LMFDB - Embedded newform 980.2.x.m.263.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.18
Character	$\chi$	$=$	980.263
Dual form			980.2.x.m.667.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41349 + 0.0450897i) q^{2} +(0.543458 + 2.02821i) q^{3} +(1.99593 + 0.127468i) q^{4} +(1.62425 + 1.53682i) q^{5} +(0.676724 + 2.89137i) q^{6} +(2.81549 + 0.270171i) q^{8} +(-1.22023 + 0.704499i) q^{9} +(2.22657 + 2.24552i) q^{10} +(0.366133 + 0.211387i) q^{11} +(0.826174 + 4.11745i) q^{12} +(1.56422 + 1.56422i) q^{13} +(-2.23429 + 4.12952i) q^{15} +(3.96750 + 0.508836i) q^{16} +(-1.18219 - 4.41198i) q^{17} +(-1.75655 + 0.940785i) q^{18} +(-3.66683 - 6.35114i) q^{19} +(3.04600 + 3.27443i) q^{20} +(0.507996 + 0.315303i) q^{22} +(-6.44210 - 1.72616i) q^{23} +(0.982138 + 5.85725i) q^{24} +(0.276371 + 4.99236i) q^{25} +(2.14049 + 2.28155i) q^{26} +(2.36225 + 2.36225i) q^{27} -4.72835i q^{29} +(-3.34435 + 5.73631i) q^{30} +(-1.70170 - 0.982474i) q^{31} +(5.58510 + 0.898130i) q^{32} +(-0.229760 + 0.857477i) q^{33} +(-1.47208 - 6.28961i) q^{34} +(-2.52529 + 1.25059i) q^{36} +(-7.20177 - 1.92971i) q^{37} +(-4.89667 - 9.14263i) q^{38} +(-2.32248 + 4.02266i) q^{39} +(4.15786 + 4.76573i) q^{40} +4.01882 q^{41} +(1.88664 - 1.88664i) q^{43} +(0.703833 + 0.468585i) q^{44} +(-3.06464 - 0.730988i) q^{45} +(-9.02804 - 2.73038i) q^{46} +(-1.70358 + 6.35786i) q^{47} +(1.12414 + 8.32348i) q^{48} +(0.165546 + 7.06913i) q^{50} +(8.30597 - 4.79545i) q^{51} +(2.92269 + 3.32147i) q^{52} +(0.780053 - 0.209015i) q^{53} +(3.23251 + 3.44554i) q^{54} +(0.269828 + 0.906026i) q^{55} +(10.8887 - 10.8887i) q^{57} +(0.213200 - 6.68350i) q^{58} +(-1.35717 + 2.35069i) q^{59} +(-4.98587 + 7.95745i) q^{60} +(-0.925760 - 1.60346i) q^{61} +(-2.36104 - 1.46545i) q^{62} +(7.85401 + 1.52133i) q^{64} +(0.136759 + 4.94461i) q^{65} +(-0.363428 + 1.20168i) q^{66} +(-8.70137 + 2.33152i) q^{67} +(-1.79718 - 8.95671i) q^{68} -14.0041i q^{69} -3.16317i q^{71} +(-3.62588 + 1.65384i) q^{72} +(-6.67113 + 1.78752i) q^{73} +(-10.0927 - 3.05236i) q^{74} +(-9.97537 + 3.27368i) q^{75} +(-6.50918 - 13.1438i) q^{76} +(-3.46420 + 5.58129i) q^{78} +(1.77995 + 3.08296i) q^{79} +(5.66223 + 6.92381i) q^{80} +(-5.62086 + 9.73561i) q^{81} +(5.68058 + 0.181207i) q^{82} +(-4.71846 + 4.71846i) q^{83} +(4.86025 - 8.98296i) q^{85} +(2.75182 - 2.58169i) q^{86} +(9.59011 - 2.56966i) q^{87} +(0.973735 + 0.694078i) q^{88} +(-10.0333 + 5.79271i) q^{89} +(-4.29889 - 1.17143i) q^{90} +(-12.6380 - 4.26646i) q^{92} +(1.06787 - 3.98534i) q^{93} +(-2.69468 + 8.90999i) q^{94} +(3.80470 - 15.9511i) q^{95} +(1.21367 + 11.8159i) q^{96} +(4.64008 - 4.64008i) q^{97} -0.595688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.41349	+	0.0450897i	0.999492	+	0.0318832i
$2$	1.41349	+	0.0450897i	0.999492	+	0.0318832i
$3$	0.543458	+	2.02821i	0.313766	+	1.17099i	0.925133	+	0.379643i	$0.123953\pi$
$3$	0.543458	+	2.02821i	0.313766	+	1.17099i	−0.611367	+	0.791347i	$0.709380\pi$
$4$	1.99593	+	0.127468i	0.997967	+	0.0637340i
$5$	1.62425	+	1.53682i	0.726386	+	0.687287i
$5$	1.62425	+	1.53682i	0.726386	+	0.687287i
$6$	0.676724	+	2.89137i	0.276271	+	1.18040i
$7$		0			0
$7$		0			0
$8$	2.81549	+	0.270171i	0.995428	+	0.0955200i
$9$	−1.22023	+	0.704499i	−0.406742	+	0.234833i
$10$	2.22657	+	2.24552i	0.704104	+	0.710097i
$11$	0.366133	+	0.211387i	0.110393	+	0.0637356i	0.554180	−	0.832397i	$-0.313032\pi$
$11$	0.366133	+	0.211387i	0.110393	+	0.0637356i	−0.443787	+	0.896132i	$0.646365\pi$
$12$	0.826174	+	4.11745i	0.238496	+	1.18861i
$13$	1.56422	+	1.56422i	0.433837	+	0.433837i	0.889931	−	0.456095i	$-0.150752\pi$
$13$	1.56422	+	1.56422i	0.433837	+	0.433837i	−0.456095	+	0.889931i	$0.650752\pi$
$14$		0			0
$15$	−2.23429	+	4.12952i	−0.576890	+	1.06624i
$16$	3.96750	+	0.508836i	0.991876	+	0.127209i
$17$	−1.18219	−	4.41198i	−0.286722	−	1.07006i	−0.947572	−	0.319544i	$-0.896470\pi$
$17$	−1.18219	−	4.41198i	−0.286722	−	1.07006i	0.660849	−	0.750519i	$-0.270196\pi$
$18$	−1.75655	+	0.940785i	−0.414023	+	0.221745i
$19$	−3.66683	−	6.35114i	−0.841228	−	1.45705i	−0.888857	−	0.458185i	$-0.848500\pi$
$19$	−3.66683	−	6.35114i	−0.841228	−	1.45705i	0.0476283	−	0.998865i	$-0.484834\pi$
$20$	3.04600	+	3.27443i	0.681106	+	0.732185i
$21$		0			0
$22$	0.507996	+	0.315303i	0.108305	+	0.0672229i
$23$	−6.44210	−	1.72616i	−1.34327	−	0.359928i	−0.485624	−	0.874168i	$-0.661408\pi$
$23$	−6.44210	−	1.72616i	−1.34327	−	0.359928i	−0.857647	+	0.514239i	$0.828074\pi$
$24$	0.982138	+	5.85725i	0.200478	+	1.19561i
$25$	0.276371	+	4.99236i	0.0552743	+	0.998471i
$26$	2.14049	+	2.28155i	0.419784	+	0.447448i
$27$	2.36225	+	2.36225i	0.454615	+	0.454615i
$28$		0			0
$29$		−	4.72835i		−	0.878033i	−0.898479	−	0.439016i	$-0.855327\pi$
$29$		−	4.72835i		−	0.878033i	0.898479	−	0.439016i	$-0.144673\pi$
$30$	−3.34435	+	5.73631i	−0.610592	+	1.04730i
$31$	−1.70170	−	0.982474i	−0.305634	−	0.176458i	0.339337	−	0.940665i	$-0.389797\pi$
$31$	−1.70170	−	0.982474i	−0.305634	−	0.176458i	−0.644971	+	0.764207i	$0.723131\pi$
$32$	5.58510	+	0.898130i	0.987316	+	0.158768i
$33$	−0.229760	+	0.857477i	−0.0399961	+	0.149268i
$34$	−1.47208	−	6.28961i	−0.252459	−	1.07866i
$35$		0			0
$36$	−2.52529	+	1.25059i	−0.420882	+	0.208432i
$37$	−7.20177	−	1.92971i	−1.18396	−	0.317242i	−0.387467	−	0.921884i	$-0.626650\pi$
$37$	−7.20177	−	1.92971i	−1.18396	−	0.317242i	−0.796498	+	0.604641i	$0.793316\pi$
$38$	−4.89667	−	9.14263i	−0.794345	−	1.48313i
$39$	−2.32248	+	4.02266i	−0.371895	+	0.644141i
$40$	4.15786	+	4.76573i	0.657415	+	0.753528i
$41$	4.01882			0.627634			0.313817	−	0.949483i	$-0.398392\pi$
$41$	4.01882			0.627634			0.313817	+	0.949483i	$0.398392\pi$
$42$		0			0
$43$	1.88664	−	1.88664i	0.287710	−	0.287710i	−0.548464	−	0.836174i	$-0.684787\pi$
$43$	1.88664	−	1.88664i	0.287710	−	0.287710i	0.836174	+	0.548464i	$0.184787\pi$
$44$	0.703833	+	0.468585i	0.106107	+	0.0706419i
$45$	−3.06464	−	0.730988i	−0.456850	−	0.108969i
$46$	−9.02804	−	2.73038i	−1.33111	−	0.402573i
$47$	−1.70358	+	6.35786i	−0.248493	+	0.927389i	0.723102	+	0.690741i	$0.242716\pi$
$47$	−1.70358	+	6.35786i	−0.248493	+	0.927389i	−0.971595	+	0.236648i	$0.923951\pi$
$48$	1.12414	+	8.32348i	0.162256	+	1.20139i
$49$		0			0
$50$	0.165546	+	7.06913i	0.0234117	+	0.999726i
$51$	8.30597	−	4.79545i	1.16307	−	0.671498i
$52$	2.92269	+	3.32147i	0.405304	+	0.460605i
$53$	0.780053	−	0.209015i	0.107149	−	0.0287104i	−0.204846	−	0.978794i	$-0.565669\pi$
$53$	0.780053	−	0.209015i	0.107149	−	0.0287104i	0.311995	+	0.950084i	$0.399003\pi$
$54$	3.23251	+	3.44554i	0.439889	+	0.468879i
$55$	0.269828	+	0.906026i	0.0363836	+	0.122169i
$56$		0			0
$57$	10.8887	−	10.8887i	1.44224	−	1.44224i
$58$	0.213200	−	6.68350i	0.0279945	−	0.877586i
$59$	−1.35717	+	2.35069i	−0.176689	+	0.306034i	−0.940744	−	0.339116i	$-0.889872\pi$
$59$	−1.35717	+	2.35069i	−0.176689	+	0.306034i	0.764056	+	0.645151i	$0.223205\pi$
$60$	−4.98587	+	7.95745i	−0.643673	+	1.02730i
$61$	−0.925760	−	1.60346i	−0.118531	−	0.205302i	0.800654	−	0.599126i	$-0.204485\pi$
$61$	−0.925760	−	1.60346i	−0.118531	−	0.205302i	−0.919186	+	0.393824i	$0.871152\pi$
$62$	−2.36104	−	1.46545i	−0.299852	−	0.186112i
$63$		0			0
$64$	7.85401	+	1.52133i	0.981752	+	0.190167i
$65$	0.136759	+	4.94461i	0.0169629	+	0.613303i
$66$	−0.363428	+	1.20168i	−0.0447349	+	0.147916i
$67$	−8.70137	+	2.33152i	−1.06304	+	0.284841i	−0.747631	−	0.664114i	$-0.768809\pi$
$67$	−8.70137	+	2.33152i	−1.06304	+	0.284841i	−0.315410	+	0.948955i	$0.602142\pi$
$68$	−1.79718	−	8.95671i	−0.217940	−	1.08616i
$69$		−	14.0041i		−	1.68589i
$70$		0			0
$71$		−	3.16317i		−	0.375400i	−0.982226	−	0.187700i	$-0.939897\pi$
$71$		−	3.16317i		−	0.375400i	0.982226	−	0.187700i	$-0.0601032\pi$
$72$	−3.62588	+	1.65384i	−0.427314	+	0.194907i
$73$	−6.67113	+	1.78752i	−0.780797	+	0.209214i	−0.627136	−	0.778910i	$-0.715773\pi$
$73$	−6.67113	+	1.78752i	−0.780797	+	0.209214i	−0.153661	+	0.988124i	$0.549106\pi$
$74$	−10.0927	−	3.05236i	−1.17325	−	0.354830i
$75$	−9.97537	+	3.27368i	−1.15186	+	0.378012i
$76$	−6.50918	−	13.1438i	−0.746654	−	1.50770i
$77$		0			0
$78$	−3.46420	+	5.58129i	−0.392243	+	0.631957i
$79$	1.77995	+	3.08296i	0.200260	+	0.346860i	0.948612	−	0.316441i	$-0.102488\pi$
$79$	1.77995	+	3.08296i	0.200260	+	0.346860i	−0.748352	+	0.663301i	$0.769155\pi$
$80$	5.66223	+	6.92381i	0.633056	+	0.774106i
$81$	−5.62086	+	9.73561i	−0.624540	+	1.08173i
$82$	5.68058	+	0.181207i	0.627315	+	0.0200110i
$83$	−4.71846	+	4.71846i	−0.517919	+	0.517919i	−0.916941	−	0.399022i	$-0.869350\pi$
$83$	−4.71846	+	4.71846i	−0.517919	+	0.517919i	0.399022	+	0.916941i	$0.369350\pi$
$84$		0			0
$85$	4.86025	−	8.98296i	0.527168	−	0.974339i
$86$	2.75182	−	2.58169i	0.296737	−	0.278391i
$87$	9.59011	−	2.56966i	1.02817	−	0.275497i
$88$	0.973735	+	0.694078i	0.103801	+	0.0739890i
$89$	−10.0333	+	5.79271i	−1.06352	+	0.614026i	−0.926405	−	0.376529i	$-0.877118\pi$
$89$	−10.0333	+	5.79271i	−1.06352	+	0.614026i	−0.137119	+	0.990555i	$0.543784\pi$
$90$	−4.29889	−	1.17143i	−0.453143	−	0.123480i
$91$		0			0
$92$	−12.6380	−	4.26646i	−1.31760	−	0.444809i
$93$	1.06787	−	3.98534i	0.110733	−	0.413260i
$94$	−2.69468	+	8.90999i	−0.277935	+	0.918995i
$95$	3.80470	−	15.9511i	0.390354	−	1.63655i
$96$	1.21367	+	11.8159i	0.123870	+	1.20595i
$97$	4.64008	−	4.64008i	0.471128	−	0.471128i	−0.431151	−	0.902280i	$-0.641892\pi$
$97$	4.64008	−	4.64008i	0.471128	−	0.471128i	0.902280	+	0.431151i	$0.141892\pi$
$98$		0			0
$99$	−0.595688			−0.0598689
$100$	−0.0847470	+	9.99964i	−0.00847470	+	0.999964i
$101$	2.12019	−	3.67228i	0.210967	−	0.365406i	−0.741050	−	0.671449i	$-0.765672\pi$
$101$	2.12019	−	3.67228i	0.210967	−	0.365406i	0.952017	+	0.306044i	$0.0990054\pi$
$102$	11.9567	−	6.40383i	1.18389	−	0.634074i
$103$	15.1879	+	4.06958i	1.49651	+	0.400987i	0.911928	−	0.410351i	$-0.134594\pi$
$103$	15.1879	+	4.06958i	1.49651	+	0.400987i	0.584577	+	0.811338i	$0.301260\pi$
$104$	3.98145	+	4.82666i	0.390413	+	0.473293i
$105$		0			0
$106$	1.11203	−	0.260269i	0.108009	−	0.0252795i
$107$	0.145422	−	0.542724i	0.0140585	−	0.0524671i	−0.958540	−	0.284957i	$-0.908021\pi$
$107$	0.145422	−	0.542724i	0.0140585	−	0.0524671i	0.972599	+	0.232490i	$0.0746873\pi$
$108$	4.41378	+	5.01601i	0.424716	+	0.482665i
$109$	4.52802	+	2.61425i	0.433706	+	0.250400i	0.700924	−	0.713236i	$-0.252771\pi$
$109$	4.52802	+	2.61425i	0.433706	+	0.250400i	−0.267218	+	0.963636i	$0.586105\pi$
$110$	0.340548	+	1.29283i	0.0324700	+	0.123266i
$111$		−	15.6555i		−	1.48595i
$112$		0			0
$113$	9.46096	+	9.46096i	0.890012	+	0.890012i	0.994524	−	0.104511i	$-0.0333278\pi$
$113$	9.46096	+	9.46096i	0.890012	+	0.890012i	−0.104511	+	0.994524i	$0.533328\pi$
$114$	15.8821	−	14.9001i	1.48749	−	1.39553i
$115$	−7.81079	−	12.7041i	−0.728360	−	1.18466i
$116$	0.602714	−	9.43748i	0.0559606	−	0.876248i
$117$	−3.01070	−	0.806713i	−0.278339	−	0.0745807i
$118$	−2.02435	+	3.26150i	−0.186357	+	0.300245i
$119$		0			0
$120$	−7.40630	+	11.0230i	−0.676100	+	1.00626i
$121$	−5.41063	−	9.37149i	−0.491876	−	0.851953i
$122$	−1.23626	−	2.30823i	−0.111925	−	0.208977i
$123$	2.18406	+	8.15103i	0.196930	+	0.734953i
$124$	−3.27124	−	2.17787i	−0.293766	−	0.195578i
$125$	−7.22345	+	8.53356i	−0.646085	+	0.763265i
$126$		0			0
$127$	15.7173	+	15.7173i	1.39469	+	1.39469i	0.814439	+	0.580249i	$0.197045\pi$
$127$	15.7173	+	15.7173i	1.39469	+	1.39469i	0.580249	+	0.814439i	$0.302955\pi$
$128$	11.0330	+	2.50453i	0.975190	+	0.221371i
$129$	4.85182	+	2.80120i	0.427179	+	0.246632i
$130$	−0.0296422	+	6.99534i	−0.00259980	+	0.613532i
$131$	15.5632	−	8.98542i	1.35976	−	0.785060i	0.370171	−	0.928963i	$-0.379299\pi$
$131$	15.5632	−	8.98542i	1.35976	−	0.785060i	0.989592	+	0.143904i	$0.0459656\pi$
$132$	−0.567887	+	1.68218i	−0.0494282	+	0.146415i
$133$		0			0
$134$	−12.4045	+	2.90326i	−1.07158	+	0.250803i
$135$	0.206531	+	7.46723i	0.0177753	+	0.642677i
$136$	−2.13645	−	12.7413i	−0.183199	−	1.09256i
$137$	−3.47858	−	12.9822i	−0.297195	−	1.10915i	−0.939458	−	0.342664i	$-0.888671\pi$
$137$	−3.47858	−	12.9822i	−0.297195	−	1.10915i	0.642263	−	0.766485i	$-0.277996\pi$
$138$	0.631438	−	19.7947i	0.0537516	−	1.68503i
$139$	6.16658			0.523043			0.261521	−	0.965198i	$-0.415776\pi$
$139$	6.16658			0.523043			0.261521	+	0.965198i	$0.415776\pi$
$140$		0			0
$141$	−13.8209			−1.16393
$142$	0.142627	−	4.47113i	0.0119690	−	0.375209i
$143$	0.242057	+	0.903369i	0.0202418	+	0.0755435i
$144$	−5.19973	+	2.17421i	−0.433311	+	0.181184i
$145$	7.26662	−	7.68002i	0.603460	−	0.637791i
$146$	−9.51021	+	2.22586i	−0.787070	+	0.184213i
$147$		0			0
$148$	−14.1283	−	4.76957i	−1.16134	−	0.392056i
$149$	−4.22837	+	2.44125i	−0.346401	+	0.199995i	−0.663099	−	0.748532i	$-0.730759\pi$
$149$	−4.22837	+	2.44125i	−0.346401	+	0.199995i	0.316698	+	0.948526i	$0.397426\pi$
$150$	−14.2477	+	4.17754i	−1.16332	+	0.341095i
$151$	3.04218	+	1.75640i	0.247569	+	0.142934i	0.618651	−	0.785666i	$-0.287680\pi$
$151$	3.04218	+	1.75640i	0.247569	+	0.142934i	−0.371082	+	0.928600i	$0.621013\pi$
$152$	−8.60804	−	18.8723i	−0.698204	−	1.53074i
$153$	4.55077	+	4.55077i	0.367908	+	0.367908i
$154$		0			0
$155$	−1.25409	−	4.21098i	−0.100731	−	0.338234i
$156$	−5.14829	+	7.73292i	−0.412193	+	0.619129i
$157$	−3.49270	−	13.0349i	−0.278748	−	1.04030i	−0.953288	−	0.302062i	$-0.902325\pi$
$157$	−3.49270	−	13.0349i	−0.278748	−	1.04030i	0.674541	−	0.738238i	$-0.264342\pi$
$158$	2.37694	+	4.43801i	0.189099	+	0.353069i
$159$	0.847853	+	1.46852i	0.0672391	+	0.116462i
$160$	7.69133	+	10.0421i	0.608053	+	0.793896i
$161$		0			0
$162$	−8.38403	+	13.5078i	−0.658712	+	1.06127i
$163$	5.57237	+	1.49311i	0.436462	+	0.116950i	0.470358	−	0.882476i	$-0.344125\pi$
$163$	5.57237	+	1.49311i	0.436462	+	0.116950i	−0.0338961	+	0.999425i	$0.510792\pi$
$164$	8.02130	+	0.512271i	0.626358	+	0.0400017i
$165$	−1.69097	+	1.03966i	−0.131642	+	0.0809371i
$166$	−6.88228	+	6.45677i	−0.534168	+	0.501143i
$167$	6.11518	+	6.11518i	0.473207	+	0.473207i	0.902951	−	0.429744i	$-0.141396\pi$
$167$	6.11518	+	6.11518i	0.473207	+	0.473207i	−0.429744	+	0.902951i	$0.641396\pi$
$168$		0			0
$169$		−	8.10643i		−	0.623572i
$170$	7.27498	−	12.4782i	0.557965	−	0.957036i
$171$	8.94873	+	5.16655i	0.684327	+	0.395096i
$172$	4.00610	−	3.52512i	0.305462	−	0.268788i
$173$	−1.13155	+	4.22300i	−0.0860302	+	0.321069i	−0.995507	−	0.0946850i	$-0.969816\pi$
$173$	−1.13155	+	4.22300i	−0.0860302	+	0.321069i	0.909477	+	0.415754i	$0.136482\pi$
$174$	13.6714	−	3.19979i	1.03643	−	0.242575i
$175$		0			0
$176$	1.34507	+	1.02498i	0.101389	+	0.0772609i
$177$	−5.50528	−	1.47513i	−0.413802	−	0.110878i
$178$	−14.4432	+	7.73556i	−1.08256	+	0.579805i
$179$	9.00305	−	15.5937i	0.672920	−	1.16553i	−0.304152	−	0.952623i	$-0.598373\pi$
$179$	9.00305	−	15.5937i	0.672920	−	1.16553i	0.977072	−	0.212908i	$-0.0682934\pi$
$180$	−6.02364	−	1.84965i	−0.448976	−	0.137865i
$181$	−14.5671			−1.08276			−0.541382	−	0.840777i	$-0.682099\pi$
$181$	−14.5671			−1.08276			−0.541382	+	0.840777i	$0.682099\pi$
$182$		0			0
$183$	2.74905	−	2.74905i	0.203216	−	0.203216i
$184$	−17.6713	−	6.60045i	−1.30275	−	0.486592i
$185$	−8.73186	−	14.2022i	−0.641979	−	1.04416i
$186$	1.68912	−	5.58510i	0.123852	−	0.409519i
$187$	0.499798	−	1.86527i	0.0365489	−	0.136402i
$188$	−4.21066	+	12.4727i	−0.307094	+	0.909666i
$189$		0			0
$190$	6.09716	−	22.3752i	0.442334	−	1.62327i
$191$	−8.77337	+	5.06530i	−0.634818	+	0.366513i	−0.782616	−	0.622505i	$-0.786115\pi$
$191$	−8.77337	+	5.06530i	−0.634818	+	0.366513i	0.147797	+	0.989018i	$0.452782\pi$
$192$	1.18274	+	16.7564i	0.0853570	+	1.20929i
$193$	20.5062	−	5.49463i	1.47607	−	0.395512i	0.571063	−	0.820907i	$-0.306531\pi$
$193$	20.5062	−	5.49463i	1.47607	−	0.395512i	0.905008	+	0.425395i	$0.139865\pi$
$194$	6.76794	−	6.34950i	0.485910	−	0.455868i
$195$	−9.95440	+	2.96456i	−0.712849	+	0.212297i
$196$		0			0
$197$	−14.1612	+	14.1612i	−1.00895	+	1.00895i	−0.00898613	+	0.999960i	$0.502860\pi$
$197$	−14.1612	+	14.1612i	−1.00895	+	1.00895i	−0.999960	+	0.00898613i	$0.997140\pi$
$198$	−0.842002	−	0.0268594i	−0.0598385	−	0.00190881i
$199$	3.64221	−	6.30849i	0.258189	−	0.447197i	−0.707568	−	0.706646i	$-0.750207\pi$
$199$	3.64221	−	6.30849i	0.258189	−	0.447197i	0.965757	+	0.259449i	$0.0835408\pi$
$200$	−0.570670	+	14.1306i	−0.0403525	+	0.999186i
$201$	−9.45766	−	16.3811i	−0.667092	−	1.15544i
$202$	3.16246	−	5.09515i	0.222510	−	0.358494i
$203$		0			0
$204$	17.1894	−	8.51266i	1.20350	−	0.596005i
$205$	6.52757	+	6.17620i	0.455905	+	0.431365i
$206$	21.2845	+	6.43714i	1.48296	+	0.448497i
$207$	9.07690	−	2.43215i	0.630888	−	0.169046i
$208$	5.41012	+	7.00198i	0.375124	+	0.485500i
$209$		−	3.10048i		−	0.214465i
$210$		0			0
$211$		−	17.4066i		−	1.19832i	−0.800630	−	0.599159i	$-0.795502\pi$
$211$		−	17.4066i		−	1.19832i	0.800630	−	0.599159i	$-0.204498\pi$
$212$	1.58358	−	0.317747i	0.108761	−	0.0218230i
$213$	6.41559	−	1.71905i	0.439589	−	0.117788i
$214$	0.230025	−	0.760580i	0.0157242	−	0.0519922i
$215$	5.96380	−	0.164948i	0.406728	−	0.0112494i
$216$	6.01269	+	7.28911i	0.409112	+	0.495961i
$217$		0			0
$218$	6.28245	+	3.89940i	0.425502	+	0.264101i
$219$	−7.25096	−	12.5590i	−0.489975	−	0.848661i
$220$	0.423069	+	1.84276i	0.0285233	+	0.124239i
$221$	5.05211	−	8.75051i	0.339842	−	0.588623i
$222$	0.705900	−	22.1289i	0.0473769	−	1.48519i
$223$	−1.68218	+	1.68218i	−0.112647	+	0.112647i	−0.761183	−	0.648537i	$-0.775381\pi$
$223$	−1.68218	+	1.68218i	−0.112647	+	0.112647i	0.648537	+	0.761183i	$0.275381\pi$
$224$		0			0
$225$	−3.85434	−	5.89711i	−0.256956	−	0.393140i
$226$	12.9464	+	13.7996i	0.861183	+	0.917936i
$227$	−15.1208	+	4.05161i	−1.00360	+	0.268915i	−0.722955	−	0.690895i	$-0.757217\pi$
$227$	−15.1208	+	4.05161i	−1.00360	+	0.268915i	−0.280650	+	0.959810i	$0.590550\pi$
$228$	23.1211	−	20.3451i	1.53123	−	1.34739i
$229$	−14.7843	+	8.53574i	−0.976976	+	0.564057i	−0.901356	−	0.433079i	$-0.857427\pi$
$229$	−14.7843	+	8.53574i	−0.976976	+	0.564057i	−0.0756201	+	0.997137i	$0.524094\pi$
$230$	−10.4677	−	18.3093i	−0.690219	−	1.20728i
$231$		0			0
$232$	1.27747	−	13.3126i	0.0838697	−	0.874018i
$233$	−3.60234	+	13.4441i	−0.235997	+	0.880753i	0.741700	+	0.670732i	$0.234020\pi$
$233$	−3.60234	+	13.4441i	−0.235997	+	0.880753i	−0.977697	+	0.210021i	$0.932647\pi$
$234$	−4.21923	−	1.27604i	−0.275820	−	0.0834171i
$235$	−12.5379	+	7.70865i	−0.817884	+	0.502857i
$236$	−3.00847	+	4.51883i	−0.195835	+	0.294151i
$237$	−5.28558	+	5.28558i	−0.343335	+	0.343335i
$238$		0			0
$239$	7.51141			0.485873			0.242936	−	0.970042i	$-0.421889\pi$
$239$	7.51141			0.485873			0.242936	+	0.970042i	$0.421889\pi$
$240$	−10.9658	+	15.2470i	−0.707839	+	0.984190i
$241$	−3.62580	+	6.28008i	−0.233559	+	0.404535i	−0.958853	−	0.283904i	$-0.908370\pi$
$241$	−3.62580	+	6.28008i	−0.233559	+	0.404535i	0.725294	+	0.688439i	$0.241704\pi$
$242$	−7.22534	−	13.4905i	−0.464462	−	0.867203i
$243$	−13.1199	−	3.51547i	−0.841644	−	0.225518i
$244$	−1.64336	−	3.31841i	−0.105206	−	0.212439i
$245$		0			0
$246$	2.71963	+	11.6199i	0.173397	+	0.740858i
$247$	4.19885	−	15.6703i	0.267166	−	0.997078i
$248$	−4.52568	−	3.22590i	−0.287381	−	0.204845i
$249$	−12.1343	−	7.00577i	−0.768983	−	0.443972i
$250$	−10.5951	+	11.7364i	−0.670092	+	0.742278i
$251$			3.63825i			0.229644i	0.993386	+	0.114822i	$0.0366298\pi$
$251$			3.63825i			0.229644i	−0.993386	+	0.114822i	$0.963370\pi$
$252$		0			0
$253$	−1.99378	−	1.99378i	−0.125348	−	0.125348i
$254$	21.5077	+	22.9251i	1.34951	+	1.43845i
$255$	20.8607	+	4.97576i	1.30635	+	0.311594i
$256$	15.4822	+	4.03762i	0.967636	+	0.252351i
$257$	−6.73562	−	1.80480i	−0.420156	−	0.112581i	0.0425454	−	0.999095i	$-0.486453\pi$
$257$	−6.73562	−	1.80480i	−0.420156	−	0.112581i	−0.462702	+	0.886514i	$0.653120\pi$
$258$	6.73171	+	4.17825i	0.419098	+	0.260126i
$259$		0			0
$260$	−0.357317	+	9.88654i	−0.0221599	+	0.613137i
$261$	3.33112	+	5.76966i	0.206191	+	0.357133i
$262$	22.4036	−	11.9991i	1.38410	−	0.741307i
$263$	6.56533	+	24.5021i	0.404836	+	1.51087i	0.804359	+	0.594144i	$0.202509\pi$
$263$	6.56533	+	24.5021i	0.404836	+	1.51087i	−0.399523	+	0.916723i	$0.630824\pi$
$264$	−0.878554	+	2.35215i	−0.0540713	+	0.144765i
$265$	1.58822	+	0.859309i	0.0975635	+	0.0527869i
$266$		0			0
$267$	−17.2015	−	17.2015i	−1.05271	−	1.05271i
$268$	−17.6646	+	3.54442i	−1.07903	+	0.216510i
$269$	16.4868	+	9.51864i	1.00522	+	0.580361i	0.909787	−	0.415075i	$-0.136245\pi$
$269$	16.4868	+	9.51864i	1.00522	+	0.580361i	0.0954283	+	0.995436i	$0.469578\pi$
$270$	−0.0447651	+	10.5642i	−0.00272431	+	0.642917i
$271$	−18.2717	+	10.5492i	−1.10993	+	0.640817i	−0.938811	−	0.344434i	$-0.888071\pi$
$271$	−18.2717	+	10.5492i	−1.10993	+	0.640817i	−0.171117	+	0.985251i	$0.554738\pi$
$272$	−2.44536	−	18.1061i	−0.148271	−	1.09784i
$273$		0			0
$274$	−4.33159	−	18.5072i	−0.261681	−	1.11806i
$275$	−0.954131	+	1.88629i	−0.0575363	+	0.113748i
$276$	1.78507	−	27.9512i	0.107449	−	1.68246i
$277$	−4.17199	−	15.5701i	−0.250670	−	0.935515i	−0.970448	−	0.241310i	$-0.922423\pi$
$277$	−4.17199	−	15.5701i	−0.250670	−	0.935515i	0.719778	−	0.694205i	$-0.244244\pi$
$278$	8.71643	+	0.278049i	0.522777	+	0.0166763i
$279$	2.76861			0.165752
$280$		0			0
$281$	−6.00749			−0.358377			−0.179189	−	0.983815i	$-0.557347\pi$
$281$	−6.00749			−0.358377			−0.179189	+	0.983815i	$0.557347\pi$
$282$	−19.5358	−	0.623181i	−1.16334	−	0.0371099i
$283$	−0.430842	−	1.60792i	−0.0256109	−	0.0955812i	0.951937	−	0.306293i	$-0.0990886\pi$
$283$	−0.430842	−	1.60792i	−0.0256109	−	0.0955812i	−0.977548	+	0.210711i	$0.932422\pi$
$284$	0.403204	−	6.31349i	0.0239257	−	0.374636i
$285$	34.4199	−	0.951995i	2.03886	−	0.0563913i
$286$	0.301414	+	1.28782i	0.0178230	+	0.0761505i
$287$		0			0
$288$	−7.44783	+	2.83877i	−0.438867	+	0.167276i
$289$	−3.34556	+	1.93156i	−0.196798	+	0.113621i
$290$	10.6176	−	10.5280i	0.623488	−	0.618226i
$291$	11.9328	+	6.88938i	0.699510	+	0.403863i
$292$	−13.5430	+	2.71742i	−0.792543	+	0.159025i
$293$	14.2453	+	14.2453i	0.832220	+	0.832220i	0.987820	−	0.155600i	$-0.0497311\pi$
$293$	14.2453	+	14.2453i	0.832220	+	0.832220i	−0.155600	+	0.987820i	$0.549731\pi$
$294$		0			0
$295$	−5.81698	+	1.73238i	−0.338678	+	0.100863i
$296$	−19.7552	−	7.37880i	−1.14825	−	0.428884i
$297$	0.365549	+	1.36425i	0.0212113	+	0.0791617i
$298$	−6.08685	+	3.26004i	−0.352602	+	0.188849i
$299$	−7.37678	−	12.7770i	−0.426610	−	0.738910i
$300$	−20.3275	+	5.26250i	−1.17361	+	0.303831i
$301$		0			0
$302$	4.22091	+	2.61984i	0.242886	+	0.150755i
$303$	8.60041	+	2.30447i	0.494081	+	0.132388i
$304$	−11.3165	−	27.0640i	−0.649044	−	1.55222i
$305$	0.960569	−	4.02715i	0.0550020	−	0.230594i
$306$	6.22730	+	6.63768i	0.355991	+	0.379451i
$307$	−3.60252	−	3.60252i	−0.205607	−	0.205607i	0.596790	−	0.802397i	$-0.296442\pi$
$307$	−3.60252	−	3.60252i	−0.205607	−	0.205607i	−0.802397	+	0.596790i	$0.796442\pi$
$308$		0			0
$309$			33.0159i			1.87821i
$310$	−1.58278	−	6.00875i	−0.0898959	−	0.341274i
$311$	−0.374701	−	0.216334i	−0.0212473	−	0.0122672i	0.489339	−	0.872094i	$-0.337238\pi$
$311$	−0.374701	−	0.216334i	−0.0212473	−	0.0122672i	−0.510586	+	0.859827i	$0.670572\pi$
$312$	−7.62575	+	10.6983i	−0.431723	+	0.605673i
$313$	−0.266609	+	0.994998i	−0.0150696	+	0.0562406i	−0.973051	−	0.230589i	$-0.925935\pi$
$313$	−0.266609	+	0.994998i	−0.0150696	+	0.0562406i	0.957982	+	0.286830i	$0.0926014\pi$
$314$	−4.34917	−	18.5823i	−0.245438	−	1.04866i
$315$		0			0
$316$	3.15968	+	6.38027i	0.177746	+	0.358918i
$317$	27.2346	+	7.29750i	1.52965	+	0.409868i	0.922905	−	0.385029i	$-0.125808\pi$
$317$	27.2346	+	7.29750i	1.52965	+	0.409868i	0.606744	+	0.794897i	$0.292475\pi$
$318$	1.13222	+	2.11398i	0.0634917	+	0.118546i
$319$	0.999513	−	1.73121i	0.0559620	−	0.0969290i
$320$	10.4189	+	14.5412i	0.582432	+	0.812879i
$321$	1.17979			0.0658495
$322$		0			0
$323$	−23.6862	+	23.6862i	−1.31794	+	1.31794i
$324$	−12.4598	+	18.7152i	−0.692214	+	1.03973i
$325$	−7.37684	+	8.24145i	−0.409193	+	0.457153i
$326$	7.80919	+	2.36176i	0.432511	+	0.130806i
$327$	−2.84147	+	10.6045i	−0.157134	+	0.586432i
$328$	11.3150	+	1.08577i	0.624765	+	0.0599517i
$329$		0			0
$330$	−2.43706	+	1.39330i	−0.134156	+	0.0766988i
$331$	−22.3187	+	12.8857i	−1.22675	+	0.708262i	−0.966348	−	0.257239i	$-0.917187\pi$
$331$	−22.3187	+	12.8857i	−1.22675	+	0.708262i	−0.260398	+	0.965501i	$0.583854\pi$
$332$	−10.0192	+	8.81629i	−0.549875	+	0.483857i
$333$	10.1473	−	2.71896i	0.556068	−	0.148998i
$334$	8.36805	+	8.91951i	0.457879	+	0.488054i
$335$	−17.7163	−	9.58546i	−0.967946	−	0.523709i
$336$		0			0
$337$	10.4788	−	10.4788i	0.570816	−	0.570816i	−0.361540	−	0.932356i	$-0.617749\pi$
$337$	10.4788	−	10.4788i	0.570816	−	0.570816i	0.932356	+	0.361540i	$0.117749\pi$
$338$	0.365516	−	11.4584i	0.0198815	−	0.623255i
$339$	−14.0472	+	24.3305i	−0.762940	+	1.32145i
$340$	10.8458	−	17.3099i	0.588195	−	0.938759i
$341$	−0.415365	−	0.719433i	−0.0224933	−	0.0389595i
$342$	12.4160	+	7.70639i	0.671382	+	0.416714i
$343$		0			0
$344$	5.82154	−	4.80211i	0.313876	−	0.258912i
$345$	21.5217	−	22.7461i	1.15869	−	1.22461i
$346$	−1.78985	+	5.91817i	−0.0962231	+	0.318163i
$347$	−18.1389	+	4.86030i	−0.973746	+	0.260914i	−0.710409	−	0.703789i	$-0.751490\pi$
$347$	−18.1389	+	4.86030i	−0.973746	+	0.260914i	−0.263337	+	0.964704i	$0.584823\pi$
$348$	19.4688	−	3.90644i	1.04364	−	0.209407i
$349$		−	7.53504i		−	0.403341i	−0.979453	−	0.201671i	$-0.935363\pi$
$349$		−	7.53504i		−	0.403341i	0.979453	−	0.201671i	$-0.0646371\pi$
$350$		0			0
$351$			7.39016i			0.394457i
$352$	1.85504	+	1.50945i	0.0988739	+	0.0804542i
$353$	35.6061	−	9.54063i	1.89512	−	0.507796i	0.897331	−	0.441358i	$-0.145503\pi$
$353$	35.6061	−	9.54063i	1.89512	−	0.507796i	0.997791	−	0.0664384i	$-0.0211636\pi$
$354$	−7.71517	−	2.33333i	−0.410056	−	0.124015i
$355$	4.86123	−	5.13778i	0.258007	−	0.272685i
$356$	−20.7641	+	10.2829i	−1.10050	+	0.544995i
$357$		0			0
$358$	13.4289	−	21.6357i	0.709739	−	1.14348i
$359$	9.04771	+	15.6711i	0.477520	+	0.827089i	0.999668	−	0.0257661i	$-0.00820252\pi$
$359$	9.04771	+	15.6711i	0.477520	+	0.827089i	−0.522148	+	0.852855i	$0.674869\pi$
$360$	−8.43099	−	2.88607i	−0.444352	−	0.152109i
$361$	−17.3913	+	30.1226i	−0.915331	+	1.58540i
$362$	−20.5905	−	0.656826i	−1.08221	−	0.0345220i
$363$	16.0669	−	16.0669i	0.843295	−	0.843295i
$364$		0			0
$365$	−13.5827	−	7.34894i	−0.710950	−	0.384661i
$366$	4.00973	−	3.76182i	0.209592	−	0.196633i
$367$	−22.6225	+	6.06169i	−1.18089	+	0.316417i	−0.795278	−	0.606245i	$-0.792675\pi$
$367$	−22.6225	+	6.06169i	−1.18089	+	0.316417i	−0.385608	+	0.922663i	$0.626008\pi$
$368$	−24.6807	−	10.1265i	−1.28657	−	0.527880i
$369$	−4.90388	+	2.83125i	−0.255286	+	0.147389i
$370$	−11.7021	−	20.4684i	−0.608362	−	1.06410i
$371$		0			0
$372$	2.63940	−	7.81835i	0.136846	−	0.405362i
$373$	1.50150	−	5.60369i	0.0777450	−	0.290148i	−0.916097	−	0.400957i	$-0.868678\pi$
$373$	1.50150	−	5.60369i	0.0777450	−	0.290148i	0.993842	+	0.110809i	$0.0353442\pi$
$374$	0.790566	−	2.61402i	0.0408792	−	0.135168i
$375$	−21.2335	−	10.0131i	−1.09650	−	0.517073i
$376$	−6.51414	+	17.4403i	−0.335941	+	0.899412i
$377$	7.39618	−	7.39618i	0.380923	−	0.380923i
$378$		0			0
$379$	−20.3909			−1.04741			−0.523706	−	0.851899i	$-0.675451\pi$
$379$	−20.3909			−1.04741			−0.523706	+	0.851899i	$0.675451\pi$
$380$	9.62719	−	31.3523i	0.493864	−	1.60834i
$381$	−23.3364	+	40.4198i	−1.19556	+	2.07077i
$382$	−12.6295	+	6.76419i	−0.646181	+	0.346086i
$383$	−10.1934	−	2.73132i	−0.520860	−	0.139564i	−0.0111957	−	0.999937i	$-0.503564\pi$
$383$	−10.1934	−	2.73132i	−0.520860	−	0.139564i	−0.509664	+	0.860373i	$0.670230\pi$
$384$	0.916257	+	23.7384i	0.0467576	+	1.21140i
$385$		0			0
$386$	29.2332	−	6.84201i	1.48793	−	0.348249i
$387$	−0.972995	+	3.63127i	−0.0494601	+	0.184588i
$388$	9.85275	−	8.66982i	0.500197	−	0.440144i
$389$	1.96021	+	1.13173i	0.0993866	+	0.0573809i	0.548869	−	0.835908i	$-0.315058\pi$
$389$	1.96021	+	1.13173i	0.0993866	+	0.0573809i	−0.449483	+	0.893289i	$0.648392\pi$
$390$	−14.2042	+	3.74156i	−0.719256	+	0.189461i
$391$			30.4631i			1.54058i
$392$		0			0
$393$	26.6823	+	26.6823i	1.34594	+	1.34594i
$394$	−20.6553	+	19.3783i	−1.04060	+	0.976264i
$395$	−1.84687	+	7.74296i	−0.0929263	+	0.389590i
$396$	−1.18895	−	0.0759312i	−0.0597472	−	0.00381569i
$397$	16.6975	+	4.47408i	0.838024	+	0.224548i	0.652211	−	0.758037i	$-0.273842\pi$
$397$	16.6975	+	4.47408i	0.838024	+	0.224548i	0.185813	+	0.982585i	$0.440508\pi$
$398$	5.43269	−	8.75279i	0.272316	−	0.438738i
$399$		0			0
$400$	−1.44378	+	19.9478i	−0.0721892	+	0.997391i
$401$	−2.49166	−	4.31568i	−0.124428	−	0.215515i	0.797081	−	0.603872i	$-0.206376\pi$
$401$	−2.49166	−	4.31568i	−0.124428	−	0.215515i	−0.921509	+	0.388357i	$0.873043\pi$
$402$	−12.6297	−	23.5811i	−0.629914	−	1.17612i
$403$	−1.12502	−	4.19863i	−0.0560413	−	0.209149i
$404$	4.69986	−	7.05937i	0.233827	−	0.351217i
$405$	−24.0916	+	7.17482i	−1.19712	+	0.356520i
$406$		0			0
$407$	−2.22889	−	2.22889i	−0.110482	−	0.110482i
$408$	24.6810	−	11.2575i	1.22189	−	0.557331i
$409$	−1.80679	−	1.04315i	−0.0893400	−	0.0515805i	0.454664	−	0.890663i	$-0.349759\pi$
$409$	−1.80679	−	1.04315i	−0.0893400	−	0.0515805i	−0.544004	+	0.839082i	$0.683093\pi$
$410$	8.94820	+	9.02435i	0.441920	+	0.445681i
$411$	24.4403	−	14.1106i	1.20555	−	0.696025i
$412$	29.7952	+	10.0586i	1.46791	+	0.495550i
$413$		0			0
$414$	12.9398	−	3.02855i	0.635957	−	0.148845i
$415$	−14.9154	+	0.412534i	−0.732168	+	0.0202505i
$416$	7.33146	+	10.1412i	0.359454	+	0.497213i
$417$	3.35128	+	12.5071i	0.164113	+	0.612477i
$418$	0.139800	−	4.38252i	0.00683783	−	0.214356i
$419$	−3.19769			−0.156217			−0.0781086	−	0.996945i	$-0.524888\pi$
$419$	−3.19769			−0.156217			−0.0781086	+	0.996945i	$0.524888\pi$
$420$		0			0
$421$	−39.6161			−1.93077			−0.965386	−	0.260824i	$-0.916006\pi$
$421$	−39.6161			−1.93077			−0.965386	+	0.260824i	$0.916006\pi$
$422$	0.784857	−	24.6041i	0.0382062	−	1.19771i
$423$	−2.40034	−	8.95821i	−0.116709	−	0.435563i
$424$	2.25270	−	0.377731i	0.109401	−	0.0183443i
$425$	21.6994	−	7.12124i	1.05258	−	0.345431i
$426$	9.14592	−	2.14059i	0.443121	−	0.103712i
$427$		0			0
$428$	0.359433	−	1.06470i	0.0173739	−	0.0514644i
$429$	−1.70068	+	0.981887i	−0.0821095	+	0.0474059i
$430$	8.43724	+	0.0357522i	0.406880	+	0.00172412i
$431$	−12.7288	−	7.34896i	−0.613123	−	0.353987i	0.161064	−	0.986944i	$-0.448508\pi$
$431$	−12.7288	−	7.34896i	−0.613123	−	0.353987i	−0.774187	+	0.632957i	$0.781841\pi$
$432$	8.17024	+	10.5742i	0.393091	+	0.508753i
$433$	−6.03281	−	6.03281i	−0.289919	−	0.289919i	0.547129	−	0.837048i	$-0.315721\pi$
$433$	−6.03281	−	6.03281i	−0.289919	−	0.289919i	−0.837048	+	0.547129i	$0.815721\pi$
$434$		0			0
$435$	19.5258	+	10.5645i	0.936192	+	0.506529i
$436$	8.70439	+	5.79505i	0.416865	+	0.277533i
$437$	12.6590	+	47.2442i	0.605564	+	2.26000i
$438$	−9.68291	−	18.0791i	−0.462667	−	0.863851i
$439$	3.31217	+	5.73685i	0.158081	+	0.273805i	0.934177	−	0.356810i	$-0.116136\pi$
$439$	3.31217	+	5.73685i	0.158081	+	0.273805i	−0.776095	+	0.630616i	$0.782802\pi$
$440$	0.514916	+	2.62381i	0.0245477	+	0.125085i
$441$		0			0
$442$	7.53568	−	12.1410i	0.358436	−	0.577488i
$443$	9.42675	+	2.52589i	0.447879	+	0.120009i	0.475707	−	0.879604i	$-0.342192\pi$
$443$	9.42675	+	2.52589i	0.447879	+	0.120009i	−0.0278280	+	0.999613i	$0.508859\pi$
$444$	1.99557	−	31.2473i	0.0947056	−	1.48293i
$445$	−25.1989	−	6.01051i	−1.19454	−	0.284926i
$446$	−2.45360	+	2.30190i	−0.116181	+	0.108998i
$447$	−7.24931	−	7.24931i	−0.342881	−	0.342881i
$448$		0			0
$449$			18.0135i			0.850109i	0.905168	+	0.425055i	$0.139745\pi$
$449$			18.0135i			0.850109i	−0.905168	+	0.425055i	$0.860255\pi$
$450$	−5.18220	−	8.50932i	−0.244291	−	0.401133i
$451$	1.47142	+	0.849527i	0.0692867	+	0.0400027i
$452$	17.6775	+	20.0894i	0.831479	+	0.944927i
$453$	−1.90906	+	7.12472i	−0.0896956	+	0.334749i
$454$	−21.5559	+	5.04514i	−1.01167	+	0.236780i
$455$		0			0
$456$	33.5989	−	27.7152i	1.57341	−	1.29788i
$457$	−1.22667	−	0.328686i	−0.0573813	−	0.0153753i	0.230014	−	0.973187i	$-0.426123\pi$
$457$	−1.22667	−	0.328686i	−0.0573813	−	0.0153753i	−0.287396	+	0.957812i	$0.592789\pi$
$458$	−21.2824	+	11.3986i	−0.994463	+	0.532621i
$459$	7.62958	−	13.2148i	0.356118	−	0.616815i
$460$	−13.9705	−	26.3521i	−0.651376	−	1.22867i
$461$	17.6021			0.819811			0.409906	−	0.912128i	$-0.365562\pi$
$461$	17.6021			0.819811			0.409906	+	0.912128i	$0.365562\pi$
$462$		0			0
$463$	13.7264	−	13.7264i	0.637919	−	0.637919i	−0.312123	−	0.950042i	$-0.601040\pi$
$463$	13.7264	−	13.7264i	0.637919	−	0.637919i	0.950042	+	0.312123i	$0.101040\pi$
$464$	2.40595	−	18.7597i	0.111694	−	0.870900i
$465$	7.85922	−	4.83206i	0.364463	−	0.224081i
$466$	−5.69808	+	18.8408i	−0.263958	+	0.872781i
$467$	3.32051	−	12.3923i	0.153655	−	0.573447i	−0.845562	−	0.533877i	$-0.820734\pi$
$467$	3.32051	−	12.3923i	0.153655	−	0.573447i	0.999217	−	0.0395701i	$-0.0125988\pi$
$468$	−5.90632	−	1.99391i	−0.273020	−	0.0921687i
$469$		0			0
$470$	−18.0699	+	10.3308i	−0.833501	+	0.476524i
$471$	24.5395	−	14.1679i	1.13072	−	0.652821i
$472$	−4.45621	+	6.25170i	−0.205113	+	0.287758i
$473$	1.08957	−	0.291950i	0.0500986	−	0.0134239i
$474$	−7.70946	+	7.23281i	−0.354107	+	0.332214i
$475$	30.6937	−	20.0614i	1.40832	−	0.920480i
$476$		0			0
$477$	−0.804592	+	0.804592i	−0.0368397	+	0.0368397i
$478$	10.6173	+	0.338687i	0.485626	+	0.0154912i
$479$	7.41948	−	12.8509i	0.339005	−	0.587173i	−0.645241	−	0.763979i	$-0.723243\pi$
$479$	7.41948	−	12.8509i	0.339005	−	0.587173i	0.984246	+	0.176806i	$0.0565764\pi$
$480$	−16.1876	+	21.0571i	−0.738858	+	0.961122i
$481$	−8.24667	−	14.2837i	−0.376016	−	0.651279i
$482$	−5.40822	+	8.71337i	−0.246338	+	0.396883i
$483$		0			0
$484$	−9.60470	−	19.3946i	−0.436577	−	0.881571i
$485$	14.6676	−	0.405681i	0.666022	−	0.0184210i
$486$	−18.3864	−	5.56068i	−0.834026	−	0.252237i
$487$	33.7505	−	9.04342i	1.52938	−	0.409796i	0.606564	−	0.795035i	$-0.292548\pi$
$487$	33.7505	−	9.04342i	1.52938	−	0.409796i	0.922817	+	0.385239i	$0.125881\pi$
$488$	−2.17326	−	4.76465i	−0.0983789	−	0.215686i
$489$			12.1134i			0.547787i
$490$		0			0
$491$			5.19048i			0.234243i	0.993118	+	0.117122i	$0.0373667\pi$
$491$			5.19048i			0.234243i	−0.993118	+	0.117122i	$0.962633\pi$
$492$	3.32025	+	16.5473i	0.149688	+	0.746010i
$493$	−20.8614	+	5.58979i	−0.939550	+	0.251752i
$494$	6.64161	−	21.9606i	0.298820	−	0.988053i
$495$	−0.967546	−	0.915465i	−0.0434879	−	0.0411471i
$496$	−6.25157	−	4.76385i	−0.280704	−	0.213903i
$497$		0			0
$498$	−16.8359	−	10.4497i	−0.754436	−	0.468264i
$499$	−5.42096	−	9.38938i	−0.242675	−	0.420326i	0.718800	−	0.695217i	$-0.244692\pi$
$499$	−5.42096	−	9.38938i	−0.242675	−	0.420326i	−0.961475	+	0.274891i	$0.911358\pi$
$500$	−15.5053	+	16.1117i	−0.693418	+	0.720536i
$501$	−9.07955	+	15.7262i	−0.405644	+	0.702597i
$502$	−0.164048	+	5.14265i	−0.00732180	+	0.229528i
$503$	−2.03813	+	2.03813i	−0.0908758	+	0.0908758i	−0.751083	−	0.660207i	$-0.770468\pi$
$503$	−2.03813	+	2.03813i	−0.0908758	+	0.0908758i	0.660207	+	0.751083i	$0.270468\pi$
$504$		0			0
$505$	9.08736	−	2.70635i	0.404382	−	0.120431i
$506$	−2.72830	−	2.90810i	−0.121288	−	0.129281i
$507$	16.4416	−	4.40551i	0.730196	−	0.195655i
$508$	29.3673	+	33.3742i	1.30296	+	1.48074i
$509$	10.5939	−	6.11641i	0.469568	−	0.271105i	−0.246491	−	0.969145i	$-0.579278\pi$
$509$	10.5939	−	6.11641i	0.469568	−	0.271105i	0.716059	+	0.698040i	$0.245944\pi$
$510$	29.2621	+	7.97382i	1.29575	+	0.353087i
$511$		0			0
$512$	21.7019	+	6.40523i	0.959098	+	0.283074i
$513$	6.34100	−	23.6649i	0.279962	−	1.04483i
$514$	−9.43939	−	2.85479i	−0.416353	−	0.125919i
$515$	18.4147	+	29.9510i	0.811448	+	1.31980i
$516$	9.32685	+	6.20946i	0.410592	+	0.273356i
$517$	−1.96771	+	1.96771i	−0.0865397	+	0.0865397i
$518$		0			0
$519$	−9.18010			−0.402962
$520$	−0.950847	+	13.9585i	−0.0416974	+	0.612119i
$521$	1.56024	−	2.70242i	0.0683554	−	0.118395i	−0.829822	−	0.558028i	$-0.811558\pi$
$521$	1.56024	−	2.70242i	0.0683554	−	0.118395i	0.898178	+	0.439633i	$0.144891\pi$
$522$	4.44836	+	8.30559i	0.194700	+	0.363526i
$523$	−6.72558	−	1.80211i	−0.294089	−	0.0788010i	0.108758	−	0.994068i	$-0.465313\pi$
$523$	−6.72558	−	1.80211i	−0.294089	−	0.0788010i	−0.402847	+	0.915267i	$0.631979\pi$
$524$	32.2085	−	15.9505i	1.40703	−	0.696800i
$525$		0			0
$526$	8.17527	+	34.9297i	0.356459	+	1.52301i
$527$	−2.32294	+	8.66931i	−0.101189	+	0.377641i
$528$	−1.34789	+	3.28513i	−0.0586593	+	0.142967i
$529$	18.6025	+	10.7401i	0.808803	+	0.466963i
$530$	2.20619	+	1.28624i	0.0958309	+	0.0558707i
$531$		−	3.82451i		−	0.165970i
$532$		0			0
$533$	6.28632	+	6.28632i	0.272291	+	0.272291i
$534$	−23.5386	−	25.0898i	−1.01862	−	1.08574i
$535$	1.07027	−	0.658030i	0.0462718	−	0.0284491i
$536$	−25.1286	+	4.21353i	−1.08539	+	0.181997i
$537$	36.5202	+	9.78557i	1.57596	+	0.422278i
$538$	22.8748	+	14.1979i	0.986201	+	0.612116i
$539$		0			0
$540$	−0.539612	+	14.9304i	−0.0232212	+	0.642503i
$541$	1.93050	+	3.34372i	0.0829986	+	0.143758i	0.904537	−	0.426396i	$-0.140217\pi$
$541$	1.93050	+	3.34372i	0.0829986	+	0.143758i	−0.821538	+	0.570154i	$0.806884\pi$
$542$	−26.3026	+	14.0873i	−1.12979	+	0.605103i
$543$	−7.91661	−	29.5452i	−0.339734	−	1.26791i
$544$	−2.64010	−	25.7031i	−0.113193	−	1.10201i
$545$	3.33700	+	11.2049i	0.142941	+	0.479967i
$546$		0			0
$547$	25.7583	+	25.7583i	1.10135	+	1.10135i	0.994249	+	0.107098i	$0.0341557\pi$
$547$	25.7583	+	25.7583i	1.10135	+	1.10135i	0.107098	+	0.994249i	$0.465844\pi$
$548$	−5.28820	−	26.3551i	−0.225901	−	1.12583i
$549$	2.25928	+	1.30439i	0.0964235	+	0.0556701i
$550$	−1.43371	+	2.62324i	−0.0611337	+	0.111855i
$551$	−30.0304	+	17.3381i	−1.27934	+	0.738626i
$552$	3.78350	−	39.4283i	0.161036	−	1.67818i
$553$		0			0
$554$	−5.19503	−	22.1963i	−0.220716	−	0.943032i
$555$	24.0596	−	25.4284i	1.02127	−	1.07937i
$556$	12.3081	+	0.786042i	0.521979	+	0.0333356i
$557$	4.34701	+	16.2233i	0.184189	+	0.687402i	0.994803	+	0.101821i	$0.0324668\pi$
$557$	4.34701	+	16.2233i	0.184189	+	0.687402i	−0.810614	+	0.585581i	$0.800866\pi$
$558$	3.91341	+	0.124836i	0.165668	+	0.00528472i
$559$	5.90224			0.249638
$560$		0			0
$561$	4.05479			0.171193
$562$	−8.49156	−	0.270876i	−0.358195	−	0.0114262i
$563$	−2.89404	−	10.8007i	−0.121969	−	0.455195i	0.877744	−	0.479129i	$-0.159047\pi$
$563$	−2.89404	−	10.8007i	−0.121969	−	0.455195i	−0.999714	+	0.0239343i	$0.992381\pi$
$564$	−27.5856	−	1.76173i	−1.16157	−	0.0741821i
$565$	0.827169	+	29.9067i	0.0347993	+	1.25819i
$566$	−0.536492	−	2.29222i	−0.0225504	−	0.0963491i
$567$		0			0
$568$	0.854600	−	8.90590i	0.0358582	−	0.373683i
$569$	−14.1920	+	8.19376i	−0.594960	+	0.343500i	−0.767056	−	0.641580i	$-0.778279\pi$
$569$	−14.1920	+	8.19376i	−0.594960	+	0.343500i	0.172096	+	0.985080i	$0.444946\pi$
$570$	48.6953	+	0.206343i	2.03962	+	0.00864274i
$571$	−39.2390	−	22.6547i	−1.64210	−	0.948068i	−0.980085	−	0.198580i	$-0.936367\pi$
$571$	−39.2390	−	22.6547i	−1.64210	−	0.948068i	−0.662018	−	0.749488i	$-0.730300\pi$
$572$	0.367979	+	1.83392i	0.0153860	+	0.0766800i
$573$	−15.0415	−	15.0415i	−0.628367	−	0.628367i
$574$		0			0
$575$	6.83717	−	32.6383i	0.285130	−	1.36111i
$576$	−10.6555	+	3.67677i	−0.443978	+	0.153199i
$577$	−8.24552	−	30.7727i	−0.343265	−	1.28108i	−0.894626	−	0.446817i	$-0.852558\pi$
$577$	−8.24552	−	30.7727i	−0.343265	−	1.28108i	0.551360	−	0.834267i	$-0.314109\pi$
$578$	−4.81603	+	2.57940i	−0.200320	+	0.107289i
$579$	22.2886	+	38.6049i	0.926281	+	1.60437i
$580$	15.4827	−	14.4026i	0.642882	−	0.598033i
$581$		0			0
$582$	16.5562	+	10.2761i	0.686278	+	0.425960i
$583$	0.329786	+	0.0883660i	0.0136584	+	0.00365975i
$584$	−19.2655	+	3.23041i	−0.797211	+	0.133675i
$585$	−3.65035	−	5.93720i	−0.150923	−	0.245473i
$586$	19.4934	+	20.7780i	0.805263	+	0.858331i
$587$	14.5087	+	14.5087i	0.598837	+	0.598837i	0.940003	−	0.341166i	$-0.110822\pi$
$587$	14.5087	+	14.5087i	0.598837	+	0.598837i	−0.341166	+	0.940003i	$0.610822\pi$
$588$		0			0
$589$			14.4103i			0.593765i
$590$	−8.30038	+	2.18643i	−0.341721	+	0.0900137i
$591$	−36.4180	−	21.0260i	−1.49804	−	0.864892i
$592$	−27.5912	−	11.3207i	−1.13399	−	0.465276i
$593$	−11.4330	+	42.6687i	−0.469498	+	1.75219i	0.172029	+	0.985092i	$0.444968\pi$
$593$	−11.4330	+	42.6687i	−0.469498	+	1.75219i	−0.641527	+	0.767100i	$0.721699\pi$
$594$	0.455188	+	1.94484i	0.0186766	+	0.0797977i
$595$		0			0
$596$	−8.75072	+	4.33359i	−0.358443	+	0.177511i
$597$	14.7744	+	3.95878i	0.604674	+	0.162022i
$598$	−9.85093	−	18.3928i	−0.402834	−	0.752136i
$599$	−20.0977	+	34.8103i	−0.821170	+	1.42231i	0.0836409	+	0.996496i	$0.473345\pi$
$599$	−20.0977	+	34.8103i	−0.821170	+	1.42231i	−0.904811	+	0.425813i	$0.859988\pi$
$600$	−28.9700	+	6.52196i	−1.18270	+	0.266258i
$601$	−17.3374			−0.707207			−0.353604	−	0.935395i	$-0.615044\pi$
$601$	−17.3374			−0.707207			−0.353604	+	0.935395i	$0.615044\pi$
$602$		0			0
$603$	8.97509	−	8.97509i	0.365494	−	0.365494i
$604$	5.84810	+	3.89344i	0.237956	+	0.158422i
$605$	5.61407	−	23.5368i	0.228244	−	0.956907i
$606$	12.0527	+	3.64515i	0.489608	+	0.148074i
$607$	0.342579	−	1.27852i	0.0139048	−	0.0518936i	−0.958625	−	0.284672i	$-0.908115\pi$
$607$	0.342579	−	1.27852i	0.0139048	−	0.0518936i	0.972530	+	0.232779i	$0.0747818\pi$
$608$	−14.7755	−	38.7650i	−0.599225	−	1.57213i
$609$		0			0
$610$	1.53934	−	5.64904i	0.0623261	−	0.228723i
$611$	−12.6099	+	7.28031i	−0.510141	+	0.294530i
$612$	8.50296	+	9.66311i	0.343712	+	0.390608i
$613$	−13.9992	+	3.75107i	−0.565422	+	0.151504i	−0.530196	−	0.847875i	$-0.677882\pi$
$613$	−13.9992	+	3.75107i	−0.565422	+	0.151504i	−0.0352258	+	0.999379i	$0.511215\pi$
$614$	−4.92970	−	5.25458i	−0.198947	−	0.212057i
$615$	−8.97920	+	16.5958i	−0.362076	+	0.669208i
$616$		0			0
$617$	11.3496	−	11.3496i	0.456918	−	0.456918i	−0.440725	−	0.897642i	$-0.645278\pi$
$617$	11.3496	−	11.3496i	0.456918	−	0.456918i	0.897642	+	0.440725i	$0.145278\pi$
$618$	−1.48868	+	46.6678i	−0.0598833	+	1.87725i
$619$	10.7582	−	18.6337i	0.432407	−	0.748951i	−0.564673	−	0.825315i	$-0.690998\pi$
$619$	10.7582	−	18.6337i	0.432407	−	0.748951i	0.997080	+	0.0763640i	$0.0243311\pi$
$620$	−1.96632	−	8.56470i	−0.0789693	−	0.343967i
$621$	−11.1402	−	19.2955i	−0.447043	−	0.774300i
$622$	−0.519883	−	0.322681i	−0.0208454	−	0.0129383i
$623$		0			0
$624$	−11.2613	+	14.7782i	−0.450814	+	0.591600i
$625$	−24.8472	+	2.75949i	−0.993890	+	0.110380i
$626$	−0.421714	+	1.39440i	−0.0168551	+	0.0557316i
$627$	6.28844	−	1.68498i	0.251136	−	0.0672917i
$628$	−5.30966	−	26.4620i	−0.211878	−	1.05595i
$629$			34.0554i			1.35788i
$630$		0			0
$631$			7.18172i			0.285900i	0.989730	+	0.142950i	$0.0456588\pi$
$631$			7.18172i			0.285900i	−0.989730	+	0.142950i	$0.954341\pi$
$632$	4.17851	+	9.16095i	0.166212	+	0.364403i
$633$	35.3042	−	9.45974i	1.40322	−	0.375991i
$634$	38.1670	+	11.5430i	1.51580	+	0.458430i
$635$	1.37416	+	49.6836i	0.0545320	+	1.97163i
$636$	1.50507	+	3.03915i	0.0596798	+	0.120510i
$637$		0			0
$638$	1.49087	−	2.40198i	0.0590239	−	0.0950955i
$639$	2.22845	+	3.85979i	0.0881562	+	0.152691i
$640$	14.0713	+	21.0237i	0.556219	+	0.831036i
$641$	13.1001	−	22.6901i	0.517425	−	0.896206i	−0.482371	−	0.875967i	$-0.660224\pi$
$641$	13.1001	−	22.6901i	0.517425	−	0.896206i	0.999795	−	0.0202384i	$-0.00644252\pi$
$642$	1.66763	+	0.0531964i	0.0658160	+	0.00209949i
$643$	−30.8400	+	30.8400i	−1.21621	+	1.21621i	−0.247263	+	0.968948i	$0.579531\pi$
$643$	−30.8400	+	30.8400i	−1.21621	+	1.21621i	−0.968948	+	0.247263i	$0.920469\pi$
$644$		0			0
$645$	3.57563	+	12.0062i	0.140790	+	0.472744i
$646$	−34.5483	+	32.4123i	−1.35929	+	1.27525i
$647$	13.9753	−	3.74467i	0.549425	−	0.147218i	0.0265817	−	0.999647i	$-0.491538\pi$
$647$	13.9753	−	3.74467i	0.549425	−	0.147218i	0.522844	+	0.852429i	$0.324871\pi$
$648$	−18.4558	+	25.8920i	−0.725012	+	1.01713i
$649$	−0.993813	+	0.573778i	−0.0390106	+	0.0225228i
$650$	−10.7987	+	11.3166i	−0.423561	+	0.443875i
$651$		0			0
$652$	10.9318	+	3.69045i	0.428121	+	0.144529i
$653$	−9.77388	+	36.4766i	−0.382481	+	1.42744i	0.459618	+	0.888117i	$0.347986\pi$
$653$	−9.77388	+	36.4766i	−0.382481	+	1.42744i	−0.842099	+	0.539323i	$0.818680\pi$
$654$	−4.49456	+	14.8613i	−0.175751	+	0.581124i
$655$	39.0875	+	9.32327i	1.52727	+	0.364290i
$656$	15.9447	+	2.04492i	0.622535	+	0.0798407i
$657$	6.88099	−	6.88099i	0.268453	−	0.268453i
$658$		0			0
$659$	5.66966			0.220859			0.110429	−	0.993884i	$-0.464777\pi$
$659$	5.66966			0.220859			0.110429	+	0.993884i	$0.464777\pi$
$660$	−3.50760	+	1.85954i	−0.136533	+	0.0723825i
$661$	−14.4408	+	25.0122i	−0.561682	+	0.972861i	0.435668	+	0.900107i	$0.356512\pi$
$661$	−14.4408	+	25.0122i	−0.561682	+	0.972861i	−0.997350	+	0.0727540i	$0.976821\pi$
$662$	−32.1284	+	17.2075i	−1.24870	+	0.668790i
$663$	20.4935	+	5.49122i	0.795902	+	0.213261i
$664$	−14.5596	+	12.0100i	−0.565022	+	0.466079i
$665$		0			0
$666$	14.4657	−	3.38569i	0.560535	−	0.131193i
$667$	−8.16187	+	30.4605i	−0.316029	+	1.17944i
$668$	11.4260	+	12.9850i	0.442086	+	0.502404i
$669$	−4.32600	−	2.49762i	−0.167253	−	0.0965636i
$670$	−24.6097	−	14.3478i	−0.950757	−	0.554304i
$671$		−	0.782775i		−	0.0302187i
$672$		0			0
$673$	−6.90378	−	6.90378i	−0.266121	−	0.266121i	0.561414	−	0.827535i	$-0.310258\pi$
$673$	−6.90378	−	6.90378i	−0.266121	−	0.266121i	−0.827535	+	0.561414i	$0.810258\pi$
$674$	15.2842	−	14.3392i	0.588725	−	0.552326i
$675$	−11.1403	+	12.4461i	−0.428792	+	0.479049i
$676$	1.03331	−	16.1799i	0.0397427	−	0.622304i
$677$	13.5776	+	3.63810i	0.521829	+	0.139824i	0.510112	−	0.860108i	$-0.329604\pi$
$677$	13.5776	+	3.63810i	0.521829	+	0.139824i	0.0117165	+	0.999931i	$0.496270\pi$
$678$	−20.9527	+	33.7576i	−0.804684	+	1.29645i
$679$		0			0
$680$	16.1109	−	23.9784i	0.617827	−	0.919529i
$681$	−16.4351	−	28.4664i	−0.629794	−	1.09083i
$682$	−0.554677	−	1.03564i	−0.0212397	−	0.0396568i
$683$	−8.40215	−	31.3572i	−0.321499	−	1.19985i	−0.917784	−	0.397079i	$-0.870024\pi$
$683$	−8.40215	−	31.3572i	−0.321499	−	1.19985i	0.596285	−	0.802773i	$-0.296643\pi$
$684$	17.2025	+	11.4528i	0.657754	+	0.437908i
$685$	14.3013	−	26.4324i	0.546424	−	1.00993i
$686$		0			0
$687$	−25.3470	−	25.3470i	−0.967047	−	0.967047i
$688$	8.44524	−	6.52526i	0.321972	−	0.248773i
$689$	1.54712	+	0.893230i	0.0589406	+	0.0340294i
$690$	31.4464	−	31.1810i	1.19714	−	1.18704i
$691$	3.27810	−	1.89261i	0.124705	−	0.0719984i	−0.436350	−	0.899777i	$-0.643729\pi$
$691$	3.27810	−	1.89261i	0.124705	−	0.0719984i	0.561055	+	0.827779i	$0.310396\pi$
$692$	−2.79680	+	8.28460i	−0.106318	+	0.314933i
$693$		0			0
$694$	−25.8583	+	6.05213i	−0.981570	+	0.229736i
$695$	10.0161	+	9.47692i	0.379931	+	0.359480i
$696$	27.6951	−	4.64389i	1.04978	−	0.176026i
$697$	−4.75099	−	17.7310i	−0.179957	−	0.671608i
$698$	0.339753	−	10.6507i	0.0128598	−	0.403136i
$699$	−29.2253			−1.10540
$700$		0			0
$701$	−5.66595			−0.214000			−0.107000	−	0.994259i	$-0.534124\pi$
$701$	−5.66595			−0.214000			−0.107000	+	0.994259i	$0.534124\pi$
$702$	−0.333220	+	10.4459i	−0.0125766	+	0.394257i
$703$	14.1518	+	52.8154i	0.533747	+	1.99197i
$704$	2.55403	+	2.21725i	0.0962585	+	0.0835657i
$705$	−22.4486	−	21.2403i	−0.845464	−	0.799955i
$706$	50.7592	−	11.8802i	1.91035	−	0.447116i
$707$		0			0
$708$	−10.8001	−	3.64602i	−0.405894	−	0.137026i
$709$	10.3830	−	5.99462i	0.389941	−	0.225133i	−0.292193	−	0.956359i	$-0.594385\pi$
$709$	10.3830	−	5.99462i	0.389941	−	0.225133i	0.682135	+	0.731227i	$0.261052\pi$
$710$	7.10298	−	7.04304i	0.266570	−	0.264320i
$711$	−4.34388	−	2.50794i	−0.162908	−	0.0940552i
$712$	−29.8136	+	13.5986i	−1.11731	+	0.509630i
$713$	9.26659	+	9.26659i	0.347037	+	0.347037i
$714$		0			0
$715$	−0.995155	+	1.83929i	−0.0372167	+	0.0687857i
$716$	19.9572	−	29.9765i	0.745836	−	1.12027i
$717$	4.08214	+	15.2348i	0.152450	+	0.568952i
$718$	12.0823	+	22.5590i	0.450907	+	0.841893i
$719$	−12.5797	−	21.7886i	−0.469142	−	0.812578i	0.530235	−	0.847850i	$-0.322104\pi$
$719$	−12.5797	−	21.7886i	−0.469142	−	0.812578i	−0.999378	+	0.0352721i	$0.988770\pi$
$720$	−11.7870	−	4.45960i	−0.439276	−	0.166199i
$721$		0			0
$722$	−25.9407	+	41.7939i	−0.965413	+	1.55541i
$723$	−14.7078	−	3.94095i	−0.546989	−	0.146565i
$724$	−29.0750	−	1.85684i	−1.08056	−	0.0690089i
$725$	23.6056	−	1.30678i	0.876690	−	0.0485326i
$726$	23.4350	−	21.9861i	0.869753	−	0.815979i
$727$	−20.9986	−	20.9986i	−0.778795	−	0.778795i	0.200831	−	0.979626i	$-0.435636\pi$
$727$	−20.9986	−	20.9986i	−0.778795	−	0.778795i	−0.979626	+	0.200831i	$0.935636\pi$
$728$		0			0
$729$			5.20463i			0.192764i
$730$	−18.8677	−	11.0001i	−0.698324	−	0.407133i
$731$	−10.5542	−	6.09346i	−0.390360	−	0.225375i
$732$	5.83735	−	5.13651i	0.215755	−	0.189851i
$733$	4.84038	−	18.0645i	0.178783	−	0.667229i	−0.817093	−	0.576506i	$-0.804416\pi$
$733$	4.84038	−	18.0645i	0.178783	−	0.667229i	0.995876	−	0.0907227i	$-0.0289177\pi$
$734$	−32.2501	+	7.54812i	−1.19037	+	0.278606i
$735$		0			0
$736$	−34.4295	−	15.4266i	−1.26909	−	0.568632i
$737$	−3.67872	−	0.985709i	−0.135507	−	0.0363091i
$738$	−7.05926	+	3.78085i	−0.259855	+	0.139175i
$739$	−8.20856	+	14.2176i	−0.301957	+	0.523004i	−0.976579	−	0.215159i	$-0.930973\pi$
$739$	−8.20856	+	14.2176i	−0.301957	+	0.523004i	0.674622	+	0.738163i	$0.264306\pi$
$740$	−15.6179	−	29.4596i	−0.574125	−	1.08296i
$741$	34.0646			1.25140
$742$		0			0
$743$	−11.1710	+	11.1710i	−0.409825	+	0.409825i	−0.881678	−	0.471852i	$-0.843586\pi$
$743$	−11.1710	+	11.1710i	−0.409825	+	0.409825i	0.471852	+	0.881678i	$0.343586\pi$
$744$	4.08330	−	10.9322i	0.149701	−	0.400793i
$745$	−10.6197	−	2.53304i	−0.389075	−	0.0928034i
$746$	2.37504	−	7.85309i	0.0869563	−	0.287522i
$747$	2.43345	−	9.08175i	0.0890352	−	0.332284i
$748$	1.23533	−	3.65925i	0.0451680	−	0.133795i
$749$		0			0
$750$	−29.5620	−	15.1108i	−1.07945	−	0.551770i
$751$	24.0345	−	13.8763i	0.877032	−	0.506355i	0.00735334	−	0.999973i	$-0.497659\pi$
$751$	24.0345	−	13.8763i	0.877032	−	0.506355i	0.869679	+	0.493618i	$0.164326\pi$
$752$	−9.99408	+	24.3580i	−0.364447	+	0.888244i
$753$	−7.37915	+	1.97724i	−0.268911	+	0.0720545i
$754$	10.7880	−	10.1210i	0.392874	−	0.368584i
$755$	2.24198	+	7.52812i	0.0815941	+	0.273976i
$756$		0			0
$757$	−4.34481	+	4.34481i	−0.157915	+	0.157915i	−0.781642	−	0.623727i	$-0.785618\pi$
$757$	−4.34481	+	4.34481i	−0.157915	+	0.157915i	0.623727	+	0.781642i	$0.285618\pi$
$758$	−28.8225	−	0.919421i	−1.04688	−	0.0333949i
$759$	2.96028	−	5.12735i	0.107451	−	0.186111i
$760$	15.0216	−	43.8823i	0.544892	−	1.59178i
$761$	−11.7897	−	20.4203i	−0.427376	−	0.740236i	0.569263	−	0.822155i	$-0.307228\pi$
$761$	−11.7897	−	20.4203i	−0.427376	−	0.740236i	−0.996639	+	0.0819190i	$0.973895\pi$
$762$	−34.8084	+	56.0810i	−1.26098	+	2.03160i
$763$		0			0
$764$	−18.1567	+	8.99169i	−0.656887	+	0.325308i
$765$	0.397873	+	14.3853i	0.0143851	+	0.520101i
$766$	−14.2852	−	4.32033i	−0.516145	−	0.156100i
$767$	−5.79992	+	1.55408i	−0.209423	+	0.0561147i
$768$	0.224767	+	33.5954i	0.00811059	+	1.21227i
$769$		−	11.6924i		−	0.421638i	−0.977525	−	0.210819i	$-0.932387\pi$
$769$		−	11.6924i		−	0.421638i	0.977525	−	0.210819i	$-0.0676131\pi$
$770$		0			0
$771$		−	14.6421i		−	0.527323i
$772$	41.6295	−	8.35302i	1.49828	−	0.300632i
$773$	−18.1569	+	4.86514i	−0.653060	+	0.174987i	−0.570112	−	0.821567i	$-0.693100\pi$
$773$	−18.1569	+	4.86514i	−0.653060	+	0.174987i	−0.0829479	+	0.996554i	$0.526434\pi$
$774$	−1.53906	+	5.08890i	−0.0553202	+	0.182917i
$775$	4.43456	−	8.76700i	0.159294	−	0.314920i
$776$	14.3177	−	11.8105i	0.513976	−	0.423972i
$777$		0			0
$778$	2.71972	+	1.68808i	0.0975066	+	0.0605205i
$779$	−14.7363	−	25.5241i	−0.527984	−	0.914495i
$780$	−20.2462	+	4.64821i	−0.724930	+	0.166433i
$781$	0.668654	−	1.15814i	0.0239263	−	0.0414416i
$782$	−1.37357	+	43.0594i	−0.0491188	+	1.53980i
$783$	11.1695	−	11.1695i	0.399167	−	0.399167i
$784$		0			0
$785$	14.3593	−	26.5396i	0.512506	−	0.947239i
$786$	36.5122	+	38.9184i	1.30235	+	1.38817i
$787$	49.6245	−	13.2968i	1.76892	−	0.473982i	0.780429	−	0.625244i	$-0.215001\pi$
$787$	49.6245	−	13.2968i	1.76892	−	0.473982i	0.988494	+	0.151262i	$0.0483338\pi$
$788$	−30.0700	+	26.4598i	−1.07120	+	0.942590i
$789$	−46.1276	+	26.6318i	−1.64219	+	0.948117i
$790$	−2.95967	+	10.8614i	−0.105301	+	0.386430i
$791$		0			0
$792$	−1.67716	−	0.160938i	−0.0595951	−	0.00571868i
$793$	1.06008	−	3.95626i	0.0376444	−	0.140491i
$794$	23.4001	+	7.07698i	0.830439	+	0.251153i
$795$	−0.879732	+	3.68825i	−0.0312009	+	0.130809i
$796$	8.07374	−	12.1271i	0.286166	−	0.429832i
$797$	−1.34897	+	1.34897i	−0.0477829	+	0.0477829i	−0.730594	−	0.682812i	$-0.760757\pi$
$797$	−1.34897	+	1.34897i	−0.0477829	+	0.0477829i	0.682812	+	0.730594i	$0.260757\pi$
$798$		0			0
$799$	30.0647			1.06361
$800$	−2.94022	+	28.1310i	−0.103953	+	0.994582i
$801$	8.16191	−	14.1368i	0.288387	−	0.499501i
$802$	−3.32736	−	6.21254i	−0.117493	−	0.219372i
$803$	−2.82038	−	0.755719i	−0.0995292	−	0.0266688i
$804$	−16.7888	−	33.9012i	−0.592095	−	1.19560i
$805$		0			0
$806$	−1.40089	−	5.98547i	−0.0493444	−	0.210829i
$807$	−10.3460	+	38.6117i	−0.364195	+	1.35919i
$808$	6.96154	−	9.76647i	0.244906	−	0.343583i
$809$	3.46174	+	1.99864i	0.121708	+	0.0702684i	0.559618	−	0.828750i	$-0.310948\pi$
$809$	3.46174	+	1.99864i	0.121708	+	0.0702684i	−0.437910	+	0.899019i	$0.644281\pi$
$810$	−34.3768	+	9.05528i	−1.20788	+	0.318170i
$811$		−	41.2999i		−	1.45024i	−0.688625	−	0.725118i	$-0.741785\pi$
$811$		−	41.2999i		−	1.45024i	0.688625	−	0.725118i	$-0.258215\pi$
$812$		0			0
$813$	−31.3259	−	31.3259i	−1.09865	−	1.09865i
$814$	−3.05003	−	3.25103i	−0.106903	−	0.113949i
$815$	6.75627	+	10.9889i	0.236662	+	0.384925i
$816$	35.3941	−	14.7996i	1.23904	−	0.518090i
$817$	−18.9003	−	5.06432i	−0.661238	−	0.177178i
$818$	−2.50685	−	1.55596i	−0.0876501	−	0.0544027i
$819$		0			0
$820$	12.2413	+	13.1593i	0.427486	+	0.459544i
$821$	26.7751	+	46.3758i	0.934457	+	1.61853i	0.775600	+	0.631225i	$0.217448\pi$
$821$	26.7751	+	46.3758i	0.934457	+	1.61853i	0.158857	+	0.987302i	$0.449219\pi$
$822$	35.1825	−	18.8433i	1.22713	−	0.657235i
$823$	0.0982095	+	0.366523i	0.00342337	+	0.0127762i	0.967616	−	0.252425i	$-0.0812282\pi$
$823$	0.0982095	+	0.366523i	0.00342337	+	0.0127762i	−0.964193	+	0.265201i	$0.914562\pi$
$824$	41.6619	+	15.5612i	1.45136	+	0.542100i
$825$	−4.34433	−	0.910063i	−0.151250	−	0.0316843i
$826$		0			0
$827$	2.07441	+	2.07441i	0.0721345	+	0.0721345i	0.742254	−	0.670119i	$-0.233757\pi$
$827$	2.07441	+	2.07441i	0.0721345	+	0.0721345i	−0.670119	+	0.742254i	$0.733757\pi$
$828$	18.4269	−	3.69739i	0.640380	−	0.128493i
$829$	23.1175	+	13.3469i	0.802903	+	0.463556i	0.844485	−	0.535579i	$-0.179906\pi$
$829$	23.1175	+	13.3469i	0.802903	+	0.463556i	−0.0415820	+	0.999135i	$0.513240\pi$
$830$	−21.1014	−	0.0894157i	−0.732441	−	0.00310367i
$831$	29.3121	−	16.9234i	1.01683	−	0.587065i
$832$	9.90571	+	14.6651i	0.343419	+	0.508421i
$833$		0			0
$834$	4.17307	+	17.8299i	0.144502	+	0.617398i
$835$	0.534649	+	19.3305i	0.0185023	+	0.668960i
$836$	0.395213	−	6.18836i	0.0136687	−	0.214029i
$837$	−1.69898	−	6.34068i	−0.0587253	−	0.219166i
$838$	−4.51991	−	0.144183i	−0.156138	−	0.00498071i
$839$	23.5830			0.814175			0.407087	−	0.913389i	$-0.366544\pi$
$839$	23.5830			0.814175			0.407087	+	0.913389i	$0.366544\pi$
$840$		0			0
$841$	6.64270			0.229059
$842$	−55.9972	−	1.78628i	−1.92979	−	0.0615593i
$843$	−3.26482	−	12.1845i	−0.112446	−	0.419656i
$844$	2.21878	−	34.7424i	0.0763736	−	1.19588i
$845$	12.4581	−	13.1669i	0.428572	−	0.452954i
$846$	−2.98895	−	12.7706i	−0.102762	−	0.439063i
$847$		0			0
$848$	3.20122	−	0.432347i	0.109930	−	0.0148469i
$849$	3.02707	−	1.74768i	0.103889	−	0.0599802i
$850$	30.9931	−	9.08741i	1.06306	−	0.311696i
$851$	43.0636	+	24.8628i	1.47620	+	0.852285i
$852$	13.0242	−	2.61333i	0.446203	−	0.0895313i
$853$	−35.4043	−	35.4043i	−1.21222	−	1.21222i	−0.970295	−	0.241926i	$-0.922221\pi$
$853$	−35.4043	−	35.4043i	−1.21222	−	1.21222i	−0.241926	−	0.970295i	$-0.577779\pi$
$854$		0			0
$855$	6.59491	+	22.1444i	0.225541	+	0.757321i
$856$	0.556064	−	1.48875i	0.0190059	−	0.0508843i
$857$	−10.1866	−	38.0169i	−0.347967	−	1.29863i	−0.889107	−	0.457699i	$-0.848674\pi$
$857$	−10.1866	−	38.0169i	−0.347967	−	1.29863i	0.541140	−	0.840932i	$-0.317993\pi$
$858$	−2.44817	+	1.31121i	−0.0835792	+	0.0447639i
$859$	−15.9154	−	27.5663i	−0.543026	−	0.940549i	−0.998728	−	0.0504166i	$-0.983945\pi$
$859$	−15.9154	−	27.5663i	−0.543026	−	0.940549i	0.455702	−	0.890132i	$-0.349388\pi$
$860$	11.9244	+	0.430968i	0.406618	+	0.0146959i
$861$		0			0
$862$	−17.6607	−	10.9616i	−0.601525	−	0.373355i
$863$	−37.4334	−	10.0303i	−1.27425	−	0.341434i	−0.442592	−	0.896723i	$-0.645941\pi$
$863$	−37.4334	−	10.0303i	−1.27425	−	0.341434i	−0.831657	+	0.555289i	$0.812608\pi$
$864$	11.0718	+	15.3150i	0.376670	+	0.521027i
$865$	−8.32791	+	5.12022i	−0.283158	+	0.174093i
$866$	−8.25533	−	8.79937i	−0.280528	−	0.299015i
$867$	−5.73580	−	5.73580i	−0.194798	−	0.194798i
$868$		0			0
$869$			1.50503i			0.0510547i
$870$	27.1233	+	15.8133i	0.919566	+	0.536120i
$871$	−17.2579	−	9.96384i	−0.584761	−	0.337612i
$872$	12.0423	+	8.58376i	0.407804	+	0.290683i
$873$	−2.39302	+	8.93088i	−0.0809915	+	0.302264i
$874$	15.7633	+	67.3502i	0.533200	+	2.27815i
$875$		0			0
$876$	−12.8716	−	25.9913i	−0.434890	−	0.878164i
$877$	−2.69021	−	0.720839i	−0.0908419	−	0.0243410i	0.213112	−	0.977028i	$-0.431640\pi$
$877$	−2.69021	−	0.720839i	−0.0908419	−	0.0243410i	−0.303954	+	0.952687i	$0.598307\pi$
$878$	4.42307	+	8.25836i	0.149271	+	0.278706i
$879$	−21.1508	+	36.6343i	−0.713399	+	1.23564i
$880$	0.609524	+	3.73196i	0.0205471	+	0.125804i
$881$	40.5035			1.36460			0.682299	−	0.731074i	$-0.260980\pi$
$881$	40.5035			1.36460			0.682299	+	0.731074i	$0.260980\pi$
$882$		0			0
$883$	−17.0113	+	17.0113i	−0.572477	+	0.572477i	−0.932820	−	0.360343i	$-0.882660\pi$
$883$	−17.0113	+	17.0113i	−0.572477	+	0.572477i	0.360343	+	0.932820i	$0.382660\pi$
$884$	11.1991	−	16.8215i	0.376666	−	0.565767i
$885$	−6.67493	−	10.8566i	−0.224375	−	0.364941i
$886$	13.2108	+	3.99538i	0.443825	+	0.134228i
$887$	10.0823	−	37.6278i	0.338532	−	1.26342i	−0.561458	−	0.827505i	$-0.689759\pi$
$887$	10.0823	−	37.6278i	0.338532	−	1.26342i	0.899989	−	0.435912i	$-0.143574\pi$
$888$	4.22966	−	44.0778i	0.141938	−	1.47916i
$889$		0			0
$890$	−35.3474	−	9.63204i	−1.18485	−	0.322867i
$891$	−4.11597	+	2.37636i	−0.137890	+	0.0796109i
$892$	−3.57194	+	3.14309i	−0.119597	+	0.105238i
$893$	46.6264	−	12.4935i	1.56029	−	0.418079i
$894$	−9.92000	−	10.5737i	−0.331774	−	0.353639i
$895$	38.5880	−	11.4921i	1.28985	−	0.384137i
$896$		0			0
$897$	21.9054	−	21.9054i	0.731401	−	0.731401i
$898$	−0.812223	+	25.4620i	−0.0271042	+	0.849677i
$899$	−4.64548	+	8.04621i	−0.154936	+	0.268356i
$900$	−6.94132	−	12.2615i	−0.231377	−	0.408718i
$901$	−1.84434	−	3.19448i	−0.0614438	−	0.106424i
$902$	2.04155	+	1.26715i	0.0679760	+	0.0421914i
$903$		0			0
$904$	24.0812	+	29.1934i	0.800929	+	0.970957i
$905$	−23.6606	−	22.3870i	−0.786505	−	0.744169i
$906$	−3.01970	+	9.98467i	−0.100323	+	0.331719i
$907$	22.1163	−	5.92604i	0.734359	−	0.196771i	0.127789	−	0.991801i	$-0.459212\pi$
$907$	22.1163	−	5.92604i	0.734359	−	0.196771i	0.606569	+	0.795030i	$0.292545\pi$
$908$	−30.6966	+	6.15933i	−1.01870	+	0.204405i
$909$			5.97469i			0.198168i
$910$		0			0
$911$			43.8022i			1.45123i	0.688100	+	0.725616i	$0.258445\pi$
$911$			43.8022i			1.45123i	−0.688100	+	0.725616i	$0.741555\pi$
$912$	48.7415	−	37.6604i	1.61399	−	1.24706i
$913$	−2.72501	+	0.730164i	−0.0901847	+	0.0241649i
$914$	−1.71907	−	0.519906i	−0.0568619	−	0.0171970i
$915$	8.68995	−	0.240349i	0.287281	−	0.00794569i
$916$	−30.5966	+	15.1522i	−1.01094	+	0.500644i
$917$		0			0
$918$	11.3802	−	18.3351i	0.375603	−	0.605147i
$919$	−16.0826	−	27.8558i	−0.530515	−	0.918879i	−0.999366	−	0.0356018i	$-0.988665\pi$
$919$	−16.0826	−	27.8558i	−0.530515	−	0.918879i	0.468851	−	0.883277i	$-0.344668\pi$
$920$	−18.5590	−	37.8784i	−0.611871	−	1.24882i
$921$	5.34886	−	9.26450i	0.176251	−	0.305276i
$922$	24.8805	+	0.793673i	0.819395	+	0.0261382i
$923$	4.94790	−	4.94790i	0.162862	−	0.162862i
$924$		0			0
$925$	7.64343	−	36.4871i	0.251315	−	1.19969i
$926$	20.0211	−	18.7832i	0.657934	−	0.617256i
$927$	−21.3997	+	5.73402i	−0.702857	+	0.188330i
$928$	4.24667	−	26.4083i	0.139404	−	0.866896i
$929$	35.6942	−	20.6080i	1.17109	−	0.676128i	0.217152	−	0.976138i	$-0.430323\pi$
$929$	35.6942	−	20.6080i	1.17109	−	0.676128i	0.953936	+	0.300010i	$0.0969900\pi$
$930$	11.3268	−	6.47572i	0.371422	−	0.212347i
$931$		0			0
$932$	−8.90373	+	26.3744i	−0.291651	+	0.863921i
$933$	0.235137	−	0.877541i	0.00769802	−	0.0287294i
$934$	5.25228	−	17.3667i	0.171860	−	0.568257i
$935$	3.67838	−	2.26157i	0.120296	−	0.0739611i
$936$	−8.25864	−	3.08470i	−0.269942	−	0.100827i
$937$	−25.3650	+	25.3650i	−0.828637	+	0.828637i	−0.987328	−	0.158691i	$-0.949273\pi$
$937$	−25.3650	+	25.3650i	−0.828637	+	0.828637i	0.158691	+	0.987328i	$0.449273\pi$
$938$		0			0
$939$	−2.16296			−0.0705855
$940$	−26.0075	+	13.7878i	−0.848270	+	0.449707i
$941$	11.4729	−	19.8717i	0.374007	−	0.647799i	−0.616171	−	0.787612i	$-0.711317\pi$
$941$	11.4729	−	19.8717i	0.374007	−	0.647799i	0.990178	+	0.139814i	$0.0446504\pi$
$942$	35.3252	−	18.9197i	1.15096	−	0.616438i
$943$	−25.8897	−	6.93711i	−0.843083	−	0.225903i
$944$	−6.58071	+	8.63581i	−0.214184	+	0.281072i
$945$		0			0
$946$	1.55327	−	0.363542i	0.0505012	−	0.0118198i
$947$	7.85278	−	29.3070i	0.255181	−	0.952348i	−0.712809	−	0.701359i	$-0.752577\pi$
$947$	7.85278	−	29.3070i	0.255181	−	0.952348i	0.967990	−	0.250990i	$-0.0807561\pi$
$948$	−11.2234	+	9.87592i	−0.364519	+	0.320755i
$949$	−13.2312	−	7.63904i	−0.429503	−	0.247974i
$950$	44.2900	−	26.9727i	1.43696	−	0.875110i
$951$			59.2035i			1.91981i
$952$		0			0
$953$	−1.41682	−	1.41682i	−0.0458953	−	0.0458953i	0.683787	−	0.729682i	$-0.260332\pi$
$953$	−1.41682	−	1.41682i	−0.0458953	−	0.0458953i	−0.729682	+	0.683787i	$0.760332\pi$
$954$	−1.17356	+	1.10101i	−0.0379956	+	0.0356464i
$955$	−22.0346	−	5.25576i	−0.713023	−	0.170072i
$956$	14.9923	+	0.957466i	0.484885	+	0.0309666i
$957$	4.05445	+	1.08639i	0.131062	+	0.0351179i
$958$	11.0668	−	17.8302i	0.357553	−	0.576066i
$959$		0			0
$960$	−23.8305	+	29.0342i	−0.769126	+	0.937076i
$961$	−13.5695	−	23.5030i	−0.437725	−	0.758163i
$962$	−11.0126	−	20.5617i	−0.355060	−	0.662936i
$963$	0.204900	+	0.764696i	0.00660280	+	0.0246420i
$964$	−8.03737	+	12.0724i	−0.258866	+	0.388827i
$965$	41.7515	+	22.5897i	1.34403	+	0.727189i
$966$		0			0
$967$	−30.6644	−	30.6644i	−0.986102	−	0.986102i	0.0138026	−	0.999905i	$-0.495606\pi$
$967$	−30.6644	−	30.6644i	−0.986102	−	0.986102i	−0.999905	+	0.0138026i	$0.995606\pi$
$968$	−12.7017	−	27.8472i	−0.408248	−	0.895042i
$969$	−60.9131	−	35.1682i	−1.95681	−	1.12977i
$970$	20.7509	+	0.0879303i	0.666270	+	0.00282327i
$971$	−24.2994	+	14.0293i	−0.779806	+	0.450221i	−0.836362	−	0.548178i	$-0.815322\pi$
$971$	−24.2994	+	14.0293i	−0.779806	+	0.450221i	0.0565554	+	0.998399i	$0.481988\pi$
$972$	−25.7384	−	8.68902i	−0.825559	−	0.278701i
$973$		0			0
$974$	48.1139	−	11.2610i	1.54167	−	0.360826i
$975$	−20.7244	−	10.4829i	−0.663713	−	0.335722i
$976$	−2.85706	−	6.83281i	−0.0914521	−	0.218713i
$977$	7.13146	+	26.6150i	0.228156	+	0.851488i	0.981116	+	0.193422i	$0.0619587\pi$
$977$	7.13146	+	26.6150i	0.228156	+	0.851488i	−0.752960	+	0.658066i	$0.771375\pi$
$978$	−0.546190	+	17.1222i	−0.0174652	+	0.547508i
$979$	−4.89802			−0.156541
$980$		0			0
$981$	−7.36695			−0.235209
$982$	−0.234037	+	7.33671i	−0.00746842	+	0.234124i
$983$	8.75124	+	32.6601i	0.279121	+	1.04169i	0.953029	+	0.302879i	$0.0979478\pi$
$983$	8.75124	+	32.6601i	0.279121	+	1.04169i	−0.673908	+	0.738815i	$0.735386\pi$
$984$	3.94704	+	23.5392i	0.125827	+	0.750404i
$985$	−44.7646	+	1.23811i	−1.42632	+	0.0394495i
$986$	−29.7395	+	6.96051i	−0.947099	+	0.221668i
$987$		0			0
$988$	10.3781	−	30.7417i	0.330171	−	0.978023i
$989$	−15.4106	+	8.89729i	−0.490027	+	0.282917i
$990$	−1.32634	−	1.33763i	−0.0421539	−	0.0425127i
$991$	−38.7625	−	22.3796i	−1.23133	−	0.710910i	−0.264025	−	0.964516i	$-0.585050\pi$
$991$	−38.7625	−	22.3796i	−1.23133	−	0.710910i	−0.967308	+	0.253605i	$0.918384\pi$
$992$	−8.62175	−	7.01556i	−0.273741	−	0.222744i
$993$	−38.2642	−	38.2642i	−1.21428	−	1.21428i
$994$		0			0
$995$	15.6109	−	4.64914i	0.494898	−	0.147388i
$996$	−23.3263	−	15.5298i	−0.739123	−	0.492080i
$997$	−2.14644	−	8.01061i	−0.0679784	−	0.253699i	0.923571	−	0.383427i	$-0.125256\pi$
$997$	−2.14644	−	8.01061i	−0.0679784	−	0.253699i	−0.991550	+	0.129728i	$0.958590\pi$
$998$	−7.23913	−	13.5163i	−0.229151	−	0.427850i
$999$	−12.4539	−	21.5708i	−0.394025	−	0.682471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.263.18		72
4.3	odd	2	inner	980.2.x.m.263.16		72
5.2	odd	4	inner	980.2.x.m.67.10		72
7.2	even	3	inner	980.2.x.m.863.8		72
7.3	odd	6		980.2.k.k.883.6		36
7.4	even	3		980.2.k.j.883.6		36
7.5	odd	6		140.2.w.b.23.8	✓	72
7.6	odd	2		140.2.w.b.123.18	yes	72
20.7	even	4	inner	980.2.x.m.67.8		72
28.3	even	6		980.2.k.k.883.5		36
28.11	odd	6		980.2.k.j.883.5		36
28.19	even	6		140.2.w.b.23.10	yes	72
28.23	odd	6	inner	980.2.x.m.863.10		72
28.27	even	2		140.2.w.b.123.16	yes	72
35.2	odd	12	inner	980.2.x.m.667.16		72
35.12	even	12		140.2.w.b.107.16	yes	72
35.13	even	4		700.2.be.e.207.9		72
35.17	even	12		980.2.k.k.687.5		36
35.19	odd	6		700.2.be.e.443.11		72
35.27	even	4		140.2.w.b.67.10	yes	72
35.32	odd	12		980.2.k.j.687.5		36
35.33	even	12		700.2.be.e.107.3		72
35.34	odd	2		700.2.be.e.543.1		72
140.19	even	6		700.2.be.e.443.9		72
140.27	odd	4		140.2.w.b.67.8	yes	72
140.47	odd	12		140.2.w.b.107.18	yes	72
140.67	even	12		980.2.k.j.687.6		36
140.83	odd	4		700.2.be.e.207.11		72
140.87	odd	12		980.2.k.k.687.6		36
140.103	odd	12		700.2.be.e.107.1		72
140.107	even	12	inner	980.2.x.m.667.18		72
140.139	even	2		700.2.be.e.543.3		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.8	✓	72	7.5	odd	6
140.2.w.b.23.10	yes	72	28.19	even	6
140.2.w.b.67.8	yes	72	140.27	odd	4
140.2.w.b.67.10	yes	72	35.27	even	4
140.2.w.b.107.16	yes	72	35.12	even	12
140.2.w.b.107.18	yes	72	140.47	odd	12
140.2.w.b.123.16	yes	72	28.27	even	2
140.2.w.b.123.18	yes	72	7.6	odd	2
700.2.be.e.107.1		72	140.103	odd	12
700.2.be.e.107.3		72	35.33	even	12
700.2.be.e.207.9		72	35.13	even	4
700.2.be.e.207.11		72	140.83	odd	4
700.2.be.e.443.9		72	140.19	even	6
700.2.be.e.443.11		72	35.19	odd	6
700.2.be.e.543.1		72	35.34	odd	2
700.2.be.e.543.3		72	140.139	even	2
980.2.k.j.687.5		36	35.32	odd	12
980.2.k.j.687.6		36	140.67	even	12
980.2.k.j.883.5		36	28.11	odd	6
980.2.k.j.883.6		36	7.4	even	3
980.2.k.k.687.5		36	35.17	even	12
980.2.k.k.687.6		36	140.87	odd	12
980.2.k.k.883.5		36	28.3	even	6
980.2.k.k.883.6		36	7.3	odd	6
980.2.x.m.67.8		72	20.7	even	4	inner
980.2.x.m.67.10		72	5.2	odd	4	inner
980.2.x.m.263.16		72	4.3	odd	2	inner
980.2.x.m.263.18		72	1.1	even	1	trivial
980.2.x.m.667.16		72	35.2	odd	12	inner
980.2.x.m.667.18		72	140.107	even	12	inner
980.2.x.m.863.8		72	7.2	even	3	inner
980.2.x.m.863.10		72	28.23	odd	6	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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41349 + 0.0450897i) q^{2} +(0.543458 + 2.02821i) q^{3} +(1.99593 + 0.127468i) q^{4} +(1.62425 + 1.53682i) q^{5} +(0.676724 + 2.89137i) q^{6} +(2.81549 + 0.270171i) q^{8} +(-1.22023 + 0.704499i) q^{9} +(2.22657 + 2.24552i) q^{10} +(0.366133 + 0.211387i) q^{11} +(0.826174 + 4.11745i) q^{12} +(1.56422 + 1.56422i) q^{13} +(-2.23429 + 4.12952i) q^{15} +(3.96750 + 0.508836i) q^{16} +(-1.18219 - 4.41198i) q^{17} +(-1.75655 + 0.940785i) q^{18} +(-3.66683 - 6.35114i) q^{19} +(3.04600 + 3.27443i) q^{20} +(0.507996 + 0.315303i) q^{22} +(-6.44210 - 1.72616i) q^{23} +(0.982138 + 5.85725i) q^{24} +(0.276371 + 4.99236i) q^{25} +(2.14049 + 2.28155i) q^{26} +(2.36225 + 2.36225i) q^{27} -4.72835i q^{29} +(-3.34435 + 5.73631i) q^{30} +(-1.70170 - 0.982474i) q^{31} +(5.58510 + 0.898130i) q^{32} +(-0.229760 + 0.857477i) q^{33} +(-1.47208 - 6.28961i) q^{34} +(-2.52529 + 1.25059i) q^{36} +(-7.20177 - 1.92971i) q^{37} +(-4.89667 - 9.14263i) q^{38} +(-2.32248 + 4.02266i) q^{39} +(4.15786 + 4.76573i) q^{40} +4.01882 q^{41} +(1.88664 - 1.88664i) q^{43} +(0.703833 + 0.468585i) q^{44} +(-3.06464 - 0.730988i) q^{45} +(-9.02804 - 2.73038i) q^{46} +(-1.70358 + 6.35786i) q^{47} +(1.12414 + 8.32348i) q^{48} +(0.165546 + 7.06913i) q^{50} +(8.30597 - 4.79545i) q^{51} +(2.92269 + 3.32147i) q^{52} +(0.780053 - 0.209015i) q^{53} +(3.23251 + 3.44554i) q^{54} +(0.269828 + 0.906026i) q^{55} +(10.8887 - 10.8887i) q^{57} +(0.213200 - 6.68350i) q^{58} +(-1.35717 + 2.35069i) q^{59} +(-4.98587 + 7.95745i) q^{60} +(-0.925760 - 1.60346i) q^{61} +(-2.36104 - 1.46545i) q^{62} +(7.85401 + 1.52133i) q^{64} +(0.136759 + 4.94461i) q^{65} +(-0.363428 + 1.20168i) q^{66} +(-8.70137 + 2.33152i) q^{67} +(-1.79718 - 8.95671i) q^{68} -14.0041i q^{69} -3.16317i q^{71} +(-3.62588 + 1.65384i) q^{72} +(-6.67113 + 1.78752i) q^{73} +(-10.0927 - 3.05236i) q^{74} +(-9.97537 + 3.27368i) q^{75} +(-6.50918 - 13.1438i) q^{76} +(-3.46420 + 5.58129i) q^{78} +(1.77995 + 3.08296i) q^{79} +(5.66223 + 6.92381i) q^{80} +(-5.62086 + 9.73561i) q^{81} +(5.68058 + 0.181207i) q^{82} +(-4.71846 + 4.71846i) q^{83} +(4.86025 - 8.98296i) q^{85} +(2.75182 - 2.58169i) q^{86} +(9.59011 - 2.56966i) q^{87} +(0.973735 + 0.694078i) q^{88} +(-10.0333 + 5.79271i) q^{89} +(-4.29889 - 1.17143i) q^{90} +(-12.6380 - 4.26646i) q^{92} +(1.06787 - 3.98534i) q^{93} +(-2.69468 + 8.90999i) q^{94} +(3.80470 - 15.9511i) q^{95} +(1.21367 + 11.8159i) q^{96} +(4.64008 - 4.64008i) q^{97} -0.595688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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