LMFDB - Embedded newform 560.2.cr.a.109.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(109,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 6, 8]))

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

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

chi := DirichletCharacter("560.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cr (of order $12$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$92$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.11
Character	$\chi$	$=$	560.109
Dual form			560.2.cr.a.149.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30660 + 0.541096i) q^{2} +(0.176005 + 0.656861i) q^{3} +(1.41443 - 1.41400i) q^{4} +(-2.08402 - 0.810465i) q^{5} +(-0.585395 - 0.763022i) q^{6} +(-2.59981 - 0.490918i) q^{7} +(-1.08299 + 2.61288i) q^{8} +(2.19759 - 1.26878i) q^{9} +(3.16153 - 0.0686997i) q^{10} +(-0.0247007 - 0.0921843i) q^{11} +(1.17775 + 0.680213i) q^{12} +(-0.965489 + 0.965489i) q^{13} +(3.66255 - 0.765310i) q^{14} +(0.165564 - 1.51156i) q^{15} +(0.00122254 - 4.00000i) q^{16} +(4.63508 + 2.67606i) q^{17} +(-2.18485 + 2.84690i) q^{18} +(-1.37477 + 5.13069i) q^{19} +(-4.09370 + 1.80046i) q^{20} +(-0.135115 - 1.79412i) q^{21} +(0.0821546 + 0.107083i) q^{22} +(2.91751 + 5.05328i) q^{23} +(-1.90691 - 0.251494i) q^{24} +(3.68629 + 3.37805i) q^{25} +(0.739089 - 1.78393i) q^{26} +(2.66277 + 2.66277i) q^{27} +(-4.37140 + 2.98175i) q^{28} +(2.43972 + 2.43972i) q^{29} +(0.601573 + 2.06460i) q^{30} +(4.28658 - 7.42458i) q^{31} +(2.16279 + 5.22708i) q^{32} +(0.0562048 - 0.0324499i) q^{33} +(-7.50422 - 0.988533i) q^{34} +(5.02018 + 3.13014i) q^{35} +(1.31428 - 4.90198i) q^{36} +(0.962819 - 3.59329i) q^{37} +(-0.979925 - 7.44767i) q^{38} +(-0.804123 - 0.464261i) q^{39} +(4.37462 - 4.56757i) q^{40} +8.38666i q^{41} +(1.14733 + 2.27109i) q^{42} +(-3.53307 - 3.53307i) q^{43} +(-0.165286 - 0.0954615i) q^{44} +(-5.60812 + 0.863093i) q^{45} +(-6.54634 - 5.02398i) q^{46} +(-7.70917 + 4.45089i) q^{47} +(2.62766 - 0.703219i) q^{48} +(6.51800 + 2.55259i) q^{49} +(-6.64438 - 2.41914i) q^{50} +(-0.942004 + 3.51561i) q^{51} +(-0.000417315 + 2.73081i) q^{52} +(6.93880 - 1.85924i) q^{53} +(-4.91999 - 2.03837i) q^{54} +(-0.0232353 + 0.212133i) q^{55} +(4.09828 - 6.26132i) q^{56} -3.61212 q^{57} +(-4.50786 - 1.86762i) q^{58} +(3.75125 + 13.9999i) q^{59} +(-1.90316 - 2.37210i) q^{60} +(-1.85274 + 6.91452i) q^{61} +(-1.58346 + 12.0204i) q^{62} +(-6.33617 + 2.21974i) q^{63} +(-5.65426 - 5.65945i) q^{64} +(2.79459 - 1.22960i) q^{65} +(-0.0558790 + 0.0728114i) q^{66} +(-1.50412 - 5.61347i) q^{67} +(10.3399 - 2.76889i) q^{68} +(-2.80581 + 2.80581i) q^{69} +(-8.25310 - 1.37345i) q^{70} +3.07469i q^{71} +(0.935193 + 7.11610i) q^{72} +(4.81409 - 8.33825i) q^{73} +(0.686292 + 5.21598i) q^{74} +(-1.57010 + 3.01594i) q^{75} +(5.31028 + 9.20092i) q^{76} +(0.0189621 + 0.251787i) q^{77} +(1.30188 + 0.171497i) q^{78} +(4.28039 + 7.41385i) q^{79} +(-3.24441 + 8.33510i) q^{80} +(2.52593 - 4.37503i) q^{81} +(-4.53799 - 10.9581i) q^{82} +(-3.47150 + 3.47150i) q^{83} +(-2.72799 - 2.34660i) q^{84} +(-7.49075 - 9.33354i) q^{85} +(6.52805 + 2.70459i) q^{86} +(-1.17315 + 2.03196i) q^{87} +(0.267617 + 0.0352949i) q^{88} +(-2.92394 + 1.68814i) q^{89} +(6.86058 - 4.16225i) q^{90} +(2.98406 - 2.03611i) q^{91} +(11.2719 + 3.02215i) q^{92} +(5.63138 + 1.50892i) q^{93} +(7.66447 - 9.98695i) q^{94} +(7.02329 - 9.57828i) q^{95} +(-3.05280 + 2.34065i) q^{96} -0.887544i q^{97} +(-9.89764 + 0.191645i) q^{98} +(-0.171243 - 0.171243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{4} - 2 q^{5} - 16 q^{6} - 8 q^{10} - 4 q^{11} + 16 q^{14} - 16 q^{15} - 4 q^{16} - 4 q^{19} - 8 q^{20} + 4 q^{21} - 4 q^{24} - 4 q^{26} - 16 q^{29} + 22 q^{30} - 56 q^{31} - 96 q^{34} + 18 q^{35}+ \cdots - 112 q^{99}+O(q^{100}) $ 368 * q - 4 * q^4 - 2 * q^5 - 16 * q^6 - 8 * q^10 - 4 * q^11 + 16 * q^14 - 16 * q^15 - 4 * q^16 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 4 * q^24 - 4 * q^26 - 16 * q^29 + 22 * q^30 - 56 * q^31 - 96 * q^34 + 18 * q^35 + 32 * q^36 - 14 * q^40 - 12 * q^44 - 16 * q^45 + 12 * q^46 - 16 * q^49 - 12 * q^50 - 28 * q^51 - 8 * q^54 - 64 * q^56 + 12 * q^59 - 54 * q^60 - 4 * q^61 - 88 * q^64 - 4 * q^65 - 44 * q^66 + 8 * q^69 + 88 * q^70 - 72 * q^74 + 10 * q^75 + 104 * q^76 - 8 * q^79 + 48 * q^80 + 112 * q^81 + 68 * q^84 - 28 * q^85 + 44 * q^86 - 92 * q^90 - 80 * q^91 - 20 * q^94 + 20 * q^95 - 36 * q^96 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.30660	+	0.541096i	−0.923909	+	0.382613i
$2$	−1.30660	+	0.541096i	−0.923909	+	0.382613i
$3$	0.176005	+	0.656861i	0.101617	+	0.379239i	0.997939	−	0.0641635i	$-0.0204379\pi$
$3$	0.176005	+	0.656861i	0.101617	+	0.379239i	−0.896323	+	0.443403i	$0.853771\pi$
$4$	1.41443	−	1.41400i	0.707215	−	0.706999i
$5$	−2.08402	−	0.810465i	−0.932003	−	0.362451i
$5$	−2.08402	−	0.810465i	−0.932003	−	0.362451i
$6$	−0.585395	−	0.763022i	−0.238986	−	0.311502i
$7$	−2.59981	−	0.490918i	−0.982635	−	0.185550i
$7$	−2.59981	−	0.490918i	−0.982635	−	0.185550i
$8$	−1.08299	+	2.61288i	−0.382895	+	0.923792i
$9$	2.19759	−	1.26878i	0.732529	−	0.422926i
$10$	3.16153	−	0.0686997i	0.999764	−	0.0217247i
$11$	−0.0247007	−	0.0921843i	−0.00744754	−	0.0277946i	0.962102	−	0.272690i	$-0.0879132\pi$
$11$	−0.0247007	−	0.0921843i	−0.00744754	−	0.0277946i	−0.969550	+	0.244895i	$0.921247\pi$
$12$	1.17775	+	0.680213i	0.339986	+	0.196361i
$13$	−0.965489	+	0.965489i	−0.267778	+	0.267778i	−0.828204	−	0.560426i	$-0.810637\pi$
$13$	−0.965489	+	0.965489i	−0.267778	+	0.267778i	0.560426	+	0.828204i	$0.310637\pi$
$14$	3.66255	−	0.765310i	0.978859	−	0.204538i
$15$	0.165564	−	1.51156i	0.0427484	−	0.390283i
$16$	0.00122254	−	4.00000i	0.000305634	−	1.00000i
$17$	4.63508	+	2.67606i	1.12417	+	0.649041i	0.942463	−	0.334311i	$-0.108504\pi$
$17$	4.63508	+	2.67606i	1.12417	+	0.649041i	0.181709	+	0.983352i	$0.441837\pi$
$18$	−2.18485	+	2.84690i	−0.514973	+	0.671020i
$19$	−1.37477	+	5.13069i	−0.315393	+	1.17706i	0.608230	+	0.793760i	$0.291880\pi$
$19$	−1.37477	+	5.13069i	−0.315393	+	1.17706i	−0.923623	+	0.383302i	$0.874787\pi$
$20$	−4.09370	+	1.80046i	−0.915379	+	0.402594i
$21$	−0.135115	−	1.79412i	−0.0294845	−	0.391508i
$22$	0.0821546	+	0.107083i	0.0175154	+	0.0228302i
$23$	2.91751	+	5.05328i	0.608343	+	1.05368i	0.991513	+	0.130004i	$0.0414989\pi$
$23$	2.91751	+	5.05328i	0.608343	+	1.05368i	−0.383170	+	0.923678i	$0.625168\pi$
$24$	−1.90691	−	0.251494i	−0.389246	−	0.0513360i
$25$	3.68629	+	3.37805i	0.737259	+	0.675610i
$26$	0.739089	−	1.78393i	0.144947	−	0.349858i
$27$	2.66277	+	2.66277i	0.512450	+	0.512450i
$28$	−4.37140	+	2.98175i	−0.826117	+	0.563498i
$29$	2.43972	+	2.43972i	0.453044	+	0.453044i	0.896364	−	0.443320i	$-0.146199\pi$
$29$	2.43972	+	2.43972i	0.453044	+	0.453044i	−0.443320	+	0.896364i	$0.646199\pi$
$30$	0.601573	+	2.06460i	0.109832	+	0.376942i
$31$	4.28658	−	7.42458i	0.769893	−	1.33349i	−0.167727	−	0.985833i	$-0.553643\pi$
$31$	4.28658	−	7.42458i	0.769893	−	1.33349i	0.937620	−	0.347661i	$-0.113024\pi$
$32$	2.16279	+	5.22708i	0.382330	+	0.924026i
$33$	0.0562048	−	0.0324499i	0.00978401	−	0.00564880i
$34$	−7.50422	−	0.988533i	−1.28696	−	0.169532i
$35$	5.02018	+	3.13014i	0.848566	+	0.529090i
$36$	1.31428	−	4.90198i	0.219047	−	0.816997i
$37$	0.962819	−	3.59329i	0.158286	−	0.590733i	−0.840515	−	0.541788i	$-0.817748\pi$
$37$	0.962819	−	3.59329i	0.158286	−	0.590733i	0.998801	−	0.0489447i	$-0.0155858\pi$
$38$	−0.979925	−	7.44767i	−0.158965	−	1.20817i
$39$	−0.804123	−	0.464261i	−0.128763	−	0.0743412i
$40$	4.37462	−	4.56757i	0.691689	−	0.722196i
$41$			8.38666i			1.30978i	0.755726	+	0.654888i	$0.227284\pi$
$41$			8.38666i			1.30978i	−0.755726	+	0.654888i	$0.772716\pi$
$42$	1.14733	+	2.27109i	0.177037	+	0.350437i
$43$	−3.53307	−	3.53307i	−0.538788	−	0.538788i	0.384385	−	0.923173i	$-0.374413\pi$
$43$	−3.53307	−	3.53307i	−0.538788	−	0.538788i	−0.923173	+	0.384385i	$0.874413\pi$
$44$	−0.165286	−	0.0954615i	−0.0249178	−	0.0143914i
$45$	−5.60812	+	0.863093i	−0.836009	+	0.128662i
$46$	−6.54634	−	5.02398i	−0.965206	−	0.740746i
$47$	−7.70917	+	4.45089i	−1.12450	+	0.649229i	−0.942545	−	0.334079i	$-0.891575\pi$
$47$	−7.70917	+	4.45089i	−1.12450	+	0.649229i	−0.181952	+	0.983307i	$0.558242\pi$
$48$	2.62766	−	0.703219i	0.379270	−	0.101501i
$49$	6.51800	+	2.55259i	0.931143	+	0.364655i
$50$	−6.64438	−	2.41914i	−0.939657	−	0.342118i
$51$	−0.942004	+	3.51561i	−0.131907	+	0.492283i
$52$	−0.000417315		2.73081i	−5.78712e−5		0.378696i
$53$	6.93880	−	1.85924i	0.953117	−	0.255387i	0.251432	−	0.967875i	$-0.419098\pi$
$53$	6.93880	−	1.85924i	0.953117	−	0.255387i	0.701684	+	0.712488i	$0.252432\pi$
$54$	−4.91999	−	2.03837i	−0.669526	−	0.277387i
$55$	−0.0232353	+	0.212133i	−0.00313305	+	0.0286040i
$56$	4.09828	−	6.26132i	0.547655	−	0.836704i
$57$	−3.61212			−0.478437
$58$	−4.50786	−	1.86762i	−0.591912	−	0.245231i
$59$	3.75125	+	13.9999i	0.488371	+	1.82263i	0.564374	+	0.825520i	$0.309118\pi$
$59$	3.75125	+	13.9999i	0.488371	+	1.82263i	−0.0760021	+	0.997108i	$0.524216\pi$
$60$	−1.90316	−	2.37210i	−0.245697	−	0.306237i
$61$	−1.85274	+	6.91452i	−0.237219	+	0.885314i	0.739917	+	0.672698i	$0.234865\pi$
$61$	−1.85274	+	6.91452i	−0.237219	+	0.885314i	−0.977136	+	0.212615i	$0.931802\pi$
$62$	−1.58346	+	12.0204i	−0.201099	+	1.52660i
$63$	−6.33617	+	2.21974i	−0.798282	+	0.279661i
$64$	−5.65426	−	5.65945i	−0.706783	−	0.707431i
$65$	2.79459	−	1.22960i	0.346627	−	0.152514i
$66$	−0.0558790	+	0.0728114i	−0.00687823	+	0.00896246i
$67$	−1.50412	−	5.61347i	−0.183758	−	0.685795i	−0.994893	−	0.100935i	$-0.967816\pi$
$67$	−1.50412	−	5.61347i	−0.183758	−	0.685795i	0.811135	−	0.584859i	$-0.198850\pi$
$68$	10.3399	−	2.76889i	1.25390	−	0.335777i
$69$	−2.80581	+	2.80581i	−0.337779	+	0.337779i
$70$	−8.25310	−	1.37345i	−0.986434	−	0.164158i
$71$			3.07469i			0.364898i	0.983215	+	0.182449i	$0.0584025\pi$
$71$			3.07469i			0.364898i	−0.983215	+	0.182449i	$0.941598\pi$
$72$	0.935193	+	7.11610i	0.110214	+	0.838641i
$73$	4.81409	−	8.33825i	0.563447	−	0.975918i	−0.433746	−	0.901035i	$-0.642808\pi$
$73$	4.81409	−	8.33825i	0.563447	−	0.975918i	0.997192	−	0.0748827i	$-0.0238582\pi$
$74$	0.686292	+	5.21598i	0.0797798	+	0.606346i
$75$	−1.57010	+	3.01594i	−0.181300	+	0.348251i
$76$	5.31028	+	9.20092i	0.609131	+	1.05542i
$77$	0.0189621	+	0.251787i	0.00216094	+	0.0286938i
$78$	1.30188	+	0.171497i	0.147409	+	0.0194182i
$79$	4.28039	+	7.41385i	0.481581	+	0.834123i	0.999777	−	0.0211394i	$-0.00672937\pi$
$79$	4.28039	+	7.41385i	0.481581	+	0.834123i	−0.518195	+	0.855262i	$0.673396\pi$
$80$	−3.24441	+	8.33510i	−0.362736	+	0.931892i
$81$	2.52593	−	4.37503i	0.280659	−	0.486115i
$82$	−4.53799	−	10.9581i	−0.501137	−	1.21011i
$83$	−3.47150	+	3.47150i	−0.381046	+	0.381046i	−0.871479	−	0.490433i	$-0.836839\pi$
$83$	−3.47150	+	3.47150i	−0.381046	+	0.381046i	0.490433	+	0.871479i	$0.336839\pi$
$84$	−2.72799	−	2.34660i	−0.297648	−	0.256035i
$85$	−7.49075	−	9.33354i	−0.812486	−	1.01237i
$86$	6.52805	+	2.70459i	0.703938	+	0.291644i
$87$	−1.17315	+	2.03196i	−0.125775	+	0.217849i
$88$	0.267617	+	0.0352949i	0.0285281	+	0.00376244i
$89$	−2.92394	+	1.68814i	−0.309937	+	0.178942i	−0.646898	−	0.762576i	$-0.723934\pi$
$89$	−2.92394	+	1.68814i	−0.309937	+	0.178942i	0.336961	+	0.941519i	$0.390601\pi$
$90$	6.86058	−	4.16225i	0.723168	−	0.438740i
$91$	2.98406	−	2.03611i	0.312815	−	0.213442i
$92$	11.2719	+	3.02215i	1.17518	+	0.315081i
$93$	5.63138	+	1.50892i	0.583947	+	0.156468i
$94$	7.66447	−	9.98695i	0.790530	−	1.03008i
$95$	7.02329	−	9.57828i	0.720574	−	0.982711i
$96$	−3.05280	+	2.34065i	−0.311575	+	0.238891i
$97$		−	0.887544i		−	0.0901165i	−0.998984	−	0.0450582i	$-0.985653\pi$
$97$		−	0.887544i		−	0.0901165i	0.998984	−	0.0450582i	$-0.0143473\pi$
$98$	−9.89764	+	0.191645i	−0.999813	+	0.0193591i
$99$	−0.171243	−	0.171243i	−0.0172106	−	0.0172106i
$100$	9.99056	−	0.434392i	0.999056	−	0.0434392i
$101$	−2.12108	−	7.91598i	−0.211055	−	0.787669i	−0.987518	−	0.157506i	$-0.949655\pi$
$101$	−2.12108	−	7.91598i	−0.211055	−	0.787669i	0.776463	−	0.630163i	$-0.217012\pi$
$102$	−0.671455	−	5.10322i	−0.0664840	−	0.505294i
$103$	2.82140	+	4.88682i	0.278001	+	0.481512i	0.970888	−	0.239534i	$-0.0769947\pi$
$103$	2.82140	+	4.88682i	0.278001	+	0.481512i	−0.692887	+	0.721046i	$0.743661\pi$
$104$	−1.47709	−	3.56832i	−0.144840	−	0.349903i
$105$	−1.17249	+	3.84849i	−0.114423	+	0.375574i
$106$	−8.06023	+	6.18385i	−0.782879	+	0.600629i
$107$	−4.84014	+	18.0637i	−0.467914	+	1.74628i	0.179127	+	0.983826i	$0.442673\pi$
$107$	−4.84014	+	18.0637i	−0.467914	+	1.74628i	−0.647042	+	0.762454i	$0.723994\pi$
$108$	7.53144	+	0.00115093i	0.724713	+	0.000110748i
$109$	−8.77324	+	2.35078i	−0.840324	+	0.225164i	−0.653212	−	0.757175i	$-0.726579\pi$
$109$	−8.77324	+	2.35078i	−0.840324	+	0.225164i	−0.187111	+	0.982339i	$0.559912\pi$
$110$	−0.0844251	−	0.289747i	−0.00804962	−	0.0276263i
$111$	2.52975			0.240114
$112$	−1.96685	+	10.3986i	−0.185850	+	0.982578i
$113$		−	17.1588i		−	1.61417i	−0.590436	−	0.807084i	$-0.701044\pi$
$113$		−	17.1588i		−	1.61417i	0.590436	−	0.807084i	$-0.298956\pi$
$114$	4.71961	−	1.95450i	0.442032	−	0.183056i
$115$	−1.98465	−	12.8957i	−0.185070	−	1.20253i
$116$	6.90056	+	0.00105452i	0.640701	+	9.79100e-5i
$117$	−0.896755	+	3.34674i	−0.0829051	+	0.309406i
$118$	−12.4767	−	16.2625i	−1.14857	−	1.49708i
$119$	−10.7366	−	9.23270i	−0.984221	−	0.846360i
$120$	3.77022	+	2.06960i	0.344172	+	0.188928i
$121$	9.51839	−	5.49545i	0.865308	−	0.499586i
$122$	−1.32062	−	10.0371i	−0.119564	−	0.908712i
$123$	−5.50887	+	1.47610i	−0.496719	+	0.133095i
$124$	−4.43527	−	16.5628i	−0.398299	−	1.48738i
$125$	−4.94452	−	10.0275i	−0.442252	−	0.896891i
$126$	7.07777	−	6.32880i	0.630538	−	0.563815i
$127$			3.39927i			0.301637i	0.988561	+	0.150818i	$0.0481909\pi$
$127$			3.39927i			0.301637i	−0.988561	+	0.150818i	$0.951809\pi$
$128$	10.4502	+	4.33516i	0.923675	+	0.383178i
$129$	1.69890	−	2.94257i	0.149579	−	0.259079i
$130$	−2.98609	+	3.11875i	−0.261898	+	0.273533i
$131$	3.39610	−	12.6744i	0.296719	−	1.10737i	−0.643124	−	0.765762i	$-0.722362\pi$
$131$	3.39610	−	12.6744i	0.296719	−	1.10737i	0.939843	−	0.341608i	$-0.110971\pi$
$132$	0.0336137	−	0.125372i	0.00292570	−	0.0109122i
$133$	6.09288	−	12.6639i	0.528319	−	1.09810i
$134$	5.00272	+	6.52071i	0.432170	+	0.563303i
$135$	−3.39118	−	7.70734i	−0.291867	−	0.663342i
$136$	−12.0120	+	9.21274i	−1.03002	+	0.789986i
$137$	8.81976	−	15.2763i	0.753523	−	1.30514i	−0.192582	−	0.981281i	$-0.561686\pi$
$137$	8.81976	−	15.2763i	0.753523	−	1.30514i	0.946105	−	0.323860i	$-0.104981\pi$
$138$	2.14787	−	5.18429i	0.182839	−	0.441316i
$139$	−0.846555	+	0.846555i	−0.0718038	+	0.0718038i	−0.742097	−	0.670293i	$-0.766168\pi$
$139$	−0.846555	+	0.846555i	−0.0718038	+	0.0718038i	0.670293	+	0.742097i	$0.266168\pi$
$140$	11.5267	−	2.67117i	0.974184	−	0.225755i
$141$	−4.28047	−	4.28047i	−0.360481	−	0.360481i
$142$	−1.66370	−	4.01740i	−0.139615	−	0.337133i
$143$	0.112851	+	0.0651547i	0.00943709	+	0.00544851i
$144$	−5.07242	−	8.79190i	−0.422702	−	0.732658i
$145$	−3.10712	−	7.06172i	−0.258032	−	0.586444i
$146$	−1.77832	+	13.4997i	−0.147174	+	1.11724i
$147$	−0.529491	+	4.73069i	−0.0436717	+	0.390181i
$148$	−3.71906	−	6.44388i	−0.305705	−	0.529683i
$149$	12.4402	+	3.33335i	1.01914	+	0.273079i	0.729445	−	0.684040i	$-0.239778\pi$
$149$	12.4402	+	3.33335i	1.01914	+	0.273079i	0.289698	+	0.957118i	$0.406445\pi$
$150$	0.419591	−	4.79022i	0.0342595	−	0.391120i
$151$	−9.08747	−	5.24666i	−0.739528	−	0.426967i	0.0823695	−	0.996602i	$-0.473751\pi$
$151$	−9.08747	−	5.24666i	−0.739528	−	0.426967i	−0.821898	+	0.569635i	$0.807085\pi$
$152$	−11.9170	−	9.14859i	−0.966598	−	0.742049i
$153$	13.5813			1.09798
$154$	−0.161017	−	0.318726i	−0.0129751	−	0.0256837i
$155$	−14.9507	+	11.9989i	−1.20087	+	0.963772i
$156$	−1.79384	+	0.480364i	−0.143622	+	0.0384599i
$157$	2.76822	+	10.3311i	0.220928	+	0.824515i	0.983995	+	0.178196i	$0.0570260\pi$
$157$	2.76822	+	10.3311i	0.220928	+	0.824515i	−0.763067	+	0.646319i	$0.776307\pi$
$158$	−9.60438	−	7.37086i	−0.764083	−	0.586394i
$159$	2.44253	+	4.23059i	0.193705	+	0.335508i
$160$	−0.270934	−	12.6462i	−0.0214192	−	0.999771i
$161$	−5.10422	−	14.5698i	−0.402269	−	1.14826i
$162$	−0.933072	+	7.08321i	−0.0733091	+	0.556509i
$163$	−1.17628	−	0.315182i	−0.0921330	−	0.0246870i	0.212458	−	0.977170i	$-0.431853\pi$
$163$	−1.17628	−	0.315182i	−0.0921330	−	0.0246870i	−0.304591	+	0.952483i	$0.598520\pi$
$164$	11.8587	+	11.8623i	0.926011	+	0.926294i
$165$	−0.143432	+	0.0220742i	−0.0111661	+	0.00171848i
$166$	2.65746	−	6.41428i	0.206259	−	0.497845i
$167$	11.7258			0.907372			0.453686	−	0.891162i	$-0.350109\pi$
$167$	11.7258			0.907372			0.453686	+	0.891162i	$0.350109\pi$
$168$	4.83414	+	1.58997i	0.372962	+	0.122669i
$169$			11.1357i			0.856589i
$170$	14.8378	+	8.14203i	1.13801	+	0.624465i
$171$	3.48854	+	13.0194i	0.266776	+	0.995620i
$172$	−9.99302	−	0.00152710i	−0.761961	−	0.000116441i
$173$	−15.0659	−	4.03689i	−1.14544	−	0.306919i	−0.364303	−	0.931281i	$-0.618693\pi$
$173$	−15.0659	−	4.03689i	−1.14544	−	0.306919i	−0.781136	+	0.624361i	$0.785359\pi$
$174$	0.433360	−	3.28975i	0.0328529	−	0.249396i
$175$	−7.92531	−	10.5920i	−0.599097	−	0.800677i
$176$	−0.368767	+	0.0986901i	−0.0277969	+	0.00743905i
$177$	−8.53573	+	4.92810i	−0.641585	+	0.370419i
$178$	2.90699	−	3.78786i	0.217888	−	0.283912i
$179$	−2.29483	+	0.614899i	−0.171524	+	0.0459597i	−0.343559	−	0.939131i	$-0.611632\pi$
$179$	−2.29483	+	0.614899i	−0.171524	+	0.0459597i	0.172035	+	0.985091i	$0.444966\pi$
$180$	−6.71188	+	9.15065i	−0.500274	+	0.682049i
$181$	1.33946	−	1.33946i	0.0995611	−	0.0995611i	−0.655572	−	0.755133i	$-0.727572\pi$
$181$	1.33946	−	1.33946i	0.0995611	−	0.0995611i	0.755133	+	0.655572i	$0.227572\pi$
$182$	−2.79726	+	4.27505i	−0.207346	+	0.316888i
$183$	−4.86797			−0.359851
$184$	−16.3632	+	2.15045i	−1.20631	+	0.158533i
$185$	−4.91877	+	6.70816i	−0.361635	+	0.493194i
$186$	−8.17446	+	1.07555i	−0.599381	+	0.0788634i
$187$	0.132201	−	0.493382i	0.00966752	−	0.0360797i
$188$	−4.61053	+	17.1962i	−0.336257	+	1.25416i
$189$	−5.61548	−	8.22988i	−0.408466	−	0.598636i
$190$	−3.99389	+	16.3153i	−0.289747	+	1.18364i
$191$	−1.22528	−	2.12225i	−0.0886584	−	0.153561i	0.818286	−	0.574811i	$-0.194925\pi$
$191$	−1.22528	−	2.12225i	−0.0886584	−	0.153561i	−0.906944	+	0.421251i	$0.861591\pi$
$192$	2.72229	−	4.71016i	0.196464	−	0.339926i
$193$	17.5525	+	10.1340i	1.26346	+	0.729458i	0.973742	−	0.227655i	$-0.0731057\pi$
$193$	17.5525	+	10.1340i	1.26346	+	0.729458i	0.289716	+	0.957113i	$0.406439\pi$
$194$	0.480247	+	1.15967i	0.0344797	+	0.0832594i
$195$	1.29954	+	1.61924i	0.0930623	+	0.115956i
$196$	12.8286	−	5.60598i	0.916329	−	0.400427i
$197$	4.69429	+	4.69429i	0.334455	+	0.334455i	0.854275	−	0.519821i	$-0.174001\pi$
$197$	4.69429	+	4.69429i	0.334455	+	0.334455i	−0.519821	+	0.854275i	$0.674001\pi$
$198$	0.316406	+	0.131088i	0.0224860	+	0.00931603i
$199$	14.4776	+	8.35863i	1.02629	+	0.592527i	0.915919	−	0.401363i	$-0.131464\pi$
$199$	14.4776	+	8.35863i	1.02629	+	0.592527i	0.110369	+	0.993891i	$0.464797\pi$
$200$	−12.8187	+	5.97343i	−0.906416	+	0.422386i
$201$	3.42254	−	1.97600i	0.241407	−	0.139376i
$202$	7.05472	+	9.19534i	0.496368	+	0.646982i
$203$	−5.14509	−	7.54049i	−0.361115	−	0.529239i
$204$	3.63866	+	6.30457i	0.254757	+	0.441408i
$205$	6.79710	−	17.4780i	0.474730	−	1.22072i
$206$	−6.33070	−	4.85848i	−0.441081	−	0.338507i
$207$	12.8230	+	7.40335i	0.891258	+	0.514568i
$208$	3.86077	+	3.86314i	0.267697	+	0.267860i
$209$	0.506927			0.0350649
$210$	−0.550426	−	5.66288i	−0.0379830	−	0.390776i
$211$	−16.5292	−	16.5292i	−1.13792	−	1.13792i	−0.988823	−	0.149094i	$-0.952364\pi$
$211$	−16.5292	−	16.5292i	−1.13792	−	1.13792i	−0.149094	−	0.988823i	$-0.547636\pi$
$212$	7.18547	−	12.4412i	0.493500	−	0.854466i
$213$	−2.01964	+	0.541162i	−0.138384	+	0.0370798i
$214$	−3.45003	−	26.2210i	−0.235839	−	1.79243i
$215$	4.49956	+	10.2264i	0.306868	+	0.697436i
$216$	−9.84123	+	4.07373i	−0.669611	+	0.277182i
$217$	−14.7892	+	17.1981i	−1.00395	+	1.16748i
$218$	10.1912	−	7.81871i	0.690232	−	0.529550i
$219$	6.32438	+	1.69461i	0.427362	+	0.114511i
$220$	0.267091	+	0.332902i	0.0180073	+	0.0224443i
$221$	−7.05883	+	1.89141i	−0.474828	+	0.127230i
$222$	−3.30539	+	1.36884i	−0.221843	+	0.0918705i
$223$		−	5.11410i		−	0.342466i	−0.985231	−	0.171233i	$-0.945225\pi$
$223$		−	5.11410i		−	0.342466i	0.985231	−	0.171233i	$-0.0547750\pi$
$224$	−3.05676	−	14.6512i	−0.204239	−	0.978921i
$225$	12.3870	+	2.74648i	0.825797	+	0.183099i
$226$	9.28459	+	22.4198i	0.617602	+	1.49134i
$227$	0.244531	+	0.912603i	0.0162301	+	0.0605716i	0.973566	−	0.228406i	$-0.0733514\pi$
$227$	0.244531	+	0.912603i	0.0162301	+	0.0605716i	−0.957336	+	0.288978i	$0.906685\pi$
$228$	−5.10909	+	5.10753i	−0.338358	+	0.338254i
$229$	2.42996	+	0.651107i	0.160577	+	0.0430264i	0.338212	−	0.941070i	$-0.390178\pi$
$229$	2.42996	+	0.651107i	0.160577	+	0.0430264i	−0.177635	+	0.984096i	$0.556845\pi$
$230$	9.57096	+	15.7757i	0.631091	+	1.04022i
$231$	−0.162052	+	0.0567715i	−0.0106622	+	0.00373529i
$232$	−9.01687	+	3.73249i	−0.591986	+	0.245050i
$233$	−11.4412	−	19.8167i	−0.749538	−	1.29824i	−0.948044	−	0.318138i	$-0.896942\pi$
$233$	−11.4412	−	19.8167i	−0.749538	−	1.29824i	0.198507	−	0.980100i	$-0.436391\pi$
$234$	−0.639202	−	4.85809i	−0.0417860	−	0.317583i
$235$	19.6734	−	3.02774i	1.28335	−	0.197508i
$236$	25.1017	+	14.4976i	1.63398	+	0.943711i
$237$	−4.11650	+	4.11650i	−0.267395	+	0.267395i
$238$	19.0242	+	6.25396i	1.23316	+	0.405384i
$239$	5.45931			0.353133			0.176567	−	0.984289i	$-0.443501\pi$
$239$	5.45931			0.353133			0.176567	+	0.984289i	$0.443501\pi$
$240$	−6.04604	−	0.664103i	−0.390270	−	0.0428676i
$241$	−6.88558	+	11.9262i	−0.443539	+	0.768232i	−0.997949	−	0.0640116i	$-0.979611\pi$
$241$	−6.88558	+	11.9262i	−0.443539	+	0.768232i	0.554410	+	0.832244i	$0.312944\pi$
$242$	−9.46321	+	12.3307i	−0.608318	+	0.792650i
$243$	14.2306	+	3.81307i	0.912892	+	0.244609i
$244$	7.15654	+	12.3999i	0.458151	+	0.793821i
$245$	−11.5149	−	10.6023i	−0.735658	−	0.677353i
$246$	6.39921	−	4.90951i	0.407999	−	0.313019i
$247$	−3.62631	−	6.28095i	−0.230736	−	0.399647i
$248$	14.7572	+	19.2411i	0.937083	+	1.22181i
$249$	−2.89129	−	1.66929i	−0.183228	−	0.105787i
$250$	11.8864	+	10.4266i	0.751762	+	0.659434i
$251$	−4.99227	+	4.99227i	−0.315109	+	0.315109i	−0.846885	−	0.531776i	$-0.821525\pi$
$251$	−4.99227	+	4.99227i	−0.315109	+	0.315109i	0.531776	+	0.846885i	$0.321525\pi$
$252$	−5.82336	+	12.0990i	−0.366837	+	0.762165i
$253$	0.393768	−	0.393768i	0.0247560	−	0.0247560i
$254$	−1.83933	−	4.44151i	−0.115410	−	0.278685i
$255$	4.81243	−	6.56314i	0.301366	−	0.411000i
$256$	−16.0000	−	0.00978029i	−1.00000	−	0.000611268i
$257$	−11.1225	+	6.42155i	−0.693799	+	0.400565i	−0.805034	−	0.593229i	$-0.797853\pi$
$257$	−11.1225	+	6.42155i	−0.693799	+	0.400565i	0.111234	+	0.993794i	$0.464520\pi$
$258$	−0.627569	+	4.76405i	−0.0390707	+	0.296597i
$259$	−4.26715	+	8.86919i	−0.265148	+	0.551105i
$260$	2.21410	−	5.69074i	0.137313	−	0.352925i
$261$	8.45694	+	2.26603i	0.523472	+	0.140264i
$262$	2.42072	+	18.3981i	0.149553	+	1.13664i
$263$	−6.39098	+	11.0695i	−0.394085	+	0.682574i	−0.992984	−	0.118250i	$-0.962272\pi$
$263$	−6.39098	+	11.0695i	−0.394085	+	0.682574i	0.598899	+	0.800824i	$0.295605\pi$
$264$	0.0239182	+	0.181999i	0.00147206	+	0.0112013i
$265$	−15.9675	−	1.74894i	−0.980873	−	0.107437i
$266$	−1.10858	+	19.8436i	−0.0679713	+	1.21669i
$267$	−1.62350	−	1.62350i	−0.0993567	−	0.0993567i
$268$	−10.0649	−	5.81303i	−0.614812	−	0.355087i
$269$	−30.2700	+	8.11081i	−1.84559	+	0.494525i	−0.999272	−	0.0381505i	$-0.987853\pi$
$269$	−30.2700	+	8.11081i	−1.84559	+	0.494525i	−0.846320	+	0.532675i	$0.821187\pi$
$270$	8.60135	+	8.23549i	0.523461	+	0.501196i
$271$	−8.59718	−	14.8908i	−0.522242	−	0.904549i	−0.999665	−	0.0258757i	$-0.991763\pi$
$271$	−8.59718	−	14.8908i	−0.522242	−	0.904549i	0.477424	−	0.878673i	$-0.341571\pi$
$272$	10.7099	−	18.5370i	0.649384	−	1.12397i
$273$	1.86265	+	1.60175i	0.112733	+	0.0969422i
$274$	−3.25800	+	24.7324i	−0.196823	+	1.49414i
$275$	0.220349	−	0.423259i	0.0132876	−	0.0255235i
$276$	−0.00121276	+	7.93602i	−7.29995e−5	+	0.477692i
$277$	−9.01392	+	2.41527i	−0.541594	+	0.145120i	−0.519237	−	0.854630i	$-0.673784\pi$
$277$	−9.01392	+	2.41527i	−0.541594	+	0.145120i	−0.0223572	+	0.999750i	$0.507117\pi$
$278$	0.648044	−	1.56418i	0.0388671	−	0.0938132i
$279$		−	21.7549i		−	1.30243i
$280$	−13.6155	+	9.72722i	−0.813680	+	0.581312i
$281$			20.2835i			1.21001i	0.796221	+	0.605005i	$0.206829\pi$
$281$			20.2835i			1.21001i	−0.796221	+	0.605005i	$0.793171\pi$
$282$	7.90903	+	3.27674i	0.470976	+	0.195127i
$283$	−19.2909	+	5.16899i	−1.14673	+	0.307264i	−0.781652	−	0.623714i	$-0.785623\pi$
$283$	−19.2909	+	5.16899i	−1.14673	+	0.307264i	−0.365074	+	0.930979i	$0.618956\pi$
$284$	4.34760	+	4.34893i	0.257983	+	0.258061i
$285$	7.52774	+	2.92750i	0.445905	+	0.173410i
$286$	−0.182707	−	0.0240680i	−0.0108037	−	0.00142317i
$287$	4.11717	−	21.8037i	0.243029	−	1.28703i
$288$	11.3849	+	8.74287i	0.670863	+	0.515178i
$289$	5.82264	+	10.0851i	0.342508	+	0.593242i
$290$	7.88084	+	7.54563i	0.462779	+	0.443095i
$291$	0.582993	−	0.156213i	0.0341757	−	0.00915735i
$292$	−4.98107	−	18.6010i	−0.291495	−	1.08854i
$293$	19.3719	+	19.3719i	1.13172	+	1.13172i	0.989891	+	0.141827i	$0.0452977\pi$
$293$	19.3719	+	19.3719i	1.13172	+	1.13172i	0.141827	+	0.989891i	$0.454702\pi$
$294$	−1.86792	−	6.46765i	−0.108939	−	0.377201i
$295$	3.52870	−	32.2163i	0.205449	−	1.87570i
$296$	8.34610	+	6.40723i	0.485107	+	0.372412i
$297$	0.179693	−	0.311237i	0.0104268	−	0.0180598i
$298$	−18.0581	+	2.37599i	−1.04608	+	0.137638i
$299$	−7.69571	−	2.06206i	−0.445054	−	0.119252i
$300$	2.04373	+	6.48596i	0.117995	+	0.374467i
$301$	7.45085	+	10.9197i	0.429460	+	0.629403i
$302$	14.7127	+	1.93810i	0.846620	+	0.111525i
$303$	4.82638	−	2.78651i	0.277268	−	0.160081i
$304$	20.5211	+	5.50533i	1.17697	+	0.315753i
$305$	9.46513	−	12.9084i	0.541972	−	0.739135i
$306$	−17.7454	+	7.34880i	−1.01444	+	0.420103i
$307$	−1.63847	+	1.63847i	−0.0935125	+	0.0935125i	−0.752315	−	0.658803i	$-0.771063\pi$
$307$	−1.63847	+	1.63847i	−0.0935125	+	0.0935125i	0.658803	+	0.752315i	$0.271063\pi$
$308$	0.382847	+	0.329323i	0.0218148	+	0.0187649i
$309$	−2.71338	+	2.71338i	−0.154359	+	0.154359i
$310$	13.0421	−	23.7675i	0.740742	−	1.34991i
$311$	−0.0830733	−	0.0479624i	−0.00471065	−	0.00271970i	0.497643	−	0.867382i	$-0.334199\pi$
$311$	−0.0830733	−	0.0479624i	−0.00471065	−	0.00271970i	−0.502353	+	0.864662i	$0.667532\pi$
$312$	2.08392	−	1.59829i	0.117978	−	0.0904851i
$313$	12.8780	+	22.3054i	0.727909	+	1.26078i	0.957765	+	0.287551i	$0.0928410\pi$
$313$	12.8780	+	22.3054i	0.727909	+	1.26078i	−0.229856	+	0.973225i	$0.573826\pi$
$314$	−9.20711	−	12.0008i	−0.519587	−	0.677247i
$315$	15.0037	+	0.509252i	0.845365	+	0.0286931i
$316$	16.5375	+	4.43391i	0.930305	+	0.249427i
$317$	14.5818	+	3.90719i	0.818997	+	0.219450i	0.643908	−	0.765103i	$-0.277312\pi$
$317$	14.5818	+	3.90719i	0.818997	+	0.219450i	0.175089	+	0.984553i	$0.443979\pi$
$318$	−5.48058	−	4.20606i	−0.307336	−	0.235864i
$319$	0.164641	−	0.285166i	0.00921811	−	0.0159662i
$320$	7.19682	+	16.3770i	0.402314	+	0.915502i
$321$	−12.7172			−0.709806
$322$	14.5529	+	16.2751i	0.811000	+	0.906976i
$323$	−20.1022	+	20.1022i	−1.11852	+	1.11852i
$324$	−2.61354	−	9.75983i	−0.145197	−	0.542213i
$325$	−6.82055	+	0.297604i	−0.378336	+	0.0165081i
$326$	1.70747	−	0.224660i	0.0945681	−	0.0124428i
$327$	−3.08828	−	5.34905i	−0.170782	−	0.295803i
$328$	−21.9133	−	9.08268i	−1.20996	−	0.501507i
$329$	22.2274	−	7.78688i	1.22543	−	0.429305i
$330$	0.175464	−	0.106453i	0.00965898	−	0.00586002i
$331$	9.41967	+	2.52399i	0.517752	+	0.138731i	0.508227	−	0.861223i	$-0.330301\pi$
$331$	9.41967	+	2.52399i	0.517752	+	0.138731i	0.00952547	+	0.999955i	$0.496968\pi$
$332$	−0.00150049	+	9.81887i	−8.23501e−5	+	0.538881i
$333$	−2.44321	−	9.11817i	−0.133887	−	0.499672i
$334$	−15.3210	+	6.34480i	−0.838329	+	0.347172i
$335$	−1.41489	+	12.9176i	−0.0773037	+	0.705766i
$336$	−7.17663	+	0.538267i	−0.391517	+	0.0293649i
$337$		−	2.37030i		−	0.129118i	−0.997914	−	0.0645591i	$-0.979436\pi$
$337$		−	2.37030i		−	0.129118i	0.997914	−	0.0645591i	$-0.0205641\pi$
$338$	−6.02547	−	14.5499i	−0.327742	−	0.791411i
$339$	11.2710	−	3.02005i	0.612156	−	0.164027i
$340$	−23.7927	−	2.60974i	−1.29034	−	0.141533i
$341$	−0.790312	−	0.211763i	−0.0427978	−	0.0114676i
$342$	−11.6029	−	15.1236i	−0.627413	−	0.817790i
$343$	−15.6924	−	9.83604i	−0.847312	−	0.531096i
$344$	13.0578	−	5.40519i	0.704027	−	0.291428i
$345$	8.12137	−	3.57335i	0.437240	−	0.192383i
$346$	21.8695	−	2.87747i	1.17571	−	0.154694i
$347$	30.6227	−	8.20533i	1.64391	−	0.440485i	0.686014	−	0.727588i	$-0.259359\pi$
$347$	30.6227	−	8.20533i	1.64391	−	0.440485i	0.957900	+	0.287103i	$0.0926923\pi$
$348$	1.21384	+	4.53289i	0.0650688	+	0.242989i
$349$	−10.8117	−	10.8117i	−0.578738	−	0.578738i	0.355817	−	0.934556i	$-0.384203\pi$
$349$	−10.8117	−	10.8117i	−0.578738	−	0.578738i	−0.934556	+	0.355817i	$0.884203\pi$
$350$	16.0865	+	9.55114i	0.859860	+	0.510530i
$351$	−5.14174			−0.274446
$352$	0.428432	−	0.328488i	0.0228355	−	0.0175085i
$353$	−9.70128	−	5.60104i	−0.516347	−	0.298113i	0.219092	−	0.975704i	$-0.429691\pi$
$353$	−9.70128	−	5.60104i	−0.516347	−	0.298113i	−0.735439	+	0.677591i	$0.763024\pi$
$354$	8.48624	−	11.0577i	0.451039	−	0.587712i
$355$	2.49193	−	6.40772i	0.132258	−	0.340086i
$356$	−1.74869	+	6.52220i	−0.0926801	+	0.345676i
$357$	4.17490	−	8.67745i	0.220959	−	0.459259i
$358$	2.66572	−	2.04516i	0.140888	−	0.108090i
$359$	−19.9754	+	11.5328i	−1.05426	+	0.608678i	−0.923839	−	0.382781i	$-0.874966\pi$
$359$	−19.9754	+	11.5328i	−1.05426	+	0.608678i	−0.130422	+	0.991459i	$0.541633\pi$
$360$	3.81839	−	15.5881i	0.201247	−	0.821563i
$361$	−7.97956	−	4.60700i	−0.419977	−	0.242474i
$362$	−1.02537	+	2.47492i	−0.0538920	+	0.130079i
$363$	5.28503	+	5.28503i	0.277392	+	0.277392i
$364$	1.34169	−	7.09939i	0.0703237	−	0.372109i
$365$	−16.7905	+	13.4754i	−0.878856	+	0.705337i
$366$	6.36052	−	2.63404i	0.332469	−	0.137684i
$367$	−3.53955	−	2.04356i	−0.184763	−	0.106673i	0.404766	−	0.914420i	$-0.367353\pi$
$367$	−3.53955	−	2.04356i	−0.184763	−	0.106673i	−0.589529	+	0.807748i	$0.700686\pi$
$368$	20.2167	−	11.6639i	1.05387	−	0.608021i
$369$	10.6408	+	18.4304i	0.553939	+	0.959450i
$370$	2.79712	−	11.4264i	0.145416	−	0.594032i
$371$	−18.9523	+	1.42730i	−0.983953	+	0.0741016i
$372$	10.0988	−	5.82849i	0.523599	−	0.302193i
$373$	−6.35492	+	23.7169i	−0.329045	+	1.22801i	0.581137	+	0.813806i	$0.302608\pi$
$373$	−6.35492	+	23.7169i	−0.329045	+	1.22801i	−0.910182	+	0.414208i	$0.864059\pi$
$374$	0.0942324	+	0.716189i	0.00487264	+	0.0370333i
$375$	5.71644	−	5.01277i	0.295196	−	0.258858i
$376$	−3.28067	−	24.9634i	−0.169188	−	1.28739i
$377$	−4.71104			−0.242631
$378$	11.7904	+	7.71468i	0.606431	+	0.396800i
$379$	−5.23930	+	5.23930i	−0.269125	+	0.269125i	−0.828748	−	0.559623i	$-0.810946\pi$
$379$	−5.23930	+	5.23930i	−0.269125	+	0.269125i	0.559623	+	0.828748i	$0.310946\pi$
$380$	−3.60972	−	23.4787i	−0.185175	−	1.20443i
$381$	−2.23285	+	0.598291i	−0.114392	+	0.0306514i
$382$	2.74930	+	2.10995i	0.140667	+	0.107954i
$383$	−9.96276	+	5.75200i	−0.509073	+	0.293914i	−0.732453	−	0.680818i	$-0.761624\pi$
$383$	−9.96276	+	5.75200i	−0.509073	+	0.293914i	0.223379	+	0.974732i	$0.428291\pi$
$384$	−1.00831	+	7.62733i	−0.0514550	+	0.389231i
$385$	0.164547	−	0.540099i	0.00838611	−	0.0275260i
$386$	−28.4176	−	3.74346i	−1.44642	−	0.190537i
$387$	−12.2469	−	3.28155i	−0.622545	−	0.166810i
$388$	−1.25499	−	1.25537i	−0.0637122	−	0.0637317i
$389$	−4.92848	−	18.3933i	−0.249884	−	0.932579i	−0.970865	−	0.239625i	$-0.922975\pi$
$389$	−4.92848	−	18.3933i	−0.249884	−	0.932579i	0.720982	−	0.692954i	$-0.243691\pi$
$390$	−2.57416	−	1.41253i	−0.130347	−	0.0715264i
$391$			31.2298i			1.57936i
$392$	−13.7285	+	14.2663i	−0.693395	+	0.720557i
$393$	8.92307			0.450110
$394$	−8.67365	−	3.59352i	−0.436972	−	0.181039i
$395$	−2.91176	−	18.9197i	−0.146506	−	0.951954i
$396$	−0.484349		7.40168e-5i	−0.0243395		3.71949e-6i
$397$	−5.55350	−	1.48806i	−0.278722	−	0.0746834i	0.116750	−	0.993161i	$-0.462752\pi$
$397$	−5.55350	−	1.48806i	−0.278722	−	0.0746834i	−0.395472	+	0.918478i	$0.629419\pi$
$398$	−23.4393	−	3.08766i	−1.17490	−	0.154770i
$399$	9.39082	+	1.77326i	0.470129	+	0.0887738i
$400$	13.5167	−	14.7410i	0.675836	−	0.737052i
$401$	−19.0438	−	32.9848i	−0.951001	−	1.64718i	−0.743266	−	0.668996i	$-0.766724\pi$
$401$	−19.0438	−	32.9848i	−0.951001	−	1.64718i	−0.207735	−	0.978185i	$-0.566609\pi$
$402$	−3.40269	+	4.43378i	−0.169711	+	0.221137i
$403$	3.02970	+	11.3070i	0.150920	+	0.563242i
$404$	−14.1933	−	8.19739i	−0.706143	−	0.407836i
$405$	−8.80990	+	7.07049i	−0.437767	+	0.351335i
$406$	10.8027	+	7.06845i	0.536130	+	0.350801i
$407$	−0.355027			−0.0175980
$408$	−8.16567	−	6.26871i	−0.404261	−	0.310347i
$409$	18.9146	+	10.9203i	0.935264	+	0.539975i	0.888473	−	0.458930i	$-0.151767\pi$
$409$	18.9146	+	10.9203i	0.935264	+	0.539975i	0.0467917	+	0.998905i	$0.485100\pi$
$410$	0.576161	+	26.5147i	0.0284546	+	1.30947i
$411$	11.5867	+	3.10465i	0.571531	+	0.153141i
$412$	10.9006	+	2.92260i	0.537035	+	0.143986i
$413$	−2.87975	−	38.2385i	−0.141703	−	1.88159i
$414$	−20.7605	−	2.73478i	−1.02032	−	0.134407i
$415$	10.0482	−	4.42115i	0.493247	−	0.217026i
$416$	−7.13483	−	2.95854i	−0.349814	−	0.145054i
$417$	−0.705067	−	0.407071i	−0.0345273	−	0.0199343i
$418$	−0.662353	+	0.274296i	−0.0323968	+	0.0134163i
$419$	−2.10427	−	2.10427i	−0.102800	−	0.102800i	0.653836	−	0.756636i	$-0.273159\pi$
$419$	−2.10427	−	2.10427i	−0.102800	−	0.102800i	−0.756636	+	0.653836i	$0.773159\pi$
$420$	3.78335	+	7.10130i	0.184609	+	0.346508i
$421$	3.61785	−	3.61785i	0.176323	−	0.176323i	−0.613428	−	0.789751i	$-0.710210\pi$
$421$	3.61785	−	3.61785i	0.176323	−	0.176323i	0.789751	+	0.613428i	$0.210210\pi$
$422$	30.5410	+	12.6532i	1.48671	+	0.615950i
$423$	−11.2944	+	19.5624i	−0.549151	+	0.951158i
$424$	−2.65668	+	20.1438i	−0.129020	+	0.978268i
$425$	8.04638	+	25.5223i	0.390307	+	1.23801i
$426$	2.34605	−	1.79991i	0.113667	−	0.0872057i
$427$	8.21123	−	17.0669i	0.397369	−	0.825924i
$428$	18.6959	+	32.3937i	0.903702	+	1.56581i
$429$	−0.0229351	+	0.0855951i	−0.00110732	+	0.00413257i
$430$	−11.4126	−	10.9272i	−0.550365	−	0.526955i
$431$	7.44446	−	12.8942i	0.358587	−	0.621091i	−0.629138	−	0.777294i	$-0.716592\pi$
$431$	7.44446	−	12.8942i	0.358587	−	0.621091i	0.987725	+	0.156202i	$0.0499252\pi$
$432$	10.6543	−	10.6478i	0.512606	−	0.512293i
$433$		−	5.59365i		−	0.268814i	−0.990926	−	0.134407i	$-0.957087\pi$
$433$		−	5.59365i		−	0.268814i	0.990926	−	0.134407i	$-0.0429129\pi$
$434$	10.0177	−	30.4735i	0.480867	−	1.46277i
$435$	4.09170	−	3.28385i	0.196182	−	0.157448i
$436$	−9.08513	+	15.7304i	−0.435099	+	0.753347i
$437$	−29.9377	+	8.02179i	−1.43212	+	0.383734i
$438$	−9.18041	+	1.20791i	−0.438657	+	0.0577162i
$439$	14.6400	−	8.45243i	0.698731	−	0.403413i	−0.108144	−	0.994135i	$-0.534491\pi$
$439$	14.6400	−	8.45243i	0.698731	−	0.403413i	0.806875	+	0.590723i	$0.201157\pi$
$440$	−0.529114	−	0.290449i	−0.0252245	−	0.0138466i
$441$	17.5625	−	2.66036i	0.836311	−	0.126684i
$442$	8.19966	−	6.29082i	0.390018	−	0.299224i
$443$	−1.07307	+	4.00477i	−0.0509833	+	0.190272i	−0.986721	−	0.162424i	$-0.948069\pi$
$443$	−1.07307	+	4.00477i	−0.0509833	+	0.190272i	0.935738	+	0.352697i	$0.114735\pi$
$444$	3.57816	−	3.57706i	0.169812	−	0.169760i
$445$	7.46173	−	1.14837i	0.353720	−	0.0544377i
$446$	2.76722	+	6.68211i	0.131032	+	0.316407i
$447$			8.75819i			0.414248i
$448$	11.9217	+	17.4893i	0.563246	+	0.826290i
$449$	7.73656			0.365111			0.182555	−	0.983196i	$-0.441563\pi$
$449$	7.73656			0.365111			0.182555	+	0.983196i	$0.441563\pi$
$450$	−17.6710	+	3.11397i	−0.833017	+	0.146794i
$451$	0.773119	−	0.207157i	0.0364047	−	0.00975462i
$452$	−24.2626	−	24.2700i	−1.14121	−	1.14156i
$453$	1.84688	−	6.89265i	0.0867740	−	0.323845i
$454$	−0.813312	−	1.06010i	−0.0381706	−	0.0497528i
$455$	−7.86904	+	1.82482i	−0.368906	+	0.0855488i
$456$	3.91189	−	9.43803i	0.183191	−	0.441976i
$457$	−5.09364	−	8.82244i	−0.238270	−	0.412696i	0.721948	−	0.691948i	$-0.243247\pi$
$457$	−5.09364	−	8.82244i	−0.238270	−	0.412696i	−0.960218	+	0.279251i	$0.909914\pi$
$458$	−3.52731	+	0.464106i	−0.164821	+	0.0216862i
$459$	5.21640	+	19.4679i	0.243481	+	0.908682i
$460$	−21.0416	−	15.4337i	−0.981071	−	0.719602i
$461$	20.1602	+	20.1602i	0.938955	+	0.938955i	0.998241	−	0.0592857i	$-0.0188823\pi$
$461$	20.1602	+	20.1602i	0.938955	+	0.938955i	−0.0592857	+	0.998241i	$0.518882\pi$
$462$	0.181019	−	0.161864i	0.00842177	−	0.00753058i
$463$		−	14.5693i		−	0.677095i	−0.940949	−	0.338547i	$-0.890064\pi$
$463$		−	14.5693i		−	0.677095i	0.940949	−	0.338547i	$-0.109936\pi$
$464$	9.76184	−	9.75588i	0.453182	−	0.452905i
$465$	−10.5130	−	7.70867i	−0.487528	−	0.357481i
$466$	25.6719	+	19.7018i	1.18923	+	0.912670i
$467$	−3.86989	−	1.03693i	−0.179077	−	0.0479836i	0.168166	−	0.985759i	$-0.446216\pi$
$467$	−3.86989	−	1.03693i	−0.179077	−	0.0479836i	−0.347243	+	0.937775i	$0.612882\pi$
$468$	3.46388	+	6.00173i	0.160118	+	0.277430i
$469$	1.15468	+	15.3323i	0.0533182	+	0.707982i
$470$	−24.0670	+	14.6012i	−1.11013	+	0.673505i
$471$	−6.29891	+	3.63668i	−0.290238	+	0.167569i
$472$	−40.6425	−	5.36017i	−1.87072	−	0.246722i
$473$	−0.238424	+	0.412963i	−0.0109627	+	0.0189880i
$474$	3.15121	−	7.60605i	0.144740	−	0.349358i
$475$	−22.3995	+	14.2692i	−1.02776	+	0.654717i
$476$	−28.2412	+	2.12250i	−1.29443	+	0.0972848i
$477$	12.8896	−	12.8896i	0.590176	−	0.590176i
$478$	−7.13316	+	2.95401i	−0.326263	+	0.135113i
$479$	13.8074	−	23.9151i	0.630876	−	1.09271i	−0.356497	−	0.934296i	$-0.616029\pi$
$479$	13.8074	−	23.9151i	0.630876	−	1.09271i	0.987373	−	0.158413i	$-0.0506377\pi$
$480$	8.25912	−	2.40377i	0.376975	−	0.109716i
$481$	2.53969	+	4.39887i	0.115800	+	0.200571i
$482$	2.54352	−	19.3085i	0.115854	−	0.879480i
$483$	8.67197	−	5.91713i	0.394589	−	0.269239i
$484$	5.69255	−	21.2319i	0.258752	−	0.965087i
$485$	−0.719323	+	1.84966i	−0.0326628	+	0.0839888i
$486$	−20.6570	+	2.71794i	−0.937020	+	0.123288i
$487$	15.7155	−	27.2200i	0.712136	−	1.23345i	−0.251918	−	0.967748i	$-0.581061\pi$
$487$	15.7155	−	27.2200i	0.712136	−	1.23345i	0.964054	−	0.265707i	$-0.0856052\pi$
$488$	−16.0603	−	12.3293i	−0.727015	−	0.558123i
$489$		−	0.828124i		−	0.0374491i
$490$	20.7822	+	7.62230i	0.938845	+	0.344340i
$491$	28.3942	−	28.3942i	1.28141	−	1.28141i	0.341549	−	0.939864i	$-0.389048\pi$
$491$	28.3942	−	28.3942i	1.28141	−	1.28141i	0.939864	−	0.341549i	$-0.110952\pi$
$492$	−5.70472	+	9.87737i	−0.257188	+	0.445306i
$493$	4.77944	+	17.8371i	0.215255	+	0.803343i
$494$	8.13675	+	6.24453i	0.366090	+	0.280955i
$495$	0.218088	+	0.495662i	0.00980234	+	0.0222783i
$496$	−29.6931	−	17.1554i	−1.33326	−	0.770301i
$497$	1.50942	−	7.99360i	0.0677067	−	0.358562i
$498$	4.68102	+	0.616632i	0.209762	+	0.0276319i
$499$	−8.19015	+	30.5661i	−0.366642	+	1.36833i	0.498540	+	0.866867i	$0.333870\pi$
$499$	−8.19015	+	30.5661i	−0.366642	+	1.36833i	−0.865182	+	0.501459i	$0.832797\pi$
$500$	−21.1726	−	7.19171i	−0.946868	−	0.321623i
$501$	2.06381	+	7.70225i	0.0922043	+	0.344111i
$502$	3.82162	−	9.22422i	0.170567	−	0.411697i
$503$	0.504940			0.0225141			0.0112571	−	0.999937i	$-0.496417\pi$
$503$	0.504940			0.0225141			0.0112571	+	0.999937i	$0.496417\pi$
$504$	1.06210	−	18.9596i	0.0473098	−	0.844528i
$505$	−1.99524	+	18.2161i	−0.0887872	+	0.810607i
$506$	−0.301433	+	0.727566i	−0.0134003	+	0.0323443i
$507$	−7.31459	+	1.95994i	−0.324852	+	0.0870439i
$508$	4.80657	+	4.80803i	0.213257	+	0.213322i
$509$	−1.12411	+	4.19524i	−0.0498253	+	0.185951i	−0.986353	−	0.164642i	$-0.947353\pi$
$509$	−1.12411	+	4.19524i	−0.0498253	+	0.185951i	0.936528	+	0.350593i	$0.114020\pi$
$510$	−2.73665	+	11.1794i	−0.121181	+	0.495033i
$511$	−16.6091	+	19.3145i	−0.734743	+	0.854424i
$512$	20.9110	−	8.64476i	0.924142	−	0.382048i
$513$	−17.3225	+	10.0012i	−0.764808	+	0.441562i
$514$	11.0580	−	14.4087i	0.487746	−	0.635542i
$515$	−1.91928	−	12.4709i	−0.0845734	−	0.549533i
$516$	−1.75782	−	6.56430i	−0.0773838	−	0.288977i
$517$	0.600724	+	0.600724i	0.0264198	+	0.0264198i
$518$	0.776395	−	13.8975i	0.0341128	−	0.610620i
$519$		−	10.6067i		−	0.465583i
$520$	0.186287	+	8.63358i	0.00816921	+	0.378608i
$521$	−8.31919	−	4.80309i	−0.364470	−	0.210427i	0.306570	−	0.951848i	$-0.400819\pi$
$521$	−8.31919	−	4.80309i	−0.364470	−	0.210427i	−0.671040	+	0.741421i	$0.734152\pi$
$522$	−12.2760	+	1.61521i	−0.537307	+	0.0706960i
$523$	4.21168	−	15.7182i	0.184164	−	0.687309i	−0.810644	−	0.585539i	$-0.800883\pi$
$523$	4.21168	−	15.7182i	0.184164	−	0.687309i	0.994808	−	0.101770i	$-0.0324504\pi$
$524$	−13.1181	−	22.7292i	−0.573065	−	0.992928i
$525$	5.56255	−	7.07007i	0.242769	−	0.308563i
$526$	2.36081	−	17.9216i	0.102936	−	0.781418i
$527$	39.7373	−	22.9423i	1.73098	−	0.999384i
$528$	−0.129731	−	0.224859i	−0.00564581	−	0.00978573i
$529$	−5.52375	+	9.56742i	−0.240163	+	0.415975i
$530$	21.8095	−	6.35475i	0.947344	−	0.276033i
$531$	26.0064	+	26.0064i	1.12858	+	1.12858i
$532$	−9.28881	−	26.5275i	−0.402721	−	1.15011i
$533$	−8.09723	−	8.09723i	−0.350730	−	0.350730i
$534$	2.99974	+	1.24280i	0.129812	+	0.0537814i
$535$	24.7269	−	33.7223i	1.06904	−	1.45794i
$536$	16.2963	+	2.14924i	0.703891	+	0.0928332i
$537$	−0.807807	−	1.39916i	−0.0348594	−	0.0603783i
$538$	35.1621	−	26.9766i	1.51595	−	1.16304i
$539$	0.0743092	−	0.663908i	0.00320072	−	0.0285965i
$540$	−15.6947	−	6.10636i	−0.675395	−	0.262776i
$541$	3.38201	−	12.6218i	0.145404	−	0.542655i	−0.854333	−	0.519726i	$-0.826034\pi$
$541$	3.38201	−	12.6218i	0.145404	−	0.542655i	0.999737	−	0.0229292i	$-0.00729923\pi$
$542$	19.2904	+	14.8044i	0.828596	+	0.635904i
$543$	1.11559	+	0.644086i	0.0478746	+	0.0276404i
$544$	−3.96331	+	30.0157i	−0.169925	+	1.28691i
$545$	20.1888	+	2.21132i	0.864795	+	0.0947225i
$546$	−3.30045	−	1.08498i	−0.141246	−	0.0464327i
$547$	29.9738	−	29.9738i	1.28159	−	1.28159i	0.341826	−	0.939763i	$-0.388955\pi$
$547$	29.9738	−	29.9738i	1.28159	−	1.28159i	0.939763	−	0.341826i	$-0.111045\pi$
$548$	−9.12568	−	34.0783i	−0.389830	−	1.45575i
$549$	4.70143	+	17.5460i	0.200652	+	0.748844i
$550$	−0.0588857	+	0.672262i	−0.00251089	+	0.0286653i
$551$	−15.8715	+	9.16340i	−0.676147	+	0.390374i
$552$	−4.29256	−	10.3699i	−0.182704	−	0.441372i
$553$	−7.48859	−	21.3759i	−0.318447	−	0.908995i
$554$	10.4707	−	8.03321i	0.444859	−	0.341298i
$555$	−5.27206	−	2.05028i	−0.223786	−	0.0870293i
$556$	−0.000365908		2.39442i	−1.55179e−5		0.101546i
$557$	−0.156224	−	0.583034i	−0.00661940	−	0.0247039i	0.962537	−	0.271150i	$-0.0874039\pi$
$557$	−0.156224	−	0.583034i	−0.00661940	−	0.0247039i	−0.969157	+	0.246446i	$0.920737\pi$
$558$	11.7715	+	28.4250i	0.498327	+	1.20333i
$559$	6.82227			0.288551
$560$	12.5267	−	20.0769i	0.529349	−	0.848404i
$561$	0.347352			0.0146652
$562$	−10.9753	−	26.5025i	−0.462966	−	1.11794i
$563$	1.59950	+	5.96942i	0.0674109	+	0.251581i	0.991406	−	0.130824i	$-0.0417624\pi$
$563$	1.59950	+	5.96942i	0.0674109	+	0.251581i	−0.923995	+	0.382405i	$0.875096\pi$
$564$	−12.1070	−	0.00185016i	−0.509797	−	7.79056e-5i
$565$	−13.9066	+	35.7594i	−0.585057	+	1.50441i
$566$	22.4087	−	17.1921i	0.941907	−	0.722636i
$567$	−8.71471	+	10.1342i	−0.365983	+	0.425597i
$568$	−8.03378	−	3.32986i	−0.337090	−	0.139718i
$569$	−37.3913	+	21.5879i	−1.56753	+	0.905012i	−0.571070	+	0.820901i	$0.693472\pi$
$569$	−37.3913	+	21.5879i	−1.56753	+	0.905012i	−0.996456	+	0.0841105i	$0.973195\pi$
$570$	−11.4198	+	0.248152i	−0.478324	+	0.0103939i
$571$	−3.65659	−	13.6466i	−0.153024	−	0.571092i	−0.999266	−	0.0382948i	$-0.987807\pi$
$571$	−3.65659	−	13.6466i	−0.153024	−	0.571092i	0.846243	−	0.532797i	$-0.178859\pi$
$572$	0.251749	−	0.0674146i	0.0105261	−	0.00281875i
$573$	1.17837	−	1.17837i	0.0492271	−	0.0492271i
$574$	6.41840	+	30.7166i	0.267899	+	1.28209i
$575$	−6.31544	+	28.4834i	−0.263372	+	1.18784i
$576$	−19.6063	−	5.26313i	−0.816930	−	0.219297i
$577$	−1.01076	−	0.583563i	−0.0420785	−	0.0242941i	0.478813	−	0.877917i	$-0.341067\pi$
$577$	−1.01076	−	0.583563i	−0.0420785	−	0.0242941i	−0.520892	+	0.853623i	$0.674400\pi$
$578$	−13.0649	−	10.0266i	−0.543428	−	0.417053i
$579$	−3.56726	+	13.3132i	−0.148250	+	0.553278i
$580$	−14.3801	−	5.59486i	−0.597099	−	0.232314i
$581$	10.7294	−	7.32100i	0.445132	−	0.303726i
$582$	−0.677216	+	0.519564i	−0.0280715	+	0.0215366i
$583$	−0.342786	−	0.593723i	−0.0141968	−	0.0245895i
$584$	16.5732	+	21.6089i	0.685804	+	0.894182i
$585$	4.58127	−	6.24788i	0.189412	−	0.258318i
$586$	−35.7935	−	14.8293i	−1.47861	−	0.612595i
$587$	−23.0989	−	23.0989i	−0.953392	−	0.953392i	0.0455689	−	0.998961i	$-0.485490\pi$
$587$	−23.0989	−	23.0989i	−0.953392	−	0.953392i	−0.998961	+	0.0455689i	$0.985490\pi$
$588$	5.94025	+	7.43993i	0.244972	+	0.306817i
$589$	32.2002	+	32.2002i	1.32679	+	1.32679i
$590$	12.8215	+	44.0033i	0.527852	+	1.81159i
$591$	−2.25728	+	3.90972i	−0.0928520	+	0.160824i
$592$	−14.3720	−	3.85567i	−0.590684	−	0.158467i
$593$	−18.7730	+	10.8386i	−0.770915	+	0.445088i	−0.833201	−	0.552970i	$-0.813494\pi$
$593$	−18.7730	+	10.8386i	−0.770915	+	0.445088i	0.0622860	+	0.998058i	$0.480161\pi$
$594$	−0.0663783	+	0.503895i	−0.00272353	+	0.0206751i
$595$	14.8925	+	27.9428i	0.610533	+	1.14554i
$596$	22.3092	−	12.8757i	0.913819	−	0.527408i
$597$	−2.94233	+	10.9809i	−0.120421	+	0.449419i
$598$	11.1710	−	1.46982i	0.456817	−	0.0601056i
$599$	11.2410	+	6.49001i	0.459296	+	0.265175i	0.711748	−	0.702435i	$-0.247904\pi$
$599$	11.2410	+	6.49001i	0.459296	+	0.265175i	−0.252452	+	0.967609i	$0.581237\pi$
$600$	−6.17987	−	7.36873i	−0.252292	−	0.300827i
$601$		−	44.6576i		−	1.82162i	−0.412826	−	0.910810i	$-0.635458\pi$
$601$		−	44.6576i		−	1.82162i	0.412826	−	0.910810i	$-0.364542\pi$
$602$	−15.6439	−	10.2362i	−0.637599	−	0.417194i
$603$	−10.4277	−	10.4277i	−0.424648	−	0.424648i
$604$	−20.2724	+	5.42864i	−0.824870	+	0.220888i
$605$	−24.2904	+	3.73831i	−0.987545	+	0.151984i
$606$	−4.79840	+	6.25240i	−0.194922	+	0.253987i
$607$	−3.62199	+	2.09116i	−0.147012	+	0.0848775i	−0.571702	−	0.820461i	$-0.693717\pi$
$607$	−3.62199	+	2.09116i	−0.147012	+	0.0848775i	0.424690	+	0.905339i	$0.360383\pi$
$608$	−29.7919	+	3.91060i	−1.20822	+	0.158596i
$609$	4.04749	−	4.70678i	0.164013	−	0.190728i
$610$	−5.38247	+	21.9878i	−0.217930	+	0.890258i
$611$	3.14583	−	11.7404i	0.127267	−	0.474966i
$612$	19.2098	−	19.2040i	0.776511	−	0.776274i
$613$	21.0556	−	5.64182i	0.850426	−	0.227871i	0.192821	−	0.981234i	$-0.438236\pi$
$613$	21.0556	−	5.64182i	0.850426	−	0.227871i	0.657605	+	0.753363i	$0.271570\pi$
$614$	1.25426	−	3.02740i	0.0506179	−	0.122176i
$615$	12.6769	+	1.38853i	0.511184	+	0.0559908i
$616$	−0.678426	−	0.223138i	−0.0273346	−	0.00899048i
$617$	27.2645			1.09763			0.548813	−	0.835945i	$-0.315080\pi$
$617$	27.2645			1.09763			0.548813	+	0.835945i	$0.315080\pi$
$618$	2.07711	−	5.01351i	0.0835537	−	0.201673i
$619$	2.87100	+	10.7147i	0.115395	+	0.430661i	0.999316	−	0.0369755i	$-0.0117724\pi$
$619$	2.87100	+	10.7147i	0.115395	+	0.430661i	−0.883921	+	0.467636i	$0.845106\pi$
$620$	−4.18034	+	38.1118i	−0.167887	+	1.53061i
$621$	−5.68705	+	21.2243i	−0.228213	+	0.851704i
$622$	0.134496	+	0.0177172i	0.00539281	+	0.000710396i
$623$	8.43042	−	2.95342i	0.337758	−	0.118326i
$624$	−1.85803	+	3.21593i	−0.0743806	+	0.128740i
$625$	2.17752	+	24.9050i	0.0871010	+	0.996199i
$626$	−28.8958	−	22.1761i	−1.15491	−	0.886334i
$627$	0.0892219	+	0.332981i	0.00356318	+	0.0132980i
$628$	18.5237	+	10.6984i	0.739175	+	0.426913i
$629$	14.0786	−	14.0786i	0.561351	−	0.561351i
$630$	−19.8795	+	7.45308i	−0.792018	+	0.296938i
$631$			18.3656i			0.731121i	0.930788	+	0.365561i	$0.119123\pi$
$631$			18.3656i			0.731121i	−0.930788	+	0.365561i	$0.880877\pi$
$632$	−24.0071	+	3.15500i	−0.954951	+	0.125499i
$633$	7.94816	−	13.7666i	0.315911	−	0.547174i
$634$	−21.1668	+	2.78502i	−0.840643	+	0.110607i
$635$	2.75499	−	7.08416i	0.109329	−	0.281126i
$636$	9.43683	+	2.53014i	0.374195	+	0.100326i
$637$	−8.75755	+	3.82856i	−0.346987	+	0.151693i
$638$	−0.0608180	+	0.461686i	−0.00240781	+	0.0182783i
$639$	3.90110	+	6.75689i	0.154325	+	0.267299i
$640$	−18.2649	−	17.5041i	−0.721984	−	0.691909i
$641$	−14.9506	+	25.8952i	−0.590513	+	1.02280i	0.403651	+	0.914913i	$0.367741\pi$
$641$	−14.9506	+	25.8952i	−0.590513	+	1.02280i	−0.994163	+	0.107885i	$0.965592\pi$
$642$	16.6164	−	6.88124i	0.655796	−	0.271581i
$643$	11.3285	−	11.3285i	0.446752	−	0.446752i	−0.447521	−	0.894273i	$-0.647693\pi$
$643$	11.3285	−	11.3285i	0.446752	−	0.446752i	0.894273	+	0.447521i	$0.147693\pi$
$644$	−27.8212	−	13.3906i	−1.09631	−	0.527664i
$645$	−5.92539	+	4.75549i	−0.233312	+	0.187247i
$646$	15.3884	−	37.1429i	0.605449	−	1.46137i
$647$	1.45887	−	2.52683i	0.0573539	−	0.0993400i	−0.835923	−	0.548847i	$-0.815067\pi$
$647$	1.45887	−	2.52683i	0.0573539	−	0.0993400i	0.893277	+	0.449507i	$0.148400\pi$
$648$	8.69587	+	11.3381i	0.341606	+	0.445401i
$649$	1.19791	−	0.691613i	0.0470221	−	0.0271482i
$650$	8.75072	−	4.07942i	0.343232	−	0.160008i
$651$	−13.8998	−	6.68746i	−0.544774	−	0.262102i
$652$	−2.10943	+	1.21745i	−0.0826115	+	0.0476789i
$653$	37.0639	+	9.93124i	1.45042	+	0.388640i	0.896171	−	0.443709i	$-0.146338\pi$
$653$	37.0639	+	9.93124i	1.45042	+	0.388640i	0.554252	+	0.832349i	$0.313004\pi$
$654$	6.92950	+	5.31804i	0.270965	+	0.207952i
$655$	−17.3497	+	23.6614i	−0.677910	+	0.924526i
$656$	33.5467	+	0.0102530i	1.30978	+	0.000400312i
$657$		−	24.4320i		−	0.953184i
$658$	−24.8289	+	22.2015i	−0.967932	+	0.865506i
$659$	−25.8866	−	25.8866i	−1.00840	−	1.00840i	−0.999964	−	0.00843384i	$-0.997315\pi$
$659$	−25.8866	−	25.8866i	−1.00840	−	1.00840i	−0.00843384	−	0.999964i	$-0.502685\pi$
$660$	−0.171661	+	0.234034i	−0.00668190	+	0.00910977i
$661$	−6.91821	−	25.8191i	−0.269087	−	1.00425i	−0.959701	−	0.281023i	$-0.909326\pi$
$661$	−6.91821	−	25.8191i	−0.269087	−	1.00425i	0.690614	−	0.723224i	$-0.257340\pi$
$662$	−13.6735	+	1.79909i	−0.531436	+	0.0699236i
$663$	−2.48478	−	4.30377i	−0.0965010	−	0.167145i
$664$	−5.31099	−	12.8302i	−0.206107	−	0.497908i
$665$	−22.9613	+	21.4538i	−0.890403	+	0.831944i
$666$	8.12611	+	10.5918i	0.314880	+	0.410425i
$667$	−5.21066	+	19.4465i	−0.201758	+	0.752970i
$668$	16.5854	−	16.5803i	0.641707	−	0.641511i
$669$	3.35926	−	0.900110i	0.129876	−	0.0348003i
$670$	−5.14098	−	17.6438i	−0.198613	−	0.681641i
$671$	0.683174			0.0263737
$672$	9.08577	−	4.58655i	0.350491	−	0.176930i
$673$			33.6326i			1.29644i	0.761452	+	0.648222i	$0.224487\pi$
$673$			33.6326i			1.29644i	−0.761452	+	0.648222i	$0.775513\pi$
$674$	1.28256	+	3.09704i	0.0494023	+	0.119293i
$675$	0.820775	+	18.8107i	0.0315916	+	0.724024i
$676$	15.7458	+	15.7506i	0.605608	+	0.605793i
$677$	−0.154367	+	0.576104i	−0.00593279	+	0.0221415i	−0.968829	−	0.247731i	$-0.920315\pi$
$677$	−0.154367	+	0.576104i	−0.00593279	+	0.0221415i	0.962896	+	0.269873i	$0.0869816\pi$
$678$	−13.0926	+	10.0447i	−0.502817	+	0.385764i
$679$	−0.435712	+	2.30744i	−0.0167211	+	0.0885516i
$680$	32.4998	−	9.46427i	1.24631	−	0.362938i
$681$	−0.556415	+	0.321246i	−0.0213219	+	0.0123102i
$682$	1.14721	−	0.150944i	0.0439289	−	0.00577993i
$683$	2.47981	−	0.664463i	0.0948873	−	0.0254250i	−0.211063	−	0.977472i	$-0.567693\pi$
$683$	2.47981	−	0.664463i	0.0948873	−	0.0254250i	0.305950	+	0.952047i	$0.401026\pi$
$684$	23.3437	+	13.4823i	0.892570	+	0.515507i
$685$	−30.7615	+	24.6880i	−1.17534	+	0.943280i
$686$	25.8260	+	4.36069i	0.986043	+	0.166492i
$687$			1.71075i			0.0652691i
$688$	−14.1366	+	14.1279i	−0.538952	+	0.538623i
$689$	−4.90425	+	8.49441i	−0.186837	+	0.323611i
$690$	−8.67788	+	9.06340i	−0.330361	+	0.345038i
$691$	9.55480	−	35.6590i	0.363482	−	1.35653i	−0.505986	−	0.862542i	$-0.668871\pi$
$691$	9.55480	−	35.6590i	0.363482	−	1.35653i	0.869467	−	0.493990i	$-0.164462\pi$
$692$	−27.0178	+	15.5932i	−1.02706	+	0.592765i
$693$	0.361133	+	0.529266i	0.0137183	+	0.0201052i
$694$	−35.5719	+	27.2910i	−1.35029	+	1.03595i
$695$	2.45034	−	1.07814i	0.0929467	−	0.0408960i
$696$	−4.03874	−	5.26589i	−0.153088	−	0.199603i
$697$	−22.4433	+	38.8728i	−0.850099	+	1.47241i
$698$	19.9768	+	8.27646i	0.756134	+	0.313269i
$699$	11.0031	−	11.0031i	0.416177	−	0.416177i
$700$	−26.1868	−	3.77521i	−0.989767	−	0.142690i
$701$	32.6287	+	32.6287i	1.23237	+	1.23237i	0.963051	+	0.269320i	$0.0867990\pi$
$701$	32.6287	+	32.6287i	1.23237	+	1.23237i	0.269320	+	0.963051i	$0.413201\pi$
$702$	6.71822	−	2.78218i	0.253563	−	0.105006i
$703$	17.1124	+	9.87986i	0.645407	+	0.372626i
$704$	−0.382048	+	0.661026i	−0.0143990	+	0.0249134i
$705$	5.45143	+	12.3898i	0.205313	+	0.466626i
$706$	15.7064	+	2.06901i	0.591119	+	0.0778683i
$707$	1.62830	+	21.6213i	0.0612386	+	0.813153i
$708$	−5.10486	+	19.0400i	−0.191852	+	0.715565i
$709$	−38.5367	−	10.3259i	−1.44728	−	0.387796i	−0.552200	−	0.833712i	$-0.686212\pi$
$709$	−38.5367	−	10.3259i	−1.44728	−	0.387796i	−0.895075	+	0.445915i	$0.852878\pi$
$710$	0.211230	+	9.72072i	0.00792732	+	0.364812i
$711$	18.8130	+	10.8617i	0.705544	+	0.407346i
$712$	−1.24430	−	9.46814i	−0.0466320	−	0.354833i
$713$	50.0246			1.87344
$714$	−0.759610	+	13.5970i	−0.0284277	+	0.508856i
$715$	−0.182379	−	0.227246i	−0.00682058	−	0.00849850i
$716$	−2.37642	+	4.11462i	−0.0888109	+	0.153771i
$717$	0.960868	+	3.58601i	0.0358843	+	0.133922i
$718$	19.8596	−	25.8774i	0.741153	−	0.965737i
$719$	4.65090	+	8.05559i	0.173449	+	0.300423i	0.939624	−	0.342210i	$-0.111175\pi$
$719$	4.65090	+	8.05559i	0.173449	+	0.300423i	−0.766174	+	0.642633i	$0.777842\pi$
$720$	3.44552	+	22.4335i	0.128407	+	0.836048i
$721$	−4.93608	−	14.0899i	−0.183829	−	0.524734i
$722$	12.9190	+	1.70182i	0.480794	+	0.0633351i
$723$	−9.04574	−	2.42380i	−0.336415	−	0.0901420i
$724$	0.000578956	−	3.78856i	2.15167e−5	−	0.140801i
$725$	0.752021	+	17.2350i	0.0279294	+	0.640092i
$726$	−9.76516	−	4.04574i	−0.362419	−	0.150151i
$727$	16.2179			0.601488			0.300744	−	0.953705i	$-0.402765\pi$
$727$	16.2179			0.601488			0.300744	+	0.953705i	$0.402765\pi$
$728$	2.08839	+	10.0021i	0.0774010	+	0.370702i
$729$		−	5.13692i		−	0.190256i
$730$	14.6471	−	26.6924i	0.542112	−	0.987928i
$731$	−6.92133	−	25.8308i	−0.255995	−	0.955385i
$732$	−6.88541	+	6.88330i	−0.254492	+	0.254414i
$733$	−19.0543	−	5.10558i	−0.703786	−	0.188579i	−0.110860	−	0.993836i	$-0.535361\pi$
$733$	−19.0543	−	5.10558i	−0.703786	−	0.188579i	−0.592926	+	0.805257i	$0.702027\pi$
$734$	5.73055	+	0.754887i	0.211519	+	0.0278634i
$735$	4.93753	−	9.42973i	0.182124	−	0.347821i
$736$	−20.1039	+	26.1792i	−0.741041	+	0.964979i
$737$	−0.480321	+	0.277313i	−0.0176928	+	0.0102150i
$738$	−23.8760	−	18.3236i	−0.878886	−	0.674500i
$739$	14.9320	−	4.00102i	0.549283	−	0.147180i	0.0265050	−	0.999649i	$-0.491562\pi$
$739$	14.9320	−	4.00102i	0.549283	−	0.147180i	0.522778	+	0.852469i	$0.324896\pi$
$740$	2.52807	+	16.4433i	0.0929337	+	0.604469i
$741$	3.48746	−	3.48746i	0.128115	−	0.128115i
$742$	23.9908	−	12.1199i	0.880730	−	0.444936i
$743$	−38.8656			−1.42584			−0.712921	−	0.701244i	$-0.752628\pi$
$743$	−38.8656			−1.42584			−0.712921	+	0.701244i	$0.752628\pi$
$744$	−10.0414	+	13.0800i	−0.368135	+	0.479535i
$745$	−23.2241	−	17.0291i	−0.850867	−	0.623899i
$746$	−4.52975	−	34.4272i	−0.165846	−	1.26047i
$747$	−3.22436	+	12.0335i	−0.117973	+	0.440282i
$748$	−0.510652	−	0.884787i	−0.0186713	−	0.0323510i
$749$	21.4512	−	44.5859i	0.783811	−	1.62913i
$750$	−4.75674	+	9.64285i	−0.173692	+	0.352107i
$751$	12.4791	+	21.6144i	0.455367	+	0.788719i	0.998709	−	0.0507921i	$-0.0161746\pi$
$751$	12.4791	+	21.6144i	0.455367	+	0.788719i	−0.543342	+	0.839512i	$0.682841\pi$
$752$	17.7941	+	30.8421i	0.648885	+	1.12470i
$753$	−4.15790	−	2.40056i	−0.151522	−	0.0874814i
$754$	6.15546	−	2.54912i	0.224169	−	0.0928336i
$755$	14.6863	+	18.2992i	0.534488	+	0.665977i
$756$	−19.5797	−	3.70031i	−0.712108	−	0.134579i
$757$	−27.2634	−	27.2634i	−0.990905	−	0.990905i	0.00905400	−	0.999959i	$-0.497118\pi$
$757$	−27.2634	−	27.2634i	−0.990905	−	0.990905i	−0.999959	+	0.00905400i	$0.997118\pi$
$758$	4.01073	−	9.68066i	0.145676	−	0.351617i
$759$	0.327957	+	0.189346i	0.0119041	+	0.00687282i
$760$	17.4207	+	28.7242i	0.631916	+	1.04194i
$761$	−18.8938	+	10.9083i	−0.684899	+	0.395427i	−0.801698	−	0.597729i	$-0.796070\pi$
$761$	−18.8938	+	10.9083i	−0.684899	+	0.395427i	0.116799	+	0.993156i	$0.462737\pi$
$762$	2.59372	−	1.98992i	0.0939606	−	0.0720871i
$763$	23.9628	−	1.80464i	0.867511	−	0.0653323i
$764$	−4.73394	−	1.26923i	−0.171268	−	0.0459191i
$765$	−28.3038	−	11.0072i	−1.02332	−	0.397966i
$766$	9.90500	−	12.9064i	0.357882	−	0.466327i
$767$	−17.1385	−	9.89492i	−0.618836	−	0.357285i
$768$	−2.80966	−	10.5115i	−0.101385	−	0.379301i
$769$	6.44813			0.232526			0.116263	−	0.993218i	$-0.462909\pi$
$769$	6.44813			0.232526			0.116263	+	0.993218i	$0.462909\pi$
$770$	0.0772471	+	0.794731i	0.00278379	+	0.0286401i
$771$	−6.17568	−	6.17568i	−0.222412	−	0.222412i
$772$	39.1562	−	10.4855i	1.40926	−	0.377380i
$773$	14.6673	−	3.93010i	0.527547	−	0.141356i	0.0147915	−	0.999891i	$-0.495292\pi$
$773$	14.6673	−	3.93010i	0.527547	−	0.141356i	0.512755	+	0.858535i	$0.328625\pi$
$774$	17.7775	−	2.33907i	0.638998	−	0.0840761i
$775$	40.8822	−	12.8889i	1.46853	−	0.462982i
$776$	2.31904	+	0.961203i	0.0832488	+	0.0345052i
$777$	−6.57687	−	1.24190i	−0.235944	−	0.0445530i
$778$	16.3921	+	21.3660i	0.587687	+	0.766010i
$779$	−43.0294	−	11.5297i	−1.54169	−	0.413094i
$780$	4.12772	+	0.452755i	0.147796	+	0.0162112i
$781$	0.283438	−	0.0759470i	0.0101422	−	0.00271760i
$782$	−16.8983	−	40.8050i	−0.604283	−	1.45918i
$783$			12.9928i			0.464324i
$784$	10.2183	−	26.0689i	0.364940	−	0.931031i
$785$	2.60399	−	23.7739i	0.0929405	−	0.848526i
$786$	−11.6589	+	4.82824i	−0.415860	+	0.172218i
$787$	−5.65474	−	21.1038i	−0.201570	−	0.752268i	−0.990468	−	0.137744i	$-0.956015\pi$
$787$	−5.65474	−	21.1038i	−0.201570	−	0.752268i	0.788898	−	0.614524i	$-0.210652\pi$
$788$	13.2775	+	0.00202902i	0.472990	+	7.22809e-5i
$789$	−8.39597	−	2.24969i	−0.298904	−	0.0800912i
$790$	14.0419	+	23.1450i	0.499588	+	0.823464i
$791$	−8.42359	+	44.6097i	−0.299508	+	1.58614i
$792$	0.632893	−	0.261983i	0.0224889	−	0.00930916i
$793$	−4.88709	−	8.46469i	−0.173546	−	0.300590i
$794$	8.06141	−	1.06068i	0.286089	−	0.0376421i
$795$	−1.66155	−	10.7962i	−0.0589290	−	0.382903i
$796$	32.2966	−	8.64855i	1.14472	−	0.306540i
$797$	−18.8306	+	18.8306i	−0.667015	+	0.667015i	−0.957024	−	0.290009i	$-0.906342\pi$
$797$	−18.8306	+	18.8306i	−0.667015	+	0.667015i	0.290009	+	0.957024i	$0.406342\pi$
$798$	−13.2296	+	2.76439i	−0.468322	+	0.0978585i
$799$	−47.6435			−1.68550
$800$	−9.68467	+	26.5746i	−0.342405	+	0.939552i
$801$	−4.28374	+	7.41966i	−0.151359	+	0.262161i
$802$	42.7306	+	32.7935i	1.50887	+	1.15798i
$803$	−0.887567	−	0.237823i	−0.0313216	−	0.00839259i
$804$	2.04688	−	7.63438i	0.0721877	−	0.269244i
$805$	−1.17101	+	34.5006i	−0.0412726	+	1.21599i
$806$	−10.0768	−	13.1344i	−0.354940	−	0.462640i
$807$	−10.6554	−	18.4556i	−0.375086	−	0.649668i
$808$	22.9806	+	3.03081i	0.808455	+	0.106624i
$809$	−19.3022	−	11.1441i	−0.678629	−	0.391807i	0.120709	−	0.992688i	$-0.461483\pi$
$809$	−19.3022	−	11.1441i	−0.678629	−	0.391807i	−0.799338	+	0.600881i	$0.794817\pi$
$810$	7.68523	−	14.0053i	0.270032	−	0.492097i
$811$	38.8598	−	38.8598i	1.36455	−	1.36455i	0.496539	−	0.868015i	$-0.334604\pi$
$811$	38.8598	−	38.8598i	1.36455	−	1.36455i	0.868015	−	0.496539i	$-0.165396\pi$
$812$	−17.9396	−	3.39035i	−0.629557	−	0.118978i
$813$	8.26801	−	8.26801i	0.289972	−	0.289972i
$814$	0.463880	−	0.192104i	0.0162590	−	0.00673324i
$815$	2.19594	+	1.61018i	0.0769204	+	0.0564020i
$816$	14.0613	+	3.77231i	0.492243	+	0.132057i
$817$	22.9842	−	13.2699i	0.804116	−	0.464257i
$818$	−30.6228	−	4.03395i	−1.07070	−	0.141044i
$819$	3.97437	−	8.26064i	0.138876	−	0.288650i
$820$	−15.0998	−	34.3325i	−0.527309	−	1.19894i
$821$	24.4030	+	6.53876i	0.851670	+	0.228204i	0.658145	−	0.752891i	$-0.271341\pi$
$821$	24.4030	+	6.53876i	0.851670	+	0.228204i	0.193525	+	0.981095i	$0.438008\pi$
$822$	−16.8192	+	2.21298i	−0.586636	+	0.0771865i
$823$	−25.6183	+	44.3721i	−0.892996	+	1.54671i	−0.0567309	+	0.998390i	$0.518068\pi$
$823$	−25.6183	+	44.3721i	−0.892996	+	1.54671i	−0.836265	+	0.548325i	$0.815266\pi$
$824$	−15.8242	+	2.07961i	−0.551262	+	0.0724465i
$825$	0.316805	+	0.0702431i	0.0110297	+	0.00244555i
$826$	24.4534	+	48.4044i	0.850843	+	1.68420i
$827$	−11.9994	−	11.9994i	−0.417261	−	0.417261i	0.466997	−	0.884259i	$-0.345336\pi$
$827$	−11.9994	−	11.9994i	−0.417261	−	0.417261i	−0.884259	+	0.466997i	$0.845336\pi$
$828$	28.6055	−	7.66014i	0.994110	−	0.266208i
$829$	25.7813	−	6.90809i	0.895423	−	0.239928i	0.218373	−	0.975865i	$-0.429925\pi$
$829$	25.7813	−	6.90809i	0.895423	−	0.239928i	0.677050	+	0.735937i	$0.263258\pi$
$830$	−10.7368	+	11.2137i	−0.372678	+	0.389234i
$831$	−3.17300	−	5.49580i	−0.110070	−	0.190647i
$832$	10.9233	+	0.00500778i	0.378696	+	0.000173613i
$833$	23.3806	+	29.2740i	0.810088	+	1.01428i
$834$	1.14151	+	0.150371i	0.0395272	+	0.00520693i
$835$	−24.4369	−	9.50337i	−0.845673	−	0.328878i
$836$	0.717013	−	0.716794i	0.0247984	−	0.0247908i
$837$	31.1841	−	8.35575i	1.07788	−	0.288817i
$838$	3.88806	+	1.61083i	0.134311	+	0.0556453i
$839$			4.35429i			0.150327i	0.997171	+	0.0751634i	$0.0239478\pi$
$839$			4.35429i			0.150327i	−0.997171	+	0.0751634i	$0.976052\pi$
$840$	−8.78583	−	7.23144i	−0.303140	−	0.249508i
$841$		−	17.0956i		−	0.589503i
$842$	−2.76949	+	6.68470i	−0.0954429	+	0.230370i
$843$	−13.3234	+	3.57000i	−0.458883	+	0.122957i
$844$	−46.7516	−	0.00714444i	−1.60926	−	0.000245922i
$845$	9.02506	−	23.2070i	0.310472	−	0.798344i
$846$	4.17212	−	31.6717i	0.143440	−	1.08890i
$847$	−27.4438	+	9.61435i	−0.942980	+	0.330353i
$848$	−7.42849	−	27.7575i	−0.255096	−	0.953195i
$849$	−6.79061	−	11.7617i	−0.233053	−	0.403660i
$850$	−24.3235	−	28.9937i	−0.834288	−	0.994475i
$851$	20.9669	−	5.61807i	0.718737	−	0.192585i
$852$	−2.09144	+	3.62121i	−0.0716516	+	0.124060i
$853$	−12.6731	−	12.6731i	−0.433919	−	0.433919i	0.456040	−	0.889959i	$-0.349267\pi$
$853$	−12.6731	−	12.6731i	−0.433919	−	0.433919i	−0.889959	+	0.456040i	$0.849267\pi$
$854$	−1.49401	+	26.7427i	−0.0511239	+	0.915117i
$855$	3.28158	−	29.9601i	0.112228	−	1.02461i
$856$	−41.9563	−	32.2095i	−1.43404	−	1.10090i
$857$	−10.2988	+	17.8380i	−0.351799	+	0.609335i	−0.986565	−	0.163370i	$-0.947763\pi$
$857$	−10.2988	+	17.8380i	−0.351799	+	0.609335i	0.634765	+	0.772705i	$0.281097\pi$
$858$	−0.0163480	−	0.124249i	−0.000558113	−	0.00424179i
$859$	−5.32758	−	1.42752i	−0.181775	−	0.0487063i	0.166783	−	0.985994i	$-0.446662\pi$
$859$	−5.32758	−	1.42752i	−0.181775	−	0.0487063i	−0.348558	+	0.937287i	$0.613329\pi$
$860$	20.8244	+	8.10217i	0.710107	+	0.276282i
$861$	15.0467	−	1.13317i	0.512789	−	0.0386182i
$862$	−2.74997	+	20.8758i	−0.0936644	+	0.711032i
$863$	11.9565	−	6.90309i	0.407004	−	0.234984i	−0.282497	−	0.959268i	$-0.591163\pi$
$863$	11.9565	−	6.90309i	0.407004	−	0.234984i	0.689502	+	0.724284i	$0.257830\pi$
$864$	−8.15949	+	19.6775i	−0.277591	+	0.669442i
$865$	28.1259	+	20.6233i	0.956309	+	0.701215i
$866$	3.02670	+	7.30869i	0.102852	+	0.248359i
$867$	−5.59970	+	5.59970i	−0.190176	+	0.190176i
$868$	3.39988	+	45.2374i	0.115399	+	1.53546i
$869$	0.577712	−	0.577712i	0.0195975	−	0.0195975i
$870$	−3.56936	+	6.50469i	−0.121013	+	0.220530i
$871$	6.87196	+	3.96753i	0.232847	+	0.134435i
$872$	3.35903	−	25.4693i	0.113751	−	0.862498i
$873$	−1.12610	−	1.95046i	−0.0381126	−	0.0660129i
$874$	34.7762	−	26.6805i	1.17632	−	0.902481i
$875$	7.93211	+	28.4970i	0.268154	+	0.963376i
$876$	11.3416	−	6.54574i	0.383196	−	0.221160i
$877$	43.1323	+	11.5573i	1.45647	+	0.390261i	0.898271	−	0.439443i	$-0.144824\pi$
$877$	43.1323	+	11.5573i	1.45647	+	0.390261i	0.558204	+	0.829704i	$0.311491\pi$
$878$	−14.5552	+	18.9657i	−0.491213	+	0.640060i
$879$	−9.31509	+	16.1342i	−0.314190	+	0.544193i
$880$	0.848504	+	0.0932006i	0.0286031	+	0.00314179i
$881$	−49.7841			−1.67727			−0.838635	−	0.544694i	$-0.816646\pi$
$881$	−49.7841			−1.67727			−0.838635	+	0.544694i	$0.816646\pi$
$882$	−21.5078	+	12.9791i	−0.724204	+	0.437028i
$883$	6.30055	−	6.30055i	0.212030	−	0.212030i	−0.593099	−	0.805130i	$-0.702096\pi$
$883$	6.30055	−	6.30055i	0.212030	−	0.212030i	0.805130	+	0.593099i	$0.202096\pi$
$884$	−7.30977	+	12.6564i	−0.245854	+	0.425682i
$885$	21.7827	−	3.35237i	0.732217	−	0.112689i
$886$	−0.764881	−	5.81328i	−0.0256967	−	0.195301i
$887$	7.22170	+	12.5083i	0.242481	+	0.419989i	0.961420	−	0.275083i	$-0.0887055\pi$
$887$	7.22170	+	12.5083i	0.242481	+	0.419989i	−0.718939	+	0.695073i	$0.755372\pi$
$888$	−2.73970	+	6.60993i	−0.0919383	+	0.221815i
$889$	1.66877	−	8.83746i	0.0559686	−	0.296399i
$890$	−9.12815	+	5.53797i	−0.305976	+	0.185633i
$891$	−0.465702	−	0.124784i	−0.0156016	−	0.00418043i
$892$	−7.23133	−	7.23354i	−0.242123	−	0.242197i
$893$	−12.2379	−	45.6723i	−0.409524	−	1.52837i
$894$	−4.73902	−	11.4435i	−0.158497	−	0.382727i
$895$	5.28084	+	0.578419i	0.176519	+	0.0193344i
$896$	−25.0403	−	16.4008i	−0.836537	−	0.547911i
$897$		−	5.41795i		−	0.180900i
$898$	−10.1086	+	4.18622i	−0.337329	+	0.139696i
$899$	28.5719	−	7.65582i	0.952927	−	0.255336i
$900$	21.4040	−	13.6304i	0.713466	−	0.454347i
$901$	37.1373	+	9.95092i	1.23722	+	0.331513i
$902$	−0.898069	+	0.689003i	−0.0299024	+	0.0229413i
$903$	−5.86136	+	6.81611i	−0.195054	+	0.226826i
$904$	44.8340	+	18.5829i	1.49116	+	0.618057i
$905$	−3.87704	+	1.70588i	−0.128877	+	0.0567052i
$906$	1.31645	+	10.0053i	0.0437360	+	0.332404i
$907$	15.9978	−	4.28659i	0.531198	−	0.142334i	0.0167565	−	0.999860i	$-0.494666\pi$
$907$	15.9978	−	4.28659i	0.531198	−	0.142334i	0.514441	+	0.857526i	$0.327999\pi$
$908$	1.63629	+	0.945047i	0.0543022	+	0.0313625i
$909$	−14.7049	−	14.7049i	−0.487730	−	0.487730i
$910$	9.29432	−	6.64223i	0.308104	−	0.220188i
$911$	−0.0663196			−0.00219727			−0.00109863	−	0.999999i	$-0.500350\pi$
$911$	−0.0663196			−0.00219727			−0.00109863	+	0.999999i	$0.500350\pi$
$912$	−0.00441595	+	14.4485i	−0.000146227	+	0.478437i
$913$	0.405766	+	0.234269i	0.0134289	+	0.00775317i
$914$	11.4292	+	8.77129i	0.378043	+	0.290129i
$915$	10.1450	+	3.94532i	0.335382	+	0.130428i
$916$	4.35768	−	2.51502i	0.143982	−	0.0830986i
$917$	−15.0513	+	31.2839i	−0.497038	+	1.03308i
$918$	−17.3498	−	22.6142i	−0.572627	−	0.746380i
$919$	11.7566	−	6.78765i	0.387813	−	0.223904i	−0.293399	−	0.955990i	$-0.594786\pi$
$919$	11.7566	−	6.78765i	0.387813	−	0.223904i	0.681212	+	0.732086i	$0.261453\pi$
$920$	35.8442	+	8.78025i	1.18175	+	0.289476i
$921$	−1.36463	−	0.787868i	−0.0449660	−	0.0259611i
$922$	−37.2501	−	15.4328i	−1.22677	−	0.508253i
$923$	−2.96858	−	2.96858i	−0.0977119	−	0.0977119i
$924$	−0.148936	+	0.309440i	−0.00489965	+	0.0101798i
$925$	15.6875	−	9.99346i	0.515803	−	0.328583i
$926$	7.88342	+	19.0364i	0.259065	+	0.625574i
$927$	12.4006	+	7.15947i	0.407288	+	0.235148i
$928$	−7.47600	+	18.0292i	−0.245412	+	0.591837i
$929$	−18.9845	−	32.8820i	−0.622860	−	1.07883i	−0.988951	−	0.148246i	$-0.952637\pi$
$929$	−18.9845	−	32.8820i	−0.622860	−	1.07883i	0.366091	−	0.930579i	$-0.380696\pi$
$930$	17.9075	+	4.38364i	0.587209	+	0.143745i
$931$	−22.0573	+	29.9327i	−0.722897	+	0.981003i
$932$	−44.2036	−	11.8516i	−1.44794	−	0.388211i
$933$	0.0168833	−	0.0630093i	0.000552734	−	0.00206283i
$934$	5.61750	−	0.739121i	0.183810	−	0.0241848i
$935$	−0.675379	+	0.921075i	−0.0220873	+	0.0301224i
$936$	−7.77343	−	5.96760i	−0.254083	−	0.195057i
$937$	31.5391			1.03034			0.515168	−	0.857089i	$-0.327730\pi$
$937$	31.5391			1.03034			0.515168	+	0.857089i	$0.327730\pi$
$938$	−9.80499	−	19.4085i	−0.320144	−	0.633710i
$939$	−12.3849	+	12.3849i	−0.404167	+	0.404167i
$940$	23.5454	−	32.1006i	0.767965	−	1.04701i
$941$	38.1626	−	10.2256i	1.24406	−	0.333346i	0.424023	−	0.905651i	$-0.360617\pi$
$941$	38.1626	−	10.2256i	1.24406	−	0.333346i	0.820041	+	0.572305i	$0.193951\pi$
$942$	6.26239	−	8.16001i	0.204040	−	0.265868i
$943$	−42.3802	+	24.4682i	−1.38009	+	0.796794i
$944$	56.0040	−	14.9879i	1.82278	−	0.487814i
$945$	5.03275	+	21.7024i	0.163715	+	0.705979i
$946$	0.0880734	−	0.668589i	0.00286351	−	0.0217377i
$947$	27.6357	+	7.40498i	0.898041	+	0.240629i	0.678175	−	0.734901i	$-0.262771\pi$
$947$	27.6357	+	7.40498i	0.898041	+	0.240629i	0.219866	+	0.975530i	$0.429438\pi$
$948$	−0.00177928	+	11.6432i	−5.77884e−5	+	0.378154i
$949$	3.40253	+	12.6984i	0.110451	+	0.412209i
$950$	21.5463	−	30.7645i	0.699055	−	0.998133i
$951$			10.2659i			0.332895i
$952$	35.7515	−	18.0545i	1.15871	−	0.585148i
$953$	−32.7210			−1.05994			−0.529968	−	0.848018i	$-0.677796\pi$
$953$	−32.7210			−1.05994			−0.529968	+	0.848018i	$0.677796\pi$
$954$	−9.86712	+	23.8162i	−0.319460	+	0.771078i
$955$	0.833506	+	5.41587i	0.0269716	+	0.175253i
$956$	7.72181	−	7.71945i	0.249741	−	0.249665i
$957$	0.216292	+	0.0579554i	0.00699174	+	0.00187343i
$958$	−5.10043	+	38.7187i	−0.164787	+	1.25094i
$959$	−30.4291	+	35.3856i	−0.982607	+	1.14266i
$960$	−9.49073	+	7.60975i	−0.306312	+	0.245604i
$961$	−21.2496	−	36.8054i	−0.685471	−	1.18727i
$962$	−5.69858	−	4.37337i	−0.183730	−	0.141003i
$963$	12.2821	+	45.8375i	0.395786	+	1.47709i
$964$	7.12441	+	26.6049i	0.229462	+	0.856886i
$965$	−28.3666	−	35.3451i	−0.913154	−	1.13780i
$966$	−8.12910	+	12.4237i	−0.261550	+	0.399727i
$967$	2.09174			0.0672657			0.0336328	−	0.999434i	$-0.489292\pi$
$967$	2.09174			0.0672657			0.0336328	+	0.999434i	$0.489292\pi$
$968$	4.05059	+	30.8219i	0.130191	+	0.990654i
$969$	−16.7425	−	9.66627i	−0.537845	−	0.310525i
$970$	−0.0609740	−	2.80600i	−0.00195776	−	0.0900952i
$971$	25.6449	+	6.87153i	0.822984	+	0.220518i	0.645651	−	0.763633i	$-0.276586\pi$
$971$	25.6449	+	6.87153i	0.822984	+	0.220518i	0.177334	+	0.984151i	$0.443253\pi$
$972$	25.5198	−	14.7287i	0.818549	−	0.472423i
$973$	2.61647	−	1.78529i	0.0838801	−	0.0572338i
$974$	−5.80526	+	44.0693i	−0.186013	+	1.41207i
$975$	−1.39594	−	4.42777i	−0.0447058	−	0.141802i
$976$	27.6558	+	7.41941i	0.885241	+	0.237490i
$977$	−6.53182	−	3.77115i	−0.208971	−	0.120650i	0.391862	−	0.920024i	$-0.371831\pi$
$977$	−6.53182	−	3.77115i	−0.208971	−	0.120650i	−0.600833	+	0.799374i	$0.705164\pi$
$978$	0.448095	+	1.08203i	0.0143285	+	0.0345995i
$979$	0.227843	+	0.227843i	0.00728190	+	0.00728190i
$980$	−31.2785	+	1.28586i	−0.999156	+	0.0410752i
$981$	−16.2973	+	16.2973i	−0.520334	+	0.520334i
$982$	−21.7360	+	52.4640i	−0.693624	+	1.67419i
$983$	7.25651	−	12.5686i	0.231447	−	0.400877i	−0.726787	−	0.686862i	$-0.758987\pi$
$983$	7.25651	−	12.5686i	0.231447	−	0.400877i	0.958234	+	0.285985i	$0.0923208\pi$
$984$	2.10920	−	15.9926i	0.0672388	−	0.509826i
$985$	−5.97845	−	13.5876i	−0.190489	−	0.432936i
$986$	−15.8964	−	20.7199i	−0.506245	−	0.659856i
$987$	9.02704	+	13.2298i	0.287334	+	0.421108i
$988$	−14.0104	−	3.75637i	−0.445730	−	0.119506i
$989$	7.54581	−	28.1613i	0.239943	−	0.895478i
$990$	−0.553156	−	0.529627i	−0.0175804	−	0.0168326i
$991$	−13.0400	+	22.5860i	−0.414229	+	0.717467i	−0.995347	−	0.0963530i	$-0.969282\pi$
$991$	−13.0400	+	22.5860i	−0.414229	+	0.717467i	0.581118	+	0.813819i	$0.302616\pi$
$992$	48.0798	+	6.34852i	1.52654	+	0.201566i
$993$			6.63166i			0.210449i
$994$	2.35309	+	11.2612i	0.0746355	+	0.357184i
$995$	−23.3972	−	29.1531i	−0.741741	−	0.924216i
$996$	−6.44990	+	1.72719i	−0.204373	+	0.0547281i
$997$	44.6934	−	11.9756i	1.41545	−	0.379270i	0.531585	−	0.847005i	$-0.321596\pi$
$997$	44.6934	−	11.9756i	1.41545	−	0.379270i	0.883869	+	0.467735i	$0.154930\pi$
$998$	−5.83790	−	44.3694i	−0.184795	−	1.40449i
$999$	12.1318	−	7.00432i	0.383835	−	0.221607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cr.a.109.11	✓	368
5.4	even	2	inner	560.2.cr.a.109.82	yes	368
7.2	even	3	inner	560.2.cr.a.429.74	yes	368
16.5	even	4	inner	560.2.cr.a.389.19	yes	368
35.9	even	6	inner	560.2.cr.a.429.19	yes	368
80.69	even	4	inner	560.2.cr.a.389.74	yes	368
112.37	even	12	inner	560.2.cr.a.149.82	yes	368
560.149	even	12	inner	560.2.cr.a.149.11	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cr.a.109.11	✓	368	1.1	even	1	trivial
560.2.cr.a.109.82	yes	368	5.4	even	2	inner
560.2.cr.a.149.11	yes	368	560.149	even	12	inner
560.2.cr.a.149.82	yes	368	112.37	even	12	inner
560.2.cr.a.389.19	yes	368	16.5	even	4	inner
560.2.cr.a.389.74	yes	368	80.69	even	4	inner
560.2.cr.a.429.19	yes	368	35.9	even	6	inner
560.2.cr.a.429.74	yes	368	7.2	even	3	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cr (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30660 + 0.541096i) q^{2} +(0.176005 + 0.656861i) q^{3} +(1.41443 - 1.41400i) q^{4} +(-2.08402 - 0.810465i) q^{5} +(-0.585395 - 0.763022i) q^{6} +(-2.59981 - 0.490918i) q^{7} +(-1.08299 + 2.61288i) q^{8} +(2.19759 - 1.26878i) q^{9} +(3.16153 - 0.0686997i) q^{10} +(-0.0247007 - 0.0921843i) q^{11} +(1.17775 + 0.680213i) q^{12} +(-0.965489 + 0.965489i) q^{13} +(3.66255 - 0.765310i) q^{14} +(0.165564 - 1.51156i) q^{15} +(0.00122254 - 4.00000i) q^{16} +(4.63508 + 2.67606i) q^{17} +(-2.18485 + 2.84690i) q^{18} +(-1.37477 + 5.13069i) q^{19} +(-4.09370 + 1.80046i) q^{20} +(-0.135115 - 1.79412i) q^{21} +(0.0821546 + 0.107083i) q^{22} +(2.91751 + 5.05328i) q^{23} +(-1.90691 - 0.251494i) q^{24} +(3.68629 + 3.37805i) q^{25} +(0.739089 - 1.78393i) q^{26} +(2.66277 + 2.66277i) q^{27} +(-4.37140 + 2.98175i) q^{28} +(2.43972 + 2.43972i) q^{29} +(0.601573 + 2.06460i) q^{30} +(4.28658 - 7.42458i) q^{31} +(2.16279 + 5.22708i) q^{32} +(0.0562048 - 0.0324499i) q^{33} +(-7.50422 - 0.988533i) q^{34} +(5.02018 + 3.13014i) q^{35} +(1.31428 - 4.90198i) q^{36} +(0.962819 - 3.59329i) q^{37} +(-0.979925 - 7.44767i) q^{38} +(-0.804123 - 0.464261i) q^{39} +(4.37462 - 4.56757i) q^{40} +8.38666i q^{41} +(1.14733 + 2.27109i) q^{42} +(-3.53307 - 3.53307i) q^{43} +(-0.165286 - 0.0954615i) q^{44} +(-5.60812 + 0.863093i) q^{45} +(-6.54634 - 5.02398i) q^{46} +(-7.70917 + 4.45089i) q^{47} +(2.62766 - 0.703219i) q^{48} +(6.51800 + 2.55259i) q^{49} +(-6.64438 - 2.41914i) q^{50} +(-0.942004 + 3.51561i) q^{51} +(-0.000417315 + 2.73081i) q^{52} +(6.93880 - 1.85924i) q^{53} +(-4.91999 - 2.03837i) q^{54} +(-0.0232353 + 0.212133i) q^{55} +(4.09828 - 6.26132i) q^{56} -3.61212 q^{57} +(-4.50786 - 1.86762i) q^{58} +(3.75125 + 13.9999i) q^{59} +(-1.90316 - 2.37210i) q^{60} +(-1.85274 + 6.91452i) q^{61} +(-1.58346 + 12.0204i) q^{62} +(-6.33617 + 2.21974i) q^{63} +(-5.65426 - 5.65945i) q^{64} +(2.79459 - 1.22960i) q^{65} +(-0.0558790 + 0.0728114i) q^{66} +(-1.50412 - 5.61347i) q^{67} +(10.3399 - 2.76889i) q^{68} +(-2.80581 + 2.80581i) q^{69} +(-8.25310 - 1.37345i) q^{70} +3.07469i q^{71} +(0.935193 + 7.11610i) q^{72} +(4.81409 - 8.33825i) q^{73} +(0.686292 + 5.21598i) q^{74} +(-1.57010 + 3.01594i) q^{75} +(5.31028 + 9.20092i) q^{76} +(0.0189621 + 0.251787i) q^{77} +(1.30188 + 0.171497i) q^{78} +(4.28039 + 7.41385i) q^{79} +(-3.24441 + 8.33510i) q^{80} +(2.52593 - 4.37503i) q^{81} +(-4.53799 - 10.9581i) q^{82} +(-3.47150 + 3.47150i) q^{83} +(-2.72799 - 2.34660i) q^{84} +(-7.49075 - 9.33354i) q^{85} +(6.52805 + 2.70459i) q^{86} +(-1.17315 + 2.03196i) q^{87} +(0.267617 + 0.0352949i) q^{88} +(-2.92394 + 1.68814i) q^{89} +(6.86058 - 4.16225i) q^{90} +(2.98406 - 2.03611i) q^{91} +(11.2719 + 3.02215i) q^{92} +(5.63138 + 1.50892i) q^{93} +(7.66447 - 9.98695i) q^{94} +(7.02329 - 9.57828i) q^{95} +(-3.05280 + 2.34065i) q^{96} -0.887544i q^{97} +(-9.89764 + 0.191645i) q^{98} +(-0.171243 - 0.171243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{4} - 2 q^{5} - 16 q^{6} - 8 q^{10} - 4 q^{11} + 16 q^{14} - 16 q^{15} - 4 q^{16} - 4 q^{19} - 8 q^{20} + 4 q^{21} - 4 q^{24} - 4 q^{26} - 16 q^{29} + 22 q^{30} - 56 q^{31} - 96 q^{34} + 18 q^{35}+ \cdots - 112 q^{99}+O(q^{100}) \) 368 * q - 4 * q^4 - 2 * q^5 - 16 * q^6 - 8 * q^10 - 4 * q^11 + 16 * q^14 - 16 * q^15 - 4 * q^16 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 4 * q^24 - 4 * q^26 - 16 * q^29 + 22 * q^30 - 56 * q^31 - 96 * q^34 + 18 * q^35 + 32 * q^36 - 14 * q^40 - 12 * q^44 - 16 * q^45 + 12 * q^46 - 16 * q^49 - 12 * q^50 - 28 * q^51 - 8 * q^54 - 64 * q^56 + 12 * q^59 - 54 * q^60 - 4 * q^61 - 88 * q^64 - 4 * q^65 - 44 * q^66 + 8 * q^69 + 88 * q^70 - 72 * q^74 + 10 * q^75 + 104 * q^76 - 8 * q^79 + 48 * q^80 + 112 * q^81 + 68 * q^84 - 28 * q^85 + 44 * q^86 - 92 * q^90 - 80 * q^91 - 20 * q^94 + 20 * q^95 - 36 * q^96 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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