LMFDB - Embedded newform 882.2.v.a.251.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(125,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 1]))

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

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

chi := DirichletCharacter("882.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.v (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.11
Character	$\chi$	$=$	882.251
Dual form			882.2.v.a.629.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-1.69731 - 0.817383i) q^{5} +(0.171452 - 2.64019i) q^{7} +(-0.433884 + 0.900969i) q^{8} +O(q^{10})$	\(q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-1.69731 - 0.817383i) q^{5} +(0.171452 - 2.64019i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.817383 - 1.69731i) q^{10} +(2.06510 + 1.64686i) q^{11} +(-5.22262 - 4.16490i) q^{13} +(1.78018 - 1.95729i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(0.735353 - 3.22179i) q^{17} -2.04317i q^{19} +(0.419202 - 1.83664i) q^{20} +(0.587757 + 2.57513i) q^{22} +(3.23083 - 0.737415i) q^{23} +(-0.904693 - 1.13445i) q^{25} +(-1.48643 - 6.51250i) q^{26} +(2.61215 - 0.420344i) q^{28} +(-1.74858 - 0.399102i) q^{29} -4.79369i q^{31} +(-0.974928 - 0.222521i) q^{32} +(2.58368 - 2.06041i) q^{34} +(-2.44905 + 4.34109i) q^{35} +(0.420577 - 1.84267i) q^{37} +(1.27389 - 1.59741i) q^{38} +(1.47287 - 1.17458i) q^{40} +(-0.136573 - 0.0657703i) q^{41} +(6.10277 - 2.93894i) q^{43} +(-1.14604 + 2.37978i) q^{44} +(2.98573 + 1.43785i) q^{46} +(-1.66088 + 2.08267i) q^{47} +(-6.94121 - 0.905333i) q^{49} -1.45102i q^{50} +(2.89833 - 6.01845i) q^{52} +(6.00728 - 1.37112i) q^{53} +(-2.15900 - 4.48321i) q^{55} +(2.30434 + 1.30001i) q^{56} +(-1.11826 - 1.40225i) q^{58} +(1.93153 - 0.930175i) q^{59} +(3.64433 + 0.831796i) q^{61} +(2.98882 - 3.74786i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(5.46010 + 11.3380i) q^{65} -14.1616 q^{67} +3.30465 q^{68} +(-4.62137 + 1.86704i) q^{70} +(-7.79700 + 1.77961i) q^{71} +(2.54900 - 2.03276i) q^{73} +(1.47771 - 1.17843i) q^{74} +(1.99194 - 0.454648i) q^{76} +(4.70209 - 5.16989i) q^{77} +11.6218 q^{79} +1.88387 q^{80} +(-0.0657703 - 0.136573i) q^{82} +(7.36863 + 9.23997i) q^{83} +(-3.88156 + 4.86732i) q^{85} +(6.60373 + 1.50726i) q^{86} +(-2.37978 + 1.14604i) q^{88} +(5.52626 + 6.92971i) q^{89} +(-11.8915 + 13.0746i) q^{91} +(1.43785 + 2.98573i) q^{92} +(-2.59705 + 0.592760i) q^{94} +(-1.67005 + 3.46789i) q^{95} +12.7672i q^{97} +(-4.86239 - 5.03559i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 16 q^{4}+O(q^{10}) $ 96 * q + 16 * q^4	$ 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) $ 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{9}{14}\right)$	$-1$

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 $

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$		0			0
$3$		0			0
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	−1.69731	−	0.817383i	−0.759061	−	0.365545i	0.0139784	−	0.999902i	$-0.495550\pi$
$5$	−1.69731	−	0.817383i	−0.759061	−	0.365545i	−0.773040	+	0.634358i	$0.781265\pi$
$6$		0			0
$7$	0.171452	−	2.64019i	0.0648028	−	0.997898i
$7$	0.171452	−	2.64019i	0.0648028	−	0.997898i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$		0			0
$10$	−0.817383	−	1.69731i	−0.258479	−	0.536737i
$11$	2.06510	+	1.64686i	0.622650	+	0.496547i	0.883251	−	0.468900i	$-0.155349\pi$
$11$	2.06510	+	1.64686i	0.622650	+	0.496547i	−0.260601	+	0.965446i	$0.583921\pi$
$12$		0			0
$13$	−5.22262	−	4.16490i	−1.44849	−	1.15513i	−0.959099	−	0.283072i	$-0.908646\pi$
$13$	−5.22262	−	4.16490i	−1.44849	−	1.15513i	−0.489394	−	0.872063i	$-0.662782\pi$
$14$	1.78018	−	1.95729i	0.475773	−	0.523106i
$15$		0			0
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	0.735353	−	3.22179i	0.178349	−	0.781399i	−0.804043	−	0.594571i	$-0.797322\pi$
$17$	0.735353	−	3.22179i	0.178349	−	0.781399i	0.982393	−	0.186829i	$-0.0598209\pi$
$18$		0			0
$19$		−	2.04317i		−	0.468735i	−0.972148	−	0.234367i	$-0.924698\pi$
$19$		−	2.04317i		−	0.468735i	0.972148	−	0.234367i	$-0.0753019\pi$
$20$	0.419202	−	1.83664i	0.0937363	−	0.410686i
$21$		0			0
$22$	0.587757	+	2.57513i	0.125310	+	0.549020i
$23$	3.23083	−	0.737415i	0.673674	−	0.153762i	0.128019	−	0.991772i	$-0.459138\pi$
$23$	3.23083	−	0.737415i	0.673674	−	0.153762i	0.545655	+	0.838010i	$0.316281\pi$
$24$		0			0
$25$	−0.904693	−	1.13445i	−0.180939	−	0.226890i
$26$	−1.48643	−	6.51250i	−0.291514	−	1.27721i
$27$		0			0
$28$	2.61215	−	0.420344i	0.493649	−	0.0794376i
$29$	−1.74858	−	0.399102i	−0.324703	−	0.0741114i	0.0570622	−	0.998371i	$-0.481827\pi$
$29$	−1.74858	−	0.399102i	−0.324703	−	0.0741114i	−0.381766	+	0.924259i	$0.624684\pi$
$30$		0			0
$31$		−	4.79369i		−	0.860973i	−0.902597	−	0.430486i	$-0.858342\pi$
$31$		−	4.79369i		−	0.860973i	0.902597	−	0.430486i	$-0.141658\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$		0			0
$34$	2.58368	−	2.06041i	0.443097	−	0.353358i
$35$	−2.44905	+	4.34109i	−0.413966	+	0.733777i
$36$		0			0
$37$	0.420577	−	1.84267i	0.0691425	−	0.302933i	−0.928519	−	0.371286i	$-0.878917\pi$
$37$	0.420577	−	1.84267i	0.0691425	−	0.302933i	0.997661	+	0.0683524i	$0.0217742\pi$
$38$	1.27389	−	1.59741i	0.206653	−	0.259135i
$39$		0			0
$40$	1.47287	−	1.17458i	0.232882	−	0.185717i
$41$	−0.136573	−	0.0657703i	−0.0213292	−	0.0102716i	0.423189	−	0.906042i	$-0.360911\pi$
$41$	−0.136573	−	0.0657703i	−0.0213292	−	0.0102716i	−0.444518	+	0.895770i	$0.646625\pi$
$42$		0			0
$43$	6.10277	−	2.93894i	0.930663	−	0.448184i	0.0937971	−	0.995591i	$-0.470100\pi$
$43$	6.10277	−	2.93894i	0.930663	−	0.448184i	0.836866	+	0.547408i	$0.184385\pi$
$44$	−1.14604	+	2.37978i	−0.172772	+	0.358766i
$45$		0			0
$46$	2.98573	+	1.43785i	0.440222	+	0.212000i
$47$	−1.66088	+	2.08267i	−0.242264	+	0.303789i	−0.888066	−	0.459715i	$-0.847951\pi$
$47$	−1.66088	+	2.08267i	−0.242264	+	0.303789i	0.645803	+	0.763504i	$0.276523\pi$
$48$		0			0
$49$	−6.94121	−	0.905333i	−0.991601	−	0.129333i
$50$		−	1.45102i		−	0.205205i
$51$		0			0
$52$	2.89833	−	6.01845i	0.401927	−	0.834609i
$53$	6.00728	−	1.37112i	0.825164	−	0.188338i	0.210969	−	0.977493i	$-0.432338\pi$
$53$	6.00728	−	1.37112i	0.825164	−	0.188338i	0.614195	+	0.789154i	$0.289481\pi$
$54$		0			0
$55$	−2.15900	−	4.48321i	−0.291120	−	0.604516i
$56$	2.30434	+	1.30001i	0.307930	+	0.173721i
$57$		0			0
$58$	−1.11826	−	1.40225i	−0.146835	−	0.184125i
$59$	1.93153	−	0.930175i	0.251463	−	0.121098i	−0.303906	−	0.952702i	$-0.598291\pi$
$59$	1.93153	−	0.930175i	0.251463	−	0.121098i	0.555370	+	0.831603i	$0.312577\pi$
$60$		0			0
$61$	3.64433	+	0.831796i	0.466609	+	0.106501i	0.449360	−	0.893351i	$-0.351652\pi$
$61$	3.64433	+	0.831796i	0.466609	+	0.106501i	0.0172491	+	0.999851i	$0.494509\pi$
$62$	2.98882	−	3.74786i	0.379580	−	0.475979i
$63$		0			0
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	5.46010	+	11.3380i	0.677242	+	1.40631i
$66$		0			0
$67$	−14.1616			−1.73012			−0.865060	−	0.501668i	$-0.832720\pi$
$67$	−14.1616			−1.73012			−0.865060	+	0.501668i	$0.832720\pi$
$68$	3.30465			0.400747
$69$		0			0
$70$	−4.62137	+	1.86704i	−0.552359	+	0.223154i
$71$	−7.79700	+	1.77961i	−0.925334	+	0.211201i	−0.658534	−	0.752551i	$-0.728823\pi$
$71$	−7.79700	+	1.77961i	−0.925334	+	0.211201i	−0.266799	+	0.963752i	$0.585966\pi$
$72$		0			0
$73$	2.54900	−	2.03276i	0.298338	−	0.237917i	−0.462867	−	0.886428i	$-0.653179\pi$
$73$	2.54900	−	2.03276i	0.298338	−	0.237917i	0.761205	+	0.648511i	$0.224608\pi$
$74$	1.47771	−	1.17843i	0.171780	−	0.136990i
$75$		0			0
$76$	1.99194	−	0.454648i	0.228491	−	0.0521516i
$77$	4.70209	−	5.16989i	0.535853	−	0.589164i
$78$		0			0
$79$	11.6218			1.30756			0.653780	−	0.756685i	$-0.273182\pi$
$79$	11.6218			1.30756			0.653780	+	0.756685i	$0.273182\pi$
$80$	1.88387			0.210624
$81$		0			0
$82$	−0.0657703	−	0.136573i	−0.00726312	−	0.0150820i
$83$	7.36863	+	9.23997i	0.808813	+	1.01422i	0.999470	+	0.0325623i	$0.0103667\pi$
$83$	7.36863	+	9.23997i	0.808813	+	1.01422i	−0.190657	+	0.981657i	$0.561062\pi$
$84$		0			0
$85$	−3.88156	+	4.86732i	−0.421014	+	0.527935i
$86$	6.60373	+	1.50726i	0.712099	+	0.162532i
$87$		0			0
$88$	−2.37978	+	1.14604i	−0.253686	+	0.122169i
$89$	5.52626	+	6.92971i	0.585782	+	0.734548i	0.983087	−	0.183139i	$-0.0586258\pi$
$89$	5.52626	+	6.92971i	0.585782	+	0.734548i	−0.397305	+	0.917687i	$0.630054\pi$
$90$		0			0
$91$	−11.8915	+	13.0746i	−1.24657	+	1.37059i
$92$	1.43785	+	2.98573i	0.149906	+	0.311284i
$93$		0			0
$94$	−2.59705	+	0.592760i	−0.267865	+	0.0611385i
$95$	−1.67005	+	3.46789i	−0.171343	+	0.355798i
$96$		0			0
$97$			12.7672i			1.29631i	0.761507	+	0.648157i	$0.224460\pi$
$97$			12.7672i			1.29631i	−0.761507	+	0.648157i	$0.775540\pi$
$98$	−4.86239	−	5.03559i	−0.491176	−	0.508671i
$99$		0			0
$100$	0.904693	−	1.13445i	0.0904693	−	0.113445i
$101$	−12.9009	−	6.21277i	−1.28369	−	0.618194i	−0.337356	−	0.941377i	$-0.609533\pi$
$101$	−12.9009	−	6.21277i	−1.28369	−	0.618194i	−0.946336	+	0.323184i	$0.895247\pi$
$102$		0			0
$103$	4.70481	−	9.76964i	0.463579	−	0.962631i	−0.529841	−	0.848097i	$-0.677748\pi$
$103$	4.70481	−	9.76964i	0.463579	−	0.962631i	0.993419	−	0.114534i	$-0.0365375\pi$
$104$	6.01845	−	2.89833i	0.590158	−	0.284205i
$105$		0			0
$106$	5.55157	+	2.67349i	0.539216	+	0.259673i
$107$	−5.56823	+	4.44051i	−0.538301	+	0.429281i	−0.854530	−	0.519402i	$-0.826155\pi$
$107$	−5.56823	+	4.44051i	−0.538301	+	0.429281i	0.316229	+	0.948683i	$0.397583\pi$
$108$		0			0
$109$	−8.62256	+	10.8123i	−0.825891	+	1.03563i	0.172824	+	0.984953i	$0.444711\pi$
$109$	−8.62256	+	10.8123i	−0.825891	+	1.03563i	−0.998715	+	0.0506819i	$0.983861\pi$
$110$	1.10726	−	4.85123i	0.105573	−	0.462547i
$111$		0			0
$112$	0.991063	+	2.45312i	0.0936466	+	0.231798i
$113$	10.2418	−	8.16753i	0.963464	−	0.768337i	−0.00934265	−	0.999956i	$-0.502974\pi$
$113$	10.2418	−	8.16753i	0.963464	−	0.768337i	0.972806	+	0.231620i	$0.0744025\pi$
$114$		0			0
$115$	−6.08647	−	1.38920i	−0.567566	−	0.129543i
$116$		−	1.79355i		−	0.166527i
$117$		0			0
$118$	2.09008	+	0.477048i	0.192408	+	0.0439158i
$119$	−8.38007	−	2.49386i	−0.768199	−	0.228611i
$120$		0			0
$121$	−0.895252	−	3.92236i	−0.0813866	−	0.356578i
$122$	2.33064	+	2.92253i	0.211006	+	0.264593i
$123$		0			0
$124$	4.67351	−	1.06670i	0.419693	−	0.0957923i
$125$	2.70428	+	11.8482i	0.241878	+	1.05974i
$126$		0			0
$127$	1.06176	−	4.65188i	0.0942162	−	0.412788i	−0.905722	−	0.423871i	$-0.860671\pi$
$127$	1.06176	−	4.65188i	0.0942162	−	0.412788i	0.999939	+	0.0110833i	$0.00352801\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−2.80026	+	12.2687i	−0.245599	+	1.07604i
$131$	−19.6343	+	9.45536i	−1.71545	+	0.826119i	−0.724923	+	0.688830i	$0.758124\pi$
$131$	−19.6343	+	9.45536i	−1.71545	+	0.826119i	−0.990531	+	0.137288i	$0.956161\pi$
$132$		0			0
$133$	−5.39435	−	0.350305i	−0.467750	−	0.0303753i
$134$	−11.0720	−	8.82964i	−0.956477	−	0.762765i
$135$		0			0
$136$	2.58368	+	2.06041i	0.221548	+	0.176679i
$137$	0.188777	+	0.392000i	0.0161283	+	0.0334908i	0.908877	−	0.417063i	$-0.136941\pi$
$137$	0.188777	+	0.392000i	0.0161283	+	0.0334908i	−0.892749	+	0.450554i	$0.851226\pi$
$138$		0			0
$139$	−2.57918	+	5.35573i	−0.218763	+	0.454267i	−0.981251	−	0.192736i	$-0.938264\pi$
$139$	−2.57918	+	5.35573i	−0.218763	+	0.454267i	0.762487	+	0.647003i	$0.223978\pi$
$140$	−4.77721	−	1.42167i	−0.403748	−	0.120153i
$141$		0			0
$142$	−7.20551	−	3.46999i	−0.604673	−	0.291195i
$143$	−3.92621	−	17.2018i	−0.328326	−	1.43849i
$144$		0			0
$145$	2.64167	+	2.10666i	0.219379	+	0.174949i
$146$	3.26030			0.269824
$147$		0			0
$148$	1.89006			0.155362
$149$	13.4799	+	10.7499i	1.10432	+	0.880662i	0.993574	−	0.113187i	$-0.0361060\pi$
$149$	13.4799	+	10.7499i	1.10432	+	0.880662i	0.110742	+	0.993849i	$0.464677\pi$
$150$		0			0
$151$	−1.31783	−	5.77381i	−0.107244	−	0.469866i	−0.999820	−	0.0189694i	$-0.993961\pi$
$151$	−1.31783	−	5.77381i	−0.107244	−	0.469866i	0.892576	−	0.450897i	$-0.148896\pi$
$152$	1.84083	+	0.886497i	0.149311	+	0.0719044i
$153$		0			0
$154$	6.89962	−	1.11028i	0.555987	−	0.0894689i
$155$	−3.91828	+	8.13640i	−0.314724	+	0.653531i
$156$		0			0
$157$	−7.13757	−	14.8213i	−0.569640	−	1.18287i	−0.964489	−	0.264124i	$-0.914917\pi$
$157$	−7.13757	−	14.8213i	−0.569640	−	1.18287i	0.394848	−	0.918746i	$-0.370797\pi$
$158$	9.08632	+	7.24610i	0.722869	+	0.576469i
$159$		0			0
$160$	1.47287	+	1.17458i	0.116441	+	0.0928585i
$161$	−1.39298	−	8.65642i	−0.109782	−	0.682222i
$162$		0			0
$163$	10.1720	−	4.89857i	0.796731	−	0.383685i	0.00919776	−	0.999958i	$-0.497072\pi$
$163$	10.1720	−	4.89857i	0.796731	−	0.383685i	0.787533	+	0.616272i	$0.211358\pi$
$164$	0.0337309	−	0.147785i	0.00263394	−	0.0115400i
$165$		0			0
$166$			11.8184i			0.917283i
$167$	4.02106	−	17.6174i	0.311159	−	1.36327i	−0.541454	−	0.840731i	$-0.682126\pi$
$167$	4.02106	−	17.6174i	0.311159	−	1.36327i	0.852612	−	0.522544i	$-0.175017\pi$
$168$		0			0
$169$	7.03658	+	30.8293i	0.541275	+	2.37148i
$170$	−6.06945	+	1.38531i	−0.465506	+	0.106249i
$171$		0			0
$172$	4.22325	+	5.29578i	0.322019	+	0.403800i
$173$	2.41967	+	10.6013i	0.183964	+	0.806000i	0.979718	+	0.200380i	$0.0642177\pi$
$173$	2.41967	+	10.6013i	0.183964	+	0.806000i	−0.795754	+	0.605620i	$0.792925\pi$
$174$		0			0
$175$	−3.15027	+	2.19406i	−0.238138	+	0.165855i
$176$	−2.57513	−	0.587757i	−0.194108	−	0.0443039i
$177$		0			0
$178$			8.86343i			0.664342i
$179$	−24.4159	−	5.57277i	−1.82493	−	0.416528i	−0.834096	−	0.551619i	$-0.814010\pi$
$179$	−24.4159	−	5.57277i	−1.82493	−	0.416528i	−0.990833	+	0.135091i	$0.956867\pi$
$180$		0			0
$181$	15.1411	−	12.0746i	1.12543	−	0.897500i	0.129860	−	0.991532i	$-0.458547\pi$
$181$	15.1411	−	12.0746i	1.12543	−	0.897500i	0.995569	+	0.0940321i	$0.0299756\pi$
$182$	−17.4491	+	2.80789i	−1.29341	+	0.208135i
$183$		0			0
$184$	−0.737415	+	3.23083i	−0.0543629	+	0.238180i
$185$	−2.22002	+	2.78382i	−0.163219	+	0.204670i
$186$		0			0
$187$	6.82442	−	5.44229i	0.499051	−	0.397980i
$188$	−2.40004	−	1.15580i	−0.175041	−	0.0842952i
$189$		0			0
$190$	−3.46789	+	1.67005i	−0.251587	+	0.121158i
$191$	−1.46526	+	3.04263i	−0.106022	+	0.220157i	−0.947230	−	0.320555i	$-0.896131\pi$
$191$	−1.46526	+	3.04263i	−0.106022	+	0.220157i	0.841208	+	0.540712i	$0.181845\pi$
$192$		0			0
$193$	18.8347	+	9.07034i	1.35575	+	0.652897i	0.963686	−	0.267039i	$-0.0860451\pi$
$193$	18.8347	+	9.07034i	1.35575	+	0.652897i	0.392069	+	0.919936i	$0.371759\pi$
$194$	−7.96022	+	9.98180i	−0.571511	+	0.716652i
$195$		0			0
$196$	−0.661930	−	6.96863i	−0.0472807	−	0.497760i
$197$		−	7.18826i		−	0.512143i	−0.966658	−	0.256071i	$-0.917572\pi$
$197$		−	7.18826i		−	0.512143i	0.966658	−	0.256071i	$-0.0824282\pi$
$198$		0			0
$199$	1.19321	−	2.47773i	0.0845846	−	0.175642i	−0.854386	−	0.519639i	$-0.826067\pi$
$199$	1.19321	−	2.47773i	0.0845846	−	0.175642i	0.938971	+	0.343997i	$0.111781\pi$
$200$	1.41464	−	0.322881i	0.100030	−	0.0228312i
$201$		0			0
$202$	−6.21277	−	12.9009i	−0.437129	−	0.907707i
$203$	−1.35350	+	4.54816i	−0.0949974	+	0.319218i
$204$		0			0
$205$	0.178048	+	0.223266i	0.0124354	+	0.0155935i
$206$	9.76964	−	4.70481i	0.680683	−	0.327800i
$207$		0			0
$208$	6.51250	+	1.48643i	0.451560	+	0.103066i
$209$	3.36481	−	4.21934i	0.232749	−	0.291858i
$210$		0			0
$211$	16.2448	+	20.3703i	1.11834	+	1.40235i	0.905020	+	0.425369i	$0.139856\pi$
$211$	16.2448	+	20.3703i	1.11834	+	1.40235i	0.213318	+	0.976983i	$0.431573\pi$
$212$	2.67349	+	5.55157i	0.183616	+	0.381283i
$213$		0			0
$214$	−7.12203			−0.486852
$215$	−12.7605			−0.870262
$216$		0			0
$217$	−12.6563	−	0.821889i	−0.859163	−	0.0557935i
$218$	−13.4828	+	3.07735i	−0.913168	+	0.208425i
$219$		0			0
$220$	3.89038	−	3.10248i	0.262290	−	0.209169i
$221$	−17.2589	+	13.7635i	−1.16096	+	0.925834i
$222$		0			0
$223$	11.7123	−	2.67326i	0.784316	−	0.179015i	0.188433	−	0.982086i	$-0.439659\pi$
$223$	11.7123	−	2.67326i	0.784316	−	0.179015i	0.595883	+	0.803071i	$0.296802\pi$
$224$	−0.754651	+	2.53584i	−0.0504222	+	0.169433i
$225$		0			0
$226$	13.0997			0.871379
$227$	23.4479			1.55629			0.778145	−	0.628085i	$-0.216161\pi$
$227$	23.4479			1.55629			0.778145	+	0.628085i	$0.216161\pi$
$228$		0			0
$229$	4.74045	+	9.84365i	0.313258	+	0.650486i	0.996844	−	0.0793831i	$-0.0252951\pi$
$229$	4.74045	+	9.84365i	0.313258	+	0.650486i	−0.683586	+	0.729870i	$0.739581\pi$
$230$	−3.89244	−	4.88097i	−0.256660	−	0.321842i
$231$		0			0
$232$	1.11826	−	1.40225i	0.0734173	−	0.0920624i
$233$	−17.9773	−	4.10321i	−1.17773	−	0.268810i	−0.411523	−	0.911399i	$-0.635003\pi$
$233$	−17.9773	−	4.10321i	−1.17773	−	0.268810i	−0.766211	+	0.642589i	$0.777860\pi$
$234$		0			0
$235$	4.52137	−	2.17738i	0.294942	−	0.142036i
$236$	1.33666	+	1.67612i	0.0870091	+	0.109106i
$237$		0			0
$238$	−4.99691	−	7.17466i	−0.323901	−	0.465064i
$239$	−4.46095	−	9.26325i	−0.288555	−	0.599190i	0.705421	−	0.708788i	$-0.250758\pi$
$239$	−4.46095	−	9.26325i	−0.288555	−	0.599190i	−0.993976	+	0.109598i	$0.965044\pi$
$240$		0			0
$241$	−5.32831	+	1.21615i	−0.343226	+	0.0783392i	−0.390660	−	0.920535i	$-0.627753\pi$
$241$	−5.32831	+	1.21615i	−0.343226	+	0.0783392i	0.0474331	+	0.998874i	$0.484896\pi$
$242$	1.74561	−	3.62480i	0.112212	−	0.233011i
$243$		0			0
$244$			3.73806i			0.239304i
$245$	11.0414	+	7.21026i	0.705409	+	0.460646i
$246$		0			0
$247$	−8.50958	+	10.6707i	−0.541452	+	0.678959i
$248$	4.31897	+	2.07991i	0.274255	+	0.132074i
$249$		0			0
$250$	−5.27295	+	10.9494i	−0.333491	+	0.692500i
$251$	15.1532	−	7.29738i	0.956460	−	0.460607i	0.110513	−	0.993875i	$-0.464750\pi$
$251$	15.1532	−	7.29738i	0.956460	−	0.460607i	0.845946	+	0.533268i	$0.179036\pi$
$252$		0			0
$253$	7.88639	+	3.79788i	0.495813	+	0.238771i
$254$	3.73052	−	2.97499i	0.234074	−	0.186668i
$255$		0			0
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	−3.93998	+	17.2622i	−0.245769	+	1.07678i	0.689900	+	0.723905i	$0.257655\pi$
$257$	−3.93998	+	17.2622i	−0.245769	+	1.07678i	−0.935669	+	0.352880i	$0.885202\pi$
$258$		0			0
$259$	−4.79289	−	1.42633i	−0.297816	−	0.0886281i
$260$	−9.83876	+	7.84615i	−0.610174	+	0.486597i
$261$		0			0
$262$	−21.2460	−	4.84926i	−1.31258	−	0.299588i
$263$		−	27.8009i		−	1.71428i	−0.515087	−	0.857138i	$-0.672241\pi$
$263$		−	27.8009i		−	1.71428i	0.515087	−	0.857138i	$-0.327759\pi$
$264$		0			0
$265$	−11.3170	−	2.58303i	−0.695196	−	0.158674i
$266$	−3.99906	−	3.63720i	−0.245198	−	0.223011i
$267$		0			0
$268$	−3.15126	−	13.8066i	−0.192494	−	0.843371i
$269$	−11.8493	−	14.8585i	−0.722464	−	0.905941i	0.276011	−	0.961155i	$-0.410987\pi$
$269$	−11.8493	−	14.8585i	−0.722464	−	0.905941i	−0.998475	+	0.0552135i	$0.982416\pi$
$270$		0			0
$271$	−1.26150	+	0.287929i	−0.0766307	+	0.0174905i	−0.260664	−	0.965429i	$-0.583942\pi$
$271$	−1.26150	+	0.287929i	−0.0766307	+	0.0174905i	0.184034	+	0.982920i	$0.441084\pi$
$272$	0.735353	+	3.22179i	0.0445873	+	0.195350i
$273$		0			0
$274$	−0.0968160	+	0.424179i	−0.00584887	+	0.0256256i
$275$		−	3.83265i		−	0.231118i
$276$		0			0
$277$	−5.29806	+	23.2123i	−0.318330	+	1.39469i	0.522151	+	0.852853i	$0.325130\pi$
$277$	−5.29806	+	23.2123i	−0.318330	+	1.39469i	−0.840481	+	0.541841i	$0.817727\pi$
$278$	−5.35573	+	2.57918i	−0.321215	+	0.154689i
$279$		0			0
$280$	−2.84858	−	4.09005i	−0.170235	−	0.244427i
$281$	25.4781	+	20.3181i	1.51990	+	1.21208i	0.906430	+	0.422355i	$0.138796\pi$
$281$	25.4781	+	20.3181i	1.51990	+	1.21208i	0.613466	+	0.789721i	$0.289775\pi$
$282$		0			0
$283$	−4.26144	−	3.39838i	−0.253316	−	0.202013i	0.488596	−	0.872510i	$-0.337509\pi$
$283$	−4.26144	−	3.39838i	−0.253316	−	0.202013i	−0.741912	+	0.670497i	$0.766081\pi$
$284$	−3.46999	−	7.20551i	−0.205906	−	0.427569i
$285$		0			0
$286$	7.65554	−	15.8969i	0.452681	−	0.940002i
$287$	−0.197062	+	0.349303i	−0.0116322	+	0.0206187i
$288$		0			0
$289$	5.47727	+	2.63771i	0.322192	+	0.155160i
$290$	0.751859	+	3.29411i	0.0441507	+	0.193437i
$291$		0			0
$292$	2.54900	+	2.03276i	0.149169	+	0.118958i
$293$	1.06781			0.0623820			0.0311910	−	0.999513i	$-0.490070\pi$
$293$	1.06781			0.0623820			0.0311910	+	0.999513i	$0.490070\pi$
$294$		0			0
$295$	−4.03871			−0.235143
$296$	1.47771	+	1.17843i	0.0858900	+	0.0684950i
$297$		0			0
$298$	3.83658	+	16.8091i	0.222247	+	0.973728i
$299$	−19.9446	−	9.60482i	−1.15343	−	0.555461i
$300$		0			0
$301$	−6.71302	−	16.6164i	−0.386932	−	0.957751i
$302$	2.56959	−	5.33580i	0.147863	−	0.307041i
$303$		0			0
$304$	0.886497	+	1.84083i	0.0508441	+	0.105579i
$305$	−5.50568	−	4.39063i	−0.315254	−	0.251407i
$306$		0			0
$307$	−8.39700	−	6.69638i	−0.479242	−	0.382183i	0.353863	−	0.935297i	$-0.384868\pi$
$307$	−8.39700	−	6.69638i	−0.479242	−	0.382183i	−0.833105	+	0.553114i	$0.813439\pi$
$308$	6.08658	+	3.43379i	0.346815	+	0.195658i
$309$		0			0
$310$	−8.13640	+	3.91828i	−0.462116	+	0.222544i
$311$	−0.991746	+	4.34512i	−0.0562367	+	0.246389i	−0.995231	−	0.0975426i	$-0.968902\pi$
$311$	−0.991746	+	4.34512i	−0.0562367	+	0.246389i	0.938995	+	0.343932i	$0.111759\pi$
$312$		0			0
$313$			6.26631i			0.354193i	0.984194	+	0.177096i	$0.0566705\pi$
$313$			6.26631i			0.354193i	−0.984194	+	0.177096i	$0.943330\pi$
$314$	3.66056	−	16.0380i	0.206578	−	0.905076i
$315$		0			0
$316$	2.58610	+	11.3305i	0.145480	+	0.637388i
$317$	14.1450	−	3.22851i	0.794464	−	0.181331i	0.194020	−	0.980998i	$-0.437847\pi$
$317$	14.1450	−	3.22851i	0.794464	−	0.181331i	0.600444	+	0.799666i	$0.294990\pi$
$318$		0			0
$319$	−2.95372	−	3.70385i	−0.165377	−	0.207376i
$320$	0.419202	+	1.83664i	0.0234341	+	0.102671i
$321$		0			0
$322$	4.30811	−	7.63638i	0.240082	−	0.425559i
$323$	−6.58266	−	1.50245i	−0.366269	−	0.0835985i
$324$		0			0
$325$			9.69275i			0.537657i
$326$	11.0070	+	2.51227i	0.609620	+	0.139142i
$327$		0			0
$328$	0.118514	−	0.0945118i	0.00654384	−	0.00521854i
$329$	5.21389	+	4.74211i	0.287451	+	0.261441i
$330$		0			0
$331$	2.52404	−	11.0585i	0.138734	−	0.607832i	−0.856980	−	0.515349i	$-0.827662\pi$
$331$	2.52404	−	11.0585i	0.138734	−	0.607832i	0.995714	−	0.0924834i	$-0.0294805\pi$
$332$	−7.36863	+	9.23997i	−0.404406	+	0.507109i
$333$		0			0
$334$	14.1281	−	11.2667i	0.773053	−	0.616489i
$335$	24.0367	+	11.5755i	1.31327	+	0.632436i
$336$		0			0
$337$	−6.74819	+	3.24976i	−0.367597	+	0.177026i	−0.608558	−	0.793509i	$-0.708252\pi$
$337$	−6.74819	+	3.24976i	−0.367597	+	0.177026i	0.240961	+	0.970535i	$0.422537\pi$
$338$	−13.7203	+	28.4905i	−0.746286	+	1.54968i
$339$		0			0
$340$	−5.60902	−	2.70116i	−0.304192	−	0.146491i
$341$	7.89454	−	9.89944i	0.427513	−	0.536085i
$342$		0			0
$343$	−3.58034	+	18.1709i	−0.193320	+	0.981136i
$344$			6.77356i			0.365206i
$345$		0			0
$346$	−4.71801	+	9.79706i	−0.253642	+	0.526693i
$347$	−18.7087	+	4.27013i	−1.00433	+	0.229232i	−0.692898	−	0.721035i	$-0.743667\pi$
$347$	−18.7087	+	4.27013i	−1.00433	+	0.229232i	−0.311435	+	0.950268i	$0.600809\pi$
$348$		0			0
$349$	−5.55847	−	11.5423i	−0.297538	−	0.617845i	0.697583	−	0.716504i	$-0.254259\pi$
$349$	−5.55847	−	11.5423i	−0.297538	−	0.617845i	−0.995121	+	0.0986594i	$0.968545\pi$
$350$	−3.83096	−	0.248780i	−0.204773	−	0.0132978i
$351$		0			0
$352$	−1.64686	−	2.06510i	−0.0877779	−	0.110070i
$353$	22.3728	−	10.7742i	1.19079	−	0.573452i	0.269750	−	0.962930i	$-0.413059\pi$
$353$	22.3728	−	10.7742i	1.19079	−	0.573452i	0.921036	+	0.389478i	$0.127345\pi$
$354$		0			0
$355$	14.6886	+	3.35257i	0.779589	+	0.177936i
$356$	−5.52626	+	6.92971i	−0.292891	+	0.367274i
$357$		0			0
$358$	−15.6145	−	19.5800i	−0.825255	−	1.03484i
$359$	−9.68905	−	20.1195i	−0.511368	−	1.06187i	−0.983595	−	0.180390i	$-0.942264\pi$
$359$	−9.68905	−	20.1195i	−0.511368	−	1.06187i	0.472227	−	0.881477i	$-0.343450\pi$
$360$		0			0
$361$	14.8255			0.780288
$362$	19.3662			1.01787
$363$		0			0
$364$	−15.3929	−	8.68403i	−0.806809	−	0.455167i
$365$	−5.98800	+	1.36672i	−0.313426	+	0.0715375i
$366$		0			0
$367$	20.7799	−	16.5714i	1.08470	−	0.865023i	0.0932712	−	0.995641i	$-0.470268\pi$
$367$	20.7799	−	16.5714i	1.08470	−	0.865023i	0.991433	+	0.130618i	$0.0416962\pi$
$368$	−2.59092	+	2.06619i	−0.135061	+	0.107708i
$369$		0			0
$370$	−3.47136	+	0.792315i	−0.180467	+	0.0411905i
$371$	−2.59006	−	16.0955i	−0.134469	−	0.835634i
$372$		0			0
$373$	29.7093			1.53829			0.769144	−	0.639076i	$-0.220683\pi$
$373$	29.7093			1.53829			0.769144	+	0.639076i	$0.220683\pi$
$374$	8.72876			0.451353
$375$		0			0
$376$	−1.15580	−	2.40004i	−0.0596057	−	0.123772i
$377$	7.46995	+	9.36702i	0.384722	+	0.482426i
$378$		0			0
$379$	14.4808	−	18.1583i	0.743827	−	0.932730i	−0.255593	−	0.966784i	$-0.582271\pi$
$379$	14.4808	−	18.1583i	0.743827	−	0.932730i	0.999420	+	0.0340549i	$0.0108421\pi$
$380$	−3.75257	−	0.856499i	−0.192503	−	0.0439375i
$381$		0			0
$382$	−3.04263	+	1.46526i	−0.155675	+	0.0749690i
$383$	10.3372	+	12.9624i	0.528205	+	0.662348i	0.972329	−	0.233618i	$-0.0750564\pi$
$383$	10.3372	+	12.9624i	0.528205	+	0.662348i	−0.444124	+	0.895965i	$0.646485\pi$
$384$		0			0
$385$	−12.2067	+	4.93152i	−0.622111	+	0.251333i
$386$	9.07034	+	18.8347i	0.461668	+	0.958663i
$387$		0			0
$388$	−12.4471	+	2.84097i	−0.631906	+	0.144228i
$389$	6.61072	−	13.7273i	0.335177	−	0.696002i	−0.663459	−	0.748213i	$-0.730912\pi$
$389$	6.61072	−	13.7273i	0.335177	−	0.696002i	0.998636	+	0.0522103i	$0.0166266\pi$
$390$		0			0
$391$		−	10.9513i		−	0.553832i
$392$	3.82735	−	5.86100i	0.193311	−	0.296025i
$393$		0			0
$394$	4.48181	−	5.62001i	0.225790	−	0.283132i
$395$	−19.7259	−	9.49949i	−0.992518	−	0.477971i
$396$		0			0
$397$	10.8242	−	22.4768i	0.543253	−	1.12808i	−0.430944	−	0.902379i	$-0.641819\pi$
$397$	10.8242	−	22.4768i	0.543253	−	1.12808i	0.974197	−	0.225698i	$-0.0724662\pi$
$398$	2.47773	−	1.19321i	0.124197	−	0.0598104i
$399$		0			0
$400$	1.30732	+	0.629572i	0.0653660	+	0.0314786i
$401$	21.9522	−	17.5063i	1.09624	−	0.874223i	0.103516	−	0.994628i	$-0.466991\pi$
$401$	21.9522	−	17.5063i	1.09624	−	0.874223i	0.992725	+	0.120405i	$0.0384193\pi$
$402$		0			0
$403$	−19.9652	+	25.0356i	−0.994540	+	1.24711i
$404$	3.18627	−	13.9600i	0.158523	−	0.694534i
$405$		0			0
$406$	−3.89394	+	2.71200i	−0.193253	+	0.134594i
$407$	3.90315	−	3.11266i	0.193472	−	0.154289i
$408$		0			0
$409$	−23.9696	−	5.47091i	−1.18522	−	0.270519i	−0.415918	−	0.909402i	$-0.636540\pi$
$409$	−23.9696	−	5.47091i	−1.18522	−	0.270519i	−0.769304	+	0.638883i	$0.779397\pi$
$410$			0.285567i			0.0141032i
$411$		0			0
$412$	10.5716	+	2.41290i	0.520826	+	0.118875i
$413$	−2.12467	−	5.25908i	−0.104548	−	0.258782i
$414$		0			0
$415$	−4.95428	−	21.7061i	−0.243196	−	1.06551i
$416$	4.16490	+	5.22262i	0.204201	+	0.256060i
$417$		0			0
$418$	5.26143	−	1.20089i	0.257345	−	0.0587373i
$419$	1.08517	+	4.75443i	0.0530139	+	0.232269i	0.994493	−	0.104802i	$-0.0334209\pi$
$419$	1.08517	+	4.75443i	0.0530139	+	0.232269i	−0.941479	+	0.337071i	$0.890564\pi$
$420$		0			0
$421$	−4.40679	+	19.3074i	−0.214774	+	0.940986i	0.746499	+	0.665387i	$0.231733\pi$
$421$	−4.40679	+	19.3074i	−0.214774	+	0.940986i	−0.961273	+	0.275599i	$0.911124\pi$
$422$			26.0546i			1.26832i
$423$		0			0
$424$	−1.37112	+	6.00728i	−0.0665876	+	0.291740i
$425$	−4.32023	+	2.08051i	−0.209562	+	0.100920i
$426$		0			0
$427$	2.82093	−	9.47912i	0.136514	−	0.458727i
$428$	−5.56823	−	4.44051i	−0.269150	−	0.214640i
$429$		0			0
$430$	−9.97659	−	7.95607i	−0.481114	−	0.383676i
$431$	−7.90717	−	16.4194i	−0.380875	−	0.790895i	−0.999984	−	0.00559044i	$-0.998220\pi$
$431$	−7.90717	−	16.4194i	−0.380875	−	0.790895i	0.619109	−	0.785305i	$-0.287494\pi$
$432$		0			0
$433$	13.4578	−	27.9453i	0.646739	−	1.34297i	−0.277343	−	0.960771i	$-0.589454\pi$
$433$	13.4578	−	27.9453i	0.646739	−	1.34297i	0.924081	−	0.382196i	$-0.124832\pi$
$434$	−9.38263	−	8.53363i	−0.450381	−	0.409627i
$435$		0			0
$436$	−12.4600	−	6.00040i	−0.596724	−	0.287367i
$437$	−1.50666	−	6.60112i	−0.0720734	−	0.315774i
$438$		0			0
$439$	−1.98774	−	1.58517i	−0.0948695	−	0.0756559i	0.574906	−	0.818219i	$-0.305038\pi$
$439$	−1.98774	−	1.58517i	−0.0948695	−	0.0756559i	−0.669776	+	0.742563i	$0.733610\pi$
$440$	4.97599			0.237221
$441$		0			0
$442$	−22.0750			−1.05000
$443$	20.3916	+	16.2618i	0.968836	+	0.772621i	0.973809	−	0.227367i	$-0.0730117\pi$
$443$	20.3916	+	16.2618i	0.968836	+	0.772621i	−0.00497340	+	0.999988i	$0.501583\pi$
$444$		0			0
$445$	−3.71556	−	16.2790i	−0.176135	−	0.771696i
$446$	10.8238	+	5.21248i	0.512523	+	0.246818i
$447$		0			0
$448$	−2.17108	+	1.51208i	−0.102574	+	0.0714393i
$449$	15.2742	−	31.7172i	0.720833	−	1.49683i	−0.141203	−	0.989981i	$-0.545097\pi$
$449$	15.2742	−	31.7172i	0.720833	−	1.49683i	0.862037	−	0.506846i	$-0.169189\pi$
$450$		0			0
$451$	−0.173723	−	0.360739i	−0.00818030	−	0.0169866i
$452$	10.2418	+	8.16753i	0.481732	+	0.384168i
$453$		0			0
$454$	18.3323	+	14.6195i	0.860376	+	0.686127i
$455$	30.8706	−	12.4718i	1.44724	−	0.584686i
$456$		0			0
$457$	24.3646	−	11.7334i	1.13973	−	0.548864i	0.233795	−	0.972286i	$-0.424886\pi$
$457$	24.3646	−	11.7334i	1.13973	−	0.548864i	0.905933	+	0.423422i	$0.139171\pi$
$458$	−2.43118	+	10.6517i	−0.113602	+	0.497721i
$459$		0			0
$460$		−	6.24300i		−	0.291081i
$461$	−6.22238	+	27.2620i	−0.289805	+	1.26972i	0.594988	+	0.803735i	$0.297157\pi$
$461$	−6.22238	+	27.2620i	−0.289805	+	1.26972i	−0.884793	+	0.465985i	$0.845700\pi$
$462$		0			0
$463$	0.736568	+	3.22712i	0.0342312	+	0.149977i	0.989155	−	0.146873i	$-0.0469210\pi$
$463$	0.736568	+	3.22712i	0.0342312	+	0.149977i	−0.954924	+	0.296850i	$0.904064\pi$
$464$	1.74858	−	0.399102i	0.0811758	−	0.0185279i
$465$		0			0
$466$	−11.4969	−	14.4167i	−0.532585	−	0.667841i
$467$	9.02483	+	39.5404i	0.417619	+	1.82971i	0.545744	+	0.837952i	$0.316247\pi$
$467$	9.02483	+	39.5404i	0.417619	+	1.82971i	−0.128125	+	0.991758i	$0.540896\pi$
$468$		0			0
$469$	−2.42804	+	37.3894i	−0.112117	+	1.72648i
$470$	4.89252	+	1.11669i	0.225675	+	0.0515089i
$471$		0			0
$472$			2.14383i			0.0986780i
$473$	17.4428	+	3.98121i	0.802022	+	0.183056i
$474$		0			0
$475$	−2.31787	+	1.84844i	−0.106351	+	0.0848122i
$476$	0.566589	−	8.72490i	0.0259696	−	0.399905i
$477$		0			0
$478$	2.28783	−	10.0237i	0.104643	−	0.458471i
$479$	5.01845	−	6.29293i	0.229299	−	0.287532i	−0.653850	−	0.756624i	$-0.726847\pi$
$479$	5.01845	−	6.29293i	0.229299	−	0.287532i	0.883149	+	0.469092i	$0.155419\pi$
$480$		0			0
$481$	−9.87105	+	7.87190i	−0.450081	+	0.358928i
$482$	−4.92410	−	2.37132i	−0.224286	−	0.108011i
$483$		0			0
$484$	3.62480	−	1.74561i	0.164764	−	0.0793460i
$485$	10.4357	−	21.6699i	0.473860	−	0.983981i
$486$		0			0
$487$	−12.7338	−	6.13229i	−0.577025	−	0.277880i	0.122524	−	0.992466i	$-0.460901\pi$
$487$	−12.7338	−	6.13229i	−0.577025	−	0.277880i	−0.699548	+	0.714585i	$0.746615\pi$
$488$	−2.33064	+	2.92253i	−0.105503	+	0.132297i
$489$		0			0
$490$	4.13699	+	12.5214i	0.186890	+	0.565659i
$491$		−	1.14449i		−	0.0516500i	−0.999666	−	0.0258250i	$-0.991779\pi$
$491$		−	1.14449i		−	0.0516500i	0.999666	−	0.0258250i	$-0.00822127\pi$
$492$		0			0
$493$	−2.57165	+	5.34008i	−0.115821	+	0.240505i
$494$	−13.3061	+	3.03703i	−0.598671	+	0.136643i
$495$		0			0
$496$	2.07991	+	4.31897i	0.0933905	+	0.193927i
$497$	3.36171	+	20.8907i	0.150793	+	0.937075i
$498$		0			0
$499$	0.982570	+	1.23210i	0.0439859	+	0.0551566i	0.803338	−	0.595524i	$-0.203055\pi$
$499$	0.982570	+	1.23210i	0.0439859	+	0.0551566i	−0.759352	+	0.650680i	$0.774484\pi$
$500$	−10.9494	+	5.27295i	−0.489672	+	0.235813i
$501$		0			0
$502$	16.3971	+	3.74252i	0.731837	+	0.167037i
$503$	−16.5559	+	20.7604i	−0.738190	+	0.925662i	−0.999213	−	0.0396712i	$-0.987369\pi$
$503$	−16.5559	+	20.7604i	−0.738190	+	0.925662i	0.261022	+	0.965333i	$0.415940\pi$
$504$		0			0
$505$	16.8187	+	21.0900i	0.748424	+	0.938494i
$506$	3.79788	+	7.88639i	0.168837	+	0.350593i
$507$		0			0
$508$	4.77152			0.211702
$509$	42.2374			1.87214			0.936070	−	0.351814i	$-0.114435\pi$
$509$	42.2374			1.87214			0.936070	+	0.351814i	$0.114435\pi$
$510$		0			0
$511$	−4.92984	−	7.07837i	−0.218083	−	0.313129i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$		0			0
$514$	−13.8432	+	11.0396i	−0.610597	+	0.486935i
$515$	−15.9711	+	12.7365i	−0.703769	+	0.561237i
$516$		0			0
$517$	−6.85974	+	1.56569i	−0.301691	+	0.0688591i
$518$	−2.85793	−	4.10347i	−0.125570	−	0.180296i
$519$		0			0
$520$	−12.5842			−0.551855
$521$	18.2136			0.797954			0.398977	−	0.916961i	$-0.369365\pi$
$521$	18.2136			0.797954			0.398977	+	0.916961i	$0.369365\pi$
$522$		0			0
$523$	0.549532	+	1.14111i	0.0240293	+	0.0498974i	0.912638	−	0.408769i	$-0.134042\pi$
$523$	0.549532	+	1.14111i	0.0240293	+	0.0498974i	−0.888609	+	0.458666i	$0.848327\pi$
$524$	−13.5873	−	17.0380i	−0.593565	−	0.744307i
$525$		0			0
$526$	17.3336	−	21.7356i	0.755779	−	0.947717i
$527$	−15.4443	−	3.52506i	−0.672764	−	0.153554i
$528$		0			0
$529$	−10.8278	+	5.21441i	−0.470775	+	0.226713i
$530$	−7.23748	−	9.07551i	−0.314376	−	0.394215i
$531$		0			0
$532$	−0.858833	−	5.33705i	−0.0372351	−	0.231391i
$533$	0.439344	+	0.912308i	0.0190301	+	0.0395164i
$534$		0			0
$535$	13.0806	−	2.98557i	0.565525	−	0.129077i
$536$	6.14451	−	12.7592i	0.265402	−	0.551114i
$537$		0			0
$538$		−	19.0048i		−	0.819354i
$539$	−12.8433	−	13.3008i	−0.553201	−	0.572906i
$540$		0			0
$541$	4.54319	−	5.69698i	0.195327	−	0.244932i	−0.674517	−	0.738259i	$-0.735648\pi$
$541$	4.54319	−	5.69698i	0.195327	−	0.244932i	0.869844	+	0.493327i	$0.164219\pi$
$542$	−1.16580	−	0.561420i	−0.0500755	−	0.0241151i
$543$		0			0
$544$	−1.43383	+	2.97738i	−0.0614751	+	0.127654i
$545$	23.4730	−	11.3040i	1.00547	−	0.484210i
$546$		0			0
$547$	−36.4975	−	17.5763i	−1.56052	−	0.751507i	−0.563317	−	0.826241i	$-0.690475\pi$
$547$	−36.4975	−	17.5763i	−1.56052	−	0.751507i	−0.997203	+	0.0747341i	$0.976189\pi$
$548$	−0.340165	+	0.271272i	−0.0145311	+	0.0115882i
$549$		0			0
$550$	2.38962	−	2.99649i	0.101894	−	0.127771i
$551$	−0.815433	+	3.57264i	−0.0347386	+	0.152200i
$552$		0			0
$553$	1.99259	−	30.6839i	0.0847336	−	1.30481i
$554$	−18.6148	+	14.8448i	−0.790869	+	0.630697i
$555$		0			0
$556$	−5.79537	−	1.32276i	−0.245779	−	0.0560973i
$557$			24.8003i			1.05082i	0.850848	+	0.525411i	$0.176089\pi$
$557$			24.8003i			1.05082i	−0.850848	+	0.525411i	$0.823911\pi$
$558$		0			0
$559$	−44.1128	−	10.0685i	−1.86577	−	0.425850i
$560$	0.322994	−	4.97379i	0.0136490	−	0.210181i
$561$		0			0
$562$	7.25145	+	31.7707i	0.305884	+	1.34016i
$563$	10.5903	+	13.2798i	0.446327	+	0.559677i	0.953199	−	0.302345i	$-0.0977694\pi$
$563$	10.5903	+	13.2798i	0.446327	+	0.559677i	−0.506871	+	0.862022i	$0.669198\pi$
$564$		0			0
$565$	−24.0595	+	5.49142i	−1.01219	+	0.231026i
$566$	−1.21287	−	5.31392i	−0.0509807	−	0.223361i
$567$		0			0
$568$	1.77961	−	7.79700i	0.0746710	−	0.327155i
$569$		−	20.1193i		−	0.843444i	−0.906725	−	0.421722i	$-0.861426\pi$
$569$		−	20.1193i		−	0.843444i	0.906725	−	0.421722i	$-0.138574\pi$
$570$		0			0
$571$	8.74302	−	38.3057i	0.365884	−	1.60304i	−0.372079	−	0.928201i	$-0.621355\pi$
$571$	8.74302	−	38.3057i	0.365884	−	1.60304i	0.737963	−	0.674841i	$-0.235788\pi$
$572$	15.8969	−	7.65554i	0.664682	−	0.320094i
$573$		0			0
$574$	−0.371856	+	0.150230i	−0.0155210	+	0.00627049i
$575$	−3.75947	−	2.99807i	−0.156781	−	0.125028i
$576$		0			0
$577$	2.58632	+	2.06252i	0.107670	+	0.0858638i	0.675845	−	0.737044i	$-0.263779\pi$
$577$	2.58632	+	2.06252i	0.107670	+	0.0858638i	−0.568175	+	0.822908i	$0.692350\pi$
$578$	2.63771	+	5.47727i	0.109714	+	0.227824i
$579$		0			0
$580$	−1.46602	+	3.04421i	−0.0608730	+	0.126404i
$581$	25.6587	−	17.8704i	1.06450	−	0.741388i
$582$		0			0
$583$	14.6637	+	7.06165i	0.607307	+	0.292464i
$584$	0.725484	+	3.17855i	0.0300207	+	0.131529i
$585$		0			0
$586$	0.834846	+	0.665768i	0.0344872	+	0.0275026i
$587$	−30.5917			−1.26266			−0.631328	−	0.775516i	$-0.717490\pi$
$587$	−30.5917			−1.26266			−0.631328	+	0.775516i	$0.717490\pi$
$588$		0			0
$589$	−9.79432			−0.403568
$590$	−3.15759	−	2.51810i	−0.129996	−	0.103668i
$591$		0			0
$592$	0.420577	+	1.84267i	0.0172856	+	0.0757333i
$593$	−19.0204	−	9.15974i	−0.781074	−	0.376145i	0.000466654	−	1.00000i	$-0.499851\pi$
$593$	−19.0204	−	9.15974i	−0.781074	−	0.376145i	−0.781540	+	0.623855i	$0.785566\pi$
$594$		0			0
$595$	12.1852	+	11.0826i	0.499543	+	0.454341i
$596$	−7.48077	+	15.5340i	−0.306424	+	0.636297i
$597$		0			0
$598$	−9.60482	−	19.9446i	−0.392770	−	0.815596i
$599$	−4.86047	−	3.87610i	−0.198594	−	0.158373i	0.519144	−	0.854687i	$-0.326251\pi$
$599$	−4.86047	−	3.87610i	−0.198594	−	0.158373i	−0.717738	+	0.696314i	$0.754822\pi$
$600$		0			0
$601$	21.9011	+	17.4655i	0.893363	+	0.712433i	0.958394	−	0.285450i	$-0.0921430\pi$
$601$	21.9011	+	17.4655i	0.893363	+	0.712433i	−0.0650304	+	0.997883i	$0.520714\pi$
$602$	5.11167	−	17.1767i	0.208336	−	0.700070i
$603$		0			0
$604$	5.33580	−	2.56959i	0.217111	−	0.104555i
$605$	−1.68654	+	7.38923i	−0.0685677	+	0.300415i
$606$		0			0
$607$			14.9005i			0.604791i	0.953183	+	0.302396i	$0.0977864\pi$
$607$			14.9005i			0.604791i	−0.953183	+	0.302396i	$0.902214\pi$
$608$	−0.454648	+	1.99194i	−0.0184384	+	0.0807839i
$609$		0			0
$610$	−1.56700	−	6.86547i	−0.0634459	−	0.277975i
$611$	17.3482	−	3.95962i	0.701835	−	0.160189i
$612$		0			0
$613$	−6.17856	−	7.74767i	−0.249550	−	0.312926i	0.641241	−	0.767340i	$-0.278420\pi$
$613$	−6.17856	−	7.74767i	−0.249550	−	0.312926i	−0.890791	+	0.454414i	$0.849849\pi$
$614$	−2.38991	−	10.4709i	−0.0964490	−	0.422571i
$615$		0			0
$616$	2.61775	+	6.47957i	0.105472	+	0.261069i
$617$	−18.3734	−	4.19360i	−0.739684	−	0.168828i	−0.163954	−	0.986468i	$-0.552425\pi$
$617$	−18.3734	−	4.19360i	−0.739684	−	0.168828i	−0.575730	+	0.817640i	$0.695282\pi$
$618$		0			0
$619$		−	16.3919i		−	0.658847i	−0.944182	−	0.329423i	$-0.893146\pi$
$619$		−	16.3919i		−	0.658847i	0.944182	−	0.329423i	$-0.106854\pi$
$620$	−8.80430	−	2.00952i	−0.353589	−	0.0807044i
$621$		0			0
$622$	−3.48452	+	2.77881i	−0.139716	+	0.111420i
$623$	19.2432	−	13.4023i	0.770964	−	0.536950i
$624$		0			0
$625$	3.48011	−	15.2474i	0.139204	−	0.609895i
$626$	−3.90698	+	4.89920i	−0.156154	+	0.195811i
$627$		0			0
$628$	12.8615	−	10.2567i	0.513228	−	0.409286i
$629$	−5.62743	−	2.71003i	−0.224380	−	0.108056i
$630$		0			0
$631$	12.1525	−	5.85233i	0.483783	−	0.232978i	−0.176062	−	0.984379i	$-0.556336\pi$
$631$	12.1525	−	5.85233i	0.483783	−	0.232978i	0.659845	+	0.751401i	$0.270622\pi$
$632$	−5.04253	+	10.4709i	−0.200581	+	0.416511i
$633$		0			0
$634$	13.0720	+	6.29513i	0.519154	+	0.250012i
$635$	−5.60451	+	7.02784i	−0.222408	+	0.278891i
$636$		0			0
$637$	32.4806	+	33.6376i	1.28693	+	1.33277i
$638$		−	4.73741i		−	0.187556i
$639$		0			0
$640$	−0.817383	+	1.69731i	−0.0323099	+	0.0670922i
$641$	−22.6727	+	5.17490i	−0.895518	+	0.204396i	−0.645423	−	0.763825i	$-0.723319\pi$
$641$	−22.6727	+	5.17490i	−0.895518	+	0.204396i	−0.250095	+	0.968221i	$0.580462\pi$
$642$		0			0
$643$	−20.7979	−	43.1873i	−0.820190	−	1.70314i	−0.704326	−	0.709876i	$-0.748751\pi$
$643$	−20.7979	−	43.1873i	−0.820190	−	1.70314i	−0.115863	−	0.993265i	$-0.536963\pi$
$644$	8.12942	−	3.28429i	0.320344	−	0.129419i
$645$		0			0
$646$	−4.20977	−	5.27888i	−0.165631	−	0.207695i
$647$	9.53132	−	4.59004i	0.374715	−	0.180453i	−0.237041	−	0.971500i	$-0.576178\pi$
$647$	9.53132	−	4.59004i	0.374715	−	0.180453i	0.611756	+	0.791046i	$0.290463\pi$
$648$		0			0
$649$	5.52066	+	1.26005i	0.216705	+	0.0494615i
$650$	−6.04333	+	7.57810i	−0.237039	+	0.297237i
$651$		0			0
$652$	7.03923	+	8.82691i	0.275677	+	0.345689i
$653$	−2.10860	−	4.37856i	−0.0825160	−	0.171346i	0.855628	−	0.517591i	$-0.173171\pi$
$653$	−2.10860	−	4.37856i	−0.0825160	−	0.171346i	−0.938144	+	0.346245i	$0.887457\pi$
$654$		0			0
$655$	41.0541			1.60412
$656$	0.151585			0.00591840
$657$		0			0
$658$	1.11973	+	6.95834i	0.0436516	+	0.271264i
$659$	−21.0308	+	4.80014i	−0.819244	+	0.186987i	−0.611549	−	0.791207i	$-0.709453\pi$
$659$	−21.0308	+	4.80014i	−0.819244	+	0.186987i	−0.207695	+	0.978194i	$0.566596\pi$
$660$		0			0
$661$	24.1911	−	19.2917i	0.940924	−	0.750362i	−0.0275126	−	0.999621i	$-0.508759\pi$
$661$	24.1911	−	19.2917i	0.940924	−	0.750362i	0.968437	+	0.249260i	$0.0801872\pi$
$662$	8.86826	−	7.07220i	0.344675	−	0.274869i
$663$		0			0
$664$	−11.5221	+	2.62983i	−0.447143	+	0.102057i
$665$	8.86957	+	5.00383i	0.343947	+	0.194040i
$666$		0			0
$667$	−5.94366			−0.230140
$668$	18.0705			0.699167
$669$		0			0
$670$	11.5755	+	24.0367i	0.447200	+	0.928620i
$671$	6.15605	+	7.71945i	0.237652	+	0.298006i
$672$		0			0
$673$	1.28952	−	1.61700i	0.0497072	−	0.0623309i	−0.756356	−	0.654160i	$-0.773022\pi$
$673$	1.28952	−	1.61700i	0.0497072	−	0.0623309i	0.806064	+	0.591829i	$0.201594\pi$
$674$	−7.30214	−	1.66666i	−0.281268	−	0.0641975i
$675$		0			0
$676$	−28.4905	+	13.7203i	−1.09579	+	0.527704i
$677$	−25.1095	−	31.4863i	−0.965036	−	1.21012i	−0.977659	−	0.210197i	$-0.932589\pi$
$677$	−25.1095	−	31.4863i	−0.965036	−	1.21012i	0.0126228	−	0.999920i	$-0.495982\pi$
$678$		0			0
$679$	33.7079	+	2.18897i	1.29359	+	0.0840048i
$680$	−2.70116	−	5.60902i	−0.103585	−	0.215096i
$681$		0			0
$682$	12.3444	−	2.81753i	0.472692	−	0.107889i
$683$	6.41982	−	13.3309i	0.245647	−	0.510092i	−0.741292	−	0.671182i	$-0.765787\pi$
$683$	6.41982	−	13.3309i	0.245647	−	0.510092i	0.986940	+	0.161090i	$0.0515010\pi$
$684$		0			0
$685$		−	0.819650i		−	0.0313172i
$686$	−14.1286	+	11.9743i	−0.539432	+	0.457180i
$687$		0			0
$688$	−4.22325	+	5.29578i	−0.161010	+	0.201900i
$689$	−37.0843	−	17.8589i	−1.41280	−	0.680369i
$690$		0			0
$691$	−4.56167	+	9.47240i	−0.173534	+	0.360347i	−0.969537	−	0.244946i	$-0.921230\pi$
$691$	−4.56167	+	9.47240i	−0.173534	+	0.360347i	0.796003	+	0.605293i	$0.206944\pi$
$692$	−9.79706	+	4.71801i	−0.372428	+	0.179352i
$693$		0			0
$694$	−17.2894	−	8.32613i	−0.656296	−	0.316056i
$695$	8.75536	−	6.98217i	0.332110	−	0.264849i
$696$		0			0
$697$	−0.312328	+	0.391647i	−0.0118303	+	0.0148347i
$698$	2.85071	−	12.4898i	0.107901	−	0.472745i
$699$		0			0
$700$	−2.84005	−	2.58307i	−0.107344	−	0.0976307i
$701$	−41.0300	+	32.7203i	−1.54968	+	1.23583i	−0.691652	+	0.722231i	$0.743117\pi$
$701$	−41.0300	+	32.7203i	−1.54968	+	1.23583i	−0.858030	+	0.513599i	$0.828312\pi$
$702$		0			0
$703$	−3.76488	−	0.859310i	−0.141995	−	0.0324095i
$704$		−	2.64136i		−	0.0995499i
$705$		0			0
$706$	24.2094	+	5.52563i	0.911132	+	0.207960i
$707$	−18.6148	+	32.9958i	−0.700081	+	1.24093i
$708$		0			0
$709$	9.78104	+	42.8535i	0.367334	+	1.60940i	0.734071	+	0.679073i	$0.237618\pi$
$709$	9.78104	+	42.8535i	0.367334	+	1.60940i	−0.366737	+	0.930325i	$0.619525\pi$
$710$	9.39370	+	11.7793i	0.352539	+	0.442070i
$711$		0			0
$712$	−8.64121	+	1.97230i	−0.323843	+	0.0739150i
$713$	−3.53494	−	15.4876i	−0.132385	−	0.580015i
$714$		0			0
$715$	−7.39648	+	32.4061i	−0.276613	+	1.21192i
$716$		−	25.0438i		−	0.935931i
$717$		0			0
$718$	4.96911	−	21.7711i	0.185445	−	0.812490i
$719$	−15.3026	+	7.36936i	−0.570692	+	0.274831i	−0.696895	−	0.717174i	$-0.745435\pi$
$719$	−15.3026	+	7.36936i	−0.570692	+	0.274831i	0.126202	+	0.992005i	$0.459721\pi$
$720$		0			0
$721$	−24.9871	−	14.0966i	−0.930567	−	0.524986i
$722$	11.5910	+	9.24353i	0.431373	+	0.344008i
$723$		0			0
$724$	15.1411	+	12.0746i	0.562715	+	0.448750i
$725$	1.12917	+	2.34474i	0.0419363	+	0.0870815i
$726$		0			0
$727$	−8.13156	+	16.8854i	−0.301583	+	0.626243i	−0.995599	−	0.0937164i	$-0.970125\pi$
$727$	−8.13156	+	16.8854i	−0.301583	+	0.626243i	0.694016	+	0.719959i	$0.255840\pi$
$728$	−6.62027	−	16.3868i	−0.245364	−	0.607334i
$729$		0			0
$730$	−5.53374	−	2.66491i	−0.204813	−	0.0986327i
$731$	−4.98096	−	21.8230i	−0.184227	−	0.807153i
$732$		0			0
$733$	2.14237	+	1.70849i	0.0791304	+	0.0631044i	0.662256	−	0.749278i	$-0.269599\pi$
$733$	2.14237	+	1.70849i	0.0791304	+	0.0631044i	−0.583126	+	0.812382i	$0.698171\pi$
$734$	26.5785			0.981032
$735$		0			0
$736$	−3.31391			−0.122152
$737$	−29.2452	−	23.3222i	−1.07726	−	0.859086i
$738$		0			0
$739$	3.57072	+	15.6443i	0.131351	+	0.575486i	0.997173	+	0.0751346i	$0.0239386\pi$
$739$	3.57072	+	15.6443i	0.131351	+	0.575486i	−0.865823	+	0.500351i	$0.833204\pi$
$740$	−3.20802	−	1.54490i	−0.117929	−	0.0567917i
$741$		0			0
$742$	8.01036	−	14.1988i	0.294070	−	0.521255i
$743$	5.63207	−	11.6951i	0.206620	−	0.429052i	−0.771746	−	0.635931i	$-0.780616\pi$
$743$	5.63207	−	11.6951i	0.206620	−	0.429052i	0.978367	+	0.206879i	$0.0663306\pi$
$744$		0			0
$745$	−14.0928	−	29.2641i	−0.516322	−	1.07215i
$746$	23.2276	+	18.5234i	0.850424	+	0.678191i
$747$		0			0
$748$	6.82442	+	5.44229i	0.249525	+	0.198990i
$749$	10.7691	+	15.4625i	0.393495	+	0.564988i
$750$		0			0
$751$	−21.7680	+	10.4829i	−0.794327	+	0.382528i	−0.786616	−	0.617443i	$-0.788169\pi$
$751$	−21.7680	+	10.4829i	−0.794327	+	0.382528i	−0.00771095	+	0.999970i	$0.502454\pi$
$752$	0.592760	−	2.59705i	0.0216157	−	0.0947047i
$753$		0			0
$754$			11.9809i			0.436317i
$755$	−2.48264	+	10.8771i	−0.0903523	+	0.395859i
$756$		0			0
$757$	2.95342	+	12.9398i	0.107344	+	0.470303i	0.999816	+	0.0192006i	$0.00611211\pi$
$757$	2.95342	+	12.9398i	0.107344	+	0.470303i	−0.892472	+	0.451103i	$0.851031\pi$
$758$	22.6430	−	5.16813i	0.822432	−	0.187715i
$759$		0			0
$760$	−2.39986	−	3.00933i	−0.0870520	−	0.109160i
$761$	0.885964	+	3.88166i	0.0321162	+	0.140710i	0.988444	−	0.151586i	$-0.0484379\pi$
$761$	0.885964	+	3.88166i	0.0321162	+	0.140710i	−0.956328	+	0.292296i	$0.905581\pi$
$762$		0			0
$763$	27.0683	+	24.6190i	0.979938	+	0.891267i
$764$	−3.29240	−	0.751468i	−0.119115	−	0.0271872i
$765$		0			0
$766$			16.5795i			0.599043i
$767$	−13.9617	−	3.18667i	−0.504128	−	0.115064i
$768$		0			0
$769$	−40.3221	+	32.1558i	−1.45405	+	1.15957i	−0.497702	+	0.867348i	$0.665823\pi$
$769$	−40.3221	+	32.1558i	−1.45405	+	1.15957i	−0.956351	+	0.292220i	$0.905606\pi$
$770$	−12.6183	−	3.75514i	−0.454733	−	0.135326i
$771$		0			0
$772$	−4.65180	+	20.3809i	−0.167422	+	0.733523i
$773$	−8.04588	+	10.0892i	−0.289390	+	0.362884i	−0.905181	−	0.425026i	$-0.860265\pi$
$773$	−8.04588	+	10.0892i	−0.289390	+	0.362884i	0.615791	+	0.787909i	$0.288837\pi$
$774$		0			0
$775$	−5.43820	+	4.33682i	−0.195346	+	0.155783i
$776$	−11.5029	−	5.53948i	−0.412928	−	0.198856i
$777$		0			0
$778$	13.7273	−	6.61072i	0.492148	−	0.237006i
$779$	−0.134380	+	0.279042i	−0.00481466	+	0.00999773i
$780$		0			0
$781$	−19.0323	−	9.16549i	−0.681031	−	0.327967i
$782$	6.82803	−	8.56208i	0.244170	−	0.306179i
$783$		0			0
$784$	6.64662	−	2.19600i	0.237379	−	0.0784286i
$785$			30.9905i			1.10610i
$786$		0			0
$787$	−4.06463	+	8.44029i	−0.144888	+	0.300864i	−0.960766	−	0.277361i	$-0.910540\pi$
$787$	−4.06463	+	8.44029i	−0.144888	+	0.300864i	0.815877	+	0.578225i	$0.196254\pi$
$788$	7.00804	−	1.59954i	0.249651	−	0.0569812i
$789$		0			0
$790$	−9.49949	−	19.7259i	−0.337977	−	0.701816i
$791$	−19.8079	−	28.4405i	−0.704287	−	1.01123i
$792$		0			0
$793$	−15.5686	−	19.5224i	−0.552858	−	0.693262i
$794$	22.4768	−	10.8242i	0.797671	−	0.384138i
$795$		0			0
$796$	2.68113	+	0.611949i	0.0950300	+	0.0216900i
$797$	−16.1058	+	20.1960i	−0.570496	+	0.715379i	−0.980459	−	0.196723i	$-0.936970\pi$
$797$	−16.1058	+	20.1960i	−0.570496	+	0.715379i	0.409963	+	0.912102i	$0.365541\pi$
$798$		0			0
$799$	5.48861	+	6.88250i	0.194173	+	0.243485i
$800$	0.629572	+	1.30732i	0.0222587	+	0.0462207i
$801$		0			0
$802$	28.0779			0.991466
$803$	8.61161			0.303897
$804$		0			0
$805$	−4.71128	+	15.8313i	−0.166051	+	0.557979i
$806$	−31.2189	+	7.12551i	−1.09964	+	0.250986i
$807$		0			0
$808$	11.1950	−	8.92773i	0.393840	−	0.314077i
$809$	−38.2072	+	30.4692i	−1.34329	+	1.07124i	−0.352505	+	0.935810i	$0.614670\pi$
$809$	−38.2072	+	30.4692i	−1.34329	+	1.07124i	−0.990787	+	0.135430i	$0.956758\pi$
$810$		0			0
$811$	−6.45499	+	1.47331i	−0.226665	+	0.0517349i	−0.334345	−	0.942451i	$-0.608515\pi$
$811$	−6.45499	+	1.47331i	−0.226665	+	0.0517349i	0.107680	+	0.994186i	$0.465658\pi$
$812$	−4.73531	−	0.307508i	−0.166177	−	0.0107914i
$813$		0			0
$814$	4.99232			0.174981
$815$	−21.2690			−0.745022
$816$		0			0
$817$	−6.00474	−	12.4690i	−0.210079	−	0.436234i
$818$	−15.3291	−	19.2221i	−0.535971	−	0.672086i
$819$		0			0
$820$	−0.178048	+	0.223266i	−0.00621772	+	0.00779677i
$821$	7.68210	+	1.75339i	0.268107	+	0.0611937i	0.354461	−	0.935071i	$-0.384664\pi$
$821$	7.68210	+	1.75339i	0.268107	+	0.0611937i	−0.0863538	+	0.996265i	$0.527522\pi$
$822$		0			0
$823$	43.7028	−	21.0462i	1.52338	−	0.733623i	0.529950	−	0.848029i	$-0.322211\pi$
$823$	43.7028	−	21.0462i	1.52338	−	0.733623i	0.993434	+	0.114405i	$0.0364962\pi$
$824$	6.76080	+	8.47778i	0.235524	+	0.295337i
$825$		0			0
$826$	1.61785	−	5.43643i	0.0562921	−	0.189157i
$827$	16.3574	+	33.9665i	0.568803	+	1.18113i	0.964826	+	0.262891i	$0.0846760\pi$
$827$	16.3574	+	33.9665i	0.568803	+	1.18113i	−0.396022	+	0.918241i	$0.629610\pi$
$828$		0			0
$829$	−22.3599	+	5.10350i	−0.776592	+	0.177252i	−0.592406	−	0.805639i	$-0.701822\pi$
$829$	−22.3599	+	5.10350i	−0.776592	+	0.177252i	−0.184186	+	0.982891i	$0.558965\pi$
$830$	9.66013	−	20.0595i	0.335308	−	0.696274i
$831$		0			0
$832$			6.67998i			0.231587i
$833$	−8.02103	+	21.6974i	−0.277912	+	0.751770i
$834$		0			0
$835$	−21.2251	+	26.6155i	−0.734526	+	0.921067i
$836$	4.86229	+	2.34156i	0.168166	+	0.0809844i
$837$		0			0
$838$	−2.11592	+	4.39375i	−0.0730932	+	0.151780i
$839$	−17.1601	+	8.26387i	−0.592432	+	0.285300i	−0.705980	−	0.708232i	$-0.749493\pi$
$839$	−17.1601	+	8.26387i	−0.592432	+	0.285300i	0.113547	+	0.993533i	$0.463779\pi$
$840$		0			0
$841$	−23.2298	−	11.1869i	−0.801029	−	0.385755i
$842$	−15.4833	+	12.3476i	−0.533591	+	0.425525i
$843$		0			0
$844$	−16.2448	+	20.3703i	−0.559169	+	0.701176i
$845$	13.2560	−	58.0785i	0.456021	−	1.99796i
$846$		0			0
$847$	−10.5093	+	1.69114i	−0.361102	+	0.0581083i
$848$	−4.81747	+	3.84180i	−0.165433	+	0.131928i
$849$		0			0
$850$	−4.67487	−	1.06701i	−0.160347	−	0.0365981i
$851$		−	6.26349i		−	0.214710i
$852$		0			0
$853$	−17.9459	−	4.09603i	−0.614455	−	0.140245i	−0.0960444	−	0.995377i	$-0.530619\pi$
$853$	−17.9459	−	4.09603i	−0.614455	−	0.140245i	−0.518411	+	0.855132i	$0.673476\pi$
$854$	8.11563	−	5.65226i	0.277711	−	0.193416i
$855$		0			0
$856$	−1.58480	−	6.94347i	−0.0541674	−	0.237323i
$857$	34.1109	+	42.7737i	1.16521	+	1.46112i	0.861065	+	0.508495i	$0.169798\pi$
$857$	34.1109	+	42.7737i	1.16521	+	1.46112i	0.304141	+	0.952627i	$0.401630\pi$
$858$		0			0
$859$	−23.0812	+	5.26814i	−0.787522	+	0.179747i	−0.597325	−	0.801999i	$-0.703770\pi$
$859$	−23.0812	+	5.26814i	−0.787522	+	0.179747i	−0.190197	+	0.981746i	$0.560913\pi$
$860$	−2.83949	−	12.4406i	−0.0968257	−	0.424221i
$861$		0			0
$862$	4.05526	−	17.7673i	0.138123	−	0.605155i
$863$			30.1072i			1.02486i	0.858728	+	0.512431i	$0.171255\pi$
$863$			30.1072i			1.02486i	−0.858728	+	0.512431i	$0.828745\pi$
$864$		0			0
$865$	4.55836	−	19.9715i	0.154989	−	0.679051i
$866$	27.9453	−	13.4578i	0.949621	−	0.457313i
$867$		0			0
$868$	−2.01500	−	12.5218i	−0.0683936	−	0.425019i
$869$	24.0002	+	19.1395i	0.814152	+	0.649265i
$870$		0			0
$871$	73.9608	+	58.9818i	2.50607	+	1.99852i
$872$	−6.00040	−	12.4600i	−0.203199	−	0.421947i
$873$		0			0
$874$	2.93777	−	6.10035i	0.0993717	−	0.206347i
$875$	31.7452	−	5.10840i	1.07318	−	0.172696i
$876$		0			0
$877$	24.3220	+	11.7128i	0.821295	+	0.395515i	0.796843	−	0.604186i	$-0.206502\pi$
$877$	24.3220	+	11.7128i	0.821295	+	0.395515i	0.0244516	+	0.999701i	$0.492216\pi$
$878$	−0.565740	−	2.47867i	−0.0190928	−	0.0836510i
$879$		0			0
$880$	3.89038	+	3.10248i	0.131145	+	0.104585i
$881$	−49.4956			−1.66755			−0.833774	−	0.552106i	$-0.813824\pi$
$881$	−49.4956			−1.66755			−0.833774	+	0.552106i	$0.813824\pi$
$882$		0			0
$883$	−5.00352			−0.168382			−0.0841909	−	0.996450i	$-0.526831\pi$
$883$	−5.00352			−0.168382			−0.0841909	+	0.996450i	$0.526831\pi$
$884$	−17.2589	−	13.7635i	−0.580480	−	0.462917i
$885$		0			0
$886$	5.80376	+	25.4280i	0.194981	+	0.854269i
$887$	−6.39054	−	3.07752i	−0.214573	−	0.103333i	0.323510	−	0.946225i	$-0.395137\pi$
$887$	−6.39054	−	3.07752i	−0.214573	−	0.103333i	−0.538083	+	0.842892i	$0.680851\pi$
$888$		0			0
$889$	−12.0998	−	3.60083i	−0.405815	−	0.120768i
$890$	7.24482	−	15.0440i	0.242847	−	0.504277i
$891$		0			0
$892$	5.21248	+	10.8238i	0.174527	+	0.362408i
$893$	4.25525	+	3.39345i	0.142397	+	0.113557i
$894$		0			0
$895$	36.8863	+	29.4159i	1.23297	+	0.983264i
$896$	−2.64019	−	0.171452i	−0.0882026	−	0.00572781i
$897$		0			0
$898$	31.7172	−	15.2742i	1.05842	−	0.509706i
$899$	−1.91317	+	8.38216i	−0.0638079	+	0.279561i
$900$		0			0
$901$		−	20.3625i		−	0.678373i
$902$	0.0890953	−	0.390352i	0.00296655	−	0.0129973i
$903$		0			0
$904$	2.91496	+	12.7713i	0.0969501	+	0.424766i
$905$	−35.5688	+	8.11834i	−1.18235	+	0.269863i
$906$		0			0
$907$	−5.19053	−	6.50872i	−0.172349	−	0.216118i	0.688154	−	0.725565i	$-0.258422\pi$
$907$	−5.19053	−	6.50872i	−0.172349	−	0.216118i	−0.860502	+	0.509447i	$0.829850\pi$
$908$	5.21764	+	22.8600i	0.173153	+	0.758635i
$909$		0			0
$910$	31.9117	+	9.49671i	1.05786	+	0.314813i
$911$	37.1966	+	8.48988i	1.23238	+	0.281282i	0.788629	−	0.614869i	$-0.210791\pi$
$911$	37.1966	+	8.48988i	1.23238	+	0.281282i	0.443749	+	0.896151i	$0.353648\pi$
$912$		0			0
$913$			31.2166i			1.03312i
$914$	26.3646	+	6.01756i	0.872065	+	0.199043i
$915$		0			0
$916$	−8.54200	+	6.81201i	−0.282235	+	0.225075i
$917$	21.5976	+	53.4593i	0.713216	+	1.76538i
$918$		0			0
$919$	−2.44796	+	10.7252i	−0.0807506	+	0.353792i	−0.999120	−	0.0419315i	$-0.986649\pi$
$919$	−2.44796	+	10.7252i	−0.0807506	+	0.353792i	0.918370	+	0.395723i	$0.129506\pi$
$920$	3.89244	−	4.88097i	0.128330	−	0.160921i
$921$		0			0
$922$	−21.8625	+	17.4347i	−0.720001	+	0.574182i
$923$	48.1327	+	23.1795i	1.58431	+	0.762961i
$924$		0			0
$925$	−2.47091	+	1.18993i	−0.0812430	+	0.0391246i
$926$	−1.43620	+	2.98230i	−0.0471965	+	0.0980046i
$927$		0			0
$928$	1.61593	+	0.778192i	0.0530456	+	0.0255454i
$929$	−14.9627	+	18.7627i	−0.490911	+	0.615583i	−0.964152	−	0.265350i	$-0.914512\pi$
$929$	−14.9627	+	18.7627i	−0.490911	+	0.615583i	0.473241	+	0.880933i	$0.343084\pi$
$930$		0			0
$931$	−1.84975	+	14.1821i	−0.0606230	+	0.464798i
$932$		−	18.4397i		−	0.604011i
$933$		0			0
$934$	−17.5971	+	36.5408i	−0.575795	+	1.19565i
$935$	−16.0316	+	3.65911i	−0.524289	+	0.119666i
$936$		0			0
$937$	19.5275	+	40.5493i	0.637936	+	1.32469i	0.929743	+	0.368210i	$0.120029\pi$
$937$	19.5275	+	40.5493i	0.637936	+	1.32469i	−0.291807	+	0.956477i	$0.594256\pi$
$938$	−25.2103	+	27.7184i	−0.823144	+	0.905037i
$939$		0			0
$940$	3.12888	+	3.92350i	0.102053	+	0.127970i
$941$	−42.4994	+	20.4666i	−1.38544	+	0.667193i	−0.970152	−	0.242496i	$-0.922034\pi$
$941$	−42.4994	+	20.4666i	−1.38544	+	0.667193i	−0.415289	+	0.909689i	$0.636320\pi$
$942$		0			0
$943$	−0.489745	−	0.111781i	−0.0159483	−	0.00364009i
$944$	−1.33666	+	1.67612i	−0.0435045	+	0.0545530i
$945$		0			0
$946$	11.1551	+	13.9881i	0.362684	+	0.454791i
$947$	19.5945	+	40.6885i	0.636737	+	1.32220i	0.930490	+	0.366316i	$0.119381\pi$
$947$	19.5945	+	40.6885i	0.636737	+	1.32220i	−0.293754	+	0.955881i	$0.594904\pi$
$948$		0			0
$949$	−21.7787			−0.706966
$950$	−2.96467			−0.0961865
$951$		0			0
$952$	5.88286	−	6.46814i	0.190665	−	0.209633i
$953$	51.7172	−	11.8041i	1.67529	−	0.382373i	0.723786	−	0.690024i	$-0.242400\pi$
$953$	51.7172	−	11.8041i	1.67529	−	0.382373i	0.951499	+	0.307651i	$0.0995431\pi$
$954$		0			0
$955$	4.97399	−	3.96663i	0.160955	−	0.128357i
$956$	8.03835	−	6.41037i	0.259979	−	0.207326i
$957$		0			0
$958$	7.84716	−	1.79106i	0.253530	−	0.0578666i
$959$	1.06732	−	0.431199i	0.0344656	−	0.0139241i
$960$		0			0
$961$	8.02049			0.258726
$962$	−12.6255			−0.407064
$963$		0			0
$964$	−2.37132	−	4.92410i	−0.0763751	−	0.158594i
$965$	−24.5545	−	30.7904i	−0.790438	−	0.991178i
$966$		0			0
$967$	28.3340	−	35.5298i	0.911161	−	1.14256i	−0.0781793	−	0.996939i	$-0.524911\pi$
$967$	28.3340	−	35.5298i	0.911161	−	1.14256i	0.989340	−	0.145621i	$-0.0465179\pi$
$968$	3.92236	+	0.895252i	0.126069	+	0.0287745i
$969$		0			0
$970$	21.6699	−	10.4357i	0.695780	−	0.335070i
$971$	33.7436	+	42.3132i	1.08288	+	1.35789i	0.929117	+	0.369787i	$0.120569\pi$
$971$	33.7436	+	42.3132i	1.08288	+	1.35789i	0.153768	+	0.988107i	$0.450859\pi$
$972$		0			0
$973$	13.6979	+	7.72779i	0.439136	+	0.247741i
$974$	−6.13229	−	12.7338i	−0.196491	−	0.408018i
$975$		0			0
$976$	−3.64433	+	0.831796i	−0.116652	+	0.0266251i
$977$	7.44374	−	15.4571i	0.238146	−	0.494516i	−0.747303	−	0.664483i	$-0.768652\pi$
$977$	7.44374	−	15.4571i	0.238146	−	0.494516i	0.985450	+	0.169967i	$0.0543661\pi$
$978$		0			0
$979$			23.4115i			0.748235i
$980$	−4.57254	+	12.3690i	−0.146064	+	0.395113i
$981$		0			0
$982$	0.713577	−	0.894797i	0.0227712	−	0.0285541i
$983$	7.36235	+	3.54552i	0.234823	+	0.113085i	0.547595	−	0.836744i	$-0.315543\pi$
$983$	7.36235	+	3.54552i	0.234823	+	0.113085i	−0.312773	+	0.949828i	$0.601258\pi$
$984$		0			0
$985$	−5.87556	+	12.2007i	−0.187211	+	0.388748i
$986$	−5.34008	+	2.57165i	−0.170063	+	0.0818980i
$987$		0			0
$988$	−12.2967	−	5.92178i	−0.391210	−	0.188397i
$989$	17.5498	−	13.9955i	0.558050	−	0.445030i
$990$		0			0
$991$	−4.17403	+	5.23406i	−0.132592	+	0.166266i	−0.843695	−	0.536822i	$-0.819625\pi$
$991$	−4.17403	+	5.23406i	−0.132592	+	0.166266i	0.711103	+	0.703088i	$0.248196\pi$
$992$	−1.06670	+	4.67351i	−0.0338677	+	0.148384i
$993$		0			0
$994$	−10.3968	+	18.4290i	−0.329768	+	0.584532i
$995$	−4.05051	+	3.23017i	−0.128410	+	0.102403i
$996$		0			0
$997$	−14.8986	−	3.40051i	−0.471843	−	0.107695i	−0.0200141	−	0.999800i	$-0.506371\pi$
$997$	−14.8986	−	3.40051i	−0.471843	−	0.107695i	−0.451829	+	0.892105i	$0.649228\pi$
$998$			1.57592i			0.0498849i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.v.a.251.11	yes	96
3.2	odd	2	inner	882.2.v.a.251.6	✓	96
49.41	odd	14	inner	882.2.v.a.629.6	yes	96
147.41	even	14	inner	882.2.v.a.629.11	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.v.a.251.6	✓	96	3.2	odd	2	inner
882.2.v.a.251.11	yes	96	1.1	even	1	trivial
882.2.v.a.629.6	yes	96	49.41	odd	14	inner
882.2.v.a.629.11	yes	96	147.41	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.v (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-1.69731 - 0.817383i) q^{5} +(0.171452 - 2.64019i) q^{7} +(-0.433884 + 0.900969i) q^{8} +O(q^{10})\)	\(q+(0.781831 + 0.623490i) q^{2} +(0.222521 + 0.974928i) q^{4} +(-1.69731 - 0.817383i) q^{5} +(0.171452 - 2.64019i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(-0.817383 - 1.69731i) q^{10} +(2.06510 + 1.64686i) q^{11} +(-5.22262 - 4.16490i) q^{13} +(1.78018 - 1.95729i) q^{14} +(-0.900969 + 0.433884i) q^{16} +(0.735353 - 3.22179i) q^{17} -2.04317i q^{19} +(0.419202 - 1.83664i) q^{20} +(0.587757 + 2.57513i) q^{22} +(3.23083 - 0.737415i) q^{23} +(-0.904693 - 1.13445i) q^{25} +(-1.48643 - 6.51250i) q^{26} +(2.61215 - 0.420344i) q^{28} +(-1.74858 - 0.399102i) q^{29} -4.79369i q^{31} +(-0.974928 - 0.222521i) q^{32} +(2.58368 - 2.06041i) q^{34} +(-2.44905 + 4.34109i) q^{35} +(0.420577 - 1.84267i) q^{37} +(1.27389 - 1.59741i) q^{38} +(1.47287 - 1.17458i) q^{40} +(-0.136573 - 0.0657703i) q^{41} +(6.10277 - 2.93894i) q^{43} +(-1.14604 + 2.37978i) q^{44} +(2.98573 + 1.43785i) q^{46} +(-1.66088 + 2.08267i) q^{47} +(-6.94121 - 0.905333i) q^{49} -1.45102i q^{50} +(2.89833 - 6.01845i) q^{52} +(6.00728 - 1.37112i) q^{53} +(-2.15900 - 4.48321i) q^{55} +(2.30434 + 1.30001i) q^{56} +(-1.11826 - 1.40225i) q^{58} +(1.93153 - 0.930175i) q^{59} +(3.64433 + 0.831796i) q^{61} +(2.98882 - 3.74786i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(5.46010 + 11.3380i) q^{65} -14.1616 q^{67} +3.30465 q^{68} +(-4.62137 + 1.86704i) q^{70} +(-7.79700 + 1.77961i) q^{71} +(2.54900 - 2.03276i) q^{73} +(1.47771 - 1.17843i) q^{74} +(1.99194 - 0.454648i) q^{76} +(4.70209 - 5.16989i) q^{77} +11.6218 q^{79} +1.88387 q^{80} +(-0.0657703 - 0.136573i) q^{82} +(7.36863 + 9.23997i) q^{83} +(-3.88156 + 4.86732i) q^{85} +(6.60373 + 1.50726i) q^{86} +(-2.37978 + 1.14604i) q^{88} +(5.52626 + 6.92971i) q^{89} +(-11.8915 + 13.0746i) q^{91} +(1.43785 + 2.98573i) q^{92} +(-2.59705 + 0.592760i) q^{94} +(-1.67005 + 3.46789i) q^{95} +12.7672i q^{97} +(-4.86239 - 5.03559i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 16 q^{4}+O(q^{10}) \) 96 * q + 16 * q^4	\( 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) \) 96 * q + 16 * q^4 - 16 * q^16 + 20 * q^22 - 8 * q^25 + 76 * q^37 + 28 * q^40 - 8 * q^43 + 112 * q^49 + 28 * q^52 + 28 * q^55 + 20 * q^58 + 84 * q^61 + 16 * q^64 - 8 * q^67 + 28 * q^70 + 112 * q^85 + 8 * q^88 - 56 * q^91 - 56 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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