LMFDB - Embedded newform 624.2.bn.a.187.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(187,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 3]))

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

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

chi := DirichletCharacter("624.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bn (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$56$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			187.32
Character	$\chi$	$=$	624.187
Dual form			624.2.bn.a.307.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.293781 - 1.38336i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.82739 - 0.812812i) q^{4} +3.07419 q^{5} +(1.18592 - 0.770451i) q^{6} +(0.857890 + 0.857890i) q^{7} +(-1.66127 + 2.28915i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.293781 - 1.38336i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.82739 - 0.812812i) q^{4} +3.07419 q^{5} +(1.18592 - 0.770451i) q^{6} +(0.857890 + 0.857890i) q^{7} +(-1.66127 + 2.28915i) q^{8} +1.00000i q^{9} +(0.903140 - 4.25272i) q^{10} +4.32633 q^{11} +(-0.717412 - 1.86690i) q^{12} +(-1.73568 + 3.16029i) q^{13} +(1.43880 - 0.934741i) q^{14} +(2.17378 + 2.17378i) q^{15} +(2.67867 + 2.97064i) q^{16} -0.759921i q^{17} +(1.38336 + 0.293781i) q^{18} -3.16005 q^{19} +(-5.61774 - 2.49874i) q^{20} +1.21324i q^{21} +(1.27099 - 5.98488i) q^{22} +1.72267i q^{23} +(-2.79336 + 0.443980i) q^{24} +4.45067 q^{25} +(3.86191 + 3.32951i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.870392 - 2.26500i) q^{28} +(3.41163 - 3.41163i) q^{29} +(3.64575 - 2.36851i) q^{30} +(1.10703 + 1.10703i) q^{31} +(4.89642 - 2.83286i) q^{32} +(3.05918 + 3.05918i) q^{33} +(-1.05125 - 0.223250i) q^{34} +(2.63732 + 2.63732i) q^{35} +(0.812812 - 1.82739i) q^{36} -11.8899i q^{37} +(-0.928362 + 4.37149i) q^{38} +(-3.46197 + 1.00735i) q^{39} +(-5.10705 + 7.03728i) q^{40} +(-5.73564 - 5.73564i) q^{41} +(1.67835 + 0.356427i) q^{42} +(2.35167 + 2.35167i) q^{43} +(-7.90587 - 3.51649i) q^{44} +3.07419i q^{45} +(2.38308 + 0.506088i) q^{46} +(-8.62371 + 8.62371i) q^{47} +(-0.206452 + 3.99467i) q^{48} -5.52805i q^{49} +(1.30752 - 6.15689i) q^{50} +(0.537345 - 0.537345i) q^{51} +(5.74047 - 4.36428i) q^{52} +(-0.861029 - 0.861029i) q^{53} +(0.770451 + 1.18592i) q^{54} +13.3000 q^{55} +(-3.38902 + 0.538654i) q^{56} +(-2.23449 - 2.23449i) q^{57} +(-3.71725 - 5.72180i) q^{58} +2.34805 q^{59} +(-2.20546 - 5.73922i) q^{60} +(7.47738 - 7.47738i) q^{61} +(1.85664 - 1.20620i) q^{62} +(-0.857890 + 0.857890i) q^{63} +(-2.48040 - 7.60576i) q^{64} +(-5.33581 + 9.71534i) q^{65} +(5.13068 - 3.33322i) q^{66} -5.99567 q^{67} +(-0.617673 + 1.38867i) q^{68} +(-1.21811 + 1.21811i) q^{69} +(4.42316 - 2.87357i) q^{70} +(2.79946 - 2.79946i) q^{71} +(-2.28915 - 1.66127i) q^{72} +(-1.41735 + 1.41735i) q^{73} +(-16.4480 - 3.49301i) q^{74} +(3.14710 + 3.14710i) q^{75} +(5.77462 + 2.56852i) q^{76} +(3.71151 + 3.71151i) q^{77} +(0.376470 + 5.08510i) q^{78} +2.19599i q^{79} +(8.23476 + 9.13233i) q^{80} -1.00000 q^{81} +(-9.61949 + 6.24945i) q^{82} -10.4271 q^{83} +(0.986136 - 2.21706i) q^{84} -2.33614i q^{85} +(3.94409 - 2.56234i) q^{86} +4.82478 q^{87} +(-7.18718 + 9.90360i) q^{88} +(2.45084 - 2.45084i) q^{89} +(4.25272 + 0.903140i) q^{90} +(-4.20020 + 1.22216i) q^{91} +(1.40021 - 3.14798i) q^{92} +1.56557i q^{93} +(9.39623 + 14.4632i) q^{94} -9.71460 q^{95} +(5.46542 + 1.45916i) q^{96} +(-0.378892 + 0.378892i) q^{97} +(-7.64730 - 1.62404i) q^{98} +4.32633i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) $ 112 * q - 8 * q^10 + 32 * q^14 + 4 * q^20 - 8 * q^22 + 12 * q^24 + 112 * q^25 - 16 * q^26 - 8 * q^28 + 60 * q^32 - 24 * q^34 - 40 * q^38 + 40 * q^40 - 16 * q^43 - 4 * q^44 - 56 * q^46 - 56 * q^50 + 56 * q^52 + 32 * q^55 + 40 * q^56 + 40 * q^58 - 64 * q^59 + 44 * q^60 - 72 * q^64 + 24 * q^68 - 64 * q^70 - 64 * q^71 - 16 * q^73 - 16 * q^75 - 16 * q^76 + 24 * q^78 + 4 * q^80 - 112 * q^81 - 72 * q^82 + 80 * q^83 + 16 * q^86 - 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.293781	−	1.38336i	0.207735	−	0.978185i
$2$	0.293781	−	1.38336i	0.207735	−	0.978185i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.82739	−	0.812812i	−0.913693	−	0.406406i
$5$	3.07419			1.37482			0.687411	−	0.726269i	$-0.258747\pi$
$5$	3.07419			1.37482			0.687411	+	0.726269i	$0.258747\pi$
$6$	1.18592	−	0.770451i	0.484150	−	0.314535i
$7$	0.857890	+	0.857890i	0.324252	+	0.324252i	0.850396	−	0.526144i	$-0.176363\pi$
$7$	0.857890	+	0.857890i	0.324252	+	0.324252i	−0.526144	+	0.850396i	$0.676363\pi$
$8$	−1.66127	+	2.28915i	−0.587346	+	0.809336i
$9$			1.00000i			0.333333i
$10$	0.903140	−	4.25272i	0.285598	−	1.34483i
$11$	4.32633			1.30444			0.652218	−	0.758031i	$-0.273838\pi$
$11$	4.32633			1.30444			0.652218	+	0.758031i	$0.273838\pi$
$12$	−0.717412	−	1.86690i	−0.207099	−	0.538928i
$13$	−1.73568	+	3.16029i	−0.481391	+	0.876506i
$13$	−1.73568	+	3.16029i	−0.481391	+	0.876506i
$14$	1.43880	−	0.934741i	0.384537	−	0.249820i
$15$	2.17378	+	2.17378i	0.561268	+	0.561268i
$16$	2.67867	+	2.97064i	0.669668	+	0.742660i
$17$		−	0.759921i		−	0.184308i	−0.995745	−	0.0921539i	$-0.970625\pi$
$17$		−	0.759921i		−	0.184308i	0.995745	−	0.0921539i	$-0.0293752\pi$
$18$	1.38336	+	0.293781i	0.326062	+	0.0692449i
$19$	−3.16005			−0.724965			−0.362482	−	0.931991i	$-0.618071\pi$
$19$	−3.16005			−0.724965			−0.362482	+	0.931991i	$0.618071\pi$
$20$	−5.61774	−	2.49874i	−1.25616	−	0.558736i
$21$			1.21324i			0.264751i
$22$	1.27099	−	5.98488i	0.270977	−	1.27598i
$23$			1.72267i			0.359201i	0.983740	+	0.179601i	$0.0574805\pi$
$23$			1.72267i			0.359201i	−0.983740	+	0.179601i	$0.942519\pi$
$24$	−2.79336	+	0.443980i	−0.570193	+	0.0906270i
$25$	4.45067			0.890133
$26$	3.86191	+	3.32951i	0.757384	+	0.652970i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−0.870392	−	2.26500i	−0.164489	−	0.428044i
$29$	3.41163	−	3.41163i	0.633524	−	0.633524i	−0.315426	−	0.948950i	$-0.602147\pi$
$29$	3.41163	−	3.41163i	0.633524	−	0.633524i	0.948950	+	0.315426i	$0.102147\pi$
$30$	3.64575	−	2.36851i	0.665619	−	0.432430i
$31$	1.10703	+	1.10703i	0.198828	+	0.198828i	0.799497	−	0.600669i	$-0.205099\pi$
$31$	1.10703	+	1.10703i	0.198828	+	0.198828i	−0.600669	+	0.799497i	$0.705099\pi$
$32$	4.89642	−	2.83286i	0.865573	−	0.500783i
$33$	3.05918	+	3.05918i	0.532534	+	0.532534i
$34$	−1.05125	−	0.223250i	−0.180287	−	0.0382871i
$35$	2.63732	+	2.63732i	0.445788	+	0.445788i
$36$	0.812812	−	1.82739i	0.135469	−	0.304564i
$37$		−	11.8899i		−	1.95468i	−0.211676	−	0.977340i	$-0.567892\pi$
$37$		−	11.8899i		−	1.95468i	0.211676	−	0.977340i	$-0.432108\pi$
$38$	−0.928362	+	4.37149i	−0.150600	+	0.709150i
$39$	−3.46197	+	1.00735i	−0.554359	+	0.161305i
$40$	−5.10705	+	7.03728i	−0.807496	+	1.11269i
$41$	−5.73564	−	5.73564i	−0.895757	−	0.895757i	0.0993009	−	0.995057i	$-0.468339\pi$
$41$	−5.73564	−	5.73564i	−0.895757	−	0.895757i	−0.995057	+	0.0993009i	$0.968339\pi$
$42$	1.67835	+	0.356427i	0.258975	+	0.0549979i
$43$	2.35167	+	2.35167i	0.358627	+	0.358627i	0.863307	−	0.504680i	$-0.168390\pi$
$43$	2.35167	+	2.35167i	0.358627	+	0.358627i	−0.504680	+	0.863307i	$0.668390\pi$
$44$	−7.90587	−	3.51649i	−1.19185	−	0.530131i
$45$			3.07419i			0.458274i
$46$	2.38308	+	0.506088i	0.351365	+	0.0746185i
$47$	−8.62371	+	8.62371i	−1.25790	+	1.25790i	−0.305802	+	0.952095i	$0.598924\pi$
$47$	−8.62371	+	8.62371i	−1.25790	+	1.25790i	−0.952095	+	0.305802i	$0.901076\pi$
$48$	−0.206452	+	3.99467i	−0.0297988	+	0.576581i
$49$		−	5.52805i		−	0.789721i
$50$	1.30752	−	6.15689i	0.184912	−	0.870715i
$51$	0.537345	−	0.537345i	0.0752434	−	0.0752434i
$52$	5.74047	−	4.36428i	0.796060	−	0.605217i
$53$	−0.861029	−	0.861029i	−0.118271	−	0.118271i	0.645494	−	0.763765i	$-0.276652\pi$
$53$	−0.861029	−	0.861029i	−0.118271	−	0.118271i	−0.763765	+	0.645494i	$0.776652\pi$
$54$	0.770451	+	1.18592i	0.104845	+	0.161383i
$55$	13.3000			1.79337
$56$	−3.38902	+	0.538654i	−0.452877	+	0.0719807i
$57$	−2.23449	−	2.23449i	−0.295966	−	0.295966i
$58$	−3.71725	−	5.72180i	−0.488099	−	0.751309i
$59$	2.34805			0.305690			0.152845	−	0.988250i	$-0.451156\pi$
$59$	2.34805			0.305690			0.152845	+	0.988250i	$0.451156\pi$
$60$	−2.20546	−	5.73922i	−0.284724	−	0.740930i
$61$	7.47738	−	7.47738i	0.957381	−	0.957381i	−0.0417472	−	0.999128i	$-0.513292\pi$
$61$	7.47738	−	7.47738i	0.957381	−	0.957381i	0.999128	+	0.0417472i	$0.0132924\pi$
$62$	1.85664	−	1.20620i	0.235794	−	0.153187i
$63$	−0.857890	+	0.857890i	−0.108084	+	0.108084i
$64$	−2.48040	−	7.60576i	−0.310049	−	0.950720i
$65$	−5.33581	+	9.71534i	−0.661826	+	1.20504i
$66$	5.13068	−	3.33322i	0.631543	−	0.410291i
$67$	−5.99567			−0.732487			−0.366244	−	0.930519i	$-0.619356\pi$
$67$	−5.99567			−0.732487			−0.366244	+	0.930519i	$0.619356\pi$
$68$	−0.617673	+	1.38867i	−0.0749038	+	0.168401i
$69$	−1.21811	+	1.21811i	−0.146643	+	0.146643i
$70$	4.42316	−	2.87357i	0.528669	−	0.343458i
$71$	2.79946	−	2.79946i	0.332235	−	0.332235i	−0.521200	−	0.853435i	$-0.674515\pi$
$71$	2.79946	−	2.79946i	0.332235	−	0.332235i	0.853435	+	0.521200i	$0.174515\pi$
$72$	−2.28915	−	1.66127i	−0.269779	−	0.195782i
$73$	−1.41735	+	1.41735i	−0.165889	+	0.165889i	−0.785170	−	0.619281i	$-0.787424\pi$
$73$	−1.41735	+	1.41735i	−0.165889	+	0.165889i	0.619281	+	0.785170i	$0.287424\pi$
$74$	−16.4480	−	3.49301i	−1.91204	−	0.406055i
$75$	3.14710	+	3.14710i	0.363395	+	0.363395i
$76$	5.77462	+	2.56852i	0.662395	+	0.294630i
$77$	3.71151	+	3.71151i	0.422966	+	0.422966i
$78$	0.376470	+	5.08510i	0.0426268	+	0.575775i
$79$			2.19599i			0.247068i	0.992340	+	0.123534i	$0.0394228\pi$
$79$			2.19599i			0.247068i	−0.992340	+	0.123534i	$0.960577\pi$
$80$	8.23476	+	9.13233i	0.920674	+	1.02103i
$81$	−1.00000			−0.111111
$82$	−9.61949	+	6.24945i	−1.06230	+	0.690136i
$83$	−10.4271			−1.14452			−0.572262	−	0.820071i	$-0.693934\pi$
$83$	−10.4271			−1.14452			−0.572262	+	0.820071i	$0.693934\pi$
$84$	0.986136	−	2.21706i	0.107596	−	0.241901i
$85$		−	2.33614i		−	0.253390i
$86$	3.94409	−	2.56234i	0.425302	−	0.276304i
$87$	4.82478			0.517271
$88$	−7.18718	+	9.90360i	−0.766156	+	1.05573i
$89$	2.45084	−	2.45084i	0.259789	−	0.259789i	−0.565179	−	0.824968i	$-0.691193\pi$
$89$	2.45084	−	2.45084i	0.259789	−	0.259789i	0.824968	+	0.565179i	$0.191193\pi$
$90$	4.25272	+	0.903140i	0.448277	+	0.0951993i
$91$	−4.20020	+	1.22216i	−0.440301	+	0.128117i
$92$	1.40021	−	3.14798i	0.145982	−	0.328199i
$93$			1.56557i			0.162342i
$94$	9.39623	+	14.4632i	0.969147	+	1.49176i
$95$	−9.71460			−0.996697
$96$	5.46542	+	1.45916i	0.557813	+	0.148925i
$97$	−0.378892	+	0.378892i	−0.0384707	+	0.0384707i	−0.726080	−	0.687610i	$-0.758660\pi$
$97$	−0.378892	+	0.378892i	−0.0384707	+	0.0384707i	0.687610	+	0.726080i	$0.258660\pi$
$98$	−7.64730	−	1.62404i	−0.772494	−	0.164053i
$99$			4.32633i			0.434812i
$100$	−8.13308	−	3.61755i	−0.813308	−	0.361755i
$101$	−11.4679	+	11.4679i	−1.14110	+	1.14110i	−0.152846	+	0.988250i	$0.548844\pi$
$101$	−11.4679	+	11.4679i	−1.14110	+	1.14110i	−0.988250	+	0.152846i	$0.951156\pi$
$102$	−0.585481	−	0.901205i	−0.0579713	−	0.0892326i
$103$		−	7.88965i		−	0.777391i	−0.921366	−	0.388695i	$-0.872926\pi$
$103$		−	7.88965i		−	0.777391i	0.921366	−	0.388695i	$-0.127074\pi$
$104$	−4.35094	−	9.22330i	−0.426645	−	0.904419i
$105$			3.72973i			0.363985i
$106$	−1.44407	+	0.938161i	−0.140260	+	0.0911222i
$107$	−5.99236	+	5.99236i	−0.579303	+	0.579303i	−0.934711	−	0.355408i	$-0.884342\pi$
$107$	−5.99236	+	5.99236i	−0.579303	+	0.579303i	0.355408	+	0.934711i	$0.384342\pi$
$108$	1.86690	−	0.717412i	0.179643	−	0.0690330i
$109$			10.1153i			0.968875i	0.874826	+	0.484437i	$0.160976\pi$
$109$			10.1153i			0.968875i	−0.874826	+	0.484437i	$0.839024\pi$
$110$	3.90728	−	18.3987i	0.372545	−	1.75425i
$111$	8.40739	−	8.40739i	0.797995	−	0.797995i
$112$	−0.250476	+	4.84649i	−0.0236678	+	0.457950i
$113$	−14.8108			−1.39329			−0.696644	−	0.717417i	$-0.745324\pi$
$113$	−14.8108			−1.39329			−0.696644	+	0.717417i	$0.745324\pi$
$114$	−3.74756	+	2.43466i	−0.350991	+	0.228027i
$115$			5.29582i			0.493837i
$116$	−9.00738	+	3.46135i	−0.836315	+	0.321378i
$117$	−3.16029	−	1.73568i	−0.292169	−	0.160464i
$118$	0.689814	−	3.24821i	0.0635025	−	0.299022i
$119$	0.651928	−	0.651928i	0.0597622	−	0.0597622i
$120$	−8.58734	+	1.36488i	−0.783913	+	0.124596i
$121$	7.71711			0.701556
$122$	−8.14722	−	12.5407i	−0.737615	−	1.13538i
$123$		−	8.11142i		−	0.731382i
$124$	−1.12316	−	2.92277i	−0.100863	−	0.262473i
$125$	−1.68876			−0.151047
$126$	0.934741	+	1.43880i	0.0832733	+	0.128179i
$127$	12.4348			1.10341			0.551707	−	0.834038i	$-0.313977\pi$
$127$	12.4348			1.10341			0.551707	+	0.834038i	$0.313977\pi$
$128$	−11.2502	+	1.19686i	−0.994389	+	0.105788i
$129$			3.32577i			0.292817i
$130$	11.8723	+	10.2355i	1.04127	+	0.897717i
$131$	−2.33919	−	2.33919i	−0.204376	−	0.204376i	0.597496	−	0.801872i	$-0.296162\pi$
$131$	−2.33919	−	2.33919i	−0.204376	−	0.204376i	−0.801872	+	0.597496i	$0.796162\pi$
$132$	−3.10376	−	8.07683i	−0.270147	−	0.702998i
$133$	−2.71097	−	2.71097i	−0.235071	−	0.235071i
$134$	−1.76141	+	8.29418i	−0.152163	+	0.716508i
$135$	−2.17378	+	2.17378i	−0.187089	+	0.187089i
$136$	1.73957	+	1.26243i	0.149167	+	0.108252i
$137$	10.0955	−	10.0955i	0.862519	−	0.862519i	−0.129111	−	0.991630i	$-0.541212\pi$
$137$	10.0955	−	10.0955i	0.862519	−	0.862519i	0.991630	+	0.129111i	$0.0412125\pi$
$138$	1.32723	+	2.04295i	0.112981	+	0.173907i
$139$	−7.64706	+	7.64706i	−0.648615	+	0.648615i	−0.952658	−	0.304043i	$-0.901663\pi$
$139$	−7.64706	+	7.64706i	−0.648615	+	0.648615i	0.304043	+	0.952658i	$0.401663\pi$
$140$	−2.67575	−	6.96304i	−0.226142	−	0.588485i
$141$	−12.1958			−1.02707
$142$	−3.05024	−	4.69509i	−0.255970	−	0.394004i
$143$	−7.50911	+	13.6724i	−0.627944	+	1.14335i
$144$	−2.97064	+	2.67867i	−0.247553	+	0.223223i
$145$	10.4880	−	10.4880i	0.870983	−	0.870983i
$146$	1.54432	+	2.37711i	0.127809	+	0.196731i
$147$	3.90892	−	3.90892i	0.322402	−	0.322402i
$148$	−9.66421	+	21.7273i	−0.794393	+	1.78598i
$149$	4.91544			0.402688			0.201344	−	0.979521i	$-0.435469\pi$
$149$	4.91544			0.402688			0.201344	+	0.979521i	$0.435469\pi$
$150$	5.27813	−	3.42902i	0.430958	−	0.279978i
$151$	15.3366	+	15.3366i	1.24808	+	1.24808i	0.956568	+	0.291511i	$0.0941579\pi$
$151$	15.3366	+	15.3366i	1.24808	+	1.24808i	0.291511	+	0.956568i	$0.405842\pi$
$152$	5.24968	−	7.23381i	0.425805	−	0.586740i
$153$	0.759921			0.0614360
$154$	6.22474	−	4.04400i	0.501604	−	0.325874i
$155$	3.40322	+	3.40322i	0.273353	+	0.273353i
$156$	7.14514	+	0.973114i	0.572069	+	0.0779114i
$157$	−17.3866	+	17.3866i	−1.38760	+	1.38760i	−0.557264	+	0.830336i	$0.688149\pi$
$157$	−17.3866	+	17.3866i	−1.38760	+	1.38760i	−0.830336	+	0.557264i	$0.811851\pi$
$158$	3.03785	+	0.645141i	0.241678	+	0.0513246i
$159$		−	1.21768i		−	0.0965682i
$160$	15.0525	−	8.70876i	1.19001	−	0.688488i
$161$	−1.47786	+	1.47786i	−0.116472	+	0.116472i
$162$	−0.293781	+	1.38336i	−0.0230816	+	0.108687i
$163$		−	10.5358i		−	0.825228i	−0.910906	−	0.412614i	$-0.864616\pi$
$163$		−	10.5358i		−	0.825228i	0.910906	−	0.412614i	$-0.135384\pi$
$164$	5.81923	+	15.1432i	0.454405	+	1.18249i
$165$	9.40450	+	9.40450i	0.732139	+	0.732139i
$166$	−3.06329	+	14.4245i	−0.237757	+	1.11956i
$167$	13.8662	+	13.8662i	1.07300	+	1.07300i	0.997117	+	0.0758838i	$0.0241778\pi$
$167$	13.8662	+	13.8662i	1.07300	+	1.07300i	0.0758838	+	0.997117i	$0.475822\pi$
$168$	−2.77728	−	2.01551i	−0.214272	−	0.155500i
$169$	−6.97484	−	10.9705i	−0.536526	−	0.843884i
$170$	−3.23173	−	0.686315i	−0.247863	−	0.0526380i
$171$		−	3.16005i		−	0.241655i
$172$	−2.38594	−	6.20888i	−0.181926	−	0.473422i
$173$	5.74035	+	5.74035i	0.436431	+	0.436431i	0.890809	−	0.454378i	$-0.150138\pi$
$173$	5.74035	+	5.74035i	0.436431	+	0.436431i	−0.454378	+	0.890809i	$0.650138\pi$
$174$	1.41743	−	6.67442i	0.107455	−	0.505986i
$175$	3.81818	+	3.81818i	0.288627	+	0.288627i
$176$	11.5888	+	12.8520i	0.873540	+	0.968753i
$177$	1.66032	+	1.66032i	0.124798	+	0.124798i
$178$	−2.67040	−	4.11042i	−0.200155	−	0.308089i
$179$	−10.5506	+	10.5506i	−0.788589	+	0.788589i	−0.981263	−	0.192674i	$-0.938284\pi$
$179$	−10.5506	+	10.5506i	−0.788589	+	0.788589i	0.192674	+	0.981263i	$0.438284\pi$
$180$	2.49874	−	5.61774i	0.186245	−	0.418721i
$181$	11.9444	−	11.9444i	0.887820	−	0.887820i	−0.106494	−	0.994313i	$-0.533962\pi$
$181$	11.9444	−	11.9444i	0.887820	−	0.887820i	0.994313	+	0.106494i	$0.0339624\pi$
$182$	0.456748	+	6.16945i	0.0338564	+	0.457310i
$183$	10.5746			0.781698
$184$	−3.94344	−	2.86181i	−0.290714	−	0.210975i
$185$		−	36.5517i		−	2.68733i
$186$	2.16576	+	0.459936i	0.158801	+	0.0337241i
$187$		−	3.28767i		−	0.240418i
$188$	22.7683	−	8.74938i	1.66055	−	0.638114i
$189$	−1.21324			−0.0882502
$190$	−2.85397	+	13.4388i	−0.207048	+	0.974954i
$191$			16.0725i			1.16297i	0.813558	+	0.581483i	$0.197527\pi$
$191$			16.0725i			1.16297i	−0.813558	+	0.581483i	$0.802473\pi$
$192$	3.62418	−	7.13199i	0.261553	−	0.514707i
$193$	2.31249	+	2.31249i	0.166457	+	0.166457i	0.785420	−	0.618963i	$-0.212447\pi$
$193$	2.31249	+	2.31249i	0.166457	+	0.166457i	−0.618963	+	0.785420i	$0.712447\pi$
$194$	0.412834	+	0.635456i	0.0296397	+	0.0456231i
$195$	−10.6428	+	3.09679i	−0.762145	+	0.221766i
$196$	−4.49327	+	10.1019i	−0.320948	+	0.721563i
$197$	15.0563			1.07272			0.536359	−	0.843990i	$-0.319799\pi$
$197$	15.0563			1.07272			0.536359	+	0.843990i	$0.319799\pi$
$198$	5.98488	+	1.27099i	0.425327	+	0.0903256i
$199$		−	21.5540i		−	1.52792i	−0.645264	−	0.763960i	$-0.723252\pi$
$199$		−	21.5540i		−	1.52792i	0.645264	−	0.763960i	$-0.276748\pi$
$200$	−7.39374	+	10.1882i	−0.522816	+	0.720417i
$201$	−4.23958	−	4.23958i	−0.299037	−	0.299037i
$202$	12.4952	+	19.2333i	0.879158	+	1.35325i
$203$	5.85361			0.410843
$204$	−1.41870	+	0.545176i	−0.0993287	+	0.0381700i
$205$	−17.6325	−	17.6325i	−1.23151	−	1.23151i
$206$	−10.9143	−	2.31783i	−0.760432	−	0.161491i
$207$	−1.72267			−0.119734
$208$	−14.0374	+	3.30930i	−0.973318	+	0.229459i
$209$	−13.6714			−0.945670
$210$	5.15957	+	1.09573i	0.356044	+	0.0756122i
$211$	0.212257	+	0.212257i	0.0146124	+	0.0146124i	0.714375	−	0.699763i	$-0.246711\pi$
$211$	0.212257	+	0.212257i	0.0146124	+	0.0146124i	−0.699763	+	0.714375i	$0.746711\pi$
$212$	0.873577	+	2.27329i	0.0599975	+	0.156130i
$213$	3.95903			0.271268
$214$	6.52917	+	10.0501i	0.446325	+	0.687007i
$215$	7.22949	+	7.22949i	0.493047	+	0.493047i
$216$	−0.443980	−	2.79336i	−0.0302090	−	0.190064i
$217$			1.89942i			0.128941i
$218$	13.9932	+	2.97170i	0.947739	+	0.201269i
$219$	−2.00444			−0.135448
$220$	−24.3042	−	10.8104i	−1.63859	−	0.728835i
$221$	2.40157	+	1.31898i	0.161547	+	0.0887241i
$222$	−9.16054	−	14.1004i	−0.614815	−	0.946358i
$223$	−17.1757	−	17.1757i	−1.15017	−	1.15017i	−0.986519	−	0.163648i	$-0.947674\pi$
$223$	−17.1757	−	17.1757i	−1.15017	−	1.15017i	−0.163648	−	0.986519i	$-0.552326\pi$
$224$	6.63087	+	1.77031i	0.443044	+	0.118284i
$225$			4.45067i			0.296711i
$226$	−4.35115	+	20.4888i	−0.289434	+	1.36289i
$227$	−11.0040			−0.730361			−0.365181	−	0.930937i	$-0.618993\pi$
$227$	−11.0040			−0.730361			−0.365181	+	0.930937i	$0.618993\pi$
$228$	2.26705	+	5.89950i	0.150139	+	0.390704i
$229$			12.2456i			0.809209i	0.914492	+	0.404605i	$0.132591\pi$
$229$			12.2456i			0.809209i	−0.914492	+	0.404605i	$0.867409\pi$
$230$	7.32604	+	1.55581i	0.483064	+	0.102587i
$231$			5.24887i			0.345350i
$232$	2.14211	+	13.4774i	0.140636	+	0.884832i
$233$	−7.89991			−0.517540			−0.258770	−	0.965939i	$-0.583317\pi$
$233$	−7.89991			−0.517540			−0.258770	+	0.965939i	$0.583317\pi$
$234$	−3.32951	+	3.86191i	−0.217657	+	0.252461i
$235$	−26.5109	+	26.5109i	−1.72938	+	1.72938i
$236$	−4.29080	−	1.90853i	−0.279307	−	0.124234i
$237$	−1.55280	+	1.55280i	−0.100865	+	0.100865i
$238$	−0.710329	−	1.09338i	−0.0460438	−	0.0708732i
$239$	12.5661	+	12.5661i	0.812832	+	0.812832i	0.985057	−	0.172226i	$-0.0550959\pi$
$239$	12.5661	+	12.5661i	0.812832	+	0.812832i	−0.172226	+	0.985057i	$0.555096\pi$
$240$	−0.634674	+	12.2804i	−0.0409681	+	0.792695i
$241$	−19.8284	−	19.8284i	−1.27726	−	1.27726i	−0.942194	−	0.335069i	$-0.891240\pi$
$241$	−19.8284	−	19.8284i	−1.27726	−	1.27726i	−0.335069	−	0.942194i	$-0.608760\pi$
$242$	2.26714	−	10.6756i	0.145737	−	0.686251i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−19.7418	+	7.58635i	−1.26384	+	0.485667i
$245$		−	16.9943i		−	1.08573i
$246$	−11.2210	−	2.38298i	−0.715427	−	0.151933i
$247$	5.48483	−	9.98666i	0.348991	−	0.635436i
$248$	−4.37322	+	0.695083i	−0.277700	+	0.0441378i
$249$	−7.37308	−	7.37308i	−0.467250	−	0.467250i
$250$	−0.496126	+	2.33617i	−0.0313777	+	0.147752i
$251$	−20.5309	−	20.5309i	−1.29590	−	1.29590i	−0.931076	−	0.364826i	$-0.881129\pi$
$251$	−20.5309	−	20.5309i	−1.29590	−	1.29590i	−0.364826	−	0.931076i	$-0.618871\pi$
$252$	2.26500	−	0.870392i	0.142681	−	0.0548295i
$253$			7.45283i			0.468555i
$254$	3.65312	−	17.2019i	0.229217	−	1.07934i
$255$	1.65190	−	1.65190i	0.103446	−	0.103446i
$256$	−1.64942	+	15.9148i	−0.103089	+	0.994672i
$257$		−	26.4166i		−	1.64782i	−0.566721	−	0.823910i	$-0.691788\pi$
$257$		−	26.4166i		−	1.64782i	0.566721	−	0.823910i	$-0.308212\pi$
$258$	4.60074	+	0.977047i	0.286430	+	0.0608283i
$259$	10.2002	−	10.2002i	0.633809	−	0.633809i
$260$	17.6473	−	13.4167i	1.09444	−	0.832065i
$261$	3.41163	+	3.41163i	0.211175	+	0.211175i
$262$	−3.92316	+	2.54874i	−0.242373	+	0.157461i
$263$	3.20322			0.197519			0.0987594	−	0.995111i	$-0.468513\pi$
$263$	3.20322			0.197519			0.0987594	+	0.995111i	$0.468513\pi$
$264$	−12.0850	+	1.92080i	−0.743781	+	0.118217i
$265$	−2.64697	−	2.64697i	−0.162602	−	0.162602i
$266$	−4.54669	+	2.95383i	−0.278775	+	0.181111i
$267$	3.46602			0.212117
$268$	10.9564	+	4.87335i	0.669268	+	0.297687i
$269$	−4.67622	+	4.67622i	−0.285114	+	0.285114i	−0.835145	−	0.550030i	$-0.814616\pi$
$269$	−4.67622	+	4.67622i	−0.285114	+	0.285114i	0.550030	+	0.835145i	$0.314616\pi$
$270$	2.36851	+	3.64575i	0.144143	+	0.221873i
$271$	17.2188	−	17.2188i	1.04597	−	1.04597i	0.0470787	−	0.998891i	$-0.485009\pi$
$271$	17.2188	−	17.2188i	1.04597	−	1.04597i	0.998891	−	0.0470787i	$-0.0149912\pi$
$272$	2.25745	−	2.03558i	0.136878	−	0.123425i
$273$	−3.83419	−	2.10579i	−0.232055	−	0.127448i
$274$	−10.9999	−	16.9316i	−0.664528	−	1.02288i
$275$	19.2550			1.16112
$276$	3.21605	−	1.23586i	0.193584	−	0.0743902i
$277$	4.49027	−	4.49027i	0.269794	−	0.269794i	−0.559223	−	0.829017i	$-0.688901\pi$
$277$	4.49027	−	4.49027i	0.269794	−	0.269794i	0.829017	+	0.559223i	$0.188901\pi$
$278$	8.33209	+	12.8252i	0.499726	+	0.769205i
$279$	−1.10703	+	1.10703i	−0.0662760	+	0.0662760i
$280$	−10.4185	+	1.65593i	−0.622625	+	0.0989606i
$281$	20.4238	−	20.4238i	1.21838	−	1.21838i	0.250185	−	0.968198i	$-0.419509\pi$
$281$	20.4238	−	20.4238i	1.21838	−	1.21838i	0.968198	−	0.250185i	$-0.0804914\pi$
$282$	−3.58289	+	16.8712i	−0.213358	+	1.00466i
$283$	4.59749	+	4.59749i	0.273292	+	0.273292i	0.830424	−	0.557132i	$-0.188098\pi$
$283$	4.59749	+	4.59749i	0.273292	+	0.273292i	−0.557132	+	0.830424i	$0.688098\pi$
$284$	−7.39112	+	2.84026i	−0.438582	+	0.168538i
$285$	−6.86926	−	6.86926i	−0.406900	−	0.406900i
$286$	16.7079	+	14.4045i	0.987959	+	0.851758i
$287$		−	9.84109i		−	0.580901i
$288$	2.83286	+	4.89642i	0.166928	+	0.288524i
$289$	16.4225			0.966031
$290$	−11.4276	−	17.5899i	−0.671049	−	1.03292i
$291$	−0.535834			−0.0314112
$292$	3.74209	−	1.43801i	0.218990	−	0.0841532i
$293$			15.5555i			0.908764i	0.890807	+	0.454382i	$0.150140\pi$
$293$			15.5555i			0.908764i	−0.890807	+	0.454382i	$0.849860\pi$
$294$	−4.25909	−	6.55582i	−0.248395	−	0.382343i
$295$	7.21837			0.420270
$296$	27.2176	+	19.7522i	1.58199	+	1.14807i
$297$	−3.05918	+	3.05918i	−0.177511	+	0.177511i
$298$	1.44406	−	6.79984i	0.0836524	−	0.393904i
$299$	−5.44413	−	2.99000i	−0.314842	−	0.172916i
$300$	−3.19296	−	8.30895i	−0.184346	−	0.479718i
$301$			4.03495i			0.232571i
$302$	25.7218	−	16.7105i	1.48012	−	0.961583i
$303$	−16.2180			−0.931701
$304$	−8.46473	−	9.38737i	−0.485486	−	0.538402i
$305$	22.9869	−	22.9869i	1.31623	−	1.31623i
$306$	0.223250	−	1.05125i	0.0127624	−	0.0600957i
$307$		−	18.0641i		−	1.03097i	−0.856897	−	0.515487i	$-0.827611\pi$
$307$		−	18.0641i		−	1.03097i	0.856897	−	0.515487i	$-0.172389\pi$
$308$	−3.76560	−	9.79912i	−0.214565	−	0.558357i
$309$	5.57883	−	5.57883i	0.317368	−	0.317368i
$310$	5.70769	−	3.70808i	0.324175	−	0.210605i
$311$			7.71182i			0.437297i	0.975804	+	0.218649i	$0.0701648\pi$
$311$			7.71182i			0.437297i	−0.975804	+	0.218649i	$0.929835\pi$
$312$	3.44528	−	9.59844i	0.195050	−	0.543405i
$313$			12.2945i			0.694928i	0.937693	+	0.347464i	$0.112957\pi$
$313$			12.2945i			0.694928i	−0.937693	+	0.347464i	$0.887043\pi$
$314$	18.9441	+	29.1598i	1.06908	+	1.64558i
$315$	−2.63732	+	2.63732i	−0.148596	+	0.148596i
$316$	1.78493	−	4.01292i	0.100410	−	0.225744i
$317$		−	2.20341i		−	0.123756i	−0.998084	−	0.0618778i	$-0.980291\pi$
$317$		−	2.20341i		−	0.123756i	0.998084	−	0.0618778i	$-0.0197089\pi$
$318$	−1.68449	−	0.357731i	−0.0944616	−	0.0200606i
$319$	14.7598	−	14.7598i	0.826393	−	0.826393i
$320$	−7.62522	−	23.3816i	−0.426263	−	1.30707i
$321$	−8.47448			−0.472999
$322$	1.61025	+	2.47858i	0.0897357	+	0.138126i
$323$			2.40139i			0.133617i
$324$	1.82739	+	0.812812i	0.101521	+	0.0451562i
$325$	−7.72493	+	14.0654i	−0.428502	+	0.780207i
$326$	−14.5748	−	3.09522i	−0.807226	−	0.171428i
$327$	−7.15263	+	7.15263i	−0.395541	+	0.395541i
$328$	22.6581	−	3.60131i	1.25109	−	0.198849i
$329$	−14.7964			−0.815751
$330$	15.7727	−	10.2470i	0.868258	−	0.564077i
$331$		−	25.8426i		−	1.42044i	−0.703981	−	0.710218i	$-0.748596\pi$
$331$		−	25.8426i		−	1.42044i	0.703981	−	0.710218i	$-0.251404\pi$
$332$	19.0543	+	8.47528i	1.04574	+	0.465141i
$333$	11.8899			0.651560
$334$	23.2557	−	15.1084i	1.27249	−	0.826694i
$335$	−18.4318			−1.00704
$336$	−3.60410	+	3.24987i	−0.196620	+	0.177295i
$337$			19.2388i			1.04800i	0.851717	+	0.524002i	$0.175562\pi$
$337$			19.2388i			1.04800i	−0.851717	+	0.524002i	$0.824438\pi$
$338$	−17.2252	+	6.42581i	−0.936930	+	0.349518i
$339$	−10.4729	−	10.4729i	−0.568807	−	0.568807i
$340$	−1.89885	+	4.26903i	−0.102979	+	0.231521i
$341$	4.78936	+	4.78936i	0.259359	+	0.259359i
$342$	−4.37149	−	0.928362i	−0.236383	−	0.0502001i
$343$	10.7477	−	10.7477i	0.580321	−	0.580321i
$344$	−9.29007	+	1.47657i	−0.500887	+	0.0796115i
$345$	−3.74471	+	3.74471i	−0.201608	+	0.201608i
$346$	9.62740	−	6.25458i	0.517572	−	0.336248i
$347$	−2.30632	+	2.30632i	−0.123810	+	0.123810i	−0.766297	−	0.642487i	$-0.777903\pi$
$347$	−2.30632	+	2.30632i	−0.123810	+	0.123810i	0.642487	+	0.766297i	$0.277903\pi$
$348$	−8.81673	−	3.92164i	−0.472626	−	0.210222i
$349$	−33.3689			−1.78620			−0.893098	−	0.449862i	$-0.851473\pi$
$349$	−33.3689			−1.78620			−0.893098	+	0.449862i	$0.851473\pi$
$350$	6.40364	−	4.16022i	0.342289	−	0.222373i
$351$	−1.00735	−	3.46197i	−0.0537684	−	0.184786i
$352$	21.1835	−	12.2559i	1.12908	−	0.653240i
$353$	7.93820	−	7.93820i	0.422508	−	0.422508i	−0.463558	−	0.886066i	$-0.653428\pi$
$353$	7.93820	−	7.93820i	0.422508	−	0.422508i	0.886066	+	0.463558i	$0.153428\pi$
$354$	2.78460	−	1.80906i	0.148000	−	0.0961504i
$355$	8.60608	−	8.60608i	0.456763	−	0.456763i
$356$	−6.47071	+	2.48656i	−0.342947	+	0.131788i
$357$	0.921966			0.0487956
$358$	11.4957	+	17.6949i	0.607568	+	0.935203i
$359$	−13.6515	−	13.6515i	−0.720499	−	0.720499i	0.248208	−	0.968707i	$-0.420159\pi$
$359$	−13.6515	−	13.6515i	−0.720499	−	0.720499i	−0.968707	+	0.248208i	$0.920159\pi$
$360$	−7.03728	−	5.10705i	−0.370897	−	0.269165i
$361$	−9.01410			−0.474426
$362$	−13.0144	−	20.0325i	−0.684021	−	1.05288i
$363$	5.45682	+	5.45682i	0.286409	+	0.286409i
$364$	8.66877	+	1.18062i	0.454367	+	0.0618813i
$365$	−4.35722	+	4.35722i	−0.228067	+	0.228067i
$366$	3.10662	−	14.6285i	0.162386	−	0.764646i
$367$		−	12.3554i		−	0.644945i	−0.946579	−	0.322473i	$-0.895486\pi$
$367$		−	12.3554i		−	0.644945i	0.946579	−	0.322473i	$-0.104514\pi$
$368$	−5.11743	+	4.61447i	−0.266764	+	0.240546i
$369$	5.73564	−	5.73564i	0.298586	−	0.298586i
$370$	−50.5643	−	10.7382i	−2.62871	−	0.558253i
$371$		−	1.47734i		−	0.0766994i
$372$	1.27252	−	2.86091i	0.0659769	−	0.148331i
$373$	3.18004	+	3.18004i	0.164656	+	0.164656i	0.784626	−	0.619970i	$-0.212855\pi$
$373$	3.18004	+	3.18004i	0.164656	+	0.164656i	−0.619970	+	0.784626i	$0.712855\pi$
$374$	−4.54804	−	0.965855i	−0.235173	−	0.0499432i
$375$	−1.19413	−	1.19413i	−0.0616648	−	0.0616648i
$376$	−5.41468	−	34.0672i	−0.279241	−	1.75688i
$377$	4.86024	+	16.7032i	0.250315	+	0.860261i
$378$	−0.356427	+	1.67835i	−0.0183326	+	0.0863250i
$379$			28.0276i			1.43968i	0.694138	+	0.719841i	$0.255786\pi$
$379$			28.0276i			1.43968i	−0.694138	+	0.719841i	$0.744214\pi$
$380$	17.7523	+	7.89614i	0.910674	+	0.405063i
$381$	8.79276	+	8.79276i	0.450467	+	0.450467i
$382$	22.2341	+	4.72180i	1.13760	+	0.241589i
$383$	25.1599	+	25.1599i	1.28561	+	1.28561i	0.937426	+	0.348184i	$0.113202\pi$
$383$	25.1599	+	25.1599i	1.28561	+	1.28561i	0.348184	+	0.937426i	$0.386798\pi$
$384$	−8.80142	−	7.10880i	−0.449145	−	0.362770i
$385$	11.4099	+	11.4099i	0.581503	+	0.581503i
$386$	3.87838	−	2.51965i	0.197404	−	0.128247i
$387$	−2.35167	+	2.35167i	−0.119542	+	0.119542i
$388$	1.00035	−	0.384414i	0.0507851	−	0.0195156i
$389$	11.3928	−	11.3928i	0.577637	−	0.577637i	−0.356615	−	0.934252i	$-0.616069\pi$
$389$	11.3928	−	11.3928i	0.577637	−	0.577637i	0.934252	+	0.356615i	$0.116069\pi$
$390$	1.15734	+	15.6326i	0.0586042	+	0.791587i
$391$	1.30909			0.0662036
$392$	12.6545	+	9.18356i	0.639150	+	0.463840i
$393$		−	3.30811i		−	0.166872i
$394$	4.42326	−	20.8284i	0.222841	−	1.04932i
$395$			6.75090i			0.339675i
$396$	3.51649	−	7.90587i	0.176710	−	0.397285i
$397$	21.8627			1.09726			0.548629	−	0.836066i	$-0.315150\pi$
$397$	21.8627			1.09726			0.548629	+	0.836066i	$0.315150\pi$
$398$	−29.8169	−	6.33215i	−1.49459	−	0.317402i
$399$		−	3.83389i		−	0.191935i
$400$	11.9219	+	13.2213i	0.596094	+	0.661067i
$401$	−0.903577	−	0.903577i	−0.0451225	−	0.0451225i	0.684186	−	0.729308i	$-0.260158\pi$
$401$	−0.903577	−	0.903577i	−0.0451225	−	0.0451225i	−0.729308	+	0.684186i	$0.760158\pi$
$402$	−7.11038	+	4.61936i	−0.354634	+	0.230393i
$403$	−5.41997	+	1.57708i	−0.269988	+	0.0785600i
$404$	30.2775	−	11.6350i	1.50636	−	0.578863i
$405$	−3.07419			−0.152758
$406$	1.71968	−	8.09767i	0.0853463	−	0.401880i
$407$		−	51.4394i		−	2.54976i
$408$	0.337390	+	2.12274i	0.0167033	+	0.105091i
$409$	7.60585	+	7.60585i	0.376085	+	0.376085i	0.869688	−	0.493602i	$-0.164320\pi$
$409$	7.60585	+	7.60585i	0.376085	+	0.376085i	−0.493602	+	0.869688i	$0.664320\pi$
$410$	−29.5722	+	19.2120i	−1.46047	+	0.948814i
$411$	14.2772			0.704244
$412$	−6.41280	+	14.4174i	−0.315936	+	0.710296i
$413$	2.01437	+	2.01437i	0.0991207	+	0.0991207i
$414$	−0.506088	+	2.38308i	−0.0248728	+	0.117122i
$415$	−32.0550			−1.57352
$416$	0.454040	+	20.3910i	0.0222611	+	0.999752i
$417$	−10.8146			−0.529592
$418$	−4.01640	+	18.9125i	−0.196449	+	0.925041i
$419$	21.4201	+	21.4201i	1.04644	+	1.04644i	0.998868	+	0.0475747i	$0.0151492\pi$
$419$	21.4201	+	21.4201i	1.04644	+	1.04644i	0.0475747	+	0.998868i	$0.484851\pi$
$420$	3.03157	−	6.81566i	0.147926	−	0.332570i
$421$	−17.4152			−0.848764			−0.424382	−	0.905483i	$-0.639509\pi$
$421$	−17.4152			−0.848764			−0.424382	+	0.905483i	$0.639509\pi$
$422$	0.355985	−	0.231271i	0.0173291	−	0.0112581i
$423$	−8.62371	−	8.62371i	−0.419299	−	0.419299i
$424$	3.40142	−	0.540625i	0.165187	−	0.0262551i
$425$		−	3.38215i		−	0.164059i
$426$	1.16309	−	5.47678i	0.0563518	−	0.265351i
$427$	12.8295			0.620865
$428$	15.8210	−	6.07969i	0.764738	−	0.293873i
$429$	−14.9776	+	4.35813i	−0.723126	+	0.210412i
$430$	12.1249	−	7.87712i	0.584715	−	0.379869i
$431$	−9.39091	−	9.39091i	−0.452344	−	0.452344i	0.443788	−	0.896132i	$-0.353634\pi$
$431$	−9.39091	−	9.39091i	−0.452344	−	0.452344i	−0.896132	+	0.443788i	$0.853634\pi$
$432$	−3.99467	−	0.206452i	−0.192194	−	0.00993294i
$433$			0.300310i			0.0144320i	0.999974	+	0.00721599i	$0.00229694\pi$
$433$			0.300310i			0.0144320i	−0.999974	+	0.00721599i	$0.997703\pi$
$434$	2.62758	+	0.558013i	0.126128	+	0.0267855i
$435$	14.8323			0.711154
$436$	8.22188	−	18.4846i	0.393756	−	0.885254i
$437$		−	5.44371i		−	0.260408i
$438$	−0.588867	+	2.77287i	−0.0281372	+	0.132493i
$439$		−	21.0823i		−	1.00621i	−0.864227	−	0.503103i	$-0.832192\pi$
$439$		−	21.0823i		−	1.00621i	0.864227	−	0.503103i	$-0.167808\pi$
$440$	−22.0948	+	30.4456i	−1.05333	+	1.45144i
$441$	5.52805			0.263240
$442$	2.53016	−	2.93475i	0.120348	−	0.139592i
$443$	−23.4721	+	23.4721i	−1.11519	+	1.11519i	−0.122757	+	0.992437i	$0.539174\pi$
$443$	−23.4721	+	23.4721i	−1.11519	+	1.11519i	−0.992437	+	0.122757i	$0.960826\pi$
$444$	−22.1972	+	8.52992i	−1.05343	+	0.404812i
$445$	7.53437	−	7.53437i	0.357163	−	0.357163i
$446$	−28.8061	+	18.7143i	−1.36401	+	0.886147i
$447$	3.47574	+	3.47574i	0.164397	+	0.164397i
$448$	4.39700	−	8.65281i	0.207739	−	0.408807i
$449$	29.9572	+	29.9572i	1.41377	+	1.41377i	0.724641	+	0.689127i	$0.242006\pi$
$449$	29.9572	+	29.9572i	1.41377	+	1.41377i	0.689127	+	0.724641i	$0.257994\pi$
$450$	6.15689	+	1.30752i	0.290238	+	0.0616372i
$451$	−24.8143	−	24.8143i	−1.16846	−	1.16846i
$452$	27.0651	+	12.0384i	1.27304	+	0.566240i
$453$			21.6893i			1.01905i
$454$	−3.23277	+	15.2225i	−0.151721	+	0.714428i
$455$	−12.9122	+	3.75715i	−0.605335	+	0.176138i
$456$	8.82716	−	1.40300i	0.413370	−	0.0657014i
$457$	2.48636	+	2.48636i	0.116307	+	0.116307i	0.762865	−	0.646558i	$-0.223792\pi$
$457$	2.48636	+	2.48636i	0.116307	+	0.116307i	−0.646558	+	0.762865i	$0.723792\pi$
$458$	16.9401	+	3.59751i	0.791557	+	0.168101i
$459$	0.537345	+	0.537345i	0.0250811	+	0.0250811i
$460$	4.30450	−	9.67750i	0.200698	−	0.451216i
$461$			34.6360i			1.61316i	0.591124	+	0.806581i	$0.298684\pi$
$461$			34.6360i			1.61316i	−0.591124	+	0.806581i	$0.701316\pi$
$462$	7.26109	+	1.54202i	0.337817	+	0.0717412i
$463$	3.19470	−	3.19470i	0.148470	−	0.148470i	−0.628964	−	0.777434i	$-0.716521\pi$
$463$	3.19470	−	3.19470i	0.148470	−	0.148470i	0.777434	+	0.628964i	$0.216521\pi$
$464$	19.2734	+	0.996087i	0.894745	+	0.0462422i
$465$			4.81288i			0.223192i
$466$	−2.32084	+	10.9284i	−0.107511	+	0.506250i
$467$	2.10588	−	2.10588i	0.0974485	−	0.0974485i	−0.656702	−	0.754150i	$-0.728049\pi$
$467$	2.10588	−	2.10588i	0.0974485	−	0.0974485i	0.754150	+	0.656702i	$0.228049\pi$
$468$	4.36428	+	5.74047i	0.201739	+	0.265353i
$469$	−5.14362	−	5.14362i	−0.237510	−	0.237510i
$470$	28.8858	+	44.4627i	1.33240	+	2.05091i
$471$	−24.5883			−1.13297
$472$	−3.90074	+	5.37504i	−0.179546	+	0.247406i
$473$	10.1741	+	10.1741i	0.467806	+	0.467806i
$474$	1.69190	+	2.60427i	0.0777116	+	0.119618i
$475$	−14.0643			−0.645315
$476$	−1.72122	+	0.661429i	−0.0788920	+	0.0303166i
$477$	0.861029	−	0.861029i	0.0394238	−	0.0394238i
$478$	21.0751	−	13.6918i	0.963953	−	0.626247i
$479$	3.93196	−	3.93196i	0.179656	−	0.179656i	−0.611550	−	0.791206i	$-0.709454\pi$
$479$	3.93196	−	3.93196i	0.179656	−	0.179656i	0.791206	+	0.611550i	$0.209454\pi$
$480$	16.8018	+	4.48573i	0.766892	+	0.204745i
$481$	37.5754	+	20.6370i	1.71329	+	0.940965i
$482$	−33.2552	+	21.6047i	−1.51473	+	0.984068i
$483$	−2.09001			−0.0950987
$484$	−14.1021	−	6.27256i	−0.641006	−	0.285116i
$485$	−1.16479	+	1.16479i	−0.0528903	+	0.0528903i
$486$	−1.18592	+	0.770451i	−0.0537944	+	0.0349483i
$487$	−3.63751	+	3.63751i	−0.164832	+	0.164832i	−0.784703	−	0.619872i	$-0.787185\pi$
$487$	−3.63751	+	3.63751i	−0.164832	+	0.164832i	0.619872	+	0.784703i	$0.287185\pi$
$488$	4.69492	+	29.5388i	0.212529	+	1.33716i
$489$	7.44994	−	7.44994i	0.336898	−	0.336898i
$490$	−23.5093	−	4.99260i	−1.06204	−	0.225543i
$491$	3.90860	+	3.90860i	0.176393	+	0.176393i	0.789781	−	0.613389i	$-0.210194\pi$
$491$	3.90860	+	3.90860i	0.176393	+	0.176393i	−0.613389	+	0.789781i	$0.710194\pi$
$492$	−6.59306	+	14.8227i	−0.297238	+	0.668258i
$493$	−2.59257	−	2.59257i	−0.116764	−	0.116764i
$494$	−12.2038	−	10.5214i	−0.549076	−	0.473380i
$495$			13.3000i			0.597789i
$496$	−0.323216	+	6.25395i	−0.0145128	+	0.280811i
$497$	4.80325			0.215455
$498$	−12.3657	+	8.03357i	−0.554121	+	0.359993i
$499$	3.13592			0.140383			0.0701915	−	0.997534i	$-0.477639\pi$
$499$	3.13592			0.140383			0.0701915	+	0.997534i	$0.477639\pi$
$500$	3.08601	+	1.37264i	0.138011	+	0.0613865i
$501$			19.6098i			0.876101i
$502$	−34.4333	+	22.3701i	−1.53684	+	0.998428i
$503$	−1.34081			−0.0597838			−0.0298919	−	0.999553i	$-0.509516\pi$
$503$	−1.34081			−0.0597838			−0.0298919	+	0.999553i	$0.509516\pi$
$504$	−0.538654	−	3.38902i	−0.0239936	−	0.150959i
$505$	−35.2545	+	35.2545i	−1.56880	+	1.56880i
$506$	10.3100	+	2.18950i	0.458334	+	0.0973352i
$507$	2.82535	−	12.6893i	0.125478	−	0.563550i
$508$	−22.7233	−	10.1072i	−1.00818	−	0.448434i
$509$		−	25.3657i		−	1.12432i	−0.827030	−	0.562159i	$-0.809971\pi$
$509$		−	25.3657i		−	1.12432i	0.827030	−	0.562159i	$-0.190029\pi$
$510$	−1.79988	−	2.77048i	−0.0797002	−	0.122679i
$511$	−2.43187			−0.107579
$512$	21.5313	+	6.95720i	0.951559	+	0.307468i
$513$	2.23449	−	2.23449i	0.0986552	−	0.0986552i
$514$	−36.5437	−	7.76069i	−1.61187	−	0.342309i
$515$		−	24.2543i		−	1.06877i
$516$	2.70322	−	6.07746i	0.119003	−	0.267545i
$517$	−37.3090	+	37.3090i	−1.64085	+	1.64085i
$518$	−11.1139	−	17.1072i	−0.488318	−	0.751646i
$519$			8.11808i			0.356344i
$520$	−13.3756	−	28.3542i	−0.586561	−	1.24341i
$521$		−	22.1881i		−	0.972077i	−0.873938	−	0.486038i	$-0.838442\pi$
$521$		−	22.1881i		−	0.972077i	0.873938	−	0.486038i	$-0.161558\pi$
$522$	5.72180	−	3.71725i	0.250436	−	0.162700i
$523$	1.01508	−	1.01508i	0.0443862	−	0.0443862i	−0.684565	−	0.728952i	$-0.740008\pi$
$523$	1.01508	−	1.01508i	0.0443862	−	0.0443862i	0.728952	+	0.684565i	$0.240008\pi$
$524$	2.37328	+	6.17592i	0.103677	+	0.269796i
$525$			5.39972i			0.235663i
$526$	0.941045	−	4.43121i	0.0410315	−	0.193210i
$527$	0.841253	−	0.841253i	0.0366456	−	0.0366456i
$528$	−0.893180	+	17.2822i	−0.0388707	+	0.752113i
$529$	20.0324			0.870974
$530$	−4.43935	+	2.88409i	−0.192833	+	0.125277i
$531$			2.34805i			0.101897i
$532$	2.75048	+	7.15750i	0.119248	+	0.310317i
$533$	28.0815	−	8.17105i	1.21634	−	0.353927i
$534$	1.01825	−	4.79476i	0.0440640	−	0.207490i
$535$	−18.4217	+	18.4217i	−0.796439	+	0.796439i
$536$	9.96039	−	13.7250i	0.430223	−	0.592828i
$537$	−14.9208			−0.643880
$538$	5.09513	+	7.84270i	0.219667	+	0.338123i
$539$		−	23.9162i		−	1.03014i
$540$	5.73922	−	2.20546i	0.246977	−	0.0949080i
$541$	26.0039			1.11800			0.558998	−	0.829169i	$-0.311186\pi$
$541$	26.0039			1.11800			0.558998	+	0.829169i	$0.311186\pi$
$542$	−18.7613	−	28.8785i	−0.805868	−	1.24044i
$543$	16.8919			0.724902
$544$	−2.15275	−	3.72089i	−0.0922983	−	0.159532i
$545$			31.0965i			1.33203i
$546$	−4.03949	+	4.68543i	−0.172874	+	0.200518i
$547$	1.14658	+	1.14658i	0.0490243	+	0.0490243i	0.731194	−	0.682170i	$-0.238963\pi$
$547$	1.14658	+	1.14658i	0.0490243	+	0.0490243i	−0.682170	+	0.731194i	$0.738963\pi$
$548$	−26.6542	+	10.2426i	−1.13861	+	0.437544i
$549$	7.47738	+	7.47738i	0.319127	+	0.319127i
$550$	5.65677	−	26.6367i	0.241205	−	1.13579i
$551$	−10.7809	+	10.7809i	−0.459283	+	0.459283i
$552$	−0.764830	−	4.81204i	−0.0325533	−	0.204814i
$553$	−1.88392	+	1.88392i	−0.0801123	+	0.0801123i
$554$	−4.89251	−	7.53082i	−0.207863	−	0.319954i
$555$	25.8460	−	25.8460i	1.09710	−	1.09710i
$556$	20.1897	−	7.75850i	0.856236	−	0.329034i
$557$	16.0757			0.681149			0.340575	−	0.940218i	$-0.389378\pi$
$557$	16.0757			0.681149			0.340575	+	0.940218i	$0.389378\pi$
$558$	1.20620	+	1.85664i	0.0510624	+	0.0785980i
$559$	−11.5137	+	3.35021i	−0.486978	+	0.141699i
$560$	−0.770012	+	14.8990i	−0.0325389	+	0.629600i
$561$	2.32473	−	2.32473i	0.0981502	−	0.0981502i
$562$	−22.2534	−	34.2537i	−0.938704	−	1.44490i
$563$	−20.8913	+	20.8913i	−0.880465	+	0.880465i	−0.993582	−	0.113116i	$-0.963917\pi$
$563$	−20.8913	+	20.8913i	−0.880465	+	0.880465i	0.113116	+	0.993582i	$0.463917\pi$
$564$	22.2864	+	9.91286i	0.938425	+	0.417407i
$565$	−45.5314			−1.91552
$566$	7.71065	−	5.00934i	0.324103	−	0.210558i
$567$	−0.857890	−	0.857890i	−0.0360280	−	0.0360280i
$568$	1.75773	+	11.0590i	0.0737527	+	0.464026i
$569$	−16.5051			−0.691928			−0.345964	−	0.938248i	$-0.612448\pi$
$569$	−16.5051			−0.691928			−0.345964	+	0.938248i	$0.612448\pi$
$570$	−11.5207	+	7.48462i	−0.482550	+	0.313496i
$571$	23.1945	+	23.1945i	0.970659	+	0.970659i	0.999582	−	0.0289227i	$-0.00920767\pi$
$571$	23.1945	+	23.1945i	0.970659	+	0.970659i	−0.0289227	+	0.999582i	$0.509208\pi$
$572$	24.8352	−	18.8813i	1.03841	−	0.789468i
$573$	−11.3650	+	11.3650i	−0.474779	+	0.474779i
$574$	−13.6138	−	2.89113i	−0.568229	−	0.120673i
$575$			7.66702i			0.319737i
$576$	7.60576	−	2.48040i	0.316907	−	0.103350i
$577$	−7.33630	+	7.33630i	−0.305414	+	0.305414i	−0.843128	−	0.537713i	$-0.819288\pi$
$577$	−7.33630	+	7.33630i	−0.305414	+	0.305414i	0.537713	+	0.843128i	$0.319288\pi$
$578$	4.82463	−	22.7183i	0.200678	−	0.944957i
$579$			3.27036i			0.135911i
$580$	−27.6904	+	10.6409i	−1.14978	+	0.441838i
$581$	−8.94531	−	8.94531i	−0.371114	−	0.371114i
$582$	−0.157418	+	0.741253i	−0.00652519	+	0.0307259i
$583$	−3.72509	−	3.72509i	−0.154278	−	0.154278i
$584$	−0.889932	−	5.59914i	−0.0368257	−	0.231694i
$585$	−9.71534	−	5.33581i	−0.401680	−	0.220609i
$586$	21.5189	+	4.56992i	0.888940	+	0.188782i
$587$		−	21.1429i		−	0.872660i	−0.899787	−	0.436330i	$-0.856278\pi$
$587$		−	21.1429i		−	0.872660i	0.899787	−	0.436330i	$-0.143722\pi$
$588$	−10.3203	+	3.96589i	−0.425603	+	0.163550i
$589$	−3.49826	−	3.49826i	−0.144143	−	0.144143i
$590$	2.12062	−	9.98562i	0.0873046	−	0.411102i
$591$	10.6464	+	10.6464i	0.437935	+	0.437935i
$592$	35.3205	−	31.8490i	1.45166	−	1.30899i
$593$	6.48073	+	6.48073i	0.266132	+	0.266132i	0.827539	−	0.561408i	$-0.189740\pi$
$593$	6.48073	+	6.48073i	0.266132	+	0.266132i	−0.561408	+	0.827539i	$0.689740\pi$
$594$	3.33322	+	5.13068i	0.136764	+	0.210514i
$595$	2.00415	−	2.00415i	0.0821623	−	0.0821623i
$596$	−8.98240	−	3.99533i	−0.367933	−	0.163655i
$597$	15.2410	−	15.2410i	0.623771	−	0.623771i
$598$	−5.73564	+	6.65280i	−0.234548	+	0.272053i
$599$	−18.4395			−0.753418			−0.376709	−	0.926332i	$-0.622944\pi$
$599$	−18.4395			−0.753418			−0.376709	+	0.926332i	$0.622944\pi$
$600$	−12.4323	+	1.97601i	−0.507548	+	0.0806701i
$601$			25.1294i			1.02505i	0.858672	+	0.512525i	$0.171290\pi$
$601$			25.1294i			1.02505i	−0.858672	+	0.512525i	$0.828710\pi$
$602$	5.58180	+	1.18539i	0.227497	+	0.0483130i
$603$		−	5.99567i		−	0.244162i
$604$	−15.5601	−	40.4918i	−0.633133	−	1.64759i
$605$	23.7239			0.964513
$606$	−4.76455	+	22.4354i	−0.193547	+	0.911376i
$607$		−	27.9518i		−	1.13453i	−0.823536	−	0.567264i	$-0.808002\pi$
$607$		−	27.9518i		−	1.13453i	0.823536	−	0.567264i	$-0.191998\pi$
$608$	−15.4729	+	8.95197i	−0.627509	+	0.363050i
$609$	4.13913	+	4.13913i	0.167726	+	0.167726i
$610$	−25.0461	−	38.5524i	−1.01409	−	1.56094i
$611$	−12.2854	−	42.2214i	−0.497015	−	1.70809i
$612$	−1.38867	−	0.617673i	−0.0561336	−	0.0249679i
$613$	22.4547			0.906937			0.453468	−	0.891272i	$-0.350187\pi$
$613$	22.4547			0.906937			0.453468	+	0.891272i	$0.350187\pi$
$614$	−24.9892	−	5.30690i	−1.00848	−	0.214169i
$615$		−	24.9361i		−	1.00552i
$616$	−14.6620	+	2.33039i	−0.590749	+	0.0938943i
$617$	21.1975	+	21.1975i	0.853379	+	0.853379i	0.990548	−	0.137169i	$-0.0438002\pi$
$617$	21.1975	+	21.1975i	0.853379	+	0.853379i	−0.137169	+	0.990548i	$0.543800\pi$
$618$	−6.07859	−	9.35650i	−0.244517	−	0.376373i
$619$	21.4228			0.861053			0.430527	−	0.902578i	$-0.358328\pi$
$619$	21.4228			0.861053			0.430527	+	0.902578i	$0.358328\pi$
$620$	−3.45281	−	8.98516i	−0.138668	−	0.360853i
$621$	−1.21811	−	1.21811i	−0.0488811	−	0.0488811i
$622$	10.6682	+	2.26559i	0.427758	+	0.0908418i
$623$	4.20511			0.168474
$624$	−12.2660	−	7.58591i	−0.491032	−	0.303679i
$625$	−27.4449			−1.09780
$626$	17.0078	+	3.61190i	0.679769	+	0.144361i
$627$	−9.66714	−	9.66714i	−0.386068	−	0.386068i
$628$	45.9040	−	17.6399i	1.83177	−	0.703911i
$629$	−9.03535			−0.360263
$630$	2.87357	+	4.42316i	0.114486	+	0.176223i
$631$	32.3769	+	32.3769i	1.28890	+	1.28890i	0.935453	+	0.353451i	$0.114992\pi$
$631$	32.3769	+	32.3769i	1.28890	+	1.28890i	0.353451	+	0.935453i	$0.385008\pi$
$632$	−5.02695	−	3.64812i	−0.199961	−	0.145114i
$633$			0.300177i			0.0119309i
$634$	−3.04811	−	0.647319i	−0.121056	−	0.0257083i
$635$	38.2271			1.51700
$636$	−0.989744	+	2.22517i	−0.0392459	+	0.0882336i
$637$	17.4702	+	9.59492i	0.692196	+	0.380165i
$638$	−16.0821	−	24.7544i	−0.636695	−	0.980035i
$639$	2.79946	+	2.79946i	0.110745	+	0.110745i
$640$	−34.5854	+	3.67937i	−1.36711	+	0.145440i
$641$			37.8821i			1.49625i	0.663557	+	0.748126i	$0.269046\pi$
$641$			37.8821i			1.49625i	−0.663557	+	0.748126i	$0.730954\pi$
$642$	−2.48964	+	11.7233i	−0.0982583	+	0.462681i
$643$	−27.5767			−1.08752			−0.543760	−	0.839241i	$-0.683000\pi$
$643$	−27.5767			−1.08752			−0.543760	+	0.839241i	$0.683000\pi$
$644$	3.90184	−	1.49940i	0.153754	−	0.0590845i
$645$			10.2240i			0.402571i
$646$	3.32199	+	0.705482i	0.130702	+	0.0277568i
$647$			21.9782i			0.864052i	0.901861	+	0.432026i	$0.142201\pi$
$647$			21.9782i			0.864052i	−0.901861	+	0.432026i	$0.857799\pi$
$648$	1.66127	−	2.28915i	0.0652607	−	0.0899262i
$649$	10.1584			0.398754
$650$	17.1881	+	14.8185i	0.674172	+	0.581230i
$651$	−1.34309	+	1.34309i	−0.0526398	+	0.0526398i
$652$	−8.56363	+	19.2530i	−0.335378	+	0.754005i
$653$	−26.2145	+	26.2145i	−1.02585	+	1.02585i	−0.0261969	+	0.999657i	$0.508340\pi$
$653$	−26.2145	+	26.2145i	−1.02585	+	1.02585i	−0.999657	+	0.0261969i	$0.991660\pi$
$654$	7.79338	+	11.9960i	0.304745	+	0.469080i
$655$	−7.19112	−	7.19112i	−0.280980	−	0.280980i
$656$	1.67462	−	32.4024i	0.0653830	−	1.26510i
$657$	−1.41735	−	1.41735i	−0.0552963	−	0.0552963i
$658$	−4.34690	+	20.4688i	−0.169460	+	0.797955i
$659$	20.6175	+	20.6175i	0.803144	+	0.803144i	0.983586	−	0.180442i	$-0.0577528\pi$
$659$	20.6175	+	20.6175i	0.803144	+	0.803144i	−0.180442	+	0.983586i	$0.557753\pi$
$660$	−9.54155	−	24.8297i	−0.371404	−	0.966496i
$661$		−	44.7303i		−	1.73981i	−0.493221	−	0.869904i	$-0.664181\pi$
$661$		−	44.7303i		−	1.73981i	0.493221	−	0.869904i	$-0.335819\pi$
$662$	−35.7497	−	7.59207i	−1.38945	−	0.295074i
$663$	0.765507	+	2.63082i	0.0297298	+	0.102173i
$664$	17.3222	−	23.8692i	0.672232	−	0.926305i
$665$	−8.33405	−	8.33405i	−0.323181	−	0.323181i
$666$	3.49301	−	16.4480i	0.135352	−	0.637346i
$667$	5.87711	+	5.87711i	0.227563	+	0.227563i
$668$	−14.0683	−	36.6096i	−0.544319	−	1.41647i
$669$		−	24.2900i		−	0.939108i
$670$	−5.41493	+	25.4979i	−0.209197	+	0.985071i
$671$	32.3496	−	32.3496i	1.24884	−	1.24884i
$672$	3.43694	+	5.94053i	0.132583	+	0.229161i
$673$		−	18.3256i		−	0.706401i	−0.935548	−	0.353200i	$-0.885093\pi$
$673$		−	18.3256i		−	0.706401i	0.935548	−	0.353200i	$-0.114907\pi$
$674$	26.6142	+	5.65200i	1.02514	+	0.217707i
$675$	−3.14710	+	3.14710i	−0.121132	+	0.121132i
$676$	3.82877	+	25.7165i	0.147260	+	0.989098i
$677$	15.3004	+	15.3004i	0.588043	+	0.588043i	0.937101	−	0.349058i	$-0.113498\pi$
$677$	15.3004	+	15.3004i	0.588043	+	0.588043i	−0.349058	+	0.937101i	$0.613498\pi$
$678$	−17.5645	+	11.4110i	−0.674560	+	0.438238i
$679$	−0.650095			−0.0249484
$680$	5.34778	+	3.88095i	0.205078	+	0.148828i
$681$	−7.78100	−	7.78100i	−0.298169	−	0.298169i
$682$	8.03245	−	5.21840i	0.307579	−	0.199823i
$683$	−1.03101			−0.0394506			−0.0197253	−	0.999805i	$-0.506279\pi$
$683$	−1.03101			−0.0394506			−0.0197253	+	0.999805i	$0.506279\pi$
$684$	−2.56852	+	5.77462i	−0.0982100	+	0.220798i
$685$	31.0356	−	31.0356i	1.18581	−	1.18581i
$686$	−11.7105	−	18.0254i	−0.447108	−	0.688214i
$687$	−8.65892	+	8.65892i	−0.330358	+	0.330358i
$688$	−0.686612	+	13.2853i	−0.0261768	+	0.506499i
$689$	4.21557	−	1.22663i	0.160600	−	0.0467309i
$690$	4.08016	+	6.28041i	0.155329	+	0.239091i
$691$	−36.3151			−1.38149			−0.690745	−	0.723098i	$-0.742717\pi$
$691$	−36.3151			−1.38149			−0.690745	+	0.723098i	$0.742717\pi$
$692$	−5.82401	−	15.1557i	−0.221396	−	0.576132i
$693$	−3.71151	+	3.71151i	−0.140989	+	0.140989i
$694$	2.51292	+	3.86803i	0.0953893	+	0.146828i
$695$	−23.5085	+	23.5085i	−0.891729	+	0.891729i
$696$	−8.01524	+	11.0446i	−0.303817	+	0.418646i
$697$	−4.35863	+	4.35863i	−0.165095	+	0.165095i
$698$	−9.80315	+	46.1613i	−0.371055	+	1.74723i
$699$	−5.58608	−	5.58608i	−0.211285	−	0.211285i
$700$	−3.87382	−	10.0808i	−0.146417	−	0.381017i
$701$	−18.4102	−	18.4102i	−0.695345	−	0.695345i	0.268058	−	0.963403i	$-0.413618\pi$
$701$	−18.4102	−	18.4102i	−0.695345	−	0.695345i	−0.963403	+	0.268058i	$0.913618\pi$
$702$	−5.08510	+	0.376470i	−0.191925	+	0.0142089i
$703$			37.5725i			1.41707i
$704$	−10.7310	−	32.9050i	−0.404440	−	1.24015i
$705$	−37.4921			−1.41204
$706$	−8.64932	−	13.3135i	−0.325521	−	0.501061i
$707$	−19.6763			−0.740005
$708$	−1.68452	−	4.38358i	−0.0633081	−	0.164745i
$709$		−	3.90623i		−	0.146702i	−0.997306	−	0.0733508i	$-0.976631\pi$
$709$		−	3.90623i		−	0.146702i	0.997306	−	0.0733508i	$-0.0233693\pi$
$710$	−9.37702	−	14.4336i	−0.351913	−	0.541684i
$711$	−2.19599			−0.0823561
$712$	1.53884	+	9.68185i	0.0576706	+	0.362843i
$713$	−1.90704	+	1.90704i	−0.0714193	+	0.0714193i
$714$	0.270856	−	1.27541i	0.0101365	−	0.0477311i
$715$	−23.0845	+	42.0317i	−0.863310	+	1.57190i
$716$	27.8557	−	10.7044i	1.04101	−	0.400040i
$717$			17.7711i			0.663674i
$718$	−22.8956	+	14.8744i	−0.854455	+	0.555109i
$719$	1.63860			0.0611096			0.0305548	−	0.999533i	$-0.490273\pi$
$719$	1.63860			0.0611096			0.0305548	+	0.999533i	$0.490273\pi$
$720$	−9.13233	+	8.23476i	−0.340342	+	0.306891i
$721$	6.76845	−	6.76845i	0.252070	−	0.252070i
$722$	−2.64817	+	12.4698i	−0.0985548	+	0.464077i
$723$		−	28.0417i		−	1.04288i
$724$	−31.5356	+	12.1185i	−1.17201	+	0.450379i
$725$	15.1840	−	15.1840i	0.563921	−	0.563921i
$726$	9.15188	−	5.94565i	0.339658	−	0.220664i
$727$			35.0817i			1.30111i	0.759460	+	0.650554i	$0.225463\pi$
$727$			35.0817i			1.30111i	−0.759460	+	0.650554i	$0.774537\pi$
$728$	4.17995	−	11.6452i	0.154919	−	0.431600i
$729$		−	1.00000i		−	0.0370370i
$730$	4.74755	+	7.30769i	0.175715	+	0.270470i
$731$	1.78708	−	1.78708i	0.0660977	−	0.0660977i
$732$	−19.3239	−	8.59518i	−0.714232	−	0.317687i
$733$			14.7820i			0.545986i	0.962016	+	0.272993i	$0.0880135\pi$
$733$			14.7820i			0.545986i	−0.962016	+	0.272993i	$0.911986\pi$
$734$	−17.0920	−	3.62978i	−0.630876	−	0.133977i
$735$	12.0168	−	12.0168i	0.443246	−	0.443246i
$736$	4.88008	+	8.43491i	0.179882	+	0.310915i
$737$	−25.9392			−0.955483
$738$	−6.24945	−	9.61949i	−0.230045	−	0.354098i
$739$		−	8.44189i		−	0.310540i	−0.987872	−	0.155270i	$-0.950375\pi$
$739$		−	8.44189i		−	0.310540i	0.987872	−	0.155270i	$-0.0496247\pi$
$740$	−29.7097	+	66.7940i	−1.09215	+	2.45540i
$741$	10.9400	−	3.18328i	0.401891	−	0.116941i
$742$	−2.04369	−	0.434013i	−0.0750262	−	0.0159331i
$743$	−7.12404	+	7.12404i	−0.261356	+	0.261356i	−0.825605	−	0.564249i	$-0.809166\pi$
$743$	−7.12404	+	7.12404i	−0.261356	+	0.261356i	0.564249	+	0.825605i	$0.309166\pi$
$744$	−3.58383	−	2.60083i	−0.131390	−	0.0953512i
$745$	15.1110			0.553625
$746$	5.33339	−	3.46492i	0.195269	−	0.126860i
$747$		−	10.4271i		−	0.381508i
$748$	−2.67225	+	6.00783i	−0.0977073	+	0.219668i
$749$	−10.2816			−0.375680
$750$	−2.00273	+	1.30111i	−0.0731295	+	0.0475096i
$751$	14.6258			0.533704			0.266852	−	0.963738i	$-0.414017\pi$
$751$	14.6258			0.533704			0.266852	+	0.963738i	$0.414017\pi$
$752$	−48.7180	−	2.51784i	−1.77656	−	0.0918163i
$753$		−	29.0351i		−	1.05810i
$754$	24.5345	−	1.81638i	0.893494	−	0.0661487i
$755$	47.1478	+	47.1478i	1.71588	+	1.71588i
$756$	2.21706	+	0.986136i	0.0806335	+	0.0358654i
$757$	11.6090	+	11.6090i	0.421937	+	0.421937i	0.885870	−	0.463933i	$-0.153562\pi$
$757$	11.6090	+	11.6090i	0.421937	+	0.421937i	−0.463933	+	0.885870i	$0.653562\pi$
$758$	38.7724	+	8.23399i	1.40828	+	0.299072i
$759$	−5.26995	+	5.26995i	−0.191287	+	0.191287i
$760$	16.1385	−	22.2381i	0.585406	−	0.806662i
$761$	−14.5944	+	14.5944i	−0.529048	+	0.529048i	−0.920288	−	0.391240i	$-0.872046\pi$
$761$	−14.5944	+	14.5944i	−0.529048	+	0.529048i	0.391240	+	0.920288i	$0.372046\pi$
$762$	14.7467	−	9.58043i	0.534218	−	0.347062i
$763$	−8.67785	+	8.67785i	−0.314159	+	0.314159i
$764$	13.0639	−	29.3707i	0.472637	−	1.06259i
$765$	2.33614			0.0844635
$766$	42.1968	−	27.4138i	1.52463	−	0.990499i
$767$	−4.07546	+	7.42052i	−0.147157	+	0.267940i
$768$	−12.4197	+	10.0871i	−0.448159	+	0.363987i
$769$	8.72969	−	8.72969i	0.314801	−	0.314801i	−0.531965	−	0.846766i	$-0.678546\pi$
$769$	8.72969	−	8.72969i	0.314801	−	0.314801i	0.846766	+	0.531965i	$0.178546\pi$
$770$	19.1361	−	12.4320i	0.689616	−	0.448019i
$771$	18.6793	−	18.6793i	0.672720	−	0.672720i
$772$	−2.34619	−	6.10543i	−0.0844413	−	0.219739i
$773$	−13.7640			−0.495058			−0.247529	−	0.968880i	$-0.579619\pi$
$773$	−13.7640			−0.495058			−0.247529	+	0.968880i	$0.579619\pi$
$774$	2.56234	+	3.94409i	0.0921013	+	0.141767i
$775$	4.92701	+	4.92701i	0.176983	+	0.176983i
$776$	−0.237900	−	1.49678i	−0.00854010	−	0.0537313i
$777$	14.4252			0.517502
$778$	−12.4134	−	19.1073i	−0.445041	−	0.685031i
$779$	18.1249	+	18.1249i	0.649392	+	0.649392i
$780$	21.9655	+	2.99154i	0.786493	+	0.107114i
$781$	12.1114	−	12.1114i	0.433379	−	0.433379i
$782$	0.384587	−	1.81095i	0.0137528	−	0.0647594i
$783$			4.82478i			0.172424i
$784$	16.4219	−	14.8078i	0.586495	−	0.528851i
$785$	−53.4497	+	53.4497i	−1.90770	+	1.90770i
$786$	−4.57632	−	0.971861i	−0.163232	−	0.0346651i
$787$			47.1256i			1.67984i	0.542706	+	0.839922i	$0.317400\pi$
$787$			47.1256i			1.67984i	−0.542706	+	0.839922i	$0.682600\pi$
$788$	−27.5137	−	12.2380i	−0.980135	−	0.435959i
$789$	2.26502	+	2.26502i	0.0806367	+	0.0806367i
$790$	9.33894	+	1.98329i	0.332265	+	0.0705622i
$791$	−12.7061	−	12.7061i	−0.451776	−	0.451776i
$792$	−9.90360	−	7.18718i	−0.351909	−	0.255385i
$793$	10.6524	+	36.6090i	0.378276	+	1.30002i
$794$	6.42286	−	30.2441i	0.227939	−	1.07332i
$795$		−	3.74338i		−	0.132764i
$796$	−17.5193	+	39.3874i	−0.620956	+	1.39605i
$797$	7.06170	+	7.06170i	0.250138	+	0.250138i	0.821027	−	0.570889i	$-0.193401\pi$
$797$	7.06170	+	7.06170i	0.250138	+	0.250138i	−0.570889	+	0.821027i	$0.693401\pi$
$798$	−5.30367	−	1.12633i	−0.187748	−	0.0398715i
$799$	6.55333	+	6.55333i	0.231840	+	0.231840i
$800$	21.7923	−	12.6081i	0.770475	−	0.445764i
$801$	2.45084	+	2.45084i	0.0865963	+	0.0865963i
$802$	−1.51543	+	0.984521i	−0.0535116	+	0.0347646i
$803$	−6.13194	+	6.13194i	−0.216391	+	0.216391i
$804$	4.30136	+	11.1933i	0.151697	+	0.394758i
$805$	−4.54323	+	4.54323i	−0.160128	+	0.160128i
$806$	0.589391	+	7.96110i	0.0207604	+	0.280418i
$807$	−6.61318			−0.232795
$808$	−7.20048	−	45.3028i	−0.253312	−	1.59375i
$809$			2.15706i			0.0758383i	0.999281	+	0.0379192i	$0.0120729\pi$
$809$			2.15706i			0.0758383i	−0.999281	+	0.0379192i	$0.987927\pi$
$810$	−0.903140	+	4.25272i	−0.0317331	+	0.149426i
$811$		−	55.9316i		−	1.96402i	−0.188822	−	0.982011i	$-0.560467\pi$
$811$		−	55.9316i		−	1.96402i	0.188822	−	0.982011i	$-0.439533\pi$
$812$	−10.6968	−	4.75788i	−0.375384	−	0.166969i
$813$	24.3511			0.854031
$814$	−71.1593	−	15.1119i	−2.49413	−	0.529673i
$815$		−	32.3891i		−	1.13454i
$816$	3.03563	+	0.156887i	0.106268	+	0.00549216i
$817$	−7.43139	−	7.43139i	−0.259992	−	0.259992i
$818$	12.7561	−	8.28720i	0.446007	−	0.289755i
$819$	−1.22216	−	4.20020i	−0.0427056	−	0.146767i
$820$	17.8894	+	46.5532i	0.624726	+	1.62571i
$821$	−21.3882			−0.746453			−0.373226	−	0.927740i	$-0.621749\pi$
$821$	−21.3882			−0.746453			−0.373226	+	0.927740i	$0.621749\pi$
$822$	4.19438	−	19.7506i	0.146296	−	0.688881i
$823$			16.1069i			0.561451i	0.959788	+	0.280726i	$0.0905751\pi$
$823$			16.1069i			0.561451i	−0.959788	+	0.280726i	$0.909425\pi$
$824$	18.0606	+	13.1068i	0.629170	+	0.456597i
$825$	13.6154	+	13.6154i	0.474026	+	0.474026i
$826$	3.37839	−	2.19482i	0.117549	−	0.0763676i
$827$	−38.7437			−1.34725			−0.673625	−	0.739073i	$-0.735264\pi$
$827$	−38.7437			−1.34725			−0.673625	+	0.739073i	$0.735264\pi$
$828$	3.14798	+	1.40021i	0.109400	+	0.0486605i
$829$	−17.9499	−	17.9499i	−0.623425	−	0.623425i	0.322980	−	0.946406i	$-0.395315\pi$
$829$	−17.9499	−	17.9499i	−0.623425	−	0.623425i	−0.946406	+	0.322980i	$0.895315\pi$
$830$	−9.41714	+	44.3436i	−0.326874	+	1.53919i
$831$	6.35020			0.220286
$832$	28.3416	+	5.36240i	0.982567	+	0.185908i
$833$	−4.20088			−0.145552
$834$	−3.17712	+	14.9605i	−0.110015	+	0.518039i
$835$	42.6274	+	42.6274i	1.47518	+	1.47518i
$836$	24.9829	+	11.1123i	0.864052	+	0.384326i
$837$	−1.56557			−0.0541141
$838$	35.9247	−	23.3390i	1.24100	−	0.806232i
$839$	24.9674	+	24.9674i	0.861970	+	0.861970i	0.991567	−	0.129597i	$-0.0413684\pi$
$839$	24.9674	+	24.9674i	0.861970	+	0.861970i	−0.129597	+	0.991567i	$0.541368\pi$
$840$	−8.53791	−	6.19608i	−0.294586	−	0.213785i
$841$			5.72152i			0.197294i
$842$	−5.11625	+	24.0915i	−0.176318	+	0.830248i
$843$	28.8836			0.994805
$844$	−0.215350	−	0.560400i	−0.00741266	−	0.0192898i
$845$	−21.4420	−	33.7254i	−0.737627	−	1.16019i
$846$	−14.4632	+	9.39623i	−0.497255	+	0.323049i
$847$	6.62043	+	6.62043i	0.227481	+	0.227481i
$848$	0.251393	−	4.86422i	0.00863285	−	0.167038i
$849$			6.50183i			0.223142i
$850$	−4.67875	−	0.993613i	−0.160480	−	0.0340807i
$851$	20.4823			0.702123
$852$	−7.23468	−	3.21795i	−0.247856	−	0.110245i
$853$			4.60176i			0.157561i	0.996892	+	0.0787807i	$0.0251027\pi$
$853$			4.60176i			0.157561i	−0.996892	+	0.0787807i	$0.974897\pi$
$854$	3.76908	−	17.7479i	0.128975	−	0.607321i
$855$		−	9.71460i		−	0.332232i
$856$	−3.76250	−	23.6723i	−0.128600	−	0.809103i
$857$	−5.67507			−0.193857			−0.0969283	−	0.995291i	$-0.530902\pi$
$857$	−5.67507			−0.193857			−0.0969283	+	0.995291i	$0.530902\pi$
$858$	1.62873	+	21.9998i	0.0556039	+	0.751062i
$859$	1.74068	−	1.74068i	0.0593913	−	0.0593913i	−0.676787	−	0.736179i	$-0.736628\pi$
$859$	1.74068	−	1.74068i	0.0593913	−	0.0593913i	0.736179	+	0.676787i	$0.236628\pi$
$860$	−7.33485	−	19.0873i	−0.250116	−	0.650871i
$861$	6.95870	−	6.95870i	0.237152	−	0.237152i
$862$	−15.7499	+	10.2322i	−0.536444	+	0.348509i
$863$	−17.4288	−	17.4288i	−0.593283	−	0.593283i	0.345234	−	0.938517i	$-0.387800\pi$
$863$	−17.4288	−	17.4288i	−0.593283	−	0.593283i	−0.938517	+	0.345234i	$0.887800\pi$
$864$	−1.45916	+	5.46542i	−0.0496415	+	0.185938i
$865$	17.6470	+	17.6470i	0.600014	+	0.600014i
$866$	0.415438	+	0.0882255i	0.0141172	+	0.00299802i
$867$	11.6125	+	11.6125i	0.394380	+	0.394380i
$868$	1.54387	−	3.47096i	0.0524023	−	0.117812i
$869$			9.50057i			0.322285i
$870$	4.35745	−	20.5185i	0.147731	−	0.695641i
$871$	10.4066	−	18.9480i	0.352613	−	0.642030i
$872$	−23.1555	−	16.8043i	−0.784145	−	0.569065i
$873$	−0.378892	−	0.378892i	−0.0128236	−	0.0128236i
$874$	−7.53063	−	1.59926i	−0.254727	−	0.0540958i
$875$	−1.44877	−	1.44877i	−0.0489773	−	0.0489773i
$876$	3.66289	+	1.62923i	0.123757	+	0.0550467i
$877$			19.3824i			0.654497i	0.944938	+	0.327248i	$0.106121\pi$
$877$			19.3824i			0.654497i	−0.944938	+	0.327248i	$0.893879\pi$
$878$	−29.1645	−	6.19360i	−0.984255	−	0.209024i
$879$	−10.9994	+	10.9994i	−0.371001	+	0.371001i
$880$	35.6263	+	39.5094i	1.20096	+	1.33186i
$881$		−	40.1234i		−	1.35179i	−0.736998	−	0.675895i	$-0.763757\pi$
$881$		−	40.1234i		−	1.35179i	0.736998	−	0.675895i	$-0.236243\pi$
$882$	1.62404	−	7.64730i	0.0546842	−	0.257498i
$883$	−11.3609	+	11.3609i	−0.382323	+	0.382323i	−0.871938	−	0.489615i	$-0.837137\pi$
$883$	−11.3609	+	11.3609i	−0.382323	+	0.382323i	0.489615	+	0.871938i	$0.337137\pi$
$884$	−3.31651	−	4.36231i	−0.111546	−	0.146720i
$885$	5.10416	+	5.10416i	0.171574	+	0.171574i
$886$	25.5748	+	39.3661i	0.859202	+	1.32253i
$887$	20.8739			0.700877			0.350439	−	0.936586i	$-0.386033\pi$
$887$	20.8739			0.700877			0.350439	+	0.936586i	$0.386033\pi$
$888$	5.27886	+	33.2127i	0.177147	+	1.11454i
$889$	10.6677	+	10.6677i	0.357784	+	0.357784i
$890$	−8.20931	−	12.6362i	−0.275177	−	0.423567i
$891$	−4.32633			−0.144937
$892$	17.4260	+	45.3471i	0.583464	+	1.51833i
$893$	27.2513	−	27.2513i	0.911931	−	0.911931i
$894$	5.82932	−	3.78710i	0.194962	−	0.126660i
$895$	−32.4346	+	32.4346i	−1.08417	+	1.08417i
$896$	−10.6782	−	8.62468i	−0.356734	−	0.288130i
$897$	−1.73533	−	5.96383i	−0.0579410	−	0.199126i
$898$	50.2425	−	32.6408i	1.67662	−	1.08924i
$899$	7.55354			0.251925
$900$	3.61755	−	8.13308i	0.120585	−	0.271103i
$901$	−0.654314	+	0.654314i	−0.0217983	+	0.0217983i
$902$	−41.6171	+	27.0372i	−1.38570	+	0.900239i
$903$	−2.85314	+	2.85314i	−0.0949466	+	0.0949466i
$904$	24.6047	−	33.9042i	0.818342	−	1.12764i
$905$	36.7194	−	36.7194i	1.22059	−	1.22059i
$906$	30.0042	+	6.37191i	0.996821	+	0.211692i
$907$	−33.1669	−	33.1669i	−1.10129	−	1.10129i	−0.994255	−	0.107034i	$-0.965865\pi$
$907$	−33.1669	−	33.1669i	−1.10129	−	1.10129i	−0.107034	−	0.994255i	$-0.534135\pi$
$908$	20.1085	+	8.94418i	0.667326	+	0.296823i
$909$	−11.4679	−	11.4679i	−0.380365	−	0.380365i
$910$	1.40413	+	18.9661i	0.0465465	+	0.628719i
$911$		−	14.6036i		−	0.483838i	−0.970296	−	0.241919i	$-0.922223\pi$
$911$		−	14.6036i		−	0.483838i	0.970296	−	0.241919i	$-0.0777769\pi$
$912$	0.652399	−	12.6233i	0.0216031	−	0.418001i
$913$	−45.1111			−1.49296
$914$	4.16998	−	2.70909i	0.137931	−	0.0896087i
$915$	32.5084			1.07470
$916$	9.95334	−	22.3774i	0.328867	−	0.739369i
$917$		−	4.01353i		−	0.132539i
$918$	0.901205	−	0.585481i	0.0297442	−	0.0193238i
$919$	2.66192			0.0878086			0.0439043	−	0.999036i	$-0.486020\pi$
$919$	2.66192			0.0878086			0.0439043	+	0.999036i	$0.486020\pi$
$920$	−12.1229	−	8.79776i	−0.399680	−	0.290053i
$921$	12.7733	−	12.7733i	0.420893	−	0.420893i
$922$	47.9142	+	10.1754i	1.57797	+	0.335110i
$923$	3.98813	+	13.7061i	0.131271	+	0.451140i
$924$	4.26635	−	9.59171i	0.140352	−	0.315544i
$925$		−	52.9178i		−	1.73993i
$926$	−3.48088	−	5.35797i	−0.114389	−	0.176074i
$927$	7.88965			0.259130
$928$	7.04011	−	26.3695i	0.231103	−	0.865620i
$929$	34.3474	−	34.3474i	1.12690	−	1.12690i	0.136225	−	0.990678i	$-0.456503\pi$
$929$	34.3474	−	34.3474i	1.12690	−	1.12690i	0.990678	−	0.136225i	$-0.0434971\pi$
$930$	6.65795	+	1.41393i	0.218323	+	0.0463647i
$931$			17.4689i			0.572520i
$932$	14.4362	+	6.42114i	0.472873	+	0.210331i
$933$	−5.45308	+	5.45308i	−0.178526	+	0.178526i
$934$	−2.29453	−	3.53186i	−0.0750792	−	0.115566i
$935$		−	10.1069i		−	0.330532i
$936$	9.22330	−	4.35094i	0.301473	−	0.142215i
$937$			43.1283i			1.40894i	0.709734	+	0.704470i	$0.248815\pi$
$937$			43.1283i			1.40894i	−0.709734	+	0.704470i	$0.751185\pi$
$938$	−8.62659	+	5.60439i	−0.281668	+	0.182990i
$939$	−8.69355	+	8.69355i	−0.283703	+	0.283703i
$940$	69.9941	−	26.8973i	2.28296	−	0.877293i
$941$		−	30.8927i		−	1.00707i	−0.863974	−	0.503536i	$-0.832032\pi$
$941$		−	30.8927i		−	1.00707i	0.863974	−	0.503536i	$-0.167968\pi$
$942$	−7.22359	+	34.0146i	−0.235357	+	1.10825i
$943$	9.88061	−	9.88061i	0.321757	−	0.321757i
$944$	6.28967	+	6.97522i	0.204711	+	0.227024i
$945$	−3.72973			−0.121328
$946$	17.0634	−	11.0855i	0.554780	−	0.360421i
$947$		−	25.9106i		−	0.841980i	−0.907065	−	0.420990i	$-0.861683\pi$
$947$		−	25.9106i		−	0.841980i	0.907065	−	0.420990i	$-0.138317\pi$
$948$	4.09970	−	1.57543i	0.133152	−	0.0511675i
$949$	−2.01918	−	6.93932i	−0.0655452	−	0.225260i
$950$	−4.13183	+	19.4560i	−0.134054	+	0.631238i
$951$	1.55804	−	1.55804i	0.0505230	−	0.0505230i
$952$	0.409334	+	2.57539i	0.0132666	+	0.0834687i
$953$	−39.4251			−1.27710			−0.638552	−	0.769579i	$-0.720466\pi$
$953$	−39.4251			−1.27710			−0.638552	+	0.769579i	$0.720466\pi$
$954$	−0.938161	−	1.44407i	−0.0303741	−	0.0467535i
$955$			49.4100i			1.59887i
$956$	−12.7492	−	33.1769i	−0.412339	−	1.07302i
$957$	20.8736			0.674747
$958$	−4.28420	−	6.59447i	−0.138416	−	0.213058i
$959$	17.3217			0.559347
$960$	11.1414	−	21.9251i	0.359588	−	0.707630i
$961$		−	28.5490i		−	0.920935i
$962$	39.5873	−	45.9176i	1.27635	−	1.48044i
$963$	−5.99236	−	5.99236i	−0.193101	−	0.193101i
$964$	20.1174	+	52.3510i	0.647938	+	1.68611i
$965$	7.10904	+	7.10904i	0.228848	+	0.228848i
$966$	−0.614005	+	2.89124i	−0.0197553	+	0.0930242i
$967$	37.6519	−	37.6519i	1.21080	−	1.21080i	0.240042	−	0.970762i	$-0.422839\pi$
$967$	37.6519	−	37.6519i	1.21080	−	1.21080i	0.970762	−	0.240042i	$-0.0771614\pi$
$968$	−12.8202	+	17.6656i	−0.412056	+	0.567794i
$969$	−1.69804	+	1.69804i	−0.0545488	+	0.0545488i
$970$	1.26913	+	1.95352i	0.0407493	+	0.0627236i
$971$	16.8015	−	16.8015i	0.539184	−	0.539184i	−0.384105	−	0.923289i	$-0.625490\pi$
$971$	16.8015	−	16.8015i	0.539184	−	0.539184i	0.923289	+	0.384105i	$0.125490\pi$
$972$	0.717412	+	1.86690i	0.0230110	+	0.0598809i
$973$	−13.1207			−0.420629
$974$	3.96337	+	6.10064i	0.126995	+	0.195477i
$975$	−15.4081	+	4.48338i	−0.493453	+	0.143583i
$976$	42.2421	+	2.18315i	1.35214	+	0.0698811i
$977$	21.2411	−	21.2411i	0.679564	−	0.679564i	−0.280338	−	0.959901i	$-0.590446\pi$
$977$	21.2411	−	21.2411i	0.679564	−	0.679564i	0.959901	+	0.280338i	$0.0904465\pi$
$978$	−8.11732	−	12.4946i	−0.259563	−	0.399534i
$979$	10.6032	−	10.6032i	0.338878	−	0.338878i
$980$	−13.8132	+	31.0551i	−0.441245	+	0.992020i
$981$	−10.1153			−0.322958
$982$	6.55529	−	4.25874i	0.209188	−	0.135902i
$983$	−35.2290	−	35.2290i	−1.12363	−	1.12363i	−0.991191	−	0.132439i	$-0.957719\pi$
$983$	−35.2290	−	35.2290i	−1.12363	−	1.12363i	−0.132439	−	0.991191i	$-0.542281\pi$
$984$	18.5682	+	13.4752i	0.591934	+	0.429574i
$985$	46.2860			1.47480
$986$	−4.34812	+	2.82482i	−0.138472	+	0.0899605i
$987$	−10.4626	−	10.4626i	−0.333029	−	0.333029i
$988$	−18.1402	+	13.7913i	−0.577116	+	0.438761i
$989$	−4.05115	+	4.05115i	−0.128819	+	0.128819i
$990$	18.3987	+	3.90728i	0.584748	+	0.124182i
$991$		−	56.3180i		−	1.78900i	−0.447067	−	0.894501i	$-0.647531\pi$
$991$		−	56.3180i		−	1.78900i	0.447067	−	0.894501i	$-0.352469\pi$
$992$	8.55652	+	2.28442i	0.271670	+	0.0725303i
$993$	18.2735	−	18.2735i	0.579891	−	0.579891i
$994$	1.41111	−	6.64464i	0.0447575	−	0.210755i
$995$		−	66.2611i		−	2.10062i
$996$	7.48053	+	19.4664i	0.237030	+	0.616816i
$997$	−11.2637	−	11.2637i	−0.356725	−	0.356725i	0.505879	−	0.862604i	$-0.331168\pi$
$997$	−11.2637	−	11.2637i	−0.356725	−	0.356725i	−0.862604	+	0.505879i	$0.831168\pi$
$998$	0.921275	−	4.33812i	0.0291624	−	0.137321i
$999$	8.40739	+	8.40739i	0.265998	+	0.265998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bn.a.187.32	yes	112
13.8	odd	4		624.2.r.a.619.53	yes	112
16.3	odd	4		624.2.r.a.499.53	✓	112
208.99	even	4	inner	624.2.bn.a.307.32	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.r.a.499.53	✓	112	16.3	odd	4
624.2.r.a.619.53	yes	112	13.8	odd	4
624.2.bn.a.187.32	yes	112	1.1	even	1	trivial
624.2.bn.a.307.32	yes	112	208.99	even	4	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bn (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.293781 - 1.38336i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.82739 - 0.812812i) q^{4} +3.07419 q^{5} +(1.18592 - 0.770451i) q^{6} +(0.857890 + 0.857890i) q^{7} +(-1.66127 + 2.28915i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.293781 - 1.38336i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.82739 - 0.812812i) q^{4} +3.07419 q^{5} +(1.18592 - 0.770451i) q^{6} +(0.857890 + 0.857890i) q^{7} +(-1.66127 + 2.28915i) q^{8} +1.00000i q^{9} +(0.903140 - 4.25272i) q^{10} +4.32633 q^{11} +(-0.717412 - 1.86690i) q^{12} +(-1.73568 + 3.16029i) q^{13} +(1.43880 - 0.934741i) q^{14} +(2.17378 + 2.17378i) q^{15} +(2.67867 + 2.97064i) q^{16} -0.759921i q^{17} +(1.38336 + 0.293781i) q^{18} -3.16005 q^{19} +(-5.61774 - 2.49874i) q^{20} +1.21324i q^{21} +(1.27099 - 5.98488i) q^{22} +1.72267i q^{23} +(-2.79336 + 0.443980i) q^{24} +4.45067 q^{25} +(3.86191 + 3.32951i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.870392 - 2.26500i) q^{28} +(3.41163 - 3.41163i) q^{29} +(3.64575 - 2.36851i) q^{30} +(1.10703 + 1.10703i) q^{31} +(4.89642 - 2.83286i) q^{32} +(3.05918 + 3.05918i) q^{33} +(-1.05125 - 0.223250i) q^{34} +(2.63732 + 2.63732i) q^{35} +(0.812812 - 1.82739i) q^{36} -11.8899i q^{37} +(-0.928362 + 4.37149i) q^{38} +(-3.46197 + 1.00735i) q^{39} +(-5.10705 + 7.03728i) q^{40} +(-5.73564 - 5.73564i) q^{41} +(1.67835 + 0.356427i) q^{42} +(2.35167 + 2.35167i) q^{43} +(-7.90587 - 3.51649i) q^{44} +3.07419i q^{45} +(2.38308 + 0.506088i) q^{46} +(-8.62371 + 8.62371i) q^{47} +(-0.206452 + 3.99467i) q^{48} -5.52805i q^{49} +(1.30752 - 6.15689i) q^{50} +(0.537345 - 0.537345i) q^{51} +(5.74047 - 4.36428i) q^{52} +(-0.861029 - 0.861029i) q^{53} +(0.770451 + 1.18592i) q^{54} +13.3000 q^{55} +(-3.38902 + 0.538654i) q^{56} +(-2.23449 - 2.23449i) q^{57} +(-3.71725 - 5.72180i) q^{58} +2.34805 q^{59} +(-2.20546 - 5.73922i) q^{60} +(7.47738 - 7.47738i) q^{61} +(1.85664 - 1.20620i) q^{62} +(-0.857890 + 0.857890i) q^{63} +(-2.48040 - 7.60576i) q^{64} +(-5.33581 + 9.71534i) q^{65} +(5.13068 - 3.33322i) q^{66} -5.99567 q^{67} +(-0.617673 + 1.38867i) q^{68} +(-1.21811 + 1.21811i) q^{69} +(4.42316 - 2.87357i) q^{70} +(2.79946 - 2.79946i) q^{71} +(-2.28915 - 1.66127i) q^{72} +(-1.41735 + 1.41735i) q^{73} +(-16.4480 - 3.49301i) q^{74} +(3.14710 + 3.14710i) q^{75} +(5.77462 + 2.56852i) q^{76} +(3.71151 + 3.71151i) q^{77} +(0.376470 + 5.08510i) q^{78} +2.19599i q^{79} +(8.23476 + 9.13233i) q^{80} -1.00000 q^{81} +(-9.61949 + 6.24945i) q^{82} -10.4271 q^{83} +(0.986136 - 2.21706i) q^{84} -2.33614i q^{85} +(3.94409 - 2.56234i) q^{86} +4.82478 q^{87} +(-7.18718 + 9.90360i) q^{88} +(2.45084 - 2.45084i) q^{89} +(4.25272 + 0.903140i) q^{90} +(-4.20020 + 1.22216i) q^{91} +(1.40021 - 3.14798i) q^{92} +1.56557i q^{93} +(9.39623 + 14.4632i) q^{94} -9.71460 q^{95} +(5.46542 + 1.45916i) q^{96} +(-0.378892 + 0.378892i) q^{97} +(-7.64730 - 1.62404i) q^{98} +4.32633i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q - 8 q^{10} + 32 q^{14} + 4 q^{20} - 8 q^{22} + 12 q^{24} + 112 q^{25} - 16 q^{26} - 8 q^{28} + 60 q^{32} - 24 q^{34} - 40 q^{38} + 40 q^{40} - 16 q^{43} - 4 q^{44} - 56 q^{46} - 56 q^{50} + 56 q^{52} + 32 q^{55} + 40 q^{56} + 40 q^{58} - 64 q^{59} + 44 q^{60} - 72 q^{64} + 24 q^{68} - 64 q^{70} - 64 q^{71} - 16 q^{73} - 16 q^{75} - 16 q^{76} + 24 q^{78} + 4 q^{80} - 112 q^{81} - 72 q^{82} + 80 q^{83} + 16 q^{86} - 16 q^{89} + 56 q^{91} - 24 q^{92} - 88 q^{94} + 40 q^{98}+O(q^{100}) \) 112 * q - 8 * q^10 + 32 * q^14 + 4 * q^20 - 8 * q^22 + 12 * q^24 + 112 * q^25 - 16 * q^26 - 8 * q^28 + 60 * q^32 - 24 * q^34 - 40 * q^38 + 40 * q^40 - 16 * q^43 - 4 * q^44 - 56 * q^46 - 56 * q^50 + 56 * q^52 + 32 * q^55 + 40 * q^56 + 40 * q^58 - 64 * q^59 + 44 * q^60 - 72 * q^64 + 24 * q^68 - 64 * q^70 - 64 * q^71 - 16 * q^73 - 16 * q^75 - 16 * q^76 + 24 * q^78 + 4 * q^80 - 112 * q^81 - 72 * q^82 + 80 * q^83 + 16 * q^86 - 16 * q^89 + 56 * q^91 - 24 * q^92 - 88 * q^94 + 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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