LMFDB - Embedded newform 552.2.q.c.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	552.25
Dual form			552.2.q.c.265.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{3} +(3.49926 + 1.02748i) q^{5} +(1.49653 - 1.72709i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{3} +(3.49926 + 1.02748i) q^{5} +(1.49653 - 1.72709i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(2.79478 - 1.79610i) q^{11} +(0.353435 + 0.407885i) q^{13} +(-0.519021 + 3.60987i) q^{15} +(-0.777239 + 1.70192i) q^{17} +(-2.95017 - 6.45997i) q^{19} +(1.92249 + 1.23551i) q^{21} +(-2.42068 - 4.14009i) q^{23} +(6.98288 + 4.48762i) q^{25} +(-0.415415 - 0.909632i) q^{27} +(-1.60631 + 3.51733i) q^{29} +(-1.07405 + 7.47017i) q^{31} +(2.17555 + 2.51072i) q^{33} +(7.01131 - 4.50590i) q^{35} +(-8.13823 + 2.38960i) q^{37} +(-0.353435 + 0.407885i) q^{39} +(1.10301 + 0.323874i) q^{41} +(1.30928 + 9.10626i) q^{43} -3.64699 q^{45} +2.73329 q^{47} +(0.252971 + 1.75945i) q^{49} +(-1.79521 - 0.527120i) q^{51} +(5.08483 - 5.86821i) q^{53} +(11.6251 - 3.41345i) q^{55} +(5.97436 - 3.83949i) q^{57} +(-2.77923 - 3.20740i) q^{59} +(0.208198 - 1.44805i) q^{61} +(-0.949335 + 2.07875i) q^{63} +(0.817669 + 1.79045i) q^{65} +(-4.35480 - 2.79866i) q^{67} +(3.75345 - 2.98524i) q^{69} +(-1.92787 - 1.23896i) q^{71} +(6.68947 + 14.6479i) q^{73} +(-3.44818 + 7.55046i) q^{75} +(1.08046 - 7.51476i) q^{77} +(-4.38593 - 5.06164i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-15.2147 + 4.46744i) q^{83} +(-4.46844 + 5.15686i) q^{85} +(-3.71013 - 1.08939i) q^{87} +(-2.52313 - 17.5487i) q^{89} +1.23338 q^{91} -7.54698 q^{93} +(-3.68595 - 25.6364i) q^{95} +(-10.3141 - 3.02848i) q^{97} +(-2.17555 + 2.51072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$		0			0
$5$	3.49926	+	1.02748i	1.56492	+	0.459502i	0.945517	−	0.325573i	$-0.105557\pi$
$5$	3.49926	+	1.02748i	1.56492	+	0.459502i	0.619402	+	0.785074i	$0.287375\pi$
$6$		0			0
$7$	1.49653	−	1.72709i	0.565636	−	0.652779i	−0.398818	−	0.917030i	$-0.630579\pi$
$7$	1.49653	−	1.72709i	0.565636	−	0.652779i	0.964454	+	0.264251i	$0.0851248\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	2.79478	−	1.79610i	0.842659	−	0.541544i	−0.0466184	−	0.998913i	$-0.514844\pi$
$11$	2.79478	−	1.79610i	0.842659	−	0.541544i	0.889277	+	0.457369i	$0.151208\pi$
$12$		0			0
$13$	0.353435	+	0.407885i	0.0980252	+	0.113127i	0.802642	−	0.596460i	$-0.203427\pi$
$13$	0.353435	+	0.407885i	0.0980252	+	0.113127i	−0.704617	+	0.709588i	$0.748881\pi$
$14$		0			0
$15$	−0.519021	+	3.60987i	−0.134011	+	0.932065i
$16$		0			0
$17$	−0.777239	+	1.70192i	−0.188508	+	0.412775i	−0.980163	−	0.198193i	$-0.936493\pi$
$17$	−0.777239	+	1.70192i	−0.188508	+	0.412775i	0.791655	+	0.610969i	$0.209220\pi$
$18$		0			0
$19$	−2.95017	−	6.45997i	−0.676815	−	1.48202i	−0.865983	−	0.500073i	$-0.833306\pi$
$19$	−2.95017	−	6.45997i	−0.676815	−	1.48202i	0.189168	−	0.981945i	$-0.439421\pi$
$20$		0			0
$21$	1.92249	+	1.23551i	0.419522	+	0.269610i
$22$		0			0
$23$	−2.42068	−	4.14009i	−0.504746	−	0.863268i
$23$	−2.42068	−	4.14009i	−0.504746	−	0.863268i
$24$		0			0
$25$	6.98288	+	4.48762i	1.39658	+	0.897524i
$26$		0			0
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$		0			0
$29$	−1.60631	+	3.51733i	−0.298284	+	0.653151i	−0.998129	−	0.0611437i	$-0.980525\pi$
$29$	−1.60631	+	3.51733i	−0.298284	+	0.653151i	0.699845	+	0.714295i	$0.253252\pi$
$30$		0			0
$31$	−1.07405	+	7.47017i	−0.192905	+	1.34168i	0.631366	+	0.775485i	$0.282495\pi$
$31$	−1.07405	+	7.47017i	−0.192905	+	1.34168i	−0.824271	+	0.566196i	$0.808414\pi$
$32$		0			0
$33$	2.17555	+	2.51072i	0.378715	+	0.437061i
$34$		0			0
$35$	7.01131	−	4.50590i	1.18513	−	0.761635i
$36$		0			0
$37$	−8.13823	+	2.38960i	−1.33792	+	0.392848i	−0.870926	−	0.491415i	$-0.836480\pi$
$37$	−8.13823	+	2.38960i	−1.33792	+	0.392848i	−0.466990	+	0.884262i	$0.654662\pi$
$38$		0			0
$39$	−0.353435	+	0.407885i	−0.0565949	+	0.0653139i
$40$		0			0
$41$	1.10301	+	0.323874i	0.172262	+	0.0505807i	0.366726	−	0.930329i	$-0.380479\pi$
$41$	1.10301	+	0.323874i	0.172262	+	0.0505807i	−0.194464	+	0.980910i	$0.562297\pi$
$42$		0			0
$43$	1.30928	+	9.10626i	0.199664	+	1.38869i	0.805261	+	0.592921i	$0.202025\pi$
$43$	1.30928	+	9.10626i	0.199664	+	1.38869i	−0.605597	+	0.795771i	$0.707066\pi$
$44$		0			0
$45$	−3.64699			−0.543662
$46$		0			0
$47$	2.73329			0.398692			0.199346	−	0.979929i	$-0.436118\pi$
$47$	2.73329			0.398692			0.199346	+	0.979929i	$0.436118\pi$
$48$		0			0
$49$	0.252971	+	1.75945i	0.0361387	+	0.251351i
$50$		0			0
$51$	−1.79521	−	0.527120i	−0.251379	−	0.0738115i
$52$		0			0
$53$	5.08483	−	5.86821i	0.698455	−	0.806060i	−0.290088	−	0.957000i	$-0.593685\pi$
$53$	5.08483	−	5.86821i	0.698455	−	0.806060i	0.988543	+	0.150940i	$0.0482300\pi$
$54$		0			0
$55$	11.6251	−	3.41345i	1.56753	−	0.460269i
$56$		0			0
$57$	5.97436	−	3.83949i	0.791323	−	0.508553i
$58$		0			0
$59$	−2.77923	−	3.20740i	−0.361825	−	0.417568i	0.545426	−	0.838159i	$-0.316368\pi$
$59$	−2.77923	−	3.20740i	−0.361825	−	0.417568i	−0.907250	+	0.420591i	$0.861823\pi$
$60$		0			0
$61$	0.208198	−	1.44805i	0.0266570	−	0.185403i	−0.972142	−	0.234391i	$-0.924690\pi$
$61$	0.208198	−	1.44805i	0.0266570	−	0.185403i	0.998799	+	0.0489876i	$0.0155995\pi$
$62$		0			0
$63$	−0.949335	+	2.07875i	−0.119605	+	0.261898i
$64$		0			0
$65$	0.817669	+	1.79045i	0.101419	+	0.222077i
$66$		0			0
$67$	−4.35480	−	2.79866i	−0.532024	−	0.341911i	0.246888	−	0.969044i	$-0.420592\pi$
$67$	−4.35480	−	2.79866i	−0.532024	−	0.341911i	−0.778912	+	0.627133i	$0.784228\pi$
$68$		0			0
$69$	3.75345	−	2.98524i	0.451862	−	0.359380i
$70$		0			0
$71$	−1.92787	−	1.23896i	−0.228795	−	0.147038i	0.421221	−	0.906958i	$-0.361602\pi$
$71$	−1.92787	−	1.23896i	−0.228795	−	0.147038i	−0.650017	+	0.759920i	$0.725238\pi$
$72$		0			0
$73$	6.68947	+	14.6479i	0.782944	+	1.71441i	0.695827	+	0.718210i	$0.255038\pi$
$73$	6.68947	+	14.6479i	0.782944	+	1.71441i	0.0871171	+	0.996198i	$0.472235\pi$
$74$		0			0
$75$	−3.44818	+	7.55046i	−0.398161	+	0.871851i
$76$		0			0
$77$	1.08046	−	7.51476i	0.123130	−	0.856387i
$78$		0			0
$79$	−4.38593	−	5.06164i	−0.493456	−	0.569479i	0.453330	−	0.891343i	$-0.350236\pi$
$79$	−4.38593	−	5.06164i	−0.493456	−	0.569479i	−0.946786	+	0.321864i	$0.895691\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	−15.2147	+	4.46744i	−1.67003	+	0.490365i	−0.973791	−	0.227444i	$-0.926963\pi$
$83$	−15.2147	+	4.46744i	−1.67003	+	0.490365i	−0.696240	+	0.717809i	$0.745145\pi$
$84$		0			0
$85$	−4.46844	+	5.15686i	−0.484671	+	0.559340i
$86$		0			0
$87$	−3.71013	−	1.08939i	−0.397767	−	0.116795i
$88$		0			0
$89$	−2.52313	−	17.5487i	−0.267451	−	1.86016i	−0.472393	−	0.881388i	$-0.656610\pi$
$89$	−2.52313	−	17.5487i	−0.267451	−	1.86016i	0.204942	−	0.978774i	$-0.434300\pi$
$90$		0			0
$91$	1.23338			0.129294
$92$		0			0
$93$	−7.54698			−0.782586
$94$		0			0
$95$	−3.68595	−	25.6364i	−0.378171	−	2.63023i
$96$		0			0
$97$	−10.3141	−	3.02848i	−1.04723	−	0.307495i	−0.287534	−	0.957770i	$-0.592836\pi$
$97$	−10.3141	−	3.02848i	−1.04723	−	0.307495i	−0.759699	+	0.650275i	$0.774654\pi$
$98$		0			0
$99$	−2.17555	+	2.51072i	−0.218651	+	0.252337i
$100$		0			0
$101$	7.85539	−	2.30655i	0.781641	−	0.229510i	0.133518	−	0.991046i	$-0.457373\pi$
$101$	7.85539	−	2.30655i	0.781641	−	0.229510i	0.648123	+	0.761536i	$0.275554\pi$
$102$		0			0
$103$	−6.40582	+	4.11677i	−0.631185	+	0.405638i	−0.816748	−	0.576995i	$-0.804225\pi$
$103$	−6.40582	+	4.11677i	−0.631185	+	0.405638i	0.185563	+	0.982632i	$0.440589\pi$
$104$		0			0
$105$	5.45785	+	6.29869i	0.532631	+	0.614689i
$106$		0			0
$107$	−0.241495	+	1.67964i	−0.0233462	+	0.162377i	−0.998159	−	0.0606470i	$-0.980684\pi$
$107$	−0.241495	+	1.67964i	−0.0233462	+	0.162377i	0.974813	+	0.223024i	$0.0715927\pi$
$108$		0			0
$109$	−5.54147	+	12.1341i	−0.530777	+	1.16224i	0.434419	+	0.900711i	$0.356954\pi$
$109$	−5.54147	+	12.1341i	−0.530777	+	1.16224i	−0.965196	+	0.261528i	$0.915774\pi$
$110$		0			0
$111$	−3.52347	−	7.71531i	−0.334433	−	0.732305i
$112$		0			0
$113$	−10.1726	−	6.53750i	−0.956953	−	0.614997i	−0.0338001	−	0.999429i	$-0.510761\pi$
$113$	−10.1726	−	6.53750i	−0.956953	−	0.614997i	−0.923153	+	0.384432i	$0.874397\pi$
$114$		0			0
$115$	−4.21675	−	16.9744i	−0.393214	−	1.58288i
$116$		0			0
$117$	−0.454033	−	0.291789i	−0.0419753	−	0.0269759i
$118$		0			0
$119$	1.77620	+	3.88933i	0.162824	+	0.356535i
$120$		0			0
$121$	0.0152769	−	0.0334517i	0.00138881	−	0.00304106i
$122$		0			0
$123$	−0.163602	+	1.13788i	−0.0147515	+	0.102599i
$124$		0			0
$125$	7.88264	+	9.09705i	0.705045	+	0.813665i
$126$		0			0
$127$	6.27210	−	4.03084i	0.556559	−	0.357679i	−0.231925	−	0.972734i	$-0.574502\pi$
$127$	6.27210	−	4.03084i	0.556559	−	0.357679i	0.788484	+	0.615055i	$0.210866\pi$
$128$		0			0
$129$	−8.82724	+	2.59191i	−0.777195	+	0.228205i
$130$		0			0
$131$	−9.98972	+	11.5288i	−0.872806	+	1.00727i	0.127075	+	0.991893i	$0.459441\pi$
$131$	−9.98972	+	11.5288i	−0.872806	+	1.00727i	−0.999882	+	0.0153791i	$0.995104\pi$
$132$		0			0
$133$	−15.5720	−	4.57234i	−1.35026	−	0.396472i
$134$		0			0
$135$	−0.519021	−	3.60987i	−0.0446702	−	0.310688i
$136$		0			0
$137$	20.7160			1.76989			0.884943	−	0.465699i	$-0.154197\pi$
$137$	20.7160			1.76989			0.884943	+	0.465699i	$0.154197\pi$
$138$		0			0
$139$	2.20763			0.187249			0.0936244	−	0.995608i	$-0.470155\pi$
$139$	2.20763			0.187249			0.0936244	+	0.995608i	$0.470155\pi$
$140$		0			0
$141$	0.388988	+	2.70547i	0.0327587	+	0.227842i
$142$		0			0
$143$	1.72038	+	0.505148i	0.143865	+	0.0422426i
$144$		0			0
$145$	−9.23487	+	10.6576i	−0.766914	+	0.885066i
$146$		0			0
$147$	−1.70554	+	0.500793i	−0.140671	+	0.0413047i
$148$		0			0
$149$	8.53375	−	5.48431i	0.699112	−	0.449292i	−0.142203	−	0.989838i	$-0.545419\pi$
$149$	8.53375	−	5.48431i	0.699112	−	0.449292i	0.841315	+	0.540546i	$0.181782\pi$
$150$		0			0
$151$	−2.75507	−	3.17952i	−0.224205	−	0.258746i	0.632492	−	0.774567i	$-0.282032\pi$
$151$	−2.75507	−	3.17952i	−0.224205	−	0.258746i	−0.856696	+	0.515821i	$0.827487\pi$
$152$		0			0
$153$	0.266270	−	1.85195i	0.0215267	−	0.149721i
$154$		0			0
$155$	−11.4338	+	25.0365i	−0.918385	+	2.01098i
$156$		0			0
$157$	−6.39138	−	13.9952i	−0.510088	−	1.11694i	−0.973058	−	0.230563i	$-0.925943\pi$
$157$	−6.39138	−	13.9952i	−0.510088	−	1.11694i	0.462970	−	0.886374i	$-0.346784\pi$
$158$		0			0
$159$	6.53212	+	4.19794i	0.518031	+	0.332918i
$160$		0			0
$161$	−10.7729	−	2.01504i	−0.849026	−	0.158808i
$162$		0			0
$163$	9.37104	+	6.02240i	0.733997	+	0.471711i	0.853480	−	0.521125i	$-0.174488\pi$
$163$	9.37104	+	6.02240i	0.733997	+	0.471711i	−0.119484	+	0.992836i	$0.538124\pi$
$164$		0			0
$165$	5.03313	+	11.0210i	0.391829	+	0.857985i
$166$		0			0
$167$	5.35007	−	11.7150i	0.414001	−	0.906536i	−0.581656	−	0.813435i	$-0.697595\pi$
$167$	5.35007	−	11.7150i	0.414001	−	0.906536i	0.995657	−	0.0931008i	$-0.0296779\pi$
$168$		0			0
$169$	1.80864	−	12.5794i	0.139126	−	0.967643i
$170$		0			0
$171$	4.65065	+	5.36713i	0.355644	+	0.410435i
$172$		0			0
$173$	15.4192	−	9.90934i	1.17230	−	0.753393i	0.198347	−	0.980132i	$-0.436443\pi$
$173$	15.4192	−	9.90934i	1.17230	−	0.753393i	0.973956	+	0.226738i	$0.0728063\pi$
$174$		0			0
$175$	18.2006	−	5.34419i	1.37584	−	0.403983i
$176$		0			0
$177$	2.77923	−	3.20740i	0.208899	−	0.241083i
$178$		0			0
$179$	1.87993	+	0.551998i	0.140513	+	0.0412582i	0.351233	−	0.936288i	$-0.385763\pi$
$179$	1.87993	+	0.551998i	0.140513	+	0.0412582i	−0.210720	+	0.977546i	$0.567581\pi$
$180$		0			0
$181$	−0.942901	−	6.55802i	−0.0700853	−	0.487454i	−0.994388	−	0.105794i	$-0.966262\pi$
$181$	−0.942901	−	6.55802i	−0.0700853	−	0.487454i	0.924303	−	0.381660i	$-0.124647\pi$
$182$		0			0
$183$	1.46294			0.108143
$184$		0			0
$185$	−30.9331			−2.27424
$186$		0			0
$187$	0.884593	+	6.15248i	0.0646879	+	0.449914i
$188$		0			0
$189$	−2.19270	−	0.643835i	−0.159495	−	0.0468321i
$190$		0			0
$191$	4.17306	−	4.81596i	0.301952	−	0.348471i	−0.584415	−	0.811455i	$-0.698676\pi$
$191$	4.17306	−	4.81596i	0.301952	−	0.348471i	0.886367	+	0.462984i	$0.153221\pi$
$192$		0			0
$193$	−15.5986	+	4.58016i	−1.12281	+	0.329687i	−0.789879	−	0.613263i	$-0.789857\pi$
$193$	−15.5986	+	4.58016i	−1.12281	+	0.329687i	−0.332933	+	0.942950i	$0.608038\pi$
$194$		0			0
$195$	−1.65585	+	1.06415i	−0.118578	+	0.0762056i
$196$		0			0
$197$	−2.15267	−	2.48431i	−0.153371	−	0.177000i	0.673864	−	0.738855i	$-0.264633\pi$
$197$	−2.15267	−	2.48431i	−0.153371	−	0.177000i	−0.827235	+	0.561855i	$0.810088\pi$
$198$		0			0
$199$	2.55580	−	17.7760i	0.181176	−	1.26011i	−0.672811	−	0.739814i	$-0.734913\pi$
$199$	2.55580	−	17.7760i	0.181176	−	1.26011i	0.853988	−	0.520293i	$-0.174177\pi$
$200$		0			0
$201$	2.15042	−	4.70877i	0.151679	−	0.332131i
$202$		0			0
$203$	3.67085	+	8.03804i	0.257643	+	0.564160i
$204$		0			0
$205$	3.52697	+	2.26664i	0.246334	+	0.158309i
$206$		0			0
$207$	3.48902	+	3.29040i	0.242504	+	0.228699i
$208$		0			0
$209$	−19.8478	−	12.7554i	−1.37290	−	0.882310i
$210$		0			0
$211$	6.03335	+	13.2112i	0.415353	+	0.909496i	0.995480	+	0.0949698i	$0.0302755\pi$
$211$	6.03335	+	13.2112i	0.415353	+	0.909496i	−0.580127	+	0.814526i	$0.696997\pi$
$212$		0			0
$213$	0.951989	−	2.08457i	0.0652292	−	0.142832i
$214$		0			0
$215$	−4.77495	+	33.2105i	−0.325649	+	2.26494i
$216$		0			0
$217$	11.2943	+	13.0343i	0.766708	+	0.884828i
$218$		0			0
$219$	−13.5468	+	8.70600i	−0.915408	+	0.588297i
$220$		0			0
$221$	−0.968890	+	0.284492i	−0.0651746	+	0.0191370i
$222$		0			0
$223$	13.0608	−	15.0730i	0.874615	−	1.00936i	−0.125236	−	0.992127i	$-0.539969\pi$
$223$	13.0608	−	15.0730i	0.874615	−	1.00936i	0.999852	−	0.0172329i	$-0.00548567\pi$
$224$		0			0
$225$	−7.96433	−	2.33854i	−0.530955	−	0.155903i
$226$		0			0
$227$	2.85629	+	19.8659i	0.189578	+	1.31855i	0.833101	+	0.553120i	$0.186563\pi$
$227$	2.85629	+	19.8659i	0.189578	+	1.31855i	−0.643523	+	0.765427i	$0.722528\pi$
$228$		0			0
$229$	−6.32229			−0.417789			−0.208894	−	0.977938i	$-0.566986\pi$
$229$	−6.32229			−0.417789			−0.208894	+	0.977938i	$0.566986\pi$
$230$		0			0
$231$	7.59204			0.499519
$232$		0			0
$233$	3.02190	+	21.0177i	0.197971	+	1.37692i	0.810161	+	0.586208i	$0.199380\pi$
$233$	3.02190	+	21.0177i	0.197971	+	1.37692i	−0.612190	+	0.790711i	$0.709711\pi$
$234$		0			0
$235$	9.56451	+	2.80839i	0.623920	+	0.183199i
$236$		0			0
$237$	4.38593	−	5.06164i	0.284897	−	0.328789i
$238$		0			0
$239$	17.0354	−	5.00205i	1.10193	−	0.323556i	0.320311	−	0.947312i	$-0.396212\pi$
$239$	17.0354	−	5.00205i	1.10193	−	0.323556i	0.781619	+	0.623756i	$0.214394\pi$
$240$		0			0
$241$	19.2242	−	12.3547i	1.23834	−	0.795833i	0.253172	−	0.967421i	$-0.418526\pi$
$241$	19.2242	−	12.3547i	1.23834	−	0.795833i	0.985169	+	0.171588i	$0.0548897\pi$
$242$		0			0
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$		0			0
$245$	−0.922584	+	6.41672i	−0.0589418	+	0.409949i
$246$		0			0
$247$	1.59223	−	3.48651i	0.101311	−	0.221841i
$248$		0			0
$249$	−6.58725	−	14.4241i	−0.417450	−	0.914088i
$250$		0			0
$251$	−18.3480	−	11.7915i	−1.15811	−	0.744275i	−0.186876	−	0.982384i	$-0.559836\pi$
$251$	−18.3480	−	11.7915i	−1.15811	−	0.744275i	−0.971239	+	0.238109i	$0.923473\pi$
$252$		0			0
$253$	−14.2013	−	7.22286i	−0.892826	−	0.454098i
$254$		0			0
$255$	−5.74029	−	3.68906i	−0.359471	−	0.231018i
$256$		0			0
$257$	1.26715	+	2.77468i	0.0790428	+	0.173080i	0.945027	−	0.326991i	$-0.106035\pi$
$257$	1.26715	+	2.77468i	0.0790428	+	0.173080i	−0.865985	+	0.500071i	$0.833307\pi$
$258$		0			0
$259$	−8.05207	+	17.6316i	−0.500331	+	1.09557i
$260$		0			0
$261$	0.550297	−	3.82740i	0.0340625	−	0.236910i
$262$		0			0
$263$	9.93196	+	11.4621i	0.612431	+	0.706783i	0.974251	−	0.225465i	$-0.0723901\pi$
$263$	9.93196	+	11.4621i	0.612431	+	0.706783i	−0.361821	+	0.932248i	$0.617845\pi$
$264$		0			0
$265$	23.8226	−	15.3099i	1.46341	−	0.940477i
$266$		0			0
$267$	17.0110	−	4.99489i	1.04106	−	0.305682i
$268$		0			0
$269$	−14.3682	+	16.5817i	−0.876043	+	1.01101i	0.123783	+	0.992309i	$0.460497\pi$
$269$	−14.3682	+	16.5817i	−0.876043	+	1.01101i	−0.999825	+	0.0186977i	$0.994048\pi$
$270$		0			0
$271$	−3.69689	−	1.08551i	−0.224570	−	0.0659398i	0.167512	−	0.985870i	$-0.446427\pi$
$271$	−3.69689	−	1.08551i	−0.224570	−	0.0659398i	−0.392082	+	0.919930i	$0.628245\pi$
$272$		0			0
$273$	0.175529	+	1.22083i	0.0106235	+	0.0738879i
$274$		0			0
$275$	27.5758			1.66288
$276$		0			0
$277$	−19.2631			−1.15741			−0.578704	−	0.815537i	$-0.696441\pi$
$277$	−19.2631			−1.15741			−0.578704	+	0.815537i	$0.696441\pi$
$278$		0			0
$279$	−1.07405	−	7.47017i	−0.0643015	−	0.447227i
$280$		0			0
$281$	18.3130	+	5.37718i	1.09246	+	0.320776i	0.777853	−	0.628446i	$-0.216309\pi$
$281$	18.3130	+	5.37718i	1.09246	+	0.320776i	0.314608	+	0.949222i	$0.398127\pi$
$282$		0			0
$283$	−15.6418	+	18.0516i	−0.929811	+	1.07306i	0.0673482	+	0.997730i	$0.478546\pi$
$283$	−15.6418	+	18.0516i	−0.929811	+	1.07306i	−0.997159	+	0.0753290i	$0.975999\pi$
$284$		0			0
$285$	24.8509	−	7.29687i	1.47204	−	0.432229i
$286$		0			0
$287$	2.21006	−	1.42032i	0.130456	−	0.0838387i
$288$		0			0
$289$	8.84022	+	10.2022i	0.520013	+	0.600127i
$290$		0			0
$291$	1.52981	−	10.6401i	0.0896791	−	0.623732i
$292$		0			0
$293$	11.9337	−	26.1312i	0.697176	−	1.52660i	−0.146187	−	0.989257i	$-0.546700\pi$
$293$	11.9337	−	26.1312i	0.697176	−	1.52660i	0.843363	−	0.537345i	$-0.180573\pi$
$294$		0			0
$295$	−6.42972	−	14.0791i	−0.374353	−	0.819719i
$296$		0			0
$297$	−2.79478	−	1.79610i	−0.162170	−	0.104220i
$298$		0			0
$299$	0.833129	−	2.45061i	0.0481811	−	0.141722i
$300$		0			0
$301$	17.6867	+	11.3666i	1.01945	+	0.655158i
$302$		0			0
$303$	3.40101	+	7.44718i	0.195383	+	0.427829i
$304$		0			0
$305$	2.21637	−	4.85318i	0.126909	−	0.277892i
$306$		0			0
$307$	−1.82556	+	12.6971i	−0.104190	+	0.724660i	0.869026	+	0.494767i	$0.164747\pi$
$307$	−1.82556	+	12.6971i	−0.104190	+	0.724660i	−0.973216	+	0.229893i	$0.926162\pi$
$308$		0			0
$309$	−4.98651	−	5.75474i	−0.283673	−	0.327376i
$310$		0			0
$311$	−2.49034	+	1.60045i	−0.141214	+	0.0907529i	−0.609340	−	0.792909i	$-0.708566\pi$
$311$	−2.49034	+	1.60045i	−0.141214	+	0.0907529i	0.468126	+	0.883662i	$0.344929\pi$
$312$		0			0
$313$	24.6683	−	7.24326i	1.39433	−	0.409413i	0.503599	−	0.863937i	$-0.332009\pi$
$313$	24.6683	−	7.24326i	1.39433	−	0.409413i	0.890734	+	0.454524i	$0.150191\pi$
$314$		0			0
$315$	−5.45785	+	6.29869i	−0.307515	+	0.354891i
$316$		0			0
$317$	−8.68882	−	2.55127i	−0.488013	−	0.143293i	0.0284638	−	0.999595i	$-0.490938\pi$
$317$	−8.68882	−	2.55127i	−0.488013	−	0.143293i	−0.516477	+	0.856301i	$0.672757\pi$
$318$		0			0
$319$	1.82818	+	12.7153i	0.102358	+	0.711917i
$320$		0			0
$321$	−1.69691			−0.0947122
$322$		0			0
$323$	13.2873			0.739325
$324$		0			0
$325$	0.637555	+	4.43429i	0.0353652	+	0.245970i
$326$		0			0
$327$	−12.7993	−	3.75820i	−0.707801	−	0.207829i
$328$		0			0
$329$	4.09046	−	4.72064i	0.225514	−	0.260257i
$330$		0			0
$331$	5.72233	−	1.68023i	0.314527	−	0.0923536i	−0.120659	−	0.992694i	$-0.538501\pi$
$331$	5.72233	−	1.68023i	0.314527	−	0.0923536i	0.435186	+	0.900340i	$0.356683\pi$
$332$		0			0
$333$	7.13534	−	4.58561i	0.391014	−	0.251290i
$334$		0			0
$335$	−12.3630	−	14.2677i	−0.675465	−	0.779528i
$336$		0			0
$337$	−1.57203	+	10.9337i	−0.0856342	+	0.595599i	0.901144	+	0.433520i	$0.142729\pi$
$337$	−1.57203	+	10.9337i	−0.0856342	+	0.595599i	−0.986778	+	0.162078i	$0.948180\pi$
$338$		0			0
$339$	5.02326	−	10.9994i	0.272826	−	0.597405i
$340$		0			0
$341$	10.4154	+	22.8066i	0.564026	+	1.23505i
$342$		0			0
$343$	16.8747	+	10.8447i	0.911151	+	0.585561i
$344$		0			0
$345$	16.2016	−	6.58955i	0.872263	−	0.354769i
$346$		0			0
$347$	−8.24691	−	5.29997i	−0.442718	−	0.284517i	0.300230	−	0.953867i	$-0.402937\pi$
$347$	−8.24691	−	5.29997i	−0.442718	−	0.284517i	−0.742948	+	0.669349i	$0.766573\pi$
$348$		0			0
$349$	−6.14215	−	13.4494i	−0.328782	−	0.719932i	0.670986	−	0.741470i	$-0.265871\pi$
$349$	−6.14215	−	13.4494i	−0.328782	−	0.719932i	−0.999768	+	0.0215379i	$0.993144\pi$
$350$		0			0
$351$	0.224204	−	0.490937i	0.0119671	−	0.0262043i
$352$		0			0
$353$	−0.874112	+	6.07958i	−0.0465243	+	0.323584i	0.953247	+	0.302193i	$0.0977186\pi$
$353$	−0.874112	+	6.07958i	−0.0465243	+	0.323584i	−0.999771	+	0.0213910i	$0.993191\pi$
$354$		0			0
$355$	−5.47310	−	6.31630i	−0.290482	−	0.335234i
$356$		0			0
$357$	−3.59697	+	2.31163i	−0.190372	+	0.122344i
$358$		0			0
$359$	18.7703	−	5.51145i	0.990658	−	0.290883i	0.254041	−	0.967193i	$-0.418240\pi$
$359$	18.7703	−	5.51145i	0.990658	−	0.290883i	0.736617	+	0.676310i	$0.236422\pi$
$360$		0			0
$361$	−20.5853	+	23.7567i	−1.08344	+	1.25035i
$362$		0			0
$363$	0.0352853	+	0.0103607i	0.00185200	+	0.000543796i
$364$		0			0
$365$	8.35786	+	58.1302i	0.437470	+	3.04267i
$366$		0			0
$367$	29.5141			1.54062			0.770311	−	0.637669i	$-0.220101\pi$
$367$	29.5141			1.54062			0.770311	+	0.637669i	$0.220101\pi$
$368$		0			0
$369$	−1.14958			−0.0598448
$370$		0			0
$371$	−2.52531	−	17.5639i	−0.131108	−	0.911874i
$372$		0			0
$373$	15.6331	+	4.59030i	0.809453	+	0.237677i	0.660168	−	0.751118i	$-0.270485\pi$
$373$	15.6331	+	4.59030i	0.809453	+	0.237677i	0.149284	+	0.988794i	$0.452303\pi$
$374$		0			0
$375$	−7.88264	+	9.09705i	−0.407058	+	0.469770i
$376$		0			0
$377$	−2.00239	+	0.587955i	−0.103128	+	0.0302812i
$378$		0			0
$379$	−0.447656	+	0.287691i	−0.0229945	+	0.0147777i	−0.552088	−	0.833786i	$-0.686169\pi$
$379$	−0.447656	+	0.287691i	−0.0229945	+	0.0147777i	0.529093	+	0.848564i	$0.322532\pi$
$380$		0			0
$381$	4.88242	+	5.63461i	0.250134	+	0.288670i
$382$		0			0
$383$	−4.74247	+	32.9846i	−0.242329	+	1.68544i	0.398040	+	0.917368i	$0.369691\pi$
$383$	−4.74247	+	32.9846i	−0.242329	+	1.68544i	−0.640369	+	0.768068i	$0.721218\pi$
$384$		0			0
$385$	11.5021	−	25.1860i	0.586199	−	1.28360i
$386$		0			0
$387$	−3.82178	−	8.36853i	−0.194272	−	0.425396i
$388$		0			0
$389$	−2.80637	−	1.80355i	−0.142289	−	0.0914434i	0.467560	−	0.883962i	$-0.345133\pi$
$389$	−2.80637	−	1.80355i	−0.142289	−	0.0914434i	−0.609848	+	0.792518i	$0.708770\pi$
$390$		0			0
$391$	8.92752	−	0.901955i	0.451484	−	0.0456138i
$392$		0			0
$393$	−12.8331	−	8.24733i	−0.647344	−	0.416023i
$394$		0			0
$395$	−10.1468	−	22.2185i	−0.510542	−	1.11793i
$396$		0			0
$397$	−9.21532	+	20.1787i	−0.462503	+	1.01274i	0.524406	+	0.851468i	$0.324287\pi$
$397$	−9.21532	+	20.1787i	−0.462503	+	1.01274i	−0.986910	+	0.161273i	$0.948440\pi$
$398$		0			0
$399$	2.30968	−	16.0642i	0.115629	−	0.804215i
$400$		0			0
$401$	−10.2331	−	11.8097i	−0.511018	−	0.589746i	0.440341	−	0.897831i	$-0.354858\pi$
$401$	−10.2331	−	11.8097i	−0.511018	−	0.589746i	−0.951359	+	0.308084i	$0.900312\pi$
$402$		0			0
$403$	−3.42658	+	2.20213i	−0.170690	+	0.109696i
$404$		0			0
$405$	3.49926	−	1.02748i	0.173880	−	0.0510557i
$406$		0			0
$407$	−18.4526	+	21.2955i	−0.914662	+	1.05558i
$408$		0			0
$409$	−19.7230	−	5.79121i	−0.975241	−	0.286357i	−0.244983	−	0.969527i	$-0.578782\pi$
$409$	−19.7230	−	5.79121i	−0.975241	−	0.286357i	−0.730259	+	0.683171i	$0.760600\pi$
$410$		0			0
$411$	2.94819	+	20.5051i	0.145424	+	1.01144i
$412$		0			0
$413$	−9.69867			−0.477241
$414$		0			0
$415$	−57.8305			−2.83879
$416$		0			0
$417$	0.314179	+	2.18516i	0.0153854	+	0.107008i
$418$		0			0
$419$	8.41863	+	2.47193i	0.411277	+	0.120762i	0.480825	−	0.876817i	$-0.340337\pi$
$419$	8.41863	+	2.47193i	0.411277	+	0.120762i	−0.0695476	+	0.997579i	$0.522156\pi$
$420$		0			0
$421$	3.10301	−	3.58107i	0.151232	−	0.174531i	−0.675079	−	0.737746i	$-0.735890\pi$
$421$	3.10301	−	3.58107i	0.151232	−	0.174531i	0.826310	+	0.563215i	$0.190436\pi$
$422$		0			0
$423$	−2.62257	+	0.770057i	−0.127514	+	0.0374415i
$424$		0			0
$425$	−13.0649	+	8.39631i	−0.633742	+	0.407281i
$426$		0			0
$427$	−2.18933	−	2.52663i	−0.105949	−	0.122272i
$428$		0			0
$429$	−0.255171	+	1.77475i	−0.0123198	+	0.0856859i
$430$		0			0
$431$	−4.00906	+	8.77863i	−0.193110	+	0.422852i	−0.981275	−	0.192612i	$-0.938304\pi$
$431$	−4.00906	+	8.77863i	−0.193110	+	0.422852i	0.788165	+	0.615464i	$0.211031\pi$
$432$		0			0
$433$	−7.28109	−	15.9434i	−0.349907	−	0.766190i	−0.999980	−	0.00631777i	$-0.997989\pi$
$433$	−7.28109	−	15.9434i	−0.349907	−	0.766190i	0.650073	−	0.759872i	$-0.274738\pi$
$434$		0			0
$435$	−11.8634	−	7.62414i	−0.568806	−	0.365549i
$436$		0			0
$437$	−19.6034	+	27.8515i	−0.937758	+	1.33232i
$438$		0			0
$439$	−33.1973	−	21.3346i	−1.58442	−	1.01824i	−0.974108	−	0.226083i	$-0.927408\pi$
$439$	−33.1973	−	21.3346i	−1.58442	−	1.01824i	−0.610312	−	0.792161i	$-0.708956\pi$
$440$		0			0
$441$	−0.738420	−	1.61691i	−0.0351628	−	0.0769959i
$442$		0			0
$443$	−7.16828	+	15.6963i	−0.340575	+	0.745756i	−0.999982	−	0.00603075i	$-0.998080\pi$
$443$	−7.16828	+	15.6963i	−0.340575	+	0.745756i	0.659407	+	0.751787i	$0.270808\pi$
$444$		0			0
$445$	9.20183	−	64.0001i	0.436209	−	3.03390i
$446$		0			0
$447$	6.64296	+	7.66639i	0.314201	+	0.362608i
$448$		0			0
$449$	11.2457	−	7.22718i	0.530718	−	0.341072i	−0.247681	−	0.968842i	$-0.579669\pi$
$449$	11.2457	−	7.22718i	0.530718	−	0.341072i	0.778399	+	0.627770i	$0.216032\pi$
$450$		0			0
$451$	3.66440	−	1.07596i	0.172550	−	0.0506651i
$452$		0			0
$453$	2.75507	−	3.17952i	0.129445	−	0.149387i
$454$		0			0
$455$	4.31593	+	1.26727i	0.202334	+	0.0594106i
$456$		0			0
$457$	−0.973905	−	6.77366i	−0.0455574	−	0.316858i	−0.999839	−	0.0179491i	$-0.994286\pi$
$457$	−0.973905	−	6.77366i	−0.0455574	−	0.316858i	0.954282	−	0.298909i	$-0.0966228\pi$
$458$		0			0
$459$	1.87099			0.0873305
$460$		0			0
$461$	7.67585			0.357500			0.178750	−	0.983895i	$-0.442795\pi$
$461$	7.67585			0.357500			0.178750	+	0.983895i	$0.442795\pi$
$462$		0			0
$463$	2.50586	+	17.4287i	0.116457	+	0.809979i	0.961406	+	0.275132i	$0.0887216\pi$
$463$	2.50586	+	17.4287i	0.116457	+	0.809979i	−0.844949	+	0.534847i	$0.820369\pi$
$464$		0			0
$465$	−26.4089	−	7.75435i	−1.22468	−	0.359599i
$466$		0			0
$467$	−15.9808	+	18.4429i	−0.739505	+	0.853435i	−0.993507	−	0.113769i	$-0.963708\pi$
$467$	−15.9808	+	18.4429i	−0.739505	+	0.853435i	0.254002	+	0.967204i	$0.418253\pi$
$468$		0			0
$469$	−11.3506	+	3.33285i	−0.524124	+	0.153897i
$470$		0			0
$471$	12.9431	−	8.31805i	0.596388	−	0.383275i
$472$		0			0
$473$	20.0149	+	23.0984i	0.920286	+	1.06207i
$474$		0			0
$475$	8.38923	−	58.3484i	0.384924	−	2.67721i
$476$		0			0
$477$	−3.22559	+	7.06306i	−0.147690	+	0.323396i
$478$		0			0
$479$	−14.0643	−	30.7965i	−0.642613	−	1.40713i	−0.897873	−	0.440254i	$-0.854889\pi$
$479$	−14.0643	−	30.7965i	−0.642613	−	1.40713i	0.255261	−	0.966872i	$-0.417839\pi$
$480$		0			0
$481$	−3.85101	−	2.47490i	−0.175591	−	0.112846i
$482$		0			0
$483$	0.461384	−	10.9500i	0.0209937	−	0.498244i
$484$		0			0
$485$	−32.9799	−	21.1949i	−1.49754	−	0.962411i
$486$		0			0
$487$	−4.36901	−	9.56680i	−0.197979	−	0.433513i	0.784440	−	0.620205i	$-0.212951\pi$
$487$	−4.36901	−	9.56680i	−0.197979	−	0.433513i	−0.982419	+	0.186692i	$0.940223\pi$
$488$		0			0
$489$	−4.62746	+	10.1327i	−0.209261	+	0.458218i
$490$		0			0
$491$	2.52130	−	17.5360i	0.113785	−	0.791391i	−0.850396	−	0.526144i	$-0.823637\pi$
$491$	2.52130	−	17.5360i	0.113785	−	0.791391i	0.964181	−	0.265247i	$-0.0854535\pi$
$492$		0			0
$493$	−4.73771	−	5.46761i	−0.213376	−	0.246249i
$494$		0			0
$495$	−10.1926	+	6.55036i	−0.458121	+	0.294417i
$496$		0			0
$497$	−5.02492	+	1.47545i	−0.225398	+	0.0661829i
$498$		0			0
$499$	16.6412	−	19.2050i	0.744964	−	0.859734i	−0.249106	−	0.968476i	$-0.580137\pi$
$499$	16.6412	−	19.2050i	0.744964	−	0.859734i	0.994070	+	0.108742i	$0.0346822\pi$
$500$		0			0
$501$	12.3572	+	3.62840i	0.552078	+	0.162105i
$502$		0			0
$503$	3.36238	+	23.3859i	0.149921	+	1.04273i	0.916345	+	0.400390i	$0.131125\pi$
$503$	3.36238	+	23.3859i	0.149921	+	1.04273i	−0.766423	+	0.642336i	$0.777966\pi$
$504$		0			0
$505$	29.8580			1.32866
$506$		0			0
$507$	12.7087			0.564414
$508$		0			0
$509$	−5.02683	−	34.9624i	−0.222810	−	1.54968i	−0.727335	−	0.686282i	$-0.759241\pi$
$509$	−5.02683	−	34.9624i	−0.222810	−	1.54968i	0.504525	−	0.863397i	$-0.331668\pi$
$510$		0			0
$511$	35.3093	+	10.3677i	1.56199	+	0.458642i
$512$		0			0
$513$	−4.65065	+	5.36713i	−0.205331	+	0.236965i
$514$		0			0
$515$	−26.6456	+	7.82384i	−1.17414	+	0.344760i
$516$		0			0
$517$	7.63896	−	4.90926i	0.335961	−	0.215909i
$518$		0			0
$519$	12.0029	+	13.8520i	0.526867	+	0.608037i
$520$		0			0
$521$	2.33411	−	16.2341i	0.102259	−	0.711228i	−0.872605	−	0.488427i	$-0.837571\pi$
$521$	2.33411	−	16.2341i	0.102259	−	0.711228i	0.974864	−	0.222801i	$-0.0715200\pi$
$522$		0			0
$523$	−12.1905	+	26.6934i	−0.533052	+	1.16722i	0.431205	+	0.902254i	$0.358089\pi$
$523$	−12.1905	+	26.6934i	−0.533052	+	1.16722i	−0.964257	+	0.264968i	$0.914639\pi$
$524$		0			0
$525$	7.88001	+	17.2548i	0.343912	+	0.753062i
$526$		0			0
$527$	−11.8788	−	7.63404i	−0.517449	−	0.332544i
$528$		0			0
$529$	−11.2806	+	20.0436i	−0.490462	+	0.871463i
$530$		0			0
$531$	3.57028	+	2.29448i	0.154937	+	0.0995719i
$532$		0			0
$533$	0.257740	+	0.564372i	0.0111640	+	0.0244457i
$534$		0			0
$535$	−2.57084	+	5.62936i	−0.111147	+	0.243379i
$536$		0			0
$537$	−0.278837	+	1.93935i	−0.0120327	+	0.0836893i
$538$		0			0
$539$	3.86715	+	4.46293i	0.166570	+	0.192232i
$540$		0			0
$541$	−16.4945	+	10.6004i	−0.709153	+	0.455745i	−0.844848	−	0.535006i	$-0.820309\pi$
$541$	−16.4945	+	10.6004i	−0.709153	+	0.455745i	0.135696	+	0.990751i	$0.456673\pi$
$542$		0			0
$543$	6.35708	−	1.86661i	0.272809	−	0.0801038i
$544$		0			0
$545$	−31.8586	+	36.7668i	−1.36467	+	1.57492i
$546$		0			0
$547$	14.9828	+	4.39934i	0.640618	+	0.188102i	0.585879	−	0.810398i	$-0.300749\pi$
$547$	14.9828	+	4.39934i	0.640618	+	0.188102i	0.0547386	+	0.998501i	$0.482567\pi$
$548$		0			0
$549$	0.208198	+	1.44805i	0.00888566	+	0.0618011i
$550$		0			0
$551$	27.4607			1.16986
$552$		0			0
$553$	−15.3056			−0.650860
$554$		0			0
$555$	−4.40223	−	30.6182i	−0.186864	−	1.29967i
$556$		0			0
$557$	21.0911	+	6.19290i	0.893657	+	0.262401i	0.696147	−	0.717899i	$-0.254896\pi$
$557$	21.0911	+	6.19290i	0.893657	+	0.262401i	0.197510	+	0.980301i	$0.436714\pi$
$558$		0			0
$559$	−3.25157	+	3.75251i	−0.137527	+	0.158714i
$560$		0			0
$561$	−5.96397	+	1.75118i	−0.251799	+	0.0739348i
$562$		0			0
$563$	−5.21636	+	3.35235i	−0.219843	+	0.141285i	−0.645927	−	0.763399i	$-0.723529\pi$
$563$	−5.21636	+	3.35235i	−0.219843	+	0.141285i	0.426084	+	0.904684i	$0.359893\pi$
$564$		0			0
$565$	−28.8793	−	33.3285i	−1.21496	−	1.40214i
$566$		0			0
$567$	0.325228	−	2.26201i	0.0136583	−	0.0949954i
$568$		0			0
$569$	15.8025	−	34.6026i	0.662474	−	1.45062i	−0.217725	−	0.976010i	$-0.569864\pi$
$569$	15.8025	−	34.6026i	0.662474	−	1.45062i	0.880199	−	0.474605i	$-0.157409\pi$
$570$		0			0
$571$	−12.1684	−	26.6450i	−0.509230	−	1.11506i	−0.973358	−	0.229290i	$-0.926360\pi$
$571$	−12.1684	−	26.6450i	−0.509230	−	1.11506i	0.464128	−	0.885768i	$-0.346368\pi$
$572$		0			0
$573$	5.36083	+	3.44520i	0.223952	+	0.143925i
$574$		0			0
$575$	1.67584	−	39.7728i	0.0698874	−	1.65864i
$576$		0			0
$577$	30.4432	+	19.5647i	1.26737	+	0.814487i	0.989275	−	0.146067i	$-0.0466616\pi$
$577$	30.4432	+	19.5647i	1.26737	+	0.814487i	0.278092	+	0.960554i	$0.410298\pi$
$578$		0			0
$579$	−6.75346	−	14.7880i	−0.280664	−	0.614569i
$580$		0			0
$581$	−15.0536	+	32.9629i	−0.624530	+	1.36753i
$582$		0			0
$583$	3.67112	−	25.5332i	0.152042	−	1.05748i
$584$		0			0
$585$	−1.28897	−	1.48756i	−0.0532925	−	0.0615029i
$586$		0			0
$587$	24.0621	−	15.4637i	0.993147	−	0.638257i	0.0601685	−	0.998188i	$-0.480836\pi$
$587$	24.0621	−	15.4637i	0.993147	−	0.638257i	0.932979	+	0.359931i	$0.117200\pi$
$588$		0			0
$589$	51.4256	−	15.0999i	2.11896	−	0.622182i
$590$		0			0
$591$	2.15267	−	2.48431i	0.0885488	−	0.102191i
$592$		0			0
$593$	26.3608	+	7.74023i	1.08251	+	0.317853i	0.773882	−	0.633330i	$-0.218313\pi$
$593$	26.3608	+	7.74023i	1.08251	+	0.317853i	0.308626	+	0.951183i	$0.400131\pi$
$594$		0			0
$595$	2.21919	+	15.4348i	0.0909780	+	0.632766i
$596$		0			0
$597$	17.9588			0.735005
$598$		0			0
$599$	−24.1796			−0.987952			−0.493976	−	0.869476i	$-0.664457\pi$
$599$	−24.1796			−0.987952			−0.493976	+	0.869476i	$0.664457\pi$
$600$		0			0
$601$	6.05134	+	42.0880i	0.246839	+	1.71681i	0.616259	+	0.787544i	$0.288647\pi$
$601$	6.05134	+	42.0880i	0.246839	+	1.71681i	−0.369419	+	0.929263i	$0.620443\pi$
$602$		0			0
$603$	4.96688	+	1.45841i	0.202267	+	0.0593909i
$604$		0			0
$605$	0.0878286	−	0.101360i	0.00357074	−	0.00412086i
$606$		0			0
$607$	−30.7941	+	9.04197i	−1.24989	+	0.367002i	−0.838724	−	0.544557i	$-0.816698\pi$
$607$	−30.7941	+	9.04197i	−1.24989	+	0.367002i	−0.411170	+	0.911559i	$0.634880\pi$
$608$		0			0
$609$	−7.43381	+	4.77742i	−0.301233	+	0.193591i
$610$		0			0
$611$	0.966040	+	1.11487i	0.0390818	+	0.0451028i
$612$		0			0
$613$	−2.65384	+	18.4578i	−0.107187	+	0.745505i	0.863359	+	0.504590i	$0.168356\pi$
$613$	−2.65384	+	18.4578i	−0.107187	+	0.745505i	−0.970546	+	0.240914i	$0.922553\pi$
$614$		0			0
$615$	−1.74163	+	3.81364i	−0.0702294	+	0.153781i
$616$		0			0
$617$	15.2370	+	33.3643i	0.613418	+	1.34320i	0.920211	+	0.391422i	$0.128017\pi$
$617$	15.2370	+	33.3643i	0.613418	+	1.34320i	−0.306794	+	0.951776i	$0.599256\pi$
$618$		0			0
$619$	−40.0384	−	25.7311i	−1.60928	−	1.03422i	−0.962402	−	0.271629i	$-0.912438\pi$
$619$	−40.0384	−	25.7311i	−1.60928	−	1.03422i	−0.646879	−	0.762593i	$-0.723926\pi$
$620$		0			0
$621$	−2.76037	+	3.92178i	−0.110770	+	0.157376i
$622$		0			0
$623$	−34.0842	−	21.9046i	−1.36555	−	0.877589i
$624$		0			0
$625$	0.995541	+	2.17993i	0.0398216	+	0.0871972i
$626$		0			0
$627$	9.80094	−	21.4611i	0.391412	−	0.857072i
$628$		0			0
$629$	2.25845	−	15.7079i	0.0900503	−	0.626313i
$630$		0			0
$631$	−19.9744	−	23.0517i	−0.795167	−	0.917672i	0.202939	−	0.979191i	$-0.434951\pi$
$631$	−19.9744	−	23.0517i	−0.795167	−	0.917672i	−0.998106	+	0.0615196i	$0.980405\pi$
$632$		0			0
$633$	−12.2181	+	7.85208i	−0.485625	+	0.312092i
$634$		0			0
$635$	26.0893	−	7.66052i	1.03532	−	0.303998i
$636$		0			0
$637$	−0.628247	+	0.725035i	−0.0248920	+	0.0287269i
$638$		0			0
$639$	2.19883	+	0.645635i	0.0869843	+	0.0255409i
$640$		0			0
$641$	1.45820	+	10.1420i	0.0575956	+	0.400586i	0.998143	+	0.0609223i	$0.0194042\pi$
$641$	1.45820	+	10.1420i	0.0575956	+	0.400586i	−0.940547	+	0.339664i	$0.889687\pi$
$642$		0			0
$643$	−18.6330			−0.734812			−0.367406	−	0.930061i	$-0.619754\pi$
$643$	−18.6330			−0.734812			−0.367406	+	0.930061i	$0.619754\pi$
$644$		0			0
$645$	−33.5520			−1.32111
$646$		0			0
$647$	4.01353	+	27.9147i	0.157788	+	1.09744i	0.902698	+	0.430275i	$0.141583\pi$
$647$	4.01353	+	27.9147i	0.157788	+	1.09744i	−0.744910	+	0.667165i	$0.767507\pi$
$648$		0			0
$649$	−13.5281	−	3.97222i	−0.531026	−	0.155923i
$650$		0			0
$651$	−11.2943	+	13.0343i	−0.442659	+	0.510855i
$652$		0			0
$653$	19.9046	−	5.84452i	0.778927	−	0.228714i	0.131984	−	0.991252i	$-0.457865\pi$
$653$	19.9046	−	5.84452i	0.778927	−	0.228714i	0.646943	+	0.762538i	$0.276047\pi$
$654$		0			0
$655$	−46.8022	+	30.0780i	−1.82871	+	1.17524i
$656$		0			0
$657$	−10.5453	−	12.1699i	−0.411411	−	0.474794i
$658$		0			0
$659$	2.13958	−	14.8811i	0.0833463	−	0.579686i	−0.904761	−	0.425920i	$-0.859951\pi$
$659$	2.13958	−	14.8811i	0.0833463	−	0.579686i	0.988107	−	0.153766i	$-0.0491403\pi$
$660$		0			0
$661$	−20.9319	+	45.8344i	−0.814156	+	1.78275i	−0.225752	+	0.974185i	$0.572484\pi$
$661$	−20.9319	+	45.8344i	−0.814156	+	1.78275i	−0.588403	+	0.808567i	$0.700243\pi$
$662$		0			0
$663$	−0.419483	−	0.918541i	−0.0162914	−	0.0356732i
$664$		0			0
$665$	−49.7925	−	31.9997i	−1.93087	−	1.24089i
$666$		0			0
$667$	18.4504	−	1.86406i	0.714402	−	0.0721767i
$668$		0			0
$669$	16.7783	+	10.7827i	0.648686	+	0.416885i
$670$		0			0
$671$	−2.01897	−	4.42092i	−0.0779413	−	0.170668i
$672$		0			0
$673$	9.58000	−	20.9773i	0.369282	−	0.808614i	−0.630200	−	0.776433i	$-0.717027\pi$
$673$	9.58000	−	20.9773i	0.369282	−	0.808614i	0.999482	−	0.0321817i	$-0.0102455\pi$
$674$		0			0
$675$	1.18129	−	8.21607i	0.0454680	−	0.316237i
$676$		0			0
$677$	−25.8443	−	29.8259i	−0.993278	−	1.14630i	−0.989239	−	0.146312i	$-0.953260\pi$
$677$	−25.8443	−	29.8259i	−0.993278	−	1.14630i	−0.00403923	−	0.999992i	$-0.501286\pi$
$678$		0			0
$679$	−20.6658	+	13.2811i	−0.793080	+	0.509681i
$680$		0			0
$681$	−19.2572	+	5.65443i	−0.737938	+	0.216678i
$682$		0			0
$683$	5.88848	−	6.79567i	0.225316	−	0.260029i	−0.631824	−	0.775112i	$-0.717693\pi$
$683$	5.88848	−	6.79567i	0.225316	−	0.260029i	0.857140	+	0.515083i	$0.172239\pi$
$684$		0			0
$685$	72.4907	+	21.2852i	2.76973	+	0.813265i
$686$		0			0
$687$	−0.899755	−	6.25794i	−0.0343278	−	0.238755i
$688$		0			0
$689$	4.19071			0.159653
$690$		0			0
$691$	−29.9869			−1.14075			−0.570377	−	0.821383i	$-0.693203\pi$
$691$	−29.9869			−1.14075			−0.570377	+	0.821383i	$0.693203\pi$
$692$		0			0
$693$	1.08046	+	7.51476i	0.0410433	+	0.285462i
$694$		0			0
$695$	7.72508	+	2.26829i	0.293029	+	0.0860411i
$696$		0			0
$697$	−1.40851	+	1.62551i	−0.0533512	+	0.0615706i
$698$		0			0
$699$	−20.3738	+	5.98228i	−0.770606	+	0.226270i
$700$		0			0
$701$	39.9971	−	25.7045i	1.51067	−	0.970847i	0.517308	−	0.855799i	$-0.326934\pi$
$701$	39.9971	−	25.7045i	1.51067	−	0.970847i	0.993360	−	0.115048i	$-0.0367023\pi$
$702$		0			0
$703$	39.4459	+	45.5229i	1.48773	+	1.71693i
$704$		0			0
$705$	−1.41864	+	9.86683i	−0.0534289	+	0.371606i
$706$		0			0
$707$	7.77223	−	17.0188i	0.292305	−	0.640058i
$708$		0			0
$709$	−11.5756	−	25.3470i	−0.434730	−	0.951926i	−0.992536	−	0.121955i	$-0.961084\pi$
$709$	−11.5756	−	25.3470i	−0.434730	−	0.951926i	0.557806	−	0.829972i	$-0.311643\pi$
$710$		0			0
$711$	5.63430	+	3.62095i	0.211303	+	0.135796i
$712$		0			0
$713$	33.5271	−	13.6362i	1.25560	−	0.510681i
$714$		0			0
$715$	5.50102	+	3.53529i	0.205727	+	0.132212i
$716$		0			0
$717$	7.37553	+	16.1502i	0.275444	+	0.603139i
$718$		0			0
$719$	6.45230	−	14.1286i	0.240630	−	0.526906i	−0.750330	−	0.661063i	$-0.770105\pi$
$719$	6.45230	−	14.1286i	0.240630	−	0.526906i	0.990960	+	0.134157i	$0.0428327\pi$
$720$		0			0
$721$	−2.47648	+	17.2243i	−0.0922291	+	0.641467i
$722$		0			0
$723$	14.9648	+	17.2703i	0.556547	+	0.642289i
$724$		0			0
$725$	−27.0011	+	17.3525i	−1.00280	+	0.644457i
$726$		0			0
$727$	24.7358	−	7.26308i	0.917400	−	0.269373i	0.211247	−	0.977433i	$-0.432247\pi$
$727$	24.7358	−	7.26308i	0.917400	−	0.269373i	0.706152	+	0.708060i	$0.250429\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	−16.5157	−	4.84945i	−0.610856	−	0.179363i
$732$		0			0
$733$	5.31608	+	36.9741i	0.196354	+	1.36567i	0.814754	+	0.579807i	$0.196872\pi$
$733$	5.31608	+	36.9741i	0.196354	+	1.36567i	−0.618400	+	0.785864i	$0.712219\pi$
$734$		0			0
$735$	−6.48270			−0.239118
$736$		0			0
$737$	−17.1974			−0.633474
$738$		0			0
$739$	4.13838	+	28.7830i	0.152233	+	1.05880i	0.912466	+	0.409152i	$0.134175\pi$
$739$	4.13838	+	28.7830i	0.152233	+	1.05880i	−0.760234	+	0.649650i	$0.774916\pi$
$740$		0			0
$741$	3.67762	+	1.07985i	0.135101	+	0.0396691i
$742$		0			0
$743$	15.3631	−	17.7300i	0.563619	−	0.650451i	−0.400383	−	0.916348i	$-0.631123\pi$
$743$	15.3631	−	17.7300i	0.563619	−	0.650451i	0.964001	+	0.265897i	$0.0856683\pi$
$744$		0			0
$745$	35.4968	−	10.4228i	1.30050	−	0.381862i
$746$		0			0
$747$	13.3398	−	8.57296i	0.488077	−	0.313668i
$748$		0			0
$749$	2.53948	+	2.93072i	0.0927906	+	0.107086i
$750$		0			0
$751$	−0.405902	+	2.82311i	−0.0148116	+	0.103017i	−0.995886	−	0.0906136i	$-0.971117\pi$
$751$	−0.405902	+	2.82311i	−0.0148116	+	0.103017i	0.981075	+	0.193630i	$0.0620263\pi$
$752$		0			0
$753$	9.06032	−	19.8393i	0.330176	−	0.722986i
$754$		0			0
$755$	−6.37384	−	13.9568i	−0.231968	−	0.507939i
$756$		0			0
$757$	−26.7621	−	17.1990i	−0.972686	−	0.625108i	−0.0452053	−	0.998978i	$-0.514394\pi$
$757$	−26.7621	−	17.1990i	−0.972686	−	0.625108i	−0.927481	+	0.373870i	$0.878031\pi$
$758$		0			0
$759$	5.12829	−	15.0846i	0.186145	−	0.547538i
$760$		0			0
$761$	37.6848	+	24.2186i	1.36607	+	0.877922i	0.998640	−	0.0521282i	$-0.0166005\pi$
$761$	37.6848	+	24.2186i	1.36607	+	0.877922i	0.367433	+	0.930050i	$0.380237\pi$
$762$		0			0
$763$	12.6638	+	27.7298i	0.458459	+	1.00388i
$764$		0			0
$765$	2.83458	−	6.20688i	0.102485	−	0.224410i
$766$		0			0
$767$	0.325976	−	2.26721i	0.0117703	−	0.0818643i
$768$		0			0
$769$	20.8339	+	24.0436i	0.751289	+	0.867034i	0.994693	−	0.102891i	$-0.0328093\pi$
$769$	20.8339	+	24.0436i	0.751289	+	0.867034i	−0.243403	+	0.969925i	$0.578264\pi$
$770$		0			0
$771$	−2.56610	+	1.64913i	−0.0924159	+	0.0593921i
$772$		0			0
$773$	11.3873	−	3.34360i	0.409571	−	0.120261i	−0.0704554	−	0.997515i	$-0.522445\pi$
$773$	11.3873	−	3.34360i	0.409571	−	0.120261i	0.480026	+	0.877254i	$0.340627\pi$
$774$		0			0
$775$	−41.0232	+	47.3433i	−1.47360	+	1.70062i
$776$		0			0
$777$	−18.5980	−	5.46088i	−0.667201	−	0.195908i
$778$		0			0
$779$	−1.16186	−	8.08092i	−0.0416280	−	0.289529i
$780$		0			0
$781$	−7.61326			−0.272424
$782$		0			0
$783$	3.86676			0.138187
$784$		0			0
$785$	−7.98542	−	55.5398i	−0.285012	−	1.98230i
$786$		0			0
$787$	19.0122	+	5.58249i	0.677712	+	0.198994i	0.602434	−	0.798169i	$-0.294198\pi$
$787$	19.0122	+	5.58249i	0.677712	+	0.198994i	0.0752775	+	0.997163i	$0.476016\pi$
$788$		0			0
$789$	−9.93196	+	11.4621i	−0.353587	+	0.408061i
$790$		0			0
$791$	−26.5144	+	7.78534i	−0.942744	+	0.276815i
$792$		0			0
$793$	0.664222	−	0.426869i	0.0235872	−	0.0151586i
$794$		0			0
$795$	18.5443	+	21.4013i	0.657700	+	0.759026i
$796$		0			0
$797$	−3.33332	+	23.1837i	−0.118072	+	0.821210i	0.841602	+	0.540097i	$0.181613\pi$
$797$	−3.33332	+	23.1837i	−0.118072	+	0.821210i	−0.959675	+	0.281113i	$0.909296\pi$
$798$		0			0
$799$	−2.12442	+	4.65183i	−0.0751566	+	0.164570i
$800$		0			0
$801$	7.36497	+	16.1270i	0.260229	+	0.569821i
$802$		0			0
$803$	45.0047	+	28.9228i	1.58818	+	1.02066i
$804$		0			0
$805$	−35.6269	−	18.1201i	−1.25568	−	0.638650i
$806$		0			0
$807$	−18.4578	−	11.8621i	−0.649744	−	0.417565i
$808$		0			0
$809$	13.4098	+	29.3634i	0.471464	+	1.03236i	0.984723	+	0.174128i	$0.0557106\pi$
$809$	13.4098	+	29.3634i	0.471464	+	1.03236i	−0.513260	+	0.858233i	$0.671562\pi$
$810$		0			0
$811$	−4.98432	+	10.9141i	−0.175023	+	0.383247i	−0.976731	−	0.214469i	$-0.931198\pi$
$811$	−4.98432	+	10.9141i	−0.175023	+	0.383247i	0.801708	+	0.597716i	$0.203925\pi$
$812$		0			0
$813$	0.548334	−	3.81375i	0.0192309	−	0.133754i
$814$		0			0
$815$	26.6039	+	30.7025i	0.931893	+	1.07546i
$816$		0			0
$817$	54.9635	−	35.3229i	1.92293	−	1.23579i
$818$		0			0
$819$	−1.18342	+	0.347484i	−0.0413521	+	0.0121421i
$820$		0			0
$821$	2.17884	−	2.51452i	0.0760421	−	0.0877573i	−0.716454	−	0.697635i	$-0.754236\pi$
$821$	2.17884	−	2.51452i	0.0760421	−	0.0877573i	0.792496	+	0.609877i	$0.208781\pi$
$822$		0			0
$823$	27.5712	+	8.09563i	0.961071	+	0.282196i	0.724389	−	0.689391i	$-0.242122\pi$
$823$	27.5712	+	8.09563i	0.961071	+	0.282196i	0.236682	+	0.971587i	$0.423940\pi$
$824$		0			0
$825$	3.92445	+	27.2951i	0.136632	+	0.950295i
$826$		0			0
$827$	−2.13512			−0.0742453			−0.0371226	−	0.999311i	$-0.511819\pi$
$827$	−2.13512			−0.0742453			−0.0371226	+	0.999311i	$0.511819\pi$
$828$		0			0
$829$	12.9706			0.450487			0.225244	−	0.974302i	$-0.427682\pi$
$829$	12.9706			0.450487			0.225244	+	0.974302i	$0.427682\pi$
$830$		0			0
$831$	−2.74143	−	19.0670i	−0.0950991	−	0.661429i
$832$		0			0
$833$	−3.19106	−	0.936980i	−0.110564	−	0.0324644i
$834$		0			0
$835$	30.7582	−	35.4969i	1.06443	−	1.22842i
$836$		0			0
$837$	7.24128	−	2.12623i	0.250295	−	0.0734933i
$838$		0			0
$839$	30.0396	−	19.3053i	1.03708	−	0.666493i	0.0928193	−	0.995683i	$-0.470412\pi$
$839$	30.0396	−	19.3053i	1.03708	−	0.666493i	0.944264	+	0.329190i	$0.106776\pi$
$840$		0			0
$841$	9.19960	+	10.6169i	0.317228	+	0.366100i
$842$		0			0
$843$	−2.71624	+	18.8918i	−0.0935522	+	0.650670i
$844$		0			0
$845$	19.2539	−	42.1602i	0.662354	−	1.45035i
$846$		0			0
$847$	−0.0349118	−	0.0764461i	−0.00119958	−	0.00262672i
$848$		0			0
$849$	−20.0940	−	12.9136i	−0.689623	−	0.443194i
$850$		0			0
$851$	29.5932	+	27.9085i	1.01444	+	0.956691i
$852$		0			0
$853$	2.56807	+	1.65040i	0.0879292	+	0.0565087i	0.583867	−	0.811850i	$-0.301539\pi$
$853$	2.56807	+	1.65040i	0.0879292	+	0.0565087i	−0.495937	+	0.868358i	$0.665175\pi$
$854$		0			0
$855$	10.7592	+	23.5595i	0.367958	+	0.805716i
$856$		0			0
$857$	5.36495	−	11.7476i	0.183263	−	0.401291i	−0.795595	−	0.605828i	$-0.792842\pi$
$857$	5.36495	−	11.7476i	0.183263	−	0.401291i	0.978859	+	0.204538i	$0.0655691\pi$
$858$		0			0
$859$	−5.51869	+	38.3833i	−0.188295	+	1.30962i	0.648126	+	0.761533i	$0.275553\pi$
$859$	−5.51869	+	38.3833i	−0.188295	+	1.30962i	−0.836421	+	0.548088i	$0.815356\pi$
$860$		0			0
$861$	1.72039	+	1.98543i	0.0586306	+	0.0676633i
$862$		0			0
$863$	38.4801	−	24.7297i	1.30988	−	0.841808i	0.315628	−	0.948883i	$-0.397785\pi$
$863$	38.4801	−	24.7297i	1.30988	−	0.841808i	0.994251	+	0.107074i	$0.0341483\pi$
$864$		0			0
$865$	64.1376	−	18.8325i	2.18074	−	0.640324i
$866$		0			0
$867$	−8.84022	+	10.2022i	−0.300229	+	0.346483i
$868$		0			0
$869$	−21.3489	−	6.26861i	−0.724213	−	0.212648i
$870$		0			0
$871$	−0.397605	−	2.76540i	−0.0134723	−	0.0937021i
$872$		0			0
$873$	10.7495			0.363815
$874$		0			0
$875$	27.5081			0.929942
$876$		0			0
$877$	−5.60981	−	39.0171i	−0.189430	−	1.31751i	−0.833488	−	0.552537i	$-0.813660\pi$
$877$	−5.60981	−	39.0171i	−0.189430	−	1.31751i	0.644059	−	0.764976i	$-0.277249\pi$
$878$		0			0
$879$	27.5636	+	8.09340i	0.929697	+	0.272984i
$880$		0			0
$881$	−7.97366	+	9.20210i	−0.268640	+	0.310027i	−0.874001	−	0.485924i	$-0.838483\pi$
$881$	−7.97366	+	9.20210i	−0.268640	+	0.310027i	0.605361	+	0.795951i	$0.293029\pi$
$882$		0			0
$883$	−19.0280	+	5.58712i	−0.640343	+	0.188022i	−0.585756	−	0.810487i	$-0.699202\pi$
$883$	−19.0280	+	5.58712i	−0.640343	+	0.188022i	−0.0545868	+	0.998509i	$0.517384\pi$
$884$		0			0
$885$	13.0208	−	8.36795i	0.437689	−	0.281285i
$886$		0			0
$887$	−8.16312	−	9.42074i	−0.274091	−	0.316318i	0.601970	−	0.798519i	$-0.294383\pi$
$887$	−8.16312	−	9.42074i	−0.274091	−	0.316318i	−0.876060	+	0.482201i	$0.839837\pi$
$888$		0			0
$889$	2.42479	−	16.8648i	0.0813248	−	0.565626i
$890$		0			0
$891$	1.38008	−	3.02195i	0.0462343	−	0.101239i
$892$		0			0
$893$	−8.06367	−	17.6570i	−0.269840	−	0.590868i
$894$		0			0
$895$	6.01121	+	3.86317i	0.200933	+	0.129132i
$896$		0			0
$897$	2.54423	+	0.475891i	0.0849495	+	0.0158895i
$898$		0			0
$899$	−24.5498	−	15.7772i	−0.818780	−	0.526198i
$900$		0			0
$901$	6.03507	+	13.2149i	0.201057	+	0.440254i
$902$		0			0
$903$	−8.73379	+	19.1243i	−0.290642	+	0.636418i
$904$		0			0
$905$	3.43876	−	23.9171i	0.114308	−	0.795030i
$906$		0			0
$907$	13.4722	+	15.5478i	0.447338	+	0.516256i	0.933970	−	0.357351i	$-0.116320\pi$
$907$	13.4722	+	15.5478i	0.447338	+	0.516256i	−0.486632	+	0.873607i	$0.661775\pi$
$908$		0			0
$909$	−6.88736	+	4.42624i	−0.228439	+	0.146809i
$910$		0			0
$911$	−24.6975	+	7.25184i	−0.818264	+	0.240264i	−0.663968	−	0.747761i	$-0.731129\pi$
$911$	−24.6975	+	7.25184i	−0.818264	+	0.240264i	−0.154296	+	0.988025i	$0.549311\pi$
$912$		0			0
$913$	−34.4978	+	39.8126i	−1.14171	+	1.31761i
$914$		0			0
$915$	5.11921	+	1.50313i	0.169236	+	0.0496921i
$916$		0			0
$917$	4.96126	+	34.5063i	0.163835	+	1.13950i
$918$		0			0
$919$	−25.7948			−0.850892			−0.425446	−	0.904984i	$-0.639883\pi$
$919$	−25.7948			−0.850892			−0.425446	+	0.904984i	$0.639883\pi$
$920$		0			0
$921$	−12.8276			−0.422685
$922$		0			0
$923$	−0.176019	−	1.22424i	−0.00579375	−	0.0402964i
$924$		0			0
$925$	−67.5518	−	19.8350i	−2.22109	−	0.652171i
$926$		0			0
$927$	4.98651	−	5.75474i	0.163779	−	0.189011i
$928$		0			0
$929$	−7.97515	+	2.34172i	−0.261656	+	0.0768292i	−0.409929	−	0.912117i	$-0.634447\pi$
$929$	−7.97515	+	2.34172i	−0.261656	+	0.0768292i	0.148273	+	0.988946i	$0.452629\pi$
$930$		0			0
$931$	10.6197	−	6.82487i	0.348047	−	0.223676i
$932$		0			0
$933$	−1.93857	−	2.23723i	−0.0634658	−	0.0732435i
$934$		0			0
$935$	−3.22611	+	22.4381i	−0.105505	+	0.733803i
$936$		0			0
$937$	−5.10449	+	11.1773i	−0.166756	+	0.365145i	−0.974500	−	0.224389i	$-0.927961\pi$
$937$	−5.10449	+	11.1773i	−0.166756	+	0.365145i	0.807743	+	0.589534i	$0.200689\pi$
$938$		0			0
$939$	10.6802	+	23.3864i	0.348535	+	0.763185i
$940$		0			0
$941$	14.8916	+	9.57023i	0.485451	+	0.311981i	0.760374	−	0.649486i	$-0.225016\pi$
$941$	14.8916	+	9.57023i	0.485451	+	0.311981i	−0.274922	+	0.961466i	$0.588652\pi$
$942$		0			0
$943$	−1.32918	−	5.35057i	−0.0432839	−	0.174239i
$944$		0			0
$945$	−7.01131	−	4.50590i	−0.228078	−	0.146577i
$946$		0			0
$947$	−4.24428	−	9.29368i	−0.137921	−	0.302004i	0.828051	−	0.560653i	$-0.189450\pi$
$947$	−4.24428	−	9.29368i	−0.137921	−	0.302004i	−0.965971	+	0.258649i	$0.916723\pi$
$948$		0			0
$949$	−3.61038	+	7.90562i	−0.117198	+	0.256627i
$950$		0			0
$951$	1.28875	−	8.96346i	0.0417906	−	0.290660i
$952$		0			0
$953$	−3.66493	−	4.22955i	−0.118719	−	0.137009i	0.693279	−	0.720669i	$-0.256165\pi$
$953$	−3.66493	−	4.22955i	−0.118719	−	0.137009i	−0.811998	+	0.583661i	$0.801620\pi$
$954$		0			0
$955$	19.5509	−	12.5646i	0.632653	−	0.406581i
$956$		0			0
$957$	−12.3257	+	3.61914i	−0.398432	+	0.116990i
$958$		0			0
$959$	31.0022	−	35.7784i	1.00111	−	1.15534i
$960$		0			0
$961$	−24.9055	−	7.31292i	−0.803403	−	0.235901i
$962$		0			0
$963$	−0.241495	−	1.67964i	−0.00778208	−	0.0541255i
$964$		0			0
$965$	−59.2897			−1.90860
$966$		0			0
$967$	27.7532			0.892482			0.446241	−	0.894913i	$-0.352762\pi$
$967$	27.7532			0.892482			0.446241	+	0.894913i	$0.352762\pi$
$968$		0			0
$969$	1.89098	+	13.1521i	0.0607470	+	0.422505i
$970$		0			0
$971$	10.2678	+	3.01491i	0.329511	+	0.0967531i	0.442304	−	0.896865i	$-0.354161\pi$
$971$	10.2678	+	3.01491i	0.329511	+	0.0967531i	−0.112793	+	0.993619i	$0.535980\pi$
$972$		0			0
$973$	3.30379	−	3.81278i	0.105915	−	0.122232i
$974$		0			0
$975$	−4.29843	+	1.26213i	−0.137660	+	0.0404206i
$976$		0			0
$977$	−13.6783	+	8.79054i	−0.437609	+	0.281234i	−0.740838	−	0.671683i	$-0.765572\pi$
$977$	−13.6783	+	8.79054i	−0.437609	+	0.281234i	0.303229	+	0.952918i	$0.401935\pi$
$978$		0			0
$979$	−38.5708	−	44.5131i	−1.23273	−	1.42265i
$980$		0			0
$981$	1.89842	−	13.2038i	0.0606120	−	0.421566i
$982$		0			0
$983$	−18.9592	+	41.5149i	−0.604706	+	1.32412i	0.321431	+	0.946933i	$0.395836\pi$
$983$	−18.9592	+	41.5149i	−0.604706	+	1.32412i	−0.926137	+	0.377188i	$0.876891\pi$
$984$		0			0
$985$	−4.98018	−	10.9051i	−0.158682	−	0.347464i
$986$		0			0
$987$	5.25473	+	3.37701i	0.167260	+	0.107491i
$988$		0			0
$989$	34.5314	−	27.4639i	1.09803	−	0.873301i
$990$		0			0
$991$	−16.9719	−	10.9072i	−0.539129	−	0.346477i	0.242569	−	0.970134i	$-0.422010\pi$
$991$	−16.9719	−	10.9072i	−0.539129	−	0.346477i	−0.781698	+	0.623657i	$0.785646\pi$
$992$		0			0
$993$	2.47750	+	5.42496i	0.0786210	+	0.172156i
$994$		0			0
$995$	27.2079	−	59.5769i	0.862547	−	1.88871i
$996$		0			0
$997$	0.997163	−	6.93542i	0.0315805	−	0.219647i	−0.967920	−	0.251260i	$-0.919155\pi$
$997$	0.997163	−	6.93542i	0.0315805	−	0.219647i	0.999500	+	0.0316126i	$0.0100643\pi$
$998$		0			0
$999$	5.55440	+	6.41011i	0.175733	+	0.202807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.c.25.3	✓	30
23.12	even	11	inner	552.2.q.c.265.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.c.25.3	✓	30	1.1	even	1	trivial
552.2.q.c.265.3	yes	30	23.12	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{3} +(3.49926 + 1.02748i) q^{5} +(1.49653 - 1.72709i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{3} +(3.49926 + 1.02748i) q^{5} +(1.49653 - 1.72709i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(2.79478 - 1.79610i) q^{11} +(0.353435 + 0.407885i) q^{13} +(-0.519021 + 3.60987i) q^{15} +(-0.777239 + 1.70192i) q^{17} +(-2.95017 - 6.45997i) q^{19} +(1.92249 + 1.23551i) q^{21} +(-2.42068 - 4.14009i) q^{23} +(6.98288 + 4.48762i) q^{25} +(-0.415415 - 0.909632i) q^{27} +(-1.60631 + 3.51733i) q^{29} +(-1.07405 + 7.47017i) q^{31} +(2.17555 + 2.51072i) q^{33} +(7.01131 - 4.50590i) q^{35} +(-8.13823 + 2.38960i) q^{37} +(-0.353435 + 0.407885i) q^{39} +(1.10301 + 0.323874i) q^{41} +(1.30928 + 9.10626i) q^{43} -3.64699 q^{45} +2.73329 q^{47} +(0.252971 + 1.75945i) q^{49} +(-1.79521 - 0.527120i) q^{51} +(5.08483 - 5.86821i) q^{53} +(11.6251 - 3.41345i) q^{55} +(5.97436 - 3.83949i) q^{57} +(-2.77923 - 3.20740i) q^{59} +(0.208198 - 1.44805i) q^{61} +(-0.949335 + 2.07875i) q^{63} +(0.817669 + 1.79045i) q^{65} +(-4.35480 - 2.79866i) q^{67} +(3.75345 - 2.98524i) q^{69} +(-1.92787 - 1.23896i) q^{71} +(6.68947 + 14.6479i) q^{73} +(-3.44818 + 7.55046i) q^{75} +(1.08046 - 7.51476i) q^{77} +(-4.38593 - 5.06164i) q^{79} +(0.841254 - 0.540641i) q^{81} +(-15.2147 + 4.46744i) q^{83} +(-4.46844 + 5.15686i) q^{85} +(-3.71013 - 1.08939i) q^{87} +(-2.52313 - 17.5487i) q^{89} +1.23338 q^{91} -7.54698 q^{93} +(-3.68595 - 25.6364i) q^{95} +(-10.3141 - 3.02848i) q^{97} +(-2.17555 + 2.51072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} - 2 q^{5} - 2 q^{7} - 3 q^{9} + 13 q^{11} - 13 q^{13} + 2 q^{15} - 11 q^{17} + 11 q^{19} - 9 q^{21} - 12 q^{23} + 17 q^{25} + 3 q^{27} + 9 q^{29} + 33 q^{31} + 9 q^{33} + 62 q^{35} + 11 q^{37} + 13 q^{39} + 2 q^{41} - 40 q^{43} - 2 q^{45} - 38 q^{47} - 13 q^{49} + 11 q^{51} - 25 q^{53} + 62 q^{55} + 22 q^{57} + 73 q^{59} + 4 q^{61} - 2 q^{63} - 12 q^{65} - 29 q^{67} - 21 q^{69} - 19 q^{71} - 38 q^{73} + 27 q^{75} + 4 q^{77} - 12 q^{79} - 3 q^{81} - 65 q^{83} + 8 q^{85} + 2 q^{87} - 61 q^{89} - 150 q^{91} - 22 q^{93} - 9 q^{95} - 9 q^{97} - 9 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 - 2 * q^5 - 2 * q^7 - 3 * q^9 + 13 * q^11 - 13 * q^13 + 2 * q^15 - 11 * q^17 + 11 * q^19 - 9 * q^21 - 12 * q^23 + 17 * q^25 + 3 * q^27 + 9 * q^29 + 33 * q^31 + 9 * q^33 + 62 * q^35 + 11 * q^37 + 13 * q^39 + 2 * q^41 - 40 * q^43 - 2 * q^45 - 38 * q^47 - 13 * q^49 + 11 * q^51 - 25 * q^53 + 62 * q^55 + 22 * q^57 + 73 * q^59 + 4 * q^61 - 2 * q^63 - 12 * q^65 - 29 * q^67 - 21 * q^69 - 19 * q^71 - 38 * q^73 + 27 * q^75 + 4 * q^77 - 12 * q^79 - 3 * q^81 - 65 * q^83 + 8 * q^85 + 2 * q^87 - 61 * q^89 - 150 * q^91 - 22 * q^93 - 9 * q^95 - 9 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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