LMFDB - Embedded newform 975.2.bu.h.232.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(7,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("975.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			232.7
Character	$\chi$	$=$	975.232
Dual form			975.2.bu.h.643.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85389 - 1.07034i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.29127 - 2.23654i) q^{4} +(2.06774 - 0.554050i) q^{6} +(-2.03627 + 3.52692i) q^{7} -1.24701i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(1.85389 - 1.07034i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.29127 - 2.23654i) q^{4} +(2.06774 - 0.554050i) q^{6} +(-2.03627 + 3.52692i) q^{7} -1.24701i q^{8} +(0.866025 + 0.500000i) q^{9} +(4.87999 + 1.30759i) q^{11} +(1.82613 - 1.82613i) q^{12} +(3.60246 + 0.149317i) q^{13} +8.71802i q^{14} +(1.24780 + 2.16125i) q^{16} +(-1.96692 - 7.34064i) q^{17} +2.14068 q^{18} +(-0.657291 - 2.45304i) q^{19} +(-2.87972 + 2.87972i) q^{21} +(10.4465 - 2.79914i) q^{22} +(-2.00925 + 7.49862i) q^{23} +(0.322751 - 1.20452i) q^{24} +(6.83837 - 3.57905i) q^{26} +(0.707107 + 0.707107i) q^{27} +(5.25873 + 9.10838i) q^{28} +(3.83371 - 2.21340i) q^{29} +(-5.01884 - 5.01884i) q^{31} +(6.78645 + 3.91816i) q^{32} +(4.37528 + 2.52607i) q^{33} +(-11.5034 - 11.5034i) q^{34} +(2.23654 - 1.29127i) q^{36} +(-2.64530 - 4.58180i) q^{37} +(-3.84414 - 3.84414i) q^{38} +(3.44106 + 1.07661i) q^{39} +(-0.523994 + 1.95557i) q^{41} +(-2.25639 + 8.42096i) q^{42} +(-1.49368 + 0.400231i) q^{43} +(9.22584 - 9.22584i) q^{44} +(4.30117 + 16.0522i) q^{46} -2.01531 q^{47} +(0.645908 + 2.41056i) q^{48} +(-4.79278 - 8.30133i) q^{49} -7.59959i q^{51} +(4.98568 - 7.86422i) q^{52} +(5.36095 - 5.36095i) q^{53} +(2.06774 + 0.554050i) q^{54} +(4.39812 + 2.53926i) q^{56} -2.53958i q^{57} +(4.73818 - 8.20677i) q^{58} +(-5.35319 + 1.43438i) q^{59} +(1.15571 - 2.00175i) q^{61} +(-14.6762 - 3.93248i) q^{62} +(-3.52692 + 2.03627i) q^{63} +11.7839 q^{64} +10.8150 q^{66} +(-13.9539 + 8.05627i) q^{67} +(-18.9574 - 5.07963i) q^{68} +(-3.88157 + 6.72308i) q^{69} +(0.802569 - 0.215048i) q^{71} +(0.623507 - 1.07995i) q^{72} +3.04966i q^{73} +(-9.80819 - 5.66276i) q^{74} +(-6.33506 - 1.69747i) q^{76} +(-14.5487 + 14.5487i) q^{77} +(7.53169 - 1.68719i) q^{78} -4.65818i q^{79} +(0.500000 + 0.866025i) q^{81} +(1.12171 + 4.18627i) q^{82} -10.0391 q^{83} +(2.72212 + 10.1591i) q^{84} +(-2.34074 + 2.34074i) q^{86} +(4.27595 - 1.14574i) q^{87} +(1.63058 - 6.08542i) q^{88} +(0.796349 - 2.97201i) q^{89} +(-7.86220 + 12.4015i) q^{91} +(14.1765 + 14.1765i) q^{92} +(-3.54885 - 6.14679i) q^{93} +(-3.73616 + 2.15708i) q^{94} +(5.54111 + 5.54111i) q^{96} +(-0.885124 - 0.511027i) q^{97} +(-17.7705 - 10.2598i) q^{98} +(3.57240 + 3.57240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 24 q^{4} - 4 q^{6}+O(q^{10}) $ 32 * q + 24 * q^4 - 4 * q^6	$ 32 q + 24 q^{4} - 4 q^{6} - 16 q^{11} - 48 q^{16} + 24 q^{19} - 8 q^{21} + 16 q^{24} + 24 q^{26} - 12 q^{29} - 8 q^{31} - 56 q^{34} - 16 q^{39} - 12 q^{41} + 88 q^{44} - 32 q^{46} + 32 q^{49} - 4 q^{54} - 96 q^{56} - 92 q^{59} - 56 q^{61} - 128 q^{64} - 12 q^{71} + 120 q^{74} - 200 q^{76} + 16 q^{81} + 48 q^{84} + 96 q^{86} - 68 q^{89} + 216 q^{94} + 136 q^{96} - 8 q^{99}+O(q^{100}) $ 32 * q + 24 * q^4 - 4 * q^6 - 16 * q^11 - 48 * q^16 + 24 * q^19 - 8 * q^21 + 16 * q^24 + 24 * q^26 - 12 * q^29 - 8 * q^31 - 56 * q^34 - 16 * q^39 - 12 * q^41 + 88 * q^44 - 32 * q^46 + 32 * q^49 - 4 * q^54 - 96 * q^56 - 92 * q^59 - 56 * q^61 - 128 * q^64 - 12 * q^71 + 120 * q^74 - 200 * q^76 + 16 * q^81 + 48 * q^84 + 96 * q^86 - 68 * q^89 + 216 * q^94 + 136 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.85389	−	1.07034i	1.31090	−	0.756846i	0.328652	−	0.944451i	$-0.393406\pi$
$2$	1.85389	−	1.07034i	1.31090	−	0.756846i	0.982245	+	0.187605i	$0.0600724\pi$
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	1.29127	−	2.23654i	0.645633	−	1.11827i
$5$		0			0
$5$		0			0
$6$	2.06774	−	0.554050i	0.844152	−	0.226190i
$7$	−2.03627	+	3.52692i	−0.769637	+	1.33305i	0.168123	+	0.985766i	$0.446229\pi$
$7$	−2.03627	+	3.52692i	−0.769637	+	1.33305i	−0.937760	+	0.347284i	$0.887104\pi$
$8$		−	1.24701i		−	0.440886i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	4.87999	+	1.30759i	1.47137	+	0.394253i	0.903402	−	0.428795i	$-0.141062\pi$
$11$	4.87999	+	1.30759i	1.47137	+	0.394253i	0.567972	+	0.823048i	$0.307728\pi$
$12$	1.82613	−	1.82613i	0.527157	−	0.527157i
$13$	3.60246	+	0.149317i	0.999142	+	0.0414132i
$13$	3.60246	+	0.149317i	0.999142	+	0.0414132i
$14$			8.71802i			2.32999i
$15$		0			0
$16$	1.24780	+	2.16125i	0.311950	+	0.540312i
$17$	−1.96692	−	7.34064i	−0.477048	−	1.78037i	−0.613473	−	0.789716i	$-0.710228\pi$
$17$	−1.96692	−	7.34064i	−0.477048	−	1.78037i	0.136425	−	0.990650i	$-0.456439\pi$
$18$	2.14068			0.504564
$19$	−0.657291	−	2.45304i	−0.150793	−	0.562767i	−0.999429	−	0.0337895i	$-0.989242\pi$
$19$	−0.657291	−	2.45304i	−0.150793	−	0.562767i	0.848636	−	0.528977i	$-0.177424\pi$
$20$		0			0
$21$	−2.87972	+	2.87972i	−0.628406	+	0.628406i
$22$	10.4465	−	2.79914i	2.22721	−	0.596778i
$23$	−2.00925	+	7.49862i	−0.418958	+	1.56357i	0.357817	+	0.933792i	$0.383521\pi$
$23$	−2.00925	+	7.49862i	−0.418958	+	1.56357i	−0.776774	+	0.629779i	$0.783145\pi$
$24$	0.322751	−	1.20452i	0.0658813	−	0.245872i
$25$		0			0
$26$	6.83837	−	3.57905i	1.34112	−	0.701909i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	5.25873	+	9.10838i	0.993806	+	1.72132i
$29$	3.83371	−	2.21340i	0.711903	−	0.411017i	−0.0998625	−	0.995001i	$-0.531840\pi$
$29$	3.83371	−	2.21340i	0.711903	−	0.411017i	0.811765	+	0.583984i	$0.198507\pi$
$30$		0			0
$31$	−5.01884	−	5.01884i	−0.901410	−	0.901410i	0.0941486	−	0.995558i	$-0.469987\pi$
$31$	−5.01884	−	5.01884i	−0.901410	−	0.901410i	−0.995558	+	0.0941486i	$0.969987\pi$
$32$	6.78645	+	3.91816i	1.19969	+	0.692639i
$33$	4.37528	+	2.52607i	0.761639	+	0.439732i
$34$	−11.5034	−	11.5034i	−1.97282	−	1.97282i
$35$		0			0
$36$	2.23654	−	1.29127i	0.372756	−	0.215211i
$37$	−2.64530	−	4.58180i	−0.434885	−	0.753243i	0.562401	−	0.826865i	$-0.309878\pi$
$37$	−2.64530	−	4.58180i	−0.434885	−	0.753243i	−0.997286	+	0.0736213i	$0.976544\pi$
$38$	−3.84414	−	3.84414i	−0.623602	−	0.623602i
$39$	3.44106	+	1.07661i	0.551011	+	0.172396i
$40$		0			0
$41$	−0.523994	+	1.95557i	−0.0818342	+	0.305409i	−0.994696	−	0.102860i	$-0.967201\pi$
$41$	−0.523994	+	1.95557i	−0.0818342	+	0.305409i	0.912862	+	0.408269i	$0.133867\pi$
$42$	−2.25639	+	8.42096i	−0.348168	+	1.29938i
$43$	−1.49368	+	0.400231i	−0.227785	+	0.0610347i	−0.370906	−	0.928670i	$-0.620953\pi$
$43$	−1.49368	+	0.400231i	−0.227785	+	0.0610347i	0.143121	+	0.989705i	$0.454286\pi$
$44$	9.22584	−	9.22584i	1.39085	−	1.39085i
$45$		0			0
$46$	4.30117	+	16.0522i	0.634173	+	2.36677i
$47$	−2.01531			−0.293964			−0.146982	−	0.989139i	$-0.546956\pi$
$47$	−2.01531			−0.293964			−0.146982	+	0.989139i	$0.546956\pi$
$48$	0.645908	+	2.41056i	0.0932288	+	0.347934i
$49$	−4.79278	−	8.30133i	−0.684682	−	1.18590i
$50$		0			0
$51$		−	7.59959i		−	1.06416i
$52$	4.98568	−	7.86422i	0.691390	−	1.09057i
$53$	5.36095	−	5.36095i	0.736383	−	0.736383i	−0.235493	−	0.971876i	$-0.575671\pi$
$53$	5.36095	−	5.36095i	0.736383	−	0.736383i	0.971876	+	0.235493i	$0.0756706\pi$
$54$	2.06774	+	0.554050i	0.281384	+	0.0753966i
$55$		0			0
$56$	4.39812	+	2.53926i	0.587724	+	0.339322i
$57$		−	2.53958i		−	0.336375i
$58$	4.73818	−	8.20677i	0.622154	−	1.07760i
$59$	−5.35319	+	1.43438i	−0.696926	+	0.186741i	−0.589853	−	0.807510i	$-0.700814\pi$
$59$	−5.35319	+	1.43438i	−0.696926	+	0.186741i	−0.107073	+	0.994251i	$0.534148\pi$
$60$		0			0
$61$	1.15571	−	2.00175i	0.147974	−	0.256298i	−0.782505	−	0.622645i	$-0.786058\pi$
$61$	1.15571	−	2.00175i	0.147974	−	0.256298i	0.930478	+	0.366347i	$0.119392\pi$
$62$	−14.6762	−	3.93248i	−1.86388	−	0.499426i
$63$	−3.52692	+	2.03627i	−0.444350	+	0.256546i
$64$	11.7839			1.47299
$65$		0			0
$66$	10.8150			1.33124
$67$	−13.9539	+	8.05627i	−1.70474	+	0.984230i	−0.763921	+	0.645310i	$0.776728\pi$
$67$	−13.9539	+	8.05627i	−1.70474	+	0.984230i	−0.940815	+	0.338920i	$0.889938\pi$
$68$	−18.9574	−	5.07963i	−2.29893	−	0.615995i
$69$	−3.88157	+	6.72308i	−0.467286	+	0.809364i
$70$		0			0
$71$	0.802569	−	0.215048i	0.0952474	−	0.0255215i	−0.210881	−	0.977512i	$-0.567633\pi$
$71$	0.802569	−	0.215048i	0.0952474	−	0.0255215i	0.306128	+	0.951990i	$0.400966\pi$
$72$	0.623507	−	1.07995i	0.0734811	−	0.127273i
$73$			3.04966i			0.356936i	0.983946	+	0.178468i	$0.0571141\pi$
$73$			3.04966i			0.356936i	−0.983946	+	0.178468i	$0.942886\pi$
$74$	−9.80819	−	5.66276i	−1.14018	−	0.658283i
$75$		0			0
$76$	−6.33506	−	1.69747i	−0.726681	−	0.194714i
$77$	−14.5487	+	14.5487i	−1.65798	+	1.65798i
$78$	7.53169	−	1.68719i	0.852795	−	0.191037i
$79$		−	4.65818i		−	0.524087i	−0.965056	−	0.262043i	$-0.915604\pi$
$79$		−	4.65818i		−	0.524087i	0.965056	−	0.262043i	$-0.0843963\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.12171	+	4.18627i	0.123872	+	0.462296i
$83$	−10.0391			−1.10194			−0.550968	−	0.834526i	$-0.685742\pi$
$83$	−10.0391			−1.10194			−0.550968	+	0.834526i	$0.685742\pi$
$84$	2.72212	+	10.1591i	0.297007	+	1.10845i
$85$		0			0
$86$	−2.34074	+	2.34074i	−0.252408	+	0.252408i
$87$	4.27595	−	1.14574i	0.458430	−	0.122836i
$88$	1.63058	−	6.08542i	0.173821	−	0.648708i
$89$	0.796349	−	2.97201i	0.0844128	−	0.315033i	−0.910790	−	0.412871i	$-0.864526\pi$
$89$	0.796349	−	2.97201i	0.0844128	−	0.315033i	0.995202	+	0.0978381i	$0.0311927\pi$
$90$		0			0
$91$	−7.86220	+	12.4015i	−0.824183	+	1.30003i
$92$	14.1765	+	14.1765i	1.47800	+	1.47800i
$93$	−3.54885	−	6.14679i	−0.367999	−	0.637393i
$94$	−3.73616	+	2.15708i	−0.385356	+	0.222485i
$95$		0			0
$96$	5.54111	+	5.54111i	0.565537	+	0.565537i
$97$	−0.885124	−	0.511027i	−0.0898707	−	0.0518869i	0.454391	−	0.890802i	$-0.349857\pi$
$97$	−0.885124	−	0.511027i	−0.0898707	−	0.0518869i	−0.544262	+	0.838915i	$0.683190\pi$
$98$	−17.7705	−	10.2598i	−1.79509	−	1.03640i
$99$	3.57240	+	3.57240i	0.359040	+	0.359040i
$100$		0			0
$101$	3.94079	−	2.27521i	0.392123	−	0.226392i	−0.290957	−	0.956736i	$-0.593974\pi$
$101$	3.94079	−	2.27521i	0.392123	−	0.226392i	0.683080	+	0.730344i	$0.260640\pi$
$102$	−8.13416	−	14.0888i	−0.805402	−	1.39500i
$103$	0.567450	+	0.567450i	0.0559125	+	0.0559125i	0.734510	−	0.678598i	$-0.237412\pi$
$103$	0.567450	+	0.567450i	0.0559125	+	0.0559125i	−0.678598	+	0.734510i	$0.737412\pi$
$104$	0.186201	−	4.49232i	0.0182585	−	0.440508i
$105$		0			0
$106$	4.20054	−	15.6766i	0.407993	−	1.52265i
$107$	−0.259313	+	0.967769i	−0.0250687	+	0.0935577i	−0.977327	−	0.211736i	$-0.932088\pi$
$107$	−0.259313	+	0.967769i	−0.0250687	+	0.0935577i	0.952258	+	0.305294i	$0.0987548\pi$
$108$	2.49453	−	0.668408i	0.240037	−	0.0643176i
$109$	11.3728	−	11.3728i	1.08931	−	1.08931i	0.0937131	−	0.995599i	$-0.470126\pi$
$109$	11.3728	−	11.3728i	1.08931	−	1.08931i	0.995599	−	0.0937131i	$-0.0298736\pi$
$110$		0			0
$111$	−1.36931	−	5.11033i	−0.129969	−	0.485051i
$112$	−10.1634			−0.960352
$113$	−2.48453	−	9.27238i	−0.233724	−	0.872272i	−0.978720	−	0.205202i	$-0.934215\pi$
$113$	−2.48453	−	9.27238i	−0.233724	−	0.872272i	0.744995	−	0.667070i	$-0.232452\pi$
$114$	−2.71822	−	4.70809i	−0.254584	−	0.440953i
$115$		0			0
$116$		−	11.4323i		−	1.06146i
$117$	3.04516	+	1.93054i	0.281525	+	0.178479i
$118$	−8.38893	+	8.38893i	−0.772264	+	0.772264i
$119$	29.8950	+	8.01034i	2.74047	+	0.734307i
$120$		0			0
$121$	12.5783	+	7.26207i	1.14348	+	0.660188i
$122$		−	4.94803i		−	0.447974i
$123$	−1.01228	+	1.75332i	−0.0912742	+	0.158091i
$124$	−17.7055	+	4.74416i	−1.59000	+	0.426039i
$125$		0			0
$126$	−4.35901	+	7.55002i	−0.388331	+	0.672610i
$127$	10.8561	+	2.90889i	0.963324	+	0.258122i	0.706007	−	0.708205i	$-0.250495\pi$
$127$	10.8561	+	2.90889i	0.963324	+	0.258122i	0.257317	+	0.966327i	$0.417161\pi$
$128$	8.27310	−	4.77648i	0.731246	−	0.422185i
$129$	−1.54638			−0.136151
$130$		0			0
$131$	−5.70291			−0.498266			−0.249133	−	0.968469i	$-0.580146\pi$
$131$	−5.70291			−0.498266			−0.249133	+	0.968469i	$0.580146\pi$
$132$	11.2993	−	6.52366i	0.983478	−	0.567811i
$133$	9.99011	+	2.67684i	0.866252	+	0.232112i
$134$	−17.2459	+	29.8708i	−1.48982	+	2.58045i
$135$		0			0
$136$	−9.15388	+	2.45278i	−0.784939	+	0.210324i
$137$	−4.10771	+	7.11476i	−0.350945	+	0.607855i	−0.986415	−	0.164271i	$-0.947473\pi$
$137$	−4.10771	+	7.11476i	−0.350945	+	0.607855i	0.635470	+	0.772125i	$0.280806\pi$
$138$			16.6184i			1.41466i
$139$	−9.74579	−	5.62673i	−0.826627	−	0.477253i	0.0260693	−	0.999660i	$-0.491701\pi$
$139$	−9.74579	−	5.62673i	−0.826627	−	0.477253i	−0.852696	+	0.522407i	$0.825034\pi$
$140$		0			0
$141$	−1.94664	−	0.521601i	−0.163937	−	0.0439268i
$142$	1.25770	−	1.25770i	0.105544	−	0.105544i
$143$	17.3847	+	5.43921i	1.45378	+	0.454849i
$144$			2.49560i			0.207966i
$145$		0			0
$146$	3.26418	+	5.65373i	0.270146	+	0.467906i
$147$	−2.48092	−	9.25893i	−0.204623	−	0.763664i
$148$	−13.6632			−1.12310
$149$	1.95251	+	7.28686i	0.159956	+	0.596963i	0.998630	+	0.0523293i	$0.0166646\pi$
$149$	1.95251	+	7.28686i	0.159956	+	0.596963i	−0.838674	+	0.544633i	$0.816669\pi$
$150$		0			0
$151$	10.8750	−	10.8750i	0.884998	−	0.884998i	−0.109040	−	0.994037i	$-0.534778\pi$
$151$	10.8750	−	10.8750i	0.884998	−	0.884998i	0.994037	+	0.109040i	$0.0347775\pi$
$152$	−3.05898	+	0.819651i	−0.248116	+	0.0664825i
$153$	1.96692	−	7.34064i	0.159016	−	0.593455i
$154$	−11.3996	+	42.5439i	−0.918605	+	3.42828i
$155$		0			0
$156$	6.85121	−	6.30587i	0.548536	−	0.504873i
$157$	3.56566	+	3.56566i	0.284570	+	0.284570i	0.834929	−	0.550358i	$-0.185509\pi$
$157$	3.56566	+	3.56566i	0.284570	+	0.284570i	−0.550358	+	0.834929i	$0.685509\pi$
$158$	−4.98585	−	8.63575i	−0.396653	−	0.687023i
$159$	6.56579	−	3.79076i	0.520701	−	0.300627i
$160$		0			0
$161$	−22.3557	−	22.3557i	−1.76187	−	1.76187i
$162$	1.85389	+	1.07034i	0.145655	+	0.0840940i
$163$	−18.0894	−	10.4439i	−1.41687	−	0.818030i	−0.420848	−	0.907131i	$-0.638267\pi$
$163$	−18.0894	−	10.4439i	−1.41687	−	0.818030i	−0.996023	+	0.0891010i	$0.971601\pi$
$164$	3.69710	+	3.69710i	0.288695	+	0.288695i
$165$		0			0
$166$	−18.6114	+	10.7453i	−1.44452	+	0.833997i
$167$	8.49100	+	14.7068i	0.657053	+	1.13805i	0.981375	+	0.192103i	$0.0615307\pi$
$167$	8.49100	+	14.7068i	0.657053	+	1.13805i	−0.324322	+	0.945947i	$0.605136\pi$
$168$	3.59105	+	3.59105i	0.277056	+	0.277056i
$169$	12.9554	+	1.07582i	0.996570	+	0.0827553i
$170$		0			0
$171$	0.657291	−	2.45304i	0.0502643	−	0.187589i
$172$	−1.03361	+	3.85749i	−0.0788120	+	0.294130i
$173$	−5.23045	+	1.40149i	−0.397664	+	0.106554i	−0.452108	−	0.891963i	$-0.649328\pi$
$173$	−5.23045	+	1.40149i	−0.397664	+	0.106554i	0.0544444	+	0.998517i	$0.482661\pi$
$174$	6.70080	−	6.70080i	0.507986	−	0.507986i
$175$		0			0
$176$	3.26322	+	12.1785i	0.245974	+	0.917989i
$177$	−5.54203			−0.416565
$178$	−1.70473	−	6.36215i	−0.127775	−	0.476863i
$179$	−11.0541	−	19.1462i	−0.826221	−	1.43106i	−0.900982	−	0.433856i	$-0.857153\pi$
$179$	−11.0541	−	19.1462i	−0.826221	−	1.43106i	0.0747607	−	0.997202i	$-0.476181\pi$
$180$		0			0
$181$		−	20.3453i		−	1.51226i	−0.654424	−	0.756128i	$-0.727089\pi$
$181$		−	20.3453i		−	1.51226i	0.654424	−	0.756128i	$-0.272911\pi$
$182$	−1.30175	+	31.4063i	−0.0964921	+	2.32799i
$183$	1.63442	−	1.63442i	0.120820	−	0.120820i
$184$	9.35089	+	2.50556i	0.689357	+	0.184713i
$185$		0			0
$186$	−13.1583	−	7.59698i	−0.964817	−	0.557037i
$187$		−	38.3942i		−	2.80766i
$188$	−2.60230	+	4.50732i	−0.189793	+	0.328730i
$189$	−3.93377	+	1.05405i	−0.286140	+	0.0766709i
$190$		0			0
$191$	−13.1768	+	22.8228i	−0.953438	+	1.65140i	−0.215535	+	0.976496i	$0.569150\pi$
$191$	−13.1768	+	22.8228i	−0.953438	+	1.65140i	−0.737903	+	0.674907i	$0.764184\pi$
$192$	11.3824	+	3.04989i	0.821451	+	0.220107i
$193$	9.61301	−	5.55007i	0.691959	−	0.399503i	−0.112386	−	0.993665i	$-0.535849\pi$
$193$	9.61301	−	5.55007i	0.691959	−	0.399503i	0.804346	+	0.594162i	$0.202516\pi$
$194$	−2.18789			−0.157082
$195$		0			0
$196$	−24.7550			−1.76821
$197$	−14.2989	+	8.25550i	−1.01876	+	0.588180i	−0.913744	−	0.406291i	$-0.866822\pi$
$197$	−14.2989	+	8.25550i	−1.01876	+	0.588180i	−0.105014	+	0.994471i	$0.533489\pi$
$198$	10.4465	+	2.79914i	0.742402	+	0.198926i
$199$	7.71221	−	13.3579i	0.546704	−	0.946920i	−0.451793	−	0.892123i	$-0.649216\pi$
$199$	7.71221	−	13.3579i	0.546704	−	0.946920i	0.998498	−	0.0547970i	$-0.0174512\pi$
$200$		0			0
$201$	−15.5635	+	4.17023i	−1.09777	+	0.294145i
$202$	4.87052	−	8.43598i	0.342688	−	0.593554i
$203$			18.0283i			1.26534i
$204$	−16.9968	−	9.81308i	−1.19001	−	0.687053i
$205$		0			0
$206$	1.65935	+	0.444623i	0.115613	+	0.0309783i
$207$	−5.48937	+	5.48937i	−0.381538	+	0.381538i
$208$	4.17243	+	7.97213i	0.289306	+	0.552768i
$209$		−	12.8303i		−	0.887490i
$210$		0			0
$211$	8.52223	+	14.7609i	0.586694	+	1.01618i	0.994662	+	0.103188i	$0.0329043\pi$
$211$	8.52223	+	14.7609i	0.586694	+	1.01618i	−0.407968	+	0.912996i	$0.633762\pi$
$212$	−5.06755	−	18.9124i	−0.348041	−	1.29891i
$213$	0.830880			0.0569310
$214$	0.555107	+	2.07169i	0.0379463	+	0.141618i
$215$		0			0
$216$	0.881773	−	0.881773i	0.0599970	−	0.0599970i
$217$	27.9207	−	7.48134i	1.89538	−	0.507866i
$218$	8.91106	−	33.2565i	0.603533	−	2.25242i
$219$	−0.789311	+	2.94575i	−0.0533367	+	0.199055i
$220$		0			0
$221$	−5.98966	−	26.7380i	−0.402908	−	1.79859i
$222$	−8.00835	−	8.00835i	−0.537485	−	0.537485i
$223$	5.25332	+	9.09902i	0.351788	+	0.609315i	0.986563	−	0.163382i	$-0.0522404\pi$
$223$	5.25332	+	9.09902i	0.351788	+	0.609315i	−0.634775	+	0.772697i	$0.718907\pi$
$224$	−27.6381	+	15.9568i	−1.84665	+	1.06616i
$225$		0			0
$226$	−14.5306	−	14.5306i	−0.966564	−	0.966564i
$227$	−8.20778	−	4.73876i	−0.544770	−	0.314523i	0.202240	−	0.979336i	$-0.435178\pi$
$227$	−8.20778	−	4.73876i	−0.544770	−	0.314523i	−0.747010	+	0.664813i	$0.768511\pi$
$228$	−5.67986	−	3.27927i	−0.376158	−	0.217175i
$229$	0.749267	+	0.749267i	0.0495130	+	0.0495130i	0.731430	−	0.681917i	$-0.238853\pi$
$229$	0.749267	+	0.749267i	0.0495130	+	0.0495130i	−0.681917	+	0.731430i	$0.738853\pi$
$230$		0			0
$231$	−17.8185	+	10.2875i	−1.17237	+	0.676869i
$232$	−2.76014	−	4.78070i	−0.181212	−	0.313868i
$233$	6.92230	+	6.92230i	0.453495	+	0.453495i	0.896513	−	0.443018i	$-0.146092\pi$
$233$	6.92230	+	6.92230i	0.453495	+	0.453495i	−0.443018	+	0.896513i	$0.646092\pi$
$234$	7.71173	+	0.319641i	0.504131	+	0.0208956i
$235$		0			0
$236$	−3.70434	+	13.8248i	−0.241132	+	0.899917i
$237$	1.20563	−	4.49946i	0.0783139	−	0.292271i
$238$	63.9958	−	17.1476i	4.14823	−	1.11152i
$239$	−0.349570	+	0.349570i	−0.0226118	+	0.0226118i	−0.718322	−	0.695711i	$-0.755090\pi$
$239$	−0.349570	+	0.349570i	−0.0226118	+	0.0226118i	0.695711	+	0.718322i	$0.255090\pi$
$240$		0			0
$241$	−3.25070	−	12.1318i	−0.209396	−	0.781476i	−0.988065	−	0.154041i	$-0.950771\pi$
$241$	−3.25070	−	12.1318i	−0.209396	−	0.781476i	0.778669	−	0.627435i	$-0.215895\pi$
$242$	31.0916			1.99864
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−2.98466	−	5.16959i	−0.191073	−	0.330949i
$245$		0			0
$246$			4.33394i			0.276322i
$247$	−2.00158	−	8.93513i	−0.127358	−	0.568529i
$248$	−6.25856	+	6.25856i	−0.397419	+	0.397419i
$249$	−9.69705	−	2.59832i	−0.614525	−	0.164662i
$250$		0			0
$251$	13.1327	+	7.58219i	0.828931	+	0.478584i	0.853487	−	0.521115i	$-0.174484\pi$
$251$	13.1327	+	7.58219i	0.828931	+	0.478584i	−0.0245553	+	0.999698i	$0.507817\pi$
$252$			10.5175i			0.662537i
$253$	−19.6103	+	33.9660i	−1.23289	+	2.13542i
$254$	23.2395	−	6.22701i	1.45818	−	0.390717i
$255$		0			0
$256$	−1.55895	+	2.70019i	−0.0974346	+	0.168762i
$257$	−0.957983	−	0.256691i	−0.0597573	−	0.0160119i	0.228817	−	0.973470i	$-0.426514\pi$
$257$	−0.957983	−	0.256691i	−0.0597573	−	0.0160119i	−0.288574	+	0.957458i	$0.593181\pi$
$258$	−2.86681	+	1.65515i	−0.178480	+	0.103045i
$259$	21.5462			1.33881
$260$		0			0
$261$	4.42679			0.274011
$262$	−10.5726	+	6.10407i	−0.653175	+	0.377111i
$263$	−1.49779	−	0.401331i	−0.0923575	−	0.0247471i	0.212344	−	0.977195i	$-0.431890\pi$
$263$	−1.49779	−	0.401331i	−0.0923575	−	0.0247471i	−0.304702	+	0.952448i	$0.598557\pi$
$264$	3.15005	−	5.45604i	0.193872	−	0.335796i
$265$		0			0
$266$	21.3857	−	5.73027i	1.31124	−	0.351346i
$267$	1.53843	−	2.66463i	0.0941502	−	0.163073i
$268$			41.6111i			2.54180i
$269$	−7.77120	−	4.48671i	−0.473819	−	0.273559i	0.244018	−	0.969771i	$-0.421534\pi$
$269$	−7.77120	−	4.48671i	−0.473819	−	0.273559i	−0.717837	+	0.696211i	$0.754868\pi$
$270$		0			0
$271$	7.09458	+	1.90099i	0.430965	+	0.115477i	0.467779	−	0.883845i	$-0.345054\pi$
$271$	7.09458	+	1.90099i	0.430965	+	0.115477i	−0.0368141	+	0.999322i	$0.511721\pi$
$272$	13.4106	−	13.4106i	0.813139	−	0.813139i
$273$	−10.8041	+	9.94407i	−0.653891	+	0.601843i
$274$			17.5866i			1.06245i
$275$		0			0
$276$	10.0243	+	17.3626i	0.603391	+	1.04510i
$277$	6.46199	+	24.1165i	0.388264	+	1.44902i	0.832958	+	0.553337i	$0.186646\pi$
$277$	6.46199	+	24.1165i	0.388264	+	1.44902i	−0.444694	+	0.895682i	$0.646688\pi$
$278$	−24.0901			−1.44483
$279$	−1.83702	−	6.85586i	−0.109980	−	0.410449i
$280$		0			0
$281$	−15.0799	+	15.0799i	−0.899592	+	0.899592i	−0.995400	−	0.0958081i	$-0.969456\pi$
$281$	−15.0799	+	15.0799i	−0.899592	+	0.899592i	0.0958081	+	0.995400i	$0.469456\pi$
$282$	−4.16715	+	1.11658i	−0.248150	+	0.0664916i
$283$	2.47772	−	9.24699i	0.147285	−	0.549677i	−0.852358	−	0.522959i	$-0.824828\pi$
$283$	2.47772	−	9.24699i	0.147285	−	0.549677i	0.999643	−	0.0267173i	$-0.00850540\pi$
$284$	0.555367	−	2.07266i	0.0329550	−	0.122990i
$285$		0			0
$286$	38.0511	−	8.52393i	2.25001	−	0.504031i
$287$	−5.83016	−	5.83016i	−0.344143	−	0.344143i
$288$	3.91816	+	6.78645i	0.230880	+	0.399895i
$289$	−35.2938	+	20.3769i	−2.07610	+	1.19864i
$290$		0			0
$291$	−0.722701	−	0.722701i	−0.0423655	−	0.0423655i
$292$	6.82068	+	3.93792i	0.399150	+	0.230450i
$293$	7.24931	+	4.18539i	0.423509	+	0.244513i	0.696578	−	0.717481i	$-0.254705\pi$
$293$	7.24931	+	4.18539i	0.423509	+	0.244513i	−0.273068	+	0.961995i	$0.588039\pi$
$294$	−14.5096	−	14.5096i	−0.846216	−	0.846216i
$295$		0			0
$296$	−5.71357	+	3.29873i	−0.332095	+	0.191735i
$297$	2.52607	+	4.37528i	0.146577	+	0.253880i
$298$	11.4192	+	11.4192i	0.661494	+	0.661494i
$299$	−8.35791	+	26.7135i	−0.483350	+	1.54488i
$300$		0			0
$301$	1.62996	−	6.08308i	0.0939492	−	0.350623i
$302$	8.52108	−	31.8011i	0.490333	−	1.82995i
$303$	4.39538	−	1.17774i	0.252508	−	0.0676593i
$304$	4.48147	−	4.48147i	0.257030	−	0.257030i
$305$		0			0
$306$	−4.21055	−	15.7140i	−0.240701	−	0.898309i
$307$	3.84610			0.219509			0.109754	−	0.993959i	$-0.464994\pi$
$307$	3.84610			0.219509			0.109754	+	0.993959i	$0.464994\pi$
$308$	13.7525	+	51.3251i	0.783622	+	2.92452i
$309$	0.401248	+	0.694982i	0.0228262	+	0.0395361i
$310$		0			0
$311$		−	8.52866i		−	0.483616i	−0.970324	−	0.241808i	$-0.922260\pi$
$311$		−	8.52866i		−	0.483616i	0.970324	−	0.241808i	$-0.0777404\pi$
$312$	1.34255	−	4.29105i	0.0760071	−	0.242933i
$313$	10.3772	−	10.3772i	0.586552	−	0.586552i	−0.350144	−	0.936696i	$-0.613867\pi$
$313$	10.3772	−	10.3772i	0.586552	−	0.586552i	0.936696	+	0.350144i	$0.113867\pi$
$314$	10.4268	+	2.79385i	0.588418	+	0.157666i
$315$		0			0
$316$	−10.4182	−	6.01495i	−0.586070	−	0.338367i
$317$		−	0.583305i		−	0.0327616i	−0.999866	−	0.0163808i	$-0.994786\pi$
$317$		−	0.583305i		−	0.0327616i	0.999866	−	0.0163808i	$-0.00521441\pi$
$318$	8.11483	−	14.0553i	0.455057	−	0.788182i
$319$	21.6027	−	5.78843i	1.20952	−	0.324090i
$320$		0			0
$321$	−0.500954	+	0.867678i	−0.0279605	+	0.0484290i
$322$	−65.3731	−	17.5167i	−3.64310	−	0.976166i
$323$	−16.7141	+	9.64987i	−0.929995	+	0.536933i
$324$	2.58253			0.143474
$325$		0			0
$326$	−44.7142			−2.47649
$327$	13.9287	−	8.04175i	0.770260	−	0.444710i
$328$	2.43863	+	0.653429i	0.134651	+	0.0360796i
$329$	4.10372	−	7.10785i	0.226245	−	0.391868i
$330$		0			0
$331$	−1.26183	+	0.338105i	−0.0693562	+	0.0185839i	−0.293330	−	0.956011i	$-0.594764\pi$
$331$	−1.26183	+	0.338105i	−0.0693562	+	0.0185839i	0.223974	+	0.974595i	$0.428097\pi$
$332$	−12.9632	+	22.4529i	−0.711446	+	1.23226i
$333$		−	5.29061i		−	0.289923i
$334$	31.4827	+	18.1766i	1.72266	+	0.994577i
$335$		0			0
$336$	−9.81710	−	2.63048i	−0.535567	−	0.143505i
$337$	12.2556	−	12.2556i	0.667606	−	0.667606i	−0.289556	−	0.957161i	$-0.593508\pi$
$337$	12.2556	−	12.2556i	0.667606	−	0.667606i	0.957161	+	0.289556i	$0.0935075\pi$
$338$	25.1694	−	11.8723i	1.36903	−	0.645767i
$339$		−	9.59947i		−	0.521372i
$340$		0			0
$341$	−17.9293	−	31.0545i	−0.970926	−	1.68169i
$342$	−1.40705	−	5.25119i	−0.0760847	−	0.283952i
$343$	10.5298			0.568553
$344$	0.499095	+	1.86265i	0.0269094	+	0.100427i
$345$		0			0
$346$	−8.19659	+	8.19659i	−0.440651	+	0.440651i
$347$	−7.18945	+	1.92641i	−0.385950	+	0.103415i	−0.446576	−	0.894746i	$-0.647357\pi$
$347$	−7.18945	+	1.92641i	−0.385950	+	0.103415i	0.0606265	+	0.998161i	$0.480690\pi$
$348$	2.95890	−	11.0428i	0.158614	−	0.591955i
$349$	−6.26650	+	23.3869i	−0.335438	+	1.25187i	0.567956	+	0.823059i	$0.307734\pi$
$349$	−6.26650	+	23.3869i	−0.335438	+	1.25187i	−0.903394	+	0.428812i	$0.858932\pi$
$350$		0			0
$351$	2.44174	+	2.65291i	0.130330	+	0.141602i
$352$	27.9945	+	27.9945i	1.49211	+	1.49211i
$353$	−4.09697	−	7.09616i	−0.218060	−	0.377690i	0.736155	−	0.676813i	$-0.236639\pi$
$353$	−4.09697	−	7.09616i	−0.218060	−	0.377690i	−0.954215	+	0.299123i	$0.903306\pi$
$354$	−10.2743	+	5.93187i	−0.546073	+	0.315275i
$355$		0			0
$356$	−5.61872	−	5.61872i	−0.297792	−	0.297792i
$357$	26.8031	+	15.4748i	1.41857	+	0.819013i
$358$	−40.9861	−	23.6633i	−2.16618	−	1.25065i
$359$	2.89818	+	2.89818i	0.152960	+	0.152960i	0.779439	−	0.626478i	$-0.215504\pi$
$359$	2.89818	+	2.89818i	0.152960	+	0.152960i	−0.626478	+	0.779439i	$0.715504\pi$
$360$		0			0
$361$	10.8691	−	6.27527i	0.572058	−	0.330278i
$362$	−21.7764	−	37.7179i	−1.14454	−	1.98241i
$363$	10.2701	+	10.2701i	0.539041	+	0.539041i
$364$	17.5843	+	33.5978i	0.921668	+	1.76100i
$365$		0			0
$366$	1.28064	−	4.77943i	0.0669404	−	0.249825i
$367$	−5.81185	+	21.6901i	−0.303376	+	1.13222i	0.630958	+	0.775817i	$0.282662\pi$
$367$	−5.81185	+	21.6901i	−0.303376	+	1.13222i	−0.934334	+	0.356398i	$0.884005\pi$
$368$	−18.7135	+	5.01428i	−0.975510	+	0.261387i
$369$	−1.43158	+	1.43158i	−0.0745250	+	0.0745250i
$370$		0			0
$371$	7.99130	+	29.8240i	0.414888	+	1.54838i
$372$	−18.3300			−0.950369
$373$	−4.09251	−	15.2735i	−0.211902	−	0.790830i	−0.987234	−	0.159276i	$-0.949084\pi$
$373$	−4.09251	−	15.2735i	−0.211902	−	0.790830i	0.775332	−	0.631554i	$-0.217583\pi$
$374$	−41.0949	−	71.1785i	−2.12497	−	3.68055i
$375$		0			0
$376$			2.51313i			0.129605i
$377$	14.1413	−	7.40122i	0.728313	−	0.381182i
$378$	−6.16457	+	6.16457i	−0.317071	+	0.317071i
$379$	14.7566	+	3.95402i	0.757995	+	0.203104i	0.617062	−	0.786915i	$-0.288323\pi$
$379$	14.7566	+	3.95402i	0.757995	+	0.203104i	0.140934	+	0.990019i	$0.454990\pi$
$380$		0			0
$381$	9.73332	+	5.61954i	0.498653	+	0.287898i
$382$			56.4146i			2.88642i
$383$	8.55450	−	14.8168i	0.437115	−	0.757105i	−0.560351	−	0.828255i	$-0.689334\pi$
$383$	8.55450	−	14.8168i	0.437115	−	0.757105i	0.997466	+	0.0711504i	$0.0226670\pi$
$384$	9.22745	−	2.47249i	0.470886	−	0.126174i
$385$		0			0
$386$	11.8810	−	20.5784i	0.604725	−	1.04741i
$387$	−1.49368	−	0.400231i	−0.0759282	−	0.0203449i
$388$	−2.28586	+	1.31974i	−0.116047	+	0.0669998i
$389$	−4.80275			−0.243509			−0.121755	−	0.992560i	$-0.538852\pi$
$389$	−4.80275			−0.243509			−0.121755	+	0.992560i	$0.538852\pi$
$390$		0			0
$391$	58.9967			2.98359
$392$	−10.3519	+	5.97666i	−0.522849	+	0.301867i
$393$	−5.50859	−	1.47602i	−0.277872	−	0.0744555i
$394$	−17.6724	+	30.6095i	−0.890324	+	1.54209i
$395$		0			0
$396$	12.6027	−	3.37689i	0.633311	−	0.169695i
$397$	−0.680810	+	1.17920i	−0.0341689	+	0.0591822i	−0.882604	−	0.470117i	$-0.844212\pi$
$397$	−0.680810	+	1.17920i	−0.0341689	+	0.0591822i	0.848435	+	0.529299i	$0.177545\pi$
$398$		−	33.0188i		−	1.65508i
$399$	8.95688	+	5.17126i	0.448405	+	0.258887i
$400$		0			0
$401$	−0.370224	−	0.0992012i	−0.0184881	−	0.00495387i	0.249563	−	0.968359i	$-0.419713\pi$
$401$	−0.370224	−	0.0992012i	−0.0184881	−	0.00495387i	−0.268051	+	0.963405i	$0.586380\pi$
$402$	−24.3894	+	24.3894i	−1.21643	+	1.21643i
$403$	−17.3307	−	18.8295i	−0.863306	−	0.937967i
$404$		−	11.7516i		−	0.584665i
$405$		0			0
$406$	19.2964	+	33.4224i	0.957665	+	1.65872i
$407$	−6.91795	−	25.8181i	−0.342910	−	1.27976i
$408$	−9.47680			−0.469171
$409$	8.23244	+	30.7239i	0.407068	+	1.51920i	0.800210	+	0.599720i	$0.204721\pi$
$409$	8.23244	+	30.7239i	0.407068	+	1.51920i	−0.393142	+	0.919478i	$0.628612\pi$
$410$		0			0
$411$	−5.80917	+	5.80917i	−0.286545	+	0.286545i
$412$	2.00185	−	0.536395i	0.0986242	−	0.0264263i
$413$	5.84158	−	21.8011i	0.287445	−	1.07276i
$414$	−4.30117	+	16.0522i	−0.211391	+	0.788922i
$415$		0			0
$416$	23.8628	+	15.1283i	1.16997	+	0.741727i
$417$	−7.95740	−	7.95740i	−0.389676	−	0.389676i
$418$	−13.7328	−	23.7859i	−0.671694	−	1.16341i
$419$	−10.1771	+	5.87575i	−0.497184	+	0.287049i	−0.727550	−	0.686055i	$-0.759341\pi$
$419$	−10.1771	+	5.87575i	−0.497184	+	0.287049i	0.230366	+	0.973104i	$0.426008\pi$
$420$		0			0
$421$	18.7052	+	18.7052i	0.911638	+	0.911638i	0.996401	−	0.0847633i	$-0.0270134\pi$
$421$	18.7052	+	18.7052i	0.911638	+	0.911638i	−0.0847633	+	0.996401i	$0.527013\pi$
$422$	31.5985	+	18.2434i	1.53819	+	0.888075i
$423$	−1.74531	−	1.00766i	−0.0848600	−	0.0489939i
$424$	−6.68518	−	6.68518i	−0.324661	−	0.324661i
$425$		0			0
$426$	1.54036	−	0.889327i	0.0746306	−	0.0430880i
$427$	4.70668	+	8.15221i	0.227772	+	0.394513i
$428$	1.82961	+	1.82961i	0.0884375	+	0.0884375i
$429$	15.3846	+	9.75337i	0.742775	+	0.470897i
$430$		0			0
$431$	−5.41749	+	20.2184i	−0.260951	+	0.973884i	0.703731	+	0.710467i	$0.251516\pi$
$431$	−5.41749	+	20.2184i	−0.260951	+	0.973884i	−0.964682	+	0.263417i	$0.915150\pi$
$432$	−0.645908	+	2.41056i	−0.0310763	+	0.115978i
$433$	−14.8867	+	3.98889i	−0.715411	+	0.191694i	−0.598123	−	0.801404i	$-0.704087\pi$
$433$	−14.8867	+	3.98889i	−0.715411	+	0.191694i	−0.117288	+	0.993098i	$0.537420\pi$
$434$	43.7543	−	43.7543i	2.10027	−	2.10027i
$435$		0			0
$436$	−10.7503	−	40.1208i	−0.514848	−	1.92144i
$437$	19.7151			0.943101
$438$	1.68967	+	6.30592i	0.0807353	+	0.301308i
$439$	−11.5106	−	19.9369i	−0.549371	−	0.951538i	−0.998318	−	0.0579797i	$-0.981534\pi$
$439$	−11.5106	−	19.9369i	−0.549371	−	0.951538i	0.448947	−	0.893558i	$-0.351799\pi$
$440$		0			0
$441$		−	9.58555i		−	0.456455i
$442$	−39.7230	−	43.1583i	−1.88943	−	2.05283i
$443$	−17.8981	+	17.8981i	−0.850366	+	0.850366i	−0.990178	−	0.139812i	$-0.955350\pi$
$443$	−17.8981	+	17.8981i	−0.850366	+	0.850366i	0.139812	+	0.990178i	$0.455350\pi$
$444$	−13.1976	−	3.53628i	−0.626330	−	0.167825i
$445$		0			0
$446$	19.4781	+	11.2457i	0.922316	+	0.532499i
$447$			7.54391i			0.356815i
$448$	−23.9952	+	41.5608i	−1.13366	+	1.96356i
$449$	−8.79239	+	2.35591i	−0.414938	+	0.111182i	−0.460248	−	0.887791i	$-0.652239\pi$
$449$	−8.79239	+	2.35591i	−0.414938	+	0.111182i	0.0453092	+	0.998973i	$0.485573\pi$
$450$		0			0
$451$	−5.11418	+	8.85802i	−0.240817	+	0.417108i
$452$	−23.9462	−	6.41636i	−1.12633	−	0.301800i
$453$	13.3191	−	7.68981i	0.625788	−	0.361299i
$454$	−20.2884			−0.952182
$455$		0			0
$456$	−3.16689			−0.148303
$457$	7.68499	−	4.43693i	0.359489	−	0.207551i	−0.309368	−	0.950942i	$-0.600117\pi$
$457$	7.68499	−	4.43693i	0.359489	−	0.207551i	0.668856	+	0.743392i	$0.266784\pi$
$458$	2.19103	+	0.587085i	0.102380	+	0.0274327i
$459$	3.79979	−	6.58144i	0.177359	−	0.307195i
$460$		0			0
$461$	7.03375	−	1.88469i	0.327594	−	0.0877786i	−0.0912735	−	0.995826i	$-0.529094\pi$
$461$	7.03375	−	1.88469i	0.327594	−	0.0877786i	0.418868	+	0.908047i	$0.362427\pi$
$462$	−22.0223	+	38.1438i	−1.02457	+	1.77461i
$463$		−	42.5422i		−	1.97710i	−0.150881	−	0.988552i	$-0.548211\pi$
$463$		−	42.5422i		−	1.97710i	0.150881	−	0.988552i	$-0.451789\pi$
$464$	9.56740	+	5.52374i	0.444155	+	0.256433i
$465$		0			0
$466$	20.2424	+	5.42393i	0.937711	+	0.251259i
$467$	14.6180	−	14.6180i	0.676441	−	0.676441i	−0.282752	−	0.959193i	$-0.591247\pi$
$467$	14.6180	−	14.6180i	0.676441	−	0.676441i	0.959193	+	0.282752i	$0.0912474\pi$
$468$	8.24984	−	4.31778i	0.381349	−	0.199589i
$469$		−	65.6189i		−	3.03000i
$470$		0			0
$471$	2.52130	+	4.36702i	0.116175	+	0.201222i
$472$	1.78870	+	6.67551i	0.0823315	+	0.307265i
$473$	−7.81251			−0.359219
$474$	−2.58087	−	9.63193i	−0.118543	−	0.442409i
$475$		0			0
$476$	56.5178	−	56.5178i	2.59049	−	2.59049i
$477$	7.32319	−	1.96224i	0.335306	−	0.0898449i
$478$	−0.273903	+	1.02222i	−0.0125281	+	0.0467553i
$479$	−1.97298	+	7.36326i	−0.0901477	+	0.336436i	−0.996239	−	0.0866460i	$-0.972385\pi$
$479$	−1.97298	+	7.36326i	−0.0901477	+	0.336436i	0.906091	+	0.423082i	$0.139052\pi$
$480$		0			0
$481$	−8.84545	−	16.9007i	−0.403318	−	0.770607i
$482$	−19.0116	−	19.0116i	−0.865954	−	0.865954i
$483$	−15.8078	−	27.3800i	−0.719282	−	1.24583i
$484$	32.4838	−	18.7545i	1.47653	−	0.852478i
$485$		0			0
$486$	1.51369	+	1.51369i	0.0686625	+	0.0686625i
$487$	−4.23530	−	2.44525i	−0.191920	−	0.110805i	0.400961	−	0.916095i	$-0.368676\pi$
$487$	−4.23530	−	2.44525i	−0.191920	−	0.110805i	−0.592881	+	0.805290i	$0.702010\pi$
$488$	−2.49622	−	1.44119i	−0.112998	−	0.0652396i
$489$	−14.7699	−	14.7699i	−0.667919	−	0.667919i
$490$		0			0
$491$	−16.3460	+	9.43738i	−0.737686	+	0.425903i	−0.821227	−	0.570601i	$-0.806710\pi$
$491$	−16.3460	+	9.43738i	−0.737686	+	0.425903i	0.0835416	+	0.996504i	$0.473377\pi$
$492$	2.61424	+	4.52800i	0.117859	+	0.204138i
$493$	−23.7883	−	23.7883i	−1.07137	−	1.07137i
$494$	−13.2744	−	14.4223i	−0.597241	−	0.648892i
$495$		0			0
$496$	4.58446	−	17.1095i	0.205849	−	0.768237i
$497$	−0.875789	+	3.26849i	−0.0392845	+	0.146612i
$498$	−20.7583	+	5.56218i	−0.930203	+	0.249247i
$499$	16.0291	−	16.0291i	0.717562	−	0.717562i	−0.250543	−	0.968105i	$-0.580609\pi$
$499$	16.0291	−	16.0291i	0.717562	−	0.717562i	0.968105	+	0.250543i	$0.0806092\pi$
$500$		0			0
$501$	4.39526	+	16.4034i	0.196366	+	0.732848i
$502$	32.4622			1.44886
$503$	2.28953	+	8.54465i	0.102085	+	0.380987i	0.997998	−	0.0632425i	$-0.0201441\pi$
$503$	2.28953	+	8.54465i	0.102085	+	0.380987i	−0.895913	+	0.444230i	$0.853477\pi$
$504$	2.53926	+	4.39812i	0.113107	+	0.195908i
$505$		0			0
$506$			83.9587i			3.73242i
$507$	12.2355	+	4.39227i	0.543399	+	0.195067i
$508$	20.5240	−	20.5240i	0.910603	−	0.910603i
$509$	24.3289	+	6.51891i	1.07836	+	0.288946i	0.753924	−	0.656962i	$-0.228159\pi$
$509$	24.3289	+	6.51891i	1.07836	+	0.288946i	0.324436	+	0.945908i	$0.394825\pi$
$510$		0			0
$511$	−10.7559	−	6.20993i	−0.475814	−	0.274711i
$512$			25.7804i			1.13934i
$513$	1.26979	−	2.19934i	0.0560625	−	0.0971031i
$514$	−2.05074	+	0.549494i	−0.0904542	+	0.0242371i
$515$		0			0
$516$	−1.99678	+	3.45853i	−0.0879034	+	0.152253i
$517$	−9.83472	−	2.63520i	−0.432530	−	0.115896i
$518$	39.9442	−	23.0618i	1.75505	−	1.01328i
$519$	−5.41496			−0.237690
$520$		0			0
$521$	−19.4960			−0.854135			−0.427067	−	0.904220i	$-0.640453\pi$
$521$	−19.4960			−0.854135			−0.427067	+	0.904220i	$0.640453\pi$
$522$	8.20677	−	4.73818i	0.359201	−	0.207385i
$523$	−18.7893	−	5.03458i	−0.821599	−	0.220147i	−0.176554	−	0.984291i	$-0.556495\pi$
$523$	−18.7893	−	5.03458i	−0.821599	−	0.220147i	−0.645046	+	0.764144i	$0.723162\pi$
$524$	−7.36397	+	12.7548i	−0.321697	+	0.557195i
$525$		0			0
$526$	−3.20629	+	0.859123i	−0.139801	+	0.0374595i
$527$	−26.9698	+	46.7131i	−1.17482	+	2.03485i
$528$			12.6081i			0.548697i
$529$	−32.2737	−	18.6332i	−1.40320	−	0.810139i
$530$		0			0
$531$	−5.35319	−	1.43438i	−0.232309	−	0.0622470i
$532$	18.8867	−	18.8867i	0.818844	−	0.818844i
$533$	−2.17967	+	6.96663i	−0.0944119	+	0.301758i
$534$		−	6.58658i		−	0.285029i
$535$		0			0
$536$	10.0463	+	17.4007i	0.433933	+	0.751595i
$537$	−5.72202	−	21.3549i	−0.246923	−	0.921530i
$538$	−19.2092			−0.828169
$539$	−12.5340	−	46.7774i	−0.539877	−	2.01485i
$540$		0			0
$541$	−19.6799	+	19.6799i	−0.846106	+	0.846106i	−0.989645	−	0.143539i	$-0.954152\pi$
$541$	−19.6799	+	19.6799i	−0.846106	+	0.846106i	0.143539	+	0.989645i	$0.454152\pi$
$542$	15.1873	−	4.06941i	0.652349	−	0.174796i
$543$	5.26575	−	19.6521i	0.225975	−	0.843351i
$544$	15.4134	−	57.5235i	0.660843	−	2.46630i
$545$		0			0
$546$	−9.38594	+	29.9992i	−0.401681	+	1.28385i
$547$	−14.9753	−	14.9753i	−0.640299	−	0.640299i	0.310330	−	0.950629i	$-0.399560\pi$
$547$	−14.9753	−	14.9753i	−0.640299	−	0.640299i	−0.950629	+	0.310330i	$0.899560\pi$
$548$	10.6083	+	18.3741i	0.453163	+	0.784902i
$549$	2.00175	−	1.15571i	0.0854327	−	0.0493246i
$550$		0			0
$551$	−7.94942	−	7.94942i	−0.338657	−	0.338657i
$552$	8.38378	+	4.84038i	0.356837	+	0.206020i
$553$	16.4290	+	9.48531i	0.698634	+	0.403356i
$554$	37.7927	+	37.7927i	1.60566	+	1.60566i
$555$		0			0
$556$	−25.1688	+	14.5312i	−1.06739	+	0.616261i
$557$	4.87264	+	8.43965i	0.206460	+	0.357600i	0.950597	−	0.310428i	$-0.100472\pi$
$557$	4.87264	+	8.43965i	0.206460	+	0.357600i	−0.744137	+	0.668027i	$0.767139\pi$
$558$	−10.7437	−	10.7437i	−0.454819	−	0.454819i
$559$	−5.44070	+	1.21878i	−0.230117	+	0.0515491i
$560$		0			0
$561$	9.93715	−	37.0859i	0.419547	−	1.56577i
$562$	−11.8158	+	44.0971i	−0.498419	+	1.86012i
$563$	41.4262	−	11.1001i	1.74591	−	0.467814i	0.762162	−	0.647386i	$-0.224138\pi$
$563$	41.4262	−	11.1001i	1.74591	−	0.467814i	0.983745	+	0.179571i	$0.0574711\pi$
$564$	−3.68021	+	3.68021i	−0.154965	+	0.154965i
$565$		0			0
$566$	−5.30403	−	19.7949i	−0.222945	−	0.832042i
$567$	−4.07254			−0.171030
$568$	−0.268168	−	1.00082i	−0.0112521	−	0.0419933i
$569$	13.9649	+	24.1879i	0.585439	+	1.01401i	0.994821	+	0.101646i	$0.0324110\pi$
$569$	13.9649	+	24.1879i	0.585439	+	1.01401i	−0.409382	+	0.912363i	$0.634256\pi$
$570$		0			0
$571$		−	18.6310i		−	0.779684i	−0.920882	−	0.389842i	$-0.872530\pi$
$571$		−	18.6310i		−	0.779684i	0.920882	−	0.389842i	$-0.127470\pi$
$572$	34.6133	−	31.8581i	1.44725	−	1.33206i
$573$	−18.6348	+	18.6348i	−0.778479	+	0.778479i
$574$	−17.0487	−	4.56819i	−0.711600	−	0.190673i
$575$		0			0
$576$	10.2051	+	5.89194i	0.425214	+	0.245498i
$577$			44.5479i			1.85455i	0.374378	+	0.927276i	$0.377856\pi$
$577$			44.5479i			1.85455i	−0.374378	+	0.927276i	$0.622144\pi$
$578$	−43.6204	+	75.5528i	−1.81437	+	3.14258i
$579$	10.7219	−	2.87293i	0.445588	−	0.119395i
$580$		0			0
$581$	20.4423	−	35.4072i	0.848091	−	1.46894i
$582$	−2.11334	−	0.566269i	−0.0876009	−	0.0234726i
$583$	33.1713	−	19.1515i	1.37382	−	0.793173i
$584$	3.80297			0.157368
$585$		0			0
$586$	17.9192			0.740235
$587$	28.2221	−	16.2940i	1.16485	−	0.672527i	0.212389	−	0.977185i	$-0.431876\pi$
$587$	28.2221	−	16.2940i	1.16485	−	0.672527i	0.952462	+	0.304658i	$0.0985423\pi$
$588$	−23.9115	−	6.40706i	−0.986093	−	0.264223i
$589$	−9.01258	+	15.6103i	−0.371357	+	0.643209i
$590$		0			0
$591$	−15.9484	+	4.27336i	−0.656030	+	0.175783i
$592$	6.60161	−	11.4343i	0.271324	−	0.469948i
$593$			20.8918i			0.857923i	0.903323	+	0.428962i	$0.141120\pi$
$593$			20.8918i			0.857923i	−0.903323	+	0.428962i	$0.858880\pi$
$594$	9.36610	+	5.40752i	0.384296	+	0.221873i
$595$		0			0
$596$	18.8185	+	5.04241i	0.770837	+	0.206545i
$597$	10.9067	−	10.9067i	0.446382	−	0.446382i
$598$	13.0979	+	58.4696i	0.535614	+	2.39100i
$599$			22.0889i			0.902528i	0.892390	+	0.451264i	$0.149027\pi$
$599$			22.0889i			0.902528i	−0.892390	+	0.451264i	$0.850973\pi$
$600$		0			0
$601$	−5.36826	−	9.29810i	−0.218976	−	0.379278i	0.735519	−	0.677504i	$-0.236938\pi$
$601$	−5.36826	−	9.29810i	−0.218976	−	0.379278i	−0.954495	+	0.298226i	$0.903605\pi$
$602$	−3.48922	−	13.0220i	−0.142210	−	0.530736i
$603$	−16.1125			−0.656153
$604$	−10.2799	−	38.3650i	−0.418282	−	1.56105i
$605$		0			0
$606$	6.88795	−	6.88795i	0.279804	−	0.279804i
$607$	30.7806	−	8.24763i	1.24934	−	0.334761i	0.427261	−	0.904128i	$-0.359478\pi$
$607$	30.7806	−	8.24763i	1.24934	−	0.334761i	0.822083	+	0.569367i	$0.192812\pi$
$608$	5.15074	−	19.2228i	0.208890	−	0.779588i
$609$	−4.66606	+	17.4140i	−0.189078	+	0.705650i
$610$		0			0
$611$	−7.26008	−	0.300921i	−0.293711	−	0.0121740i
$612$	−13.8778	−	13.8778i	−0.560977	−	0.560977i
$613$	18.5022	+	32.0468i	0.747297	+	1.29436i	0.949114	+	0.314933i	$0.101982\pi$
$613$	18.5022	+	32.0468i	0.747297	+	1.29436i	−0.201817	+	0.979423i	$0.564685\pi$
$614$	7.13024	−	4.11664i	0.287753	−	0.166134i
$615$		0			0
$616$	18.1425	+	18.1425i	0.730982	+	0.730982i
$617$	9.63246	+	5.56130i	0.387788	+	0.223890i	0.681201	−	0.732096i	$-0.261458\pi$
$617$	9.63246	+	5.56130i	0.387788	+	0.223890i	−0.293413	+	0.955986i	$0.594791\pi$
$618$	1.48774	+	0.858945i	0.0598455	+	0.0345518i
$619$	20.8314	+	20.8314i	0.837286	+	0.837286i	0.988501	−	0.151215i	$-0.0483184\pi$
$619$	20.8314	+	20.8314i	0.837286	+	0.837286i	−0.151215	+	0.988501i	$0.548318\pi$
$620$		0			0
$621$	−6.72308	+	3.88157i	−0.269788	+	0.155762i
$622$	−9.12859	−	15.8112i	−0.366023	−	0.633971i
$623$	8.86048	+	8.86048i	0.354987	+	0.354987i
$624$	1.96692	+	8.78039i	0.0787397	+	0.351497i
$625$		0			0
$626$	8.13097	−	30.3452i	0.324979	−	1.21284i
$627$	3.32073	−	12.3931i	0.132617	−	0.494933i
$628$	12.5789	−	3.37051i	0.501954	−	0.134498i
$629$	−28.4302	+	28.4302i	−1.13359	+	1.13359i
$630$		0			0
$631$	8.10371	+	30.2435i	0.322604	+	1.20397i	0.916699	+	0.399579i	$0.130844\pi$
$631$	8.10371	+	30.2435i	0.322604	+	1.20397i	−0.594095	+	0.804395i	$0.702490\pi$
$632$	−5.80882			−0.231063
$633$	4.41143	+	16.4637i	0.175339	+	0.654372i
$634$	−0.624336	−	1.08138i	−0.0247955	−	0.0429471i
$635$		0			0
$636$		−	19.5795i		−	0.776378i
$637$	−16.0262	−	30.6208i	−0.634983	−	1.21324i
$638$	33.8534	−	33.8534i	1.34027	−	1.34027i
$639$	0.802569	+	0.215048i	0.0317491	+	0.00850715i
$640$		0			0
$641$	43.6702	+	25.2130i	1.72487	+	0.995854i	0.907918	+	0.419148i	$0.137671\pi$
$641$	43.6702	+	25.2130i	1.72487	+	0.995854i	0.816952	+	0.576706i	$0.195662\pi$
$642$			2.14477i			0.0846473i
$643$	−4.15944	+	7.20436i	−0.164032	+	0.284112i	−0.936311	−	0.351171i	$-0.885783\pi$
$643$	−4.15944	+	7.20436i	−0.164032	+	0.284112i	0.772279	+	0.635284i	$0.219117\pi$
$644$	−78.8664	+	21.1322i	−3.10777	+	0.832725i
$645$		0			0
$646$	−20.6573	+	35.7795i	−0.812751	+	1.40773i
$647$	18.1328	+	4.85868i	0.712876	+	0.191014i	0.596991	−	0.802248i	$-0.296363\pi$
$647$	18.1328	+	4.85868i	0.712876	+	0.191014i	0.115885	+	0.993263i	$0.463030\pi$
$648$	1.07995	−	0.623507i	0.0424243	−	0.0244937i
$649$	−27.9991			−1.09906
$650$		0			0
$651$	28.9057			1.13290
$652$	−46.7164	+	26.9717i	−1.82956	+	1.05629i
$653$	−5.65830	−	1.51614i	−0.221426	−	0.0593310i	0.146400	−	0.989225i	$-0.453231\pi$
$653$	−5.65830	−	1.51614i	−0.221426	−	0.0593310i	−0.367826	+	0.929894i	$0.619898\pi$
$654$	17.2149	−	29.8170i	0.673154	−	1.16594i
$655$		0			0
$656$	−4.88032	+	1.30768i	−0.190545	+	0.0510563i
$657$	−1.52483	+	2.64109i	−0.0594893	+	0.103039i
$658$		−	17.5695i		−	0.684932i
$659$	4.26630	+	2.46315i	0.166191	+	0.0959507i	0.580789	−	0.814054i	$-0.302744\pi$
$659$	4.26630	+	2.46315i	0.166191	+	0.0959507i	−0.414597	+	0.910005i	$0.636078\pi$
$660$		0			0
$661$	−9.27020	−	2.48394i	−0.360569	−	0.0966142i	0.0739864	−	0.997259i	$-0.476428\pi$
$661$	−9.27020	−	2.48394i	−0.360569	−	0.0966142i	−0.434556	+	0.900645i	$0.643095\pi$
$662$	−1.97740	+	1.97740i	−0.0768536	+	0.0768536i
$663$	1.13475	−	27.3772i	0.0440700	−	1.06324i
$664$			12.5189i			0.485829i
$665$		0			0
$666$	−5.66276	−	9.80819i	−0.219428	−	0.380060i
$667$	8.89453	+	33.1948i	0.344397	+	1.28531i
$668$	43.8565			1.69686
$669$	2.71932	+	10.1486i	0.105135	+	0.392369i
$670$		0			0
$671$	8.25734	−	8.25734i	0.318771	−	0.318771i
$672$	−30.8262	+	8.25987i	−1.18915	+	0.318631i
$673$	1.27960	−	4.77554i	0.0493251	−	0.184084i	−0.936868	−	0.349683i	$-0.886289\pi$
$673$	1.27960	−	4.77554i	0.0493251	−	0.184084i	0.986193	+	0.165600i	$0.0529559\pi$
$674$	9.60282	−	35.8382i	0.369887	−	1.38044i
$675$		0			0
$676$	19.1350	−	27.5861i	0.735961	−	1.06100i
$677$	−18.4058	−	18.4058i	−0.707393	−	0.707393i	0.258593	−	0.965986i	$-0.416741\pi$
$677$	−18.4058	−	18.4058i	−0.707393	−	0.707393i	−0.965986	+	0.258593i	$0.916741\pi$
$678$	−10.2747	−	17.7963i	−0.394598	−	0.683464i
$679$	3.60470	−	2.08117i	0.138336	−	0.0798681i
$680$		0			0
$681$	−6.70163	−	6.70163i	−0.256807	−	0.256807i
$682$	−66.4778	−	38.3810i	−2.54557	−	1.46968i
$683$	5.48209	+	3.16508i	0.209766	+	0.121109i	0.601203	−	0.799097i	$-0.294688\pi$
$683$	5.48209	+	3.16508i	0.209766	+	0.121109i	−0.391437	+	0.920205i	$0.628022\pi$
$684$	−4.63758	−	4.63758i	−0.177322	−	0.177322i
$685$		0			0
$686$	19.5210	−	11.2704i	0.745314	−	0.430307i
$687$	0.529812	+	0.917661i	0.0202136	+	0.0350110i
$688$	−2.72882	−	2.72882i	−0.104035	−	0.104035i
$689$	20.1131	−	18.5121i	0.766247	−	0.705255i
$690$		0			0
$691$	−5.32307	+	19.8660i	−0.202499	+	0.755737i	0.787698	+	0.616061i	$0.211273\pi$
$691$	−5.32307	+	19.8660i	−0.202499	+	0.755737i	−0.990197	+	0.139676i	$0.955394\pi$
$692$	−3.61940	+	13.5078i	−0.137589	+	0.513489i
$693$	−19.8740	+	5.32521i	−0.754949	+	0.202288i
$694$	−11.2665	+	11.2665i	−0.427671	+	0.427671i
$695$		0			0
$696$	−1.42875	−	5.33218i	−0.0541567	−	0.202116i
$697$	15.3858			0.582779
$698$	13.4146	+	50.0639i	0.507750	+	1.89495i
$699$	4.89481	+	8.47805i	0.185139	+	0.320669i
$700$		0			0
$701$		−	28.7357i		−	1.08533i	−0.839949	−	0.542665i	$-0.817415\pi$
$701$		−	28.7357i		−	1.08533i	0.839949	−	0.542665i	$-0.182585\pi$
$702$	7.36623	+	2.30469i	0.278020	+	0.0869850i
$703$	−9.50062	+	9.50062i	−0.358323	+	0.358323i
$704$	57.5053	+	15.4085i	2.16731	+	0.580730i
$705$		0			0
$706$	−15.1906	−	8.77032i	−0.571707	−	0.330075i
$707$			18.5318i			0.696960i
$708$	−7.15624	+	12.3950i	−0.268948	+	0.465831i
$709$	18.7237	−	5.01701i	0.703184	−	0.188418i	0.110528	−	0.993873i	$-0.464746\pi$
$709$	18.7237	−	5.01701i	0.703184	−	0.188418i	0.592656	+	0.805455i	$0.298079\pi$
$710$		0			0
$711$	2.32909	−	4.03411i	0.0873478	−	0.151291i
$712$	−3.70615	−	0.993059i	−0.138894	−	0.0372165i
$713$	47.7184	−	27.5503i	1.78707	−	1.03177i
$714$	66.2533			2.47947
$715$		0			0
$716$	−57.0951			−2.13374
$717$	−0.428134	+	0.247183i	−0.0159889	+	0.00923122i
$718$	8.47495	+	2.27086i	0.316282	+	0.0847476i
$719$	−15.7788	+	27.3296i	−0.588448	+	1.01922i	0.405988	+	0.913878i	$0.366928\pi$
$719$	−15.7788	+	27.3296i	−0.588448	+	1.01922i	−0.994436	+	0.105344i	$0.966406\pi$
$720$		0			0
$721$	−3.15683	+	0.845871i	−0.117567	+	0.0315019i
$722$	13.4334	−	23.2673i	0.499939	−	0.865919i
$723$		−	12.5597i		−	0.467101i
$724$	−45.5031	−	26.2712i	−1.69111	−	0.976361i
$725$		0			0
$726$	30.0322	+	8.04710i	1.11460	+	0.298656i
$727$	32.8891	−	32.8891i	1.21979	−	1.21979i	0.252083	−	0.967706i	$-0.418884\pi$
$727$	32.8891	−	32.8891i	1.21979	−	1.21979i	0.967706	−	0.252083i	$-0.0811156\pi$
$728$	15.4649	+	9.80428i	0.573167	+	0.363371i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	5.87591	+	10.1774i	0.217328	+	0.376424i
$732$	−1.54498	−	5.76593i	−0.0571039	−	0.213115i
$733$	−39.8536			−1.47202			−0.736012	−	0.676968i	$-0.763294\pi$
$733$	−39.8536			−1.47202			−0.736012	+	0.676968i	$0.763294\pi$
$734$	12.4413	+	46.4317i	0.459218	+	1.71383i
$735$		0			0
$736$	−43.0164	+	43.0164i	−1.58561	+	1.58561i
$737$	−78.6291	+	21.0686i	−2.89634	+	0.776072i
$738$	−1.12171	+	4.18627i	−0.0412906	+	0.154099i
$739$	−3.54794	+	13.2411i	−0.130513	+	0.487082i	−0.999976	−	0.00691649i	$-0.997798\pi$
$739$	−3.54794	+	13.2411i	−0.130513	+	0.487082i	0.869463	+	0.493998i	$0.164465\pi$
$740$		0			0
$741$	0.379203	−	9.14872i	0.0139304	−	0.336087i
$742$	46.7368	+	46.7368i	1.71576	+	1.71576i
$743$	14.1060	+	24.4324i	0.517501	+	0.896338i	0.999793	+	0.0203274i	$0.00647087\pi$
$743$	14.1060	+	24.4324i	0.517501	+	0.896338i	−0.482293	+	0.876010i	$0.660196\pi$
$744$	−7.66514	+	4.42547i	−0.281018	+	0.162246i
$745$		0			0
$746$	−23.9349	−	23.9349i	−0.876319	−	0.876319i
$747$	−8.69413	−	5.01956i	−0.318102	−	0.183656i
$748$	−85.8700	−	49.5771i	−3.13972	−	1.81272i
$749$	−2.88521	−	2.88521i	−0.105423	−	0.105423i
$750$		0			0
$751$	−6.76144	+	3.90372i	−0.246728	+	0.142449i	−0.618265	−	0.785970i	$-0.712164\pi$
$751$	−6.76144	+	3.90372i	−0.246728	+	0.142449i	0.371537	+	0.928418i	$0.378831\pi$
$752$	−2.51470	−	4.35560i	−0.0917018	−	0.158832i
$753$	10.7228	+	10.7228i	0.390762	+	0.390762i
$754$	18.2945	−	28.8571i	0.666247	−	1.05091i
$755$		0			0
$756$	−2.72212	+	10.1591i	−0.0990024	+	0.369482i
$757$	10.6445	−	39.7258i	0.386881	−	1.44386i	−0.448300	−	0.893883i	$-0.647970\pi$
$757$	10.6445	−	39.7258i	0.386881	−	1.44386i	0.835180	−	0.549976i	$-0.185363\pi$
$758$	31.5892	−	8.46430i	1.14737	−	0.307437i
$759$	−27.7331	+	27.7331i	−1.00665	+	1.00665i
$760$		0			0
$761$	12.4358	+	46.4110i	0.450797	+	1.68240i	0.700159	+	0.713987i	$0.253113\pi$
$761$	12.4358	+	46.4110i	0.450797	+	1.68240i	−0.249362	+	0.968410i	$0.580221\pi$
$762$	24.0593			0.871577
$763$	16.9528	+	63.2688i	0.613733	+	2.29048i
$764$	34.0294	+	58.9407i	1.23114	+	2.13240i
$765$		0			0
$766$		−	36.6250i		−	1.32331i
$767$	−19.4988	+	4.36798i	−0.704062	+	0.157719i
$768$	−2.20469	+	2.20469i	−0.0795550	+	0.0795550i
$769$	−38.2338	−	10.2447i	−1.37874	−	0.369434i	−0.508080	−	0.861310i	$-0.669645\pi$
$769$	−38.2338	−	10.2447i	−1.37874	−	0.369434i	−0.870665	+	0.491876i	$0.836311\pi$
$770$		0			0
$771$	−0.858904	−	0.495888i	−0.0309327	−	0.0178590i
$772$		−	28.6665i		−	1.03173i
$773$	20.2355	−	35.0488i	0.727819	−	1.26062i	−0.229984	−	0.973194i	$-0.573867\pi$
$773$	20.2355	−	35.0488i	0.727819	−	1.26062i	0.957803	−	0.287425i	$-0.0927992\pi$
$774$	−3.19751	+	0.856769i	−0.114932	+	0.0307959i
$775$		0			0
$776$	−0.637258	+	1.10376i	−0.0228762	+	0.0396228i
$777$	20.8120	+	5.57656i	0.746627	+	0.200058i
$778$	−8.90377	+	5.14059i	−0.319215	+	0.184299i
$779$	5.14152			0.184214
$780$		0			0
$781$	4.19773			0.150206
$782$	109.373	−	63.1467i	3.91118	−	2.25812i
$783$	4.27595	+	1.14574i	0.152810	+	0.0409453i
$784$	11.9608	−	20.7168i	0.427173	−	0.739885i
$785$		0			0
$786$	−11.7922	+	3.15970i	−0.420612	+	0.112703i
$787$	12.6652	−	21.9368i	0.451466	−	0.781963i	−0.547011	−	0.837125i	$-0.684234\pi$
$787$	12.6652	−	21.9368i	0.451466	−	0.781963i	0.998477	+	0.0551626i	$0.0175677\pi$
$788$			42.6402i			1.51899i
$789$	−1.34288	−	0.775312i	−0.0478078	−	0.0276018i
$790$		0			0
$791$	37.7621	+	10.1183i	1.34267	+	0.359766i
$792$	4.45484	−	4.45484i	0.158296	−	0.158296i
$793$	4.46230	−	7.03866i	0.158461	−	0.249950i
$794$			2.91480i			0.103442i
$795$		0			0
$796$	−19.9170	−	34.4973i	−0.705940	−	1.22272i
$797$	−3.99042	−	14.8925i	−0.141348	−	0.527518i	−0.999891	−	0.0147760i	$-0.995296\pi$
$797$	−3.99042	−	14.8925i	−0.141348	−	0.527518i	0.858543	−	0.512742i	$-0.171370\pi$
$798$	22.1401			0.783750
$799$	3.96396	+	14.7937i	0.140235	+	0.523363i
$800$		0			0
$801$	2.17567	−	2.17567i	0.0768734	−	0.0768734i
$802$	−0.792533	+	0.212358i	−0.0279853	+	0.00749864i
$803$	−3.98771	+	14.8823i	−0.140723	+	0.525186i
$804$	−10.7698	+	40.1933i	−0.379820	+	1.41751i
$805$		0			0
$806$	−52.2833	−	16.3580i	−1.84160	−	0.576187i
$807$	−6.34516	−	6.34516i	−0.223360	−	0.223360i
$808$	−2.83723	−	4.91422i	−0.0998133	−	0.172882i
$809$	−24.0660	+	13.8945i	−0.846116	+	0.488506i	−0.859339	−	0.511407i	$-0.829124\pi$
$809$	−24.0660	+	13.8945i	−0.846116	+	0.488506i	0.0132222	+	0.999913i	$0.495791\pi$
$810$		0			0
$811$	17.7053	+	17.7053i	0.621719	+	0.621719i	0.945971	−	0.324252i	$-0.105113\pi$
$811$	17.7053	+	17.7053i	0.621719	+	0.621719i	−0.324252	+	0.945971i	$0.605113\pi$
$812$	40.3209	+	23.2793i	1.41499	+	0.816942i
$813$	6.36083	+	3.67243i	0.223084	+	0.128798i
$814$	−40.4593	−	40.4593i	−1.41810	−	1.41810i
$815$		0			0
$816$	16.4246	−	9.48275i	0.574976	−	0.331963i
$817$	1.96357	+	3.40100i	0.0686966	+	0.118986i
$818$	48.1471	+	48.1471i	1.68342	+	1.68342i
$819$	−13.0096	+	6.80894i	−0.454593	+	0.237924i
$820$		0			0
$821$	0.589019	−	2.19825i	0.0205569	−	0.0767194i	−0.954885	−	0.296975i	$-0.904022\pi$
$821$	0.589019	−	2.19825i	0.0205569	−	0.0767194i	0.975442	+	0.220255i	$0.0706890\pi$
$822$	−4.55175	+	16.9874i	−0.158760	+	0.592502i
$823$	48.9214	−	13.1085i	1.70529	−	0.456932i	0.731031	−	0.682345i	$-0.239040\pi$
$823$	48.9214	−	13.1085i	1.70529	−	0.456932i	0.974263	+	0.225413i	$0.0723730\pi$
$824$	0.707619	−	0.707619i	0.0246511	−	0.0246511i
$825$		0			0
$826$	−12.5050	−	46.6692i	−0.435104	−	1.62383i
$827$	−30.0403			−1.04460			−0.522302	−	0.852761i	$-0.674927\pi$
$827$	−30.0403			−1.04460			−0.522302	+	0.852761i	$0.674927\pi$
$828$	5.18895	+	19.3654i	0.180328	+	0.672995i
$829$	10.6656	+	18.4733i	0.370430	+	0.641604i	0.989632	−	0.143628i	$-0.0458770\pi$
$829$	10.6656	+	18.4733i	0.370430	+	0.641604i	−0.619202	+	0.785232i	$0.712544\pi$
$830$		0			0
$831$			24.9672i			0.866103i
$832$	42.4510	+	1.75954i	1.47172	+	0.0610010i
$833$	−51.5101	+	51.5101i	−1.78472	+	1.78472i
$834$	−23.2693	−	6.23498i	−0.805749	−	0.215900i
$835$		0			0
$836$	−28.6954	−	16.5673i	−0.992453	−	0.572993i
$837$		−	7.09771i		−	0.245333i
$838$	−12.5781	+	21.7860i	−0.434504	+	0.752584i
$839$	44.8268	−	12.0113i	1.54759	−	0.414677i	0.618884	−	0.785482i	$-0.287585\pi$
$839$	44.8268	−	12.0113i	1.54759	−	0.414677i	0.928710	+	0.370806i	$0.120918\pi$
$840$		0			0
$841$	−4.70176	+	8.14369i	−0.162130	+	0.280817i
$842$	54.6984	+	14.6564i	1.88503	+	0.505093i
$843$	−18.4690	+	10.6631i	−0.636107	+	0.367257i
$844$	44.0178			1.51516
$845$		0			0
$846$	−4.31415			−0.148324
$847$	−51.2255	+	29.5750i	−1.76013	+	1.01621i
$848$	18.2757	+	4.89696i	0.627591	+	0.168162i
$849$	4.78660	−	8.29063i	0.164276	−	0.284534i
$850$		0			0
$851$	39.6723	−	10.6301i	1.35995	−	0.364397i
$852$	1.07289	−	1.85830i	0.0367565	−	0.0636641i
$853$			38.9423i			1.33336i	0.745345	+	0.666679i	$0.232285\pi$
$853$			38.9423i			1.33336i	−0.745345	+	0.666679i	$0.767715\pi$
$854$	17.4513	+	10.0755i	0.597172	+	0.344777i
$855$		0			0
$856$	1.20682	+	0.323367i	0.0412483	+	0.0110525i
$857$	−40.1598	+	40.1598i	−1.37183	+	1.37183i	−0.514103	+	0.857728i	$0.671875\pi$
$857$	−40.1598	+	40.1598i	−1.37183	+	1.37183i	−0.857728	+	0.514103i	$0.828125\pi$
$858$	38.9607	+	1.61487i	1.33010	+	0.0551308i
$859$			44.8615i			1.53066i	0.643641	+	0.765328i	$0.277423\pi$
$859$			44.8615i			1.53066i	−0.643641	+	0.765328i	$0.722577\pi$
$860$		0			0
$861$	−4.12254	−	7.14046i	−0.140496	−	0.243346i
$862$	11.5971	+	43.2811i	0.395000	+	1.47416i
$863$	32.3427			1.10096			0.550479	−	0.834849i	$-0.314445\pi$
$863$	32.3427			1.10096			0.550479	+	0.834849i	$0.314445\pi$
$864$	2.02819	+	7.56930i	0.0690003	+	0.257513i
$865$		0			0
$866$	−23.3288	+	23.3288i	−0.792746	+	0.792746i
$867$	−39.3651	+	10.5478i	−1.33691	+	0.358223i
$868$	19.3208	−	72.1061i	0.655790	−	2.44744i
$869$	6.09100	−	22.7319i	0.206623	−	0.771127i
$870$		0			0
$871$	−51.4712	+	26.9388i	−1.74403	+	0.912787i
$872$	−14.1820	−	14.1820i	−0.480263	−	0.480263i
$873$	−0.511027	−	0.885124i	−0.0172956	−	0.0299569i
$874$	36.5496	−	21.1019i	1.23631	−	0.713783i
$875$		0			0
$876$	5.56907	+	5.56907i	0.188161	+	0.188161i
$877$	−25.3319	−	14.6254i	−0.855398	−	0.493864i	0.00707071	−	0.999975i	$-0.497749\pi$
$877$	−25.3319	−	14.6254i	−0.855398	−	0.493864i	−0.862468	+	0.506111i	$0.831083\pi$
$878$	−42.6787	−	24.6406i	−1.44034	−	0.831579i
$879$	5.91904	+	5.91904i	0.199644	+	0.199644i
$880$		0			0
$881$	34.3407	−	19.8266i	1.15697	−	0.667976i	0.206393	−	0.978469i	$-0.433827\pi$
$881$	34.3407	−	19.8266i	1.15697	−	0.667976i	0.950576	+	0.310493i	$0.100494\pi$
$882$	−10.2598	−	17.7705i	−0.345466	−	0.598365i
$883$	−14.5229	−	14.5229i	−0.488735	−	0.488735i	0.419172	−	0.907907i	$-0.362320\pi$
$883$	−14.5229	−	14.5229i	−0.488735	−	0.488735i	−0.907907	+	0.419172i	$0.862320\pi$
$884$	−67.5348	−	21.1298i	−2.27144	−	0.710672i
$885$		0			0
$886$	−14.0240	+	52.3383i	−0.471145	+	1.75834i
$887$	5.11275	−	19.0810i	0.171669	−	0.640679i	−0.825426	−	0.564511i	$-0.809065\pi$
$887$	5.11275	−	19.0810i	0.171669	−	0.640679i	0.997095	−	0.0761680i	$-0.0242685\pi$
$888$	−6.37266	+	1.70755i	−0.213853	+	0.0573016i
$889$	−32.3654	+	32.3654i	−1.08550	+	1.08550i
$890$		0			0
$891$	1.30759	+	4.87999i	0.0438059	+	0.163486i
$892$	27.1337			0.908504
$893$	1.32465	+	4.94365i	0.0443276	+	0.165433i
$894$	8.07457	+	13.9856i	0.270054	+	0.467747i
$895$		0			0
$896$			38.9048i			1.29972i
$897$	−14.9871	+	23.6400i	−0.500404	+	0.789318i
$898$	−13.7785	+	13.7785i	−0.459793	+	0.459793i
$899$	−30.3494	−	8.13211i	−1.01221	−	0.271221i
$900$		0			0
$901$	−49.8973	−	28.8082i	−1.66232	−	0.959741i
$902$			21.8957i			0.729047i
$903$	3.14884	−	5.45394i	0.104787	−	0.181496i
$904$	−11.5628	+	3.09824i	−0.384573	+	0.103046i
$905$		0			0
$906$	16.4615	−	28.5121i	0.546895	−	0.947251i
$907$	−34.4063	−	9.21915i	−1.14244	−	0.306117i	−0.362511	−	0.931980i	$-0.618080\pi$
$907$	−34.4063	−	9.21915i	−1.14244	−	0.306117i	−0.779933	+	0.625863i	$0.784747\pi$
$908$	−21.1968	+	12.2380i	−0.703442	+	0.406133i
$909$	4.55043			0.150928
$910$		0			0
$911$	32.5748			1.07925			0.539626	−	0.841905i	$-0.318566\pi$
$911$	32.5748			1.07925			0.539626	+	0.841905i	$0.318566\pi$
$912$	5.48866	−	3.16888i	0.181748	−	0.104932i
$913$	−48.9909	−	13.1271i	−1.62136	−	0.434442i
$914$	9.49807	−	16.4511i	0.314168	−	0.544156i
$915$		0			0
$916$	2.64327	−	0.708261i	0.0873360	−	0.0234016i
$917$	11.6127	−	20.1137i	0.383484	−	0.664213i
$918$		−	16.2683i		−	0.536935i
$919$	−33.3360	−	19.2465i	−1.09965	−	0.634885i	−0.163523	−	0.986540i	$-0.552286\pi$
$919$	−33.3360	−	19.2465i	−1.09965	−	0.634885i	−0.936130	+	0.351655i	$0.885619\pi$
$920$		0			0
$921$	3.71505	+	0.995444i	0.122415	+	0.0328010i
$922$	11.0225	−	11.0225i	0.363007	−	0.363007i
$923$	2.92333	−	0.654863i	0.0962226	−	0.0215551i
$924$			53.1356i			1.74803i
$925$		0			0
$926$	−45.5347	−	78.8685i	−1.49636	−	2.59178i
$927$	0.207701	+	0.775151i	0.00682180	+	0.0254593i
$928$	34.6897			1.13875
$929$	−7.17856	−	26.7907i	−0.235521	−	0.878976i	−0.977913	−	0.209011i	$-0.932976\pi$
$929$	−7.17856	−	26.7907i	−0.235521	−	0.878976i	0.742393	−	0.669965i	$-0.233691\pi$
$930$		0			0
$931$	−17.2133	+	17.2133i	−0.564142	+	0.564142i
$932$	24.4205	−	6.54346i	0.799920	−	0.214338i
$933$	2.20738	−	8.23806i	0.0722664	−	0.269702i
$934$	11.4539	−	42.7464i	0.374782	−	1.39871i
$935$		0			0
$936$	2.40741	−	3.79736i	0.0786888	−	0.124121i
$937$	−19.5019	−	19.5019i	−0.637100	−	0.637100i	0.312739	−	0.949839i	$-0.398753\pi$
$937$	−19.5019	−	19.5019i	−0.637100	−	0.637100i	−0.949839	+	0.312739i	$0.898753\pi$
$938$	−70.2347	−	121.650i	−2.29324	−	3.97201i
$939$	12.7094	−	7.33776i	0.414755	−	0.239459i
$940$		0			0
$941$	−10.7083	−	10.7083i	−0.349081	−	0.349081i	0.510686	−	0.859767i	$-0.329391\pi$
$941$	−10.7083	−	10.7083i	−0.349081	−	0.349081i	−0.859767	+	0.510686i	$0.829391\pi$
$942$	9.34841	+	5.39731i	0.304588	+	0.175854i
$943$	−13.6113	−	7.85847i	−0.443244	−	0.255907i
$944$	−9.77976	−	9.77976i	−0.318304	−	0.318304i
$945$		0			0
$946$	−14.4835	+	8.36206i	−0.470899	+	0.271874i
$947$	21.8088	+	37.7739i	0.708689	+	1.22749i	0.965344	+	0.260983i	$0.0840465\pi$
$947$	21.8088	+	37.7739i	0.708689	+	1.22749i	−0.256654	+	0.966503i	$0.582620\pi$
$948$	−8.50643	−	8.50643i	−0.276276	−	0.276276i
$949$	−0.455367	+	10.9863i	−0.0147818	+	0.356630i
$950$		0			0
$951$	0.150970	−	0.563429i	0.00489555	−	0.0182704i
$952$	9.98902	−	37.2795i	0.323746	−	1.20824i
$953$	3.98308	−	1.06726i	0.129025	−	0.0345720i	−0.193729	−	0.981055i	$-0.562058\pi$
$953$	3.98308	−	1.06726i	0.129025	−	0.0345720i	0.322753	+	0.946483i	$0.395392\pi$
$954$	11.4761	−	11.4761i	0.371552	−	0.371552i
$955$		0			0
$956$	0.330438	+	1.23321i	0.0106871	+	0.0398849i
$957$	22.3648			0.722950
$958$	4.22353	+	15.7624i	0.136456	+	0.509261i
$959$	−16.7288	−	28.9751i	−0.540201	−	0.935655i
$960$		0			0
$961$			19.3774i			0.625079i
$962$	−34.4880	−	21.8644i	−1.11194	−	0.704936i
$963$	−0.708456	+	0.708456i	−0.0228297	+	0.0228297i
$964$	−31.3307	−	8.39503i	−1.00909	−	0.270386i
$965$		0			0
$966$	−58.6119	−	33.8396i	−1.88581	−	1.08877i
$967$			29.4367i			0.946621i	0.880896	+	0.473310i	$0.156941\pi$
$967$			29.4367i			0.946621i	−0.880896	+	0.473310i	$0.843059\pi$
$968$	9.05590	−	15.6853i	0.291068	−	0.504144i
$969$	−18.6421	+	4.99514i	−0.598871	+	0.160467i
$970$		0			0
$971$	−21.5962	+	37.4057i	−0.693054	+	1.20041i	0.277778	+	0.960645i	$0.410402\pi$
$971$	−21.5962	+	37.4057i	−0.693054	+	1.20041i	−0.970832	+	0.239760i	$0.922931\pi$
$972$	2.49453	+	0.668408i	0.0800122	+	0.0214392i
$973$	39.6901	−	22.9151i	1.27241	−	0.734624i
$974$	−10.4690			−0.335450
$975$		0			0
$976$	5.76838			0.184641
$977$	−18.4375	+	10.6449i	−0.589869	+	0.340561i	−0.765046	−	0.643976i	$-0.777284\pi$
$977$	−18.4375	+	10.6449i	−0.589869	+	0.340561i	0.175177	+	0.984537i	$0.443950\pi$
$978$	−43.1906	−	11.5729i	−1.38108	−	0.370061i
$979$	7.77235	−	13.4621i	0.248406	−	0.430251i
$980$		0			0
$981$	15.5355	−	4.16272i	0.496009	−	0.132905i
$982$	−20.2025	+	34.9917i	−0.644686	+	1.11663i
$983$			44.7807i			1.42828i	0.700001	+	0.714142i	$0.253183\pi$
$983$			44.7807i			1.42828i	−0.700001	+	0.714142i	$0.746817\pi$
$984$	2.18642	+	1.26233i	0.0697004	+	0.0402415i
$985$		0			0
$986$	−69.5625	−	18.6392i	−2.21532	−	0.593594i
$987$	5.80353	−	5.80353i	0.184729	−	0.184729i
$988$	−22.5683	−	7.06101i	−0.717994	−	0.224641i
$989$		−	12.0047i		−	0.381728i
$990$		0			0
$991$	−19.0759	−	33.0405i	−0.605966	−	1.04956i	−0.991898	−	0.127037i	$-0.959453\pi$
$991$	−19.0759	−	33.0405i	−0.605966	−	1.04956i	0.385931	−	0.922527i	$-0.373880\pi$
$992$	−14.3955	−	53.7247i	−0.457057	−	1.70576i
$993$	−1.30634			−0.0414554
$994$	1.87479	+	6.99681i	0.0594647	+	0.221925i
$995$		0			0
$996$	−18.3327	+	18.3327i	−0.580894	+	0.580894i
$997$	12.3249	−	3.30245i	0.390334	−	0.104590i	−0.0583140	−	0.998298i	$-0.518572\pi$
$997$	12.3249	−	3.30245i	0.390334	−	0.104590i	0.448648	+	0.893709i	$0.351906\pi$
$998$	12.5595	−	46.8728i	0.397565	−	1.48373i
$999$	1.36931	−	5.11033i	0.0433230	−	0.161684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bu.h.232.7	yes	32
5.2	odd	4		975.2.bl.h.193.7	yes	32
5.3	odd	4		975.2.bl.h.193.2	✓	32
5.4	even	2	inner	975.2.bu.h.232.2	yes	32
13.6	odd	12		975.2.bl.h.682.2	yes	32
65.19	odd	12		975.2.bl.h.682.7	yes	32
65.32	even	12	inner	975.2.bu.h.643.2	yes	32
65.58	even	12	inner	975.2.bu.h.643.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.bl.h.193.2	✓	32	5.3	odd	4
975.2.bl.h.193.7	yes	32	5.2	odd	4
975.2.bl.h.682.2	yes	32	13.6	odd	12
975.2.bl.h.682.7	yes	32	65.19	odd	12
975.2.bu.h.232.2	yes	32	5.4	even	2	inner
975.2.bu.h.232.7	yes	32	1.1	even	1	trivial
975.2.bu.h.643.2	yes	32	65.32	even	12	inner
975.2.bu.h.643.7	yes	32	65.58	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.85389 - 1.07034i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.29127 - 2.23654i) q^{4} +(2.06774 - 0.554050i) q^{6} +(-2.03627 + 3.52692i) q^{7} -1.24701i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.85389 - 1.07034i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.29127 - 2.23654i) q^{4} +(2.06774 - 0.554050i) q^{6} +(-2.03627 + 3.52692i) q^{7} -1.24701i q^{8} +(0.866025 + 0.500000i) q^{9} +(4.87999 + 1.30759i) q^{11} +(1.82613 - 1.82613i) q^{12} +(3.60246 + 0.149317i) q^{13} +8.71802i q^{14} +(1.24780 + 2.16125i) q^{16} +(-1.96692 - 7.34064i) q^{17} +2.14068 q^{18} +(-0.657291 - 2.45304i) q^{19} +(-2.87972 + 2.87972i) q^{21} +(10.4465 - 2.79914i) q^{22} +(-2.00925 + 7.49862i) q^{23} +(0.322751 - 1.20452i) q^{24} +(6.83837 - 3.57905i) q^{26} +(0.707107 + 0.707107i) q^{27} +(5.25873 + 9.10838i) q^{28} +(3.83371 - 2.21340i) q^{29} +(-5.01884 - 5.01884i) q^{31} +(6.78645 + 3.91816i) q^{32} +(4.37528 + 2.52607i) q^{33} +(-11.5034 - 11.5034i) q^{34} +(2.23654 - 1.29127i) q^{36} +(-2.64530 - 4.58180i) q^{37} +(-3.84414 - 3.84414i) q^{38} +(3.44106 + 1.07661i) q^{39} +(-0.523994 + 1.95557i) q^{41} +(-2.25639 + 8.42096i) q^{42} +(-1.49368 + 0.400231i) q^{43} +(9.22584 - 9.22584i) q^{44} +(4.30117 + 16.0522i) q^{46} -2.01531 q^{47} +(0.645908 + 2.41056i) q^{48} +(-4.79278 - 8.30133i) q^{49} -7.59959i q^{51} +(4.98568 - 7.86422i) q^{52} +(5.36095 - 5.36095i) q^{53} +(2.06774 + 0.554050i) q^{54} +(4.39812 + 2.53926i) q^{56} -2.53958i q^{57} +(4.73818 - 8.20677i) q^{58} +(-5.35319 + 1.43438i) q^{59} +(1.15571 - 2.00175i) q^{61} +(-14.6762 - 3.93248i) q^{62} +(-3.52692 + 2.03627i) q^{63} +11.7839 q^{64} +10.8150 q^{66} +(-13.9539 + 8.05627i) q^{67} +(-18.9574 - 5.07963i) q^{68} +(-3.88157 + 6.72308i) q^{69} +(0.802569 - 0.215048i) q^{71} +(0.623507 - 1.07995i) q^{72} +3.04966i q^{73} +(-9.80819 - 5.66276i) q^{74} +(-6.33506 - 1.69747i) q^{76} +(-14.5487 + 14.5487i) q^{77} +(7.53169 - 1.68719i) q^{78} -4.65818i q^{79} +(0.500000 + 0.866025i) q^{81} +(1.12171 + 4.18627i) q^{82} -10.0391 q^{83} +(2.72212 + 10.1591i) q^{84} +(-2.34074 + 2.34074i) q^{86} +(4.27595 - 1.14574i) q^{87} +(1.63058 - 6.08542i) q^{88} +(0.796349 - 2.97201i) q^{89} +(-7.86220 + 12.4015i) q^{91} +(14.1765 + 14.1765i) q^{92} +(-3.54885 - 6.14679i) q^{93} +(-3.73616 + 2.15708i) q^{94} +(5.54111 + 5.54111i) q^{96} +(-0.885124 - 0.511027i) q^{97} +(-17.7705 - 10.2598i) q^{98} +(3.57240 + 3.57240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 24 q^{4} - 4 q^{6}+O(q^{10}) \) 32 * q + 24 * q^4 - 4 * q^6	\( 32 q + 24 q^{4} - 4 q^{6} - 16 q^{11} - 48 q^{16} + 24 q^{19} - 8 q^{21} + 16 q^{24} + 24 q^{26} - 12 q^{29} - 8 q^{31} - 56 q^{34} - 16 q^{39} - 12 q^{41} + 88 q^{44} - 32 q^{46} + 32 q^{49} - 4 q^{54} - 96 q^{56} - 92 q^{59} - 56 q^{61} - 128 q^{64} - 12 q^{71} + 120 q^{74} - 200 q^{76} + 16 q^{81} + 48 q^{84} + 96 q^{86} - 68 q^{89} + 216 q^{94} + 136 q^{96} - 8 q^{99}+O(q^{100}) \) 32 * q + 24 * q^4 - 4 * q^6 - 16 * q^11 - 48 * q^16 + 24 * q^19 - 8 * q^21 + 16 * q^24 + 24 * q^26 - 12 * q^29 - 8 * q^31 - 56 * q^34 - 16 * q^39 - 12 * q^41 + 88 * q^44 - 32 * q^46 + 32 * q^49 - 4 * q^54 - 96 * q^56 - 92 * q^59 - 56 * q^61 - 128 * q^64 - 12 * q^71 + 120 * q^74 - 200 * q^76 + 16 * q^81 + 48 * q^84 + 96 * q^86 - 68 * q^89 + 216 * q^94 + 136 * q^96 - 8 * q^99

Introduction

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