LMFDB - Embedded newform 69.7.f.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	69.37
Dual form			69.7.f.a.28.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.33856 + 1.27392i) q^{2} +(10.2083 + 11.7810i) q^{3} +(-36.6400 + 23.5471i) q^{4} +(168.459 - 24.2208i) q^{5} +(-59.2972 - 38.1080i) q^{6} +(49.4387 + 22.5779i) q^{7} +(318.478 - 367.543i) q^{8} +(-34.5825 + 240.527i) q^{9} +O(q^{10})$	\(q+(-4.33856 + 1.27392i) q^{2} +(10.2083 + 11.7810i) q^{3} +(-36.6400 + 23.5471i) q^{4} +(168.459 - 24.2208i) q^{5} +(-59.2972 - 38.1080i) q^{6} +(49.4387 + 22.5779i) q^{7} +(318.478 - 367.543i) q^{8} +(-34.5825 + 240.527i) q^{9} +(-700.015 + 319.686i) q^{10} +(579.039 - 1972.03i) q^{11} +(-651.438 - 191.279i) q^{12} +(484.540 + 1060.99i) q^{13} +(-243.255 - 34.9748i) q^{14} +(2005.02 + 1737.36i) q^{15} +(244.433 - 535.234i) q^{16} +(84.9691 - 132.215i) q^{17} +(-156.373 - 1087.60i) q^{18} +(1870.69 + 2910.84i) q^{19} +(-5602.00 + 4854.16i) q^{20} +(238.694 + 812.917i) q^{21} +9293.41i q^{22} +(12161.5 + 366.977i) q^{23} +7581.13 q^{24} +(12799.7 - 3758.34i) q^{25} +(-3453.83 - 3985.93i) q^{26} +(-3186.66 + 2047.94i) q^{27} +(-2343.08 + 336.883i) q^{28} +(32774.5 + 21062.9i) q^{29} +(-10912.2 - 4983.41i) q^{30} +(-8922.48 + 10297.1i) q^{31} +(-4808.21 + 33441.8i) q^{32} +(29143.4 - 13309.3i) q^{33} +(-200.214 + 681.865i) q^{34} +(8875.25 + 2606.01i) q^{35} +(-4396.60 - 9627.20i) q^{36} +(46637.2 + 6705.42i) q^{37} +(-11824.3 - 10245.8i) q^{38} +(-7553.23 + 16539.3i) q^{39} +(44748.3 - 69629.8i) q^{40} +(17115.4 + 119040. i) q^{41} +(-2071.18 - 3222.82i) q^{42} +(48224.6 - 41786.8i) q^{43} +(25219.5 + 85889.6i) q^{44} +41356.5i q^{45} +(-53230.8 + 13900.5i) q^{46} -22285.9 q^{47} +(8800.82 - 2584.15i) q^{48} +(-75109.3 - 86680.7i) q^{49} +(-50744.6 + 32611.6i) q^{50} +(2425.00 - 348.663i) q^{51} +(-42736.8 - 27465.3i) q^{52} +(-201513. - 92027.9i) q^{53} +(11216.6 - 12944.7i) q^{54} +(49780.4 - 346230. i) q^{55} +(24043.5 - 10980.3i) q^{56} +(-15196.1 + 51753.2i) q^{57} +(-169027. - 49630.7i) q^{58} +(-107233. - 234807. i) q^{59} +(-114374. - 16444.4i) q^{60} +(-178080. - 154307. i) q^{61} +(25593.1 - 56041.1i) q^{62} +(-7140.30 + 11110.5i) q^{63} +(-16382.1 - 113940. i) q^{64} +(107323. + 166998. i) q^{65} +(-109485. + 94869.6i) q^{66} +(153087. + 521366. i) q^{67} +6845.11i q^{68} +(119824. + 147020. i) q^{69} -41825.7 q^{70} +(50291.1 - 14766.8i) q^{71} +(77390.2 + 89313.0i) q^{72} +(221875. - 142591. i) q^{73} +(-210881. + 30320.1i) q^{74} +(174940. + 112427. i) q^{75} +(-137084. - 62604.1i) q^{76} +(73151.1 - 84420.9i) q^{77} +(11700.5 - 81378.8i) q^{78} +(174150. - 79531.8i) q^{79} +(28213.2 - 96085.4i) q^{80} +(-56657.1 - 16636.0i) q^{81} +(-225903. - 494659. i) q^{82} +(696070. + 100080. i) q^{83} +(-27887.6 - 24164.7i) q^{84} +(11111.5 - 24330.7i) q^{85} +(-155992. + 242729. i) q^{86} +(86429.5 + 601131. i) q^{87} +(-540394. - 840869. i) q^{88} +(-443656. + 384430. i) q^{89} +(-52684.7 - 179428. i) q^{90} +63394.1i q^{91} +(-454237. + 272921. i) q^{92} -212393. q^{93} +(96688.7 - 28390.4i) q^{94} +(385637. + 445049. i) q^{95} +(-443061. + 284738. i) q^{96} +(187681. - 26984.4i) q^{97} +(436290. + 280387. i) q^{98} +(454300. + 207472. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−4.33856	+	1.27392i	−0.542320	+	0.159240i	−0.541408	−	0.840760i	$-0.682109\pi$
$2$	−4.33856	+	1.27392i	−0.542320	+	0.159240i	−0.000912330		1.00000i	$0.500290\pi$
$3$	10.2083	+	11.7810i	0.378084	+	0.436332i
$3$	10.2083	+	11.7810i	0.378084	+	0.436332i
$4$	−36.6400	+	23.5471i	−0.572499	+	0.367923i
$5$	168.459	−	24.2208i	1.34767	−	0.193766i	0.569590	−	0.821929i	$-0.307102\pi$
$5$	168.459	−	24.2208i	1.34767	−	0.193766i	0.778082	+	0.628163i	$0.216193\pi$
$6$	−59.2972	−	38.1080i	−0.274524	−	0.176426i
$7$	49.4387	+	22.5779i	0.144136	+	0.0658248i	0.486177	−	0.873860i	$-0.338391\pi$
$7$	49.4387	+	22.5779i	0.144136	+	0.0658248i	−0.342041	+	0.939685i	$0.611118\pi$
$8$	318.478	−	367.543i	0.622028	−	0.717858i
$9$	−34.5825	+	240.527i	−0.0474383	+	0.329940i
$10$	−700.015	+	319.686i	−0.700015	+	0.319686i
$11$	579.039	−	1972.03i	0.435041	−	1.48161i	−0.392261	−	0.919854i	$-0.628307\pi$
$11$	579.039	−	1972.03i	0.435041	−	1.48161i	0.827301	−	0.561758i	$-0.189875\pi$
$12$	−651.438	−	191.279i	−0.376990	−	0.110694i
$13$	484.540	+	1060.99i	0.220546	+	0.482929i	0.987271	−	0.159047i	$-0.0508422\pi$
$13$	484.540	+	1060.99i	0.220546	+	0.482929i	−0.766725	+	0.641976i	$0.778115\pi$
$14$	−243.255	−	34.9748i	−0.0886499	−	0.0127459i
$15$	2005.02	+	1737.36i	0.594080	+	0.514773i
$16$	244.433	−	535.234i	0.0596761	−	0.130672i
$17$	84.9691	−	132.215i	0.0172948	−	0.0269112i	−0.832499	−	0.554027i	$-0.813090\pi$
$17$	84.9691	−	132.215i	0.0172948	−	0.0269112i	0.849793	+	0.527116i	$0.176727\pi$
$18$	−156.373	−	1087.60i	−0.0268129	−	0.186488i
$19$	1870.69	+	2910.84i	0.272735	+	0.424383i	0.950420	−	0.310968i	$-0.100653\pi$
$19$	1870.69	+	2910.84i	0.272735	+	0.424383i	−0.677686	+	0.735352i	$0.737017\pi$
$20$	−5602.00	+	4854.16i	−0.700251	+	0.606771i
$21$	238.694	+	812.917i	0.0257741	+	0.0877785i
$22$			9293.41i			0.872784i
$23$	12161.5	+	366.977i	0.999545	+	0.0301616i
$23$	12161.5	+	366.977i	0.999545	+	0.0301616i
$24$	7581.13			0.548403
$25$	12799.7	−	3758.34i	0.819182	−	0.240534i
$26$	−3453.83	−	3985.93i	−0.196508	−	0.226782i
$27$	−3186.66	+	2047.94i	−0.161899	+	0.104046i
$28$	−2343.08	+	336.883i	−0.106736	+	0.0153464i
$29$	32774.5	+	21062.9i	1.34382	+	0.863622i	0.997229	−	0.0743934i	$-0.0237021\pi$
$29$	32774.5	+	21062.9i	1.34382	+	0.863622i	0.346593	+	0.938016i	$0.387338\pi$
$30$	−10912.2	−	4983.41i	−0.404154	−	0.184571i
$31$	−8922.48	+	10297.1i	−0.299503	+	0.345644i	−0.885475	−	0.464686i	$-0.846167\pi$
$31$	−8922.48	+	10297.1i	−0.299503	+	0.345644i	0.585973	+	0.810331i	$0.300713\pi$
$32$	−4808.21	+	33441.8i	−0.146735	+	1.02056i
$33$	29143.4	−	13309.3i	0.810957	−	0.370352i
$34$	−200.214	+	681.865i	−0.00509397	+	0.0173485i
$35$	8875.25	+	2606.01i	0.207003	+	0.0607815i
$36$	−4396.60	−	9627.20i	−0.0942343	−	0.206344i
$37$	46637.2	+	6705.42i	0.920720	+	0.132380i	0.586346	−	0.810061i	$-0.300566\pi$
$37$	46637.2	+	6705.42i	0.920720	+	0.132380i	0.334374	+	0.942440i	$0.391475\pi$
$38$	−11824.3	−	10245.8i	−0.215488	−	0.186722i
$39$	−7553.23	+	16539.3i	−0.127332	+	0.278819i
$40$	44748.3	−	69629.8i	0.699193	−	1.08797i
$41$	17115.4	+	119040.i	0.248333	+	1.72720i	0.607845	+	0.794055i	$0.292034\pi$
$41$	17115.4	+	119040.i	0.248333	+	1.72720i	−0.359512	+	0.933140i	$0.617057\pi$
$42$	−2071.18	−	3222.82i	−0.0279556	−	0.0434998i
$43$	48224.6	−	41786.8i	0.606545	−	0.525574i	−0.296549	−	0.955018i	$-0.595836\pi$
$43$	48224.6	−	41786.8i	0.606545	−	0.525574i	0.903094	+	0.429444i	$0.141290\pi$
$44$	25219.5	+	85889.6i	0.296059	+	1.00828i
$45$			41356.5i			0.453844i
$46$	−53230.8	+	13900.5i	−0.546877	+	0.142810i
$47$	−22285.9			−0.214653			−0.107326	−	0.994224i	$-0.534229\pi$
$47$	−22285.9			−0.214653			−0.107326	+	0.994224i	$0.534229\pi$
$48$	8800.82	−	2584.15i	0.0795792	−	0.0233665i
$49$	−75109.3	−	86680.7i	−0.638418	−	0.736774i
$50$	−50744.6	+	32611.6i	−0.405957	+	0.260893i
$51$	2425.00	−	348.663i	0.0182811	−	0.00262842i
$52$	−42736.8	−	27465.3i	−0.303943	−	0.195332i
$53$	−201513.	−	92027.9i	−1.35355	−	0.618147i	−0.399210	−	0.916859i	$-0.630716\pi$
$53$	−201513.	−	92027.9i	−1.35355	−	0.618147i	−0.954343	+	0.298712i	$0.903443\pi$
$54$	11216.6	−	12944.7i	0.0712330	−	0.0822073i
$55$	49780.4	−	346230.i	0.299206	−	2.08102i
$56$	24043.5	−	10980.3i	0.136910	−	0.0625245i
$57$	−15196.1	+	51753.2i	−0.0820555	+	0.279455i
$58$	−169027.	−	49630.7i	−0.866305	−	0.254370i
$59$	−107233.	−	234807.i	−0.522122	−	1.14329i	−0.968630	−	0.248508i	$-0.920060\pi$
$59$	−107233.	−	234807.i	−0.522122	−	1.14329i	0.446507	−	0.894780i	$-0.352668\pi$
$60$	−114374.	−	16444.4i	−0.529507	−	0.0761316i
$61$	−178080.	−	154307.i	−0.784560	−	0.679825i	0.167454	−	0.985880i	$-0.446446\pi$
$61$	−178080.	−	154307.i	−0.784560	−	0.679825i	−0.952014	+	0.306055i	$0.900991\pi$
$62$	25593.1	−	56041.1i	0.107386	−	0.235143i
$63$	−7140.30	+	11110.5i	−0.0285558	+	0.0444337i
$64$	−16382.1	−	113940.i	−0.0624927	−	0.434646i
$65$	107323.	+	166998.i	0.390799	+	0.608095i
$66$	−109485.	+	94869.6i	−0.380824	+	0.329986i
$67$	153087.	+	521366.i	0.508995	+	1.73348i	0.666069	+	0.745890i	$0.267976\pi$
$67$	153087.	+	521366.i	0.508995	+	1.73348i	−0.157074	+	0.987587i	$0.550206\pi$
$68$			6845.11i			0.0217698i
$69$	119824.	+	147020.i	0.364752	+	0.447537i
$70$	−41825.7			−0.121941
$71$	50291.1	−	14766.8i	0.140513	−	0.0412583i	−0.210720	−	0.977547i	$-0.567581\pi$
$71$	50291.1	−	14766.8i	0.140513	−	0.0412583i	0.351233	+	0.936288i	$0.385763\pi$
$72$	77390.2	+	89313.0i	0.207343	+	0.239286i
$73$	221875.	−	142591.i	0.570349	−	0.366541i	−0.223455	−	0.974714i	$-0.571734\pi$
$73$	221875.	−	142591.i	0.570349	−	0.366541i	0.793804	+	0.608173i	$0.208097\pi$
$74$	−210881.	+	30320.1i	−0.520405	+	0.0748230i
$75$	174940.	+	112427.i	0.414672	+	0.266494i
$76$	−137084.	−	62604.1i	−0.312281	−	0.142614i
$77$	73151.1	−	84420.9i	0.160232	−	0.184917i
$78$	11700.5	−	81378.8i	0.0246559	−	0.171486i
$79$	174150.	−	79531.8i	0.353218	−	0.161309i	−0.230901	−	0.972977i	$-0.574167\pi$
$79$	174150.	−	79531.8i	0.353218	−	0.161309i	0.584119	+	0.811668i	$0.301440\pi$
$80$	28213.2	−	96085.4i	0.0551039	−	0.187667i
$81$	−56657.1	−	16636.0i	−0.106610	−	0.0313036i
$82$	−225903.	−	494659.i	−0.409714	−	0.897149i
$83$	696070.	+	100080.i	1.21736	+	0.175030i	0.720906	−	0.693033i	$-0.243726\pi$
$83$	696070.	+	100080.i	1.21736	+	0.175030i	0.496454	+	0.868063i	$0.334635\pi$
$84$	−27887.6	−	24164.7i	−0.0470514	−	0.0407703i
$85$	11111.5	−	24330.7i	0.0180932	−	0.0396186i
$86$	−155992.	+	242729.i	−0.245249	+	0.381616i
$87$	86429.5	+	601131.i	0.131252	+	0.912875i
$88$	−540394.	−	840869.i	−0.792980	−	1.23390i
$89$	−443656.	+	384430.i	−0.629327	+	0.545315i	−0.910063	−	0.414470i	$-0.863967\pi$
$89$	−443656.	+	384430.i	−0.629327	+	0.545315i	0.280736	+	0.959785i	$0.409422\pi$
$90$	−52684.7	−	179428.i	−0.0722699	−	0.246129i
$91$			63394.1i			0.0841249i
$92$	−454237.	+	272921.i	−0.583336	+	0.350488i
$93$	−212393.			−0.264053
$94$	96688.7	−	28390.4i	0.116410	−	0.0341812i
$95$	385637.	+	445049.i	0.449788	+	0.519083i
$96$	−443061.	+	284738.i	−0.500783	+	0.321834i
$97$	187681.	−	26984.4i	0.205638	−	0.0295663i	−0.0387258	−	0.999250i	$-0.512330\pi$
$97$	187681.	−	26984.4i	0.205638	−	0.0295663i	0.244364	+	0.969684i	$0.421421\pi$
$98$	436290.	+	280387.i	0.463551	+	0.297906i
$99$	454300.	+	207472.i	0.468206	+	0.213823i
$100$	−380484.	+	439101.i	−0.380484	+	0.439101i
$101$	195830.	−	1.36203e6i	0.190070	−	1.32197i	−0.641746	−	0.766917i	$-0.721790\pi$
$101$	195830.	−	1.36203e6i	0.190070	−	1.32197i	0.831816	−	0.555051i	$-0.187301\pi$
$102$	−10076.9	+	4601.95i	−0.00949565	+	0.00433652i
$103$	210114.	−	715582.i	0.192284	−	0.654859i	−0.805754	−	0.592250i	$-0.798240\pi$
$103$	210114.	−	715582.i	0.192284	−	0.654859i	0.998038	−	0.0626090i	$-0.0199421\pi$
$104$	544277.	+	159814.i	0.483860	+	0.142074i
$105$	59899.6	+	131162.i	0.0517435	+	0.113303i
$106$	991513.	+	142558.i	0.832493	+	0.119694i
$107$	475332.	+	411878.i	0.388013	+	0.336215i	0.826922	−	0.562316i	$-0.190090\pi$
$107$	475332.	+	411878.i	0.388013	+	0.336215i	−0.438910	+	0.898531i	$0.644635\pi$
$108$	68536.1	−	150073.i	0.0544062	−	0.119133i
$109$	56133.8	−	87345.9i	0.0433456	−	0.0674471i	−0.818905	−	0.573930i	$-0.805418\pi$
$109$	56133.8	−	87345.9i	0.0433456	−	0.0674471i	0.862250	+	0.506483i	$0.169055\pi$
$110$	225093.	+	1.56556e6i	0.169116	+	1.17623i
$111$	397089.	+	617883.i	0.290348	+	0.451790i
$112$	24168.9	−	20942.5i	0.0172030	−	0.0149065i
$113$	285561.	+	972532.i	0.197908	+	0.674014i	0.997316	+	0.0732242i	$0.0233289\pi$
$113$	285561.	+	972532.i	0.197908	+	0.674014i	−0.799407	+	0.600790i	$0.794853\pi$
$114$		−	243893.i		−	0.164621i
$115$	2.05760e6	−	232739.i	1.35290	−	0.153030i
$116$	−1.69682e6			−1.08708
$117$	−271954.	+	79852.9i	−0.169800	+	0.0498578i
$118$	764362.	+	882121.i	0.465214	+	0.536886i
$119$	7185.89	−	4618.09i	0.00426422	−	0.00274045i
$120$	1.27711e6	−	183621.i	0.739068	−	0.106262i
$121$	−2.06327e6	−	1.32598e6i	−1.16466	−	0.748482i
$122$	969187.	+	442613.i	0.533738	+	0.243750i
$123$	−1.22769e6	+	1.41683e6i	−0.659740	+	0.761381i
$124$	84453.0	−	587383.i	0.0442945	−	0.308075i
$125$	−353730.	+	161543.i	−0.181110	+	0.0827100i
$126$	16824.8	−	57299.9i	0.00841080	−	0.0286445i
$127$	1.13381e6	+	332917.i	0.553515	+	0.162527i	0.546516	−	0.837449i	$-0.315954\pi$
$127$	1.13381e6	+	332917.i	0.553515	+	0.162527i	0.00699936	+	0.999976i	$0.497772\pi$
$128$	−682021.	−	1.49342e6i	−0.325213	−	0.712117i
$129$	984578.	+	141561.i	0.458650	+	0.0659439i
$130$	−678370.	−	587811.i	−0.308771	−	0.267552i
$131$	1.41514e6	−	3.09873e6i	0.629487	−	1.37838i	−0.278926	−	0.960312i	$-0.589979\pi$
$131$	1.41514e6	−	3.09873e6i	0.629487	−	1.37838i	0.908414	−	0.418072i	$-0.137294\pi$
$132$	−754416.	+	1.17389e6i	−0.328012	+	0.510396i
$133$	26763.5	+	186145.i	0.0113760	+	0.0791217i
$134$	−1.32835e6	−	2.06696e6i	−0.552077	−	0.859048i
$135$	−487220.	+	422178.i	−0.198027	+	0.171591i
$136$	−21533.8	−	73337.3i	−0.00856058	−	0.0291547i
$137$		−	17212.7i		−	0.00669401i	−0.999994	−	0.00334700i	$-0.998935\pi$
$137$		−	17212.7i		−	0.00669401i	0.999994	−	0.00334700i	$-0.00106539\pi$
$138$	−707156.	−	485210.i	−0.269078	−	0.184626i
$139$	−4.67345e6			−1.74018			−0.870089	−	0.492895i	$-0.835939\pi$
$139$	−4.67345e6			−1.74018			−0.870089	+	0.492895i	$0.835939\pi$
$140$	−386553.	+	113502.i	−0.140872	+	0.0413637i
$141$	−227500.	−	262549.i	−0.0811567	−	0.0936598i
$142$	−199380.	+	128133.i	−0.0696331	+	0.0447505i
$143$	2.37288e6	−	341168.i	0.811460	−	0.116670i
$144$	120285.	+	77302.4i	0.0402832	+	0.0258884i
$145$	6.03132e6	+	2.75441e6i	1.97837	+	0.903493i
$146$	−780972.	+	901290.i	−0.250944	+	0.289605i
$147$	254447.	−	1.76972e6i	0.0801025	−	0.557125i
$148$	−1.86668e6	+	852484.i	−0.575817	+	0.262967i
$149$	−942728.	+	3.21064e6i	−0.284989	+	0.970582i	0.685225	+	0.728331i	$0.259704\pi$
$149$	−942728.	+	3.21064e6i	−0.284989	+	0.970582i	−0.970214	+	0.242251i	$0.922114\pi$
$150$	−902211.	−	264913.i	−0.267322	−	0.0784927i
$151$	−296923.	−	650172.i	−0.0862410	−	0.188841i	0.861598	−	0.507592i	$-0.169464\pi$
$151$	−296923.	−	650172.i	−0.0862410	−	0.188841i	−0.947839	+	0.318750i	$0.896737\pi$
$152$	1.66563e6	+	239482.i	0.474295	+	0.0681934i
$153$	28862.7	+	25009.6i	0.00805865	+	0.00698286i
$154$	−209826.	+	459454.i	−0.0574508	+	0.125800i
$155$	−1.25367e6	+	1.95075e6i	−0.336657	+	0.523849i
$156$	−112701.	−	783854.i	−0.0296862	−	0.206472i
$157$	−2.87793e6	−	4.47814e6i	−0.743671	−	1.15718i	−0.982527	−	0.186120i	$-0.940409\pi$
$157$	−2.87793e6	−	4.47814e6i	−0.743671	−	1.15718i	0.238856	−	0.971055i	$-0.423228\pi$
$158$	−654245.	+	566907.i	−0.165871	+	0.143728i
$159$	−972921.	−	3.31346e6i	−0.242039	−	0.824311i
$160$			5.75004e6i			1.40382i
$161$	592961.	+	292723.i	0.142085	+	0.0701422i
$162$	267003.			0.0628017
$163$	−2.12563e6	+	624141.i	−0.490823	+	0.144119i	−0.517773	−	0.855518i	$-0.673239\pi$
$163$	−2.12563e6	+	624141.i	−0.490823	+	0.144119i	0.0269498	+	0.999637i	$0.491421\pi$
$164$	−3.43015e6	−	3.95861e6i	−0.777646	−	0.897451i
$165$	4.58710e6	−	2.94795e6i	1.02114	−	0.656249i
$166$	−3.14744e6	+	452533.i	−0.688071	+	0.0989296i
$167$	−1.11154e6	−	714345.i	−0.238658	−	0.153376i	0.415845	−	0.909436i	$-0.363486\pi$
$167$	−1.11154e6	−	714345.i	−0.238658	−	0.153376i	−0.654503	+	0.756059i	$0.727122\pi$
$168$	374801.	+	171166.i	0.0790447	+	0.0360985i
$169$	2.26996e6	−	2.61967e6i	0.470281	−	0.542734i
$170$	−17212.5	+	119716.i	−0.00350346	+	0.0243671i
$171$	−764829.	+	349286.i	−0.152959	+	0.0698542i
$172$	−782989.	+	2.66661e6i	−0.153876	+	0.524053i
$173$	−8.61668e6	−	2.53009e6i	−1.66419	−	0.488649i	−0.691812	−	0.722078i	$-0.743187\pi$
$173$	−8.61668e6	−	2.53009e6i	−1.66419	−	0.488649i	−0.972374	+	0.233429i	$0.925005\pi$
$174$	−1.14077e6	−	2.49794e6i	−0.216546	−	0.474170i
$175$	717657.	+	103184.i	0.133907	+	0.0192529i
$176$	−913959.	−	791950.i	−0.167644	−	0.145265i
$177$	1.67160e6	−	3.66029e6i	0.301447	−	0.660078i
$178$	1.43510e6	−	2.23306e6i	0.254461	−	0.395950i
$179$	725210.	+	5.04395e6i	0.126446	+	0.879451i	0.950008	+	0.312225i	$0.101074\pi$
$179$	725210.	+	5.04395e6i	0.126446	+	0.879451i	−0.823562	+	0.567226i	$0.808017\pi$
$180$	−973824.	−	1.51530e6i	−0.166979	−	0.259825i
$181$	−3.01606e6	+	2.61343e6i	−0.508632	+	0.440732i	−0.870986	−	0.491308i	$-0.836519\pi$
$181$	−3.01606e6	+	2.61343e6i	−0.508632	+	0.440732i	0.362353	+	0.932041i	$0.381973\pi$
$182$	−80758.8	−	275039.i	−0.0133960	−	0.0456226i
$183$		−	3.67317e6i		−	0.599360i
$184$	4.00804e6	−	4.35299e6i	0.643396	−	0.698770i
$185$	8.01887e6			1.26648
$186$	921480.	−	270571.i	0.143201	−	0.0420477i
$187$	−211530.	−	244119.i	−0.0323480	−	0.0373316i
$188$	816554.	−	524767.i	0.122888	−	0.0789756i
$189$	−203783.	+	29299.5i	−0.0301844	+	0.00433986i
$190$	−2.24007e6	−	1.43960e6i	−0.326588	−	0.209885i
$191$	−1.48953e6	−	680243.i	−0.213771	−	0.0976257i	0.305652	−	0.952143i	$-0.401126\pi$
$191$	−1.48953e6	−	680243.i	−0.213771	−	0.0976257i	−0.519422	+	0.854518i	$0.673853\pi$
$192$	1.17509e6	−	1.35613e6i	0.166023	−	0.191600i
$193$	190209.	−	1.32293e6i	0.0264581	−	0.184020i	−0.972307	−	0.233709i	$-0.924914\pi$
$193$	190209.	−	1.32293e6i	0.0264581	−	0.184020i	0.998765	+	0.0496884i	$0.0158228\pi$
$194$	−779888.	+	356163.i	−0.106814	+	0.0487802i
$195$	−871816.	+	2.96913e6i	−0.117577	+	0.400429i
$196$	4.79308e6	+	1.40737e6i	0.636570	+	0.186914i
$197$	−2.08603e6	−	4.56776e6i	−0.272848	−	0.597454i	0.722757	−	0.691102i	$-0.242875\pi$
$197$	−2.08603e6	−	4.56776e6i	−0.272848	−	0.597454i	−0.995605	+	0.0936477i	$0.970147\pi$
$198$	−2.23531e6	−	321389.i	−0.287967	−	0.0414034i
$199$	5.08119e6	+	4.40287e6i	0.644772	+	0.558698i	0.914675	−	0.404189i	$-0.132446\pi$
$199$	5.08119e6	+	4.40287e6i	0.644772	+	0.558698i	−0.269904	+	0.962887i	$0.586992\pi$
$200$	2.69508e6	−	5.90140e6i	0.336885	−	0.737675i
$201$	−4.57944e6	+	7.12575e6i	−0.563929	+	0.877491i
$202$	885488.	+	6.15870e6i	0.107431	+	0.747197i
$203$	1.14477e6	+	1.78130e6i	0.136846	+	0.212936i
$204$	−80642.0	+	69876.7i	−0.00949885	+	0.00823080i
$205$	5.76648e6	+	1.96388e7i	0.669344	+	2.27958i
$206$			3.37227e6i			0.385763i
$207$	−508842.	+	2.91246e6i	−0.0573682	+	0.328360i
$208$	686318.			0.0762668
$209$	6.82346e6	−	2.00355e6i	0.747422	−	0.219463i
$210$	−426968.	−	492747.i	−0.0461038	−	0.0532067i
$211$	−9.12412e6	+	5.86372e6i	−0.971278	+	0.624203i	−0.927097	−	0.374821i	$-0.877704\pi$
$211$	−9.12412e6	+	5.86372e6i	−0.971278	+	0.624203i	−0.0441811	+	0.999024i	$0.514068\pi$
$212$	9.55041e6	−	1.37314e6i	1.00234	−	0.144115i
$213$	687353.	+	441735.i	0.0711280	+	0.0457112i
$214$	−2.58696e6	−	1.18142e6i	−0.263966	−	0.120549i
$215$	7.11175e6	−	8.20740e6i	0.715585	−	0.825829i
$216$	−262174.	+	1.82346e6i	−0.0260153	+	0.180940i
$217$	−673603.	+	307624.i	−0.0659211	+	0.0301052i
$218$	−132269.	+	450466.i	−0.0127670	+	0.0434803i
$219$	3.94482e6	+	1.15830e6i	0.375574	+	0.110278i
$220$	6.32876e6	+	1.38580e7i	0.594361	+	1.30147i
$221$	181450.	+	26088.5i	0.0168105	+	0.00241698i
$222$	−2.50993e6	−	2.17486e6i	−0.229405	−	0.198780i
$223$	−2.99242e6	+	6.55249e6i	−0.269841	+	0.590870i	−0.995239	−	0.0974595i	$-0.968928\pi$
$223$	−2.99242e6	+	6.55249e6i	−0.269841	+	0.590870i	0.725398	+	0.688329i	$0.241656\pi$
$224$	−992758.	+	1.54476e6i	−0.0883281	+	0.137441i
$225$	461334.	+	3.20865e6i	0.0405012	+	0.281692i
$226$	−2.47785e6	−	3.85561e6i	−0.214659	−	0.334017i
$227$	188417.	−	163264.i	0.0161080	−	0.0139577i	−0.646770	−	0.762686i	$-0.723880\pi$
$227$	188417.	−	163264.i	0.0161080	−	0.0139577i	0.662878	+	0.748728i	$0.269335\pi$
$228$	−661851.	−	2.25406e6i	−0.0558413	−	0.190178i
$229$		−	1.01676e7i		−	0.846670i	−0.905973	−	0.423335i	$-0.860859\pi$
$229$		−	1.01676e7i		−	0.846670i	0.905973	−	0.423335i	$-0.139141\pi$
$230$	−8.63052e6	+	3.63096e6i	−0.709339	+	0.298427i
$231$	1.74131e6			0.141267
$232$	1.81795e7	−	5.33798e6i	1.45585	−	0.427477i
$233$	−1.43265e7	−	1.65336e7i	−1.13259	−	1.30708i	−0.945827	−	0.324671i	$-0.894747\pi$
$233$	−1.43265e7	−	1.65336e7i	−1.13259	−	1.30708i	−0.186761	−	0.982405i	$-0.559799\pi$
$234$	1.07816e6	−	692894.i	0.0841467	−	0.0540778i
$235$	−3.75426e6	+	539781.i	−0.289281	+	0.0415924i
$236$	9.45804e6	+	6.07831e6i	0.719557	+	0.462431i
$237$	2.71473e6	+	1.23978e6i	0.203931	+	0.0931320i
$238$	−25293.4	+	29190.1i	−0.00187619	+	0.00216523i
$239$	−1.31303e6	+	9.13231e6i	−0.0961790	+	0.668940i	0.883509	+	0.468414i	$0.155174\pi$
$239$	−1.31303e6	+	9.13231e6i	−0.0961790	+	0.668940i	−0.979688	+	0.200526i	$0.935735\pi$
$240$	1.41999e6	−	648486.i	0.102719	−	0.0469102i
$241$	−3.68886e6	+	1.25631e7i	−0.263537	+	0.897524i	0.716312	+	0.697781i	$0.245829\pi$
$241$	−3.68886e6	+	1.25631e7i	−0.263537	+	0.897524i	−0.979848	+	0.199743i	$0.935989\pi$
$242$	1.06408e7	+	3.12442e6i	0.750808	+	0.220457i
$243$	−382382.	−	837301.i	−0.0266489	−	0.0583529i
$244$	1.01583e7	+	1.46055e6i	0.699284	+	0.100542i
$245$	−1.47523e7	−	1.27830e7i	−1.00314	−	0.869226i
$246$	3.52148e6	−	7.71097e6i	0.236549	−	0.517969i
$247$	−2.18197e6	+	3.39521e6i	−0.144796	+	0.225307i
$248$	943013.	+	6.55880e6i	0.0618248	+	0.430001i
$249$	5.92664e6	+	9.22202e6i	0.383893	+	0.597349i
$250$	1.32889e6	−	1.15149e6i	0.0850488	−	0.0736952i
$251$	4.19182e6	+	1.42760e7i	0.265083	+	0.902790i	0.979223	+	0.202787i	$0.0649998\pi$
$251$	4.19182e6	+	1.42760e7i	0.265083	+	0.902790i	−0.714140	+	0.700003i	$0.753182\pi$
$252$		−	575222.i		−	0.0359446i
$253$	7.76565e6	−	2.37702e7i	0.479531	−	1.46782i
$254$	−5.34322e6			−0.326063
$255$	400069.	−	117471.i	0.0241276	−	0.00708450i
$256$	9.68594e6	+	1.11782e7i	0.577327	+	0.666271i
$257$	1.14498e7	−	7.35833e6i	0.674525	−	0.433491i	−0.158029	−	0.987434i	$-0.550514\pi$
$257$	1.14498e7	−	7.35833e6i	0.674525	−	0.433491i	0.832554	+	0.553944i	$0.186878\pi$
$258$	−4.45199e6	+	640100.i	−0.259236	+	0.0372725i
$259$	2.15429e6	+	1.38448e6i	0.123995	+	0.0796869i
$260$	−7.86463e6	−	3.59166e6i	−0.447464	−	0.204350i
$261$	−6.19961e6	+	7.15473e6i	−0.348693	+	0.402413i
$262$	−2.19216e6	+	1.52468e7i	−0.121890	+	0.847766i
$263$	8.51516e6	−	3.88874e6i	0.468086	−	0.213768i	−0.167386	−	0.985891i	$-0.553533\pi$
$263$	8.51516e6	−	3.88874e6i	0.468086	−	0.213768i	0.635472	+	0.772124i	$0.280805\pi$
$264$	4.38977e6	−	1.49502e7i	0.238578	−	0.812521i
$265$	−3.61757e7	−	1.06221e7i	−1.94392	−	0.570787i
$266$	−353248.	−	773505.i	−0.0187687	−	0.0410978i
$267$	−9.05793e6	−	1.30233e6i	−0.475877	−	0.0684208i
$268$	−1.78857e7	−	1.54981e7i	−0.929185	−	0.805144i
$269$	−5.73674e6	+	1.25617e7i	−0.294719	+	0.645344i	−0.997838	−	0.0657281i	$-0.979063\pi$
$269$	−5.73674e6	+	1.25617e7i	−0.294719	+	0.645344i	0.703119	+	0.711073i	$0.251790\pi$
$270$	1.57601e6	−	2.45232e6i	0.0800698	−	0.124591i
$271$	−5.42475e6	−	3.77300e7i	−0.272566	−	1.89574i	−0.421397	−	0.906876i	$-0.638460\pi$
$271$	−5.42475e6	−	3.77300e7i	−0.272566	−	1.89574i	0.148831	−	0.988863i	$-0.452449\pi$
$272$	−49996.5	−	77796.0i	−0.00248446	−	0.00386590i
$273$	−746843.	+	647144.i	−0.0367064	+	0.0318063i
$274$	21927.5	+	74678.2i	0.00106595	+	0.00363030i
$275$		−	2.74176e7i		−	1.31835i
$276$	−7.85224e6	−	2.56530e6i	−0.373479	−	0.122014i
$277$	4.84946e6			0.228168			0.114084	−	0.993471i	$-0.463607\pi$
$277$	4.84946e6			0.228168			0.114084	+	0.993471i	$0.463607\pi$
$278$	2.02761e7	−	5.95359e6i	0.943734	−	0.277105i
$279$	−2.16816e6	−	2.50219e6i	−0.0998342	−	0.115215i
$280$	3.78439e6	−	2.43208e6i	0.172394	−	0.110791i
$281$	−1.13733e7	+	1.63523e6i	−0.512587	+	0.0736988i	−0.393755	−	0.919216i	$-0.628824\pi$
$281$	−1.13733e7	+	1.63523e6i	−0.512587	+	0.0736988i	−0.118832	+	0.992914i	$0.537915\pi$
$282$	1.32149e6	+	849270.i	0.0589273	+	0.0378703i
$283$	−1.20881e7	−	5.52045e6i	−0.533333	−	0.243565i	0.130497	−	0.991449i	$-0.458343\pi$
$283$	−1.20881e7	−	5.52045e6i	−0.533333	−	0.243565i	−0.663830	+	0.747884i	$0.731070\pi$
$284$	−1.49495e6	+	1.72526e6i	−0.0652637	+	0.0753183i
$285$	−1.30642e6	+	9.08635e6i	−0.0564350	+	0.392514i
$286$	−9.86025e6	+	4.50303e6i	−0.421493	+	0.192489i
$287$	−1.84151e6	+	6.27161e6i	−0.0778985	+	0.265298i
$288$	−7.87737e6	−	2.31300e6i	−0.329764	−	0.0968275i
$289$	1.00168e7	+	2.19338e7i	0.414990	+	0.908701i
$290$	−2.96761e7	−	4.26678e6i	−1.21678	−	0.174947i
$291$	2.23380e6	+	1.93560e6i	0.0906493	+	0.0785481i
$292$	−4.77191e6	+	1.04490e7i	−0.191666	+	0.419689i
$293$	−2.62623e7	+	4.08649e7i	−1.04407	+	1.62460i	−0.303234	+	0.952916i	$0.598066\pi$
$293$	−2.62623e7	+	4.08649e7i	−1.04407	+	1.62460i	−0.740835	+	0.671687i	$0.765570\pi$
$294$	1.15054e6	+	8.00219e6i	0.0452752	+	0.314896i
$295$	−2.37516e7	−	3.69582e7i	−0.925180	−	1.43961i
$296$	1.73175e7	−	1.50057e7i	0.667743	−	0.578603i
$297$	2.19340e6	+	7.47002e6i	0.0837236	+	0.285136i
$298$		−	1.51305e7i		−	0.571748i
$299$	5.50335e6	+	1.30811e7i	0.205880	+	0.489361i
$300$	−9.05712e6			−0.335449
$301$	3.32762e6	−	977077.i	0.122021	−	0.0358285i
$302$	2.11649e6	+	2.44256e6i	0.0768413	+	0.0886796i
$303$	1.80451e7	−	1.15969e7i	0.648680	−	0.416881i
$304$	2.01524e6	−	289748.i	0.0717309	−	0.0103133i
$305$	−3.37367e7	−	2.16812e7i	−1.18906	−	0.764161i
$306$	−157083.	−	71737.3i	−0.00548232	−	0.00250369i
$307$	1.60086e6	−	1.84749e6i	0.0553271	−	0.0638509i	−0.727411	−	0.686202i	$-0.759277\pi$
$307$	1.60086e6	−	1.84749e6i	0.0553271	−	0.0638509i	0.782738	+	0.622351i	$0.213822\pi$
$308$	−692389.	+	4.81567e6i	−0.0236973	+	0.164818i
$309$	1.05752e7	−	4.82951e6i	0.358436	−	0.163692i
$310$	2.95403e6	−	1.00605e7i	0.0991586	−	0.337703i
$311$	1.30384e7	+	3.82841e6i	0.433453	+	0.127273i	0.491178	−	0.871059i	$-0.336566\pi$
$311$	1.30384e7	+	3.82841e6i	0.433453	+	0.127273i	−0.0577249	+	0.998333i	$0.518385\pi$
$312$	3.67336e6	+	8.04353e6i	0.120948	+	0.264840i
$313$	−3.60638e7	−	5.18520e6i	−1.17609	−	0.169096i	−0.473565	−	0.880759i	$-0.657033\pi$
$313$	−3.60638e7	−	5.18520e6i	−1.17609	−	0.169096i	−0.702521	+	0.711663i	$0.747942\pi$
$314$	1.81909e7	+	1.57625e7i	0.587576	+	0.509138i
$315$	−933743.	+	2.04461e6i	−0.0298741	+	0.0654153i
$316$	−4.50812e6	+	7.01477e6i	−0.142868	+	0.222307i
$317$	218201.	+	1.51762e6i	0.00684981	+	0.0476415i	0.992960	−	0.118453i	$-0.0377935\pi$
$317$	218201.	+	1.51762e6i	0.00684981	+	0.0476415i	−0.986110	+	0.166094i	$0.946884\pi$
$318$	8.44216e6	+	1.31363e7i	0.262526	+	0.408498i
$319$	6.05143e7	−	5.24359e7i	1.86417	−	1.61531i
$320$	−5.51942e6	−	1.87974e7i	−0.168439	−	0.573652i
$321$			9.80443e6i			0.296420i
$322$	−2.94551e6	−	514614.i	−0.0882251	−	0.0154140i
$323$	543807.			0.0161375
$324$	2.46764e6	−	724566.i	0.0725517	−	0.0213031i
$325$	1.01896e7	+	1.17594e7i	0.296828	+	0.342558i
$326$	8.42708e6	−	5.41575e6i	0.243234	−	0.156317i
$327$	1.60205e6	−	230340.i	0.0458176	−	0.00658758i
$328$	4.92033e7	+	3.16210e7i	1.39435	+	0.896095i
$329$	−1.10178e6	−	503168.i	−0.0309392	−	0.0141295i
$330$	−1.61460e7	+	1.86335e7i	−0.449286	+	0.518503i
$331$	6.92128e6	−	4.81386e7i	0.190855	−	1.32742i	−0.638898	−	0.769292i	$-0.720609\pi$
$331$	6.92128e6	−	4.81386e7i	0.190855	−	1.32742i	0.829752	−	0.558132i	$-0.188482\pi$
$332$	−2.78606e7	+	1.27235e7i	−0.761335	+	0.347690i
$333$	−3.22566e6	+	1.09856e7i	−0.0873547	+	0.297503i
$334$	5.73251e6	+	1.68322e6i	0.153853	+	0.0451753i
$335$	3.84167e7	+	8.41209e7i	1.02185	+	2.23753i
$336$	493446.	+	70946.8i	0.0130083	+	0.00187032i
$337$	−3.32368e7	−	2.87999e7i	−0.868421	−	0.752491i	0.101777	−	0.994807i	$-0.467547\pi$
$337$	−3.32368e7	−	2.87999e7i	−0.868421	−	0.752491i	−0.970197	+	0.242317i	$0.922093\pi$
$338$	−6.51111e6	+	1.42573e7i	−0.168618	+	0.369223i
$339$	−8.54229e6	+	1.32921e7i	−0.219268	+	0.341188i
$340$	165794.	+	1.15312e6i	0.00421824	+	0.0293385i
$341$	1.51397e7	+	2.35578e7i	0.381815	+	0.594116i
$342$	2.87330e6	−	2.48973e6i	0.0718294	−	0.0622405i
$343$	−3.55770e6	−	1.21164e7i	−0.0881632	−	0.300256i
$344$		−	3.10328e7i		−	0.762335i
$345$	2.37464e7	+	2.18646e7i	0.578283	+	0.532457i
$346$	4.06071e7			0.980334
$347$	1.39217e7	−	4.08778e6i	0.333199	−	0.0978361i	−0.110854	−	0.993837i	$-0.535358\pi$
$347$	1.39217e7	−	4.08778e6i	0.333199	−	0.0978361i	0.444053	+	0.896001i	$0.353540\pi$
$348$	−1.73216e7	−	1.99902e7i	−0.411009	−	0.474330i
$349$	−4.80680e7	+	3.08914e7i	−1.13078	+	0.726711i	−0.965724	−	0.259572i	$-0.916418\pi$
$349$	−4.80680e7	+	3.08914e7i	−1.13078	+	0.726711i	−0.165061	+	0.986283i	$0.552782\pi$
$350$	−3.24505e6	+	466567.i	−0.0756863	+	0.0108820i
$351$	−3.71692e6	−	2.38872e6i	−0.0859532	−	0.0552388i
$352$	6.31640e7	+	2.88460e7i	1.44824	+	0.661391i
$353$	−5.01340e7	+	5.78577e7i	−1.13975	+	1.31534i	−0.197542	+	0.980294i	$0.563296\pi$
$353$	−5.01340e7	+	5.78577e7i	−1.13975	+	1.31534i	−0.942203	+	0.335042i	$0.891250\pi$
$354$	−2.58943e6	+	1.80099e7i	−0.0583706	+	0.405976i
$355$	8.11433e6	−	3.70569e6i	0.181371	−	0.0828293i
$356$	7.20334e6	−	2.45323e7i	0.159656	−	0.543737i
$357$	127761.	+	37514.0i	0.00280798	+	0.000824497i
$358$	−9.57194e6	−	2.09596e7i	−0.208618	−	0.456809i
$359$	6.21040e7	+	8.92921e6i	1.34226	+	0.192988i	0.775736	−	0.631058i	$-0.217379\pi$
$359$	6.21040e7	+	8.92921e6i	1.34226	+	0.192988i	0.566524	+	0.824045i	$0.308288\pi$
$360$	1.52003e7	+	1.31711e7i	0.325795	+	0.282303i
$361$	1.45700e7	−	3.19039e7i	0.309698	−	0.678144i
$362$	9.75607e6	−	1.51807e7i	0.205660	−	0.320013i
$363$	−5.44104e6	−	3.78433e7i	−0.113753	−	0.791168i
$364$	−1.49274e6	−	2.32276e6i	−0.0309515	−	0.0481614i
$365$	3.39233e7	−	2.93947e7i	0.697620	−	0.604492i
$366$	4.67931e6	+	1.59363e7i	0.0954419	+	0.325045i
$367$		−	7.30704e7i		−	1.47824i	−0.673576	−	0.739118i	$-0.735243\pi$
$367$		−	7.30704e7i		−	1.47824i	0.673576	−	0.739118i	$-0.264757\pi$
$368$	3.16908e6	−	6.41953e6i	0.0635902	−	0.128813i
$369$	−2.92242e7			−0.581652
$370$	−3.47904e7	+	1.02154e7i	−0.686838	+	0.201674i
$371$	−7.88474e6	−	9.09948e6i	−0.154407	−	0.178195i
$372$	7.78206e6	−	5.00123e6i	0.151170	−	0.0971512i
$373$	−3.80726e7	+	5.47401e6i	−0.733644	+	0.105482i	−0.499003	−	0.866600i	$-0.666300\pi$
$373$	−3.80726e7	+	5.47401e6i	−0.733644	+	0.105482i	−0.234641	+	0.972082i	$0.575391\pi$
$374$	1.22872e6	+	789653.i	0.0234876	+	0.0150946i
$375$	−5.51410e6	−	2.51821e6i	−0.104564	−	0.0477527i
$376$	−7.09757e6	+	8.19103e6i	−0.133520	+	0.154090i
$377$	−6.46705e6	+	4.49793e7i	−0.120693	+	0.839439i
$378$	846799.	−	386720.i	0.0156785	−	0.00716014i
$379$	−3.00841e7	+	1.02457e8i	−0.552610	+	1.88202i	−0.0888796	+	0.996042i	$0.528329\pi$
$379$	−3.00841e7	+	1.02457e8i	−0.552610	+	1.88202i	−0.463731	+	0.885976i	$0.653490\pi$
$380$	−2.46093e7	−	7.22595e6i	−0.448486	−	0.131687i
$381$	7.65216e6	+	1.67559e7i	0.138360	+	0.302965i
$382$	7.32897e6	+	1.05375e6i	0.131478	+	0.0189037i
$383$	4.28751e7	+	3.71515e7i	0.763148	+	0.661271i	0.946837	−	0.321713i	$-0.104259\pi$
$383$	4.28751e7	+	3.71515e7i	0.763148	+	0.661271i	−0.183690	+	0.982984i	$0.558804\pi$
$384$	1.06317e7	−	2.32801e7i	0.187762	−	0.411141i
$385$	1.02782e7	−	1.59932e7i	0.180109	−	0.280256i
$386$	860073.	+	5.98194e6i	0.0149546	+	0.104011i
$387$	8.38312e6	+	1.30444e7i	0.144635	+	0.225056i
$388$	−6.24121e6	+	5.40804e6i	−0.106850	+	0.0925858i
$389$	6.70730e6	+	2.28430e7i	0.113946	+	0.388064i	0.996642	−	0.0818796i	$-0.0260923\pi$
$389$	6.70730e6	+	2.28430e7i	0.113946	+	0.388064i	−0.882696	+	0.469944i	$0.844274\pi$
$390$		−	1.39924e7i		−	0.235884i
$391$	1.08187e6	−	1.57674e6i	0.0180986	−	0.0263773i
$392$	−5.57796e7			−0.926013
$393$	5.09523e7	−	1.49609e7i	0.839433	−	0.246480i
$394$	1.48693e7	+	1.71601e7i	0.243110	+	0.280563i
$395$	2.74109e7	−	1.76159e7i	0.444766	−	0.285834i
$396$	−2.15309e7	+	3.09568e6i	−0.346718	+	0.0498505i
$397$	6.70021e7	+	4.30596e7i	1.07082	+	0.688175i	0.952419	−	0.304791i	$-0.0985866\pi$
$397$	6.70021e7	+	4.30596e7i	1.07082	+	0.688175i	0.118402	+	0.992966i	$0.462223\pi$
$398$	−2.76540e7	−	1.26291e7i	−0.438640	−	0.200320i
$399$	−1.91975e6	+	2.21551e6i	−0.0302223	+	0.0348783i
$400$	1.11709e6	−	7.76951e6i	0.0174545	−	0.121399i
$401$	−8.74224e7	+	3.99245e7i	−1.35578	+	0.619165i	−0.954890	−	0.296960i	$-0.904027\pi$
$401$	−8.74224e7	+	3.99245e7i	−1.35578	+	0.619165i	−0.400892	+	0.916125i	$0.631300\pi$
$402$	1.07906e7	−	3.67494e7i	0.166099	−	0.565681i
$403$	−1.52485e7	−	4.47735e6i	−0.232976	−	0.0684078i
$404$	2.48965e7	+	5.45158e7i	0.377567	+	0.826757i
$405$	−9.94734e6	−	1.43021e6i	−0.149741	−	0.0215296i
$406$	−7.23589e6	−	6.26994e6i	−0.108122	−	0.0936883i
$407$	4.02280e7	−	8.80871e7i	0.596686	−	1.30656i
$408$	644162.	−	1.00234e6i	0.00948450	−	0.0147582i
$409$	−3.71799e6	−	2.58592e7i	−0.0543423	−	0.377959i	−0.998785	−	0.0492827i	$-0.984306\pi$
$409$	−3.71799e6	−	2.58592e7i	−0.0543423	−	0.377959i	0.944443	−	0.328677i	$-0.106603\pi$
$410$	−5.00365e7	−	7.78583e7i	−0.725998	−	1.12967i
$411$	202782.	−	175711.i	0.00292081	−	0.00253090i
$412$	9.15130e6	+	3.11665e7i	0.130855	+	0.445652i
$413$		−	1.40297e7i		−	0.199158i
$414$	−1.50260e6	−	1.32841e7i	−0.0211759	−	0.187211i
$415$	1.19683e8			1.67452
$416$	−3.78113e7	+	1.11024e7i	−0.525221	+	0.154219i
$417$	−4.77079e7	−	5.50578e7i	−0.657933	−	0.759295i
$418$	−2.70517e7	+	1.73851e7i	−0.370395	+	0.238038i
$419$	1.13465e8	−	1.63138e7i	1.54248	−	0.221775i	0.682034	−	0.731320i	$-0.261095\pi$
$419$	1.13465e8	−	1.63138e7i	1.54248	−	0.221775i	0.860444	+	0.509545i	$0.170186\pi$
$420$	−5.28320e6	−	3.39530e6i	−0.0713098	−	0.0458280i
$421$	−6.28915e7	−	2.87216e7i	−0.842841	−	0.384912i	−0.0532760	−	0.998580i	$-0.516966\pi$
$421$	−6.28915e7	−	2.87216e7i	−0.842841	−	0.384912i	−0.789565	+	0.613667i	$0.789694\pi$
$422$	3.21157e7	−	3.70635e7i	0.427346	−	0.493184i
$423$	770701.	−	5.36035e6i	0.0101828	−	0.0708226i
$424$	−9.80017e7	+	4.47559e7i	−1.28569	+	0.587155i
$425$	590674.	−	2.01165e6i	0.00769452	−	0.0262051i
$426$	−3.54486e6	−	1.04086e6i	−0.0458532	−	0.0134637i
$427$	−5.32012e6	−	1.16494e7i	−0.0683341	−	0.149631i
$428$	−2.71147e7	−	3.89850e6i	−0.345838	−	0.0497240i
$429$	2.82422e7	+	2.44720e7i	0.357707	+	0.309955i
$430$	−2.03992e7	+	4.46681e7i	−0.256572	+	0.561814i
$431$	2.57279e7	−	4.00334e7i	0.321346	−	0.500024i	−0.642572	−	0.766226i	$-0.722132\pi$
$431$	2.57279e7	−	4.00334e7i	0.321346	−	0.500024i	0.963917	+	0.266202i	$0.0857688\pi$
$432$	317203.	+	2.20620e6i	0.00393447	+	0.0273649i
$433$	−3.24093e7	−	5.04299e7i	−0.399215	−	0.621190i	0.582210	−	0.813038i	$-0.302188\pi$
$433$	−3.24093e7	−	5.04299e7i	−0.399215	−	0.621190i	−0.981425	+	0.191848i	$0.938552\pi$
$434$	2.53058e6	−	2.19276e6i	0.0309564	−	0.0268239i
$435$	2.91197e7	+	9.91725e7i	0.353768	+	1.20482i
$436$			4.52214e6i			0.0545612i
$437$	2.16821e7	+	3.60866e7i	0.259810	+	0.432416i
$438$	−1.85904e7			−0.221242
$439$	−1.12322e7	+	3.29807e6i	−0.132761	+	0.0389822i	−0.347438	−	0.937703i	$-0.612948\pi$
$439$	−1.12322e7	+	3.29807e6i	−0.132761	+	0.0389822i	0.214677	+	0.976685i	$0.431130\pi$
$440$	−1.11401e8	−	1.28563e8i	−1.30777	−	1.50924i
$441$	2.34465e7	−	1.50681e7i	0.273377	−	0.175689i
$442$	−820466.	+	117965.i	−0.00950153	+	0.00136611i
$443$	−1.04077e8	−	6.68864e7i	−1.19714	−	0.769355i	−0.218681	−	0.975797i	$-0.570175\pi$
$443$	−1.04077e8	−	6.68864e7i	−1.19714	−	0.769355i	−0.978459	+	0.206442i	$0.933812\pi$
$444$	−2.90986e7	−	1.32889e7i	−0.332448	−	0.151824i
$445$	−6.54267e7	+	7.55065e7i	−0.742464	+	0.856849i
$446$	4.63548e6	−	3.22405e7i	0.0522505	−	0.363410i
$447$	−4.74480e7	+	2.16688e7i	−0.531246	+	0.242612i
$448$	1.76262e6	−	6.00292e6i	0.0196030	−	0.0667618i
$449$	1.38088e8	+	4.05462e7i	1.52551	+	0.447931i	0.933674	−	0.358124i	$-0.116584\pi$
$449$	1.38088e8	+	4.05462e7i	1.52551	+	0.447931i	0.591840	+	0.806055i	$0.298402\pi$
$450$	−6.08908e6	−	1.33332e7i	−0.0668211	−	0.146318i
$451$	2.44661e8	+	3.51769e7i	2.66707	+	0.383467i
$452$	−3.33632e7	−	2.89094e7i	−0.361288	−	0.313057i
$453$	4.62858e6	−	1.01352e7i	0.0497912	−	0.109028i
$454$	−609474.	+	948360.i	−0.00651310	+	0.0101346i
$455$	1.53545e6	+	1.06793e7i	0.0163005	+	0.113373i
$456$	1.41819e7	+	2.20675e7i	0.149569	+	0.232733i
$457$	−1.10633e8	+	9.58641e7i	−1.15914	+	1.00440i	−0.159289	+	0.987232i	$0.550920\pi$
$457$	−1.10633e8	+	9.58641e7i	−1.15914	+	1.00440i	−0.999853	+	0.0171696i	$0.994534\pi$
$458$	1.29527e7	+	4.41130e7i	0.134823	+	0.459166i
$459$			595335.i			0.00615635i
$460$	−6.99099e7	+	5.69779e7i	−0.718233	+	0.585374i
$461$	7.02674e7			0.717218			0.358609	−	0.933488i	$-0.383251\pi$
$461$	7.02674e7			0.717218			0.358609	+	0.933488i	$0.383251\pi$
$462$	−7.55477e6	+	2.21828e6i	−0.0766117	+	0.0224952i
$463$	−3.96059e7	−	4.57076e7i	−0.399040	−	0.460517i	0.520298	−	0.853985i	$-0.325821\pi$
$463$	−3.96059e7	−	4.57076e7i	−0.399040	−	0.460517i	−0.919338	+	0.393468i	$0.871275\pi$
$464$	1.92847e7	−	1.23936e7i	0.193046	−	0.124063i
$465$	−3.57795e7	+	5.14431e6i	−0.355857	+	0.0511645i
$466$	8.32189e7	+	5.34815e7i	0.822364	+	0.528501i
$467$	−1.71105e7	−	7.81409e6i	−0.168001	−	0.0767234i	0.329640	−	0.944107i	$-0.393073\pi$
$467$	−1.71105e7	−	7.81409e6i	−0.168001	−	0.0767234i	−0.497640	+	0.867383i	$0.665800\pi$
$468$	8.08408e6	−	9.32953e6i	0.0788666	−	0.0910169i
$469$	−4.20293e6	+	2.92320e7i	−0.0407412	+	0.283361i
$470$	1.56004e7	−	7.12449e6i	0.150260	−	0.0686215i
$471$	2.33782e7	−	7.96189e7i	0.223743	−	0.761997i
$472$	−1.20453e8	−	3.53683e7i	−1.14549	−	0.336347i
$473$	−5.44808e7	−	1.19296e8i	−0.514825	−	1.12731i
$474$	−1.33574e7	−	1.92051e6i	−0.125426	−	0.0180335i
$475$	3.48842e7	+	3.02273e7i	0.325498	+	0.282045i
$476$	−154548.	+	338413.i	−0.00143299	+	0.00313781i
$477$	2.91040e7	−	4.52867e7i	0.268162	−	0.417268i
$478$	−5.93715e6	−	4.12938e7i	−0.0543619	−	0.378095i
$479$	−9.41086e7	−	1.46436e8i	−0.856294	−	1.33242i	−0.941832	−	0.336085i	$-0.890897\pi$
$479$	−9.41086e7	−	1.46436e8i	−0.856294	−	1.33242i	0.0855375	−	0.996335i	$-0.472739\pi$
$480$	−6.77410e7	+	5.86979e7i	−0.612531	+	0.530761i
$481$	1.54832e7	+	5.27309e7i	0.139131	+	0.473838i
$482$		−	5.92051e7i		−	0.528711i
$483$	2.60455e6	+	9.97386e6i	0.0231148	+	0.0885160i
$484$	1.06821e8			0.942152
$485$	3.09629e7	−	9.09153e6i	0.271404	−	0.0796915i
$486$	2.72564e6	+	3.14556e6i	0.0237443	+	0.0274024i
$487$	−9.13718e7	+	5.87211e7i	−0.791089	+	0.508402i	−0.872697	−	0.488262i	$-0.837631\pi$
$487$	−9.13718e7	+	5.87211e7i	−0.791089	+	0.508402i	0.0816077	+	0.996665i	$0.473995\pi$
$488$	−1.13429e8	+	1.63087e7i	−0.976036	+	0.140333i
$489$	−2.90520e7	−	1.86706e7i	−0.248456	−	0.159673i
$490$	8.02883e7	+	3.66664e7i	0.682439	+	0.311659i
$491$	−1.43517e8	+	1.65627e8i	−1.21244	+	1.39923i	−0.320386	+	0.947287i	$0.603813\pi$
$491$	−1.43517e8	+	1.65627e8i	−1.21244	+	1.39923i	−0.892049	+	0.451938i	$0.850733\pi$
$492$	1.16203e7	−	8.08210e7i	0.0975714	−	0.678624i
$493$	5.56964e6	−	2.54357e6i	0.0464821	−	0.0212277i
$494$	5.14139e6	−	1.75100e7i	0.0426481	−	0.145246i
$495$	8.15561e7	+	2.39470e7i	0.672420	+	0.197440i
$496$	3.33040e6	+	7.29257e6i	0.0272930	+	0.0597634i
$497$	2.81973e6	+	405416.i	0.0229688	+	0.00330242i
$498$	−3.74612e7	−	3.24603e7i	−0.303315	−	0.262824i
$499$	−856660.	+	1.87582e6i	−0.00689457	+	0.0150970i	−0.913048	−	0.407852i	$-0.866278\pi$
$499$	−856660.	+	1.87582e6i	−0.00689457	+	0.0150970i	0.906153	+	0.422949i	$0.139005\pi$
$500$	9.15678e6	−	1.42482e7i	0.0732543	−	0.113986i
$501$	−2.93125e6	−	2.03873e7i	−0.0233098	−	0.162124i
$502$	−3.63730e7	−	5.65975e7i	−0.287520	−	0.447390i
$503$	4.83693e7	−	4.19122e7i	0.380072	−	0.329334i	−0.443784	−	0.896134i	$-0.646364\pi$
$503$	4.83693e7	−	4.19122e7i	0.380072	−	0.329334i	0.823856	+	0.566800i	$0.191819\pi$
$504$	1.80957e6	+	6.16283e6i	0.0141346	+	0.0481380i
$505$		−	2.34189e8i		−	1.81841i
$506$	−3.41046e6	+	1.13021e8i	−0.0263246	+	0.872387i
$507$	5.40346e7			0.414618
$508$	−4.93820e7	+	1.44999e7i	−0.376684	+	0.110605i
$509$	−5.10895e7	−	5.89604e7i	−0.387417	−	0.447103i	0.528221	−	0.849107i	$-0.322859\pi$
$509$	−5.10895e7	−	5.89604e7i	−0.387417	−	0.447103i	−0.915638	+	0.402004i	$0.868314\pi$
$510$	−1.58608e6	+	1.01931e6i	−0.0119568	+	0.00768414i
$511$	1.41886e7	−	2.04002e6i	0.106335	−	0.0152887i
$512$	3.21308e7	+	2.06492e7i	0.239393	+	0.153849i
$513$	−1.19225e7	−	5.44482e6i	−0.0883111	−	0.0403303i
$514$	−4.03017e7	+	4.65107e7i	−0.296780	+	0.342502i
$515$	1.80636e7	−	1.25635e8i	0.132246	−	0.919794i
$516$	−3.94083e7	+	1.79972e7i	−0.286839	+	0.130995i
$517$	−1.29044e7	+	4.39483e7i	−0.0933826	+	0.318032i
$518$	−1.11102e7	−	3.26226e6i	−0.0799344	−	0.0234709i
$519$	−5.81545e7	−	1.27341e8i	−0.415989	−	0.910888i
$520$	9.55592e7	+	1.37393e7i	0.679614	+	0.0977137i
$521$	2.08701e8	+	1.80840e8i	1.47575	+	1.27874i	0.879464	+	0.475965i	$0.157901\pi$
$521$	2.08701e8	+	1.80840e8i	1.47575	+	1.27874i	0.596281	+	0.802776i	$0.296644\pi$
$522$	1.77829e7	−	3.89390e7i	0.125023	−	0.273762i
$523$	2.22578e7	−	3.46338e7i	0.155588	−	0.242100i	−0.754705	−	0.656065i	$-0.772220\pi$
$523$	2.22578e7	−	3.46338e7i	0.155588	−	0.242100i	0.910293	+	0.413965i	$0.135856\pi$
$524$	2.11153e7	+	1.46860e8i	0.146758	+	1.02073i
$525$	6.11043e6	+	9.50802e6i	0.0422274	+	0.0657071i
$526$	−3.19896e7	+	2.77192e7i	−0.219812	+	0.190468i
$527$	603290.	+	2.05462e6i	0.00412187	+	0.0140378i
$528$		−	1.88518e7i		−	0.128071i
$529$	1.47767e8	+	8.92594e6i	0.998181	+	0.0602958i
$530$	1.70482e8			1.14512
$531$	6.01858e7	−	1.76722e7i	0.401986	−	0.118034i
$532$	−5.36377e6	−	6.19013e6i	−0.0356234	−	0.0411116i
$533$	−1.18008e8	+	7.58390e7i	−0.779343	+	0.500854i
$534$	4.09575e7	−	5.88879e6i	0.268973	−	0.0386725i
$535$	9.00500e7	+	5.78716e7i	0.588061	+	0.377924i
$536$	2.40379e8	+	1.09778e8i	1.56100	+	0.712885i
$537$	−5.20195e7	+	6.00337e7i	−0.335926	+	0.387679i
$538$	8.88663e6	−	6.18079e7i	0.0570677	−	0.396914i
$539$	−2.14428e8	+	9.79259e7i	−1.36935	+	0.625362i
$540$	7.91065e6	−	2.69412e7i	0.0502378	−	0.171094i
$541$	−1.03713e8	−	3.04530e7i	−0.655002	−	0.192326i	−0.0626881	−	0.998033i	$-0.519967\pi$
$541$	−1.03713e8	−	3.04530e7i	−0.655002	−	0.192326i	−0.592314	+	0.805707i	$0.701786\pi$
$542$	7.16005e7	+	1.56783e8i	0.449695	+	0.984695i
$543$	−6.15775e7	−	8.85350e6i	−0.384611	−	0.0552988i
$544$	4.01295e6	+	3.47724e6i	0.0249268	+	0.0215992i
$545$	7.34066e6	−	1.60738e7i	0.0453467	−	0.0992954i
$546$	2.41582e6	−	3.75909e6i	0.0148418	−	0.0230943i
$547$	3.81977e7	+	2.65671e8i	0.233386	+	1.62323i	0.683282	+	0.730154i	$0.260552\pi$
$547$	3.81977e7	+	2.65671e8i	0.233386	+	1.62323i	−0.449896	+	0.893081i	$0.648539\pi$
$548$	405308.	+	630671.i	0.00246288	+	0.00383231i
$549$	4.32735e7	−	3.74967e7i	0.261520	−	0.226608i
$550$	3.49278e7	+	1.18953e8i	0.209934	+	0.714970i
$551$			1.34803e8i			0.805835i
$552$	9.21976e7	+	2.78210e6i	0.548154	+	0.0165407i
$553$	1.04054e7			0.0615296
$554$	−2.10397e7	+	6.17781e6i	−0.123740	+	0.0363333i
$555$	8.18588e7	+	9.44701e7i	0.478836	+	0.552606i
$556$	1.71235e8	−	1.10046e8i	0.996250	−	0.640251i
$557$	2.71399e7	−	3.90213e6i	0.157052	−	0.0225806i	−0.0633404	−	0.997992i	$-0.520175\pi$
$557$	2.71399e7	−	3.90213e6i	0.157052	−	0.0225806i	0.220392	+	0.975411i	$0.429266\pi$
$558$	1.25943e7	+	8.09387e6i	0.0724889	+	0.0465858i
$559$	6.77023e7	+	3.09186e7i	0.387586	+	0.177005i
$560$	3.56423e6	−	4.11334e6i	0.0202956	−	0.0234224i
$561$	716599.	−	4.98406e6i	0.00405871	−	0.0282289i
$562$	4.72606e7	−	2.15832e7i	0.266250	−	0.121592i
$563$	7.76067e7	−	2.64304e8i	0.434884	−	1.48108i	−0.392662	−	0.919683i	$-0.628446\pi$
$563$	7.76067e7	−	2.64304e8i	0.434884	−	1.48108i	0.827546	−	0.561398i	$-0.189736\pi$
$564$	1.45179e7	+	4.26283e6i	0.0809218	+	0.0237608i
$565$	7.16608e7	+	1.56915e8i	0.397316	+	0.870002i
$566$	5.94776e7	+	8.55159e6i	0.328023	+	0.0471626i
$567$	−2.42545e6	−	2.10166e6i	−0.0133058	−	0.0115296i
$568$	1.05892e7	−	2.31871e7i	0.0577853	−	0.126532i
$569$	−1.46840e8	+	2.28488e8i	−0.797092	+	1.24030i	0.169893	+	0.985463i	$0.445658\pi$
$569$	−1.46840e8	+	2.28488e8i	−0.797092	+	1.24030i	−0.966984	+	0.254836i	$0.917978\pi$
$570$	−5.90727e6	−	4.10860e7i	−0.0318979	−	0.221855i
$571$	−1.40207e8	−	2.18166e8i	−0.753115	−	1.17187i	−0.980203	−	0.197995i	$-0.936557\pi$
$571$	−1.40207e8	−	2.18166e8i	−0.753115	−	1.17187i	0.227088	−	0.973874i	$-0.427079\pi$
$572$	−7.89086e7	+	6.83747e7i	−0.421634	+	0.365348i
$573$	−7.19155e6	−	2.44922e7i	−0.0382260	−	0.130186i
$574$		−	2.95557e7i		−	0.156281i
$575$	1.57043e8	−	4.10097e7i	0.826065	−	0.215716i
$576$	2.79721e7			0.146372
$577$	2.21824e8	−	6.51335e7i	1.15473	−	0.339060i	0.352349	−	0.935869i	$-0.385383\pi$
$577$	2.21824e8	−	6.51335e7i	1.15473	−	0.339060i	0.802384	+	0.596809i	$0.203565\pi$
$578$	−7.14006e7	−	8.24007e7i	−0.369759	−	0.426724i
$579$	1.75271e7	−	1.12640e7i	0.0902975	−	0.0580307i
$580$	−2.85845e8	+	4.10984e7i	−1.46503	+	0.210640i
$581$	3.21532e7	+	2.06636e7i	0.163944	+	0.105361i
$582$	−1.21573e7	−	5.55203e6i	−0.0616690	−	0.0281633i
$583$	−2.98165e8	+	3.44101e8i	−1.50471	+	1.73652i
$584$	1.82542e7	−	1.26961e8i	0.0916484	−	0.637428i
$585$	−4.38790e7	+	2.00389e7i	−0.219174	+	0.100093i
$586$	6.18820e7	−	2.10751e8i	0.307519	−	1.04731i
$587$	−5.39648e7	−	1.58455e7i	−0.266806	−	0.0783414i	0.145593	−	0.989345i	$-0.453491\pi$
$587$	−5.39648e7	−	1.58455e7i	−0.266806	−	0.0783414i	−0.412399	+	0.911003i	$0.635309\pi$
$588$	3.23488e7	+	7.08340e7i	0.159120	+	0.348425i
$589$	−4.66644e7	−	6.70933e6i	−0.228370	−	0.0328347i
$590$	1.50129e8	+	1.30088e8i	0.730987	+	0.633404i
$591$	3.25179e7	−	7.12044e7i	0.157529	−	0.344940i
$592$	1.49887e7	−	2.33228e7i	0.0722433	−	0.112413i
$593$	−2.04623e7	−	1.42318e8i	−0.0981273	−	0.682490i	−0.978202	−	0.207655i	$-0.933417\pi$
$593$	−2.04623e7	−	1.42318e8i	−0.0981273	−	0.682490i	0.880075	−	0.474835i	$-0.157492\pi$
$594$	−1.90324e7	−	2.96150e7i	−0.0908100	−	0.141303i
$595$	1.09867e6	−	952007.i	0.00521576	−	0.00451949i
$596$	−4.10596e7	−	1.39836e8i	−0.193944	−	0.660512i
$597$			1.04807e8i			0.492569i
$598$	−4.05408e7	−	4.97422e7i	−0.189579	−	0.232606i
$599$	9.76212e7			0.454217			0.227109	−	0.973869i	$-0.427073\pi$
$599$	9.76212e7			0.454217			0.227109	+	0.973869i	$0.427073\pi$
$600$	9.70364e7	−	2.84924e7i	0.449242	−	0.131909i
$601$	−2.89736e7	−	3.34373e7i	−0.133468	−	0.154031i	0.685081	−	0.728467i	$-0.259767\pi$
$601$	−2.89736e7	−	3.34373e7i	−0.133468	−	0.154031i	−0.818549	+	0.574436i	$0.805221\pi$
$602$	−1.31924e7	+	8.47822e6i	−0.0604691	+	0.0388611i
$603$	−1.30696e8	+	1.87913e7i	−0.596090	+	0.0857048i
$604$	2.61889e7	+	1.68306e7i	0.118852	+	0.0763815i
$605$	−3.79692e8	−	1.73400e8i	−1.71461	−	0.783037i
$606$	−6.35162e7	+	7.33016e7i	−0.285408	+	0.329379i
$607$	−1.43308e7	+	9.96727e7i	−0.0640772	+	0.445666i	0.932374	+	0.361495i	$0.117733\pi$
$607$	−1.43308e7	+	9.96727e7i	−0.0640772	+	0.445666i	−0.996451	+	0.0841716i	$0.973176\pi$
$608$	−1.06339e8	+	4.85632e7i	−0.473130	+	0.216071i
$609$	−9.29930e6	+	3.16705e7i	−0.0411717	+	0.140218i
$610$	1.73989e8	+	5.10877e7i	0.766535	+	0.225075i
$611$	−1.07984e7	−	2.36452e7i	−0.0473408	−	0.103662i
$612$	−1.64643e6	−	236721.i	−0.00718272	−	0.00103272i
$613$	−2.55388e8	−	2.21295e8i	−1.10871	−	0.960706i	−0.109268	−	0.994012i	$-0.534851\pi$
$613$	−2.55388e8	−	2.21295e8i	−1.10871	−	0.960706i	−0.999445	+	0.0333066i	$0.989396\pi$
$614$	−4.59188e6	+	1.00548e7i	−0.0198374	+	0.0434379i
$615$	−1.72499e8	+	2.68413e8i	−0.741584	+	1.15393i
$616$	−7.73131e6	−	5.37724e7i	−0.0330758	−	0.230048i
$617$	−1.13544e8	−	1.76677e8i	−0.483400	−	0.752185i	0.510804	−	0.859697i	$-0.329348\pi$
$617$	−1.13544e8	−	1.76677e8i	−0.483400	−	0.752185i	−0.994204	+	0.107512i	$0.965712\pi$
$618$	−3.97286e7	+	3.44250e7i	−0.168321	+	0.145851i
$619$	−7.72341e7	−	2.63035e8i	−0.325639	−	1.10903i	−0.945854	−	0.324594i	$-0.894772\pi$
$619$	−7.72341e7	−	2.63035e8i	−0.325639	−	1.10903i	0.620214	−	0.784433i	$-0.287046\pi$
$620$		−	1.00996e8i		−	0.423767i
$621$	−3.95061e7	+	2.37366e7i	−0.164964	+	0.0991159i
$622$	−6.14449e7			−0.255337
$623$	−3.06134e7	+	8.98891e6i	−0.126604	+	0.0371743i
$624$	7.00612e6	+	8.08549e6i	0.0288352	+	0.0332776i
$625$	−2.31026e8	+	1.48472e8i	−0.946284	+	0.608140i
$626$	1.63071e8	−	2.34460e7i	0.664742	−	0.0955755i
$627$	9.32595e7	+	5.99342e7i	0.378347	+	0.243149i
$628$	2.10894e8	+	9.63122e7i	0.851503	+	0.388868i
$629$	4.84928e6	−	5.59637e6i	0.0194861	−	0.0224882i
$630$	1.44644e6	−	1.00602e7i	0.00578466	−	0.0402332i
$631$	2.80486e8	−	1.28094e8i	1.11641	−	0.509847i	0.230206	−	0.973142i	$-0.426060\pi$
$631$	2.80486e8	−	1.28094e8i	1.11641	−	0.509847i	0.886204	+	0.463295i	$0.153333\pi$
$632$	2.62317e7	−	8.93369e7i	0.103914	−	0.353899i
$633$	−1.62222e8	−	4.76326e7i	−0.639585	−	0.187799i
$634$	−2.88000e6	−	6.30632e6i	−0.0113012	−	0.0247462i
$635$	1.99064e8	+	2.86211e7i	0.777449	+	0.111780i
$636$	1.13670e8	+	9.84957e7i	0.441850	+	0.382865i
$637$	5.55743e7	−	1.21691e8i	0.215009	−	0.470803i
$638$	−1.95746e8	+	3.04587e8i	−0.753756	+	1.17287i
$639$	1.81262e6	+	1.26070e7i	0.00694710	+	0.0483181i
$640$	−1.51064e8	−	2.35061e8i	−0.576265	−	0.896685i
$641$	3.19396e8	−	2.76759e8i	1.21271	−	1.05082i	0.215472	−	0.976510i	$-0.430871\pi$
$641$	3.19396e8	−	2.76759e8i	1.21271	−	1.05082i	0.997235	−	0.0743070i	$-0.0236745\pi$
$642$	−1.24900e7	−	4.25371e7i	−0.0472018	−	0.160755i
$643$		−	1.46153e8i		−	0.549762i	−0.961478	−	0.274881i	$-0.911362\pi$
$643$		−	1.46153e8i		−	0.549762i	0.961478	−	0.274881i	$-0.0886384\pi$
$644$	−2.86189e7	+	3.23714e6i	−0.107151	+	0.0121200i
$645$	1.69290e8			0.630887
$646$	−2.35934e6	+	692764.i	−0.00875171	+	0.00256973i
$647$	8.73165e7	+	1.00769e8i	0.322392	+	0.372060i	0.893692	−	0.448682i	$-0.148106\pi$
$647$	8.73165e7	+	1.00769e8i	0.322392	+	0.372060i	−0.571300	+	0.820741i	$0.693561\pi$
$648$	−2.41585e7	+	1.55257e7i	−0.0887861	+	0.0570594i
$649$	−5.25138e8	+	7.55035e7i	−1.92105	+	0.276206i
$650$	−5.91885e7	−	3.80381e7i	−0.215525	−	0.138509i
$651$	−1.05004e7	−	4.79538e6i	−0.0380596	−	0.0173812i
$652$	6.31863e7	−	7.29209e7i	0.227971	−	0.263093i
$653$	−5.57865e7	+	3.88004e8i	−0.200350	+	1.39347i	0.602897	+	0.797819i	$0.294013\pi$
$653$	−5.57865e7	+	3.88004e8i	−0.200350	+	1.39347i	−0.803247	+	0.595646i	$0.796896\pi$
$654$	−6.65715e6	+	3.04022e6i	−0.0237988	+	0.0108686i
$655$	1.63340e8	−	5.56286e8i	0.581258	−	1.97958i
$656$	6.78979e7	+	1.99366e7i	0.240516	+	0.0706220i
$657$	2.66238e7	+	5.82981e7i	0.0938804	+	0.205569i
$658$	5.42116e6	+	779445.i	0.0190289	+	0.00273595i
$659$	−2.33463e8	−	2.02296e8i	−0.815757	−	0.706858i	0.143420	−	0.989662i	$-0.454190\pi$
$659$	−2.33463e8	−	2.02296e8i	−0.815757	−	0.706858i	−0.959178	+	0.282804i	$0.908735\pi$
$660$	−9.86556e7	+	2.16026e8i	−0.343155	+	0.751404i
$661$	4.97170e7	−	7.73611e7i	0.172147	−	0.267866i	−0.744450	−	0.667678i	$-0.767288\pi$
$661$	4.97170e7	−	7.73611e7i	0.172147	−	0.267866i	0.916597	+	0.399812i	$0.130925\pi$
$662$	3.12961e7	+	2.17669e8i	0.107874	+	0.750280i
$663$	1.54494e6	+	2.40397e6i	0.00530116	+	0.00824877i
$664$	2.58467e8	−	2.23963e8i	0.882878	−	0.765018i
$665$	9.01712e6	+	3.07095e7i	0.0306622	+	0.104426i
$666$		−	5.17710e7i		−	0.175252i
$667$	3.90856e8	+	2.68183e8i	1.31716	+	0.903761i
$668$	5.75476e7			0.193062
$669$	−1.07742e8	+	3.16360e7i	−0.359838	+	0.105658i
$670$	−2.73836e8	−	3.16024e8i	−0.910473	−	1.05074i
$671$	−4.07414e8	+	2.61829e8i	−1.34855	+	0.866662i
$672$	−2.83331e7	+	4.07369e6i	−0.0933655	+	0.0134239i
$673$	−4.65910e8	−	2.99422e8i	−1.52847	−	0.982289i	−0.990222	−	0.139503i	$-0.955450\pi$
$673$	−4.65910e8	−	2.99422e8i	−1.52847	−	0.982289i	−0.538249	−	0.842786i	$-0.680914\pi$
$674$	1.80889e8	+	8.26092e7i	0.590789	+	0.269804i
$675$	−3.30916e7	+	3.81897e7i	−0.107598	+	0.124175i
$676$	−2.14856e7	+	1.49435e8i	−0.0695516	+	0.483742i
$677$	−3.86512e8	+	1.76514e8i	−1.24565	+	0.568870i	−0.925590	−	0.378527i	$-0.876431\pi$
$677$	−3.86512e8	+	1.76514e8i	−1.24565	+	0.568870i	−0.320061	+	0.947397i	$0.603703\pi$
$678$	2.01283e7	−	6.85506e7i	0.0645829	−	0.219949i
$679$	9.88793e6	+	2.90336e6i	0.0315861	+	0.00927452i
$680$	−5.40384e6	−	1.18328e7i	−0.0171860	−	0.0376322i
$681$	3.84682e6	+	553090.i	0.0121804	+	0.00175128i
$682$	−9.56951e7	−	8.29203e7i	−0.301673	−	0.261401i
$683$	1.36799e8	−	2.99549e8i	0.429360	−	0.940168i	−0.564070	−	0.825727i	$-0.690765\pi$
$683$	1.36799e8	−	2.99549e8i	0.429360	−	0.940168i	0.993430	−	0.114441i	$-0.0365075\pi$
$684$	1.97986e7	−	3.08073e7i	0.0618681	−	0.0962687i
$685$	−416903.	−	2.89963e6i	−0.00129707	−	0.00902133i
$686$	3.08707e7	+	4.80357e7i	0.0956254	+	0.148796i
$687$	1.19785e8	−	1.03794e8i	0.369429	−	0.320112i
$688$	−1.05780e7	−	3.60255e7i	−0.0324818	−	0.110623i
$689$		−	2.58395e8i		−	0.790000i
$690$	−1.30879e8	−	6.46101e7i	−0.398403	−	0.196677i
$691$	3.02188e8			0.915890			0.457945	−	0.888981i	$-0.348586\pi$
$691$	3.02188e8			0.915890			0.457945	+	0.888981i	$0.348586\pi$
$692$	3.75291e8	−	1.10195e8i	1.13253	−	0.332541i
$693$	1.77757e7	+	2.05143e7i	0.0534106	+	0.0616391i
$694$	−5.51927e7	+	3.54702e7i	−0.165121	+	0.106117i
$695$	−7.87285e8	+	1.13195e8i	−2.34519	+	0.337187i
$696$	2.48468e8	+	1.59680e8i	0.736957	+	0.473613i
$697$	1.71931e7	+	7.85183e6i	0.0507757	+	0.0231885i
$698$	1.69193e8	−	1.95259e8i	0.497526	−	0.574176i
$699$	4.85338e7	−	3.37560e8i	0.142106	−	0.988369i
$700$	−2.87246e7	+	1.31181e7i	−0.0837452	+	0.0382451i
$701$	−6.86852e7	+	2.33920e8i	−0.199393	+	0.679069i	0.797713	+	0.603037i	$0.206043\pi$
$701$	−6.86852e7	+	2.33920e8i	−0.199393	+	0.679069i	−0.997105	+	0.0760313i	$0.975775\pi$
$702$	1.91691e7	+	5.62857e6i	0.0554104	+	0.0162700i
$703$	6.77252e7	+	1.48297e8i	0.194933	+	0.426843i
$704$	−2.34178e8	−	3.36698e7i	−0.671164	−	0.0964989i
$705$	−4.46836e7	−	3.87186e7i	−0.127521	−	0.110497i
$706$	1.43803e8	−	3.14886e8i	0.408654	−	0.894826i
$707$	4.04332e7	−	6.29153e7i	0.114414	−	0.178032i
$708$	2.49418e7	+	1.73474e8i	0.0702794	+	0.488804i
$709$	5.54950e7	+	8.63519e7i	0.155709	+	0.242289i	0.910340	−	0.413861i	$-0.135820\pi$
$709$	5.54950e7	+	8.63519e7i	0.155709	+	0.242289i	−0.754630	+	0.656150i	$0.772184\pi$
$710$	−3.04838e7	+	2.64144e7i	−0.0851715	+	0.0738015i
$711$	1.31070e7	+	4.46382e7i	0.0364664	+	0.124193i
$712$			2.85496e8i			0.790969i
$713$	−1.12289e8	+	1.21953e8i	−0.309792	+	0.336454i
$714$	−602089.			−0.00165412
$715$	3.91469e8	−	1.14946e8i	1.07097	−	0.314467i
$716$	−1.45342e8	−	1.67734e8i	−0.395960	−	0.456963i
$717$	−1.20991e8	+	7.77563e7i	−0.328244	+	0.210949i
$718$	−2.80817e8	+	4.03754e7i	−0.758666	+	0.109080i
$719$	3.07174e8	+	1.97409e8i	0.826415	+	0.531104i	0.884137	−	0.467228i	$-0.154747\pi$
$719$	3.07174e8	+	1.97409e8i	0.826415	+	0.531104i	−0.0577221	+	0.998333i	$0.518384\pi$
$720$	2.21354e7	+	1.01089e7i	0.0593048	+	0.0270836i
$721$	2.65441e7	−	3.06335e7i	0.0708210	−	0.0817318i
$722$	−2.25700e7	+	1.56978e8i	−0.0599681	+	0.417088i
$723$	−1.85662e8	+	8.47892e7i	−0.491257	+	0.224350i
$724$	4.89696e7	−	1.66775e8i	0.129036	−	0.439456i
$725$	4.98666e8	+	1.46421e8i	1.30857	+	0.384230i
$726$	7.18155e7	+	1.57254e8i	0.187676	+	0.410953i
$727$	−5.17031e8	−	7.43378e7i	−1.34559	−	0.193467i	−0.568411	−	0.822745i	$-0.692441\pi$
$727$	−5.17031e8	−	7.43378e7i	−1.34559	−	0.193467i	−0.777180	+	0.629278i	$0.783351\pi$
$728$	2.33001e7	+	2.01896e7i	0.0603897	+	0.0523280i
$729$	5.96075e6	−	1.30522e7i	0.0153857	−	0.0336901i
$730$	−1.09732e8	+	1.70746e8i	−0.282075	+	0.438917i
$731$	−1.42723e6	−	9.92658e6i	−0.00365377	−	0.0254125i
$732$	8.64924e7	+	1.34585e8i	0.220518	+	0.343133i
$733$	−9.83986e7	+	8.52628e7i	−0.249849	+	0.216495i	−0.770776	−	0.637106i	$-0.780131\pi$
$733$	−9.83986e7	+	8.52628e7i	−0.249849	+	0.216495i	0.520928	+	0.853601i	$0.325586\pi$
$734$	9.30857e7	+	3.17021e8i	0.235394	+	0.801677i
$735$		−	3.04288e8i		−	0.766343i
$736$	−7.07472e7	+	4.04937e8i	−0.177450	+	1.01567i
$737$	1.11679e9			2.78977
$738$	1.26791e8	−	3.72292e7i	0.315442	−	0.0926221i
$739$	1.70826e8	+	1.97144e8i	0.423273	+	0.488483i	0.926831	−	0.375478i	$-0.122521\pi$
$739$	1.70826e8	+	1.97144e8i	0.423273	+	0.488483i	−0.503558	+	0.863961i	$0.667976\pi$
$740$	−2.93811e8	+	1.88821e8i	−0.725059	+	0.465967i
$741$	−6.22730e7	+	8.95350e6i	−0.153054	+	0.0220059i
$742$	4.58004e7	+	2.94342e7i	0.112114	+	0.0720510i
$743$	1.70083e8	+	7.76744e7i	0.414663	+	0.189370i	0.611812	−	0.791003i	$-0.290441\pi$
$743$	1.70083e8	+	7.76744e7i	0.414663	+	0.189370i	−0.197149	+	0.980374i	$0.563168\pi$
$744$	−6.76425e7	+	7.80636e7i	−0.164248	+	0.189553i
$745$	−8.10470e7	+	5.63694e8i	−0.196005	+	1.36325i
$746$	1.58207e8	−	7.22506e7i	0.381073	−	0.174030i
$747$	−4.81437e7	+	1.63962e8i	−0.115499	+	0.393353i
$748$	1.34987e7	+	3.96359e6i	0.0322543	+	0.00947073i
$749$	1.42005e7	+	3.10947e7i	0.0337954	+	0.0740015i
$750$	2.71313e7	+	3.90089e6i	0.0643112	+	0.00924655i
$751$	5.45906e8	+	4.73030e8i	1.28884	+	1.11678i	0.986531	+	0.163573i	$0.0523020\pi$
$751$	5.45906e8	+	4.73030e8i	1.28884	+	1.11678i	0.302306	+	0.953211i	$0.402243\pi$
$752$	−5.44741e6	+	1.19282e7i	−0.0128096	+	0.0280492i
$753$	−1.25394e8	+	1.95117e8i	−0.293693	+	0.456995i
$754$	−2.92422e7	−	2.03384e8i	−0.0682176	−	0.474464i
$755$	−6.57671e7	−	1.02336e8i	−0.152816	−	0.237786i
$756$	6.77668e6	−	5.87202e6i	0.0156838	−	0.0135901i
$757$	1.72857e8	+	5.88695e8i	0.398472	+	1.35707i	0.877628	+	0.479342i	$0.159125\pi$
$757$	1.72857e8	+	5.88695e8i	0.398472	+	1.35707i	−0.479156	+	0.877730i	$0.659057\pi$
$758$		−	4.82841e8i		−	1.10865i
$759$	3.59310e8	−	1.51166e8i	0.821759	−	0.345723i
$760$	2.86392e8			0.652408
$761$	7.50686e8	−	2.20421e8i	1.70335	−	0.500149i	0.721922	−	0.691974i	$-0.243259\pi$
$761$	7.50686e8	−	2.20421e8i	1.70335	−	0.500149i	0.981429	+	0.191825i	$0.0614407\pi$
$762$	−5.45450e7	−	6.29483e7i	−0.123279	−	0.142272i
$763$	4.74727e6	−	3.05088e6i	0.0106874	−	0.00686835i
$764$	7.05939e7	−	1.01499e7i	0.158302	−	0.0227604i
$765$	5.46793e6	+	3.51402e6i	0.0122135	+	0.00784911i
$766$	−2.33344e8	−	1.06565e8i	−0.519171	−	0.237098i
$767$	1.97171e8	−	2.27547e8i	0.436975	−	0.504296i
$768$	−3.28130e7	+	2.28219e8i	−0.0724373	+	0.503813i
$769$	1.29640e8	−	5.92046e7i	0.285076	−	0.130190i	−0.267745	−	0.963490i	$-0.586279\pi$
$769$	1.29640e8	−	5.92046e7i	0.285076	−	0.130190i	0.552821	+	0.833300i	$0.313551\pi$
$770$	−2.42187e7	+	8.24813e7i	−0.0530492	+	0.180669i
$771$	2.03571e8	+	5.97738e7i	0.444173	+	0.130421i
$772$	2.41820e7	+	5.29511e7i	0.0525581	+	0.115086i
$773$	−2.76672e8	−	3.97794e7i	−0.598999	−	0.0861231i	−0.163856	−	0.986484i	$-0.552393\pi$
$773$	−2.76672e8	−	3.97794e7i	−0.598999	−	0.0861231i	−0.435143	+	0.900361i	$0.643302\pi$
$774$	−5.29881e7	−	4.59145e7i	−0.114276	−	0.0990209i
$775$	−7.55054e7	+	1.65334e8i	−0.162208	+	0.355186i
$776$	4.98542e7	−	7.75747e7i	0.106688	−	0.166010i
$777$	5.68107e6	+	3.95127e7i	0.0121106	+	0.0842314i
$778$	−5.82001e7	−	9.05611e7i	−0.123590	−	0.192310i
$779$	−3.14490e8	+	2.72507e8i	−0.665264	+	0.576454i
$780$	−3.79711e7	−	1.29318e8i	−0.0800146	−	0.272505i
$781$		−	1.07726e8i		−	0.226135i
$782$	−2.68512e6	+	8.21900e6i	−0.00561491	+	0.0171869i
$783$	−1.47577e8			−0.307421
$784$	−6.47537e7	+	1.90134e7i	−0.134374	+	0.0394559i
$785$	−5.93277e8	−	6.84678e8i	−1.22645	−	1.41539i
$786$	−2.02001e8	+	1.29818e8i	−0.415992	+	0.267342i
$787$	5.42862e8	−	7.80517e7i	1.11369	−	0.160125i	0.439187	−	0.898395i	$-0.355266\pi$
$787$	5.42862e8	−	7.80517e7i	1.11369	−	0.160125i	0.674504	+	0.738271i	$0.264357\pi$
$788$	1.83989e8	+	1.18243e8i	0.376023	+	0.241655i
$789$	1.32738e8	+	6.06195e7i	0.270249	+	0.123419i
$790$	−9.64826e7	+	1.11347e8i	−0.195690	+	0.225838i
$791$	−7.83996e6	+	5.45281e7i	−0.0158411	+	0.110177i
$792$	2.20940e8	−	1.00900e8i	0.444732	−	0.203102i
$793$	7.74323e7	−	2.63710e8i	0.155275	−	0.528819i
$794$	−3.45547e8	−	1.01462e8i	−0.690313	−	0.202694i
$795$	−2.44152e8	−	5.34618e8i	−0.485913	−	1.06400i
$796$	−2.89849e8	−	4.16740e7i	−0.574689	−	0.0826278i
$797$	−6.10271e7	−	5.28803e7i	−0.120545	−	0.104453i	0.592503	−	0.805569i	$-0.298140\pi$
$797$	−6.10271e7	−	5.28803e7i	−0.120545	−	0.104453i	−0.713047	+	0.701116i	$0.752685\pi$
$798$	5.50659e6	−	1.20578e7i	0.0108361	−	0.0237278i
$799$	−1.89361e6	+	2.94652e6i	−0.00371236	+	0.00577655i
$800$	6.41419e7	+	4.46117e8i	0.125277	+	0.871322i
$801$	−7.71230e7	−	1.20006e8i	−0.150067	−	0.233509i
$802$	3.28427e8	−	2.84584e8i	0.636673	−	0.551680i
$803$	−1.52718e8	−	5.20110e8i	−0.294947	−	1.00450i
$804$		−	3.68920e8i		−	0.709845i
$805$	1.06980e8	+	3.49499e7i	0.205075	+	0.0669974i
$806$	7.18602e7			0.137241
$807$	−2.06551e8	+	6.06489e7i	−0.393013	+	0.115399i
$808$	−4.38236e8	−	5.05751e8i	−0.830757	−	0.958745i
$809$	−8.77072e7	+	5.63660e7i	−0.165649	+	0.106456i	−0.620839	−	0.783938i	$-0.713208\pi$
$809$	−8.77072e7	+	5.63660e7i	−0.165649	+	0.106456i	0.455190	+	0.890395i	$0.349571\pi$
$810$	4.49791e7	−	6.46702e6i	0.0846362	−	0.0121688i
$811$	−1.83028e7	−	1.17625e7i	−0.0343127	−	0.0220514i	0.523372	−	0.852104i	$-0.324674\pi$
$811$	−1.83028e7	−	1.17625e7i	−0.0343127	−	0.0220514i	−0.557685	+	0.830053i	$0.688310\pi$
$812$	−8.38888e7	−	3.83107e7i	−0.156688	−	0.0715570i
$813$	3.89118e8	−	4.49066e8i	0.724119	−	0.835678i
$814$	−6.23162e7	+	4.33419e8i	−0.115539	+	0.803590i
$815$	−3.42964e8	+	1.56627e8i	−0.633543	+	0.289330i
$816$	406135.	−	1.38317e6i	0.000747481	−	0.00254569i
$817$	2.11848e8	+	6.22042e7i	0.388471	+	0.114065i
$818$	4.90732e7	+	1.07455e8i	0.0896571	+	0.196322i
$819$	−1.52480e7	−	2.19233e6i	−0.0277562	−	0.00399074i
$820$	−6.73720e8	−	5.83782e8i	−1.22191	−	1.05879i
$821$	−2.96528e8	+	6.49306e8i	−0.535841	+	1.17333i	0.427245	+	0.904136i	$0.359484\pi$
$821$	−2.96528e8	+	6.49306e8i	−0.535841	+	1.17333i	−0.963086	+	0.269193i	$0.913243\pi$
$822$	−655940.	+	1.02066e6i	−0.00118100	+	0.00183767i
$823$	1.21404e8	+	8.44383e8i	0.217788	+	1.51475i	0.746179	+	0.665746i	$0.231886\pi$
$823$	1.21404e8	+	8.44383e8i	0.217788	+	1.51475i	−0.528391	+	0.849001i	$0.677204\pi$
$824$	−1.96091e8	−	3.05123e8i	−0.350490	−	0.545373i
$825$	3.23006e8	−	2.79886e8i	0.575240	−	0.498448i
$826$	1.78726e7	+	6.08686e7i	0.0317138	+	0.108007i
$827$		−	5.74104e8i		−	1.01502i	−0.861646	−	0.507510i	$-0.830566\pi$
$827$		−	5.74104e8i		−	1.01502i	0.861646	−	0.507510i	$-0.169434\pi$
$828$	−4.99361e7	−	1.18694e8i	−0.0879678	−	0.209093i
$829$	4.59769e8			0.807005			0.403503	−	0.914979i	$-0.367793\pi$
$829$	4.59769e8			0.807005			0.403503	+	0.914979i	$0.367793\pi$
$830$	−5.19254e8	+	1.52467e8i	−0.908124	+	0.266649i
$831$	4.95046e7	+	5.71313e7i	0.0862665	+	0.0995569i
$832$	1.12952e8	−	7.25898e7i	0.196121	−	0.126039i
$833$	−1.78424e7	+	2.56535e6i	−0.0308687	+	0.00443825i
$834$	2.77123e8	+	1.78096e8i	0.477721	+	0.307012i
$835$	−2.04551e8	−	9.34155e7i	−0.351352	−	0.160457i
$836$	−2.02834e8	+	2.34083e8i	−0.347153	+	0.400636i
$837$	7.34508e6	−	5.10861e7i	0.0125262	−	0.0871218i
$838$	−4.71492e8	+	2.15323e8i	−0.801202	+	0.365897i
$839$	−1.81389e8	+	6.17754e8i	−0.307132	+	1.04600i	0.650859	+	0.759198i	$0.274409\pi$
$839$	−1.81389e8	+	6.17754e8i	−0.307132	+	1.04600i	−0.957991	+	0.286797i	$0.907409\pi$
$840$	6.72844e7	+	1.97565e7i	0.113521	+	0.0333328i
$841$	3.83423e8	+	8.39580e8i	0.644600	+	1.41148i
$842$	3.09448e8	+	4.44918e7i	0.518383	+	0.0745322i
$843$	−1.35366e8	−	1.17296e8i	−0.225958	−	0.195794i
$844$	1.96234e8	−	4.29693e8i	0.326398	−	0.714711i
$845$	3.18945e8	−	4.96287e8i	0.528622	−	0.822551i
$846$	3.48490e6	+	2.42380e7i	0.00575545	+	0.0400300i
$847$	−7.20674e7	−	1.12139e8i	−0.118601	−	0.184547i
$848$	−9.85129e7	+	8.53620e7i	−0.161550	+	0.139983i
$849$	−5.83623e7	−	1.98764e8i	−0.0953695	−	0.324799i
$850$			9.48015e6i			0.0154368i
$851$	5.64716e8	+	9.86625e7i	0.916308	+	0.160090i
$852$	−3.55861e7			−0.0575390
$853$	5.53232e8	−	1.62443e8i	0.891374	−	0.261731i	0.196192	−	0.980565i	$-0.437142\pi$
$853$	5.53232e8	−	1.62443e8i	0.891374	−	0.261731i	0.695181	+	0.718834i	$0.255324\pi$
$854$	3.79221e7	+	4.37644e7i	0.0608862	+	0.0702664i
$855$	−1.20382e8	+	7.73650e7i	−0.192604	+	0.123779i
$856$	3.02766e8	−	4.35311e7i	0.482709	−	0.0694031i
$857$	−1.43686e8	−	9.23411e7i	−0.228282	−	0.146708i	0.421501	−	0.906828i	$-0.361504\pi$
$857$	−1.43686e8	−	9.23411e7i	−0.228282	−	0.146708i	−0.649782	+	0.760120i	$0.725140\pi$
$858$	−1.53706e8	−	7.01952e7i	−0.243349	−	0.111134i
$859$	−4.14713e8	+	4.78605e8i	−0.654288	+	0.755088i	−0.981833	−	0.189747i	$-0.939233\pi$
$859$	−4.14713e8	+	4.78605e8i	−0.654288	+	0.755088i	0.327545	+	0.944835i	$0.393779\pi$
$860$	−6.73141e7	+	4.68180e8i	−0.105830	+	0.736067i
$861$	−9.26843e7	+	4.23275e7i	−0.145210	+	0.0663152i
$862$	−6.06229e7	+	2.06463e8i	−0.0946488	+	0.322344i
$863$	3.10262e8	+	9.11010e7i	0.482720	+	0.141739i	0.514033	−	0.857770i	$-0.328151\pi$
$863$	3.10262e8	+	9.11010e7i	0.482720	+	0.141739i	−0.0313131	+	0.999510i	$0.509969\pi$
$864$	−5.31649e7	−	1.16415e8i	−0.0824296	−	0.180496i
$865$	−1.51284e9	−	2.17513e8i	−2.33746	−	0.336076i
$866$	2.04853e8	+	1.77507e8i	0.315420	+	0.273313i
$867$	−1.56147e8	+	3.41915e8i	−0.239595	+	0.524639i
$868$	1.74371e7	−	2.71327e7i	0.0266634	−	0.0414891i
$869$	−5.59989e7	−	3.89481e8i	−0.0853336	−	0.593508i
$870$	−2.52675e8	−	3.93170e8i	−0.383711	−	0.597067i
$871$	−4.78989e8	+	4.15047e8i	−0.724889	+	0.628120i
$872$	−1.42260e7	−	4.84494e7i	−0.0214553	−	0.0730699i
$873$			4.60754e7i			0.0692510i
$874$	−1.40040e8	−	1.28943e8i	−0.209758	−	0.193136i
$875$	−2.11352e7			−0.0315488
$876$	−1.71813e8	+	5.04488e7i	−0.255590	+	0.0750479i
$877$	3.10489e8	+	3.58323e8i	0.460307	+	0.531222i	0.937690	−	0.347473i	$-0.112960\pi$
$877$	3.10489e8	+	3.58323e8i	0.460307	+	0.531222i	−0.477383	+	0.878695i	$0.658415\pi$
$878$	4.45301e7	−	2.86178e7i	0.0657916	−	0.0422817i
$879$	−7.49520e8	+	1.07765e8i	−1.10361	+	0.158676i
$880$	−1.73146e8	−	1.11274e8i	−0.254077	−	0.163285i
$881$	8.01271e8	+	3.65928e8i	1.17180	+	0.535141i	0.903664	−	0.428242i	$-0.140867\pi$
$881$	8.01271e8	+	3.65928e8i	1.17180	+	0.535141i	0.268131	+	0.963382i	$0.413594\pi$
$882$	−8.25285e7	+	9.52430e7i	−0.120281	+	0.138812i
$883$	1.90265e8	−	1.32332e9i	0.276361	−	1.92213i	−0.0986673	−	0.995120i	$-0.531458\pi$
$883$	1.90265e8	−	1.32332e9i	0.276361	−	1.92213i	0.375028	−	0.927013i	$-0.377633\pi$
$884$	−7.26262e6	+	3.31673e6i	−0.0105132	+	0.00480124i
$885$	1.92941e8	−	6.57096e8i	0.278352	−	0.947979i
$886$	5.36754e8	+	1.57605e8i	0.771745	+	0.226605i
$887$	−5.44524e8	−	1.19234e9i	−0.780273	−	1.70856i	−0.702605	−	0.711580i	$-0.747980\pi$
$887$	−5.44524e8	−	1.19234e9i	−0.780273	−	1.70856i	−0.0776676	−	0.996979i	$-0.524747\pi$
$888$	3.53563e8	+	5.08347e7i	0.504926	+	0.0725974i
$889$	4.85376e7	+	4.20580e7i	0.0690833	+	0.0598610i
$890$	1.87669e8	−	4.10938e8i	0.266209	−	0.582916i
$891$	−6.56134e7	+	1.02096e8i	−0.0927597	+	0.144337i
$892$	−4.46497e7	−	3.10546e8i	−0.0629107	−	0.437553i
$893$	−4.16899e7	−	6.48707e7i	−0.0585432	−	0.0910950i
$894$	1.78252e8	−	1.54456e8i	0.249472	−	0.216169i
$895$	2.44337e8	+	8.32134e8i	0.340815	+	1.16071i
$896$		−	8.92312e7i		−	0.124049i
$897$	−9.79278e7	+	1.98370e8i	−0.135684	+	0.274852i
$898$	−6.50755e8			−0.898646
$899$	−5.09316e8	+	1.49549e8i	−0.700984	+	0.205828i
$900$	−9.24575e7	−	1.06702e8i	−0.126828	−	0.146367i
$901$	−2.92898e7	+	1.88234e7i	−0.0400444	+	0.0257350i
$902$	−1.10629e9	+	1.59060e8i	−1.50747	+	0.216741i
$903$	4.54801e7	+	2.92283e7i	0.0617673	+	0.0396954i
$904$	4.48393e8	+	2.04774e8i	0.606951	+	0.277185i
$905$	−4.44783e8	+	5.13307e8i	−0.600071	+	0.692518i
$906$	−7.17001e6	+	4.98685e7i	−0.00964129	+	0.0670566i
$907$	−5.10284e8	+	2.33039e8i	−0.683896	+	0.312325i	−0.726893	−	0.686751i	$-0.759036\pi$
$907$	−5.10284e8	+	2.33039e8i	−0.683896	+	0.312325i	0.0429977	+	0.999075i	$0.486309\pi$
$908$	−3.05920e6	+	1.04187e7i	−0.00408649	+	0.0139173i
$909$	3.20831e8	+	9.42045e7i	0.427154	+	0.125424i
$910$	−2.02662e7	−	4.43768e7i	−0.0268936	−	0.0588887i
$911$	−8.45416e8	−	1.21553e8i	−1.11819	−	0.160771i	−0.441657	−	0.897184i	$-0.645609\pi$
$911$	−8.45416e8	−	1.21553e8i	−1.11819	−	0.160771i	−0.676533	+	0.736413i	$0.736518\pi$
$912$	2.39856e7	+	2.07837e7i	0.0316204	+	0.0273992i
$913$	6.00412e8	−	1.31472e9i	0.788927	−	1.72751i
$914$	3.57866e8	−	5.56850e8i	0.468685	−	0.729289i
$915$	−8.89669e7	−	6.18779e8i	−0.116136	−	0.807741i
$916$	2.39418e8	+	3.72542e8i	0.311509	+	0.484718i
$917$	1.39926e8	−	1.21246e8i	0.181464	−	0.157239i
$918$	−758408.	−	2.58290e6i	−0.000980336	−	0.00333872i
$919$		−	2.11340e8i		−	0.272292i	−0.990689	−	0.136146i	$-0.956528\pi$
$919$		−	2.11340e8i		−	0.272292i	0.990689	−	0.136146i	$-0.0434716\pi$
$920$	5.69758e8	−	8.30379e8i	0.731690	−	1.06638i
$921$	3.81072e7			0.0487785
$922$	−3.04860e8	+	8.95149e7i	−0.388962	+	0.114210i
$923$	4.00356e7	+	4.62035e7i	0.0509144	+	0.0587584i
$924$	−6.38014e7	+	4.10027e7i	−0.0808750	+	0.0519752i
$925$	6.22145e8	−	8.94509e7i	0.786079	−	0.113021i
$926$	2.30060e8	+	1.47851e8i	0.289740	+	0.186205i
$927$	1.64850e8	+	7.52846e7i	0.206943	+	0.0945077i
$928$	−8.61968e8	+	9.94764e8i	−1.07857	+	1.24473i
$929$	2.33344e7	−	1.62294e8i	0.0291037	−	0.202421i	−0.970082	−	0.242779i	$-0.921941\pi$
$929$	2.33344e7	−	1.62294e8i	0.0291037	−	0.202421i	0.999185	+	0.0403584i	$0.0128500\pi$
$930$	1.48678e8	−	6.78990e7i	0.184841	−	0.0844141i
$931$	1.11808e8	−	3.80784e8i	0.138556	−	0.471878i
$932$	9.14241e8	+	2.68445e8i	1.12931	+	0.331595i
$933$	8.79968e7	+	1.92686e8i	0.108348	+	0.237250i
$934$	8.41894e7	+	1.21046e7i	0.103328	+	0.0148563i
$935$	−4.15469e7	−	3.60006e7i	−0.0508281	−	0.0440428i
$936$	−5.72620e7	+	1.25386e8i	−0.0698295	+	0.152905i
$937$	−2.17755e8	+	3.38833e8i	−0.264697	+	0.411877i	−0.948006	−	0.318253i	$-0.896904\pi$
$937$	−2.17755e8	+	3.38833e8i	−0.264697	+	0.411877i	0.683309	+	0.730130i	$0.260540\pi$
$938$	−1.90045e7	−	1.32179e8i	−0.0230276	−	0.160160i
$939$	−3.07063e8	−	4.77799e8i	−0.370877	−	0.577096i
$940$	1.24846e8	−	1.08179e8i	0.150311	−	0.130245i
$941$	−4.03109e7	−	1.37286e8i	−0.0483787	−	0.164763i	0.931760	−	0.363074i	$-0.118273\pi$
$941$	−4.03109e7	−	1.37286e8i	−0.0483787	−	0.164763i	−0.980139	+	0.198311i	$0.936454\pi$
$942$			3.75213e8i			0.448875i
$943$	1.64463e8	+	1.45398e9i	0.196125	+	1.73390i
$944$	−1.51888e8			−0.180554
$945$	−3.36194e7	+	9.87155e6i	−0.0398377	+	0.0116974i
$946$	3.88342e8	+	4.48170e8i	0.458713	+	0.529383i
$947$	8.19318e8	−	5.26544e8i	0.964723	−	0.619990i	0.0394219	−	0.999223i	$-0.487448\pi$
$947$	8.19318e8	−	5.26544e8i	0.964723	−	0.619990i	0.925301	+	0.379233i	$0.123812\pi$
$948$	−1.28661e8	+	1.84986e7i	−0.151016	+	0.0217128i
$949$	2.58795e8	+	1.66318e8i	0.302801	+	0.194599i
$950$	−1.89855e8	−	8.67036e7i	−0.221437	−	0.101127i
$951$	−1.56516e7	+	1.80629e7i	−0.0181977	+	0.0210013i
$952$	591200.	−	4.11189e6i	0.000685210	−	0.00476574i
$953$	−1.92227e8	+	8.77871e7i	−0.222093	+	0.101427i	−0.523355	−	0.852115i	$-0.675320\pi$
$953$	−1.92227e8	+	8.77871e7i	−0.222093	+	0.101427i	0.301261	+	0.953542i	$0.402592\pi$
$954$	−6.85780e7	+	2.33555e8i	−0.0789841	+	0.268995i
$955$	−2.67400e8	−	7.85157e7i	−0.307009	−	0.0901460i
$956$	−1.66930e8	−	3.65525e8i	−0.191056	−	0.418354i
$957$	1.23549e9	+	1.77637e8i	1.40963	+	0.202674i
$958$	5.94844e8	+	5.15435e8i	0.676560	+	0.586242i
$959$	388625.	−	850971.i	0.000440631	−	0.000964848i
$960$	1.65108e8	−	2.56913e8i	0.186619	−	0.290384i
$961$	9.98855e7	+	6.94719e8i	0.112547	+	0.782779i
$962$	−1.34350e8	−	2.09052e8i	−0.150908	−	0.234817i
$963$	−1.15506e8	+	1.00086e8i	−0.129338	+	0.112072i
$964$	−1.60665e8	−	5.47173e8i	−0.179345	−	0.610793i
$965$		−	2.27467e8i		−	0.253126i
$966$	−2.40059e7	−	3.99542e7i	−0.0266309	−	0.0443232i
$967$	−3.97437e8			−0.439530			−0.219765	−	0.975553i	$-0.570529\pi$
$967$	−3.97437e8			−0.439530			−0.219765	+	0.975553i	$0.570529\pi$
$968$	−1.14446e9	+	3.36044e8i	−1.26176	+	0.370485i
$969$	5.55132e6	+	6.40657e6i	0.00610134	+	0.00704132i
$970$	−1.22753e8	+	7.88884e7i	−0.134498	+	0.0864366i
$971$	3.89326e8	−	5.59766e7i	0.425261	−	0.0611433i	0.0736380	−	0.997285i	$-0.476539\pi$
$971$	3.89326e8	−	5.59766e7i	0.425261	−	0.0611433i	0.351623	+	0.936142i	$0.385630\pi$
$972$	3.37265e7	+	2.16747e7i	0.0367259	+	0.0236023i
$973$	−2.31049e8	−	1.05517e8i	−0.250822	−	0.114547i
$974$	3.21617e8	−	3.71165e8i	0.348066	−	0.401690i
$975$	−3.45191e7	+	2.40086e8i	−0.0372431	+	0.259031i
$976$	−1.26119e8	+	5.75968e7i	−0.135654	+	0.0619511i
$977$	1.32674e8	−	4.51845e8i	0.142266	−	0.484513i	−0.857273	−	0.514861i	$-0.827843\pi$
$977$	1.32674e8	−	4.51845e8i	0.142266	−	0.484513i	0.999539	+	0.0303481i	$0.00966158\pi$
$978$	1.49829e8	+	4.39937e7i	0.160169	+	0.0470299i
$979$	5.01212e8	+	1.09750e9i	0.534163	+	1.16965i
$980$	8.41525e8	+	1.20993e8i	0.894106	+	0.128553i
$981$	1.90678e7	+	1.65223e7i	0.0201973	+	0.0175010i
$982$	4.11662e8	−	9.01413e8i	0.434716	−	0.951896i
$983$	−5.83743e8	+	9.08321e8i	−0.614555	+	0.956267i	0.384890	+	0.922962i	$0.374239\pi$
$983$	−5.83743e8	+	9.08321e8i	−0.614555	+	0.956267i	−0.999445	+	0.0333041i	$0.989397\pi$
$984$	1.29754e8	+	9.02458e8i	0.136187	+	0.947200i
$985$	−4.62045e8	−	7.18956e8i	−0.483476	−	0.752304i
$986$	−2.09239e7	+	1.81307e7i	−0.0218279	+	0.0189140i
$987$	−5.31950e6	−	1.81166e7i	−0.00553248	−	0.0188419i
$988$		−	1.75779e8i		−	0.182262i
$989$	6.01816e8	−	4.90492e8i	0.622121	−	0.507041i
$990$	−3.84343e8			−0.396108
$991$	−7.57540e8	+	2.22434e8i	−0.778368	+	0.228549i	−0.646700	−	0.762745i	$-0.723851\pi$
$991$	−7.57540e8	+	2.22434e8i	−0.778368	+	0.228549i	−0.131668	+	0.991294i	$0.542033\pi$
$992$	−3.01452e8	−	3.47895e8i	−0.308805	−	0.356379i
$993$	6.37774e8	−	4.09872e8i	0.651357	−	0.418601i
$994$	−1.27501e7	+	1.83318e6i	−0.0129823	+	0.00186658i
$995$	9.62613e8	+	6.18634e8i	0.977198	+	0.628007i
$996$	−4.34303e8	−	1.98340e8i	−0.439557	−	0.200739i
$997$	7.18857e8	−	8.29605e8i	0.725365	−	0.837116i	−0.266576	−	0.963814i	$-0.585892\pi$
$997$	7.18857e8	−	8.29605e8i	0.725365	−	0.837116i	0.991941	+	0.126698i	$0.0404378\pi$
$998$	1.32703e6	−	9.22969e6i	0.00133502	−	0.00928530i
$999$	−1.62350e8	+	7.41425e7i	−0.162838	+	0.0743654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.37.10	yes	240
23.5	odd	22	inner	69.7.f.a.28.10	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.28.10	✓	240	23.5	odd	22	inner
69.7.f.a.37.10	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.33856 + 1.27392i) q^{2} +(10.2083 + 11.7810i) q^{3} +(-36.6400 + 23.5471i) q^{4} +(168.459 - 24.2208i) q^{5} +(-59.2972 - 38.1080i) q^{6} +(49.4387 + 22.5779i) q^{7} +(318.478 - 367.543i) q^{8} +(-34.5825 + 240.527i) q^{9} +O(q^{10})\)	\(q+(-4.33856 + 1.27392i) q^{2} +(10.2083 + 11.7810i) q^{3} +(-36.6400 + 23.5471i) q^{4} +(168.459 - 24.2208i) q^{5} +(-59.2972 - 38.1080i) q^{6} +(49.4387 + 22.5779i) q^{7} +(318.478 - 367.543i) q^{8} +(-34.5825 + 240.527i) q^{9} +(-700.015 + 319.686i) q^{10} +(579.039 - 1972.03i) q^{11} +(-651.438 - 191.279i) q^{12} +(484.540 + 1060.99i) q^{13} +(-243.255 - 34.9748i) q^{14} +(2005.02 + 1737.36i) q^{15} +(244.433 - 535.234i) q^{16} +(84.9691 - 132.215i) q^{17} +(-156.373 - 1087.60i) q^{18} +(1870.69 + 2910.84i) q^{19} +(-5602.00 + 4854.16i) q^{20} +(238.694 + 812.917i) q^{21} +9293.41i q^{22} +(12161.5 + 366.977i) q^{23} +7581.13 q^{24} +(12799.7 - 3758.34i) q^{25} +(-3453.83 - 3985.93i) q^{26} +(-3186.66 + 2047.94i) q^{27} +(-2343.08 + 336.883i) q^{28} +(32774.5 + 21062.9i) q^{29} +(-10912.2 - 4983.41i) q^{30} +(-8922.48 + 10297.1i) q^{31} +(-4808.21 + 33441.8i) q^{32} +(29143.4 - 13309.3i) q^{33} +(-200.214 + 681.865i) q^{34} +(8875.25 + 2606.01i) q^{35} +(-4396.60 - 9627.20i) q^{36} +(46637.2 + 6705.42i) q^{37} +(-11824.3 - 10245.8i) q^{38} +(-7553.23 + 16539.3i) q^{39} +(44748.3 - 69629.8i) q^{40} +(17115.4 + 119040. i) q^{41} +(-2071.18 - 3222.82i) q^{42} +(48224.6 - 41786.8i) q^{43} +(25219.5 + 85889.6i) q^{44} +41356.5i q^{45} +(-53230.8 + 13900.5i) q^{46} -22285.9 q^{47} +(8800.82 - 2584.15i) q^{48} +(-75109.3 - 86680.7i) q^{49} +(-50744.6 + 32611.6i) q^{50} +(2425.00 - 348.663i) q^{51} +(-42736.8 - 27465.3i) q^{52} +(-201513. - 92027.9i) q^{53} +(11216.6 - 12944.7i) q^{54} +(49780.4 - 346230. i) q^{55} +(24043.5 - 10980.3i) q^{56} +(-15196.1 + 51753.2i) q^{57} +(-169027. - 49630.7i) q^{58} +(-107233. - 234807. i) q^{59} +(-114374. - 16444.4i) q^{60} +(-178080. - 154307. i) q^{61} +(25593.1 - 56041.1i) q^{62} +(-7140.30 + 11110.5i) q^{63} +(-16382.1 - 113940. i) q^{64} +(107323. + 166998. i) q^{65} +(-109485. + 94869.6i) q^{66} +(153087. + 521366. i) q^{67} +6845.11i q^{68} +(119824. + 147020. i) q^{69} -41825.7 q^{70} +(50291.1 - 14766.8i) q^{71} +(77390.2 + 89313.0i) q^{72} +(221875. - 142591. i) q^{73} +(-210881. + 30320.1i) q^{74} +(174940. + 112427. i) q^{75} +(-137084. - 62604.1i) q^{76} +(73151.1 - 84420.9i) q^{77} +(11700.5 - 81378.8i) q^{78} +(174150. - 79531.8i) q^{79} +(28213.2 - 96085.4i) q^{80} +(-56657.1 - 16636.0i) q^{81} +(-225903. - 494659. i) q^{82} +(696070. + 100080. i) q^{83} +(-27887.6 - 24164.7i) q^{84} +(11111.5 - 24330.7i) q^{85} +(-155992. + 242729. i) q^{86} +(86429.5 + 601131. i) q^{87} +(-540394. - 840869. i) q^{88} +(-443656. + 384430. i) q^{89} +(-52684.7 - 179428. i) q^{90} +63394.1i q^{91} +(-454237. + 272921. i) q^{92} -212393. q^{93} +(96688.7 - 28390.4i) q^{94} +(385637. + 445049. i) q^{95} +(-443061. + 284738. i) q^{96} +(187681. - 26984.4i) q^{97} +(436290. + 280387. i) q^{98} +(454300. + 207472. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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