LMFDB - Embedded newform 510.2.bi.b.97.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(37,510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("510.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(510, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bi (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.10
Character	$\chi$	$=$	510.97
Dual form			510.2.bi.b.163.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 + 0.923880i) q^{2} +(0.195090 - 0.980785i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(2.19567 - 0.423144i) q^{5} +(0.831470 + 0.555570i) q^{6} +(-3.65460 - 2.44193i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-0.449311 + 2.19046i) q^{10} +(0.736823 - 1.10273i) q^{11} +(-0.831470 + 0.555570i) q^{12} -3.30428 q^{13} +(3.65460 - 2.44193i) q^{14} +(0.0133395 - 2.23603i) q^{15} +1.00000i q^{16} +(0.0712911 - 4.12249i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.60430 - 0.664522i) q^{19} +(-1.85178 - 1.25336i) q^{20} +(-3.10799 + 3.10799i) q^{21} +(0.736823 + 1.10273i) q^{22} +(-6.53289 + 1.29947i) q^{23} +(-0.195090 - 0.980785i) q^{24} +(4.64190 - 1.85817i) q^{25} +(1.26449 - 3.05276i) q^{26} +(-0.555570 + 0.831470i) q^{27} +(0.857491 + 4.31090i) q^{28} +(-9.32914 - 1.85568i) q^{29} +(2.06072 + 0.868015i) q^{30} +(0.267072 + 0.399702i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(-0.937798 - 0.937798i) q^{33} +(3.78140 + 1.64347i) q^{34} +(-9.05758 - 3.81523i) q^{35} +(0.382683 + 0.923880i) q^{36} +(10.1305 + 2.01508i) q^{37} +1.73648i q^{38} +(-0.644633 + 3.24079i) q^{39} +(1.86660 - 1.23118i) q^{40} +(10.4444 - 2.07751i) q^{41} +(-1.68203 - 4.06078i) q^{42} +(-4.41265 - 10.6531i) q^{43} +(-1.30076 + 0.258738i) q^{44} +(-2.19046 - 0.449311i) q^{45} +(1.29947 - 6.53289i) q^{46} -4.79630i q^{47} +(0.980785 + 0.195090i) q^{48} +(4.71433 + 11.3814i) q^{49} +(-0.0596551 + 4.99964i) q^{50} +(-4.02937 - 0.874179i) q^{51} +(2.33648 + 2.33648i) q^{52} +(7.07539 + 2.93072i) q^{53} +(-0.555570 - 0.831470i) q^{54} +(1.15120 - 2.73302i) q^{55} +(-4.31090 - 0.857491i) q^{56} +(-0.338770 - 1.70311i) q^{57} +(5.28453 - 7.90886i) q^{58} +(5.05368 - 12.2007i) q^{59} +(-1.59054 + 1.57168i) q^{60} +(0.887221 + 4.46036i) q^{61} +(-0.471480 + 0.0937833i) q^{62} +(2.44193 + 3.65460i) q^{63} +(0.707107 - 0.707107i) q^{64} +(-7.25510 + 1.39819i) q^{65} +(1.22529 - 0.507533i) q^{66} +(0.963997 - 0.963997i) q^{67} +(-2.96545 + 2.86463i) q^{68} +6.66087i q^{69} +(6.99100 - 6.90808i) q^{70} +(-6.15628 + 4.11350i) q^{71} -1.00000 q^{72} +(-5.03866 + 3.36672i) q^{73} +(-5.73847 + 8.58823i) q^{74} +(-0.916873 - 4.91522i) q^{75} +(-1.60430 - 0.664522i) q^{76} +(-5.38559 + 2.23079i) q^{77} +(-2.74741 - 1.83576i) q^{78} +(10.5819 + 7.07062i) q^{79} +(0.423144 + 2.19567i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-2.07751 + 10.4444i) q^{82} +(1.03554 - 2.50001i) q^{83} +4.39536 q^{84} +(-1.58788 - 9.08178i) q^{85} +11.5308 q^{86} +(-3.64005 + 8.78786i) q^{87} +(0.258738 - 1.30076i) q^{88} +(2.86526 + 2.86526i) q^{89} +(1.25336 - 1.85178i) q^{90} +(12.0758 + 8.06882i) q^{91} +(5.53831 + 3.70058i) q^{92} +(0.444125 - 0.183963i) q^{93} +(4.43120 + 1.83546i) q^{94} +(3.24132 - 2.13792i) q^{95} +(-0.555570 + 0.831470i) q^{96} +(4.23482 - 2.82962i) q^{97} -12.3192 q^{98} +(-1.10273 + 0.736823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 48 q^{25} + 16 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} - 16 q^{33} - 32 q^{34} - 32 q^{35} + 48 q^{37} + 32 q^{41} + 32 q^{43} + 16 q^{44} - 64 q^{49} + 48 q^{50} - 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 144 q^{98}+O(q^{100}) $ 80 * q + 48 * q^25 + 16 * q^28 + 32 * q^29 + 16 * q^30 + 16 * q^31 - 16 * q^33 - 32 * q^34 - 32 * q^35 + 48 * q^37 + 32 * q^41 + 32 * q^43 + 16 * q^44 - 64 * q^49 + 48 * q^50 - 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 - 16 * q^56 + 32 * q^57 + 32 * q^58 - 16 * q^60 + 48 * q^61 + 32 * q^62 - 32 * q^65 - 16 * q^67 - 16 * q^70 - 80 * q^72 - 80 * q^73 - 32 * q^74 - 48 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 32 * q^82 - 32 * q^83 - 32 * q^85 - 48 * q^87 - 16 * q^88 - 32 * q^89 - 32 * q^92 - 48 * q^93 - 16 * q^94 - 96 * q^95 + 80 * q^97 - 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$3$	0.195090	−	0.980785i	0.112635	−	0.566257i
$3$	0.195090	−	0.980785i	0.112635	−	0.566257i
$4$	−0.707107	−	0.707107i	−0.353553	−	0.353553i
$5$	2.19567	−	0.423144i	0.981932	−	0.189236i
$5$	2.19567	−	0.423144i	0.981932	−	0.189236i
$6$	0.831470	+	0.555570i	0.339446	+	0.226811i
$7$	−3.65460	−	2.44193i	−1.38131	−	0.922962i	−0.381312	−	0.924446i	$-0.624528\pi$
$7$	−3.65460	−	2.44193i	−1.38131	−	0.922962i	−0.999999	+	0.00148419i	$0.999528\pi$
$8$	0.923880	−	0.382683i	0.326641	−	0.135299i
$9$	−0.923880	−	0.382683i	−0.307960	−	0.127561i
$10$	−0.449311	+	2.19046i	−0.142085	+	0.692685i
$11$	0.736823	−	1.10273i	0.222161	−	0.332487i	−0.703601	−	0.710596i	$-0.748426\pi$
$11$	0.736823	−	1.10273i	0.222161	−	0.332487i	0.925761	+	0.378109i	$0.123426\pi$
$12$	−0.831470	+	0.555570i	−0.240025	+	0.160379i
$13$	−3.30428			−0.916443			−0.458221	−	0.888838i	$-0.651513\pi$
$13$	−3.30428			−0.916443			−0.458221	+	0.888838i	$0.651513\pi$
$14$	3.65460	−	2.44193i	0.976734	−	0.652633i
$15$	0.0133395	−	2.23603i	0.00344425	−	0.577340i
$16$			1.00000i			0.250000i
$17$	0.0712911	−	4.12249i	0.0172906	−	0.999851i
$17$	0.0712911	−	4.12249i	0.0172906	−	0.999851i
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	1.60430	−	0.664522i	0.368051	−	0.152452i	−0.190989	−	0.981592i	$-0.561170\pi$
$19$	1.60430	−	0.664522i	0.368051	−	0.152452i	0.559041	+	0.829140i	$0.311170\pi$
$20$	−1.85178	−	1.25336i	−0.414070	−	0.280260i
$21$	−3.10799	+	3.10799i	−0.678218	+	0.678218i
$22$	0.736823	+	1.10273i	0.157091	+	0.235104i
$23$	−6.53289	+	1.29947i	−1.36220	+	0.270959i	−0.821477	−	0.570242i	$-0.806850\pi$
$23$	−6.53289	+	1.29947i	−1.36220	+	0.270959i	−0.540724	+	0.841200i	$0.681850\pi$
$24$	−0.195090	−	0.980785i	−0.0398226	−	0.200202i
$25$	4.64190	−	1.85817i	0.928380	−	0.371633i
$26$	1.26449	−	3.05276i	0.247988	−	0.598695i
$27$	−0.555570	+	0.831470i	−0.106920	+	0.160016i
$28$	0.857491	+	4.31090i	0.162051	+	0.814684i
$29$	−9.32914	−	1.85568i	−1.73238	−	0.344591i	−0.774677	−	0.632357i	$-0.782088\pi$
$29$	−9.32914	−	1.85568i	−1.73238	−	0.344591i	−0.957701	+	0.287765i	$0.907088\pi$
$30$	2.06072	+	0.868015i	0.376234	+	0.158477i
$31$	0.267072	+	0.399702i	0.0479676	+	0.0717886i	0.854678	−	0.519158i	$-0.173754\pi$
$31$	0.267072	+	0.399702i	0.0479676	+	0.0717886i	−0.806711	+	0.590947i	$0.798754\pi$
$32$	−0.923880	−	0.382683i	−0.163320	−	0.0676495i
$33$	−0.937798	−	0.937798i	−0.163250	−	0.163250i
$34$	3.78140	+	1.64347i	0.648505	+	0.281853i
$35$	−9.05758	−	3.81523i	−1.53101	−	0.644892i
$36$	0.382683	+	0.923880i	0.0637806	+	0.153980i
$37$	10.1305	+	2.01508i	1.66545	+	0.331278i	0.935796	−	0.352543i	$-0.114683\pi$
$37$	10.1305	+	2.01508i	1.66545	+	0.331278i	0.729650	+	0.683821i	$0.239683\pi$
$38$			1.73648i			0.281694i
$39$	−0.644633	+	3.24079i	−0.103224	+	0.518942i
$40$	1.86660	−	1.23118i	0.295135	−	0.194667i
$41$	10.4444	−	2.07751i	1.63114	−	0.324453i	0.707204	−	0.707009i	$-0.249956\pi$
$41$	10.4444	−	2.07751i	1.63114	−	0.324453i	0.923932	+	0.382556i	$0.124956\pi$
$42$	−1.68203	−	4.06078i	−0.259543	−	0.626592i
$43$	−4.41265	−	10.6531i	−0.672923	−	1.62458i	−0.776619	−	0.629970i	$-0.783067\pi$
$43$	−4.41265	−	10.6531i	−0.672923	−	1.62458i	0.103697	−	0.994609i	$-0.466933\pi$
$44$	−1.30076	+	0.258738i	−0.196097	+	0.0390062i
$45$	−2.19046	−	0.449311i	−0.326535	−	0.0669793i
$46$	1.29947	−	6.53289i	0.191597	−	0.963221i
$47$		−	4.79630i		−	0.699612i	−0.936822	−	0.349806i	$-0.886247\pi$
$47$		−	4.79630i		−	0.699612i	0.936822	−	0.349806i	$-0.113753\pi$
$48$	0.980785	+	0.195090i	0.141564	+	0.0281589i
$49$	4.71433	+	11.3814i	0.673476	+	1.62592i
$50$	−0.0596551	+	4.99964i	−0.00843650	+	0.707056i
$51$	−4.02937	−	0.874179i	−0.564224	−	0.122410i
$52$	2.33648	+	2.33648i	0.324011	+	0.324011i
$53$	7.07539	+	2.93072i	0.971879	+	0.402566i	0.811411	−	0.584476i	$-0.198700\pi$
$53$	7.07539	+	2.93072i	0.971879	+	0.402566i	0.160468	+	0.987041i	$0.448700\pi$
$54$	−0.555570	−	0.831470i	−0.0756035	−	0.113149i
$55$	1.15120	−	2.73302i	0.155228	−	0.368520i
$56$	−4.31090	−	0.857491i	−0.576068	−	0.114587i
$57$	−0.338770	−	1.70311i	−0.0448712	−	0.225583i
$58$	5.28453	−	7.90886i	0.693893	−	1.03848i
$59$	5.05368	−	12.2007i	0.657934	−	1.58839i	−0.143056	−	0.989715i	$-0.545693\pi$
$59$	5.05368	−	12.2007i	0.657934	−	1.58839i	0.800990	−	0.598678i	$-0.204307\pi$
$60$	−1.59054	+	1.57168i	−0.205338	+	0.202903i
$61$	0.887221	+	4.46036i	0.113597	+	0.571091i	0.995097	+	0.0989064i	$0.0315344\pi$
$61$	0.887221	+	4.46036i	0.113597	+	0.571091i	−0.881500	+	0.472185i	$0.843466\pi$
$62$	−0.471480	+	0.0937833i	−0.0598781	+	0.0119105i
$63$	2.44193	+	3.65460i	0.307654	+	0.460437i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$	−7.25510	+	1.39819i	−0.899884	+	0.173424i
$66$	1.22529	−	0.507533i	0.150823	−	0.0624729i
$67$	0.963997	−	0.963997i	0.117771	−	0.117771i	−0.645765	−	0.763536i	$-0.723461\pi$
$67$	0.963997	−	0.963997i	0.117771	−	0.117771i	0.763536	+	0.645765i	$0.223461\pi$
$68$	−2.96545	+	2.86463i	−0.359614	+	0.347387i
$69$			6.66087i			0.801875i
$70$	6.99100	−	6.90808i	0.835585	−	0.825674i
$71$	−6.15628	+	4.11350i	−0.730616	+	0.488182i	−0.864385	−	0.502830i	$-0.832292\pi$
$71$	−6.15628	+	4.11350i	−0.730616	+	0.488182i	0.133769	+	0.991013i	$0.457292\pi$
$72$	−1.00000			−0.117851
$73$	−5.03866	+	3.36672i	−0.589730	+	0.394045i	−0.814327	−	0.580407i	$-0.802894\pi$
$73$	−5.03866	+	3.36672i	−0.589730	+	0.394045i	0.224597	+	0.974452i	$0.427894\pi$
$74$	−5.73847	+	8.58823i	−0.667084	+	0.998362i
$75$	−0.916873	−	4.91522i	−0.105871	−	0.567560i
$76$	−1.60430	−	0.664522i	−0.184026	−	0.0762259i
$77$	−5.38559	+	2.23079i	−0.613745	+	0.254222i
$78$	−2.74741	−	1.83576i	−0.311083	−	0.207859i
$79$	10.5819	+	7.07062i	1.19056	+	0.795507i	0.983160	−	0.182749i	$-0.0584996\pi$
$79$	10.5819	+	7.07062i	1.19056	+	0.795507i	0.207401	+	0.978256i	$0.433500\pi$
$80$	0.423144	+	2.19567i	0.0473090	+	0.245483i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	−2.07751	+	10.4444i	−0.229423	+	1.15339i
$83$	1.03554	−	2.50001i	0.113665	−	0.274411i	−0.856802	−	0.515645i	$-0.827552\pi$
$83$	1.03554	−	2.50001i	0.113665	−	0.274411i	0.970467	+	0.241234i	$0.0775522\pi$
$84$	4.39536			0.479573
$85$	−1.58788	−	9.08178i	−0.172229	−	0.985057i
$86$	11.5308			1.24340
$87$	−3.64005	+	8.78786i	−0.390254	+	0.942157i
$88$	0.258738	−	1.30076i	0.0275816	−	0.138662i
$89$	2.86526	+	2.86526i	0.303717	+	0.303717i	0.842466	−	0.538749i	$-0.181103\pi$
$89$	2.86526	+	2.86526i	0.303717	+	0.303717i	−0.538749	+	0.842466i	$0.681103\pi$
$90$	1.25336	−	1.85178i	0.132116	−	0.195195i
$91$	12.0758	+	8.06882i	1.26589	+	0.845842i
$92$	5.53831	+	3.70058i	0.577409	+	0.385812i
$93$	0.444125	−	0.183963i	0.0460536	−	0.0190760i
$94$	4.43120	+	1.83546i	0.457044	+	0.189314i
$95$	3.24132	−	2.13792i	0.332552	−	0.219346i
$96$	−0.555570	+	0.831470i	−0.0567026	+	0.0848615i
$97$	4.23482	−	2.82962i	0.429981	−	0.287304i	−0.321687	−	0.946846i	$-0.604250\pi$
$97$	4.23482	−	2.82962i	0.429981	−	0.287304i	0.751668	+	0.659542i	$0.229250\pi$
$98$	−12.3192			−1.24442
$99$	−1.10273	+	0.736823i	−0.110829	+	0.0740535i
$100$	−4.59624	−	1.96840i	−0.459624	−	0.196840i
$101$		−	9.85997i		−	0.981103i	−0.871412	−	0.490552i	$-0.836795\pi$
$101$		−	9.85997i		−	0.981103i	0.871412	−	0.490552i	$-0.163205\pi$
$102$	2.34961	−	3.38812i	0.232646	−	0.335474i
$103$	−8.05048	+	8.05048i	−0.793237	+	0.793237i	−0.982019	−	0.188782i	$-0.939546\pi$
$103$	−8.05048	+	8.05048i	−0.793237	+	0.793237i	0.188782	+	0.982019i	$0.439546\pi$
$104$	−3.05276	+	1.26449i	−0.299347	+	0.123994i
$105$	−5.50897	+	8.13922i	−0.537621	+	0.794307i
$106$	−5.41527	+	5.41527i	−0.525977	+	0.525977i
$107$	0.475230	+	0.711233i	0.0459423	+	0.0687575i	0.853730	−	0.520716i	$-0.174335\pi$
$107$	0.475230	+	0.711233i	0.0459423	+	0.0687575i	−0.807787	+	0.589474i	$0.799335\pi$
$108$	0.980785	−	0.195090i	0.0943761	−	0.0187726i
$109$	3.20245	+	16.0998i	0.306739	+	1.54208i	0.759534	+	0.650467i	$0.225427\pi$
$109$	3.20245	+	16.0998i	0.306739	+	1.54208i	−0.452795	+	0.891615i	$0.649573\pi$
$110$	2.08443	+	2.10945i	0.198743	+	0.201128i
$111$	3.95273	−	9.54273i	0.375177	−	0.905756i
$112$	2.44193	−	3.65460i	0.230741	−	0.345328i
$113$	1.36095	+	6.84196i	0.128027	+	0.643637i	0.990498	+	0.137529i	$0.0439162\pi$
$113$	1.36095	+	6.84196i	0.128027	+	0.643637i	−0.862470	+	0.506108i	$0.831084\pi$
$114$	1.70311	+	0.338770i	0.159511	+	0.0317288i
$115$	−13.7942	+	5.61756i	−1.28631	+	0.523840i
$116$	5.28453	+	7.90886i	0.490657	+	0.734320i
$117$	3.05276	+	1.26449i	0.282228	+	0.116902i
$118$	9.33799	+	9.33799i	0.859632	+	0.859632i
$119$	−10.3274	+	14.8920i	−0.946708	+	1.36515i
$120$	−0.843367	−	2.07093i	−0.0769885	−	0.189049i
$121$	3.53640	+	8.53764i	0.321491	+	0.776149i
$122$	−4.46036	−	0.887221i	−0.403822	−	0.0803252i
$123$		−	10.6490i		−	0.960187i
$124$	0.0937833	−	0.471480i	0.00842199	−	0.0423402i
$125$	9.40578	−	6.04411i	0.841279	−	0.540601i
$126$	−4.31090	+	0.857491i	−0.384045	+	0.0763914i
$127$	−1.07769	−	2.60177i	−0.0956296	−	0.230870i	0.868825	−	0.495120i	$-0.164876\pi$
$127$	−1.07769	−	2.60177i	−0.0956296	−	0.230870i	−0.964454	+	0.264249i	$0.914876\pi$
$128$	0.382683	+	0.923880i	0.0338248	+	0.0816602i
$129$	−11.3092	+	2.24955i	−0.995724	+	0.198062i
$130$	1.48465	−	7.23790i	0.130212	−	0.634806i
$131$	−2.39285	+	12.0296i	−0.209064	+	1.05104i	0.723581	+	0.690240i	$0.242495\pi$
$131$	−2.39285	+	12.0296i	−0.209064	+	1.05104i	−0.932645	+	0.360796i	$0.882505\pi$
$132$			1.32625i			0.115435i
$133$	−7.48579	−	1.48902i	−0.649101	−	0.129114i
$134$	0.521712	+	1.25952i	0.0450690	+	0.108806i
$135$	−0.868015	+	2.06072i	−0.0747068	+	0.177358i
$136$	−1.51174	−	3.83597i	−0.129631	−	0.328931i
$137$	−12.7416	−	12.7416i	−1.08859	−	1.08859i	−0.995674	−	0.0929122i	$-0.970382\pi$
$137$	−12.7416	−	12.7416i	−1.08859	−	1.08859i	−0.0929122	−	0.995674i	$-0.529618\pi$
$138$	−6.15384	−	2.54901i	−0.523850	−	0.216986i
$139$	−4.79231	−	7.17220i	−0.406478	−	0.608338i	0.570597	−	0.821230i	$-0.306712\pi$
$139$	−4.79231	−	7.17220i	−0.406478	−	0.608338i	−0.977076	+	0.212892i	$0.931712\pi$
$140$	3.70690	+	9.10245i	0.313290	+	0.769298i
$141$	−4.70414	−	0.935712i	−0.396160	−	0.0788011i
$142$	−1.44447	−	7.26183i	−0.121217	−	0.609399i
$143$	−2.43467	+	3.64374i	−0.203597	+	0.304705i
$144$	0.382683	−	0.923880i	0.0318903	−	0.0769900i
$145$	−21.2689	−	0.126884i	−1.76629	−	0.0105372i
$146$	−1.18224	−	5.94350i	−0.0978425	−	0.491887i
$147$	12.0824	−	2.40335i	0.996543	−	0.198225i
$148$	−5.73847	−	8.58823i	−0.471700	−	0.705948i
$149$	5.11636	−	5.11636i	0.419149	−	0.419149i	−0.465761	−	0.884910i	$-0.654220\pi$
$149$	5.11636	−	5.11636i	0.419149	−	0.419149i	0.884910	+	0.465761i	$0.154220\pi$
$150$	4.89194	+	1.03389i	0.399425	+	0.0844168i
$151$	3.06381	−	1.26907i	0.249329	−	0.103276i	−0.254519	−	0.967068i	$-0.581917\pi$
$151$	3.06381	−	1.26907i	0.249329	−	0.103276i	0.503848	+	0.863792i	$0.331917\pi$
$152$	1.22788	−	1.22788i	0.0995940	−	0.0995940i
$153$	−1.64347	+	3.78140i	−0.132867	+	0.305708i
$154$		−	5.82933i		−	0.469740i
$155$	0.755533	+	0.764602i	0.0606859	+	0.0614143i
$156$	2.74741	−	1.83576i	0.219969	−	0.146978i
$157$	3.22468			0.257358			0.128679	−	0.991686i	$-0.458926\pi$
$157$	3.22468			0.257358			0.128679	+	0.991686i	$0.458926\pi$
$158$	−10.5819	+	7.07062i	−0.841853	+	0.562508i
$159$	4.25475	−	6.36768i	0.337423	−	0.504990i
$160$	−2.19046	−	0.449311i	−0.173171	−	0.0355211i
$161$	27.0483	+	11.2038i	2.13171	+	0.882982i
$162$	−0.923880	+	0.382683i	−0.0725868	+	0.0300665i
$163$	8.30448	+	5.54887i	0.650457	+	0.434621i	0.836535	−	0.547914i	$-0.184578\pi$
$163$	8.30448	+	5.54887i	0.650457	+	0.434621i	−0.186078	+	0.982535i	$0.559578\pi$
$164$	−8.85431	−	5.91626i	−0.691405	−	0.461982i
$165$	−2.45591	−	1.66227i	−0.191193	−	0.129407i
$166$	1.91342	+	1.91342i	0.148510	+	0.148510i
$167$	1.40570	−	7.06691i	0.108776	−	0.546854i	−0.887513	−	0.460783i	$-0.847569\pi$
$167$	1.40570	−	7.06691i	0.108776	−	0.546854i	0.996289	−	0.0860711i	$-0.0274312\pi$
$168$	−1.68203	+	4.06078i	−0.129771	+	0.313296i
$169$	−2.08173			−0.160133
$170$	8.99812	+	2.00844i	0.690124	+	0.154040i
$171$	−1.73648			−0.132792
$172$	−4.41265	+	10.6531i	−0.336461	+	0.812290i
$173$	−0.295247	+	1.48431i	−0.0224472	+	0.112850i	−0.990384	−	0.138342i	$-0.955823\pi$
$173$	−0.295247	+	1.48431i	−0.0224472	+	0.112850i	0.967937	+	0.251192i	$0.0808226\pi$
$174$	−6.72594	−	6.72594i	−0.509892	−	0.509892i
$175$	−21.5018	−	4.54432i	−1.62538	−	0.343518i
$176$	1.10273	+	0.736823i	0.0831217	+	0.0555401i
$177$	−10.9803	−	7.33681i	−0.825331	−	0.551469i
$178$	−3.74364	+	1.55067i	−0.280598	+	0.116228i
$179$	−4.02438	−	1.66695i	−0.300796	−	0.124594i	0.227181	−	0.973853i	$-0.427049\pi$
$179$	−4.02438	−	1.66695i	−0.300796	−	0.124594i	−0.527977	+	0.849259i	$0.677049\pi$
$180$	1.23118	+	1.86660i	0.0917667	+	0.139128i
$181$	4.76322	−	7.12867i	0.354047	−	0.529870i	−0.611108	−	0.791547i	$-0.709276\pi$
$181$	4.76322	−	7.12867i	0.354047	−	0.529870i	0.965155	+	0.261678i	$0.0842758\pi$
$182$	−12.0758	+	8.06882i	−0.895121	+	0.598101i
$183$	4.54775			0.336179
$184$	−5.53831	+	3.70058i	−0.408290	+	0.272811i
$185$	23.0959	+	0.137784i	1.69804	+	0.0101301i
$186$			0.480717i			0.0352479i
$187$	−4.49348	−	3.11616i	−0.328596	−	0.227876i
$188$	−3.39150	+	3.39150i	−0.247350	+	0.247350i
$189$	4.06078	−	1.68203i	0.295378	−	0.122350i
$190$	0.734782	+	3.81273i	0.0533067	+	0.276605i
$191$	4.37246	−	4.37246i	0.316380	−	0.316380i	−0.530995	−	0.847375i	$-0.678182\pi$
$191$	4.37246	−	4.37246i	0.316380	−	0.316380i	0.847375	+	0.530995i	$0.178182\pi$
$192$	−0.555570	−	0.831470i	−0.0400948	−	0.0600062i
$193$	−14.7569	+	2.93532i	−1.06222	+	0.211289i	−0.695122	−	0.718892i	$-0.744649\pi$
$193$	−14.7569	+	2.93532i	−1.06222	+	0.211289i	−0.367100	+	0.930181i	$0.619649\pi$
$194$	0.993629	+	4.99531i	0.0713384	+	0.358643i
$195$	−0.0440775	+	7.38846i	−0.00315646	+	0.529099i
$196$	4.71433	−	11.3814i	0.336738	−	0.812958i
$197$	−1.29403	+	1.93666i	−0.0921959	+	0.137981i	−0.874700	−	0.484664i	$-0.838942\pi$
$197$	−1.29403	+	1.93666i	−0.0921959	+	0.137981i	0.782504	+	0.622645i	$0.213942\pi$
$198$	−0.258738	−	1.30076i	−0.0183877	−	0.0924412i
$199$	23.0179	+	4.57854i	1.63170	+	0.324564i	0.924129	−	0.382082i	$-0.124793\pi$
$199$	23.0179	+	4.57854i	1.63170	+	0.324564i	0.707567	+	0.706646i	$0.249793\pi$
$200$	3.57746	−	3.49310i	0.252965	−	0.246999i
$201$	−0.757408	−	1.13354i	−0.0534234	−	0.0799538i
$202$	9.10942	+	3.77325i	0.640937	+	0.265485i
$203$	29.5629	+	29.5629i	2.07491	+	2.07491i
$204$	2.23106	+	3.46733i	0.156205	+	0.242762i
$205$	22.0533	−	8.98100i	1.54027	−	0.627260i
$206$	−4.35689	−	10.5185i	−0.303559	−	0.732856i
$207$	6.53289	+	1.29947i	0.454067	+	0.0903195i
$208$		−	3.30428i		−	0.229111i
$209$	0.449293	−	2.25875i	0.0310783	−	0.156241i
$210$	−5.41147	−	8.20437i	−0.373427	−	0.566156i
$211$	11.4509	−	2.27772i	0.788312	−	0.156805i	0.215513	−	0.976501i	$-0.430858\pi$
$211$	11.4509	−	2.27772i	0.788312	−	0.156805i	0.572799	+	0.819696i	$0.305858\pi$
$212$	−2.93072	−	7.07539i	−0.201283	−	0.485940i
$213$	2.83343	+	6.84049i	0.194143	+	0.468703i
$214$	−0.838956	+	0.166879i	−0.0573499	+	0.0114076i
$215$	−14.1965	−	21.5234i	−0.968193	−	1.46788i
$216$	−0.195090	+	0.980785i	−0.0132742	+	0.0667340i
$217$		−	2.11292i		−	0.143435i
$218$	−16.0998	−	3.20245i	−1.09042	−	0.216897i
$219$	2.31904	+	5.59865i	0.156706	+	0.378322i
$220$	−2.74656	+	1.11851i	−0.185173	+	0.0754101i
$221$	−0.235566	+	13.6219i	−0.0158459	+	0.916306i
$222$	7.30369	+	7.30369i	0.490192	+	0.490192i
$223$	23.9983	+	9.94043i	1.60705	+	0.665660i	0.992390	−	0.123135i	$-0.0392948\pi$
$223$	23.9983	+	9.94043i	1.60705	+	0.665660i	0.614656	+	0.788795i	$0.289295\pi$
$224$	2.44193	+	3.65460i	0.163158	+	0.244184i
$225$	−4.99964	−	0.0596551i	−0.333310	−	0.00397700i
$226$	−6.84196	−	1.36095i	−0.455120	−	0.0905290i
$227$	0.133557	+	0.671438i	0.00886452	+	0.0445649i	0.984964	−	0.172757i	$-0.0552677\pi$
$227$	0.133557	+	0.671438i	0.00886452	+	0.0445649i	−0.976100	+	0.217322i	$0.930268\pi$
$228$	−0.964737	+	1.44383i	−0.0638913	+	0.0956200i
$229$	1.85900	−	4.48804i	0.122847	−	0.296578i	−0.850478	−	0.526011i	$-0.823687\pi$
$229$	1.85900	−	4.48804i	0.122847	−	0.296578i	0.973324	+	0.229433i	$0.0736872\pi$
$230$	0.0888528	−	14.8939i	0.00585878	−	0.982075i
$231$	1.13724	+	5.71732i	0.0748252	+	0.376172i
$232$	−9.32914	+	1.85568i	−0.612488	+	0.121831i
$233$	2.37700	+	3.55743i	0.155722	+	0.233055i	0.901125	−	0.433560i	$-0.142743\pi$
$233$	2.37700	+	3.55743i	0.155722	+	0.233055i	−0.745402	+	0.666615i	$0.767743\pi$
$234$	−2.33648	+	2.33648i	−0.152740	+	0.152740i
$235$	−2.02953	−	10.5311i	−0.132392	−	0.686971i
$236$	−12.2007	+	5.05368i	−0.794196	+	0.328967i
$237$	8.99919	−	8.99919i	0.584560	−	0.584560i
$238$	−9.80628	−	15.2402i	−0.635647	−	0.987873i
$239$		−	24.3391i		−	1.57437i	−0.616719	−	0.787184i	$-0.711538\pi$
$239$		−	24.3391i		−	1.57437i	0.616719	−	0.787184i	$-0.288462\pi$
$240$	2.23603	+	0.0133395i	0.144335	+	0.000861062i
$241$	5.21379	−	3.48375i	0.335850	−	0.224408i	−0.376197	−	0.926540i	$-0.622768\pi$
$241$	5.21379	−	3.48375i	0.335850	−	0.224408i	0.712047	+	0.702132i	$0.247768\pi$
$242$	−9.24107			−0.594038
$243$	0.831470	−	0.555570i	0.0533388	−	0.0356398i
$244$	2.52659	−	3.78131i	0.161749	−	0.242074i
$245$	15.1671	+	22.9949i	0.968989	+	1.46909i
$246$	9.83838	+	4.07519i	0.627272	+	0.259825i
$247$	−5.30105	+	2.19577i	−0.337298	+	0.139713i
$248$	0.399702	+	0.267072i	0.0253811	+	0.0169591i
$249$	−2.24995	−	1.50337i	−0.142585	−	0.0952720i
$250$	1.98459	+	11.0028i	0.125516	+	0.695878i
$251$	−5.04989	−	5.04989i	−0.318747	−	0.318747i	0.529539	−	0.848286i	$-0.322365\pi$
$251$	−5.04989	−	5.04989i	−0.318747	−	0.318747i	−0.848286	+	0.529539i	$0.822365\pi$
$252$	0.857491	−	4.31090i	0.0540169	−	0.271561i
$253$	−3.38061	+	8.16151i	−0.212537	+	0.513110i
$254$	2.81614			0.176700
$255$	−9.21705	−	0.214401i	−0.577194	−	0.0134263i
$256$	−1.00000			−0.0625000
$257$	2.88047	−	6.95408i	0.179679	−	0.433784i	−0.808220	−	0.588880i	$-0.799569\pi$
$257$	2.88047	−	6.95408i	0.179679	−	0.433784i	0.987899	+	0.155097i	$0.0495689\pi$
$258$	2.24955	−	11.3092i	0.140051	−	0.704083i
$259$	−32.1023	−	32.1023i	−1.99474	−	1.99474i
$260$	6.11880	+	4.14146i	0.379472	+	0.256842i
$261$	7.90886	+	5.28453i	0.489546	+	0.327104i
$262$	−10.1982	−	6.81425i	−0.630050	−	0.420986i
$263$	10.7357	−	4.44688i	0.661993	−	0.274207i	−0.0262838	−	0.999655i	$-0.508367\pi$
$263$	10.7357	−	4.44688i	0.661993	−	0.274207i	0.688277	+	0.725448i	$0.258367\pi$
$264$	−1.22529	−	0.507533i	−0.0754115	−	0.0312365i
$265$	16.7753	+	3.44098i	1.03050	+	0.211377i
$266$	4.24036	−	6.34615i	0.259993	−	0.389107i
$267$	3.36919	−	2.25122i	0.206191	−	0.137773i
$268$	−1.36330			−0.0832767
$269$	−14.5979	+	9.75398i	−0.890047	+	0.594710i	−0.914319	−	0.404995i	$-0.867273\pi$
$269$	−14.5979	+	9.75398i	−0.890047	+	0.594710i	0.0242719	+	0.999705i	$0.492273\pi$
$270$	−1.57168	−	1.59054i	−0.0956493	−	0.0967974i
$271$		−	1.73289i		−	0.105265i	−0.998614	−	0.0526327i	$-0.983239\pi$
$271$		−	1.73289i		−	0.105265i	0.998614	−	0.0526327i	$-0.0167612\pi$
$272$	4.12249	+	0.0712911i	0.249963	+	0.00432266i
$273$	10.2697	−	10.2697i	0.621548	−	0.621548i
$274$	16.6477	−	6.89569i	1.00572	−	0.416584i
$275$	1.37119	−	6.48792i	0.0826861	−	0.391236i
$276$	4.70995	−	4.70995i	0.283506	−	0.283506i
$277$	−9.95490	−	14.8986i	−0.598132	−	0.895168i	0.401655	−	0.915791i	$-0.368435\pi$
$277$	−9.95490	−	14.8986i	−0.598132	−	0.895168i	−0.999787	+	0.0206231i	$0.993435\pi$
$278$	8.46018	−	1.68283i	0.507408	−	0.100930i
$279$	−0.0937833	−	0.471480i	−0.00561466	−	0.0282268i
$280$	−9.82814	−	0.0586319i	−0.587344	−	0.00350393i
$281$	12.1850	−	29.4172i	0.726897	−	1.75489i	0.0742292	−	0.997241i	$-0.476350\pi$
$281$	12.1850	−	29.4172i	0.726897	−	1.75489i	0.652668	−	0.757644i	$-0.273650\pi$
$282$	2.66468	−	3.98798i	0.158679	−	0.237481i
$283$	−2.19840	−	11.0521i	−0.130681	−	0.656978i	−0.989480	−	0.144666i	$-0.953789\pi$
$283$	−2.19840	−	11.0521i	−0.130681	−	0.656978i	0.858799	−	0.512312i	$-0.171211\pi$
$284$	7.26183	+	1.44447i	0.430910	+	0.0857134i
$285$	−1.46449	−	3.59612i	−0.0867489	−	0.213016i
$286$	−2.43467	−	3.64374i	−0.143965	−	0.215459i
$287$	−43.2432	−	17.9119i	−2.55256	−	1.05731i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	−16.9898	−	0.587794i	−0.999402	−	0.0345761i
$290$	8.25648	−	19.6013i	0.484837	−	1.15103i
$291$	−1.94907	−	4.70548i	−0.114257	−	0.275840i
$292$	5.94350	+	1.18224i	0.347817	+	0.0691851i
$293$		−	7.48509i		−	0.437284i	−0.975805	−	0.218642i	$-0.929837\pi$
$293$		−	7.48509i		−	0.437284i	0.975805	−	0.218642i	$-0.0701626\pi$
$294$	−2.40335	+	12.0824i	−0.140166	+	0.704662i
$295$	5.93356	−	28.9270i	0.345465	−	1.68420i
$296$	10.1305	−	2.01508i	0.588824	−	0.117124i
$297$	0.507533	+	1.22529i	0.0294500	+	0.0710987i
$298$	2.76896	+	6.68485i	0.160401	+	0.387243i
$299$	21.5865	−	4.29382i	1.24838	−	0.248318i
$300$	−2.82725	+	4.12391i	−0.163232	+	0.238094i
$301$	−9.88757	+	49.7082i	−0.569910	+	2.86513i
$302$			3.31624i			0.190828i
$303$	−9.67051	−	1.92358i	−0.555556	−	0.110507i
$304$	0.664522	+	1.60430i	0.0381130	+	0.0920128i
$305$	3.83542	+	9.41804i	0.219615	+	0.539276i
$306$	−2.86463	−	2.96545i	−0.163760	−	0.169524i
$307$	0.616321	+	0.616321i	0.0351753	+	0.0351753i	0.724476	−	0.689300i	$-0.242082\pi$
$307$	0.616321	+	0.616321i	0.0351753	+	0.0351753i	−0.689300	+	0.724476i	$0.742082\pi$
$308$	5.38559	+	2.23079i	0.306873	+	0.127111i
$309$	6.32522	+	9.46636i	0.359829	+	0.538523i
$310$	−0.995530	+	0.405421i	−0.0565423	+	0.0230264i
$311$	−14.9000	−	2.96379i	−0.844900	−	0.168061i	−0.246385	−	0.969172i	$-0.579243\pi$
$311$	−14.9000	−	2.96379i	−0.844900	−	0.168061i	−0.598516	+	0.801111i	$0.704243\pi$
$312$	0.644633	+	3.24079i	0.0364952	+	0.183474i
$313$	12.2909	−	18.3946i	0.694723	−	1.03973i	−0.301548	−	0.953451i	$-0.597503\pi$
$313$	12.2909	−	18.3946i	0.694723	−	1.03973i	0.996271	−	0.0862760i	$-0.0274967\pi$
$314$	−1.23403	+	2.97922i	−0.0696405	+	0.168127i
$315$	6.90808	+	6.99100i	0.389226	+	0.393898i
$316$	−2.48287	−	12.4822i	−0.139672	−	0.702181i
$317$	0.860841	−	0.171232i	0.0483496	−	0.00961734i	−0.170856	−	0.985296i	$-0.554653\pi$
$317$	0.860841	−	0.171232i	0.0483496	−	0.00961734i	0.219206	+	0.975679i	$0.429653\pi$
$318$	4.25475	+	6.36768i	0.238594	+	0.357082i
$319$	−8.92025	+	8.92025i	−0.499438	+	0.499438i
$320$	1.25336	−	1.85178i	0.0700651	−	0.103518i
$321$	0.790279	−	0.327344i	0.0441091	−	0.0182706i
$322$	−20.7019	+	20.7019i	−1.15367	+	1.15367i
$323$	−2.62511	−	6.66108i	−0.146065	−	0.370632i
$324$		−	1.00000i		−	0.0555556i
$325$	−15.3381	+	6.13990i	−0.850807	+	0.340581i
$326$	−8.30448	+	5.54887i	−0.459942	+	0.307324i
$327$	16.4152			0.907764
$328$	8.85431	−	5.91626i	0.488897	−	0.326671i
$329$	−11.7122	+	17.5286i	−0.645716	+	0.966382i
$330$	2.47557	−	1.63285i	0.136276	−	0.0898853i
$331$	−11.5589	−	4.78787i	−0.635337	−	0.263165i	0.0416818	−	0.999131i	$-0.486728\pi$
$331$	−11.5589	−	4.78787i	−0.635337	−	0.263165i	−0.677019	+	0.735966i	$0.736728\pi$
$332$	−2.50001	+	1.03554i	−0.137206	+	0.0568325i
$333$	−8.58823	−	5.73847i	−0.470632	−	0.314466i
$334$	5.99103	+	4.00308i	0.327815	+	0.219039i
$335$	1.70871	−	2.52453i	0.0933566	−	0.137930i
$336$	−3.10799	−	3.10799i	−0.169555	−	0.169555i
$337$	−2.04014	+	10.2565i	−0.111133	+	0.558706i	0.884594	+	0.466362i	$0.154436\pi$
$337$	−2.04014	+	10.2565i	−0.111133	+	0.558706i	−0.995727	+	0.0923433i	$0.970564\pi$
$338$	0.796644	−	1.92327i	0.0433317	−	0.104612i
$339$	6.97600			0.378884
$340$	−5.29899	+	7.54458i	−0.287378	+	0.409162i
$341$	0.637550			0.0345253
$342$	0.664522	−	1.60430i	0.0359332	−	0.0867505i
$343$	4.56113	−	22.9303i	0.246278	−	1.23812i
$344$	−8.15351	−	8.15351i	−0.439608	−	0.439608i
$345$	2.81851	+	14.6251i	0.151743	+	0.787386i
$346$	−1.25834	−	0.840794i	−0.0676486	−	0.0452013i
$347$	14.5748	+	9.73857i	0.782416	+	0.522794i	0.881443	−	0.472291i	$-0.156573\pi$
$347$	14.5748	+	9.73857i	0.782416	+	0.522794i	−0.0990267	+	0.995085i	$0.531573\pi$
$348$	8.78786	−	3.64005i	0.471079	−	0.195127i
$349$	−0.563986	−	0.233611i	−0.0301895	−	0.0125049i	0.367538	−	0.930009i	$-0.380201\pi$
$349$	−0.563986	−	0.233611i	−0.0301895	−	0.0125049i	−0.397727	+	0.917504i	$0.630201\pi$
$350$	12.4268	−	18.1260i	0.664240	−	0.968878i
$351$	1.83576	−	2.74741i	0.0979856	−	0.146646i
$352$	−1.10273	+	0.736823i	−0.0587759	+	0.0392728i
$353$	13.8674			0.738087			0.369043	−	0.929412i	$-0.379685\pi$
$353$	13.8674			0.738087			0.369043	+	0.929412i	$0.379685\pi$
$354$	10.9803	−	7.33681i	0.583597	−	0.389947i
$355$	−11.7765	+	11.6369i	−0.625034	+	0.617620i
$356$		−	4.05209i		−	0.214760i
$357$	12.5911	+	13.0342i	0.666390	+	0.689844i
$358$	3.08013	−	3.08013i	0.162790	−	0.162790i
$359$	−17.5283	+	7.26045i	−0.925108	+	0.383192i	−0.793820	−	0.608152i	$-0.791911\pi$
$359$	−17.5283	+	7.26045i	−0.925108	+	0.383192i	−0.131287	+	0.991344i	$0.541911\pi$
$360$	−2.19567	+	0.423144i	−0.115722	+	0.0223017i
$361$	−11.3028	+	11.3028i	−0.594887	+	0.594887i
$362$	4.76322	+	7.12867i	0.250349	+	0.374674i
$363$	9.06351	−	1.80284i	0.475711	−	0.0946247i
$364$	−2.83339	−	14.2444i	−0.148510	−	0.746611i
$365$	−9.63859	+	9.52427i	−0.504507	+	0.498523i
$366$	−1.74035	+	4.20157i	−0.0909694	+	0.219620i
$367$	−13.9243	+	20.8392i	−0.726842	+	1.08780i	0.265480	+	0.964116i	$0.414470\pi$
$367$	−13.9243	+	20.8392i	−0.726842	+	1.08780i	−0.992322	+	0.123680i	$0.960530\pi$
$368$	−1.29947	−	6.53289i	−0.0677396	−	0.340550i
$369$	−10.4444	−	2.07751i	−0.543712	−	0.108151i
$370$	−8.96571	+	21.2851i	−0.466105	+	1.10656i
$371$	−18.7011	−	27.9882i	−0.970914	−	1.45308i
$372$	−0.444125	−	0.183963i	−0.0230268	−	0.00953801i
$373$	−2.12926	−	2.12926i	−0.110249	−	0.110249i	0.649830	−	0.760079i	$-0.274840\pi$
$373$	−2.12926	−	2.12926i	−0.110249	−	0.110249i	−0.760079	+	0.649830i	$0.774840\pi$
$374$	4.59854	−	2.95893i	0.237785	−	0.153003i
$375$	−4.09299	−	10.4042i	−0.211361	−	0.537271i
$376$	−1.83546	−	4.43120i	−0.0946569	−	0.228522i
$377$	30.8261	+	6.13169i	1.58763	+	0.315798i
$378$			4.39536i			0.226073i
$379$	−3.70120	+	18.6072i	−0.190118	+	0.955787i	0.761421	+	0.648258i	$0.224502\pi$
$379$	−3.70120	+	18.6072i	−0.190118	+	0.955787i	−0.951539	+	0.307529i	$0.900498\pi$
$380$	−3.80369	−	0.780219i	−0.195125	−	0.0400244i
$381$	−2.76203	+	0.549402i	−0.141503	+	0.0281467i
$382$	2.36636	+	5.71289i	0.121073	+	0.292297i
$383$	12.9613	+	31.2913i	0.662290	+	1.59891i	0.794207	+	0.607648i	$0.207887\pi$
$383$	12.9613	+	31.2913i	0.662290	+	1.59891i	−0.131917	+	0.991261i	$0.542113\pi$
$384$	0.980785	−	0.195090i	0.0500505	−	0.00995566i
$385$	−10.8810	+	7.17694i	−0.554548	+	0.365771i
$386$	2.93532	−	14.7569i	0.149404	−	0.751104i
$387$			11.5308i			0.586144i
$388$	−4.99531	−	0.993629i	−0.253599	−	0.0504439i
$389$	−5.43127	−	13.1122i	−0.275376	−	0.664817i	0.724320	−	0.689464i	$-0.242154\pi$
$389$	−5.43127	−	13.1122i	−0.275376	−	0.664817i	−0.999696	+	0.0246468i	$0.992154\pi$
$390$	−6.80918	−	2.86817i	−0.344796	−	0.145235i
$391$	4.89132	+	27.0244i	0.247365	+	1.36668i
$392$	8.71095	+	8.71095i	0.439970	+	0.439970i
$393$	11.3317	+	4.69374i	0.571608	+	0.236768i
$394$	−1.29403	−	1.93666i	−0.0651924	−	0.0975673i
$395$	26.2263	+	11.0470i	1.31959	+	0.555837i
$396$	1.30076	+	0.258738i	0.0653658	+	0.0130021i
$397$	−1.17198	−	5.89194i	−0.0588199	−	0.295708i	0.940167	−	0.340715i	$-0.110669\pi$
$397$	−1.17198	−	5.89194i	−0.0588199	−	0.295708i	−0.998987	+	0.0450069i	$0.985669\pi$
$398$	−13.0386	+	19.5136i	−0.653566	+	0.978130i
$399$	−2.92081	+	7.05146i	−0.146223	+	0.353015i
$400$	1.85817	+	4.64190i	0.0929083	+	0.232095i
$401$	1.61816	+	8.13504i	0.0808070	+	0.406244i	0.999925	+	0.0122615i	$0.00390306\pi$
$401$	1.61816	+	8.13504i	0.0808070	+	0.406244i	−0.919118	+	0.393983i	$0.871097\pi$
$402$	1.33710	−	0.265966i	0.0666886	−	0.0132652i
$403$	−0.882482	−	1.32073i	−0.0439595	−	0.0657901i
$404$	−6.97205	+	6.97205i	−0.346872	+	0.346872i
$405$	1.85178	+	1.25336i	0.0920156	+	0.0622801i
$406$	−38.6258	+	15.9993i	−1.91696	+	0.794033i
$407$	9.68650	−	9.68650i	0.480142	−	0.480142i
$408$	−4.05718	+	0.734336i	−0.200861	+	0.0363551i
$409$		−	13.2249i		−	0.653932i	−0.945036	−	0.326966i	$-0.893974\pi$
$409$		−	13.2249i		−	0.653932i	0.945036	−	0.326966i	$-0.106026\pi$
$410$	−0.142052	+	23.8114i	−0.00701546	+	1.17596i
$411$	−14.9825	+	10.0110i	−0.739033	+	0.493806i
$412$	11.3851			0.560904
$413$	−48.2624	+	32.2479i	−2.37484	+	1.58682i
$414$	−3.70058	+	5.53831i	−0.181874	+	0.272193i
$415$	1.21583	−	5.92736i	0.0596827	−	0.290963i
$416$	3.05276	+	1.26449i	0.149674	+	0.0619969i
$417$	−7.96932	+	3.30100i	−0.390259	+	0.161651i
$418$	1.91488	+	1.27948i	0.0936596	+	0.0625814i
$419$	−7.86976	−	5.25840i	−0.384463	−	0.256890i	0.348287	−	0.937388i	$-0.386763\pi$
$419$	−7.86976	−	5.25840i	−0.384463	−	0.256890i	−0.732750	+	0.680498i	$0.761763\pi$
$420$	9.65073	−	1.85987i	0.470908	−	0.0907523i
$421$	−2.77824	−	2.77824i	−0.135403	−	0.135403i	0.636157	−	0.771560i	$-0.280523\pi$
$421$	−2.77824	−	2.77824i	−0.135403	−	0.135403i	−0.771560	+	0.636157i	$0.780523\pi$
$422$	−2.27772	+	11.4509i	−0.110878	+	0.557421i
$423$	−1.83546	+	4.43120i	−0.0892433	+	0.215453i
$424$	7.65834			0.371922
$425$	−7.32935	−	19.2686i	−0.355526	−	0.934667i
$426$	−7.40410			−0.358730
$427$	7.64944	−	18.4674i	0.370183	−	0.893700i
$428$	0.166879	−	0.838956i	0.00806639	−	0.0405525i
$429$	3.09875	+	3.09875i	0.149609	+	0.149609i
$430$	25.3178	−	4.87920i	1.22093	−	0.235296i
$431$	−17.2953	−	11.5563i	−0.833083	−	0.556648i	0.0642846	−	0.997932i	$-0.479523\pi$
$431$	−17.2953	−	11.5563i	−0.833083	−	0.556648i	−0.897368	+	0.441283i	$0.854523\pi$
$432$	−0.831470	−	0.555570i	−0.0400041	−	0.0267299i
$433$	16.5159	−	6.84112i	0.793705	−	0.328763i	0.0512728	−	0.998685i	$-0.483672\pi$
$433$	16.5159	−	6.84112i	0.793705	−	0.328763i	0.742432	+	0.669921i	$0.233672\pi$
$434$	1.95209	+	0.808581i	0.0937032	+	0.0388131i
$435$	−4.27380	+	20.8355i	−0.204913	+	0.998984i
$436$	9.11981	−	13.6488i	0.436760	−	0.653657i
$437$	−9.61717	+	6.42599i	−0.460052	+	0.307397i
$438$	−6.05994			−0.289555
$439$	−5.24270	+	3.50306i	−0.250220	+	0.167192i	−0.674355	−	0.738407i	$-0.735578\pi$
$439$	−5.24270	+	3.50306i	−0.250220	+	0.167192i	0.424135	+	0.905599i	$0.360578\pi$
$440$	0.0176915	−	2.96552i	0.000843409	−	0.141376i
$441$		−	12.3192i		−	0.586626i
$442$	−12.4948	−	5.43049i	−0.594318	−	0.258302i
$443$	−4.20395	+	4.20395i	−0.199736	+	0.199736i	−0.799887	−	0.600151i	$-0.795107\pi$
$443$	−4.20395	+	4.20395i	−0.199736	+	0.199736i	0.600151	+	0.799887i	$0.295107\pi$
$444$	−9.54273	+	3.95273i	−0.452878	+	0.187588i
$445$	7.50358	+	5.07874i	0.355704	+	0.240755i
$446$	−18.3675	+	18.3675i	−0.869727	+	0.869727i
$447$	−4.01990	−	6.01621i	−0.190135	−	0.284557i
$448$	−4.31090	+	0.857491i	−0.203671	+	0.0405127i
$449$	−7.50130	−	37.7116i	−0.354008	−	1.77972i	−0.589423	−	0.807824i	$-0.700645\pi$
$449$	−7.50130	−	37.7116i	−0.354008	−	1.77972i	0.235415	−	0.971895i	$-0.424355\pi$
$450$	1.96840	−	4.59624i	0.0927910	−	0.216669i
$451$	5.40471	−	13.0481i	0.254498	−	0.614412i
$452$	3.87566	−	5.80033i	0.182296	−	0.272825i
$453$	−0.646967	−	3.25252i	−0.0303972	−	0.152817i
$454$	−0.671438	−	0.133557i	−0.0315122	−	0.00626816i
$455$	29.9288	+	12.6066i	1.40308	+	0.591007i
$456$	−0.964737	−	1.44383i	−0.0451779	−	0.0676136i
$457$	25.7551	+	10.6681i	1.20477	+	0.499034i	0.892539	−	0.450971i	$-0.148922\pi$
$457$	25.7551	+	10.6681i	1.20477	+	0.499034i	0.312236	+	0.950005i	$0.398922\pi$
$458$	3.43499	+	3.43499i	0.160507	+	0.160507i
$459$	3.38812	+	2.34961i	0.158144	+	0.109670i
$460$	13.7262	+	5.78174i	0.639986	+	0.269575i
$461$	6.12535	+	14.7879i	0.285286	+	0.688741i	0.999942	−	0.0107344i	$-0.00341692\pi$
$461$	6.12535	+	14.7879i	0.285286	+	0.688741i	−0.714656	+	0.699476i	$0.753417\pi$
$462$	−5.71732	−	1.13724i	−0.265994	−	0.0529094i
$463$		−	6.71620i		−	0.312128i	−0.987747	−	0.156064i	$-0.950119\pi$
$463$		−	6.71620i		−	0.312128i	0.987747	−	0.156064i	$-0.0498807\pi$
$464$	1.85568	−	9.32914i	0.0861479	−	0.433095i
$465$	0.897307	−	0.591849i	0.0416116	−	0.0274464i
$466$	−4.19627	+	0.834691i	−0.194389	+	0.0386663i
$467$	4.03513	+	9.74166i	0.186723	+	0.450790i	0.989325	−	0.145725i	$-0.0465515\pi$
$467$	4.03513	+	9.74166i	0.186723	+	0.450790i	−0.802602	+	0.596515i	$0.796551\pi$
$468$	−1.26449	−	3.05276i	−0.0584512	−	0.141114i
$469$	−5.87704	+	1.16902i	−0.271377	+	0.0539802i
$470$	10.5061	+	2.15503i	0.484611	+	0.0994041i
$471$	0.629104	−	3.16272i	0.0289876	−	0.145731i
$472$		−	13.2059i		−	0.607851i
$473$	−14.9989	−	2.98346i	−0.689648	−	0.137179i
$474$	4.87033	+	11.7580i	0.223702	+	0.540063i
$475$	6.21220	−	6.06570i	0.285035	−	0.278313i
$476$	17.8328	−	3.22767i	0.817364	−	0.147940i
$477$	−5.41527	−	5.41527i	−0.247948	−	0.247948i
$478$	22.4864	+	9.31418i	1.02851	+	0.426021i
$479$	−7.80687	−	11.6838i	−0.356705	−	0.533847i	0.609108	−	0.793087i	$-0.291528\pi$
$479$	−7.80687	−	11.6838i	−0.356705	−	0.533847i	−0.965813	+	0.259241i	$0.916528\pi$
$480$	−0.868015	+	2.06072i	−0.0396193	+	0.0940584i
$481$	−33.4741	−	6.65840i	−1.52629	−	0.303597i
$482$	1.22333	+	6.15009i	0.0557211	+	0.280129i
$483$	16.2654	−	24.3429i	0.740100	−	1.10764i
$484$	3.53640	−	8.53764i	0.160746	−	0.388074i
$485$	8.10092	−	8.00483i	0.367844	−	0.363481i
$486$	0.195090	+	0.980785i	0.00884948	+	0.0444893i
$487$	24.1210	−	4.79796i	1.09303	−	0.217416i	0.384517	−	0.923118i	$-0.374368\pi$
$487$	24.1210	−	4.79796i	1.09303	−	0.217416i	0.708509	+	0.705702i	$0.249368\pi$
$488$	2.52659	+	3.78131i	0.114373	+	0.171172i
$489$	7.06238	−	7.06238i	0.319372	−	0.319372i
$490$	−27.0487	+	5.21278i	−1.22194	+	0.235489i
$491$	−0.905863	+	0.375221i	−0.0408810	+	0.0169335i	−0.403030	−	0.915187i	$-0.632043\pi$
$491$	−0.905863	+	0.375221i	−0.0408810	+	0.0169335i	0.362149	+	0.932120i	$0.382043\pi$
$492$	−7.52997	+	7.52997i	−0.339477	+	0.339477i
$493$	−8.31511	+	38.3270i	−0.374494	+	1.72616i
$494$		−	5.73782i		−	0.258157i
$495$	−2.10945	+	2.08443i	−0.0948128	+	0.0936883i
$496$	−0.399702	+	0.267072i	−0.0179471	+	0.0119919i
$497$	32.5436			1.45978
$498$	2.24995	−	1.50337i	0.100823	−	0.0673675i
$499$	−12.1110	+	18.1254i	−0.542163	+	0.811405i	−0.996855	−	0.0792439i	$-0.974749\pi$
$499$	−12.1110	+	18.1254i	−0.542163	+	0.811405i	0.454692	+	0.890649i	$0.349749\pi$
$500$	−10.9247	−	2.37707i	−0.488568	−	0.106306i
$501$	−6.65688	−	2.75737i	−0.297407	−	0.123190i
$502$	6.59801	−	2.73298i	0.294483	−	0.121979i
$503$	−24.7922	−	16.5656i	−1.10543	−	0.738624i	−0.137664	−	0.990479i	$-0.543959\pi$
$503$	−24.7922	−	16.5656i	−1.10543	−	0.738624i	−0.967765	+	0.251855i	$0.918959\pi$
$504$	3.65460	+	2.44193i	0.162789	+	0.108772i
$505$	−4.17219	−	21.6492i	−0.185660	−	0.963377i
$506$	−6.24655	−	6.24655i	−0.277693	−	0.277693i
$507$	−0.406125	+	2.04173i	−0.0180367	+	0.0906764i
$508$	−1.07769	+	2.60177i	−0.0478148	+	0.115435i
$509$	42.5707			1.88691			0.943457	−	0.331496i	$-0.107553\pi$
$509$	42.5707			1.88691			0.943457	+	0.331496i	$0.107553\pi$
$510$	3.72529	−	8.43340i	0.164959	−	0.373437i
$511$	26.6356			1.17829
$512$	0.382683	−	0.923880i	0.0169124	−	0.0408301i
$513$	−0.338770	+	1.70311i	−0.0149571	+	0.0751943i
$514$	5.32242	+	5.32242i	0.234762	+	0.234762i
$515$	−14.2697	+	21.0827i	−0.628796	+	0.929014i
$516$	9.58752	+	6.40617i	0.422067	+	0.282016i
$517$	−5.28904	−	3.53403i	−0.232612	−	0.155426i
$518$	41.9437	−	17.3737i	1.84290	−	0.763355i
$519$	1.39819	+	0.579149i	0.0613737	+	0.0254218i
$520$	−6.16777	+	4.06816i	−0.270475	+	0.178401i
$521$	8.81866	−	13.1981i	0.386352	−	0.578217i	−0.586412	−	0.810013i	$-0.699460\pi$
$521$	8.81866	−	13.1981i	0.386352	−	0.578217i	0.972765	+	0.231796i	$0.0744600\pi$
$522$	−7.90886	+	5.28453i	−0.346162	+	0.231298i
$523$	−0.644078			−0.0281636			−0.0140818	−	0.999901i	$-0.504483\pi$
$523$	−0.644078			−0.0281636			−0.0140818	+	0.999901i	$0.504483\pi$
$524$	10.1982	−	6.81425i	0.445512	−	0.297682i
$525$	−8.65180	+	20.2021i	−0.377595	+	0.881692i
$526$			11.6203i			0.506668i
$527$	1.66681	−	1.07251i	0.0726072	−	0.0467192i
$528$	0.937798	−	0.937798i	0.0408124	−	0.0408124i
$529$	19.7407	−	8.17688i	0.858293	−	0.355517i
$530$	−9.59868	+	14.1816i	−0.416940	+	0.616007i
$531$	−9.33799	+	9.33799i	−0.405234	+	0.405234i
$532$	4.24036	+	6.34615i	0.183843	+	0.275140i
$533$	−34.5111	+	6.86469i	−1.49484	+	0.297343i
$534$	0.790524	+	3.97423i	0.0342093	+	0.171982i
$535$	1.34440	+	1.36054i	0.0581235	+	0.0588212i
$536$	0.521712	−	1.25952i	0.0225345	−	0.0544031i
$537$	−2.42004	+	3.62184i	−0.104432	+	0.156294i
$538$	−3.42514	−	17.2193i	−0.147668	−	0.742379i
$539$	16.0243	+	3.18743i	0.690215	+	0.137292i
$540$	2.07093	−	0.843367i	0.0891184	−	0.0362927i
$541$	−4.94722	−	7.40404i	−0.212698	−	0.318324i	0.709745	−	0.704459i	$-0.248810\pi$
$541$	−4.94722	−	7.40404i	−0.212698	−	0.318324i	−0.922443	+	0.386134i	$0.873810\pi$
$542$	1.60098	+	0.663147i	0.0687679	+	0.0284846i
$543$	−6.06243	−	6.06243i	−0.260164	−	0.260164i
$544$	−1.64347	+	3.78140i	−0.0704633	+	0.162126i
$545$	13.8441	+	33.9947i	0.593014	+	1.45617i
$546$	5.55790	+	13.4180i	0.237856	+	0.574235i
$547$	−7.38935	−	1.46983i	−0.315946	−	0.0628455i	0.0345701	−	0.999402i	$-0.488994\pi$
$547$	−7.38935	−	1.46983i	−0.315946	−	0.0628455i	−0.350516	+	0.936557i	$0.613994\pi$
$548$			18.0193i			0.769747i
$549$	0.887221	−	4.46036i	0.0378657	−	0.190364i
$550$	5.46932	+	3.74964i	0.233213	+	0.159885i
$551$	−16.1999	+	3.22235i	−0.690138	+	0.137277i
$552$	2.54901	+	6.15384i	0.108493	+	0.261925i
$553$	−21.4068	−	51.6806i	−0.910311	−	2.19768i
$554$	17.5741	−	3.49570i	0.746650	−	0.148518i
$555$	4.64092	−	22.6252i	0.196996	−	0.960388i
$556$	−1.68283	+	8.46018i	−0.0713681	+	0.358792i
$557$			16.3464i			0.692620i	0.938120	+	0.346310i	$0.112565\pi$
$557$			16.3464i			0.692620i	−0.938120	+	0.346310i	$0.887435\pi$
$558$	0.471480	+	0.0937833i	0.0199594	+	0.00397016i
$559$	14.5806	+	35.2008i	0.616695	+	1.48883i
$560$	3.81523	−	9.05758i	0.161223	−	0.382753i
$561$	−3.93292	+	3.79921i	−0.166048	+	0.160403i
$562$	22.5150	+	22.5150i	0.949737	+	0.949737i
$563$	11.7850	+	4.88151i	0.496678	+	0.205731i	0.616938	−	0.787012i	$-0.288373\pi$
$563$	11.7850	+	4.88151i	0.496678	+	0.205731i	−0.120260	+	0.992742i	$0.538373\pi$
$564$	2.66468	+	3.98798i	0.112203	+	0.167924i
$565$	5.88333	+	14.4468i	0.247513	+	0.607780i
$566$	11.0521	+	2.19840i	0.464554	+	0.0924055i
$567$	−0.857491	−	4.31090i	−0.0360113	−	0.181041i
$568$	−4.11350	+	6.15628i	−0.172598	+	0.258312i
$569$	2.36415	−	5.70756i	0.0991102	−	0.239273i	−0.866546	−	0.499098i	$-0.833665\pi$
$569$	2.36415	−	5.70756i	0.0991102	−	0.239273i	0.965656	+	0.259825i	$0.0836648\pi$
$570$	3.88282	+	0.0231638i	0.162633	+	0.000970225i
$571$	−1.82607	−	9.18029i	−0.0764188	−	0.384183i	−1.00000		0.000779666i	$-0.999752\pi$
$571$	−1.82607	−	9.18029i	−0.0764188	−	0.384183i	0.923581	−	0.383404i	$-0.125248\pi$
$572$	4.29809	−	0.854943i	0.179712	−	0.0357469i
$573$	−3.43542	−	5.14147i	−0.143517	−	0.214788i
$574$	33.0969	−	33.0969i	1.38144	−	1.38144i
$575$	−27.9104	+	18.1712i	−1.16394	+	0.757792i
$576$	−0.923880	+	0.382683i	−0.0384950	+	0.0159451i
$577$	−30.7734	+	30.7734i	−1.28112	+	1.28112i	−0.341082	+	0.940034i	$0.610793\pi$
$577$	−30.7734	+	30.7734i	−1.28112	+	1.28112i	−0.940034	+	0.341082i	$0.889207\pi$
$578$	7.04478	−	15.4716i	0.293024	−	0.643535i
$579$			15.0460i			0.625289i
$580$	14.9497	+	15.1291i	0.620751	+	0.628202i
$581$	−9.88932	+	6.60783i	−0.410278	+	0.274139i
$582$	5.09318			0.211119
$583$	8.44511	−	5.64284i	0.349761	−	0.233703i
$584$	−3.36672	+	5.03866i	−0.139316	+	0.208501i
$585$	7.23790	+	1.48465i	0.299250	+	0.0613827i
$586$	6.91532	+	2.86442i	0.285669	+	0.118328i
$587$	−19.8554	+	8.22439i	−0.819521	+	0.339457i	−0.752746	−	0.658311i	$-0.771271\pi$
$587$	−19.8554	+	8.22439i	−0.819521	+	0.339457i	−0.0667755	+	0.997768i	$0.521271\pi$
$588$	−10.2430	−	6.84415i	−0.422414	−	0.282248i
$589$	0.694074	+	0.463766i	0.0285988	+	0.0191091i
$590$	24.4544	+	16.5518i	1.00677	+	0.681426i
$591$	1.64699	+	1.64699i	0.0677481	+	0.0677481i
$592$	−2.01508	+	10.1305i	−0.0828195	+	0.416362i
$593$	−0.0139667	+	0.0337186i	−0.000573544	+	0.00138466i	−0.924166	−	0.381991i	$-0.875239\pi$
$593$	−0.0139667	+	0.0337186i	−0.000573544	+	0.00138466i	0.923593	+	0.383376i	$0.125239\pi$
$594$	−1.32625			−0.0544166
$595$	−16.3740	+	37.0678i	−0.671268	+	1.51963i
$596$	−7.23563			−0.296383
$597$	8.98114	−	21.6824i	0.367574	−	0.887401i
$598$	−4.29382	+	21.5865i	−0.175587	+	0.882737i
$599$	−8.71071	−	8.71071i	−0.355910	−	0.355910i	0.506393	−	0.862303i	$-0.330979\pi$
$599$	−8.71071	−	8.71071i	−0.355910	−	0.355910i	−0.862303	+	0.506393i	$0.830979\pi$
$600$	−2.72805	−	4.19019i	−0.111372	−	0.171064i
$601$	−22.9907	−	15.3619i	−0.937809	−	0.626624i	−0.0101081	−	0.999949i	$-0.503218\pi$
$601$	−22.9907	−	15.3619i	−0.937809	−	0.626624i	−0.927701	+	0.373325i	$0.878218\pi$
$602$	−42.1405	−	28.1574i	−1.71752	−	1.14761i
$603$	−1.25952	+	0.521712i	−0.0512917	+	0.0212457i
$604$	−3.06381	−	1.26907i	−0.124665	−	0.0516378i
$605$	11.3774	+	17.2494i	0.462558	+	0.701287i
$606$	5.47790	−	8.19826i	0.222525	−	0.333032i
$607$	10.0122	−	6.68996i	0.406384	−	0.271537i	−0.335533	−	0.942028i	$-0.608917\pi$
$607$	10.0122	−	6.68996i	0.406384	−	0.271537i	0.741918	+	0.670491i	$0.233917\pi$
$608$	−1.73648			−0.0704236
$609$	34.7623	−	23.2274i	1.40864	−	0.941222i
$610$	−10.1689	−	0.0606647i	−0.411726	−	0.00245624i
$611$			15.8483i			0.641154i
$612$	3.83597	−	1.51174i	0.155060	−	0.0611086i
$613$	−26.7555	+	26.7555i	−1.08064	+	1.08064i	−0.0841944	+	0.996449i	$0.526832\pi$
$613$	−26.7555	+	26.7555i	−1.08064	+	1.08064i	−0.996449	+	0.0841944i	$0.973168\pi$
$614$	−0.805262	+	0.333550i	−0.0324977	+	0.0134610i
$615$	−4.50606	−	23.3816i	−0.181702	−	0.942838i
$616$	−4.12196	+	4.12196i	−0.166078	+	0.166078i
$617$	−2.75373	−	4.12125i	−0.110861	−	0.165915i	0.771890	−	0.635756i	$-0.219311\pi$
$617$	−2.75373	−	4.12125i	−0.110861	−	0.165915i	−0.882751	+	0.469841i	$0.844311\pi$
$618$	−11.1663	+	2.22112i	−0.449176	+	0.0893467i
$619$	6.74822	+	33.9256i	0.271234	+	1.36359i	0.840669	+	0.541549i	$0.182162\pi$
$619$	6.74822	+	33.9256i	0.271234	+	1.36359i	−0.569435	+	0.822036i	$0.692838\pi$
$620$	0.00641254	−	1.07490i	0.000257534	−	0.0431689i
$621$	2.54901	−	6.15384i	0.102288	−	0.246945i
$622$	8.44016	−	12.6316i	0.338420	−	0.506481i
$623$	−3.47463	−	17.4682i	−0.139208	−	0.699847i
$624$	−3.24079	−	0.644633i	−0.129735	−	0.0258060i
$625$	18.0944	−	17.2508i	0.723777	−	0.690034i
$626$	12.2909	+	18.3946i	0.491244	+	0.735198i
$627$	−2.12770	−	0.881320i	−0.0849720	−	0.0351965i
$628$	−2.28019	−	2.28019i	−0.0909897	−	0.0909897i
$629$	9.02938	−	41.6193i	0.360025	−	1.65947i
$630$	−9.10245	+	3.70690i	−0.362650	+	0.147686i
$631$	−15.1406	−	36.5527i	−0.602738	−	1.45514i	−0.870751	−	0.491724i	$-0.836367\pi$
$631$	−15.1406	−	36.5527i	−0.602738	−	1.45514i	0.268013	−	0.963415i	$-0.413633\pi$
$632$	12.4822	+	2.48287i	0.496517	+	0.0987633i
$633$		−	11.6752i		−	0.464049i
$634$	−0.171232	+	0.860841i	−0.00680049	+	0.0341884i
$635$	−3.46717	−	5.25661i	−0.137591	−	0.208602i
$636$	−7.51119	+	1.49407i	−0.297838	+	0.0592437i
$637$	−15.5775	−	37.6074i	−0.617202	−	1.49006i
$638$	−4.82760	−	11.6549i	−0.191127	−	0.461421i
$639$	7.26183	−	1.44447i	0.287274	−	0.0571423i
$640$	1.23118	+	1.86660i	0.0486666	+	0.0737839i
$641$	6.06401	−	30.4858i	0.239514	−	1.20412i	−0.654494	−	0.756067i	$-0.727118\pi$
$641$	6.06401	−	30.4858i	0.239514	−	1.20412i	0.894008	−	0.448050i	$-0.147882\pi$
$642$			0.855392i			0.0337596i
$643$	47.7399	+	9.49605i	1.88268	+	0.374488i	0.996110	−	0.0881141i	$-0.0280840\pi$
$643$	47.7399	+	9.49605i	1.88268	+	0.374488i	0.886566	+	0.462602i	$0.153084\pi$
$644$	−11.2038	−	27.0483i	−0.441491	−	1.06585i
$645$	−23.8794	+	9.72470i	−0.940252	+	0.382910i
$646$	7.15862	+	0.123796i	0.281652	+	0.00487067i
$647$	13.6334	+	13.6334i	0.535983	+	0.535983i	0.922347	−	0.386363i	$-0.126269\pi$
$647$	13.6334	+	13.6334i	0.535983	+	0.535983i	−0.386363	+	0.922347i	$0.626269\pi$
$648$	0.923880	+	0.382683i	0.0362934	+	0.0150332i
$649$	−9.73042	−	14.5626i	−0.381952	−	0.571632i
$650$	0.197117	−	16.5202i	0.00773157	−	0.647977i
$651$	−2.07232	−	0.412211i	−0.0812208	−	0.0161558i
$652$	−1.94851	−	9.79580i	−0.0763094	−	0.383633i
$653$	24.0012	−	35.9203i	0.939238	−	1.40567i	0.0253609	−	0.999678i	$-0.491927\pi$
$653$	24.0012	−	35.9203i	0.939238	−	1.40567i	0.913877	−	0.405991i	$-0.133073\pi$
$654$	−6.28183	+	15.1657i	−0.245639	+	0.593025i
$655$	−0.163613	+	27.4256i	−0.00639291	+	1.07161i
$656$	2.07751	+	10.4444i	0.0811133	+	0.407784i
$657$	5.94350	−	1.18224i	0.231878	−	0.0461234i
$658$	−11.7122	−	17.5286i	−0.456590	−	0.683335i
$659$	−29.3177	+	29.3177i	−1.14205	+	1.14205i	−0.153981	+	0.988074i	$0.549209\pi$
$659$	−29.3177	+	29.3177i	−1.14205	+	1.14205i	−0.988074	+	0.153981i	$0.950791\pi$
$660$	0.561194	+	2.91199i	0.0218444	+	0.113349i
$661$	−26.8225	+	11.1102i	−1.04327	+	0.432138i	−0.837486	−	0.546459i	$-0.815975\pi$
$661$	−26.8225	+	11.1102i	−1.04327	+	0.432138i	−0.205787	+	0.978597i	$0.565975\pi$
$662$	8.84683	−	8.84683i	0.343842	−	0.343842i
$663$	13.3142	+	2.88853i	0.517079	+	0.112181i
$664$		−	2.70599i		−	0.105013i
$665$	−17.0664	−	0.101813i	−0.661805	−	0.00394814i
$666$	8.58823	−	5.73847i	0.332787	−	0.222361i
$667$	63.3576			2.45322
$668$	−5.99103	+	4.00308i	−0.231800	+	0.154884i
$669$	14.4313	−	21.5979i	0.557945	−	0.835024i
$670$	1.67846	+	2.54473i	0.0648447	+	0.0983116i
$671$	5.57232	+	2.30813i	0.215117	+	0.0891044i
$672$	4.06078	−	1.68203i	0.156648	−	0.0648857i
$673$	−16.9978	−	11.3576i	−0.655216	−	0.437802i	0.183020	−	0.983109i	$-0.441413\pi$
$673$	−16.9978	−	11.3576i	−0.655216	−	0.437802i	−0.838236	+	0.545308i	$0.816413\pi$
$674$	−8.69502	−	5.80982i	−0.334920	−	0.223786i
$675$	−1.03389	+	4.89194i	−0.0397945	+	0.188291i
$676$	1.47201	+	1.47201i	0.0566156	+	0.0566156i
$677$	−3.74460	+	18.8254i	−0.143917	+	0.723518i	0.839672	+	0.543094i	$0.182747\pi$
$677$	−3.74460	+	18.8254i	−0.143917	+	0.723518i	−0.983589	+	0.180424i	$0.942253\pi$
$678$	−2.66960	+	6.44498i	−0.102525	+	0.247518i
$679$	−22.3863			−0.859108
$680$	−4.94245	−	7.78281i	−0.189534	−	0.298457i
$681$	0.684593			0.0262336
$682$	−0.243980	+	0.589019i	−0.00934247	+	0.0225547i
$683$	−3.93124	+	19.7637i	−0.150425	+	0.756235i	0.829756	+	0.558127i	$0.188480\pi$
$683$	−3.93124	+	19.7637i	−0.150425	+	0.756235i	−0.980180	+	0.198108i	$0.936520\pi$
$684$	1.22788	+	1.22788i	0.0469491	+	0.0469491i
$685$	−33.3678	−	22.5847i	−1.27492	−	0.862918i
$686$	19.4394	+	12.9890i	0.742199	+	0.495922i
$687$	−4.03912	−	2.69886i	−0.154102	−	0.102968i
$688$	10.6531	−	4.41265i	0.406145	−	0.168231i
$689$	−23.3791	−	9.68393i	−0.890671	−	0.368928i
$690$	−14.5904	−	2.99280i	−0.555446	−	0.113934i
$691$	−16.9769	+	25.4077i	−0.645831	+	0.966555i	0.353682	+	0.935366i	$0.384929\pi$
$691$	−16.9769	+	25.4077i	−0.645831	+	0.966555i	−0.999513	+	0.0311893i	$0.990071\pi$
$692$	1.25834	−	0.840794i	0.0478348	−	0.0319622i
$693$	5.82933			0.221438
$694$	−14.5748	+	9.73857i	−0.553252	+	0.369671i
$695$	−13.5572	−	13.7199i	−0.514253	−	0.520426i
$696$			9.51191i			0.360548i
$697$	−7.81994	−	43.2049i	−0.296201	−	1.63650i
$698$	0.431656	−	0.431656i	0.0163384	−	0.0163384i
$699$	3.95280	−	1.63731i	0.149509	−	0.0619286i
$700$	11.9908	+	18.4174i	0.453208	+	0.696112i
$701$	−13.8997	+	13.8997i	−0.524983	+	0.524983i	−0.919072	−	0.394089i	$-0.871060\pi$
$701$	−13.8997	+	13.8997i	−0.524983	+	0.524983i	0.394089	+	0.919072i	$0.371060\pi$
$702$	1.83576	+	2.74741i	0.0692863	+	0.103694i
$703$	17.5914	−	3.49915i	0.663474	−	0.131973i
$704$	−0.258738	−	1.30076i	−0.00975155	−	0.0490244i
$705$	−10.7247	−	0.0639803i	−0.403914	−	0.00240964i
$706$	−5.30682	+	12.8118i	−0.199725	+	0.482178i
$707$	−24.0773	+	36.0343i	−0.905521	+	1.35521i
$708$	2.57635	+	12.9522i	0.0968250	+	0.486772i
$709$	8.06608	+	1.60444i	0.302928	+	0.0602562i	0.344214	−	0.938891i	$-0.388145\pi$
$709$	8.06608	+	1.60444i	0.302928	+	0.0602562i	−0.0412858	+	0.999147i	$0.513145\pi$
$710$	−6.24437	−	15.3333i	−0.234347	−	0.575450i
$711$	−7.07062	−	10.5819i	−0.265169	−	0.396853i
$712$	3.74364	+	1.55067i	0.140299	+	0.0581138i
$713$	−2.26415	−	2.26415i	−0.0847932	−	0.0847932i
$714$	−16.8604	+	6.64465i	−0.630986	+	0.248670i
$715$	−3.80389	+	9.03066i	−0.142258	+	0.337727i
$716$	1.66695	+	4.02438i	0.0622969	+	0.150398i
$717$	−23.8715	−	4.74833i	−0.891496	−	0.177330i
$718$		−	18.9725i		−	0.708047i
$719$	−1.56612	+	7.87340i	−0.0584063	+	0.293628i	−0.998938	−	0.0460781i	$-0.985328\pi$
$719$	−1.56612	+	7.87340i	−0.0584063	+	0.293628i	0.940532	+	0.339706i	$0.110328\pi$
$720$	0.449311	−	2.19046i	0.0167448	−	0.0816337i
$721$	49.0800	−	9.76262i	1.82784	−	0.363579i
$722$	−6.11706	−	14.7679i	−0.227653	−	0.549604i
$723$	−2.39965	−	5.79326i	−0.0892438	−	0.215454i
$724$	−8.40883	+	1.67262i	−0.312512	+	0.0621625i
$725$	−46.7531	+	8.72122i	−1.73637	+	0.323898i
$726$	−1.80284	+	9.06351i	−0.0669098	+	0.336378i
$727$			21.2108i			0.786664i	0.919397	+	0.393332i	$0.128678\pi$
$727$			21.2108i			0.786664i	−0.919397	+	0.393332i	$0.871322\pi$
$728$	14.2444	+	2.83339i	0.527933	+	0.105012i
$729$	−0.382683	−	0.923880i	−0.0141735	−	0.0342178i
$730$	−5.11075	−	12.5497i	−0.189157	−	0.464485i
$731$	−44.2318	+	17.4316i	−1.63597	+	0.644732i
$732$	−3.21574	−	3.21574i	−0.118857	−	0.118857i
$733$	26.7655	+	11.0866i	0.988605	+	0.409493i	0.817606	−	0.575778i	$-0.195301\pi$
$733$	26.7655	+	11.0866i	0.988605	+	0.409493i	0.170998	+	0.985271i	$0.445301\pi$
$734$	−13.9243	−	20.8392i	−0.513955	−	0.769188i
$735$	25.5120	−	10.3896i	0.941026	−	0.383225i
$736$	6.53289	+	1.29947i	0.240805	+	0.0478992i
$737$	−0.352737	−	1.77333i	−0.0129932	−	0.0653214i
$738$	5.91626	−	8.85431i	0.217781	−	0.325932i
$739$	15.2129	−	36.7272i	0.559615	−	1.35103i	−0.350456	−	0.936579i	$-0.613973\pi$
$739$	15.2129	−	36.7272i	0.559615	−	1.35103i	0.910071	−	0.414452i	$-0.136027\pi$
$740$	−16.2338	−	16.4287i	−0.596768	−	0.603931i
$741$	1.11939	+	5.62757i	0.0411219	+	0.206734i
$742$	33.0144	−	6.56696i	1.21200	−	0.241081i
$743$	0.589803	+	0.882702i	0.0216378	+	0.0323832i	0.842131	−	0.539273i	$-0.181301\pi$
$743$	0.589803	+	0.882702i	0.0216378	+	0.0323832i	−0.820493	+	0.571656i	$0.806301\pi$
$744$	0.339918	−	0.339918i	0.0124620	−	0.0124620i
$745$	9.06887	−	13.3988i	0.332258	−	0.490894i
$746$	2.78202	−	1.15235i	0.101857	−	0.0421905i
$747$	−1.91342	+	1.91342i	−0.0700085	+	0.0700085i
$748$	0.973911	+	5.38083i	0.0356097	+	0.196743i
$749$		−	3.75975i		−	0.137378i
$750$	11.1785	+	0.200083i	0.408183	+	0.00730601i
$751$	22.4210	−	14.9812i	0.818152	−	0.546672i	−0.0746033	−	0.997213i	$-0.523769\pi$
$751$	22.4210	−	14.9812i	0.818152	−	0.546672i	0.892755	+	0.450541i	$0.148769\pi$
$752$	4.79630			0.174903
$753$	−5.93805	+	3.96768i	−0.216394	+	0.144590i
$754$	−17.4616	+	26.1331i	−0.635913	+	0.951712i
$755$	6.19010	−	4.08289i	0.225281	−	0.148592i
$756$	−4.06078	−	1.68203i	−0.147689	−	0.0611748i
$757$	19.9107	−	8.24727i	0.723665	−	0.299752i	0.00971929	−	0.999953i	$-0.496906\pi$
$757$	19.9107	−	8.24727i	0.723665	−	0.299752i	0.713946	+	0.700201i	$0.246906\pi$
$758$	−15.7744	−	10.5401i	−0.572952	−	0.382834i
$759$	7.34517	+	4.90788i	0.266613	+	0.178145i
$760$	2.17644	−	3.21558i	0.0789477	−	0.116641i
$761$	30.5567	+	30.5567i	1.10768	+	1.10768i	0.993455	+	0.114223i	$0.0364378\pi$
$761$	30.5567	+	30.5567i	1.10768	+	1.10768i	0.114223	+	0.993455i	$0.463562\pi$
$762$	0.549402	−	2.76203i	0.0199027	−	0.100058i
$763$	27.6109	−	66.6586i	0.999582	−	2.41320i
$764$	−6.18359			−0.223714
$765$	−2.00844	+	8.99812i	−0.0726153	+	0.325328i
$766$	−33.8694			−1.22375
$767$	−16.6988	+	40.3144i	−0.602958	+	1.45567i
$768$	−0.195090	+	0.980785i	−0.00703972	+	0.0353910i
$769$	4.31226	+	4.31226i	0.155504	+	0.155504i	0.780571	−	0.625067i	$-0.214928\pi$
$769$	4.31226	+	4.31226i	0.155504	+	0.155504i	−0.625067	+	0.780571i	$0.714928\pi$
$770$	−2.46665	−	12.7993i	−0.0888917	−	0.461253i
$771$	−6.25851	−	4.18180i	−0.225395	−	0.150604i
$772$	12.5103	+	8.35909i	0.450254	+	0.300850i
$773$	0.0800706	−	0.0331663i	0.00287994	−	0.00119291i	−0.381243	−	0.924475i	$-0.624504\pi$
$773$	0.0800706	−	0.0331663i	0.00287994	−	0.00119291i	0.384123	+	0.923282i	$0.374504\pi$
$774$	−10.6531	−	4.41265i	−0.382917	−	0.158609i
$775$	1.98243	+	1.35911i	0.0712112	+	0.0488207i
$776$	2.82962	−	4.23482i	0.101577	−	0.152021i
$777$	−37.7483	+	25.2226i	−1.35421	+	0.904857i
$778$	14.1926			0.508829
$779$	15.3753	−	10.2735i	0.550878	−	0.368085i
$780$	5.25560	−	5.19327i	0.188181	−	0.185949i
$781$			9.81966i			0.351375i
$782$	−26.8391	−	5.82279i	−0.959765	−	0.208223i
$783$	6.72594	−	6.72594i	0.240365	−	0.240365i
$784$	−11.3814	+	4.71433i	−0.406479	+	0.168369i
$785$	7.08033	−	1.36451i	0.252708	−	0.0487013i
$786$	−8.67289	+	8.67289i	−0.309352	+	0.309352i
$787$	11.9414	+	17.8715i	0.425664	+	0.637051i	0.980870	−	0.194662i	$-0.0623608\pi$
$787$	11.9414	+	17.8715i	0.425664	+	0.637051i	−0.555207	+	0.831712i	$0.687361\pi$
$788$	2.28444	−	0.454403i	0.0813798	−	0.0161875i
$789$	−2.26700	−	11.3970i	−0.0807074	−	0.405743i
$790$	−20.2425	+	20.0024i	−0.720196	+	0.711654i
$791$	11.7338	−	28.3280i	0.417207	−	1.00723i
$792$	−0.736823	+	1.10273i	−0.0261819	+	0.0391839i
$793$	−2.93163	−	14.7383i	−0.104105	−	0.523372i
$794$	5.89194	+	1.17198i	0.209097	+	0.0415920i
$795$	6.64756	−	15.7817i	0.235765	−	0.559718i
$796$	−13.0386	−	19.5136i	−0.462141	−	0.691642i
$797$	−2.13720	−	0.885256i	−0.0757034	−	0.0313574i	0.344510	−	0.938783i	$-0.388045\pi$
$797$	−2.13720	−	0.885256i	−0.0757034	−	0.0313574i	−0.420214	+	0.907425i	$0.638045\pi$
$798$	−5.39696	−	5.39696i	−0.191050	−	0.191050i
$799$	−19.7727	−	0.341934i	−0.699508	−	0.0120967i
$800$	−4.99964	−	0.0596551i	−0.176764	−	0.00210912i
$801$	−1.55067	−	3.74364i	−0.0547902	−	0.132275i
$802$	−8.13504	−	1.61816i	−0.287258	−	0.0571392i
$803$			8.03697i			0.283619i
$804$	−0.265966	+	1.33710i	−0.00937991	+	0.0471560i
$805$	64.1299	+	13.1544i	2.26028	+	0.463633i
$806$	1.55790	−	0.309886i	0.0548748	−	0.0109153i
$807$	6.71866	+	16.2203i	0.236508	+	0.570980i
$808$	−3.77325	−	9.10942i	−0.132742	−	0.320468i
$809$	43.9097	−	8.73419i	1.54378	−	0.307078i	0.651534	−	0.758620i	$-0.274126\pi$
$809$	43.9097	−	8.73419i	1.54378	−	0.307078i	0.892250	+	0.451542i	$0.149126\pi$
$810$	−1.86660	+	1.23118i	−0.0655857	+	0.0432592i
$811$	2.89956	−	14.5771i	0.101817	−	0.511870i	−0.895895	−	0.444266i	$-0.853465\pi$
$811$	2.89956	−	14.5771i	0.101817	−	0.511870i	0.997712	−	0.0676038i	$-0.0215354\pi$
$812$		−	41.8082i		−	1.46718i
$813$	−1.69959	−	0.338069i	−0.0596072	−	0.0118566i
$814$	5.24229	+	12.6560i	0.183742	+	0.443593i
$815$	20.5818	+	8.66948i	0.720950	+	0.303679i
$816$	0.874179	−	4.02937i	0.0306024	−	0.141056i
$817$	−14.1584	−	14.1584i	−0.495340	−	0.495340i
$818$	12.2183	+	5.06097i	0.427201	+	0.176953i
$819$	−8.06882	−	12.0758i	−0.281947	−	0.421964i
$820$	−21.9445	−	9.24348i	−0.766336	−	0.322796i
$821$	34.4107	+	6.84472i	1.20094	+	0.238882i	0.754725	−	0.656042i	$-0.227771\pi$
$821$	34.4107	+	6.84472i	1.20094	+	0.238882i	0.446218	+	0.894924i	$0.352771\pi$
$822$	−3.51539	−	17.6731i	−0.122613	−	0.616419i
$823$	5.14206	−	7.69563i	0.179241	−	0.268253i	−0.730960	−	0.682421i	$-0.760927\pi$
$823$	5.14206	−	7.69563i	0.179241	−	0.268253i	0.910201	+	0.414168i	$0.135927\pi$
$824$	−4.35689	+	10.5185i	−0.151779	+	0.366428i
$825$	−6.09575	−	2.61058i	−0.212227	−	0.0908886i
$826$	−11.3240	−	56.9294i	−0.394011	−	1.98083i
$827$	19.3366	−	3.84629i	0.672399	−	0.133749i	0.152929	−	0.988237i	$-0.451129\pi$
$827$	19.3366	−	3.84629i	0.672399	−	0.133749i	0.519470	+	0.854489i	$0.326129\pi$
$828$	−3.70058	−	5.53831i	−0.128604	−	0.192470i
$829$	9.57107	−	9.57107i	0.332417	−	0.332417i	−0.521087	−	0.853504i	$-0.674473\pi$
$829$	9.57107	−	9.57107i	0.332417	−	0.332417i	0.853504	+	0.521087i	$0.174473\pi$
$830$	5.01089	+	3.39158i	0.173931	+	0.117724i
$831$	−16.5544	+	6.85705i	−0.574266	+	0.237869i
$832$	−2.33648	+	2.33648i	−0.0810028	+	0.0810028i
$833$	47.2558	−	18.6234i	1.63732	−	0.645263i
$834$		−	8.62593i		−	0.298691i
$835$	0.0961160	−	16.1114i	0.00332623	−	0.557557i
$836$	−1.91488	+	1.27948i	−0.0662274	+	0.0442517i
$837$	−0.480717			−0.0166160
$838$	7.86976	−	5.25840i	0.271856	−	0.181649i
$839$	−22.3836	+	33.4994i	−0.772767	+	1.15653i	0.211072	+	0.977471i	$0.432305\pi$
$839$	−22.3836	+	33.4994i	−0.772767	+	1.15653i	−0.983839	+	0.179057i	$0.942695\pi$
$840$	−1.97488	+	9.62786i	−0.0681398	+	0.332193i
$841$	56.7968	+	23.5260i	1.95851	+	0.811242i
$842$	3.62995	−	1.50357i	0.125096	−	0.0518165i
$843$	−26.4748	−	17.6899i	−0.911841	−	0.609273i
$844$	−9.70760	−	6.48641i	−0.334149	−	0.223271i
$845$	−4.57078	+	0.880872i	−0.157240	+	0.0303029i
$846$	−3.39150	−	3.39150i	−0.116602	−	0.116602i
$847$	7.92414	−	39.8373i	0.272277	−	1.36883i
$848$	−2.93072	+	7.07539i	−0.100641	+	0.242970i
$849$	−11.2686			−0.386738
$850$	20.6067	+	0.602358i	0.706805	+	0.0206607i
$851$	−68.8000			−2.35843
$852$	2.83343	−	6.84049i	0.0970716	−	0.234351i
$853$	−7.93795	+	39.9068i	−0.271790	+	1.36638i	0.567802	+	0.823165i	$0.307794\pi$
$853$	−7.93795	+	39.9068i	−0.271790	+	1.36638i	−0.839592	+	0.543217i	$0.817206\pi$
$854$	14.1343	+	14.1343i	0.483667	+	0.483667i
$855$	−3.81273	+	0.734782i	−0.130393	+	0.0251290i
$856$	0.711233	+	0.475230i	0.0243094	+	0.0162430i
$857$	−37.5029	−	25.0586i	−1.28107	−	0.855986i	−0.286305	−	0.958139i	$-0.592427\pi$
$857$	−37.5029	−	25.0586i	−1.28107	−	0.855986i	−0.994769	+	0.102153i	$0.967427\pi$
$858$	−4.04871	+	1.67703i	−0.138221	+	0.0572529i
$859$	16.1258	+	6.67951i	0.550204	+	0.227902i	0.640426	−	0.768020i	$-0.278758\pi$
$859$	16.1258	+	6.67951i	0.550204	+	0.227902i	−0.0902223	+	0.995922i	$0.528758\pi$
$860$	−5.18092	+	25.2578i	−0.176668	+	0.861283i
$861$	−26.0041	+	38.9178i	−0.886216	+	1.32632i
$862$	17.2953	−	11.5563i	0.589079	−	0.393610i
$863$	39.6699			1.35038			0.675190	−	0.737644i	$-0.264061\pi$
$863$	39.6699			1.35038			0.675190	+	0.737644i	$0.264061\pi$
$864$	0.831470	−	0.555570i	0.0282872	−	0.0189009i
$865$	−0.0201879	+	3.38398i	−0.000686408	+	0.115059i
$866$			17.8767i			0.607475i
$867$	−3.89105	+	16.5487i	−0.132147	+	0.562024i
$868$	−1.49406	+	1.49406i	−0.0507118	+	0.0507118i
$869$	15.5940	−	6.45926i	0.528991	−	0.219115i
$870$	−17.6140	−	11.9219i	−0.597169	−	0.404189i
$871$	−3.18532	+	3.18532i	−0.107930	+	0.107930i
$872$	9.11981	+	13.6488i	0.308836	+	0.462205i
$873$	−4.99531	+	0.993629i	−0.169066	+	0.0336293i
$874$	−2.25651	−	11.3442i	−0.0763275	−	0.383724i
$875$	−49.1337	−	0.879437i	−1.66102	−	0.0297304i
$876$	2.31904	−	5.59865i	0.0783530	−	0.189161i
$877$	−27.6654	+	41.4042i	−0.934194	+	1.39812i	−0.0169236	+	0.999857i	$0.505387\pi$
$877$	−27.6654	+	41.4042i	−0.934194	+	1.39812i	−0.917271	+	0.398264i	$0.869613\pi$
$878$	−1.23011	−	6.18418i	−0.0415142	−	0.208706i
$879$	−7.34127	−	1.46027i	−0.247615	−	0.0492536i
$880$	2.73302	+	1.15120i	0.0921300	+	0.0388070i
$881$	−8.23750	−	12.3283i	−0.277529	−	0.415351i	0.666352	−	0.745637i	$-0.267855\pi$
$881$	−8.23750	−	12.3283i	−0.277529	−	0.415351i	−0.943881	+	0.330286i	$0.892855\pi$
$882$	11.3814	+	4.71433i	0.383232	+	0.158740i
$883$	−10.5514	−	10.5514i	−0.355084	−	0.355084i	0.506913	−	0.861997i	$-0.330786\pi$
$883$	−10.5514	−	10.5514i	−0.355084	−	0.355084i	−0.861997	+	0.506913i	$0.830786\pi$
$884$	9.79868	−	9.46554i	0.329565	−	0.318361i
$885$	−27.2136	−	11.4629i	−0.914776	−	0.385322i
$886$	−2.27516	−	5.49273i	−0.0764356	−	0.184532i
$887$	−40.2487	−	8.00597i	−1.35142	−	0.268814i	−0.534306	−	0.845291i	$-0.679427\pi$
$887$	−40.2487	−	8.00597i	−1.35142	−	0.268814i	−0.817114	+	0.576477i	$0.804427\pi$
$888$		−	10.3290i		−	0.346618i
$889$	−2.41482	+	12.1401i	−0.0809903	+	0.407166i
$890$	−7.56364	+	4.98885i	−0.253534	+	0.167227i
$891$	1.30076	−	0.258738i	0.0435772	−	0.00866804i
$892$	−9.94043	−	23.9983i	−0.332830	−	0.803523i
$893$	−3.18725	−	7.69470i	−0.106657	−	0.257493i
$894$	7.09660	−	1.41160i	0.237346	−	0.0472110i
$895$	−9.54155	−	1.95718i	−0.318939	−	0.0654212i
$896$	0.857491	−	4.31090i	0.0286468	−	0.144017i
$897$		−	22.0094i		−	0.734872i
$898$	37.7116	+	7.50130i	1.25845	+	0.250322i
$899$	−1.74984	−	4.22448i	−0.0583603	−	0.140894i
$900$	3.49310	+	3.57746i	0.116437	+	0.119249i
$901$	12.5863	−	28.9593i	0.419310	−	0.964773i
$902$	9.98660	+	9.98660i	0.332517	+	0.332517i
$903$	46.8241	+	19.3952i	1.55821	+	0.645431i
$904$	3.87566	+	5.80033i	0.128902	+	0.192916i
$905$	7.44199	−	17.6677i	0.247380	−	0.587294i
$906$	3.25252	+	0.646967i	0.108058	+	0.0214940i
$907$	9.66199	+	48.5741i	0.320821	+	1.61288i	0.718619	+	0.695404i	$0.244774\pi$
$907$	9.66199	+	48.5741i	0.320821	+	1.61288i	−0.397798	+	0.917473i	$0.630226\pi$
$908$	0.380339	−	0.569218i	0.0126220	−	0.0188902i
$909$	−3.77325	+	9.10942i	−0.125151	+	0.302140i
$910$	−23.1002	+	22.8262i	−0.765765	+	0.756683i
$911$	3.28551	+	16.5174i	0.108854	+	0.547246i	0.996271	+	0.0862784i	$0.0274975\pi$
$911$	3.28551	+	16.5174i	0.108854	+	0.547246i	−0.887417	+	0.460967i	$0.847503\pi$
$912$	1.70311	−	0.338770i	0.0563958	−	0.0112178i
$913$	−1.99383	−	2.98398i	−0.0659863	−	0.0987555i
$914$	−19.7121	+	19.7121i	−0.652019	+	0.652019i
$915$	9.98533	−	1.92435i	0.330105	−	0.0636171i
$916$	−4.48804	+	1.85900i	−0.148289	+	0.0614233i
$917$	38.1204	−	38.1204i	1.25885	−	1.25885i
$918$	−3.46733	+	2.23106i	−0.114439	+	0.0736358i
$919$			13.0619i			0.430874i	0.976518	+	0.215437i	$0.0691176\pi$
$919$			13.0619i			0.430874i	−0.976518	+	0.215437i	$0.930882\pi$
$920$	−10.5944	+	10.4687i	−0.349287	+	0.345144i
$921$	0.724717	−	0.484240i	0.0238802	−	0.0159563i
$922$	−16.0063			−0.527140
$923$	20.3421	−	13.5921i	0.669568	−	0.447391i
$924$	3.23860	−	4.84691i	0.106542	−	0.159452i
$925$	50.7692	−	9.47037i	1.66928	−	0.311384i
$926$	6.20496	+	2.57018i	0.203908	+	0.0844613i
$927$	10.5185	−	4.35689i	0.345472	−	0.143099i
$928$	7.90886	+	5.28453i	0.259621	+	0.173473i
$929$	−45.6106	−	30.4760i	−1.49644	−	0.999887i	−0.990530	−	0.137298i	$-0.956158\pi$
$929$	−45.6106	−	30.4760i	−1.49644	−	0.999887i	−0.505906	−	0.862589i	$-0.668842\pi$
$930$	0.203413	+	1.05549i	0.00667017	+	0.0346110i
$931$	15.1264	+	15.1264i	0.495748	+	0.495748i
$932$	0.834691	−	4.19627i	0.0273412	−	0.137454i
$933$	−5.81368	+	14.0355i	−0.190331	+	0.459501i
$934$	−10.5443			−0.345020
$935$	−11.1848	−	4.94066i	−0.365781	−	0.161577i
$936$	3.30428			0.108004
$937$	7.82337	−	18.8873i	0.255578	−	0.617021i	−0.743058	−	0.669227i	$-0.766625\pi$
$937$	7.82337	−	18.8873i	0.255578	−	0.617021i	0.998636	+	0.0522063i	$0.0166253\pi$
$938$	1.16902	−	5.87704i	0.0381697	−	0.191892i
$939$	−15.6434	−	15.6434i	−0.510502	−	0.510502i
$940$	−6.01150	+	8.88169i	−0.196074	+	0.289689i
$941$	−26.9836	−	18.0299i	−0.879641	−	0.587757i	0.0316597	−	0.999499i	$-0.489921\pi$
$941$	−26.9836	−	18.0299i	−0.879641	−	0.587757i	−0.911301	+	0.411741i	$0.864921\pi$
$942$	2.68123	+	1.79154i	0.0873591	+	0.0583715i
$943$	−65.5322	+	27.1443i	−2.13402	+	0.883941i
$944$	12.2007	+	5.05368i	0.397098	+	0.164483i
$945$	8.20437	−	5.41147i	0.266888	−	0.176035i
$946$	8.49617	−	12.7154i	0.276234	−	0.413414i
$947$	−2.15217	+	1.43804i	−0.0699362	+	0.0467299i	−0.590047	−	0.807369i	$-0.700891\pi$
$947$	−2.15217	+	1.43804i	−0.0699362	+	0.0467299i	0.520111	+	0.854099i	$0.325891\pi$
$948$	−12.7268			−0.413347
$949$	16.6491	−	11.1246i	0.540454	−	0.361120i
$950$	3.22667	+	8.06056i	0.104687	+	0.261519i
$951$		−	0.877706i		−	0.0284616i
$952$	−3.84233	+	17.7105i	−0.124531	+	0.574001i
$953$	15.8517	−	15.8517i	0.513487	−	0.513487i	−0.402106	−	0.915593i	$-0.631722\pi$
$953$	15.8517	−	15.8517i	0.513487	−	0.513487i	0.915593	+	0.402106i	$0.131722\pi$
$954$	7.07539	−	2.93072i	0.229074	−	0.0948856i
$955$	7.75028	−	11.4506i	0.250793	−	0.370534i
$956$	−17.2104	+	17.2104i	−0.556623	+	0.556623i
$957$	7.00860	+	10.4891i	0.226556	+	0.339065i
$958$	13.7820	−	2.74141i	0.445276	−	0.0885709i
$959$	15.4514	+	77.6795i	0.498952	+	2.50840i
$960$	−1.57168	−	1.59054i	−0.0507257	−	0.0513346i
$961$	11.7748	−	28.4268i	0.379831	−	0.916992i
$962$	18.9615	−	28.3779i	0.611344	−	0.914941i
$963$	−0.166879	−	0.838956i	−0.00537759	−	0.0270350i
$964$	−6.15009	−	1.22333i	−0.198081	−	0.0394008i
$965$	−31.1591	+	12.6893i	−1.00305	+	0.408482i
$966$	16.2654	+	24.3429i	0.523330	+	0.783218i
$967$	28.8627	+	11.9553i	0.928161	+	0.384457i	0.794981	−	0.606635i	$-0.207481\pi$
$967$	28.8627	+	11.9553i	0.928161	+	0.384457i	0.133181	+	0.991092i	$0.457481\pi$
$968$	6.53442	+	6.53442i	0.210024	+	0.210024i
$969$	−7.04522	+	1.27516i	−0.226325	+	0.0409641i
$970$	4.29542	+	10.5476i	0.137917	+	0.338663i
$971$	12.9067	+	31.1595i	0.414195	+	0.999955i	0.983999	+	0.178174i	$0.0570191\pi$
$971$	12.9067	+	31.1595i	0.414195	+	0.999955i	−0.569804	+	0.821781i	$0.692981\pi$
$972$	−0.980785	−	0.195090i	−0.0314587	−	0.00625752i
$973$			37.9140i			1.21547i
$974$	−4.79796	+	24.1210i	−0.153737	+	0.772886i
$975$	3.02961	+	16.2413i	0.0970251	+	0.520136i
$976$	−4.46036	+	0.887221i	−0.142773	+	0.0283993i
$977$	0.310967	+	0.750742i	0.00994873	+	0.0240184i	0.928776	−	0.370642i	$-0.120862\pi$
$977$	0.310967	+	0.750742i	0.00994873	+	0.0240184i	−0.918827	+	0.394660i	$0.870862\pi$
$978$	3.82213	+	9.22744i	0.122218	+	0.295061i
$979$	5.27081	−	1.04843i	0.168456	−	0.0335080i
$980$	5.53513	−	26.9846i	0.176813	−	0.861992i
$981$	3.20245	−	16.0998i	0.102246	−	0.514027i
$982$		−	0.980500i		−	0.0312890i
$983$	−36.6201	−	7.28419i	−1.16800	−	0.232330i	−0.427264	−	0.904127i	$-0.640523\pi$
$983$	−36.6201	−	7.28419i	−1.16800	−	0.232330i	−0.740735	+	0.671797i	$0.765523\pi$
$984$	−4.07519	−	9.83838i	−0.129912	−	0.313636i
$985$	−2.02178	+	4.79981i	−0.0644192	+	0.152935i
$986$	−32.2275	−	22.3493i	−1.02633	−	0.711746i
$987$	14.9068	+	14.9068i	0.474490	+	0.474490i
$988$	5.30105	+	2.19577i	0.168649	+	0.0698567i
$989$	42.6707	+	63.8612i	1.35685	+	2.03067i
$990$	−1.11851	−	2.74656i	−0.0355487	−	0.0872913i
$991$	21.4646	+	4.26958i	0.681847	+	0.135628i	0.523848	−	0.851812i	$-0.324496\pi$
$991$	21.4646	+	4.26958i	0.681847	+	0.135628i	0.157999	+	0.987439i	$0.449496\pi$
$992$	−0.0937833	−	0.471480i	−0.00297762	−	0.0149695i
$993$	−6.95091	+	10.4028i	−0.220580	+	0.330122i
$994$	−12.4539	+	30.0664i	−0.395014	+	0.953648i
$995$	52.4770	+	0.313063i	1.66363	+	0.00992477i
$996$	0.527912	+	2.65399i	0.0167275	+	0.0840950i
$997$	−1.25601	+	0.249836i	−0.0397782	+	0.00791238i	−0.214939	−	0.976627i	$-0.568955\pi$
$997$	−1.25601	+	0.249836i	−0.0397782	+	0.00791238i	0.175161	+	0.984540i	$0.443955\pi$
$998$	−12.1110	−	18.1254i	−0.383367	−	0.573750i
$999$	−7.30369	+	7.30369i	−0.231079	+	0.231079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.bi.b.97.10	yes	80
5.3	odd	4		510.2.bd.b.403.9	yes	80
17.10	odd	16		510.2.bd.b.367.9	✓	80
85.78	even	16	inner	510.2.bi.b.163.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.b.367.9	✓	80	17.10	odd	16
510.2.bd.b.403.9	yes	80	5.3	odd	4
510.2.bi.b.97.10	yes	80	1.1	even	1	trivial
510.2.bi.b.163.10	yes	80	85.78	even	16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bi (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{2} +(0.195090 - 0.980785i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(2.19567 - 0.423144i) q^{5} +(0.831470 + 0.555570i) q^{6} +(-3.65460 - 2.44193i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-0.449311 + 2.19046i) q^{10} +(0.736823 - 1.10273i) q^{11} +(-0.831470 + 0.555570i) q^{12} -3.30428 q^{13} +(3.65460 - 2.44193i) q^{14} +(0.0133395 - 2.23603i) q^{15} +1.00000i q^{16} +(0.0712911 - 4.12249i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.60430 - 0.664522i) q^{19} +(-1.85178 - 1.25336i) q^{20} +(-3.10799 + 3.10799i) q^{21} +(0.736823 + 1.10273i) q^{22} +(-6.53289 + 1.29947i) q^{23} +(-0.195090 - 0.980785i) q^{24} +(4.64190 - 1.85817i) q^{25} +(1.26449 - 3.05276i) q^{26} +(-0.555570 + 0.831470i) q^{27} +(0.857491 + 4.31090i) q^{28} +(-9.32914 - 1.85568i) q^{29} +(2.06072 + 0.868015i) q^{30} +(0.267072 + 0.399702i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(-0.937798 - 0.937798i) q^{33} +(3.78140 + 1.64347i) q^{34} +(-9.05758 - 3.81523i) q^{35} +(0.382683 + 0.923880i) q^{36} +(10.1305 + 2.01508i) q^{37} +1.73648i q^{38} +(-0.644633 + 3.24079i) q^{39} +(1.86660 - 1.23118i) q^{40} +(10.4444 - 2.07751i) q^{41} +(-1.68203 - 4.06078i) q^{42} +(-4.41265 - 10.6531i) q^{43} +(-1.30076 + 0.258738i) q^{44} +(-2.19046 - 0.449311i) q^{45} +(1.29947 - 6.53289i) q^{46} -4.79630i q^{47} +(0.980785 + 0.195090i) q^{48} +(4.71433 + 11.3814i) q^{49} +(-0.0596551 + 4.99964i) q^{50} +(-4.02937 - 0.874179i) q^{51} +(2.33648 + 2.33648i) q^{52} +(7.07539 + 2.93072i) q^{53} +(-0.555570 - 0.831470i) q^{54} +(1.15120 - 2.73302i) q^{55} +(-4.31090 - 0.857491i) q^{56} +(-0.338770 - 1.70311i) q^{57} +(5.28453 - 7.90886i) q^{58} +(5.05368 - 12.2007i) q^{59} +(-1.59054 + 1.57168i) q^{60} +(0.887221 + 4.46036i) q^{61} +(-0.471480 + 0.0937833i) q^{62} +(2.44193 + 3.65460i) q^{63} +(0.707107 - 0.707107i) q^{64} +(-7.25510 + 1.39819i) q^{65} +(1.22529 - 0.507533i) q^{66} +(0.963997 - 0.963997i) q^{67} +(-2.96545 + 2.86463i) q^{68} +6.66087i q^{69} +(6.99100 - 6.90808i) q^{70} +(-6.15628 + 4.11350i) q^{71} -1.00000 q^{72} +(-5.03866 + 3.36672i) q^{73} +(-5.73847 + 8.58823i) q^{74} +(-0.916873 - 4.91522i) q^{75} +(-1.60430 - 0.664522i) q^{76} +(-5.38559 + 2.23079i) q^{77} +(-2.74741 - 1.83576i) q^{78} +(10.5819 + 7.07062i) q^{79} +(0.423144 + 2.19567i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-2.07751 + 10.4444i) q^{82} +(1.03554 - 2.50001i) q^{83} +4.39536 q^{84} +(-1.58788 - 9.08178i) q^{85} +11.5308 q^{86} +(-3.64005 + 8.78786i) q^{87} +(0.258738 - 1.30076i) q^{88} +(2.86526 + 2.86526i) q^{89} +(1.25336 - 1.85178i) q^{90} +(12.0758 + 8.06882i) q^{91} +(5.53831 + 3.70058i) q^{92} +(0.444125 - 0.183963i) q^{93} +(4.43120 + 1.83546i) q^{94} +(3.24132 - 2.13792i) q^{95} +(-0.555570 + 0.831470i) q^{96} +(4.23482 - 2.82962i) q^{97} -12.3192 q^{98} +(-1.10273 + 0.736823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 48 q^{25} + 16 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} - 16 q^{33} - 32 q^{34} - 32 q^{35} + 48 q^{37} + 32 q^{41} + 32 q^{43} + 16 q^{44} - 64 q^{49} + 48 q^{50} - 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 144 q^{98}+O(q^{100}) \) 80 * q + 48 * q^25 + 16 * q^28 + 32 * q^29 + 16 * q^30 + 16 * q^31 - 16 * q^33 - 32 * q^34 - 32 * q^35 + 48 * q^37 + 32 * q^41 + 32 * q^43 + 16 * q^44 - 64 * q^49 + 48 * q^50 - 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 - 16 * q^56 + 32 * q^57 + 32 * q^58 - 16 * q^60 + 48 * q^61 + 32 * q^62 - 32 * q^65 - 16 * q^67 - 16 * q^70 - 80 * q^72 - 80 * q^73 - 32 * q^74 - 48 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 32 * q^82 - 32 * q^83 - 32 * q^85 - 48 * q^87 - 16 * q^88 - 32 * q^89 - 32 * q^92 - 48 * q^93 - 16 * q^94 - 96 * q^95 + 80 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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