LMFDB - Embedded newform 72.7.j.a.29.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(5,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("72.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.j (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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$70$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.17
Character	$\chi$	$=$	72.29
Dual form			72.7.j.a.5.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.34800 + 4.86856i) q^{2} +(15.8845 - 21.8331i) q^{3} +(16.5943 - 61.8112i) q^{4} +(122.026 + 211.355i) q^{5} +(5.46045 + 215.931i) q^{6} +(-28.5227 + 49.4028i) q^{7} +(195.591 + 473.168i) q^{8} +(-224.364 - 693.615i) q^{9} +O(q^{10})$	\(q+(-6.34800 + 4.86856i) q^{2} +(15.8845 - 21.8331i) q^{3} +(16.5943 - 61.8112i) q^{4} +(122.026 + 211.355i) q^{5} +(5.46045 + 215.931i) q^{6} +(-28.5227 + 49.4028i) q^{7} +(195.591 + 473.168i) q^{8} +(-224.364 - 693.615i) q^{9} +(-1803.62 - 747.594i) q^{10} +(-529.794 + 917.630i) q^{11} +(-1085.93 - 1344.15i) q^{12} +(1072.25 - 619.067i) q^{13} +(-59.4579 - 452.473i) q^{14} +(6552.86 + 693.076i) q^{15} +(-3545.26 - 2051.43i) q^{16} +6617.79i q^{17} +(4801.17 + 3310.74i) q^{18} -3342.42i q^{19} +(15089.1 - 4035.28i) q^{20} +(625.544 + 1407.48i) q^{21} +(-1104.40 - 8404.45i) q^{22} +(5525.65 - 3190.23i) q^{23} +(13437.6 + 3245.71i) q^{24} +(-21968.2 + 38050.1i) q^{25} +(-3792.72 + 9150.17i) q^{26} +(-18707.6 - 6119.18i) q^{27} +(2580.33 + 2582.83i) q^{28} +(-10797.1 + 18701.2i) q^{29} +(-44971.9 + 27503.3i) q^{30} +(10636.5 + 18422.9i) q^{31} +(32492.8 - 4237.78i) q^{32} +(11619.1 + 26143.1i) q^{33} +(-32219.1 - 42009.7i) q^{34} -13922.1 q^{35} +(-46596.4 + 2358.16i) q^{36} +35838.8i q^{37} +(16272.8 + 21217.7i) q^{38} +(3516.13 - 33244.2i) q^{39} +(-76139.6 + 99078.0i) q^{40} +(13932.0 - 8043.65i) q^{41} +(-10823.3 - 5889.17i) q^{42} +(122952. + 70986.1i) q^{43} +(47928.3 + 47974.7i) q^{44} +(119221. - 132060. i) q^{45} +(-19545.0 + 47153.5i) q^{46} +(-11817.8 - 6823.00i) q^{47} +(-101104. + 44817.8i) q^{48} +(57197.4 + 99068.8i) q^{49} +(-45794.6 - 348496. i) q^{50} +(144487. + 105120. i) q^{51} +(-20471.9 - 76550.4i) q^{52} +145311. q^{53} +(148548. - 52234.7i) q^{54} -258595. q^{55} +(-28954.6 - 3833.33i) q^{56} +(-72975.2 - 53092.7i) q^{57} +(-22507.5 - 171282. i) q^{58} +(-125868. - 218010. i) q^{59} +(151580. - 393539. i) q^{60} +(-183328. - 105845. i) q^{61} +(-157213. - 65164.5i) q^{62} +(40666.0 + 8699.55i) q^{63} +(-185633. + 185095. i) q^{64} +(261686. + 151085. i) q^{65} +(-201038. - 109388. i) q^{66} +(239882. - 138496. i) q^{67} +(409054. + 109818. i) q^{68} +(18119.7 - 171317. i) q^{69} +(88377.3 - 67780.3i) q^{70} +590317. i q^{71} +(284313. - 241827. i) q^{72} -479905. q^{73} +(-174483. - 227505. i) q^{74} +(481795. + 1.08404e6i) q^{75} +(-206599. - 55465.2i) q^{76} +(-30222.3 - 52346.6i) q^{77} +(139531. + 228153. i) q^{78} +(414018. - 717100. i) q^{79} +(967.282 - 999638. i) q^{80} +(-430762. + 311245. i) q^{81} +(-49279.5 + 118890. i) q^{82} +(246200. - 426431. i) q^{83} +(97378.4 - 15309.5i) q^{84} +(-1.39871e6 + 807543. i) q^{85} +(-1.12610e6 + 147976. i) q^{86} +(236797. + 532794. i) q^{87} +(-537816. - 71202.0i) q^{88} -380195. i q^{89} +(-113875. + 1.41875e6i) q^{90} +70629.8i q^{91} +(-105498. - 394487. i) q^{92} +(571184. + 60412.4i) q^{93} +(108237. - 14223.1i) q^{94} +(706439. - 407863. i) q^{95} +(423609. - 776732. i) q^{96} +(241248. - 417854. i) q^{97} +(-845412. - 350421. i) q^{98} +(755349. + 161590. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 140 * q - 3 * q^2 - q^4 + 317 * q^6 - 2 * q^7 - 4 * q^9	$ 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9} + 124 q^{10} - 6946 q^{12} - 7428 q^{14} + 1454 q^{15} - q^{16} + 20878 q^{18} - 35346 q^{20} + 127 q^{22} - 6 q^{23} + 50209 q^{24} - 193752 q^{25} + 8188 q^{28} - 21344 q^{30} - 2 q^{31} - 180093 q^{32} + 45534 q^{33} + 20061 q^{34} + 39831 q^{36} + 274239 q^{38} + 125738 q^{39} - 58376 q^{40} + 31314 q^{41} - 213688 q^{42} - 22560 q^{46} - 6 q^{47} - 114411 q^{48} - 974808 q^{49} + 723249 q^{50} - 79338 q^{52} - 231173 q^{54} + 62492 q^{55} + 1294542 q^{56} + 125032 q^{57} - 221138 q^{58} - 1156344 q^{60} + 275294 q^{63} - 804478 q^{64} - 6 q^{65} + 1782258 q^{66} + 2100195 q^{68} - 86464 q^{70} + 1113091 q^{72} - 8 q^{73} - 1886976 q^{74} + 432081 q^{76} + 1658428 q^{78} - 2 q^{79} + 597124 q^{81} - 965382 q^{82} + 4997288 q^{84} - 1041879 q^{86} - 1337970 q^{87} - 536717 q^{88} - 4261994 q^{90} - 737184 q^{92} - 72534 q^{94} + 93744 q^{95} + 1053622 q^{96} - 2 q^{97}+O(q^{100}) $ 140 * q - 3 * q^2 - q^4 + 317 * q^6 - 2 * q^7 - 4 * q^9 + 124 * q^10 - 6946 * q^12 - 7428 * q^14 + 1454 * q^15 - q^16 + 20878 * q^18 - 35346 * q^20 + 127 * q^22 - 6 * q^23 + 50209 * q^24 - 193752 * q^25 + 8188 * q^28 - 21344 * q^30 - 2 * q^31 - 180093 * q^32 + 45534 * q^33 + 20061 * q^34 + 39831 * q^36 + 274239 * q^38 + 125738 * q^39 - 58376 * q^40 + 31314 * q^41 - 213688 * q^42 - 22560 * q^46 - 6 * q^47 - 114411 * q^48 - 974808 * q^49 + 723249 * q^50 - 79338 * q^52 - 231173 * q^54 + 62492 * q^55 + 1294542 * q^56 + 125032 * q^57 - 221138 * q^58 - 1156344 * q^60 + 275294 * q^63 - 804478 * q^64 - 6 * q^65 + 1782258 * q^66 + 2100195 * q^68 - 86464 * q^70 + 1113091 * q^72 - 8 * q^73 - 1886976 * q^74 + 432081 * q^76 + 1658428 * q^78 - 2 * q^79 + 597124 * q^81 - 965382 * q^82 + 4997288 * q^84 - 1041879 * q^86 - 1337970 * q^87 - 536717 * q^88 - 4261994 * q^90 - 737184 * q^92 - 72534 * q^94 + 93744 * q^95 + 1053622 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−6.34800	+	4.86856i	−0.793501	+	0.608569i
$2$	−6.34800	+	4.86856i	−0.793501	+	0.608569i
$3$	15.8845	−	21.8331i	0.588315	−	0.808632i
$3$	15.8845	−	21.8331i	0.588315	−	0.808632i
$4$	16.5943	−	61.8112i	0.259286	−	0.965800i
$5$	122.026	+	211.355i	0.976209	+	1.69084i	0.675886	+	0.737006i	$0.263761\pi$
$5$	122.026	+	211.355i	0.976209	+	1.69084i	0.300323	+	0.953838i	$0.402906\pi$
$6$	5.46045	+	215.931i	0.0252799	+	0.999680i
$7$	−28.5227	+	49.4028i	−0.0831566	+	0.144031i	−0.904604	−	0.426253i	$-0.859833\pi$
$7$	−28.5227	+	49.4028i	−0.0831566	+	0.144031i	0.821448	+	0.570284i	$0.193167\pi$
$8$	195.591	+	473.168i	0.382013	+	0.924157i
$9$	−224.364	−	693.615i	−0.307770	−	0.951461i
$10$	−1803.62	−	747.594i	−1.80362	−	0.747594i
$11$	−529.794	+	917.630i	−0.398042	+	0.689429i	−0.993484	−	0.113969i	$-0.963644\pi$
$11$	−529.794	+	917.630i	−0.398042	+	0.689429i	0.595442	+	0.803398i	$0.296977\pi$
$12$	−1085.93	−	1344.15i	−0.628435	−	0.777862i
$13$	1072.25	−	619.067i	0.488054	−	0.281778i	−0.235713	−	0.971823i	$-0.575742\pi$
$13$	1072.25	−	619.067i	0.488054	−	0.281778i	0.723767	+	0.690045i	$0.242409\pi$
$14$	−59.4579	−	452.473i	−0.0216683	−	0.164896i
$15$	6552.86	+	693.076i	1.94159	+	0.205356i
$16$	−3545.26	−	2051.43i	−0.865541	−	0.500838i
$17$			6617.79i			1.34700i	0.739189	+	0.673498i	$0.235209\pi$
$17$			6617.79i			1.34700i	−0.739189	+	0.673498i	$0.764791\pi$
$18$	4801.17	+	3310.74i	0.823246	+	0.567685i
$19$		−	3342.42i		−	0.487304i	−0.969863	−	0.243652i	$-0.921654\pi$
$19$		−	3342.42i		−	0.487304i	0.969863	−	0.243652i	$-0.0783455\pi$
$20$	15089.1	−	4035.28i	1.88614	−	0.504410i
$21$	625.544	+	1407.48i	0.0675461	+	0.151979i
$22$	−1104.40	−	8404.45i	−0.103719	−	0.789299i
$23$	5525.65	−	3190.23i	0.454150	−	0.262204i	−0.255431	−	0.966827i	$-0.582217\pi$
$23$	5525.65	−	3190.23i	0.454150	−	0.262204i	0.709581	+	0.704623i	$0.248884\pi$
$24$	13437.6	+	3245.71i	0.972047	+	0.234788i
$25$	−21968.2	+	38050.1i	−1.40597	+	2.43521i
$26$	−3792.72	+	9150.17i	−0.215790	+	0.520606i
$27$	−18707.6	−	6119.18i	−0.950447	−	0.310887i
$28$	2580.33	+	2582.83i	0.117544	+	0.117658i
$29$	−10797.1	+	18701.2i	−0.442705	+	0.766788i	−0.997889	−	0.0649394i	$-0.979315\pi$
$29$	−10797.1	+	18701.2i	−0.442705	+	0.766788i	0.555184	+	0.831728i	$0.312648\pi$
$30$	−44971.9	+	27503.3i	−1.66562	+	1.01864i
$31$	10636.5	+	18422.9i	0.357037	+	0.618405i	0.987464	−	0.157843i	$-0.0504538\pi$
$31$	10636.5	+	18422.9i	0.357037	+	0.618405i	−0.630428	+	0.776248i	$0.717121\pi$
$32$	32492.8	−	4237.78i	0.991602	−	0.129327i
$33$	11619.1	+	26143.1i	0.323320	+	0.727471i
$34$	−32219.1	−	42009.7i	−0.819740	−	1.06884i
$35$	−13922.1			−0.324713
$36$	−46596.4	+	2358.16i	−0.998722	+	0.0505436i
$37$			35838.8i			0.707536i	0.935333	+	0.353768i	$0.115100\pi$
$37$			35838.8i			0.707536i	−0.935333	+	0.353768i	$0.884900\pi$
$38$	16272.8	+	21217.7i	0.296558	+	0.386676i
$39$	3516.13	−	33244.2i	0.0592750	−	0.560430i
$40$	−76139.6	+	99078.0i	−1.18968	+	1.54809i
$41$	13932.0	−	8043.65i	0.202145	−	0.116708i	−0.395511	−	0.918461i	$-0.629432\pi$
$41$	13932.0	−	8043.65i	0.202145	−	0.116708i	0.597655	+	0.801753i	$0.296099\pi$
$42$	−10823.3	−	5889.17i	−0.146088	−	0.0794889i
$43$	122952.	+	70986.1i	1.54642	+	0.892829i	0.998411	+	0.0563597i	$0.0179493\pi$
$43$	122952.	+	70986.1i	1.54642	+	0.892829i	0.548014	+	0.836469i	$0.315384\pi$
$44$	47928.3	+	47974.7i	0.562644	+	0.563189i
$45$	119221.	−	132060.i	1.30832	−	1.44922i
$46$	−19545.0	+	47153.5i	−0.200799	+	0.484441i
$47$	−11817.8	−	6823.00i	−0.113826	−	0.0657176i	0.442006	−	0.897012i	$-0.354267\pi$
$47$	−11817.8	−	6823.00i	−0.113826	−	0.0657176i	−0.555832	+	0.831295i	$0.687600\pi$
$48$	−101104.	+	44817.8i	−0.914204	+	0.405253i
$49$	57197.4	+	99068.8i	0.486170	+	0.842071i
$50$	−45794.6	−	348496.i	−0.366357	−	2.78797i
$51$	144487.	+	105120.i	1.08922	+	0.792458i
$52$	−20471.9	−	76550.4i	−0.145596	−	0.544424i
$53$	145311.			0.976044			0.488022	−	0.872831i	$-0.337719\pi$
$53$	145311.			0.976044			0.488022	+	0.872831i	$0.337719\pi$
$54$	148548.	−	52234.7i	0.943376	−	0.331724i
$55$	−258595.			−1.55429
$56$	−28954.6	−	3833.33i	−0.164875	−	0.0218279i
$57$	−72975.2	−	53092.7i	−0.394050	−	0.286689i
$58$	−22507.5	−	171282.i	−0.115357	−	0.877864i
$59$	−125868.	−	218010.i	−0.612857	−	1.06150i	−0.990756	−	0.135653i	$-0.956687\pi$
$59$	−125868.	−	218010.i	−0.612857	−	1.06150i	0.377900	−	0.925847i	$-0.376646\pi$
$60$	151580.	−	393539.i	0.701760	−	1.82194i
$61$	−183328.	−	105845.i	−0.807681	−	0.466315i	0.0384688	−	0.999260i	$-0.487752\pi$
$61$	−183328.	−	105845.i	−0.807681	−	0.466315i	−0.846150	+	0.532945i	$0.821085\pi$
$62$	−157213.	−	65164.5i	−0.659651	−	0.273424i
$63$	40666.0	+	8699.55i	0.162633	+	0.0347917i
$64$	−185633.	+	185095.i	−0.708132	+	0.706080i
$65$	261686.	+	151085.i	0.952885	+	0.550149i
$66$	−201038.	−	109388.i	−0.699271	−	0.380486i
$67$	239882.	−	138496.i	0.797578	−	0.460482i	−0.0450454	−	0.998985i	$-0.514343\pi$
$67$	239882.	−	138496.i	0.797578	−	0.460482i	0.842624	+	0.538503i	$0.181010\pi$
$68$	409054.	+	109818.i	1.30093	+	0.349257i
$69$	18119.7	−	171317.i	0.0551574	−	0.521499i
$70$	88377.3	−	67780.3i	0.257660	−	0.197610i
$71$			590317.i			1.64934i	0.565614	+	0.824670i	$0.308639\pi$
$71$			590317.i			1.64934i	−0.565614	+	0.824670i	$0.691361\pi$
$72$	284313.	−	241827.i	0.761727	−	0.647898i
$73$	−479905.			−1.23364			−0.616818	−	0.787106i	$-0.711579\pi$
$73$	−479905.			−1.23364			−0.616818	+	0.787106i	$0.711579\pi$
$74$	−174483.	−	227505.i	−0.430585	−	0.561430i
$75$	481795.	+	1.08404e6i	1.14203	+	2.56958i
$76$	−206599.	−	55465.2i	−0.470639	−	0.126351i
$77$	−30222.3	−	52346.6i	−0.0661996	−	0.114661i
$78$	139531.	+	228153.i	0.294026	+	0.480775i
$79$	414018.	−	717100.i	0.839727	−	1.45445i	−0.0503964	−	0.998729i	$-0.516048\pi$
$79$	414018.	−	717100.i	0.839727	−	1.45445i	0.890123	−	0.455720i	$-0.150618\pi$
$80$	967.282	−	999638.i	0.00188922	−	1.95242i
$81$	−430762.	+	311245.i	−0.810555	+	0.585662i
$82$	−49279.5	+	118890.i	−0.0893768	+	0.215627i
$83$	246200.	−	426431.i	0.430580	−	0.745786i	−0.566344	−	0.824169i	$-0.691642\pi$
$83$	246200.	−	426431.i	0.430580	−	0.745786i	0.996923	+	0.0783834i	$0.0249758\pi$
$84$	97378.4	−	15309.5i	0.164295	−	0.0258300i
$85$	−1.39871e6	+	807543.i	−2.27756	+	1.31495i
$86$	−1.12610e6	+	147976.i	−1.77044	+	0.232647i
$87$	236797.	+	532794.i	0.359599	+	0.809099i
$88$	−537816.	−	71202.0i	−0.789198	−	0.104483i
$89$		−	380195.i		−	0.539307i	−0.962957	−	0.269654i	$-0.913091\pi$
$89$		−	380195.i		−	0.539307i	0.962957	−	0.269654i	$-0.0869092\pi$
$90$	−113875.	+	1.41875e6i	−0.156207	+	1.94616i
$91$			70629.8i			0.0937268i
$92$	−105498.	−	394487.i	−0.135482	−	0.506605i
$93$	571184.	+	60412.4i	0.710112	+	0.0751064i
$94$	108237.	−	14223.1i	0.130315	−	0.0171242i
$95$	706439.	−	407863.i	0.823955	−	0.475711i
$96$	423609.	−	776732.i	0.478797	−	0.877926i
$97$	241248.	−	417854.i	0.264331	−	0.457835i	−0.703057	−	0.711134i	$-0.748182\pi$
$97$	241248.	−	417854.i	0.264331	−	0.457835i	0.967388	+	0.253298i	$0.0815155\pi$
$98$	−845412.	−	350421.i	−0.898235	−	0.372316i
$99$	755349.	+	161590.i	0.778470	+	0.166536i
$100$	1.98738e6	+	1.98930e6i	1.98738	+	1.98930i
$101$	470173.	−	814364.i	0.456345	−	0.790413i	−0.542419	−	0.840108i	$-0.682491\pi$
$101$	470173.	−	814364.i	0.456345	−	0.790413i	0.998764	+	0.0496946i	$0.0158248\pi$
$102$	−1.42899e6	+	36136.1i	−1.34656	+	0.0340519i
$103$	−118324.	−	204943.i	−0.108283	−	0.187551i	0.806792	−	0.590836i	$-0.201202\pi$
$103$	−118324.	−	204943.i	−0.108283	−	0.187551i	−0.915075	+	0.403284i	$0.867869\pi$
$104$	502646.	+	386273.i	0.446850	+	0.343396i
$105$	−221145.	+	303961.i	−0.191034	+	0.262573i
$106$	−922432.	+	707452.i	−0.774492	+	0.593991i
$107$	−796217.			−0.649951			−0.324975	−	0.945723i	$-0.605356\pi$
$107$	−796217.			−0.649951			−0.324975	+	0.945723i	$0.605356\pi$
$108$	−688675.	+	1.05480e6i	−0.546692	+	0.837334i
$109$		−	2.24985e6i		−	1.73729i	−0.495432	−	0.868647i	$-0.664990\pi$
$109$		−	2.24985e6i		−	1.73729i	0.495432	−	0.868647i	$-0.335010\pi$
$110$	1.64156e6	−	1.25898e6i	1.23333	−	0.945893i
$111$	782471.	+	569283.i	0.572136	+	0.416255i
$112$	202467.	−	116633.i	0.144112	−	0.0830172i
$113$	−1.49832e6	+	865054.i	−1.03841	+	0.599526i	−0.919382	−	0.393365i	$-0.871311\pi$
$113$	−1.49832e6	+	865054.i	−1.03841	+	0.599526i	−0.119027	+	0.992891i	$0.537977\pi$
$114$	721732.	−	18251.1i	0.487148	−	0.0123190i
$115$	1.34855e6	+	778584.i	0.886691	+	0.511931i
$116$	976773.	+	977718.i	0.625777	+	0.626383i
$117$	−669969.	−	604835.i	−0.418309	−	0.377641i
$118$	1.86040e6	+	771131.i	1.13230	+	0.469334i
$119$	−326937.	−	188757.i	−0.194010	−	0.112012i
$120$	953736.	+	3.23617e6i	0.551931	+	1.87278i
$121$	324417.	+	561907.i	0.183125	+	0.317182i
$122$	1.67908e6	−	220642.i	0.924681	−	0.121509i
$123$	45685.8	−	431948.i	0.0245508	−	0.232122i
$124$	1.31525e6	−	351738.i	0.689831	−	0.184482i
$125$	−6.90948e6			−3.53766
$126$	−300502.	+	142760.i	−0.150223	+	0.0713665i
$127$	−1.92900e6			−0.941718			−0.470859	−	0.882208i	$-0.656056\pi$
$127$	−1.92900e6			−0.941718			−0.470859	+	0.882208i	$0.656056\pi$
$128$	277254.	−	2.07874e6i	0.132205	−	0.991222i
$129$	3.50287e6	−	1.55683e6i	1.63175	−	0.725223i
$130$	−2.39675e6	+	314948.i	−1.09092	+	0.143354i
$131$	989910.	+	1.71457e6i	0.440334	+	0.762680i	0.997714	−	0.0675770i	$-0.0215268\pi$
$131$	989910.	+	1.71457e6i	0.440334	+	0.762680i	−0.557380	+	0.830257i	$0.688194\pi$
$132$	1.80875e6	−	284366.i	0.786425	−	0.123639i
$133$	165125.	+	95334.9i	0.0701871	+	0.0405226i
$134$	−848497.	+	2.04705e6i	−0.352643	+	0.850775i
$135$	−989500.	−	4.70066e6i	−0.402174	−	1.91055i
$136$	−3.13133e6	+	1.29438e6i	−1.24484	+	0.514570i
$137$	1.55369e6	+	897022.i	0.604230	+	0.348852i	0.770704	−	0.637194i	$-0.219905\pi$
$137$	1.55369e6	+	897022.i	0.604230	+	0.348852i	−0.166474	+	0.986046i	$0.553238\pi$
$138$	719043.	+	1.17574e6i	0.273601	+	0.447377i
$139$	−2.85851e6	+	1.65036e6i	−1.06438	+	0.614518i	−0.926640	−	0.375951i	$-0.877316\pi$
$139$	−2.85851e6	+	1.65036e6i	−1.06438	+	0.614518i	−0.137737	+	0.990469i	$0.543983\pi$
$140$	−231027.	+	860540.i	−0.0841936	+	0.313608i
$141$	−336686.	+	149638.i	−0.120107	+	0.0533808i
$142$	−2.87399e6	−	3.74734e6i	−1.00374	−	1.30875i
$143$			1.31191e6i			0.448638i
$144$	−627474.	+	2.91931e6i	−0.210140	+	0.977671i
$145$	−5.27013e6			−1.72869
$146$	3.04644e6	−	2.33645e6i	0.978891	−	0.750753i
$147$	3.07153e6	+	324866.i	0.966947	+	0.102271i
$148$	2.21524e6	+	594721.i	0.683339	+	0.183455i
$149$	−616155.	−	1.06721e6i	−0.186265	−	0.322620i	0.757737	−	0.652560i	$-0.226305\pi$
$149$	−616155.	−	1.06721e6i	−0.186265	−	0.322620i	−0.944002	+	0.329940i	$0.892972\pi$
$150$	−8.33616e6	−	4.53585e6i	−2.46997	−	1.34396i
$151$	966767.	−	1.67449e6i	0.280796	−	0.486353i	−0.690785	−	0.723060i	$-0.742735\pi$
$151$	966767.	−	1.67449e6i	0.280796	−	0.486353i	0.971581	+	0.236707i	$0.0760682\pi$
$152$	1.58153e6	−	653746.i	0.450346	−	0.186156i
$153$	4.59020e6	−	1.48480e6i	1.28161	−	0.414565i
$154$	446704.	+	185157.i	0.122309	+	0.0506966i
$155$	−2.59586e6	+	4.49615e6i	−0.697085	+	1.20739i
$156$	−1.99651e6	−	769001.i	−0.525895	−	0.202560i
$157$	6.12636e6	−	3.53705e6i	1.58308	−	0.913993i	0.588676	−	0.808369i	$-0.299649\pi$
$157$	6.12636e6	−	3.53705e6i	1.58308	−	0.913993i	0.994406	−	0.105624i	$-0.0336839\pi$
$158$	863054.	+	6.56783e6i	0.218810	+	1.66514i
$159$	2.30819e6	−	3.17257e6i	0.574222	−	0.789260i
$160$	4.86065e6	+	6.35041e6i	1.18668	+	1.55039i
$161$			363976.i			0.0872159i
$162$	1.21917e6	−	4.07297e6i	0.286760	−	0.958002i
$163$		−	5.34853e6i		−	1.23501i	−0.786566	−	0.617507i	$-0.788143\pi$
$163$		−	5.34853e6i		−	1.23501i	0.786566	−	0.617507i	$-0.211857\pi$
$164$	−265995.	−	994633.i	−0.0603035	−	0.225492i
$165$	−4.10765e6	+	5.64592e6i	−0.914412	+	1.25685i
$166$	513224.	+	3.90562e6i	0.112197	+	0.853819i
$167$	5.93465e6	−	3.42637e6i	1.27422	−	0.735673i	0.298443	−	0.954427i	$-0.403533\pi$
$167$	5.93465e6	−	3.42637e6i	1.27422	−	0.735673i	0.975780	+	0.218754i	$0.0701992\pi$
$168$	−543623.	+	571277.i	−0.114649	+	0.120481i
$169$	−1.64692e6	+	2.85255e6i	−0.341202	+	0.590980i
$170$	4.94742e6	−	1.19360e7i	1.00701	−	2.42947i
$171$	−2.31835e6	+	749920.i	−0.463651	+	0.149978i
$172$	6.42804e6	−	6.42182e6i	1.26326	−	1.26204i
$173$	−328585.	+	569126.i	−0.0634613	+	0.109918i	−0.896010	−	0.444033i	$-0.853547\pi$
$173$	−328585.	+	569126.i	−0.0634613	+	0.109918i	0.832549	+	0.553951i	$0.186881\pi$
$174$	−4.09713e6	−	2.22932e6i	−0.777735	−	0.423180i
$175$	−1.25319e6	−	2.17059e6i	−0.233831	−	0.405007i
$176$	3.76071e6	−	2.16640e6i	0.689814	−	0.397375i
$177$	−6.75917e6	−	714897.i	−1.21891	−	0.128921i
$178$	1.85100e6	+	2.41348e6i	0.328206	+	0.427941i
$179$	6.58978e6			1.14898			0.574489	−	0.818512i	$-0.305201\pi$
$179$	6.58978e6			1.14898			0.574489	+	0.818512i	$0.305201\pi$
$180$	−6.18438e6	−	9.56064e6i	−1.06042	−	1.63934i
$181$		−	5.36105e6i		−	0.904095i	−0.891994	−	0.452048i	$-0.850694\pi$
$181$		−	5.36105e6i		−	0.904095i	0.891994	−	0.452048i	$-0.149306\pi$
$182$	−343865.	−	448358.i	−0.0570393	−	0.0743723i
$183$	−5.22299e6	+	2.32133e6i	−0.852248	+	0.378776i
$184$	2.59028e6	+	1.99058e6i	0.415809	+	0.319541i
$185$	−7.57473e6	+	4.37327e6i	−1.19633	+	0.690703i
$186$	−3.92000e6	+	2.39734e6i	−0.609182	+	0.372556i
$187$	−6.07268e6	−	3.50607e6i	−0.928658	−	0.536161i
$188$	−617846.	+	617248.i	−0.0929836	+	0.0928937i
$189$	835897.	−	749674.i	0.123813	−	0.111042i
$190$	−2.49877e6	+	6.02845e6i	−0.364306	+	0.878911i
$191$	4.07906e6	+	2.35505e6i	0.585410	+	0.337986i	0.763280	−	0.646068i	$-0.223588\pi$
$191$	4.07906e6	+	2.35505e6i	0.585410	+	0.337986i	−0.177871	+	0.984054i	$0.556921\pi$
$192$	1.09249e6	+	6.99306e6i	0.154353	+	0.988016i
$193$	−361403.	−	625969.i	−0.0502713	−	0.0870725i	0.839795	−	0.542904i	$-0.182675\pi$
$193$	−361403.	−	625969.i	−0.0502713	−	0.0870725i	−0.890066	+	0.455832i	$0.849342\pi$
$194$	502901.	+	3.82707e6i	0.0688775	+	0.524156i
$195$	7.45540e6	−	3.31350e6i	1.00546	−	0.446872i
$196$	7.07272e6	−	1.89146e6i	0.939330	−	0.251206i
$197$	−1.00491e6			−0.131440			−0.0657200	−	0.997838i	$-0.520934\pi$
$197$	−1.00491e6			−0.131440			−0.0657200	+	0.997838i	$0.520934\pi$
$198$	−5.58167e6	+	2.65169e6i	−0.719065	+	0.341607i
$199$	−1.26262e6			−0.160218			−0.0801092	−	0.996786i	$-0.525527\pi$
$199$	−1.26262e6			−0.160218			−0.0801092	+	0.996786i	$0.525527\pi$
$200$	−2.23009e7	−	2.95244e6i	−2.78761	−	0.369054i
$201$	786621.	−	7.43730e6i	0.0968673	−	0.915856i
$202$	980114.	+	7.45865e6i	0.118911	+	0.904911i
$203$	−615927.	−	1.06682e6i	−0.0736277	−	0.127527i
$204$	8.89527e6	−	7.18649e6i	1.04778	−	0.846498i
$205$	3.40014e6	+	1.96307e6i	0.394671	+	0.227863i
$206$	1.74889e6	+	724911.i	0.200061	+	0.0829245i
$207$	−3.45255e6	−	3.11690e6i	−0.389251	−	0.351408i
$208$	−5.07139e6	−	4907.24i	−0.563556	−	0.000545315i
$209$	3.06711e6	+	1.77079e6i	0.335962	+	0.193968i
$210$	−76020.8	−	3.00620e6i	−0.00820870	−	0.324609i
$211$	1.19190e7	−	6.88144e6i	1.26880	−	0.732541i	0.294037	−	0.955794i	$-0.405001\pi$
$211$	1.19190e7	−	6.88144e6i	1.26880	−	0.732541i	0.974760	+	0.223253i	$0.0716677\pi$
$212$	2.41133e6	−	8.98182e6i	0.253075	−	0.942664i
$213$	1.28884e7	+	9.37690e6i	1.33371	+	0.970332i
$214$	5.05439e6	−	3.87643e6i	0.515736	−	0.395540i
$215$			3.46486e7i			3.48635i
$216$	−763638.	−	1.00487e7i	−0.0757750	−	0.997125i
$217$	−1.21352e6			−0.118760
$218$	1.09535e7	+	1.42820e7i	1.05726	+	1.37854i
$219$	−7.62307e6	+	1.04778e7i	−0.725767	+	0.997557i
$220$	−4.29121e6	+	1.59841e7i	−0.403006	+	1.50113i
$221$	4.09685e6	+	7.09595e6i	0.379554	+	0.657406i
$222$	−7.73871e6	+	195696.i	−0.707310	+	0.0178864i
$223$	193821.	−	335707.i	0.0174777	−	0.0302723i	−0.857154	−	0.515060i	$-0.827770\pi$
$223$	193821.	−	335707.i	0.0174777	−	0.0302723i	0.874632	+	0.484787i	$0.161103\pi$
$224$	−717425.	+	1.72611e6i	−0.0638311	+	0.153576i
$225$	3.13210e7	+	6.70042e6i	2.74972	+	0.588239i
$226$	5.29976e6	−	1.27860e7i	0.459125	−	1.10767i
$227$	−852647.	+	1.47683e6i	−0.0728940	+	0.126256i	−0.900169	−	0.435542i	$-0.856557\pi$
$227$	−852647.	+	1.47683e6i	−0.0728940	+	0.126256i	0.827275	+	0.561798i	$0.189890\pi$
$228$	−4.49270e6	+	3.62965e6i	−0.379056	+	0.306239i
$229$	5.84638e6	−	3.37541e6i	0.486834	−	0.281073i	−0.236426	−	0.971649i	$-0.575976\pi$
$229$	5.84638e6	−	3.37541e6i	0.486834	−	0.281073i	0.723260	+	0.690576i	$0.242643\pi$
$230$	−1.23512e7	+	1.62302e6i	−1.01514	+	0.133395i
$231$	−1.62295e6	−	171655.i	−0.131665	−	0.0139258i
$232$	−1.09606e7	−	1.45109e6i	−0.877752	−	0.116206i
$233$		−	9.86477e6i		−	0.779865i	−0.920844	−	0.389932i	$-0.872498\pi$
$233$		−	9.86477e6i		−	0.779865i	0.920844	−	0.389932i	$-0.127502\pi$
$234$	7.19764e6	+	577714.i	0.561750	+	0.0450885i
$235$		−	3.33033e6i		−	0.256616i
$236$	−1.55641e7	+	4.16233e6i	−1.18410	+	0.316665i
$237$	−9.08001e6	−	2.04301e7i	−0.682089	−	1.53470i
$238$	2.99437e6	−	393480.i	0.222114	−	0.0291871i
$239$	−3.19874e6	+	1.84680e6i	−0.234307	+	0.135277i	−0.612557	−	0.790426i	$-0.709859\pi$
$239$	−3.19874e6	+	1.84680e6i	−0.234307	+	0.135277i	0.378250	+	0.925703i	$0.376526\pi$
$240$	−2.18098e7	−	1.58999e7i	−1.57767	−	1.15016i
$241$	−2.20907e6	+	3.82622e6i	−0.157818	+	0.273350i	−0.934082	−	0.357059i	$-0.883779\pi$
$241$	−2.20907e6	+	3.82622e6i	−0.157818	+	0.273350i	0.776263	+	0.630409i	$0.217113\pi$
$242$	−4.79507e6	−	1.98754e6i	−0.338337	−	0.140240i
$243$	−47025.2	+	1.43488e7i	−0.00327726	+	0.999995i
$244$	−9.58460e6	+	9.57533e6i	−0.659788	+	0.659150i
$245$	−1.39592e7	+	2.41780e7i	−0.949207	+	1.64407i
$246$	1.81295e6	+	2.96443e6i	0.121781	+	0.199130i
$247$	−2.06918e6	−	3.58393e6i	−0.137312	−	0.237831i
$248$	−6.63675e6	+	8.63619e6i	−0.435111	+	0.566197i
$249$	−5.39952e6	−	1.21489e7i	−0.349749	−	0.786938i
$250$	4.38614e7	−	3.36392e7i	2.80713	−	2.15291i
$251$	−1.37812e7			−0.871495			−0.435747	−	0.900069i	$-0.643516\pi$
$251$	−1.37812e7			−0.871495			−0.435747	+	0.900069i	$0.643516\pi$
$252$	1.21255e6	−	2.36925e6i	0.0757704	−	0.148050i
$253$			6.76067e6i			0.417473i
$254$	1.22453e7	−	9.39144e6i	0.747254	−	0.573101i
$255$	−4.58663e6	+	4.33654e7i	−0.276613	+	2.61531i
$256$	8.36047e6	+	1.45457e7i	0.498323	+	0.866991i
$257$	−964311.	+	556745.i	−0.0568091	+	0.0327988i	−0.528136	−	0.849160i	$-0.677109\pi$
$257$	−964311.	+	556745.i	−0.0568091	+	0.0327988i	0.471326	+	0.881959i	$0.343775\pi$
$258$	−1.46567e7	+	2.69367e7i	−0.853450	+	1.56850i
$259$	−1.77054e6	−	1.02222e6i	−0.101907	−	0.0588363i
$260$	1.36812e7	−	1.36680e7i	0.778404	−	0.777651i
$261$	1.53939e7	+	3.29318e6i	0.865820	+	0.185222i
$262$	−1.46315e7	−	6.06469e6i	−0.813549	−	0.337214i
$263$	−1.50165e7	−	8.66978e6i	−0.825471	−	0.476586i	0.0268288	−	0.999640i	$-0.491459\pi$
$263$	−1.50165e7	−	8.66978e6i	−0.825471	−	0.476586i	−0.852299	+	0.523054i	$0.824792\pi$
$264$	−1.00975e7	+	1.06112e7i	−0.548785	+	0.576702i
$265$	1.77317e7	+	3.07122e7i	0.952823	+	1.65034i
$266$	−1.51236e6	+	198733.i	−0.0803543	+	0.0105591i
$267$	−8.30082e6	−	6.03921e6i	−0.436101	−	0.317283i
$268$	−4.57992e6	−	1.71257e7i	−0.237933	−	0.889698i
$269$	2.44758e7			1.25742			0.628710	−	0.777640i	$-0.283583\pi$
$269$	2.44758e7			1.25742			0.628710	+	0.777640i	$0.283583\pi$
$270$	2.91668e7	+	2.50224e7i	1.48183	+	1.27127i
$271$	−1.09005e7			−0.547693			−0.273847	−	0.961773i	$-0.588296\pi$
$271$	−1.09005e7			−0.547693			−0.273847	+	0.961773i	$0.588296\pi$
$272$	1.35759e7	−	2.34618e7i	0.674626	−	1.16588i
$273$	1.54206e6	+	1.12192e6i	0.0757905	+	0.0551409i
$274$	−1.42300e7	+	1.86992e6i	−0.691757	+	0.0909014i
$275$	−2.32773e7	−	4.03175e7i	−1.11927	−	1.93863i
$276$	−1.02886e7	−	3.96289e6i	−0.489362	−	0.188489i
$277$	1.05520e7	+	6.09222e6i	0.496474	+	0.286640i	0.727256	−	0.686366i	$-0.240795\pi$
$277$	1.05520e7	+	6.09222e6i	0.496474	+	0.286640i	−0.230782	+	0.973005i	$0.574128\pi$
$278$	1.01110e7	−	2.43933e7i	0.470606	−	1.13537i
$279$	1.03920e7	−	1.15111e7i	0.478503	−	0.530033i
$280$	−2.72302e6	−	6.58748e6i	−0.124044	−	0.300086i
$281$	−2.45972e7	−	1.42012e7i	−1.10858	−	0.640038i	−0.170117	−	0.985424i	$-0.554415\pi$
$281$	−2.45972e7	−	1.42012e7i	−1.10858	−	0.640038i	−0.938461	+	0.345386i	$0.887748\pi$
$282$	1.40877e6	−	2.58908e6i	0.0628191	−	0.115451i
$283$	−3.45365e6	+	1.99396e6i	−0.152377	+	0.0879747i	−0.574250	−	0.818680i	$-0.694706\pi$
$283$	−3.45365e6	+	1.99396e6i	−0.152377	+	0.0879747i	0.421873	+	0.906655i	$0.361373\pi$
$284$	3.64882e7	+	9.79591e6i	1.59293	+	0.427651i
$285$	2.31655e6	−	2.19024e7i	0.100071	−	0.946144i
$286$	−6.38711e6	−	8.32802e6i	−0.273028	−	0.355995i
$287$			917706.i			0.0388202i
$288$	−1.02296e7	−	2.15867e7i	−0.428235	−	0.903667i
$289$	−1.96575e7			−0.814396
$290$	3.34548e7	−	2.56579e7i	1.37172	−	1.05203i
$291$	−5.29091e6	−	1.19046e7i	−0.214710	−	0.483098i
$292$	−7.96371e6	+	2.96635e7i	−0.319865	+	1.19145i
$293$	1.36961e7	+	2.37223e7i	0.544494	+	0.943091i	0.998639	+	0.0521632i	$0.0166116\pi$
$293$	1.36961e7	+	2.37223e7i	0.544494	+	0.943091i	−0.454145	+	0.890928i	$0.650055\pi$
$294$	−2.10797e7	+	1.28917e7i	−0.829512	+	0.507302i
$295$	3.07183e7	−	5.32057e7i	1.19655	−	2.07249i
$296$	−1.69578e7	+	7.00974e6i	−0.653875	+	0.270288i
$297$	1.55263e7	−	1.39248e7i	0.592652	−	0.531520i
$298$	9.10713e6	+	3.77488e6i	0.344138	+	0.142644i
$299$	3.94993e6	−	6.84149e6i	0.147767	−	0.255939i
$300$	7.50010e7	−	1.17914e7i	2.77782	−	0.436719i
$301$	−7.01382e6	+	4.04943e6i	−0.257191	+	0.148489i
$302$	2.01531e6	+	1.53364e7i	0.0731678	+	0.556805i
$303$	−1.03116e7	−	2.32011e7i	−0.370678	−	0.834028i
$304$	−6.85674e6	+	1.18497e7i	−0.244060	+	0.421782i
$305$		−	5.16632e7i		−	1.82088i
$306$	−2.19098e7	+	3.17731e7i	−0.764669	+	1.10891i
$307$		−	2.17680e7i		−	0.752320i	−0.926555	−	0.376160i	$-0.877244\pi$
$307$		−	2.17680e7i		−	0.752320i	0.926555	−	0.376160i	$-0.122756\pi$
$308$	−3.73713e6	+	999423.i	−0.127904	+	0.0342056i
$309$	−6.35404e6	−	672047.i	−0.215365	−	0.0227785i
$310$	−5.41127e6	−	4.11797e7i	−0.181641	−	1.38229i
$311$	3.76298e7	−	2.17256e7i	1.25098	−	0.722254i	0.279676	−	0.960094i	$-0.409773\pi$
$311$	3.76298e7	−	2.17256e7i	1.25098	−	0.722254i	0.971304	+	0.237840i	$0.0764395\pi$
$312$	1.64178e7	−	4.83852e6i	0.540569	−	0.159312i
$313$	−1.47066e7	+	2.54726e7i	−0.479600	+	0.830691i	−0.999726	−	0.0233980i	$-0.992552\pi$
$313$	−1.47066e7	+	2.54726e7i	−0.479600	+	0.830691i	0.520126	+	0.854089i	$0.325885\pi$
$314$	−2.16698e7	+	5.22798e7i	−0.699948	+	1.68867i
$315$	3.12361e6	+	9.65655e6i	0.0999369	+	0.308951i
$316$	−3.74545e7	−	3.74908e7i	−1.18698	−	1.18813i
$317$	8.99488e6	−	1.55796e7i	0.282369	−	0.489078i	−0.689599	−	0.724192i	$-0.742213\pi$
$317$	8.99488e6	−	1.55796e7i	0.282369	−	0.489078i	0.971968	+	0.235114i	$0.0755463\pi$
$318$	793461.	+	3.13770e7i	0.0246743	+	0.975732i
$319$	−1.14405e7	−	1.98156e7i	−0.352431	−	0.610428i
$320$	−6.17728e7	−	1.66481e7i	−1.88516	−	0.508060i
$321$	−1.26475e7	+	1.73839e7i	−0.382376	+	0.525571i
$322$	−1.77204e6	−	2.31052e6i	−0.0530769	−	0.0692059i
$323$	2.21194e7			0.656396
$324$	1.20902e7	+	3.17908e7i	0.355467	+	0.934689i
$325$			5.43992e7i			1.58468i
$326$	2.60396e7	+	3.39525e7i	0.751591	+	0.979984i
$327$	−4.91210e7	−	3.57377e7i	−1.40483	−	1.02208i
$328$	6.53097e6	+	5.01892e6i	0.185079	+	0.142229i
$329$	674150.	−	389221.i	0.0189308	−	0.0109297i
$330$	−1.41205e6	−	5.58386e7i	−0.0392923	−	1.55379i
$331$	−1.73246e7	−	1.00024e7i	−0.477726	−	0.275815i	0.241742	−	0.970340i	$-0.422281\pi$
$331$	−1.73246e7	−	1.00024e7i	−0.477726	−	0.275815i	−0.719468	+	0.694525i	$0.755614\pi$
$332$	−2.22727e7	−	2.22942e7i	−0.608637	−	0.609226i
$333$	2.48584e7	−	8.04096e6i	0.673193	−	0.217758i
$334$	−2.09917e7	+	5.06438e7i	−0.563389	+	1.35921i
$335$	5.85437e7	+	3.38002e7i	1.55721	+	0.899053i
$336$	669628.	−	6.27313e6i	0.0176529	−	0.165374i
$337$	−5.08635e6	−	8.80981e6i	−0.132897	−	0.230185i	0.791895	−	0.610657i	$-0.209095\pi$
$337$	−5.08635e6	−	8.80981e6i	−0.132897	−	0.230185i	−0.924792	+	0.380472i	$0.875761\pi$
$338$	−3.43313e6	−	2.61261e7i	−0.0889080	−	0.676588i
$339$	−4.91328e6	+	4.64538e7i	−0.126117	+	1.19240i
$340$	2.67047e7	+	9.98563e7i	0.679439	+	2.54062i
$341$	−2.25406e7			−0.568462
$342$	1.10659e7	−	1.60475e7i	0.276635	−	0.401171i
$343$	−1.32370e7			−0.328026
$344$	−9.54022e6	+	7.20610e7i	−0.234360	+	1.77021i
$345$	3.84199e7	−	1.70755e7i	0.935618	−	0.415829i
$346$	−684962.	−	5.21255e6i	−0.0165363	−	0.125841i
$347$	−2.22772e7	−	3.85853e7i	−0.533178	−	0.923492i	−0.999249	−	0.0387446i	$-0.987664\pi$
$347$	−2.22772e7	−	3.85853e7i	−0.533178	−	0.923492i	0.466071	−	0.884747i	$-0.345669\pi$
$348$	3.68621e7	−	5.79535e6i	0.874667	−	0.137512i
$349$	−9.90868e6	−	5.72078e6i	−0.233099	−	0.134580i	0.378902	−	0.925437i	$-0.376302\pi$
$349$	−9.90868e6	−	5.72078e6i	−0.233099	−	0.134580i	−0.612001	+	0.790857i	$0.709635\pi$
$350$	1.85229e7	+	7.67767e6i	0.432020	+	0.179071i
$351$	−2.38475e7	+	5.01996e6i	−0.551471	+	0.116086i
$352$	−1.33258e7	+	3.20615e7i	−0.305538	+	0.735117i
$353$	−1.09677e7	−	6.33218e6i	−0.249339	−	0.143956i	0.370123	−	0.928983i	$-0.379316\pi$
$353$	−1.09677e7	−	6.33218e6i	−0.249339	−	0.143956i	−0.619461	+	0.785027i	$0.712649\pi$
$354$	4.63877e7	−	2.83692e7i	1.04567	−	0.639495i
$355$	−1.24767e8	+	7.20341e7i	−2.78878	+	1.61010i
$356$	−2.35003e7	−	6.30908e6i	−0.520863	−	0.139835i
$357$	−9.31438e6	+	4.13972e6i	−0.204715	+	0.0909842i
$358$	−4.18320e7	+	3.20827e7i	−0.911715	+	0.699233i
$359$			4.24097e7i			0.916605i	0.888796	+	0.458302i	$0.151542\pi$
$359$			4.24097e7i			0.916605i	−0.888796	+	0.458302i	$0.848458\pi$
$360$	8.58050e7	+	3.05820e7i	1.83910	+	0.655477i
$361$	3.58741e7			0.762535
$362$	2.61006e7	+	3.40320e7i	0.550205	+	0.717400i
$363$	1.74213e7	+	1.84260e6i	0.364218	+	0.0385223i
$364$	4.36572e6	+	1.17205e6i	0.0905214	+	0.0243021i
$365$	−5.85610e7	−	1.01431e8i	−1.20429	−	2.08589i
$366$	2.18541e7	−	4.01642e7i	0.445748	−	0.819212i
$367$	1.54241e7	−	2.67153e7i	0.312033	−	0.540457i	−0.666769	−	0.745264i	$-0.732323\pi$
$367$	1.54241e7	−	2.67153e7i	0.312033	−	0.540457i	0.978802	+	0.204807i	$0.0656567\pi$
$368$	−2.61344e7	−	25288.5i	−0.524407	−	0.000507434i
$369$	−8.70504e6	−	7.85874e6i	−0.173257	−	0.156413i
$370$	2.67929e7	−	6.46396e7i	0.528950	−	1.27613i
$371$	−4.14465e6	+	7.17874e6i	−0.0811645	+	0.140581i
$372$	1.32126e7	−	3.43031e7i	0.256660	−	0.666353i
$373$	−2.51097e7	+	1.44971e7i	−0.483855	+	0.279354i	−0.722021	−	0.691871i	$-0.756787\pi$
$373$	−2.51097e7	+	1.44971e7i	−0.483855	+	0.279354i	0.238167	+	0.971224i	$0.423453\pi$
$374$	5.56189e7	−	7.30868e6i	1.06318	−	0.139709i
$375$	−1.09754e8	+	1.50855e8i	−2.08126	+	2.86066i
$376$	916980.	−	6.92631e6i	0.0172503	−	0.130298i
$377$			2.67366e7i			0.498979i
$378$	−1.65645e6	+	8.82855e6i	−0.0306692	+	0.163461i
$379$			4.12189e7i			0.757144i	0.925572	+	0.378572i	$0.123585\pi$
$379$			4.12189e7i			0.757144i	−0.925572	+	0.378572i	$0.876415\pi$
$380$	−1.34876e7	−	5.04340e7i	−0.245801	−	0.919122i
$381$	−3.06412e7	+	4.21159e7i	−0.554027	+	0.761503i
$382$	−3.73595e7	+	4.90928e6i	−0.670211	+	0.0880700i
$383$	3.69740e7	−	2.13470e7i	0.658113	−	0.379962i	−0.133444	−	0.991056i	$-0.542604\pi$
$383$	3.69740e7	−	2.13470e7i	0.658113	−	0.379962i	0.791558	+	0.611094i	$0.209270\pi$
$384$	−4.09813e7	−	3.90731e7i	−0.723756	−	0.690056i
$385$	7.37583e6	−	1.27753e7i	0.129249	−	0.223866i
$386$	5.34176e6	+	2.21414e6i	0.0928800	+	0.0384985i
$387$	2.16511e7	−	1.01208e8i	0.373548	−	1.74615i
$388$	−2.18247e7	−	2.18458e7i	−0.373640	−	0.374002i
$389$	−7.43138e6	+	1.28715e7i	−0.126247	+	0.218666i	−0.922220	−	0.386666i	$-0.873626\pi$
$389$	−7.43138e6	+	1.28715e7i	−0.126247	+	0.218666i	0.795973	+	0.605332i	$0.206960\pi$
$390$	−3.11949e7	+	5.73311e7i	−0.525884	+	0.966489i
$391$	2.11123e7	+	3.65676e7i	0.353187	+	0.611738i
$392$	−3.56890e7	+	4.64409e7i	−0.592483	+	0.770979i
$393$	5.31586e7	+	5.62243e6i	0.875782	+	0.0926288i
$394$	6.37916e6	−	4.89245e6i	0.104298	−	0.0799904i
$395$	2.02084e8			3.27900
$396$	2.25226e7	−	4.40076e7i	0.362687	−	0.708667i
$397$		−	6.91670e7i		−	1.10542i	−0.833373	−	0.552710i	$-0.813594\pi$
$397$		−	6.91670e7i		−	1.10542i	0.833373	−	0.552710i	$-0.186406\pi$
$398$	8.01510e6	−	6.14712e6i	0.127133	−	0.0975040i
$399$	4.70438e6	−	2.09083e6i	0.0740600	−	0.0329155i
$400$	1.55940e8	−	8.98311e7i	2.43657	−	1.40361i
$401$	7.16368e7	−	4.13596e7i	1.11097	−	0.641420i	0.171891	−	0.985116i	$-0.445012\pi$
$401$	7.16368e7	−	4.13596e7i	1.11097	−	0.641420i	0.939081	+	0.343696i	$0.111679\pi$
$402$	3.12154e7	+	5.10417e7i	0.480498	+	0.785682i
$403$	2.28100e7	+	1.31694e7i	0.348506	+	0.201210i
$404$	−4.25346e7	−	4.25758e7i	−0.645058	−	0.645682i
$405$	−1.18348e8	−	5.30640e7i	−1.78153	−	0.798794i
$406$	9.10377e6	+	3.77349e6i	0.136033	+	0.0563851i
$407$	−3.28868e7	−	1.89872e7i	−0.487796	−	0.281629i
$408$	−2.14794e7	+	8.89270e7i	−0.316259	+	1.30934i
$409$	5.79151e7	+	1.00312e8i	0.846490	+	1.46616i	0.884321	+	0.466879i	$0.154622\pi$
$409$	5.79151e7	+	1.00312e8i	0.846490	+	1.46616i	−0.0378313	+	0.999284i	$0.512045\pi$
$410$	−3.11414e7	+	4.09218e6i	−0.451842	+	0.0593749i
$411$	4.42643e7	−	1.96730e7i	0.637571	−	0.283364i
$412$	−1.46313e7	+	3.91285e6i	−0.209214	+	0.0559501i
$413$	1.43604e7			0.203852
$414$	3.70916e7	+	2.97713e6i	0.522727	+	0.0419563i
$415$	1.20171e8			1.68134
$416$	3.22171e7	−	2.46592e7i	0.447514	−	0.342530i
$417$	−9.37362e6	+	8.86252e7i	−0.129270	+	1.22222i
$418$	−2.80912e7	+	3.69137e6i	−0.384629	+	0.0505427i
$419$	6.99444e7	+	1.21147e8i	0.950848	+	1.64692i	0.743596	+	0.668629i	$0.233119\pi$
$419$	6.99444e7	+	1.21147e8i	0.950848	+	1.64692i	0.207252	+	0.978288i	$0.433548\pi$
$420$	1.51185e7	+	1.87133e7i	0.204061	+	0.252582i
$421$	1.19562e8	+	6.90294e7i	1.60232	+	0.925098i	0.991023	+	0.133695i	$0.0426841\pi$
$421$	1.19562e8	+	6.90294e7i	1.60232	+	0.925098i	0.611294	+	0.791403i	$0.290649\pi$
$422$	−4.21592e7	+	1.01712e8i	−0.560990	+	1.35342i
$423$	−2.08104e6	+	9.72782e6i	−0.0274954	+	0.128527i
$424$	2.84214e7	+	6.87563e7i	0.372861	+	0.902018i
$425$	−2.51808e8	−	1.45381e8i	−3.28021	−	1.89383i
$426$	−1.27468e8	+	3.22340e6i	−1.64881	+	0.0416951i
$427$	1.04580e7	−	6.03795e6i	0.134328	−	0.0775543i
$428$	−1.32127e7	+	4.92152e7i	−0.168523	+	0.627723i
$429$	2.86430e7	+	2.08391e7i	0.362783	+	0.263941i
$430$	−1.68689e8	−	2.19950e8i	−2.12169	−	2.76642i
$431$		−	3.79427e7i		−	0.473910i	−0.971521	−	0.236955i	$-0.923851\pi$
$431$		−	3.79427e7i		−	0.473910i	0.971521	−	0.236955i	$-0.0761494\pi$
$432$	5.37703e7	+	6.00715e7i	0.666947	+	0.745105i
$433$	−1.11501e8			−1.37345			−0.686726	−	0.726916i	$-0.740953\pi$
$433$	−1.11501e8			−1.37345			−0.686726	+	0.726916i	$0.740953\pi$
$434$	7.70346e6	−	5.90811e6i	0.0942359	−	0.0722736i
$435$	−8.37135e7	+	1.15063e8i	−1.01702	+	1.39787i
$436$	−1.39066e8	−	3.73347e7i	−1.67788	−	0.450457i
$437$	−1.06631e7	−	1.84690e7i	−0.127773	−	0.221309i
$438$	−2.62050e6	−	1.03626e8i	−0.0311862	−	1.23324i
$439$	4.80116e7	−	8.31586e7i	0.567483	−	0.982910i	−0.429331	−	0.903147i	$-0.641250\pi$
$439$	4.80116e7	−	8.31586e7i	0.567483	−	0.982910i	0.996814	−	0.0797625i	$-0.0254162\pi$
$440$	−5.05787e7	−	1.22359e8i	−0.593758	−	1.43641i
$441$	5.58826e7	−	6.19005e7i	0.651569	−	0.721736i
$442$	−6.05539e7	−	2.50994e7i	−0.701254	−	0.290668i
$443$	2.80371e7	−	4.85616e7i	0.322494	−	0.558576i	−0.658508	−	0.752574i	$-0.728812\pi$
$443$	2.80371e7	−	4.85616e7i	0.322494	−	0.558576i	0.981002	+	0.193998i	$0.0621455\pi$
$444$	4.81726e7	−	3.89186e7i	0.550366	−	0.444640i
$445$	8.03563e7	−	4.63937e7i	0.911885	−	0.526477i
$446$	404035.	+	3.07470e6i	0.00455422	+	0.0346575i
$447$	−3.30878e7	−	3.49960e6i	−0.370464	−	0.0391828i
$448$	−3.84944e6	−	1.44502e7i	−0.0428118	−	0.160708i
$449$			1.43500e7i			0.158531i	0.996854	+	0.0792653i	$0.0252574\pi$
$449$			1.43500e7i			0.158531i	−0.996854	+	0.0792653i	$0.974743\pi$
$450$	−2.31447e8	+	1.09954e8i	−2.53989	+	1.20663i
$451$			1.70459e7i			0.185819i
$452$	2.86065e7	+	1.06968e8i	0.309777	+	1.15834i
$453$	−2.12026e7	−	4.77059e7i	−0.228084	−	0.513190i
$454$	−1.77741e6	−	1.35261e7i	−0.0189942	−	0.144545i
$455$	−1.49280e7	+	8.61868e6i	−0.158477	+	0.0914970i
$456$	1.08485e7	−	4.49140e7i	0.114413	−	0.473682i
$457$	−5.13371e7	+	8.89185e7i	−0.537877	+	0.931630i	0.461141	+	0.887327i	$0.347440\pi$
$457$	−5.13371e7	+	8.89185e7i	−0.537877	+	0.931630i	−0.999018	+	0.0443032i	$0.985893\pi$
$458$	−2.06795e7	+	4.98905e7i	−0.215250	+	0.519304i
$459$	4.04954e7	−	1.23803e8i	0.418763	−	1.28025i
$460$	7.05034e7	−	7.04353e7i	0.724331	−	0.723630i
$461$	−7.20263e7	+	1.24753e8i	−0.735171	+	1.27335i	0.219477	+	0.975618i	$0.429565\pi$
$461$	−7.20263e7	+	1.24753e8i	−0.735171	+	1.27335i	−0.954648	+	0.297736i	$0.903768\pi$
$462$	1.11382e7	−	6.81177e6i	0.112951	−	0.0690771i
$463$	1.06605e7	+	1.84646e7i	0.107408	+	0.186036i	0.914719	−	0.404090i	$-0.132412\pi$
$463$	1.06605e7	+	1.84646e7i	0.107408	+	0.186036i	−0.807312	+	0.590125i	$0.799078\pi$
$464$	7.66429e7	−	4.41510e7i	0.767216	−	0.441963i
$465$	5.69309e7	+	1.28095e8i	0.566225	+	1.27401i
$466$	4.80272e7	+	6.26216e7i	0.474602	+	0.618823i
$467$	−9.33020e7			−0.916095			−0.458047	−	0.888928i	$-0.651451\pi$
$467$	−9.33020e7			−0.916095			−0.458047	+	0.888928i	$0.651451\pi$
$468$	−4.85033e7	+	3.13748e7i	−0.473188	+	0.306086i
$469$			1.58011e7i			0.153168i
$470$	1.62139e7	+	2.11410e7i	0.156169	+	0.203625i
$471$	2.00895e7	−	1.89942e8i	0.192268	−	1.81785i
$472$	7.85367e7	−	1.02197e8i	0.746873	−	0.971882i
$473$	−1.30278e8	+	7.52161e7i	−1.23108	+	0.710767i
$474$	1.57105e8	+	8.54836e7i	1.47521	+	0.802690i
$475$	1.27179e8	+	7.34271e7i	1.18669	+	0.685134i
$476$	−1.70926e7	+	1.70761e7i	−0.158485	+	0.158332i
$477$	−3.26025e7	−	1.00790e8i	−0.300397	−	0.928668i
$478$	1.13144e7	−	2.72967e7i	0.103597	−	0.249935i
$479$	7.03570e7	+	4.06206e7i	0.640178	+	0.369607i	0.784683	−	0.619897i	$-0.212826\pi$
$479$	7.03570e7	+	4.06206e7i	0.640178	+	0.369607i	−0.144505	+	0.989504i	$0.546159\pi$
$480$	2.15858e8	−	5.24961e6i	1.95184	−	0.0474683i
$481$	2.21866e7	+	3.84284e7i	0.199368	+	0.345316i
$482$	−4.60498e6	−	3.50438e7i	−0.0411232	−	0.312947i
$483$	7.94672e6	+	5.78159e6i	0.0705255	+	0.0513105i
$484$	4.01156e7	−	1.07281e7i	0.353816	−	0.0946212i
$485$	1.17754e8			1.03217
$486$	−6.95596e7	−	9.13154e7i	−0.605966	−	0.795491i
$487$	−9.41235e7			−0.814913			−0.407457	−	0.913225i	$-0.633584\pi$
$487$	−9.41235e7			−0.814913			−0.407457	+	0.913225i	$0.633584\pi$
$488$	1.42251e7	−	1.07447e8i	0.122404	−	0.924563i
$489$	−1.16775e8	−	8.49588e7i	−0.998671	−	0.726577i
$490$	−2.90990e7	−	2.21443e8i	−0.247337	−	1.88223i
$491$	4.86836e7	+	8.43224e7i	0.411280	+	0.712359i	0.995030	−	0.0995751i	$-0.0317483\pi$
$491$	4.86836e7	+	8.43224e7i	0.411280	+	0.712359i	−0.583750	+	0.811934i	$0.698415\pi$
$492$	−2.59411e7	−	9.99177e6i	−0.217818	−	0.0838972i
$493$	−1.23761e8	−	7.14532e7i	−1.03286	−	0.596322i
$494$	3.05837e7	+	1.26769e7i	0.253693	+	0.105155i
$495$	5.80195e7	+	1.79365e8i	0.478364	+	1.47885i
$496$	84313.7	−	8.71340e7i	0.000690960	−	0.714073i
$497$	−2.91633e7	−	1.68374e7i	−0.237557	−	0.137154i
$498$	9.34239e7	+	5.08337e7i	0.756433	+	0.411589i
$499$	1.09120e8	−	6.30003e7i	0.878217	−	0.507039i	0.00814681	−	0.999967i	$-0.497407\pi$
$499$	1.09120e8	−	6.30003e7i	0.878217	−	0.507039i	0.870070	+	0.492928i	$0.164073\pi$
$500$	−1.14658e8	+	4.27084e8i	−0.917266	+	3.41667i
$501$	1.94609e7	−	1.83998e8i	0.154757	−	1.46319i
$502$	8.74829e7	−	6.70944e7i	0.691531	−	0.530365i
$503$		−	9.33109e7i		−	0.733210i	−0.930377	−	0.366605i	$-0.880520\pi$
$503$		−	9.33109e7i		−	0.733210i	0.930377	−	0.366605i	$-0.119480\pi$
$504$	3.83753e6	+	2.09434e7i	0.0299751	+	0.163590i
$505$	2.29494e8			1.78195
$506$	−3.29147e7	−	4.29168e7i	−0.254061	−	0.331265i
$507$	3.61193e7	+	8.12685e7i	0.277150	+	0.623589i
$508$	−3.20104e7	+	1.19234e8i	−0.244175	+	0.909512i
$509$	2.97666e7	+	5.15573e7i	0.225723	+	0.390964i	0.956536	−	0.291614i	$-0.0941922\pi$
$509$	2.97666e7	+	5.15573e7i	0.225723	+	0.390964i	−0.730813	+	0.682578i	$0.760859\pi$
$510$	−1.82011e8	−	2.97614e8i	−1.37211	−	2.24359i
$511$	1.36882e7	−	2.37087e7i	0.102585	−	0.177682i
$512$	−1.23889e8	−	5.16328e7i	−0.923044	−	0.384694i
$513$	−2.04529e7	+	6.25288e7i	−0.151496	+	0.463157i
$514$	3.41091e6	−	8.22903e6i	0.0251177	−	0.0605981i
$515$	2.88772e7	−	5.00167e7i	0.211413	−	0.366179i
$516$	−3.81017e7	−	2.42351e8i	−0.277329	−	1.76399i
$517$	1.25220e7	−	7.22957e6i	0.0906152	−	0.0523167i
$518$	1.62161e7	−	2.13090e6i	0.116670	−	0.0153311i
$519$	7.20634e6	+	1.62143e7i	0.0515481	+	0.115983i
$520$	−2.03051e7	+	1.53372e8i	−0.144409	+	1.09078i
$521$			1.83155e8i			1.29511i	0.762020	+	0.647554i	$0.224208\pi$
$521$			1.83155e8i			1.29511i	−0.762020	+	0.647554i	$0.775792\pi$
$522$	−1.13754e8	+	5.40411e7i	−0.799750	+	0.379938i
$523$		−	1.21735e8i		−	0.850965i	−0.904967	−	0.425483i	$-0.860104\pi$
$523$		−	1.21735e8i		−	0.850965i	0.904967	−	0.425483i	$-0.139896\pi$
$524$	1.22407e8	−	3.27353e7i	0.850769	−	0.227522i
$525$	−6.72968e7	−	7.11778e6i	−0.465068	−	0.0491888i
$526$	1.37534e8	−	1.80729e7i	0.945047	−	0.124185i
$527$	−1.21919e8	+	7.03899e7i	−0.832989	+	0.480927i
$528$	1.24380e7	−	1.16520e8i	0.0844984	−	0.791587i
$529$	−5.36628e7	+	9.29466e7i	−0.362498	+	0.627865i
$530$	−2.62085e8	−	1.08633e8i	−1.76041	−	0.729685i
$531$	−1.22974e8	+	1.36217e8i	−0.821356	+	0.909807i
$532$	8.63290e6	−	8.62455e6i	0.0573353	−	0.0572798i
$533$	9.95910e6	−	1.72497e7i	0.0657716	−	0.113920i
$534$	8.20959e7	−	2.07604e6i	0.539135	−	0.0136336i
$535$	−9.71593e7	−	1.68285e8i	−0.634488	−	1.09896i
$536$	1.12451e8	+	8.64161e7i	0.730243	+	0.561177i
$537$	1.04675e8	−	1.43875e8i	0.675962	−	0.929100i
$538$	−1.55373e8	+	1.19162e8i	−0.997764	+	0.765228i
$539$	−1.21211e8			−0.774065
$540$	−3.06974e8	−	1.68421e7i	−1.94949	−	0.106959i
$541$			2.63952e8i			1.66699i	0.552525	+	0.833496i	$0.313664\pi$
$541$			2.63952e8i			1.66699i	−0.552525	+	0.833496i	$0.686336\pi$
$542$	6.91963e7	−	5.30696e7i	0.434595	−	0.333309i
$543$	−1.17048e8	−	8.51577e7i	−0.731080	−	0.531893i
$544$	2.80448e7	+	2.15031e8i	0.174203	+	1.33568i
$545$	4.75517e8	−	2.74540e8i	2.93749	−	1.69596i
$546$	−1.52512e7	+	385671.i	−0.0936969	+	0.00236940i
$547$	−3.02067e7	−	1.74399e7i	−0.184562	−	0.106557i	0.404872	−	0.914373i	$-0.367316\pi$
$547$	−3.02067e7	−	1.74399e7i	−0.184562	−	0.106557i	−0.589434	+	0.807816i	$0.700649\pi$
$548$	8.12284e7	−	8.11499e7i	0.493590	−	0.493113i
$549$	−3.22831e7	+	1.50907e8i	−0.195100	+	0.911995i
$550$	3.44052e8	+	1.42609e8i	2.06793	+	0.857152i
$551$	6.25073e7	+	3.60886e7i	0.373659	+	0.215732i
$552$	8.46059e7	−	2.49343e7i	0.503018	−	0.148245i
$553$	2.36178e7	+	4.09073e7i	0.139658	+	0.241894i
$554$	−9.66446e7	+	1.26997e7i	−0.568393	+	0.0746904i
$555$	−2.48390e7	+	2.34847e8i	−0.145297	+	1.37374i
$556$	5.45758e7	+	2.04075e8i	0.317524	+	1.18731i
$557$	1.32047e8			0.764123			0.382062	−	0.924137i	$-0.375214\pi$
$557$	1.32047e8			0.764123			0.382062	+	0.924137i	$0.375214\pi$
$558$	−9.92598e6	+	1.23666e8i	−0.0571309	+	0.711784i
$559$	1.75781e8			1.00632
$560$	4.93573e7	+	2.85602e7i	0.281052	+	0.162628i
$561$	−1.73010e8	+	7.68931e7i	−0.979900	+	0.435510i
$562$	2.25282e8	−	2.96035e7i	1.26917	−	0.166776i
$563$	−1.09706e8	−	1.90016e8i	−0.614757	−	1.06479i	−0.990427	−	0.138037i	$-0.955921\pi$
$563$	−1.09706e8	−	1.90016e8i	−0.614757	−	1.06479i	0.375670	−	0.926753i	$-0.377413\pi$
$564$	3.66223e6	+	2.32941e7i	0.0204131	+	0.129840i
$565$	−3.65668e8	−	2.11118e8i	−2.02741	−	1.17052i
$566$	1.22160e7	−	2.94720e7i	0.0673723	−	0.162540i
$567$	−3.08985e6	−	3.01584e7i	−0.0169507	−	0.165447i
$568$	−2.79319e8	+	1.15460e8i	−1.52425	+	0.630069i
$569$	3.85613e6	+	2.22634e6i	0.0209322	+	0.0120852i	0.510430	−	0.859920i	$-0.329486\pi$
$569$	3.85613e6	+	2.22634e6i	0.0209322	+	0.0120852i	−0.489497	+	0.872005i	$0.662820\pi$
$570$	9.19276e7	+	1.50315e8i	0.496388	+	0.811666i
$571$	4.62830e6	−	2.67215e6i	0.0248607	−	0.0143533i	−0.487518	−	0.873113i	$-0.662098\pi$
$571$	4.62830e6	−	2.67215e6i	0.0248607	−	0.0143533i	0.512379	+	0.858760i	$0.328764\pi$
$572$	8.10908e7	+	2.17703e7i	0.433295	+	0.116326i
$573$	1.16212e8	−	5.16495e7i	0.617712	−	0.274538i
$574$	−4.46790e6	−	5.82560e6i	−0.0236248	−	0.0308039i
$575$			2.80335e8i			1.47460i
$576$	1.70034e8	+	8.72290e7i	0.889749	+	0.456450i
$577$	−5.80873e7			−0.302380			−0.151190	−	0.988505i	$-0.548311\pi$
$577$	−5.80873e7			−0.302380			−0.151190	+	0.988505i	$0.548311\pi$
$578$	1.24786e8	−	9.57039e7i	0.646224	−	0.495617i
$579$	−1.94075e7	−	2.05268e6i	−0.0999849	−	0.0105751i
$580$	−8.74543e7	+	3.25753e8i	−0.448226	+	1.66957i
$581$	1.40446e7	+	2.43259e7i	0.0716111	+	0.124034i
$582$	9.15449e7	+	4.98112e7i	0.464371	+	0.252673i
$583$	−7.69847e7	+	1.33341e8i	−0.388507	+	0.672913i
$584$	−9.38650e7	−	2.27076e8i	−0.471265	−	1.14007i
$585$	4.60815e7	−	2.15407e8i	0.230175	−	1.07595i
$586$	−2.02436e8	−	8.39091e7i	−1.00599	−	0.416981i
$587$	−6.45403e7	+	1.11787e8i	−0.319093	+	0.552685i	−0.980299	−	0.197519i	$-0.936711\pi$
$587$	−6.45403e7	+	1.11787e8i	−0.319093	+	0.552685i	0.661206	+	0.750204i	$0.270045\pi$
$588$	7.10503e7	−	1.84464e8i	0.349489	−	0.907360i
$589$	6.15771e7	−	3.55516e7i	0.301352	−	0.173985i
$590$	6.40349e7	+	4.87304e8i	0.311789	+	2.37271i
$591$	−1.59625e7	+	2.19402e7i	−0.0773282	+	0.106287i
$592$	7.35209e7	−	1.27058e8i	0.354361	−	0.612402i
$593$			1.17804e8i			0.564934i	0.959277	+	0.282467i	$0.0911527\pi$
$593$			1.17804e8i			0.564934i	−0.959277	+	0.282467i	$0.908847\pi$
$594$	−3.07677e7	+	1.63986e8i	−0.146803	+	0.782432i
$595$		−	9.21332e7i		−	0.437387i
$596$	−7.61904e7	+	2.03756e7i	−0.359883	+	0.0962437i
$597$	−2.00561e7	+	2.75668e7i	−0.0942589	+	0.129558i
$598$	8.23396e6	+	6.26603e7i	0.0385039	+	0.293014i
$599$	6.80007e7	−	3.92602e7i	0.316397	−	0.182672i	−0.333388	−	0.942790i	$-0.608192\pi$
$599$	6.80007e7	−	3.92602e7i	0.316397	−	0.182672i	0.649786	+	0.760118i	$0.274859\pi$
$600$	−4.18700e8	+	4.39999e8i	−1.93842	+	2.03703i
$601$	−6.14440e7	+	1.06424e8i	−0.283045	+	0.490249i	−0.972133	−	0.234429i	$-0.924678\pi$
$601$	−6.14440e7	+	1.06424e8i	−0.283045	+	0.490249i	0.689088	+	0.724678i	$0.258011\pi$
$602$	2.48089e7	−	5.98530e7i	0.113715	−	0.274345i
$603$	−1.49884e8	−	1.35312e8i	−0.683601	−	0.617142i
$604$	−8.74594e7	−	8.75441e7i	−0.396913	−	0.397298i
$605$	−7.91747e7	+	1.37135e8i	−0.357536	+	0.619271i
$606$	1.78414e8	+	9.70781e7i	0.801697	+	0.436218i
$607$	−5.11020e7	−	8.85113e7i	−0.228493	−	0.395761i	0.728869	−	0.684653i	$-0.240046\pi$
$607$	−5.11020e7	−	8.85113e7i	−0.228493	−	0.395761i	−0.957362	+	0.288893i	$0.906713\pi$
$608$	−1.41645e7	−	1.08605e8i	−0.0630215	−	0.483212i
$609$	−3.30756e7	−	3.49831e6i	−0.146439	−	0.0154884i
$610$	2.51525e8	+	3.27959e8i	1.10813	+	1.44487i
$611$	−1.68956e7			−0.0740711
$612$	−1.56058e7	−	3.08365e8i	−0.0680820	−	1.34527i
$613$		−	1.52425e8i		−	0.661721i	−0.943680	−	0.330861i	$-0.892661\pi$
$613$		−	1.52425e8i		−	0.661721i	0.943680	−	0.330861i	$-0.107339\pi$
$614$	1.05979e8	+	1.38183e8i	0.457839	+	0.596966i
$615$	9.68693e7	−	4.30530e7i	0.416448	−	0.185088i
$616$	1.88576e7	−	2.45388e7i	0.0806758	−	0.104981i
$617$	−1.46835e8	+	8.47753e7i	−0.625136	+	0.360923i	−0.778866	−	0.627190i	$-0.784205\pi$
$617$	−1.46835e8	+	8.47753e7i	−0.625136	+	0.360923i	0.153730	+	0.988113i	$0.450871\pi$
$618$	4.36074e7	−	2.66688e7i	0.184754	−	0.112990i
$619$	−2.35563e8	−	1.36002e8i	−0.993197	−	0.573422i	−0.0869684	−	0.996211i	$-0.527718\pi$
$619$	−2.35563e8	−	1.36002e8i	−0.993197	−	0.573422i	−0.906228	+	0.422789i	$0.861051\pi$
$620$	2.34836e8	+	2.35064e8i	0.985349	+	0.986303i
$621$	−1.22893e8	+	2.58694e7i	−0.513162	+	0.108022i
$622$	−1.33102e8	+	3.21117e8i	−0.553112	+	1.33442i
$623$	1.87827e7	+	1.08442e7i	0.0776772	+	0.0448470i
$624$	−8.06637e7	+	1.10646e8i	−0.331990	+	0.455388i
$625$	−4.99884e8	−	8.65824e8i	−2.04752	−	3.54642i
$626$	−3.06571e7	−	2.33300e8i	−0.124971	−	0.951024i
$627$	8.73813e7	−	3.88361e7i	0.354500	−	0.157555i
$628$	−1.16967e8	−	4.37373e8i	−0.472263	−	1.76593i
$629$	−2.37174e8			−0.953048
$630$	−6.68422e7	−	4.60923e7i	−0.267318	−	0.184335i
$631$	−2.32746e8			−0.926392			−0.463196	−	0.886256i	$-0.653297\pi$
$631$	−2.32746e8			−0.926392			−0.463196	+	0.886256i	$0.653297\pi$
$632$	4.20287e8	+	5.56422e7i	1.66493	+	0.220421i
$633$	3.90848e7	−	3.69536e8i	0.154098	−	1.45695i
$634$	1.87506e7	+	1.42691e8i	0.0735777	+	0.559925i
$635$	−2.35388e8	−	4.07704e8i	−0.919314	−	1.59230i
$636$	−1.57798e8	−	1.95319e8i	−0.613380	−	0.759228i
$637$	1.22660e8	+	7.08180e7i	0.474554	+	0.273984i
$638$	1.69098e8	+	7.00905e7i	0.651142	+	0.269896i
$639$	4.09453e8	−	1.32446e8i	1.56928	−	0.507617i
$640$	4.73186e8	−	1.95062e8i	1.80506	−	0.744102i
$641$	3.90283e7	+	2.25330e7i	0.148186	+	0.0855549i	0.572259	−	0.820073i	$-0.306067\pi$
$641$	3.90283e7	+	2.25330e7i	0.148186	+	0.0855549i	−0.424074	+	0.905628i	$0.639400\pi$
$642$	−4.34771e6	−	1.71928e8i	−0.0164307	−	0.649743i
$643$	7.25549e6	−	4.18896e6i	0.0272919	−	0.0157570i	−0.486292	−	0.873796i	$-0.661651\pi$
$643$	7.25549e6	−	4.18896e6i	0.0272919	−	0.0157570i	0.513584	+	0.858039i	$0.328318\pi$
$644$	2.24978e7	+	6.03994e6i	0.0842332	+	0.0226139i
$645$	7.56486e8	+	5.50377e8i	2.81917	+	2.05107i
$646$	−1.40414e8	+	1.07690e8i	−0.520851	+	0.399463i
$647$		−	1.65500e8i		−	0.611061i	−0.952182	−	0.305530i	$-0.901166\pi$
$647$		−	1.65500e8i		−	0.611061i	0.952182	−	0.305530i	$-0.0988338\pi$
$648$	−2.31524e8	−	1.42947e8i	−0.850886	−	0.525350i
$649$	2.66736e8			0.975771
$650$	−2.64846e8	−	3.45327e8i	−0.964390	−	1.25745i
$651$	−1.92762e7	+	2.64949e7i	−0.0698682	+	0.0960329i
$652$	−3.30599e8	−	8.87553e7i	−1.19278	−	0.320222i
$653$	−3.37546e7	−	5.84646e7i	−0.121225	−	0.209968i	0.799026	−	0.601297i	$-0.205349\pi$
$653$	−3.37546e7	−	5.84646e7i	−0.121225	−	0.209968i	−0.920251	+	0.391328i	$0.872016\pi$
$654$	4.85811e8	−	1.22852e7i	1.73674	−	0.0439186i
$655$	−2.41590e8	+	4.18446e8i	−0.859715	+	1.48907i
$656$	−6.58935e7	−	63760.7i	−0.233416	−	0.000225861i
$657$	1.07674e8	+	3.32870e8i	0.379676	+	1.17376i
$658$	−2.38456e6	+	5.75291e6i	−0.00837011	+	0.0201934i
$659$	−1.04575e8	+	1.81128e8i	−0.365401	+	0.632893i	−0.988840	−	0.148979i	$-0.952401\pi$
$659$	−1.04575e8	+	1.81128e8i	−0.365401	+	0.632893i	0.623439	+	0.781872i	$0.285735\pi$
$660$	2.80817e8	+	3.47589e8i	0.976769	+	1.20902i
$661$	2.63495e8	−	1.52129e8i	0.912365	−	0.526754i	0.0311737	−	0.999514i	$-0.490075\pi$
$661$	2.63495e8	−	1.52129e8i	0.912365	−	0.526754i	0.881191	+	0.472760i	$0.156742\pi$
$662$	1.58674e8	−	2.08507e7i	0.546929	−	0.0718699i
$663$	2.20003e8	+	2.32690e7i	0.754897	+	0.0798432i
$664$	2.49928e8	+	3.30882e7i	0.853710	+	0.113023i
$665$			4.65334e7i			0.158234i
$666$	−1.18653e8	+	1.72068e8i	−0.401658	+	0.582476i
$667$			1.37782e8i			0.464316i
$668$	−1.13307e8	−	4.23686e8i	−0.380125	−	1.42140i
$669$	−4.25076e6	−	9.56424e6i	−0.0141967	−	0.0319427i
$670$	−5.36194e8	+	7.04594e7i	−1.78278	+	0.234269i
$671$	1.94253e8	−	1.12152e8i	0.642982	−	0.371226i
$672$	2.62903e7	+	4.30820e7i	0.0866338	+	0.141967i
$673$	4.69112e7	−	8.12525e7i	0.153897	−	0.266558i	−0.778760	−	0.627322i	$-0.784151\pi$
$673$	4.69112e7	−	8.12525e7i	0.153897	−	0.266558i	0.932657	+	0.360764i	$0.117484\pi$
$674$	7.51792e7	+	3.11616e7i	0.245538	+	0.101775i
$675$	6.43810e8	−	5.77401e8i	2.09337	−	1.87744i
$676$	1.48990e8	+	1.49134e8i	0.482299	+	0.482766i
$677$	−1.67159e7	+	2.89529e7i	−0.0538722	+	0.0933094i	−0.891704	−	0.452619i	$-0.850490\pi$
$677$	−1.67159e7	+	2.89529e7i	−0.0538722	+	0.0933094i	0.837832	+	0.545929i	$0.183823\pi$
$678$	−1.94973e8	−	3.18810e8i	−0.625585	−	1.02292i
$679$	1.37621e7	+	2.38366e7i	0.0439618	+	0.0761440i
$680$	−6.55677e8	−	5.03875e8i	−2.08528	−	1.60249i
$681$	1.86998e7	+	4.20746e7i	0.0592100	+	0.133223i
$682$	1.43088e8	−	1.09740e8i	0.451075	−	0.345949i
$683$	−4.15206e7			−0.130317			−0.0651585	−	0.997875i	$-0.520755\pi$
$683$	−4.15206e7			−0.130317			−0.0651585	+	0.997875i	$0.520755\pi$
$684$	7.88197e6	+	1.55745e8i	0.0246301	+	0.486681i
$685$			4.37841e8i			1.36221i
$686$	8.40288e7	−	6.44452e7i	0.260289	−	0.199627i
$687$	1.91714e7	−	1.81261e8i	0.0591268	−	0.559029i
$688$	−2.90272e8	−	5.03891e8i	−0.891332	−	1.54729i
$689$	1.55810e8	−	8.99569e7i	0.476362	−	0.275028i
$690$	−1.60757e8	+	2.95444e8i	−0.489352	+	0.899350i
$691$	5.44107e7	+	3.14140e7i	0.164911	+	0.0952115i	0.580184	−	0.814485i	$-0.302981\pi$
$691$	5.44107e7	+	3.14140e7i	0.164911	+	0.0952115i	−0.415273	+	0.909697i	$0.636314\pi$
$692$	2.97257e7	+	2.97545e7i	0.0897044	+	0.0897913i
$693$	−2.95276e7	+	3.27074e7i	−0.0887213	+	0.0982756i
$694$	3.29270e8	+	1.36482e8i	0.985086	+	0.408315i
$695$	−6.97626e8	−	4.02774e8i	−2.07811	−	1.19980i
$696$	−2.05786e8	+	2.16254e8i	−0.610363	+	0.641412i
$697$	5.32311e7	+	9.21990e7i	0.157205	+	0.272288i
$698$	9.07523e7	−	1.19254e7i	0.266865	−	0.0350677i
$699$	−2.15378e8	−	1.56697e8i	−0.630623	−	0.458806i
$700$	−1.54962e8	+	4.14417e7i	−0.451785	+	0.120821i
$701$	2.32346e7			0.0674497			0.0337249	−	0.999431i	$-0.489263\pi$
$701$	2.32346e7			0.0674497			0.0337249	+	0.999431i	$0.489263\pi$
$702$	1.26944e8	−	1.47970e8i	0.366946	−	0.427722i
$703$	1.19788e8			0.344785
$704$	−7.15013e7	−	2.68404e8i	−0.204925	−	0.769257i
$705$	−7.27114e7	−	5.29008e7i	−0.207508	−	0.150971i
$706$	1.00451e8	−	1.32000e7i	0.285458	−	0.0375110i
$707$	2.68212e7	+	4.64557e7i	0.0758962	+	0.131456i
$708$	−1.56352e8	+	4.05929e8i	−0.440560	+	1.14380i
$709$	2.63366e8	+	1.52055e8i	0.738961	+	0.426639i	0.821691	−	0.569933i	$-0.193031\pi$
$709$	2.63366e8	+	1.52055e8i	0.738961	+	0.426639i	−0.0827305	+	0.996572i	$0.526364\pi$
$710$	4.41318e8	−	1.06471e9i	1.23304	−	2.97478i
$711$	−5.90282e8	−	1.26277e8i	−1.64229	−	0.351331i
$712$	1.79896e8	−	7.43626e7i	0.498405	−	0.206022i
$713$	1.17547e8	+	6.78657e7i	0.324297	+	0.187233i
$714$	3.89733e7	−	7.16265e7i	0.107071	−	0.196779i
$715$	−2.77280e8	+	1.60087e8i	−0.758577	+	0.437965i
$716$	1.09353e8	−	4.07322e8i	0.297914	−	1.10968i
$717$	−1.04893e7	+	9.91738e7i	−0.0284570	+	0.269054i
$718$	−2.06474e8	−	2.69217e8i	−0.557818	−	0.727326i
$719$			5.00247e8i			1.34585i	0.739709	+	0.672927i	$0.234963\pi$
$719$			5.00247e8i			1.34585i	−0.739709	+	0.672927i	$0.765037\pi$
$720$	−6.93581e8	+	2.23612e8i	−1.85823	+	0.599098i
$721$	1.34996e7			0.0360177
$722$	−2.27729e8	+	1.74655e8i	−0.605072	+	0.464055i
$723$	4.84480e7	+	1.09008e8i	0.128192	+	0.288433i
$724$	−3.31373e8	−	8.89630e7i	−0.873175	−	0.234420i
$725$	−4.74389e8	−	8.21665e8i	−1.24486	−	2.15616i
$726$	−1.19562e8	+	7.31199e7i	−0.312451	+	0.191085i
$727$	−4.94691e7	+	8.56830e7i	−0.128745	+	0.222993i	−0.923191	−	0.384342i	$-0.874428\pi$
$727$	−4.94691e7	+	8.56830e7i	−0.128745	+	0.222993i	0.794446	+	0.607335i	$0.207762\pi$
$728$	−3.34198e7	+	1.38145e7i	−0.0866183	+	0.0358048i
$729$	3.12532e8	+	2.28951e8i	0.806699	+	0.590962i
$730$	8.65566e8	+	3.58775e8i	2.22501	+	0.922259i
$731$	−4.69771e8	+	8.13668e8i	−1.20264	+	2.08303i
$732$	5.68119e7	+	3.61360e8i	0.144846	+	0.921313i
$733$	2.76067e8	−	1.59388e8i	0.700976	−	0.404709i	−0.106735	−	0.994288i	$-0.534040\pi$
$733$	2.76067e8	−	1.59388e8i	0.700976	−	0.404709i	0.807711	+	0.589579i	$0.200706\pi$
$734$	3.21527e7	+	2.44681e8i	0.0813073	+	0.618747i
$735$	3.06144e8	+	6.88826e8i	0.771018	+	1.73479i
$736$	1.66024e8	−	1.27076e8i	0.416426	−	0.318736i
$737$			2.93497e8i			0.733165i
$738$	9.35203e7	+	7.50635e6i	0.232668	+	0.0186750i
$739$		−	4.34664e8i		−	1.07701i	−0.842622	−	0.538505i	$-0.818989\pi$
$739$		−	4.34664e8i		−	1.07701i	0.842622	−	0.538505i	$-0.181011\pi$
$740$	1.44620e8	+	5.40775e8i	0.356889	+	1.33451i
$741$	−1.11116e8	−	1.17524e7i	−0.273100	−	0.0288850i
$742$	−8.63986e6	−	6.57491e7i	−0.0211492	−	0.160945i
$743$	−1.84463e8	+	1.06500e8i	−0.449720	+	0.259646i	−0.707712	−	0.706501i	$-0.750273\pi$
$743$	−1.84463e8	+	1.06500e8i	−0.449720	+	0.259646i	0.257992	+	0.966147i	$0.416939\pi$
$744$	8.31329e7	+	2.82082e8i	0.201862	+	0.684947i
$745$	1.50374e8	−	2.60455e8i	0.363667	−	0.629890i
$746$	8.88165e7	−	2.14275e8i	0.213933	−	0.516126i
$747$	−3.51017e8	−	7.50921e7i	−0.842105	−	0.180149i
$748$	−3.17486e8	+	3.17179e8i	−0.758613	+	0.757879i
$749$	2.27103e7	−	3.93353e7i	0.0540477	−	0.0936133i
$750$	−3.77289e7	−	1.49197e9i	−0.0894315	−	3.53653i
$751$	2.90660e8	+	5.03438e8i	0.686223	+	1.18857i	0.973051	+	0.230591i	$0.0740661\pi$
$751$	2.90660e8	+	5.03438e8i	0.686223	+	1.18857i	−0.286827	+	0.957982i	$0.592601\pi$
$752$	2.79001e7	+	4.84326e7i	0.0656074	+	0.113890i
$753$	−2.18907e8	+	3.00885e8i	−0.512714	+	0.704718i
$754$	−1.30169e8	−	1.69724e8i	−0.303663	−	0.395940i
$755$	4.71883e8			1.09646
$756$	−3.24671e7	−	6.41082e7i	−0.0751413	−	0.148371i
$757$		−	2.79393e8i		−	0.644063i	−0.946729	−	0.322031i	$-0.895634\pi$
$757$		−	2.79393e8i		−	0.644063i	0.946729	−	0.322031i	$-0.104366\pi$
$758$	−2.00676e8	−	2.61658e8i	−0.460775	−	0.600795i
$759$	1.47606e8	+	1.07390e8i	0.337582	+	0.245606i
$760$	3.31160e8	+	2.54490e8i	0.754393	+	0.579736i
$761$	−4.94388e8	+	2.85435e8i	−1.12180	+	0.647669i	−0.941859	−	0.336009i	$-0.890923\pi$
$761$	−4.94388e8	+	2.85435e8i	−1.12180	+	0.647669i	−0.179937	+	0.983678i	$0.557589\pi$
$762$	−1.05332e7	−	4.16531e8i	−0.0238065	−	0.941417i
$763$	1.11149e8	+	6.41717e7i	0.250225	+	0.144467i
$764$	2.13257e8	−	2.13051e8i	0.478216	−	0.477754i
$765$	8.73943e8	+	7.88979e8i	1.95209	+	1.76231i
$766$	−1.30782e8	+	3.15521e8i	−0.290980	+	0.702008i
$767$	−2.69925e8	−	1.55841e8i	−0.598214	−	0.345379i
$768$	4.50379e8	+	4.85168e7i	0.994248	+	0.107105i
$769$	−1.32322e8	−	2.29188e8i	−0.290973	−	0.503979i	0.683067	−	0.730355i	$-0.260645\pi$
$769$	−1.32322e8	−	2.29188e8i	−0.290973	−	0.503979i	−0.974040	+	0.226376i	$0.927312\pi$
$770$	1.53755e7	+	1.17007e8i	0.0336789	+	0.256295i
$771$	−3.16217e6	+	2.98975e7i	−0.00689957	+	0.0652336i
$772$	−4.46892e7	+	1.19513e7i	−0.0971293	+	0.0259754i
$773$	7.45128e8			1.61321			0.806607	−	0.591088i	$-0.201301\pi$
$773$	7.45128e8			1.61321			0.806607	+	0.591088i	$0.201301\pi$
$774$	3.55295e8	+	7.47877e8i	0.766242	+	1.61290i
$775$	−9.34659e8			−2.00793
$776$	2.44901e8	+	3.24227e7i	0.524089	+	0.0693847i
$777$	−5.04423e7	+	2.24188e7i	−0.107531	+	0.0477913i
$778$	−1.54913e7	−	1.17889e8i	−0.0328965	−	0.250341i
$779$	−2.68852e7	−	4.65666e7i	−0.0568724	−	0.0985059i
$780$	−8.10944e7	−	5.15813e8i	−0.170886	−	1.08695i
$781$	−5.41693e8	−	3.12747e8i	−1.13710	−	0.656507i
$782$	−3.12052e8	−	1.29345e8i	−0.652540	−	0.270476i
$783$	3.16425e8	−	2.83786e8i	0.659152	−	0.591160i
$784$	453395.	−	4.68561e8i	0.000940868	−	0.972339i
$785$	1.49515e9	+	8.63226e8i	3.09084	+	1.78450i
$786$	−3.64824e8	+	2.23115e8i	−0.751305	+	0.459473i
$787$	−4.37871e8	+	2.52805e8i	−0.898301	+	0.518635i	−0.876649	−	0.481131i	$-0.840226\pi$
$787$	−4.37871e8	+	2.52805e8i	−0.898301	+	0.518635i	−0.0216526	+	0.999766i	$0.506893\pi$
$788$	−1.66758e7	+	6.21146e7i	−0.0340806	+	0.126945i
$789$	−4.27818e8	+	1.90141e8i	−0.871019	+	0.387119i
$790$	−1.28283e9	+	9.83858e8i	−2.60188	+	1.99550i
$791$		−	9.86947e7i		−	0.199418i
$792$	7.12801e7	+	3.89013e8i	0.143480	+	0.783048i
$793$	−2.62099e8			−0.525589
$794$	3.36744e8	+	4.39073e8i	0.672725	+	0.877152i
$795$	9.52199e8	+	1.00711e8i	1.89508	+	0.200436i
$796$	−2.09523e7	+	7.80439e7i	−0.0415424	+	0.154739i
$797$	2.76754e8	+	4.79351e8i	0.546661	+	0.946845i	0.998500	+	0.0547458i	$0.0174348\pi$
$797$	2.76754e8	+	4.79351e8i	0.546661	+	0.946845i	−0.451839	+	0.892100i	$0.649232\pi$
$798$	−1.96841e7	+	3.61761e7i	−0.0387353	+	0.0711891i
$799$	4.51531e7	−	7.82075e7i	0.0885213	−	0.153323i
$800$	−5.52562e8	+	1.32945e9i	−1.07922	+	2.59659i
$801$	−2.63709e8	+	8.53022e7i	−0.513130	+	0.165983i
$802$	−2.53390e8	+	6.11319e8i	−0.491209	+	1.18507i
$803$	2.54251e8	−	4.40376e8i	0.491039	−	0.850505i
$804$	−4.46655e8	−	1.72039e8i	−0.859417	−	0.331023i
$805$	−7.69284e7	+	4.44146e7i	−0.147468	+	0.0851409i
$806$	−2.08914e8	+	2.74526e7i	−0.398990	+	0.0524299i
$807$	3.88787e8	−	5.34382e8i	0.739760	−	1.01679i
$808$	4.77293e8	+	6.31892e7i	0.904796	+	0.119787i
$809$			2.63924e8i			0.498463i	0.968444	+	0.249232i	$0.0801781\pi$
$809$			2.63924e8i			0.498463i	−0.968444	+	0.249232i	$0.919822\pi$
$810$	1.00962e9	−	2.39331e8i	1.89977	−	0.450344i
$811$		−	6.56970e8i		−	1.23164i	−0.787888	−	0.615818i	$-0.788825\pi$
$811$		−	6.56970e8i		−	1.23164i	0.787888	−	0.615818i	$-0.211175\pi$
$812$	−7.61622e7	+	2.03681e7i	−0.142256	+	0.0380437i
$813$	−1.73149e8	+	2.37991e8i	−0.322216	+	0.442882i
$814$	3.01206e8	−	3.95804e7i	0.558458	−	0.0733849i
$815$	1.13044e9	−	6.52660e8i	2.08821	−	1.20563i
$816$	−2.96595e8	−	6.69083e8i	−0.545874	−	1.23143i
$817$	2.37265e8	−	4.10956e8i	0.435079	−	0.753579i
$818$	−8.56019e8	−	3.54817e8i	−1.56395	−	0.648254i
$819$	4.89899e7	−	1.58468e7i	0.0891774	−	0.0288463i
$820$	1.77763e8	−	1.77591e8i	0.322403	−	0.322091i
$821$	2.66676e8	−	4.61896e8i	0.481896	−	0.834669i	−0.517888	−	0.855449i	$-0.673281\pi$
$821$	2.66676e8	−	4.61896e8i	0.481896	−	0.834669i	0.999784	+	0.0207795i	$0.00661479\pi$
$822$	−1.85211e8	+	3.40387e8i	−0.333466	+	0.612856i
$823$	1.74595e8	+	3.02407e8i	0.313207	+	0.542490i	0.979055	−	0.203597i	$-0.0652634\pi$
$823$	1.74595e8	+	3.02407e8i	0.313207	+	0.542490i	−0.665848	+	0.746088i	$0.731930\pi$
$824$	7.38294e7	−	9.60719e7i	0.131962	−	0.171717i
$825$	−1.25000e9	−	1.32209e8i	−2.22612	−	0.235450i
$826$	−9.11597e7	+	6.99143e7i	−0.161757	+	0.124058i
$827$	−7.69277e7			−0.136009			−0.0680043	−	0.997685i	$-0.521663\pi$
$827$	−7.69277e7			−0.136009			−0.0680043	+	0.997685i	$0.521663\pi$
$828$	−2.49952e8	+	1.61684e8i	−0.440317	+	0.284823i
$829$		−	1.06728e8i		−	0.187333i	−0.995604	−	0.0936666i	$-0.970141\pi$
$829$		−	1.06728e8i		−	0.187333i	0.995604	−	0.0936666i	$-0.0298588\pi$
$830$	−7.62848e8	+	5.85060e8i	−1.33415	+	1.02321i
$831$	3.00626e8	−	1.33611e8i	0.523869	−	0.232830i
$832$	−8.44596e7	+	3.13387e8i	−0.146649	+	0.544141i
$833$	−6.55616e8	+	3.78520e8i	−1.13427	+	0.654869i
$834$	−3.71973e8	−	6.08229e8i	−0.641229	−	1.04850i
$835$	1.44836e9	+	8.36214e8i	2.48782	+	1.43634i
$836$	1.60352e8	−	1.60196e8i	0.274444	−	0.274179i
$837$	−8.62503e7	−	4.09736e8i	−0.147090	−	0.698759i
$838$	−1.03382e9	−	4.28515e8i	−1.75676	−	0.728173i
$839$	−1.00133e7	−	5.78120e6i	−0.0169548	−	0.00978886i	0.491499	−	0.870878i	$-0.336449\pi$
$839$	−1.00133e7	−	5.78120e6i	−0.0169548	−	0.00978886i	−0.508453	+	0.861089i	$0.669783\pi$
$840$	−1.87079e8	−	4.51870e7i	−0.315636	−	0.0762387i
$841$	6.42551e7	+	1.11293e8i	0.108024	+	0.187103i
$842$	−1.09506e9	+	1.43897e8i	−1.83443	+	0.241055i
$843$	−7.00770e8	+	3.11453e8i	−1.16975	+	0.519887i
$844$	−2.27562e8	−	8.50921e8i	−0.378506	−	1.41534i
$845$	−8.03868e8			−1.33234
$846$	−3.41500e7	−	7.18839e7i	−0.0564000	−	0.118719i
$847$	−3.70130e7			−0.0609122
$848$	−5.15163e8	−	2.98095e8i	−0.844806	−	0.488840i
$849$	−1.13252e7	+	1.07077e8i	−0.0185064	+	0.174974i
$850$	2.30627e9	−	3.03059e8i	3.75538	−	0.493481i
$851$	1.14334e8	+	1.98033e8i	0.185519	+	0.321328i
$852$	7.93473e8	−	6.41046e8i	1.28296	−	1.03650i
$853$	−6.29442e8	−	3.63408e8i	−1.01416	−	0.585528i	−0.101756	−	0.994809i	$-0.532446\pi$
$853$	−6.29442e8	−	3.63408e8i	−1.01416	−	0.585528i	−0.912408	+	0.409281i	$0.865780\pi$
$854$	−3.69916e7	+	8.92445e7i	−0.0593922	+	0.143287i
$855$	−4.41399e8	−	3.98487e8i	−0.706209	−	0.637552i
$856$	−1.55733e8	−	3.76745e8i	−0.248289	−	0.600656i
$857$	1.41583e8	+	8.17430e7i	0.224941	+	0.129870i	0.608236	−	0.793756i	$-0.291877\pi$
$857$	1.41583e8	+	8.17430e7i	0.224941	+	0.129870i	−0.383295	+	0.923626i	$0.625211\pi$
$858$	−2.83282e8	+	7.16363e6i	−0.448495	+	0.0113415i
$859$	−5.34155e7	+	3.08394e7i	−0.0842728	+	0.0486549i	−0.541544	−	0.840672i	$-0.682160\pi$
$859$	−5.34155e7	+	3.08394e7i	−0.0842728	+	0.0486549i	0.457271	+	0.889327i	$0.348827\pi$
$860$	2.14168e9	+	5.74971e8i	3.36712	+	0.903963i
$861$	2.00363e7	+	1.45773e7i	0.0313913	+	0.0228385i
$862$	1.84726e8	+	2.40860e8i	0.288407	+	0.376048i
$863$			3.22243e8i			0.501361i	0.968070	+	0.250680i	$0.0806543\pi$
$863$			3.22243e8i			0.501361i	−0.968070	+	0.250680i	$0.919346\pi$
$864$	−6.33796e8	−	1.19550e8i	−0.982671	−	0.185357i
$865$	−1.60384e8			−0.247806
$866$	7.07807e8	−	5.42847e8i	1.08984	−	0.835841i
$867$	−3.12251e8	+	4.29184e8i	−0.479122	+	0.658547i
$868$	−2.01376e7	+	7.50094e7i	−0.0307928	+	0.114698i
$869$	4.38689e8	+	7.59831e8i	0.668493	+	1.15786i
$870$	−2.87773e7	−	1.13799e9i	−0.0437011	−	1.72814i
$871$	1.71476e8	−	2.97006e8i	0.259508	−	0.449480i
$872$	1.06456e9	−	4.40049e8i	1.60553	−	0.663669i
$873$	−3.43957e8	−	7.35817e7i	−0.516965	−	0.110593i
$874$	1.57607e8	+	6.53276e7i	0.236070	+	0.0978504i
$875$	1.97077e8	−	3.41348e8i	0.294179	−	0.509534i
$876$	5.21146e8	+	6.45063e8i	0.775260	+	0.959599i
$877$	−3.07278e7	+	1.77407e7i	−0.0455547	+	0.0263010i	−0.522604	−	0.852575i	$-0.675040\pi$
$877$	−3.07278e7	+	1.77407e7i	−0.0455547	+	0.0263010i	0.477050	+	0.878876i	$0.341706\pi$
$878$	1.00084e8	+	7.61639e8i	0.147871	+	1.12529i
$879$	7.35485e8	+	7.77901e7i	1.08295	+	0.114540i
$880$	9.16785e8	+	5.30490e8i	1.34530	+	0.778447i
$881$		−	1.12082e9i		−	1.63911i	−0.573003	−	0.819553i	$-0.694222\pi$
$881$		−	1.12082e9i		−	1.63911i	0.573003	−	0.819553i	$-0.305778\pi$
$882$	−5.33767e7	+	6.65012e8i	−0.0777940	+	0.969223i
$883$		−	5.27118e8i		−	0.765642i	−0.923822	−	0.382821i	$-0.874953\pi$
$883$		−	5.27118e8i		−	0.765642i	0.923822	−	0.382821i	$-0.125047\pi$
$884$	5.06594e8	−	1.35479e8i	0.733337	−	0.196117i
$885$	−6.73698e8	−	1.51582e9i	−0.971930	−	2.18685i
$886$	5.84456e7	+	4.44770e8i	0.0840331	+	0.639490i
$887$	−1.07145e9	+	6.18602e8i	−1.53533	+	0.886421i	−0.536224	+	0.844076i	$0.680150\pi$
$887$	−1.07145e9	+	6.18602e8i	−1.53533	+	0.886421i	−0.999103	+	0.0423458i	$0.986517\pi$
$888$	−1.16323e8	+	4.81587e8i	−0.166121	+	0.687758i
$889$	5.50203e7	−	9.52979e7i	0.0783100	−	0.135637i
$890$	−2.84232e8	+	6.85727e8i	−0.403183	+	0.972705i
$891$	−5.73924e7	−	5.60176e8i	−0.0811374	−	0.791939i
$892$	−1.75341e7	−	1.75511e7i	−0.0247053	−	0.0247292i
$893$	−2.28053e7	+	3.95000e7i	−0.0320244	+	0.0554680i
$894$	2.27080e8	−	1.38874e8i	0.317809	−	0.194361i
$895$	8.04125e8	+	1.39279e9i	1.12164	+	1.94274i
$896$	9.47877e7	+	7.29885e7i	0.131773	+	0.101468i
$897$	−8.66277e7	−	1.94913e8i	−0.120027	−	0.270062i
$898$	−6.98638e7	−	9.10939e7i	−0.0964769	−	0.125794i
$899$	−4.59374e8			−0.632248
$900$	9.33912e8	−	1.82480e9i	1.28109	−	2.50316i
$901$			9.61634e8i			1.31473i
$902$	−8.29889e7	−	1.08207e8i	−0.113084	−	0.147448i
$903$	−2.29997e7	+	2.17456e8i	−0.0312363	+	0.295331i
$904$	−7.02373e8	−	5.39760e8i	−0.950742	−	0.730626i
$905$	1.13309e9	−	6.54188e8i	1.52868	−	0.882586i
$906$	3.66853e8	+	1.99611e8i	0.493296	+	0.268411i
$907$	1.02963e9	+	5.94459e8i	1.37994	+	0.796709i	0.992152	−	0.125039i	$-0.0399056\pi$
$907$	1.02963e9	+	5.94459e8i	1.37994	+	0.796709i	0.387789	+	0.921748i	$0.373239\pi$
$908$	7.71355e7	+	7.72102e7i	0.103038	+	0.103138i
$909$	−6.70345e8	−	1.43405e8i	−0.892497	−	0.190929i
$910$	5.28024e7	−	1.27389e8i	0.0700696	−	0.169047i
$911$	−1.08577e9	−	6.26870e8i	−1.43609	−	0.829130i	−0.438519	−	0.898722i	$-0.644497\pi$
$911$	−1.08577e9	−	6.26870e8i	−1.43609	−	0.829130i	−0.997576	+	0.0695923i	$0.977830\pi$
$912$	1.49800e8	+	3.37931e8i	0.197482	+	0.445496i
$913$	2.60870e8	+	4.51841e8i	0.342778	+	0.593708i
$914$	−1.07016e8	−	8.14392e8i	−0.140156	−	1.06658i
$915$	−1.12797e9	−	8.20646e8i	−1.47242	−	1.07125i
$916$	−1.11621e8	−	4.17384e8i	−0.145232	−	0.543063i
$917$	−1.12940e8			−0.146467
$918$	3.45678e8	+	9.83058e8i	0.446831	+	1.27072i
$919$	3.67605e8			0.473625			0.236813	−	0.971555i	$-0.423897\pi$
$919$	3.67605e8			0.473625			0.236813	+	0.971555i	$0.423897\pi$
$920$	−1.04638e8	+	7.90373e8i	−0.134378	+	1.01501i
$921$	−4.75261e8	−	3.45774e8i	−0.608350	−	0.442602i
$922$	−1.50145e8	−	1.14260e9i	−0.191566	−	1.45781i
$923$	3.65446e8	+	6.32970e8i	0.464748	+	0.804967i
$924$	−3.75420e7	+	9.74682e7i	−0.0475885	+	0.123551i
$925$	−1.36367e9	−	7.87316e8i	−1.72300	−	0.994773i
$926$	−1.57569e8	−	6.53118e7i	−0.198444	−	0.0822543i
$927$	−1.15604e8	+	1.28053e8i	−0.145122	+	0.160750i
$928$	−2.71578e8	+	6.53411e8i	−0.339821	+	0.817602i
$929$	−8.98791e8	−	5.18917e8i	−1.12101	−	0.647218i	−0.179355	−	0.983784i	$-0.557401\pi$
$929$	−8.98791e8	−	5.18917e8i	−1.12101	−	0.647218i	−0.941660	+	0.336566i	$0.890734\pi$
$930$	−9.85033e8	−	5.35975e8i	−1.22462	−	0.666339i
$931$	3.31130e8	−	1.91178e8i	0.410345	−	0.236913i
$932$	−6.09754e8	−	1.63699e8i	−0.753194	−	0.202208i
$933$	1.23396e8	−	1.16667e9i	0.151934	−	1.43650i
$934$	5.92282e8	−	4.54246e8i	0.726922	−	0.557507i
$935$		−	1.71133e9i		−	2.09362i
$936$	1.55149e8	−	4.35308e8i	0.189200	−	0.530847i
$937$	8.80462e8			1.07027			0.535133	−	0.844768i	$-0.320261\pi$
$937$	8.80462e8			1.07027			0.535133	+	0.844768i	$0.320261\pi$
$938$	−7.69286e7	−	1.00306e8i	−0.0932136	−	0.121539i
$939$	3.22537e8	+	7.25709e8i	0.389567	+	0.876528i
$940$	−2.05852e8	−	5.52647e7i	−0.247840	−	0.0665371i
$941$	2.29124e7	+	3.96855e7i	0.0274981	+	0.0476280i	0.879447	−	0.475997i	$-0.157913\pi$
$941$	2.29124e7	+	3.96855e7i	0.0274981	+	0.0476280i	−0.851949	+	0.523625i	$0.824579\pi$
$942$	7.97212e8	+	1.30356e9i	0.953721	+	1.55947i
$943$	5.13222e7	−	8.88927e7i	0.0612027	−	0.106006i
$944$	−997735.	+	1.03111e9i	−0.00118604	+	1.22571i
$945$	2.60449e8	+	8.51916e7i	0.308622	+	0.100949i
$946$	4.60812e8	−	1.11174e9i	0.544315	−	1.31319i
$947$	−7.67440e8	+	1.32924e9i	−0.903638	+	1.56515i	−0.0809025	+	0.996722i	$0.525780\pi$
$947$	−7.67440e8	+	1.32924e9i	−0.903638	+	1.56515i	−0.822735	+	0.568425i	$0.807553\pi$
$948$	−1.41348e9	+	2.22223e8i	−1.65907	+	0.260834i
$949$	−5.14581e8	+	2.97093e8i	−0.602081	+	0.347612i
$950$	−1.16482e9	+	1.53065e8i	−1.35859	+	0.178527i
$951$	−1.97271e8	−	4.43860e8i	−0.229362	−	0.516065i
$952$	2.53681e7	−	1.91615e8i	0.0294021	−	0.222085i
$953$		−	1.33729e8i		−	0.154507i	−0.997011	−	0.0772534i	$-0.975385\pi$
$953$		−	1.33729e8i		−	0.154507i	0.997011	−	0.0772534i	$-0.0246150\pi$
$954$	6.97660e8	+	4.81085e8i	0.803524	+	0.554086i
$955$			1.14951e9i			1.31978i
$956$	6.10717e7	+	2.28365e8i	0.0698982	+	0.261370i
$957$	−6.14362e8	−	6.49792e7i	−0.700952	−	0.0741376i
$958$	−6.44390e8	+	8.46770e7i	−0.732913	+	0.0963095i
$959$	−8.86308e7	+	5.11710e7i	−0.100491	+	0.0580187i
$960$	−1.34471e9	+	1.08424e9i	−1.51990	+	1.22550i
$961$	2.17483e8	−	3.76691e8i	0.245050	−	0.424439i
$962$	−3.27931e8	−	1.35927e8i	−0.368348	−	0.152679i
$963$	1.78643e8	+	5.52268e8i	0.200035	+	0.618402i
$964$	1.99845e8	+	2.00039e8i	0.223081	+	0.223297i
$965$	8.82013e7	−	1.52769e8i	0.0981506	−	0.170002i
$966$	−7.85938e7	+	1.98748e6i	−0.0871880	+	0.00220481i
$967$	−6.63153e8	−	1.14861e9i	−0.733389	−	1.27027i	−0.955427	−	0.295228i	$-0.904604\pi$
$967$	−6.63153e8	−	1.14861e9i	−0.733389	−	1.27027i	0.222038	−	0.975038i	$-0.428729\pi$
$968$	−2.02424e8	+	2.63407e8i	−0.223170	+	0.290404i
$969$	3.51356e8	−	4.82935e8i	0.386168	−	0.530783i
$970$	−7.47504e8	+	5.73293e8i	−0.819027	+	0.628147i
$971$	3.79723e8			0.414772			0.207386	−	0.978259i	$-0.433504\pi$
$971$	3.79723e8			0.414772			0.207386	+	0.978259i	$0.433504\pi$
$972$	8.86138e8	+	2.41016e8i	0.964946	+	0.262450i
$973$		−	1.88291e8i		−	0.204405i
$974$	5.97497e8	−	4.58246e8i	0.646634	−	0.495931i
$975$	1.18770e9	+	8.64105e8i	1.28143	+	0.932294i
$976$	4.32813e8	+	7.51332e8i	0.465533	+	0.808132i
$977$	−1.04749e8	+	6.04768e7i	−0.112322	+	0.0648493i	−0.555109	−	0.831778i	$-0.687323\pi$
$977$	−1.04749e8	+	6.04768e7i	−0.112322	+	0.0648493i	0.442786	+	0.896627i	$0.353990\pi$
$978$	1.15491e9	−	2.92054e7i	1.23462	−	0.0312210i
$979$	3.48879e8	+	2.01425e8i	0.371814	+	0.214667i
$980$	1.26283e9	+	1.26405e9i	1.34173	+	1.34303i
$981$	−1.56053e9	+	5.04785e8i	−1.65297	+	0.534687i
$982$	−7.19572e8	−	2.98261e8i	−0.759871	−	0.314964i
$983$	−9.70647e8	−	5.60403e8i	−1.02188	−	0.589984i	−0.107233	−	0.994234i	$-0.534199\pi$
$983$	−9.70647e8	−	5.60403e8i	−1.02188	−	0.589984i	−0.914649	+	0.404250i	$0.867533\pi$
$984$	2.13320e8	−	6.28678e7i	0.223896	−	0.0659847i
$985$	−1.22625e8	−	2.12393e8i	−0.128313	−	0.222244i
$986$	1.13351e9	−	1.48950e8i	1.18248	−	0.155385i
$987$	2.21067e6	−	2.09013e7i	0.00229918	−	0.0217381i
$988$	−2.55863e8	+	6.84258e7i	−0.265300	+	0.0709494i
$989$	9.05850e8			0.936412
$990$	−1.24156e9	−	8.56141e8i	−1.27956	−	0.882347i
$991$	−5.88652e8			−0.604836			−0.302418	−	0.953175i	$-0.597794\pi$
$991$	−5.88652e8			−0.604836			−0.302418	+	0.953175i	$0.597794\pi$
$992$	4.23681e8	+	5.53537e8i	0.434015	+	0.567038i
$993$	−4.93575e8	+	2.19366e8i	−0.504086	+	0.224038i
$994$	2.67103e8	−	3.50990e7i	0.271969	−	0.0357385i
$995$	−1.54072e8	−	2.66861e8i	−0.156407	−	0.270904i
$996$	−8.40542e8	+	1.32147e8i	−0.850710	+	0.133746i
$997$	8.59345e8	+	4.96143e8i	0.867126	+	0.500635i	0.866392	−	0.499364i	$-0.166433\pi$
$997$	8.59345e8	+	4.96143e8i	0.867126	+	0.500635i	0.000733751		1.00000i	$0.499766\pi$
$998$	−3.85972e8	+	9.31182e8i	−0.388297	+	0.936792i
$999$	2.19304e8	−	6.70460e8i	0.219963	−	0.672476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.j.a.29.17	yes	140
8.5	even	2	inner	72.7.j.a.29.39	yes	140
9.5	odd	6	inner	72.7.j.a.5.39	yes	140
72.5	odd	6	inner	72.7.j.a.5.17	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.j.a.5.17	✓	140	72.5	odd	6	inner
72.7.j.a.5.39	yes	140	9.5	odd	6	inner
72.7.j.a.29.17	yes	140	1.1	even	1	trivial
72.7.j.a.29.39	yes	140	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.34800 + 4.86856i) q^{2} +(15.8845 - 21.8331i) q^{3} +(16.5943 - 61.8112i) q^{4} +(122.026 + 211.355i) q^{5} +(5.46045 + 215.931i) q^{6} +(-28.5227 + 49.4028i) q^{7} +(195.591 + 473.168i) q^{8} +(-224.364 - 693.615i) q^{9} +O(q^{10})\)	\(q+(-6.34800 + 4.86856i) q^{2} +(15.8845 - 21.8331i) q^{3} +(16.5943 - 61.8112i) q^{4} +(122.026 + 211.355i) q^{5} +(5.46045 + 215.931i) q^{6} +(-28.5227 + 49.4028i) q^{7} +(195.591 + 473.168i) q^{8} +(-224.364 - 693.615i) q^{9} +(-1803.62 - 747.594i) q^{10} +(-529.794 + 917.630i) q^{11} +(-1085.93 - 1344.15i) q^{12} +(1072.25 - 619.067i) q^{13} +(-59.4579 - 452.473i) q^{14} +(6552.86 + 693.076i) q^{15} +(-3545.26 - 2051.43i) q^{16} +6617.79i q^{17} +(4801.17 + 3310.74i) q^{18} -3342.42i q^{19} +(15089.1 - 4035.28i) q^{20} +(625.544 + 1407.48i) q^{21} +(-1104.40 - 8404.45i) q^{22} +(5525.65 - 3190.23i) q^{23} +(13437.6 + 3245.71i) q^{24} +(-21968.2 + 38050.1i) q^{25} +(-3792.72 + 9150.17i) q^{26} +(-18707.6 - 6119.18i) q^{27} +(2580.33 + 2582.83i) q^{28} +(-10797.1 + 18701.2i) q^{29} +(-44971.9 + 27503.3i) q^{30} +(10636.5 + 18422.9i) q^{31} +(32492.8 - 4237.78i) q^{32} +(11619.1 + 26143.1i) q^{33} +(-32219.1 - 42009.7i) q^{34} -13922.1 q^{35} +(-46596.4 + 2358.16i) q^{36} +35838.8i q^{37} +(16272.8 + 21217.7i) q^{38} +(3516.13 - 33244.2i) q^{39} +(-76139.6 + 99078.0i) q^{40} +(13932.0 - 8043.65i) q^{41} +(-10823.3 - 5889.17i) q^{42} +(122952. + 70986.1i) q^{43} +(47928.3 + 47974.7i) q^{44} +(119221. - 132060. i) q^{45} +(-19545.0 + 47153.5i) q^{46} +(-11817.8 - 6823.00i) q^{47} +(-101104. + 44817.8i) q^{48} +(57197.4 + 99068.8i) q^{49} +(-45794.6 - 348496. i) q^{50} +(144487. + 105120. i) q^{51} +(-20471.9 - 76550.4i) q^{52} +145311. q^{53} +(148548. - 52234.7i) q^{54} -258595. q^{55} +(-28954.6 - 3833.33i) q^{56} +(-72975.2 - 53092.7i) q^{57} +(-22507.5 - 171282. i) q^{58} +(-125868. - 218010. i) q^{59} +(151580. - 393539. i) q^{60} +(-183328. - 105845. i) q^{61} +(-157213. - 65164.5i) q^{62} +(40666.0 + 8699.55i) q^{63} +(-185633. + 185095. i) q^{64} +(261686. + 151085. i) q^{65} +(-201038. - 109388. i) q^{66} +(239882. - 138496. i) q^{67} +(409054. + 109818. i) q^{68} +(18119.7 - 171317. i) q^{69} +(88377.3 - 67780.3i) q^{70} +590317. i q^{71} +(284313. - 241827. i) q^{72} -479905. q^{73} +(-174483. - 227505. i) q^{74} +(481795. + 1.08404e6i) q^{75} +(-206599. - 55465.2i) q^{76} +(-30222.3 - 52346.6i) q^{77} +(139531. + 228153. i) q^{78} +(414018. - 717100. i) q^{79} +(967.282 - 999638. i) q^{80} +(-430762. + 311245. i) q^{81} +(-49279.5 + 118890. i) q^{82} +(246200. - 426431. i) q^{83} +(97378.4 - 15309.5i) q^{84} +(-1.39871e6 + 807543. i) q^{85} +(-1.12610e6 + 147976. i) q^{86} +(236797. + 532794. i) q^{87} +(-537816. - 71202.0i) q^{88} -380195. i q^{89} +(-113875. + 1.41875e6i) q^{90} +70629.8i q^{91} +(-105498. - 394487. i) q^{92} +(571184. + 60412.4i) q^{93} +(108237. - 14223.1i) q^{94} +(706439. - 407863. i) q^{95} +(423609. - 776732. i) q^{96} +(241248. - 417854. i) q^{97} +(-845412. - 350421. i) q^{98} +(755349. + 161590. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 140 * q - 3 * q^2 - q^4 + 317 * q^6 - 2 * q^7 - 4 * q^9	\( 140 q - 3 q^{2} - q^{4} + 317 q^{6} - 2 q^{7} - 4 q^{9} + 124 q^{10} - 6946 q^{12} - 7428 q^{14} + 1454 q^{15} - q^{16} + 20878 q^{18} - 35346 q^{20} + 127 q^{22} - 6 q^{23} + 50209 q^{24} - 193752 q^{25} + 8188 q^{28} - 21344 q^{30} - 2 q^{31} - 180093 q^{32} + 45534 q^{33} + 20061 q^{34} + 39831 q^{36} + 274239 q^{38} + 125738 q^{39} - 58376 q^{40} + 31314 q^{41} - 213688 q^{42} - 22560 q^{46} - 6 q^{47} - 114411 q^{48} - 974808 q^{49} + 723249 q^{50} - 79338 q^{52} - 231173 q^{54} + 62492 q^{55} + 1294542 q^{56} + 125032 q^{57} - 221138 q^{58} - 1156344 q^{60} + 275294 q^{63} - 804478 q^{64} - 6 q^{65} + 1782258 q^{66} + 2100195 q^{68} - 86464 q^{70} + 1113091 q^{72} - 8 q^{73} - 1886976 q^{74} + 432081 q^{76} + 1658428 q^{78} - 2 q^{79} + 597124 q^{81} - 965382 q^{82} + 4997288 q^{84} - 1041879 q^{86} - 1337970 q^{87} - 536717 q^{88} - 4261994 q^{90} - 737184 q^{92} - 72534 q^{94} + 93744 q^{95} + 1053622 q^{96} - 2 q^{97}+O(q^{100}) \) 140 * q - 3 * q^2 - q^4 + 317 * q^6 - 2 * q^7 - 4 * q^9 + 124 * q^10 - 6946 * q^12 - 7428 * q^14 + 1454 * q^15 - q^16 + 20878 * q^18 - 35346 * q^20 + 127 * q^22 - 6 * q^23 + 50209 * q^24 - 193752 * q^25 + 8188 * q^28 - 21344 * q^30 - 2 * q^31 - 180093 * q^32 + 45534 * q^33 + 20061 * q^34 + 39831 * q^36 + 274239 * q^38 + 125738 * q^39 - 58376 * q^40 + 31314 * q^41 - 213688 * q^42 - 22560 * q^46 - 6 * q^47 - 114411 * q^48 - 974808 * q^49 + 723249 * q^50 - 79338 * q^52 - 231173 * q^54 + 62492 * q^55 + 1294542 * q^56 + 125032 * q^57 - 221138 * q^58 - 1156344 * q^60 + 275294 * q^63 - 804478 * q^64 - 6 * q^65 + 1782258 * q^66 + 2100195 * q^68 - 86464 * q^70 + 1113091 * q^72 - 8 * q^73 - 1886976 * q^74 + 432081 * q^76 + 1658428 * q^78 - 2 * q^79 + 597124 * q^81 - 965382 * q^82 + 4997288 * q^84 - 1041879 * q^86 - 1337970 * q^87 - 536717 * q^88 - 4261994 * q^90 - 737184 * q^92 - 72534 * q^94 + 93744 * q^95 + 1053622 * q^96 - 2 * q^97

Introduction

L-functions

Modular forms

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