LMFDB - Embedded newform 96.2.n.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("96.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	96.13
Dual form			96.2.n.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.603367 + 1.27904i) q^{2} +(0.382683 - 0.923880i) q^{3} +(-1.27190 - 1.54346i) q^{4} +(3.68816 - 1.52768i) q^{5} +(0.950782 + 1.04691i) q^{6} +(-1.63704 + 1.63704i) q^{7} +(2.74158 - 0.695531i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.603367 + 1.27904i) q^{2} +(0.382683 - 0.923880i) q^{3} +(-1.27190 - 1.54346i) q^{4} +(3.68816 - 1.52768i) q^{5} +(0.950782 + 1.04691i) q^{6} +(-1.63704 + 1.63704i) q^{7} +(2.74158 - 0.695531i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-0.271341 + 5.63906i) q^{10} +(1.20420 + 2.90719i) q^{11} +(-1.91271 + 0.584420i) q^{12} +(-3.30127 - 1.36743i) q^{13} +(-1.10611 - 3.08158i) q^{14} -3.99203i q^{15} +(-0.764563 + 3.92625i) q^{16} +0.511560i q^{17} +(1.33106 - 0.477774i) q^{18} +(-0.254077 - 0.105242i) q^{19} +(-7.04888 - 3.74948i) q^{20} +(0.885960 + 2.13890i) q^{21} +(-4.44500 - 0.213885i) q^{22} +(-3.17185 - 3.17185i) q^{23} +(0.406568 - 2.79905i) q^{24} +(7.73315 - 7.73315i) q^{25} +(3.74088 - 3.39740i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(4.60886 + 0.444569i) q^{28} +(-2.75087 + 6.64118i) q^{29} +(5.10598 + 2.40866i) q^{30} -5.82083 q^{31} +(-4.56053 - 3.34688i) q^{32} +3.14672 q^{33} +(-0.654306 - 0.308659i) q^{34} +(-3.53678 + 8.53855i) q^{35} +(-0.192028 + 1.99076i) q^{36} +(-5.53467 + 2.29253i) q^{37} +(0.287911 - 0.261476i) q^{38} +(-2.52668 + 2.52668i) q^{39} +(9.04881 - 6.75349i) q^{40} +(3.94823 + 3.94823i) q^{41} +(-3.27030 - 0.157361i) q^{42} +(1.30801 + 3.15781i) q^{43} +(2.95553 - 5.55628i) q^{44} +(-3.68816 - 1.52768i) q^{45} +(5.97071 - 2.14313i) q^{46} -9.41403i q^{47} +(3.33480 + 2.20888i) q^{48} +1.64019i q^{49} +(5.22509 + 14.5570i) q^{50} +(0.472620 + 0.195765i) q^{51} +(2.08829 + 6.83462i) q^{52} +(2.50482 + 6.04717i) q^{53} +(0.0679707 - 1.41258i) q^{54} +(8.88255 + 8.88255i) q^{55} +(-3.34946 + 5.62669i) q^{56} +(-0.194462 + 0.194462i) q^{57} +(-6.83457 - 7.52555i) q^{58} +(13.3423 - 5.52657i) q^{59} +(-6.16156 + 5.07745i) q^{60} +(3.35835 - 8.10777i) q^{61} +(3.51210 - 7.44509i) q^{62} +2.31513 q^{63} +(7.03247 - 3.81370i) q^{64} -14.2646 q^{65} +(-1.89863 + 4.02479i) q^{66} +(-1.11643 + 2.69530i) q^{67} +(0.789574 - 0.650651i) q^{68} +(-4.14422 + 1.71659i) q^{69} +(-8.78718 - 9.67558i) q^{70} +(1.26611 - 1.26611i) q^{71} +(-2.43040 - 1.44677i) q^{72} +(-7.51616 - 7.51616i) q^{73} +(0.407191 - 8.46231i) q^{74} +(-4.18515 - 10.1038i) q^{75} +(0.160722 + 0.526017i) q^{76} +(-6.73052 - 2.78787i) q^{77} +(-1.70721 - 4.75625i) q^{78} -0.709730i q^{79} +(3.17824 + 15.6486i) q^{80} +1.00000i q^{81} +(-7.43218 + 2.66772i) q^{82} +(-1.40823 - 0.583309i) q^{83} +(2.17446 - 4.08790i) q^{84} +(0.781502 + 1.88671i) q^{85} +(-4.82818 - 0.232323i) q^{86} +(5.08294 + 5.08294i) q^{87} +(5.32345 + 7.13273i) q^{88} +(-0.0856897 + 0.0856897i) q^{89} +(4.17929 - 3.79555i) q^{90} +(7.64285 - 3.16577i) q^{91} +(-0.861374 + 8.92989i) q^{92} +(-2.22754 + 5.37775i) q^{93} +(12.0409 + 5.68012i) q^{94} -1.09785 q^{95} +(-4.83735 + 2.93258i) q^{96} -0.677647 q^{97} +(-2.09787 - 0.989638i) q^{98} +(1.20420 - 2.90719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) $ 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$37$	$65$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.603367	+	1.27904i	−0.426645	+	0.904419i
$2$	−0.603367	+	1.27904i	−0.426645	+	0.904419i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$4$	−1.27190	−	1.54346i	−0.635948	−	0.771732i
$5$	3.68816	−	1.52768i	1.64939	−	0.683201i	0.652199	−	0.758048i	$-0.273847\pi$
$5$	3.68816	−	1.52768i	1.64939	−	0.683201i	0.997195	+	0.0748462i	$0.0238466\pi$
$6$	0.950782	+	1.04691i	0.388155	+	0.427398i
$7$	−1.63704	+	1.63704i	−0.618743	+	0.618743i	−0.945209	−	0.326466i	$-0.894142\pi$
$7$	−1.63704	+	1.63704i	−0.618743	+	0.618743i	0.326466	+	0.945209i	$0.394142\pi$
$8$	2.74158	−	0.695531i	0.969293	−	0.245908i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−0.271341	+	5.63906i	−0.0858057	+	1.78323i
$11$	1.20420	+	2.90719i	0.363080	+	0.876552i	0.994846	+	0.101393i	$0.0323300\pi$
$11$	1.20420	+	2.90719i	0.363080	+	0.876552i	−0.631767	+	0.775158i	$0.717670\pi$
$12$	−1.91271	+	0.584420i	−0.552151	+	0.168708i
$13$	−3.30127	−	1.36743i	−0.915607	−	0.379257i	−0.125407	−	0.992105i	$-0.540024\pi$
$13$	−3.30127	−	1.36743i	−0.915607	−	0.379257i	−0.790200	+	0.612849i	$0.790024\pi$
$14$	−1.10611	−	3.08158i	−0.295619	−	0.823587i
$15$		−	3.99203i		−	1.03074i
$16$	−0.764563	+	3.92625i	−0.191141	+	0.981563i
$17$			0.511560i			0.124071i	0.998074	+	0.0620357i	$0.0197593\pi$
$17$			0.511560i			0.124071i	−0.998074	+	0.0620357i	$0.980241\pi$
$18$	1.33106	−	0.477774i	0.313735	−	0.112612i
$19$	−0.254077	−	0.105242i	−0.0582894	−	0.0241442i	0.353348	−	0.935492i	$-0.385043\pi$
$19$	−0.254077	−	0.105242i	−0.0582894	−	0.0241442i	−0.411638	+	0.911348i	$0.635043\pi$
$20$	−7.04888	−	3.74948i	−1.57618	−	0.838410i
$21$	0.885960	+	2.13890i	0.193332	+	0.466746i
$22$	−4.44500	−	0.213885i	−0.947676	−	0.0456004i
$23$	−3.17185	−	3.17185i	−0.661376	−	0.661376i	0.294329	−	0.955704i	$-0.404904\pi$
$23$	−3.17185	−	3.17185i	−0.661376	−	0.661376i	−0.955704	+	0.294329i	$0.904904\pi$
$24$	0.406568	−	2.79905i	0.0829904	−	0.571354i
$25$	7.73315	−	7.73315i	1.54663	−	1.54663i
$26$	3.74088	−	3.39740i	0.733646	−	0.666284i
$27$	−0.923880	+	0.382683i	−0.177801	+	0.0736475i
$28$	4.60886	+	0.444569i	0.870993	+	0.0840157i
$29$	−2.75087	+	6.64118i	−0.510823	+	1.23324i	0.432582	+	0.901595i	$0.357603\pi$
$29$	−2.75087	+	6.64118i	−0.510823	+	1.23324i	−0.943405	+	0.331642i	$0.892397\pi$
$30$	5.10598	+	2.40866i	0.932220	+	0.439760i
$31$	−5.82083			−1.04545			−0.522726	−	0.852501i	$-0.675085\pi$
$31$	−5.82083			−1.04545			−0.522726	+	0.852501i	$0.675085\pi$
$32$	−4.56053	−	3.34688i	−0.806195	−	0.591650i
$33$	3.14672			0.547774
$34$	−0.654306	−	0.308659i	−0.112213	−	0.0529345i
$35$	−3.53678	+	8.53855i	−0.597825	+	1.44328i
$36$	−0.192028	+	1.99076i	−0.0320047	+	0.331793i
$37$	−5.53467	+	2.29253i	−0.909894	+	0.376890i	−0.788016	−	0.615655i	$-0.788892\pi$
$37$	−5.53467	+	2.29253i	−0.909894	+	0.376890i	−0.121878	+	0.992545i	$0.538892\pi$
$38$	0.287911	−	0.261476i	0.0467054	−	0.0424170i
$39$	−2.52668	+	2.52668i	−0.404593	+	0.404593i
$40$	9.04881	−	6.75349i	1.43074	−	1.06782i
$41$	3.94823	+	3.94823i	0.616610	+	0.616610i	0.944660	−	0.328050i	$-0.106392\pi$
$41$	3.94823	+	3.94823i	0.616610	+	0.616610i	−0.328050	+	0.944660i	$0.606392\pi$
$42$	−3.27030	−	0.157361i	−0.504618	−	0.0242813i
$43$	1.30801	+	3.15781i	0.199469	+	0.481561i	0.991686	−	0.128678i	$-0.0410733\pi$
$43$	1.30801	+	3.15781i	0.199469	+	0.481561i	−0.792217	+	0.610239i	$0.791073\pi$
$44$	2.95553	−	5.55628i	0.445563	−	0.837641i
$45$	−3.68816	−	1.52768i	−0.549798	−	0.227734i
$46$	5.97071	−	2.14313i	0.880333	−	0.315988i
$47$		−	9.41403i		−	1.37318i	−0.727046	−	0.686589i	$-0.759107\pi$
$47$		−	9.41403i		−	1.37318i	0.727046	−	0.686589i	$-0.240893\pi$
$48$	3.33480	+	2.20888i	0.481336	+	0.318824i
$49$			1.64019i			0.234313i
$50$	5.22509	+	14.5570i	0.738940	+	2.05866i
$51$	0.472620	+	0.195765i	0.0661800	+	0.0274127i
$52$	2.08829	+	6.83462i	0.289594	+	0.947791i
$53$	2.50482	+	6.04717i	0.344063	+	0.830642i	0.997296	+	0.0734852i	$0.0234122\pi$
$53$	2.50482	+	6.04717i	0.344063	+	0.830642i	−0.653233	+	0.757157i	$0.726588\pi$
$54$	0.0679707	−	1.41258i	0.00924964	−	0.192228i
$55$	8.88255	+	8.88255i	1.19772	+	1.19772i
$56$	−3.34946	+	5.62669i	−0.447590	+	0.751898i
$57$	−0.194462	+	0.194462i	−0.0257572	+	0.0257572i
$58$	−6.83457	−	7.52555i	−0.897423	−	0.988153i
$59$	13.3423	−	5.52657i	1.73702	−	0.719498i	0.738023	−	0.674775i	$-0.235759\pi$
$59$	13.3423	−	5.52657i	1.73702	−	0.719498i	0.998999	−	0.0447232i	$-0.0142406\pi$
$60$	−6.16156	+	5.07745i	−0.795454	+	0.655496i
$61$	3.35835	−	8.10777i	0.429992	−	1.03809i	−0.549297	−	0.835627i	$-0.685104\pi$
$61$	3.35835	−	8.10777i	0.429992	−	1.03809i	0.979289	−	0.202466i	$-0.0648955\pi$
$62$	3.51210	−	7.44509i	0.446037	−	0.945527i
$63$	2.31513			0.291678
$64$	7.03247	−	3.81370i	0.879059	−	0.476713i
$65$	−14.2646			−1.76931
$66$	−1.89863	+	4.02479i	−0.233705	+	0.495417i
$67$	−1.11643	+	2.69530i	−0.136394	+	0.329283i	−0.977288	−	0.211916i	$-0.932030\pi$
$67$	−1.11643	+	2.69530i	−0.136394	+	0.329283i	0.840894	+	0.541199i	$0.182030\pi$
$68$	0.789574	−	0.650651i	0.0957500	−	0.0789030i
$69$	−4.14422	+	1.71659i	−0.498905	+	0.206653i
$70$	−8.78718	−	9.67558i	−1.05027	−	1.15645i
$71$	1.26611	−	1.26611i	0.150259	−	0.150259i	−0.627975	−	0.778234i	$-0.716116\pi$
$71$	1.26611	−	1.26611i	0.150259	−	0.150259i	0.778234	+	0.627975i	$0.216116\pi$
$72$	−2.43040	−	1.44677i	−0.286426	−	0.170504i
$73$	−7.51616	−	7.51616i	−0.879700	−	0.879700i	0.113804	−	0.993503i	$-0.463697\pi$
$73$	−7.51616	−	7.51616i	−0.879700	−	0.879700i	−0.993503	+	0.113804i	$0.963697\pi$
$74$	0.407191	−	8.46231i	0.0473350	−	0.983723i
$75$	−4.18515	−	10.1038i	−0.483260	−	1.16669i
$76$	0.160722	+	0.526017i	0.0184361	+	0.0603383i
$77$	−6.73052	−	2.78787i	−0.767014	−	0.317707i
$78$	−1.70721	−	4.75625i	−0.193304	−	0.538539i
$79$		−	0.709730i		−	0.0798509i	−0.999203	−	0.0399254i	$-0.987288\pi$
$79$		−	0.709730i		−	0.0798509i	0.999203	−	0.0399254i	$-0.0127120\pi$
$80$	3.17824	+	15.6486i	0.355338	+	1.74957i
$81$			1.00000i			0.111111i
$82$	−7.43218	+	2.66772i	−0.820747	+	0.294600i
$83$	−1.40823	−	0.583309i	−0.154574	−	0.0640265i	0.304055	−	0.952654i	$-0.401659\pi$
$83$	−1.40823	−	0.583309i	−0.154574	−	0.0640265i	−0.458629	+	0.888628i	$0.651659\pi$
$84$	2.17446	−	4.08790i	0.237253	−	0.446027i
$85$	0.781502	+	1.88671i	0.0847658	+	0.204643i
$86$	−4.82818	−	0.232323i	−0.520636	−	0.0250520i
$87$	5.08294	+	5.08294i	0.544949	+	0.544949i
$88$	5.32345	+	7.13273i	0.567481	+	0.760352i
$89$	−0.0856897	+	0.0856897i	−0.00908309	+	0.00908309i	−0.711634	−	0.702551i	$-0.752044\pi$
$89$	−0.0856897	+	0.0856897i	−0.00908309	+	0.00908309i	0.702551	+	0.711634i	$0.252044\pi$
$90$	4.17929	−	3.79555i	0.440536	−	0.400086i
$91$	7.64285	−	3.16577i	0.801188	−	0.331863i
$92$	−0.861374	+	8.92989i	−0.0898044	+	0.931005i
$93$	−2.22754	+	5.37775i	−0.230985	+	0.557646i
$94$	12.0409	+	5.68012i	1.24193	+	0.585860i
$95$	−1.09785			−0.112638
$96$	−4.83735	+	2.93258i	−0.493710	+	0.299305i
$97$	−0.677647			−0.0688046			−0.0344023	−	0.999408i	$-0.510953\pi$
$97$	−0.677647			−0.0688046			−0.0344023	+	0.999408i	$0.510953\pi$
$98$	−2.09787	−	0.989638i	−0.211917	−	0.0999686i
$99$	1.20420	−	2.90719i	0.121027	−	0.292184i
$100$	−21.7716	−	2.10008i	−2.17716	−	0.210008i
$101$	10.0095	−	4.14605i	0.995978	−	0.412548i	0.175657	−	0.984451i	$-0.443795\pi$
$101$	10.0095	−	4.14605i	0.995978	−	0.412548i	0.820321	+	0.571904i	$0.193795\pi$
$102$	−0.535556	+	0.486382i	−0.0530279	+	0.0481590i
$103$	8.25191	−	8.25191i	0.813085	−	0.813085i	−0.172010	−	0.985095i	$-0.555026\pi$
$103$	8.25191	−	8.25191i	0.813085	−	0.813085i	0.985095	+	0.172010i	$0.0550263\pi$
$104$	−10.0018	−	1.45278i	−0.980754	−	0.142456i
$105$	6.53512	+	6.53512i	0.637763	+	0.637763i
$106$	−9.24590	−	0.444896i	−0.898041	−	0.0432121i
$107$	−0.162056	−	0.391238i	−0.0156665	−	0.0378224i	0.915853	−	0.401514i	$-0.131516\pi$
$107$	−0.162056	−	0.391238i	−0.0156665	−	0.0378224i	−0.931519	+	0.363692i	$0.881516\pi$
$108$	1.76574	+	0.939242i	0.169908	+	0.0903786i
$109$	5.41943	+	2.24480i	0.519087	+	0.215013i	0.626816	−	0.779167i	$-0.284358\pi$
$109$	5.41943	+	2.24480i	0.519087	+	0.215013i	−0.107729	+	0.994180i	$0.534358\pi$
$110$	−16.7206	+	6.00171i	−1.59425	+	0.572241i
$111$			5.99068i			0.568610i
$112$	−5.17581	−	7.67906i	−0.489068	−	0.725603i
$113$			3.60406i			0.339041i	0.985527	+	0.169521i	$0.0542219\pi$
$113$			3.60406i			0.339041i	−0.985527	+	0.169521i	$0.945778\pi$
$114$	−0.131393	−	0.366058i	−0.0123061	−	0.0342845i
$115$	−16.5438	−	6.85269i	−1.54272	−	0.639016i
$116$	13.7492	−	4.20103i	1.27659	−	0.390055i
$117$	1.36743	+	3.30127i	0.126419	+	0.305202i
$118$	−0.981608	+	20.3999i	−0.0903643	+	1.87797i
$119$	−0.837445	−	0.837445i	−0.0767684	−	0.0767684i
$120$	−2.77658	−	10.9445i	−0.253466	−	0.999088i
$121$	0.776498	−	0.776498i	0.0705908	−	0.0705908i
$122$	8.34385	+	9.18743i	0.755417	+	0.831791i
$123$	5.15861	−	2.13677i	0.465136	−	0.192666i
$124$	7.40349	+	8.98425i	0.664853	+	0.806809i
$125$	9.06884	−	21.8941i	0.811142	−	1.95827i
$126$	−1.39687	+	2.96114i	−0.124443	+	0.263800i
$127$	−0.146652			−0.0130133			−0.00650663	−	0.999979i	$-0.502071\pi$
$127$	−0.146652			−0.0130133			−0.00650663	+	0.999979i	$0.502071\pi$
$128$	0.634722	+	11.2959i	0.0561021	+	0.998425i
$129$	3.41799			0.300937
$130$	8.60679	−	18.2450i	0.754866	−	1.60019i
$131$	1.16280	−	2.80726i	0.101595	−	0.245271i	−0.864907	−	0.501933i	$-0.832623\pi$
$131$	1.16280	−	2.80726i	0.101595	−	0.245271i	0.966501	+	0.256661i	$0.0826225\pi$
$132$	−4.00230	−	4.85685i	−0.348356	−	0.422735i
$133$	0.588221	−	0.243649i	0.0510053	−	0.0211271i
$134$	−2.77378	−	3.05421i	−0.239618	−	0.263844i
$135$	−2.82279	+	2.82279i	−0.242947	+	0.242947i
$136$	0.355806	+	1.40248i	0.0305101	+	0.120262i
$137$	−11.6890	−	11.6890i	−0.998662	−	0.998662i	0.00133685	−	0.999999i	$-0.499574\pi$
$137$	−11.6890	−	11.6890i	−0.998662	−	0.998662i	−0.999999	+	0.00133685i	$0.999574\pi$
$138$	0.304894	−	6.33636i	0.0259543	−	0.539387i
$139$	7.96071	+	19.2188i	0.675218	+	1.63012i	0.772615	+	0.634875i	$0.218949\pi$
$139$	7.96071	+	19.2188i	0.675218	+	1.63012i	−0.0973963	+	0.995246i	$0.531051\pi$
$140$	17.6774	−	5.40124i	1.49401	−	0.456489i
$141$	−8.69743	−	3.60259i	−0.732456	−	0.303393i
$142$	0.855476	+	2.38333i	0.0717900	+	0.200005i
$143$		−	11.2441i		−	0.940277i
$144$	3.31691	−	2.23565i	0.276409	−	0.186304i
$145$			28.6962i			2.38309i
$146$	14.1485	−	5.07847i	1.17094	−	0.420297i
$147$	1.51534	+	0.627674i	0.124983	+	0.0517697i
$148$	10.5780	+	5.62670i	0.869503	+	0.462512i
$149$	−0.110593	−	0.266995i	−0.00906011	−	0.0218730i	0.919285	−	0.393593i	$-0.128768\pi$
$149$	−0.110593	−	0.266995i	−0.00906011	−	0.0218730i	−0.928345	+	0.371720i	$0.878768\pi$
$150$	15.4484	+	0.743350i	1.26136	+	0.0606943i
$151$	−4.70680	−	4.70680i	−0.383034	−	0.383034i	0.489160	−	0.872194i	$-0.337303\pi$
$151$	−4.70680	−	4.70680i	−0.383034	−	0.383034i	−0.872194	+	0.489160i	$0.837303\pi$
$152$	−0.769772	−	0.111811i	−0.0624367	−	0.00906906i
$153$	0.361727	−	0.361727i	0.0292439	−	0.0292439i
$154$	7.62678	−	6.92650i	0.614583	−	0.558153i
$155$	−21.4681	+	8.89240i	−1.72436	+	0.714255i
$156$	7.11352	+	0.686167i	0.569537	+	0.0549374i
$157$	−7.43264	+	17.9440i	−0.593189	+	1.43208i	0.287218	+	0.957865i	$0.407270\pi$
$157$	−7.43264	+	17.9440i	−0.593189	+	1.43208i	−0.880407	+	0.474220i	$0.842730\pi$
$158$	0.907774	+	0.428228i	0.0722186	+	0.0340680i
$159$	6.54540			0.519084
$160$	−21.9329	−	5.37678i	−1.73395	−	0.425071i
$161$	10.3849			0.818444
$162$	−1.27904	−	0.603367i	−0.100491	−	0.0474050i
$163$	5.94686	−	14.3570i	0.465794	−	1.12453i	−0.500188	−	0.865917i	$-0.666736\pi$
$163$	5.94686	−	14.3570i	0.465794	−	1.12453i	0.965982	−	0.258609i	$-0.0832641\pi$
$164$	1.07222	−	11.1157i	0.0837260	−	0.867989i
$165$	11.6056	−	4.80720i	0.903496	−	0.374240i
$166$	1.59576	−	1.44924i	0.123855	−	0.112483i
$167$	−10.7086	+	10.7086i	−0.828655	+	0.828655i	−0.987331	−	0.158676i	$-0.949277\pi$
$167$	−10.7086	+	10.7086i	−0.828655	+	0.828655i	0.158676	+	0.987331i	$0.449277\pi$
$168$	3.91660	+	5.24774i	0.302172	+	0.404872i
$169$	−0.163883	−	0.163883i	−0.0126064	−	0.0126064i
$170$	−2.88472	−	0.138807i	−0.221248	−	0.0106460i
$171$	0.105242	+	0.254077i	0.00804808	+	0.0194298i
$172$	3.21032	−	6.03526i	0.244784	−	0.460185i
$173$	2.46513	+	1.02109i	0.187420	+	0.0776320i	0.474420	−	0.880299i	$-0.342658\pi$
$173$	2.46513	+	1.02109i	0.187420	+	0.0776320i	−0.287000	+	0.957931i	$0.592658\pi$
$174$	−9.56818	+	3.43441i	−0.725362	+	0.260362i
$175$			25.3190i			1.91393i
$176$	−12.3351	+	2.50525i	−0.929790	+	0.188840i
$177$		−	14.4416i		−	1.08550i
$178$	−0.0578983	−	0.161303i	−0.00433966	−	0.0120902i
$179$	9.77295	+	4.04809i	0.730465	+	0.302568i	0.716743	−	0.697337i	$-0.245632\pi$
$179$	9.77295	+	4.04809i	0.730465	+	0.302568i	0.0137219	+	0.999906i	$0.495632\pi$
$180$	2.33302	+	7.63559i	0.173893	+	0.569124i
$181$	−7.36413	−	17.7786i	−0.547371	−	1.32147i	−0.919427	−	0.393261i	$-0.871347\pi$
$181$	−7.36413	−	17.7786i	−0.547371	−	1.32147i	0.372056	−	0.928210i	$-0.378653\pi$
$182$	−0.562292	+	11.6856i	−0.0416799	+	0.866198i
$183$	−6.20542	−	6.20542i	−0.458718	−	0.458718i
$184$	−10.9020	−	6.48974i	−0.803704	−	0.478430i
$185$	−16.9105	+	16.9105i	−1.24328	+	1.24328i
$186$	−5.53434	−	6.09387i	−0.405798	−	0.446824i
$187$	−1.48720	+	0.616020i	−0.108755	+	0.0450478i
$188$	−14.5302	+	11.9737i	−1.05973	+	0.873269i
$189$	0.885960	−	2.13890i	0.0644441	−	0.155582i
$190$	0.662410	−	1.40420i	0.0480563	−	0.101872i
$191$	10.1764			0.736335			0.368168	−	0.929759i	$-0.379985\pi$
$191$	10.1764			0.736335			0.368168	+	0.929759i	$0.379985\pi$
$192$	−0.832193	−	7.95660i	−0.0600583	−	0.574218i
$193$	−7.17480			−0.516454			−0.258227	−	0.966084i	$-0.583138\pi$
$193$	−7.17480			−0.516454			−0.258227	+	0.966084i	$0.583138\pi$
$194$	0.408870	−	0.866739i	0.0293552	−	0.0622282i
$195$	−5.45883	+	13.1788i	−0.390915	+	0.943751i
$196$	2.53158	−	2.08615i	0.180827	−	0.149011i
$197$	9.81153	−	4.06407i	0.699042	−	0.289553i	−0.00471943	−	0.999989i	$-0.501502\pi$
$197$	9.81153	−	4.06407i	0.699042	−	0.289553i	0.703762	+	0.710436i	$0.251502\pi$
$198$	2.99185	+	3.29433i	0.212621	+	0.234118i
$199$	−7.92887	+	7.92887i	−0.562063	+	0.562063i	−0.929893	−	0.367830i	$-0.880101\pi$
$199$	−7.92887	+	7.92887i	−0.562063	+	0.562063i	0.367830	+	0.929893i	$0.380101\pi$
$200$	15.8224	−	26.5797i	1.11881	−	1.87947i
$201$	2.06289	+	2.06289i	0.145505	+	0.145505i
$202$	−0.736405	+	15.3041i	−0.0518133	+	1.07679i
$203$	−6.36861	−	15.3752i	−0.446989	−	1.07913i
$204$	−0.298966	−	0.978465i	−0.0209318	−	0.0685062i
$205$	20.5933	+	8.53004i	1.43830	+	0.595764i
$206$	5.57560	+	15.5335i	0.388471	+	1.08227i
$207$			4.48567i			0.311775i
$208$	7.89290	−	11.9161i	0.547274	−	0.826234i
$209$		−	0.865385i		−	0.0598599i
$210$	−12.3018	+	4.41561i	−0.848903	+	0.304706i
$211$	−23.9700	−	9.92869i	−1.65016	−	0.683519i	−0.652898	−	0.757446i	$-0.726447\pi$
$211$	−23.9700	−	9.92869i	−1.65016	−	0.683519i	−0.997264	+	0.0739270i	$0.976447\pi$
$212$	6.14772	−	11.5575i	0.422227	−	0.793770i
$213$	−0.685213	−	1.65425i	−0.0469500	−	0.113347i
$214$	0.598189	+	0.0287837i	0.0408913	+	0.00196762i
$215$	9.64827	+	9.64827i	0.658007	+	0.658007i
$216$	−2.26672	+	1.69174i	−0.154231	+	0.115109i
$217$	9.52894	−	9.52894i	0.646867	−	0.646867i
$218$	−6.14110	+	5.57724i	−0.415928	+	0.377738i
$219$	−9.82033	+	4.06771i	−0.663597	+	0.274871i
$220$	2.41222	−	25.0076i	0.162632	−	1.68601i
$221$	0.699522	−	1.68880i	0.0470550	−	0.113601i
$222$	−7.66233	−	3.61458i	−0.514262	−	0.242595i
$223$	−0.573216			−0.0383854			−0.0191927	−	0.999816i	$-0.506110\pi$
$223$	−0.573216			−0.0383854			−0.0191927	+	0.999816i	$0.506110\pi$
$224$	12.9447	−	1.98679i	0.864907	−	0.132748i
$225$	−10.9363			−0.729089
$226$	−4.60974	−	2.17457i	−0.306635	−	0.144650i
$227$	−1.44349	+	3.48488i	−0.0958075	+	0.231300i	−0.964516	−	0.264023i	$-0.914950\pi$
$227$	−1.44349	+	3.48488i	−0.0958075	+	0.231300i	0.868709	+	0.495323i	$0.164950\pi$
$228$	0.547482	+	0.0528099i	0.0362579	+	0.00349742i
$229$	−7.10429	+	2.94269i	−0.469465	+	0.194459i	−0.604858	−	0.796333i	$-0.706770\pi$
$229$	−7.10429	+	2.94269i	−0.469465	+	0.194459i	0.135393	+	0.990792i	$0.456770\pi$
$230$	18.7469	−	17.0256i	1.23613	−	1.12263i
$231$	−5.15132	+	5.15132i	−0.338932	+	0.338932i
$232$	−2.92256	+	20.1206i	−0.191876	+	1.32098i
$233$	1.38129	+	1.38129i	0.0904912	+	0.0904912i	0.750903	−	0.660412i	$-0.229618\pi$
$233$	1.38129	+	1.38129i	0.0904912	+	0.0904912i	−0.660412	+	0.750903i	$0.729618\pi$
$234$	−5.04752	−	0.242878i	−0.329967	−	0.0158774i
$235$	−14.3817	−	34.7204i	−0.938157	−	2.26491i
$236$	−25.5001	−	13.5642i	−1.65992	−	0.882953i
$237$	−0.655705	−	0.271602i	−0.0425926	−	0.0176424i
$238$	1.57641	−	0.565840i	0.102184	−	0.0366779i
$239$			4.58455i			0.296550i	0.988946	+	0.148275i	$0.0473721\pi$
$239$			4.58455i			0.296550i	−0.988946	+	0.148275i	$0.952628\pi$
$240$	15.6737	+	3.05216i	1.01173	+	0.197016i
$241$		−	15.9551i		−	1.02776i	−0.857862	−	0.513880i	$-0.828208\pi$
$241$		−	15.9551i		−	1.02776i	0.857862	−	0.513880i	$-0.171792\pi$
$242$	0.524660	+	1.46169i	0.0337264	+	0.0939608i
$243$	0.923880	+	0.382683i	0.0592669	+	0.0245492i
$244$	−16.7855	+	5.12874i	−1.07458	+	0.328334i
$245$	2.50570	+	6.04929i	0.160083	+	0.386475i
$246$	−0.379524	+	7.88733i	−0.0241976	+	0.502878i
$247$	0.694866	+	0.694866i	0.0442133	+	0.0442133i
$248$	−15.9583	+	4.04857i	−1.01335	+	0.257085i
$249$	−1.07781	+	1.07781i	−0.0683037	+	0.0683037i
$250$	22.5316	+	24.8096i	1.42503	+	1.56910i
$251$	−20.0790	+	8.31700i	−1.26738	+	0.524964i	−0.912166	−	0.409822i	$-0.865591\pi$
$251$	−20.0790	+	8.31700i	−1.26738	+	0.524964i	−0.355211	+	0.934786i	$0.615591\pi$
$252$	−2.94460	−	3.57331i	−0.185492	−	0.225098i
$253$	5.40164	−	13.0407i	0.339598	−	0.819862i
$254$	0.0884851	−	0.187574i	0.00555205	−	0.0117694i
$255$	2.04216			0.127885
$256$	−14.8309	−	6.00374i	−0.926930	−	0.375233i
$257$	0.677979			0.0422912			0.0211456	−	0.999776i	$-0.493269\pi$
$257$	0.677979			0.0422912			0.0211456	+	0.999776i	$0.493269\pi$
$258$	−2.06230	+	4.37175i	−0.128393	+	0.272173i
$259$	5.30750	−	12.8134i	0.329792	−	0.796189i
$260$	18.1431	+	22.0169i	1.12519	+	1.36543i
$261$	6.64118	−	2.75087i	0.411079	−	0.170274i
$262$	2.88900	+	3.18108i	0.178483	+	0.196528i
$263$	7.67357	−	7.67357i	0.473173	−	0.473173i	−0.429767	−	0.902940i	$-0.641404\pi$
$263$	7.67357	−	7.67357i	0.473173	−	0.473173i	0.902940	+	0.429767i	$0.141404\pi$
$264$	8.62698	−	2.18864i	0.530954	−	0.134702i
$265$	18.4763	+	18.4763i	1.13499	+	1.13499i
$266$	−0.0432760	+	0.899370i	−0.00265342	+	0.0551439i
$267$	0.0463749	+	0.111959i	0.00283810	+	0.00685178i
$268$	5.58008	−	1.70497i	0.340857	−	0.104148i
$269$	22.0482	+	9.13266i	1.34430	+	0.556828i	0.934701	−	0.355436i	$-0.115668\pi$
$269$	22.0482	+	9.13266i	1.34430	+	0.556828i	0.409602	+	0.912264i	$0.365668\pi$
$270$	−1.90729	−	5.31365i	−0.116074	−	0.323379i
$271$		−	0.778886i		−	0.0473140i	−0.999720	−	0.0236570i	$-0.992469\pi$
$271$		−	0.778886i		−	0.0473140i	0.999720	−	0.0236570i	$-0.00753096\pi$
$272$	−2.00851	−	0.391120i	−0.121784	−	0.0237151i
$273$		−	8.27256i		−	0.500678i
$274$	22.0036	−	7.89799i	1.32928	−	0.477135i
$275$	31.7940	+	13.1695i	1.91725	+	0.794151i
$276$	7.92051	+	4.21313i	0.476758	+	0.253600i
$277$	1.47054	+	3.55020i	0.0883564	+	0.213311i	0.961881	−	0.273469i	$-0.0881712\pi$
$277$	1.47054	+	3.55020i	0.0883564	+	0.213311i	−0.873524	+	0.486780i	$0.838171\pi$
$278$	−29.3849	−	1.41395i	−1.76239	−	0.0848030i
$279$	4.11595	+	4.11595i	0.246415	+	0.246415i
$280$	−3.75753	+	25.8690i	−0.224555	+	1.54597i
$281$	−3.60771	+	3.60771i	−0.215218	+	0.215218i	−0.806480	−	0.591262i	$-0.798630\pi$
$281$	−3.60771	+	3.60771i	−0.215218	+	0.215218i	0.591262	+	0.806480i	$0.298630\pi$
$282$	9.85562	−	8.95069i	0.586893	−	0.533006i
$283$	12.3134	−	5.10036i	0.731953	−	0.303185i	0.0145986	−	0.999893i	$-0.495353\pi$
$283$	12.3134	−	5.10036i	0.731953	−	0.303185i	0.717354	+	0.696709i	$0.245353\pi$
$284$	−3.56455	−	0.343835i	−0.211517	−	0.0204029i
$285$	−0.420131	+	1.01429i	−0.0248864	+	0.0600811i
$286$	14.3816	+	6.78431i	0.850405	+	0.401165i
$287$	−12.9268			−0.763047
$288$	0.858177	+	5.59138i	0.0505686	+	0.329475i
$289$	16.7383			0.984606
$290$	−36.7036	−	17.3143i	−2.15531	−	1.01673i
$291$	−0.259324	+	0.626064i	−0.0152019	+	0.0367005i
$292$	−2.04115	+	21.1607i	−0.119449	+	1.23834i
$293$	−21.1509	+	8.76099i	−1.23565	+	0.511822i	−0.902352	−	0.431000i	$-0.858161\pi$
$293$	−21.1509	+	8.76099i	−1.23565	+	0.511822i	−0.333297	+	0.942822i	$0.608161\pi$
$294$	−1.71713	+	1.55946i	−0.100145	+	0.0909498i
$295$	40.7657	−	40.7657i	2.37347	−	2.37347i
$296$	−13.5792	+	10.1347i	−0.789274	+	0.589067i
$297$	−2.22507	−	2.22507i	−0.129112	−	0.129112i
$298$	0.408225	+	0.0196430i	0.0236479	+	0.00113789i
$299$	6.13384	+	14.8084i	0.354729	+	0.856391i
$300$	−10.2719	+	19.3107i	−0.593046	+	1.11490i
$301$	−7.31072	−	3.02820i	−0.421383	−	0.174543i
$302$	8.86013	−	3.18027i	0.509843	−	0.183004i
$303$		−	10.8342i		−	0.622406i
$304$	0.607466	−	0.917107i	0.0348406	−	0.0525997i
$305$		−	35.0332i		−	2.00600i
$306$	0.244410	+	0.680919i	0.0139720	+	0.0389256i
$307$	29.7333	+	12.3159i	1.69697	+	0.702908i	0.999901	−	0.0140946i	$-0.00448661\pi$
$307$	29.7333	+	12.3159i	1.69697	+	0.702908i	0.697070	+	0.717003i	$0.254487\pi$
$308$	4.25754	+	13.9342i	0.242596	+	0.793974i
$309$	−4.46590	−	10.7816i	−0.254056	−	0.613346i
$310$	1.57943	−	32.8240i	0.0897057	−	1.86428i
$311$	−5.08789	−	5.08789i	−0.288508	−	0.288508i	0.547982	−	0.836490i	$-0.315396\pi$
$311$	−5.08789	−	5.08789i	−0.288508	−	0.288508i	−0.836490	+	0.547982i	$0.815396\pi$
$312$	−5.16970	+	8.68447i	−0.292677	+	0.491661i
$313$	−10.3695	+	10.3695i	−0.586117	+	0.586117i	−0.936578	−	0.350460i	$-0.886025\pi$
$313$	−10.3695	+	10.3695i	−0.586117	+	0.586117i	0.350460	+	0.936578i	$0.386025\pi$
$314$	−18.4665	−	20.3335i	−1.04212	−	1.14748i
$315$	8.53855	−	3.53678i	0.481093	−	0.199275i
$316$	−1.09544	+	0.902702i	−0.0616235	+	0.0507810i
$317$	−6.18851	+	14.9404i	−0.347582	+	0.839136i	0.649323	+	0.760513i	$0.275052\pi$
$317$	−6.18851	+	14.9404i	−0.347582	+	0.839136i	−0.996904	+	0.0786232i	$0.974948\pi$
$318$	−3.94928	+	8.37185i	−0.221465	+	0.469470i
$319$	−22.6198			−1.26647
$320$	20.1107	−	24.8089i	1.12422	−	1.38686i
$321$	−0.423473			−0.0236359
$322$	−6.26590	+	13.2827i	−0.349185	+	0.740216i
$323$	0.0538378	−	0.129976i	0.00299561	−	0.00723205i
$324$	1.54346	−	1.27190i	0.0857480	−	0.0706609i
$325$	−36.1037	+	14.9547i	−2.00268	+	0.829535i
$326$	14.7750	+	16.2688i	0.818314	+	0.901046i
$327$	4.14785	−	4.14785i	0.229377	−	0.229377i
$328$	13.5705	+	8.07825i	0.749305	+	0.446047i
$329$	15.4112	+	15.4112i	0.849645	+	0.849645i
$330$	−0.853836	+	17.7446i	−0.0470021	+	0.976806i
$331$	12.0185	+	29.0153i	0.660599	+	1.59483i	0.796867	+	0.604155i	$0.206489\pi$
$331$	12.0185	+	29.0153i	0.660599	+	1.59483i	−0.136268	+	0.990672i	$0.543511\pi$
$332$	0.890808	+	2.91547i	0.0488895	+	0.160007i
$333$	5.53467	+	2.29253i	0.303298	+	0.125630i
$334$	−7.23551	−	20.1579i	−0.395910	−	1.10299i
$335$			11.6462i			0.636302i
$336$	−9.07522	+	1.84318i	−0.495094	+	0.100554i
$337$			2.12023i			0.115496i	0.998331	+	0.0577480i	$0.0183920\pi$
$337$			2.12023i			0.115496i	−0.998331	+	0.0577480i	$0.981608\pi$
$338$	0.308494	−	0.110731i	0.0167799	−	0.00602299i
$339$	3.32971	+	1.37921i	0.180845	+	0.0749085i
$340$	1.91809	−	3.60592i	0.104023	−	0.195559i
$341$	−7.00944	−	16.9223i	−0.379582	−	0.916393i
$342$	−0.388475	−	0.0186927i	−0.0210063	−	0.00101079i
$343$	−14.1444	−	14.1444i	−0.763723	−	0.763723i
$344$	5.78235	+	7.74761i	0.311764	+	0.417723i
$345$	−12.6621	+	12.6621i	−0.681705	+	0.681705i
$346$	−2.79340	+	2.53691i	−0.150174	+	0.136385i
$347$	15.6587	−	6.48607i	0.840606	−	0.348190i	0.0795133	−	0.996834i	$-0.474663\pi$
$347$	15.6587	−	6.48607i	0.840606	−	0.348190i	0.761092	+	0.648644i	$0.224663\pi$
$348$	1.38037	−	14.3103i	0.0739955	−	0.767113i
$349$	−2.54342	+	6.14035i	−0.136146	+	0.328685i	−0.977218	−	0.212238i	$-0.931925\pi$
$349$	−2.54342	+	6.14035i	−0.136146	+	0.328685i	0.841072	+	0.540923i	$0.181925\pi$
$350$	−32.3840	−	15.2766i	−1.73100	−	0.816571i
$351$	3.57327			0.190727
$352$	4.23825	−	17.2886i	0.225899	−	0.921487i
$353$	26.7822			1.42547			0.712737	−	0.701431i	$-0.247455\pi$
$353$	26.7822			1.42547			0.712737	+	0.701431i	$0.247455\pi$
$354$	18.4714	+	8.71361i	0.981746	+	0.463123i
$355$	2.73539	−	6.60382i	0.145179	−	0.350494i
$356$	0.241247	+	0.0232706i	0.0127861	+	0.00123334i
$357$	−1.09417	+	0.453222i	−0.0579098	+	0.0239870i
$358$	−11.0744	+	10.0575i	−0.585298	+	0.531557i
$359$	−21.9626	+	21.9626i	−1.15914	+	1.15914i	−0.174480	+	0.984661i	$0.555824\pi$
$359$	−21.9626	+	21.9626i	−1.15914	+	1.15914i	−0.984661	+	0.174480i	$0.944176\pi$
$360$	−11.1739	−	1.62303i	−0.588917	−	0.0855414i
$361$	−13.3815	−	13.3815i	−0.704292	−	0.704292i
$362$	27.1828	+	1.30799i	1.42870	+	0.0687463i
$363$	−0.420238	−	1.01454i	−0.0220568	−	0.0532498i
$364$	−14.6072	−	7.76993i	−0.765623	−	0.407255i
$365$	−39.2031	−	16.2385i	−2.05198	−	0.849959i
$366$	11.6811	−	4.19284i	0.610583	−	0.219163i
$367$		−	20.1290i		−	1.05073i	−0.850878	−	0.525363i	$-0.823929\pi$
$367$		−	20.1290i		−	1.05073i	0.850878	−	0.525363i	$-0.176071\pi$
$368$	14.8785	−	10.0284i	0.775597	−	0.522766i
$369$		−	5.58364i		−	0.290673i
$370$	−11.4260	−	31.8324i	−0.594007	−	1.65489i
$371$	−13.9999	−	5.79897i	−0.726841	−	0.301067i
$372$	11.1336	−	3.40181i	0.577248	−	0.176376i
$373$	0.278651	+	0.672724i	0.0144280	+	0.0348323i	0.930929	−	0.365199i	$-0.118999\pi$
$373$	0.278651	+	0.672724i	0.0144280	+	0.0348323i	−0.916501	+	0.400032i	$0.868999\pi$
$374$	0.109415	−	2.27388i	0.00565771	−	0.117580i
$375$	−16.7570	−	16.7570i	−0.865329	−	0.865329i
$376$	−6.54776	−	25.8093i	−0.337675	−	1.33101i
$377$	18.1627	−	18.1627i	0.935427	−	0.935427i
$378$	2.20118	+	2.42372i	0.113216	+	0.124663i
$379$	−33.2934	+	13.7906i	−1.71017	+	0.708375i	−0.710177	+	0.704023i	$0.751385\pi$
$379$	−33.2934	+	13.7906i	−1.71017	+	0.708375i	−0.999991	+	0.00435195i	$0.998615\pi$
$380$	1.39636	+	1.69450i	0.0716316	+	0.0869260i
$381$	−0.0561213	+	0.135489i	−0.00287518	+	0.00694130i
$382$	−6.14008	+	13.0160i	−0.314154	+	0.665955i
$383$	30.6643			1.56687			0.783435	−	0.621473i	$-0.213466\pi$
$383$	30.6643			1.56687			0.783435	+	0.621473i	$0.213466\pi$
$384$	10.6789	+	3.73634i	0.544957	+	0.190669i
$385$	−29.0822			−1.48217
$386$	4.32904	−	9.17687i	0.220342	−	0.467091i
$387$	1.30801	−	3.15781i	0.0664897	−	0.160520i
$388$	0.861896	+	1.04592i	0.0437561	+	0.0530987i
$389$	−9.95840	+	4.12490i	−0.504911	+	0.209141i	−0.620575	−	0.784147i	$-0.713101\pi$
$389$	−9.95840	+	4.12490i	−0.504911	+	0.209141i	0.115664	+	0.993288i	$0.463101\pi$
$390$	−13.5625	−	14.9337i	−0.686765	−	0.756198i
$391$	1.62259	−	1.62259i	0.0820579	−	0.0820579i
$392$	1.14081	+	4.49671i	0.0576194	+	0.227118i
$393$	−2.14858	−	2.14858i	−0.108382	−	0.108382i
$394$	−0.721844	+	15.0015i	−0.0363660	+	0.755764i
$395$	−1.08424	−	2.61760i	−0.0545542	−	0.131706i
$396$	−6.01876	+	1.83901i	−0.302454	+	0.0924136i
$397$	33.1225	+	13.7198i	1.66237	+	0.688577i	0.998255	−	0.0590504i	$-0.0188073\pi$
$397$	33.1225	+	13.7198i	1.66237	+	0.688577i	0.664118	+	0.747628i	$0.268807\pi$
$398$	−5.35733	−	14.9254i	−0.268539	−	0.748142i
$399$		−	0.636686i		−	0.0318742i
$400$	24.4498	+	36.2748i	1.22249	+	1.81374i
$401$		−	1.21160i		−	0.0605046i	−0.999542	−	0.0302523i	$-0.990369\pi$
$401$		−	1.21160i		−	0.0605046i	0.999542	−	0.0302523i	$-0.00963107\pi$
$402$	−3.88321	+	1.39384i	−0.193677	+	0.0695186i
$403$	19.2161	+	7.95958i	0.957224	+	0.396495i
$404$	−19.1303	−	10.1759i	−0.951766	−	0.506269i
$405$	1.52768	+	3.68816i	0.0759113	+	0.183266i
$406$	23.5081	+	1.13117i	1.16669	+	0.0561389i
$407$	−13.3297	−	13.3297i	−0.660728	−	0.660728i
$408$	1.43188	+	0.207984i	0.0708888	+	0.0102967i
$409$	−20.0380	+	20.0380i	−0.990817	+	0.990817i	−0.999958	−	0.00914144i	$-0.997090\pi$
$409$	−20.0380	+	20.0380i	−0.990817	+	0.990817i	0.00914144	+	0.999958i	$0.497090\pi$
$410$	−23.3356	+	21.1930i	−1.15246	+	1.04665i
$411$	−15.2725	+	6.32606i	−0.753335	+	0.312042i
$412$	−23.2321	−	2.24096i	−1.14456	−	0.110404i
$413$	−12.7947	+	30.8892i	−0.629587	+	1.51996i
$414$	−5.73736	−	2.70651i	−0.281976	−	0.133017i
$415$	−6.08490			−0.298696
$416$	10.4789	+	17.2851i	0.513770	+	0.847474i
$417$	20.8023			1.01869
$418$	1.10686	+	0.522145i	0.0541385	+	0.0255390i
$419$	1.34843	−	3.25539i	0.0658749	−	0.159036i	−0.887514	−	0.460781i	$-0.847569\pi$
$419$	1.34843	−	3.25539i	0.0658749	−	0.159036i	0.953389	+	0.301745i	$0.0975692\pi$
$420$	1.77473	−	18.3987i	0.0865982	−	0.897766i
$421$	10.4207	−	4.31639i	0.507873	−	0.210368i	−0.114008	−	0.993480i	$-0.536369\pi$
$421$	10.4207	−	4.31639i	0.507873	−	0.210368i	0.621881	+	0.783112i	$0.286369\pi$
$422$	27.1619	−	24.6680i	1.32222	−	1.20082i
$423$	−6.65673	+	6.65673i	−0.323661	+	0.323661i
$424$	11.0731	+	14.8366i	0.537759	+	0.720528i
$425$	3.95597	+	3.95597i	0.191893	+	0.191893i
$426$	2.52929	+	0.121705i	0.122544	+	0.00589661i
$427$	7.77500	+	18.7705i	0.376258	+	0.908368i
$428$	−0.397743	+	0.747741i	−0.0192256	+	0.0361434i
$429$	−10.3882	−	4.30292i	−0.501546	−	0.207747i
$430$	−18.1620	+	6.51909i	−0.875849	+	0.314378i
$431$			35.6433i			1.71688i	0.512914	+	0.858440i	$0.328566\pi$
$431$			35.6433i			1.71688i	−0.512914	+	0.858440i	$0.671434\pi$
$432$	−0.796146	−	3.91997i	−0.0383046	−	0.188600i
$433$			9.75449i			0.468771i	0.972144	+	0.234385i	$0.0753078\pi$
$433$			9.75449i			0.468771i	−0.972144	+	0.234385i	$0.924692\pi$
$434$	6.43846	+	17.9374i	0.309056	+	0.861021i
$435$	26.5118	+	10.9816i	1.27114	+	0.526525i
$436$	−3.42818	−	11.2198i	−0.164180	−	0.537333i
$437$	0.472082	+	1.13971i	0.0225828	+	0.0545196i
$438$	0.722491	−	15.0149i	0.0345220	−	0.717442i
$439$	−11.2645	−	11.2645i	−0.537625	−	0.537625i	0.385206	−	0.922831i	$-0.374130\pi$
$439$	−11.2645	−	11.2645i	−0.537625	−	0.537625i	−0.922831	+	0.385206i	$0.874130\pi$
$440$	30.5303	+	18.1741i	1.45547	+	0.866416i
$441$	1.15979	−	1.15979i	0.0552281	−	0.0552281i
$442$	1.73797	+	1.91368i	0.0826669	+	0.0910246i
$443$	22.1985	−	9.19492i	1.05468	−	0.436864i	0.213122	−	0.977026i	$-0.431637\pi$
$443$	22.1985	−	9.19492i	1.05468	−	0.436864i	0.841561	+	0.540162i	$0.181637\pi$
$444$	9.24640	−	7.61952i	0.438815	−	0.361606i
$445$	−0.185130	+	0.446944i	−0.00877601	+	0.0211872i
$446$	0.345860	−	0.733168i	0.0163769	−	0.0347165i
$447$	−0.288993			−0.0136689
$448$	−5.26926	+	17.7556i	−0.248949	+	0.838875i
$449$	−12.5831			−0.593834			−0.296917	−	0.954903i	$-0.595958\pi$
$449$	−12.5831			−0.593834			−0.296917	+	0.954903i	$0.595958\pi$
$450$	6.59862	−	13.9880i	0.311062	−	0.659402i
$451$	−6.72381	+	16.2327i	−0.316612	+	0.764369i
$452$	5.56273	−	4.58398i	0.261649	−	0.215612i
$453$	−6.14974	+	2.54730i	−0.288940	+	0.119683i
$454$	−3.58636	−	3.94894i	−0.168316	−	0.185333i
$455$	23.3517	−	23.3517i	1.09475	−	1.09475i
$456$	−0.397879	+	0.668388i	−0.0186324	+	0.0313002i
$457$	−28.8488	−	28.8488i	−1.34949	−	1.34949i	−0.886216	−	0.463273i	$-0.846675\pi$
$457$	−28.8488	−	28.8488i	−1.34949	−	1.34949i	−0.463273	−	0.886216i	$-0.653325\pi$
$458$	0.522670	−	10.8622i	0.0244227	−	0.507558i
$459$	−0.195765	−	0.472620i	−0.00913755	−	0.0220600i
$460$	10.4652	+	34.2507i	0.487941	+	1.59695i
$461$	11.8188	+	4.89549i	0.550454	+	0.228006i	0.640535	−	0.767929i	$-0.278713\pi$
$461$	11.8188	+	4.89549i	0.550454	+	0.228006i	−0.0900809	+	0.995934i	$0.528713\pi$
$462$	−3.48061	−	9.69688i	−0.161933	−	0.451140i
$463$			18.0311i			0.837976i	0.907992	+	0.418988i	$0.137615\pi$
$463$			18.0311i			0.837976i	−0.907992	+	0.418988i	$0.862385\pi$
$464$	−23.9717	−	15.8782i	−1.11286	−	0.737127i
$465$			23.2370i			1.07759i
$466$	−2.60015	+	0.933301i	−0.120450	+	0.0432343i
$467$	−22.2527	−	9.21739i	−1.02973	−	0.426530i	−0.197118	−	0.980380i	$-0.563158\pi$
$467$	−22.2527	−	9.21739i	−1.02973	−	0.426530i	−0.832616	+	0.553850i	$0.813158\pi$
$468$	3.35616	−	6.30945i	0.155139	−	0.291654i
$469$	−2.58467	−	6.23995i	−0.119349	−	0.288134i
$470$	53.0863	+	2.55442i	2.44869	+	0.117826i
$471$	13.7337	+	13.7337i	0.632817	+	0.632817i
$472$	32.7351	−	24.4315i	1.50675	−	1.12455i
$473$	−7.60526	+	7.60526i	−0.349690	+	0.349690i
$474$	0.743021	−	0.674798i	0.0341281	−	0.0309945i
$475$	−2.77867	+	1.15096i	−0.127494	+	0.0528099i
$476$	−0.227424	+	2.35771i	−0.0104239	+	0.108065i
$477$	2.50482	−	6.04717i	0.114688	−	0.276881i
$478$	−5.86383	−	2.76617i	−0.268206	−	0.126522i
$479$	11.2525			0.514141			0.257070	−	0.966393i	$-0.417243\pi$
$479$	11.2525			0.514141			0.257070	+	0.966393i	$0.417243\pi$
$480$	−13.3609	+	18.2058i	−0.609837	+	0.830976i
$481$	21.4063			0.976043
$482$	20.4073	+	9.62681i	0.929526	+	0.438489i
$483$	3.97412	−	9.59438i	0.180829	−	0.436560i
$484$	−2.18612	−	0.210873i	−0.0993692	−	0.00958512i
$485$	−2.49927	+	1.03523i	−0.113486	+	0.0470074i
$486$	−1.04691	+	0.950782i	−0.0474887	+	0.0431283i
$487$	−23.1247	+	23.1247i	−1.04788	+	1.04788i	−0.0490867	+	0.998795i	$0.515631\pi$
$487$	−23.1247	+	23.1247i	−1.04788	+	1.04788i	−0.998795	+	0.0490867i	$0.984369\pi$
$488$	3.56795	−	24.5639i	0.161514	−	1.11195i
$489$	−10.9884	−	10.9884i	−0.496911	−	0.496911i
$490$	−9.24915	−	0.445052i	−0.417834	−	0.0201054i
$491$	−9.92916	−	23.9711i	−0.448097	−	1.08180i	−0.973034	−	0.230661i	$-0.925911\pi$
$491$	−9.92916	−	23.9711i	−0.448097	−	1.08180i	0.524937	−	0.851141i	$-0.324089\pi$
$492$	−9.85924	−	5.24439i	−0.444489	−	0.236435i
$493$	−3.39736	−	1.40723i	−0.153010	−	0.0633786i
$494$	−1.30802	+	0.469503i	−0.0588507	+	0.0211240i
$495$		−	12.5618i		−	0.564612i
$496$	4.45040	−	22.8540i	0.199829	−	1.02618i
$497$			4.14534i			0.185944i
$498$	−0.728252	−	2.02889i	−0.0326337	−	0.0909167i
$499$	−0.662766	−	0.274527i	−0.0296695	−	0.0122895i	0.367799	−	0.929905i	$-0.380111\pi$
$499$	−0.662766	−	0.274527i	−0.0296695	−	0.0122895i	−0.397469	+	0.917616i	$0.630111\pi$
$500$	−45.3274	+	13.8496i	−2.02710	+	0.619373i
$501$	5.79544	+	13.9914i	0.258921	+	0.625091i
$502$	1.47723	−	30.7001i	0.0659321	−	1.37021i
$503$	−5.46400	−	5.46400i	−0.243628	−	0.243628i	0.574721	−	0.818349i	$-0.305110\pi$
$503$	−5.46400	−	5.46400i	−0.243628	−	0.243628i	−0.818349	+	0.574721i	$0.805110\pi$
$504$	6.34709	−	1.61024i	0.282722	−	0.0717259i
$505$	30.5826	−	30.5826i	1.36091	−	1.36091i
$506$	13.4204	+	14.7773i	0.596611	+	0.656929i
$507$	−0.214123	+	0.0886927i	−0.00950954	+	0.00393898i
$508$	0.186526	+	0.226352i	0.00827576	+	0.0100428i
$509$	−3.15891	+	7.62628i	−0.140016	+	0.338029i	−0.978296	−	0.207211i	$-0.933561\pi$
$509$	−3.15891	+	7.62628i	−0.140016	+	0.338029i	0.838280	+	0.545240i	$0.183561\pi$
$510$	−1.23218	+	2.61201i	−0.0545616	+	0.115662i
$511$	24.6085			1.08862
$512$	16.6275	−	15.3469i	0.734839	−	0.678242i
$513$	0.275011			0.0121421
$514$	−0.409070	+	0.867163i	−0.0180433	+	0.0382489i
$515$	17.8280	−	43.0407i	0.785597	−	1.89660i
$516$	−4.34732	−	5.27554i	−0.191380	−	0.232243i
$517$	27.3684	−	11.3364i	1.20366	−	0.498573i
$518$	13.1866	+	14.5197i	0.579384	+	0.637961i
$519$	1.88673	−	1.88673i	0.0828182	−	0.0828182i
$520$	−39.1075	+	9.92148i	−1.71498	+	0.435086i
$521$	17.3737	+	17.3737i	0.761157	+	0.761157i	0.976531	−	0.215375i	$-0.0690973\pi$
$521$	17.3737	+	17.3737i	0.761157	+	0.761157i	−0.215375	+	0.976531i	$0.569097\pi$
$522$	−0.488598	+	10.1541i	−0.0213854	+	0.444434i
$523$	6.26194	+	15.1177i	0.273816	+	0.661049i	0.999640	−	0.0268308i	$-0.00854153\pi$
$523$	6.26194	+	15.1177i	0.273816	+	0.661049i	−0.725824	+	0.687880i	$0.758542\pi$
$524$	−5.81187	+	1.77579i	−0.253893	+	0.0775758i
$525$	23.3917	+	9.68915i	1.02090	+	0.422869i
$526$	5.18484	+	14.4448i	0.226070	+	0.629823i
$527$		−	2.97770i		−	0.129711i
$528$	−2.40587	+	12.3548i	−0.104702	+	0.537675i
$529$		−	2.87879i		−	0.125165i
$530$	−34.7800	+	12.4840i	−1.51075	+	0.542269i
$531$	−13.3423	−	5.52657i	−0.579008	−	0.239833i
$532$	−1.12422	−	0.598002i	−0.0487411	−	0.0259267i
$533$	−7.63524	−	18.4331i	−0.330719	−	0.798426i
$534$	−0.171181	−	0.00823693i	−0.00740774	−	0.000356447i
$535$	−1.19538	−	1.19538i	−0.0516806	−	0.0516806i
$536$	−1.18611	+	8.16588i	−0.0512321	+	0.352712i
$537$	7.47990	−	7.47990i	0.322781	−	0.322781i
$538$	−24.9842	+	22.6902i	−1.07715	+	0.978244i
$539$	−4.76835	+	1.97512i	−0.205388	+	0.0850743i
$540$	7.94718	+	0.766582i	0.341992	+	0.0329884i
$541$	10.7750	−	26.0132i	0.463255	−	1.11840i	−0.503799	−	0.863821i	$-0.668065\pi$
$541$	10.7750	−	26.0132i	0.463255	−	1.11840i	0.967053	−	0.254574i	$-0.0819354\pi$
$542$	0.996228	+	0.469955i	0.0427917	+	0.0201863i
$543$	−19.2434			−0.825813
$544$	1.71213	−	2.33298i	0.0734069	−	0.100026i
$545$	23.4171			1.00308
$546$	10.5810	+	4.99139i	0.452823	+	0.213612i
$547$	−13.7101	+	33.0991i	−0.586201	+	1.41521i	0.300908	+	0.953653i	$0.402710\pi$
$547$	−13.7101	+	33.0991i	−0.586201	+	1.41521i	−0.887109	+	0.461561i	$0.847290\pi$
$548$	−3.17438	+	32.9089i	−0.135603	+	1.40580i
$549$	−8.10777	+	3.35835i	−0.346031	+	0.143331i
$550$	−36.0278	+	32.7198i	−1.53623	+	1.39518i
$551$	1.39787	−	1.39787i	0.0595512	−	0.0595512i
$552$	−10.1677	+	7.58860i	−0.432768	+	0.322992i
$553$	1.16186	+	1.16186i	0.0494072	+	0.0494072i
$554$	−5.42814	−	0.261192i	−0.230619	−	0.0110970i
$555$	9.15187	+	22.0946i	0.388475	+	0.937862i
$556$	19.5384	−	36.7314i	0.828613	−	1.55776i
$557$	−21.4363	−	8.87921i	−0.908286	−	0.376224i	−0.120886	−	0.992666i	$-0.538573\pi$
$557$	−21.4363	−	8.87921i	−0.908286	−	0.376224i	−0.787400	+	0.616442i	$0.788573\pi$
$558$	−7.74790	+	2.78104i	−0.327995	+	0.117731i
$559$		−	12.2134i		−	0.516571i
$560$	−30.8204	−	20.4146i	−1.30240	−	0.862673i
$561$			1.60974i			0.0679632i
$562$	−2.43764	−	6.79118i	−0.102825	−	0.286469i
$563$	−41.3211	−	17.1158i	−1.74148	−	0.721343i	−0.998655	−	0.0518544i	$-0.983487\pi$
$563$	−41.3211	−	17.1158i	−1.74148	−	0.721343i	−0.742822	−	0.669489i	$-0.766513\pi$
$564$	5.50175	+	18.0063i	0.231665	+	0.758202i
$565$	5.50586	+	13.2923i	0.231633	+	0.559212i
$566$	−0.905905	+	18.8267i	−0.0380780	+	0.791344i
$567$	−1.63704	−	1.63704i	−0.0687493	−	0.0687493i
$568$	2.59051	−	4.35175i	0.108695	−	0.182595i
$569$	29.0924	−	29.0924i	1.21962	−	1.21962i	0.251848	−	0.967767i	$-0.418962\pi$
$569$	29.0924	−	29.0924i	1.21962	−	1.21962i	0.967767	−	0.251848i	$-0.0810384\pi$
$570$	−1.04382	−	1.14935i	−0.0437208	−	0.0481411i
$571$	0.414172	−	0.171556i	0.0173326	−	0.00717938i	−0.374000	−	0.927429i	$-0.622014\pi$
$571$	0.414172	−	0.171556i	0.0173326	−	0.00717938i	0.391333	+	0.920249i	$0.372014\pi$
$572$	−17.3548	+	14.3013i	−0.725642	+	0.597967i
$573$	3.89432	−	9.40172i	0.162688	−	0.392763i
$574$	7.79963	−	16.5340i	0.325550	−	0.690114i
$575$	−49.0567			−2.04581
$576$	−7.66940	−	2.27601i	−0.319559	−	0.0948339i
$577$	23.7041			0.986813			0.493406	−	0.869799i	$-0.335752\pi$
$577$	23.7041			0.986813			0.493406	+	0.869799i	$0.335752\pi$
$578$	−10.0993	+	21.4090i	−0.420078	+	0.890497i
$579$	−2.74568	+	6.62865i	−0.114107	+	0.275477i
$580$	44.2915	−	36.4986i	1.83911	−	1.51552i
$581$	3.26024	−	1.35043i	0.135257	−	0.0560255i
$582$	−0.644294	−	0.709433i	−0.0267069	−	0.0294070i
$583$	−14.5640	+	14.5640i	−0.603178	+	0.603178i
$584$	−25.8338	−	15.3784i	−1.06901	−	0.636362i
$585$	10.0866	+	10.0866i	0.417029	+	0.417029i
$586$	1.55609	−	32.3390i	0.0642816	−	1.33591i
$587$	−6.09999	−	14.7267i	−0.251773	−	0.607835i	0.746574	−	0.665302i	$-0.231697\pi$
$587$	−6.09999	−	14.7267i	−0.251773	−	0.607835i	−0.998347	+	0.0574676i	$0.981697\pi$
$588$	−0.958561	−	3.13721i	−0.0395304	−	0.129376i
$589$	1.47894	+	0.612598i	0.0609388	+	0.0252417i
$590$	27.5444	+	76.7378i	1.13398	+	3.15925i
$591$		−	10.6199i		−	0.436845i
$592$	−4.76946	−	23.4833i	−0.196024	−	0.965157i
$593$			6.36035i			0.261188i	0.991436	+	0.130594i	$0.0416885\pi$
$593$			6.36035i			0.261188i	−0.991436	+	0.130594i	$0.958312\pi$
$594$	4.18849	−	1.50342i	0.171856	−	0.0616862i
$595$	−4.36798	−	1.80928i	−0.179070	−	0.0741731i
$596$	−0.271434	+	0.510285i	−0.0111184	+	0.0209021i
$597$	4.29107	+	10.3596i	0.175622	+	0.423989i
$598$	−22.6415	−	1.08947i	−0.925880	−	0.0445516i
$599$	−4.61895	−	4.61895i	−0.188725	−	0.188725i	0.606420	−	0.795145i	$-0.292605\pi$
$599$	−4.61895	−	4.61895i	−0.188725	−	0.188725i	−0.795145	+	0.606420i	$0.792605\pi$
$600$	−18.5015	−	24.7896i	−0.755319	−	1.01203i
$601$	−10.9077	+	10.9077i	−0.444936	+	0.444936i	−0.893667	−	0.448731i	$-0.851876\pi$
$601$	−10.9077	+	10.9077i	−0.444936	+	0.444936i	0.448731	+	0.893667i	$0.351876\pi$
$602$	8.28425	−	7.52360i	0.337641	−	0.306639i
$603$	2.69530	−	1.11643i	0.109761	−	0.0454645i
$604$	−1.27822	+	13.2513i	−0.0520101	+	0.539190i
$605$	1.67760	−	4.05009i	0.0682043	−	0.164660i
$606$	13.8573	+	6.53698i	0.562916	+	0.265547i
$607$	−0.957019			−0.0388442			−0.0194221	−	0.999811i	$-0.506183\pi$
$607$	−0.957019			−0.0388442			−0.0194221	+	0.999811i	$0.506183\pi$
$608$	0.806493	+	1.33033i	0.0327076	+	0.0539519i
$609$	−16.6420			−0.674367
$610$	44.8089	+	21.1379i	1.81426	+	0.855849i
$611$	−12.8730	+	31.0782i	−0.520787	+	1.25729i
$612$	−1.01839	−	0.0982338i	−0.0411661	−	0.00397087i
$613$	−2.24424	+	0.929594i	−0.0906440	+	0.0375460i	−0.427545	−	0.903994i	$-0.640621\pi$
$613$	−2.24424	+	0.929594i	−0.0906440	+	0.0375460i	0.336901	+	0.941540i	$0.390621\pi$
$614$	−33.6927	+	30.5991i	−1.35973	+	1.23488i
$615$	15.7615	−	15.7615i	0.635564	−	0.635564i
$616$	−20.3913	−	2.96187i	−0.821588	−	0.119337i
$617$	−22.5163	−	22.5163i	−0.906472	−	0.906472i	0.0895138	−	0.995986i	$-0.471469\pi$
$617$	−22.5163	−	22.5163i	−0.906472	−	0.906472i	−0.995986	+	0.0895138i	$0.971469\pi$
$618$	16.4847	+	0.793216i	0.663114	+	0.0319078i
$619$	−3.44381	−	8.31410i	−0.138419	−	0.334172i	0.839436	−	0.543459i	$-0.182886\pi$
$619$	−3.44381	−	8.31410i	−0.138419	−	0.334172i	−0.977854	+	0.209287i	$0.932886\pi$
$620$	41.0303	+	21.8251i	1.64782	+	0.876518i
$621$	4.14422	+	1.71659i	0.166302	+	0.0688844i
$622$	9.57750	−	3.43776i	0.384023	−	0.137842i
$623$		−	0.280555i		−	0.0112402i
$624$	−7.98857	−	11.8522i	−0.319799	−	0.474467i
$625$		−	39.9216i		−	1.59687i
$626$	−7.00639	−	19.5196i	−0.280031	−	0.780160i
$627$	−0.799511	−	0.331168i	−0.0319294	−	0.0132256i
$628$	37.1494	−	11.3509i	1.48242	−	0.452948i
$629$	−1.17277	−	2.83131i	−0.0467613	−	0.112892i
$630$	−0.628189	+	13.0551i	−0.0250277	+	0.520129i
$631$	28.2240	+	28.2240i	1.12358	+	1.12358i	0.991199	+	0.132379i	$0.0422617\pi$
$631$	28.2240	+	28.2240i	1.12358	+	1.12358i	0.132379	+	0.991199i	$0.457738\pi$
$632$	−0.493640	−	1.94578i	−0.0196359	−	0.0773989i
$633$	−18.3458	+	18.3458i	−0.729181	+	0.729181i
$634$	−15.3754	−	16.9299i	−0.610637	−	0.672373i
$635$	−0.540876	+	0.224038i	−0.0214640	+	0.00889068i
$636$	−8.32507	−	10.1026i	−0.330111	−	0.400594i
$637$	2.24285	−	5.41471i	0.0888649	−	0.214539i
$638$	13.6480	−	28.9317i	0.540331	−	1.14542i
$639$	−1.79055			−0.0708329
$640$	19.5975	+	40.6914i	0.774660	+	1.60847i
$641$	−30.2846			−1.19617			−0.598084	−	0.801433i	$-0.704071\pi$
$641$	−30.2846			−1.19617			−0.598084	+	0.801433i	$0.704071\pi$
$642$	0.255510	−	0.541639i	0.0100842	−	0.0213768i
$643$	0.944867	−	2.28111i	0.0372619	−	0.0899582i	−0.904153	−	0.427209i	$-0.859497\pi$
$643$	0.944867	−	2.28111i	0.0372619	−	0.0899582i	0.941415	+	0.337251i	$0.109497\pi$
$644$	−13.2085	−	16.0287i	−0.520487	−	0.631619i
$645$	12.6061	−	5.22161i	0.496364	−	0.205601i
$646$	0.133761	+	0.147284i	0.00526274	+	0.00579481i
$647$	8.32184	−	8.32184i	0.327165	−	0.327165i	−0.524342	−	0.851508i	$-0.675689\pi$
$647$	8.32184	−	8.32184i	0.327165	−	0.327165i	0.851508	+	0.524342i	$0.175689\pi$
$648$	0.695531	+	2.74158i	0.0273231	+	0.107699i
$649$	32.1336	+	32.1336i	1.26136	+	1.26136i
$650$	2.65619	−	55.2014i	0.104184	−	2.16518i
$651$	−5.15703	−	12.4502i	−0.202120	−	0.487960i
$652$	−29.7233	+	9.08182i	−1.16405	+	0.355672i
$653$	19.1159	+	7.91806i	0.748062	+	0.309858i	0.723951	−	0.689852i	$-0.242324\pi$
$653$	19.1159	+	7.91806i	0.748062	+	0.309858i	0.0241116	+	0.999709i	$0.492324\pi$
$654$	2.80260	+	7.80795i	0.109590	+	0.305315i
$655$		−	12.1300i		−	0.473959i
$656$	−18.5204	+	12.4831i	−0.723101	+	0.487382i
$657$			10.6295i			0.414694i
$658$	−29.0101	+	10.4129i	−1.13093	+	0.405938i
$659$	29.0382	+	12.0280i	1.13117	+	0.468546i	0.868178	−	0.496253i	$-0.165291\pi$
$659$	29.0382	+	12.0280i	1.13117	+	0.468546i	0.262991	+	0.964798i	$0.415291\pi$
$660$	−22.1809	−	11.7986i	−0.863389	−	0.459259i
$661$	−6.92538	−	16.7193i	−0.269366	−	0.650307i	0.730088	−	0.683353i	$-0.239479\pi$
$661$	−6.92538	−	16.7193i	−0.269366	−	0.650307i	−0.999454	+	0.0330463i	$0.989479\pi$
$662$	−44.3634	−	2.13469i	−1.72423	−	0.0829669i
$663$	−1.29255	−	1.29255i	−0.0501984	−	0.0501984i
$664$	−4.26649	−	0.619716i	−0.165572	−	0.0240496i
$665$	1.79723	−	1.79723i	0.0696937	−	0.0696937i
$666$	−6.27168	+	5.69583i	−0.243023	+	0.220709i
$667$	29.7901	−	12.3395i	1.15348	−	0.477787i
$668$	30.1485	+	2.90811i	1.16648	+	0.112518i
$669$	−0.219360	+	0.529583i	−0.00848096	+	0.0204749i
$670$	−14.8960	−	7.02696i	−0.575484	−	0.271475i
$671$	27.6150			1.06606
$672$	3.11819	−	12.7197i	0.120287	−	0.490673i
$673$	−19.3968			−0.747691			−0.373846	−	0.927491i	$-0.621961\pi$
$673$	−19.3968			−0.747691			−0.373846	+	0.927491i	$0.621961\pi$
$674$	−2.71186	−	1.27928i	−0.104457	−	0.0492758i
$675$	−4.18515	+	10.1038i	−0.161087	+	0.388897i
$676$	−0.0445054	+	0.461389i	−0.00171175	+	0.0177457i
$677$	−1.10973	+	0.459664i	−0.0426503	+	0.0176663i	−0.403907	−	0.914800i	$-0.632348\pi$
$677$	−1.10973	+	0.459664i	−0.0426503	+	0.0176663i	0.361256	+	0.932467i	$0.382348\pi$
$678$	−3.77311	+	3.42667i	−0.144905	+	0.131600i
$679$	1.10934	−	1.10934i	0.0425724	−	0.0425724i
$680$	3.45482	+	4.62901i	0.132486	+	0.177514i
$681$	2.66721	+	2.66721i	0.102208	+	0.102208i
$682$	25.8736	+	1.24499i	0.990750	+	0.0476731i
$683$	−2.49553	−	6.02475i	−0.0954889	−	0.230531i	0.868916	−	0.494959i	$-0.164817\pi$
$683$	−2.49553	−	6.02475i	−0.0954889	−	0.230531i	−0.964405	+	0.264428i	$0.914817\pi$
$684$	0.258302	−	0.485598i	0.00987643	−	0.0185673i
$685$	−60.9682	−	25.2539i	−2.32948	−	0.964900i
$686$	26.6255	−	9.55697i	1.01656	−	0.364887i
$687$			7.68963i			0.293378i
$688$	−13.3984	+	2.72122i	−0.510809	+	0.103745i
$689$		−	23.3885i		−	0.891030i
$690$	−8.55547	−	23.8353i	−0.325701	−	0.907394i
$691$	−12.2382	−	5.06922i	−0.465563	−	0.192842i	0.137556	−	0.990494i	$-0.456075\pi$
$691$	−12.2382	−	5.06922i	−0.465563	−	0.192842i	−0.603118	+	0.797652i	$0.706075\pi$
$692$	−1.55937	−	5.10356i	−0.0592784	−	0.194008i
$693$	2.78787	+	6.73052i	0.105902	+	0.255671i
$694$	−1.15203	+	23.9417i	−0.0437304	+	0.908813i
$695$	58.7207	+	58.7207i	2.22740	+	2.22740i
$696$	17.4706	+	10.3999i	0.662222	+	0.394208i
$697$	−2.01976	+	2.01976i	−0.0765037	+	0.0765037i
$698$	−6.31915	−	6.95802i	−0.239183	−	0.263365i
$699$	1.80474	−	0.747548i	0.0682615	−	0.0282748i
$700$	39.0789	−	32.2031i	1.47704	−	1.21716i
$701$	14.9505	−	36.0936i	0.564671	−	1.36324i	−0.341322	−	0.939946i	$-0.610875\pi$
$701$	14.9505	−	36.0936i	0.564671	−	1.36324i	0.905994	−	0.423291i	$-0.139125\pi$
$702$	−2.15599	+	4.57036i	−0.0813727	+	0.172497i
$703$	1.64751			0.0621369
$704$	19.5557	+	15.8523i	0.737032	+	0.597456i
$705$	−37.5811			−1.41539
$706$	−16.1595	+	34.2556i	−0.608172	+	1.28923i
$707$	−9.59863	+	23.1731i	−0.360994	+	0.871516i
$708$	−22.2901	+	18.3682i	−0.837715	+	0.690321i
$709$	31.0545	−	12.8632i	1.16627	−	0.483087i	0.286315	−	0.958136i	$-0.407570\pi$
$709$	31.0545	−	12.8632i	1.16627	−	0.483087i	0.879959	+	0.475049i	$0.157570\pi$
$710$	6.79611	+	7.48321i	0.255054	+	0.280840i
$711$	−0.501855	+	0.501855i	−0.0188210	+	0.0188210i
$712$	−0.175325	+	0.294525i	−0.00657058	+	0.0110378i
$713$	18.4628	+	18.4628i	0.691437	+	0.691437i
$714$	0.0804995	−	1.67295i	0.00301262	−	0.0626087i
$715$	−17.1774	−	41.4699i	−0.642399	−	1.55089i
$716$	−6.18209	−	20.2330i	−0.231036	−	0.756141i
$717$	4.23557	+	1.75443i	0.158180	+	0.0655205i
$718$	−14.8395	−	41.3426i	−0.553807	−	1.54289i
$719$			12.6636i			0.472274i	0.971720	+	0.236137i	$0.0758815\pi$
$719$			12.6636i			0.472274i	−0.971720	+	0.236137i	$0.924119\pi$
$720$	8.81790	−	13.3126i	0.328624	−	0.496132i
$721$			27.0174i			1.00618i
$722$	25.1896	−	9.04157i	0.937458	−	0.336492i
$723$	−14.7406	−	6.10576i	−0.548209	−	0.227076i
$724$	−18.0742	+	33.9787i	−0.671722	+	1.26281i
$725$	30.0844	+	72.6302i	1.11731	+	2.69742i
$726$	1.55120	+	0.0746410i	0.0575705	+	0.00277019i
$727$	33.0425	+	33.0425i	1.22548	+	1.22548i	0.965657	+	0.259821i	$0.0836636\pi$
$727$	33.0425	+	33.0425i	1.22548	+	1.22548i	0.259821	+	0.965657i	$0.416336\pi$
$728$	18.7516	−	13.9950i	0.694979	−	0.518691i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	44.4235	−	40.3446i	1.64419	−	1.49322i
$731$	−1.61541	+	0.669124i	−0.0597480	+	0.0247484i
$732$	−1.68520	+	17.4705i	−0.0622867	+	0.645727i
$733$	1.87261	−	4.52088i	0.0691664	−	0.166982i	−0.885516	−	0.464609i	$-0.846195\pi$
$733$	1.87261	−	4.52088i	0.0691664	−	0.166982i	0.954682	+	0.297626i	$0.0961950\pi$
$734$	25.7459	+	12.1452i	0.950297	+	0.448288i
$735$	6.54770			0.241516
$736$	3.84950	+	25.0811i	0.141894	+	0.924501i
$737$	−9.18015			−0.338155
$738$	7.14171	+	3.36899i	0.262890	+	0.124014i
$739$	15.0628	−	36.3648i	0.554093	−	1.33770i	−0.360287	−	0.932842i	$-0.617321\pi$
$739$	15.0628	−	36.3648i	0.554093	−	1.33770i	0.914380	−	0.404857i	$-0.132679\pi$
$740$	47.6090	+	4.59235i	1.75014	+	0.168818i
$741$	0.907887	−	0.376059i	0.0333520	−	0.0138149i
$742$	15.8642	−	14.4076i	0.582394	−	0.528920i
$743$	−20.9250	+	20.9250i	−0.767664	+	0.767664i	−0.977695	−	0.210031i	$-0.932644\pi$
$743$	−20.9250	+	20.9250i	−0.767664	+	0.767664i	0.210031	+	0.977695i	$0.432644\pi$
$744$	−2.36657	+	16.2928i	−0.0867625	+	0.597324i
$745$	−0.815767	−	0.815767i	−0.0298874	−	0.0298874i
$746$	−1.02857	−	0.0494929i	−0.0376587	−	0.00181207i
$747$	0.583309	+	1.40823i	0.0213422	+	0.0515246i
$748$	2.84237	+	1.51193i	0.103927	+	0.0552817i
$749$	0.905765	+	0.375180i	0.0330959	+	0.0137088i
$750$	31.5436	−	11.3223i	1.15181	−	0.413432i
$751$		−	2.47050i		−	0.0901497i	−0.998984	−	0.0450749i	$-0.985647\pi$
$751$		−	2.47050i		−	0.0901497i	0.998984	−	0.0450749i	$-0.0143526\pi$
$752$	36.9618	+	7.19763i	1.34786	+	0.262470i
$753$			21.7334i			0.792008i
$754$	12.2721	+	34.1896i	0.446923	+	1.24511i
$755$	−24.5499	−	10.1689i	−0.893464	−	0.370085i
$756$	−4.42816	+	1.35301i	−0.161051	+	0.0492084i
$757$	2.84324	+	6.86420i	0.103339	+	0.249483i	0.967089	−	0.254437i	$-0.0818903\pi$
$757$	2.84324	+	6.86420i	0.103339	+	0.249483i	−0.863750	+	0.503921i	$0.831890\pi$
$758$	2.44943	−	50.9045i	0.0889673	−	1.84893i
$759$	−9.98092	−	9.98092i	−0.362284	−	0.362284i
$760$	−3.00985	+	0.763593i	−0.109179	+	0.0276984i
$761$	−29.8039	+	29.8039i	−1.08039	+	1.08039i	−0.0839198	+	0.996473i	$0.526744\pi$
$761$	−29.8039	+	29.8039i	−1.08039	+	1.08039i	−0.996473	+	0.0839198i	$0.973256\pi$
$762$	−0.139434	−	0.153531i	−0.00505116	−	0.00556184i
$763$	−12.5467	+	5.19700i	−0.454220	+	0.188144i
$764$	−12.9433	−	15.7068i	−0.468271	−	0.568253i
$765$	0.781502	−	1.88671i	0.0282553	−	0.0682143i
$766$	−18.5018	+	39.2209i	−0.668498	+	1.41711i
$767$	−51.6038			−1.86330
$768$	−11.2223	+	11.4044i	−0.404949	+	0.411522i
$769$	−50.3024			−1.81395			−0.906976	−	0.421182i	$-0.861615\pi$
$769$	−50.3024			−1.81395			−0.906976	+	0.421182i	$0.861615\pi$
$770$	17.5473	−	37.1973i	0.632359	−	1.34050i
$771$	0.259451	−	0.626371i	0.00934391	−	0.0225582i
$772$	9.12560	+	11.0741i	0.328438	+	0.398564i
$773$	−0.373623	+	0.154760i	−0.0134383	+	0.00556632i	−0.389392	−	0.921072i	$-0.627315\pi$
$773$	−0.373623	+	0.154760i	−0.0134383	+	0.00556632i	0.375954	+	0.926638i	$0.377315\pi$
$774$	3.24976	+	3.57831i	0.116810	+	0.128620i
$775$	−45.0134	+	45.0134i	−1.61693	+	1.61693i
$776$	−1.85782	+	0.471325i	−0.0666919	+	0.0169196i
$777$	−9.80699	−	9.80699i	−0.351824	−	0.351824i
$778$	0.732649	−	15.2260i	0.0262667	−	0.545880i
$779$	−0.587635	−	1.41868i	−0.0210542	−	0.0508294i
$780$	27.2840	−	8.33652i	0.976925	−	0.298495i
$781$	5.20546	+	2.15617i	0.186266	+	0.0771540i
$782$	1.09634	+	3.05438i	0.0392051	+	0.109224i
$783$		−	7.18837i		−	0.256891i
$784$	−6.43980	−	1.25403i	−0.229993	−	0.0447868i
$785$			77.5349i			2.76734i
$786$	4.04451	−	1.45174i	0.144263	−	0.0517819i
$787$	−13.9620	−	5.78325i	−0.497692	−	0.206151i	0.119695	−	0.992811i	$-0.461808\pi$
$787$	−13.9620	−	5.78325i	−0.497692	−	0.206151i	−0.617386	+	0.786660i	$0.711808\pi$
$788$	−18.7520	−	9.97467i	−0.668012	−	0.355333i
$789$	−4.15291	−	10.0260i	−0.147847	−	0.356935i
$790$	4.00221	+	0.192579i	0.142392	+	0.00685166i
$791$	−5.89999	−	5.89999i	−0.209779	−	0.209779i
$792$	1.27936	−	8.80785i	0.0454600	−	0.312973i
$793$	−22.1736	+	22.1736i	−0.787408	+	0.787408i
$794$	−37.5333	+	34.0870i	−1.33201	+	1.20970i
$795$	24.1405	−	9.99932i	0.856175	−	0.354639i
$796$	22.3226	+	2.15323i	0.791204	+	0.0763193i
$797$	−1.14025	+	2.75280i	−0.0403896	+	0.0975092i	−0.942787	−	0.333396i	$-0.891806\pi$
$797$	−1.14025	+	2.75280i	−0.0403896	+	0.0975092i	0.902397	+	0.430905i	$0.141806\pi$
$798$	0.814348	+	0.384156i	0.0288276	+	0.0135990i
$799$	4.81584			0.170372
$800$	−61.1492	+	9.38530i	−2.16195	+	0.331821i
$801$	0.121183			0.00428181
$802$	1.54969	+	0.731042i	0.0547215	+	0.0258140i
$803$	12.8000	−	30.9019i	0.451701	−	1.09050i
$804$	0.560217	−	5.80778i	0.0197573	−	0.204825i
$805$	38.3011	−	15.8648i	1.34994	−	0.559162i
$806$	−21.7750	+	19.7757i	−0.766992	+	0.696569i
$807$	16.8750	−	16.8750i	0.594027	−	0.594027i
$808$	24.5580	−	18.3286i	0.863946	−	0.644798i
$809$	−15.2034	−	15.2034i	−0.534524	−	0.534524i	0.387392	−	0.921915i	$-0.373376\pi$
$809$	−15.2034	−	15.2034i	−0.534524	−	0.534524i	−0.921915	+	0.387392i	$0.873376\pi$
$810$	−5.63906	−	0.271341i	−0.198136	−	0.00953396i
$811$	−1.72375	−	4.16149i	−0.0605289	−	0.146130i	0.890721	−	0.454550i	$-0.150200\pi$
$811$	−1.72375	−	4.16149i	−0.0605289	−	0.146130i	−0.951250	+	0.308420i	$0.900200\pi$
$812$	−15.6308	+	29.3853i	−0.548535	+	1.03122i
$813$	−0.719597	−	0.298067i	−0.0252374	−	0.0104537i
$814$	25.0919	−	9.00652i	0.879471	−	0.315678i
$815$		−	62.0357i		−	2.17302i
$816$	−1.12997	+	1.70595i	−0.0395569	+	0.0597201i
$817$		−	0.939986i		−	0.0328859i
$818$	−13.5392	−	37.7198i	−0.473386	−	1.31884i
$819$	−7.64285	−	3.16577i	−0.267063	−	0.110621i
$820$	−13.0268	−	42.6344i	−0.454914	−	1.48886i
$821$	−18.5191	−	44.7092i	−0.646323	−	1.56036i	−0.818007	−	0.575209i	$-0.804921\pi$
$821$	−18.5191	−	44.7092i	−0.646323	−	1.56036i	0.171684	−	0.985152i	$-0.445079\pi$
$822$	1.12361	−	23.3511i	0.0391904	−	0.814462i
$823$	−9.78250	−	9.78250i	−0.340996	−	0.340996i	0.515745	−	0.856742i	$-0.327515\pi$
$823$	−9.78250	−	9.78250i	−0.340996	−	0.340996i	−0.856742	+	0.515745i	$0.827515\pi$
$824$	16.8838	−	28.3627i	0.588174	−	0.988061i
$825$	24.3341	−	24.3341i	0.847204	−	0.847204i
$826$	−31.7886	−	35.0025i	−1.10607	−	1.21789i
$827$	21.3770	−	8.85466i	0.743352	−	0.307907i	0.0213264	−	0.999773i	$-0.493211\pi$
$827$	21.3770	−	8.85466i	0.743352	−	0.307907i	0.722026	+	0.691866i	$0.243211\pi$
$828$	6.92347	−	5.70530i	0.240607	−	0.198273i
$829$	−4.53604	+	10.9510i	−0.157543	+	0.380343i	−0.982867	−	0.184317i	$-0.940993\pi$
$829$	−4.53604	+	10.9510i	−0.157543	+	0.380343i	0.825324	+	0.564660i	$0.190993\pi$
$830$	3.67143	−	7.78284i	0.127437	−	0.270146i
$831$	3.84271			0.133302
$832$	−28.4310	+	2.97365i	−0.985669	+	0.103093i
$833$	−0.839056			−0.0290716
$834$	−12.5514	+	26.6070i	−0.434621	+	0.921327i
$835$	−23.1356	+	55.8543i	−0.800640	+	1.93292i
$836$	−1.33569	+	1.10068i	−0.0461958	+	0.0380678i
$837$	5.37775	−	2.22754i	0.185882	−	0.0769949i
$838$	3.35018	+	3.68889i	0.115730	+	0.127430i
$839$	2.23832	−	2.23832i	0.0772752	−	0.0772752i	−0.667413	−	0.744688i	$-0.732598\pi$
$839$	2.23832	−	2.23832i	0.0772752	−	0.0772752i	0.744688	+	0.667413i	$0.232598\pi$
$840$	22.4619	+	13.3711i	0.775010	+	0.461348i
$841$	−16.0319	−	16.0319i	−0.552826	−	0.552826i
$842$	−0.766660	+	15.9329i	−0.0264208	+	0.549082i
$843$	1.95248	+	4.71370i	0.0672469	+	0.162348i
$844$	15.1627	+	49.6251i	0.521923	+	1.70816i
$845$	−0.854786	−	0.354064i	−0.0294055	−	0.0121802i
$846$	−4.49778	−	12.5307i	−0.154637	−	0.430814i
$847$			2.54232i			0.0873551i
$848$	−25.6578	+	5.21110i	−0.881092	+	0.178950i
$849$		−	13.3279i		−	0.457412i
$850$	−7.44675	+	2.67295i	−0.255422	+	0.0916813i
$851$	24.8267	+	10.2835i	0.851047	+	0.352515i
$852$	−1.68176	+	3.16163i	−0.0576160	+	0.108316i
$853$	8.29470	+	20.0252i	0.284005	+	0.685649i	0.999921	−	0.0125373i	$-0.00399085\pi$
$853$	8.29470	+	20.0252i	0.284005	+	0.685649i	−0.715916	+	0.698186i	$0.753991\pi$
$854$	−28.6994	−	1.38096i	−0.982074	−	0.0472556i
$855$	0.776301	+	0.776301i	0.0265489	+	0.0265489i
$856$	−0.716407	−	0.959893i	−0.0244863	−	0.0328085i
$857$	20.9308	−	20.9308i	0.714984	−	0.714984i	−0.252590	−	0.967574i	$-0.581282\pi$
$857$	20.9308	−	20.9308i	0.714984	−	0.714984i	0.967574	+	0.252590i	$0.0812823\pi$
$858$	11.7715	−	10.6907i	0.401873	−	0.364973i
$859$	4.72981	−	1.95915i	0.161379	−	0.0668453i	−0.300532	−	0.953772i	$-0.597164\pi$
$859$	4.72981	−	1.95915i	0.161379	−	0.0668453i	0.461911	+	0.886927i	$0.347164\pi$
$860$	2.62017	−	27.1634i	0.0893470	−	0.926263i
$861$	−4.94688	+	11.9428i	−0.168589	+	0.407011i
$862$	−45.5893	−	21.5060i	−1.55278	−	0.732498i
$863$	52.6045			1.79068			0.895340	−	0.445384i	$-0.146933\pi$
$863$	52.6045			1.79068			0.895340	+	0.445384i	$0.146933\pi$
$864$	5.49417	+	1.34688i	0.186916	+	0.0458217i
$865$	10.6517			0.362168
$866$	−12.4764	−	5.88554i	−0.423965	−	0.199999i
$867$	6.40547	−	15.4642i	0.217541	−	0.525191i
$868$	−26.8274	−	2.58776i	−0.910581	−	0.0878344i
$869$	2.06332	−	0.854656i	0.0699934	−	0.0289922i
$870$	−30.0422	+	27.2838i	−1.01853	+	0.925008i
$871$	7.37126	−	7.37126i	0.249766	−	0.249766i
$872$	16.4191	+	2.38491i	0.556021	+	0.0807632i
$873$	0.479169	+	0.479169i	0.0162174	+	0.0162174i
$874$	−1.74257	−	0.0838494i	−0.0589434	−	0.00283625i
$875$	20.9955	+	50.6876i	0.709778	+	1.71355i
$876$	18.7688	+	9.98362i	0.634139	+	0.337315i
$877$	−41.7255	−	17.2833i	−1.40897	−	0.583614i	−0.456906	−	0.889515i	$-0.651042\pi$
$877$	−41.7255	−	17.2833i	−1.40897	−	0.583614i	−0.952063	+	0.305901i	$0.901042\pi$
$878$	21.2044	−	7.61112i	0.715613	−	0.256863i
$879$			22.8936i			0.772181i
$880$	−41.6664	+	28.0838i	−1.40457	+	0.946706i
$881$			51.6942i			1.74162i	0.491619	+	0.870811i	$0.336405\pi$
$881$			51.6942i			1.74162i	−0.491619	+	0.870811i	$0.663595\pi$
$882$	0.783641	+	2.18320i	0.0263866	+	0.0735122i
$883$	28.5743	+	11.8358i	0.961601	+	0.398308i	0.807579	−	0.589760i	$-0.200777\pi$
$883$	28.5743	+	11.8358i	0.961601	+	0.398308i	0.154022	+	0.988067i	$0.450777\pi$
$884$	−3.49632	+	1.06828i	−0.117594	+	0.0359303i
$885$	−22.0623	−	53.2630i	−0.741615	−	1.79042i
$886$	−1.63317	+	33.9407i	−0.0548673	+	1.14026i
$887$	10.8240	+	10.8240i	0.363433	+	0.363433i	0.865075	−	0.501642i	$-0.167271\pi$
$887$	10.8240	+	10.8240i	0.363433	+	0.363433i	−0.501642	+	0.865075i	$0.667271\pi$
$888$	4.16671	+	16.4239i	0.139826	+	0.551150i
$889$	0.240075	−	0.240075i	0.00805187	−	0.00805187i
$890$	−0.459958	−	0.506461i	−0.0154178	−	0.0169766i
$891$	−2.90719	+	1.20420i	−0.0973946	+	0.0403422i
$892$	0.729071	+	0.884739i	0.0244111	+	0.0296232i
$893$	−0.990755	+	2.39189i	−0.0331543	+	0.0800417i
$894$	0.174369	−	0.369634i	0.00583177	−	0.0123624i
$895$	42.2284			1.41154
$896$	−19.5309	−	17.4528i	−0.652482	−	0.583056i
$897$	16.0285			0.535176
$898$	7.59224	−	16.0943i	0.253356	−	0.537075i
$899$	16.0123	−	38.6572i	0.534042	−	1.28929i
$900$	13.9099	+	16.8798i	0.463662	+	0.562661i
$901$	−3.09349	+	1.28136i	−0.103059	+	0.0426884i
$902$	−16.7054	−	18.3943i	−0.556229	−	0.612464i
$903$	−5.59539	+	5.59539i	−0.186203	+	0.186203i
$904$	2.50673	+	9.88079i	0.0833727	+	0.328630i
$905$	−54.3201	−	54.3201i	−1.80566	−	1.80566i
$906$	0.452442	−	9.40273i	0.0150314	−	0.312385i
$907$	−12.4155	−	29.9736i	−0.412249	−	0.995257i	−0.984533	−	0.175201i	$-0.943942\pi$
$907$	−12.4155	−	29.9736i	−0.412249	−	0.995257i	0.572284	−	0.820056i	$-0.306058\pi$
$908$	7.21475	−	2.20444i	0.239430	−	0.0731568i
$909$	−10.0095	−	4.14605i	−0.331993	−	0.137516i
$910$	15.7782	+	43.9575i	0.523041	+	1.45718i
$911$		−	27.7454i		−	0.919247i	−0.888114	−	0.459623i	$-0.847984\pi$
$911$		−	27.7454i		−	0.919247i	0.888114	−	0.459623i	$-0.152016\pi$
$912$	−0.614829	−	0.912187i	−0.0203590	−	0.0302055i
$913$		−	4.79643i		−	0.158739i
$914$	54.3052	−	19.4924i	1.79626	−	0.644750i
$915$	−32.3665	−	13.4066i	−1.07000	−	0.443210i
$916$	13.5779	+	7.22242i	0.448625	+	0.238635i
$917$	2.69204	+	6.49915i	0.0888989	+	0.214621i
$918$	0.722619	+	0.0347711i	0.0238500	+	0.00114762i
$919$	−22.9579	−	22.9579i	−0.757311	−	0.757311i	0.218521	−	0.975832i	$-0.429877\pi$
$919$	−22.9579	−	22.9579i	−0.757311	−	0.757311i	−0.975832	+	0.218521i	$0.929877\pi$
$920$	−50.1225	−	7.28039i	−1.65249	−	0.240027i
$921$	22.7569	−	22.7569i	0.749866	−	0.749866i
$922$	−13.3926	+	12.1629i	−0.441061	+	0.400564i
$923$	−5.91107	+	2.44845i	−0.194565	+	0.0805916i
$924$	14.5028	+	1.39894i	0.477107	+	0.0460216i
$925$	−25.0719	+	60.5289i	−0.824359	+	1.99018i
$926$	−23.0625	−	10.8794i	−0.757881	−	0.357518i
$927$	−11.6700			−0.383292
$928$	34.7727	−	21.0805i	1.14147	−	0.692000i
$929$	−14.7767			−0.484807			−0.242404	−	0.970175i	$-0.577936\pi$
$929$	−14.7767			−0.484807			−0.242404	+	0.970175i	$0.577936\pi$
$930$	−29.7210	−	14.0204i	−0.974591	−	0.459748i
$931$	0.172618	−	0.416736i	0.00565731	−	0.0136580i
$932$	0.375114	−	3.88882i	0.0122873	−	0.127383i
$933$	−6.64765	+	2.75355i	−0.217634	+	0.0901471i
$934$	25.2160	−	22.9007i	0.825093	−	0.749334i
$935$	−4.54396	+	4.54396i	−0.148603	+	0.148603i
$936$	6.04505	+	8.09958i	0.197589	+	0.264743i
$937$	25.7038	+	25.7038i	0.839707	+	0.839707i	0.988820	−	0.149113i	$-0.0476418\pi$
$937$	25.7038	+	25.7038i	0.839707	+	0.839707i	−0.149113	+	0.988820i	$0.547642\pi$
$938$	9.54067	+	0.459080i	0.311514	+	0.0149895i
$939$	5.61192	+	13.5484i	0.183138	+	0.442134i
$940$	−35.2978	+	66.3584i	−1.15129	+	2.16437i
$941$	−4.00523	−	1.65902i	−0.130567	−	0.0540826i	0.316443	−	0.948611i	$-0.397511\pi$
$941$	−4.00523	−	1.65902i	−0.130567	−	0.0540826i	−0.447010	+	0.894529i	$0.647511\pi$
$942$	−25.8525	+	9.27952i	−0.842319	+	0.302343i
$943$		−	25.0464i		−	0.815622i
$944$	11.4977	+	56.6107i	0.374217	+	1.84252i
$945$		−	9.24206i		−	0.300644i
$946$	−5.13868	−	14.3162i	−0.167073	−	0.465460i
$947$	−15.2678	−	6.32413i	−0.496136	−	0.205506i	0.120562	−	0.992706i	$-0.461530\pi$
$947$	−15.2678	−	6.32413i	−0.496136	−	0.205506i	−0.616699	+	0.787199i	$0.711530\pi$
$948$	0.414780	+	1.35751i	0.0134714	+	0.0440898i
$949$	14.5350	+	35.0907i	0.471827	+	1.13909i
$950$	0.204430	−	4.24850i	0.00663258	−	0.137839i
$951$	11.4349	+	11.4349i	0.370801	+	0.370801i
$952$	−2.87839	−	1.71345i	−0.0932890	−	0.0555332i
$953$	19.6560	−	19.6560i	0.636719	−	0.636719i	−0.313026	−	0.949745i	$-0.601343\pi$
$953$	19.6560	−	19.6560i	0.636719	−	0.636719i	0.949745	+	0.313026i	$0.101343\pi$
$954$	6.22325	+	6.85243i	0.201485	+	0.221856i
$955$	37.5320	−	15.5463i	1.21451	−	0.503065i
$956$	7.07609	−	5.83107i	0.228857	−	0.188590i
$957$	−8.65622	+	20.8980i	−0.279816	+	0.675535i
$958$	−6.78941	+	14.3924i	−0.219356	+	0.464999i
$959$	38.2709			1.23583
$960$	−15.2244	−	28.0739i	−0.491366	−	0.906080i
$961$	2.88209			0.0929707
$962$	−12.9159	+	27.3795i	−0.416424	+	0.882752i
$963$	−0.162056	+	0.391238i	−0.00522218	+	0.0126075i
$964$	−24.6262	+	20.2933i	−0.793156	+	0.653602i
$965$	−26.4618	+	10.9608i	−0.851836	+	0.352842i
$966$	9.87376	+	10.8720i	0.317683	+	0.349801i
$967$	13.4891	−	13.4891i	0.433781	−	0.433781i	−0.456131	−	0.889912i	$-0.650765\pi$
$967$	13.4891	−	13.4891i	0.433781	−	0.433781i	0.889912	+	0.456131i	$0.150765\pi$
$968$	1.58875	−	2.66891i	0.0510644	−	0.0857820i
$969$	−0.0994792	−	0.0994792i	−0.00319573	−	0.00319573i
$970$	0.183874	−	3.82129i	0.00590383	−	0.122694i
$971$	16.3983	+	39.5889i	0.526246	+	1.27047i	0.933966	+	0.357362i	$0.116324\pi$
$971$	16.3983	+	39.5889i	0.526246	+	1.27047i	−0.407720	+	0.913107i	$0.633676\pi$
$972$	−0.584420	−	1.91271i	−0.0187453	−	0.0613501i
$973$	−44.4940	−	18.4300i	−1.42641	−	0.590840i
$974$	−15.6248	−	43.5302i	−0.500650	−	1.39480i
$975$			39.0784i			1.25151i
$976$	29.2655	+	19.3846i	0.936764	+	0.620486i
$977$			15.7216i			0.502979i	0.967860	+	0.251489i	$0.0809203\pi$
$977$			15.7216i			0.502979i	−0.967860	+	0.251489i	$0.919080\pi$
$978$	20.6846	−	7.42455i	0.661420	−	0.237411i
$979$	−0.352304	−	0.145929i	−0.0112597	−	0.00466391i
$980$	6.14987	−	11.5615i	0.196451	−	0.369319i
$981$	−2.24480	−	5.41943i	−0.0716710	−	0.173029i
$982$	36.6510	+	1.76358i	1.16958	+	0.0562781i
$983$	10.9749	+	10.9749i	0.350046	+	0.350046i	0.860127	−	0.510080i	$-0.170384\pi$
$983$	10.9749	+	10.9749i	0.350046	+	0.350046i	−0.510080	+	0.860127i	$0.670384\pi$
$984$	12.6565	−	9.44608i	0.403476	−	0.301130i
$985$	29.9778	−	29.9778i	0.955173	−	0.955173i
$986$	3.84977	−	3.49629i	0.122602	−	0.111345i
$987$	20.1357	−	8.34046i	0.640925	−	0.265480i
$988$	0.188704	−	1.95630i	0.00600347	−	0.0622382i
$989$	5.86728	−	14.1649i	0.186569	−	0.450417i
$990$	16.0671	+	7.57939i	0.510646	+	0.240889i
$991$	32.2476			1.02438			0.512190	−	0.858872i	$-0.328834\pi$
$991$	32.2476			1.02438			0.512190	+	0.858872i	$0.328834\pi$
$992$	26.5461	+	19.4816i	0.842838	+	0.618542i
$993$	31.4060			0.996638
$994$	−5.30206	−	2.50116i	−0.168171	−	0.0793321i
$995$	−17.1301	+	41.3557i	−0.543061	+	1.31107i
$996$	3.03444	+	0.292701i	0.0961498	+	0.00927458i
$997$	22.2570	−	9.21915i	0.704886	−	0.291973i	−0.00130036	−	0.999999i	$-0.500414\pi$
$997$	22.2570	−	9.21915i	0.704886	−	0.291973i	0.706187	+	0.708026i	$0.250414\pi$
$998$	0.751023	−	0.682065i	0.0237732	−	0.0215904i
$999$	4.23605	−	4.23605i	0.134023	−	0.134023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.2.n.a.13.3	✓	32
3.2	odd	2		288.2.v.d.109.6		32
4.3	odd	2		384.2.n.a.145.4		32
8.3	odd	2		768.2.n.b.289.5		32
8.5	even	2		768.2.n.a.289.1		32
12.11	even	2		1152.2.v.c.145.1		32
32.5	even	8	inner	96.2.n.a.37.3	yes	32
32.11	odd	8		768.2.n.b.481.5		32
32.21	even	8		768.2.n.a.481.1		32
32.27	odd	8		384.2.n.a.241.4		32
96.5	odd	8		288.2.v.d.37.6		32
96.59	even	8		1152.2.v.c.1009.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.3	✓	32	1.1	even	1	trivial
96.2.n.a.37.3	yes	32	32.5	even	8	inner
288.2.v.d.37.6		32	96.5	odd	8
288.2.v.d.109.6		32	3.2	odd	2
384.2.n.a.145.4		32	4.3	odd	2
384.2.n.a.241.4		32	32.27	odd	8
768.2.n.a.289.1		32	8.5	even	2
768.2.n.a.481.1		32	32.21	even	8
768.2.n.b.289.5		32	8.3	odd	2
768.2.n.b.481.5		32	32.11	odd	8
1152.2.v.c.145.1		32	12.11	even	2
1152.2.v.c.1009.1		32	96.59	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.603367 + 1.27904i) q^{2} +(0.382683 - 0.923880i) q^{3} +(-1.27190 - 1.54346i) q^{4} +(3.68816 - 1.52768i) q^{5} +(0.950782 + 1.04691i) q^{6} +(-1.63704 + 1.63704i) q^{7} +(2.74158 - 0.695531i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.603367 + 1.27904i) q^{2} +(0.382683 - 0.923880i) q^{3} +(-1.27190 - 1.54346i) q^{4} +(3.68816 - 1.52768i) q^{5} +(0.950782 + 1.04691i) q^{6} +(-1.63704 + 1.63704i) q^{7} +(2.74158 - 0.695531i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-0.271341 + 5.63906i) q^{10} +(1.20420 + 2.90719i) q^{11} +(-1.91271 + 0.584420i) q^{12} +(-3.30127 - 1.36743i) q^{13} +(-1.10611 - 3.08158i) q^{14} -3.99203i q^{15} +(-0.764563 + 3.92625i) q^{16} +0.511560i q^{17} +(1.33106 - 0.477774i) q^{18} +(-0.254077 - 0.105242i) q^{19} +(-7.04888 - 3.74948i) q^{20} +(0.885960 + 2.13890i) q^{21} +(-4.44500 - 0.213885i) q^{22} +(-3.17185 - 3.17185i) q^{23} +(0.406568 - 2.79905i) q^{24} +(7.73315 - 7.73315i) q^{25} +(3.74088 - 3.39740i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(4.60886 + 0.444569i) q^{28} +(-2.75087 + 6.64118i) q^{29} +(5.10598 + 2.40866i) q^{30} -5.82083 q^{31} +(-4.56053 - 3.34688i) q^{32} +3.14672 q^{33} +(-0.654306 - 0.308659i) q^{34} +(-3.53678 + 8.53855i) q^{35} +(-0.192028 + 1.99076i) q^{36} +(-5.53467 + 2.29253i) q^{37} +(0.287911 - 0.261476i) q^{38} +(-2.52668 + 2.52668i) q^{39} +(9.04881 - 6.75349i) q^{40} +(3.94823 + 3.94823i) q^{41} +(-3.27030 - 0.157361i) q^{42} +(1.30801 + 3.15781i) q^{43} +(2.95553 - 5.55628i) q^{44} +(-3.68816 - 1.52768i) q^{45} +(5.97071 - 2.14313i) q^{46} -9.41403i q^{47} +(3.33480 + 2.20888i) q^{48} +1.64019i q^{49} +(5.22509 + 14.5570i) q^{50} +(0.472620 + 0.195765i) q^{51} +(2.08829 + 6.83462i) q^{52} +(2.50482 + 6.04717i) q^{53} +(0.0679707 - 1.41258i) q^{54} +(8.88255 + 8.88255i) q^{55} +(-3.34946 + 5.62669i) q^{56} +(-0.194462 + 0.194462i) q^{57} +(-6.83457 - 7.52555i) q^{58} +(13.3423 - 5.52657i) q^{59} +(-6.16156 + 5.07745i) q^{60} +(3.35835 - 8.10777i) q^{61} +(3.51210 - 7.44509i) q^{62} +2.31513 q^{63} +(7.03247 - 3.81370i) q^{64} -14.2646 q^{65} +(-1.89863 + 4.02479i) q^{66} +(-1.11643 + 2.69530i) q^{67} +(0.789574 - 0.650651i) q^{68} +(-4.14422 + 1.71659i) q^{69} +(-8.78718 - 9.67558i) q^{70} +(1.26611 - 1.26611i) q^{71} +(-2.43040 - 1.44677i) q^{72} +(-7.51616 - 7.51616i) q^{73} +(0.407191 - 8.46231i) q^{74} +(-4.18515 - 10.1038i) q^{75} +(0.160722 + 0.526017i) q^{76} +(-6.73052 - 2.78787i) q^{77} +(-1.70721 - 4.75625i) q^{78} -0.709730i q^{79} +(3.17824 + 15.6486i) q^{80} +1.00000i q^{81} +(-7.43218 + 2.66772i) q^{82} +(-1.40823 - 0.583309i) q^{83} +(2.17446 - 4.08790i) q^{84} +(0.781502 + 1.88671i) q^{85} +(-4.82818 - 0.232323i) q^{86} +(5.08294 + 5.08294i) q^{87} +(5.32345 + 7.13273i) q^{88} +(-0.0856897 + 0.0856897i) q^{89} +(4.17929 - 3.79555i) q^{90} +(7.64285 - 3.16577i) q^{91} +(-0.861374 + 8.92989i) q^{92} +(-2.22754 + 5.37775i) q^{93} +(12.0409 + 5.68012i) q^{94} -1.09785 q^{95} +(-4.83735 + 2.93258i) q^{96} -0.677647 q^{97} +(-2.09787 - 0.989638i) q^{98} +(1.20420 - 2.90719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} - 16 q^{12} - 32 q^{14} - 8 q^{16} - 8 q^{18} - 32 q^{20} - 8 q^{22} - 16 q^{23} - 8 q^{24} + 40 q^{26} + 40 q^{28} - 48 q^{31} + 40 q^{32} + 40 q^{34} - 48 q^{35} + 40 q^{38} + 8 q^{40} - 16 q^{43} + 8 q^{44} - 32 q^{46} + 24 q^{50} + 16 q^{51} - 8 q^{52} - 32 q^{53} + 8 q^{54} + 32 q^{55} + 56 q^{56} - 32 q^{58} + 64 q^{59} + 48 q^{60} - 32 q^{61} + 48 q^{62} + 16 q^{63} + 24 q^{64} + 48 q^{66} + 16 q^{67} - 8 q^{68} - 32 q^{69} - 24 q^{70} + 64 q^{71} - 32 q^{74} + 32 q^{75} - 56 q^{76} - 32 q^{77} + 24 q^{78} - 56 q^{80} - 40 q^{82} - 64 q^{86} - 48 q^{88} - 48 q^{91} - 80 q^{92} - 32 q^{94} - 40 q^{96} - 80 q^{98}+O(q^{100}) \) 32 * q - 8 * q^10 - 16 * q^12 - 32 * q^14 - 8 * q^16 - 8 * q^18 - 32 * q^20 - 8 * q^22 - 16 * q^23 - 8 * q^24 + 40 * q^26 + 40 * q^28 - 48 * q^31 + 40 * q^32 + 40 * q^34 - 48 * q^35 + 40 * q^38 + 8 * q^40 - 16 * q^43 + 8 * q^44 - 32 * q^46 + 24 * q^50 + 16 * q^51 - 8 * q^52 - 32 * q^53 + 8 * q^54 + 32 * q^55 + 56 * q^56 - 32 * q^58 + 64 * q^59 + 48 * q^60 - 32 * q^61 + 48 * q^62 + 16 * q^63 + 24 * q^64 + 48 * q^66 + 16 * q^67 - 8 * q^68 - 32 * q^69 - 24 * q^70 + 64 * q^71 - 32 * q^74 + 32 * q^75 - 56 * q^76 - 32 * q^77 + 24 * q^78 - 56 * q^80 - 40 * q^82 - 64 * q^86 - 48 * q^88 - 48 * q^91 - 80 * q^92 - 32 * q^94 - 40 * q^96 - 80 * q^98

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