LMFDB - Embedded newform 460.2.o.a.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label			199.3
Character	$\chi$	$=$	460.199
Dual form			460.2.o.a.319.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.201264 - 1.39982i) q^{2} +(-1.21668 - 2.66415i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(-1.68991 + 1.46431i) q^{5} +(-3.97421 + 1.16693i) q^{6} +(0.198162 - 0.308347i) q^{7} +(-1.17497 + 2.57283i) q^{8} +(-3.65283 + 4.21559i) q^{9} +O(q^{10})$	\(q+(0.201264 - 1.39982i) q^{2} +(-1.21668 - 2.66415i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(-1.68991 + 1.46431i) q^{5} +(-3.97421 + 1.16693i) q^{6} +(0.198162 - 0.308347i) q^{7} +(-1.17497 + 2.57283i) q^{8} +(-3.65283 + 4.21559i) q^{9} +(1.70966 + 2.66028i) q^{10} +(0.833631 + 5.79803i) q^{12} +(-0.391747 - 0.339451i) q^{14} +(5.95723 + 2.72058i) q^{15} +(3.36501 + 2.16256i) q^{16} +(5.16588 + 5.96175i) q^{18} +(4.06800 - 1.85779i) q^{20} +(-1.06258 - 0.152776i) q^{21} +(-4.59450 - 1.37497i) q^{23} +8.28397 q^{24} +(0.711574 - 4.94911i) q^{25} +(7.24474 + 2.12725i) q^{27} +(-0.554014 + 0.480056i) q^{28} +(-10.2558 + 3.01138i) q^{29} +(5.00729 - 7.79149i) q^{30} +(3.70445 - 4.27517i) q^{32} +(0.116640 + 0.811249i) q^{35} +(9.38507 - 6.03142i) q^{36} +(-1.78183 - 6.06837i) q^{40} +(8.19418 + 9.45659i) q^{41} +(-0.427719 + 1.45668i) q^{42} +(-6.02181 + 2.75007i) q^{43} -12.4728i q^{45} +(-2.84941 + 6.15474i) q^{46} -0.686879 q^{47} +(1.66726 - 11.5961i) q^{48} +(2.85210 + 6.24522i) q^{49} +(-6.78464 - 1.99215i) q^{50} +(4.43586 - 9.71318i) q^{54} +(0.560488 + 0.872136i) q^{56} +(2.15126 + 14.9624i) q^{58} +(-9.89889 - 8.57744i) q^{60} +(-13.7598 - 6.28390i) q^{61} +(0.576010 + 1.96171i) q^{63} +(-5.23889 - 6.04600i) q^{64} +(10.3214 + 1.48399i) q^{67} +(1.92691 + 13.9134i) q^{69} +1.15908 q^{70} +(-6.55402 - 14.3513i) q^{72} +(-14.0509 + 4.12573i) q^{75} +(-8.85323 + 1.27290i) q^{80} +(-0.765695 - 5.32553i) q^{81} +(14.8867 - 9.56710i) q^{82} +(-13.6727 - 11.8474i) q^{83} +(1.95300 + 0.891905i) q^{84} +(2.63763 + 8.98294i) q^{86} +(20.5008 + 23.6592i) q^{87} +(-7.71799 + 3.52469i) q^{89} +(-17.4597 - 2.51033i) q^{90} +(8.04204 + 5.22739i) q^{92} +(-0.138244 + 0.961507i) q^{94} +(-15.8968 - 4.66773i) q^{96} +(9.31620 - 2.73548i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	$ 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) $ 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	0.201264	−	1.39982i	0.142315	−	0.989821i
$2$	0.201264	−	1.39982i	0.142315	−	0.989821i
$3$	−1.21668	−	2.66415i	−0.702450	−	1.53815i	−0.836976	−	0.547240i	$-0.815678\pi$
$3$	−1.21668	−	2.66415i	−0.702450	−	1.53815i	0.134526	−	0.990910i	$-0.457049\pi$
$4$	−1.91899	−	0.563465i	−0.959493	−	0.281733i
$5$	−1.68991	+	1.46431i	−0.755750	+	0.654861i
$5$	−1.68991	+	1.46431i	−0.755750	+	0.654861i
$6$	−3.97421	+	1.16693i	−1.62246	+	0.476398i
$7$	0.198162	−	0.308347i	0.0748984	−	0.116544i	−0.801784	−	0.597614i	$-0.796115\pi$
$7$	0.198162	−	0.308347i	0.0748984	−	0.116544i	0.876682	+	0.481070i	$0.159752\pi$
$8$	−1.17497	+	2.57283i	−0.415415	+	0.909632i
$9$	−3.65283	+	4.21559i	−1.21761	+	1.40520i
$10$	1.70966	+	2.66028i	0.540641	+	0.841254i
$11$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$11$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$12$	0.833631	+	5.79803i	0.240649	+	1.67375i
$13$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$13$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$14$	−0.391747	−	0.339451i	−0.104699	−	0.0907220i
$15$	5.95723	+	2.72058i	1.53815	+	0.702450i
$16$	3.36501	+	2.16256i	0.841254	+	0.540641i
$17$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$17$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$18$	5.16588	+	5.96175i	1.21761	+	1.40520i
$19$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$19$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$20$	4.06800	−	1.85779i	0.909632	−	0.415415i
$21$	−1.06258	−	0.152776i	−0.231875	−	0.0333386i
$22$		0			0
$23$	−4.59450	−	1.37497i	−0.958020	−	0.286701i
$23$	−4.59450	−	1.37497i	−0.958020	−	0.286701i
$24$	8.28397			1.69096
$25$	0.711574	−	4.94911i	0.142315	−	0.989821i
$26$		0			0
$27$	7.24474	+	2.12725i	1.39425	+	0.409389i
$28$	−0.554014	+	0.480056i	−0.104699	+	0.0907220i
$29$	−10.2558	+	3.01138i	−1.90446	+	0.559199i	−0.917628	+	0.397440i	$0.869899\pi$
$29$	−10.2558	+	3.01138i	−1.90446	+	0.559199i	−0.986830	+	0.161760i	$0.948283\pi$
$30$	5.00729	−	7.79149i	0.914201	−	1.42253i
$31$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$31$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$32$	3.70445	−	4.27517i	0.654861	−	0.755750i
$33$		0			0
$34$		0			0
$35$	0.116640	+	0.811249i	0.0197158	+	0.137126i
$36$	9.38507	−	6.03142i	1.56418	−	1.00524i
$37$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$37$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$38$		0			0
$39$		0			0
$40$	−1.78183	−	6.06837i	−0.281733	−	0.959493i
$41$	8.19418	+	9.45659i	1.27972	+	1.47687i	0.800700	+	0.599065i	$0.204461\pi$
$41$	8.19418	+	9.45659i	1.27972	+	1.47687i	0.479016	+	0.877806i	$0.340994\pi$
$42$	−0.427719	+	1.45668i	−0.0659984	+	0.224770i
$43$	−6.02181	+	2.75007i	−0.918318	+	0.419382i	−0.817766	−	0.575550i	$-0.804788\pi$
$43$	−6.02181	+	2.75007i	−0.918318	+	0.419382i	−0.100551	+	0.994932i	$0.532061\pi$
$44$		0			0
$45$		−	12.4728i		−	1.85934i
$46$	−2.84941	+	6.15474i	−0.420123	+	0.907467i
$47$	−0.686879			−0.100192			−0.0500958	−	0.998744i	$-0.515953\pi$
$47$	−0.686879			−0.100192			−0.0500958	+	0.998744i	$0.515953\pi$
$48$	1.66726	−	11.5961i	0.240649	−	1.67375i
$49$	2.85210	+	6.24522i	0.407442	+	0.892174i
$50$	−6.78464	−	1.99215i	−0.959493	−	0.281733i
$51$		0			0
$52$		0			0
$53$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$53$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$54$	4.43586	−	9.71318i	0.603644	−	1.32180i
$55$		0			0
$56$	0.560488	+	0.872136i	0.0748984	+	0.116544i
$57$		0			0
$58$	2.15126	+	14.9624i	0.282475	+	1.96466i
$59$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$59$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$60$	−9.89889	−	8.57744i	−1.27794	−	1.10734i
$61$	−13.7598	−	6.28390i	−1.76177	−	0.804571i	−0.984497	−	0.175403i	$-0.943877\pi$
$61$	−13.7598	−	6.28390i	−1.76177	−	0.804571i	−0.777269	−	0.629168i	$-0.783396\pi$
$62$		0			0
$63$	0.576010	+	1.96171i	0.0725704	+	0.247152i
$64$	−5.23889	−	6.04600i	−0.654861	−	0.755750i
$65$		0			0
$66$		0			0
$67$	10.3214	+	1.48399i	1.26096	+	0.181299i	0.740189	−	0.672399i	$-0.234736\pi$
$67$	10.3214	+	1.48399i	1.26096	+	0.181299i	0.520770	+	0.853697i	$0.325645\pi$
$68$		0			0
$69$	1.92691	+	13.9134i	0.231972	+	1.67497i
$70$	1.15908			0.138536
$71$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$71$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$72$	−6.55402	−	14.3513i	−0.772399	−	1.69132i
$73$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$73$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$74$		0			0
$75$	−14.0509	+	4.12573i	−1.62246	+	0.476398i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$79$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$80$	−8.85323	+	1.27290i	−0.989821	+	0.142315i
$81$	−0.765695	−	5.32553i	−0.0850773	−	0.591725i
$82$	14.8867	−	9.56710i	1.64396	−	1.05651i
$83$	−13.6727	−	11.8474i	−1.50077	−	1.30042i	−0.828274	−	0.560324i	$-0.810677\pi$
$83$	−13.6727	−	11.8474i	−1.50077	−	1.30042i	−0.672496	−	0.740101i	$-0.734778\pi$
$84$	1.95300	+	0.891905i	0.213090	+	0.0973148i
$85$		0			0
$86$	2.63763	+	8.98294i	0.284423	+	0.968655i
$87$	20.5008	+	23.6592i	2.19792	+	2.53653i
$88$		0			0
$89$	−7.71799	+	3.52469i	−0.818105	+	0.373616i	−0.780095	−	0.625661i	$-0.784829\pi$
$89$	−7.71799	+	3.52469i	−0.818105	+	0.373616i	−0.0380101	+	0.999277i	$0.512102\pi$
$90$	−17.4597	−	2.51033i	−1.84042	−	0.264612i
$91$		0			0
$92$	8.04204	+	5.22739i	0.838441	+	0.544993i
$93$		0			0
$94$	−0.138244	+	0.961507i	−0.0142588	+	0.0991719i
$95$		0			0
$96$	−15.8968	−	4.66773i	−1.62246	−	0.476398i
$97$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$97$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$98$	9.31620	−	2.73548i	0.941078	−	0.276325i
$99$		0			0
$100$	−4.15415	+	9.09632i	−0.415415	+	0.909632i
$101$	−10.2246	+	11.7999i	−1.01739	+	1.17413i	−0.0327629	+	0.999463i	$0.510431\pi$
$101$	−10.2246	+	11.7999i	−1.01739	+	1.17413i	−0.984627	+	0.174668i	$0.944115\pi$
$102$		0			0
$103$	−19.7701	+	2.84251i	−1.94800	+	0.280081i	−0.999344	−	0.0362175i	$-0.988469\pi$
$103$	−19.7701	+	2.84251i	−1.94800	+	0.280081i	−0.948660	+	0.316298i	$0.897560\pi$
$104$		0			0
$105$	2.01938	−	1.29778i	0.197071	−	0.126650i
$106$		0			0
$107$	−6.98755	−	3.19111i	−0.675512	−	0.308496i	0.0479605	−	0.998849i	$-0.484728\pi$
$107$	−6.98755	−	3.19111i	−0.675512	−	0.308496i	−0.723472	+	0.690353i	$0.757455\pi$
$108$	−12.7039	−	8.16431i	−1.22244	−	0.785612i
$109$	−4.99977	−	17.0276i	−0.478891	−	1.63095i	−0.745040	−	0.667020i	$-0.767569\pi$
$109$	−4.99977	−	17.0276i	−0.478891	−	1.63095i	0.266149	−	0.963932i	$-0.414249\pi$
$110$		0			0
$111$		0			0
$112$	1.33364	−	0.609052i	0.126017	−	0.0575500i
$113$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$113$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$114$		0			0
$115$	9.77767	−	4.40422i	0.911772	−	0.410696i
$116$	21.3776			1.98486
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−13.9991	+	12.1303i	−1.27794	+	1.10734i
$121$	10.5544	−	3.09906i	0.959493	−	0.281733i
$122$	−11.5657	+	17.9965i	−1.04711	+	1.62933i
$123$	15.2241	−	33.3362i	1.37271	−	3.00582i
$124$		0			0
$125$	6.04455	+	9.40550i	0.540641	+	0.841254i
$126$	2.86197	−	0.411489i	0.254964	−	0.0366584i
$127$	−2.61477	−	18.1861i	−0.232023	−	1.61375i	−0.689331	−	0.724447i	$-0.742095\pi$
$127$	−2.61477	−	18.1861i	−0.232023	−	1.61375i	0.457308	−	0.889308i	$-0.348814\pi$
$128$	−9.51770	+	6.11665i	−0.841254	+	0.540641i
$129$	14.6532	+	12.6971i	1.29014	+	1.11792i
$130$		0			0
$131$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$131$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$132$		0			0
$133$		0			0
$134$	4.15464	−	14.1494i	0.358906	−	1.22232i
$135$	−15.3579	+	7.01371i	−1.32180	+	0.603644i
$136$		0			0
$137$		0			0			−	1.00000i	$-0.5\pi$
$137$		0			0				1.00000i	$0.5\pi$
$138$	19.8640	+	0.102932i	1.69094	+	0.00876216i
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$	0.233280	−	1.62250i	0.0197158	−	0.137126i
$141$	0.835712	+	1.82995i	0.0703796	+	0.154110i
$142$		0			0
$143$		0			0
$144$	−21.4083	+	6.28605i	−1.78403	+	0.523837i
$145$	12.9218	−	20.1067i	1.07310	−	1.66977i
$146$		0			0
$147$	13.1681	−	15.1968i	1.08609	−	1.25341i
$148$		0			0
$149$	15.0546	−	2.16452i	1.23332	−	0.177324i	0.505337	−	0.862922i	$-0.331368\pi$
$149$	15.0546	−	2.16452i	1.23332	−	0.177324i	0.727980	+	0.685598i	$0.240459\pi$
$150$	2.94733	+	20.4991i	0.240649	+	1.67375i
$151$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$151$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$157$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$158$		0			0
$159$		0			0
$160$			12.6491i			1.00000i
$161$	−1.33443	+	1.14423i	−0.105167	+	0.0901782i
$162$	−7.60888			−0.597810
$163$	2.62553	−	18.2610i	0.205648	−	1.43031i	−0.581500	−	0.813546i	$-0.697534\pi$
$163$	2.62553	−	18.2610i	0.205648	−	1.43031i	0.787148	−	0.616764i	$-0.211557\pi$
$164$	−10.3961	−	22.7642i	−0.811796	−	1.77759i
$165$		0			0
$166$	−19.3361	+	16.7548i	−1.50077	+	1.30042i
$167$	−24.6979	+	7.25194i	−1.91118	+	0.561172i	−0.930199	+	0.367057i	$0.880366\pi$
$167$	−24.6979	+	7.25194i	−1.91118	+	0.561172i	−0.980979	+	0.194116i	$0.937816\pi$
$168$	1.64157	−	2.55434i	0.126650	−	0.197071i
$169$	5.40040	−	11.8252i	0.415415	−	0.909632i
$170$		0			0
$171$		0			0
$172$	13.1053	−	1.88426i	0.999273	−	0.143674i
$173$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$173$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$174$	37.2447	−	23.9357i	2.82351	−	1.81456i
$175$	−1.38503	−	1.20014i	−0.104699	−	0.0907220i
$176$		0			0
$177$		0			0
$178$	3.38057	+	11.5132i	0.253385	+	0.862949i
$179$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$179$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$180$	−7.02801	+	23.9352i	−0.523837	+	1.78403i
$181$	8.48458	−	3.87478i	0.630654	−	0.288010i	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	8.48458	−	3.87478i	0.630654	−	0.288010i	0.704984	+	0.709224i	$0.250954\pi$
$182$		0			0
$183$			44.3038i			3.27503i
$184$	8.93596	−	10.2053i	0.658768	−	0.752346i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.31811	+	0.387033i	0.0961332	+	0.0282273i
$189$	2.09156	−	1.81235i	0.152139	−	0.131829i
$190$		0			0
$191$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$191$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$192$	−9.73343	+	21.3132i	−0.702450	+	1.53815i
$193$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$193$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$194$		0			0
$195$		0			0
$196$	−1.95417	−	13.5915i	−0.139583	−	0.970824i
$197$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$197$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$198$		0			0
$199$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$199$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$200$	11.8971	+	7.64582i	0.841254	+	0.540641i
$201$	−8.60423	−	29.3033i	−0.606896	−	2.06690i
$202$	14.4598	+	16.6875i	1.01739	+	1.17413i
$203$	−1.10377	+	3.75909i	−0.0774694	+	0.263837i
$204$		0			0
$205$	−27.6948	−	3.98191i	−1.93429	−	0.278109i
$206$			28.2466i			1.96804i
$207$	22.5792	−	14.3460i	1.56937	−	0.997117i
$208$		0			0
$209$		0			0
$210$	−1.41022	−	3.08796i	−0.0973148	−	0.213090i
$211$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$211$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$212$		0			0
$213$		0			0
$214$	−5.87331	+	9.13905i	−0.401491	+	0.624733i
$215$	6.14934	−	13.4652i	0.419382	−	0.918318i
$216$	−13.9854	+	16.1400i	−0.951586	+	1.09819i
$217$		0			0
$218$	−24.8419	+	3.57172i	−1.68250	+	0.241908i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	24.7214	+	15.8875i	1.65547	+	1.06390i	0.924269	+	0.381741i	$0.124675\pi$
$223$	24.7214	+	15.8875i	1.65547	+	1.06390i	0.731199	+	0.682164i	$0.238961\pi$
$224$	−0.584150	−	1.98943i	−0.0390302	−	0.132925i
$225$	18.2641	+	21.0780i	1.21761	+	1.40520i
$226$		0			0
$227$	−23.7589	+	10.8503i	−1.57693	+	0.720160i	−0.995617	−	0.0935193i	$-0.970188\pi$
$227$	−23.7589	+	10.8503i	−1.57693	+	0.720160i	−0.581314	+	0.813680i	$0.697461\pi$
$228$		0			0
$229$		−	10.0388i		−	0.663382i	−0.943388	−	0.331691i	$-0.892381\pi$
$229$		−	10.0388i		−	0.663382i	0.943388	−	0.331691i	$-0.107619\pi$
$230$	−4.19723	−	14.5734i	−0.276757	−	0.960940i
$231$		0			0
$232$	4.30253	−	29.9248i	0.282475	−	1.96466i
$233$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$233$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$234$		0			0
$235$	1.16076	−	1.00581i	0.0757198	−	0.0656116i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$239$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$240$	14.1627	+	22.0377i	0.914201	+	1.42253i
$241$	26.1556	−	3.76060i	1.68483	−	0.242242i	0.767693	−	0.640817i	$-0.221404\pi$
$241$	26.1556	−	3.76060i	1.68483	−	0.242242i	0.917136	+	0.398575i	$0.130495\pi$
$242$	−2.21390	−	15.3980i	−0.142315	−	0.989821i
$243$	5.79945	−	3.72708i	0.372035	−	0.239093i
$244$	22.8642	+	19.8119i	1.46373	+	1.26833i
$245$	−13.9647	−	6.37748i	−0.892174	−	0.407442i
$246$	−43.6006	−	28.0204i	−2.77987	−	1.78651i
$247$		0			0
$248$		0			0
$249$	−14.9281	+	50.8406i	−0.946033	+	3.22189i
$250$	14.3825	−	6.56829i	0.909632	−	0.415415i
$251$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$251$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$252$		−	4.08906i		−	0.257586i
$253$		0			0
$254$	−25.9835			−1.63035
$255$		0			0
$256$	6.64664	+	14.5541i	0.415415	+	0.909632i
$257$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$257$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$258$	20.7228	−	17.9564i	1.29014	−	1.11792i
$259$		0			0
$260$		0			0
$261$	24.7680	−	54.2344i	1.53310	−	3.35703i
$262$		0			0
$263$	12.3941	+	19.2857i	0.764256	+	1.18921i	0.977237	+	0.212149i	$0.0680462\pi$
$263$	12.3941	+	19.2857i	0.764256	+	1.18921i	−0.212981	+	0.977056i	$0.568317\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	18.7806	+	16.2735i	1.14935	+	0.995922i
$268$	−18.9704	−	8.66350i	−1.15880	−	0.529208i
$269$	−8.72382	−	5.60646i	−0.531901	−	0.341832i	0.246963	−	0.969025i	$-0.420567\pi$
$269$	−8.72382	−	5.60646i	−0.531901	−	0.341832i	−0.778864	+	0.627193i	$0.784204\pi$
$270$	6.72695	+	22.9099i	0.409389	+	1.39425i
$271$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$271$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	4.14199	−	27.7853i	0.249318	−	1.67248i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$	−2.22425	−	0.653100i	−0.132925	−	0.0390302i
$281$	20.1453	−	17.4560i	1.20177	−	1.04134i	0.203713	−	0.979031i	$-0.434699\pi$
$281$	20.1453	−	17.4560i	1.20177	−	1.04134i	0.998057	−	0.0623085i	$-0.0198463\pi$
$282$	2.72980	−	0.801542i	0.162557	−	0.0477311i
$283$	−17.1093	+	26.6226i	−1.01704	+	1.58255i	−0.222882	+	0.974845i	$0.571547\pi$
$283$	−17.1093	+	26.6226i	−1.01704	+	1.58255i	−0.794162	+	0.607706i	$0.792090\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.53969	−	0.652709i	0.267969	−	0.0385282i
$288$	4.49061	+	31.2329i	0.264612	+	1.84042i
$289$	−14.3013	+	9.19089i	−0.841254	+	0.540641i
$290$	−25.5450	−	22.1349i	−1.50006	−	1.29981i
$291$		0			0
$292$		0			0
$293$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$293$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$294$	−18.6226	−	21.4916i	−1.08609	−	1.25341i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		−	21.5093i		−	1.24600i
$299$		0			0
$300$	29.2883			1.69096
$301$	−0.345322	+	2.40177i	−0.0199040	+	0.138436i
$302$		0			0
$303$	43.8768	+	12.8834i	2.52066	+	0.740131i
$304$		0			0
$305$	32.4544	−	9.52948i	1.85834	−	0.545657i
$306$		0			0
$307$	−6.32971	+	13.8601i	−0.361256	+	0.791040i	0.638515	+	0.769610i	$0.279549\pi$
$307$	−6.32971	+	13.8601i	−0.361256	+	0.791040i	−0.999770	+	0.0214301i	$0.993178\pi$
$308$		0			0
$309$	31.6267	+	49.2121i	1.79918	+	2.79958i
$310$		0			0
$311$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$311$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$312$		0			0
$313$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$313$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$314$		0			0
$315$	−3.84596	−	2.47165i	−0.216695	−	0.139262i
$316$		0			0
$317$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$317$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$318$		0			0
$319$		0			0
$320$	17.7065	+	2.54581i	0.989821	+	0.142315i
$321$			22.4985i			1.25574i
$322$	1.33315	+	2.09825i	0.0742935	+	0.116931i
$323$		0			0
$324$	−1.53139	+	10.6511i	−0.0850773	+	0.591725i
$325$		0			0
$326$	−25.0336	−	7.35054i	−1.38649	−	0.407109i
$327$	−39.2812	+	34.0373i	−2.17225	+	1.88227i
$328$	−33.9581	+	9.97100i	−1.87502	+	0.550556i
$329$	−0.136114	+	0.211797i	−0.00750419	+	0.0116768i
$330$		0			0
$331$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$331$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$332$	19.5620	+	30.4391i	1.07361	+	1.67056i
$333$		0			0
$334$	5.18063	+	36.0321i	0.283471	+	1.97159i
$335$	−19.6152	+	12.6059i	−1.07169	+	0.688736i
$336$	−3.24522	−	2.81200i	−0.177041	−	0.153407i
$337$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$337$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$338$	−15.4663	−	9.93956i	−0.841254	−	0.540641i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	5.03048	+	0.723274i	0.271621	+	0.0390531i
$344$		−	18.7243i		−	1.00955i
$345$	−23.6298	−	20.6907i	−1.27219	−	1.11395i
$346$		0			0
$347$	2.26299	−	15.7395i	0.121484	−	0.844939i	−0.834393	−	0.551171i	$-0.814181\pi$
$347$	2.26299	−	15.7395i	0.121484	−	0.844939i	0.955877	−	0.293769i	$-0.0949095\pi$
$348$	−26.0097	−	56.9532i	−1.39426	−	3.05301i
$349$	34.9059	+	10.2493i	1.86847	+	0.548632i	0.998453	+	0.0556092i	$0.0177101\pi$
$349$	34.9059	+	10.2493i	1.86847	+	0.548632i	0.870016	+	0.493023i	$0.164108\pi$
$350$	−1.95873	+	1.69725i	−0.104699	+	0.0907220i
$351$		0			0
$352$		0			0
$353$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$353$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$354$		0			0
$355$		0			0
$356$	16.7967	−	2.41501i	0.890226	−	0.127995i
$357$		0			0
$358$		0			0
$359$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$359$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$360$	32.0905	+	14.6552i	1.69132	+	0.772399i
$361$	−15.9838	−	10.2722i	−0.841254	−	0.540641i
$362$	−3.71635	−	12.6567i	−0.195327	−	0.665223i
$363$	−21.0977	−	24.3481i	−1.10734	−	1.27794i
$364$		0			0
$365$		0			0
$366$	62.0173	+	8.91674i	3.24170	+	0.466086i
$367$		−	33.4195i		−	1.74448i	−0.489074	−	0.872242i	$-0.662665\pi$
$367$		−	33.4195i		−	1.74448i	0.489074	−	0.872242i	$-0.337335\pi$
$368$	−12.4871	−	14.5627i	−0.650936	−	0.759133i
$369$	−69.7971			−3.63349
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$373$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$374$		0			0
$375$	17.7034	−	27.5471i	0.914201	−	1.42253i
$376$	0.807064	−	1.76722i	0.0416211	−	0.0911375i
$377$		0			0
$378$	−2.11601	−	3.29257i	−0.108836	−	0.169352i
$379$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$379$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$380$		0			0
$381$	−45.2692	+	29.0928i	−2.31921	+	1.49047i
$382$		0			0
$383$	−34.9931	−	15.9808i	−1.78807	−	0.816582i	−0.970636	−	0.240553i	$-0.922671\pi$
$383$	−34.9931	−	15.9808i	−1.78807	−	0.816582i	−0.817429	−	0.576029i	$-0.804602\pi$
$384$	27.8757	+	17.9146i	1.42253	+	0.914201i
$385$		0			0
$386$		0			0
$387$	10.4035	−	35.4310i	0.528839	−	1.80106i
$388$		0			0
$389$	−19.1041	−	2.74676i	−0.968617	−	0.139266i	−0.360192	−	0.932878i	$-0.617289\pi$
$389$	−19.1041	−	2.74676i	−0.968617	−	0.139266i	−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$		0			0
$392$	−19.4190			−0.980808
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$397$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$398$		0			0
$399$		0			0
$400$	13.0972	−	15.1150i	0.654861	−	0.755750i
$401$	0.816928	+	1.27116i	0.0407954	+	0.0634789i	0.861052	−	0.508516i	$-0.169806\pi$
$401$	0.816928	+	1.27116i	0.0407954	+	0.0634789i	−0.820257	+	0.571995i	$0.806170\pi$
$402$	−42.7511	+	6.14668i	−2.13223	+	0.306568i
$403$		0			0
$404$	26.2698	−	16.8826i	1.30697	−	0.839938i
$405$	9.09220	+	7.87843i	0.451795	+	0.391482i
$406$	5.03990	+	2.30165i	0.250126	+	0.114229i
$407$		0			0
$408$		0			0
$409$	−21.6351	−	24.9683i	−1.06979	−	1.23460i	−0.970895	−	0.239504i	$-0.923015\pi$
$409$	−21.6351	−	24.9683i	−1.06979	−	1.23460i	−0.0988936	−	0.995098i	$-0.531530\pi$
$410$	−11.1479	+	37.9663i	−0.550556	+	1.87502i
$411$		0			0
$412$	39.5402	+	5.68502i	1.94800	+	0.280081i
$413$		0			0
$414$	−15.5375	−	34.4942i	−0.763624	−	1.69530i
$415$	40.4539			1.98580
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$419$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$420$	−4.60641	+	1.35257i	−0.224770	+	0.0659984i
$421$	−15.9677	+	24.8461i	−0.778216	+	1.21093i	0.194948	+	0.980814i	$0.437546\pi$
$421$	−15.9677	+	24.8461i	−0.778216	+	1.21093i	−0.973164	+	0.230114i	$0.926090\pi$
$422$		0			0
$423$	2.50905	−	2.89560i	0.121994	−	0.140789i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.66430	+	2.99757i	−0.225721	+	0.145062i
$428$	11.6109	+	10.0609i	0.561236	+	0.486313i
$429$		0			0
$430$	−17.6112	−	11.3180i	−0.849286	−	0.545803i
$431$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$431$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$432$	19.7783	+	22.8254i	0.951586	+	1.09819i
$433$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$433$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$434$		0			0
$435$	−69.2890	−	9.96225i	−3.32215	−	0.477653i
$436$			35.4930i			1.69981i
$437$		0			0
$438$		0			0
$439$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$439$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$440$		0			0
$441$	−36.7455	−	10.7895i	−1.74979	−	0.513783i
$442$		0			0
$443$	35.1924	−	10.3334i	1.67204	−	0.490956i	0.697769	−	0.716323i	$-0.254176\pi$
$443$	35.1924	−	10.3334i	1.67204	−	0.490956i	0.974274	+	0.225367i	$0.0723580\pi$
$444$		0			0
$445$	7.88144	−	17.2579i	0.373616	−	0.818105i
$446$	27.2151	−	31.4079i	1.28867	−	1.48721i
$447$	−24.0832	−	37.4741i	−1.13909	−	1.77247i
$448$	−2.90241	+	0.417304i	−0.137126	+	0.0197158i
$449$	3.87899	+	26.9790i	0.183061	+	1.27322i	0.849473	+	0.527633i	$0.176920\pi$
$449$	3.87899	+	26.9790i	0.183061	+	1.27322i	−0.666412	+	0.745584i	$0.732171\pi$
$450$	33.1812	−	21.3243i	1.56418	−	1.00524i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	10.4067	+	35.4419i	0.488409	+	1.66337i
$455$		0			0
$456$		0			0
$457$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$457$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$458$	−14.0525	−	2.02044i	−0.656630	−	0.0944091i
$459$		0			0
$460$	−21.2448	+	2.94227i	−0.990546	+	0.137184i
$461$	14.8305			0.690723			0.345362	−	0.938470i	$-0.387756\pi$
$461$	14.8305			0.690723			0.345362	+	0.938470i	$0.387756\pi$
$462$		0			0
$463$	13.6808	+	29.9569i	0.635802	+	1.39221i	0.903449	+	0.428696i	$0.141027\pi$
$463$	13.6808	+	29.9569i	0.635802	+	1.39221i	−0.267646	+	0.963517i	$0.586246\pi$
$464$	−41.0233	−	12.0455i	−1.90446	−	0.559199i
$465$		0			0
$466$		0			0
$467$	−15.3869	+	23.9425i	−0.712021	+	1.10793i	0.277103	+	0.960840i	$0.410626\pi$
$467$	−15.3869	+	23.9425i	−0.712021	+	1.10793i	−0.989124	+	0.147086i	$0.953011\pi$
$468$		0			0
$469$	2.50290	−	2.88850i	0.115573	−	0.133378i
$470$	−1.17433	−	1.82729i	−0.0541677	−	0.0842866i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$479$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$480$	33.6992	−	15.3899i	1.53815	−	0.702450i
$481$		0			0
$482$		−	37.3699i		−	1.70215i
$483$	4.67198	+	2.16295i	0.212582	+	0.0984176i
$484$	−22.0000			−1.00000
$485$		0			0
$486$	−4.05002	−	8.86831i	−0.183713	−	0.402275i
$487$	−19.3382	−	5.67822i	−0.876299	−	0.257305i	−0.187507	−	0.982263i	$-0.560041\pi$
$487$	−19.3382	−	5.67822i	−0.876299	−	0.257305i	−0.688792	+	0.724959i	$0.741859\pi$
$488$	32.3348	−	28.0183i	1.46373	−	1.26833i
$489$	−51.8445	+	15.2229i	−2.34449	+	0.688404i
$490$	−11.7379	+	18.2645i	−0.530265	+	0.825108i
$491$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$491$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$492$	−47.9987	+	55.3934i	−2.16395	+	2.49733i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	68.1631	+	31.1291i	3.05446	+	1.39493i
$499$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$499$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$500$	−6.29973	−	21.4549i	−0.281733	−	0.959493i
$501$	49.3696	+	56.9756i	2.20567	+	2.54548i
$502$		0			0
$503$	40.7010	−	18.5875i	1.81477	−	0.828777i	0.878202	−	0.478291i	$-0.158743\pi$
$503$	40.7010	−	18.5875i	1.81477	−	0.828777i	0.936568	−	0.350487i	$-0.113984\pi$
$504$	−5.72394	−	0.822978i	−0.254964	−	0.0366584i
$505$		−	34.9128i		−	1.55360i
$506$		0			0
$507$	−38.0747			−1.69096
$508$	−5.22953	+	36.3722i	−0.232023	+	1.61375i
$509$	7.62553	+	16.6976i	0.337996	+	0.740108i	0.999956	−	0.00943185i	$-0.00300230\pi$
$509$	7.62553	+	16.6976i	0.337996	+	0.740108i	−0.661960	+	0.749539i	$0.730275\pi$
$510$		0			0
$511$		0			0
$512$	21.7108	−	6.37488i	0.959493	−	0.281733i
$513$		0			0
$514$		0			0
$515$	29.2473	−	33.7532i	1.28879	−	1.48734i
$516$	−20.9650	−	32.6221i	−0.922931	−	1.43611i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−39.5290	−	18.0523i	−1.73180	−	0.790884i	−0.993158	−	0.116781i	$-0.962742\pi$
$521$	−39.5290	−	18.0523i	−1.73180	−	0.790884i	−0.738637	−	0.674103i	$-0.764530\pi$
$522$	−70.9335	−	45.5862i	−3.10467	−	1.99525i
$523$	−3.53982	−	12.0555i	−0.154785	−	0.527151i	0.845188	−	0.534469i	$-0.179489\pi$
$523$	−3.53982	−	12.0555i	−0.154785	−	0.527151i	−0.999973	+	0.00731877i	$0.997670\pi$
$524$		0			0
$525$	−1.51221	+	5.15013i	−0.0659984	+	0.224770i
$526$	29.4909	−	13.4681i	1.28587	−	0.587235i
$527$		0			0
$528$		0			0
$529$	19.2189	+	12.6346i	0.835605	+	0.549330i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	26.5598	−	23.0142i	1.14935	−	0.995922i
$535$	16.4811	−	4.83929i	0.712540	−	0.209221i
$536$	−15.9454	+	24.8115i	−0.688736	+	1.07169i
$537$		0			0
$538$	−9.60382	+	11.0834i	−0.414050	+	0.477839i
$539$		0			0
$540$	33.4236	−	4.80558i	1.43832	−	0.206799i
$541$	−1.22707	−	8.53446i	−0.0527558	−	0.366925i	−0.999048	−	0.0436135i	$-0.986113\pi$
$541$	−1.22707	−	8.53446i	−0.0527558	−	0.366925i	0.946293	−	0.323311i	$-0.104796\pi$
$542$		0			0
$543$	−20.6460	−	17.8899i	−0.886006	−	0.767728i
$544$		0			0
$545$	33.3829	+	21.4539i	1.42997	+	0.918985i
$546$		0			0
$547$	−18.4486	−	21.2909i	−0.788806	−	0.910331i	0.208906	−	0.977936i	$-0.433010\pi$
$547$	−18.4486	−	21.2909i	−0.788806	−	0.910331i	−0.997712	+	0.0676046i	$0.978464\pi$
$548$		0			0
$549$	76.7527	−	35.0518i	3.27572	−	1.49597i
$550$		0			0
$551$		0			0
$552$	−38.0607	−	11.3902i	−1.61997	−	0.484799i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$557$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$558$		0			0
$559$		0			0
$560$	−1.36188	+	2.98211i	−0.0575500	+	0.126017i
$561$		0			0
$562$	−20.3808	−	31.7131i	−0.859710	−	1.33774i
$563$	40.2548	−	5.78777i	1.69654	−	0.243925i	0.774929	−	0.632048i	$-0.217785\pi$
$563$	40.2548	−	5.78777i	1.69654	−	0.243925i	0.921608	+	0.388123i	$0.126876\pi$
$564$	−0.572604	−	3.98255i	−0.0241110	−	0.167696i
$565$		0			0
$566$	33.8234	+	29.3081i	1.42170	+	1.23191i
$567$	−1.79384	−	0.819220i	−0.0753343	−	0.0344040i
$568$		0			0
$569$	−12.8896	−	43.8980i	−0.540361	−	1.84030i	−0.542116	−	0.840304i	$-0.682377\pi$
$569$	−12.8896	−	43.8980i	−0.540361	−	1.84030i	0.00175481	−	0.999998i	$-0.499441\pi$
$570$		0			0
$571$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$571$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$572$		0			0
$573$		0			0
$574$		−	6.48611i		−	0.270725i
$575$	−10.0742	+	21.7603i	−0.420123	+	0.907467i
$576$	44.6242			1.85934
$577$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$577$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$578$	9.98725	+	21.8690i	0.415415	+	0.909632i
$579$		0			0
$580$	−36.1261	+	31.3035i	−1.50006	+	1.29981i
$581$	−6.36253	+	1.86821i	−0.263962	+	0.0775062i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.550083	+	3.82591i	0.0227043	+	0.157912i	0.998020	−	0.0629052i	$-0.0200366\pi$
$587$	0.550083	+	3.82591i	0.0227043	+	0.157912i	−0.975315	+	0.220817i	$0.929127\pi$
$588$	−33.8324	+	21.7427i	−1.39522	+	0.896656i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$593$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$594$		0			0
$595$		0			0
$596$	−30.1091	−	4.32904i	−1.23332	−	0.177324i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	5.89466	−	40.9983i	0.240649	−	1.67375i
$601$	18.2053	+	39.8640i	0.742610	+	1.62609i	0.779214	+	0.626758i	$0.215619\pi$
$601$	18.2053	+	39.8640i	0.742610	+	1.62609i	−0.0366042	+	0.999330i	$0.511654\pi$
$602$	3.29254	+	0.966776i	0.134194	+	0.0394029i
$603$	−43.9582	+	38.0900i	−1.79012	+	1.55114i
$604$		0			0
$605$	−13.2980	+	20.6921i	−0.540641	+	0.841254i
$606$	26.8652	−	58.8266i	1.09132	−	2.38967i
$607$	−26.4066	+	30.4749i	−1.07181	+	1.23694i	−0.101563	+	0.994829i	$0.532384\pi$
$607$	−26.4066	+	30.4749i	−1.07181	+	1.23694i	−0.970249	+	0.242108i	$0.922161\pi$
$608$		0			0
$609$	11.3577	−	1.63300i	0.460239	−	0.0661723i
$610$	−6.80765	−	47.3483i	−0.275634	−	1.91708i
$611$		0			0
$612$		0			0
$613$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$613$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$614$	18.1277	+	11.6500i	0.731576	+	0.470155i
$615$	23.0873	+	78.6280i	0.930968	+	3.17059i
$616$		0			0
$617$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$617$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$618$	75.2534	−	34.3671i	3.02713	−	1.38245i
$619$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$619$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$620$		0			0
$621$	−30.3611	−	19.7349i	−1.21835	−	0.791935i
$622$		0			0
$623$	−0.442589	+	3.07828i	−0.0177320	+	0.123329i
$624$		0			0
$625$	−23.9873	−	7.04331i	−0.959493	−	0.281733i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−4.23391	+	4.88620i	−0.168683	+	0.194671i
$631$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$631$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	31.0488	+	26.9040i	1.23214	+	1.06765i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	7.12733	−	24.2735i	0.281733	−	0.959493i
$641$	−37.5531	+	17.1499i	−1.48326	+	0.677382i	−0.982167	−	0.188011i	$-0.939796\pi$
$641$	−37.5531	+	17.1499i	−1.48326	+	0.677382i	−0.501093	+	0.865393i	$0.667069\pi$
$642$	31.4938	+	4.52812i	1.24296	+	0.178711i
$643$			31.0774i			1.22557i	0.790249	+	0.612786i	$0.209951\pi$
$643$			31.0774i			1.22557i	−0.790249	+	0.612786i	$0.790049\pi$
$644$	3.20548	−	1.44387i	0.126314	−	0.0568963i
$645$	−43.3551			−1.70711
$646$		0			0
$647$	14.7515	+	32.3013i	0.579942	+	1.26990i	0.941332	+	0.337481i	$0.109575\pi$
$647$	14.7515	+	32.3013i	0.579942	+	1.26990i	−0.361390	+	0.932415i	$0.617698\pi$
$648$	14.6013	+	4.28734i	0.573595	+	0.168423i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−15.3278	+	33.5632i	−0.600283	+	1.31444i
$653$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$653$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$654$	39.7402	+	61.8370i	1.55397	+	2.41802i
$655$		0			0
$656$	7.12306	+	49.5420i	0.278109	+	1.93429i
$657$		0			0
$658$	0.269083	+	0.233162i	0.0104899	+	0.00908958i
$659$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$659$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$660$		0			0
$661$	0.612388	+	2.08560i	0.0238191	+	0.0811205i	0.970545	−	0.240920i	$-0.0774493\pi$
$661$	0.612388	+	2.08560i	0.0238191	+	0.0811205i	−0.946726	+	0.322041i	$0.895631\pi$
$662$		0			0
$663$		0			0
$664$	46.5464	−	21.2570i	1.80635	−	0.824932i
$665$		0			0
$666$		0			0
$667$	51.2610	+	0.265626i	1.98483	+	0.0102851i
$668$	51.4811			1.99186
$669$	12.2487	−	85.1916i	0.473562	−	3.29370i
$670$	13.6982	+	29.9949i	0.529208	+	1.15880i
$671$		0			0
$672$	−4.58943	+	3.97677i	−0.177041	+	0.153407i
$673$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$673$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$674$		0			0
$675$	15.6831	−	34.3413i	0.603644	−	1.32180i
$676$	−17.0264	+	19.6495i	−0.654861	+	0.755750i
$677$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$677$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	57.8138	+	50.0959i	2.21543	+	1.91968i
$682$		0			0
$683$	43.9706	+	28.2582i	1.68249	+	1.08127i	0.843732	+	0.536765i	$0.180354\pi$
$683$	43.9706	+	28.2582i	1.68249	+	1.08127i	0.838757	+	0.544505i	$0.183283\pi$
$684$		0			0
$685$		0			0
$686$	2.02491	−	6.89620i	0.0773113	−	0.263298i
$687$	−26.7449	+	12.2140i	−1.02038	+	0.465993i
$688$	−26.2107	−	3.76853i	−0.999273	−	0.143674i
$689$		0			0
$690$	−33.7190	+	28.9132i	−1.28366	+	1.10071i
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	−21.5770	−	6.33557i	−0.819050	−	0.240495i
$695$		0			0
$696$	−84.9590	+	24.9462i	−3.22036	+	0.945583i
$697$		0			0
$698$	21.3724	−	46.7991i	0.808959	−	1.77137i
$699$		0			0
$700$	1.98162	+	3.08347i	0.0748984	+	0.116544i
$701$	7.85102	−	1.12881i	0.296529	−	0.0426344i	0.00755520	−	0.999971i	$-0.497595\pi$
$701$	7.85102	−	1.12881i	0.296529	−	0.0426344i	0.288974	+	0.957337i	$0.406686\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−4.09190	−	1.86871i	−0.154110	−	0.0703796i
$706$		0			0
$707$	1.61231	+	5.49103i	0.0606372	+	0.206511i
$708$		0			0
$709$	−7.55968	+	25.7459i	−0.283910	+	0.966908i	0.686839	+	0.726810i	$0.258998\pi$
$709$	−7.55968	+	25.7459i	−0.283910	+	0.966908i	−0.970749	+	0.240098i	$0.922820\pi$
$710$		0			0
$711$		0			0
$712$		−	23.9985i		−	0.899380i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$719$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$720$	26.9733	−	41.9713i	1.00524	−	1.56418i
$721$	−3.04121	+	6.65932i	−0.113261	+	0.248006i
$722$	−17.5961	+	20.3070i	−0.654861	+	0.755750i
$723$	−41.8418	−	65.1071i	−1.55611	−	2.42136i
$724$	−18.4651	+	2.65488i	−0.686250	+	0.0986679i
$725$	7.60587	+	52.9000i	0.282475	+	1.96466i
$726$	−38.3291	+	24.6326i	−1.42253	+	0.914201i
$727$	29.0290	+	25.1538i	1.07663	+	0.932901i	0.997950	−	0.0639991i	$-0.0203855\pi$
$727$	29.0290	+	25.1538i	1.07663	+	0.932901i	0.0786754	+	0.996900i	$0.474931\pi$
$728$		0			0
$729$	−30.5642	−	19.6424i	−1.13201	−	0.727496i
$730$		0			0
$731$		0			0
$732$	24.9636	−	85.0184i	0.922683	−	3.14237i
$733$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$733$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$734$	−46.7813	−	6.72613i	−1.72673	−	0.248266i
$735$			44.9635i			1.65851i
$736$	−22.8983	+	14.5488i	−0.844044	+	0.536274i
$737$		0			0
$738$	−14.0476	+	97.7032i	−0.517100	+	3.59651i
$739$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$739$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.81499	−	9.04830i	0.213331	−	0.331950i	−0.718052	−	0.695989i	$-0.754966\pi$
$743$	5.81499	−	9.04830i	0.213331	−	0.331950i	0.931384	+	0.364039i	$0.118603\pi$
$744$		0			0
$745$	−22.2713	+	25.7024i	−0.815956	+	0.941664i
$746$		0			0
$747$	99.8878	−	14.3617i	3.65470	−	0.525467i
$748$		0			0
$749$	−2.36864	+	1.52223i	−0.0865481	+	0.0556211i
$750$	−34.9979	−	30.3258i	−1.27794	−	1.10734i
$751$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$751$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$752$	−2.31136	−	1.48542i	−0.0842866	−	0.0541677i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−5.03488	+	2.29935i	−0.183117	+	0.0836266i
$757$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$757$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.27563	+	15.8273i	−0.0824914	+	0.573741i	0.906094	+	0.423077i	$0.139050\pi$
$761$	−2.27563	+	15.8273i	−0.0824914	+	0.573741i	−0.988585	+	0.150663i	$0.951859\pi$
$762$	31.6136	+	69.2240i	1.14524	+	2.50772i
$763$	−6.24118	−	1.83258i	−0.225946	−	0.0663437i
$764$		0			0
$765$		0			0
$766$	−29.4131	+	45.7677i	−1.06274	+	1.65365i
$767$		0			0
$768$	30.6876	−	35.4154i	1.10734	−	1.27794i
$769$	−25.7061	−	39.9995i	−0.926987	−	1.44242i	−0.896580	−	0.442883i	$-0.853956\pi$
$769$	−25.7061	−	39.9995i	−0.926987	−	1.44242i	−0.0304075	−	0.999538i	$-0.509681\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$773$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$774$	−47.5032	−	21.6940i	−1.70747	−	0.779774i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−7.68992	+	26.1895i	−0.275697	+	0.938938i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−80.7067			−2.88422
$784$	−3.90834	+	27.1831i	−0.139583	+	0.970824i
$785$		0			0
$786$		0			0
$787$	−32.9852	+	28.5818i	−1.17579	+	1.01883i	−0.176390	+	0.984320i	$0.556442\pi$
$787$	−32.9852	+	28.5818i	−1.17579	+	1.01883i	−0.999404	+	0.0345107i	$0.989013\pi$
$788$		0			0
$789$	36.3003	−	56.4844i	1.29233	−	2.01090i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$797$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$798$		0			0
$799$		0			0
$800$	−18.5223	−	21.3758i	−0.654861	−	0.755750i
$801$	13.3339	−	45.4109i	0.471129	−	1.60452i
$802$	1.94382	−	0.887712i	0.0686386	−	0.0313462i
$803$		0			0
$804$			61.0809i			2.15416i
$805$	0.579539	−	3.88766i	0.0204261	−	0.137022i
$806$		0			0
$807$	−4.32239	+	30.0629i	−0.152155	+	1.05826i
$808$	−18.3454	−	40.1708i	−0.645388	−	1.41320i
$809$	−9.61552	−	2.82337i	−0.338064	−	0.0992645i	0.108294	−	0.994119i	$-0.465461\pi$
$809$	−9.61552	−	2.82337i	−0.338064	−	0.0992645i	−0.446358	+	0.894854i	$0.647279\pi$
$810$	12.8583	−	11.1418i	0.451795	−	0.391482i
$811$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$811$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$812$	4.23624	−	6.59171i	0.148663	−	0.231324i
$813$		0			0
$814$		0			0
$815$	22.3029	+	34.7040i	0.781236	+	1.21563i
$816$		0			0
$817$		0			0
$818$	−39.3054	+	25.2601i	−1.37428	+	0.883198i
$819$		0			0
$820$	50.9023	+	23.2463i	1.77759	+	0.811796i
$821$	6.54042	+	4.20327i	0.228262	+	0.146695i	0.649773	−	0.760128i	$-0.274864\pi$
$821$	6.54042	+	4.20327i	0.228262	+	0.146695i	−0.421511	+	0.906823i	$0.638500\pi$
$822$		0			0
$823$	−24.7868	−	28.6055i	−0.864014	−	0.997125i	−0.999979	−	0.00641129i	$-0.997959\pi$
$823$	−24.7868	−	28.6055i	−0.864014	−	0.997125i	0.135966	−	0.990714i	$-0.456586\pi$
$824$	15.9160	−	54.2049i	0.554460	−	1.88832i
$825$		0			0
$826$		0			0
$827$		−	47.4342i		−	1.64945i	−0.565536	−	0.824724i	$-0.691331\pi$
$827$		−	47.4342i		−	1.64945i	0.565536	−	0.824724i	$-0.308669\pi$
$828$	−51.4127	+	14.8072i	−1.78672	+	0.514586i
$829$	39.8567			1.38428			0.692141	−	0.721762i	$-0.256668\pi$
$829$	39.8567			1.38428			0.692141	+	0.721762i	$0.256668\pi$
$830$	8.14189	−	56.6281i	0.282609	−	1.96559i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	31.1180	−	48.4205i	1.07688	−	1.67566i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$839$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$840$	0.966243	+	6.72037i	0.0333386	+	0.231875i
$841$	71.7171	−	46.0898i	2.47300	−	1.58930i
$842$	31.5664	+	27.3524i	1.08785	+	0.942627i
$843$	−71.0159	−	32.4319i	−2.44592	−	1.11701i
$844$		0			0
$845$	8.18965	+	27.8914i	0.281733	+	0.959493i
$846$	−3.54834	−	4.09500i	−0.121994	−	0.140789i
$847$	1.13591	−	3.86854i	0.0390302	−	0.132925i
$848$		0			0
$849$	91.7434	+	13.1907i	3.14862	+	0.452704i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$853$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$854$	3.25729	+	7.13248i	0.111462	+	0.244068i
$855$		0			0
$856$	16.4203	−	14.2283i	0.561236	−	0.486313i
$857$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$857$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$858$		0			0
$859$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$859$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$860$	−19.3877	+	22.3746i	−0.661114	+	0.762966i
$861$	−7.26226	−	11.3003i	−0.247497	−	0.385113i
$862$		0			0
$863$	−7.67179	−	53.3585i	−0.261151	−	1.81634i	−0.524238	−	0.851572i	$-0.675650\pi$
$863$	−7.67179	−	53.3585i	−0.261151	−	1.81634i	0.263088	−	0.964772i	$-0.415259\pi$
$864$	35.9321	−	23.0922i	1.22244	−	0.785612i
$865$		0			0
$866$		0			0
$867$	41.8861	+	26.9185i	1.42253	+	0.914201i
$868$		0			0
$869$		0			0
$870$	−27.8907	+	94.9870i	−0.945583	+	3.22036i
$871$		0			0
$872$	49.6838	+	7.14345i	1.68250	+	0.241908i
$873$		0			0
$874$		0			0
$875$	4.09796			0.138536
$876$		0			0
$877$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$877$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	7.15577	−	11.1346i	0.241084	−	0.375134i	−0.699535	−	0.714598i	$-0.746609\pi$
$881$	7.15577	−	11.1346i	0.241084	−	0.375134i	0.940619	+	0.339464i	$0.110246\pi$
$882$	−22.4988	+	49.2655i	−0.757574	+	1.65886i
$883$	−19.4886	+	22.4910i	−0.655844	+	0.756884i	−0.982092	−	0.188400i	$-0.939670\pi$
$883$	−19.4886	+	22.4910i	−0.655844	+	0.756884i	0.326249	+	0.945284i	$0.394215\pi$
$884$		0			0
$885$		0			0
$886$	−7.38198	−	51.3428i	−0.248002	−	1.72489i
$887$	−29.9634	+	19.2563i	−1.00607	+	0.646564i	−0.936374	−	0.351005i	$-0.885840\pi$
$887$	−29.9634	+	19.2563i	−1.00607	+	0.646564i	−0.0696988	+	0.997568i	$0.522204\pi$
$888$		0			0
$889$	−6.12577	−	2.79755i	−0.205452	−	0.0938267i
$890$	−22.5717	−	14.5060i	−0.756607	−	0.486242i
$891$		0			0
$892$	−38.4880	−	44.4175i	−1.28867	−	1.48721i
$893$		0			0
$894$	−57.3041	+	26.1699i	−1.91653	+	0.875252i
$895$		0			0
$896$			4.14684i			0.138536i
$897$		0			0
$898$	38.5464			1.28631
$899$		0			0
$900$	−23.1720	−	50.7395i	−0.772399	−	1.69132i
$901$		0			0
$902$		0			0
$903$	6.81882	−	2.00219i	0.226916	−	0.0666286i
$904$		0			0
$905$	−8.66427	+	18.9721i	−0.288010	+	0.630654i
$906$		0			0
$907$	2.35248	+	3.66053i	0.0781129	+	0.121546i	0.878112	−	0.478455i	$-0.158803\pi$
$907$	2.35248	+	3.66053i	0.0781129	+	0.121546i	−0.799999	+	0.600001i	$0.795167\pi$
$908$	51.7067	−	7.43430i	1.71595	−	0.246716i
$909$	−12.3945	−	86.2058i	−0.411101	−	2.85927i
$910$		0			0
$911$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$911$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−64.8746	−	74.8693i	−2.14469	−	2.47510i
$916$	−5.65651	+	19.2643i	−0.186896	+	0.636510i
$917$		0			0
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	−0.157171	+	30.3311i	−0.00518177	+	0.999987i
$921$	44.6268			1.47050
$922$	2.98483	−	20.7600i	0.0983002	−	0.683693i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	44.6876	−	13.1215i	1.46853	−	0.431198i
$927$	60.2339	−	93.7258i	1.97834	−	3.07836i
$928$	−25.1180	+	55.0009i	−0.824540	+	1.80549i
$929$	8.90806	−	10.2804i	0.292264	−	0.337290i	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	8.90806	−	10.2804i	0.292264	−	0.337290i	0.882825	+	0.469703i	$0.155639\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	30.4183	+	26.3576i	0.995318	+	0.862448i
$935$		0			0
$936$		0			0
$937$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$937$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$938$	−3.53963	−	4.08495i	−0.115573	−	0.133378i
$939$		0			0
$940$	−2.79422	+	1.27608i	−0.0911375	+	0.0416211i
$941$	−54.1854	−	7.79068i	−1.76639	−	0.253969i	−0.818944	−	0.573874i	$-0.805440\pi$
$941$	−54.1854	−	7.79068i	−1.76639	−	0.253969i	−0.947450	+	0.319905i	$0.896349\pi$
$942$		0			0
$943$	−24.6457	−	54.7151i	−0.802574	−	1.78177i
$944$		0			0
$945$	−0.880701	+	6.12541i	−0.0286492	+	0.199260i
$946$		0			0
$947$	17.3137	+	5.08375i	0.562619	+	0.165200i	0.550661	−	0.834729i	$-0.314376\pi$
$947$	17.3137	+	5.08375i	0.562619	+	0.165200i	0.0119574	+	0.999929i	$0.496194\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$953$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−14.7607	−	50.2702i	−0.476398	−	1.62246i
$961$	−20.3007	−	23.4282i	−0.654861	−	0.755750i
$962$		0			0
$963$	38.9767	−	17.8001i	1.25601	−	0.573599i
$964$	−52.3112	−	7.52121i	−1.68483	−	0.242242i
$965$		0			0
$966$	3.96804	−	6.10460i	0.127670	−	0.196412i
$967$	−47.3329			−1.52212			−0.761061	−	0.648680i	$-0.775321\pi$
$967$	−47.3329			−1.52212			−0.761061	+	0.648680i	$0.775321\pi$
$968$	−4.42780	+	30.7960i	−0.142315	+	0.989821i
$969$		0			0
$970$		0			0
$971$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$971$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$972$	−13.2292	+	3.88443i	−0.424325	+	0.124593i
$973$		0			0
$974$	−11.8406	+	25.9272i	−0.379396	+	0.830761i
$975$		0			0
$976$	−32.7127	−	50.9019i	−1.04711	−	1.62933i
$977$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$977$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$978$	10.8749	+	75.6368i	0.347742	+	2.41860i
$979$		0			0
$980$	23.2046	+	20.1069i	0.741245	+	0.642292i
$981$	90.0448	+	41.1221i	2.87491	+	1.31293i
$982$		0			0
$983$	9.53500	+	32.4732i	0.304119	+	1.03574i	0.959797	+	0.280695i	$0.0905648\pi$
$983$	9.53500	+	32.4732i	0.304119	+	1.03574i	−0.655678	+	0.755041i	$0.727617\pi$
$984$	67.8804	+	78.3381i	2.16395	+	2.49733i
$985$		0			0
$986$		0			0
$987$	0.729867	+	0.104939i	0.0232319	+	0.00334025i
$988$		0			0
$989$	31.4485	−	4.35540i	1.00000	−	0.138494i
$990$		0			0
$991$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$991$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	57.2938	−	89.1509i	1.81542	−	2.82485i
$997$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$997$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.a.199.3	yes	40
4.3	odd	2	inner	460.2.o.a.199.2	✓	40
5.4	even	2	inner	460.2.o.a.199.2	✓	40
20.19	odd	2	CM	460.2.o.a.199.3	yes	40
23.20	odd	22	inner	460.2.o.a.319.3	yes	40
92.43	even	22	inner	460.2.o.a.319.2	yes	40
115.89	odd	22	inner	460.2.o.a.319.2	yes	40
460.319	even	22	inner	460.2.o.a.319.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.a.199.2	✓	40	4.3	odd	2	inner
460.2.o.a.199.2	✓	40	5.4	even	2	inner
460.2.o.a.199.3	yes	40	1.1	even	1	trivial
460.2.o.a.199.3	yes	40	20.19	odd	2	CM
460.2.o.a.319.2	yes	40	92.43	even	22	inner
460.2.o.a.319.2	yes	40	115.89	odd	22	inner
460.2.o.a.319.3	yes	40	23.20	odd	22	inner
460.2.o.a.319.3	yes	40	460.319	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.201264 - 1.39982i) q^{2} +(-1.21668 - 2.66415i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(-1.68991 + 1.46431i) q^{5} +(-3.97421 + 1.16693i) q^{6} +(0.198162 - 0.308347i) q^{7} +(-1.17497 + 2.57283i) q^{8} +(-3.65283 + 4.21559i) q^{9} +O(q^{10})\)	\(q+(0.201264 - 1.39982i) q^{2} +(-1.21668 - 2.66415i) q^{3} +(-1.91899 - 0.563465i) q^{4} +(-1.68991 + 1.46431i) q^{5} +(-3.97421 + 1.16693i) q^{6} +(0.198162 - 0.308347i) q^{7} +(-1.17497 + 2.57283i) q^{8} +(-3.65283 + 4.21559i) q^{9} +(1.70966 + 2.66028i) q^{10} +(0.833631 + 5.79803i) q^{12} +(-0.391747 - 0.339451i) q^{14} +(5.95723 + 2.72058i) q^{15} +(3.36501 + 2.16256i) q^{16} +(5.16588 + 5.96175i) q^{18} +(4.06800 - 1.85779i) q^{20} +(-1.06258 - 0.152776i) q^{21} +(-4.59450 - 1.37497i) q^{23} +8.28397 q^{24} +(0.711574 - 4.94911i) q^{25} +(7.24474 + 2.12725i) q^{27} +(-0.554014 + 0.480056i) q^{28} +(-10.2558 + 3.01138i) q^{29} +(5.00729 - 7.79149i) q^{30} +(3.70445 - 4.27517i) q^{32} +(0.116640 + 0.811249i) q^{35} +(9.38507 - 6.03142i) q^{36} +(-1.78183 - 6.06837i) q^{40} +(8.19418 + 9.45659i) q^{41} +(-0.427719 + 1.45668i) q^{42} +(-6.02181 + 2.75007i) q^{43} -12.4728i q^{45} +(-2.84941 + 6.15474i) q^{46} -0.686879 q^{47} +(1.66726 - 11.5961i) q^{48} +(2.85210 + 6.24522i) q^{49} +(-6.78464 - 1.99215i) q^{50} +(4.43586 - 9.71318i) q^{54} +(0.560488 + 0.872136i) q^{56} +(2.15126 + 14.9624i) q^{58} +(-9.89889 - 8.57744i) q^{60} +(-13.7598 - 6.28390i) q^{61} +(0.576010 + 1.96171i) q^{63} +(-5.23889 - 6.04600i) q^{64} +(10.3214 + 1.48399i) q^{67} +(1.92691 + 13.9134i) q^{69} +1.15908 q^{70} +(-6.55402 - 14.3513i) q^{72} +(-14.0509 + 4.12573i) q^{75} +(-8.85323 + 1.27290i) q^{80} +(-0.765695 - 5.32553i) q^{81} +(14.8867 - 9.56710i) q^{82} +(-13.6727 - 11.8474i) q^{83} +(1.95300 + 0.891905i) q^{84} +(2.63763 + 8.98294i) q^{86} +(20.5008 + 23.6592i) q^{87} +(-7.71799 + 3.52469i) q^{89} +(-17.4597 - 2.51033i) q^{90} +(8.04204 + 5.22739i) q^{92} +(-0.138244 + 0.961507i) q^{94} +(-15.8968 - 4.66773i) q^{96} +(9.31620 - 2.73548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9	\( 40 q - 8 q^{4} - 8 q^{6} + 4 q^{9} - 16 q^{16} - 16 q^{24} + 20 q^{25} + 24 q^{29} + 8 q^{36} + 48 q^{41} - 4 q^{46} + 100 q^{49} - 276 q^{54} - 264 q^{56} - 32 q^{64} - 4 q^{69} - 40 q^{70} + 20 q^{81} + 352 q^{84} + 396 q^{86} - 56 q^{94} - 32 q^{96}+O(q^{100}) \) 40 * q - 8 * q^4 - 8 * q^6 + 4 * q^9 - 16 * q^16 - 16 * q^24 + 20 * q^25 + 24 * q^29 + 8 * q^36 + 48 * q^41 - 4 * q^46 + 100 * q^49 - 276 * q^54 - 264 * q^56 - 32 * q^64 - 4 * q^69 - 40 * q^70 + 20 * q^81 + 352 * q^84 + 396 * q^86 - 56 * q^94 - 32 * q^96

Introduction

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