LMFDB - Embedded newform 425.2.m.b.76.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(26,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,-8,0,0,-24,0,-8,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			76.5
Character	$\chi$	$=$	425.76
Dual form			425.2.m.b.151.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.528855 - 0.528855i) q^{2} +(-1.17676 + 2.84096i) q^{3} +1.44062i q^{4} +(0.880118 + 2.12479i) q^{6} +(-2.98655 + 1.23707i) q^{7} +(1.81959 + 1.81959i) q^{8} +(-4.56494 - 4.56494i) q^{9} +(1.04667 + 2.52689i) q^{11} +(-4.09275 - 1.69527i) q^{12} -4.31833i q^{13} +(-0.925222 + 2.23368i) q^{14} -0.956646 q^{16} +(3.47152 - 2.22453i) q^{17} -4.82839 q^{18} +(-0.897260 + 0.897260i) q^{19} -9.94040i q^{21} +(1.88990 + 0.782821i) q^{22} +(0.188421 + 0.454888i) q^{23} +(-7.31061 + 3.02815i) q^{24} +(-2.28377 - 2.28377i) q^{26} +(9.81779 - 4.06666i) q^{27} +(-1.78215 - 4.30250i) q^{28} +(-0.410535 - 0.170049i) q^{29} +(-2.11561 + 5.10754i) q^{31} +(-4.14511 + 4.14511i) q^{32} -8.41047 q^{33} +(0.659477 - 3.01239i) q^{34} +(6.57637 - 6.57637i) q^{36} +(-4.09469 + 9.88545i) q^{37} +0.949042i q^{38} +(12.2682 + 5.08165i) q^{39} +(-2.00526 + 0.830608i) q^{41} +(-5.25703 - 5.25703i) q^{42} +(-1.52864 - 1.52864i) q^{43} +(-3.64030 + 1.50786i) q^{44} +(0.340217 + 0.140922i) q^{46} +8.39597i q^{47} +(1.12575 - 2.71779i) q^{48} +(2.43940 - 2.43940i) q^{49} +(2.23464 + 12.4802i) q^{51} +6.22109 q^{52} +(-1.28480 + 1.28480i) q^{53} +(3.04152 - 7.34287i) q^{54} +(-7.68527 - 3.18334i) q^{56} +(-1.49321 - 3.60494i) q^{57} +(-0.307045 + 0.127182i) q^{58} +(-2.13537 - 2.13537i) q^{59} +(11.2928 - 4.67764i) q^{61} +(1.58230 + 3.82000i) q^{62} +(19.2806 + 7.98628i) q^{63} +2.47104i q^{64} +(-4.44792 + 4.44792i) q^{66} +4.21389 q^{67} +(3.20471 + 5.00116i) q^{68} -1.51404 q^{69} +(-1.48927 + 3.59542i) q^{71} -16.6127i q^{72} +(5.97807 + 2.47620i) q^{73} +(3.06247 + 7.39347i) q^{74} +(-1.29261 - 1.29261i) q^{76} +(-6.25188 - 6.25188i) q^{77} +(9.17555 - 3.80064i) q^{78} +(-2.76355 - 6.67180i) q^{79} +13.3100i q^{81} +(-0.621223 + 1.49977i) q^{82} +(-0.160866 + 0.160866i) q^{83} +14.3204 q^{84} -1.61686 q^{86} +(0.966206 - 0.966206i) q^{87} +(-2.69339 + 6.50243i) q^{88} +13.3408i q^{89} +(5.34208 + 12.8969i) q^{91} +(-0.655322 + 0.271443i) q^{92} +(-12.0207 - 12.0207i) q^{93} +(4.44025 + 4.44025i) q^{94} +(-6.89827 - 16.6539i) q^{96} +(13.6803 + 5.66657i) q^{97} -2.58018i q^{98} +(6.75711 - 16.3131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} - 24 q^{12} - 24 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 32 q^{22} + 16 q^{23} - 8 q^{24} + 16 q^{26} - 24 q^{27} - 48 q^{28} - 8 q^{29} + 16 q^{34} - 24 q^{36} - 24 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 - 24 * q^12 - 24 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 32 * q^22 + 16 * q^23 - 8 * q^24 + 16 * q^26 - 24 * q^27 - 48 * q^28 - 8 * q^29 + 16 * q^34 - 24 * q^36 - 24 * q^37 + 8 * q^39 + 16 * q^41 + 24 * q^42 - 8 * q^43 + 16 * q^44 + 8 * q^46 - 80 * q^48 - 56 * q^51 + 48 * q^52 - 24 * q^53 - 32 * q^54 + 64 * q^56 - 32 * q^57 + 64 * q^58 + 32 * q^59 + 32 * q^61 + 32 * q^62 + 56 * q^63 + 96 * q^66 - 16 * q^67 + 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^76 - 24 * q^77 + 112 * q^78 + 80 * q^82 + 96 * q^83 - 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 - 80 * q^92 - 64 * q^93 + 56 * q^94 - 168 * q^96 + 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

Coefficient data

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

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

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

$2$	0.528855	−	0.528855i	0.373957	−	0.373957i	−0.494959	−	0.868916i	$-0.664817\pi$
$2$	0.528855	−	0.528855i	0.373957	−	0.373957i	0.868916	+	0.494959i	$0.164817\pi$
$3$	−1.17676	+	2.84096i	−0.679404	+	1.64023i	0.0857002	+	0.996321i	$0.472687\pi$
$3$	−1.17676	+	2.84096i	−0.679404	+	1.64023i	−0.765105	+	0.643906i	$0.777313\pi$
$4$			1.44062i			0.720312i
$5$		0			0
$5$		0			0
$6$	0.880118	+	2.12479i	0.359307	+	0.867443i
$7$	−2.98655	+	1.23707i	−1.12881	+	0.467569i	−0.867376	−	0.497653i	$-0.834195\pi$
$7$	−2.98655	+	1.23707i	−1.12881	+	0.467569i	−0.261434	+	0.965221i	$0.584195\pi$
$8$	1.81959	+	1.81959i	0.643323	+	0.643323i
$9$	−4.56494	−	4.56494i	−1.52165	−	1.52165i
$10$		0			0
$11$	1.04667	+	2.52689i	0.315584	+	0.761886i	0.999478	+	0.0323052i	$0.0102849\pi$
$11$	1.04667	+	2.52689i	0.315584	+	0.761886i	−0.683894	+	0.729581i	$0.739715\pi$
$12$	−4.09275	−	1.69527i	−1.18148	−	0.489383i
$13$		−	4.31833i		−	1.19769i	−0.800865	−	0.598845i	$-0.795627\pi$
$13$		−	4.31833i		−	1.19769i	0.800865	−	0.598845i	$-0.204373\pi$
$14$	−0.925222	+	2.23368i	−0.247276	+	0.596977i
$15$		0			0
$16$	−0.956646			−0.239162
$17$	3.47152	−	2.22453i	0.841968	−	0.539528i
$17$	3.47152	−	2.22453i	0.841968	−	0.539528i
$18$	−4.82839			−1.13806
$19$	−0.897260	+	0.897260i	−0.205846	+	0.205846i	−0.802499	−	0.596653i	$-0.796497\pi$
$19$	−0.897260	+	0.897260i	−0.205846	+	0.205846i	0.596653	+	0.802499i	$0.296497\pi$
$20$		0			0
$21$		−	9.94040i		−	2.16917i
$22$	1.88990	+	0.782821i	0.402928	+	0.166898i
$23$	0.188421	+	0.454888i	0.0392884	+	0.0948506i	0.942306	−	0.334754i	$-0.108653\pi$
$23$	0.188421	+	0.454888i	0.0392884	+	0.0948506i	−0.903017	+	0.429604i	$0.858653\pi$
$24$	−7.31061	+	3.02815i	−1.49227	+	0.618119i
$25$		0			0
$26$	−2.28377	−	2.28377i	−0.447884	−	0.447884i
$27$	9.81779	−	4.06666i	1.88943	−	0.782630i
$28$	−1.78215	−	4.30250i	−0.336795	−	0.813096i
$29$	−0.410535	−	0.170049i	−0.0762345	−	0.0315774i	0.344240	−	0.938882i	$-0.388137\pi$
$29$	−0.410535	−	0.170049i	−0.0762345	−	0.0315774i	−0.420475	+	0.907304i	$0.638137\pi$
$30$		0			0
$31$	−2.11561	+	5.10754i	−0.379975	+	0.917342i	0.611994	+	0.790862i	$0.290368\pi$
$31$	−2.11561	+	5.10754i	−0.379975	+	0.917342i	−0.991969	+	0.126479i	$0.959632\pi$
$32$	−4.14511	+	4.14511i	−0.732759	+	0.732759i
$33$	−8.41047			−1.46408
$34$	0.659477	−	3.01239i	0.113099	−	0.516620i
$35$		0			0
$36$	6.57637	−	6.57637i	1.09606	−	1.09606i
$37$	−4.09469	+	9.88545i	−0.673162	+	1.62516i	0.103043	+	0.994677i	$0.467142\pi$
$37$	−4.09469	+	9.88545i	−0.673162	+	1.62516i	−0.776205	+	0.630481i	$0.782858\pi$
$38$			0.949042i			0.153955i
$39$	12.2682	+	5.08165i	1.96448	+	0.813715i
$40$		0			0
$41$	−2.00526	+	0.830608i	−0.313170	+	0.129719i	−0.533732	−	0.845654i	$-0.679211\pi$
$41$	−2.00526	+	0.830608i	−0.313170	+	0.129719i	0.220562	+	0.975373i	$0.429211\pi$
$42$	−5.25703	−	5.25703i	−0.811178	−	0.811178i
$43$	−1.52864	−	1.52864i	−0.233115	−	0.233115i	0.580876	−	0.813992i	$-0.302710\pi$
$43$	−1.52864	−	1.52864i	−0.233115	−	0.233115i	−0.813992	+	0.580876i	$0.802710\pi$
$44$	−3.64030	+	1.50786i	−0.548796	+	0.227319i
$45$		0			0
$46$	0.340217	+	0.140922i	0.0501622	+	0.0207779i
$47$			8.39597i			1.22468i	0.790595	+	0.612339i	$0.209771\pi$
$47$			8.39597i			1.22468i	−0.790595	+	0.612339i	$0.790229\pi$
$48$	1.12575	−	2.71779i	0.162487	−	0.392279i
$49$	2.43940	−	2.43940i	0.348485	−	0.348485i
$50$		0			0
$51$	2.23464	+	12.4802i	0.312912	+	1.74758i
$52$	6.22109			0.862710
$53$	−1.28480	+	1.28480i	−0.176481	+	0.176481i	−0.789820	−	0.613339i	$-0.789826\pi$
$53$	−1.28480	+	1.28480i	−0.176481	+	0.176481i	0.613339	+	0.789820i	$0.289826\pi$
$54$	3.04152	−	7.34287i	0.413898	−	0.999238i
$55$		0			0
$56$	−7.68527	−	3.18334i	−1.02699	−	0.425392i
$57$	−1.49321	−	3.60494i	−0.197781	−	0.477486i
$58$	−0.307045	+	0.127182i	−0.0403170	+	0.0166999i
$59$	−2.13537	−	2.13537i	−0.278001	−	0.278001i	0.554309	−	0.832311i	$-0.312982\pi$
$59$	−2.13537	−	2.13537i	−0.278001	−	0.278001i	−0.832311	+	0.554309i	$0.812982\pi$
$60$		0			0
$61$	11.2928	−	4.67764i	1.44590	−	0.598910i	0.484677	−	0.874693i	$-0.338937\pi$
$61$	11.2928	−	4.67764i	1.44590	−	0.598910i	0.961220	+	0.275783i	$0.0889371\pi$
$62$	1.58230	+	3.82000i	0.200952	+	0.485141i
$63$	19.2806	+	7.98628i	2.42913	+	1.00618i
$64$			2.47104i			0.308880i
$65$		0			0
$66$	−4.44792	+	4.44792i	−0.547501	+	0.547501i
$67$	4.21389			0.514808			0.257404	−	0.966304i	$-0.417133\pi$
$67$	4.21389			0.514808			0.257404	+	0.966304i	$0.417133\pi$
$68$	3.20471	+	5.00116i	0.388629	+	0.606479i
$69$	−1.51404			−0.182269
$70$		0			0
$71$	−1.48927	+	3.59542i	−0.176744	+	0.426698i	−0.987280	−	0.158991i	$-0.949176\pi$
$71$	−1.48927	+	3.59542i	−0.176744	+	0.426698i	0.810536	+	0.585689i	$0.199176\pi$
$72$		−	16.6127i		−	1.95782i
$73$	5.97807	+	2.47620i	0.699680	+	0.289817i	0.704027	−	0.710173i	$-0.251383\pi$
$73$	5.97807	+	2.47620i	0.699680	+	0.289817i	−0.00434632	+	0.999991i	$0.501383\pi$
$74$	3.06247	+	7.39347i	0.356005	+	0.859473i
$75$		0			0
$76$	−1.29261	−	1.29261i	−0.148273	−	0.148273i
$77$	−6.25188	−	6.25188i	−0.712468	−	0.712468i
$78$	9.17555	−	3.80064i	1.03893	−	0.430338i
$79$	−2.76355	−	6.67180i	−0.310923	−	0.750636i	−0.999671	−	0.0256347i	$-0.991839\pi$
$79$	−2.76355	−	6.67180i	−0.310923	−	0.750636i	0.688748	−	0.725001i	$-0.258161\pi$
$80$		0			0
$81$			13.3100i			1.47889i
$82$	−0.621223	+	1.49977i	−0.0686026	+	0.165621i
$83$	−0.160866	+	0.160866i	−0.0176574	+	0.0176574i	−0.715880	−	0.698223i	$-0.753974\pi$
$83$	−0.160866	+	0.160866i	−0.0176574	+	0.0176574i	0.698223	+	0.715880i	$0.253974\pi$
$84$	14.3204			1.56248
$85$		0			0
$86$	−1.61686			−0.174350
$87$	0.966206	−	0.966206i	0.103588	−	0.103588i
$88$	−2.69339	+	6.50243i	−0.287117	+	0.693161i
$89$			13.3408i			1.41413i	0.707150	+	0.707064i	$0.249981\pi$
$89$			13.3408i			1.41413i	−0.707150	+	0.707064i	$0.750019\pi$
$90$		0			0
$91$	5.34208	+	12.8969i	0.560002	+	1.35196i
$92$	−0.655322	+	0.271443i	−0.0683220	+	0.0282999i
$93$	−12.0207	−	12.0207i	−1.24649	−	1.24649i
$94$	4.44025	+	4.44025i	0.457977	+	0.457977i
$95$		0			0
$96$	−6.89827	−	16.6539i	−0.704052	−	1.69973i
$97$	13.6803	+	5.66657i	1.38902	+	0.575353i	0.946879	−	0.321591i	$-0.104218\pi$
$97$	13.6803	+	5.66657i	1.38902	+	0.575353i	0.442145	+	0.896943i	$0.354218\pi$
$98$		−	2.58018i		−	0.260637i
$99$	6.75711	−	16.3131i	0.679115	−	1.63953i
$100$		0			0
$101$	−0.284213			−0.0282803			−0.0141401	−	0.999900i	$-0.504501\pi$
$101$	−0.284213			−0.0282803			−0.0141401	+	0.999900i	$0.504501\pi$
$102$	7.78201	+	5.41841i	0.770534	+	0.536503i
$103$	14.0842			1.38775			0.693877	−	0.720093i	$-0.255901\pi$
$103$	14.0842			1.38775			0.693877	+	0.720093i	$0.255901\pi$
$104$	7.85760	−	7.85760i	0.770501	−	0.770501i
$105$		0			0
$106$			1.35894i			0.131992i
$107$	−17.2857	−	7.15995i	−1.67107	−	0.692179i	−0.672228	−	0.740344i	$-0.734663\pi$
$107$	−17.2857	−	7.15995i	−1.67107	−	0.692179i	−0.998839	+	0.0481649i	$0.984663\pi$
$108$	5.85853	+	14.1437i	0.563738	+	1.36098i
$109$	−3.26202	+	1.35117i	−0.312444	+	0.129419i	−0.533395	−	0.845866i	$-0.679084\pi$
$109$	−3.26202	+	1.35117i	−0.312444	+	0.129419i	0.220951	+	0.975285i	$0.429084\pi$
$110$		0			0
$111$	−23.2657	−	23.2657i	−2.20828	−	2.20828i
$112$	2.85707	−	1.18344i	0.269968	−	0.111824i
$113$	−1.08741	−	2.62525i	−0.102295	−	0.246963i	0.864443	−	0.502731i	$-0.167671\pi$
$113$	−1.08741	−	2.62525i	−0.102295	−	0.246963i	−0.966738	+	0.255769i	$0.917671\pi$
$114$	−2.69619	−	1.11680i	−0.252521	−	0.104598i
$115$		0			0
$116$	0.244977	−	0.591427i	0.0227456	−	0.0549126i
$117$	−19.7129	+	19.7129i	−1.82246	+	1.82246i
$118$	−2.25860			−0.207921
$119$	−7.61598	+	10.9382i	−0.698155	+	1.00270i
$120$		0			0
$121$	2.48852	−	2.48852i	0.226229	−	0.226229i
$122$	3.49847	−	8.44606i	0.316737	−	0.764670i
$123$		−	6.67430i		−	0.601801i
$124$	−7.35805	−	3.04780i	−0.660772	−	0.273701i
$125$		0			0
$126$	14.4202	−	5.97306i	1.28466	−	0.532122i
$127$	−3.86444	−	3.86444i	−0.342914	−	0.342914i	0.514548	−	0.857462i	$-0.327960\pi$
$127$	−3.86444	−	3.86444i	−0.342914	−	0.342914i	−0.857462	+	0.514548i	$0.827960\pi$
$128$	−6.98340	−	6.98340i	−0.617251	−	0.617251i
$129$	6.14164	−	2.54395i	0.540742	−	0.223983i
$130$		0			0
$131$	9.21986	+	3.81899i	0.805543	+	0.333667i	0.747174	−	0.664628i	$-0.231410\pi$
$131$	9.21986	+	3.81899i	0.805543	+	0.333667i	0.0583689	+	0.998295i	$0.481410\pi$
$132$		−	12.1163i		−	1.05459i
$133$	1.56974	−	3.78969i	0.136114	−	0.328608i
$134$	2.22854	−	2.22854i	0.192516	−	0.192516i
$135$		0			0
$136$	10.3645	+	2.26901i	0.888748	+	0.194566i
$137$	3.07772			0.262947			0.131474	−	0.991320i	$-0.458029\pi$
$137$	3.07772			0.262947			0.131474	+	0.991320i	$0.458029\pi$
$138$	−0.800709	+	0.800709i	−0.0681609	+	0.0681609i
$139$	−2.56777	+	6.19915i	−0.217796	+	0.525805i	−0.994582	−	0.103960i	$-0.966849\pi$
$139$	−2.56777	+	6.19915i	−0.217796	+	0.525805i	0.776786	+	0.629765i	$0.216849\pi$
$140$		0			0
$141$	−23.8526	−	9.88006i	−2.00875	−	0.832051i
$142$	1.11385	+	2.68907i	0.0934720	+	0.225661i
$143$	10.9119	−	4.51988i	0.912503	−	0.377971i
$144$	4.36704	+	4.36704i	0.363920	+	0.363920i
$145$		0			0
$146$	4.47109	−	1.85198i	0.370030	−	0.153271i
$147$	4.05963	+	9.80082i	0.334833	+	0.808358i
$148$	−14.2412	−	5.89890i	−1.17062	−	0.484887i
$149$		−	22.9914i		−	1.88353i	−0.336276	−	0.941764i	$-0.609167\pi$
$149$		−	22.9914i		−	1.88353i	0.336276	−	0.941764i	$-0.390833\pi$
$150$		0			0
$151$	0.138411	−	0.138411i	0.0112638	−	0.0112638i	−0.701452	−	0.712716i	$-0.747465\pi$
$151$	0.138411	−	0.138411i	0.0112638	−	0.0112638i	0.712716	+	0.701452i	$0.247465\pi$
$152$	−3.26530			−0.264850
$153$	−26.0022	−	5.69244i	−2.10215	−	0.460207i
$154$	−6.61268			−0.532865
$155$		0			0
$156$	−7.32075	+	17.6738i	−0.586129	+	1.41504i
$157$			11.8582i			0.946391i	0.880957	+	0.473196i	$0.156900\pi$
$157$			11.8582i			0.946391i	−0.880957	+	0.473196i	$0.843100\pi$
$158$	−4.98993	−	2.06690i	−0.396978	−	0.164434i
$159$	−2.13815	−	5.16196i	−0.169567	−	0.409370i
$160$		0			0
$161$	−1.12546	−	1.12546i	−0.0886983	−	0.0886983i
$162$	7.03907	+	7.03907i	0.553041	+	0.553041i
$163$	4.93787	−	2.04533i	0.386764	−	0.160203i	−0.180824	−	0.983515i	$-0.557877\pi$
$163$	4.93787	−	2.04533i	0.386764	−	0.160203i	0.567588	+	0.823312i	$0.307877\pi$
$164$	−1.19659	−	2.88883i	−0.0934382	−	0.225580i
$165$		0			0
$166$			0.170150i			0.0132062i
$167$	4.43529	−	10.7077i	0.343213	−	0.828589i	−0.654174	−	0.756344i	$-0.726984\pi$
$167$	4.43529	−	10.7077i	0.343213	−	0.828589i	0.997387	−	0.0722453i	$-0.0230164\pi$
$168$	18.0875	−	18.0875i	1.39548	−	1.39548i
$169$	−5.64797			−0.434459
$170$		0			0
$171$	8.19188			0.626449
$172$	2.20220	−	2.20220i	0.167916	−	0.167916i
$173$	−4.21988	+	10.1877i	−0.320832	+	0.774556i	0.678375	+	0.734716i	$0.262685\pi$
$173$	−4.21988	+	10.1877i	−0.320832	+	0.774556i	−0.999206	+	0.0398396i	$0.987315\pi$
$174$		−	1.02197i		−	0.0774750i
$175$		0			0
$176$	−1.00130	−	2.41734i	−0.0754755	−	0.182214i
$177$	8.57932	−	3.55367i	0.644861	−	0.267110i
$178$	7.05538	+	7.05538i	0.528823	+	0.528823i
$179$	14.9009	+	14.9009i	1.11375	+	1.11375i	0.992639	+	0.121109i	$0.0386451\pi$
$179$	14.9009	+	14.9009i	1.11375	+	1.11375i	0.121109	+	0.992639i	$0.461355\pi$
$180$		0			0
$181$	8.67131	+	20.9344i	0.644533	+	1.55604i	0.820501	+	0.571645i	$0.193695\pi$
$181$	8.67131	+	20.9344i	0.644533	+	1.55604i	−0.175968	+	0.984396i	$0.556305\pi$
$182$	9.64579	+	3.99542i	0.714993	+	0.296160i
$183$			37.5869i			2.77850i
$184$	−0.484861	+	1.17056i	−0.0357444	+	0.0862947i
$185$		0			0
$186$	−12.7145			−0.932269
$187$	9.25469	+	6.44380i	0.676770	+	0.471217i
$188$	−12.0954			−0.882150
$189$	−24.2906	+	24.2906i	−1.76688	+	1.76688i
$190$		0			0
$191$			3.50162i			0.253368i	0.991943	+	0.126684i	$0.0404335\pi$
$191$			3.50162i			0.253368i	−0.991943	+	0.126684i	$0.959567\pi$
$192$	−7.02011	−	2.90782i	−0.506633	−	0.209854i
$193$	4.70480	+	11.3584i	0.338659	+	0.817595i	0.997845	+	0.0656152i	$0.0209010\pi$
$193$	4.70480	+	11.3584i	0.338659	+	0.817595i	−0.659186	+	0.751980i	$0.729099\pi$
$194$	10.2317	−	4.23811i	0.734593	−	0.304278i
$195$		0			0
$196$	3.51426	+	3.51426i	0.251018	+	0.251018i
$197$	−15.6835	+	6.49632i	−1.11740	+	0.462843i	−0.863481	−	0.504381i	$-0.831721\pi$
$197$	−15.6835	+	6.49632i	−1.11740	+	0.462843i	−0.253922	+	0.967225i	$0.581721\pi$
$198$	−5.05374	−	12.2008i	−0.359154	−	0.867074i
$199$	10.6966	+	4.43067i	0.758260	+	0.314082i	0.728107	−	0.685464i	$-0.240400\pi$
$199$	10.6966	+	4.43067i	0.758260	+	0.314082i	0.0301533	+	0.999545i	$0.490400\pi$
$200$		0			0
$201$	−4.95875	+	11.9715i	−0.349763	+	0.844403i
$202$	−0.150308	+	0.150308i	−0.0105756	+	0.0105756i
$203$	1.43645			0.100819
$204$	−17.9793	+	3.21928i	−1.25880	+	0.225394i
$205$		0			0
$206$	7.44849	−	7.44849i	0.518961	−	0.518961i
$207$	1.21641	−	2.93667i	0.0845461	−	0.204112i
$208$			4.13111i			0.286441i
$209$	−3.20642	−	1.32814i	−0.221792	−	0.0918694i
$210$		0			0
$211$	6.15655	−	2.55013i	0.423834	−	0.175558i	−0.160563	−	0.987026i	$-0.551331\pi$
$211$	6.15655	−	2.55013i	0.423834	−	0.175558i	0.584397	+	0.811468i	$0.301331\pi$
$212$	−1.85091	−	1.85091i	−0.127121	−	0.127121i
$213$	−8.46191	−	8.46191i	−0.579800	−	0.579800i
$214$	−12.9282	+	5.35503i	−0.883753	+	0.366063i
$215$		0			0
$216$	25.2640	+	10.4647i	1.71900	+	0.712033i
$217$		−	17.8711i		−	1.21317i
$218$	−1.01056	+	2.43971i	−0.0684438	+	0.165238i
$219$	−14.0695	+	14.0695i	−0.950732	+	0.950732i
$220$		0			0
$221$	−9.60626	−	14.9912i	−0.646187	−	1.00842i
$222$	−24.6083			−1.65160
$223$	−8.90442	+	8.90442i	−0.596284	+	0.596284i	−0.939322	−	0.343037i	$-0.888544\pi$
$223$	−8.90442	+	8.90442i	−0.596284	+	0.596284i	0.343037	+	0.939322i	$0.388544\pi$
$224$	7.25180	−	17.5074i	0.484531	−	1.16976i
$225$		0			0
$226$	−1.96346	−	0.813292i	−0.130607	−	0.0540994i
$227$	−3.07779	−	7.43044i	−0.204280	−	0.493176i	0.788224	−	0.615389i	$-0.211001\pi$
$227$	−3.07779	−	7.43044i	−0.204280	−	0.493176i	−0.992504	+	0.122213i	$0.961001\pi$
$228$	5.19336	−	2.15116i	0.343939	−	0.142464i
$229$	−15.2944	−	15.2944i	−1.01068	−	1.01068i	−0.999942	−	0.0107373i	$-0.996582\pi$
$229$	−15.2944	−	15.2944i	−1.01068	−	1.01068i	−0.0107373	−	0.999942i	$-0.503418\pi$
$230$		0			0
$231$	25.1183	−	10.4043i	1.65266	−	0.684555i
$232$	−0.437587	−	1.05643i	−0.0287290	−	0.0693579i
$233$	20.2797	+	8.40011i	1.32857	+	0.550310i	0.930246	−	0.366937i	$-0.119594\pi$
$233$	20.2797	+	8.40011i	1.32857	+	0.550310i	0.398320	+	0.917247i	$0.369594\pi$
$234$			20.8506i			1.36304i
$235$		0			0
$236$	3.07626	−	3.07626i	0.200248	−	0.200248i
$237$	22.2063			1.44246
$238$	1.75697	+	9.81247i	0.113888	+	0.636048i
$239$	5.90132			0.381725			0.190862	−	0.981617i	$-0.438872\pi$
$239$	5.90132			0.381725			0.190862	+	0.981617i	$0.438872\pi$
$240$		0			0
$241$	5.09407	−	12.2982i	0.328138	−	0.792195i	−0.670593	−	0.741826i	$-0.733960\pi$
$241$	5.09407	−	12.2982i	0.328138	−	0.792195i	0.998731	−	0.0503696i	$-0.0160399\pi$
$242$		−	2.63214i		−	0.169200i
$243$	−8.35977	−	3.46273i	−0.536279	−	0.222134i
$244$	6.73872	+	16.2687i	0.431402	+	1.04150i
$245$		0			0
$246$	−3.52974	−	3.52974i	−0.225048	−	0.225048i
$247$	3.87467	+	3.87467i	0.246539	+	0.246539i
$248$	−13.1432	+	5.44409i	−0.834594	+	0.345700i
$249$	−0.267712	−	0.646315i	−0.0169656	−	0.0409586i
$250$		0			0
$251$			3.59367i			0.226831i	0.993548	+	0.113415i	$0.0361790\pi$
$251$			3.59367i			0.226831i	−0.993548	+	0.113415i	$0.963821\pi$
$252$	−11.5052	+	27.7761i	−0.724761	+	1.74973i
$253$	−0.952236	+	0.952236i	−0.0598666	+	0.0598666i
$254$	−4.08746			−0.256470
$255$		0			0
$256$	−12.3285			−0.770531
$257$	17.3588	−	17.3588i	1.08281	−	1.08281i	0.0865680	−	0.996246i	$-0.472410\pi$
$257$	17.3588	−	17.3588i	1.08281	−	1.08281i	0.996246	−	0.0865680i	$-0.0275900\pi$
$258$	1.90266	−	4.59342i	0.118454	−	0.285974i
$259$		−	34.5888i		−	2.14924i
$260$		0			0
$261$	1.09781	+	2.65034i	0.0679524	+	0.164052i
$262$	6.89567	−	2.85628i	0.426016	−	0.176462i
$263$	−10.3521	−	10.3521i	−0.638340	−	0.638340i	0.311806	−	0.950146i	$-0.399066\pi$
$263$	−10.3521	−	10.3521i	−0.638340	−	0.638340i	−0.950146	+	0.311806i	$0.899066\pi$
$264$	−15.3036	−	15.3036i	−0.941873	−	0.941873i
$265$		0			0
$266$	−1.17403	−	2.83436i	−0.0719845	−	0.173786i
$267$	−37.9008	−	15.6990i	−2.31949	−	0.960764i
$268$			6.07063i			0.370823i
$269$	−7.17904	+	17.3317i	−0.437714	+	1.05673i	0.539023	+	0.842291i	$0.318794\pi$
$269$	−7.17904	+	17.3317i	−0.437714	+	1.05673i	−0.976736	+	0.214443i	$0.931206\pi$
$270$		0			0
$271$	5.76388			0.350131			0.175065	−	0.984557i	$-0.443986\pi$
$271$	5.76388			0.350131			0.175065	+	0.984557i	$0.443986\pi$
$272$	−3.32102	+	2.12809i	−0.201366	+	0.129034i
$273$	−42.9259			−2.59800
$274$	1.62767	−	1.62767i	0.0983311	−	0.0983311i
$275$		0			0
$276$		−	2.18117i		−	0.131291i
$277$	−0.113870	−	0.0471663i	−0.00684176	−	0.00283395i	0.379260	−	0.925290i	$-0.376179\pi$
$277$	−0.113870	−	0.0471663i	−0.00684176	−	0.00283395i	−0.386102	+	0.922456i	$0.626179\pi$
$278$	1.92047	+	4.63643i	0.115182	+	0.278075i
$279$	32.9733	−	13.6580i	1.97406	−	0.817682i
$280$		0			0
$281$	−1.28950	−	1.28950i	−0.0769253	−	0.0769253i	0.667597	−	0.744523i	$-0.267323\pi$
$281$	−1.28950	−	1.28950i	−0.0769253	−	0.0769253i	−0.744523	+	0.667597i	$0.767323\pi$
$282$	−17.8397	+	7.38944i	−1.06234	+	0.440035i
$283$	−10.9554	−	26.4486i	−0.651229	−	1.57221i	−0.810996	−	0.585052i	$-0.801074\pi$
$283$	−10.9554	−	26.4486i	−0.651229	−	1.57221i	0.159767	−	0.987155i	$-0.448926\pi$
$284$	−5.17965	−	2.14548i	−0.307355	−	0.127311i
$285$		0			0
$286$	3.38048	−	8.16120i	0.199892	−	0.482582i
$287$	4.96130	−	4.96130i	0.292856	−	0.292856i
$288$	37.8444			2.23000
$289$	7.10292	−	15.4450i	0.417819	−	0.908530i
$290$		0			0
$291$	−32.1969	+	32.1969i	−1.88742	+	1.88742i
$292$	−3.56727	+	8.61216i	−0.208759	+	0.503988i
$293$		−	1.41607i		−	0.0827278i	−0.999144	−	0.0413639i	$-0.986830\pi$
$293$		−	1.41607i		−	0.0827278i	0.999144	−	0.0413639i	$-0.0131703\pi$
$294$	7.33017	+	3.03626i	0.427504	+	0.177078i
$295$		0			0
$296$	−25.4381	+	10.5368i	−1.47856	+	0.612440i
$297$	20.5520	+	20.5520i	1.19255	+	1.19255i
$298$	−12.1591	−	12.1591i	−0.704358	−	0.704358i
$299$	1.96435	−	0.813662i	0.113602	−	0.0470553i
$300$		0			0
$301$	6.45639	+	2.67433i	0.372140	+	0.154146i
$302$		−	0.146399i		−	0.00842433i
$303$	0.334452	−	0.807438i	0.0192138	−	0.0463861i
$304$	0.858361	−	0.858361i	0.0492304	−	0.0492304i
$305$		0			0
$306$	−16.7619	+	10.7409i	−0.958212	+	0.614017i
$307$	21.7364			1.24056			0.620281	−	0.784379i	$-0.287018\pi$
$307$	21.7364			1.24056			0.620281	+	0.784379i	$0.287018\pi$
$308$	9.00661	−	9.00661i	0.513199	−	0.513199i
$309$	−16.5737	+	40.0125i	−0.942846	+	2.27623i
$310$		0			0
$311$	7.99250	+	3.31060i	0.453213	+	0.187727i	0.597600	−	0.801794i	$-0.296121\pi$
$311$	7.99250	+	3.31060i	0.453213	+	0.187727i	−0.144387	+	0.989521i	$0.546121\pi$
$312$	13.0766	+	31.5696i	0.740315	+	1.78728i
$313$	−9.49936	+	3.93476i	−0.536936	+	0.222406i	−0.634638	−	0.772810i	$-0.718851\pi$
$313$	−9.49936	+	3.93476i	−0.536936	+	0.222406i	0.0977022	+	0.995216i	$0.468851\pi$
$314$	6.27130	+	6.27130i	0.353910	+	0.353910i
$315$		0			0
$316$	9.61155	−	3.98123i	0.540692	−	0.223962i
$317$	0.431538	+	1.04183i	0.0242376	+	0.0585147i	0.935535	−	0.353234i	$-0.114918\pi$
$317$	0.431538	+	1.04183i	0.0242376	+	0.0585147i	−0.911297	+	0.411749i	$0.864918\pi$
$318$	−3.86070	−	1.59916i	−0.216497	−	0.0896762i
$319$		−	1.21536i		−	0.0680473i
$320$		0			0
$321$	40.6822	−	40.6822i	2.27066	−	2.27066i
$322$	−1.19041			−0.0663387
$323$	−1.11887	+	5.11084i	−0.0622559	+	0.284375i
$324$	−19.1747			−1.06526
$325$		0			0
$326$	1.52974	−	3.69311i	0.0847242	−	0.204542i
$327$		−	10.8573i		−	0.600407i
$328$	−5.16013	−	2.13740i	−0.284921	−	0.118018i
$329$	−10.3864	−	25.0750i	−0.572621	−	1.38243i
$330$		0			0
$331$	−24.2254	−	24.2254i	−1.33155	−	1.33155i	−0.903984	−	0.427567i	$-0.859371\pi$
$331$	−24.2254	−	24.2254i	−1.33155	−	1.33155i	−0.427567	−	0.903984i	$-0.640629\pi$
$332$	−0.231748	−	0.231748i	−0.0127188	−	0.0127188i
$333$	63.8185	−	26.4345i	3.49723	−	1.44860i
$334$	−3.31722	−	8.00847i	−0.181510	−	0.438204i
$335$		0			0
$336$			9.50945i			0.518783i
$337$	5.26046	−	12.6999i	0.286556	−	0.691807i	−0.713404	−	0.700753i	$-0.752848\pi$
$337$	5.26046	−	12.6999i	0.286556	−	0.691807i	0.999960	+	0.00894611i	$0.00284767\pi$
$338$	−2.98696	+	2.98696i	−0.162469	+	0.162469i
$339$	8.73784			0.474574
$340$		0			0
$341$	−15.1206			−0.818824
$342$	4.33232	−	4.33232i	0.234265	−	0.234265i
$343$	4.39181	−	10.6028i	0.237135	−	0.572495i
$344$		−	5.56300i		−	0.299937i
$345$		0			0
$346$	3.15611	+	7.61952i	0.169673	+	0.409628i
$347$	−17.4415	+	7.22453i	−0.936311	+	0.387833i	−0.798069	−	0.602566i	$-0.794145\pi$
$347$	−17.4415	+	7.22453i	−0.936311	+	0.387833i	−0.138242	+	0.990398i	$0.544145\pi$
$348$	1.39194	+	1.39194i	0.0746158	+	0.0746158i
$349$	4.98501	+	4.98501i	0.266842	+	0.266842i	0.827826	−	0.560985i	$-0.189577\pi$
$349$	4.98501	+	4.98501i	0.266842	+	0.266842i	−0.560985	+	0.827826i	$0.689577\pi$
$350$		0			0
$351$	−17.5612	−	42.3965i	−0.937347	−	2.26296i
$352$	−14.8128	−	6.13567i	−0.789526	−	0.327032i
$353$		−	8.60779i		−	0.458146i	−0.973409	−	0.229073i	$-0.926431\pi$
$353$		−	8.60779i		−	0.458146i	0.973409	−	0.229073i	$-0.0735695\pi$
$354$	2.65784	−	6.41659i	0.141263	−	0.341038i
$355$		0			0
$356$	−19.2191			−1.01861
$357$	−22.1127	−	34.5083i	−1.17033	−	1.82637i
$358$	15.7609			0.832988
$359$	−6.49195	+	6.49195i	−0.342632	+	0.342632i	−0.857356	−	0.514724i	$-0.827894\pi$
$359$	−6.49195	+	6.49195i	−0.342632	+	0.342632i	0.514724	+	0.857356i	$0.327894\pi$
$360$		0			0
$361$			17.3898i			0.915255i
$362$	15.6571	+	6.48540i	0.822921	+	0.340865i
$363$	4.14138	+	9.99818i	0.217366	+	0.524769i
$364$	−18.5796	+	7.69592i	−0.973836	+	0.403376i
$365$		0			0
$366$	19.8780	+	19.8780i	1.03904	+	1.03904i
$367$	6.29722	−	2.60840i	0.328712	−	0.136157i	−0.212223	−	0.977221i	$-0.568070\pi$
$367$	6.29722	−	2.60840i	0.328712	−	0.136157i	0.540935	+	0.841064i	$0.318070\pi$
$368$	−0.180252	−	0.435166i	−0.00939628	−	0.0226846i
$369$	12.9456	+	5.36224i	0.673921	+	0.279147i
$370$		0			0
$371$	2.24773	−	5.42650i	0.116696	−	0.281730i
$372$	17.3174	−	17.3174i	0.897863	−	0.897863i
$373$	−10.4647			−0.541841			−0.270920	−	0.962602i	$-0.587328\pi$
$373$	−10.4647			−0.541841			−0.270920	+	0.962602i	$0.587328\pi$
$374$	8.30223	−	1.48656i	0.429298	−	0.0768680i
$375$		0			0
$376$	−15.2772	+	15.2772i	−0.787863	+	0.787863i
$377$	−0.734329	+	1.77283i	−0.0378199	+	0.0913053i
$378$			25.6924i			1.32148i
$379$	23.4129	+	9.69794i	1.20264	+	0.498150i	0.891851	−	0.452330i	$-0.149407\pi$
$379$	23.4129	+	9.69794i	1.20264	+	0.498150i	0.310789	+	0.950479i	$0.399407\pi$
$380$		0			0
$381$	15.5263	−	6.43119i	0.795434	−	0.329480i
$382$	1.85185	+	1.85185i	0.0947489	+	0.0947489i
$383$	5.43799	+	5.43799i	0.277868	+	0.277868i	0.832258	−	0.554389i	$-0.187048\pi$
$383$	5.43799	+	5.43799i	0.277868	+	0.277868i	−0.554389	+	0.832258i	$0.687048\pi$
$384$	28.0574	−	11.6217i	1.43180	−	0.593069i
$385$		0			0
$386$	8.49511	+	3.51879i	0.432389	+	0.179102i
$387$			13.9563i			0.709439i
$388$	−8.16339	+	19.7082i	−0.414433	+	1.00053i
$389$	11.1991	−	11.1991i	0.567816	−	0.567816i	−0.363700	−	0.931516i	$-0.618487\pi$
$389$	11.1991	−	11.1991i	0.567816	−	0.567816i	0.931516	+	0.363700i	$0.118487\pi$
$390$		0			0
$391$	1.66602	+	1.16000i	0.0842541	+	0.0586639i
$392$	8.87742			0.448377
$393$	−21.6992	+	21.6992i	−1.09458	+	1.09458i
$394$	−4.85869	+	11.7299i	−0.244777	+	0.590944i
$395$		0			0
$396$	23.5011	+	9.73446i	1.18097	+	0.489175i
$397$	−11.1606	−	26.9440i	−0.560133	−	1.35228i	−0.909659	−	0.415355i	$-0.863657\pi$
$397$	−11.1606	−	26.9440i	−0.560133	−	1.35228i	0.349526	−	0.936927i	$-0.386343\pi$
$398$	8.00012	−	3.31376i	0.401010	−	0.166104i
$399$	8.91913	+	8.91913i	0.446515	+	0.446515i
$400$		0			0
$401$	−15.1386	+	6.27060i	−0.755984	+	0.313139i	−0.727181	−	0.686446i	$-0.759170\pi$
$401$	−15.1386	+	6.27060i	−0.755984	+	0.313139i	−0.0288034	+	0.999585i	$0.509170\pi$
$402$	3.70872	+	8.95364i	0.184974	+	0.446567i
$403$	22.0561	+	9.13592i	1.09869	+	0.455092i
$404$		−	0.409445i		−	0.0203706i
$405$		0			0
$406$	0.759673	−	0.759673i	0.0377019	−	0.0377019i
$407$	−29.2652			−1.45062
$408$	−18.6427	+	26.7750i	−0.922952	+	1.32556i
$409$	33.9971			1.68105			0.840525	−	0.541772i	$-0.182247\pi$
$409$	33.9971			1.68105			0.840525	+	0.541772i	$0.182247\pi$
$410$		0			0
$411$	−3.62175	+	8.74367i	−0.178648	+	0.431294i
$412$			20.2900i			0.999616i
$413$	9.01899	+	3.73579i	0.443796	+	0.183826i
$414$	−0.909768	−	2.19637i	−0.0447127	−	0.107946i
$415$		0			0
$416$	17.9000	+	17.9000i	0.877618	+	0.877618i
$417$	−14.5899	−	14.5899i	−0.714468	−	0.714468i
$418$	−2.39812	+	0.993336i	−0.117296	+	0.0485856i
$419$	0.341711	+	0.824964i	0.0166937	+	0.0403021i	0.932007	−	0.362441i	$-0.118057\pi$
$419$	0.341711	+	0.824964i	0.0166937	+	0.0403021i	−0.915313	+	0.402743i	$0.868057\pi$
$420$		0			0
$421$			33.6725i			1.64110i	0.571575	+	0.820550i	$0.306332\pi$
$421$			33.6725i			1.64110i	−0.571575	+	0.820550i	$0.693668\pi$
$422$	1.90728	−	4.60457i	0.0928448	−	0.224147i
$423$	38.3271	−	38.3271i	1.86353	−	1.86353i
$424$	−4.67562			−0.227068
$425$		0			0
$426$	−8.95025			−0.433641
$427$	−27.9400	+	27.9400i	−1.35211	+	1.35211i
$428$	10.3148	−	24.9021i	0.498585	−	1.20369i
$429$			36.3192i			1.75351i
$430$		0			0
$431$	−6.23658	−	15.0564i	−0.300405	−	0.725243i	−0.999943	−	0.0106472i	$-0.996611\pi$
$431$	−6.23658	−	15.0564i	−0.300405	−	0.725243i	0.699538	−	0.714595i	$-0.253389\pi$
$432$	−9.39215	+	3.89036i	−0.451880	+	0.187175i
$433$	24.7450	+	24.7450i	1.18917	+	1.18917i	0.977298	+	0.211871i	$0.0679556\pi$
$433$	24.7450	+	24.7450i	1.18917	+	1.18917i	0.211871	+	0.977298i	$0.432044\pi$
$434$	−9.45122	−	9.45122i	−0.453673	−	0.453673i
$435$		0			0
$436$	−1.94653	−	4.69934i	−0.0932219	−	0.225057i
$437$	−0.577215	−	0.239090i	−0.0276119	−	0.0114372i
$438$			14.8815i			0.711066i
$439$	8.52530	−	20.5819i	0.406891	−	0.982321i	−0.579060	−	0.815285i	$-0.696580\pi$
$439$	8.52530	−	20.5819i	0.406891	−	0.982321i	0.985951	−	0.167036i	$-0.0534196\pi$
$440$		0			0
$441$	−22.2714			−1.06054
$442$	−13.0085	−	2.84784i	−0.618750	−	0.135458i
$443$	8.79907			0.418056			0.209028	−	0.977910i	$-0.432970\pi$
$443$	8.79907			0.418056			0.209028	+	0.977910i	$0.432970\pi$
$444$	33.5171	−	33.5171i	1.59065	−	1.59065i
$445$		0			0
$446$			9.41830i			0.445970i
$447$	65.3175	+	27.0554i	3.08941	+	1.27968i
$448$	−3.05685	−	7.37988i	−0.144422	−	0.348666i
$449$	−8.19189	+	3.39319i	−0.386599	+	0.160135i	−0.567513	−	0.823364i	$-0.692094\pi$
$449$	−8.19189	+	3.39319i	−0.386599	+	0.160135i	0.180914	+	0.983499i	$0.442094\pi$
$450$		0			0
$451$	−4.19771	−	4.19771i	−0.197662	−	0.197662i
$452$	3.78200	−	1.56655i	0.177890	−	0.0736845i
$453$	0.230343	+	0.556098i	0.0108225	+	0.0261278i
$454$	−5.55733	−	2.30192i	−0.260819	−	0.108035i
$455$		0			0
$456$	3.84248	−	9.27656i	0.179941	−	0.434415i
$457$	13.0643	−	13.0643i	0.611120	−	0.611120i	−0.332118	−	0.943238i	$-0.607763\pi$
$457$	13.0643	−	13.0643i	0.611120	−	0.611120i	0.943238	+	0.332118i	$0.107763\pi$
$458$	−16.1770			−0.755902
$459$	25.0363	−	35.9575i	1.16859	−	1.67835i
$460$		0			0
$461$	17.3736	−	17.3736i	0.809169	−	0.809169i	−0.175339	−	0.984508i	$-0.556102\pi$
$461$	17.3736	−	17.3736i	0.809169	−	0.809169i	0.984508	+	0.175339i	$0.0561022\pi$
$462$	7.78156	−	18.7863i	0.362031	−	0.874020i
$463$		−	9.90931i		−	0.460525i	−0.973129	−	0.230262i	$-0.926042\pi$
$463$		−	9.90931i		−	0.460525i	0.973129	−	0.230262i	$-0.0739584\pi$
$464$	0.392737	+	0.162677i	0.0182324	+	0.00755209i
$465$		0			0
$466$	15.1675	−	6.28257i	0.702619	−	0.291034i
$467$	20.7918	+	20.7918i	0.962131	+	0.962131i	0.999309	−	0.0371777i	$-0.0118367\pi$
$467$	20.7918	+	20.7918i	0.962131	+	0.962131i	−0.0371777	+	0.999309i	$0.511837\pi$
$468$	−28.3989	−	28.3989i	−1.31274	−	1.31274i
$469$	−12.5850	+	5.21287i	−0.581121	+	0.240708i
$470$		0			0
$471$	−33.6888	−	13.9543i	−1.55230	−	0.642982i
$472$		−	7.77100i		−	0.357689i
$473$	2.26272	−	5.46269i	0.104040	−	0.251175i
$474$	11.7439	−	11.7439i	0.539417	−	0.539417i
$475$		0			0
$476$	−15.7578	−	10.9718i	−0.722259	−	0.502890i
$477$	11.7301			0.537083
$478$	3.12095	−	3.12095i	0.142749	−	0.142749i
$479$	−10.9449	+	26.4232i	−0.500083	+	1.20731i	0.449354	+	0.893354i	$0.351654\pi$
$479$	−10.9449	+	26.4232i	−0.500083	+	1.20731i	−0.949438	+	0.313955i	$0.898346\pi$
$480$		0			0
$481$	42.6886	+	17.6822i	1.94643	+	0.806239i
$482$	−3.80993	−	9.19799i	−0.173538	−	0.418957i
$483$	4.52176	−	1.87298i	0.205747	−	0.0852234i
$484$	3.58503	+	3.58503i	0.162956	+	0.162956i
$485$		0			0
$486$	−6.25239	+	2.58982i	−0.283614	+	0.117477i
$487$	0.236454	+	0.570849i	0.0107147	+	0.0258677i	0.929146	−	0.369712i	$-0.120544\pi$
$487$	0.236454	+	0.570849i	0.0107147	+	0.0258677i	−0.918432	+	0.395580i	$0.870544\pi$
$488$	29.0597	+	12.0369i	1.31547	+	0.544886i
$489$			16.4352i			0.743224i
$490$		0			0
$491$	18.0077	−	18.0077i	0.812675	−	0.812675i	−0.172359	−	0.985034i	$-0.555139\pi$
$491$	18.0077	−	18.0077i	0.812675	−	0.812675i	0.985034	+	0.172359i	$0.0551390\pi$
$492$	9.61515			0.433485
$493$	−1.80346	+	0.322919i	−0.0812239	+	0.0145435i
$494$	4.09827			0.184390
$495$		0			0
$496$	2.02389	−	4.88611i	0.0908755	−	0.219393i
$497$		−	12.5802i		−	0.564301i
$498$	−0.483388	−	0.200226i	−0.0216611	−	0.00897234i
$499$	13.9527	+	33.6849i	0.624611	+	1.50794i	0.846234	+	0.532811i	$0.178864\pi$
$499$	13.9527	+	33.6849i	0.624611	+	1.50794i	−0.221624	+	0.975132i	$0.571136\pi$
$500$		0			0
$501$	25.2009	+	25.2009i	1.12589	+	1.12589i
$502$	1.90053	+	1.90053i	0.0848249	+	0.0848249i
$503$	−27.8902	+	11.5525i	−1.24356	+	0.515100i	−0.904826	−	0.425781i	$-0.859999\pi$
$503$	−27.8902	+	11.5525i	−1.24356	+	0.515100i	−0.338736	+	0.940881i	$0.609999\pi$
$504$	20.5510	+	49.6146i	0.915416	+	2.21001i
$505$		0			0
$506$			1.00719i			0.0447751i
$507$	6.64632	−	16.0456i	0.295174	−	0.712612i
$508$	5.56721	−	5.56721i	0.247005	−	0.247005i
$509$	−40.1857			−1.78120			−0.890600	−	0.454787i	$-0.849715\pi$
$509$	−40.1857			−1.78120			−0.890600	+	0.454787i	$0.849715\pi$
$510$		0			0
$511$	−20.9171			−0.925316
$512$	7.44682	−	7.44682i	0.329106	−	0.329106i
$513$	−5.16026	+	12.4580i	−0.227831	+	0.550033i
$514$		−	18.3606i		−	0.809852i
$515$		0			0
$516$	3.66488	+	8.84780i	0.161337	+	0.389503i
$517$	−21.2157	+	8.78783i	−0.933065	+	0.386488i
$518$	−18.2925	−	18.2925i	−0.803725	−	0.803725i
$519$	−23.9770	−	23.9770i	−1.05247	−	1.05247i
$520$		0			0
$521$	−13.5302	−	32.6647i	−0.592767	−	1.43107i	−0.880820	−	0.473451i	$-0.843008\pi$
$521$	−13.5302	−	32.6647i	−0.592767	−	1.43107i	0.288053	−	0.957614i	$-0.406992\pi$
$522$	1.98222	+	0.821064i	0.0867596	+	0.0359370i
$523$		−	24.5035i		−	1.07146i	−0.844388	−	0.535732i	$-0.820036\pi$
$523$		−	24.5035i		−	1.07146i	0.844388	−	0.535732i	$-0.179964\pi$
$524$	−5.50173	+	13.2824i	−0.240344	+	0.580243i
$525$		0			0
$526$	−10.9496			−0.477424
$527$	4.01749	+	22.4372i	0.175005	+	0.977379i
$528$	8.04585			0.350150
$529$	16.0920	−	16.0920i	0.699654	−	0.699654i
$530$		0			0
$531$			19.4957i			0.846041i
$532$	5.45951	+	2.26140i	0.236700	+	0.0980443i
$533$	3.58684	+	8.65939i	0.155363	+	0.375080i
$534$	−28.3465	+	11.7415i	−1.22667	+	0.508105i
$535$		0			0
$536$	7.66756	+	7.66756i	0.331188	+	0.331188i
$537$	−59.8678	+	24.7981i	−2.58349	+	1.07011i
$538$	5.36930	+	12.9626i	0.231487	+	0.558859i
$539$	8.71734	+	3.61084i	0.375483	+	0.155530i
$540$		0			0
$541$	9.77786	−	23.6058i	0.420383	−	1.01489i	−0.561852	−	0.827238i	$-0.689911\pi$
$541$	9.77786	−	23.6058i	0.420383	−	1.01489i	0.982235	−	0.187657i	$-0.0600892\pi$
$542$	3.04826	−	3.04826i	0.130934	−	0.130934i
$543$	−69.6778			−2.99016
$544$	−5.16891	+	23.6108i	−0.221615	+	1.01230i
$545$		0			0
$546$	−22.7016	+	22.7016i	−0.971539	+	0.971539i
$547$	4.50103	−	10.8664i	0.192450	−	0.464616i	−0.797971	−	0.602696i	$-0.794093\pi$
$547$	4.50103	−	10.8664i	0.192450	−	0.464616i	0.990421	+	0.138080i	$0.0440932\pi$
$548$			4.43384i			0.189404i
$549$	−72.9042	−	30.1979i	−3.11148	−	1.28882i
$550$		0			0
$551$	0.520936	−	0.215779i	0.0221926	−	0.00919248i
$552$	−2.75494	−	2.75494i	−0.117258	−	0.117258i
$553$	16.5070	+	16.5070i	0.701947	+	0.701947i
$554$	−0.0851647	+	0.0352764i	−0.00361830	+	0.00149875i
$555$		0			0
$556$	−8.93065	−	3.69919i	−0.378744	−	0.156881i
$557$			35.6812i			1.51186i	0.654651	+	0.755931i	$0.272816\pi$
$557$			35.6812i			1.51186i	−0.654651	+	0.755931i	$0.727184\pi$
$558$	10.2150	−	24.6612i	0.432436	−	1.04399i
$559$	−6.60117	+	6.60117i	−0.279200	+	0.279200i
$560$		0			0
$561$	−29.1971	+	18.7094i	−1.23270	+	0.789910i
$562$	−1.36392			−0.0575335
$563$	21.3003	−	21.3003i	0.897702	−	0.897702i	−0.0975306	−	0.995233i	$-0.531094\pi$
$563$	21.3003	−	21.3003i	0.897702	−	0.897702i	0.995233	+	0.0975306i	$0.0310944\pi$
$564$	14.2335	−	34.3626i	0.599337	−	1.44693i
$565$		0			0
$566$	−19.7813	−	8.19368i	−0.831470	−	0.344406i
$567$	−16.4654	−	39.7510i	−0.691482	−	1.66939i
$568$	−9.25206	+	3.83233i	−0.388208	+	0.160801i
$569$	−17.2524	−	17.2524i	−0.723257	−	0.723257i	0.246010	−	0.969267i	$-0.420880\pi$
$569$	−17.2524	−	17.2524i	−0.723257	−	0.723257i	−0.969267	+	0.246010i	$0.920880\pi$
$570$		0			0
$571$	−30.7483	+	12.7364i	−1.28678	+	0.533001i	−0.918024	−	0.396526i	$-0.870216\pi$
$571$	−30.7483	+	12.7364i	−1.28678	+	0.533001i	−0.368755	+	0.929527i	$0.620216\pi$
$572$	6.51144	+	15.7200i	0.272257	+	0.657287i
$573$	−9.94795	−	4.12058i	−0.415582	−	0.172140i
$574$		−	5.24762i		−	0.219032i
$575$		0			0
$576$	11.2801	−	11.2801i	0.470006	−	0.470006i
$577$	18.0611			0.751895			0.375947	−	0.926641i	$-0.377317\pi$
$577$	18.0611			0.751895			0.375947	+	0.926641i	$0.377317\pi$
$578$	−4.41176	−	11.9246i	−0.183505	−	0.495998i
$579$	−37.8051			−1.57113
$580$		0			0
$581$	0.281432	−	0.679438i	0.0116758	−	0.0281878i
$582$			34.0550i			1.41163i
$583$	−4.59131	−	1.90178i	−0.190152	−	0.0787637i
$584$	6.37198	+	15.3833i	0.263675	+	0.636567i
$585$		0			0
$586$	−0.748897	−	0.748897i	−0.0309366	−	0.0309366i
$587$	29.5785	+	29.5785i	1.22084	+	1.22084i	0.967335	+	0.253500i	$0.0815817\pi$
$587$	29.5785	+	29.5785i	1.22084	+	1.22084i	0.253500	+	0.967335i	$0.418418\pi$
$588$	−14.1193	+	5.84840i	−0.582270	+	0.241184i
$589$	−2.68454	−	6.48105i	−0.110614	−	0.267047i
$590$		0			0
$591$		−	52.2008i		−	2.14725i
$592$	3.91717	−	9.45688i	0.160995	−	0.388675i
$593$	−14.6130	+	14.6130i	−0.600085	+	0.600085i	−0.940335	−	0.340250i	$-0.889488\pi$
$593$	−14.6130	+	14.6130i	−0.600085	+	0.600085i	0.340250	+	0.940335i	$0.389488\pi$
$594$	21.7381			0.891925
$595$		0			0
$596$	33.1219			1.35673
$597$	−25.1747	+	25.1747i	−1.03033	+	1.03033i
$598$	0.608550	−	1.46917i	0.0248854	−	0.0600788i
$599$		−	9.21817i		−	0.376644i	−0.982107	−	0.188322i	$-0.939695\pi$
$599$		−	9.21817i		−	0.376644i	0.982107	−	0.188322i	$-0.0603049\pi$
$600$		0			0
$601$	−0.620216	−	1.49733i	−0.0252991	−	0.0610775i	0.910725	−	0.413013i	$-0.135524\pi$
$601$	−0.620216	−	1.49733i	−0.0252991	−	0.0610775i	−0.936024	+	0.351936i	$0.885524\pi$
$602$	4.82883	−	2.00017i	0.196808	−	0.0815207i
$603$	−19.2362	−	19.2362i	−0.783357	−	0.783357i
$604$	0.199399	+	0.199399i	0.00811342	+	0.00811342i
$605$		0			0
$606$	−0.250141	−	0.603894i	−0.0101613	−	0.0245315i
$607$	−23.1115	−	9.57311i	−0.938068	−	0.388560i	−0.139334	−	0.990245i	$-0.544496\pi$
$607$	−23.1115	−	9.57311i	−0.938068	−	0.388560i	−0.798733	+	0.601685i	$0.794496\pi$
$608$		−	7.43849i		−	0.301671i
$609$	−1.69036	+	4.08089i	−0.0684968	+	0.165366i
$610$		0			0
$611$	36.2566			1.46678
$612$	8.20067	−	37.4593i	0.331492	−	1.51420i
$613$	−4.83538			−0.195299			−0.0976495	−	0.995221i	$-0.531132\pi$
$613$	−4.83538			−0.195299			−0.0976495	+	0.995221i	$0.531132\pi$
$614$	11.4954	−	11.4954i	0.463917	−	0.463917i
$615$		0			0
$616$		−	22.7517i		−	0.916694i
$617$	−15.5336	−	6.43422i	−0.625358	−	0.259032i	0.0474212	−	0.998875i	$-0.484900\pi$
$617$	−15.5336	−	6.43422i	−0.625358	−	0.259032i	−0.672779	+	0.739843i	$0.734900\pi$
$618$	12.3957	+	29.9259i	0.498629	+	1.20380i
$619$	11.7540	−	4.86865i	0.472431	−	0.195687i	−0.133748	−	0.991015i	$-0.542701\pi$
$619$	11.7540	−	4.86865i	0.472431	−	0.195687i	0.606179	+	0.795328i	$0.292701\pi$
$620$		0			0
$621$	3.69975	+	3.69975i	0.148466	+	0.148466i
$622$	5.97771	−	2.47605i	0.239684	−	0.0992804i
$623$	−16.5036	−	39.8431i	−0.661201	−	1.59628i
$624$	−11.7363	−	4.86134i	−0.469829	−	0.194609i
$625$		0			0
$626$	−2.94287	+	7.10471i	−0.117621	+	0.283961i
$627$	7.54638	−	7.54638i	0.301373	−	0.301373i
$628$	−17.0833			−0.681697
$629$	7.77569	+	43.4263i	0.310037	+	1.73152i
$630$		0			0
$631$	−2.99812	+	2.99812i	−0.119353	+	0.119353i	−0.764261	−	0.644907i	$-0.776896\pi$
$631$	−2.99812	+	2.99812i	−0.119353	+	0.119353i	0.644907	+	0.764261i	$0.276896\pi$
$632$	7.11142	−	17.1685i	0.282877	−	0.682925i
$633$			20.4914i			0.814459i
$634$	0.779196	+	0.322754i	0.0309458	+	0.0128182i
$635$		0			0
$636$	7.43644	−	3.08028i	0.294874	−	0.122141i
$637$	−10.5341	−	10.5341i	−0.417377	−	0.417377i
$638$	−0.642752	−	0.642752i	−0.0254468	−	0.0254468i
$639$	23.2113	−	9.61444i	0.918226	−	0.380342i
$640$		0			0
$641$	19.6050	+	8.12065i	0.774350	+	0.320746i	0.734633	−	0.678465i	$-0.237354\pi$
$641$	19.6050	+	8.12065i	0.774350	+	0.320746i	0.0397171	+	0.999211i	$0.487354\pi$
$642$		−	43.0300i		−	1.69826i
$643$	3.12525	−	7.54502i	0.123248	−	0.297547i	−0.850198	−	0.526462i	$-0.823518\pi$
$643$	3.12525	−	7.54502i	0.123248	−	0.297547i	0.973446	+	0.228916i	$0.0735181\pi$
$644$	1.62136	−	1.62136i	0.0638905	−	0.0638905i
$645$		0			0
$646$	2.11117	+	3.29462i	0.0830630	+	0.129625i
$647$	−23.4331			−0.921249			−0.460624	−	0.887595i	$-0.652374\pi$
$647$	−23.4331			−0.921249			−0.460624	+	0.887595i	$0.652374\pi$
$648$	−24.2188	+	24.2188i	−0.951404	+	0.951404i
$649$	3.16081	−	7.63088i	0.124073	−	0.299538i
$650$		0			0
$651$	50.7710	+	21.0300i	1.98987	+	0.824232i
$652$	2.94656	+	7.11362i	0.115396	+	0.278591i
$653$	−15.5279	+	6.43188i	−0.607655	+	0.251699i	−0.665225	−	0.746643i	$-0.731665\pi$
$653$	−15.5279	+	6.43188i	−0.607655	+	0.251699i	0.0575706	+	0.998341i	$0.481665\pi$
$654$	−5.74192	−	5.74192i	−0.224527	−	0.224527i
$655$		0			0
$656$	1.91833	−	0.794598i	0.0748981	−	0.0310238i
$657$	−15.9859	−	38.5933i	−0.623668	−	1.50567i
$658$	−18.7539	−	7.76814i	−0.731105	−	0.302833i
$659$			14.0972i			0.549150i	0.961566	+	0.274575i	$0.0885371\pi$
$659$			14.0972i			0.549150i	−0.961566	+	0.274575i	$0.911463\pi$
$660$		0			0
$661$	−7.34734	+	7.34734i	−0.285779	+	0.285779i	−0.835408	−	0.549630i	$-0.814769\pi$
$661$	−7.34734	+	7.34734i	−0.285779	+	0.285779i	0.549630	+	0.835408i	$0.314769\pi$
$662$	−25.6235			−0.995886
$663$	53.8936	−	9.64991i	2.09305	−	0.374771i
$664$	−0.585422			−0.0227188
$665$		0			0
$666$	19.7707	−	47.7308i	0.766101	−	1.84953i
$667$		−	0.218788i		−	0.00847151i
$668$	15.4258	+	6.38959i	0.596843	+	0.247220i
$669$	−14.8187	−	35.7755i	−0.572923	−	1.38316i
$670$		0			0
$671$	23.6398	+	23.6398i	0.912603	+	0.912603i
$672$	41.2041	+	41.2041i	1.58948	+	1.58948i
$673$	18.3153	−	7.58646i	0.706005	−	0.292437i	−0.000645530	−	1.00000i	$-0.500205\pi$
$673$	18.3153	−	7.58646i	0.706005	−	0.292437i	0.706650	+	0.707563i	$0.250205\pi$
$674$	−3.93438	−	9.49842i	−0.151546	−	0.365866i
$675$		0			0
$676$		−	8.13660i		−	0.312946i
$677$	−1.28043	+	3.09124i	−0.0492111	+	0.118806i	−0.946573	−	0.322489i	$-0.895481\pi$
$677$	−1.28043	+	3.09124i	−0.0492111	+	0.118806i	0.897362	+	0.441295i	$0.145481\pi$
$678$	4.62105	−	4.62105i	0.177471	−	0.177471i
$679$	−47.8669			−1.83696
$680$		0			0
$681$	24.7314			0.947709
$682$	−7.99658	+	7.99658i	−0.306205	+	0.306205i
$683$	−19.2424	+	46.4553i	−0.736290	+	1.77756i	−0.115910	+	0.993260i	$0.536978\pi$
$683$	−19.2424	+	46.4553i	−0.736290	+	1.77756i	−0.620380	+	0.784302i	$0.713022\pi$
$684$			11.8014i			0.451239i
$685$		0			0
$686$	−3.28470	−	7.92996i	−0.125410	−	0.302767i
$687$	61.4484	−	25.4528i	2.34440	−	0.971084i
$688$	1.46237	+	1.46237i	0.0557522	+	0.0557522i
$689$	5.54818	+	5.54818i	0.211369	+	0.211369i
$690$		0			0
$691$	−14.8926	−	35.9539i	−0.566540	−	1.36775i	−0.904454	−	0.426572i	$-0.859721\pi$
$691$	−14.8926	−	35.9539i	−0.566540	−	1.36775i	0.337913	−	0.941177i	$-0.390279\pi$
$692$	−14.6766	−	6.07926i	−0.557922	−	0.231099i
$693$			57.0790i			2.16825i
$694$	−5.40333	+	13.0448i	−0.205107	+	0.495173i
$695$		0			0
$696$	3.51620			0.133281
$697$	−5.11360	+	7.34424i	−0.193692	+	0.278183i
$698$	5.27270			0.199575
$699$	−47.7287	+	47.7287i	−1.80527	+	1.80527i
$700$		0			0
$701$			37.5419i			1.41794i	0.705239	+	0.708969i	$0.250840\pi$
$701$			37.5419i			1.41794i	−0.705239	+	0.708969i	$0.749160\pi$
$702$	−31.7089	−	13.1343i	−1.19678	−	0.495721i
$703$	−5.19582	−	12.5438i	−0.195964	−	0.473099i
$704$	−6.24404	+	2.58637i	−0.235331	+	0.0974773i
$705$		0			0
$706$	−4.55227	−	4.55227i	−0.171327	−	0.171327i
$707$	0.848818	−	0.351592i	0.0319231	−	0.0132230i
$708$	5.11950	+	12.3596i	0.192403	+	0.464501i
$709$	12.7076	+	5.26367i	0.477245	+	0.197681i	0.608321	−	0.793691i	$-0.291843\pi$
$709$	12.7076	+	5.26367i	0.477245	+	0.197681i	−0.131076	+	0.991372i	$0.541843\pi$
$710$		0			0
$711$	−17.8409	+	43.0718i	−0.669087	+	1.61532i
$712$	−24.2749	+	24.2749i	−0.909741	+	0.909741i
$713$	−2.72198			−0.101939
$714$	−29.9443	−	6.55547i	−1.12064	−	0.245332i
$715$		0			0
$716$	−21.4667	+	21.4667i	−0.802246	+	0.802246i
$717$	−6.94446	+	16.7654i	−0.259346	+	0.626116i
$718$			6.86660i			0.256259i
$719$	−0.488717	−	0.202433i	−0.0182261	−	0.00754949i	0.373552	−	0.927609i	$-0.378140\pi$
$719$	−0.488717	−	0.202433i	−0.0182261	−	0.00754949i	−0.391778	+	0.920060i	$0.628140\pi$
$720$		0			0
$721$	−42.0631	+	17.4231i	−1.56651	+	0.648870i
$722$	9.19671	+	9.19671i	0.342266	+	0.342266i
$723$	28.9441	+	28.9441i	1.07644	+	1.07644i
$724$	−30.1586	+	12.4921i	−1.12084	+	0.464265i
$725$		0			0
$726$	7.47778	+	3.09740i	0.277527	+	0.114955i
$727$		−	26.7632i		−	0.992591i	−0.868154	−	0.496296i	$-0.834693\pi$
$727$		−	26.7632i		−	0.992591i	0.868154	−	0.496296i	$-0.165307\pi$
$728$	−13.7467	+	33.1875i	−0.509487	+	1.23001i
$729$	−8.55986	+	8.55986i	−0.317032	+	0.317032i
$730$		0			0
$731$	−8.70721	−	1.90620i	−0.322048	−	0.0705033i
$732$	−54.1486			−2.00139
$733$	12.2673	−	12.2673i	0.453105	−	0.453105i	−0.443279	−	0.896384i	$-0.646185\pi$
$733$	12.2673	−	12.2673i	0.453105	−	0.453105i	0.896384	+	0.443279i	$0.146185\pi$
$734$	1.95086	−	4.70978i	0.0720074	−	0.173841i
$735$		0			0
$736$	−2.66658	−	1.10454i	−0.0982916	−	0.0407137i
$737$	4.41056	+	10.6480i	0.162465	+	0.392225i
$738$	9.68219	−	4.01050i	0.356407	−	0.147628i
$739$	21.3876	+	21.3876i	0.786757	+	0.786757i	0.980961	−	0.194204i	$-0.0622124\pi$
$739$	21.3876	+	21.3876i	0.786757	+	0.786757i	−0.194204	+	0.980961i	$0.562212\pi$
$740$		0			0
$741$	−15.5673	+	6.44819i	−0.571880	+	0.236880i
$742$	−1.68111	−	4.05856i	−0.0617155	−	0.148994i
$743$	−6.63416	−	2.74796i	−0.243384	−	0.100813i	0.257657	−	0.966236i	$-0.417049\pi$
$743$	−6.63416	−	2.74796i	−0.243384	−	0.100813i	−0.501041	+	0.865424i	$0.667049\pi$
$744$		−	43.7457i		−	1.60379i
$745$		0			0
$746$	−5.53430	+	5.53430i	−0.202625	+	0.202625i
$747$	1.46869			0.0537366
$748$	−9.28309	+	13.3325i	−0.339423	+	0.487486i
$749$	60.4819			2.20996
$750$		0			0
$751$	11.9767	−	28.9144i	0.437037	−	1.05510i	−0.539930	−	0.841710i	$-0.681549\pi$
$751$	11.9767	−	28.9144i	0.437037	−	1.05510i	0.976967	−	0.213390i	$-0.0684505\pi$
$752$		−	8.03197i		−	0.292896i
$753$	−10.2095	−	4.22890i	−0.372054	−	0.154110i
$754$	0.549215	+	1.32592i	0.0200012	+	0.0482873i
$755$		0			0
$756$	−34.9936	−	34.9936i	−1.27271	−	1.27271i
$757$	7.61956	+	7.61956i	0.276938	+	0.276938i	0.831885	−	0.554948i	$-0.187262\pi$
$757$	7.61956	+	7.61956i	0.276938	+	0.276938i	−0.554948	+	0.831885i	$0.687262\pi$
$758$	17.5108	−	7.25323i	0.636022	−	0.263449i
$759$	−1.58471	−	3.82582i	−0.0575212	−	0.138868i
$760$		0			0
$761$			33.1409i			1.20136i	0.799491	+	0.600678i	$0.205102\pi$
$761$			33.1409i			1.20136i	−0.799491	+	0.600678i	$0.794898\pi$
$762$	4.80998	−	11.6123i	0.174247	−	0.420670i
$763$	8.07068	−	8.07068i	0.292178	−	0.292178i
$764$	−5.04452			−0.182504
$765$		0			0
$766$	5.75182			0.207822
$767$	−9.22123	+	9.22123i	−0.332959	+	0.332959i
$768$	14.5077	−	35.0247i	0.523502	−	1.26385i
$769$			11.4864i			0.414210i	0.978319	+	0.207105i	$0.0664042\pi$
$769$			11.4864i			0.414210i	−0.978319	+	0.207105i	$0.933596\pi$
$770$		0			0
$771$	28.8885	+	69.7429i	1.04039	+	2.51173i
$772$	−16.3632	+	6.77785i	−0.588924	+	0.243940i
$773$	2.26913	+	2.26913i	0.0816149	+	0.0816149i	0.746736	−	0.665121i	$-0.231620\pi$
$773$	2.26913	+	2.26913i	0.0816149	+	0.0816149i	−0.665121	+	0.746736i	$0.731620\pi$
$774$	7.38087	+	7.38087i	0.265300	+	0.265300i
$775$		0			0
$776$	14.5817	+	35.2034i	0.523454	+	1.26373i
$777$	98.2653	+	40.7028i	3.52525	+	1.46021i
$778$		−	11.8454i		−	0.424678i
$779$	1.05397	−	2.54451i	0.0377625	−	0.0911667i
$780$		0			0
$781$	−10.6440			−0.380873
$782$	1.49456	−	0.267608i	0.0534452	−	0.00956963i
$783$	−4.72208			−0.168754
$784$	−2.33364	+	2.33364i	−0.0833443	+	0.0833443i
$785$		0			0
$786$			22.9515i			0.818651i
$787$	−3.11375	−	1.28976i	−0.110993	−	0.0459748i	0.326496	−	0.945199i	$-0.394132\pi$
$787$	−3.11375	−	1.28976i	−0.110993	−	0.0459748i	−0.437489	+	0.899224i	$0.644132\pi$
$788$	−9.35875	−	22.5940i	−0.333392	−	0.804879i
$789$	41.5920	−	17.2280i	1.48071	−	0.613332i
$790$		0			0
$791$	6.49523	+	6.49523i	0.230944	+	0.230944i
$792$	41.9784	−	17.3880i	1.49164	−	0.617857i
$793$	−20.1996	−	48.7661i	−0.717308	−	1.73174i
$794$	−20.1518	−	8.34716i	−0.715161	−	0.296230i
$795$		0			0
$796$	−6.38293	+	15.4097i	−0.226237	+	0.546184i
$797$	15.0966	−	15.0966i	0.534747	−	0.534747i	−0.387234	−	0.921981i	$-0.626569\pi$
$797$	15.0966	−	15.0966i	0.534747	−	0.534747i	0.921981	+	0.387234i	$0.126569\pi$
$798$	9.43385			0.333955
$799$	18.6771	+	29.1468i	0.660748	+	1.03114i
$800$		0			0
$801$	60.9002	−	60.9002i	2.15180	−	2.15180i
$802$	−4.68987	+	11.3224i	−0.165605	+	0.399806i
$803$			17.6977i			0.624538i
$804$	−17.2464	−	7.14369i	−0.608233	−	0.251939i
$805$		0			0
$806$	16.4960	−	6.83288i	0.581048	−	0.240678i
$807$	−40.7907	−	40.7907i	−1.43590	−	1.43590i
$808$	−0.517153	−	0.517153i	−0.0181934	−	0.0181934i
$809$	−2.52190	+	1.04460i	−0.0886652	+	0.0367263i	−0.426575	−	0.904452i	$-0.640280\pi$
$809$	−2.52190	+	1.04460i	−0.0886652	+	0.0367263i	0.337910	+	0.941178i	$0.390280\pi$
$810$		0			0
$811$	−34.4933	−	14.2876i	−1.21122	−	0.501705i	−0.316614	−	0.948554i	$-0.602546\pi$
$811$	−34.4933	−	14.2876i	−1.21122	−	0.501705i	−0.894609	+	0.446849i	$0.852546\pi$
$812$			2.06938i			0.0726211i
$813$	−6.78272	+	16.3749i	−0.237880	+	0.574294i
$814$	−15.4771	+	15.4771i	−0.542471	+	0.542471i
$815$		0			0
$816$	−2.13776	−	11.9391i	−0.0748365	−	0.417953i
$817$	2.74317			0.0959715
$818$	17.9796	−	17.9796i	0.628641	−	0.628641i
$819$	34.4874	−	83.2600i	1.20509	−	2.90934i
$820$		0			0
$821$	−39.0148	−	16.1605i	−1.36163	−	0.564004i	−0.422121	−	0.906540i	$-0.638714\pi$
$821$	−39.0148	−	16.1605i	−1.36163	−	0.564004i	−0.939505	+	0.342536i	$0.888714\pi$
$822$	2.70876	+	6.53952i	0.0944788	+	0.228092i
$823$	−19.1803	+	7.94473i	−0.668582	+	0.276936i	−0.691045	−	0.722812i	$-0.742849\pi$
$823$	−19.1803	+	7.94473i	−0.668582	+	0.276936i	0.0224627	+	0.999748i	$0.492849\pi$
$824$	25.6275	+	25.6275i	0.892775	+	0.892775i
$825$		0			0
$826$	6.74543	−	2.79405i	0.234704	−	0.0972174i
$827$	4.40367	+	10.6314i	0.153131	+	0.369690i	0.981765	−	0.190101i	$-0.0608815\pi$
$827$	4.40367	+	10.6314i	0.153131	+	0.369690i	−0.828634	+	0.559791i	$0.810881\pi$
$828$	4.23063	+	1.75238i	0.147025	+	0.0608996i
$829$		−	11.7508i		−	0.408121i	−0.978958	−	0.204060i	$-0.934586\pi$
$829$		−	11.7508i		−	0.408121i	0.978958	−	0.204060i	$-0.0654139\pi$
$830$		0			0
$831$	0.267995	−	0.267995i	0.00929664	−	0.00929664i
$832$	10.6708			0.369942
$833$	3.04191	−	13.8949i	0.105396	−	0.481431i
$834$	−15.4318			−0.534361
$835$		0			0
$836$	1.91335	−	4.61924i	0.0661747	−	0.159760i
$837$			58.7483i			2.03064i
$838$	0.617003	+	0.255571i	0.0213140	+	0.00882855i
$839$	−14.0060	−	33.8134i	−0.483540	−	1.16737i	−0.957917	−	0.287046i	$-0.907327\pi$
$839$	−14.0060	−	33.8134i	−0.483540	−	1.16737i	0.474377	−	0.880322i	$-0.342673\pi$
$840$		0			0
$841$	−20.3665	−	20.3665i	−0.702292	−	0.702292i
$842$	17.8079	+	17.8079i	0.613701	+	0.613701i
$843$	5.18086	−	2.14598i	0.178438	−	0.0739116i
$844$	3.67377	+	8.86927i	0.126457	+	0.305293i
$845$		0			0
$846$		−	40.5390i		−	1.39376i
$847$	−4.35362	+	10.5106i	−0.149592	+	0.361148i
$848$	1.22910	−	1.22910i	0.0422074	−	0.0422074i
$849$	88.0312			3.02122
$850$		0			0
$851$	−5.26829			−0.180595
$852$	12.1904	−	12.1904i	0.417637	−	0.417637i
$853$	−14.5715	+	35.1787i	−0.498918	+	1.20450i	0.451149	+	0.892449i	$0.351014\pi$
$853$	−14.5715	+	35.1787i	−0.498918	+	1.20450i	−0.950067	+	0.312046i	$0.898986\pi$
$854$			29.5524i			1.01126i
$855$		0			0
$856$	−18.4247	−	44.4811i	−0.629742	−	1.52033i
$857$	18.6880	−	7.74080i	0.638368	−	0.264421i	−0.0399356	−	0.999202i	$-0.512715\pi$
$857$	18.6880	−	7.74080i	0.638368	−	0.264421i	0.678304	+	0.734781i	$0.262715\pi$
$858$	19.2076	+	19.2076i	0.655736	+	0.655736i
$859$	1.84360	+	1.84360i	0.0629028	+	0.0629028i	0.737858	−	0.674956i	$-0.235837\pi$
$859$	1.84360	+	1.84360i	0.0629028	+	0.0629028i	−0.674956	+	0.737858i	$0.735837\pi$
$860$		0			0
$861$	8.25657	+	19.9331i	0.281383	+	0.679319i
$862$	−11.2609	−	4.66443i	−0.383548	−	0.158871i
$863$		−	11.2563i		−	0.383169i	−0.981476	−	0.191584i	$-0.938637\pi$
$863$		−	11.2563i		−	0.383169i	0.981476	−	0.191584i	$-0.0613626\pi$
$864$	−23.8391	+	57.5526i	−0.811022	+	1.95798i
$865$		0			0
$866$	26.1730			0.889396
$867$	35.5202	+	38.3542i	1.20633	+	1.30258i
$868$	25.7455			0.873860
$869$	13.9664	−	13.9664i	0.473777	−	0.473777i
$870$		0			0
$871$		−	18.1970i		−	0.616580i
$872$	−8.39412	−	3.47696i	−0.284261	−	0.117745i
$873$	−36.5822	−	88.3174i	−1.23812	−	2.98909i
$874$	−0.431707	+	0.178819i	−0.0146027	+	0.00604864i
$875$		0			0
$876$	−20.2689	−	20.2689i	−0.684824	−	0.684824i
$877$	5.54426	−	2.29651i	0.187216	−	0.0775476i	−0.287106	−	0.957899i	$-0.592693\pi$
$877$	5.54426	−	2.29651i	0.187216	−	0.0775476i	0.474322	+	0.880351i	$0.342693\pi$
$878$	−6.37620	−	15.3935i	−0.215186	−	0.519506i
$879$	4.02300	+	1.66638i	0.135692	+	0.0562056i
$880$		0			0
$881$	13.1380	−	31.7181i	0.442632	−	1.06861i	−0.532390	−	0.846499i	$-0.678706\pi$
$881$	13.1380	−	31.7181i	0.442632	−	1.06861i	0.975022	−	0.222109i	$-0.0712941\pi$
$882$	−11.7784	+	11.7784i	−0.396598	+	0.396598i
$883$	11.8244			0.397921			0.198961	−	0.980007i	$-0.436243\pi$
$883$	11.8244			0.397921			0.198961	+	0.980007i	$0.436243\pi$
$884$	21.5966	−	13.8390i	0.726374	−	0.465456i
$885$		0			0
$886$	4.65343	−	4.65343i	0.156335	−	0.156335i
$887$	9.27440	−	22.3904i	0.311404	−	0.751796i	−0.688250	−	0.725474i	$-0.741621\pi$
$887$	9.27440	−	22.3904i	0.311404	−	0.751796i	0.999654	−	0.0263216i	$-0.00837938\pi$
$888$		−	84.6680i		−	2.84127i
$889$	16.3220	+	6.76077i	0.547421	+	0.226749i
$890$		0			0
$891$	−33.6329	+	13.9312i	−1.12675	+	0.466713i
$892$	−12.8279	−	12.8279i	−0.429511	−	0.429511i
$893$	−7.53337	−	7.53337i	−0.252095	−	0.252095i
$894$	48.8519	−	20.2351i	1.63385	−	0.676764i
$895$		0			0
$896$	29.4952	+	12.2173i	0.985367	+	0.408152i
$897$			6.53813i			0.218302i
$898$	−2.53782	+	6.12683i	−0.0846880	+	0.204455i
$899$	1.73707	−	1.73707i	0.0579345	−	0.0579345i
$900$		0			0
$901$	−1.60213	+	7.31828i	−0.0533747	+	0.243807i
$902$	−4.43996			−0.147835
$903$	−15.1953	+	15.1953i	−0.505668	+	0.505668i
$904$	2.79823	−	6.75553i	0.0930678	−	0.224686i
$905$		0			0
$906$	0.415914	+	0.172277i	0.0138178	+	0.00572353i
$907$	17.1364	+	41.3709i	0.569005	+	1.37370i	0.902395	+	0.430910i	$0.141808\pi$
$907$	17.1364	+	41.3709i	0.569005	+	1.37370i	−0.333390	+	0.942789i	$0.608192\pi$
$908$	10.7045	−	4.43394i	0.355240	−	0.147145i
$909$	1.29742	+	1.29742i	0.0430326	+	0.0430326i
$910$		0			0
$911$	9.19129	−	3.80716i	0.304521	−	0.126137i	−0.225190	−	0.974315i	$-0.572300\pi$
$911$	9.19129	−	3.80716i	0.304521	−	0.126137i	0.529711	+	0.848178i	$0.322300\pi$
$912$	1.42848	+	3.44865i	0.0473016	+	0.114196i
$913$	−0.574865	−	0.238117i	−0.0190253	−	0.00788052i
$914$		−	13.8182i		−	0.457066i
$915$		0			0
$916$	22.0334	−	22.0334i	0.728005	−	0.728005i
$917$	−32.2600			−1.06532
$918$	−5.77575	−	32.2569i	−0.190628	−	1.06464i
$919$	−33.3601			−1.10045			−0.550224	−	0.835017i	$-0.685458\pi$
$919$	−33.3601			−1.10045			−0.550224	+	0.835017i	$0.685458\pi$
$920$		0			0
$921$	−25.5786	+	61.7522i	−0.842844	+	2.03480i
$922$		−	18.3762i		−	0.605189i
$923$	15.5262	+	6.43116i	0.511051	+	0.211684i
$924$	14.9887	+	36.1860i	0.493094	+	1.19043i
$925$		0			0
$926$	−5.24059	−	5.24059i	−0.172217	−	0.172217i
$927$	−64.2934	−	64.2934i	−2.11167	−	2.11167i
$928$	2.40659	−	0.996842i	0.0790001	−	0.0327229i
$929$	−9.52731	−	23.0010i	−0.312581	−	0.754637i	−0.999608	−	0.0280049i	$-0.991085\pi$
$929$	−9.52731	−	23.0010i	−0.312581	−	0.754637i	0.687027	−	0.726632i	$-0.258915\pi$
$930$		0			0
$931$			4.37755i			0.143468i
$932$	−12.1014	+	29.2154i	−0.396395	+	0.956982i
$933$	−18.8106	+	18.8106i	−0.615830	+	0.615830i
$934$	21.9917			0.719592
$935$		0			0
$936$	−71.7390			−2.34486
$937$	22.0943	−	22.0943i	0.721788	−	0.721788i	−0.247181	−	0.968969i	$-0.579504\pi$
$937$	22.0943	−	22.0943i	0.721788	−	0.721788i	0.968969	+	0.247181i	$0.0795043\pi$
$938$	−3.89878	+	9.41250i	−0.127300	+	0.307329i
$939$		−	31.6176i		−	1.03180i
$940$		0			0
$941$	−0.663467	−	1.60175i	−0.0216284	−	0.0522156i	0.912696	−	0.408638i	$-0.133996\pi$
$941$	−0.663467	−	1.60175i	−0.0216284	−	0.0522156i	−0.934325	+	0.356423i	$0.883996\pi$
$942$	−25.1963	+	10.4367i	−0.820940	+	0.340045i
$943$	−0.755666	−	0.755666i	−0.0246079	−	0.0246079i
$944$	2.04279	+	2.04279i	0.0664873	+	0.0664873i
$945$		0			0
$946$	−1.69232	−	4.08562i	−0.0550221	−	0.132835i
$947$	−10.0253	−	4.15260i	−0.325777	−	0.134941i	0.213800	−	0.976877i	$-0.431416\pi$
$947$	−10.0253	−	4.15260i	−0.325777	−	0.134941i	−0.539577	+	0.841936i	$0.681416\pi$
$948$			31.9910i			1.03902i
$949$	10.6930	−	25.8153i	0.347111	−	0.838000i
$950$		0			0
$951$	−3.46760			−0.112445
$952$	−33.7610	+	6.04508i	−1.09420	+	0.195922i
$953$	16.9007			0.547466			0.273733	−	0.961806i	$-0.411742\pi$
$953$	16.9007			0.547466			0.273733	+	0.961806i	$0.411742\pi$
$954$	6.20351	−	6.20351i	0.200846	−	0.200846i
$955$		0			0
$956$			8.50159i			0.274961i
$957$	3.45280	+	1.43020i	0.111613	+	0.0462316i
$958$	8.18582	+	19.7623i	0.264472	+	0.638491i
$959$	−9.19177	+	3.80736i	−0.296818	+	0.122946i
$960$		0			0
$961$	0.309144	+	0.309144i	0.00997239	+	0.00997239i
$962$	31.9274	−	13.2248i	1.02938	−	0.426384i
$963$	46.2233	+	111.593i	1.48952	+	3.59603i
$964$	17.7171	+	7.33864i	0.570628	+	0.236362i
$965$		0			0
$966$	1.40083	−	3.38189i	0.0450708	−	0.108811i
$967$	−22.0869	+	22.0869i	−0.710267	+	0.710267i	−0.966591	−	0.256324i	$-0.917489\pi$
$967$	−22.0869	+	22.0869i	−0.710267	+	0.710267i	0.256324	+	0.966591i	$0.417489\pi$
$968$	9.05619			0.291077
$969$	−13.2030	−	9.19292i	−0.424142	−	0.295319i
$970$		0			0
$971$	−12.2957	+	12.2957i	−0.394589	+	0.394589i	−0.876319	−	0.481731i	$-0.840008\pi$
$971$	−12.2957	+	12.2957i	−0.394589	+	0.394589i	0.481731	+	0.876319i	$0.340008\pi$
$972$	4.98849	−	12.0433i	0.160006	−	0.386288i
$973$		−	21.6906i		−	0.695368i
$974$	0.426947	+	0.176847i	0.0136802	+	0.00566654i
$975$		0			0
$976$	−10.8032	+	4.47485i	−0.345803	+	0.143236i
$977$	6.48656	+	6.48656i	0.207523	+	0.207523i	0.803214	−	0.595691i	$-0.203122\pi$
$977$	6.48656	+	6.48656i	0.207523	+	0.207523i	−0.595691	+	0.803214i	$0.703122\pi$
$978$	8.69182	+	8.69182i	0.277934	+	0.277934i
$979$	−33.7109	+	13.9635i	−1.07740	+	0.446275i
$980$		0			0
$981$	21.0589	+	8.72290i	0.672360	+	0.278501i
$982$		−	19.0469i		−	0.607811i
$983$	−14.2729	+	34.4578i	−0.455235	+	1.09903i	0.515070	+	0.857148i	$0.327766\pi$
$983$	−14.2729	+	34.4578i	−0.455235	+	1.09903i	−0.970305	+	0.241886i	$0.922234\pi$
$984$	12.1445	−	12.1445i	0.387152	−	0.387152i
$985$		0			0
$986$	−0.782993	+	1.12455i	−0.0249356	+	0.0358129i
$987$	83.4593			2.65654
$988$	−5.58194	+	5.58194i	−0.177585	+	0.177585i
$989$	0.407332	−	0.983386i	0.0129524	−	0.0312699i
$990$		0			0
$991$	−32.3988	−	13.4200i	−1.02918	−	0.426301i	−0.196765	−	0.980451i	$-0.563044\pi$
$991$	−32.3988	−	13.4200i	−1.02918	−	0.426301i	−0.832417	+	0.554149i	$0.813044\pi$
$992$	−12.4019	−	29.9408i	−0.393760	−	0.950621i
$993$	97.3310	−	40.3158i	3.08871	−	1.27938i
$994$	−6.65312	−	6.65312i	−0.211024	−	0.211024i
$995$		0			0
$996$	0.931097	−	0.385673i	0.0295029	−	0.0122205i
$997$	−14.2961	−	34.5139i	−0.452763	−	1.09307i	−0.971267	−	0.237991i	$-0.923511\pi$
$997$	−14.2961	−	34.5139i	−0.452763	−	1.09307i	0.518505	−	0.855075i	$-0.326489\pi$
$998$	25.1934	+	10.4355i	0.797484	+	0.330329i
$999$			113.705i			3.59747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.b.76.5		24
5.2	odd	4		425.2.n.c.399.5		24
5.3	odd	4		425.2.n.f.399.2		24
5.4	even	2		85.2.l.a.76.2	yes	24
15.14	odd	2		765.2.be.b.586.5		24
17.7	odd	16		7225.2.a.bs.1.4		12
17.10	odd	16		7225.2.a.bq.1.4		12
17.15	even	8	inner	425.2.m.b.151.5		24
85.24	odd	16		1445.2.a.p.1.9		12
85.32	odd	8		425.2.n.f.49.2		24
85.44	odd	16		1445.2.a.q.1.9		12
85.49	even	8		85.2.l.a.66.2	✓	24
85.74	odd	16		1445.2.d.j.866.8		24
85.79	odd	16		1445.2.d.j.866.7		24
85.83	odd	8		425.2.n.c.49.5		24
255.134	odd	8		765.2.be.b.406.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.2	✓	24	85.49	even	8
85.2.l.a.76.2	yes	24	5.4	even	2
425.2.m.b.76.5		24	1.1	even	1	trivial
425.2.m.b.151.5		24	17.15	even	8	inner
425.2.n.c.49.5		24	85.83	odd	8
425.2.n.c.399.5		24	5.2	odd	4
425.2.n.f.49.2		24	85.32	odd	8
425.2.n.f.399.2		24	5.3	odd	4
765.2.be.b.406.5		24	255.134	odd	8
765.2.be.b.586.5		24	15.14	odd	2
1445.2.a.p.1.9		12	85.24	odd	16
1445.2.a.q.1.9		12	85.44	odd	16
1445.2.d.j.866.7		24	85.79	odd	16
1445.2.d.j.866.8		24	85.74	odd	16
7225.2.a.bq.1.4		12	17.10	odd	16
7225.2.a.bs.1.4		12	17.7	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.528855 - 0.528855i) q^{2} +(-1.17676 + 2.84096i) q^{3} +1.44062i q^{4} +(0.880118 + 2.12479i) q^{6} +(-2.98655 + 1.23707i) q^{7} +(1.81959 + 1.81959i) q^{8} +(-4.56494 - 4.56494i) q^{9} +(1.04667 + 2.52689i) q^{11} +(-4.09275 - 1.69527i) q^{12} -4.31833i q^{13} +(-0.925222 + 2.23368i) q^{14} -0.956646 q^{16} +(3.47152 - 2.22453i) q^{17} -4.82839 q^{18} +(-0.897260 + 0.897260i) q^{19} -9.94040i q^{21} +(1.88990 + 0.782821i) q^{22} +(0.188421 + 0.454888i) q^{23} +(-7.31061 + 3.02815i) q^{24} +(-2.28377 - 2.28377i) q^{26} +(9.81779 - 4.06666i) q^{27} +(-1.78215 - 4.30250i) q^{28} +(-0.410535 - 0.170049i) q^{29} +(-2.11561 + 5.10754i) q^{31} +(-4.14511 + 4.14511i) q^{32} -8.41047 q^{33} +(0.659477 - 3.01239i) q^{34} +(6.57637 - 6.57637i) q^{36} +(-4.09469 + 9.88545i) q^{37} +0.949042i q^{38} +(12.2682 + 5.08165i) q^{39} +(-2.00526 + 0.830608i) q^{41} +(-5.25703 - 5.25703i) q^{42} +(-1.52864 - 1.52864i) q^{43} +(-3.64030 + 1.50786i) q^{44} +(0.340217 + 0.140922i) q^{46} +8.39597i q^{47} +(1.12575 - 2.71779i) q^{48} +(2.43940 - 2.43940i) q^{49} +(2.23464 + 12.4802i) q^{51} +6.22109 q^{52} +(-1.28480 + 1.28480i) q^{53} +(3.04152 - 7.34287i) q^{54} +(-7.68527 - 3.18334i) q^{56} +(-1.49321 - 3.60494i) q^{57} +(-0.307045 + 0.127182i) q^{58} +(-2.13537 - 2.13537i) q^{59} +(11.2928 - 4.67764i) q^{61} +(1.58230 + 3.82000i) q^{62} +(19.2806 + 7.98628i) q^{63} +2.47104i q^{64} +(-4.44792 + 4.44792i) q^{66} +4.21389 q^{67} +(3.20471 + 5.00116i) q^{68} -1.51404 q^{69} +(-1.48927 + 3.59542i) q^{71} -16.6127i q^{72} +(5.97807 + 2.47620i) q^{73} +(3.06247 + 7.39347i) q^{74} +(-1.29261 - 1.29261i) q^{76} +(-6.25188 - 6.25188i) q^{77} +(9.17555 - 3.80064i) q^{78} +(-2.76355 - 6.67180i) q^{79} +13.3100i q^{81} +(-0.621223 + 1.49977i) q^{82} +(-0.160866 + 0.160866i) q^{83} +14.3204 q^{84} -1.61686 q^{86} +(0.966206 - 0.966206i) q^{87} +(-2.69339 + 6.50243i) q^{88} +13.3408i q^{89} +(5.34208 + 12.8969i) q^{91} +(-0.655322 + 0.271443i) q^{92} +(-12.0207 - 12.0207i) q^{93} +(4.44025 + 4.44025i) q^{94} +(-6.89827 - 16.6539i) q^{96} +(13.6803 + 5.66657i) q^{97} -2.58018i q^{98} +(6.75711 - 16.3131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} - 24 q^{12} - 24 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 32 q^{22} + 16 q^{23} - 8 q^{24} + 16 q^{26} - 24 q^{27} - 48 q^{28} - 8 q^{29} + 16 q^{34} - 24 q^{36} - 24 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 - 24 * q^12 - 24 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 32 * q^22 + 16 * q^23 - 8 * q^24 + 16 * q^26 - 24 * q^27 - 48 * q^28 - 8 * q^29 + 16 * q^34 - 24 * q^36 - 24 * q^37 + 8 * q^39 + 16 * q^41 + 24 * q^42 - 8 * q^43 + 16 * q^44 + 8 * q^46 - 80 * q^48 - 56 * q^51 + 48 * q^52 - 24 * q^53 - 32 * q^54 + 64 * q^56 - 32 * q^57 + 64 * q^58 + 32 * q^59 + 32 * q^61 + 32 * q^62 + 56 * q^63 + 96 * q^66 - 16 * q^67 + 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^76 - 24 * q^77 + 112 * q^78 + 80 * q^82 + 96 * q^83 - 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 - 80 * q^92 - 64 * q^93 + 56 * q^94 - 168 * q^96 + 40 * q^97 - 8 * q^99

Introduction

L-functions

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