LMFDB - Embedded newform 624.2.cn.d.401.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(305,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))

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

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

chi := DirichletCharacter("624.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.cn (of order $12$, degree $4$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			401.4
Root			$0.500000 + 0.331082i$ of defining polynomial
Character	$\chi$	$=$	624.401
Dual form			624.2.cn.d.305.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73022 - 0.0795432i) q^{3} +(2.76293 - 2.76293i) q^{5} +(0.657464 + 2.45369i) q^{7} +(2.98735 - 0.275255i) q^{9} +(-0.150860 + 0.563016i) q^{11} +(-1.20856 + 3.39697i) q^{13} +(4.56072 - 5.00027i) q^{15} +(-0.547000 + 0.947432i) q^{17} +(-1.32717 + 0.355613i) q^{19} +(1.33273 + 4.19313i) q^{21} +(-0.876460 - 1.51807i) q^{23} -10.2676i q^{25} +(5.14688 - 0.713876i) q^{27} +(-5.12973 + 2.96165i) q^{29} +(-6.49983 - 6.49983i) q^{31} +(-0.216237 + 0.986144i) q^{33} +(8.59591 + 4.96285i) q^{35} +(-2.98942 - 0.801012i) q^{37} +(-1.82088 + 5.97364i) q^{39} +(5.11781 + 1.37131i) q^{41} +(-3.26299 - 1.88389i) q^{43} +(7.49333 - 9.01435i) q^{45} +(-5.51114 - 5.51114i) q^{47} +(0.473846 - 0.273575i) q^{49} +(-0.871071 + 1.68278i) q^{51} -3.04435i q^{53} +(1.13876 + 1.97239i) q^{55} +(-2.26801 + 0.720857i) q^{57} +(8.19009 - 2.19453i) q^{59} +(-4.67266 + 8.09329i) q^{61} +(2.63946 + 7.14905i) q^{63} +(6.04642 + 12.7248i) q^{65} +(-1.70856 + 6.37644i) q^{67} +(-1.63722 - 2.55689i) q^{69} +(0.220122 + 0.821505i) q^{71} +(-5.18078 + 5.18078i) q^{73} +(-0.816719 - 17.7653i) q^{75} -1.48065 q^{77} +13.1089 q^{79} +(8.84847 - 1.64456i) q^{81} +(-5.15394 + 5.15394i) q^{83} +(1.10637 + 4.12902i) q^{85} +(-8.63999 + 5.53235i) q^{87} +(2.50797 - 9.35988i) q^{89} +(-9.12969 - 0.732051i) q^{91} +(-11.7632 - 10.7291i) q^{93} +(-2.68434 + 4.64941i) q^{95} +(-0.592450 + 0.158747i) q^{97} +(-0.295697 + 1.72345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73}+ \cdots + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.73022	−	0.0795432i	0.998945	−	0.0459243i
$3$	1.73022	−	0.0795432i	0.998945	−	0.0459243i
$4$		0			0
$5$	2.76293	−	2.76293i	1.23562	−	1.23562i	0.273849	−	0.961773i	$-0.411703\pi$
$5$	2.76293	−	2.76293i	1.23562	−	1.23562i	0.961773	−	0.273849i	$-0.0882968\pi$
$6$		0			0
$7$	0.657464	+	2.45369i	0.248498	+	0.927407i	0.971593	+	0.236659i	$0.0760523\pi$
$7$	0.657464	+	2.45369i	0.248498	+	0.927407i	−0.723095	+	0.690749i	$0.757281\pi$
$8$		0			0
$9$	2.98735	−	0.275255i	0.995782	−	0.0917517i
$10$		0			0
$11$	−0.150860	+	0.563016i	−0.0454859	+	0.169756i	−0.984932	−	0.172940i	$-0.944673\pi$
$11$	−0.150860	+	0.563016i	−0.0454859	+	0.169756i	0.939446	+	0.342696i	$0.111340\pi$
$12$		0			0
$13$	−1.20856	+	3.39697i	−0.335195	+	0.942149i
$13$	−1.20856	+	3.39697i	−0.335195	+	0.942149i
$14$		0			0
$15$	4.56072	−	5.00027i	1.17757	−	1.29106i
$16$		0			0
$17$	−0.547000	+	0.947432i	−0.132667	+	0.229786i	−0.924704	−	0.380687i	$-0.875687\pi$
$17$	−0.547000	+	0.947432i	−0.132667	+	0.229786i	0.792037	+	0.610473i	$0.209021\pi$
$18$		0			0
$19$	−1.32717	+	0.355613i	−0.304473	+	0.0815832i	−0.407821	−	0.913062i	$-0.633711\pi$
$19$	−1.32717	+	0.355613i	−0.304473	+	0.0815832i	0.103348	+	0.994645i	$0.467044\pi$
$20$		0			0
$21$	1.33273	+	4.19313i	0.290826	+	0.915017i
$22$		0			0
$23$	−0.876460	−	1.51807i	−0.182755	−	0.316540i	0.760063	−	0.649849i	$-0.225168\pi$
$23$	−0.876460	−	1.51807i	−0.182755	−	0.316540i	−0.942818	+	0.333309i	$0.891835\pi$
$24$		0			0
$25$		−	10.2676i		−	2.05352i
$26$		0			0
$27$	5.14688	−	0.713876i	0.990518	−	0.137386i
$28$		0			0
$29$	−5.12973	+	2.96165i	−0.952566	+	0.549965i	−0.893877	−	0.448312i	$-0.852025\pi$
$29$	−5.12973	+	2.96165i	−0.952566	+	0.549965i	−0.0586892	+	0.998276i	$0.518692\pi$
$30$		0			0
$31$	−6.49983	−	6.49983i	−1.16740	−	1.16740i	−0.982816	−	0.184588i	$-0.940905\pi$
$31$	−6.49983	−	6.49983i	−1.16740	−	1.16740i	−0.184588	−	0.982816i	$-0.559095\pi$
$32$		0			0
$33$	−0.216237	+	0.986144i	−0.0376420	+	0.171666i
$34$		0			0
$35$	8.59591	+	4.96285i	1.45297	+	0.838875i
$36$		0			0
$37$	−2.98942	−	0.801012i	−0.491457	−	0.131686i	0.00457534	−	0.999990i	$-0.498544\pi$
$37$	−2.98942	−	0.801012i	−0.491457	−	0.131686i	−0.496032	+	0.868304i	$0.665210\pi$
$38$		0			0
$39$	−1.82088	+	5.97364i	−0.291573	+	0.956548i
$40$		0			0
$41$	5.11781	+	1.37131i	0.799268	+	0.214163i	0.635262	−	0.772296i	$-0.280892\pi$
$41$	5.11781	+	1.37131i	0.799268	+	0.214163i	0.164005	+	0.986459i	$0.447559\pi$
$42$		0			0
$43$	−3.26299	−	1.88389i	−0.497602	−	0.287290i	0.230121	−	0.973162i	$-0.426088\pi$
$43$	−3.26299	−	1.88389i	−0.497602	−	0.287290i	−0.727723	+	0.685872i	$0.759421\pi$
$44$		0			0
$45$	7.49333	−	9.01435i	1.11704	−	1.34378i
$46$		0			0
$47$	−5.51114	−	5.51114i	−0.803883	−	0.803883i	0.179817	−	0.983700i	$-0.442449\pi$
$47$	−5.51114	−	5.51114i	−0.803883	−	0.803883i	−0.983700	+	0.179817i	$0.942449\pi$
$48$		0			0
$49$	0.473846	−	0.273575i	0.0676922	−	0.0390821i
$50$		0			0
$51$	−0.871071	+	1.68278i	−0.121974	+	0.235636i
$52$		0			0
$53$		−	3.04435i		−	0.418173i	−0.977897	−	0.209087i	$-0.932951\pi$
$53$		−	3.04435i		−	0.418173i	0.977897	−	0.209087i	$-0.0670490\pi$
$54$		0			0
$55$	1.13876	+	1.97239i	0.153551	+	0.265957i
$56$		0			0
$57$	−2.26801	+	0.720857i	−0.300405	+	0.0954799i
$58$		0			0
$59$	8.19009	−	2.19453i	1.06626	−	0.285703i	0.317304	−	0.948324i	$-0.397223\pi$
$59$	8.19009	−	2.19453i	1.06626	−	0.285703i	0.748955	+	0.662621i	$0.230556\pi$
$60$		0			0
$61$	−4.67266	+	8.09329i	−0.598273	+	1.03624i	0.394803	+	0.918766i	$0.370813\pi$
$61$	−4.67266	+	8.09329i	−0.598273	+	1.03624i	−0.993076	+	0.117474i	$0.962520\pi$
$62$		0			0
$63$	2.63946	+	7.14905i	0.332541	+	0.900695i
$64$		0			0
$65$	6.04642	+	12.7248i	0.749966	+	1.57831i
$66$		0			0
$67$	−1.70856	+	6.37644i	−0.208734	+	0.779006i	0.779545	+	0.626346i	$0.215450\pi$
$67$	−1.70856	+	6.37644i	−0.208734	+	0.779006i	−0.988279	+	0.152659i	$0.951216\pi$
$68$		0			0
$69$	−1.63722	−	2.55689i	−0.197099	−	0.307813i
$70$		0			0
$71$	0.220122	+	0.821505i	0.0261236	+	0.0974947i	0.977757	−	0.209742i	$-0.0672624\pi$
$71$	0.220122	+	0.821505i	0.0261236	+	0.0974947i	−0.951633	+	0.307237i	$0.900596\pi$
$72$		0			0
$73$	−5.18078	+	5.18078i	−0.606365	+	0.606365i	−0.941994	−	0.335629i	$-0.891051\pi$
$73$	−5.18078	+	5.18078i	−0.606365	+	0.606365i	0.335629	+	0.941994i	$0.391051\pi$
$74$		0			0
$75$	−0.816719	−	17.7653i	−0.0943066	−	2.05135i
$76$		0			0
$77$	−1.48065			−0.168736
$78$		0			0
$79$	13.1089			1.47486			0.737431	−	0.675422i	$-0.236039\pi$
$79$	13.1089			1.47486			0.737431	+	0.675422i	$0.236039\pi$
$80$		0			0
$81$	8.84847	−	1.64456i	0.983163	−	0.182729i
$82$		0			0
$83$	−5.15394	+	5.15394i	−0.565719	+	0.565719i	−0.930926	−	0.365208i	$-0.880998\pi$
$83$	−5.15394	+	5.15394i	−0.565719	+	0.565719i	0.365208	+	0.930926i	$0.380998\pi$
$84$		0			0
$85$	1.10637	+	4.12902i	0.120002	+	0.447855i
$86$		0			0
$87$	−8.63999	+	5.53235i	−0.926305	+	0.593130i
$88$		0			0
$89$	2.50797	−	9.35988i	0.265844	−	0.992145i	−0.695887	−	0.718151i	$-0.744989\pi$
$89$	2.50797	−	9.35988i	0.265844	−	0.992145i	0.961731	−	0.273994i	$-0.0883448\pi$
$90$		0			0
$91$	−9.12969	−	0.732051i	−0.957051	−	0.0767398i
$92$		0			0
$93$	−11.7632	−	10.7291i	−1.21978	−	1.11256i
$94$		0			0
$95$	−2.68434	+	4.64941i	−0.275407	+	0.477019i
$96$		0			0
$97$	−0.592450	+	0.158747i	−0.0601542	+	0.0161183i	−0.288771	−	0.957398i	$-0.593247\pi$
$97$	−0.592450	+	0.158747i	−0.0601542	+	0.0161183i	0.228616	+	0.973517i	$0.426580\pi$
$98$		0			0
$99$	−0.295697	+	1.72345i	−0.0297187	+	0.173213i
$100$		0			0
$101$	−2.91789	−	5.05394i	−0.290341	−	0.502886i	0.683549	−	0.729904i	$-0.260435\pi$
$101$	−2.91789	−	5.05394i	−0.290341	−	0.502886i	−0.973890	+	0.227019i	$0.927102\pi$
$102$		0			0
$103$			2.07313i			0.204272i	0.994770	+	0.102136i	$0.0325677\pi$
$103$			2.07313i			0.204272i	−0.994770	+	0.102136i	$0.967432\pi$
$104$		0			0
$105$	15.2676	+	7.90310i	1.48997	+	0.771263i
$106$		0			0
$107$	2.99520	−	1.72928i	0.289557	−	0.167176i	−0.348185	−	0.937426i	$-0.613202\pi$
$107$	2.99520	−	1.72928i	0.289557	−	0.167176i	0.637742	+	0.770250i	$0.279869\pi$
$108$		0			0
$109$	−10.9901	−	10.9901i	−1.05266	−	1.05266i	−0.998534	−	0.0541251i	$-0.982763\pi$
$109$	−10.9901	−	10.9901i	−1.05266	−	1.05266i	−0.0541251	−	0.998534i	$-0.517237\pi$
$110$		0			0
$111$	−5.23607	−	1.14814i	−0.496986	−	0.108977i
$112$		0			0
$113$	9.43719	+	5.44856i	0.887776	+	0.512558i	0.873214	−	0.487336i	$-0.162031\pi$
$113$	9.43719	+	5.44856i	0.887776	+	0.512558i	0.0145614	+	0.999894i	$0.495365\pi$
$114$		0			0
$115$	−6.61594	−	1.77274i	−0.616940	−	0.165308i
$116$		0			0
$117$	−2.67536	+	10.4806i	−0.247337	+	0.968930i
$118$		0			0
$119$	−2.68434	−	0.719266i	−0.246073	−	0.0659350i
$120$		0			0
$121$	9.23205	+	5.33013i	0.839277	+	0.484557i
$122$		0			0
$123$	8.96403	+	1.96559i	0.808260	+	0.177231i
$124$		0			0
$125$	−14.5541	−	14.5541i	−1.30175	−	1.30175i
$126$		0			0
$127$	−8.06551	+	4.65662i	−0.715698	+	0.413209i	−0.813167	−	0.582030i	$-0.802259\pi$
$127$	−8.06551	+	4.65662i	−0.715698	+	0.413209i	0.0974690	+	0.995239i	$0.468925\pi$
$128$		0			0
$129$	−5.79555	−	3.00000i	−0.510270	−	0.264135i
$130$		0			0
$131$			0.917828i			0.0801910i	0.999196	+	0.0400955i	$0.0127662\pi$
$131$			0.917828i			0.0801910i	−0.999196	+	0.0400955i	$0.987234\pi$
$132$		0			0
$133$	−1.74513	−	3.02265i	−0.151322	−	0.262097i
$134$		0			0
$135$	12.2481	−	16.1929i	1.05415	−	1.39366i
$136$		0			0
$137$	−8.32493	+	2.23066i	−0.711247	+	0.190578i	−0.596263	−	0.802789i	$-0.703348\pi$
$137$	−8.32493	+	2.23066i	−0.711247	+	0.190578i	−0.114984	+	0.993367i	$0.536682\pi$
$138$		0			0
$139$	1.65662	−	2.86936i	0.140513	−	0.243376i	−0.787177	−	0.616727i	$-0.788458\pi$
$139$	1.65662	−	2.86936i	0.140513	−	0.243376i	0.927690	+	0.373352i	$0.121791\pi$
$140$		0			0
$141$	−9.97388	−	9.09713i	−0.839952	−	0.766117i
$142$		0			0
$143$	−1.73022	−	1.19291i	−0.144689	−	0.0997557i
$144$		0			0
$145$	−5.99026	+	22.3559i	−0.497464	+	1.85656i
$146$		0			0
$147$	0.798098	−	0.511037i	0.0658260	−	0.0421496i
$148$		0			0
$149$	−2.03304	−	7.58742i	−0.166553	−	0.621585i	−0.997837	−	0.0657369i	$-0.979060\pi$
$149$	−2.03304	−	7.58742i	−0.166553	−	0.621585i	0.831284	−	0.555848i	$-0.187606\pi$
$150$		0			0
$151$	−10.2600	+	10.2600i	−0.834946	+	0.834946i	−0.988189	−	0.153243i	$-0.951028\pi$
$151$	−10.2600	+	10.2600i	−0.834946	+	0.834946i	0.153243	+	0.988189i	$0.451028\pi$
$152$		0			0
$153$	−1.37329	+	2.98087i	−0.111024	+	0.240989i
$154$		0			0
$155$	−35.9172			−2.88494
$156$		0			0
$157$	−6.71547			−0.535953			−0.267976	−	0.963425i	$-0.586355\pi$
$157$	−6.71547			−0.535953			−0.267976	+	0.963425i	$0.586355\pi$
$158$		0			0
$159$	−0.242157	−	5.26740i	−0.0192043	−	0.417732i
$160$		0			0
$161$	3.14864	−	3.14864i	0.248148	−	0.248148i
$162$		0			0
$163$	0.407550	+	1.52100i	0.0319217	+	0.119134i	0.980048	−	0.198760i	$-0.0636913\pi$
$163$	0.407550	+	1.52100i	0.0319217	+	0.119134i	−0.948127	+	0.317893i	$0.897025\pi$
$164$		0			0
$165$	2.12720	+	3.32210i	0.165602	+	0.258625i
$166$		0			0
$167$	6.32673	−	23.6117i	0.489577	−	1.82713i	−0.0689223	−	0.997622i	$-0.521956\pi$
$167$	6.32673	−	23.6117i	0.489577	−	1.82713i	0.558499	−	0.829505i	$-0.311377\pi$
$168$		0			0
$169$	−10.0788	−	8.21088i	−0.775289	−	0.631606i
$170$		0			0
$171$	−3.86682	+	1.42765i	−0.295703	+	0.109175i
$172$		0			0
$173$	−10.3837	+	17.9850i	−0.789456	+	1.36738i	0.136845	+	0.990593i	$0.456304\pi$
$173$	−10.3837	+	17.9850i	−0.789456	+	1.36738i	−0.926301	+	0.376785i	$0.877029\pi$
$174$		0			0
$175$	25.1935	−	6.75058i	1.90445	−	0.510296i
$176$		0			0
$177$	13.9961	−	4.44849i	1.05201	−	0.334369i
$178$		0			0
$179$	7.00018	+	12.1247i	0.523218	+	0.906241i	0.999635	+	0.0270211i	$0.00860212\pi$
$179$	7.00018	+	12.1247i	0.523218	+	0.906241i	−0.476416	+	0.879220i	$0.658065\pi$
$180$		0			0
$181$			25.5405i			1.89841i	0.314653	+	0.949207i	$0.398112\pi$
$181$			25.5405i			1.89841i	−0.314653	+	0.949207i	$0.601888\pi$
$182$		0			0
$183$	−7.44098	+	14.3749i	−0.550053	+	1.06262i
$184$		0			0
$185$	−10.4727	+	6.04642i	−0.769968	+	0.444541i
$186$		0			0
$187$	−0.450899	−	0.450899i	−0.0329730	−	0.0329730i
$188$		0			0
$189$	5.13552	+	12.1595i	0.373554	+	0.884473i
$190$		0			0
$191$	20.4783	+	11.8231i	1.48176	+	0.855493i	0.999786	−	0.0206939i	$-0.00658754\pi$
$191$	20.4783	+	11.8231i	1.48176	+	0.855493i	0.481972	+	0.876187i	$0.339921\pi$
$192$		0			0
$193$	10.2375	+	2.74313i	0.736912	+	0.197455i	0.607705	−	0.794163i	$-0.292090\pi$
$193$	10.2375	+	2.74313i	0.736912	+	0.197455i	0.129207	+	0.991618i	$0.458757\pi$
$194$		0			0
$195$	11.4738	+	21.5357i	0.821658	+	1.54221i
$196$		0			0
$197$	−3.34959	−	0.897520i	−0.238649	−	0.0639457i	0.137512	−	0.990500i	$-0.456089\pi$
$197$	−3.34959	−	0.897520i	−0.238649	−	0.0639457i	−0.376161	+	0.926554i	$0.622756\pi$
$198$		0			0
$199$	2.67432	+	1.54402i	0.189577	+	0.109453i	0.591785	−	0.806096i	$-0.298424\pi$
$199$	2.67432	+	1.54402i	0.189577	+	0.109453i	−0.402207	+	0.915549i	$0.631757\pi$
$200$		0			0
$201$	−2.44899	+	11.1686i	−0.172738	+	0.787770i
$202$		0			0
$203$	−10.6396	−	10.6396i	−0.746752	−	0.746752i
$204$		0			0
$205$	17.9290	−	10.3513i	1.25222	−	0.722968i
$206$		0			0
$207$	−3.03615	−	4.29376i	−0.211027	−	0.298437i
$208$		0			0
$209$		−	0.800864i		−	0.0553969i
$210$		0			0
$211$	−2.47900	−	4.29376i	−0.170662	−	0.295595i	0.767990	−	0.640462i	$-0.221257\pi$
$211$	−2.47900	−	4.29376i	−0.170662	−	0.295595i	−0.938651	+	0.344867i	$0.887924\pi$
$212$		0			0
$213$	0.446205	+	1.40388i	0.0305734	+	0.0961921i
$214$		0			0
$215$	−14.2205	+	3.81037i	−0.969829	+	0.259865i
$216$		0			0
$217$	11.6752	−	20.2220i	0.792561	−	1.37276i
$218$		0			0
$219$	−8.55181	+	9.37601i	−0.577878	+	0.633572i
$220$		0			0
$221$	−2.55731	−	3.00317i	−0.172023	−	0.202015i
$222$		0			0
$223$	−4.93415	+	18.4145i	−0.330415	+	1.23313i	0.578340	+	0.815796i	$0.303701\pi$
$223$	−4.93415	+	18.4145i	−0.330415	+	1.23313i	−0.908755	+	0.417330i	$0.862966\pi$
$224$		0			0
$225$	−2.82621	−	30.6729i	−0.188414	−	2.04486i
$226$		0			0
$227$	−1.38733	−	5.17758i	−0.0920803	−	0.343648i	0.904480	−	0.426515i	$-0.140259\pi$
$227$	−1.38733	−	5.17758i	−0.0920803	−	0.343648i	−0.996561	+	0.0828671i	$0.973592\pi$
$228$		0			0
$229$	2.78436	−	2.78436i	0.183996	−	0.183996i	−0.609099	−	0.793094i	$-0.708469\pi$
$229$	2.78436	−	2.78436i	0.183996	−	0.183996i	0.793094	+	0.609099i	$0.208469\pi$
$230$		0			0
$231$	−2.56186	+	0.117776i	−0.168558	+	0.00774908i
$232$		0			0
$233$	3.83663			0.251346			0.125673	−	0.992072i	$-0.459891\pi$
$233$	3.83663			0.251346			0.125673	+	0.992072i	$0.459891\pi$
$234$		0			0
$235$	−30.4538			−1.98659
$236$		0			0
$237$	22.6813	−	1.04272i	1.47331	−	0.0677320i
$238$		0			0
$239$	−0.751524	+	0.751524i	−0.0486121	+	0.0486121i	−0.730995	−	0.682383i	$-0.760944\pi$
$239$	−0.751524	+	0.751524i	−0.0486121	+	0.0486121i	0.682383	+	0.730995i	$0.260944\pi$
$240$		0			0
$241$	−7.23751	−	27.0107i	−0.466209	−	1.73991i	−0.652851	−	0.757487i	$-0.726427\pi$
$241$	−7.23751	−	27.0107i	−0.466209	−	1.73991i	0.186642	−	0.982428i	$-0.440240\pi$
$242$		0			0
$243$	15.1790	−	3.54930i	0.973734	−	0.227688i
$244$		0			0
$245$	0.553335	−	2.06507i	0.0353513	−	0.131933i
$246$		0			0
$247$	0.395956	−	4.93812i	0.0251941	−	0.314205i
$248$		0			0
$249$	−8.50751	+	9.32743i	−0.539141	+	0.591102i
$250$		0			0
$251$	7.56320	−	13.0998i	0.477385	−	0.826855i	−0.522279	−	0.852775i	$-0.674918\pi$
$251$	7.56320	−	13.0998i	0.477385	−	0.826855i	0.999664	+	0.0259196i	$0.00825138\pi$
$252$		0			0
$253$	0.986923	−	0.264445i	0.0620473	−	0.0166255i
$254$		0			0
$255$	2.24270	+	7.05612i	0.140443	+	0.441871i
$256$		0			0
$257$	−0.178601	−	0.309345i	−0.0111408	−	0.0192964i	0.860401	−	0.509617i	$-0.170213\pi$
$257$	−0.178601	−	0.309345i	−0.0111408	−	0.0192964i	−0.871542	+	0.490321i	$0.836880\pi$
$258$		0			0
$259$		−	7.86174i		−	0.488505i
$260$		0			0
$261$	−14.5091	+	10.2595i	−0.898088	+	0.635044i
$262$		0			0
$263$	−1.86002	+	1.07389i	−0.114694	+	0.0662186i	−0.556250	−	0.831015i	$-0.687760\pi$
$263$	−1.86002	+	1.07389i	−0.114694	+	0.0662186i	0.441556	+	0.897234i	$0.354427\pi$
$264$		0			0
$265$	−8.41133	−	8.41133i	−0.516704	−	0.516704i
$266$		0			0
$267$	3.59484	−	16.3942i	0.220000	−	1.00331i
$268$		0			0
$269$	21.2380	+	12.2618i	1.29490	+	0.747612i	0.979519	−	0.201352i	$-0.0645335\pi$
$269$	21.2380	+	12.2618i	1.29490	+	0.747612i	0.315384	+	0.948964i	$0.397867\pi$
$270$		0			0
$271$	21.1790	+	5.67488i	1.28653	+	0.344725i	0.836341	−	0.548209i	$-0.184690\pi$
$271$	21.1790	+	5.67488i	1.28653	+	0.344725i	0.450189	+	0.892934i	$0.351357\pi$
$272$		0			0
$273$	−15.8546	−	0.540407i	−0.959566	−	0.0327069i
$274$		0			0
$275$	5.78083	+	1.54897i	0.348597	+	0.0934063i
$276$		0			0
$277$	−16.1517	−	9.32517i	−0.970460	−	0.560295i	−0.0710833	−	0.997470i	$-0.522646\pi$
$277$	−16.1517	−	9.32517i	−0.970460	−	0.560295i	−0.899376	+	0.437175i	$0.855979\pi$
$278$		0			0
$279$	−21.2063	−	17.6281i	−1.26959	−	1.05537i
$280$		0			0
$281$	−11.2782	−	11.2782i	−0.672801	−	0.672801i	0.285560	−	0.958361i	$-0.407820\pi$
$281$	−11.2782	−	11.2782i	−0.672801	−	0.672801i	−0.958361	+	0.285560i	$0.907820\pi$
$282$		0			0
$283$	−4.08342	+	2.35756i	−0.242734	+	0.140143i	−0.616433	−	0.787408i	$-0.711423\pi$
$283$	−4.08342	+	2.35756i	−0.242734	+	0.140143i	0.373699	+	0.927550i	$0.378089\pi$
$284$		0			0
$285$	−4.27467	+	8.25803i	−0.253210	+	0.489164i
$286$		0			0
$287$			13.4591i			0.794466i
$288$		0			0
$289$	7.90158	+	13.6859i	0.464799	+	0.805055i
$290$		0			0
$291$	−1.01244	+	0.321793i	−0.0593505	+	0.0188638i
$292$		0			0
$293$	20.6276	−	5.52716i	1.20508	−	0.322900i	0.400250	−	0.916406i	$-0.368923\pi$
$293$	20.6276	−	5.52716i	1.20508	−	0.322900i	0.804830	+	0.593506i	$0.202257\pi$
$294$		0			0
$295$	16.5653	−	28.6920i	0.964471	−	1.67051i
$296$		0			0
$297$	−0.374533	+	3.00547i	−0.0217326	+	0.174395i
$298$		0			0
$299$	6.21610	−	1.14262i	0.359486	−	0.0660795i
$300$		0			0
$301$	2.47718	−	9.24496i	0.142782	−	0.532870i
$302$		0			0
$303$	−5.45061	−	8.51234i	−0.313130	−	0.489021i
$304$		0			0
$305$	9.45097	+	35.2715i	0.541161	+	2.01964i
$306$		0			0
$307$	16.2259	−	16.2259i	0.926063	−	0.926063i	−0.0713857	−	0.997449i	$-0.522742\pi$
$307$	16.2259	−	16.2259i	0.926063	−	0.926063i	0.997449	+	0.0713857i	$0.0227421\pi$
$308$		0			0
$309$	0.164904	+	3.58698i	0.00938104	+	0.204056i
$310$		0			0
$311$	32.8464			1.86255			0.931275	−	0.364317i	$-0.118697\pi$
$311$	32.8464			1.86255			0.931275	+	0.364317i	$0.118697\pi$
$312$		0			0
$313$	11.0629			0.625311			0.312655	−	0.949867i	$-0.398782\pi$
$313$	11.0629			0.625311			0.312655	+	0.949867i	$0.398782\pi$
$314$		0			0
$315$	27.0450	+	12.4597i	1.52381	+	0.702024i
$316$		0			0
$317$	17.5500	−	17.5500i	0.985704	−	0.985704i	−0.0141948	−	0.999899i	$-0.504519\pi$
$317$	17.5500	−	17.5500i	0.985704	−	0.985704i	0.999899	+	0.0141948i	$0.00451851\pi$
$318$		0			0
$319$	−0.893587	−	3.33491i	−0.0500313	−	0.186719i
$320$		0			0
$321$	5.04481	−	3.23029i	0.281574	−	0.180297i
$322$		0			0
$323$	0.389041	−	1.45192i	0.0216468	−	0.0807870i
$324$		0			0
$325$	34.8787	+	12.4090i	1.93472	+	0.688329i
$326$		0			0
$327$	−19.8895	−	18.1411i	−1.09989	−	1.00321i
$328$		0			0
$329$	9.89925	−	17.1460i	0.545763	−	0.945290i
$330$		0			0
$331$	−4.46639	+	1.19677i	−0.245495	+	0.0657803i	−0.379468	−	0.925205i	$-0.623893\pi$
$331$	−4.46639	+	1.19677i	−0.245495	+	0.0657803i	0.133973	+	0.990985i	$0.457226\pi$
$332$		0			0
$333$	−9.15090	−	1.57005i	−0.501466	−	0.0860380i
$334$		0			0
$335$	12.8970	+	22.3383i	0.704640	+	1.22047i
$336$		0			0
$337$			7.78436i			0.424041i	0.977265	+	0.212021i	$0.0680044\pi$
$337$			7.78436i			0.424041i	−0.977265	+	0.212021i	$0.931996\pi$
$338$		0			0
$339$	16.7618	+	8.67656i	0.910378	+	0.471246i
$340$		0			0
$341$	4.64007	−	2.67895i	0.251274	−	0.145073i
$342$		0			0
$343$	13.5564	+	13.5564i	0.731976	+	0.731976i
$344$		0			0
$345$	−11.5881	−	2.54098i	−0.623880	−	0.136802i
$346$		0			0
$347$	9.39077	+	5.42177i	0.504123	+	0.291056i	0.730415	−	0.683004i	$-0.239327\pi$
$347$	9.39077	+	5.42177i	0.504123	+	0.291056i	−0.226292	+	0.974060i	$0.572660\pi$
$348$		0			0
$349$	14.8487	+	3.97869i	0.794830	+	0.212974i	0.633313	−	0.773896i	$-0.281695\pi$
$349$	14.8487	+	3.97869i	0.794830	+	0.212974i	0.161517	+	0.986870i	$0.448361\pi$
$350$		0			0
$351$	−3.79531	+	18.3465i	−0.202579	+	0.979266i
$352$		0			0
$353$	1.80378	+	0.483321i	0.0960054	+	0.0257246i	0.306502	−	0.951870i	$-0.400841\pi$
$353$	1.80378	+	0.483321i	0.0960054	+	0.0257246i	−0.210497	+	0.977595i	$0.567508\pi$
$354$		0			0
$355$	2.87795	+	1.66158i	0.152745	+	0.0881876i
$356$		0			0
$357$	−4.70171	−	1.03097i	−0.248841	−	0.0545647i
$358$		0			0
$359$	−12.1336	−	12.1336i	−0.640387	−	0.640387i	0.310264	−	0.950650i	$-0.399583\pi$
$359$	−12.1336	−	12.1336i	−0.640387	−	0.640387i	−0.950650	+	0.310264i	$0.899583\pi$
$360$		0			0
$361$	−14.8196	+	8.55608i	−0.779978	+	0.450320i
$362$		0			0
$363$	16.3975	+	8.48796i	0.860645	+	0.445503i
$364$		0			0
$365$			28.6283i			1.49847i
$366$		0			0
$367$	−4.53141	−	7.84863i	−0.236538	−	0.409695i	0.723181	−	0.690659i	$-0.242679\pi$
$367$	−4.53141	−	7.84863i	−0.236538	−	0.409695i	−0.959718	+	0.280964i	$0.909346\pi$
$368$		0			0
$369$	15.6661	+	2.68788i	0.815546	+	0.139926i
$370$		0			0
$371$	7.46988	−	2.00155i	0.387817	−	0.103915i
$372$		0			0
$373$	3.78793	−	6.56090i	0.196132	−	0.339710i	−0.751139	−	0.660144i	$-0.770495\pi$
$373$	3.78793	−	6.56090i	0.196132	−	0.339710i	0.947271	+	0.320434i	$0.103829\pi$
$374$		0			0
$375$	−26.3394	−	24.0241i	−1.36016	−	1.24060i
$376$		0			0
$377$	−3.86103	−	21.0048i	−0.198853	−	1.08180i
$378$		0			0
$379$	−3.12578	+	11.6656i	−0.160561	+	0.599221i	0.838004	+	0.545664i	$0.183722\pi$
$379$	−3.12578	+	11.6656i	−0.160561	+	0.599221i	−0.998565	+	0.0535568i	$0.982944\pi$
$380$		0			0
$381$	−13.5847	+	8.69856i	−0.695967	+	0.445641i
$382$		0			0
$383$	9.53291	+	35.5773i	0.487109	+	1.81792i	0.570371	+	0.821387i	$0.306800\pi$
$383$	9.53291	+	35.5773i	0.487109	+	1.81792i	−0.0832617	+	0.996528i	$0.526534\pi$
$384$		0			0
$385$	−4.09094	+	4.09094i	−0.208494	+	0.208494i
$386$		0			0
$387$	−10.2662	−	4.72967i	−0.521862	−	0.240423i
$388$		0			0
$389$	−14.1012			−0.714961			−0.357481	−	0.933921i	$-0.616364\pi$
$389$	−14.1012			−0.714961			−0.357481	+	0.933921i	$0.616364\pi$
$390$		0			0
$391$	1.91770			0.0969820
$392$		0			0
$393$	0.0730070	+	1.58805i	0.00368272	+	0.0801064i
$394$		0			0
$395$	36.2189	−	36.2189i	1.82237	−	1.82237i
$396$		0			0
$397$	−2.03222	−	7.58436i	−0.101994	−	0.380648i	0.895992	−	0.444069i	$-0.146466\pi$
$397$	−2.03222	−	7.58436i	−0.101994	−	0.380648i	−0.997987	+	0.0634210i	$0.979799\pi$
$398$		0			0
$399$	−3.25989	−	5.09105i	−0.163199	−	0.254871i
$400$		0			0
$401$	5.65677	−	21.1113i	0.282485	−	1.05425i	−0.668172	−	0.744007i	$-0.732923\pi$
$401$	5.65677	−	21.1113i	0.282485	−	1.05425i	0.950657	−	0.310243i	$-0.100410\pi$
$402$		0			0
$403$	29.9351	−	14.2243i	1.49118	−	0.708561i
$404$		0			0
$405$	19.9039	−	28.9916i	0.989033	−	1.44060i
$406$		0			0
$407$	0.901965	−	1.56225i	0.0447088	−	0.0774378i
$408$		0			0
$409$	2.16512	−	0.580141i	0.107058	−	0.0286861i	−0.204892	−	0.978785i	$-0.565684\pi$
$409$	2.16512	−	0.580141i	0.107058	−	0.0286861i	0.311950	+	0.950098i	$0.399018\pi$
$410$		0			0
$411$	−14.2266	+	4.52173i	−0.701744	+	0.223041i
$412$		0			0
$413$	10.7694	+	18.6531i	0.529926	+	0.917860i
$414$		0			0
$415$			28.4800i			1.39803i
$416$		0			0
$417$	2.63809	−	5.09640i	0.129188	−	0.249572i
$418$		0			0
$419$	−28.9126	+	16.6927i	−1.41247	+	0.815491i	−0.995621	−	0.0934844i	$-0.970199\pi$
$419$	−28.9126	+	16.6927i	−1.41247	+	0.815491i	−0.416851	+	0.908975i	$0.636866\pi$
$420$		0			0
$421$	2.25285	+	2.25285i	0.109797	+	0.109797i	0.759871	−	0.650074i	$-0.225262\pi$
$421$	2.25285	+	2.25285i	0.109797	+	0.109797i	−0.650074	+	0.759871i	$0.725262\pi$
$422$		0			0
$423$	−17.9807	−	14.9467i	−0.874250	−	0.726734i
$424$		0			0
$425$	9.72786	+	5.61638i	0.471870	+	0.272435i
$426$		0			0
$427$	−22.9305	−	6.14422i	−1.10969	−	0.297339i
$428$		0			0
$429$	−3.08856	−	1.92636i	−0.149117	−	0.0930058i
$430$		0			0
$431$	−20.9452	−	5.61224i	−1.00889	−	0.270332i	−0.283727	−	0.958905i	$-0.591571\pi$
$431$	−20.9452	−	5.61224i	−1.00889	−	0.270332i	−0.725167	+	0.688573i	$0.758238\pi$
$432$		0			0
$433$	26.0258	+	15.0260i	1.25072	+	0.722103i	0.971252	−	0.238053i	$-0.0765091\pi$
$433$	26.0258	+	15.0260i	1.25072	+	0.722103i	0.279466	+	0.960155i	$0.409842\pi$
$434$		0			0
$435$	−8.58622	+	39.1573i	−0.411678	+	1.87745i
$436$		0			0
$437$	1.70306	+	1.70306i	0.0814682	+	0.0814682i
$438$		0			0
$439$	18.0531	−	10.4229i	0.861626	−	0.497460i	−0.00293019	−	0.999996i	$-0.500933\pi$
$439$	18.0531	−	10.4229i	0.861626	−	0.497460i	0.864557	+	0.502535i	$0.167599\pi$
$440$		0			0
$441$	1.34024	−	0.947691i	0.0638209	−	0.0451282i
$442$		0			0
$443$			13.0363i			0.619374i	0.950839	+	0.309687i	$0.100224\pi$
$443$			13.0363i			0.619374i	−0.950839	+	0.309687i	$0.899776\pi$
$444$		0			0
$445$	−18.9314	−	32.7901i	−0.897433	−	1.55440i
$446$		0			0
$447$	−4.12114	−	12.9662i	−0.194923	−	0.613281i
$448$		0			0
$449$	−18.3916	+	4.92801i	−0.867953	+	0.232567i	−0.665202	−	0.746663i	$-0.731655\pi$
$449$	−18.3916	+	4.92801i	−0.867953	+	0.232567i	−0.202750	+	0.979230i	$0.564988\pi$
$450$		0			0
$451$	−1.54414	+	2.67453i	−0.0727109	+	0.125939i
$452$		0			0
$453$	−16.9360	+	18.5682i	−0.795720	+	0.872409i
$454$		0			0
$455$	−27.2473	+	23.2021i	−1.27737	+	1.08773i
$456$		0			0
$457$	−5.50257	+	20.5359i	−0.257399	+	0.960627i	0.709341	+	0.704866i	$0.248993\pi$
$457$	−5.50257	+	20.5359i	−0.257399	+	0.960627i	−0.966740	+	0.255761i	$0.917674\pi$
$458$		0			0
$459$	−2.13900	+	5.26681i	−0.0998398	+	0.245834i
$460$		0			0
$461$	0.395195	+	1.47489i	0.0184061	+	0.0686924i	0.974518	−	0.224309i	$-0.0720125\pi$
$461$	0.395195	+	1.47489i	0.0184061	+	0.0686924i	−0.956112	+	0.293002i	$0.905346\pi$
$462$		0			0
$463$	21.3272	−	21.3272i	0.991159	−	0.991159i	−0.00880240	−	0.999961i	$-0.502802\pi$
$463$	21.3272	−	21.3272i	0.991159	−	0.991159i	0.999961	+	0.00880240i	$0.00280193\pi$
$464$		0			0
$465$	−62.1448	+	2.85697i	−2.88189	+	0.132489i
$466$		0			0
$467$	−11.2935			−0.522601			−0.261300	−	0.965258i	$-0.584151\pi$
$467$	−11.2935			−0.522601			−0.261300	+	0.965258i	$0.584151\pi$
$468$		0			0
$469$	−16.7691			−0.774326
$470$		0			0
$471$	−11.6193	+	0.534170i	−0.535387	+	0.0246133i
$472$		0			0
$473$	1.55291	−	1.55291i	0.0714031	−	0.0714031i
$474$		0			0
$475$	3.65130	+	13.6268i	0.167533	+	0.625241i
$476$		0			0
$477$	−0.837972	−	9.09451i	−0.0383681	−	0.416409i
$478$		0			0
$479$	7.52517	−	28.0843i	0.343834	−	1.28320i	−0.550135	−	0.835076i	$-0.685424\pi$
$479$	7.52517	−	28.0843i	0.343834	−	1.28320i	0.893969	−	0.448129i	$-0.147910\pi$
$480$		0			0
$481$	6.33390	−	9.18688i	0.288801	−	0.418885i
$482$		0			0
$483$	5.19740	−	5.69830i	0.236490	−	0.259282i
$484$		0			0
$485$	−1.19829	+	2.07551i	−0.0544118	+	0.0942440i
$486$		0			0
$487$	−2.44743	+	0.655786i	−0.110903	+	0.0297165i	−0.313844	−	0.949475i	$-0.601617\pi$
$487$	−2.44743	+	0.655786i	−0.110903	+	0.0297165i	0.202940	+	0.979191i	$0.434950\pi$
$488$		0			0
$489$	0.826137	+	2.59924i	0.0373592	+	0.117542i
$490$		0			0
$491$	−18.4575	−	31.9694i	−0.832978	−	1.44276i	−0.895667	−	0.444726i	$-0.853301\pi$
$491$	−18.4575	−	31.9694i	−0.832978	−	1.44276i	0.0626890	−	0.998033i	$-0.480032\pi$
$492$		0			0
$493$		−	6.48009i		−	0.291849i
$494$		0			0
$495$	3.94478	+	5.57877i	0.177305	+	0.250747i
$496$		0			0
$497$	−1.87100	+	1.08022i	−0.0839256	+	0.0484545i
$498$		0			0
$499$	−22.3461	−	22.3461i	−1.00035	−	1.00035i	−1.00000		0.000347536i	$-0.999889\pi$
$499$	−22.3461	−	22.3461i	−1.00035	−	1.00035i	−0.000347536	−	1.00000i	$-0.500111\pi$
$500$		0			0
$501$	9.06851	−	41.3567i	0.405151	−	1.84768i
$502$		0			0
$503$	−20.2177	−	11.6727i	−0.901464	−	0.520460i	−0.0237889	−	0.999717i	$-0.507573\pi$
$503$	−20.2177	−	11.6727i	−0.901464	−	0.520460i	−0.877675	+	0.479257i	$0.840906\pi$
$504$		0			0
$505$	−22.0256	−	5.90175i	−0.980128	−	0.262625i
$506$		0			0
$507$	−18.0916	−	13.4050i	−0.803477	−	0.595335i
$508$		0			0
$509$	−18.0113	−	4.82612i	−0.798338	−	0.213914i	−0.163484	−	0.986546i	$-0.552273\pi$
$509$	−18.0113	−	4.82612i	−0.798338	−	0.213914i	−0.634854	+	0.772632i	$0.718940\pi$
$510$		0			0
$511$	−16.1182	−	9.30585i	−0.713028	−	0.411667i
$512$		0			0
$513$	−6.57690	+	2.77773i	−0.290377	+	0.122640i
$514$		0			0
$515$	5.72793	+	5.72793i	0.252403	+	0.252403i
$516$		0			0
$517$	3.93427	−	2.27145i	0.173029	−	0.0998984i
$518$		0			0
$519$	−16.5355	+	31.9441i	−0.725827	+	1.40219i
$520$		0			0
$521$			20.1922i			0.884637i	0.896858	+	0.442318i	$0.145844\pi$
$521$			20.1922i			0.884637i	−0.896858	+	0.442318i	$0.854156\pi$
$522$		0			0
$523$	14.1118	+	24.4424i	0.617066	+	1.06879i	0.990018	+	0.140939i	$0.0450121\pi$
$523$	14.1118	+	24.4424i	0.617066	+	1.06879i	−0.372952	+	0.927850i	$0.621655\pi$
$524$		0			0
$525$	43.0534	−	13.6840i	1.87901	−	0.597218i
$526$		0			0
$527$	9.71355	−	2.60274i	0.423129	−	0.113377i
$528$		0			0
$529$	9.96363	−	17.2575i	0.433201	−	0.750327i
$530$		0			0
$531$	23.8626	−	8.81018i	1.03555	−	0.382329i
$532$		0			0
$533$	−10.8435	+	15.7277i	−0.469684	+	0.681243i
$534$		0			0
$535$	3.49765	−	13.0534i	0.151217	−	0.564349i
$536$		0			0
$537$	13.0763	+	20.4216i	0.564285	+	0.881256i
$538$		0			0
$539$	0.0825429	+	0.308054i	0.00355537	+	0.0132688i
$540$		0			0
$541$	−13.2334	+	13.2334i	−0.568947	+	0.568947i	−0.931833	−	0.362887i	$-0.881791\pi$
$541$	−13.2334	+	13.2334i	−0.568947	+	0.568947i	0.362887	+	0.931833i	$0.381791\pi$
$542$		0			0
$543$	2.03158	+	44.1908i	0.0871833	+	1.89641i
$544$		0			0
$545$	−60.7298			−2.60138
$546$		0			0
$547$	14.7212			0.629433			0.314717	−	0.949186i	$-0.398091\pi$
$547$	14.7212			0.629433			0.314717	+	0.949186i	$0.398091\pi$
$548$		0			0
$549$	−11.7311	+	25.4636i	−0.500673	+	1.08676i
$550$		0			0
$551$	5.75480	−	5.75480i	0.245163	−	0.245163i
$552$		0			0
$553$	8.61860	+	32.1651i	0.366500	+	1.36780i
$554$		0			0
$555$	−17.6392	+	11.2947i	−0.748741	+	0.479433i
$556$		0			0
$557$	−3.19111	+	11.9094i	−0.135212	+	0.504616i	0.864785	+	0.502142i	$0.167454\pi$
$557$	−3.19111	+	11.9094i	−0.135212	+	0.504616i	−0.999997	+	0.00247467i	$0.999212\pi$
$558$		0			0
$559$	10.3430	−	8.80748i	0.437464	−	0.372517i
$560$		0			0
$561$	−0.816022	−	0.744291i	−0.0344525	−	0.0314240i
$562$		0			0
$563$	−9.86628	+	17.0889i	−0.415814	+	0.720211i	−0.995514	−	0.0946194i	$-0.969837\pi$
$563$	−9.86628	+	17.0889i	−0.415814	+	0.720211i	0.579700	+	0.814830i	$0.303170\pi$
$564$		0			0
$565$	41.1283	−	11.0203i	1.73028	−	0.463628i
$566$		0			0
$567$	9.85280	+	20.6302i	0.413779	+	0.866385i
$568$		0			0
$569$	−17.4503	−	30.2248i	−0.731555	−	1.26709i	−0.956218	−	0.292654i	$-0.905462\pi$
$569$	−17.4503	−	30.2248i	−0.731555	−	1.26709i	0.224663	−	0.974436i	$-0.427872\pi$
$570$		0			0
$571$		−	2.37582i		−	0.0994248i	−0.998764	−	0.0497124i	$-0.984170\pi$
$571$		−	2.37582i		−	0.0994248i	0.998764	−	0.0497124i	$-0.0158305\pi$
$572$		0			0
$573$	36.3725	+	18.8278i	1.51948	+	0.786542i
$574$		0			0
$575$	−15.5870	+	8.99915i	−0.650022	+	0.375291i
$576$		0			0
$577$	3.78848	+	3.78848i	0.157716	+	0.157716i	0.781554	−	0.623838i	$-0.214427\pi$
$577$	3.78848	+	3.78848i	0.157716	+	0.157716i	−0.623838	+	0.781554i	$0.714427\pi$
$578$		0			0
$579$	17.9314	+	3.93191i	0.745202	+	0.163404i
$580$		0			0
$581$	−16.0347	−	9.25764i	−0.665232	−	0.384072i
$582$		0			0
$583$	1.71402	+	0.459269i	0.0709873	+	0.0190210i
$584$		0			0
$585$	21.5653	+	36.3490i	0.891615	+	1.50285i
$586$		0			0
$587$	−9.81579	−	2.63013i	−0.405141	−	0.108557i	0.0504929	−	0.998724i	$-0.483921\pi$
$587$	−9.81579	−	2.63013i	−0.405141	−	0.108557i	−0.455634	+	0.890167i	$0.650587\pi$
$588$		0			0
$589$	10.9378	+	6.31493i	0.450683	+	0.260202i
$590$		0			0
$591$	−5.86693	−	1.28647i	−0.241333	−	0.0529184i
$592$		0			0
$593$	−9.76893	−	9.76893i	−0.401162	−	0.401162i	0.477481	−	0.878642i	$-0.341550\pi$
$593$	−9.76893	−	9.76893i	−0.401162	−	0.401162i	−0.878642	+	0.477481i	$0.841550\pi$
$594$		0			0
$595$	−9.40393	+	5.42936i	−0.385523	+	0.222582i
$596$		0			0
$597$	4.74998	+	2.45877i	0.194404	+	0.100631i
$598$		0			0
$599$		−	35.2538i		−	1.44043i	−0.693750	−	0.720216i	$-0.744043\pi$
$599$		−	35.2538i		−	1.44043i	0.693750	−	0.720216i	$-0.255957\pi$
$600$		0			0
$601$	−4.57192	−	7.91880i	−0.186493	−	0.323015i	0.757586	−	0.652736i	$-0.226379\pi$
$601$	−4.57192	−	7.91880i	−0.186493	−	0.323015i	−0.944078	+	0.329721i	$0.893045\pi$
$602$		0			0
$603$	−3.34892	+	19.5189i	−0.136378	+	0.794872i
$604$		0			0
$605$	40.2343	−	10.7808i	1.63576	−	0.438300i
$606$		0			0
$607$	−9.96393	+	17.2580i	−0.404423	+	0.700482i	−0.994254	−	0.107045i	$-0.965861\pi$
$607$	−9.96393	+	17.2580i	−0.404423	+	0.700482i	0.589831	+	0.807527i	$0.299194\pi$
$608$		0			0
$609$	−19.2552	−	17.5625i	−0.780258	−	0.711670i
$610$		0			0
$611$	25.3817	−	12.0606i	1.02683	−	0.487920i
$612$		0			0
$613$	−3.88890	+	14.5136i	−0.157071	+	0.586198i	0.841848	+	0.539715i	$0.181468\pi$
$613$	−3.88890	+	14.5136i	−0.157071	+	0.586198i	−0.998919	+	0.0464829i	$0.985199\pi$
$614$		0			0
$615$	30.1978	−	19.3362i	1.21769	−	0.779712i
$616$		0			0
$617$	−2.63629	−	9.83876i	−0.106133	−	0.396094i	0.892338	−	0.451367i	$-0.149064\pi$
$617$	−2.63629	−	9.83876i	−0.106133	−	0.396094i	−0.998471	+	0.0552736i	$0.982397\pi$
$618$		0			0
$619$	−18.1131	+	18.1131i	−0.728027	+	0.728027i	−0.970226	−	0.242199i	$-0.922131\pi$
$619$	−18.1131	+	18.1131i	−0.728027	+	0.728027i	0.242199	+	0.970226i	$0.422131\pi$
$620$		0			0
$621$	−5.59475	−	7.18766i	−0.224510	−	0.288431i
$622$		0			0
$623$	24.6151			0.986185
$624$		0			0
$625$	−29.0857			−1.16343
$626$		0			0
$627$	−0.0637033	−	1.38567i	−0.00254406	−	0.0553385i
$628$		0			0
$629$	2.39412	−	2.39412i	0.0954596	−	0.0954596i
$630$		0			0
$631$	5.19785	+	19.3987i	0.206923	+	0.772248i	0.988855	+	0.148884i	$0.0475680\pi$
$631$	5.19785	+	19.3987i	0.206923	+	0.772248i	−0.781931	+	0.623364i	$0.785765\pi$
$632$		0			0
$633$	−4.63077	−	7.23198i	−0.184057	−	0.287445i
$634$		0			0
$635$	−9.41853	+	35.1504i	−0.373763	+	1.39490i
$636$		0			0
$637$	0.356653	+	1.94027i	0.0141311	+	0.0768763i
$638$		0			0
$639$	0.883703	+	2.39353i	0.0349587	+	0.0946866i
$640$		0			0
$641$	22.3417	−	38.6969i	0.882443	−	1.52844i	0.0338257	−	0.999428i	$-0.489231\pi$
$641$	22.3417	−	38.6969i	0.882443	−	1.52844i	0.848617	−	0.529008i	$-0.177436\pi$
$642$		0			0
$643$	−8.68244	+	2.32645i	−0.342402	+	0.0917463i	−0.425922	−	0.904760i	$-0.640050\pi$
$643$	−8.68244	+	2.32645i	−0.342402	+	0.0917463i	0.0835204	+	0.996506i	$0.473384\pi$
$644$		0			0
$645$	−24.3015	+	7.72393i	−0.956872	+	0.304130i
$646$		0			0
$647$	−18.9869	−	32.8862i	−0.746451	−	1.29289i	−0.949514	−	0.313725i	$-0.898423\pi$
$647$	−18.9869	−	32.8862i	−0.746451	−	1.29289i	0.203063	−	0.979166i	$-0.434910\pi$
$648$		0			0
$649$			4.94222i			0.193999i
$650$		0			0
$651$	18.5921	−	35.9172i	0.728682	−	1.40771i
$652$		0			0
$653$	−16.0116	+	9.24428i	−0.626581	+	0.361757i	−0.779427	−	0.626493i	$-0.784490\pi$
$653$	−16.0116	+	9.24428i	−0.626581	+	0.361757i	0.152846	+	0.988250i	$0.451156\pi$
$654$		0			0
$655$	2.53590	+	2.53590i	0.0990857	+	0.0990857i
$656$		0			0
$657$	−14.0508	+	16.9028i	−0.548172	+	0.659442i
$658$		0			0
$659$	0.644195	+	0.371926i	0.0250943	+	0.0144882i	0.512495	−	0.858690i	$-0.328721\pi$
$659$	0.644195	+	0.371926i	0.0250943	+	0.0144882i	−0.487400	+	0.873179i	$0.662055\pi$
$660$		0			0
$661$	27.0849	+	7.25737i	1.05348	+	0.282279i	0.743689	−	0.668526i	$-0.233075\pi$
$661$	27.0849	+	7.25737i	1.05348	+	0.282279i	0.309790	+	0.950805i	$0.399741\pi$
$662$		0			0
$663$	−4.66360	−	4.99274i	−0.181119	−	0.193902i
$664$		0			0
$665$	−13.1731	−	3.52971i	−0.510829	−	0.136876i
$666$		0			0
$667$	8.99201	+	5.19154i	0.348172	+	0.201017i
$668$		0			0
$669$	−7.07243	+	32.2537i	−0.273436	+	1.24700i
$670$		0			0
$671$	−3.85174	−	3.85174i	−0.148695	−	0.148695i
$672$		0			0
$673$	23.9347	−	13.8187i	0.922615	−	0.532672i	0.0381465	−	0.999272i	$-0.487855\pi$
$673$	23.9347	−	13.8187i	0.922615	−	0.532672i	0.884468	+	0.466600i	$0.154521\pi$
$674$		0			0
$675$	−7.32980	−	52.8461i	−0.282124	−	2.03405i
$676$		0			0
$677$		−	34.0927i		−	1.31029i	−0.755504	−	0.655145i	$-0.772608\pi$
$677$		−	34.0927i		−	1.31029i	0.755504	−	0.655145i	$-0.227392\pi$
$678$		0			0
$679$	−0.779030	−	1.34932i	−0.0298964	−	0.0517821i
$680$		0			0
$681$	−2.81223	−	8.84802i	−0.107765	−	0.339057i
$682$		0			0
$683$	−22.5100	+	6.03154i	−0.861322	+	0.230790i	−0.662331	−	0.749211i	$-0.730433\pi$
$683$	−22.5100	+	6.03154i	−0.861322	+	0.230790i	−0.198990	+	0.980001i	$0.563766\pi$
$684$		0			0
$685$	−16.8381	+	29.1644i	−0.643350	+	1.11431i
$686$		0			0
$687$	4.59609	−	5.03904i	0.175352	−	0.192251i
$688$		0			0
$689$	10.3415	+	3.67928i	0.393981	+	0.140169i
$690$		0			0
$691$	−2.64500	+	9.87128i	−0.100621	+	0.375521i	−0.997812	−	0.0661216i	$-0.978937\pi$
$691$	−2.64500	+	9.87128i	−0.100621	+	0.375521i	0.897191	+	0.441643i	$0.145604\pi$
$692$		0			0
$693$	−4.42322	+	0.407557i	−0.168024	+	0.0154818i
$694$		0			0
$695$	−3.35070	−	12.5050i	−0.127099	−	0.474341i
$696$		0			0
$697$	−4.09867	+	4.09867i	−0.155248	+	0.155248i
$698$		0			0
$699$	6.63822	−	0.305178i	0.251081	−	0.0115429i
$700$		0			0
$701$	31.9420			1.20643			0.603217	−	0.797577i	$-0.293885\pi$
$701$	31.9420			1.20643			0.603217	+	0.797577i	$0.293885\pi$
$702$		0			0
$703$	4.25230			0.160379
$704$		0			0
$705$	−52.6920	+	2.42240i	−1.98449	+	0.0912328i
$706$		0			0
$707$	10.4824	−	10.4824i	0.394231	−	0.394231i
$708$		0			0
$709$	1.92196	+	7.17283i	0.0721805	+	0.269381i	0.992579	−	0.121600i	$-0.0388024\pi$
$709$	1.92196	+	7.17283i	0.0721805	+	0.269381i	−0.920399	+	0.390981i	$0.872136\pi$
$710$		0			0
$711$	39.1607	−	3.60828i	1.46864	−	0.135321i
$712$		0			0
$713$	−4.17038	+	15.5641i	−0.156182	+	0.582879i
$714$		0			0
$715$	−8.07641	+	1.48458i	−0.302041	+	0.0555200i
$716$		0			0
$717$	−1.24053	+	1.36008i	−0.0463283	+	0.0507933i
$718$		0			0
$719$	−14.4593	+	25.0442i	−0.539240	+	0.933992i	0.459705	+	0.888072i	$0.347955\pi$
$719$	−14.4593	+	25.0442i	−0.539240	+	0.933992i	−0.998945	+	0.0459198i	$0.985378\pi$
$720$		0			0
$721$	−5.08682	+	1.36301i	−0.189443	+	0.0507612i
$722$		0			0
$723$	−14.6710	−	46.1589i	−0.545621	−	1.71667i
$724$		0			0
$725$	30.4091	+	52.6700i	1.12936	+	1.95612i
$726$		0			0
$727$		−	13.5518i		−	0.502608i	−0.967908	−	0.251304i	$-0.919141\pi$
$727$		−	13.5518i		−	0.502608i	0.967908	−	0.251304i	$-0.0808594\pi$
$728$		0			0
$729$	25.9808	−	7.34847i	0.962250	−	0.272166i
$730$		0			0
$731$	3.56971	−	2.06098i	0.132031	−	0.0762279i
$732$		0			0
$733$	−13.9665	−	13.9665i	−0.515864	−	0.515864i	0.400453	−	0.916317i	$-0.368853\pi$
$733$	−13.9665	−	13.9665i	−0.515864	−	0.515864i	−0.916317	+	0.400453i	$0.868853\pi$
$734$		0			0
$735$	0.793130	−	3.61705i	0.0292551	−	0.133417i
$736$		0			0
$737$	−3.33228	−	1.92390i	−0.122746	−	0.0708676i
$738$		0			0
$739$	1.90239	+	0.509744i	0.0699806	+	0.0187512i	0.293639	−	0.955916i	$-0.405133\pi$
$739$	1.90239	+	0.509744i	0.0699806	+	0.0187512i	−0.223659	+	0.974667i	$0.571800\pi$
$740$		0			0
$741$	0.292298	−	8.57554i	0.0107378	−	0.315030i
$742$		0			0
$743$	−5.78030	−	1.54883i	−0.212059	−	0.0568210i	0.151226	−	0.988499i	$-0.451678\pi$
$743$	−5.78030	−	1.54883i	−0.212059	−	0.0568210i	−0.363284	+	0.931678i	$0.618345\pi$
$744$		0			0
$745$	−26.5807	−	15.3464i	−0.973841	−	0.562247i
$746$		0			0
$747$	−13.9780	+	16.8153i	−0.511427	+	0.615238i
$748$		0			0
$749$	6.21235	+	6.21235i	0.226994	+	0.226994i
$750$		0			0
$751$	15.1590	−	8.75204i	0.553159	−	0.319366i	−0.197236	−	0.980356i	$-0.563197\pi$
$751$	15.1590	−	8.75204i	0.553159	−	0.319366i	0.750395	+	0.660990i	$0.229863\pi$
$752$		0			0
$753$	12.0440	−	23.2673i	0.438909	−	0.847906i
$754$		0			0
$755$			56.6953i			2.06335i
$756$		0			0
$757$	−4.00168	−	6.93111i	−0.145443	−	0.251915i	0.784095	−	0.620641i	$-0.213128\pi$
$757$	−4.00168	−	6.93111i	−0.145443	−	0.251915i	−0.929538	+	0.368726i	$0.879794\pi$
$758$		0			0
$759$	1.68656	−	0.536052i	0.0612183	−	0.0194575i
$760$		0			0
$761$	−18.9310	+	5.07254i	−0.686247	+	0.183879i	−0.585062	−	0.810988i	$-0.698930\pi$
$761$	−18.9310	+	5.07254i	−0.686247	+	0.183879i	−0.101185	+	0.994868i	$0.532263\pi$
$762$		0			0
$763$	19.7407	−	34.1918i	0.714660	−	1.23783i
$764$		0			0
$765$	4.44163	+	12.0303i	0.160588	+	0.434955i
$766$		0			0
$767$	−2.44349	+	30.4737i	−0.0882293	+	1.10034i
$768$		0			0
$769$	11.1131	−	41.4747i	0.400749	−	1.49561i	−0.411015	−	0.911629i	$-0.634826\pi$
$769$	11.1131	−	41.4747i	0.400749	−	1.49561i	0.811764	−	0.583986i	$-0.198508\pi$
$770$		0			0
$771$	−0.333625	−	0.521030i	−0.0120152	−	0.0187644i
$772$		0			0
$773$	2.39809	+	8.94981i	0.0862535	+	0.321902i	0.995549	−	0.0942495i	$-0.0300451\pi$
$773$	2.39809	+	8.94981i	0.0862535	+	0.321902i	−0.909295	+	0.416152i	$0.863378\pi$
$774$		0			0
$775$	−66.7377	+	66.7377i	−2.39729	+	2.39729i
$776$		0			0
$777$	−0.625348	−	13.6026i	−0.0224342	−	0.487989i
$778$		0			0
$779$	−7.27984			−0.260827
$780$		0			0
$781$	−0.495728			−0.0177385
$782$		0			0
$783$	−24.2878	+	18.9052i	−0.867977	+	0.675618i
$784$		0			0
$785$	−18.5544	+	18.5544i	−0.662235	+	0.662235i
$786$		0			0
$787$	11.0255	+	41.1479i	0.393018	+	1.46676i	0.825130	+	0.564943i	$0.191102\pi$
$787$	11.0255	+	41.1479i	0.393018	+	1.46676i	−0.432112	+	0.901820i	$0.642231\pi$
$788$		0			0
$789$	−3.13284	+	2.00601i	−0.111532	+	0.0714160i
$790$		0			0
$791$	−7.16447	+	26.7382i	−0.254739	+	0.950699i
$792$		0			0
$793$	−21.8454	−	25.6541i	−0.775754	−	0.911004i
$794$		0			0
$795$	−15.2225	−	13.8844i	−0.539888	−	0.492429i
$796$		0			0
$797$	10.5161	−	18.2144i	0.372499	−	0.645187i	−0.617450	−	0.786610i	$-0.711834\pi$
$797$	10.5161	−	18.2144i	0.372499	−	0.645187i	0.989949	+	0.141423i	$0.0451677\pi$
$798$		0			0
$799$	8.23603	−	2.20684i	0.291370	−	0.0780723i
$800$		0			0
$801$	4.91582	−	28.6515i	0.173692	−	1.01235i
$802$		0			0
$803$	−2.13529	−	3.69844i	−0.0753529	−	0.130515i
$804$		0			0
$805$		−	17.3990i		−	0.613233i
$806$		0			0
$807$	37.7218	+	19.5262i	1.32787	+	0.687356i
$808$		0			0
$809$	23.4871	−	13.5603i	0.825762	−	0.476754i	−0.0266373	−	0.999645i	$-0.508480\pi$
$809$	23.4871	−	13.5603i	0.825762	−	0.476754i	0.852399	+	0.522891i	$0.175147\pi$
$810$		0			0
$811$	−39.1597	−	39.1597i	−1.37508	−	1.37508i	−0.852726	−	0.522359i	$-0.825052\pi$
$811$	−39.1597	−	39.1597i	−1.37508	−	1.37508i	−0.522359	−	0.852726i	$-0.674948\pi$
$812$		0			0
$813$	37.0957	+	8.13417i	1.30100	+	0.285278i
$814$		0			0
$815$	5.32844	+	3.07638i	0.186647	+	0.107761i
$816$		0			0
$817$	5.00047	+	1.33987i	0.174944	+	0.0468762i
$818$		0			0
$819$	−27.4750	+	0.326104i	−0.960055	+	0.0113950i
$820$		0			0
$821$	8.30053	+	2.22412i	0.289690	+	0.0776223i	0.400738	−	0.916193i	$-0.368754\pi$
$821$	8.30053	+	2.22412i	0.289690	+	0.0776223i	−0.111047	+	0.993815i	$0.535421\pi$
$822$		0			0
$823$	7.37175	+	4.25608i	0.256963	+	0.148358i	0.622948	−	0.782263i	$-0.285935\pi$
$823$	7.37175	+	4.25608i	0.256963	+	0.148358i	−0.365985	+	0.930621i	$0.619268\pi$
$824$		0			0
$825$	10.1253	+	2.22024i	0.352519	+	0.0772987i
$826$		0			0
$827$	18.9976	+	18.9976i	0.660613	+	0.660613i	0.955524	−	0.294912i	$-0.0952903\pi$
$827$	18.9976	+	18.9976i	0.660613	+	0.660613i	−0.294912	+	0.955524i	$0.595290\pi$
$828$		0			0
$829$	14.3179	−	8.26645i	0.497282	−	0.287106i	−0.230309	−	0.973118i	$-0.573974\pi$
$829$	14.3179	−	8.26645i	0.497282	−	0.287106i	0.727590	+	0.686012i	$0.240640\pi$
$830$		0			0
$831$	−28.6877	−	14.8499i	−0.995167	−	0.515136i
$832$		0			0
$833$			0.598582i			0.0207396i
$834$		0			0
$835$	−47.7572	−	82.7179i	−1.65271	−	2.86257i
$836$		0			0
$837$	−38.0939	−	28.8138i	−1.31672	−	0.995950i
$838$		0			0
$839$	40.0647	−	10.7353i	1.38319	−	0.370623i	0.510908	−	0.859635i	$-0.329309\pi$
$839$	40.0647	−	10.7353i	1.38319	−	0.370623i	0.872277	+	0.489012i	$0.162643\pi$
$840$		0			0
$841$	3.04274	−	5.27017i	0.104922	−	0.181730i
$842$		0			0
$843$	−20.4109	−	18.6167i	−0.702989	−	0.641193i
$844$		0			0
$845$	−50.5331	+	5.16081i	−1.73839	+	0.177537i
$846$		0			0
$847$	−7.00873	+	26.1570i	−0.240823	+	0.898763i
$848$		0			0
$849$	−6.87770	+	4.40392i	−0.236042	+	0.151142i
$850$		0			0
$851$	1.40411	+	5.24021i	0.0481323	+	0.179632i
$852$		0			0
$853$	−13.7858	+	13.7858i	−0.472018	+	0.472018i	−0.902567	−	0.430549i	$-0.858320\pi$
$853$	−13.7858	+	13.7858i	−0.472018	+	0.472018i	0.430549	+	0.902567i	$0.358320\pi$
$854$		0			0
$855$	−6.73927	+	14.6283i	−0.230478	+	0.500276i
$856$		0			0
$857$	41.5499			1.41932			0.709659	−	0.704545i	$-0.248849\pi$
$857$	41.5499			1.41932			0.709659	+	0.704545i	$0.248849\pi$
$858$		0			0
$859$	−44.2270			−1.50900			−0.754502	−	0.656298i	$-0.772122\pi$
$859$	−44.2270			−1.50900			−0.754502	+	0.656298i	$0.772122\pi$
$860$		0			0
$861$	1.07058	+	23.2873i	0.0364853	+	0.793628i
$862$		0			0
$863$	14.7459	−	14.7459i	0.501956	−	0.501956i	−0.410089	−	0.912045i	$-0.634502\pi$
$863$	14.7459	−	14.7459i	0.501956	−	0.501956i	0.912045	+	0.410089i	$0.134502\pi$
$864$		0			0
$865$	21.0021	+	78.3809i	0.714093	+	2.66503i
$866$		0			0
$867$	14.7601	+	23.0512i	0.501280	+	0.782860i
$868$		0			0
$869$	−1.97760	+	7.38050i	−0.0670855	+	0.250366i
$870$		0			0
$871$	−19.5956	−	13.5102i	−0.663973	−	0.457777i
$872$		0			0
$873$	−1.72616	+	0.637306i	−0.0584216	+	0.0215695i
$874$		0			0
$875$	26.1424	−	45.2799i	0.883773	−	1.53074i
$876$		0			0
$877$	−43.6140	+	11.6863i	−1.47274	+	0.394620i	−0.903870	−	0.427808i	$-0.859286\pi$
$877$	−43.6140	+	11.6863i	−1.47274	+	0.394620i	−0.568870	+	0.822427i	$0.692619\pi$
$878$		0			0
$879$	35.2508	−	11.2040i	1.18898	−	0.377902i
$880$		0			0
$881$	−15.5665	−	26.9620i	−0.524448	−	0.908371i	−0.999595	−	0.0284646i	$-0.990938\pi$
$881$	−15.5665	−	26.9620i	−0.524448	−	0.908371i	0.475146	−	0.879907i	$-0.342395\pi$
$882$		0			0
$883$			45.7983i			1.54123i	0.637298	+	0.770617i	$0.280052\pi$
$883$			45.7983i			1.54123i	−0.637298	+	0.770617i	$0.719948\pi$
$884$		0			0
$885$	26.3795	−	50.9612i	0.886737	−	1.71304i
$886$		0			0
$887$	25.6110	−	14.7865i	0.859933	−	0.496482i	−0.00405708	−	0.999992i	$-0.501291\pi$
$887$	25.6110	−	14.7865i	0.859933	−	0.496482i	0.863990	+	0.503509i	$0.167958\pi$
$888$		0			0
$889$	−16.7287	−	16.7287i	−0.561062	−	0.561062i
$890$		0			0
$891$	−0.408961	+	5.22993i	−0.0137007	+	0.175209i
$892$		0			0
$893$	9.27404	+	5.35437i	0.310344	+	0.179177i
$894$		0			0
$895$	52.8407	+	14.1586i	1.76627	+	0.473271i
$896$		0			0
$897$	10.6644	−	2.47144i	0.356073	−	0.0825189i
$898$		0			0
$899$	52.5926	+	14.0921i	1.75406	+	0.469999i
$900$		0			0
$901$	2.88431	+	1.66526i	0.0960903	+	0.0554778i
$902$		0			0
$903$	3.55070	−	16.1929i	0.118160	−	0.538865i
$904$		0			0
$905$	70.5668	+	70.5668i	2.34572	+	2.34572i
$906$		0			0
$907$	50.3199	−	29.0522i	1.67085	−	0.964663i	0.703679	−	0.710518i	$-0.251539\pi$
$907$	50.3199	−	29.0522i	1.67085	−	0.964663i	0.967166	−	0.254145i	$-0.0817942\pi$
$908$		0			0
$909$	−10.1079	−	14.2947i	−0.335257	−	0.474125i
$910$		0			0
$911$		−	52.8673i		−	1.75157i	−0.482701	−	0.875785i	$-0.660344\pi$
$911$		−	52.8673i		−	1.75157i	0.482701	−	0.875785i	$-0.339656\pi$
$912$		0			0
$913$	−2.12423	−	3.67928i	−0.0703018	−	0.121766i
$914$		0			0
$915$	19.1579	+	60.2758i	0.633340	+	1.99266i
$916$		0			0
$917$	−2.25207	+	0.603439i	−0.0743697	+	0.0199273i
$918$		0			0
$919$	−3.07508	+	5.32620i	−0.101438	+	0.175695i	−0.912277	−	0.409573i	$-0.865678\pi$
$919$	−3.07508	+	5.32620i	−0.101438	+	0.175695i	0.810840	+	0.585269i	$0.199011\pi$
$920$		0			0
$921$	26.7838	−	29.3652i	0.882557	−	0.967615i
$922$		0			0
$923$	−3.05665	−	0.245094i	−0.100611	−	0.00806735i
$924$		0			0
$925$	−8.22447	+	30.6942i	−0.270419	+	1.00922i
$926$		0			0
$927$	0.570641	+	6.19317i	0.0187423	+	0.203410i
$928$		0			0
$929$	9.26432	+	34.5749i	0.303952	+	1.13437i	0.933843	+	0.357682i	$0.116433\pi$
$929$	9.26432	+	34.5749i	0.303952	+	1.13437i	−0.629891	+	0.776684i	$0.716900\pi$
$930$		0			0
$931$	−0.531585	+	0.531585i	−0.0174220	+	0.0174220i
$932$		0			0
$933$	56.8317	−	2.61271i	1.86059	−	0.0855363i
$934$		0			0
$935$	−2.49161			−0.0814844
$936$		0			0
$937$	−13.8585			−0.452737			−0.226369	−	0.974042i	$-0.572685\pi$
$937$	−13.8585			−0.452737			−0.226369	+	0.974042i	$0.572685\pi$
$938$		0			0
$939$	19.1412	−	0.879977i	0.624651	−	0.0287170i
$940$		0			0
$941$	10.8257	−	10.8257i	0.352908	−	0.352908i	−0.508283	−	0.861190i	$-0.669719\pi$
$941$	10.8257	−	10.8257i	0.352908	−	0.352908i	0.861190	+	0.508283i	$0.169719\pi$
$942$		0			0
$943$	−2.40380	−	8.97112i	−0.0782786	−	0.292140i
$944$		0			0
$945$	47.7850	+	19.4068i	1.55445	+	0.631303i
$946$		0			0
$947$	−5.50870	+	20.5588i	−0.179009	+	0.668070i	0.816825	+	0.576885i	$0.195732\pi$
$947$	−5.50870	+	20.5588i	−0.179009	+	0.668070i	−0.995834	+	0.0911846i	$0.970935\pi$
$948$		0			0
$949$	−11.3376	−	23.8602i	−0.368036	−	0.774536i
$950$		0			0
$951$	28.9694	−	31.7613i	0.939397	−	1.02993i
$952$		0			0
$953$	−10.3217	+	17.8776i	−0.334351	+	0.579114i	−0.983360	−	0.181667i	$-0.941851\pi$
$953$	−10.3217	+	17.8776i	−0.334351	+	0.579114i	0.649009	+	0.760781i	$0.275184\pi$
$954$		0			0
$955$	89.2468	−	23.9136i	2.88796	−	0.773826i
$956$		0			0
$957$	−1.81138	−	5.69907i	−0.0585535	−	0.184225i
$958$		0			0
$959$	−10.9467	−	18.9602i	−0.353487	−	0.612257i
$960$		0			0
$961$			53.4956i			1.72566i
$962$		0			0
$963$	8.47170	−	5.99040i	0.272997	−	0.193038i
$964$		0			0
$965$	35.8646	−	20.7065i	1.15452	−	0.666565i
$966$		0			0
$967$	3.56933	+	3.56933i	0.114782	+	0.114782i	0.762165	−	0.647383i	$-0.224137\pi$
$967$	3.56933	+	3.56933i	0.114782	+	0.114782i	−0.647383	+	0.762165i	$0.724137\pi$
$968$		0			0
$969$	0.557637	−	2.54309i	0.0179139	−	0.0816959i
$970$		0			0
$971$	−32.0913	−	18.5279i	−1.02986	−	0.594590i	−0.112916	−	0.993605i	$-0.536019\pi$
$971$	−32.0913	−	18.5279i	−1.02986	−	0.594590i	−0.916945	+	0.399014i	$0.869352\pi$
$972$		0			0
$973$	8.12969	+	2.17834i	0.260626	+	0.0698345i
$974$		0			0
$975$	61.3350	+	18.6960i	1.96429	+	0.598752i
$976$		0			0
$977$	−47.1501	−	12.6338i	−1.50847	−	0.404192i	−0.592540	−	0.805541i	$-0.701875\pi$
$977$	−47.1501	−	12.6338i	−1.50847	−	0.404192i	−0.915925	+	0.401349i	$0.868542\pi$
$978$		0			0
$979$	4.89141	+	2.82406i	0.156330	+	0.0902573i
$980$		0			0
$981$	−35.8563	−	29.8061i	−1.14480	−	0.951636i
$982$		0			0
$983$	33.9032	+	33.9032i	1.08134	+	1.08134i	0.996384	+	0.0849587i	$0.0270758\pi$
$983$	33.9032	+	33.9032i	1.08134	+	1.08134i	0.0849587	+	0.996384i	$0.472924\pi$
$984$		0			0
$985$	−11.7345	+	6.77491i	−0.373892	+	0.215867i
$986$		0			0
$987$	15.7641	−	30.4538i	0.501776	−	0.969357i
$988$		0			0
$989$			6.60462i			0.210015i
$990$		0			0
$991$	−24.3508	−	42.1768i	−0.773529	−	1.33979i	−0.935618	−	0.353015i	$-0.885156\pi$
$991$	−24.3508	−	42.1768i	−0.773529	−	1.33979i	0.162089	−	0.986776i	$-0.448177\pi$
$992$		0			0
$993$	−7.63267	+	2.42595i	−0.242215	+	0.0769850i
$994$		0			0
$995$	11.6550	−	3.12294i	0.369488	−	0.0990039i
$996$		0			0
$997$	2.76696	−	4.79252i	0.0876306	−	0.151781i	−0.818879	−	0.573967i	$-0.805404\pi$
$997$	2.76696	−	4.79252i	0.0876306	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$998$		0			0
$999$	−15.9580	−	1.98864i	−0.504889	−	0.0629178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.cn.d.401.4		16
3.2	odd	2	inner	624.2.cn.d.401.2		16
4.3	odd	2		78.2.k.a.11.1	✓	16
12.11	even	2		78.2.k.a.11.4	yes	16
13.6	odd	12	inner	624.2.cn.d.305.2		16
39.32	even	12	inner	624.2.cn.d.305.4		16
52.3	odd	6		1014.2.g.c.437.7		16
52.11	even	12		1014.2.g.d.239.7		16
52.15	even	12		1014.2.g.c.239.3		16
52.19	even	12		78.2.k.a.71.4	yes	16
52.23	odd	6		1014.2.g.d.437.3		16
156.11	odd	12		1014.2.g.d.239.3		16
156.23	even	6		1014.2.g.d.437.7		16
156.71	odd	12		78.2.k.a.71.1	yes	16
156.107	even	6		1014.2.g.c.437.3		16
156.119	odd	12		1014.2.g.c.239.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.11.1	✓	16	4.3	odd	2
78.2.k.a.11.4	yes	16	12.11	even	2
78.2.k.a.71.1	yes	16	156.71	odd	12
78.2.k.a.71.4	yes	16	52.19	even	12
624.2.cn.d.305.2		16	13.6	odd	12	inner
624.2.cn.d.305.4		16	39.32	even	12	inner
624.2.cn.d.401.2		16	3.2	odd	2	inner
624.2.cn.d.401.4		16	1.1	even	1	trivial
1014.2.g.c.239.3		16	52.15	even	12
1014.2.g.c.239.7		16	156.119	odd	12
1014.2.g.c.437.3		16	156.107	even	6
1014.2.g.c.437.7		16	52.3	odd	6
1014.2.g.d.239.3		16	156.11	odd	12
1014.2.g.d.239.7		16	52.11	even	12
1014.2.g.d.437.3		16	52.23	odd	6
1014.2.g.d.437.7		16	156.23	even	6

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.cn (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73022 - 0.0795432i) q^{3} +(2.76293 - 2.76293i) q^{5} +(0.657464 + 2.45369i) q^{7} +(2.98735 - 0.275255i) q^{9} +(-0.150860 + 0.563016i) q^{11} +(-1.20856 + 3.39697i) q^{13} +(4.56072 - 5.00027i) q^{15} +(-0.547000 + 0.947432i) q^{17} +(-1.32717 + 0.355613i) q^{19} +(1.33273 + 4.19313i) q^{21} +(-0.876460 - 1.51807i) q^{23} -10.2676i q^{25} +(5.14688 - 0.713876i) q^{27} +(-5.12973 + 2.96165i) q^{29} +(-6.49983 - 6.49983i) q^{31} +(-0.216237 + 0.986144i) q^{33} +(8.59591 + 4.96285i) q^{35} +(-2.98942 - 0.801012i) q^{37} +(-1.82088 + 5.97364i) q^{39} +(5.11781 + 1.37131i) q^{41} +(-3.26299 - 1.88389i) q^{43} +(7.49333 - 9.01435i) q^{45} +(-5.51114 - 5.51114i) q^{47} +(0.473846 - 0.273575i) q^{49} +(-0.871071 + 1.68278i) q^{51} -3.04435i q^{53} +(1.13876 + 1.97239i) q^{55} +(-2.26801 + 0.720857i) q^{57} +(8.19009 - 2.19453i) q^{59} +(-4.67266 + 8.09329i) q^{61} +(2.63946 + 7.14905i) q^{63} +(6.04642 + 12.7248i) q^{65} +(-1.70856 + 6.37644i) q^{67} +(-1.63722 - 2.55689i) q^{69} +(0.220122 + 0.821505i) q^{71} +(-5.18078 + 5.18078i) q^{73} +(-0.816719 - 17.7653i) q^{75} -1.48065 q^{77} +13.1089 q^{79} +(8.84847 - 1.64456i) q^{81} +(-5.15394 + 5.15394i) q^{83} +(1.10637 + 4.12902i) q^{85} +(-8.63999 + 5.53235i) q^{87} +(2.50797 - 9.35988i) q^{89} +(-9.12969 - 0.732051i) q^{91} +(-11.7632 - 10.7291i) q^{93} +(-2.68434 + 4.64941i) q^{95} +(-0.592450 + 0.158747i) q^{97} +(-0.295697 + 1.72345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{13} + 16 q^{19} - 24 q^{21} - 16 q^{31} - 24 q^{33} + 16 q^{37} - 48 q^{39} + 24 q^{45} + 24 q^{49} + 24 q^{55} - 24 q^{57} - 24 q^{61} + 24 q^{63} - 32 q^{67} - 48 q^{69} + 56 q^{73}+ \cdots + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^13 + 16 * q^19 - 24 * q^21 - 16 * q^31 - 24 * q^33 + 16 * q^37 - 48 * q^39 + 24 * q^45 + 24 * q^49 + 24 * q^55 - 24 * q^57 - 24 * q^61 + 24 * q^63 - 32 * q^67 - 48 * q^69 + 56 * q^73 + 96 * q^79 + 24 * q^81 - 24 * q^85 - 48 * q^87 + 16 * q^91 - 24 * q^93 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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