LMFDB - Embedded newform 61.6.g.a.41.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,6,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, 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:	$9.78341300859$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.15
Character	$\chi$	$=$	61.41
Dual form			61.6.g.a.3.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.632478 - 0.205504i) q^{2} +(8.01843 + 24.6782i) q^{3} +(-25.5307 + 18.5492i) q^{4} +(-4.43129 + 3.21952i) q^{5} +(10.1430 + 13.9606i) q^{6} +(128.232 + 41.6652i) q^{7} +(-24.8443 + 34.1952i) q^{8} +(-348.127 + 252.929i) q^{9} +O(q^{10})$	\(q+(0.632478 - 0.205504i) q^{2} +(8.01843 + 24.6782i) q^{3} +(-25.5307 + 18.5492i) q^{4} +(-4.43129 + 3.21952i) q^{5} +(10.1430 + 13.9606i) q^{6} +(128.232 + 41.6652i) q^{7} +(-24.8443 + 34.1952i) q^{8} +(-348.127 + 252.929i) q^{9} +(-2.14107 + 2.94692i) q^{10} -82.9904i q^{11} +(-662.477 - 481.318i) q^{12} -526.185 q^{13} +89.6665 q^{14} +(-114.984 - 83.5407i) q^{15} +(303.374 - 933.689i) q^{16} +(-347.717 - 478.592i) q^{17} +(-168.205 + 231.514i) q^{18} +(144.764 + 445.539i) q^{19} +(53.4147 - 164.394i) q^{20} +3498.63i q^{21} +(-17.0549 - 52.4896i) q^{22} +(-812.982 - 1118.97i) q^{23} +(-1043.09 - 338.920i) q^{24} +(-956.407 + 2943.52i) q^{25} +(-332.800 + 108.133i) q^{26} +(-3932.08 - 2856.83i) q^{27} +(-4046.72 + 1314.86i) q^{28} +5340.16i q^{29} +(-89.8928 - 29.2079i) q^{30} +(7314.52 + 2376.63i) q^{31} -2005.44i q^{32} +(2048.05 - 665.453i) q^{33} +(-318.276 - 231.241i) q^{34} +(-702.377 + 228.216i) q^{35} +(4196.32 - 12914.9i) q^{36} +(7607.74 + 2471.90i) q^{37} +(183.121 + 252.044i) q^{38} +(-4219.18 - 12985.3i) q^{39} -231.515i q^{40} +(351.123 - 1080.65i) q^{41} +(718.985 + 2212.81i) q^{42} +(-2713.16 + 3734.34i) q^{43} +(1539.40 + 2118.81i) q^{44} +(728.341 - 2241.60i) q^{45} +(-744.147 - 540.654i) q^{46} +17515.3 q^{47} +25474.3 q^{48} +(1110.40 + 806.752i) q^{49} +2058.26i q^{50} +(9022.64 - 12418.6i) q^{51} +(13433.9 - 9760.30i) q^{52} +(-20367.3 + 28033.2i) q^{53} +(-3074.05 - 998.818i) q^{54} +(267.189 + 367.754i) q^{55} +(-4610.59 + 3349.79i) q^{56} +(-9834.32 + 7145.05i) q^{57} +(1097.43 + 3377.53i) q^{58} +(-32312.1 + 10498.8i) q^{59} +4485.24 q^{60} +(22523.2 - 18365.8i) q^{61} +5114.68 q^{62} +(-55179.5 + 17928.9i) q^{63} +(9295.84 + 28609.6i) q^{64} +(2331.68 - 1694.06i) q^{65} +(1158.59 - 841.768i) q^{66} +(-1811.94 - 2493.92i) q^{67} +(17755.0 + 5768.94i) q^{68} +(21095.4 - 29035.3i) q^{69} +(-397.338 + 288.683i) q^{70} +(29521.4 - 40632.7i) q^{71} -18188.1i q^{72} +(12472.9 + 9062.07i) q^{73} +5319.71 q^{74} -80309.6 q^{75} +(-11960.3 - 8689.69i) q^{76} +(3457.81 - 10642.1i) q^{77} +(-5337.08 - 7345.85i) q^{78} +(-42670.8 + 58731.3i) q^{79} +(1661.69 + 5114.16i) q^{80} +(6659.81 - 20496.8i) q^{81} -755.642i q^{82} +(1596.27 + 4912.81i) q^{83} +(-64896.8 - 89322.7i) q^{84} +(3081.67 + 1001.30i) q^{85} +(-948.588 + 2919.45i) q^{86} +(-131785. + 42819.7i) q^{87} +(2837.87 + 2061.83i) q^{88} +(67185.3 - 21829.8i) q^{89} -1567.44i q^{90} +(-67474.0 - 21923.6i) q^{91} +(41512.1 + 13488.1i) q^{92} +199566. i q^{93} +(11078.1 - 3599.48i) q^{94} +(-2075.92 - 1508.24i) q^{95} +(49490.7 - 16080.5i) q^{96} +(-56848.2 + 174961. i) q^{97} +(868.094 + 282.061i) q^{98} +(20990.7 + 28891.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) $ 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.632478	−	0.205504i	0.111807	−	0.0363284i	−0.252579	−	0.967576i	$-0.581279\pi$
$2$	0.632478	−	0.205504i	0.111807	−	0.0363284i	0.364386	+	0.931248i	$0.381279\pi$
$3$	8.01843	+	24.6782i	0.514383	+	1.58311i	0.784402	+	0.620252i	$0.212970\pi$
$3$	8.01843	+	24.6782i	0.514383	+	1.58311i	−0.270020	+	0.962855i	$0.587030\pi$
$4$	−25.5307	+	18.5492i	−0.797836	+	0.579662i
$5$	−4.43129	+	3.21952i	−0.0792693	+	0.0575925i	−0.626714	−	0.779249i	$-0.715601\pi$
$5$	−4.43129	+	3.21952i	−0.0792693	+	0.0575925i	0.547445	+	0.836842i	$0.315601\pi$
$6$	10.1430	+	13.9606i	0.115023	+	0.158316i
$7$	128.232	+	41.6652i	0.989128	+	0.321387i	0.758513	−	0.651658i	$-0.225926\pi$
$7$	128.232	+	41.6652i	0.989128	+	0.321387i	0.230615	+	0.973045i	$0.425926\pi$
$8$	−24.8443	+	34.1952i	−0.137246	+	0.188903i
$9$	−348.127	+	252.929i	−1.43262	+	1.04086i
$10$	−2.14107	+	2.94692i	−0.00677064	+	0.00931899i
$11$		−	82.9904i		−	0.206798i	−0.994640	−	0.103399i	$-0.967028\pi$
$11$		−	82.9904i		−	0.206798i	0.994640	−	0.103399i	$-0.0329718\pi$
$12$	−662.477	−	481.318i	−1.32806	−	0.964892i
$13$	−526.185			−0.863536			−0.431768	−	0.901985i	$-0.642110\pi$
$13$	−526.185			−0.863536			−0.431768	+	0.901985i	$0.642110\pi$
$14$	89.6665			0.122267
$15$	−114.984	−	83.5407i	−0.131950	−	0.0958672i
$16$	303.374	−	933.689i	0.296264	−	0.911806i
$17$	−347.717	−	478.592i	−0.291813	−	0.401646i	0.637789	−	0.770211i	$-0.279849\pi$
$17$	−347.717	−	478.592i	−0.291813	−	0.401646i	−0.929602	+	0.368565i	$0.879849\pi$
$18$	−168.205	+	231.514i	−0.122365	+	0.168421i
$19$	144.764	+	445.539i	0.0919979	+	0.283140i	0.986460	−	0.164004i	$-0.0524410\pi$
$19$	144.764	+	445.539i	0.0919979	+	0.283140i	−0.894462	+	0.447144i	$0.852441\pi$
$20$	53.4147	−	164.394i	0.0298597	−	0.0918988i
$21$			3498.63i			1.73121i
$22$	−17.0549	−	52.4896i	−0.00751263	−	0.0231215i
$23$	−812.982	−	1118.97i	−0.320451	−	0.441063i	0.618154	−	0.786057i	$-0.287881\pi$
$23$	−812.982	−	1118.97i	−0.320451	−	0.441063i	−0.938605	+	0.344994i	$0.887881\pi$
$24$	−1043.09	−	338.920i	−0.369652	−	0.120107i
$25$	−956.407	+	2943.52i	−0.306050	+	0.941926i
$26$	−332.800	+	108.133i	−0.0965496	+	0.0313709i
$27$	−3932.08	−	2856.83i	−1.03804	−	0.754179i
$28$	−4046.72	+	1314.86i	−0.975458	+	0.316945i
$29$			5340.16i			1.17912i	0.807723	+	0.589561i	$0.200699\pi$
$29$			5340.16i			1.17912i	−0.807723	+	0.589561i	$0.799301\pi$
$30$	−89.8928	−	29.2079i	−0.0182357	−	0.00592513i
$31$	7314.52	+	2376.63i	1.36704	+	0.444179i	0.898388	−	0.439203i	$-0.144739\pi$
$31$	7314.52	+	2376.63i	1.36704	+	0.444179i	0.468654	+	0.883382i	$0.344739\pi$
$32$		−	2005.44i		−	0.346207i
$33$	2048.05	−	665.453i	0.327383	−	0.106373i
$34$	−318.276	−	231.241i	−0.0472179	−	0.0343058i
$35$	−702.377	+	228.216i	−0.0969170	+	0.0314902i
$36$	4196.32	−	12914.9i	0.539650	−	1.66087i
$37$	7607.74	+	2471.90i	0.913590	+	0.296843i	0.727835	−	0.685753i	$-0.240527\pi$
$37$	7607.74	+	2471.90i	0.913590	+	0.296843i	0.185755	+	0.982596i	$0.440527\pi$
$38$	183.121	+	252.044i	0.0205721	+	0.0283150i
$39$	−4219.18	−	12985.3i	−0.444188	−	1.36707i
$40$		−	231.515i		−	0.0228786i
$41$	351.123	−	1080.65i	0.0326212	−	0.100398i	−0.933420	−	0.358785i	$-0.883191\pi$
$41$	351.123	−	1080.65i	0.0326212	−	0.100398i	0.966041	+	0.258387i	$0.0831911\pi$
$42$	718.985	+	2212.81i	0.0628921	+	0.193562i
$43$	−2713.16	+	3734.34i	−0.223771	+	0.307994i	−0.906111	−	0.423041i	$-0.860963\pi$
$43$	−2713.16	+	3734.34i	−0.223771	+	0.307994i	0.682339	+	0.731035i	$0.260963\pi$
$44$	1539.40	+	2118.81i	0.119873	+	0.164991i
$45$	728.341	−	2241.60i	0.0536172	−	0.165017i
$46$	−744.147	−	540.654i	−0.0518518	−	0.0376726i
$47$	17515.3			1.15657			0.578287	−	0.815833i	$-0.303721\pi$
$47$	17515.3			1.15657			0.578287	+	0.815833i	$0.303721\pi$
$48$	25474.3			1.59588
$49$	1110.40	+	806.752i	0.0660676	+	0.0480010i
$50$			2058.26i			0.116432i
$51$	9022.64	−	12418.6i	0.485745	−	0.668570i
$52$	13433.9	−	9760.30i	0.688960	−	0.500559i
$53$	−20367.3	+	28033.2i	−0.995964	+	1.37083i	−0.0681949	+	0.997672i	$0.521724\pi$
$53$	−20367.3	+	28033.2i	−0.995964	+	1.37083i	−0.927769	+	0.373155i	$0.878276\pi$
$54$	−3074.05	−	998.818i	−0.143458	−	0.0466124i
$55$	267.189	+	367.754i	0.0119100	+	0.0163927i
$56$	−4610.59	+	3349.79i	−0.196465	+	0.142740i
$57$	−9834.32	+	7145.05i	−0.400920	+	0.291285i
$58$	1097.43	+	3377.53i	0.0428356	+	0.131835i
$59$	−32312.1	+	10498.8i	−1.20847	+	0.392655i	−0.842870	−	0.538117i	$-0.819136\pi$
$59$	−32312.1	+	10498.8i	−1.20847	+	0.392655i	−0.365599	+	0.930772i	$0.619136\pi$
$60$	4485.24			0.160845
$61$	22523.2	−	18365.8i	0.775006	−	0.631954i
$61$	22523.2	−	18365.8i	0.775006	−	0.631954i
$62$	5114.68			0.168982
$63$	−55179.5	+	17928.9i	−1.75157	+	0.569118i
$64$	9295.84	+	28609.6i	0.283686	+	0.873097i
$65$	2331.68	−	1694.06i	0.0684519	−	0.0497332i
$66$	1158.59	−	841.768i	0.0327395	−	0.0237866i
$67$	−1811.94	−	2493.92i	−0.0493125	−	0.0678728i	0.783649	−	0.621204i	$-0.213356\pi$
$67$	−1811.94	−	2493.92i	−0.0493125	−	0.0678728i	−0.832961	+	0.553331i	$0.813356\pi$
$68$	17755.0	+	5768.94i	0.465637	+	0.151295i
$69$	21095.4	−	29035.3i	0.533415	−	0.734183i
$70$	−397.338	+	288.683i	−0.00969204	+	0.00704168i
$71$	29521.4	−	40632.7i	0.695010	−	0.956599i	−0.304981	−	0.952358i	$-0.598650\pi$
$71$	29521.4	−	40632.7i	0.695010	−	0.956599i	0.999991	−	0.00424055i	$-0.00134981\pi$
$72$		−	18188.1i		−	0.413482i
$73$	12472.9	+	9062.07i	0.273942	+	0.199031i	0.716271	−	0.697822i	$-0.245847\pi$
$73$	12472.9	+	9062.07i	0.273942	+	0.199031i	−0.442328	+	0.896853i	$0.645847\pi$
$74$	5319.71			0.112930
$75$	−80309.6			−1.64860
$76$	−11960.3	−	8689.69i	−0.237525	−	0.172572i
$77$	3457.81	−	10642.1i	0.0664622	−	0.204550i
$78$	−5337.08	−	7345.85i	−0.0993269	−	0.136712i
$79$	−42670.8	+	58731.3i	−0.769241	+	1.05877i	0.227147	+	0.973860i	$0.427060\pi$
$79$	−42670.8	+	58731.3i	−0.769241	+	1.05877i	−0.996389	+	0.0849094i	$0.972940\pi$
$80$	1661.69	+	5114.16i	0.0290286	+	0.0893408i
$81$	6659.81	−	20496.8i	0.112784	−	0.347115i
$82$		−	755.642i		−	0.0124103i
$83$	1596.27	+	4912.81i	0.0254338	+	0.0782771i	0.962968	−	0.269617i	$-0.0868970\pi$
$83$	1596.27	+	4912.81i	0.0254338	+	0.0782771i	−0.937534	+	0.347894i	$0.886897\pi$
$84$	−64896.8	−	89322.7i	−1.00352	−	1.38122i
$85$	3081.67	+	1001.30i	0.0462636	+	0.0150319i
$86$	−948.588	+	2919.45i	−0.0138303	+	0.0425653i
$87$	−131785.	+	42819.7i	−1.86668	+	0.606520i
$88$	2837.87	+	2061.83i	0.0390648	+	0.0283823i
$89$	67185.3	−	21829.8i	0.899081	−	0.292129i	0.177223	−	0.984171i	$-0.443288\pi$
$89$	67185.3	−	21829.8i	0.899081	−	0.292129i	0.721858	+	0.692041i	$0.243288\pi$
$90$		−	1567.44i		−	0.0203979i
$91$	−67474.0	−	21923.6i	−0.854148	−	0.277529i
$92$	41512.1	+	13488.1i	0.511334	+	0.166143i
$93$			199566.i			2.39265i
$94$	11078.1	−	3599.48i	0.129313	−	0.0420165i
$95$	−2075.92	−	1508.24i	−0.0235994	−	0.0171460i
$96$	49490.7	−	16080.5i	0.548082	−	0.178083i
$97$	−56848.2	+	174961.i	−0.613461	+	1.88804i	−0.191255	+	0.981540i	$0.561256\pi$
$97$	−56848.2	+	174961.i	−0.613461	+	1.88804i	−0.422206	+	0.906500i	$0.638744\pi$
$98$	868.094	+	282.061i	0.00913064	+	0.00296673i
$99$	20990.7	+	28891.2i	0.215248	+	0.296263i
$100$	−30182.0	−	92890.8i	−0.301820	−	0.928908i
$101$		−	125029.i		−	1.21958i	−0.792565	−	0.609788i	$-0.791255\pi$
$101$		−	125029.i		−	1.21958i	0.792565	−	0.609788i	$-0.208745\pi$
$102$	3154.54	−	9708.67i	0.0300217	−	0.0923973i
$103$	1434.99	+	4416.44i	0.0133277	+	0.0410184i	0.957499	−	0.288436i	$-0.0931352\pi$
$103$	1434.99	+	4416.44i	0.0133277	+	0.0410184i	−0.944172	+	0.329454i	$0.893135\pi$
$104$	13072.7	−	17993.0i	0.118517	−	0.163125i
$105$	−11263.9	−	15503.5i	−0.0997049	−	0.137232i
$106$	−7120.91	+	21915.9i	−0.0615561	+	0.189450i
$107$	93958.1	+	68264.6i	0.793369	+	0.576416i	0.908961	−	0.416881i	$-0.136877\pi$
$107$	93958.1	+	68264.6i	0.793369	+	0.576416i	−0.115593	+	0.993297i	$0.536877\pi$
$108$	153381.			1.26535
$109$	−62338.6			−0.502563			−0.251282	−	0.967914i	$-0.580852\pi$
$109$	−62338.6			−0.502563			−0.251282	+	0.967914i	$0.580852\pi$
$110$	244.566	+	177.688i	0.00192715	+	0.00140015i
$111$			207566.i			1.59900i
$112$	77804.7	−	107089.i	0.586085	−	0.806677i
$113$	184091.	−	133750.i	1.35624	−	0.985365i	0.357565	−	0.933888i	$-0.383607\pi$
$113$	184091.	−	133750.i	1.35624	−	0.985365i	0.998674	−	0.0514772i	$-0.0163929\pi$
$114$	−4751.65	+	6540.08i	−0.0342438	+	0.0471326i
$115$	7205.12	+	2341.08i	0.0508038	+	0.0165072i
$116$	−99055.5	−	136338.i	−0.683492	−	0.940747i
$117$	183179.	−	133088.i	1.23712	−	0.898821i
$118$	−18279.1	+	13280.6i	−0.120851	+	0.0878035i
$119$	−24648.0	−	75858.7i	−0.159556	−	0.491064i
$120$	5713.38	−	1856.39i	0.0362193	−	0.0117684i
$121$	154164.			0.957235
$122$	10471.1	−	16244.6i	0.0636934	−	0.0988118i
$123$	29483.9			0.175720
$124$	−230830.	+	75001.1i	−1.34815	+	0.438040i
$125$	−10528.0	−	32401.8i	−0.0602657	−	0.185479i
$126$	−31215.3	+	22679.3i	−0.175163	+	0.127263i
$127$	142842.	−	103781.i	0.785864	−	0.570964i	−0.120869	−	0.992668i	$-0.538568\pi$
$127$	142842.	−	103781.i	0.785864	−	0.570964i	0.906733	+	0.421705i	$0.138568\pi$
$128$	49479.5	+	68102.7i	0.266932	+	0.367400i
$129$	−113912.	−	37012.3i	−0.602692	−	0.195827i
$130$	1126.60	−	1550.63i	0.00584669	−	0.00804728i
$131$	231986.	−	168547.i	1.18109	−	0.858112i	0.188795	−	0.982016i	$-0.439542\pi$
$131$	231986.	−	168547.i	1.18109	−	0.858112i	0.992294	+	0.123905i	$0.0395418\pi$
$132$	−39944.7	+	54979.2i	−0.199538	+	0.274640i
$133$			63164.2i			0.309629i
$134$	−1658.52	−	1204.99i	−0.00797920	−	0.00579723i
$135$	26621.8			0.125720
$136$	25004.3			0.115922
$137$	−190692.	−	138545.i	−0.868020	−	0.630654i	0.0620346	−	0.998074i	$-0.480241\pi$
$137$	−190692.	−	138545.i	−0.868020	−	0.630654i	−0.930055	+	0.367420i	$0.880241\pi$
$138$	7375.48	−	22699.4i	0.0329680	−	0.101465i
$139$	−226886.	−	312282.i	−0.996026	−	1.37091i	−0.927732	−	0.373248i	$-0.878244\pi$
$139$	−226886.	−	312282.i	−0.996026	−	1.37091i	−0.0682947	−	0.997665i	$-0.521756\pi$
$140$	13699.0	−	18855.0i	0.0590702	−	0.0813031i
$141$	140445.	+	432247.i	0.594922	+	1.83098i
$142$	10321.4	−	31766.1i	0.0429555	−	0.132203i
$143$			43668.3i			0.178577i
$144$	130544.	+	401775.i	0.524629	+	1.61464i
$145$	−17192.7	−	23663.8i	−0.0679087	−	0.0934683i
$146$	9751.11	+	3168.33i	0.0378592	+	0.0123012i
$147$	−11005.5	+	33871.5i	−0.0420066	+	0.129283i
$148$	−240083.	+	78007.7i	−0.900964	+	0.292741i
$149$	−60492.9	−	43950.6i	−0.223223	−	0.162181i	0.470553	−	0.882372i	$-0.344054\pi$
$149$	−60492.9	−	43950.6i	−0.223223	−	0.162181i	−0.693776	+	0.720191i	$0.744054\pi$
$150$	−50794.0	+	16504.0i	−0.184325	+	0.0598909i
$151$			489528.i			1.74717i	0.486671	+	0.873586i	$0.338211\pi$
$151$			489528.i			1.74717i	−0.486671	+	0.873586i	$0.661789\pi$
$152$	−18831.9	−	6118.84i	−0.0661126	−	0.0214813i
$153$	242100.	+	78662.9i	0.836114	+	0.271670i
$154$		−	7441.46i		−	0.0252846i
$155$	−40064.4	+	13017.7i	−0.133946	+	0.0435216i
$156$	348586.	+	253262.i	1.14683	+	0.833219i
$157$	73401.3	−	23849.5i	0.237659	−	0.0772202i	−0.187766	−	0.982214i	$-0.560125\pi$
$157$	73401.3	−	23849.5i	0.237659	−	0.0772202i	0.425425	+	0.904994i	$0.360125\pi$
$158$	−14918.8	+	45915.2i	−0.0475434	+	0.146323i
$159$	−855122.	−	277846.i	−2.68247	−	0.871588i
$160$	6456.57	+	8886.70i	0.0199389	+	0.0274436i
$161$	−57628.3	−	177362.i	−0.175215	−	0.539256i
$162$		−	14332.4i		−	0.0429072i
$163$	72147.8	−	222048.i	0.212693	−	0.654603i	−0.786616	−	0.617443i	$-0.788169\pi$
$163$	72147.8	−	222048.i	0.212693	−	0.654603i	0.999309	−	0.0371605i	$-0.0118313\pi$
$164$	11080.7	+	34102.8i	0.0321704	+	0.0990102i
$165$	−6933.08	+	9542.56i	−0.0198251	+	0.0272870i
$166$	2019.21	+	2779.20i	0.00568737	+	0.00782799i
$167$	23086.7	−	71053.5i	0.0640576	−	0.197149i	−0.913905	−	0.405927i	$-0.866949\pi$
$167$	23086.7	−	71053.5i	0.0640576	−	0.197149i	0.977963	+	0.208778i	$0.0669487\pi$
$168$	−119636.	−	86920.9i	−0.327032	−	0.237603i
$169$	−94421.9			−0.254306
$170$	2154.86			0.00571869
$171$	−163086.	−	118489.i	−0.426508	−	0.309876i
$172$		−	145667.i		−	0.375440i
$173$	132423.	−	182264.i	0.336393	−	0.463005i	−0.606991	−	0.794709i	$-0.707624\pi$
$173$	132423.	−	182264.i	0.336393	−	0.463005i	0.943384	+	0.331704i	$0.107624\pi$
$174$	−74551.7	+	54165.0i	−0.186674	+	0.135627i
$175$	−245285.	+	337605.i	−0.605446	+	0.833325i
$176$	−77487.2	−	25177.1i	−0.188559	−	0.0612667i
$177$	−518185.	−	713221.i	−1.24323	−	1.71116i
$178$	38007.0	−	27613.7i	0.0899113	−	0.0653244i
$179$	353276.	−	256670.i	0.824103	−	0.598746i	−0.0937817	−	0.995593i	$-0.529896\pi$
$179$	353276.	−	256670.i	0.824103	−	0.598746i	0.917885	+	0.396847i	$0.129896\pi$
$180$	22984.8	+	70740.0i	0.0528761	+	0.162736i
$181$	−188590.	+	61276.7i	−0.427881	+	0.139027i	−0.515038	−	0.857168i	$-0.672222\pi$
$181$	−188590.	+	61276.7i	−0.427881	+	0.139027i	0.0871563	+	0.996195i	$0.472222\pi$
$182$	−47181.2			−0.105582
$183$	633836.	+	408566.i	1.39910	+	0.901850i
$184$	58461.4			0.127299
$185$	−41670.4	+	13539.5i	−0.0895156	+	0.0290854i
$186$	41011.7	+	126221.i	0.0869212	+	0.267516i
$187$	−39718.5	+	28857.2i	−0.0830595	+	0.0603462i
$188$	−447179.	+	324895.i	−0.922757	+	0.670422i
$189$	−385190.	−	530169.i	−0.784369	−	1.07959i
$190$	−1622.92	−	527.319i	−0.00326147	−	0.00105972i
$191$	292461.	−	402538.i	0.580076	−	0.798406i	−0.413628	−	0.910446i	$-0.635739\pi$
$191$	292461.	−	402538.i	0.580076	−	0.798406i	0.993704	+	0.112040i	$0.0357386\pi$
$192$	−631497.	+	458809.i	−1.23628	+	0.898212i
$193$	69986.5	−	96328.1i	0.135245	−	0.186149i	−0.736023	−	0.676957i	$-0.763298\pi$
$193$	69986.5	−	96328.1i	0.135245	−	0.186149i	0.871268	+	0.490808i	$0.163298\pi$
$194$			122341.i			0.233383i
$195$	60502.9	+	43957.9i	0.113943	+	0.0827848i
$196$	−43313.9			−0.0805355
$197$	484043.			0.888625			0.444312	−	0.895872i	$-0.353448\pi$
$197$	484043.			0.888625			0.444312	+	0.895872i	$0.353448\pi$
$198$	19213.4	+	13959.4i	0.0348290	+	0.0253048i
$199$	−11321.4	+	34843.6i	−0.0202659	+	0.0623721i	−0.960678	−	0.277665i	$-0.910440\pi$
$199$	−11321.4	+	34843.6i	−0.0202659	+	0.0623721i	0.940412	+	0.340037i	$0.110440\pi$
$200$	−76892.9	−	105834.i	−0.135929	−	0.187090i
$201$	47016.6	−	64712.7i	0.0820844	−	0.112979i
$202$	−25694.1	−	79078.3i	−0.0443052	−	0.136357i
$203$	−222499.	+	684781.i	−0.378955	+	1.16630i
$204$			484418.i			0.814977i
$205$	1923.23	+	5919.11i	0.00319630	+	0.00983720i
$206$	1815.20	+	2498.40i	0.00298027	+	0.00410199i
$207$	566042.	+	183918.i	0.918169	+	0.298331i
$208$	−159631.	+	491293.i	−0.255834	+	0.787377i
$209$	36975.5	−	12014.1i	0.0585528	−	0.0190250i
$210$	−10310.2	−	7490.80i	−0.0161331	−	0.0117214i
$211$	344192.	−	111835.i	0.532225	−	0.172930i	−0.0305613	−	0.999533i	$-0.509729\pi$
$211$	344192.	−	111835.i	0.532225	−	0.172930i	0.562786	+	0.826603i	$0.309729\pi$
$212$		−	1.09350e6i		−	1.67102i
$213$	1.23946e6	+	402724.i	1.87190	+	0.608217i
$214$	73455.1	+	23867.0i	0.109645	+	0.0356257i
$215$		−	25283.0i		−	0.0373020i
$216$	195379.	−	63482.6i	0.284934	−	0.0925807i
$217$	838936.	+	609522.i	1.20943	+	0.878699i
$218$	−39427.8	+	12810.9i	−0.0561903	+	0.0182573i
$219$	−123623.	+	380472.i	−0.174176	+	0.536058i
$220$	−13643.1	−	4432.91i	−0.0190045	−	0.00617493i
$221$	182964.	+	251828.i	0.251991	+	0.346835i
$222$	42655.7	+	131281.i	0.0580892	+	0.178780i
$223$			690984.i			0.930477i	0.885185	+	0.465239i	$0.154031\pi$
$223$			690984.i			0.930477i	−0.885185	+	0.465239i	$0.845969\pi$
$224$	83557.3	−	257163.i	0.111266	−	0.342443i
$225$	−411550.	−	1.26662e6i	−0.541959	−	1.66798i
$226$	88947.2	−	122425.i	0.115841	−	0.159441i
$227$	509241.	+	700910.i	0.655932	+	0.902813i	0.999338	−	0.0363739i	$-0.0115807\pi$
$227$	509241.	+	700910.i	0.655932	+	0.902813i	−0.343406	+	0.939187i	$0.611581\pi$
$228$	118543.	−	364837.i	0.151021	−	0.464795i
$229$	−691038.	−	502069.i	−0.870790	−	0.632666i	0.0600091	−	0.998198i	$-0.480887\pi$
$229$	−691038.	−	502069.i	−0.870790	−	0.632666i	−0.930799	+	0.365532i	$0.880887\pi$
$230$	5038.18			0.00627992
$231$	290353.			0.358011
$232$	−182608.	−	132672.i	−0.222740	−	0.161830i
$233$		−	1.23556e6i		−	1.49098i	−0.666515	−	0.745491i	$-0.732215\pi$
$233$		−	1.23556e6i		−	1.49098i	0.666515	−	0.745491i	$-0.267785\pi$
$234$	88506.8	−	121819.i	0.105666	−	0.145437i
$235$	−77615.5	+	56391.0i	−0.0916809	+	0.0666101i
$236$	630208.	−	867407.i	0.736553	−	1.01378i
$237$	−1.79153e6	−	582105.i	−2.07183	−	0.673179i
$238$	−31178.6	−	42913.6i	−0.0356791	−	0.0491081i
$239$	792499.	−	575785.i	0.897438	−	0.652027i	−0.0403690	−	0.999185i	$-0.512853\pi$
$239$	792499.	−	575785.i	0.897438	−	0.652027i	0.937807	+	0.347158i	$0.112853\pi$
$240$	−112884.	+	82015.2i	−0.126504	+	0.0919107i
$241$	204494.	+	629367.i	0.226797	+	0.698009i	0.998104	+	0.0615462i	$0.0196032\pi$
$241$	204494.	+	629367.i	0.226797	+	0.698009i	−0.771307	+	0.636463i	$0.780397\pi$
$242$	97505.0	−	31681.3i	0.107026	−	0.0347748i
$243$	−621834.			−0.675552
$244$	−234362.	+	886679.i	−0.252007	+	0.953437i
$245$	−7517.85			−0.00800163
$246$	18647.9	−	6059.06i	0.0196468	−	0.00638363i
$247$	−76172.9	−	234436.i	−0.0794435	−	0.244502i
$248$	−262993.	+	191076.i	−0.271528	+	0.197277i
$249$	−108440.	+	78786.1i	−0.110838	+	0.0805288i
$250$	−13317.4	−	18329.9i	−0.0134763	−	0.0185485i
$251$	314649.	+	102236.i	0.315241	+	0.102428i	0.462364	−	0.886690i	$-0.347001\pi$
$251$	314649.	+	102236.i	0.315241	+	0.102428i	−0.147123	+	0.989118i	$0.547001\pi$
$252$	1.07621e6	−	1.48127e6i	1.06757	−	1.46938i
$253$	−92864.1	+	67469.7i	−0.0912108	+	0.0662685i
$254$	69017.1	−	94993.8i	0.0671231	−	0.0923871i
$255$			84079.0i			0.0809724i
$256$	−733488.	−	532910.i	−0.699509	−	0.508223i
$257$	1.69708e6			1.60276			0.801380	−	0.598156i	$-0.204100\pi$
$257$	1.69708e6			1.60276			0.801380	+	0.598156i	$0.204100\pi$
$258$	−79653.0			−0.0744994
$259$	872566.	+	633956.i	0.808256	+	0.587232i
$260$	−28106.0	+	86501.5i	−0.0257849	+	0.0793579i
$261$	−1.35068e6	−	1.85905e6i	−1.22730	−	1.68924i
$262$	112088.	−	154276.i	0.100881	−	0.138850i
$263$	598429.	+	1.84178e6i	0.533487	+	1.64190i	0.746896	+	0.664940i	$0.231543\pi$
$263$	598429.	+	1.84178e6i	0.533487	+	1.64190i	−0.213410	+	0.976963i	$0.568457\pi$
$264$	−28127.1	+	86566.2i	−0.0248379	+	0.0764432i
$265$		−	189796.i		−	0.166025i
$266$	12980.5	+	39949.9i	0.0112483	+	0.0346188i
$267$	1.07744e6	+	1.48297e6i	0.924944	+	1.27308i
$268$	92520.3	+	30061.7i	0.0786865	+	0.0255668i
$269$	−569412.	+	1.75247e6i	−0.479785	+	1.47662i	0.359610	+	0.933103i	$0.382910\pi$
$269$	−569412.	+	1.75247e6i	−0.479785	+	1.47662i	−0.839395	+	0.543522i	$0.817090\pi$
$270$	16837.7	−	5470.90i	0.0140564	−	0.00456719i
$271$	1.02684e6	+	746044.i	0.849337	+	0.617079i	0.924963	−	0.380057i	$-0.124096\pi$
$271$	1.02684e6	+	746044.i	0.849337	+	0.617079i	−0.0756262	+	0.997136i	$0.524096\pi$
$272$	−552344.	+	179468.i	−0.452676	+	0.147083i
$273$		−	1.84093e6i		−	1.49496i
$274$	−149080.	−	48439.0i	−0.119962	−	0.0389779i
$275$	244284.	+	79372.6i	0.194788	+	0.0632905i
$276$			1.13260e6i			0.894958i
$277$	−1.59767e6	+	519114.i	−1.25109	+	0.406503i	−0.858310	−	0.513132i	$-0.828485\pi$
$277$	−1.59767e6	+	519114.i	−1.25109	+	0.406503i	−0.392776	+	0.919634i	$0.628485\pi$
$278$	−207676.	−	150885.i	−0.161166	−	0.117094i
$279$	−3.14750e6	+	1.02269e6i	−2.42078	+	0.786560i
$280$	9646.14	−	29687.8i	0.00735289	−	0.0226299i
$281$	150087.	+	48766.4i	0.113391	+	0.0368430i	0.365163	−	0.930944i	$-0.381013\pi$
$281$	150087.	+	48766.4i	0.113391	+	0.0368430i	−0.251772	+	0.967787i	$0.581013\pi$
$282$	177657.	+	244524.i	0.133033	+	0.183105i
$283$	113265.	+	348595.i	0.0840682	+	0.258735i	0.984251	−	0.176777i	$-0.0565672\pi$
$283$	113265.	+	348595.i	0.0840682	+	0.258735i	−0.900183	+	0.435512i	$0.856567\pi$
$284$			1.58498e6i			1.16608i
$285$	20575.1	−	63323.6i	0.0150048	−	0.0461799i
$286$	8974.03	+	27619.2i	0.00648743	+	0.0199663i
$287$	90050.7	−	123944.i	0.0645331	−	0.0888222i
$288$	507235.	+	698149.i	0.360353	+	0.495983i
$289$	330617.	−	1.01753e6i	0.232852	−	0.716646i
$290$	−15737.0	−	11433.6i	−0.0109882	−	0.00798342i
$291$	−4.77355e6			−3.30452
$292$	−486536.			−0.333932
$293$	−2.26100e6	−	1.64271e6i	−1.53862	−	1.11787i	−0.951195	−	0.308592i	$-0.900142\pi$
$293$	−2.26100e6	−	1.64271e6i	−1.53862	−	1.11787i	−0.587424	−	0.809280i	$-0.699858\pi$
$294$			23684.7i			0.0159808i
$295$	109383.	−	150553.i	0.0731805	−	0.100724i
$296$	−273536.	+	198735.i	−0.181462	+	0.131840i
$297$	−237089.	+	326325.i	−0.155963	+	0.214664i
$298$	−47292.4	−	15366.2i	−0.0308497	−	0.0100237i
$299$	427779.	+	588788.i	0.276721	+	0.380873i
$300$	2.05036e6	−	1.48968e6i	1.31531	−	0.955628i
$301$	−503507.	+	365819.i	−0.320324	+	0.232729i
$302$	100600.	+	309616.i	0.0634719	+	0.195346i
$303$	3.08550e6	−	1.00254e6i	1.93072	−	0.627329i
$304$	459913.			0.285425
$305$	−40677.5	+	153898.i	−0.0250383	+	0.0947291i
$306$	169288.			0.103353
$307$	−373752.	+	121439.i	−0.226328	+	0.0735384i	−0.419986	−	0.907531i	$-0.637965\pi$
$307$	−373752.	+	121439.i	−0.226328	+	0.0735384i	0.193658	+	0.981069i	$0.437965\pi$
$308$	109121.	+	335839.i	0.0655436	+	0.201723i
$309$	−97483.4	+	70825.8i	−0.0580811	+	0.0421984i
$310$	−22664.6	+	16466.8i	−0.0133950	+	0.00973207i
$311$	−1.25222e6	−	1.72354e6i	−0.734143	−	1.01046i	−0.998934	−	0.0461555i	$-0.985303\pi$
$311$	−1.25222e6	−	1.72354e6i	−0.734143	−	1.01046i	0.264791	−	0.964306i	$-0.414697\pi$
$312$	548857.	+	178335.i	0.319207	+	0.103717i
$313$	728633.	−	1.00288e6i	0.420386	−	0.578611i	−0.545327	−	0.838223i	$-0.683595\pi$
$313$	728633.	−	1.00288e6i	0.420386	−	0.578611i	0.965713	+	0.259612i	$0.0835946\pi$
$314$	41523.5	−	30168.6i	0.0237668	−	0.0172676i
$315$	186794.	−	257100.i	0.106068	−	0.145991i
$316$		−	2.29096e6i		−	1.29062i
$317$	−2.32730e6	−	1.69089e6i	−1.30078	−	0.945074i	−0.300820	−	0.953681i	$-0.597260\pi$
$317$	−2.32730e6	−	1.69089e6i	−1.30078	−	0.945074i	−0.999963	+	0.00860646i	$0.997260\pi$
$318$	−597944.			−0.331583
$319$	443182.			0.243840
$320$	−133302.	−	96849.5i	−0.0727715	−	0.0528716i
$321$	−931250.	+	2.86609e6i	−0.504433	+	1.55249i
$322$	−72897.2	−	100334.i	−0.0391806	−	0.0539275i
$323$	162894.	−	224205.i	0.0868760	−	0.119575i
$324$	210168.	+	646832.i	0.111226	+	0.342317i
$325$	503247.	−	1.54884e6i	0.264285	−	0.813387i
$326$		−	155267.i		−	0.0809162i
$327$	−499858.	−	1.53840e6i	−0.258510	−	0.795612i
$328$	28229.5	+	38854.6i	0.0144883	+	0.0199415i
$329$	2.24603e6	+	729780.i	1.14400	+	0.371708i
$330$	−2423.98	+	7460.24i	−0.00122530	+	0.00377110i
$331$	−2.00745e6	+	652261.i	−1.00711	+	0.327229i	−0.765702	−	0.643196i	$-0.777608\pi$
$331$	−2.00745e6	+	652261.i	−1.00711	+	0.327229i	−0.241405	+	0.970424i	$0.577608\pi$
$332$	−131883.	−	95818.3i	−0.0656662	−	0.0477093i
$333$	−3.27368e6	+	1.06368e6i	−1.61780	+	0.525656i
$334$		−	49684.2i		−	0.0243698i
$335$	16058.5	+	5217.71i	0.00781793	+	0.00254020i
$336$	3.26664e6	+	1.06139e6i	1.57853	+	0.512895i
$337$		−	1.41899e6i		−	0.680622i	−0.940313	−	0.340311i	$-0.889468\pi$
$337$		−	1.41899e6i		−	0.680622i	0.940313	−	0.340311i	$-0.110532\pi$
$338$	−59719.8	+	19404.1i	−0.0284332	+	0.00923852i
$339$	4.77683e6	+	3.47057e6i	2.25757	+	1.64022i
$340$	−97250.6	+	31598.6i	−0.0456242	+	0.0148242i
$341$	197238.	−	607035.i	0.0918552	−	0.282701i
$342$	−127498.	−	41426.8i	−0.0589440	−	0.0191521i
$343$	−1.22321e6	−	1.68361e6i	−0.561392	−	0.772690i
$344$	−60290.1	−	185554.i	−0.0274694	−	0.0845422i
$345$			196581.i			0.0889189i
$346$	46298.2	−	142491.i	0.0207909	−	0.0639879i
$347$	566254.	+	1.74275e6i	0.252457	+	0.776983i	0.994320	+	0.106432i	$0.0339425\pi$
$347$	566254.	+	1.74275e6i	0.252457	+	0.776983i	−0.741863	+	0.670552i	$0.766057\pi$
$348$	2.57031e6	−	3.53773e6i	1.13773	−	1.56595i
$349$	2.39902e6	+	3.30197e6i	1.05432	+	1.45114i	0.885006	+	0.465579i	$0.154154\pi$
$349$	2.39902e6	+	3.30197e6i	1.05432	+	1.45114i	0.169310	+	0.985563i	$0.445846\pi$
$350$	−85757.7	+	263935.i	−0.0374199	+	0.115167i
$351$	2.06901e6	+	1.50322e6i	0.896383	+	0.651261i
$352$	−166433.			−0.0715948
$353$	−95137.3			−0.0406363			−0.0203181	−	0.999794i	$-0.506468\pi$
$353$	−95137.3			−0.0406363			−0.0203181	+	0.999794i	$0.506468\pi$
$354$	−474311.	−	344607.i	−0.201166	−	0.146156i
$355$			275100.i			0.115856i
$356$	−1.31036e6	+	1.80356e6i	−0.547983	+	0.754234i
$357$	1.67442e6	−	1.21654e6i	0.695334	−	0.505189i
$358$	170692.	−	234938.i	0.0703893	−	0.0968825i
$359$	1.03759e6	+	337133.i	0.424902	+	0.138059i	0.513659	−	0.857994i	$-0.328290\pi$
$359$	1.03759e6	+	337133.i	0.424902	+	0.138059i	−0.0887571	+	0.996053i	$0.528290\pi$
$360$	58557.0	+	80596.8i	0.0238135	+	0.0327764i
$361$	1.82566e6	−	1.32642e6i	0.737312	−	0.535689i
$362$	−106687.	+	77512.3i	−0.0427896	+	0.0310885i
$363$	1.23615e6	+	3.80448e6i	0.492385	+	1.51541i
$364$	2.12933e6	−	691860.i	0.842343	−	0.273694i
$365$	−84446.4			−0.0331779
$366$	484849.	+	128153.i	0.189192	+	0.0500063i
$367$	−3.87440e6			−1.50155			−0.750774	−	0.660559i	$-0.770319\pi$
$367$	−3.87440e6			−1.50155			−0.750774	+	0.660559i	$0.770319\pi$
$368$	−1.29141e6	+	419605.i	−0.497101	+	0.161518i
$369$	151091.	+	465012.i	0.0577662	+	0.177786i
$370$	−23573.2	+	17126.9i	−0.00895187	+	0.00650392i
$371$	−3.77975e6	+	2.74615e6i	−1.42570	+	1.03583i
$372$	−3.70179e6	−	5.09507e6i	−1.38693	−	1.90894i
$373$	2.50178e6	+	812878.i	0.931060	+	0.302520i	0.734996	−	0.678072i	$-0.237184\pi$
$373$	2.50178e6	+	812878.i	0.931060	+	0.302520i	0.196064	+	0.980591i	$0.437184\pi$
$374$	−19190.8	+	26413.9i	−0.00709437	+	0.00976456i
$375$	715200.	−	519623.i	0.262633	−	0.190814i
$376$	−435155.	+	598940.i	−0.158736	+	0.218481i
$377$		−	2.80991e6i		−	1.01822i
$378$	−352576.	−	256162.i	−0.126918	−	0.0922114i
$379$	2.26421e6			0.809688			0.404844	−	0.914386i	$-0.367326\pi$
$379$	2.26421e6			0.809688			0.404844	+	0.914386i	$0.367326\pi$
$380$	80976.3			0.0287673
$381$	3.70650e6	+	2.69293e6i	1.30813	+	0.950413i
$382$	102252.	−	314698.i	0.0358519	−	0.110341i
$383$	−2.76346e6	−	3.80357e6i	−0.962622	−	1.32494i	−0.945687	−	0.325080i	$-0.894609\pi$
$383$	−2.76346e6	−	3.80357e6i	−0.962622	−	1.32494i	−0.0169358	−	0.999857i	$-0.505391\pi$
$384$	−1.28390e6	+	1.76714e6i	−0.444328	+	0.611566i
$385$	18939.7	+	58290.5i	0.00651212	+	0.0200422i
$386$	24469.0	−	75307.9i	0.00835888	−	0.0257260i
$387$		−	1.98626e6i		−	0.674154i
$388$	−1.79400e6	−	5.52136e6i	−0.604983	−	1.86195i
$389$	−1.64591e6	−	2.26541e6i	−0.551485	−	0.759053i	0.438728	−	0.898620i	$-0.355429\pi$
$389$	−1.64591e6	−	2.26541e6i	−0.551485	−	0.759053i	−0.990213	+	0.139566i	$0.955429\pi$
$390$	47300.3	+	15368.8i	0.0157472	+	0.00511656i
$391$	−252844.	+	778173.i	−0.0836393	+	0.257415i
$392$	−55174.1	+	17927.1i	−0.0181351	+	0.00589245i
$393$	6.01961e6	+	4.37350e6i	1.96601	+	1.42839i
$394$	306146.	−	99473.0i	0.0993547	−	0.0322823i
$395$		−	397635.i		−	0.128231i
$396$	−1.07182e6	−	348254.i	−0.343465	−	0.111598i
$397$	2.72734e6	+	886168.i	0.868488	+	0.282189i	0.709169	−	0.705038i	$-0.249070\pi$
$397$	2.72734e6	+	886168.i	0.868488	+	0.282189i	0.159319	+	0.987227i	$0.449070\pi$
$398$			24364.4i			0.00770988i
$399$	−1.55878e6	+	506478.i	−0.490176	+	0.159268i
$400$	2.45818e6	+	1.78597e6i	0.768182	+	0.558117i
$401$	−650886.	+	211486.i	−0.202136	+	0.0656781i	−0.408335	−	0.912832i	$-0.633891\pi$
$401$	−650886.	+	211486.i	−0.202136	+	0.0656781i	0.206199	+	0.978510i	$0.433891\pi$
$402$	16438.2	−	50591.5i	0.00507327	−	0.0156139i
$403$	−3.84879e6	−	1.25055e6i	−1.18049	−	0.383564i
$404$	2.31919e6	+	3.19209e6i	0.706941	+	0.973021i
$405$	36478.3	+	112269.i	0.0110509	+	0.0340111i
$406$			478833.i			0.144168i
$407$	205144.	−	631369.i	0.0613866	−	0.188928i
$408$	200495.	+	617061.i	0.0596285	+	0.183518i
$409$	360979.	−	496845.i	0.106702	−	0.146863i	−0.752326	−	0.658791i	$-0.771068\pi$
$409$	360979.	−	496845.i	0.106702	−	0.146863i	0.859029	+	0.511927i	$0.171068\pi$
$410$	2432.80	+	3348.47i	0.000714739	+	0.000983754i
$411$	1.89001e6	−	5.81684e6i	0.551898	−	1.69857i
$412$	−118558.	−	86137.2i	−0.0344101	−	0.0250004i
$413$	−4.58090e6			−1.32153
$414$	395805.			0.113496
$415$	−22890.4	−	16630.9i	−0.00652430	−	0.00474018i
$416$			1.05524e6i			0.298962i
$417$	5.88728e6	−	8.10315e6i	1.65796	−	2.28199i
$418$	20917.2	−	15197.2i	0.00585549	−	0.00425426i
$419$	−3.29605e6	+	4.53662e6i	−0.917189	+	1.26240i	0.0474628	+	0.998873i	$0.484886\pi$
$419$	−3.29605e6	+	4.53662e6i	−0.917189	+	1.26240i	−0.964651	+	0.263529i	$0.915114\pi$
$420$	575153.	+	186878.i	0.159096	+	0.0516935i
$421$	−1.39474e6	−	1.91969e6i	−0.383520	−	0.527869i	0.572993	−	0.819560i	$-0.305782\pi$
$421$	−1.39474e6	−	1.91969e6i	−0.383520	−	0.527869i	−0.956513	+	0.291691i	$0.905782\pi$
$422$	194711.	−	141466.i	0.0532243	−	0.0386697i
$423$	−6.09756e6	+	4.43014e6i	−1.65693	+	1.20383i
$424$	−452589.	−	1.39293e6i	−0.122261	−	0.376282i
$425$	1.74130e6	−	565784.i	0.467630	−	0.151942i
$426$	866690.			0.231388
$427$	3.65341e6	−	1.41666e6i	0.969682	−	0.376007i
$428$	−3.66507e6			−0.967104
$429$	−1.07766e6	+	350152.i	−0.282707	+	0.0918571i
$430$	−5195.77	−	15990.9i	−0.00135512	−	0.00417064i
$431$	−3.78730e6	+	2.75164e6i	−0.982057	+	0.713506i	−0.958167	−	0.286208i	$-0.907605\pi$
$431$	−3.78730e6	+	2.75164e6i	−0.982057	+	0.713506i	−0.0238896	+	0.999715i	$0.507605\pi$
$432$	−3.86028e6	+	2.80466e6i	−0.995198	+	0.723053i
$433$	1.61928e6	+	2.22875e6i	0.415051	+	0.571269i	0.964441	−	0.264297i	$-0.0851399\pi$
$433$	1.61928e6	+	2.22875e6i	0.415051	+	0.571269i	−0.549390	+	0.835566i	$0.685140\pi$
$434$	655867.	+	213104.i	0.167144	+	0.0543085i
$435$	446121.	−	614033.i	0.113039	−	0.155585i
$436$	1.59155e6	−	1.15633e6i	0.400963	−	0.291317i
$437$	380856.	−	524203.i	0.0954019	−	0.131309i
$438$			266045.i			0.0662628i
$439$	−3.75915e6	−	2.73118e6i	−0.930953	−	0.676377i	0.0152728	−	0.999883i	$-0.495138\pi$
$439$	−3.75915e6	−	2.73118e6i	−0.930953	−	0.676377i	−0.946226	+	0.323506i	$0.895138\pi$
$440$	−19213.5			−0.00473125
$441$	−590611.			−0.144612
$442$	167472.	+	121676.i	0.0407744	+	0.0296243i
$443$	−1.20869e6	+	3.71997e6i	−0.292621	+	0.900595i	0.691389	+	0.722483i	$0.256999\pi$
$443$	−1.20869e6	+	3.71997e6i	−0.292621	+	0.900595i	−0.984010	+	0.178113i	$0.943001\pi$
$444$	−3.85018e6	−	5.29932e6i	−0.926880	−	1.27574i
$445$	−227436.	+	313039.i	−0.0544451	+	0.0749373i
$446$	142000.	+	437032.i	0.0338027	+	0.104034i
$447$	599565.	−	1.84527e6i	0.141928	−	0.436809i
$448$			4.05600e6i			0.954778i
$449$	2.28701e6	+	7.03868e6i	0.535367	+	1.64769i	0.742855	+	0.669452i	$0.233471\pi$
$449$	2.28701e6	+	7.03868e6i	0.535367	+	1.64769i	−0.207488	+	0.978238i	$0.566529\pi$
$450$	−520593.	−	716534.i	−0.121190	−	0.166804i
$451$	−89683.3	−	29139.9i	−0.0207620	−	0.00674600i
$452$	−2.21903e6	+	6.82947e6i	−0.510878	+	1.57232i
$453$	−1.20807e7	+	3.92525e6i	−2.76596	+	0.898715i
$454$	466124.	+	338659.i	0.106136	+	0.0771121i
$455$	369580.	−	120084.i	0.0836913	−	0.0271930i
$456$		−	513800.i		−	0.115713i
$457$	4.13708e6	+	1.34422e6i	0.926623	+	0.301078i	0.733181	−	0.680033i	$-0.238035\pi$
$457$	4.13708e6	+	1.34422e6i	0.926623	+	0.301078i	0.193442	+	0.981112i	$0.438035\pi$
$458$	−540243.	−	175536.i	−0.120344	−	0.0391023i
$459$			2.87523e6i			0.637002i
$460$	−227377.	+	73879.3i	−0.0501017	+	0.0162790i
$461$	−2.95874e6	−	2.14965e6i	−0.648417	−	0.471102i	0.214315	−	0.976765i	$-0.431248\pi$
$461$	−2.95874e6	−	2.14965e6i	−0.648417	−	0.471102i	−0.862732	+	0.505662i	$0.831248\pi$
$462$	183642.	−	59668.8i	0.0400282	−	0.0130060i
$463$	−227635.	+	700589.i	−0.0493500	+	0.151884i	−0.972695	−	0.232088i	$-0.925444\pi$
$463$	−227635.	+	700589.i	−0.0493500	+	0.151884i	0.923345	+	0.383972i	$0.125444\pi$
$464$	4.98605e6	+	1.62006e6i	1.07513	+	0.349331i
$465$	−642507.	−	884335.i	−0.137799	−	0.189664i
$466$	−253912.	−	781461.i	−0.0541650	−	0.166703i
$467$		−	2.52934e6i		−	0.536679i	−0.963324	−	0.268340i	$-0.913525\pi$
$467$		−	2.52934e6i		−	0.536679i	0.963324	−	0.268340i	$-0.0864749\pi$
$468$	−2.20804e6	+	6.79565e6i	−0.466007	+	1.43422i
$469$	−128440.	−	395296.i	−0.0269629	−	0.0829833i
$470$	−37501.5	+	51616.3i	−0.00783075	+	0.0107781i
$471$	1.17713e6	+	1.62018e6i	0.244496	+	0.336519i
$472$	443761.	−	1.36576e6i	0.0916841	−	0.282175i
$473$	309914.	+	225166.i	0.0636926	+	0.0462754i
$474$	−1.25273e6			−0.256101
$475$	−1.44991e6			−0.294853
$476$	2.03640e6	+	1.47953e6i	0.411951	+	0.299300i
$477$		−	1.49106e7i		−	3.00054i
$478$	382912.	−	527033.i	0.0766530	−	0.105504i
$479$	6.74952e6	−	4.90382e6i	1.34411	−	0.976552i	0.344826	−	0.938667i	$-0.387938\pi$
$479$	6.74952e6	−	4.90382e6i	1.34411	−	0.976552i	0.999282	−	0.0378853i	$-0.0120622\pi$
$480$	−167536.	+	230594.i	−0.0331899	+	0.0456820i
$481$	−4.00308e6	−	1.30068e6i	−0.788918	−	0.256335i
$482$	258675.	+	356036.i	0.0507151	+	0.0698033i
$483$	3.91488e6	−	2.84433e6i	0.763573	−	0.554768i
$484$	−3.93591e6	+	2.85961e6i	−0.763716	+	0.554872i
$485$	−311379.	−	958326.i	−0.0601083	−	0.184994i
$486$	−393296.	+	127790.i	−0.0755316	+	0.0245417i
$487$	180713.			0.0345277			0.0172639	−	0.999851i	$-0.494504\pi$
$487$	180713.			0.0345277			0.0172639	+	0.999851i	$0.494504\pi$
$488$	68451.5	+	1.22647e6i	0.0130117	+	0.233135i
$489$	6.05826e6			1.14571
$490$	−4754.87	+	1544.95i	−0.000894641	+	0.000290686i
$491$	−1.89116e6	−	5.82038e6i	−0.354017	−	1.08955i	−0.956577	−	0.291478i	$-0.905853\pi$
$491$	−1.89116e6	−	5.82038e6i	−0.354017	−	1.08955i	0.602561	−	0.798073i	$-0.294147\pi$
$492$	−752745.	+	546901.i	−0.140196	+	0.101858i
$493$	2.55576e6	−	1.85687e6i	0.473590	−	0.344083i
$494$	−96355.4	−	132622.i	−0.0177647	−	0.0244510i
$495$	−186032.	−	60445.3i	−0.0341251	−	0.0110879i
$496$	4.43807e6	−	6.10848e6i	0.810009	−	1.11488i
$497$	5.47857e6	−	3.98041e6i	0.994892	−	0.722832i
$498$	−52394.8	+	72115.3i	−0.00946706	+	0.0130303i
$499$			3.53688e6i			0.635871i	0.948112	+	0.317935i	$0.102990\pi$
$499$			3.53688e6i			0.635871i	−0.948112	+	0.317935i	$0.897010\pi$
$500$	869814.	+	631957.i	0.155597	+	0.113048i
$501$	1.93859e6			0.345058
$502$	220018.			0.0389673
$503$	2.65028e6	+	1.92554e6i	0.467059	+	0.339338i	0.796294	−	0.604910i	$-0.206791\pi$
$503$	2.65028e6	+	1.92554e6i	0.467059	+	0.339338i	−0.329235	+	0.944248i	$0.606791\pi$
$504$	757811.	−	2.33230e6i	0.132888	−	0.408986i
$505$	402535.	+	554041.i	0.0702384	+	0.0966749i
$506$	−44869.1	+	61757.0i	−0.00779061	+	0.0107228i
$507$	−757116.	−	2.33016e6i	−0.130810	−	0.402593i
$508$	−1.72182e6	+	5.29921e6i	−0.296025	+	0.911070i
$509$			8.75831e6i			1.49839i	0.662348	+	0.749197i	$0.269560\pi$
$509$			8.75831e6i			1.49839i	−0.662348	+	0.749197i	$0.730440\pi$
$510$	17278.6	+	53178.0i	0.00294160	+	0.00905330i
$511$	1.22185e6	+	1.68174e6i	0.206998	+	0.284909i
$512$	−3.13533e6	−	1.01873e6i	−0.528578	−	0.171745i
$513$	703602.	−	2.16546e6i	0.118041	−	0.363294i
$514$	1.07336e6	−	348756.i	0.179200	−	0.0582257i
$515$	−20577.7	−	14950.5i	−0.00341883	−	0.00248393i
$516$	3.59481e6	−	1.16802e6i	0.594363	−	0.193120i
$517$		−	1.45360e6i		−	0.239177i
$518$	682159.	+	221647.i	0.111702	+	0.0362942i
$519$	5.55977e6	+	1.80648e6i	0.906021	+	0.294384i
$520$			121820.i			0.0197565i
$521$	2.32294e6	−	754767.i	0.374924	−	0.121820i	−0.115493	−	0.993308i	$-0.536845\pi$
$521$	2.32294e6	−	754767.i	0.374924	−	0.121820i	0.490416	+	0.871488i	$0.336845\pi$
$522$	−1.23632e6	−	898239.i	−0.198589	−	0.144283i
$523$	2.43692e6	−	791802.i	0.389571	−	0.126579i	−0.107681	−	0.994186i	$-0.534343\pi$
$523$	2.43692e6	−	791802.i	0.389571	−	0.126579i	0.497252	+	0.867606i	$0.334343\pi$
$524$	−2.79635e6	+	8.60628e6i	−0.444901	+	1.36926i
$525$	−1.02983e7	−	3.34612e6i	−1.63067	−	0.529838i
$526$	756986.	+	1.04190e6i	0.119295	+	0.164196i
$527$	−1.40595e6	−	4.32707e6i	−0.220518	−	0.678683i
$528$		−	2.11413e6i		−	0.330024i
$529$	1.39778e6	−	4.30192e6i	0.217169	−	0.668379i
$530$	−39003.9	−	120042.i	−0.00603141	−	0.0185628i
$531$	8.59326e6	−	1.18276e7i	1.32258	−	1.82037i
$532$	−1.17164e6	−	1.61263e6i	−0.179480	−	0.247033i
$533$	−184756.	+	568620.i	−0.0281696	+	0.0866971i
$534$	986214.	+	716526.i	0.149664	+	0.108737i
$535$	−636135.			−0.0960870
$536$	130296.			0.0195894
$537$	9.16687e6	+	6.66012e6i	1.37178	+	0.996659i
$538$			1.22542e6i			0.182527i
$539$	66952.7	−	92152.4i	0.00992650	−	0.0136626i
$540$	−679675.	+	493813.i	−0.100304	+	0.0728749i
$541$	−3.87289e6	+	5.33058e6i	−0.568908	+	0.783035i	−0.992425	−	0.122853i	$-0.960796\pi$
$541$	−3.87289e6	+	5.33058e6i	−0.568908	+	0.783035i	0.423517	+	0.905888i	$0.360796\pi$
$542$	802769.	+	260836.i	0.117380	+	0.0381389i
$543$	−3.02440e6	−	4.16273e6i	−0.440189	−	0.605869i
$544$	−959789.	+	697328.i	−0.139052	+	0.101028i
$545$	276240.	−	200700.i	0.0398379	−	0.0289439i
$546$	−378319.	−	1.16435e6i	−0.0543096	−	0.167148i
$547$	−8.69075e6	+	2.82380e6i	−1.24191	+	0.403520i	−0.855014	−	0.518604i	$-0.826452\pi$
$547$	−8.69075e6	+	2.82380e6i	−1.24191	+	0.403520i	−0.386893	+	0.922125i	$0.626452\pi$
$548$	7.43840e6			1.05810
$549$	−3.19567e6	+	1.20904e7i	−0.452513	+	1.71202i
$550$	170815.			0.0240780
$551$	−2.37925e6	+	773065.i	−0.333857	+	0.108477i
$552$	468769.	+	1.44272e6i	0.0654804	+	0.201528i
$553$	−7.91882e6	+	5.75336e6i	−1.10115	+	0.800035i
$554$	−903809.	+	656656.i	−0.125113	+	0.0908999i
$555$	−668263.	−	919786.i	−0.0920906	−	0.126752i
$556$	1.15851e7	+	3.76424e6i	1.58933	+	0.516405i
$557$	2.24027e6	−	3.08346e6i	0.305958	−	0.421115i	−0.628157	−	0.778086i	$-0.716191\pi$
$557$	2.24027e6	−	3.08346e6i	0.305958	−	0.421115i	0.934115	+	0.356971i	$0.116191\pi$
$558$	−1.78056e6	+	1.29365e6i	−0.242087	+	0.175886i
$559$	1.42762e6	−	1.96496e6i	0.193234	−	0.265964i
$560$			725036.i			0.0976989i
$561$	−1.03062e6	−	748792.i	−0.138259	−	0.100451i
$562$	104949.			0.0140164
$563$	4.91911e6			0.654057			0.327028	−	0.945015i	$-0.393953\pi$
$563$	4.91911e6			0.654057			0.327028	+	0.945015i	$0.393953\pi$
$564$	−1.16035e7	−	8.43044e6i	−1.53600	−	1.11597i
$565$	−385150.	+	1.18537e6i	−0.0507585	+	0.156218i
$566$	143276.	+	197202.i	0.0187989	+	0.0258744i
$567$	1.70801e6	−	2.35087e6i	0.223116	−	0.307093i
$568$	656006.	+	2.01898e6i	0.0853173	+	0.262580i
$569$	288844.	−	888969.i	0.0374009	−	0.115108i	−0.930613	−	0.366005i	$-0.880725\pi$
$569$	288844.	−	888969.i	0.0374009	−	0.115108i	0.968014	+	0.250897i	$0.0807254\pi$
$570$		−	44279.0i		−	0.00570835i
$571$	3.09724e6	+	9.53232e6i	0.397543	+	1.22351i	0.926963	+	0.375152i	$0.122410\pi$
$571$	3.09724e6	+	9.53232e6i	0.397543	+	1.22351i	−0.529420	+	0.848360i	$0.677590\pi$
$572$	−810011.	−	1.11489e6i	−0.103514	−	0.142475i
$573$	1.22790e7	+	3.98969e6i	1.56234	+	0.507636i
$574$	31484.0	−	96897.8i	0.00398850	−	0.0122754i
$575$	4.07126e6	−	1.32283e6i	0.513522	−	0.166854i
$576$	−1.04723e7	−	7.60860e6i	−1.31519	−	0.955540i
$577$	6.12470e6	−	1.99003e6i	0.765852	−	0.248840i	0.100064	−	0.994981i	$-0.468095\pi$
$577$	6.12470e6	−	1.99003e6i	0.765852	−	0.248840i	0.665788	+	0.746141i	$0.268095\pi$
$578$		−	711511.i		−	0.0885854i
$579$	2.93839e6	+	954739.i	0.364261	+	0.118355i
$580$	877887.	+	285243.i	0.108360	+	0.0352083i
$581$			696490.i			0.0856002i
$582$	−3.01916e6	+	980985.i	−0.369470	+	0.120048i
$583$	2.32648e6	+	1.69029e6i	0.283484	+	0.205963i
$584$	−619758.	+	201372.i	−0.0751952	+	0.0244324i
$585$	−383243.	+	1.17950e6i	−0.0463003	+	0.142498i
$586$	−1.76761e6	−	574333.i	−0.212639	−	0.0690907i
$587$	−2.30981e6	−	3.17918e6i	−0.276682	−	0.380820i	0.647949	−	0.761683i	$-0.275627\pi$
$587$	−2.30981e6	−	3.17918e6i	−0.276682	−	0.380820i	−0.924631	+	0.380863i	$0.875627\pi$
$588$	−347310.	−	1.06891e6i	−0.0414260	−	0.127496i
$589$			3.60296e6i			0.427928i
$590$	38243.1	−	117700.i	0.00452296	−	0.0139202i
$591$	3.88127e6	+	1.19453e7i	0.457093	+	1.40679i
$592$	4.61598e6	−	6.35335e6i	0.541327	−	0.745073i
$593$	−4.99593e6	−	6.87631e6i	−0.583418	−	0.803006i	0.410647	−	0.911794i	$-0.365303\pi$
$593$	−4.99593e6	−	6.87631e6i	−0.583418	−	0.803006i	−0.994065	+	0.108789i	$0.965303\pi$
$594$	−82892.3	+	255116.i	−0.00963936	+	0.0296669i
$595$	353451.	+	256797.i	0.0409295	+	0.0297370i
$596$	2.35968e6			0.272105
$597$	−950656.			−0.109166
$598$	391559.	+	284484.i	0.0447759	+	0.0325316i
$599$		−	3.43074e6i		−	0.390680i	−0.980736	−	0.195340i	$-0.937419\pi$
$599$		−	3.43074e6i		−	0.390680i	0.980736	−	0.195340i	$-0.0625810\pi$
$600$	1.99523e6	−	2.74620e6i	0.226264	−	0.311426i
$601$	−7.53643e6	+	5.47554e6i	−0.851098	+	0.618359i	−0.925449	−	0.378873i	$-0.876312\pi$
$601$	−7.53643e6	+	5.47554e6i	−0.851098	+	0.618359i	0.0743503	+	0.997232i	$0.476312\pi$
$602$	−243279.	+	334845.i	−0.0273599	+	0.0376576i
$603$	1.26157e6	+	409909.i	0.141292	+	0.0459086i
$604$	−9.08035e6	−	1.24980e7i	−1.01277	−	1.39396i
$605$	−683144.	+	496333.i	−0.0758793	+	0.0551296i
$606$	1.74548e6	−	1.26817e6i	0.193079	−	0.140280i
$607$	−653742.	−	2.01201e6i	−0.0720170	−	0.221645i	0.908569	−	0.417735i	$-0.137176\pi$
$607$	−653742.	−	2.01201e6i	−0.0720170	−	0.221645i	−0.980586	+	0.196089i	$0.937176\pi$
$608$	893504.	−	290317.i	0.0980252	−	0.0318503i
$609$	−1.86833e7			−2.04131
$610$	5899.11	+	105696.i	0.000641892	+	0.0115010i
$611$	−9.21631e6			−0.998744
$612$	−7.64012e6	+	2.48242e6i	−0.824559	+	0.267915i
$613$	−3.90861e6	−	1.20295e7i	−0.420118	−	1.29299i	−0.907592	−	0.419852i	$-0.862082\pi$
$613$	−3.90861e6	−	1.20295e7i	−0.420118	−	1.29299i	0.487475	−	0.873137i	$-0.337918\pi$
$614$	−211434.	+	153615.i	−0.0226336	+	0.0164443i
$615$	−130652.	+	94923.9i	−0.0139292	+	0.0101202i
$616$	278000.	+	382634.i	0.0295184	+	0.0406286i
$617$	5.74648e6	+	1.86714e6i	0.607700	+	0.197454i	0.596671	−	0.802486i	$-0.296490\pi$
$617$	5.74648e6	+	1.86714e6i	0.607700	+	0.197454i	0.0110282	+	0.999939i	$0.496490\pi$
$618$	−47101.0	+	64829.0i	−0.00496089	+	0.00682808i
$619$	1.17343e6	−	852546.i	0.123092	−	0.0894316i	−0.524536	−	0.851388i	$-0.675761\pi$
$619$	1.17343e6	−	852546.i	0.123092	−	0.0894316i	0.647628	+	0.761957i	$0.275761\pi$
$620$	781406.	−	1.07551e6i	0.0816390	−	0.112366i
$621$			6.72245e6i			0.699517i
$622$	−1.14620e6	−	832761.i	−0.118791	−	0.0863067i
$623$	9.52487e6			0.983193
$624$	−1.34042e7			−1.37810
$625$	−7.67374e6	−	5.57530e6i	−0.785791	−	0.570910i
$626$	254748.	−	784035.i	0.0259822	−	0.0799649i
$627$	592971.	+	816154.i	0.0602371	+	0.0829093i
$628$	−1.43160e6	+	1.97043e6i	−0.144852	+	0.199371i
$629$	−1.46231e6	−	4.50053e6i	−0.147371	−	0.453562i
$630$	65307.8	−	200997.i	0.00655562	−	0.0201761i
$631$		−	6.06287e6i		−	0.606185i	−0.952961	−	0.303092i	$-0.901981\pi$
$631$		−	6.06287e6i		−	0.606185i	0.952961	−	0.303092i	$-0.0980191\pi$
$632$	−948203.	−	2.91827e6i	−0.0944297	−	0.290625i
$633$	5.51977e6	+	7.59731e6i	0.547535	+	0.753617i
$634$	−1.81945e6	−	591176.i	−0.179770	−	0.0584108i
$635$	−298850.	+	919767.i	−0.0294117	+	0.0905198i
$636$	2.69857e7	−	8.76819e6i	2.64540	−	0.859542i
$637$	−584276.	−	424501.i	−0.0570518	−	0.0414505i
$638$	280303.	−	91075.8i	0.0272631	−	0.00885832i
$639$			2.16122e7i			2.09385i
$640$	−438516.	−	142482.i	−0.0423190	−	0.0137503i
$641$	−8.62562e6	−	2.80263e6i	−0.829173	−	0.269415i	−0.136476	−	0.990643i	$-0.543578\pi$
$641$	−8.62562e6	−	2.80263e6i	−0.829173	−	0.269415i	−0.692697	+	0.721229i	$0.743578\pi$
$642$			2.00412e6i			0.191904i
$643$	8.27792e6	−	2.68966e6i	0.789576	−	0.256549i	0.113652	−	0.993521i	$-0.463745\pi$
$643$	8.27792e6	−	2.68966e6i	0.789576	−	0.256549i	0.675924	+	0.736972i	$0.263745\pi$
$644$	4.76121e6	+	3.45922e6i	0.452379	+	0.328673i
$645$	623939.	−	202730.i	0.0590531	−	0.0191875i
$646$	56951.9	−	175280.i	0.00536942	−	0.0165254i
$647$	−1.69946e7	−	5.52188e6i	−1.59606	−	0.518592i	−0.629933	−	0.776649i	$-0.716918\pi$
$647$	−1.69946e7	−	5.52188e6i	−1.59606	−	0.518592i	−0.966130	+	0.258057i	$0.916918\pi$
$648$	535433.	+	736960.i	0.0500919	+	0.0689456i
$649$	871303.	+	2.68160e6i	0.0812003	+	0.249909i
$650$		−	1.08302e6i		−	0.100544i
$651$	−8.31496e6	+	2.55908e7i	−0.768967	+	2.36664i
$652$	2.27682e6	+	7.00734e6i	0.209754	+	0.645556i
$653$	2.39727e6	−	3.29955e6i	0.220005	−	0.302811i	−0.684720	−	0.728806i	$-0.740076\pi$
$653$	2.39727e6	−	3.29955e6i	0.220005	−	0.302811i	0.904726	+	0.425994i	$0.140076\pi$
$654$	−632298.	−	870283.i	−0.0578066	−	0.0795640i
$655$	−485354.	+	1.49376e6i	−0.0442033	+	0.136044i
$656$	−902466.	−	655680.i	−0.0818788	−	0.0594884i
$657$	−6.63421e6			−0.599619
$658$	1.57054e6			0.141411
$659$	−1.49579e7	−	1.08675e7i	−1.34171	−	0.974806i	−0.999379	−	0.0352244i	$-0.988785\pi$
$659$	−1.49579e7	−	1.08675e7i	−1.34171	−	0.974806i	−0.342326	−	0.939581i	$-0.611215\pi$
$660$		−	372232.i		−	0.0332624i
$661$	−7.47735e6	+	1.02917e7i	−0.665647	+	0.916185i	−0.999652	−	0.0263867i	$-0.991600\pi$
$661$	−7.47735e6	+	1.02917e7i	−0.665647	+	0.916185i	0.334005	+	0.942571i	$0.391600\pi$
$662$	−1.13563e6	+	825081.i	−0.100714	+	0.0731731i
$663$	−4.74758e6	+	6.53448e6i	−0.419458	+	0.577334i
$664$	−207653.	−	67470.4i	−0.0182775	−	0.00593873i
$665$	−203358.	−	279899.i	−0.0178323	−	0.0245441i
$666$	−1.85194e6	+	1.34551e6i	−0.161786	+	0.117544i
$667$	5.97550e6	−	4.34145e6i	0.520067	−	0.377851i
$668$	728564.	+	2.24229e6i	0.0631722	+	0.194424i
$669$	−1.70522e7	+	5.54061e6i	−1.47305	+	0.478621i
$670$	11228.9			0.000966383
$671$	−1.52419e6	−	1.86921e6i	−0.130687	−	0.160269i
$672$	7.01631e6			0.599357
$673$	2.39848e6	−	779313.i	0.204126	−	0.0663245i	−0.205169	−	0.978726i	$-0.565775\pi$
$673$	2.39848e6	−	779313.i	0.204126	−	0.0663245i	0.409295	+	0.912402i	$0.365775\pi$
$674$	−291610.	−	897482.i	−0.0247259	−	0.0760985i
$675$	1.21698e7	−	8.84187e6i	1.02807	−	0.746938i
$676$	2.41066e6	−	1.75145e6i	0.202894	−	0.147411i
$677$	5.66043e6	+	7.79092e6i	0.474655	+	0.653306i	0.977467	−	0.211090i	$-0.0677012\pi$
$677$	5.66043e6	+	7.79092e6i	0.474655	+	0.653306i	−0.502812	+	0.864396i	$0.667701\pi$
$678$	3.73445e6	+	1.21340e6i	0.311999	+	0.101375i
$679$	−1.45796e7	+	2.00670e7i	−1.21358	+	1.67035i
$680$	−110801.	+	80501.9i	−0.00918910	+	0.00667627i
$681$	−1.32139e7	+	1.81874e7i	−1.09185	+	1.50280i
$682$		−	424469.i		−	0.0349450i
$683$	5.91158e6	+	4.29501e6i	0.484899	+	0.352300i	0.803219	−	0.595683i	$-0.203119\pi$
$683$	5.91158e6	+	4.29501e6i	0.484899	+	0.352300i	−0.318320	+	0.947983i	$0.603119\pi$
$684$	6.36159e6			0.519907
$685$	1.29106e6			0.105128
$686$	−1.11964e6	−	813468.i	−0.0908383	−	0.0659979i
$687$	6.84910e6	−	2.10794e7i	0.553658	−	1.70399i
$688$	2.66361e6	+	3.66615e6i	0.214536	+	0.295283i
$689$	1.07170e7	−	1.47506e7i	0.860051	−	1.18376i
$690$	40398.3	+	124333.i	0.00323028	+	0.00994178i
$691$	3.54361e6	−	1.09061e7i	0.282326	−	0.868911i	−0.704861	−	0.709345i	$-0.748991\pi$
$691$	3.54361e6	−	1.09061e7i	0.282326	−	0.868911i	0.987187	−	0.159565i	$-0.0510093\pi$
$692$			7.10966e6i			0.564396i
$693$	1.48793e6	+	4.57937e6i	0.117692	+	0.362220i
$694$	716286.	+	985883.i	0.0564531	+	0.0777010i
$695$	2.01080e6	+	653347.i	0.157909	+	0.0513076i
$696$	1.80988e6	−	5.57025e6i	0.141621	−	0.435865i
$697$	−639280.	+	207715.i	−0.0498436	+	0.0161952i
$698$	2.19590e6	+	1.59541e6i	0.170598	+	0.123947i
$699$	3.04913e7	−	9.90722e6i	2.36039	−	0.766936i
$700$		−	1.31691e7i		−	1.01581i
$701$	6.69835e6	+	2.17643e6i	0.514841	+	0.167282i	0.554903	−	0.831915i	$-0.312756\pi$
$701$	6.69835e6	+	2.17643e6i	0.514841	+	0.167282i	−0.0400619	+	0.999197i	$0.512756\pi$
$702$	1.61752e6	+	525563.i	0.123881	+	0.0402515i
$703$			3.74739e6i			0.285983i
$704$	2.37433e6	−	771465.i	0.180555	−	0.0586658i
$705$	−2.01398e6	−	1.46324e6i	−0.152610	−	0.110878i
$706$	−60172.2	+	19551.1i	−0.00454343	+	0.00147625i
$707$	5.20938e6	−	1.60328e7i	0.391956	−	1.20632i
$708$	2.64593e7	+	8.59715e6i	1.98379	+	0.644572i
$709$	−2.31432e6	−	3.18538e6i	−0.172905	−	0.237983i	0.713766	−	0.700384i	$-0.246988\pi$
$709$	−2.31432e6	−	3.18538e6i	−0.172905	−	0.237983i	−0.886671	+	0.462401i	$0.846988\pi$
$710$	56534.3	+	173995.i	0.00420887	+	0.0129536i
$711$		−	3.12386e7i		−	2.31749i
$712$	−922693.	+	2.83976e6i	−0.0682114	+	0.209933i
$713$	−3.28719e6	−	1.01169e7i	−0.242159	−	0.745288i
$714$	809028.	−	1.11353e6i	0.0593906	−	0.0817442i
$715$	−140591.	−	193507.i	−0.0102847	−	0.0141557i
$716$	−4.25838e6	+	1.31060e7i	−0.310429	+	0.955402i
$717$	2.05639e7	+	1.49406e7i	1.49385	+	1.08535i
$718$	725534.			0.0525226
$719$	2.41157e6			0.173971			0.0869855	−	0.996210i	$-0.472277\pi$
$719$	2.41157e6			0.173971			0.0869855	+	0.996210i	$0.472277\pi$
$720$	−1.87200e6	−	1.36009e6i	−0.134578	−	0.0977768i
$721$			626120.i			0.0448559i
$722$	882103.	−	1.21411e6i	0.0629762	−	0.0866793i
$723$	−1.38919e7	+	1.00931e7i	−0.988363	+	0.718088i
$724$	3.67822e6	−	5.06264e6i	0.260790	−	0.358947i
$725$	−1.57189e7	−	5.10736e6i	−1.11065	−	0.360871i
$726$	1.56367e6	+	2.15221e6i	0.110104	+	0.151546i
$727$	−1.29778e6	+	942891.i	−0.0910677	+	0.0661646i	−0.632387	−	0.774652i	$-0.717925\pi$
$727$	−1.29778e6	+	942891.i	−0.0910677	+	0.0661646i	0.541320	+	0.840817i	$0.317925\pi$
$728$	2.42602e6	−	1.76261e6i	0.169655	−	0.123262i
$729$	−6.60447e6	−	2.03265e7i	−0.460277	−	1.41659i
$730$	−53410.5	+	17354.1i	−0.00370953	+	0.00120530i
$731$	2.73064e6			0.189004
$732$	−2.37609e7	+	1.32614e6i	−1.63902	+	0.0914768i
$733$	1.28047e7			0.880260			0.440130	−	0.897934i	$-0.354932\pi$
$733$	1.28047e7			0.880260			0.440130	+	0.897934i	$0.354932\pi$
$734$	−2.45047e6	+	796206.i	−0.167884	+	0.0545488i
$735$	−60281.4	−	185527.i	−0.00411590	−	0.0126674i
$736$	−2.24404e6	+	1.63039e6i	−0.152699	+	0.110942i
$737$	−206971.	+	150374.i	−0.0140359	+	0.0101977i
$738$	191124.	+	263059.i	0.0129174	+	0.0177792i
$739$	−9.94685e6	−	3.23193e6i	−0.669999	−	0.217696i	−0.0457876	−	0.998951i	$-0.514580\pi$
$739$	−9.94685e6	−	3.23193e6i	−0.669999	−	0.217696i	−0.624212	+	0.781255i	$0.714580\pi$
$740$	812730.	−	1.11863e6i	0.0545591	−	0.0750941i
$741$	5.17468e6	−	3.75962e6i	0.346208	−	0.251535i
$742$	−1.82626e6	+	2.51364e6i	−0.121774	+	0.167607i
$743$		−	6.18851e6i		−	0.411258i	−0.978630	−	0.205629i	$-0.934076\pi$
$743$		−	6.18851e6i		−	0.411258i	0.978630	−	0.205629i	$-0.0659240\pi$
$744$	−6.82420e6	−	4.95807e6i	−0.451980	−	0.328383i
$745$	409561.			0.0270351
$746$	1.74937e6			0.115089
$747$	−1.79830e6	−	1.30654e6i	−0.117913	−	0.0856685i
$748$	478766.	−	1.47349e6i	0.0312874	−	0.0962928i
$749$	9.20422e6	+	1.26685e7i	0.599490	+	0.825128i
$750$	345563.	−	475627.i	0.0224323	−	0.0308754i
$751$	−8.90900e6	−	2.74191e7i	−0.576407	−	1.77400i	−0.631339	−	0.775507i	$-0.717494\pi$
$751$	−8.90900e6	−	2.74191e7i	−0.576407	−	1.77400i	0.0549322	−	0.998490i	$-0.482506\pi$
$752$	5.31369e6	−	1.63539e7i	0.342651	−	1.05457i
$753$			8.58475e6i			0.551747i
$754$	−577450.	−	1.77721e6i	−0.0369901	−	0.113844i
$755$	−1.57605e6	−	2.16924e6i	−0.100624	−	0.138497i
$756$	1.96684e7	+	6.39065e6i	1.25160	+	0.406668i
$757$	−5.50305e6	+	1.69366e7i	−0.349031	+	1.07421i	0.610360	+	0.792124i	$0.291025\pi$
$757$	−5.50305e6	+	1.69366e7i	−0.349031	+	1.07421i	−0.959390	+	0.282081i	$0.908975\pi$
$758$	1.43206e6	−	465304.i	0.0905291	−	0.0294147i
$759$	−2.40965e6	−	1.75072e6i	−0.151827	−	0.110309i
$760$	103149.	−	33515.2i	0.00647786	−	0.00210478i
$761$			1.08099e7i			0.676646i	0.941030	+	0.338323i	$0.109860\pi$
$761$			1.08099e7i			0.676646i	−0.941030	+	0.338323i	$0.890140\pi$
$762$	2.89769e6	+	941515.i	0.180786	+	0.0587408i
$763$	−7.99383e6	−	2.59735e6i	−0.497100	−	0.161517i
$764$			1.57020e7i			0.973244i
$765$	−1.32607e6	+	430866.i	−0.0819244	+	0.0266188i
$766$	−2.52948e6	−	1.83777e6i	−0.155761	−	0.113167i
$767$	1.70022e7	−	5.52434e6i	1.04356	−	0.339072i
$768$	7.26984e6	−	2.23743e7i	0.444756	−	1.36882i
$769$	1.66045e7	+	5.39514e6i	1.01254	+	0.328993i	0.767864	−	0.640613i	$-0.221320\pi$
$769$	1.66045e7	+	5.39514e6i	1.01254	+	0.328993i	0.244672	+	0.969606i	$0.421320\pi$
$770$	23957.9	+	32975.2i	0.00145620	+	0.00200429i
$771$	1.36079e7	+	4.18808e7i	0.824432	+	2.53734i
$772$			3.75752e6i			0.226912i
$773$	7.15055e6	−	2.20071e7i	0.430418	−	1.32469i	−0.467291	−	0.884104i	$-0.654770\pi$
$773$	7.15055e6	−	2.20071e7i	0.430418	−	1.32469i	0.897709	−	0.440588i	$-0.145230\pi$
$774$	−408186.	−	1.25627e6i	−0.0244909	−	0.0753753i
$775$	−1.39913e7	+	1.92574e7i	−0.836767	+	1.15171i
$776$	−4.57046e6	−	6.29070e6i	−0.272462	−	0.375012i
$777$	−8.64829e6	+	2.66167e7i	−0.513899	+	1.58162i
$778$	−1.50656e6	−	1.09458e6i	−0.0892352	−	0.0648332i
$779$	532301.			0.0314277
$780$	−2.36007e6			−0.138895
$781$	−3.37212e6	−	2.44999e6i	−0.197823	−	0.143727i
$782$			544138.i			0.0318194i
$783$	1.52559e7	−	2.09980e7i	0.889270	−	1.22397i
$784$	1.09012e6	−	792020.i	0.0633410	−	0.0460199i
$785$	−248478.	+	342001.i	−0.0143918	+	0.0198086i
$786$	4.70604e6	+	1.52908e6i	0.271706	+	0.0882826i
$787$	1.85088e7	+	2.54752e7i	1.06523	+	1.46616i	0.874817	+	0.484453i	$0.160981\pi$
$787$	1.85088e7	+	2.54752e7i	1.06523	+	1.46616i	0.190409	+	0.981705i	$0.439019\pi$
$788$	−1.23580e7	+	8.97860e6i	−0.708977	+	0.515102i
$789$	−4.06533e7	+	2.95363e7i	−2.32489	+	1.68913i
$790$	−81715.7	−	251495.i	−0.00465841	−	0.0143371i
$791$	2.91791e7	−	9.48087e6i	1.65818	−	0.538775i
$792$	−1.50944e6			−0.0855071
$793$	−1.18514e7	+	9.66383e6i	−0.669245	+	0.545715i
$794$	1.90710e6			0.107355
$795$	4.68382e6	−	1.52187e6i	0.262835	−	0.0854002i
$796$	−357277.	−	1.09958e6i	−0.0199858	−	0.0615100i
$797$	2.58307e7	−	1.87671e7i	1.44042	−	1.04653i	0.452471	−	0.891779i	$-0.350543\pi$
$797$	2.58307e7	−	1.87671e7i	1.44042	−	1.04653i	0.987954	−	0.154750i	$-0.0494574\pi$
$798$	−881809.	+	640672.i	−0.0490193	+	0.0356146i
$799$	−6.09038e6	−	8.38269e6i	−0.337503	−	0.464533i
$800$	5.90306e6	+	1.91802e6i	0.326101	+	0.105957i
$801$	−1.78676e7	+	2.45927e7i	−0.983978	+	1.35433i
$802$	−368210.	+	267520.i	−0.0202143	+	0.0146866i
$803$	752065.	−	1.03513e6i	0.0411592	−	0.0566507i
$804$			2.52428e6i			0.137720i
$805$	826387.	+	600406.i	0.0449463	+	0.0326554i
$806$	−2.69127e6			−0.145922
$807$	−4.78136e7			−2.58445
$808$	4.27540e6	+	3.10626e6i	0.230382	+	0.167382i
$809$	−773837.	+	2.38163e6i	−0.0415698	+	0.127939i	−0.969688	−	0.244348i	$-0.921426\pi$
$809$	−773837.	+	2.38163e6i	−0.0415698	+	0.127939i	0.928118	+	0.372287i	$0.121426\pi$
$810$	46143.4	+	63510.9i	0.00247114	+	0.00340123i
$811$	−1.54314e7	+	2.12395e7i	−0.823860	+	1.13395i	0.165175	+	0.986264i	$0.447181\pi$
$811$	−1.54314e7	+	2.12395e7i	−0.823860	+	1.13395i	−0.989035	+	0.147682i	$0.952819\pi$
$812$	−7.02156e6	−	2.16101e7i	−0.373718	−	1.15018i
$813$	−1.01774e7	+	3.13227e7i	−0.540019	+	1.66201i
$814$		−	441485.i		−	0.0233537i
$815$	395181.	+	1.21624e6i	0.0208402	+	0.0641395i
$816$	−8.85787e6	−	1.21918e7i	−0.465698	−	0.640978i
$817$	−2.05656e6	−	668218.i	−0.107792	−	0.0350238i
$818$	126207.	−	388426.i	0.00659479	−	0.0202967i
$819$	2.90346e7	−	9.43393e6i	1.51254	−	0.491454i
$820$	−158896.	−	115445.i	−0.00825237	−	0.00599570i
$821$	1.69000e7	−	5.49115e6i	0.875044	−	0.284319i	0.163146	−	0.986602i	$-0.447836\pi$
$821$	1.69000e7	−	5.49115e6i	0.875044	−	0.284319i	0.711898	+	0.702283i	$0.247836\pi$
$822$		−	4.06743e6i		−	0.209962i
$823$	−7.57594e6	−	2.46157e6i	−0.389885	−	0.126681i	0.107513	−	0.994204i	$-0.465711\pi$
$823$	−7.57594e6	−	2.46157e6i	−0.389885	−	0.126681i	−0.497398	+	0.867522i	$0.665711\pi$
$824$	−186672.	−	60653.5i	−0.00957771	−	0.00311199i
$825$			6.66493e6i			0.340926i
$826$	−2.89732e6	+	941395.i	−0.147756	+	0.0480089i
$827$	−1.27465e7	−	9.26084e6i	−0.648076	−	0.470855i	0.214539	−	0.976715i	$-0.431175\pi$
$827$	−1.27465e7	−	9.26084e6i	−0.648076	−	0.470855i	−0.862615	+	0.505861i	$0.831175\pi$
$828$	−1.78630e7	+	5.80404e6i	−0.905480	+	0.294208i
$829$	1.10063e7	−	3.38740e7i	0.556232	−	1.71191i	−0.136434	−	0.990649i	$-0.543564\pi$
$829$	1.10063e7	−	3.38740e7i	0.556232	−	1.71191i	0.692666	−	0.721258i	$-0.256436\pi$
$830$	−17895.4	−	5814.57i	−0.000901667	−	0.000292969i
$831$	−2.56216e7	−	3.52651e7i	−1.28707	−	1.77151i
$832$	−4.89133e6	−	1.50540e7i	−0.244973	−	0.753951i
$833$		−	811950.i		−	0.0405431i
$834$	2.05834e6	−	6.33492e6i	0.102471	−	0.315374i
$835$	126454.	+	389187.i	0.00627650	+	0.0193171i
$836$	−721161.	+	992592.i	−0.0356875	+	0.0491196i
$837$	−2.19717e7	−	3.02414e7i	−1.08405	−	1.49207i
$838$	−1.15238e6	+	3.54667e6i	−0.0566874	+	0.174466i
$839$	−1.26787e7	−	9.21163e6i	−0.621828	−	0.451785i	0.231731	−	0.972780i	$-0.425561\pi$
$839$	−1.26787e7	−	9.21163e6i	−0.621828	−	0.451785i	−0.853560	+	0.520995i	$0.825561\pi$
$840$	809987.			0.0396077
$841$	−8.00614e6			−0.390331
$842$	−1.27665e6	−	927538.i	−0.0620569	−	0.0450870i
$843$			4.09492e6i			0.198461i
$844$	−6.71304e6	+	9.23971e6i	−0.324387	+	0.446480i
$845$	418411.	−	303993.i	0.0201586	−	0.0146461i
$846$	−2.94616e6	+	4.05504e6i	−0.141524	+	0.194791i
$847$	1.97688e7	+	6.42326e6i	0.946828	+	0.307643i
$848$	1.99954e7	+	2.75212e7i	0.954860	+	1.31425i
$849$	−7.69449e6	+	5.59038e6i	−0.366362	+	0.266178i
$850$	985064.	−	715691.i	0.0467646	−	0.0339765i
$851$	−3.41896e6	−	1.05225e7i	−0.161834	−	0.498074i
$852$	−3.91145e7	+	1.27091e7i	−1.84603	+	0.599811i
$853$	3.35878e7			1.58055			0.790277	−	0.612749i	$-0.209936\pi$
$853$	3.35878e7			1.58055			0.790277	+	0.612749i	$0.209936\pi$
$854$	2.01957e6	−	1.64680e6i	0.0947578	−	0.0772673i
$855$	1.10416e6			0.0516555
$856$	−4.66864e6	+	1.51693e6i	−0.217774	+	0.0707590i
$857$	6.24152e6	+	1.92094e7i	0.290294	+	0.893434i	0.984762	+	0.173910i	$0.0556401\pi$
$857$	6.24152e6	+	1.92094e7i	0.290294	+	0.893434i	−0.694467	+	0.719524i	$0.744360\pi$
$858$	−609635.	+	442926.i	−0.0282717	+	0.0205406i
$859$	−8.40041e6	+	6.10325e6i	−0.388434	+	0.282214i	−0.764814	−	0.644252i	$-0.777169\pi$
$859$	−8.40041e6	+	6.10325e6i	−0.388434	+	0.282214i	0.376379	+	0.926466i	$0.377169\pi$
$860$	468979.	+	645494.i	0.0216226	+	0.0297609i
$861$	3.78079e6	+	1.22845e6i	0.173810	+	0.0564742i
$862$	−1.82991e6	+	2.51865e6i	−0.0838806	+	0.115452i
$863$	−4.81410e6	+	3.49765e6i	−0.220033	+	0.159863i	−0.692342	−	0.721570i	$-0.743421\pi$
$863$	−4.81410e6	+	3.49765e6i	−0.220033	+	0.159863i	0.472308	+	0.881433i	$0.343421\pi$
$864$	−5.72921e6	+	7.88557e6i	−0.261102	+	0.359376i
$865$			1.23400e6i			0.0560758i
$866$	1.48217e6	+	1.07686e6i	0.0671590	+	0.0487939i
$867$	2.77620e7			1.25430
$868$	−3.27248e7			−1.47427
$869$	4.87413e6	+	3.54126e6i	0.218951	+	0.159077i
$870$	155975.	−	480042.i	0.00698645	−	0.0215021i
$871$	953416.	+	1.31226e6i	0.0425831	+	0.0586106i
$872$	1.54876e6	−	2.13168e6i	0.0689750	−	0.0949360i
$873$	−2.44623e7	−	7.52871e7i	−1.08633	−	3.34338i
$874$	133157.	−	409814.i	0.00589637	−	0.0181471i
$875$		−	4.59361e6i		−	0.202831i
$876$	−3.90125e6	−	1.20068e7i	−0.171769	−	0.528650i
$877$	1.97603e7	+	2.71977e7i	0.867550	+	1.19408i	0.979716	+	0.200391i	$0.0642212\pi$
$877$	1.97603e7	+	2.71977e7i	0.867550	+	1.19408i	−0.112166	+	0.993690i	$0.535779\pi$
$878$	−2.93884e6	−	954889.i	−0.128659	−	0.0418039i
$879$	2.24095e7	−	6.89693e7i	0.978272	−	3.01081i
$880$	424427.	−	137905.i	0.0184755	−	0.00600305i
$881$	1.58233e7	+	1.14963e7i	0.686841	+	0.499019i	0.875620	−	0.483000i	$-0.160453\pi$
$881$	1.58233e7	+	1.14963e7i	0.686841	+	0.499019i	−0.188779	+	0.982020i	$0.560453\pi$
$882$	−373548.	+	121373.i	−0.0161687	+	0.00525353i
$883$			1.75040e7i			0.755504i	0.925907	+	0.377752i	$0.123303\pi$
$883$			1.75040e7i			0.755504i	−0.925907	+	0.377752i	$0.876697\pi$
$884$	−9.34240e6	−	3.03553e6i	−0.402094	−	0.130648i
$885$	4.59246e6	+	1.49218e6i	0.197100	+	0.0640417i
$886$			2.60119e6i			0.111324i
$887$	−9.70318e6	+	3.15275e6i	−0.414100	+	0.134549i	−0.508655	−	0.860970i	$-0.669857\pi$
$887$	−9.70318e6	+	3.15275e6i	−0.414100	+	0.134549i	0.0945552	+	0.995520i	$0.469857\pi$
$888$	−7.09776e6	−	5.15682e6i	−0.302057	−	0.219457i
$889$	2.26411e7	−	7.35652e6i	0.960821	−	0.312190i
$890$	−79517.2	+	244729.i	−0.00336501	+	0.0103564i
$891$	−1.70104e6	−	552700.i	−0.0717826	−	0.0233236i
$892$	−1.28172e7	−	1.76413e7i	−0.539362	−	0.742368i
$893$	2.53560e6	+	7.80377e6i	0.106402	+	0.327473i
$894$		−	1.29031e6i		−	0.0539944i
$895$	−739114.	+	2.27476e6i	−0.0308428	+	0.0949244i
$896$	3.50736e6	+	1.07945e7i	0.145952	+	0.449194i
$897$	−1.11001e7	+	1.52780e7i	−0.460623	+	0.633993i
$898$	2.89296e6	+	3.98182e6i	0.119716	+	0.164775i
$899$	−1.26916e7	+	3.90607e7i	−0.523741	+	1.61191i
$900$	3.40020e7	+	2.47039e7i	1.39926	+	1.01662i
$901$	2.04985e7			0.841221
$902$	−62711.0			−0.00256642
$903$	−1.30651e7	−	9.49234e6i	−0.533204	−	0.387395i
$904$			9.61794e6i			0.391436i
$905$	638417.	−	878706.i	0.0259109	−	0.0356633i
$906$	−6.83410e6	+	4.96526e6i	−0.276606	+	0.200966i
$907$	−8.05311e6	+	1.10842e7i	−0.325047	+	0.447388i	−0.940000	−	0.341175i	$-0.889175\pi$
$907$	−8.05311e6	+	1.10842e7i	−0.325047	+	0.447388i	0.614953	+	0.788564i	$0.289175\pi$
$908$	−2.60026e7	−	8.44876e6i	−1.04665	−	0.340078i
$909$	3.16236e7	+	4.35261e7i	1.26941	+	1.74719i
$910$	209074.	−	151901.i	0.00836942	−	0.00608074i
$911$	−1.83038e7	+	1.32985e7i	−0.730711	+	0.530892i	−0.889788	−	0.456374i	$-0.849148\pi$
$911$	−1.83038e7	+	1.32985e7i	−0.730711	+	0.530892i	0.159078	+	0.987266i	$0.449148\pi$
$912$	3.68778e6	+	1.13498e7i	0.146818	+	0.451858i
$913$	407716.	−	132475.i	0.0161875	−	0.00525965i
$914$	2.89285e6			0.114541
$915$	−4.12410e6	+	230173.i	−0.162846	+	0.00908871i
$916$	2.69557e7			1.06148
$917$	3.67706e7	−	1.19475e7i	1.44403	−	0.469195i
$918$	590873.	+	1.81852e6i	0.0231413	+	0.0712215i
$919$	2.51669e6	−	1.82848e6i	0.0982971	−	0.0714170i	−0.537551	−	0.843231i	$-0.680650\pi$
$919$	2.51669e6	−	1.82848e6i	0.0982971	−	0.0714170i	0.635848	+	0.771814i	$0.280650\pi$
$920$	−259060.	+	188218.i	−0.0100909	+	0.00733147i
$921$	−5.99382e6	−	8.24978e6i	−0.232838	−	0.320474i
$922$	−2.31310e6	−	751571.i	−0.0896121	−	0.0291167i
$923$	−1.55337e7	+	2.13803e7i	−0.600166	+	0.826058i
$924$	−7.41293e6	+	5.38581e6i	−0.285634	+	0.207525i
$925$	−1.45522e7	+	2.00294e7i	−0.559209	+	0.769685i
$926$			489887.i			0.0187745i
$927$	−1.61660e6	−	1.17453e6i	−0.0617880	−	0.0448916i
$928$	1.07094e7			0.408220
$929$	5.03603e6			0.191447			0.0957236	−	0.995408i	$-0.469483\pi$
$929$	5.03603e6			0.191447			0.0957236	+	0.995408i	$0.469483\pi$
$930$	−588106.	−	427284.i	−0.0222971	−	0.0161998i
$931$	−198693.	+	611515.i	−0.00751293	+	0.0231224i
$932$	2.29185e7	+	3.15447e7i	0.864266	+	1.18956i
$933$	3.24929e7	−	4.47227e7i	1.22204	−	1.68199i
$934$	−519790.	−	1.59975e6i	−0.0194967	−	0.0600047i
$935$	83098.0	−	255749.i	0.00310857	−	0.00956721i
$936$			9.57031e6i			0.357056i
$937$	−6.87709e6	−	2.11655e7i	−0.255891	−	0.787553i	−0.993653	−	0.112491i	$-0.964117\pi$
$937$	−6.87709e6	−	2.11655e7i	−0.255891	−	0.787553i	0.737761	−	0.675062i	$-0.235883\pi$
$938$	−162470.	−	223621.i	−0.00602930	−	0.00829862i
$939$	3.05917e7	+	9.93984e6i	1.13224	+	0.367888i
$940$	935576.	−	2.87941e6i	0.0345350	−	0.106288i
$941$	1.43614e7	−	4.66630e6i	0.528716	−	0.171790i	−0.0324810	−	0.999472i	$-0.510341\pi$
$941$	1.43614e7	−	4.66630e6i	0.528716	−	0.171790i	0.561197	+	0.827682i	$0.310341\pi$
$942$	1.07746e6	+	782820.i	0.0395616	+	0.0287432i
$943$	−1.49467e6	+	485648.i	−0.0547352	+	0.0177845i
$944$			3.33546e7i			1.21822i
$945$	3.41378e6	+	1.10920e6i	0.124353	+	0.0404047i
$946$	242287.	+	78723.7i	0.00880241	+	0.00286008i
$947$		−	1.90897e7i		−	0.691711i	−0.938288	−	0.345856i	$-0.887589\pi$
$947$		−	1.90897e7i		−	0.691711i	0.938288	−	0.345856i	$-0.112411\pi$
$948$	5.65368e7	−	1.83699e7i	2.04320	−	0.663875i
$949$	−6.56304e6	−	4.76833e6i	−0.236559	−	0.171870i
$950$	−917033.	+	297962.i	−0.0329667	+	0.0107115i
$951$	2.30667e7	−	7.09919e7i	0.827054	−	2.54541i
$952$	3.20636e6	+	1.04181e6i	0.114662	+	0.0372560i
$953$	−1.04725e7	−	1.44142e7i	−0.373525	−	0.514113i	0.580330	−	0.814382i	$-0.302924\pi$
$953$	−1.04725e7	−	1.44142e7i	−0.373525	−	0.514113i	−0.953855	+	0.300268i	$0.902924\pi$
$954$	−3.06419e6	−	9.43061e6i	−0.109005	−	0.335482i
$955$			2.72535e6i			0.0966971i
$956$	−9.55278e6	+	2.94004e7i	−0.338053	+	1.04042i
$957$	3.55362e6	+	1.09369e7i	0.125427	+	0.386025i
$958$	3.26117e6	−	4.48861e6i	0.114805	−	0.158015i
$959$	−1.86803e7	−	2.57112e7i	−0.655899	−	0.902768i
$960$	1.32120e6	−	4.06623e6i	0.0462690	−	0.142401i
$961$	2.46924e7	+	1.79401e7i	0.862491	+	0.626636i
$962$	−2.79915e6			−0.0975190
$963$	−4.99755e7			−1.73657
$964$	−1.68951e7	−	1.22750e7i	−0.585556	−	0.425431i
$965$			652181.i			0.0225450i
$966$	1.89155e6	−	2.60350e6i	0.0652192	−	0.0897665i
$967$	2.36170e7	−	1.71588e7i	0.812192	−	0.590092i	−0.102274	−	0.994756i	$-0.532612\pi$
$967$	2.36170e7	−	1.71588e7i	0.812192	−	0.590092i	0.914465	+	0.404665i	$0.132612\pi$
$968$	−3.83008e6	+	5.27165e6i	−0.131377	+	0.180825i
$969$	6.83913e6	+	2.22217e6i	0.233987	+	0.0760269i
$970$	−393880.	−	542130.i	−0.0134411	−	0.0185001i
$971$	−3.95003e7	+	2.86987e7i	−1.34447	+	0.976818i	−0.345208	+	0.938526i	$0.612192\pi$
$971$	−3.95003e7	+	2.86987e7i	−1.34447	+	0.976818i	−0.999267	+	0.0382916i	$0.987808\pi$
$972$	1.58759e7	−	1.15345e7i	0.538979	−	0.391592i
$973$	−1.60828e7	−	4.94979e7i	−0.544604	−	1.67612i
$974$	114297.	−	37137.4i	0.00386045	−	0.00125434i
$975$	4.22577e7			1.42362
$976$	−1.03150e7	−	2.66013e7i	−0.346614	−	0.893879i
$977$	−2.31454e7			−0.775761			−0.387880	−	0.921710i	$-0.626793\pi$
$977$	−2.31454e7			−0.775761			−0.387880	+	0.921710i	$0.626793\pi$
$978$	3.83171e6	−	1.24500e6i	0.128099	−	0.0416219i
$979$	−1.81166e6	−	5.57573e6i	−0.0604117	−	0.185928i
$980$	191936.	−	139450.i	0.00638399	−	0.00463824i
$981$	2.17018e7	−	1.57673e7i	0.719983	−	0.523099i
$982$	−2.39223e6	−	3.29262e6i	−0.0791633	−	0.108959i
$983$	−1.80142e7	−	5.85316e6i	−0.594608	−	0.193200i	−0.00377369	−	0.999993i	$-0.501201\pi$
$983$	−1.80142e7	−	5.85316e6i	−0.594608	−	0.193200i	−0.590834	+	0.806793i	$0.701201\pi$
$984$	−732505.	+	1.00821e6i	−0.0241170	+	0.0331942i
$985$	−2.14493e6	+	1.55839e6i	−0.0704407	+	0.0511782i
$986$	1.23486e6	−	1.69964e6i	0.0404508	−	0.0556757i
$987$			6.12797e7i			2.00228i
$988$	6.29335e6	+	4.57239e6i	0.205111	+	0.149022i
$989$	6.38438e6			0.207552
$990$	−130083.			−0.00421824
$991$	−2.73018e7	−	1.98359e7i	−0.883096	−	0.641607i	0.0509730	−	0.998700i	$-0.483768\pi$
$991$	−2.73018e7	−	1.98359e7i	−0.883096	−	0.641607i	−0.934069	+	0.357093i	$0.883768\pi$
$992$	4.76620e6	−	1.46689e7i	0.153778	−	0.473279i
$993$	−3.21933e7	−	4.43102e7i	−1.03608	−	1.42604i
$994$	2.64708e6	−	3.64339e6i	0.0849769	−	0.116961i
$995$	−62011.4	−	190851.i	−0.00198570	−	0.00611136i
$996$	1.30713e6	−	4.02294e6i	0.0417514	−	0.128498i
$997$			1.61292e7i			0.513896i	0.966425	+	0.256948i	$0.0827169\pi$
$997$			1.61292e7i			0.513896i	−0.966425	+	0.256948i	$0.917283\pi$
$998$	726844.	+	2.23700e6i	0.0231002	+	0.0710950i
$999$	−2.28525e7	−	3.14537e7i	−0.724468	−	0.997145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.6.g.a.41.15	yes	104
61.3	even	10	inner	61.6.g.a.3.15	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.6.g.a.3.15	✓	104	61.3	even	10	inner
61.6.g.a.41.15	yes	104	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.632478 - 0.205504i) q^{2} +(8.01843 + 24.6782i) q^{3} +(-25.5307 + 18.5492i) q^{4} +(-4.43129 + 3.21952i) q^{5} +(10.1430 + 13.9606i) q^{6} +(128.232 + 41.6652i) q^{7} +(-24.8443 + 34.1952i) q^{8} +(-348.127 + 252.929i) q^{9} +O(q^{10})\)	\(q+(0.632478 - 0.205504i) q^{2} +(8.01843 + 24.6782i) q^{3} +(-25.5307 + 18.5492i) q^{4} +(-4.43129 + 3.21952i) q^{5} +(10.1430 + 13.9606i) q^{6} +(128.232 + 41.6652i) q^{7} +(-24.8443 + 34.1952i) q^{8} +(-348.127 + 252.929i) q^{9} +(-2.14107 + 2.94692i) q^{10} -82.9904i q^{11} +(-662.477 - 481.318i) q^{12} -526.185 q^{13} +89.6665 q^{14} +(-114.984 - 83.5407i) q^{15} +(303.374 - 933.689i) q^{16} +(-347.717 - 478.592i) q^{17} +(-168.205 + 231.514i) q^{18} +(144.764 + 445.539i) q^{19} +(53.4147 - 164.394i) q^{20} +3498.63i q^{21} +(-17.0549 - 52.4896i) q^{22} +(-812.982 - 1118.97i) q^{23} +(-1043.09 - 338.920i) q^{24} +(-956.407 + 2943.52i) q^{25} +(-332.800 + 108.133i) q^{26} +(-3932.08 - 2856.83i) q^{27} +(-4046.72 + 1314.86i) q^{28} +5340.16i q^{29} +(-89.8928 - 29.2079i) q^{30} +(7314.52 + 2376.63i) q^{31} -2005.44i q^{32} +(2048.05 - 665.453i) q^{33} +(-318.276 - 231.241i) q^{34} +(-702.377 + 228.216i) q^{35} +(4196.32 - 12914.9i) q^{36} +(7607.74 + 2471.90i) q^{37} +(183.121 + 252.044i) q^{38} +(-4219.18 - 12985.3i) q^{39} -231.515i q^{40} +(351.123 - 1080.65i) q^{41} +(718.985 + 2212.81i) q^{42} +(-2713.16 + 3734.34i) q^{43} +(1539.40 + 2118.81i) q^{44} +(728.341 - 2241.60i) q^{45} +(-744.147 - 540.654i) q^{46} +17515.3 q^{47} +25474.3 q^{48} +(1110.40 + 806.752i) q^{49} +2058.26i q^{50} +(9022.64 - 12418.6i) q^{51} +(13433.9 - 9760.30i) q^{52} +(-20367.3 + 28033.2i) q^{53} +(-3074.05 - 998.818i) q^{54} +(267.189 + 367.754i) q^{55} +(-4610.59 + 3349.79i) q^{56} +(-9834.32 + 7145.05i) q^{57} +(1097.43 + 3377.53i) q^{58} +(-32312.1 + 10498.8i) q^{59} +4485.24 q^{60} +(22523.2 - 18365.8i) q^{61} +5114.68 q^{62} +(-55179.5 + 17928.9i) q^{63} +(9295.84 + 28609.6i) q^{64} +(2331.68 - 1694.06i) q^{65} +(1158.59 - 841.768i) q^{66} +(-1811.94 - 2493.92i) q^{67} +(17755.0 + 5768.94i) q^{68} +(21095.4 - 29035.3i) q^{69} +(-397.338 + 288.683i) q^{70} +(29521.4 - 40632.7i) q^{71} -18188.1i q^{72} +(12472.9 + 9062.07i) q^{73} +5319.71 q^{74} -80309.6 q^{75} +(-11960.3 - 8689.69i) q^{76} +(3457.81 - 10642.1i) q^{77} +(-5337.08 - 7345.85i) q^{78} +(-42670.8 + 58731.3i) q^{79} +(1661.69 + 5114.16i) q^{80} +(6659.81 - 20496.8i) q^{81} -755.642i q^{82} +(1596.27 + 4912.81i) q^{83} +(-64896.8 - 89322.7i) q^{84} +(3081.67 + 1001.30i) q^{85} +(-948.588 + 2919.45i) q^{86} +(-131785. + 42819.7i) q^{87} +(2837.87 + 2061.83i) q^{88} +(67185.3 - 21829.8i) q^{89} -1567.44i q^{90} +(-67474.0 - 21923.6i) q^{91} +(41512.1 + 13488.1i) q^{92} +199566. i q^{93} +(11078.1 - 3599.48i) q^{94} +(-2075.92 - 1508.24i) q^{95} +(49490.7 - 16080.5i) q^{96} +(-56848.2 + 174961. i) q^{97} +(868.094 + 282.061i) q^{98} +(20990.7 + 28891.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9}+O(q^{10}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9	\( 104 q - 5 q^{2} + 15 q^{3} + 465 q^{4} - 122 q^{5} + 445 q^{6} + 230 q^{7} - 5 q^{8} - 2841 q^{9} - 595 q^{10} + 1982 q^{12} + 2372 q^{13} - 4474 q^{14} - 1149 q^{15} - 8631 q^{16} + 950 q^{17} + 4340 q^{18} - 5597 q^{19} - 6627 q^{20} - 8639 q^{22} + 9065 q^{23} + 17220 q^{24} - 7694 q^{25} + 14810 q^{26} + 4500 q^{27} + 19835 q^{28} - 44585 q^{30} + 10905 q^{31} - 19205 q^{33} - 15376 q^{34} - 43790 q^{35} - 25135 q^{36} - 5 q^{37} + 17555 q^{38} + 29401 q^{39} - 21014 q^{41} + 62197 q^{42} - 31625 q^{43} + 146190 q^{44} + 153742 q^{45} + 13387 q^{46} + 27326 q^{47} - 82968 q^{48} + 14694 q^{49} + 34090 q^{51} + 90072 q^{52} - 40270 q^{53} - 13760 q^{54} + 25140 q^{55} - 97860 q^{56} + 114893 q^{57} - 18003 q^{58} - 117435 q^{59} - 536650 q^{60} - 121867 q^{61} - 157388 q^{62} - 160825 q^{63} + 132509 q^{64} - 155852 q^{65} + 308443 q^{66} + 101665 q^{67} + 303780 q^{68} + 281945 q^{69} + 264985 q^{70} + 160970 q^{71} + 127669 q^{73} - 133952 q^{74} - 139592 q^{75} - 641111 q^{76} + 128917 q^{77} + 1670 q^{78} + 187940 q^{79} + 785373 q^{80} - 453473 q^{81} - 301209 q^{83} + 100475 q^{84} - 340045 q^{85} - 462669 q^{86} + 189245 q^{87} - 881635 q^{88} - 201970 q^{89} + 93865 q^{91} - 622085 q^{92} - 285265 q^{94} - 113308 q^{95} + 1215465 q^{96} - 342131 q^{97} - 616150 q^{98} + 714235 q^{99}+O(q^{100}) \) 104 * q - 5 * q^2 + 15 * q^3 + 465 * q^4 - 122 * q^5 + 445 * q^6 + 230 * q^7 - 5 * q^8 - 2841 * q^9 - 595 * q^10 + 1982 * q^12 + 2372 * q^13 - 4474 * q^14 - 1149 * q^15 - 8631 * q^16 + 950 * q^17 + 4340 * q^18 - 5597 * q^19 - 6627 * q^20 - 8639 * q^22 + 9065 * q^23 + 17220 * q^24 - 7694 * q^25 + 14810 * q^26 + 4500 * q^27 + 19835 * q^28 - 44585 * q^30 + 10905 * q^31 - 19205 * q^33 - 15376 * q^34 - 43790 * q^35 - 25135 * q^36 - 5 * q^37 + 17555 * q^38 + 29401 * q^39 - 21014 * q^41 + 62197 * q^42 - 31625 * q^43 + 146190 * q^44 + 153742 * q^45 + 13387 * q^46 + 27326 * q^47 - 82968 * q^48 + 14694 * q^49 + 34090 * q^51 + 90072 * q^52 - 40270 * q^53 - 13760 * q^54 + 25140 * q^55 - 97860 * q^56 + 114893 * q^57 - 18003 * q^58 - 117435 * q^59 - 536650 * q^60 - 121867 * q^61 - 157388 * q^62 - 160825 * q^63 + 132509 * q^64 - 155852 * q^65 + 308443 * q^66 + 101665 * q^67 + 303780 * q^68 + 281945 * q^69 + 264985 * q^70 + 160970 * q^71 + 127669 * q^73 - 133952 * q^74 - 139592 * q^75 - 641111 * q^76 + 128917 * q^77 + 1670 * q^78 + 187940 * q^79 + 785373 * q^80 - 453473 * q^81 - 301209 * q^83 + 100475 * q^84 - 340045 * q^85 - 462669 * q^86 + 189245 * q^87 - 881635 * q^88 - 201970 * q^89 + 93865 * q^91 - 622085 * q^92 - 285265 * q^94 - 113308 * q^95 + 1215465 * q^96 - 342131 * q^97 - 616150 * q^98 + 714235 * q^99

Introduction

L-functions

Modular forms

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