LMFDB - Embedded newform 187.2.h.a.100.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(100,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([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("187.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.h (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			100.8
Character	$\chi$	$=$	187.100
Dual form			187.2.h.a.144.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.131056 + 0.131056i) q^{2} +(0.554134 + 1.33780i) q^{3} -1.96565i q^{4} +(1.85179 - 0.767036i) q^{5} +(-0.102704 + 0.247949i) q^{6} +(-0.551118 - 0.228280i) q^{7} +(0.519723 - 0.519723i) q^{8} +(0.638682 - 0.638682i) q^{9} +O(q^{10})$	\(q+(0.131056 + 0.131056i) q^{2} +(0.554134 + 1.33780i) q^{3} -1.96565i q^{4} +(1.85179 - 0.767036i) q^{5} +(-0.102704 + 0.247949i) q^{6} +(-0.551118 - 0.228280i) q^{7} +(0.519723 - 0.519723i) q^{8} +(0.638682 - 0.638682i) q^{9} +(0.343213 + 0.142164i) q^{10} +(-0.382683 + 0.923880i) q^{11} +(2.62964 - 1.08923i) q^{12} +2.18007i q^{13} +(-0.0423098 - 0.102145i) q^{14} +(2.05228 + 2.05228i) q^{15} -3.79507 q^{16} +(-3.90011 - 1.33758i) q^{17} +0.167407 q^{18} +(6.03686 + 6.03686i) q^{19} +(-1.50772 - 3.63997i) q^{20} -0.863782i q^{21} +(-0.171233 + 0.0709271i) q^{22} +(0.245547 - 0.592803i) q^{23} +(0.983280 + 0.407288i) q^{24} +(-0.694756 + 0.694756i) q^{25} +(-0.285712 + 0.285712i) q^{26} +(5.22174 + 2.16291i) q^{27} +(-0.448719 + 1.08330i) q^{28} +(-7.81225 + 3.23594i) q^{29} +0.537928i q^{30} +(-3.47763 - 8.39575i) q^{31} +(-1.53681 - 1.53681i) q^{32} -1.44802 q^{33} +(-0.335836 - 0.686432i) q^{34} -1.19565 q^{35} +(-1.25542 - 1.25542i) q^{36} +(-1.36283 - 3.29015i) q^{37} +1.58234i q^{38} +(-2.91649 + 1.20805i) q^{39} +(0.563771 - 1.36106i) q^{40} +(-5.32899 - 2.20734i) q^{41} +(0.113204 - 0.113204i) q^{42} +(2.16470 - 2.16470i) q^{43} +(1.81602 + 0.752221i) q^{44} +(0.692812 - 1.67260i) q^{45} +(0.109871 - 0.0455101i) q^{46} +10.6708i q^{47} +(-2.10298 - 5.07704i) q^{48} +(-4.69813 - 4.69813i) q^{49} -0.182104 q^{50} +(-0.371777 - 5.95876i) q^{51} +4.28525 q^{52} +(2.64883 + 2.64883i) q^{53} +(0.400878 + 0.967804i) q^{54} +2.00436i q^{55} +(-0.405071 + 0.167786i) q^{56} +(-4.73087 + 11.4213i) q^{57} +(-1.44793 - 0.599754i) q^{58} +(-4.38591 + 4.38591i) q^{59} +(4.03406 - 4.03406i) q^{60} +(-0.0140470 - 0.00581845i) q^{61} +(0.644550 - 1.55608i) q^{62} +(-0.497788 + 0.206190i) q^{63} +7.18732i q^{64} +(1.67219 + 4.03703i) q^{65} +(-0.189772 - 0.189772i) q^{66} +6.00539 q^{67} +(-2.62921 + 7.66625i) q^{68} +0.929117 q^{69} +(-0.156698 - 0.156698i) q^{70} +(-1.91924 - 4.63346i) q^{71} -0.663876i q^{72} +(9.50711 - 3.93797i) q^{73} +(0.252588 - 0.609802i) q^{74} +(-1.31443 - 0.544455i) q^{75} +(11.8663 - 11.8663i) q^{76} +(0.421807 - 0.421807i) q^{77} +(-0.540547 - 0.223902i) q^{78} +(-3.73551 + 9.01833i) q^{79} +(-7.02767 + 2.91096i) q^{80} +5.47447i q^{81} +(-0.409112 - 0.987683i) q^{82} +(6.56549 + 6.56549i) q^{83} -1.69789 q^{84} +(-8.24816 + 0.514616i) q^{85} +0.567394 q^{86} +(-8.65806 - 8.65806i) q^{87} +(0.281272 + 0.679051i) q^{88} -16.2031i q^{89} +(0.310002 - 0.128407i) q^{90} +(0.497668 - 1.20148i) q^{91} +(-1.16524 - 0.482659i) q^{92} +(9.30474 - 9.30474i) q^{93} +(-1.39848 + 1.39848i) q^{94} +(15.8095 + 6.54850i) q^{95} +(1.20435 - 2.90755i) q^{96} +(12.9060 - 5.34582i) q^{97} -1.23144i q^{98} +(0.345652 + 0.834479i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 16 q^{6}+O(q^{10}) $ 56 * q - 16 * q^6	$ 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) $ 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.131056	+	0.131056i	0.0926707	+	0.0926707i	0.751922	−	0.659252i	$-0.229127\pi$
$2$	0.131056	+	0.131056i	0.0926707	+	0.0926707i	−0.659252	+	0.751922i	$0.729127\pi$
$3$	0.554134	+	1.33780i	0.319929	+	0.772378i	0.999257	+	0.0385427i	$0.0122716\pi$
$3$	0.554134	+	1.33780i	0.319929	+	0.772378i	−0.679328	+	0.733835i	$0.737728\pi$
$4$		−	1.96565i		−	0.982824i
$5$	1.85179	−	0.767036i	0.828145	−	0.343029i	0.0719770	−	0.997406i	$-0.477069\pi$
$5$	1.85179	−	0.767036i	0.828145	−	0.343029i	0.756168	+	0.654377i	$0.227069\pi$
$6$	−0.102704	+	0.247949i	−0.0419287	+	0.101225i
$7$	−0.551118	−	0.228280i	−0.208303	−	0.0862819i	0.276093	−	0.961131i	$-0.410960\pi$
$7$	−0.551118	−	0.228280i	−0.208303	−	0.0862819i	−0.484395	+	0.874849i	$0.660960\pi$
$8$	0.519723	−	0.519723i	0.183750	−	0.183750i
$9$	0.638682	−	0.638682i	0.212894	−	0.212894i
$10$	0.343213	+	0.142164i	0.108534	+	0.0449561i
$11$	−0.382683	+	0.923880i	−0.115383	+	0.278560i
$11$	−0.382683	+	0.923880i	−0.115383	+	0.278560i
$12$	2.62964	−	1.08923i	0.759112	−	0.314434i
$13$			2.18007i			0.604643i	0.953206	+	0.302322i	$0.0977616\pi$
$13$			2.18007i			0.604643i	−0.953206	+	0.302322i	$0.902238\pi$
$14$	−0.0423098	−	0.102145i	−0.0113078	−	0.0272994i
$15$	2.05228	+	2.05228i	0.529896	+	0.529896i
$16$	−3.79507			−0.948768
$17$	−3.90011	−	1.33758i	−0.945916	−	0.324410i
$17$	−3.90011	−	1.33758i	−0.945916	−	0.324410i
$18$	0.167407			0.0394581
$19$	6.03686	+	6.03686i	1.38495	+	1.38495i	0.835577	+	0.549373i	$0.185134\pi$
$19$	6.03686	+	6.03686i	1.38495	+	1.38495i	0.549373	+	0.835577i	$0.314866\pi$
$20$	−1.50772	−	3.63997i	−0.337137	−	0.813921i
$21$		−	0.863782i		−	0.188493i
$22$	−0.171233	+	0.0709271i	−0.0365070	+	0.0151217i
$23$	0.245547	−	0.592803i	0.0512001	−	0.123608i	−0.896210	−	0.443630i	$-0.853690\pi$
$23$	0.245547	−	0.592803i	0.0512001	−	0.123608i	0.947410	+	0.320022i	$0.103690\pi$
$24$	0.983280	+	0.407288i	0.200711	+	0.0831373i
$25$	−0.694756	+	0.694756i	−0.138951	+	0.138951i
$26$	−0.285712	+	0.285712i	−0.0560327	+	0.0560327i
$27$	5.22174	+	2.16291i	1.00492	+	0.416253i
$28$	−0.448719	+	1.08330i	−0.0847999	+	0.204725i
$29$	−7.81225	+	3.23594i	−1.45070	+	0.600899i	−0.962365	−	0.271759i	$-0.912395\pi$
$29$	−7.81225	+	3.23594i	−1.45070	+	0.600899i	−0.488332	+	0.872658i	$0.662395\pi$
$30$			0.537928i			0.0982117i
$31$	−3.47763	−	8.39575i	−0.624601	−	1.50792i	−0.846245	−	0.532793i	$-0.821142\pi$
$31$	−3.47763	−	8.39575i	−0.624601	−	1.50792i	0.221644	−	0.975128i	$-0.428858\pi$
$32$	−1.53681	−	1.53681i	−0.271673	−	0.271673i
$33$	−1.44802			−0.252068
$34$	−0.335836	−	0.686432i	−0.0575954	−	0.117722i
$35$	−1.19565			−0.202102
$36$	−1.25542	−	1.25542i	−0.209237	−	0.209237i
$37$	−1.36283	−	3.29015i	−0.224047	−	0.540898i	0.771385	−	0.636369i	$-0.219564\pi$
$37$	−1.36283	−	3.29015i	−0.224047	−	0.540898i	−0.995432	+	0.0954709i	$0.969564\pi$
$38$			1.58234i			0.256689i
$39$	−2.91649	+	1.20805i	−0.467013	+	0.193443i
$40$	0.563771	−	1.36106i	0.0891400	−	0.215203i
$41$	−5.32899	−	2.20734i	−0.832249	−	0.344729i	−0.0744561	−	0.997224i	$-0.523722\pi$
$41$	−5.32899	−	2.20734i	−0.832249	−	0.344729i	−0.757792	+	0.652496i	$0.773722\pi$
$42$	0.113204	−	0.113204i	0.0174677	−	0.0174677i
$43$	2.16470	−	2.16470i	0.330113	−	0.330113i	−0.522516	−	0.852629i	$-0.675007\pi$
$43$	2.16470	−	2.16470i	0.330113	−	0.330113i	0.852629	+	0.522516i	$0.175007\pi$
$44$	1.81602	+	0.752221i	0.273776	+	0.113402i
$45$	0.692812	−	1.67260i	0.103278	−	0.249336i
$46$	0.109871	−	0.0455101i	0.0161996	−	0.00671009i
$47$			10.6708i			1.55650i	0.627956	+	0.778249i	$0.283892\pi$
$47$			10.6708i			1.55650i	−0.627956	+	0.778249i	$0.716108\pi$
$48$	−2.10298	−	5.07704i	−0.303539	−	0.732807i
$49$	−4.69813	−	4.69813i	−0.671161	−	0.671161i
$50$	−0.182104			−0.0257534
$51$	−0.371777	−	5.95876i	−0.0520591	−	0.834393i
$52$	4.28525			0.594258
$53$	2.64883	+	2.64883i	0.363845	+	0.363845i	0.865226	−	0.501382i	$-0.167175\pi$
$53$	2.64883	+	2.64883i	0.363845	+	0.363845i	−0.501382	+	0.865226i	$0.667175\pi$
$54$	0.400878	+	0.967804i	0.0545525	+	0.131701i
$55$			2.00436i			0.270268i
$56$	−0.405071	+	0.167786i	−0.0541299	+	0.0224213i
$57$	−4.73087	+	11.4213i	−0.626619	+	1.51279i
$58$	−1.44793	−	0.599754i	−0.190123	−	0.0787515i
$59$	−4.38591	+	4.38591i	−0.570997	+	0.570997i	−0.932407	−	0.361410i	$-0.882295\pi$
$59$	−4.38591	+	4.38591i	−0.570997	+	0.570997i	0.361410	+	0.932407i	$0.382295\pi$
$60$	4.03406	−	4.03406i	0.520795	−	0.520795i
$61$	−0.0140470	−	0.00581845i	−0.00179853	−	0.000744977i	0.381784	−	0.924252i	$-0.375310\pi$
$61$	−0.0140470	−	0.00581845i	−0.00179853	−	0.000744977i	−0.383583	+	0.923507i	$0.625310\pi$
$62$	0.644550	−	1.55608i	0.0818579	−	0.197622i
$63$	−0.497788	+	0.206190i	−0.0627153	+	0.0259775i
$64$			7.18732i			0.898416i
$65$	1.67219	+	4.03703i	0.207410	+	0.500732i
$66$	−0.189772	−	0.189772i	−0.0233594	−	0.0233594i
$67$	6.00539			0.733675			0.366838	−	0.930285i	$-0.380440\pi$
$67$	6.00539			0.733675			0.366838	+	0.930285i	$0.380440\pi$
$68$	−2.62921	+	7.66625i	−0.318838	+	0.929670i
$69$	0.929117			0.111853
$70$	−0.156698	−	0.156698i	−0.0187290	−	0.0187290i
$71$	−1.91924	−	4.63346i	−0.227772	−	0.549890i	0.768134	−	0.640290i	$-0.221186\pi$
$71$	−1.91924	−	4.63346i	−0.227772	−	0.549890i	−0.995906	+	0.0903994i	$0.971186\pi$
$72$		−	0.663876i		−	0.0782385i
$73$	9.50711	−	3.93797i	1.11272	−	0.460905i	0.250848	−	0.968026i	$-0.419291\pi$
$73$	9.50711	−	3.93797i	1.11272	−	0.460905i	0.861874	+	0.507122i	$0.169291\pi$
$74$	0.252588	−	0.609802i	0.0293628	−	0.0708880i
$75$	−1.31443	−	0.544455i	−0.151777	−	0.0628683i
$76$	11.8663	−	11.8663i	1.36116	−	1.36116i
$77$	0.421807	−	0.421807i	0.0480694	−	0.0480694i
$78$	−0.540547	−	0.223902i	−0.0612049	−	0.0253519i
$79$	−3.73551	+	9.01833i	−0.420278	+	1.01464i	0.561987	+	0.827146i	$0.310037\pi$
$79$	−3.73551	+	9.01833i	−0.420278	+	1.01464i	−0.982266	+	0.187495i	$0.939963\pi$
$80$	−7.02767	+	2.91096i	−0.785717	+	0.325455i
$81$			5.47447i			0.608275i
$82$	−0.409112	−	0.987683i	−0.0451788	−	0.109071i
$83$	6.56549	+	6.56549i	0.720657	+	0.720657i	0.968739	−	0.248082i	$-0.0798003\pi$
$83$	6.56549	+	6.56549i	0.720657	+	0.720657i	−0.248082	+	0.968739i	$0.579800\pi$
$84$	−1.69789			−0.185255
$85$	−8.24816	+	0.514616i	−0.894638	+	0.0558179i
$86$	0.567394			0.0611837
$87$	−8.65806	−	8.65806i	−0.928242	−	0.928242i
$88$	0.281272	+	0.679051i	0.0299837	+	0.0723871i
$89$		−	16.2031i		−	1.71753i	−0.512370	−	0.858765i	$-0.671232\pi$
$89$		−	16.2031i		−	1.71753i	0.512370	−	0.858765i	$-0.328768\pi$
$90$	0.310002	−	0.128407i	0.0326770	−	0.0135353i
$91$	0.497668	−	1.20148i	0.0521697	−	0.125949i
$92$	−1.16524	−	0.482659i	−0.121485	−	0.0503207i
$93$	9.30474	−	9.30474i	0.964857	−	0.964857i
$94$	−1.39848	+	1.39848i	−0.144242	+	0.144242i
$95$	15.8095	+	6.54850i	1.62202	+	0.671862i
$96$	1.20435	−	2.90755i	0.122918	−	0.296750i
$97$	12.9060	−	5.34582i	1.31040	−	0.542786i	0.385400	−	0.922750i	$-0.374064\pi$
$97$	12.9060	−	5.34582i	1.31040	−	0.542786i	0.925001	+	0.379964i	$0.124064\pi$
$98$		−	1.23144i		−	0.124394i
$99$	0.345652	+	0.834479i	0.0347394	+	0.0838682i
$100$	1.36565	+	1.36565i	0.136565	+	0.136565i
$101$	0.666064			0.0662759			0.0331379	−	0.999451i	$-0.489450\pi$
$101$	0.666064			0.0662759			0.0331379	+	0.999451i	$0.489450\pi$
$102$	0.732209	−	0.829656i	0.0724995	−	0.0821482i
$103$	10.3950			1.02425			0.512126	−	0.858910i	$-0.328858\pi$
$103$	10.3950			1.02425			0.512126	+	0.858910i	$0.328858\pi$
$104$	1.13303	+	1.13303i	0.111103	+	0.111103i
$105$	−0.662552	−	1.59954i	−0.0646584	−	0.156099i
$106$			0.694291i			0.0674355i
$107$	−5.24085	+	2.17083i	−0.506652	+	0.209862i	−0.621342	−	0.783539i	$-0.713412\pi$
$107$	−5.24085	+	2.17083i	−0.506652	+	0.209862i	0.114690	+	0.993401i	$0.463412\pi$
$108$	4.25153	−	10.2641i	0.409104	−	0.987663i
$109$	−1.18338	−	0.490174i	−0.113348	−	0.0469501i	0.325289	−	0.945615i	$-0.394538\pi$
$109$	−1.18338	−	0.490174i	−0.113348	−	0.0469501i	−0.438637	+	0.898665i	$0.644538\pi$
$110$	−0.262684	+	0.262684i	−0.0250459	+	0.0250459i
$111$	3.64637	−	3.64637i	0.346098	−	0.346098i
$112$	2.09153	+	0.866340i	0.197631	+	0.0818615i
$113$	−2.79231	+	6.74122i	−0.262678	+	0.634161i	−0.999102	−	0.0423589i	$-0.986513\pi$
$113$	−2.79231	+	6.74122i	−0.262678	+	0.634161i	0.736424	+	0.676520i	$0.236513\pi$
$114$	−2.11685	+	0.876826i	−0.198261	+	0.0821223i
$115$		−	1.28609i		−	0.119929i
$116$	6.36072	+	15.3561i	0.590578	+	1.42578i
$117$	1.39237	+	1.39237i	0.128725	+	0.128725i
$118$	−1.14960			−0.105829
$119$	1.84408	+	1.62748i	0.169046	+	0.149191i
$120$	2.13323			0.194737
$121$	−0.707107	−	0.707107i	−0.0642824	−	0.0642824i
$122$	−0.00107840	−	0.00260349i	−9.76338e−5	−	0.000235709i
$123$		−	8.35227i		−	0.753099i
$124$	−16.5031	+	6.83580i	−1.48202	+	0.613873i
$125$	−4.58882	+	11.0784i	−0.410436	+	0.990881i
$126$	−0.0922607	−	0.0382156i	−0.00821924	−	0.00340452i
$127$	4.86726	−	4.86726i	0.431900	−	0.431900i	−0.457374	−	0.889274i	$-0.651210\pi$
$127$	4.86726	−	4.86726i	0.431900	−	0.431900i	0.889274	+	0.457374i	$0.151210\pi$
$128$	−4.01557	+	4.01557i	−0.354930	+	0.354930i
$129$	4.09546	+	1.69639i	0.360585	+	0.149359i
$130$	−0.309927	+	0.748230i	−0.0271824	+	0.0656241i
$131$	1.96785	−	0.815109i	0.171932	−	0.0712164i	−0.295057	−	0.955480i	$-0.595339\pi$
$131$	1.96785	−	0.815109i	0.171932	−	0.0712164i	0.466989	+	0.884263i	$0.345339\pi$
$132$			2.84630i			0.247739i
$133$	−1.94892	−	4.70511i	−0.168993	−	0.407985i
$134$	0.787044	+	0.787044i	0.0679903	+	0.0679903i
$135$	11.3286			0.975009
$136$	−2.72215	+	1.33181i	−0.233422	+	0.114202i
$137$	−2.02146			−0.172705			−0.0863524	−	0.996265i	$-0.527521\pi$
$137$	−2.02146			−0.172705			−0.0863524	+	0.996265i	$0.527521\pi$
$138$	0.121767	+	0.121767i	0.0103655	+	0.0103655i
$139$	−2.21678	−	5.35178i	−0.188025	−	0.453932i	0.801554	−	0.597922i	$-0.204007\pi$
$139$	−2.21678	−	5.35178i	−0.188025	−	0.453932i	−0.989579	+	0.143990i	$0.954007\pi$
$140$			2.35023i			0.198631i
$141$	−14.2754	+	5.91306i	−1.20220	+	0.497969i
$142$	0.355715	−	0.858772i	0.0298509	−	0.0720665i
$143$	−2.01412	−	0.834277i	−0.168429	−	0.0697658i
$144$	−2.42384	+	2.42384i	−0.201987	+	0.201987i
$145$	−11.9845	+	11.9845i	−0.995263	+	0.995263i
$146$	1.76206	+	0.729870i	0.145829	+	0.0604044i
$147$	3.68175	−	8.88854i	0.303666	−	0.733114i
$148$	−6.46729	+	2.67884i	−0.531608	+	0.220199i
$149$		−	1.27339i		−	0.104320i	−0.998639	−	0.0521600i	$-0.983389\pi$
$149$		−	1.27339i		−	0.104320i	0.998639	−	0.0521600i	$-0.0166106\pi$
$150$	−0.100910	−	0.243619i	−0.00823928	−	0.0198914i
$151$	−9.13270	−	9.13270i	−0.743208	−	0.743208i	0.229986	−	0.973194i	$-0.426132\pi$
$151$	−9.13270	−	9.13270i	−0.743208	−	0.743208i	−0.973194	+	0.229986i	$0.926132\pi$
$152$	6.27499			0.508969
$153$	−3.34522	+	1.63665i	−0.270445	+	0.132315i
$154$	0.110561			0.00890925
$155$	−12.8797	−	12.8797i	−1.03452	−	1.03452i
$156$	2.37460	+	5.73280i	0.190121	+	0.458992i
$157$			8.79938i			0.702267i	0.936325	+	0.351133i	$0.114204\pi$
$157$			8.79938i			0.702267i	−0.936325	+	0.351133i	$0.885796\pi$
$158$	−1.67147	+	0.692346i	−0.132975	+	0.0550801i
$159$	−2.07579	+	5.01141i	−0.164621	+	0.397430i
$160$	−4.02465	−	1.66706i	−0.318176	−	0.131793i
$161$	−0.270651	+	0.270651i	−0.0213303	+	0.0213303i
$162$	−0.717464	+	0.717464i	−0.0563693	+	0.0563693i
$163$	15.3882	+	6.37402i	1.20530	+	0.499252i	0.892708	−	0.450636i	$-0.148803\pi$
$163$	15.3882	+	6.37402i	1.20530	+	0.499252i	0.312592	+	0.949887i	$0.398803\pi$
$164$	−4.33886	+	10.4749i	−0.338808	+	0.817954i
$165$	−2.68143	+	1.11068i	−0.208749	+	0.0864667i
$166$			1.72090i			0.133568i
$167$	−5.33570	−	12.8815i	−0.412889	−	0.996802i	−0.984358	−	0.176178i	$-0.943626\pi$
$167$	−5.33570	−	12.8815i	−0.412889	−	0.996802i	0.571469	−	0.820623i	$-0.306374\pi$
$168$	−0.448927	−	0.448927i	−0.0346355	−	0.0346355i
$169$	8.24729			0.634407
$170$	−1.14842	−	1.01353i	−0.0880795	−	0.0777341i
$171$	7.71127			0.589695
$172$	−4.25503	−	4.25503i	−0.324443	−	0.324443i
$173$	−6.78604	−	16.3829i	−0.515933	−	1.24557i	−0.940382	−	0.340120i	$-0.889532\pi$
$173$	−6.78604	−	16.3829i	−0.515933	−	1.24557i	0.424449	−	0.905452i	$-0.360468\pi$
$174$		−	2.26939i		−	0.172042i
$175$	0.541492	−	0.224293i	0.0409329	−	0.0169550i
$176$	1.45231	−	3.50619i	0.109472	−	0.264289i
$177$	−8.29784	−	3.43708i	−0.623704	−	0.258347i
$178$	2.12352	−	2.12352i	0.159165	−	0.159165i
$179$	2.70049	−	2.70049i	0.201844	−	0.201844i	−0.598946	−	0.800790i	$-0.704413\pi$
$179$	2.70049	−	2.70049i	0.201844	−	0.201844i	0.800790	+	0.598946i	$0.204413\pi$
$180$	−3.28774	−	1.36183i	−0.245053	−	0.101504i
$181$	5.13352	−	12.3934i	0.381571	−	0.921194i	−0.610091	−	0.792331i	$-0.708867\pi$
$181$	5.13352	−	12.3934i	0.381571	−	0.921194i	0.991662	−	0.128863i	$-0.0411328\pi$
$182$	0.222683	−	0.0922384i	0.0165064	−	0.00683717i
$183$		−	0.0220162i		−	0.00162749i
$184$	−0.180477	−	0.435710i	−0.0133049	−	0.0321210i
$185$	−5.04733	−	5.04733i	−0.371087	−	0.371087i
$186$	2.43889			0.178828
$187$	2.72827	−	3.09137i	0.199511	−	0.226063i
$188$	20.9751			1.52976
$189$	−2.38404	−	2.38404i	−0.173413	−	0.173413i
$190$	1.21371	+	2.93015i	0.0880517	+	0.212576i
$191$		−	8.85486i		−	0.640715i	−0.947297	−	0.320358i	$-0.896197\pi$
$191$		−	8.85486i		−	0.640715i	0.947297	−	0.320358i	$-0.103803\pi$
$192$	−9.61519	+	3.98274i	−0.693916	+	0.287430i
$193$	−4.47646	+	10.8071i	−0.322223	+	0.777914i	0.676902	+	0.736073i	$0.263322\pi$
$193$	−4.47646	+	10.8071i	−0.322223	+	0.777914i	−0.999124	+	0.0418407i	$0.986678\pi$
$194$	2.39201	+	0.990803i	0.171736	+	0.0711355i
$195$	−4.47411	+	4.47411i	−0.320398	+	0.320398i
$196$	−9.23487	+	9.23487i	−0.659634	+	0.659634i
$197$	−12.5528	−	5.19954i	−0.894350	−	0.370452i	−0.112305	−	0.993674i	$-0.535823\pi$
$197$	−12.5528	−	5.19954i	−0.894350	−	0.370452i	−0.782045	+	0.623222i	$0.785823\pi$
$198$	−0.0640637	+	0.154663i	−0.00455281	+	0.0109915i
$199$	−12.9657	+	5.37059i	−0.919117	+	0.380711i	−0.791540	−	0.611118i	$-0.790720\pi$
$199$	−12.9657	+	5.37059i	−0.919117	+	0.380711i	−0.127578	+	0.991829i	$0.540720\pi$
$200$			0.722162i			0.0510645i
$201$	3.32779	+	8.03400i	0.234724	+	0.566675i
$202$	0.0872919	+	0.0872919i	0.00614183	+	0.00614183i
$203$	5.04417			0.354031
$204$	−11.7128	+	0.730782i	−0.820062	+	0.0511650i
$205$	−11.5613			−0.807474
$206$	1.36233	+	1.36233i	0.0949181	+	0.0949181i
$207$	−0.221786	−	0.535439i	−0.0154152	−	0.0372156i
$208$		−	8.27353i		−	0.573666i
$209$	−7.88754	+	3.26712i	−0.545592	+	0.225992i
$210$	0.122798	−	0.296461i	0.00847389	−	0.0204578i
$211$	12.2399	+	5.06994i	0.842630	+	0.349029i	0.761890	−	0.647706i	$-0.224272\pi$
$211$	12.2399	+	5.06994i	0.842630	+	0.349029i	0.0807402	+	0.996735i	$0.474272\pi$
$212$	5.20667	−	5.20667i	0.357595	−	0.357595i
$213$	5.13511	−	5.13511i	0.351852	−	0.351852i
$214$	−0.971347	−	0.402345i	−0.0663999	−	0.0275037i
$215$	2.34816	−	5.66896i	0.160143	−	0.386620i
$216$	3.83797	−	1.58974i	0.261141	−	0.108168i
$217$			5.42092i			0.367996i
$218$	−0.0908495	−	0.219330i	−0.00615310	−	0.0148549i
$219$	10.5364	+	10.5364i	0.711985	+	0.711985i
$220$	3.93987			0.265626
$221$	2.91602	−	8.50253i	0.196152	−	0.571942i
$222$	0.955759			0.0641464
$223$	−13.1660	−	13.1660i	−0.881662	−	0.881662i	0.112042	−	0.993703i	$-0.464261\pi$
$223$	−13.1660	−	13.1660i	−0.881662	−	0.881662i	−0.993703	+	0.112042i	$0.964261\pi$
$224$	0.496141	+	1.19779i	0.0331498	+	0.0800307i
$225$			0.887457i			0.0591638i
$226$	−1.24943	+	0.517530i	−0.0831108	+	0.0344256i
$227$	−10.4777	+	25.2954i	−0.695430	+	1.67892i	0.0381133	+	0.999273i	$0.487865\pi$
$227$	−10.4777	+	25.2954i	−0.695430	+	1.67892i	−0.733543	+	0.679643i	$0.762135\pi$
$228$	22.4503	+	9.29922i	1.48681	+	0.615856i
$229$	12.1157	−	12.1157i	0.800627	−	0.800627i	−0.182567	−	0.983193i	$-0.558441\pi$
$229$	12.1157	−	12.1157i	0.800627	−	0.800627i	0.983193	+	0.182567i	$0.0584405\pi$
$230$	0.168550	−	0.168550i	0.0111139	−	0.0111139i
$231$	0.798030	+	0.330555i	0.0525065	+	0.0217489i
$232$	−2.37841	+	5.74200i	−0.156150	+	0.376980i
$233$	−7.90060	+	3.27254i	−0.517586	+	0.214391i	−0.626156	−	0.779698i	$-0.715373\pi$
$233$	−7.90060	+	3.27254i	−0.517586	+	0.214391i	0.108570	+	0.994089i	$0.465373\pi$
$234$			0.364958i			0.0238581i
$235$	8.18489	+	19.7601i	0.533924	+	1.28901i
$236$	8.62115	+	8.62115i	0.561189	+	0.561189i
$237$	−14.1347			−0.918146
$238$	0.0283863	+	0.454970i	0.00184001	+	0.0294913i
$239$	−4.48889			−0.290362			−0.145181	−	0.989405i	$-0.546376\pi$
$239$	−4.48889			−0.290362			−0.145181	+	0.989405i	$0.546376\pi$
$240$	−7.78854	−	7.78854i	−0.502748	−	0.502748i
$241$	−0.701006	−	1.69238i	−0.0451558	−	0.109016i	0.899692	−	0.436525i	$-0.143791\pi$
$241$	−0.701006	−	1.69238i	−0.0451558	−	0.109016i	−0.944848	+	0.327509i	$0.893791\pi$
$242$		−	0.185341i		−	0.0119142i
$243$	8.34147	−	3.45515i	0.535106	−	0.221648i
$244$	−0.0114370	+	0.0276114i	−0.000732181	+	0.00176764i
$245$	−12.3036	−	5.09631i	−0.786047	−	0.325591i
$246$	1.09462	−	1.09462i	0.0697903	−	0.0697903i
$247$	−13.1608	+	13.1608i	−0.837401	+	0.837401i
$248$	−6.17087	−	2.55606i	−0.391851	−	0.162310i
$249$	−5.14514	+	12.4215i	−0.326060	+	0.787178i
$250$	−2.05329	+	0.850499i	−0.129861	+	0.0537903i
$251$		−	12.7038i		−	0.801858i	−0.916109	−	0.400929i	$-0.868687\pi$
$251$		−	12.7038i		−	0.801858i	0.916109	−	0.400929i	$-0.131313\pi$
$252$	0.405298	+	0.978475i	0.0255314	+	0.0616382i
$253$	0.453712	+	0.453712i	0.0285246	+	0.0285246i
$254$	1.27577			0.0800490
$255$	−5.25904	−	10.7492i	−0.329334	−	0.673141i
$256$	13.3221			0.832632
$257$	15.2784	+	15.2784i	0.953042	+	0.953042i	0.998946	−	0.0459043i	$-0.0146169\pi$
$257$	15.2784	+	15.2784i	0.953042	+	0.953042i	−0.0459043	+	0.998946i	$0.514617\pi$
$258$	0.314412	+	0.759058i	0.0195745	+	0.0472569i
$259$			2.12437i			0.132002i
$260$	7.93539	−	3.28694i	0.492132	−	0.203848i
$261$	−2.92281	+	7.05628i	−0.180917	+	0.436773i
$262$	0.364724	+	0.151074i	0.0225327	+	0.00933336i
$263$	10.8224	−	10.8224i	0.667341	−	0.667341i	−0.289759	−	0.957100i	$-0.593575\pi$
$263$	10.8224	−	10.8224i	0.667341	−	0.667341i	0.957100	+	0.289759i	$0.0935751\pi$
$264$	−0.752570	+	0.752570i	−0.0463175	+	0.0463175i
$265$	6.93682	+	2.87333i	0.426126	+	0.176507i
$266$	0.361216	−	0.872053i	0.0221476	−	0.0534690i
$267$	21.6765	−	8.97871i	1.32658	−	0.549488i
$268$		−	11.8045i		−	0.721074i
$269$	0.495279	+	1.19571i	0.0301977	+	0.0729036i	0.938259	−	0.345934i	$-0.112438\pi$
$269$	0.495279	+	1.19571i	0.0301977	+	0.0729036i	−0.908061	+	0.418837i	$0.862438\pi$
$270$	1.48468	+	1.48468i	0.0903548	+	0.0903548i
$271$	15.4512			0.938594			0.469297	−	0.883040i	$-0.344507\pi$
$271$	15.4512			0.938594			0.469297	+	0.883040i	$0.344507\pi$
$272$	14.8012	+	5.07620i	0.897455	+	0.307790i
$273$	1.88311			0.113971
$274$	−0.264925	−	0.264925i	−0.0160047	−	0.0160047i
$275$	−0.375999	−	0.907743i	−0.0226736	−	0.0547390i
$276$		−	1.82632i		−	0.109931i
$277$	20.2729	−	8.39732i	1.21808	−	0.504546i	0.321282	−	0.946984i	$-0.395886\pi$
$277$	20.2729	−	8.39732i	1.21808	−	0.504546i	0.896799	+	0.442438i	$0.145886\pi$
$278$	0.410861	−	0.991907i	0.0246418	−	0.0594906i
$279$	−7.58332	−	3.14111i	−0.454001	−	0.188054i
$280$	−0.621408	+	0.621408i	−0.0371362	+	0.0371362i
$281$	11.9930	−	11.9930i	0.715445	−	0.715445i	−0.252224	−	0.967669i	$-0.581162\pi$
$281$	11.9930	−	11.9930i	0.715445	−	0.715445i	0.967669	+	0.252224i	$0.0811619\pi$
$282$	−2.64582	−	1.09593i	−0.157556	−	0.0652620i
$283$	8.45391	−	20.4095i	0.502533	−	1.21322i	−0.445567	−	0.895249i	$-0.646998\pi$
$283$	8.45391	−	20.4095i	0.502533	−	1.21322i	0.948100	−	0.317973i	$-0.103002\pi$
$284$	−9.10775	+	3.77255i	−0.540445	+	0.223860i
$285$			24.7786i			1.46776i
$286$	−0.154626	−	0.373301i	−0.00914324	−	0.0220737i
$287$	2.43301	+	2.43301i	0.143616	+	0.143616i
$288$	−1.96307			−0.115675
$289$	13.4218	+	10.4334i	0.789516	+	0.613730i
$290$	−3.14130			−0.184463
$291$	14.3033	+	14.3033i	0.838472	+	0.838472i
$292$	−7.74067	−	18.6876i	−0.452988	−	1.09361i
$293$		−	30.6582i		−	1.79107i	−0.444993	−	0.895534i	$-0.646794\pi$
$293$		−	30.6582i		−	1.79107i	0.444993	−	0.895534i	$-0.353206\pi$
$294$	1.64741	−	0.682382i	0.0960792	−	0.0397973i
$295$	−4.75763	+	11.4859i	−0.277000	+	0.668736i
$296$	−2.41826	−	1.00168i	−0.140559	−	0.0582212i
$297$	−3.99654	+	3.99654i	−0.231903	+	0.231903i
$298$	0.166885	−	0.166885i	0.00966741	−	0.00966741i
$299$	1.29235	+	0.535310i	0.0747387	+	0.0309578i
$300$	−1.07021	+	2.58371i	−0.0617885	+	0.149171i
$301$	−1.68716	+	0.698845i	−0.0972463	+	0.0402807i
$302$		−	2.39379i		−	0.137747i
$303$	0.369089	+	0.891059i	0.0212036	+	0.0511900i
$304$	−22.9103	−	22.9103i	−1.31400	−	1.31400i
$305$	−0.0304750			−0.00174499
$306$	−0.652905	−	0.223919i	−0.0373241	−	0.0128006i
$307$	−0.553753			−0.0316044			−0.0158022	−	0.999875i	$-0.505030\pi$
$307$	−0.553753			−0.0316044			−0.0158022	+	0.999875i	$0.505030\pi$
$308$	−0.829124	−	0.829124i	−0.0472438	−	0.0472438i
$309$	5.76023	+	13.9064i	0.327688	+	0.791109i
$310$		−	3.37593i		−	0.191740i
$311$	7.29880	−	3.02326i	0.413877	−	0.171433i	−0.166022	−	0.986122i	$-0.553092\pi$
$311$	7.29880	−	3.02326i	0.413877	−	0.171433i	0.579899	+	0.814689i	$0.303092\pi$
$312$	−0.887917	+	2.14362i	−0.0502684	+	0.121359i
$313$	2.18052	+	0.903201i	0.123250	+	0.0510520i	0.443456	−	0.896296i	$-0.353752\pi$
$313$	2.18052	+	0.903201i	0.123250	+	0.0510520i	−0.320206	+	0.947348i	$0.603752\pi$
$314$	−1.15321	+	1.15321i	−0.0650796	+	0.0650796i
$315$	−0.763642	+	0.763642i	−0.0430264	+	0.0430264i
$316$	17.7269	+	7.34271i	0.997214	+	0.413059i
$317$	1.89179	−	4.56717i	0.106253	−	0.256518i	−0.861807	−	0.507237i	$-0.830667\pi$
$317$	1.89179	−	4.56717i	0.106253	−	0.256518i	0.968060	+	0.250719i	$0.0806669\pi$
$318$	−0.928821	+	0.384730i	−0.0520857	+	0.0215746i
$319$		−	8.45591i		−	0.473440i
$320$	5.51294	+	13.3094i	0.308183	+	0.744018i
$321$	−5.80826	−	5.80826i	−0.324186	−	0.324186i
$322$	−0.0709409			−0.00395338
$323$	−15.4697	−	31.6192i	−0.860755	−	1.75934i
$324$	10.7609			0.597827
$325$	−1.51462	−	1.51462i	−0.0840159	−	0.0840159i
$326$	1.18137	+	2.85208i	0.0654300	+	0.157962i
$327$		−	1.85475i		−	0.102568i
$328$	−3.91680	+	1.62239i	−0.216269	+	0.0895817i
$329$	2.43594	−	5.88087i	0.134297	−	0.324223i
$330$	−0.496980	−	0.205856i	−0.0273579	−	0.0113320i
$331$	−19.1924	+	19.1924i	−1.05491	+	1.05491i	−0.0565075	+	0.998402i	$0.517996\pi$
$331$	−19.1924	+	19.1924i	−1.05491	+	1.05491i	−0.998402	+	0.0565075i	$0.982004\pi$
$332$	12.9055	−	12.9055i	0.708279	−	0.708279i
$333$	−2.97178	−	1.23095i	−0.162852	−	0.0674556i
$334$	0.988926	−	2.38748i	0.0541116	−	0.130637i
$335$	11.1207	−	4.60635i	0.607590	−	0.251672i
$336$			3.27811i			0.178836i
$337$	−10.2369	−	24.7140i	−0.557639	−	1.34626i	−0.911630	−	0.411011i	$-0.865176\pi$
$337$	−10.2369	−	24.7140i	−0.557639	−	1.34626i	0.353991	−	0.935249i	$-0.384824\pi$
$338$	1.08086	+	1.08086i	0.0587909	+	0.0587909i
$339$	−10.5657			−0.573850
$340$	1.01155	+	16.2130i	0.0548592	+	0.879272i
$341$	9.08749			0.492115
$342$	1.01061	+	1.01061i	0.0546475	+	0.0546475i
$343$	3.11469	+	7.51953i	0.168178	+	0.406017i
$344$		−	2.25009i		−	0.121316i
$345$	1.72053	−	0.712666i	0.0926301	−	0.0383687i
$346$	1.25773	−	3.03644i	0.0676162	−	0.163240i
$347$	13.2301	+	5.48008i	0.710228	+	0.294186i	0.708399	−	0.705812i	$-0.249418\pi$
$347$	13.2301	+	5.48008i	0.710228	+	0.294186i	0.00182908	+	0.999998i	$0.499418\pi$
$348$	−17.0187	+	17.0187i	−0.912298	+	0.912298i
$349$	−21.6075	+	21.6075i	−1.15662	+	1.15662i	−0.171423	+	0.985197i	$0.554837\pi$
$349$	−21.6075	+	21.6075i	−1.15662	+	1.15662i	−0.985197	+	0.171423i	$0.945163\pi$
$350$	0.100361	+	0.0415708i	0.00536451	+	0.00222205i
$351$	−4.71531	+	11.3838i	−0.251684	+	0.607620i
$352$	2.00794	−	0.831718i	0.107024	−	0.0443307i
$353$			11.5249i			0.613409i	0.951805	+	0.306705i	$0.0992264\pi$
$353$			11.5249i			0.613409i	−0.951805	+	0.306705i	$0.900774\pi$
$354$	−0.637033	−	1.53793i	−0.0338579	−	0.0817403i
$355$	−7.10806	−	7.10806i	−0.377256	−	0.377256i
$356$	−31.8497			−1.68803
$357$	−1.15538	+	3.36885i	−0.0611489	+	0.178298i
$358$	0.707832			0.0374101
$359$	23.8971	+	23.8971i	1.26124	+	1.26124i	0.950493	+	0.310745i	$0.100578\pi$
$359$	23.8971	+	23.8971i	1.26124	+	1.26124i	0.310745	+	0.950493i	$0.399422\pi$
$360$	−0.509216	−	1.22936i	−0.0268381	−	0.0647928i
$361$			53.8873i			2.83617i
$362$	2.29701	−	0.951453i	0.120728	−	0.0500073i
$363$	0.554134	−	1.33780i	0.0290845	−	0.0702162i
$364$	−2.36168	−	0.978239i	−0.123786	−	0.0512737i
$365$	14.5846	−	14.5846i	0.763392	−	0.763392i
$366$	0.00288536	−	0.00288536i	0.000150820	−	0.000150820i
$367$	4.73463	+	1.96115i	0.247145	+	0.102371i	0.502818	−	0.864393i	$-0.332297\pi$
$367$	4.73463	+	1.96115i	0.247145	+	0.102371i	−0.255672	+	0.966764i	$0.582297\pi$
$368$	−0.931869	+	2.24973i	−0.0485770	+	0.117275i
$369$	−4.81332	+	1.99374i	−0.250571	+	0.103790i
$370$		−	1.32297i		−	0.0687779i
$371$	−0.855141	−	2.06449i	−0.0443967	−	0.107183i
$372$	−18.2898	−	18.2898i	−0.948284	−	0.948284i
$373$	−13.4961			−0.698802			−0.349401	−	0.936973i	$-0.613615\pi$
$373$	−13.4961			−0.698802			−0.349401	+	0.936973i	$0.613615\pi$
$374$	0.762700	−	0.0475860i	0.0394383	−	0.00246062i
$375$	−17.3635			−0.896645
$376$	5.54586	+	5.54586i	0.286006	+	0.286006i
$377$	−7.05458	−	17.0313i	−0.363329	−	0.877154i
$378$		−	0.624886i		−	0.0321407i
$379$	−21.3590	+	8.84719i	−1.09714	+	0.454450i	−0.856491	−	0.516163i	$-0.827360\pi$
$379$	−21.3590	+	8.84719i	−1.09714	+	0.454450i	−0.240648	+	0.970612i	$0.577360\pi$
$380$	12.8720	−	31.0759i	0.660322	−	1.59416i
$381$	9.20853	+	3.81430i	0.471767	+	0.195412i
$382$	1.16048	−	1.16048i	0.0593756	−	0.0593756i
$383$	−14.4275	+	14.4275i	−0.737209	+	0.737209i	−0.972037	−	0.234828i	$-0.924547\pi$
$383$	−14.4275	+	14.4275i	−0.737209	+	0.737209i	0.234828	+	0.972037i	$0.424547\pi$
$384$	−7.59719	−	3.14686i	−0.387692	−	0.160587i
$385$	0.457556	−	1.10464i	0.0233192	−	0.0562976i
$386$	−2.00301	+	0.829674i	−0.101950	+	0.0422293i
$387$		−	2.76511i		−	0.140558i
$388$	−10.5080	−	25.3686i	−0.533463	−	1.28789i
$389$	12.1700	+	12.1700i	0.617043	+	0.617043i	0.944772	−	0.327729i	$-0.106283\pi$
$389$	12.1700	+	12.1700i	0.617043	+	0.617043i	−0.327729	+	0.944772i	$0.606283\pi$
$390$	−1.17272			−0.0593830
$391$	−1.75058	+	1.98356i	−0.0885308	+	0.100313i
$392$	−4.88345			−0.246652
$393$	2.18090	+	2.18090i	0.110012	+	0.110012i
$394$	−0.963690	−	2.32655i	−0.0485500	−	0.117210i
$395$			19.5653i			0.984438i
$396$	1.64029	−	0.679431i	0.0824277	−	0.0341427i
$397$	−3.76439	+	9.08803i	−0.188929	+	0.456115i	−0.989754	−	0.142783i	$-0.954395\pi$
$397$	−3.76439	+	9.08803i	−0.188929	+	0.456115i	0.800825	+	0.598899i	$0.204395\pi$
$398$	−2.40309	−	0.995393i	−0.120456	−	0.0498945i
$399$	5.21453	−	5.21453i	0.261053	−	0.261053i
$400$	2.63665	−	2.63665i	0.131833	−	0.131833i
$401$	−16.1173	−	6.67600i	−0.804859	−	0.333383i	−0.0579581	−	0.998319i	$-0.518459\pi$
$401$	−16.1173	−	6.67600i	−0.804859	−	0.333383i	−0.746901	+	0.664936i	$0.768459\pi$
$402$	−0.616778	+	1.48903i	−0.0307621	+	0.0742662i
$403$	18.3033	−	7.58149i	0.911754	−	0.377661i
$404$		−	1.30925i		−	0.0651375i
$405$	4.19912	+	10.1376i	0.208656	+	0.503740i
$406$	0.661070	+	0.661070i	0.0328083	+	0.0328083i
$407$	3.56124			0.176524
$408$	−3.29012	−	2.90368i	−0.162885	−	0.143754i
$409$	−23.0150			−1.13802			−0.569008	−	0.822332i	$-0.692673\pi$
$409$	−23.0150			−1.13802			−0.569008	+	0.822332i	$0.692673\pi$
$410$	−1.51518	−	1.51518i	−0.0748293	−	0.0748293i
$411$	−1.12016	−	2.70430i	−0.0552533	−	0.133393i
$412$		−	20.4330i		−	1.00666i
$413$	3.41837	−	1.41593i	0.168207	−	0.0696736i
$414$	0.0411062	−	0.0992392i	0.00202026	−	0.00487734i
$415$	17.1939	+	7.12194i	0.844014	+	0.349602i
$416$	3.35036	−	3.35036i	0.164265	−	0.164265i
$417$	5.93121	−	5.93121i	0.290452	−	0.290452i
$418$	−1.46189	−	0.605534i	−0.0715033	−	0.0296176i
$419$	−12.6943	+	30.6467i	−0.620156	+	1.49719i	0.231365	+	0.972867i	$0.425681\pi$
$419$	−12.6943	+	30.6467i	−0.620156	+	1.49719i	−0.851520	+	0.524321i	$0.824319\pi$
$420$	−3.14414	+	1.30234i	−0.153418	+	0.0635479i
$421$		−	20.4782i		−	0.998045i	−0.866589	−	0.499023i	$-0.833692\pi$
$421$		−	20.4782i		−	0.998045i	0.866589	−	0.499023i	$-0.166308\pi$
$422$	0.939670	+	2.26856i	0.0457424	+	0.110432i
$423$	6.81526	+	6.81526i	0.331369	+	0.331369i
$424$	2.75332			0.133713
$425$	3.63892	−	1.78034i	0.176514	−	0.0863591i
$426$	1.34598			0.0652128
$427$	0.00641330	+	0.00641330i	0.000310362	+	0.000310362i
$428$	4.26709	+	10.3017i	0.206258	+	0.497950i
$429$		−	3.15679i		−	0.152411i
$430$	1.05069	−	0.435212i	0.0506690	−	0.0209878i
$431$	2.04914	−	4.94706i	0.0987035	−	0.238291i	−0.866813	−	0.498633i	$-0.833835\pi$
$431$	2.04914	−	4.94706i	0.0987035	−	0.238291i	0.965516	+	0.260342i	$0.0838354\pi$
$432$	−19.8169	−	8.20841i	−0.953439	−	0.394927i
$433$	−22.3708	+	22.3708i	−1.07507	+	1.07507i	−0.0781293	+	0.996943i	$0.524895\pi$
$433$	−22.3708	+	22.3708i	−1.07507	+	1.07507i	−0.996943	+	0.0781293i	$0.975105\pi$
$434$	−0.710445	+	0.710445i	−0.0341025	+	0.0341025i
$435$	−22.6739	−	9.39186i	−1.08713	−	0.450305i
$436$	−0.963509	+	2.32612i	−0.0461437	+	0.111401i
$437$	5.06100	−	2.09634i	0.242101	−	0.100281i
$438$			2.76173i			0.131960i
$439$	−9.30329	−	22.4601i	−0.444022	−	1.07196i	−0.974525	−	0.224281i	$-0.927997\pi$
$439$	−9.30329	−	22.4601i	−0.444022	−	1.07196i	0.530503	−	0.847683i	$-0.322003\pi$
$440$	1.04171	+	1.04171i	0.0496617	+	0.0496617i
$441$	−6.00122			−0.285773
$442$	1.49647	−	0.732147i	0.0711799	−	0.0348247i
$443$	−3.68500			−0.175080			−0.0875399	−	0.996161i	$-0.527901\pi$
$443$	−3.68500			−0.175080			−0.0875399	+	0.996161i	$0.527901\pi$
$444$	−7.16748	−	7.16748i	−0.340154	−	0.340154i
$445$	−12.4284	−	30.0048i	−0.589162	−	1.42236i
$446$		−	3.45098i		−	0.163408i
$447$	1.70353	−	0.705627i	0.0805744	−	0.0333750i
$448$	1.64072	−	3.96106i	0.0775170	−	0.187143i
$449$	0.792880	+	0.328422i	0.0374183	+	0.0154992i	0.401314	−	0.915940i	$-0.368554\pi$
$449$	0.792880	+	0.328422i	0.0374183	+	0.0154992i	−0.363896	+	0.931440i	$0.618554\pi$
$450$	−0.116307	+	0.116307i	−0.00548275	+	0.00548275i
$451$	4.07863	−	4.07863i	0.192055	−	0.192055i
$452$	13.2509	+	5.48869i	0.623269	+	0.258166i
$453$	7.15696	−	17.2784i	0.336264	−	0.811812i
$454$	−4.68829	+	1.94195i	−0.220032	+	0.0911404i
$455$		−	2.60661i		−	0.122200i
$456$	3.47718	+	8.39466i	0.162834	+	0.393116i
$457$	27.2529	+	27.2529i	1.27484	+	1.27484i	0.943518	+	0.331320i	$0.107494\pi$
$457$	27.2529	+	27.2529i	1.27484	+	1.27484i	0.331320	+	0.943518i	$0.392506\pi$
$458$	3.17567			0.148389
$459$	−17.4723	−	15.4201i	−0.815537	−	0.719748i
$460$	−2.52800			−0.117869
$461$	−9.57279	−	9.57279i	−0.445849	−	0.445849i	0.448123	−	0.893972i	$-0.352093\pi$
$461$	−9.57279	−	9.57279i	−0.445849	−	0.445849i	−0.893972	+	0.448123i	$0.852093\pi$
$462$	0.0612655	+	0.147908i	0.00285033	+	0.00688131i
$463$			15.7275i			0.730921i	0.930827	+	0.365461i	$0.119088\pi$
$463$			15.7275i			0.730921i	−0.930827	+	0.365461i	$0.880912\pi$
$464$	29.6480	−	12.2806i	1.37638	−	0.570113i
$465$	10.0933	−	24.3675i	0.468068	−	1.13001i
$466$	−1.46431	−	0.606537i	−0.0678328	−	0.0280973i
$467$	−23.4310	+	23.4310i	−1.08426	+	1.08426i	−0.0881526	+	0.996107i	$0.528096\pi$
$467$	−23.4310	+	23.4310i	−1.08426	+	1.08426i	−0.996107	+	0.0881526i	$0.971904\pi$
$468$	2.73692	−	2.73692i	0.126514	−	0.126514i
$469$	−3.30968	−	1.37091i	−0.152827	−	0.0633029i
$470$	−1.51700	+	3.66236i	−0.0699740	+	0.168932i
$471$	−11.7718	+	4.87603i	−0.542415	+	0.224676i
$472$			4.55891i			0.209841i
$473$	1.17153	+	2.82831i	0.0538668	+	0.130046i
$474$	−1.85244	−	1.85244i	−0.0850852	−	0.0850852i
$475$	−8.38829			−0.384881
$476$	3.19906	−	3.62481i	0.146629	−	0.166143i
$477$	3.38352			0.154921
$478$	−0.588297	−	0.588297i	−0.0269081	−	0.0269081i
$479$	1.38279	+	3.33835i	0.0631812	+	0.152533i	0.952317	−	0.305111i	$-0.0986935\pi$
$479$	1.38279	+	3.33835i	0.0631812	+	0.152533i	−0.889136	+	0.457644i	$0.848694\pi$
$480$		−	6.30794i		−	0.287917i
$481$	7.17277	−	2.97106i	0.327050	−	0.135469i
$482$	0.129926	−	0.313668i	0.00591795	−	0.0142872i
$483$	−0.512053	−	0.212099i	−0.0232992	−	0.00965084i
$484$	−1.38992	+	1.38992i	−0.0631783	+	0.0631783i
$485$	19.7987	−	19.7987i	0.899011	−	0.899011i
$486$	1.54602	+	0.640383i	0.0701289	+	0.0290484i
$487$	−13.9298	+	33.6295i	−0.631219	+	1.52390i	0.206872	+	0.978368i	$0.433672\pi$
$487$	−13.9298	+	33.6295i	−0.631219	+	1.52390i	−0.838091	+	0.545530i	$0.816328\pi$
$488$	−0.0103245	+	0.00427656i	−0.000467369	+	0.000193591i
$489$			24.1184i			1.09067i
$490$	−0.944557	−	2.28036i	−0.0426708	−	0.103016i
$491$	−7.13805	−	7.13805i	−0.322136	−	0.322136i	0.527450	−	0.849586i	$-0.323148\pi$
$491$	−7.13805	−	7.13805i	−0.322136	−	0.322136i	−0.849586	+	0.527450i	$0.823148\pi$
$492$	−16.4176			−0.740164
$493$	34.7970	−	2.17104i	1.56718	−	0.0977786i
$494$	−3.44961			−0.155205
$495$	1.28015	+	1.28015i	0.0575385	+	0.0575385i
$496$	13.1979	+	31.8625i	0.592602	+	1.43067i
$497$			2.99170i			0.134196i
$498$	−2.30221	+	0.953608i	−0.103165	+	0.0427322i
$499$	2.75253	−	6.64519i	0.123220	−	0.297480i	−0.850218	−	0.526431i	$-0.823530\pi$
$499$	2.75253	−	6.64519i	0.123220	−	0.297480i	0.973438	+	0.228952i	$0.0735298\pi$
$500$	21.7762	+	9.02001i	0.973862	+	0.403387i
$501$	14.2762	−	14.2762i	0.637812	−	0.637812i
$502$	1.66491	−	1.66491i	0.0743088	−	0.0743088i
$503$	−35.5675	−	14.7325i	−1.58588	−	0.656891i	−0.596545	−	0.802580i	$-0.703460\pi$
$503$	−35.5675	−	14.7325i	−1.58588	−	0.656891i	−0.989331	+	0.145688i	$0.953460\pi$
$504$	−0.151550	+	0.365873i	−0.00675056	+	0.0162973i
$505$	1.23341	−	0.510895i	0.0548860	−	0.0227345i
$506$			0.118924i			0.00528680i
$507$	4.57010	+	11.0332i	0.202965	+	0.490002i
$508$	−9.56733	−	9.56733i	−0.424482	−	0.424482i
$509$	30.6548			1.35875			0.679376	−	0.733790i	$-0.262251\pi$
$509$	30.6548			1.35875			0.679376	+	0.733790i	$0.262251\pi$
$510$	0.719520	−	2.09798i	0.0318609	−	0.0929001i
$511$	−6.13849			−0.271551
$512$	9.77709	+	9.77709i	0.432090	+	0.432090i
$513$	18.4657	+	44.5801i	0.815280	+	1.96826i
$514$			4.00466i			0.176638i
$515$	19.2494	−	7.97335i	0.848229	−	0.351348i
$516$	3.33452	−	8.05023i	0.146794	−	0.354392i
$517$	−9.85854	−	4.08354i	−0.433578	−	0.179594i
$518$	−0.278412	+	0.278412i	−0.0122327	+	0.0122327i
$519$	18.1567	−	18.1567i	0.796990	−	0.796990i
$520$	2.96722	+	1.22906i	0.130121	+	0.0538979i
$521$	11.6188	−	28.0502i	0.509027	−	1.22890i	−0.435418	−	0.900229i	$-0.643399\pi$
$521$	11.6188	−	28.0502i	0.509027	−	1.22890i	0.944444	−	0.328671i	$-0.106601\pi$
$522$	−1.30782	+	0.541717i	−0.0572418	+	0.0237103i
$523$			13.9575i			0.610317i	0.952302	+	0.305158i	$0.0987094\pi$
$523$			13.9575i			0.610317i	−0.952302	+	0.305158i	$0.901291\pi$
$524$	−1.60222	−	3.86810i	−0.0699932	−	0.168979i
$525$	0.600118	+	0.600118i	0.0261913	+	0.0261913i
$526$	2.83670			0.123686
$527$	2.33319	+	37.3960i	0.101636	+	1.62899i
$528$	5.49535			0.239154
$529$	15.9723	+	15.9723i	0.694449	+	0.694449i
$530$	0.532546	+	1.28568i	0.0231323	+	0.0558464i
$531$			5.60240i			0.243124i
$532$	−9.24860	+	3.83090i	−0.400978	+	0.166090i
$533$	4.81216	−	11.6176i	0.208438	−	0.503213i
$534$	4.01756	+	1.66413i	0.173857	+	0.0720139i
$535$	−8.03984	+	8.03984i	−0.347593	+	0.347593i
$536$	3.12114	−	3.12114i	0.134813	−	0.134813i
$537$	5.10914	+	2.11628i	0.220476	+	0.0913240i
$538$	−0.0917957	+	0.221614i	−0.00395759	+	0.00955447i
$539$	6.13840	−	2.54261i	0.264400	−	0.109518i
$540$		−	22.2680i		−	0.958263i
$541$	−5.28478	−	12.7586i	−0.227210	−	0.548534i	0.768626	−	0.639699i	$-0.220941\pi$
$541$	−5.28478	−	12.7586i	−0.227210	−	0.548534i	−0.995836	+	0.0911648i	$0.970941\pi$
$542$	2.02498	+	2.02498i	0.0869802	+	0.0869802i
$543$	19.4245			0.833586
$544$	3.93814	+	8.04936i	0.168846	+	0.345113i
$545$	−2.56736			−0.109974
$546$	0.246793	+	0.246793i	0.0105618	+	0.0105618i
$547$	−1.70168	−	4.10823i	−0.0727587	−	0.175655i	0.883316	−	0.468778i	$-0.155306\pi$
$547$	−1.70168	−	4.10823i	−0.0727587	−	0.175655i	−0.956075	+	0.293123i	$0.905306\pi$
$548$			3.97348i			0.169738i
$549$	−0.0126877	+	0.00525542i	−0.000541498	+	0.000224296i
$550$	0.0696883	−	0.168242i	0.00297152	−	0.00717388i
$551$	−66.6963	−	27.6265i	−2.84136	−	1.17693i
$552$	0.482883	−	0.482883i	0.0205529	−	0.0205529i
$553$	4.11741	−	4.11741i	0.175090	−	0.175090i
$554$	3.75741	+	1.55637i	0.159637	+	0.0661239i
$555$	3.95541	−	9.54921i	0.167898	−	0.405341i
$556$	−10.5197	+	4.35741i	−0.446136	+	0.184795i
$557$		−	0.297000i		−	0.0125843i	−0.999980	−	0.00629215i	$-0.997997\pi$
$557$		−	0.297000i		−	0.0125843i	0.999980	−	0.00629215i	$-0.00200287\pi$
$558$	−0.582179	−	1.40550i	−0.0246456	−	0.0594997i
$559$	4.71919	+	4.71919i	0.199601	+	0.199601i
$560$	4.53759			0.191748
$561$	5.64745	+	1.93684i	0.238435	+	0.0817735i
$562$	3.14353			0.132602
$563$	−15.1680	−	15.1680i	−0.639255	−	0.639255i	0.311117	−	0.950372i	$-0.399297\pi$
$563$	−15.1680	−	15.1680i	−0.639255	−	0.639255i	−0.950372	+	0.311117i	$0.899297\pi$
$564$	11.6230	+	28.0604i	0.489416	+	1.18156i
$565$			14.6251i			0.615284i
$566$	3.78274	−	1.56686i	0.159000	−	0.0658601i
$567$	1.24971	−	3.01708i	0.0524831	−	0.126705i
$568$	−3.40559	−	1.41064i	−0.142895	−	0.0591892i
$569$	11.9519	−	11.9519i	0.501050	−	0.501050i	−0.410714	−	0.911764i	$-0.634721\pi$
$569$	11.9519	−	11.9519i	0.501050	−	0.501050i	0.911764	+	0.410714i	$0.134721\pi$
$570$	−3.24739	+	3.24739i	−0.136018	+	0.136018i
$571$	−2.52953	−	1.04777i	−0.105858	−	0.0438477i	0.329126	−	0.944286i	$-0.393246\pi$
$571$	−2.52953	−	1.04777i	−0.105858	−	0.0438477i	−0.434984	+	0.900438i	$0.643246\pi$
$572$	−1.63990	+	3.95906i	−0.0685675	+	0.165537i
$573$	11.8460	−	4.90678i	0.494874	−	0.204984i
$574$			0.637722i			0.0266180i
$575$	0.241258	+	0.582449i	0.0100612	+	0.0242898i
$576$	4.59042	+	4.59042i	0.191267	+	0.191267i
$577$	−23.0499			−0.959580			−0.479790	−	0.877383i	$-0.659287\pi$
$577$	−23.0499			−0.959580			−0.479790	+	0.877383i	$0.659287\pi$
$578$	0.391643	+	3.12637i	0.0162902	+	0.130040i
$579$	−16.9383			−0.703932
$580$	23.5574	+	23.5574i	0.978168	+	0.978168i
$581$	−2.11959	−	5.11713i	−0.0879352	−	0.212294i
$582$			3.74906i			0.155404i
$583$	−3.46086	+	1.43354i	−0.143334	+	0.0593710i
$584$	2.89441	−	6.98772i	0.119771	−	0.289154i
$585$	3.64638	+	1.51038i	0.150759	+	0.0624465i
$586$	4.01794	−	4.01794i	0.165980	−	0.165980i
$587$	23.1412	−	23.1412i	0.955139	−	0.955139i	−0.0438970	−	0.999036i	$-0.513977\pi$
$587$	23.1412	−	23.1412i	0.955139	−	0.955139i	0.999036	+	0.0438970i	$0.0139773\pi$
$588$	−17.4717	−	7.23703i	−0.720523	−	0.298450i
$589$	29.6900	−	71.6779i	1.22335	−	2.95344i
$590$	−2.12882	+	0.881785i	−0.0876421	+	0.0363025i
$591$		−	19.6743i		−	0.809294i
$592$	5.17202	+	12.4864i	0.212569	+	0.513187i
$593$	25.5524	+	25.5524i	1.04931	+	1.04931i	0.998719	+	0.0505934i	$0.0161112\pi$
$593$	25.5524	+	25.5524i	1.04931	+	1.04931i	0.0505934	+	0.998719i	$0.483889\pi$
$594$	−1.04754			−0.0429812
$595$	4.66318	+	1.59928i	0.191172	+	0.0655640i
$596$	−2.50303			−0.102528
$597$	−14.3695	−	14.3695i	−0.588105	−	0.588105i
$598$	0.0992152	+	0.239527i	0.00405721	+	0.00979498i
$599$			46.1615i			1.88611i	0.332642	+	0.943053i	$0.392060\pi$
$599$			46.1615i			1.88611i	−0.332642	+	0.943053i	$0.607940\pi$
$600$	−0.966106	+	0.400174i	−0.0394411	+	0.0163370i
$601$	−1.11299	+	2.68700i	−0.0453999	+	0.109605i	−0.944953	−	0.327207i	$-0.893893\pi$
$601$	−1.11299	+	2.68700i	−0.0453999	+	0.109605i	0.899553	+	0.436812i	$0.143893\pi$
$602$	−0.312701	−	0.129525i	−0.0127447	−	0.00527904i
$603$	3.83554	−	3.83554i	0.156195	−	0.156195i
$604$	−17.9517	+	17.9517i	−0.730443	+	0.730443i
$605$	−1.85179	−	0.767036i	−0.0752859	−	0.0311844i
$606$	−0.0684075	+	0.165150i	−0.00277886	+	0.00670877i
$607$	27.8846	−	11.5502i	1.13180	−	0.468807i	0.263409	−	0.964684i	$-0.415153\pi$
$607$	27.8846	−	11.5502i	1.13180	−	0.468807i	0.868393	+	0.495877i	$0.165153\pi$
$608$		−	18.5551i		−	0.752507i
$609$	2.79514	+	6.74807i	0.113265	+	0.273446i
$610$	−0.00399394	−	0.00399394i	−0.000161710	−	0.000161710i
$611$	−23.2631			−0.941125
$612$	3.21707	+	6.57553i	0.130042	+	0.265800i
$613$	−22.3208			−0.901529			−0.450765	−	0.892643i	$-0.648849\pi$
$613$	−22.3208			−0.901529			−0.450765	+	0.892643i	$0.648849\pi$
$614$	−0.0725728	−	0.0725728i	−0.00292880	−	0.00292880i
$615$	−6.40649	−	15.4666i	−0.258335	−	0.623675i
$616$		−	0.438446i		−	0.0176655i
$617$	−18.8814	+	7.82094i	−0.760138	+	0.314859i	−0.728870	−	0.684652i	$-0.759954\pi$
$617$	−18.8814	+	7.82094i	−0.760138	+	0.314859i	−0.0312673	+	0.999511i	$0.509954\pi$
$618$	−1.06761	+	2.57744i	−0.0429456	+	0.103680i
$619$	−3.40671	−	1.41111i	−0.136927	−	0.0567172i	0.313168	−	0.949698i	$-0.398610\pi$
$619$	−3.40671	−	1.41111i	−0.136927	−	0.0567172i	−0.450095	+	0.892981i	$0.648610\pi$
$620$	−25.3169	+	25.3169i	−1.01675	+	1.01675i
$621$	2.56436	−	2.56436i	0.102904	−	0.102904i
$622$	1.35277	+	0.560336i	0.0542412	+	0.0224674i
$623$	−3.69886	+	8.92984i	−0.148192	+	0.357766i
$624$	11.0683	−	4.58464i	0.443087	−	0.183533i
$625$			19.1220i			0.764878i
$626$	0.167401	+	0.404141i	0.00669068	+	0.0161527i
$627$	−8.74150	−	8.74150i	−0.349102	−	0.349102i
$628$	17.2965			0.690205
$629$	0.914340	+	14.6549i	0.0364571	+	0.584327i
$630$	−0.200160			−0.00797457
$631$	8.23198	+	8.23198i	0.327710	+	0.327710i	0.851715	−	0.524005i	$-0.175563\pi$
$631$	8.23198	+	8.23198i	0.327710	+	0.327710i	−0.524005	+	0.851715i	$0.675563\pi$
$632$	2.74560	+	6.62846i	0.109214	+	0.263666i
$633$			19.1840i			0.762494i
$634$	0.846487	−	0.350626i	0.0336183	−	0.0139252i
$635$	5.27978	−	12.7465i	0.209522	−	0.505830i
$636$	9.85066	+	4.08028i	0.390604	+	0.161794i
$637$	10.2423	−	10.2423i	0.405813	−	0.405813i
$638$	1.10820	−	1.10820i	0.0438741	−	0.0438741i
$639$	−4.18509	−	1.73352i	−0.165560	−	0.0685771i
$640$	−4.35590	+	10.5161i	−0.172182	+	0.415684i
$641$	7.56293	−	3.13267i	0.298718	−	0.123733i	−0.228291	−	0.973593i	$-0.573314\pi$
$641$	7.56293	−	3.13267i	0.298718	−	0.123733i	0.527008	+	0.849860i	$0.323314\pi$
$642$		−	1.52242i		−	0.0600851i
$643$	−3.43015	−	8.28111i	−0.135272	−	0.326575i	0.841699	−	0.539946i	$-0.181556\pi$
$643$	−3.43015	−	8.28111i	−0.135272	−	0.326575i	−0.976971	+	0.213371i	$0.931556\pi$
$644$	0.532004	+	0.532004i	0.0209639	+	0.0209639i
$645$	8.88512			0.349851
$646$	2.11650	−	6.17129i	0.0832725	−	0.242806i
$647$	−12.5224			−0.492306			−0.246153	−	0.969231i	$-0.579167\pi$
$647$	−12.5224			−0.492306			−0.246153	+	0.969231i	$0.579167\pi$
$648$	2.84521	+	2.84521i	0.111770	+	0.111770i
$649$	−2.37364	−	5.73047i	−0.0931734	−	0.224940i
$650$		−	0.397000i		−	0.0155716i
$651$	−7.25209	+	3.00392i	−0.284232	+	0.117733i
$652$	12.5291	−	30.2479i	0.490677	−	1.18460i
$653$	11.4043	+	4.72381i	0.446285	+	0.184857i	0.594496	−	0.804099i	$-0.297352\pi$
$653$	11.4043	+	4.72381i	0.446285	+	0.184857i	−0.148211	+	0.988956i	$0.547352\pi$
$654$	0.243076	−	0.243076i	0.00950504	−	0.00950504i
$655$	3.01882	−	3.01882i	0.117955	−	0.117955i
$656$	20.2239	+	8.37701i	0.789611	+	0.327067i
$657$	3.55691	−	8.58713i	0.138768	−	0.335016i
$658$	1.08997	−	0.451480i	0.0424914	−	0.0176005i
$659$		−	29.3851i		−	1.14468i	−0.820016	−	0.572340i	$-0.806036\pi$
$659$		−	29.3851i		−	1.14468i	0.820016	−	0.572340i	$-0.193964\pi$
$660$	2.18322	+	5.27075i	0.0849816	+	0.205164i
$661$	−20.4931	−	20.4931i	−0.797089	−	0.797089i	0.185546	−	0.982636i	$-0.440595\pi$
$661$	−20.4931	−	20.4931i	−0.797089	−	0.797089i	−0.982636	+	0.185546i	$0.940595\pi$
$662$	−5.03057			−0.195519
$663$	12.9905	−	0.810499i	0.504510	−	0.0314772i
$664$	6.82448			0.264841
$665$	−7.21799	−	7.21799i	−0.279901	−	0.279901i
$666$	−0.228146	−	0.550793i	−0.00884048	−	0.0213428i
$667$			5.42570i			0.210084i
$668$	−25.3205	+	10.4881i	−0.979681	+	0.405797i
$669$	10.3177	−	24.9092i	0.398906	−	0.963045i
$670$	2.06113	+	0.853748i	0.0796284	+	0.0329832i
$671$	0.0107511	−	0.0107511i	0.000415042	−	0.000415042i
$672$	−1.32747	+	1.32747i	−0.0512083	+	0.0512083i
$673$	19.5511	+	8.09834i	0.753640	+	0.312168i	0.726226	−	0.687456i	$-0.241273\pi$
$673$	19.5511	+	8.09834i	0.753640	+	0.312168i	0.0274144	+	0.999624i	$0.491273\pi$
$674$	1.89732	−	4.58054i	0.0730821	−	0.176436i
$675$	−5.13053	+	2.12514i	−0.197474	+	0.0817965i
$676$		−	16.2113i		−	0.623510i
$677$	8.89234	+	21.4680i	0.341760	+	0.825082i	0.997538	+	0.0701284i	$0.0223409\pi$
$677$	8.89234	+	21.4680i	0.341760	+	0.825082i	−0.655778	+	0.754954i	$0.727659\pi$
$678$	−1.38470	−	1.38470i	−0.0531791	−	0.0531791i
$679$	−8.33304			−0.319793
$680$	−4.01930	+	4.55421i	−0.154133	+	0.174646i
$681$	−39.6462			−1.51925
$682$	1.19097	+	1.19097i	0.0456047	+	0.0456047i
$683$	8.77395	+	21.1822i	0.335726	+	0.810514i	0.998116	+	0.0613547i	$0.0195421\pi$
$683$	8.77395	+	21.1822i	0.335726	+	0.810514i	−0.662390	+	0.749159i	$0.730458\pi$
$684$		−	15.1576i		−	0.579567i
$685$	−3.74331	+	1.55053i	−0.143025	+	0.0592427i
$686$	−0.577282	+	1.39368i	−0.0220407	+	0.0532110i
$687$	22.9220	+	9.49462i	0.874530	+	0.362242i
$688$	−8.21518	+	8.21518i	−0.313201	+	0.313201i
$689$	−5.77464	+	5.77464i	−0.219996	+	0.219996i
$690$	0.318885	+	0.132087i	0.0121398	+	0.00502845i
$691$	−9.03891	+	21.8218i	−0.343856	+	0.830142i	0.653462	+	0.756959i	$0.273316\pi$
$691$	−9.03891	+	21.8218i	−0.343856	+	0.830142i	−0.997319	+	0.0731832i	$0.976684\pi$
$692$	−32.2031	+	13.3390i	−1.22418	+	0.507071i
$693$		−	0.538801i		−	0.0204674i
$694$	1.01569	+	2.45208i	0.0385549	+	0.0930798i
$695$	−8.21002	−	8.21002i	−0.311424	−	0.311424i
$696$	−8.99959			−0.341128
$697$	17.8312	+	15.7368i	0.675404	+	0.596074i
$698$	−5.66358			−0.214370
$699$	−8.75599	−	8.75599i	−0.331182	−	0.331182i
$700$	−0.440882	−	1.06438i	−0.0166638	−	0.0402299i
$701$			12.4090i			0.468682i	0.972155	+	0.234341i	$0.0752932\pi$
$701$			12.4090i			0.468682i	−0.972155	+	0.234341i	$0.924707\pi$
$702$	−2.10988	+	0.873942i	−0.0796324	+	0.0329848i
$703$	11.6350	−	28.0894i	0.438822	−	1.05941i
$704$	−6.64022	−	2.75047i	−0.250263	−	0.103662i
$705$	−21.8995	+	21.8995i	−0.824782	+	0.824782i
$706$	−1.51041	+	1.51041i	−0.0568451	+	0.0568451i
$707$	−0.367080	−	0.152049i	−0.0138055	−	0.00571841i
$708$	−6.75609	+	16.3106i	−0.253909	+	0.612991i
$709$	15.0811	−	6.24678i	0.566381	−	0.234603i	−0.0810719	−	0.996708i	$-0.525834\pi$
$709$	15.0811	−	6.24678i	0.566381	−	0.234603i	0.647453	+	0.762106i	$0.275834\pi$
$710$		−	1.86311i		−	0.0699213i
$711$	3.37404	+	8.14565i	0.126536	+	0.305486i
$712$	−8.42115	−	8.42115i	−0.315596	−	0.315596i
$713$	−5.83095			−0.218371
$714$	−0.592927	+	0.290089i	−0.0221898	+	0.0108563i
$715$	−4.36965			−0.163416
$716$	−5.30821	−	5.30821i	−0.198377	−	0.198377i
$717$	−2.48745	−	6.00523i	−0.0928954	−	0.224269i
$718$			6.26371i			0.233760i
$719$	8.28958	−	3.43366i	0.309149	−	0.128054i	−0.222715	−	0.974884i	$-0.571492\pi$
$719$	8.28958	−	3.43366i	0.309149	−	0.128054i	0.531864	+	0.846830i	$0.321492\pi$
$720$	−2.62927	+	6.34762i	−0.0979872	+	0.236562i
$721$	−5.72888	−	2.37298i	−0.213354	−	0.0883743i
$722$	−7.06227	+	7.06227i	−0.262830	+	0.262830i
$723$	1.87561	−	1.87561i	0.0697546	−	0.0697546i
$724$	−24.3611	−	10.0907i	−0.905372	−	0.375017i
$725$	3.17942	−	7.67580i	0.118081	−	0.285072i
$726$	0.247949	−	0.102704i	0.00920227	−	0.00381170i
$727$		−	51.7088i		−	1.91777i	−0.283791	−	0.958886i	$-0.591592\pi$
$727$		−	51.7088i		−	1.91777i	0.283791	−	0.958886i	$-0.408408\pi$
$728$	−0.365785	−	0.883084i	−0.0135569	−	0.0327293i
$729$	20.8577	+	20.8577i	0.772507	+	0.772507i
$730$	3.82280			0.141488
$731$	−11.3380	+	5.54711i	−0.419352	+	0.205167i
$732$	−0.0432762			−0.00159953
$733$	−14.7147	−	14.7147i	−0.543501	−	0.543501i	0.381053	−	0.924553i	$-0.375562\pi$
$733$	−14.7147	−	14.7147i	−0.543501	−	0.543501i	−0.924553	+	0.381053i	$0.875562\pi$
$734$	0.363482	+	0.877522i	0.0134164	+	0.0323899i
$735$		−	19.2837i		−	0.711291i
$736$	−1.28839	+	0.533668i	−0.0474906	+	0.0196713i
$737$	−2.29816	+	5.54826i	−0.0846540	+	0.204373i
$738$	−0.892108	−	0.369523i	−0.0328389	−	0.0136023i
$739$	−9.11969	+	9.11969i	−0.335473	+	0.335473i	−0.854660	−	0.519187i	$-0.826235\pi$
$739$	−9.11969	+	9.11969i	−0.335473	+	0.335473i	0.519187	+	0.854660i	$0.326235\pi$
$740$	−9.92128	+	9.92128i	−0.364714	+	0.364714i
$741$	−24.8993	−	10.3136i	−0.914699	−	0.378881i
$742$	0.158493	−	0.382636i	0.00581846	−	0.0140470i
$743$	−35.6986	+	14.7868i	−1.30965	+	0.542477i	−0.924784	−	0.380493i	$-0.875754\pi$
$743$	−35.6986	+	14.7868i	−1.30965	+	0.542477i	−0.384871	+	0.922970i	$0.625754\pi$
$744$		−	9.67177i		−	0.354584i
$745$	−0.976734	−	2.35804i	−0.0357848	−	0.0863921i
$746$	−1.76875	−	1.76875i	−0.0647585	−	0.0647585i
$747$	8.38653			0.306847
$748$	−6.07654	−	5.36282i	−0.222180	−	0.196084i
$749$	3.38388			0.123644
$750$	−2.27559	−	2.27559i	−0.0830928	−	0.0830928i
$751$	6.63762	+	16.0246i	0.242210	+	0.584747i	0.997502	−	0.0706420i	$-0.0225048\pi$
$751$	6.63762	+	16.0246i	0.242210	+	0.584747i	−0.755292	+	0.655389i	$0.772505\pi$
$752$		−	40.4965i		−	1.47675i
$753$	16.9951	−	7.03962i	0.619337	−	0.256538i
$754$	1.30751	−	3.15660i	0.0476166	−	0.114957i
$755$	−23.9169	−	9.90672i	−0.870426	−	0.360542i
$756$	−4.68618	+	4.68618i	−0.170435	+	0.170435i
$757$	1.42718	−	1.42718i	0.0518716	−	0.0518716i	−0.680695	−	0.732567i	$-0.738322\pi$
$757$	1.42718	−	1.42718i	0.0518716	−	0.0518716i	0.732567	+	0.680695i	$0.238322\pi$
$758$	−3.95871	−	1.63975i	−0.143787	−	0.0595585i
$759$	−0.355558	+	0.858392i	−0.0129059	+	0.0311577i
$760$	11.6200	−	4.81314i	0.421500	−	0.174591i
$761$		−	31.8985i		−	1.15632i	−0.815924	−	0.578160i	$-0.803771\pi$
$761$		−	31.8985i		−	1.15632i	0.815924	−	0.578160i	$-0.196229\pi$
$762$	0.706948	+	1.70672i	0.0256100	+	0.0618280i
$763$	0.540286	+	0.540286i	0.0195597	+	0.0195597i
$764$	−17.4055			−0.629711
$765$	−4.93928	+	5.59663i	−0.178580	+	0.202346i
$766$	−3.78162			−0.136635
$767$	−9.56159	−	9.56159i	−0.345249	−	0.345249i
$768$	7.38224	+	17.8223i	0.266384	+	0.643107i
$769$			25.7904i			0.930026i	0.885304	+	0.465013i	$0.153950\pi$
$769$			25.7904i			0.930026i	−0.885304	+	0.465013i	$0.846050\pi$
$770$	0.204735	−	0.0848042i	0.00737815	−	0.00305613i
$771$	−11.9731	+	28.9057i	−0.431202	+	1.04101i
$772$	21.2430	+	8.79915i	0.764553	+	0.316688i
$773$	−23.2460	+	23.2460i	−0.836101	+	0.836101i	−0.988343	−	0.152243i	$-0.951351\pi$
$773$	−23.2460	+	23.2460i	−0.836101	+	0.836101i	0.152243	+	0.988343i	$0.451351\pi$
$774$	0.362384	−	0.362384i	0.0130256	−	0.0130256i
$775$	8.24911	+	3.41689i	0.296317	+	0.122738i
$776$	3.92917	−	9.48587i	0.141049	−	0.340523i
$777$	−2.84197	+	1.17718i	−0.101955	+	0.0422312i
$778$			3.18990i			0.114364i
$779$	−18.8450	−	45.4958i	−0.675191	−	1.63005i
$780$	8.79453	+	8.79453i	0.314895	+	0.314895i
$781$	5.01522			0.179459
$782$	−0.489383	+	0.0305334i	−0.0175003	+	0.00109187i
$783$	−47.7925			−1.70797
$784$	17.8297	+	17.8297i	0.636776	+	0.636776i
$785$	6.74944	+	16.2946i	0.240898	+	0.581579i
$786$			0.571642i			0.0203898i
$787$	−17.5631	+	7.27488i	−0.626058	+	0.259322i	−0.673077	−	0.739572i	$-0.735028\pi$
$787$	−17.5631	+	7.27488i	−0.626058	+	0.259322i	0.0470194	+	0.998894i	$0.485028\pi$
$788$	−10.2205	+	24.6744i	−0.364089	+	0.878989i
$789$	20.4753	+	8.48116i	0.728941	+	0.301937i
$790$	−2.56416	+	2.56416i	−0.0912286	+	0.0912286i
$791$	3.07778	−	3.07778i	0.109433	−	0.109433i
$792$	0.613341	+	0.254054i	0.0217941	+	0.00902742i
$793$	0.0126846	−	0.0306234i	0.000450445	−	0.00108747i
$794$	−1.68439	+	0.697697i	−0.0597767	+	0.0247603i
$795$			10.8723i			0.385600i
$796$	10.5567	+	25.4861i	0.374172	+	0.903331i
$797$	13.5592	+	13.5592i	0.480291	+	0.480291i	0.905225	−	0.424933i	$-0.139703\pi$
$797$	13.5592	+	13.5592i	0.480291	+	0.480291i	−0.424933	+	0.905225i	$0.639703\pi$
$798$	1.36679			0.0483839
$799$	14.2730	−	41.6174i	0.504944	−	1.47232i
$800$	2.13542			0.0754986
$801$	−10.3487	−	10.3487i	−0.365652	−	0.365652i
$802$	−1.23734	−	2.98720i	−0.0436920	−	0.105482i
$803$			10.2904i			0.363141i
$804$	15.7920	−	6.54127i	0.556942	−	0.230693i
$805$	−0.293589	+	0.708787i	−0.0103477	+	0.0249814i
$806$	3.39237	+	1.40516i	0.119491	+	0.0494948i
$807$	−1.32517	+	1.32517i	−0.0466480	+	0.0466480i
$808$	0.346169	−	0.346169i	0.0121782	−	0.0121782i
$809$	−52.1544	−	21.6031i	−1.83365	−	0.759524i	−0.964023	−	0.265820i	$-0.914357\pi$
$809$	−52.1544	−	21.6031i	−1.83365	−	0.759524i	−0.869630	−	0.493704i	$-0.835643\pi$
$810$	−0.778271	+	1.87891i	−0.0273456	+	0.0660182i
$811$	−8.70390	+	3.60527i	−0.305635	+	0.126598i	−0.530230	−	0.847854i	$-0.677894\pi$
$811$	−8.70390	+	3.60527i	−0.305635	+	0.126598i	0.224594	+	0.974452i	$0.427894\pi$
$812$		−	9.91506i		−	0.347950i
$813$	8.56204	+	20.6706i	0.300284	+	0.724949i
$814$	0.466722	+	0.466722i	0.0163586	+	0.0163586i
$815$	33.3849			1.16942
$816$	1.41092	+	22.6139i	0.0493920	+	0.791645i
$817$	26.1359			0.914381
$818$	−3.01625	−	3.01625i	−0.105461	−	0.105461i
$819$	−0.449510	−	1.08521i	−0.0157071	−	0.0379204i
$820$			22.7254i			0.793605i
$821$	44.4602	−	18.4160i	1.55167	−	0.642723i	0.568053	−	0.822992i	$-0.307697\pi$
$821$	44.4602	−	18.4160i	1.55167	−	0.642723i	0.983617	+	0.180269i	$0.0576968\pi$
$822$	0.207612	−	0.501219i	0.00724129	−	0.0174820i
$823$	10.8859	+	4.50911i	0.379460	+	0.157178i	0.564257	−	0.825599i	$-0.309163\pi$
$823$	10.8859	+	4.50911i	0.379460	+	0.157178i	−0.184797	+	0.982777i	$0.559163\pi$
$824$	5.40253	−	5.40253i	0.188206	−	0.188206i
$825$	1.00602	−	1.00602i	0.0350252	−	0.0350252i
$826$	0.633565	+	0.262431i	0.0220446	+	0.00913115i
$827$	−11.5802	+	27.9571i	−0.402683	+	0.972163i	0.584329	+	0.811517i	$0.301358\pi$
$827$	−11.5802	+	27.9571i	−0.402683	+	0.972163i	−0.987012	+	0.160646i	$0.948642\pi$
$828$	−1.05249	+	0.435954i	−0.0365764	+	0.0151504i
$829$		−	4.82405i		−	0.167546i	−0.996485	−	0.0837731i	$-0.973303\pi$
$829$		−	4.82405i		−	0.167546i	0.996485	−	0.0837731i	$-0.0266971\pi$
$830$	1.31999	+	3.18674i	0.0458175	+	0.110613i
$831$	22.4678	+	22.4678i	0.779400	+	0.779400i
$832$	−15.6689			−0.543221
$833$	12.0391	+	24.6073i	0.417131	+	0.852594i
$834$	1.55464			0.0538329
$835$	−19.7612	−	19.7612i	−0.683864	−	0.683864i
$836$	6.42202	+	15.5041i	0.222110	+	0.536221i
$837$		−	51.3622i		−	1.77534i
$838$	−5.68010	+	2.35278i	−0.196216	+	0.0812753i
$839$	−18.1179	+	43.7406i	−0.625501	+	1.51009i	0.219658	+	0.975577i	$0.429506\pi$
$839$	−18.1179	+	43.7406i	−0.625501	+	1.51009i	−0.845159	+	0.534516i	$0.820494\pi$
$840$	−1.17566	−	0.486975i	−0.0405642	−	0.0168022i
$841$	30.0538	−	30.0538i	1.03634	−	1.03634i
$842$	2.68379	−	2.68379i	0.0924896	−	0.0924896i
$843$	22.6900	+	9.39852i	0.781486	+	0.323702i
$844$	9.96572	−	24.0594i	0.343034	−	0.828158i
$845$	15.2722	−	6.32597i	0.525381	−	0.217620i
$846$			1.78636i			0.0614164i
$847$	0.228280	+	0.551118i	0.00784381	+	0.0189366i
$848$	−10.0525	−	10.0525i	−0.345204	−	0.345204i
$849$	31.9884			1.09784
$850$	0.710227	+	0.243579i	0.0243606	+	0.00835468i
$851$	−2.28505			−0.0783306
$852$	−10.0938	−	10.0938i	−0.345809	−	0.345809i
$853$	−12.0474	−	29.0850i	−0.412495	−	0.995850i	−0.984466	−	0.175576i	$-0.943821\pi$
$853$	−12.0474	−	29.0850i	−0.412495	−	0.995850i	0.571971	−	0.820274i	$-0.306179\pi$
$854$			0.00168101i			5.75229e-5i
$855$	14.2796	−	5.91482i	0.488353	−	0.202283i
$856$	−1.59556	+	3.85202i	−0.0545351	+	0.131659i
$857$	34.4497	+	14.2696i	1.17678	+	0.487439i	0.883429	−	0.468566i	$-0.155229\pi$
$857$	34.4497	+	14.2696i	1.17678	+	0.487439i	0.293352	+	0.956004i	$0.405229\pi$
$858$	0.413717	−	0.413717i	0.0141241	−	0.0141241i
$859$	18.3048	−	18.3048i	0.624552	−	0.624552i	−0.322140	−	0.946692i	$-0.604402\pi$
$859$	18.3048	−	18.3048i	0.624552	−	0.624552i	0.946692	+	0.322140i	$0.104402\pi$
$860$	−11.1432	−	4.61566i	−0.379980	−	0.157393i
$861$	−1.90666	+	4.60308i	−0.0649788	+	0.156873i
$862$	0.916895	−	0.379790i	0.0312296	−	0.0129357i
$863$			7.00354i			0.238403i	0.992870	+	0.119202i	$0.0380335\pi$
$863$			7.00354i			0.238403i	−0.992870	+	0.119202i	$0.961967\pi$
$864$	−4.70084	−	11.3488i	−0.159926	−	0.386095i
$865$	−25.1326	−	25.1326i	−0.854535	−	0.854535i
$866$	−5.86367			−0.199256
$867$	−6.52034	+	23.7371i	−0.221442	+	0.806155i
$868$	10.6556			0.361675
$869$	−6.90233	−	6.90233i	−0.234145	−	0.234145i
$870$	−1.74070	−	4.20242i	−0.0590153	−	0.142475i
$871$			13.0922i			0.443612i
$872$	−0.869786	+	0.360277i	−0.0294547	+	0.0122005i
$873$	4.82852	−	11.6571i	0.163421	−	0.394533i
$874$	0.938014	+	0.388538i	0.0317288	+	0.0131425i
$875$	5.05796	−	5.05796i	0.170990	−	0.170990i
$876$	20.7109	−	20.7109i	0.699756	−	0.699756i
$877$	−17.5964	−	7.28866i	−0.594187	−	0.246120i	0.0652637	−	0.997868i	$-0.479211\pi$
$877$	−17.5964	−	7.28866i	−0.594187	−	0.246120i	−0.659451	+	0.751748i	$0.729211\pi$
$878$	1.72429	−	4.16279i	0.0581918	−	0.140488i
$879$	41.0144	−	16.9887i	1.38338	−	0.573015i
$880$		−	7.60670i		−	0.256422i
$881$	3.60457	+	8.70221i	0.121441	+	0.293185i	0.972896	−	0.231243i	$-0.0742792\pi$
$881$	3.60457	+	8.70221i	0.121441	+	0.293185i	−0.851455	+	0.524428i	$0.824279\pi$
$882$	−0.786498	−	0.786498i	−0.0264828	−	0.0264828i
$883$	−9.67910			−0.325728			−0.162864	−	0.986649i	$-0.552073\pi$
$883$	−9.67910			−0.325728			−0.162864	+	0.986649i	$0.552073\pi$
$884$	−16.7130	−	5.73186i	−0.562118	−	0.192783i
$885$	−18.0022			−0.605138
$886$	−0.482943	−	0.482943i	−0.0162248	−	0.0162248i
$887$	14.3805	+	34.7176i	0.482849	+	1.16570i	0.958250	+	0.285932i	$0.0923031\pi$
$887$	14.3805	+	34.7176i	0.482849	+	1.16570i	−0.475401	+	0.879769i	$0.657697\pi$
$888$		−	3.79021i		−	0.127191i
$889$	−3.79354	+	1.57133i	−0.127231	+	0.0527008i
$890$	2.30350	−	5.56114i	0.0772134	−	0.186410i
$891$	−5.05775	−	2.09499i	−0.169441	−	0.0701848i
$892$	−25.8798	+	25.8798i	−0.866518	+	0.866518i
$893$	−64.4182	+	64.4182i	−2.15567	+	2.15567i
$894$	0.315736	+	0.130782i	0.0105598	+	0.00437400i
$895$	2.92936	−	7.07211i	0.0979178	−	0.236395i
$896$	3.12973	−	1.29638i	0.104557	−	0.0433089i
$897$			2.02554i			0.0676309i
$898$	0.0608702	+	0.146954i	0.00203126	+	0.00490390i
$899$	54.3363	+	54.3363i	1.81222	+	1.81222i
$900$	1.74443			0.0581476
$901$	−6.78772	−	13.8738i	−0.226132	−	0.462202i
$902$	1.06906			0.0355958
$903$	−1.86983	−	1.86983i	−0.0622239	−	0.0622239i
$904$	2.05234	+	4.95479i	0.0682599	+	0.164794i
$905$		−	26.8876i		−	0.893773i
$906$	3.20241	−	1.32648i	0.106393	−	0.0440694i
$907$	13.3874	−	32.3200i	0.444521	−	1.07317i	−0.529824	−	0.848108i	$-0.677742\pi$
$907$	13.3874	−	32.3200i	0.444521	−	1.07317i	0.974345	−	0.225061i	$-0.0722580\pi$
$908$	49.7219	+	20.5955i	1.65008	+	0.683485i
$909$	0.425403	−	0.425403i	0.0141097	−	0.0141097i
$910$	0.341612	−	0.341612i	0.0113243	−	0.0113243i
$911$	−24.2088	−	10.0276i	−0.802074	−	0.332230i	−0.0562874	−	0.998415i	$-0.517926\pi$
$911$	−24.2088	−	10.0276i	−0.802074	−	0.332230i	−0.745787	+	0.666185i	$0.767926\pi$
$912$	17.9540	−	43.3447i	0.594516	−	1.43529i
$913$	−8.57823	+	3.55322i	−0.283898	+	0.117594i
$914$			7.14333i			0.236281i
$915$	−0.0168872	−	0.0407694i	−0.000558275	−	0.00134780i
$916$	−23.8152	−	23.8152i	−0.786875	−	0.786875i
$917$	−1.27059			−0.0419585
$918$	−0.268955	−	4.31075i	−0.00887683	−	0.142276i
$919$	6.09791			0.201152			0.100576	−	0.994929i	$-0.467932\pi$
$919$	6.09791			0.201152			0.100576	+	0.994929i	$0.467932\pi$
$920$	−0.668410	−	0.668410i	−0.0220368	−	0.0220368i
$921$	−0.306853	−	0.740809i	−0.0101112	−	0.0244105i
$922$		−	2.50915i		−	0.0826344i
$923$	10.1013	−	4.18408i	0.332487	−	0.137721i
$924$	0.649755	−	1.56865i	0.0213754	−	0.0516047i
$925$	3.23269	+	1.33902i	0.106290	+	0.0440268i
$926$	−2.06119	+	2.06119i	−0.0677350	+	0.0677350i
$927$	6.63911	−	6.63911i	0.218057	−	0.218057i
$928$	16.9790	+	7.03293i	0.557363	+	0.230867i
$929$	14.6692	−	35.4145i	0.481280	−	1.16191i	−0.477722	−	0.878511i	$-0.658537\pi$
$929$	14.6692	−	35.4145i	0.481280	−	1.16191i	0.959002	−	0.283401i	$-0.0914626\pi$
$930$	4.51631	−	1.87071i	0.148095	−	0.0613432i
$931$		−	56.7239i		−	1.85905i
$932$	6.43266	+	15.5298i	0.210709	+	0.508696i
$933$	8.08903	+	8.08903i	0.264823	+	0.264823i
$934$	−6.14157			−0.200958
$935$	2.68099	−	7.81724i	0.0876778	−	0.255651i
$936$	1.44730			0.0473064
$937$	40.8743	+	40.8743i	1.33530	+	1.33530i	0.900548	+	0.434756i	$0.143166\pi$
$937$	40.8743	+	40.8743i	1.33530	+	1.33530i	0.434756	+	0.900548i	$0.356834\pi$
$938$	−0.254087	−	0.613420i	−0.00829624	−	0.0200289i
$939$			3.41759i			0.111529i
$940$	38.8414	−	16.0886i	1.26687	−	0.524753i
$941$	−1.62183	+	3.91544i	−0.0528701	+	0.127640i	−0.948108	−	0.317949i	$-0.897006\pi$
$941$	−1.62183	+	3.91544i	−0.0528701	+	0.127640i	0.895238	+	0.445589i	$0.147006\pi$
$942$	−2.18180	−	0.903731i	−0.0710869	−	0.0294452i
$943$	−2.61704	+	2.61704i	−0.0852225	+	0.0852225i
$944$	16.6448	−	16.6448i	0.541743	−	0.541743i
$945$	−6.24338	−	2.58609i	−0.203097	−	0.0841256i
$946$	−0.217132	+	0.524204i	−0.00705958	+	0.0170433i
$947$	17.9207	−	7.42301i	0.582345	−	0.241215i	−0.0720084	−	0.997404i	$-0.522941\pi$
$947$	17.9207	−	7.42301i	0.582345	−	0.241215i	0.654354	+	0.756189i	$0.272941\pi$
$948$			27.7838i			0.902376i
$949$	8.58506	+	20.7262i	0.278683	+	0.672800i
$950$	−1.09934	−	1.09934i	−0.0356672	−	0.0356672i
$951$	7.15826			0.232122
$952$	1.80425	−	0.112570i	0.0584761	−	0.00364841i
$953$	−8.61141			−0.278951			−0.139475	−	0.990226i	$-0.544542\pi$
$953$	−8.61141			−0.278951			−0.139475	+	0.990226i	$0.544542\pi$
$954$	0.443432	+	0.443432i	0.0143566	+	0.0143566i
$955$	−6.79200	−	16.3973i	−0.219784	−	0.530605i
$956$			8.82358i			0.285375i
$957$	11.3123	−	4.68571i	0.365675	−	0.151467i
$958$	−0.256288	+	0.618734i	−0.00828029	+	0.0199904i
$959$	1.11406	+	0.461459i	0.0359749	+	0.0149013i
$960$	−14.7504	+	14.7504i	−0.476067	+	0.476067i
$961$	−36.4744	+	36.4744i	−1.17659	+	1.17659i
$962$	1.32941	+	0.550660i	0.0428620	+	0.0177540i
$963$	−1.96077	+	4.73371i	−0.0631848	+	0.152542i
$964$	−3.32662	+	1.37793i	−0.107143	+	0.0443802i
$965$			23.4461i			0.754757i
$966$	−0.0393108	−	0.0949046i	−0.00126480	−	0.00305350i
$967$	−36.0986	−	36.0986i	−1.16085	−	1.16085i	−0.984289	−	0.176563i	$-0.943502\pi$
$967$	−36.0986	−	36.0986i	−1.16085	−	1.16085i	−0.176563	−	0.984289i	$-0.556498\pi$
$968$	−0.734999			−0.0236238
$969$	33.7278	−	38.2166i	1.08349	−	1.22769i
$970$	5.18948			0.166624
$971$	−1.31533	−	1.31533i	−0.0422109	−	0.0422109i	0.685686	−	0.727897i	$-0.259502\pi$
$971$	−1.31533	−	1.31533i	−0.0422109	−	0.0422109i	−0.727897	+	0.685686i	$0.759502\pi$
$972$	−6.79161	−	16.3964i	−0.217841	−	0.525915i
$973$			3.45551i			0.110778i
$974$	−6.23294	+	2.58177i	−0.199716	+	0.0827252i
$975$	1.18695	−	2.86556i	0.0380129	−	0.0917712i
$976$	0.0533093	+	0.0220814i	0.00170639	+	0.000706810i
$977$	−7.12449	+	7.12449i	−0.227933	+	0.227933i	−0.811829	−	0.583896i	$-0.801528\pi$
$977$	−7.12449	+	7.12449i	−0.227933	+	0.227933i	0.583896	+	0.811829i	$0.301528\pi$
$978$	−3.16087	+	3.16087i	−0.101073	+	0.101073i
$979$	14.9698	+	6.20068i	0.478435	+	0.198174i
$980$	−10.0176	+	24.1845i	−0.319999	+	0.772546i
$981$	−1.06887	+	0.442741i	−0.0341264	+	0.0141356i
$982$		−	1.87097i		−	0.0597051i
$983$	−10.4310	−	25.1826i	−0.332697	−	0.803201i	−0.998376	−	0.0569632i	$-0.981858\pi$
$983$	−10.4310	−	25.1826i	−0.332697	−	0.803201i	0.665680	−	0.746238i	$-0.268142\pi$
$984$	−4.34087	−	4.34087i	−0.138382	−	0.138382i
$985$	−27.2334			−0.867727
$986$	4.84489	+	4.27583i	0.154293	+	0.136170i
$987$	9.21725			0.293388
$988$	25.8695	+	25.8695i	0.823018	+	0.823018i
$989$	−0.751704	−	1.81477i	−0.0239028	−	0.0577065i
$990$			0.335543i			0.0106643i
$991$	2.89202	−	1.19791i	0.0918680	−	0.0380530i	−0.336276	−	0.941763i	$-0.609168\pi$
$991$	2.89202	−	1.19791i	0.0918680	−	0.0380530i	0.428144	+	0.903710i	$0.359168\pi$
$992$	−7.55823	+	18.2472i	−0.239974	+	0.579348i
$993$	−36.3107	−	15.0404i	−1.15229	−	0.477292i
$994$	−0.392081	+	0.392081i	−0.0124361	+	0.0124361i
$995$	−19.8904	+	19.8904i	−0.630568	+	0.630568i
$996$	24.4162	+	10.1135i	0.773658	+	0.320460i
$997$	−8.98503	+	21.6918i	−0.284559	+	0.686986i	−0.999931	−	0.0117581i	$-0.996257\pi$
$997$	−8.98503	+	21.6918i	−0.284559	+	0.686986i	0.715372	+	0.698744i	$0.246257\pi$
$998$	1.23163	−	0.510158i	0.0389865	−	0.0161488i
$999$		−	20.1280i		−	0.636821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.h.a.100.8	✓	56
17.5	odd	16		3179.2.a.bi.1.13		28
17.8	even	8	inner	187.2.h.a.144.8	yes	56
17.12	odd	16		3179.2.a.bh.1.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.8	✓	56	1.1	even	1	trivial
187.2.h.a.144.8	yes	56	17.8	even	8	inner
3179.2.a.bh.1.13		28	17.12	odd	16
3179.2.a.bi.1.13		28	17.5	odd	16

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.131056 + 0.131056i) q^{2} +(0.554134 + 1.33780i) q^{3} -1.96565i q^{4} +(1.85179 - 0.767036i) q^{5} +(-0.102704 + 0.247949i) q^{6} +(-0.551118 - 0.228280i) q^{7} +(0.519723 - 0.519723i) q^{8} +(0.638682 - 0.638682i) q^{9} +O(q^{10})\)	\(q+(0.131056 + 0.131056i) q^{2} +(0.554134 + 1.33780i) q^{3} -1.96565i q^{4} +(1.85179 - 0.767036i) q^{5} +(-0.102704 + 0.247949i) q^{6} +(-0.551118 - 0.228280i) q^{7} +(0.519723 - 0.519723i) q^{8} +(0.638682 - 0.638682i) q^{9} +(0.343213 + 0.142164i) q^{10} +(-0.382683 + 0.923880i) q^{11} +(2.62964 - 1.08923i) q^{12} +2.18007i q^{13} +(-0.0423098 - 0.102145i) q^{14} +(2.05228 + 2.05228i) q^{15} -3.79507 q^{16} +(-3.90011 - 1.33758i) q^{17} +0.167407 q^{18} +(6.03686 + 6.03686i) q^{19} +(-1.50772 - 3.63997i) q^{20} -0.863782i q^{21} +(-0.171233 + 0.0709271i) q^{22} +(0.245547 - 0.592803i) q^{23} +(0.983280 + 0.407288i) q^{24} +(-0.694756 + 0.694756i) q^{25} +(-0.285712 + 0.285712i) q^{26} +(5.22174 + 2.16291i) q^{27} +(-0.448719 + 1.08330i) q^{28} +(-7.81225 + 3.23594i) q^{29} +0.537928i q^{30} +(-3.47763 - 8.39575i) q^{31} +(-1.53681 - 1.53681i) q^{32} -1.44802 q^{33} +(-0.335836 - 0.686432i) q^{34} -1.19565 q^{35} +(-1.25542 - 1.25542i) q^{36} +(-1.36283 - 3.29015i) q^{37} +1.58234i q^{38} +(-2.91649 + 1.20805i) q^{39} +(0.563771 - 1.36106i) q^{40} +(-5.32899 - 2.20734i) q^{41} +(0.113204 - 0.113204i) q^{42} +(2.16470 - 2.16470i) q^{43} +(1.81602 + 0.752221i) q^{44} +(0.692812 - 1.67260i) q^{45} +(0.109871 - 0.0455101i) q^{46} +10.6708i q^{47} +(-2.10298 - 5.07704i) q^{48} +(-4.69813 - 4.69813i) q^{49} -0.182104 q^{50} +(-0.371777 - 5.95876i) q^{51} +4.28525 q^{52} +(2.64883 + 2.64883i) q^{53} +(0.400878 + 0.967804i) q^{54} +2.00436i q^{55} +(-0.405071 + 0.167786i) q^{56} +(-4.73087 + 11.4213i) q^{57} +(-1.44793 - 0.599754i) q^{58} +(-4.38591 + 4.38591i) q^{59} +(4.03406 - 4.03406i) q^{60} +(-0.0140470 - 0.00581845i) q^{61} +(0.644550 - 1.55608i) q^{62} +(-0.497788 + 0.206190i) q^{63} +7.18732i q^{64} +(1.67219 + 4.03703i) q^{65} +(-0.189772 - 0.189772i) q^{66} +6.00539 q^{67} +(-2.62921 + 7.66625i) q^{68} +0.929117 q^{69} +(-0.156698 - 0.156698i) q^{70} +(-1.91924 - 4.63346i) q^{71} -0.663876i q^{72} +(9.50711 - 3.93797i) q^{73} +(0.252588 - 0.609802i) q^{74} +(-1.31443 - 0.544455i) q^{75} +(11.8663 - 11.8663i) q^{76} +(0.421807 - 0.421807i) q^{77} +(-0.540547 - 0.223902i) q^{78} +(-3.73551 + 9.01833i) q^{79} +(-7.02767 + 2.91096i) q^{80} +5.47447i q^{81} +(-0.409112 - 0.987683i) q^{82} +(6.56549 + 6.56549i) q^{83} -1.69789 q^{84} +(-8.24816 + 0.514616i) q^{85} +0.567394 q^{86} +(-8.65806 - 8.65806i) q^{87} +(0.281272 + 0.679051i) q^{88} -16.2031i q^{89} +(0.310002 - 0.128407i) q^{90} +(0.497668 - 1.20148i) q^{91} +(-1.16524 - 0.482659i) q^{92} +(9.30474 - 9.30474i) q^{93} +(-1.39848 + 1.39848i) q^{94} +(15.8095 + 6.54850i) q^{95} +(1.20435 - 2.90755i) q^{96} +(12.9060 - 5.34582i) q^{97} -1.23144i q^{98} +(0.345652 + 0.834479i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 16 q^{6}+O(q^{10}) \) 56 * q - 16 * q^6	\( 56 q - 16 q^{6} - 16 q^{10} - 16 q^{14} + 24 q^{15} - 32 q^{16} + 8 q^{17} - 24 q^{19} + 16 q^{20} - 24 q^{24} - 8 q^{25} - 48 q^{27} - 40 q^{32} + 16 q^{33} + 64 q^{34} + 32 q^{35} + 64 q^{36} + 8 q^{37} - 32 q^{39} + 96 q^{40} - 24 q^{41} - 8 q^{42} - 32 q^{43} + 16 q^{44} - 32 q^{45} - 16 q^{46} - 24 q^{48} - 112 q^{50} - 48 q^{51} + 8 q^{53} - 72 q^{54} + 64 q^{56} + 40 q^{57} + 16 q^{58} + 16 q^{59} - 8 q^{60} - 64 q^{61} + 56 q^{62} + 16 q^{63} + 56 q^{65} + 24 q^{67} - 88 q^{68} - 64 q^{69} - 96 q^{70} - 16 q^{71} + 8 q^{73} - 48 q^{74} + 40 q^{75} + 88 q^{76} + 136 q^{78} - 32 q^{80} + 104 q^{82} - 56 q^{83} + 80 q^{84} - 8 q^{85} - 32 q^{86} + 56 q^{87} - 32 q^{91} + 40 q^{92} + 8 q^{93} + 16 q^{94} + 48 q^{95} + 64 q^{96} - 16 q^{97}+O(q^{100}) \) 56 * q - 16 * q^6 - 16 * q^10 - 16 * q^14 + 24 * q^15 - 32 * q^16 + 8 * q^17 - 24 * q^19 + 16 * q^20 - 24 * q^24 - 8 * q^25 - 48 * q^27 - 40 * q^32 + 16 * q^33 + 64 * q^34 + 32 * q^35 + 64 * q^36 + 8 * q^37 - 32 * q^39 + 96 * q^40 - 24 * q^41 - 8 * q^42 - 32 * q^43 + 16 * q^44 - 32 * q^45 - 16 * q^46 - 24 * q^48 - 112 * q^50 - 48 * q^51 + 8 * q^53 - 72 * q^54 + 64 * q^56 + 40 * q^57 + 16 * q^58 + 16 * q^59 - 8 * q^60 - 64 * q^61 + 56 * q^62 + 16 * q^63 + 56 * q^65 + 24 * q^67 - 88 * q^68 - 64 * q^69 - 96 * q^70 - 16 * q^71 + 8 * q^73 - 48 * q^74 + 40 * q^75 + 88 * q^76 + 136 * q^78 - 32 * q^80 + 104 * q^82 - 56 * q^83 + 80 * q^84 - 8 * q^85 - 32 * q^86 + 56 * q^87 - 32 * q^91 + 40 * q^92 + 8 * q^93 + 16 * q^94 + 48 * q^95 + 64 * q^96 - 16 * q^97

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