LMFDB - Embedded newform 882.2.v.a.251.6

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			251.6
Character	$\chi$	$=$	882.251
Dual form			882.2.v.a.629.6

$q$-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	0.773040	−	0.634358i	$-0.218735\pi$
$5$	1.69731	+	0.817383i	0.759061	+	0.365545i	−0.0139784	+	0.999902i	$0.504450\pi$
$6$		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	0.260601	−	0.965446i	$-0.416079\pi$
$11$	−2.06510	−	1.64686i	−0.622650	−	0.496547i	−0.883251	+	0.468900i	$0.844651\pi$
$12$		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	$0.202678\pi$
$17$	−0.735353	+	3.22179i	−0.178349	+	0.781399i	−0.982393	+	0.186829i	$0.940179\pi$
$18$		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	−0.545655	−	0.838010i	$-0.683719\pi$
$23$	−3.23083	+	0.737415i	−0.673674	+	0.153762i	−0.128019	+	0.991772i	$0.540862\pi$
$24$		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	0.381766	−	0.924259i	$-0.375316\pi$
$29$	1.74858	+	0.399102i	0.324703	+	0.0741114i	−0.0570622	+	0.998371i	$0.518173\pi$
$30$		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	0.444518	−	0.895770i	$-0.353375\pi$
$41$	0.136573	+	0.0657703i	0.0213292	+	0.0102716i	−0.423189	+	0.906042i	$0.639089\pi$
$42$		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	−0.645803	−	0.763504i	$-0.723477\pi$
$47$	1.66088	−	2.08267i	0.242264	−	0.303789i	0.888066	+	0.459715i	$0.152049\pi$
$48$		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	−0.614195	−	0.789154i	$-0.710519\pi$
$53$	−6.00728	+	1.37112i	−0.825164	+	0.188338i	−0.210969	+	0.977493i	$0.567662\pi$
$54$		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	−0.555370	−	0.831603i	$-0.687423\pi$
$59$	−1.93153	+	0.930175i	−0.251463	+	0.121098i	0.303906	+	0.952702i	$0.401709\pi$
$60$		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	0.266799	−	0.963752i	$-0.414034\pi$
$71$	7.79700	−	1.77961i	0.925334	−	0.211201i	0.658534	+	0.752551i	$0.271177\pi$
$72$		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	$-0.989633\pi$
$83$	−7.36863	−	9.23997i	−0.808813	−	1.01422i	0.190657	−	0.981657i	$-0.438938\pi$
$84$		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	0.397305	−	0.917687i	$-0.369946\pi$
$89$	−5.52626	−	6.92971i	−0.585782	−	0.734548i	−0.983087	+	0.183139i	$0.941374\pi$
$90$		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	0.946336	−	0.323184i	$-0.104753\pi$
$101$	12.9009	+	6.21277i	1.28369	+	0.618194i	0.337356	+	0.941377i	$0.390467\pi$
$102$		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	−0.316229	−	0.948683i	$-0.602417\pi$
$107$	5.56823	−	4.44051i	0.538301	−	0.429281i	0.854530	+	0.519402i	$0.173845\pi$
$108$		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	−0.972806	−	0.231620i	$-0.925598\pi$
$113$	−10.2418	+	8.16753i	−0.963464	+	0.768337i	0.00934265	+	0.999956i	$0.497026\pi$
$114$		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	$-0.241876\pi$
$131$	19.6343	−	9.45536i	1.71545	−	0.826119i	0.990531	−	0.137288i	$-0.0438387\pi$
$132$		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	0.892749	−	0.450554i	$-0.148774\pi$
$137$	−0.188777	−	0.392000i	−0.0161283	−	0.0334908i	−0.908877	+	0.417063i	$0.863059\pi$
$138$		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	−0.110742	−	0.993849i	$-0.535323\pi$
$149$	−13.4799	−	10.7499i	−1.10432	−	0.880662i	−0.993574	+	0.113187i	$0.963894\pi$
$150$		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	$0.317874\pi$
$167$	−4.02106	+	17.6174i	−0.311159	+	1.36327i	−0.852612	+	0.522544i	$0.824983\pi$
$168$		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	$-0.935782\pi$
$173$	−2.41967	−	10.6013i	−0.183964	−	0.806000i	0.795754	−	0.605620i	$-0.207075\pi$
$174$		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	0.990833	−	0.135091i	$-0.0431325\pi$
$179$	24.4159	+	5.57277i	1.82493	+	0.416528i	0.834096	+	0.551619i	$0.185990\pi$
$180$		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	−0.841208	−	0.540712i	$-0.818155\pi$
$191$	1.46526	−	3.04263i	0.106022	−	0.220157i	0.947230	+	0.320555i	$0.103869\pi$
$192$		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	$0.0824282\pi$
$197$			7.18826i			0.512143i	−0.966658	+	0.256071i	$0.917572\pi$
$198$		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	$-0.783839\pi$
$227$	−23.4479			−1.55629			−0.778145	+	0.628085i	$0.783839\pi$
$228$		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	0.766211	−	0.642589i	$-0.222140\pi$
$233$	17.9773	+	4.10321i	1.17773	+	0.268810i	0.411523	+	0.911399i	$0.364997\pi$
$234$		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	0.993976	−	0.109598i	$-0.0349565\pi$
$239$	4.46095	+	9.26325i	0.288555	+	0.599190i	−0.705421	+	0.708788i	$0.749242\pi$
$240$		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	−0.845946	−	0.533268i	$-0.820964\pi$
$251$	−15.1532	+	7.29738i	−0.956460	+	0.460607i	−0.110513	+	0.993875i	$0.535250\pi$
$252$		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	$-0.742345\pi$
$257$	3.93998	−	17.2622i	0.245769	−	1.07678i	0.935669	−	0.352880i	$-0.114798\pi$
$258$		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	$0.327759\pi$
$263$			27.8009i			1.71428i	−0.515087	+	0.857138i	$0.672241\pi$
$264$		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	0.998475	−	0.0552135i	$-0.0175840\pi$
$269$	11.8493	+	14.8585i	0.722464	+	0.905941i	−0.276011	+	0.961155i	$0.589013\pi$
$270$		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	$-0.861204\pi$
$281$	−25.4781	−	20.3181i	−1.51990	−	1.21208i	−0.613466	−	0.789721i	$-0.710225\pi$
$282$		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	$-0.509930\pi$
$293$	−1.06781			−0.0623820			−0.0311910	+	0.999513i	$0.509930\pi$
$294$		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	−0.938995	−	0.343932i	$-0.888241\pi$
$311$	0.991746	−	4.34512i	0.0562367	−	0.246389i	0.995231	+	0.0975426i	$0.0310982\pi$
$312$		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	−0.600444	−	0.799666i	$-0.705010\pi$
$317$	−14.1450	+	3.22851i	−0.794464	+	0.181331i	−0.194020	+	0.980998i	$0.562153\pi$
$318$		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	0.311435	−	0.950268i	$-0.399191\pi$
$347$	18.7087	−	4.27013i	1.00433	−	0.229232i	0.692898	+	0.721035i	$0.256333\pi$
$348$		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	−0.921036	−	0.389478i	$-0.872655\pi$
$353$	−22.3728	+	10.7742i	−1.19079	+	0.573452i	−0.269750	+	0.962930i	$0.586941\pi$
$354$		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	$0.0577360\pi$
$359$	9.68905	+	20.1195i	0.511368	+	1.06187i	−0.472227	+	0.881477i	$0.656550\pi$
$360$		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	0.444124	−	0.895965i	$-0.353515\pi$
$383$	−10.3372	−	12.9624i	−0.528205	−	0.662348i	−0.972329	+	0.233618i	$0.924944\pi$
$384$		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	−0.998636	−	0.0522103i	$-0.983373\pi$
$389$	−6.61072	+	13.7273i	−0.335177	+	0.696002i	0.663459	+	0.748213i	$0.269088\pi$
$390$		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	−0.992725	−	0.120405i	$-0.961581\pi$
$401$	−21.9522	+	17.5063i	−1.09624	+	0.874223i	−0.103516	+	0.994628i	$0.533009\pi$
$402$		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	0.941479	−	0.337071i	$-0.109436\pi$
$419$	−1.08517	−	4.75443i	−0.0530139	−	0.232269i	−0.994493	+	0.104802i	$0.966579\pi$
$420$		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	$0.00177950\pi$
$431$	7.90717	+	16.4194i	0.380875	+	0.790895i	−0.619109	+	0.785305i	$0.712506\pi$
$432$		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	0.00497340	−	0.999988i	$-0.498417\pi$
$443$	−20.3916	−	16.2618i	−0.968836	−	0.772621i	−0.973809	+	0.227367i	$0.926988\pi$
$444$		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	$0.454903\pi$
$449$	−15.2742	+	31.7172i	−0.720833	+	1.49683i	−0.862037	+	0.506846i	$0.830811\pi$
$450$		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	$-0.702843\pi$
$461$	6.22238	−	27.2620i	0.289805	−	1.26972i	0.884793	−	0.465985i	$-0.154300\pi$
$462$		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	$-0.683753\pi$
$467$	−9.02483	−	39.5404i	−0.417619	−	1.82971i	0.128125	−	0.991758i	$-0.459104\pi$
$468$		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	−0.883149	−	0.469092i	$-0.844581\pi$
$479$	−5.01845	+	6.29293i	−0.229299	+	0.287532i	0.653850	+	0.756624i	$0.273153\pi$
$480$		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	$0.00822127\pi$
$491$			1.14449i			0.0516500i	−0.999666	+	0.0258250i	$0.991779\pi$
$492$		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	−0.261022	−	0.965333i	$-0.584060\pi$
$503$	16.5559	−	20.7604i	0.738190	−	0.925662i	0.999213	+	0.0396712i	$0.0126310\pi$
$504$		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	$-0.885565\pi$
$509$	−42.2374			−1.87214			−0.936070	+	0.351814i	$0.885565\pi$
$510$		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	$-0.630635\pi$
$521$	−18.2136			−0.797954			−0.398977	+	0.916961i	$0.630635\pi$
$522$		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	$-0.823911\pi$
$557$		−	24.8003i		−	1.05082i	0.850848	−	0.525411i	$-0.176089\pi$
$558$		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	0.506871	−	0.862022i	$-0.330802\pi$
$563$	−10.5903	−	13.2798i	−0.446327	−	0.559677i	−0.953199	+	0.302345i	$0.902231\pi$
$564$		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	$0.138574\pi$
$569$			20.1193i			0.843444i	−0.906725	+	0.421722i	$0.861426\pi$
$570$		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	$-0.282510\pi$
$587$	30.5917			1.26266			0.631328	+	0.775516i	$0.282510\pi$
$588$		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	0.781540	−	0.623855i	$-0.214434\pi$
$593$	19.0204	+	9.15974i	0.781074	+	0.376145i	−0.000466654		1.00000i	$0.500149\pi$
$594$		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	0.717738	−	0.696314i	$-0.245178\pi$
$599$	4.86047	+	3.87610i	0.198594	+	0.158373i	−0.519144	+	0.854687i	$0.673749\pi$
$600$		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	0.575730	−	0.817640i	$-0.304718\pi$
$617$	18.3734	+	4.19360i	0.739684	+	0.168828i	0.163954	+	0.986468i	$0.447575\pi$
$618$		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	0.250095	−	0.968221i	$-0.419538\pi$
$641$	22.6727	−	5.17490i	0.895518	−	0.204396i	0.645423	+	0.763825i	$0.276681\pi$
$642$		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	−0.611756	−	0.791046i	$-0.709537\pi$
$647$	−9.53132	+	4.59004i	−0.374715	+	0.180453i	0.237041	+	0.971500i	$0.423822\pi$
$648$		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	0.938144	−	0.346245i	$-0.112543\pi$
$653$	2.10860	+	4.37856i	0.0825160	+	0.171346i	−0.855628	+	0.517591i	$0.826829\pi$
$654$		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	0.207695	−	0.978194i	$-0.433404\pi$
$659$	21.0308	−	4.80014i	0.819244	−	0.186987i	0.611549	+	0.791207i	$0.290547\pi$
$660$		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	$0.0674105\pi$
$677$	25.1095	+	31.4863i	0.965036	+	1.21012i	−0.0126228	+	0.999920i	$0.504018\pi$
$678$		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	−0.986940	−	0.161090i	$-0.948499\pi$
$683$	−6.41982	+	13.3309i	−0.245647	+	0.510092i	0.741292	+	0.671182i	$0.234213\pi$
$684$		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	$-0.256883\pi$
$701$	41.0300	−	32.7203i	1.54968	−	1.23583i	0.858030	−	0.513599i	$-0.171688\pi$
$702$		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	−0.126202	−	0.992005i	$-0.540279\pi$
$719$	15.3026	−	7.36936i	0.570692	−	0.274831i	0.696895	+	0.717174i	$0.254565\pi$
$720$		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	−0.978367	−	0.206879i	$-0.933669\pi$
$743$	−5.63207	+	11.6951i	−0.206620	+	0.429052i	0.771746	+	0.635931i	$0.219384\pi$
$744$		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	0.956328	−	0.292296i	$-0.0944192\pi$
$761$	−0.885964	−	3.88166i	−0.0321162	−	0.140710i	−0.988444	+	0.151586i	$0.951562\pi$
$762$		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	−0.615791	−	0.787909i	$-0.711163\pi$
$773$	8.04588	−	10.0892i	0.289390	−	0.362884i	0.905181	+	0.425026i	$0.139735\pi$
$774$		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	−0.409963	−	0.912102i	$-0.634459\pi$
$797$	16.1058	−	20.1960i	0.570496	−	0.715379i	0.980459	+	0.196723i	$0.0630300\pi$
$798$		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	$-0.385330\pi$
$809$	38.2072	−	30.4692i	1.34329	−	1.07124i	0.990787	−	0.135430i	$-0.0432416\pi$
$810$		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	0.0863538	−	0.996265i	$-0.472478\pi$
$821$	−7.68210	−	1.75339i	−0.268107	−	0.0611937i	−0.354461	+	0.935071i	$0.615336\pi$
$822$		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	$-0.915324\pi$
$827$	−16.3574	−	33.9665i	−0.568803	−	1.18113i	0.396022	−	0.918241i	$-0.370390\pi$
$828$		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	−0.113547	−	0.993533i	$-0.536221\pi$
$839$	17.1601	−	8.26387i	0.592432	−	0.285300i	0.705980	+	0.708232i	$0.250507\pi$
$840$		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	$-0.830202\pi$
$857$	−34.1109	−	42.7737i	−1.16521	−	1.46112i	−0.304141	−	0.952627i	$-0.598370\pi$
$858$		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	$-0.828745\pi$
$863$		−	30.1072i		−	1.02486i	0.858728	−	0.512431i	$-0.171255\pi$
$864$		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	$-0.186176\pi$
$881$	49.4956			1.66755			0.833774	+	0.552106i	$0.186176\pi$
$882$		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	0.538083	−	0.842892i	$-0.319149\pi$
$887$	6.39054	+	3.07752i	0.214573	+	0.103333i	−0.323510	+	0.946225i	$0.604863\pi$
$888$		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	−0.443749	−	0.896151i	$-0.646352\pi$
$911$	−37.1966	−	8.48988i	−1.23238	−	0.281282i	−0.788629	+	0.614869i	$0.789209\pi$
$912$		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	−0.473241	−	0.880933i	$-0.656916\pi$
$929$	14.9627	−	18.7627i	0.490911	−	0.615583i	0.964152	+	0.265350i	$0.0854876\pi$
$930$		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	0.415289	−	0.909689i	$-0.363680\pi$
$941$	42.4994	−	20.4666i	1.38544	−	0.667193i	0.970152	+	0.242496i	$0.0779661\pi$
$942$		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	$-0.880619\pi$
$947$	−19.5945	−	40.6885i	−0.636737	−	1.32220i	0.293754	−	0.955881i	$-0.405096\pi$
$948$		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	−0.951499	−	0.307651i	$-0.900457\pi$
$953$	−51.7172	+	11.8041i	−1.67529	+	0.382373i	−0.723786	+	0.690024i	$0.757600\pi$
$954$		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	$-0.879431\pi$
$971$	−33.7436	−	42.3132i	−1.08288	−	1.35789i	−0.153768	−	0.988107i	$-0.549141\pi$
$972$		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	−0.985450	−	0.169967i	$-0.945634\pi$
$977$	−7.44374	+	15.4571i	−0.238146	+	0.494516i	0.747303	+	0.664483i	$0.231348\pi$
$978$		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	0.312773	−	0.949828i	$-0.398742\pi$
$983$	−7.36235	−	3.54552i	−0.234823	−	0.113085i	−0.547595	+	0.836744i	$0.684457\pi$
$984$		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.251.6	✓	96
3.2	odd	2	inner	882.2.v.a.251.11	yes	96
49.41	odd	14	inner	882.2.v.a.629.11	yes	96
147.41	even	14	inner	882.2.v.a.629.6	yes	96

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

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Database

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