LMFDB - Embedded newform 21.7.h.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(2,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("21.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.h (of order $6$, degree $2$, 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:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	21.11
Dual form			21.7.h.a.2.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.69684 + 3.28907i) q^{2} +(2.79228 + 26.8552i) q^{3} +(-10.3640 + 17.9510i) q^{4} +(57.4599 - 33.1745i) q^{5} +(-104.236 - 143.806i) q^{6} +(-329.948 + 93.7191i) q^{7} -557.353i q^{8} +(-713.406 + 149.974i) q^{9} +O(q^{10})$	\(q+(-5.69684 + 3.28907i) q^{2} +(2.79228 + 26.8552i) q^{3} +(-10.3640 + 17.9510i) q^{4} +(57.4599 - 33.1745i) q^{5} +(-104.236 - 143.806i) q^{6} +(-329.948 + 93.7191i) q^{7} -557.353i q^{8} +(-713.406 + 149.974i) q^{9} +(-218.227 + 377.979i) q^{10} +(-603.143 - 348.225i) q^{11} +(-511.016 - 228.203i) q^{12} -824.771 q^{13} +(1571.41 - 1619.13i) q^{14} +(1051.35 + 1450.47i) q^{15} +(1169.88 + 2026.29i) q^{16} +(4784.05 + 2762.07i) q^{17} +(3570.89 - 3200.83i) q^{18} +(2527.23 + 4377.29i) q^{19} +1375.28i q^{20} +(-3438.15 - 8599.14i) q^{21} +4581.35 q^{22} +(-17221.4 + 9942.79i) q^{23} +(14967.8 - 1556.28i) q^{24} +(-5611.41 + 9719.25i) q^{25} +(4698.59 - 2712.73i) q^{26} +(-6019.63 - 18739.9i) q^{27} +(1737.23 - 6894.19i) q^{28} -23408.7i q^{29} +(-10760.1 - 4805.10i) q^{30} +(-23180.0 + 40149.0i) q^{31} +(17562.4 + 10139.7i) q^{32} +(7667.51 - 17169.9i) q^{33} -36338.6 q^{34} +(-15849.7 + 16330.9i) q^{35} +(4701.55 - 14360.7i) q^{36} +(24177.8 + 41877.2i) q^{37} +(-28794.4 - 16624.5i) q^{38} +(-2302.99 - 22149.4i) q^{39} +(-18489.9 - 32025.4i) q^{40} +15904.7i q^{41} +(47869.8 + 37679.6i) q^{42} +21757.0 q^{43} +(12501.9 - 7217.99i) q^{44} +(-36016.9 + 32284.4i) q^{45} +(65405.1 - 113285. i) q^{46} +(33042.5 - 19077.1i) q^{47} +(-51149.9 + 37075.4i) q^{48} +(100082. - 61844.9i) q^{49} -73825.4i q^{50} +(-60817.6 + 136189. i) q^{51} +(8547.91 - 14805.4i) q^{52} +(193312. + 111609. i) q^{53} +(95929.8 + 86959.4i) q^{54} -46208.7 q^{55} +(52234.6 + 183898. i) q^{56} +(-110496. + 80091.9i) q^{57} +(76992.9 + 133356. i) q^{58} +(-271755. - 156898. i) q^{59} +(-36933.4 + 3840.16i) q^{60} +(-126472. - 219056. i) q^{61} -304963. i q^{62} +(221332. - 116344. i) q^{63} -283145. q^{64} +(-47391.2 + 27361.3i) q^{65} +(12792.4 + 123033. i) q^{66} +(82947.6 - 143669. i) q^{67} +(-99163.6 + 57252.1i) q^{68} +(-315103. - 434722. i) q^{69} +(36579.5 - 145166. i) q^{70} +298965. i q^{71} +(83588.7 + 397619. i) q^{72} +(-2216.28 + 3838.71i) q^{73} +(-275474. - 159045. i) q^{74} +(-276681. - 123557. i) q^{75} -104769. q^{76} +(231641. + 58370.1i) q^{77} +(85970.8 + 118607. i) q^{78} +(310276. + 537413. i) q^{79} +(134442. + 77620.3i) q^{80} +(486456. - 213985. i) q^{81} +(-52311.7 - 90606.6i) q^{82} +414931. i q^{83} +(189996. + 27403.2i) q^{84} +366521. q^{85} +(-123946. + 71560.3i) q^{86} +(628645. - 65363.5i) q^{87} +(-194084. + 336164. i) q^{88} +(649685. - 375096. i) q^{89} +(98996.9 - 302381. i) q^{90} +(272131. - 77296.8i) q^{91} -412188. i q^{92} +(-1.14293e6 - 510398. i) q^{93} +(-125492. + 217359. i) q^{94} +(290428. + 167679. i) q^{95} +(-223264. + 499955. i) q^{96} +212245. q^{97} +(-366742. + 681499. i) q^{98} +(482511. + 157970. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−5.69684	+	3.28907i	−0.712105	+	0.411134i	−0.811840	−	0.583880i	$-0.801534\pi$
$2$	−5.69684	+	3.28907i	−0.712105	+	0.411134i	0.0997347	+	0.995014i	$0.468201\pi$
$3$	2.79228	+	26.8552i	0.103418	+	0.994638i
$3$	2.79228	+	26.8552i	0.103418	+	0.994638i
$4$	−10.3640	+	17.9510i	−0.161937	+	0.280484i
$5$	57.4599	−	33.1745i	0.459679	−	0.265396i	−0.252230	−	0.967667i	$-0.581164\pi$
$5$	57.4599	−	33.1745i	0.459679	−	0.265396i	0.711909	+	0.702271i	$0.247831\pi$
$6$	−104.236	−	143.806i	−0.482574	−	0.665769i
$7$	−329.948	+	93.7191i	−0.961948	+	0.273234i
$7$	−329.948	+	93.7191i	−0.961948	+	0.273234i
$8$		−	557.353i		−	1.08858i
$9$	−713.406	+	149.974i	−0.978610	+	0.205726i
$10$	−218.227	+	377.979i	−0.218227	+	0.377979i
$11$	−603.143	−	348.225i	−0.453150	−	0.261626i	0.256010	−	0.966674i	$-0.417592\pi$
$11$	−603.143	−	348.225i	−0.453150	−	0.261626i	−0.709160	+	0.705048i	$0.750925\pi$
$12$	−511.016	−	228.203i	−0.295727	−	0.132062i
$13$	−824.771			−0.375408			−0.187704	−	0.982226i	$-0.560105\pi$
$13$	−824.771			−0.375408			−0.187704	+	0.982226i	$0.560105\pi$
$14$	1571.41	−	1619.13i	0.572672	−	0.590061i
$15$	1051.35	+	1450.47i	0.311512	+	0.429768i
$16$	1169.88	+	2026.29i	0.285615	+	0.494700i
$17$	4784.05	+	2762.07i	0.973752	+	0.562196i	0.900378	−	0.435108i	$-0.143290\pi$
$17$	4784.05	+	2762.07i	0.973752	+	0.562196i	0.0733743	+	0.997304i	$0.476623\pi$
$18$	3570.89	−	3200.83i	0.612292	−	0.548839i
$19$	2527.23	+	4377.29i	0.368454	+	0.638182i	0.989324	−	0.145732i	$-0.0465538\pi$
$19$	2527.23	+	4377.29i	0.368454	+	0.638182i	−0.620870	+	0.783914i	$0.713220\pi$
$20$			1375.28i			0.171910i
$21$	−3438.15	−	8599.14i	−0.371251	−	0.928533i
$22$	4581.35			0.430254
$23$	−17221.4	+	9942.79i	−1.41542	+	0.817193i	−0.995892	−	0.0905491i	$-0.971138\pi$
$23$	−17221.4	+	9942.79i	−1.41542	+	0.817193i	−0.419528	+	0.907742i	$0.637804\pi$
$24$	14967.8	−	1556.28i	1.08274	−	0.112578i
$25$	−5611.41	+	9719.25i	−0.359130	+	0.622032i
$26$	4698.59	−	2712.73i	0.267330	−	0.154343i
$27$	−6019.63	−	18739.9i	−0.305829	−	0.952087i
$28$	1737.23	−	6894.19i	0.0791377	−	0.314057i
$29$		−	23408.7i		−	0.959805i	−0.877322	−	0.479902i	$-0.840672\pi$
$29$		−	23408.7i		−	0.959805i	0.877322	−	0.479902i	$-0.159328\pi$
$30$	−10760.1	−	4805.10i	−0.398521	−	0.177967i
$31$	−23180.0	+	40149.0i	−0.778088	+	1.34769i	0.154954	+	0.987922i	$0.450477\pi$
$31$	−23180.0	+	40149.0i	−0.778088	+	1.34769i	−0.933042	+	0.359767i	$0.882856\pi$
$32$	17562.4	+	10139.7i	0.535962	+	0.309438i
$33$	7667.51	−	17169.9i	0.213360	−	0.477777i
$34$	−36338.6			−0.924552
$35$	−15849.7	+	16330.9i	−0.369672	+	0.380897i
$36$	4701.55	−	14360.7i	0.100771	−	0.307799i
$37$	24177.8	+	41877.2i	0.477323	+	0.826747i	0.999662	−	0.0259906i	$-0.00827401\pi$
$37$	24177.8	+	41877.2i	0.477323	+	0.826747i	−0.522340	+	0.852738i	$0.674941\pi$
$38$	−28794.4	−	16624.5i	−0.524757	−	0.302968i
$39$	−2302.99	−	22149.4i	−0.0388238	−	0.373395i
$40$	−18489.9	−	32025.4i	−0.288905	−	0.500397i
$41$			15904.7i			0.230767i	0.993321	+	0.115384i	$0.0368097\pi$
$41$			15904.7i			0.230767i	−0.993321	+	0.115384i	$0.963190\pi$
$42$	47869.8	+	37679.6i	0.646121	+	0.508579i
$43$	21757.0			0.273649			0.136824	−	0.990595i	$-0.456310\pi$
$43$	21757.0			0.273649			0.136824	+	0.990595i	$0.456310\pi$
$44$	12501.9	−	7217.99i	0.146764	−	0.0847341i
$45$	−36016.9	+	32284.4i	−0.395247	+	0.354287i
$46$	65405.1	−	113285.i	0.671952	−	1.16386i
$47$	33042.5	−	19077.1i	0.318258	−	0.183747i	−0.332358	−	0.943153i	$-0.607844\pi$
$47$	33042.5	−	19077.1i	0.318258	−	0.183747i	0.650616	+	0.759407i	$0.274511\pi$
$48$	−51149.9	+	37075.4i	−0.462510	+	0.335245i
$49$	100082.	−	61844.9i	0.850687	−	0.525673i
$50$		−	73825.4i		−	0.590603i
$51$	−60817.6	+	136189.i	−0.458479	+	1.02667i
$52$	8547.91	−	14805.4i	0.0607925	−	0.105296i
$53$	193312.	+	111609.i	1.29847	+	0.749670i	0.980139	−	0.198310i	$-0.0635454\pi$
$53$	193312.	+	111609.i	1.29847	+	0.749670i	0.318328	+	0.947981i	$0.396879\pi$
$54$	95929.8	+	86959.4i	0.609218	+	0.552249i
$55$	−46208.7			−0.277738
$56$	52234.6	+	183898.i	0.297437	+	1.04716i
$57$	−110496.	+	80091.9i	−0.596655	+	0.432478i
$58$	76992.9	+	133356.i	0.394609	+	0.683482i
$59$	−271755.	−	156898.i	−1.32319	−	0.763944i	−0.338953	−	0.940803i	$-0.610073\pi$
$59$	−271755.	−	156898.i	−1.32319	−	0.763944i	−0.984236	+	0.176860i	$0.943406\pi$
$60$	−36933.4	+	3840.16i	−0.170988	+	0.0177785i
$61$	−126472.	−	219056.i	−0.557192	−	0.965085i	−0.997729	−	0.0673504i	$-0.978545\pi$
$61$	−126472.	−	219056.i	−0.557192	−	0.965085i	0.440538	−	0.897734i	$-0.354788\pi$
$62$		−	304963.i		−	1.27959i
$63$	221332.	−	116344.i	0.885160	−	0.465287i
$64$	−283145.			−1.08011
$65$	−47391.2	+	27361.3i	−0.172567	+	0.0996316i
$66$	12792.4	+	123033.i	0.0444959	+	0.427947i
$67$	82947.6	−	143669.i	0.275791	−	0.477683i	−0.694544	−	0.719451i	$-0.744394\pi$
$67$	82947.6	−	143669.i	0.275791	−	0.477683i	0.970334	+	0.241767i	$0.0777270\pi$
$68$	−99163.6	+	57252.1i	−0.315374	+	0.182081i
$69$	−315103.	−	434722.i	−0.959191	−	1.32332i
$70$	36579.5	−	145166.i	0.106646	−	0.423223i
$71$			298965.i			0.835307i	0.908606	+	0.417653i	$0.137147\pi$
$71$			298965.i			0.835307i	−0.908606	+	0.417653i	$0.862853\pi$
$72$	83588.7	+	397619.i	0.223950	+	1.06530i
$73$	−2216.28	+	3838.71i	−0.00569714	+	0.00986773i	−0.868860	−	0.495058i	$-0.835147\pi$
$73$	−2216.28	+	3838.71i	−0.00569714	+	0.00986773i	0.863163	+	0.504926i	$0.168480\pi$
$74$	−275474.	−	159045.i	−0.679808	−	0.392487i
$75$	−276681.	−	123557.i	−0.655837	−	0.292875i
$76$	−104769.			−0.238666
$77$	231641.	+	58370.1i	0.507392	+	0.127855i
$78$	85970.8	+	118607.i	0.181162	+	0.249935i
$79$	310276.	+	537413.i	0.629313	+	1.09000i	0.987690	+	0.156425i	$0.0499969\pi$
$79$	310276.	+	537413.i	0.629313	+	1.09000i	−0.358377	+	0.933577i	$0.616670\pi$
$80$	134442.	+	77620.3i	0.262583	+	0.151602i
$81$	486456.	−	213985.i	0.915353	−	0.402651i
$82$	−52311.7	−	90606.6i	−0.0948762	−	0.164330i
$83$			414931.i			0.725674i	0.931853	+	0.362837i	$0.118192\pi$
$83$			414931.i			0.725674i	−0.931853	+	0.362837i	$0.881808\pi$
$84$	189996.	+	27403.2i	0.320558	+	0.0462343i
$85$	366521.			0.596818
$86$	−123946.	+	71560.3i	−0.194867	+	0.112506i
$87$	628645.	−	65363.5i	0.954658	−	0.0992608i
$88$	−194084.	+	336164.i	−0.284801	+	0.493290i
$89$	649685.	−	375096.i	0.921580	−	0.532074i	0.0374412	−	0.999299i	$-0.488079\pi$
$89$	649685.	−	375096.i	0.921580	−	0.532074i	0.884139	+	0.467224i	$0.154746\pi$
$90$	98996.9	−	302381.i	0.135798	−	0.414789i
$91$	272131.	−	77296.8i	0.361123	−	0.102574i
$92$		−	412188.i		−	0.529336i
$93$	−1.14293e6	−	510398.i	−1.42093	−	0.634541i
$94$	−125492.	+	217359.i	−0.151089	+	0.261694i
$95$	290428.	+	167679.i	0.338741	+	0.195572i
$96$	−223264.	+	499955.i	−0.252351	+	0.565089i
$97$	212245.			0.232553			0.116276	−	0.993217i	$-0.462904\pi$
$97$	212245.			0.232553			0.116276	+	0.993217i	$0.462904\pi$
$98$	−366742.	+	681499.i	−0.389657	+	0.724081i
$99$	482511.	+	157970.i	0.497281	+	0.162805i
$100$	−116313.	−	201460.i	−0.116313	−	0.201460i
$101$	−1.27401e6	−	735552.i	−1.23654	−	0.713920i	−0.268159	−	0.963375i	$-0.586415\pi$
$101$	−1.27401e6	−	735552.i	−1.23654	−	0.713920i	−0.968386	+	0.249455i	$0.919748\pi$
$102$	−101467.	−	975882.i	−0.0956151	−	0.919595i
$103$	372502.	+	645192.i	0.340892	+	0.590442i	0.984599	−	0.174830i	$-0.0559377\pi$
$103$	372502.	+	645192.i	0.340892	+	0.590442i	−0.643707	+	0.765272i	$0.722604\pi$
$104$			459688.i			0.408661i
$105$	−482828.	−	380047.i	−0.417085	−	0.328298i
$106$	−1.46836e6			−1.23286
$107$	1.33788e6	−	772428.i	1.09211	−	0.630531i	0.157974	−	0.987443i	$-0.449504\pi$
$107$	1.33788e6	−	772428.i	1.09211	−	0.630531i	0.934138	+	0.356912i	$0.116170\pi$
$108$	398787.	+	86162.2i	0.316570	+	0.0683984i
$109$	−958591.	+	1.66033e6i	−0.740208	+	1.28208i	0.212192	+	0.977228i	$0.431940\pi$
$109$	−958591.	+	1.66033e6i	−0.740208	+	1.28208i	−0.952400	+	0.304850i	$0.901394\pi$
$110$	263244.	−	151984.i	0.197779	−	0.114188i
$111$	−1.05711e6	+	766234.i	−0.772950	+	0.560263i
$112$	−575902.	−	558931.i	−0.409916	−	0.397836i
$113$		−	1.61984e6i		−	1.12263i	−0.827601	−	0.561317i	$-0.810295\pi$
$113$		−	1.61984e6i		−	1.12263i	0.827601	−	0.561317i	$-0.189705\pi$
$114$	366052.	−	819702.i	0.247075	−	0.553275i
$115$	−659694.	+	1.14262e6i	−0.433759	+	0.751293i
$116$	420208.	+	242607.i	0.269209	+	0.155428i
$117$	588397.	−	123695.i	0.367378	−	0.0772312i
$118$	2.06420e6			1.25633
$119$	−1.83735e6	−	462983.i	−1.09031	−	0.274742i
$120$	808421.	−	585974.i	0.467836	−	0.339105i
$121$	−643260.	−	1.11416e6i	−0.363103	−	0.628913i
$122$	1.44098e6	+	831951.i	0.793559	+	0.458161i
$123$	−427124.	+	44410.3i	−0.229530	+	0.0238654i
$124$	−480475.	−	832207.i	−0.252003	−	0.436482i
$125$			1.78132e6i			0.912038i
$126$	−878229.	+	1.39077e6i	−0.439032	+	0.695253i
$127$	2.34506e6			1.14484			0.572418	−	0.819962i	$-0.306005\pi$
$127$	2.34506e6			1.14484			0.572418	+	0.819962i	$0.306005\pi$
$128$	489039.	−	282347.i	0.233192	−	0.134634i
$129$	60751.5	+	584289.i	0.0283001	+	0.272181i
$130$	179987.	−	311746.i	0.0819239	−	0.141896i
$131$	−3.22497e6	+	1.86194e6i	−1.43454	+	0.828229i	−0.997462	−	0.0711964i	$-0.977318\pi$
$131$	−3.22497e6	+	1.86194e6i	−1.43454	+	0.828229i	−0.437073	+	0.899426i	$0.643985\pi$
$132$	228750.	+	315588.i	0.0994578	+	0.137214i
$133$	−1.24409e6	−	1.20743e6i	−0.528806	−	0.513223i
$134$			1.09128e6i			0.453548i
$135$	−967574.	−	877095.i	−0.393263	−	0.356488i
$136$	1.53945e6	−	2.66640e6i	0.611996	−	1.06001i
$137$	66461.5	+	38371.6i	0.0258469	+	0.0149227i	0.512868	−	0.858468i	$-0.328583\pi$
$137$	66461.5	+	38371.6i	0.0258469	+	0.0149227i	−0.487021	+	0.873390i	$0.661916\pi$
$138$	3.22492e6	+	1.44015e6i	1.22711	+	0.547986i
$139$	4.61947e6			1.72008			0.860038	−	0.510230i	$-0.170440\pi$
$139$	4.61947e6			1.72008			0.860038	+	0.510230i	$0.170440\pi$
$140$	−128890.	−	453771.i	−0.0469715	−	0.165368i
$141$	604584.	+	834096.i	0.215675	+	0.297549i
$142$	−983319.	−	1.70316e6i	−0.343423	−	0.594826i
$143$	497455.	+	287205.i	0.170116	+	0.0982165i
$144$	−1.13849e6	−	1.27012e6i	−0.381279	−	0.425360i
$145$	−776570.	−	1.34506e6i	−0.254728	−	0.441202i
$146$		−	29158.1i		−	0.00936915i
$147$	1.94032e6	+	2.51505e6i	0.610830	+	0.791762i
$148$	−1.00231e6			−0.309185
$149$	1.08263e6	−	625060.i	0.327283	−	0.188957i	−0.327351	−	0.944903i	$-0.606156\pi$
$149$	1.08263e6	−	625060.i	0.327283	−	0.188957i	0.654634	+	0.755946i	$0.272823\pi$
$150$	1.98260e6	−	206141.i	0.587436	−	0.0610788i
$151$	−2.72866e6	+	4.72617e6i	−0.792534	+	1.37271i	0.131859	+	0.991268i	$0.457905\pi$
$151$	−2.72866e6	+	4.72617e6i	−0.792534	+	1.37271i	−0.924393	+	0.381441i	$0.875428\pi$
$152$	2.43970e6	−	1.40856e6i	0.694712	−	0.401092i
$153$	−3.82721e6	−	1.25299e6i	−1.06858	−	0.349844i
$154$	−1.51161e6	+	429360.i	−0.413882	+	0.117560i
$155$			3.07594e6i			0.826005i
$156$	421471.	+	188215.i	0.111018	+	0.0495771i
$157$	1.44836e6	−	2.50863e6i	0.374263	−	0.648243i	−0.615953	−	0.787783i	$-0.711229\pi$
$157$	1.44836e6	−	2.50863e6i	0.374263	−	0.648243i	0.990216	+	0.139540i	$0.0445623\pi$
$158$	−3.53519e6	−	2.04104e6i	−0.896274	−	0.517464i
$159$	−2.45750e6	+	5.50308e6i	−0.611366	+	1.36903i
$160$	1.34551e6			0.328494
$161$	4.75034e6	−	4.89458e6i	1.13828	−	1.17284i
$162$	−2.06745e6	+	2.81903e6i	−0.486284	+	0.663063i
$163$	244572.	+	423611.i	0.0564734	+	0.0978149i	0.892880	−	0.450295i	$-0.148681\pi$
$163$	244572.	+	423611.i	0.0564734	+	0.0978149i	−0.836407	+	0.548109i	$0.815348\pi$
$164$	−285504.	−	164836.i	−0.0647264	−	0.0373698i
$165$	−129027.	−	1.24094e6i	−0.0287230	−	0.276249i
$166$	−1.36474e6	−	2.36380e6i	−0.298349	−	0.516756i
$167$		−	2.69550e6i		−	0.578749i	−0.957216	−	0.289375i	$-0.906553\pi$
$167$		−	2.69550e6i		−	0.578749i	0.957216	−	0.289375i	$-0.0934473\pi$
$168$	−4.79276e6	+	1.91627e6i	−1.01078	+	0.404136i
$169$	−4.14656e6			−0.859069
$170$	−2.08801e6	+	1.20551e6i	−0.424997	+	0.245372i
$171$	−2.45942e6	−	2.74377e6i	−0.491864	−	0.548730i
$172$	−225489.	+	390559.i	−0.0443139	+	0.0767540i
$173$	−546938.	+	315775.i	−0.105633	+	0.0609873i	−0.551886	−	0.833920i	$-0.686092\pi$
$173$	−546938.	+	315775.i	−0.105633	+	0.0609873i	0.446253	+	0.894907i	$0.352758\pi$
$174$	−3.36631e6	+	2.44003e6i	−0.639008	+	0.463177i
$175$	940595.	−	3.73274e6i	0.175505	−	0.696488i
$176$		−	1.62953e6i		−	0.298898i
$177$	3.45471e6	−	7.73615e6i	0.623006	−	1.39510i
$178$	−2.46744e6	+	4.27373e6i	−0.437508	+	0.757786i
$179$	−1.23874e6	−	715187.i	−0.215984	−	0.124698i	0.388105	−	0.921615i	$-0.373130\pi$
$179$	−1.23874e6	−	715187.i	−0.215984	−	0.124698i	−0.604089	+	0.796917i	$0.706463\pi$
$180$	−206257.	−	981133.i	−0.0353664	−	0.168233i
$181$	3.92186e6			0.661388			0.330694	−	0.943738i	$-0.392717\pi$
$181$	3.92186e6			0.661388			0.330694	+	0.943738i	$0.392717\pi$
$182$	−1.29606e6	+	1.33541e6i	−0.214986	+	0.221513i
$183$	5.52965e6	−	4.00810e6i	0.902286	−	0.654011i
$184$	5.54165e6	+	9.59841e6i	0.889580	+	1.54080i
$185$	2.77851e6	+	1.60417e6i	0.438830	+	0.253359i
$186$	8.18986e6	−	851542.i	1.27273	−	0.132333i
$187$	−1.92364e6	−	3.33185e6i	−0.294171	−	0.509519i
$188$			790860.i			0.119022i
$189$	3.74245e6	+	5.61905e6i	0.554333	+	0.832295i
$190$	−2.20603e6			−0.321626
$191$	−410709.	+	237123.i	−0.0589432	+	0.0340309i	−0.529182	−	0.848508i	$-0.677501\pi$
$191$	−410709.	+	237123.i	−0.0589432	+	0.0340309i	0.470239	+	0.882539i	$0.344168\pi$
$192$	−790619.	−	7.60392e6i	−0.111703	−	1.07432i
$193$	109690.	−	189988.i	0.0152579	−	0.0264274i	−0.858296	−	0.513156i	$-0.828476\pi$
$193$	109690.	−	189988.i	0.0152579	−	0.0264274i	0.873554	+	0.486728i	$0.161810\pi$
$194$	−1.20912e6	+	698088.i	−0.165602	+	0.0956104i
$195$	−867124.	−	1.19630e6i	−0.116944	−	0.161338i
$196$	72921.1	+	2.43753e6i	0.00968468	+	0.323730i
$197$			7.90337e6i			1.03374i	0.856062	+	0.516872i	$0.172904\pi$
$197$			7.90337e6i			1.03374i	−0.856062	+	0.516872i	$0.827096\pi$
$198$	−3.26836e6	+	687085.i	−0.421051	+	0.0885146i
$199$	−4.44349e6	+	7.69635e6i	−0.563852	+	0.976620i	0.433304	+	0.901248i	$0.357348\pi$
$199$	−4.44349e6	+	7.69635e6i	−0.563852	+	0.976620i	−0.997155	+	0.0753721i	$0.975986\pi$
$200$	5.41705e6	+	3.12754e6i	0.677132	+	0.390942i
$201$	4.08989e6	+	1.82641e6i	0.503644	+	0.224911i
$202$	9.67714e6			1.17407
$203$	2.19384e6	+	7.72365e6i	0.262251	+	0.923282i
$204$	−1.81441e6	−	2.50320e6i	−0.213720	−	0.294852i
$205$	527630.	+	913882.i	0.0612446	+	0.106079i
$206$	−4.24417e6	−	2.45037e6i	−0.485502	−	0.280304i
$207$	1.07947e7	−	9.67602e6i	1.21703	−	1.09090i
$208$	−964883.	−	1.67123e6i	−0.107222	−	0.185714i
$209$		−	3.52017e6i		−	0.385589i
$210$	4.00060e6	+	577009.i	0.431983	+	0.0623053i
$211$	3.95802e6			0.421337			0.210669	−	0.977558i	$-0.432436\pi$
$211$	3.95802e6			0.421337			0.210669	+	0.977558i	$0.432436\pi$
$212$	−4.00696e6	+	2.31342e6i	−0.420540	+	0.242799i
$213$	−8.02878e6	+	834794.i	−0.830828	+	0.0863855i
$214$	−5.08114e6	+	8.80080e6i	−0.518466	+	0.898009i
$215$	1.25015e6	−	721776.i	0.125791	−	0.0726252i
$216$	−1.04448e7	+	3.35506e6i	−1.03642	+	0.332919i
$217$	3.88548e6	−	1.54195e7i	0.380246	−	1.50901i
$218$		−	1.26115e7i		−	1.21730i
$219$	−109278.	−	48800.0i	−0.0104040	−	0.00464609i
$220$	478906.	−	829490.i	0.0449762	−	0.0779010i
$221$	−3.94574e6	−	2.27807e6i	−0.365554	−	0.211053i
$222$	3.50200e6	−	7.84203e6i	0.320079	−	0.716753i
$223$	−2.07065e7			−1.86720			−0.933601	−	0.358313i	$-0.883352\pi$
$223$	−2.07065e7			−1.86720			−0.933601	+	0.358313i	$0.883352\pi$
$224$	−6.74496e6	−	1.69963e6i	−0.600116	−	0.151220i
$225$	2.54558e6	−	7.77534e6i	0.223480	−	0.682609i
$226$	5.32779e6	+	9.22800e6i	0.461553	+	0.799433i
$227$	4.71060e6	+	2.71967e6i	0.402716	+	0.232508i	0.687655	−	0.726038i	$-0.258640\pi$
$227$	4.71060e6	+	2.71967e6i	0.402716	+	0.232508i	−0.284939	+	0.958546i	$0.591973\pi$
$228$	−292543.	−	2.81359e6i	−0.0246823	−	0.237386i
$229$	636788.	+	1.10295e6i	0.0530259	+	0.0918436i	0.891320	−	0.453375i	$-0.149780\pi$
$229$	636788.	+	1.10295e6i	0.0530259	+	0.0918436i	−0.838294	+	0.545218i	$0.816447\pi$
$230$		−	8.67912e6i		−	0.713333i
$231$	−920735.	+	6.38376e6i	−0.0746962	+	0.517894i
$232$	−1.30469e7			−1.04482
$233$	−1.16591e7	+	6.73138e6i	−0.921716	+	0.532153i	−0.884182	−	0.467142i	$-0.845284\pi$
$233$	−1.16591e7	+	6.73138e6i	−0.921716	+	0.532153i	−0.0375341	+	0.999295i	$0.511950\pi$
$234$	−2.94516e6	+	2.63995e6i	−0.229859	+	0.206038i
$235$	1.26575e6	−	2.19234e6i	0.0975311	−	0.168929i
$236$	5.63294e6	−	3.25218e6i	0.428547	−	0.247422i
$237$	−1.35660e7	+	9.83313e6i	−1.01908	+	0.738664i
$238$	1.19899e7	−	3.40562e6i	0.889371	−	0.252619i
$239$			1.37101e6i			0.100426i	0.998739	+	0.0502132i	$0.0159901\pi$
$239$			1.37101e6i			0.100426i	−0.998739	+	0.0502132i	$0.984010\pi$
$240$	−1.70911e6	+	3.82722e6i	−0.123634	+	0.276853i
$241$	−6.49292e6	+	1.12461e7i	−0.463862	+	0.803432i	−0.999149	−	0.0412376i	$-0.986870\pi$
$241$	−6.49292e6	+	1.12461e7i	−0.463862	+	0.803432i	0.535287	+	0.844670i	$0.320203\pi$
$242$	7.32910e6	+	4.23146e6i	0.517136	+	0.298568i
$243$	7.10495e6	+	1.24664e7i	0.495156	+	0.868804i
$244$	5.24301e6			0.360921
$245$	3.69905e6	−	6.87378e6i	0.251531	−	0.467409i
$246$	2.28719e6	−	1.65784e6i	0.153637	−	0.111362i
$247$	−2.08438e6	−	3.61026e6i	−0.138321	−	0.239578i
$248$	2.23772e7	+	1.29195e7i	1.46707	+	0.847011i
$249$	−1.11431e7	+	1.15860e6i	−0.721783	+	0.0750475i
$250$	−5.85891e6	−	1.01479e7i	−0.374970	−	0.649467i
$251$		−	1.87672e7i		−	1.18680i	−0.804907	−	0.593401i	$-0.797785\pi$
$251$		−	1.87672e7i		−	1.18680i	0.804907	−	0.593401i	$-0.202215\pi$
$252$	−205399.	+	5.17890e6i	−0.0128350	+	0.323620i
$253$	1.38493e7			0.855197
$254$	−1.33595e7	+	7.71309e6i	−0.815244	+	0.470681i
$255$	1.02343e6	+	9.84300e6i	0.0617215	+	0.593618i
$256$	7.20332e6	−	1.24765e7i	0.429351	−	0.743658i
$257$	7.23297e6	−	4.17596e6i	0.426105	−	0.246012i	−0.271581	−	0.962416i	$-0.587546\pi$
$257$	7.23297e6	−	4.17596e6i	0.426105	−	0.246012i	0.697686	+	0.716404i	$0.254213\pi$
$258$	−2.26786e6	−	3.12878e6i	−0.132056	−	0.182187i
$259$	−1.19021e7	−	1.15514e7i	−0.685054	−	0.664867i
$260$		−	1.13429e6i		−	0.0645363i
$261$	3.51070e6	+	1.66999e7i	0.197457	+	0.939274i
$262$	1.22481e7	−	2.12143e7i	0.681027	−	1.17957i
$263$	5.57378e6	+	3.21803e6i	0.306396	+	0.176898i	0.645313	−	0.763919i	$-0.276727\pi$
$263$	5.57378e6	+	3.21803e6i	0.306396	+	0.176898i	−0.338917	+	0.940816i	$0.610060\pi$
$264$	−9.56969e6	−	4.27351e6i	−0.520099	−	0.232259i
$265$	1.48102e7			0.795837
$266$	1.10587e7	+	2.78663e6i	0.587570	+	0.148059i
$267$	1.18874e7	+	1.64001e7i	0.624529	+	0.861613i
$268$	1.71934e6	+	2.97798e6i	0.0893216	+	0.154710i
$269$	−2.66372e7	−	1.53790e7i	−1.36846	−	0.790080i	−0.377728	−	0.925917i	$-0.623295\pi$
$269$	−2.66372e7	−	1.53790e7i	−1.36846	−	0.790080i	−0.990731	+	0.135836i	$0.956628\pi$
$270$	8.39695e6	+	1.81425e6i	0.426609	+	0.0921736i
$271$	−2.63106e6	−	4.55713e6i	−0.132197	−	0.228973i	0.792326	−	0.610098i	$-0.208870\pi$
$271$	−2.63106e6	−	4.55713e6i	−0.132197	−	0.228973i	−0.924523	+	0.381125i	$0.875537\pi$
$272$			1.29252e7i			0.642287i
$273$	2.83569e6	+	7.09232e6i	0.139370	+	0.348578i
$274$	−504828.			−0.0245410
$275$	6.76896e6	−	3.90806e6i	0.325480	−	0.187916i
$276$	1.10694e7	−	1.15094e6i	0.526498	−	0.0547427i
$277$	−369234.	+	639531.i	−0.0173725	+	0.0300900i	−0.874581	−	0.484880i	$-0.838863\pi$
$277$	−369234.	+	639531.i	−0.0173725	+	0.0300900i	0.857208	+	0.514970i	$0.172197\pi$
$278$	−2.63164e7	+	1.51938e7i	−1.22488	+	0.707182i
$279$	1.05155e7	−	3.21189e7i	0.484190	−	1.47893i
$280$	9.10210e6	+	8.83387e6i	0.414636	+	0.402418i
$281$			2.15513e7i			0.971300i	0.874153	+	0.485650i	$0.161417\pi$
$281$			2.15513e7i			0.971300i	−0.874153	+	0.485650i	$0.838583\pi$
$282$	−6.18762e6	−	2.76319e6i	−0.275916	−	0.123215i
$283$	2.00616e6	−	3.47477e6i	0.0885128	−	0.153309i	−0.818370	−	0.574692i	$-0.805122\pi$
$283$	2.00616e6	−	3.47477e6i	0.0885128	−	0.153309i	0.906883	+	0.421383i	$0.138455\pi$
$284$	−5.36671e6	−	3.09847e6i	−0.234290	−	0.135267i
$285$	−3.69210e6	+	8.26773e6i	−0.159492	+	0.357151i
$286$	−3.77856e6			−0.161521
$287$	−1.49057e6	−	5.24772e6i	−0.0630533	−	0.221986i
$288$	−1.40498e7	−	4.59978e6i	−0.588157	−	0.192557i
$289$	3.18928e6	+	5.52399e6i	0.132129	+	0.228854i
$290$	8.84800e6	+	5.10839e6i	0.362786	+	0.209455i
$291$	592646.	+	5.69988e6i	0.0240501	+	0.231306i
$292$	−45939.0	−	79568.8i	−0.00184516	−	0.00319591i
$293$			3.06845e7i			1.21988i	0.792448	+	0.609940i	$0.208806\pi$
$293$			3.06845e7i			1.21988i	−0.792448	+	0.609940i	$0.791194\pi$
$294$	−1.93259e7	−	7.94600e6i	−0.760496	−	0.312685i
$295$	−2.08200e7			−0.810990
$296$	2.33404e7	−	1.34756e7i	0.899980	−	0.519604i
$297$	−2.89501e6	+	1.33990e7i	−0.110505	+	0.511451i
$298$	−4.11173e6	+	7.12173e6i	−0.155373	+	0.269114i
$299$	1.42037e7	−	8.20052e6i	0.531360	−	0.306781i
$300$	5.08548e6	−	3.68615e6i	0.188351	−	0.136524i
$301$	−7.17867e6	+	2.03905e6i	−0.263236	+	0.0747700i
$302$		−	3.58990e7i		−	1.30335i
$303$	1.61960e7	−	3.62678e7i	0.582211	−	1.30375i
$304$	−5.91311e6	+	1.02418e7i	−0.210472	+	0.364549i
$305$	−1.45341e7	−	8.39128e6i	−0.512259	−	0.295753i
$306$	2.59242e7	−	5.44986e6i	0.904776	−	0.190205i
$307$	−7.56198e6			−0.261349			−0.130674	−	0.991425i	$-0.541714\pi$
$307$	−7.56198e6			−0.261349			−0.130674	+	0.991425i	$0.541714\pi$
$308$	−3.44852e6	+	3.55323e6i	−0.118027	+	0.121611i
$309$	−1.62866e7	+	1.18052e7i	−0.552022	+	0.400126i
$310$	−1.01170e7	−	1.75231e7i	−0.339599	−	0.588203i
$311$	−4.11760e7	−	2.37730e7i	−1.36887	−	0.790319i	−0.378089	−	0.925769i	$-0.623419\pi$
$311$	−4.11760e7	−	2.37730e7i	−1.36887	−	0.790319i	−0.990784	+	0.135450i	$0.956752\pi$
$312$	−1.23450e7	+	1.28358e6i	−0.406470	+	0.0422628i
$313$	1.45386e7	+	2.51816e7i	0.474121	+	0.821201i	0.999561	−	0.0296294i	$-0.00943270\pi$
$313$	1.45386e7	+	2.51816e7i	0.474121	+	0.821201i	−0.525440	+	0.850831i	$0.676099\pi$
$314$			1.90550e7i			0.615490i
$315$	8.85805e6	−	1.40276e7i	0.283404	−	0.448800i
$316$	−1.28628e7			−0.407637
$317$	2.54469e7	−	1.46918e7i	0.798834	−	0.461207i	−0.0442294	−	0.999021i	$-0.514083\pi$
$317$	2.54469e7	−	1.46918e7i	0.798834	−	0.461207i	0.843063	+	0.537814i	$0.180750\pi$
$318$	−4.10006e6	−	3.94331e7i	−0.127500	−	1.22625i
$319$	−8.15148e6	+	1.41188e7i	−0.251110	+	0.434936i
$320$	−1.62695e7	+	9.39318e6i	−0.496505	+	0.286657i
$321$	2.44795e7	+	3.37723e7i	0.740094	+	1.02105i
$322$	−1.09633e7	+	4.35079e7i	−0.328379	+	1.30317i
$323$			2.79215e7i			0.828575i
$324$	−1.20038e6	+	1.09501e7i	−0.0352927	+	0.321946i
$325$	4.62813e6	−	8.01615e6i	0.134820	−	0.233515i
$326$	−2.78658e6	−	1.60883e6i	−0.0804301	−	0.0464363i
$327$	−4.72652e7	−	2.11071e7i	−1.35175	−	0.603650i
$328$	8.86453e6			0.251208
$329$	−9.11443e6	+	9.39117e6i	−0.255942	+	0.263713i
$330$	4.81661e6	+	6.64509e6i	0.134029	+	0.184909i
$331$	−1.71441e7	−	2.96945e7i	−0.472749	−	0.818826i	0.526764	−	0.850011i	$-0.323405\pi$
$331$	−1.71441e7	−	2.96945e7i	−0.472749	−	0.818826i	−0.999514	+	0.0311858i	$0.990072\pi$
$332$	−7.44840e6	−	4.30034e6i	−0.203540	−	0.117514i
$333$	−2.35291e7	−	2.62494e7i	−0.637196	−	0.710865i
$334$	8.86571e6	+	1.53559e7i	0.237944	+	0.412130i
$335$		−	1.10070e7i		−	0.292775i
$336$	1.34021e7	−	1.70267e7i	0.353310	−	0.448861i
$337$	5.34960e7			1.39776			0.698878	−	0.715241i	$-0.253683\pi$
$337$	5.34960e7			1.39776			0.698878	+	0.715241i	$0.253683\pi$
$338$	2.36223e7	−	1.36384e7i	0.611748	−	0.353193i
$339$	4.35013e7	−	4.52305e6i	1.11661	−	0.116100i
$340$	−3.79862e6	+	6.57940e6i	−0.0966471	+	0.167398i
$341$	2.79617e7	−	1.61437e7i	0.705182	−	0.407137i
$342$	2.30354e7	+	7.54158e6i	0.575860	+	0.188532i
$343$	−2.72260e7	+	2.97852e7i	−0.674685	+	0.738106i
$344$		−	1.21263e7i		−	0.297889i
$345$	−3.25274e7	−	1.45257e7i	−0.792123	−	0.353736i
$346$	2.07721e6	−	3.59784e6i	0.0501479	−	0.0868587i
$347$	3.17861e7	+	1.83517e7i	0.760762	+	0.439226i	0.829569	−	0.558404i	$-0.188586\pi$
$347$	3.17861e7	+	1.83517e7i	0.760762	+	0.439226i	−0.0688072	+	0.997630i	$0.521919\pi$
$348$	−5.34193e6	+	1.19622e7i	−0.126754	+	0.283840i
$349$	3.14402e7			0.739620			0.369810	−	0.929107i	$-0.379423\pi$
$349$	3.14402e7			0.739620			0.369810	+	0.929107i	$0.379423\pi$
$350$	6.91885e6	+	2.43585e7i	0.161373	+	0.568129i
$351$	4.96481e6	+	1.54561e7i	0.114810	+	0.357421i
$352$	−7.06176e6	−	1.22313e7i	−0.161914	−	0.280443i
$353$	2.35735e7	+	1.36102e7i	0.535920	+	0.309414i	0.743424	−	0.668820i	$-0.233201\pi$
$353$	2.35735e7	+	1.36102e7i	0.535920	+	0.309414i	−0.207503	+	0.978234i	$0.566534\pi$
$354$	5.76381e6	+	5.54345e7i	0.129927	+	1.24960i
$355$	9.91802e6	+	1.71785e7i	0.221687	+	0.383973i
$356$			1.55500e7i			0.344651i
$357$	7.30314e6	−	5.06351e7i	0.160511	−	1.11288i
$358$	9.40921e6			0.205071
$359$	3.24692e7	−	1.87461e7i	0.701760	−	0.405162i	−0.106242	−	0.994340i	$-0.533882\pi$
$359$	3.24692e7	−	1.87461e7i	0.701760	−	0.405162i	0.808003	+	0.589179i	$0.200549\pi$
$360$	1.79938e7	+	2.00741e7i	0.385670	+	0.430258i
$361$	1.07492e7	−	1.86181e7i	0.228483	−	0.395744i
$362$	−2.23422e7	+	1.28993e7i	−0.470978	+	0.271919i
$363$	2.81248e7	−	2.03859e7i	0.587990	−	0.426197i
$364$	−1.43282e6	+	5.68612e6i	−0.0297089	+	0.117899i
$365$			294096.i			0.00604798i
$366$	−1.83186e7	+	4.10209e7i	−0.373637	+	0.836686i
$367$	1.03822e6	−	1.79824e6i	0.0210034	−	0.0363789i	−0.855333	−	0.518079i	$-0.826647\pi$
$367$	1.03822e6	−	1.79824e6i	0.0210034	−	0.0363789i	0.876336	+	0.481700i	$0.159981\pi$
$368$	−4.02940e7	−	2.32638e7i	−0.808531	−	0.466806i
$369$	−2.38530e6	−	1.13465e7i	−0.0474748	−	0.225831i
$370$	−2.11050e7			−0.416658
$371$	−7.42428e7	−	1.87080e7i	−1.45389	−	0.366359i
$372$	2.10075e7	−	1.52270e7i	0.408080	−	0.295792i
$373$	−5.00434e6	−	8.66777e6i	−0.0964318	−	0.167025i	0.813773	−	0.581182i	$-0.197410\pi$
$373$	−5.00434e6	−	8.66777e6i	−0.0964318	−	0.167025i	−0.910205	+	0.414157i	$0.864076\pi$
$374$	2.19174e7	+	1.26540e7i	0.418961	+	0.241887i
$375$	−4.78379e7	+	4.97395e6i	−0.907148	+	0.0943208i
$376$	−1.06327e7	−	1.84164e7i	−0.200023	−	0.346450i
$377$			1.93068e7i			0.360318i
$378$	−3.98016e7	−	1.97016e7i	−0.736929	−	0.364776i
$379$	3.16574e7			0.581511			0.290755	−	0.956797i	$-0.406093\pi$
$379$	3.16574e7			0.581511			0.290755	+	0.956797i	$0.406093\pi$
$380$	−6.01999e6	+	3.47564e6i	−0.109710	+	0.0633409i
$381$	6.54807e6	+	6.29772e7i	0.118396	+	1.13870i
$382$	1.55983e6	−	2.70170e6i	0.0279825	−	0.0484672i
$383$	7.81038e6	−	4.50932e6i	0.139020	−	0.0802629i	−0.428877	−	0.903363i	$-0.641091\pi$
$383$	7.81038e6	−	4.50932e6i	0.139020	−	0.0802629i	0.567897	+	0.823100i	$0.307757\pi$
$384$	8.94802e6	+	1.23449e7i	0.158028	+	0.218018i
$385$	1.52465e7	−	4.33064e6i	0.267170	−	0.0758874i
$386$			1.44311e6i			0.0250922i
$387$	−1.55216e7	+	3.26299e6i	−0.267795	+	0.0562967i
$388$	−2.19970e6	+	3.80999e6i	−0.0376589	+	0.0652272i
$389$	6.99549e6	+	4.03885e6i	0.118842	+	0.0686134i	0.558243	−	0.829678i	$-0.311476\pi$
$389$	6.99549e6	+	4.03885e6i	0.118842	+	0.0686134i	−0.439401	+	0.898291i	$0.644809\pi$
$390$	8.87459e6	+	3.96311e6i	0.149608	+	0.0668100i
$391$	−1.09851e8			−1.83769
$392$	−3.44694e7	−	5.57813e7i	−0.572237	−	0.926041i
$393$	−5.90077e7	−	8.14082e7i	−0.972145	−	1.34119i
$394$	−2.59948e7	−	4.50242e7i	−0.425008	−	0.736135i
$395$	3.56568e7	+	2.05865e7i	0.578564	+	0.334034i
$396$	−7.83644e6	+	7.02433e6i	−0.126192	+	0.113115i
$397$	2.40751e7	+	4.16992e7i	0.384765	+	0.666433i	0.991737	−	0.128291i	$-0.0409490\pi$
$397$	2.40751e7	+	4.16992e7i	0.384765	+	0.666433i	−0.606971	+	0.794724i	$0.707616\pi$
$398$		−	5.84599e7i		−	0.927275i
$399$	2.89519e7	−	3.67818e7i	0.455783	−	0.579047i
$400$	−2.62587e7			−0.410292
$401$	−8.72146e7	+	5.03534e7i	−1.35256	+	0.780900i	−0.988607	−	0.150518i	$-0.951906\pi$
$401$	−8.72146e7	+	5.03534e7i	−1.35256	+	0.780900i	−0.363951	+	0.931418i	$0.618572\pi$
$402$	−2.93067e7	+	3.04717e6i	−0.451116	+	0.0469049i
$403$	1.91182e7	−	3.31137e7i	0.292100	−	0.505932i
$404$	2.64077e7	−	1.52465e7i	0.400485	−	0.231220i
$405$	2.08529e7	−	2.84335e7i	0.313907	−	0.428021i
$406$	−3.79016e7	−	3.67847e7i	−0.566343	−	0.549654i
$407$		−	3.36773e7i		−	0.499521i
$408$	7.59054e7	+	3.38969e7i	1.11762	+	0.499091i
$409$	2.83875e7	−	4.91687e7i	0.414914	−	0.718652i	−0.580506	−	0.814256i	$-0.697145\pi$
$409$	2.83875e7	−	4.91687e7i	0.414914	−	0.718652i	0.995419	+	0.0956046i	$0.0304784\pi$
$410$	−6.01165e6	−	3.47083e6i	−0.0872252	−	0.0503595i
$411$	−844898.	+	1.89198e6i	−0.0121697	+	0.0272516i
$412$	−1.54424e7			−0.220812
$413$	1.04369e8	+	2.62995e7i	1.48157	+	0.373334i
$414$	−2.96706e7	+	9.06274e7i	−0.418143	+	1.27720i
$415$	1.37651e7	+	2.38419e7i	0.192591	+	0.333577i
$416$	−1.44849e7	−	8.36289e6i	−0.201204	−	0.116165i
$417$	1.28988e7	+	1.24057e8i	0.177886	+	1.71085i
$418$	1.15781e7	+	2.00539e7i	0.158529	+	0.274580i
$419$			4.76327e7i			0.647535i	0.946137	+	0.323767i	$0.104950\pi$
$419$			4.76327e7i			0.647535i	−0.946137	+	0.323767i	$0.895050\pi$
$420$	1.18262e7	−	4.72842e6i	0.159624	−	0.0638217i
$421$	4.52744e7			0.606745			0.303373	−	0.952872i	$-0.401887\pi$
$421$	4.52744e7			0.606745			0.303373	+	0.952872i	$0.401887\pi$
$422$	−2.25482e7	+	1.30182e7i	−0.300037	+	0.173226i
$423$	−2.07117e7	+	1.85653e7i	−0.273649	+	0.245290i
$424$	6.22054e7	−	1.07743e8i	0.816076	−	1.41349i
$425$	−5.36905e7	+	3.09982e7i	−0.699408	+	0.403803i
$426$	4.29930e7	−	3.11630e7i	0.556121	−	0.403097i
$427$	6.22589e7	+	6.04242e7i	0.799683	+	0.776117i
$428$			3.20217e7i			0.408426i
$429$	−6.32394e6	+	1.41612e7i	−0.0800969	+	0.179361i
$430$	−4.74795e6	+	8.22369e6i	−0.0597174	+	0.103434i
$431$	3.09039e7	+	1.78424e7i	0.385995	+	0.222855i	0.680424	−	0.732819i	$-0.261796\pi$
$431$	3.09039e7	+	1.78424e7i	0.385995	+	0.222855i	−0.294428	+	0.955674i	$0.595129\pi$
$432$	3.09303e7	−	3.41210e7i	0.383648	−	0.423224i
$433$	−4.90389e7			−0.604056			−0.302028	−	0.953299i	$-0.597664\pi$
$433$	−4.90389e7			−0.604056			−0.302028	+	0.953299i	$0.597664\pi$
$434$	2.85809e7	+	1.00622e8i	0.349628	+	1.23090i
$435$	3.39535e7	−	2.46107e7i	0.412493	−	0.298990i
$436$	−1.98697e7	−	3.44153e7i	−0.239735	−	0.415233i
$437$	−8.70449e7	−	5.02554e7i	−1.04304	−	0.602197i
$438$	783047.	−	81417.4i	0.00931891	−	0.000968936i
$439$	−1.80621e6	−	3.12844e6i	−0.0213488	−	0.0369772i	0.855154	−	0.518375i	$-0.173463\pi$
$439$	−1.80621e6	−	3.12844e6i	−0.0213488	−	0.0369772i	−0.876502	+	0.481397i	$0.840129\pi$
$440$			2.57546e7i			0.302340i
$441$	−6.21243e7	+	5.91303e7i	−0.724346	+	0.689437i
$442$	2.99710e7			0.347084
$443$	−6.88023e6	+	3.97230e6i	−0.0791392	+	0.0456911i	−0.539047	−	0.842275i	$-0.681216\pi$
$443$	−6.88023e6	+	3.97230e6i	−0.0791392	+	0.0456911i	0.459908	+	0.887966i	$0.347882\pi$
$444$	−2.79874e6	−	2.69174e7i	−0.0319752	−	0.307527i
$445$	2.48872e7	−	4.31059e7i	0.282421	−	0.489167i
$446$	1.17962e8	−	6.81051e7i	1.32965	−	0.767671i
$447$	1.98091e7	+	2.73291e7i	0.221790	+	0.305986i
$448$	9.34231e7	−	2.65361e7i	1.03901	−	0.295123i
$449$		−	8.36672e7i		−	0.924306i	−0.886800	−	0.462153i	$-0.847077\pi$
$449$		−	8.36672e7i		−	0.924306i	0.886800	−	0.462153i	$-0.152923\pi$
$450$	1.10719e7	+	5.26675e7i	0.121503	+	0.577970i
$451$	5.53841e6	−	9.59280e6i	0.0603747	−	0.104572i
$452$	2.90777e7	+	1.67880e7i	0.314880	+	0.181796i
$453$	−1.34542e8	−	6.00819e7i	−1.44731	−	0.646322i
$454$	−3.57807e7			−0.382368
$455$	1.30724e7	−	1.34693e7i	0.138778	−	0.142991i
$456$	4.46395e7	+	6.15855e7i	0.470787	+	0.649507i
$457$	6.93037e7	+	1.20038e8i	0.726119	+	1.25768i	0.958512	+	0.285053i	$0.0920113\pi$
$457$	6.93037e7	+	1.20038e8i	0.726119	+	1.25768i	−0.232392	+	0.972622i	$0.574655\pi$
$458$	−7.25536e6	−	4.18888e6i	−0.0755201	−	0.0436016i
$459$	2.29628e7	−	1.06279e8i	0.237458	−	1.09903i
$460$	−1.36741e7	−	2.36843e7i	−0.140484	−	0.243325i
$461$		−	6.46347e7i		−	0.659725i	−0.944029	−	0.329862i	$-0.892998\pi$
$461$		−	6.46347e7i		−	0.659725i	0.944029	−	0.329862i	$-0.107002\pi$
$462$	−1.57514e7	−	3.93956e7i	−0.159732	−	0.399505i
$463$	−1.21889e8			−1.22807			−0.614035	−	0.789279i	$-0.710455\pi$
$463$	−1.21889e8			−1.22807			−0.614035	+	0.789279i	$0.710455\pi$
$464$	4.74328e7	−	2.73853e7i	0.474816	−	0.274135i
$465$	−8.26051e7	+	8.58888e6i	−0.821576	+	0.0854235i
$466$	4.42800e7	−	7.66953e7i	0.437573	−	0.757898i
$467$	−4.43386e7	+	2.55989e7i	−0.435343	+	0.251345i	−0.701620	−	0.712551i	$-0.747540\pi$
$467$	−4.43386e7	+	2.55989e7i	−0.435343	+	0.251345i	0.266277	+	0.963896i	$0.414206\pi$
$468$	−3.87770e6	+	1.18442e7i	−0.0378300	+	0.115550i
$469$	−1.39038e7	+	5.51773e7i	−0.134777	+	0.534862i
$470$			1.66525e7i			0.160393i
$471$	7.14141e7	+	3.18912e7i	0.683472	+	0.305217i
$472$	−8.74476e7	+	1.51464e8i	−0.831614	+	1.44040i
$473$	−1.31226e7	−	7.57632e6i	−0.124004	−	0.0715937i
$474$	4.49414e7	−	1.00637e8i	0.421999	−	0.944983i
$475$	−5.67253e7			−0.529292
$476$	2.73532e7	−	2.81837e7i	0.253622	−	0.261323i
$477$	−1.54648e8	−	5.06305e7i	−1.42492	−	0.466506i
$478$	−4.50936e6	−	7.81045e6i	−0.0412887	−	0.0715142i
$479$	1.69759e7	+	9.80106e6i	0.154464	+	0.0891798i	0.575240	−	0.817985i	$-0.304909\pi$
$479$	1.69759e7	+	9.80106e6i	0.154464	+	0.0891798i	−0.420776	+	0.907165i	$0.638242\pi$
$480$	3.75704e6	+	3.61340e7i	0.0339721	+	0.326732i
$481$	−1.99412e7	−	3.45391e7i	−0.179191	−	0.310367i
$482$		−	8.54227e7i		−	0.762838i
$483$	1.44709e8	+	1.13905e8i	1.28427	+	1.01088i
$484$	2.66669e7			0.235200
$485$	1.21955e7	−	7.04110e6i	0.106900	−	0.0617185i
$486$	−8.14787e7	−	4.76504e7i	−0.709798	−	0.415104i
$487$	−9.65961e7	+	1.67309e8i	−0.836320	+	1.44855i	0.0566307	+	0.998395i	$0.481964\pi$
$487$	−9.65961e7	+	1.67309e8i	−0.836320	+	1.44855i	−0.892951	+	0.450154i	$0.851369\pi$
$488$	−1.22091e8	+	7.04895e7i	−1.05057	+	0.606548i
$489$	−1.06933e7	+	7.75088e6i	−0.0914500	+	0.0662864i
$490$	1.53544e6	+	5.13253e7i	0.0130511	+	0.436258i
$491$			1.00270e8i			0.847085i	0.905876	+	0.423543i	$0.139214\pi$
$491$			1.00270e8i			0.847085i	−0.905876	+	0.423543i	$0.860786\pi$
$492$	3.62950e6	−	8.12755e6i	0.0304756	−	0.0682440i
$493$	6.46564e7	−	1.11988e8i	0.539598	−	0.934612i
$494$	2.37488e7	+	1.37114e7i	0.196998	+	0.113737i
$495$	3.29656e7	−	6.93012e6i	0.271797	−	0.0571380i
$496$	−1.08471e8			−0.888936
$497$	−2.80188e7	−	9.86431e7i	−0.228234	−	0.803521i
$498$	5.96696e7	−	4.32507e7i	0.483131	−	0.350191i
$499$	4.87188e7	+	8.43834e7i	0.392098	+	0.679134i	0.992726	−	0.120395i	$-0.0384161\pi$
$499$	4.87188e7	+	8.43834e7i	0.392098	+	0.679134i	−0.600628	+	0.799529i	$0.705083\pi$
$500$	−3.19765e7	−	1.84616e7i	−0.255812	−	0.147693i
$501$	7.23883e7	−	7.52659e6i	0.575646	−	0.0598529i
$502$	6.17267e7	+	1.06914e8i	0.487935	+	0.845128i
$503$		−	1.14370e8i		−	0.898685i	−0.893360	−	0.449342i	$-0.851658\pi$
$503$		−	1.14370e8i		−	0.898685i	0.893360	−	0.449342i	$-0.148342\pi$
$504$	−6.48445e7	−	1.23360e8i	−0.506502	−	0.963568i
$505$	−9.76062e7			−0.757885
$506$	−7.88973e7	+	4.55514e7i	−0.608991	+	0.351601i
$507$	−1.15784e7	−	1.11357e8i	−0.0888429	−	0.854463i
$508$	−2.43042e7	+	4.20961e7i	−0.185392	+	0.321108i
$509$	7.07146e7	−	4.08271e7i	0.536236	−	0.309596i	−0.207316	−	0.978274i	$-0.566473\pi$
$509$	7.07146e7	−	4.08271e7i	0.536236	−	0.309596i	0.743552	+	0.668678i	$0.233140\pi$
$510$	−3.82047e7	−	5.27079e7i	−0.288009	−	0.397343i
$511$	371497.	−	1.47428e6i	0.00278415	−	0.0110489i
$512$			1.30909e8i			0.975351i
$513$	6.68171e7	−	7.37097e7i	0.494920	−	0.545975i
$514$	−2.74701e7	+	4.75795e7i	−0.202288	+	0.350373i
$515$	4.28078e7	+	2.47151e7i	0.313401	+	0.180942i
$516$	−1.11182e7	−	4.96501e6i	−0.0809252	−	0.0361386i
$517$	−2.65725e7			−0.192292
$518$	1.05798e8	+	2.66595e7i	0.761180	+	0.191806i
$519$	−1.00074e7	−	1.38064e7i	−0.0715846	−	0.0987595i
$520$	1.52499e7	+	2.64136e7i	0.108457	+	0.187853i
$521$	1.11407e8	+	6.43207e7i	0.787768	+	0.454818i	0.839176	−	0.543860i	$-0.183038\pi$
$521$	1.11407e8	+	6.43207e7i	0.787768	+	0.454818i	−0.0514085	+	0.998678i	$0.516371\pi$
$522$	−7.49271e7	−	8.35897e7i	−0.526778	−	0.587681i
$523$	−1.29930e7	−	2.25046e7i	−0.0908250	−	0.157314i	0.817033	−	0.576590i	$-0.195617\pi$
$523$	−1.29930e7	−	2.25046e7i	−0.0908250	−	0.157314i	−0.907859	+	0.419277i	$0.862284\pi$
$524$		−	7.71883e7i		−	0.536485i
$525$	1.02870e8	+	1.48370e7i	0.710904	+	0.102534i
$526$	−4.23373e7			−0.290915
$527$	−2.21789e8	+	1.28050e8i	−1.51533	+	0.874876i
$528$	4.37613e7	−	4.55009e6i	0.297295	−	0.0309113i
$529$	1.23700e8	−	2.14255e8i	0.835610	−	1.44732i
$530$	−8.43716e7	+	4.87120e7i	−0.566720	+	0.327196i
$531$	2.17403e8	+	7.11757e7i	1.45205	+	0.475388i
$532$	3.45682e7	−	9.81882e6i	0.229584	−	0.0652116i
$533$		−	1.31177e7i		−	0.0866317i
$534$	−1.21662e8	−	5.43302e7i	−0.798969	−	0.356794i
$535$	5.12498e7	−	8.87672e7i	0.334681	−	0.579684i
$536$	−8.00746e7	−	4.62311e7i	−0.519997	−	0.300220i
$537$	1.57476e7	−	3.52636e7i	0.101693	−	0.227722i
$538$	2.02331e8			1.29932
$539$	−8.18999e7	+	2.45011e6i	−0.523019	+	0.0156466i
$540$	2.57726e7	−	8.27867e6i	0.163673	−	0.0525750i
$541$	−1.12905e7	−	1.95558e7i	−0.0713055	−	0.123505i	0.828168	−	0.560480i	$-0.189383\pi$
$541$	−1.12905e7	−	1.95558e7i	−0.0713055	−	0.123505i	−0.899474	+	0.436975i	$0.856050\pi$
$542$	2.99775e7	+	1.73075e7i	0.188277	+	0.108702i
$543$	1.09509e7	+	1.05322e8i	0.0683992	+	0.657842i
$544$	5.60129e7	+	9.70171e7i	0.347929	+	0.602631i
$545$			1.27203e8i			0.785793i
$546$	−3.94816e7	−	3.10770e7i	−0.242559	−	0.190924i
$547$	2.44583e8			1.49439			0.747197	−	0.664603i	$-0.231399\pi$
$547$	2.44583e8			1.49439			0.747197	+	0.664603i	$0.231399\pi$
$548$	−1.37761e6	+	795365.i	−0.00837115	+	0.00483309i
$549$	1.23079e8	+	1.37308e8i	0.743817	+	0.829812i
$550$	−2.57078e7	+	4.45272e7i	−0.154517	+	0.267632i
$551$	1.02467e8	−	5.91591e7i	0.612530	−	0.353644i
$552$	−2.42294e8	+	1.75624e8i	−1.44054	+	1.04416i
$553$	−1.52741e8	−	1.48240e8i	−0.903191	−	0.876575i
$554$		−	4.85775e6i		−	0.0285697i
$555$	−3.53221e7	+	7.90968e7i	−0.206617	+	0.462679i
$556$	−4.78761e7	+	8.29239e7i	−0.278545	+	0.482453i
$557$	4.19332e6	+	2.42102e6i	0.0242657	+	0.0140098i	0.512084	−	0.858936i	$-0.328874\pi$
$557$	4.19332e6	+	2.42102e6i	0.0242657	+	0.0140098i	−0.487818	+	0.872945i	$0.662207\pi$
$558$	4.57367e7	+	2.17563e8i	0.263246	+	1.25222i
$559$	−1.79445e7			−0.102730
$560$	−5.16335e7	−	1.30109e7i	−0.294014	−	0.0740870i
$561$	8.41061e7	−	6.09633e7i	0.476364	−	0.345287i
$562$	−7.08837e7	−	1.22774e8i	−0.399335	−	0.691668i
$563$	2.58387e8	+	1.49180e8i	1.44792	+	0.835958i	0.998358	−	0.0572897i	$-0.0182459\pi$
$563$	2.58387e8	+	1.49180e8i	1.44792	+	0.835958i	0.449564	+	0.893248i	$0.351579\pi$
$564$	−2.12387e7	+	2.20830e6i	−0.118383	+	0.0123089i
$565$	−5.37375e7	−	9.30760e7i	−0.297942	−	0.516051i
$566$			2.63936e7i			0.145563i
$567$	−1.40451e8	+	1.16194e8i	−0.770504	+	0.637435i
$568$	1.66629e8			0.909298
$569$	1.64780e8	−	9.51358e7i	0.894475	−	0.516425i	0.0190711	−	0.999818i	$-0.493929\pi$
$569$	1.64780e8	−	9.51358e7i	0.894475	−	0.516425i	0.875403	+	0.483393i	$0.160596\pi$
$570$	−6.15986e6	−	5.92435e7i	−0.0332618	−	0.319902i
$571$	−6.56426e7	+	1.13696e8i	−0.352596	+	0.610714i	−0.986703	−	0.162531i	$-0.948034\pi$
$571$	−6.56426e7	+	1.13696e8i	−0.352596	+	0.610714i	0.634108	+	0.773245i	$0.281368\pi$
$572$	−1.03112e7	+	5.95319e6i	−0.0550963	+	0.0318098i
$573$	−7.51480e6	−	1.03676e7i	−0.0399442	−	0.0551078i
$574$	2.57517e7	+	2.49928e7i	0.136167	+	0.132154i
$575$		−	2.23172e8i		−	1.17392i
$576$	2.01997e8	−	4.24645e7i	1.05701	−	0.222208i
$577$	1.39506e7	−	2.41632e7i	0.0726216	−	0.125784i	−0.827428	−	0.561572i	$-0.810197\pi$
$577$	1.39506e7	−	2.41632e7i	0.0726216	−	0.125784i	0.900050	+	0.435788i	$0.143530\pi$
$578$	−3.63376e7	−	2.09795e7i	−0.188180	−	0.108646i
$579$	5.40847e6	+	2.41525e6i	0.0278637	+	0.0124430i
$580$	3.21935e7			0.165000
$581$	−3.88870e7	−	1.36906e8i	−0.198278	−	0.698060i
$582$	−2.21235e7	−	3.05220e7i	−0.112224	−	0.154826i
$583$	−7.77298e7	−	1.34632e8i	−0.392267	−	0.679427i
$584$	2.13952e6	+	1.23525e6i	0.0107418	+	0.00620179i
$585$	2.97057e7	−	2.66272e7i	0.148379	−	0.133002i
$586$	−1.00924e8	−	1.74805e8i	−0.501534	−	0.868682i
$587$			4.50405e7i			0.222684i	0.993782	+	0.111342i	$0.0355149\pi$
$587$			4.50405e7i			0.222684i	−0.993782	+	0.111342i	$0.964485\pi$
$588$	−6.52569e7	+	8.76459e6i	−0.320992	+	0.0431121i
$589$	−2.34325e8			−1.14676
$590$	1.18608e8	−	6.84786e7i	0.577510	−	0.333426i
$591$	−2.12247e8	+	2.20684e7i	−1.02820	+	0.106907i
$592$	−5.65703e7	+	9.79827e7i	−0.272661	+	0.472263i
$593$	−4.76852e6	+	2.75311e6i	−0.0228675	+	0.0132026i	−0.511390	−	0.859349i	$-0.670869\pi$
$593$	−4.76852e6	+	2.75311e6i	−0.0228675	+	0.0132026i	0.488523	+	0.872551i	$0.337536\pi$
$594$	−2.75780e7	−	8.58541e7i	−0.131584	−	0.409639i
$595$	−1.20933e8	+	3.43500e7i	−0.574108	+	0.163071i
$596$			2.59124e7i			0.122397i
$597$	−2.19095e8	−	9.78406e7i	−1.02970	−	0.459829i
$598$	−5.39442e7	+	9.34342e7i	−0.252256	+	0.436920i
$599$	−3.14579e8	−	1.81622e8i	−1.46369	−	0.845062i	−0.464512	−	0.885567i	$-0.653770\pi$
$599$	−3.14579e8	−	1.81622e8i	−1.46369	−	0.845062i	−0.999179	+	0.0405046i	$0.987103\pi$
$600$	−6.88648e7	+	1.54209e8i	−0.318818	+	0.713931i
$601$	2.03084e8			0.935517			0.467759	−	0.883856i	$-0.345062\pi$
$601$	2.03084e8			0.935517			0.467759	+	0.883856i	$0.345062\pi$
$602$	3.41892e7	−	3.52273e7i	0.156711	−	0.161469i
$603$	−3.76286e7	+	1.14935e8i	−0.171619	+	0.524203i
$604$	−5.65595e7	−	9.79639e7i	−0.256682	−	0.444586i
$605$	−7.39232e7	−	4.26796e7i	−0.333822	−	0.192732i
$606$	2.70213e7	+	2.59882e8i	0.121419	+	1.16777i
$607$	−5.60658e7	−	9.71089e7i	−0.250687	−	0.434203i	0.713028	−	0.701136i	$-0.247323\pi$
$607$	−5.60658e7	−	9.71089e7i	−0.250687	−	0.434203i	−0.963715	+	0.266933i	$0.913990\pi$
$608$			1.02501e8i			0.456055i
$609$	−2.01294e8	+	8.04826e7i	−0.891210	+	0.356328i
$610$	1.10398e8			0.486376
$611$	−2.72525e7	+	1.57342e7i	−0.119477	+	0.0689798i
$612$	6.21576e7	−	5.57160e7i	0.271169	−	0.243067i
$613$	−3.83093e7	+	6.63536e7i	−0.166311	+	0.288060i	−0.937120	−	0.349007i	$-0.886519\pi$
$613$	−3.83093e7	+	6.63536e7i	−0.166311	+	0.288060i	0.770809	+	0.637067i	$0.219852\pi$
$614$	4.30794e7	−	2.48719e7i	0.186108	−	0.107449i
$615$	−2.30692e7	+	1.67214e7i	−0.0991762	+	0.0718866i
$616$	3.25327e7	−	1.29106e8i	0.139181	−	0.552337i
$617$		−	1.59298e7i		−	0.0678196i	−0.999425	−	0.0339098i	$-0.989204\pi$
$617$		−	1.59298e7i		−	0.0678196i	0.999425	−	0.0339098i	$-0.0107959\pi$
$618$	5.39544e7	−	1.20820e8i	0.228592	−	0.511887i
$619$	1.30151e8	−	2.25428e8i	0.548751	−	0.950465i	−0.449609	−	0.893225i	$-0.648437\pi$
$619$	1.30151e8	−	2.25428e8i	0.548751	−	0.950465i	0.998360	−	0.0572397i	$-0.0182299\pi$
$620$	−5.52160e7	−	3.18790e7i	−0.231681	−	0.133761i
$621$	2.89994e8	+	2.62876e8i	1.21091	+	1.09768i
$622$	3.12764e8			1.29971
$623$	−1.79209e8	+	1.84650e8i	−0.741131	+	0.763634i
$624$	4.21869e7	−	3.05787e7i	0.173630	−	0.125853i
$625$	−2.85838e7	−	4.95086e7i	−0.117079	−	0.202787i
$626$	−1.65648e8	−	9.56369e7i	−0.675248	−	0.389855i
$627$	9.45351e7	−	9.82930e6i	0.383522	−	0.0398768i
$628$	3.00215e7	+	5.19988e7i	0.121214	+	0.209949i
$629$			2.67123e8i			1.07340i
$630$	−4.32494e6	+	1.09048e8i	−0.0172965	+	0.436110i
$631$	−8.31931e7			−0.331130			−0.165565	−	0.986199i	$-0.552945\pi$
$631$	−8.31931e7			−0.331130			−0.165565	+	0.986199i	$0.552945\pi$
$632$	2.99529e8	−	1.72933e8i	1.18655	−	0.685058i
$633$	1.10519e7	+	1.06293e8i	0.0435737	+	0.419078i
$634$	−9.66445e7	+	1.67393e8i	−0.379236	+	0.656856i
$635$	1.34747e8	−	7.77962e7i	0.526257	−	0.303835i
$636$	−7.33160e7	−	1.01148e8i	−0.284989	−	0.393176i
$637$	−8.25451e7	+	5.10078e7i	−0.319354	+	0.197342i
$638$		−	1.07243e8i		−	0.412960i
$639$	−4.48372e7	−	2.13284e8i	−0.171845	−	0.817439i
$640$	1.87334e7	−	3.24472e7i	0.0714623	−	0.123776i
$641$	4.13537e8	+	2.38755e8i	1.57015	+	0.906524i	0.996150	+	0.0876653i	$0.0279406\pi$
$641$	4.13537e8	+	2.38755e8i	1.57015	+	0.906524i	0.573995	+	0.818859i	$0.305393\pi$
$642$	−2.50535e8	−	1.11881e8i	−0.946813	−	0.422816i
$643$	1.79150e8			0.673880			0.336940	−	0.941526i	$-0.390608\pi$
$643$	1.79150e8			0.673880			0.336940	+	0.941526i	$0.390608\pi$
$644$	3.86299e7	+	1.36001e8i	0.144632	+	0.509194i
$645$	2.28742e7	+	3.15578e7i	0.0852447	+	0.117605i
$646$	−9.18360e7	−	1.59065e8i	−0.340655	−	0.590032i
$647$	−1.90784e8	−	1.10149e8i	−0.704415	−	0.406694i	0.104575	−	0.994517i	$-0.466652\pi$
$647$	−1.90784e8	−	1.10149e8i	−0.704415	−	0.406694i	−0.808990	+	0.587823i	$0.799985\pi$
$648$	−1.19265e8	−	2.71128e8i	−0.438318	−	0.996436i
$649$	1.09272e8	+	1.89264e8i	0.399736	+	0.692362i
$650$			6.08890e7i			0.221717i
$651$	4.24943e8	+	6.12899e7i	1.54024	+	0.222150i
$652$	−1.01390e7			−0.0365806
$653$	1.16639e8	−	6.73418e7i	0.418895	−	0.241849i	−0.275709	−	0.961241i	$-0.588913\pi$
$653$	1.16639e8	−	6.73418e7i	0.418895	−	0.241849i	0.694605	+	0.719392i	$0.255579\pi$
$654$	3.38685e8	−	3.52148e7i	1.21077	−	0.125890i
$655$	−1.23537e8	+	2.13973e8i	−0.439617	+	0.761439i
$656$	−3.22276e7	+	1.86066e7i	−0.114161	+	0.0659106i
$657$	1.00540e6	−	3.07095e6i	0.00354522	−	0.0108287i
$658$	2.10352e7	−	8.34781e7i	0.0738362	−	0.293018i
$659$			3.76030e8i			1.31391i	0.753928	+	0.656957i	$0.228157\pi$
$659$			3.76030e8i			1.31391i	−0.753928	+	0.656957i	$0.771843\pi$
$660$	2.36134e7	+	1.05450e7i	0.0821346	+	0.0366787i
$661$	2.90919e7	−	5.03887e7i	0.100732	−	0.174473i	−0.811254	−	0.584693i	$-0.801215\pi$
$661$	2.90919e7	−	5.03887e7i	0.100732	−	0.174473i	0.911987	+	0.410220i	$0.134548\pi$
$662$	1.95335e8	+	1.12776e8i	0.673294	+	0.388727i
$663$	5.01606e7	−	1.12325e8i	0.172116	−	0.385421i
$664$	2.31263e8			0.789954
$665$	−1.11541e8	−	2.81066e7i	−0.379288	−	0.0955749i
$666$	2.20378e8	+	7.21498e7i	0.746011	+	0.244237i
$667$	2.32748e8	+	4.03131e8i	0.784346	+	1.35853i
$668$	4.83868e7	+	2.79361e7i	0.162330	+	0.0937210i
$669$	−5.78182e7	−	5.56077e8i	−0.193102	−	1.85719i
$670$	3.62027e7	+	6.27050e7i	0.120370	+	0.208486i
$671$			1.76163e8i			0.583104i
$672$	2.68101e7	−	1.85883e8i	0.0883467	−	0.612537i
$673$	−1.71549e8			−0.562786			−0.281393	−	0.959593i	$-0.590796\pi$
$673$	−1.71549e8			−0.562786			−0.281393	+	0.959593i	$0.590796\pi$
$674$	−3.04758e8	+	1.75952e8i	−0.995350	+	0.574665i
$675$	2.15916e8	+	4.66511e7i	0.702060	+	0.151688i
$676$	4.29749e7	−	7.44347e7i	0.139115	−	0.240955i
$677$	−4.36085e8	+	2.51774e8i	−1.40542	+	0.811417i	−0.994942	−	0.100455i	$-0.967970\pi$
$677$	−4.36085e8	+	2.51774e8i	−1.40542	+	0.811417i	−0.410475	+	0.911872i	$0.634637\pi$
$678$	−2.32943e8	+	1.68846e8i	−0.747414	+	0.541754i
$679$	−7.00297e7	+	1.98914e7i	−0.223704	+	0.0635412i
$680$		−	2.04282e8i		−	0.649684i
$681$	−5.98839e7	+	1.34098e8i	−0.189613	+	0.424602i
$682$	−1.06196e8	+	1.83936e8i	−0.334776	+	0.579849i
$683$	−4.47198e8	−	2.58190e8i	−1.40358	−	0.810359i	−0.408824	−	0.912613i	$-0.634061\pi$
$683$	−4.47198e8	−	2.58190e8i	−1.40358	−	0.810359i	−0.994758	+	0.102255i	$0.967394\pi$
$684$	7.47426e7	−	1.57126e7i	0.233561	−	0.0490999i
$685$	5.09183e6			0.0158417
$686$	5.71362e7	−	2.59230e8i	0.176986	−	0.802995i
$687$	−2.78419e7	+	2.01808e7i	−0.0858673	+	0.0622399i
$688$	2.54531e7	+	4.40860e7i	0.0781583	+	0.135374i
$689$	−1.59438e8	−	9.20516e7i	−0.487455	−	0.281432i
$690$	2.33080e8	−	2.42345e7i	0.709508	−	0.0737712i
$691$	−2.03098e8	−	3.51777e8i	−0.615563	−	1.06619i	−0.990285	−	0.139049i	$-0.955595\pi$
$691$	−2.03098e8	−	3.51777e8i	−0.615563	−	1.06619i	0.374722	−	0.927137i	$-0.377738\pi$
$692$		−	1.30907e7i		−	0.0395045i
$693$	−1.74008e8	−	6.90131e6i	−0.522842	−	0.0207363i
$694$	−2.41441e8			−0.722324
$695$	2.65434e8	−	1.53248e8i	0.790683	−	0.456501i
$696$	−3.64306e7	−	3.50377e8i	−0.108053	−	1.03922i
$697$	−4.39299e7	+	7.60888e7i	−0.129736	+	0.224710i
$698$	−1.79110e8	+	1.03409e8i	−0.526688	+	0.304083i
$699$	−2.13328e8	−	2.94312e8i	−0.624622	−	0.861740i
$700$	5.72580e7	+	5.55707e7i	0.166933	+	0.162014i
$701$			1.61640e8i			0.469239i	0.972087	+	0.234619i	$0.0753843\pi$
$701$			1.61640e8i			0.469239i	−0.972087	+	0.234619i	$0.924616\pi$
$702$	−7.91201e7	−	7.17215e7i	−0.228705	−	0.207319i
$703$	−1.22206e8	+	2.11667e8i	−0.351743	+	0.609237i
$704$	1.70777e8	+	9.85981e7i	0.489453	+	0.282586i
$705$	6.24100e7	+	2.78703e7i	0.178109	+	0.0795379i
$706$	−1.79060e8			−0.508842
$707$	4.89294e8	+	1.23295e8i	1.38456	+	0.348888i
$708$	1.03067e8	+	1.42193e8i	0.290415	+	0.400662i
$709$	2.99324e8	+	5.18444e8i	0.839851	+	1.45466i	0.890019	+	0.455923i	$0.150691\pi$
$709$	2.99324e8	+	5.18444e8i	0.839851	+	1.45466i	−0.0501682	+	0.998741i	$0.515976\pi$
$710$	−1.13003e8	−	6.52422e7i	−0.315729	−	0.182286i
$711$	−3.01951e8	−	3.36861e8i	−0.840094	−	0.937220i
$712$	−2.09061e8	−	3.62104e8i	−0.579206	−	1.00321i
$713$		−	9.21896e8i		−	2.54339i
$714$	1.24938e8	+	3.12481e8i	0.343241	+	0.858477i
$715$	3.81116e7			0.104265
$716$	2.56766e7	−	1.48244e7i	0.0699517	−	0.0403866i
$717$	−3.68189e7	+	3.82825e6i	−0.0998879	+	0.0103859i
$718$	−1.23315e8	+	2.13588e8i	−0.333152	+	0.577035i
$719$	5.37512e8	−	3.10332e8i	1.44611	−	0.834912i	0.447863	−	0.894102i	$-0.352185\pi$
$719$	5.37512e8	−	3.10332e8i	1.44611	−	0.834912i	0.998247	+	0.0591908i	$0.0188520\pi$
$720$	−1.07553e8	−	3.52119e7i	−0.288155	−	0.0943392i
$721$	−1.83373e8	−	1.77969e8i	−0.489248	−	0.474831i
$722$			1.41419e8i			0.375748i
$723$	−3.20146e8	−	1.42967e8i	−0.847096	−	0.378286i
$724$	−4.06461e7	+	7.04011e7i	−0.107103	+	0.185509i
$725$	2.27515e8	+	1.31356e8i	0.597029	+	0.344695i
$726$	−9.31719e7	+	2.08640e8i	−0.243487	+	0.545240i
$727$	−1.61816e8			−0.421132			−0.210566	−	0.977580i	$-0.567531\pi$
$727$	−1.61816e8			−0.421132			−0.210566	+	0.977580i	$0.567531\pi$
$728$	−4.30816e7	−	1.51673e8i	−0.111660	−	0.393111i
$729$	−3.14949e8	+	2.25615e8i	−0.812938	+	0.582351i
$730$	−967303.	−	1.67542e6i	−0.00248653	−	0.00430680i
$731$	1.04086e8	+	6.00943e7i	0.266466	+	0.153844i
$732$	1.46399e7	+	1.40802e8i	0.0373256	+	0.358985i
$733$	2.88495e8	+	4.99689e8i	0.732532	+	1.26878i	0.955798	+	0.294026i	$0.0949951\pi$
$733$	2.88495e8	+	4.99689e8i	0.732532	+	1.26878i	−0.223265	+	0.974758i	$0.571672\pi$
$734$			1.36591e7i			0.0345409i
$735$	1.94926e8	+	8.01454e7i	0.490916	+	0.201844i
$736$	−4.03266e8			−1.01148
$737$	−1.00059e8	+	5.77688e7i	−0.249949	+	0.144308i
$738$	5.09082e7	+	5.67939e7i	0.126654	+	0.141297i
$739$	−5.88627e7	+	1.01953e8i	−0.145850	+	0.252620i	−0.929690	−	0.368343i	$-0.879925\pi$
$739$	−5.88627e7	+	1.01953e8i	−0.145850	+	0.252620i	0.783840	+	0.620963i	$0.213258\pi$
$740$	−5.75928e7	+	3.32512e7i	−0.142126	+	0.0820565i
$741$	9.11341e7	−	6.60574e7i	0.223989	−	0.162356i
$742$	4.84481e8	−	1.37613e8i	1.18595	−	0.336859i
$743$		−	4.99500e8i		−	1.21778i	−0.793255	−	0.608890i	$-0.791615\pi$
$743$		−	4.99500e8i		−	1.21778i	0.793255	−	0.608890i	$-0.208385\pi$
$744$	−2.84472e8	+	6.37018e8i	−0.690749	+	1.54680i
$745$	4.14720e7	−	7.18317e7i	0.100297	−	0.173719i
$746$	5.70179e7	+	3.29193e7i	0.137339	+	0.0792929i
$747$	−6.22290e7	−	2.96014e8i	−0.149290	−	0.710152i
$748$	7.97464e7			0.190549
$749$	−3.69041e8	+	3.80246e8i	−0.878272	+	0.904940i
$750$	2.56165e8	−	1.85678e8i	0.607206	−	0.440126i
$751$	1.86246e7	+	3.22587e7i	0.0439711	+	0.0761601i	0.887173	−	0.461436i	$-0.152666\pi$
$751$	1.86246e7	+	3.22587e7i	0.0439711	+	0.0761601i	−0.843202	+	0.537596i	$0.819332\pi$
$752$	7.73116e7	+	4.46359e7i	0.181799	+	0.104962i
$753$	5.03997e8	−	5.24032e7i	1.18044	−	0.122736i
$754$	−6.35014e7	−	1.09988e8i	−0.148139	−	0.256584i
$755$			3.62087e8i			0.841341i
$756$	−1.39654e8	+	8.94487e6i	−0.323212	+	0.0207018i
$757$	3.37798e8			0.778699			0.389350	−	0.921090i	$-0.372700\pi$
$757$	3.37798e8			0.778699			0.389350	+	0.921090i	$0.372700\pi$
$758$	−1.80347e8	+	1.04124e8i	−0.414097	+	0.239079i
$759$	3.86711e7	+	3.71926e8i	0.0884425	+	0.850612i
$760$	9.34564e7	−	1.61871e8i	0.212896	−	0.368747i
$761$	−3.20644e8	+	1.85124e8i	−0.727561	+	0.420058i	−0.817529	−	0.575887i	$-0.804657\pi$
$761$	−3.20644e8	+	1.85124e8i	−0.727561	+	0.420058i	0.0899682	+	0.995945i	$0.471323\pi$
$762$	−2.44440e8	−	3.37234e8i	−0.552468	−	0.762196i
$763$	1.60681e8	−	6.37661e8i	0.361735	−	1.43554i
$764$		−	9.83015e6i		−	0.0220435i
$765$	−2.61478e8	+	5.49688e7i	−0.584052	+	0.122781i
$766$	−2.96630e7	+	5.13778e7i	−0.0659977	+	0.114311i
$767$	2.24136e8	+	1.29405e8i	0.496735	+	0.286790i
$768$	3.55173e8	+	1.58609e8i	0.784073	+	0.350142i
$769$	2.18577e8			0.480646			0.240323	−	0.970693i	$-0.422747\pi$
$769$	2.18577e8			0.480646			0.240323	+	0.970693i	$0.422747\pi$
$770$	−7.26129e7	+	7.48177e7i	−0.159053	+	0.163882i
$771$	1.32343e8	+	1.82583e8i	0.288760	+	0.398379i
$772$	2.27365e6	+	3.93807e6i	0.00494164	+	0.00855918i
$773$	−9.67046e7	−	5.58324e7i	−0.209367	−	0.120878i	0.391650	−	0.920114i	$-0.371904\pi$
$773$	−9.67046e7	−	5.58324e7i	−0.209367	−	0.120878i	−0.601017	+	0.799236i	$0.705238\pi$
$774$	7.76917e7	−	6.96403e7i	0.167553	−	0.150189i
$775$	−2.60145e8	−	4.50585e8i	−0.558870	−	0.967991i
$776$		−	1.18295e8i		−	0.253152i
$777$	2.76981e8	−	3.51889e8i	0.590455	−	0.750140i
$778$	−5.31363e7			−0.112837
$779$	−6.96194e7	+	4.01948e7i	−0.147271	+	0.0850271i
$780$	3.04616e7	−	3.16725e6i	0.0641902	−	0.00667419i
$781$	1.04107e8	−	1.80319e8i	0.218538	−	0.378519i
$782$	6.25802e8	−	3.61307e8i	1.30863	−	0.755538i
$783$	−4.38677e8	+	1.40911e8i	−0.913817	+	0.293536i
$784$	2.42400e8	+	1.30445e8i	0.503020	+	0.270695i
$785$		−	1.92194e8i		−	0.397311i
$786$	6.03915e8	+	2.69689e8i	1.24368	+	0.555387i
$787$	3.55944e8	−	6.16513e8i	0.730226	−	1.26479i	−0.226560	−	0.973997i	$-0.572748\pi$
$787$	3.55944e8	−	6.16513e8i	0.730226	−	1.26479i	0.956786	−	0.290792i	$-0.0939186\pi$
$788$	−1.41873e8	−	8.19104e7i	−0.289948	−	0.167402i
$789$	−7.08572e7	+	1.58671e8i	−0.144262	+	0.323047i
$790$	−2.70842e8			−0.549331
$791$	1.51810e8	+	5.34465e8i	0.306741	+	1.07991i
$792$	8.80449e7	−	2.68929e8i	0.177227	−	0.541330i
$793$	1.04310e8	+	1.80671e8i	0.209174	+	0.362300i
$794$	−2.74304e8	−	1.58369e8i	−0.547987	−	0.316380i
$795$	4.13543e7	+	3.97732e8i	0.0823036	+	0.791570i
$796$	−9.21046e7	−	1.59530e8i	−0.182617	−	0.316302i
$797$			4.14474e8i			0.818695i	0.912379	+	0.409348i	$0.134244\pi$
$797$			4.14474e8i			0.818695i	−0.912379	+	0.409348i	$0.865756\pi$
$798$	−4.39565e7	+	3.04765e8i	−0.0864997	+	0.599731i
$799$	2.10769e8			0.413206
$800$	−1.97100e8	+	1.13795e8i	−0.384960	+	0.222257i
$801$	−4.07235e8	+	3.65032e8i	−0.792405	+	0.710286i
$802$	3.31232e8	−	5.73710e8i	0.642109	−	1.11217i
$803$	2.67347e6	−	1.54353e6i	0.00516332	−	0.00298104i
$804$	−7.51734e7	+	5.44885e7i	−0.144643	+	0.104842i
$805$	1.10579e8	−	4.38832e8i	0.211975	−	0.841222i
$806$			2.51525e8i			0.480370i
$807$	3.38628e8	−	7.58291e8i	0.644321	−	1.44283i
$808$	−4.09962e8	+	7.10075e8i	−0.777159	+	1.34608i
$809$	1.03739e8	+	5.98936e7i	0.195927	+	0.113119i	0.594754	−	0.803907i	$-0.297249\pi$
$809$	1.03739e8	+	5.98936e7i	0.195927	+	0.113119i	−0.398827	+	0.917026i	$0.630583\pi$
$810$	−2.52756e7	+	2.30568e8i	−0.0475604	+	0.433854i
$811$	−1.83712e8			−0.344410			−0.172205	−	0.985061i	$-0.555089\pi$
$811$	−1.83712e8			−0.344410			−0.172205	+	0.985061i	$0.555089\pi$
$812$	−1.61384e8	−	4.06663e7i	−0.301434	−	0.0759567i
$813$	1.15036e8	−	8.33825e7i	0.214073	−	0.155168i
$814$	1.10767e8	+	1.91854e8i	0.205370	+	0.355711i
$815$	2.81062e7	+	1.62271e7i	0.0519193	+	0.0299756i
$816$	−3.47108e8	+	3.60906e7i	−0.638844	+	0.0664239i
$817$	5.49849e7	+	9.52366e7i	0.100827	+	0.174638i
$818$			3.73475e8i			0.682341i
$819$	−1.82548e8	+	9.59568e7i	−0.332296	+	0.174672i
$820$	−2.18734e7			−0.0396711
$821$	−2.73208e8	+	1.57737e8i	−0.493701	+	0.285038i	−0.726108	−	0.687580i	$-0.758673\pi$
$821$	−2.73208e8	+	1.57737e8i	−0.493701	+	0.285038i	0.232408	+	0.972618i	$0.425340\pi$
$822$	−1.40962e6	−	1.35573e7i	−0.00253797	−	0.0244094i
$823$	−1.92392e7	+	3.33232e7i	−0.0345133	+	0.0597788i	−0.882766	−	0.469813i	$-0.844321\pi$
$823$	−1.92392e7	+	3.33232e7i	−0.0345133	+	0.0597788i	0.848253	+	0.529592i	$0.177655\pi$
$824$	3.59600e8	−	2.07615e8i	0.642743	−	0.371088i
$825$	1.23853e8	+	1.70870e8i	0.220569	+	0.304301i
$826$	−6.81078e8	+	1.93455e8i	−1.20853	+	0.343272i
$827$		−	6.64958e8i		−	1.17565i	−0.808988	−	0.587825i	$-0.799984\pi$
$827$		−	6.64958e8i		−	1.17565i	0.808988	−	0.587825i	$-0.200016\pi$
$828$	6.18176e7	+	2.94057e8i	0.108898	+	0.518013i
$829$	−3.05620e8	+	5.29350e8i	−0.536437	+	0.929136i	0.462656	+	0.886538i	$0.346897\pi$
$829$	−3.05620e8	+	5.29350e8i	−0.536437	+	0.929136i	−0.999092	+	0.0425975i	$0.986437\pi$
$830$	−1.56835e8	−	9.05489e7i	−0.274290	−	0.158361i
$831$	−1.82058e7	−	8.13010e6i	−0.0317253	−	0.0141675i
$832$	2.33530e8			0.405482
$833$	6.49619e8	−	1.94340e7i	1.12389	−	0.0336222i
$834$	−4.81515e8	−	6.64308e8i	−0.830064	−	1.14517i
$835$	−8.94219e7	−	1.54883e8i	−0.153598	−	0.266039i
$836$	6.31905e7	+	3.64830e7i	0.108152	+	0.0624413i
$837$	8.91924e8	+	1.92710e8i	1.52108	+	0.328646i
$838$	−1.56667e8	−	2.71356e8i	−0.266224	−	0.461113i
$839$		−	7.78319e8i		−	1.31787i	−0.752201	−	0.658934i	$-0.771008\pi$
$839$		−	7.78319e8i		−	1.31787i	0.752201	−	0.658934i	$-0.228992\pi$
$840$	−2.11820e8	+	2.69106e8i	−0.357379	+	0.454030i
$841$	4.68573e7			0.0787752
$842$	−2.57921e8	+	1.48911e8i	−0.432067	+	0.249454i
$843$	−5.78764e8	+	6.01771e7i	−0.966092	+	0.100450i
$844$	−4.10208e7	+	7.10501e7i	−0.0682302	+	0.118178i
$845$	−2.38261e8	+	1.37560e8i	−0.394896	+	0.227993i
$846$	5.69286e7	−	1.73886e8i	0.0940198	−	0.287179i
$847$	3.16660e8	+	3.07329e8i	0.521127	+	0.505770i
$848$			5.22275e8i			0.856469i
$849$	9.89175e7	+	4.41733e7i	0.161640	+	0.0721834i
$850$	2.03911e8	−	3.53184e8i	0.332035	−	0.575101i
$851$	−8.32753e8	−	4.80790e8i	−1.35122	−	0.780129i
$852$	6.82249e7	−	1.52776e8i	0.110312	−	0.247023i
$853$	−7.77463e8			−1.25266			−0.626329	−	0.779559i	$-0.715443\pi$
$853$	−7.77463e8			−1.25266			−0.626329	+	0.779559i	$0.715443\pi$
$854$	−5.53419e8	−	1.39453e8i	−0.888547	−	0.223900i
$855$	−2.32341e8	−	7.60664e7i	−0.371730	−	0.121701i
$856$	−4.30515e8	−	7.45674e8i	−0.686384	−	1.18885i
$857$	1.34313e8	+	7.75458e7i	0.213391	+	0.123201i	0.602886	−	0.797827i	$-0.294017\pi$
$857$	1.34313e8	+	7.75458e7i	0.213391	+	0.123201i	−0.389495	+	0.921028i	$0.627351\pi$
$858$	−1.05508e7	−	1.01474e8i	−0.0167041	−	0.160655i
$859$	1.49561e8	+	2.59048e8i	0.235961	+	0.408696i	0.959551	−	0.281533i	$-0.0908430\pi$
$859$	1.49561e8	+	2.59048e8i	0.235961	+	0.408696i	−0.723591	+	0.690229i	$0.757510\pi$
$860$			2.99219e7i			0.0470429i
$861$	1.36767e8	−	5.46828e7i	0.214275	−	0.0856725i
$862$	−2.34740e8			−0.366493
$863$	1.56018e8	−	9.00769e7i	0.242740	−	0.140146i	−0.373695	−	0.927552i	$-0.621909\pi$
$863$	1.56018e8	−	9.00769e7i	0.242740	−	0.140146i	0.616436	+	0.787405i	$0.288576\pi$
$864$	8.42972e7	−	3.90155e8i	0.130699	−	0.604917i
$865$	−2.09513e7	+	3.62888e7i	−0.0323715	+	0.0560691i
$866$	2.79367e8	−	1.61293e8i	0.430151	−	0.248348i
$867$	−1.39443e8	+	1.01073e8i	−0.213963	+	0.155088i
$868$	2.36525e8	+	2.29555e8i	0.361675	+	0.351017i
$869$		−	4.32183e8i		−	0.658579i
$870$	−1.12481e8	+	2.51879e8i	−0.170813	+	0.382503i
$871$	−6.84128e7	+	1.18494e8i	−0.103534	+	0.179326i
$872$	9.25389e8	+	5.34274e8i	1.39565	+	0.805776i
$873$	−1.51417e8	+	3.18313e7i	−0.227578	+	0.0478422i
$874$	6.61175e8			0.990335
$875$	−1.66944e8	−	5.87744e8i	−0.249199	−	0.877333i
$876$	2.00856e6	−	1.45588e6i	0.00298795	−	0.00216578i
$877$	−1.11962e8	−	1.93924e8i	−0.165986	−	0.287496i	0.771019	−	0.636812i	$-0.219747\pi$
$877$	−1.11962e8	−	1.93924e8i	−0.165986	−	0.287496i	−0.937005	+	0.349316i	$0.886414\pi$
$878$	2.05793e7	+	1.18815e7i	0.0304052	+	0.0175545i
$879$	−8.24040e8	+	8.56797e7i	−1.21334	+	0.126157i
$880$	−5.40586e7	−	9.36323e7i	−0.0793263	−	0.137397i
$881$		−	2.77136e8i		−	0.405289i	−0.979252	−	0.202645i	$-0.935046\pi$
$881$		−	2.77136e8i		−	0.405289i	0.979252	−	0.202645i	$-0.0649537\pi$
$882$	1.59428e8	−	5.41188e8i	0.232359	−	0.788755i
$883$	1.26602e9			1.83890			0.919452	−	0.393203i	$-0.128633\pi$
$883$	1.26602e9			1.83890			0.919452	+	0.393203i	$0.128633\pi$
$884$	8.17872e7	−	4.72199e7i	0.118394	−	0.0683546i
$885$	−5.81353e7	−	5.59127e8i	−0.0838707	−	0.806641i
$886$	2.61304e7	−	4.52592e7i	0.0375703	−	0.0650737i
$887$	−5.24508e8	+	3.02825e8i	−0.751591	+	0.433931i	−0.826269	−	0.563276i	$-0.809541\pi$
$887$	−5.24508e8	+	3.02825e8i	−0.751591	+	0.433931i	0.0746774	+	0.997208i	$0.476207\pi$
$888$	4.27063e8	+	5.89184e8i	0.609892	+	0.841418i
$889$	−7.73749e8	+	2.19777e8i	−1.10127	+	0.312808i
$890$			3.27424e8i			0.464451i
$891$	−3.67918e8	−	4.03323e7i	−0.520137	−	0.0570190i
$892$	2.14602e8	−	3.71701e8i	0.302370	−	0.523720i
$893$	1.67012e8	+	9.64245e7i	0.234527	+	0.135404i
$894$	−2.02737e8	−	9.05357e7i	−0.283740	−	0.126709i
$895$	−9.49038e7			−0.132378
$896$	−1.34896e8	+	1.38992e8i	−0.187532	+	0.193226i
$897$	2.59888e8	+	3.58546e8i	0.360088	+	0.496784i
$898$	2.75187e8	+	4.76639e8i	0.380014	+	0.658204i
$899$	9.39834e8	+	5.42614e8i	1.29352	+	0.746813i
$900$	1.13192e8	+	1.26279e8i	0.155271	+	0.173222i
$901$	6.16542e8	+	1.06788e9i	0.842924	+	1.45999i
$902$			7.28649e7i			0.0992885i
$903$	−7.48039e7	−	1.87091e8i	−0.101592	−	0.254092i
$904$	−9.02825e8			−1.22208
$905$	2.25350e8	−	1.30106e8i	0.304026	−	0.175530i
$906$	9.64076e8	−	1.00240e8i	1.29636	−	0.134790i
$907$	−3.94123e8	+	6.82642e8i	−0.528214	+	0.914894i	0.471245	+	0.882003i	$0.343805\pi$
$907$	−3.94123e8	+	6.82642e8i	−0.528214	+	0.914894i	−0.999459	+	0.0328915i	$0.989528\pi$
$908$	−9.76412e7	+	5.63732e7i	−0.130429	+	0.0753034i
$909$	1.01920e9	+	3.33678e8i	1.35697	+	0.444259i
$910$	−3.01697e7	+	1.19728e8i	−0.0400357	+	0.158881i
$911$			1.49408e9i			1.97615i	0.153976	+	0.988075i	$0.450792\pi$
$911$			1.49408e9i			1.97615i	−0.153976	+	0.988075i	$0.549208\pi$
$912$	−2.91557e8	−	1.30200e8i	−0.384361	−	0.171643i
$913$	1.44489e8	−	2.50263e8i	0.189855	−	0.328839i
$914$	−7.89625e8	−	4.55890e8i	−1.03415	−	0.597065i
$915$	1.84766e8	−	4.13748e8i	0.241190	−	0.540098i
$916$	−2.63986e7			−0.0343475
$917$	8.89573e8	−	9.16583e8i	1.15365	−	1.18868i
$918$	2.18745e8	+	6.80983e8i	0.282755	+	0.880254i
$919$	2.98707e8	+	5.17375e8i	0.384856	+	0.666590i	0.991749	−	0.128193i	$-0.0409178\pi$
$919$	2.98707e8	+	5.17375e8i	0.384856	+	0.666590i	−0.606893	+	0.794783i	$0.707584\pi$
$920$	6.36844e8	+	3.67682e8i	0.817843	+	0.472182i
$921$	−2.11152e7	−	2.03079e8i	−0.0270281	−	0.259947i
$922$	2.12588e8	+	3.68214e8i	0.271235	+	0.469794i
$923$		−	2.46578e8i		−	0.313580i
$924$	−1.05052e8	−	8.26893e7i	−0.133165	−	0.104817i
$925$	−5.42687e8			−0.685684
$926$	6.94385e8	−	4.00903e8i	0.874515	−	0.504902i
$927$	−3.62507e8	−	4.04418e8i	−0.455069	−	0.507682i
$928$	2.37356e8	−	4.11112e8i	0.297000	−	0.514419i
$929$	−1.07426e9	+	6.20222e8i	−1.33986	+	0.773571i	−0.986787	−	0.162023i	$-0.948198\pi$
$929$	−1.07426e9	+	6.20222e8i	−1.33986	+	0.773571i	−0.353078	+	0.935594i	$0.614865\pi$
$930$	4.42339e8	−	3.20624e8i	0.549928	−	0.398609i
$931$	5.23644e8	+	2.81794e8i	0.648914	+	0.349206i
$932$		−	2.79056e8i		−	0.344702i
$933$	5.23454e8	−	1.17217e9i	0.644516	−	1.44327i
$934$	1.68393e8	−	2.91666e8i	0.206673	−	0.357968i
$935$	−2.21064e8	−	1.27632e8i	−0.270448	−	0.156143i
$936$	−6.89415e7	−	3.27945e8i	−0.0840724	−	0.399920i
$937$	−1.45542e8			−0.176917			−0.0884585	−	0.996080i	$-0.528194\pi$
$937$	−1.45542e8			−0.176917			−0.0884585	+	0.996080i	$0.528194\pi$
$938$	−1.02274e8	−	3.60067e8i	−0.123925	−	0.436289i
$939$	−6.35661e8	+	4.60751e8i	−0.767765	+	0.556505i
$940$	2.62364e7	+	4.54427e7i	0.0315878	+	0.0547117i
$941$	−2.91954e8	−	1.68560e8i	−0.350386	−	0.202295i	0.314470	−	0.949268i	$-0.398173\pi$
$941$	−2.91954e8	−	1.68560e8i	−0.350386	−	0.202295i	−0.664855	+	0.746972i	$0.731507\pi$
$942$	−5.11727e8	+	5.32069e7i	−0.612189	+	0.0636525i
$943$	−1.58137e8	−	2.73901e8i	−0.188581	−	0.326632i
$944$		−	7.34208e8i		−	0.872776i
$945$	4.01450e8	+	1.98716e8i	0.475703	+	0.235471i
$946$	9.96763e7			0.117738
$947$	−3.13694e7	+	1.81111e7i	−0.0369365	+	0.0213253i	−0.518355	−	0.855166i	$-0.673455\pi$
$947$	−3.13694e7	+	1.81111e7i	−0.0369365	+	0.0213253i	0.481418	+	0.876491i	$0.340122\pi$
$948$	−3.59164e7	−	3.45433e8i	−0.0421569	−	0.405451i
$949$	1.82792e6	−	3.16606e6i	0.00213875	−	0.00370442i
$950$	3.23155e8	−	1.86574e8i	0.376912	−	0.217610i
$951$	4.65605e8	+	6.42358e8i	0.541347	+	0.746854i
$952$	−2.58045e8	+	1.02405e9i	−0.299078	+	1.18689i
$953$			1.20343e9i			1.39041i	0.718811	+	0.695205i	$0.244687\pi$
$953$			1.20343e9i			1.39041i	−0.718811	+	0.695205i	$0.755313\pi$
$954$	1.04754e9	−	2.20216e8i	1.20649	−	0.253632i
$955$	−1.57329e7	+	2.72501e7i	−0.0180633	+	0.0312866i
$956$	−2.46110e7	−	1.42092e7i	−0.0281680	−	0.0162628i
$957$	−4.01924e8	−	1.79486e8i	−0.458573	−	0.204784i
$958$	−1.28946e8			−0.146660
$959$	−2.55250e7	−	6.43191e6i	−0.0289408	−	0.00729263i
$960$	−2.97685e8	−	4.10692e8i	−0.336468	−	0.464197i
$961$	−6.30875e8	−	1.09271e9i	−0.710842	−	1.23121i
$962$	2.27203e8	+	1.31176e8i	0.255205	+	0.147343i
$963$	−8.38611e8	+	7.51703e8i	−0.939034	+	0.841720i
$964$	−1.34585e8	−	2.33108e8i	−0.150233	−	0.260211i
$965$		−	1.45556e7i		−	0.0161975i
$966$	−1.19903e9	−	1.72937e8i	−1.33014	−	0.191847i
$967$	1.16933e9			1.29317			0.646586	−	0.762841i	$-0.276196\pi$
$967$	1.16933e9			1.29317			0.646586	+	0.762841i	$0.276196\pi$
$968$	−6.20980e8	+	3.58523e8i	−0.684623	+	0.395267i
$969$	−7.49839e8	+	7.79646e7i	−0.824132	+	0.0856892i
$970$	−4.63174e7	+	8.02241e7i	−0.0507492	+	0.0879001i
$971$	−2.74967e8	+	1.58752e8i	−0.300347	+	0.173405i	−0.642599	−	0.766203i	$-0.722144\pi$
$971$	−2.74967e8	+	1.58752e8i	−0.300347	+	0.173405i	0.342252	+	0.939608i	$0.388810\pi$
$972$	−2.97419e8	−	1.66088e6i	−0.323870	−	0.00180858i
$973$	−1.52419e9	+	4.32933e8i	−1.65462	+	0.469983i
$974$		−	1.27085e9i		−	1.37536i
$975$	2.28198e8	+	1.01906e8i	0.246206	+	0.109948i
$976$	2.95914e8	−	5.12538e8i	0.318285	−	0.551286i
$977$	−1.04559e8	−	6.03673e7i	−0.112119	−	0.0647319i	0.442892	−	0.896575i	$-0.353953\pi$
$977$	−1.04559e8	−	6.03673e7i	−0.112119	−	0.0647319i	−0.555011	+	0.831843i	$0.687286\pi$
$978$	3.54246e7	−	7.93265e7i	0.0378694	−	0.0848011i
$979$	−5.22471e8			−0.556819
$980$	8.50540e7	+	1.37641e8i	0.0903683	+	0.146241i
$981$	4.34858e8	−	1.32825e9i	0.460618	−	1.40693i
$982$	−3.29796e8	−	5.71223e8i	−0.348266	−	0.603214i
$983$	−1.02296e9	−	5.90608e8i	−1.07696	−	0.621783i	−0.146884	−	0.989154i	$-0.546925\pi$
$983$	−1.02296e9	−	5.90608e8i	−1.07696	−	0.621783i	−0.930074	+	0.367371i	$0.880258\pi$
$984$	2.47522e7	+	2.38059e8i	0.0259794	+	0.249861i
$985$	2.62190e8	+	4.54126e8i	0.274351	+	0.475191i
$986$			8.50639e8i			0.887390i
$987$	−2.77652e8	−	2.18547e8i	−0.288768	−	0.227297i
$988$	8.64101e7			0.0895970
$989$	−3.74686e8	+	2.16325e8i	−0.387328	+	0.223624i
$990$	−1.65006e8	+	1.47906e8i	−0.170057	+	0.152433i
$991$	−5.41017e7	+	9.37069e7i	−0.0555892	+	0.0962833i	−0.892481	−	0.451085i	$-0.851037\pi$
$991$	−5.41017e7	+	9.37069e7i	−0.0555892	+	0.0962833i	0.836892	+	0.547368i	$0.184370\pi$
$992$	−8.14193e8	+	4.70075e8i	−0.834051	+	0.481540i
$993$	7.49580e8	−	5.43324e8i	0.765544	−	0.554895i
$994$	4.84063e8	+	4.69798e8i	0.492882	+	0.478357i
$995$			5.89642e8i			0.598576i
$996$	9.46886e7	−	2.12036e8i	0.0958340	−	0.214601i
$997$	−1.44590e8	+	2.50437e8i	−0.145899	+	0.252705i	−0.929708	−	0.368297i	$-0.879941\pi$
$997$	−1.44590e8	+	2.50437e8i	−0.145899	+	0.252705i	0.783809	+	0.621002i	$0.213274\pi$
$998$	−5.55086e8	−	3.20479e8i	−0.558430	−	0.322410i
$999$	6.39234e8	−	7.05176e8i	0.641156	−	0.707295i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.h.a.11.5	yes	28
3.2	odd	2	inner	21.7.h.a.11.10	yes	28
7.2	even	3	inner	21.7.h.a.2.10	yes	28
7.3	odd	6		147.7.b.d.50.5		14
7.4	even	3		147.7.b.e.50.5		14
21.2	odd	6	inner	21.7.h.a.2.5	✓	28
21.11	odd	6		147.7.b.e.50.10		14
21.17	even	6		147.7.b.d.50.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.h.a.2.5	✓	28	21.2	odd	6	inner
21.7.h.a.2.10	yes	28	7.2	even	3	inner
21.7.h.a.11.5	yes	28	1.1	even	1	trivial
21.7.h.a.11.10	yes	28	3.2	odd	2	inner
147.7.b.d.50.5		14	7.3	odd	6
147.7.b.d.50.10		14	21.17	even	6
147.7.b.e.50.5		14	7.4	even	3
147.7.b.e.50.10		14	21.11	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.69684 + 3.28907i) q^{2} +(2.79228 + 26.8552i) q^{3} +(-10.3640 + 17.9510i) q^{4} +(57.4599 - 33.1745i) q^{5} +(-104.236 - 143.806i) q^{6} +(-329.948 + 93.7191i) q^{7} -557.353i q^{8} +(-713.406 + 149.974i) q^{9} +O(q^{10})\)	\(q+(-5.69684 + 3.28907i) q^{2} +(2.79228 + 26.8552i) q^{3} +(-10.3640 + 17.9510i) q^{4} +(57.4599 - 33.1745i) q^{5} +(-104.236 - 143.806i) q^{6} +(-329.948 + 93.7191i) q^{7} -557.353i q^{8} +(-713.406 + 149.974i) q^{9} +(-218.227 + 377.979i) q^{10} +(-603.143 - 348.225i) q^{11} +(-511.016 - 228.203i) q^{12} -824.771 q^{13} +(1571.41 - 1619.13i) q^{14} +(1051.35 + 1450.47i) q^{15} +(1169.88 + 2026.29i) q^{16} +(4784.05 + 2762.07i) q^{17} +(3570.89 - 3200.83i) q^{18} +(2527.23 + 4377.29i) q^{19} +1375.28i q^{20} +(-3438.15 - 8599.14i) q^{21} +4581.35 q^{22} +(-17221.4 + 9942.79i) q^{23} +(14967.8 - 1556.28i) q^{24} +(-5611.41 + 9719.25i) q^{25} +(4698.59 - 2712.73i) q^{26} +(-6019.63 - 18739.9i) q^{27} +(1737.23 - 6894.19i) q^{28} -23408.7i q^{29} +(-10760.1 - 4805.10i) q^{30} +(-23180.0 + 40149.0i) q^{31} +(17562.4 + 10139.7i) q^{32} +(7667.51 - 17169.9i) q^{33} -36338.6 q^{34} +(-15849.7 + 16330.9i) q^{35} +(4701.55 - 14360.7i) q^{36} +(24177.8 + 41877.2i) q^{37} +(-28794.4 - 16624.5i) q^{38} +(-2302.99 - 22149.4i) q^{39} +(-18489.9 - 32025.4i) q^{40} +15904.7i q^{41} +(47869.8 + 37679.6i) q^{42} +21757.0 q^{43} +(12501.9 - 7217.99i) q^{44} +(-36016.9 + 32284.4i) q^{45} +(65405.1 - 113285. i) q^{46} +(33042.5 - 19077.1i) q^{47} +(-51149.9 + 37075.4i) q^{48} +(100082. - 61844.9i) q^{49} -73825.4i q^{50} +(-60817.6 + 136189. i) q^{51} +(8547.91 - 14805.4i) q^{52} +(193312. + 111609. i) q^{53} +(95929.8 + 86959.4i) q^{54} -46208.7 q^{55} +(52234.6 + 183898. i) q^{56} +(-110496. + 80091.9i) q^{57} +(76992.9 + 133356. i) q^{58} +(-271755. - 156898. i) q^{59} +(-36933.4 + 3840.16i) q^{60} +(-126472. - 219056. i) q^{61} -304963. i q^{62} +(221332. - 116344. i) q^{63} -283145. q^{64} +(-47391.2 + 27361.3i) q^{65} +(12792.4 + 123033. i) q^{66} +(82947.6 - 143669. i) q^{67} +(-99163.6 + 57252.1i) q^{68} +(-315103. - 434722. i) q^{69} +(36579.5 - 145166. i) q^{70} +298965. i q^{71} +(83588.7 + 397619. i) q^{72} +(-2216.28 + 3838.71i) q^{73} +(-275474. - 159045. i) q^{74} +(-276681. - 123557. i) q^{75} -104769. q^{76} +(231641. + 58370.1i) q^{77} +(85970.8 + 118607. i) q^{78} +(310276. + 537413. i) q^{79} +(134442. + 77620.3i) q^{80} +(486456. - 213985. i) q^{81} +(-52311.7 - 90606.6i) q^{82} +414931. i q^{83} +(189996. + 27403.2i) q^{84} +366521. q^{85} +(-123946. + 71560.3i) q^{86} +(628645. - 65363.5i) q^{87} +(-194084. + 336164. i) q^{88} +(649685. - 375096. i) q^{89} +(98996.9 - 302381. i) q^{90} +(272131. - 77296.8i) q^{91} -412188. i q^{92} +(-1.14293e6 - 510398. i) q^{93} +(-125492. + 217359. i) q^{94} +(290428. + 167679. i) q^{95} +(-223264. + 499955. i) q^{96} +212245. q^{97} +(-366742. + 681499. i) q^{98} +(482511. + 157970. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Introduction

L-functions

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