LMFDB - Embedded newform 76.7.g.a.7.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(7,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, 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("76.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.g (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:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.4
Character	$\chi$	$=$	76.7
Dual form			76.7.g.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.83923 - 1.59575i) q^{2} +(36.3885 - 21.0089i) q^{3} +(58.9072 + 25.0189i) q^{4} +(30.8964 + 53.5142i) q^{5} +(-318.783 + 106.627i) q^{6} -234.954i q^{7} +(-421.863 - 290.130i) q^{8} +(518.249 - 897.634i) q^{9} +O(q^{10})$	\(q+(-7.83923 - 1.59575i) q^{2} +(36.3885 - 21.0089i) q^{3} +(58.9072 + 25.0189i) q^{4} +(30.8964 + 53.5142i) q^{5} +(-318.783 + 106.627i) q^{6} -234.954i q^{7} +(-421.863 - 290.130i) q^{8} +(518.249 - 897.634i) q^{9} +(-156.809 - 468.813i) q^{10} -653.265i q^{11} +(2669.16 - 327.174i) q^{12} +(503.075 - 871.351i) q^{13} +(-374.928 + 1841.86i) q^{14} +(2248.55 + 1298.20i) q^{15} +(2844.11 + 2947.59i) q^{16} +(-2181.65 - 3778.74i) q^{17} +(-5495.08 + 6209.77i) q^{18} +(3411.88 + 5950.21i) q^{19} +(481.154 + 3925.36i) q^{20} +(-4936.13 - 8549.63i) q^{21} +(-1042.45 + 5121.10i) q^{22} +(3922.37 + 2264.58i) q^{23} +(-21446.3 - 1694.53i) q^{24} +(5903.32 - 10224.9i) q^{25} +(-5334.18 + 6027.94i) q^{26} -12920.4i q^{27} +(5878.30 - 13840.5i) q^{28} +(14772.9 - 25587.5i) q^{29} +(-15555.3 - 13765.0i) q^{30} -31339.0i q^{31} +(-17592.0 - 27645.3i) q^{32} +(-13724.4 - 23771.4i) q^{33} +(11072.6 + 33103.8i) q^{34} +(12573.4 - 7259.25i) q^{35} +(52986.4 - 39911.0i) q^{36} -10832.2 q^{37} +(-17251.5 - 52089.6i) q^{38} -42276.2i q^{39} +(2492.03 - 31539.6i) q^{40} +(-16506.6 - 28590.3i) q^{41} +(25052.4 + 74899.4i) q^{42} +(-86238.5 + 49789.8i) q^{43} +(16344.0 - 38482.0i) q^{44} +64048.2 q^{45} +(-27134.6 - 24011.7i) q^{46} +(-40341.1 - 23291.0i) q^{47} +(165418. + 47506.7i) q^{48} +62445.5 q^{49} +(-62593.8 + 70734.8i) q^{50} +(-158774. - 91668.4i) q^{51} +(51435.0 - 38742.4i) q^{52} +(-6267.71 + 10856.0i) q^{53} +(-20617.8 + 101286. i) q^{54} +(34959.0 - 20183.6i) q^{55} +(-68167.3 + 99118.5i) q^{56} +(249161. + 144839. i) q^{57} +(-156640. + 177012. i) q^{58} +(-273348. + 157818. i) q^{59} +(99976.1 + 132730. i) q^{60} +(59167.9 - 102482. i) q^{61} +(-50009.2 + 245673. i) q^{62} +(-210903. - 121765. i) q^{63} +(93792.8 + 244791. i) q^{64} +62172.9 q^{65} +(69655.6 + 208250. i) q^{66} +(452139. + 261042. i) q^{67} +(-33975.1 - 277177. i) q^{68} +190305. q^{69} +(-110150. + 36842.9i) q^{70} +(-14107.7 + 8145.11i) q^{71} +(-479061. + 228319. i) q^{72} +(-99516.3 - 172367. i) q^{73} +(84916.2 + 17285.5i) q^{74} -496090. i q^{75} +(52116.2 + 435871. i) q^{76} -153487. q^{77} +(-67462.3 + 331413. i) q^{78} +(570791. - 329546. i) q^{79} +(-69865.0 + 243270. i) q^{80} +(106360. + 184220. i) q^{81} +(83776.4 + 250467. i) q^{82} -44853.2i q^{83} +(-76870.9 - 627131. i) q^{84} +(134811. - 233499. i) q^{85} +(755496. - 252699. i) q^{86} -1.24145e6i q^{87} +(-189532. + 275589. i) q^{88} +(318944. - 552427. i) q^{89} +(-502089. - 102205. i) q^{90} +(-204728. - 118200. i) q^{91} +(174398. + 231533. i) q^{92} +(-658398. - 1.14038e6i) q^{93} +(279077. + 246958. i) q^{94} +(-213006. + 366424. i) q^{95} +(-1.22094e6 - 636383. i) q^{96} +(653102. + 1.13121e6i) q^{97} +(-489525. - 99647.5i) q^{98} +(-586393. - 338554. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9}+O(q^{10}) $ 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9} - 812 q^{10} - 1462 q^{12} + 2518 q^{13} - 2742 q^{14} + 461 q^{16} + 6838 q^{17} - 13948 q^{18} - 24396 q^{20} + 11176 q^{21} + 22293 q^{22} + 33905 q^{24} - 156252 q^{25} - 78080 q^{26} - 34362 q^{28} - 2 q^{29} + 208344 q^{30} - 10941 q^{32} + 110316 q^{33} + 64648 q^{34} + 78574 q^{36} + 55432 q^{37} + 221994 q^{38} + 242590 q^{40} - 9126 q^{41} + 187550 q^{42} + 138081 q^{44} + 59576 q^{45} - 686052 q^{46} - 141617 q^{48} - 1306636 q^{49} + 167498 q^{50} - 35414 q^{52} + 60758 q^{53} - 348601 q^{54} + 543732 q^{56} - 466566 q^{57} + 1208536 q^{58} - 319142 q^{60} - 839474 q^{61} + 628548 q^{62} - 470026 q^{64} + 151836 q^{65} + 1471119 q^{66} + 341484 q^{68} - 2169836 q^{69} - 68364 q^{70} + 1236042 q^{72} + 207538 q^{73} + 336144 q^{74} - 97437 q^{76} + 1977632 q^{77} - 2740948 q^{78} + 1250050 q^{80} - 3334682 q^{81} - 2244893 q^{82} - 2404612 q^{84} + 788426 q^{85} + 910490 q^{86} + 5123058 q^{88} + 360166 q^{89} + 2446616 q^{90} + 2518692 q^{92} + 2079592 q^{93} - 2221200 q^{94} - 5927450 q^{96} + 3567778 q^{97} + 5270703 q^{98}+O(q^{100}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9 - 812 * q^10 - 1462 * q^12 + 2518 * q^13 - 2742 * q^14 + 461 * q^16 + 6838 * q^17 - 13948 * q^18 - 24396 * q^20 + 11176 * q^21 + 22293 * q^22 + 33905 * q^24 - 156252 * q^25 - 78080 * q^26 - 34362 * q^28 - 2 * q^29 + 208344 * q^30 - 10941 * q^32 + 110316 * q^33 + 64648 * q^34 + 78574 * q^36 + 55432 * q^37 + 221994 * q^38 + 242590 * q^40 - 9126 * q^41 + 187550 * q^42 + 138081 * q^44 + 59576 * q^45 - 686052 * q^46 - 141617 * q^48 - 1306636 * q^49 + 167498 * q^50 - 35414 * q^52 + 60758 * q^53 - 348601 * q^54 + 543732 * q^56 - 466566 * q^57 + 1208536 * q^58 - 319142 * q^60 - 839474 * q^61 + 628548 * q^62 - 470026 * q^64 + 151836 * q^65 + 1471119 * q^66 + 341484 * q^68 - 2169836 * q^69 - 68364 * q^70 + 1236042 * q^72 + 207538 * q^73 + 336144 * q^74 - 97437 * q^76 + 1977632 * q^77 - 2740948 * q^78 + 1250050 * q^80 - 3334682 * q^81 - 2244893 * q^82 - 2404612 * q^84 + 788426 * q^85 + 910490 * q^86 + 5123058 * q^88 + 360166 * q^89 + 2446616 * q^90 + 2518692 * q^92 + 2079592 * q^93 - 2221200 * q^94 - 5927450 * q^96 + 3567778 * q^97 + 5270703 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−7.83923	−	1.59575i	−0.979904	−	0.199469i
$2$	−7.83923	−	1.59575i	−0.979904	−	0.199469i
$3$	36.3885	−	21.0089i	1.34772	−	0.778108i	0.359796	−	0.933031i	$-0.382846\pi$
$3$	36.3885	−	21.0089i	1.34772	−	0.778108i	0.987927	+	0.154923i	$0.0495129\pi$
$4$	58.9072	+	25.0189i	0.920424	+	0.390921i
$5$	30.8964	+	53.5142i	0.247171	+	0.428114i	0.962740	−	0.270429i	$-0.0871656\pi$
$5$	30.8964	+	53.5142i	0.247171	+	0.428114i	−0.715568	+	0.698543i	$0.753832\pi$
$6$	−318.783	+	106.627i	−1.47585	+	0.493643i
$7$		−	234.954i		−	0.684998i	−0.939518	−	0.342499i	$-0.888727\pi$
$7$		−	234.954i		−	0.684998i	0.939518	−	0.342499i	$-0.111273\pi$
$8$	−421.863	−	290.130i	−0.823951	−	0.566661i
$9$	518.249	−	897.634i	0.710904	−	1.23132i
$10$	−156.809	−	468.813i	−0.156809	−	0.468813i
$11$		−	653.265i		−	0.490808i	−0.969421	−	0.245404i	$-0.921079\pi$
$11$		−	653.265i		−	0.490808i	0.969421	−	0.245404i	$-0.0789206\pi$
$12$	2669.16	−	327.174i	1.54466	−	0.189337i
$13$	503.075	−	871.351i	0.228983	−	0.396609i	−0.728524	−	0.685020i	$-0.759793\pi$
$13$	503.075	−	871.351i	0.228983	−	0.396609i	0.957507	+	0.288411i	$0.0931268\pi$
$14$	−374.928	+	1841.86i	−0.136636	+	0.671232i
$15$	2248.55	+	1298.20i	0.666237	+	0.384652i
$16$	2844.11	+	2947.59i	0.694362	+	0.719626i
$17$	−2181.65	−	3778.74i	−0.444057	−	0.769130i	0.553929	−	0.832564i	$-0.313128\pi$
$17$	−2181.65	−	3778.74i	−0.444057	−	0.769130i	−0.997986	+	0.0634341i	$0.979795\pi$
$18$	−5495.08	+	6209.77i	−0.942229	+	1.06477i
$19$	3411.88	+	5950.21i	0.497431	+	0.867504i
$19$	3411.88	+	5950.21i	0.497431	+	0.867504i
$20$	481.154	+	3925.36i	0.0601442	+	0.490671i
$21$	−4936.13	−	8549.63i	−0.533002	−	0.923187i
$22$	−1042.45	+	5121.10i	−0.0979009	+	0.480945i
$23$	3922.37	+	2264.58i	0.322377	+	0.186125i	0.652452	−	0.757830i	$-0.273740\pi$
$23$	3922.37	+	2264.58i	0.322377	+	0.186125i	−0.330074	+	0.943955i	$0.607074\pi$
$24$	−21446.3	−	1694.53i	−1.55138	−	0.122579i
$25$	5903.32	−	10224.9i	0.377813	−	0.654391i
$26$	−5334.18	+	6027.94i	−0.303492	+	0.342964i
$27$		−	12920.4i		−	0.656426i
$28$	5878.30	−	13840.5i	0.267780	−	0.630488i
$29$	14772.9	−	25587.5i	0.605721	−	1.04914i	−0.386216	−	0.922408i	$-0.626218\pi$
$29$	14772.9	−	25587.5i	0.605721	−	1.04914i	0.991937	−	0.126731i	$-0.0404485\pi$
$30$	−15555.3	−	13765.0i	−0.576122	−	0.509816i
$31$		−	31339.0i		−	1.05196i	−0.850497	−	0.525980i	$-0.823698\pi$
$31$		−	31339.0i		−	1.05196i	0.850497	−	0.525980i	$-0.176302\pi$
$32$	−17592.0	−	27645.3i	−0.536865	−	0.843668i
$33$	−13724.4	−	23771.4i	−0.381902	−	0.661473i
$34$	11072.6	+	33103.8i	0.281716	+	0.842249i
$35$	12573.4	−	7259.25i	0.293257	−	0.169312i
$36$	52986.4	−	39911.0i	1.13568	−	0.855432i
$37$	−10832.2			−0.213851			−0.106926	−	0.994267i	$-0.534101\pi$
$37$	−10832.2			−0.213851			−0.106926	+	0.994267i	$0.534101\pi$
$38$	−17251.5	−	52089.6i	−0.314394	−	0.949292i
$39$		−	42276.2i		−	0.712693i
$40$	2492.03	−	31539.6i	0.0389379	−	0.492807i
$41$	−16506.6	−	28590.3i	−0.239501	−	0.414828i	0.721070	−	0.692862i	$-0.243650\pi$
$41$	−16506.6	−	28590.3i	−0.239501	−	0.414828i	−0.960571	+	0.278034i	$0.910317\pi$
$42$	25052.4	+	74899.4i	0.338144	+	1.01095i
$43$	−86238.5	+	49789.8i	−1.08467	+	0.626232i	−0.932151	−	0.362069i	$-0.882070\pi$
$43$	−86238.5	+	49789.8i	−1.08467	+	0.626232i	−0.152514	+	0.988301i	$0.548737\pi$
$44$	16344.0	−	38482.0i	0.191867	−	0.451752i
$45$	64048.2			0.702861
$46$	−27134.6	−	24011.7i	−0.278773	−	0.246689i
$47$	−40341.1	−	23291.0i	−0.388557	−	0.224333i	0.292978	−	0.956119i	$-0.405354\pi$
$47$	−40341.1	−	23291.0i	−0.388557	−	0.224333i	−0.681535	+	0.731786i	$0.738687\pi$
$48$	165418.	+	47506.7i	1.49575	+	0.429567i
$49$	62445.5			0.530778
$50$	−62593.8	+	70734.8i	−0.500751	+	0.565878i
$51$	−158774.	−	91668.4i	−1.19693	−	0.691049i
$52$	51435.0	−	38742.4i	0.365804	−	0.275535i
$53$	−6267.71	+	10856.0i	−0.0420999	+	0.0729192i	−0.886308	−	0.463097i	$-0.846738\pi$
$53$	−6267.71	+	10856.0i	−0.0420999	+	0.0729192i	0.844208	+	0.536016i	$0.180071\pi$
$54$	−20617.8	+	101286.i	−0.130936	+	0.643234i
$55$	34959.0	−	20183.6i	0.210122	−	0.121314i
$56$	−68167.3	+	99118.5i	−0.388161	+	0.564405i
$57$	249161.	+	144839.i	1.34541	+	0.782100i
$58$	−156640.	+	177012.i	−0.802819	+	0.907234i
$59$	−273348.	+	157818.i	−1.33095	+	0.768422i	−0.985445	−	0.169997i	$-0.945624\pi$
$59$	−273348.	+	157818.i	−1.33095	+	0.768422i	−0.345501	+	0.938419i	$0.612291\pi$
$60$	99976.1	+	132730.i	0.462852	+	0.614489i
$61$	59167.9	−	102482.i	0.260674	−	0.451500i	−0.705748	−	0.708463i	$-0.749389\pi$
$61$	59167.9	−	102482.i	0.260674	−	0.451500i	0.966421	+	0.256964i	$0.0827220\pi$
$62$	−50009.2	+	245673.i	−0.209833	+	1.03082i
$63$	−210903.	−	121765.i	−0.843453	−	0.486968i
$64$	93792.8	+	244791.i	0.357791	+	0.933802i
$65$	62172.9			0.226392
$66$	69655.6	+	208250.i	0.242284	+	0.724358i
$67$	452139.	+	261042.i	1.50331	+	0.867934i	0.999993	+	0.00382963i	$0.00121901\pi$
$67$	452139.	+	261042.i	1.50331	+	0.867934i	0.503313	+	0.864104i	$0.332114\pi$
$68$	−33975.1	−	277177.i	−0.108052	−	0.881517i
$69$	190305.			0.579301
$70$	−110150.	+	36842.9i	−0.321136	+	0.107414i
$71$	−14107.7	+	8145.11i	−0.0394169	+	0.0227574i	−0.519579	−	0.854422i	$-0.673911\pi$
$71$	−14107.7	+	8145.11i	−0.0394169	+	0.0227574i	0.480162	+	0.877180i	$0.340578\pi$
$72$	−479061.	+	228319.i	−1.28349	+	0.611708i
$73$	−99516.3	−	172367.i	−0.255815	−	0.443084i	0.709302	−	0.704905i	$-0.249010\pi$
$73$	−99516.3	−	172367.i	−0.255815	−	0.443084i	−0.965117	+	0.261821i	$0.915677\pi$
$74$	84916.2	+	17285.5i	0.209554	+	0.0426567i
$75$		−	496090.i		−	1.17592i
$76$	52116.2	+	435871.i	0.118722	+	0.992928i
$77$	−153487.			−0.336202
$78$	−67462.3	+	331413.i	−0.142160	+	0.698371i
$79$	570791.	−	329546.i	1.15770	−	0.668398i	0.206948	−	0.978352i	$-0.433647\pi$
$79$	570791.	−	329546.i	1.15770	−	0.668398i	0.950752	+	0.309954i	$0.100314\pi$
$80$	−69865.0	+	243270.i	−0.136455	+	0.475137i
$81$	106360.	+	184220.i	0.200134	+	0.346643i
$82$	83776.4	+	250467.i	0.151943	+	0.454264i
$83$		−	44853.2i		−	0.0784438i	−0.999231	−	0.0392219i	$-0.987512\pi$
$83$		−	44853.2i		−	0.0784438i	0.999231	−	0.0392219i	$-0.0124879\pi$
$84$	−76870.9	−	627131.i	−0.129695	−	1.05809i
$85$	134811.	−	233499.i	0.219517	−	0.380214i
$86$	755496.	−	252699.i	1.18778	−	0.397290i
$87$		−	1.24145e6i		−	1.88527i
$88$	−189532.	+	275589.i	−0.278122	+	0.404402i
$89$	318944.	−	552427.i	0.452423	−	0.783619i	−0.546113	−	0.837711i	$-0.683893\pi$
$89$	318944.	−	552427.i	0.452423	−	0.783619i	0.998536	+	0.0540920i	$0.0172264\pi$
$90$	−502089.	−	102205.i	−0.688737	−	0.140199i
$91$	−204728.	−	118200.i	−0.271677	−	0.156853i
$92$	174398.	+	231533.i	0.223964	+	0.297338i
$93$	−658398.	−	1.14038e6i	−0.818539	−	1.41775i
$94$	279077.	+	246958.i	0.336001	+	0.297330i
$95$	−213006.	+	366424.i	−0.248439	+	0.427379i
$96$	−1.22094e6	−	636383.i	−1.38001	−	0.719291i
$97$	653102.	+	1.13121e6i	0.715592	+	1.23944i	0.962731	+	0.270462i	$0.0871763\pi$
$97$	653102.	+	1.13121e6i	0.715592	+	1.23944i	−0.247139	+	0.968980i	$0.579490\pi$
$98$	−489525.	−	99647.5i	−0.520112	−	0.105874i
$99$	−586393.	−	338554.i	−0.604343	−	0.348918i
$100$	603563.	−	454622.i	0.603563	−	0.454622i
$101$	−770769.	+	1.33501e6i	−0.748101	+	1.29575i	0.200631	+	0.979667i	$0.435701\pi$
$101$	−770769.	+	1.33501e6i	−0.748101	+	1.29575i	−0.948732	+	0.316081i	$0.897633\pi$
$102$	1.09839e6	+	971974.i	1.03504	+	0.915913i
$103$			1.66822e6i			1.52665i	0.646012	+	0.763327i	$0.276436\pi$
$103$			1.66822e6i			1.52665i	−0.646012	+	0.763327i	$0.723564\pi$
$104$	−465034.	+	221634.i	−0.413414	+	0.197031i
$105$	305018.	−	528306.i	0.263486	−	0.456371i
$106$	66457.5	−	75101.0i	0.0557990	−	0.0630562i
$107$			1.60093e6i			1.30683i	0.756999	+	0.653416i	$0.226665\pi$
$107$			1.60093e6i			1.30683i	−0.756999	+	0.653416i	$0.773335\pi$
$108$	323255.	−	761106.i	0.256610	−	0.604190i
$109$	−395762.	−	685480.i	−0.305601	−	0.529317i	0.671794	−	0.740738i	$-0.265524\pi$
$109$	−395762.	−	685480.i	−0.305601	−	0.529317i	−0.977395	+	0.211422i	$0.932191\pi$
$110$	−306259.	+	102438.i	−0.230097	+	0.0769631i
$111$	−394168.	+	227573.i	−0.288212	+	0.166399i
$112$	692548.	−	668235.i	0.492942	−	0.475636i
$113$	−944613.			−0.654664			−0.327332	−	0.944909i	$-0.606150\pi$
$113$	−944613.			−0.654664			−0.327332	+	0.944909i	$0.606150\pi$
$114$	−1.72210e6	−	1.53303e6i	−1.16237	−	1.03475i
$115$			279870.i			0.184019i
$116$	1.51040e6	−	1.13768e6i	0.967651	−	0.728865i
$117$	−521436.	−	903154.i	−0.325569	−	0.563903i
$118$	2.39468e6	−	800974.i	1.45747	−	0.487497i
$119$	−887830.	+	512589.i	−0.526852	+	0.304178i
$120$	−571933.	−	1.20004e6i	−0.330980	−	0.694465i
$121$	1.34481e6			0.759108
$122$	−627367.	+	708962.i	−0.345495	+	0.390430i
$123$	−1.20130e6	−	693573.i	−0.645562	−	0.372715i
$124$	784067.	−	1.84609e6i	0.411233	−	0.968251i
$125$	1.69508e6			0.867881
$126$	1.45901e6	+	1.29109e6i	0.729368	+	0.645424i
$127$	3.07349e6	+	1.77448e6i	1.50045	+	0.866283i	1.00000		0.000515688i	$0.000164149\pi$
$127$	3.07349e6	+	1.77448e6i	1.50045	+	0.866283i	0.500447	+	0.865767i	$0.333169\pi$
$128$	−344639.	−	2.06864e6i	−0.164337	−	0.986404i
$129$	−2.09206e6	+	3.62355e6i	−0.974552	+	1.68797i
$130$	−487388.	−	99212.4i	−0.221842	−	0.0451581i
$131$	2.13191e6	−	1.23086e6i	0.948322	−	0.547514i	0.0557627	−	0.998444i	$-0.482241\pi$
$131$	2.13191e6	−	1.23086e6i	0.948322	−	0.547514i	0.892559	+	0.450930i	$0.148908\pi$
$132$	−213732.	−	1.74367e6i	−0.0929281	−	0.758129i
$133$	1.39803e6	−	801635.i	0.594238	−	0.340739i
$134$	−3.12786e6	−	2.76787e6i	−1.29997	−	1.15035i
$135$	691426.	−	399195.i	0.281025	−	0.162250i
$136$	−175967.	+	2.22707e6i	−0.0699542	+	0.885356i
$137$	−2.09056e6	+	3.62096e6i	−0.813021	+	1.40819i	0.0977193	+	0.995214i	$0.468845\pi$
$137$	−2.09056e6	+	3.62096e6i	−0.813021	+	1.40819i	−0.910740	+	0.412980i	$0.864488\pi$
$138$	−1.49185e6	−	303680.i	−0.567659	−	0.115552i
$139$	−1.22880e6	−	709449.i	−0.457549	−	0.264166i	0.253464	−	0.967345i	$-0.418430\pi$
$139$	−1.22880e6	−	709449.i	−0.457549	−	0.264166i	−0.711013	+	0.703179i	$0.751763\pi$
$140$	922281.	−	113049.i	0.336108	−	0.0411986i
$141$	−1.95727e6			−0.698222
$142$	123591.	−	41339.0i	0.0431642	−	0.0144376i
$143$	−569224.	−	328641.i	−0.194659	−	0.112386i
$144$	4.11981e6	−	1.02538e6i	1.37972	−	0.343398i
$145$	1.82572e6			0.598868
$146$	505076.	+	1.51003e6i	0.162292	+	0.485207i
$147$	2.27230e6	−	1.31191e6i	0.715342	−	0.413003i
$148$	−638095.	−	271010.i	−0.196834	−	0.0835989i
$149$	−2.63066e6	−	4.55644e6i	−0.795254	−	1.37742i	−0.922678	−	0.385572i	$-0.874004\pi$
$149$	−2.63066e6	−	4.55644e6i	−0.795254	−	1.37742i	0.127424	−	0.991848i	$-0.459329\pi$
$150$	−791635.	+	3.88896e6i	−0.234559	+	1.15228i
$151$			1.31032e6i			0.380582i	0.981728	+	0.190291i	$0.0609431\pi$
$151$			1.31032e6i			0.380582i	−0.981728	+	0.190291i	$0.939057\pi$
$152$	286991.	−	3.50006e6i	0.0817218	−	0.996655i
$153$	−4.52256e6			−1.26273
$154$	1.20322e6	+	244928.i	0.329446	+	0.0670619i
$155$	1.67708e6	−	968262.i	0.450359	−	0.260015i
$156$	1.05771e6	−	2.49037e6i	0.278606	−	0.655980i
$157$	−866484.	−	1.50079e6i	−0.223904	−	0.387813i	0.732086	−	0.681212i	$-0.238547\pi$
$157$	−866484.	−	1.50079e6i	−0.223904	−	0.387813i	−0.955990	+	0.293399i	$0.905213\pi$
$158$	−5.00044e6	+	1.67255e6i	−1.26776	+	0.424041i
$159$			526711.i			0.131033i
$160$	935886.	−	1.79556e6i	0.228488	−	0.438370i
$161$	532072.	−	921576.i	0.127495	−	0.220828i
$162$	−539808.	−	1.61387e6i	−0.126968	−	0.379597i
$163$			6.83258e6i			1.57769i	0.614592	+	0.788845i	$0.289321\pi$
$163$			6.83258e6i			1.57769i	−0.614592	+	0.788845i	$0.710679\pi$
$164$	−257060.	−	2.09715e6i	−0.0582777	−	0.475443i
$165$	848070.	−	1.46890e6i	0.188790	−	0.326995i
$166$	−71574.5	+	351614.i	−0.0156471	+	0.0768674i
$167$	658774.	+	380343.i	0.141445	+	0.0816632i	0.569052	−	0.822301i	$-0.307310\pi$
$167$	658774.	+	380343.i	0.141445	+	0.0816632i	−0.427608	+	0.903964i	$0.640643\pi$
$168$	−398136.	+	5.03890e6i	−0.0839660	+	1.06269i
$169$	1.90724e6	+	3.30343e6i	0.395134	+	0.684392i
$170$	−1.42942e6	+	1.61533e6i	−0.290946	+	0.328787i
$171$	7.10931e6	+	21074.1i	1.42180	+	0.00421463i
$172$	−6.32575e6	+	775382.i	−1.24316	+	0.152381i
$173$	2.03431e6	+	3.52352e6i	0.392896	+	0.680516i	0.992830	−	0.119533i	$-0.0381398\pi$
$173$	2.03431e6	+	3.52352e6i	0.392896	+	0.680516i	−0.599934	+	0.800050i	$0.704806\pi$
$174$	−1.98105e6	+	9.73204e6i	−0.376052	+	1.84738i
$175$	−2.40237e6	−	1.38701e6i	−0.448256	−	0.258801i
$176$	1.92556e6	−	1.85796e6i	0.353198	−	0.340798i
$177$	−6.63116e6	+	1.14855e7i	−1.19583	+	2.07124i
$178$	−3.38181e6	+	3.82165e6i	−0.599639	+	0.677628i
$179$			2.92695e6i			0.510336i	0.966897	+	0.255168i	$0.0821307\pi$
$179$			2.92695e6i			0.510336i	−0.966897	+	0.255168i	$0.917869\pi$
$180$	3.77290e6	+	1.60242e6i	0.646930	+	0.274763i
$181$	4.62988e6	−	8.01919e6i	0.780790	−	1.35237i	−0.150692	−	0.988581i	$-0.548150\pi$
$181$	4.62988e6	−	8.01919e6i	0.780790	−	1.35237i	0.931482	−	0.363788i	$-0.118517\pi$
$182$	1.41629e6	+	1.25329e6i	0.234930	+	0.207891i
$183$		−	4.97222e6i		−	0.811329i
$184$	−997678.	−	2.09334e6i	−0.160154	−	0.336036i
$185$	−334677.	−	579677.i	−0.0528580	−	0.0915527i
$186$	3.34157e6	+	9.99033e6i	0.519293	+	1.55253i
$187$	−2.46852e6	+	1.42520e6i	−0.377495	+	0.217947i
$188$	−1.79367e6	−	2.38130e6i	−0.269941	−	0.358377i
$189$	−3.03571e6			−0.449650
$190$	2.25452e6	−	2.53258e6i	0.328696	−	0.369235i
$191$			1.32477e6i			0.190125i	0.995471	+	0.0950624i	$0.0303051\pi$
$191$			1.32477e6i			0.190125i	−0.995471	+	0.0950624i	$0.969695\pi$
$192$	8.55576e6	+	6.93708e6i	1.20880	+	0.980106i
$193$	6.35054e6	+	1.09995e7i	0.883362	+	1.53003i	0.847580	+	0.530668i	$0.178059\pi$
$193$	6.35054e6	+	1.09995e7i	0.883362	+	1.53003i	0.0357816	+	0.999360i	$0.488608\pi$
$194$	−3.31469e6	−	9.90997e6i	−0.453982	−	1.35727i
$195$	2.26238e6	−	1.30618e6i	0.305113	−	0.176157i
$196$	3.67849e6	+	1.56232e6i	0.488541	+	0.207492i
$197$	−6.42272e6			−0.840079			−0.420039	−	0.907506i	$-0.637984\pi$
$197$	−6.42272e6			−0.840079			−0.420039	+	0.907506i	$0.637984\pi$
$198$	4.05663e6	+	3.58974e6i	0.522600	+	0.462453i
$199$	−8.57515e6	−	4.95087e6i	−1.08813	−	0.628235i	−0.155056	−	0.987906i	$-0.549556\pi$
$199$	−8.57515e6	−	4.95087e6i	−1.08813	−	0.628235i	−0.933079	+	0.359671i	$0.882889\pi$
$200$	−5.45693e6	+	2.60075e6i	−0.682117	+	0.325094i
$201$	2.19369e7			2.70139
$202$	8.17258e6	−	9.23551e6i	0.991528	−	1.12049i
$203$	−6.01188e6	−	3.47096e6i	−0.718658	−	0.414917i
$204$	−7.05950e6	−	9.37229e6i	−0.831541	−	1.10396i
$205$	1.01999e6	−	1.76668e6i	0.118396	−	0.205067i
$206$	2.66206e6	−	1.30775e7i	0.304520	−	1.49598i
$207$	4.06553e6	−	2.34723e6i	0.458359	−	0.264634i
$208$	3.99918e6	−	995358.i	0.444407	−	0.110609i
$209$	3.88707e6	−	2.22886e6i	0.425778	−	0.244143i
$210$	−3.23415e6	+	3.65478e6i	−0.349223	+	0.394643i
$211$	−6.71498e6	+	3.87690e6i	−0.714821	+	0.412702i	−0.812844	−	0.582482i	$-0.802082\pi$
$211$	−6.71498e6	+	3.87690e6i	−0.714821	+	0.412702i	0.0980223	+	0.995184i	$0.468748\pi$
$212$	−640818.	+	482684.i	−0.0672554	+	0.0506589i
$213$	−342240.	+	592777.i	−0.0354154	+	0.0613412i
$214$	2.55468e6	−	1.25500e7i	0.260672	−	1.28057i
$215$	−5.32892e6	−	3.07666e6i	−0.536197	−	0.309573i
$216$	−3.74861e6	+	5.45065e6i	−0.371971	+	0.540863i
$217$	−7.36322e6			−0.720591
$218$	2.00862e6	+	6.00518e6i	0.193878	+	0.579637i
$219$	−7.24250e6	−	4.18146e6i	−0.689535	−	0.398103i
$220$	2.56430e6	−	314321.i	0.240825	−	0.0295192i
$221$	−4.39014e6			−0.406726
$222$	3.45313e6	−	1.15500e6i	0.315612	−	0.105566i
$223$	−4.22494e6	+	2.43927e6i	−0.380983	+	0.219961i	−0.678246	−	0.734835i	$-0.737260\pi$
$223$	−4.22494e6	+	2.43927e6i	−0.380983	+	0.219961i	0.297263	+	0.954796i	$0.403926\pi$
$224$	−6.49538e6	+	4.13331e6i	−0.577911	+	0.367751i
$225$	−6.11878e6	−	1.05980e7i	−0.537177	−	0.930418i
$226$	7.40504e6	+	1.50737e6i	0.641508	+	0.130585i
$227$			1.14923e7i			0.982493i	0.871021	+	0.491247i	$0.163459\pi$
$227$			1.14923e7i			0.982493i	−0.871021	+	0.491247i	$0.836541\pi$
$228$	1.10536e7	+	1.47658e7i	0.932609	+	1.24581i
$229$	1.69700e6			0.141311			0.0706554	−	0.997501i	$-0.477491\pi$
$229$	1.69700e6			0.141311			0.0706554	+	0.997501i	$0.477491\pi$
$230$	446602.	−	2.19396e6i	0.0367060	−	0.180321i
$231$	−5.58518e6	+	3.22461e6i	−0.453107	+	0.261602i
$232$	−1.36558e7	+	6.50833e6i	−1.09359	+	0.521201i
$233$	−3.41112e6	−	5.90824e6i	−0.269668	−	0.467079i	0.699108	−	0.715016i	$-0.253581\pi$
$233$	−3.41112e6	−	5.90824e6i	−0.269668	−	0.467079i	−0.968776	+	0.247937i	$0.920247\pi$
$234$	2.64645e6	+	7.91212e6i	0.206546	+	0.617512i
$235$		−	2.87843e6i		−	0.221795i
$236$	−2.00506e7	+	2.45771e6i	−1.52543	+	0.186980i
$237$	1.38468e7	−	2.39834e7i	1.04017	−	1.80163i
$238$	7.77787e6	−	2.60155e6i	0.576939	−	0.192975i
$239$		−	1.91421e7i		−	1.40215i	−0.713087	−	0.701076i	$-0.752704\pi$
$239$		−	1.91421e7i		−	1.40215i	0.713087	−	0.701076i	$-0.247296\pi$
$240$	2.56856e6	+	1.03200e7i	0.185804	+	0.746529i
$241$	1.19219e6	−	2.06493e6i	0.0851712	−	0.147521i	−0.820293	−	0.571944i	$-0.806190\pi$
$241$	1.19219e6	−	2.06493e6i	0.0851712	−	0.147521i	0.905464	+	0.424423i	$0.139523\pi$
$242$	−1.05422e7	−	2.14597e6i	−0.743853	−	0.151418i
$243$	1.58976e7	+	9.17849e6i	1.10793	+	0.639665i
$244$	6.04940e6	−	4.55660e6i	0.416431	−	0.313669i
$245$	1.92934e6	+	3.34172e6i	0.131193	+	0.227233i
$246$	8.31054e6	+	7.35407e6i	0.558244	+	0.493995i
$247$	6.90115e6	+	20457.0i	0.457963	+	0.00135754i
$248$	−9.09239e6	+	1.32208e7i	−0.596105	+	0.866764i
$249$	−942316.	−	1.63214e6i	−0.0610378	−	0.105721i
$250$	−1.32881e7	−	2.70492e6i	−0.850440	−	0.173115i
$251$	2.99976e6	+	1.73191e6i	0.189699	+	0.109523i	0.591842	−	0.806054i	$-0.298401\pi$
$251$	2.99976e6	+	1.73191e6i	0.189699	+	0.109523i	−0.402142	+	0.915577i	$0.631734\pi$
$252$	−9.37726e6	−	1.24494e7i	−0.585969	−	0.777940i
$253$	1.47937e6	−	2.56235e6i	0.0913515	−	0.158225i
$254$	−2.12622e7	−	1.88151e7i	−1.29750	−	1.14817i
$255$		−	1.13289e7i		−	0.683231i
$256$	−599329.	+	1.67665e7i	−0.0357228	+	0.999362i
$257$	1.21687e7	−	2.10769e7i	0.716880	−	1.24167i	−0.245350	−	0.969434i	$-0.578903\pi$
$257$	1.21687e7	−	2.10769e7i	0.716880	−	1.24167i	0.962230	−	0.272238i	$-0.0877636\pi$
$258$	2.21824e7	−	2.50675e7i	1.29167	−	1.45966i
$259$			2.54507e6i			0.146488i
$260$	3.66243e6	+	1.55550e6i	0.208377	+	0.0885013i
$261$	−1.53121e7	−	2.65214e7i	−0.861219	−	1.49168i
$262$	−1.86767e7	+	6.24700e6i	−1.03848	+	0.347350i
$263$	6.60578e6	−	3.81385e6i	0.363126	−	0.209651i	−0.307325	−	0.951604i	$-0.599434\pi$
$263$	6.60578e6	−	3.81385e6i	0.363126	−	0.209651i	0.670451	+	0.741954i	$0.266101\pi$
$264$	−1.10698e6	+	1.40101e7i	−0.0601626	+	0.761430i
$265$	−774600.			−0.0416236
$266$	−1.22387e7	+	4.05330e6i	−0.650263	+	0.215359i
$267$		−	2.68027e7i		−	1.40814i
$268$	2.01032e7	+	2.66893e7i	1.04439	+	1.38654i
$269$	6.81903e6	+	1.18109e7i	0.350320	+	0.606773i	0.986306	−	0.164929i	$-0.0527393\pi$
$269$	6.81903e6	+	1.18109e7i	0.350320	+	0.606773i	−0.635985	+	0.771701i	$0.719406\pi$
$270$	−6.05727e6	+	2.02604e6i	−0.307741	+	0.102933i
$271$	9.23495e6	−	5.33180e6i	0.464009	−	0.267896i	−0.249719	−	0.968318i	$-0.580338\pi$
$271$	9.23495e6	−	5.33180e6i	0.464009	−	0.267896i	0.713729	+	0.700422i	$0.247005\pi$
$272$	4.93330e6	−	1.71777e7i	0.245149	−	0.853610i
$273$	−9.93298e6			−0.488193
$274$	2.21666e7	−	2.50496e7i	1.07757	−	1.21772i
$275$	−6.67954e6	−	3.85644e6i	−0.321180	−	0.185433i
$276$	1.12104e7	+	4.76124e6i	0.533202	+	0.226461i
$277$	1.44801e7			0.681289			0.340644	−	0.940192i	$-0.389355\pi$
$277$	1.44801e7			0.681289			0.340644	+	0.940192i	$0.389355\pi$
$278$	8.50076e6	+	7.52240e6i	0.395661	+	0.350124i
$279$	−2.81309e7	−	1.62414e7i	−1.29530	−	0.747844i
$280$	−7.41037e6	−	585513.i	−0.337572	−	0.0266724i
$281$	−2.60667e6	+	4.51488e6i	−0.117481	+	0.203483i	−0.918769	−	0.394796i	$-0.870815\pi$
$281$	−2.60667e6	+	4.51488e6i	−0.117481	+	0.203483i	0.801288	+	0.598279i	$0.204148\pi$
$282$	1.53435e7	+	3.12332e6i	0.684191	+	0.139274i
$283$	9.76135e6	−	5.63572e6i	0.430676	−	0.248651i	−0.268959	−	0.963152i	$-0.586680\pi$
$283$	9.76135e6	−	5.63572e6i	0.430676	−	0.248651i	0.699635	+	0.714501i	$0.253346\pi$
$284$	−1.03483e6	+	126845.i	−0.0451766	+	0.00553755i
$285$	−52790.0	+	1.78086e7i	−0.00228043	+	0.769301i
$286$	3.93785e6	+	3.48463e6i	0.168330	+	0.148956i
$287$	−6.71742e6	+	3.87831e6i	−0.284156	+	0.164058i
$288$	−3.39324e7	+	1.46402e6i	−1.42049	+	0.0612870i
$289$	2.54955e6	−	4.41595e6i	0.105626	−	0.182949i
$290$	−1.43123e7	−	2.91340e6i	−0.586833	−	0.119455i
$291$	4.75308e7	+	2.74419e7i	1.92884	+	1.11362i
$292$	−1.54978e6	−	1.26435e7i	−0.0622474	−	0.507829i
$293$	−3.40777e7			−1.35478			−0.677388	−	0.735626i	$-0.736888\pi$
$293$	−3.40777e7			−1.35478			−0.677388	+	0.735626i	$0.736888\pi$
$294$	−1.99066e7	+	6.65837e6i	−0.783348	+	0.262015i
$295$	−1.68910e7	−	9.75200e6i	−0.657943	−	0.379864i
$296$	4.56971e6	+	3.14275e6i	0.176203	+	0.121181i
$297$	−8.44047e6			−0.322179
$298$	1.33514e7	+	3.99168e7i	0.504520	+	1.50837i
$299$	3.94649e6	−	2.27851e6i	0.147638	−	0.0852386i
$300$	1.24116e7	−	2.92232e7i	0.459690	−	1.08234i
$301$	1.16983e7	+	2.02621e7i	0.428967	+	0.742993i
$302$	2.09095e6	−	1.02719e7i	0.0759142	−	0.372934i
$303$			6.47721e7i			2.32841i
$304$	−7.83502e6	+	2.69798e7i	−0.278881	+	0.960326i
$305$	7.31231e6			0.257724
$306$	3.54534e7	+	7.21688e6i	1.23735	+	0.251875i
$307$	−9.01924e6	+	5.20726e6i	−0.311713	+	0.179967i	−0.647693	−	0.761902i	$-0.724266\pi$
$307$	−9.01924e6	+	5.20726e6i	−0.311713	+	0.179967i	0.335980	+	0.941869i	$0.390933\pi$
$308$	−9.04151e6	−	3.84009e6i	−0.309449	−	0.131428i
$309$	3.50474e7	+	6.07039e7i	1.18790	+	2.05751i
$310$	−1.46921e7	+	4.91423e6i	−0.493173	+	0.164957i
$311$			4.71094e7i			1.56613i	0.621942	+	0.783063i	$0.286344\pi$
$311$			4.71094e7i			1.56613i	−0.621942	+	0.783063i	$0.713656\pi$
$312$	−1.22656e7	+	1.78348e7i	−0.403855	+	0.587224i
$313$	1.54709e7	−	2.67963e7i	0.504524	−	0.873861i	−0.495463	−	0.868629i	$-0.665001\pi$
$313$	1.54709e7	−	2.67963e7i	0.504524	−	0.873861i	0.999986	−	0.00523133i	$-0.00166519\pi$
$314$	4.39768e6	+	1.31478e7i	0.142048	+	0.424681i
$315$		−	1.50484e7i		−	0.481458i
$316$	4.18686e7	−	5.13206e6i	1.32687	−	0.162641i
$317$	−2.29745e7	+	3.97930e7i	−0.721221	+	1.24919i	0.239290	+	0.970948i	$0.423085\pi$
$317$	−2.29745e7	+	3.97930e7i	−0.721221	+	1.24919i	−0.960511	+	0.278243i	$0.910248\pi$
$318$	840500.	−	4.12901e6i	0.0261370	−	0.128400i
$319$	−1.67154e7	−	9.65064e6i	−0.514926	−	0.297293i
$320$	−1.02019e7	+	1.25824e7i	−0.311337	+	0.383984i
$321$	3.36337e7	+	5.82553e7i	1.01686	+	1.76125i
$322$	−5.64165e6	+	6.37540e6i	−0.168981	+	0.190959i
$323$	1.50407e7	−	2.58739e7i	0.446335	−	0.767810i
$324$	1.65635e6	+	1.35129e7i	0.0486987	+	0.397295i
$325$	−5.93962e6	−	1.02877e7i	−0.173025	−	0.299688i
$326$	1.09031e7	−	5.35622e7i	0.314700	−	1.54599i
$327$	−2.88024e7	−	1.66291e7i	−0.823731	−	0.475581i
$328$	−1.33138e6	+	1.68503e7i	−0.0377296	+	0.477514i
$329$	−5.47231e6	+	9.47832e6i	−0.153668	+	0.266160i
$330$	−8.99222e6	+	1.01617e7i	−0.250222	+	0.282765i
$331$			6.92959e7i			1.91084i	0.295255	+	0.955419i	$0.404595\pi$
$331$			6.92959e7i			1.91084i	−0.295255	+	0.955419i	$0.595405\pi$
$332$	1.12218e6	−	2.64217e6i	0.0306653	−	0.0722016i
$333$	−5.61379e6	+	9.72336e6i	−0.152028	+	0.263320i
$334$	−4.55735e6	−	4.03284e6i	−0.122313	−	0.108236i
$335$			3.22611e7i			0.858114i
$336$	1.11619e7	−	3.88658e7i	0.294253	−	1.02459i
$337$	−2.49799e7	−	4.32664e7i	−0.652681	−	1.13048i	−0.982470	−	0.186421i	$-0.940311\pi$
$337$	−2.49799e7	−	4.32664e7i	−0.652681	−	1.13048i	0.329789	−	0.944055i	$-0.393022\pi$
$338$	−9.67982e6	−	2.89398e7i	−0.250679	−	0.749456i
$339$	−3.43731e7	+	1.98453e7i	−0.882306	+	0.509400i
$340$	1.37832e7	−	1.03819e7i	0.350682	−	0.264145i
$341$	−2.04727e7			−0.516311
$342$	−5.56979e7	−	1.15099e7i	−1.39239	−	0.287735i
$343$		−	4.23140e7i		−	1.04858i
$344$	5.08264e7	+	4.01592e6i	1.24857	+	0.0986529i
$345$	5.87976e6	+	1.01840e7i	0.143187	+	0.248006i
$346$	−1.03247e7	−	3.08679e7i	−0.249259	−	0.745211i
$347$	1.32894e7	−	7.67263e6i	0.318065	−	0.183635i	−0.332465	−	0.943116i	$-0.607880\pi$
$347$	1.32894e7	−	7.67263e6i	0.318065	−	0.183635i	0.650530	+	0.759481i	$0.274547\pi$
$348$	3.10598e7	−	7.31305e7i	0.736989	−	1.73524i
$349$	−4.19297e6			−0.0986383			−0.0493192	−	0.998783i	$-0.515705\pi$
$349$	−4.19297e6			−0.0986383			−0.0493192	+	0.998783i	$0.515705\pi$
$350$	1.66194e7	+	1.47067e7i	0.387625	+	0.343013i
$351$	−1.12582e7	−	6.49994e6i	−0.260345	−	0.150310i
$352$	−1.80597e7	+	1.14922e7i	−0.414079	+	0.263498i
$353$	−5.70174e7			−1.29623			−0.648116	−	0.761541i	$-0.724443\pi$
$353$	−5.70174e7			−1.29623			−0.648116	+	0.761541i	$0.724443\pi$
$354$	7.03112e7	−	7.94558e7i	1.58495	−	1.79108i
$355$	−871758.	−	503310.i	−0.0194855	−	0.0112499i
$356$	3.26092e7	−	2.45623e7i	0.722754	−	0.544401i
$357$	−2.15379e7	+	3.73047e7i	−0.473367	+	0.819896i
$358$	4.67068e6	−	2.29450e7i	0.101796	−	0.500080i
$359$	3.11561e7	−	1.79880e7i	0.673380	−	0.388776i	−0.123976	−	0.992285i	$-0.539565\pi$
$359$	3.11561e7	−	1.79880e7i	0.673380	−	0.388776i	0.797356	+	0.603509i	$0.206231\pi$
$360$	−2.70196e7	−	1.85823e7i	−0.579123	−	0.398284i
$361$	−2.37641e7	+	4.06028e7i	−0.505125	+	0.863046i
$362$	−4.90914e7	+	5.54762e7i	−1.03485	+	1.16945i
$363$	4.89355e7	−	2.82529e7i	1.02307	−	0.590668i
$364$	−9.10269e6	−	1.20849e7i	−0.188741	−	0.250575i
$365$	6.14940e6	−	1.06511e7i	0.126460	−	0.219036i
$366$	−7.93442e6	+	3.89784e7i	−0.161835	+	0.795025i
$367$	−4.13085e7	−	2.38495e7i	−0.835683	−	0.482482i	0.0201113	−	0.999798i	$-0.493598\pi$
$367$	−4.13085e7	−	2.38495e7i	−0.835683	−	0.482482i	−0.855795	+	0.517316i	$0.826931\pi$
$368$	4.48058e6	+	1.80022e7i	0.0899065	+	0.361229i
$369$	−3.42182e7			−0.681049
$370$	1.69859e6	+	5.07828e6i	0.0335338	+	0.100256i
$371$	2.55066e6	+	1.47263e6i	0.0499495	+	0.0288384i
$372$	−1.02533e7	−	8.36489e7i	−0.199175	−	1.62492i
$373$	−9.32094e7			−1.79611			−0.898056	−	0.439882i	$-0.855020\pi$
$373$	−9.32094e7			−1.79611			−0.898056	+	0.439882i	$0.855020\pi$
$374$	2.16255e7	−	7.23333e6i	0.413383	−	0.138269i
$375$	6.16814e7	−	3.56118e7i	1.16966	−	0.675305i
$376$	1.02610e7	+	2.15298e7i	0.193031	+	0.405020i
$377$	−1.48638e7	−	2.57448e7i	−0.277399	−	0.480469i
$378$	2.37976e7	+	4.84423e6i	0.440614	+	0.0896912i
$379$			2.66098e7i			0.488791i	0.969676	+	0.244395i	$0.0785895\pi$
$379$			2.66098e7i			0.488791i	−0.969676	+	0.244395i	$0.921410\pi$
$380$	−2.17151e7	+	1.62558e7i	−0.395741	+	0.296250i
$381$	1.49120e8			2.69625
$382$	2.11400e6	−	1.03851e7i	0.0379240	−	0.186304i
$383$	8.76834e7	−	5.06240e7i	1.56071	−	0.901074i	0.563520	−	0.826103i	$-0.309447\pi$
$383$	8.76834e7	−	5.06240e7i	1.56071	−	0.901074i	0.997186	−	0.0749710i	$-0.0238864\pi$
$384$	−5.60008e7	−	6.80342e7i	−0.989009	−	1.20153i
$385$	−4.74221e6	−	8.21376e6i	−0.0830996	−	0.143933i
$386$	−3.22310e7	−	9.63612e7i	−0.560417	−	1.67548i
$387$			1.03214e8i			1.78076i
$388$	1.01708e7	+	8.29760e7i	0.174125	+	1.42055i
$389$	3.55313e7	−	6.15421e7i	0.603619	−	1.04550i	−0.388649	−	0.921386i	$-0.627058\pi$
$389$	3.55313e7	−	6.15421e7i	0.603619	−	1.04550i	0.992268	−	0.124113i	$-0.0396084\pi$
$390$	−1.98197e7	+	6.62929e6i	−0.334120	+	0.111757i
$391$		−	1.97621e7i		−	0.330600i
$392$	−2.63435e7	−	1.81173e7i	−0.437335	−	0.300771i
$393$	5.17181e7	−	8.95784e7i	0.852050	−	1.47579i
$394$	5.03492e7	+	1.02491e7i	0.823197	+	0.167570i
$395$	3.52708e7	+	2.03636e7i	0.572300	+	0.330418i
$396$	−2.60725e7	−	3.46142e7i	−0.419853	−	0.557402i
$397$	1.11111e7	+	1.92450e7i	0.177577	+	0.307572i	0.941050	−	0.338267i	$-0.109841\pi$
$397$	1.11111e7	+	1.92450e7i	0.177577	+	0.307572i	−0.763473	+	0.645840i	$0.776508\pi$
$398$	5.93223e7	+	5.24948e7i	0.940955	+	0.832659i
$399$	3.40306e7	−	5.85413e7i	0.535736	−	0.921603i
$400$	4.69283e7	−	1.16800e7i	0.733255	−	0.182500i
$401$	−3.99192e7	−	6.91421e7i	−0.619083	−	1.07228i	−0.989653	−	0.143479i	$-0.954171\pi$
$401$	−3.99192e7	−	6.91421e7i	−0.619083	−	1.07228i	0.370570	−	0.928804i	$-0.379162\pi$
$402$	−1.71968e8	−	3.50058e7i	−2.64710	−	0.538842i
$403$	−2.73072e7	−	1.57658e7i	−0.417218	−	0.240881i
$404$	−7.88043e7	+	5.93579e7i	−1.19510	+	0.900190i
$405$	−6.57226e6	+	1.13835e7i	−0.0989350	+	0.171360i
$406$	4.15897e7	+	3.68031e7i	0.621453	+	0.549929i
$407$			7.07631e6i			0.104960i
$408$	4.03852e7	+	8.47368e7i	0.594623	+	1.24765i
$409$	3.41293e7	−	5.91137e7i	0.498835	−	0.864008i	−0.501164	−	0.865353i	$-0.667095\pi$
$409$	3.41293e7	−	5.91137e7i	0.498835	−	0.864008i	0.999999	+	0.00134420i	$0.000427871\pi$
$410$	−1.08151e7	+	1.22218e7i	−0.156921	+	0.177330i
$411$			1.75682e8i			2.53047i
$412$	−4.17370e7	+	9.82699e7i	−0.596801	+	1.40517i
$413$	3.70799e7	+	6.42243e7i	0.526367	+	0.911694i
$414$	−3.56162e7	+	1.19129e7i	−0.501934	+	0.167887i
$415$	2.40028e6	−	1.38580e6i	0.0335829	−	0.0193891i
$416$	−3.29389e7	+	1.42115e6i	−0.457540	+	0.0197406i
$417$	−5.96190e7			−0.822198
$418$	−3.40283e7	+	1.12698e7i	−0.465920	+	0.154307i
$419$			7.22515e6i			0.0982210i	0.998793	+	0.0491105i	$0.0156387\pi$
$419$			7.22515e6i			0.0982210i	−0.998793	+	0.0491105i	$0.984361\pi$
$420$	3.11854e7	−	2.34898e7i	0.420924	−	0.317053i
$421$	−3.80991e7	−	6.59896e7i	−0.510586	−	0.884361i	−0.999925	−	0.0122669i	$-0.996095\pi$
$421$	−3.80991e7	−	6.59896e7i	−0.510586	−	0.884361i	0.489339	−	0.872094i	$-0.337238\pi$
$422$	5.88269e7	−	1.96765e7i	0.782778	−	0.261824i
$423$	−4.18135e7	+	2.41411e7i	−0.552453	+	0.318959i
$424$	5.79377e6	−	2.76129e6i	0.0760088	−	0.0362255i
$425$	−5.15160e7			−0.671082
$426$	3.62882e6	−	4.10079e6i	0.0469393	−	0.0530443i
$427$	−2.40785e7	−	1.39018e7i	−0.309276	−	0.178561i
$428$	−4.00534e7	+	9.43060e7i	−0.510868	+	1.20284i
$429$	−2.76176e7			−0.349795
$430$	3.68651e7	+	3.26223e7i	0.463671	+	0.410307i
$431$	5.71751e6	+	3.30100e6i	0.0714126	+	0.0412301i	0.535281	−	0.844674i	$-0.320206\pi$
$431$	5.71751e6	+	3.30100e6i	0.0714126	+	0.0412301i	−0.463869	+	0.885904i	$0.653539\pi$
$432$	3.80841e7	−	3.67471e7i	0.472381	−	0.455797i
$433$	−4.00685e6	+	6.94006e6i	−0.0493559	+	0.0854869i	−0.889648	−	0.456647i	$-0.849050\pi$
$433$	−4.00685e6	+	6.94006e6i	−0.0493559	+	0.0854869i	0.840292	+	0.542134i	$0.182384\pi$
$434$	5.77220e7	+	1.17499e7i	0.706110	+	0.143735i
$435$	6.64353e7	−	3.83565e7i	0.807108	−	0.465984i
$436$	−6.16325e6	−	5.02812e7i	−0.0743619	−	0.606662i
$437$	−92086.7	+	3.10654e7i	−0.00110345	+	0.372248i
$438$	5.01031e7	+	4.43367e7i	0.596269	+	0.527644i
$439$	−1.05768e8	+	6.10650e7i	−1.25014	+	0.721770i	−0.971138	−	0.238520i	$-0.923338\pi$
$439$	−1.05768e8	+	6.10650e7i	−1.25014	+	0.721770i	−0.279005	+	0.960290i	$0.590005\pi$
$440$	−2.06038e7	−	1.62796e6i	−0.241874	−	0.0191111i
$441$	3.23624e7	−	5.60532e7i	0.377333	−	0.653559i
$442$	3.44153e7	+	7.00557e6i	0.398552	+	0.0811291i
$443$	3.47242e7	+	2.00480e7i	0.399411	+	0.230600i	0.686230	−	0.727385i	$-0.259264\pi$
$443$	3.47242e7	+	2.00480e7i	0.399411	+	0.230600i	−0.286819	+	0.957985i	$0.592598\pi$
$444$	−2.89130e7	+	3.54402e6i	−0.330327	+	0.0404900i
$445$	3.94169e7			0.447304
$446$	3.70127e7	−	1.23801e7i	0.417202	−	0.139546i
$447$	−1.91452e8	−	1.10535e8i	−2.14356	−	1.23759i
$448$	5.75146e7	−	2.20370e7i	0.639652	−	0.245086i
$449$	−6.26815e7			−0.692469			−0.346234	−	0.938148i	$-0.612540\pi$
$449$	−6.26815e7			−0.692469			−0.346234	+	0.938148i	$0.612540\pi$
$450$	3.10547e7	+	9.28446e7i	0.340793	+	1.01887i
$451$	−1.86771e7	+	1.07832e7i	−0.203601	+	0.117549i
$452$	−5.56445e7	−	2.36332e7i	−0.602569	−	0.255922i
$453$	2.75285e7	+	4.76807e7i	0.296134	+	0.512918i
$454$	1.83389e7	−	9.00909e7i	0.195977	−	0.962749i
$455$		−	1.46078e7i		−	0.155078i
$456$	−6.30893e7	−	1.33391e8i	−0.665367	−	1.40680i
$457$	1.18835e8			1.24507			0.622537	−	0.782591i	$-0.286102\pi$
$457$	1.18835e8			1.24507			0.622537	+	0.782591i	$0.286102\pi$
$458$	−1.33032e7	−	2.70799e6i	−0.138471	−	0.0281871i
$459$	−4.88229e7	+	2.81879e7i	−0.504877	+	0.291491i
$460$	−7.00204e6	+	1.64863e7i	−0.0719368	+	0.169375i
$461$	6.50806e7	+	1.12723e8i	0.664277	+	1.15056i	0.979481	+	0.201537i	$0.0645936\pi$
$461$	6.50806e7	+	1.12723e8i	0.664277	+	1.15056i	−0.315204	+	0.949024i	$0.602073\pi$
$462$	4.89292e7	−	1.63659e7i	0.496183	−	0.165964i
$463$		−	1.85794e8i		−	1.87192i	−0.352102	−	0.935962i	$-0.614533\pi$
$463$		−	1.85794e8i		−	1.87192i	0.352102	−	0.935962i	$-0.385467\pi$
$464$	1.17437e8	−	2.92290e7i	1.17558	−	0.292590i
$465$	4.06843e7	−	7.04673e7i	0.404639	−	0.700856i
$466$	1.73125e7	+	5.17594e7i	0.171081	+	0.511483i
$467$		−	1.26043e8i		−	1.23757i	−0.785562	−	0.618783i	$-0.787626\pi$
$467$		−	1.26043e8i		−	1.23757i	0.785562	−	0.618783i	$-0.212374\pi$
$468$	−8.12038e6	−	6.62480e7i	−0.0792208	−	0.646302i
$469$	6.13330e7	−	1.06232e8i	0.594533	−	1.02976i
$470$	−4.59326e6	+	2.25647e7i	−0.0442412	+	0.217338i
$471$	−6.30601e7	−	3.64078e7i	−0.603521	−	0.348443i
$472$	1.61103e8	+	1.27292e7i	1.53207	+	0.121053i
$473$	3.25260e7	+	5.63366e7i	0.307360	+	0.532362i
$474$	−1.46820e8	+	1.65915e8i	−1.37864	+	1.55794i
$475$	8.09814e7	+	240052.i	0.755622	+	0.00223988i
$476$	−6.51240e7	+	7.98260e6i	−0.603837	+	0.0740157i
$477$	6.49647e6	+	1.12522e7i	0.0598581	+	0.103677i
$478$	−3.05459e7	+	1.50059e8i	−0.279685	+	1.37397i
$479$	−1.18260e8	−	6.82777e7i	−1.07605	−	0.621259i	−0.146223	−	0.989252i	$-0.546712\pi$
$479$	−1.18260e8	−	6.82777e7i	−1.07605	−	0.621259i	−0.929829	+	0.367993i	$0.880045\pi$
$480$	−3.66732e6	−	8.49998e7i	−0.0331609	−	0.768589i
$481$	−5.44941e6	+	9.43866e6i	−0.0489682	+	0.0848155i
$482$	−1.26409e7	+	1.42850e7i	−0.112885	+	0.127567i
$483$		−	4.47131e7i		−	0.396820i
$484$	7.92187e7	+	3.36456e7i	0.698701	+	0.296751i
$485$	−4.03570e7	+	6.99004e7i	−0.353748	+	0.612709i
$486$	−1.09979e8	−	9.73210e7i	−0.958074	−	0.847808i
$487$			1.18541e8i			1.02632i	0.858294	+	0.513158i	$0.171525\pi$
$487$			1.18541e8i			1.02632i	−0.858294	+	0.513158i	$0.828475\pi$
$488$	−5.46939e7	+	2.60669e7i	−0.470630	+	0.224300i
$489$	1.43545e8	+	2.48627e8i	1.22761	+	2.12629i
$490$	−9.79202e6	−	2.92753e7i	−0.0832308	−	0.248836i
$491$	7.56454e7	−	4.36739e7i	0.639055	−	0.368958i	−0.145196	−	0.989403i	$-0.546381\pi$
$491$	7.56454e7	−	4.36739e7i	0.639055	−	0.368958i	0.784250	+	0.620445i	$0.213048\pi$
$492$	−5.34130e7	−	7.09118e7i	−0.448489	−	0.595420i
$493$	−1.28918e8			−1.07590
$494$	−5.40671e7	−	1.11729e7i	−0.448489	−	0.0926796i
$495$		−	4.18405e7i		−	0.344970i
$496$	9.23744e7	−	8.91314e7i	0.757018	−	0.730442i
$497$	1.91373e6	+	3.31467e6i	0.0155887	+	0.0270005i
$498$	4.78255e6	+	1.42984e7i	0.0387232	+	0.115771i
$499$	2.10404e7	−	1.21477e7i	0.169337	−	0.0977670i	−0.412936	−	0.910760i	$-0.635497\pi$
$499$	2.10404e7	−	1.21477e7i	0.169337	−	0.0977670i	0.582273	+	0.812993i	$0.302163\pi$
$500$	9.98523e7	+	4.24091e7i	0.798819	+	0.339273i
$501$	3.19624e7			0.254171
$502$	−2.07521e7	−	1.83638e7i	−0.164041	−	0.145161i
$503$	−9.05353e7	−	5.22706e7i	−0.711400	−	0.410727i	0.100179	−	0.994969i	$-0.468058\pi$
$503$	−9.05353e7	−	5.22706e7i	−0.711400	−	0.410727i	−0.811579	+	0.584242i	$0.801392\pi$
$504$	5.36444e7	+	1.12557e8i	0.419018	+	0.879189i
$505$	−9.52560e7			−0.739636
$506$	−1.56860e7	+	1.77261e7i	−0.121077	+	0.136824i
$507$	1.38803e8	+	8.01379e7i	1.06506	+	0.614914i
$508$	1.36655e8	+	1.81425e8i	1.04240	+	1.38390i
$509$	2.72058e7	−	4.71219e7i	0.206305	−	0.357330i	−0.744243	−	0.667909i	$-0.767190\pi$
$509$	2.72058e7	−	4.71219e7i	0.206305	−	0.357330i	0.950548	+	0.310579i	$0.100523\pi$
$510$	−1.80781e7	+	8.88099e7i	−0.136283	+	0.669501i
$511$	−4.04984e7	+	2.33818e7i	−0.303512	+	0.175233i
$512$	3.14535e7	−	1.30480e8i	0.234346	−	0.972153i
$513$	7.68792e7	−	4.40829e7i	0.569452	−	0.326526i
$514$	−1.29027e8	+	1.45808e8i	−0.950148	+	1.07372i
$515$	−8.92733e7	+	5.15420e7i	−0.653582	+	0.377345i
$516$	−2.13895e8	+	1.61112e8i	−1.55687	+	1.17268i
$517$	−1.52152e7	+	2.63535e7i	−0.110105	+	0.190707i
$518$	4.06130e6	−	1.99514e7i	0.0292197	−	0.143544i
$519$	1.48051e8	+	8.54771e7i	1.05903	+	0.611432i
$520$	−2.62284e7	−	1.80382e7i	−0.186536	−	0.128287i
$521$	1.18017e8			0.834509			0.417254	−	0.908790i	$-0.362992\pi$
$521$	1.18017e8			0.834509			0.417254	+	0.908790i	$0.362992\pi$
$522$	7.77138e7	+	2.32341e8i	0.546370	+	1.63349i
$523$	−2.66803e7	−	1.54039e7i	−0.186503	−	0.107678i	0.403841	−	0.914829i	$-0.367675\pi$
$523$	−2.66803e7	−	1.54039e7i	−0.186503	−	0.107678i	−0.590344	+	0.807151i	$0.701008\pi$
$524$	1.56380e8	−	1.91683e7i	1.08689	−	0.133226i
$525$	−1.16558e8			−0.805500
$526$	−5.78702e7	+	1.93565e7i	−0.397647	+	0.133005i
$527$	−1.18422e8	+	6.83708e7i	−0.809095	+	0.467131i
$528$	3.10345e7	−	1.08062e8i	0.210835	−	0.734128i
$529$	−6.37613e7	−	1.10438e8i	−0.430715	−	0.746021i
$530$	6.07227e6	+	1.23607e6i	0.0407871	+	0.00830261i
$531$			3.27156e8i			2.18510i
$532$	1.02410e8	−	1.22449e7i	0.680153	−	0.0813244i
$533$	−3.32163e7			−0.219366
$534$	−4.27704e7	+	2.10112e8i	−0.280879	+	1.37984i
$535$	−8.56723e7	+	4.94629e7i	−0.559473	+	0.323012i
$536$	−1.15004e8	−	2.41303e8i	−0.746826	−	1.56700i
$537$	6.14920e7	+	1.06507e8i	0.397096	+	0.687791i
$538$	−3.46087e7	−	1.03470e8i	−0.222248	−	0.664457i
$539$		−	4.07935e7i		−	0.260510i
$540$	5.07174e7	−	6.21671e6i	0.322089	−	0.0394802i
$541$	1.24884e8	−	2.16305e8i	0.788704	−	1.36608i	−0.138058	−	0.990424i	$-0.544086\pi$
$541$	1.24884e8	−	2.16305e8i	0.788704	−	1.36608i	0.926761	−	0.375651i	$-0.122581\pi$
$542$	−8.09032e7	+	2.70606e7i	−0.508122	+	0.169957i
$543$		−	3.89075e8i		−	2.43016i
$544$	−6.60847e7	+	1.26788e8i	−0.410491	+	0.787556i
$545$	2.44553e7	−	4.23578e7i	0.151072	−	0.261664i
$546$	7.78669e7	+	1.58506e7i	0.478382	+	0.0973793i
$547$	−7.40560e7	−	4.27562e7i	−0.452479	−	0.261239i	0.256398	−	0.966571i	$-0.417464\pi$
$547$	−7.40560e7	−	4.27562e7i	−0.452479	−	0.261239i	−0.708877	+	0.705333i	$0.750798\pi$
$548$	−2.13742e8	+	1.60997e8i	−1.29882	+	0.978309i
$549$	−6.13275e7	−	1.06222e8i	−0.370628	−	0.641946i
$550$	4.62086e7	+	4.08904e7i	0.277738	+	0.245772i
$551$	2.02654e8	+	600725.i	1.21144	+	0.00359105i
$552$	−8.02828e7	−	5.52134e7i	−0.477315	−	0.328267i
$553$	−7.74283e7	−	1.34110e8i	−0.457851	−	0.793021i
$554$	−1.13513e8	−	2.31066e7i	−0.667598	−	0.135896i
$555$	−2.43568e7	−	1.40624e7i	−0.142476	−	0.0822584i
$556$	−5.46356e7	−	7.25349e7i	−0.317871	−	0.422010i
$557$	1.61996e6	−	2.80586e6i	0.00937431	−	0.0162368i	−0.861300	−	0.508096i	$-0.830349\pi$
$557$	1.61996e6	−	2.80586e6i	0.00937431	−	0.0162368i	0.870675	+	0.491860i	$0.163683\pi$
$558$	1.94608e8	+	1.72210e8i	1.12010	+	0.991188i
$559$			1.00192e8i			0.573585i
$560$	5.71573e7	+	1.64151e7i	0.325468	+	0.0934714i
$561$	−5.98838e7	+	1.03722e8i	−0.339173	+	0.587464i
$562$	2.76389e7	−	3.12336e7i	0.155708	−	0.175960i
$563$		−	2.64818e7i		−	0.148396i	−0.997244	−	0.0741980i	$-0.976360\pi$
$563$		−	2.64818e7i		−	0.148396i	0.997244	−	0.0741980i	$-0.0236397\pi$
$564$	−1.15297e8	−	4.89688e7i	−0.642661	−	0.272950i
$565$	−2.91852e7	−	5.05502e7i	−0.161814	−	0.280271i
$566$	−8.55147e7	+	2.86030e7i	−0.471619	+	0.157748i
$567$	4.32833e7	−	2.49896e7i	0.237450	−	0.137092i
$568$	8.31468e6	+	656964.i	0.0453733	+	0.00358506i
$569$	2.45010e8			1.32998			0.664992	−	0.746851i	$-0.268435\pi$
$569$	2.45010e8			1.32998			0.664992	+	0.746851i	$0.268435\pi$
$570$	2.88320e7	−	1.39522e8i	0.155686	−	0.753386i
$571$		−	1.26463e8i		−	0.679288i	−0.940554	−	0.339644i	$-0.889693\pi$
$571$		−	1.26463e8i		−	0.679288i	0.940554	−	0.339644i	$-0.110307\pi$
$572$	−2.53091e7	−	3.36007e7i	−0.135235	−	0.179540i
$573$	2.78319e7	+	4.82062e7i	0.147938	+	0.256236i
$574$	5.88482e7	−	1.96836e7i	0.311170	−	0.104080i
$575$	4.63100e7	−	2.67371e7i	0.243596	−	0.140641i
$576$	2.68340e8	+	4.26709e7i	1.40417	+	0.223288i
$577$	−1.94565e8			−1.01283			−0.506415	−	0.862290i	$-0.669030\pi$
$577$	−1.94565e8			−1.01283			−0.506415	+	0.862290i	$0.669030\pi$
$578$	−2.70333e7	+	3.05492e7i	−0.139996	+	0.158204i
$579$	4.62173e8	+	2.66836e8i	2.38105	+	1.37470i
$580$	1.07548e8	+	4.56776e7i	0.551212	+	0.234110i
$581$	−1.05384e7			−0.0537338
$582$	−3.28814e8	−	2.90971e8i	−1.66795	−	1.47598i
$583$	7.09185e6	+	4.09448e6i	0.0357893	+	0.0206630i
$584$	−8.02674e6	+	1.01588e8i	−0.0402996	+	0.510040i
$585$	3.22210e7	−	5.58085e7i	0.160943	−	0.278761i
$586$	2.67143e8	+	5.43796e7i	1.32755	+	0.270236i
$587$	7.50983e7	−	4.33580e7i	0.371292	−	0.214366i	−0.302731	−	0.953076i	$-0.597898\pi$
$587$	7.50983e7	−	4.33580e7i	0.371292	−	0.214366i	0.674023	+	0.738711i	$0.264565\pi$
$588$	1.66677e8	−	2.04306e7i	0.819870	−	0.100496i
$589$	1.86473e8	−	1.06925e8i	0.912580	−	0.523278i
$590$	1.16850e8	+	1.03402e8i	0.568950	+	0.503469i
$591$	−2.33713e8	+	1.34934e8i	−1.13219	+	0.653672i
$592$	−3.08080e7	−	3.19289e7i	−0.148490	−	0.153893i
$593$	−6.42735e7	+	1.11325e8i	−0.308225	+	0.533861i	−0.977974	−	0.208726i	$-0.933068\pi$
$593$	−6.42735e7	+	1.11325e8i	−0.308225	+	0.533861i	0.669749	+	0.742587i	$0.266402\pi$
$594$	6.61668e7	+	1.34689e7i	0.315704	+	0.0642647i
$595$	−5.48616e7	−	3.16743e7i	−0.260446	−	0.150368i
$596$	−4.09675e7	−	3.34223e8i	−0.193509	−	1.57869i
$597$	−4.16049e8			−1.95534
$598$	−3.45734e7	+	1.15641e7i	−0.161673	+	0.0540766i
$599$	−4.55407e7	−	2.62929e7i	−0.211894	−	0.122337i	0.390297	−	0.920689i	$-0.372372\pi$
$599$	−4.55407e7	−	2.62929e7i	−0.211894	−	0.122337i	−0.602191	+	0.798352i	$0.705706\pi$
$600$	−1.43931e8	+	2.09282e8i	−0.666345	+	0.968897i
$601$	1.34220e8			0.618290			0.309145	−	0.951015i	$-0.399957\pi$
$601$	1.34220e8			0.618290			0.309145	+	0.951015i	$0.399957\pi$
$602$	−5.93726e7	−	1.77507e8i	−0.272143	−	0.813628i
$603$	4.68641e8	−	2.70570e8i	2.13741	−	1.23404i
$604$	−3.27829e7	+	7.71875e7i	−0.148777	+	0.350297i
$605$	4.15497e7	+	7.19662e7i	0.187630	+	0.324984i
$606$	1.03360e8	−	5.07763e8i	0.464446	−	2.28162i
$607$			2.21760e8i			0.991556i	0.868449	+	0.495778i	$0.165117\pi$
$607$			2.21760e8i			0.991556i	−0.868449	+	0.495778i	$0.834883\pi$
$608$	1.04474e8	−	1.98998e8i	0.464832	−	0.885399i
$609$	−2.91685e8			−1.29140
$610$	−5.73229e7	−	1.16686e7i	−0.252545	−	0.0514080i
$611$	−4.05892e7	+	2.34342e7i	−0.177945	+	0.102737i
$612$	−2.66411e8	−	1.13150e8i	−1.16225	−	0.493627i
$613$	−2.05576e8	−	3.56068e8i	−0.892464	−	1.54579i	−0.836912	−	0.547337i	$-0.815642\pi$
$613$	−2.05576e8	−	3.56068e8i	−0.892464	−	1.54579i	−0.0555514	−	0.998456i	$-0.517692\pi$
$614$	7.90134e7	−	2.64285e7i	0.341347	−	0.114174i
$615$		−	8.57158e7i		−	0.368498i
$616$	6.47507e7	+	4.45314e7i	0.277014	+	0.190513i
$617$	−1.37975e8	+	2.38980e8i	−0.587416	+	1.01743i	0.407153	+	0.913360i	$0.366521\pi$
$617$	−1.37975e8	+	2.38980e8i	−0.587416	+	1.01743i	−0.994569	+	0.104075i	$0.966812\pi$
$618$	−1.77877e8	−	5.31799e8i	−0.753622	−	2.25311i
$619$			3.08270e8i			1.29975i	0.760041	+	0.649875i	$0.225179\pi$
$619$			3.08270e8i			1.29975i	−0.760041	+	0.649875i	$0.774821\pi$
$620$	1.23017e8	−	1.50789e7i	0.516166	−	0.0632693i
$621$	2.92593e7	−	5.06786e7i	0.122177	−	0.211617i
$622$	7.51749e7	−	3.69302e8i	0.312393	−	1.53465i
$623$	−1.29795e8	−	7.49373e7i	−0.536777	−	0.309909i
$624$	1.24613e8	−	1.20238e8i	0.512872	−	0.494867i
$625$	−3.98675e7	−	6.90525e7i	−0.163297	−	0.282839i
$626$	−1.64040e8	+	1.85375e8i	−0.668693	+	0.755663i
$627$	9.46186e7	−	1.62768e8i	0.383861	−	0.660338i
$628$	−1.34938e7	−	1.10086e8i	−0.0544825	−	0.444481i
$629$	2.36321e7	+	4.09321e7i	0.0949623	+	0.164480i
$630$	−2.40135e7	+	1.17968e8i	−0.0960359	+	0.471783i
$631$	−3.03701e8	−	1.75342e8i	−1.20881	−	0.697906i	−0.246309	−	0.969191i	$-0.579218\pi$
$631$	−3.03701e8	−	1.75342e8i	−1.20881	−	0.697906i	−0.962499	+	0.271285i	$0.912551\pi$
$632$	−3.36407e8	−	2.65804e7i	−1.33264	−	0.105296i
$633$	−1.62899e8	+	2.82149e8i	−0.642254	+	1.11242i
$634$	2.43602e8	−	2.75285e8i	0.955902	−	1.08023i
$635$			2.19300e8i			0.856482i
$636$	−1.31778e7	+	3.10271e7i	−0.0512236	+	0.120606i
$637$	3.14148e7	−	5.44120e7i	0.121539	−	0.210512i
$638$	1.15636e8	+	1.02327e8i	0.445277	+	0.394030i
$639$			1.68848e7i			0.0647132i
$640$	1.00053e8	−	8.23567e7i	0.381674	−	0.314166i
$641$	1.96223e8	+	3.39868e8i	0.745032	+	1.29043i	0.950180	+	0.311703i	$0.100899\pi$
$641$	1.96223e8	+	3.39868e8i	0.745032	+	1.29043i	−0.205147	+	0.978731i	$0.565767\pi$
$642$	−1.70702e8	−	5.10348e8i	−0.645108	−	1.92869i
$643$	−1.72732e8	+	9.97268e7i	−0.649740	+	0.375128i	−0.788357	−	0.615218i	$-0.789068\pi$
$643$	−1.72732e8	+	9.97268e7i	−0.649740	+	0.375128i	0.138617	+	0.990346i	$0.455734\pi$
$644$	5.43997e7	−	4.09756e7i	0.203676	−	0.153415i
$645$	−2.58549e8			−0.963526
$646$	−1.59196e8	+	1.78830e8i	−0.590520	+	0.663351i
$647$			7.97911e7i			0.294606i	0.989091	+	0.147303i	$0.0470592\pi$
$647$			7.97911e7i			0.294606i	−0.989091	+	0.147303i	$0.952941\pi$
$648$	8.57870e6	−	1.08574e8i	0.0315280	−	0.399025i
$649$	1.03097e8	+	1.78569e8i	0.377147	+	0.653238i
$650$	3.01454e7	+	9.01261e7i	0.109769	+	0.328179i
$651$	−2.67937e8	+	1.54693e8i	−0.971157	+	0.560697i
$652$	−1.70944e8	+	4.02488e8i	−0.616752	+	1.45214i
$653$	5.32124e8			1.91106			0.955528	−	0.294901i	$-0.0952867\pi$
$653$	5.32124e8			1.91106			0.955528	+	0.294901i	$0.0952867\pi$
$654$	1.99253e8	+	1.76321e8i	0.712314	+	0.630333i
$655$	1.31737e8	+	7.60584e7i	0.468796	+	0.270660i
$656$	3.73259e7	−	1.29969e8i	0.132220	−	0.460392i
$657$	−2.06297e8			−0.727439
$658$	5.80237e7	−	6.55703e7i	0.203670	−	0.230160i
$659$	2.12160e8	+	1.22491e8i	0.741324	+	0.428004i	0.822550	−	0.568692i	$-0.192550\pi$
$659$	2.12160e8	+	1.22491e8i	0.741324	+	0.428004i	−0.0812266	+	0.996696i	$0.525884\pi$
$660$	8.67077e7	−	6.53109e7i	0.301596	−	0.227172i
$661$	4.85020e7	−	8.40080e7i	0.167941	−	0.290881i	−0.769755	−	0.638339i	$-0.779622\pi$
$661$	4.85020e7	−	8.40080e7i	0.167941	−	0.290881i	0.937696	+	0.347458i	$0.112955\pi$
$662$	1.10579e8	−	5.43227e8i	0.381152	−	1.87244i
$663$	−1.59751e8	+	9.22321e7i	−0.548154	+	0.316477i
$664$	−1.30133e7	+	1.89219e7i	−0.0444510	+	0.0646339i
$665$	8.60929e7	+	5.00466e7i	0.292754	+	0.170180i
$666$	5.95238e7	−	6.72655e7i	0.201497	−	0.227704i
$667$	1.15890e8	−	6.69089e7i	0.390542	−	0.225479i
$668$	2.92907e7	+	3.88868e7i	0.0982654	+	0.130459i
$669$	−1.02493e8	+	1.77523e8i	−0.342306	+	0.592892i
$670$	5.14807e7	−	2.52902e8i	0.171167	−	0.840869i
$671$	−6.69479e7	−	3.86524e7i	−0.221600	−	0.127941i
$672$	−1.49521e8	+	2.86866e8i	−0.492713	+	0.945304i
$673$	−3.54378e8			−1.16258			−0.581288	−	0.813698i	$-0.697451\pi$
$673$	−3.54378e8			−1.16258			−0.581288	+	0.813698i	$0.697451\pi$
$674$	1.26781e8	+	3.79037e8i	0.414070	+	1.23795i
$675$	−1.32109e8	−	7.62734e7i	−0.429559	−	0.248006i
$676$	2.97016e7	+	2.42313e8i	0.0961479	+	0.784397i
$677$	2.14252e8			0.690491			0.345246	−	0.938512i	$-0.387796\pi$
$677$	2.14252e8			0.690491			0.345246	+	0.938512i	$0.387796\pi$
$678$	3.01127e8	−	1.00721e8i	0.966185	−	0.323170i
$679$	2.65781e8	−	1.53449e8i	0.849015	−	0.490179i
$680$	−1.24617e8	+	5.93919e7i	−0.396323	+	0.188886i
$681$	2.41441e8	+	4.18188e8i	0.764486	+	1.32413i
$682$	1.60490e8	+	3.26693e7i	0.505935	+	0.102988i
$683$			3.14169e8i			0.986055i	0.870014	+	0.493027i	$0.164110\pi$
$683$			3.14169e8i			0.986055i	−0.870014	+	0.493027i	$0.835890\pi$
$684$	4.18262e8	+	1.79109e8i	1.30701	+	0.559691i
$685$	−2.58364e8			−0.803822
$686$	−6.75225e7	+	3.31709e8i	−0.209159	+	1.02751i
$687$	6.17513e7	−	3.56521e7i	0.190448	−	0.109955i
$688$	−3.92031e8	−	1.12588e8i	−1.20380	−	0.345722i
$689$	6.30626e6	+	1.09228e7i	0.0192803	+	0.0333945i
$690$	−2.98416e7	−	8.92177e7i	−0.0908396	−	0.271584i
$691$			3.33161e8i			1.00976i	0.863189	+	0.504882i	$0.168464\pi$
$691$			3.33161e8i			1.00976i	−0.863189	+	0.504882i	$0.831536\pi$
$692$	3.16805e7	+	2.58457e8i	0.0956034	+	0.779955i
$693$	−7.95448e7	+	1.37776e8i	−0.239008	+	0.413973i
$694$	−1.16422e8	+	3.89410e7i	−0.348303	+	0.116501i
$695$		−	8.76777e7i		−	0.261177i
$696$	−3.60183e8	+	5.23723e8i	−1.06831	+	1.55337i
$697$	−7.20236e7	+	1.24749e8i	−0.212704	+	0.368415i
$698$	3.28697e7	+	6.69094e6i	0.0966561	+	0.0196753i
$699$	−2.48251e8	−	1.43328e8i	−0.726876	−	0.419662i
$700$	−1.06815e8	−	1.41810e8i	−0.311415	−	0.413439i
$701$	1.69609e8	+	2.93771e8i	0.492373	+	0.852816i	0.999961	−	0.00878422i	$-0.00279614\pi$
$701$	1.69609e8	+	2.93771e8i	0.492373	+	0.852816i	−0.507588	+	0.861600i	$0.669463\pi$
$702$	7.78836e7	+	6.89199e7i	0.225131	+	0.199220i
$703$	−3.69582e7	−	6.44539e7i	−0.106376	−	0.185517i
$704$	1.59913e8	−	6.12716e7i	0.458317	−	0.175607i
$705$	−6.04727e7	−	1.04742e8i	−0.172581	−	0.298918i
$706$	4.46972e8	+	9.09855e7i	1.27018	+	0.258558i
$707$	3.13666e8	+	1.81095e8i	0.887584	+	0.512447i
$708$	−6.77977e8	+	5.10674e8i	−1.91036	+	1.43894i
$709$	−1.89484e8	+	3.28196e8i	−0.531660	+	0.920861i	0.467658	+	0.883910i	$0.345098\pi$
$709$	−1.89484e8	+	3.28196e8i	−0.531660	+	0.920861i	−0.999317	+	0.0369516i	$0.988235\pi$
$710$	6.03076e6	+	5.33667e6i	0.0168499	+	0.0149106i
$711$		−	6.83148e8i		−	1.90067i
$712$	−2.94827e8	+	1.40513e8i	−0.816821	+	0.389294i
$713$	7.09696e7	−	1.22923e8i	0.195796	−	0.339129i
$714$	2.28369e8	−	2.58071e8i	0.627398	−	0.708998i
$715$		−	4.06154e7i		−	0.111115i
$716$	−7.32291e7	+	1.72418e8i	−0.199501	+	0.469725i
$717$	−4.02154e8	−	6.96551e8i	−1.09103	−	1.88971i
$718$	−2.72945e8	+	9.12948e7i	−0.737397	+	0.246645i
$719$	6.58358e7	−	3.80103e7i	0.177123	−	0.102262i	−0.408817	−	0.912616i	$-0.634059\pi$
$719$	6.58358e7	−	3.80103e7i	0.177123	−	0.102262i	0.585940	+	0.810354i	$0.300725\pi$
$720$	1.82160e8	+	1.88788e8i	0.488040	+	0.505797i
$721$	3.91955e8			1.04575
$722$	2.51084e8	−	2.80373e8i	0.667125	−	0.744946i
$723$		−	1.00186e8i		−	0.265090i
$724$	4.73365e8	−	3.56553e8i	1.24733	−	0.939526i
$725$	−1.74419e8	−	3.02102e8i	−0.457698	−	0.792756i
$726$	−4.28701e8	+	1.43392e8i	−1.12033	+	0.374728i
$727$	−2.52469e8	+	1.45763e8i	−0.657059	+	0.379353i	−0.791156	−	0.611615i	$-0.790520\pi$
$727$	−2.52469e8	+	1.45763e8i	−0.657059	+	0.379353i	0.134096	+	0.990968i	$0.457187\pi$
$728$	5.20737e7	+	1.09262e8i	0.134966	+	0.283187i
$729$	6.16249e8			1.59065
$730$	−6.52030e7	+	7.36833e7i	−0.167610	+	0.189409i
$731$	3.76285e8	+	2.17248e8i	0.963308	+	0.556166i
$732$	1.24400e8	−	2.92899e8i	0.317165	−	0.746767i
$733$	1.53124e8			0.388805			0.194403	−	0.980922i	$-0.437723\pi$
$733$	1.53124e8			0.388805			0.194403	+	0.980922i	$0.437723\pi$
$734$	2.85769e8	+	2.52880e8i	0.722649	+	0.639479i
$735$	1.40412e8	+	8.10669e7i	0.353624	+	0.204165i
$736$	−6.39727e6	−	1.48274e8i	−0.0160458	−	0.371903i
$737$	1.70530e8	−	2.95367e8i	0.425989	−	0.737834i
$738$	2.68245e8	+	5.46038e7i	0.667363	+	0.135848i
$739$	−5.75218e8	+	3.32102e8i	−1.42528	+	0.822884i	−0.996743	−	0.0806419i	$-0.974303\pi$
$739$	−5.75218e8	+	3.32102e8i	−1.42528	+	0.822884i	−0.428534	+	0.903526i	$0.640970\pi$
$740$	−5.21196e6	−	4.25204e7i	−0.0128619	−	0.104931i
$741$	2.51552e8	−	1.44241e8i	0.618264	−	0.354515i
$742$	−1.76453e7	−	1.56145e7i	−0.0431934	−	0.0382222i
$743$	6.99412e8	−	4.03805e8i	1.70516	−	0.984477i	0.764827	−	0.644236i	$-0.222825\pi$
$743$	6.99412e8	−	4.03805e8i	1.70516	−	0.984477i	0.940338	−	0.340241i	$-0.110509\pi$
$744$	−5.31047e7	+	6.72105e8i	−0.128948	+	1.63199i
$745$	1.62556e8	−	2.81555e8i	0.393128	−	0.680918i
$746$	7.30690e8	+	1.48739e8i	1.76002	+	0.358268i
$747$	−4.02617e7	−	2.32451e7i	−0.0965896	−	0.0557661i
$748$	−1.81070e8	+	2.21948e7i	−0.432656	+	0.0530330i
$749$	3.76144e8			0.895177
$750$	−5.40363e8	+	1.80741e8i	−1.28086	+	0.428423i
$751$	2.23158e8	+	1.28840e8i	0.526856	+	0.304181i	0.739735	−	0.672898i	$-0.234951\pi$
$751$	2.23158e8	+	1.28840e8i	0.526856	+	0.304181i	−0.212879	+	0.977079i	$0.568284\pi$
$752$	−4.60823e7	−	1.85151e8i	−0.108363	−	0.435384i
$753$	1.45543e8			0.340883
$754$	7.54383e7	+	2.25538e8i	0.175986	+	0.526146i
$755$	−7.01209e7	+	4.04843e7i	−0.162932	+	0.0940689i
$756$	−1.78825e8	−	7.59501e7i	−0.413869	−	0.175777i
$757$	−1.70505e8	−	2.95323e8i	−0.393051	−	0.680785i	0.599799	−	0.800151i	$-0.295247\pi$
$757$	−1.70505e8	−	2.95323e8i	−0.393051	−	0.680785i	−0.992850	+	0.119366i	$0.961914\pi$
$758$	4.24625e7	−	2.08600e8i	0.0974986	−	0.478968i
$759$		−	1.24320e8i		−	0.284325i
$760$	1.96170e8	−	9.27813e7i	0.446881	−	0.211359i
$761$	−5.21764e8			−1.18391			−0.591957	−	0.805970i	$-0.701644\pi$
$761$	−5.21764e8			−1.18391			−0.591957	+	0.805970i	$0.701644\pi$
$762$	−1.16898e9	−	2.37958e8i	−2.64206	−	0.537817i
$763$	−1.61056e8	+	9.29860e7i	−0.362581	+	0.209336i
$764$	−3.31442e7	+	7.80382e7i	−0.0743237	+	0.174996i
$765$	−1.39731e8	−	2.42021e8i	−0.312111	−	0.540592i
$766$	−7.68154e8	+	2.56933e8i	−1.70908	+	0.571654i
$767$			3.17576e8i			0.703821i
$768$	3.30437e8	+	6.22700e8i	0.729467	+	1.37466i
$769$	−2.37462e8	+	4.11297e8i	−0.522175	+	0.904433i	0.477493	+	0.878636i	$0.341546\pi$
$769$	−2.37462e8	+	4.11297e8i	−0.522175	+	0.904433i	−0.999667	+	0.0257972i	$0.991788\pi$
$770$	2.40682e7	+	7.19569e7i	0.0527196	+	0.157616i
$771$		−	1.02261e9i		−	2.23124i
$772$	9.88976e7	+	8.06830e8i	0.214948	+	1.75360i
$773$	−4.33097e8	+	7.50146e8i	−0.937662	+	1.62408i	−0.167846	+	0.985813i	$0.553681\pi$
$773$	−4.33097e8	+	7.50146e8i	−0.937662	+	1.62408i	−0.769816	+	0.638265i	$0.779652\pi$
$774$	1.64704e8	−	8.09120e8i	0.355207	−	1.74498i
$775$	−3.20436e8	−	1.85004e8i	−0.688393	−	0.397444i
$776$	5.26775e7	−	6.66698e8i	0.112730	−	1.42674i
$777$	5.34692e7	+	9.26114e7i	0.113983	+	0.197425i
$778$	−3.76744e8	+	4.25744e8i	−0.800033	+	0.904085i
$779$	1.13800e8	−	1.95765e8i	0.240730	−	0.414116i
$780$	1.65950e8	−	2.03414e7i	0.349697	−	0.0428643i
$781$	5.32092e6	+	9.21610e6i	0.0111695	+	0.0193461i
$782$	−3.15354e7	+	1.54920e8i	−0.0659445	+	0.323957i
$783$	−3.30601e8	−	1.90872e8i	−0.688682	−	0.397611i
$784$	1.77602e8	+	1.84064e8i	0.368552	+	0.381962i
$785$	5.35425e7	−	9.27384e7i	0.110685	−	0.191713i
$786$	−5.48375e8	+	6.19697e8i	−1.12930	+	1.27618i
$787$		−	4.38705e8i		−	0.900011i	−0.893026	−	0.450006i	$-0.851422\pi$
$787$		−	4.38705e8i		−	0.900011i	0.893026	−	0.450006i	$-0.148578\pi$
$788$	−3.78344e8	−	1.60689e8i	−0.773229	−	0.328404i
$789$	1.60250e8	−	2.77561e8i	0.326262	−	0.565102i
$790$	−2.44001e8	−	2.15918e8i	−0.494891	−	0.437934i
$791$			2.21941e8i			0.448443i
$792$	1.49153e8	+	3.12954e8i	0.300231	+	0.629948i
$793$	−5.95318e7	−	1.03112e8i	−0.119379	−	0.206771i
$794$	−5.63924e7	−	1.68597e8i	−0.112657	−	0.336812i
$795$	−2.81865e7	+	1.62735e7i	−0.0560971	+	0.0323877i
$796$	−3.81273e8	−	5.06183e8i	−0.755956	−	1.00362i
$797$	8.55147e8			1.68914			0.844570	−	0.535444i	$-0.179856\pi$
$797$	8.55147e8			1.68914			0.844570	+	0.535444i	$0.179856\pi$
$798$	−3.60191e8	+	4.04615e8i	−0.708801	+	0.796220i
$799$			2.03251e8i			0.398468i
$800$	−3.86520e8	+	1.66765e7i	−0.754923	+	0.0325712i
$801$	−3.30585e8	−	5.72590e8i	−0.643259	−	1.11416i
$802$	2.02603e8	+	6.05722e8i	0.392755	+	1.17422i
$803$	−1.12602e8	+	6.50106e7i	−0.217469	+	0.125556i
$804$	1.29224e9	+	5.48837e8i	2.48642	+	1.05603i
$805$	6.57566e7			0.126052
$806$	1.88909e8	+	1.67168e8i	0.360785	+	0.319262i
$807$	4.96268e8	+	2.86521e8i	0.944270	+	0.545174i
$808$	7.12486e8	−	3.39568e8i	1.35065	−	0.643714i
$809$	4.06544e8			0.767825			0.383913	−	0.923369i	$-0.374576\pi$
$809$	4.06544e8			0.767825			0.383913	+	0.923369i	$0.374576\pi$
$810$	6.96867e7	−	7.87502e7i	0.131128	−	0.148182i
$811$	−3.39186e8	−	1.95829e8i	−0.635880	−	0.367126i	0.147146	−	0.989115i	$-0.452991\pi$
$811$	−3.39186e8	−	1.95829e8i	−0.635880	−	0.367126i	−0.783026	+	0.621989i	$0.786325\pi$
$812$	−2.67303e8	−	3.54875e8i	−0.499270	−	0.662838i
$813$	2.24031e8	−	3.88033e8i	0.416904	−	0.722099i
$814$	1.12920e7	−	5.54728e7i	0.0209362	−	0.102851i
$815$	−3.65640e8	+	2.11102e8i	−0.675431	+	0.389960i
$816$	−1.81370e8	−	7.28716e8i	−0.333808	−	1.34118i
$817$	−5.90495e8	−	3.43260e8i	−1.08280	−	0.629444i
$818$	−3.61878e8	+	4.08944e8i	−0.661154	+	0.747143i
$819$	−2.12200e8	+	1.22514e8i	−0.386272	+	0.223014i
$820$	1.04285e8	−	7.85509e7i	0.189139	−	0.142466i
$821$	2.88076e7	−	4.98962e7i	0.0520568	−	0.0901651i	−0.838823	−	0.544405i	$-0.816756\pi$
$821$	2.88076e7	−	4.98962e7i	0.0520568	−	0.0901651i	0.890880	+	0.454240i	$0.150089\pi$
$822$	2.80345e8	−	1.37721e9i	0.504750	−	2.47962i
$823$	−7.16010e8	−	4.13389e8i	−1.28446	−	0.741582i	−0.306797	−	0.951775i	$-0.599257\pi$
$823$	−7.16010e8	−	4.13389e8i	−1.28446	−	0.741582i	−0.977660	+	0.210193i	$0.932591\pi$
$824$	4.84000e8	−	7.03759e8i	0.865095	−	1.25789i
$825$	−3.24078e8			−0.577149
$826$	−1.88192e8	−	5.62640e8i	−0.333935	−	0.998367i
$827$	−2.18592e8	−	1.26204e8i	−0.386471	−	0.223129i	0.294159	−	0.955757i	$-0.404961\pi$
$827$	−2.18592e8	−	1.26204e8i	−0.386471	−	0.223129i	−0.680630	+	0.732627i	$0.738294\pi$
$828$	2.98214e8	−	3.65537e7i	0.525336	−	0.0643933i
$829$	8.47974e8			1.48840			0.744199	−	0.667958i	$-0.232832\pi$
$829$	8.47974e8			1.48840			0.744199	+	0.667958i	$0.232832\pi$
$830$	−2.10278e7	+	7.03338e6i	−0.0367755	+	0.0123007i
$831$	5.26908e8	−	3.04211e8i	0.918188	−	0.530116i
$832$	2.60483e8	+	4.14215e7i	0.452283	+	0.0719210i
$833$	−1.36235e8	−	2.35965e8i	−0.235696	−	0.408238i
$834$	4.67367e8	+	9.51371e7i	0.805676	+	0.164003i
$835$			4.70050e7i			0.0807392i
$836$	2.84740e8	−	3.40457e7i	0.487337	−	0.0582698i
$837$	−4.04913e8			−0.690534
$838$	1.15295e7	−	5.66396e7i	0.0195920	−	0.0962472i
$839$	−4.60419e8	+	2.65823e8i	−0.779592	+	0.450097i	−0.836286	−	0.548294i	$-0.815277\pi$
$839$	−4.60419e8	+	2.65823e8i	−0.779592	+	0.450097i	0.0566940	+	0.998392i	$0.481944\pi$
$840$	−2.81953e8	+	1.34378e8i	−0.475707	+	0.226720i
$841$	−1.39067e8	−	2.40871e8i	−0.233796	−	0.404946i
$842$	1.93365e8	+	5.78105e8i	0.323923	+	0.968435i
$843$			2.19053e8i			0.365651i
$844$	−4.92556e8	+	6.03753e7i	−0.819273	+	0.100423i
$845$	−1.17854e8	+	2.04128e8i	−0.195332	+	0.338324i
$846$	3.66309e8	−	1.22523e8i	0.604974	−	0.202352i
$847$		−	3.15968e8i		−	0.519987i
$848$	−4.98250e7	+	1.24010e7i	−0.0817072	+	0.0203361i
$849$	2.36801e8	−	4.10151e8i	0.386954	−	0.670225i
$850$	4.03846e8	+	8.22067e7i	0.657596	+	0.133860i
$851$	−4.24879e7	−	2.45304e7i	−0.0689409	−	0.0398030i
$852$	−3.49910e7	+	2.63563e7i	−0.0565767	+	0.0426154i
$853$	4.74367e8	+	8.21628e8i	0.764306	+	1.32382i	0.940613	+	0.339482i	$0.110252\pi$
$853$	4.74367e8	+	8.21628e8i	0.764306	+	1.32382i	−0.176306	+	0.984335i	$0.556415\pi$
$854$	1.66574e8	+	1.47402e8i	0.267444	+	0.236663i
$855$	2.18525e8	+	3.81100e8i	0.349625	+	0.609735i
$856$	4.64477e8	−	6.75371e8i	0.740531	−	1.07677i
$857$	5.37053e7	+	9.30202e7i	0.0853246	+	0.147787i	0.905529	−	0.424283i	$-0.139474\pi$
$857$	5.37053e7	+	9.30202e7i	0.0853246	+	0.147787i	−0.820205	+	0.572070i	$0.806141\pi$
$858$	2.16501e8	+	4.40708e7i	0.342766	+	0.0697733i
$859$	−2.08124e8	−	1.20160e8i	−0.328354	−	0.189575i	0.326756	−	0.945109i	$-0.394044\pi$
$859$	−2.08124e8	−	1.20160e8i	−0.328354	−	0.189575i	−0.655110	+	0.755533i	$0.727378\pi$
$860$	−2.36937e8	−	3.14561e8i	−0.372510	−	0.494549i
$861$	−1.62958e8	+	2.82252e8i	−0.255309	+	0.442208i
$862$	−3.95533e7	−	3.50010e7i	−0.0617534	−	0.0546461i
$863$		−	2.03019e7i		−	0.0315867i	−0.999875	−	0.0157933i	$-0.994973\pi$
$863$		−	2.03019e7i		−	0.0315867i	0.999875	−	0.0157933i	$-0.00502739\pi$
$864$	−3.57189e8	+	2.27296e8i	−0.553805	+	0.352412i
$865$	−1.25706e8	+	2.17728e8i	−0.194225	+	0.336408i
$866$	4.24852e7	−	4.80108e7i	0.0654160	−	0.0739240i
$867$		−	2.14253e8i		−	0.328753i
$868$	−4.33746e8	−	1.84220e8i	−0.663249	−	0.281694i
$869$	−2.15281e8	−	3.72878e8i	−0.328055	−	0.568208i
$870$	−5.82010e8	+	1.94671e8i	−0.883837	+	0.295627i
$871$	4.54919e8	−	2.62648e8i	0.688462	−	0.397484i
$872$	−3.19212e7	+	4.04001e8i	−0.0481426	+	0.609303i
$873$	1.35388e9			2.03487
$874$	5.02945e7	−	2.43382e8i	0.0753331	−	0.364547i
$875$		−	3.98266e8i		−	0.594496i
$876$	−3.22020e8	−	4.27518e8i	−0.479038	−	0.635977i
$877$	−1.18367e8	−	2.05018e8i	−0.175482	−	0.303943i	0.764846	−	0.644213i	$-0.222815\pi$
$877$	−1.18367e8	−	2.05018e8i	−0.175482	−	0.303943i	−0.940328	+	0.340270i	$0.889482\pi$
$878$	9.26582e8	−	3.09924e8i	1.36899	−	0.457901i
$879$	−1.24004e9	+	7.15936e8i	−1.82586	+	1.05416i
$880$	1.58920e8	+	4.56404e7i	0.233201	+	0.0669733i
$881$	−6.81648e8			−0.996857			−0.498428	−	0.866931i	$-0.666089\pi$
$881$	−6.81648e8			−0.996857			−0.498428	+	0.866931i	$0.666089\pi$
$882$	−3.43143e8	+	3.87772e8i	−0.500114	+	0.565159i
$883$	9.36234e8	+	5.40535e8i	1.35989	+	0.785130i	0.989608	−	0.143791i	$-0.0459294\pi$
$883$	9.36234e8	+	5.40535e8i	1.35989	+	0.785130i	0.370277	+	0.928921i	$0.379263\pi$
$884$	−2.58611e8	−	1.09837e8i	−0.374360	−	0.158998i
$885$	−8.19516e8			−1.18230
$886$	−2.40219e8	−	2.12572e8i	−0.345387	−	0.305636i
$887$	−2.43393e8	−	1.40523e8i	−0.348769	−	0.201362i	0.315374	−	0.948967i	$-0.397870\pi$
$887$	−2.43393e8	−	1.40523e8i	−0.348769	−	0.201362i	−0.664143	+	0.747606i	$0.731203\pi$
$888$	2.32311e8	+	1.83555e7i	0.331765	+	0.0262136i
$889$	4.16921e8	−	7.22129e8i	0.593402	−	1.02780i
$890$	−3.08999e8	−	6.28996e7i	−0.438315	−	0.0892232i
$891$	1.20345e8	−	6.94810e7i	0.170135	−	0.0982275i
$892$	−3.09907e8	+	3.79870e7i	−0.436653	+	0.0535230i
$893$	947102.	−	3.19504e8i	0.00132997	−	0.448665i
$894$	1.32445e9	+	1.17202e9i	1.85363	+	1.64029i
$895$	−1.56633e8	+	9.04322e7i	−0.218482	+	0.126140i
$896$	−4.86036e8	+	8.09743e7i	−0.675685	+	0.112570i
$897$	9.57379e7	−	1.65823e8i	0.132650	−	0.229756i
$898$	4.91375e8	+	1.00024e8i	0.678553	+	0.138126i
$899$	−8.01885e8	−	4.62968e8i	−1.10365	−	0.637195i
$900$	−9.52885e7	−	7.77386e8i	−0.130711	−	1.06637i
$901$	5.46959e7			0.0747792
$902$	1.63621e8	−	5.47282e7i	0.222957	−	0.0745747i
$903$	8.51369e8	+	4.91538e8i	1.15626	+	0.667566i
$904$	3.98497e8	+	2.74061e8i	0.539411	+	0.370973i
$905$	5.72188e8			0.771956
$906$	−1.39716e8	−	4.17709e8i	−0.187871	−	0.561680i
$907$	−2.56794e8	+	1.48260e8i	−0.344162	+	0.198702i	−0.662111	−	0.749406i	$-0.730339\pi$
$907$	−2.56794e8	+	1.48260e8i	−0.344162	+	0.198702i	0.317949	+	0.948108i	$0.397006\pi$
$908$	−2.87525e8	+	6.76979e8i	−0.384077	+	0.904311i
$909$	7.98901e8	+	1.38374e9i	1.06366	+	1.84231i
$910$	−2.33104e7	+	1.14514e8i	−0.0309332	+	0.151961i
$911$			2.75083e8i			0.363839i	0.983313	+	0.181919i	$0.0582310\pi$
$911$			2.75083e8i			0.363839i	−0.983313	+	0.181919i	$0.941769\pi$
$912$	2.81712e8	+	1.14636e9i	0.371383	+	1.51125i
$913$	−2.93010e7			−0.0385009
$914$	−9.31573e8	−	1.89631e8i	−1.22005	−	0.248353i
$915$	2.66084e8	−	1.53624e8i	0.347341	−	0.200537i
$916$	9.99655e7	+	4.24571e7i	0.130066	+	0.0552413i
$917$	−2.89196e8	−	5.00902e8i	−0.375046	−	0.649598i
$918$	4.27715e8	−	1.43062e8i	0.552874	−	0.184926i
$919$		−	7.45485e8i		−	0.960488i	−0.877135	−	0.480244i	$-0.840548\pi$
$919$		−	7.45485e8i		−	0.960488i	0.877135	−	0.480244i	$-0.159452\pi$
$920$	8.11987e7	−	1.18067e8i	0.104276	−	0.151623i
$921$	−2.18798e8	+	3.78969e8i	−0.280068	+	0.485092i
$922$	−3.30305e8	−	9.87514e8i	−0.421426	−	1.25994i
$923$			1.63904e7i			0.0208442i
$924$	−4.09683e8	+	5.02171e7i	−0.519317	+	0.0636555i
$925$	−6.39460e7	+	1.10758e8i	−0.0807957	+	0.139942i
$926$	−2.96480e8	+	1.45648e9i	−0.373390	+	1.83431i
$927$	1.49745e9	+	8.64552e8i	1.87980	+	1.08531i
$928$	−9.67259e8	+	4.17325e7i	−1.21032	+	0.0522192i
$929$	−5.39109e8	−	9.33764e8i	−0.672403	−	1.16464i	−0.977221	−	0.212225i	$-0.931929\pi$
$929$	−5.39109e8	−	9.33764e8i	−0.672403	−	1.16464i	0.304818	−	0.952411i	$-0.401404\pi$
$930$	−4.31382e8	+	4.87487e8i	−0.536306	+	0.606058i
$931$	2.13056e8	+	3.71564e8i	0.264025	+	0.460452i
$932$	−5.31218e7	−	4.33380e8i	−0.0656183	−	0.535330i
$933$	9.89718e8	+	1.71424e9i	1.21862	+	2.11070i
$934$	−2.01133e8	+	9.88081e8i	−0.246856	+	1.21270i
$935$	−1.52537e8	−	8.80672e7i	−0.186612	−	0.107741i
$936$	−4.20577e7	+	5.32292e8i	−0.0512883	+	0.649116i
$937$	−2.84677e8	+	4.93075e8i	−0.346046	+	0.599369i	−0.985543	−	0.169424i	$-0.945809\pi$
$937$	−2.84677e8	+	4.93075e8i	−0.346046	+	0.599369i	0.639497	+	0.768793i	$0.279143\pi$
$938$	−6.50323e8	+	7.34904e8i	−0.787990	+	0.890476i
$939$		−	1.30010e9i		−	1.57030i
$940$	7.20152e7	−	1.69560e8i	0.0867043	−	0.204146i
$941$	−7.62210e8	+	1.32019e9i	−0.914757	+	1.58441i	−0.107500	+	0.994205i	$0.534284\pi$
$941$	−7.62210e8	+	1.32019e9i	−0.914757	+	1.58441i	−0.807257	+	0.590200i	$0.799049\pi$
$942$	4.36245e8	+	3.86037e8i	0.521889	+	0.461824i
$943$		−	1.49522e8i		−	0.178308i
$944$	−1.24261e9	−	3.56867e8i	−1.47713	−	0.424220i
$945$	−9.37925e7	−	1.62453e8i	−0.111141	−	0.192501i
$946$	−1.65079e8	−	4.93539e8i	−0.194993	−	0.582973i
$947$	−1.01959e8	+	5.88660e7i	−0.120054	+	0.0693130i	−0.558824	−	0.829286i	$-0.688747\pi$
$947$	−1.01959e8	+	5.88660e7i	−0.120054	+	0.0693130i	0.438771	+	0.898599i	$0.355414\pi$
$948$	1.41572e9	−	1.06636e9i	1.66169	−	1.25164i
$949$	−2.00257e8			−0.234309
$950$	−6.34449e8	−	1.31108e8i	−0.739990	−	0.152918i
$951$			1.93068e9i			2.24475i
$952$	5.23260e8	+	4.13441e7i	0.606466	+	0.0479185i
$953$	−7.28248e8	−	1.26136e9i	−0.841396	−	1.45734i	−0.888715	−	0.458461i	$-0.848401\pi$
$953$	−7.28248e8	−	1.26136e9i	−0.841396	−	1.45734i	0.0473189	−	0.998880i	$-0.484932\pi$
$954$	−3.29716e7	−	9.85756e7i	−0.0379748	−	0.113534i
$955$	−7.08937e7	+	4.09305e7i	−0.0813950	+	0.0469934i
$956$	4.78914e8	−	1.12760e9i	0.548130	−	1.29057i
$957$	−8.10998e8			−0.925303
$958$	8.18117e8	+	7.23959e8i	0.930506	+	0.823413i
$959$	8.50760e8	+	4.91187e8i	0.964609	+	0.556917i
$960$	−1.06890e8	+	6.72186e8i	−0.120815	+	0.759759i
$961$	−9.46273e7			−0.106622
$962$	5.77810e7	−	6.52960e7i	0.0649022	−	0.0733434i
$963$	1.43705e9	+	8.29679e8i	1.60913	+	0.929033i
$964$	1.21890e8	−	9.18117e7i	0.136063	−	0.102487i
$965$	−3.92418e8	+	6.79688e8i	−0.436684	+	0.756358i
$966$	−7.13509e7	+	3.50516e8i	−0.0791531	+	0.388845i
$967$	6.89998e8	−	3.98370e8i	0.763077	−	0.440563i	−0.0673226	−	0.997731i	$-0.521446\pi$
$967$	6.89998e8	−	3.98370e8i	0.763077	−	0.440563i	0.830399	+	0.557169i	$0.188112\pi$
$968$	−5.67324e8	−	3.90169e8i	−0.625468	−	0.430156i
$969$	3.72760e6	−	1.25750e9i	0.00409692	−	1.38209i
$970$	4.27912e8	−	4.83566e8i	0.468855	−	0.529835i
$971$	3.12321e8	−	1.80318e8i	0.341148	−	0.196962i	−0.319631	−	0.947542i	$-0.603559\pi$
$971$	3.12321e8	−	1.80318e8i	0.341148	−	0.196962i	0.660780	+	0.750580i	$0.270226\pi$
$972$	7.06847e8	+	9.38420e8i	0.769710	+	1.02188i
$973$	−1.66688e8	+	2.88712e8i	−0.180953	+	0.313420i
$974$	1.89162e8	−	9.29270e8i	0.204718	−	1.00569i
$975$	−4.32268e8	−	2.49570e8i	−0.466379	−	0.269264i
$976$	4.70354e8	−	1.17067e8i	0.505913	−	0.125917i
$977$	−9.48531e8			−1.01711			−0.508555	−	0.861030i	$-0.669820\pi$
$977$	−9.48531e8			−1.01711			−0.508555	+	0.861030i	$0.669820\pi$
$978$	−7.28536e8	−	2.17811e9i	−0.778815	−	2.32843i
$979$	−3.60882e8	−	2.08355e8i	−0.384607	−	0.222053i
$980$	3.00459e7	+	2.45121e8i	0.0319232	+	0.260437i
$981$	−8.20414e8			−0.869013
$982$	−6.62695e8	+	2.21659e8i	−0.699808	+	0.234072i
$983$	−6.00549e8	+	3.46727e8i	−0.632249	+	0.365029i	−0.781623	−	0.623752i	$-0.785608\pi$
$983$	−6.00549e8	+	3.46727e8i	−0.632249	+	0.365029i	0.149374	+	0.988781i	$0.452274\pi$
$984$	3.05559e8	+	6.41128e8i	0.320708	+	0.672914i
$985$	−1.98439e8	−	3.43707e8i	−0.207644	−	0.359649i
$986$	1.01062e9	+	2.05720e8i	1.05428	+	0.214608i
$987$			4.59869e8i			0.478281i
$988$	4.06015e8	+	1.73864e8i	0.420990	+	0.180277i
$989$	−4.51012e8			−0.466229
$990$	−6.67670e7	+	3.27997e8i	−0.0688107	+	0.338037i
$991$	6.83503e8	−	3.94620e8i	0.702295	−	0.405470i	−0.105907	−	0.994376i	$-0.533775\pi$
$991$	6.83503e8	−	3.94620e8i	0.702295	−	0.405470i	0.808201	+	0.588906i	$0.200441\pi$
$992$	−8.66376e8	+	5.51315e8i	−0.887506	+	0.564761i
$993$	1.45583e9	+	2.52158e9i	1.48684	+	2.57528i
$994$	−9.71276e6	−	2.90383e7i	−0.00988971	−	0.0295674i
$995$		−	6.11857e8i		−	0.621127i
$996$	−1.46748e7	−	1.19720e8i	−0.0148523	−	0.121169i
$997$	5.77101e8	−	9.99568e8i	0.582326	−	1.00862i	−0.412877	−	0.910787i	$-0.635476\pi$
$997$	5.77101e8	−	9.99568e8i	0.582326	−	1.00862i	0.995203	−	0.0978312i	$-0.0311905\pi$
$998$	−1.84325e8	+	6.16533e7i	−0.185436	+	0.0620247i
$999$			1.39957e8i			0.140378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.g.a.7.4	✓	116
4.3	odd	2	inner	76.7.g.a.7.37	yes	116
19.11	even	3	inner	76.7.g.a.11.37	yes	116
76.11	odd	6	inner	76.7.g.a.11.4	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.g.a.7.4	✓	116	1.1	even	1	trivial
76.7.g.a.7.37	yes	116	4.3	odd	2	inner
76.7.g.a.11.4	yes	116	76.11	odd	6	inner
76.7.g.a.11.37	yes	116	19.11	even	3	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.83923 - 1.59575i) q^{2} +(36.3885 - 21.0089i) q^{3} +(58.9072 + 25.0189i) q^{4} +(30.8964 + 53.5142i) q^{5} +(-318.783 + 106.627i) q^{6} -234.954i q^{7} +(-421.863 - 290.130i) q^{8} +(518.249 - 897.634i) q^{9} +O(q^{10})\)	\(q+(-7.83923 - 1.59575i) q^{2} +(36.3885 - 21.0089i) q^{3} +(58.9072 + 25.0189i) q^{4} +(30.8964 + 53.5142i) q^{5} +(-318.783 + 106.627i) q^{6} -234.954i q^{7} +(-421.863 - 290.130i) q^{8} +(518.249 - 897.634i) q^{9} +(-156.809 - 468.813i) q^{10} -653.265i q^{11} +(2669.16 - 327.174i) q^{12} +(503.075 - 871.351i) q^{13} +(-374.928 + 1841.86i) q^{14} +(2248.55 + 1298.20i) q^{15} +(2844.11 + 2947.59i) q^{16} +(-2181.65 - 3778.74i) q^{17} +(-5495.08 + 6209.77i) q^{18} +(3411.88 + 5950.21i) q^{19} +(481.154 + 3925.36i) q^{20} +(-4936.13 - 8549.63i) q^{21} +(-1042.45 + 5121.10i) q^{22} +(3922.37 + 2264.58i) q^{23} +(-21446.3 - 1694.53i) q^{24} +(5903.32 - 10224.9i) q^{25} +(-5334.18 + 6027.94i) q^{26} -12920.4i q^{27} +(5878.30 - 13840.5i) q^{28} +(14772.9 - 25587.5i) q^{29} +(-15555.3 - 13765.0i) q^{30} -31339.0i q^{31} +(-17592.0 - 27645.3i) q^{32} +(-13724.4 - 23771.4i) q^{33} +(11072.6 + 33103.8i) q^{34} +(12573.4 - 7259.25i) q^{35} +(52986.4 - 39911.0i) q^{36} -10832.2 q^{37} +(-17251.5 - 52089.6i) q^{38} -42276.2i q^{39} +(2492.03 - 31539.6i) q^{40} +(-16506.6 - 28590.3i) q^{41} +(25052.4 + 74899.4i) q^{42} +(-86238.5 + 49789.8i) q^{43} +(16344.0 - 38482.0i) q^{44} +64048.2 q^{45} +(-27134.6 - 24011.7i) q^{46} +(-40341.1 - 23291.0i) q^{47} +(165418. + 47506.7i) q^{48} +62445.5 q^{49} +(-62593.8 + 70734.8i) q^{50} +(-158774. - 91668.4i) q^{51} +(51435.0 - 38742.4i) q^{52} +(-6267.71 + 10856.0i) q^{53} +(-20617.8 + 101286. i) q^{54} +(34959.0 - 20183.6i) q^{55} +(-68167.3 + 99118.5i) q^{56} +(249161. + 144839. i) q^{57} +(-156640. + 177012. i) q^{58} +(-273348. + 157818. i) q^{59} +(99976.1 + 132730. i) q^{60} +(59167.9 - 102482. i) q^{61} +(-50009.2 + 245673. i) q^{62} +(-210903. - 121765. i) q^{63} +(93792.8 + 244791. i) q^{64} +62172.9 q^{65} +(69655.6 + 208250. i) q^{66} +(452139. + 261042. i) q^{67} +(-33975.1 - 277177. i) q^{68} +190305. q^{69} +(-110150. + 36842.9i) q^{70} +(-14107.7 + 8145.11i) q^{71} +(-479061. + 228319. i) q^{72} +(-99516.3 - 172367. i) q^{73} +(84916.2 + 17285.5i) q^{74} -496090. i q^{75} +(52116.2 + 435871. i) q^{76} -153487. q^{77} +(-67462.3 + 331413. i) q^{78} +(570791. - 329546. i) q^{79} +(-69865.0 + 243270. i) q^{80} +(106360. + 184220. i) q^{81} +(83776.4 + 250467. i) q^{82} -44853.2i q^{83} +(-76870.9 - 627131. i) q^{84} +(134811. - 233499. i) q^{85} +(755496. - 252699. i) q^{86} -1.24145e6i q^{87} +(-189532. + 275589. i) q^{88} +(318944. - 552427. i) q^{89} +(-502089. - 102205. i) q^{90} +(-204728. - 118200. i) q^{91} +(174398. + 231533. i) q^{92} +(-658398. - 1.14038e6i) q^{93} +(279077. + 246958. i) q^{94} +(-213006. + 366424. i) q^{95} +(-1.22094e6 - 636383. i) q^{96} +(653102. + 1.13121e6i) q^{97} +(-489525. - 99647.5i) q^{98} +(-586393. - 338554. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9}+O(q^{10}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9	\( 116 q - q^{2} - 67 q^{4} - 2 q^{5} + 33 q^{6} + 962 q^{8} + 12660 q^{9} - 812 q^{10} - 1462 q^{12} + 2518 q^{13} - 2742 q^{14} + 461 q^{16} + 6838 q^{17} - 13948 q^{18} - 24396 q^{20} + 11176 q^{21} + 22293 q^{22} + 33905 q^{24} - 156252 q^{25} - 78080 q^{26} - 34362 q^{28} - 2 q^{29} + 208344 q^{30} - 10941 q^{32} + 110316 q^{33} + 64648 q^{34} + 78574 q^{36} + 55432 q^{37} + 221994 q^{38} + 242590 q^{40} - 9126 q^{41} + 187550 q^{42} + 138081 q^{44} + 59576 q^{45} - 686052 q^{46} - 141617 q^{48} - 1306636 q^{49} + 167498 q^{50} - 35414 q^{52} + 60758 q^{53} - 348601 q^{54} + 543732 q^{56} - 466566 q^{57} + 1208536 q^{58} - 319142 q^{60} - 839474 q^{61} + 628548 q^{62} - 470026 q^{64} + 151836 q^{65} + 1471119 q^{66} + 341484 q^{68} - 2169836 q^{69} - 68364 q^{70} + 1236042 q^{72} + 207538 q^{73} + 336144 q^{74} - 97437 q^{76} + 1977632 q^{77} - 2740948 q^{78} + 1250050 q^{80} - 3334682 q^{81} - 2244893 q^{82} - 2404612 q^{84} + 788426 q^{85} + 910490 q^{86} + 5123058 q^{88} + 360166 q^{89} + 2446616 q^{90} + 2518692 q^{92} + 2079592 q^{93} - 2221200 q^{94} - 5927450 q^{96} + 3567778 q^{97} + 5270703 q^{98}+O(q^{100}) \) 116 * q - q^2 - 67 * q^4 - 2 * q^5 + 33 * q^6 + 962 * q^8 + 12660 * q^9 - 812 * q^10 - 1462 * q^12 + 2518 * q^13 - 2742 * q^14 + 461 * q^16 + 6838 * q^17 - 13948 * q^18 - 24396 * q^20 + 11176 * q^21 + 22293 * q^22 + 33905 * q^24 - 156252 * q^25 - 78080 * q^26 - 34362 * q^28 - 2 * q^29 + 208344 * q^30 - 10941 * q^32 + 110316 * q^33 + 64648 * q^34 + 78574 * q^36 + 55432 * q^37 + 221994 * q^38 + 242590 * q^40 - 9126 * q^41 + 187550 * q^42 + 138081 * q^44 + 59576 * q^45 - 686052 * q^46 - 141617 * q^48 - 1306636 * q^49 + 167498 * q^50 - 35414 * q^52 + 60758 * q^53 - 348601 * q^54 + 543732 * q^56 - 466566 * q^57 + 1208536 * q^58 - 319142 * q^60 - 839474 * q^61 + 628548 * q^62 - 470026 * q^64 + 151836 * q^65 + 1471119 * q^66 + 341484 * q^68 - 2169836 * q^69 - 68364 * q^70 + 1236042 * q^72 + 207538 * q^73 + 336144 * q^74 - 97437 * q^76 + 1977632 * q^77 - 2740948 * q^78 + 1250050 * q^80 - 3334682 * q^81 - 2244893 * q^82 - 2404612 * q^84 + 788426 * q^85 + 910490 * q^86 + 5123058 * q^88 + 360166 * q^89 + 2446616 * q^90 + 2518692 * q^92 + 2079592 * q^93 - 2221200 * q^94 - 5927450 * q^96 + 3567778 * q^97 + 5270703 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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