LMFDB - Embedded newform 966.2.f.c.461.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (of order $2$, degree $1$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.4
Character	$\chi$	$=$	966.461
Dual form			966.2.f.c.461.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.18002 - 1.26789i) q^{3} -1.00000 q^{4} +3.87735 q^{5} +(-1.26789 + 1.18002i) q^{6} +(0.302862 - 2.62836i) q^{7} +1.00000i q^{8} +(-0.215085 + 2.99228i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.18002 - 1.26789i) q^{3} -1.00000 q^{4} +3.87735 q^{5} +(-1.26789 + 1.18002i) q^{6} +(0.302862 - 2.62836i) q^{7} +1.00000i q^{8} +(-0.215085 + 2.99228i) q^{9} -3.87735i q^{10} -5.48161i q^{11} +(1.18002 + 1.26789i) q^{12} +4.05132i q^{13} +(-2.62836 - 0.302862i) q^{14} +(-4.57537 - 4.91605i) q^{15} +1.00000 q^{16} +2.53578 q^{17} +(2.99228 + 0.215085i) q^{18} -1.59206i q^{19} -3.87735 q^{20} +(-3.68985 + 2.71753i) q^{21} -5.48161 q^{22} -1.00000i q^{23} +(1.26789 - 1.18002i) q^{24} +10.0338 q^{25} +4.05132 q^{26} +(4.04768 - 3.25826i) q^{27} +(-0.302862 + 2.62836i) q^{28} -9.78700i q^{29} +(-4.91605 + 4.57537i) q^{30} +6.36714i q^{31} -1.00000i q^{32} +(-6.95008 + 6.46844i) q^{33} -2.53578i q^{34} +(1.17430 - 10.1911i) q^{35} +(0.215085 - 2.99228i) q^{36} +3.09394 q^{37} -1.59206 q^{38} +(5.13662 - 4.78066i) q^{39} +3.87735i q^{40} +2.14736 q^{41} +(2.71753 + 3.68985i) q^{42} -6.76726 q^{43} +5.48161i q^{44} +(-0.833961 + 11.6021i) q^{45} -1.00000 q^{46} +0.573582 q^{47} +(-1.18002 - 1.26789i) q^{48} +(-6.81655 - 1.59206i) q^{49} -10.0338i q^{50} +(-2.99228 - 3.21509i) q^{51} -4.05132i q^{52} -6.95621i q^{53} +(-3.25826 - 4.04768i) q^{54} -21.2541i q^{55} +(2.62836 + 0.302862i) q^{56} +(-2.01855 + 1.87867i) q^{57} -9.78700 q^{58} -4.91543 q^{59} +(4.57537 + 4.91605i) q^{60} +12.1027i q^{61} +6.36714 q^{62} +(7.79965 + 1.47157i) q^{63} -1.00000 q^{64} +15.7084i q^{65} +(6.46844 + 6.95008i) q^{66} -12.4303 q^{67} -2.53578 q^{68} +(-1.26789 + 1.18002i) q^{69} +(-10.1911 - 1.17430i) q^{70} +8.75597i q^{71} +(-2.99228 - 0.215085i) q^{72} +0.527845i q^{73} -3.09394i q^{74} +(-11.8402 - 12.7218i) q^{75} +1.59206i q^{76} +(-14.4077 - 1.66017i) q^{77} +(-4.78066 - 5.13662i) q^{78} -1.78905 q^{79} +3.87735 q^{80} +(-8.90748 - 1.28719i) q^{81} -2.14736i q^{82} +0.461416 q^{83} +(3.68985 - 2.71753i) q^{84} +9.83210 q^{85} +6.76726i q^{86} +(-12.4088 + 11.5489i) q^{87} +5.48161 q^{88} +12.2137 q^{89} +(11.6021 + 0.833961i) q^{90} +(10.6483 + 1.22699i) q^{91} +1.00000i q^{92} +(8.07282 - 7.51338i) q^{93} -0.573582i q^{94} -6.17297i q^{95} +(-1.26789 + 1.18002i) q^{96} -8.09621i q^{97} +(-1.59206 + 6.81655i) q^{98} +(16.4025 + 1.17901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	$ 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.18002	−	1.26789i	−0.681287	−	0.732016i
$3$	−1.18002	−	1.26789i	−0.681287	−	0.732016i
$4$	−1.00000			−0.500000
$5$	3.87735			1.73400			0.867002	−	0.498305i	$-0.166044\pi$
$5$	3.87735			1.73400			0.867002	+	0.498305i	$0.166044\pi$
$6$	−1.26789	+	1.18002i	−0.517614	+	0.481743i
$7$	0.302862	−	2.62836i	0.114471	−	0.993427i
$7$	0.302862	−	2.62836i	0.114471	−	0.993427i
$8$			1.00000i			0.353553i
$9$	−0.215085	+	2.99228i	−0.0716951	+	0.997427i
$10$		−	3.87735i		−	1.22613i
$11$		−	5.48161i		−	1.65277i	−0.563106	−	0.826384i	$-0.690394\pi$
$11$		−	5.48161i		−	1.65277i	0.563106	−	0.826384i	$-0.309606\pi$
$12$	1.18002	+	1.26789i	0.340644	+	0.366008i
$13$			4.05132i			1.12363i	0.827262	+	0.561817i	$0.189897\pi$
$13$			4.05132i			1.12363i	−0.827262	+	0.561817i	$0.810103\pi$
$14$	−2.62836	−	0.302862i	−0.702459	−	0.0809432i
$15$	−4.57537	−	4.91605i	−1.18135	−	1.26932i
$16$	1.00000			0.250000
$17$	2.53578			0.615017			0.307508	−	0.951545i	$-0.400505\pi$
$17$	2.53578			0.615017			0.307508	+	0.951545i	$0.400505\pi$
$18$	2.99228	+	0.215085i	0.705287	+	0.0506961i
$19$		−	1.59206i		−	0.365243i	−0.983183	−	0.182622i	$-0.941542\pi$
$19$		−	1.59206i		−	0.365243i	0.983183	−	0.182622i	$-0.0584583\pi$
$20$	−3.87735			−0.867002
$21$	−3.68985	+	2.71753i	−0.805192	+	0.593014i
$22$	−5.48161			−1.16868
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	1.26789	−	1.18002i	0.258807	−	0.240871i
$25$	10.0338			2.00677
$26$	4.05132			0.794529
$27$	4.04768	−	3.25826i	0.778977	−	0.627052i
$28$	−0.302862	+	2.62836i	−0.0572355	+	0.496713i
$29$		−	9.78700i		−	1.81740i	−0.417450	−	0.908700i	$-0.637076\pi$
$29$		−	9.78700i		−	1.81740i	0.417450	−	0.908700i	$-0.362924\pi$
$30$	−4.91605	+	4.57537i	−0.897544	+	0.835344i
$31$			6.36714i			1.14357i	0.820403	+	0.571786i	$0.193749\pi$
$31$			6.36714i			1.14357i	−0.820403	+	0.571786i	$0.806251\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−6.95008	+	6.46844i	−1.20985	+	1.12601i
$34$		−	2.53578i		−	0.434882i
$35$	1.17430	−	10.1911i	0.198493	−	1.72261i
$36$	0.215085	−	2.99228i	0.0358475	−	0.498713i
$37$	3.09394			0.508640			0.254320	−	0.967120i	$-0.418148\pi$
$37$	3.09394			0.508640			0.254320	+	0.967120i	$0.418148\pi$
$38$	−1.59206			−0.258266
$39$	5.13662	−	4.78066i	0.822518	−	0.765518i
$40$			3.87735i			0.613063i
$41$	2.14736			0.335361			0.167681	−	0.985841i	$-0.446372\pi$
$41$	2.14736			0.335361			0.167681	+	0.985841i	$0.446372\pi$
$42$	2.71753	+	3.68985i	0.419325	+	0.569357i
$43$	−6.76726			−1.03200			−0.515999	−	0.856589i	$-0.672579\pi$
$43$	−6.76726			−1.03200			−0.515999	+	0.856589i	$0.672579\pi$
$44$			5.48161i			0.826384i
$45$	−0.833961	+	11.6021i	−0.124320	+	1.72954i
$46$	−1.00000			−0.147442
$47$	0.573582			0.0836656			0.0418328	−	0.999125i	$-0.486680\pi$
$47$	0.573582			0.0836656			0.0418328	+	0.999125i	$0.486680\pi$
$48$	−1.18002	−	1.26789i	−0.170322	−	0.183004i
$49$	−6.81655	−	1.59206i	−0.973793	−	0.227437i
$50$		−	10.0338i		−	1.41900i
$51$	−2.99228	−	3.21509i	−0.419003	−	0.450202i
$52$		−	4.05132i		−	0.561817i
$53$		−	6.95621i		−	0.955509i	−0.878493	−	0.477754i	$-0.841451\pi$
$53$		−	6.95621i		−	0.955509i	0.878493	−	0.477754i	$-0.158549\pi$
$54$	−3.25826	−	4.04768i	−0.443393	−	0.550820i
$55$		−	21.2541i		−	2.86591i
$56$	2.62836	+	0.302862i	0.351229	+	0.0404716i
$57$	−2.01855	+	1.87867i	−0.267364	+	0.248836i
$58$	−9.78700			−1.28510
$59$	−4.91543			−0.639934			−0.319967	−	0.947429i	$-0.603672\pi$
$59$	−4.91543			−0.639934			−0.319967	+	0.947429i	$0.603672\pi$
$60$	4.57537	+	4.91605i	0.590677	+	0.634659i
$61$			12.1027i			1.54959i	0.632210	+	0.774797i	$0.282148\pi$
$61$			12.1027i			1.54959i	−0.632210	+	0.774797i	$0.717852\pi$
$62$	6.36714			0.808627
$63$	7.79965	+	1.47157i	0.982663	+	0.185400i
$64$	−1.00000			−0.125000
$65$			15.7084i			1.94839i
$66$	6.46844	+	6.95008i	0.796210	+	0.855496i
$67$	−12.4303			−1.51860			−0.759300	−	0.650740i	$-0.774459\pi$
$67$	−12.4303			−1.51860			−0.759300	+	0.650740i	$0.774459\pi$
$68$	−2.53578			−0.307508
$69$	−1.26789	+	1.18002i	−0.152636	+	0.142058i
$70$	−10.1911	−	1.17430i	−1.21807	−	0.140356i
$71$			8.75597i			1.03914i	0.854427	+	0.519571i	$0.173908\pi$
$71$			8.75597i			1.03914i	−0.854427	+	0.519571i	$0.826092\pi$
$72$	−2.99228	−	0.215085i	−0.352644	−	0.0253480i
$73$			0.527845i			0.0617796i	0.999523	+	0.0308898i	$0.00983409\pi$
$73$			0.527845i			0.0617796i	−0.999523	+	0.0308898i	$0.990166\pi$
$74$		−	3.09394i		−	0.359663i
$75$	−11.8402	−	12.7218i	−1.36719	−	1.46899i
$76$			1.59206i			0.182622i
$77$	−14.4077	−	1.66017i	−1.64190	−	0.189194i
$78$	−4.78066	−	5.13662i	−0.541303	−	0.581608i
$79$	−1.78905			−0.201283			−0.100642	−	0.994923i	$-0.532090\pi$
$79$	−1.78905			−0.201283			−0.100642	+	0.994923i	$0.532090\pi$
$80$	3.87735			0.433501
$81$	−8.90748	−	1.28719i	−0.989720	−	0.143021i
$82$		−	2.14736i		−	0.237136i
$83$	0.461416			0.0506470			0.0253235	−	0.999679i	$-0.491938\pi$
$83$	0.461416			0.0506470			0.0253235	+	0.999679i	$0.491938\pi$
$84$	3.68985	−	2.71753i	0.402596	−	0.296507i
$85$	9.83210			1.06644
$86$			6.76726i			0.729733i
$87$	−12.4088	+	11.5489i	−1.33037	+	1.23817i
$88$	5.48161			0.584342
$89$	12.2137			1.29465			0.647325	−	0.762214i	$-0.275888\pi$
$89$	12.2137			1.29465			0.647325	+	0.762214i	$0.275888\pi$
$90$	11.6021	+	0.833961i	1.22297	+	0.0879072i
$91$	10.6483	+	1.22699i	1.11625	+	0.128623i
$92$			1.00000i			0.104257i
$93$	8.07282	−	7.51338i	0.837113	−	0.779101i
$94$		−	0.573582i		−	0.0591605i
$95$		−	6.17297i		−	0.633333i
$96$	−1.26789	+	1.18002i	−0.129403	+	0.120436i
$97$		−	8.09621i		−	0.822045i	−0.911625	−	0.411023i	$-0.865172\pi$
$97$		−	8.09621i		−	0.822045i	0.911625	−	0.411023i	$-0.134828\pi$
$98$	−1.59206	+	6.81655i	−0.160822	+	0.688575i
$99$	16.4025	+	1.17901i	1.64852	+	0.118495i
$100$	−10.0338			−1.00338
$101$	−17.3577			−1.72715			−0.863576	−	0.504218i	$-0.831781\pi$
$101$	−17.3577			−1.72715			−0.863576	+	0.504218i	$0.831781\pi$
$102$	−3.21509	+	2.99228i	−0.318341	+	0.296280i
$103$		−	5.76721i		−	0.568260i	−0.958786	−	0.284130i	$-0.908295\pi$
$103$		−	5.76721i		−	0.568260i	0.958786	−	0.284130i	$-0.0917047\pi$
$104$	−4.05132			−0.397265
$105$	−14.3069	+	10.5368i	−1.39621	+	1.02829i
$106$	−6.95621			−0.675647
$107$			17.5647i			1.69805i	0.528354	+	0.849024i	$0.322809\pi$
$107$			17.5647i			1.69805i	−0.528354	+	0.849024i	$0.677191\pi$
$108$	−4.04768	+	3.25826i	−0.389489	+	0.313526i
$109$	0.554958			0.0531553			0.0265776	−	0.999647i	$-0.491539\pi$
$109$	0.554958			0.0531553			0.0265776	+	0.999647i	$0.491539\pi$
$110$	−21.2541			−2.02650
$111$	−3.65092	−	3.92277i	−0.346530	−	0.372333i
$112$	0.302862	−	2.62836i	0.0286177	−	0.248357i
$113$		−	7.29007i		−	0.685792i	−0.939373	−	0.342896i	$-0.888592\pi$
$113$		−	7.29007i		−	0.685792i	0.939373	−	0.342896i	$-0.111408\pi$
$114$	1.87867	+	2.01855i	0.175953	+	0.189055i
$115$		−	3.87735i		−	0.361565i
$116$			9.78700i			0.908700i
$117$	−12.1227	−	0.871379i	−1.12074	−	0.0805590i
$118$			4.91543i			0.452502i
$119$	0.767990	−	6.66494i	0.0704015	−	0.610974i
$120$	4.91605	−	4.57537i	0.448772	−	0.417672i
$121$	−19.0481			−1.73165
$122$	12.1027			1.09573
$123$	−2.53394	−	2.72261i	−0.228477	−	0.245490i
$124$		−	6.36714i		−	0.571786i
$125$	19.5180			1.74574
$126$	1.47157	−	7.79965i	0.131098	−	0.694848i
$127$	10.0647			0.893098			0.446549	−	0.894759i	$-0.352653\pi$
$127$	10.0647			0.893098			0.446549	+	0.894759i	$0.352653\pi$
$128$			1.00000i			0.0883883i
$129$	7.98554	+	8.58014i	0.703087	+	0.755439i
$130$	15.7084			1.37772
$131$	14.5965			1.27530			0.637649	−	0.770327i	$-0.279907\pi$
$131$	14.5965			1.27530			0.637649	+	0.770327i	$0.279907\pi$
$132$	6.95008	−	6.46844i	0.604927	−	0.563005i
$133$	−4.18450	−	0.482174i	−0.362842	−	0.0418097i
$134$			12.4303i			1.07381i
$135$	15.6943	−	12.6334i	1.35075	−	1.08731i
$136$			2.53578i			0.217441i
$137$		−	1.09814i		−	0.0938206i	−0.998899	−	0.0469103i	$-0.985062\pi$
$137$		−	1.09814i		−	0.0938206i	0.998899	−	0.0469103i	$-0.0149375\pi$
$138$	1.18002	+	1.26789i	0.100450	+	0.107930i
$139$			3.04117i			0.257949i	0.991648	+	0.128974i	$0.0411685\pi$
$139$			3.04117i			0.257949i	−0.991648	+	0.128974i	$0.958831\pi$
$140$	−1.17430	+	10.1911i	−0.0992465	+	0.861303i
$141$	−0.676841	−	0.727239i	−0.0570003	−	0.0612446i
$142$	8.75597			0.734784
$143$	22.2078			1.85711
$144$	−0.215085	+	2.99228i	−0.0179238	+	0.249357i
$145$		−	37.9476i		−	3.15138i
$146$	0.527845			0.0436848
$147$	6.02514	+	10.5213i	0.496945	+	0.867782i
$148$	−3.09394			−0.254320
$149$		−	1.07201i		−	0.0878228i	−0.999035	−	0.0439114i	$-0.986018\pi$
$149$		−	1.07201i		−	0.0878228i	0.999035	−	0.0439114i	$-0.0139819\pi$
$150$	−12.7218	+	11.8402i	−1.03873	+	0.966747i
$151$	7.03831			0.572769			0.286385	−	0.958115i	$-0.407546\pi$
$151$	7.03831			0.572769			0.286385	+	0.958115i	$0.407546\pi$
$152$	1.59206			0.129133
$153$	−0.545408	+	7.58776i	−0.0440937	+	0.613434i
$154$	−1.66017	+	14.4077i	−0.133780	+	1.16100i
$155$			24.6876i			1.98296i
$156$	−5.13662	+	4.78066i	−0.411259	+	0.382759i
$157$		−	0.588084i		−	0.0469342i	−0.999725	−	0.0234671i	$-0.992530\pi$
$157$		−	0.588084i		−	0.0469342i	0.999725	−	0.0234671i	$-0.00747050\pi$
$158$			1.78905i			0.142329i
$159$	−8.81970	+	8.20850i	−0.699448	+	0.650976i
$160$		−	3.87735i		−	0.306531i
$161$	−2.62836	−	0.302862i	−0.207144	−	0.0238688i
$162$	−1.28719	+	8.90748i	−0.101131	+	0.699837i
$163$	5.47111			0.428530			0.214265	−	0.976776i	$-0.431264\pi$
$163$	5.47111			0.428530			0.214265	+	0.976776i	$0.431264\pi$
$164$	−2.14736			−0.167681
$165$	−26.9479	+	25.0804i	−2.09789	+	1.95251i
$166$		−	0.461416i		−	0.0358128i
$167$	15.1296			1.17076			0.585380	−	0.810759i	$-0.300945\pi$
$167$	15.1296			1.17076			0.585380	+	0.810759i	$0.300945\pi$
$168$	−2.71753	−	3.68985i	−0.209662	−	0.284678i
$169$	−3.41319			−0.262553
$170$		−	9.83210i		−	0.754088i
$171$	4.76389	+	0.342428i	0.364303	+	0.0261861i
$172$	6.76726			0.515999
$173$	21.3342			1.62201			0.811006	−	0.585038i	$-0.198920\pi$
$173$	21.3342			1.62201			0.811006	+	0.585038i	$0.198920\pi$
$174$	11.5489	+	12.4088i	0.875520	+	0.940711i
$175$	3.03887	−	26.3726i	0.229717	−	1.99358i
$176$		−	5.48161i		−	0.413192i
$177$	5.80032	+	6.23222i	0.435979	+	0.468442i
$178$		−	12.2137i		−	0.915456i
$179$		−	15.0706i		−	1.12643i	−0.826311	−	0.563215i	$-0.809564\pi$
$179$		−	15.0706i		−	1.12643i	0.826311	−	0.563215i	$-0.190436\pi$
$180$	0.833961	−	11.6021i	0.0621598	−	0.864771i
$181$			6.92160i			0.514479i	0.966348	+	0.257239i	$0.0828129\pi$
$181$			6.92160i			0.514479i	−0.966348	+	0.257239i	$0.917187\pi$
$182$	1.22699	−	10.6483i	0.0909505	−	0.789306i
$183$	15.3449	−	14.2815i	1.13433	−	1.05572i
$184$	1.00000			0.0737210
$185$	11.9963			0.881984
$186$	−7.51338	−	8.07282i	−0.550908	−	0.591928i
$187$		−	13.9002i		−	1.01648i
$188$	−0.573582			−0.0418328
$189$	−7.33799	−	11.6256i	−0.533760	−	0.845636i
$190$	−6.17297			−0.447834
$191$			27.5414i			1.99283i	0.0846212	+	0.996413i	$0.473032\pi$
$191$			27.5414i			1.99283i	−0.0846212	+	0.996413i	$0.526968\pi$
$192$	1.18002	+	1.26789i	0.0851609	+	0.0915020i
$193$	9.28333			0.668229			0.334114	−	0.942532i	$-0.391563\pi$
$193$	9.28333			0.668229			0.334114	+	0.942532i	$0.391563\pi$
$194$	−8.09621			−0.581274
$195$	19.9165	−	18.5363i	1.42625	−	1.32741i
$196$	6.81655	+	1.59206i	0.486896	+	0.113718i
$197$			0.671664i			0.0478541i	0.999714	+	0.0239270i	$0.00761694\pi$
$197$			0.671664i			0.0478541i	−0.999714	+	0.0239270i	$0.992383\pi$
$198$	1.17901	−	16.4025i	0.0837889	−	1.16568i
$199$			23.6028i			1.67316i	0.547845	+	0.836580i	$0.315448\pi$
$199$			23.6028i			1.67316i	−0.547845	+	0.836580i	$0.684552\pi$
$200$			10.0338i			0.709500i
$201$	14.6680	+	15.7602i	1.03460	+	1.11164i
$202$			17.3577i			1.22128i
$203$	−25.7238	−	2.96411i	−1.80545	−	0.208039i
$204$	2.99228	+	3.21509i	0.209501	+	0.225101i
$205$	8.32606			0.581517
$206$	−5.76721			−0.401820
$207$	2.99228	+	0.215085i	0.207978	+	0.0149495i
$208$			4.05132i			0.280908i
$209$	−8.72705			−0.603663
$210$	10.5368	+	14.3069i	0.727110	+	0.987267i
$211$	12.6220			0.868934			0.434467	−	0.900688i	$-0.356937\pi$
$211$	12.6220			0.868934			0.434467	+	0.900688i	$0.356937\pi$
$212$			6.95621i			0.477754i
$213$	11.1016	−	10.3323i	0.760669	−	0.707954i
$214$	17.5647			1.20070
$215$	−26.2391			−1.78949
$216$	3.25826	+	4.04768i	0.221696	+	0.275410i
$217$	16.7351	+	1.92836i	1.13605	+	0.130906i
$218$		−	0.554958i		−	0.0375865i
$219$	0.669249	−	0.622870i	0.0452236	−	0.0420896i
$220$			21.2541i			1.43295i
$221$			10.2732i			0.691053i
$222$	−3.92277	+	3.65092i	−0.263279	+	0.245034i
$223$		−	0.0999946i		−	0.00669613i	−0.999994	−	0.00334807i	$-0.998934\pi$
$223$		−	0.0999946i		−	0.00669613i	0.999994	−	0.00334807i	$-0.00106572\pi$
$224$	−2.62836	−	0.302862i	−0.175615	−	0.0202358i
$225$	−2.15813	+	30.0241i	−0.143875	+	2.00160i
$226$	−7.29007			−0.484928
$227$	26.4176			1.75340			0.876700	−	0.481037i	$-0.159740\pi$
$227$	26.4176			1.75340			0.876700	+	0.481037i	$0.159740\pi$
$228$	2.01855	−	1.87867i	0.133682	−	0.124418i
$229$			10.5636i			0.698064i	0.937111	+	0.349032i	$0.113490\pi$
$229$			10.5636i			0.698064i	−0.937111	+	0.349032i	$0.886510\pi$
$230$	−3.87735			−0.255665
$231$	14.8965	+	20.2263i	0.980116	+	1.33080i
$232$	9.78700			0.642548
$233$		−	18.6512i		−	1.22188i	−0.791676	−	0.610942i	$-0.790791\pi$
$233$		−	18.6512i		−	1.22188i	0.791676	−	0.610942i	$-0.209209\pi$
$234$	−0.871379	+	12.1227i	−0.0569638	+	0.792485i
$235$	2.22398			0.145076
$236$	4.91543			0.319967
$237$	2.11112	+	2.26831i	0.137132	+	0.147343i
$238$	−6.66494	−	0.767990i	−0.432024	−	0.0497814i
$239$		−	29.1333i		−	1.88448i	−0.334940	−	0.942239i	$-0.608716\pi$
$239$		−	29.1333i		−	1.88448i	0.334940	−	0.942239i	$-0.391284\pi$
$240$	−4.57537	−	4.91605i	−0.295339	−	0.317330i
$241$		−	5.46589i		−	0.352089i	−0.984382	−	0.176044i	$-0.943670\pi$
$241$		−	5.46589i		−	0.352089i	0.984382	−	0.176044i	$-0.0563302\pi$
$242$			19.0481i			1.22446i
$243$	8.87902	+	12.8126i	0.569590	+	0.821929i
$244$		−	12.1027i		−	0.774797i
$245$	−26.4302	−	6.17297i	−1.68856	−	0.394377i
$246$	−2.72261	+	2.53394i	−0.173587	+	0.161558i
$247$	6.44994			0.410400
$248$	−6.36714			−0.404314
$249$	−0.544482	−	0.585024i	−0.0345052	−	0.0370744i
$250$		−	19.5180i		−	1.23443i
$251$	−10.3699			−0.654543			−0.327271	−	0.944930i	$-0.606129\pi$
$251$	−10.3699			−0.654543			−0.327271	+	0.944930i	$0.606129\pi$
$252$	−7.79965	−	1.47157i	−0.491332	−	0.0927001i
$253$	−5.48161			−0.344626
$254$		−	10.0647i		−	0.631516i
$255$	−11.6021	−	12.4660i	−0.726553	−	0.780652i
$256$	1.00000			0.0625000
$257$	−1.79485			−0.111960			−0.0559798	−	0.998432i	$-0.517828\pi$
$257$	−1.79485			−0.111960			−0.0559798	+	0.998432i	$0.517828\pi$
$258$	8.58014	−	7.98554i	0.534176	−	0.497158i
$259$	0.937035	−	8.13198i	0.0582245	−	0.505297i
$260$		−	15.7084i		−	0.974193i
$261$	29.2854	+	2.10504i	1.81272	+	0.130299i
$262$		−	14.5965i		−	0.901772i
$263$			12.9422i			0.798050i	0.916940	+	0.399025i	$0.130651\pi$
$263$			12.9422i			0.798050i	−0.916940	+	0.399025i	$0.869349\pi$
$264$	−6.46844	−	6.95008i	−0.398105	−	0.427748i
$265$		−	26.9717i		−	1.65686i
$266$	−0.482174	+	4.18450i	−0.0295640	+	0.256568i
$267$	−14.4125	−	15.4856i	−0.882028	−	0.947704i
$268$	12.4303			0.759300
$269$	−14.8549			−0.905719			−0.452859	−	0.891582i	$-0.649596\pi$
$269$	−14.8549			−0.905719			−0.452859	+	0.891582i	$0.649596\pi$
$270$	−12.6334	−	15.6943i	−0.768845	−	0.955124i
$271$			19.5724i			1.18894i	0.804119	+	0.594469i	$0.202638\pi$
$271$			19.5724i			1.18894i	−0.804119	+	0.594469i	$0.797362\pi$
$272$	2.53578			0.153754
$273$	−11.0096	−	14.9488i	−0.666331	−	0.904741i
$274$	−1.09814			−0.0663412
$275$		−	55.0017i		−	3.31673i
$276$	1.26789	−	1.18002i	0.0763180	−	0.0710291i
$277$	−9.80788			−0.589298			−0.294649	−	0.955605i	$-0.595203\pi$
$277$	−9.80788			−0.589298			−0.294649	+	0.955605i	$0.595203\pi$
$278$	3.04117			0.182397
$279$	−19.0523	−	1.36948i	−1.14063	−	0.0819885i
$280$	10.1911	+	1.17430i	0.609033	+	0.0701779i
$281$			8.17582i			0.487729i	0.969809	+	0.243864i	$0.0784151\pi$
$281$			8.17582i			0.487729i	−0.969809	+	0.243864i	$0.921585\pi$
$282$	−0.727239	+	0.676841i	−0.0433064	+	0.0403053i
$283$			6.82716i			0.405833i	0.979196	+	0.202916i	$0.0650420\pi$
$283$			6.82716i			0.405833i	−0.979196	+	0.202916i	$0.934958\pi$
$284$		−	8.75597i		−	0.519571i
$285$	−7.82664	+	7.28425i	−0.463610	+	0.431482i
$286$		−	22.2078i		−	1.31317i
$287$	0.650353	−	5.64403i	0.0383891	−	0.333157i
$288$	2.99228	+	0.215085i	0.176322	+	0.0126740i
$289$	−10.5698			−0.621755
$290$	−37.9476			−2.22836
$291$	−10.2651	+	9.55372i	−0.601750	+	0.560049i
$292$		−	0.527845i		−	0.0308898i
$293$	4.03638			0.235808			0.117904	−	0.993025i	$-0.462383\pi$
$293$	4.03638			0.235808			0.117904	+	0.993025i	$0.462383\pi$
$294$	10.5213	−	6.02514i	0.613614	−	0.351393i
$295$	−19.0588			−1.10965
$296$			3.09394i			0.179831i
$297$	−17.8605	−	22.1878i	−1.03637	−	1.28747i
$298$	−1.07201			−0.0621001
$299$	4.05132			0.234294
$300$	11.8402	+	12.7218i	0.683593	+	0.734494i
$301$	−2.04954	+	17.7868i	−0.118134	+	1.02521i
$302$		−	7.03831i		−	0.405009i
$303$	20.4825	+	22.0076i	1.17669	+	1.26430i
$304$		−	1.59206i		−	0.0913108i
$305$			46.9265i			2.68700i
$306$	7.58776	+	0.545408i	0.433763	+	0.0311789i
$307$		−	11.8749i		−	0.677734i	−0.940834	−	0.338867i	$-0.889956\pi$
$307$		−	11.8749i		−	0.677734i	0.940834	−	0.338867i	$-0.110044\pi$
$308$	14.4077	+	1.66017i	0.820952	+	0.0945970i
$309$	−7.31218	+	6.80544i	−0.415975	+	0.387148i
$310$	24.6876			1.40216
$311$	−21.9913			−1.24701			−0.623507	−	0.781818i	$-0.714293\pi$
$311$	−21.9913			−1.24701			−0.623507	+	0.781818i	$0.714293\pi$
$312$	4.78066	+	5.13662i	0.270651	+	0.290804i
$313$		−	6.93834i		−	0.392178i	−0.980586	−	0.196089i	$-0.937176\pi$
$313$		−	6.93834i		−	0.392178i	0.980586	−	0.196089i	$-0.0628242\pi$
$314$	−0.588084			−0.0331875
$315$	30.2420	+	5.70579i	1.70394	+	0.321485i
$316$	1.78905			0.100642
$317$			24.9558i			1.40166i	0.713330	+	0.700828i	$0.247186\pi$
$317$			24.9558i			1.40166i	−0.713330	+	0.700828i	$0.752814\pi$
$318$	8.20850	+	8.81970i	0.460310	+	0.494584i
$319$	−53.6485			−3.00374
$320$	−3.87735			−0.216750
$321$	22.2701	−	20.7268i	1.24300	−	1.15686i
$322$	−0.302862	+	2.62836i	−0.0168778	+	0.146473i
$323$		−	4.03711i		−	0.224631i
$324$	8.90748	+	1.28719i	0.494860	+	0.0715106i
$325$			40.6503i			2.25487i
$326$		−	5.47111i		−	0.303017i
$327$	−0.654863	−	0.703625i	−0.0362140	−	0.0389105i
$328$			2.14736i			0.118568i
$329$	0.173716	−	1.50758i	0.00957728	−	0.0831156i
$330$	25.0804	+	26.9479i	1.38063	+	1.48343i
$331$	6.74735			0.370868			0.185434	−	0.982657i	$-0.440631\pi$
$331$	6.74735			0.370868			0.185434	+	0.982657i	$0.440631\pi$
$332$	−0.461416			−0.0253235
$333$	−0.665460	+	9.25792i	−0.0364670	+	0.507331i
$334$		−	15.1296i		−	0.827853i
$335$	−48.1966			−2.63326
$336$	−3.68985	+	2.71753i	−0.201298	+	0.148254i
$337$	16.5741			0.902849			0.451425	−	0.892309i	$-0.350916\pi$
$337$	16.5741			0.902849			0.451425	+	0.892309i	$0.350916\pi$
$338$			3.41319i			0.185653i
$339$	−9.24300	+	8.60246i	−0.502011	+	0.467222i
$340$	−9.83210			−0.533220
$341$	34.9022			1.89006
$342$	0.342428	−	4.76389i	0.0185164	−	0.257601i
$343$	−6.24897	+	17.4342i	−0.337413	+	0.941357i
$344$		−	6.76726i		−	0.364866i
$345$	−4.91605	+	4.57537i	−0.264671	+	0.246330i
$346$		−	21.3342i		−	1.14694i
$347$		−	17.3061i		−	0.929039i	−0.885563	−	0.464519i	$-0.846227\pi$
$347$		−	17.3061i		−	0.929039i	0.885563	−	0.464519i	$-0.153773\pi$
$348$	12.4088	−	11.5489i	0.665183	−	0.619086i
$349$		−	13.0219i		−	0.697047i	−0.937300	−	0.348523i	$-0.886683\pi$
$349$		−	13.0219i		−	0.697047i	0.937300	−	0.348523i	$-0.113317\pi$
$350$	−26.3726	−	3.03887i	−1.40967	−	0.162434i
$351$	13.2002	+	16.3985i	0.704577	+	0.875285i
$352$	−5.48161			−0.292171
$353$	20.9771			1.11650			0.558249	−	0.829674i	$-0.311474\pi$
$353$	20.9771			1.11650			0.558249	+	0.829674i	$0.311474\pi$
$354$	6.23222	−	5.80032i	0.331239	−	0.308284i
$355$			33.9499i			1.80188i
$356$	−12.2137			−0.647325
$357$	−9.35665	+	6.89106i	−0.495206	+	0.364714i
$358$	−15.0706			−0.796506
$359$			23.6584i			1.24864i	0.781167	+	0.624322i	$0.214625\pi$
$359$			23.6584i			1.24864i	−0.781167	+	0.624322i	$0.785375\pi$
$360$	−11.6021	−	0.833961i	−0.611485	−	0.0439536i
$361$	16.4653			0.866597
$362$	6.92160			0.363791
$363$	22.4772	+	24.1509i	1.17975	+	1.26759i
$364$	−10.6483	−	1.22699i	−0.558124	−	0.0643117i
$365$			2.04664i			0.107126i
$366$	−14.2815	−	15.3449i	−0.746506	−	0.802091i
$367$			32.0746i			1.67428i	0.546987	+	0.837141i	$0.315775\pi$
$367$			32.0746i			1.67428i	−0.546987	+	0.837141i	$0.684225\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	−0.461865	+	6.42550i	−0.0240437	+	0.334498i
$370$		−	11.9963i		−	0.623657i
$371$	−18.2834	−	2.10677i	−0.949228	−	0.109378i
$372$	−8.07282	+	7.51338i	−0.418556	+	0.389550i
$373$	−19.3797			−1.00344			−0.501722	−	0.865029i	$-0.667300\pi$
$373$	−19.3797			−1.00344			−0.501722	+	0.865029i	$0.667300\pi$
$374$	−13.9002			−0.718760
$375$	−23.0317	−	24.7466i	−1.18935	−	1.27791i
$376$			0.573582i			0.0295803i
$377$	39.6503			2.04209
$378$	−11.6256	+	7.33799i	−0.597955	+	0.377425i
$379$	25.0421			1.28632			0.643162	−	0.765730i	$-0.277622\pi$
$379$	25.0421			1.28632			0.643162	+	0.765730i	$0.277622\pi$
$380$			6.17297i			0.316667i
$381$	−11.8766	−	12.7609i	−0.608457	−	0.653762i
$382$	27.5414			1.40914
$383$	28.4246			1.45243			0.726216	−	0.687467i	$-0.241277\pi$
$383$	28.4246			1.45243			0.726216	+	0.687467i	$0.241277\pi$
$384$	1.26789	−	1.18002i	0.0647017	−	0.0602179i
$385$	−55.8635	−	6.43706i	−2.84707	−	0.328063i
$386$		−	9.28333i		−	0.472509i
$387$	1.45554	−	20.2495i	0.0739892	−	1.02934i
$388$			8.09621i			0.411023i
$389$			19.7035i			0.999009i	0.866311	+	0.499505i	$0.166485\pi$
$389$			19.7035i			0.999009i	−0.866311	+	0.499505i	$0.833515\pi$
$390$	−18.5363	−	19.9165i	−0.938621	−	1.00851i
$391$		−	2.53578i		−	0.128240i
$392$	1.59206	−	6.81655i	0.0804111	−	0.344288i
$393$	−17.2242	−	18.5067i	−0.868845	−	0.933539i
$394$	0.671664			0.0338379
$395$	−6.93676			−0.349026
$396$	−16.4025	−	1.17901i	−0.824258	−	0.0592477i
$397$		−	24.3072i		−	1.21995i	−0.792422	−	0.609973i	$-0.791180\pi$
$397$		−	24.3072i		−	1.21995i	0.792422	−	0.609973i	$-0.208820\pi$
$398$	23.6028			1.18310
$399$	4.32647	+	5.87446i	0.216595	+	0.294091i
$400$	10.0338			0.501692
$401$		−	14.9262i		−	0.745377i	−0.927957	−	0.372688i	$-0.878436\pi$
$401$		−	14.9262i		−	0.745377i	0.927957	−	0.372688i	$-0.121564\pi$
$402$	15.7602	−	14.6680i	0.786048	−	0.731575i
$403$	−25.7953			−1.28496
$404$	17.3577			0.863576
$405$	−34.5374	−	4.99089i	−1.71618	−	0.247999i
$406$	−2.96411	+	25.7238i	−0.147106	+	1.27665i
$407$		−	16.9598i		−	0.840665i
$408$	3.21509	−	2.99228i	0.159170	−	0.148140i
$409$			20.2559i			1.00159i	0.865566	+	0.500795i	$0.166959\pi$
$409$			20.2559i			1.00159i	−0.865566	+	0.500795i	$0.833041\pi$
$410$		−	8.32606i		−	0.411195i
$411$	−1.39232	+	1.29583i	−0.0686782	+	0.0639188i
$412$			5.76721i			0.284130i
$413$	−1.48869	+	12.9195i	−0.0732539	+	0.635728i
$414$	0.215085	−	2.99228i	0.0105709	−	0.147063i
$415$	1.78907			0.0878221
$416$	4.05132			0.198632
$417$	3.85587	−	3.58866i	0.188823	−	0.175737i
$418$			8.72705i			0.426854i
$419$	−21.1668			−1.03406			−0.517032	−	0.855966i	$-0.672963\pi$
$419$	−21.1668			−1.03406			−0.517032	+	0.855966i	$0.672963\pi$
$420$	14.3069	−	10.5368i	0.698103	−	0.514145i
$421$	−24.7598			−1.20672			−0.603360	−	0.797469i	$-0.706172\pi$
$421$	−24.7598			−1.20672			−0.603360	+	0.797469i	$0.706172\pi$
$422$		−	12.6220i		−	0.614429i
$423$	−0.123369	+	1.71632i	−0.00599841	+	0.0834503i
$424$	6.95621			0.337823
$425$	25.4436			1.23420
$426$	−10.3323	−	11.1016i	−0.500599	−	0.537874i
$427$	31.8103	+	3.66545i	1.53941	+	0.177383i
$428$		−	17.5647i		−	0.849024i
$429$	−26.2057	−	28.1570i	−1.26522	−	1.35943i
$430$			26.2391i			1.26536i
$431$		−	14.4976i		−	0.698325i	−0.937062	−	0.349163i	$-0.886466\pi$
$431$		−	14.4976i		−	0.698325i	0.937062	−	0.349163i	$-0.113534\pi$
$432$	4.04768	−	3.25826i	0.194744	−	0.156763i
$433$			18.9525i			0.910801i	0.890287	+	0.455400i	$0.150504\pi$
$433$			18.9525i			0.910801i	−0.890287	+	0.455400i	$0.849496\pi$
$434$	1.92836	−	16.7351i	0.0925643	−	0.803312i
$435$	−48.1134	+	44.7791i	−2.30686	+	2.14699i
$436$	−0.554958			−0.0265776
$437$	−1.59206			−0.0761585
$438$	−0.622870	−	0.669249i	−0.0297619	−	0.0319779i
$439$			5.13220i			0.244946i	0.992472	+	0.122473i	$0.0390826\pi$
$439$			5.13220i			0.244946i	−0.992472	+	0.122473i	$0.960917\pi$
$440$	21.2541			1.01325
$441$	6.23002	−	20.0546i	0.296668	−	0.954981i
$442$	10.2732			0.488649
$443$		−	7.28414i		−	0.346080i	−0.984915	−	0.173040i	$-0.944641\pi$
$443$		−	7.28414i		−	0.346080i	0.984915	−	0.173040i	$-0.0553590\pi$
$444$	3.65092	+	3.92277i	0.173265	+	0.186166i
$445$	47.3568			2.24493
$446$	−0.0999946			−0.00473488
$447$	−1.35919	+	1.26500i	−0.0642877	+	0.0598326i
$448$	−0.302862	+	2.62836i	−0.0143089	+	0.124178i
$449$			28.5459i			1.34717i	0.739112	+	0.673583i	$0.235246\pi$
$449$			28.5459i			1.34717i	−0.739112	+	0.673583i	$0.764754\pi$
$450$	30.0241	+	2.15813i	1.41535	+	0.101735i
$451$		−	11.7710i		−	0.554274i
$452$			7.29007i			0.342896i
$453$	−8.30538	−	8.92379i	−0.390221	−	0.419276i
$454$		−	26.4176i		−	1.23984i
$455$	41.2873	+	4.75747i	1.93558	+	0.223034i
$456$	−1.87867	−	2.01855i	−0.0879767	−	0.0945274i
$457$	4.70548			0.220113			0.110057	−	0.993925i	$-0.464897\pi$
$457$	4.70548			0.220113			0.110057	+	0.993925i	$0.464897\pi$
$458$	10.5636			0.493606
$459$	10.2640	−	8.26222i	0.479084	−	0.385647i
$460$			3.87735i			0.180782i
$461$	14.1607			0.659529			0.329764	−	0.944063i	$-0.393031\pi$
$461$	14.1607			0.659529			0.329764	+	0.944063i	$0.393031\pi$
$462$	20.2263	−	14.8965i	0.941015	−	0.693047i
$463$	−1.54127			−0.0716288			−0.0358144	−	0.999358i	$-0.511403\pi$
$463$	−1.54127			−0.0716288			−0.0358144	+	0.999358i	$0.511403\pi$
$464$		−	9.78700i		−	0.454350i
$465$	31.3012	−	29.1320i	1.45156	−	1.35096i
$466$	−18.6512			−0.864002
$467$	−18.4584			−0.854152			−0.427076	−	0.904216i	$-0.640456\pi$
$467$	−18.4584			−0.854152			−0.427076	+	0.904216i	$0.640456\pi$
$468$	12.1227	+	0.871379i	0.560371	+	0.0402795i
$469$	−3.76466	+	32.6712i	−0.173836	+	1.50862i
$470$		−	2.22398i		−	0.102585i
$471$	−0.745625	+	0.693953i	−0.0343566	+	0.0319757i
$472$		−	4.91543i		−	0.226251i
$473$			37.0955i			1.70565i
$474$	2.26831	−	2.11112i	0.104187	−	0.0969668i
$475$		−	15.9745i		−	0.732959i
$476$	−0.767990	+	6.66494i	−0.0352008	+	0.305487i
$477$	20.8149	+	1.49618i	0.953050	+	0.0685053i
$478$	−29.1333			−1.33253
$479$	4.34248			0.198413			0.0992066	−	0.995067i	$-0.468370\pi$
$479$	4.34248			0.198413			0.0992066	+	0.995067i	$0.468370\pi$
$480$	−4.91605	+	4.57537i	−0.224386	+	0.208836i
$481$			12.5345i			0.571525i
$482$	−5.46589			−0.248964
$483$	2.71753	+	3.68985i	0.123652	+	0.167894i
$484$	19.0481			0.865823
$485$		−	31.3918i		−	1.42543i
$486$	12.8126	−	8.87902i	0.581192	−	0.402761i
$487$	41.2175			1.86774			0.933872	−	0.357608i	$-0.116408\pi$
$487$	41.2175			1.86774			0.933872	+	0.357608i	$0.116408\pi$
$488$	−12.1027			−0.547864
$489$	−6.45604	−	6.93676i	−0.291952	−	0.313691i
$490$	−6.17297	+	26.4302i	−0.278866	+	1.19399i
$491$			16.9407i			0.764524i	0.924054	+	0.382262i	$0.124855\pi$
$491$			16.9407i			0.764524i	−0.924054	+	0.382262i	$0.875145\pi$
$492$	2.53394	+	2.72261i	0.114239	+	0.122745i
$493$		−	24.8177i		−	1.11773i
$494$		−	6.44994i		−	0.290196i
$495$	63.5983	+	4.57145i	2.85853	+	0.205471i
$496$			6.36714i			0.285893i
$497$	23.0138	+	2.65185i	1.03231	+	0.118952i
$498$	−0.585024	+	0.544482i	−0.0262156	+	0.0243988i
$499$	−40.2538			−1.80201			−0.901004	−	0.433811i	$-0.857169\pi$
$499$	−40.2538			−1.80201			−0.901004	+	0.433811i	$0.857169\pi$
$500$	−19.5180			−0.872871
$501$	−17.8533	−	19.1826i	−0.797625	−	0.857016i
$502$			10.3699i			0.462832i
$503$	−2.46742			−0.110017			−0.0550085	−	0.998486i	$-0.517519\pi$
$503$	−2.46742			−0.110017			−0.0550085	+	0.998486i	$0.517519\pi$
$504$	−1.47157	+	7.79965i	−0.0655489	+	0.347424i
$505$	−67.3018			−2.99489
$506$			5.48161i			0.243687i
$507$	4.02765	+	4.32755i	0.178874	+	0.192193i
$508$	−10.0647			−0.446549
$509$	−0.835122			−0.0370161			−0.0185081	−	0.999829i	$-0.505892\pi$
$509$	−0.835122			−0.0370161			−0.0185081	+	0.999829i	$0.505892\pi$
$510$	−12.4660	+	11.6021i	−0.552004	+	0.513750i
$511$	1.38737	+	0.159864i	0.0613735	+	0.00707197i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.18734	−	6.44415i	−0.229027	−	0.284516i
$514$			1.79485i			0.0791674i
$515$		−	22.3615i		−	0.985364i
$516$	−7.98554	−	8.58014i	−0.351544	−	0.377720i
$517$		−	3.14416i		−	0.138280i
$518$	−8.13198	−	0.937035i	−0.357299	−	0.0411709i
$519$	−25.1749	−	27.0494i	−1.10506	−	1.18734i
$520$	−15.7084			−0.688858
$521$	23.9058			1.04733			0.523666	−	0.851923i	$-0.324564\pi$
$521$	23.9058			1.04733			0.523666	+	0.851923i	$0.324564\pi$
$522$	2.10504	−	29.2854i	0.0921350	−	1.28179i
$523$		−	25.5556i		−	1.11747i	−0.829347	−	0.558733i	$-0.811288\pi$
$523$		−	25.5556i		−	1.11747i	0.829347	−	0.558733i	$-0.188712\pi$
$524$	−14.5965			−0.637649
$525$	−37.0234	+	27.2673i	−1.61583	+	1.19004i
$526$	12.9422			0.564307
$527$			16.1456i			0.703315i
$528$	−6.95008	+	6.46844i	−0.302463	+	0.281503i
$529$	−1.00000			−0.0434783
$530$	−26.9717			−1.17157
$531$	1.05724	−	14.7083i	0.0458801	−	0.638287i
$532$	4.18450	+	0.482174i	0.181421	+	0.0209049i
$533$			8.69964i			0.376823i
$534$	−15.4856	+	14.4125i	−0.670128	+	0.623688i
$535$			68.1047i			2.94442i
$536$		−	12.4303i		−	0.536906i
$537$	−19.1078	+	17.7837i	−0.824564	+	0.767422i
$538$			14.8549i			0.640440i
$539$	−8.72705	+	37.3657i	−0.375901	+	1.60945i
$540$	−15.6943	+	12.6334i	−0.675375	+	0.543655i
$541$	7.35253			0.316110			0.158055	−	0.987430i	$-0.449478\pi$
$541$	7.35253			0.316110			0.158055	+	0.987430i	$0.449478\pi$
$542$	19.5724			0.840706
$543$	8.77582	−	8.16766i	0.376607	−	0.350508i
$544$		−	2.53578i		−	0.108721i
$545$	2.15176			0.0921715
$546$	−14.9488	+	11.0096i	−0.639748	+	0.471167i
$547$	14.1086			0.603238			0.301619	−	0.953428i	$-0.402473\pi$
$547$	14.1086			0.603238			0.301619	+	0.953428i	$0.402473\pi$
$548$			1.09814i			0.0469103i
$549$	−36.2147	−	2.60311i	−1.54561	−	0.111098i
$550$	−55.0017			−2.34528
$551$	−15.5815			−0.663793
$552$	−1.18002	−	1.26789i	−0.0502252	−	0.0539649i
$553$	−0.541833	+	4.70226i	−0.0230411	+	0.199960i
$554$			9.80788i			0.416697i
$555$	−14.1559	−	15.2099i	−0.600884	−	0.645626i
$556$		−	3.04117i		−	0.128974i
$557$		−	21.9546i		−	0.930248i	−0.885246	−	0.465124i	$-0.846010\pi$
$557$		−	21.9546i		−	0.930248i	0.885246	−	0.465124i	$-0.153990\pi$
$558$	−1.36948	+	19.0523i	−0.0579746	+	0.806546i
$559$		−	27.4163i		−	1.15959i
$560$	1.17430	−	10.1911i	0.0496233	−	0.430651i
$561$	−17.6239	+	16.4025i	−0.744080	+	0.692515i
$562$	8.17582			0.344876
$563$	−43.9089			−1.85054			−0.925271	−	0.379308i	$-0.876162\pi$
$563$	−43.9089			−1.85054			−0.925271	+	0.379308i	$0.876162\pi$
$564$	0.676841	+	0.727239i	0.0285002	+	0.0306223i
$565$		−	28.2662i		−	1.18917i
$566$	6.82716			0.286967
$567$	−6.08093	+	23.0222i	−0.255375	+	0.966842i
$568$	−8.75597			−0.367392
$569$		−	8.36193i		−	0.350551i	−0.984519	−	0.175275i	$-0.943918\pi$
$569$		−	8.36193i		−	0.350551i	0.984519	−	0.175275i	$-0.0560815\pi$
$570$	7.28425	+	7.82664i	0.305104	+	0.327822i
$571$	−17.2548			−0.722090			−0.361045	−	0.932548i	$-0.617580\pi$
$571$	−17.2548			−0.722090			−0.361045	+	0.932548i	$0.617580\pi$
$572$	−22.2078			−0.928554
$573$	34.9194	−	32.4995i	1.45878	−	1.35769i
$574$	−5.64403	−	0.650353i	−0.235577	−	0.0271452i
$575$		−	10.0338i		−	0.418440i
$576$	0.215085	−	2.99228i	0.00896188	−	0.124678i
$577$		−	45.7993i		−	1.90665i	−0.301943	−	0.953326i	$-0.597635\pi$
$577$		−	45.7993i		−	1.90665i	0.301943	−	0.953326i	$-0.402365\pi$
$578$			10.5698i			0.439647i
$579$	−10.9546	−	11.7702i	−0.455256	−	0.489154i
$580$			37.9476i			1.57569i
$581$	0.139745	−	1.21277i	0.00579761	−	0.0503141i
$582$	9.55372	+	10.2651i	0.396014	+	0.425502i
$583$	−38.1313			−1.57924
$584$	−0.527845			−0.0218424
$585$	−47.0039	−	3.37864i	−1.94337	−	0.139690i
$586$		−	4.03638i		−	0.166741i
$587$	−5.46189			−0.225436			−0.112718	−	0.993627i	$-0.535956\pi$
$587$	−5.46189			−0.225436			−0.112718	+	0.993627i	$0.535956\pi$
$588$	−6.02514	−	10.5213i	−0.248473	−	0.433891i
$589$	10.1369			0.417682
$590$			19.0588i			0.784640i
$591$	0.851595	−	0.792580i	0.0350299	−	0.0326024i
$592$	3.09394			0.127160
$593$	−34.9784			−1.43639			−0.718194	−	0.695842i	$-0.755031\pi$
$593$	−34.9784			−1.43639			−0.718194	+	0.695842i	$0.755031\pi$
$594$	−22.1878	+	17.8605i	−0.910378	+	0.732826i
$595$	2.97777	−	25.8423i	0.122077	−	1.05943i
$596$			1.07201i			0.0439114i
$597$	29.9258	−	27.8519i	1.22478	−	1.13990i
$598$		−	4.05132i		−	0.165671i
$599$			23.4153i			0.956725i	0.878163	+	0.478362i	$0.158769\pi$
$599$			23.4153i			0.956725i	−0.878163	+	0.478362i	$0.841231\pi$
$600$	12.7218	−	11.8402i	0.519365	−	0.483373i
$601$			24.8353i			1.01305i	0.862225	+	0.506526i	$0.169070\pi$
$601$			24.8353i			1.01305i	−0.862225	+	0.506526i	$0.830930\pi$
$602$	17.7868	+	2.04954i	0.724936	+	0.0835332i
$603$	2.67357	−	37.1949i	0.108876	−	1.51469i
$604$	−7.03831			−0.286385
$605$	−73.8561			−3.00268
$606$	22.0076	−	20.4825i	0.893998	−	0.832044i
$607$		−	6.72695i		−	0.273038i	−0.990637	−	0.136519i	$-0.956408\pi$
$607$		−	6.72695i		−	0.273038i	0.990637	−	0.136519i	$-0.0435915\pi$
$608$	−1.59206			−0.0645665
$609$	26.5965	+	36.1126i	1.07774	+	1.46336i
$610$	46.9265			1.90000
$611$			2.32377i			0.0940095i
$612$	0.545408	−	7.58776i	0.0220468	−	0.306717i
$613$	36.2102			1.46252			0.731259	−	0.682100i	$-0.238933\pi$
$613$	36.2102			1.46252			0.731259	+	0.682100i	$0.238933\pi$
$614$	−11.8749			−0.479231
$615$	−9.82496	−	10.5565i	−0.396181	−	0.425680i
$616$	1.66017	−	14.4077i	0.0668902	−	0.580501i
$617$			20.4103i			0.821689i	0.911705	+	0.410845i	$0.134766\pi$
$617$			20.4103i			0.821689i	−0.911705	+	0.410845i	$0.865234\pi$
$618$	6.80544	+	7.31218i	0.273755	+	0.294139i
$619$		−	31.4720i		−	1.26497i	−0.774574	−	0.632483i	$-0.782036\pi$
$619$		−	31.4720i		−	1.26497i	0.774574	−	0.632483i	$-0.217964\pi$
$620$		−	24.6876i		−	0.991479i
$621$	−3.25826	−	4.04768i	−0.130749	−	0.162428i
$622$			21.9913i			0.881772i
$623$	3.69906	−	32.1020i	0.148200	−	1.28614i
$624$	5.13662	−	4.78066i	0.205630	−	0.191379i
$625$	25.5088			1.02035
$626$	−6.93834			−0.277312
$627$	10.2981	+	11.0649i	0.411268	+	0.441891i
$628$			0.588084i			0.0234671i
$629$	7.84554			0.312822
$630$	5.70579	−	30.2420i	0.227324	−	1.20487i
$631$	−33.0258			−1.31474			−0.657368	−	0.753570i	$-0.728330\pi$
$631$	−33.0258			−1.31474			−0.657368	+	0.753570i	$0.728330\pi$
$632$		−	1.78905i		−	0.0711644i
$633$	−14.8943	−	16.0033i	−0.591994	−	0.636074i
$634$	24.9558			0.991121
$635$	39.0244			1.54864
$636$	8.81970	−	8.20850i	0.349724	−	0.325488i
$637$	6.44994	−	27.6160i	0.255556	−	1.09419i
$638$			53.6485i			2.12397i
$639$	−26.2003	−	1.88328i	−1.03647	−	0.0745014i
$640$			3.87735i			0.153266i
$641$			6.73717i			0.266102i	0.991109	+	0.133051i	$0.0424774\pi$
$641$			6.73717i			0.266102i	−0.991109	+	0.133051i	$0.957523\pi$
$642$	−20.7268	−	22.2701i	−0.818023	−	0.878933i
$643$		−	12.3313i		−	0.486298i	−0.969989	−	0.243149i	$-0.921820\pi$
$643$		−	12.3313i		−	0.486298i	0.969989	−	0.243149i	$-0.0781805\pi$
$644$	2.62836	+	0.302862i	0.103572	+	0.0119344i
$645$	30.9627	+	33.2682i	1.21916	+	1.30993i
$646$	−4.03711			−0.158838
$647$	−16.5816			−0.651889			−0.325944	−	0.945389i	$-0.605682\pi$
$647$	−16.5816			−0.651889			−0.325944	+	0.945389i	$0.605682\pi$
$648$	1.28719	−	8.90748i	0.0505656	−	0.349919i
$649$			26.9445i			1.05766i
$650$	40.6503			1.59444
$651$	−17.3029	−	23.4938i	−0.678154	−	0.920795i
$652$	−5.47111			−0.214265
$653$		−	36.0008i		−	1.40882i	−0.709794	−	0.704409i	$-0.751212\pi$
$653$		−	36.0008i		−	1.40882i	0.709794	−	0.704409i	$-0.248788\pi$
$654$	−0.703625	+	0.654863i	−0.0275139	+	0.0256072i
$655$	56.5956			2.21137
$656$	2.14736			0.0838403
$657$	−1.57946	−	0.113532i	−0.0616206	−	0.00442929i
$658$	−1.50758	−	0.173716i	−0.0587716	−	0.00677216i
$659$		−	17.0146i		−	0.662793i	−0.943492	−	0.331396i	$-0.892480\pi$
$659$		−	17.0146i		−	0.662793i	0.943492	−	0.331396i	$-0.107520\pi$
$660$	26.9479	−	25.0804i	1.04895	−	0.976253i
$661$			47.2095i			1.83623i	0.396308	+	0.918117i	$0.370291\pi$
$661$			47.2095i			1.83623i	−0.396308	+	0.918117i	$0.629709\pi$
$662$		−	6.74735i		−	0.262243i
$663$	13.0253	−	12.1227i	0.505862	−	0.470806i
$664$			0.461416i			0.0179064i
$665$	−16.2248	−	1.86956i	−0.629170	−	0.0724983i
$666$	9.25792	+	0.665460i	0.358737	+	0.0257861i
$667$	−9.78700			−0.378954
$668$	−15.1296			−0.585380
$669$	−0.126782	+	0.117996i	−0.00490168	+	0.00456199i
$670$			48.1966i			1.86200i
$671$	66.3424			2.56112
$672$	2.71753	+	3.68985i	0.104831	+	0.142339i
$673$	−32.1543			−1.23946			−0.619729	−	0.784816i	$-0.712757\pi$
$673$	−32.1543			−1.23946			−0.619729	+	0.784816i	$0.712757\pi$
$674$		−	16.5741i		−	0.638411i
$675$	40.6138	−	32.6929i	1.56323	−	1.25835i
$676$	3.41319			0.131277
$677$	16.5283			0.635233			0.317617	−	0.948219i	$-0.397118\pi$
$677$	16.5283			0.635233			0.317617	+	0.948219i	$0.397118\pi$
$678$	8.60246	+	9.24300i	0.330376	+	0.354975i
$679$	−21.2797	−	2.45203i	−0.816642	−	0.0941003i
$680$			9.83210i			0.377044i
$681$	−31.1735	−	33.4946i	−1.19457	−	1.28352i
$682$		−	34.9022i		−	1.33647i
$683$		−	0.467428i		−	0.0178856i	−0.999960	−	0.00894281i	$-0.997153\pi$
$683$		−	0.467428i		−	0.0178856i	0.999960	−	0.00894281i	$-0.00284662\pi$
$684$	−4.76389	−	0.342428i	−0.182152	−	0.0130931i
$685$		−	4.25788i		−	0.162685i
$686$	17.4342	+	6.24897i	0.665640	+	0.238587i
$687$	13.3935	−	12.4653i	0.510994	−	0.475582i
$688$	−6.76726			−0.258000
$689$	28.1818			1.07364
$690$	4.57537	+	4.91605i	0.174181	+	0.187151i
$691$			10.4702i			0.398304i	0.979969	+	0.199152i	$0.0638188\pi$
$691$			10.4702i			0.398304i	−0.979969	+	0.199152i	$0.936181\pi$
$692$	−21.3342			−0.811006
$693$	8.06657	−	42.7547i	0.306424	−	1.62412i
$694$	−17.3061			−0.656930
$695$			11.7917i			0.447284i
$696$	−11.5489	−	12.4088i	−0.437760	−	0.470355i
$697$	5.44523			0.206253
$698$	−13.0219			−0.492886
$699$	−23.6477	+	22.0089i	−0.894438	+	0.832454i
$700$	−3.03887	+	26.3726i	−0.114858	+	0.996789i
$701$		−	48.9190i		−	1.84765i	−0.382821	−	0.923823i	$-0.625047\pi$
$701$		−	48.9190i		−	1.84765i	0.382821	−	0.923823i	$-0.374953\pi$
$702$	16.3985	−	13.2002i	0.618920	−	0.498211i
$703$		−	4.92573i		−	0.185777i
$704$			5.48161i			0.206596i
$705$	−2.62435	−	2.81976i	−0.0988387	−	0.106198i
$706$		−	20.9771i		−	0.789483i
$707$	−5.25697	+	45.6222i	−0.197709	+	1.71580i
$708$	−5.80032	−	6.23222i	−0.217990	−	0.234221i
$709$	−34.6151			−1.30000			−0.649998	−	0.759936i	$-0.725230\pi$
$709$	−34.6151			−1.30000			−0.649998	+	0.759936i	$0.725230\pi$
$710$	33.9499			1.27412
$711$	0.384797	−	5.35333i	0.0144310	−	0.200765i
$712$			12.2137i			0.457728i
$713$	6.36714			0.238451
$714$	6.89106	+	9.35665i	0.257892	+	0.350164i
$715$	86.1073			3.22023
$716$			15.0706i			0.563215i
$717$	−36.9378	+	34.3780i	−1.37947	+	1.28387i
$718$	23.6584			0.882925
$719$	−12.5885			−0.469470			−0.234735	−	0.972059i	$-0.575422\pi$
$719$	−12.5885			−0.469470			−0.234735	+	0.972059i	$0.575422\pi$
$720$	−0.833961	+	11.6021i	−0.0310799	+	0.432385i
$721$	−15.1583	−	1.74667i	−0.564524	−	0.0650492i
$722$		−	16.4653i		−	0.612777i
$723$	−6.93014	+	6.44988i	−0.257735	+	0.239874i
$724$		−	6.92160i		−	0.257239i
$725$		−	98.2012i		−	3.64710i
$726$	24.1509	−	22.4772i	0.896323	−	0.834208i
$727$			21.6999i			0.804804i	0.915463	+	0.402402i	$0.131825\pi$
$727$			21.6999i			0.804804i	−0.915463	+	0.402402i	$0.868175\pi$
$728$	−1.22699	+	10.6483i	−0.0454753	+	0.394653i
$729$	5.76750	−	26.3768i	0.213611	−	0.976919i
$730$	2.04664			0.0757495
$731$	−17.1603			−0.634696
$732$	−15.3449	+	14.2815i	−0.567164	+	0.527859i
$733$			39.1763i			1.44701i	0.690319	+	0.723505i	$0.257470\pi$
$733$			39.1763i			1.44701i	−0.690319	+	0.723505i	$0.742530\pi$
$734$	32.0746			1.18390
$735$	23.3616	+	40.7948i	0.861705	+	1.50474i
$736$	−1.00000			−0.0368605
$737$			68.1380i			2.50990i
$738$	6.42550	+	0.461865i	0.236526	+	0.0170015i
$739$	35.7175			1.31389			0.656945	−	0.753938i	$-0.271848\pi$
$739$	35.7175			1.31389			0.656945	+	0.753938i	$0.271848\pi$
$740$	−11.9963			−0.440992
$741$	−7.61108	−	8.17781i	−0.279600	−	0.300419i
$742$	−2.10677	+	18.2834i	−0.0773419	+	0.671205i
$743$		−	17.4669i		−	0.640799i	−0.947283	−	0.320399i	$-0.896183\pi$
$743$		−	17.4669i		−	0.640799i	0.947283	−	0.320399i	$-0.103817\pi$
$744$	7.51338	+	8.07282i	0.275454	+	0.295964i
$745$		−	4.15657i		−	0.152285i
$746$			19.3797i			0.709543i
$747$	−0.0992438	+	1.38069i	−0.00363114	+	0.0505167i
$748$			13.9002i			0.508240i
$749$	46.1665	+	5.31969i	1.68689	+	0.194377i
$750$	−24.7466	+	23.0317i	−0.903619	+	0.840999i
$751$	20.2274			0.738107			0.369053	−	0.929408i	$-0.379682\pi$
$751$	20.2274			0.738107			0.369053	+	0.929408i	$0.379682\pi$
$752$	0.573582			0.0209164
$753$	12.2367	+	13.1479i	0.445932	+	0.479136i
$754$		−	39.6503i		−	1.44398i
$755$	27.2900			0.993184
$756$	7.33799	+	11.6256i	0.266880	+	0.422818i
$757$	12.0119			0.436578			0.218289	−	0.975884i	$-0.429952\pi$
$757$	12.0119			0.436578			0.218289	+	0.975884i	$0.429952\pi$
$758$		−	25.0421i		−	0.909568i
$759$	6.46844	+	6.95008i	0.234789	+	0.252272i
$760$	6.17297			0.223917
$761$	22.7541			0.824837			0.412418	−	0.910995i	$-0.364684\pi$
$761$	22.7541			0.824837			0.412418	+	0.910995i	$0.364684\pi$
$762$	−12.7609	+	11.8766i	−0.462280	+	0.430244i
$763$	0.168075	−	1.45863i	0.00608474	−	0.0528059i
$764$		−	27.5414i		−	0.996413i
$765$	−2.11474	+	29.4204i	−0.0764586	+	1.06370i
$766$		−	28.4246i		−	1.02702i
$767$		−	19.9140i		−	0.719052i
$768$	−1.18002	−	1.26789i	−0.0425805	−	0.0457510i
$769$			28.8898i			1.04179i	0.853620	+	0.520896i	$0.174402\pi$
$769$			28.8898i			1.04179i	−0.853620	+	0.520896i	$0.825598\pi$
$770$	−6.43706	+	55.8635i	−0.231976	+	2.01318i
$771$	2.11797	+	2.27567i	0.0762767	+	0.0819562i
$772$	−9.28333			−0.334114
$773$	14.5743			0.524200			0.262100	−	0.965041i	$-0.415585\pi$
$773$	14.5743			0.524200			0.262100	+	0.965041i	$0.415585\pi$
$774$	−20.2495	−	1.45554i	−0.727855	−	0.0523182i
$775$			63.8869i			2.29488i
$776$	8.09621			0.290637
$777$	−11.4162	+	8.40788i	−0.409553	+	0.301631i
$778$	19.7035			0.706406
$779$		−	3.41872i		−	0.122488i
$780$	−19.9165	+	18.5363i	−0.713125	+	0.663705i
$781$	47.9968			1.71746
$782$	−2.53578			−0.0906792
$783$	−31.8886	−	39.6147i	−1.13960	−	1.41571i
$784$	−6.81655	−	1.59206i	−0.243448	−	0.0568592i
$785$		−	2.28021i		−	0.0813841i
$786$	−18.5067	+	17.2242i	−0.660112	+	0.614366i
$787$			3.66338i			0.130585i	0.997866	+	0.0652927i	$0.0207981\pi$
$787$			3.66338i			0.130585i	−0.997866	+	0.0652927i	$0.979202\pi$
$788$		−	0.671664i		−	0.0239270i
$789$	16.4093	−	15.2721i	0.584185	−	0.543701i
$790$			6.93676i			0.246799i
$791$	−19.1609	−	2.20788i	−0.681284	−	0.0785033i
$792$	−1.17901	+	16.4025i	−0.0418944	+	0.582838i
$793$	−49.0320			−1.74118
$794$	−24.3072			−0.862632
$795$	−34.1971	+	31.8272i	−1.21285	+	1.12879i
$796$		−	23.6028i		−	0.836580i
$797$	−39.2481			−1.39024			−0.695120	−	0.718894i	$-0.744649\pi$
$797$	−39.2481			−1.39024			−0.695120	+	0.718894i	$0.744649\pi$
$798$	5.87446	−	4.32647i	0.207954	−	0.153155i
$799$	1.45448			0.0514557
$800$		−	10.0338i		−	0.354750i
$801$	−2.62699	+	36.5468i	−0.0928200	+	1.29132i
$802$	−14.9262			−0.527061
$803$	2.89344			0.102107
$804$	−14.6680	−	15.7602i	−0.517302	−	0.555820i
$805$	−10.1911	−	1.17430i	−0.359188	−	0.0413887i
$806$			25.7953i			0.908601i
$807$	17.5291	+	18.8344i	0.617055	+	0.663001i
$808$		−	17.3577i		−	0.610641i
$809$		−	5.36364i		−	0.188575i	−0.995545	−	0.0942877i	$-0.969943\pi$
$809$		−	5.36364i		−	0.188575i	0.995545	−	0.0942877i	$-0.0300574\pi$
$810$	−4.99089	+	34.5374i	−0.175362	+	1.21352i
$811$		−	8.17676i		−	0.287125i	−0.989641	−	0.143562i	$-0.954144\pi$
$811$		−	8.17676i		−	0.287125i	0.989641	−	0.143562i	$-0.0458558\pi$
$812$	25.7238	+	2.96411i	0.902727	+	0.104020i
$813$	24.8156	−	23.0959i	0.870321	−	0.810008i
$814$	−16.9598			−0.594440
$815$	21.2134			0.743073
$816$	−2.99228	−	3.21509i	−0.104751	−	0.112550i
$817$			10.7739i			0.376930i
$818$	20.2559			0.708231
$819$	−5.96179	+	31.5989i	−0.208322	+	1.10415i
$820$	−8.32606			−0.290759
$821$			48.4373i			1.69047i	0.534393	+	0.845236i	$0.320540\pi$
$821$			48.4373i			1.69047i	−0.534393	+	0.845236i	$0.679460\pi$
$822$	1.29583	+	1.39232i	0.0451974	+	0.0485628i
$823$	18.4351			0.642609			0.321304	−	0.946976i	$-0.395879\pi$
$823$	18.4351			0.642609			0.321304	+	0.946976i	$0.395879\pi$
$824$	5.76721			0.200910
$825$	−69.7360	+	64.9033i	−2.42790	+	2.25964i
$826$	12.9195	+	1.48869i	0.449527	+	0.0517983i
$827$		−	16.5808i		−	0.576571i	−0.957544	−	0.288286i	$-0.906915\pi$
$827$		−	16.5808i		−	0.576571i	0.957544	−	0.288286i	$-0.0930852\pi$
$828$	−2.99228	−	0.215085i	−0.103989	−	0.00747473i
$829$			2.74513i			0.0953422i	0.998863	+	0.0476711i	$0.0151799\pi$
$829$			2.74513i			0.0953422i	−0.998863	+	0.0476711i	$0.984820\pi$
$830$		−	1.78907i		−	0.0620996i
$831$	11.5735	+	12.4353i	0.401482	+	0.431376i
$832$		−	4.05132i		−	0.140454i
$833$	−17.2853	−	4.03711i	−0.598899	−	0.139877i
$834$	−3.58866	−	3.85587i	−0.124265	−	0.133518i
$835$	58.6626			2.03010
$836$	8.72705			0.301831
$837$	20.7458	+	25.7722i	0.717079	+	0.890816i
$838$			21.1668i			0.731194i
$839$	−33.5960			−1.15986			−0.579932	−	0.814665i	$-0.696921\pi$
$839$	−33.5960			−1.15986			−0.579932	+	0.814665i	$0.696921\pi$
$840$	−10.5368	−	14.3069i	−0.363555	−	0.493633i
$841$	−66.7853			−2.30294
$842$			24.7598i			0.853280i
$843$	10.3660	−	9.64767i	0.357025	−	0.332283i
$844$	−12.6220			−0.434467
$845$	−13.2341			−0.455268
$846$	1.71632	+	0.123369i	0.0590083	+	0.00424152i
$847$	−5.76894	+	50.0653i	−0.198223	+	1.72026i
$848$		−	6.95621i		−	0.238877i
$849$	8.65609	−	8.05622i	0.297076	−	0.276489i
$850$		−	25.4436i		−	0.872708i
$851$		−	3.09394i		−	0.106059i
$852$	−11.1016	+	10.3323i	−0.380334	+	0.353977i
$853$			28.3818i			0.971775i	0.874021	+	0.485887i	$0.161503\pi$
$853$			28.3818i			0.971775i	−0.874021	+	0.485887i	$0.838497\pi$
$854$	3.66545	−	31.8103i	0.125429	−	1.08853i
$855$	18.4713	+	1.32771i	0.631703	+	0.0454069i
$856$	−17.5647			−0.600351
$857$	−6.84983			−0.233986			−0.116993	−	0.993133i	$-0.537325\pi$
$857$	−6.84983			−0.233986			−0.116993	+	0.993133i	$0.537325\pi$
$858$	−28.1570	+	26.2057i	−0.961264	+	0.894648i
$859$			34.0403i			1.16144i	0.814103	+	0.580720i	$0.197229\pi$
$859$			34.0403i			1.16144i	−0.814103	+	0.580720i	$0.802771\pi$
$860$	26.2391			0.894744
$861$	−7.92344	+	5.83552i	−0.270030	+	0.198874i
$862$	−14.4976			−0.493790
$863$		−	1.37996i		−	0.0469745i	−0.999724	−	0.0234872i	$-0.992523\pi$
$863$		−	1.37996i		−	0.0469745i	0.999724	−	0.0234872i	$-0.00747690\pi$
$864$	−3.25826	−	4.04768i	−0.110848	−	0.137705i
$865$	82.7203			2.81257
$866$	18.9525			0.644034
$867$	12.4727	+	13.4014i	0.423594	+	0.455134i
$868$	−16.7351	−	1.92836i	−0.568027	−	0.0654529i
$869$			9.80686i			0.332675i
$870$	44.7791	+	48.1134i	1.51815	+	1.63120i
$871$		−	50.3590i		−	1.70635i
$872$			0.554958i			0.0187932i
$873$	24.2261	+	1.74137i	0.819930	+	0.0589366i
$874$			1.59206i			0.0538522i
$875$	5.91125	−	51.3003i	0.199837	−	1.73427i
$876$	−0.669249	+	0.622870i	−0.0226118	+	0.0210448i
$877$	18.2061			0.614775			0.307387	−	0.951584i	$-0.400545\pi$
$877$	18.2061			0.614775			0.307387	+	0.951584i	$0.400545\pi$
$878$	5.13220			0.173203
$879$	−4.76302	−	5.11768i	−0.160653	−	0.172615i
$880$		−	21.2541i		−	0.716477i
$881$	−25.7395			−0.867187			−0.433593	−	0.901109i	$-0.642755\pi$
$881$	−25.7395			−0.867187			−0.433593	+	0.901109i	$0.642755\pi$
$882$	−20.0546	−	6.23002i	−0.675273	−	0.209776i
$883$	46.8161			1.57549			0.787743	−	0.616004i	$-0.211250\pi$
$883$	46.8161			1.57549			0.787743	+	0.616004i	$0.211250\pi$
$884$		−	10.2732i		−	0.345527i
$885$	22.4899	+	24.1645i	0.755989	+	0.812280i
$886$	−7.28414			−0.244715
$887$	−24.7708			−0.831722			−0.415861	−	0.909428i	$-0.636520\pi$
$887$	−24.7708			−0.831722			−0.415861	+	0.909428i	$0.636520\pi$
$888$	3.92277	−	3.65092i	0.131639	−	0.122517i
$889$	3.04821	−	26.4537i	0.102234	−	0.887228i
$890$		−	47.3568i		−	1.58740i
$891$	−7.05588	+	48.8274i	−0.236381	+	1.63578i
$892$			0.0999946i			0.00334807i
$893$		−	0.913177i		−	0.0305583i
$894$	1.26500	+	1.35919i	0.0423080	+	0.0454583i
$895$		−	58.4340i		−	1.95323i
$896$	2.62836	+	0.302862i	0.0878073	+	0.0101179i
$897$	−4.78066	−	5.13662i	−0.159621	−	0.171507i
$898$	28.5459			0.952590
$899$	62.3152			2.07833
$900$	2.15813	−	30.0241i	0.0719377	−	1.00080i
$901$		−	17.6394i		−	0.587654i
$902$	−11.7710			−0.391931
$903$	24.9702	−	18.3903i	0.830956	−	0.611990i
$904$	7.29007			0.242464
$905$			26.8375i			0.892108i
$906$	−8.92379	+	8.30538i	−0.296473	+	0.275928i
$907$	36.6141			1.21575			0.607876	−	0.794032i	$-0.292022\pi$
$907$	36.6141			1.21575			0.607876	+	0.794032i	$0.292022\pi$
$908$	−26.4176			−0.876700
$909$	3.73338	−	51.9390i	0.123828	−	1.72271i
$910$	4.75747	−	41.2873i	0.157709	−	1.36866i
$911$		−	21.3903i		−	0.708693i	−0.935114	−	0.354346i	$-0.884703\pi$
$911$		−	21.3903i		−	0.708693i	0.935114	−	0.354346i	$-0.115297\pi$
$912$	−2.01855	+	1.87867i	−0.0668410	+	0.0622089i
$913$		−	2.52931i		−	0.0837078i
$914$		−	4.70548i		−	0.155643i
$915$	59.4975	−	55.3744i	1.96693	−	1.83062i
$916$		−	10.5636i		−	0.349032i
$917$	4.42071	−	38.3648i	0.145985	−	1.26692i
$918$	−8.26222	−	10.2640i	−0.272694	−	0.338763i
$919$	8.52949			0.281362			0.140681	−	0.990055i	$-0.455071\pi$
$919$	8.52949			0.281362			0.140681	+	0.990055i	$0.455071\pi$
$920$	3.87735			0.127832
$921$	−15.0560	+	14.0126i	−0.496112	+	0.461732i
$922$		−	14.1607i		−	0.466357i
$923$	−35.4732			−1.16762
$924$	−14.8965	−	20.2263i	−0.490058	−	0.665398i
$925$	31.0441			1.02072
$926$			1.54127i			0.0506492i
$927$	17.2571	+	1.24044i	0.566797	+	0.0407414i
$928$	−9.78700			−0.321274
$929$	−48.3584			−1.58659			−0.793293	−	0.608840i	$-0.791635\pi$
$929$	−48.3584			−1.58659			−0.793293	+	0.608840i	$0.791635\pi$
$930$	−29.1320	−	31.3012i	−0.955276	−	1.02641i
$931$	−2.53465	+	10.8523i	−0.0830698	+	0.355671i
$932$			18.6512i			0.610942i
$933$	25.9503	+	27.8826i	0.849575	+	0.912834i
$934$			18.4584i			0.603976i
$935$		−	53.8958i		−	1.76258i
$936$	0.871379	−	12.1227i	0.0284819	−	0.396242i
$937$			33.7502i			1.10257i	0.834317	+	0.551285i	$0.185862\pi$
$937$			33.7502i			1.10257i	−0.834317	+	0.551285i	$0.814138\pi$
$938$	32.6712	+	3.76466i	1.06675	+	0.122920i
$939$	−8.79705	+	8.18741i	−0.287081	+	0.267186i
$940$	−2.22398			−0.0725382
$941$	27.5070			0.896701			0.448351	−	0.893858i	$-0.352012\pi$
$941$	27.5070			0.896701			0.448351	+	0.893858i	$0.352012\pi$
$942$	0.693953	+	0.745625i	0.0226102	+	0.0242938i
$943$		−	2.14736i		−	0.0699276i
$944$	−4.91543			−0.159984
$945$	−28.4519	−	45.0764i	−0.925542	−	1.46634i
$946$	37.0955			1.20608
$947$			11.0106i			0.357796i	0.983868	+	0.178898i	$0.0572532\pi$
$947$			11.0106i			0.357796i	−0.983868	+	0.178898i	$0.942747\pi$
$948$	−2.11112	−	2.26831i	−0.0685659	−	0.0736713i
$949$	−2.13847			−0.0694176
$950$	−15.9745			−0.518280
$951$	31.6412	−	29.4484i	1.02604	−	0.954931i
$952$	6.66494	+	0.767990i	0.216012	+	0.0248907i
$953$			41.4210i			1.34176i	0.741567	+	0.670879i	$0.234083\pi$
$953$			41.4210i			1.34176i	−0.741567	+	0.670879i	$0.765917\pi$
$954$	1.49618	−	20.8149i	0.0484405	−	0.673908i
$955$			106.788i			3.45557i
$956$			29.1333i			0.942239i
$957$	63.3066	+	68.0204i	2.04641	+	2.19879i
$958$		−	4.34248i		−	0.140299i
$959$	−2.88631	−	0.332585i	−0.0932039	−	0.0107397i
$960$	4.57537	+	4.91605i	0.147669	+	0.158665i
$961$	−9.54044			−0.307756
$962$	12.5345			0.404129
$963$	−52.5586	−	3.77792i	−1.69368	−	0.121742i
$964$			5.46589i			0.176044i
$965$	35.9947			1.15871
$966$	3.68985	−	2.71753i	0.118719	−	0.0874352i
$967$	−25.3262			−0.814437			−0.407218	−	0.913331i	$-0.633501\pi$
$967$	−25.3262			−0.814437			−0.407218	+	0.913331i	$0.633501\pi$
$968$		−	19.0481i		−	0.612229i
$969$	−5.11860	+	4.76389i	−0.164433	+	0.153038i
$970$	−31.3918			−1.00793
$971$	−0.639049			−0.0205081			−0.0102540	−	0.999947i	$-0.503264\pi$
$971$	−0.639049			−0.0205081			−0.0102540	+	0.999947i	$0.503264\pi$
$972$	−8.87902	−	12.8126i	−0.284795	−	0.410965i
$973$	7.99329	+	0.921054i	0.256253	+	0.0295276i
$974$		−	41.2175i		−	1.32069i
$975$	51.5401	−	47.9684i	1.65060	−	1.53622i
$976$			12.1027i			0.387398i
$977$			28.1788i			0.901519i	0.892646	+	0.450759i	$0.148847\pi$
$977$			28.1788i			0.901519i	−0.892646	+	0.450759i	$0.851153\pi$
$978$	−6.93676	+	6.45604i	−0.221813	+	0.206441i
$979$		−	66.9508i		−	2.13976i
$980$	26.4302	+	6.17297i	0.844280	+	0.197188i
$981$	−0.119363	+	1.66059i	−0.00381097	+	0.0530185i
$982$	16.9407			0.540600
$983$	−47.8001			−1.52459			−0.762294	−	0.647231i	$-0.775927\pi$
$983$	−47.8001			−1.52459			−0.762294	+	0.647231i	$0.775927\pi$
$984$	2.72261	−	2.53394i	0.0867937	−	0.0807789i
$985$			2.60428i			0.0829791i
$986$	−24.8177			−0.790355
$987$	−2.11643	+	1.55873i	−0.0673668	+	0.0496149i
$988$	−6.44994			−0.205200
$989$			6.76726i			0.215186i
$990$	4.57145	−	63.5983i	0.145290	−	2.02129i
$991$	−15.8113			−0.502263			−0.251131	−	0.967953i	$-0.580803\pi$
$991$	−15.8113			−0.502263			−0.251131	+	0.967953i	$0.580803\pi$
$992$	6.36714			0.202157
$993$	−7.96204	−	8.55489i	−0.252668	−	0.271481i
$994$	2.65185	−	23.0138i	0.0841115	−	0.729954i
$995$			91.5164i			2.90127i
$996$	0.544482	+	0.585024i	0.0172526	+	0.0185372i
$997$		−	55.5747i		−	1.76007i	−0.474911	−	0.880034i	$-0.657520\pi$
$997$		−	55.5747i		−	1.76007i	0.474911	−	0.880034i	$-0.342480\pi$
$998$			40.2538i			1.27421i
$999$	12.5233	−	10.0808i	0.396219	−	0.318944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.c.461.4	✓	28
3.2	odd	2	inner	966.2.f.c.461.25	yes	28
7.6	odd	2	inner	966.2.f.c.461.11	yes	28
21.20	even	2	inner	966.2.f.c.461.18	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.c.461.4	✓	28	1.1	even	1	trivial
966.2.f.c.461.11	yes	28	7.6	odd	2	inner
966.2.f.c.461.18	yes	28	21.20	even	2	inner
966.2.f.c.461.25	yes	28	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.18002 - 1.26789i) q^{3} -1.00000 q^{4} +3.87735 q^{5} +(-1.26789 + 1.18002i) q^{6} +(0.302862 - 2.62836i) q^{7} +1.00000i q^{8} +(-0.215085 + 2.99228i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.18002 - 1.26789i) q^{3} -1.00000 q^{4} +3.87735 q^{5} +(-1.26789 + 1.18002i) q^{6} +(0.302862 - 2.62836i) q^{7} +1.00000i q^{8} +(-0.215085 + 2.99228i) q^{9} -3.87735i q^{10} -5.48161i q^{11} +(1.18002 + 1.26789i) q^{12} +4.05132i q^{13} +(-2.62836 - 0.302862i) q^{14} +(-4.57537 - 4.91605i) q^{15} +1.00000 q^{16} +2.53578 q^{17} +(2.99228 + 0.215085i) q^{18} -1.59206i q^{19} -3.87735 q^{20} +(-3.68985 + 2.71753i) q^{21} -5.48161 q^{22} -1.00000i q^{23} +(1.26789 - 1.18002i) q^{24} +10.0338 q^{25} +4.05132 q^{26} +(4.04768 - 3.25826i) q^{27} +(-0.302862 + 2.62836i) q^{28} -9.78700i q^{29} +(-4.91605 + 4.57537i) q^{30} +6.36714i q^{31} -1.00000i q^{32} +(-6.95008 + 6.46844i) q^{33} -2.53578i q^{34} +(1.17430 - 10.1911i) q^{35} +(0.215085 - 2.99228i) q^{36} +3.09394 q^{37} -1.59206 q^{38} +(5.13662 - 4.78066i) q^{39} +3.87735i q^{40} +2.14736 q^{41} +(2.71753 + 3.68985i) q^{42} -6.76726 q^{43} +5.48161i q^{44} +(-0.833961 + 11.6021i) q^{45} -1.00000 q^{46} +0.573582 q^{47} +(-1.18002 - 1.26789i) q^{48} +(-6.81655 - 1.59206i) q^{49} -10.0338i q^{50} +(-2.99228 - 3.21509i) q^{51} -4.05132i q^{52} -6.95621i q^{53} +(-3.25826 - 4.04768i) q^{54} -21.2541i q^{55} +(2.62836 + 0.302862i) q^{56} +(-2.01855 + 1.87867i) q^{57} -9.78700 q^{58} -4.91543 q^{59} +(4.57537 + 4.91605i) q^{60} +12.1027i q^{61} +6.36714 q^{62} +(7.79965 + 1.47157i) q^{63} -1.00000 q^{64} +15.7084i q^{65} +(6.46844 + 6.95008i) q^{66} -12.4303 q^{67} -2.53578 q^{68} +(-1.26789 + 1.18002i) q^{69} +(-10.1911 - 1.17430i) q^{70} +8.75597i q^{71} +(-2.99228 - 0.215085i) q^{72} +0.527845i q^{73} -3.09394i q^{74} +(-11.8402 - 12.7218i) q^{75} +1.59206i q^{76} +(-14.4077 - 1.66017i) q^{77} +(-4.78066 - 5.13662i) q^{78} -1.78905 q^{79} +3.87735 q^{80} +(-8.90748 - 1.28719i) q^{81} -2.14736i q^{82} +0.461416 q^{83} +(3.68985 - 2.71753i) q^{84} +9.83210 q^{85} +6.76726i q^{86} +(-12.4088 + 11.5489i) q^{87} +5.48161 q^{88} +12.2137 q^{89} +(11.6021 + 0.833961i) q^{90} +(10.6483 + 1.22699i) q^{91} +1.00000i q^{92} +(8.07282 - 7.51338i) q^{93} -0.573582i q^{94} -6.17297i q^{95} +(-1.26789 + 1.18002i) q^{96} -8.09621i q^{97} +(-1.59206 + 6.81655i) q^{98} +(16.4025 + 1.17901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9	\( 28 q - 28 q^{4} + 4 q^{7} - 4 q^{9} + 16 q^{15} + 28 q^{16} - 16 q^{18} + 4 q^{21} + 80 q^{25} - 4 q^{28} + 12 q^{30} + 4 q^{36} + 20 q^{37} - 20 q^{39} + 28 q^{42} - 28 q^{43} - 28 q^{46} - 28 q^{49} + 16 q^{51} - 8 q^{57} - 36 q^{58} - 16 q^{60} + 36 q^{63} - 28 q^{64} - 8 q^{67} - 60 q^{70} + 16 q^{72} + 16 q^{78} - 76 q^{81} - 4 q^{84} - 24 q^{85} + 36 q^{91} + 48 q^{93} + 72 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 4 * q^7 - 4 * q^9 + 16 * q^15 + 28 * q^16 - 16 * q^18 + 4 * q^21 + 80 * q^25 - 4 * q^28 + 12 * q^30 + 4 * q^36 + 20 * q^37 - 20 * q^39 + 28 * q^42 - 28 * q^43 - 28 * q^46 - 28 * q^49 + 16 * q^51 - 8 * q^57 - 36 * q^58 - 16 * q^60 + 36 * q^63 - 28 * q^64 - 8 * q^67 - 60 * q^70 + 16 * q^72 + 16 * q^78 - 76 * q^81 - 4 * q^84 - 24 * q^85 + 36 * q^91 + 48 * q^93 + 72 * q^99

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