LMFDB - Embedded newform 875.2.u.b.424.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(74,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([9, 20]))

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

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

chi := DirichletCharacter("875.74");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.u (of order $30$, degree $8$, not 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			424.31
Character	$\chi$	$=$	875.424
Dual form			875.2.u.b.324.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.11556 + 0.222354i) q^{2} +(0.483252 - 2.27352i) q^{3} +(2.46986 + 0.524984i) q^{4} +(1.52788 - 4.70232i) q^{6} +(-0.0903750 - 2.64421i) q^{7} +(1.06219 + 0.345128i) q^{8} +(-2.19474 - 0.977159i) q^{9} +O(q^{10})$	\(q+(2.11556 + 0.222354i) q^{2} +(0.483252 - 2.27352i) q^{3} +(2.46986 + 0.524984i) q^{4} +(1.52788 - 4.70232i) q^{6} +(-0.0903750 - 2.64421i) q^{7} +(1.06219 + 0.345128i) q^{8} +(-2.19474 - 0.977159i) q^{9} +(-2.44955 + 1.09061i) q^{11} +(2.38713 - 5.36157i) q^{12} +(-1.74792 - 2.40580i) q^{13} +(0.396757 - 5.61407i) q^{14} +(-2.44307 - 1.08773i) q^{16} +(0.836817 - 0.753473i) q^{17} +(-4.42582 - 2.55525i) q^{18} +(3.59536 - 0.764218i) q^{19} +(-6.05534 - 1.07235i) q^{21} +(-5.42467 + 1.76258i) q^{22} +(7.22218 + 0.759081i) q^{23} +(1.29796 - 2.24814i) q^{24} +(-3.16288 - 5.47827i) q^{26} +(0.816389 - 1.12366i) q^{27} +(1.16495 - 6.57825i) q^{28} +(3.16693 + 9.74681i) q^{29} +(3.56421 + 3.95846i) q^{31} +(-6.86105 - 3.96123i) q^{32} +(1.29578 + 6.09615i) q^{33} +(1.93787 - 1.40795i) q^{34} +(-4.90769 - 3.56564i) q^{36} +(-1.82513 + 4.09931i) q^{37} +(7.77613 - 0.817304i) q^{38} +(-6.31433 + 2.81132i) q^{39} +(3.05046 - 2.21629i) q^{41} +(-12.5720 - 3.61505i) q^{42} -8.46953i q^{43} +(-6.62259 + 1.40767i) q^{44} +(15.1102 + 3.21176i) q^{46} +(3.85492 + 3.47099i) q^{47} +(-3.65359 + 5.02873i) q^{48} +(-6.98366 + 0.477940i) q^{49} +(-1.30864 - 2.26664i) q^{51} +(-3.05410 - 6.85961i) q^{52} +(-0.495113 + 2.32932i) q^{53} +(1.97697 - 2.19565i) q^{54} +(0.816594 - 2.83985i) q^{56} -8.54345i q^{57} +(4.53258 + 21.3241i) q^{58} +(-0.0789064 - 0.750745i) q^{59} +(-0.0500232 + 0.475939i) q^{61} +(6.66012 + 9.16687i) q^{62} +(-2.38546 + 5.89165i) q^{63} +(-9.30711 - 6.76201i) q^{64} +(1.38579 + 13.1849i) q^{66} +(-2.55052 + 2.29650i) q^{67} +(2.46238 - 1.42165i) q^{68} +(5.21592 - 16.0530i) q^{69} +(-3.56107 - 10.9599i) q^{71} +(-1.99399 - 1.79540i) q^{72} +(3.95548 + 8.88415i) q^{73} +(-4.77267 + 8.26651i) q^{74} +9.28123 q^{76} +(3.10518 + 6.37856i) q^{77} +(-13.9834 + 4.54350i) q^{78} +(-2.83673 + 3.15051i) q^{79} +(-6.98278 - 7.75517i) q^{81} +(6.94623 - 4.01041i) q^{82} +(13.2413 + 4.30236i) q^{83} +(-14.3928 - 5.82750i) q^{84} +(1.88324 - 17.9178i) q^{86} +(23.6900 - 2.48992i) q^{87} +(-2.97830 + 0.313032i) q^{88} +(-0.850889 + 8.09567i) q^{89} +(-6.20347 + 4.83928i) q^{91} +(17.4392 + 5.66635i) q^{92} +(10.7221 - 6.19038i) q^{93} +(7.38353 + 8.20024i) q^{94} +(-12.3216 + 13.6845i) q^{96} +(-2.53425 + 0.823427i) q^{97} +(-14.8806 - 0.541736i) q^{98} +6.44182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 26 q^{4} - 24 q^{6} - 22 q^{9}+O(q^{10}) $ 288 * q - 26 * q^4 - 24 * q^6 - 22 * q^9	$ 288 q - 26 q^{4} - 24 q^{6} - 22 q^{9} - 12 q^{11} + 12 q^{14} + 26 q^{16} + 22 q^{19} - 6 q^{21} - 92 q^{24} + 88 q^{26} + 48 q^{29} - 42 q^{31} + 72 q^{34} - 208 q^{36} - 50 q^{39} + 76 q^{41} + 14 q^{44} + 42 q^{46} + 76 q^{49} - 16 q^{51} - 30 q^{54} - 120 q^{56} + 78 q^{59} - 26 q^{61} - 84 q^{64} + 14 q^{66} - 100 q^{69} + 44 q^{71} + 20 q^{74} - 552 q^{76} - 18 q^{79} + 114 q^{81} + 58 q^{84} - 34 q^{86} + 84 q^{89} - 68 q^{91} + 22 q^{94} + 26 q^{96} + 136 q^{99}+O(q^{100}) $ 288 * q - 26 * q^4 - 24 * q^6 - 22 * q^9 - 12 * q^11 + 12 * q^14 + 26 * q^16 + 22 * q^19 - 6 * q^21 - 92 * q^24 + 88 * q^26 + 48 * q^29 - 42 * q^31 + 72 * q^34 - 208 * q^36 - 50 * q^39 + 76 * q^41 + 14 * q^44 + 42 * q^46 + 76 * q^49 - 16 * q^51 - 30 * q^54 - 120 * q^56 + 78 * q^59 - 26 * q^61 - 84 * q^64 + 14 * q^66 - 100 * q^69 + 44 * q^71 + 20 * q^74 - 552 * q^76 - 18 * q^79 + 114 * q^81 + 58 * q^84 - 34 * q^86 + 84 * q^89 - 68 * q^91 + 22 * q^94 + 26 * q^96 + 136 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.11556	+	0.222354i	1.49593	+	0.157228i	0.816855	−	0.576844i	$-0.195716\pi$
$2$	2.11556	+	0.222354i	1.49593	+	0.157228i	0.679072	+	0.734072i	$0.262382\pi$
$3$	0.483252	−	2.27352i	0.279006	−	1.31262i	−0.585777	−	0.810472i	$-0.699211\pi$
$3$	0.483252	−	2.27352i	0.279006	−	1.31262i	0.864783	−	0.502146i	$-0.167456\pi$
$4$	2.46986	+	0.524984i	1.23493	+	0.262492i
$5$		0			0
$5$		0			0
$6$	1.52788	−	4.70232i	0.623753	−	1.91971i
$7$	−0.0903750	−	2.64421i	−0.0341585	−	0.999416i
$7$	−0.0903750	−	2.64421i	−0.0341585	−	0.999416i
$8$	1.06219	+	0.345128i	0.375542	+	0.122021i
$9$	−2.19474	−	0.977159i	−0.731579	−	0.325720i
$10$		0			0
$11$	−2.44955	+	1.09061i	−0.738567	+	0.328831i	−0.741308	−	0.671165i	$-0.765794\pi$
$11$	−2.44955	+	1.09061i	−0.738567	+	0.328831i	0.00274080	+	0.999996i	$0.499128\pi$
$12$	2.38713	−	5.36157i	0.689104	−	1.54775i
$13$	−1.74792	−	2.40580i	−0.484785	−	0.667249i	0.494631	−	0.869103i	$-0.335303\pi$
$13$	−1.74792	−	2.40580i	−0.484785	−	0.667249i	−0.979416	+	0.201854i	$0.935303\pi$
$14$	0.396757	−	5.61407i	0.106038	−	1.50042i
$15$		0			0
$16$	−2.44307	−	1.08773i	−0.610768	−	0.271931i
$17$	0.836817	−	0.753473i	0.202958	−	0.182744i	−0.561384	−	0.827556i	$-0.689731\pi$
$17$	0.836817	−	0.753473i	0.202958	−	0.182744i	0.764342	+	0.644812i	$0.223064\pi$
$18$	−4.42582	−	2.55525i	−1.04318	−	0.602278i
$19$	3.59536	−	0.764218i	0.824833	−	0.175324i	0.223889	−	0.974615i	$-0.428125\pi$
$19$	3.59536	−	0.764218i	0.824833	−	0.175324i	0.600944	+	0.799291i	$0.294791\pi$
$20$		0			0
$21$	−6.05534	−	1.07235i	−1.32138	−	0.234006i
$22$	−5.42467	+	1.76258i	−1.15654	+	0.375784i
$23$	7.22218	+	0.759081i	1.50593	+	0.158279i	0.821251	−	0.570567i	$-0.193277\pi$
$23$	7.22218	+	0.759081i	1.50593	+	0.158279i	0.684677	+	0.728847i	$0.259943\pi$
$24$	1.29796	−	2.24814i	0.264946	−	0.458899i
$25$		0			0
$26$	−3.16288	−	5.47827i	−0.620292	−	1.07438i
$27$	0.816389	−	1.12366i	0.157114	−	0.216249i
$28$	1.16495	−	6.57825i	0.220155	−	1.24317i
$29$	3.16693	+	9.74681i	0.588084	+	1.80994i	0.586515	+	0.809938i	$0.300499\pi$
$29$	3.16693	+	9.74681i	0.588084	+	1.80994i	0.00156889	+	0.999999i	$0.499501\pi$
$30$		0			0
$31$	3.56421	+	3.95846i	0.640151	+	0.710960i	0.972684	−	0.232132i	$-0.0745700\pi$
$31$	3.56421	+	3.95846i	0.640151	+	0.710960i	−0.332533	+	0.943092i	$0.607903\pi$
$32$	−6.86105	−	3.96123i	−1.21287	−	0.700253i
$33$	1.29578	+	6.09615i	0.225566	+	1.06120i
$34$	1.93787	−	1.40795i	0.332342	−	0.241461i
$35$		0			0
$36$	−4.90769	−	3.56564i	−0.817948	−	0.594274i
$37$	−1.82513	+	4.09931i	−0.300050	+	0.673923i	−0.999155	−	0.0410958i	$-0.986915\pi$
$37$	−1.82513	+	4.09931i	−0.300050	+	0.673923i	0.699105	+	0.715019i	$0.253582\pi$
$38$	7.77613	−	0.817304i	1.26145	−	0.132584i
$39$	−6.31433	+	2.81132i	−1.01110	+	0.450172i
$40$		0			0
$41$	3.05046	−	2.21629i	0.476402	−	0.346126i	−0.323529	−	0.946218i	$-0.604869\pi$
$41$	3.05046	−	2.21629i	0.476402	−	0.346126i	0.799931	+	0.600092i	$0.204869\pi$
$42$	−12.5720	−	3.61505i	−1.93990	−	0.557814i
$43$		−	8.46953i		−	1.29159i	−0.763510	−	0.645796i	$-0.776526\pi$
$43$		−	8.46953i		−	1.29159i	0.763510	−	0.645796i	$-0.223474\pi$
$44$	−6.62259	+	1.40767i	−0.998393	+	0.212215i
$45$		0			0
$46$	15.1102	+	3.21176i	2.22787	+	0.473549i
$47$	3.85492	+	3.47099i	0.562298	+	0.506295i	0.900545	−	0.434762i	$-0.143167\pi$
$47$	3.85492	+	3.47099i	0.562298	+	0.506295i	−0.338247	+	0.941057i	$0.609834\pi$
$48$	−3.65359	+	5.02873i	−0.527350	+	0.725835i
$49$	−6.98366	+	0.477940i	−0.997666	+	0.0682772i
$50$		0			0
$51$	−1.30864	−	2.26664i	−0.183247	−	0.317393i
$52$	−3.05410	−	6.85961i	−0.423527	−	0.951257i
$53$	−0.495113	+	2.32932i	−0.0680090	+	0.319957i	−0.998981	−	0.0451335i	$-0.985629\pi$
$53$	−0.495113	+	2.32932i	−0.0680090	+	0.319957i	0.930972	+	0.365091i	$0.118962\pi$
$54$	1.97697	−	2.19565i	0.269032	−	0.298790i
$55$		0			0
$56$	0.816594	−	2.83985i	0.109122	−	0.379491i
$57$		−	8.54345i		−	1.13161i
$58$	4.53258	+	21.3241i	0.595157	+	2.80000i
$59$	−0.0789064	−	0.750745i	−0.0102727	−	0.0977386i	0.988184	−	0.153272i	$-0.0489809\pi$
$59$	−0.0789064	−	0.750745i	−0.0102727	−	0.0977386i	−0.998457	+	0.0555329i	$0.982314\pi$
$60$		0			0
$61$	−0.0500232	+	0.475939i	−0.00640481	+	0.0609377i	−0.997257	−	0.0740105i	$-0.976420\pi$
$61$	−0.0500232	+	0.475939i	−0.00640481	+	0.0609377i	0.990853	+	0.134948i	$0.0430868\pi$
$62$	6.66012	+	9.16687i	0.845836	+	1.16419i
$63$	−2.38546	+	5.89165i	−0.300540	+	0.742278i
$64$	−9.30711	−	6.76201i	−1.16339	−	0.845251i
$65$		0			0
$66$	1.38579	+	13.1849i	0.170579	+	1.62295i
$67$	−2.55052	+	2.29650i	−0.311596	+	0.280562i	−0.810059	−	0.586349i	$-0.800565\pi$
$67$	−2.55052	+	2.29650i	−0.311596	+	0.280562i	0.498463	+	0.866911i	$0.333898\pi$
$68$	2.46238	−	1.42165i	0.298607	−	0.172401i
$69$	5.21592	−	16.0530i	0.627923	−	1.93255i
$70$		0			0
$71$	−3.56107	−	10.9599i	−0.422622	−	1.30070i	−0.905253	−	0.424873i	$-0.860319\pi$
$71$	−3.56107	−	10.9599i	−0.422622	−	1.30070i	0.482631	−	0.875824i	$-0.339681\pi$
$72$	−1.99399	−	1.79540i	−0.234994	−	0.211590i
$73$	3.95548	+	8.88415i	0.462954	+	1.03981i	0.982652	+	0.185461i	$0.0593779\pi$
$73$	3.95548	+	8.88415i	0.462954	+	1.03981i	−0.519698	+	0.854350i	$0.673955\pi$
$74$	−4.77267	+	8.26651i	−0.554812	+	0.960963i
$75$		0			0
$76$	9.28123			1.06463
$77$	3.10518	+	6.37856i	0.353868	+	0.726904i
$78$	−13.9834	+	4.54350i	−1.58331	+	0.514450i
$79$	−2.83673	+	3.15051i	−0.319158	+	0.354460i	−0.881281	−	0.472593i	$-0.843318\pi$
$79$	−2.83673	+	3.15051i	−0.319158	+	0.354460i	0.562123	+	0.827054i	$0.309985\pi$
$80$		0			0
$81$	−6.98278	−	7.75517i	−0.775865	−	0.861685i
$82$	6.94623	−	4.01041i	0.767083	−	0.442875i
$83$	13.2413	+	4.30236i	1.45342	+	0.472246i	0.926054	−	0.377391i	$-0.123179\pi$
$83$	13.2413	+	4.30236i	1.45342	+	0.472246i	0.527369	+	0.849637i	$0.323179\pi$
$84$	−14.3928	−	5.82750i	−1.57039	−	0.635833i
$85$		0			0
$86$	1.88324	−	17.9178i	0.203075	−	1.93213i
$87$	23.6900	−	2.48992i	2.53984	−	0.266948i
$88$	−2.97830	+	0.313032i	−0.317488	+	0.0333693i
$89$	−0.850889	+	8.09567i	−0.0901941	+	0.858139i	0.852106	+	0.523369i	$0.175325\pi$
$89$	−0.850889	+	8.09567i	−0.0901941	+	0.858139i	−0.942300	+	0.334770i	$0.891341\pi$
$90$		0			0
$91$	−6.20347	+	4.83928i	−0.650301	+	0.507294i
$92$	17.4392	+	5.66635i	1.81816	+	0.590758i
$93$	10.7221	−	6.19038i	1.11183	−	0.641913i
$94$	7.38353	+	8.20024i	0.761553	+	0.845790i
$95$		0			0
$96$	−12.3216	+	13.6845i	−1.25756	+	1.39667i
$97$	−2.53425	+	0.823427i	−0.257314	+	0.0836063i	−0.434833	−	0.900511i	$-0.643193\pi$
$97$	−2.53425	+	0.823427i	−0.257314	+	0.0836063i	0.177520	+	0.984117i	$0.443193\pi$
$98$	−14.8806	−	0.541736i	−1.50317	−	0.0547236i
$99$	6.44182			0.647427
$100$		0			0
$101$	8.22057	−	14.2384i	0.817977	−	1.41678i	−0.0891934	−	0.996014i	$-0.528429\pi$
$101$	8.22057	−	14.2384i	0.817977	−	1.41678i	0.907170	−	0.420763i	$-0.138238\pi$
$102$	−2.26452	−	5.08619i	−0.224221	−	0.503608i
$103$	−7.69823	−	6.93152i	−0.758529	−	0.682983i	0.196165	−	0.980571i	$-0.437151\pi$
$103$	−7.69823	−	6.93152i	−0.758529	−	0.682983i	−0.954694	+	0.297588i	$0.903818\pi$
$104$	−1.02632	−	3.15868i	−0.100639	−	0.309734i
$105$		0			0
$106$	−1.56538	+	4.81773i	−0.152043	+	0.467940i
$107$	0.365594	−	0.211076i	0.0353433	−	0.0204055i	−0.482224	−	0.876048i	$-0.660171\pi$
$107$	0.365594	−	0.211076i	0.0353433	−	0.0204055i	0.517568	+	0.855642i	$0.326838\pi$
$108$	2.60627	−	2.34669i	0.250788	−	0.225811i
$109$	0.0105013	+	0.0999129i	0.00100584	+	0.00956992i	0.995013	−	0.0997423i	$-0.0318018\pi$
$109$	0.0105013	+	0.0999129i	0.00100584	+	0.00956992i	−0.994007	+	0.109312i	$0.965135\pi$
$110$		0			0
$111$	8.43788	+	6.13048i	0.800888	+	0.581879i
$112$	−2.65538	+	6.55829i	−0.250910	+	0.619700i
$113$	5.05111	+	6.95226i	0.475169	+	0.654013i	0.977567	−	0.210623i	$-0.0675491\pi$
$113$	5.05111	+	6.95226i	0.475169	+	0.654013i	−0.502399	+	0.864636i	$0.667549\pi$
$114$	1.89967	−	18.0742i	0.177921	−	1.69280i
$115$		0			0
$116$	2.70494	+	25.7358i	0.251147	+	2.38951i
$117$	1.48537	+	6.98809i	0.137322	+	0.646049i
$118$		−	1.60579i		−	0.147825i
$119$	−2.06797	−	2.14462i	−0.189570	−	0.196597i
$120$		0			0
$121$	−2.54957	+	2.83158i	−0.231779	+	0.257417i
$122$	−0.211654	+	0.995754i	−0.0191623	+	0.0901513i
$123$	−3.56464	−	8.00631i	−0.321413	−	0.721905i
$124$	6.72496	+	11.6480i	0.603919	+	1.04602i
$125$		0			0
$126$	−6.35662	+	11.9337i	−0.566293	+	1.06314i
$127$	−9.64769	+	13.2789i	−0.856094	+	1.17831i	0.126392	+	0.991980i	$0.459660\pi$
$127$	−9.64769	+	13.2789i	−0.856094	+	1.17831i	−0.982487	+	0.186332i	$0.940340\pi$
$128$	−6.41110	−	5.77258i	−0.566666	−	0.510229i
$129$	−19.2557	−	4.09292i	−1.69537	−	0.360361i
$130$		0			0
$131$	−20.2180	+	4.29746i	−1.76645	+	0.375471i	−0.972572	−	0.232602i	$-0.925276\pi$
$131$	−20.2180	+	4.29746i	−1.76645	+	0.375471i	−0.793881	+	0.608073i	$0.791943\pi$
$132$			15.7369i			1.36972i
$133$	−2.34568	−	9.43782i	−0.203396	−	0.818363i
$134$	−5.90642	+	4.29126i	−0.510237	+	0.370709i
$135$		0			0
$136$	1.14891	−	0.511526i	0.0985179	−	0.0438630i
$137$	−6.74599	+	0.709033i	−0.576349	+	0.0605767i	−0.388219	−	0.921567i	$-0.626909\pi$
$137$	−6.74599	+	0.709033i	−0.576349	+	0.0605767i	−0.188131	+	0.982144i	$0.560243\pi$
$138$	14.6040	−	32.8012i	1.24318	−	2.79222i
$139$	5.48003	+	3.98148i	0.464810	+	0.337704i	0.795415	−	0.606065i	$-0.207253\pi$
$139$	5.48003	+	3.98148i	0.464810	+	0.337704i	−0.330605	+	0.943769i	$0.607253\pi$
$140$		0			0
$141$	9.75426	−	7.08689i	0.821457	−	0.596824i
$142$	−5.09669	−	23.9781i	−0.427705	−	2.01219i
$143$	6.90540	+	3.98684i	0.577459	+	0.333396i
$144$	4.29901	+	4.77454i	0.358251	+	0.397878i
$145$		0			0
$146$	6.39262	+	19.6745i	0.529057	+	1.62827i
$147$	−2.28826	+	16.1085i	−0.188733	+	1.32861i
$148$	−6.65988	+	9.16654i	−0.547439	+	0.753485i
$149$	−4.16733	−	7.21802i	−0.341401	−	0.591324i	0.643292	−	0.765621i	$-0.277568\pi$
$149$	−4.16733	−	7.21802i	−0.341401	−	0.591324i	−0.984693	+	0.174297i	$0.944235\pi$
$150$		0			0
$151$	−11.3516	+	19.6616i	−0.923781	+	1.60003i	−0.130270	+	0.991479i	$0.541584\pi$
$151$	−11.3516	+	19.6616i	−0.923781	+	1.60003i	−0.793511	+	0.608556i	$0.791749\pi$
$152$	4.08273	+	0.429112i	0.331153	+	0.0348056i
$153$	−2.57285	+	0.835971i	−0.208003	+	0.0675842i
$154$	5.15089	+	14.1847i	0.415070	+	1.14303i
$155$		0			0
$156$	−17.0714	+	3.62863i	−1.36680	+	0.290523i
$157$	9.98874	+	5.76700i	0.797188	+	0.460257i	0.842487	−	0.538717i	$-0.181091\pi$
$157$	9.98874	+	5.76700i	0.797188	+	0.460257i	−0.0452987	+	0.998973i	$0.514424\pi$
$158$	−6.70181	+	6.03434i	−0.533167	+	0.480066i
$159$	5.05651	+	2.25130i	0.401007	+	0.178540i
$160$		0			0
$161$	1.35446	−	19.1655i	0.106747	−	1.51046i
$162$	−13.0481	−	17.9592i	−1.02516	−	1.41101i
$163$	3.83703	−	8.61811i	0.300539	−	0.675023i	−0.698642	−	0.715471i	$-0.746212\pi$
$163$	3.83703	−	8.61811i	0.300539	−	0.675023i	0.999182	+	0.0404486i	$0.0128787\pi$
$164$	8.69771	−	3.87247i	0.679177	−	0.302389i
$165$		0			0
$166$	27.0561	+	12.0462i	2.09996	+	0.934964i
$167$	15.5186	+	5.04231i	1.20087	+	0.390186i	0.840080	−	0.542462i	$-0.182508\pi$
$167$	15.5186	+	5.04231i	1.20087	+	0.390186i	0.360788	+	0.932648i	$0.382508\pi$
$168$	−6.06185	−	3.22891i	−0.467682	−	0.249116i
$169$	1.28455	−	3.95345i	0.0988118	−	0.304111i
$170$		0			0
$171$	−8.63763	−	1.83599i	−0.660536	−	0.140401i
$172$	4.44637	−	20.9185i	0.339032	−	1.59502i
$173$	−14.5837	−	1.53281i	−1.10878	−	0.116537i	−0.467608	−	0.883936i	$-0.654884\pi$
$173$	−14.5837	−	1.53281i	−1.10878	−	0.116537i	−0.641170	+	0.767399i	$0.721551\pi$
$174$	50.6713			3.84138
$175$		0			0
$176$	7.17071			0.540513
$177$	−1.74497	−	0.183403i	−0.131160	−	0.0137854i
$178$	−3.60021	+	16.9377i	−0.269847	+	1.26953i
$179$	12.9742	+	2.75776i	0.969740	+	0.206125i	0.665440	−	0.746452i	$-0.268244\pi$
$179$	12.9742	+	2.75776i	0.969740	+	0.206125i	0.304300	+	0.952576i	$0.401577\pi$
$180$		0			0
$181$	3.73433	−	11.4931i	0.277571	−	0.854275i	−0.710957	−	0.703235i	$-0.751738\pi$
$181$	3.73433	−	11.4931i	0.277571	−	0.854275i	0.988528	−	0.151039i	$-0.0482620\pi$
$182$	−14.1998	+	8.85842i	−1.05256	+	0.656630i
$183$	1.05788	+	0.343727i	0.0782010	+	0.0254091i
$184$	7.40937	+	3.29887i	0.546226	+	0.243196i
$185$		0			0
$186$	24.0596	−	10.7120i	1.76414	−	0.785444i
$187$	−1.22808	+	2.75831i	−0.0898060	+	0.201708i
$188$	7.69888	+	10.5966i	0.561499	+	0.772837i
$189$	−3.04498	−	2.05715i	−0.221490	−	0.149636i
$190$		0			0
$191$	8.93385	+	3.97761i	0.646431	+	0.287810i	0.703644	−	0.710552i	$-0.251555\pi$
$191$	8.93385	+	3.97761i	0.646431	+	0.287810i	−0.0572133	+	0.998362i	$0.518222\pi$
$192$	−19.8713	+	17.8922i	−1.43408	+	1.29126i
$193$	−14.1929	−	8.19428i	−1.02163	−	0.589837i	−0.107053	−	0.994253i	$-0.534142\pi$
$193$	−14.1929	−	8.19428i	−1.02163	−	0.589837i	−0.914575	+	0.404416i	$0.867475\pi$
$194$	−5.54444	+	1.17851i	−0.398068	+	0.0846119i
$195$		0			0
$196$	−17.4996	−	2.48587i	−1.24997	−	0.177562i
$197$	−6.73048	+	2.18687i	−0.479527	+	0.155808i	−0.538799	−	0.842434i	$-0.681122\pi$
$197$	−6.73048	+	2.18687i	−0.479527	+	0.155808i	0.0592724	+	0.998242i	$0.481122\pi$
$198$	13.6280	+	1.43237i	0.968503	+	0.101794i
$199$	−3.64345	+	6.31065i	−0.258278	+	0.447350i	−0.965781	−	0.259360i	$-0.916488\pi$
$199$	−3.64345	+	6.31065i	−0.258278	+	0.447350i	0.707503	+	0.706710i	$0.249822\pi$
$200$		0			0
$201$	3.98860	+	6.90846i	0.281334	+	0.487285i
$202$	20.5571	−	28.2944i	1.44639	−	1.99079i
$203$	25.4864	−	9.25489i	1.78879	−	0.649566i
$204$	−2.04221	−	6.28529i	−0.142984	−	0.440058i
$205$		0			0
$206$	−14.7448	−	16.3758i	−1.02732	−	1.14095i
$207$	−15.1090	−	8.72320i	−1.05015	−	0.606304i
$208$	1.65343	+	7.77880i	0.114645	+	0.539363i
$209$	−7.97356	+	5.79313i	−0.551543	+	0.400719i
$210$		0			0
$211$	17.5042	+	12.7175i	1.20504	+	0.875512i	0.994771	−	0.102132i	$-0.0325664\pi$
$211$	17.5042	+	12.7175i	1.20504	+	0.875512i	0.210268	+	0.977644i	$0.432566\pi$
$212$	−2.44572	+	5.49317i	−0.167972	+	0.377272i
$213$	−26.6384	+	2.79981i	−1.82523	+	0.191840i
$214$	0.820369	−	0.365252i	0.0560793	−	0.0249681i
$215$		0			0
$216$	1.25497	−	0.911790i	0.0853899	−	0.0620394i
$217$	10.1449	−	9.78226i	0.688678	−	0.664063i
$218$			0.213707i			0.0144740i
$219$	22.1098	−	4.69959i	1.49404	−	0.317569i
$220$		0			0
$221$	−3.27539	−	0.696206i	−0.220327	−	0.0468319i
$222$	16.4877	+	14.8456i	1.10658	+	0.996371i
$223$	4.35513	−	5.99432i	0.291641	−	0.401409i	−0.637905	−	0.770115i	$-0.720199\pi$
$223$	4.35513	−	5.99432i	0.291641	−	0.401409i	0.929546	+	0.368705i	$0.120199\pi$
$224$	−9.85425	+	18.5000i	−0.658415	+	1.23609i
$225$		0			0
$226$	9.14006	+	15.8310i	0.607988	+	1.05307i
$227$	−6.41085	−	14.3990i	−0.425503	−	0.955696i	−0.991357	−	0.131190i	$-0.958120\pi$
$227$	−6.41085	−	14.3990i	−0.425503	−	0.955696i	0.565854	−	0.824505i	$-0.308547\pi$
$228$	4.48517	−	21.1011i	0.297038	−	1.39745i
$229$	5.76428	−	6.40188i	0.380914	−	0.423048i	−0.521949	−	0.852977i	$-0.674795\pi$
$229$	5.76428	−	6.40188i	0.380914	−	0.423048i	0.902863	+	0.429929i	$0.141461\pi$
$230$		0			0
$231$	16.0024	−	3.97724i	1.05288	−	0.261683i
$232$			11.4460i			0.751467i
$233$	−0.283024	−	1.33153i	−0.0185416	−	0.0872311i	0.967904	−	0.251320i	$-0.0808648\pi$
$233$	−0.283024	−	1.33153i	−0.0185416	−	0.0872311i	−0.986445	+	0.164089i	$0.947531\pi$
$234$	1.58855	+	15.1140i	0.103846	+	0.988033i
$235$		0			0
$236$	0.199241	−	1.89565i	0.0129695	−	0.123397i
$237$	5.79190	+	7.97187i	0.376225	+	0.517829i
$238$	−3.89804	−	4.99689i	−0.252672	−	0.323901i
$239$	15.7418	+	11.4371i	1.01826	+	0.739806i	0.965924	−	0.258824i	$-0.0833350\pi$
$239$	15.7418	+	11.4371i	1.01826	+	0.739806i	0.0523308	+	0.998630i	$0.483335\pi$
$240$		0			0
$241$	−1.36582	−	12.9949i	−0.0879802	−	0.837075i	−0.946154	−	0.323716i	$-0.895068\pi$
$241$	−1.36582	−	12.9949i	−0.0879802	−	0.837075i	0.858174	−	0.513359i	$-0.171599\pi$
$242$	−6.02338	+	5.42348i	−0.387198	+	0.348634i
$243$	−17.3975	+	10.0444i	−1.11605	+	0.644350i
$244$	−0.373410	+	1.14924i	−0.0239051	+	0.0735725i
$245$		0			0
$246$	−5.76097	−	17.7304i	−0.367306	−	1.13045i
$247$	−8.12295	−	7.31394i	−0.516851	−	0.465375i
$248$	2.41971	+	5.43476i	0.153652	+	0.345107i
$249$	16.1804	−	28.0253i	1.02539	−	1.77603i
$250$		0			0
$251$	−21.9011			−1.38238			−0.691192	−	0.722671i	$-0.742914\pi$
$251$	−21.9011			−1.38238			−0.691192	+	0.722671i	$0.742914\pi$
$252$	−8.98477	+	13.2992i	−0.565987	+	0.837770i
$253$	−18.5189	+	6.01717i	−1.16428	+	0.378296i
$254$	−23.3629	+	25.9471i	−1.46592	+	1.62807i
$255$		0			0
$256$	3.11614	+	3.46083i	0.194759	+	0.216302i
$257$	−6.99088	+	4.03619i	−0.436079	+	0.251770i	−0.701933	−	0.712243i	$-0.747679\pi$
$257$	−6.99088	+	4.03619i	−0.436079	+	0.251770i	0.265854	+	0.964013i	$0.414346\pi$
$258$	−39.8264	−	12.9404i	−2.47949	−	0.805634i
$259$	11.0044	+	4.45555i	0.683779	+	0.276854i
$260$		0			0
$261$	2.57361	−	24.4863i	0.159302	−	1.51566i
$262$	−43.7279	+	4.59599i	−2.70152	+	0.283941i
$263$	−5.31312	+	0.558432i	−0.327621	+	0.0344344i	−0.266911	−	0.963721i	$-0.586003\pi$
$263$	−5.31312	+	0.558432i	−0.327621	+	0.0344344i	−0.0607099	+	0.998155i	$0.519336\pi$
$264$	−0.727584	+	6.92250i	−0.0447797	+	0.426050i
$265$		0			0
$266$	−2.86389	−	20.4878i	−0.175596	−	1.25619i
$267$	17.9945	+	5.84676i	1.10124	+	0.357816i
$268$	−7.50505	+	4.33304i	−0.458444	+	0.264683i
$269$	−8.17799	−	9.08258i	−0.498621	−	0.553775i	0.440325	−	0.897838i	$-0.354863\pi$
$269$	−8.17799	−	9.08258i	−0.498621	−	0.553775i	−0.938946	+	0.344064i	$0.888196\pi$
$270$		0			0
$271$	−2.13857	+	2.37512i	−0.129909	+	0.144278i	−0.804589	−	0.593831i	$-0.797615\pi$
$271$	−2.13857	+	2.37512i	−0.129909	+	0.144278i	0.674681	+	0.738110i	$0.264281\pi$
$272$	−2.86397	+	0.930561i	−0.173654	+	0.0564236i
$273$	8.00437	+	16.4423i	0.484447	+	0.995135i
$274$	−14.4292			−0.871700
$275$		0			0
$276$	21.3101	−	36.9102i	1.28272	−	2.22173i
$277$	2.12471	+	4.77218i	0.127662	+	0.286733i	0.966057	−	0.258330i	$-0.0831723\pi$
$277$	2.12471	+	4.77218i	0.127662	+	0.286733i	−0.838395	+	0.545063i	$0.816506\pi$
$278$	10.7080	+	9.64156i	0.642225	+	0.578262i
$279$	−3.95446	−	12.1706i	−0.236747	−	0.728633i
$280$		0			0
$281$	−6.54737	+	20.1507i	−0.390583	+	1.20209i	0.541765	+	0.840530i	$0.317756\pi$
$281$	−6.54737	+	20.1507i	−0.390583	+	1.20209i	−0.932348	+	0.361561i	$0.882244\pi$
$282$	22.2115	−	12.8238i	1.32268	−	0.763648i
$283$	−4.57979	+	4.12366i	−0.272240	+	0.245126i	−0.793930	−	0.608009i	$-0.791969\pi$
$283$	−4.57979	+	4.12366i	−0.272240	+	0.245126i	0.521690	+	0.853135i	$0.325302\pi$
$284$	−3.04159	−	28.9388i	−0.180485	−	1.71720i
$285$		0			0
$286$	13.7223	+	9.96984i	0.811417	+	0.589529i
$287$	−6.13601	−	7.86575i	−0.362197	−	0.464300i
$288$	11.1874	+	15.3982i	0.659227	+	0.907348i
$289$	−1.64444	+	15.6458i	−0.0967320	+	0.920343i
$290$		0			0
$291$	0.647399	+	6.15959i	0.0379512	+	0.361082i
$292$	5.10542	+	24.0191i	0.298772	+	1.40561i
$293$		−	24.5603i		−	1.43483i	−0.696648	−	0.717413i	$-0.745326\pi$
$293$		−	24.5603i		−	1.43483i	0.696648	−	0.717413i	$-0.254674\pi$
$294$	−8.42275	+	33.5697i	−0.491224	+	1.95782i
$295$		0			0
$296$	−3.35343	+	3.72436i	−0.194914	+	0.216474i
$297$	−0.774308	+	3.64283i	−0.0449299	+	0.211379i
$298$	−7.21127	−	16.1968i	−0.417738	−	0.938254i
$299$	−10.7976	−	18.7019i	−0.624440	−	1.08156i
$300$		0			0
$301$	−22.3952	+	0.765434i	−1.29084	+	0.0441189i
$302$	−28.3868	+	39.0711i	−1.63348	+	2.24829i
$303$	−28.3988	−	25.5704i	−1.63147	−	1.46898i
$304$	−9.61499	−	2.04373i	−0.551457	−	0.117216i
$305$		0			0
$306$	−5.62891	+	1.19646i	−0.321783	+	0.0683971i
$307$			8.71345i			0.497303i	0.968593	+	0.248651i	$0.0799873\pi$
$307$			8.71345i			0.497303i	−0.968593	+	0.248651i	$0.920013\pi$
$308$	4.32070	+	17.3843i	0.246195	+	0.990561i
$309$	−19.4791	+	14.1524i	−1.10813	+	0.805104i
$310$		0			0
$311$	−21.1140	+	9.40056i	−1.19727	+	0.533057i	−0.905874	−	0.423547i	$-0.860785\pi$
$311$	−21.1140	+	9.40056i	−1.19727	+	0.533057i	−0.291392	+	0.956604i	$0.594118\pi$
$312$	−7.67731	+	0.806918i	−0.434642	+	0.0456827i
$313$	3.04097	−	6.83014i	0.171886	−	0.386062i	−0.806976	−	0.590584i	$-0.798897\pi$
$313$	3.04097	−	6.83014i	0.171886	−	0.386062i	0.978862	+	0.204522i	$0.0655640\pi$
$314$	19.8495	+	14.4215i	1.12017	+	0.813851i
$315$		0			0
$316$	−8.66029	+	6.29207i	−0.487179	+	0.353957i
$317$	−5.98610	−	28.1624i	−0.336213	−	1.58176i	−0.743678	−	0.668538i	$-0.766921\pi$
$317$	−5.98610	−	28.1624i	−0.336213	−	1.58176i	0.407465	−	0.913221i	$-0.366413\pi$
$318$	10.1968	+	5.88710i	0.571805	+	0.330132i
$319$	−18.3875	−	20.4214i	−1.02950	−	1.14338i
$320$		0			0
$321$	−0.303211	−	0.933188i	−0.0169236	−	0.0520855i
$322$	7.12699	−	40.2447i	0.397172	−	2.24275i
$323$	2.43284	−	3.34852i	0.135367	−	0.186317i
$324$	−13.1751	−	22.8200i	−0.731951	−	1.26778i
$325$		0			0
$326$	10.0337	−	17.3789i	0.555717	−	0.962531i
$327$	0.232229	+	0.0244083i	0.0128423	+	0.00134978i
$328$	4.00508	−	1.30133i	0.221144	−	0.0718539i
$329$	8.82962	−	10.5069i	0.486793	−	0.579264i
$330$		0			0
$331$	−3.94864	+	0.839310i	−0.217037	+	0.0461326i	−0.315147	−	0.949043i	$-0.602054\pi$
$331$	−3.94864	+	0.839310i	−0.217037	+	0.0461326i	0.0981097	+	0.995176i	$0.468720\pi$
$332$	30.4454	+	17.5777i	1.67091	+	0.964701i
$333$	8.01136	−	7.21346i	0.439020	−	0.395295i
$334$	31.7094	+	14.1179i	1.73506	+	0.772500i
$335$		0			0
$336$	13.6272	+	9.20637i	0.743425	+	0.502249i
$337$	−8.19713	−	11.2824i	−0.446526	−	0.614590i	0.525121	−	0.851028i	$-0.324020\pi$
$337$	−8.19713	−	11.2824i	−0.446526	−	0.614590i	−0.971647	+	0.236437i	$0.924020\pi$
$338$	3.59661	−	8.07813i	0.195630	−	0.439392i
$339$	18.2471	−	8.12412i	0.991045	−	0.441242i
$340$		0			0
$341$	−13.0478	−	5.80928i	−0.706581	−	0.314590i
$342$	−17.8652	−	5.80475i	−0.966039	−	0.313885i
$343$	1.89492	+	18.4231i	0.102316	+	0.994752i
$344$	2.92307	−	8.99628i	0.157601	−	0.485047i
$345$		0			0
$346$	−30.5118	−	6.48549i	−1.64033	−	0.348662i
$347$	0.143294	−	0.674146i	0.00769243	−	0.0361901i	−0.974134	−	0.225971i	$-0.927444\pi$
$347$	0.143294	−	0.674146i	0.00769243	−	0.0361901i	0.981826	+	0.189781i	$0.0607778\pi$
$348$	59.8181	+	6.28713i	3.20659	+	0.337026i
$349$	−19.3610			−1.03637			−0.518186	−	0.855268i	$-0.673393\pi$
$349$	−19.3610			−1.03637			−0.518186	+	0.855268i	$0.673393\pi$
$350$		0			0
$351$	−4.13029			−0.220459
$352$	21.1267	+	2.22050i	1.12605	+	0.118353i
$353$	2.46473	−	11.5956i	0.131184	−	0.617173i	−0.862604	−	0.505881i	$-0.831168\pi$
$353$	2.46473	−	11.5956i	0.131184	−	0.617173i	0.993788	−	0.111292i	$-0.0354990\pi$
$354$	−3.65080	−	0.776001i	−0.194038	−	0.0412440i
$355$		0			0
$356$	−6.35167	+	19.5484i	−0.336638	+	1.03606i
$357$	−5.87519	+	3.66517i	−0.310948	+	0.193982i
$358$	26.8346	+	8.71908i	1.41825	+	0.460818i
$359$	11.0514	+	4.92038i	0.583268	+	0.259688i	0.677089	−	0.735901i	$-0.263241\pi$
$359$	11.0514	+	4.92038i	0.583268	+	0.259688i	−0.0938206	+	0.995589i	$0.529908\pi$
$360$		0			0
$361$	−5.01476	+	2.23271i	−0.263935	+	0.117511i
$362$	10.4557	−	23.4840i	0.549541	−	1.23429i
$363$	5.20558	+	7.16487i	0.273222	+	0.376058i
$364$	−17.8622	+	8.69560i	−0.936235	+	0.455773i
$365$		0			0
$366$	2.16159	+	0.962401i	0.112988	+	0.0503055i
$367$	10.9546	−	9.86355i	0.571825	−	0.514873i	−0.331714	−	0.943380i	$-0.607627\pi$
$367$	10.9546	−	9.86355i	0.571825	−	0.514873i	0.903539	+	0.428507i	$0.140960\pi$
$368$	−16.8186	−	9.71023i	−0.876731	−	0.506181i
$369$	−8.86062	+	1.88338i	−0.461265	+	0.0980450i
$370$		0			0
$371$	6.20396	+	1.09867i	0.322094	+	0.0570401i
$372$	29.7318	−	9.66044i	1.54152	−	0.500870i
$373$	34.8601	+	3.66394i	1.80499	+	0.189712i	0.946409	−	0.322972i	$-0.104682\pi$
$373$	34.8601	+	3.66394i	1.80499	+	0.189712i	0.858578	+	0.512684i	$0.171349\pi$
$374$	−3.21140	+	5.56230i	−0.166057	+	0.287620i
$375$		0			0
$376$	2.89674	+	5.01730i	0.149388	+	0.258748i
$377$	17.9134	−	24.6556i	0.922585	−	1.26983i
$378$	−5.98442	−	5.02909i	−0.307805	−	0.258668i
$379$	−6.00030	−	18.4670i	−0.308215	−	0.948587i	−0.978458	−	0.206446i	$-0.933810\pi$
$379$	−6.00030	−	18.4670i	−0.308215	−	0.948587i	0.670243	−	0.742141i	$-0.266190\pi$
$380$		0			0
$381$	25.5276	+	28.3513i	1.30782	+	1.45248i
$382$	18.0157	+	10.4013i	0.921761	+	0.532179i
$383$	−3.15281	−	14.8328i	−0.161101	−	0.757920i	−0.982305	−	0.187286i	$-0.940031\pi$
$383$	−3.15281	−	14.8328i	−0.161101	−	0.757920i	0.821204	−	0.570634i	$-0.193303\pi$
$384$	−16.2223	+	11.7862i	−0.827839	+	0.601460i
$385$		0			0
$386$	−28.2039	−	20.4913i	−1.43554	−	1.04298i
$387$	−8.27608	+	18.5884i	−0.420697	+	0.944900i
$388$	−6.69151	+	0.703306i	−0.339710	+	0.0357049i
$389$	−18.1841	+	8.09607i	−0.921968	+	0.410487i	−0.812139	−	0.583464i	$-0.801697\pi$
$389$	−18.1841	+	8.09607i	−0.921968	+	0.410487i	−0.109829	+	0.993950i	$0.535030\pi$
$390$		0			0
$391$	6.61558	−	4.80650i	0.334564	−	0.243075i
$392$	−7.58296	−	1.90259i	−0.382997	−	0.0960954i
$393$			48.0428i			2.42344i
$394$	−14.7250	+	3.12989i	−0.741835	+	0.157682i
$395$		0			0
$396$	15.9104	+	3.38185i	0.799525	+	0.169944i
$397$	−15.3310	−	13.8041i	−0.769442	−	0.692809i	0.187764	−	0.982214i	$-0.439876\pi$
$397$	−15.3310	−	13.8041i	−0.769442	−	0.692809i	−0.957207	+	0.289405i	$0.906542\pi$
$398$	−9.11114	+	12.5404i	−0.456700	+	0.628594i
$399$	−22.5906	+	0.772114i	−1.13095	+	0.0386541i
$400$		0			0
$401$	7.44973	+	12.9033i	0.372022	+	0.644361i	0.989876	−	0.141932i	$-0.0453313\pi$
$401$	7.44973	+	12.9033i	0.372022	+	0.644361i	−0.617855	+	0.786292i	$0.711998\pi$
$402$	6.90200	+	15.5021i	0.344240	+	0.773176i
$403$	3.29332	−	15.4938i	0.164052	−	0.771803i
$404$	27.7786	−	30.8512i	1.38204	−	1.53491i
$405$		0			0
$406$	55.9758	−	13.9123i	2.77803	−	0.690454i
$407$		−	12.0320i		−	0.596403i
$408$	−0.607754	−	2.85926i	−0.0300883	−	0.141554i
$409$	−3.16422	−	30.1055i	−0.156460	−	1.48862i	−0.737832	−	0.674984i	$-0.764151\pi$
$409$	−3.16422	−	30.1055i	−0.156460	−	1.48862i	0.581372	−	0.813638i	$-0.302516\pi$
$410$		0			0
$411$	−1.64801	+	15.6798i	−0.0812906	+	0.773428i
$412$	−15.3746	−	21.1613i	−0.757451	−	1.04254i
$413$	−1.97799	+	0.276494i	−0.0973307	+	0.0136054i
$414$	−30.0244	−	21.8140i	−1.47562	−	1.07210i
$415$		0			0
$416$	2.46262	+	23.4302i	0.120740	+	1.14876i
$417$	11.7002	−	10.5349i	0.572962	−	0.515897i
$418$	−18.1567	+	10.4828i	−0.888071	+	0.512728i
$419$	−4.26455	+	13.1249i	−0.208337	+	0.641196i	0.791223	+	0.611528i	$0.209445\pi$
$419$	−4.26455	+	13.1249i	−0.208337	+	0.641196i	−0.999560	+	0.0296676i	$0.990555\pi$
$420$		0			0
$421$	2.65296	+	8.16496i	0.129297	+	0.397936i	0.994659	−	0.103211i	$-0.0329117\pi$
$421$	2.65296	+	8.16496i	0.129297	+	0.397936i	−0.865362	+	0.501147i	$0.832912\pi$
$422$	34.2034	+	30.7969i	1.66499	+	1.49917i
$423$	−5.06883	−	11.3848i	−0.246455	−	0.553546i
$424$	−1.32982	+	2.30332i	−0.0645818	+	0.111859i
$425$		0			0
$426$	−56.9776			−2.76058
$427$	1.26300	+	0.0892587i	0.0611210	+	0.00431953i
$428$	1.01377	−	0.329395i	0.0490027	−	0.0159219i
$429$	12.4012	−	13.7729i	0.598736	−	0.664964i
$430$		0			0
$431$	6.12966	+	6.80768i	0.295255	+	0.327914i	0.872460	−	0.488685i	$-0.162523\pi$
$431$	6.12966	+	6.80768i	0.295255	+	0.327914i	−0.577205	+	0.816599i	$0.695857\pi$
$432$	−3.21673	+	1.85718i	−0.154765	+	0.0893537i
$433$	−3.84295	−	1.24865i	−0.184680	−	0.0600063i	0.215217	−	0.976566i	$-0.430954\pi$
$433$	−3.84295	−	1.24865i	−0.184680	−	0.0600063i	−0.399897	+	0.916560i	$0.630954\pi$
$434$	23.6372	−	18.4392i	1.13462	−	0.885110i
$435$		0			0
$436$	−0.0265161	+	0.252283i	−0.00126989	+	0.0120822i
$437$	26.5464	−	2.79014i	1.26989	−	0.133471i
$438$	47.8196	−	5.02604i	2.28491	−	0.240154i
$439$	−1.21075	+	11.5195i	−0.0577860	+	0.549797i	0.926881	+	0.375355i	$0.122479\pi$
$439$	−1.21075	+	11.5195i	−0.0577860	+	0.549797i	−0.984667	+	0.174443i	$0.944188\pi$
$440$		0			0
$441$	15.7943	+	5.77520i	0.752111	+	0.275009i
$442$	−6.77448	−	2.20116i	−0.322229	−	0.104699i
$443$	−16.0411	+	9.26133i	−0.762135	+	0.440019i	−0.830062	−	0.557671i	$-0.811695\pi$
$443$	−16.0411	+	9.26133i	−0.762135	+	0.440019i	0.0679265	+	0.997690i	$0.478362\pi$
$444$	17.6219	+	19.5711i	0.836300	+	0.928805i
$445$		0			0
$446$	10.5464	−	11.7130i	0.499386	−	0.554625i
$447$	−18.4242	+	5.98639i	−0.871435	+	0.283146i
$448$	−17.0390	+	25.2210i	−0.805018	+	1.19158i
$449$	7.62529			0.359860			0.179930	−	0.983679i	$-0.442413\pi$
$449$	7.62529			0.359860			0.179930	+	0.983679i	$0.442413\pi$
$450$		0			0
$451$	−5.05515	+	8.75577i	−0.238038	+	0.412293i
$452$	8.82569	+	19.8228i	0.415125	+	0.932387i
$453$	39.2153	+	35.3096i	1.84250	+	1.65899i
$454$	−10.3609	−	31.8874i	−0.486259	−	1.49655i
$455$		0			0
$456$	2.94858	−	9.07480i	0.138080	−	0.424966i
$457$	−10.9307	+	6.31085i	−0.511317	+	0.295209i	−0.733375	−	0.679824i	$-0.762056\pi$
$457$	−10.9307	+	6.31085i	−0.511317	+	0.295209i	0.222058	+	0.975034i	$0.428723\pi$
$458$	13.6182	−	12.2618i	0.636335	−	0.572958i
$459$	−0.163482	−	1.55543i	−0.00763068	−	0.0726011i
$460$		0			0
$461$	10.9007	+	7.91981i	0.507695	+	0.368862i	0.811949	−	0.583729i	$-0.198407\pi$
$461$	10.9007	+	7.91981i	0.507695	+	0.368862i	−0.304253	+	0.952591i	$0.598407\pi$
$462$	34.7383	−	4.85589i	1.61617	−	0.225917i
$463$	10.1270	+	13.9386i	0.470639	+	0.647780i	0.976672	−	0.214734i	$-0.0688886\pi$
$463$	10.1270	+	13.9386i	0.470639	+	0.647780i	−0.506033	+	0.862514i	$0.668889\pi$
$464$	2.86482	−	27.2569i	0.132996	−	1.26537i
$465$		0			0
$466$	−0.302685	−	2.87985i	−0.0140216	−	0.133407i
$467$	5.34623	+	25.1520i	0.247394	+	1.16390i	0.909896	+	0.414837i	$0.136162\pi$
$467$	5.34623	+	25.1520i	0.247394	+	1.16390i	−0.662501	+	0.749061i	$0.730505\pi$
$468$			18.0394i			0.833870i
$469$	6.30293	+	6.53656i	0.291042	+	0.301831i
$470$		0			0
$471$	17.9385	−	19.9227i	0.826562	−	0.917990i
$472$	0.175289	−	0.824669i	0.00806832	−	0.0379585i
$473$	9.23696	+	20.7465i	0.424716	+	0.953927i
$474$	10.4805	+	18.1528i	0.481387	+	0.833787i
$475$		0			0
$476$	−3.98168	−	6.38255i	−0.182500	−	0.292544i
$477$	3.36276	−	4.62845i	0.153970	−	0.211922i
$478$	30.7597	+	27.6962i	1.40692	+	1.26679i
$479$	26.6604	+	5.66684i	1.21814	+	0.258925i	0.771758	−	0.635916i	$-0.219377\pi$
$479$	26.6604	+	5.66684i	1.21814	+	0.258925i	0.446386	+	0.894840i	$0.352711\pi$
$480$		0			0
$481$	13.0523	−	2.77435i	0.595134	−	0.126500i
$482$		−	27.7952i		−	1.26604i
$483$	−42.9187	−	12.3412i	−1.95287	−	0.561544i
$484$	−7.78360	+	5.65512i	−0.353800	+	0.257051i
$485$		0			0
$486$	−39.0388	+	17.3812i	−1.77084	+	0.788427i
$487$	12.5393	−	1.31793i	0.568209	−	0.0597212i	0.183932	−	0.982939i	$-0.441117\pi$
$487$	12.5393	−	1.31793i	0.568209	−	0.0597212i	0.384277	+	0.923218i	$0.374451\pi$
$488$	−0.217394	+	0.488275i	−0.00984097	+	0.0221032i
$489$	−17.7392	−	12.8883i	−0.802195	−	0.582829i
$490$		0			0
$491$	22.9004	−	16.6381i	1.03348	−	0.750867i	0.0644778	−	0.997919i	$-0.479462\pi$
$491$	22.9004	−	16.6381i	1.03348	−	0.750867i	0.969002	+	0.247052i	$0.0794618\pi$
$492$	−4.60096	−	21.6458i	−0.207427	−	0.975868i
$493$	9.99410	+	5.77009i	0.450111	+	0.259872i
$494$	−15.5583	−	17.2793i	−0.700001	−	0.777430i
$495$		0			0
$496$	−4.40191	−	13.5477i	−0.197651	−	0.608309i
$497$	−28.6583	+	10.4067i	−1.28550	+	0.466805i
$498$	40.4622	−	55.6914i	1.81315	−	2.49559i
$499$	13.0184	+	22.5485i	0.582783	+	1.00941i	0.995148	+	0.0983912i	$0.0313697\pi$
$499$	13.0184	+	22.5485i	0.582783	+	1.00941i	−0.412365	+	0.911019i	$0.635297\pi$
$500$		0			0
$501$	18.9632	−	32.8453i	0.847214	−	1.46742i
$502$	−46.3331	−	4.86980i	−2.06795	−	0.217350i
$503$	17.9094	−	5.81912i	0.798542	−	0.259462i	0.118804	−	0.992918i	$-0.462094\pi$
$503$	17.9094	−	5.81912i	0.798542	−	0.259462i	0.679737	+	0.733456i	$0.262094\pi$
$504$	−4.56719	+	5.43478i	−0.203439	+	0.242084i
$505$		0			0
$506$	−40.5159	+	8.61192i	−1.80115	+	0.382846i
$507$	−8.36749	−	4.83097i	−0.371613	−	0.214551i
$508$	−30.7996	+	27.7321i	−1.36651	+	1.23041i
$509$	−7.54950	−	3.36125i	−0.334626	−	0.148985i	0.232544	−	0.972586i	$-0.425295\pi$
$509$	−7.54950	−	3.36125i	−0.334626	−	0.148985i	−0.567170	+	0.823601i	$0.691962\pi$
$510$		0			0
$511$	23.1341	−	11.2620i	1.02339	−	0.498202i
$512$	15.9645	+	21.9732i	0.705537	+	0.971089i
$513$	2.07649	−	4.66388i	0.0916793	−	0.205915i
$514$	−15.6871	+	6.98434i	−0.691928	+	0.308066i
$515$		0			0
$516$	−45.4100	−	20.2178i	−1.99906	−	0.890040i
$517$	−13.2283	−	4.29814i	−0.581781	−	0.189032i
$518$	22.2897	+	11.8729i	0.979353	+	0.521663i
$519$	−10.5325	+	32.4156i	−0.462324	+	1.42289i
$520$		0			0
$521$	2.78693	+	0.592379i	0.122097	+	0.0259526i	0.268555	−	0.963264i	$-0.413454\pi$
$521$	2.78693	+	0.592379i	0.122097	+	0.0259526i	−0.146458	+	0.989217i	$0.546787\pi$
$522$	10.8892	−	51.2299i	0.476609	−	2.24227i
$523$	−21.5638	−	2.26644i	−0.942917	−	0.0991046i	−0.379422	−	0.925224i	$-0.623877\pi$
$523$	−21.5638	−	2.26644i	−0.942917	−	0.0991046i	−0.563495	+	0.826119i	$0.690544\pi$
$524$	−52.1916			−2.28000
$525$		0			0
$526$	−11.3644			−0.495511
$527$	5.96518	+	0.626966i	0.259847	+	0.0273111i
$528$	3.46526	−	16.3028i	0.150806	−	0.709487i
$529$	29.0862	+	6.18247i	1.26462	+	0.268803i
$530$		0			0
$531$	−0.560418	+	1.72479i	−0.0243201	+	0.0748495i
$532$	−0.838791	−	24.5415i	−0.0363662	−	1.06401i
$533$	−10.6639	−	3.46491i	−0.461905	−	0.150082i
$534$	36.7684	+	16.3703i	1.59112	+	0.708413i
$535$		0			0
$536$	−3.50174	+	1.55907i	−0.151252	+	0.0673417i
$537$	12.5397	−	28.1645i	0.541126	−	1.21539i
$538$	−15.2815	−	21.0331i	−0.658831	−	0.906803i
$539$	16.5856	−	8.78720i	0.714392	−	0.378491i
$540$		0			0
$541$	−18.4184	−	8.20040i	−0.791869	−	0.352563i	−0.0293837	−	0.999568i	$-0.509354\pi$
$541$	−18.4184	−	8.20040i	−0.791869	−	0.352563i	−0.762485	+	0.647005i	$0.776021\pi$
$542$	−5.05238	+	4.54918i	−0.217018	+	0.195404i
$543$	−24.3252	−	14.0441i	−1.04389	−	0.602692i
$544$	−8.72612	+	1.85480i	−0.374130	+	0.0795237i
$545$		0			0
$546$	13.2777	+	36.5645i	0.568233	+	1.56482i
$547$	−3.04493	+	0.989356i	−0.130192	+	0.0423018i	−0.373388	−	0.927675i	$-0.621804\pi$
$547$	−3.04493	+	0.989356i	−0.130192	+	0.0423018i	0.243196	+	0.969977i	$0.421804\pi$
$548$	−17.0339	−	1.79033i	−0.727650	−	0.0764791i
$549$	0.574856	−	0.995679i	0.0245342	−	0.0424946i
$550$		0			0
$551$	18.8349	+	32.6231i	0.802396	+	1.38979i
$552$	11.0806	−	15.2512i	0.471623	−	0.649134i
$553$	8.58698	+	7.21619i	0.365155	+	0.306863i
$554$	3.43384	+	10.5683i	0.145890	+	0.449003i
$555$		0			0
$556$	11.4447	+	12.7106i	0.485362	+	0.539049i
$557$	−15.6619	−	9.04243i	−0.663618	−	0.383140i	0.130036	−	0.991509i	$-0.458491\pi$
$557$	−15.6619	−	9.04243i	−0.663618	−	0.383140i	−0.793654	+	0.608369i	$0.791824\pi$
$558$	−5.65971	−	26.6269i	−0.239595	−	1.12720i
$559$	−20.3760	+	14.8040i	−0.861814	+	0.626144i
$560$		0			0
$561$	5.67761	+	4.12502i	0.239709	+	0.174159i
$562$	−18.3319	+	41.1742i	−0.773286	+	1.73683i
$563$	−20.9369	+	2.20056i	−0.882387	+	0.0927426i	−0.534873	−	0.844932i	$-0.679641\pi$
$563$	−20.9369	+	2.20056i	−0.882387	+	0.0927426i	−0.347513	+	0.937675i	$0.612974\pi$
$564$	27.8121	−	12.3828i	1.17110	−	0.521408i
$565$		0			0
$566$	−10.6057	+	7.70552i	−0.445792	+	0.323887i
$567$	−19.8752	+	19.1648i	−0.834680	+	0.804846i
$568$		−	12.8705i		−	0.540035i
$569$	4.05388	−	0.861678i	0.169947	−	0.0361234i	−0.122152	−	0.992511i	$-0.538980\pi$
$569$	4.05388	−	0.861678i	0.169947	−	0.0361234i	0.292099	+	0.956388i	$0.405646\pi$
$570$		0			0
$571$	−26.9756	−	5.73384i	−1.12889	−	0.239954i	−0.394644	−	0.918834i	$-0.629132\pi$
$571$	−26.9756	−	5.73384i	−1.12889	−	0.239954i	−0.734249	+	0.678880i	$0.762466\pi$
$572$	14.9623	+	13.4721i	0.625606	+	0.563298i
$573$	13.3605	−	18.3891i	0.558142	−	0.768217i
$574$	−11.2321	−	18.0048i	−0.468819	−	0.751507i
$575$		0			0
$576$	13.8191	+	23.9353i	0.575795	+	0.997306i
$577$	−1.66193	−	3.73276i	−0.0691871	−	0.155397i	0.875642	−	0.482961i	$-0.160439\pi$
$577$	−1.66193	−	3.73276i	−0.0691871	−	0.155397i	−0.944829	+	0.327564i	$0.893772\pi$
$578$	−6.95784	+	32.7340i	−0.289408	+	1.36156i
$579$	−25.4886	+	28.3080i	−1.05927	+	1.17644i
$580$		0			0
$581$	10.1797	−	35.4016i	0.422323	−	1.46871i
$582$			13.1749i			0.546119i
$583$	−1.32758	−	6.24577i	−0.0549827	−	0.258673i
$584$	1.13532	+	10.8018i	0.0469798	+	0.446983i
$585$		0			0
$586$	5.46108	−	51.9587i	0.225595	−	2.14640i
$587$	−12.3204	−	16.9576i	−0.508519	−	0.699916i	0.475150	−	0.879905i	$-0.342394\pi$
$587$	−12.3204	−	16.9576i	−0.508519	−	0.699916i	−0.983669	+	0.179989i	$0.942394\pi$
$588$	−14.1084	+	38.5843i	−0.581819	+	1.59119i
$589$	15.8398	+	11.5083i	0.652666	+	0.474189i
$590$		0			0
$591$	1.71937	+	16.3587i	0.0707254	+	0.672908i
$592$	8.91785	−	8.02967i	0.366521	−	0.330017i
$593$	20.6351	−	11.9137i	0.847383	−	0.489237i	−0.0123842	−	0.999923i	$-0.503942\pi$
$593$	20.6351	−	11.9137i	0.847383	−	0.489237i	0.859767	+	0.510687i	$0.170609\pi$
$594$	−2.44809	+	7.53446i	−0.100446	+	0.309142i
$595$		0			0
$596$	−6.50335	−	20.0153i	−0.266388	−	0.819857i
$597$	12.5867	+	11.3331i	0.515139	+	0.463833i
$598$	−18.6844	−	41.9660i	−0.764064	−	1.71612i
$599$	−2.74663	+	4.75730i	−0.112224	+	0.194378i	−0.916667	−	0.399652i	$-0.869131\pi$
$599$	−2.74663	+	4.75730i	−0.112224	+	0.194378i	0.804443	+	0.594030i	$0.202464\pi$
$600$		0			0
$601$	10.0631			0.410482			0.205241	−	0.978711i	$-0.434202\pi$
$601$	10.0631			0.410482			0.205241	+	0.978711i	$0.434202\pi$
$602$	−47.5486	−	3.36035i	−1.93793	−	0.136957i
$603$	7.84177	−	2.54795i	0.319342	−	0.103760i
$604$	−38.3588	+	42.6018i	−1.56080	+	1.73344i
$605$		0			0
$606$	−54.3937	−	60.4103i	−2.20959	−	2.45400i
$607$	19.5086	−	11.2633i	0.791831	−	0.457164i	−0.0487757	−	0.998810i	$-0.515532\pi$
$607$	19.5086	−	11.2633i	0.791831	−	0.457164i	0.840607	+	0.541646i	$0.182199\pi$
$608$	−27.6952	−	8.99872i	−1.12319	−	0.364946i
$609$	−8.72485	−	62.4163i	−0.353549	−	2.52924i
$610$		0			0
$611$	1.61242	−	15.3412i	0.0652316	−	0.620638i
$612$	−6.79345	+	0.714020i	−0.274609	+	0.0288626i
$613$	2.09941	−	0.220657i	0.0847943	−	0.00891224i	−0.0620363	−	0.998074i	$-0.519759\pi$
$613$	2.09941	−	0.220657i	0.0847943	−	0.00891224i	0.146831	+	0.989162i	$0.453093\pi$
$614$	−1.93747	+	18.4338i	−0.0781900	+	0.743928i
$615$		0			0
$616$	1.09688	+	7.84695i	0.0441947	+	0.316162i
$617$	−29.2447	−	9.50219i	−1.17735	−	0.382544i	−0.345967	−	0.938247i	$-0.612449\pi$
$617$	−29.2447	−	9.50219i	−1.17735	−	0.382544i	−0.831381	+	0.555703i	$0.812449\pi$
$618$	−44.3561	+	25.6090i	−1.78427	+	1.03015i
$619$	9.85617	+	10.9464i	0.396153	+	0.439972i	0.907915	−	0.419155i	$-0.137674\pi$
$619$	9.85617	+	10.9464i	0.396153	+	0.439972i	−0.511762	+	0.859127i	$0.671007\pi$
$620$		0			0
$621$	6.74906	−	7.49559i	0.270830	−	0.300788i
$622$	−46.7582	+	15.1927i	−1.87483	+	0.609170i
$623$	21.4835	+	1.51828i	0.860719	+	0.0608286i
$624$	18.4843			0.739964
$625$		0			0
$626$	7.95207	−	13.7734i	0.317829	−	0.550495i
$627$	9.31757	+	20.9276i	0.372108	+	0.835768i
$628$	21.6432	+	19.4876i	0.863656	+	0.777639i
$629$	1.56142	+	4.80556i	0.0622579	+	0.191610i
$630$		0			0
$631$	−2.75377	+	8.47524i	−0.109626	+	0.337394i	−0.990788	−	0.135420i	$-0.956762\pi$
$631$	−2.75377	+	8.47524i	−0.109626	+	0.337394i	0.881162	+	0.472814i	$0.156762\pi$
$632$	−4.10049	+	2.36742i	−0.163109	+	0.0941709i
$633$	37.3726	−	33.6504i	1.48543	−	1.33748i
$634$	−6.40193	−	60.9103i	−0.254253	−	2.41906i
$635$		0			0
$636$	11.3069	+	8.21497i	0.448349	+	0.325745i
$637$	13.3567	+	15.9659i	0.529212	+	0.632593i
$638$	−34.3591	−	47.2913i	−1.36029	−	1.87228i
$639$	−2.89391	+	27.5337i	−0.114481	+	1.08922i
$640$		0			0
$641$	−0.932548	−	8.87261i	−0.0368334	−	0.350447i	−0.997381	−	0.0723302i	$-0.976956\pi$
$641$	−0.932548	−	8.87261i	−0.0368334	−	0.350447i	0.960547	−	0.278117i	$-0.0897102\pi$
$642$	−0.433963	−	2.04164i	−0.0171272	−	0.0805769i
$643$		−	8.25030i		−	0.325360i	−0.986679	−	0.162680i	$-0.947986\pi$
$643$		−	8.25030i		−	0.325360i	0.986679	−	0.162680i	$-0.0520138\pi$
$644$	13.4069	−	46.6250i	0.528307	−	1.83728i
$645$		0			0
$646$	5.89138	−	6.54304i	0.231793	−	0.257432i
$647$	−3.77858	+	17.7768i	−0.148551	+	0.698879i	0.839324	+	0.543631i	$0.182951\pi$
$647$	−3.77858	+	17.7768i	−0.148551	+	0.698879i	−0.987876	+	0.155248i	$0.950382\pi$
$648$	−4.74055	−	10.6474i	−0.186226	−	0.418271i
$649$	1.01206	+	1.75293i	0.0397266	+	0.0688085i
$650$		0			0
$651$	−17.3377	−	27.7919i	−0.679516	−	1.08925i
$652$	14.0013	−	19.2711i	0.548332	−	0.754715i
$653$	−22.6838	−	20.4246i	−0.887685	−	0.799275i	0.0928374	−	0.995681i	$-0.470406\pi$
$653$	−22.6838	−	20.4246i	−0.887685	−	0.799275i	−0.980523	+	0.196406i	$0.937073\pi$
$654$	0.485867	+	0.103274i	0.0189989	+	0.00403834i
$655$		0			0
$656$	−9.86320	+	2.09649i	−0.385093	+	0.0818541i
$657$		−	23.3635i		−	0.911497i
$658$	21.0158	−	20.2647i	0.819283	−	0.789999i
$659$	4.57123	−	3.32120i	0.178070	−	0.129375i	−0.495180	−	0.868790i	$-0.664898\pi$
$659$	4.57123	−	3.32120i	0.178070	−	0.129375i	0.673250	+	0.739415i	$0.264898\pi$
$660$		0			0
$661$	−7.00951	+	3.12084i	−0.272638	+	0.121386i	−0.538502	−	0.842624i	$-0.681010\pi$
$661$	−7.00951	+	3.12084i	−0.272638	+	0.121386i	0.265864	+	0.964011i	$0.414343\pi$
$662$	−8.54021	+	0.897612i	−0.331925	+	0.0348867i
$663$	−3.16568	+	7.11024i	−0.122945	+	0.276139i
$664$	12.5800	+	9.13989i	0.488198	+	0.354696i
$665$		0			0
$666$	18.5525	−	13.4791i	0.718893	−	0.522306i
$667$	15.4735	+	72.7971i	0.599137	+	2.81872i
$668$	35.6817	+	20.6008i	1.38056	+	0.797069i
$669$	−11.5236	−	12.7983i	−0.445528	−	0.494809i
$670$		0			0
$671$	−0.396529	−	1.22039i	−0.0153079	−	0.0471127i
$672$	37.2982	+	31.3440i	1.43881	+	1.20912i
$673$	−7.32449	+	10.0813i	−0.282338	+	0.388606i	−0.926507	−	0.376278i	$-0.877204\pi$
$673$	−7.32449	+	10.0813i	−0.282338	+	0.388606i	0.644168	+	0.764884i	$0.277204\pi$
$674$	−14.8328	−	25.6912i	−0.571339	−	0.989589i
$675$		0			0
$676$	5.24816	−	9.09007i	0.201852	−	0.349618i
$677$	44.0683	+	4.63176i	1.69368	+	0.178013i	0.901650	−	0.432467i	$-0.142357\pi$
$677$	44.0683	+	4.63176i	1.69368	+	0.178013i	0.792032	+	0.610480i	$0.209023\pi$
$678$	40.4092	−	13.1297i	1.55191	−	0.504245i
$679$	2.40634	+	6.62666i	0.0923470	+	0.254308i
$680$		0			0
$681$	−35.8345	+	7.61686i	−1.37318	+	0.291879i
$682$	−26.3118	−	15.1911i	−1.00753	−	0.581698i
$683$	−2.50575	+	2.25619i	−0.0958798	+	0.0863306i	−0.715677	−	0.698432i	$-0.753882\pi$
$683$	−2.50575	+	2.25619i	−0.0958798	+	0.0863306i	0.619797	+	0.784762i	$0.287215\pi$
$684$	−20.3698	−	9.06924i	−0.778860	−	0.346771i
$685$		0			0
$686$	−0.0876255	+	39.3964i	−0.00334556	+	1.50416i
$687$	−11.7692	−	16.1989i	−0.449024	−	0.618028i
$688$	−9.21252	+	20.6917i	−0.351224	+	0.788862i
$689$	6.46931	−	2.88032i	0.246461	−	0.109732i
$690$		0			0
$691$	−9.86060	−	4.39022i	−0.375115	−	0.167012i	0.210515	−	0.977591i	$-0.432486\pi$
$691$	−9.86060	−	4.39022i	−0.375115	−	0.167012i	−0.585630	+	0.810579i	$0.699153\pi$
$692$	−35.2149	−	11.4420i	−1.33867	−	0.434960i
$693$	−0.582179	−	17.0335i	−0.0221152	−	0.647049i
$694$	0.453047	−	1.39433i	0.0171974	−	0.0529282i
$695$		0			0
$696$	26.0227	+	5.53130i	0.986389	+	0.209663i
$697$	0.882761	−	4.15306i	0.0334370	−	0.157309i
$698$	−40.9594	−	4.30501i	−1.55034	−	0.162947i
$699$	−3.16403			−0.119674
$700$		0			0
$701$	18.3376			0.692601			0.346301	−	0.938124i	$-0.387438\pi$
$701$	18.3376			0.692601			0.346301	+	0.938124i	$0.387438\pi$
$702$	−8.73788	−	0.918388i	−0.329790	−	0.0346623i
$703$	−3.42924	+	16.1333i	−0.129336	+	0.608479i
$704$	30.1729	+	6.41346i	1.13719	+	0.241716i
$705$		0			0
$706$	7.79261	−	23.9832i	0.293279	−	0.902619i
$707$	−38.3923	−	20.4501i	−1.44389	−	0.769105i
$708$	−4.21353	−	1.36906i	−0.158354	−	0.0514524i
$709$	37.2742	+	16.5955i	1.39986	+	0.623259i	0.961316	−	0.275449i	$-0.0888267\pi$
$709$	37.2742	+	16.5955i	1.39986	+	0.623259i	0.438547	+	0.898708i	$0.355493\pi$
$710$		0			0
$711$	9.30443	−	4.14260i	0.348944	−	0.155360i
$712$	−3.69785	+	8.30551i	−0.138583	+	0.311262i
$713$	22.7366	+	31.2942i	0.851491	+	1.17198i
$714$	−13.2443	+	6.44752i	−0.495655	+	0.241292i
$715$		0			0
$716$	30.5967	+	13.6225i	1.14345	+	0.509098i
$717$	33.6098	−	30.2624i	1.25518	−	1.13017i
$718$	22.2857	+	12.8667i	0.831696	+	0.480180i
$719$	23.2416	−	4.94015i	0.866765	−	0.184237i	0.246992	−	0.969018i	$-0.420558\pi$
$719$	23.2416	−	4.94015i	0.866765	−	0.184237i	0.619773	+	0.784781i	$0.287225\pi$
$720$		0			0
$721$	−17.6326	+	20.9822i	−0.656674	+	0.781416i
$722$	−11.1055	+	3.60839i	−0.413303	+	0.134290i
$723$	−30.2042	−	3.17459i	−1.12331	−	0.118064i
$724$	15.2569	−	26.4258i	0.567020	−	0.982107i
$725$		0			0
$726$	9.41958	+	16.3152i	0.349594	+	0.605514i
$727$	6.69898	−	9.22036i	0.248452	−	0.341964i	−0.666517	−	0.745490i	$-0.732215\pi$
$727$	6.69898	−	9.22036i	0.248452	−	0.341964i	0.914968	+	0.403526i	$0.132215\pi$
$728$	−8.25946	+	2.99926i	−0.306116	+	0.111160i
$729$	4.75454	+	14.6330i	0.176094	+	0.541961i
$730$		0			0
$731$	−6.38156	−	7.08744i	−0.236031	−	0.262139i
$732$	2.43237	+	1.40433i	0.0899029	+	0.0519055i
$733$	9.82343	+	46.2156i	0.362837	+	1.70701i	0.659226	+	0.751945i	$0.270884\pi$
$733$	9.82343	+	46.2156i	0.362837	+	1.70701i	−0.296390	+	0.955067i	$0.595783\pi$
$734$	25.3683	−	18.4311i	0.936360	−	0.680305i
$735$		0			0
$736$	−46.5449	−	33.8168i	−1.71567	−	1.24650i
$737$	3.74305	−	8.40702i	0.137877	−	0.309677i
$738$	−19.1639	+	2.01421i	−0.705434	+	0.0741441i
$739$	−7.02198	+	3.12639i	−0.258308	+	0.115006i	−0.531805	−	0.846867i	$-0.678486\pi$
$739$	−7.02198	+	3.12639i	−0.258308	+	0.115006i	0.273498	+	0.961873i	$0.411819\pi$
$740$		0			0
$741$	−20.5538	+	14.9332i	−0.755064	+	0.548586i
$742$	12.8806	+	3.70378i	0.472860	+	0.135970i
$743$		−	16.6970i		−	0.612554i	−0.951942	−	0.306277i	$-0.900917\pi$
$743$		−	16.6970i		−	0.612554i	0.951942	−	0.306277i	$-0.0990834\pi$
$744$	13.5254	−	2.87491i	0.495864	−	0.105399i
$745$		0			0
$746$	72.9339	+	15.5026i	2.67030	+	0.567589i
$747$	−24.8571	−	22.3814i	−0.909473	−	0.818893i
$748$	−4.48125	+	6.16791i	−0.163851	+	0.225521i
$749$	−0.591168	−	0.947630i	−0.0216008	−	0.0346256i
$750$		0			0
$751$	13.1673	+	22.8064i	0.480481	+	0.832218i	0.999749	−	0.0223936i	$-0.00712869\pi$
$751$	13.1673	+	22.8064i	0.480481	+	0.832218i	−0.519268	+	0.854611i	$0.673795\pi$
$752$	−5.64237	−	12.6730i	−0.205756	−	0.462135i
$753$	−10.5838	+	49.7926i	−0.385693	+	1.81454i
$754$	43.3791	−	48.1773i	1.57977	−	1.75451i
$755$		0			0
$756$	−6.44069	−	6.67943i	−0.234245	−	0.242928i
$757$			25.9220i			0.942150i	0.882093	+	0.471075i	$0.156134\pi$
$757$			25.9220i			0.942150i	−0.882093	+	0.471075i	$0.843866\pi$
$758$	−8.58777	−	40.4023i	−0.311922	−	1.46748i
$759$	4.73085	+	45.0111i	0.171719	+	1.63380i
$760$		0			0
$761$	2.35580	−	22.4139i	0.0853976	−	0.812504i	−0.865064	−	0.501662i	$-0.832722\pi$
$761$	2.35580	−	22.4139i	0.0853976	−	0.812504i	0.950462	−	0.310842i	$-0.100611\pi$
$762$	47.7012	+	65.6551i	1.72803	+	2.37843i
$763$	0.263241	−	0.0367972i	0.00952998	−	0.00133215i
$764$	19.9771	+	14.5142i	0.722748	+	0.525107i
$765$		0			0
$766$	−3.37182	−	32.0807i	−0.121829	−	1.15912i
$767$	−1.66822	+	1.50207i	−0.0602360	+	0.0542367i
$768$	9.37415	−	5.41217i	0.338261	−	0.195295i
$769$	−11.9612	+	36.8128i	−0.431333	+	1.32750i	0.465466	+	0.885066i	$0.345887\pi$
$769$	−11.9612	+	36.8128i	−0.431333	+	1.32750i	−0.896798	+	0.442439i	$0.854113\pi$
$770$		0			0
$771$	5.79800	+	17.8444i	0.208810	+	0.642651i
$772$	−30.7526	−	27.6897i	−1.10681	−	0.996576i
$773$	−9.95858	−	22.3673i	−0.358185	−	0.804498i	−0.999313	−	0.0370632i	$-0.988200\pi$
$773$	−9.95858	−	22.3673i	−0.358185	−	0.804498i	0.641128	−	0.767434i	$-0.278467\pi$
$774$	−21.6417	+	37.4846i	−0.777896	+	1.34736i
$775$		0			0
$776$	−2.97605			−0.106834
$777$	15.4477	−	22.8655i	0.554183	−	0.820297i
$778$	−40.2697	+	13.0844i	−1.44374	+	0.469099i
$779$	9.27378	−	10.2996i	0.332268	−	0.369021i
$780$		0			0
$781$	20.6760	+	22.9630i	0.739844	+	0.821680i
$782$	15.0644	−	8.69744i	0.538702	−	0.311020i
$783$	13.5376	+	4.39862i	0.483793	+	0.157194i
$784$	17.5815	+	6.42867i	0.627909	+	0.229595i
$785$		0			0
$786$	−10.6825	+	101.637i	−0.381033	+	3.62529i
$787$	−54.9617	+	5.77671i	−1.95917	+	0.205917i	−0.997634	−	0.0687476i	$-0.978100\pi$
$787$	−54.9617	+	5.77671i	−1.95917	+	0.205917i	−0.961540	+	0.274665i	$0.911433\pi$
$788$	−17.7714	+	1.86785i	−0.633080	+	0.0665393i
$789$	−1.29797	+	12.3494i	−0.0462090	+	0.439649i
$790$		0			0
$791$	17.9267	−	13.9845i	0.637401	−	0.497231i
$792$	6.84246	+	2.22325i	0.243136	+	0.0789997i
$793$	1.23245	−	0.711556i	0.0437656	−	0.0252681i
$794$	−29.3643	−	32.6124i	−1.04210	−	1.15737i
$795$		0			0
$796$	−12.3118	+	13.6736i	−0.436380	+	0.484649i
$797$	18.2526	−	5.93061i	0.646539	−	0.210073i	0.0326513	−	0.999467i	$-0.489605\pi$
$797$	18.2526	−	5.93061i	0.646539	−	0.210073i	0.613887	+	0.789394i	$0.289605\pi$
$798$	−47.9635	−	3.38967i	−1.69789	−	0.119993i
$799$	5.84116			0.206645
$800$		0			0
$801$	9.77823	−	16.9364i	0.345497	−	0.598418i
$802$	12.8912	+	28.9542i	0.455206	+	1.02241i
$803$	−19.3783	−	17.4483i	−0.683845	−	0.615737i
$804$	6.22444	+	19.1568i	0.219519	+	0.675610i
$805$		0			0
$806$	10.4123	−	32.0459i	0.366759	−	1.12877i
$807$	−24.6015	+	14.2037i	−0.866013	+	0.499993i
$808$	13.6459	−	12.2868i	0.480062	−	0.432250i
$809$	5.00156	+	47.5866i	0.175845	+	1.67306i	0.625783	+	0.779997i	$0.284780\pi$
$809$	5.00156	+	47.5866i	0.175845	+	1.67306i	−0.449938	+	0.893060i	$0.648554\pi$
$810$		0			0
$811$	10.1349	+	7.36343i	0.355884	+	0.258565i	0.751333	−	0.659923i	$-0.229411\pi$
$811$	10.1349	+	7.36343i	0.355884	+	0.258565i	−0.395449	+	0.918488i	$0.629411\pi$
$812$	67.8063	−	9.47830i	2.37953	−	0.332623i
$813$	4.36642	+	6.00986i	0.153137	+	0.210775i
$814$	2.67536	−	25.4544i	0.0937714	−	0.892175i
$815$		0			0
$816$	0.731631	+	6.96100i	0.0256122	+	0.243684i
$817$	−6.47257	−	30.4510i	−0.226446	−	1.06535i
$818$		−	64.3936i		−	2.25147i
$819$	18.3437	−	4.55916i	0.640982	−	0.159310i
$820$		0			0
$821$	4.04209	−	4.48920i	0.141070	−	0.156674i	−0.668469	−	0.743740i	$-0.733050\pi$
$821$	4.04209	−	4.48920i	0.141070	−	0.156674i	0.809539	+	0.587066i	$0.199717\pi$
$822$	−6.97295	+	32.8051i	−0.243209	+	1.14421i
$823$	16.1108	+	36.1854i	0.561586	+	1.26134i	0.941716	+	0.336410i	$0.109213\pi$
$823$	16.1108	+	36.1854i	0.561586	+	1.26134i	−0.380130	+	0.924933i	$0.624121\pi$
$824$	−5.78476	−	10.0195i	−0.201521	−	0.349045i
$825$		0			0
$826$	−4.24604	+	0.145123i	−0.147739	+	0.00504948i
$827$	8.49914	−	11.6981i	0.295544	−	0.406782i	−0.635261	−	0.772298i	$-0.719107\pi$
$827$	8.49914	−	11.6981i	0.295544	−	0.406782i	0.930805	+	0.365516i	$0.119107\pi$
$828$	−32.7376	−	29.4770i	−1.13771	−	1.02440i
$829$	−37.7643	−	8.02705i	−1.31161	−	0.278791i	−0.501544	−	0.865132i	$-0.667234\pi$
$829$	−37.7643	−	8.02705i	−1.31161	−	0.278791i	−0.810064	+	0.586341i	$0.800568\pi$
$830$		0			0
$831$	11.8764	−	2.52442i	0.411989	−	0.0875710i
$832$			34.2105i			1.18604i
$833$	−5.48393	+	5.66195i	−0.190007	+	0.196175i
$834$	27.0950	−	19.6857i	0.938222	−	0.681658i
$835$		0			0
$836$	−22.7348	+	10.1222i	−0.786301	+	0.350084i
$837$	7.35775	−	0.773331i	0.254321	−	0.0267302i
$838$	−11.9403	+	26.8184i	−0.412471	+	0.926425i
$839$	−4.52632	−	3.28857i	−0.156266	−	0.113534i	0.506905	−	0.862002i	$-0.330790\pi$
$839$	−4.52632	−	3.28857i	−0.156266	−	0.113534i	−0.663171	+	0.748468i	$0.730790\pi$
$840$		0			0
$841$	−61.5093	+	44.6892i	−2.12101	+	1.54101i
$842$	3.79697	+	17.8633i	0.130852	+	0.615612i
$843$	42.6491	+	24.6235i	1.46891	+	0.848077i
$844$	36.5563	+	40.5999i	1.25832	+	1.39751i
$845$		0			0
$846$	−8.19195	−	25.2122i	−0.281645	−	0.866814i
$847$	7.71771	+	6.48569i	0.265184	+	0.222851i
$848$	3.74326	−	5.15216i	0.128544	−	0.176926i
$849$	7.16205	+	12.4050i	0.245801	+	0.425740i
$850$		0			0
$851$	−16.2931	+	28.2205i	−0.558521	+	0.967387i
$852$	−67.2628	−	7.06961i	−2.30439	−	0.242201i
$853$	−26.8891	+	8.73679i	−0.920664	+	0.299142i	−0.730739	−	0.682657i	$-0.760824\pi$
$853$	−26.8891	+	8.73679i	−0.920664	+	0.299142i	−0.189925	+	0.981799i	$0.560824\pi$
$854$	2.65211	+	0.469666i	0.0907533	+	0.0160716i
$855$		0			0
$856$	0.461180	−	0.0980267i	0.0157628	−	0.00335048i
$857$	−7.58589	−	4.37971i	−0.259129	−	0.149608i	0.364808	−	0.931083i	$-0.381135\pi$
$857$	−7.58589	−	4.37971i	−0.259129	−	0.149608i	−0.623937	+	0.781475i	$0.714468\pi$
$858$	29.2980	−	26.3800i	1.00022	−	0.900599i
$859$	−17.7128	−	7.88627i	−0.604355	−	0.269076i	0.0816641	−	0.996660i	$-0.473977\pi$
$859$	−17.7128	−	7.88627i	−0.604355	−	0.269076i	−0.686019	+	0.727584i	$0.740643\pi$
$860$		0			0
$861$	−20.8482	+	10.1492i	−0.710505	+	0.345884i
$862$	11.4540	+	15.7650i	0.390123	+	0.536958i
$863$	23.1669	−	52.0338i	0.788611	−	1.77125i	0.170177	−	0.985413i	$-0.445566\pi$
$863$	23.1669	−	52.0338i	0.788611	−	1.77125i	0.618434	−	0.785837i	$-0.287767\pi$
$864$	−10.0524	+	4.47561i	−0.341989	+	0.152263i
$865$		0			0
$866$	−7.85235	−	3.49609i	−0.266834	−	0.118802i
$867$	34.7765	+	11.2996i	1.18107	+	0.383753i
$868$	30.1919	−	18.8349i	1.02478	−	0.639297i
$869$	3.51274	−	10.8111i	0.119162	−	0.366742i
$870$		0			0
$871$	9.98303	+	2.12196i	0.338262	+	0.0718998i
$872$	−0.0233283	+	0.109751i	−0.000789997	+	0.00371664i
$873$	6.36662	+	0.669159i	0.215477	+	0.0226476i
$874$	56.7810			1.92065
$875$		0			0
$876$	57.0752			1.92839
$877$	−12.4336	−	1.30682i	−0.419851	−	0.0441282i	−0.107752	−	0.994178i	$-0.534365\pi$
$877$	−12.4336	−	1.30682i	−0.419851	−	0.0441282i	−0.312099	+	0.950050i	$0.601032\pi$
$878$	−5.12283	+	24.1010i	−0.172887	+	0.813371i
$879$	−55.8383	−	11.8688i	−1.88338	−	0.400325i
$880$		0			0
$881$	−7.65963	+	23.5739i	−0.258059	+	0.794225i	0.735152	+	0.677902i	$0.237111\pi$
$881$	−7.65963	+	23.5739i	−0.258059	+	0.794225i	−0.993211	+	0.116323i	$0.962889\pi$
$882$	32.1297	+	15.7297i	1.08186	+	0.529647i
$883$	−46.5243	−	15.1166i	−1.56567	−	0.508716i	−0.607352	−	0.794433i	$-0.707768\pi$
$883$	−46.5243	−	15.1166i	−1.56567	−	0.508716i	−0.958314	+	0.285717i	$0.907768\pi$
$884$	−7.72425	−	3.43906i	−0.259795	−	0.115668i
$885$		0			0
$886$	−35.9952	+	16.0261i	−1.20928	+	0.538407i
$887$	16.2042	−	36.3951i	0.544082	−	1.22203i	−0.407096	−	0.913386i	$-0.633458\pi$
$887$	16.2042	−	36.3951i	0.544082	−	1.22203i	0.951178	−	0.308643i	$-0.0998749\pi$
$888$	6.84687	+	9.42390i	0.229766	+	0.316246i
$889$	35.9841	+	24.3104i	1.20687	+	0.815345i
$890$		0			0
$891$	25.5625	+	11.3812i	0.856378	+	0.381284i
$892$	13.9035	−	12.5187i	0.465522	−	0.419158i
$893$	16.5124	+	9.53346i	0.552567	+	0.319025i
$894$	−40.3086	+	8.56786i	−1.34812	+	0.286552i
$895$		0			0
$896$	−14.6845	+	17.4740i	−0.490574	+	0.583764i
$897$	−47.7372	+	15.5108i	−1.59390	+	0.517889i
$898$	16.1317	+	1.69552i	0.538323	+	0.0565801i
$899$	−27.2947	+	47.2758i	−0.910330	+	1.57674i
$900$		0			0
$901$	1.34076	+	2.32227i	0.0446673	+	0.0773661i
$902$	−12.6413	+	17.3993i	−0.420911	+	0.579334i
$903$	−9.08229	+	51.2859i	−0.302240	+	1.70669i
$904$	2.96584	+	9.12792i	0.0986425	+	0.303590i
$905$		0			0
$906$	75.1111	+	83.4193i	2.49540	+	2.77142i
$907$	27.9882	+	16.1590i	0.929332	+	0.536550i	0.886600	−	0.462536i	$-0.153061\pi$
$907$	27.9882	+	16.1590i	0.929332	+	0.536550i	0.0427318	+	0.999087i	$0.486394\pi$
$908$	−8.27462	−	38.9290i	−0.274603	−	1.29191i
$909$	−31.9552	+	23.2168i	−1.05989	+	0.770053i
$910$		0			0
$911$	25.3724	+	18.4341i	0.840624	+	0.610749i	0.922545	−	0.385889i	$-0.126105\pi$
$911$	25.3724	+	18.4341i	0.840624	+	0.610749i	−0.0819206	+	0.996639i	$0.526105\pi$
$912$	−9.29292	+	20.8723i	−0.307719	+	0.691149i
$913$	−37.1275	+	3.90225i	−1.22874	+	0.129146i
$914$	−24.5278	+	10.9205i	−0.811308	+	0.361218i
$915$		0			0
$916$	17.5978	−	12.7856i	0.581448	−	0.422447i
$917$	13.1906	+	53.0721i	0.435592	+	1.75260i
$918$		−	3.32695i		−	0.109806i
$919$	14.7600	−	3.13733i	0.486887	−	0.103491i	0.0420741	−	0.999114i	$-0.486603\pi$
$919$	14.7600	−	3.13733i	0.486887	−	0.103491i	0.444813	+	0.895623i	$0.353270\pi$
$920$		0			0
$921$	19.8102	+	4.21079i	0.652769	+	0.138750i
$922$	21.3000	+	19.1786i	0.701479	+	0.631615i
$923$	−20.1428	+	27.7242i	−0.663008	+	0.912552i
$924$	41.6115	−	1.42222i	1.36892	−	0.0467876i
$925$		0			0
$926$	18.3249	+	31.7396i	0.602193	+	1.04303i
$927$	10.1224	+	22.7352i	0.332463	+	0.746723i
$928$	16.8809	−	79.4183i	0.554142	−	2.60703i
$929$	−14.6305	+	16.2489i	−0.480012	+	0.533108i	−0.933702	−	0.358052i	$-0.883441\pi$
$929$	−14.6305	+	16.2489i	−0.480012	+	0.533108i	0.453689	+	0.891160i	$0.350108\pi$
$930$		0			0
$931$	−24.7436	+	7.05541i	−0.810937	+	0.231232i
$932$		−	3.43726i		−	0.112591i
$933$	11.1690	+	52.5460i	0.365657	+	1.72028i
$934$	5.71761	+	54.3994i	0.187086	+	1.78000i
$935$		0			0
$936$	−0.834039	+	7.93535i	−0.0272614	+	0.259375i
$937$	27.0301	+	37.2038i	0.883035	+	1.21539i	0.975571	+	0.219684i	$0.0705028\pi$
$937$	27.0301	+	37.2038i	0.883035	+	1.21539i	−0.0925358	+	0.995709i	$0.529497\pi$
$938$	11.8808	+	15.2300i	0.387921	+	0.497276i
$939$	−14.0589	−	10.2144i	−0.458795	−	0.333334i
$940$		0			0
$941$	−4.14631	−	39.4495i	−0.135166	−	1.28602i	−0.826275	−	0.563267i	$-0.809544\pi$
$941$	−4.14631	−	39.4495i	−0.135166	−	1.28602i	0.691109	−	0.722751i	$-0.257123\pi$
$942$	42.3798	−	38.1590i	1.38081	−	1.24329i
$943$	23.7133	−	13.6909i	0.772211	−	0.445836i
$944$	−0.623830	+	1.91995i	−0.0203039	+	0.0624891i
$945$		0			0
$946$	14.9282	+	45.9444i	0.485359	+	1.49378i
$947$	6.94158	+	6.25022i	0.225571	+	0.203105i	0.774165	−	0.632984i	$-0.218170\pi$
$947$	6.94158	+	6.25022i	0.225571	+	0.203105i	−0.548594	+	0.836089i	$0.684837\pi$
$948$	10.1201	+	22.7300i	0.328684	+	0.738237i
$949$	14.4597	−	25.0449i	0.469380	−	0.812991i
$950$		0			0
$951$	−66.9207			−2.17005
$952$	−1.45641	−	2.99172i	−0.0472026	−	0.0969621i
$953$	21.3981	−	6.95267i	0.693153	−	0.225219i	0.0588083	−	0.998269i	$-0.481270\pi$
$953$	21.3981	−	6.95267i	0.693153	−	0.225219i	0.634345	+	0.773050i	$0.281270\pi$
$954$	8.14328	−	9.04403i	0.263648	−	0.292811i
$955$		0			0
$956$	32.8758	+	36.5122i	1.06328	+	1.18089i
$957$	−55.3144	+	31.9358i	−1.78806	+	1.03234i
$958$	55.1416	+	17.9166i	1.78154	+	0.578859i
$959$	2.48450	+	17.7737i	0.0802286	+	0.573944i
$960$		0			0
$961$	0.274598	−	2.61262i	0.00885799	−	0.0842781i
$962$	28.2298	−	2.96708i	0.910166	−	0.0956623i
$963$	−1.00864	+	0.106012i	−0.0325028	+	0.00341619i
$964$	3.44874	−	32.8126i	0.111076	−	1.05682i
$965$		0			0
$966$	−88.0530	−	35.6517i	−2.83306	−	1.14707i
$967$	−6.87975	−	2.23537i	−0.221238	−	0.0718845i	0.196301	−	0.980544i	$-0.437107\pi$
$967$	−6.87975	−	2.23537i	−0.221238	−	0.0718845i	−0.417538	+	0.908659i	$0.637107\pi$
$968$	−3.68540	+	2.12776i	−0.118453	+	0.0683889i
$969$	−6.43726	−	7.14930i	−0.206794	−	0.229669i
$970$		0			0
$971$	−15.0750	+	16.7425i	−0.483781	+	0.537293i	−0.934778	−	0.355232i	$-0.884402\pi$
$971$	−15.0750	+	16.7425i	−0.483781	+	0.537293i	0.450997	+	0.892525i	$0.351068\pi$
$972$	−48.2424	+	15.6749i	−1.54737	+	0.502773i
$973$	10.0326	−	14.8502i	0.321630	−	0.476074i
$974$	26.8206			0.859389
$975$		0			0
$976$	0.639901	−	1.10834i	0.0204827	−	0.0354771i
$977$	−7.80715	−	17.5351i	−0.249773	−	0.560999i	0.744530	−	0.667589i	$-0.232673\pi$
$977$	−7.80715	−	17.5351i	−0.249773	−	0.560999i	−0.994303	+	0.106590i	$0.966007\pi$
$978$	−34.6626	−	31.2103i	−1.10839	−	0.997997i
$979$	−6.74492	−	20.7587i	−0.215569	−	0.663452i
$980$		0			0
$981$	0.0745833	−	0.229544i	0.00238126	−	0.00732877i
$982$	52.1467	−	30.1069i	1.66407	−	0.960750i
$983$	−9.05775	+	8.15564i	−0.288897	+	0.260124i	−0.800817	−	0.598909i	$-0.795601\pi$
$983$	−9.05775	+	8.15564i	−0.288897	+	0.260124i	0.511920	+	0.859033i	$0.328934\pi$
$984$	−1.02314	−	9.73451i	−0.0326165	−	0.310325i
$985$		0			0
$986$	19.8601	+	14.4292i	0.632474	+	0.459520i
$987$	−19.6207	−	25.1518i	−0.624535	−	0.800591i
$988$	−16.2228	−	22.3288i	−0.516117	−	0.710374i
$989$	6.42906	−	61.1684i	0.204432	−	1.94504i
$990$		0			0
$991$	−1.16780	−	11.1108i	−0.0370963	−	0.352947i	−0.997288	−	0.0736040i	$-0.976550\pi$
$991$	−1.16780	−	11.1108i	−0.0370963	−	0.352947i	0.960191	−	0.279343i	$-0.0901168\pi$
$992$	−8.77388	−	41.2779i	−0.278571	−	1.31057i
$993$			9.38293i			0.297758i
$994$	−62.9423	+	15.6437i	−1.99641	+	0.496189i
$995$		0			0
$996$	54.6761	−	60.7239i	1.73248	−	1.92411i
$997$	3.86265	−	18.1723i	0.122331	−	0.575524i	−0.873696	−	0.486473i	$-0.838283\pi$
$997$	3.86265	−	18.1723i	0.122331	−	0.575524i	0.996027	−	0.0890509i	$-0.0283834\pi$
$998$	22.5274	+	50.5974i	0.713093	+	1.60163i
$999$	3.11623	+	5.39747i	0.0985931	+	0.170768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.u.b.424.31		288
5.2	odd	4		875.2.q.a.326.4		144
5.3	odd	4		175.2.q.a.116.15	yes	144
5.4	even	2	inner	875.2.u.b.424.6		288
7.2	even	3	inner	875.2.u.b.674.6		288
25.2	odd	20		875.2.q.a.676.15		144
25.11	even	5	inner	875.2.u.b.74.31		288
25.14	even	10	inner	875.2.u.b.74.6		288
25.23	odd	20		175.2.q.a.11.4	✓	144
35.2	odd	12		875.2.q.a.576.15		144
35.9	even	6	inner	875.2.u.b.674.31		288
35.23	odd	12		175.2.q.a.16.4	yes	144
175.2	odd	60		875.2.q.a.51.4		144
175.23	odd	60		175.2.q.a.86.15	yes	144
175.86	even	15	inner	875.2.u.b.324.6		288
175.114	even	30	inner	875.2.u.b.324.31		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.q.a.11.4	✓	144	25.23	odd	20
175.2.q.a.16.4	yes	144	35.23	odd	12
175.2.q.a.86.15	yes	144	175.23	odd	60
175.2.q.a.116.15	yes	144	5.3	odd	4
875.2.q.a.51.4		144	175.2	odd	60
875.2.q.a.326.4		144	5.2	odd	4
875.2.q.a.576.15		144	35.2	odd	12
875.2.q.a.676.15		144	25.2	odd	20
875.2.u.b.74.6		288	25.14	even	10	inner
875.2.u.b.74.31		288	25.11	even	5	inner
875.2.u.b.324.6		288	175.86	even	15	inner
875.2.u.b.324.31		288	175.114	even	30	inner
875.2.u.b.424.6		288	5.4	even	2	inner
875.2.u.b.424.31		288	1.1	even	1	trivial
875.2.u.b.674.6		288	7.2	even	3	inner
875.2.u.b.674.31		288	35.9	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.11556 + 0.222354i) q^{2} +(0.483252 - 2.27352i) q^{3} +(2.46986 + 0.524984i) q^{4} +(1.52788 - 4.70232i) q^{6} +(-0.0903750 - 2.64421i) q^{7} +(1.06219 + 0.345128i) q^{8} +(-2.19474 - 0.977159i) q^{9} +O(q^{10})\)	\(q+(2.11556 + 0.222354i) q^{2} +(0.483252 - 2.27352i) q^{3} +(2.46986 + 0.524984i) q^{4} +(1.52788 - 4.70232i) q^{6} +(-0.0903750 - 2.64421i) q^{7} +(1.06219 + 0.345128i) q^{8} +(-2.19474 - 0.977159i) q^{9} +(-2.44955 + 1.09061i) q^{11} +(2.38713 - 5.36157i) q^{12} +(-1.74792 - 2.40580i) q^{13} +(0.396757 - 5.61407i) q^{14} +(-2.44307 - 1.08773i) q^{16} +(0.836817 - 0.753473i) q^{17} +(-4.42582 - 2.55525i) q^{18} +(3.59536 - 0.764218i) q^{19} +(-6.05534 - 1.07235i) q^{21} +(-5.42467 + 1.76258i) q^{22} +(7.22218 + 0.759081i) q^{23} +(1.29796 - 2.24814i) q^{24} +(-3.16288 - 5.47827i) q^{26} +(0.816389 - 1.12366i) q^{27} +(1.16495 - 6.57825i) q^{28} +(3.16693 + 9.74681i) q^{29} +(3.56421 + 3.95846i) q^{31} +(-6.86105 - 3.96123i) q^{32} +(1.29578 + 6.09615i) q^{33} +(1.93787 - 1.40795i) q^{34} +(-4.90769 - 3.56564i) q^{36} +(-1.82513 + 4.09931i) q^{37} +(7.77613 - 0.817304i) q^{38} +(-6.31433 + 2.81132i) q^{39} +(3.05046 - 2.21629i) q^{41} +(-12.5720 - 3.61505i) q^{42} -8.46953i q^{43} +(-6.62259 + 1.40767i) q^{44} +(15.1102 + 3.21176i) q^{46} +(3.85492 + 3.47099i) q^{47} +(-3.65359 + 5.02873i) q^{48} +(-6.98366 + 0.477940i) q^{49} +(-1.30864 - 2.26664i) q^{51} +(-3.05410 - 6.85961i) q^{52} +(-0.495113 + 2.32932i) q^{53} +(1.97697 - 2.19565i) q^{54} +(0.816594 - 2.83985i) q^{56} -8.54345i q^{57} +(4.53258 + 21.3241i) q^{58} +(-0.0789064 - 0.750745i) q^{59} +(-0.0500232 + 0.475939i) q^{61} +(6.66012 + 9.16687i) q^{62} +(-2.38546 + 5.89165i) q^{63} +(-9.30711 - 6.76201i) q^{64} +(1.38579 + 13.1849i) q^{66} +(-2.55052 + 2.29650i) q^{67} +(2.46238 - 1.42165i) q^{68} +(5.21592 - 16.0530i) q^{69} +(-3.56107 - 10.9599i) q^{71} +(-1.99399 - 1.79540i) q^{72} +(3.95548 + 8.88415i) q^{73} +(-4.77267 + 8.26651i) q^{74} +9.28123 q^{76} +(3.10518 + 6.37856i) q^{77} +(-13.9834 + 4.54350i) q^{78} +(-2.83673 + 3.15051i) q^{79} +(-6.98278 - 7.75517i) q^{81} +(6.94623 - 4.01041i) q^{82} +(13.2413 + 4.30236i) q^{83} +(-14.3928 - 5.82750i) q^{84} +(1.88324 - 17.9178i) q^{86} +(23.6900 - 2.48992i) q^{87} +(-2.97830 + 0.313032i) q^{88} +(-0.850889 + 8.09567i) q^{89} +(-6.20347 + 4.83928i) q^{91} +(17.4392 + 5.66635i) q^{92} +(10.7221 - 6.19038i) q^{93} +(7.38353 + 8.20024i) q^{94} +(-12.3216 + 13.6845i) q^{96} +(-2.53425 + 0.823427i) q^{97} +(-14.8806 - 0.541736i) q^{98} +6.44182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 26 q^{4} - 24 q^{6} - 22 q^{9}+O(q^{10}) \) 288 * q - 26 * q^4 - 24 * q^6 - 22 * q^9	\( 288 q - 26 q^{4} - 24 q^{6} - 22 q^{9} - 12 q^{11} + 12 q^{14} + 26 q^{16} + 22 q^{19} - 6 q^{21} - 92 q^{24} + 88 q^{26} + 48 q^{29} - 42 q^{31} + 72 q^{34} - 208 q^{36} - 50 q^{39} + 76 q^{41} + 14 q^{44} + 42 q^{46} + 76 q^{49} - 16 q^{51} - 30 q^{54} - 120 q^{56} + 78 q^{59} - 26 q^{61} - 84 q^{64} + 14 q^{66} - 100 q^{69} + 44 q^{71} + 20 q^{74} - 552 q^{76} - 18 q^{79} + 114 q^{81} + 58 q^{84} - 34 q^{86} + 84 q^{89} - 68 q^{91} + 22 q^{94} + 26 q^{96} + 136 q^{99}+O(q^{100}) \) 288 * q - 26 * q^4 - 24 * q^6 - 22 * q^9 - 12 * q^11 + 12 * q^14 + 26 * q^16 + 22 * q^19 - 6 * q^21 - 92 * q^24 + 88 * q^26 + 48 * q^29 - 42 * q^31 + 72 * q^34 - 208 * q^36 - 50 * q^39 + 76 * q^41 + 14 * q^44 + 42 * q^46 + 76 * q^49 - 16 * q^51 - 30 * q^54 - 120 * q^56 + 78 * q^59 - 26 * q^61 - 84 * q^64 + 14 * q^66 - 100 * q^69 + 44 * q^71 + 20 * q^74 - 552 * q^76 - 18 * q^79 + 114 * q^81 + 58 * q^84 - 34 * q^86 + 84 * q^89 - 68 * q^91 + 22 * q^94 + 26 * q^96 + 136 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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