LMFDB - Embedded newform 37.8.e.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(11,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("37.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.e (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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	37.11
Dual form			37.8.e.a.27.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.1223 - 6.99882i) q^{2} +(43.2891 - 74.9789i) q^{3} +(33.9669 - 58.8324i) q^{4} +(-221.481 - 127.872i) q^{5} -1211.89i q^{6} +(-32.7203 + 56.6733i) q^{7} +840.785i q^{8} +(-2654.39 - 4597.54i) q^{9} +O(q^{10})$	\(q+(12.1223 - 6.99882i) q^{2} +(43.2891 - 74.9789i) q^{3} +(33.9669 - 58.8324i) q^{4} +(-221.481 - 127.872i) q^{5} -1211.89i q^{6} +(-32.7203 + 56.6733i) q^{7} +840.785i q^{8} +(-2654.39 - 4597.54i) q^{9} -3579.82 q^{10} +4266.03 q^{11} +(-2940.79 - 5093.60i) q^{12} +(3545.97 + 2047.27i) q^{13} +916.015i q^{14} +(-19175.5 + 11071.0i) q^{15} +(10232.3 + 17722.8i) q^{16} +(8925.01 - 5152.86i) q^{17} +(-64354.7 - 37155.2i) q^{18} +(5493.86 + 3171.88i) q^{19} +(-15046.1 + 8686.85i) q^{20} +(2832.87 + 4906.67i) q^{21} +(51714.1 - 29857.1i) q^{22} -108131. i q^{23} +(63041.2 + 36396.8i) q^{24} +(-6359.85 - 11015.6i) q^{25} +57313.8 q^{26} -270278. q^{27} +(2222.82 + 3850.03i) q^{28} +179652. i q^{29} +(-154967. + 268411. i) q^{30} -230057. i q^{31} +(154875. + 89417.2i) q^{32} +(184672. - 319862. i) q^{33} +(72127.8 - 124929. i) q^{34} +(14493.9 - 8368.05i) q^{35} -360646. q^{36} +(232570. + 202097. i) q^{37} +88797.6 q^{38} +(307004. - 177249. i) q^{39} +(107513. - 186218. i) q^{40} +(-211962. + 367128. i) q^{41} +(68681.8 + 39653.5i) q^{42} +692764. i q^{43} +(144904. - 250980. i) q^{44} +1.35769e6i q^{45} +(-756788. - 1.31080e6i) q^{46} +964442. q^{47} +1.77178e6 q^{48} +(409630. + 709500. i) q^{49} +(-154192. - 89022.8i) q^{50} -892250. i q^{51} +(240891. - 139079. i) q^{52} +(-73966.9 - 128114. i) q^{53} +(-3.27640e6 + 1.89163e6i) q^{54} +(-944845. - 545507. i) q^{55} +(-47650.1 - 27510.8i) q^{56} +(475648. - 274616. i) q^{57} +(1.25735e6 + 2.17780e6i) q^{58} +(476246. - 274961. i) q^{59} +1.50418e6i q^{60} +(63470.3 + 36644.6i) q^{61} +(-1.61013e6 - 2.78883e6i) q^{62} +347411. q^{63} -116200. q^{64} +(-523578. - 906863. i) q^{65} -5.16995e6i q^{66} +(-1.07414e6 + 1.86046e6i) q^{67} -700106. i q^{68} +(-8.10754e6 - 4.68089e6i) q^{69} +(117133. - 202880. i) q^{70} +(35395.9 - 61307.5i) q^{71} +(3.86555e6 - 2.23177e6i) q^{72} -279398. q^{73} +(4.23372e6 + 822161. i) q^{74} -1.10125e6 q^{75} +(373218. - 215478. i) q^{76} +(-139586. + 241770. i) q^{77} +(2.48106e6 - 4.29733e6i) q^{78} +(-3.45505e6 - 1.99477e6i) q^{79} -5.23369e6i q^{80} +(-5.89496e6 + 1.02104e7i) q^{81} +5.93392e6i q^{82} +(2.19364e6 + 3.79950e6i) q^{83} +384895. q^{84} -2.63563e6 q^{85} +(4.84853e6 + 8.39790e6i) q^{86} +(1.34701e7 + 7.77698e6i) q^{87} +3.58681e6i q^{88} +(-3.28266e6 + 1.89524e6i) q^{89} +(9.50225e6 + 1.64584e7i) q^{90} +(-232051. + 133975. i) q^{91} +(-6.36160e6 - 3.67287e6i) q^{92} +(-1.72495e7 - 9.95898e6i) q^{93} +(1.16913e7 - 6.74996e6i) q^{94} +(-811191. - 1.40502e6i) q^{95} +(1.34088e7 - 7.74158e6i) q^{96} +1.70342e7i q^{97} +(9.93133e6 + 5.73385e6i) q^{98} +(-1.13237e7 - 1.96132e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) $ 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9 - 5124 * q^10 + 12468 * q^11 + 6926 * q^12 + 10512 * q^13 + 36402 * q^15 - 31094 * q^16 - 22440 * q^17 - 153504 * q^18 + 49086 * q^19 + 28662 * q^20 + 7736 * q^21 + 132018 * q^22 + 2754 * q^24 + 72328 * q^25 - 680244 * q^26 + 42984 * q^27 + 105488 * q^28 + 382084 * q^30 + 523656 * q^32 + 9228 * q^33 + 276914 * q^34 - 904452 * q^35 - 204828 * q^36 + 1333776 * q^37 + 50208 * q^38 + 122040 * q^39 - 1205236 * q^40 - 871440 * q^41 + 1436094 * q^42 - 994326 * q^44 - 987942 * q^46 - 586932 * q^47 + 3984388 * q^48 - 1766072 * q^49 + 1818708 * q^50 - 2745228 * q^52 + 1661988 * q^53 + 1102554 * q^54 - 2733258 * q^55 - 5943924 * q^56 + 3920592 * q^57 + 5021672 * q^58 + 5296632 * q^59 - 4588524 * q^61 - 8143398 * q^62 - 2503648 * q^63 + 10662964 * q^64 - 1652736 * q^65 + 1940622 * q^67 - 10266552 * q^69 - 5038546 * q^70 + 6420528 * q^71 - 6576036 * q^72 - 3313032 * q^73 + 16192386 * q^74 - 5168536 * q^75 + 10328022 * q^76 - 8599404 * q^77 + 18210222 * q^78 - 15094374 * q^79 + 1733956 * q^81 - 191670 * q^83 + 1175224 * q^84 - 18053592 * q^85 + 18575940 * q^86 - 3762762 * q^87 - 14873004 * q^89 + 37293212 * q^90 - 76496700 * q^91 + 27846618 * q^92 + 26687652 * q^93 + 35421402 * q^94 + 14310774 * q^95 - 30894534 * q^96 - 13793868 * q^98 - 37141758 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	12.1223	−	6.99882i	1.07147	−	0.618614i	0.142888	−	0.989739i	$-0.454361\pi$
$2$	12.1223	−	6.99882i	1.07147	−	0.618614i	0.928583	+	0.371125i	$0.121028\pi$
$3$	43.2891	−	74.9789i	0.925666	−	1.60330i	0.135179	−	0.990821i	$-0.456839\pi$
$3$	43.2891	−	74.9789i	0.925666	−	1.60330i	0.790487	−	0.612479i	$-0.209827\pi$
$4$	33.9669	−	58.8324i	0.265366	−	0.459628i
$5$	−221.481	−	127.872i	−0.792396	−	0.457490i	0.0484096	−	0.998828i	$-0.484585\pi$
$5$	−221.481	−	127.872i	−0.792396	−	0.457490i	−0.840805	+	0.541338i	$0.817918\pi$
$6$		−	1211.89i		−	2.29052i
$7$	−32.7203	+	56.6733i	−0.0360558	+	0.0624504i	−0.883490	−	0.468450i	$-0.844813\pi$
$7$	−32.7203	+	56.6733i	−0.0360558	+	0.0624504i	0.847434	+	0.530900i	$0.178146\pi$
$8$			840.785i			0.580591i
$9$	−2654.39	−	4597.54i	−1.21371	−	2.10221i
$10$	−3579.82			−1.13204
$11$	4266.03			0.966383			0.483191	−	0.875515i	$-0.339478\pi$
$11$	4266.03			0.966383			0.483191	+	0.875515i	$0.339478\pi$
$12$	−2940.79	−	5093.60i	−0.491281	−	0.850923i
$13$	3545.97	+	2047.27i	0.447645	+	0.258448i	0.706835	−	0.707378i	$-0.250122\pi$
$13$	3545.97	+	2047.27i	0.447645	+	0.258448i	−0.259190	+	0.965826i	$0.583456\pi$
$14$			916.015i			0.0892184i
$15$	−19175.5	+	11071.0i	−1.46699	+	0.846965i
$16$	10232.3	+	17722.8i	0.624528	+	1.08171i
$17$	8925.01	−	5152.86i	0.440593	−	0.254376i	−0.263256	−	0.964726i	$-0.584796\pi$
$17$	8925.01	−	5152.86i	0.440593	−	0.254376i	0.703849	+	0.710350i	$0.251463\pi$
$18$	−64354.7	−	37155.2i	−2.60092	−	1.50164i
$19$	5493.86	+	3171.88i	0.183755	+	0.106091i	0.589056	−	0.808092i	$-0.299500\pi$
$19$	5493.86	+	3171.88i	0.183755	+	0.106091i	−0.405301	+	0.914183i	$0.632833\pi$
$20$	−15046.1	+	8686.85i	−0.420550	+	0.242805i
$21$	2832.87	+	4906.67i	0.0667512	+	0.115616i
$22$	51714.1	−	29857.1i	1.03545	−	0.597818i
$23$		−	108131.i		−	1.85311i	−0.376154	−	0.926557i	$-0.622753\pi$
$23$		−	108131.i		−	1.85311i	0.376154	−	0.926557i	$-0.377247\pi$
$24$	63041.2	+	36396.8i	0.930861	+	0.537433i
$25$	−6359.85	−	11015.6i	−0.0814060	−	0.140999i
$26$	57313.8			0.639518
$27$	−270278.			−2.64264
$28$	2222.82	+	3850.03i	0.0191360	+	0.0331445i
$29$			179652.i			1.36785i	0.729551	+	0.683927i	$0.239729\pi$
$29$			179652.i			1.36785i	−0.729551	+	0.683927i	$0.760271\pi$
$30$	−154967.	+	268411.i	−1.04789	+	1.81500i
$31$		−	230057.i		−	1.38698i	−0.720466	−	0.693490i	$-0.756072\pi$
$31$		−	230057.i		−	1.38698i	0.720466	−	0.693490i	$-0.243928\pi$
$32$	154875.	+	89417.2i	0.835520	+	0.482388i
$33$	184672.	−	319862.i	0.894547	−	1.54940i
$34$	72127.8	−	124929.i	0.314722	−	0.545114i
$35$	14493.9	−	8368.05i	0.0571409	−	0.0329903i
$36$	−360646.			−1.28831
$37$	232570.	+	202097.i	0.754828	+	0.655923i
$37$	232570.	+	202097.i	0.754828	+	0.655923i
$38$	88797.6			0.262518
$39$	307004.	−	177249.i	0.828739	−	0.478473i
$40$	107513.	−	186218.i	0.265614	−	0.460058i
$41$	−211962.	+	367128.i	−0.480301	+	0.831906i	−0.999745	−	0.0225987i	$-0.992806\pi$
$41$	−211962.	+	367128.i	−0.480301	+	0.831906i	0.519443	+	0.854505i	$0.326139\pi$
$42$	68681.8	+	39653.5i	0.143044	+	0.0825864i
$43$			692764.i			1.32876i	0.747396	+	0.664379i	$0.231304\pi$
$43$			692764.i			1.32876i	−0.747396	+	0.664379i	$0.768696\pi$
$44$	144904.	−	250980.i	0.256445	−	0.444176i
$45$			1.35769e6i			2.22105i
$46$	−756788.	−	1.31080e6i	−1.14636	−	1.98556i
$47$	964442.			1.35498			0.677491	−	0.735531i	$-0.263067\pi$
$47$	964442.			1.35498			0.677491	+	0.735531i	$0.263067\pi$
$48$	1.77178e6			2.31242
$49$	409630.	+	709500.i	0.497400	+	0.861522i
$50$	−154192.	−	89022.8i	−0.174448	−	0.100718i
$51$		−	892250.i		−	0.941870i
$52$	240891.	−	139079.i	0.237580	−	0.137167i
$53$	−73966.9	−	128114.i	−0.0682451	−	0.118204i	0.829884	−	0.557936i	$-0.188407\pi$
$53$	−73966.9	−	128114.i	−0.0682451	−	0.118204i	−0.898129	+	0.439732i	$0.855073\pi$
$54$	−3.27640e6	+	1.89163e6i	−2.83151	+	1.63477i
$55$	−944845.	−	545507.i	−0.765758	−	0.442110i
$56$	−47650.1	−	27510.8i	−0.0362581	−	0.0209336i
$57$	475648.	−	274616.i	0.340192	−	0.196410i
$58$	1.25735e6	+	2.17780e6i	0.846173	+	1.46561i
$59$	476246.	−	274961.i	0.301890	−	0.174297i	−0.341401	−	0.939918i	$-0.610902\pi$
$59$	476246.	−	274961.i	0.301890	−	0.174297i	0.643292	+	0.765621i	$0.277568\pi$
$60$			1.50418e6i			0.899024i
$61$	63470.3	+	36644.6i	0.0358027	+	0.0206707i	0.517795	−	0.855505i	$-0.326753\pi$
$61$	63470.3	+	36644.6i	0.0358027	+	0.0206707i	−0.481992	+	0.876176i	$0.660087\pi$
$62$	−1.61013e6	−	2.78883e6i	−0.858005	−	1.48611i
$63$	347411.			0.175046
$64$	−116200.			−0.0554085
$65$	−523578.	−	906863.i	−0.236475	−	0.409586i
$66$		−	5.16995e6i		−	2.21352i
$67$	−1.07414e6	+	1.86046e6i	−0.436312	+	0.755715i	−0.997402	−	0.0720400i	$-0.977049\pi$
$67$	−1.07414e6	+	1.86046e6i	−0.436312	+	0.755715i	0.561089	+	0.827755i	$0.310382\pi$
$68$		−	700106.i		−	0.270012i
$69$	−8.10754e6	−	4.68089e6i	−2.97110	−	1.71536i
$70$	117133.	−	202880.i	0.0408165	−	0.0706963i
$71$	35395.9	−	61307.5i	0.0117368	−	0.0203287i	−0.860097	−	0.510130i	$-0.829597\pi$
$71$	35395.9	−	61307.5i	0.0117368	−	0.0203287i	0.871834	+	0.489801i	$0.162931\pi$
$72$	3.86555e6	−	2.23177e6i	1.22053	−	0.704671i
$73$	−279398.			−0.0840608			−0.0420304	−	0.999116i	$-0.513383\pi$
$73$	−279398.			−0.0840608			−0.0420304	+	0.999116i	$0.513383\pi$
$74$	4.23372e6	+	822161.i	1.21454	+	0.235855i
$75$	−1.10125e6			−0.301419
$76$	373218.	−	215478.i	0.0975249	−	0.0563060i
$77$	−139586.	+	241770.i	−0.0348437	+	0.0603510i
$78$	2.48106e6	−	4.29733e6i	0.591980	−	1.02534i
$79$	−3.45505e6	−	1.99477e6i	−0.788424	−	0.455197i	0.0509836	−	0.998699i	$-0.483764\pi$
$79$	−3.45505e6	−	1.99477e6i	−0.788424	−	0.455197i	−0.839407	+	0.543503i	$0.817098\pi$
$80$		−	5.23369e6i		−	1.14286i
$81$	−5.89496e6	+	1.02104e7i	−1.23249	+	2.13473i
$82$			5.93392e6i			1.18848i
$83$	2.19364e6	+	3.79950e6i	0.421107	+	0.729378i	0.996048	−	0.0888165i	$-0.0283085\pi$
$83$	2.19364e6	+	3.79950e6i	0.421107	+	0.729378i	−0.574941	+	0.818195i	$0.694975\pi$
$84$	384895.			0.0708540
$85$	−2.63563e6			−0.465498
$86$	4.84853e6	+	8.39790e6i	0.821988	+	1.42372i
$87$	1.34701e7	+	7.77698e6i	2.19308	+	1.26617i
$88$			3.58681e6i			0.561073i
$89$	−3.28266e6	+	1.89524e6i	−0.493583	+	0.284970i	−0.726060	−	0.687632i	$-0.758650\pi$
$89$	−3.28266e6	+	1.89524e6i	−0.493583	+	0.284970i	0.232477	+	0.972602i	$0.425317\pi$
$90$	9.50225e6	+	1.64584e7i	1.37397	+	2.37979i
$91$	−232051.	+	133975.i	−0.0322804	+	0.0186371i
$92$	−6.36160e6	−	3.67287e6i	−0.851743	−	0.491754i
$93$	−1.72495e7	−	9.95898e6i	−2.22375	−	1.28388i
$94$	1.16913e7	−	6.74996e6i	1.45182	−	0.838211i
$95$	−811191.	−	1.40502e6i	−0.0970712	−	0.168132i
$96$	1.34088e7	−	7.74158e6i	1.54682	−	0.893060i
$97$			1.70342e7i			1.89505i	0.319683	+	0.947525i	$0.396424\pi$
$97$			1.70342e7i			1.89505i	−0.319683	+	0.947525i	$0.603576\pi$
$98$	9.93133e6	+	5.73385e6i	1.06590	+	0.615397i
$99$	−1.13237e7	−	1.96132e7i	−1.17291	−	2.03154i
$100$	−864097.			−0.0864097
$101$	1.26448e7			1.22120			0.610600	−	0.791939i	$-0.290928\pi$
$101$	1.26448e7			1.22120			0.610600	+	0.791939i	$0.290928\pi$
$102$	−6.24469e6	−	1.08161e7i	−0.582654	−	1.00919i
$103$		−	1.55811e7i		−	1.40498i	−0.711696	−	0.702488i	$-0.752072\pi$
$103$		−	1.55811e7i		−	1.40498i	0.711696	−	0.702488i	$-0.247928\pi$
$104$	−1.72131e6	+	2.98140e6i	−0.150052	+	0.259898i
$105$		−	1.44898e6i		−	0.122152i
$106$	−1.79330e6	−	1.03536e6i	−0.146245	−	0.0844348i
$107$	8.44138e6	−	1.46209e7i	0.666147	−	1.15380i	−0.312825	−	0.949811i	$-0.601275\pi$
$107$	8.44138e6	−	1.46209e7i	0.666147	−	1.15380i	0.978973	−	0.203991i	$-0.0653912\pi$
$108$	−9.18052e6	+	1.59011e7i	−0.701268	+	1.21463i
$109$	−2.03782e7	+	1.17654e7i	−1.50721	+	0.870186i	−0.507242	+	0.861804i	$0.669335\pi$
$109$	−2.03782e7	+	1.17654e7i	−1.50721	+	0.870186i	−0.999965	+	0.00838237i	$0.997332\pi$
$110$	−1.52716e7			−1.09398
$111$	2.52207e7	−	8.68928e6i	1.75036	−	0.603050i
$112$	−1.33921e6			−0.0900713
$113$	4.66147e6	−	2.69130e6i	0.303913	−	0.175464i	−0.340287	−	0.940322i	$-0.610524\pi$
$113$	4.66147e6	−	2.69130e6i	0.303913	−	0.175464i	0.644199	+	0.764858i	$0.277191\pi$
$114$	3.84397e6	−	6.65795e6i	0.243004	−	0.420895i
$115$	−1.38269e7	+	2.39490e7i	−0.847781	+	1.46840i
$116$	1.05694e7	+	6.10223e6i	0.628704	+	0.362982i
$117$		−	2.17370e7i		−	1.25473i
$118$	3.84880e6	−	6.66632e6i	0.215645	−	0.373507i
$119$			674413.i			0.0366869i
$120$	−9.30829e6	−	1.61224e7i	−0.491740	−	0.851719i
$121$	−1.28819e6			−0.0661044
$122$	1.02588e6			0.0511488
$123$	1.83513e7	+	3.17853e7i	0.889197	+	1.54013i
$124$	−1.35348e7	−	7.81433e6i	−0.637495	−	0.368058i
$125$			2.32330e7i			1.06395i
$126$	4.21142e6	−	2.43146e6i	0.187556	−	0.108286i
$127$	−1.29050e7	−	2.23521e7i	−0.559041	−	0.968288i	−0.997577	−	0.0695742i	$-0.977836\pi$
$127$	−1.29050e7	−	2.23521e7i	−0.559041	−	0.968288i	0.438535	−	0.898714i	$-0.355497\pi$
$128$	−2.12326e7	+	1.22587e7i	−0.894889	+	0.516664i
$129$	5.19427e7	+	2.99891e7i	2.13040	+	1.22998i
$130$	−1.26939e7	−	7.32885e6i	−0.506751	−	0.292573i
$131$	−4.08317e7	+	2.35742e7i	−1.58689	+	0.916193i	−0.593078	+	0.805145i	$0.702088\pi$
$131$	−4.08317e7	+	2.35742e7i	−1.58689	+	0.916193i	−0.993815	+	0.111049i	$0.964579\pi$
$132$	−1.25455e7	−	2.17294e7i	−0.474765	−	0.822318i
$133$	−359522.	+	207570.i	−0.0132509	+	0.00765039i
$134$			3.00707e7i			1.07964i
$135$	5.98616e7	+	3.45611e7i	2.09402	+	1.20898i
$136$	4.33244e6	+	7.50401e6i	0.147689	+	0.255804i
$137$	−5.42261e7			−1.80172			−0.900858	−	0.434113i	$-0.857062\pi$
$137$	−5.42261e7			−1.80172			−0.900858	+	0.434113i	$0.857062\pi$
$138$	−1.31043e8			−4.24459
$139$	−8.27571e6	−	1.43339e7i	−0.261369	−	0.452704i	0.705237	−	0.708971i	$-0.250840\pi$
$139$	−8.27571e6	−	1.43339e7i	−0.261369	−	0.452704i	−0.966606	+	0.256268i	$0.917507\pi$
$140$		−	1.13695e6i		−	0.0350181i
$141$	4.17498e7	−	7.23128e7i	1.25426	−	2.17244i
$142$		−	990918.i		−	0.0290421i
$143$	1.51272e7	+	8.73370e6i	0.432596	+	0.249760i
$144$	5.43209e7	−	9.40865e7i	1.51600	−	2.62578i
$145$	2.29725e7	−	3.97896e7i	0.625779	−	1.08388i
$146$	−3.38695e6	+	1.95546e6i	−0.0900687	+	0.0520012i
$147$	7.09301e7			1.84170
$148$	1.97895e7	−	6.81806e6i	0.501786	−	0.172880i
$149$	2.24349e7			0.555614			0.277807	−	0.960637i	$-0.410392\pi$
$149$	2.24349e7			0.555614			0.277807	+	0.960637i	$0.410392\pi$
$150$	−1.33497e7	+	7.70744e6i	−0.322962	+	0.186462i
$151$	2.04341e7	−	3.53929e7i	0.482988	−	0.836559i	−0.516821	−	0.856093i	$-0.672885\pi$
$151$	2.04341e7	−	3.53929e7i	0.482988	−	0.836559i	0.999809	+	0.0195339i	$0.00621822\pi$
$152$	−2.66687e6	+	4.61915e6i	−0.0615955	+	0.106687i
$153$	−4.73809e7	−	2.73554e7i	−1.06951	−	0.617480i
$154$			3.90774e6i			0.0862191i
$155$	−2.94180e7	+	5.09534e7i	−0.634529	+	1.09904i
$156$		−	2.40824e7i		−	0.507882i
$157$	9.02490e6	+	1.56316e7i	0.186120	+	0.322370i	0.943953	−	0.330079i	$-0.107075\pi$
$157$	9.02490e6	+	1.56316e7i	0.186120	+	0.322370i	−0.757833	+	0.652448i	$0.773742\pi$
$158$	−5.58443e7			−1.12636
$159$	−1.28078e7			−0.252689
$160$	−2.28680e7	−	3.96085e7i	−0.441375	−	0.764484i
$161$	6.12813e6	+	3.53808e6i	0.115728	+	0.0668155i
$162$			1.65031e8i			3.04974i
$163$	−1.02985e7	+	5.94584e6i	−0.186259	+	0.107537i	−0.590230	−	0.807235i	$-0.700963\pi$
$163$	−1.02985e7	+	5.94584e6i	−0.186259	+	0.107537i	0.403971	+	0.914772i	$0.367630\pi$
$164$	1.43994e7	+	2.49404e7i	0.254912	+	0.441520i
$165$	−8.18030e7	+	4.72290e7i	−1.41767	+	0.818493i
$166$	5.31840e7	+	3.07058e7i	0.902407	+	0.521005i
$167$	3.61507e7	+	2.08716e7i	0.600634	+	0.346776i	0.769291	−	0.638899i	$-0.220610\pi$
$167$	3.61507e7	+	2.08716e7i	0.600634	+	0.346776i	−0.168657	+	0.985675i	$0.553943\pi$
$168$	−4.12546e6	+	2.38183e6i	−0.0671258	+	0.0387551i
$169$	−2.29916e7	−	3.98227e7i	−0.366409	−	0.634640i
$170$	−3.19499e7	+	1.84463e7i	−0.498768	+	0.287964i
$171$		−	3.36776e7i		−	0.515057i
$172$	4.07569e7	+	2.35310e7i	0.610734	+	0.352607i
$173$	2.58470e6	+	4.47683e6i	0.0379532	+	0.0657368i	0.884378	−	0.466771i	$-0.154583\pi$
$173$	2.58470e6	+	4.47683e6i	0.0379532	+	0.0657368i	−0.846425	+	0.532508i	$0.821250\pi$
$174$	2.17719e8			3.13309
$175$	832386.			0.0117406
$176$	4.36511e7	+	7.56059e7i	0.603533	+	1.04535i
$177$		−	4.76112e7i		−	0.645361i
$178$	−2.65289e7	+	4.59494e7i	−0.352573	+	0.610675i
$179$			3.45973e7i			0.450876i	0.974258	+	0.225438i	$0.0723812\pi$
$179$			3.45973e7i			0.450876i	−0.974258	+	0.225438i	$0.927619\pi$
$180$	7.98763e7	+	4.61166e7i	1.02086	+	0.589391i
$181$	4.59651e7	−	7.96138e7i	0.576173	−	0.997961i	−0.419740	−	0.907644i	$-0.637879\pi$
$181$	4.59651e7	−	7.96138e7i	0.576173	−	0.997961i	0.995913	−	0.0903164i	$-0.0287878\pi$
$182$	−1.87533e6	+	3.24816e6i	−0.0230583	+	0.0399382i
$183$	5.49514e6	−	3.17262e6i	0.0662827	−	0.0382683i
$184$	9.09148e7			1.07590
$185$	−2.56674e7	−	7.44999e7i	−0.298044	−	0.865077i
$186$	−2.78804e8			−3.17690
$187$	3.80743e7	−	2.19822e7i	0.425781	−	0.245825i
$188$	3.27591e7	−	5.67404e7i	0.359567	−	0.622788i
$189$	8.84361e6	−	1.53176e7i	0.0952825	−	0.165034i
$190$	−1.96670e7	−	1.13548e7i	−0.208018	−	0.120099i
$191$		−	5.99105e7i		−	0.622137i	−0.950387	−	0.311069i	$-0.899313\pi$
$191$		−	5.99105e7i		−	0.622137i	0.950387	−	0.311069i	$-0.100687\pi$
$192$	−5.03020e6	+	8.71256e6i	−0.0512898	+	0.0888365i
$193$		−	1.23402e8i		−	1.23558i	−0.786343	−	0.617790i	$-0.788028\pi$
$193$		−	1.23402e8i		−	1.23558i	0.786343	−	0.617790i	$-0.211972\pi$
$194$	1.19219e8	+	2.06494e8i	1.17230	+	2.03049i
$195$	−9.06608e7			−0.875585
$196$	5.56555e7			0.527973
$197$	7.18017e7	+	1.24364e8i	0.669118	+	1.15895i	0.978151	+	0.207895i	$0.0666613\pi$
$197$	7.18017e7	+	1.24364e8i	0.669118	+	1.15895i	−0.309033	+	0.951051i	$0.600005\pi$
$198$	−2.74539e8	−	1.58505e8i	−2.51348	−	1.45116i
$199$			2.18634e7i			0.196667i	0.995154	+	0.0983335i	$0.0313512\pi$
$199$			2.18634e7i			0.196667i	−0.995154	+	0.0983335i	$0.968649\pi$
$200$	9.26174e6	−	5.34727e6i	0.0818629	−	0.0472636i
$201$	9.29968e7	+	1.61075e8i	0.807759	+	1.39908i
$202$	1.53284e8	−	8.84986e7i	1.30848	−	0.755452i
$203$	−1.01815e7	−	5.87828e6i	−0.0854230	−	0.0493190i
$204$	−5.24932e7	−	3.03069e7i	−0.432910	−	0.249941i
$205$	9.38911e7	−	5.42080e7i	0.761177	−	0.439466i
$206$	−1.09050e8	−	1.88879e8i	−0.869138	−	1.50539i
$207$	−4.97136e8	+	2.87022e8i	−3.89564	+	2.24915i
$208$			8.37927e7i			0.645631i
$209$	2.34369e7	+	1.35313e7i	0.177578	+	0.102525i
$210$	−1.01412e7	−	1.75650e7i	−0.0755649	−	0.130882i
$211$	−3.70575e7			−0.271574			−0.135787	−	0.990738i	$-0.543356\pi$
$211$	−3.70575e7			−0.271574			−0.135787	+	0.990738i	$0.543356\pi$
$212$	−1.00497e7			−0.0724398
$213$	−3.06452e6	−	5.30790e6i	−0.0217287	−	0.0376352i
$214$		−	2.36319e8i		−	1.64835i
$215$	8.85853e7	−	1.53434e8i	0.607893	−	1.05290i
$216$		−	2.27246e8i		−	1.53429i
$217$	1.30381e7	+	7.52756e6i	0.0866175	+	0.0500086i
$218$	−1.64687e8	+	2.85246e8i	−1.07662	+	1.86476i
$219$	−1.20949e7	+	2.09490e7i	−0.0778122	+	0.134775i
$220$	−6.41869e7	+	3.70583e7i	−0.406412	+	0.234642i
$221$	4.21971e7			0.262972
$222$	2.44919e8	−	2.81849e8i	1.50240	−	1.72895i
$223$	−1.13701e8			−0.686592			−0.343296	−	0.939227i	$-0.611543\pi$
$223$	−1.13701e8			−0.686592			−0.343296	+	0.939227i	$0.611543\pi$
$224$	−1.01351e7	+	5.85153e6i	−0.0602506	+	0.0347857i
$225$	−3.37631e7	+	5.84793e7i	−0.197607	+	0.342266i
$226$	3.76719e7	−	6.52496e7i	0.217089	−	0.376009i
$227$	1.78404e8	+	1.03001e8i	1.01231	+	0.584457i	0.911867	−	0.410486i	$-0.134641\pi$
$227$	1.78404e8	+	1.03001e8i	1.01231	+	0.584457i	0.100442	+	0.994943i	$0.467974\pi$
$228$		−	3.73113e7i		−	0.208482i
$229$	1.63820e8	−	2.83744e8i	0.901450	−	1.56136i	0.0758366	−	0.997120i	$-0.475837\pi$
$229$	1.63820e8	−	2.83744e8i	0.901450	−	1.56136i	0.825613	−	0.564237i	$-0.190829\pi$
$230$			3.87089e8i			2.09780i
$231$	1.20851e7	+	2.09320e7i	0.0645072	+	0.111730i
$232$	−1.51049e8			−0.794163
$233$	2.41349e8			1.24997			0.624984	−	0.780637i	$-0.285105\pi$
$233$	2.41349e8			1.24997			0.624984	+	0.780637i	$0.285105\pi$
$234$	−1.52133e8	−	2.63503e8i	−0.776191	−	1.34440i
$235$	−2.13606e8	−	1.23325e8i	−1.07368	−	0.619891i
$236$		−	3.73583e7i		−	0.185010i
$237$	−2.99132e8	+	1.72704e8i	−1.45963	+	0.842720i
$238$	4.72009e6	+	8.17544e6i	0.0226951	+	0.0393090i
$239$	−2.07863e8	+	1.20010e8i	−0.984882	+	0.568622i	−0.903741	−	0.428081i	$-0.859190\pi$
$239$	−2.07863e8	+	1.20010e8i	−0.984882	+	0.568622i	−0.0811415	+	0.996703i	$0.525857\pi$
$240$	−3.92417e8	−	2.26562e8i	−1.83235	−	1.05791i
$241$	1.85550e8	+	1.07127e8i	0.853887	+	0.492992i	0.861961	−	0.506975i	$-0.169237\pi$
$241$	1.85550e8	+	1.07127e8i	0.853887	+	0.492992i	−0.00807333	+	0.999967i	$0.502570\pi$
$242$	−1.56158e7	+	9.01579e6i	−0.0708289	+	0.0408931i
$243$	2.14825e8	+	3.72088e8i	0.960424	+	1.66350i
$244$	4.31178e6	−	2.48941e6i	0.0190017	−	0.0109706i
$245$		−	2.09521e8i		−	0.910222i
$246$	4.44919e8	+	2.56874e8i	1.90550	+	1.10014i
$247$	1.29874e7	+	2.24948e7i	0.0548380	+	0.0949823i
$248$	1.93429e8			0.805268
$249$	3.79843e8			1.55922
$250$	1.62604e8	+	2.81638e8i	0.658174	+	1.13999i
$251$		−	1.49022e8i		−	0.594828i	−0.954749	−	0.297414i	$-0.903876\pi$
$251$		−	1.49022e8i		−	0.594828i	0.954749	−	0.297414i	$-0.0961241\pi$
$252$	1.18005e7	−	2.04390e7i	0.0464512	−	0.0804558i
$253$		−	4.61289e8i		−	1.79082i
$254$	−3.12876e8	−	1.80639e8i	−1.19799	−	0.691662i
$255$	−1.14094e8	+	1.97617e8i	−0.430896	+	0.746334i
$256$	−1.64156e8	+	2.84326e8i	−0.611527	+	1.05920i
$257$	−3.96013e8	+	2.28638e8i	−1.45527	+	0.840200i	−0.998773	−	0.0495249i	$-0.984229\pi$
$257$	−3.96013e8	+	2.28638e8i	−1.45527	+	0.840200i	−0.456497	+	0.889725i	$0.650896\pi$
$258$	8.39554e8			3.04354
$259$	−1.90633e7	+	6.56785e6i	−0.0681786	+	0.0234895i
$260$	−7.11372e7			−0.251009
$261$	8.25959e8	−	4.76867e8i	2.87552	−	1.66018i
$262$	−3.29983e8	+	5.71547e8i	−1.13354	+	1.96335i
$263$	1.77386e7	−	3.07242e7i	0.0601278	−	0.104144i	−0.834395	−	0.551168i	$-0.814183\pi$
$263$	1.77386e7	−	3.07242e7i	0.0601278	−	0.104144i	0.894522	+	0.447023i	$0.147516\pi$
$264$	2.68935e8	+	1.55270e8i	0.899568	+	0.519366i
$265$			3.78333e7i			0.124886i
$266$	−2.90549e6	+	5.03245e6i	−0.00946528	+	0.0163943i
$267$			3.28173e8i			1.05515i
$268$	7.29701e7	+	1.26388e8i	0.231565	+	0.401083i
$269$	−80369.0			−0.000251742			−0.000125871	−	1.00000i	$-0.500040\pi$
$269$	−80369.0			−0.000251742			−0.000125871		1.00000i	$0.500040\pi$
$270$	9.67548e8			2.99157
$271$	−8.98141e7	−	1.55563e8i	−0.274127	−	0.474802i	0.695787	−	0.718248i	$-0.255056\pi$
$271$	−8.98141e7	−	1.55563e8i	−0.274127	−	0.474802i	−0.969915	+	0.243446i	$0.921722\pi$
$272$	1.82646e8	+	1.05451e8i	0.550325	+	0.317730i
$273$			2.31986e7i			0.0690068i
$274$	−6.57346e8	+	3.79519e8i	−1.93049	+	1.11457i
$275$	−2.71313e7	−	4.69928e7i	−0.0786694	−	0.136259i
$276$	−5.50775e8	+	3.17990e8i	−1.57686	+	0.910400i
$277$	−4.02569e8	−	2.32424e8i	−1.13805	−	0.657054i	−0.192104	−	0.981375i	$-0.561531\pi$
$277$	−4.02569e8	−	2.32424e8i	−1.13805	−	0.657054i	−0.945947	+	0.324321i	$0.894864\pi$
$278$	−2.00641e8	−	1.15840e8i	−0.560097	−	0.323372i
$279$	−1.05770e9	+	6.10663e8i	−2.91573	+	1.68340i
$280$	7.03573e6	+	1.21862e7i	0.0191539	+	0.0331755i
$281$	−1.67114e8	+	9.64836e7i	−0.449306	+	0.259407i	−0.707537	−	0.706676i	$-0.750194\pi$
$281$	−1.67114e8	+	9.64836e7i	−0.449306	+	0.259407i	0.258231	+	0.966083i	$0.416860\pi$
$282$		−	1.16880e9i		−	3.10361i
$283$	2.00208e8	+	1.15590e8i	0.525084	+	0.303158i	0.739012	−	0.673692i	$-0.235292\pi$
$283$	2.00208e8	+	1.15590e8i	0.525084	+	0.303158i	−0.213928	+	0.976849i	$0.568626\pi$
$284$	−2.40458e6	−	4.16485e6i	−0.00622909	−	0.0107891i
$285$	−1.40463e8			−0.359422
$286$	2.44502e8			0.618019
$287$	−1.38709e7	−	2.40251e7i	−0.0346353	−	0.0599900i
$288$		−	9.49393e8i		−	2.34192i
$289$	−1.52065e8	+	2.63385e8i	−0.370585	+	0.641873i
$290$		−	6.43122e8i		−	1.54846i
$291$	1.27721e9	+	7.37395e8i	3.03833	+	1.75418i
$292$	−9.49029e6	+	1.64377e7i	−0.0223069	+	0.0386367i
$293$	9.00384e7	−	1.55951e8i	0.209118	−	0.362203i	−0.742319	−	0.670047i	$-0.766274\pi$
$293$	9.00384e7	−	1.55951e8i	0.209118	−	0.362203i	0.951437	+	0.307844i	$0.0996074\pi$
$294$	8.59836e8	−	4.96427e8i	1.97333	−	1.13930i
$295$	−1.40640e8			−0.318956
$296$	−1.69920e8	+	1.95541e8i	−0.380823	+	0.438246i
$297$	−1.15302e9			−2.55380
$298$	2.71963e8	−	1.57018e8i	0.595324	−	0.343711i
$299$	2.21373e8	−	3.83429e8i	0.478933	−	0.829537i
$300$	−3.74060e7	+	6.47890e7i	−0.0799865	+	0.138541i
$301$	−3.92612e7	−	2.26675e7i	−0.0829815	−	0.0479094i
$302$		−	5.72058e8i		−	1.19513i
$303$	5.47382e8	−	9.48093e8i	1.13042	−	1.95795i
$304$			1.29822e8i			0.265027i
$305$	−9.37166e6	−	1.62322e7i	−0.0189133	−	0.0327588i
$306$	−7.65822e8			−1.52793
$307$	−2.47354e7			−0.0487905			−0.0243952	−	0.999702i	$-0.507766\pi$
$307$	−2.47354e7			−0.0487905			−0.0243952	+	0.999702i	$0.507766\pi$
$308$	9.48259e6	+	1.64243e7i	0.0184927	+	0.0320302i
$309$	−1.16826e9	−	6.74493e8i	−2.25260	−	1.30054i
$310$			8.23564e8i			1.57011i
$311$	−4.16336e7	+	2.40372e7i	−0.0784843	+	0.0453129i	−0.538729	−	0.842479i	$-0.681095\pi$
$311$	−4.16336e7	+	2.40372e7i	−0.0784843	+	0.0453129i	0.460244	+	0.887792i	$0.347762\pi$
$312$	1.49028e8	+	2.58124e8i	0.277797	+	0.481158i
$313$	1.23389e8	−	7.12388e7i	0.227443	−	0.131314i	−0.381949	−	0.924183i	$-0.624747\pi$
$313$	1.23389e8	−	7.12388e7i	0.227443	−	0.131314i	0.609392	+	0.792869i	$0.291414\pi$
$314$	2.18805e8	+	1.26327e8i	0.398845	+	0.230273i
$315$	−7.69449e7	−	4.44242e7i	−0.138705	−	0.0800816i
$316$	−2.34715e8	+	1.35513e8i	−0.418442	+	0.241588i
$317$	4.29123e8	+	7.43262e8i	0.756614	+	1.31049i	0.944568	+	0.328316i	$0.106481\pi$
$317$	4.29123e8	+	7.43262e8i	0.756614	+	1.31049i	−0.187954	+	0.982178i	$0.560186\pi$
$318$	−1.55261e8	+	8.96397e7i	−0.270749	+	0.156317i
$319$			7.66401e8i			1.32187i
$320$	2.57362e7	+	1.48588e7i	0.0439055	+	0.0253488i
$321$	−7.30840e8	−	1.26585e9i	−1.23326	−	2.13607i
$322$	9.90495e7			0.165332
$323$	6.53769e7			0.107948
$324$	4.00467e8	+	6.93628e8i	0.654122	+	1.13297i
$325$		−	5.20812e7i		−	0.0841569i
$326$	−8.32277e7	+	1.44155e8i	−0.133047	+	0.230445i
$327$			2.03725e9i			3.22201i
$328$	−3.08676e8	−	1.78214e8i	−0.482997	−	0.278858i
$329$	−3.15569e7	+	5.46581e7i	−0.0488549	+	0.0846193i
$330$	−6.61094e8	+	1.14505e9i	−1.01266	+	1.75398i
$331$	−1.54313e8	+	8.90927e7i	−0.233886	+	0.135034i	−0.612364	−	0.790576i	$-0.709781\pi$
$331$	−1.54313e8	+	8.90927e7i	−0.233886	+	0.135034i	0.378477	+	0.925611i	$0.376448\pi$
$332$	2.98045e8			0.446990
$333$	3.11815e8	−	1.60569e9i	0.462746	−	2.38291i
$334$	5.84307e8			0.858082
$335$	4.75802e8	−	2.74705e8i	0.691464	−	0.399217i
$336$	−5.79733e7	+	1.00413e8i	−0.0833759	+	0.144411i
$337$	−2.22725e7	+	3.85772e7i	−0.0317004	+	0.0549068i	−0.881440	−	0.472295i	$-0.843426\pi$
$337$	−2.22725e7	+	3.85772e7i	−0.0317004	+	0.0549068i	0.849740	+	0.527202i	$0.176759\pi$
$338$	−5.57424e8	−	3.21829e8i	−0.785194	−	0.453332i
$339$		−	4.66016e8i		−	0.649684i
$340$	−8.95241e7	+	1.55060e8i	−0.123528	+	0.213956i
$341$		−	9.81431e8i		−	1.34035i
$342$	−2.35704e8	−	4.08251e8i	−0.318621	−	0.551869i
$343$	−1.07506e8			−0.143848
$344$	−5.82466e8			−0.771464
$345$	1.19711e9	+	2.07346e9i	1.56952	+	2.71850i
$346$	6.26650e7	+	3.61796e7i	0.0813315	+	0.0469567i
$347$		−	2.00704e8i		−	0.257871i	−0.991653	−	0.128936i	$-0.958844\pi$
$347$		−	2.00704e8i		−	0.257871i	0.991653	−	0.128936i	$-0.0411561\pi$
$348$	9.15077e8	−	5.28320e8i	1.16394	−	0.672000i
$349$	2.55971e8	+	4.43354e8i	0.322330	+	0.558292i	0.980968	−	0.194168i	$-0.0622005\pi$
$349$	2.55971e8	+	4.43354e8i	0.322330	+	0.558292i	−0.658638	+	0.752460i	$0.728867\pi$
$350$	1.00904e7	−	5.82571e6i	0.0125797	−	0.00726292i
$351$	−9.58400e8	−	5.53332e8i	−1.18296	−	0.682985i
$352$	6.60702e8	+	3.81456e8i	0.807432	+	0.466171i
$353$	−2.68013e8	+	1.54738e8i	−0.324298	+	0.187234i	−0.653307	−	0.757093i	$-0.726619\pi$
$353$	−2.68013e8	+	1.54738e8i	−0.324298	+	0.187234i	0.329008	+	0.944327i	$0.393286\pi$
$354$	−3.33222e8	−	5.77158e8i	−0.399229	−	0.691486i
$355$	−1.56791e7	+	9.05232e6i	−0.0186003	+	0.0107389i
$356$			2.57502e8i			0.302486i
$357$	5.05668e7	+	2.91947e7i	0.0588202	+	0.0339598i
$358$	2.42140e8	+	4.19399e8i	0.278918	+	0.483100i
$359$	7.16291e8			0.817069			0.408535	−	0.912743i	$-0.366040\pi$
$359$	7.16291e8			0.817069			0.408535	+	0.912743i	$0.366040\pi$
$360$	−1.14153e9			−1.28952
$361$	−4.26814e8	−	7.39264e8i	−0.477489	−	0.827036i
$362$		−	1.28680e9i		−	1.42571i
$363$	−5.57645e7	+	9.65869e7i	−0.0611906	+	0.105985i
$364$			1.82028e7i			0.0197826i
$365$	6.18815e7	+	3.57273e7i	0.0666094	+	0.0384570i
$366$	4.44092e7	−	7.69190e7i	0.0473467	−	0.0820068i
$367$	−2.30103e8	+	3.98550e8i	−0.242992	+	0.420874i	−0.961565	−	0.274577i	$-0.911462\pi$
$367$	−2.30103e8	+	3.98550e8i	−0.242992	+	0.420874i	0.718573	+	0.695451i	$0.244795\pi$
$368$	1.91638e9	−	1.10642e9i	2.00454	−	1.15732i
$369$	2.25052e9			2.33179
$370$	−8.32559e8	−	7.23469e8i	−0.854494	−	0.742530i
$371$	9.68089e6			0.00984252
$372$	−1.17182e9	+	6.76551e8i	−1.18021	+	0.681397i
$373$	2.33112e8	−	4.03761e8i	0.232586	−	0.402851i	−0.725982	−	0.687713i	$-0.758615\pi$
$373$	2.33112e8	−	4.03761e8i	0.232586	−	0.402851i	0.958568	+	0.284863i	$0.0919480\pi$
$374$	3.07699e8	−	5.32950e8i	0.304141	−	0.526788i
$375$	1.74199e9	+	1.00574e9i	1.70583	+	0.984862i
$376$			8.10889e8i			0.786690i
$377$	−3.67796e8	+	6.37042e8i	−0.353519	+	0.612312i
$378$		−	2.47579e8i		−	0.235772i
$379$	−3.21046e8	−	5.56067e8i	−0.302921	−	0.524675i	0.673875	−	0.738845i	$-0.264629\pi$
$379$	−3.21046e8	−	5.56067e8i	−0.302921	−	0.524675i	−0.976796	+	0.214170i	$0.931295\pi$
$380$	−1.10215e8			−0.103038
$381$	−2.23458e9			−2.06994
$382$	−4.19303e8	−	7.26253e8i	−0.384863	−	0.666602i
$383$	−5.07236e8	−	2.92853e8i	−0.461333	−	0.266351i	0.251272	−	0.967917i	$-0.419151\pi$
$383$	−5.07236e8	−	2.92853e8i	−0.461333	−	0.266351i	−0.712605	+	0.701566i	$0.752485\pi$
$384$			2.12267e9i			1.91303i
$385$	6.18313e7	−	3.56983e7i	0.0552200	−	0.0318813i
$386$	−8.63667e8	−	1.49592e9i	−0.764347	−	1.32389i
$387$	3.18501e9	−	1.83887e9i	2.79333	−	1.61273i
$388$	1.00216e9	+	5.78598e8i	0.871017	+	0.502882i
$389$	−7.93771e8	−	4.58284e8i	−0.683709	−	0.394740i	0.117542	−	0.993068i	$-0.462499\pi$
$389$	−7.93771e8	−	4.58284e8i	−0.683709	−	0.394740i	−0.801251	+	0.598328i	$0.795832\pi$
$390$	−1.09902e9	+	6.34519e8i	−0.938164	+	0.541649i
$391$	−5.57183e8	−	9.65069e8i	−0.471389	−	0.816469i
$392$	−5.96537e8	+	3.44411e8i	−0.500192	+	0.288786i
$393$			4.08202e9i			3.39235i
$394$	1.74080e9	+	1.00505e9i	1.43388	+	0.827852i
$395$	5.10153e8	+	8.83611e8i	0.416496	+	0.721392i
$396$	−1.53852e9			−1.24501
$397$	−5.14472e8			−0.412662			−0.206331	−	0.978482i	$-0.566152\pi$
$397$	−5.14472e8			−0.412662			−0.206331	+	0.978482i	$0.566152\pi$
$398$	1.53018e8	+	2.65035e8i	0.121661	+	0.210723i
$399$			3.59421e7i			0.0283268i
$400$	1.30151e8	−	2.25429e8i	0.101681	−	0.176116i
$401$		−	8.79070e8i		−	0.680798i	−0.940281	−	0.340399i	$-0.889438\pi$
$401$		−	8.79070e8i		−	0.680798i	0.940281	−	0.340399i	$-0.110562\pi$
$402$	2.25467e9	+	1.30174e9i	1.73098	+	0.999382i
$403$	4.70989e8	−	8.15777e8i	0.358462	−	0.620874i
$404$	4.29504e8	−	7.43923e8i	0.324065	−	0.561298i
$405$	2.61125e9	−	1.50760e9i	1.95324	−	1.12770i
$406$	−1.64564e8			−0.122038
$407$	9.92150e8	+	8.62149e8i	0.729453	+	0.633873i
$408$	7.50191e8			0.546841
$409$	3.52065e7	−	2.03265e7i	0.0254444	−	0.0146903i	−0.487224	−	0.873277i	$-0.661990\pi$
$409$	3.52065e7	−	2.03265e7i	0.0254444	−	0.0146903i	0.512668	+	0.858587i	$0.328657\pi$
$410$	7.58784e8	−	1.31425e9i	0.543719	−	0.941750i
$411$	−2.34740e9	+	4.06582e9i	−1.66779	+	2.88869i
$412$	−9.16675e8	−	5.29243e8i	−0.645766	−	0.372833i
$413$			3.59873e7i			0.0251376i
$414$	−4.01763e9	+	6.95873e9i	−2.78271	+	4.81980i
$415$		−	1.12202e9i		−	0.770608i
$416$	3.66122e8	+	6.34142e8i	0.249344	+	0.431877i
$417$	−1.43299e9			−0.967759
$418$	3.78813e8			0.253693
$419$	8.80145e8	+	1.52446e9i	0.584528	+	1.01243i	0.994934	+	0.100529i	$0.0320536\pi$
$419$	8.80145e8	+	1.52446e9i	0.584528	+	1.01243i	−0.410406	+	0.911903i	$0.634613\pi$
$420$	−8.52470e7	−	4.92174e7i	−0.0561444	−	0.0324150i
$421$		−	6.21617e8i		−	0.406009i	−0.979178	−	0.203004i	$-0.934929\pi$
$421$		−	6.21617e8i		−	0.406009i	0.979178	−	0.203004i	$-0.0650706\pi$
$422$	−4.49223e8	+	2.59359e8i	−0.290983	+	0.167999i
$423$	−2.56001e9	−	4.43406e9i	−1.64456	−	2.84846i
$424$	1.07717e8	−	6.21902e7i	0.0686282	−	0.0396225i
$425$	−1.13523e8	−	6.55428e7i	−0.0717338	−	0.0414155i
$426$	−7.42980e7	−	4.28960e7i	−0.0465633	−	0.0268833i
$427$	−4.15354e6	+	2.39805e6i	−0.00258179	+	0.00149060i
$428$	−5.73455e8	−	9.93253e8i	−0.353546	−	0.612360i
$429$	1.30969e9	−	7.56148e8i	0.800879	−	0.462388i
$430$		−	2.47997e9i		−	1.50420i
$431$	2.31273e9	+	1.33526e9i	1.39141	+	0.803331i	0.993471	−	0.114081i	$-0.0363924\pi$
$431$	2.31273e9	+	1.33526e9i	1.39141	+	0.803331i	0.397938	+	0.917412i	$0.369726\pi$
$432$	−2.76556e9	−	4.79009e9i	−1.65040	−	2.85858i
$433$	−9.47319e8			−0.560775			−0.280387	−	0.959887i	$-0.590463\pi$
$433$	−9.47319e8			−0.560775			−0.280387	+	0.959887i	$0.590463\pi$
$434$	2.10736e8			0.123744
$435$	−1.98892e9	−	3.44491e9i	−1.15852	−	2.00662i
$436$			1.59853e9i			0.923672i
$437$	3.42978e8	−	5.94055e8i	0.196599	−	0.340519i
$438$			3.38600e8i			0.192543i
$439$	4.01657e8	+	2.31897e8i	0.226584	+	0.130819i	0.608995	−	0.793174i	$-0.291573\pi$
$439$	4.01657e8	+	2.31897e8i	0.226584	+	0.130819i	−0.382411	+	0.923992i	$0.624906\pi$
$440$	4.58654e8	−	7.94412e8i	0.256685	−	0.444592i
$441$	2.17464e9	−	3.76658e9i	1.20740	−	2.09128i
$442$	5.11526e8	−	2.95330e8i	0.281767	−	0.162678i
$443$	−2.90299e9			−1.58647			−0.793237	−	0.608913i	$-0.791606\pi$
$443$	−2.90299e9			−1.58647			−0.793237	+	0.608913i	$0.791606\pi$
$444$	3.45459e8	−	1.77894e9i	0.187308	−	0.964543i
$445$	9.69396e8			0.521484
$446$	−1.37832e9	+	7.95775e8i	−0.735663	+	0.424735i
$447$	9.71189e8	−	1.68215e9i	0.514313	−	0.890816i
$448$	3.80211e6	−	6.58545e6i	0.00199780	−	0.00346029i
$449$	3.36171e8	+	1.94088e8i	0.175266	+	0.101190i	0.585067	−	0.810985i	$-0.301068\pi$
$449$	3.36171e8	+	1.94088e8i	0.175266	+	0.101190i	−0.409800	+	0.912175i	$0.634402\pi$
$450$			9.45206e8i			0.488970i
$451$	−9.04234e8	+	1.56618e9i	−0.464155	+	0.803940i
$452$		−	3.65661e8i		−	0.186249i
$453$	−1.76915e9	−	3.06425e9i	−0.894170	−	1.54875i
$454$	2.88355e9			1.44621
$455$	6.85266e7			0.0341051
$456$	2.30893e8	+	3.99918e8i	0.114034	+	0.197512i
$457$	−1.09501e9	−	6.32207e8i	−0.536677	−	0.309851i	0.207054	−	0.978329i	$-0.433612\pi$
$457$	−1.09501e9	−	6.32207e8i	−0.536677	−	0.309851i	−0.743731	+	0.668479i	$0.766946\pi$
$458$		−	4.58617e9i		−	2.23060i
$459$	−2.41224e9	+	1.39271e9i	−1.16433	+	0.672226i
$460$	9.39316e8	+	1.62694e9i	0.449945	+	0.779328i
$461$	−2.50922e9	+	1.44870e9i	−1.19285	+	0.688692i	−0.958952	−	0.283569i	$-0.908481\pi$
$461$	−2.50922e9	+	1.44870e9i	−1.19285	+	0.688692i	−0.233898	+	0.972261i	$0.575148\pi$
$462$	2.92998e8	+	1.69163e8i	0.138235	+	0.0798101i
$463$	2.20528e9	+	1.27322e9i	1.03260	+	0.596169i	0.917727	−	0.397211i	$-0.130022\pi$
$463$	2.20528e9	+	1.27322e9i	1.03260	+	0.596169i	0.114868	+	0.993381i	$0.463355\pi$
$464$	−3.18394e9	+	1.83825e9i	−1.47963	+	0.854262i
$465$	2.54695e9	+	4.41146e9i	1.17472	+	2.03468i
$466$	2.92570e9	−	1.68915e9i	1.33930	−	0.773248i
$467$			2.57896e9i			1.17175i	0.810401	+	0.585876i	$0.199249\pi$
$467$			2.57896e9i			1.17175i	−0.810401	+	0.585876i	$0.800751\pi$
$468$	−1.27884e9	−	7.38338e8i	−0.576707	−	0.332962i
$469$	−7.02922e7	−	1.21750e8i	−0.0314632	−	0.0544958i
$470$	−3.45253e9			−1.53389
$471$	1.56272e9			0.689141
$472$	2.31183e8	+	4.00421e8i	0.101195	+	0.175275i
$473$			2.95535e9i			1.28409i
$474$	−2.41745e9	+	4.18714e9i	−1.04264	+	1.80590i
$475$		−	8.06907e7i		−	0.0345458i
$476$	3.96773e7	+	2.29077e7i	0.0168623	+	0.00973548i
$477$	−3.92674e8	+	6.80132e8i	−0.165660	+	0.286932i
$478$	−1.67985e9	+	2.90959e9i	−0.703515	+	1.21852i
$479$	1.68797e9	−	9.74552e8i	0.701764	−	0.405164i	−0.106240	−	0.994341i	$-0.533881\pi$
$479$	1.68797e9	−	9.74552e8i	0.701764	−	0.405164i	0.808004	+	0.589177i	$0.200548\pi$
$480$	−3.95974e9			−1.63426
$481$	4.10941e8	+	1.19276e9i	0.168373	+	0.488704i
$482$	2.99905e9			1.21989
$483$	5.30563e8	−	3.06321e8i	0.214251	−	0.123698i
$484$	−4.37557e7	+	7.57871e7i	−0.0175419	+	0.0303834i
$485$	2.17820e9	−	3.77276e9i	0.866966	−	1.50163i
$486$	5.20835e9	+	3.00704e9i	2.05813	+	1.18826i
$487$		−	1.07413e9i		−	0.421409i	−0.977550	−	0.210704i	$-0.932424\pi$
$487$		−	1.07413e9i		−	0.421409i	0.977550	−	0.210704i	$-0.0675758\pi$
$488$	−3.08102e7	+	5.33649e7i	−0.0120012	+	0.0207867i
$489$			1.02956e9i			0.398172i
$490$	−1.46640e9	−	2.53988e9i	−0.563076	−	0.975276i
$491$	3.46234e9			1.32003			0.660016	−	0.751252i	$-0.270549\pi$
$491$	3.46234e9			1.32003			0.660016	+	0.751252i	$0.270549\pi$
$492$	2.49334e9			0.943851
$493$	9.25722e8	+	1.60340e9i	0.347950	+	0.602666i
$494$	3.14874e8	+	1.81792e8i	0.117515	+	0.0678472i
$495$			5.79195e9i			2.14638i
$496$	4.07726e9	−	2.35401e9i	1.50032	−	0.866208i
$497$	2.31633e6	+	4.01201e6i	0.000846357	+	0.00146593i
$498$	4.60457e9	−	2.65845e9i	1.67065	−	0.964553i
$499$	−6.94584e8	−	4.01018e8i	−0.250249	−	0.144481i	0.369629	−	0.929179i	$-0.379485\pi$
$499$	−6.94584e8	−	4.01018e8i	−0.250249	−	0.144481i	−0.619878	+	0.784698i	$0.712818\pi$
$500$	1.36685e9	+	7.89154e8i	0.489021	+	0.282336i
$501$	3.12987e9	−	1.80703e9i	1.11197	−	0.641997i
$502$	−1.04297e9	−	1.80649e9i	−0.367969	−	0.637340i
$503$	−2.36589e9	+	1.36595e9i	−0.828909	+	0.478571i	−0.853479	−	0.521127i	$-0.825512\pi$
$503$	−2.36589e9	+	1.36595e9i	−0.828909	+	0.478571i	0.0245701	+	0.999698i	$0.492178\pi$
$504$			2.92098e8i			0.101630i
$505$	−2.80059e9	−	1.61692e9i	−0.967674	−	0.558687i
$506$	−3.22848e9	−	5.59189e9i	−1.10782	−	1.91881i
$507$	−3.98115e9			−1.35669
$508$	−1.75337e9			−0.593403
$509$	5.91705e8	+	1.02486e9i	0.198881	+	0.344472i	0.948166	−	0.317776i	$-0.102936\pi$
$509$	5.91705e8	+	1.02486e9i	0.198881	+	0.344472i	−0.749285	+	0.662248i	$0.769603\pi$
$510$			3.19409e9i			1.06623i
$511$	9.14201e6	−	1.58344e7i	0.00303088	−	0.00524963i
$512$			1.45736e9i			0.479868i
$513$	−1.48487e9	−	8.57291e8i	−0.485599	−	0.280361i
$514$	−3.20039e9	+	5.54324e9i	−1.03952	+	1.80050i
$515$	−1.99240e9	+	3.45093e9i	−0.642762	+	1.11330i
$516$	3.52866e9	−	2.03727e9i	1.13067	−	0.652793i
$517$	4.11434e9			1.30943
$518$	−1.85123e8	+	2.13038e8i	−0.0585204	+	0.0673445i
$519$	4.47557e8			0.140528
$520$	7.62477e8	−	4.40216e8i	0.237802	−	0.137295i
$521$	−1.90524e9	+	3.29998e9i	−0.590226	+	1.02230i	0.403976	+	0.914770i	$0.367628\pi$
$521$	−1.90524e9	+	3.29998e9i	−0.590226	+	1.02230i	−0.994202	+	0.107532i	$0.965705\pi$
$522$	6.67502e9	−	1.15615e10i	2.05402	−	3.55767i
$523$	5.28615e8	+	3.05196e8i	0.161579	+	0.0932874i	0.578609	−	0.815605i	$-0.303596\pi$
$523$	5.28615e8	+	3.05196e8i	0.161579	+	0.0932874i	−0.417030	+	0.908893i	$0.636929\pi$
$524$			3.20297e9i			0.972507i
$525$	3.60332e7	−	6.24114e7i	0.0108679	−	0.0188238i
$526$		−	4.96598e8i		−	0.148784i
$527$	−1.18545e9	−	2.05326e9i	−0.352815	−	0.611094i
$528$	7.55847e9			2.23468
$529$	−8.28746e9			−2.43403
$530$	2.64788e8	+	4.58626e8i	0.0772561	+	0.133811i
$531$	−2.52829e9	−	1.45971e9i	−0.732817	−	0.423092i
$532$			2.82020e7i			0.00812063i
$533$	−1.50322e9	+	8.67884e8i	−0.430009	+	0.248266i
$534$	2.29682e9	+	3.97822e9i	0.652730	+	1.13056i
$535$	−3.73922e9	+	2.15884e9i	−1.05570	+	0.609511i
$536$	−1.56425e9	−	9.03118e8i	−0.438761	−	0.253319i
$537$	2.59407e9	+	1.49769e9i	0.722889	+	0.417360i
$538$	−974257.	+	562488.i	−0.000269734	+	0.000155731i
$539$	1.74749e9	+	3.02675e9i	0.480679	+	0.832560i
$540$	4.06663e9	−	2.34787e9i	1.11136	−	0.641646i
$541$		−	6.37749e9i		−	1.73165i	−0.500350	−	0.865823i	$-0.666795\pi$
$541$		−	6.37749e9i		−	1.73165i	0.500350	−	0.865823i	$-0.333205\pi$
$542$	−2.17751e9	−	1.25718e9i	−0.587438	−	0.339158i
$543$	−3.97957e9	−	6.89282e9i	−1.06669	−	1.84756i
$544$	1.84302e9			0.490832
$545$	6.01785e9			1.59241
$546$	1.62363e8	+	2.81220e8i	0.0426886	+	0.0739388i
$547$			2.01091e9i			0.525335i	0.964886	+	0.262667i	$0.0846022\pi$
$547$			2.01091e9i			0.525335i	−0.964886	+	0.262667i	$0.915398\pi$
$548$	−1.84189e9	+	3.19025e9i	−0.478115	+	0.828119i
$549$		−	3.89076e8i		−	0.100353i
$550$	−6.57787e8	−	3.79774e8i	−0.168584	−	0.0973320i
$551$	−5.69835e8	+	9.86983e8i	−0.145117	+	0.251350i
$552$	3.93562e9	−	6.81670e9i	0.995925	−	1.72499i
$553$	2.26101e8	−	1.30539e8i	0.0568544	−	0.0328249i
$554$	−6.50676e9			−1.62585
$555$	−6.69704e9	−	1.30052e9i	−1.66287	−	0.322918i
$556$	−1.12440e9			−0.277434
$557$	2.49128e9	−	1.43834e9i	0.610844	−	0.352671i	−0.162452	−	0.986716i	$-0.551940\pi$
$557$	2.49128e9	−	1.43834e9i	0.610844	−	0.352671i	0.773296	+	0.634046i	$0.218607\pi$
$558$	−8.54783e9	+	1.48053e10i	−2.08275	+	3.60742i
$559$	−1.41827e9	+	2.45652e9i	−0.343414	+	0.594811i
$560$	2.96611e8	+	1.71248e8i	0.0713721	+	0.0412067i
$561$		−	3.80636e9i		−	0.910207i
$562$	−1.35054e9	+	2.33921e9i	−0.320945	+	0.555893i
$563$		−	6.37504e9i		−	1.50558i	−0.658261	−	0.752789i	$-0.728708\pi$
$563$		−	6.37504e9i		−	1.50558i	0.658261	−	0.752789i	$-0.271292\pi$
$564$	−2.83622e9	−	4.91248e9i	−0.665677	−	1.15299i
$565$	−1.37657e9			−0.321092
$566$	3.23598e9			0.750150
$567$	−3.85770e8	−	6.68173e8i	−0.0888767	−	0.153939i
$568$	5.15465e7	+	2.97604e7i	0.0118027	+	0.00681427i
$569$			4.47250e9i			1.01779i	0.860829	+	0.508894i	$0.169945\pi$
$569$			4.47250e9i			1.01779i	−0.860829	+	0.508894i	$0.830055\pi$
$570$	−1.70273e9	+	9.83074e8i	−0.385110	+	0.222343i
$571$	−3.87943e8	−	6.71937e8i	−0.0872051	−	0.151044i	0.819124	−	0.573617i	$-0.194460\pi$
$571$	−3.87943e8	−	6.71937e8i	−0.0872051	−	0.151044i	−0.906329	+	0.422573i	$0.861127\pi$
$572$	1.02765e9	−	5.93313e8i	0.229593	−	0.132556i
$573$	−4.49202e9	−	2.59347e9i	−0.997472	−	0.575891i
$574$	−3.36295e8	−	1.94160e8i	−0.0742213	−	0.0428517i
$575$	−1.19112e9	+	6.87696e8i	−0.261288	+	0.150855i
$576$	3.08441e8	+	5.34235e8i	0.0672501	+	0.116481i
$577$	−4.63677e8	+	2.67704e8i	−0.100485	+	0.0580150i	−0.549400	−	0.835559i	$-0.685144\pi$
$577$	−4.63677e8	+	2.67704e8i	−0.100485	+	0.0580150i	0.448915	+	0.893574i	$0.351810\pi$
$578$			4.25711e9i			0.916997i
$579$	−9.25254e9	−	5.34195e9i	−1.98101	−	1.14373i
$580$	−1.56061e9	−	2.70306e9i	−0.332121	−	0.575251i
$581$	−2.87107e8			−0.0607333
$582$	2.06436e10			4.34065
$583$	−3.15545e8	−	5.46539e8i	−0.0659509	−	0.114230i
$584$		−	2.34914e8i		−	0.0488049i
$585$	−2.77956e9	+	4.81434e9i	−0.574025	+	0.994240i
$586$		−	2.52065e9i		−	0.517453i
$587$	−2.52081e9	−	1.45539e9i	−0.514406	−	0.296993i	0.220237	−	0.975446i	$-0.429317\pi$
$587$	−2.52081e9	−	1.45539e9i	−0.514406	−	0.296993i	−0.734643	+	0.678454i	$0.762650\pi$
$588$	2.40927e9	−	4.17299e9i	0.488726	−	0.846499i
$589$	7.29714e8	−	1.26390e9i	0.147146	−	0.254865i
$590$	−1.70488e9	+	9.84310e8i	−0.341752	+	0.197310i
$591$	1.24329e10			2.47752
$592$	−1.20200e9	+	6.18970e9i	−0.238110	+	1.22615i
$593$	5.91637e9			1.16510			0.582551	−	0.812794i	$-0.302055\pi$
$593$	5.91637e9			1.16510			0.582551	+	0.812794i	$0.302055\pi$
$594$	−1.39772e10	+	8.06974e9i	−2.73633	+	1.57982i
$595$	8.62387e7	−	1.49370e8i	0.0167839	−	0.0290706i
$596$	7.62045e8	−	1.31990e9i	0.147441	−	0.255376i
$597$	1.63929e9	+	9.46446e8i	0.315316	+	0.182048i
$598$		−	6.19739e9i		−	1.18510i
$599$	4.05768e9	−	7.02810e9i	0.771407	−	1.33612i	−0.165385	−	0.986229i	$-0.552887\pi$
$599$	4.05768e9	−	7.02810e9i	0.771407	−	1.33612i	0.936792	−	0.349887i	$-0.113780\pi$
$600$		−	9.25913e8i		−	0.175001i
$601$	1.27306e9	+	2.20500e9i	0.239214	+	0.414331i	0.960489	−	0.278318i	$-0.0897769\pi$
$601$	1.27306e9	+	2.20500e9i	0.239214	+	0.414331i	−0.721275	+	0.692649i	$0.756444\pi$
$602$	−6.34582e8			−0.118550
$603$	1.14047e10			2.11823
$604$	−1.38817e9	−	2.40437e9i	−0.256337	−	0.443989i
$605$	2.85310e8	+	1.64724e8i	0.0523809	+	0.0302421i
$606$		−	1.53241e10i		−	2.79718i
$607$	−9.36566e9	+	5.40727e9i	−1.69972	+	0.981335i	−0.753709	+	0.657209i	$0.771737\pi$
$607$	−9.36566e9	+	5.40727e9i	−1.69972	+	0.981335i	−0.946014	+	0.324127i	$0.894930\pi$
$608$	5.67241e8	+	9.82491e8i	0.102354	+	0.177283i
$609$	−8.81495e8	+	5.08931e8i	−0.158146	+	0.0913058i
$610$	−2.27212e8	−	1.31181e8i	−0.0405301	−	0.0234000i
$611$	3.41989e9	+	1.97447e9i	0.606551	+	0.350192i
$612$	−3.21877e9	+	1.85836e9i	−0.567622	+	0.327717i
$613$	−3.31296e9	−	5.73821e9i	−0.580903	−	1.00615i	−0.995373	−	0.0960908i	$-0.969366\pi$
$613$	−3.31296e9	−	5.73821e9i	−0.580903	−	1.00615i	0.414469	−	0.910063i	$-0.363967\pi$
$614$	−2.99851e8	+	1.73119e8i	−0.0522776	+	0.0301825i
$615$		−	9.38647e9i		−	1.62719i
$616$	−2.03276e8	−	1.17362e8i	−0.0350392	−	0.0202299i
$617$	4.71774e9	+	8.17137e9i	0.808605	+	1.40054i	0.913830	+	0.406096i	$0.133110\pi$
$617$	4.71774e9	+	8.17137e9i	0.808605	+	1.40054i	−0.105226	+	0.994448i	$0.533556\pi$
$618$	−1.88826e10			−3.21812
$619$	6.89850e9			1.16906			0.584530	−	0.811372i	$-0.301279\pi$
$619$	6.89850e9			1.16906			0.584530	+	0.811372i	$0.301279\pi$
$620$	1.99847e9	+	3.46146e9i	0.336765	+	0.583295i
$621$			2.92254e10i			4.89712i
$622$	−3.36464e8	+	5.82772e8i	−0.0560624	+	0.0971030i
$623$		−	2.48052e8i		−	0.0410993i
$624$	6.28269e9	+	3.62731e9i	1.03514	+	0.597639i
$625$	2.47400e9	−	4.28509e9i	0.405340	−	0.702070i
$626$	9.97174e8	−	1.72716e9i	0.162465	−	0.281398i
$627$	2.02913e9	−	1.17152e9i	0.328755	−	0.189807i
$628$	1.22619e9			0.197560
$629$	3.11706e9	+	6.05313e8i	0.499423	+	0.0969846i
$630$	−1.24367e9			−0.198158
$631$	−5.46953e8	+	3.15784e8i	−0.0866657	+	0.0500365i	−0.542707	−	0.839922i	$-0.682600\pi$
$631$	−5.46953e8	+	3.15784e8i	−0.0866657	+	0.0500365i	0.456041	+	0.889959i	$0.349267\pi$
$632$	1.67718e9	−	2.90496e9i	0.264283	−	0.457751i
$633$	−1.60419e9	+	2.77853e9i	−0.251387	+	0.435414i
$634$	1.04039e10	+	6.00670e9i	1.62138	+	0.936103i
$635$			6.60075e9i			1.02302i
$636$	−4.35042e8	+	7.53515e8i	−0.0670551	+	0.116143i
$637$			3.35449e9i			0.514208i
$638$	5.36390e9	+	9.29055e9i	0.817727	+	1.41634i
$639$	−3.75819e8			−0.0569804
$640$	6.27018e9			0.945475
$641$	−3.57587e9	−	6.19359e9i	−0.536264	−	0.928837i	−0.999101	−	0.0423936i	$-0.986502\pi$
$641$	−3.57587e9	−	6.19359e9i	−0.536264	−	0.928837i	0.462837	−	0.886444i	$-0.346832\pi$
$642$	−1.77189e10	−	1.02300e10i	−2.64280	−	1.52582i
$643$			7.21343e9i			1.07005i	0.844837	+	0.535024i	$0.179698\pi$
$643$			7.21343e9i			1.07005i	−0.844837	+	0.535024i	$0.820302\pi$
$644$	4.16307e8	−	2.40355e8i	0.0614205	−	0.0354611i
$645$	−7.66956e9	−	1.32841e10i	−1.12541	−	1.94927i
$646$	7.92519e8	−	4.57561e8i	0.115663	−	0.0667783i
$647$	−3.04820e8	−	1.75988e8i	−0.0442465	−	0.0255457i	0.477714	−	0.878516i	$-0.341466\pi$
$647$	−3.04820e8	−	1.75988e8i	−0.0442465	−	0.0255457i	−0.521960	+	0.852970i	$0.674799\pi$
$648$	−8.58472e9	−	4.95639e9i	−1.23941	−	0.715572i
$649$	2.03168e9	−	1.17299e9i	0.291742	−	0.168437i
$650$	−3.64507e8	−	6.31345e8i	−0.0520606	−	0.0901716i
$651$	1.12882e9	−	6.51722e8i	0.160358	−	0.0925826i
$652$			8.07846e8i			0.114146i
$653$	−3.11174e9	−	1.79657e9i	−0.437328	−	0.252492i	0.265135	−	0.964211i	$-0.414583\pi$
$653$	−3.11174e9	−	1.79657e9i	−0.437328	−	0.252492i	−0.702464	+	0.711720i	$0.747917\pi$
$654$	1.42583e10	+	2.46961e10i	1.99318	+	3.45228i
$655$	1.20579e10			1.67660
$656$	−8.67539e9			−1.19985
$657$	7.41632e8	+	1.28455e9i	0.102026	+	0.176714i
$658$			8.83444e8i			0.120889i
$659$	4.66129e9	−	8.07359e9i	0.634464	−	1.09892i	−0.352164	−	0.935938i	$-0.614554\pi$
$659$	4.66129e9	−	8.07359e9i	0.634464	−	1.09892i	0.986628	−	0.162986i	$-0.0521125\pi$
$660$			6.41689e9i			0.868801i
$661$	−5.27073e9	−	3.04306e9i	−0.709848	−	0.409831i	0.101157	−	0.994871i	$-0.467746\pi$
$661$	−5.27073e9	−	3.04306e9i	−0.709848	−	0.409831i	−0.811005	+	0.585040i	$0.801079\pi$
$662$	−1.24709e9	+	2.16002e9i	−0.167068	+	0.289370i
$663$	1.82667e9	−	3.16389e9i	0.243424	−	0.421623i
$664$	−3.19456e9	+	1.84438e9i	−0.423470	+	0.244491i
$665$	1.06170e8			0.0139999
$666$	−7.45804e9	−	2.16471e10i	−0.978284	−	2.83948i
$667$	1.94260e10			2.53479
$668$	2.45586e9	−	1.41789e9i	0.318776	−	0.184045i
$669$	−4.92203e9	+	8.52521e9i	−0.635555	+	1.10081i
$670$	3.84521e9	−	6.66011e9i	0.493922	−	0.855499i
$671$	2.70766e8	+	1.56327e8i	0.0345991	+	0.0199758i
$672$			1.01323e9i			0.128800i
$673$	−6.55703e8	+	1.13571e9i	−0.0829191	+	0.143620i	−0.904503	−	0.426468i	$-0.859758\pi$
$673$	−6.55703e8	+	1.13571e9i	−0.0829191	+	0.143620i	0.821583	+	0.570088i	$0.193091\pi$
$674$			6.23526e8i			0.0784413i
$675$	1.71893e9	+	2.97727e9i	0.215127	+	0.372611i
$676$	−3.12382e9			−0.388931
$677$	−3.52519e9			−0.436639			−0.218319	−	0.975877i	$-0.570057\pi$
$677$	−3.52519e9			−0.436639			−0.218319	+	0.975877i	$0.570057\pi$
$678$	−3.26156e9	−	5.64919e9i	−0.401904	−	0.696117i
$679$	−9.65384e8	−	5.57365e8i	−0.118347	−	0.0683275i
$680$		−	2.21600e9i		−	0.270264i
$681$	1.54459e10	−	8.91768e9i	1.87412	−	1.08202i
$682$	−6.86886e9	−	1.18972e10i	−0.829161	−	1.43615i
$683$	9.78967e9	−	5.65207e9i	1.17570	−	0.678790i	0.220683	−	0.975346i	$-0.429172\pi$
$683$	9.78967e9	−	5.65207e9i	1.17570	−	0.678790i	0.955015	+	0.296556i	$0.0958382\pi$
$684$	−1.98134e9	−	1.14392e9i	−0.236735	−	0.136679i
$685$	1.20101e10	+	6.93402e9i	1.42767	+	0.824267i
$686$	−1.30322e9	+	7.52416e8i	−0.154129	+	0.0889864i
$687$	−1.41832e10	−	2.45660e10i	−1.66888	−	2.89059i
$688$	−1.22777e10	+	7.08854e9i	−1.43734	+	0.829846i
$689$		−	6.05720e8i		−	0.0705512i
$690$	2.90235e10	+	1.67567e10i	3.36340	+	1.94186i
$691$	−7.05176e9	−	1.22140e10i	−0.813064	−	1.40827i	−0.910710	−	0.413047i	$-0.864465\pi$
$691$	−7.05176e9	−	1.22140e10i	−0.813064	−	1.40827i	0.0976462	−	0.995221i	$-0.468869\pi$
$692$	3.51176e8			0.0402860
$693$	1.48206e9			0.169161
$694$	−1.40469e9	−	2.43300e9i	−0.159523	−	0.276301i
$695$			4.23293e9i			0.478294i
$696$	−6.53877e9	+	1.13255e10i	−0.735129	+	1.27328i
$697$			4.36883e9i			0.488709i
$698$	6.20591e9	+	3.58298e9i	0.690735	+	0.398796i
$699$	1.04478e10	−	1.80961e10i	1.15705	−	2.00407i
$700$	2.82735e7	−	4.89712e7i	0.00311557	−	0.00539632i
$701$	−2.79352e9	+	1.61284e9i	−0.306294	+	0.176839i	−0.645267	−	0.763957i	$-0.723254\pi$
$701$	−2.79352e9	+	1.61284e9i	−0.306294	+	0.176839i	0.338973	+	0.940796i	$0.389920\pi$
$702$	−1.54907e10			−1.69002
$703$	6.36681e8	+	1.84797e9i	0.0691159	+	0.200610i
$704$	−4.95713e8			−0.0535459
$705$	−1.84936e10	+	1.06773e10i	−1.98774	+	1.14762i
$706$	−2.16596e9	+	3.75155e9i	−0.231651	+	0.401231i
$707$	−4.13742e8	+	7.16622e8i	−0.0440313	+	0.0762645i
$708$	−2.80108e9	−	1.61721e9i	−0.296626	−	0.171257i
$709$			9.20125e9i			0.969583i	0.874630	+	0.484792i	$0.161105\pi$
$709$			9.20125e9i			0.969583i	−0.874630	+	0.484792i	$0.838895\pi$
$710$	−1.26711e8	+	2.19470e8i	−0.0132865	+	0.0230129i
$711$			2.11797e10i			2.20991i
$712$	−1.59349e9	−	2.76001e9i	−0.165451	−	0.286570i
$713$	−2.48763e10			−2.57023
$714$	8.17314e8			0.0840321
$715$	−2.23360e9	−	3.86870e9i	−0.228525	−	0.395817i
$716$	2.03544e9	+	1.17516e9i	0.207235	+	0.119647i
$717$			2.07804e10i			2.10542i
$718$	8.68310e9	−	5.01319e9i	0.875466	−	0.505450i
$719$	7.29091e9	+	1.26282e10i	0.731527	+	1.26704i	0.956230	+	0.292615i	$0.0945253\pi$
$719$	7.29091e9	+	1.26282e10i	0.731527	+	1.26704i	−0.224703	+	0.974427i	$0.572141\pi$
$720$	−2.40621e10	+	1.38923e10i	−2.40254	+	1.38711i
$721$	8.83035e8	+	5.09820e8i	0.0877413	+	0.0506575i
$722$	−1.03479e10	−	5.97439e9i	−1.02323	−	0.590763i
$723$	1.60646e10	−	9.27487e9i	1.58083	−	0.912692i
$724$	−3.12258e9	−	5.40847e9i	−0.305794	−	0.529650i
$725$	1.97897e9	−	1.14256e9i	0.192867	−	0.111352i
$726$			1.56114e9i			0.151413i
$727$	8.98117e9	+	5.18528e9i	0.866887	+	0.500497i	0.866312	−	0.499503i	$-0.166484\pi$
$727$	8.98117e9	+	5.18528e9i	0.866887	+	0.500497i	0.000574237		1.00000i	$0.499817\pi$
$728$	−1.12644e8	−	1.95105e8i	−0.0108205	−	0.0187417i
$729$	1.14138e10			1.09115
$730$	1.00020e9			0.0951601
$731$	3.56971e9	+	6.18292e9i	0.338004	+	0.585441i
$732$		−	4.31056e8i		−	0.0406205i
$733$	2.30746e9	−	3.99663e9i	0.216406	−	0.374827i	−0.737300	−	0.675565i	$-0.763900\pi$
$733$	2.30746e9	−	3.99663e9i	0.216406	−	0.374827i	0.953707	+	0.300738i	$0.0972331\pi$
$734$			6.44180e9i			0.601272i
$735$	−1.57097e10	−	9.07000e9i	−1.45936	−	0.842561i
$736$	9.66876e9	−	1.67468e10i	0.893920	−	1.54831i
$737$	−4.58229e9	+	7.93677e9i	−0.421645	+	0.730310i
$738$	2.72815e10	−	1.57510e10i	2.49845	−	1.44248i
$739$	−1.26213e10			−1.15040			−0.575200	−	0.818013i	$-0.695076\pi$
$739$	−1.26213e10			−1.15040			−0.575200	+	0.818013i	$0.695076\pi$
$740$	−5.25485e9	−	1.02046e9i	−0.476704	−	0.0925728i
$741$	2.24885e9			0.203047
$742$	1.17355e8	−	6.77547e7i	0.0105460	−	0.00608872i
$743$	6.87742e8	−	1.19120e9i	0.0615127	−	0.106543i	−0.833629	−	0.552325i	$-0.813741\pi$
$743$	6.87742e8	−	1.19120e9i	0.0615127	−	0.106543i	0.895142	+	0.445782i	$0.147074\pi$
$744$	8.37336e9	−	1.45031e10i	0.745409	−	1.29109i
$745$	−4.96892e9	−	2.86881e9i	−0.440266	−	0.254188i
$746$		−	6.52603e9i		−	0.575523i
$747$	1.16456e10	−	2.01707e10i	1.02221	−	1.77051i
$748$		−	2.98667e9i		−	0.260935i
$749$	5.52410e8	+	9.56802e8i	0.0480369	+	0.0832024i
$750$	2.81559e10			2.43700
$751$	−1.70299e10			−1.46714			−0.733572	−	0.679611i	$-0.762148\pi$
$751$	−1.70299e10			−1.46714			−0.733572	+	0.679611i	$0.762148\pi$
$752$	9.86843e9	+	1.70926e10i	0.846224	+	1.46570i
$753$	−1.11735e10	−	6.45101e9i	−0.953687	−	0.550612i
$754$			1.02966e10i			0.874766i
$755$	−9.05154e9	+	5.22591e9i	−0.765435	+	0.441924i
$756$	−6.00779e8	−	1.04058e9i	−0.0505695	−	0.0875890i
$757$	3.71193e9	−	2.14308e9i	0.311003	−	0.179557i	−0.336372	−	0.941729i	$-0.609200\pi$
$757$	3.71193e9	−	2.14308e9i	0.311003	−	0.179557i	0.647375	+	0.762172i	$0.275867\pi$
$758$	−7.78363e9	−	4.49388e9i	−0.649142	−	0.374782i
$759$	−3.45870e10	−	1.99688e10i	−2.87122	−	1.65770i
$760$	1.18132e9	−	6.82037e8i	0.0976161	−	0.0563587i
$761$	−7.31412e9	−	1.26684e10i	−0.601611	−	1.04202i	−0.992577	−	0.121616i	$-0.961192\pi$
$761$	−7.31412e9	−	1.26684e10i	−0.601611	−	1.04202i	0.390966	−	0.920405i	$-0.372141\pi$
$762$	−2.70882e10	+	1.56394e10i	−2.21788	+	1.28049i
$763$		−	1.53987e9i		−	0.125501i
$764$	−3.52468e9	−	2.03497e9i	−0.285952	−	0.165094i
$765$	6.99600e9	+	1.21174e10i	0.564982	+	0.978577i
$766$	−8.19849e9			−0.659073
$767$	2.25167e9			0.180186
$768$	1.42123e10	+	2.46164e10i	1.13214	+	1.96092i
$769$		−	2.22573e10i		−	1.76494i	−0.470364	−	0.882472i	$-0.655878\pi$
$769$		−	2.22573e10i		−	1.76494i	0.470364	−	0.882472i	$-0.344122\pi$
$770$	4.99692e8	−	8.65492e8i	0.0394444	−	0.0683197i
$771$			3.95902e10i			3.11098i
$772$	−7.26002e9	−	4.19158e9i	−0.567907	−	0.327881i
$773$	4.38170e9	−	7.58933e9i	0.341204	−	0.590983i	−0.643452	−	0.765486i	$-0.722499\pi$
$773$	4.38170e9	−	7.58933e9i	0.341204	−	0.590983i	0.984657	+	0.174503i	$0.0558319\pi$
$774$	2.57398e10	−	4.45826e10i	1.99532	−	3.45599i
$775$	−2.53422e9	+	1.46313e9i	−0.195563	+	0.112909i
$776$	−1.43221e10			−1.10025
$777$	−3.32781e8	+	1.71366e9i	−0.0254498	+	0.131054i
$778$	−1.28298e10			−0.976766
$779$	−2.32897e9	+	1.34463e9i	−0.176516	+	0.101911i
$780$	−3.07947e9	+	5.33379e9i	−0.232351	+	0.402443i
$781$	1.51000e8	−	2.61540e8i	0.0113422	−	0.0196453i
$782$	−1.35087e10	−	7.79924e9i	−1.01016	−	0.583215i
$783$		−	4.85561e10i		−	3.61475i
$784$	−8.38289e9	+	1.45196e10i	−0.621280	+	1.07609i
$785$		−	4.61614e9i		−	0.340593i
$786$	2.85693e10	+	4.94835e10i	2.09856	+	3.63481i
$787$	2.18961e9			0.160123			0.0800616	−	0.996790i	$-0.474488\pi$
$787$	2.18961e9			0.160123			0.0800616	+	0.996790i	$0.474488\pi$
$788$	9.75552e9			0.710246
$789$	−1.53578e9	−	2.66005e9i	−0.111316	−	0.192806i
$790$	1.23685e10	+	7.14093e9i	0.892526	+	0.515300i
$791$			3.52242e8i			0.0253060i
$792$	1.64905e10	−	9.52081e9i	1.17950	−	0.680982i
$793$	1.50043e8	+	2.59881e8i	0.0106846	+	0.0185063i
$794$	−6.23659e9	+	3.60069e9i	−0.442156	+	0.255279i
$795$	2.83670e9	+	1.63777e9i	0.200229	+	0.115603i
$796$	1.28627e9	+	7.42631e8i	0.0903937	+	0.0521888i
$797$	−9.32563e9	+	5.38415e9i	−0.652490	+	0.376715i	−0.789410	−	0.613867i	$-0.789613\pi$
$797$	−9.32563e9	+	5.38415e9i	−0.652490	+	0.376715i	0.136919	+	0.990582i	$0.456280\pi$
$798$	2.51552e8	+	4.35701e8i	0.0175234	+	0.0303514i
$799$	8.60766e9	−	4.96963e9i	0.596996	−	0.344676i
$800$		−	2.27472e9i		−	0.157077i
$801$	1.74269e10	+	1.00614e10i	1.19814	+	0.691745i
$802$	−6.15245e9	−	1.06564e10i	−0.421151	−	0.729455i
$803$	−1.19192e9			−0.0812349
$804$	1.26352e10			0.857408
$805$	−9.04845e8	−	1.56724e9i	−0.0611348	−	0.105889i
$806$		−	1.31855e10i		−	0.886998i
$807$	−3.47910e6	+	6.02598e6i	−0.000233029	+	0.000403618i
$808$			1.06316e10i			0.709018i
$809$	1.37749e10	+	7.95292e9i	0.914677	+	0.528089i	0.881933	−	0.471375i	$-0.156242\pi$
$809$	1.37749e10	+	7.95292e9i	0.914677	+	0.528089i	0.0327438	+	0.999464i	$0.489575\pi$
$810$	2.11029e10	−	3.65513e10i	1.39522	−	2.41660i
$811$	−2.16956e9	+	3.75779e9i	−0.142823	+	0.247377i	−0.928559	−	0.371186i	$-0.878951\pi$
$811$	−2.16956e9	+	3.75779e9i	−0.142823	+	0.247377i	0.785736	+	0.618563i	$0.212285\pi$
$812$	−6.91667e8	+	3.99334e8i	−0.0453368	+	0.0261752i
$813$	−1.55519e10			−1.01500
$814$	1.80612e10	+	3.50736e9i	1.17371	+	0.227927i
$815$	3.04123e9			0.196788
$816$	1.58132e10	−	9.12974e9i	1.01883	−	0.588224i
$817$	−2.19736e9	+	3.80595e9i	−0.140969	+	0.244166i
$818$	2.84523e8	−	4.92808e8i	0.0181753	−	0.0314805i
$819$	1.23191e9	+	7.11242e8i	0.0783582	+	0.0452401i
$820$		−	7.36511e9i		−	0.466478i
$821$	2.27254e9	−	3.93615e9i	0.143321	−	0.248239i	−0.785424	−	0.618958i	$-0.787555\pi$
$821$	2.27254e9	−	3.93615e9i	0.143321	−	0.248239i	0.928745	+	0.370718i	$0.120889\pi$
$822$			6.57161e10i			4.12687i
$823$	7.80003e9	+	1.35100e10i	0.487749	+	0.844807i	0.999901	−	0.0140885i	$-0.00448466\pi$
$823$	7.80003e9	+	1.35100e10i	0.487749	+	0.844807i	−0.512151	+	0.858895i	$0.671151\pi$
$824$	1.31004e10			0.815716
$825$	−4.69795e9			−0.291286
$826$	2.51868e8	+	4.36249e8i	0.0155505	+	0.0269342i
$827$	1.76432e10	+	1.01863e10i	1.08469	+	0.626248i	0.932159	−	0.362050i	$-0.117923\pi$
$827$	1.76432e10	+	1.01863e10i	1.08469	+	0.626248i	0.152535	+	0.988298i	$0.451256\pi$
$828$			3.89969e10i			2.38740i
$829$	−1.51562e9	+	8.75041e8i	−0.0923949	+	0.0533442i	−0.545486	−	0.838120i	$-0.683655\pi$
$829$	−1.51562e9	+	8.75041e8i	−0.0923949	+	0.0533442i	0.453091	+	0.891464i	$0.350321\pi$
$830$	−7.85284e9	−	1.36015e10i	−0.476709	−	0.825684i
$831$	−3.48537e10	+	2.01228e10i	−2.10691	+	1.21642i
$832$	−4.12042e8	−	2.37893e8i	−0.0248033	−	0.0143202i
$833$	7.31191e9	+	4.22153e9i	0.438302	+	0.253054i
$834$	−1.73712e10	+	1.00292e10i	−1.03693	+	0.598669i
$835$	−5.33781e9	−	9.24536e9i	−0.317293	−	0.549567i
$836$	1.59216e9	−	9.19234e8i	0.0942464	−	0.0544132i
$837$			6.21796e10i			3.66529i
$838$	2.13388e10	+	1.23200e10i	1.25261	+	0.723194i
$839$	−1.51311e9	−	2.62078e9i	−0.0884509	−	0.153201i	0.818406	−	0.574641i	$-0.194858\pi$
$839$	−1.51311e9	−	2.62078e9i	−0.0884509	−	0.153201i	−0.906857	+	0.421440i	$0.861525\pi$
$840$	1.21828e9			0.0709203
$841$	−1.50250e10			−0.871023
$842$	−4.35058e9	−	7.53543e9i	−0.251163	−	0.435026i
$843$			1.67067e10i			0.960496i
$844$	−1.25873e9	+	2.18018e9i	−0.0720665	+	0.124823i
$845$			1.17600e10i			0.670514i
$846$	−6.20664e10	−	3.58341e10i	−3.52420	−	2.03470i
$847$	4.21500e7	−	7.30059e7i	0.00238345	−	0.00412825i
$848$	1.51370e9	−	2.62180e9i	0.0852419	−	0.147643i
$849$	1.73337e10	−	1.00076e10i	0.972105	−	0.561245i
$850$	−1.83489e9			−0.102481
$851$	2.18529e10	−	2.51480e10i	1.21550	−	1.39878i
$852$	−4.16368e8			−0.0230642
$853$	1.21356e10	−	7.00648e9i	0.669482	−	0.386526i	−0.126398	−	0.991980i	$-0.540342\pi$
$853$	1.21356e10	−	7.00648e9i	0.669482	−	0.386526i	0.795880	+	0.605454i	$0.207008\pi$
$854$	−3.35670e7	+	5.81397e7i	−0.00184421	+	0.00319426i
$855$	−4.30644e9	+	7.45897e9i	−0.235633	+	0.408129i
$856$	1.22930e10	+	7.09739e9i	0.669886	+	0.386759i
$857$		−	5.00321e8i		−	0.0271529i	−0.999908	−	0.0135764i	$-0.995678\pi$
$857$		−	5.00321e8i		−	0.0271529i	0.999908	−	0.0135764i	$-0.00432164\pi$
$858$	1.05843e10	−	1.83325e10i	0.572079	−	0.990870i
$859$			2.84397e10i			1.53091i	0.643491	+	0.765453i	$0.277485\pi$
$859$			2.84397e10i			1.53091i	−0.643491	+	0.765453i	$0.722515\pi$
$860$	−6.01793e9	−	1.04234e10i	−0.322629	−	0.558809i
$861$	−2.40184e9			−0.128243
$862$	3.73809e10			1.98781
$863$	1.83368e9	+	3.17603e9i	0.0971149	+	0.168208i	0.910489	−	0.413533i	$-0.135705\pi$
$863$	1.83368e9	+	3.17603e9i	0.0971149	+	0.168208i	−0.813374	+	0.581741i	$0.802372\pi$
$864$	−4.18594e10	−	2.41675e10i	−2.20798	−	1.27478i
$865$		−	1.32204e9i		−	0.0694528i
$866$	−1.14837e10	+	6.63011e9i	−0.600854	+	0.346903i
$867$	1.31656e10	+	2.28034e10i	0.686076	+	1.18832i
$868$	8.85728e8	−	5.11375e8i	0.0459707	−	0.0265412i
$869$	−1.47393e10	−	8.50976e9i	−0.761919	−	0.439894i
$870$	−4.82206e10	−	2.78402e10i	−2.48265	−	1.43336i
$871$	−7.61771e9	+	4.39809e9i	−0.390626	+	0.225528i
$872$	−9.89213e9	−	1.71337e10i	−0.505222	−	0.875070i
$873$	7.83154e10	−	4.52154e10i	3.98380	−	2.30005i
$874$		−	9.60176e9i		−	0.486476i
$875$	−1.31669e9	−	7.60193e8i	−0.0664441	−	0.0383615i
$876$	8.21652e8	+	1.42314e9i	0.0412975	+	0.0715293i
$877$	−2.36488e10			−1.18389			−0.591943	−	0.805979i	$-0.701639\pi$
$877$	−2.36488e10			−1.18389			−0.591943	+	0.805979i	$0.701639\pi$
$878$	6.49202e9			0.323705
$879$	−7.79537e9	−	1.35020e10i	−0.387147	−	0.670558i
$880$		−	2.23271e10i		−	1.10444i
$881$	1.51071e10	−	2.61663e10i	0.744332	−	1.28922i	−0.206174	−	0.978515i	$-0.566101\pi$
$881$	1.51071e10	−	2.61663e10i	0.744332	−	1.28922i	0.950506	−	0.310706i	$-0.100565\pi$
$882$		−	6.08796e10i		−	2.98766i
$883$	9.25271e9	+	5.34205e9i	0.452279	+	0.261123i	0.708792	−	0.705417i	$-0.249240\pi$
$883$	9.25271e9	+	5.34205e9i	0.452279	+	0.261123i	−0.256513	+	0.966541i	$0.582574\pi$
$884$	1.43330e9	−	2.48256e9i	0.0697839	−	0.120869i
$885$	−6.08816e9	+	1.05450e10i	−0.295246	+	0.511382i
$886$	−3.51910e10	+	2.03175e10i	−1.69986	+	0.981415i
$887$	1.55115e10			0.746313			0.373156	−	0.927768i	$-0.378275\pi$
$887$	1.55115e10			0.746313			0.373156	+	0.927768i	$0.378275\pi$
$888$	7.30582e9	+	2.12052e10i	0.350125	+	1.01624i
$889$	1.68902e9			0.0806267
$890$	1.17513e10	−	6.78462e9i	0.558755	−	0.322597i
$891$	−2.51480e10	+	4.35577e10i	−1.19106	+	2.06297i
$892$	−3.86208e9	+	6.68932e9i	−0.182198	+	0.315577i
$893$	5.29851e9	+	3.05909e9i	0.248985	+	0.143752i
$894$		−	2.71887e10i		−	1.27264i
$895$	4.42404e9	−	7.66266e9i	0.206271	−	0.357272i
$896$		−	1.60443e9i		−	0.0745149i
$897$	−1.91661e10	−	3.31966e10i	−0.886665	−	1.53575i
$898$	5.43356e9			0.250390
$899$	4.13303e10			1.89719
$900$	2.29365e9	+	3.97272e9i	0.104877	+	0.181652i
$901$	−1.32031e9	−	7.62281e8i	−0.0601366	−	0.0347199i
$902$			2.53143e10i			1.14853i
$903$	−3.39917e9	+	1.96251e9i	−0.153626	+	0.0886961i
$904$	2.26281e9	+	3.91930e9i	0.101873	+	0.176449i
$905$	−2.03608e10	+	1.17553e10i	−0.913114	+	0.527186i
$906$	−4.28923e10	−	2.47639e10i	−1.91615	−	1.10629i
$907$	−1.74344e10	−	1.00657e10i	−0.775856	−	0.447940i	0.0591039	−	0.998252i	$-0.481176\pi$
$907$	−1.74344e10	−	1.00657e10i	−0.775856	−	0.447940i	−0.834959	+	0.550311i	$0.814509\pi$
$908$	1.21196e10	−	6.99727e9i	0.537266	−	0.310190i
$909$	−3.35642e10	−	5.81350e10i	−1.48219	−	2.56723i
$910$	8.30700e8	−	4.79605e8i	0.0365426	−	0.0210979i
$911$		−	3.12499e10i		−	1.36941i	−0.728818	−	0.684707i	$-0.759930\pi$
$911$		−	3.12499e10i		−	1.36941i	0.728818	−	0.684707i	$-0.240070\pi$
$912$	9.73391e9	+	5.61988e9i	0.424918	+	0.245327i
$913$	9.35813e9	+	1.62088e10i	0.406950	+	0.704858i
$914$	−1.76988e10			−0.766711
$915$	−1.62276e9			−0.0700295
$916$	−1.11289e10	−	1.92758e10i	−0.478429	−	0.828663i
$917$		−	3.08542e9i		−	0.132136i
$918$	−1.94946e10	+	3.37656e10i	−0.831696	+	1.44054i
$919$			4.73421e9i			0.201207i	0.994927	+	0.100604i	$0.0320774\pi$
$919$			4.73421e9i			0.201207i	−0.994927	+	0.100604i	$0.967923\pi$
$920$	−2.01359e10	−	1.16255e10i	−0.852539	−	0.492214i
$921$	−1.07077e9	+	1.85464e9i	−0.0451637	+	0.0782258i
$922$	−2.02784e10	+	3.51232e10i	−0.852069	+	1.47583i
$923$	2.51026e8	−	1.44930e8i	0.0105078	−	0.00606669i
$924$	1.64197e9			0.0684721
$925$	7.47100e8	−	3.84720e9i	0.0310372	−	0.159826i
$926$	3.56441e10			1.47519
$927$	−7.16349e10	+	4.13585e10i	−2.95356	+	1.70524i
$928$	−1.60640e10	+	2.78237e10i	−0.659836	+	1.14287i
$929$	6.72606e9	−	1.16499e10i	0.275236	−	0.476723i	−0.694958	−	0.719050i	$-0.744577\pi$
$929$	6.72606e9	−	1.16499e10i	0.275236	−	0.476723i	0.970195	+	0.242327i	$0.0779105\pi$
$930$	6.17499e10	+	3.56513e10i	2.51737	+	1.45340i
$931$			5.19719e9i			0.211079i
$932$	8.19786e9	−	1.41991e10i	0.331699	−	0.574520i
$933$			4.16219e9i			0.167779i
$934$	1.80497e10	+	3.12630e10i	0.724862	+	1.25550i
$935$	−1.12437e10			−0.449850
$936$	1.82762e10			0.728483
$937$	−2.47538e9	−	4.28749e9i	−0.0983000	−	0.170261i	0.812681	−	0.582709i	$-0.198007\pi$
$937$	−2.47538e9	−	4.28749e9i	−0.0983000	−	0.170261i	−0.910981	+	0.412448i	$0.864674\pi$
$938$	−1.70421e9	−	9.83925e8i	−0.0674237	−	0.0389271i
$939$		−	1.23354e10i		−	0.486212i
$940$	−1.45111e10	+	8.37796e9i	−0.569838	+	0.328996i
$941$	−1.84401e10	−	3.19392e10i	−0.721439	−	1.24957i	−0.960423	−	0.278545i	$-0.910148\pi$
$941$	−1.84401e10	−	3.19392e10i	−0.721439	−	1.24957i	0.238985	−	0.971023i	$-0.423185\pi$
$942$	1.89438e10	−	1.09372e10i	0.738394	−	0.426312i
$943$	3.96979e10	+	2.29196e10i	1.54162	+	0.890053i
$944$	9.74615e9	+	5.62694e9i	0.377078	+	0.217706i
$945$	−3.91739e9	+	2.26170e9i	−0.151003	+	0.0871815i
$946$	2.06839e10	+	3.58257e10i	0.794355	+	1.37586i
$947$	−2.67692e10	+	1.54552e10i	−1.02426	+	0.591357i	−0.915335	−	0.402693i	$-0.868074\pi$
$947$	−2.67692e10	+	1.54552e10i	−1.02426	+	0.591357i	−0.108926	+	0.994050i	$0.534741\pi$
$948$			2.34649e10i			0.894518i
$949$	−9.90738e8	−	5.72003e8i	−0.0376294	−	0.0217253i
$950$	−5.64739e8	−	9.78157e8i	−0.0213705	−	0.0370148i
$951$	7.43054e10			2.80149
$952$	−5.67036e8			−0.0213001
$953$	−2.28191e10	−	3.95238e10i	−0.854030	−	1.47922i	−0.877542	−	0.479501i	$-0.840818\pi$
$953$	−2.28191e10	−	3.95238e10i	−0.854030	−	1.47922i	0.0235110	−	0.999724i	$-0.492516\pi$
$954$			1.09930e10i			0.409919i
$955$	−7.66089e9	+	1.32691e10i	−0.284621	+	0.492979i
$956$			1.63054e10i			0.603572i
$957$	5.74639e10	+	3.31768e10i	2.11935	+	1.22361i
$958$	1.36414e10	−	2.36276e10i	0.501280	−	0.868242i
$959$	1.77430e9	−	3.07317e9i	0.0649623	−	0.112518i
$960$	2.22819e9	−	1.28645e9i	0.0812836	−	0.0469291i
$961$	−2.54138e10			−0.923714
$962$	1.33295e10	+	1.15829e10i	0.482726	+	0.419474i
$963$	−8.96270e10			−3.23405
$964$	1.26051e10	−	7.27755e9i	0.453186	−	0.261647i
$965$	−1.57797e10	+	2.73312e10i	−0.565266	+	0.979069i
$966$	4.28776e9	−	7.42662e9i	0.153042	−	0.265077i
$967$	−3.53806e10	−	2.04270e10i	−1.25827	−	0.726461i	−0.285530	−	0.958370i	$-0.592170\pi$
$967$	−3.53806e10	−	2.04270e10i	−1.25827	−	0.726461i	−0.972738	+	0.231908i	$0.925503\pi$
$968$		−	1.08309e9i		−	0.0383796i
$969$	2.83011e9	−	4.90189e9i	0.0999240	−	0.173074i
$970$		−	6.09793e10i		−	2.14527i
$971$	4.82008e9	+	8.34862e9i	0.168961	+	0.292649i	0.938055	−	0.346487i	$-0.112625\pi$
$971$	4.82008e9	+	8.34862e9i	0.168961	+	0.292649i	−0.769094	+	0.639136i	$0.779292\pi$
$972$	2.91878e10			1.01946
$973$	1.08314e9			0.0376954
$974$	−7.51761e9	−	1.30209e10i	−0.260689	−	0.451527i
$975$	−3.90500e9	−	2.25455e9i	−0.134929	−	0.0779011i
$976$			1.49983e9i			0.0516377i
$977$	−5.54750e9	+	3.20285e9i	−0.190312	+	0.109877i	−0.592129	−	0.805843i	$-0.701712\pi$
$977$	−5.54750e9	+	3.20285e9i	−0.190312	+	0.109877i	0.401817	+	0.915720i	$0.368379\pi$
$978$	7.20570e9	+	1.24806e10i	0.246315	+	0.426629i
$979$	−1.40039e10	+	8.08515e9i	−0.476990	+	0.275390i
$980$	−1.23266e10	−	7.11679e9i	−0.418363	−	0.241542i
$981$	1.08183e11	+	6.24597e10i	3.65864	+	2.11231i
$982$	4.19715e10	−	2.42323e10i	1.41438	−	0.816590i
$983$	−8.90498e9	−	1.54239e10i	−0.299017	−	0.517912i	0.676895	−	0.736080i	$-0.263325\pi$
$983$	−8.90498e9	−	1.54239e10i	−0.299017	−	0.517912i	−0.975911	+	0.218168i	$0.929992\pi$
$984$	−2.67246e10	+	1.54295e10i	−0.894188	+	0.516259i
$985$		−	3.67258e10i		−	1.22446i
$986$	2.24438e10	+	1.29579e10i	0.745636	+	0.430493i
$987$	2.73214e9	+	4.73220e9i	0.0904467	+	0.156658i
$988$	1.76456e9			0.0582087
$989$	7.49092e10			2.46234
$990$	4.05368e10	+	7.02118e10i	1.32778	+	2.29978i
$991$			4.23940e10i			1.38372i	0.722033	+	0.691858i	$0.243208\pi$
$991$			4.23940e10i			1.38372i	−0.722033	+	0.691858i	$0.756792\pi$
$992$	2.05711e10	−	3.56302e10i	0.669062	−	1.15885i
$993$			1.54270e10i			0.499986i
$994$	5.61586e7	+	3.24232e7i	0.00181369	+	0.00104714i
$995$	2.79572e9	−	4.84233e9i	0.0899732	−	0.155838i
$996$	1.29021e10	−	2.23471e10i	0.413763	−	0.716659i
$997$	−1.00964e10	+	5.82918e9i	−0.322653	+	0.186284i	−0.652574	−	0.757725i	$-0.726311\pi$
$997$	−1.00964e10	+	5.82918e9i	−0.322653	+	0.186284i	0.329922	+	0.944008i	$0.392978\pi$
$998$	−1.12266e10			−0.357513
$999$	−6.28587e10	−	5.46224e10i	−1.99474	−	1.73337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.e.a.11.15	✓	40
37.27	even	6	inner	37.8.e.a.27.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.e.a.11.15	✓	40	1.1	even	1	trivial
37.8.e.a.27.15	yes	40	37.27	even	6	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(12.1223 - 6.99882i) q^{2} +(43.2891 - 74.9789i) q^{3} +(33.9669 - 58.8324i) q^{4} +(-221.481 - 127.872i) q^{5} -1211.89i q^{6} +(-32.7203 + 56.6733i) q^{7} +840.785i q^{8} +(-2654.39 - 4597.54i) q^{9} +O(q^{10})\)	\(q+(12.1223 - 6.99882i) q^{2} +(43.2891 - 74.9789i) q^{3} +(33.9669 - 58.8324i) q^{4} +(-221.481 - 127.872i) q^{5} -1211.89i q^{6} +(-32.7203 + 56.6733i) q^{7} +840.785i q^{8} +(-2654.39 - 4597.54i) q^{9} -3579.82 q^{10} +4266.03 q^{11} +(-2940.79 - 5093.60i) q^{12} +(3545.97 + 2047.27i) q^{13} +916.015i q^{14} +(-19175.5 + 11071.0i) q^{15} +(10232.3 + 17722.8i) q^{16} +(8925.01 - 5152.86i) q^{17} +(-64354.7 - 37155.2i) q^{18} +(5493.86 + 3171.88i) q^{19} +(-15046.1 + 8686.85i) q^{20} +(2832.87 + 4906.67i) q^{21} +(51714.1 - 29857.1i) q^{22} -108131. i q^{23} +(63041.2 + 36396.8i) q^{24} +(-6359.85 - 11015.6i) q^{25} +57313.8 q^{26} -270278. q^{27} +(2222.82 + 3850.03i) q^{28} +179652. i q^{29} +(-154967. + 268411. i) q^{30} -230057. i q^{31} +(154875. + 89417.2i) q^{32} +(184672. - 319862. i) q^{33} +(72127.8 - 124929. i) q^{34} +(14493.9 - 8368.05i) q^{35} -360646. q^{36} +(232570. + 202097. i) q^{37} +88797.6 q^{38} +(307004. - 177249. i) q^{39} +(107513. - 186218. i) q^{40} +(-211962. + 367128. i) q^{41} +(68681.8 + 39653.5i) q^{42} +692764. i q^{43} +(144904. - 250980. i) q^{44} +1.35769e6i q^{45} +(-756788. - 1.31080e6i) q^{46} +964442. q^{47} +1.77178e6 q^{48} +(409630. + 709500. i) q^{49} +(-154192. - 89022.8i) q^{50} -892250. i q^{51} +(240891. - 139079. i) q^{52} +(-73966.9 - 128114. i) q^{53} +(-3.27640e6 + 1.89163e6i) q^{54} +(-944845. - 545507. i) q^{55} +(-47650.1 - 27510.8i) q^{56} +(475648. - 274616. i) q^{57} +(1.25735e6 + 2.17780e6i) q^{58} +(476246. - 274961. i) q^{59} +1.50418e6i q^{60} +(63470.3 + 36644.6i) q^{61} +(-1.61013e6 - 2.78883e6i) q^{62} +347411. q^{63} -116200. q^{64} +(-523578. - 906863. i) q^{65} -5.16995e6i q^{66} +(-1.07414e6 + 1.86046e6i) q^{67} -700106. i q^{68} +(-8.10754e6 - 4.68089e6i) q^{69} +(117133. - 202880. i) q^{70} +(35395.9 - 61307.5i) q^{71} +(3.86555e6 - 2.23177e6i) q^{72} -279398. q^{73} +(4.23372e6 + 822161. i) q^{74} -1.10125e6 q^{75} +(373218. - 215478. i) q^{76} +(-139586. + 241770. i) q^{77} +(2.48106e6 - 4.29733e6i) q^{78} +(-3.45505e6 - 1.99477e6i) q^{79} -5.23369e6i q^{80} +(-5.89496e6 + 1.02104e7i) q^{81} +5.93392e6i q^{82} +(2.19364e6 + 3.79950e6i) q^{83} +384895. q^{84} -2.63563e6 q^{85} +(4.84853e6 + 8.39790e6i) q^{86} +(1.34701e7 + 7.77698e6i) q^{87} +3.58681e6i q^{88} +(-3.28266e6 + 1.89524e6i) q^{89} +(9.50225e6 + 1.64584e7i) q^{90} +(-232051. + 133975. i) q^{91} +(-6.36160e6 - 3.67287e6i) q^{92} +(-1.72495e7 - 9.95898e6i) q^{93} +(1.16913e7 - 6.74996e6i) q^{94} +(-811191. - 1.40502e6i) q^{95} +(1.34088e7 - 7.74158e6i) q^{96} +1.70342e7i q^{97} +(9.93133e6 + 5.73385e6i) q^{98} +(-1.13237e7 - 1.96132e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9 - 5124 * q^10 + 12468 * q^11 + 6926 * q^12 + 10512 * q^13 + 36402 * q^15 - 31094 * q^16 - 22440 * q^17 - 153504 * q^18 + 49086 * q^19 + 28662 * q^20 + 7736 * q^21 + 132018 * q^22 + 2754 * q^24 + 72328 * q^25 - 680244 * q^26 + 42984 * q^27 + 105488 * q^28 + 382084 * q^30 + 523656 * q^32 + 9228 * q^33 + 276914 * q^34 - 904452 * q^35 - 204828 * q^36 + 1333776 * q^37 + 50208 * q^38 + 122040 * q^39 - 1205236 * q^40 - 871440 * q^41 + 1436094 * q^42 - 994326 * q^44 - 987942 * q^46 - 586932 * q^47 + 3984388 * q^48 - 1766072 * q^49 + 1818708 * q^50 - 2745228 * q^52 + 1661988 * q^53 + 1102554 * q^54 - 2733258 * q^55 - 5943924 * q^56 + 3920592 * q^57 + 5021672 * q^58 + 5296632 * q^59 - 4588524 * q^61 - 8143398 * q^62 - 2503648 * q^63 + 10662964 * q^64 - 1652736 * q^65 + 1940622 * q^67 - 10266552 * q^69 - 5038546 * q^70 + 6420528 * q^71 - 6576036 * q^72 - 3313032 * q^73 + 16192386 * q^74 - 5168536 * q^75 + 10328022 * q^76 - 8599404 * q^77 + 18210222 * q^78 - 15094374 * q^79 + 1733956 * q^81 - 191670 * q^83 + 1175224 * q^84 - 18053592 * q^85 + 18575940 * q^86 - 3762762 * q^87 - 14873004 * q^89 + 37293212 * q^90 - 76496700 * q^91 + 27846618 * q^92 + 26687652 * q^93 + 35421402 * q^94 + 14310774 * q^95 - 30894534 * q^96 - 13793868 * q^98 - 37141758 * q^99

Introduction

L-functions

Modular forms

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