LMFDB - Embedded newform 950.2.w.a.113.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.44
Character	$\chi$	$=$	950.113
Dual form			950.2.w.a.227.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 + 0.987688i) q^{2} +(1.49304 + 0.760743i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.0580574 - 2.23531i) q^{5} +(-0.517814 + 1.59367i) q^{6} +(-3.23452 + 3.23452i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.112910 - 0.155407i) q^{9} +O(q^{10})$	\(q+(0.156434 + 0.987688i) q^{2} +(1.49304 + 0.760743i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.0580574 - 2.23531i) q^{5} +(-0.517814 + 1.59367i) q^{6} +(-3.23452 + 3.23452i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.112910 - 0.155407i) q^{9} +(2.19871 - 0.407023i) q^{10} +(-2.45597 - 1.78436i) q^{11} +(-1.65505 - 0.262134i) q^{12} +(-0.941505 + 5.94443i) q^{13} +(-3.70069 - 2.68871i) q^{14} +(1.61382 - 3.38159i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.63180 + 3.20258i) q^{17} +(0.135830 - 0.135830i) q^{18} +(-3.95629 - 1.82969i) q^{19} +(0.745966 + 2.10797i) q^{20} +(-7.28992 + 2.36864i) q^{21} +(1.37820 - 2.70486i) q^{22} +(0.863660 + 5.45294i) q^{23} -1.67568i q^{24} +(-4.99326 + 0.259553i) q^{25} -6.01853 q^{26} +(-0.836757 - 5.28308i) q^{27} +(2.07669 - 4.07574i) q^{28} +(-0.130709 - 0.402281i) q^{29} +(3.59241 + 1.06495i) q^{30} +(-3.31636 - 1.07755i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.30942 - 4.53249i) q^{33} +(-2.90788 + 2.11270i) q^{34} +(7.41796 + 7.04239i) q^{35} +(0.155407 + 0.112910i) q^{36} +(-7.68778 - 1.21762i) q^{37} +(1.18826 - 4.19381i) q^{38} +(-5.92789 + 8.15905i) q^{39} +(-1.96532 + 1.06654i) q^{40} +(-0.859241 - 1.18264i) q^{41} +(-3.47987 - 6.82963i) q^{42} +(4.43125 + 4.43125i) q^{43} +(2.88716 + 0.938095i) q^{44} +(-0.340828 + 0.261411i) q^{45} +(-5.25070 + 1.70605i) q^{46} +(-2.88053 - 1.46770i) q^{47} +(1.65505 - 0.262134i) q^{48} -13.9243i q^{49} +(-1.03748 - 4.89118i) q^{50} +6.02297i q^{51} +(-0.941505 - 5.94443i) q^{52} +(5.41254 + 2.75783i) q^{53} +(5.08713 - 1.65291i) q^{54} +(-3.84603 + 5.59345i) q^{55} +(4.35042 + 1.41354i) q^{56} +(-4.51499 - 5.74153i) q^{57} +(0.376881 - 0.192031i) q^{58} +(2.71432 - 1.97207i) q^{59} +(-0.489865 + 3.71478i) q^{60} +(4.23186 + 3.07463i) q^{61} +(0.545491 - 3.44409i) q^{62} +(0.867875 + 0.137458i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(13.3423 + 1.75944i) q^{65} +(4.11542 - 2.99002i) q^{66} +(-11.4427 + 5.83033i) q^{67} +(-2.54158 - 2.54158i) q^{68} +(-2.85880 + 8.79849i) q^{69} +(-5.79526 + 8.42831i) q^{70} +(3.76930 - 1.22472i) q^{71} +(-0.0872085 + 0.171156i) q^{72} +(1.95845 + 12.3652i) q^{73} -7.78361i q^{74} +(-7.65260 - 3.41106i) q^{75} +(4.32806 + 0.517577i) q^{76} +(13.7154 - 2.17231i) q^{77} +(-8.98592 - 4.57856i) q^{78} +(4.18130 + 12.8687i) q^{79} +(-1.36085 - 1.77428i) q^{80} +(2.59167 - 7.97634i) q^{81} +(1.03367 - 1.03367i) q^{82} +(-4.75828 + 2.42447i) q^{83} +(6.20118 - 4.50542i) q^{84} +(7.06404 - 3.83351i) q^{85} +(-3.68349 + 5.06989i) q^{86} +(0.110879 - 0.700059i) q^{87} +(-0.474894 + 2.99837i) q^{88} +(-0.823413 - 0.598244i) q^{89} +(-0.311510 - 0.295738i) q^{90} +(-16.1821 - 22.2727i) q^{91} +(-2.50644 - 4.91916i) q^{92} +(-4.13172 - 4.13172i) q^{93} +(0.999019 - 3.07466i) q^{94} +(-3.86024 + 8.94978i) q^{95} +(0.517814 + 1.59367i) q^{96} +(5.07201 - 9.95438i) q^{97} +(13.7528 - 2.17824i) q^{98} +0.583145i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$-1$

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 $

$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$2$	0.156434	+	0.987688i	0.110616	+	0.698401i
$3$	1.49304	+	0.760743i	0.862009	+	0.439215i	0.828345	−	0.560218i	$-0.189283\pi$
$3$	1.49304	+	0.760743i	0.862009	+	0.439215i	0.0336633	+	0.999433i	$0.489283\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−0.0580574	−	2.23531i	−0.0259641	−	0.999663i
$5$	−0.0580574	−	2.23531i	−0.0259641	−	0.999663i
$6$	−0.517814	+	1.59367i	−0.211397	+	0.650612i
$7$	−3.23452	+	3.23452i	−1.22253	+	1.22253i	−0.255806	+	0.966728i	$0.582341\pi$
$7$	−3.23452	+	3.23452i	−1.22253	+	1.22253i	−0.966728	+	0.255806i	$0.917659\pi$
$8$	−0.453990	−	0.891007i	−0.160510	−	0.315018i
$9$	−0.112910	−	0.155407i	−0.0376365	−	0.0518022i
$10$	2.19871	−	0.407023i	0.695294	−	0.128712i
$11$	−2.45597	−	1.78436i	−0.740502	−	0.538006i	0.152367	−	0.988324i	$-0.451311\pi$
$11$	−2.45597	−	1.78436i	−0.740502	−	0.538006i	−0.892868	+	0.450318i	$0.851311\pi$
$12$	−1.65505	−	0.262134i	−0.477772	−	0.0756716i
$13$	−0.941505	+	5.94443i	−0.261127	+	1.64869i	0.413481	+	0.910513i	$0.364313\pi$
$13$	−0.941505	+	5.94443i	−0.261127	+	1.64869i	−0.674608	+	0.738176i	$0.735687\pi$
$14$	−3.70069	−	2.68871i	−0.989051	−	0.718588i
$15$	1.61382	−	3.38159i	0.416686	−	0.873122i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	1.63180	+	3.20258i	0.395769	+	0.776740i	0.999795	−	0.0202239i	$-0.00643791\pi$
$17$	1.63180	+	3.20258i	0.395769	+	0.776740i	−0.604027	+	0.796964i	$0.706438\pi$
$18$	0.135830	−	0.135830i	0.0320155	−	0.0320155i
$19$	−3.95629	−	1.82969i	−0.907635	−	0.419759i
$19$	−3.95629	−	1.82969i	−0.907635	−	0.419759i
$20$	0.745966	+	2.10797i	0.166803	+	0.471356i
$21$	−7.28992	+	2.36864i	−1.59079	+	0.516879i
$22$	1.37820	−	2.70486i	0.293833	−	0.576679i
$23$	0.863660	+	5.45294i	0.180086	+	1.13702i	0.897710	+	0.440586i	$0.145229\pi$
$23$	0.863660	+	5.45294i	0.180086	+	1.13702i	−0.717625	+	0.696430i	$0.754771\pi$
$24$		−	1.67568i		−	0.342047i
$25$	−4.99326	+	0.259553i	−0.998652	+	0.0519106i
$26$	−6.01853			−1.18033
$27$	−0.836757	−	5.28308i	−0.161034	−	1.01673i
$28$	2.07669	−	4.07574i	0.392458	−	0.770242i
$29$	−0.130709	−	0.402281i	−0.0242721	−	0.0747018i	0.938187	−	0.346129i	$-0.112504\pi$
$29$	−0.130709	−	0.402281i	−0.0242721	−	0.0747018i	−0.962459	+	0.271428i	$0.912504\pi$
$30$	3.59241	+	1.06495i	0.655881	+	0.194433i
$31$	−3.31636	−	1.07755i	−0.595635	−	0.193534i	−0.00434249	−	0.999991i	$-0.501382\pi$
$31$	−3.31636	−	1.07755i	−0.595635	−	0.193534i	−0.591293	+	0.806457i	$0.701382\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−2.30942	−	4.53249i	−0.402018	−	0.789005i
$34$	−2.90788	+	2.11270i	−0.498698	+	0.362325i
$35$	7.41796	+	7.04239i	1.25386	+	1.19038i
$36$	0.155407	+	0.112910i	0.0259011	+	0.0188183i
$37$	−7.68778	−	1.21762i	−1.26386	−	0.200176i	−0.511706	−	0.859161i	$-0.670986\pi$
$37$	−7.68778	−	1.21762i	−1.26386	−	0.200176i	−0.752157	+	0.658984i	$0.770986\pi$
$38$	1.18826	−	4.19381i	0.192762	−	0.680326i
$39$	−5.92789	+	8.15905i	−0.949223	+	1.30649i
$40$	−1.96532	+	1.06654i	−0.310745	+	0.168635i
$41$	−0.859241	−	1.18264i	−0.134191	−	0.184698i	0.736633	−	0.676292i	$-0.236414\pi$
$41$	−0.859241	−	1.18264i	−0.134191	−	0.184698i	−0.870824	+	0.491594i	$0.836414\pi$
$42$	−3.47987	−	6.82963i	−0.536956	−	1.05384i
$43$	4.43125	+	4.43125i	0.675759	+	0.675759i	0.959038	−	0.283279i	$-0.0914222\pi$
$43$	4.43125	+	4.43125i	0.675759	+	0.675759i	−0.283279	+	0.959038i	$0.591422\pi$
$44$	2.88716	+	0.938095i	0.435256	+	0.141423i
$45$	−0.340828	+	0.261411i	−0.0508076	+	0.0389688i
$46$	−5.25070	+	1.70605i	−0.774173	+	0.251544i
$47$	−2.88053	−	1.46770i	−0.420168	−	0.214086i	0.231106	−	0.972928i	$-0.425765\pi$
$47$	−2.88053	−	1.46770i	−0.420168	−	0.214086i	−0.651275	+	0.758842i	$0.725765\pi$
$48$	1.65505	−	0.262134i	0.238886	−	0.0378358i
$49$		−	13.9243i		−	1.98918i
$50$	−1.03748	−	4.89118i	−0.146721	−	0.691717i
$51$			6.02297i			0.843385i
$52$	−0.941505	−	5.94443i	−0.130563	−	0.824344i
$53$	5.41254	+	2.75783i	0.743469	+	0.378816i	0.784326	−	0.620349i	$-0.213009\pi$
$53$	5.41254	+	2.75783i	0.743469	+	0.378816i	−0.0408571	+	0.999165i	$0.513009\pi$
$54$	5.08713	−	1.65291i	0.692271	−	0.224933i
$55$	−3.84603	+	5.59345i	−0.518598	+	0.754221i
$56$	4.35042	+	1.41354i	0.581350	+	0.188892i
$57$	−4.51499	−	5.74153i	−0.598025	−	0.760484i
$58$	0.376881	−	0.192031i	0.0494869	−	0.0252149i
$59$	2.71432	−	1.97207i	0.353374	−	0.256741i	−0.396909	−	0.917858i	$-0.629917\pi$
$59$	2.71432	−	1.97207i	0.353374	−	0.256741i	0.750283	+	0.661117i	$0.229917\pi$
$60$	−0.489865	+	3.71478i	−0.0632412	+	0.479576i
$61$	4.23186	+	3.07463i	0.541834	+	0.393666i	0.824766	−	0.565475i	$-0.191307\pi$
$61$	4.23186	+	3.07463i	0.541834	+	0.393666i	−0.282932	+	0.959140i	$0.591307\pi$
$62$	0.545491	−	3.44409i	0.0692774	−	0.437400i
$63$	0.867875	+	0.137458i	0.109342	+	0.0173181i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	13.3423	+	1.75944i	1.65491	+	0.218232i
$66$	4.11542	−	2.99002i	0.506573	−	0.368047i
$67$	−11.4427	+	5.83033i	−1.39794	+	0.712288i	−0.980519	−	0.196424i	$-0.937067\pi$
$67$	−11.4427	+	5.83033i	−1.39794	+	0.712288i	−0.417424	+	0.908712i	$0.637067\pi$
$68$	−2.54158	−	2.54158i	−0.308212	−	0.308212i
$69$	−2.85880	+	8.79849i	−0.344159	+	1.05921i
$70$	−5.79526	+	8.42831i	−0.692666	+	1.00738i
$71$	3.76930	−	1.22472i	0.447334	−	0.145348i	−0.0766827	−	0.997056i	$-0.524433\pi$
$71$	3.76930	−	1.22472i	0.447334	−	0.145348i	0.524017	+	0.851708i	$0.324433\pi$
$72$	−0.0872085	+	0.171156i	−0.0102776	+	0.0201710i
$73$	1.95845	+	12.3652i	0.229219	+	1.44723i	0.786850	+	0.617144i	$0.211711\pi$
$73$	1.95845	+	12.3652i	0.229219	+	1.44723i	−0.557631	+	0.830089i	$0.688289\pi$
$74$		−	7.78361i		−	0.904826i
$75$	−7.65260	−	3.41106i	−0.883646	−	0.393876i
$76$	4.32806	+	0.517577i	0.496463	+	0.0593701i
$77$	13.7154	−	2.17231i	1.56302	−	0.247558i
$78$	−8.98592	−	4.57856i	−1.01746	−	0.518419i
$79$	4.18130	+	12.8687i	0.470433	+	1.44785i	0.852019	+	0.523512i	$0.175378\pi$
$79$	4.18130	+	12.8687i	0.470433	+	1.44785i	−0.381585	+	0.924334i	$0.624622\pi$
$80$	−1.36085	−	1.77428i	−0.152148	−	0.198371i
$81$	2.59167	−	7.97634i	0.287963	−	0.886260i
$82$	1.03367	−	1.03367i	0.114150	−	0.114150i
$83$	−4.75828	+	2.42447i	−0.522289	+	0.266120i	−0.695198	−	0.718818i	$-0.744683\pi$
$83$	−4.75828	+	2.42447i	−0.522289	+	0.266120i	0.172909	+	0.984938i	$0.444683\pi$
$84$	6.20118	−	4.50542i	0.676604	−	0.491581i
$85$	7.06404	−	3.83351i	0.766203	−	0.415803i
$86$	−3.68349	+	5.06989i	−0.397201	+	0.546700i
$87$	0.110879	−	0.700059i	0.0118874	−	0.0750543i
$88$	−0.474894	+	2.99837i	−0.0506239	+	0.319627i
$89$	−0.823413	−	0.598244i	−0.0872816	−	0.0634138i	0.543289	−	0.839546i	$-0.317179\pi$
$89$	−0.823413	−	0.598244i	−0.0872816	−	0.0634138i	−0.630570	+	0.776132i	$0.717179\pi$
$90$	−0.311510	−	0.295738i	−0.0328360	−	0.0311735i
$91$	−16.1821	−	22.2727i	−1.69634	−	2.33482i
$92$	−2.50644	−	4.91916i	−0.261314	−	0.512858i
$93$	−4.13172	−	4.13172i	−0.428440	−	0.428440i
$94$	0.999019	−	3.07466i	0.103041	−	0.317127i
$95$	−3.86024	+	8.94978i	−0.396052	+	0.918228i
$96$	0.517814	+	1.59367i	0.0528492	+	0.162653i
$97$	5.07201	−	9.95438i	0.514985	−	1.01071i	−0.476338	−	0.879262i	$-0.658036\pi$
$97$	5.07201	−	9.95438i	0.514985	−	1.01071i	0.991323	−	0.131452i	$-0.0419640\pi$
$98$	13.7528	−	2.17824i	1.38925	−	0.220035i
$99$			0.583145i			0.0586083i
$100$	4.66866	−	1.78985i	0.466866	−	0.178985i
$101$	8.38540			0.834378			0.417189	−	0.908820i	$-0.363015\pi$
$101$	8.38540			0.834378			0.417189	+	0.908820i	$0.363015\pi$
$102$	−5.94882	+	0.942200i	−0.589021	+	0.0932917i
$103$	−1.77190	−	0.902828i	−0.174590	−	0.0889583i	0.364511	−	0.931199i	$-0.381236\pi$
$103$	−1.77190	−	0.902828i	−0.174590	−	0.0889583i	−0.539102	+	0.842241i	$0.681236\pi$
$104$	5.72396	−	1.85983i	0.561281	−	0.182371i
$105$	5.71789	+	16.1577i	0.558009	+	1.57683i
$106$	−1.87716	+	5.77732i	−0.182326	+	0.561143i
$107$	4.86286	+	4.86286i	0.470111	+	0.470111i	0.901950	−	0.431840i	$-0.142135\pi$
$107$	4.86286	+	4.86286i	0.470111	+	0.470111i	−0.431840	+	0.901950i	$0.642135\pi$
$108$	2.42836	+	4.76593i	0.233669	+	0.458602i
$109$	15.9340	−	11.5767i	1.52620	−	1.10885i	0.567895	−	0.823101i	$-0.307758\pi$
$109$	15.9340	−	11.5767i	1.52620	−	1.10885i	0.958305	−	0.285748i	$-0.0922420\pi$
$110$	−6.12624	−	2.92367i	−0.584114	−	0.278761i
$111$	−10.5519	−	7.66639i	−1.00154	−	0.727662i
$112$	−0.715579	+	4.51799i	−0.0676159	+	0.426910i
$113$	2.81930	−	17.8004i	0.265218	−	1.67452i	−0.391343	−	0.920245i	$-0.627989\pi$
$113$	2.81930	−	17.8004i	0.265218	−	1.67452i	0.656560	−	0.754273i	$-0.272011\pi$
$114$	4.96454	−	5.35757i	0.464972	−	0.501783i
$115$	12.1389	−	2.24714i	1.13196	−	0.209546i
$116$	0.248624	+	0.342201i	0.0230841	+	0.0317726i
$117$	1.03011	−	0.524867i	0.0952336	−	0.0485240i
$118$	2.37240	+	2.37240i	0.218397	+	0.218397i
$119$	−15.6369	−	5.08074i	−1.43343	−	0.465751i
$120$	−3.74567	+	0.0972857i	−0.341932	+	0.00888092i
$121$	−0.551373	−	1.69695i	−0.0501248	−	0.154268i
$122$	−2.37476	+	4.66074i	−0.215001	+	0.421963i
$123$	−0.383195	−	2.41940i	−0.0345516	−	0.218150i
$124$	3.48702			0.313144
$125$	0.870078	+	11.1464i	0.0778221	+	0.996967i
$126$			0.878693i			0.0782802i
$127$	0.113146	+	0.714373i	0.0100400	+	0.0633903i	0.992200	−	0.124659i	$-0.0397836\pi$
$127$	0.113146	+	0.714373i	0.0100400	+	0.0633903i	−0.982160	+	0.188049i	$0.939784\pi$
$128$	−0.891007	−	0.453990i	−0.0787546	−	0.0401275i
$129$	3.24500	+	9.98708i	0.285706	+	0.879313i
$130$	0.349420	+	13.4533i	0.0306462	+	1.17993i
$131$	−2.30047	+	7.08012i	−0.200993	+	0.618593i	0.798861	+	0.601515i	$0.205436\pi$
$131$	−2.30047	+	7.08012i	−0.200993	+	0.618593i	−0.999854	+	0.0170772i	$0.994564\pi$
$132$	3.59700	+	3.59700i	0.313079	+	0.313079i
$133$	18.7149	−	6.87854i	1.62279	−	0.596445i
$134$	−7.54857	−	10.3897i	−0.652097	−	0.897535i
$135$	−11.7608	+	2.17714i	−1.01220	+	0.187378i
$136$	2.11270	−	2.90788i	0.181163	−	0.249349i
$137$	−2.32465	+	14.6772i	−0.198608	+	1.25396i	0.663862	+	0.747855i	$0.268916\pi$
$137$	−2.32465	+	14.6772i	−0.198608	+	1.25396i	−0.862471	+	0.506107i	$0.831084\pi$
$138$	−9.13738	−	1.44722i	−0.777826	−	0.123195i
$139$	2.41131	−	3.31889i	0.204525	−	0.281504i	−0.694417	−	0.719573i	$-0.744337\pi$
$139$	2.41131	−	3.31889i	0.204525	−	0.281504i	0.898941	+	0.438069i	$0.144337\pi$
$140$	−9.23112	−	4.40543i	−0.780172	−	0.372327i
$141$	−3.18421	−	4.38269i	−0.268159	−	0.369089i
$142$	1.79929	+	3.53131i	0.150993	+	0.296341i
$143$	12.9193	−	12.9193i	1.08037	−	1.08037i
$144$	−0.182692	−	0.0593601i	−0.0152243	−	0.00494667i
$145$	−0.891637	+	0.315531i	−0.0740464	+	0.0262035i
$146$	−11.9066	+	3.86868i	−0.985394	+	0.320174i
$147$	10.5928	−	20.7895i	0.873679	−	1.71469i
$148$	7.68778	−	1.21762i	0.631931	−	0.100088i
$149$		−	9.21964i		−	0.755303i	−0.925948	−	0.377651i	$-0.876732\pi$
$149$		−	9.21964i		−	0.755303i	0.925948	−	0.377651i	$-0.123268\pi$
$150$	2.17194	−	8.09199i	0.177338	−	0.660708i
$151$		−	6.69157i		−	0.544552i	−0.962219	−	0.272276i	$-0.912224\pi$
$151$		−	6.69157i		−	0.544552i	0.962219	−	0.272276i	$-0.0877764\pi$
$152$	0.165854	+	4.35574i	0.0134525	+	0.353297i
$153$	0.313457	−	0.615194i	0.0253415	−	0.0497355i
$154$	4.29113	+	13.2068i	0.345789	+	1.06423i
$155$	−2.21612	+	7.47566i	−0.178003	+	0.600459i
$156$	3.11648	−	9.59153i	0.249518	−	0.767937i
$157$	−11.8699	+	11.8699i	−0.947325	+	0.947325i	−0.998680	−	0.0513554i	$-0.983646\pi$
$157$	−11.8699	+	11.8699i	−0.947325	+	0.947325i	0.0513554	+	0.998680i	$0.483646\pi$
$158$	−12.0562	+	6.14294i	−0.959139	+	0.488706i
$159$	5.98315	+	8.23510i	0.474495	+	0.653086i
$160$	1.53955	−	1.62166i	0.121712	−	0.128203i
$161$	−20.4312	−	14.8441i	−1.61020	−	1.16988i
$162$	8.28356	+	1.31199i	0.650818	+	0.103079i
$163$	0.174120	+	0.0275779i	0.0136381	+	0.00216007i	0.163250	−	0.986585i	$-0.447802\pi$
$163$	0.174120	+	0.0275779i	0.0136381	+	0.00216007i	−0.149612	+	0.988745i	$0.547802\pi$
$164$	1.18264	+	0.859241i	0.0923490	+	0.0670955i
$165$	−9.99746	+	5.42542i	−0.778301	+	0.422369i
$166$	−3.13898	−	4.32043i	−0.243632	−	0.335330i
$167$	−8.42465	+	4.29257i	−0.651919	+	0.332169i	−0.748480	−	0.663158i	$-0.769216\pi$
$167$	−8.42465	+	4.29257i	−0.651919	+	0.332169i	0.0965607	+	0.995327i	$0.469216\pi$
$168$	5.42003	+	5.42003i	0.418164	+	0.418164i
$169$	−22.0861	−	7.17621i	−1.69893	−	0.552016i
$170$	4.89138	+	6.37738i	0.375151	+	0.489122i
$171$	0.162357	+	0.821423i	0.0124158	+	0.0628158i
$172$	−5.58370	−	2.84503i	−0.425753	−	0.216932i
$173$	−1.80440	+	0.285789i	−0.137186	+	0.0217282i	−0.224650	−	0.974440i	$-0.572124\pi$
$173$	−1.80440	+	0.285789i	−0.137186	+	0.0217282i	0.0874637	+	0.996168i	$0.472124\pi$
$174$	0.708786			0.0537329
$175$	15.3113	−	16.9903i	1.15742	−	1.28435i
$176$	−3.03574			−0.228828
$177$	5.55283	−	0.879482i	0.417376	−	0.0661059i
$178$	0.462069	−	0.906861i	0.0346335	−	0.0679721i
$179$	7.31242	+	22.5053i	0.546556	+	1.68213i	0.717261	+	0.696805i	$0.245396\pi$
$179$	7.31242	+	22.5053i	0.546556	+	1.68213i	−0.170704	+	0.985322i	$0.554604\pi$
$180$	0.243366	−	0.353938i	0.0181394	−	0.0263810i
$181$	7.29410	+	2.37000i	0.542166	+	0.176160i	0.567281	−	0.823524i	$-0.307995\pi$
$181$	7.29410	+	2.37000i	0.542166	+	0.176160i	−0.0251151	+	0.999685i	$0.507995\pi$
$182$	19.4671	−	19.4671i	1.44300	−	1.44300i
$183$	3.97935	+	7.80991i	0.294162	+	0.577325i
$184$	4.46651	−	3.24511i	0.329275	−	0.239233i
$185$	−2.27544	+	17.2553i	−0.167294	+	1.26863i
$186$	3.43451	−	4.72720i	0.251831	−	0.346615i
$187$	1.70693	−	10.7772i	0.124823	−	0.788103i
$188$	3.19309	+	0.505736i	0.232880	+	0.0368846i
$189$	19.7947	+	14.3817i	1.43986	+	1.04612i
$190$	−9.44347	−	2.41266i	−0.685101	−	0.175033i
$191$	−21.0734	+	15.3107i	−1.52482	+	1.10784i	−0.565782	+	0.824555i	$0.691426\pi$
$191$	−21.0734	+	15.3107i	−1.52482	+	1.10784i	−0.959034	+	0.283289i	$0.908574\pi$
$192$	−1.49304	+	0.760743i	−0.107751	+	0.0549019i
$193$	−2.22876	+	2.22876i	−0.160429	+	0.160429i	−0.782757	−	0.622327i	$-0.786187\pi$
$193$	−2.22876	+	2.22876i	−0.160429	+	0.160429i	0.622327	+	0.782757i	$0.286187\pi$
$194$	10.6253	+	3.45236i	0.762850	+	0.247865i
$195$	18.5822	+	12.7770i	1.33070	+	0.914981i
$196$	4.30284	+	13.2428i	0.307345	+	0.945912i
$197$	−9.56881	−	4.87555i	−0.681750	−	0.347369i	0.0785785	−	0.996908i	$-0.474962\pi$
$197$	−9.56881	−	4.87555i	−0.681750	−	0.347369i	−0.760328	+	0.649539i	$0.774962\pi$
$198$	−0.575966	+	0.0912240i	−0.0409321	+	0.00648301i
$199$			18.1446i			1.28624i	0.765767	+	0.643118i	$0.222360\pi$
$199$			18.1446i			1.28624i	−0.765767	+	0.643118i	$0.777640\pi$
$200$	2.49816	+	4.33119i	0.176646	+	0.306261i
$201$	−21.5198			−1.51789
$202$	1.31177	+	8.28216i	0.0922955	+	0.582731i
$203$	1.72397	+	0.878407i	0.120999	+	0.0616521i
$204$	−1.86120	−	5.72819i	−0.130310	−	0.401053i
$205$	−2.59370	+	1.98933i	−0.181152	+	0.138941i
$206$	0.614526	−	1.89132i	0.0428161	−	0.131774i
$207$	0.749907	−	0.749907i	0.0521222	−	0.0521222i
$208$	2.73236	+	5.36255i	0.189455	+	0.371826i
$209$	6.45168	+	11.5531i	0.446272	+	0.799146i
$210$	−15.0643	+	8.17512i	−1.03954	+	0.564137i
$211$	4.27037	−	5.87766i	0.293984	−	0.404635i	−0.636319	−	0.771426i	$-0.719544\pi$
$211$	4.27037	−	5.87766i	0.293984	−	0.404635i	0.930303	+	0.366791i	$0.119544\pi$
$212$	−5.99984	−	0.950282i	−0.412071	−	0.0652656i
$213$	6.55943	+	1.03891i	0.449445	+	0.0711851i
$214$	−4.04227	+	5.56371i	−0.276324	+	0.380328i
$215$	9.64796	−	10.1625i	0.657985	−	0.693076i
$216$	−4.32738	+	3.14402i	−0.294441	+	0.213924i
$217$	14.2122	−	7.24147i	0.964786	−	0.491583i
$218$	13.9268	+	13.9268i	0.943243	+	0.943243i
$219$	−6.48267	+	19.9516i	−0.438058	+	1.34820i
$220$	1.92932	−	6.50817i	0.130075	−	0.438781i
$221$	−20.5739	+	6.68486i	−1.38395	+	0.449672i
$222$	5.92133	−	11.6213i	0.397413	−	0.779968i
$223$	−1.43862	+	0.227854i	−0.0963368	+	0.0152583i	−0.204417	−	0.978884i	$-0.565530\pi$
$223$	−1.43862	+	0.227854i	−0.0963368	+	0.0152583i	0.108080	+	0.994142i	$0.465530\pi$
$224$	−4.57431			−0.305634
$225$	0.604123	+	0.746680i	0.0402749	+	0.0497786i
$226$	18.0223			1.19882
$227$	−1.65064	−	10.4217i	−0.109557	−	0.691714i	−0.979933	−	0.199327i	$-0.936124\pi$
$227$	−1.65064	−	10.4217i	−0.109557	−	0.691714i	0.870376	−	0.492387i	$-0.163876\pi$
$228$	6.06824	+	4.06531i	0.401879	+	0.269232i
$229$	18.4581	−	5.99740i	1.21975	−	0.396320i	0.372757	−	0.927929i	$-0.378413\pi$
$229$	18.4581	−	5.99740i	1.21975	−	0.396320i	0.846990	+	0.531610i	$0.178413\pi$
$230$	4.11841	+	11.6379i	0.271560	+	0.767381i
$231$	22.1303	+	7.19057i	1.45607	+	0.473105i
$232$	−0.299095	+	0.299095i	−0.0196365	+	0.0196365i
$233$	−3.07482	+	1.56670i	−0.201438	+	0.102638i	−0.551800	−	0.833977i	$-0.686059\pi$
$233$	−3.07482	+	1.56670i	−0.201438	+	0.102638i	0.350362	+	0.936615i	$0.386059\pi$
$234$	0.679550	+	0.935320i	0.0444235	+	0.0611438i
$235$	−3.11354	+	6.52410i	−0.203105	+	0.425585i
$236$	−1.97207	+	2.71432i	−0.128371	+	0.176687i
$237$	−3.54693	+	22.3945i	−0.230398	+	1.45468i
$238$	2.57204	−	16.2392i	0.166720	−	1.05263i
$239$	−9.55434	+	13.1504i	−0.618019	+	0.850630i	−0.997207	−	0.0746898i	$-0.976203\pi$
$239$	−9.55434	+	13.1504i	−0.618019	+	0.850630i	0.379188	+	0.925320i	$0.376203\pi$
$240$	−0.682040	−	3.68434i	−0.0440255	−	0.237823i
$241$	16.8493	+	23.1911i	1.08536	+	1.49387i	0.853481	+	0.521123i	$0.174487\pi$
$241$	16.8493	+	23.1911i	1.08536	+	1.49387i	0.231878	+	0.972745i	$0.425513\pi$
$242$	1.58980	−	0.810046i	0.102197	−	0.0520717i
$243$	−1.40937	+	1.40937i	−0.0904113	+	0.0904113i
$244$	−4.97485	−	1.61643i	−0.318482	−	0.103481i
$245$	−31.1251	+	0.808407i	−1.98851	+	0.0516472i
$246$	2.32967	−	0.756955i	0.148534	−	0.0482617i
$247$	14.6013	−	21.7952i	0.929060	−	1.38680i
$248$	0.545491	+	3.44409i	0.0346387	+	0.218700i
$249$	−8.94872			−0.567102
$250$	−10.8731	+	2.60305i	−0.687675	+	0.164631i
$251$	9.64675			0.608897			0.304449	−	0.952529i	$-0.401528\pi$
$251$	9.64675			0.608897			0.304449	+	0.952529i	$0.401528\pi$
$252$	−0.867875	+	0.137458i	−0.0546710	+	0.00865903i
$253$	7.60890	−	14.9333i	0.478367	−	0.938849i
$254$	−0.687878	+	0.223505i	−0.0431613	+	0.0140240i
$255$	13.4632	−	0.349678i	0.843100	−	0.0218977i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	12.7430	+	12.7430i	0.794885	+	0.794885i	0.982284	−	0.187399i	$-0.0600056\pi$
$257$	12.7430	+	12.7430i	0.794885	+	0.794885i	−0.187399	+	0.982284i	$0.560006\pi$
$258$	−9.35649	+	4.76737i	−0.582510	+	0.296804i
$259$	28.8047	−	20.9279i	1.78984	−	1.30039i
$260$	−13.2330	+	2.44968i	−0.820676	+	0.151923i
$261$	−0.0477589	+	0.0657345i	−0.00295620	+	0.00406886i
$262$	−7.35282	−	1.16457i	−0.454259	−	0.0719475i
$263$	−10.0245	−	1.58773i	−0.618138	−	0.0979034i	−0.160491	−	0.987037i	$-0.551308\pi$
$263$	−10.0245	−	1.58773i	−0.618138	−	0.0979034i	−0.457647	+	0.889134i	$0.651308\pi$
$264$	−2.99002	+	4.11542i	−0.184023	+	0.253286i
$265$	5.85037	−	12.2588i	0.359385	−	0.753054i
$266$	9.72151	+	17.4084i	0.596064	+	1.06738i
$267$	−0.774280	−	1.51961i	−0.0473852	−	0.0929986i
$268$	9.08095	−	9.08095i	0.554707	−	0.554707i
$269$	6.22508	−	19.1588i	0.379550	−	1.16813i	−0.560808	−	0.827946i	$-0.689509\pi$
$269$	6.22508	−	19.1588i	0.379550	−	1.16813i	0.940357	−	0.340188i	$-0.110491\pi$
$270$	−3.99012	−	11.2754i	−0.242831	−	0.686198i
$271$	−1.81183	−	5.57624i	−0.110061	−	0.338733i	0.880824	−	0.473444i	$-0.156989\pi$
$271$	−1.81183	−	5.57624i	−0.110061	−	0.338733i	−0.990885	+	0.134711i	$0.956989\pi$
$272$	3.20258	+	1.63180i	0.194185	+	0.0989422i
$273$	−7.21671	−	45.5645i	−0.436775	−	2.75769i
$274$	−14.8602			−0.897738
$275$	12.7264	+	8.27234i	0.767431	+	0.498841i
$276$		−	9.25128i		−	0.556862i
$277$	2.42885	−	0.384692i	0.145935	−	0.0231139i	−0.0830393	−	0.996546i	$-0.526463\pi$
$277$	2.42885	−	0.384692i	0.145935	−	0.0231139i	0.228975	+	0.973432i	$0.426463\pi$
$278$	3.65524	+	1.86244i	0.219227	+	0.111702i
$279$	0.206990	+	0.637050i	0.0123922	+	0.0381392i
$280$	2.90713	−	9.80663i	0.173734	−	0.586058i
$281$	−27.3937	−	8.90075i	−1.63417	−	0.530974i	−0.658945	−	0.752191i	$-0.728997\pi$
$281$	−27.3937	−	8.90075i	−1.63417	−	0.530974i	−0.975225	+	0.221217i	$0.928997\pi$
$282$	3.83061	−	3.83061i	0.228109	−	0.228109i
$283$	−21.8537	+	11.1350i	−1.29907	+	0.661908i	−0.960302	−	0.278962i	$-0.910010\pi$
$283$	−21.8537	+	11.1350i	−1.29907	+	0.661908i	−0.338766	+	0.940871i	$0.610010\pi$
$284$	−3.20636	+	2.32956i	−0.190263	+	0.138234i
$285$	−12.5720	+	10.4258i	−0.744700	+	0.617568i
$286$	14.7813	+	10.7392i	0.874037	+	0.635025i
$287$	6.60452	+	1.04605i	0.389853	+	0.0617466i
$288$	0.0300500	−	0.189728i	0.00177071	−	0.0111798i
$289$	2.39858	−	3.30136i	0.141093	−	0.194198i
$290$	−0.451129	−	0.831299i	−0.0264912	−	0.0488156i
$291$	15.1455	−	11.0038i	0.887843	−	0.645055i
$292$	−5.68364	−	11.1548i	−0.332610	−	0.652784i
$293$	13.5583	−	13.5583i	0.792083	−	0.792083i	−0.189750	−	0.981833i	$-0.560768\pi$
$293$	13.5583	−	13.5583i	0.792083	−	0.792083i	0.981833	+	0.189750i	$0.0607676\pi$
$294$	22.1907	+	7.21018i	1.29419	+	0.420506i
$295$	−4.56578	−	5.95286i	−0.265830	−	0.346589i
$296$	2.40527	+	7.40265i	0.139803	+	0.430270i
$297$	−7.37188	+	14.4681i	−0.427760	+	0.839526i
$298$	9.10613	−	1.44227i	0.527504	−	0.0835484i
$299$	−33.2277			−1.92161
$300$	8.33213	+	0.879331i	0.481056	+	0.0507682i
$301$	−28.6659			−1.65228
$302$	6.60918	−	1.04679i	0.380316	−	0.0602361i
$303$	12.5198	+	6.37914i	0.719241	+	0.366472i
$304$	−4.27617	+	0.845200i	−0.245255	+	0.0484755i
$305$	6.62707	−	9.63804i	0.379465	−	0.551873i
$306$	0.656656	+	0.213360i	0.0375385	+	0.0121970i
$307$	−9.26924	−	9.26924i	−0.529024	−	0.529024i	0.391258	−	0.920281i	$-0.372040\pi$
$307$	−9.26924	−	9.26924i	−0.529024	−	0.529024i	−0.920281	+	0.391258i	$0.872040\pi$
$308$	−12.3729	+	6.30430i	−0.705010	+	0.359221i
$309$	−1.95870	−	2.69592i	−0.111427	−	0.153366i
$310$	−7.73030	−	1.01939i	−0.439052	−	0.0578974i
$311$	27.2287	+	19.7828i	1.54400	+	1.12178i	0.947767	+	0.318965i	$0.103335\pi$
$311$	27.2287	+	19.7828i	1.54400	+	1.12178i	0.596229	+	0.802814i	$0.296665\pi$
$312$	9.96097	+	1.57766i	0.563929	+	0.0893176i
$313$	−25.3513	−	4.01525i	−1.43294	−	0.226955i	−0.608791	−	0.793330i	$-0.708345\pi$
$313$	−25.3513	−	4.01525i	−1.43294	−	0.226955i	−0.824148	+	0.566375i	$0.808345\pi$
$314$	−13.5807	−	9.86694i	−0.766402	−	0.556824i
$315$	0.256875	−	1.94795i	0.0144733	−	0.109755i
$316$	−7.95331	−	10.9468i	−0.447409	−	0.615805i
$317$	−10.3231	+	5.25990i	−0.579805	+	0.295426i	−0.719191	−	0.694813i	$-0.755487\pi$
$317$	−10.3231	+	5.25990i	−0.579805	+	0.295426i	0.139385	+	0.990238i	$0.455487\pi$
$318$	−7.19774	+	7.19774i	−0.403629	+	0.403629i
$319$	−0.396799	+	1.22122i	−0.0222165	+	0.0683753i
$320$	1.84253	+	1.26692i	0.103001	+	0.0708227i
$321$	3.56107	+	10.9599i	0.198760	+	0.611719i
$322$	11.4652	−	22.5018i	0.638932	−	1.25397i
$323$	−0.596135	−	15.6560i	−0.0331698	−	0.871125i
$324$			8.38682i			0.465934i
$325$	3.15829	−	29.9265i	0.175190	−	1.66002i
$326$			0.176291i			0.00976383i
$327$	32.5970	−	5.16286i	1.80262	−	0.285507i
$328$	−0.663656	+	1.30250i	−0.0366443	+	0.0719184i
$329$	14.0645	−	4.56982i	0.775398	−	0.251942i
$330$	−6.92257	−	9.02565i	−0.381075	−	0.496846i
$331$	−17.3653	−	5.64234i	−0.954486	−	0.310131i	−0.209949	−	0.977712i	$-0.567330\pi$
$331$	−17.3653	−	5.64234i	−0.954486	−	0.310131i	−0.744537	+	0.667581i	$0.767330\pi$
$332$	3.77620	−	3.77620i	0.207246	−	0.207246i
$333$	0.678797	+	1.33221i	0.0371978	+	0.0730048i
$334$	−5.55763	−	7.64942i	−0.304100	−	0.418558i
$335$	13.6969	+	25.2394i	0.748344	+	1.37898i
$336$	−4.50542	+	6.20118i	−0.245791	+	0.338302i
$337$	−31.9950	−	5.06751i	−1.74288	−	0.276045i	−0.797809	−	0.602910i	$-0.794008\pi$
$337$	−31.9950	−	5.06751i	−1.74288	−	0.276045i	−0.945071	+	0.326865i	$0.894008\pi$
$338$	3.63283	−	22.9368i	0.197600	−	1.24760i
$339$	17.7509	−	24.4320i	0.964094	−	1.32696i
$340$	−5.53368	+	5.82880i	−0.300106	+	0.316111i
$341$	6.22212	+	8.56401i	0.336947	+	0.463767i
$342$	−0.785912	+	0.288857i	−0.0424973	+	0.0156196i
$343$	22.3967	+	22.3967i	1.20931	+	1.20931i
$344$	1.93653	−	5.96001i	0.104410	−	0.321342i
$345$	19.8334	+	5.87951i	1.06779	+	0.316542i
$346$	−0.564541	−	1.73748i	−0.0303499	−	0.0934075i
$347$	−17.3768	−	8.85395i	−0.932838	−	0.475305i	−0.0796002	−	0.996827i	$-0.525364\pi$
$347$	−17.3768	−	8.85395i	−0.932838	−	0.475305i	−0.853238	+	0.521522i	$0.825364\pi$
$348$	0.110879	+	0.700059i	0.00594371	+	0.0375271i
$349$			24.6873i			1.32148i	0.750615	+	0.660740i	$0.229758\pi$
$349$			24.6873i			1.32148i	−0.750615	+	0.660740i	$0.770242\pi$
$350$	19.1764	+	12.4649i	1.02502	+	0.666277i
$351$	32.1927			1.71832
$352$	−0.474894	−	2.99837i	−0.0253120	−	0.159813i
$353$	5.15643	−	10.1201i	0.274449	−	0.538637i	−0.712105	−	0.702073i	$-0.752258\pi$
$353$	5.15643	−	10.1201i	0.274449	−	0.538637i	0.986554	+	0.163436i	$0.0522578\pi$
$354$	1.73731	+	5.34688i	0.0923369	+	0.284184i
$355$	−2.95647	−	8.35448i	−0.156913	−	0.443410i
$356$	0.967980	+	0.314516i	0.0513028	+	0.0166693i
$357$	−19.4814	−	19.4814i	−1.03107	−	1.03107i
$358$	−21.0843	+	10.7430i	−1.11434	+	0.567785i
$359$	10.8066	+	14.8741i	0.570352	+	0.785023i	0.992596	−	0.121459i	$-0.0387574\pi$
$359$	10.8066	+	14.8741i	0.570352	+	0.785023i	−0.422244	+	0.906482i	$0.638757\pi$
$360$	0.387651	+	0.185001i	0.0204310	+	0.00975043i
$361$	12.3045	+	14.4776i	0.647604	+	0.761977i
$362$	−1.19977	+	7.57505i	−0.0630585	+	0.398136i
$363$	0.467721	−	2.95307i	0.0245490	−	0.154996i
$364$	22.2727	+	16.1821i	1.16741	+	0.848171i
$365$	27.5263	−	5.09564i	1.44079	−	0.266718i
$366$	−7.09125	+	5.15209i	−0.370665	+	0.269304i
$367$	−3.65286	−	7.16915i	−0.190678	−	0.374226i	0.775799	−	0.630980i	$-0.217347\pi$
$367$	−3.65286	−	7.16915i	−0.190678	−	0.374226i	−0.966477	+	0.256754i	$0.917347\pi$
$368$	3.90387	+	3.90387i	0.203503	+	0.203503i
$369$	−0.0867742	+	0.267064i	−0.00451729	+	0.0139028i
$370$	−17.3988	+	0.451896i	−0.904521	+	0.0234929i
$371$	−26.4272	+	8.58672i	−1.37203	+	0.445800i
$372$	5.20628	+	2.65273i	0.269933	+	0.137538i
$373$	19.1551	−	3.03388i	0.991815	−	0.157088i	0.360621	−	0.932713i	$-0.382565\pi$
$373$	19.1551	−	3.03388i	0.991815	−	0.157088i	0.631195	+	0.775624i	$0.282565\pi$
$374$	10.9115			0.564220
$375$	−7.18051	+	17.3040i	−0.370800	+	0.893575i
$376$			3.23289i			0.166724i
$377$	2.51440	−	0.398242i	0.129498	−	0.0205105i
$378$	−11.1081	+	21.8008i	−0.571338	+	1.12131i
$379$	4.43373	+	13.6456i	0.227745	+	0.700928i	0.998001	+	0.0631933i	$0.0201285\pi$
$379$	4.43373	+	13.6456i	0.227745	+	0.700928i	−0.770256	+	0.637735i	$0.779872\pi$
$380$	0.905670	−	9.70463i	0.0464599	−	0.497837i
$381$	−0.374523	+	1.15266i	−0.0191874	+	0.0590528i
$382$	−18.4188	−	18.4188i	−0.942389	−	0.942389i
$383$	12.9159	+	25.3489i	0.659971	+	1.29527i	0.941920	+	0.335837i	$0.109019\pi$
$383$	12.9159	+	25.3489i	0.659971	+	1.29527i	−0.281949	+	0.959429i	$0.590981\pi$
$384$	−0.984941	−	1.35565i	−0.0502625	−	0.0691804i
$385$	−5.65208	−	30.5322i	−0.288057	−	1.55606i
$386$	−2.54997	−	1.85266i	−0.129790	−	0.0942981i
$387$	0.188315	−	1.18898i	0.00957260	−	0.0604390i
$388$	−1.74770	+	11.0345i	−0.0887258	+	0.560193i
$389$	−1.49135	+	2.05266i	−0.0756143	+	0.104074i	−0.845149	−	0.534531i	$-0.820488\pi$
$389$	−1.49135	+	2.05266i	−0.0756143	+	0.104074i	0.769535	+	0.638605i	$0.220488\pi$
$390$	−9.71281	+	20.3522i	−0.491827	+	1.03057i
$391$	−16.0542	+	11.6640i	−0.811894	+	0.589875i
$392$	−12.4066	+	6.32149i	−0.626629	+	0.319283i
$393$	−8.82085	+	8.82085i	−0.444953	+	0.444953i
$394$	3.31864	−	10.2137i	0.167190	−	0.514559i
$395$	28.5229	−	10.0937i	1.43514	−	0.507867i
$396$	−0.180202	−	0.554604i	−0.00905548	−	0.0278699i
$397$	10.2247	+	5.20974i	0.513163	+	0.261469i	0.691341	−	0.722529i	$-0.257020\pi$
$397$	10.2247	+	5.20974i	0.513163	+	0.261469i	−0.178178	+	0.983998i	$0.557020\pi$
$398$	−17.9212	+	2.83844i	−0.898309	+	0.142278i
$399$	33.1749	+	3.96726i	1.66082	+	0.198612i
$400$	−3.88707	+	3.14495i	−0.194353	+	0.157247i
$401$		−	5.84511i		−	0.291891i	−0.989293	−	0.145946i	$-0.953378\pi$
$401$		−	5.84511i		−	0.291891i	0.989293	−	0.145946i	$-0.0466224\pi$
$402$	−3.36643	−	21.2548i	−0.167902	−	1.06009i
$403$	9.52779	−	18.6993i	0.474613	−	0.931480i
$404$	−7.97499	+	2.59123i	−0.396771	+	0.128919i
$405$	−17.9801	−	5.33011i	−0.893438	−	0.264855i
$406$	−0.597904	+	1.84016i	−0.0296735	+	0.0913255i
$407$	16.7082	+	16.7082i	0.828196	+	0.828196i
$408$	5.36651	−	2.73437i	0.265682	−	0.135372i
$409$	−29.6816	+	21.5650i	−1.46766	+	1.06632i	−0.486380	+	0.873747i	$0.661683\pi$
$409$	−29.6816	+	21.5650i	−1.46766	+	1.06632i	−0.981283	+	0.192572i	$0.938317\pi$
$410$	−2.37059	−	2.25056i	−0.117075	−	0.111147i
$411$	−14.6364	+	20.1453i	−0.721961	+	0.993694i
$412$	1.96417	+	0.311093i	0.0967675	+	0.0153265i
$413$	−2.40083	+	15.1582i	−0.118137	+	0.745887i
$414$	0.857986	+	0.623363i	0.0421677	+	0.0306366i
$415$	5.69570	+	10.4955i	0.279591	+	0.515204i
$416$	−4.86909	+	3.53760i	−0.238727	+	0.173445i
$417$	6.12501	−	3.12085i	0.299943	−	0.152829i
$418$	−10.4016	+	8.17956i	−0.508759	+	0.400075i
$419$	−17.4730	−	5.67734i	−0.853614	−	0.277356i	−0.150655	−	0.988586i	$-0.548138\pi$
$419$	−17.4730	−	5.67734i	−0.853614	−	0.277356i	−0.702959	+	0.711230i	$0.748138\pi$
$420$	−10.4311	−	13.6000i	−0.508983	−	0.663612i
$421$	−2.16597	+	0.703766i	−0.105563	+	0.0342995i	−0.361322	−	0.932441i	$-0.617675\pi$
$421$	−2.16597	+	0.703766i	−0.105563	+	0.0342995i	0.255759	+	0.966740i	$0.417675\pi$
$422$	6.47333	+	3.29833i	0.315117	+	0.160560i
$423$	0.0971484	+	0.613371i	0.00472352	+	0.0298231i
$424$		−	6.07463i		−	0.295010i
$425$	−8.97922	−	15.5678i	−0.435556	−	0.755148i
$426$			6.64120i			0.321767i
$427$	−23.6330	+	3.74310i	−1.14368	+	0.181141i
$428$	−6.12757	−	3.12215i	−0.296187	−	0.150915i
$429$	29.1174	−	9.46082i	1.40580	−	0.456773i
$430$	11.5466	+	7.93941i	0.556829	+	0.382872i
$431$	−10.1349	−	3.29304i	−0.488183	−	0.158620i	0.0545745	−	0.998510i	$-0.482620\pi$
$431$	−10.1349	−	3.29304i	−0.488183	−	0.158620i	−0.542758	+	0.839889i	$0.682620\pi$
$432$	−3.78226	−	3.78226i	−0.181974	−	0.181974i
$433$	−13.5006	−	26.4963i	−0.648795	−	1.27333i	−0.947734	−	0.319060i	$-0.896633\pi$
$433$	−13.5006	−	26.4963i	−0.648795	−	1.27333i	0.298939	−	0.954272i	$-0.403367\pi$
$434$	9.37559	+	12.9044i	0.450043	+	0.619431i
$435$	−1.57129	−	0.207205i	−0.0753376	−	0.00993471i
$436$	−11.5767	+	15.9340i	−0.554424	+	0.763100i
$437$	6.56029	−	23.1536i	0.313821	−	1.10759i
$438$	−20.7201	−	3.28174i	−0.990044	−	0.156808i
$439$	−21.6654	−	15.7408i	−1.03403	−	0.751268i	−0.0649200	−	0.997890i	$-0.520679\pi$
$439$	−21.6654	−	15.7408i	−1.03403	−	0.751268i	−0.969112	+	0.246622i	$0.920679\pi$
$440$	6.72986	+	0.887461i	0.320833	+	0.0423080i
$441$	−2.16392	+	1.57218i	−0.103044	+	0.0748659i
$442$	−9.82102	−	19.2748i	−0.467138	−	0.916810i
$443$	−22.7839	−	22.7839i	−1.08250	−	1.08250i	−0.996276	−	0.0862210i	$-0.972521\pi$
$443$	−22.7839	−	22.7839i	−1.08250	−	1.08250i	−0.0862210	−	0.996276i	$-0.527479\pi$
$444$	12.4045	+	4.03046i	0.588691	+	0.191277i
$445$	−1.28946	+	1.87532i	−0.0611262	+	0.0888986i
$446$	−0.450098	−	1.38526i	−0.0213128	−	0.0655940i
$447$	7.01378	−	13.7653i	0.331740	−	0.651077i
$448$	−0.715579	−	4.51799i	−0.0338079	−	0.213455i
$449$	−3.88060			−0.183137			−0.0915685	−	0.995799i	$-0.529188\pi$
$449$	−3.88060			−0.183137			−0.0915685	+	0.995799i	$0.529188\pi$
$450$	−0.642981	+	0.713492i	−0.0303104	+	0.0336343i
$451$			4.43773i			0.208965i
$452$	2.81930	+	17.8004i	0.132609	+	0.837259i
$453$	5.09057	−	9.99080i	0.239176	−	0.469409i
$454$	10.0352	−	3.26063i	0.470975	−	0.153029i
$455$	−48.8470	+	37.4651i	−2.28998	+	1.75639i
$456$	−3.06598	+	6.62948i	−0.143577	+	0.310454i
$457$	1.96534	−	1.96534i	0.0919349	−	0.0919349i	−0.659644	−	0.751579i	$-0.729293\pi$
$457$	1.96534	−	1.96534i	0.0919349	−	0.0919349i	0.751579	+	0.659644i	$0.229293\pi$
$458$	8.81105	+	17.2927i	0.411713	+	0.808033i
$459$	15.5541	−	11.3007i	0.726002	−	0.527471i
$460$	−10.8504	+	5.88827i	−0.505901	+	0.274542i
$461$	−11.7638	−	8.54691i	−0.547895	−	0.398069i	0.279113	−	0.960258i	$-0.409959\pi$
$461$	−11.7638	−	8.54691i	−0.547895	−	0.398069i	−0.827009	+	0.562189i	$0.809959\pi$
$462$	−3.64010	+	22.9827i	−0.169353	+	1.06925i
$463$	39.4471	+	6.24781i	1.83326	+	0.290361i	0.974894	−	0.222670i	$-0.0714772\pi$
$463$	39.4471	+	6.24781i	1.83326	+	0.290361i	0.858370	+	0.513030i	$0.171477\pi$
$464$	−0.342201	−	0.248624i	−0.0158863	−	0.0115421i
$465$	−8.99582	+	9.47558i	−0.417171	+	0.439419i
$466$	−2.02842	−	2.79188i	−0.0939647	−	0.129331i
$467$	1.69086	+	3.31849i	0.0782435	+	0.153561i	0.926814	−	0.375521i	$-0.122536\pi$
$467$	1.69086	+	3.31849i	0.0782435	+	0.153561i	−0.848570	+	0.529082i	$0.822536\pi$
$468$	−0.817499	+	0.817499i	−0.0377889	+	0.0377889i
$469$	18.1532	−	55.8699i	0.838238	−	2.57983i
$470$	−6.93084	−	2.05461i	−0.319696	−	0.0947723i
$471$	−26.7523	+	8.69236i	−1.23268	+	0.400523i
$472$	−2.98940	−	1.52317i	−0.137598	−	0.0701098i
$473$	−2.97603	−	18.7899i	−0.136838	−	0.863962i
$474$	−22.6736			−1.04143
$475$	20.2297	+	8.10924i	0.928202	+	0.372078i
$476$	16.4416			0.753600
$477$	−0.182543	−	1.15253i	−0.00835806	−	0.0527707i
$478$	−14.4831	−	7.37953i	−0.662443	−	0.337532i
$479$	−39.7841	+	12.9266i	−1.81778	+	0.590633i	−0.817898	+	0.575364i	$0.804861\pi$
$479$	−39.7841	+	12.9266i	−1.81778	+	0.590633i	−0.999883	+	0.0152693i	$0.995139\pi$
$480$	3.53228	−	1.25000i	0.161226	−	0.0570545i
$481$	14.4762	−	44.5531i	0.660057	−	2.03145i
$482$	−20.2697	+	20.2697i	−0.923261	+	0.923261i
$483$	−19.2121	−	37.7058i	−0.874179	−	1.71567i
$484$	1.04877	+	1.44351i	0.0476715	+	0.0656142i
$485$	−22.5456	−	10.7596i	−1.02374	−	0.488569i
$486$	−1.61250	−	1.17155i	−0.0731443	−	0.0531424i
$487$	5.17695	+	0.819948i	0.234590	+	0.0371554i	0.272622	−	0.962121i	$-0.412109\pi$
$487$	5.17695	+	0.819948i	0.234590	+	0.0371554i	−0.0380325	+	0.999277i	$0.512109\pi$
$488$	0.818288	−	5.16647i	0.0370422	−	0.233875i
$489$	0.238989	+	0.173636i	0.0108075	+	0.00785208i
$490$	−5.66749	−	30.6154i	−0.256031	−	1.38307i
$491$	−13.8470	+	10.0605i	−0.624908	+	0.454023i	−0.854633	−	0.519233i	$-0.826218\pi$
$491$	−13.8470	+	10.0605i	−0.624908	+	0.454023i	0.229724	+	0.973256i	$0.426218\pi$
$492$	1.11208	+	2.18257i	0.0501363	+	0.0983979i
$493$	1.07505	−	1.07505i	0.0484178	−	0.0484178i
$494$	23.8111	+	11.0120i	1.07131	+	0.495455i
$495$	1.30351	−	0.0338559i	0.0585885	−	0.00152171i
$496$	−3.31636	+	1.07755i	−0.148909	+	0.0483834i
$497$	−8.23051	+	16.1533i	−0.369189	+	0.724574i
$498$	−1.39989	−	8.83854i	−0.0627305	−	0.396065i
$499$		−	16.4828i		−	0.737871i	−0.929455	−	0.368935i	$-0.879722\pi$
$499$		−	16.4828i		−	0.737871i	0.929455	−	0.368935i	$-0.120278\pi$
$500$	−4.27193	−	10.3320i	−0.191047	−	0.462062i
$501$	−15.8439			−0.707854
$502$	1.50908	+	9.52798i	0.0673537	+	0.425255i
$503$	0.560537	−	1.10012i	0.0249931	−	0.0490517i	−0.878172	−	0.478344i	$-0.841237\pi$
$503$	0.560537	−	1.10012i	0.0249931	−	0.0490517i	0.903165	+	0.429293i	$0.141237\pi$
$504$	−0.271531	−	0.835687i	−0.0120950	−	0.0372244i
$505$	−0.486834	−	18.7440i	−0.0216638	−	0.834097i
$506$	15.9397	+	5.17914i	0.708608	+	0.230241i
$507$	−27.5162	−	27.5162i	−1.22204	−	1.22204i
$508$	−0.328361	−	0.644445i	−0.0145687	−	0.0285926i
$509$	−5.76661	+	4.18969i	−0.255600	+	0.185705i	−0.708205	−	0.706007i	$-0.750495\pi$
$509$	−5.76661	+	4.18969i	−0.255600	+	0.185705i	0.452605	+	0.891711i	$0.350495\pi$
$510$	2.45149	+	13.2428i	0.108554	+	0.586400i
$511$	−46.3301	−	33.6608i	−2.04952	−	1.48906i
$512$	0.987688	+	0.156434i	0.0436501	+	0.00691349i
$513$	−6.35593	+	22.4324i	−0.280621	+	0.990414i
$514$	−10.5927	+	14.5795i	−0.467222	+	0.643076i
$515$	−1.91523	+	4.01317i	−0.0843952	+	0.176841i
$516$	−6.17235	−	8.49552i	−0.271723	−	0.373994i
$517$	4.45556	+	8.74454i	0.195956	+	0.384584i
$518$	25.1762	+	25.1762i	1.10618	+	1.10618i
$519$	−2.91146	−	0.945991i	−0.127799	−	0.0415244i
$520$	−4.48962	−	12.6869i	−0.196883	−	0.556356i
$521$	34.9825	−	11.3665i	1.53261	−	0.497976i	0.583286	−	0.812267i	$-0.301767\pi$
$521$	34.9825	−	11.3665i	1.53261	−	0.497976i	0.949327	+	0.314291i	$0.101767\pi$
$522$	−0.0723963	−	0.0368878i	−0.00316870	−	0.00161453i
$523$	34.9290	−	5.53221i	1.52734	−	0.241907i	0.664462	−	0.747322i	$-0.268661\pi$
$523$	34.9290	−	5.53221i	1.52734	−	0.241907i	0.862876	+	0.505415i	$0.168661\pi$
$524$		−	7.44447i		−	0.325213i
$525$	35.7857	−	13.7193i	1.56181	−	0.598761i
$526$		−	10.1495i		−	0.442538i
$527$	−1.96068	−	12.3792i	−0.0854086	−	0.539249i
$528$	−4.53249	−	2.30942i	−0.197251	−	0.100505i
$529$	−7.11431	+	2.31158i	−0.309318	+	0.100503i
$530$	13.0231	+	3.86064i	0.565688	+	0.167695i
$531$	−0.612945	−	0.199158i	−0.0265995	−	0.00864271i
$532$	−15.6733	+	12.3251i	−0.679525	+	0.534361i
$533$	7.83913	−	3.99423i	0.339550	−	0.173009i
$534$	1.37978	−	1.00247i	0.0597088	−	0.0433810i
$535$	10.5877	−	11.1524i	0.457746	−	0.482158i
$536$	10.3897	+	7.54857i	0.448767	+	0.326049i
$537$	−6.20301	+	39.1643i	−0.267680	+	1.69006i
$538$	19.8968	+	3.15134i	0.857811	+	0.135864i
$539$	−24.8460	+	34.1975i	−1.07019	+	1.47299i
$540$	10.5124	−	5.70485i	0.452380	−	0.245498i
$541$	12.4880	−	9.07310i	0.536903	−	0.390083i	−0.286031	−	0.958221i	$-0.592336\pi$
$541$	12.4880	−	9.07310i	0.536903	−	0.390083i	0.822934	+	0.568138i	$0.192336\pi$
$542$	5.22416	−	2.66184i	0.224397	−	0.114336i
$543$	9.08745	+	9.08745i	0.389980	+	0.389980i
$544$	−1.11071	+	3.41842i	−0.0476214	+	0.146564i
$545$	−26.8027	−	34.9454i	−1.14810	−	1.49689i
$546$	43.8746	−	14.2557i	1.87766	−	0.610089i
$547$	−13.0056	+	25.5249i	−0.556079	+	1.09137i	0.426320	+	0.904573i	$0.359810\pi$
$547$	−13.0056	+	25.5249i	−0.556079	+	1.09137i	−0.982399	+	0.186794i	$0.940190\pi$
$548$	−2.32465	−	14.6772i	−0.0993040	−	0.626981i
$549$		−	1.00481i		−	0.0428844i
$550$	−6.17964	+	13.8638i	−0.263501	+	0.591155i
$551$	−0.218926	+	1.83070i	−0.00932658	+	0.0779904i
$552$	9.13738	−	1.44722i	0.388913	−	0.0615977i
$553$	−55.1487	−	28.0997i	−2.34516	−	1.19492i
$554$	0.759911	+	2.33877i	0.0322855	+	0.0993647i
$555$	−16.5242	+	24.0319i	−0.701412	+	1.02010i
$556$	−1.26770	+	3.90159i	−0.0537625	+	0.165464i
$557$	−0.270599	+	0.270599i	−0.0114656	+	0.0114656i	−0.712816	−	0.701351i	$-0.752581\pi$
$557$	−0.270599	+	0.270599i	−0.0114656	+	0.0114656i	0.701351	+	0.712816i	$0.252581\pi$
$558$	−0.596826	+	0.304098i	−0.0252657	+	0.0128735i
$559$	−30.5133	+	22.1692i	−1.29057	+	0.937657i
$560$	10.1407	+	1.33724i	0.428521	+	0.0565088i
$561$	10.7472	−	14.7922i	0.453746	−	0.624528i
$562$	4.50585	−	28.4488i	0.190068	−	1.20004i
$563$	3.39594	−	21.4411i	0.143122	−	0.903635i	−0.806727	−	0.590924i	$-0.798763\pi$
$563$	3.39594	−	21.4411i	0.143122	−	0.903635i	0.949849	−	0.312710i	$-0.101237\pi$
$564$	4.38269	+	3.18421i	0.184544	+	0.134079i
$565$	−39.9531	−	5.26858i	−1.68084	−	0.221651i
$566$	−14.4166	−	19.8428i	−0.605975	−	0.834053i
$567$	17.4168	+	34.1825i	0.731438	+	1.43553i
$568$	−2.80246	−	2.80246i	−0.117589	−	0.117589i
$569$	−1.47408	+	4.53676i	−0.0617967	+	0.190191i	−0.977189	−	0.212373i	$-0.931881\pi$
$569$	−1.47408	+	4.53676i	−0.0617967	+	0.190191i	0.915392	+	0.402564i	$0.131881\pi$
$570$	−12.2641	−	10.7863i	−0.513686	−	0.451787i
$571$	3.11488	+	9.58661i	0.130354	+	0.401187i	0.994838	−	0.101472i	$-0.0323552\pi$
$571$	3.11488	+	9.58661i	0.130354	+	0.401187i	−0.864485	+	0.502659i	$0.832355\pi$
$572$	−8.29472	+	16.2793i	−0.346820	+	0.680672i
$573$	−43.1110	+	6.82811i	−1.80099	+	0.285248i
$574$			6.68685i			0.279104i
$575$	−5.72781	−	27.0038i	−0.238866	−	1.12613i
$576$	0.192093			0.00800388
$577$	−26.9795	+	4.27313i	−1.12317	+	0.177893i	−0.690272	−	0.723550i	$-0.742509\pi$
$577$	−26.9795	+	4.27313i	−1.12317	+	0.177893i	−0.432899	+	0.901442i	$0.642509\pi$
$578$	3.63594	+	1.85260i	0.151235	+	0.0770581i
$579$	−5.02314	+	1.63212i	−0.208755	+	0.0678285i
$580$	0.750492	−	0.575619i	0.0311625	−	0.0239013i
$581$	7.54878	−	23.2328i	0.313176	−	0.963857i
$582$	13.2376	+	13.2376i	0.548717	+	0.548717i
$583$	−8.37204	−	16.4311i	−0.346735	−	0.680505i
$584$	10.1283	−	7.35866i	0.419113	−	0.304504i
$585$	−1.23305	−	2.27215i	−0.0509803	−	0.0939417i
$586$	15.5123	+	11.2704i	0.640809	+	0.465575i
$587$	−2.11547	+	13.3566i	−0.0873148	+	0.551284i	0.904789	+	0.425861i	$0.140029\pi$
$587$	−2.11547	+	13.3566i	−0.0873148	+	0.551284i	−0.992103	+	0.125423i	$0.959971\pi$
$588$	−3.65003	+	23.0454i	−0.150525	+	0.950375i
$589$	11.1489	+	10.3310i	0.459382	+	0.425682i
$590$	5.16533	−	5.44080i	0.212653	−	0.223994i
$591$	−10.5776	−	14.5588i	−0.435104	−	0.598870i
$592$	−6.93524	+	3.53368i	−0.285037	+	0.145234i
$593$	−1.94143	−	1.94143i	−0.0797251	−	0.0797251i	0.666120	−	0.745845i	$-0.267954\pi$
$593$	−1.94143	−	1.94143i	−0.0797251	−	0.0797251i	−0.745845	+	0.666120i	$0.767954\pi$
$594$	−15.4432	−	5.01781i	−0.633643	−	0.205883i
$595$	−10.4492	+	35.2484i	−0.428376	+	1.44504i
$596$	2.84903	+	8.76840i	0.116701	+	0.359168i
$597$	−13.8034	+	27.0907i	−0.564935	+	1.10875i
$598$	−5.19796	−	32.8187i	−0.212561	−	1.34205i
$599$	−11.2621			−0.460156			−0.230078	−	0.973172i	$-0.573898\pi$
$599$	−11.2621			−0.460156			−0.230078	+	0.973172i	$0.573898\pi$
$600$	0.434928	+	8.36711i	0.0177559	+	0.341586i
$601$		−	32.6038i		−	1.32994i	−0.746872	−	0.664968i	$-0.768445\pi$
$601$		−	32.6038i		−	1.32994i	0.746872	−	0.664968i	$-0.231555\pi$
$602$	−4.48434	−	28.3130i	−0.182768	−	1.15395i
$603$	2.19806	+	1.11997i	0.0895118	+	0.0456085i
$604$	2.06781	+	6.36406i	0.0841379	+	0.258950i
$605$	−3.76121	+	1.33101i	−0.152915	+	0.0541133i
$606$	−4.34208	+	13.3635i	−0.176385	+	0.542857i
$607$	−15.1743	−	15.1743i	−0.615904	−	0.615904i	0.328574	−	0.944478i	$-0.393432\pi$
$607$	−15.1743	−	15.1743i	−0.615904	−	0.615904i	−0.944478	+	0.328574i	$0.893432\pi$
$608$	−1.50373	−	4.09131i	−0.0609845	−	0.165924i
$609$	1.90572	+	2.62300i	0.0772236	+	0.106289i
$610$	10.5561	+	5.03775i	0.427403	+	0.203973i
$611$	11.4367	−	15.7413i	0.462679	−	0.636823i
$612$	−0.108010	+	0.681948i	−0.00436604	+	0.0275661i
$613$	31.8263	+	5.04079i	1.28545	+	0.203595i	0.761507	−	0.648157i	$-0.224460\pi$
$613$	31.8263	+	5.04079i	1.28545	+	0.203595i	0.523944	+	0.851752i	$0.324460\pi$
$614$	7.70509	−	10.6052i	0.310952	−	0.427989i
$615$	−5.38587	+	0.997026i	−0.217179	+	0.0402040i
$616$	−8.16222	−	11.2343i	−0.328865	−	0.452644i
$617$	2.81758	+	5.52980i	0.113431	+	0.222621i	0.940742	−	0.339123i	$-0.110130\pi$
$617$	2.81758	+	5.52980i	0.113431	+	0.222621i	−0.827311	+	0.561745i	$0.810130\pi$
$618$	2.35632	−	2.35632i	0.0947852	−	0.0947852i
$619$	12.4488	+	4.04485i	0.500359	+	0.162576i	0.548313	−	0.836273i	$-0.315270\pi$
$619$	12.4488	+	4.04485i	0.500359	+	0.162576i	−0.0479544	+	0.998850i	$0.515270\pi$
$620$	−0.202448	−	7.79460i	−0.00813049	−	0.313038i
$621$	28.0856	−	9.12557i	1.12704	−	0.366196i
$622$	−15.2797	+	29.9881i	−0.612661	+	1.20242i
$623$	4.59838	−	0.728312i	0.184230	−	0.0291792i
$624$			10.0851i			0.403729i
$625$	24.8653	−	2.59203i	0.994611	−	0.103681i
$626$		−	25.6673i		−	1.02587i
$627$	0.843686	+	22.1574i	0.0336936	+	0.884880i
$628$	7.62098	−	14.9570i	0.304110	−	0.596850i
$629$	−8.64535	−	26.6077i	−0.344713	−	1.06092i
$630$	1.96415	−	0.0510146i	0.0782538	−	0.00203247i
$631$	0.970701	−	2.98751i	0.0386430	−	0.118931i	−0.929874	−	0.367878i	$-0.880084\pi$
$631$	0.970701	−	2.98751i	0.0386430	−	0.118931i	0.968517	+	0.248947i	$0.0800845\pi$
$632$	9.56785	−	9.56785i	0.380589	−	0.380589i
$633$	10.8472	−	5.52694i	0.431139	−	0.219676i
$634$	−6.81004	−	9.37322i	−0.270461	−	0.372258i
$635$	1.59028	−	0.294390i	0.0631083	−	0.0116825i
$636$	−8.23510	−	5.98315i	−0.326543	−	0.237247i
$637$	82.7719	+	13.1098i	3.27954	+	0.519428i
$638$	−1.26826	−	0.200873i	−0.0502109	−	0.00795262i
$639$	−0.615920	−	0.447492i	−0.0243654	−	0.0177025i
$640$	−0.963082	+	2.01804i	−0.0380692	+	0.0797699i
$641$	16.6031	+	22.8522i	0.655783	+	0.902608i	0.999333	−	0.0365267i	$-0.0116294\pi$
$641$	16.6031	+	22.8522i	0.655783	+	0.902608i	−0.343550	+	0.939134i	$0.611629\pi$
$642$	−10.2678	+	5.23173i	−0.405239	+	0.206480i
$643$	5.34571	+	5.34571i	0.210814	+	0.210814i	0.804613	−	0.593799i	$-0.202373\pi$
$643$	5.34571	+	5.34571i	0.210814	+	0.210814i	−0.593799	+	0.804613i	$0.702373\pi$
$644$	24.0183	+	7.80401i	0.946453	+	0.307521i
$645$	22.1359	−	7.83341i	0.871599	−	0.308440i
$646$	15.3700	−	3.03794i	0.604725	−	0.119526i
$647$	−31.2039	−	15.8992i	−1.22675	−	0.625062i	−0.284086	−	0.958799i	$-0.591690\pi$
$647$	−31.2039	−	15.8992i	−1.22675	−	0.625062i	−0.942666	+	0.333737i	$0.891690\pi$
$648$	−8.28356	+	1.31199i	−0.325409	+	0.0515397i
$649$	−10.1852			−0.399802
$650$	30.0521	−	1.56213i	1.17874	−	0.0612717i
$651$	26.7283			1.04756
$652$	−0.174120	+	0.0275779i	−0.00681907	+	0.00108003i
$653$	−0.199467	+	0.391476i	−0.00780574	+	0.0153196i	−0.894876	−	0.446314i	$-0.852736\pi$
$653$	−0.199467	+	0.391476i	−0.00780574	+	0.0153196i	0.887071	+	0.461634i	$0.152736\pi$
$654$	10.1986	+	31.3881i	0.398797	+	1.22737i
$655$	15.9598	+	4.73122i	0.623603	+	0.184864i
$656$	−1.39028	−	0.451730i	−0.0542814	−	0.0176371i
$657$	1.70050	−	1.70050i	0.0663429	−	0.0663429i
$658$	6.71372	+	13.1764i	0.261728	+	0.513670i
$659$	29.7032	−	21.5806i	1.15707	−	0.840662i	0.167667	−	0.985844i	$-0.446377\pi$
$659$	29.7032	−	21.5806i	1.15707	−	0.840662i	0.989405	+	0.145181i	$0.0463766\pi$
$660$	7.83160	−	8.24927i	0.304845	−	0.321102i
$661$	−3.93533	+	5.41652i	−0.153067	+	0.210678i	−0.878663	−	0.477442i	$-0.841564\pi$
$661$	−3.93533	+	5.41652i	−0.153067	+	0.210678i	0.725596	+	0.688120i	$0.241564\pi$
$662$	2.85634	−	18.0342i	0.111015	−	0.700919i
$663$	−35.8031	−	5.67066i	−1.39048	−	0.220230i
$664$	4.32043	+	3.13898i	0.167665	+	0.121816i
$665$	−16.4622	−	41.4343i	−0.638378	−	1.60675i
$666$	−1.20962	+	0.878844i	−0.0468720	+	0.0340545i
$667$	2.08073	−	1.06018i	0.0805661	−	0.0410505i
$668$	6.68584	−	6.68584i	0.258683	−	0.258683i
$669$	−2.32125	−	0.754221i	−0.0897448	−	0.0291599i
$670$	−22.7860	+	17.4766i	−0.880301	+	0.675181i
$671$	−4.90705	−	15.1024i	−0.189435	−	0.583020i
$672$	−6.82963	−	3.47987i	−0.263459	−	0.134239i
$673$	−12.1852	+	1.92995i	−0.469706	+	0.0743942i	−0.386801	−	0.922163i	$-0.626420\pi$
$673$	−12.1852	+	1.92995i	−0.469706	+	0.0743942i	−0.0829055	+	0.996557i	$0.526420\pi$
$674$		−	32.3938i		−	1.24776i
$675$	5.54938	+	26.1626i	0.213596	+	1.00700i
$676$	23.2227			0.893181
$677$	7.70627	+	48.6554i	0.296176	+	1.86998i	0.466398	+	0.884575i	$0.345551\pi$
$677$	7.70627	+	48.6554i	0.296176	+	1.86998i	−0.170222	+	0.985406i	$0.554449\pi$
$678$	26.9080	+	13.7103i	1.03340	+	0.526541i
$679$	15.7921	+	48.6032i	0.606047	+	1.86522i
$680$	−6.62269	−	4.55373i	−0.253969	−	0.174627i
$681$	5.46378	−	16.8158i	0.209373	−	0.644382i
$682$	−7.48522	+	7.48522i	−0.286624	+	0.286624i
$683$	7.29014	+	14.3077i	0.278950	+	0.547469i	0.987391	−	0.158300i	$-0.0506014\pi$
$683$	7.29014	+	14.3077i	0.278950	+	0.547469i	−0.708441	+	0.705770i	$0.750601\pi$
$684$	−0.408245	−	0.731049i	−0.0156096	−	0.0279524i
$685$	32.9432	+	4.34420i	1.25870	+	0.165983i
$686$	−18.6173	+	25.6246i	−0.710813	+	0.978351i
$687$	32.1212	+	5.08750i	1.22550	+	0.194100i
$688$	6.18957	+	0.980332i	0.235975	+	0.0373748i
$689$	−21.4896	+	29.5779i	−0.818690	+	1.12683i
$690$	−2.70450	+	20.5089i	−0.102958	+	0.780762i
$691$	4.24943	−	3.08739i	0.161656	−	0.117450i	−0.504016	−	0.863694i	$-0.668145\pi$
$691$	4.24943	−	3.08739i	0.161656	−	0.117450i	0.665672	+	0.746244i	$0.268145\pi$
$692$	1.62777	−	0.829393i	0.0618787	−	0.0315288i
$693$	−1.88620	−	1.88620i	−0.0716507	−	0.0716507i
$694$	6.02660	−	18.5480i	0.228767	−	0.704071i
$695$	−7.55875	−	5.19736i	−0.286720	−	0.197147i
$696$	−0.674095	+	0.219027i	−0.0255515	+	0.00830219i
$697$	2.38541	−	4.68163i	0.0903537	−	0.177329i
$698$	−24.3834	+	3.86194i	−0.922923	+	0.146177i
$699$	−5.78269			−0.218722
$700$	−9.31159	+	20.8902i	−0.351945	+	0.789576i
$701$	32.7170			1.23570			0.617851	−	0.786295i	$-0.288003\pi$
$701$	32.7170			1.23570			0.617851	+	0.786295i	$0.288003\pi$
$702$	5.03605	+	31.7963i	0.190073	+	1.20008i
$703$	28.1872	+	18.8835i	1.06310	+	0.712205i
$704$	2.88716	−	0.938095i	0.108814	−	0.0353558i
$705$	−9.61181	+	7.37215i	−0.362002	+	0.277651i
$706$	10.8021	+	3.50982i	0.406543	+	0.132094i
$707$	−27.1228	+	27.1228i	−1.02006	+	1.02006i
$708$	−5.00928	+	2.55236i	−0.188260	+	0.0959234i
$709$	2.69750	+	3.71279i	0.101307	+	0.139437i	0.856661	−	0.515880i	$-0.172535\pi$
$709$	2.69750	+	3.71279i	0.101307	+	0.139437i	−0.755354	+	0.655317i	$0.772535\pi$
$710$	7.78912	−	4.22700i	0.292321	−	0.158637i
$711$	1.52778	−	2.10281i	0.0572961	−	0.0788614i
$712$	−0.159218	+	1.00526i	−0.00596695	+	0.0376738i
$713$	3.01160	−	19.0145i	0.112785	−	0.712099i
$714$	16.1940	−	22.2892i	0.606046	−	0.834151i
$715$	−29.6288	−	28.1287i	−1.10806	−	1.05195i
$716$	−13.9091	−	19.1442i	−0.519806	−	0.715451i
$717$	−24.2691	+	12.3657i	−0.906347	+	0.461807i
$718$	−13.0004	+	13.0004i	−0.485171	+	0.485171i
$719$	−14.9422	−	4.85501i	−0.557249	−	0.181061i	0.0168340	−	0.999858i	$-0.494641\pi$
$719$	−14.9422	−	4.85501i	−0.557249	−	0.181061i	−0.574083	+	0.818797i	$0.694641\pi$
$720$	−0.122082	+	0.411819i	−0.00454972	+	0.0153476i
$721$	8.65147	−	2.81103i	0.322197	−	0.104688i
$722$	−12.3745	+	14.4178i	−0.460530	+	0.536574i
$723$	7.51427	+	47.4433i	0.279459	+	1.76443i
$724$	−7.66947			−0.285034
$725$	0.757078	+	1.97477i	0.0281172	+	0.0733411i
$726$	2.98988			0.110965
$727$	47.8526	−	7.57911i	1.77475	−	0.281094i	0.818687	−	0.574240i	$-0.194702\pi$
$727$	47.8526	−	7.57911i	1.77475	−	0.281094i	0.956068	+	0.293146i	$0.0947022\pi$
$728$	−12.4986	+	24.5299i	−0.463230	+	0.909140i
$729$	−27.1054	+	8.80709i	−1.00391	+	0.326189i
$730$	9.33897	+	26.3903i	0.345651	+	0.976749i
$731$	−6.96053	+	21.4223i	−0.257445	+	0.792333i
$732$	−6.19798	−	6.19798i	−0.229084	−	0.229084i
$733$	−18.2205	+	9.28379i	−0.672988	+	0.342905i	−0.756865	−	0.653571i	$-0.773270\pi$
$733$	−18.2205	+	9.28379i	−0.672988	+	0.342905i	0.0838765	+	0.996476i	$0.473270\pi$
$734$	6.50945	−	4.72939i	0.240268	−	0.174565i
$735$	−47.0861	−	22.4712i	−1.73680	−	0.828864i
$736$	−3.24511	+	4.46651i	−0.119616	+	0.164638i
$737$	38.5062	+	6.09878i	1.41839	+	0.224652i
$738$	−0.277350	−	0.0439279i	−0.0102094	−	0.00161701i
$739$	14.0547	−	19.3447i	0.517011	−	0.711605i	−0.468071	−	0.883691i	$-0.655051\pi$
$739$	14.0547	−	19.3447i	0.517011	−	0.711605i	0.985082	+	0.172086i	$0.0550507\pi$
$740$	−3.16811	−	17.1139i	−0.116462	−	0.629120i
$741$	38.3810	−	21.4334i	1.40996	−	0.787374i
$742$	−12.6151	−	24.7586i	−0.463116	−	0.908917i
$743$	14.8295	−	14.8295i	0.544042	−	0.544042i	−0.380669	−	0.924711i	$-0.624306\pi$
$743$	14.8295	−	14.8295i	0.544042	−	0.544042i	0.924711	+	0.380669i	$0.124306\pi$
$744$	−1.80563	+	5.55716i	−0.0661976	+	0.203735i
$745$	−20.6088	+	0.535268i	−0.755048	+	0.0196107i
$746$	5.99305	+	18.4447i	0.219421	+	0.675309i
$747$	0.914034	+	0.465724i	0.0334428	+	0.0170399i
$748$	1.70693	+	10.7772i	0.0624117	+	0.394052i
$749$	−31.4581			−1.14945
$750$	−18.2142	−	4.38516i	−0.665090	−	0.160124i
$751$			8.92506i			0.325680i	0.986652	+	0.162840i	$0.0520655\pi$
$751$			8.92506i			0.325680i	−0.986652	+	0.162840i	$0.947935\pi$
$752$	−3.19309	+	0.505736i	−0.116440	+	0.0184423i
$753$	14.4030	+	7.33870i	0.524875	+	0.267437i
$754$	0.786677	+	2.42114i	0.0286491	+	0.0881728i
$755$	−14.9578	+	0.388495i	−0.544368	+	0.0141388i
$756$	−23.2701	−	7.56092i	−0.846326	−	0.274988i
$757$	−25.8093	+	25.8093i	−0.938053	+	0.938053i	−0.998190	−	0.0601369i	$-0.980846\pi$
$757$	−25.8093	+	25.8093i	−0.938053	+	0.938053i	0.0601369	+	0.998190i	$0.480846\pi$
$758$	−12.7840	+	6.51379i	−0.464337	+	0.236591i
$759$	22.7208	−	16.5076i	0.824714	−	0.599190i
$760$	9.72682	−	0.623618i	0.352829	−	0.0226210i
$761$	0.837600	+	0.608552i	0.0303630	+	0.0220600i	0.602863	−	0.797845i	$-0.294026\pi$
$761$	0.837600	+	0.608552i	0.0303630	+	0.0220600i	−0.572500	+	0.819905i	$0.694026\pi$
$762$	−1.19706	−	0.189596i	−0.0433649	−	0.00686833i
$763$	−14.0937	+	88.9840i	−0.510226	+	3.22144i
$764$	15.3107	−	21.0734i	0.553922	−	0.762408i
$765$	−1.39335	−	0.664959i	−0.0503767	−	0.0240416i
$766$	−23.0163	+	16.7223i	−0.831612	+	0.604202i
$767$	9.16727	+	17.9918i	0.331011	+	0.649646i
$768$	1.18489	−	1.18489i	0.0427559	−	0.0427559i
$769$	−39.4408	−	12.8151i	−1.42227	−	0.462124i	−0.505949	−	0.862563i	$-0.668858\pi$
$769$	−39.4408	−	12.8151i	−1.42227	−	0.462124i	−0.916324	+	0.400439i	$0.868858\pi$
$770$	29.2721	−	10.3588i	1.05489	−	0.373305i
$771$	9.33168	+	28.7199i	0.336072	+	1.03432i
$772$	1.43095	−	2.80840i	0.0515010	−	0.101076i
$773$	−13.9055	+	2.20241i	−0.500145	+	0.0792152i	−0.401410	−	0.915898i	$-0.631480\pi$
$773$	−13.9055	+	2.20241i	−0.500145	+	0.0792152i	−0.0987353	+	0.995114i	$0.531480\pi$
$774$	1.20380			0.0432695
$775$	16.8391	+	4.51971i	0.604879	+	0.162353i
$776$	−11.1721			−0.401054
$777$	58.9274	−	9.33318i	2.11401	−	0.334826i
$778$	−2.26069	−	1.15188i	−0.0810496	−	0.0412968i
$779$	1.23554	+	6.25103i	0.0442677	+	0.223966i
$780$	−21.6210	−	6.40945i	−0.774157	−	0.229495i
$781$	−11.4426	−	3.71794i	−0.409450	−	0.133038i
$782$	−14.0318	−	14.0318i	−0.501778	−	0.501778i
$783$	−2.01591	+	1.02716i	−0.0720428	+	0.0367076i
$784$	−8.18448	−	11.2650i	−0.292303	−	0.402320i
$785$	27.2222	+	25.8439i	0.971602	+	0.922409i
$786$	−10.0921	−	7.33236i	−0.359974	−	0.261537i
$787$	−3.18227	−	0.504022i	−0.113436	−	0.0179664i	0.0994585	−	0.995042i	$-0.468289\pi$
$787$	−3.18227	−	0.504022i	−0.113436	−	0.0179664i	−0.212894	+	0.977075i	$0.568289\pi$
$788$	10.6071	+	1.68000i	0.377863	+	0.0598476i
$789$	−13.7592	−	9.99662i	−0.489839	−	0.355889i
$790$	14.4313	+	26.5927i	0.513444	+	0.946127i
$791$	48.4566	+	66.6948i	1.72292	+	2.37139i
$792$	0.519586	−	0.264742i	0.0184627	−	0.00940721i
$793$	−22.2612	+	22.2612i	−0.790519	+	0.790519i
$794$	−3.54611	+	10.9138i	−0.125847	+	0.387316i
$795$	18.0607	−	13.8523i	0.640546	−	0.491292i
$796$	−5.60699	−	17.2565i	−0.198734	−	0.611642i
$797$	17.1749	−	33.7076i	0.608366	−	1.19399i	−0.357249	−	0.934009i	$-0.616285\pi$
$797$	17.1749	−	33.7076i	0.608366	−	1.19399i	0.965615	−	0.259977i	$-0.0837149\pi$
$798$	1.27128	+	33.3871i	0.0450028	+	1.18189i
$799$		−	11.6201i		−	0.411090i
$800$	−3.71430	−	3.34724i	−0.131320	−	0.118343i
$801$			0.195511i			0.00690805i
$802$	5.77315	−	0.914377i	0.203857	−	0.0322878i
$803$	17.2541	−	33.8630i	0.608883	−	1.19500i
$804$	20.4665	−	6.64997i	0.721798	−	0.234526i
$805$	−31.9951	+	46.5319i	−1.12768	+	1.64003i
$806$	19.9596	+	6.48527i	0.703047	+	0.228434i
$807$	23.8693	−	23.8693i	0.840238	−	0.840238i
$808$	−3.80689	−	7.47145i	−0.133926	−	0.262845i
$809$	21.7699	+	29.9637i	0.765389	+	1.05347i	0.996747	+	0.0805986i	$0.0256832\pi$
$809$	21.7699	+	29.9637i	0.765389	+	1.05347i	−0.231358	+	0.972869i	$0.574317\pi$
$810$	2.45178	−	18.5925i	0.0861469	−	0.653275i
$811$	29.2827	−	40.3041i	1.02825	−	1.41527i	0.122002	−	0.992530i	$-0.461069\pi$
$811$	29.2827	−	40.3041i	1.02825	−	1.41527i	0.906251	−	0.422739i	$-0.138931\pi$
$812$	−1.91104	−	0.302678i	−0.0670642	−	0.0106219i
$813$	1.53695	−	9.70390i	0.0539031	−	0.340331i
$814$	−13.8888	+	19.1163i	−0.486802	+	0.670025i
$815$	0.0515364	−	0.390814i	0.00180524	−	0.0136896i
$816$	3.54021	+	4.87269i	0.123932	+	0.170578i
$817$	−9.42349	−	25.6391i	−0.329686	−	0.896998i
$818$	−25.9427	−	25.9427i	−0.907065	−	0.907065i
$819$	−1.63422	+	5.02961i	−0.0571042	+	0.175749i
$820$	1.85201	−	2.69347i	0.0646751	−	0.0940599i
$821$	12.6179	+	38.8338i	0.440367	+	1.35531i	0.887485	+	0.460836i	$0.152450\pi$
$821$	12.6179	+	38.8338i	0.440367	+	1.35531i	−0.447118	+	0.894475i	$0.647550\pi$
$822$	−22.1869	−	11.3048i	−0.773858	−	0.394300i
$823$	4.99280	+	31.5233i	0.174038	+	1.09883i	0.907793	+	0.419419i	$0.137766\pi$
$823$	4.99280	+	31.5233i	0.174038	+	1.09883i	−0.733755	+	0.679415i	$0.762234\pi$
$824$			1.98865i			0.0692779i
$825$	12.7079	+	22.0325i	0.442434	+	0.767072i
$826$	−15.3472			−0.533996
$827$	3.89032	+	24.5625i	0.135280	+	0.854123i	0.958228	+	0.286006i	$0.0923279\pi$
$827$	3.89032	+	24.5625i	0.135280	+	0.854123i	−0.822948	+	0.568117i	$0.807672\pi$
$828$	−0.481470	+	0.944938i	−0.0167322	+	0.0328389i
$829$	−6.27861	−	19.3236i	−0.218065	−	0.671136i	−0.998922	−	0.0464253i	$-0.985217\pi$
$829$	−6.27861	−	19.3236i	−0.218065	−	0.671136i	0.780857	−	0.624710i	$-0.214783\pi$
$830$	−9.47528	+	7.26743i	−0.328892	+	0.252256i
$831$	3.91903	+	1.27337i	0.135950	+	0.0441727i
$832$	−4.25574	−	4.25574i	−0.147541	−	0.147541i
$833$	44.5936	−	22.7216i	1.54508	−	0.787256i
$834$	4.04059	+	5.56140i	0.139914	+	0.192575i
$835$	10.0844	+	18.5825i	0.348984	+	0.643075i
$836$	−9.70603	−	8.99398i	−0.335690	−	0.311063i
$837$	−2.91779	+	18.4222i	−0.100854	+	0.636765i
$838$	2.87405	−	18.1461i	0.0992825	−	0.626845i
$839$	37.4273	+	27.1925i	1.29213	+	0.938791i	0.999846	−	0.0175392i	$-0.00558318\pi$
$839$	37.4273	+	27.1925i	1.29213	+	0.938791i	0.292289	+	0.956330i	$0.405583\pi$
$840$	11.8008	−	12.4301i	0.407166	−	0.428880i
$841$	23.3167	−	16.9406i	0.804026	−	0.584159i
$842$	−1.03393	−	2.02921i	−0.0356317	−	0.0699312i
$843$	−34.1287	−	34.1287i	−1.17546	−	1.17546i
$844$	−2.24507	+	6.90960i	−0.0772783	+	0.237838i
$845$	−14.7588	+	49.7860i	−0.507719	+	1.71269i
$846$	−0.590622	+	0.191905i	−0.0203060	+	0.00659782i
$847$	7.27225	+	3.70540i	0.249878	+	0.127319i
$848$	5.99984	−	0.950282i	0.206035	−	0.0326328i
$849$	−41.0994			−1.41053
$850$	13.9715	−	11.3040i	0.479217	−	0.387724i
$851$		−	42.9726i		−	1.47308i
$852$	−6.55943	+	1.03891i	−0.224722	+	0.0355925i
$853$	−21.1989	+	41.6052i	−0.725837	+	1.42453i	0.172402	+	0.985027i	$0.444847\pi$
$853$	−21.1989	+	41.6052i	−0.725837	+	1.42453i	−0.898239	+	0.439508i	$0.855153\pi$
$854$	−7.39403	−	22.7565i	−0.253018	−	0.778711i
$855$	1.82671	−	0.410609i	0.0624723	−	0.0140425i
$856$	2.12515	−	6.54054i	0.0726361	−	0.223551i
$857$	−28.1041	−	28.1041i	−0.960016	−	0.960016i	0.0392145	−	0.999231i	$-0.487514\pi$
$857$	−28.1041	−	28.1041i	−0.960016	−	0.960016i	−0.999231	+	0.0392145i	$0.987514\pi$
$858$	13.8993	+	27.2789i	0.474515	+	0.931287i
$859$	−3.97907	−	5.47672i	−0.135764	−	0.186863i	0.735722	−	0.677284i	$-0.236843\pi$
$859$	−3.97907	−	5.47672i	−0.135764	−	0.186863i	−0.871486	+	0.490421i	$0.836843\pi$
$860$	−6.03537	+	12.6465i	−0.205804	+	0.431242i
$861$	9.06506	+	6.58615i	0.308936	+	0.224455i
$862$	1.66705	−	10.5253i	0.0567798	−	0.358493i
$863$	5.55203	−	35.0541i	0.188993	−	1.19326i	−0.692627	−	0.721296i	$-0.743547\pi$
$863$	5.55203	−	35.0541i	0.188993	−	1.19326i	0.881620	−	0.471960i	$-0.156453\pi$
$864$	3.14402	−	4.32738i	0.106962	−	0.147220i
$865$	0.743588	+	4.01681i	0.0252827	+	0.136576i
$866$	24.0582	−	17.4793i	0.817530	−	0.593970i
$867$	6.09267	−	3.10437i	0.206918	−	0.105430i
$868$	−11.2789	+	11.2789i	−0.382829	+	0.382829i
$869$	12.6934	−	39.0661i	0.430593	−	1.32523i
$870$	−0.0411502	−	1.58436i	−0.00139512	−	0.0537148i
$871$	−23.8846	−	73.5094i	−0.809300	−	2.49077i
$872$	−17.5488	−	8.94157i	−0.594278	−	0.302800i
$873$	−2.11966	+	0.335721i	−0.0717395	+	0.0113624i
$874$	23.8948	+	2.85749i	0.808255	+	0.0966561i
$875$	−38.8677	−	33.2391i	−1.31397	−	1.12369i
$876$		−	20.9784i		−	0.708793i
$877$	1.28858	+	8.13576i	0.0435122	+	0.274725i	0.999846	−	0.0175517i	$-0.00558716\pi$
$877$	1.28858	+	8.13576i	0.0435122	+	0.274725i	−0.956334	+	0.292277i	$0.905587\pi$
$878$	12.1578	−	23.8610i	0.410306	−	0.805271i
$879$	30.5574	−	9.92872i	1.03068	−	0.334887i
$880$	0.176247	+	6.78583i	0.00594129	+	0.228750i
$881$	6.19767	−	19.0745i	0.208805	−	0.642635i	−0.790731	−	0.612164i	$-0.790299\pi$
$881$	6.19767	−	19.0745i	0.208805	−	0.642635i	0.999536	−	0.0304712i	$-0.00970078\pi$
$882$	−1.89134	−	1.89134i	−0.0636847	−	0.0636847i
$883$	33.4939	−	17.0660i	1.12716	−	0.574317i	0.211945	−	0.977282i	$-0.432020\pi$
$883$	33.4939	−	17.0660i	1.12716	−	0.574317i	0.915216	+	0.402965i	$0.132020\pi$
$884$	17.5012	−	12.7154i	0.588629	−	0.427664i
$885$	−2.28830	−	12.3613i	−0.0769204	−	0.415519i
$886$	18.9392	−	26.0676i	0.636276	−	0.875758i
$887$	44.1000	+	6.98475i	1.48073	+	0.234525i	0.843910	−	0.536485i	$-0.180248\pi$
$887$	44.1000	+	6.98475i	1.48073	+	0.234525i	0.636823	+	0.771010i	$0.280248\pi$
$888$	−2.04035	+	12.8823i	−0.0684697	+	0.432300i
$889$	−2.67663	−	1.94468i	−0.0897712	−	0.0652226i
$890$	−2.05395	−	0.980219i	−0.0688484	−	0.0328570i
$891$	−20.5977	+	14.9651i	−0.690050	+	0.501351i
$892$	1.29779	−	0.661259i	0.0434534	−	0.0221406i
$893$	8.71077	+	11.0771i	0.291495	+	0.370682i
$894$	14.6930	+	4.77406i	0.491409	+	0.159668i
$895$	49.8819	−	17.6522i	1.66737	−	0.590047i
$896$	4.35042	−	1.41354i	0.145337	−	0.0472230i
$897$	−49.6104	−	25.2778i	−1.65644	−	0.844001i
$898$	−0.607060	−	3.83283i	−0.0202579	−	0.127903i
$899$			1.47495i			0.0491925i
$900$	−0.805292	−	0.523450i	−0.0268431	−	0.0174483i
$901$			21.8343i			0.727406i
$902$	−4.38310	+	0.694214i	−0.145941	+	0.0231148i
$903$	−42.7994	−	21.8074i	−1.42428	−	0.725705i
$904$	−17.1402	+	5.56918i	−0.570074	+	0.185228i
$905$	4.87421	−	16.4422i	0.162024	−	0.546557i
$906$	10.6641	+	3.46499i	0.354292	+	0.115116i
$907$	−6.36697	−	6.36697i	−0.211412	−	0.211412i	0.593455	−	0.804867i	$-0.297763\pi$
$907$	−6.36697	−	6.36697i	−0.211412	−	0.211412i	−0.804867	+	0.593455i	$0.797763\pi$
$908$	4.79034	+	9.40157i	0.158973	+	0.312002i
$909$	−0.946792	−	1.30315i	−0.0314031	−	0.0432227i
$910$	−44.6452	−	42.3848i	−1.47997	−	1.40504i
$911$	−23.0289	+	31.6966i	−0.762982	+	1.05015i	0.233978	+	0.972242i	$0.424825\pi$
$911$	−23.0289	+	31.6966i	−0.762982	+	1.05015i	−0.996960	+	0.0779125i	$0.975175\pi$
$912$	−7.02749	−	1.99115i	−0.232703	−	0.0659335i
$913$	16.0123	+	2.53610i	0.529930	+	0.0839327i
$914$	2.24860	+	1.63370i	0.0743769	+	0.0540380i
$915$	17.2266	−	9.34851i	0.569493	−	0.309052i
$916$	−15.7014	+	11.4077i	−0.518789	+	0.376922i
$917$	−15.4599	−	30.3417i	−0.510530	−	1.00197i
$918$	13.5948	+	13.5948i	0.448694	+	0.448694i
$919$	−25.2970	−	8.21950i	−0.834472	−	0.271136i	−0.139544	−	0.990216i	$-0.544564\pi$
$919$	−25.2970	−	8.21950i	−0.834472	−	0.271136i	−0.694928	+	0.719079i	$0.744564\pi$
$920$	−7.51315	−	9.79565i	−0.247701	−	0.322953i
$921$	−6.78786	−	20.8909i	−0.223668	−	0.688378i
$922$	6.60142	−	12.9560i	0.217406	−	0.426684i
$923$	3.73145	+	23.5595i	0.122822	+	0.775469i
$924$	−23.2692			−0.765500
$925$	38.7031	+	4.08453i	1.27255	+	0.134298i
$926$			39.9389i			1.31247i
$927$	0.0597589	+	0.377303i	0.00196274	+	0.0123923i
$928$	0.192031	−	0.376881i	0.00630371	−	0.0123717i
$929$	26.6406	−	8.65606i	0.874050	−	0.283996i	0.162565	−	0.986698i	$-0.448023\pi$
$929$	26.6406	−	8.65606i	0.874050	−	0.283996i	0.711485	+	0.702702i	$0.248023\pi$
$930$	−10.7662	−	7.40276i	−0.353037	−	0.242746i
$931$	−25.4771	+	55.0885i	−0.834978	+	1.80545i
$932$	2.44019	−	2.44019i	0.0799311	−	0.0799311i
$933$	25.6039	+	50.2506i	0.838235	+	1.64513i
$934$	−3.01313	+	2.18917i	−0.0985925	+	0.0716317i
$935$	−24.1894	−	3.18984i	−0.791079	−	0.104319i
$936$	−0.935320	−	0.679550i	−0.0305719	−	0.0222118i
$937$	−7.43541	+	46.9454i	−0.242904	+	1.53364i	0.501056	+	0.865415i	$0.332945\pi$
$937$	−7.43541	+	46.9454i	−0.242904	+	1.53364i	−0.743961	+	0.668223i	$0.767055\pi$
$938$	58.0218	+	9.18975i	1.89448	+	0.300056i
$939$	−34.7960	−	25.2808i	−1.13552	−	0.825006i
$940$	0.945096	−	7.16692i	0.0308256	−	0.233759i
$941$	24.7313	+	34.0397i	0.806218	+	1.10966i	0.991896	+	0.127053i	$0.0405519\pi$
$941$	24.7313	+	34.0397i	0.806218	+	1.10966i	−0.185678	+	0.982611i	$0.559448\pi$
$942$	−12.7703	−	25.0632i	−0.416080	−	0.816602i
$943$	5.70679	−	5.70679i	0.185839	−	0.185839i
$944$	1.03678	−	3.19087i	0.0337442	−	0.103854i
$945$	30.9984	−	45.0824i	1.00838	−	1.46653i
$946$	18.0930	−	5.87879i	0.588256	−	0.191136i
$947$	43.3141	+	22.0697i	1.40752	+	0.717168i	0.982193	−	0.187872i	$-0.0601591\pi$
$947$	43.3141	+	22.0697i	1.40752	+	0.717168i	0.425327	+	0.905040i	$0.360159\pi$
$948$	−3.54693	−	22.3945i	−0.115199	−	0.727338i
$949$	−75.3478			−2.44589
$950$	−4.84479	+	21.2492i	−0.157186	+	0.689415i
$951$	−19.4143			−0.629553
$952$	2.57204	+	16.2392i	0.0833602	+	0.526315i
$953$	40.4506	+	20.6106i	1.31032	+	0.667644i	0.962848	−	0.270045i	$-0.0870385\pi$
$953$	40.4506	+	20.6106i	1.31032	+	0.667644i	0.347477	+	0.937689i	$0.387039\pi$
$954$	1.10978	−	0.360591i	0.0359306	−	0.0116746i
$955$	35.4477	+	46.2167i	1.14706	+	1.49554i
$956$	5.02301	−	15.4592i	0.162456	−	0.499988i
$957$	−1.52147	+	1.52147i	−0.0491823	+	0.0491823i
$958$	−18.9911	−	37.2721i	−0.613574	−	1.20421i
$959$	−39.9548	−	54.9930i	−1.29021	−	1.77582i
$960$	1.78718	+	3.29325i	0.0576811	+	0.106289i
$961$	−15.2424	−	11.0743i	−0.491691	−	0.357234i
$962$	46.2691	+	7.32831i	1.49178	+	0.236274i
$963$	0.206658	−	1.30479i	0.00665945	−	0.0420461i
$964$	−23.1911	−	16.8493i	−0.746934	−	0.542679i
$965$	5.11137	+	4.85258i	0.164541	+	0.156210i
$966$	34.2361	−	24.8740i	1.10153	−	0.800308i
$967$	−22.9132	−	44.9696i	−0.736838	−	1.44613i	−0.889065	−	0.457780i	$-0.848645\pi$
$967$	−22.9132	−	44.9696i	−0.736838	−	1.44613i	0.152227	−	0.988346i	$-0.451355\pi$
$968$	−1.26168	+	1.26168i	−0.0405518	+	0.0405518i
$969$	11.0202	−	23.8286i	0.354019	−	0.765486i
$970$	7.10023	−	23.9512i	0.227975	−	0.769028i
$971$	13.3464	−	4.33650i	0.428305	−	0.139165i	−0.0869285	−	0.996215i	$-0.527705\pi$
$971$	13.3464	−	4.33650i	0.428305	−	0.139165i	0.515234	+	0.857050i	$0.327705\pi$
$972$	0.904873	−	1.77591i	0.0290238	−	0.0569624i
$973$	2.93557	+	18.5345i	0.0941100	+	0.594187i
$974$			5.24148i			0.167948i
$975$	27.4818	−	42.2788i	0.880122	−	1.35401i
$976$	5.23087			0.167436
$977$	8.33437	+	52.6211i	0.266640	+	1.68350i	0.650027	+	0.759911i	$0.274758\pi$
$977$	8.33437	+	52.6211i	0.266640	+	1.68350i	−0.383387	+	0.923588i	$0.625242\pi$
$978$	−0.134112	+	0.263209i	−0.00428842	+	0.00841651i
$979$	0.954788	+	2.93854i	0.0305152	+	0.0939160i
$980$	29.3519	−	10.3870i	0.937613	−	0.331801i
$981$	−3.59820	−	1.16913i	−0.114882	−	0.0373273i
$982$	−12.1028	−	12.1028i	−0.386215	−	0.386215i
$983$	−16.6889	−	32.7539i	−0.532294	−	1.04469i	−0.987985	−	0.154548i	$-0.950608\pi$
$983$	−16.6889	−	32.7539i	−0.532294	−	1.04469i	0.455691	−	0.890138i	$-0.349392\pi$
$984$	−1.98173	+	1.43981i	−0.0631754	+	0.0458996i
$985$	−10.3429	+	21.6724i	−0.329551	+	0.690539i
$986$	1.22999	+	0.893638i	0.0391708	+	0.0284592i
$987$	24.4753	+	3.87650i	0.779057	+	0.123390i
$988$	−7.15159	+	25.2406i	−0.227522	+	0.803009i
$989$	−20.3362	+	27.9904i	−0.646654	+	0.890043i
$990$	0.237353	+	1.28217i	0.00754358	+	0.0407500i
$991$	3.66891	+	5.04983i	0.116547	+	0.160413i	0.863305	−	0.504683i	$-0.168391\pi$
$991$	3.66891	+	5.04983i	0.116547	+	0.160413i	−0.746758	+	0.665096i	$0.768391\pi$
$992$	−1.58308	−	3.10696i	−0.0502627	−	0.0986461i
$993$	−21.6348	−	21.6348i	−0.686561	−	0.686561i
$994$	−17.2420	−	5.60225i	−0.546881	−	0.177693i
$995$	40.5589	−	1.05343i	1.28580	−	0.0333959i
$996$	8.51074	−	2.76531i	0.269673	−	0.0876221i
$997$	52.3750	+	26.6864i	1.65873	+	0.845167i	0.995290	+	0.0969396i	$0.0309054\pi$
$997$	52.3750	+	26.6864i	1.65873	+	0.845167i	0.663443	+	0.748227i	$0.269095\pi$
$998$	16.2799	−	2.57848i	0.515330	−	0.0816202i
$999$			41.6340i			1.31724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.113.44	yes	400
19.18	odd	2	inner	950.2.w.a.113.7	✓	400
25.2	odd	20	inner	950.2.w.a.227.7	yes	400
475.227	even	20	inner	950.2.w.a.227.44	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.113.7	✓	400	19.18	odd	2	inner
950.2.w.a.113.44	yes	400	1.1	even	1	trivial
950.2.w.a.227.7	yes	400	25.2	odd	20	inner
950.2.w.a.227.44	yes	400	475.227	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 + 0.987688i) q^{2} +(1.49304 + 0.760743i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.0580574 - 2.23531i) q^{5} +(-0.517814 + 1.59367i) q^{6} +(-3.23452 + 3.23452i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.112910 - 0.155407i) q^{9} +O(q^{10})\)	\(q+(0.156434 + 0.987688i) q^{2} +(1.49304 + 0.760743i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-0.0580574 - 2.23531i) q^{5} +(-0.517814 + 1.59367i) q^{6} +(-3.23452 + 3.23452i) q^{7} +(-0.453990 - 0.891007i) q^{8} +(-0.112910 - 0.155407i) q^{9} +(2.19871 - 0.407023i) q^{10} +(-2.45597 - 1.78436i) q^{11} +(-1.65505 - 0.262134i) q^{12} +(-0.941505 + 5.94443i) q^{13} +(-3.70069 - 2.68871i) q^{14} +(1.61382 - 3.38159i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.63180 + 3.20258i) q^{17} +(0.135830 - 0.135830i) q^{18} +(-3.95629 - 1.82969i) q^{19} +(0.745966 + 2.10797i) q^{20} +(-7.28992 + 2.36864i) q^{21} +(1.37820 - 2.70486i) q^{22} +(0.863660 + 5.45294i) q^{23} -1.67568i q^{24} +(-4.99326 + 0.259553i) q^{25} -6.01853 q^{26} +(-0.836757 - 5.28308i) q^{27} +(2.07669 - 4.07574i) q^{28} +(-0.130709 - 0.402281i) q^{29} +(3.59241 + 1.06495i) q^{30} +(-3.31636 - 1.07755i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-2.30942 - 4.53249i) q^{33} +(-2.90788 + 2.11270i) q^{34} +(7.41796 + 7.04239i) q^{35} +(0.155407 + 0.112910i) q^{36} +(-7.68778 - 1.21762i) q^{37} +(1.18826 - 4.19381i) q^{38} +(-5.92789 + 8.15905i) q^{39} +(-1.96532 + 1.06654i) q^{40} +(-0.859241 - 1.18264i) q^{41} +(-3.47987 - 6.82963i) q^{42} +(4.43125 + 4.43125i) q^{43} +(2.88716 + 0.938095i) q^{44} +(-0.340828 + 0.261411i) q^{45} +(-5.25070 + 1.70605i) q^{46} +(-2.88053 - 1.46770i) q^{47} +(1.65505 - 0.262134i) q^{48} -13.9243i q^{49} +(-1.03748 - 4.89118i) q^{50} +6.02297i q^{51} +(-0.941505 - 5.94443i) q^{52} +(5.41254 + 2.75783i) q^{53} +(5.08713 - 1.65291i) q^{54} +(-3.84603 + 5.59345i) q^{55} +(4.35042 + 1.41354i) q^{56} +(-4.51499 - 5.74153i) q^{57} +(0.376881 - 0.192031i) q^{58} +(2.71432 - 1.97207i) q^{59} +(-0.489865 + 3.71478i) q^{60} +(4.23186 + 3.07463i) q^{61} +(0.545491 - 3.44409i) q^{62} +(0.867875 + 0.137458i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(13.3423 + 1.75944i) q^{65} +(4.11542 - 2.99002i) q^{66} +(-11.4427 + 5.83033i) q^{67} +(-2.54158 - 2.54158i) q^{68} +(-2.85880 + 8.79849i) q^{69} +(-5.79526 + 8.42831i) q^{70} +(3.76930 - 1.22472i) q^{71} +(-0.0872085 + 0.171156i) q^{72} +(1.95845 + 12.3652i) q^{73} -7.78361i q^{74} +(-7.65260 - 3.41106i) q^{75} +(4.32806 + 0.517577i) q^{76} +(13.7154 - 2.17231i) q^{77} +(-8.98592 - 4.57856i) q^{78} +(4.18130 + 12.8687i) q^{79} +(-1.36085 - 1.77428i) q^{80} +(2.59167 - 7.97634i) q^{81} +(1.03367 - 1.03367i) q^{82} +(-4.75828 + 2.42447i) q^{83} +(6.20118 - 4.50542i) q^{84} +(7.06404 - 3.83351i) q^{85} +(-3.68349 + 5.06989i) q^{86} +(0.110879 - 0.700059i) q^{87} +(-0.474894 + 2.99837i) q^{88} +(-0.823413 - 0.598244i) q^{89} +(-0.311510 - 0.295738i) q^{90} +(-16.1821 - 22.2727i) q^{91} +(-2.50644 - 4.91916i) q^{92} +(-4.13172 - 4.13172i) q^{93} +(0.999019 - 3.07466i) q^{94} +(-3.86024 + 8.94978i) q^{95} +(0.517814 + 1.59367i) q^{96} +(5.07201 - 9.95438i) q^{97} +(13.7528 - 2.17824i) q^{98} +0.583145i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

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