LMFDB - Embedded newform 966.2.f.c.461.12

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			461.12
Character	$\chi$	$=$	966.461
Dual form			966.2.f.c.461.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.37202 - 1.05715i) q^{3} -1.00000 q^{4} +2.38722 q^{5} +(-1.05715 - 1.37202i) q^{6} +(-2.59254 + 0.527932i) q^{7} +1.00000i q^{8} +(0.764872 - 2.90086i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.37202 - 1.05715i) q^{3} -1.00000 q^{4} +2.38722 q^{5} +(-1.05715 - 1.37202i) q^{6} +(-2.59254 + 0.527932i) q^{7} +1.00000i q^{8} +(0.764872 - 2.90086i) q^{9} -2.38722i q^{10} -4.24529i q^{11} +(-1.37202 + 1.05715i) q^{12} +0.530418i q^{13} +(0.527932 + 2.59254i) q^{14} +(3.27531 - 2.52365i) q^{15} +1.00000 q^{16} +2.11430 q^{17} +(-2.90086 - 0.764872i) q^{18} -2.73737i q^{19} -2.38722 q^{20} +(-2.99892 + 3.46504i) q^{21} -4.24529 q^{22} -1.00000i q^{23} +(1.05715 + 1.37202i) q^{24} +0.698814 q^{25} +0.530418 q^{26} +(-2.01722 - 4.78861i) q^{27} +(2.59254 - 0.527932i) q^{28} +4.13294i q^{29} +(-2.52365 - 3.27531i) q^{30} -8.63102i q^{31} -1.00000i q^{32} +(-4.48791 - 5.82462i) q^{33} -2.11430i q^{34} +(-6.18897 + 1.26029i) q^{35} +(-0.764872 + 2.90086i) q^{36} +1.99195 q^{37} -2.73737 q^{38} +(0.560730 + 0.727743i) q^{39} +2.38722i q^{40} -8.92450 q^{41} +(3.46504 + 2.99892i) q^{42} +8.94310 q^{43} +4.24529i q^{44} +(1.82592 - 6.92498i) q^{45} -1.00000 q^{46} +5.75433 q^{47} +(1.37202 - 1.05715i) q^{48} +(6.44258 - 2.73737i) q^{49} -0.698814i q^{50} +(2.90086 - 2.23513i) q^{51} -0.530418i q^{52} +2.38309i q^{53} +(-4.78861 + 2.01722i) q^{54} -10.1344i q^{55} +(-0.527932 - 2.59254i) q^{56} +(-2.89381 - 3.75573i) q^{57} +4.13294 q^{58} +4.97056 q^{59} +(-3.27531 + 2.52365i) q^{60} +3.14015i q^{61} -8.63102 q^{62} +(-0.451509 + 7.92440i) q^{63} -1.00000 q^{64} +1.26622i q^{65} +(-5.82462 + 4.48791i) q^{66} -7.15841 q^{67} -2.11430 q^{68} +(-1.05715 - 1.37202i) q^{69} +(1.26029 + 6.18897i) q^{70} +11.1811i q^{71} +(2.90086 + 0.764872i) q^{72} +5.68336i q^{73} -1.99195i q^{74} +(0.958786 - 0.738750i) q^{75} +2.73737i q^{76} +(2.24123 + 11.0061i) q^{77} +(0.727743 - 0.560730i) q^{78} +10.5466 q^{79} +2.38722 q^{80} +(-7.82994 - 4.43757i) q^{81} +8.92450i q^{82} +1.92977 q^{83} +(2.99892 - 3.46504i) q^{84} +5.04729 q^{85} -8.94310i q^{86} +(4.36913 + 5.67047i) q^{87} +4.24529 q^{88} -17.8501 q^{89} +(-6.92498 - 1.82592i) q^{90} +(-0.280024 - 1.37513i) q^{91} +1.00000i q^{92} +(-9.12427 - 11.8419i) q^{93} -5.75433i q^{94} -6.53471i q^{95} +(-1.05715 - 1.37202i) q^{96} +9.07256i q^{97} +(-2.73737 - 6.44258i) q^{98} +(-12.3150 - 3.24710i) 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
$3$	1.37202	−	1.05715i	0.792135	−	0.610345i
$3$	1.37202	−	1.05715i	0.792135	−	0.610345i
$4$	−1.00000			−0.500000
$5$	2.38722			1.06760			0.533798	−	0.845612i	$-0.320764\pi$
$5$	2.38722			1.06760			0.533798	+	0.845612i	$0.320764\pi$
$6$	−1.05715	−	1.37202i	−0.431579	−	0.560124i
$7$	−2.59254	+	0.527932i	−0.979890	+	0.199540i
$7$	−2.59254	+	0.527932i	−0.979890	+	0.199540i
$8$			1.00000i			0.353553i
$9$	0.764872	−	2.90086i	0.254957	−	0.966952i
$10$		−	2.38722i		−	0.754905i
$11$		−	4.24529i		−	1.28000i	−0.768373	−	0.640002i	$-0.778934\pi$
$11$		−	4.24529i		−	1.28000i	0.768373	−	0.640002i	$-0.221066\pi$
$12$	−1.37202	+	1.05715i	−0.396068	+	0.305173i
$13$			0.530418i			0.147111i	0.997291	+	0.0735557i	$0.0234347\pi$
$13$			0.530418i			0.147111i	−0.997291	+	0.0735557i	$0.976565\pi$
$14$	0.527932	+	2.59254i	0.141096	+	0.692887i
$15$	3.27531	−	2.52365i	0.845681	−	0.651603i
$16$	1.00000			0.250000
$17$	2.11430			0.512793			0.256396	−	0.966572i	$-0.417465\pi$
$17$	2.11430			0.512793			0.256396	+	0.966572i	$0.417465\pi$
$18$	−2.90086	−	0.764872i	−0.683739	−	0.180282i
$19$		−	2.73737i		−	0.627997i	−0.949424	−	0.313998i	$-0.898331\pi$
$19$		−	2.73737i		−	0.627997i	0.949424	−	0.313998i	$-0.101669\pi$
$20$	−2.38722			−0.533798
$21$	−2.99892	+	3.46504i	−0.654417	+	0.756133i
$22$	−4.24529			−0.905099
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	1.05715	+	1.37202i	0.215790	+	0.280062i
$25$	0.698814			0.139763
$26$	0.530418			0.104023
$27$	−2.01722	−	4.78861i	−0.388214	−	0.921569i
$28$	2.59254	−	0.527932i	0.489945	−	0.0997698i
$29$			4.13294i			0.767468i	0.923444	+	0.383734i	$0.125362\pi$
$29$			4.13294i			0.767468i	−0.923444	+	0.383734i	$0.874638\pi$
$30$	−2.52365	−	3.27531i	−0.460753	−	0.597987i
$31$		−	8.63102i		−	1.55018i	−0.631853	−	0.775088i	$-0.717705\pi$
$31$		−	8.63102i		−	1.55018i	0.631853	−	0.775088i	$-0.282295\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.48791	−	5.82462i	−0.781244	−	1.01394i
$34$		−	2.11430i		−	0.362599i
$35$	−6.18897	+	1.26029i	−1.04613	+	0.213028i
$36$	−0.764872	+	2.90086i	−0.127479	+	0.483476i
$37$	1.99195			0.327474			0.163737	−	0.986504i	$-0.447645\pi$
$37$	1.99195			0.327474			0.163737	+	0.986504i	$0.447645\pi$
$38$	−2.73737			−0.444061
$39$	0.560730	+	0.727743i	0.0897887	+	0.116532i
$40$			2.38722i			0.377452i
$41$	−8.92450			−1.39377			−0.696886	−	0.717182i	$-0.745432\pi$
$41$	−8.92450			−1.39377			−0.696886	+	0.717182i	$0.745432\pi$
$42$	3.46504	+	2.99892i	0.534667	+	0.462743i
$43$	8.94310			1.36381			0.681905	−	0.731441i	$-0.261152\pi$
$43$	8.94310			1.36381			0.681905	+	0.731441i	$0.261152\pi$
$44$			4.24529i			0.640002i
$45$	1.82592	−	6.92498i	0.272191	−	1.03232i
$46$	−1.00000			−0.147442
$47$	5.75433			0.839356			0.419678	−	0.907673i	$-0.362143\pi$
$47$	5.75433			0.839356			0.419678	+	0.907673i	$0.362143\pi$
$48$	1.37202	−	1.05715i	0.198034	−	0.152586i
$49$	6.44258	−	2.73737i	0.920368	−	0.391054i
$50$		−	0.698814i		−	0.0988272i
$51$	2.90086	−	2.23513i	0.406201	−	0.312981i
$52$		−	0.530418i		−	0.0735557i
$53$			2.38309i			0.327342i	0.986515	+	0.163671i	$0.0523336\pi$
$53$			2.38309i			0.327342i	−0.986515	+	0.163671i	$0.947666\pi$
$54$	−4.78861	+	2.01722i	−0.651648	+	0.274509i
$55$		−	10.1344i		−	1.36653i
$56$	−0.527932	−	2.59254i	−0.0705479	−	0.346443i
$57$	−2.89381	−	3.75573i	−0.383295	−	0.497459i
$58$	4.13294			0.542682
$59$	4.97056			0.647112			0.323556	−	0.946209i	$-0.395122\pi$
$59$	4.97056			0.647112			0.323556	+	0.946209i	$0.395122\pi$
$60$	−3.27531	+	2.52365i	−0.422841	+	0.325801i
$61$			3.14015i			0.402054i	0.979586	+	0.201027i	$0.0644280\pi$
$61$			3.14015i			0.402054i	−0.979586	+	0.201027i	$0.935572\pi$
$62$	−8.63102			−1.09614
$63$	−0.451509	+	7.92440i	−0.0568848	+	0.998381i
$64$	−1.00000			−0.125000
$65$			1.26622i			0.157056i
$66$	−5.82462	+	4.48791i	−0.716961	+	0.552423i
$67$	−7.15841			−0.874539			−0.437270	−	0.899331i	$-0.644054\pi$
$67$	−7.15841			−0.874539			−0.437270	+	0.899331i	$0.644054\pi$
$68$	−2.11430			−0.256396
$69$	−1.05715	−	1.37202i	−0.127266	−	0.165172i
$70$	1.26029	+	6.18897i	0.150633	+	0.739724i
$71$			11.1811i			1.32695i	0.748200	+	0.663474i	$0.230919\pi$
$71$			11.1811i			1.32695i	−0.748200	+	0.663474i	$0.769081\pi$
$72$	2.90086	+	0.764872i	0.341869	+	0.0901410i
$73$			5.68336i			0.665187i	0.943070	+	0.332594i	$0.107924\pi$
$73$			5.68336i			0.665187i	−0.943070	+	0.332594i	$0.892076\pi$
$74$		−	1.99195i		−	0.231559i
$75$	0.958786	−	0.738750i	0.110711	−	0.0853035i
$76$			2.73737i			0.313998i
$77$	2.24123	+	11.0061i	0.255411	+	1.25426i
$78$	0.727743	−	0.560730i	0.0824007	−	0.0634902i
$79$	10.5466			1.18658			0.593292	−	0.804987i	$-0.297828\pi$
$79$	10.5466			1.18658			0.593292	+	0.804987i	$0.297828\pi$
$80$	2.38722			0.266899
$81$	−7.82994	−	4.43757i	−0.869994	−	0.493063i
$82$			8.92450i			0.985546i
$83$	1.92977			0.211820			0.105910	−	0.994376i	$-0.466224\pi$
$83$	1.92977			0.211820			0.105910	+	0.994376i	$0.466224\pi$
$84$	2.99892	−	3.46504i	0.327209	−	0.378067i
$85$	5.04729			0.547456
$86$		−	8.94310i		−	0.964360i
$87$	4.36913	+	5.67047i	0.468420	+	0.607938i
$88$	4.24529			0.452550
$89$	−17.8501			−1.89211			−0.946055	−	0.324007i	$-0.894970\pi$
$89$	−17.8501			−1.89211			−0.946055	+	0.324007i	$0.894970\pi$
$90$	−6.92498	−	1.82592i	−0.729957	−	0.192468i
$91$	−0.280024	−	1.37513i	−0.0293545	−	0.144153i
$92$			1.00000i			0.104257i
$93$	−9.12427	−	11.8419i	−0.946143	−	1.22795i
$94$		−	5.75433i		−	0.593514i
$95$		−	6.53471i		−	0.670447i
$96$	−1.05715	−	1.37202i	−0.107895	−	0.140031i
$97$			9.07256i			0.921179i	0.887613	+	0.460590i	$0.152362\pi$
$97$			9.07256i			0.921179i	−0.887613	+	0.460590i	$0.847638\pi$
$98$	−2.73737	−	6.44258i	−0.276517	−	0.650798i
$99$	−12.3150	−	3.24710i	−1.23770	−	0.326346i
$100$	−0.698814			−0.0698814
$101$	4.63086			0.460787			0.230394	−	0.973098i	$-0.425999\pi$
$101$	4.63086			0.460787			0.230394	+	0.973098i	$0.425999\pi$
$102$	−2.23513	−	2.90086i	−0.221311	−	0.287228i
$103$			1.03544i			0.102025i	0.998698	+	0.0510125i	$0.0162448\pi$
$103$			1.03544i			0.102025i	−0.998698	+	0.0510125i	$0.983755\pi$
$104$	−0.530418			−0.0520117
$105$	−7.15907	+	8.27181i	−0.698654	+	0.807246i
$106$	2.38309			0.231466
$107$			9.44463i			0.913047i	0.889711	+	0.456524i	$0.150906\pi$
$107$			9.44463i			0.913047i	−0.889711	+	0.456524i	$0.849094\pi$
$108$	2.01722	+	4.78861i	0.194107	+	0.460785i
$109$	9.31875			0.892574			0.446287	−	0.894890i	$-0.352746\pi$
$109$	9.31875			0.892574			0.446287	+	0.894890i	$0.352746\pi$
$110$	−10.1344			−0.966281
$111$	2.73299	−	2.10578i	0.259404	−	0.199872i
$112$	−2.59254	+	0.527932i	−0.244972	+	0.0498849i
$113$		−	2.62413i		−	0.246857i	−0.992353	−	0.123429i	$-0.960611\pi$
$113$		−	2.62413i		−	0.246857i	0.992353	−	0.123429i	$-0.0393890\pi$
$114$	−3.75573	+	2.89381i	−0.351756	+	0.271030i
$115$		−	2.38722i		−	0.222609i
$116$		−	4.13294i		−	0.383734i
$117$	1.53867	+	0.405701i	0.142250	+	0.0375071i
$118$		−	4.97056i		−	0.457577i
$119$	−5.48141	+	1.11621i	−0.502480	+	0.102322i
$120$	2.52365	+	3.27531i	0.230376	+	0.298993i
$121$	−7.02250			−0.638409
$122$	3.14015			0.284295
$123$	−12.2446	+	9.43452i	−1.10406	+	0.850682i
$124$			8.63102i			0.775088i
$125$	−10.2679			−0.918386
$126$	7.92440	+	0.451509i	0.705962	+	0.0402236i
$127$	1.18632			0.105269			0.0526346	−	0.998614i	$-0.483238\pi$
$127$	1.18632			0.105269			0.0526346	+	0.998614i	$0.483238\pi$
$128$			1.00000i			0.0883883i
$129$	12.2701	−	9.45419i	1.08032	−	0.832395i
$130$	1.26622			0.111055
$131$	14.4222			1.26008			0.630038	−	0.776564i	$-0.283039\pi$
$131$	14.4222			1.26008			0.630038	+	0.776564i	$0.283039\pi$
$132$	4.48791	+	5.82462i	0.390622	+	0.506968i
$133$	1.44515	+	7.09677i	0.125310	+	0.615368i
$134$			7.15841i			0.618392i
$135$	−4.81555	−	11.4315i	−0.414456	−	0.983864i
$136$			2.11430i			0.181300i
$137$			0.147193i			0.0125755i	0.999980	+	0.00628776i	$0.00200147\pi$
$137$			0.147193i			0.0125755i	−0.999980	+	0.00628776i	$0.997999\pi$
$138$	−1.37202	+	1.05715i	−0.116794	+	0.0899905i
$139$		−	2.60010i		−	0.220537i	−0.993902	−	0.110269i	$-0.964829\pi$
$139$		−	2.60010i		−	0.220537i	0.993902	−	0.110269i	$-0.0351711\pi$
$140$	6.18897	−	1.26029i	0.523064	−	0.106514i
$141$	7.89505	−	6.08319i	0.664883	−	0.512297i
$142$	11.1811			0.938294
$143$	2.25178			0.188303
$144$	0.764872	−	2.90086i	0.0637393	−	0.241738i
$145$			9.86623i			0.819346i
$146$	5.68336			0.470359
$147$	5.94552	−	10.5665i	0.490378	−	0.871510i
$148$	−1.99195			−0.163737
$149$			11.8396i			0.969939i	0.874531	+	0.484969i	$0.161169\pi$
$149$			11.8396i			0.969939i	−0.874531	+	0.484969i	$0.838831\pi$
$150$	−0.738750	−	0.958786i	−0.0603187	−	0.0782845i
$151$	11.8966			0.968133			0.484066	−	0.875031i	$-0.339159\pi$
$151$	11.8966			0.968133			0.484066	+	0.875031i	$0.339159\pi$
$152$	2.73737			0.222030
$153$	1.61717	−	6.13328i	0.130740	−	0.495846i
$154$	11.0061	−	2.24123i	0.886898	−	0.180603i
$155$		−	20.6041i		−	1.65496i
$156$	−0.560730	−	0.727743i	−0.0448944	−	0.0582661i
$157$			14.8784i			1.18742i	0.804678	+	0.593712i	$0.202338\pi$
$157$			14.8784i			1.18742i	−0.804678	+	0.593712i	$0.797662\pi$
$158$		−	10.5466i		−	0.839041i
$159$	2.51928	+	3.26964i	0.199792	+	0.259300i
$160$		−	2.38722i		−	0.188726i
$161$	0.527932	+	2.59254i	0.0416069	+	0.204321i
$162$	−4.43757	+	7.82994i	−0.348648	+	0.615178i
$163$	−23.8160			−1.86541			−0.932705	−	0.360641i	$-0.882558\pi$
$163$	−23.8160			−1.86541			−0.932705	+	0.360641i	$0.882558\pi$
$164$	8.92450			0.696886
$165$	−10.7136	−	13.9046i	−0.834054	−	1.08248i
$166$		−	1.92977i		−	0.149780i
$167$	5.42417			0.419735			0.209868	−	0.977730i	$-0.432697\pi$
$167$	5.42417			0.419735			0.209868	+	0.977730i	$0.432697\pi$
$168$	−3.46504	−	2.99892i	−0.267334	−	0.231372i
$169$	12.7187			0.978358
$170$		−	5.04729i		−	0.387110i
$171$	−7.94073	−	2.09374i	−0.607243	−	0.160112i
$172$	−8.94310			−0.681905
$173$	−1.70656			−0.129747			−0.0648735	−	0.997893i	$-0.520664\pi$
$173$	−1.70656			−0.129747			−0.0648735	+	0.997893i	$0.520664\pi$
$174$	5.67047	−	4.36913i	0.429877	−	0.331223i
$175$	−1.81171	+	0.368926i	−0.136952	+	0.0278882i
$176$		−	4.24529i		−	0.320001i
$177$	6.81970	−	5.25462i	0.512600	−	0.394962i
$178$			17.8501i			1.33792i
$179$			14.9077i			1.11425i	0.830428	+	0.557127i	$0.188096\pi$
$179$			14.9077i			1.11425i	−0.830428	+	0.557127i	$0.811904\pi$
$180$	−1.82592	+	6.92498i	−0.136096	+	0.516158i
$181$		−	15.2548i		−	1.13388i	−0.823760	−	0.566939i	$-0.808128\pi$
$181$		−	15.2548i		−	1.13388i	0.823760	−	0.566939i	$-0.191872\pi$
$182$	−1.37513	+	0.280024i	−0.101932	+	0.0207568i
$183$	3.31960	+	4.30834i	0.245392	+	0.318482i
$184$	1.00000			0.0737210
$185$	4.75521			0.349610
$186$	−11.8419	+	9.12427i	−0.868292	+	0.669024i
$187$		−	8.97581i		−	0.656376i
$188$	−5.75433			−0.419678
$189$	7.75780	+	11.3497i	0.564297	+	0.825572i
$190$	−6.53471			−0.474078
$191$		−	9.45500i		−	0.684140i	−0.939674	−	0.342070i	$-0.888872\pi$
$191$		−	9.45500i		−	0.684140i	0.939674	−	0.342070i	$-0.111128\pi$
$192$	−1.37202	+	1.05715i	−0.0990169	+	0.0762932i
$193$	27.2408			1.96083			0.980417	−	0.196933i	$-0.0630981\pi$
$193$	27.2408			1.96083			0.980417	+	0.196933i	$0.0630981\pi$
$194$	9.07256			0.651372
$195$	1.33859	+	1.73728i	0.0958582	+	0.124409i
$196$	−6.44258	+	2.73737i	−0.460184	+	0.195527i
$197$			18.6196i			1.32659i	0.748357	+	0.663296i	$0.230843\pi$
$197$			18.6196i			1.32659i	−0.748357	+	0.663296i	$0.769157\pi$
$198$	−3.24710	+	12.3150i	−0.230762	+	0.875188i
$199$			2.99081i			0.212013i	0.994365	+	0.106006i	$0.0338064\pi$
$199$			2.99081i			0.212013i	−0.994365	+	0.106006i	$0.966194\pi$
$200$			0.698814i			0.0494136i
$201$	−9.82147	+	7.56751i	−0.692753	+	0.533771i
$202$		−	4.63086i		−	0.325826i
$203$	−2.18191	−	10.7148i	−0.153140	−	0.752034i
$204$	−2.90086	+	2.23513i	−0.203101	+	0.156490i
$205$	−21.3047			−1.48799
$206$	1.03544			0.0721426
$207$	−2.90086	−	0.764872i	−0.201623	−	0.0531623i
$208$			0.530418i			0.0367778i
$209$	−11.6210			−0.803838
$210$	8.27181	+	7.15907i	0.570809	+	0.494023i
$211$	−6.02193			−0.414567			−0.207283	−	0.978281i	$-0.566462\pi$
$211$	−6.02193			−0.414567			−0.207283	+	0.978281i	$0.566462\pi$
$212$		−	2.38309i		−	0.163671i
$213$	11.8200	+	15.3406i	0.809896	+	1.05112i
$214$	9.44463			0.645622
$215$	21.3491			1.45600
$216$	4.78861	−	2.01722i	0.325824	−	0.137254i
$217$	4.55659	+	22.3763i	0.309321	+	1.51900i
$218$		−	9.31875i		−	0.631145i
$219$	6.00816	+	7.79768i	0.405994	+	0.526919i
$220$			10.1344i			0.683264i
$221$			1.12146i			0.0754376i
$222$	−2.10578	−	2.73299i	−0.141331	−	0.183426i
$223$		−	5.48938i		−	0.367596i	−0.982964	−	0.183798i	$-0.941161\pi$
$223$		−	5.48938i		−	0.367596i	0.982964	−	0.183798i	$-0.0588392\pi$
$224$	0.527932	+	2.59254i	0.0352739	+	0.173222i
$225$	0.534503	−	2.02716i	0.0356335	−	0.135144i
$226$	−2.62413			−0.174554
$227$	9.80484			0.650770			0.325385	−	0.945582i	$-0.394506\pi$
$227$	9.80484			0.650770			0.325385	+	0.945582i	$0.394506\pi$
$228$	2.89381	+	3.75573i	0.191647	+	0.248729i
$229$		−	25.2542i		−	1.66885i	−0.551123	−	0.834424i	$-0.685801\pi$
$229$		−	25.2542i		−	1.66885i	0.551123	−	0.834424i	$-0.314199\pi$
$230$	−2.38722			−0.157409
$231$	14.7101	+	12.7313i	0.967854	+	0.837657i
$232$	−4.13294			−0.271341
$233$		−	5.02747i		−	0.329361i	−0.986347	−	0.164680i	$-0.947341\pi$
$233$		−	5.02747i		−	0.329361i	0.986347	−	0.164680i	$-0.0526593\pi$
$234$	0.405701	−	1.53867i	0.0265215	−	0.100586i
$235$	13.7369			0.896093
$236$	−4.97056			−0.323556
$237$	14.4701	−	11.1493i	0.939935	−	0.724226i
$238$	1.11621	+	5.48141i	0.0723529	+	0.355307i
$239$			23.5462i			1.52308i	0.648121	+	0.761538i	$0.275555\pi$
$239$			23.5462i			1.52308i	−0.648121	+	0.761538i	$0.724445\pi$
$240$	3.27531	−	2.52365i	0.211420	−	0.162901i
$241$			8.30568i			0.535016i	0.963556	+	0.267508i	$0.0862002\pi$
$241$			8.30568i			0.535016i	−0.963556	+	0.267508i	$0.913800\pi$
$242$			7.02250i			0.451424i
$243$	−15.4340	+	2.18899i	−0.990091	+	0.140424i
$244$		−	3.14015i		−	0.201027i
$245$	15.3798	−	6.53471i	0.982582	−	0.417487i
$246$	9.43452	+	12.2446i	0.601523	+	0.780686i
$247$	1.45195			0.0923855
$248$	8.63102			0.548070
$249$	2.64769	−	2.04006i	0.167790	−	0.129283i
$250$			10.2679i			0.649397i
$251$	−27.5152			−1.73675			−0.868373	−	0.495912i	$-0.834834\pi$
$251$	−27.5152			−1.73675			−0.868373	+	0.495912i	$0.834834\pi$
$252$	0.451509	−	7.92440i	0.0284424	−	0.499190i
$253$	−4.24529			−0.266899
$254$		−	1.18632i		−	0.0744365i
$255$	6.92498	−	5.33574i	0.433659	−	0.334137i
$256$	1.00000			0.0625000
$257$	24.6363			1.53677			0.768384	−	0.639989i	$-0.221061\pi$
$257$	24.6363			1.53677			0.768384	+	0.639989i	$0.221061\pi$
$258$	−9.45419	−	12.2701i	−0.588592	−	0.763903i
$259$	−5.16421	+	1.05161i	−0.320888	+	0.0653440i
$260$		−	1.26622i		−	0.0785278i
$261$	11.9891	+	3.16117i	0.742105	+	0.195671i
$262$		−	14.4222i		−	0.891009i
$263$		−	2.48576i		−	0.153278i	−0.997059	−	0.0766392i	$-0.975581\pi$
$263$		−	2.48576i		−	0.153278i	0.997059	−	0.0766392i	$-0.0244190\pi$
$264$	5.82462	−	4.48791i	0.358481	−	0.276212i
$265$			5.68895i			0.349470i
$266$	7.09677	−	1.44515i	0.435131	−	0.0886077i
$267$	−24.4907	+	18.8702i	−1.49881	+	1.15484i
$268$	7.15841			0.437270
$269$	27.7234			1.69032			0.845162	−	0.534511i	$-0.179504\pi$
$269$	27.7234			1.69032			0.845162	+	0.534511i	$0.179504\pi$
$270$	−11.4315	+	4.81555i	−0.695697	+	0.293065i
$271$			1.95150i			0.118545i	0.998242	+	0.0592726i	$0.0188781\pi$
$271$			1.95150i			0.118545i	−0.998242	+	0.0592726i	$0.981122\pi$
$272$	2.11430			0.128198
$273$	−1.83792	−	1.59068i	−0.111236	−	0.0962722i
$274$	0.147193			0.00889224
$275$		−	2.96667i		−	0.178897i
$276$	1.05715	+	1.37202i	0.0636329	+	0.0825858i
$277$	17.5012			1.05155			0.525774	−	0.850624i	$-0.323776\pi$
$277$	17.5012			1.05155			0.525774	+	0.850624i	$0.323776\pi$
$278$	−2.60010			−0.155943
$279$	−25.0373	−	6.60162i	−1.49895	−	0.395229i
$280$	−1.26029	−	6.18897i	−0.0753167	−	0.369862i
$281$		−	29.6709i		−	1.77002i	−0.465576	−	0.885008i	$-0.654153\pi$
$281$		−	29.6709i		−	1.77002i	0.465576	−	0.885008i	$-0.345847\pi$
$282$	−6.08319	−	7.89505i	−0.362249	−	0.470144i
$283$		−	13.7544i		−	0.817613i	−0.912621	−	0.408806i	$-0.865945\pi$
$283$		−	13.7544i		−	0.817613i	0.912621	−	0.408806i	$-0.134055\pi$
$284$		−	11.1811i		−	0.663474i
$285$	−6.90816	−	8.96575i	−0.409204	−	0.531085i
$286$		−	2.25178i		−	0.133150i
$287$	23.1372	−	4.71153i	1.36574	−	0.278113i
$288$	−2.90086	−	0.764872i	−0.170935	−	0.0450705i
$289$	−12.5297			−0.737044
$290$	9.86623			0.579365
$291$	9.59105	+	12.4477i	0.562238	+	0.729699i
$292$		−	5.68336i		−	0.332594i
$293$	−7.30903			−0.426998			−0.213499	−	0.976943i	$-0.568486\pi$
$293$	−7.30903			−0.426998			−0.213499	+	0.976943i	$0.568486\pi$
$294$	−10.5665	−	5.94552i	−0.616250	−	0.346750i
$295$	11.8658			0.690854
$296$			1.99195i			0.115780i
$297$	−20.3291	+	8.56369i	−1.17961	+	0.496916i
$298$	11.8396			0.685850
$299$	0.530418			0.0306748
$300$	−0.958786	+	0.738750i	−0.0553555	+	0.0426518i
$301$	−23.1854	+	4.72135i	−1.33638	+	0.272134i
$302$		−	11.8966i		−	0.684573i
$303$	6.35362	−	4.89550i	0.365006	−	0.281239i
$304$		−	2.73737i		−	0.156999i
$305$			7.49621i			0.429232i
$306$	−6.13328	−	1.61717i	−0.350616	−	0.0924473i
$307$		−	6.88194i		−	0.392773i	−0.980527	−	0.196386i	$-0.937079\pi$
$307$		−	6.88194i		−	0.392773i	0.980527	−	0.196386i	$-0.0629207\pi$
$308$	−2.24123	−	11.0061i	−0.127706	−	0.627131i
$309$	1.09462	+	1.42064i	0.0622705	+	0.0808176i
$310$	−20.6041			−1.17024
$311$	15.1958			0.861674			0.430837	−	0.902430i	$-0.358218\pi$
$311$	15.1958			0.861674			0.430837	+	0.902430i	$0.358218\pi$
$312$	−0.727743	+	0.560730i	−0.0412003	+	0.0317451i
$313$		−	30.1231i		−	1.70266i	−0.524633	−	0.851329i	$-0.675797\pi$
$313$		−	30.1231i		−	1.70266i	0.524633	−	0.851329i	$-0.324203\pi$
$314$	14.8784			0.839635
$315$	−1.07785	+	18.9173i	−0.0607300	+	1.06587i
$316$	−10.5466			−0.593292
$317$			18.0815i			1.01556i	0.861488	+	0.507778i	$0.169533\pi$
$317$			18.0815i			1.01556i	−0.861488	+	0.507778i	$0.830467\pi$
$318$	3.26964	−	2.51928i	0.183352	−	0.141274i
$319$	17.5455			0.982362
$320$	−2.38722			−0.133450
$321$	9.98439	+	12.9582i	0.557274	+	0.723257i
$322$	2.59254	−	0.527932i	0.144477	−	0.0294205i
$323$		−	5.78763i		−	0.322032i
$324$	7.82994	+	4.43757i	0.434997	+	0.246531i
$325$			0.370663i			0.0205607i
$326$			23.8160i			1.31904i
$327$	12.7855	−	9.85130i	0.707039	−	0.544778i
$328$		−	8.92450i		−	0.492773i
$329$	−14.9184	+	3.03790i	−0.822476	+	0.167485i
$330$	−13.9046	+	10.7136i	−0.765425	+	0.589765i
$331$	13.4098			0.737072			0.368536	−	0.929614i	$-0.379859\pi$
$331$	13.4098			0.737072			0.368536	+	0.929614i	$0.379859\pi$
$332$	−1.92977			−0.105910
$333$	1.52358	−	5.77835i	0.0834918	−	0.316652i
$334$		−	5.42417i		−	0.296798i
$335$	−17.0887			−0.933655
$336$	−2.99892	+	3.46504i	−0.163604	+	0.189033i
$337$	−5.36398			−0.292195			−0.146097	−	0.989270i	$-0.546671\pi$
$337$	−5.36398			−0.292195			−0.146097	+	0.989270i	$0.546671\pi$
$338$		−	12.7187i		−	0.691804i
$339$	−2.77409	−	3.60035i	−0.150668	−	0.195544i
$340$	−5.04729			−0.273728
$341$	−36.6412			−1.98423
$342$	−2.09374	+	7.94073i	−0.113217	+	0.429386i
$343$	−15.2575	+	10.4980i	−0.823828	+	0.566839i
$344$			8.94310i			0.482180i
$345$	−2.52365	−	3.27531i	−0.135869	−	0.176337i
$346$			1.70656i			0.0917450i
$347$			28.4518i			1.52737i	0.645587	+	0.763687i	$0.276613\pi$
$347$			28.4518i			1.52737i	−0.645587	+	0.763687i	$0.723387\pi$
$348$	−4.36913	−	5.67047i	−0.234210	−	0.303969i
$349$			29.2240i			1.56433i	0.623073	+	0.782164i	$0.285884\pi$
$349$			29.2240i			1.56433i	−0.623073	+	0.782164i	$0.714116\pi$
$350$	0.368926	+	1.81171i	0.0197199	+	0.0968398i
$351$	2.53997	−	1.06997i	0.135573	−	0.0571107i
$352$	−4.24529			−0.226275
$353$	−5.61185			−0.298689			−0.149344	−	0.988785i	$-0.547716\pi$
$353$	−5.61185			−0.298689			−0.149344	+	0.988785i	$0.547716\pi$
$354$	−5.25462	−	6.81970i	−0.279280	−	0.362463i
$355$			26.6916i			1.41664i
$356$	17.8501			0.946055
$357$	−6.34061	+	7.32613i	−0.335580	+	0.387740i
$358$	14.9077			0.787896
$359$		−	2.05565i		−	0.108493i	−0.998528	−	0.0542465i	$-0.982724\pi$
$359$		−	2.05565i		−	0.108493i	0.998528	−	0.0542465i	$-0.0172757\pi$
$360$	6.92498	+	1.82592i	0.364979	+	0.0962342i
$361$	11.5068			0.605620
$362$	−15.2548			−0.801772
$363$	−9.63501	+	7.42383i	−0.505707	+	0.389650i
$364$	0.280024	+	1.37513i	0.0146773	+	0.0720765i
$365$			13.5674i			0.710152i
$366$	4.30834	−	3.31960i	0.225200	−	0.173518i
$367$		−	33.3452i		−	1.74061i	−0.492517	−	0.870303i	$-0.663923\pi$
$367$		−	33.3452i		−	1.74061i	0.492517	−	0.870303i	$-0.336077\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	−6.82609	+	25.8887i	−0.355352	+	1.34771i
$370$		−	4.75521i		−	0.247212i
$371$	−1.25811	−	6.17826i	−0.0653178	−	0.320760i
$372$	9.12427	+	11.8419i	0.473071	+	0.613975i
$373$	−13.4898			−0.698475			−0.349238	−	0.937034i	$-0.613559\pi$
$373$	−13.4898			−0.698475			−0.349238	+	0.937034i	$0.613559\pi$
$374$	−8.97581			−0.464128
$375$	−14.0877	+	10.8547i	−0.727486	+	0.560533i
$376$			5.75433i			0.296757i
$377$	−2.19218			−0.112903
$378$	11.3497	−	7.75780i	0.583768	−	0.399018i
$379$	−29.2116			−1.50050			−0.750248	−	0.661156i	$-0.770066\pi$
$379$	−29.2116			−1.50050			−0.750248	+	0.661156i	$0.770066\pi$
$380$			6.53471i			0.335224i
$381$	1.62766	−	1.25412i	0.0833874	−	0.0642505i
$382$	−9.45500			−0.483760
$383$	−5.51748			−0.281930			−0.140965	−	0.990015i	$-0.545021\pi$
$383$	−5.51748			−0.281930			−0.140965	+	0.990015i	$0.545021\pi$
$384$	1.05715	+	1.37202i	0.0539474	+	0.0700155i
$385$	5.35030	+	26.2740i	0.272676	+	1.33905i
$386$		−	27.2408i		−	1.38652i
$387$	6.84033	−	25.9427i	0.347713	−	1.31874i
$388$		−	9.07256i		−	0.460590i
$389$		−	2.08173i		−	0.105548i	−0.998606	−	0.0527740i	$-0.983194\pi$
$389$		−	2.08173i		−	0.105548i	0.998606	−	0.0527740i	$-0.0168063\pi$
$390$	1.73728	−	1.33859i	0.0879707	−	0.0677820i
$391$		−	2.11430i		−	0.106925i
$392$	2.73737	+	6.44258i	0.138258	+	0.325399i
$393$	19.7876	−	15.2465i	0.998151	−	0.769082i
$394$	18.6196			0.938042
$395$	25.1770			1.26679
$396$	12.3150	+	3.24710i	0.618851	+	0.163173i
$397$			3.52438i			0.176884i	0.996081	+	0.0884418i	$0.0281887\pi$
$397$			3.52438i			0.176884i	−0.996081	+	0.0884418i	$0.971811\pi$
$398$	2.99081			0.149916
$399$	9.48511	+	8.20916i	0.474849	+	0.410972i
$400$	0.698814			0.0349407
$401$			26.0497i			1.30086i	0.759566	+	0.650430i	$0.225411\pi$
$401$			26.0497i			1.30086i	−0.759566	+	0.650430i	$0.774589\pi$
$402$	7.56751	+	9.82147i	0.377433	+	0.489851i
$403$	4.57804			0.228049
$404$	−4.63086			−0.230394
$405$	−18.6918	−	10.5934i	−0.928802	−	0.526392i
$406$	−10.7148	+	2.18191i	−0.531768	+	0.108286i
$407$		−	8.45639i		−	0.419168i
$408$	2.23513	+	2.90086i	0.110655	+	0.143614i
$409$			36.7589i			1.81761i	0.417221	+	0.908805i	$0.363004\pi$
$409$			36.7589i			1.81761i	−0.417221	+	0.908805i	$0.636996\pi$
$410$			21.3047i			1.05217i
$411$	0.155605	+	0.201951i	0.00767541	+	0.00996152i
$412$		−	1.03544i		−	0.0510125i
$413$	−12.8864	+	2.62412i	−0.634098	+	0.129124i
$414$	−0.764872	+	2.90086i	−0.0375914	+	0.142569i
$415$	4.60679			0.226139
$416$	0.530418			0.0260059
$417$	−2.74869	−	3.56738i	−0.134604	−	0.174695i
$418$			11.6210i			0.568399i
$419$	−34.1180			−1.66677			−0.833387	−	0.552690i	$-0.813601\pi$
$419$	−34.1180			−1.66677			−0.833387	+	0.552690i	$0.813601\pi$
$420$	7.15907	−	8.27181i	0.349327	−	0.403623i
$421$	−11.0413			−0.538118			−0.269059	−	0.963124i	$-0.586713\pi$
$421$	−11.0413			−0.538118			−0.269059	+	0.963124i	$0.586713\pi$
$422$			6.02193i			0.293143i
$423$	4.40133	−	16.6925i	0.214000	−	0.811617i
$424$	−2.38309			−0.115733
$425$	1.47750			0.0716693
$426$	15.3406	−	11.8200i	0.743256	−	0.572683i
$427$	−1.65778	−	8.14097i	−0.0802258	−	0.393969i
$428$		−	9.44463i		−	0.456524i
$429$	3.08948	−	2.38046i	0.149162	−	0.114930i
$430$		−	21.3491i		−	1.02955i
$431$		−	16.5144i		−	0.795469i	−0.917500	−	0.397735i	$-0.869796\pi$
$431$		−	16.5144i		−	0.795469i	0.917500	−	0.397735i	$-0.130204\pi$
$432$	−2.01722	−	4.78861i	−0.0970535	−	0.230392i
$433$			10.8168i			0.519820i	0.965633	+	0.259910i	$0.0836929\pi$
$433$			10.8168i			0.519820i	−0.965633	+	0.259910i	$0.916307\pi$
$434$	22.3763	−	4.55659i	1.07410	−	0.218723i
$435$	10.4301	+	13.5367i	0.500084	+	0.649033i
$436$	−9.31875			−0.446287
$437$	−2.73737			−0.130946
$438$	7.79768	−	6.00816i	0.372588	−	0.287081i
$439$		−	38.2864i		−	1.82731i	−0.406493	−	0.913654i	$-0.633248\pi$
$439$		−	38.2864i		−	1.82731i	0.406493	−	0.913654i	$-0.366752\pi$
$440$	10.1344			0.483141
$441$	−3.01299	−	20.7827i	−0.143476	−	0.989654i
$442$	1.12146			0.0533425
$443$			14.5512i			0.691347i	0.938355	+	0.345673i	$0.112349\pi$
$443$			14.5512i			0.691347i	−0.938355	+	0.345673i	$0.887651\pi$
$444$	−2.73299	+	2.10578i	−0.129702	+	0.0999361i
$445$	−42.6121			−2.02001
$446$	−5.48938			−0.259929
$447$	12.5162	+	16.2442i	0.591997	+	0.768323i
$448$	2.59254	−	0.527932i	0.122486	−	0.0249424i
$449$		−	23.2181i		−	1.09573i	−0.836567	−	0.547865i	$-0.815441\pi$
$449$		−	23.2181i		−	1.09573i	0.836567	−	0.547865i	$-0.184559\pi$
$450$	−2.02716	−	0.534503i	−0.0955612	−	0.0251967i
$451$			37.8871i			1.78403i
$452$			2.62413i			0.123429i
$453$	16.3224	−	12.5765i	0.766892	−	0.590895i
$454$		−	9.80484i		−	0.460164i
$455$	−0.668480	−	3.28274i	−0.0313388	−	0.153897i
$456$	3.75573	−	2.89381i	0.175878	−	0.135515i
$457$	1.57154			0.0735135			0.0367568	−	0.999324i	$-0.488297\pi$
$457$	1.57154			0.0735135			0.0367568	+	0.999324i	$0.488297\pi$
$458$	−25.2542			−1.18005
$459$	−4.26500	−	10.1246i	−0.199073	−	0.472574i
$460$			2.38722i			0.111305i
$461$	−30.3724			−1.41458			−0.707292	−	0.706922i	$-0.750083\pi$
$461$	−30.3724			−1.41458			−0.707292	+	0.706922i	$0.750083\pi$
$462$	12.7313	−	14.7101i	0.592313	−	0.684376i
$463$	2.89918			0.134736			0.0673682	−	0.997728i	$-0.478540\pi$
$463$	2.89918			0.134736			0.0673682	+	0.997728i	$0.478540\pi$
$464$			4.13294i			0.191867i
$465$	−21.7816	−	28.2692i	−1.01010	−	1.31096i
$466$	−5.02747			−0.232893
$467$	13.1117			0.606736			0.303368	−	0.952874i	$-0.401889\pi$
$467$	13.1117			0.606736			0.303368	+	0.952874i	$0.401889\pi$
$468$	−1.53867	−	0.405701i	−0.0711248	−	0.0187536i
$469$	18.5585	−	3.77915i	0.856952	−	0.174505i
$470$		−	13.7369i		−	0.633634i
$471$	15.7287	+	20.4134i	0.724739	+	0.940601i
$472$			4.97056i			0.228789i
$473$		−	37.9661i		−	1.74568i
$474$	−11.1493	−	14.4701i	−0.512105	−	0.664634i
$475$		−	1.91292i		−	0.0877706i
$476$	5.48141	−	1.11621i	0.251240	−	0.0511612i
$477$	6.91300	+	1.82276i	0.316525	+	0.0834583i
$478$	23.5462			1.07698
$479$	−38.8150			−1.77350			−0.886751	−	0.462247i	$-0.847043\pi$
$479$	−38.8150			−1.77350			−0.886751	+	0.462247i	$0.847043\pi$
$480$	−2.52365	−	3.27531i	−0.115188	−	0.149497i
$481$			1.05656i			0.0481751i
$482$	8.30568			0.378313
$483$	3.46504	+	2.99892i	0.157665	+	0.136455i
$484$	7.02250			0.319205
$485$			21.6582i			0.983448i
$486$	2.18899	+	15.4340i	0.0992947	+	0.700100i
$487$	24.6155			1.11544			0.557718	−	0.830031i	$-0.311677\pi$
$487$	24.6155			1.11544			0.557718	+	0.830031i	$0.311677\pi$
$488$	−3.14015			−0.142148
$489$	−32.6759	+	25.1770i	−1.47766	+	1.13854i
$490$	−6.53471	−	15.3798i	−0.295208	−	0.694790i
$491$		−	22.4723i		−	1.01416i	−0.861899	−	0.507079i	$-0.830725\pi$
$491$		−	22.4723i		−	1.01416i	0.861899	−	0.507079i	$-0.169275\pi$
$492$	12.2446	−	9.43452i	0.552028	−	0.425341i
$493$			8.73827i			0.393552i
$494$		−	1.45195i		−	0.0653264i
$495$	−29.3986	−	7.75155i	−1.32137	−	0.348406i
$496$		−	8.63102i		−	0.387544i
$497$	−5.90284	−	28.9874i	−0.264778	−	1.30026i
$498$	−2.04006	−	2.64769i	−0.0914172	−	0.118646i
$499$	1.06698			0.0477645			0.0238822	−	0.999715i	$-0.492397\pi$
$499$	1.06698			0.0477645			0.0238822	+	0.999715i	$0.492397\pi$
$500$	10.2679			0.459193
$501$	7.44207	−	5.73416i	0.332487	−	0.256183i
$502$			27.5152i			1.22806i
$503$	−11.0618			−0.493222			−0.246611	−	0.969115i	$-0.579317\pi$
$503$	−11.0618			−0.493222			−0.246611	+	0.969115i	$0.579317\pi$
$504$	−7.92440	−	0.451509i	−0.352981	−	0.0201118i
$505$	11.0549			0.491935
$506$			4.24529i			0.188726i
$507$	17.4502	−	13.4455i	0.774992	−	0.597136i
$508$	−1.18632			−0.0526346
$509$	−31.7609			−1.40778			−0.703888	−	0.710311i	$-0.748554\pi$
$509$	−31.7609			−1.40778			−0.703888	+	0.710311i	$0.748554\pi$
$510$	−5.33574	−	6.92498i	−0.236271	−	0.306643i
$511$	−3.00043	−	14.7344i	−0.132731	−	0.651810i
$512$		−	1.00000i		−	0.0441942i
$513$	−13.1082	+	5.52189i	−0.578743	+	0.243797i
$514$		−	24.6363i		−	1.08666i
$515$			2.47182i			0.108922i
$516$	−12.2701	+	9.45419i	−0.540161	+	0.416198i
$517$		−	24.4288i		−	1.07438i
$518$	1.05161	+	5.16421i	0.0462052	+	0.226902i
$519$	−2.34143	+	1.80408i	−0.102777	+	0.0791905i
$520$	−1.26622			−0.0555275
$521$	−35.1037			−1.53792			−0.768961	−	0.639296i	$-0.779226\pi$
$521$	−35.1037			−1.53792			−0.768961	+	0.639296i	$0.779226\pi$
$522$	3.16117	−	11.9891i	0.138361	−	0.524747i
$523$		−	23.0638i		−	1.00851i	−0.863555	−	0.504254i	$-0.831768\pi$
$523$		−	23.0638i		−	1.00851i	0.863555	−	0.504254i	$-0.168232\pi$
$524$	−14.4222			−0.630038
$525$	−2.09568	+	2.42142i	−0.0914632	+	0.105679i
$526$	−2.48576			−0.108384
$527$		−	18.2485i		−	0.794919i
$528$	−4.48791	−	5.82462i	−0.195311	−	0.253484i
$529$	−1.00000			−0.0434783
$530$	5.68895			0.247112
$531$	3.80184	−	14.4189i	0.164986	−	0.625726i
$532$	−1.44515	−	7.09677i	−0.0626551	−	0.307684i
$533$		−	4.73371i		−	0.205040i
$534$	18.8702	+	24.4907i	0.816595	+	1.05982i
$535$			22.5464i			0.974766i
$536$		−	7.15841i		−	0.309196i
$537$	15.7596	+	20.4536i	0.680079	+	0.882639i
$538$		−	27.7234i		−	1.19524i
$539$	−11.6210	−	27.3506i	−0.500550	−	1.17807i
$540$	4.81555	+	11.4315i	0.207228	+	0.491932i
$541$	−35.6025			−1.53067			−0.765336	−	0.643631i	$-0.777427\pi$
$541$	−35.6025			−1.53067			−0.765336	+	0.643631i	$0.777427\pi$
$542$	1.95150			0.0838241
$543$	−16.1266	−	20.9298i	−0.692057	−	0.898185i
$544$		−	2.11430i		−	0.0906498i
$545$	22.2459			0.952909
$546$	−1.59068	+	1.83792i	−0.0680748	+	0.0786556i
$547$	33.9610			1.45207			0.726033	−	0.687660i	$-0.241362\pi$
$547$	33.9610			1.45207			0.726033	+	0.687660i	$0.241362\pi$
$548$		−	0.147193i		−	0.00628776i
$549$	9.10911	+	2.40181i	0.388767	+	0.102507i
$550$	−2.96667			−0.126499
$551$	11.3134			0.481967
$552$	1.37202	−	1.05715i	0.0583970	−	0.0449953i
$553$	−27.3425	+	5.56788i	−1.16272	+	0.236770i
$554$		−	17.5012i		−	0.743556i
$555$	6.52424	−	5.02697i	0.276939	−	0.213383i
$556$			2.60010i			0.110269i
$557$		−	30.2599i		−	1.28215i	−0.767476	−	0.641077i	$-0.778488\pi$
$557$		−	30.2599i		−	1.28215i	0.767476	−	0.641077i	$-0.221512\pi$
$558$	−6.60162	+	25.0373i	−0.279469	+	1.05992i
$559$			4.74358i			0.200632i
$560$	−6.18897	+	1.26029i	−0.261532	+	0.0532569i
$561$	−9.48877	−	12.3150i	−0.400616	−	0.519939i
$562$	−29.6709			−1.25159
$563$	9.61003			0.405015			0.202507	−	0.979281i	$-0.435091\pi$
$563$	9.61003			0.405015			0.202507	+	0.979281i	$0.435091\pi$
$564$	−7.89505	+	6.08319i	−0.332442	+	0.256148i
$565$		−	6.26436i		−	0.263544i
$566$	−13.7544			−0.578139
$567$	22.6422	+	7.37091i	0.950883	+	0.309549i
$568$	−11.1811			−0.469147
$569$			10.2889i			0.431334i	0.976467	+	0.215667i	$0.0691925\pi$
$569$			10.2889i			0.431334i	−0.976467	+	0.215667i	$0.930807\pi$
$570$	−8.96575	+	6.90816i	−0.375534	+	0.289351i
$571$	−42.7140			−1.78753			−0.893763	−	0.448539i	$-0.851944\pi$
$571$	−42.7140			−1.78753			−0.893763	+	0.448539i	$0.851944\pi$
$572$	−2.25178			−0.0941515
$573$	−9.99535	−	12.9724i	−0.417562	−	0.541932i
$574$	−4.71153	−	23.1372i	−0.196655	−	0.965726i
$575$		−	0.698814i		−	0.0291426i
$576$	−0.764872	+	2.90086i	−0.0318697	+	0.120869i
$577$			0.941440i			0.0391926i	0.999808	+	0.0195963i	$0.00623810\pi$
$577$			0.941440i			0.0391926i	−0.999808	+	0.0195963i	$0.993762\pi$
$578$			12.5297i			0.521169i
$579$	37.3749	−	28.7976i	1.55325	−	1.19679i
$580$		−	9.86623i		−	0.409673i
$581$	−5.00303	+	1.01879i	−0.207560	+	0.0422665i
$582$	12.4477	−	9.59105i	0.515975	−	0.397562i
$583$	10.1169			0.419000
$584$	−5.68336			−0.235179
$585$	3.67313	+	0.968498i	0.151865	+	0.0400425i
$586$			7.30903i			0.301933i
$587$	8.99079			0.371090			0.185545	−	0.982636i	$-0.440595\pi$
$587$	8.99079			0.371090			0.185545	+	0.982636i	$0.440595\pi$
$588$	−5.94552	+	10.5665i	−0.245189	+	0.435755i
$589$	−23.6263			−0.973506
$590$		−	11.8658i		−	0.488508i
$591$	19.6837	+	25.5465i	0.809679	+	1.05084i
$592$	1.99195			0.0818685
$593$	−32.0136			−1.31464			−0.657321	−	0.753611i	$-0.728310\pi$
$593$	−32.0136			−1.31464			−0.657321	+	0.753611i	$0.728310\pi$
$594$	8.56369	+	20.3291i	0.351372	+	0.834112i
$595$	−13.0853	+	2.66463i	−0.536446	+	0.109239i
$596$		−	11.8396i		−	0.484969i
$597$	3.16173	+	4.10345i	0.129401	+	0.167943i
$598$		−	0.530418i		−	0.0216904i
$599$			37.1859i			1.51937i	0.650289	+	0.759687i	$0.274648\pi$
$599$			37.1859i			1.51937i	−0.650289	+	0.759687i	$0.725352\pi$
$600$	0.738750	+	0.958786i	0.0301594	+	0.0391423i
$601$		−	17.2573i		−	0.703938i	−0.936012	−	0.351969i	$-0.885512\pi$
$601$		−	17.2573i		−	0.703938i	0.936012	−	0.351969i	$-0.114488\pi$
$602$	4.72135	+	23.1854i	0.192428	+	0.944966i
$603$	−5.47527	+	20.7655i	−0.222970	+	0.845638i
$604$	−11.8966			−0.484066
$605$	−16.7643			−0.681564
$606$	−4.89550	−	6.35362i	−0.198866	−	0.258098i
$607$		−	10.1629i		−	0.412500i	−0.978499	−	0.206250i	$-0.933874\pi$
$607$		−	10.1629i		−	0.412500i	0.978499	−	0.206250i	$-0.0661260\pi$
$608$	−2.73737			−0.111015
$609$	−14.3208	−	12.3943i	−0.580308	−	0.502244i
$610$	7.49621			0.303513
$611$			3.05220i			0.123479i
$612$	−1.61717	+	6.13328i	−0.0653701	+	0.247923i
$613$	7.01773			0.283443			0.141722	−	0.989907i	$-0.454736\pi$
$613$	7.01773			0.283443			0.141722	+	0.989907i	$0.454736\pi$
$614$	−6.88194			−0.277732
$615$	−29.2305	+	22.5223i	−1.17869	+	0.908186i
$616$	−11.0061	+	2.24123i	−0.443449	+	0.0903015i
$617$			12.0094i			0.483480i	0.970341	+	0.241740i	$0.0777182\pi$
$617$			12.0094i			0.483480i	−0.970341	+	0.241740i	$0.922282\pi$
$618$	1.42064	−	1.09462i	0.0571467	−	0.0440319i
$619$			11.0457i			0.443966i	0.975051	+	0.221983i	$0.0712529\pi$
$619$			11.0457i			0.443966i	−0.975051	+	0.221983i	$0.928747\pi$
$620$			20.6041i			0.827482i
$621$	−4.78861	+	2.01722i	−0.192160	+	0.0809482i
$622$		−	15.1958i		−	0.609296i
$623$	46.2772	−	9.42365i	1.85406	−	0.377551i
$624$	0.560730	+	0.727743i	0.0224472	+	0.0291330i
$625$	−28.0057			−1.12023
$626$	−30.1231			−1.20396
$627$	−15.9442	+	12.2851i	−0.636749	+	0.490619i
$628$		−	14.8784i		−	0.593712i
$629$	4.21157			0.167926
$630$	18.9173	+	1.07785i	0.753683	+	0.0429426i
$631$	−25.9355			−1.03248			−0.516239	−	0.856445i	$-0.672668\pi$
$631$	−25.9355			−1.03248			−0.516239	+	0.856445i	$0.672668\pi$
$632$			10.5466i			0.419521i
$633$	−8.26220	+	6.36608i	−0.328393	+	0.253029i
$634$	18.0815			0.718107
$635$	2.83201			0.112385
$636$	−2.51928	−	3.26964i	−0.0998960	−	0.129650i
$637$	1.45195	+	3.41726i	0.0575284	+	0.135397i
$638$		−	17.5455i		−	0.694635i
$639$	32.4346	+	8.55207i	1.28309	+	0.338315i
$640$			2.38722i			0.0943631i
$641$			36.9867i			1.46089i	0.682973	+	0.730444i	$0.260687\pi$
$641$			36.9867i			1.46089i	−0.682973	+	0.730444i	$0.739313\pi$
$642$	12.9582	−	9.98439i	0.511420	−	0.394052i
$643$		−	48.1118i		−	1.89734i	−0.316263	−	0.948672i	$-0.602428\pi$
$643$		−	48.1118i		−	1.89734i	0.316263	−	0.948672i	$-0.397572\pi$
$644$	−0.527932	−	2.59254i	−0.0208034	−	0.102161i
$645$	29.2914	−	22.5692i	1.15335	−	0.888663i
$646$	−5.78763			−0.227711
$647$	10.7637			0.423163			0.211582	−	0.977360i	$-0.432139\pi$
$647$	10.7637			0.423163			0.211582	+	0.977360i	$0.432139\pi$
$648$	4.43757	−	7.82994i	0.174324	−	0.307589i
$649$		−	21.1015i		−	0.828305i
$650$	0.370663			0.0145386
$651$	29.9068	+	25.8837i	1.17214	+	1.01446i
$652$	23.8160			0.932705
$653$			29.8948i			1.16988i	0.811078	+	0.584938i	$0.198881\pi$
$653$			29.8948i			1.16988i	−0.811078	+	0.584938i	$0.801119\pi$
$654$	−9.85130	−	12.7855i	−0.385216	−	0.499952i
$655$	34.4290			1.34525
$656$	−8.92450			−0.348443
$657$	16.4866	+	4.34704i	0.643205	+	0.169594i
$658$	3.03790	+	14.9184i	0.118430	+	0.581578i
$659$		−	0.667865i		−	0.0260163i	−0.999915	−	0.0130082i	$-0.995859\pi$
$659$		−	0.667865i		−	0.0260163i	0.999915	−	0.0130082i	$-0.00414074\pi$
$660$	10.7136	+	13.9046i	0.417027	+	0.541238i
$661$		−	5.76252i		−	0.224136i	−0.993701	−	0.112068i	$-0.964253\pi$
$661$		−	5.76252i		−	0.224136i	0.993701	−	0.112068i	$-0.0357474\pi$
$662$		−	13.4098i		−	0.521188i
$663$	1.18555	+	1.53867i	0.0460430	+	0.0597568i
$664$			1.92977i			0.0748898i
$665$	3.44988	+	16.9415i	0.133781	+	0.656964i
$666$	−5.77835	−	1.52358i	−0.223907	−	0.0590377i
$667$	4.13294			0.160028
$668$	−5.42417			−0.209868
$669$	−5.80309	−	7.53153i	−0.224360	−	0.291186i
$670$			17.0887i			0.660194i
$671$	13.3308			0.514631
$672$	3.46504	+	2.99892i	0.133667	+	0.115686i
$673$	−34.1780			−1.31747			−0.658733	−	0.752377i	$-0.728907\pi$
$673$	−34.1780			−1.31747			−0.658733	+	0.752377i	$0.728907\pi$
$674$			5.36398i			0.206613i
$675$	−1.40966	−	3.34635i	−0.0542579	−	0.128801i
$676$	−12.7187			−0.489179
$677$	49.0360			1.88460			0.942302	−	0.334763i	$-0.108656\pi$
$677$	49.0360			1.88460			0.942302	+	0.334763i	$0.108656\pi$
$678$	−3.60035	+	2.77409i	−0.138271	+	0.106538i
$679$	−4.78970	−	23.5210i	−0.183812	−	0.902654i
$680$			5.04729i			0.193555i
$681$	13.4524	−	10.3652i	0.515498	−	0.397195i
$682$			36.6412i			1.40306i
$683$		−	26.6025i		−	1.01792i	−0.860791	−	0.508959i	$-0.830031\pi$
$683$		−	26.6025i		−	1.01792i	0.860791	−	0.508959i	$-0.169969\pi$
$684$	7.94073	+	2.09374i	0.303621	+	0.0800562i
$685$			0.351381i			0.0134256i
$686$	10.4980	+	15.2575i	0.400816	+	0.582535i
$687$	−26.6975	−	34.6493i	−1.01857	−	1.32195i
$688$	8.94310			0.340953
$689$	−1.26403			−0.0481558
$690$	−3.27531	+	2.52365i	−0.124689	+	0.0960736i
$691$			34.0474i			1.29522i	0.761970	+	0.647612i	$0.224232\pi$
$691$			34.0474i			1.29522i	−0.761970	+	0.647612i	$0.775768\pi$
$692$	1.70656			0.0648735
$693$	33.6414	+	1.91679i	1.27793	+	0.0728127i
$694$	28.4518			1.08002
$695$		−	6.20700i		−	0.235445i
$696$	−5.67047	+	4.36913i	−0.214939	+	0.165612i
$697$	−18.8690			−0.714716
$698$	29.2240			1.10615
$699$	−5.31479	−	6.89779i	−0.201024	−	0.260898i
$700$	1.81171	−	0.368926i	0.0684761	−	0.0139441i
$701$			40.5922i			1.53315i	0.642158	+	0.766573i	$0.278039\pi$
$701$			40.5922i			1.53315i	−0.642158	+	0.766573i	$0.721961\pi$
$702$	−1.06997	−	2.53997i	−0.0403834	−	0.0958648i
$703$		−	5.45270i		−	0.205653i
$704$			4.24529i			0.160000i
$705$	18.8472	−	14.5219i	0.709827	−	0.546926i
$706$			5.61185i			0.211205i
$707$	−12.0057	+	2.44478i	−0.451521	+	0.0919453i
$708$	−6.81970	+	5.25462i	−0.256300	+	0.197481i
$709$	−2.65848			−0.0998413			−0.0499206	−	0.998753i	$-0.515897\pi$
$709$	−2.65848			−0.0998413			−0.0499206	+	0.998753i	$0.515897\pi$
$710$	26.6916			1.00172
$711$	8.06679	−	30.5941i	0.302528	−	1.14737i
$712$		−	17.8501i		−	0.668962i
$713$	−8.63102			−0.323234
$714$	7.32613	+	6.34061i	0.274173	+	0.237291i
$715$	5.37549			0.201032
$716$		−	14.9077i		−	0.557127i
$717$	24.8918	+	32.3058i	0.929602	+	1.20648i
$718$	−2.05565			−0.0767161
$719$	−42.5540			−1.58700			−0.793498	−	0.608573i	$-0.791742\pi$
$719$	−42.5540			−1.58700			−0.793498	+	0.608573i	$0.791742\pi$
$720$	1.82592	−	6.92498i	0.0680479	−	0.258079i
$721$	−0.546642	−	2.68443i	−0.0203580	−	0.0999733i
$722$		−	11.5068i		−	0.428238i
$723$	8.78034	+	11.3956i	0.326544	+	0.423805i
$724$			15.2548i			0.566939i
$725$			2.88816i			0.107263i
$726$	7.42383	+	9.63501i	0.275524	+	0.357589i
$727$			49.6978i			1.84319i	0.388152	+	0.921595i	$0.373114\pi$
$727$			49.6978i			1.84319i	−0.388152	+	0.921595i	$0.626886\pi$
$728$	1.37513	−	0.280024i	0.0509658	−	0.0103784i
$729$	−18.8616	+	19.3194i	−0.698580	+	0.715532i
$730$	13.5674			0.502153
$731$	18.9084			0.699352
$732$	−3.31960	−	4.30834i	−0.122696	−	0.159241i
$733$		−	35.3495i		−	1.30566i	−0.757503	−	0.652832i	$-0.773581\pi$
$733$		−	35.3495i		−	1.30566i	0.757503	−	0.652832i	$-0.226419\pi$
$734$	−33.3452			−1.23079
$735$	14.1933	−	25.2245i	0.523526	−	0.930421i
$736$	−1.00000			−0.0368605
$737$			30.3895i			1.11941i
$738$	25.8887	+	6.82609i	0.952976	+	0.251272i
$739$	−27.5105			−1.01199			−0.505995	−	0.862536i	$-0.668875\pi$
$739$	−27.5105			−1.01199			−0.505995	+	0.862536i	$0.668875\pi$
$740$	−4.75521			−0.174805
$741$	1.99211	−	1.53493i	0.0731818	−	0.0563870i
$742$	−6.17826	+	1.25811i	−0.226811	+	0.0461866i
$743$			28.2522i			1.03647i	0.855238	+	0.518236i	$0.173411\pi$
$743$			28.2522i			1.03647i	−0.855238	+	0.518236i	$0.826589\pi$
$744$	11.8419	−	9.12427i	0.434146	−	0.334512i
$745$			28.2637i			1.03550i
$746$			13.4898i			0.493897i
$747$	1.47603	−	5.59800i	0.0540051	−	0.204820i
$748$			8.97581i			0.328188i
$749$	−4.98612	−	24.4856i	−0.182189	−	0.894686i
$750$	10.8547	+	14.0877i	0.396357	+	0.514411i
$751$	48.1266			1.75617			0.878083	−	0.478509i	$-0.158822\pi$
$751$	48.1266			1.75617			0.878083	+	0.478509i	$0.158822\pi$
$752$	5.75433			0.209839
$753$	−37.7514	+	29.0877i	−1.37574	+	1.06001i
$754$			2.19218i			0.0798346i
$755$	28.3998			1.03358
$756$	−7.75780	−	11.3497i	−0.282148	−	0.412786i
$757$	3.25281			0.118225			0.0591126	−	0.998251i	$-0.481173\pi$
$757$	3.25281			0.118225			0.0591126	+	0.998251i	$0.481173\pi$
$758$			29.2116i			1.06101i
$759$	−5.82462	+	4.48791i	−0.211420	+	0.162901i
$760$	6.53471			0.237039
$761$	18.2124			0.660198			0.330099	−	0.943946i	$-0.392918\pi$
$761$	18.2124			0.660198			0.330099	+	0.943946i	$0.392918\pi$
$762$	−1.25412	−	1.62766i	−0.0454320	−	0.0589638i
$763$	−24.1593	+	4.91966i	−0.874624	+	0.178104i
$764$			9.45500i			0.342070i
$765$	3.86053	−	14.6415i	0.139578	−	0.529364i
$766$			5.51748i			0.199355i
$767$			2.63647i			0.0951975i
$768$	1.37202	−	1.05715i	0.0495085	−	0.0381466i
$769$			9.31871i			0.336041i	0.985783	+	0.168021i	$0.0537375\pi$
$769$			9.31871i			0.336041i	−0.985783	+	0.168021i	$0.946262\pi$
$770$	26.2740	−	5.35030i	0.946849	−	0.192811i
$771$	33.8014	−	26.0442i	1.21733	−	0.937959i
$772$	−27.2408			−0.980417
$773$	17.0860			0.614542			0.307271	−	0.951622i	$-0.400584\pi$
$773$	17.0860			0.614542			0.307271	+	0.951622i	$0.400584\pi$
$774$	−25.9427	−	6.84033i	−0.932490	−	0.245870i
$775$		−	6.03147i		−	0.216657i
$776$	−9.07256			−0.325686
$777$	−5.97368	+	6.90217i	−0.214305	+	0.247614i
$778$	−2.08173			−0.0746338
$779$			24.4297i			0.875284i
$780$	−1.33859	−	1.73728i	−0.0479291	−	0.0622047i
$781$	47.4669			1.69850
$782$	−2.11430			−0.0756071
$783$	19.7911	−	8.33705i	0.707275	−	0.297942i
$784$	6.44258	−	2.73737i	0.230092	−	0.0977634i
$785$			35.5179i			1.26769i
$786$	−15.2465	−	19.7876i	−0.543823	−	0.705800i
$787$		−	7.62517i		−	0.271808i	−0.990722	−	0.135904i	$-0.956606\pi$
$787$		−	7.62517i		−	0.271808i	0.990722	−	0.135904i	$-0.0433938\pi$
$788$		−	18.6196i		−	0.663296i
$789$	−2.62782	−	3.41051i	−0.0935527	−	0.121417i
$790$		−	25.1770i		−	0.895758i
$791$	1.38536	+	6.80317i	0.0492577	+	0.241893i
$792$	3.24710	−	12.3150i	0.115381	−	0.437594i
$793$	−1.66559			−0.0591468
$794$	3.52438			0.125076
$795$	6.01407	+	7.80535i	0.213297	+	0.276827i
$796$		−	2.99081i		−	0.106006i
$797$	21.4708			0.760533			0.380267	−	0.924877i	$-0.375832\pi$
$797$	21.4708			0.760533			0.380267	+	0.924877i	$0.375832\pi$
$798$	8.20916	−	9.48511i	0.290601	−	0.335769i
$799$	12.1664			0.430415
$800$		−	0.698814i		−	0.0247068i
$801$	−13.6531	+	51.7807i	−0.482407	+	1.82958i
$802$	26.0497			0.919848
$803$	24.1275			0.851442
$804$	9.82147	−	7.56751i	0.346377	−	0.266885i
$805$	1.26029	+	6.18897i	0.0444194	+	0.218133i
$806$		−	4.57804i		−	0.161255i
$807$	38.0370	−	29.3077i	1.33896	−	1.03168i
$808$			4.63086i			0.162913i
$809$			41.4583i			1.45760i	0.684729	+	0.728798i	$0.259921\pi$
$809$			41.4583i			1.45760i	−0.684729	+	0.728798i	$0.740079\pi$
$810$	−10.5934	+	18.6918i	−0.372216	+	0.656762i
$811$			52.8572i			1.85607i	0.372497	+	0.928034i	$0.378502\pi$
$811$			52.8572i			1.85607i	−0.372497	+	0.928034i	$0.621498\pi$
$812$	2.18191	+	10.7148i	0.0765701	+	0.376017i
$813$	2.06303	+	2.67750i	0.0723535	+	0.0939039i
$814$	−8.45639			−0.296396
$815$	−56.8539			−1.99150
$816$	2.90086	−	2.23513i	0.101550	−	0.0782451i
$817$		−	24.4806i		−	0.856469i
$818$	36.7589			1.28524
$819$	−4.20324	−	0.239488i	−0.146873	−	0.00836839i
$820$	21.3047			0.743993
$821$			22.9087i			0.799520i	0.916620	+	0.399760i	$0.130907\pi$
$821$			22.9087i			0.799520i	−0.916620	+	0.399760i	$0.869093\pi$
$822$	0.201951	−	0.155605i	0.00704386	−	0.00542734i
$823$	−32.9884			−1.14990			−0.574951	−	0.818188i	$-0.694979\pi$
$823$	−32.9884			−1.14990			−0.574951	+	0.818188i	$0.694979\pi$
$824$	−1.03544			−0.0360713
$825$	−3.13621	−	4.07033i	−0.109189	−	0.141711i
$826$	2.62412	+	12.8864i	0.0913047	+	0.448375i
$827$			5.73106i			0.199288i	0.995023	+	0.0996442i	$0.0317704\pi$
$827$			5.73106i			0.199288i	−0.995023	+	0.0996442i	$0.968230\pi$
$828$	2.90086	+	0.764872i	0.100812	+	0.0265811i
$829$		−	1.28200i		−	0.0445257i	−0.999752	−	0.0222628i	$-0.992913\pi$
$829$		−	1.28200i		−	0.0445257i	0.999752	−	0.0222628i	$-0.00708707\pi$
$830$		−	4.60679i		−	0.159904i
$831$	24.0120	−	18.5014i	0.832968	−	0.641807i
$832$		−	0.530418i		−	0.0183889i
$833$	13.6215	−	5.78763i	0.471958	−	0.200529i
$834$	−3.56738	+	2.74869i	−0.123528	+	0.0951793i
$835$	12.9487			0.448108
$836$	11.6210			0.401919
$837$	−41.3306	+	17.4107i	−1.42859	+	0.601800i
$838$			34.1180i			1.17859i
$839$	−7.93031			−0.273785			−0.136892	−	0.990586i	$-0.543711\pi$
$839$	−7.93031			−0.273785			−0.136892	+	0.990586i	$0.543711\pi$
$840$	−8.27181	−	7.15907i	−0.285404	−	0.247011i
$841$	11.9188			0.410993
$842$			11.0413i			0.380507i
$843$	−31.3665	−	40.7090i	−1.08032	−	1.40209i
$844$	6.02193			0.207283
$845$	30.3622			1.04449
$846$	−16.6925	−	4.40133i	−0.573900	−	0.151321i
$847$	18.2062	−	3.70740i	0.625571	−	0.127388i
$848$			2.38309i			0.0818356i
$849$	−14.5404	−	18.8713i	−0.499026	−	0.647660i
$850$		−	1.47750i		−	0.0506779i
$851$		−	1.99195i		−	0.0682830i
$852$	−11.8200	−	15.3406i	−0.404948	−	0.525561i
$853$		−	55.7011i		−	1.90717i	−0.301126	−	0.953584i	$-0.597362\pi$
$853$		−	55.7011i		−	1.90717i	0.301126	−	0.953584i	$-0.402638\pi$
$854$	−8.14097	+	1.65778i	−0.278578	+	0.0567282i
$855$	−18.9563	−	4.99822i	−0.648291	−	0.170935i
$856$	−9.44463			−0.322811
$857$	−32.2545			−1.10179			−0.550896	−	0.834574i	$-0.685714\pi$
$857$	−32.2545			−1.10179			−0.550896	+	0.834574i	$0.685714\pi$
$858$	−2.38046	−	3.08948i	−0.0812677	−	0.105473i
$859$		−	21.5419i		−	0.734999i	−0.930024	−	0.367499i	$-0.880214\pi$
$859$		−	21.5419i		−	0.734999i	0.930024	−	0.367499i	$-0.119786\pi$
$860$	−21.3491			−0.728000
$861$	26.7638	−	30.9237i	0.912109	−	1.05388i
$862$	−16.5144			−0.562482
$863$		−	14.7382i		−	0.501696i	−0.968027	−	0.250848i	$-0.919291\pi$
$863$		−	14.7382i		−	0.501696i	0.968027	−	0.250848i	$-0.0807094\pi$
$864$	−4.78861	+	2.01722i	−0.162912	+	0.0686272i
$865$	−4.07392			−0.138518
$866$	10.8168			0.367568
$867$	−17.1910	+	13.2458i	−0.583838	+	0.449851i
$868$	−4.55659	−	22.3763i	−0.154661	−	0.759501i
$869$		−	44.7733i		−	1.51883i
$870$	13.5367	−	10.4301i	0.458936	−	0.353613i
$871$		−	3.79695i		−	0.128655i
$872$			9.31875i			0.315573i
$873$	26.3182	+	6.93935i	0.890737	+	0.234861i
$874$			2.73737i			0.0925931i
$875$	26.6199	−	5.42074i	0.899917	−	0.183254i
$876$	−6.00816	−	7.79768i	−0.202997	−	0.263459i
$877$	−12.8513			−0.433958			−0.216979	−	0.976176i	$-0.569620\pi$
$877$	−12.8513			−0.433958			−0.216979	+	0.976176i	$0.569620\pi$
$878$	−38.2864			−1.29210
$879$	−10.0281	+	7.72673i	−0.338240	+	0.260616i
$880$		−	10.1344i		−	0.341632i
$881$	47.4552			1.59881			0.799404	−	0.600794i	$-0.205149\pi$
$881$	47.4552			1.59881			0.799404	+	0.600794i	$0.205149\pi$
$882$	−20.7827	+	3.01299i	−0.699791	+	0.101453i
$883$	−0.239120			−0.00804704			−0.00402352	−	0.999992i	$-0.501281\pi$
$883$	−0.239120			−0.00804704			−0.00402352	+	0.999992i	$0.501281\pi$
$884$		−	1.12146i		−	0.0377188i
$885$	16.2801	−	12.5439i	0.547250	−	0.421660i
$886$	14.5512			0.488856
$887$	−8.75627			−0.294007			−0.147003	−	0.989136i	$-0.546963\pi$
$887$	−8.75627			−0.294007			−0.147003	+	0.989136i	$0.546963\pi$
$888$	2.10578	+	2.73299i	0.0706655	+	0.0917131i
$889$	−3.07559	+	0.626298i	−0.103152	+	0.0210053i
$890$			42.6121i			1.42836i
$891$	−18.8388	+	33.2404i	−0.631122	+	1.11360i
$892$			5.48938i			0.183798i
$893$		−	15.7518i		−	0.527113i
$894$	16.2442	−	12.5162i	0.543286	−	0.418605i
$895$			35.5879i			1.18957i
$896$	−0.527932	−	2.59254i	−0.0176370	−	0.0866108i
$897$	0.727743	−	0.560730i	0.0242986	−	0.0187222i
$898$	−23.2181			−0.774798
$899$	35.6715			1.18971
$900$	−0.534503	+	2.02716i	−0.0178168	+	0.0675720i
$901$			5.03856i			0.167859i
$902$	37.8871			1.26150
$903$	−26.8196	+	30.9882i	−0.892501	+	1.03122i
$904$	2.62413			0.0872772
$905$		−	36.4165i		−	1.21052i
$906$	−12.5765	−	16.3224i	−0.417826	−	0.542275i
$907$	7.27362			0.241516			0.120758	−	0.992682i	$-0.461467\pi$
$907$	7.27362			0.241516			0.120758	+	0.992682i	$0.461467\pi$
$908$	−9.80484			−0.325385
$909$	3.54201	−	13.4335i	0.117481	−	0.445559i
$910$	−3.28274	+	0.668480i	−0.108822	+	0.0221599i
$911$			9.82537i			0.325529i	0.986665	+	0.162764i	$0.0520411\pi$
$911$			9.82537i			0.325529i	−0.986665	+	0.162764i	$0.947959\pi$
$912$	−2.89381	−	3.75573i	−0.0958237	−	0.124365i
$913$		−	8.19245i		−	0.271131i
$914$		−	1.57154i		−	0.0519819i
$915$	7.92462	+	10.2849i	0.261980	+	0.340010i
$916$			25.2542i			0.834424i
$917$	−37.3903	+	7.61396i	−1.23474	+	0.251435i
$918$	−10.1246	+	4.26500i	−0.334160	+	0.140766i
$919$	−7.32226			−0.241539			−0.120770	−	0.992681i	$-0.538536\pi$
$919$	−7.32226			−0.241539			−0.120770	+	0.992681i	$0.538536\pi$
$920$	2.38722			0.0787043
$921$	−7.27523	−	9.44215i	−0.239727	−	0.311129i
$922$			30.3724i			1.00026i
$923$	−5.93063			−0.195209
$924$	−14.7101	−	12.7313i	−0.483927	−	0.418828i
$925$	1.39200			0.0457687
$926$		−	2.89918i		−	0.0952730i
$927$	3.00367	+	0.791980i	0.0986533	+	0.0260120i
$928$	4.13294			0.135670
$929$	31.9322			1.04766			0.523830	−	0.851823i	$-0.324503\pi$
$929$	31.9322			1.04766			0.523830	+	0.851823i	$0.324503\pi$
$930$	−28.2692	+	21.7816i	−0.926985	+	0.714248i
$931$	−7.49322	−	17.6357i	−0.245580	−	0.577988i
$932$			5.02747i			0.164680i
$933$	20.8489	−	16.0642i	0.682563	−	0.525919i
$934$		−	13.1117i		−	0.429027i
$935$		−	21.4272i		−	0.700745i
$936$	−0.405701	+	1.53867i	−0.0132608	+	0.0502929i
$937$			58.3670i			1.90677i	0.301763	+	0.953383i	$0.402425\pi$
$937$			58.3670i			1.90677i	−0.301763	+	0.953383i	$0.597575\pi$
$938$	−3.77915	−	18.5585i	−0.123394	−	0.605956i
$939$	−31.8446	−	41.3294i	−1.03921	−	1.34874i
$940$	−13.7369			−0.448047
$941$	0.898173			0.0292796			0.0146398	−	0.999893i	$-0.495340\pi$
$941$	0.898173			0.0292796			0.0146398	+	0.999893i	$0.495340\pi$
$942$	20.4134	−	15.7287i	0.665105	−	0.512468i
$943$			8.92450i			0.290622i
$944$	4.97056			0.161778
$945$	18.5196	+	27.0943i	0.602441	+	0.881378i
$946$	−37.9661			−1.23438
$947$		−	45.6660i		−	1.48395i	−0.670429	−	0.741974i	$-0.733890\pi$
$947$		−	45.6660i		−	1.48395i	0.670429	−	0.741974i	$-0.266110\pi$
$948$	−14.4701	+	11.1493i	−0.469968	+	0.362113i
$949$	−3.01456			−0.0978566
$950$	−1.91292			−0.0620632
$951$	19.1148	+	24.8081i	0.619840	+	0.804459i
$952$	−1.11621	−	5.48141i	−0.0361764	−	0.177654i
$953$			32.7530i			1.06097i	0.847693	+	0.530487i	$0.177991\pi$
$953$			32.7530i			1.06097i	−0.847693	+	0.530487i	$0.822009\pi$
$954$	1.82276	−	6.91300i	0.0590139	−	0.223817i
$955$		−	22.5712i		−	0.730386i
$956$		−	23.5462i		−	0.761538i
$957$	24.0728	−	18.5483i	0.778163	−	0.599580i
$958$			38.8150i			1.25406i
$959$	−0.0777078	−	0.381604i	−0.00250931	−	0.0123226i
$960$	−3.27531	+	2.52365i	−0.105710	+	0.0814503i
$961$	−43.4944			−1.40305
$962$	1.05656			0.0340650
$963$	27.3975	+	7.22393i	0.882873	+	0.232788i
$964$		−	8.30568i		−	0.267508i
$965$	65.0297			2.09338
$966$	2.99892	−	3.46504i	0.0964886	−	0.111486i
$967$	−42.2525			−1.35875			−0.679375	−	0.733792i	$-0.737749\pi$
$967$	−42.2525			−1.35875			−0.679375	+	0.733792i	$0.737749\pi$
$968$		−	7.02250i		−	0.225712i
$969$	−6.11838	−	7.94073i	−0.196551	−	0.255093i
$970$	21.6582			0.695403
$971$	4.27368			0.137149			0.0685745	−	0.997646i	$-0.478155\pi$
$971$	4.27368			0.137149			0.0685745	+	0.997646i	$0.478155\pi$
$972$	15.4340	−	2.18899i	0.495046	−	0.0702119i
$973$	1.37267	+	6.74086i	0.0440059	+	0.216102i
$974$		−	24.6155i		−	0.788732i
$975$	0.391846	+	0.508557i	0.0125491	+	0.0162869i
$976$			3.14015i			0.100514i
$977$		−	54.2583i		−	1.73588i	−0.496672	−	0.867939i	$-0.665445\pi$
$977$		−	54.2583i		−	1.73588i	0.496672	−	0.867939i	$-0.334555\pi$
$978$	25.1770	+	32.6759i	0.805072	+	1.04486i
$979$			75.7790i			2.42191i
$980$	−15.3798	+	6.53471i	−0.491291	+	0.208744i
$981$	7.12764	−	27.0323i	0.227568	−	0.863076i
$982$	−22.4723			−0.717118
$983$	7.40681			0.236240			0.118120	−	0.992999i	$-0.462313\pi$
$983$	7.40681			0.236240			0.118120	+	0.992999i	$0.462313\pi$
$984$	−9.43452	−	12.2446i	−0.300762	−	0.390343i
$985$			44.4491i			1.41627i
$986$	8.73827			0.278283
$987$	−17.2568	+	19.9390i	−0.549289	+	0.634665i
$988$	−1.45195			−0.0461927
$989$		−	8.94310i		−	0.284374i
$990$	−7.75155	+	29.3986i	−0.246360	+	0.934348i
$991$	−15.6673			−0.497688			−0.248844	−	0.968544i	$-0.580051\pi$
$991$	−15.6673			−0.497688			−0.248844	+	0.968544i	$0.580051\pi$
$992$	−8.63102			−0.274035
$993$	18.3986	−	14.1762i	0.583861	−	0.449868i
$994$	−28.9874	+	5.90284i	−0.919424	+	0.187227i
$995$			7.13972i			0.226344i
$996$	−2.64769	+	2.04006i	−0.0838952	+	0.0646417i
$997$		−	47.3637i		−	1.50002i	−0.661424	−	0.750012i	$-0.730047\pi$
$997$		−	47.3637i		−	1.50002i	0.661424	−	0.750012i	$-0.269953\pi$
$998$		−	1.06698i		−	0.0337746i
$999$	−4.01819	−	9.53866i	−0.127130	−	0.301790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.c.461.12	yes	28
3.2	odd	2	inner	966.2.f.c.461.17	yes	28
7.6	odd	2	inner	966.2.f.c.461.3	✓	28
21.20	even	2	inner	966.2.f.c.461.26	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.c.461.3	✓	28	7.6	odd	2	inner
966.2.f.c.461.12	yes	28	1.1	even	1	trivial
966.2.f.c.461.17	yes	28	3.2	odd	2	inner
966.2.f.c.461.26	yes	28	21.20	even	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.37202 - 1.05715i) q^{3} -1.00000 q^{4} +2.38722 q^{5} +(-1.05715 - 1.37202i) q^{6} +(-2.59254 + 0.527932i) q^{7} +1.00000i q^{8} +(0.764872 - 2.90086i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.37202 - 1.05715i) q^{3} -1.00000 q^{4} +2.38722 q^{5} +(-1.05715 - 1.37202i) q^{6} +(-2.59254 + 0.527932i) q^{7} +1.00000i q^{8} +(0.764872 - 2.90086i) q^{9} -2.38722i q^{10} -4.24529i q^{11} +(-1.37202 + 1.05715i) q^{12} +0.530418i q^{13} +(0.527932 + 2.59254i) q^{14} +(3.27531 - 2.52365i) q^{15} +1.00000 q^{16} +2.11430 q^{17} +(-2.90086 - 0.764872i) q^{18} -2.73737i q^{19} -2.38722 q^{20} +(-2.99892 + 3.46504i) q^{21} -4.24529 q^{22} -1.00000i q^{23} +(1.05715 + 1.37202i) q^{24} +0.698814 q^{25} +0.530418 q^{26} +(-2.01722 - 4.78861i) q^{27} +(2.59254 - 0.527932i) q^{28} +4.13294i q^{29} +(-2.52365 - 3.27531i) q^{30} -8.63102i q^{31} -1.00000i q^{32} +(-4.48791 - 5.82462i) q^{33} -2.11430i q^{34} +(-6.18897 + 1.26029i) q^{35} +(-0.764872 + 2.90086i) q^{36} +1.99195 q^{37} -2.73737 q^{38} +(0.560730 + 0.727743i) q^{39} +2.38722i q^{40} -8.92450 q^{41} +(3.46504 + 2.99892i) q^{42} +8.94310 q^{43} +4.24529i q^{44} +(1.82592 - 6.92498i) q^{45} -1.00000 q^{46} +5.75433 q^{47} +(1.37202 - 1.05715i) q^{48} +(6.44258 - 2.73737i) q^{49} -0.698814i q^{50} +(2.90086 - 2.23513i) q^{51} -0.530418i q^{52} +2.38309i q^{53} +(-4.78861 + 2.01722i) q^{54} -10.1344i q^{55} +(-0.527932 - 2.59254i) q^{56} +(-2.89381 - 3.75573i) q^{57} +4.13294 q^{58} +4.97056 q^{59} +(-3.27531 + 2.52365i) q^{60} +3.14015i q^{61} -8.63102 q^{62} +(-0.451509 + 7.92440i) q^{63} -1.00000 q^{64} +1.26622i q^{65} +(-5.82462 + 4.48791i) q^{66} -7.15841 q^{67} -2.11430 q^{68} +(-1.05715 - 1.37202i) q^{69} +(1.26029 + 6.18897i) q^{70} +11.1811i q^{71} +(2.90086 + 0.764872i) q^{72} +5.68336i q^{73} -1.99195i q^{74} +(0.958786 - 0.738750i) q^{75} +2.73737i q^{76} +(2.24123 + 11.0061i) q^{77} +(0.727743 - 0.560730i) q^{78} +10.5466 q^{79} +2.38722 q^{80} +(-7.82994 - 4.43757i) q^{81} +8.92450i q^{82} +1.92977 q^{83} +(2.99892 - 3.46504i) q^{84} +5.04729 q^{85} -8.94310i q^{86} +(4.36913 + 5.67047i) q^{87} +4.24529 q^{88} -17.8501 q^{89} +(-6.92498 - 1.82592i) q^{90} +(-0.280024 - 1.37513i) q^{91} +1.00000i q^{92} +(-9.12427 - 11.8419i) q^{93} -5.75433i q^{94} -6.53471i q^{95} +(-1.05715 - 1.37202i) q^{96} +9.07256i q^{97} +(-2.73737 - 6.44258i) q^{98} +(-12.3150 - 3.24710i) 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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