LMFDB - Embedded newform 260.2.bk.c.33.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(33,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 11]))

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

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

chi := DirichletCharacter("260.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bk (of order $12$, degree $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + \cdots + 9 $ x^20 + 30x^18 + 371x^16 + 2460x^14 + 9517x^12 + 21870x^10 + 29001x^8 + 20400x^6 + 6399x^4 + 666*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.3
Root			$-2.27790i$ of defining polynomial
Character	$\chi$	$=$	260.33
Dual form			260.2.bk.c.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.243028 - 0.0651192i) q^{3} +(0.356684 + 2.20744i) q^{5} +(-4.30824 + 2.48736i) q^{7} +(-2.54325 + 1.46835i) q^{9} +O(q^{10})$	\(q+(0.243028 - 0.0651192i) q^{3} +(0.356684 + 2.20744i) q^{5} +(-4.30824 + 2.48736i) q^{7} +(-2.54325 + 1.46835i) q^{9} +(1.07571 + 4.01459i) q^{11} +(3.20328 - 1.65499i) q^{13} +(0.230431 + 0.513242i) q^{15} +(1.65147 - 6.16338i) q^{17} +(1.01061 + 0.270792i) q^{19} +(-0.885048 + 0.885048i) q^{21} +(0.195793 + 0.730708i) q^{23} +(-4.74555 + 1.57472i) q^{25} +(-1.05619 + 1.05619i) q^{27} +(6.59295 + 3.80644i) q^{29} +(2.17449 + 2.17449i) q^{31} +(0.522853 + 0.905608i) q^{33} +(-7.02737 - 8.62296i) q^{35} +(5.36518 + 3.09759i) q^{37} +(0.670715 - 0.610805i) q^{39} +(-2.57347 + 0.689559i) q^{41} +(-2.90779 - 0.779141i) q^{43} +(-4.14842 - 5.09034i) q^{45} -1.62865i q^{47} +(8.87394 - 15.3701i) q^{49} -1.60542i q^{51} +(-5.32012 - 5.32012i) q^{53} +(-8.47826 + 3.80649i) q^{55} +0.263240 q^{57} +(2.52700 - 9.43090i) q^{59} +(5.39215 + 9.33947i) q^{61} +(7.30463 - 12.6520i) q^{63} +(4.79585 + 6.48073i) q^{65} +(-3.04802 + 5.27932i) q^{67} +(0.0951662 + 0.164833i) q^{69} +(-1.15621 + 4.31503i) q^{71} +5.98834 q^{73} +(-1.05076 + 0.691727i) q^{75} +(-14.6201 - 14.6201i) q^{77} +14.0944i q^{79} +(4.21714 - 7.30430i) q^{81} -8.32705i q^{83} +(14.1943 + 1.44714i) q^{85} +(1.85015 + 0.495745i) q^{87} +(-1.99308 + 0.534044i) q^{89} +(-9.68392 + 15.0978i) q^{91} +(0.670065 + 0.386862i) q^{93} +(-0.237288 + 2.32744i) q^{95} +(4.17921 + 7.23861i) q^{97} +(-8.63060 - 8.63060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	$ 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.243028	−	0.0651192i	0.140312	−	0.0375966i	−0.187979	−	0.982173i	$-0.560194\pi$
$3$	0.243028	−	0.0651192i	0.140312	−	0.0375966i	0.328292	+	0.944576i	$0.393527\pi$
$4$		0			0
$5$	0.356684	+	2.20744i	0.159514	+	0.987196i
$5$	0.356684	+	2.20744i	0.159514	+	0.987196i
$6$		0			0
$7$	−4.30824	+	2.48736i	−1.62836	+	0.940134i	−0.643778	+	0.765212i	$0.722634\pi$
$7$	−4.30824	+	2.48736i	−1.62836	+	0.940134i	−0.984582	+	0.174922i	$0.944033\pi$
$8$		0			0
$9$	−2.54325	+	1.46835i	−0.847751	+	0.489449i
$10$		0			0
$11$	1.07571	+	4.01459i	0.324337	+	1.21044i	0.914976	+	0.403508i	$0.132209\pi$
$11$	1.07571	+	4.01459i	0.324337	+	1.21044i	−0.590639	+	0.806936i	$0.701124\pi$
$12$		0			0
$13$	3.20328	−	1.65499i	0.888430	−	0.459012i
$13$	3.20328	−	1.65499i	0.888430	−	0.459012i
$14$		0			0
$15$	0.230431	+	0.513242i	0.0594970	+	0.132519i
$16$		0			0
$17$	1.65147	−	6.16338i	0.400541	−	1.49484i	−0.411592	−	0.911368i	$-0.635027\pi$
$17$	1.65147	−	6.16338i	0.400541	−	1.49484i	0.812133	−	0.583472i	$-0.198306\pi$
$18$		0			0
$19$	1.01061	+	0.270792i	0.231850	+	0.0621239i	0.372873	−	0.927882i	$-0.378373\pi$
$19$	1.01061	+	0.270792i	0.231850	+	0.0621239i	−0.141024	+	0.990006i	$0.545039\pi$
$20$		0			0
$21$	−0.885048	+	0.885048i	−0.193133	+	0.193133i
$22$		0			0
$23$	0.195793	+	0.730708i	0.0408256	+	0.152363i	0.983330	−	0.181831i	$-0.0582025\pi$
$23$	0.195793	+	0.730708i	0.0408256	+	0.152363i	−0.942504	+	0.334194i	$0.891536\pi$
$24$		0			0
$25$	−4.74555	+	1.57472i	−0.949111	+	0.314943i
$26$		0			0
$27$	−1.05619	+	1.05619i	−0.203264	+	0.203264i
$28$		0			0
$29$	6.59295	+	3.80644i	1.22428	+	0.706839i	0.965828	−	0.259185i	$-0.0834539\pi$
$29$	6.59295	+	3.80644i	1.22428	+	0.706839i	0.258453	+	0.966024i	$0.416787\pi$
$30$		0			0
$31$	2.17449	+	2.17449i	0.390551	+	0.390551i	0.874884	−	0.484333i	$-0.160938\pi$
$31$	2.17449	+	2.17449i	0.390551	+	0.390551i	−0.484333	+	0.874884i	$0.660938\pi$
$32$		0			0
$33$	0.522853	+	0.905608i	0.0910171	+	0.157646i
$34$		0			0
$35$	−7.02737	−	8.62296i	−1.18784	−	1.45755i
$36$		0			0
$37$	5.36518	+	3.09759i	0.882030	+	0.509240i	0.871327	−	0.490702i	$-0.163260\pi$
$37$	5.36518	+	3.09759i	0.882030	+	0.509240i	0.0107029	+	0.999943i	$0.496593\pi$
$38$		0			0
$39$	0.670715	−	0.610805i	0.107400	−	0.0978070i
$40$		0			0
$41$	−2.57347	+	0.689559i	−0.401908	+	0.107691i	−0.454110	−	0.890946i	$-0.650043\pi$
$41$	−2.57347	+	0.689559i	−0.401908	+	0.107691i	0.0522020	+	0.998637i	$0.483376\pi$
$42$		0			0
$43$	−2.90779	−	0.779141i	−0.443435	−	0.118818i	0.0301912	−	0.999544i	$-0.490388\pi$
$43$	−2.90779	−	0.779141i	−0.443435	−	0.118818i	−0.473626	+	0.880726i	$0.657055\pi$
$44$		0			0
$45$	−4.14842	−	5.09034i	−0.618411	−	0.758822i
$46$		0			0
$47$		−	1.62865i		−	0.237563i	−0.992920	−	0.118781i	$-0.962101\pi$
$47$		−	1.62865i		−	0.237563i	0.992920	−	0.118781i	$-0.0378988\pi$
$48$		0			0
$49$	8.87394	−	15.3701i	1.26771	−	2.19573i
$50$		0			0
$51$		−	1.60542i		−	0.224804i
$52$		0			0
$53$	−5.32012	−	5.32012i	−0.730775	−	0.730775i	0.239998	−	0.970773i	$-0.422853\pi$
$53$	−5.32012	−	5.32012i	−0.730775	−	0.730775i	−0.970773	+	0.239998i	$0.922853\pi$
$54$		0			0
$55$	−8.47826	+	3.80649i	−1.14321	+	0.513267i
$56$		0			0
$57$	0.263240			0.0348670
$58$		0			0
$59$	2.52700	−	9.43090i	0.328988	−	1.22780i	−0.581254	−	0.813722i	$-0.697438\pi$
$59$	2.52700	−	9.43090i	0.328988	−	1.22780i	0.910242	−	0.414077i	$-0.135895\pi$
$60$		0			0
$61$	5.39215	+	9.33947i	0.690394	+	1.19580i	0.971709	+	0.236182i	$0.0758961\pi$
$61$	5.39215	+	9.33947i	0.690394	+	1.19580i	−0.281315	+	0.959615i	$0.590771\pi$
$62$		0			0
$63$	7.30463	−	12.6520i	0.920297	−	1.59400i
$64$		0			0
$65$	4.79585	+	6.48073i	0.594852	+	0.803835i
$66$		0			0
$67$	−3.04802	+	5.27932i	−0.372375	+	0.644972i	−0.989930	−	0.141555i	$-0.954790\pi$
$67$	−3.04802	+	5.27932i	−0.372375	+	0.644972i	0.617556	+	0.786527i	$0.288123\pi$
$68$		0			0
$69$	0.0951662	+	0.164833i	0.0114567	+	0.0198435i
$70$		0			0
$71$	−1.15621	+	4.31503i	−0.137217	+	0.512100i	0.862762	+	0.505610i	$0.168733\pi$
$71$	−1.15621	+	4.31503i	−0.137217	+	0.512100i	−0.999979	+	0.00649007i	$0.997934\pi$
$72$		0			0
$73$	5.98834			0.700882			0.350441	−	0.936585i	$-0.386032\pi$
$73$	5.98834			0.700882			0.350441	+	0.936585i	$0.386032\pi$
$74$		0			0
$75$	−1.05076	+	0.691727i	−0.121331	+	0.0798737i
$76$		0			0
$77$	−14.6201	−	14.6201i	−1.66612	−	1.66612i
$78$		0			0
$79$			14.0944i			1.58574i	0.609390	+	0.792871i	$0.291415\pi$
$79$			14.0944i			1.58574i	−0.609390	+	0.792871i	$0.708585\pi$
$80$		0			0
$81$	4.21714	−	7.30430i	0.468571	−	0.811589i
$82$		0			0
$83$		−	8.32705i		−	0.914013i	−0.889463	−	0.457006i	$-0.848922\pi$
$83$		−	8.32705i		−	0.914013i	0.889463	−	0.457006i	$-0.151078\pi$
$84$		0			0
$85$	14.1943	+	1.44714i	1.53959	+	0.156965i
$86$		0			0
$87$	1.85015	+	0.495745i	0.198356	+	0.0531494i
$88$		0			0
$89$	−1.99308	+	0.534044i	−0.211266	+	0.0566086i	−0.362900	−	0.931828i	$-0.618213\pi$
$89$	−1.99308	+	0.534044i	−0.211266	+	0.0566086i	0.151634	+	0.988437i	$0.451547\pi$
$90$		0			0
$91$	−9.68392	+	15.0978i	−1.01515	+	1.58268i
$92$		0			0
$93$	0.670065	+	0.386862i	0.0694825	+	0.0401157i
$94$		0			0
$95$	−0.237288	+	2.32744i	−0.0243452	+	0.238791i
$96$		0			0
$97$	4.17921	+	7.23861i	0.424335	+	0.734970i	0.996358	−	0.0852678i	$-0.0271746\pi$
$97$	4.17921	+	7.23861i	0.424335	+	0.734970i	−0.572023	+	0.820237i	$0.693841\pi$
$98$		0			0
$99$	−8.63060	−	8.63060i	−0.867408	−	0.867408i
$100$		0			0
$101$	1.46818	+	0.847656i	0.146090	+	0.0843449i	0.571263	−	0.820767i	$-0.306454\pi$
$101$	1.46818	+	0.847656i	0.146090	+	0.0843449i	−0.425173	+	0.905112i	$0.639787\pi$
$102$		0			0
$103$	−1.53574	+	1.53574i	−0.151321	+	0.151321i	−0.778708	−	0.627387i	$-0.784125\pi$
$103$	−1.53574	+	1.53574i	−0.151321	+	0.151321i	0.627387	+	0.778708i	$0.284125\pi$
$104$		0			0
$105$	−2.26937	−	1.63800i	−0.221468	−	0.159853i
$106$		0			0
$107$	−3.68950	−	13.7694i	−0.356677	−	1.33114i	−0.878361	−	0.477998i	$-0.841363\pi$
$107$	−3.68950	−	13.7694i	−0.356677	−	1.33114i	0.521684	−	0.853139i	$-0.325304\pi$
$108$		0			0
$109$	3.49190	−	3.49190i	0.334464	−	0.334464i	−0.519815	−	0.854279i	$-0.673999\pi$
$109$	3.49190	−	3.49190i	0.334464	−	0.334464i	0.854279	+	0.519815i	$0.173999\pi$
$110$		0			0
$111$	1.50560	+	0.403425i	0.142905	+	0.0382914i
$112$		0			0
$113$	−1.02987	+	3.84351i	−0.0968817	+	0.361567i	−0.997298	−	0.0734619i	$-0.976595\pi$
$113$	−1.02987	+	3.84351i	−0.0968817	+	0.361567i	0.900416	+	0.435029i	$0.143262\pi$
$114$		0			0
$115$	−1.54316	+	0.692832i	−0.143900	+	0.0646069i
$116$		0			0
$117$	−5.71665	+	8.91260i	−0.528504	+	0.823970i
$118$		0			0
$119$	8.21563	+	30.6611i	0.753125	+	2.81070i
$120$		0			0
$121$	−5.43349	+	3.13702i	−0.493953	+	0.285184i
$122$		0			0
$123$	−0.580521	+	0.335164i	−0.0523439	+	0.0302207i
$124$		0			0
$125$	−5.16875	−	9.91383i	−0.462307	−	0.886720i
$126$		0			0
$127$	13.9209	−	3.73009i	1.23528	−	0.330992i	0.418646	−	0.908149i	$-0.362505\pi$
$127$	13.9209	−	3.73009i	1.23528	−	0.330992i	0.816633	+	0.577157i	$0.195838\pi$
$128$		0			0
$129$	−0.757413			−0.0666865
$130$		0			0
$131$	13.6069			1.18884			0.594418	−	0.804156i	$-0.297382\pi$
$131$	13.6069			1.18884			0.594418	+	0.804156i	$0.297382\pi$
$132$		0			0
$133$	−5.02750	+	1.34712i	−0.435940	+	0.116810i
$134$		0			0
$135$	−2.70820	−	1.95475i	−0.233085	−	0.168238i
$136$		0			0
$137$	−8.63357	+	4.98459i	−0.737616	+	0.425863i	−0.821202	−	0.570638i	$-0.806696\pi$
$137$	−8.63357	+	4.98459i	−0.737616	+	0.425863i	0.0835860	+	0.996501i	$0.473363\pi$
$138$		0			0
$139$	−14.3180	+	8.26649i	−1.21443	+	0.701154i	−0.963722	−	0.266907i	$-0.913998\pi$
$139$	−14.3180	+	8.26649i	−1.21443	+	0.701154i	−0.250713	+	0.968062i	$0.580665\pi$
$140$		0			0
$141$	−0.106056	−	0.395808i	−0.00893155	−	0.0333330i
$142$		0			0
$143$	10.0899	+	11.0796i	0.843760	+	0.926519i
$144$		0			0
$145$	−6.05088	+	15.9112i	−0.502498	+	1.32136i
$146$		0			0
$147$	1.15573	−	4.31323i	0.0953228	−	0.355749i
$148$		0			0
$149$	−4.94306	−	1.32449i	−0.404951	−	0.108506i	0.0505933	−	0.998719i	$-0.483889\pi$
$149$	−4.94306	−	1.32449i	−0.404951	−	0.108506i	−0.455545	+	0.890213i	$0.650555\pi$
$150$		0			0
$151$	10.2431	−	10.2431i	0.833572	−	0.833572i	−0.154432	−	0.988003i	$-0.549355\pi$
$151$	10.2431	−	10.2431i	0.833572	−	0.833572i	0.988003	+	0.154432i	$0.0493547\pi$
$152$		0			0
$153$	4.84988	+	18.1000i	0.392089	+	1.46330i
$154$		0			0
$155$	−4.02445	+	5.57567i	−0.323252	+	0.447848i
$156$		0			0
$157$	−9.17805	+	9.17805i	−0.732488	+	0.732488i	−0.971112	−	0.238624i	$-0.923304\pi$
$157$	−9.17805	+	9.17805i	−0.732488	+	0.732488i	0.238624	+	0.971112i	$0.423304\pi$
$158$		0			0
$159$	−1.63938	−	0.946497i	−0.130011	−	0.0750621i
$160$		0			0
$161$	−2.66106	−	2.66106i	−0.209721	−	0.209721i
$162$		0			0
$163$	0.301606	+	0.522396i	0.0236236	+	0.0409172i	0.877596	−	0.479402i	$-0.159146\pi$
$163$	0.301606	+	0.522396i	0.0236236	+	0.0409172i	−0.853972	+	0.520319i	$0.825813\pi$
$164$		0			0
$165$	−1.81258	+	1.47718i	−0.141109	+	0.114998i
$166$		0			0
$167$	9.55141	+	5.51451i	0.739111	+	0.426726i	0.821746	−	0.569854i	$-0.193000\pi$
$167$	9.55141	+	5.51451i	0.739111	+	0.426726i	−0.0826352	+	0.996580i	$0.526334\pi$
$168$		0			0
$169$	7.52200	−	10.6028i	0.578615	−	0.815601i
$170$		0			0
$171$	−2.96785	+	0.795234i	−0.226957	+	0.0608130i
$172$		0			0
$173$	−2.32352	−	0.622584i	−0.176654	−	0.0473342i	0.169408	−	0.985546i	$-0.445814\pi$
$173$	−2.32352	−	0.622584i	−0.176654	−	0.0473342i	−0.346062	+	0.938212i	$0.612481\pi$
$174$		0			0
$175$	16.5281	−	18.5882i	1.24941	−	1.40513i
$176$		0			0
$177$		−	2.45653i		−	0.184644i
$178$		0			0
$179$	4.18307	−	7.24528i	0.312657	−	0.541538i	−0.666280	−	0.745702i	$-0.732114\pi$
$179$	4.18307	−	7.24528i	0.312657	−	0.541538i	0.978937	+	0.204164i	$0.0654476\pi$
$180$		0			0
$181$		−	4.76362i		−	0.354077i	−0.984204	−	0.177038i	$-0.943348\pi$
$181$		−	4.76362i		−	0.354077i	0.984204	−	0.177038i	$-0.0566517\pi$
$182$		0			0
$183$	1.91862	+	1.91862i	0.141829	+	0.141829i
$184$		0			0
$185$	−4.92406	+	12.9482i	−0.362024	+	0.951967i
$186$		0			0
$187$	26.5199			1.93933
$188$		0			0
$189$	1.92319	−	7.17745i	0.139892	−	0.522083i
$190$		0			0
$191$	−8.87644	−	15.3744i	−0.642277	−	1.11246i	−0.984923	−	0.172992i	$-0.944657\pi$
$191$	−8.87644	−	15.3744i	−0.642277	−	1.11246i	0.342647	−	0.939464i	$-0.388677\pi$
$192$		0			0
$193$	0.533644	−	0.924299i	0.0384126	−	0.0665325i	−0.846180	−	0.532897i	$-0.821103\pi$
$193$	0.533644	−	0.924299i	0.0384126	−	0.0665325i	0.884593	+	0.466365i	$0.154437\pi$
$194$		0			0
$195$	1.58755	+	1.26270i	0.113687	+	0.0904236i
$196$		0			0
$197$	−1.86172	+	3.22459i	−0.132642	+	0.229742i	−0.924694	−	0.380711i	$-0.875679\pi$
$197$	−1.86172	+	3.22459i	−0.132642	+	0.229742i	0.792052	+	0.610453i	$0.209013\pi$
$198$		0			0
$199$	−8.66514	−	15.0085i	−0.614256	−	1.06392i	−0.990515	−	0.137407i	$-0.956123\pi$
$199$	−8.66514	−	15.0085i	−0.614256	−	1.06392i	0.376259	−	0.926515i	$-0.377210\pi$
$200$		0			0
$201$	−0.396969	+	1.48151i	−0.0280000	+	0.104498i
$202$		0			0
$203$	−37.8720			−2.65809
$204$		0			0
$205$	−2.44007	−	5.43481i	−0.170422	−	0.379584i
$206$		0			0
$207$	−1.57088	−	1.57088i	−0.109184	−	0.109184i
$208$		0			0
$209$			4.34847i			0.300790i
$210$		0			0
$211$	−3.27838	+	5.67831i	−0.225693	+	0.390911i	−0.956527	−	0.291644i	$-0.905798\pi$
$211$	−3.27838	+	5.67831i	−0.225693	+	0.390911i	0.730834	+	0.682555i	$0.239131\pi$
$212$		0			0
$213$			1.12397i			0.0770128i
$214$		0			0
$215$	0.682741	−	6.69668i	0.0465625	−	0.456710i
$216$		0			0
$217$	−14.7770	−	3.95948i	−1.00313	−	0.268787i
$218$		0			0
$219$	1.45533	−	0.389956i	0.0983424	−	0.0263508i
$220$		0			0
$221$	−4.91022	−	22.4762i	−0.330297	−	1.51191i
$222$		0			0
$223$	4.31040	+	2.48861i	0.288646	+	0.166650i	0.637331	−	0.770590i	$-0.280038\pi$
$223$	4.31040	+	2.48861i	0.288646	+	0.166650i	−0.348685	+	0.937240i	$0.613372\pi$
$224$		0			0
$225$	9.75692	−	10.9730i	0.650461	−	0.731535i
$226$		0			0
$227$	3.56183	+	6.16926i	0.236407	+	0.409468i	0.959681	−	0.281093i	$-0.0906969\pi$
$227$	3.56183	+	6.16926i	0.236407	+	0.409468i	−0.723274	+	0.690561i	$0.757364\pi$
$228$		0			0
$229$	15.5515	+	15.5515i	1.02767	+	1.02767i	0.999606	+	0.0280672i	$0.00893525\pi$
$229$	15.5515	+	15.5515i	1.02767	+	1.02767i	0.0280672	+	0.999606i	$0.491065\pi$
$230$		0			0
$231$	−4.50515	−	2.60105i	−0.296417	−	0.171137i
$232$		0			0
$233$	−1.10223	+	1.10223i	−0.0722092	+	0.0722092i	−0.742289	−	0.670080i	$-0.766260\pi$
$233$	−1.10223	+	1.10223i	−0.0722092	+	0.0722092i	0.670080	+	0.742289i	$0.266260\pi$
$234$		0			0
$235$	3.59514	−	0.580913i	0.234521	−	0.0378946i
$236$		0			0
$237$	0.917815	+	3.42533i	0.0596185	+	0.222499i
$238$		0			0
$239$	3.75486	−	3.75486i	0.242882	−	0.242882i	−0.575160	−	0.818041i	$-0.695060\pi$
$239$	3.75486	−	3.75486i	0.242882	−	0.242882i	0.818041	+	0.575160i	$0.195060\pi$
$240$		0			0
$241$	−23.3970	−	6.26920i	−1.50713	−	0.403834i	−0.591650	−	0.806195i	$-0.701523\pi$
$241$	−23.3970	−	6.26920i	−1.50713	−	0.403834i	−0.915481	+	0.402361i	$0.868190\pi$
$242$		0			0
$243$	1.70901	−	6.37812i	0.109633	−	0.409157i
$244$		0			0
$245$	37.0937	+	14.1064i	2.36983	+	0.901224i
$246$		0			0
$247$	3.68542	−	0.805129i	0.234498	−	0.0512291i
$248$		0			0
$249$	−0.542251	−	2.02371i	−0.0343637	−	0.128247i
$250$		0			0
$251$	18.3191	−	10.5765i	1.15629	−	0.667584i	0.205878	−	0.978578i	$-0.433995\pi$
$251$	18.3191	−	10.5765i	1.15629	−	0.667584i	0.950412	+	0.310993i	$0.100662\pi$
$252$		0			0
$253$	−2.72288	+	1.57205i	−0.171186	+	0.0988341i
$254$		0			0
$255$	3.54386	−	0.572627i	0.221925	−	0.0358593i
$256$		0			0
$257$	15.6872	−	4.20336i	0.978538	−	0.262198i	0.266109	−	0.963943i	$-0.414262\pi$
$257$	15.6872	−	4.20336i	0.978538	−	0.262198i	0.712429	+	0.701745i	$0.247595\pi$
$258$		0			0
$259$	−30.8193			−1.91502
$260$		0			0
$261$	−22.3567			−1.38385
$262$		0			0
$263$	24.6930	−	6.61647i	1.52264	−	0.407989i	0.602028	−	0.798475i	$-0.294360\pi$
$263$	24.6930	−	6.61647i	1.52264	−	0.407989i	0.920609	+	0.390486i	$0.127693\pi$
$264$		0			0
$265$	9.84623	−	13.6414i	0.604849	−	0.837987i
$266$		0			0
$267$	−0.449598	+	0.259576i	−0.0275149	+	0.0158858i
$268$		0			0
$269$	−2.52850	+	1.45983i	−0.154166	+	0.0890076i	−0.575098	−	0.818084i	$-0.695036\pi$
$269$	−2.52850	+	1.45983i	−0.154166	+	0.0890076i	0.420933	+	0.907092i	$0.361703\pi$
$270$		0			0
$271$	4.61686	+	17.2303i	0.280454	+	1.04667i	0.952098	+	0.305794i	$0.0989220\pi$
$271$	4.61686	+	17.2303i	0.280454	+	1.04667i	−0.671643	+	0.740875i	$0.734411\pi$
$272$		0			0
$273$	−1.37031	+	4.29980i	−0.0829348	+	0.260236i
$274$		0			0
$275$	−11.4266	−	17.3575i	−0.689053	−	1.04670i
$276$		0			0
$277$	−0.632426	+	2.36025i	−0.0379988	+	0.141813i	−0.982319	−	0.187214i	$-0.940054\pi$
$277$	−0.632426	+	2.36025i	−0.0379988	+	0.141813i	0.944320	+	0.329027i	$0.106721\pi$
$278$		0			0
$279$	−8.72321	−	2.33738i	−0.522245	−	0.139935i
$280$		0			0
$281$	7.70513	−	7.70513i	0.459649	−	0.459649i	−0.438891	−	0.898540i	$-0.644629\pi$
$281$	7.70513	−	7.70513i	0.459649	−	0.459649i	0.898540	+	0.438891i	$0.144629\pi$
$282$		0			0
$283$	−5.35341	−	19.9792i	−0.318227	−	1.18764i	−0.920947	−	0.389687i	$-0.872583\pi$
$283$	−5.35341	−	19.9792i	−0.318227	−	1.18764i	0.602721	−	0.797952i	$-0.294083\pi$
$284$		0			0
$285$	0.0938936	+	0.581086i	0.00556178	+	0.0344206i
$286$		0			0
$287$	9.37193	−	9.37193i	0.553207	−	0.553207i
$288$		0			0
$289$	−20.5375	−	11.8573i	−1.20809	−	0.697490i
$290$		0			0
$291$	1.48704	+	1.48704i	0.0871718	+	0.0871718i
$292$		0			0
$293$	−3.32754	−	5.76347i	−0.194397	−	0.336705i	0.752306	−	0.658814i	$-0.228942\pi$
$293$	−3.32754	−	5.76347i	−0.194397	−	0.336705i	−0.946703	+	0.322109i	$0.895608\pi$
$294$		0			0
$295$	21.7195	+	2.21434i	1.26456	+	0.128924i
$296$		0			0
$297$	−5.37632	−	3.10402i	−0.311966	−	0.180114i
$298$		0			0
$299$	1.83649	+	2.01663i	0.106207	+	0.116625i
$300$		0			0
$301$	14.4655	−	3.87601i	0.833776	−	0.223410i
$302$		0			0
$303$	0.412009	+	0.110397i	0.0236693	+	0.00634216i
$304$		0			0
$305$	−18.6930	+	15.2341i	−1.07036	+	0.872300i
$306$		0			0
$307$			20.2894i			1.15798i	0.815336	+	0.578988i	$0.196552\pi$
$307$			20.2894i			1.15798i	−0.815336	+	0.578988i	$0.803448\pi$
$308$		0			0
$309$	−0.273222	+	0.473235i	−0.0155431	+	0.0269214i
$310$		0			0
$311$		−	16.7888i		−	0.952005i	−0.879444	−	0.476003i	$-0.842085\pi$
$311$		−	16.7888i		−	0.952005i	0.879444	−	0.476003i	$-0.157915\pi$
$312$		0			0
$313$	−3.96737	−	3.96737i	−0.224249	−	0.224249i	0.586036	−	0.810285i	$-0.300688\pi$
$313$	−3.96737	−	3.96737i	−0.224249	−	0.224249i	−0.810285	+	0.586036i	$0.800688\pi$
$314$		0			0
$315$	30.5339	+	11.6117i	1.72039	+	0.654247i
$316$		0			0
$317$	−14.0049			−0.786596			−0.393298	−	0.919411i	$-0.628666\pi$
$317$	−14.0049			−0.786596			−0.393298	+	0.919411i	$0.628666\pi$
$318$		0			0
$319$	−8.18922	+	30.5626i	−0.458508	+	1.71118i
$320$		0			0
$321$	−1.79330	−	3.10609i	−0.100092	−	0.173365i
$322$		0			0
$323$	3.33799	−	5.78157i	0.185731	−	0.321695i
$324$		0			0
$325$	−12.5952	+	12.8981i	−0.698655	+	0.715458i
$326$		0			0
$327$	0.621241	−	1.07602i	0.0343547	−	0.0595041i
$328$		0			0
$329$	4.05104	+	7.01661i	0.223341	+	0.386838i
$330$		0			0
$331$	4.64068	−	17.3193i	0.255075	−	0.951953i	−0.712974	−	0.701191i	$-0.752652\pi$
$331$	4.64068	−	17.3193i	0.255075	−	0.951953i	0.968049	−	0.250762i	$-0.0806812\pi$
$332$		0			0
$333$	−18.1934			−0.996990
$334$		0			0
$335$	−12.7409	−	4.84526i	−0.696112	−	0.264725i
$336$		0			0
$337$	−5.10238	−	5.10238i	−0.277944	−	0.277944i	0.554344	−	0.832288i	$-0.312969\pi$
$337$	−5.10238	−	5.10238i	−0.277944	−	0.277944i	−0.832288	+	0.554344i	$0.812969\pi$
$338$		0			0
$339$			1.00115i			0.0543748i
$340$		0			0
$341$	−6.39058	+	11.0688i	−0.346069	+	0.599410i
$342$		0			0
$343$			53.4677i			2.88699i
$344$		0			0
$345$	−0.329914	+	0.268867i	−0.0177619	+	0.0144753i
$346$		0			0
$347$	−5.64882	−	1.51360i	−0.303245	−	0.0812541i	0.103988	−	0.994579i	$-0.466840\pi$
$347$	−5.64882	−	1.51360i	−0.303245	−	0.0812541i	−0.407233	+	0.913324i	$0.633506\pi$
$348$		0			0
$349$	−10.5635	+	2.83049i	−0.565453	+	0.151513i	−0.530210	−	0.847866i	$-0.677887\pi$
$349$	−10.5635	+	2.83049i	−0.565453	+	0.151513i	−0.0352425	+	0.999379i	$0.511220\pi$
$350$		0			0
$351$	−1.63529	+	5.13127i	−0.0872852	+	0.273887i
$352$		0			0
$353$	4.17880	+	2.41263i	0.222415	+	0.128411i	0.607068	−	0.794650i	$-0.292346\pi$
$353$	4.17880	+	2.41263i	0.222415	+	0.128411i	−0.384653	+	0.923061i	$0.625679\pi$
$354$		0			0
$355$	−9.93756	−	1.01316i	−0.527431	−	0.0537727i
$356$		0			0
$357$	3.99326	+	6.91652i	0.211346	+	0.366061i
$358$		0			0
$359$	14.0711	+	14.0711i	0.742643	+	0.742643i	0.973086	−	0.230443i	$-0.0740175\pi$
$359$	14.0711	+	14.0711i	0.742643	+	0.742643i	−0.230443	+	0.973086i	$0.574017\pi$
$360$		0			0
$361$	−15.5065	−	8.95267i	−0.816131	−	0.471193i
$362$		0			0
$363$	−1.11621	+	1.11621i	−0.0585858	+	0.0585858i
$364$		0			0
$365$	2.13594	+	13.2189i	0.111800	+	0.691907i
$366$		0			0
$367$	0.521841	+	1.94754i	0.0272399	+	0.101661i	0.978207	−	0.207630i	$-0.0665751\pi$
$367$	0.521841	+	1.94754i	0.0272399	+	0.101661i	−0.950968	+	0.309291i	$0.899908\pi$
$368$		0			0
$369$	5.53247	−	5.53247i	0.288009	−	0.288009i
$370$		0			0
$371$	36.1534	+	9.68728i	1.87699	+	0.502939i
$372$		0			0
$373$	−2.91290	+	10.8711i	−0.150824	+	0.562884i	0.848603	+	0.529031i	$0.177444\pi$
$373$	−2.91290	+	10.8711i	−0.150824	+	0.562884i	−0.999427	+	0.0338529i	$0.989222\pi$
$374$		0			0
$375$	−1.90173	−	2.07276i	−0.0982050	−	0.107037i
$376$		0			0
$377$	27.4187	+	1.28181i	1.41214	+	0.0660167i
$378$		0			0
$379$	−5.25775	−	19.6222i	−0.270072	−	1.00792i	−0.959072	−	0.283162i	$-0.908617\pi$
$379$	−5.25775	−	19.6222i	−0.270072	−	1.00792i	0.689000	−	0.724762i	$-0.258050\pi$
$380$		0			0
$381$	3.14027	−	1.81303i	0.160881	−	0.0928846i
$382$		0			0
$383$	−26.8722	+	15.5147i	−1.37310	+	0.792762i	−0.991318	−	0.131489i	$-0.958024\pi$
$383$	−26.8722	+	15.5147i	−1.37310	+	0.792762i	−0.381786	+	0.924251i	$0.624691\pi$
$384$		0			0
$385$	27.0582	−	37.4878i	1.37902	−	1.91055i
$386$		0			0
$387$	8.53931	−	2.28810i	0.434078	−	0.116311i
$388$		0			0
$389$	−1.63490			−0.0828926			−0.0414463	−	0.999141i	$-0.513197\pi$
$389$	−1.63490			−0.0828926			−0.0414463	+	0.999141i	$0.513197\pi$
$390$		0			0
$391$	4.82698			0.244111
$392$		0			0
$393$	3.30685	−	0.886068i	0.166808	−	0.0446962i
$394$		0			0
$395$	−31.1125	+	5.02724i	−1.56544	+	0.252948i
$396$		0			0
$397$	23.6174	−	13.6355i	1.18532	−	0.684347i	0.228084	−	0.973642i	$-0.426754\pi$
$397$	23.6174	−	13.6355i	1.18532	−	0.684347i	0.957240	+	0.289295i	$0.0934207\pi$
$398$		0			0
$399$	−1.13410	+	0.654774i	−0.0567761	+	0.0327797i
$400$		0			0
$401$	−6.48832	−	24.2147i	−0.324011	−	1.20923i	−0.915302	−	0.402768i	$-0.868048\pi$
$401$	−6.48832	−	24.2147i	−0.324011	−	1.20923i	0.591291	−	0.806458i	$-0.298618\pi$
$402$		0			0
$403$	10.5643	+	3.36674i	0.526245	+	0.167709i
$404$		0			0
$405$	17.6280	+	6.70374i	0.875941	+	0.333112i
$406$		0			0
$407$	−6.66418	+	24.8711i	−0.330331	+	1.23281i
$408$		0			0
$409$	18.8874	+	5.06087i	0.933923	+	0.250244i	0.693527	−	0.720431i	$-0.256056\pi$
$409$	18.8874	+	5.06087i	0.933923	+	0.250244i	0.240396	+	0.970675i	$0.422723\pi$
$410$		0			0
$411$	−1.77361	+	1.77361i	−0.0874856	+	0.0874856i
$412$		0			0
$413$	12.5711	+	46.9161i	0.618585	+	2.30859i
$414$		0			0
$415$	18.3814	−	2.97013i	0.902309	−	0.145798i
$416$		0			0
$417$	−2.94136	+	2.94136i	−0.144039	+	0.144039i
$418$		0			0
$419$	−4.39265	−	2.53610i	−0.214595	−	0.123896i	0.388850	−	0.921301i	$-0.372872\pi$
$419$	−4.39265	−	2.53610i	−0.214595	−	0.123896i	−0.603445	+	0.797405i	$0.706206\pi$
$420$		0			0
$421$	−17.3139	−	17.3139i	−0.843829	−	0.843829i	0.145526	−	0.989354i	$-0.453513\pi$
$421$	−17.3139	−	17.3139i	−0.843829	−	0.843829i	−0.989354	+	0.145526i	$0.953513\pi$
$422$		0			0
$423$	2.39142	+	4.14207i	0.116275	+	0.201394i
$424$		0			0
$425$	1.86842	+	31.8493i	0.0906316	+	1.54492i
$426$		0			0
$427$	−46.4613	−	26.8244i	−2.24842	−	1.29813i
$428$		0			0
$429$	3.17362	+	2.03560i	0.153224	+	0.0982796i
$430$		0			0
$431$	−34.0567	+	9.12548i	−1.64046	+	0.439559i	−0.956918	−	0.290357i	$-0.906226\pi$
$431$	−34.0567	+	9.12548i	−1.64046	+	0.439559i	−0.683537	+	0.729916i	$0.739559\pi$
$432$		0			0
$433$	7.36406	+	1.97319i	0.353894	+	0.0948256i	0.431386	−	0.902167i	$-0.358025\pi$
$433$	7.36406	+	1.97319i	0.353894	+	0.0948256i	−0.0774922	+	0.996993i	$0.524691\pi$
$434$		0			0
$435$	−0.434408	+	4.26090i	−0.0208283	+	0.204295i
$436$		0			0
$437$			0.791479i			0.0378616i
$438$		0			0
$439$	6.65410	−	11.5252i	0.317583	−	0.550070i	−0.662400	−	0.749150i	$-0.730462\pi$
$439$	6.65410	−	11.5252i	0.317583	−	0.550070i	0.979983	+	0.199080i	$0.0637955\pi$
$440$		0			0
$441$			52.1201i			2.48191i
$442$		0			0
$443$	−3.68354	−	3.68354i	−0.175010	−	0.175010i	0.614166	−	0.789177i	$-0.289492\pi$
$443$	−3.68354	−	3.68354i	−0.175010	−	0.175010i	−0.789177	+	0.614166i	$0.789492\pi$
$444$		0			0
$445$	−1.88977	−	4.20911i	−0.0895836	−	0.199531i
$446$		0			0
$447$	−1.28755			−0.0608991
$448$		0			0
$449$	−8.69575	+	32.4530i	−0.410378	+	1.53155i	0.383539	+	0.923525i	$0.374705\pi$
$449$	−8.69575	+	32.4530i	−0.410378	+	1.53155i	−0.793917	+	0.608026i	$0.791961\pi$
$450$		0			0
$451$	−5.53659	−	9.58965i	−0.260708	−	0.451559i
$452$		0			0
$453$	1.82234	−	3.15638i	0.0856210	−	0.148300i
$454$		0			0
$455$	−36.7816	−	15.9915i	−1.72435	−	0.749693i
$456$		0			0
$457$	−12.7773	+	22.1309i	−0.597697	+	1.03524i	0.395464	+	0.918482i	$0.370584\pi$
$457$	−12.7773	+	22.1309i	−0.597697	+	1.03524i	−0.993160	+	0.116759i	$0.962749\pi$
$458$		0			0
$459$	4.76544	+	8.25399i	0.222432	+	0.385263i
$460$		0			0
$461$	3.88759	−	14.5087i	0.181063	−	0.675736i	−0.814376	−	0.580337i	$-0.802921\pi$
$461$	3.88759	−	14.5087i	0.181063	−	0.675736i	0.995439	−	0.0953989i	$-0.0304126\pi$
$462$		0			0
$463$	−18.4587			−0.857850			−0.428925	−	0.903340i	$-0.641107\pi$
$463$	−18.4587			−0.857850			−0.428925	+	0.903340i	$0.641107\pi$
$464$		0			0
$465$	−0.614972	+	1.61711i	−0.0285186	+	0.0749918i
$466$		0			0
$467$	19.6509	+	19.6509i	0.909333	+	0.909333i	0.996218	−	0.0868854i	$-0.0276914\pi$
$467$	19.6509	+	19.6509i	0.909333	+	0.909333i	−0.0868854	+	0.996218i	$0.527691\pi$
$468$		0			0
$469$		−	30.3261i		−	1.40033i
$470$		0			0
$471$	−1.63286	+	2.82819i	−0.0752381	+	0.130316i
$472$		0			0
$473$		−	12.5117i		−	0.575289i
$474$		0			0
$475$	−5.22232	+	0.306364i	−0.239616	+	0.0140570i
$476$		0			0
$477$	21.3422	+	5.71863i	0.977193	+	0.261838i
$478$		0			0
$479$	−15.7117	+	4.20993i	−0.717885	+	0.192357i	−0.599228	−	0.800579i	$-0.704526\pi$
$479$	−15.7117	+	4.20993i	−0.717885	+	0.192357i	−0.118657	+	0.992935i	$0.537859\pi$
$480$		0			0
$481$	22.3127	+	1.04311i	1.01737	+	0.0475615i
$482$		0			0
$483$	−0.819997	−	0.473426i	−0.0373112	−	0.0215416i
$484$		0			0
$485$	−14.4881	+	11.8072i	−0.657872	+	0.536140i
$486$		0			0
$487$	−20.1697	−	34.9350i	−0.913977	−	1.58306i	−0.808392	−	0.588645i	$-0.799662\pi$
$487$	−20.1697	−	34.9350i	−0.913977	−	1.58306i	−0.105586	−	0.994410i	$-0.533672\pi$
$488$		0			0
$489$	0.107317	+	0.107317i	0.00485303	+	0.00485303i
$490$		0			0
$491$	0.241005	+	0.139144i	0.0108764	+	0.00627949i	0.505428	−	0.862869i	$-0.331334\pi$
$491$	0.241005	+	0.139144i	0.0108764	+	0.00627949i	−0.494552	+	0.869148i	$0.664668\pi$
$492$		0			0
$493$	34.3487	−	34.3487i	1.54699	−	1.54699i
$494$		0			0
$495$	15.9731	−	22.1299i	0.717938	−	0.994666i
$496$		0			0
$497$	−5.75182	−	21.4661i	−0.258004	−	0.962886i
$498$		0			0
$499$	−5.97274	+	5.97274i	−0.267377	+	0.267377i	−0.828042	−	0.560666i	$-0.810545\pi$
$499$	−5.97274	+	5.97274i	−0.267377	+	0.267377i	0.560666	+	0.828042i	$0.310545\pi$
$500$		0			0
$501$	2.68036	+	0.718201i	0.119750	+	0.0320869i
$502$		0			0
$503$	8.52299	−	31.8082i	0.380021	−	1.41826i	−0.465846	−	0.884866i	$-0.654250\pi$
$503$	8.52299	−	31.8082i	0.380021	−	1.41826i	0.845867	−	0.533393i	$-0.179083\pi$
$504$		0			0
$505$	−1.34747	+	3.54327i	−0.0599616	+	0.157673i
$506$		0			0
$507$	1.13761	−	3.06661i	0.0505231	−	0.136193i
$508$		0			0
$509$	−8.47308	−	31.6220i	−0.375562	−	1.40162i	−0.852521	−	0.522693i	$-0.824928\pi$
$509$	−8.47308	−	31.6220i	−0.375562	−	1.40162i	0.476959	−	0.878926i	$-0.341739\pi$
$510$		0			0
$511$	−25.7992	+	14.8952i	−1.14129	+	0.658923i
$512$		0			0
$513$	−1.35340	+	0.781389i	−0.0597543	+	0.0344992i
$514$		0			0
$515$	−3.93783	−	2.84228i	−0.173521	−	0.125246i
$516$		0			0
$517$	6.53835	−	1.75195i	0.287556	−	0.0770505i
$518$		0			0
$519$	−0.605222			−0.0265663
$520$		0			0
$521$	24.2134			1.06081			0.530405	−	0.847744i	$-0.322040\pi$
$521$	24.2134			1.06081			0.530405	+	0.847744i	$0.322040\pi$
$522$		0			0
$523$	34.0608	−	9.12656i	1.48937	−	0.399076i	0.579848	−	0.814725i	$-0.303112\pi$
$523$	34.0608	−	9.12656i	1.48937	−	0.399076i	0.909525	+	0.415648i	$0.136445\pi$
$524$		0			0
$525$	2.80634	−	5.59374i	0.122479	−	0.244131i
$526$		0			0
$527$	16.9934	−	9.81113i	0.740243	−	0.427379i
$528$		0			0
$529$	19.4230	−	11.2139i	0.844478	−	0.487559i
$530$		0			0
$531$	7.42104	+	27.6957i	0.322046	+	1.20189i
$532$		0			0
$533$	−7.10232	+	6.46792i	−0.307636	+	0.280157i
$534$		0			0
$535$	29.0791	−	13.0556i	1.25720	−	0.564445i
$536$		0			0
$537$	0.544796	−	2.03321i	0.0235097	−	0.0877393i
$538$		0			0
$539$	71.2504	+	19.0915i	3.06897	+	0.822328i
$540$		0			0
$541$	16.9720	−	16.9720i	0.729682	−	0.729682i	−0.240874	−	0.970556i	$-0.577434\pi$
$541$	16.9720	−	16.9720i	0.729682	−	0.729682i	0.970556	+	0.240874i	$0.0774342\pi$
$542$		0			0
$543$	−0.310203	−	1.15769i	−0.0133121	−	0.0496814i
$544$		0			0
$545$	8.95366	+	6.46265i	0.383533	+	0.276829i
$546$		0			0
$547$	−23.4672	+	23.4672i	−1.00339	+	1.00339i	−0.00339103	+	0.999994i	$0.501079\pi$
$547$	−23.4672	+	23.4672i	−1.00339	+	1.00339i	−0.999994	+	0.00339103i	$0.998921\pi$
$548$		0			0
$549$	−27.4272	−	15.8351i	−1.17056	−	0.675826i
$550$		0			0
$551$	5.63215	+	5.63215i	0.239937	+	0.239937i
$552$		0			0
$553$	−35.0578	−	60.7219i	−1.49081	−	2.58216i
$554$		0			0
$555$	−0.353511	+	3.46742i	−0.0150057	+	0.147184i
$556$		0			0
$557$	−23.3777	−	13.4971i	−0.990547	−	0.571893i	−0.0851092	−	0.996372i	$-0.527124\pi$
$557$	−23.3777	−	13.4971i	−0.990547	−	0.571893i	−0.905438	+	0.424479i	$0.860457\pi$
$558$		0			0
$559$	−10.6040	+	2.31657i	−0.448499	+	0.0979806i
$560$		0			0
$561$	6.44509	−	1.72696i	0.272112	−	0.0729122i
$562$		0			0
$563$	−27.8306	−	7.45719i	−1.17292	−	0.314283i	−0.380806	−	0.924655i	$-0.624353\pi$
$563$	−27.8306	−	7.45719i	−1.17292	−	0.314283i	−0.792115	+	0.610372i	$0.791020\pi$
$564$		0			0
$565$	−8.85165	−	0.902444i	−0.372392	−	0.0379661i
$566$		0			0
$567$			41.9582i			1.76208i
$568$		0			0
$569$	−5.73227	+	9.92858i	−0.240309	+	0.416228i	−0.960802	−	0.277234i	$-0.910582\pi$
$569$	−5.73227	+	9.92858i	−0.240309	+	0.416228i	0.720493	+	0.693462i	$0.243915\pi$
$570$		0			0
$571$		−	6.41332i		−	0.268389i	−0.990955	−	0.134195i	$-0.957155\pi$
$571$		−	6.41332i		−	0.268389i	0.990955	−	0.134195i	$-0.0428447\pi$
$572$		0			0
$573$	−3.15840	−	3.15840i	−0.131944	−	0.131944i
$574$		0			0
$575$	−2.07980	−	3.15930i	−0.0867337	−	0.131752i
$576$		0			0
$577$	−11.3236			−0.471407			−0.235704	−	0.971825i	$-0.575739\pi$
$577$	−11.3236			−0.471407			−0.235704	+	0.971825i	$0.575739\pi$
$578$		0			0
$579$	0.0695010	−	0.259381i	0.00288836	−	0.0107795i
$580$		0			0
$581$	20.7124	+	35.8749i	0.859295	+	1.48834i
$582$		0			0
$583$	15.6352	−	27.0810i	0.647544	−	1.12158i
$584$		0			0
$585$	−21.7130	−	9.44015i	−0.897723	−	0.390302i
$586$		0			0
$587$	17.2749	−	29.9211i	0.713013	−	1.23497i	−0.250708	−	0.968063i	$-0.580664\pi$
$587$	17.2749	−	29.9211i	0.713013	−	1.23497i	0.963721	−	0.266911i	$-0.0860031\pi$
$588$		0			0
$589$	1.60873	+	2.78640i	0.0662865	+	0.114812i
$590$		0			0
$591$	−0.242467	+	0.904898i	−0.00997375	+	0.0372225i
$592$		0			0
$593$	9.05726			0.371937			0.185969	−	0.982556i	$-0.440458\pi$
$593$	9.05726			0.371937			0.185969	+	0.982556i	$0.440458\pi$
$594$		0			0
$595$	−64.7521	+	29.0718i	−2.65458	+	1.19183i
$596$		0			0
$597$	−3.08321	−	3.08321i	−0.126187	−	0.126187i
$598$		0			0
$599$			5.99982i			0.245146i	0.992459	+	0.122573i	$0.0391146\pi$
$599$			5.99982i			0.245146i	−0.992459	+	0.122573i	$0.960885\pi$
$600$		0			0
$601$	−19.2508	+	33.3433i	−0.785256	+	1.36010i	0.143590	+	0.989637i	$0.454135\pi$
$601$	−19.2508	+	33.3433i	−0.785256	+	1.36010i	−0.928846	+	0.370466i	$0.879198\pi$
$602$		0			0
$603$		−	17.9022i		−	0.729034i
$604$		0			0
$605$	−8.86282	−	10.8751i	−0.360325	−	0.442138i
$606$		0			0
$607$	6.53668	+	1.75150i	0.265316	+	0.0710911i	0.389024	−	0.921227i	$-0.372812\pi$
$607$	6.53668	+	1.75150i	0.265316	+	0.0710911i	−0.123709	+	0.992319i	$0.539479\pi$
$608$		0			0
$609$	−9.20396	+	2.46619i	−0.372963	+	0.0999352i
$610$		0			0
$611$	−2.69540	−	5.21702i	−0.109044	−	0.211058i
$612$		0			0
$613$	−18.1115	−	10.4567i	−0.731517	−	0.422342i	0.0874596	−	0.996168i	$-0.472125\pi$
$613$	−18.1115	−	10.4567i	−0.731517	−	0.422342i	−0.818977	+	0.573826i	$0.805458\pi$
$614$		0			0
$615$	−0.946917	−	1.16192i	−0.0381834	−	0.0468530i
$616$		0			0
$617$	6.32411	+	10.9537i	0.254599	+	0.440978i	0.964786	−	0.263034i	$-0.0847232\pi$
$617$	6.32411	+	10.9537i	0.254599	+	0.440978i	−0.710188	+	0.704012i	$0.751390\pi$
$618$		0			0
$619$	1.45857	+	1.45857i	0.0586247	+	0.0586247i	0.735811	−	0.677187i	$-0.236801\pi$
$619$	1.45857	+	1.45857i	0.0586247	+	0.0586247i	−0.677187	+	0.735811i	$0.736801\pi$
$620$		0			0
$621$	−0.978562	−	0.564973i	−0.0392683	−	0.0226716i
$622$		0			0
$623$	7.25830	−	7.25830i	0.290798	−	0.290798i
$624$		0			0
$625$	20.0405	−	14.9458i	0.801622	−	0.597831i
$626$		0			0
$627$	0.283169	+	1.05680i	0.0113087	+	0.0422046i
$628$		0			0
$629$	27.9521	−	27.9521i	1.11452	−	1.11452i
$630$		0			0
$631$	−13.4552	−	3.60532i	−0.535644	−	0.143525i	−0.0191508	−	0.999817i	$-0.506096\pi$
$631$	−13.4552	−	3.60532i	−0.535644	−	0.143525i	−0.516493	+	0.856291i	$0.672763\pi$
$632$		0			0
$633$	−0.426970	+	1.59347i	−0.0169705	+	0.0633349i
$634$		0			0
$635$	13.1993	+	29.3990i	0.523798	+	1.16666i
$636$		0			0
$637$	2.98828	−	63.9211i	0.118400	−	2.53264i
$638$		0			0
$639$	−3.39544	−	12.6719i	−0.134321	−	0.501294i
$640$		0			0
$641$	24.8804	−	14.3647i	0.982716	−	0.567371i	0.0796269	−	0.996825i	$-0.474627\pi$
$641$	24.8804	−	14.3647i	0.982716	−	0.567371i	0.903089	+	0.429453i	$0.141294\pi$
$642$		0			0
$643$	−8.92050	+	5.15025i	−0.351790	+	0.203106i	−0.665473	−	0.746422i	$-0.731770\pi$
$643$	−8.92050	+	5.15025i	−0.351790	+	0.203106i	0.313683	+	0.949528i	$0.398437\pi$
$644$		0			0
$645$	−0.270157	−	1.67194i	−0.0106374	−	0.0658326i
$646$		0			0
$647$	−8.63436	+	2.31357i	−0.339452	+	0.0909558i	−0.424518	−	0.905420i	$-0.639556\pi$
$647$	−8.63436	+	2.31357i	−0.339452	+	0.0909558i	0.0850664	+	0.996375i	$0.472890\pi$
$648$		0			0
$649$	40.5795			1.59288
$650$		0			0
$651$	−3.84906			−0.150857
$652$		0			0
$653$	9.13021	−	2.44643i	0.357293	−	0.0957363i	−0.0757076	−	0.997130i	$-0.524122\pi$
$653$	9.13021	−	2.44643i	0.357293	−	0.0957363i	0.433000	+	0.901394i	$0.357455\pi$
$654$		0			0
$655$	4.85335	+	30.0363i	0.189636	+	1.17361i
$656$		0			0
$657$	−15.2299	+	8.79296i	−0.594173	+	0.343046i
$658$		0			0
$659$	34.4663	−	19.8991i	1.34262	−	0.775160i	0.355426	−	0.934704i	$-0.384336\pi$
$659$	34.4663	−	19.8991i	1.34262	−	0.775160i	0.987191	+	0.159544i	$0.0510025\pi$
$660$		0			0
$661$	4.86551	+	18.1583i	0.189246	+	0.706277i	0.993682	+	0.112236i	$0.0358014\pi$
$661$	4.86551	+	18.1583i	0.189246	+	0.706277i	−0.804435	+	0.594040i	$0.797532\pi$
$662$		0			0
$663$	−2.65696	−	5.14260i	−0.103188	−	0.199722i
$664$		0			0
$665$	−4.76690	−	10.6174i	−0.184852	−	0.411725i
$666$		0			0
$667$	−1.49055	+	5.56280i	−0.0577142	+	0.215392i
$668$		0			0
$669$	1.20961	+	0.324113i	0.0467660	+	0.0125309i
$670$		0			0
$671$	−31.6938	+	31.6938i	−1.22352	+	1.22352i
$672$		0			0
$673$	11.5669	+	43.1681i	0.445870	+	1.66401i	0.713630	+	0.700522i	$0.247050\pi$
$673$	11.5669	+	43.1681i	0.445870	+	1.66401i	−0.267761	+	0.963485i	$0.586284\pi$
$674$		0			0
$675$	3.34901	−	6.67541i	0.128904	−	0.256937i
$676$		0			0
$677$	−1.55951	+	1.55951i	−0.0599367	+	0.0599367i	−0.736440	−	0.676503i	$-0.763495\pi$
$677$	−1.55951	+	1.55951i	−0.0599367	+	0.0599367i	0.676503	+	0.736440i	$0.263495\pi$
$678$		0			0
$679$	−36.0101	−	20.7904i	−1.38194	−	0.797864i
$680$		0			0
$681$	1.26736	+	1.26736i	0.0485654	+	0.0485654i
$682$		0			0
$683$	−0.814127	−	1.41011i	−0.0311517	−	0.0539563i	0.850029	−	0.526735i	$-0.176584\pi$
$683$	−0.814127	−	1.41011i	−0.0311517	−	0.0539563i	−0.881181	+	0.472779i	$0.843251\pi$
$684$		0			0
$685$	−14.0826	−	17.2801i	−0.538070	−	0.660240i
$686$		0			0
$687$	4.79216	+	2.76675i	0.182832	+	0.105558i
$688$		0			0
$689$	−25.8466	−	8.23708i	−0.984677	−	0.313808i
$690$		0			0
$691$	30.4385	−	8.15597i	1.15793	−	0.310268i	0.371794	−	0.928315i	$-0.378743\pi$
$691$	30.4385	−	8.15597i	1.15793	−	0.310268i	0.786141	+	0.618047i	$0.212076\pi$
$692$		0			0
$693$	58.6501	+	15.7153i	2.22793	+	0.596973i
$694$		0			0
$695$	−23.3547	−	28.6575i	−0.885896	−	1.08704i
$696$		0			0
$697$			17.0001i			0.643923i
$698$		0			0
$699$	−0.196096	+	0.339648i	−0.00741702	+	0.0128467i
$700$		0			0
$701$			43.9348i			1.65939i	0.558215	+	0.829697i	$0.311487\pi$
$701$			43.9348i			1.65939i	−0.558215	+	0.829697i	$0.688513\pi$
$702$		0			0
$703$	4.58330	+	4.58330i	0.172862	+	0.172862i
$704$		0			0
$705$	0.835891	−	0.375291i	0.0314815	−	0.0141343i
$706$		0			0
$707$	−8.43371			−0.317182
$708$		0			0
$709$	−3.94108	+	14.7083i	−0.148011	+	0.552383i	0.851592	+	0.524205i	$0.175637\pi$
$709$	−3.94108	+	14.7083i	−0.148011	+	0.552383i	−0.999603	+	0.0281782i	$0.991029\pi$
$710$		0			0
$711$	−20.6955	−	35.8456i	−0.776140	−	1.34431i
$712$		0			0
$713$	−1.16317	+	2.01467i	−0.0435611	+	0.0754500i
$714$		0			0
$715$	−20.8585	+	26.2247i	−0.780064	+	0.980749i
$716$		0			0
$717$	0.668023	−	1.15705i	0.0249478	−	0.0432108i
$718$		0			0
$719$	9.45929	+	16.3840i	0.352772	+	0.611019i	0.986734	−	0.162345i	$-0.0519057\pi$
$719$	9.45929	+	16.3840i	0.352772	+	0.611019i	−0.633962	+	0.773364i	$0.718572\pi$
$720$		0			0
$721$	2.79639	−	10.4363i	0.104143	−	0.388668i
$722$		0			0
$723$	−6.09436			−0.226652
$724$		0			0
$725$	−37.2813	−	7.68166i	−1.38459	−	0.285290i
$726$		0			0
$727$	12.2973	+	12.2973i	0.456082	+	0.456082i	0.897367	−	0.441285i	$-0.145477\pi$
$727$	12.2973	+	12.2973i	0.456082	+	0.456082i	−0.441285	+	0.897367i	$0.645477\pi$
$728$		0			0
$729$			23.6415i			0.875611i
$730$		0			0
$731$	−9.60429	+	16.6351i	−0.355228	+	0.615272i
$732$		0			0
$733$			28.9122i			1.06790i	0.845517	+	0.533948i	$0.179292\pi$
$733$			28.9122i			1.06790i	−0.845517	+	0.533948i	$0.820708\pi$
$734$		0			0
$735$	9.93342	+	1.01273i	0.366400	+	0.0373552i
$736$		0			0
$737$	−24.4731	−	6.55754i	−0.901477	−	0.241550i
$738$		0			0
$739$	3.63268	−	0.973373i	0.133630	−	0.0358061i	−0.191384	−	0.981515i	$-0.561298\pi$
$739$	3.63268	−	0.973373i	0.133630	−	0.0358061i	0.325014	+	0.945709i	$0.394631\pi$
$740$		0			0
$741$	0.843232	−	0.435661i	0.0309769	−	0.0160044i
$742$		0			0
$743$	30.7182	+	17.7352i	1.12694	+	0.650641i	0.943164	−	0.332327i	$-0.107834\pi$
$743$	30.7182	+	17.7352i	1.12694	+	0.650641i	0.183779	+	0.982968i	$0.441167\pi$
$744$		0			0
$745$	1.16061	−	11.3839i	0.0425216	−	0.417074i
$746$		0			0
$747$	12.2270	+	21.1778i	0.447363	+	0.774855i
$748$		0			0
$749$	50.1447	+	50.1447i	1.83225	+	1.83225i
$750$		0			0
$751$	−12.5593	−	7.25111i	−0.458295	−	0.264597i	0.253032	−	0.967458i	$-0.418572\pi$
$751$	−12.5593	−	7.25111i	−0.458295	−	0.264597i	−0.711327	+	0.702861i	$0.751906\pi$
$752$		0			0
$753$	3.76332	−	3.76332i	0.137143	−	0.137143i
$754$		0			0
$755$	26.2645	+	18.9574i	0.955865	+	0.689932i
$756$		0			0
$757$	9.92051	+	37.0239i	0.360567	+	1.34566i	0.873332	+	0.487126i	$0.161955\pi$
$757$	9.92051	+	37.0239i	0.360567	+	1.34566i	−0.512765	+	0.858529i	$0.671379\pi$
$758$		0			0
$759$	−0.559364	+	0.559364i	−0.0203036	+	0.0203036i
$760$		0			0
$761$	36.7432	+	9.84532i	1.33194	+	0.356892i	0.853438	−	0.521194i	$-0.174513\pi$
$761$	36.7432	+	9.84532i	1.33194	+	0.356892i	0.478502	+	0.878086i	$0.341180\pi$
$762$		0			0
$763$	−6.35832	+	23.7296i	−0.230187	+	0.859068i
$764$		0			0
$765$	−38.2247	+	17.1618i	−1.38202	+	0.620485i
$766$		0			0
$767$	−7.51338	−	34.3920i	−0.271292	−	1.24182i
$768$		0			0
$769$	−7.83503	−	29.2407i	−0.282538	−	1.05445i	−0.950619	−	0.310359i	$-0.899551\pi$
$769$	−7.83503	−	29.2407i	−0.282538	−	1.05445i	0.668081	−	0.744089i	$-0.267116\pi$
$770$		0			0
$771$	3.53870	−	2.04307i	0.127443	−	0.0735793i
$772$		0			0
$773$	−16.0681	+	9.27689i	−0.577928	+	0.333667i	−0.760309	−	0.649561i	$-0.774953\pi$
$773$	−16.0681	+	9.27689i	−0.577928	+	0.333667i	0.182382	+	0.983228i	$0.441619\pi$
$774$		0			0
$775$	−13.7434	−	6.89497i	−0.493677	−	0.247675i
$776$		0			0
$777$	−7.48995	+	2.00693i	−0.268701	+	0.0719981i
$778$		0			0
$779$	−2.78750			−0.0998724
$780$		0			0
$781$	−18.5668			−0.664373
$782$		0			0
$783$	−10.9838	+	2.94309i	−0.392527	+	0.105177i
$784$		0			0
$785$	−23.5336	−	16.9863i	−0.839951	−	0.606267i
$786$		0			0
$787$	−26.8837	+	15.5213i	−0.958302	+	0.553276i	−0.895650	−	0.444759i	$-0.853289\pi$
$787$	−26.8837	+	15.5213i	−0.958302	+	0.553276i	−0.0626520	+	0.998035i	$0.519956\pi$
$788$		0			0
$789$	5.57024	−	3.21598i	0.198306	−	0.114492i
$790$		0			0
$791$	−5.12330	−	19.1204i	−0.182164	−	0.679844i
$792$		0			0
$793$	32.7293	+	20.9930i	1.16225	+	0.745483i
$794$		0			0
$795$	1.50459	−	3.95643i	0.0533624	−	0.140320i
$796$		0			0
$797$	6.19057	−	23.1035i	0.219281	−	0.818368i	−0.765334	−	0.643633i	$-0.777426\pi$
$797$	6.19057	−	23.1035i	0.219281	−	0.818368i	0.984615	−	0.174735i	$-0.0559070\pi$
$798$		0			0
$799$	−10.0380	−	2.68967i	−0.355119	−	0.0951537i
$800$		0			0
$801$	4.28475	−	4.28475i	0.151394	−	0.151394i
$802$		0			0
$803$	6.44169	+	24.0407i	0.227322	+	0.848378i
$804$		0			0
$805$	4.92496	−	6.82327i	0.173582	−	0.240489i
$806$		0			0
$807$	−0.519434	+	0.519434i	−0.0182850	+	0.0182850i
$808$		0			0
$809$	32.8616	+	18.9726i	1.15535	+	0.667043i	0.950186	−	0.311684i	$-0.100893\pi$
$809$	32.8616	+	18.9726i	1.15535	+	0.667043i	0.205166	+	0.978727i	$0.434227\pi$
$810$		0			0
$811$	26.4061	+	26.4061i	0.927242	+	0.927242i	0.997527	−	0.0702846i	$-0.0223907\pi$
$811$	26.4061	+	26.4061i	0.927242	+	0.927242i	−0.0702846	+	0.997527i	$0.522391\pi$
$812$		0			0
$813$	2.24405	+	3.88681i	0.0787023	+	0.136316i
$814$		0			0
$815$	−1.04558	+	0.852106i	−0.0366250	+	0.0298480i
$816$		0			0
$817$	−2.72766	−	1.57481i	−0.0954287	−	0.0550958i
$818$		0			0
$819$	2.45982	−	52.6170i	0.0859530	−	1.83859i
$820$		0			0
$821$	9.49104	−	2.54312i	0.331240	−	0.0887554i	−0.0893662	−	0.995999i	$-0.528484\pi$
$821$	9.49104	−	2.54312i	0.331240	−	0.0887554i	0.420606	+	0.907243i	$0.361817\pi$
$822$		0			0
$823$	−13.0556	−	3.49823i	−0.455089	−	0.121941i	0.0239906	−	0.999712i	$-0.492363\pi$
$823$	−13.0556	−	3.49823i	−0.455089	−	0.121941i	−0.479080	+	0.877771i	$0.659030\pi$
$824$		0			0
$825$	−3.90730	−	3.47427i	−0.136035	−	0.120958i
$826$		0			0
$827$		−	19.5815i		−	0.680916i	−0.940260	−	0.340458i	$-0.889418\pi$
$827$		−	19.5815i		−	0.680916i	0.940260	−	0.340458i	$-0.110582\pi$
$828$		0			0
$829$	−6.60308	+	11.4369i	−0.229335	+	0.397219i	−0.957611	−	0.288064i	$-0.906988\pi$
$829$	−6.60308	+	11.4369i	−0.229335	+	0.397219i	0.728277	+	0.685283i	$0.240322\pi$
$830$		0			0
$831$			0.614789i			0.0213268i
$832$		0			0
$833$	−80.0768	−	80.0768i	−2.77450	−	2.77450i
$834$		0			0
$835$	−8.76610	+	23.0511i	−0.303363	+	0.797716i
$836$		0			0
$837$	−4.59337			−0.158770
$838$		0			0
$839$	−3.51806	+	13.1296i	−0.121457	+	0.453283i	−0.999689	−	0.0249523i	$-0.992057\pi$
$839$	−3.51806	+	13.1296i	−0.121457	+	0.453283i	0.878232	+	0.478235i	$0.158723\pi$
$840$		0			0
$841$	14.4780	+	25.0767i	0.499242	+	0.864713i
$842$		0			0
$843$	1.37081	−	2.37431i	0.0472132	−	0.0817757i
$844$		0			0
$845$	26.0880	+	12.8225i	0.897455	+	0.441107i
$846$		0			0
$847$	15.6058	−	27.0301i	0.536223	−	0.928765i
$848$		0			0
$849$	−2.60206	−	4.50689i	−0.0893023	−	0.154676i
$850$		0			0
$851$	−1.21297	+	4.52686i	−0.0415801	+	0.155179i
$852$		0			0
$853$	1.37110			0.0469457			0.0234728	−	0.999724i	$-0.492528\pi$
$853$	1.37110			0.0469457			0.0234728	+	0.999724i	$0.492528\pi$
$854$		0			0
$855$	−2.81401	−	6.26770i	−0.0962373	−	0.214351i
$856$		0			0
$857$	19.5377	+	19.5377i	0.667395	+	0.667395i	0.957112	−	0.289718i	$-0.0935614\pi$
$857$	19.5377	+	19.5377i	0.667395	+	0.667395i	−0.289718	+	0.957112i	$0.593561\pi$
$858$		0			0
$859$			6.82578i			0.232893i	0.993197	+	0.116446i	$0.0371503\pi$
$859$			6.82578i			0.232893i	−0.993197	+	0.116446i	$0.962850\pi$
$860$		0			0
$861$	1.66735	−	2.88793i	0.0568231	−	0.0984205i
$862$		0			0
$863$		−	24.6002i		−	0.837401i	−0.908124	−	0.418701i	$-0.862486\pi$
$863$		−	24.6002i		−	0.837401i	0.908124	−	0.418701i	$-0.137514\pi$
$864$		0			0
$865$	0.545554	−	5.35108i	0.0185494	−	0.181942i
$866$		0			0
$867$	−5.76333	−	1.54428i	−0.195733	−	0.0524465i
$868$		0			0
$869$	−56.5831	+	15.1614i	−1.91945	+	0.514315i
$870$		0			0
$871$	−1.02641	+	21.9556i	−0.0347787	+	0.743937i
$872$		0			0
$873$	−21.2576	−	12.2731i	−0.719461	−	0.415381i
$874$		0			0
$875$	46.9275	+	29.8546i	1.58644	+	1.00927i
$876$		0			0
$877$	19.4286	+	33.6513i	0.656057	+	1.13632i	0.981628	+	0.190806i	$0.0611103\pi$
$877$	19.4286	+	33.6513i	0.656057	+	1.13632i	−0.325571	+	0.945518i	$0.605556\pi$
$878$		0			0
$879$	−1.18400	−	1.18400i	−0.0399353	−	0.0399353i
$880$		0			0
$881$	−24.9837	−	14.4243i	−0.841721	−	0.485968i	0.0161277	−	0.999870i	$-0.494866\pi$
$881$	−24.9837	−	14.4243i	−0.841721	−	0.485968i	−0.857849	+	0.513902i	$0.828200\pi$
$882$		0			0
$883$	38.2512	−	38.2512i	1.28725	−	1.28725i	0.350806	−	0.936448i	$-0.385908\pi$
$883$	38.2512	−	38.2512i	1.28725	−	1.28725i	0.936448	−	0.350806i	$-0.114092\pi$
$884$		0			0
$885$	5.42263	−	0.876205i	0.182280	−	0.0294533i
$886$		0			0
$887$	−11.6937	−	43.6417i	−0.392638	−	1.46534i	−0.825767	−	0.564012i	$-0.809257\pi$
$887$	−11.6937	−	43.6417i	−0.392638	−	1.46534i	0.433129	−	0.901332i	$-0.357409\pi$
$888$		0			0
$889$	−50.6964	+	50.6964i	−1.70030	+	1.70030i
$890$		0			0
$891$	33.8601	+	9.07280i	1.13436	+	0.303950i
$892$		0			0
$893$	0.441025	−	1.64593i	0.0147583	−	0.0550789i
$894$		0			0
$895$	17.4855	+	6.64958i	0.584477	+	0.222271i
$896$		0			0
$897$	0.577641	+	0.370506i	0.0192869	+	0.0123708i
$898$		0			0
$899$	6.05925	+	22.6134i	0.202087	+	0.754200i
$900$		0			0
$901$	−41.5760	+	24.0039i	−1.38510	+	0.799687i
$902$		0			0
$903$	3.26311	−	1.88396i	0.108590	−	0.0626943i
$904$		0			0
$905$	10.5154	−	1.69911i	0.349543	−	0.0564802i
$906$		0			0
$907$	−22.3497	+	5.98857i	−0.742108	+	0.198847i	−0.610015	−	0.792390i	$-0.708837\pi$
$907$	−22.3497	+	5.98857i	−0.742108	+	0.198847i	−0.132093	+	0.991237i	$0.542170\pi$
$908$		0			0
$909$	−4.97862			−0.165130
$910$		0			0
$911$	50.3382			1.66778			0.833890	−	0.551931i	$-0.186109\pi$
$911$	50.3382			1.66778			0.833890	+	0.551931i	$0.186109\pi$
$912$		0			0
$913$	33.4297	−	8.95745i	1.10636	−	0.296448i
$914$		0			0
$915$	−3.55090	+	4.91958i	−0.117389	+	0.162636i
$916$		0			0
$917$	−58.6216	+	33.8452i	−1.93586	+	1.11767i
$918$		0			0
$919$	27.9629	−	16.1444i	0.922412	−	0.532555i	0.0380085	−	0.999277i	$-0.487899\pi$
$919$	27.9629	−	16.1444i	0.922412	−	0.532555i	0.884404	+	0.466722i	$0.154565\pi$
$920$		0			0
$921$	1.32123	+	4.93089i	0.0435359	+	0.162478i
$922$		0			0
$923$	3.43769	+	15.7358i	0.113153	+	0.517949i
$924$		0			0
$925$	−30.3386	−	6.25114i	−0.997526	−	0.205536i
$926$		0			0
$927$	1.65078	−	6.16079i	0.0542187	−	0.202347i
$928$		0			0
$929$	−18.2130	−	4.88016i	−0.597549	−	0.160113i	−0.0526479	−	0.998613i	$-0.516766\pi$
$929$	−18.2130	−	4.88016i	−0.597549	−	0.160113i	−0.544901	+	0.838500i	$0.683433\pi$
$930$		0			0
$931$	13.1302	−	13.1302i	0.430324	−	0.430324i
$932$		0			0
$933$	−1.09327	−	4.08015i	−0.0357921	−	0.133578i
$934$		0			0
$935$	9.45924	+	58.5411i	0.309350	+	1.91450i
$936$		0			0
$937$	28.7938	−	28.7938i	0.940651	−	0.940651i	−0.0576835	−	0.998335i	$-0.518371\pi$
$937$	28.7938	−	28.7938i	0.940651	−	0.940651i	0.998335	+	0.0576835i	$0.0183714\pi$
$938$		0			0
$939$	−1.22253	−	0.705830i	−0.0398959	−	0.0230339i
$940$		0			0
$941$	−15.7400	−	15.7400i	−0.513111	−	0.513111i	0.402367	−	0.915478i	$-0.368187\pi$
$941$	−15.7400	−	15.7400i	−0.513111	−	0.513111i	−0.915478	+	0.402367i	$0.868187\pi$
$942$		0			0
$943$	−1.00773	−	1.74544i	−0.0328163	−	0.0568394i
$944$		0			0
$945$	16.5297	+	1.68524i	0.537713	+	0.0548210i
$946$		0			0
$947$	−46.4702	−	26.8296i	−1.51008	−	0.871845i	−0.999931	−	0.0117590i	$-0.996257\pi$
$947$	−46.4702	−	26.8296i	−1.51008	−	0.871845i	−0.510149	−	0.860086i	$-0.670410\pi$
$948$		0			0
$949$	19.1823	−	9.91065i	0.622684	−	0.321713i
$950$		0			0
$951$	−3.40360	+	0.911991i	−0.110369	+	0.0295733i
$952$		0			0
$953$	−17.7036	−	4.74366i	−0.573475	−	0.153662i	−0.0395854	−	0.999216i	$-0.512604\pi$
$953$	−17.7036	−	4.74366i	−0.573475	−	0.153662i	−0.533890	+	0.845554i	$0.679270\pi$
$954$		0			0
$955$	30.7720	−	25.0780i	0.995760	−	0.811505i
$956$		0			0
$957$			7.96085i			0.257338i
$958$		0			0
$959$	24.7970	−	42.9496i	0.800736	−	1.38692i
$960$		0			0
$961$		−	21.5431i		−	0.694940i
$962$		0			0
$963$	29.6016	+	29.6016i	0.953898	+	0.953898i
$964$		0			0
$965$	2.23067	+	0.848303i	0.0718079	+	0.0273078i
$966$		0			0
$967$	29.0099			0.932894			0.466447	−	0.884549i	$-0.345534\pi$
$967$	29.0099			0.932894			0.466447	+	0.884549i	$0.345534\pi$
$968$		0			0
$969$	0.434734	−	1.62245i	0.0139657	−	0.0521206i
$970$		0			0
$971$	7.94826	+	13.7668i	0.255072	+	0.441797i	0.964915	−	0.262562i	$-0.0845676\pi$
$971$	7.94826	+	13.7668i	0.255072	+	0.441797i	−0.709843	+	0.704360i	$0.751234\pi$
$972$		0			0
$973$	41.1235	−	71.2280i	1.31836	−	2.28346i
$974$		0			0
$975$	−2.22107	+	3.95479i	−0.0711312	+	0.126655i
$976$		0			0
$977$	20.9877	−	36.3517i	0.671454	−	1.16299i	−0.306037	−	0.952020i	$-0.599003\pi$
$977$	20.9877	−	36.3517i	0.671454	−	1.16299i	0.977492	−	0.210974i	$-0.0676634\pi$
$978$		0			0
$979$	−4.28793	−	7.42692i	−0.137043	−	0.237365i
$980$		0			0
$981$	−3.75347	+	14.0081i	−0.119839	+	0.447245i
$982$		0			0
$983$	−34.2861			−1.09356			−0.546779	−	0.837277i	$-0.684146\pi$
$983$	−34.2861			−1.09356			−0.546779	+	0.837277i	$0.684146\pi$
$984$		0			0
$985$	−7.78211	−	2.95946i	−0.247959	−	0.0942962i
$986$		0			0
$987$	1.44143	+	1.44143i	0.0458813	+	0.0458813i
$988$		0			0
$989$		−	2.27730i		−	0.0724139i
$990$		0			0
$991$	20.4379	−	35.3995i	0.649231	−	1.12450i	−0.334076	−	0.942546i	$-0.608424\pi$
$991$	20.4379	−	35.3995i	0.649231	−	1.12450i	0.983307	−	0.181955i	$-0.0582424\pi$
$992$		0			0
$993$		−	4.51127i		−	0.143161i
$994$		0			0
$995$	30.0395	−	24.4810i	0.952317	−	0.776101i
$996$		0			0
$997$	34.5952	+	9.26975i	1.09564	+	0.293576i	0.760988	−	0.648766i	$-0.224715\pi$
$997$	34.5952	+	9.26975i	1.09564	+	0.293576i	0.334652	+	0.942342i	$0.391381\pi$
$998$		0			0
$999$	−8.93830	+	2.39501i	−0.282795	+	0.0757748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bk.c.33.3	yes	20
5.2	odd	4		260.2.bf.c.137.3	yes	20
5.3	odd	4		1300.2.bn.d.657.3		20
5.4	even	2		1300.2.bs.d.293.3		20
13.2	odd	12		260.2.bf.c.93.3	✓	20
65.2	even	12	inner	260.2.bk.c.197.3	yes	20
65.28	even	12		1300.2.bs.d.457.3		20
65.54	odd	12		1300.2.bn.d.93.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bf.c.93.3	✓	20	13.2	odd	12
260.2.bf.c.137.3	yes	20	5.2	odd	4
260.2.bk.c.33.3	yes	20	1.1	even	1	trivial
260.2.bk.c.197.3	yes	20	65.2	even	12	inner
1300.2.bn.d.93.3		20	65.54	odd	12
1300.2.bn.d.657.3		20	5.3	odd	4
1300.2.bs.d.293.3		20	5.4	even	2
1300.2.bs.d.457.3		20	65.28	even	12

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bk (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.243028 - 0.0651192i) q^{3} +(0.356684 + 2.20744i) q^{5} +(-4.30824 + 2.48736i) q^{7} +(-2.54325 + 1.46835i) q^{9} +O(q^{10})\)	\(q+(0.243028 - 0.0651192i) q^{3} +(0.356684 + 2.20744i) q^{5} +(-4.30824 + 2.48736i) q^{7} +(-2.54325 + 1.46835i) q^{9} +(1.07571 + 4.01459i) q^{11} +(3.20328 - 1.65499i) q^{13} +(0.230431 + 0.513242i) q^{15} +(1.65147 - 6.16338i) q^{17} +(1.01061 + 0.270792i) q^{19} +(-0.885048 + 0.885048i) q^{21} +(0.195793 + 0.730708i) q^{23} +(-4.74555 + 1.57472i) q^{25} +(-1.05619 + 1.05619i) q^{27} +(6.59295 + 3.80644i) q^{29} +(2.17449 + 2.17449i) q^{31} +(0.522853 + 0.905608i) q^{33} +(-7.02737 - 8.62296i) q^{35} +(5.36518 + 3.09759i) q^{37} +(0.670715 - 0.610805i) q^{39} +(-2.57347 + 0.689559i) q^{41} +(-2.90779 - 0.779141i) q^{43} +(-4.14842 - 5.09034i) q^{45} -1.62865i q^{47} +(8.87394 - 15.3701i) q^{49} -1.60542i q^{51} +(-5.32012 - 5.32012i) q^{53} +(-8.47826 + 3.80649i) q^{55} +0.263240 q^{57} +(2.52700 - 9.43090i) q^{59} +(5.39215 + 9.33947i) q^{61} +(7.30463 - 12.6520i) q^{63} +(4.79585 + 6.48073i) q^{65} +(-3.04802 + 5.27932i) q^{67} +(0.0951662 + 0.164833i) q^{69} +(-1.15621 + 4.31503i) q^{71} +5.98834 q^{73} +(-1.05076 + 0.691727i) q^{75} +(-14.6201 - 14.6201i) q^{77} +14.0944i q^{79} +(4.21714 - 7.30430i) q^{81} -8.32705i q^{83} +(14.1943 + 1.44714i) q^{85} +(1.85015 + 0.495745i) q^{87} +(-1.99308 + 0.534044i) q^{89} +(-9.68392 + 15.0978i) q^{91} +(0.670065 + 0.386862i) q^{93} +(-0.237288 + 2.32744i) q^{95} +(4.17921 + 7.23861i) q^{97} +(-8.63060 - 8.63060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9	\( 20 q - 2 q^{3} + 12 q^{5} + 6 q^{7} - 12 q^{9} + 8 q^{13} - 20 q^{15} + 20 q^{19} - 12 q^{21} + 6 q^{23} + 2 q^{25} - 20 q^{27} + 24 q^{29} + 8 q^{31} - 10 q^{33} - 36 q^{35} + 4 q^{39} + 6 q^{41} + 38 q^{43} - 16 q^{45} + 14 q^{49} + 30 q^{53} + 2 q^{55} - 76 q^{57} - 24 q^{59} - 32 q^{61} - 24 q^{63} - 30 q^{65} + 22 q^{67} - 16 q^{69} - 44 q^{73} - 2 q^{75} - 12 q^{77} + 2 q^{81} + 50 q^{85} + 38 q^{87} - 30 q^{89} - 72 q^{91} - 48 q^{93} - 30 q^{95} + 46 q^{97} + 20 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 12 * q^5 + 6 * q^7 - 12 * q^9 + 8 * q^13 - 20 * q^15 + 20 * q^19 - 12 * q^21 + 6 * q^23 + 2 * q^25 - 20 * q^27 + 24 * q^29 + 8 * q^31 - 10 * q^33 - 36 * q^35 + 4 * q^39 + 6 * q^41 + 38 * q^43 - 16 * q^45 + 14 * q^49 + 30 * q^53 + 2 * q^55 - 76 * q^57 - 24 * q^59 - 32 * q^61 - 24 * q^63 - 30 * q^65 + 22 * q^67 - 16 * q^69 - 44 * q^73 - 2 * q^75 - 12 * q^77 + 2 * q^81 + 50 * q^85 + 38 * q^87 - 30 * q^89 - 72 * q^91 - 48 * q^93 - 30 * q^95 + 46 * q^97 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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