LMFDB - Embedded newform 805.2.i.d.116.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(116,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("805.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.i (of order $3$, 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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.7
Character	$\chi$	$=$	805.116
Dual form			805.2.i.d.576.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.331631 + 0.574401i) q^{2} +(0.0704605 - 0.122041i) q^{3} +(0.780042 - 1.35107i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.0934675 q^{6} +(2.61178 - 0.422600i) q^{7} +2.36127 q^{8} +(1.49007 + 2.58088i) q^{9} +O(q^{10})$	\(q+(0.331631 + 0.574401i) q^{2} +(0.0704605 - 0.122041i) q^{3} +(0.780042 - 1.35107i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.0934675 q^{6} +(2.61178 - 0.422600i) q^{7} +2.36127 q^{8} +(1.49007 + 2.58088i) q^{9} +(0.331631 - 0.574401i) q^{10} +(1.14839 - 1.98906i) q^{11} +(-0.109924 - 0.190395i) q^{12} -2.34924 q^{13} +(1.10889 + 1.36006i) q^{14} -0.140921 q^{15} +(-0.777015 - 1.34583i) q^{16} +(0.591704 - 1.02486i) q^{17} +(-0.988307 + 1.71180i) q^{18} +(-0.219488 - 0.380164i) q^{19} -1.56008 q^{20} +(0.132453 - 0.348522i) q^{21} +1.52336 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.166376 - 0.288172i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.779079 - 1.34941i) q^{26} +0.842728 q^{27} +(1.46634 - 3.85835i) q^{28} +1.75146 q^{29} +(-0.0467337 - 0.0809452i) q^{30} +(-4.39607 + 7.61422i) q^{31} +(2.87663 - 4.98247i) q^{32} +(-0.161832 - 0.280301i) q^{33} +0.784909 q^{34} +(-1.67187 - 2.05057i) q^{35} +4.64927 q^{36} +(-3.22433 - 5.58470i) q^{37} +(0.145578 - 0.252148i) q^{38} +(-0.165528 + 0.286704i) q^{39} +(-1.18063 - 2.04492i) q^{40} +0.492791 q^{41} +(0.244117 - 0.0394993i) q^{42} +11.3064 q^{43} +(-1.79158 - 3.10311i) q^{44} +(1.49007 - 2.58088i) q^{45} +(0.331631 - 0.574401i) q^{46} +(0.154951 + 0.268382i) q^{47} -0.218996 q^{48} +(6.64282 - 2.20748i) q^{49} -0.663262 q^{50} +(-0.0833835 - 0.144424i) q^{51} +(-1.83250 + 3.17399i) q^{52} +(3.24756 - 5.62493i) q^{53} +(0.279474 + 0.484064i) q^{54} -2.29677 q^{55} +(6.16712 - 0.997870i) q^{56} -0.0618609 q^{57} +(0.580837 + 1.00604i) q^{58} +(3.21092 - 5.56148i) q^{59} +(-0.109924 + 0.190395i) q^{60} +(-0.966187 - 1.67348i) q^{61} -5.83149 q^{62} +(4.98242 + 6.11099i) q^{63} +0.707856 q^{64} +(1.17462 + 2.03450i) q^{65} +(0.107337 - 0.185913i) q^{66} +(-4.29682 + 7.44230i) q^{67} +(-0.923108 - 1.59887i) q^{68} -0.140921 q^{69} +(0.623406 - 1.64036i) q^{70} -9.22786 q^{71} +(3.51845 + 6.09414i) q^{72} +(2.10264 - 3.64188i) q^{73} +(2.13857 - 3.70411i) q^{74} +(0.0704605 + 0.122041i) q^{75} -0.684838 q^{76} +(2.15876 - 5.68031i) q^{77} -0.219577 q^{78} +(7.17687 + 12.4307i) q^{79} +(-0.777015 + 1.34583i) q^{80} +(-4.41083 + 7.63979i) q^{81} +(0.163425 + 0.283060i) q^{82} -14.3627 q^{83} +(-0.367559 - 0.450815i) q^{84} -1.18341 q^{85} +(3.74955 + 6.49440i) q^{86} +(0.123409 - 0.213750i) q^{87} +(2.71165 - 4.69671i) q^{88} +(2.47813 + 4.29225i) q^{89} +1.97661 q^{90} +(-6.13570 + 0.992787i) q^{91} -1.56008 q^{92} +(0.619499 + 1.07300i) q^{93} +(-0.102773 + 0.178008i) q^{94} +(-0.219488 + 0.380164i) q^{95} +(-0.405378 - 0.702135i) q^{96} -6.11976 q^{97} +(3.47094 + 3.08358i) q^{98} +6.84470 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 5 q^{2} + 2 q^{3} - 13 q^{4} - 13 q^{5} - 8 q^{6} - 30 q^{8} - 5 q^{9}+O(q^{10}) $ 26 * q + 5 * q^2 + 2 * q^3 - 13 * q^4 - 13 * q^5 - 8 * q^6 - 30 * q^8 - 5 * q^9	\( 26 q + 5 q^{2} + 2 q^{3} - 13 q^{4} - 13 q^{5} - 8 q^{6} - 30 q^{8} - 5 q^{9} + 5 q^{10} + 17 q^{11} - 6 q^{12} + 2 q^{13} + 11 q^{14} - 4 q^{15} - 21 q^{16} - 2 q^{17} + 25 q^{18} + 13 q^{19} + 26 q^{20} + 5 q^{21} + 6 q^{22} - 13 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 10 q^{27} + 23 q^{28} - 52 q^{29} + 4 q^{30} - 8 q^{31} + 40 q^{32} + 6 q^{33} - 84 q^{34} + 3 q^{35} + 34 q^{36} + 29 q^{37} - 40 q^{38} + 20 q^{39} + 15 q^{40} - 56 q^{41} - 18 q^{42} - 20 q^{43} + 31 q^{44} - 5 q^{45} + 5 q^{46} - q^{47} + 16 q^{48} - 4 q^{49} - 10 q^{50} + 3 q^{51} - 27 q^{52} + 43 q^{53} + 24 q^{54} - 34 q^{55} - 24 q^{56} + 4 q^{57} - 24 q^{58} + q^{59} - 6 q^{60} + 30 q^{61} - 4 q^{62} + 8 q^{63} + 70 q^{64} - q^{65} - 71 q^{66} + 21 q^{67} - 11 q^{68} - 4 q^{69} + 5 q^{70} + 47 q^{72} - 5 q^{73} + 10 q^{74} + 2 q^{75} - 174 q^{76} - 2 q^{77} + 58 q^{78} + 36 q^{79} - 21 q^{80} + 35 q^{81} - 8 q^{82} - 22 q^{84} + 4 q^{85} + 20 q^{86} - 6 q^{87} + 24 q^{88} + 10 q^{89} - 50 q^{90} + 36 q^{91} + 26 q^{92} + 15 q^{93} - 38 q^{94} + 13 q^{95} + 31 q^{96} - 16 q^{97} + 41 q^{98} - 18 q^{99}+O(q^{100}) \) 26 * q + 5 * q^2 + 2 * q^3 - 13 * q^4 - 13 * q^5 - 8 * q^6 - 30 * q^8 - 5 * q^9 + 5 * q^10 + 17 * q^11 - 6 * q^12 + 2 * q^13 + 11 * q^14 - 4 * q^15 - 21 * q^16 - 2 * q^17 + 25 * q^18 + 13 * q^19 + 26 * q^20 + 5 * q^21 + 6 * q^22 - 13 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 10 * q^27 + 23 * q^28 - 52 * q^29 + 4 * q^30 - 8 * q^31 + 40 * q^32 + 6 * q^33 - 84 * q^34 + 3 * q^35 + 34 * q^36 + 29 * q^37 - 40 * q^38 + 20 * q^39 + 15 * q^40 - 56 * q^41 - 18 * q^42 - 20 * q^43 + 31 * q^44 - 5 * q^45 + 5 * q^46 - q^47 + 16 * q^48 - 4 * q^49 - 10 * q^50 + 3 * q^51 - 27 * q^52 + 43 * q^53 + 24 * q^54 - 34 * q^55 - 24 * q^56 + 4 * q^57 - 24 * q^58 + q^59 - 6 * q^60 + 30 * q^61 - 4 * q^62 + 8 * q^63 + 70 * q^64 - q^65 - 71 * q^66 + 21 * q^67 - 11 * q^68 - 4 * q^69 + 5 * q^70 + 47 * q^72 - 5 * q^73 + 10 * q^74 + 2 * q^75 - 174 * q^76 - 2 * q^77 + 58 * q^78 + 36 * q^79 - 21 * q^80 + 35 * q^81 - 8 * q^82 - 22 * q^84 + 4 * q^85 + 20 * q^86 - 6 * q^87 + 24 * q^88 + 10 * q^89 - 50 * q^90 + 36 * q^91 + 26 * q^92 + 15 * q^93 - 38 * q^94 + 13 * q^95 + 31 * q^96 - 16 * q^97 + 41 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.331631	+	0.574401i	0.234498	+	0.406163i	0.959127	−	0.282977i	$-0.0913219\pi$
$2$	0.331631	+	0.574401i	0.234498	+	0.406163i	−0.724628	+	0.689140i	$0.757989\pi$
$3$	0.0704605	−	0.122041i	0.0406804	−	0.0704605i	−0.844968	−	0.534816i	$-0.820381\pi$
$3$	0.0704605	−	0.122041i	0.0406804	−	0.0704605i	0.885649	+	0.464356i	$0.153714\pi$
$4$	0.780042	−	1.35107i	0.390021	−	0.675536i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.0934675			0.0381579
$7$	2.61178	−	0.422600i	0.987161	−	0.159728i
$7$	2.61178	−	0.422600i	0.987161	−	0.159728i
$8$	2.36127			0.834834
$9$	1.49007	+	2.58088i	0.496690	+	0.860293i
$10$	0.331631	−	0.574401i	0.104871	−	0.181642i
$11$	1.14839	−	1.98906i	0.346251	−	0.599725i	−0.639329	−	0.768933i	$-0.720788\pi$
$11$	1.14839	−	1.98906i	0.346251	−	0.599725i	0.985580	+	0.169208i	$0.0541211\pi$
$12$	−0.109924	−	0.190395i	−0.0317324	−	0.0549622i
$13$	−2.34924			−0.651561			−0.325781	−	0.945445i	$-0.605627\pi$
$13$	−2.34924			−0.651561			−0.325781	+	0.945445i	$0.605627\pi$
$14$	1.10889	+	1.36006i	0.296363	+	0.363493i
$15$	−0.140921			−0.0363857
$16$	−0.777015	−	1.34583i	−0.194254	−	0.336458i
$17$	0.591704	−	1.02486i	0.143509	−	0.248565i	−0.785307	−	0.619107i	$-0.787495\pi$
$17$	0.591704	−	1.02486i	0.143509	−	0.248565i	0.928816	+	0.370542i	$0.120828\pi$
$18$	−0.988307	+	1.71180i	−0.232946	+	0.403474i
$19$	−0.219488	−	0.380164i	−0.0503539	−	0.0872156i	0.839750	−	0.542973i	$-0.182702\pi$
$19$	−0.219488	−	0.380164i	−0.0503539	−	0.0872156i	−0.890104	+	0.455758i	$0.849368\pi$
$20$	−1.56008			−0.348845
$21$	0.132453	−	0.348522i	0.0289036	−	0.0760537i
$22$	1.52336			0.324782
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	0.166376	−	0.288172i	0.0339614	−	0.0588228i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.779079	−	1.34941i	−0.152790	−	0.264640i
$27$	0.842728			0.162183
$28$	1.46634	−	3.85835i	0.277112	−	0.729160i
$29$	1.75146			0.325238			0.162619	−	0.986689i	$-0.448006\pi$
$29$	1.75146			0.325238			0.162619	+	0.986689i	$0.448006\pi$
$30$	−0.0467337	−	0.0809452i	−0.00853238	−	0.0147785i
$31$	−4.39607	+	7.61422i	−0.789558	+	1.36755i	0.136681	+	0.990615i	$0.456357\pi$
$31$	−4.39607	+	7.61422i	−0.789558	+	1.36755i	−0.926238	+	0.376939i	$0.876977\pi$
$32$	2.87663	−	4.98247i	0.508521	−	0.880785i
$33$	−0.161832	−	0.280301i	−0.0281713	−	0.0487941i
$34$	0.784909			0.134611
$35$	−1.67187	−	2.05057i	−0.282598	−	0.346610i
$36$	4.64927			0.774879
$37$	−3.22433	−	5.58470i	−0.530076	−	0.918119i	−0.999384	−	0.0350842i	$-0.988830\pi$
$37$	−3.22433	−	5.58470i	−0.530076	−	0.918119i	0.469308	−	0.883034i	$-0.344503\pi$
$38$	0.145578	−	0.252148i	0.0236158	−	0.0409038i
$39$	−0.165528	+	0.286704i	−0.0265058	+	0.0459093i
$40$	−1.18063	−	2.04492i	−0.186675	−	0.323330i
$41$	0.492791			0.0769610			0.0384805	−	0.999259i	$-0.487748\pi$
$41$	0.492791			0.0769610			0.0384805	+	0.999259i	$0.487748\pi$
$42$	0.244117	−	0.0394993i	0.0376680	−	0.00609488i
$43$	11.3064			1.72421			0.862104	−	0.506732i	$-0.169147\pi$
$43$	11.3064			1.72421			0.862104	+	0.506732i	$0.169147\pi$
$44$	−1.79158	−	3.10311i	−0.270091	−	0.467811i
$45$	1.49007	−	2.58088i	0.222127	−	0.384735i
$46$	0.331631	−	0.574401i	0.0488963	−	0.0846909i
$47$	0.154951	+	0.268382i	0.0226019	+	0.0391476i	0.877105	−	0.480298i	$-0.159472\pi$
$47$	0.154951	+	0.268382i	0.0226019	+	0.0391476i	−0.854503	+	0.519446i	$0.826138\pi$
$48$	−0.218996			−0.0316093
$49$	6.64282	−	2.20748i	0.948974	−	0.315354i
$50$	−0.663262			−0.0937993
$51$	−0.0833835	−	0.144424i	−0.0116760	−	0.0202235i
$52$	−1.83250	+	3.17399i	−0.254123	+	0.440153i
$53$	3.24756	−	5.62493i	0.446086	−	0.772644i	−0.552041	−	0.833817i	$-0.686151\pi$
$53$	3.24756	−	5.62493i	0.446086	−	0.772644i	0.998127	+	0.0611731i	$0.0194842\pi$
$54$	0.279474	+	0.484064i	0.0380317	+	0.0658728i
$55$	−2.29677			−0.309697
$56$	6.16712	−	0.997870i	0.824116	−	0.133346i
$57$	−0.0618609			−0.00819367
$58$	0.580837	+	1.00604i	0.0762677	+	0.132100i
$59$	3.21092	−	5.56148i	0.418027	−	0.724043i	−0.577714	−	0.816239i	$-0.696055\pi$
$59$	3.21092	−	5.56148i	0.418027	−	0.724043i	0.995741	+	0.0921957i	$0.0293885\pi$
$60$	−0.109924	+	0.190395i	−0.0141912	+	0.0245798i
$61$	−0.966187	−	1.67348i	−0.123708	−	0.214268i	0.797519	−	0.603293i	$-0.206145\pi$
$61$	−0.966187	−	1.67348i	−0.123708	−	0.214268i	−0.921227	+	0.389026i	$0.872812\pi$
$62$	−5.83149			−0.740600
$63$	4.98242	+	6.11099i	0.627726	+	0.769912i
$64$	0.707856			0.0884820
$65$	1.17462	+	2.03450i	0.145694	+	0.252349i
$66$	0.107337	−	0.185913i	0.0132122	−	0.0228843i
$67$	−4.29682	+	7.44230i	−0.524940	+	0.909222i	0.474639	+	0.880181i	$0.342579\pi$
$67$	−4.29682	+	7.44230i	−0.524940	+	0.909222i	−0.999578	+	0.0290412i	$0.990755\pi$
$68$	−0.923108	−	1.59887i	−0.111943	−	0.193891i
$69$	−0.140921			−0.0169649
$70$	0.623406	−	1.64036i	0.0745112	−	0.196060i
$71$	−9.22786			−1.09515			−0.547573	−	0.836758i	$-0.684448\pi$
$71$	−9.22786			−1.09515			−0.547573	+	0.836758i	$0.684448\pi$
$72$	3.51845	+	6.09414i	0.414654	+	0.718202i
$73$	2.10264	−	3.64188i	0.246095	−	0.426250i	−0.716344	−	0.697748i	$-0.754186\pi$
$73$	2.10264	−	3.64188i	0.246095	−	0.426250i	0.962439	+	0.271498i	$0.0875190\pi$
$74$	2.13857	−	3.70411i	0.248604	−	0.430595i
$75$	0.0704605	+	0.122041i	0.00813608	+	0.0140921i
$76$	−0.684838			−0.0785564
$77$	2.15876	−	5.68031i	0.246013	−	0.647331i
$78$	−0.219577			−0.0248622
$79$	7.17687	+	12.4307i	0.807461	+	1.39856i	0.914617	+	0.404321i	$0.132492\pi$
$79$	7.17687	+	12.4307i	0.807461	+	1.39856i	−0.107156	+	0.994242i	$0.534174\pi$
$80$	−0.777015	+	1.34583i	−0.0868730	+	0.150468i
$81$	−4.41083	+	7.63979i	−0.490093	+	0.848865i
$82$	0.163425	+	0.283060i	0.0180472	+	0.0312587i
$83$	−14.3627			−1.57651			−0.788257	−	0.615347i	$-0.789016\pi$
$83$	−14.3627			−1.57651			−0.788257	+	0.615347i	$0.789016\pi$
$84$	−0.367559	−	0.450815i	−0.0401040	−	0.0491880i
$85$	−1.18341			−0.128359
$86$	3.74955	+	6.49440i	0.404324	+	0.700309i
$87$	0.123409	−	0.213750i	0.0132308	−	0.0229164i
$88$	2.71165	−	4.69671i	0.289062	−	0.500671i
$89$	2.47813	+	4.29225i	0.262682	+	0.454978i	0.966954	−	0.254952i	$-0.0820597\pi$
$89$	2.47813	+	4.29225i	0.262682	+	0.454978i	−0.704272	+	0.709930i	$0.748726\pi$
$90$	1.97661			0.208353
$91$	−6.13570	+	0.992787i	−0.643196	+	0.104072i
$92$	−1.56008			−0.162650
$93$	0.619499	+	1.07300i	0.0642390	+	0.111265i
$94$	−0.102773	+	0.178008i	−0.0106002	+	0.0183601i
$95$	−0.219488	+	0.380164i	−0.0225190	+	0.0390040i
$96$	−0.405378	−	0.702135i	−0.0413737	−	0.0716614i
$97$	−6.11976			−0.621368			−0.310684	−	0.950513i	$-0.600558\pi$
$97$	−6.11976			−0.621368			−0.310684	+	0.950513i	$0.600558\pi$
$98$	3.47094	+	3.08358i	0.350618	+	0.311488i
$99$	6.84470			0.687919
$100$	0.780042	+	1.35107i	0.0780042	+	0.135107i
$101$	−8.75997	+	15.1727i	−0.871650	+	1.50974i	−0.0113609	+	0.999935i	$0.503616\pi$
$101$	−8.75997	+	15.1727i	−0.871650	+	1.50974i	−0.860289	+	0.509807i	$0.829717\pi$
$102$	0.0553051	−	0.0957912i	0.00547602	−	0.00948474i
$103$	5.93503	+	10.2798i	0.584796	+	1.01290i	0.994901	+	0.100857i	$0.0321586\pi$
$103$	5.93503	+	10.2798i	0.584796	+	1.01290i	−0.410105	+	0.912038i	$0.634508\pi$
$104$	−5.54718			−0.543945
$105$	−0.368055	+	0.0595532i	−0.0359185	+	0.00581179i
$106$	4.30796			0.418426
$107$	−5.26729	−	9.12321i	−0.509208	−	0.881974i	−0.999943	−	0.0106654i	$-0.996605\pi$
$107$	−5.26729	−	9.12321i	−0.509208	−	0.881974i	0.490735	−	0.871309i	$-0.336728\pi$
$108$	0.657363	−	1.13859i	0.0632548	−	0.109560i
$109$	−7.96603	+	13.7976i	−0.763008	+	1.32157i	0.178286	+	0.983979i	$0.442945\pi$
$109$	−7.96603	+	13.7976i	−0.763008	+	1.32157i	−0.941294	+	0.337589i	$0.890389\pi$
$110$	−0.761680	−	1.31927i	−0.0726234	−	0.125787i
$111$	−0.908751			−0.0862548
$112$	−2.59814	−	3.18665i	−0.245501	−	0.301110i
$113$	0.688562			0.0647744			0.0323872	−	0.999475i	$-0.489689\pi$
$113$	0.688562			0.0647744			0.0323872	+	0.999475i	$0.489689\pi$
$114$	−0.0205150	−	0.0355330i	−0.00192140	−	0.00332797i
$115$	−0.500000	+	0.866025i	−0.0466252	+	0.0807573i
$116$	1.36621	−	2.36635i	0.126850	−	0.219710i
$117$	−3.50053	−	6.06310i	−0.323624	−	0.560533i
$118$	4.25936			0.392106
$119$	1.11230	−	2.92677i	0.101964	−	0.268296i
$120$	−0.332752			−0.0303760
$121$	2.86242	+	4.95786i	0.260220	+	0.450714i
$122$	0.640834	−	1.10996i	0.0580184	−	0.100491i
$123$	0.0347223	−	0.0601407i	0.00313080	−	0.00542271i
$124$	6.85824	+	11.8788i	0.615888	+	1.06675i
$125$	1.00000			0.0894427
$126$	−1.85784	+	4.88850i	−0.165509	+	0.435502i
$127$	−10.8425			−0.962120			−0.481060	−	0.876688i	$-0.659748\pi$
$127$	−10.8425			−0.962120			−0.481060	+	0.876688i	$0.659748\pi$
$128$	−5.51852	−	9.55835i	−0.487772	−	0.844847i
$129$	0.796654	−	1.37984i	0.0701414	−	0.121489i
$130$	−0.779079	+	1.34941i	−0.0683298	+	0.118351i
$131$	−3.53365	−	6.12046i	−0.308736	−	0.534747i	0.669350	−	0.742947i	$-0.266573\pi$
$131$	−3.53365	−	6.12046i	−0.308736	−	0.534747i	−0.978086	+	0.208200i	$0.933239\pi$
$132$	−0.504942			−0.0439496
$133$	−0.733911	−	0.900150i	−0.0636382	−	0.0780529i
$134$	−5.69982			−0.492390
$135$	−0.421364	−	0.729824i	−0.0362652	−	0.0628132i
$136$	1.39717	−	2.41997i	0.119806	−	0.207511i
$137$	7.01647	−	12.1529i	0.599457	−	1.03829i	−0.393444	−	0.919349i	$-0.628717\pi$
$137$	7.01647	−	12.1529i	0.599457	−	1.03829i	0.992901	−	0.118942i	$-0.0379502\pi$
$138$	−0.0467337	−	0.0809452i	−0.00397824	−	0.00689052i
$139$	10.2949			0.873200			0.436600	−	0.899656i	$-0.356182\pi$
$139$	10.2949			0.873200			0.436600	+	0.899656i	$0.356182\pi$
$140$	−4.07460	+	0.659291i	−0.344367	+	0.0557202i
$141$	0.0436716			0.00367781
$142$	−3.06024	−	5.30050i	−0.256810	−	0.444808i
$143$	−2.69783	+	4.67278i	−0.225604	+	0.390758i
$144$	2.31562	−	4.01076i	0.192968	−	0.334230i
$145$	−0.875729	−	1.51681i	−0.0727254	−	0.125964i
$146$	2.78920			0.230836
$147$	0.198653	−	0.966237i	0.0163847	−	0.0796939i
$148$	−10.0604			−0.826963
$149$	5.15362	+	8.92634i	0.422201	+	0.731274i	0.996155	−	0.0876139i	$-0.0279242\pi$
$149$	5.15362	+	8.92634i	0.422201	+	0.731274i	−0.573953	+	0.818888i	$0.694591\pi$
$150$	−0.0467337	+	0.0809452i	−0.00381579	+	0.00660915i
$151$	5.97589	−	10.3505i	0.486311	−	0.842315i	−0.513565	−	0.858050i	$-0.671676\pi$
$151$	5.97589	−	10.3505i	0.486311	−	0.842315i	0.999876	+	0.0157356i	$0.00500899\pi$
$152$	−0.518269	−	0.897668i	−0.0420372	−	0.0728105i
$153$	3.52672			0.285119
$154$	3.97869	−	0.643771i	0.320612	−	0.0518766i
$155$	8.79214			0.706202
$156$	0.258238	+	0.447282i	0.0206756	+	0.0358112i
$157$	−3.70861	+	6.42351i	−0.295980	+	0.512652i	−0.975212	−	0.221271i	$-0.928979\pi$
$157$	−3.70861	+	6.42351i	−0.295980	+	0.512652i	0.679233	+	0.733923i	$0.262313\pi$
$158$	−4.76014	+	8.24481i	−0.378697	+	0.655922i
$159$	−0.457649	−	0.792671i	−0.0362939	−	0.0628629i
$160$	−5.75326			−0.454835
$161$	−1.67187	−	2.05057i	−0.131762	−	0.161608i
$162$	−5.85107			−0.459704
$163$	6.42354	+	11.1259i	0.503130	+	0.871447i	0.999993	+	0.00361839i	$0.00115177\pi$
$163$	6.42354	+	11.1259i	0.503130	+	0.871447i	−0.496863	+	0.867829i	$0.665515\pi$
$164$	0.384397	−	0.665796i	0.0300164	−	0.0519899i
$165$	−0.161832	+	0.280301i	−0.0125986	+	0.0218214i
$166$	−4.76312	−	8.24997i	−0.369690	−	0.640322i
$167$	−22.7005			−1.75662			−0.878308	−	0.478095i	$-0.841327\pi$
$167$	−22.7005			−1.75662			−0.878308	+	0.478095i	$0.841327\pi$
$168$	0.312757	−	0.822953i	0.0241297	−	0.0634922i
$169$	−7.48108			−0.575468
$170$	−0.392454	−	0.679751i	−0.0300999	−	0.0521345i
$171$	0.654104	−	1.13294i	0.0500206	−	0.0866382i
$172$	8.81946	−	15.2757i	0.672477	−	1.16476i
$173$	−6.10094	−	10.5671i	−0.463846	−	0.803404i	0.535303	−	0.844660i	$-0.320197\pi$
$173$	−6.10094	−	10.5671i	−0.463846	−	0.803404i	−0.999149	+	0.0412557i	$0.986864\pi$
$174$	0.163704			0.0124104
$175$	−0.939909	+	2.47317i	−0.0710505	+	0.186954i
$176$	−3.56925			−0.269043
$177$	−0.452487	−	0.783730i	−0.0340110	−	0.0589087i
$178$	−1.64365	+	2.84689i	−0.123197	+	0.213383i
$179$	−1.54663	+	2.67884i	−0.115600	+	0.200226i	−0.918020	−	0.396535i	$-0.870213\pi$
$179$	−1.54663	+	2.67884i	−0.115600	+	0.200226i	0.802419	+	0.596761i	$0.203546\pi$
$180$	−2.32464	−	4.02639i	−0.173268	−	0.300109i
$181$	10.9643			0.814970			0.407485	−	0.913212i	$-0.366406\pi$
$181$	10.9643			0.814970			0.407485	+	0.913212i	$0.366406\pi$
$182$	−2.60504	−	3.19511i	−0.193099	−	0.236838i
$183$	−0.272312			−0.0201299
$184$	−1.18063	−	2.04492i	−0.0870375	−	0.150753i
$185$	−3.22433	+	5.58470i	−0.237057	+	0.410595i
$186$	−0.410890	+	0.711682i	−0.0301279	+	0.0521830i
$187$	−1.35901	−	2.35387i	−0.0993806	−	0.172132i
$188$	0.483472			0.0352608
$189$	2.20102	−	0.356136i	0.160101	−	0.0259051i
$190$	−0.291155			−0.0211226
$191$	3.26835	+	5.66095i	0.236489	+	0.409612i	0.959704	−	0.281011i	$-0.0906698\pi$
$191$	3.26835	+	5.66095i	0.236489	+	0.409612i	−0.723215	+	0.690623i	$0.757336\pi$
$192$	0.0498759	−	0.0863876i	0.00359948	−	0.00623449i
$193$	−6.88020	+	11.9169i	−0.495248	+	0.857794i	−0.999985	−	0.00547885i	$-0.998256\pi$
$193$	−6.88020	+	11.9169i	−0.495248	+	0.857794i	0.504737	+	0.863273i	$0.331589\pi$
$194$	−2.02950	−	3.51520i	−0.145710	−	0.252377i
$195$	0.331057			0.0237075
$196$	2.19922	−	10.6969i	0.157087	−	0.764061i
$197$	−1.09733			−0.0781816			−0.0390908	−	0.999236i	$-0.512446\pi$
$197$	−1.09733			−0.0781816			−0.0390908	+	0.999236i	$0.512446\pi$
$198$	2.26991	+	3.93161i	0.161316	+	0.279407i
$199$	−7.34629	+	12.7241i	−0.520764	+	0.901991i	0.478944	+	0.877845i	$0.341020\pi$
$199$	−7.34629	+	12.7241i	−0.520764	+	0.901991i	−0.999708	+	0.0241451i	$0.992314\pi$
$200$	−1.18063	+	2.04492i	−0.0834834	+	0.144597i
$201$	0.605512	+	1.04878i	0.0427095	+	0.0739750i
$202$	−11.6203			−0.817602
$203$	4.57443	−	0.740166i	0.321062	−	0.0519494i
$204$	−0.260171			−0.0182156
$205$	−0.246395	−	0.426769i	−0.0172090	−	0.0298068i
$206$	−3.93647	+	6.81817i	−0.274267	+	0.475045i
$207$	1.49007	−	2.58088i	0.103567	−	0.179383i
$208$	1.82539	+	3.16167i	0.126568	+	0.219223i
$209$	−1.00823			−0.0697405
$210$	−0.156266	−	0.191662i	−0.0107834	−	0.0132259i
$211$	−10.4407			−0.718767			−0.359384	−	0.933190i	$-0.617013\pi$
$211$	−10.4407			−0.718767			−0.359384	+	0.933190i	$0.617013\pi$
$212$	−5.06646	−	8.77537i	−0.347966	−	0.602695i
$213$	−0.650200	+	1.12618i	−0.0445510	+	0.0771645i
$214$	3.49359	−	6.05108i	0.238817	−	0.413643i
$215$	−5.65319	−	9.79162i	−0.385545	−	0.667783i
$216$	1.98990			0.135396
$217$	−8.26382	+	21.7445i	−0.560984	+	1.47611i
$218$	−10.5671			−0.715696
$219$	−0.296306	−	0.513217i	−0.0200225	−	0.0346800i
$220$	−1.79158	+	3.10311i	−0.120788	+	0.209211i
$221$	−1.39005	+	2.40764i	−0.0935051	+	0.161956i
$222$	−0.301370	−	0.521988i	−0.0202266	−	0.0350335i
$223$	−20.3135			−1.36029			−0.680147	−	0.733076i	$-0.738084\pi$
$223$	−20.3135			−1.36029			−0.680147	+	0.733076i	$0.738084\pi$
$224$	5.40755	−	14.2288i	0.361307	−	0.950701i
$225$	−2.98014			−0.198676
$226$	0.228348	+	0.395511i	0.0151895	+	0.0263090i
$227$	3.49359	−	6.05107i	0.231877	−	0.401624i	−0.726483	−	0.687184i	$-0.758846\pi$
$227$	3.49359	−	6.05107i	0.231877	−	0.401624i	0.958361	+	0.285561i	$0.0921798\pi$
$228$	−0.0482541	+	0.0835785i	−0.00319570	+	0.00553512i
$229$	14.1058	+	24.4320i	0.932140	+	1.61451i	0.779655	+	0.626209i	$0.215394\pi$
$229$	14.1058	+	24.4320i	0.932140	+	1.61451i	0.152485	+	0.988306i	$0.451272\pi$
$230$	−0.663262			−0.0437342
$231$	−0.541124	−	0.663695i	−0.0356034	−	0.0436679i
$232$	4.13566			0.271519
$233$	10.5596	+	18.2897i	0.691781	+	1.19820i	0.971254	+	0.238047i	$0.0765071\pi$
$233$	10.5596	+	18.2897i	0.691781	+	1.19820i	−0.279472	+	0.960154i	$0.590160\pi$
$234$	2.32177	−	4.02142i	0.151779	−	0.262888i
$235$	0.154951	−	0.268382i	0.0101079	−	0.0175073i
$236$	−5.00931	−	8.67638i	−0.326078	−	0.564784i
$237$	2.02274			0.131391
$238$	2.05001	−	0.331702i	0.132883	−	0.0215011i
$239$	7.90675			0.511445			0.255723	−	0.966750i	$-0.417687\pi$
$239$	7.90675			0.511445			0.255723	+	0.966750i	$0.417687\pi$
$240$	0.109498	+	0.189656i	0.00706805	+	0.0122422i
$241$	−3.85105	+	6.67022i	−0.248068	+	0.429667i	−0.962990	−	0.269538i	$-0.913129\pi$
$241$	−3.85105	+	6.67022i	−0.248068	+	0.429667i	0.714922	+	0.699205i	$0.246462\pi$
$242$	−1.89853	+	3.28836i	−0.122042	+	0.211384i
$243$	1.88567	+	3.26608i	0.120966	+	0.209519i
$244$	−3.01466			−0.192994
$245$	−5.23314	−	4.64911i	−0.334333	−	0.297021i
$246$	0.0460599			0.00293667
$247$	0.515629	+	0.893095i	0.0328087	+	0.0568263i
$248$	−10.3803	+	17.9792i	−0.659149	+	1.14168i
$249$	−1.01200	+	1.75284i	−0.0641332	+	0.111082i
$250$	0.331631	+	0.574401i	0.0209742	+	0.0363283i
$251$	6.85380			0.432608			0.216304	−	0.976326i	$-0.430600\pi$
$251$	6.85380			0.432608			0.216304	+	0.976326i	$0.430600\pi$
$252$	12.1429	−	1.96478i	0.764930	−	0.123769i
$253$	−2.29677			−0.144397
$254$	−3.59572	−	6.22797i	−0.225616	−	0.390778i
$255$	−0.0833835	+	0.144424i	−0.00522168	+	0.00904421i
$256$	4.36808	−	7.56573i	0.273005	−	0.472858i
$257$	−6.91946	−	11.9849i	−0.431624	−	0.747594i	0.565389	−	0.824824i	$-0.308726\pi$
$257$	−6.91946	−	11.9849i	−0.431624	−	0.747594i	−0.997013	+	0.0772296i	$0.975393\pi$
$258$	1.05678			0.0657922
$259$	−10.7813	−	13.2234i	−0.669919	−	0.821663i
$260$	3.66501			0.227294
$261$	2.60980	+	4.52030i	0.161542	+	0.279800i
$262$	2.34373	−	4.05947i	0.144796	−	0.250795i
$263$	7.99226	−	13.8430i	0.492824	−	0.853596i	−0.507142	−	0.861863i	$-0.669298\pi$
$263$	7.99226	−	13.8430i	0.492824	−	0.853596i	0.999966	+	0.00826659i	$0.00263137\pi$
$264$	−0.382128	−	0.661865i	−0.0235183	−	0.0407350i
$265$	−6.49511			−0.398992
$266$	0.273660	−	0.720077i	0.0167792	−	0.0441507i
$267$	0.698442			0.0427440
$268$	6.70339	+	11.6106i	0.409475	+	0.709231i
$269$	3.44528	−	5.96739i	0.210062	−	0.363838i	−0.741672	−	0.670763i	$-0.765967\pi$
$269$	3.44528	−	5.96739i	0.210062	−	0.363838i	0.951734	+	0.306925i	$0.0993000\pi$
$270$	0.279474	−	0.484064i	0.0170083	−	0.0294592i
$271$	−7.40115	−	12.8192i	−0.449588	−	0.778709i	0.548771	−	0.835973i	$-0.315096\pi$
$271$	−7.40115	−	12.8192i	−0.449588	−	0.778709i	−0.998359	+	0.0572635i	$0.981762\pi$
$272$	−1.83905			−0.111509
$273$	−0.311164	+	0.818760i	−0.0188325	+	0.0495536i
$274$	9.30750			0.562287
$275$	1.14839	+	1.98906i	0.0692503	+	0.119945i
$276$	−0.109924	+	0.190395i	−0.00661667	+	0.0114604i
$277$	2.27246	−	3.93601i	0.136539	−	0.236492i	−0.789645	−	0.613563i	$-0.789736\pi$
$277$	2.27246	−	3.93601i	0.136539	−	0.236492i	0.926184	+	0.377071i	$0.123069\pi$
$278$	3.41410	+	5.91339i	0.204764	+	0.354662i
$279$	−26.2018			−1.56866
$280$	−3.94774	−	4.84194i	−0.235923	−	0.289362i
$281$	−6.52122			−0.389023			−0.194512	−	0.980900i	$-0.562312\pi$
$281$	−6.52122			−0.389023			−0.194512	+	0.980900i	$0.562312\pi$
$282$	0.0144828	+	0.0250850i	0.000862441	+	0.00149379i
$283$	8.35754	−	14.4757i	0.496804	−	0.860491i	−0.503189	−	0.864177i	$-0.667840\pi$
$283$	8.35754	−	14.4757i	0.496804	−	0.860491i	0.999993	+	0.00368595i	$0.00117328\pi$
$284$	−7.19812	+	12.4675i	−0.427130	+	0.739811i
$285$	0.0309304	+	0.0535731i	0.00183216	+	0.00317339i
$286$	−3.57874			−0.211615
$287$	1.28706	−	0.208253i	0.0759729	−	0.0122928i
$288$	17.1455			1.01031
$289$	7.79977	+	13.5096i	0.458810	+	0.794683i
$290$	0.580837	−	1.00604i	0.0341080	−	0.0590767i
$291$	−0.431202	+	0.746863i	−0.0252775	+	0.0437819i
$292$	−3.28029	−	5.68164i	−0.191965	−	0.332493i
$293$	24.3140			1.42044			0.710218	−	0.703981i	$-0.248596\pi$
$293$	24.3140			1.42044			0.710218	+	0.703981i	$0.248596\pi$
$294$	0.620888	−	0.206327i	0.0362109	−	0.0120333i
$295$	−6.42185			−0.373894
$296$	−7.61350	−	13.1870i	−0.442525	−	0.766476i
$297$	0.967776	−	1.67624i	0.0561561	−	0.0972652i
$298$	−3.41820	+	5.92050i	−0.198011	+	0.342965i
$299$	1.17462	+	2.03450i	0.0679300	+	0.117658i
$300$	0.219849			0.0126930
$301$	29.5298	−	4.77807i	1.70207	−	0.275404i
$302$	7.92715			0.456156
$303$	1.23446	+	2.13816i	0.0709181	+	0.122834i
$304$	−0.341091	+	0.590786i	−0.0195629	+	0.0338839i
$305$	−0.966187	+	1.67348i	−0.0553237	+	0.0958234i
$306$	1.16957	+	2.02575i	0.0668599	+	0.115805i
$307$	−9.94603			−0.567650			−0.283825	−	0.958876i	$-0.591603\pi$
$307$	−9.94603			−0.567650			−0.283825	+	0.958876i	$0.591603\pi$
$308$	−5.99058	−	7.34752i	−0.341345	−	0.418664i
$309$	1.67274			0.0951589
$310$	2.91574	+	5.05022i	0.165603	+	0.286833i
$311$	−3.06401	+	5.30702i	−0.173744	+	0.300933i	−0.939726	−	0.341929i	$-0.888920\pi$
$311$	−3.06401	+	5.30702i	−0.173744	+	0.300933i	0.765982	+	0.642862i	$0.222253\pi$
$312$	−0.390857	+	0.676984i	−0.0221279	+	0.0383267i
$313$	7.27165	+	12.5949i	0.411018	+	0.711904i	0.995001	−	0.0998614i	$-0.0318399\pi$
$313$	7.27165	+	12.5949i	0.411018	+	0.711904i	−0.583983	+	0.811766i	$0.698507\pi$
$314$	−4.91956			−0.277627
$315$	2.80106	−	7.37040i	0.157822	−	0.415275i
$316$	22.3930			1.25971
$317$	8.61567	+	14.9228i	0.483904	+	0.838146i	0.999829	−	0.0184874i	$-0.00588506\pi$
$317$	8.61567	+	14.9228i	0.483904	+	0.838146i	−0.515925	+	0.856634i	$0.672552\pi$
$318$	0.303541	−	0.525748i	0.0170217	−	0.0294825i
$319$	2.01135	−	3.48376i	0.112614	−	0.195053i
$320$	−0.353928	−	0.613021i	−0.0197852	−	0.0342689i
$321$	−1.48454			−0.0828591
$322$	0.623406	−	1.64036i	0.0347410	−	0.0914136i
$323$	−0.519487			−0.0289050
$324$	6.88127	+	11.9187i	0.382293	+	0.662151i
$325$	1.17462	−	2.03450i	0.0651561	−	0.112854i
$326$	−4.26049	+	7.37938i	−0.235966	+	0.408706i
$327$	1.12258	+	1.94437i	0.0620789	+	0.107524i
$328$	1.16361			0.0642496
$329$	0.518115	+	0.635474i	0.0285646	+	0.0350348i
$330$	−0.214673			−0.0118174
$331$	−9.00356	−	15.5946i	−0.494880	−	0.857158i	0.505102	−	0.863059i	$-0.331455\pi$
$331$	−9.00356	−	15.5946i	−0.494880	−	0.857158i	−0.999983	+	0.00590175i	$0.998121\pi$
$332$	−11.2035	+	19.4051i	−0.614873	+	1.06499i
$333$	9.60895	−	16.6432i	0.526567	−	0.912041i
$334$	−7.52818	−	13.0392i	−0.411924	−	0.713473i
$335$	8.59363			0.469520
$336$	−0.571969	+	0.0925474i	−0.0312035	+	0.00504888i
$337$	−12.1855			−0.663786			−0.331893	−	0.943317i	$-0.607687\pi$
$337$	−12.1855			−0.663786			−0.331893	+	0.943317i	$0.607687\pi$
$338$	−2.48096	−	4.29714i	−0.134946	−	0.233734i
$339$	0.0485164	−	0.0840329i	0.00263505	−	0.00456404i
$340$	−0.923108	+	1.59887i	−0.0500626	+	0.0867109i
$341$	10.0968	+	17.4881i	0.546771	+	0.947035i
$342$	0.867684			0.0469190
$343$	16.4167	−	8.57270i	0.886420	−	0.462882i
$344$	26.6974			1.43943
$345$	0.0704605	+	0.122041i	0.00379347	+	0.00657048i
$346$	4.04652	−	7.00877i	0.217542	−	0.376794i
$347$	9.53122	−	16.5086i	0.511663	−	0.886226i	−0.488246	−	0.872706i	$-0.662363\pi$
$347$	9.53122	−	16.5086i	0.511663	−	0.886226i	0.999909	−	0.0135199i	$-0.00430366\pi$
$348$	−0.192528	−	0.333468i	−0.0103206	−	0.0178758i
$349$	9.30609			0.498144			0.249072	−	0.968485i	$-0.419874\pi$
$349$	9.30609			0.498144			0.249072	+	0.968485i	$0.419874\pi$
$350$	−1.73230	+	0.280294i	−0.0925951	+	0.0149823i
$351$	−1.97977			−0.105672
$352$	−6.60697	−	11.4436i	−0.352152	−	0.609946i
$353$	−8.54616	+	14.8024i	−0.454866	+	0.787852i	−0.998681	−	0.0513540i	$-0.983646\pi$
$353$	−8.54616	+	14.8024i	−0.454866	+	0.787852i	0.543814	+	0.839206i	$0.316980\pi$
$354$	0.300117	−	0.519818i	0.0159510	−	0.0276280i
$355$	4.61393	+	7.99156i	0.244882	+	0.424148i
$356$	7.73220			0.409806
$357$	−0.278813	−	0.341968i	−0.0147564	−	0.0180988i
$358$	−2.05164			−0.108432
$359$	16.8301	+	29.1506i	0.888259	+	1.53851i	0.841932	+	0.539583i	$0.181418\pi$
$359$	16.8301	+	29.1506i	0.888259	+	1.53851i	0.0463264	+	0.998926i	$0.485249\pi$
$360$	3.51845	−	6.09414i	0.185439	−	0.321189i
$361$	9.40365	−	16.2876i	0.494929	−	0.857242i
$362$	3.63610	+	6.29791i	0.191109	+	0.331011i
$363$	0.806750			0.0423434
$364$	−3.44478	+	9.06419i	−0.180555	+	0.475093i
$365$	−4.20528			−0.220114
$366$	−0.0903070	−	0.156416i	−0.00472042	−	0.00817602i
$367$	−15.5765	+	26.9793i	−0.813088	+	1.40831i	0.0976040	+	0.995225i	$0.468882\pi$
$367$	−15.5765	+	26.9793i	−0.813088	+	1.40831i	−0.910692	+	0.413085i	$0.864451\pi$
$368$	−0.777015	+	1.34583i	−0.0405047	+	0.0701562i
$369$	0.734293	+	1.27183i	0.0382258	+	0.0662089i
$370$	−4.27714			−0.222358
$371$	6.10482	−	16.0635i	0.316946	−	0.833976i
$372$	1.93294			0.100218
$373$	−5.54575	−	9.60552i	−0.287148	−	0.497355i	0.685980	−	0.727621i	$-0.259374\pi$
$373$	−5.54575	−	9.60552i	−0.287148	−	0.497355i	−0.973128	+	0.230266i	$0.926040\pi$
$374$	0.901378	−	1.56123i	0.0466092	−	0.0807294i
$375$	0.0704605	−	0.122041i	0.00363857	−	0.00630218i
$376$	0.365880	+	0.633722i	0.0188688	+	0.0326817i
$377$	−4.11459			−0.211912
$378$	0.934492	+	1.14616i	0.0480651	+	0.0589523i
$379$	−4.75235			−0.244112			−0.122056	−	0.992523i	$-0.538949\pi$
$379$	−4.75235			−0.244112			−0.122056	+	0.992523i	$0.538949\pi$
$380$	0.342419	+	0.593087i	0.0175657	+	0.0304247i
$381$	−0.763971	+	1.32324i	−0.0391394	+	0.0677915i
$382$	−2.16777	+	3.75469i	−0.110913	+	0.192107i
$383$	−4.93825	−	8.55330i	−0.252333	−	0.437053i	0.711835	−	0.702347i	$-0.247864\pi$
$383$	−4.93825	−	8.55330i	−0.252333	−	0.437053i	−0.964168	+	0.265294i	$0.914531\pi$
$384$	−1.55535			−0.0793711
$385$	−5.99867	+	0.970615i	−0.305720	+	0.0494671i
$386$	−9.12674			−0.464539
$387$	16.8473	+	29.1804i	0.856397	+	1.48332i
$388$	−4.77367	+	8.26824i	−0.242346	+	0.419756i
$389$	13.3296	−	23.0876i	0.675839	−	1.17059i	−0.300384	−	0.953818i	$-0.597115\pi$
$389$	13.3296	−	23.0876i	0.675839	−	1.17059i	0.976223	−	0.216769i	$-0.0695519\pi$
$390$	0.109789	+	0.190160i	0.00555937	+	0.00962910i
$391$	−1.18341			−0.0598475
$392$	15.6855	−	5.21244i	0.792236	−	0.263268i
$393$	−0.995931			−0.0502381
$394$	−0.363909	−	0.630308i	−0.0183335	−	0.0317545i
$395$	7.17687	−	12.4307i	0.361108	−	0.625457i
$396$	5.33916	−	9.24769i	0.268303	−	0.464714i
$397$	5.40643	+	9.36422i	0.271341	+	0.469977i	0.969206	−	0.246253i	$-0.0791995\pi$
$397$	5.40643	+	9.36422i	0.271341	+	0.469977i	−0.697864	+	0.716230i	$0.745866\pi$
$398$	−9.74502			−0.488474
$399$	−0.161567	+	0.0261424i	−0.00808847	+	0.00130876i
$400$	1.55403			0.0777015
$401$	5.33711	+	9.24414i	0.266522	+	0.461630i	0.967961	−	0.251099i	$-0.0807921\pi$
$401$	5.33711	+	9.24414i	0.266522	+	0.461630i	−0.701439	+	0.712729i	$0.747459\pi$
$402$	−0.401613	+	0.695613i	−0.0200306	+	0.0346940i
$403$	10.3274	−	17.8876i	0.514445	−	0.891045i
$404$	13.6663	+	23.6707i	0.679924	+	1.17766i
$405$	8.82167			0.438352
$406$	1.94217	+	2.38210i	0.0963884	+	0.118221i
$407$	−14.8111			−0.734158
$408$	−0.196891	−	0.341025i	−0.00974754	−	0.0168832i
$409$	16.7642	−	29.0364i	0.828936	−	1.43576i	−0.0699383	−	0.997551i	$-0.522280\pi$
$409$	16.7642	−	29.0364i	0.828936	−	1.43576i	0.898874	−	0.438207i	$-0.144386\pi$
$410$	0.163425	−	0.283060i	0.00807096	−	0.0139793i
$411$	−0.988768	−	1.71260i	−0.0487723	−	0.0844761i
$412$	18.5183			0.912330
$413$	6.03595	−	15.8823i	0.297010	−	0.781518i
$414$	1.97661			0.0971452
$415$	7.18136	+	12.4385i	0.352519	+	0.610581i
$416$	−6.75789	+	11.7050i	−0.331333	+	0.573885i
$417$	0.725383	−	1.25640i	0.0355221	−	0.0615261i
$418$	−0.334359	−	0.579126i	−0.0163540	−	0.0283260i
$419$	−36.1527			−1.76618			−0.883088	−	0.469208i	$-0.844539\pi$
$419$	−36.1527			−1.76618			−0.883088	+	0.469208i	$0.844539\pi$
$420$	−0.206638	+	0.543723i	−0.0100829	+	0.0265310i
$421$	−30.5700			−1.48989			−0.744946	−	0.667124i	$-0.767525\pi$
$421$	−30.5700			−1.48989			−0.744946	+	0.667124i	$0.767525\pi$
$422$	−3.46246	−	5.99715i	−0.168550	−	0.291937i
$423$	−0.461775	+	0.799817i	−0.0224522	+	0.0388884i
$424$	7.66835	−	13.2820i	0.372408	−	0.645029i
$425$	0.591704	+	1.02486i	0.0287019	+	0.0497131i
$426$	−0.862505			−0.0417885
$427$	−3.23068	−	3.96247i	−0.156344	−	0.191757i
$428$	−16.4348			−0.794407
$429$	0.380181	+	0.658493i	0.0183553	+	0.0317923i
$430$	3.74955	−	6.49440i	0.180819	−	0.313188i
$431$	−1.57847	+	2.73399i	−0.0760323	+	0.131692i	−0.901535	−	0.432707i	$-0.857559\pi$
$431$	−1.57847	+	2.73399i	−0.0760323	+	0.131692i	0.825502	+	0.564399i	$0.190892\pi$
$432$	−0.654812	−	1.13417i	−0.0315047	−	0.0545677i
$433$	23.2592			1.11777			0.558883	−	0.829247i	$-0.311230\pi$
$433$	23.2592			1.11777			0.558883	+	0.829247i	$0.311230\pi$
$434$	−15.2306	+	2.46438i	−0.731091	+	0.118294i
$435$	−0.246817			−0.0118340
$436$	12.4277	+	21.5254i	0.595178	+	1.03088i
$437$	−0.219488	+	0.380164i	−0.0104995	+	0.0181857i
$438$	0.196528	−	0.340397i	0.00939049	−	0.0162648i
$439$	−15.3744	−	26.6292i	−0.733779	−	1.27094i	−0.955257	−	0.295777i	$-0.904421\pi$
$439$	−15.3744	−	26.6292i	−0.733779	−	1.27094i	0.221478	−	0.975165i	$-0.428912\pi$
$440$	−5.42329			−0.258545
$441$	15.5955	+	13.8550i	0.742643	+	0.659762i
$442$	−1.84394			−0.0877072
$443$	−18.5131	−	32.0656i	−0.879584	−	1.52348i	−0.851798	−	0.523871i	$-0.824487\pi$
$443$	−18.5131	−	32.0656i	−0.879584	−	1.52348i	−0.0277865	−	0.999614i	$-0.508846\pi$
$444$	−0.708864	+	1.22779i	−0.0336412	+	0.0582682i
$445$	2.47813	−	4.29225i	0.117475	−	0.203472i
$446$	−6.73658	−	11.6681i	−0.318987	−	0.552501i
$447$	1.45251			0.0687013
$448$	1.84877	−	0.299140i	0.0873460	−	0.0141330i
$449$	−25.1215			−1.18556			−0.592778	−	0.805366i	$-0.701969\pi$
$449$	−25.1215			−1.18556			−0.592778	+	0.805366i	$0.701969\pi$
$450$	−0.988307	−	1.71180i	−0.0465892	−	0.0806949i
$451$	0.565914	−	0.980191i	0.0266478	−	0.0461554i
$452$	0.537107	−	0.930297i	0.0252634	−	0.0437575i
$453$	−0.842128	−	1.45861i	−0.0395666	−	0.0685314i
$454$	4.63432			0.217500
$455$	3.92763	+	4.81728i	0.184130	+	0.225837i
$456$	−0.146070			−0.00684035
$457$	−7.07132	−	12.2479i	−0.330782	−	0.572932i	0.651883	−	0.758320i	$-0.273979\pi$
$457$	−7.07132	−	12.2479i	−0.330782	−	0.572932i	−0.982665	+	0.185388i	$0.940646\pi$
$458$	−9.35586	+	16.2048i	−0.437171	+	0.757202i
$459$	0.498645	−	0.863679i	0.0232748	−	0.0403131i
$460$	0.780042	+	1.35107i	0.0363696	+	0.0629941i
$461$	−7.44572			−0.346782			−0.173391	−	0.984853i	$-0.555472\pi$
$461$	−7.44572			−0.346782			−0.173391	+	0.984853i	$0.555472\pi$
$462$	0.201774	−	0.530924i	0.00938736	−	0.0247008i
$463$	5.45782			0.253646			0.126823	−	0.991925i	$-0.459522\pi$
$463$	5.45782			0.253646			0.126823	+	0.991925i	$0.459522\pi$
$464$	−1.36091	−	2.35717i	−0.0631787	−	0.109429i
$465$	0.619499	−	1.07300i	0.0287286	−	0.0497593i
$466$	−7.00377	+	12.1309i	−0.324443	+	0.561952i
$467$	−16.0100	−	27.7302i	−0.740856	−	1.28320i	−0.952106	−	0.305768i	$-0.901087\pi$
$467$	−16.0100	−	27.7302i	−0.740856	−	1.28320i	0.211251	−	0.977432i	$-0.432246\pi$
$468$	−10.9222			−0.504881
$469$	−8.07723	+	21.2535i	−0.372972	+	0.981396i
$470$	0.205545			0.00948111
$471$	0.522622	+	0.905208i	0.0240811	+	0.0417098i
$472$	7.58185	−	13.1321i	0.348983	−	0.604456i
$473$	12.9841	−	22.4891i	0.597009	−	1.03405i
$474$	0.670804	+	1.16187i	0.0308111	+	0.0533663i
$475$	0.438975			0.0201416
$476$	−3.08664	−	3.78580i	−0.141476	−	0.173522i
$477$	19.3564			0.886267
$478$	2.62212	+	4.54165i	0.119933	+	0.207730i
$479$	9.91377	−	17.1712i	0.452972	−	0.784570i	−0.545597	−	0.838048i	$-0.683697\pi$
$479$	9.91377	−	17.1712i	0.452972	−	0.784570i	0.998569	+	0.0534773i	$0.0170305\pi$
$480$	−0.405378	+	0.702135i	−0.0185029	+	0.0320479i
$481$	7.57471	+	13.1198i	0.345377	+	0.598210i
$482$	−5.10851			−0.232686
$483$	−0.368055	+	0.0595532i	−0.0167471	+	0.00270976i
$484$	8.93123			0.405965
$485$	3.05988	+	5.29987i	0.138942	+	0.240655i
$486$	−1.25069	+	2.16626i	−0.0567326	+	0.0982637i
$487$	0.657313	−	1.13850i	0.0297857	−	0.0515904i	−0.850748	−	0.525573i	$-0.823851\pi$
$487$	0.657313	−	1.13850i	0.0297857	−	0.0515904i	0.880534	+	0.473983i	$0.157184\pi$
$488$	−2.28142	−	3.95154i	−0.103275	−	0.178878i
$489$	1.81042			0.0818702
$490$	0.934986	−	4.54771i	0.0422384	−	0.205445i
$491$	9.69013			0.437309			0.218655	−	0.975802i	$-0.429833\pi$
$491$	9.69013			0.437309			0.218655	+	0.975802i	$0.429833\pi$
$492$	−0.0541697	−	0.0938246i	−0.00244216	−	0.00422994i
$493$	1.03634	−	1.79500i	0.0466746	−	0.0808428i
$494$	−0.341997	+	0.592356i	−0.0153872	+	0.0266513i
$495$	−3.42235	−	5.92769i	−0.153823	−	0.266430i
$496$	13.6633			0.613498
$497$	−24.1012	+	3.89969i	−1.08109	+	0.174925i
$498$	−1.34245			−0.0601565
$499$	13.5108	+	23.4013i	0.604825	+	1.04759i	0.992079	+	0.125614i	$0.0400901\pi$
$499$	13.5108	+	23.4013i	0.604825	+	1.04759i	−0.387255	+	0.921973i	$0.626577\pi$
$500$	0.780042	−	1.35107i	0.0348845	−	0.0604218i
$501$	−1.59949	+	2.77039i	−0.0714598	+	0.123772i
$502$	2.27293	+	3.93683i	0.101446	+	0.175709i
$503$	9.93624			0.443035			0.221517	−	0.975156i	$-0.428899\pi$
$503$	9.93624			0.443035			0.221517	+	0.975156i	$0.428899\pi$
$504$	11.7648	+	14.4297i	0.524047	+	0.642749i
$505$	17.5199			0.779627
$506$	−0.761680	−	1.31927i	−0.0338608	−	0.0586486i
$507$	−0.527121	+	0.913000i	−0.0234103	+	0.0405478i
$508$	−8.45764	+	14.6491i	−0.375247	+	0.649947i
$509$	21.0715	+	36.4969i	0.933977	+	1.61769i	0.776449	+	0.630180i	$0.217019\pi$
$509$	21.0715	+	36.4969i	0.933977	+	1.61769i	0.157528	+	0.987515i	$0.449648\pi$
$510$	−0.110610			−0.00489790
$511$	3.95258	−	10.4004i	0.174852	−	0.460085i
$512$	−16.2797			−0.719468
$513$	−0.184968	−	0.320375i	−0.00816655	−	0.0141449i
$514$	4.58941	−	7.94909i	0.202430	−	0.350619i
$515$	5.93503	−	10.2798i	0.261529	−	0.452981i
$516$	−1.24285	−	2.15267i	−0.0547133	−	0.0947662i
$517$	0.711772			0.0313037
$518$	4.02013	−	10.5781i	0.176634	−	0.464775i
$519$	−1.71950			−0.0754777
$520$	2.77359	+	4.80400i	0.121630	+	0.210669i
$521$	13.7013	−	23.7314i	0.600266	−	1.03969i	−0.392514	−	0.919746i	$-0.628395\pi$
$521$	13.7013	−	23.7314i	0.600266	−	1.03969i	0.992780	−	0.119945i	$-0.0382720\pi$
$522$	−1.73098	+	2.99814i	−0.0757628	+	0.131225i
$523$	7.05247	+	12.2152i	0.308383	+	0.534135i	0.978009	−	0.208564i	$-0.0668789\pi$
$523$	7.05247	+	12.2152i	0.308383	+	0.534135i	−0.669626	+	0.742699i	$0.733546\pi$
$524$	−11.0256			−0.481655
$525$	0.235602	+	0.288968i	0.0102825	+	0.0126116i
$526$	10.6019			0.462266
$527$	5.20234	+	9.01072i	0.226618	+	0.392513i
$528$	−0.251491	+	0.435596i	−0.0109448	+	0.0189569i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−2.15398	−	3.73080i	−0.0935629	−	0.162056i
$531$	19.1380			0.830519
$532$	−1.78865	+	0.289412i	−0.0775478	+	0.0125476i
$533$	−1.15768			−0.0501448
$534$	0.231625	+	0.401186i	0.0100234	+	0.0173610i
$535$	−5.26729	+	9.12321i	−0.227725	+	0.394431i
$536$	−10.1459	+	17.5733i	−0.438237	+	0.759049i
$537$	0.217952	+	0.377504i	0.00940533	+	0.0162905i
$538$	4.57024			0.197037
$539$	3.23771	−	15.7480i	0.139458	−	0.678315i
$540$	−1.31473			−0.0565768
$541$	11.3961	+	19.7386i	0.489955	+	0.848627i	0.999933	−	0.0115606i	$-0.00367994\pi$
$541$	11.3961	+	19.7386i	0.489955	+	0.848627i	−0.509978	+	0.860187i	$0.670347\pi$
$542$	4.90890	−	8.50246i	0.210855	−	0.365212i
$543$	0.772551	−	1.33810i	0.0331533	−	0.0574232i
$544$	−3.40423	−	5.89630i	−0.145955	−	0.252802i
$545$	15.9321			0.682455
$546$	−0.573488	+	0.0927933i	−0.0245430	+	0.00397119i
$547$	23.4443			1.00241			0.501204	−	0.865329i	$-0.332891\pi$
$547$	23.4443			1.00241			0.501204	+	0.865329i	$0.332891\pi$
$548$	−10.9463	−	18.9595i	−0.467602	−	0.809910i
$549$	2.87937	−	4.98722i	0.122889	−	0.212849i
$550$	−0.761680	+	1.31927i	−0.0324782	+	0.0562538i
$551$	−0.384423	−	0.665841i	−0.0163770	−	0.0283658i
$552$	−0.332752			−0.0141629
$553$	23.9976	+	29.4334i	1.02048	+	1.25163i
$554$	3.01447			0.128072
$555$	0.454375	+	0.787001i	0.0192872	+	0.0334063i
$556$	8.03044	−	13.9091i	0.340567	−	0.589878i
$557$	5.35227	−	9.27040i	0.226783	−	0.392800i	−0.730070	−	0.683372i	$-0.760513\pi$
$557$	5.35227	−	9.27040i	0.226783	−	0.392800i	0.956853	+	0.290573i	$0.0938459\pi$
$558$	−8.68933	−	15.0504i	−0.367849	−	0.637133i
$559$	−26.5614			−1.12343
$560$	−1.46065	+	3.84338i	−0.0617237	+	0.162413i
$561$	−0.383026			−0.0161714
$562$	−2.16264	−	3.74580i	−0.0912253	−	0.158007i
$563$	5.11162	−	8.85359i	0.215429	−	0.373134i	−0.737976	−	0.674827i	$-0.764218\pi$
$563$	5.11162	−	8.85359i	0.215429	−	0.373134i	0.953405	+	0.301693i	$0.0975516\pi$
$564$	0.0340657	−	0.0590035i	0.00143442	−	0.00248449i
$565$	−0.344281	−	0.596312i	−0.0144840	−	0.0250870i
$566$	11.0865			0.465999
$567$	−8.29157	+	21.8175i	−0.348213	+	0.916248i
$568$	−21.7894			−0.914265
$569$	2.86304	+	4.95894i	0.120025	+	0.207890i	0.919777	−	0.392441i	$-0.128369\pi$
$569$	2.86304	+	4.95894i	0.120025	+	0.207890i	−0.799752	+	0.600330i	$0.795036\pi$
$570$	−0.0205150	+	0.0355330i	−0.000859277	+	0.00148831i
$571$	−8.46183	+	14.6563i	−0.354116	+	0.613348i	−0.986966	−	0.160927i	$-0.948552\pi$
$571$	−8.46183	+	14.6563i	−0.354116	+	0.613348i	0.632850	+	0.774275i	$0.281885\pi$
$572$	4.20884	+	7.28993i	0.175981	+	0.304807i
$573$	0.921158			0.0384819
$574$	0.546450	+	0.670227i	0.0228084	+	0.0279747i
$575$	1.00000			0.0417029
$576$	1.05476	+	1.82689i	0.0439482	+	0.0761204i
$577$	10.0617	−	17.4274i	0.418874	−	0.725512i	−0.576952	−	0.816778i	$-0.695758\pi$
$577$	10.0617	−	17.4274i	0.418874	−	0.725512i	0.995827	+	0.0912662i	$0.0290914\pi$
$578$	−5.17329	+	8.96040i	−0.215180	+	0.372704i
$579$	0.969565	+	1.67934i	0.0402937	+	0.0697908i
$580$	−2.73242			−0.113458
$581$	−37.5123	+	6.06968i	−1.55627	+	0.251813i
$582$	−0.571999			−0.0237101
$583$	−7.45890	−	12.9192i	−0.308916	−	0.535058i
$584$	4.96489	−	8.59945i	0.205449	−	0.355848i
$585$	−3.50053	+	6.06310i	−0.144729	+	0.250678i
$586$	8.06326	+	13.9660i	0.333090	+	0.576929i
$587$	−8.43540			−0.348166			−0.174083	−	0.984731i	$-0.555696\pi$
$587$	−8.43540			−0.348166			−0.174083	+	0.984731i	$0.555696\pi$
$588$	−1.15050	−	1.02210i	−0.0474458	−	0.0421507i
$589$	3.85953			0.159029
$590$	−2.12968	−	3.68872i	−0.0876776	−	0.151862i
$591$	−0.0773185	+	0.133920i	−0.00318046	+	0.00550872i
$592$	−5.01070	+	8.67879i	−0.205939	+	0.356696i
$593$	−16.0013	−	27.7150i	−0.657093	−	1.13812i	−0.981365	−	0.192155i	$-0.938453\pi$
$593$	−16.0013	−	27.7150i	−0.657093	−	1.13812i	0.324272	−	0.945964i	$-0.394881\pi$
$594$	1.28378			0.0526740
$595$	−3.09080	+	0.500108i	−0.126711	+	0.0205024i
$596$	16.0802			0.658670
$597$	1.03525	+	1.79310i	0.0423698	+	0.0733867i
$598$	−0.779079	+	1.34941i	−0.0318589	+	0.0551813i
$599$	−8.01629	+	13.8846i	−0.327537	+	0.567310i	−0.982022	−	0.188764i	$-0.939552\pi$
$599$	−8.01629	+	13.8846i	−0.327537	+	0.567310i	0.654486	+	0.756074i	$0.272885\pi$
$600$	0.166376	+	0.288172i	0.00679227	+	0.0117646i
$601$	8.60174			0.350872			0.175436	−	0.984491i	$-0.443866\pi$
$601$	8.60174			0.350872			0.175436	+	0.984491i	$0.443866\pi$
$602$	12.5375	+	15.3774i	0.510992	+	0.626737i
$603$	−25.6102			−1.04293
$604$	−9.32288	−	16.1477i	−0.379343	−	0.657041i
$605$	2.86242	−	4.95786i	0.116374	−	0.201566i
$606$	−0.818773	+	1.41816i	−0.0332604	+	0.0576087i
$607$	−9.97427	−	17.2759i	−0.404843	−	0.701209i	0.589460	−	0.807798i	$-0.299341\pi$
$607$	−9.97427	−	17.2759i	−0.404843	−	0.701209i	−0.994303	+	0.106589i	$0.966007\pi$
$608$	−2.52554			−0.102424
$609$	0.231986	−	0.610421i	0.00940054	−	0.0247355i
$610$	−1.28167			−0.0518933
$611$	−0.364016	−	0.630494i	−0.0147265	−	0.0255070i
$612$	2.75099	−	4.76486i	0.111202	−	0.192608i
$613$	14.8750	−	25.7643i	0.600796	−	1.04061i	−0.391905	−	0.920006i	$-0.628184\pi$
$613$	14.8750	−	25.7643i	0.600796	−	1.04061i	0.992701	−	0.120604i	$-0.0384830\pi$
$614$	−3.29841	−	5.71301i	−0.133113	−	0.230558i
$615$	−0.0694445			−0.00280027
$616$	5.09740	−	13.4127i	0.205380	−	0.540414i
$617$	17.9270			0.721713			0.360857	−	0.932621i	$-0.382484\pi$
$617$	17.9270			0.721713			0.360857	+	0.932621i	$0.382484\pi$
$618$	0.554732	+	0.960824i	0.0223146	+	0.0386500i
$619$	18.4811	−	32.0102i	0.742818	−	1.28660i	−0.208389	−	0.978046i	$-0.566822\pi$
$619$	18.4811	−	32.0102i	0.742818	−	1.28660i	0.951207	−	0.308553i	$-0.0998447\pi$
$620$	6.85824	−	11.8788i	0.275434	−	0.477065i
$621$	−0.421364	−	0.729824i	−0.0169087	−	0.0292868i
$622$	−4.06448			−0.162971
$623$	8.28625	+	10.1632i	0.331982	+	0.407179i
$624$	0.514473			0.0205954
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.82301	+	8.35369i	−0.192766	+	0.333881i
$627$	−0.0710401	+	0.123045i	−0.00283707	+	0.00491395i
$628$	5.78575	+	10.0212i	0.230877	+	0.399890i
$629$	−7.63139			−0.304283
$630$	5.16248	−	0.835316i	0.205678	−	0.0332798i
$631$	−32.6900			−1.30137			−0.650684	−	0.759349i	$-0.725518\pi$
$631$	−32.6900			−1.30137			−0.650684	+	0.759349i	$0.725518\pi$
$632$	16.9465	+	29.3522i	0.674096	+	1.16757i
$633$	−0.735657	+	1.27420i	−0.0292397	+	0.0506447i
$634$	−5.71444	+	9.89770i	−0.226949	+	0.393088i
$635$	5.42127	+	9.38992i	0.215137	+	0.372627i
$636$	−1.42794			−0.0566216
$637$	−15.6056	+	5.18589i	−0.618315	+	0.205472i
$638$	2.66810			0.105631
$639$	−13.7502	−	23.8160i	−0.543948	−	0.942146i
$640$	−5.51852	+	9.55835i	−0.218138	+	0.377827i
$641$	12.3164	−	21.3327i	0.486470	−	0.842591i	−0.513409	−	0.858144i	$-0.671617\pi$
$641$	12.3164	−	21.3327i	0.486470	−	0.842591i	0.999879	+	0.0155529i	$0.00495083\pi$
$642$	−0.492320	−	0.852724i	−0.0194303	−	0.0336543i
$643$	31.4947			1.24203			0.621016	−	0.783798i	$-0.286720\pi$
$643$	31.4947			1.24203			0.621016	+	0.783798i	$0.286720\pi$
$644$	−4.07460	+	0.659291i	−0.160562	+	0.0259797i
$645$	−1.59331			−0.0627364
$646$	−0.172278	−	0.298394i	−0.00677818	−	0.0117402i
$647$	−12.8382	+	22.2365i	−0.504723	+	0.874206i	0.495262	+	0.868744i	$0.335072\pi$
$647$	−12.8382	+	22.2365i	−0.504723	+	0.874206i	−0.999985	+	0.00546216i	$0.998261\pi$
$648$	−10.4152	+	18.0396i	−0.409146	+	0.708661i
$649$	−7.37476	−	12.7735i	−0.289485	−	0.501402i
$650$	1.55816			0.0611160
$651$	2.07145	+	2.54065i	0.0811864	+	0.0995760i
$652$	20.0425			0.784926
$653$	−11.3329	−	19.6292i	−0.443492	−	0.768151i	0.554453	−	0.832215i	$-0.312927\pi$
$653$	−11.3329	−	19.6292i	−0.443492	−	0.768151i	−0.997946	+	0.0640635i	$0.979594\pi$
$654$	−0.744565	+	1.28962i	−0.0291148	+	0.0504283i
$655$	−3.53365	+	6.12046i	−0.138071	+	0.239146i
$656$	−0.382906	−	0.663212i	−0.0149500	−	0.0258941i
$657$	12.5323			0.488933
$658$	−0.193194	+	0.508349i	−0.00753149	+	0.0198175i
$659$	−47.1731			−1.83760			−0.918802	−	0.394719i	$-0.870842\pi$
$659$	−47.1731			−1.83760			−0.918802	+	0.394719i	$0.870842\pi$
$660$	0.252471	+	0.437293i	0.00982742	+	0.0170216i
$661$	10.8183	−	18.7379i	0.420784	−	0.728818i	−0.575233	−	0.817990i	$-0.695089\pi$
$661$	10.8183	−	18.7379i	0.420784	−	0.728818i	0.996016	+	0.0891713i	$0.0284219\pi$
$662$	5.97171	−	10.3433i	0.232097	−	0.402004i
$663$	0.195888	+	0.339287i	0.00760765	+	0.0131768i
$664$	−33.9142			−1.31613
$665$	−0.412597	+	1.08566i	−0.0159998	+	0.0421001i
$666$	12.7465			0.493917
$667$	−0.875729	−	1.51681i	−0.0339084	−	0.0587310i
$668$	−17.7073	+	30.6700i	−0.685117	+	1.18666i
$669$	−1.43130	+	2.47908i	−0.0553373	+	0.0958470i
$670$	2.84991	+	4.93619i	0.110102	+	0.190702i
$671$	−4.43822			−0.171336
$672$	−1.35548	−	1.66251i	−0.0522888	−	0.0641328i
$673$	−29.3457			−1.13119			−0.565597	−	0.824682i	$-0.691354\pi$
$673$	−29.3457			−1.13119			−0.565597	+	0.824682i	$0.691354\pi$
$674$	−4.04108	−	6.99936i	−0.155657	−	0.269605i
$675$	−0.421364	+	0.729824i	−0.0162183	+	0.0280909i
$676$	−5.83556	+	10.1075i	−0.224445	+	0.388749i
$677$	1.44793	+	2.50788i	0.0556484	+	0.0963858i	0.892508	−	0.451032i	$-0.148944\pi$
$677$	1.44793	+	2.50788i	0.0556484	+	0.0963858i	−0.836859	+	0.547418i	$0.815611\pi$
$678$	0.0643581			0.00247166
$679$	−15.9835	+	2.58621i	−0.613390	+	0.0992496i
$680$	−2.79434			−0.107158
$681$	−0.492320	−	0.852723i	−0.0188657	−	0.0326764i
$682$	−6.69680	+	11.5992i	−0.256434	+	0.444156i
$683$	11.7586	−	20.3664i	0.449929	−	0.779300i	−0.548452	−	0.836182i	$-0.684783\pi$
$683$	11.7586	−	20.3664i	0.449929	−	0.779300i	0.998381	+	0.0568822i	$0.0181159\pi$
$684$	−1.02046	−	1.76748i	−0.0390182	−	0.0675815i
$685$	−14.0329			−0.536171
$686$	10.3685	+	6.58682i	0.395870	+	0.251486i
$687$	3.97562			0.151679
$688$	−8.78523	−	15.2165i	−0.334934	−	0.580123i
$689$	−7.62928	+	13.2143i	−0.290652	+	0.503425i
$690$	−0.0467337	+	0.0809452i	−0.00177912	+	0.00308153i
$691$	−19.3239	−	33.4700i	−0.735117	−	1.27326i	−0.954672	−	0.297660i	$-0.903794\pi$
$691$	−19.3239	−	33.4700i	−0.735117	−	1.27326i	0.219555	−	0.975600i	$-0.429539\pi$
$692$	−19.0360			−0.723638
$693$	17.8769	−	2.89257i	0.679087	−	0.109880i
$694$	12.6434			0.479936
$695$	−5.14744	−	8.91563i	−0.195254	−	0.338189i
$696$	0.291401	−	0.504721i	0.0110455	−	0.0191314i
$697$	0.291586	−	0.505042i	0.0110446	−	0.0191298i
$698$	3.08619	+	5.34543i	0.116814	+	0.202328i
$699$	2.97613			0.112568
$700$	2.60826	+	3.19906i	0.0985831	+	0.120913i
$701$	−8.43425			−0.318557			−0.159279	−	0.987234i	$-0.550917\pi$
$701$	−8.43425			−0.318557			−0.159279	+	0.987234i	$0.550917\pi$
$702$	−0.656552	−	1.13718i	−0.0247799	−	0.0429201i
$703$	−1.41540	+	2.45154i	−0.0533828	+	0.0924617i
$704$	0.812892	−	1.40797i	0.0306370	−	0.0530649i
$705$	−0.0218358	−	0.0378207i	−0.000822383	−	0.00142441i
$706$	−11.3367			−0.426662
$707$	−16.4672	+	43.3298i	−0.619311	+	1.62959i
$708$	−1.41183			−0.0530600
$709$	−1.89119	−	3.27563i	−0.0710250	−	0.123019i	0.828326	−	0.560247i	$-0.189294\pi$
$709$	−1.89119	−	3.27563i	−0.0710250	−	0.123019i	−0.899351	+	0.437228i	$0.855960\pi$
$710$	−3.06024	+	5.30050i	−0.114849	+	0.198924i
$711$	−21.3881	+	37.0453i	−0.802116	+	1.38931i
$712$	5.85154	+	10.1352i	0.219296	+	0.379831i
$713$	8.79214			0.329268
$714$	0.103964	−	0.273558i	0.00389074	−	0.0102376i
$715$	5.39566			0.201786
$716$	2.41287	+	4.17921i	0.0901731	+	0.156184i
$717$	0.557114	−	0.964949i	0.0208058	−	0.0360367i
$718$	−11.1628	+	19.3345i	−0.416590	+	0.721556i
$719$	−18.1597	−	31.4536i	−0.677244	−	1.17302i	−0.975808	−	0.218631i	$-0.929841\pi$
$719$	−18.1597	−	31.4536i	−0.677244	−	1.17302i	0.298564	−	0.954390i	$-0.403492\pi$
$720$	−4.63123			−0.172596
$721$	19.8452	+	24.3404i	0.739075	+	0.906483i
$722$	12.4742			0.464240
$723$	0.542694	+	0.939974i	0.0201830	+	0.0349580i
$724$	8.55262	−	14.8136i	0.317856	−	0.550542i
$725$	−0.875729	+	1.51681i	−0.0325238	+	0.0563328i
$726$	0.267543	+	0.463398i	0.00992946	+	0.0171983i
$727$	42.0694			1.56027			0.780134	−	0.625613i	$-0.215151\pi$
$727$	42.0694			1.56027			0.780134	+	0.625613i	$0.215151\pi$
$728$	−14.4880	+	2.34423i	−0.536962	+	0.0868831i
$729$	−25.9335			−0.960501
$730$	−1.39460	−	2.41552i	−0.0516165	−	0.0894023i
$731$	6.69003	−	11.5875i	0.247440	−	0.428578i
$732$	−0.212415	+	0.367913i	−0.00785108	+	0.0135985i
$733$	6.63560	+	11.4932i	0.245092	+	0.424511i	0.962157	−	0.272494i	$-0.0878486\pi$
$733$	6.63560	+	11.4932i	0.245092	+	0.424511i	−0.717066	+	0.697006i	$0.754515\pi$
$734$	−20.6626			−0.762672
$735$	−0.936113	+	0.311080i	−0.0345290	+	0.0114744i
$736$	−5.75326			−0.212068
$737$	9.86880	+	17.0933i	0.363522	+	0.629639i
$738$	−0.487028	+	0.843557i	−0.0179278	+	0.0310518i
$739$	−0.152579	+	0.264274i	−0.00561270	+	0.00972148i	−0.868818	−	0.495131i	$-0.835120\pi$
$739$	−0.152579	+	0.264274i	−0.00561270	+	0.00972148i	0.863205	+	0.504853i	$0.168453\pi$
$740$	5.03022	+	8.71260i	0.184915	+	0.320281i
$741$	0.145326			0.00533868
$742$	11.2515	−	1.82054i	0.413054	−	0.0668342i
$743$	−22.5046			−0.825614			−0.412807	−	0.910819i	$-0.635452\pi$
$743$	−22.5046			−0.825614			−0.412807	+	0.910819i	$0.635452\pi$
$744$	1.46280	+	2.53365i	0.0536289	+	0.0928880i
$745$	5.15362	−	8.92634i	0.188814	−	0.327036i
$746$	3.67828	−	6.37097i	0.134671	−	0.233258i
$747$	−21.4015	−	37.0684i	−0.783039	−	1.35626i
$748$	−4.24034			−0.155042
$749$	−17.6125	−	21.6019i	−0.643546	−	0.789316i
$750$	0.0934675			0.00341295
$751$	−21.1286	−	36.5959i	−0.770995	−	1.33540i	−0.937018	−	0.349281i	$-0.886426\pi$
$751$	−21.1286	−	36.5959i	−0.770995	−	1.33540i	0.166023	−	0.986122i	$-0.446907\pi$
$752$	0.240798	−	0.417074i	0.00878100	−	0.0152091i
$753$	0.482922	−	0.836446i	0.0175987	−	0.0304818i
$754$	−1.36453	−	2.36343i	−0.0496931	−	0.0860709i
$755$	−11.9518			−0.434970
$756$	1.23572	−	3.25154i	0.0449428	−	0.118257i
$757$	28.2230			1.02578			0.512892	−	0.858453i	$-0.328574\pi$
$757$	28.2230			1.02578			0.512892	+	0.858453i	$0.328574\pi$
$758$	−1.57603	−	2.72976i	−0.0572438	−	0.0991492i
$759$	−0.161832	+	0.280301i	−0.00587412	+	0.0101743i
$760$	−0.518269	+	0.897668i	−0.0187996	+	0.0325618i
$761$	7.84453	+	13.5871i	0.284364	+	0.492533i	0.972455	−	0.233092i	$-0.0748843\pi$
$761$	7.84453	+	13.5871i	0.284364	+	0.492533i	−0.688091	+	0.725625i	$0.741551\pi$
$762$	−1.01343			−0.0367125
$763$	−14.9747	+	39.4027i	−0.542120	+	1.42647i
$764$	10.1978			0.368943
$765$	−1.76336	−	3.05423i	−0.0637545	−	0.110426i
$766$	3.27535	−	5.67307i	0.118343	−	0.204976i
$767$	−7.54322	+	13.0652i	−0.272370	+	0.471759i
$768$	−0.615554	−	1.06617i	−0.0222119	−	0.0384721i
$769$	12.6533			0.456290			0.228145	−	0.973627i	$-0.426734\pi$
$769$	12.6533			0.456290			0.228145	+	0.973627i	$0.426734\pi$
$770$	−2.54687	−	3.12376i	−0.0917827	−	0.112572i
$771$	−1.95019			−0.0702345
$772$	10.7337	+	18.5913i	0.386314	+	0.669116i
$773$	−5.46530	+	9.46618i	−0.196573	+	0.340475i	−0.947415	−	0.320007i	$-0.896315\pi$
$773$	−5.46530	+	9.46618i	−0.196573	+	0.340475i	0.750842	+	0.660482i	$0.229648\pi$
$774$	−11.1742	+	19.3542i	−0.401647	+	0.695674i
$775$	−4.39607	−	7.61422i	−0.157912	−	0.273511i
$776$	−14.4504			−0.518739
$777$	−2.37346	+	0.384038i	−0.0851474	+	0.0137773i
$778$	17.6821			0.633933
$779$	−0.108161	−	0.187341i	−0.00387529	−	0.00671219i
$780$	0.258238	−	0.447282i	0.00924642	−	0.0160153i
$781$	−10.5971	+	18.3548i	−0.379196	+	0.656786i
$782$	−0.392454	−	0.679751i	−0.0140341	−	0.0243078i
$783$	1.47600			0.0527480
$784$	−8.13246	−	7.22486i	−0.290445	−	0.258031i
$785$	7.41723			0.264732
$786$	−0.330281	−	0.572064i	−0.0117807	−	0.0204048i
$787$	−5.05761	+	8.76004i	−0.180284	+	0.312262i	−0.941977	−	0.335677i	$-0.891035\pi$
$787$	−5.05761	+	8.76004i	−0.180284	+	0.312262i	0.761693	+	0.647938i	$0.224368\pi$
$788$	−0.855964	+	1.48257i	−0.0304925	+	0.0528145i
$789$	−1.12628	−	1.95077i	−0.0400965	−	0.0694492i
$790$	9.52029			0.338717
$791$	1.79837	−	0.290986i	0.0639428	−	0.0103463i
$792$	16.1622			0.574298
$793$	2.26980	+	3.93141i	0.0806030	+	0.139609i
$794$	−3.58588	+	6.21093i	−0.127258	+	0.220417i
$795$	−0.457649	+	0.792671i	−0.0162311	+	0.0281132i
$796$	11.4608	+	19.8507i	0.406218	+	0.703591i
$797$	26.6699			0.944697			0.472349	−	0.881412i	$-0.343406\pi$
$797$	26.6699			0.944697			0.472349	+	0.881412i	$0.343406\pi$
$798$	−0.0685968	−	0.0841348i	−0.00242830	−	0.00297834i
$799$	0.366739			0.0129743
$800$	2.87663	+	4.98247i	0.101704	+	0.176157i
$801$	−7.38519	+	12.7915i	−0.260943	+	0.451966i
$802$	−3.53990	+	6.13128i	−0.124998	+	0.216503i
$803$	−4.82928	−	8.36456i	−0.170422	−	0.295179i
$804$	1.88930			0.0666304
$805$	−0.939909	+	2.47317i	−0.0331275	+	0.0871678i
$806$	13.6996			0.482546
$807$	−0.485512	−	0.840931i	−0.0170908	−	0.0296022i
$808$	−20.6846	+	35.8268i	−0.727683	+	1.26038i
$809$	−18.6598	+	32.3198i	−0.656045	+	1.13630i	0.325586	+	0.945513i	$0.394439\pi$
$809$	−18.6598	+	32.3198i	−0.656045	+	1.13630i	−0.981631	+	0.190791i	$0.938895\pi$
$810$	2.92554	+	5.06718i	0.102793	+	0.178042i
$811$	−44.0052			−1.54523			−0.772616	−	0.634873i	$-0.781052\pi$
$811$	−44.0052			−1.54523			−0.772616	+	0.634873i	$0.781052\pi$
$812$	2.56823	−	6.75775i	0.0901272	−	0.237150i
$813$	−2.08596			−0.0731577
$814$	−4.91181	−	8.50751i	−0.172159	−	0.298188i
$815$	6.42354	−	11.1259i	0.225007	−	0.389723i
$816$	−0.129581	+	0.224440i	−0.00453623	+	0.00785698i
$817$	−2.48161	−	4.29828i	−0.0868206	−	0.150378i
$818$	22.2381			0.777536
$819$	−11.7049	−	14.3562i	−0.409002	−	0.501645i
$820$	−0.768795			−0.0268475
$821$	−15.5108	−	26.8655i	−0.541331	−	0.937613i	−0.998828	−	0.0484018i	$-0.984587\pi$
$821$	−15.5108	−	26.8655i	−0.541331	−	0.937613i	0.457497	−	0.889211i	$-0.348746\pi$
$822$	0.655812	−	1.13590i	0.0228741	−	0.0396190i
$823$	−21.8332	+	37.8162i	−0.761057	+	1.31819i	0.181249	+	0.983437i	$0.441986\pi$
$823$	−21.8332	+	37.8162i	−0.761057	+	1.31819i	−0.942306	+	0.334752i	$0.891347\pi$
$824$	14.0142	+	24.2733i	0.488207	+	0.845600i
$825$	0.323663			0.0112685
$826$	11.1245	−	1.80001i	0.387072	−	0.0626302i
$827$	3.97442			0.138204			0.0691020	−	0.997610i	$-0.477987\pi$
$827$	3.97442			0.138204			0.0691020	+	0.997610i	$0.477987\pi$
$828$	−2.32464	−	4.02639i	−0.0807867	−	0.139927i
$829$	19.2762	−	33.3873i	0.669488	−	1.15959i	−0.308559	−	0.951205i	$-0.599847\pi$
$829$	19.2762	−	33.3873i	0.669488	−	1.15959i	0.978047	−	0.208383i	$-0.0668200\pi$
$830$	−4.76312	+	8.24997i	−0.165330	+	0.286361i
$831$	−0.320237	−	0.554667i	−0.0111089	−	0.0192412i
$832$	−1.66292			−0.0576515
$833$	1.66823	−	8.11414i	0.0578006	−	0.281138i
$834$	0.962237			0.0333195
$835$	11.3502	+	19.6592i	0.392791	+	0.680334i
$836$	−0.786459	+	1.36219i	−0.0272002	+	0.0471122i
$837$	−3.70469	+	6.41671i	−0.128053	+	0.221794i
$838$	−11.9893	−	20.7662i	−0.414165	−	0.717355i
$839$	16.4765			0.568832			0.284416	−	0.958701i	$-0.408200\pi$
$839$	16.4765			0.568832			0.284416	+	0.958701i	$0.408200\pi$
$840$	−0.869076	+	0.140621i	−0.0299860	+	0.00485188i
$841$	−25.9324			−0.894220
$842$	−10.1380	−	17.5595i	−0.349377	−	0.605139i
$843$	−0.459488	+	0.795857i	−0.0158256	+	0.0274108i
$844$	−8.14418	+	14.1061i	−0.280334	+	0.485553i
$845$	3.74054	+	6.47881i	0.128679	+	0.222878i
$846$	−0.612555			−0.0210601
$847$	9.57121	+	11.7392i	0.328871	+	0.403363i
$848$	−10.0936			−0.346616
$849$	−1.17775	−	2.03993i	−0.0404204	−	0.0700102i
$850$	−0.392454	+	0.679751i	−0.0134611	+	0.0233153i
$851$	−3.22433	+	5.58470i	−0.110528	+	0.191441i
$852$	1.01437	+	1.75693i	0.0347516	+	0.0601916i
$853$	−9.16031			−0.313643			−0.156822	−	0.987627i	$-0.550125\pi$
$853$	−9.16031			−0.313643			−0.156822	+	0.987627i	$0.550125\pi$
$854$	1.20465	−	3.16979i	0.0412224	−	0.108468i
$855$	−1.30821			−0.0447398
$856$	−12.4375	−	21.5423i	−0.425104	−	0.736302i
$857$	19.0971	−	33.0772i	0.652346	−	1.12990i	−0.330206	−	0.943909i	$-0.607118\pi$
$857$	19.0971	−	33.0772i	0.652346	−	1.12990i	0.982552	−	0.185987i	$-0.0595483\pi$
$858$	−0.252160	+	0.436753i	−0.00860858	+	0.0149105i
$859$	−2.09661	−	3.63144i	−0.0715355	−	0.123903i	0.828039	−	0.560671i	$-0.189457\pi$
$859$	−2.09661	−	3.63144i	−0.0715355	−	0.123903i	−0.899574	+	0.436767i	$0.856123\pi$
$860$	−17.6389			−0.601482
$861$	0.0652716	−	0.171748i	0.00222445	−	0.00585316i
$862$	−2.09388			−0.0713178
$863$	−15.7615	−	27.2997i	−0.536527	−	0.929293i	−0.999088	−	0.0427048i	$-0.986403\pi$
$863$	−15.7615	−	27.2997i	−0.536527	−	0.929293i	0.462560	−	0.886588i	$-0.346931\pi$
$864$	2.42422	−	4.19887i	0.0824735	−	0.142848i
$865$	−6.10094	+	10.5671i	−0.207438	+	0.359293i
$866$	7.71346	+	13.3601i	0.262114	+	0.453995i
$867$	2.19830			0.0746583
$868$	22.9322	+	28.1266i	0.778370	+	0.954679i
$869$	32.9673			1.11834
$870$	−0.0818522	−	0.141772i	−0.00277505	−	0.00480653i
$871$	10.0942	−	17.4837i	0.342030	−	0.592414i
$872$	−18.8099	+	32.5798i	−0.636985	+	1.10329i
$873$	−9.11888	−	15.7944i	−0.308627	−	0.534558i
$874$	−0.291155			−0.00984848
$875$	2.61178	−	0.422600i	0.0882944	−	0.0142865i
$876$	−0.924525			−0.0312368
$877$	2.50821	+	4.34434i	0.0846961	+	0.146698i	0.905262	−	0.424854i	$-0.139675\pi$
$877$	2.50821	+	4.34434i	0.0846961	+	0.146698i	−0.820566	+	0.571552i	$0.806341\pi$
$878$	10.1972	−	17.6621i	0.344140	−	0.596068i
$879$	1.71317	−	2.96730i	0.0577839	−	0.100085i
$880$	1.78463	+	3.09106i	0.0601598	+	0.104200i
$881$	−27.0033			−0.909763			−0.454882	−	0.890552i	$-0.650318\pi$
$881$	−27.0033			−0.909763			−0.454882	+	0.890552i	$0.650318\pi$
$882$	−2.78639	+	13.5528i	−0.0938226	+	0.456347i
$883$	−14.9452			−0.502946			−0.251473	−	0.967864i	$-0.580915\pi$
$883$	−14.9452			−0.502946			−0.251473	+	0.967864i	$0.580915\pi$
$884$	2.16860	+	3.75612i	0.0729379	+	0.126332i
$885$	−0.452487	+	0.783730i	−0.0152102	+	0.0263448i
$886$	12.2790	−	21.2679i	0.412522	−	0.714509i
$887$	28.5407	+	49.4340i	0.958304	+	1.65983i	0.726620	+	0.687039i	$0.241090\pi$
$887$	28.5407	+	49.4340i	0.958304	+	1.65983i	0.231683	+	0.972791i	$0.425577\pi$
$888$	−2.14580			−0.0720084
$889$	−28.3184	+	4.58205i	−0.949767	+	0.153677i
$890$	3.28730			0.110191
$891$	10.1307	+	17.5468i	0.339390	+	0.587841i
$892$	−15.8454	+	27.4450i	−0.530543	+	0.918927i
$893$	0.0680195	−	0.117813i	0.00227618	−	0.00394247i
$894$	0.481696	+	0.834323i	0.0161103	+	0.0279039i
$895$	3.09325			0.103396
$896$	−18.4525	−	22.6322i	−0.616455	−	0.756089i
$897$	0.331057			0.0110537
$898$	−8.33105	−	14.4298i	−0.278011	−	0.481529i
$899$	−7.69953	+	13.3360i	−0.256794	+	0.444780i
$900$	−2.32464	+	4.02639i	−0.0774879	+	0.134213i
$901$	−3.84318	−	6.65659i	−0.128035	−	0.221763i
$902$	0.750698			0.0249955
$903$	1.49756	−	3.94052i	0.0498358	−	0.131132i
$904$	1.62588			0.0540759
$905$	−5.48215	−	9.49537i	−0.182233	−	0.315637i
$906$	0.558551	−	0.967439i	0.0185566	−	0.0321410i
$907$	4.44353	−	7.69641i	0.147545	−	0.255555i	−0.782775	−	0.622305i	$-0.786196\pi$
$907$	4.44353	−	7.69641i	0.147545	−	0.255555i	0.930320	+	0.366750i	$0.119530\pi$
$908$	−5.45029	−	9.44018i	−0.180874	−	0.313283i
$909$	−52.2119			−1.73176
$910$	−1.46453	+	3.85359i	−0.0485486	+	0.127745i
$911$	−32.0804			−1.06287			−0.531435	−	0.847099i	$-0.678347\pi$
$911$	−32.0804			−1.06287			−0.531435	+	0.847099i	$0.678347\pi$
$912$	0.0480668	+	0.0832542i	0.00159165	+	0.00275682i
$913$	−16.4939	+	28.5684i	−0.545870	+	0.945474i
$914$	4.69014	−	8.12355i	0.155136	−	0.268703i
$915$	0.136156	+	0.235829i	0.00450118	+	0.00779627i
$916$	44.0126			1.45422
$917$	−11.8156	−	14.4920i	−0.390186	−	0.478568i
$918$	0.661464			0.0218316
$919$	7.37795	+	12.7790i	0.243376	+	0.421540i	0.961674	−	0.274196i	$-0.0884117\pi$
$919$	7.37795	+	12.7790i	0.243376	+	0.421540i	−0.718298	+	0.695736i	$0.755078\pi$
$920$	−1.18063	+	2.04492i	−0.0389243	+	0.0674189i
$921$	−0.700803	+	1.21383i	−0.0230922	+	0.0399969i
$922$	−2.46923	−	4.27683i	−0.0813198	−	0.140850i
$923$	21.6784			0.713554
$924$	−1.31880	+	0.213388i	−0.0433853	+	0.00701996i
$925$	6.44865			0.212030
$926$	1.80998	+	3.13498i	0.0594796	+	0.103022i
$927$	−17.6872	+	30.6352i	−0.580924	+	1.00619i
$928$	5.03830	−	8.72659i	0.165390	−	0.286464i
$929$	1.65113	+	2.85985i	0.0541720	+	0.0938286i	0.891840	−	0.452352i	$-0.149415\pi$
$929$	1.65113	+	2.85985i	0.0541720	+	0.0938286i	−0.837668	+	0.546180i	$0.816081\pi$
$930$	0.821779			0.0269472
$931$	−2.29722	−	2.04085i	−0.0752883	−	0.0668860i
$932$	32.9477			1.07924
$933$	0.431783	+	0.747870i	0.0141359	+	0.0244842i
$934$	10.6188	−	18.3924i	0.347459	−	0.601816i
$935$	−1.35901	+	2.35387i	−0.0444443	+	0.0769799i
$936$	−8.26568	−	14.3166i	−0.270172	−	0.467952i
$937$	34.9652			1.14226			0.571132	−	0.820858i	$-0.306504\pi$
$937$	34.9652			1.14226			0.571132	+	0.820858i	$0.306504\pi$
$938$	−14.8867	+	2.40874i	−0.486068	+	0.0786483i
$939$	2.04946			0.0668815
$940$	−0.241736	−	0.418699i	−0.00788456	−	0.0136565i
$941$	−24.8079	+	42.9685i	−0.808713	+	1.40073i	0.105042	+	0.994468i	$0.466502\pi$
$941$	−24.8079	+	42.9685i	−0.808713	+	1.40073i	−0.913756	+	0.406264i	$0.866831\pi$
$942$	−0.346635	+	0.600389i	−0.0112940	+	0.0195617i
$943$	−0.246395	−	0.426769i	−0.00802373	−	0.0138975i
$944$	−9.97975			−0.324813
$945$	−1.40893	−	1.72807i	−0.0458326	−	0.0562142i
$946$	17.2237			0.559991
$947$	15.6163	+	27.0482i	0.507460	+	0.878947i	0.999963	+	0.00863588i	$0.00274892\pi$
$947$	15.6163	+	27.0482i	0.507460	+	0.878947i	−0.492502	+	0.870311i	$0.663918\pi$
$948$	1.57783	−	2.73287i	0.0512454	−	0.0887596i
$949$	−4.93960	+	8.55564i	−0.160346	+	0.277728i
$950$	0.145578	+	0.252148i	0.00472316	+	0.00818076i
$951$	2.42826			0.0787416
$952$	2.62643	−	6.91088i	0.0851230	−	0.223983i
$953$	31.9297			1.03431			0.517153	−	0.855893i	$-0.326992\pi$
$953$	31.9297			1.03431			0.517153	+	0.855893i	$0.326992\pi$
$954$	6.41916	+	11.1183i	0.207828	+	0.359969i
$955$	3.26835	−	5.66095i	0.105761	−	0.183184i
$956$	6.16760	−	10.6826i	0.199474	−	0.345500i
$957$	−0.283442	−	0.490935i	−0.00916236	−	0.0158697i
$958$	13.1508			0.424885
$959$	13.1897	−	34.7058i	0.425917	−	1.12071i
$960$	−0.0997518			−0.00321948
$961$	−23.1509	−	40.0985i	−0.746802	−	1.29350i
$962$	−5.02401	+	8.70184i	−0.161981	+	0.280559i
$963$	15.6973	−	27.1885i	0.505837	−	0.876136i
$964$	6.00797	+	10.4061i	0.193504	+	0.335158i
$965$	13.7604			0.442963
$966$	−0.156266	−	0.191662i	−0.00502777	−	0.00616661i
$967$	−5.29114			−0.170152			−0.0850758	−	0.996374i	$-0.527113\pi$
$967$	−5.29114			−0.170152			−0.0850758	+	0.996374i	$0.527113\pi$
$968$	6.75894	+	11.7068i	0.217240	+	0.376272i
$969$	−0.0366033	+	0.0633988i	−0.00117587	+	0.00203666i
$970$	−2.02950	+	3.51520i	−0.0651634	+	0.112866i
$971$	−6.00208	−	10.3959i	−0.192616	−	0.333620i	0.753501	−	0.657447i	$-0.228364\pi$
$971$	−6.00208	−	10.3959i	−0.192616	−	0.333620i	−0.946116	+	0.323827i	$0.895030\pi$
$972$	5.88361			0.188717
$973$	26.8880	−	4.35061i	0.861989	−	0.139474i
$974$	0.871941			0.0279388
$975$	−0.165528	−	0.286704i	−0.00530115	−	0.00918187i
$976$	−1.50148	+	2.60065i	−0.0480613	+	0.0832447i
$977$	26.1920	−	45.3659i	0.837957	−	1.45138i	−0.0536424	−	0.998560i	$-0.517083\pi$
$977$	26.1920	−	45.3659i	0.837957	−	1.45138i	0.891600	−	0.452824i	$-0.149584\pi$
$978$	0.600392	+	1.03991i	0.0191984	+	0.0332526i
$979$	11.3834			0.363816
$980$	−10.3634	+	3.44385i	−0.331045	+	0.110010i
$981$	−47.4798			−1.51591
$982$	3.21354	+	5.56602i	0.102548	+	0.177619i
$983$	10.3669	−	17.9560i	0.330653	−	0.572707i	−0.651987	−	0.758230i	$-0.726065\pi$
$983$	10.3669	−	17.9560i	0.330653	−	0.572707i	0.982640	+	0.185523i	$0.0593979\pi$
$984$	0.0819886	−	0.142008i	0.00261370	−	0.00452706i
$985$	0.548666	+	0.950317i	0.0174819	+	0.0302796i
$986$	1.37474			0.0437805
$987$	0.114061	−	0.0184556i	0.00363059	−	0.000587448i
$988$	1.60885			0.0511843
$989$	−5.65319	−	9.79162i	−0.179761	−	0.311355i
$990$	2.26991	−	3.93161i	0.0721426	−	0.124955i
$991$	2.89837	−	5.02012i	0.0920697	−	0.159469i	−0.816312	−	0.577611i	$-0.803985\pi$
$991$	2.89837	−	5.02012i	0.0920697	−	0.159469i	0.908382	+	0.418142i	$0.137318\pi$
$992$	25.2917	+	43.8066i	0.803014	+	1.39086i
$993$	−2.53758			−0.0805277
$994$	−10.2327	−	12.5505i	−0.324561	−	0.398077i
$995$	14.6926			0.465786
$996$	1.57881	+	2.73458i	0.0500266	+	0.0866486i
$997$	13.4885	−	23.3627i	0.427184	−	0.739904i	−0.569438	−	0.822034i	$-0.692839\pi$
$997$	13.4885	−	23.3627i	0.427184	−	0.739904i	0.996622	+	0.0821304i	$0.0261724\pi$
$998$	−8.96117	+	15.5212i	−0.283661	+	0.491315i
$999$	−2.71723	−	4.70638i	−0.0859693	−	0.148903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.i.d.116.7	✓	26
7.2	even	3	inner	805.2.i.d.576.7	yes	26
7.3	odd	6		5635.2.a.bf.1.7		13
7.4	even	3		5635.2.a.be.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.i.d.116.7	✓	26	1.1	even	1	trivial
805.2.i.d.576.7	yes	26	7.2	even	3	inner
5635.2.a.be.1.7		13	7.4	even	3
5635.2.a.bf.1.7		13	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.331631 + 0.574401i) q^{2} +(0.0704605 - 0.122041i) q^{3} +(0.780042 - 1.35107i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.0934675 q^{6} +(2.61178 - 0.422600i) q^{7} +2.36127 q^{8} +(1.49007 + 2.58088i) q^{9} +O(q^{10})\)	\(q+(0.331631 + 0.574401i) q^{2} +(0.0704605 - 0.122041i) q^{3} +(0.780042 - 1.35107i) q^{4} +(-0.500000 - 0.866025i) q^{5} +0.0934675 q^{6} +(2.61178 - 0.422600i) q^{7} +2.36127 q^{8} +(1.49007 + 2.58088i) q^{9} +(0.331631 - 0.574401i) q^{10} +(1.14839 - 1.98906i) q^{11} +(-0.109924 - 0.190395i) q^{12} -2.34924 q^{13} +(1.10889 + 1.36006i) q^{14} -0.140921 q^{15} +(-0.777015 - 1.34583i) q^{16} +(0.591704 - 1.02486i) q^{17} +(-0.988307 + 1.71180i) q^{18} +(-0.219488 - 0.380164i) q^{19} -1.56008 q^{20} +(0.132453 - 0.348522i) q^{21} +1.52336 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.166376 - 0.288172i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.779079 - 1.34941i) q^{26} +0.842728 q^{27} +(1.46634 - 3.85835i) q^{28} +1.75146 q^{29} +(-0.0467337 - 0.0809452i) q^{30} +(-4.39607 + 7.61422i) q^{31} +(2.87663 - 4.98247i) q^{32} +(-0.161832 - 0.280301i) q^{33} +0.784909 q^{34} +(-1.67187 - 2.05057i) q^{35} +4.64927 q^{36} +(-3.22433 - 5.58470i) q^{37} +(0.145578 - 0.252148i) q^{38} +(-0.165528 + 0.286704i) q^{39} +(-1.18063 - 2.04492i) q^{40} +0.492791 q^{41} +(0.244117 - 0.0394993i) q^{42} +11.3064 q^{43} +(-1.79158 - 3.10311i) q^{44} +(1.49007 - 2.58088i) q^{45} +(0.331631 - 0.574401i) q^{46} +(0.154951 + 0.268382i) q^{47} -0.218996 q^{48} +(6.64282 - 2.20748i) q^{49} -0.663262 q^{50} +(-0.0833835 - 0.144424i) q^{51} +(-1.83250 + 3.17399i) q^{52} +(3.24756 - 5.62493i) q^{53} +(0.279474 + 0.484064i) q^{54} -2.29677 q^{55} +(6.16712 - 0.997870i) q^{56} -0.0618609 q^{57} +(0.580837 + 1.00604i) q^{58} +(3.21092 - 5.56148i) q^{59} +(-0.109924 + 0.190395i) q^{60} +(-0.966187 - 1.67348i) q^{61} -5.83149 q^{62} +(4.98242 + 6.11099i) q^{63} +0.707856 q^{64} +(1.17462 + 2.03450i) q^{65} +(0.107337 - 0.185913i) q^{66} +(-4.29682 + 7.44230i) q^{67} +(-0.923108 - 1.59887i) q^{68} -0.140921 q^{69} +(0.623406 - 1.64036i) q^{70} -9.22786 q^{71} +(3.51845 + 6.09414i) q^{72} +(2.10264 - 3.64188i) q^{73} +(2.13857 - 3.70411i) q^{74} +(0.0704605 + 0.122041i) q^{75} -0.684838 q^{76} +(2.15876 - 5.68031i) q^{77} -0.219577 q^{78} +(7.17687 + 12.4307i) q^{79} +(-0.777015 + 1.34583i) q^{80} +(-4.41083 + 7.63979i) q^{81} +(0.163425 + 0.283060i) q^{82} -14.3627 q^{83} +(-0.367559 - 0.450815i) q^{84} -1.18341 q^{85} +(3.74955 + 6.49440i) q^{86} +(0.123409 - 0.213750i) q^{87} +(2.71165 - 4.69671i) q^{88} +(2.47813 + 4.29225i) q^{89} +1.97661 q^{90} +(-6.13570 + 0.992787i) q^{91} -1.56008 q^{92} +(0.619499 + 1.07300i) q^{93} +(-0.102773 + 0.178008i) q^{94} +(-0.219488 + 0.380164i) q^{95} +(-0.405378 - 0.702135i) q^{96} -6.11976 q^{97} +(3.47094 + 3.08358i) q^{98} +6.84470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 5 q^{2} + 2 q^{3} - 13 q^{4} - 13 q^{5} - 8 q^{6} - 30 q^{8} - 5 q^{9}+O(q^{10}) \) 26 * q + 5 * q^2 + 2 * q^3 - 13 * q^4 - 13 * q^5 - 8 * q^6 - 30 * q^8 - 5 * q^9	\( 26 q + 5 q^{2} + 2 q^{3} - 13 q^{4} - 13 q^{5} - 8 q^{6} - 30 q^{8} - 5 q^{9} + 5 q^{10} + 17 q^{11} - 6 q^{12} + 2 q^{13} + 11 q^{14} - 4 q^{15} - 21 q^{16} - 2 q^{17} + 25 q^{18} + 13 q^{19} + 26 q^{20} + 5 q^{21} + 6 q^{22} - 13 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 10 q^{27} + 23 q^{28} - 52 q^{29} + 4 q^{30} - 8 q^{31} + 40 q^{32} + 6 q^{33} - 84 q^{34} + 3 q^{35} + 34 q^{36} + 29 q^{37} - 40 q^{38} + 20 q^{39} + 15 q^{40} - 56 q^{41} - 18 q^{42} - 20 q^{43} + 31 q^{44} - 5 q^{45} + 5 q^{46} - q^{47} + 16 q^{48} - 4 q^{49} - 10 q^{50} + 3 q^{51} - 27 q^{52} + 43 q^{53} + 24 q^{54} - 34 q^{55} - 24 q^{56} + 4 q^{57} - 24 q^{58} + q^{59} - 6 q^{60} + 30 q^{61} - 4 q^{62} + 8 q^{63} + 70 q^{64} - q^{65} - 71 q^{66} + 21 q^{67} - 11 q^{68} - 4 q^{69} + 5 q^{70} + 47 q^{72} - 5 q^{73} + 10 q^{74} + 2 q^{75} - 174 q^{76} - 2 q^{77} + 58 q^{78} + 36 q^{79} - 21 q^{80} + 35 q^{81} - 8 q^{82} - 22 q^{84} + 4 q^{85} + 20 q^{86} - 6 q^{87} + 24 q^{88} + 10 q^{89} - 50 q^{90} + 36 q^{91} + 26 q^{92} + 15 q^{93} - 38 q^{94} + 13 q^{95} + 31 q^{96} - 16 q^{97} + 41 q^{98} - 18 q^{99}+O(q^{100}) \) 26 * q + 5 * q^2 + 2 * q^3 - 13 * q^4 - 13 * q^5 - 8 * q^6 - 30 * q^8 - 5 * q^9 + 5 * q^10 + 17 * q^11 - 6 * q^12 + 2 * q^13 + 11 * q^14 - 4 * q^15 - 21 * q^16 - 2 * q^17 + 25 * q^18 + 13 * q^19 + 26 * q^20 + 5 * q^21 + 6 * q^22 - 13 * q^23 + 20 * q^24 - 13 * q^25 + 2 * q^26 - 10 * q^27 + 23 * q^28 - 52 * q^29 + 4 * q^30 - 8 * q^31 + 40 * q^32 + 6 * q^33 - 84 * q^34 + 3 * q^35 + 34 * q^36 + 29 * q^37 - 40 * q^38 + 20 * q^39 + 15 * q^40 - 56 * q^41 - 18 * q^42 - 20 * q^43 + 31 * q^44 - 5 * q^45 + 5 * q^46 - q^47 + 16 * q^48 - 4 * q^49 - 10 * q^50 + 3 * q^51 - 27 * q^52 + 43 * q^53 + 24 * q^54 - 34 * q^55 - 24 * q^56 + 4 * q^57 - 24 * q^58 + q^59 - 6 * q^60 + 30 * q^61 - 4 * q^62 + 8 * q^63 + 70 * q^64 - q^65 - 71 * q^66 + 21 * q^67 - 11 * q^68 - 4 * q^69 + 5 * q^70 + 47 * q^72 - 5 * q^73 + 10 * q^74 + 2 * q^75 - 174 * q^76 - 2 * q^77 + 58 * q^78 + 36 * q^79 - 21 * q^80 + 35 * q^81 - 8 * q^82 - 22 * q^84 + 4 * q^85 + 20 * q^86 - 6 * q^87 + 24 * q^88 + 10 * q^89 - 50 * q^90 + 36 * q^91 + 26 * q^92 + 15 * q^93 - 38 * q^94 + 13 * q^95 + 31 * q^96 - 16 * q^97 + 41 * q^98 - 18 * q^99

Introduction

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