LMFDB - Embedded newform 96.2.n.a.61.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [96,2,Mod(13,96)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(96, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 0]))

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

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

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	96.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.766563859404$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			61.5
Character	$\chi$	$=$	96.61
Dual form			96.2.n.a.85.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.126318 + 1.40856i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(-1.96809 - 0.355853i) q^{4} +(1.36206 + 3.28830i) q^{5} +(0.655736 - 1.25300i) q^{6} +(-2.73097 + 2.73097i) q^{7} +(0.749846 - 2.72722i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.126318 + 1.40856i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(-1.96809 - 0.355853i) q^{4} +(1.36206 + 3.28830i) q^{5} +(0.655736 - 1.25300i) q^{6} +(-2.73097 + 2.73097i) q^{7} +(0.749846 - 2.72722i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-4.80383 + 1.50317i) q^{10} +(3.01609 - 1.24931i) q^{11} +(1.68210 + 1.08192i) q^{12} +(0.932498 - 2.25125i) q^{13} +(-3.50176 - 4.19170i) q^{14} -3.55923i q^{15} +(3.74674 + 1.40070i) q^{16} +0.517450i q^{17} +(-1.08532 + 0.906683i) q^{18} +(1.52739 - 3.68744i) q^{19} +(-1.51050 - 6.95636i) q^{20} +(3.56818 - 1.47799i) q^{21} +(1.37874 + 4.40616i) q^{22} +(2.39792 + 2.39792i) q^{23} +(-1.73643 + 2.23267i) q^{24} +(-5.42220 + 5.42220i) q^{25} +(3.05323 + 1.59785i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(6.34660 - 4.40296i) q^{28} +(7.09056 + 2.93701i) q^{29} +(5.01340 + 0.449595i) q^{30} -1.50132 q^{31} +(-2.44625 + 5.10057i) q^{32} -3.26460 q^{33} +(-0.728859 - 0.0653632i) q^{34} +(-12.7000 - 5.26051i) q^{35} +(-1.14002 - 1.64327i) q^{36} +(-3.40814 - 8.22797i) q^{37} +(5.00104 + 2.61721i) q^{38} +(-1.72303 + 1.72303i) q^{39} +(9.98927 - 1.24892i) q^{40} +(-3.21656 - 3.21656i) q^{41} +(1.63111 + 5.21269i) q^{42} +(-1.31346 + 0.544054i) q^{43} +(-6.38051 + 1.38546i) q^{44} +(-1.36206 + 3.28830i) q^{45} +(-3.68051 + 3.07471i) q^{46} +4.67448i q^{47} +(-2.92551 - 2.72789i) q^{48} -7.91635i q^{49} +(-6.95258 - 8.32242i) q^{50} +(0.198019 - 0.478061i) q^{51} +(-2.63635 + 4.09882i) q^{52} +(-4.19534 + 1.73777i) q^{53} +(1.34968 - 0.422330i) q^{54} +(8.21621 + 8.21621i) q^{55} +(5.40014 + 9.49575i) q^{56} +(-2.82224 + 2.82224i) q^{57} +(-5.03262 + 9.61649i) q^{58} +(-0.680868 - 1.64376i) q^{59} +(-1.26656 + 7.00489i) q^{60} +(6.71487 + 2.78139i) q^{61} +(0.189643 - 2.11470i) q^{62} -3.86217 q^{63} +(-6.87546 - 4.08999i) q^{64} +8.67291 q^{65} +(0.412377 - 4.59838i) q^{66} +(11.1312 + 4.61070i) q^{67} +(0.184136 - 1.01839i) q^{68} +(-1.29774 - 3.13303i) q^{69} +(9.01398 - 17.2242i) q^{70} +(1.86620 - 1.86620i) q^{71} +(2.45866 - 1.39822i) q^{72} +(-9.06859 - 9.06859i) q^{73} +(12.0201 - 3.76123i) q^{74} +(7.08445 - 2.93447i) q^{75} +(-4.31822 + 6.71367i) q^{76} +(-4.82504 + 11.6487i) q^{77} +(-2.20935 - 2.64465i) q^{78} -10.4412i q^{79} +(0.497353 + 14.2282i) q^{80} +1.00000i q^{81} +(4.93702 - 4.12441i) q^{82} +(-1.89340 + 4.57106i) q^{83} +(-7.54843 + 1.63906i) q^{84} +(-1.70153 + 0.704798i) q^{85} +(-0.600420 - 1.91882i) q^{86} +(-5.42688 - 5.42688i) q^{87} +(-1.14553 - 9.16234i) q^{88} +(-2.70762 + 2.70762i) q^{89} +(-4.45972 - 2.33392i) q^{90} +(3.60147 + 8.69471i) q^{91} +(-3.86600 - 5.57262i) q^{92} +(1.38704 + 0.574529i) q^{93} +(-6.58429 - 0.590470i) q^{94} +14.2058 q^{95} +(4.21195 - 3.77618i) q^{96} +3.73293 q^{97} +(11.1507 + 0.999977i) q^{98} +(3.01609 + 1.24931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	−0.126318	+	1.40856i	−0.0893203	+	0.996003i
$2$	−0.126318	+	1.40856i	−0.0893203	+	0.996003i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$4$	−1.96809	−	0.355853i	−0.984044	−	0.177927i
$5$	1.36206	+	3.28830i	0.609132	+	1.47057i	0.863946	+	0.503584i	$0.167986\pi$
$5$	1.36206	+	3.28830i	0.609132	+	1.47057i	−0.254814	+	0.966990i	$0.582014\pi$
$6$	0.655736	−	1.25300i	0.267703	−	0.511535i
$7$	−2.73097	+	2.73097i	−1.03221	+	1.03221i	−0.0327442	+	0.999464i	$0.510425\pi$
$7$	−2.73097	+	2.73097i	−1.03221	+	1.03221i	−0.999464	+	0.0327442i	$0.989575\pi$
$8$	0.749846	−	2.72722i	0.265110	−	0.964218i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$	−4.80383	+	1.50317i	−1.51910	+	0.475345i
$11$	3.01609	−	1.24931i	0.909387	−	0.376680i	0.121565	−	0.992583i	$-0.461209\pi$
$11$	3.01609	−	1.24931i	0.909387	−	0.376680i	0.787822	+	0.615903i	$0.211209\pi$
$12$	1.68210	+	1.08192i	0.485579	+	0.312323i
$13$	0.932498	−	2.25125i	0.258628	−	0.624384i	−0.740220	−	0.672365i	$-0.765279\pi$
$13$	0.932498	−	2.25125i	0.258628	−	0.624384i	0.998848	+	0.0479806i	$0.0152786\pi$
$14$	−3.50176	−	4.19170i	−0.935885	−	1.12028i
$15$		−	3.55923i		−	0.918990i
$16$	3.74674	+	1.40070i	0.936684	+	0.350175i
$17$			0.517450i			0.125500i	0.998029	+	0.0627500i	$0.0199871\pi$
$17$			0.517450i			0.125500i	−0.998029	+	0.0627500i	$0.980013\pi$
$18$	−1.08532	+	0.906683i	−0.255813	+	0.213707i
$19$	1.52739	−	3.68744i	0.350407	−	0.845956i	−0.646163	−	0.763199i	$-0.723627\pi$
$19$	1.52739	−	3.68744i	0.350407	−	0.845956i	0.996570	−	0.0827570i	$-0.0263725\pi$
$20$	−1.51050	−	6.95636i	−0.337758	−	1.55549i
$21$	3.56818	−	1.47799i	0.778640	−	0.322523i
$22$	1.37874	+	4.40616i	0.293948	+	0.939397i
$23$	2.39792	+	2.39792i	0.500000	+	0.500000i	0.911438	−	0.411438i	$-0.134973\pi$
$23$	2.39792	+	2.39792i	0.500000	+	0.500000i	−0.411438	+	0.911438i	$0.634973\pi$
$24$	−1.73643	+	2.23267i	−0.354447	+	0.455742i
$25$	−5.42220	+	5.42220i	−1.08444	+	1.08444i
$26$	3.05323	+	1.59785i	0.598788	+	0.313365i
$27$	−0.382683	−	0.923880i	−0.0736475	−	0.177801i
$28$	6.34660	−	4.40296i	1.19939	−	0.832081i
$29$	7.09056	+	2.93701i	1.31668	+	0.545389i	0.926828	−	0.375487i	$-0.122524\pi$
$29$	7.09056	+	2.93701i	1.31668	+	0.545389i	0.389857	+	0.920875i	$0.372524\pi$
$30$	5.01340	+	0.449595i	0.915317	+	0.0820845i
$31$	−1.50132			−0.269644			−0.134822	−	0.990870i	$-0.543046\pi$
$31$	−1.50132			−0.269644			−0.134822	+	0.990870i	$0.543046\pi$
$32$	−2.44625	+	5.10057i	−0.432440	+	0.901663i
$33$	−3.26460			−0.568293
$34$	−0.728859	−	0.0653632i	−0.124998	−	0.0112097i
$35$	−12.7000	−	5.26051i	−2.14669	−	0.889188i
$36$	−1.14002	−	1.64327i	−0.190004	−	0.273879i
$37$	−3.40814	−	8.22797i	−0.560294	−	1.35267i	−0.909531	−	0.415635i	$-0.863559\pi$
$37$	−3.40814	−	8.22797i	−0.560294	−	1.35267i	0.349237	−	0.937034i	$-0.386441\pi$
$38$	5.00104	+	2.61721i	0.811276	+	0.424567i
$39$	−1.72303	+	1.72303i	−0.275906	+	0.275906i
$40$	9.98927	−	1.24892i	1.57944	−	0.197471i
$41$	−3.21656	−	3.21656i	−0.502342	−	0.502342i	0.409823	−	0.912165i	$-0.365590\pi$
$41$	−3.21656	−	3.21656i	−0.502342	−	0.502342i	−0.912165	+	0.409823i	$0.865590\pi$
$42$	1.63111	+	5.21269i	0.251686	+	0.804336i
$43$	−1.31346	+	0.544054i	−0.200301	+	0.0829675i	−0.480579	−	0.876951i	$-0.659573\pi$
$43$	−1.31346	+	0.544054i	−0.200301	+	0.0829675i	0.280278	+	0.959919i	$0.409573\pi$
$44$	−6.38051	+	1.38546i	−0.961898	+	0.208866i
$45$	−1.36206	+	3.28830i	−0.203044	+	0.490191i
$46$	−3.68051	+	3.07471i	−0.542662	+	0.453342i
$47$			4.67448i			0.681843i	0.940092	+	0.340921i	$0.110739\pi$
$47$			4.67448i			0.681843i	−0.940092	+	0.340921i	$0.889261\pi$
$48$	−2.92551	−	2.72789i	−0.422261	−	0.393737i
$49$		−	7.91635i		−	1.13091i
$50$	−6.95258	−	8.32242i	−0.983243	−	1.17697i
$51$	0.198019	−	0.478061i	0.0277283	−	0.0669419i
$52$	−2.63635	+	4.09882i	−0.365596	+	0.568405i
$53$	−4.19534	+	1.73777i	−0.576275	+	0.238701i	−0.651733	−	0.758448i	$-0.725958\pi$
$53$	−4.19534	+	1.73777i	−0.576275	+	0.238701i	0.0754586	+	0.997149i	$0.475958\pi$
$54$	1.34968	−	0.422330i	0.183668	−	0.0574719i
$55$	8.21621	+	8.21621i	1.10787	+	1.10787i
$56$	5.40014	+	9.49575i	0.721624	+	1.26892i
$57$	−2.82224	+	2.82224i	−0.373815	+	0.373815i
$58$	−5.03262	+	9.61649i	−0.660815	+	1.26271i
$59$	−0.680868	−	1.64376i	−0.0886415	−	0.213999i	0.873342	−	0.487108i	$-0.161948\pi$
$59$	−0.680868	−	1.64376i	−0.0886415	−	0.213999i	−0.961983	+	0.273109i	$0.911948\pi$
$60$	−1.26656	+	7.00489i	−0.163513	+	0.904327i
$61$	6.71487	+	2.78139i	0.859751	+	0.356121i	0.768610	−	0.639717i	$-0.220949\pi$
$61$	6.71487	+	2.78139i	0.859751	+	0.356121i	0.0911409	+	0.995838i	$0.470949\pi$
$62$	0.189643	−	2.11470i	0.0240847	−	0.268567i
$63$	−3.86217			−0.486587
$64$	−6.87546	−	4.08999i	−0.859433	−	0.511249i
$65$	8.67291			1.07574
$66$	0.412377	−	4.59838i	0.0507601	−	0.566022i
$67$	11.1312	+	4.61070i	1.35989	+	0.563286i	0.939029	−	0.343837i	$-0.111727\pi$
$67$	11.1312	+	4.61070i	1.35989	+	0.563286i	0.420864	+	0.907124i	$0.361727\pi$
$68$	0.184136	−	1.01839i	0.0223298	−	0.123497i
$69$	−1.29774	−	3.13303i	−0.156230	−	0.377172i
$70$	9.01398	−	17.2242i	1.07738	−	2.05869i
$71$	1.86620	−	1.86620i	0.221477	−	0.221477i	−0.587643	−	0.809120i	$-0.699944\pi$
$71$	1.86620	−	1.86620i	0.221477	−	0.221477i	0.809120	+	0.587643i	$0.199944\pi$
$72$	2.45866	−	1.39822i	0.289756	−	0.164781i
$73$	−9.06859	−	9.06859i	−1.06140	−	1.06140i	−0.997988	−	0.0634101i	$-0.979802\pi$
$73$	−9.06859	−	9.06859i	−1.06140	−	1.06140i	−0.0634101	−	0.997988i	$-0.520198\pi$
$74$	12.0201	−	3.76123i	1.39731	−	0.437234i
$75$	7.08445	−	2.93447i	0.818042	−	0.338844i
$76$	−4.31822	+	6.71367i	−0.495333	+	0.770111i
$77$	−4.82504	+	11.6487i	−0.549864	+	1.32749i
$78$	−2.20935	−	2.64465i	−0.250159	−	0.299447i
$79$		−	10.4412i		−	1.17473i	−0.809323	−	0.587364i	$-0.800166\pi$
$79$		−	10.4412i		−	1.17473i	0.809323	−	0.587364i	$-0.199834\pi$
$80$	0.497353	+	14.2282i	0.0556058	+	1.59077i
$81$			1.00000i			0.111111i
$82$	4.93702	−	4.12441i	0.545203	−	0.455464i
$83$	−1.89340	+	4.57106i	−0.207827	+	0.501739i	−0.993081	−	0.117435i	$-0.962533\pi$
$83$	−1.89340	+	4.57106i	−0.207827	+	0.501739i	0.785253	+	0.619175i	$0.212533\pi$
$84$	−7.54843	+	1.63906i	−0.823602	+	0.178836i
$85$	−1.70153	+	0.704798i	−0.184557	+	0.0764460i
$86$	−0.600420	−	1.91882i	−0.0647449	−	0.206911i
$87$	−5.42688	−	5.42688i	−0.581823	−	0.581823i
$88$	−1.14553	−	9.16234i	−0.122114	−	0.976709i
$89$	−2.70762	+	2.70762i	−0.287007	+	0.287007i	−0.835896	−	0.548888i	$-0.815051\pi$
$89$	−2.70762	+	2.70762i	−0.287007	+	0.287007i	0.548888	+	0.835896i	$0.315051\pi$
$90$	−4.45972	−	2.33392i	−0.470096	−	0.246016i
$91$	3.60147	+	8.69471i	0.377536	+	0.911453i
$92$	−3.86600	−	5.57262i	−0.403059	−	0.580985i
$93$	1.38704	+	0.574529i	0.143829	+	0.0595759i
$94$	−6.58429	−	0.590470i	−0.679117	−	0.0609024i
$95$	14.2058			1.45749
$96$	4.21195	−	3.77618i	0.429880	−	0.385404i
$97$	3.73293			0.379022			0.189511	−	0.981879i	$-0.439310\pi$
$97$	3.73293			0.379022			0.189511	+	0.981879i	$0.439310\pi$
$98$	11.1507	+	0.999977i	1.12639	+	0.101013i
$99$	3.01609	+	1.24931i	0.303129	+	0.125560i
$100$	12.6009	−	8.74186i	1.26009	−	0.874186i
$101$	−6.36949	−	15.3773i	−0.633788	−	1.53010i	−0.834824	−	0.550517i	$-0.814431\pi$
$101$	−6.36949	−	15.3773i	−0.633788	−	1.53010i	0.201036	−	0.979584i	$-0.435569\pi$
$102$	0.648365	+	0.339310i	0.0641977	+	0.0335967i
$103$	−7.42244	+	7.42244i	−0.731355	+	0.731355i	−0.970888	−	0.239533i	$-0.923006\pi$
$103$	−7.42244	+	7.42244i	−0.731355	+	0.731355i	0.239533	+	0.970888i	$0.423006\pi$
$104$	−5.44043	−	4.23122i	−0.533478	−	0.414905i
$105$	9.72015	+	9.72015i	0.948589	+	0.948589i
$106$	−1.91781	−	6.12891i	−0.186274	−	0.595292i
$107$	7.85343	−	3.25300i	0.759220	−	0.314479i	0.0307226	−	0.999528i	$-0.490219\pi$
$107$	7.85343	−	3.25300i	0.759220	−	0.314479i	0.728497	+	0.685049i	$0.240219\pi$
$108$	0.424389	+	1.95445i	0.0408369	+	0.188068i
$109$	3.33028	−	8.04001i	0.318983	−	0.770094i	−0.680325	−	0.732910i	$-0.738161\pi$
$109$	3.33028	−	8.04001i	0.318983	−	0.770094i	0.999308	−	0.0371832i	$-0.0118385\pi$
$110$	−12.6109	+	10.5352i	−1.20240	+	1.00449i
$111$			8.90589i			0.845310i
$112$	−14.0575	+	6.40695i	−1.32831	+	0.605400i
$113$		−	17.4463i		−	1.64121i	−0.571494	−	0.820606i	$-0.693636\pi$
$113$		−	17.4463i		−	1.64121i	0.571494	−	0.820606i	$-0.306364\pi$
$114$	−3.61880	−	4.33180i	−0.338932	−	0.405710i
$115$	−4.61897	+	11.1512i	−0.430721	+	1.03985i
$116$	−12.9097	−	8.30349i	−1.19864	−	0.770959i
$117$	2.25125	−	0.932498i	0.208128	−	0.0862095i
$118$	2.40134	−	0.751408i	0.221062	−	0.0691727i
$119$	−1.41314	−	1.41314i	−0.129542	−	0.129542i
$120$	−9.70682	−	2.66888i	−0.886107	−	0.243634i
$121$	−0.242116	+	0.242116i	−0.0220105	+	0.0220105i
$122$	−4.76597	+	9.10696i	−0.431490	+	0.824506i
$123$	1.74079	+	4.20263i	0.156962	+	0.378939i
$124$	2.95472	+	0.534248i	0.265342	+	0.0479769i
$125$	−8.77369	−	3.63418i	−0.784743	−	0.325051i
$126$	0.487861	−	5.44010i	0.0434621	−	0.484643i
$127$	1.84791			0.163975			0.0819876	−	0.996633i	$-0.473873\pi$
$127$	1.84791			0.163975			0.0819876	+	0.996633i	$0.473873\pi$
$128$	6.62949	−	9.16787i	0.585970	−	0.810333i
$129$	1.42168			0.125172
$130$	−1.09554	+	12.2163i	−0.0960856	+	1.07144i
$131$	−7.59353	−	3.14534i	−0.663450	−	0.274810i	0.0254395	−	0.999676i	$-0.491901\pi$
$131$	−7.59353	−	3.14534i	−0.663450	−	0.274810i	−0.688889	+	0.724866i	$0.741901\pi$
$132$	6.42501	+	1.16172i	0.559226	+	0.101114i
$133$	5.89902	+	14.2415i	0.511510	+	1.23490i
$134$	−7.90052	+	15.0966i	−0.682501	+	1.30415i
$135$	2.51676	−	2.51676i	0.216608	−	0.216608i
$136$	1.41120	+	0.388007i	0.121009	+	0.0332714i
$137$	7.98582	+	7.98582i	0.682274	+	0.682274i	0.960512	−	0.278238i	$-0.0897503\pi$
$137$	7.98582	+	7.98582i	0.682274	+	0.682274i	−0.278238	+	0.960512i	$0.589750\pi$
$138$	4.57699	−	1.43219i	0.389619	−	0.121916i
$139$	1.52261	−	0.630686i	0.129146	−	0.0534941i	−0.317174	−	0.948367i	$-0.602734\pi$
$139$	1.52261	−	0.630686i	0.129146	−	0.0534941i	0.446321	+	0.894873i	$0.352734\pi$
$140$	23.1227	+	14.8725i	1.95423	+	1.25695i
$141$	1.78885	−	4.31865i	0.150648	−	0.363696i
$142$	2.39292	+	2.86439i	0.200809	+	0.240374i
$143$		−	7.95496i		−	0.665227i
$144$	1.65890	+	3.63979i	0.138242	+	0.303316i
$145$			27.3163i			2.26850i
$146$	13.9192	−	11.6281i	1.15196	−	0.962351i
$147$	−3.02945	+	7.31375i	−0.249865	+	0.603228i
$148$	3.77956	+	17.4062i	0.310678	+	1.43078i
$149$	−3.85004	+	1.59474i	−0.315408	+	0.130646i	−0.534771	−	0.844997i	$-0.679602\pi$
$149$	−3.85004	+	1.59474i	−0.315408	+	0.130646i	0.219363	+	0.975643i	$0.429602\pi$
$150$	3.23849	+	10.3496i	0.264422	+	0.845038i
$151$	−0.409447	−	0.409447i	−0.0333203	−	0.0333203i	0.690250	−	0.723571i	$-0.257500\pi$
$151$	−0.409447	−	0.409447i	−0.0333203	−	0.0333203i	−0.723571	+	0.690250i	$0.757500\pi$
$152$	−8.91115	−	6.93053i	−0.722790	−	0.562140i
$153$	−0.365892	+	0.365892i	−0.0295806	+	0.0295806i
$154$	−15.7984	−	8.26779i	−1.27307	−	0.666238i
$155$	−2.04488	−	4.93678i	−0.164249	−	0.396532i
$156$	4.00422	−	2.77793i	0.320595	−	0.222413i
$157$	−12.1456	−	5.03087i	−0.969324	−	0.401507i	−0.158864	−	0.987301i	$-0.550783\pi$
$157$	−12.1456	−	5.03087i	−0.969324	−	0.401507i	−0.810461	+	0.585793i	$0.800783\pi$
$158$	14.7071	+	1.31891i	1.17003	+	0.104927i
$159$	4.54101			0.360125
$160$	−20.1042	−	1.09673i	−1.58937	−	0.0867042i
$161$	−13.0973			−1.03221
$162$	−1.40856	−	0.126318i	−0.110667	−	0.00992448i
$163$	−15.6056	−	6.46405i	−1.22233	−	0.506304i	−0.324177	−	0.945996i	$-0.605087\pi$
$163$	−15.6056	−	6.46405i	−1.22233	−	0.506304i	−0.898148	+	0.439693i	$0.855087\pi$
$164$	5.18584	+	7.47508i	0.404946	+	0.583706i
$165$	−4.44658	−	10.7350i	−0.346166	−	0.835718i
$166$	−6.19945	−	3.24437i	−0.481171	−	0.251812i
$167$	−3.65825	+	3.65825i	−0.283084	+	0.283084i	−0.834338	−	0.551254i	$-0.814150\pi$
$167$	−3.65825	+	3.65825i	−0.283084	+	0.283084i	0.551254	+	0.834338i	$0.314150\pi$
$168$	−1.35522	−	10.8395i	−0.104557	−	0.836283i
$169$	4.99382	+	4.99382i	0.384140	+	0.384140i
$170$	−0.777816	−	2.48574i	−0.0596558	−	0.190648i
$171$	3.68744	−	1.52739i	0.281985	−	0.116802i
$172$	2.77862	−	0.603347i	0.211867	−	0.0460048i
$173$	−4.69766	+	11.3412i	−0.357156	+	0.862252i	0.638541	+	0.769588i	$0.279538\pi$
$173$	−4.69766	+	11.3412i	−0.357156	+	0.862252i	−0.995697	+	0.0926640i	$0.970462\pi$
$174$	8.32961	−	6.95858i	0.631466	−	0.527529i
$175$		−	29.6157i		−	2.23874i
$176$	13.0504	−	0.456182i	0.983712	−	0.0343860i
$177$			1.77919i			0.133732i
$178$	−3.47183	−	4.15587i	−0.260224	−	0.311496i
$179$	2.26551	−	5.46943i	0.169332	−	0.408804i	−0.816318	−	0.577602i	$-0.803989\pi$
$179$	2.26551	−	5.46943i	0.169332	−	0.408804i	0.985651	+	0.168798i	$0.0539885\pi$
$180$	3.85081	−	5.98698i	0.287022	−	0.446243i
$181$	−14.5765	+	6.03777i	−1.08346	+	0.448784i	−0.851722	−	0.523994i	$-0.824441\pi$
$181$	−14.5765	+	6.03777i	−1.08346	+	0.448784i	−0.231738	+	0.972778i	$0.574441\pi$
$182$	−12.7020	+	3.97459i	−0.941531	+	0.294616i
$183$	−5.13934	−	5.13934i	−0.379911	−	0.379911i
$184$	8.33772	−	4.74158i	0.614665	−	0.349554i
$185$	22.4140	−	22.4140i	1.64791	−	1.64791i
$186$	−0.984466	+	1.88115i	−0.0721846	+	0.137933i
$187$	0.646454	+	1.56068i	0.0472734	+	0.114128i
$188$	1.66343	−	9.19978i	0.121318	−	0.670963i
$189$	3.56818	+	1.47799i	0.259547	+	0.107508i
$190$	−1.79445	+	20.0097i	−0.130183	+	1.45166i
$191$	−12.3765			−0.895535			−0.447768	−	0.894150i	$-0.647781\pi$
$191$	−12.3765			−0.895535			−0.447768	+	0.894150i	$0.647781\pi$
$192$	4.78693	+	6.40978i	0.345467	+	0.462586i
$193$	21.9343			1.57887			0.789434	−	0.613835i	$-0.210374\pi$
$193$	21.9343			1.57887			0.789434	+	0.613835i	$0.210374\pi$
$194$	−0.471536	+	5.25806i	−0.0338543	+	0.377507i
$195$	−8.01273	−	3.31898i	−0.573803	−	0.237677i
$196$	−2.81706	+	15.5801i	−0.201218	+	1.11286i
$197$	6.52756	+	15.7589i	0.465070	+	1.12278i	0.966290	+	0.257458i	$0.0828847\pi$
$197$	6.52756	+	15.7589i	0.465070	+	1.12278i	−0.501220	+	0.865320i	$0.667115\pi$
$198$	−2.14071	+	4.09054i	−0.152134	+	0.290702i
$199$	5.80270	−	5.80270i	0.411343	−	0.411343i	−0.470863	−	0.882206i	$-0.656058\pi$
$199$	5.80270	−	5.80270i	0.411343	−	0.411343i	0.882206	+	0.470863i	$0.156058\pi$
$200$	10.7217	+	18.8534i	0.758141	+	1.33313i
$201$	−8.51946	−	8.51946i	−0.600916	−	0.600916i
$202$	22.4645	−	7.02939i	1.58059	−	0.494586i
$203$	−27.3850	+	11.3432i	−1.92205	+	0.796138i
$204$	−0.559839	+	0.870400i	−0.0391966	+	0.0609402i
$205$	6.19587	−	14.9582i	0.432738	−	1.04472i
$206$	−9.51738	−	11.3926i	−0.663107	−	0.793757i
$207$			3.39117i			0.235702i
$208$	6.64715	−	7.12869i	0.460897	−	0.494286i
$209$		−	13.0298i		−	0.901293i
$210$	−14.9192	+	12.4636i	−1.02953	+	0.860069i
$211$	7.65444	−	18.4794i	0.526953	−	1.27218i	−0.406557	−	0.913626i	$-0.633271\pi$
$211$	7.65444	−	18.4794i	0.526953	−	1.27218i	0.933510	−	0.358552i	$-0.116729\pi$
$212$	8.87519	−	1.92715i	0.609551	−	0.132357i
$213$	−2.43831	+	1.00998i	−0.167070	+	0.0692026i
$214$	3.59002	+	11.4729i	0.245408	+	0.784274i
$215$	−3.57803	−	3.57803i	−0.244020	−	0.244020i
$216$	−2.80658	+	0.350895i	−0.190963	+	0.0238754i
$217$	4.10004	−	4.10004i	0.278329	−	0.278329i
$218$	10.9042	+	5.70650i	0.738524	+	0.386493i
$219$	4.90788	+	11.8487i	0.331644	+	0.800659i
$220$	−13.2464	−	19.0940i	−0.893075	−	1.28732i
$221$	1.16491	+	0.482521i	0.0783602	+	0.0324579i
$222$	−12.5445	−	1.12497i	−0.841931	−	0.0755033i
$223$	−29.0773			−1.94716			−0.973580	−	0.228346i	$-0.926668\pi$
$223$	−29.0773			−1.94716			−0.973580	+	0.228346i	$0.926668\pi$
$224$	−7.24886	−	20.6101i	−0.484335	−	1.37707i
$225$	−7.66815			−0.511210
$226$	24.5742	+	2.20379i	1.63465	+	0.146594i
$227$	23.2583	+	9.63391i	1.54371	+	0.639425i	0.982165	−	0.188022i	$-0.0602077\pi$
$227$	23.2583	+	9.63391i	1.54371	+	0.639425i	0.561544	+	0.827447i	$0.310208\pi$
$228$	6.55872	−	4.55012i	0.434362	−	0.301339i
$229$	2.92749	+	7.06760i	0.193454	+	0.467040i	0.990607	−	0.136737i	$-0.0436616\pi$
$229$	2.92749	+	7.06760i	0.193454	+	0.467040i	−0.797153	+	0.603777i	$0.793662\pi$
$230$	−15.1237	−	7.91470i	−0.997225	−	0.521880i
$231$	8.91550	−	8.91550i	0.586597	−	0.586597i
$232$	13.3267	−	17.1352i	0.874940	−	1.12498i
$233$	13.0873	+	13.0873i	0.857375	+	0.857375i	0.991028	−	0.133653i	$-0.0426708\pi$
$233$	13.0873	+	13.0873i	0.857375	+	0.857375i	−0.133653	+	0.991028i	$0.542671\pi$
$234$	1.02911	+	3.28881i	0.0672748	+	0.214996i
$235$	−15.3711	+	6.36692i	−1.00270	+	0.415332i
$236$	0.755070	+	3.47735i	0.0491509	+	0.226356i
$237$	−3.99568	+	9.64642i	−0.259547	+	0.626602i
$238$	2.16899	−	1.81199i	0.140595	−	0.117454i
$239$			4.10909i			0.265795i	0.991130	+	0.132897i	$0.0424281\pi$
$239$			4.10909i			0.265795i	−0.991130	+	0.132897i	$0.957572\pi$
$240$	4.98542	−	13.3355i	0.321808	−	0.860804i
$241$			14.2144i			0.915632i	0.889047	+	0.457816i	$0.151368\pi$
$241$			14.2144i			0.915632i	−0.889047	+	0.457816i	$0.848632\pi$
$242$	−0.310451	−	0.371618i	−0.0199566	−	0.0238885i
$243$	0.382683	−	0.923880i	0.0245492	−	0.0592669i
$244$	−12.2257	−	7.86353i	−0.782669	−	0.503411i
$245$	26.0314	−	10.7825i	1.66308	−	0.688871i
$246$	−6.13956	+	1.92114i	−0.391444	+	0.122487i
$247$	−6.87706	−	6.87706i	−0.437577	−	0.437577i
$248$	−1.12576	+	4.09442i	−0.0714855	+	0.259996i
$249$	3.49854	−	3.49854i	0.221711	−	0.221711i
$250$	6.22724	−	11.8992i	0.393845	−	0.752573i
$251$	2.36893	+	5.71910i	0.149525	+	0.360986i	0.980840	−	0.194816i	$-0.0624110\pi$
$251$	2.36893	+	5.71910i	0.149525	+	0.360986i	−0.831314	+	0.555803i	$0.812411\pi$
$252$	7.60109	+	1.37436i	0.478823	+	0.0865768i
$253$	10.2281	+	4.23661i	0.643034	+	0.266353i
$254$	−0.233424	+	2.60289i	−0.0146463	+	0.163320i
$255$	1.84172			0.115333
$256$	12.0761	+	10.4961i	0.754755	+	0.656007i
$257$	−8.28191			−0.516612			−0.258306	−	0.966063i	$-0.583164\pi$
$257$	−8.28191			−0.516612			−0.258306	+	0.966063i	$0.583164\pi$
$258$	−0.179584	+	2.00253i	−0.0111804	+	0.124672i
$259$	31.7778	+	13.1628i	1.97458	+	0.817896i
$260$	−17.0691	−	3.08628i	−1.05858	−	0.191403i
$261$	2.93701	+	7.09056i	0.181796	+	0.438895i
$262$	5.38961	−	10.2986i	0.332971	−	0.636252i
$263$	15.4068	−	15.4068i	0.950023	−	0.950023i	−0.0487861	−	0.998809i	$-0.515535\pi$
$263$	15.4068	−	15.4068i	0.950023	−	0.950023i	0.998809	+	0.0487861i	$0.0155353\pi$
$264$	−2.44794	+	8.90328i	−0.150661	+	0.547959i
$265$	−11.4286	−	11.4286i	−0.702055	−	0.702055i
$266$	−20.8052	+	6.51018i	−1.27565	+	0.399165i
$267$	3.53768	−	1.46535i	0.216502	−	0.0896782i
$268$	−20.2665	−	13.0353i	−1.23797	−	0.796260i
$269$	−3.09893	+	7.48148i	−0.188945	+	0.456154i	−0.989757	−	0.142762i	$-0.954402\pi$
$269$	−3.09893	+	7.48148i	−0.188945	+	0.456154i	0.800812	+	0.598916i	$0.204402\pi$
$270$	3.22710	+	3.86292i	0.196395	+	0.235090i
$271$			28.7832i			1.74846i	0.485515	+	0.874228i	$0.338632\pi$
$271$			28.7832i			1.74846i	−0.485515	+	0.874228i	$0.661368\pi$
$272$	−0.724792	+	1.93875i	−0.0439470	+	0.117554i
$273$		−	9.41108i		−	0.569585i
$274$	−12.2573	+	10.2398i	−0.740488	+	0.618606i
$275$	−9.57988	+	23.1279i	−0.577688	+	1.39466i
$276$	1.43917	+	6.62788i	0.0866281	+	0.398952i
$277$	−12.1515	+	5.03333i	−0.730115	+	0.302424i	−0.716599	−	0.697485i	$-0.754302\pi$
$277$	−12.1515	+	5.03333i	−0.730115	+	0.302424i	−0.0135158	+	0.999909i	$0.504302\pi$
$278$	0.696026	+	2.22436i	0.0417449	+	0.133408i
$279$	−1.06159	−	1.06159i	−0.0635558	−	0.0635558i
$280$	−23.8696	+	30.6911i	−1.42648	+	1.83414i
$281$	−21.6306	+	21.6306i	−1.29037	+	1.29037i	−0.355820	+	0.934555i	$0.615798\pi$
$281$	−21.6306	+	21.6306i	−1.29037	+	1.29037i	−0.934555	+	0.355820i	$0.884202\pi$
$282$	5.85712	+	3.06522i	0.348787	+	0.182531i
$283$	−11.4777	−	27.7097i	−0.682281	−	1.64717i	−0.759781	−	0.650179i	$-0.774694\pi$
$283$	−11.4777	−	27.7097i	−0.682281	−	1.64717i	0.0775002	−	0.996992i	$-0.475306\pi$
$284$	−4.33693	+	3.00875i	−0.257350	+	0.178536i
$285$	−13.1245	−	5.43633i	−0.777426	−	0.322020i
$286$	11.2050	+	1.00485i	0.662568	+	0.0594183i
$287$	17.5686			1.03704
$288$	−5.33641	+	1.87689i	−0.314451	+	0.110597i
$289$	16.7322			0.984250
$290$	−38.4767	−	3.45054i	−2.25943	−	0.202623i
$291$	−3.44878	−	1.42853i	−0.202171	−	0.0837420i
$292$	14.6207	+	21.0749i	0.855611	+	1.23331i
$293$	−1.84257	−	4.44836i	−0.107644	−	0.259876i	0.860874	−	0.508818i	$-0.169917\pi$
$293$	−1.84257	−	4.44836i	−0.107644	−	0.259876i	−0.968519	+	0.248942i	$0.919917\pi$
$294$	−9.91919	−	5.19103i	−0.578499	−	0.302747i
$295$	4.47780	−	4.47780i	0.260708	−	0.260708i
$296$	−24.9951	+	3.12503i	−1.45281	+	0.181639i
$297$	−2.30842	−	2.30842i	−0.133948	−	0.133948i
$298$	−1.75996	−	5.62447i	−0.101952	−	0.325817i
$299$	7.63436	−	3.16226i	0.441507	−	0.182878i
$300$	−14.9871	+	3.25428i	−0.865278	+	0.187886i
$301$	2.10123	−	5.07282i	0.121113	−	0.292392i
$302$	0.628451	−	0.525010i	0.0361633	−	0.0302110i
$303$			16.6443i			0.956190i
$304$	10.8877	−	11.6764i	0.624453	−	0.669690i
$305$			25.8690i			1.48125i
$306$	−0.469163	−	0.561600i	−0.0268202	−	0.0321045i
$307$	11.7403	−	28.3435i	0.670052	−	1.61765i	−0.111467	−	0.993768i	$-0.535555\pi$
$307$	11.7403	−	28.3435i	0.670052	−	1.61765i	0.781519	−	0.623881i	$-0.214445\pi$
$308$	13.6413	−	21.2086i	0.777286	−	1.20847i
$309$	9.69789	−	4.01700i	0.551694	−	0.228519i
$310$	7.21207	−	2.25674i	0.409618	−	0.128174i
$311$	11.6121	+	11.6121i	0.658459	+	0.658459i	0.955015	−	0.296556i	$-0.0958382\pi$
$311$	11.6121	+	11.6121i	0.658459	+	0.658459i	−0.296556	+	0.955015i	$0.595838\pi$
$312$	3.40708	+	5.99110i	0.192888	+	0.339179i
$313$	−6.84409	+	6.84409i	−0.386851	+	0.386851i	−0.873563	−	0.486712i	$-0.838196\pi$
$313$	−6.84409	+	6.84409i	−0.386851	+	0.386851i	0.486712	+	0.873563i	$0.338196\pi$
$314$	8.62050	−	16.4723i	0.486483	−	0.929587i
$315$	−5.26051	−	12.7000i	−0.296396	−	0.715563i
$316$	−3.71554	+	20.5492i	−0.209015	+	1.15598i
$317$	−23.6795	−	9.80835i	−1.32997	−	0.550892i	−0.399324	−	0.916810i	$-0.630755\pi$
$317$	−23.6795	−	9.80835i	−1.32997	−	0.550892i	−0.930647	+	0.365918i	$0.880755\pi$
$318$	−0.573611	+	6.39629i	−0.0321665	+	0.358686i
$319$	25.0550			1.40281
$320$	4.08433	−	28.1794i	0.228321	−	1.57528i
$321$	−8.50049			−0.474451
$322$	1.65442	−	18.4483i	0.0921972	−	1.02808i
$323$	1.90806	+	0.790346i	0.106167	+	0.0439760i
$324$	0.355853	−	1.96809i	0.0197696	−	0.109338i
$325$	7.15054	+	17.2629i	0.396640	+	0.957575i
$326$	11.0763	−	21.1649i	0.613458	−	1.17222i
$327$	−6.15356	+	6.15356i	−0.340293	+	0.340293i
$328$	−11.1842	+	6.36034i	−0.617543	+	0.351191i
$329$	−12.7658	−	12.7658i	−0.703803	−	0.703803i
$330$	15.6826	−	4.90725i	0.863297	−	0.270135i
$331$	−21.7107	+	8.99285i	−1.19333	+	0.494292i	−0.888837	−	0.458224i	$-0.848486\pi$
$331$	−21.7107	+	8.99285i	−1.19333	+	0.494292i	−0.304489	+	0.952516i	$0.598486\pi$
$332$	5.35300	−	8.32248i	0.293784	−	0.456755i
$333$	3.40814	−	8.22797i	0.186765	−	0.450890i
$334$	−4.69076	−	5.61497i	−0.256667	−	0.307237i
$335$			42.8828i			2.34294i
$336$	15.4392	−	0.539684i	0.842280	−	0.0294422i
$337$		−	24.2394i		−	1.32040i	−0.751088	−	0.660202i	$-0.770471\pi$
$337$		−	24.2394i		−	1.32040i	0.751088	−	0.660202i	$-0.229529\pi$
$338$	−7.66490	+	6.40328i	−0.416916	+	0.348293i
$339$	−6.67642	+	16.1183i	−0.362613	+	0.875426i
$340$	3.59957	−	0.781608i	0.195214	−	0.0423886i
$341$	−4.52811	+	1.87561i	−0.245211	+	0.101570i
$342$	1.68563	+	5.38692i	0.0911483	+	0.291291i
$343$	2.50251	+	2.50251i	0.135123	+	0.135123i
$344$	0.498862	+	3.99006i	0.0268968	+	0.215130i
$345$	8.53475	−	8.53475i	0.459495	−	0.459495i
$346$	−15.3813	−	8.04953i	−0.826904	−	0.432745i
$347$	−1.42236	−	3.43389i	−0.0763565	−	0.184341i	0.881092	−	0.472945i	$-0.156809\pi$
$347$	−1.42236	−	3.43389i	−0.0763565	−	0.184341i	−0.957449	+	0.288604i	$0.906809\pi$
$348$	8.74941	+	12.6118i	0.469017	+	0.676061i
$349$	3.17452	+	1.31493i	0.169928	+	0.0703866i	0.466026	−	0.884771i	$-0.345685\pi$
$349$	3.17452	+	1.31493i	0.169928	+	0.0703866i	−0.296098	+	0.955158i	$0.595685\pi$
$350$	41.7155	+	3.74099i	2.22979	+	0.199965i
$351$	−2.43674			−0.130063
$352$	−1.00594	+	18.4399i	−0.0536169	+	0.982852i
$353$	−7.88845			−0.419860			−0.209930	−	0.977716i	$-0.567324\pi$
$353$	−7.88845			−0.419860			−0.209930	+	0.977716i	$0.567324\pi$
$354$	−2.50610	−	0.224744i	−0.133198	−	0.0119450i
$355$	8.67850	+	3.59475i	0.460607	+	0.190790i
$356$	6.29235	−	4.36532i	0.333494	−	0.231361i
$357$	0.764784	+	1.84635i	0.0404767	+	0.0977193i
$358$	7.41785	+	3.88200i	0.392045	+	0.205170i
$359$	−2.60336	+	2.60336i	−0.137400	+	0.137400i	−0.772462	−	0.635062i	$-0.780975\pi$
$359$	−2.60336	+	2.60336i	−0.137400	+	0.137400i	0.635062	+	0.772462i	$0.280975\pi$
$360$	7.94660	+	6.18036i	0.418822	+	0.325734i
$361$	2.17074	+	2.17074i	0.114250	+	0.114250i
$362$	−6.66330	−	21.2945i	−0.350215	−	1.11922i
$363$	0.316339	−	0.131032i	0.0166035	−	0.00687740i
$364$	−3.99396	−	18.3935i	−0.209340	−	0.964083i
$365$	17.4683	−	42.1722i	0.914333	−	2.20740i
$366$	7.88826	−	6.58988i	0.412326	−	0.344459i
$367$			1.41682i			0.0739575i	0.999316	+	0.0369787i	$0.0117734\pi$
$367$			1.41682i			0.0739575i	−0.999316	+	0.0369787i	$0.988227\pi$
$368$	5.62560	+	12.3431i	0.293255	+	0.643430i
$369$		−	4.54890i		−	0.236806i
$370$	28.7402	+	34.4027i	1.49413	+	1.78851i
$371$	6.71155	−	16.2031i	0.348447	−	0.841224i
$372$	−2.52536	−	1.62430i	−0.130934	−	0.0842162i
$373$	30.8483	−	12.7778i	1.59726	−	0.661609i	0.606239	−	0.795282i	$-0.292677\pi$
$373$	30.8483	−	12.7778i	1.59726	−	0.661609i	0.991025	+	0.133674i	$0.0426774\pi$
$374$	−2.27997	+	0.713428i	−0.117894	+	0.0368905i
$375$	6.71510	+	6.71510i	0.346766	+	0.346766i
$376$	12.7483	+	3.50514i	0.657445	+	0.180764i
$377$	13.2239	−	13.2239i	0.681064	−	0.681064i
$378$	−2.53256	+	4.83930i	−0.130261	+	0.248907i
$379$	−4.79982	−	11.5878i	−0.246550	−	0.595224i	0.751357	−	0.659896i	$-0.229400\pi$
$379$	−4.79982	−	11.5878i	−0.246550	−	0.595224i	−0.997907	+	0.0646720i	$0.979400\pi$
$380$	−27.9583	−	5.05518i	−1.43423	−	0.259325i
$381$	−1.70724	−	0.707163i	−0.0874647	−	0.0362291i
$382$	1.56338	−	17.4331i	0.0799895	−	0.891956i
$383$	−13.2502			−0.677053			−0.338527	−	0.940957i	$-0.609929\pi$
$383$	−13.2502			−0.677053			−0.338527	+	0.940957i	$0.609929\pi$
$384$	−9.63324	+	5.93301i	−0.491594	+	0.302768i
$385$	−44.8763			−2.28711
$386$	−2.77070	+	30.8959i	−0.141025	+	1.57256i
$387$	−1.31346	−	0.544054i	−0.0667671	−	0.0276558i
$388$	−7.34674	−	1.32838i	−0.372974	−	0.0674380i
$389$	−1.30717	−	3.15579i	−0.0662762	−	0.160005i	0.887271	−	0.461248i	$-0.152598\pi$
$389$	−1.30717	−	3.15579i	−0.0662762	−	0.160005i	−0.953547	+	0.301243i	$0.902598\pi$
$390$	5.68714	−	10.8672i	0.287979	−	0.550280i
$391$	−1.24080	+	1.24080i	−0.0627500	+	0.0627500i
$392$	−21.5896	−	5.93604i	−1.09044	−	0.299815i
$393$	5.81184	+	5.81184i	0.293168	+	0.293168i
$394$	−23.0220	+	7.20383i	−1.15983	+	0.362924i
$395$	34.3339	−	14.2215i	1.72752	−	0.715564i
$396$	−5.49137	−	3.53203i	−0.275952	−	0.177491i
$397$	−2.75561	+	6.65262i	−0.138300	+	0.333886i	−0.977821	−	0.209441i	$-0.932836\pi$
$397$	−2.75561	+	6.65262i	−0.138300	+	0.333886i	0.839521	+	0.543327i	$0.182836\pi$
$398$	7.44047	+	8.90645i	0.372957	+	0.446440i
$399$		−	15.4149i		−	0.771710i
$400$	−27.9104	+	12.7207i	−1.39552	+	0.636034i
$401$			22.5969i			1.12844i	0.825626	+	0.564218i	$0.190822\pi$
$401$			22.5969i			1.12844i	−0.825626	+	0.564218i	$0.809178\pi$
$402$	13.0763	−	10.9240i	0.652188	−	0.544840i
$403$	−1.39997	+	3.37984i	−0.0697377	+	0.168362i
$404$	7.06366	+	32.5305i	0.351430	+	1.61845i
$405$	−3.28830	+	1.36206i	−0.163397	+	0.0676813i
$406$	−12.5184	−	40.0062i	−0.621278	−	1.98548i
$407$	−20.5585	−	20.5585i	−1.01905	−	1.01905i
$408$	−1.15529	−	0.898515i	−0.0571956	−	0.0444831i
$409$	−3.48618	+	3.48618i	−0.172380	+	0.172380i	−0.788024	−	0.615644i	$-0.788896\pi$
$409$	−3.48618	+	3.48618i	−0.172380	+	0.172380i	0.615644	+	0.788024i	$0.288896\pi$
$410$	20.2868	+	10.6167i	1.00189	+	0.524324i
$411$	−4.32189	−	10.4340i	−0.213183	−	0.514670i
$412$	17.2493	−	11.9667i	0.849813	−	0.589558i
$413$	6.34848	+	2.62963i	0.312388	+	0.129395i
$414$	−4.77666	−	0.428365i	−0.234760	−	0.0210530i
$415$	−17.6100			−0.864439
$416$	9.20154	+	10.2634i	0.451143	+	0.503205i
$417$	−1.64806			−0.0807059
$418$	18.3533	+	1.64590i	0.897690	+	0.0805037i
$419$	9.10369	+	3.77087i	0.444744	+	0.184219i	0.593805	−	0.804609i	$-0.297625\pi$
$419$	9.10369	+	3.77087i	0.444744	+	0.184219i	−0.149061	+	0.988828i	$0.547625\pi$
$420$	−15.6712	−	22.5890i	−0.764674	−	1.10223i
$421$	−0.766817	−	1.85126i	−0.0373724	−	0.0902249i	0.904091	−	0.427339i	$-0.140549\pi$
$421$	−0.766817	−	1.85126i	−0.0373724	−	0.0902249i	−0.941464	+	0.337114i	$0.890549\pi$
$422$	25.0625	+	13.1160i	1.22002	+	0.638478i
$423$	−3.30535	+	3.30535i	−0.160712	+	0.160712i
$424$	1.59342	+	12.7447i	0.0773832	+	0.618937i
$425$	−2.80572	−	2.80572i	−0.136097	−	0.136097i
$426$	−1.11462	−	3.56208i	−0.0540033	−	0.172583i
$427$	−25.9340	+	10.7422i	−1.25503	+	0.519851i
$428$	−16.6138	+	3.60752i	−0.803060	+	0.174376i
$429$	−3.04423	+	7.34942i	−0.146977	+	0.354834i
$430$	5.49185	−	4.58791i	0.264840	−	0.221249i
$431$		−	11.5510i		−	0.556394i	−0.960524	−	0.278197i	$-0.910263\pi$
$431$		−	11.5510i		−	0.556394i	0.960524	−	0.278197i	$-0.0897368\pi$
$432$	−0.139736	−	3.99756i	−0.00672305	−	0.192333i
$433$			3.12797i			0.150321i	0.997171	+	0.0751603i	$0.0239468\pi$
$433$			3.12797i			0.150321i	−0.997171	+	0.0751603i	$0.976053\pi$
$434$	5.25725	+	6.29307i	0.252356	+	0.302077i
$435$	10.4535	−	25.2370i	0.501207	−	1.21002i
$436$	−9.41535	+	14.6384i	−0.450914	+	0.701050i
$437$	12.5047	−	5.17962i	0.598182	−	0.247775i
$438$	−17.3095	+	5.41635i	−0.827082	+	0.258803i
$439$	8.10867	+	8.10867i	0.387006	+	0.387006i	0.873618	−	0.486612i	$-0.161768\pi$
$439$	8.10867	+	8.10867i	0.387006	+	0.387006i	−0.486612	+	0.873618i	$0.661768\pi$
$440$	28.5683	−	16.2465i	1.36194	−	0.774522i
$441$	5.59770	−	5.59770i	0.266557	−	0.266557i
$442$	−0.826809	+	1.57989i	−0.0393273	+	0.0751479i
$443$	9.34973	+	22.5722i	0.444219	+	1.07244i	0.974454	+	0.224588i	$0.0721037\pi$
$443$	9.34973	+	22.5722i	0.444219	+	1.07244i	−0.530235	+	0.847851i	$0.677896\pi$
$444$	3.16919	−	17.5276i	0.150403	−	0.831822i
$445$	−12.5914	−	5.21554i	−0.596891	−	0.247240i
$446$	3.67299	−	40.9571i	0.173921	−	1.93938i
$447$	4.16726			0.197105
$448$	29.9463	−	7.60704i	1.41483	−	0.359399i
$449$	−28.6259			−1.35094			−0.675469	−	0.737388i	$-0.736059\pi$
$449$	−28.6259			−1.35094			−0.675469	+	0.737388i	$0.736059\pi$
$450$	0.968625	−	10.8011i	0.0456614	−	0.509167i
$451$	−13.7199	−	5.68297i	−0.646045	−	0.267601i
$452$	−6.20833	+	34.3359i	−0.292015	+	1.61503i
$453$	0.221591	+	0.534968i	0.0104113	+	0.0251350i
$454$	−16.5079	+	31.5438i	−0.774754	+	1.48042i
$455$	−23.6854	+	23.6854i	−1.11039	+	1.11039i
$456$	5.58063	+	9.81312i	0.261337	+	0.459542i
$457$	−18.7182	−	18.7182i	−0.875602	−	0.875602i	0.117474	−	0.993076i	$-0.462520\pi$
$457$	−18.7182	−	18.7182i	−0.875602	−	0.875602i	−0.993076	+	0.117474i	$0.962520\pi$
$458$	−10.3249	+	3.23079i	−0.482452	+	0.150965i
$459$	0.478061	−	0.198019i	0.0223140	−	0.00924275i
$460$	13.0587	−	20.3028i	0.608866	−	0.946625i
$461$	2.60820	−	6.29674i	0.121476	−	0.293268i	−0.851431	−	0.524467i	$-0.824265\pi$
$461$	2.60820	−	6.29674i	0.121476	−	0.293268i	0.972907	+	0.231198i	$0.0742647\pi$
$462$	11.4318	+	13.6842i	0.531857	+	0.636647i
$463$			5.96406i			0.277174i	0.990350	+	0.138587i	$0.0442560\pi$
$463$			5.96406i			0.277174i	−0.990350	+	0.138587i	$0.955744\pi$
$464$	22.4526	+	20.9359i	1.04234	+	0.971927i
$465$			5.34354i			0.247801i
$466$	−20.0874	+	16.7811i	−0.930529	+	0.777367i
$467$	8.88493	−	21.4501i	0.411146	−	0.992593i	−0.573685	−	0.819076i	$-0.694487\pi$
$467$	8.88493	−	21.4501i	0.411146	−	0.992593i	0.984831	−	0.173518i	$-0.0555133\pi$
$468$	−4.76249	+	1.03412i	−0.220146	+	0.0478024i
$469$	−42.9906	+	17.8073i	−1.98512	+	0.822264i
$470$	−7.02655	−	22.4554i	−0.324110	−	1.03579i
$471$	9.29584	+	9.29584i	0.428330	+	0.428330i
$472$	−4.99344	+	0.624310i	−0.229842	+	0.0287362i
$473$	−3.28184	+	3.28184i	−0.150899	+	0.150899i
$474$	−13.0828	−	6.84667i	−0.600915	−	0.314478i
$475$	11.7122	+	28.2758i	0.537394	+	1.29738i
$476$	2.27831	+	3.28405i	0.104426	+	0.150524i
$477$	−4.19534	−	1.73777i	−0.192092	−	0.0795669i
$478$	−5.78790	−	0.519052i	−0.264733	−	0.0237409i
$479$	−22.6413			−1.03451			−0.517254	−	0.855832i	$-0.673046\pi$
$479$	−22.6413			−1.03451			−0.517254	+	0.855832i	$0.673046\pi$
$480$	18.1541	+	8.70678i	0.828619	+	0.397408i
$481$	−21.7013			−0.989494
$482$	−20.0219	−	1.79554i	−0.911972	−	0.0817845i
$483$	12.1003	+	5.01210i	0.550582	+	0.228059i
$484$	0.562662	−	0.390347i	0.0255756	−	0.0177431i
$485$	5.08448	+	12.2750i	0.230874	+	0.557380i
$486$	1.25300	+	0.655736i	0.0568373	+	0.0297448i
$487$	2.79015	−	2.79015i	0.126434	−	0.126434i	−0.641058	−	0.767492i	$-0.721504\pi$
$487$	2.79015	−	2.79015i	0.126434	−	0.126434i	0.767492	+	0.641058i	$0.221504\pi$
$488$	12.6206	−	16.2273i	0.571307	−	0.734576i
$489$	11.9440	+	11.9440i	0.540127	+	0.540127i
$490$	11.8996	+	38.0288i	0.537571	+	1.71796i
$491$	19.9243	−	8.25292i	0.899172	−	0.372449i	0.115270	−	0.993334i	$-0.463227\pi$
$491$	19.9243	−	8.25292i	0.899172	−	0.372449i	0.783902	+	0.620885i	$0.213227\pi$
$492$	−1.93050	−	8.89061i	−0.0870338	−	0.400820i
$493$	−1.51975	+	3.66901i	−0.0684463	+	0.165244i
$494$	10.5555	−	8.81806i	0.474912	−	0.396743i
$495$			11.6195i			0.522256i
$496$	−5.62504	−	2.10289i	−0.252572	−	0.0944227i
$497$			10.1930i			0.457221i
$498$	4.48598	+	5.36983i	0.201021	+	0.240628i
$499$	−14.7704	+	35.6588i	−0.661212	+	1.59631i	0.134695	+	0.990887i	$0.456995\pi$
$499$	−14.7704	+	35.6588i	−0.661212	+	1.59631i	−0.795907	+	0.605419i	$0.793005\pi$
$500$	15.9742	+	10.2745i	0.714386	+	0.459491i
$501$	4.77973	−	1.97983i	0.213543	−	0.0884523i
$502$	−8.35494	+	2.61436i	−0.372899	+	0.116684i
$503$	−26.5194	−	26.5194i	−1.18244	−	1.18244i	−0.979110	−	0.203333i	$-0.934823\pi$
$503$	−26.5194	−	26.5194i	−1.18244	−	1.18244i	−0.203333	−	0.979110i	$-0.565177\pi$
$504$	−2.89603	+	10.5330i	−0.128999	+	0.469176i
$505$	41.8897	−	41.8897i	1.86407	−	1.86407i
$506$	−7.25951	+	13.8717i	−0.322725	+	0.616673i
$507$	−2.70263	−	6.52473i	−0.120028	−	0.289774i
$508$	−3.63684	−	0.657583i	−0.161359	−	0.0291755i
$509$	33.0361	+	13.6840i	1.46430	+	0.606534i	0.965551	−	0.260212i	$-0.0837926\pi$
$509$	33.0361	+	13.6840i	1.46430	+	0.606534i	0.498750	+	0.866746i	$0.333793\pi$
$510$	−0.232643	+	2.59418i	−0.0103016	+	0.114872i
$511$	49.5320			2.19117
$512$	−16.3098	+	15.6840i	−0.720800	+	0.693143i
$513$	−3.99125			−0.176218
$514$	1.04615	−	11.6656i	0.0461439	−	0.514547i
$515$	−34.5171	−	14.2974i	−1.52100	−	0.630020i
$516$	−2.79800	−	0.505910i	−0.123175	−	0.0222715i
$517$	5.83986	+	14.0987i	0.256837	+	0.620059i
$518$	−22.5547	+	43.0983i	−0.990997	+	1.89363i
$519$	8.68014	−	8.68014i	0.381016	−	0.381016i
$520$	6.50335	−	23.6529i	0.285191	−	1.03725i
$521$	−2.51581	−	2.51581i	−0.110220	−	0.110220i	0.649846	−	0.760066i	$-0.274833\pi$
$521$	−2.51581	−	2.51581i	−0.110220	−	0.110220i	−0.760066	+	0.649846i	$0.774833\pi$
$522$	−10.3585	+	3.24129i	−0.453379	+	0.141867i
$523$	21.6449	−	8.96561i	0.946465	−	0.392039i	0.144564	−	0.989495i	$-0.453822\pi$
$523$	21.6449	−	8.96561i	0.946465	−	0.392039i	0.801901	+	0.597457i	$0.203822\pi$
$524$	13.8255	+	8.89249i	0.603968	+	0.388470i
$525$	−11.3334	+	27.3613i	−0.494632	+	1.19415i
$526$	19.7552	+	23.6476i	0.861370	+	1.03108i
$527$		−	0.776856i		−	0.0338404i
$528$	−12.2316	−	4.57272i	−0.532312	−	0.199002i
$529$		−	11.5000i		−	0.500000i
$530$	17.5415	−	14.6543i	0.761956	−	0.636541i
$531$	0.680868	−	1.64376i	0.0295472	−	0.0713331i
$532$	−6.54191	−	30.1277i	−0.283628	−	1.30620i
$533$	−10.2407	+	4.24184i	−0.443574	+	0.183734i
$534$	1.61717	+	5.16813i	0.0699817	+	0.223647i
$535$	21.3937	+	21.3937i	0.924930	+	0.924930i
$536$	20.9211	−	26.8999i	0.903653	−	1.16190i
$537$	−4.18612	+	4.18612i	−0.180644	+	0.180644i
$538$	−10.1467	−	5.31008i	−0.437454	−	0.228934i
$539$	−9.88995	−	23.8764i	−0.425990	−	1.02843i
$540$	−5.84880	+	4.05761i	−0.251692	+	0.174612i
$541$	9.88526	+	4.09461i	0.425001	+	0.176041i	0.584924	−	0.811088i	$-0.301125\pi$
$541$	9.88526	+	4.09461i	0.425001	+	0.176041i	−0.159923	+	0.987130i	$0.551125\pi$
$542$	−40.5429	−	3.63584i	−1.74147	−	0.156173i
$543$	15.7775			0.677075
$544$	−2.63929	−	1.26581i	−0.113159	−	0.0542712i
$545$	30.9741			1.32678
$546$	13.2561	+	1.18879i	0.567308	+	0.0508755i
$547$	−4.92501	−	2.04001i	−0.210578	−	0.0872244i	0.274901	−	0.961473i	$-0.411355\pi$
$547$	−4.92501	−	2.04001i	−0.210578	−	0.0872244i	−0.485479	+	0.874248i	$0.661355\pi$
$548$	−12.8750	−	18.5586i	−0.549993	−	0.792783i
$549$	2.78139	+	6.71487i	0.118707	+	0.286584i
$550$	−31.3669	−	16.4153i	−1.33749	−	0.699951i
$551$	21.6601	−	21.6601i	0.922750	−	0.922750i
$552$	−9.51757	+	1.18994i	−0.405095	+	0.0506474i
$553$	28.5146	+	28.5146i	1.21256	+	1.21256i
$554$	−5.55480	−	17.7520i	−0.236001	−	0.754209i
$555$	−29.2853	+	12.1304i	−1.24309	+	0.514905i
$556$	−3.22106	+	0.699419i	−0.136603	+	0.0296620i
$557$	−1.88066	+	4.54032i	−0.0796862	+	0.192380i	−0.958702	−	0.284414i	$-0.908201\pi$
$557$	−1.88066	+	4.54032i	−0.0796862	+	0.192380i	0.879015	+	0.476793i	$0.158201\pi$
$558$	1.62941	−	1.36122i	0.0689786	−	0.0576249i
$559$			3.46426i			0.146523i
$560$	−40.2151	−	37.4986i	−1.69940	−	1.58461i
$561$		−	1.68926i		−	0.0713208i
$562$	−27.7357	−	33.2004i	−1.16996	−	1.40047i
$563$	−4.16303	+	10.0504i	−0.175451	+	0.423575i	−0.987002	−	0.160705i	$-0.948623\pi$
$563$	−4.16303	+	10.0504i	−0.175451	+	0.423575i	0.811552	+	0.584281i	$0.198623\pi$
$564$	−5.05741	+	7.86292i	−0.212955	+	0.331089i
$565$	57.3688	−	23.7630i	2.41353	−	0.999715i
$566$	40.4807	−	12.6669i	1.70153	−	0.532428i
$567$	−2.73097	−	2.73097i	−0.114690	−	0.114690i
$568$	−3.69017	−	6.48890i	−0.154836	−	0.272268i
$569$	−1.48801	+	1.48801i	−0.0623805	+	0.0623805i	−0.737609	−	0.675228i	$-0.764045\pi$
$569$	−1.48801	+	1.48801i	−0.0623805	+	0.0623805i	0.675228	+	0.737609i	$0.264045\pi$
$570$	9.31525	−	17.7999i	0.390173	−	0.745555i
$571$	−10.9476	−	26.4299i	−0.458145	−	1.10606i	−0.969148	−	0.246480i	$-0.920726\pi$
$571$	−10.9476	−	26.4299i	−0.458145	−	1.10606i	0.511003	−	0.859579i	$-0.329274\pi$
$572$	−2.83080	+	15.6561i	−0.118362	+	0.654613i
$573$	11.4344	+	4.73630i	0.477680	+	0.197862i
$574$	−2.21923	+	24.7464i	−0.0926289	+	1.03290i
$575$	−26.0040			−1.08444
$576$	−1.96963	−	7.75375i	−0.0820678	−	0.323073i
$577$	28.1723			1.17283			0.586413	−	0.810012i	$-0.300539\pi$
$577$	28.1723			1.17283			0.586413	+	0.810012i	$0.300539\pi$
$578$	−2.11358	+	23.5684i	−0.0879135	+	0.980316i
$579$	−20.2647	−	8.39391i	−0.842172	−	0.348839i
$580$	9.72059	−	53.7609i	0.403626	−	2.23230i
$581$	−7.31261	−	17.6542i	−0.303378	−	0.732420i
$582$	2.44782	−	4.67737i	0.101465	−	0.193883i
$583$	−10.4825	+	10.4825i	−0.434143	+	0.434143i
$584$	−31.5321	+	17.9320i	−1.30481	+	0.742031i
$585$	6.13268	+	6.13268i	0.253555	+	0.253555i
$586$	6.49854	−	2.03347i	0.268452	−	0.0840018i
$587$	−26.4589	+	10.9597i	−1.09208	+	0.452353i	−0.854731	−	0.519072i	$-0.826278\pi$
$587$	−26.4589	+	10.9597i	−1.09208	+	0.452353i	−0.237347	+	0.971425i	$0.576278\pi$
$588$	8.56485	−	13.3161i	0.353209	−	0.549145i
$589$	−2.29309	+	5.53601i	−0.0944851	+	0.228107i
$590$	5.74163	+	6.87288i	0.236379	+	0.282952i
$591$		−	17.0573i		−	0.701645i
$592$	−1.24447	−	35.6018i	−0.0511476	−	1.46323i
$593$		−	1.34616i		−	0.0552802i	−0.999618	−	0.0276401i	$-0.991201\pi$
$593$		−	1.34616i		−	0.0552802i	0.999618	−	0.0276401i	$-0.00879924\pi$
$594$	3.54314	−	2.95995i	0.145377	−	0.121448i
$595$	2.72205	−	6.57160i	0.111593	−	0.269409i
$596$	8.14472	−	1.76854i	0.333621	−	0.0724422i
$597$	−7.58160	+	3.14040i	−0.310294	+	0.128528i
$598$	3.48987	+	11.1529i	0.142712	+	0.456077i
$599$	−8.34761	−	8.34761i	−0.341074	−	0.341074i	0.515697	−	0.856771i	$-0.327533\pi$
$599$	−8.34761	−	8.34761i	−0.341074	−	0.341074i	−0.856771	+	0.515697i	$0.827533\pi$
$600$	−2.69072	−	21.5213i	−0.109848	−	0.878602i
$601$	−25.9145	+	25.9145i	−1.05707	+	1.05707i	−0.0588044	+	0.998270i	$0.518729\pi$
$601$	−25.9145	+	25.9145i	−1.05707	+	1.05707i	−0.998270	+	0.0588044i	$0.981271\pi$
$602$	6.87995	+	3.60050i	0.280406	+	0.146745i
$603$	4.61070	+	11.1312i	0.187762	+	0.453298i
$604$	0.660124	+	0.951530i	0.0268601	+	0.0387172i
$605$	−1.12593	−	0.466374i	−0.0457754	−	0.0189608i
$606$	−23.4445	−	2.10247i	−0.952368	−	0.0854071i
$607$	−2.09569			−0.0850615			−0.0425307	−	0.999095i	$-0.513542\pi$
$607$	−2.09569			−0.0850615			−0.0425307	+	0.999095i	$0.513542\pi$
$608$	15.0717	+	16.8109i	0.611237	+	0.681774i
$609$	29.6413			1.20112
$610$	−36.4380	−	3.26771i	−1.47533	−	0.132306i
$611$	10.5234	+	4.35894i	0.425732	+	0.176344i
$612$	0.850312	−	0.589904i	0.0343718	−	0.0238455i
$613$	−8.75402	−	21.1341i	−0.353572	−	0.853597i	−0.996174	−	0.0873972i	$-0.972145\pi$
$613$	−8.75402	−	21.1341i	−0.353572	−	0.853597i	0.642602	−	0.766200i	$-0.277855\pi$
$614$	38.4405	+	20.1172i	1.55133	+	0.811863i
$615$	−11.4485	+	11.4485i	−0.461647	+	0.461647i
$616$	28.1504	+	21.8936i	1.13421	+	0.882120i
$617$	7.54724	+	7.54724i	0.303841	+	0.303841i	0.842514	−	0.538674i	$-0.181074\pi$
$617$	7.54724	+	7.54724i	0.303841	+	0.303841i	−0.538674	+	0.842514i	$0.681074\pi$
$618$	4.43317	+	14.1675i	0.178328	+	0.569900i
$619$	30.8044	−	12.7596i	1.23813	−	0.512851i	0.335002	−	0.942217i	$-0.391263\pi$
$619$	30.8044	−	12.7596i	1.23813	−	0.512851i	0.903130	+	0.429366i	$0.141263\pi$
$620$	2.26774	+	10.4437i	0.0910746	+	0.419429i
$621$	1.29774	−	3.13303i	0.0520766	−	0.125724i
$622$	−17.8231	+	14.8895i	−0.714641	+	0.597014i
$623$		−	14.7888i		−	0.592502i
$624$	−8.86920	+	4.04230i	−0.355052	+	0.161821i
$625$			4.54021i			0.181608i
$626$	−8.77578	−	10.5048i	−0.350751	−	0.419858i
$627$	−4.98630	+	12.0380i	−0.199134	+	0.480751i
$628$	22.1134	+	14.2232i	0.882419	+	0.567569i
$629$	4.25756	−	1.76354i	0.169760	−	0.0703169i
$630$	18.5532	−	5.80551i	0.739177	−	0.231297i
$631$	4.03006	+	4.03006i	0.160434	+	0.160434i	0.782759	−	0.622325i	$-0.213812\pi$
$631$	4.03006	+	4.03006i	0.160434	+	0.160434i	−0.622325	+	0.782759i	$0.713812\pi$
$632$	−28.4755	−	7.82929i	−1.13269	−	0.311432i
$633$	−14.1436	+	14.1436i	−0.562156	+	0.562156i
$634$	16.8068	−	32.1150i	0.667483	−	1.27545i
$635$	2.51696	+	6.07648i	0.0998825	+	0.241138i
$636$	−8.93710	−	1.61593i	−0.354379	−	0.0640759i
$637$	−17.8217	−	7.38198i	−0.706120	−	0.292485i
$638$	−3.16490	+	35.2915i	−0.125300	+	1.39721i
$639$	2.63920			0.104405
$640$	39.1765	+	9.31260i	1.54859	+	0.368113i
$641$	10.3489			0.408757			0.204378	−	0.978892i	$-0.434483\pi$
$641$	10.3489			0.408757			0.204378	+	0.978892i	$0.434483\pi$
$642$	1.07376	−	11.9735i	0.0423781	−	0.472555i
$643$	−8.10100	−	3.35554i	−0.319472	−	0.132330i	0.217184	−	0.976131i	$-0.430313\pi$
$643$	−8.10100	−	3.35554i	−0.319472	−	0.132330i	−0.536656	+	0.843801i	$0.680313\pi$
$644$	25.7765	+	4.66070i	1.01574	+	0.183657i
$645$	1.93642	+	4.67493i	0.0762464	+	0.184075i
$646$	−1.35427	+	2.58779i	−0.0532831	+	0.101815i
$647$	20.0358	−	20.0358i	0.787689	−	0.787689i	−0.193426	−	0.981115i	$-0.561960\pi$
$647$	20.0358	−	20.0358i	0.787689	−	0.787689i	0.981115	+	0.193426i	$0.0619600\pi$
$648$	2.72722	+	0.749846i	0.107135	+	0.0294567i
$649$	−4.10712	−	4.10712i	−0.161219	−	0.161219i
$650$	−25.2191	+	7.89135i	−0.989175	+	0.309524i
$651$	−5.35696	+	2.21893i	−0.209956	+	0.0869666i
$652$	28.4129	+	18.2751i	1.11274	+	0.715709i
$653$	11.1811	−	26.9936i	0.437552	−	1.05634i	−0.539240	−	0.842152i	$-0.681289\pi$
$653$	11.1811	−	26.9936i	0.437552	−	1.05634i	0.976792	−	0.214191i	$-0.0687115\pi$
$654$	−7.89036	−	9.44497i	−0.308537	−	0.369327i
$655$		−	29.2540i		−	1.14305i
$656$	−7.54616	−	16.5570i	−0.294628	−	0.646443i
$657$		−	12.8249i		−	0.500348i
$658$	19.5940	−	16.3689i	0.763854	−	0.638126i
$659$	−10.0306	+	24.2161i	−0.390738	+	0.943325i	0.599041	+	0.800718i	$0.295549\pi$
$659$	−10.0306	+	24.2161i	−0.390738	+	0.943325i	−0.989779	+	0.142607i	$0.954451\pi$
$660$	4.93118	+	22.7097i	0.191946	+	0.883975i
$661$	−13.8010	+	5.71657i	−0.536798	+	0.222349i	−0.634578	−	0.772859i	$-0.718826\pi$
$661$	−13.8010	+	5.71657i	−0.536798	+	0.222349i	0.0977799	+	0.995208i	$0.468826\pi$
$662$	−9.92453	−	31.7168i	−0.385728	−	1.23271i
$663$	−0.891582	−	0.891582i	−0.0346262	−	0.0346262i
$664$	11.0465	+	8.59130i	0.428689	+	0.333407i
$665$	−38.7956	+	38.7956i	−1.50443	+	1.50443i
$666$	11.1591	+	5.83991i	0.432406	+	0.226292i
$667$	9.95988	+	24.0453i	0.385648	+	0.931037i
$668$	8.50155	−	5.89795i	0.328935	−	0.228199i
$669$	26.8639	+	11.1274i	1.03862	+	0.430210i
$670$	−60.4031	−	5.41687i	−2.33358	−	0.209272i
$671$	23.7275			0.915990
$672$	−1.19008	+	21.8153i	−0.0459082	+	0.841543i
$673$	31.4646			1.21287			0.606436	−	0.795132i	$-0.292599\pi$
$673$	31.4646			1.21287			0.606436	+	0.795132i	$0.292599\pi$
$674$	34.1427	+	3.06187i	1.31513	+	0.117939i
$675$	7.08445	+	2.93447i	0.272681	+	0.112948i
$676$	−8.05120	−	11.6053i	−0.309662	−	0.446359i
$677$	−6.25070	−	15.0905i	−0.240234	−	0.579976i	0.757072	−	0.653332i	$-0.226629\pi$
$677$	−6.25070	−	15.0905i	−0.240234	−	0.579976i	−0.997306	+	0.0733553i	$0.976629\pi$
$678$	−21.8603	−	11.4402i	−0.839538	−	0.439357i
$679$	−10.1945	+	10.1945i	−0.391229	+	0.391229i
$680$	0.646252	+	5.16894i	0.0247826	+	0.198220i
$681$	−17.8011	−	17.8011i	−0.682141	−	0.682141i
$682$	−2.06992	−	6.61504i	−0.0792614	−	0.253303i
$683$	−13.3397	+	5.52548i	−0.510429	+	0.211426i	−0.623007	−	0.782216i	$-0.714089\pi$
$683$	−13.3397	+	5.52548i	−0.510429	+	0.211426i	0.112578	+	0.993643i	$0.464089\pi$
$684$	−7.80073	+	1.69384i	−0.298268	+	0.0647658i
$685$	−15.3826	+	37.1370i	−0.587740	+	1.41893i
$686$	−3.84105	+	3.20882i	−0.146652	+	0.122513i
$687$		−	7.64991i		−	0.291862i
$688$	−5.68326	+	0.198660i	−0.216672	+	0.00757386i
$689$			11.0652i			0.421552i
$690$	10.9436	+	13.0998i	0.416617	+	0.498701i
$691$	−9.47463	+	22.8738i	−0.360432	+	0.870160i	0.634805	+	0.772673i	$0.281081\pi$
$691$	−9.47463	+	22.8738i	−0.360432	+	0.870160i	−0.995237	+	0.0974874i	$0.968919\pi$
$692$	13.2812	−	20.6487i	0.504875	−	0.784946i
$693$	−11.6487	+	4.82504i	−0.442496	+	0.183288i
$694$	5.01651	−	1.56972i	0.190424	−	0.0595859i
$695$	4.14777	+	4.14777i	0.157334	+	0.157334i
$696$	−18.8696	+	10.7310i	−0.715251	+	0.406757i
$697$	1.66441	−	1.66441i	0.0630439	−	0.0630439i
$698$	−2.25316	+	4.30541i	−0.0852833	+	0.162962i
$699$	−7.08278	−	17.0993i	−0.267895	−	0.646756i
$700$	−10.5388	+	58.2863i	−0.398331	+	2.20301i
$701$	−5.36748	−	2.22328i	−0.202727	−	0.0839723i	0.279010	−	0.960288i	$-0.409994\pi$
$701$	−5.36748	−	2.22328i	−0.202727	−	0.0839723i	−0.481737	+	0.876316i	$0.659994\pi$
$702$	0.307803	−	3.43229i	0.0116173	−	0.129543i
$703$	−35.5457			−1.34063
$704$	−25.8467	−	3.74623i	−0.974134	−	0.141191i
$705$	16.6376			0.626607
$706$	0.996453	−	11.1114i	0.0375020	−	0.418181i
$707$	59.3898	+	24.6001i	2.23358	+	0.925180i
$708$	0.633132	−	3.50161i	0.0237945	−	0.131599i
$709$	−14.4269	−	34.8295i	−0.541812	−	1.30805i	−0.923443	−	0.383735i	$-0.874638\pi$
$709$	−14.4269	−	34.8295i	−0.541812	−	1.30805i	0.381631	−	0.924315i	$-0.375362\pi$
$710$	−6.15968	+	11.7701i	−0.231169	+	0.441725i
$711$	7.38305	−	7.38305i	0.276886	−	0.276886i
$712$	5.35398	+	9.41458i	0.200649	+	0.352826i
$713$	−3.60003	−	3.60003i	−0.134822	−	0.134822i
$714$	−2.69731	+	0.844018i	−0.100944	+	0.0315866i
$715$	26.1583	−	10.8351i	0.978266	−	0.405211i
$716$	−6.40504	+	9.95812i	−0.239367	+	0.372152i
$717$	1.57248	−	3.79630i	0.0587254	−	0.141776i
$718$	−3.33814	−	3.99584i	−0.124578	−	0.149123i
$719$		−	38.6849i		−	1.44270i	−0.692569	−	0.721351i	$-0.743521\pi$
$719$		−	38.6849i		−	1.44270i	0.692569	−	0.721351i	$-0.256479\pi$
$720$	−9.70921	+	10.4126i	−0.361841	+	0.388054i
$721$		−	40.5409i		−	1.50982i
$722$	−3.33183	+	2.78342i	−0.123998	+	0.103588i
$723$	5.43963	−	13.1324i	0.202302	−	0.488400i
$724$	30.8363	−	6.69578i	1.14602	−	0.248847i
$725$	−54.3715	+	22.5214i	−2.01931	+	0.836425i
$726$	0.144607	+	0.462135i	0.00536688	+	0.0171514i
$727$	−31.8871	−	31.8871i	−1.18263	−	1.18263i	−0.979061	−	0.203566i	$-0.934747\pi$
$727$	−31.8871	−	31.8871i	−1.18263	−	1.18263i	−0.203566	−	0.979061i	$-0.565253\pi$
$728$	26.4129	−	3.30230i	0.978928	−	0.122391i
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$	57.1956	+	29.9323i	2.11690	+	1.10784i
$731$	−0.281521	−	0.679651i	−0.0104124	−	0.0251378i
$732$	8.28582	+	11.9435i	0.306253	+	0.441445i
$733$	−18.4333	−	7.63532i	−0.680849	−	0.282017i	0.0153326	−	0.999882i	$-0.495119\pi$
$733$	−18.4333	−	7.63532i	−0.680849	−	0.282017i	−0.696182	+	0.717865i	$0.745119\pi$
$734$	−1.99568	−	0.178970i	−0.0736619	−	0.00660590i
$735$	−28.1761			−1.03929
$736$	−18.0967	+	6.36484i	−0.667052	+	0.234611i
$737$	39.3330			1.44885
$738$	6.40740	+	0.574607i	0.235860	+	0.0211516i
$739$	−19.0069	−	7.87292i	−0.699180	−	0.289610i	0.00463865	−	0.999989i	$-0.498523\pi$
$739$	−19.0069	−	7.87292i	−0.699180	−	0.289610i	−0.703819	+	0.710379i	$0.748523\pi$
$740$	−52.0888	+	36.1366i	−1.91482	+	1.32841i
$741$	3.72184	+	8.98531i	0.136725	+	0.330084i
$742$	21.9753	+	11.5004i	0.806739	+	0.422192i
$743$	−17.5266	+	17.5266i	−0.642987	+	0.642987i	−0.951289	−	0.308302i	$-0.900239\pi$
$743$	−17.5266	+	17.5266i	−0.642987	+	0.642987i	0.308302	+	0.951289i	$0.400239\pi$
$744$	2.60693	−	3.35194i	0.0955747	−	0.122888i
$745$	−10.4880	−	10.4880i	−0.384250	−	0.384250i
$746$	14.1016	+	45.0658i	0.516296	+	1.64998i
$747$	−4.57106	+	1.89340i	−0.167246	+	0.0692757i
$748$	−0.716906	−	3.30159i	−0.0262127	−	0.120718i
$749$	−12.5636	+	30.3313i	−0.459065	+	1.10828i
$750$	−10.3069	+	8.61038i	−0.376353	+	0.314407i
$751$			40.4908i			1.47753i	0.673963	+	0.738765i	$0.264591\pi$
$751$			40.4908i			1.47753i	−0.673963	+	0.738765i	$0.735409\pi$
$752$	−6.54754	+	17.5140i	−0.238764	+	0.638671i
$753$		−	6.19031i		−	0.225587i
$754$	16.9562	+	20.2970i	0.617509	+	0.739175i
$755$	0.788695	−	1.90408i	0.0287035	−	0.0692965i
$756$	−6.49654	−	4.17856i	−0.236277	−	0.151973i
$757$	−29.7102	+	12.3064i	−1.07984	+	0.447283i	−0.850452	−	0.526053i	$-0.823671\pi$
$757$	−29.7102	+	12.3064i	−1.07984	+	0.447283i	−0.229385	+	0.973336i	$0.573671\pi$
$758$	16.9284	−	5.29709i	0.614867	−	0.192399i
$759$	−7.82823	−	7.82823i	−0.284147	−	0.284147i
$760$	10.6522	−	38.7424i	0.386395	−	1.40533i
$761$	−15.8052	+	15.8052i	−0.572939	+	0.572939i	−0.932949	−	0.360010i	$-0.882773\pi$
$761$	−15.8052	+	15.8052i	−0.572939	+	0.572939i	0.360010	+	0.932949i	$0.382773\pi$
$762$	1.21174	−	2.31543i	0.0438966	−	0.0838791i
$763$	12.8621	+	31.0519i	0.465640	+	1.12415i
$764$	24.3581	+	4.40423i	0.881246	+	0.159339i
$765$	−1.70153	−	0.704798i	−0.0615190	−	0.0254820i
$766$	1.67374	−	18.6637i	0.0604746	−	0.674347i
$767$	−4.33542			−0.156543
$768$	−7.14015	−	14.3185i	−0.257648	−	0.516673i
$769$	2.99003			0.107823			0.0539116	−	0.998546i	$-0.482831\pi$
$769$	2.99003			0.107823			0.0539116	+	0.998546i	$0.482831\pi$
$770$	5.66869	−	63.2111i	0.204285	−	2.27797i
$771$	7.65149	+	3.16935i	0.275562	+	0.114141i
$772$	−43.1687	−	7.80540i	−1.55368	−	0.280923i
$773$	1.59236	+	3.84429i	0.0572731	+	0.138269i	0.949926	−	0.312476i	$-0.101158\pi$
$773$	1.59236	+	3.84429i	0.0572731	+	0.138269i	−0.892653	+	0.450745i	$0.851158\pi$
$774$	0.932248	−	1.78137i	0.0335090	−	0.0640300i
$775$	8.14044	−	8.14044i	0.292413	−	0.292413i
$776$	2.79912	−	10.1805i	0.100483	−	0.365460i
$777$	−24.3217	−	24.3217i	−0.872535	−	0.872535i
$778$	4.61024	−	1.44260i	0.165285	−	0.0517196i
$779$	−16.7738	+	6.94792i	−0.600983	+	0.248935i
$780$	14.5887	+	9.38340i	0.522358	+	0.335980i
$781$	3.29718	−	7.96009i	0.117982	−	0.284834i
$782$	−1.59101	−	1.90448i	−0.0568943	−	0.0681040i
$783$		−	7.67477i		−	0.274274i
$784$	11.0884	−	29.6605i	0.396015	−	1.05930i
$785$		−	46.7908i		−	1.67003i
$786$	−8.92047	+	7.45219i	−0.318183	+	0.265811i
$787$	3.14740	−	7.59851i	0.112193	−	0.270857i	−0.857803	−	0.513978i	$-0.828171\pi$
$787$	3.14740	−	7.59851i	0.112193	−	0.270857i	0.969996	+	0.243121i	$0.0781712\pi$
$788$	−7.23895	−	33.3378i	−0.257877	−	1.18761i
$789$	−20.1299	+	8.33809i	−0.716645	+	0.296844i
$790$	15.6949	+	50.1578i	0.558401	+	1.78453i
$791$	47.6453	+	47.6453i	1.69407	+	1.69407i
$792$	5.66874	−	7.28877i	0.201430	−	0.258995i
$793$	12.5232	−	12.5232i	0.444712	−	0.444712i
$794$	−9.02254	−	4.72179i	−0.320198	−	0.167570i
$795$	6.18513	+	14.9322i	0.219364	+	0.529591i
$796$	−13.4851	+	9.35532i	−0.477968	+	0.331590i
$797$	−13.9175	−	5.76480i	−0.492982	−	0.204200i	0.122321	−	0.992491i	$-0.460966\pi$
$797$	−13.9175	−	5.76480i	−0.492982	−	0.204200i	−0.615303	+	0.788291i	$0.710966\pi$
$798$	21.7128	+	1.94718i	0.768625	+	0.0689294i
$799$	−2.41881			−0.0855712
$800$	−14.3923	−	40.9204i	−0.508844	−	1.44676i
$801$	−3.82915			−0.135297
$802$	−31.8292	−	2.85440i	−1.12393	−	0.100792i
$803$	−38.6812	−	16.0223i	−1.36503	−	0.565413i
$804$	13.7354	+	19.7987i	0.484409	+	0.698247i
$805$	−17.8393	−	43.0678i	−0.628751	−	1.51794i
$806$	−4.58387	−	2.39888i	−0.161460	−	0.0844971i
$807$	5.72608	−	5.72608i	0.201568	−	0.201568i
$808$	−46.7135	+	5.84040i	−1.64337	+	0.205465i
$809$	30.4595	+	30.4595i	1.07090	+	1.07090i	0.997287	+	0.0736122i	$0.0234527\pi$
$809$	30.4595	+	30.4595i	1.07090	+	1.07090i	0.0736122	+	0.997287i	$0.476547\pi$
$810$	−1.50317	−	4.80383i	−0.0528161	−	0.168789i
$811$	19.1190	−	7.91934i	0.671358	−	0.278086i	−0.0208509	−	0.999783i	$-0.506638\pi$
$811$	19.1190	−	7.91934i	0.671358	−	0.278086i	0.692209	+	0.721697i	$0.256638\pi$
$812$	57.9325	−	12.5794i	2.03303	−	0.441451i
$813$	11.0149	−	26.5922i	0.386308	−	0.932631i
$814$	31.5548	−	26.3610i	1.10600	−	0.923953i
$815$		−	60.1204i		−	2.10593i
$816$	1.41155	−	1.51380i	0.0494140	−	0.0529937i
$817$			5.67430i			0.198519i
$818$	−4.47013	−	5.35086i	−0.156294	−	0.187088i
$819$	−3.60147	+	8.69471i	−0.125845	+	0.303818i
$820$	−17.5169	+	27.2341i	−0.611717	+	0.951057i
$821$	32.8139	−	13.5920i	1.14521	−	0.474363i	0.272287	−	0.962216i	$-0.412220\pi$
$821$	32.8139	−	13.5920i	1.14521	−	0.474363i	0.872926	+	0.487853i	$0.162220\pi$
$822$	15.2428	−	4.76965i	0.531654	−	0.166361i
$823$	5.67489	+	5.67489i	0.197814	+	0.197814i	0.799062	−	0.601248i	$-0.205330\pi$
$823$	5.67489	+	5.67489i	0.197814	+	0.197814i	−0.601248	+	0.799062i	$0.705330\pi$
$824$	14.6770	+	25.8083i	0.511296	+	0.899076i
$825$	17.7013	−	17.7013i	0.616280	−	0.616280i
$826$	−4.50592	+	8.61005i	−0.156781	+	0.299582i
$827$	21.2654	+	51.3392i	0.739471	+	1.78524i	0.608027	+	0.793916i	$0.291961\pi$
$827$	21.2654	+	51.3392i	0.739471	+	1.78524i	0.131443	+	0.991324i	$0.458039\pi$
$828$	1.20676	−	6.67411i	0.0419377	−	0.231941i
$829$	−14.6369	−	6.06280i	−0.508361	−	0.210570i	0.113735	−	0.993511i	$-0.463719\pi$
$829$	−14.6369	−	6.06280i	−0.508361	−	0.210570i	−0.622096	+	0.782941i	$0.713719\pi$
$830$	2.22445	−	24.8047i	0.0772120	−	0.860984i
$831$	13.1527			0.456263
$832$	−15.6189	+	11.6645i	−0.541489	+	0.404393i
$833$	4.09631			0.141929
$834$	0.208180	−	2.32140i	0.00720868	−	0.0803833i
$835$	−17.0122	−	7.04668i	−0.588731	−	0.243860i
$836$	−4.63671	+	25.6439i	−0.160364	+	0.886911i
$837$	0.574529	+	1.38704i	0.0198586	+	0.0479430i
$838$	−6.46146	+	12.3468i	−0.223207	+	0.426512i
$839$	−39.7201	+	39.7201i	−1.37129	+	1.37129i	−0.512756	+	0.858535i	$0.671375\pi$
$839$	−39.7201	+	39.7201i	−1.37129	+	1.37129i	−0.858535	+	0.512756i	$0.828625\pi$
$840$	33.7976	−	19.2204i	1.16613	−	0.663166i
$841$	21.1440	+	21.1440i	0.729103	+	0.729103i
$842$	2.70448	−	0.846261i	0.0932024	−	0.0291641i
$843$	28.2618	−	11.7064i	0.973387	−	0.403190i
$844$	−21.6406	+	33.6453i	−0.744899	+	1.15812i
$845$	−9.61931	+	23.2231i	−0.330914	+	0.798898i
$846$	−4.23827	−	5.07332i	−0.145715	−	0.174424i
$847$		−	1.32242i		−	0.0454389i
$848$	−18.1529	+	0.634543i	−0.623375	+	0.0217903i
$849$			29.9928i			1.02935i
$850$	4.30643	−	3.59761i	0.147709	−	0.123397i
$851$	11.5576	−	27.9024i	0.396188	−	0.956482i
$852$	5.15820	−	1.12005i	0.176717	−	0.0383722i
$853$	17.7015	−	7.33222i	0.606089	−	0.251050i	−0.0584662	−	0.998289i	$-0.518621\pi$
$853$	17.7015	−	7.33222i	0.606089	−	0.251050i	0.664555	+	0.747239i	$0.268621\pi$
$854$	−11.8551	−	37.8865i	−0.405674	−	1.29645i
$855$	10.0450	+	10.0450i	0.343533	+	0.343533i
$856$	−2.98278	−	23.8573i	−0.101949	−	0.815425i
$857$	34.8578	−	34.8578i	1.19072	−	1.19072i	0.213853	−	0.976866i	$-0.431399\pi$
$857$	34.8578	−	34.8578i	1.19072	−	1.19072i	0.976866	−	0.213853i	$-0.0686015\pi$
$858$	−9.96757	−	5.21635i	−0.340287	−	0.178083i
$859$	13.9729	+	33.7335i	0.476748	+	1.15097i	0.961125	+	0.276112i	$0.0890461\pi$
$859$	13.9729	+	33.7335i	0.476748	+	1.15097i	−0.484378	+	0.874859i	$0.660954\pi$
$860$	5.76863	+	8.31514i	0.196709	+	0.283544i
$861$	−16.2313	−	6.72321i	−0.553160	−	0.229127i
$862$	16.2703	+	1.45910i	0.554170	+	0.0496973i
$863$	35.2947			1.20144			0.600722	−	0.799458i	$-0.294880\pi$
$863$	35.2947			1.20144			0.600722	+	0.799458i	$0.294880\pi$
$864$	5.64846	+	0.308137i	0.192164	+	0.0104830i
$865$	−43.6916			−1.48556
$866$	−4.40593	−	0.395119i	−0.149720	−	0.0134267i
$867$	−15.4586	−	6.40315i	−0.525001	−	0.217462i
$868$	−9.52826	+	6.61023i	−0.323410	+	0.224366i
$869$	−13.0443	−	31.4917i	−0.442497	−	1.06828i
$870$	34.2274	+	17.9123i	1.16042	+	0.607283i
$871$	20.7597	−	20.7597i	0.703414	−	0.703414i
$872$	−19.4297	−	15.1112i	−0.657972	−	0.511729i
$873$	2.63958	+	2.63958i	0.0893363	+	0.0893363i
$874$	5.71624	+	18.2679i	0.193355	+	0.617922i
$875$	33.8855	−	14.0358i	1.14554	−	0.474498i
$876$	−5.44275	−	25.0657i	−0.183894	−	0.846892i
$877$	−3.81781	+	9.21700i	−0.128918	+	0.311236i	−0.975138	−	0.221598i	$-0.928873\pi$
$877$	−3.81781	+	9.21700i	−0.128918	+	0.311236i	0.846220	+	0.532834i	$0.178873\pi$
$878$	−12.4458	+	10.3973i	−0.420026	+	0.350892i
$879$			4.81487i			0.162402i
$880$	19.2755	+	42.2924i	0.649778	+	1.42568i
$881$		−	20.1037i		−	0.677312i	−0.940910	−	0.338656i	$-0.890028\pi$
$881$		−	20.1037i		−	0.677312i	0.940910	−	0.338656i	$-0.109972\pi$
$882$	7.17761	+	8.59179i	0.241683	+	0.289301i
$883$	−9.85279	+	23.7867i	−0.331573	+	0.800487i	0.666895	+	0.745152i	$0.267623\pi$
$883$	−9.85279	+	23.7867i	−0.331573	+	0.800487i	−0.998468	+	0.0553357i	$0.982377\pi$
$884$	−2.12094	−	1.36418i	−0.0713348	−	0.0458823i
$885$	−5.85053	+	2.42337i	−0.196663	+	0.0814607i
$886$	−32.9754	+	10.3184i	−1.10783	+	0.346653i
$887$	14.1672	+	14.1672i	0.475688	+	0.475688i	0.903749	−	0.428062i	$-0.140803\pi$
$887$	14.1672	+	14.1672i	0.475688	+	0.475688i	−0.428062	+	0.903749i	$0.640803\pi$
$888$	24.2883	+	6.67804i	0.815063	+	0.224100i
$889$	−5.04657	+	5.04657i	−0.169256	+	0.169256i
$890$	8.93693	−	17.0770i	0.299566	−	0.572421i
$891$	1.24931	+	3.01609i	0.0418534	+	0.101043i
$892$	57.2267	+	10.3472i	1.91609	+	0.346451i
$893$	17.2368	+	7.13973i	0.576809	+	0.238922i
$894$	−0.526400	+	5.86984i	−0.0176054	+	0.196317i
$895$	21.0709			0.704322
$896$	6.93222	+	43.1421i	0.231589	+	1.44127i
$897$	−8.26337			−0.275906
$898$	3.61596	−	40.3213i	0.120666	−	1.34554i
$899$	−10.6452	−	4.40938i	−0.355037	−	0.147061i
$900$	15.0916	+	2.72874i	0.503053	+	0.0909579i
$901$	−0.899208	−	2.17088i	−0.0299569	−	0.0723225i
$902$	9.73788	−	18.6075i	0.324236	−	0.619561i
$903$	−3.88257	+	3.88257i	−0.129204	+	0.129204i
$904$	−47.5800	−	13.0821i	−1.58249	−	0.435103i
$905$	−39.7080	−	39.7080i	−1.31994	−	1.31994i
$906$	−0.781526	+	0.244548i	−0.0259645	+	0.00812458i
$907$	−1.27402	+	0.527716i	−0.0423031	+	0.0175225i	−0.403735	−	0.914876i	$-0.632288\pi$
$907$	−1.27402	+	0.527716i	−0.0423031	+	0.0175225i	0.361432	+	0.932399i	$0.382288\pi$
$908$	−42.3461	−	27.2369i	−1.40531	−	0.903889i
$909$	6.36949	−	15.3773i	0.211263	−	0.510033i
$910$	−30.3705	−	36.3543i	−1.00677	−	1.20513i
$911$			3.64101i			0.120632i	0.998179	+	0.0603161i	$0.0192109\pi$
$911$			3.64101i			0.120632i	−0.998179	+	0.0603161i	$0.980789\pi$
$912$	−14.5273	+	6.62109i	−0.481048	+	0.219246i
$913$			16.1522i			0.534560i
$914$	28.7302	−	24.0013i	0.950312	−	0.793893i
$915$	9.89962	−	23.8998i	0.327271	−	0.790103i
$916$	−3.24654	−	14.9514i	−0.107269	−	0.494008i
$917$	29.3275	−	12.1478i	0.968479	−	0.401157i
$918$	0.218535	+	0.698392i	0.00721272	+	0.0230504i
$919$	16.8542	+	16.8542i	0.555970	+	0.555970i	0.928158	−	0.372187i	$-0.121392\pi$
$919$	16.8542	+	16.8542i	0.555970	+	0.555970i	−0.372187	+	0.928158i	$0.621392\pi$
$920$	26.9482	+	20.9586i	0.888457	+	0.690985i
$921$	−21.6932	+	21.6932i	−0.714815	+	0.714815i
$922$	8.53988	+	4.46919i	0.281246	+	0.147185i
$923$	−2.46105	−	5.94151i	−0.0810065	−	0.195567i
$924$	−20.7191	+	14.3739i	−0.681608	+	0.472866i
$925$	63.0933	+	26.1341i	2.07450	+	0.859284i
$926$	−8.40075	−	0.753368i	−0.276066	−	0.0247572i
$927$	−10.4969			−0.344764
$928$	−32.3257	+	28.9813i	−1.06114	+	0.951357i
$929$	−29.1718			−0.957096			−0.478548	−	0.878061i	$-0.658837\pi$
$929$	−29.1718			−0.957096			−0.478548	+	0.878061i	$0.658837\pi$
$930$	−7.52670	−	0.674985i	−0.246810	−	0.0221336i
$931$	−29.1910	−	12.0913i	−0.956697	−	0.396277i
$932$	−21.0997	−	30.4140i	−0.691145	−	0.996244i
$933$	−6.28440	−	15.1719i	−0.205742	−	0.496705i
$934$	29.0915	+	15.2245i	0.951902	+	0.498161i
$935$	−4.25147	+	4.25147i	−0.139038	+	0.139038i
$936$	−0.855039	−	6.83888i	−0.0279478	−	0.223536i
$937$	16.6591	+	16.6591i	0.544230	+	0.544230i	0.924766	−	0.380536i	$-0.124261\pi$
$937$	16.6591	+	16.6591i	0.544230	+	0.544230i	−0.380536	+	0.924766i	$0.624261\pi$
$938$	−19.6522	−	62.8043i	−0.641666	−	2.05063i
$939$	8.94223	−	3.70399i	0.291819	−	0.120875i
$940$	32.5174	−	7.06080i	1.06060	−	0.230298i
$941$	2.44955	−	5.91373i	0.0798529	−	0.192782i	−0.878911	−	0.476986i	$-0.841729\pi$
$941$	2.44955	−	5.91373i	0.0798529	−	0.192782i	0.958764	+	0.284204i	$0.0917293\pi$
$942$	−14.2680	+	11.9195i	−0.464876	+	0.388359i
$943$		−	15.4261i		−	0.502342i
$944$	−0.248618	−	7.11243i	−0.00809181	−	0.231490i
$945$			13.7464i			0.447169i
$946$	−4.20812	−	5.03723i	−0.136818	−	0.163774i
$947$	−4.96711	+	11.9917i	−0.161409	+	0.389676i	−0.983806	−	0.179238i	$-0.942637\pi$
$947$	−4.96711	+	11.9917i	−0.161409	+	0.389676i	0.822396	+	0.568915i	$0.192637\pi$
$948$	11.2965	−	17.5631i	0.366895	−	0.570423i
$949$	−28.8721	+	11.9592i	−0.937228	+	0.388212i
$950$	−41.3077	+	12.9256i	−1.34020	+	0.419363i
$951$	18.1235	+	18.1235i	0.587694	+	0.587694i
$952$	−4.91357	+	2.79430i	−0.159250	+	0.0905638i
$953$	−6.25983	+	6.25983i	−0.202776	+	0.202776i	−0.801188	−	0.598412i	$-0.795798\pi$
$953$	−6.25983	+	6.25983i	−0.202776	+	0.202776i	0.598412	+	0.801188i	$0.295798\pi$
$954$	2.97770	−	5.68989i	0.0964066	−	0.184217i
$955$	−16.8576	−	40.6978i	−0.545499	−	1.31695i
$956$	1.46223	−	8.08705i	0.0472920	−	0.261554i
$957$	−23.1478	−	9.58815i	−0.748263	−	0.309941i
$958$	2.86001	−	31.8917i	0.0924026	−	1.03037i
$959$	−43.6180			−1.40850
$960$	−14.5572	+	24.4714i	−0.469833	+	0.789811i
$961$	−28.7460			−0.927292
$962$	2.74126	−	30.5676i	0.0883819	−	0.985539i
$963$	7.85343	+	3.25300i	0.253073	+	0.104826i
$964$	5.05825	−	27.9752i	0.162915	−	0.901022i
$965$	29.8759	+	72.1268i	0.961739	+	2.32184i
$966$	−8.58834	+	16.4109i	−0.276325	+	0.528011i
$967$	4.21628	−	4.21628i	0.135586	−	0.135586i	−0.636056	−	0.771643i	$-0.719435\pi$
$967$	4.21628	−	4.21628i	0.135586	−	0.135586i	0.771643	+	0.636056i	$0.219435\pi$
$968$	0.478753	+	0.841852i	0.0153877	+	0.0270582i
$969$	−1.46037	−	1.46037i	−0.0469138	−	0.0469138i
$970$	−17.9324	+	5.61124i	−0.575774	+	0.180166i
$971$	−35.3365	+	14.6369i	−1.13400	+	0.469720i	−0.869140	−	0.494566i	$-0.835327\pi$
$971$	−35.3365	+	14.6369i	−1.13400	+	0.469720i	−0.264864	+	0.964286i	$0.585327\pi$
$972$	−1.08192	+	1.68210i	−0.0347026	+	0.0539533i
$973$	−2.43582	+	5.88058i	−0.0780887	+	0.188523i
$974$	3.57765	+	4.28255i	0.114635	+	0.137222i
$975$		−	18.6853i		−	0.598407i
$976$	21.2630	+	19.8267i	0.680611	+	0.634636i
$977$			60.3138i			1.92961i	0.262970	+	0.964804i	$0.415298\pi$
$977$			60.3138i			1.92961i	−0.262970	+	0.964804i	$0.584702\pi$
$978$	−18.3326	+	15.3151i	−0.586212	+	0.489724i
$979$	−4.78379	+	11.5491i	−0.152891	+	0.369111i
$980$	−55.0690	+	11.9576i	−1.75911	+	0.381973i
$981$	8.04001	−	3.33028i	0.256698	−	0.106328i
$982$	9.10794	+	29.1071i	0.290646	+	0.928845i
$983$	38.0148	+	38.0148i	1.21248	+	1.21248i	0.970207	+	0.242277i	$0.0778944\pi$
$983$	38.0148	+	38.0148i	1.21248	+	1.21248i	0.242277	+	0.970207i	$0.422106\pi$
$984$	12.7668	−	1.59619i	0.406992	−	0.0508845i
$985$	−42.9292	+	42.9292i	−1.36784	+	1.36784i
$986$	−4.97605	−	2.60413i	−0.158470	−	0.0829323i
$987$	6.90882	+	16.6794i	0.219910	+	0.530910i
$988$	11.0874	+	15.9819i	0.352738	+	0.508451i
$989$	−4.45417	−	1.84498i	−0.141634	−	0.0586669i
$990$	−16.3667	−	1.46775i	−0.520169	−	0.0466481i
$991$	51.7734			1.64464			0.822319	−	0.569027i	$-0.192680\pi$
$991$	51.7734			1.64464			0.822319	+	0.569027i	$0.192680\pi$
$992$	3.67260	−	7.65757i	0.116605	−	0.243128i
$993$	23.4995			0.745733
$994$	−14.3575	−	1.28757i	−0.455393	−	0.0408391i
$995$	26.9847	+	11.1774i	0.855472	+	0.354348i
$996$	−8.13040	+	5.64047i	−0.257622	+	0.178725i
$997$	13.2018	+	31.8719i	0.418105	+	1.00939i	0.982896	+	0.184161i	$0.0589567\pi$
$997$	13.2018	+	31.8719i	0.418105	+	1.00939i	−0.564791	+	0.825234i	$0.691043\pi$
$998$	−48.3618	−	25.3093i	−1.53087	−	0.801151i
$999$	−6.29742	+	6.29742i	−0.199241	+	0.199241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.61.5	✓	32
3.2	odd	2		288.2.v.d.253.4		32
4.3	odd	2		384.2.n.a.337.8		32
8.3	odd	2		768.2.n.b.673.1		32
8.5	even	2		768.2.n.a.673.5		32
12.11	even	2		1152.2.v.c.721.1		32
32.5	even	8		768.2.n.a.97.5		32
32.11	odd	8		384.2.n.a.49.8		32
32.21	even	8	inner	96.2.n.a.85.5	yes	32
32.27	odd	8		768.2.n.b.97.1		32
96.11	even	8		1152.2.v.c.433.1		32
96.53	odd	8		288.2.v.d.181.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.61.5	✓	32	1.1	even	1	trivial
96.2.n.a.85.5	yes	32	32.21	even	8	inner
288.2.v.d.181.4		32	96.53	odd	8
288.2.v.d.253.4		32	3.2	odd	2
384.2.n.a.49.8		32	32.11	odd	8
384.2.n.a.337.8		32	4.3	odd	2
768.2.n.a.97.5		32	32.5	even	8
768.2.n.a.673.5		32	8.5	even	2
768.2.n.b.97.1		32	32.27	odd	8
768.2.n.b.673.1		32	8.3	odd	2
1152.2.v.c.433.1		32	96.11	even	8
1152.2.v.c.721.1		32	12.11	even	2

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:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	96.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.126318 + 1.40856i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(-1.96809 - 0.355853i) q^{4} +(1.36206 + 3.28830i) q^{5} +(0.655736 - 1.25300i) q^{6} +(-2.73097 + 2.73097i) q^{7} +(0.749846 - 2.72722i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.126318 + 1.40856i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(-1.96809 - 0.355853i) q^{4} +(1.36206 + 3.28830i) q^{5} +(0.655736 - 1.25300i) q^{6} +(-2.73097 + 2.73097i) q^{7} +(0.749846 - 2.72722i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-4.80383 + 1.50317i) q^{10} +(3.01609 - 1.24931i) q^{11} +(1.68210 + 1.08192i) q^{12} +(0.932498 - 2.25125i) q^{13} +(-3.50176 - 4.19170i) q^{14} -3.55923i q^{15} +(3.74674 + 1.40070i) q^{16} +0.517450i q^{17} +(-1.08532 + 0.906683i) q^{18} +(1.52739 - 3.68744i) q^{19} +(-1.51050 - 6.95636i) q^{20} +(3.56818 - 1.47799i) q^{21} +(1.37874 + 4.40616i) q^{22} +(2.39792 + 2.39792i) q^{23} +(-1.73643 + 2.23267i) q^{24} +(-5.42220 + 5.42220i) q^{25} +(3.05323 + 1.59785i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(6.34660 - 4.40296i) q^{28} +(7.09056 + 2.93701i) q^{29} +(5.01340 + 0.449595i) q^{30} -1.50132 q^{31} +(-2.44625 + 5.10057i) q^{32} -3.26460 q^{33} +(-0.728859 - 0.0653632i) q^{34} +(-12.7000 - 5.26051i) q^{35} +(-1.14002 - 1.64327i) q^{36} +(-3.40814 - 8.22797i) q^{37} +(5.00104 + 2.61721i) q^{38} +(-1.72303 + 1.72303i) q^{39} +(9.98927 - 1.24892i) q^{40} +(-3.21656 - 3.21656i) q^{41} +(1.63111 + 5.21269i) q^{42} +(-1.31346 + 0.544054i) q^{43} +(-6.38051 + 1.38546i) q^{44} +(-1.36206 + 3.28830i) q^{45} +(-3.68051 + 3.07471i) q^{46} +4.67448i q^{47} +(-2.92551 - 2.72789i) q^{48} -7.91635i q^{49} +(-6.95258 - 8.32242i) q^{50} +(0.198019 - 0.478061i) q^{51} +(-2.63635 + 4.09882i) q^{52} +(-4.19534 + 1.73777i) q^{53} +(1.34968 - 0.422330i) q^{54} +(8.21621 + 8.21621i) q^{55} +(5.40014 + 9.49575i) q^{56} +(-2.82224 + 2.82224i) q^{57} +(-5.03262 + 9.61649i) q^{58} +(-0.680868 - 1.64376i) q^{59} +(-1.26656 + 7.00489i) q^{60} +(6.71487 + 2.78139i) q^{61} +(0.189643 - 2.11470i) q^{62} -3.86217 q^{63} +(-6.87546 - 4.08999i) q^{64} +8.67291 q^{65} +(0.412377 - 4.59838i) q^{66} +(11.1312 + 4.61070i) q^{67} +(0.184136 - 1.01839i) q^{68} +(-1.29774 - 3.13303i) q^{69} +(9.01398 - 17.2242i) q^{70} +(1.86620 - 1.86620i) q^{71} +(2.45866 - 1.39822i) q^{72} +(-9.06859 - 9.06859i) q^{73} +(12.0201 - 3.76123i) q^{74} +(7.08445 - 2.93447i) q^{75} +(-4.31822 + 6.71367i) q^{76} +(-4.82504 + 11.6487i) q^{77} +(-2.20935 - 2.64465i) q^{78} -10.4412i q^{79} +(0.497353 + 14.2282i) q^{80} +1.00000i q^{81} +(4.93702 - 4.12441i) q^{82} +(-1.89340 + 4.57106i) q^{83} +(-7.54843 + 1.63906i) q^{84} +(-1.70153 + 0.704798i) q^{85} +(-0.600420 - 1.91882i) q^{86} +(-5.42688 - 5.42688i) q^{87} +(-1.14553 - 9.16234i) q^{88} +(-2.70762 + 2.70762i) q^{89} +(-4.45972 - 2.33392i) q^{90} +(3.60147 + 8.69471i) q^{91} +(-3.86600 - 5.57262i) q^{92} +(1.38704 + 0.574529i) q^{93} +(-6.58429 - 0.590470i) q^{94} +14.2058 q^{95} +(4.21195 - 3.77618i) q^{96} +3.73293 q^{97} +(11.1507 + 0.999977i) q^{98} +(3.01609 + 1.24931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more