LMFDB - Embedded newform 975.2.bn.d.218.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			218.11
Character	$\chi$	$=$	975.218
Dual form			975.2.bn.d.407.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.254998 - 0.0683265i) q^{2} +(-1.56121 - 0.750075i) q^{3} +(-1.67170 - 0.965154i) q^{4} +(0.346856 + 0.297940i) q^{6} +(-3.34011 + 0.894980i) q^{7} +(0.733676 + 0.733676i) q^{8} +(1.87477 + 2.34206i) q^{9} +(0.378689 + 0.655909i) q^{11} +(1.88593 + 2.76071i) q^{12} +(-3.19278 + 1.67516i) q^{13} +0.912873 q^{14} +(1.79335 + 3.10618i) q^{16} +(7.08724 - 1.89902i) q^{17} +(-0.318039 - 0.725316i) q^{18} +(-2.37830 + 4.11934i) q^{19} +(5.88593 + 1.10808i) q^{21} +(-0.0517490 - 0.193130i) q^{22} +(-1.15395 - 0.309199i) q^{23} +(-0.595113 - 1.69574i) q^{24} +(0.928610 - 0.209011i) q^{26} +(-1.17020 - 5.06267i) q^{27} +(6.44744 + 1.72759i) q^{28} +(-3.57287 - 6.18840i) q^{29} -3.75546i q^{31} +(-0.782155 - 2.91904i) q^{32} +(-0.0992334 - 1.30806i) q^{33} -1.93698 q^{34} +(-0.873607 - 5.72465i) q^{36} +(0.717836 - 2.67900i) q^{37} +(0.887922 - 0.887922i) q^{38} +(6.24111 - 0.220453i) q^{39} +(2.69593 + 4.66949i) q^{41} +(-1.42519 - 0.684723i) q^{42} +(-5.52432 + 1.48024i) q^{43} -1.46197i q^{44} +(0.273128 + 0.157690i) q^{46} +(2.28189 - 2.28189i) q^{47} +(-0.469938 - 6.19455i) q^{48} +(4.29318 - 2.47867i) q^{49} +(-12.4891 - 2.35119i) q^{51} +(6.95414 + 0.281170i) q^{52} +(5.30126 - 5.30126i) q^{53} +(-0.0475149 + 1.37093i) q^{54} +(-3.10719 - 1.79394i) q^{56} +(6.80285 - 4.64726i) q^{57} +(0.488244 + 1.82215i) q^{58} +(4.58287 + 2.64592i) q^{59} +(-1.28268 + 2.22167i) q^{61} +(-0.256597 + 0.957635i) q^{62} +(-8.35805 - 6.14484i) q^{63} -6.37561i q^{64} +(-0.0640708 + 0.340333i) q^{66} +(1.50179 - 5.60475i) q^{67} +(-13.6805 - 3.66569i) q^{68} +(1.56964 + 1.34827i) q^{69} +(-0.328162 + 0.568393i) q^{71} +(-0.342833 + 3.09379i) q^{72} +(8.39721 - 8.39721i) q^{73} +(-0.366094 + 0.634093i) q^{74} +(7.95159 - 4.59085i) q^{76} +(-1.85189 - 1.85189i) q^{77} +(-1.60653 - 0.370218i) q^{78} -6.35343i q^{79} +(-1.97045 + 8.78165i) q^{81} +(-0.368407 - 1.37491i) q^{82} +(2.33630 + 2.33630i) q^{83} +(-8.77001 - 7.53320i) q^{84} +1.50983 q^{86} +(0.936252 + 12.3413i) q^{87} +(-0.203390 + 0.759060i) q^{88} +(9.05197 - 5.22616i) q^{89} +(9.16501 - 8.45269i) q^{91} +(1.63062 + 1.63062i) q^{92} +(-2.81688 + 5.86307i) q^{93} +(-0.737790 + 0.425963i) q^{94} +(-0.968391 + 5.14392i) q^{96} +(-8.55305 + 2.29178i) q^{97} +(-1.26411 + 0.338717i) q^{98} +(-0.826218 + 2.11659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.254998	−	0.0683265i	−0.180311	−	0.0483141i	0.167534	−	0.985866i	$-0.446420\pi$
$2$	−0.254998	−	0.0683265i	−0.180311	−	0.0483141i	−0.347845	+	0.937552i	$0.613086\pi$
$3$	−1.56121	−	0.750075i	−0.901367	−	0.433056i
$3$	−1.56121	−	0.750075i	−0.901367	−	0.433056i
$4$	−1.67170	−	0.965154i	−0.835848	−	0.482577i
$5$		0			0
$5$		0			0
$6$	0.346856	+	0.297940i	0.141603	+	0.121634i
$7$	−3.34011	+	0.894980i	−1.26244	+	0.338271i	−0.827131	−	0.562009i	$-0.810029\pi$
$7$	−3.34011	+	0.894980i	−1.26244	+	0.338271i	−0.435312	+	0.900280i	$0.643362\pi$
$8$	0.733676	+	0.733676i	0.259394	+	0.259394i
$9$	1.87477	+	2.34206i	0.624925	+	0.780685i
$10$		0			0
$11$	0.378689	+	0.655909i	0.114179	+	0.197764i	0.917451	−	0.397848i	$-0.130243\pi$
$11$	0.378689	+	0.655909i	0.114179	+	0.197764i	−0.803272	+	0.595612i	$0.796910\pi$
$12$	1.88593	+	2.76071i	0.544423	+	0.796948i
$13$	−3.19278	+	1.67516i	−0.885518	+	0.464605i
$13$	−3.19278	+	1.67516i	−0.885518	+	0.464605i
$14$	0.912873			0.243975
$15$		0			0
$16$	1.79335	+	3.10618i	0.448338	+	0.776544i
$17$	7.08724	−	1.89902i	1.71891	−	0.460580i	0.741327	−	0.671144i	$-0.234197\pi$
$17$	7.08724	−	1.89902i	1.71891	−	0.460580i	0.977580	+	0.210564i	$0.0675299\pi$
$18$	−0.318039	−	0.725316i	−0.0749625	−	0.170959i
$19$	−2.37830	+	4.11934i	−0.545620	+	0.945041i	0.452948	+	0.891537i	$0.350372\pi$
$19$	−2.37830	+	4.11934i	−0.545620	+	0.945041i	−0.998568	+	0.0535042i	$0.982961\pi$
$20$		0			0
$21$	5.88593	+	1.10808i	1.28442	+	0.241803i
$22$	−0.0517490	−	0.193130i	−0.0110329	−	0.0411754i
$23$	−1.15395	−	0.309199i	−0.240615	−	0.0644725i	0.136496	−	0.990641i	$-0.456416\pi$
$23$	−1.15395	−	0.309199i	−0.240615	−	0.0644725i	−0.377111	+	0.926168i	$0.623082\pi$
$24$	−0.595113	−	1.69574i	−0.121477	−	0.346141i
$25$		0			0
$26$	0.928610	−	0.209011i	0.182115	−	0.0409903i
$27$	−1.17020	−	5.06267i	−0.225206	−	0.974311i
$28$	6.44744	+	1.72759i	1.21845	+	0.326483i
$29$	−3.57287	−	6.18840i	−0.663466	−	1.14916i	−0.979699	−	0.200475i	$-0.935751\pi$
$29$	−3.57287	−	6.18840i	−0.663466	−	1.14916i	0.316233	−	0.948682i	$-0.397582\pi$
$30$		0			0
$31$		−	3.75546i		−	0.674500i	−0.941415	−	0.337250i	$-0.890503\pi$
$31$		−	3.75546i		−	0.674500i	0.941415	−	0.337250i	$-0.109497\pi$
$32$	−0.782155	−	2.91904i	−0.138267	−	0.516019i
$33$	−0.0992334	−	1.30806i	−0.0172743	−	0.227704i
$34$	−1.93698			−0.332190
$35$		0			0
$36$	−0.873607	−	5.72465i	−0.145601	−	0.954108i
$37$	0.717836	−	2.67900i	0.118012	−	0.440425i	−0.881483	−	0.472216i	$-0.843454\pi$
$37$	0.717836	−	2.67900i	0.118012	−	0.440425i	0.999495	+	0.0317906i	$0.0101210\pi$
$38$	0.887922	−	0.887922i	0.144040	−	0.144040i
$39$	6.24111	−	0.220453i	0.999377	−	0.0353008i
$40$		0			0
$41$	2.69593	+	4.66949i	0.421033	+	0.729251i	0.996041	−	0.0888969i	$-0.0283342\pi$
$41$	2.69593	+	4.66949i	0.421033	+	0.729251i	−0.575007	+	0.818148i	$0.695001\pi$
$42$	−1.42519	−	0.684723i	−0.219911	−	0.105655i
$43$	−5.52432	+	1.48024i	−0.842451	+	0.225734i	−0.654138	−	0.756375i	$-0.726968\pi$
$43$	−5.52432	+	1.48024i	−0.842451	+	0.225734i	−0.188313	+	0.982109i	$0.560302\pi$
$44$		−	1.46197i		−	0.220401i
$45$		0			0
$46$	0.273128	+	0.157690i	0.0402705	+	0.0232502i
$47$	2.28189	−	2.28189i	0.332847	−	0.332847i	−0.520819	−	0.853667i	$-0.674374\pi$
$47$	2.28189	−	2.28189i	0.332847	−	0.332847i	0.853667	+	0.520819i	$0.174374\pi$
$48$	−0.469938	−	6.19455i	−0.0678297	−	0.894106i
$49$	4.29318	−	2.47867i	0.613311	−	0.354095i
$50$		0			0
$51$	−12.4891	−	2.35119i	−1.74882	−	0.329232i
$52$	6.95414	+	0.281170i	0.964366	+	0.0389912i
$53$	5.30126	−	5.30126i	0.728185	−	0.728185i	−0.242073	−	0.970258i	$-0.577827\pi$
$53$	5.30126	−	5.30126i	0.728185	−	0.728185i	0.970258	+	0.242073i	$0.0778275\pi$
$54$	−0.0475149	+	1.37093i	−0.00646596	+	0.186559i
$55$		0			0
$56$	−3.10719	−	1.79394i	−0.415215	−	0.239725i
$57$	6.80285	−	4.64726i	0.901060	−	0.615545i
$58$	0.488244	+	1.82215i	0.0641096	+	0.239260i
$59$	4.58287	+	2.64592i	0.596639	+	0.344470i	0.767718	−	0.640787i	$-0.221392\pi$
$59$	4.58287	+	2.64592i	0.596639	+	0.344470i	−0.171079	+	0.985257i	$0.554725\pi$
$60$		0			0
$61$	−1.28268	+	2.22167i	−0.164231	+	0.284456i	−0.936382	−	0.350983i	$-0.885847\pi$
$61$	−1.28268	+	2.22167i	−0.164231	+	0.284456i	0.772151	+	0.635439i	$0.219181\pi$
$62$	−0.256597	+	0.957635i	−0.0325879	+	0.121620i
$63$	−8.35805	−	6.14484i	−1.05301	−	0.774177i
$64$		−	6.37561i		−	0.796951i
$65$		0			0
$66$	−0.0640708	+	0.340333i	−0.00788657	+	0.0418921i
$67$	1.50179	−	5.60475i	0.183473	−	0.684729i	−0.811480	−	0.584381i	$-0.801338\pi$
$67$	1.50179	−	5.60475i	0.183473	−	0.684729i	0.994952	−	0.100349i	$-0.0319958\pi$
$68$	−13.6805	−	3.66569i	−1.65901	−	0.444530i
$69$	1.56964	+	1.34827i	0.188962	+	0.162313i
$70$		0			0
$71$	−0.328162	+	0.568393i	−0.0389456	+	0.0674558i	−0.884841	−	0.465893i	$-0.845733\pi$
$71$	−0.328162	+	0.568393i	−0.0389456	+	0.0674558i	0.845896	+	0.533349i	$0.179067\pi$
$72$	−0.342833	+	3.09379i	−0.0404033	+	0.364606i
$73$	8.39721	−	8.39721i	0.982819	−	0.982819i	−0.0170357	−	0.999855i	$-0.505423\pi$
$73$	8.39721	−	8.39721i	0.982819	−	0.982819i	0.999855	+	0.0170357i	$0.00542289\pi$
$74$	−0.366094	+	0.634093i	−0.0425575	+	0.0737118i
$75$		0			0
$76$	7.95159	−	4.59085i	0.912110	−	0.526607i
$77$	−1.85189	−	1.85189i	−0.211042	−	0.211042i
$78$	−1.60653	−	0.370218i	−0.181904	−	0.0419189i
$79$		−	6.35343i		−	0.714816i	−0.933948	−	0.357408i	$-0.883660\pi$
$79$		−	6.35343i		−	0.714816i	0.933948	−	0.357408i	$-0.116340\pi$
$80$		0			0
$81$	−1.97045	+	8.78165i	−0.218938	+	0.975739i
$82$	−0.368407	−	1.37491i	−0.0406837	−	0.151834i
$83$	2.33630	+	2.33630i	0.256442	+	0.256442i	0.823605	−	0.567163i	$-0.191959\pi$
$83$	2.33630	+	2.33630i	0.256442	+	0.256442i	−0.567163	+	0.823605i	$0.691959\pi$
$84$	−8.77001	−	7.53320i	−0.956887	−	0.821939i
$85$		0			0
$86$	1.50983			0.162809
$87$	0.936252	+	12.3413i	0.100377	+	1.32313i
$88$	−0.203390	+	0.759060i	−0.0216814	+	0.0809161i
$89$	9.05197	−	5.22616i	0.959507	−	0.553971i	0.0634855	−	0.997983i	$-0.479778\pi$
$89$	9.05197	−	5.22616i	0.959507	−	0.553971i	0.896021	+	0.444011i	$0.146445\pi$
$90$		0			0
$91$	9.16501	−	8.45269i	0.960754	−	0.886083i
$92$	1.63062	+	1.63062i	0.170004	+	0.170004i
$93$	−2.81688	+	5.86307i	−0.292097	+	0.607972i
$94$	−0.737790	+	0.425963i	−0.0760972	+	0.0439348i
$95$		0			0
$96$	−0.968391	+	5.14392i	−0.0988360	+	0.525000i
$97$	−8.55305	+	2.29178i	−0.868430	+	0.232695i	−0.665409	−	0.746479i	$-0.731743\pi$
$97$	−8.55305	+	2.29178i	−0.868430	+	0.232695i	−0.203022	+	0.979174i	$0.565076\pi$
$98$	−1.26411	+	0.338717i	−0.127694	+	0.0342156i
$99$	−0.826218	+	2.11659i	−0.0830381	+	0.212725i
$100$		0			0
$101$	10.7112	−	6.18411i	1.06580	−	0.615342i	0.138772	−	0.990324i	$-0.455685\pi$
$101$	10.7112	−	6.18411i	1.06580	−	0.615342i	0.927032	+	0.374983i	$0.122351\pi$
$102$	3.02405	+	1.45288i	0.299425	+	0.143857i
$103$	11.9113	+	11.9113i	1.17365	+	1.17365i	0.981332	+	0.192322i	$0.0616018\pi$
$103$	11.9113	+	11.9113i	1.17365	+	1.17365i	0.192322	+	0.981332i	$0.438398\pi$
$104$	−3.57149	−	1.11344i	−0.350214	−	0.109182i
$105$		0			0
$106$	−1.71403	+	0.989595i	−0.166481	+	0.0961180i
$107$	0.496016	−	1.85116i	0.0479517	−	0.178958i	−0.937797	−	0.347185i	$-0.887138\pi$
$107$	0.496016	−	1.85116i	0.0479517	−	0.178958i	0.985748	+	0.168227i	$0.0538042\pi$
$108$	−2.93003	+	9.59267i	−0.281942	+	0.923055i
$109$	7.27602			0.696916			0.348458	−	0.937324i	$-0.386705\pi$
$109$	7.27602			0.696916			0.348458	+	0.937324i	$0.386705\pi$
$110$		0			0
$111$	−3.13015	+	3.64406i	−0.297101	+	0.345879i
$112$	−8.76996	−	8.76996i	−0.828683	−	0.828683i
$113$	0.759173	+	2.83327i	0.0714170	+	0.266532i	0.992397	−	0.123078i	$-0.0392765\pi$
$113$	0.759173	+	2.83327i	0.0714170	+	0.266532i	−0.920980	+	0.389610i	$0.872610\pi$
$114$	−2.05224	+	0.720227i	−0.192210	+	0.0674555i
$115$		0			0
$116$			13.7935i			1.28069i
$117$	−9.90905	−	4.33712i	−0.916092	−	0.400967i
$118$	−0.987837	−	0.987837i	−0.0909378	−	0.0909378i
$119$	−21.9726	+	12.6859i	−2.01422	+	1.16291i
$120$		0			0
$121$	5.21319	−	9.02951i	0.473926	−	0.820864i
$122$	0.478880	−	0.478880i	0.0433558	−	0.0433558i
$123$	−0.706454	−	9.31221i	−0.0636988	−	0.839654i
$124$	−3.62460	+	6.27798i	−0.325498	+	0.563780i
$125$		0			0
$126$	1.71143	+	2.13800i	0.152466	+	0.190468i
$127$	12.3901	+	3.31991i	1.09944	+	0.294594i	0.762537	−	0.646945i	$-0.223954\pi$
$127$	12.3901	+	3.31991i	1.09944	+	0.294594i	0.336904	+	0.941539i	$0.390620\pi$
$128$	−1.99993	+	7.46386i	−0.176771	+	0.659718i
$129$	9.73493	+	1.83269i	0.857112	+	0.161359i
$130$		0			0
$131$		−	17.7409i		−	1.55003i	−0.631943	−	0.775015i	$-0.717742\pi$
$131$		−	17.7409i		−	1.55003i	0.631943	−	0.775015i	$-0.282258\pi$
$132$	−1.09659	+	2.28245i	−0.0954459	+	0.198662i
$133$	4.25707	−	15.8876i	0.369134	−	1.37763i
$134$	−0.765906	+	1.32659i	−0.0661642	+	0.114600i
$135$		0			0
$136$	6.59301	+	3.80647i	0.565346	+	0.326402i
$137$	5.55583	+	20.7346i	0.474666	+	1.77148i	0.622663	+	0.782490i	$0.286051\pi$
$137$	5.55583	+	20.7346i	0.474666	+	1.77148i	−0.147996	+	0.988988i	$0.547282\pi$
$138$	−0.308131	−	0.451055i	−0.0262299	−	0.0383964i
$139$	−8.79884	−	5.08001i	−0.746308	−	0.430881i	0.0780503	−	0.996949i	$-0.475131\pi$
$139$	−8.79884	−	5.08001i	−0.746308	−	0.430881i	−0.824358	+	0.566068i	$0.808464\pi$
$140$		0			0
$141$	−5.27410	+	1.85092i	−0.444159	+	0.155876i
$142$	0.122517	−	0.122517i	0.0102814	−	0.0102814i
$143$	−2.30782	−	1.45981i	−0.192990	−	0.122075i
$144$	−3.91271	+	10.0235i	−0.326059	+	0.835292i
$145$		0			0
$146$	−2.71502	+	1.56752i	−0.224697	+	0.129729i
$147$	−8.56175	+	0.649521i	−0.706161	+	0.0535716i
$148$	−3.78565	+	3.78565i	−0.311179	+	0.311179i
$149$	11.4427	+	6.60643i	0.937420	+	0.541220i	0.889151	−	0.457615i	$-0.151296\pi$
$149$	11.4427	+	6.60643i	0.937420	+	0.541220i	0.0482693	+	0.998834i	$0.484629\pi$
$150$		0			0
$151$			7.62730i			0.620701i	0.950622	+	0.310350i	$0.100446\pi$
$151$			7.62730i			0.620701i	−0.950622	+	0.310350i	$0.899554\pi$
$152$	−4.76717	+	1.27736i	−0.386668	+	0.103607i
$153$	17.7346	+	13.0385i	1.43376	+	1.05410i
$154$	0.345695	+	0.598761i	0.0278569	+	0.0482496i
$155$		0			0
$156$	−10.6460	−	5.65510i	−0.852362	−	0.452770i
$157$	2.99534	−	2.99534i	0.239054	−	0.239054i	−0.577404	−	0.816458i	$-0.695934\pi$
$157$	2.99534	−	2.99534i	0.239054	−	0.239054i	0.816458	+	0.577404i	$0.195934\pi$
$158$	−0.434108	+	1.62011i	−0.0345357	+	0.128889i
$159$	−12.2528	+	4.30006i	−0.971706	+	0.341017i
$160$		0			0
$161$	4.13104			0.325572
$162$	1.10248	−	2.10467i	0.0866190	−	0.165358i
$163$	4.23491	+	15.8049i	0.331704	+	1.23794i	0.907399	+	0.420271i	$0.138065\pi$
$163$	4.23491	+	15.8049i	0.331704	+	1.23794i	−0.575695	+	0.817665i	$0.695268\pi$
$164$		−	10.4079i		−	0.812724i
$165$		0			0
$166$	−0.436121	−	0.755383i	−0.0338495	−	0.0586291i
$167$	−7.96743	−	2.13487i	−0.616538	−	0.165201i	−0.0629845	−	0.998015i	$-0.520062\pi$
$167$	−7.96743	−	2.13487i	−0.616538	−	0.165201i	−0.553553	+	0.832814i	$0.686729\pi$
$168$	3.50539	+	5.13134i	0.270447	+	0.395891i
$169$	7.38769	−	10.6968i	0.568284	−	0.822833i
$170$		0			0
$171$	−14.1065	+	2.15272i	−1.07875	+	0.164622i
$172$	10.6636	+	2.85731i	0.813094	+	0.217868i
$173$	−3.14446	−	11.7353i	−0.239069	−	0.892217i	−0.976272	−	0.216546i	$-0.930521\pi$
$173$	−3.14446	−	11.7353i	−0.239069	−	0.892217i	0.737204	−	0.675671i	$-0.236146\pi$
$174$	0.604498	−	3.21099i	0.0458269	−	0.243424i
$175$		0			0
$176$	−1.35825	+	2.35255i	−0.102382	+	0.177330i
$177$	−5.17020	−	7.56835i	−0.388616	−	0.568872i
$178$	−2.66532	+	0.714170i	−0.199774	+	0.0535293i
$179$	6.88190	+	11.9198i	0.514377	+	0.890927i	0.999861	+	0.0166817i	$0.00531018\pi$
$179$	6.88190	+	11.9198i	0.514377	+	0.890927i	−0.485484	+	0.874246i	$0.661356\pi$
$180$		0			0
$181$	−5.09406			−0.378639			−0.189319	−	0.981916i	$-0.560628\pi$
$181$	−5.09406			−0.378639			−0.189319	+	0.981916i	$0.560628\pi$
$182$	−2.91460	+	1.52921i	−0.216045	+	0.113352i
$183$	3.66896	−	2.50639i	0.271217	−	0.185278i
$184$	−0.619772	−	1.07348i	−0.0456902	−	0.0791378i
$185$		0			0
$186$	1.11890	−	1.30260i	0.0820419	−	0.0955116i
$187$	3.92944	+	3.92944i	0.287349	+	0.287349i
$188$	−6.01699	+	1.61225i	−0.438834	+	0.117585i
$189$	8.43960	+	15.8626i	0.613891	+	1.15383i
$190$		0			0
$191$	−7.24923	−	4.18535i	−0.524536	−	0.302841i	0.214252	−	0.976778i	$-0.431268\pi$
$191$	−7.24923	−	4.18535i	−0.524536	−	0.302841i	−0.738789	+	0.673937i	$0.764602\pi$
$192$	−4.78219	+	9.95369i	−0.345125	+	0.718346i
$193$	7.26170	+	1.94577i	0.522708	+	0.140059i	0.510519	−	0.859866i	$-0.329453\pi$
$193$	7.26170	+	1.94577i	0.522708	+	0.140059i	0.0121893	+	0.999926i	$0.496120\pi$
$194$	2.33760			0.167830
$195$		0			0
$196$	−9.56918			−0.683513
$197$	−18.0324	−	4.83176i	−1.28475	−	0.344249i	−0.449089	−	0.893487i	$-0.648251\pi$
$197$	−18.0324	−	4.83176i	−1.28475	−	0.344249i	−0.835666	+	0.549238i	$0.814918\pi$
$198$	0.355303	−	0.483274i	0.0252503	−	0.0343448i
$199$	−0.308520	−	0.178124i	−0.0218704	−	0.0126269i	0.489025	−	0.872270i	$-0.337353\pi$
$199$	−0.308520	−	0.178124i	−0.0218704	−	0.0126269i	−0.510895	+	0.859643i	$0.670686\pi$
$200$		0			0
$201$	−6.54860	+	7.62376i	−0.461902	+	0.537738i
$202$	−3.15387	+	0.845077i	−0.221906	+	0.0594594i
$203$	17.4723	+	17.4723i	1.22631	+	1.22631i
$204$	18.6087	+	15.9844i	1.30287	+	1.11913i
$205$		0			0
$206$	−2.22350	−	3.85121i	−0.154918	−	0.268327i
$207$	−1.43923	−	3.28229i	−0.100033	−	0.228135i
$208$	−10.9291	−	6.91319i	−0.757797	−	0.479343i
$209$	−3.60255			−0.249193
$210$		0			0
$211$	4.03683	+	6.99199i	0.277907	+	0.481349i	0.970864	−	0.239630i	$-0.0770260\pi$
$211$	4.03683	+	6.99199i	0.277907	+	0.481349i	−0.692958	+	0.720978i	$0.743693\pi$
$212$	−13.9786	+	3.74556i	−0.960056	+	0.257246i
$213$	0.938668	−	0.641236i	0.0643165	−	0.0439368i
$214$	−0.252966	+	0.438150i	−0.0172924	+	0.0299513i
$215$		0			0
$216$	2.85581	−	4.57291i	0.194313	−	0.311147i
$217$	3.36106	+	12.5437i	0.228164	+	0.851519i
$218$	−1.85537	−	0.497145i	−0.125662	−	0.0336709i
$219$	−19.4084	+	6.81130i	−1.31150	+	0.460265i
$220$		0			0
$221$	−19.4468	+	17.9354i	−1.30814	+	1.20647i
$222$	1.04717	−	0.715356i	0.0702813	−	0.0480116i
$223$	−5.60827	−	1.50273i	−0.375557	−	0.100630i	0.0661025	−	0.997813i	$-0.478944\pi$
$223$	−5.60827	−	1.50273i	−0.375557	−	0.100630i	−0.441660	+	0.897183i	$0.645610\pi$
$224$	5.22497	+	9.04992i	0.349108	+	0.604673i
$225$		0			0
$226$		−	0.774351i		−	0.0515091i
$227$	1.34293	+	5.01188i	0.0891333	+	0.332650i	0.996065	−	0.0886282i	$-0.0282483\pi$
$227$	1.34293	+	5.01188i	0.0891333	+	0.332650i	−0.906931	+	0.421278i	$0.861582\pi$
$228$	−15.8576	+	1.20301i	−1.05020	+	0.0796712i
$229$	−16.0682			−1.06182			−0.530908	−	0.847429i	$-0.678149\pi$
$229$	−16.0682			−1.06182			−0.530908	+	0.847429i	$0.678149\pi$
$230$		0			0
$231$	1.50214	+	4.28025i	0.0988334	+	0.281620i
$232$	1.91895	−	7.16161i	0.125985	−	0.470183i
$233$	5.72175	−	5.72175i	0.374844	−	0.374844i	−0.494394	−	0.869238i	$-0.664610\pi$
$233$	5.72175	−	5.72175i	0.374844	−	0.374844i	0.869238	+	0.494394i	$0.164610\pi$
$234$	2.23045	+	1.78301i	0.145809	+	0.116559i
$235$		0			0
$236$	−5.10745	−	8.84636i	−0.332466	−	0.575849i
$237$	−4.76555	+	9.91906i	−0.309556	+	0.644312i
$238$	6.46975	−	1.73356i	0.419371	−	0.112370i
$239$		−	14.1799i		−	0.917222i	−0.888637	−	0.458611i	$-0.848347\pi$
$239$		−	14.1799i		−	0.917222i	0.888637	−	0.458611i	$-0.151653\pi$
$240$		0			0
$241$	−1.38091	−	0.797270i	−0.0889523	−	0.0513567i	0.454864	−	0.890561i	$-0.349688\pi$
$241$	−1.38091	−	0.797270i	−0.0889523	−	0.0513567i	−0.543816	+	0.839204i	$0.683021\pi$
$242$	−1.94631	+	1.94631i	−0.125113	+	0.125113i
$243$	9.66318	−	12.2320i	0.619894	−	0.784686i
$244$	4.28851	−	2.47597i	0.274543	−	0.158508i
$245$		0			0
$246$	−0.456127	+	2.42287i	−0.0290816	+	0.154476i
$247$	0.692849	−	17.1362i	0.0440849	−	1.09035i
$248$	2.75529	−	2.75529i	0.174961	−	0.174961i
$249$	−1.89506	−	5.39987i	−0.120095	−	0.342203i
$250$		0			0
$251$	−10.7131	−	6.18523i	−0.676207	−	0.390408i	0.122217	−	0.992503i	$-0.461000\pi$
$251$	−10.7131	−	6.18523i	−0.676207	−	0.390408i	−0.798424	+	0.602095i	$0.794333\pi$
$252$	8.04139	+	18.3391i	0.506560	+	1.15525i
$253$	−0.234181	−	0.873975i	−0.0147228	−	0.0549463i
$254$	−2.93260	−	1.69314i	−0.184008	−	0.106237i
$255$		0			0
$256$	−5.35565	+	9.27626i	−0.334728	+	0.579766i
$257$	4.49358	−	16.7703i	0.280302	−	1.04610i	−0.671903	−	0.740639i	$-0.734523\pi$
$257$	4.49358	−	16.7703i	0.280302	−	1.04610i	0.952205	−	0.305461i	$-0.0988105\pi$
$258$	−2.35717	−	1.13249i	−0.146751	−	0.0705055i
$259$			9.59061i			0.595932i
$260$		0			0
$261$	7.79524	−	19.9697i	0.482513	−	1.23609i
$262$	−1.21217	+	4.52390i	−0.0748884	+	0.279487i
$263$	16.9287	+	4.53603i	1.04387	+	0.279704i	0.739716	−	0.672920i	$-0.234960\pi$
$263$	16.9287	+	4.53603i	1.04387	+	0.279704i	0.304153	+	0.952623i	$0.401627\pi$
$264$	0.886887	−	1.03250i	0.0545841	−	0.0635458i
$265$		0			0
$266$	−2.17109	+	3.76043i	−0.133118	+	0.230567i
$267$	−18.0521	+	1.36949i	−1.10477	+	0.0838112i
$268$	−7.91998	+	7.91998i	−0.483790	+	0.483790i
$269$	−2.88285	+	4.99325i	−0.175771	+	0.304444i	−0.940428	−	0.339994i	$-0.889575\pi$
$269$	−2.88285	+	4.99325i	−0.175771	+	0.304444i	0.764657	+	0.644437i	$0.222908\pi$
$270$		0			0
$271$	18.2632	−	10.5443i	1.10941	−	0.640518i	0.170733	−	0.985317i	$-0.445386\pi$
$271$	18.2632	−	10.5443i	1.10941	−	0.640518i	0.938676	+	0.344800i	$0.112053\pi$
$272$	18.6086	+	18.6086i	1.12831	+	1.12831i
$273$	−20.6487	+	6.32201i	−1.24972	+	0.382625i
$274$		−	5.66690i		−	0.342350i
$275$		0			0
$276$	−1.32266	−	3.76884i	−0.0796149	−	0.226858i
$277$	1.43776	+	5.36578i	0.0863865	+	0.322399i	0.995573	−	0.0939901i	$-0.0299622\pi$
$277$	1.43776	+	5.36578i	0.0863865	+	0.322399i	−0.909187	+	0.416389i	$0.863296\pi$
$278$	1.89659	+	1.89659i	0.113750	+	0.113750i
$279$	8.79549	−	7.04064i	0.526572	−	0.421512i
$280$		0			0
$281$	13.3268			0.795013			0.397506	−	0.917599i	$-0.369876\pi$
$281$	13.3268			0.795013			0.397506	+	0.917599i	$0.369876\pi$
$282$	1.47135	−	0.111621i	0.0876177	−	0.00664696i
$283$	3.60372	−	13.4493i	0.214219	−	0.799475i	−0.772221	−	0.635354i	$-0.780854\pi$
$283$	3.60372	−	13.4493i	0.214219	−	0.799475i	0.986440	−	0.164122i	$-0.0524789\pi$
$284$	1.09717	−	0.633453i	0.0651052	−	0.0375885i
$285$		0			0
$286$	0.488746	+	0.529934i	0.0289002	+	0.0313356i
$287$	−13.1838	−	13.1838i	−0.778215	−	0.778215i
$288$	5.37020	−	7.30440i	0.316442	−	0.430416i
$289$	31.9002	−	18.4176i	1.87648	−	1.08339i
$290$		0			0
$291$	15.0721	+	2.83747i	0.883545	+	0.166335i
$292$	−22.1422	+	5.93298i	−1.29577	+	0.347201i
$293$	14.4405	−	3.86933i	0.843626	−	0.226049i	0.188976	−	0.981982i	$-0.439483\pi$
$293$	14.4405	−	3.86933i	0.843626	−	0.226049i	0.654649	+	0.755933i	$0.272816\pi$
$294$	2.22761	+	0.419368i	0.129917	+	0.0244580i
$295$		0			0
$296$	2.49218	−	1.43886i	0.144855	−	0.0836321i
$297$	2.87751	−	2.68472i	0.166970	−	0.155784i
$298$	−2.46646	−	2.46646i	−0.142878	−	0.142878i
$299$	4.20226	−	0.945840i	0.243023	−	0.0546993i
$300$		0			0
$301$	17.1271	−	9.88831i	0.987187	−	0.569953i
$302$	0.521147	−	1.94495i	0.0299886	−	0.111919i
$303$	−21.3610	+	1.62051i	−1.22716	+	0.0930960i
$304$	−17.0605			−0.978488
$305$		0			0
$306$	−3.63141	−	4.53653i	−0.207594	−	0.259336i
$307$	7.71849	+	7.71849i	0.440517	+	0.440517i	0.892186	−	0.451668i	$-0.149171\pi$
$307$	7.71849	+	7.71849i	0.440517	+	0.440517i	−0.451668	+	0.892186i	$0.649171\pi$
$308$	1.30844	+	4.88315i	0.0745551	+	0.278243i
$309$	−9.66170	−	27.5304i	−0.549635	−	1.56615i
$310$		0			0
$311$		−	4.84533i		−	0.274753i	−0.990519	−	0.137377i	$-0.956133\pi$
$311$		−	4.84533i		−	0.274753i	0.990519	−	0.137377i	$-0.0438671\pi$
$312$	4.74069	+	4.41721i	0.268389	+	0.250075i
$313$	1.11868	+	1.11868i	0.0632313	+	0.0632313i	0.738015	−	0.674784i	$-0.235763\pi$
$313$	1.11868	+	1.11868i	0.0632313	+	0.0632313i	−0.674784	+	0.738015i	$0.735763\pi$
$314$	−0.968466	+	0.559144i	−0.0546537	+	0.0315543i
$315$		0			0
$316$	−6.13203	+	10.6210i	−0.344954	+	0.597478i
$317$	3.06846	−	3.06846i	0.172342	−	0.172342i	−0.615666	−	0.788007i	$-0.711113\pi$
$317$	3.06846	−	3.06846i	0.172342	−	0.172342i	0.788007	+	0.615666i	$0.211113\pi$
$318$	3.41824	−	0.259318i	0.191685	−	0.0145418i
$319$	2.70602	−	4.68696i	0.151508	−	0.262419i
$320$		0			0
$321$	−2.16289	+	2.51800i	−0.120721	+	0.140541i
$322$	−1.05341	−	0.282260i	−0.0587041	−	0.0157297i
$323$	−9.03288	+	33.7112i	−0.502603	+	1.87574i
$324$	11.7696	−	12.7785i	0.653868	−	0.709914i
$325$		0			0
$326$		−	4.31958i		−	0.239239i
$327$	−11.3594	−	5.45756i	−0.628177	−	0.301804i
$328$	−1.44795	+	5.40383i	−0.0799498	+	0.298377i
$329$	−5.57951	+	9.66400i	−0.307608	+	0.532794i
$330$		0			0
$331$	−13.7926	−	7.96315i	−0.758109	−	0.437694i	0.0705077	−	0.997511i	$-0.477538\pi$
$331$	−13.7926	−	7.96315i	−0.758109	−	0.437694i	−0.828616	+	0.559817i	$0.810871\pi$
$332$	−1.65069	−	6.16047i	−0.0905936	−	0.338100i
$333$	7.62015	−	3.34131i	0.417582	−	0.183103i
$334$	1.88581	+	1.08877i	0.103187	+	0.0595750i
$335$		0			0
$336$	7.11364	+	20.2699i	0.388081	+	1.10581i
$337$	−5.75666	+	5.75666i	−0.313585	+	0.313585i	−0.846297	−	0.532712i	$-0.821173\pi$
$337$	−5.75666	+	5.75666i	−0.313585	+	0.313585i	0.532712	+	0.846297i	$0.321173\pi$
$338$	−2.61472	+	2.22289i	−0.142222	+	0.120909i
$339$	0.939937	−	4.99278i	0.0510504	−	0.271171i
$340$		0			0
$341$	2.46324	−	1.42215i	0.133392	−	0.0770138i
$342$	3.74422	+	0.414910i	0.202464	+	0.0224357i
$343$	4.99459	−	4.99459i	0.269682	−	0.269682i
$344$	−5.13908	−	2.96705i	−0.277080	−	0.159972i
$345$		0			0
$346$			3.20732i			0.172427i
$347$	−2.62597	+	0.703627i	−0.140970	+	0.0377727i	−0.328614	−	0.944464i	$-0.606581\pi$
$347$	−2.62597	+	0.703627i	−0.140970	+	0.0377727i	0.187644	+	0.982237i	$0.439915\pi$
$348$	10.3462	−	21.5346i	0.554612	−	1.15437i
$349$	10.1053	+	17.5028i	0.540922	+	0.936905i	0.998851	+	0.0479160i	$0.0152580\pi$
$349$	10.1053	+	17.5028i	0.540922	+	0.936905i	−0.457929	+	0.888989i	$0.651409\pi$
$350$		0			0
$351$	12.2170	+	14.2037i	0.652094	+	0.758138i
$352$	1.61843	−	1.61843i	0.0862627	−	0.0862627i
$353$	7.55673	−	28.2021i	0.402204	−	1.50105i	−0.406951	−	0.913450i	$-0.633408\pi$
$353$	7.55673	−	28.2021i	0.402204	−	1.50105i	0.809155	−	0.587596i	$-0.199925\pi$
$354$	0.801272	+	2.28318i	0.0425871	+	0.121349i
$355$		0			0
$356$	−20.1762			−1.06934
$357$	43.8192	−	3.32426i	2.31916	−	0.175939i
$358$	−0.940432	−	3.50974i	−0.0497034	−	0.185496i
$359$		−	29.4575i		−	1.55471i	−0.629063	−	0.777355i	$-0.716561\pi$
$359$		−	29.4575i		−	1.55471i	0.629063	−	0.777355i	$-0.283439\pi$
$360$		0			0
$361$	−1.81264	−	3.13958i	−0.0954020	−	0.165241i
$362$	1.29898	+	0.348060i	0.0682727	+	0.0182936i
$363$	−14.9117	+	10.1867i	−0.782662	+	0.534663i
$364$	−23.4792	+	5.28468i	−1.23065	+	0.276993i
$365$		0			0
$366$	−1.10683	+	0.388438i	−0.0578549	+	0.0203040i
$367$	−6.21790	−	1.66608i	−0.324572	−	0.0869688i	0.0928540	−	0.995680i	$-0.470401\pi$
$367$	−6.21790	−	1.66608i	−0.324572	−	0.0869688i	−0.417426	+	0.908711i	$0.637068\pi$
$368$	−1.10901	−	4.13887i	−0.0578109	−	0.215753i
$369$	−5.88194	+	15.0682i	−0.306201	+	0.784422i
$370$		0			0
$371$	−12.9623	+	22.4513i	−0.672968	+	1.16562i
$372$	10.3677	−	7.08255i	0.537542	−	0.367213i
$373$	−9.33338	+	2.50087i	−0.483264	+	0.129490i	−0.492222	−	0.870470i	$-0.663815\pi$
$373$	−9.33338	+	2.50087i	−0.483264	+	0.129490i	0.00895787	+	0.999960i	$0.497149\pi$
$374$	−0.733515	−	1.27049i	−0.0379292	−	0.0656952i
$375$		0			0
$376$	3.34833			0.172677
$377$	21.7739	+	13.7731i	1.12142	+	0.709349i
$378$	−1.06825	−	4.62157i	−0.0549447	−	0.237708i
$379$	7.67284	+	13.2897i	0.394127	+	0.682649i	0.992989	−	0.118204i	$-0.0377136\pi$
$379$	7.67284	+	13.2897i	0.394127	+	0.682649i	−0.598862	+	0.800852i	$0.704380\pi$
$380$		0			0
$381$	−16.8534	−	14.4766i	−0.863423	−	0.741657i
$382$	1.56257	+	1.56257i	0.0799481	+	0.0799481i
$383$	−21.8543	+	5.85583i	−1.11670	+	0.299219i	−0.769548	−	0.638589i	$-0.779518\pi$
$383$	−21.8543	+	5.85583i	−1.11670	+	0.299219i	−0.347153	+	0.937808i	$0.612852\pi$
$384$	8.72078	−	10.1526i	0.445030	−	0.518096i
$385$		0			0
$386$	−1.71877	−	0.992333i	−0.0874832	−	0.0505084i
$387$	−13.8236	−	10.1631i	−0.702695	−	0.516622i
$388$	16.5100	+	4.42384i	0.838169	+	0.224587i
$389$	−11.0104			−0.558251			−0.279126	−	0.960255i	$-0.590045\pi$
$389$	−11.0104			−0.558251			−0.279126	+	0.960255i	$0.590045\pi$
$390$		0			0
$391$	−8.76548			−0.443289
$392$	4.96834	+	1.33126i	0.250939	+	0.0672390i
$393$	−13.3070	+	27.6973i	−0.671250	+	1.39715i
$394$	4.26809	+	2.46418i	0.215023	+	0.124144i
$395$		0			0
$396$	3.42402	−	2.74087i	0.172064	−	0.137734i
$397$	7.77969	−	2.08456i	0.390451	−	0.104621i	−0.0582519	−	0.998302i	$-0.518553\pi$
$397$	7.77969	−	2.08456i	0.390451	−	0.104621i	0.448703	+	0.893681i	$0.351886\pi$
$398$	0.0665015	+	0.0665015i	0.00333342	+	0.00333342i
$399$	−18.5631	+	21.6108i	−0.929316	+	1.08189i
$400$		0			0
$401$	18.6776	+	32.3506i	0.932716	+	1.61551i	0.778656	+	0.627451i	$0.215902\pi$
$401$	18.6776	+	32.3506i	0.932716	+	1.61551i	0.154060	+	0.988061i	$0.450765\pi$
$402$	2.19078	−	1.49660i	0.109266	−	0.0746436i
$403$	6.29099	+	11.9904i	0.313376	+	0.597282i
$404$	−23.8745			−1.18780
$405$		0			0
$406$	−3.26158	−	5.64922i	−0.161869	−	0.280366i
$407$	2.02902	−	0.543674i	0.100575	−	0.0269489i
$408$	−7.43795	−	10.8880i	−0.368233	−	0.539035i
$409$	−6.94769	+	12.0338i	−0.343541	+	0.595031i	−0.985088	−	0.172053i	$-0.944960\pi$
$409$	−6.94769	+	12.0338i	−0.343541	+	0.595031i	0.641546	+	0.767084i	$0.278293\pi$
$410$		0			0
$411$	6.87870	−	36.5385i	0.339301	−	1.80231i
$412$	−8.41582	−	31.4083i	−0.414618	−	1.54737i
$413$	−17.6754	−	4.73610i	−0.869748	−	0.233048i
$414$	0.142733	+	0.935315i	0.00701496	+	0.0459682i
$415$		0			0
$416$	7.38711	+	8.00963i	0.362183	+	0.392704i
$417$	9.92648	+	14.5308i	0.486102	+	0.711575i
$418$	0.918643	+	0.246150i	0.0449323	+	0.0120396i
$419$	16.7332	+	28.9828i	0.817472	+	1.41590i	0.907539	+	0.419967i	$0.137958\pi$
$419$	16.7332	+	28.9828i	0.817472	+	1.41590i	−0.0900677	+	0.995936i	$0.528708\pi$
$420$		0			0
$421$			16.6235i			0.810182i	0.914276	+	0.405091i	$0.132760\pi$
$421$			16.6235i			0.810182i	−0.914276	+	0.405091i	$0.867240\pi$
$422$	−0.551645	−	2.05877i	−0.0268537	−	0.100219i
$423$	9.62233	+	1.06628i	0.467854	+	0.0518445i
$424$	7.77882			0.377773
$425$		0			0
$426$	−0.283172	+	0.0993781i	−0.0137197	+	0.00481489i
$427$	2.29595	−	8.56860i	0.111109	−	0.414664i
$428$	−2.61584	+	2.61584i	−0.126441	+	0.126441i
$429$	2.50804	+	4.01011i	0.121089	+	0.193610i
$430$		0			0
$431$	−17.3517	−	30.0540i	−0.835801	−	1.44765i	−0.893377	−	0.449309i	$-0.851670\pi$
$431$	−17.3517	−	30.0540i	−0.835801	−	1.44765i	0.0575757	−	0.998341i	$-0.481663\pi$
$432$	13.6270	−	12.7140i	0.655627	−	0.611703i
$433$	20.4894	−	5.49011i	0.984656	−	0.263838i	0.269652	−	0.962958i	$-0.413091\pi$
$433$	20.4894	−	5.49011i	0.984656	−	0.263838i	0.715004	+	0.699120i	$0.246425\pi$
$434$		−	3.42826i		−	0.164562i
$435$		0			0
$436$	−12.1633	−	7.02248i	−0.582516	−	0.336316i
$437$	4.01813	−	4.01813i	0.192213	−	0.192213i
$438$	5.41449	−	0.410760i	0.258714	−	0.0196269i
$439$	−15.3686	+	8.87309i	−0.733505	+	0.423489i	−0.819703	−	0.572789i	$-0.805862\pi$
$439$	−15.3686	+	8.87309i	−0.733505	+	0.423489i	0.0861981	+	0.996278i	$0.472528\pi$
$440$		0			0
$441$	13.8539	+	5.40792i	0.659710	+	0.257520i
$442$	6.18437	−	3.24476i	0.294160	−	0.154337i
$443$	12.3374	−	12.3374i	0.586169	−	0.586169i	−0.350422	−	0.936592i	$-0.613962\pi$
$443$	12.3374	−	12.3374i	0.586169	−	0.586169i	0.936592	+	0.350422i	$0.113962\pi$
$444$	8.74973	−	3.07069i	0.415244	−	0.145728i
$445$		0			0
$446$	1.32742	+	0.766387i	0.0628552	+	0.0362895i
$447$	−12.9091	−	18.8969i	−0.610581	−	0.893793i
$448$	5.70605	+	21.2953i	0.269585	+	1.00611i
$449$	11.9704	+	6.91114i	0.564920	+	0.326157i	0.755118	−	0.655589i	$-0.227580\pi$
$449$	11.9704	+	6.91114i	0.564920	+	0.326157i	−0.190198	+	0.981746i	$0.560913\pi$
$450$		0			0
$451$	−2.04184	+	3.53657i	−0.0961464	+	0.166530i
$452$	1.46544	−	5.46909i	0.0689284	−	0.257244i
$453$	5.72105	−	11.9078i	0.268798	−	0.559479i
$454$		−	1.36978i		−	0.0642868i
$455$		0			0
$456$	8.40068	+	1.58151i	0.393398	+	0.0740608i
$457$	−0.341127	+	1.27310i	−0.0159572	+	0.0595532i	−0.973445	−	0.228919i	$-0.926481\pi$
$457$	−0.341127	+	1.27310i	−0.0159572	+	0.0595532i	0.957488	+	0.288473i	$0.0931474\pi$
$458$	4.09736	+	1.09788i	0.191457	+	0.0513008i
$459$	−17.9076	−	33.6581i	−0.835856	−	1.57103i
$460$		0			0
$461$	5.56011	−	9.63039i	0.258960	−	0.448532i	−0.707003	−	0.707210i	$-0.749954\pi$
$461$	5.56011	−	9.63039i	0.258960	−	0.448532i	0.965964	+	0.258678i	$0.0832868\pi$
$462$	−0.0905875	−	1.19409i	−0.00421451	−	0.0555542i
$463$	−20.2693	+	20.2693i	−0.941994	+	0.941994i	−0.998407	−	0.0564134i	$-0.982034\pi$
$463$	−20.2693	+	20.2693i	−0.941994	+	0.941994i	0.0564134	+	0.998407i	$0.482034\pi$
$464$	12.8148	−	22.1959i	0.594914	−	1.03042i
$465$		0			0
$466$	−1.84998	+	1.06809i	−0.0856987	+	0.0494782i
$467$	−6.97119	−	6.97119i	−0.322588	−	0.322588i	0.527171	−	0.849759i	$-0.323253\pi$
$467$	−6.97119	−	6.97119i	−0.322588	−	0.322588i	−0.849759	+	0.527171i	$0.823253\pi$
$468$	12.3789	+	16.8141i	0.572216	+	0.777233i
$469$			20.0646i			0.926495i
$470$		0			0
$471$	−6.92309	+	2.42963i	−0.318999	+	0.111952i
$472$	1.42110	+	5.30360i	0.0654112	+	0.244118i
$473$	−3.06290	−	3.06290i	−0.140832	−	0.140832i
$474$	1.89294	−	2.20373i	0.0869456	−	0.101221i
$475$		0			0
$476$	48.9753			2.24478
$477$	22.3545	+	2.47718i	1.02354	+	0.113422i
$478$	−0.968864	+	3.61585i	−0.0443148	+	0.165385i
$479$	29.8923	−	17.2583i	1.36582	−	0.788554i	0.375425	−	0.926853i	$-0.377497\pi$
$479$	29.8923	−	17.2583i	1.36582	−	0.788554i	0.990391	+	0.138299i	$0.0441635\pi$
$480$		0			0
$481$	2.19586	+	9.75595i	0.100123	+	0.444833i
$482$	0.297655	+	0.297655i	0.0135578	+	0.0135578i
$483$	−6.44944	−	3.09859i	−0.293460	−	0.140991i
$484$	−17.4297	+	10.0631i	−0.792260	+	0.457412i
$485$		0			0
$486$	−3.29987	+	2.45889i	−0.149685	+	0.111538i
$487$	−5.95347	+	1.59523i	−0.269778	+	0.0722867i	−0.391172	−	0.920318i	$-0.627930\pi$
$487$	−5.95347	+	1.59523i	−0.269778	+	0.0722867i	0.121394	+	0.992604i	$0.461264\pi$
$488$	−2.57106	+	0.688913i	−0.116386	+	0.0311856i
$489$	5.24327	−	27.8513i	0.237109	−	1.25948i
$490$		0			0
$491$	33.2103	−	19.1739i	1.49876	−	0.865308i	0.498759	−	0.866741i	$-0.333789\pi$
$491$	33.2103	−	19.1739i	1.49876	−	0.865308i	0.999999	+	0.00143268i	$0.000456037\pi$
$492$	−7.80674	+	16.2490i	−0.351955	+	0.732562i
$493$	−37.0737	−	37.0737i	−1.66971	−	1.66971i
$494$	−1.34753	+	4.32235i	−0.0606283	+	0.194472i
$495$		0			0
$496$	11.6651	−	6.73486i	0.523779	−	0.302404i
$497$	0.587397	−	2.19219i	0.0263483	−	0.0983333i
$498$	0.114283	+	1.50644i	0.00512115	+	0.0675051i
$499$	15.3354			0.686509			0.343254	−	0.939242i	$-0.388471\pi$
$499$	15.3354			0.686509			0.343254	+	0.939242i	$0.388471\pi$
$500$		0			0
$501$	10.8375	+	9.30915i	0.484186	+	0.415902i
$502$	2.30921	+	2.30921i	0.103065	+	0.103065i
$503$	−3.77227	−	14.0783i	−0.168197	−	0.627721i	−0.997611	−	0.0690858i	$-0.977992\pi$
$503$	−3.77227	−	14.0783i	−0.168197	−	0.627721i	0.829413	−	0.558635i	$-0.188675\pi$
$504$	−1.62378	−	10.6404i	−0.0723288	−	0.473962i
$505$		0			0
$506$			0.238863i			0.0106187i
$507$	−19.5572	+	11.1587i	−0.868565	+	0.495575i
$508$	−17.5082	−	17.5082i	−0.776800	−	0.776800i
$509$	14.2026	−	8.19989i	0.629520	−	0.363454i	−0.151046	−	0.988527i	$-0.548264\pi$
$509$	14.2026	−	8.19989i	0.629520	−	0.363454i	0.780566	+	0.625073i	$0.214931\pi$
$510$		0			0
$511$	−20.5323	+	35.5630i	−0.908295	+	1.57321i
$512$	12.9273	−	12.9273i	0.571313	−	0.571313i
$513$	23.6380	+	7.22009i	1.04364	+	0.318775i
$514$	−2.29171	+	3.96935i	−0.101083	+	0.175081i
$515$		0			0
$516$	−14.5050	−	12.4594i	−0.638547	−	0.548494i
$517$	2.36084	+	0.632584i	0.103829	+	0.0278210i
$518$	0.655293	−	2.44559i	0.0287919	−	0.107453i
$519$	−3.89317	+	20.6799i	−0.170891	+	0.907745i
$520$		0			0
$521$			1.84827i			0.0809740i	0.999180	+	0.0404870i	$0.0128909\pi$
$521$			1.84827i			0.0809740i	−0.999180	+	0.0404870i	$0.987109\pi$
$522$	−3.35223	+	4.55962i	−0.146723	+	0.199569i
$523$	6.03412	−	22.5196i	0.263854	−	0.984715i	−0.699095	−	0.715029i	$-0.746413\pi$
$523$	6.03412	−	22.5196i	0.263854	−	0.984715i	0.962948	−	0.269686i	$-0.0869200\pi$
$524$	−17.1227	+	29.6574i	−0.748009	+	1.29559i
$525$		0			0
$526$	−4.00685	−	2.31336i	−0.174707	−	0.100867i
$527$	−7.13169	−	26.6158i	−0.310661	−	1.15940i
$528$	3.88510	−	2.65405i	0.169077	−	0.115502i
$529$	−18.6826	−	10.7864i	−0.812287	−	0.468974i
$530$		0			0
$531$	2.39495	+	15.6939i	0.103932	+	0.681055i
$532$	−22.4505	+	22.4505i	−0.973352	+	0.973352i
$533$	−16.4296	−	10.3925i	−0.711647	−	0.450151i
$534$	4.69681	+	0.884218i	0.203251	+	0.0382639i
$535$		0			0
$536$	5.21390	−	3.01025i	0.225206	−	0.130023i
$537$	−1.80336	−	23.7713i	−0.0778209	−	1.02581i
$538$	1.07629	−	1.07629i	0.0464023	−	0.0464023i
$539$	3.25156	+	1.87729i	0.140055	+	0.0808605i
$540$		0			0
$541$		−	30.2686i		−	1.30135i	−0.759357	−	0.650674i	$-0.774487\pi$
$541$		−	30.2686i		−	1.30135i	0.759357	−	0.650674i	$-0.225513\pi$
$542$	−5.37753	+	1.44090i	−0.230985	+	0.0618921i
$543$	7.95292	+	3.82093i	0.341292	+	0.163972i
$544$	−11.0866	−	19.2026i	−0.475336	−	0.823306i
$545$		0			0
$546$	5.69734	−	0.201246i	0.243823	−	0.00861253i
$547$	−22.9924	+	22.9924i	−0.983084	+	0.983084i	−0.999859	−	0.0167753i	$-0.994660\pi$
$547$	−22.9924	+	22.9924i	−0.983084	+	0.983084i	0.0167753	+	0.999859i	$0.494660\pi$
$548$	10.7245	−	40.0242i	0.458126	−	1.70975i
$549$	−7.60801	+	1.16102i	−0.324702	+	0.0495510i
$550$		0			0
$551$	33.9895			1.44800
$552$	0.162408	+	2.14080i	0.00691254	+	0.0911186i
$553$	5.68619	+	21.2212i	0.241801	+	0.902415i
$554$		−	1.46650i		−	0.0623057i
$555$		0			0
$556$	9.80599	+	16.9845i	0.415867	+	0.720302i
$557$	27.3100	+	7.31770i	1.15716	+	0.310061i	0.785832	−	0.618440i	$-0.212235\pi$
$557$	27.3100	+	7.31770i	1.15716	+	0.310061i	0.371331	+	0.928501i	$0.378902\pi$
$558$	−2.72390	+	1.19438i	−0.115312	+	0.0505623i
$559$	15.1583	−	13.9802i	0.641128	−	0.591298i
$560$		0			0
$561$	−3.18732	−	9.08208i	−0.134569	−	0.383446i
$562$	−3.39832	−	0.910577i	−0.143349	−	0.0384104i
$563$	−6.99906	−	26.1208i	−0.294975	−	1.10086i	−0.941237	−	0.337747i	$-0.890335\pi$
$563$	−6.99906	−	26.1208i	−0.294975	−	1.10086i	0.646262	−	0.763116i	$-0.276331\pi$
$564$	10.6031	+	1.99613i	0.446472	+	0.0840524i
$565$		0			0
$566$	−1.83788	+	3.18330i	−0.0772519	+	0.133804i
$567$	−1.27789	−	31.0952i	−0.0536664	−	1.30588i
$568$	−0.657781	+	0.176252i	−0.0275999	+	0.00739537i
$569$	−4.95492	−	8.58218i	−0.207721	−	0.359784i	0.743275	−	0.668986i	$-0.233271\pi$
$569$	−4.95492	−	8.58218i	−0.207721	−	0.359784i	−0.950996	+	0.309202i	$0.899938\pi$
$570$		0			0
$571$	23.1555			0.969026			0.484513	−	0.874784i	$-0.338997\pi$
$571$	23.1555			0.969026			0.484513	+	0.874784i	$0.338997\pi$
$572$	2.44904	+	4.66776i	0.102399	+	0.195169i
$573$	8.17828	+	11.9717i	0.341652	+	0.500125i
$574$	2.46104	+	4.26265i	0.102722	+	0.177919i
$575$		0			0
$576$	14.9320	−	11.9528i	0.622168	−	0.498035i
$577$	−7.88984	−	7.88984i	−0.328458	−	0.328458i	0.523542	−	0.852000i	$-0.324610\pi$
$577$	−7.88984	−	7.88984i	−0.328458	−	0.328458i	−0.852000	+	0.523542i	$0.824610\pi$
$578$	−9.39291	+	2.51682i	−0.390693	+	0.104686i
$579$	−9.87759	−	8.48458i	−0.410499	−	0.352607i
$580$		0			0
$581$	−9.89445	−	5.71256i	−0.410491	−	0.236997i
$582$	−3.64949	−	1.75338i	−0.151276	−	0.0726798i
$583$	5.48468	+	1.46961i	0.227152	+	0.0608652i
$584$	12.3217			0.509874
$585$		0			0
$586$	−3.94669			−0.163036
$587$	17.2891	+	4.63260i	0.713597	+	0.191208i	0.597313	−	0.802008i	$-0.296235\pi$
$587$	17.2891	+	4.63260i	0.713597	+	0.191208i	0.116284	+	0.993216i	$0.462902\pi$
$588$	14.9395	+	7.17761i	0.616096	+	0.295999i
$589$	15.4700	+	8.93162i	0.637431	+	0.368021i
$590$		0			0
$591$	24.5282	+	21.0691i	1.00896	+	0.866665i
$592$	9.60878	−	2.57466i	0.394918	−	0.105818i
$593$	18.2825	+	18.2825i	0.750773	+	0.750773i	0.974623	−	0.223851i	$-0.0718628\pi$
$593$	18.2825	+	18.2825i	0.750773	+	0.750773i	−0.223851	+	0.974623i	$0.571863\pi$
$594$	−0.917196	+	0.487990i	−0.0376330	+	0.0200225i
$595$		0			0
$596$	−12.7524	−	22.0879i	−0.522360	−	0.904754i
$597$	0.348060	+	0.509504i	0.0142451	+	0.0208526i
$598$	−1.13619	−	0.0459385i	−0.0464624	−	0.00187857i
$599$	−28.6851			−1.17204			−0.586021	−	0.810296i	$-0.699306\pi$
$599$	−28.6851			−1.17204			−0.586021	+	0.810296i	$0.699306\pi$
$600$		0			0
$601$	−22.4909	−	38.9554i	−0.917423	−	1.58902i	−0.803315	−	0.595554i	$-0.796933\pi$
$601$	−22.4909	−	38.9554i	−0.917423	−	1.58902i	−0.114107	−	0.993468i	$-0.536401\pi$
$602$	−5.04300	+	1.35127i	−0.205537	+	0.0550735i
$603$	15.9422	−	6.99037i	0.649215	−	0.284670i
$604$	7.36152	−	12.7505i	0.299536	−	0.518811i
$605$		0			0
$606$	5.55774	+	1.04630i	0.225768	+	0.0425028i
$607$	6.14482	+	22.9328i	0.249411	+	0.930813i	0.971115	+	0.238612i	$0.0766924\pi$
$607$	6.14482	+	22.9328i	0.249411	+	0.930813i	−0.721704	+	0.692201i	$0.756641\pi$
$608$	13.8847	+	3.72040i	0.563100	+	0.150882i
$609$	−14.1724	−	40.3835i	−0.574296	−	1.63642i
$610$		0			0
$611$	−3.46304	+	11.1081i	−0.140100	+	0.449385i
$612$	−17.0627	−	38.9129i	−0.689718	−	1.57296i
$613$	−34.7467	−	9.31036i	−1.40341	−	0.376042i	−0.523840	−	0.851817i	$-0.675501\pi$
$613$	−34.7467	−	9.31036i	−1.40341	−	0.376042i	−0.879567	+	0.475775i	$0.842168\pi$
$614$	−1.44082	−	2.49558i	−0.0581468	−	0.100713i
$615$		0			0
$616$		−	2.71738i		−	0.109486i
$617$	4.62410	+	17.2574i	0.186159	+	0.694756i	0.994379	+	0.105876i	$0.0337646\pi$
$617$	4.62410	+	17.2574i	0.186159	+	0.694756i	−0.808220	+	0.588881i	$0.799569\pi$
$618$	0.582656	+	7.68035i	0.0234378	+	0.308949i
$619$	−2.34719			−0.0943415			−0.0471707	−	0.998887i	$-0.515020\pi$
$619$	−2.34719			−0.0943415			−0.0471707	+	0.998887i	$0.515020\pi$
$620$		0			0
$621$	−0.215020	+	6.20388i	−0.00862847	+	0.248953i
$622$	−0.331065	+	1.23555i	−0.0132745	+	0.0495410i
$623$	−25.5573	+	25.5573i	−1.02393	+	1.02393i
$624$	11.8773	+	18.9906i	0.475471	+	0.760233i
$625$		0			0
$626$	−0.208825	−	0.361695i	−0.00834632	−	0.0144563i
$627$	5.62435	+	2.70218i	0.224615	+	0.107915i
$628$	−7.89826	+	2.11633i	−0.315175	+	0.0844508i
$629$		−	20.3499i		−	0.811404i
$630$		0			0
$631$	11.6065	+	6.70099i	0.462046	+	0.266762i	0.712904	−	0.701262i	$-0.247379\pi$
$631$	11.6065	+	6.70099i	0.462046	+	0.266762i	−0.250858	+	0.968024i	$0.580713\pi$
$632$	4.66136	−	4.66136i	0.185419	−	0.185419i
$633$	−1.05783	−	13.9439i	−0.0420449	−	0.554221i
$634$	−0.992107	+	0.572793i	−0.0394016	+	0.0227485i
$635$		0			0
$636$	24.6331	+	4.63740i	0.976765	+	0.183885i
$637$	−9.55501	+	15.1056i	−0.378583	+	0.598505i
$638$	−1.01027	+	1.01027i	−0.0399971	+	0.0399971i
$639$	−1.94644	+	0.297035i	−0.0769998	+	0.0117505i
$640$		0			0
$641$	7.29316	+	4.21071i	0.288062	+	0.166313i	0.637068	−	0.770808i	$-0.280147\pi$
$641$	7.29316	+	4.21071i	0.288062	+	0.166313i	−0.349005	+	0.937121i	$0.613480\pi$
$642$	0.723580	−	0.494303i	0.0285574	−	0.0195086i
$643$	−7.26793	−	27.1243i	−0.286619	−	1.06968i	−0.947648	−	0.319316i	$-0.896547\pi$
$643$	−7.26793	−	27.1243i	−0.286619	−	1.06968i	0.661029	−	0.750360i	$-0.270120\pi$
$644$	−6.90584	−	3.98709i	−0.272128	−	0.157113i
$645$		0			0
$646$	4.60673	−	7.97910i	0.181250	−	0.313933i
$647$	3.43885	−	12.8340i	0.135195	−	0.504555i	−0.864802	−	0.502113i	$-0.832556\pi$
$647$	3.43885	−	12.8340i	0.135195	−	0.504555i	0.999997	−	0.00244197i	$-0.000777304\pi$
$648$	−7.88856	+	4.99722i	−0.309892	+	0.196309i
$649$			4.00793i			0.157325i
$650$		0			0
$651$	4.16135	−	22.1044i	0.163096	−	0.866338i
$652$	8.17468	−	30.5083i	0.320145	−	1.19480i
$653$	−37.7391	−	10.1122i	−1.47685	−	0.395719i	−0.571573	−	0.820551i	$-0.693667\pi$
$653$	−37.7391	−	10.1122i	−1.47685	−	0.395719i	−0.905272	+	0.424832i	$0.860333\pi$
$654$	2.52373	+	2.16782i	0.0986858	+	0.0847684i
$655$		0			0
$656$	−9.66949	+	16.7481i	−0.377530	+	0.653902i
$657$	35.4096	+	3.92386i	1.38146	+	0.153084i
$658$	2.08307	−	2.08307i	0.0812066	−	0.0812066i
$659$	0.692965	−	1.20025i	0.0269941	−	0.0467551i	−0.852213	−	0.523195i	$-0.824740\pi$
$659$	0.692965	−	1.20025i	0.0269941	−	0.0467551i	0.879207	+	0.476440i	$0.158073\pi$
$660$		0			0
$661$	−36.2520	+	20.9301i	−1.41004	+	0.814087i	−0.995392	−	0.0958938i	$-0.969429\pi$
$661$	−36.2520	+	20.9301i	−1.41004	+	0.814087i	−0.414649	+	0.909981i	$0.636096\pi$
$662$	2.97299	+	2.97299i	0.115548	+	0.115548i
$663$	43.8136	−	13.4144i	1.70158	−	0.520972i
$664$			3.42818i			0.133039i
$665$		0			0
$666$	−2.17142	+	0.331369i	−0.0841409	+	0.0128403i
$667$	2.20946	+	8.24582i	0.0855507	+	0.319279i
$668$	11.2586	+	11.2586i	0.435610	+	0.435610i
$669$	7.62854	+	6.55271i	0.294936	+	0.253342i
$670$		0			0
$671$	−1.94295			−0.0750068
$672$	−1.36918	−	18.0480i	−0.0528171	−	0.696216i
$673$	−5.82222	+	21.7288i	−0.224430	+	0.837585i	0.758202	+	0.652020i	$0.226078\pi$
$673$	−5.82222	+	21.7288i	−0.224430	+	0.837585i	−0.982632	+	0.185565i	$0.940588\pi$
$674$	1.86127	−	1.07460i	0.0716934	−	0.0413922i
$675$		0			0
$676$	−22.6740	+	10.7516i	−0.872079	+	0.413522i
$677$	−9.66307	−	9.66307i	−0.371382	−	0.371382i	0.496599	−	0.867980i	$-0.334582\pi$
$677$	−9.66307	−	9.66307i	−0.371382	−	0.371382i	−0.867980	+	0.496599i	$0.834582\pi$
$678$	−0.580822	+	1.20893i	−0.0223063	+	0.0464286i
$679$	26.5170	−	15.3096i	1.01763	−	0.587529i
$680$		0			0
$681$	1.66269	−	8.83191i	0.0637143	−	0.338439i
$682$	−0.725292	+	0.194341i	−0.0277729	+	0.00744171i
$683$	−39.5275	+	10.5914i	−1.51248	+	0.405267i	−0.917257	−	0.398295i	$-0.869602\pi$
$683$	−39.5275	+	10.5914i	−1.51248	+	0.405267i	−0.595221	+	0.803562i	$0.702935\pi$
$684$	25.6595	+	10.0163i	0.981114	+	0.382981i
$685$		0			0
$686$	−1.61487	+	0.932347i	−0.0616561	+	0.0355972i
$687$	25.0859	+	12.0524i	0.957086	+	0.459826i
$688$	−14.5049	−	14.5049i	−0.552995	−	0.552995i
$689$	−8.04531	+	25.8062i	−0.306502	+	0.983139i
$690$		0			0
$691$	−35.2096	+	20.3283i	−1.33944	+	0.773323i	−0.986724	−	0.162409i	$-0.948074\pi$
$691$	−35.2096	+	20.3283i	−1.33944	+	0.773323i	−0.352712	+	0.935732i	$0.614740\pi$
$692$	−6.06977	+	22.6527i	−0.230738	+	0.861127i
$693$	0.865354	−	7.80910i	0.0328721	−	0.296643i
$694$	0.717694			0.0272433
$695$		0			0
$696$	−8.36764	+	9.74145i	−0.317175	+	0.369249i
$697$	27.9741	+	27.9741i	1.05960	+	1.05960i
$698$	−1.38091	−	5.15364i	−0.0522684	−	0.195068i
$699$	−13.2246	+	4.64113i	−0.500201	+	0.175543i
$700$		0			0
$701$			49.6743i			1.87617i	0.346401	+	0.938086i	$0.387404\pi$
$701$			49.6743i			1.87617i	−0.346401	+	0.938086i	$0.612596\pi$
$702$	−2.14481	−	4.45666i	−0.0809508	−	0.168206i
$703$	9.32848	+	9.32848i	0.351830	+	0.351830i
$704$	4.18182	−	2.41437i	0.157608	−	0.0909952i
$705$		0			0
$706$	−3.85390	+	6.67515i	−0.145044	+	0.251223i
$707$	−30.2419	+	30.2419i	−1.13736	+	1.13736i
$708$	1.33838	+	17.6420i	0.0502994	+	0.663028i
$709$	0.0385950	−	0.0668486i	0.00144947	−	0.00251055i	−0.865300	−	0.501255i	$-0.832872\pi$
$709$	0.0385950	−	0.0668486i	0.00144947	−	0.00251055i	0.866749	+	0.498744i	$0.166205\pi$
$710$		0			0
$711$	14.8801	−	11.9112i	0.558047	−	0.446706i
$712$	10.4755	+	2.80691i	0.392587	+	0.105193i
$713$	−1.16119	+	4.33360i	−0.0434868	+	0.162295i
$714$	−11.4010	−	2.14634i	−0.426670	−	0.0803246i
$715$		0			0
$716$		−	26.5684i		−	0.992906i
$717$	−10.6360	+	22.1379i	−0.397209	+	0.826754i
$718$	−2.01273	+	7.51161i	−0.0751144	+	0.280331i
$719$	1.97524	−	3.42122i	0.0736641	−	0.127590i	−0.826840	−	0.562437i	$-0.809864\pi$
$719$	1.97524	−	3.42122i	0.0736641	−	0.127590i	0.900505	+	0.434847i	$0.143197\pi$
$720$		0			0
$721$	−50.4454	−	29.1247i	−1.87868	−	1.08466i
$722$	0.247702	+	0.924438i	0.00921853	+	0.0344040i
$723$	1.55789	+	2.28050i	0.0579384	+	0.0848126i
$724$	8.51572	+	4.91655i	0.316484	+	0.182722i
$725$		0			0
$726$	4.49848	−	1.57872i	0.166954	−	0.0585919i
$727$	26.2031	−	26.2031i	0.971818	−	0.971818i	−0.0277959	−	0.999614i	$-0.508849\pi$
$727$	26.2031	−	26.2031i	0.971818	−	0.971818i	0.999614	+	0.0277959i	$0.00884884\pi$
$728$	12.9257	+	0.522611i	0.479058	+	0.0193693i
$729$	−24.2612	+	11.8487i	−0.898565	+	0.438841i
$730$		0			0
$731$	−36.3412	+	20.9816i	−1.34413	+	0.776032i
$732$	−8.55243	+	0.648814i	−0.316107	+	0.0239809i
$733$	−4.40376	+	4.40376i	−0.162656	+	0.162656i	−0.783742	−	0.621086i	$-0.786692\pi$
$733$	−4.40376	+	4.40376i	−0.162656	+	0.162656i	0.621086	+	0.783742i	$0.286692\pi$
$734$	1.47172	+	0.849695i	0.0543220	+	0.0313628i
$735$		0			0
$736$			3.61027i			0.133076i
$737$	4.24492	−	1.13742i	0.156364	−	0.0418975i
$738$	2.52944	−	3.44048i	0.0931101	−	0.126646i
$739$	19.3253	+	33.4724i	0.710892	+	1.23130i	0.964523	+	0.264000i	$0.0850420\pi$
$739$	19.3253	+	33.4724i	0.710892	+	1.23130i	−0.253630	+	0.967301i	$0.581625\pi$
$740$		0			0
$741$	−13.9351	+	26.2335i	−0.511919	+	0.963713i
$742$	4.83938	−	4.83938i	0.177659	−	0.177659i
$743$	−10.9045	+	40.6962i	−0.400048	+	1.49300i	0.412961	+	0.910749i	$0.364494\pi$
$743$	−10.9045	+	40.6962i	−0.400048	+	1.49300i	−0.813009	+	0.582251i	$0.802172\pi$
$744$	−6.36828	+	2.23492i	−0.233472	+	0.0819362i
$745$		0			0
$746$	2.55087			0.0933940
$747$	−1.09171	+	9.85178i	−0.0399436	+	0.360458i
$748$	−2.77632	−	10.3613i	−0.101512	−	0.378848i
$749$			6.62700i			0.242145i
$750$		0			0
$751$	8.97373	+	15.5430i	0.327456	+	0.567170i	0.982006	−	0.188848i	$-0.0604754\pi$
$751$	8.97373	+	15.5430i	0.327456	+	0.567170i	−0.654550	+	0.756018i	$0.727142\pi$
$752$	11.1802	+	2.99572i	0.407699	+	0.109243i
$753$	12.0861	+	17.6921i	0.440442	+	0.644737i
$754$	−4.61125	−	4.99984i	−0.167932	−	0.182084i
$755$		0			0
$756$	1.20138	−	34.6629i	0.0436938	−	1.26068i
$757$	−6.17589	−	1.65482i	−0.224466	−	0.0601456i	0.144833	−	0.989456i	$-0.453736\pi$
$757$	−6.17589	−	1.65482i	−0.224466	−	0.0601456i	−0.369299	+	0.929311i	$0.620402\pi$
$758$	−1.04852	−	3.91312i	−0.0380838	−	0.142131i
$759$	−0.289941	+	1.54011i	−0.0105242	+	0.0559026i
$760$		0			0
$761$	1.79494	−	3.10892i	0.0650664	−	0.112698i	−0.831657	−	0.555290i	$-0.812607\pi$
$761$	1.79494	−	3.10892i	0.0650664	−	0.112698i	0.896723	+	0.442591i	$0.145941\pi$
$762$	3.30844	+	4.84303i	0.119852	+	0.175444i
$763$	−24.3027	+	6.51189i	−0.879818	+	0.235746i
$764$	8.07901	+	13.9933i	0.292288	+	0.506258i
$765$		0			0
$766$	5.97290			0.215810
$767$	−19.0645	−	0.770813i	−0.688377	−	0.0278324i
$768$	15.3192	−	10.4651i	0.552785	−	0.377626i
$769$	−3.66193	−	6.34265i	−0.132053	−	0.228722i	0.792415	−	0.609982i	$-0.208823\pi$
$769$	−3.66193	−	6.34265i	−0.132053	−	0.228722i	−0.924468	+	0.381260i	$0.875490\pi$
$770$		0			0
$771$	−19.5944	+	22.8114i	−0.705675	+	0.821533i
$772$	−10.2614	−	10.2614i	−0.369315	−	0.369315i
$773$	31.5967	−	8.46631i	1.13645	−	0.304512i	0.358930	−	0.933364i	$-0.383142\pi$
$773$	31.5967	−	8.46631i	1.13645	−	0.304512i	0.777525	+	0.628852i	$0.216475\pi$
$774$	2.83059	+	3.53610i	0.101743	+	0.127103i
$775$		0			0
$776$	−7.95660	−	4.59374i	−0.285625	−	0.164906i
$777$	7.19368	−	14.9730i	0.258072	−	0.537153i
$778$	2.80764	+	0.752305i	0.100659	+	0.0269714i
$779$	−25.6469			−0.918897
$780$		0			0
$781$	−0.497085			−0.0177871
$782$	2.23518	+	0.598915i	0.0799299	+	0.0214171i
$783$	−27.1488	+	25.3300i	−0.970220	+	0.905219i
$784$	15.3983	+	8.89024i	0.549941	+	0.317509i
$785$		0			0
$786$	5.28573	−	6.15355i	0.188536	−	0.219490i
$787$	24.6663	−	6.60933i	0.879260	−	0.235597i	0.209172	−	0.977879i	$-0.432923\pi$
$787$	24.6663	−	6.60933i	0.879260	−	0.235597i	0.670088	+	0.742282i	$0.266256\pi$
$788$	25.4813	+	25.4813i	0.907732	+	0.907732i
$789$	−23.0269	−	19.7795i	−0.819781	−	0.704169i
$790$		0			0
$791$	−5.07145	−	8.78400i	−0.180320	−	0.312323i
$792$	−2.15907	+	0.946716i	−0.0767192	+	0.0336401i
$793$	0.373672	−	9.24200i	0.0132695	−	0.328193i
$794$	−2.12624			−0.0754573
$795$		0			0
$796$	0.343835	+	0.595539i	0.0121869	+	0.0211083i
$797$	−1.26147	+	0.338010i	−0.0446836	+	0.0119729i	−0.281092	−	0.959681i	$-0.590696\pi$
$797$	−1.26147	+	0.338010i	−0.0446836	+	0.0119729i	0.236408	+	0.971654i	$0.424030\pi$
$798$	6.21014	−	4.24236i	0.219836	−	0.150178i
$799$	11.8389	−	20.5056i	0.418831	−	0.725437i
$800$		0			0
$801$	29.2103	+	11.4023i	1.03210	+	0.402882i
$802$	−2.55235	−	9.52552i	−0.0901268	−	0.336358i
$803$	8.68774	+	2.32787i	0.306584	+	0.0821488i
$804$	18.3054	−	6.42420i	0.645580	−	0.226564i
$805$		0			0
$806$	−0.784930	−	3.48736i	−0.0276480	−	0.122837i
$807$	8.24606	−	5.63317i	0.290275	−	0.198297i
$808$	12.3957	+	3.32141i	0.436079	+	0.116847i
$809$	−14.5548	−	25.2097i	−0.511720	−	0.886326i	−0.999908	−	0.0135868i	$-0.995675\pi$
$809$	−14.5548	−	25.2097i	−0.511720	−	0.886326i	0.488187	−	0.872739i	$-0.337658\pi$
$810$		0			0
$811$		−	40.2274i		−	1.41257i	−0.707926	−	0.706287i	$-0.750369\pi$
$811$		−	40.2274i		−	1.41257i	0.707926	−	0.706287i	$-0.249631\pi$
$812$	−12.3449	−	46.0718i	−0.433221	−	1.61680i
$813$	−36.4217	+	2.76306i	−1.27736	+	0.0969049i
$814$	−0.554543			−0.0194367
$815$		0			0
$816$	−15.0941	−	43.0098i	−0.528400	−	1.50565i
$817$	7.04090	−	26.2770i	0.246330	−	0.919315i
$818$	2.59387	−	2.59387i	0.0906927	−	0.0906927i
$819$	36.9790	+	5.61807i	1.29215	+	0.196311i
$820$		0			0
$821$	−10.4818	−	18.1550i	−0.365818	−	0.633615i	0.623089	−	0.782151i	$-0.285877\pi$
$821$	−10.4818	−	18.1550i	−0.365818	−	0.633615i	−0.988907	+	0.148536i	$0.952544\pi$
$822$	−4.25060	+	8.84724i	−0.148257	+	0.308583i
$823$	38.6043	−	10.3440i	1.34566	−	0.360569i	0.487130	−	0.873329i	$-0.338044\pi$
$823$	38.6043	−	10.3440i	1.34566	−	0.360569i	0.858532	+	0.512760i	$0.171377\pi$
$824$			17.4781i			0.608877i
$825$		0			0
$826$	4.18358	+	2.41539i	0.145565	+	0.0840422i
$827$	−0.968029	+	0.968029i	−0.0336617	+	0.0336617i	−0.723737	−	0.690076i	$-0.757577\pi$
$827$	−0.968029	+	0.968029i	−0.0336617	+	0.0336617i	0.690076	+	0.723737i	$0.257577\pi$
$828$	−0.761961	+	6.87606i	−0.0264800	+	0.238960i
$829$	−23.0443	+	13.3046i	−0.800362	+	0.462089i	−0.843598	−	0.536976i	$-0.819567\pi$
$829$	−23.0443	+	13.3046i	−0.800362	+	0.462089i	0.0432359	+	0.999065i	$0.486233\pi$
$830$		0			0
$831$	1.78010	−	9.45556i	0.0617509	−	0.328010i
$832$	10.6802	+	20.3559i	0.370268	+	0.705715i
$833$	25.7197	−	25.7197i	0.891136	−	0.891136i
$834$	−1.53839	−	4.38356i	−0.0532702	−	0.151790i
$835$		0			0
$836$	6.02236	+	3.47701i	0.208288	+	0.120255i
$837$	−19.0127	+	4.39465i	−0.657173	+	0.151901i
$838$	−2.28665	−	8.53388i	−0.0789909	−	0.294798i
$839$	−10.1710	−	5.87220i	−0.351140	−	0.202731i	0.314047	−	0.949407i	$-0.398315\pi$
$839$	−10.1710	−	5.87220i	−0.351140	−	0.202731i	−0.665187	+	0.746676i	$0.731648\pi$
$840$		0			0
$841$	−11.0308	+	19.1060i	−0.380374	+	0.658827i
$842$	1.13583	−	4.23897i	0.0391432	−	0.146085i
$843$	−20.8060	−	9.99614i	−0.716598	−	0.344285i
$844$		−	15.5846i		−	0.536446i
$845$		0			0
$846$	−2.38082	−	0.929360i	−0.0818542	−	0.0319521i
$847$	−9.33140	+	34.8253i	−0.320631	+	1.19661i
$848$	25.9737	+	6.95963i	0.891940	+	0.238995i
$849$	−15.7141	+	18.2941i	−0.539307	+	0.627852i
$850$		0			0
$851$	−1.65669	+	2.86947i	−0.0567907	+	0.0983643i
$852$	−2.18806	+	0.165993i	−0.0749617	+	0.00568683i
$853$	12.6463	−	12.6463i	0.433001	−	0.433001i	−0.456647	−	0.889648i	$-0.650950\pi$
$853$	12.6463	−	12.6463i	0.433001	−	0.433001i	0.889648	+	0.456647i	$0.150950\pi$
$854$	−1.17092	+	2.02810i	−0.0400682	+	0.0694002i
$855$		0			0
$856$	1.72207	−	0.994235i	0.0588590	−	0.0339823i
$857$	−17.5943	−	17.5943i	−0.601008	−	0.601008i	0.339572	−	0.940580i	$-0.389718\pi$
$857$	−17.5943	−	17.5943i	−0.601008	−	0.601008i	−0.940580	+	0.339572i	$0.889718\pi$
$858$	−0.365547	−	1.19394i	−0.0124796	−	0.0407603i
$859$			0.150593i			0.00513817i	0.999997	+	0.00256909i	$0.000817767\pi$
$859$			0.150593i			0.00513817i	−0.999997	+	0.00256909i	$0.999182\pi$
$860$		0			0
$861$	10.6939	+	30.4716i	0.364446	+	1.03847i
$862$	2.37116	+	8.84929i	0.0807620	+	0.301408i
$863$	21.1115	+	21.1115i	0.718643	+	0.718643i	0.968327	−	0.249685i	$-0.0803269\pi$
$863$	21.1115	+	21.1115i	0.718643	+	0.718643i	−0.249685	+	0.968327i	$0.580327\pi$
$864$	−13.8629	+	7.37567i	−0.471624	+	0.250925i
$865$		0			0
$866$	−5.59987			−0.190291
$867$	−63.6176	+	4.82623i	−2.16057	+	0.163907i
$868$	6.48788	−	24.2131i	0.220213	−	0.821846i
$869$	4.16727	−	2.40597i	0.141365	−	0.0816171i
$870$		0			0
$871$	4.59396	+	20.4105i	0.155661	+	0.691582i
$872$	5.33824	+	5.33824i	0.180776	+	0.180776i
$873$	−21.4025	−	15.7351i	−0.724365	−	0.532554i
$874$	−1.29916	+	0.750071i	−0.0439448	+	0.0253715i
$875$		0			0
$876$	39.0188	+	7.34566i	1.31832	+	0.248187i
$877$	−9.57243	+	2.56493i	−0.323238	+	0.0866114i	−0.416789	−	0.909003i	$-0.636845\pi$
$877$	−9.57243	+	2.56493i	−0.323238	+	0.0866114i	0.0935514	+	0.995614i	$0.470178\pi$
$878$	4.52524	−	1.21253i	0.152719	−	0.0409210i
$879$	−25.4471	−	4.79064i	−0.858308	−	0.161584i
$880$		0			0
$881$	−41.0035	+	23.6734i	−1.38144	+	0.797576i	−0.992330	−	0.123614i	$-0.960551\pi$
$881$	−41.0035	+	23.6734i	−1.38144	+	0.797576i	−0.389112	+	0.921190i	$0.627218\pi$
$882$	−3.16322	−	2.32560i	−0.106511	−	0.0783070i
$883$	8.67634	+	8.67634i	0.291982	+	0.291982i	0.837863	−	0.545881i	$-0.183805\pi$
$883$	8.67634	+	8.67634i	0.291982	+	0.291982i	−0.545881	+	0.837863i	$0.683805\pi$
$884$	49.8196	−	11.2133i	1.67561	−	0.377145i
$885$		0			0
$886$	−3.98900	+	2.30305i	−0.134013	+	0.0773724i
$887$	−4.44848	+	16.6020i	−0.149365	+	0.557439i	0.850157	+	0.526530i	$0.176507\pi$
$887$	−4.44848	+	16.6020i	−0.149365	+	0.557439i	−0.999522	+	0.0309097i	$0.990160\pi$
$888$	−4.97008	+	0.377046i	−0.166785	+	0.0126528i
$889$	−44.3554			−1.48763
$890$		0			0
$891$	−6.50615	+	2.03308i	−0.217964	+	0.0681108i
$892$	7.92495	+	7.92495i	0.265347	+	0.265347i
$893$	3.97285	+	14.8269i	0.132946	+	0.496163i
$894$	2.00064	+	5.70071i	0.0669115	+	0.190660i
$895$		0			0
$896$		−	26.7200i		−	0.892653i
$897$	−7.27008	−	1.67535i	−0.242741	−	0.0559385i
$898$	−2.58022	−	2.58022i	−0.0861032	−	0.0861032i
$899$	−23.2403	+	13.4178i	−0.775107	+	0.447508i
$900$		0			0
$901$	27.5041	−	47.6385i	0.916295	−	1.58707i
$902$	0.762306	−	0.762306i	0.0253820	−	0.0253820i
$903$	−34.1560	+	2.59118i	−1.13664	+	0.0862290i
$904$	−1.52172	+	2.63569i	−0.0506116	+	0.0876619i
$905$		0			0
$906$	−2.27248	+	2.64558i	−0.0754980	+	0.0878934i
$907$	−42.1187	−	11.2857i	−1.39853	−	0.374735i	−0.520713	−	0.853732i	$-0.674334\pi$
$907$	−42.1187	−	11.2857i	−1.39853	−	0.374735i	−0.877817	+	0.478997i	$0.841001\pi$
$908$	2.59226	−	9.67446i	0.0860273	−	0.321058i
$909$	34.5646	+	13.4924i	1.14644	+	0.447515i
$910$		0			0
$911$		−	17.9743i		−	0.595516i	−0.954641	−	0.297758i	$-0.903761\pi$
$911$		−	17.9743i		−	0.595516i	0.954641	−	0.297758i	$-0.0962388\pi$
$912$	26.6351	+	12.7967i	0.881977	+	0.423740i
$913$	−0.647668	+	2.41713i	−0.0214347	+	0.0799954i
$914$	0.173973	−	0.301331i	0.00575452	−	0.00996713i
$915$		0			0
$916$	26.8611	+	15.5083i	0.887517	+	0.512408i
$917$	15.8778	+	59.2566i	0.524330	+	1.95683i
$918$	2.26667	+	9.80631i	0.0748112	+	0.323657i
$919$	26.6383	+	15.3796i	0.878716	+	0.507327i	0.870235	−	0.492637i	$-0.163967\pi$
$919$	26.6383	+	15.3796i	0.878716	+	0.507327i	0.00848144	+	0.999964i	$0.497300\pi$
$920$		0			0
$921$	−6.26076	−	17.8397i	−0.206299	−	0.587837i
$922$	−2.07583	+	2.07583i	−0.0683638	+	0.0683638i
$923$	0.0956004	−	2.36448i	0.00314673	−	0.0778277i
$924$	1.61998	−	8.60507i	0.0532935	−	0.283086i
$925$		0			0
$926$	6.55356	−	3.78370i	0.215363	−	0.124340i
$927$	−5.56592	+	50.2279i	−0.182809	+	1.64970i
$928$	−15.2697	+	15.2697i	−0.501251	+	0.501251i
$929$	35.1545	+	20.2965i	1.15338	+	0.665906i	0.949709	−	0.313133i	$-0.101379\pi$
$929$	35.1545	+	20.2965i	1.15338	+	0.665906i	0.203673	+	0.979039i	$0.434712\pi$
$930$		0			0
$931$			23.5801i			0.772806i
$932$	−15.0874	+	4.04265i	−0.494204	+	0.132421i
$933$	−3.63436	+	7.56459i	−0.118984	+	0.247654i
$934$	1.30132	+	2.25396i	0.0425806	+	0.0737517i
$935$		0			0
$936$	−4.08799	−	10.4521i	−0.133620	−	0.341637i
$937$	−25.1017	+	25.1017i	−0.820037	+	0.820037i	−0.986113	−	0.166076i	$-0.946890\pi$
$937$	−25.1017	+	25.1017i	−0.820037	+	0.820037i	0.166076	+	0.986113i	$0.446890\pi$
$938$	1.37094	−	5.11642i	0.0447628	−	0.167057i
$939$	−0.907400	−	2.58558i	−0.0296119	−	0.0843773i
$940$		0			0
$941$	−8.19014			−0.266991			−0.133495	−	0.991049i	$-0.542620\pi$
$941$	−8.19014			−0.266991			−0.133495	+	0.991049i	$0.542620\pi$
$942$	1.93138	−	0.146521i	0.0629279	−	0.00477390i
$943$	−1.66716	−	6.22192i	−0.0542902	−	0.202614i
$944$			18.9803i			0.617756i
$945$		0			0
$946$	0.571756	+	0.990310i	0.0185894	+	0.0321978i
$947$	−37.4781	−	10.0422i	−1.21787	−	0.326328i	−0.408027	−	0.912970i	$-0.633783\pi$
$947$	−37.4781	−	10.0422i	−1.21787	−	0.326328i	−0.809847	+	0.586642i	$0.800450\pi$
$948$	17.5400	−	11.9822i	0.569671	−	0.389162i
$949$	−12.7438	+	40.8771i	−0.413681	+	1.32693i
$950$		0			0
$951$	−7.09209	+	2.48894i	−0.229977	+	0.0807094i
$952$	−25.4281	−	6.81344i	−0.824129	−	0.220825i
$953$	8.38243	+	31.2837i	0.271534	+	1.01338i	0.958129	+	0.286338i	$0.0924379\pi$
$953$	8.38243	+	31.2837i	0.271534	+	1.01338i	−0.686595	+	0.727040i	$0.740895\pi$
$954$	−5.53110	−	2.15908i	−0.179076	−	0.0699029i
$955$		0			0
$956$	−13.6858	+	23.7045i	−0.442630	+	0.766658i
$957$	−7.74024	+	5.28762i	−0.250206	+	0.170925i
$958$	−8.80169	+	2.35841i	−0.284370	+	0.0761966i
$959$	−37.1142	−	64.2836i	−1.19848	−	2.07583i
$960$		0			0
$961$	16.8965			0.545049
$962$	0.106651	−	2.63778i	0.00343856	−	0.0850456i
$963$	5.26543	−	2.30880i	0.169676	−	0.0744002i
$964$	1.53898	+	2.66558i	0.0495671	+	0.0858527i
$965$		0			0
$966$	1.43288	+	1.23080i	0.0461021	+	0.0396004i
$967$	−0.363600	−	0.363600i	−0.0116926	−	0.0116926i	0.701236	−	0.712929i	$-0.252632\pi$
$967$	−0.363600	−	0.363600i	−0.0116926	−	0.0116926i	−0.712929	+	0.701236i	$0.752632\pi$
$968$	10.4495	−	2.79994i	0.335861	−	0.0899936i
$969$	39.3882	−	45.8550i	1.26533	−	1.47307i
$970$		0			0
$971$	−51.2520	−	29.5904i	−1.64476	−	0.949600i	−0.979110	−	0.203332i	$-0.934823\pi$
$971$	−51.2520	−	29.5904i	−1.64476	−	0.949600i	−0.665645	−	0.746268i	$-0.731844\pi$
$972$	−27.9597	+	11.1218i	−0.896808	+	0.356732i
$973$	33.9356	+	9.09302i	1.08793	+	0.291509i
$974$	1.62712			0.0521363
$975$		0			0
$976$	−9.20119			−0.294523
$977$	7.43926	+	1.99334i	0.238003	+	0.0637727i	0.375849	−	0.926681i	$-0.377351\pi$
$977$	7.43926	+	1.99334i	0.238003	+	0.0637727i	−0.137846	+	0.990454i	$0.544018\pi$
$978$	−3.24001	+	6.74378i	−0.103604	+	0.215642i
$979$	6.85576	+	3.95818i	0.219111	+	0.126504i
$980$		0			0
$981$	13.6409	+	17.0408i	0.435520	+	0.544072i
$982$	−9.77864	+	2.62018i	−0.312049	+	0.0836132i
$983$	−0.396618	−	0.396618i	−0.0126502	−	0.0126502i	0.700753	−	0.713404i	$-0.252847\pi$
$983$	−0.396618	−	0.396618i	−0.0126502	−	0.0126502i	−0.713404	+	0.700753i	$0.752847\pi$
$984$	6.31384	−	7.35046i	0.201278	−	0.234324i
$985$		0			0
$986$	6.92060	+	11.9868i	0.220397	+	0.381739i
$987$	15.9595	−	10.9025i	0.507998	−	0.347031i
$988$	−17.6973	+	27.9778i	−0.563025	+	0.890091i
$989$	6.83246			0.217260
$990$		0			0
$991$	17.3190	+	29.9974i	0.550157	+	0.952900i	0.998263	+	0.0589191i	$0.0187654\pi$
$991$	17.3190	+	29.9974i	0.550157	+	0.952900i	−0.448106	+	0.893980i	$0.647901\pi$
$992$	−10.9623	+	2.93735i	−0.348055	+	0.0932610i
$993$	15.5602	+	22.7776i	0.493788	+	0.722827i
$994$	−0.299570	+	0.518870i	−0.00950178	+	0.0164576i
$995$		0			0
$996$	−2.04373	+	10.8560i	−0.0647582	+	0.343984i
$997$	−4.90330	−	18.2994i	−0.155289	−	0.579546i	−0.999080	−	0.0428751i	$-0.986348\pi$
$997$	−4.90330	−	18.2994i	−0.155289	−	0.579546i	0.843791	−	0.536671i	$-0.180318\pi$
$998$	−3.91051	−	1.04782i	−0.123785	−	0.0331681i
$999$	−14.4029	−	0.499190i	−0.455688	−	0.0157937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.218.11		96
3.2	odd	2	inner	975.2.bn.d.218.14		96
5.2	odd	4	inner	975.2.bn.d.257.14		96
5.3	odd	4		195.2.bf.a.62.11	yes	96
5.4	even	2		195.2.bf.a.23.14	yes	96
13.4	even	6	inner	975.2.bn.d.368.11		96
15.2	even	4	inner	975.2.bn.d.257.11		96
15.8	even	4		195.2.bf.a.62.14	yes	96
15.14	odd	2		195.2.bf.a.23.11	yes	96
39.17	odd	6	inner	975.2.bn.d.368.14		96
65.4	even	6		195.2.bf.a.173.14	yes	96
65.17	odd	12	inner	975.2.bn.d.407.14		96
65.43	odd	12		195.2.bf.a.17.11	✓	96
195.17	even	12	inner	975.2.bn.d.407.11		96
195.134	odd	6		195.2.bf.a.173.11	yes	96
195.173	even	12		195.2.bf.a.17.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.11	✓	96	65.43	odd	12
195.2.bf.a.17.14	yes	96	195.173	even	12
195.2.bf.a.23.11	yes	96	15.14	odd	2
195.2.bf.a.23.14	yes	96	5.4	even	2
195.2.bf.a.62.11	yes	96	5.3	odd	4
195.2.bf.a.62.14	yes	96	15.8	even	4
195.2.bf.a.173.11	yes	96	195.134	odd	6
195.2.bf.a.173.14	yes	96	65.4	even	6
975.2.bn.d.218.11		96	1.1	even	1	trivial
975.2.bn.d.218.14		96	3.2	odd	2	inner
975.2.bn.d.257.11		96	15.2	even	4	inner
975.2.bn.d.257.14		96	5.2	odd	4	inner
975.2.bn.d.368.11		96	13.4	even	6	inner
975.2.bn.d.368.14		96	39.17	odd	6	inner
975.2.bn.d.407.11		96	195.17	even	12	inner
975.2.bn.d.407.14		96	65.17	odd	12	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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.254998 - 0.0683265i) q^{2} +(-1.56121 - 0.750075i) q^{3} +(-1.67170 - 0.965154i) q^{4} +(0.346856 + 0.297940i) q^{6} +(-3.34011 + 0.894980i) q^{7} +(0.733676 + 0.733676i) q^{8} +(1.87477 + 2.34206i) q^{9} +(0.378689 + 0.655909i) q^{11} +(1.88593 + 2.76071i) q^{12} +(-3.19278 + 1.67516i) q^{13} +0.912873 q^{14} +(1.79335 + 3.10618i) q^{16} +(7.08724 - 1.89902i) q^{17} +(-0.318039 - 0.725316i) q^{18} +(-2.37830 + 4.11934i) q^{19} +(5.88593 + 1.10808i) q^{21} +(-0.0517490 - 0.193130i) q^{22} +(-1.15395 - 0.309199i) q^{23} +(-0.595113 - 1.69574i) q^{24} +(0.928610 - 0.209011i) q^{26} +(-1.17020 - 5.06267i) q^{27} +(6.44744 + 1.72759i) q^{28} +(-3.57287 - 6.18840i) q^{29} -3.75546i q^{31} +(-0.782155 - 2.91904i) q^{32} +(-0.0992334 - 1.30806i) q^{33} -1.93698 q^{34} +(-0.873607 - 5.72465i) q^{36} +(0.717836 - 2.67900i) q^{37} +(0.887922 - 0.887922i) q^{38} +(6.24111 - 0.220453i) q^{39} +(2.69593 + 4.66949i) q^{41} +(-1.42519 - 0.684723i) q^{42} +(-5.52432 + 1.48024i) q^{43} -1.46197i q^{44} +(0.273128 + 0.157690i) q^{46} +(2.28189 - 2.28189i) q^{47} +(-0.469938 - 6.19455i) q^{48} +(4.29318 - 2.47867i) q^{49} +(-12.4891 - 2.35119i) q^{51} +(6.95414 + 0.281170i) q^{52} +(5.30126 - 5.30126i) q^{53} +(-0.0475149 + 1.37093i) q^{54} +(-3.10719 - 1.79394i) q^{56} +(6.80285 - 4.64726i) q^{57} +(0.488244 + 1.82215i) q^{58} +(4.58287 + 2.64592i) q^{59} +(-1.28268 + 2.22167i) q^{61} +(-0.256597 + 0.957635i) q^{62} +(-8.35805 - 6.14484i) q^{63} -6.37561i q^{64} +(-0.0640708 + 0.340333i) q^{66} +(1.50179 - 5.60475i) q^{67} +(-13.6805 - 3.66569i) q^{68} +(1.56964 + 1.34827i) q^{69} +(-0.328162 + 0.568393i) q^{71} +(-0.342833 + 3.09379i) q^{72} +(8.39721 - 8.39721i) q^{73} +(-0.366094 + 0.634093i) q^{74} +(7.95159 - 4.59085i) q^{76} +(-1.85189 - 1.85189i) q^{77} +(-1.60653 - 0.370218i) q^{78} -6.35343i q^{79} +(-1.97045 + 8.78165i) q^{81} +(-0.368407 - 1.37491i) q^{82} +(2.33630 + 2.33630i) q^{83} +(-8.77001 - 7.53320i) q^{84} +1.50983 q^{86} +(0.936252 + 12.3413i) q^{87} +(-0.203390 + 0.759060i) q^{88} +(9.05197 - 5.22616i) q^{89} +(9.16501 - 8.45269i) q^{91} +(1.63062 + 1.63062i) q^{92} +(-2.81688 + 5.86307i) q^{93} +(-0.737790 + 0.425963i) q^{94} +(-0.968391 + 5.14392i) q^{96} +(-8.55305 + 2.29178i) q^{97} +(-1.26411 + 0.338717i) q^{98} +(-0.826218 + 2.11659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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