LMFDB - Embedded newform 360.2.bi.b.49.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(49,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

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

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

chi := DirichletCharacter("360.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bi (of order $6$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.10
Character	$\chi$	$=$	360.49
Dual form			360.2.bi.b.169.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.557359 - 1.63992i) q^{3} +(-2.18221 + 0.487830i) q^{5} +(-3.90215 + 2.25291i) q^{7} +(-2.37870 - 1.82805i) q^{9} +O(q^{10})$	\(q+(0.557359 - 1.63992i) q^{3} +(-2.18221 + 0.487830i) q^{5} +(-3.90215 + 2.25291i) q^{7} +(-2.37870 - 1.82805i) q^{9} +(0.631800 + 1.09431i) q^{11} +(-4.31068 - 2.48877i) q^{13} +(-0.416267 + 3.85055i) q^{15} -4.59329i q^{17} -6.38235 q^{19} +(1.51970 + 7.65491i) q^{21} +(5.34103 + 3.08364i) q^{23} +(4.52404 - 2.12909i) q^{25} +(-4.32366 + 2.88201i) q^{27} +(1.95380 + 3.38408i) q^{29} +(1.08560 - 1.88031i) q^{31} +(2.14672 - 0.426181i) q^{33} +(7.41626 - 6.81990i) q^{35} +0.516341i q^{37} +(-6.48400 + 5.68205i) q^{39} +(1.11882 - 1.93786i) q^{41} +(-5.09669 + 2.94257i) q^{43} +(6.08260 + 2.82878i) q^{45} +(-5.95343 + 3.43722i) q^{47} +(6.65119 - 11.5202i) q^{49} +(-7.53264 - 2.56011i) q^{51} -6.92003i q^{53} +(-1.91255 - 2.07980i) q^{55} +(-3.55726 + 10.4666i) q^{57} +(3.91777 - 6.78578i) q^{59} +(-6.62192 - 11.4695i) q^{61} +(13.4005 + 1.77434i) q^{63} +(10.6209 + 3.32814i) q^{65} +(-2.63495 - 1.52129i) q^{67} +(8.03381 - 7.04018i) q^{69} -9.06407 q^{71} +6.90760i q^{73} +(-0.970034 - 8.60576i) q^{75} +(-4.93076 - 2.84677i) q^{77} +(4.09326 + 7.08973i) q^{79} +(2.31645 + 8.69679i) q^{81} +(5.71353 - 3.29871i) q^{83} +(2.24074 + 10.0235i) q^{85} +(6.63860 - 1.31793i) q^{87} +0.969826 q^{89} +22.4279 q^{91} +(-2.47850 - 2.82831i) q^{93} +(13.9276 - 3.11350i) q^{95} +(-10.8174 + 6.24543i) q^{97} +(0.497592 - 3.75800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 4 * q^9	$ 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) $ 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.557359	−	1.63992i	0.321791	−	0.946811i
$3$	0.557359	−	1.63992i	0.321791	−	0.946811i
$4$		0			0
$5$	−2.18221	+	0.487830i	−0.975912	+	0.218164i
$5$	−2.18221	+	0.487830i	−0.975912	+	0.218164i
$6$		0			0
$7$	−3.90215	+	2.25291i	−1.47487	+	0.851519i	−0.999599	−	0.0283175i	$-0.990985\pi$
$7$	−3.90215	+	2.25291i	−1.47487	+	0.851519i	−0.475276	+	0.879837i	$0.657652\pi$
$8$		0			0
$9$	−2.37870	−	1.82805i	−0.792901	−	0.609351i
$10$		0			0
$11$	0.631800	+	1.09431i	0.190495	+	0.329947i	0.945414	−	0.325871i	$-0.105657\pi$
$11$	0.631800	+	1.09431i	0.190495	+	0.329947i	−0.754919	+	0.655817i	$0.772324\pi$
$12$		0			0
$13$	−4.31068	−	2.48877i	−1.19557	−	0.690262i	−0.236005	−	0.971752i	$-0.575838\pi$
$13$	−4.31068	−	2.48877i	−1.19557	−	0.690262i	−0.959564	+	0.281490i	$0.909171\pi$
$14$		0			0
$15$	−0.416267	+	3.85055i	−0.107480	+	0.994207i
$16$		0			0
$17$		−	4.59329i		−	1.11404i	−0.830501	−	0.557018i	$-0.811946\pi$
$17$		−	4.59329i		−	1.11404i	0.830501	−	0.557018i	$-0.188054\pi$
$18$		0			0
$19$	−6.38235			−1.46421			−0.732106	−	0.681191i	$-0.761462\pi$
$19$	−6.38235			−1.46421			−0.732106	+	0.681191i	$0.761462\pi$
$20$		0			0
$21$	1.51970	+	7.65491i	0.331626	+	1.67044i
$22$		0			0
$23$	5.34103	+	3.08364i	1.11368	+	0.642984i	0.939780	−	0.341779i	$-0.111029\pi$
$23$	5.34103	+	3.08364i	1.11368	+	0.642984i	0.173901	+	0.984763i	$0.444363\pi$
$24$		0			0
$25$	4.52404	−	2.12909i	0.904809	−	0.425818i
$26$		0			0
$27$	−4.32366	+	2.88201i	−0.832088	+	0.554643i
$28$		0			0
$29$	1.95380	+	3.38408i	0.362811	+	0.628407i	0.988422	−	0.151728i	$-0.0484836\pi$
$29$	1.95380	+	3.38408i	0.362811	+	0.628407i	−0.625611	+	0.780135i	$0.715150\pi$
$30$		0			0
$31$	1.08560	−	1.88031i	0.194979	−	0.337714i	−0.751915	−	0.659261i	$-0.770869\pi$
$31$	1.08560	−	1.88031i	0.194979	−	0.337714i	0.946894	+	0.321547i	$0.104203\pi$
$32$		0			0
$33$	2.14672	−	0.426181i	0.373697	−	0.0741885i
$34$		0			0
$35$	7.41626	−	6.81990i	1.25358	−	1.15277i
$36$		0			0
$37$			0.516341i			0.0848860i	0.999099	+	0.0424430i	$0.0135141\pi$
$37$			0.516341i			0.0848860i	−0.999099	+	0.0424430i	$0.986486\pi$
$38$		0			0
$39$	−6.48400	+	5.68205i	−1.03827	+	0.909857i
$40$		0			0
$41$	1.11882	−	1.93786i	0.174731	−	0.302643i	−0.765337	−	0.643630i	$-0.777428\pi$
$41$	1.11882	−	1.93786i	0.174731	−	0.302643i	0.940068	+	0.340987i	$0.110761\pi$
$42$		0			0
$43$	−5.09669	+	2.94257i	−0.777237	+	0.448738i	−0.835450	−	0.549566i	$-0.814793\pi$
$43$	−5.09669	+	2.94257i	−0.777237	+	0.448738i	0.0582130	+	0.998304i	$0.481460\pi$
$44$		0			0
$45$	6.08260	+	2.82878i	0.906740	+	0.421690i
$46$		0			0
$47$	−5.95343	+	3.43722i	−0.868398	+	0.501370i	−0.866815	−	0.498629i	$-0.833837\pi$
$47$	−5.95343	+	3.43722i	−0.868398	+	0.501370i	−0.00158216	+	0.999999i	$0.500504\pi$
$48$		0			0
$49$	6.65119	−	11.5202i	0.950170	−	1.64574i
$50$		0			0
$51$	−7.53264	−	2.56011i	−1.05478	−	0.358487i
$52$		0			0
$53$		−	6.92003i		−	0.950540i	−0.879840	−	0.475270i	$-0.842350\pi$
$53$		−	6.92003i		−	0.950540i	0.879840	−	0.475270i	$-0.157650\pi$
$54$		0			0
$55$	−1.91255	−	2.07980i	−0.257889	−	0.280440i
$56$		0			0
$57$	−3.55726	+	10.4666i	−0.471171	+	1.38633i
$58$		0			0
$59$	3.91777	−	6.78578i	0.510050	−	0.883433i	−0.489882	−	0.871789i	$-0.662960\pi$
$59$	3.91777	−	6.78578i	0.510050	−	0.883433i	0.999932	−	0.0116444i	$-0.00370660\pi$
$60$		0			0
$61$	−6.62192	−	11.4695i	−0.847850	−	1.46852i	−0.883123	−	0.469142i	$-0.844563\pi$
$61$	−6.62192	−	11.4695i	−0.847850	−	1.46852i	0.0352721	−	0.999378i	$-0.488770\pi$
$62$		0			0
$63$	13.4005	+	1.77434i	1.68830	+	0.223546i
$64$		0			0
$65$	10.6209	+	3.32814i	1.31736	+	0.412804i
$66$		0			0
$67$	−2.63495	−	1.52129i	−0.321911	−	0.185855i	0.330333	−	0.943864i	$-0.392839\pi$
$67$	−2.63495	−	1.52129i	−0.321911	−	0.185855i	−0.652244	+	0.758009i	$0.726172\pi$
$68$		0			0
$69$	8.03381	−	7.04018i	0.967157	−	0.847538i
$70$		0			0
$71$	−9.06407			−1.07571			−0.537853	−	0.843038i	$-0.680765\pi$
$71$	−9.06407			−1.07571			−0.537853	+	0.843038i	$0.680765\pi$
$72$		0			0
$73$			6.90760i			0.808473i	0.914654	+	0.404237i	$0.132463\pi$
$73$			6.90760i			0.808473i	−0.914654	+	0.404237i	$0.867537\pi$
$74$		0			0
$75$	−0.970034	−	8.60576i	−0.112010	−	0.993707i
$76$		0			0
$77$	−4.93076	−	2.84677i	−0.561912	−	0.324420i
$78$		0			0
$79$	4.09326	+	7.08973i	0.460527	+	0.797657i	0.998987	−	0.0449945i	$-0.0143270\pi$
$79$	4.09326	+	7.08973i	0.460527	+	0.797657i	−0.538460	+	0.842651i	$0.680994\pi$
$80$		0			0
$81$	2.31645	+	8.69679i	0.257383	+	0.966309i
$82$		0			0
$83$	5.71353	−	3.29871i	0.627141	−	0.362080i	−0.152503	−	0.988303i	$-0.548733\pi$
$83$	5.71353	−	3.29871i	0.627141	−	0.362080i	0.779644	+	0.626223i	$0.215400\pi$
$84$		0			0
$85$	2.24074	+	10.0235i	0.243043	+	1.08720i
$86$		0			0
$87$	6.63860	−	1.31793i	0.711732	−	0.141297i
$88$		0			0
$89$	0.969826			0.102801			0.0514007	−	0.998678i	$-0.483631\pi$
$89$	0.969826			0.102801			0.0514007	+	0.998678i	$0.483631\pi$
$90$		0			0
$91$	22.4279			2.35109
$92$		0			0
$93$	−2.47850	−	2.82831i	−0.257008	−	0.293282i
$94$		0			0
$95$	13.9276	−	3.11350i	1.42894	−	0.319439i
$96$		0			0
$97$	−10.8174	+	6.24543i	−1.09834	+	0.634128i	−0.935785	−	0.352571i	$-0.885307\pi$
$97$	−10.8174	+	6.24543i	−1.09834	+	0.634128i	−0.162557	+	0.986699i	$0.551974\pi$
$98$		0			0
$99$	0.497592	−	3.75800i	0.0500098	−	0.377693i
$100$		0			0
$101$	−0.979696	−	1.69688i	−0.0974834	−	0.168846i	0.813159	−	0.582042i	$-0.197746\pi$
$101$	−0.979696	−	1.69688i	−0.0974834	−	0.168846i	−0.910642	+	0.413195i	$0.864413\pi$
$102$		0			0
$103$	−0.885468	−	0.511225i	−0.0872478	−	0.0503725i	0.455741	−	0.890112i	$-0.349374\pi$
$103$	−0.885468	−	0.511225i	−0.0872478	−	0.0503725i	−0.542989	+	0.839740i	$0.682708\pi$
$104$		0			0
$105$	−7.05060	−	15.9632i	−0.688068	−	1.55785i
$106$		0			0
$107$			8.51447i			0.823125i	0.911382	+	0.411562i	$0.135017\pi$
$107$			8.51447i			0.823125i	−0.911382	+	0.411562i	$0.864983\pi$
$108$		0			0
$109$	−10.7130			−1.02612			−0.513058	−	0.858354i	$-0.671487\pi$
$109$	−10.7130			−1.02612			−0.513058	+	0.858354i	$0.671487\pi$
$110$		0			0
$111$	0.846761	+	0.287787i	0.0803710	+	0.0273156i
$112$		0			0
$113$	3.14209	+	1.81409i	0.295583	+	0.170655i	0.640457	−	0.767994i	$-0.278745\pi$
$113$	3.14209	+	1.81409i	0.295583	+	0.170655i	−0.344874	+	0.938649i	$0.612078\pi$
$114$		0			0
$115$	−13.1595	−	4.12363i	−1.22713	−	0.384530i
$116$		0			0
$117$	5.70422	+	13.8002i	0.527356	+	1.27583i
$118$		0			0
$119$	10.3483	+	17.9237i	0.948623	+	1.64306i
$120$		0			0
$121$	4.70166	−	8.14351i	0.427423	−	0.740319i
$122$		0			0
$123$	−2.55436	−	2.91487i	−0.230319	−	0.262825i
$124$		0			0
$125$	−8.83376	+	6.85308i	−0.790115	+	0.612958i
$126$		0			0
$127$		−	0.378129i		−	0.0335535i	−0.999859	−	0.0167768i	$-0.994660\pi$
$127$		−	0.378129i		−	0.0335535i	0.999859	−	0.0167768i	$-0.00534046\pi$
$128$		0			0
$129$	1.98491	+	9.99825i	0.174762	+	0.880297i
$130$		0			0
$131$	4.04395	−	7.00433i	0.353322	−	0.611972i	−0.633507	−	0.773737i	$-0.718385\pi$
$131$	4.04395	−	7.00433i	0.353322	−	0.611972i	0.986829	+	0.161765i	$0.0517187\pi$
$132$		0			0
$133$	24.9049	−	14.3789i	2.15953	−	1.24680i
$134$		0			0
$135$	8.02918	−	8.39835i	0.691042	−	0.722815i
$136$		0			0
$137$	−5.78131	+	3.33784i	−0.493930	+	0.285171i	−0.726203	−	0.687480i	$-0.758717\pi$
$137$	−5.78131	+	3.33784i	−0.493930	+	0.285171i	0.232273	+	0.972651i	$0.425384\pi$
$138$		0			0
$139$	−9.23568	+	15.9967i	−0.783360	+	1.35682i	0.146614	+	0.989194i	$0.453162\pi$
$139$	−9.23568	+	15.9967i	−0.783360	+	1.35682i	−0.929974	+	0.367625i	$0.880171\pi$
$140$		0			0
$141$	2.31858	+	11.6789i	0.195259	+	0.983544i
$142$		0			0
$143$		−	6.28963i		−	0.525965i
$144$		0			0
$145$	−5.91445	−	6.43163i	−0.491168	−	0.534118i
$146$		0			0
$147$	−15.1852	−	17.3283i	−1.25245	−	1.42922i
$148$		0			0
$149$	3.37010	−	5.83719i	0.276090	−	0.478201i	−0.694320	−	0.719666i	$-0.744295\pi$
$149$	3.37010	−	5.83719i	0.276090	−	0.478201i	0.970409	+	0.241465i	$0.0776280\pi$
$150$		0			0
$151$	−1.30517	−	2.26062i	−0.106213	−	0.183966i	0.808020	−	0.589155i	$-0.200539\pi$
$151$	−1.30517	−	2.26062i	−0.106213	−	0.183966i	−0.914233	+	0.405189i	$0.867206\pi$
$152$		0			0
$153$	−8.39677	+	10.9261i	−0.678838	+	0.883319i
$154$		0			0
$155$	−1.45173	+	4.63281i	−0.116605	+	0.372117i
$156$		0			0
$157$	−8.04733	−	4.64613i	−0.642247	−	0.370801i	0.143233	−	0.989689i	$-0.454250\pi$
$157$	−8.04733	−	4.64613i	−0.642247	−	0.370801i	−0.785480	+	0.618888i	$0.787584\pi$
$158$		0			0
$159$	−11.3483	−	3.85694i	−0.899981	−	0.305875i
$160$		0			0
$161$	−27.7887			−2.19005
$162$		0			0
$163$		−	4.95234i		−	0.387897i	−0.981012	−	0.193949i	$-0.937871\pi$
$163$		−	4.95234i		−	0.387897i	0.981012	−	0.193949i	$-0.0621295\pi$
$164$		0			0
$165$	−4.47669	+	1.97725i	−0.348510	+	0.153929i
$166$		0			0
$167$	9.29759	+	5.36796i	0.719469	+	0.415386i	0.814557	−	0.580083i	$-0.196980\pi$
$167$	9.29759	+	5.36796i	0.719469	+	0.415386i	−0.0950883	+	0.995469i	$0.530313\pi$
$168$		0			0
$169$	5.88800	+	10.1983i	0.452923	+	0.784486i
$170$		0			0
$171$	15.1817	+	11.6673i	1.16097	+	0.892219i
$172$		0			0
$173$	−21.0459	+	12.1508i	−1.60009	+	0.923811i	−0.608619	+	0.793462i	$0.708276\pi$
$173$	−21.0459	+	12.1508i	−1.60009	+	0.923811i	−0.991468	+	0.130349i	$0.958390\pi$
$174$		0			0
$175$	−12.8569	+	18.5003i	−0.971887	+	1.39849i
$176$		0			0
$177$	−8.94456	−	10.2070i	−0.672314	−	0.767202i
$178$		0			0
$179$	−0.821382			−0.0613930			−0.0306965	−	0.999529i	$-0.509773\pi$
$179$	−0.821382			−0.0613930			−0.0306965	+	0.999529i	$0.509773\pi$
$180$		0			0
$181$	3.35574			0.249430			0.124715	−	0.992193i	$-0.460198\pi$
$181$	3.35574			0.249430			0.124715	+	0.992193i	$0.460198\pi$
$182$		0			0
$183$	−22.4999	+	4.46682i	−1.66324	+	0.330197i
$184$		0			0
$185$	−0.251887	−	1.12676i	−0.0185191	−	0.0828413i
$186$		0			0
$187$	5.02648	−	2.90204i	0.367572	−	0.212218i
$188$		0			0
$189$	10.3787	−	20.9868i	0.754937	−	1.52657i
$190$		0			0
$191$	−9.57297	−	16.5809i	−0.692676	−	1.19975i	−0.970958	−	0.239250i	$-0.923098\pi$
$191$	−9.57297	−	16.5809i	−0.692676	−	1.19975i	0.278283	−	0.960499i	$-0.410235\pi$
$192$		0			0
$193$	8.59931	+	4.96481i	0.618992	+	0.357375i	0.776476	−	0.630146i	$-0.217005\pi$
$193$	8.59931	+	4.96481i	0.618992	+	0.357375i	−0.157485	+	0.987521i	$0.550338\pi$
$194$		0			0
$195$	11.3775	−	15.5625i	0.814763	−	1.11445i
$196$		0			0
$197$		−	11.3402i		−	0.807953i	−0.914769	−	0.403977i	$-0.867628\pi$
$197$		−	11.3402i		−	0.807953i	0.914769	−	0.403977i	$-0.132372\pi$
$198$		0			0
$199$	3.24887			0.230306			0.115153	−	0.993348i	$-0.463264\pi$
$199$	3.24887			0.230306			0.115153	+	0.993348i	$0.463264\pi$
$200$		0			0
$201$	−3.96341	+	3.47322i	−0.279558	+	0.244982i
$202$		0			0
$203$	−15.2480	−	8.80346i	−1.07020	−	0.617882i
$204$		0			0
$205$	−1.49616	+	4.77460i	−0.104496	+	0.333473i
$206$		0			0
$207$	−7.06765	−	17.0987i	−0.491236	−	1.18845i
$208$		0			0
$209$	−4.03237	−	6.98427i	−0.278925	−	0.483112i
$210$		0			0
$211$	2.96885	−	5.14221i	0.204384	−	0.354004i	−0.745552	−	0.666447i	$-0.767814\pi$
$211$	2.96885	−	5.14221i	0.204384	−	0.354004i	0.949936	+	0.312443i	$0.101147\pi$
$212$		0			0
$213$	−5.05194	+	14.8644i	−0.346153	+	1.01849i
$214$		0			0
$215$	9.68654	−	8.90762i	0.660617	−	0.607494i
$216$		0			0
$217$			9.78301i			0.664114i
$218$		0			0
$219$	11.3279	+	3.85001i	0.765471	+	0.260160i
$220$		0			0
$221$	−11.4317	+	19.8002i	−0.768976	+	1.33191i
$222$		0			0
$223$	10.0223	−	5.78635i	0.671140	−	0.387483i	−0.125368	−	0.992110i	$-0.540011\pi$
$223$	10.0223	−	5.78635i	0.671140	−	0.387483i	0.796508	+	0.604627i	$0.206678\pi$
$224$		0			0
$225$	−14.6534	−	3.20571i	−0.976896	−	0.213714i
$226$		0			0
$227$	−13.1724	+	7.60511i	−0.874285	+	0.504769i	−0.868770	−	0.495216i	$-0.835089\pi$
$227$	−13.1724	+	7.60511i	−0.874285	+	0.504769i	−0.00551546	+	0.999985i	$0.501756\pi$
$228$		0			0
$229$	−1.73884	+	3.01176i	−0.114906	+	0.199023i	−0.917742	−	0.397177i	$-0.869990\pi$
$229$	−1.73884	+	3.01176i	−0.114906	+	0.199023i	0.802836	+	0.596200i	$0.203323\pi$
$230$		0			0
$231$	−7.41670	+	6.49939i	−0.487983	+	0.427629i
$232$		0			0
$233$		−	9.49649i		−	0.622136i	−0.950388	−	0.311068i	$-0.899313\pi$
$233$		−	9.49649i		−	0.622136i	0.950388	−	0.311068i	$-0.100687\pi$
$234$		0			0
$235$	11.3148	−	10.4050i	0.738099	−	0.678746i
$236$		0			0
$237$	13.9080	−	2.76111i	0.903423	−	0.179353i
$238$		0			0
$239$	−11.9689	+	20.7307i	−0.774202	+	1.34096i	0.161039	+	0.986948i	$0.448515\pi$
$239$	−11.9689	+	20.7307i	−0.774202	+	1.34096i	−0.935242	+	0.354010i	$0.884818\pi$
$240$		0			0
$241$	15.2919	+	26.4863i	0.985037	+	1.70613i	0.641774	+	0.766894i	$0.278199\pi$
$241$	15.2919	+	26.4863i	0.985037	+	1.70613i	0.343263	+	0.939239i	$0.388468\pi$
$242$		0			0
$243$	15.5532	+	1.04843i	0.997736	+	0.0672570i
$244$		0			0
$245$	−8.89437	+	28.3841i	−0.568240	+	1.81339i
$246$		0			0
$247$	27.5123	+	15.8842i	1.75057	+	1.01069i
$248$		0			0
$249$	−2.22514	−	11.2083i	−0.141013	−	0.710298i
$250$		0			0
$251$	−21.3298			−1.34633			−0.673163	−	0.739494i	$-0.735065\pi$
$251$	−21.3298			−1.34633			−0.673163	+	0.739494i	$0.735065\pi$
$252$		0			0
$253$			7.79298i			0.489941i
$254$		0			0
$255$	17.6867	+	1.91203i	1.10758	+	0.119736i
$256$		0			0
$257$	18.4067	+	10.6271i	1.14818	+	0.662899i	0.948442	−	0.316951i	$-0.102659\pi$
$257$	18.4067	+	10.6271i	1.14818	+	0.662899i	0.199733	+	0.979850i	$0.435992\pi$
$258$		0			0
$259$	−1.16327	−	2.01484i	−0.0722821	−	0.125196i
$260$		0			0
$261$	1.53877	−	11.6214i	0.0952474	−	0.719344i
$262$		0			0
$263$	−5.49833	+	3.17446i	−0.339042	+	0.195746i	−0.659848	−	0.751399i	$-0.729379\pi$
$263$	−5.49833	+	3.17446i	−0.339042	+	0.195746i	0.320806	+	0.947145i	$0.396046\pi$
$264$		0			0
$265$	3.37580	+	15.1009i	0.207374	+	0.927643i
$266$		0			0
$267$	0.540541	−	1.59044i	0.0330806	−	0.0973334i
$268$		0			0
$269$	−0.830098			−0.0506120			−0.0253060	−	0.999680i	$-0.508056\pi$
$269$	−0.830098			−0.0506120			−0.0253060	+	0.999680i	$0.508056\pi$
$270$		0			0
$271$	−8.84383			−0.537225			−0.268612	−	0.963248i	$-0.586565\pi$
$271$	−8.84383			−0.537225			−0.268612	+	0.963248i	$0.586565\pi$
$272$		0			0
$273$	12.5004	−	36.7801i	0.756559	−	2.22603i
$274$		0			0
$275$	5.18818	+	3.60554i	0.312859	+	0.217422i
$276$		0			0
$277$	14.1198	−	8.15208i	0.848377	−	0.489811i	−0.0117258	−	0.999931i	$-0.503733\pi$
$277$	14.1198	−	8.15208i	0.848377	−	0.489811i	0.860103	+	0.510120i	$0.170399\pi$
$278$		0			0
$279$	−6.01962	+	2.48817i	−0.360385	+	0.148963i
$280$		0			0
$281$	−12.5316	−	21.7054i	−0.747572	−	1.29483i	−0.948983	−	0.315326i	$-0.897886\pi$
$281$	−12.5316	−	21.7054i	−0.747572	−	1.29483i	0.201411	−	0.979507i	$-0.435447\pi$
$282$		0			0
$283$	−9.62212	−	5.55534i	−0.571976	−	0.330230i	0.185962	−	0.982557i	$-0.440460\pi$
$283$	−9.62212	−	5.55534i	−0.571976	−	0.330230i	−0.757938	+	0.652326i	$0.773793\pi$
$284$		0			0
$285$	2.65676	−	24.5756i	0.157373	−	1.45573i
$286$		0			0
$287$			10.0824i			0.595147i
$288$		0			0
$289$	−4.09827			−0.241075
$290$		0			0
$291$	4.21286	+	21.2207i	0.246962	+	1.24398i
$292$		0			0
$293$	22.5627	+	13.0266i	1.31812	+	0.761019i	0.983427	−	0.181306i	$-0.0580325\pi$
$293$	22.5627	+	13.0266i	1.31812	+	0.761019i	0.334697	+	0.942326i	$0.391366\pi$
$294$		0			0
$295$	−5.23907	+	16.7192i	−0.305031	+	0.973428i
$296$		0			0
$297$	−5.88550	−	2.91057i	−0.341511	−	0.168888i
$298$		0			0
$299$	−15.3490	−	26.5852i	−0.887655	−	1.53746i
$300$		0			0
$301$	13.2587	−	22.9647i	0.764219	−	1.32367i
$302$		0			0
$303$	−3.32880	+	0.660854i	−0.191235	+	0.0379651i
$304$		0			0
$305$	20.0456	+	21.7985i	1.14781	+	1.24818i
$306$		0			0
$307$		−	22.7847i		−	1.30039i	−0.759766	−	0.650197i	$-0.774686\pi$
$307$		−	22.7847i		−	1.30039i	0.759766	−	0.650197i	$-0.225314\pi$
$308$		0			0
$309$	−1.33189	+	1.16716i	−0.0757688	+	0.0663977i
$310$		0			0
$311$	12.3951	−	21.4689i	0.702861	−	1.21739i	−0.264597	−	0.964359i	$-0.585239\pi$
$311$	12.3951	−	21.4689i	0.702861	−	1.21739i	0.967458	−	0.253032i	$-0.0814278\pi$
$312$		0			0
$313$	−5.63759	+	3.25487i	−0.318656	+	0.183976i	−0.650793	−	0.759255i	$-0.725563\pi$
$313$	−5.63759	+	3.25487i	−0.318656	+	0.183976i	0.332138	+	0.943231i	$0.392230\pi$
$314$		0			0
$315$	−30.1082	+	2.66519i	−1.69641	+	0.150166i
$316$		0			0
$317$	21.8673	−	12.6251i	1.22819	−	0.709095i	0.261538	−	0.965193i	$-0.415770\pi$
$317$	21.8673	−	12.6251i	1.22819	−	0.709095i	0.966651	+	0.256098i	$0.0824371\pi$
$318$		0			0
$319$	−2.46882	+	4.27612i	−0.138227	+	0.239417i
$320$		0			0
$321$	13.9631	+	4.74562i	0.779343	+	0.264874i
$322$		0			0
$323$			29.3160i			1.63118i
$324$		0			0
$325$	−24.8006	−	2.08148i	−1.37569	−	0.115460i
$326$		0			0
$327$	−5.97096	+	17.5684i	−0.330195	+	0.971537i
$328$		0			0
$329$	15.4875	−	26.8251i	0.853852	−	1.47891i
$330$		0			0
$331$	−5.51425	−	9.55097i	−0.303091	−	0.524969i	0.673744	−	0.738965i	$-0.264685\pi$
$331$	−5.51425	−	9.55097i	−0.303091	−	0.524969i	−0.976834	+	0.213996i	$0.931352\pi$
$332$		0			0
$333$	0.943899	−	1.22822i	0.0517253	−	0.0673062i
$334$		0			0
$335$	6.49214	+	2.03436i	0.354703	+	0.111149i
$336$		0			0
$337$	−14.1788	−	8.18614i	−0.772369	−	0.445927i	0.0613501	−	0.998116i	$-0.480459\pi$
$337$	−14.1788	−	8.18614i	−0.772369	−	0.445927i	−0.833719	+	0.552189i	$0.813793\pi$
$338$		0			0
$339$	4.72624	−	4.14169i	0.256694	−	0.224946i
$340$		0			0
$341$	2.74352			0.148570
$342$		0			0
$343$			28.3974i			1.53332i
$344$		0			0
$345$	−14.0970	+	19.2823i	−0.758958	+	1.03812i
$346$		0			0
$347$	2.81815	+	1.62706i	0.151286	+	0.0873453i	0.573732	−	0.819043i	$-0.305495\pi$
$347$	2.81815	+	1.62706i	0.151286	+	0.0873453i	−0.422446	+	0.906388i	$0.638828\pi$
$348$		0			0
$349$	−8.69215	−	15.0553i	−0.465280	−	0.805889i	0.533934	−	0.845526i	$-0.320713\pi$
$349$	−8.69215	−	15.0553i	−0.465280	−	0.805889i	−0.999214	+	0.0396372i	$0.987380\pi$
$350$		0			0
$351$	25.8106	−	1.66282i	1.37767	−	0.0887549i
$352$		0			0
$353$	5.76193	−	3.32665i	0.306677	−	0.177060i	−0.338762	−	0.940872i	$-0.610008\pi$
$353$	5.76193	−	3.32665i	0.306677	−	0.177060i	0.645438	+	0.763812i	$0.276675\pi$
$354$		0			0
$355$	19.7797	−	4.42173i	1.04980	−	0.234681i
$356$		0			0
$357$	35.1612	−	6.98041i	1.86093	−	0.369443i
$358$		0			0
$359$	0.786305			0.0414996			0.0207498	−	0.999785i	$-0.493395\pi$
$359$	0.786305			0.0414996			0.0207498	+	0.999785i	$0.493395\pi$
$360$		0			0
$361$	21.7344			1.14392
$362$		0			0
$363$	−10.7342	−	12.2492i	−0.563401	−	0.642917i
$364$		0			0
$365$	−3.36973	−	15.0738i	−0.176380	−	0.788999i
$366$		0			0
$367$	18.8240	−	10.8681i	0.982607	−	0.567308i	0.0795507	−	0.996831i	$-0.474651\pi$
$367$	18.8240	−	10.8681i	0.982607	−	0.567308i	0.903056	+	0.429523i	$0.141318\pi$
$368$		0			0
$369$	−6.20386	+	2.56432i	−0.322960	+	0.133493i
$370$		0			0
$371$	15.5902	+	27.0030i	0.809403	+	1.40193i
$372$		0			0
$373$	−27.9332	−	16.1272i	−1.44633	−	0.835036i	−0.448065	−	0.894001i	$-0.647887\pi$
$373$	−27.9332	−	16.1272i	−1.44633	−	0.835036i	−0.998260	+	0.0589648i	$0.981220\pi$
$374$		0			0
$375$	6.31496	+	18.3063i	0.326103	+	0.945334i
$376$		0			0
$377$		−	19.4503i		−	1.00174i
$378$		0			0
$379$	−3.30273			−0.169650			−0.0848249	−	0.996396i	$-0.527033\pi$
$379$	−3.30273			−0.169650			−0.0848249	+	0.996396i	$0.527033\pi$
$380$		0			0
$381$	−0.620103	−	0.210754i	−0.0317688	−	0.0107972i
$382$		0			0
$383$	−3.48996	−	2.01493i	−0.178329	−	0.102958i	0.408178	−	0.912902i	$-0.366164\pi$
$383$	−3.48996	−	2.01493i	−0.178329	−	0.102958i	−0.586507	+	0.809944i	$0.699497\pi$
$384$		0			0
$385$	12.1487	+	3.80687i	0.619154	+	0.194016i
$386$		0			0
$387$	17.5027	+	2.31751i	0.889711	+	0.117805i
$388$		0			0
$389$	17.7678	+	30.7748i	0.900865	+	1.56034i	0.826374	+	0.563122i	$0.190400\pi$
$389$	17.7678	+	30.7748i	0.900865	+	1.56034i	0.0744906	+	0.997222i	$0.476267\pi$
$390$		0			0
$391$	14.1641	−	24.5329i	0.716307	−	1.24068i
$392$		0			0
$393$	−9.23264	−	10.5357i	−0.465725	−	0.531456i
$394$		0			0
$395$	−12.3909	−	13.4744i	−0.623454	−	0.677972i
$396$		0			0
$397$		−	15.3547i		−	0.770629i	−0.922785	−	0.385315i	$-0.874093\pi$
$397$		−	15.3547i		−	0.770629i	0.922785	−	0.385315i	$-0.125907\pi$
$398$		0			0
$399$	−9.69926	−	48.8563i	−0.485570	−	2.44588i
$400$		0			0
$401$	5.82535	−	10.0898i	0.290904	−	0.503861i	−0.683120	−	0.730306i	$-0.739377\pi$
$401$	5.82535	−	10.0898i	0.290904	−	0.503861i	0.974024	+	0.226446i	$0.0727106\pi$
$402$		0			0
$403$	−9.35934	+	5.40362i	−0.466222	+	0.269173i
$404$		0			0
$405$	−9.29752	−	17.8481i	−0.461997	−	0.886881i
$406$		0			0
$407$	−0.565037	+	0.326224i	−0.0280079	+	0.0161703i
$408$		0			0
$409$	−6.19607	+	10.7319i	−0.306376	+	0.530659i	−0.977567	−	0.210626i	$-0.932450\pi$
$409$	−6.19607	+	10.7319i	−0.306376	+	0.530659i	0.671191	+	0.741285i	$0.265783\pi$
$410$		0			0
$411$	2.25154	+	11.3413i	0.111060	+	0.559424i
$412$		0			0
$413$			35.3055i			1.73727i
$414$		0			0
$415$	−10.8589	+	9.98569i	−0.533042	+	0.490178i
$416$		0			0
$417$	21.0857	+	24.0617i	1.03257	+	1.17831i
$418$		0			0
$419$	−3.13331	+	5.42705i	−0.153072	+	0.265129i	−0.932355	−	0.361543i	$-0.882250\pi$
$419$	−3.13331	+	5.42705i	−0.153072	+	0.265129i	0.779283	+	0.626672i	$0.215583\pi$
$420$		0			0
$421$	11.1245	+	19.2681i	0.542173	+	0.939070i	0.998779	+	0.0494016i	$0.0157314\pi$
$421$	11.1245	+	19.2681i	0.542173	+	0.939070i	−0.456606	+	0.889669i	$0.650935\pi$
$422$		0			0
$423$	20.4449	+	2.70708i	0.994063	+	0.131623i
$424$		0			0
$425$	−9.77953	−	20.7802i	−0.474377	−	1.00799i
$426$		0			0
$427$	51.6795	+	29.8372i	2.50095	+	1.44392i
$428$		0			0
$429$	−10.3145	−	3.50558i	−0.497990	−	0.169251i
$430$		0			0
$431$	−24.7545			−1.19238			−0.596191	−	0.802842i	$-0.703320\pi$
$431$	−24.7545			−1.19238			−0.596191	+	0.802842i	$0.703320\pi$
$432$		0			0
$433$			26.5725i			1.27700i	0.769624	+	0.638498i	$0.220444\pi$
$433$			26.5725i			1.27700i	−0.769624	+	0.638498i	$0.779556\pi$
$434$		0			0
$435$	−13.8439	+	6.11451i	−0.663762	+	0.293169i
$436$		0			0
$437$	−34.0883	−	19.6809i	−1.63067	−	0.941465i
$438$		0			0
$439$	−9.84063	−	17.0445i	−0.469668	−	0.813488i	0.529731	−	0.848166i	$-0.322293\pi$
$439$	−9.84063	−	17.0445i	−0.469668	−	0.813488i	−0.999399	+	0.0346776i	$0.988960\pi$
$440$		0			0
$441$	−36.8807	+	15.2444i	−1.75623	+	0.725924i
$442$		0			0
$443$	28.8058	−	16.6310i	1.36861	−	0.790165i	0.377856	−	0.925864i	$-0.376661\pi$
$443$	28.8058	−	16.6310i	1.36861	−	0.790165i	0.990750	+	0.135699i	$0.0433281\pi$
$444$		0			0
$445$	−2.11636	+	0.473111i	−0.100325	+	0.0224276i
$446$		0			0
$447$	−7.69419	−	8.78012i	−0.363923	−	0.415285i
$448$		0			0
$449$	10.8999			0.514396			0.257198	−	0.966359i	$-0.417201\pi$
$449$	10.8999			0.514396			0.257198	+	0.966359i	$0.417201\pi$
$450$		0			0
$451$	2.82749			0.133141
$452$		0			0
$453$	−4.43468	+	0.880401i	−0.208360	+	0.0413648i
$454$		0			0
$455$	−48.9424	+	10.9410i	−2.29445	+	0.512923i
$456$		0			0
$457$	−22.6241	+	13.0621i	−1.05831	+	0.611017i	−0.924965	−	0.380052i	$-0.875906\pi$
$457$	−22.6241	+	13.0621i	−1.05831	+	0.611017i	−0.133348	+	0.991069i	$0.542573\pi$
$458$		0			0
$459$	13.2379	+	19.8598i	0.617892	+	0.926976i
$460$		0			0
$461$	−4.69817	−	8.13747i	−0.218816	−	0.379000i	0.735630	−	0.677383i	$-0.236886\pi$
$461$	−4.69817	−	8.13747i	−0.218816	−	0.379000i	−0.954446	+	0.298383i	$0.903553\pi$
$462$		0			0
$463$	−35.1541	−	20.2963i	−1.63375	−	0.943247i	−0.982922	−	0.184023i	$-0.941088\pi$
$463$	−35.1541	−	20.2963i	−1.63375	−	0.943247i	−0.650830	−	0.759224i	$-0.725579\pi$
$464$		0			0
$465$	6.78833	+	4.96286i	0.314801	+	0.230147i
$466$		0			0
$467$		−	9.24300i		−	0.427715i	−0.976865	−	0.213858i	$-0.931397\pi$
$467$		−	9.24300i		−	0.427715i	0.976865	−	0.213858i	$-0.0686028\pi$
$468$		0			0
$469$	13.7093			0.633037
$470$		0			0
$471$	−12.1045	+	10.6074i	−0.557748	+	0.488765i
$472$		0			0
$473$	−6.44017	−	3.71824i	−0.296119	−	0.170965i
$474$		0			0
$475$	−28.8740	+	13.5886i	−1.32483	+	0.623488i
$476$		0			0
$477$	−12.6502	+	16.4607i	−0.579212	+	0.753684i
$478$		0			0
$479$	8.91795	+	15.4463i	0.407471	+	0.705761i	0.994606	−	0.103728i	$-0.0330773\pi$
$479$	8.91795	+	15.4463i	0.407471	+	0.705761i	−0.587134	+	0.809490i	$0.699744\pi$
$480$		0			0
$481$	1.28506	−	2.22578i	0.0585936	−	0.101487i
$482$		0			0
$483$	−15.4883	+	45.5713i	−0.704740	+	2.07357i
$484$		0			0
$485$	20.5591	−	18.9059i	0.933541	−	0.858472i
$486$		0			0
$487$		−	35.8484i		−	1.62445i	−0.583347	−	0.812223i	$-0.698257\pi$
$487$		−	35.8484i		−	1.62445i	0.583347	−	0.812223i	$-0.301743\pi$
$488$		0			0
$489$	−8.12146	−	2.76023i	−0.367265	−	0.124822i
$490$		0			0
$491$	−17.4427	+	30.2117i	−0.787179	+	1.36343i	0.140509	+	0.990079i	$0.455126\pi$
$491$	−17.4427	+	30.2117i	−0.787179	+	1.36343i	−0.927689	+	0.373355i	$0.878207\pi$
$492$		0			0
$493$	15.5440	−	8.97435i	0.700068	−	0.404185i
$494$		0			0
$495$	0.747419	+	8.44347i	0.0335940	+	0.379506i
$496$		0			0
$497$	35.3694	−	20.4205i	1.58653	−	0.915985i
$498$		0			0
$499$	−10.4353	+	18.0745i	−0.467149	+	0.809125i	−0.999296	−	0.0375267i	$-0.988052\pi$
$499$	−10.4353	+	18.0745i	−0.467149	+	0.809125i	0.532147	+	0.846652i	$0.321385\pi$
$500$		0			0
$501$	13.9851	−	12.2555i	0.624810	−	0.547533i
$502$		0			0
$503$		−	30.0613i		−	1.34037i	−0.742196	−	0.670183i	$-0.766216\pi$
$503$		−	30.0613i		−	1.34037i	0.742196	−	0.670183i	$-0.233784\pi$
$504$		0			0
$505$	2.96569	+	3.22502i	0.131971	+	0.143512i
$506$		0			0
$507$	20.0062	−	3.97175i	0.888506	−	0.176392i
$508$		0			0
$509$	−6.90596	+	11.9615i	−0.306101	+	0.530183i	−0.977506	−	0.210908i	$-0.932358\pi$
$509$	−6.90596	+	11.9615i	−0.306101	+	0.530183i	0.671405	+	0.741091i	$0.265691\pi$
$510$		0			0
$511$	−15.5622	−	26.9545i	−0.688430	−	1.19240i
$512$		0			0
$513$	27.5951	−	18.3940i	1.21835	−	0.812115i
$514$		0			0
$515$	2.18166	+	0.683640i	0.0961356	+	0.0301248i
$516$		0			0
$517$	−7.52276	−	4.34327i	−0.330851	−	0.191017i
$518$		0			0
$519$	8.19635	+	41.2860i	0.359780	+	1.81225i
$520$		0			0
$521$	31.6849			1.38814			0.694070	−	0.719908i	$-0.255816\pi$
$521$	31.6849			1.38814			0.694070	+	0.719908i	$0.255816\pi$
$522$		0			0
$523$			9.20648i			0.402571i	0.979533	+	0.201286i	$0.0645120\pi$
$523$			9.20648i			0.402571i	−0.979533	+	0.201286i	$0.935488\pi$
$524$		0			0
$525$	23.1732	+	31.3956i	1.01136	+	1.37022i
$526$		0			0
$527$	−8.63681	−	4.98646i	−0.376225	−	0.217214i
$528$		0			0
$529$	7.51771	+	13.0211i	0.326857	+	0.566133i
$530$		0			0
$531$	−21.7240	+	8.97946i	−0.942740	+	0.389675i
$532$		0			0
$533$	−9.64579	+	5.56900i	−0.417806	+	0.241220i
$534$		0			0
$535$	−4.15362	−	18.5803i	−0.179576	−	0.803297i
$536$		0			0
$537$	−0.457805	+	1.34700i	−0.0197557	+	0.0581275i
$538$		0			0
$539$	16.8089			0.724010
$540$		0			0
$541$	−25.7154			−1.10559			−0.552796	−	0.833317i	$-0.686439\pi$
$541$	−25.7154			−1.10559			−0.552796	+	0.833317i	$0.686439\pi$
$542$		0			0
$543$	1.87035	−	5.50316i	0.0802644	−	0.236163i
$544$		0			0
$545$	23.3779	−	5.22610i	1.00140	−	0.223862i
$546$		0			0
$547$	−4.36999	+	2.52301i	−0.186847	+	0.107876i	−0.590506	−	0.807033i	$-0.701072\pi$
$547$	−4.36999	+	2.52301i	−0.186847	+	0.107876i	0.403659	+	0.914910i	$0.367738\pi$
$548$		0			0
$549$	−5.21528	+	39.3878i	−0.222583	+	1.68103i
$550$		0			0
$551$	−12.4698	−	21.5984i	−0.531233	−	0.920122i
$552$		0			0
$553$	−31.9450	−	18.4435i	−1.35844	−	0.784296i
$554$		0			0
$555$	−1.98820	−	0.214936i	−0.0843943	−	0.00912352i
$556$		0			0
$557$			11.0624i			0.468731i	0.972149	+	0.234365i	$0.0753012\pi$
$557$			11.0624i			0.468731i	−0.972149	+	0.234365i	$0.924699\pi$
$558$		0			0
$559$	29.2936			1.23899
$560$		0			0
$561$	−1.95757	−	9.86052i	−0.0826487	−	0.416311i
$562$		0			0
$563$	−11.9334	−	6.88976i	−0.502934	−	0.290369i	0.226991	−	0.973897i	$-0.427111\pi$
$563$	−11.9334	−	6.88976i	−0.502934	−	0.290369i	−0.729924	+	0.683528i	$0.760445\pi$
$564$		0			0
$565$	−7.74165	−	2.42590i	−0.325694	−	0.102059i
$566$		0			0
$567$	−28.6322	−	28.7174i	−1.20244	−	1.20602i
$568$		0			0
$569$	−0.296278	−	0.513168i	−0.0124206	−	0.0215131i	0.859748	−	0.510718i	$-0.170620\pi$
$569$	−0.296278	−	0.513168i	−0.0124206	−	0.0215131i	−0.872169	+	0.489205i	$0.837287\pi$
$570$		0			0
$571$	−9.03431	+	15.6479i	−0.378074	+	0.654843i	−0.990782	−	0.135466i	$-0.956747\pi$
$571$	−9.03431	+	15.6479i	−0.378074	+	0.654843i	0.612708	+	0.790309i	$0.290080\pi$
$572$		0			0
$573$	−32.5269	+	6.45745i	−1.35883	+	0.269764i
$574$		0			0
$575$	30.7284	+	2.57900i	1.28146	+	0.107552i
$576$		0			0
$577$			20.3195i			0.845910i	0.906151	+	0.422955i	$0.139007\pi$
$577$			20.3195i			0.845910i	−0.906151	+	0.422955i	$0.860993\pi$
$578$		0			0
$579$	12.9348	−	11.3350i	0.537553	−	0.471068i
$580$		0			0
$581$	−14.8634	+	25.7441i	−0.616637	+	1.06805i
$582$		0			0
$583$	7.57266	−	4.37208i	0.313628	−	0.181073i
$584$		0			0
$585$	−19.1799	−	27.3322i	−0.792993	−	1.13005i
$586$		0			0
$587$	3.07205	−	1.77365i	0.126797	−	0.0732064i	−0.435260	−	0.900305i	$-0.643343\pi$
$587$	3.07205	−	1.77365i	0.126797	−	0.0732064i	0.562057	+	0.827099i	$0.310010\pi$
$588$		0			0
$589$	−6.92867	+	12.0008i	−0.285491	+	0.494485i
$590$		0			0
$591$	−18.5970	−	6.32054i	−0.764979	−	0.259992i
$592$		0			0
$593$		−	10.1123i		−	0.415261i	−0.978207	−	0.207630i	$-0.933425\pi$
$593$		−	10.1123i		−	0.415261i	0.978207	−	0.207630i	$-0.0665751\pi$
$594$		0			0
$595$	−31.3257	−	34.0650i	−1.28423	−	1.39653i
$596$		0			0
$597$	1.81079	−	5.32790i	0.0741106	−	0.218057i
$598$		0			0
$599$	8.03413	−	13.9155i	0.328266	−	0.568573i	−0.653902	−	0.756579i	$-0.726869\pi$
$599$	8.03413	−	13.9155i	0.328266	−	0.568573i	0.982168	+	0.188006i	$0.0602025\pi$
$600$		0			0
$601$	−23.6961	−	41.0429i	−0.966585	−	1.67417i	−0.705294	−	0.708915i	$-0.749185\pi$
$601$	−23.6961	−	41.0429i	−0.966585	−	1.67417i	−0.261291	−	0.965260i	$-0.584148\pi$
$602$		0			0
$603$	3.48677	+	8.43553i	0.141992	+	0.343521i
$604$		0			0
$605$	−6.28733	+	20.0644i	−0.255616	+	0.815735i
$606$		0			0
$607$	−27.4993	−	15.8767i	−1.11616	−	0.644417i	−0.175744	−	0.984436i	$-0.556233\pi$
$607$	−27.4993	−	15.8767i	−1.11616	−	0.644417i	−0.940419	+	0.340019i	$0.889567\pi$
$608$		0			0
$609$	−22.9356	+	20.0989i	−0.929399	+	0.814450i
$610$		0			0
$611$	34.2178			1.38431
$612$		0			0
$613$		−	9.56267i		−	0.386233i	−0.981176	−	0.193116i	$-0.938141\pi$
$613$		−	9.56267i		−	0.386233i	0.981176	−	0.193116i	$-0.0618595\pi$
$614$		0			0
$615$	6.99609	+	5.11475i	0.282110	+	0.206247i
$616$		0			0
$617$	27.2861	+	15.7536i	1.09850	+	0.634217i	0.935825	−	0.352464i	$-0.114656\pi$
$617$	27.2861	+	15.7536i	1.09850	+	0.634217i	0.162670	+	0.986681i	$0.447989\pi$
$618$		0			0
$619$	−22.5040	−	38.9781i	−0.904513	−	1.56666i	−0.821569	−	0.570109i	$-0.806901\pi$
$619$	−22.5040	−	38.9781i	−0.904513	−	1.56666i	−0.0829440	−	0.996554i	$-0.526432\pi$
$620$		0			0
$621$	−31.9799	+	2.06027i	−1.28331	+	0.0826758i
$622$		0			0
$623$	−3.78441	+	2.18493i	−0.151619	+	0.0875374i
$624$		0			0
$625$	15.9339	−	19.2642i	0.637357	−	0.770568i
$626$		0			0
$627$	−13.7011	+	2.72004i	−0.547171	+	0.108628i
$628$		0			0
$629$	2.37170			0.0945660
$630$		0			0
$631$	4.68299			0.186427			0.0932135	−	0.995646i	$-0.470286\pi$
$631$	4.68299			0.186427			0.0932135	+	0.995646i	$0.470286\pi$
$632$		0			0
$633$	−6.77811	−	7.73475i	−0.269406	−	0.307429i
$634$		0			0
$635$	0.184463	+	0.825156i	0.00732019	+	0.0327453i
$636$		0			0
$637$	−57.3424	+	33.1066i	−2.27199	+	1.31173i
$638$		0			0
$639$	21.5607	+	16.5696i	0.852929	+	0.655483i
$640$		0			0
$641$	−4.05316	−	7.02029i	−0.160090	−	0.277285i	0.774811	−	0.632194i	$-0.217845\pi$
$641$	−4.05316	−	7.02029i	−0.160090	−	0.277285i	−0.934901	+	0.354909i	$0.884512\pi$
$642$		0			0
$643$	26.6845	+	15.4063i	1.05233	+	0.607564i	0.923301	−	0.384076i	$-0.125480\pi$
$643$	26.6845	+	15.4063i	1.05233	+	0.607564i	0.129031	+	0.991641i	$0.458813\pi$
$644$		0			0
$645$	−9.20894	−	20.8499i	−0.362602	−	0.820965i
$646$		0			0
$647$			10.2266i			0.402051i	0.979586	+	0.201025i	$0.0644274\pi$
$647$			10.2266i			0.402051i	−0.979586	+	0.201025i	$0.935573\pi$
$648$		0			0
$649$	9.90099			0.388648
$650$		0			0
$651$	16.0434	+	5.45265i	0.628790	+	0.213706i
$652$		0			0
$653$	−16.0678	−	9.27674i	−0.628781	−	0.363027i	0.151499	−	0.988457i	$-0.451590\pi$
$653$	−16.0678	−	9.27674i	−0.628781	−	0.363027i	−0.780280	+	0.625430i	$0.784923\pi$
$654$		0			0
$655$	−5.40781	+	17.2577i	−0.211301	+	0.674313i
$656$		0			0
$657$	12.6274	−	16.4311i	0.492644	−	0.641039i
$658$		0			0
$659$	−2.24532	−	3.88902i	−0.0874654	−	0.151495i	0.818974	−	0.573831i	$-0.194543\pi$
$659$	−2.24532	−	3.88902i	−0.0874654	−	0.151495i	−0.906439	+	0.422337i	$0.861210\pi$
$660$		0			0
$661$	−16.1772	+	28.0197i	−0.629219	+	1.08984i	0.358490	+	0.933534i	$0.383292\pi$
$661$	−16.1772	+	28.0197i	−0.629219	+	1.08984i	−0.987709	+	0.156306i	$0.950042\pi$
$662$		0			0
$663$	26.0993	+	29.7829i	1.01361	+	1.15667i
$664$		0			0
$665$	−47.3332	+	43.5270i	−1.83550	+	1.68790i
$666$		0			0
$667$			24.0993i			0.933127i
$668$		0			0
$669$	−3.90319	−	19.6608i	−0.150906	−	0.760131i
$670$		0			0
$671$	8.36746	−	14.4929i	0.323022	−	0.559491i
$672$		0			0
$673$	3.24386	−	1.87284i	0.125041	−	0.0721927i	−0.436175	−	0.899862i	$-0.643667\pi$
$673$	3.24386	−	1.87284i	0.125041	−	0.0721927i	0.561216	+	0.827669i	$0.310334\pi$
$674$		0			0
$675$	−13.4244	+	22.2438i	−0.516704	+	0.856164i
$676$		0			0
$677$	31.5958	−	18.2419i	1.21433	−	0.701091i	0.250627	−	0.968084i	$-0.419363\pi$
$677$	31.5958	−	18.2419i	1.21433	−	0.701091i	0.963699	+	0.266992i	$0.0860298\pi$
$678$		0			0
$679$	28.1408	−	48.7413i	1.07994	−	1.87052i
$680$		0			0
$681$	5.13003	+	25.8406i	0.196583	+	0.990213i
$682$		0			0
$683$		−	40.6438i		−	1.55519i	−0.628765	−	0.777595i	$-0.716439\pi$
$683$		−	40.6438i		−	1.55519i	0.628765	−	0.777595i	$-0.283561\pi$
$684$		0			0
$685$	10.9877	−	10.1041i	0.419818	−	0.386060i
$686$		0			0
$687$	3.96990	+	4.53020i	0.151461	+	0.172838i
$688$		0			0
$689$	−17.2224	+	29.8301i	−0.656122	+	1.13644i
$690$		0			0
$691$	18.2372	+	31.5878i	0.693776	+	1.20166i	0.970592	+	0.240732i	$0.0773876\pi$
$691$	18.2372	+	31.5878i	0.693776	+	1.20166i	−0.276816	+	0.960923i	$0.589279\pi$
$692$		0			0
$693$	6.52475	+	15.7853i	0.247855	+	0.599635i
$694$		0			0
$695$	12.3505	−	39.4134i	0.468481	−	1.49504i
$696$		0			0
$697$	−8.90114	−	5.13908i	−0.337155	−	0.194656i
$698$		0			0
$699$	−15.5735	−	5.29295i	−0.589045	−	0.200198i
$700$		0			0
$701$	49.7764			1.88003			0.940014	−	0.341136i	$-0.110812\pi$
$701$	49.7764			1.88003			0.940014	+	0.341136i	$0.110812\pi$
$702$		0			0
$703$		−	3.29547i		−	0.124291i
$704$		0			0
$705$	−10.7569	−	24.3548i	−0.405130	−	0.917254i
$706$		0			0
$707$	7.64585	+	4.41433i	0.287552	+	0.166018i
$708$		0			0
$709$	−1.35844	−	2.35289i	−0.0510174	−	0.0883647i	0.839389	−	0.543531i	$-0.182913\pi$
$709$	−1.35844	−	2.35289i	−0.0510174	−	0.0883647i	−0.890406	+	0.455167i	$0.849580\pi$
$710$		0			0
$711$	3.22376	−	24.3470i	0.120900	−	0.913085i
$712$		0			0
$713$	11.5964	−	6.69520i	0.434289	−	0.250737i
$714$		0			0
$715$	3.06827	+	13.7253i	0.114747	+	0.513296i
$716$		0			0
$717$	27.3258	+	31.1825i	1.02050	+	1.16453i
$718$		0			0
$719$	25.2525			0.941759			0.470880	−	0.882197i	$-0.343937\pi$
$719$	25.2525			0.941759			0.470880	+	0.882197i	$0.343937\pi$
$720$		0			0
$721$	4.60697			0.171573
$722$		0			0
$723$	51.9586	−	10.3151i	1.93236	−	0.383624i
$724$		0			0
$725$	16.0441	+	11.1499i	0.595862	+	0.414097i
$726$		0			0
$727$	8.79799	−	5.07952i	0.326299	−	0.188389i	−0.327898	−	0.944713i	$-0.606340\pi$
$727$	8.79799	−	5.07952i	0.326299	−	0.188389i	0.654197	+	0.756324i	$0.273007\pi$
$728$		0			0
$729$	10.3880	−	24.9216i	0.384742	−	0.923024i
$730$		0			0
$731$	13.5161	+	23.4105i	0.499910	+	0.865870i
$732$		0			0
$733$	20.7730	+	11.9933i	0.767268	+	0.442983i	0.831899	−	0.554927i	$-0.187254\pi$
$733$	20.7730	+	11.9933i	0.767268	+	0.442983i	−0.0646310	+	0.997909i	$0.520587\pi$
$734$		0			0
$735$	41.5904	+	30.4062i	1.53409	+	1.12155i
$736$		0			0
$737$		−	3.84460i		−	0.141618i
$738$		0			0
$739$	16.5460			0.608656			0.304328	−	0.952567i	$-0.401568\pi$
$739$	16.5460			0.608656			0.304328	+	0.952567i	$0.401568\pi$
$740$		0			0
$741$	41.3832	−	36.2649i	1.52025	−	1.33222i
$742$		0			0
$743$	5.52100	+	3.18755i	0.202546	+	0.116940i	0.597842	−	0.801614i	$-0.296025\pi$
$743$	5.52100	+	3.18755i	0.202546	+	0.116940i	−0.395297	+	0.918554i	$0.629358\pi$
$744$		0			0
$745$	−4.50670	+	14.3820i	−0.165113	+	0.526915i
$746$		0			0
$747$	−19.6210	−	2.59799i	−0.717895	−	0.0950555i
$748$		0			0
$749$	−19.1823	−	33.2248i	−0.700907	−	1.21401i
$750$		0			0
$751$	−1.03374	+	1.79049i	−0.0377217	+	0.0653359i	−0.884270	−	0.466976i	$-0.845343\pi$
$751$	−1.03374	+	1.79049i	−0.0377217	+	0.0653359i	0.846548	+	0.532312i	$0.178677\pi$
$752$		0			0
$753$	−11.8884	+	34.9793i	−0.433236	+	1.27472i
$754$		0			0
$755$	3.95094	+	4.29643i	0.143789	+	0.156363i
$756$		0			0
$757$		−	3.09824i		−	0.112607i	−0.998414	−	0.0563037i	$-0.982068\pi$
$757$		−	3.09824i		−	0.112607i	0.998414	−	0.0563037i	$-0.0179315\pi$
$758$		0			0
$759$	12.7799	+	4.34349i	0.463881	+	0.157659i
$760$		0			0
$761$	−3.63122	+	6.28946i	−0.131632	+	0.227993i	−0.924306	−	0.381653i	$-0.875355\pi$
$761$	−3.63122	+	6.28946i	−0.131632	+	0.227993i	0.792674	+	0.609646i	$0.208688\pi$
$762$		0			0
$763$	41.8036	−	24.1353i	1.51339	−	0.873757i
$764$		0			0
$765$	12.9934	−	27.9391i	0.469778	−	1.01014i
$766$		0			0
$767$	−33.7766	+	19.5009i	−1.21960	+	0.704137i
$768$		0			0
$769$	−15.9830	+	27.6834i	−0.576362	+	0.998289i	0.419530	+	0.907742i	$0.362195\pi$
$769$	−15.9830	+	27.6834i	−0.576362	+	0.998289i	−0.995892	+	0.0905475i	$0.971138\pi$
$770$		0			0
$771$	27.6867	−	24.2624i	0.997113	−	0.873789i
$772$		0			0
$773$			16.5784i			0.596283i	0.954522	+	0.298142i	$0.0963668\pi$
$773$			16.5784i			0.596283i	−0.954522	+	0.298142i	$0.903633\pi$
$774$		0			0
$775$	0.907938	−	10.8179i	0.0326141	−	0.388592i
$776$		0			0
$777$	−3.95255	+	0.784684i	−0.141797	+	0.0281504i
$778$		0			0
$779$	−7.14073	+	12.3681i	−0.255843	+	0.443133i
$780$		0			0
$781$	−5.72668	−	9.91889i	−0.204917	−	0.354926i
$782$		0			0
$783$	−18.2005	−	9.00073i	−0.650433	−	0.321660i
$784$		0			0
$785$	19.8275	+	6.21308i	0.707672	+	0.221754i
$786$		0			0
$787$	−15.3953	−	8.88849i	−0.548784	−	0.316840i	0.199848	−	0.979827i	$-0.435955\pi$
$787$	−15.3953	−	8.88849i	−0.548784	−	0.316840i	−0.748631	+	0.662987i	$0.769289\pi$
$788$		0			0
$789$	2.14133	+	10.7862i	0.0762335	+	0.383998i
$790$		0			0
$791$	−16.3479			−0.581264
$792$		0			0
$793$			65.9219i			2.34096i
$794$		0			0
$795$	26.6459	+	2.88058i	0.945034	+	0.102164i
$796$		0			0
$797$	−28.5522	−	16.4846i	−1.01137	−	0.583915i	−0.0997774	−	0.995010i	$-0.531813\pi$
$797$	−28.5522	−	16.4846i	−1.01137	−	0.583915i	−0.911592	+	0.411095i	$0.865146\pi$
$798$		0			0
$799$	15.7881	+	27.3458i	0.558543	+	0.967426i
$800$		0			0
$801$	−2.30693	−	1.77289i	−0.0815113	−	0.0626421i
$802$		0			0
$803$	−7.55905	+	4.36422i	−0.266753	+	0.154010i
$804$		0			0
$805$	60.6406	−	13.5562i	2.13730	−	0.477792i
$806$		0			0
$807$	−0.462663	+	1.36130i	−0.0162865	+	0.0479200i
$808$		0			0
$809$	−16.1251			−0.566929			−0.283464	−	0.958983i	$-0.591484\pi$
$809$	−16.1251			−0.566929			−0.283464	+	0.958983i	$0.591484\pi$
$810$		0			0
$811$	23.5077			0.825467			0.412733	−	0.910852i	$-0.364574\pi$
$811$	23.5077			0.825467			0.412733	+	0.910852i	$0.364574\pi$
$812$		0			0
$813$	−4.92919	+	14.5032i	−0.172874	+	0.508650i
$814$		0			0
$815$	2.41590	+	10.8070i	0.0846253	+	0.378553i
$816$		0			0
$817$	32.5288	−	18.7805i	1.13804	−	0.657048i
$818$		0			0
$819$	−53.3494	−	40.9994i	−1.86418	−	1.43264i
$820$		0			0
$821$	−18.7377	−	32.4547i	−0.653952	−	1.13268i	−0.982156	−	0.188071i	$-0.939777\pi$
$821$	−18.7377	−	32.4547i	−0.653952	−	1.13268i	0.328204	−	0.944607i	$-0.393557\pi$
$822$		0			0
$823$	−10.9338	−	6.31265i	−0.381129	−	0.220045i	0.297180	−	0.954821i	$-0.403954\pi$
$823$	−10.9338	−	6.31265i	−0.381129	−	0.220045i	−0.678310	+	0.734776i	$0.737287\pi$
$824$		0			0
$825$	8.80449	−	6.49863i	0.306533	−	0.226253i
$826$		0			0
$827$			28.7120i			0.998415i	0.866482	+	0.499208i	$0.166376\pi$
$827$			28.7120i			0.998415i	−0.866482	+	0.499208i	$0.833624\pi$
$828$		0			0
$829$	−36.7202			−1.27534			−0.637672	−	0.770308i	$-0.720103\pi$
$829$	−36.7202			−1.27534			−0.637672	+	0.770308i	$0.720103\pi$
$830$		0			0
$831$	−5.49898	−	27.6990i	−0.190758	−	0.960869i
$832$		0			0
$833$	−52.9156	−	30.5508i	−1.83342	−	1.05852i
$834$		0			0
$835$	−22.9079	−	7.17836i	−0.792761	−	0.248417i
$836$		0			0
$837$	0.725319	+	11.2585i	0.0250707	+	0.389152i
$838$		0			0
$839$	−19.5871	−	33.9259i	−0.676223	−	1.17125i	−0.976110	−	0.217277i	$-0.930282\pi$
$839$	−19.5871	−	33.9259i	−0.676223	−	1.17125i	0.299887	−	0.953975i	$-0.403051\pi$
$840$		0			0
$841$	6.86534	−	11.8911i	0.236736	−	0.410039i
$842$		0			0
$843$	−42.5797	+	8.45319i	−1.46652	+	0.291143i
$844$		0			0
$845$	−17.8239	−	19.3825i	−0.613160	−	0.666777i
$846$		0			0
$847$			42.3696i			1.45584i
$848$		0			0
$849$	−14.4733	+	12.6832i	−0.496723	+	0.435288i
$850$		0			0
$851$	−1.59221	+	2.75779i	−0.0545803	+	0.0945359i
$852$		0			0
$853$	46.5322	−	26.8654i	1.59323	−	0.919853i	0.600485	−	0.799636i	$-0.294974\pi$
$853$	46.5322	−	26.8654i	1.59323	−	0.919853i	0.992748	−	0.120217i	$-0.0383592\pi$
$854$		0			0
$855$	−38.8213	−	18.0543i	−1.32766	−	0.617444i
$856$		0			0
$857$	−39.1673	+	22.6133i	−1.33793	+	0.772454i	−0.986500	−	0.163760i	$-0.947638\pi$
$857$	−39.1673	+	22.6133i	−1.33793	+	0.772454i	−0.351430	+	0.936214i	$0.614304\pi$
$858$		0			0
$859$	12.2589	−	21.2331i	0.418269	−	0.724463i	−0.577497	−	0.816393i	$-0.695970\pi$
$859$	12.2589	−	21.2331i	0.418269	−	0.724463i	0.995765	+	0.0919301i	$0.0293036\pi$
$860$		0			0
$861$	16.5344	+	5.61953i	0.563492	+	0.191513i
$862$		0			0
$863$			18.1003i			0.616141i	0.951363	+	0.308071i	$0.0996833\pi$
$863$			18.1003i			0.616141i	−0.951363	+	0.308071i	$0.900317\pi$
$864$		0			0
$865$	39.9989	−	36.7824i	1.36000	−	1.25064i
$866$		0			0
$867$	−2.28421	+	6.72085i	−0.0775758	+	0.228252i
$868$		0			0
$869$	−5.17224	+	8.95858i	−0.175456	+	0.303899i
$870$		0			0
$871$	7.57230	+	13.1156i	0.256578	+	0.444405i
$872$		0			0
$873$	37.1484	+	4.91877i	1.25728	+	0.166475i
$874$		0			0
$875$	19.0313	−	46.6434i	0.643375	−	1.57684i
$876$		0			0
$877$	20.4266	+	11.7933i	0.689756	+	0.398231i	0.803521	−	0.595277i	$-0.202958\pi$
$877$	20.4266	+	11.7933i	0.689756	+	0.398231i	−0.113764	+	0.993508i	$0.536291\pi$
$878$		0			0
$879$	33.9381	−	29.7406i	1.14470	−	1.00312i
$880$		0			0
$881$	53.3253			1.79658			0.898288	−	0.439407i	$-0.144811\pi$
$881$	53.3253			1.79658			0.898288	+	0.439407i	$0.144811\pi$
$882$		0			0
$883$			3.16348i			0.106460i	0.998582	+	0.0532298i	$0.0169516\pi$
$883$			3.16348i			0.106460i	−0.998582	+	0.0532298i	$0.983048\pi$
$884$		0			0
$885$	24.4981	+	17.9103i	0.823496	+	0.602047i
$886$		0			0
$887$	−15.5435	−	8.97406i	−0.521900	−	0.301319i	0.215811	−	0.976435i	$-0.430760\pi$
$887$	−15.5435	−	8.97406i	−0.521900	−	0.301319i	−0.737712	+	0.675116i	$0.764094\pi$
$888$		0			0
$889$	0.851890	+	1.47552i	0.0285715	+	0.0494873i
$890$		0			0
$891$	−8.05344	+	8.02954i	−0.269801	+	0.269000i
$892$		0			0
$893$	37.9969	−	21.9375i	1.27152	−	0.734111i
$894$		0			0
$895$	1.79242	−	0.400695i	0.0599141	−	0.0133938i
$896$		0			0
$897$	−52.1527	+	10.3537i	−1.74133	+	0.345699i
$898$		0			0
$899$	8.48416			0.282963
$900$		0			0
$901$	−31.7857			−1.05894
$902$		0			0
$903$	−30.2706	−	34.5429i	−1.00734	−	1.14951i
$904$		0			0
$905$	−7.32291	+	1.63703i	−0.243422	+	0.0544168i
$906$		0			0
$907$	−2.12812	+	1.22867i	−0.0706632	+	0.0407974i	−0.534915	−	0.844906i	$-0.679656\pi$
$907$	−2.12812	+	1.22867i	−0.0706632	+	0.0407974i	0.464252	+	0.885703i	$0.346323\pi$
$908$		0			0
$909$	−0.771587	+	5.82732i	−0.0255919	+	0.193280i
$910$		0			0
$911$	26.7512	+	46.3344i	0.886306	+	1.53513i	0.844210	+	0.536013i	$0.180070\pi$
$911$	26.7512	+	46.3344i	0.886306	+	1.53513i	0.0420962	+	0.999114i	$0.486596\pi$
$912$		0			0
$913$	7.21962	+	4.16825i	0.238934	+	0.137949i
$914$		0			0
$915$	46.9204	−	20.7237i	1.55114	−	0.685103i
$916$		0			0
$917$			36.4426i			1.20344i
$918$		0			0
$919$	−46.9236			−1.54787			−0.773933	−	0.633267i	$-0.781713\pi$
$919$	−46.9236			−1.54787			−0.773933	+	0.633267i	$0.781713\pi$
$920$		0			0
$921$	−37.3653	−	12.6993i	−1.23123	−	0.418456i
$922$		0			0
$923$	39.0723	+	22.5584i	1.28608	+	0.742519i
$924$		0			0
$925$	1.09934	+	2.33595i	0.0361460	+	0.0768056i
$926$		0			0
$927$	1.17172	+	2.83473i	0.0384843	+	0.0931049i
$928$		0			0
$929$	−4.47672	−	7.75391i	−0.146877	−	0.254398i	0.783195	−	0.621776i	$-0.213589\pi$
$929$	−4.47672	−	7.75391i	−0.146877	−	0.254398i	−0.930071	+	0.367379i	$0.880255\pi$
$930$		0			0
$931$	−42.4503	+	73.5260i	−1.39125	+	2.40972i
$932$		0			0
$933$	−28.2989	−	32.2929i	−0.926464	−	1.05722i
$934$		0			0
$935$	−9.55310	+	8.78491i	−0.312420	+	0.287297i
$936$		0			0
$937$		−	57.7860i		−	1.88779i	−0.330251	−	0.943893i	$-0.607134\pi$
$937$		−	57.7860i		−	1.88779i	0.330251	−	0.943893i	$-0.392866\pi$
$938$		0			0
$939$	2.19557	+	11.0594i	0.0716497	+	0.360908i
$940$		0			0
$941$	23.8942	−	41.3859i	0.778927	−	1.34914i	−0.153633	−	0.988128i	$-0.549097\pi$
$941$	23.8942	−	41.3859i	0.778927	−	1.34914i	0.932560	−	0.361014i	$-0.117569\pi$
$942$		0			0
$943$	11.9513	−	6.90011i	0.389189	−	0.224698i
$944$		0			0
$945$	−12.4104	+	50.8606i	−0.403709	+	1.65450i
$946$		0			0
$947$	−16.0247	+	9.25189i	−0.520734	+	0.300646i	−0.737235	−	0.675636i	$-0.763869\pi$
$947$	−16.0247	+	9.25189i	−0.520734	+	0.300646i	0.216501	+	0.976282i	$0.430536\pi$
$948$		0			0
$949$	17.1915	−	29.7765i	0.558058	−	0.966585i
$950$		0			0
$951$	−8.51625	−	42.8974i	−0.276158	−	1.39104i
$952$		0			0
$953$			27.7246i			0.898088i	0.893510	+	0.449044i	$0.148235\pi$
$953$			27.7246i			0.898088i	−0.893510	+	0.449044i	$0.851765\pi$
$954$		0			0
$955$	28.9788	+	31.5129i	0.937733	+	1.01973i
$956$		0			0
$957$	5.63649	+	6.43201i	0.182202	+	0.207917i
$958$		0			0
$959$	15.0397	−	26.0495i	0.485657	−	0.841182i
$960$		0			0
$961$	13.1430	+	22.7643i	0.423966	+	0.734331i
$962$		0			0
$963$	15.5649	−	20.2534i	0.501572	−	0.652656i
$964$		0			0
$965$	−21.1874	−	6.63924i	−0.682048	−	0.213725i
$966$		0			0
$967$	10.5049	+	6.06498i	0.337813	+	0.195037i	0.659305	−	0.751876i	$-0.270851\pi$
$967$	10.5049	+	6.06498i	0.337813	+	0.195037i	−0.321491	+	0.946913i	$0.604184\pi$
$968$		0			0
$969$	48.0760	+	16.3395i	1.54442	+	0.524901i
$970$		0			0
$971$	−40.5273			−1.30058			−0.650291	−	0.759685i	$-0.725353\pi$
$971$	−40.5273			−1.30058			−0.650291	+	0.759685i	$0.725353\pi$
$972$		0			0
$973$		−	83.2285i		−	2.66818i
$974$		0			0
$975$	−17.2363	+	39.5109i	−0.552003	+	1.26536i
$976$		0			0
$977$	−18.1332	−	10.4692i	−0.580132	−	0.334939i	0.181054	−	0.983473i	$-0.442049\pi$
$977$	−18.1332	−	10.4692i	−0.580132	−	0.334939i	−0.761186	+	0.648534i	$0.775382\pi$
$978$		0			0
$979$	0.612736	+	1.06129i	0.0195831	+	0.0339190i
$980$		0			0
$981$	25.4829	+	19.5838i	0.813607	+	0.625264i
$982$		0			0
$983$	−1.24120	+	0.716607i	−0.0395881	+	0.0228562i	−0.519663	−	0.854371i	$-0.673943\pi$
$983$	−1.24120	+	0.716607i	−0.0395881	+	0.0228562i	0.480075	+	0.877227i	$0.340609\pi$
$984$		0			0
$985$	5.53208	+	24.7466i	0.176267	+	0.788491i
$986$		0			0
$987$	−35.3590	−	40.3495i	−1.12549	−	1.28434i
$988$		0			0
$989$	−36.2954			−1.15413
$990$		0			0
$991$	−55.4821			−1.76245			−0.881223	−	0.472700i	$-0.843279\pi$
$991$	−55.4821			−1.76245			−0.881223	+	0.472700i	$0.843279\pi$
$992$		0			0
$993$	−18.7363	+	3.71964i	−0.594578	+	0.118039i
$994$		0			0
$995$	−7.08971	+	1.58490i	−0.224759	+	0.0502447i
$996$		0			0
$997$	−37.8252	+	21.8384i	−1.19794	+	0.691629i	−0.960095	−	0.279675i	$-0.909773\pi$
$997$	−37.8252	+	21.8384i	−1.19794	+	0.691629i	−0.237842	+	0.971304i	$0.576440\pi$
$998$		0			0
$999$	−1.48810	−	2.23248i	−0.0470814	−	0.0706326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.b.49.10	yes	32
3.2	odd	2		1080.2.bi.b.1009.16		32
4.3	odd	2		720.2.by.f.49.7		32
5.4	even	2	inner	360.2.bi.b.49.7	✓	32
9.2	odd	6		1080.2.bi.b.289.7		32
9.4	even	3		3240.2.f.k.649.12		16
9.5	odd	6		3240.2.f.i.649.5		16
9.7	even	3	inner	360.2.bi.b.169.7	yes	32
12.11	even	2		2160.2.by.f.1009.16		32
15.14	odd	2		1080.2.bi.b.1009.7		32
20.19	odd	2		720.2.by.f.49.10		32
36.7	odd	6		720.2.by.f.529.10		32
36.11	even	6		2160.2.by.f.289.7		32
45.4	even	6		3240.2.f.k.649.11		16
45.14	odd	6		3240.2.f.i.649.6		16
45.29	odd	6		1080.2.bi.b.289.16		32
45.34	even	6	inner	360.2.bi.b.169.10	yes	32
60.59	even	2		2160.2.by.f.1009.7		32
180.79	odd	6		720.2.by.f.529.7		32
180.119	even	6		2160.2.by.f.289.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.b.49.7	✓	32	5.4	even	2	inner
360.2.bi.b.49.10	yes	32	1.1	even	1	trivial
360.2.bi.b.169.7	yes	32	9.7	even	3	inner
360.2.bi.b.169.10	yes	32	45.34	even	6	inner
720.2.by.f.49.7		32	4.3	odd	2
720.2.by.f.49.10		32	20.19	odd	2
720.2.by.f.529.7		32	180.79	odd	6
720.2.by.f.529.10		32	36.7	odd	6
1080.2.bi.b.289.7		32	9.2	odd	6
1080.2.bi.b.289.16		32	45.29	odd	6
1080.2.bi.b.1009.7		32	15.14	odd	2
1080.2.bi.b.1009.16		32	3.2	odd	2
2160.2.by.f.289.7		32	36.11	even	6
2160.2.by.f.289.16		32	180.119	even	6
2160.2.by.f.1009.7		32	60.59	even	2
2160.2.by.f.1009.16		32	12.11	even	2
3240.2.f.i.649.5		16	9.5	odd	6
3240.2.f.i.649.6		16	45.14	odd	6
3240.2.f.k.649.11		16	45.4	even	6
3240.2.f.k.649.12		16	9.4	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.557359 - 1.63992i) q^{3} +(-2.18221 + 0.487830i) q^{5} +(-3.90215 + 2.25291i) q^{7} +(-2.37870 - 1.82805i) q^{9} +O(q^{10})\)	\(q+(0.557359 - 1.63992i) q^{3} +(-2.18221 + 0.487830i) q^{5} +(-3.90215 + 2.25291i) q^{7} +(-2.37870 - 1.82805i) q^{9} +(0.631800 + 1.09431i) q^{11} +(-4.31068 - 2.48877i) q^{13} +(-0.416267 + 3.85055i) q^{15} -4.59329i q^{17} -6.38235 q^{19} +(1.51970 + 7.65491i) q^{21} +(5.34103 + 3.08364i) q^{23} +(4.52404 - 2.12909i) q^{25} +(-4.32366 + 2.88201i) q^{27} +(1.95380 + 3.38408i) q^{29} +(1.08560 - 1.88031i) q^{31} +(2.14672 - 0.426181i) q^{33} +(7.41626 - 6.81990i) q^{35} +0.516341i q^{37} +(-6.48400 + 5.68205i) q^{39} +(1.11882 - 1.93786i) q^{41} +(-5.09669 + 2.94257i) q^{43} +(6.08260 + 2.82878i) q^{45} +(-5.95343 + 3.43722i) q^{47} +(6.65119 - 11.5202i) q^{49} +(-7.53264 - 2.56011i) q^{51} -6.92003i q^{53} +(-1.91255 - 2.07980i) q^{55} +(-3.55726 + 10.4666i) q^{57} +(3.91777 - 6.78578i) q^{59} +(-6.62192 - 11.4695i) q^{61} +(13.4005 + 1.77434i) q^{63} +(10.6209 + 3.32814i) q^{65} +(-2.63495 - 1.52129i) q^{67} +(8.03381 - 7.04018i) q^{69} -9.06407 q^{71} +6.90760i q^{73} +(-0.970034 - 8.60576i) q^{75} +(-4.93076 - 2.84677i) q^{77} +(4.09326 + 7.08973i) q^{79} +(2.31645 + 8.69679i) q^{81} +(5.71353 - 3.29871i) q^{83} +(2.24074 + 10.0235i) q^{85} +(6.63860 - 1.31793i) q^{87} +0.969826 q^{89} +22.4279 q^{91} +(-2.47850 - 2.82831i) q^{93} +(13.9276 - 3.11350i) q^{95} +(-10.8174 + 6.24543i) q^{97} +(0.497592 - 3.75800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 4 * q^9	\( 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) \) 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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