LMFDB - Embedded newform 400.2.bi.d.223.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

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

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.7
Character	$\chi$	$=$	400.223
Dual form			400.2.bi.d.287.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.630190 + 1.23682i) q^{3} +(2.13375 - 0.668655i) q^{5} +(1.04788 + 1.04788i) q^{7} +(0.630777 - 0.868191i) q^{9} +O(q^{10})$	\(q+(0.630190 + 1.23682i) q^{3} +(2.13375 - 0.668655i) q^{5} +(1.04788 + 1.04788i) q^{7} +(0.630777 - 0.868191i) q^{9} +(0.0991587 + 0.136480i) q^{11} +(-0.0572924 - 0.361730i) q^{13} +(2.17167 + 2.21768i) q^{15} +(-1.20651 - 0.614748i) q^{17} +(-0.488134 - 1.50232i) q^{19} +(-0.635676 + 1.95641i) q^{21} +(-1.02277 + 6.45752i) q^{23} +(4.10580 - 2.85349i) q^{25} +(5.58437 + 0.884478i) q^{27} +(-3.38386 - 1.09948i) q^{29} +(-3.16642 + 1.02883i) q^{31} +(-0.106312 + 0.208650i) q^{33} +(2.93660 + 1.53525i) q^{35} +(-3.57850 + 0.566779i) q^{37} +(0.411289 - 0.298819i) q^{39} +(6.74026 + 4.89709i) q^{41} +(-4.31359 + 4.31359i) q^{43} +(0.765403 - 2.27428i) q^{45} +(3.72094 - 1.89591i) q^{47} -4.80388i q^{49} -1.87964i q^{51} +(-2.34369 + 1.19417i) q^{53} +(0.302838 + 0.224912i) q^{55} +(1.55048 - 1.55048i) q^{57} +(-10.3539 - 7.52257i) q^{59} +(-7.31975 + 5.31811i) q^{61} +(1.57075 - 0.248782i) q^{63} +(-0.364120 - 0.733533i) q^{65} +(5.12992 - 10.0680i) q^{67} +(-8.63132 + 2.80448i) q^{69} +(-15.4722 - 5.02722i) q^{71} +(14.1235 + 2.23694i) q^{73} +(6.11668 + 3.27989i) q^{75} +(-0.0391087 + 0.246922i) q^{77} +(4.87493 - 15.0035i) q^{79} +(1.43042 + 4.40238i) q^{81} +(-11.4971 - 5.85808i) q^{83} +(-2.98545 - 0.504980i) q^{85} +(-0.772615 - 4.87810i) q^{87} +(2.77813 + 3.82377i) q^{89} +(0.319015 - 0.439087i) q^{91} +(-3.26793 - 3.26793i) q^{93} +(-2.04609 - 2.87919i) q^{95} +(-5.33666 - 10.4738i) q^{97} +0.181038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{5}+O(q^{10}) $ 80 * q + 4 * q^5	$ 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) $ 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{11}{20}\right)$	$-1$

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			0
$2$		0			0
$3$	0.630190	+	1.23682i	0.363840	+	0.714077i	0.998263	−	0.0589091i	$-0.0187622\pi$
$3$	0.630190	+	1.23682i	0.363840	+	0.714077i	−0.634423	+	0.772986i	$0.718762\pi$
$4$		0			0
$5$	2.13375	−	0.668655i	0.954243	−	0.299032i
$5$	2.13375	−	0.668655i	0.954243	−	0.299032i
$6$		0			0
$7$	1.04788	+	1.04788i	0.396063	+	0.396063i	0.876842	−	0.480779i	$-0.159646\pi$
$7$	1.04788	+	1.04788i	0.396063	+	0.396063i	−0.480779	+	0.876842i	$0.659646\pi$
$8$		0			0
$9$	0.630777	−	0.868191i	0.210259	−	0.289397i
$10$		0			0
$11$	0.0991587	+	0.136480i	0.0298975	+	0.0411503i	0.823704	−	0.567020i	$-0.191904\pi$
$11$	0.0991587	+	0.136480i	0.0298975	+	0.0411503i	−0.793807	+	0.608170i	$0.791904\pi$
$12$		0			0
$13$	−0.0572924	−	0.361730i	−0.0158901	−	0.100326i	0.978469	−	0.206396i	$-0.0661733\pi$
$13$	−0.0572924	−	0.361730i	−0.0158901	−	0.100326i	−0.994359	+	0.106070i	$0.966173\pi$
$14$		0			0
$15$	2.17167	+	2.21768i	0.560724	+	0.572603i
$16$		0			0
$17$	−1.20651	−	0.614748i	−0.292622	−	0.149098i	0.301517	−	0.953461i	$-0.402507\pi$
$17$	−1.20651	−	0.614748i	−0.292622	−	0.149098i	−0.594139	+	0.804363i	$0.702507\pi$
$18$		0			0
$19$	−0.488134	−	1.50232i	−0.111986	−	0.344656i	0.879321	−	0.476230i	$-0.157997\pi$
$19$	−0.488134	−	1.50232i	−0.111986	−	0.344656i	−0.991306	+	0.131574i	$0.957997\pi$
$20$		0			0
$21$	−0.635676	+	1.95641i	−0.138716	+	0.426923i
$22$		0			0
$23$	−1.02277	+	6.45752i	−0.213262	+	1.34649i	0.616053	+	0.787705i	$0.288731\pi$
$23$	−1.02277	+	6.45752i	−0.213262	+	1.34649i	−0.829315	+	0.558781i	$0.811269\pi$
$24$		0			0
$25$	4.10580	−	2.85349i	0.821160	−	0.570698i
$26$		0			0
$27$	5.58437	+	0.884478i	1.07471	+	0.170218i
$28$		0			0
$29$	−3.38386	−	1.09948i	−0.628367	−	0.204169i	−0.0225152	−	0.999747i	$-0.507167\pi$
$29$	−3.38386	−	1.09948i	−0.628367	−	0.204169i	−0.605851	+	0.795578i	$0.707167\pi$
$30$		0			0
$31$	−3.16642	+	1.02883i	−0.568706	+	0.184784i	−0.579235	−	0.815161i	$-0.696649\pi$
$31$	−3.16642	+	1.02883i	−0.568706	+	0.184784i	0.0105286	+	0.999945i	$0.496649\pi$
$32$		0			0
$33$	−0.106312	+	0.208650i	−0.0185066	+	0.0363212i
$34$		0			0
$35$	2.93660	+	1.53525i	0.496376	+	0.259505i
$36$		0			0
$37$	−3.57850	+	0.566779i	−0.588302	+	0.0931779i	−0.443487	−	0.896281i	$-0.646259\pi$
$37$	−3.57850	+	0.566779i	−0.588302	+	0.0931779i	−0.144815	+	0.989459i	$0.546259\pi$
$38$		0			0
$39$	0.411289	−	0.298819i	0.0658589	−	0.0478493i
$40$		0			0
$41$	6.74026	+	4.89709i	1.05265	+	0.764796i	0.972715	−	0.232004i	$-0.0745281\pi$
$41$	6.74026	+	4.89709i	1.05265	+	0.764796i	0.0799369	+	0.996800i	$0.474528\pi$
$42$		0			0
$43$	−4.31359	+	4.31359i	−0.657817	+	0.657817i	−0.954863	−	0.297046i	$-0.903998\pi$
$43$	−4.31359	+	4.31359i	−0.657817	+	0.657817i	0.297046	+	0.954863i	$0.403998\pi$
$44$		0			0
$45$	0.765403	−	2.27428i	0.114100	−	0.339029i
$46$		0			0
$47$	3.72094	−	1.89591i	0.542754	−	0.276547i	−0.161044	−	0.986947i	$-0.551486\pi$
$47$	3.72094	−	1.89591i	0.542754	−	0.276547i	0.703798	+	0.710400i	$0.251486\pi$
$48$		0			0
$49$		−	4.80388i		−	0.686268i
$50$		0			0
$51$		−	1.87964i		−	0.263202i
$52$		0			0
$53$	−2.34369	+	1.19417i	−0.321930	+	0.164032i	−0.607486	−	0.794330i	$-0.707822\pi$
$53$	−2.34369	+	1.19417i	−0.321930	+	0.164032i	0.285555	+	0.958362i	$0.407822\pi$
$54$		0			0
$55$	0.302838	+	0.224912i	0.0408347	+	0.0303271i
$56$		0			0
$57$	1.55048	−	1.55048i	0.205366	−	0.205366i
$58$		0			0
$59$	−10.3539	−	7.52257i	−1.34797	−	0.979356i	−0.999110	−	0.0421796i	$-0.986570\pi$
$59$	−10.3539	−	7.52257i	−1.34797	−	0.979356i	−0.348857	−	0.937176i	$-0.613430\pi$
$60$		0			0
$61$	−7.31975	+	5.31811i	−0.937198	+	0.680915i	−0.947745	−	0.319030i	$-0.896643\pi$
$61$	−7.31975	+	5.31811i	−0.937198	+	0.680915i	0.0105462	+	0.999944i	$0.496643\pi$
$62$		0			0
$63$	1.57075	−	0.248782i	0.197895	−	0.0313435i
$64$		0			0
$65$	−0.364120	−	0.733533i	−0.0451636	−	0.0909836i
$66$		0			0
$67$	5.12992	−	10.0680i	0.626720	−	1.23001i	−0.331359	−	0.943505i	$-0.607507\pi$
$67$	5.12992	−	10.0680i	0.626720	−	1.23001i	0.958079	−	0.286503i	$-0.0924927\pi$
$68$		0			0
$69$	−8.63132	+	2.80448i	−1.03909	+	0.337620i
$70$		0			0
$71$	−15.4722	−	5.02722i	−1.83621	−	0.596622i	−0.998742	−	0.0501387i	$-0.984034\pi$
$71$	−15.4722	−	5.02722i	−1.83621	−	0.596622i	−0.837470	−	0.546483i	$-0.815966\pi$
$72$		0			0
$73$	14.1235	+	2.23694i	1.65303	+	0.261814i	0.912158	−	0.409838i	$-0.134415\pi$
$73$	14.1235	+	2.23694i	1.65303	+	0.261814i	0.740867	+	0.671651i	$0.234415\pi$
$74$		0			0
$75$	6.11668	+	3.27989i	0.706293	+	0.378729i
$76$		0			0
$77$	−0.0391087	+	0.246922i	−0.00445684	+	0.0281394i
$78$		0			0
$79$	4.87493	−	15.0035i	0.548472	−	1.68802i	−0.164115	−	0.986441i	$-0.552477\pi$
$79$	4.87493	−	15.0035i	0.548472	−	1.68802i	0.712587	−	0.701583i	$-0.247523\pi$
$80$		0			0
$81$	1.43042	+	4.40238i	0.158936	+	0.489153i
$82$		0			0
$83$	−11.4971	−	5.85808i	−1.26197	−	0.643007i	−0.310451	−	0.950589i	$-0.600480\pi$
$83$	−11.4971	−	5.85808i	−1.26197	−	0.643007i	−0.951522	+	0.307582i	$0.900480\pi$
$84$		0			0
$85$	−2.98545	−	0.504980i	−0.323817	−	0.0547728i
$86$		0			0
$87$	−0.772615	−	4.87810i	−0.0828330	−	0.522987i
$88$		0			0
$89$	2.77813	+	3.82377i	0.294481	+	0.405319i	0.930463	−	0.366385i	$-0.119405\pi$
$89$	2.77813	+	3.82377i	0.294481	+	0.405319i	−0.635982	+	0.771704i	$0.719405\pi$
$90$		0			0
$91$	0.319015	−	0.439087i	0.0334419	−	0.0460288i
$92$		0			0
$93$	−3.26793	−	3.26793i	−0.338868	−	0.338868i
$94$		0			0
$95$	−2.04609	−	2.87919i	−0.209925	−	0.295399i
$96$		0			0
$97$	−5.33666	−	10.4738i	−0.541856	−	1.06345i	−0.985883	−	0.167438i	$-0.946451\pi$
$97$	−5.33666	−	10.4738i	−0.541856	−	1.06345i	0.444027	−	0.896013i	$-0.353549\pi$
$98$		0			0
$99$	0.181038			0.0181950
$100$		0			0
$101$	−11.6784			−1.16204			−0.581021	−	0.813889i	$-0.697346\pi$
$101$	−11.6784			−1.16204			−0.581021	+	0.813889i	$0.697346\pi$
$102$		0			0
$103$	3.37989	+	6.63340i	0.333030	+	0.653609i	0.995425	−	0.0955464i	$-0.0304598\pi$
$103$	3.37989	+	6.63340i	0.333030	+	0.653609i	−0.662395	+	0.749155i	$0.730460\pi$
$104$		0			0
$105$	−0.0482118	+	4.59954i	−0.00470499	+	0.448869i
$106$		0			0
$107$	−1.06357	−	1.06357i	−0.102819	−	0.102819i	0.653826	−	0.756645i	$-0.273163\pi$
$107$	−1.06357	−	1.06357i	−0.102819	−	0.102819i	−0.756645	+	0.653826i	$0.773163\pi$
$108$		0			0
$109$	−6.98398	+	9.61263i	−0.668944	+	0.920723i	−0.999736	−	0.0229811i	$-0.992684\pi$
$109$	−6.98398	+	9.61263i	−0.668944	+	0.920723i	0.330792	+	0.943704i	$0.392684\pi$
$110$		0			0
$111$	−2.95614	−	4.06878i	−0.280584	−	0.386191i
$112$		0			0
$113$	1.79674	+	11.3442i	0.169023	+	1.06717i	0.915664	+	0.401944i	$0.131666\pi$
$113$	1.79674	+	11.3442i	0.169023	+	1.06717i	−0.746641	+	0.665228i	$0.768334\pi$
$114$		0			0
$115$	2.13552	+	14.4626i	0.199138	+	1.34865i
$116$		0			0
$117$	−0.350189	−	0.178430i	−0.0323750	−	0.0164959i
$118$		0			0
$119$	−0.620099	−	1.90847i	−0.0568444	−	0.174949i
$120$		0			0
$121$	3.39039	−	10.4346i	0.308218	−	0.948596i
$122$		0			0
$123$	−1.80916	+	11.4226i	−0.163126	+	1.02994i
$124$		0			0
$125$	6.85276	−	8.83401i	0.612930	−	0.790138i
$126$		0			0
$127$	0.700687	+	0.110978i	0.0621759	+	0.00984769i	0.187445	−	0.982275i	$-0.439979\pi$
$127$	0.700687	+	0.110978i	0.0621759	+	0.00984769i	−0.125269	+	0.992123i	$0.539979\pi$
$128$		0			0
$129$	−8.05351	−	2.61674i	−0.709072	−	0.230391i
$130$		0			0
$131$	−12.2227	+	3.97139i	−1.06790	+	0.346982i	−0.789670	−	0.613532i	$-0.789748\pi$
$131$	−12.2227	+	3.97139i	−1.06790	+	0.346982i	−0.278231	+	0.960514i	$0.589748\pi$
$132$		0			0
$133$	1.06275	−	2.08577i	0.0921523	−	0.180859i
$134$		0			0
$135$	12.5071	−	1.84676i	1.07644	−	0.158944i
$136$		0			0
$137$	−2.64979	+	0.419685i	−0.226387	+	0.0358561i	−0.268597	−	0.963253i	$-0.586560\pi$
$137$	−2.64979	+	0.419685i	−0.226387	+	0.0358561i	0.0422104	+	0.999109i	$0.486560\pi$
$138$		0			0
$139$	2.07298	−	1.50611i	0.175828	−	0.127746i	−0.496391	−	0.868099i	$-0.665342\pi$
$139$	2.07298	−	1.50611i	0.175828	−	0.127746i	0.672218	+	0.740353i	$0.265342\pi$
$140$		0			0
$141$	4.68979	+	3.40733i	0.394952	+	0.286949i
$142$		0			0
$143$	0.0436879	−	0.0436879i	0.00365337	−	0.00365337i
$144$		0			0
$145$	−7.95549	−	0.0833884i	−0.660668	−	0.00692503i
$146$		0			0
$147$	5.94152	−	3.02735i	0.490048	−	0.249692i
$148$		0			0
$149$			8.69912i			0.712660i	0.934360	+	0.356330i	$0.115972\pi$
$149$			8.69912i			0.712660i	−0.934360	+	0.356330i	$0.884028\pi$
$150$		0			0
$151$			5.73756i			0.466916i	0.972367	+	0.233458i	$0.0750042\pi$
$151$			5.73756i			0.466916i	−0.972367	+	0.233458i	$0.924996\pi$
$152$		0			0
$153$	−1.29476	+	0.659712i	−0.104675	+	0.0533346i
$154$		0			0
$155$	−6.06843	+	4.31252i	−0.487428	+	0.346390i
$156$		0			0
$157$	4.72527	−	4.72527i	0.377117	−	0.377117i	−0.492944	−	0.870061i	$-0.664079\pi$
$157$	4.72527	−	4.72527i	0.377117	−	0.377117i	0.870061	+	0.492944i	$0.164079\pi$
$158$		0			0
$159$	−2.95394	−	2.14616i	−0.234263	−	0.170202i
$160$		0			0
$161$	−7.83848	+	5.69499i	−0.617759	+	0.448828i
$162$		0			0
$163$	15.2729	−	2.41899i	1.19627	−	0.189470i	0.473646	−	0.880715i	$-0.342938\pi$
$163$	15.2729	−	2.41899i	1.19627	−	0.189470i	0.722620	+	0.691245i	$0.242938\pi$
$164$		0			0
$165$	−0.0873295	+	0.516293i	−0.00679859	+	0.0401934i
$166$		0			0
$167$	−2.49073	+	4.88833i	−0.192738	+	0.378271i	−0.967070	−	0.254509i	$-0.918086\pi$
$167$	−2.49073	+	4.88833i	−0.192738	+	0.378271i	0.774332	+	0.632780i	$0.218086\pi$
$168$		0			0
$169$	12.2362	−	3.97577i	0.941244	−	0.305829i
$170$		0			0
$171$	−1.61221	−	0.523837i	−0.123288	−	0.0400589i
$172$		0			0
$173$	19.4562	+	3.08157i	1.47923	+	0.234287i	0.843294	−	0.537453i	$-0.180614\pi$
$173$	19.4562	+	3.08157i	1.47923	+	0.234287i	0.635938	+	0.771740i	$0.280614\pi$
$174$		0			0
$175$	7.29253	+	1.31228i	0.551264	+	0.0991988i
$176$		0			0
$177$	2.77910	−	17.5466i	0.208890	−	1.31888i
$178$		0			0
$179$	1.59155	−	4.89827i	0.118958	−	0.366114i	−0.873794	−	0.486296i	$-0.838348\pi$
$179$	1.59155	−	4.89827i	0.118958	−	0.366114i	0.992752	+	0.120182i	$0.0383477\pi$
$180$		0			0
$181$	−4.79058	−	14.7439i	−0.356081	−	1.09590i	−0.955380	−	0.295379i	$-0.904554\pi$
$181$	−4.79058	−	14.7439i	−0.356081	−	1.09590i	0.599300	−	0.800525i	$-0.295446\pi$
$182$		0			0
$183$	−11.1904	−	5.70178i	−0.827216	−	0.421488i
$184$		0			0
$185$	−7.25666	+	3.60215i	−0.533520	+	0.264835i
$186$		0			0
$187$	−0.0357351	−	0.225622i	−0.00261321	−	0.0164991i
$188$		0			0
$189$	4.92495	+	6.77861i	0.358237	+	0.493071i
$190$		0			0
$191$	−0.0492519	+	0.0677894i	−0.00356374	+	0.00490507i	−0.810795	−	0.585330i	$-0.800965\pi$
$191$	−0.0492519	+	0.0677894i	−0.00356374	+	0.00490507i	0.807231	+	0.590235i	$0.200965\pi$
$192$		0			0
$193$	3.97741	+	3.97741i	0.286300	+	0.286300i	0.835615	−	0.549315i	$-0.185111\pi$
$193$	3.97741	+	3.97741i	0.286300	+	0.286300i	−0.549315	+	0.835615i	$0.685111\pi$
$194$		0			0
$195$	0.677782	−	0.912616i	0.0485370	−	0.0653538i
$196$		0			0
$197$	3.92599	+	7.70518i	0.279715	+	0.548971i	0.987531	−	0.157425i	$-0.0503194\pi$
$197$	3.92599	+	7.70518i	0.279715	+	0.548971i	−0.707816	+	0.706397i	$0.750319\pi$
$198$		0			0
$199$	21.5679			1.52891			0.764455	−	0.644677i	$-0.223008\pi$
$199$	21.5679			1.52891			0.764455	+	0.644677i	$0.223008\pi$
$200$		0			0
$201$	15.6852			1.10635
$202$		0			0
$203$	−2.39376	−	4.69802i	−0.168009	−	0.329737i
$204$		0			0
$205$	17.6565	+	5.94226i	1.23318	+	0.415025i
$206$		0			0
$207$	4.96122	+	4.96122i	0.344829	+	0.344829i
$208$		0			0
$209$	0.156634	−	0.215589i	0.0108346	−	0.0149126i
$210$		0			0
$211$	8.43098	+	11.6042i	0.580413	+	0.798869i	0.993741	−	0.111713i	$-0.0356337\pi$
$211$	8.43098	+	11.6042i	0.580413	+	0.798869i	−0.413328	+	0.910582i	$0.635634\pi$
$212$		0			0
$213$	−3.53267	−	22.3044i	−0.242055	−	1.52827i
$214$		0			0
$215$	−6.31983	+	12.0884i	−0.431009	+	0.824425i
$216$		0			0
$217$	−4.39614	−	2.23995i	−0.298430	−	0.152058i
$218$		0			0
$219$	6.13378	+	18.8778i	0.414483	+	1.27565i
$220$		0			0
$221$	−0.153249	+	0.471651i	−0.0103086	+	0.0317267i
$222$		0			0
$223$	−4.12520	+	26.0455i	−0.276244	+	1.74414i	0.325587	+	0.945512i	$0.394438\pi$
$223$	−4.12520	+	26.0455i	−0.276244	+	1.74414i	−0.601831	+	0.798624i	$0.705562\pi$
$224$		0			0
$225$	0.112473	−	5.36453i	0.00749821	−	0.357636i
$226$		0			0
$227$	2.07011	+	0.327874i	0.137398	+	0.0217617i	0.224755	−	0.974415i	$-0.427842\pi$
$227$	2.07011	+	0.327874i	0.137398	+	0.0217617i	−0.0873565	+	0.996177i	$0.527842\pi$
$228$		0			0
$229$	−2.31694	−	0.752818i	−0.153107	−	0.0497476i	0.231461	−	0.972844i	$-0.425650\pi$
$229$	−2.31694	−	0.752818i	−0.153107	−	0.0497476i	−0.384568	+	0.923097i	$0.625650\pi$
$230$		0			0
$231$	−0.330044	+	0.107238i	−0.0217153	+	0.00705572i
$232$		0			0
$233$	−7.03310	+	13.8032i	−0.460754	+	0.904280i	0.537388	+	0.843335i	$0.319411\pi$
$233$	−7.03310	+	13.8032i	−0.460754	+	0.904280i	−0.998141	+	0.0609444i	$0.980589\pi$
$234$		0			0
$235$	6.67185	−	6.53343i	0.435223	−	0.426194i
$236$		0			0
$237$	21.6287	−	3.42565i	1.40494	−	0.222520i
$238$		0			0
$239$	−20.7984	+	15.1109i	−1.34533	+	0.977443i	−0.346105	+	0.938196i	$0.612496\pi$
$239$	−20.7984	+	15.1109i	−1.34533	+	0.977443i	−0.999230	+	0.0392474i	$0.987504\pi$
$240$		0			0
$241$	4.70353	+	3.41732i	0.302981	+	0.220129i	0.728879	−	0.684643i	$-0.240042\pi$
$241$	4.70353	+	3.41732i	0.302981	+	0.220129i	−0.425898	+	0.904771i	$0.640042\pi$
$242$		0			0
$243$	7.45040	−	7.45040i	0.477943	−	0.477943i
$244$		0			0
$245$	−3.21214	−	10.2503i	−0.205216	−	0.654867i
$246$		0			0
$247$	−0.515469	+	0.262644i	−0.0327985	+	0.0167117i
$248$		0			0
$249$		−	17.9115i		−	1.13510i
$250$		0			0
$251$		−	1.03379i		−	0.0652522i	−0.999468	−	0.0326261i	$-0.989613\pi$
$251$		−	1.03379i		−	0.0652522i	0.999468	−	0.0326261i	$-0.0103870\pi$
$252$		0			0
$253$	−0.982740	+	0.500731i	−0.0617844	+	0.0314807i
$254$		0			0
$255$	−1.25683	−	4.01069i	−0.0787059	−	0.251159i
$256$		0			0
$257$	−11.1538	+	11.1538i	−0.695754	+	0.695754i	−0.963492	−	0.267738i	$-0.913724\pi$
$257$	−11.1538	+	11.1538i	−0.695754	+	0.695754i	0.267738	+	0.963492i	$0.413724\pi$
$258$		0			0
$259$	−4.34378	−	3.15594i	−0.269909	−	0.196100i
$260$		0			0
$261$	−3.08902	+	2.24431i	−0.191206	+	0.138919i
$262$		0			0
$263$	22.9196	−	3.63010i	1.41328	−	0.223842i	0.597345	−	0.801984i	$-0.296222\pi$
$263$	22.9196	−	3.63010i	1.41328	−	0.223842i	0.815936	+	0.578143i	$0.196222\pi$
$264$		0			0
$265$	−4.20237	+	4.11518i	−0.258149	+	0.252794i
$266$		0			0
$267$	−2.97855	+	5.84574i	−0.182285	+	0.357754i
$268$		0			0
$269$	12.2538	−	3.98149i	0.747125	−	0.242755i	0.0893811	−	0.995998i	$-0.471511\pi$
$269$	12.2538	−	3.98149i	0.747125	−	0.242755i	0.657743	+	0.753242i	$0.271511\pi$
$270$		0			0
$271$	19.1563	+	6.22426i	1.16366	+	0.378097i	0.826274	−	0.563268i	$-0.190456\pi$
$271$	19.1563	+	6.22426i	1.16366	+	0.378097i	0.337389	+	0.941365i	$0.390456\pi$
$272$		0			0
$273$	0.744111	+	0.117856i	0.0450356	+	0.00713295i
$274$		0			0
$275$	0.796570	+	0.277412i	0.0480350	+	0.0167286i
$276$		0			0
$277$	−4.07240	+	25.7121i	−0.244687	+	1.54489i	0.493170	+	0.869933i	$0.335838\pi$
$277$	−4.07240	+	25.7121i	−0.244687	+	1.54489i	−0.737857	+	0.674957i	$0.764162\pi$
$278$		0			0
$279$	−1.10408	+	3.39802i	−0.0660998	+	0.203434i
$280$		0			0
$281$	1.96162	+	6.03725i	0.117021	+	0.360152i	0.992363	−	0.123351i	$-0.0393641\pi$
$281$	1.96162	+	6.03725i	0.117021	+	0.360152i	−0.875343	+	0.483503i	$0.839364\pi$
$282$		0			0
$283$	−16.5487	−	8.43199i	−0.983719	−	0.501230i	−0.113310	−	0.993560i	$-0.536145\pi$
$283$	−16.5487	−	8.43199i	−0.983719	−	0.501230i	−0.870409	+	0.492330i	$0.836145\pi$
$284$		0			0
$285$	2.27161	−	4.34508i	0.134558	−	0.257380i
$286$		0			0
$287$	1.93143	+	12.1946i	0.114009	+	0.719824i
$288$		0			0
$289$	−8.91460	−	12.2699i	−0.524388	−	0.721758i
$290$		0			0
$291$	9.59105	−	13.2009i	0.562237	−	0.773853i
$292$		0			0
$293$	−20.3728	−	20.3728i	−1.19019	−	1.19019i	−0.977014	−	0.213177i	$-0.931619\pi$
$293$	−20.3728	−	20.3728i	−1.19019	−	1.19019i	−0.213177	−	0.977014i	$-0.568381\pi$
$294$		0			0
$295$	−27.1227	−	9.12810i	−1.57915	−	0.531458i
$296$		0			0
$297$	0.433025	+	0.849860i	0.0251267	+	0.0493139i
$298$		0			0
$299$	2.39448			0.138476
$300$		0			0
$301$	−9.04029			−0.521074
$302$		0			0
$303$	−7.35959	−	14.4440i	−0.422798	−	0.829787i
$304$		0			0
$305$	−12.0626	+	16.2419i	−0.690700	+	0.930010i
$306$		0			0
$307$	−10.4358	−	10.4358i	−0.595603	−	0.595603i	0.343536	−	0.939139i	$-0.388375\pi$
$307$	−10.4358	−	10.4358i	−0.595603	−	0.595603i	−0.939139	+	0.343536i	$0.888375\pi$
$308$		0			0
$309$	−6.07434	+	8.36061i	−0.345557	+	0.475618i
$310$		0			0
$311$	−0.526932	−	0.725259i	−0.0298796	−	0.0411257i	0.793816	−	0.608158i	$-0.208091\pi$
$311$	−0.526932	−	0.725259i	−0.0298796	−	0.0411257i	−0.823695	+	0.567033i	$0.808091\pi$
$312$		0			0
$313$	−0.227697	−	1.43762i	−0.0128702	−	0.0812593i	0.980417	−	0.196932i	$-0.0630977\pi$
$313$	−0.227697	−	1.43762i	−0.0128702	−	0.0812593i	−0.993287	+	0.115672i	$0.963098\pi$
$314$		0			0
$315$	3.18523	−	1.58113i	0.179468	−	0.0890863i
$316$		0			0
$317$	5.01284	+	2.55417i	0.281549	+	0.143457i	0.589063	−	0.808087i	$-0.299497\pi$
$317$	5.01284	+	2.55417i	0.281549	+	0.143457i	−0.307514	+	0.951544i	$0.599497\pi$
$318$		0			0
$319$	−0.185481	−	0.570853i	−0.0103850	−	0.0319616i
$320$		0			0
$321$	0.645188	−	1.98569i	0.0360109	−	0.110830i
$322$		0			0
$323$	−0.334610	+	2.11265i	−0.0186182	+	0.117551i
$324$		0			0
$325$	−1.26742	−	1.32171i	−0.0703040	−	0.0733152i
$326$		0			0
$327$	−16.2903	−	2.58013i	−0.900856	−	0.142682i
$328$		0			0
$329$	5.88581	+	1.91241i	0.324495	+	0.105435i
$330$		0			0
$331$	17.9746	−	5.84029i	0.987971	−	0.321011i	0.229922	−	0.973209i	$-0.426153\pi$
$331$	17.9746	−	5.84029i	0.987971	−	0.321011i	0.758049	+	0.652198i	$0.226153\pi$
$332$		0			0
$333$	−1.76517	+	3.46433i	−0.0967305	+	0.189844i
$334$		0			0
$335$	4.21394	−	24.9129i	0.230232	−	1.36114i
$336$		0			0
$337$	−22.6084	+	3.58082i	−1.23156	+	0.195059i	−0.738088	−	0.674704i	$-0.764271\pi$
$337$	−22.6084	+	3.58082i	−1.23156	+	0.195059i	−0.493469	+	0.869764i	$0.664271\pi$
$338$		0			0
$339$	−12.8984	+	9.37124i	−0.700545	+	0.508976i
$340$		0			0
$341$	−0.454394	−	0.330136i	−0.0246068	−	0.0178779i
$342$		0			0
$343$	12.3691	−	12.3691i	0.667869	−	0.667869i
$344$		0			0
$345$	−16.5419	+	11.7555i	−0.890584	+	0.632892i
$346$		0			0
$347$	−10.8348	+	5.52060i	−0.581642	+	0.296361i	−0.719948	−	0.694028i	$-0.755834\pi$
$347$	−10.8348	+	5.52060i	−0.581642	+	0.296361i	0.138306	+	0.990390i	$0.455834\pi$
$348$		0			0
$349$		−	7.55962i		−	0.404657i	−0.979318	−	0.202329i	$-0.935149\pi$
$349$		−	7.55962i		−	0.404657i	0.979318	−	0.202329i	$-0.0648509\pi$
$350$		0			0
$351$		−	2.07071i		−	0.110526i
$352$		0			0
$353$	−22.7197	+	11.5763i	−1.20925	+	0.616142i	−0.938090	−	0.346393i	$-0.887406\pi$
$353$	−22.7197	+	11.5763i	−1.20925	+	0.616142i	−0.271158	+	0.962535i	$0.587406\pi$
$354$		0			0
$355$	−36.3753	−	0.381282i	−1.93060	−	0.0202363i
$356$		0			0
$357$	1.96965	−	1.96965i	0.104245	−	0.104245i
$358$		0			0
$359$	−0.0972255	−	0.0706384i	−0.00513136	−	0.00372815i	0.585217	−	0.810877i	$-0.301009\pi$
$359$	−0.0972255	−	0.0706384i	−0.00513136	−	0.00372815i	−0.590348	+	0.807149i	$0.701009\pi$
$360$		0			0
$361$	13.3526	−	9.70125i	0.702770	−	0.510592i
$362$		0			0
$363$	15.0422	−	2.38246i	0.789512	−	0.125046i
$364$		0			0
$365$	31.6317	−	4.67066i	1.65568	−	0.244473i
$366$		0			0
$367$	−2.25797	+	4.43152i	−0.117865	+	0.231323i	−0.942400	−	0.334488i	$-0.891437\pi$
$367$	−2.25797	+	4.43152i	−0.117865	+	0.231323i	0.824535	+	0.565811i	$0.191437\pi$
$368$		0			0
$369$	8.50321	−	2.76286i	0.442659	−	0.143829i
$370$		0			0
$371$	−3.70727	−	1.20456i	−0.192472	−	0.0625379i
$372$		0			0
$373$	−0.329633	−	0.0522088i	−0.0170678	−	0.00270327i	0.147895	−	0.989003i	$-0.452750\pi$
$373$	−0.329633	−	0.0522088i	−0.0170678	−	0.00270327i	−0.164963	+	0.986300i	$0.552750\pi$
$374$		0			0
$375$	15.2446	+	2.90851i	0.787228	+	0.150195i
$376$		0			0
$377$	−0.203846	+	1.28703i	−0.0104986	+	0.0662857i
$378$		0			0
$379$	5.21049	−	16.0362i	0.267645	−	0.823726i	−0.723428	−	0.690400i	$-0.757434\pi$
$379$	5.21049	−	16.0362i	0.267645	−	0.823726i	0.991072	−	0.133325i	$-0.0425655\pi$
$380$		0			0
$381$	0.304306	+	0.936559i	0.0155901	+	0.0479814i
$382$		0			0
$383$	−22.9034	−	11.6698i	−1.17031	−	0.596301i	−0.242789	−	0.970079i	$-0.578062\pi$
$383$	−22.9034	−	11.6698i	−1.17031	−	0.596301i	−0.927518	+	0.373778i	$0.878062\pi$
$384$		0			0
$385$	0.0816577	+	0.553021i	0.00416166	+	0.0281846i
$386$		0			0
$387$	1.02410	+	6.46594i	0.0520581	+	0.328682i
$388$		0			0
$389$	7.44948	+	10.2533i	0.377704	+	0.519865i	0.954974	−	0.296688i	$-0.0958822\pi$
$389$	7.44948	+	10.2533i	0.377704	+	0.519865i	−0.577271	+	0.816553i	$0.695882\pi$
$390$		0			0
$391$	5.20373	−	7.16232i	0.263164	−	0.362214i
$392$		0			0
$393$	−12.6145	−	12.6145i	−0.636317	−	0.636317i
$394$		0			0
$395$	0.369731	−	35.2734i	0.0186032	−	1.77480i
$396$		0			0
$397$	12.9530	+	25.4218i	0.650094	+	1.27588i	0.947079	+	0.320999i	$0.104019\pi$
$397$	12.9530	+	25.4218i	0.650094	+	1.27588i	−0.296985	+	0.954882i	$0.595981\pi$
$398$		0			0
$399$	3.24945			0.162676
$400$		0			0
$401$	0.192908			0.00963338			0.00481669	−	0.999988i	$-0.498467\pi$
$401$	0.192908			0.00963338			0.00481669	+	0.999988i	$0.498467\pi$
$402$		0			0
$403$	0.553572	+	1.08645i	0.0275754	+	0.0541197i
$404$		0			0
$405$	5.99584	+	8.43713i	0.297936	+	0.419244i
$406$		0			0
$407$	−0.432194	−	0.432194i	−0.0214230	−	0.0214230i
$408$		0			0
$409$	4.25450	−	5.85582i	0.210371	−	0.289552i	−0.690772	−	0.723073i	$-0.742729\pi$
$409$	4.25450	−	5.85582i	0.210371	−	0.289552i	0.901143	+	0.433521i	$0.142729\pi$
$410$		0			0
$411$	−2.18894	−	3.01282i	−0.107973	−	0.148612i
$412$		0			0
$413$	−2.96694	−	18.7325i	−0.145994	−	0.921767i
$414$		0			0
$415$	−28.4490	−	4.81207i	−1.39651	−	0.236215i
$416$		0			0
$417$	3.16915	+	1.61476i	0.155194	+	0.0790752i
$418$		0			0
$419$	10.9889	+	33.8203i	0.536842	+	1.65223i	0.739634	+	0.673009i	$0.234999\pi$
$419$	10.9889	+	33.8203i	0.536842	+	1.65223i	−0.202791	+	0.979222i	$0.565001\pi$
$420$		0			0
$421$	2.74774	−	8.45666i	0.133916	−	0.412152i	−0.861503	−	0.507752i	$-0.830477\pi$
$421$	2.74774	−	8.45666i	0.133916	−	0.412152i	0.995420	+	0.0955993i	$0.0304768\pi$
$422$		0			0
$423$	0.701070	−	4.42638i	0.0340872	−	0.215218i
$424$		0			0
$425$	−6.70787	+	0.918733i	−0.325379	+	0.0445651i
$426$		0			0
$427$	−13.2430	−	2.09749i	−0.640875	−	0.101505i
$428$		0			0
$429$	0.0815657	+	0.0265023i	0.00393803	+	0.00127954i
$430$		0			0
$431$	27.3276	−	8.87927i	1.31632	−	0.427699i	0.435093	−	0.900386i	$-0.356716\pi$
$431$	27.3276	−	8.87927i	1.31632	−	0.427699i	0.881231	+	0.472686i	$0.156716\pi$
$432$		0			0
$433$	−11.4519	+	22.4756i	−0.550342	+	1.08011i	0.433514	+	0.901147i	$0.357274\pi$
$433$	−11.4519	+	22.4756i	−0.550342	+	1.08011i	−0.983856	+	0.178961i	$0.942726\pi$
$434$		0			0
$435$	−4.91033	−	9.89204i	−0.235433	−	0.474287i
$436$		0			0
$437$	10.2005	−	1.61560i	0.487957	−	0.0772849i
$438$		0			0
$439$	−17.4647	+	12.6889i	−0.833547	+	0.605607i	−0.920561	−	0.390600i	$-0.872268\pi$
$439$	−17.4647	+	12.6889i	−0.833547	+	0.605607i	0.0870138	+	0.996207i	$0.472268\pi$
$440$		0			0
$441$	−4.17068	−	3.03018i	−0.198604	−	0.144294i
$442$		0			0
$443$	20.2111	−	20.2111i	0.960257	−	0.960257i	−0.0389829	−	0.999240i	$-0.512412\pi$
$443$	20.2111	−	20.2111i	0.960257	−	0.960257i	0.999240	+	0.0389829i	$0.0124118\pi$
$444$		0			0
$445$	8.48463	+	6.30136i	0.402210	+	0.298713i
$446$		0			0
$447$	−10.7592	+	5.48210i	−0.508894	+	0.259294i
$448$		0			0
$449$		−	10.9202i		−	0.515358i	−0.966231	−	0.257679i	$-0.917042\pi$
$449$		−	10.9202i		−	0.515358i	0.966231	−	0.257679i	$-0.0829576\pi$
$450$		0			0
$451$			1.40550i			0.0661824i
$452$		0			0
$453$	−7.09632	+	3.61575i	−0.333414	+	0.169883i
$454$		0			0
$455$	0.387102	−	1.15021i	0.0181476	−	0.0539229i
$456$		0			0
$457$	−19.0896	+	19.0896i	−0.892976	+	0.892976i	−0.994802	−	0.101826i	$-0.967531\pi$
$457$	−19.0896	+	19.0896i	−0.892976	+	0.892976i	0.101826	+	0.994802i	$0.467531\pi$
$458$		0			0
$459$	−6.19387	−	4.50011i	−0.289105	−	0.210047i
$460$		0			0
$461$	9.71821	−	7.06069i	0.452622	−	0.328849i	−0.338008	−	0.941143i	$-0.609753\pi$
$461$	9.71821	−	7.06069i	0.452622	−	0.328849i	0.790630	+	0.612294i	$0.209753\pi$
$462$		0			0
$463$	13.6775	−	2.16630i	0.635646	−	0.100676i	0.169709	−	0.985494i	$-0.445717\pi$
$463$	13.6775	−	2.16630i	0.635646	−	0.100676i	0.465937	+	0.884818i	$0.345717\pi$
$464$		0			0
$465$	−9.15806	−	4.78783i	−0.424695	−	0.222030i
$466$		0			0
$467$	−8.92743	+	17.5211i	−0.413112	+	0.810779i	0.586887	+	0.809669i	$0.300353\pi$
$467$	−8.92743	+	17.5211i	−0.413112	+	0.810779i	−0.999999	+	0.00110978i	$0.999647\pi$
$468$		0			0
$469$	15.9257	−	5.17458i	0.735381	−	0.238940i
$470$		0			0
$471$	8.82211	+	2.86648i	0.406501	+	0.132080i
$472$		0			0
$473$	−1.01645	−	0.160990i	−0.0467364	−	0.00740232i
$474$		0			0
$475$	−6.29104	−	4.77535i	−0.288653	−	0.219108i
$476$		0			0
$477$	−0.441580	+	2.78802i	−0.0202185	+	0.127655i
$478$		0			0
$479$	−2.63365	+	8.10555i	−0.120335	+	0.370352i	−0.993022	−	0.117927i	$-0.962375\pi$
$479$	−2.63365	+	8.10555i	−0.120335	+	0.370352i	0.872688	+	0.488279i	$0.162375\pi$
$480$		0			0
$481$	0.410042	+	1.26198i	0.0186963	+	0.0575413i
$482$		0			0
$483$	−11.9834	−	6.10585i	−0.545264	−	0.277826i
$484$		0			0
$485$	−18.3905	−	18.7801i	−0.835068	−	0.852759i
$486$		0			0
$487$	−4.59603	−	29.0182i	−0.208266	−	1.31494i	−0.841195	−	0.540731i	$-0.818148\pi$
$487$	−4.59603	−	29.0182i	−0.208266	−	1.31494i	0.632929	−	0.774210i	$-0.281852\pi$
$488$		0			0
$489$	12.6167	+	17.3654i	0.570546	+	0.785289i
$490$		0			0
$491$	−6.47867	+	8.91713i	−0.292378	+	0.402424i	−0.929785	−	0.368103i	$-0.880007\pi$
$491$	−6.47867	+	8.91713i	−0.292378	+	0.402424i	0.637407	+	0.770528i	$0.280007\pi$
$492$		0			0
$493$	3.40676	+	3.40676i	0.153433	+	0.153433i
$494$		0			0
$495$	0.386290	−	0.121052i	0.0173624	−	0.00544088i
$496$		0			0
$497$	−10.9451	−	21.4810i	−0.490956	−	0.963556i
$498$		0			0
$499$	30.4320			1.36232			0.681161	−	0.732134i	$-0.261475\pi$
$499$	30.4320			1.36232			0.681161	+	0.732134i	$0.261475\pi$
$500$		0			0
$501$	−7.61561			−0.340240
$502$		0			0
$503$	−12.4208	−	24.3771i	−0.553815	−	1.08692i	−0.982983	−	0.183698i	$-0.941193\pi$
$503$	−12.4208	−	24.3771i	−0.553815	−	1.08692i	0.429168	−	0.903225i	$-0.358807\pi$
$504$		0			0
$505$	−24.9188	+	7.80880i	−1.10887	+	0.347487i
$506$		0			0
$507$	12.6284	+	12.6284i	0.560848	+	0.560848i
$508$		0			0
$509$	−7.53440	+	10.3702i	−0.333956	+	0.459651i	−0.942664	−	0.333743i	$-0.891688\pi$
$509$	−7.53440	+	10.3702i	−0.333956	+	0.459651i	0.608708	+	0.793394i	$0.291688\pi$
$510$		0			0
$511$	12.4557	+	17.1438i	0.551008	+	0.758397i
$512$		0			0
$513$	−1.39715	−	8.82127i	−0.0616858	−	0.389469i
$514$		0			0
$515$	11.6473	+	11.8941i	0.513242	+	0.524115i
$516$		0			0
$517$	0.627717	+	0.319838i	0.0276070	+	0.0140665i
$518$		0			0
$519$	8.44980	+	26.0058i	0.370905	+	1.14153i
$520$		0			0
$521$	3.41175	−	10.5003i	0.149472	−	0.460026i	−0.848087	−	0.529857i	$-0.822246\pi$
$521$	3.41175	−	10.5003i	0.149472	−	0.460026i	0.997559	+	0.0698302i	$0.0222457\pi$
$522$		0			0
$523$	−6.46921	+	40.8450i	−0.282879	+	1.78603i	0.280527	+	0.959846i	$0.409491\pi$
$523$	−6.46921	+	40.8450i	−0.282879	+	1.78603i	−0.563406	+	0.826180i	$0.690509\pi$
$524$		0			0
$525$	2.97263	+	9.84652i	0.129736	+	0.429737i
$526$		0			0
$527$	4.45279	+	0.705253i	0.193967	+	0.0307213i
$528$		0			0
$529$	−18.7792	−	6.10174i	−0.816488	−	0.265293i
$530$		0			0
$531$	−13.0621	+	4.24412i	−0.566845	+	0.184179i
$532$		0			0
$533$	1.38526	−	2.71872i	0.0600021	−	0.117761i
$534$		0			0
$535$	−2.98055	−	1.55823i	−0.128860	−	0.0673681i
$536$		0			0
$537$	7.06125	−	1.11839i	0.304715	−	0.0482622i
$538$		0			0
$539$	0.655634	−	0.476346i	0.0282402	−	0.0205177i
$540$		0			0
$541$	−25.4223	−	18.4704i	−1.09299	−	0.794104i	−0.113088	−	0.993585i	$-0.536074\pi$
$541$	−25.4223	−	18.4704i	−1.09299	−	0.794104i	−0.979902	+	0.199481i	$0.936074\pi$
$542$		0			0
$543$	15.2165	−	15.2165i	0.653003	−	0.653003i
$544$		0			0
$545$	−8.47456	+	25.1808i	−0.363010	+	1.07863i
$546$		0			0
$547$	−29.4471	+	15.0040i	−1.25907	+	0.641526i	−0.950809	−	0.309777i	$-0.899745\pi$
$547$	−29.4471	+	15.0040i	−1.25907	+	0.641526i	−0.308256	+	0.951303i	$0.599745\pi$
$548$		0			0
$549$			9.70949i			0.414391i
$550$		0			0
$551$			5.62034i			0.239434i
$552$		0			0
$553$	20.8303	−	10.6136i	0.885794	−	0.451335i
$554$		0			0
$555$	−9.02828	−	6.70513i	−0.383229	−	0.284617i
$556$		0			0
$557$	24.5284	−	24.5284i	1.03930	−	1.03930i	0.0401049	−	0.999195i	$-0.487231\pi$
$557$	24.5284	−	24.5284i	1.03930	−	1.03930i	0.999195	−	0.0401049i	$-0.0127692\pi$
$558$		0			0
$559$	1.80749	+	1.31322i	0.0764488	+	0.0555433i
$560$		0			0
$561$	0.256534	−	0.186383i	0.0108309	−	0.00786908i
$562$		0			0
$563$	32.1270	−	5.08842i	1.35399	−	0.214451i	0.563091	−	0.826395i	$-0.309612\pi$
$563$	32.1270	−	5.08842i	1.35399	−	0.214451i	0.790901	+	0.611944i	$0.209612\pi$
$564$		0			0
$565$	11.4192	+	23.0043i	0.480408	+	0.967798i
$566$		0			0
$567$	−3.11427	+	6.11210i	−0.130787	+	0.256684i
$568$		0			0
$569$	31.5276	−	10.2439i	1.32171	−	0.429448i	0.438625	−	0.898670i	$-0.355466\pi$
$569$	31.5276	−	10.2439i	1.32171	−	0.429448i	0.883080	+	0.469222i	$0.155466\pi$
$570$		0			0
$571$	34.4177	+	11.1830i	1.44033	+	0.467993i	0.922002	−	0.387186i	$-0.126553\pi$
$571$	34.4177	+	11.1830i	1.44033	+	0.467993i	0.518333	+	0.855179i	$0.326553\pi$
$572$		0			0
$573$	−0.114881	−	0.0181954i	−0.00479923	−	0.000760123i
$574$		0			0
$575$	14.2272	+	29.4318i	0.593314	+	1.22739i
$576$		0			0
$577$	3.64976	−	23.0437i	0.151942	−	0.959321i	−0.787426	−	0.616409i	$-0.788587\pi$
$577$	3.64976	−	23.0437i	0.151942	−	0.959321i	0.939368	−	0.342912i	$-0.111413\pi$
$578$		0			0
$579$	−2.41281	+	7.42585i	−0.100273	+	0.308608i
$580$		0			0
$581$	−5.90907	−	18.1862i	−0.245149	−	0.754492i
$582$		0			0
$583$	−0.395378	−	0.201455i	−0.0163749	−	0.00834341i
$584$		0			0
$585$	−0.866526	−	0.146570i	−0.0358264	−	0.00605994i
$586$		0			0
$587$	4.78783	+	30.2291i	0.197615	+	1.24769i	0.864539	+	0.502565i	$0.167610\pi$
$587$	4.78783	+	30.2291i	0.197615	+	1.24769i	−0.666925	+	0.745125i	$0.732390\pi$
$588$		0			0
$589$	3.09128	+	4.25478i	0.127374	+	0.175315i
$590$		0			0
$591$	−7.05579	+	9.71146i	−0.290236	+	0.399476i
$592$		0			0
$593$	18.5760	+	18.5760i	0.762825	+	0.762825i	0.976832	−	0.214007i	$-0.0686514\pi$
$593$	18.5760	+	18.5760i	0.762825	+	0.762825i	−0.214007	+	0.976832i	$0.568651\pi$
$594$		0			0
$595$	−2.59924	−	3.65757i	−0.106559	−	0.149946i
$596$		0			0
$597$	13.5919	+	26.6756i	0.556279	+	1.09176i
$598$		0			0
$599$	21.7167			0.887321			0.443661	−	0.896195i	$-0.353680\pi$
$599$	21.7167			0.887321			0.443661	+	0.896195i	$0.353680\pi$
$600$		0			0
$601$	42.0559			1.71550			0.857748	−	0.514071i	$-0.171863\pi$
$601$	42.0559			1.71550			0.857748	+	0.514071i	$0.171863\pi$
$602$		0			0
$603$	−5.50514	−	10.8044i	−0.224187	−	0.439991i
$604$		0			0
$605$	0.257139	−	24.5318i	0.0104542	−	0.997358i
$606$		0			0
$607$	−5.14209	−	5.14209i	−0.208711	−	0.208711i	0.595008	−	0.803719i	$-0.297149\pi$
$607$	−5.14209	−	5.14209i	−0.208711	−	0.208711i	−0.803719	+	0.595008i	$0.797149\pi$
$608$		0			0
$609$	4.30207	−	5.92129i	0.174329	−	0.239943i
$610$		0			0
$611$	−0.898989	−	1.23735i	−0.0363692	−	0.0500579i
$612$		0			0
$613$	−4.62115	−	29.1768i	−0.186646	−	1.17844i	−0.886008	−	0.463671i	$-0.846532\pi$
$613$	−4.62115	−	29.1768i	−0.186646	−	1.17844i	0.699361	−	0.714768i	$-0.253468\pi$
$614$		0			0
$615$	3.77747	+	25.5826i	0.152322	+	1.03159i
$616$		0			0
$617$	30.4600	+	15.5201i	1.22627	+	0.624817i	0.942542	−	0.334087i	$-0.108428\pi$
$617$	30.4600	+	15.5201i	1.22627	+	0.624817i	0.283731	+	0.958904i	$0.408428\pi$
$618$		0			0
$619$	4.49710	+	13.8407i	0.180754	+	0.556303i	0.999849	−	0.0173539i	$-0.00552420\pi$
$619$	4.49710	+	13.8407i	0.180754	+	0.556303i	−0.819096	+	0.573657i	$0.805524\pi$
$620$		0			0
$621$	−11.4231	+	35.1566i	−0.458392	+	1.41079i
$622$		0			0
$623$	−1.09571	+	6.91803i	−0.0438986	+	0.277165i
$624$		0			0
$625$	8.71519	−	23.4317i	0.348608	−	0.937269i
$626$		0			0
$627$	0.365354	+	0.0578663i	0.0145908	+	0.00231096i
$628$		0			0
$629$	4.66593	+	1.51605i	0.186043	+	0.0604489i
$630$		0			0
$631$	8.67575	−	2.81892i	0.345376	−	0.112220i	−0.131192	−	0.991357i	$-0.541880\pi$
$631$	8.67575	−	2.81892i	0.345376	−	0.112220i	0.476568	+	0.879137i	$0.341880\pi$
$632$		0			0
$633$	−9.03922	+	17.7405i	−0.359277	+	0.705120i
$634$		0			0
$635$	1.56930	−	0.231718i	0.0622757	−	0.00919547i
$636$		0			0
$637$	−1.73771	+	0.275226i	−0.0688504	+	0.0109048i
$638$		0			0
$639$	−14.1241	+	10.2618i	−0.558741	+	0.405949i
$640$		0			0
$641$	−19.1690	−	13.9271i	−0.757131	−	0.550088i	0.140898	−	0.990024i	$-0.455001\pi$
$641$	−19.1690	−	13.9271i	−0.757131	−	0.550088i	−0.898029	+	0.439936i	$0.855001\pi$
$642$		0			0
$643$	−1.28119	+	1.28119i	−0.0505252	+	0.0505252i	−0.731918	−	0.681393i	$-0.761375\pi$
$643$	−1.28119	+	1.28119i	−0.0505252	+	0.0505252i	0.681393	+	0.731918i	$0.261375\pi$
$644$		0			0
$645$	−18.9339	−	0.198463i	−0.745521	−	0.00781446i
$646$		0			0
$647$	24.6793	−	12.5747i	0.970242	−	0.494363i	0.104321	−	0.994544i	$-0.466733\pi$
$647$	24.6793	−	12.5747i	0.970242	−	0.494363i	0.865921	+	0.500181i	$0.166733\pi$
$648$		0			0
$649$		−	2.15903i		−	0.0847495i
$650$		0			0
$651$		−	6.84882i		−	0.268426i
$652$		0			0
$653$	22.8434	−	11.6393i	0.893933	−	0.455482i	0.0542307	−	0.998528i	$-0.482729\pi$
$653$	22.8434	−	11.6393i	0.893933	−	0.455482i	0.839702	+	0.543047i	$0.182729\pi$
$654$		0			0
$655$	−23.4247	+	16.6467i	−0.915278	+	0.650441i
$656$		0			0
$657$	10.8508	−	10.8508i	0.423332	−	0.423332i
$658$		0			0
$659$	−7.46387	−	5.42282i	−0.290751	−	0.211243i	0.432842	−	0.901470i	$-0.357511\pi$
$659$	−7.46387	−	5.42282i	−0.290751	−	0.211243i	−0.723593	+	0.690227i	$0.757511\pi$
$660$		0			0
$661$	26.7691	−	19.4489i	1.04120	−	0.756475i	0.0706791	−	0.997499i	$-0.477483\pi$
$661$	26.7691	−	19.4489i	1.04120	−	0.756475i	0.970519	+	0.241024i	$0.0774834\pi$
$662$		0			0
$663$	−0.679923	+	0.107689i	−0.0264060	+	0.00418230i
$664$		0			0
$665$	0.872990	−	5.16113i	0.0338531	−	0.200140i
$666$		0			0
$667$	10.5608	−	20.7268i	0.408917	−	0.802546i
$668$		0			0
$669$	−34.8132	+	11.3115i	−1.34596	+	0.437328i
$670$		0			0
$671$	−1.45163	−	0.471664i	−0.0560397	−	0.0182084i
$672$		0			0
$673$	37.5793	+	5.95197i	1.44857	+	0.229432i	0.830645	−	0.556802i	$-0.187972\pi$
$673$	37.5793	+	5.95197i	1.44857	+	0.229432i	0.617930	+	0.786234i	$0.287972\pi$
$674$		0			0
$675$	25.4522	−	12.3035i	0.979654	−	0.473560i
$676$		0			0
$677$	−3.05193	+	19.2691i	−0.117295	+	0.740573i	0.857003	+	0.515312i	$0.172324\pi$
$677$	−3.05193	+	19.2691i	−0.117295	+	0.740573i	−0.974298	+	0.225262i	$0.927676\pi$
$678$		0			0
$679$	5.38311	−	16.5675i	0.206585	−	0.635803i
$680$		0			0
$681$	0.899045	+	2.76698i	0.0344515	+	0.106031i
$682$		0			0
$683$	−0.565299	−	0.288034i	−0.0216306	−	0.0110213i	0.443142	−	0.896452i	$-0.353864\pi$
$683$	−0.565299	−	0.288034i	−0.0216306	−	0.0110213i	−0.464772	+	0.885430i	$0.653864\pi$
$684$		0			0
$685$	−5.37337	+	2.66730i	−0.205306	+	0.101912i
$686$		0			0
$687$	−0.529011	−	3.34005i	−0.0201830	−	0.127431i
$688$		0			0
$689$	0.566242	+	0.779366i	0.0215721	+	0.0296915i
$690$		0			0
$691$	−12.9621	+	17.8408i	−0.493101	+	0.678695i	−0.980956	−	0.194230i	$-0.937779\pi$
$691$	−12.9621	+	17.8408i	−0.493101	+	0.678695i	0.487856	+	0.872924i	$0.337779\pi$
$692$		0			0
$693$	0.189707	+	0.189707i	0.00720637	+	0.00720637i
$694$		0			0
$695$	3.41615	−	4.59976i	0.129582	−	0.174479i
$696$		0			0
$697$	−5.12172	−	10.0519i	−0.193999	−	0.380745i
$698$		0			0
$699$	−21.5043			−0.813366
$700$		0			0
$701$	−34.5682			−1.30562			−0.652811	−	0.757521i	$-0.726411\pi$
$701$	−34.5682			−1.30562			−0.652811	+	0.757521i	$0.726411\pi$
$702$		0			0
$703$	2.59827	+	5.09940i	0.0979958	+	0.192328i
$704$		0			0
$705$	12.2852	+	4.13455i	0.462687	+	0.155716i
$706$		0			0
$707$	−12.2376	−	12.2376i	−0.460242	−	0.460242i
$708$		0			0
$709$	1.87104	−	2.57526i	0.0702682	−	0.0967159i	−0.772436	−	0.635092i	$-0.780962\pi$
$709$	1.87104	−	2.57526i	0.0702682	−	0.0967159i	0.842705	+	0.538376i	$0.180962\pi$
$710$		0			0
$711$	−9.95090	−	13.6962i	−0.373188	−	0.513649i
$712$		0			0
$713$	−3.40519	−	21.4995i	−0.127525	−	0.805163i
$714$		0			0
$715$	0.0640071	−	0.122431i	0.00239373	−	0.00457868i
$716$		0			0
$717$	−31.7964	−	16.2011i	−1.18746	−	0.605039i
$718$		0			0
$719$	−1.75241	−	5.39338i	−0.0653540	−	0.201139i	0.913047	−	0.407854i	$-0.133723\pi$
$719$	−1.75241	−	5.39338i	−0.0653540	−	0.201139i	−0.978401	+	0.206715i	$0.933723\pi$
$720$		0			0
$721$	−3.40931	+	10.4928i	−0.126969	+	0.390771i
$722$		0			0
$723$	−1.26248	+	7.97097i	−0.0469520	+	0.296444i
$724$		0			0
$725$	−17.0308	+	5.14155i	−0.632508	+	0.190952i
$726$		0			0
$727$	−15.8391	−	2.50866i	−0.587439	−	0.0930412i	−0.144362	−	0.989525i	$-0.546113\pi$
$727$	−15.8391	−	2.50866i	−0.587439	−	0.0930412i	−0.443077	+	0.896484i	$0.646113\pi$
$728$		0			0
$729$	27.1171	+	8.81088i	1.00434	+	0.326329i
$730$		0			0
$731$	7.85616	−	2.55262i	0.290571	−	0.0944122i
$732$		0			0
$733$	−13.8779	+	27.2368i	−0.512590	+	1.00602i	0.479148	+	0.877734i	$0.340946\pi$
$733$	−13.8779	+	27.2368i	−0.512590	+	1.00602i	−0.991738	+	0.128281i	$0.959054\pi$
$734$		0			0
$735$	10.6535	−	10.4325i	0.392959	−	0.384807i
$736$		0			0
$737$	1.88276	−	0.298201i	0.0693525	−	0.0109844i
$738$		0			0
$739$	37.7235	−	27.4077i	1.38768	−	1.00821i	0.391564	−	0.920151i	$-0.371934\pi$
$739$	37.7235	−	27.4077i	1.38768	−	1.00821i	0.996115	−	0.0880575i	$-0.0280659\pi$
$740$		0			0
$741$	−0.649686	−	0.472025i	−0.0238668	−	0.0173403i
$742$		0			0
$743$	13.4374	−	13.4374i	0.492969	−	0.492969i	−0.416272	−	0.909240i	$-0.636663\pi$
$743$	13.4374	−	13.4374i	0.492969	−	0.492969i	0.909240	+	0.416272i	$0.136663\pi$
$744$		0			0
$745$	5.81671	+	18.5618i	0.213108	+	0.680051i
$746$		0			0
$747$	−12.3381	+	6.28655i	−0.451426	+	0.230013i
$748$		0			0
$749$		−	2.22899i		−	0.0814455i
$750$		0			0
$751$		−	3.94636i		−	0.144005i	−0.997404	−	0.0720023i	$-0.977061\pi$
$751$		−	3.94636i		−	0.144005i	0.997404	−	0.0720023i	$-0.0229389\pi$
$752$		0			0
$753$	1.27861	−	0.651483i	0.0465951	−	0.0237414i
$754$		0			0
$755$	3.83645	+	12.2425i	0.139623	+	0.445552i
$756$		0			0
$757$	4.06131	−	4.06131i	0.147611	−	0.147611i	−0.629439	−	0.777050i	$-0.716715\pi$
$757$	4.06131	−	4.06131i	0.147611	−	0.147611i	0.777050	+	0.629439i	$0.216715\pi$
$758$		0			0
$759$	−1.23863	−	0.899915i	−0.0449593	−	0.0326648i
$760$		0			0
$761$	8.43570	−	6.12889i	0.305794	−	0.222172i	−0.424296	−	0.905524i	$-0.639478\pi$
$761$	8.43570	−	6.12889i	0.305794	−	0.222172i	0.730090	+	0.683351i	$0.239478\pi$
$762$		0			0
$763$	−17.3913	+	2.75452i	−0.629608	+	0.0997202i
$764$		0			0
$765$	−2.32157	+	2.27341i	−0.0839366	+	0.0821953i
$766$		0			0
$767$	−2.12794	+	4.17631i	−0.0768354	+	0.150798i
$768$		0			0
$769$	−26.6666	+	8.66449i	−0.961621	+	0.312450i	−0.747429	−	0.664342i	$-0.768712\pi$
$769$	−26.6666	+	8.66449i	−0.961621	+	0.312450i	−0.214192	+	0.976792i	$0.568712\pi$
$770$		0			0
$771$	−20.8242	−	6.76619i	−0.749965	−	0.243678i
$772$		0			0
$773$	−16.6206	−	2.63244i	−0.597801	−	0.0946823i	−0.149801	−	0.988716i	$-0.547863\pi$
$773$	−16.6206	−	2.63244i	−0.597801	−	0.0946823i	−0.447999	+	0.894034i	$0.647863\pi$
$774$		0			0
$775$	−10.0649	+	13.2595i	−0.361543	+	0.476297i
$776$		0			0
$777$	1.16592	−	7.36130i	0.0418270	−	0.264085i
$778$		0			0
$779$	4.06685	−	12.5165i	0.145710	−	0.448449i
$780$		0			0
$781$	−0.848086	−	2.61014i	−0.0303469	−	0.0933982i
$782$		0			0
$783$	−17.9243	−	9.13286i	−0.640561	−	0.326382i
$784$		0			0
$785$	6.92298	−	13.2421i	0.247092	−	0.472632i
$786$		0			0
$787$	−3.27675	−	20.6886i	−0.116803	−	0.737468i	−0.974679	−	0.223610i	$-0.928216\pi$
$787$	−3.27675	−	20.6886i	−0.116803	−	0.737468i	0.857875	−	0.513858i	$-0.171784\pi$
$788$		0			0
$789$	18.9335	+	26.0597i	0.674049	+	0.927748i
$790$		0			0
$791$	−10.0046	+	13.7702i	−0.355724	+	0.489611i
$792$		0			0
$793$	2.34309	+	2.34309i	0.0832055	+	0.0832055i
$794$		0			0
$795$	−7.73802	−	2.60421i	−0.274439	−	0.0923619i
$796$		0			0
$797$	−21.9788	−	43.1359i	−0.778530	−	1.52795i	−0.847778	−	0.530351i	$-0.822060\pi$
$797$	−21.9788	−	43.1359i	−0.778530	−	1.52795i	0.0692485	−	0.997599i	$-0.477940\pi$
$798$		0			0
$799$	−5.65485			−0.200054
$800$		0			0
$801$	5.07214			0.179215
$802$		0			0
$803$	1.09517	+	2.14938i	0.0386476	+	0.0758501i
$804$		0			0
$805$	−12.9174	+	17.3929i	−0.455278	+	0.613021i
$806$		0			0
$807$	12.6466	+	12.6466i	0.445180	+	0.445180i
$808$		0			0
$809$	−7.74316	+	10.6576i	−0.272235	+	0.374700i	−0.923143	−	0.384457i	$-0.874389\pi$
$809$	−7.74316	+	10.6576i	−0.272235	+	0.374700i	0.650908	+	0.759157i	$0.274389\pi$
$810$		0			0
$811$	−16.6964	−	22.9807i	−0.586291	−	0.806961i	0.408076	−	0.912948i	$-0.366200\pi$
$811$	−16.6964	−	22.9807i	−0.586291	−	0.806961i	−0.994368	+	0.105987i	$0.966200\pi$
$812$		0			0
$813$	4.37384	+	27.6153i	0.153397	+	0.968512i
$814$		0			0
$815$	30.9711	−	15.3738i	1.08487	−	0.538522i
$816$		0			0
$817$	8.58602	+	4.37479i	0.300387	+	0.153055i
$818$		0			0
$819$	−0.179984	−	0.553933i	−0.00628914	−	0.0193560i
$820$		0			0
$821$	−7.70688	+	23.7193i	−0.268972	+	0.827810i	0.721780	+	0.692123i	$0.243324\pi$
$821$	−7.70688	+	23.7193i	−0.268972	+	0.827810i	−0.990752	+	0.135688i	$0.956676\pi$
$822$		0			0
$823$	−7.58149	+	47.8677i	−0.264274	+	1.66856i	0.396544	+	0.918016i	$0.370209\pi$
$823$	−7.58149	+	47.8677i	−0.264274	+	1.66856i	−0.660818	+	0.750546i	$0.729791\pi$
$824$		0			0
$825$	0.158883	+	1.16003i	0.00553158	+	0.0403872i
$826$		0			0
$827$	46.2370	+	7.32322i	1.60782	+	0.254653i	0.894792	−	0.446484i	$-0.147324\pi$
$827$	46.2370	+	7.32322i	1.60782	+	0.254653i	0.713027	+	0.701137i	$0.247324\pi$
$828$		0			0
$829$	−48.4214	−	15.7331i	−1.68175	−	0.546432i	−0.696497	−	0.717560i	$-0.745259\pi$
$829$	−48.4214	−	15.7331i	−1.68175	−	0.546432i	−0.985249	+	0.171127i	$0.945259\pi$
$830$		0			0
$831$	−34.3676	+	11.1667i	−1.19220	+	0.387368i
$832$		0			0
$833$	−2.95317	+	5.79593i	−0.102321	+	0.200817i
$834$		0			0
$835$	−2.04599	+	12.0959i	−0.0708045	+	0.418597i
$836$		0			0
$837$	−18.5925	+	2.94476i	−0.642650	+	0.101786i
$838$		0			0
$839$	−26.1961	+	19.0326i	−0.904389	+	0.657077i	−0.939589	−	0.342303i	$-0.888793\pi$
$839$	−26.1961	+	19.0326i	−0.904389	+	0.657077i	0.0352007	+	0.999380i	$0.488793\pi$
$840$		0			0
$841$	−13.2199	−	9.60479i	−0.455857	−	0.331200i
$842$		0			0
$843$	−6.23078	+	6.23078i	−0.214600	+	0.214600i
$844$		0			0
$845$	23.4505	−	16.6651i	0.806723	−	0.573297i
$846$		0			0
$847$	14.4869	−	7.38147i	0.497777	−	0.253630i
$848$		0			0
$849$		−	25.7815i		−	0.884818i
$850$		0			0
$851$		−	23.6879i		−	0.812012i
$852$		0			0
$853$	−7.93377	+	4.04246i	−0.271647	+	0.138411i	−0.584508	−	0.811388i	$-0.698713\pi$
$853$	−7.93377	+	4.04246i	−0.271647	+	0.138411i	0.312861	+	0.949799i	$0.398713\pi$
$854$		0			0
$855$	−3.79032	−	0.0397296i	−0.129626	−	0.00135872i
$856$		0			0
$857$	−15.9682	+	15.9682i	−0.545463	+	0.545463i	−0.925125	−	0.379662i	$-0.876040\pi$
$857$	−15.9682	+	15.9682i	−0.545463	+	0.545463i	0.379662	+	0.925125i	$0.376040\pi$
$858$		0			0
$859$	−34.8688	−	25.3336i	−1.18971	−	0.864373i	−0.196474	−	0.980509i	$-0.562949\pi$
$859$	−34.8688	−	25.3336i	−1.18971	−	0.864373i	−0.993233	+	0.116136i	$0.962949\pi$
$860$		0			0
$861$	−13.8653	+	10.0737i	−0.472529	+	0.343312i
$862$		0			0
$863$	0.685477	−	0.108569i	0.0233339	−	0.00369573i	−0.144757	−	0.989467i	$-0.546240\pi$
$863$	0.685477	−	0.108569i	0.0233339	−	0.00369573i	0.168091	+	0.985772i	$0.446240\pi$
$864$		0			0
$865$	43.5753	−	6.43422i	1.48161	−	0.218770i
$866$		0			0
$867$	9.55773	−	18.7581i	0.324597	−	0.637058i
$868$		0			0
$869$	2.53107	−	0.822395i	0.0858607	−	0.0278978i
$870$		0			0
$871$	−3.93582	−	1.27883i	−0.133360	−	0.0433313i
$872$		0			0
$873$	−12.4595	−	1.97339i	−0.421690	−	0.0667891i
$874$		0			0
$875$	16.4379	−	2.07612i	0.555703	−	0.0701855i
$876$		0			0
$877$	−5.16592	+	32.6163i	−0.174441	+	1.10138i	0.732701	+	0.680550i	$0.238259\pi$
$877$	−5.16592	+	32.6163i	−0.174441	+	1.10138i	−0.907142	+	0.420825i	$0.861741\pi$
$878$		0			0
$879$	12.3587	−	38.0361i	0.416848	−	1.28293i
$880$		0			0
$881$	16.9854	+	52.2756i	0.572251	+	1.76121i	0.645353	+	0.763884i	$0.276710\pi$
$881$	16.9854	+	52.2756i	0.572251	+	1.76121i	−0.0731019	+	0.997324i	$0.523290\pi$
$882$		0			0
$883$	−4.63963	−	2.36401i	−0.156136	−	0.0795553i	0.374177	−	0.927357i	$-0.377925\pi$
$883$	−4.63963	−	2.36401i	−0.156136	−	0.0795553i	−0.530313	+	0.847802i	$0.677925\pi$
$884$		0			0
$885$	−5.80269	−	39.2983i	−0.195055	−	1.32100i
$886$		0			0
$887$	1.30072	+	8.21242i	0.0436739	+	0.275746i	0.999855	−	0.0170299i	$-0.00542104\pi$
$887$	1.30072	+	8.21242i	0.0436739	+	0.275746i	−0.956181	+	0.292776i	$0.905421\pi$
$888$		0			0
$889$	0.617947	+	0.850531i	0.0207253	+	0.0285259i
$890$		0			0
$891$	−0.458999	+	0.631758i	−0.0153771	+	0.0211647i
$892$		0			0
$893$	−4.66458	−	4.66458i	−0.156094	−	0.156094i
$894$		0			0
$895$	0.120708	−	11.5159i	0.00403483	−	0.384934i
$896$		0			0
$897$	1.50898	+	2.96153i	0.0503832	+	0.0988826i
$898$		0			0
$899$	11.8459			0.395083
$900$		0			0
$901$	3.56180			0.118661
$902$		0			0
$903$	−5.69710	−	11.1812i	−0.189588	−	0.372087i
$904$		0			0
$905$	−20.0805	−	28.2565i	−0.667497	−	0.939279i
$906$		0			0
$907$	−18.5451	−	18.5451i	−0.615780	−	0.615780i	0.328666	−	0.944446i	$-0.393401\pi$
$907$	−18.5451	−	18.5451i	−0.615780	−	0.615780i	−0.944446	+	0.328666i	$0.893401\pi$
$908$		0			0
$909$	−7.36645	+	10.1391i	−0.244330	+	0.336291i
$910$		0			0
$911$	−7.72876	−	10.6377i	−0.256065	−	0.352444i	0.661559	−	0.749893i	$-0.269895\pi$
$911$	−7.72876	−	10.6377i	−0.256065	−	0.352444i	−0.917624	+	0.397450i	$0.869895\pi$
$912$		0			0
$913$	−0.340528	−	2.15001i	−0.0112698	−	0.0711549i
$914$		0			0
$915$	−27.6900	−	4.68369i	−0.915403	−	0.154838i
$916$		0			0
$917$	−16.9695	−	8.64640i	−0.560383	−	0.285529i
$918$		0			0
$919$	−15.3555	−	47.2594i	−0.506532	−	1.55894i	−0.798180	−	0.602419i	$-0.794204\pi$
$919$	−15.3555	−	47.2594i	−0.506532	−	1.55894i	0.291648	−	0.956526i	$-0.405796\pi$
$920$		0			0
$921$	6.33065	−	19.4837i	0.208602	−	0.642011i
$922$		0			0
$923$	−0.932058	+	5.88478i	−0.0306791	+	0.193700i
$924$		0			0
$925$	−13.0753	+	12.5383i	−0.429914	+	0.412257i
$926$		0			0
$927$	7.89102	+	1.24981i	0.259175	+	0.0410493i
$928$		0			0
$929$	−19.1811	−	6.23232i	−0.629312	−	0.204476i	−0.0230417	−	0.999735i	$-0.507335\pi$
$929$	−19.1811	−	6.23232i	−0.629312	−	0.204476i	−0.606270	+	0.795259i	$0.707335\pi$
$930$		0			0
$931$	−7.21697	+	2.34494i	−0.236527	+	0.0768522i
$932$		0			0
$933$	0.564946	−	1.10877i	0.0184955	−	0.0362995i
$934$		0			0
$935$	−0.227113	−	0.457528i	−0.00742740	−	0.0149628i
$936$		0			0
$937$	−26.7613	+	4.23858i	−0.874255	+	0.138468i	−0.577407	−	0.816456i	$-0.695935\pi$
$937$	−26.7613	+	4.23858i	−0.874255	+	0.138468i	−0.296848	+	0.954925i	$0.595935\pi$
$938$		0			0
$939$	1.63459	−	1.18760i	0.0533427	−	0.0387557i
$940$		0			0
$941$	33.8070	+	24.5622i	1.10208	+	0.800706i	0.981398	−	0.191986i	$-0.0614927\pi$
$941$	33.8070	+	24.5622i	1.10208	+	0.800706i	0.120679	+	0.992692i	$0.461493\pi$
$942$		0			0
$943$	−38.5168	+	38.5168i	−1.25428	+	1.25428i
$944$		0			0
$945$	15.0412	+	11.1708i	0.489289	+	0.363386i
$946$		0			0
$947$	37.9696	−	19.3465i	1.23385	−	0.628676i	0.289358	−	0.957221i	$-0.406558\pi$
$947$	37.9696	−	19.3465i	1.23385	−	0.628676i	0.944488	+	0.328545i	$0.106558\pi$
$948$		0			0
$949$		−	5.23704i		−	0.170001i
$950$		0			0
$951$			7.80959i			0.253243i
$952$		0			0
$953$	−12.5874	+	6.41359i	−0.407745	+	0.207756i	−0.645819	−	0.763491i	$-0.723484\pi$
$953$	−12.5874	+	6.41359i	−0.407745	+	0.207756i	0.238074	+	0.971247i	$0.423484\pi$
$954$		0			0
$955$	−0.0597636	+	0.177578i	−0.00193390	+	0.00574630i
$956$		0			0
$957$	0.589152	−	0.589152i	0.0190446	−	0.0190446i
$958$		0			0
$959$	−3.21645	−	2.33689i	−0.103865	−	0.0754621i
$960$		0			0
$961$	−16.1118	+	11.7059i	−0.519735	+	0.377610i
$962$		0			0
$963$	−1.59425	+	0.252505i	−0.0513740	+	0.00813685i
$964$		0			0
$965$	11.1463	+	5.82729i	0.358813	+	0.187587i
$966$		0			0
$967$	13.1346	−	25.7782i	0.422381	−	0.828970i	−0.577539	−	0.816363i	$-0.695987\pi$
$967$	13.1346	−	25.7782i	0.422381	−	0.828970i	0.999921	−	0.0126072i	$-0.00401311\pi$
$968$		0			0
$969$	−2.82383	+	0.917517i	−0.0907144	+	0.0294749i
$970$		0			0
$971$	−35.7849	−	11.6272i	−1.14839	−	0.373135i	−0.327855	−	0.944728i	$-0.606326\pi$
$971$	−35.7849	−	11.6272i	−1.14839	−	0.373135i	−0.820537	+	0.571593i	$0.806326\pi$
$972$		0			0
$973$	3.75047	+	0.594015i	0.120234	+	0.0190433i
$974$		0			0
$975$	0.835994	−	2.40050i	0.0267732	−	0.0768775i
$976$		0			0
$977$	6.21052	−	39.2117i	0.198692	−	1.25449i	−0.663602	−	0.748086i	$-0.730973\pi$
$977$	6.21052	−	39.2117i	0.198692	−	1.25449i	0.862294	−	0.506407i	$-0.169027\pi$
$978$		0			0
$979$	−0.246393	+	0.758320i	−0.00787475	+	0.0242360i
$980$		0			0
$981$	3.94025	+	12.1269i	0.125803	+	0.387181i
$982$		0			0
$983$	3.18791	+	1.62432i	0.101679	+	0.0518079i	0.504090	−	0.863651i	$-0.331828\pi$
$983$	3.18791	+	1.62432i	0.101679	+	0.0518079i	−0.402412	+	0.915459i	$0.631828\pi$
$984$		0			0
$985$	13.5292	+	13.8158i	0.431076	+	0.440209i
$986$		0			0
$987$	1.34387	+	8.48485i	0.0427758	+	0.270076i
$988$		0			0
$989$	−23.4433	−	32.2669i	−0.745454	−	1.02603i
$990$		0			0
$991$	21.5059	−	29.6004i	0.683158	−	0.940287i	−0.316808	−	0.948490i	$-0.602611\pi$
$991$	21.5059	−	29.6004i	0.683158	−	0.940287i	0.999966	+	0.00820303i	$0.00261113\pi$
$992$		0			0
$993$	18.5508	+	18.5508i	0.588690	+	0.588690i
$994$		0			0
$995$	46.0206	−	14.4215i	1.45895	−	0.457193i
$996$		0			0
$997$	8.03054	+	15.7608i	0.254330	+	0.499150i	0.982504	−	0.186242i	$-0.0596308\pi$
$997$	8.03054	+	15.7608i	0.254330	+	0.499150i	−0.728174	+	0.685392i	$0.759631\pi$
$998$		0			0
$999$	−20.4850			−0.648117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.223.7	yes	80
4.3	odd	2	inner	400.2.bi.d.223.4	✓	80
25.12	odd	20	inner	400.2.bi.d.287.4	yes	80
100.87	even	20	inner	400.2.bi.d.287.7	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.223.4	✓	80	4.3	odd	2	inner
400.2.bi.d.223.7	yes	80	1.1	even	1	trivial
400.2.bi.d.287.4	yes	80	25.12	odd	20	inner
400.2.bi.d.287.7	yes	80	100.87	even	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.630190 + 1.23682i) q^{3} +(2.13375 - 0.668655i) q^{5} +(1.04788 + 1.04788i) q^{7} +(0.630777 - 0.868191i) q^{9} +O(q^{10})\)	\(q+(0.630190 + 1.23682i) q^{3} +(2.13375 - 0.668655i) q^{5} +(1.04788 + 1.04788i) q^{7} +(0.630777 - 0.868191i) q^{9} +(0.0991587 + 0.136480i) q^{11} +(-0.0572924 - 0.361730i) q^{13} +(2.17167 + 2.21768i) q^{15} +(-1.20651 - 0.614748i) q^{17} +(-0.488134 - 1.50232i) q^{19} +(-0.635676 + 1.95641i) q^{21} +(-1.02277 + 6.45752i) q^{23} +(4.10580 - 2.85349i) q^{25} +(5.58437 + 0.884478i) q^{27} +(-3.38386 - 1.09948i) q^{29} +(-3.16642 + 1.02883i) q^{31} +(-0.106312 + 0.208650i) q^{33} +(2.93660 + 1.53525i) q^{35} +(-3.57850 + 0.566779i) q^{37} +(0.411289 - 0.298819i) q^{39} +(6.74026 + 4.89709i) q^{41} +(-4.31359 + 4.31359i) q^{43} +(0.765403 - 2.27428i) q^{45} +(3.72094 - 1.89591i) q^{47} -4.80388i q^{49} -1.87964i q^{51} +(-2.34369 + 1.19417i) q^{53} +(0.302838 + 0.224912i) q^{55} +(1.55048 - 1.55048i) q^{57} +(-10.3539 - 7.52257i) q^{59} +(-7.31975 + 5.31811i) q^{61} +(1.57075 - 0.248782i) q^{63} +(-0.364120 - 0.733533i) q^{65} +(5.12992 - 10.0680i) q^{67} +(-8.63132 + 2.80448i) q^{69} +(-15.4722 - 5.02722i) q^{71} +(14.1235 + 2.23694i) q^{73} +(6.11668 + 3.27989i) q^{75} +(-0.0391087 + 0.246922i) q^{77} +(4.87493 - 15.0035i) q^{79} +(1.43042 + 4.40238i) q^{81} +(-11.4971 - 5.85808i) q^{83} +(-2.98545 - 0.504980i) q^{85} +(-0.772615 - 4.87810i) q^{87} +(2.77813 + 3.82377i) q^{89} +(0.319015 - 0.439087i) q^{91} +(-3.26793 - 3.26793i) q^{93} +(-2.04609 - 2.87919i) q^{95} +(-5.33666 - 10.4738i) q^{97} +0.181038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5}+O(q^{10}) \) 80 * q + 4 * q^5	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) \) 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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