LMFDB - Embedded newform 360.2.bi.b.169.4

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			169.4
Character	$\chi$	$=$	360.169
Dual form			360.2.bi.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27766 - 1.16944i) q^{3} +(0.307984 - 2.21476i) q^{5} +(-3.28422 - 1.89614i) q^{7} +(0.264813 + 2.98829i) q^{9} +O(q^{10})$	\(q+(-1.27766 - 1.16944i) q^{3} +(0.307984 - 2.21476i) q^{5} +(-3.28422 - 1.89614i) q^{7} +(0.264813 + 2.98829i) q^{9} +(-1.86561 + 3.23134i) q^{11} +(-1.09954 + 0.634820i) q^{13} +(-2.98353 + 2.46953i) q^{15} -0.973091i q^{17} +2.74455 q^{19} +(1.97867 + 6.26332i) q^{21} +(-5.83699 + 3.36999i) q^{23} +(-4.81029 - 1.36422i) q^{25} +(3.15629 - 4.12769i) q^{27} +(-1.99547 + 3.45625i) q^{29} +(-5.36108 - 9.28566i) q^{31} +(6.16247 - 1.94681i) q^{33} +(-5.21098 + 6.68976i) q^{35} -7.59511i q^{37} +(2.14722 + 0.474767i) q^{39} +(-2.92955 - 5.07413i) q^{41} +(4.95478 + 2.86065i) q^{43} +(6.69989 + 0.333848i) q^{45} +(-4.18344 - 2.41531i) q^{47} +(3.69072 + 6.39251i) q^{49} +(-1.13797 + 1.24328i) q^{51} +10.1260i q^{53} +(6.58205 + 5.12708i) q^{55} +(-3.50659 - 3.20959i) q^{57} +(-3.98987 - 6.91066i) q^{59} +(4.29821 - 7.44471i) q^{61} +(4.79652 - 10.3163i) q^{63} +(1.06733 + 2.63073i) q^{65} +(0.993211 - 0.573431i) q^{67} +(11.3987 + 2.52033i) q^{69} +9.20350 q^{71} +0.990931i q^{73} +(4.55053 + 7.36836i) q^{75} +(12.2542 - 7.07494i) q^{77} +(7.83472 - 13.5701i) q^{79} +(-8.85975 + 1.58267i) q^{81} +(1.08329 + 0.625439i) q^{83} +(-2.15516 - 0.299696i) q^{85} +(6.59140 - 2.08232i) q^{87} -8.97031 q^{89} +4.81484 q^{91} +(-4.00942 + 18.1334i) q^{93} +(0.845275 - 6.07851i) q^{95} +(-5.56207 - 3.21126i) q^{97} +(-10.1502 - 4.71929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.27766	−	1.16944i	−0.737655	−	0.675177i
$3$	−1.27766	−	1.16944i	−0.737655	−	0.675177i
$4$		0			0
$5$	0.307984	−	2.21476i	0.137734	−	0.990469i
$5$	0.307984	−	2.21476i	0.137734	−	0.990469i
$6$		0			0
$7$	−3.28422	−	1.89614i	−1.24132	−	0.716675i	−0.271955	−	0.962310i	$-0.587670\pi$
$7$	−3.28422	−	1.89614i	−1.24132	−	0.716675i	−0.969362	+	0.245635i	$0.921003\pi$
$8$		0			0
$9$	0.264813	+	2.98829i	0.0882709	+	0.996097i
$10$		0			0
$11$	−1.86561	+	3.23134i	−0.562504	+	0.974285i	0.434773	+	0.900540i	$0.356828\pi$
$11$	−1.86561	+	3.23134i	−0.562504	+	0.974285i	−0.997277	+	0.0737451i	$0.976505\pi$
$12$		0			0
$13$	−1.09954	+	0.634820i	−0.304958	+	0.176067i	−0.644668	−	0.764463i	$-0.723004\pi$
$13$	−1.09954	+	0.634820i	−0.304958	+	0.176067i	0.339710	+	0.940530i	$0.389671\pi$
$14$		0			0
$15$	−2.98353	+	2.46953i	−0.770343	+	0.637630i
$16$		0			0
$17$		−	0.973091i		−	0.236009i	−0.993013	−	0.118005i	$-0.962350\pi$
$17$		−	0.973091i		−	0.236009i	0.993013	−	0.118005i	$-0.0376498\pi$
$18$		0			0
$19$	2.74455			0.629642			0.314821	−	0.949151i	$-0.398055\pi$
$19$	2.74455			0.629642			0.314821	+	0.949151i	$0.398055\pi$
$20$		0			0
$21$	1.97867	+	6.26332i	0.431782	+	1.36677i
$22$		0			0
$23$	−5.83699	+	3.36999i	−1.21710	+	0.702691i	−0.964296	−	0.264828i	$-0.914685\pi$
$23$	−5.83699	+	3.36999i	−1.21710	+	0.702691i	−0.252800	+	0.967518i	$0.581352\pi$
$24$		0			0
$25$	−4.81029	−	1.36422i	−0.962058	−	0.272843i
$26$		0			0
$27$	3.15629	−	4.12769i	0.607428	−	0.794374i
$28$		0			0
$29$	−1.99547	+	3.45625i	−0.370549	+	0.641809i	−0.989650	−	0.143502i	$-0.954164\pi$
$29$	−1.99547	+	3.45625i	−0.370549	+	0.641809i	0.619101	+	0.785311i	$0.287497\pi$
$30$		0			0
$31$	−5.36108	−	9.28566i	−0.962878	−	1.66775i	−0.715211	−	0.698909i	$-0.753669\pi$
$31$	−5.36108	−	9.28566i	−0.962878	−	1.66775i	−0.247668	−	0.968845i	$-0.579664\pi$
$32$		0			0
$33$	6.16247	−	1.94681i	1.07275	−	0.338897i
$34$		0			0
$35$	−5.21098	+	6.68976i	−0.880816	+	1.13078i
$36$		0			0
$37$		−	7.59511i		−	1.24863i	−0.781173	−	0.624314i	$-0.785379\pi$
$37$		−	7.59511i		−	1.24863i	0.781173	−	0.624314i	$-0.214621\pi$
$38$		0			0
$39$	2.14722	+	0.474767i	0.343830	+	0.0760235i
$40$		0			0
$41$	−2.92955	−	5.07413i	−0.457519	−	0.792446i	0.541310	−	0.840823i	$-0.317928\pi$
$41$	−2.92955	−	5.07413i	−0.457519	−	0.792446i	−0.998829	+	0.0483769i	$0.984595\pi$
$42$		0			0
$43$	4.95478	+	2.86065i	0.755597	+	0.436244i	0.827713	−	0.561152i	$-0.189642\pi$
$43$	4.95478	+	2.86065i	0.755597	+	0.436244i	−0.0721154	+	0.997396i	$0.522975\pi$
$44$		0			0
$45$	6.69989	+	0.333848i	0.998761	+	0.0497672i
$46$		0			0
$47$	−4.18344	−	2.41531i	−0.610217	−	0.352309i	0.162833	−	0.986654i	$-0.447937\pi$
$47$	−4.18344	−	2.41531i	−0.610217	−	0.352309i	−0.773051	+	0.634344i	$0.781270\pi$
$48$		0			0
$49$	3.69072	+	6.39251i	0.527245	+	0.913215i
$50$		0			0
$51$	−1.13797	+	1.24328i	−0.159348	+	0.174094i
$52$		0			0
$53$			10.1260i			1.39091i	0.718570	+	0.695455i	$0.244797\pi$
$53$			10.1260i			1.39091i	−0.718570	+	0.695455i	$0.755203\pi$
$54$		0			0
$55$	6.58205	+	5.12708i	0.887523	+	0.691335i
$56$		0			0
$57$	−3.50659	−	3.20959i	−0.464459	−	0.425120i
$58$		0			0
$59$	−3.98987	−	6.91066i	−0.519437	−	0.899691i	−0.999745	−	0.0225909i	$-0.992808\pi$
$59$	−3.98987	−	6.91066i	−0.519437	−	0.899691i	0.480308	−	0.877100i	$-0.340525\pi$
$60$		0			0
$61$	4.29821	−	7.44471i	0.550329	−	0.953198i	−0.447922	−	0.894073i	$-0.647836\pi$
$61$	4.29821	−	7.44471i	0.550329	−	0.953198i	0.998251	−	0.0591248i	$-0.0188310\pi$
$62$		0			0
$63$	4.79652	−	10.3163i	0.604305	−	1.29973i
$64$		0			0
$65$	1.06733	+	2.63073i	0.132386	+	0.326302i
$66$		0			0
$67$	0.993211	−	0.573431i	0.121340	−	0.0700557i	−0.438102	−	0.898926i	$-0.644349\pi$
$67$	0.993211	−	0.573431i	0.121340	−	0.0700557i	0.559442	+	0.828870i	$0.311016\pi$
$68$		0			0
$69$	11.3987	+	2.52033i	1.37224	+	0.303412i
$70$		0			0
$71$	9.20350			1.09225			0.546127	−	0.837702i	$-0.316101\pi$
$71$	9.20350			1.09225			0.546127	+	0.837702i	$0.316101\pi$
$72$		0			0
$73$			0.990931i			0.115980i	0.998317	+	0.0579899i	$0.0184691\pi$
$73$			0.990931i			0.115980i	−0.998317	+	0.0579899i	$0.981531\pi$
$74$		0			0
$75$	4.55053	+	7.36836i	0.525450	+	0.850825i
$76$		0			0
$77$	12.2542	−	7.07494i	1.39649	−	0.806264i
$78$		0			0
$79$	7.83472	−	13.5701i	0.881474	−	1.52676i	0.0317725	−	0.999495i	$-0.489885\pi$
$79$	7.83472	−	13.5701i	0.881474	−	1.52676i	0.849702	−	0.527263i	$-0.176782\pi$
$80$		0			0
$81$	−8.85975	+	1.58267i	−0.984417	+	0.175853i
$82$		0			0
$83$	1.08329	+	0.625439i	0.118907	+	0.0686509i	0.558274	−	0.829657i	$-0.311464\pi$
$83$	1.08329	+	0.625439i	0.118907	+	0.0686509i	−0.439367	+	0.898308i	$0.644797\pi$
$84$		0			0
$85$	−2.15516	−	0.299696i	−0.233760	−	0.0325066i
$86$		0			0
$87$	6.59140	−	2.08232i	0.706672	−	0.223248i
$88$		0			0
$89$	−8.97031			−0.950851			−0.475425	−	0.879756i	$-0.657706\pi$
$89$	−8.97031			−0.950851			−0.475425	+	0.879756i	$0.657706\pi$
$90$		0			0
$91$	4.81484			0.504732
$92$		0			0
$93$	−4.00942	+	18.1334i	−0.415758	+	1.88034i
$94$		0			0
$95$	0.845275	−	6.07851i	0.0867234	−	0.623641i
$96$		0			0
$97$	−5.56207	−	3.21126i	−0.564743	−	0.326054i	0.190304	−	0.981725i	$-0.439053\pi$
$97$	−5.56207	−	3.21126i	−0.564743	−	0.326054i	−0.755047	+	0.655671i	$0.772386\pi$
$98$		0			0
$99$	−10.1502	−	4.71929i	−1.02013	−	0.474307i
$100$		0			0
$101$	4.57733	−	7.92817i	0.455462	−	0.788883i	−0.543253	−	0.839569i	$-0.682808\pi$
$101$	4.57733	−	7.92817i	0.455462	−	0.788883i	0.998715	+	0.0506864i	$0.0161409\pi$
$102$		0			0
$103$	−4.09661	+	2.36518i	−0.403651	+	0.233048i	−0.688058	−	0.725656i	$-0.741537\pi$
$103$	−4.09661	+	2.36518i	−0.403651	+	0.233048i	0.284407	+	0.958704i	$0.408203\pi$
$104$		0			0
$105$	14.4811	−	2.45328i	1.41321	−	0.239415i
$106$		0			0
$107$			9.92233i			0.959228i	0.877480	+	0.479614i	$0.159223\pi$
$107$			9.92233i			0.959228i	−0.877480	+	0.479614i	$0.840777\pi$
$108$		0			0
$109$	−16.8233			−1.61138			−0.805688	−	0.592340i	$-0.798204\pi$
$109$	−16.8233			−1.61138			−0.805688	+	0.592340i	$0.798204\pi$
$110$		0			0
$111$	−8.88204	+	9.70394i	−0.843045	+	0.921057i
$112$		0			0
$113$	11.1494	−	6.43709i	1.04884	−	0.605550i	0.126519	−	0.991964i	$-0.459620\pi$
$113$	11.1494	−	6.43709i	1.04884	−	0.605550i	0.922326	+	0.386414i	$0.126286\pi$
$114$		0			0
$115$	5.66600	+	13.9654i	0.528358	+	1.30228i
$116$		0			0
$117$	−2.18820	−	3.11764i	−0.202299	−	0.288226i
$118$		0			0
$119$	−1.84512	+	3.19584i	−0.169142	+	0.292962i
$120$		0			0
$121$	−1.46103	−	2.53058i	−0.132821	−	0.230052i
$122$		0			0
$123$	−2.19094	+	9.90893i	−0.197550	+	0.893458i
$124$		0			0
$125$	−4.50290	+	10.2335i	−0.402752	+	0.915309i
$126$		0			0
$127$		−	7.91379i		−	0.702235i	−0.936331	−	0.351118i	$-0.885802\pi$
$127$		−	7.91379i		−	0.702235i	0.936331	−	0.351118i	$-0.114198\pi$
$128$		0			0
$129$	−2.98515	−	9.44925i	−0.262828	−	0.831960i
$130$		0			0
$131$	10.7079	+	18.5466i	0.935554	+	1.62043i	0.773643	+	0.633622i	$0.218432\pi$
$131$	10.7079	+	18.5466i	0.935554	+	1.62043i	0.161911	+	0.986805i	$0.448234\pi$
$132$		0			0
$133$	−9.01369	−	5.20405i	−0.781586	−	0.451249i
$134$		0			0
$135$	−8.16974	−	8.26168i	−0.703140	−	0.711052i
$136$		0			0
$137$	−14.2066	−	8.20220i	−1.21375	−	0.700761i	−0.250179	−	0.968200i	$-0.580489\pi$
$137$	−14.2066	−	8.20220i	−1.21375	−	0.700761i	−0.963575	+	0.267439i	$0.913823\pi$
$138$		0			0
$139$	2.66492	+	4.61578i	0.226036	+	0.391505i	0.956630	−	0.291307i	$-0.0940901\pi$
$139$	2.66492	+	4.61578i	0.226036	+	0.391505i	−0.730594	+	0.682812i	$0.760757\pi$
$140$		0			0
$141$	2.52044	+	7.97823i	0.212259	+	0.671888i
$142$		0			0
$143$		−	4.73732i		−	0.396154i
$144$		0			0
$145$	7.04018	+	5.48394i	0.584655	+	0.455416i
$146$		0			0
$147$	2.76020	−	12.4835i	0.227657	−	1.02962i
$148$		0			0
$149$	−3.81487	−	6.60754i	−0.312526	−	0.541311i	0.666382	−	0.745610i	$-0.267842\pi$
$149$	−3.81487	−	6.60754i	−0.312526	−	0.541311i	−0.978909	+	0.204299i	$0.934509\pi$
$150$		0			0
$151$	−2.99814	+	5.19292i	−0.243985	+	0.422594i	−0.961846	−	0.273592i	$-0.911788\pi$
$151$	−2.99814	+	5.19292i	−0.243985	+	0.422594i	0.717861	+	0.696187i	$0.245121\pi$
$152$		0			0
$153$	2.90788	−	0.257687i	0.235088	−	0.0208328i
$154$		0			0
$155$	−22.2166	+	9.01365i	−1.78448	+	0.723994i
$156$		0			0
$157$	10.2887	−	5.94016i	0.821125	−	0.474077i	−0.0296795	−	0.999559i	$-0.509449\pi$
$157$	10.2887	−	5.94016i	0.821125	−	0.474077i	0.850804	+	0.525483i	$0.176115\pi$
$158$		0			0
$159$	11.8417	−	12.9375i	0.939111	−	1.02601i
$160$		0			0
$161$	25.5599			2.01440
$162$		0			0
$163$		−	8.45806i		−	0.662487i	−0.943545	−	0.331243i	$-0.892532\pi$
$163$		−	8.45806i		−	0.662487i	0.943545	−	0.331243i	$-0.107468\pi$
$164$		0			0
$165$	−2.41378	−	14.2480i	−0.187912	−	1.10920i
$166$		0			0
$167$	−3.48250	+	2.01062i	−0.269484	+	0.155587i	−0.628653	−	0.777686i	$-0.716393\pi$
$167$	−3.48250	+	2.01062i	−0.269484	+	0.155587i	0.359169	+	0.933272i	$0.383060\pi$
$168$		0			0
$169$	−5.69401	+	9.86231i	−0.438001	+	0.758639i
$170$		0			0
$171$	0.726791	+	8.20150i	0.0555791	+	0.627185i
$172$		0			0
$173$	−4.15204	−	2.39718i	−0.315674	−	0.182254i	0.333789	−	0.942648i	$-0.391673\pi$
$173$	−4.15204	−	2.39718i	−0.315674	−	0.182254i	−0.649463	+	0.760393i	$0.725006\pi$
$174$		0			0
$175$	13.2113	+	13.6014i	0.998679	+	1.02817i
$176$		0			0
$177$	−2.98393	+	13.4954i	−0.224286	+	1.01437i
$178$		0			0
$179$	11.2763			0.842828			0.421414	−	0.906868i	$-0.361534\pi$
$179$	11.2763			0.842828			0.421414	+	0.906868i	$0.361534\pi$
$180$		0			0
$181$	−21.2372			−1.57855			−0.789275	−	0.614040i	$-0.789543\pi$
$181$	−21.2372			−1.57855			−0.789275	+	0.614040i	$0.789543\pi$
$182$		0			0
$183$	−14.1978	+	4.48528i	−1.04953	+	0.331562i
$184$		0			0
$185$	−16.8213	−	2.33917i	−1.23673	−	0.171979i
$186$		0			0
$187$	3.14439	+	1.81541i	0.229940	+	0.132756i
$188$		0			0
$189$	−18.1926	+	7.57145i	−1.32332	+	0.550742i
$190$		0			0
$191$	2.33607	−	4.04618i	0.169032	−	0.292772i	−0.769048	−	0.639191i	$-0.779269\pi$
$191$	2.33607	−	4.04618i	0.169032	−	0.292772i	0.938080	+	0.346420i	$0.112603\pi$
$192$		0			0
$193$	−9.20871	+	5.31665i	−0.662857	+	0.382701i	−0.793365	−	0.608746i	$-0.791673\pi$
$193$	−9.20871	+	5.31665i	−0.662857	+	0.382701i	0.130508	+	0.991447i	$0.458339\pi$
$194$		0			0
$195$	1.71280	−	4.60935i	0.122656	−	0.330082i
$196$		0			0
$197$		−	19.4334i		−	1.38457i	−0.721622	−	0.692287i	$-0.756603\pi$
$197$		−	19.4334i		−	1.38457i	0.721622	−	0.692287i	$-0.243397\pi$
$198$		0			0
$199$	0.778360			0.0551765			0.0275882	−	0.999619i	$-0.491217\pi$
$199$	0.778360			0.0551765			0.0275882	+	0.999619i	$0.491217\pi$
$200$		0			0
$201$	−1.93958	−	0.428855i	−0.136807	−	0.0302491i
$202$		0			0
$203$	13.1071	−	7.56738i	0.919937	−	0.531126i
$204$		0			0
$205$	−12.1402	+	4.92549i	−0.847909	+	0.344011i
$206$		0			0
$207$	−11.6162	−	16.5502i	−0.807382	−	1.15032i
$208$		0			0
$209$	−5.12027	+	8.86856i	−0.354176	+	0.613451i
$210$		0			0
$211$	−10.6242	−	18.4017i	−0.731403	−	1.26683i	−0.956284	−	0.292441i	$-0.905533\pi$
$211$	−10.6242	−	18.4017i	−0.731403	−	1.26683i	0.224881	−	0.974386i	$-0.427801\pi$
$212$		0			0
$213$	−11.7589	−	10.7630i	−0.805708	−	0.737466i
$214$		0			0
$215$	7.86162	−	10.0926i	0.536158	−	0.688310i
$216$		0			0
$217$			40.6615i			2.76028i
$218$		0			0
$219$	1.15884	−	1.26607i	0.0783069	−	0.0855531i
$220$		0			0
$221$	0.617738	+	1.06995i	0.0415536	+	0.0719729i
$222$		0			0
$223$	24.0876	+	13.9070i	1.61303	+	0.931281i	0.988664	+	0.150147i	$0.0479746\pi$
$223$	24.0876	+	13.9070i	1.61303	+	0.931281i	0.624363	+	0.781135i	$0.285359\pi$
$224$		0			0
$225$	2.80285	−	14.7358i	0.186857	−	0.982387i
$226$		0			0
$227$	−4.48981	−	2.59220i	−0.297999	−	0.172050i	0.343544	−	0.939136i	$-0.388372\pi$
$227$	−4.48981	−	2.59220i	−0.297999	−	0.172050i	−0.641544	+	0.767086i	$0.721706\pi$
$228$		0			0
$229$	12.5022	+	21.6545i	0.826170	+	1.43097i	0.901022	+	0.433774i	$0.142819\pi$
$229$	12.5022	+	21.6545i	0.826170	+	1.43097i	−0.0748511	+	0.997195i	$0.523848\pi$
$230$		0			0
$231$	−23.9303	−	5.29118i	−1.57450	−	0.348134i
$232$		0			0
$233$		−	1.61032i		−	0.105496i	−0.998608	−	0.0527479i	$-0.983202\pi$
$233$		−	1.61032i		−	0.105496i	0.998608	−	0.0527479i	$-0.0167980\pi$
$234$		0			0
$235$	−6.63775	+	8.52142i	−0.432999	+	0.555876i
$236$		0			0
$237$	−25.8795	+	8.17572i	−1.68106	+	0.531070i
$238$		0			0
$239$	−1.27688	−	2.21162i	−0.0825944	−	0.143058i	0.821769	−	0.569821i	$-0.192987\pi$
$239$	−1.27688	−	2.21162i	−0.0825944	−	0.143058i	−0.904364	+	0.426763i	$0.859654\pi$
$240$		0			0
$241$	8.11330	−	14.0527i	0.522624	−	0.905211i	−0.477030	−	0.878887i	$-0.658287\pi$
$241$	8.11330	−	14.0527i	0.522624	−	0.905211i	0.999653	−	0.0263238i	$-0.00838010\pi$
$242$		0			0
$243$	13.1706	+	8.33884i	0.844892	+	0.534937i
$244$		0			0
$245$	15.2945	−	6.20525i	0.977131	−	0.396439i
$246$		0			0
$247$	−3.01774	+	1.74229i	−0.192014	+	0.110860i
$248$		0			0
$249$	−0.652661	−	2.06594i	−0.0413607	−	0.130924i
$250$		0			0
$251$	15.7288			0.992791			0.496395	−	0.868096i	$-0.334657\pi$
$251$	15.7288			0.992791			0.496395	+	0.868096i	$0.334657\pi$
$252$		0			0
$253$		−	25.1484i		−	1.58106i
$254$		0			0
$255$	2.40308	+	2.90324i	0.150487	+	0.181808i
$256$		0			0
$257$	1.09479	−	0.632077i	0.0682911	−	0.0394279i	−0.465466	−	0.885066i	$-0.654113\pi$
$257$	1.09479	−	0.632077i	0.0682911	−	0.0394279i	0.533757	+	0.845638i	$0.320780\pi$
$258$		0			0
$259$	−14.4014	+	24.9440i	−0.894860	+	1.54994i
$260$		0			0
$261$	−10.8567	−	5.04777i	−0.672012	−	0.312449i
$262$		0			0
$263$	−6.32659	−	3.65266i	−0.390114	−	0.225233i	0.292095	−	0.956389i	$-0.405648\pi$
$263$	−6.32659	−	3.65266i	−0.390114	−	0.225233i	−0.682210	+	0.731157i	$0.738981\pi$
$264$		0			0
$265$	22.4266	+	3.11863i	1.37765	+	0.191576i
$266$		0			0
$267$	11.4610	+	10.4903i	0.701400	+	0.641993i
$268$		0			0
$269$	9.85871			0.601096			0.300548	−	0.953767i	$-0.402830\pi$
$269$	9.85871			0.601096			0.300548	+	0.953767i	$0.402830\pi$
$270$		0			0
$271$	−7.99866			−0.485884			−0.242942	−	0.970041i	$-0.578112\pi$
$271$	−7.99866			−0.485884			−0.242942	+	0.970041i	$0.578112\pi$
$272$		0			0
$273$	−6.15171	−	5.63067i	−0.372318	−	0.340784i
$274$		0			0
$275$	13.3824	−	12.9986i	0.806989	−	0.783844i
$276$		0			0
$277$	14.3068	+	8.26005i	0.859614	+	0.496298i	0.863883	−	0.503693i	$-0.168026\pi$
$277$	14.3068	+	8.26005i	0.859614	+	0.496298i	−0.00426933	+	0.999991i	$0.501359\pi$
$278$		0			0
$279$	26.3286	−	18.4794i	1.57625	−	1.10633i
$280$		0			0
$281$	−11.6622	+	20.1996i	−0.695711	+	1.20501i	0.274230	+	0.961664i	$0.411577\pi$
$281$	−11.6622	+	20.1996i	−0.695711	+	1.20501i	−0.969940	+	0.243342i	$0.921756\pi$
$282$		0			0
$283$	−18.4247	+	10.6375i	−1.09524	+	0.632335i	−0.934966	−	0.354738i	$-0.884570\pi$
$283$	−18.4247	+	10.6375i	−1.09524	+	0.632335i	−0.160271	+	0.987073i	$0.551237\pi$
$284$		0			0
$285$	−8.18843	+	6.77774i	−0.485041	+	0.401479i
$286$		0			0
$287$			22.2194i			1.31157i
$288$		0			0
$289$	16.0531			0.944300
$290$		0			0
$291$	3.35103	+	10.6074i	0.196441	+	0.621817i
$292$		0			0
$293$	2.15049	−	1.24158i	0.125633	−	0.0725342i	−0.435867	−	0.900011i	$-0.643558\pi$
$293$	2.15049	−	1.24158i	0.125633	−	0.0725342i	0.561499	+	0.827477i	$0.310225\pi$
$294$		0			0
$295$	−16.5342	+	6.70822i	−0.962660	+	0.390568i
$296$		0			0
$297$	7.44954	+	17.8997i	0.432266	+	1.03865i
$298$		0			0
$299$	4.27867	−	7.41088i	0.247442	−	0.428582i
$300$		0			0
$301$	−10.8484	−	18.7900i	−0.625291	−	1.08303i
$302$		0			0
$303$	−15.1198	+	4.77656i	−0.868609	+	0.274406i
$304$		0			0
$305$	−15.1644	−	11.8123i	−0.868314	−	0.676372i
$306$		0			0
$307$		−	10.7398i		−	0.612955i	−0.951878	−	0.306478i	$-0.900850\pi$
$307$		−	10.7398i		−	0.612955i	0.951878	−	0.306478i	$-0.0991504\pi$
$308$		0			0
$309$	8.00000	+	1.76886i	0.455104	+	0.100627i
$310$		0			0
$311$	−2.41774	−	4.18764i	−0.137097	−	0.237460i	0.789299	−	0.614009i	$-0.210444\pi$
$311$	−2.41774	−	4.18764i	−0.137097	−	0.237460i	−0.926397	+	0.376549i	$0.877111\pi$
$312$		0			0
$313$	16.2023	+	9.35443i	0.915811	+	0.528744i	0.882296	−	0.470695i	$-0.155997\pi$
$313$	16.2023	+	9.35443i	0.915811	+	0.528744i	0.0335146	+	0.999438i	$0.489330\pi$
$314$		0			0
$315$	−21.3709	−	13.8004i	−1.20411	−	0.777563i
$316$		0			0
$317$	26.2517	+	15.1564i	1.47444	+	0.851270i	0.999585	−	0.0287919i	$-0.00916602\pi$
$317$	26.2517	+	15.1564i	1.47444	+	0.851270i	0.474858	+	0.880062i	$0.342499\pi$
$318$		0			0
$319$	−7.44554	−	12.8960i	−0.416870	−	0.722040i
$320$		0			0
$321$	11.6036	−	12.6773i	0.647649	−	0.707580i
$322$		0			0
$323$		−	2.67070i		−	0.148601i
$324$		0			0
$325$	6.15514	−	1.55366i	0.341426	−	0.0861815i
$326$		0			0
$327$	21.4944	+	19.6738i	1.18864	+	1.08796i
$328$		0			0
$329$	9.15955	+	15.8648i	0.504982	+	0.874655i
$330$		0			0
$331$	4.17353	−	7.22877i	0.229398	−	0.397329i	−0.728232	−	0.685331i	$-0.759658\pi$
$331$	4.17353	−	7.22877i	0.229398	−	0.397329i	0.957630	+	0.288002i	$0.0929909\pi$
$332$		0			0
$333$	22.6964	−	2.01128i	1.24375	−	0.110218i
$334$		0			0
$335$	−0.964117	−	2.37633i	−0.0526753	−	0.129833i
$336$		0			0
$337$	11.8323	−	6.83137i	0.644546	−	0.372129i	−0.141818	−	0.989893i	$-0.545295\pi$
$337$	11.8323	−	6.83137i	0.644546	−	0.372129i	0.786363	+	0.617764i	$0.211961\pi$
$338$		0			0
$339$	−21.7729	−	4.81414i	−1.18254	−	0.261468i
$340$		0			0
$341$	40.0068			2.16649
$342$		0			0
$343$		−	1.44650i		−	0.0781035i
$344$		0			0
$345$	9.09252	−	24.4691i	0.489525	−	1.31737i
$346$		0			0
$347$	1.31113	−	0.756981i	0.0703851	−	0.0406368i	−0.464394	−	0.885628i	$-0.653728\pi$
$347$	1.31113	−	0.756981i	0.0703851	−	0.0406368i	0.534780	+	0.844992i	$0.320395\pi$
$348$		0			0
$349$	1.48031	−	2.56397i	0.0792392	−	0.137246i	−0.823683	−	0.567051i	$-0.808084\pi$
$349$	1.48031	−	2.56397i	0.0792392	−	0.137246i	0.902922	+	0.429805i	$0.141418\pi$
$350$		0			0
$351$	−0.850129	+	6.54224i	−0.0453765	+	0.349199i
$352$		0			0
$353$	−20.7247	−	11.9654i	−1.10307	−	0.636855i	−0.166041	−	0.986119i	$-0.553098\pi$
$353$	−20.7247	−	11.9654i	−1.10307	−	0.636855i	−0.937025	+	0.349263i	$0.886432\pi$
$354$		0			0
$355$	2.83453	−	20.3835i	0.150441	−	1.08184i
$356$		0			0
$357$	6.09478	−	1.92543i	0.322570	−	0.101904i
$358$		0			0
$359$	−8.76880			−0.462800			−0.231400	−	0.972859i	$-0.574331\pi$
$359$	−8.76880			−0.462800			−0.231400	+	0.972859i	$0.574331\pi$
$360$		0			0
$361$	−11.4675			−0.603550
$362$		0			0
$363$	−1.09267	+	4.94180i	−0.0573502	+	0.259377i
$364$		0			0
$365$	2.19467	+	0.305190i	0.114874	+	0.0159744i
$366$		0			0
$367$	−22.9301	−	13.2387i	−1.19694	−	0.691055i	−0.237070	−	0.971493i	$-0.576187\pi$
$367$	−22.9301	−	13.2387i	−1.19694	−	0.691055i	−0.959872	+	0.280438i	$0.909520\pi$
$368$		0			0
$369$	14.3872	−	10.0980i	0.748967	−	0.525683i
$370$		0			0
$371$	19.2003	−	33.2559i	0.996830	−	1.72656i
$372$		0			0
$373$	16.0449	−	9.26355i	0.830776	−	0.479648i	−0.0233426	−	0.999728i	$-0.507431\pi$
$373$	16.0449	−	9.26355i	0.830776	−	0.479648i	0.854118	+	0.520079i	$0.174098\pi$
$374$		0			0
$375$	17.7206	−	7.80898i	0.915088	−	0.403254i
$376$		0			0
$377$		−	5.06705i		−	0.260966i
$378$		0			0
$379$	23.5529			1.20983			0.604917	−	0.796289i	$-0.293206\pi$
$379$	23.5529			1.20983			0.604917	+	0.796289i	$0.293206\pi$
$380$		0			0
$381$	−9.25472	+	10.1111i	−0.474133	+	0.518008i
$382$		0			0
$383$	0.456831	−	0.263751i	0.0233430	−	0.0134771i	−0.488283	−	0.872685i	$-0.662377\pi$
$383$	0.456831	−	0.263751i	0.0233430	−	0.0134771i	0.511626	+	0.859208i	$0.329043\pi$
$384$		0			0
$385$	−11.8952	−	29.3189i	−0.606235	−	1.49423i
$386$		0			0
$387$	−7.23635	+	15.5639i	−0.367844	+	0.791156i
$388$		0			0
$389$	3.21656	−	5.57125i	0.163086	−	0.282473i	−0.772888	−	0.634543i	$-0.781188\pi$
$389$	3.21656	−	5.57125i	0.163086	−	0.282473i	0.935974	+	0.352069i	$0.114522\pi$
$390$		0			0
$391$	3.27931	+	5.67992i	0.165842	+	0.287246i
$392$		0			0
$393$	8.00818	−	36.2185i	0.403959	−	1.82698i
$394$		0			0
$395$	−27.6416	−	21.5314i	−1.39080	−	1.08336i
$396$		0			0
$397$			17.9480i			0.900782i	0.892831	+	0.450391i	$0.148715\pi$
$397$			17.9480i			0.900782i	−0.892831	+	0.450391i	$0.851285\pi$
$398$		0			0
$399$	5.43056	+	17.1900i	0.271868	+	0.860575i
$400$		0			0
$401$	12.3216	+	21.3416i	0.615310	+	1.06575i	0.990330	+	0.138732i	$0.0443026\pi$
$401$	12.3216	+	21.3416i	0.615310	+	1.06575i	−0.375020	+	0.927017i	$0.622364\pi$
$402$		0			0
$403$	11.7894	+	6.80664i	0.587274	+	0.339063i
$404$		0			0
$405$	0.776581	+	20.1096i	0.0385886	+	0.999255i
$406$		0			0
$407$	24.5424	+	14.1695i	1.21652	+	0.702358i
$408$		0			0
$409$	−4.99246	−	8.64719i	−0.246861	−	0.427576i	0.715792	−	0.698313i	$-0.246066\pi$
$409$	−4.99246	−	8.64719i	−0.246861	−	0.427576i	−0.962653	+	0.270737i	$0.912732\pi$
$410$		0			0
$411$	8.55919	+	27.0934i	0.422194	+	1.33642i
$412$		0			0
$413$			30.2614i			1.48907i
$414$		0			0
$415$	1.71883	−	2.20660i	0.0843741	−	0.108318i
$416$		0			0
$417$	1.99303	−	9.01385i	0.0975991	−	0.441410i
$418$		0			0
$419$	−5.35550	−	9.27599i	−0.261633	−	0.453162i	0.705043	−	0.709165i	$-0.250928\pi$
$419$	−5.35550	−	9.27599i	−0.261633	−	0.453162i	−0.966676	+	0.256003i	$0.917594\pi$
$420$		0			0
$421$	−0.204268	+	0.353803i	−0.00995543	+	0.0172433i	−0.870960	−	0.491354i	$-0.836502\pi$
$421$	−0.204268	+	0.353803i	−0.00995543	+	0.0172433i	0.861005	+	0.508597i	$0.169836\pi$
$422$		0			0
$423$	6.10982	−	13.1409i	0.297070	−	0.638934i
$424$		0			0
$425$	−1.32751	+	4.68085i	−0.0643936	+	0.227055i
$426$		0			0
$427$	−28.2325	+	16.3000i	−1.36627	+	0.788814i
$428$		0			0
$429$	−5.54001	+	6.05266i	−0.267474	+	0.292225i
$430$		0			0
$431$	−31.2522			−1.50536			−0.752682	−	0.658384i	$-0.771240\pi$
$431$	−31.2522			−1.50536			−0.752682	+	0.658384i	$0.771240\pi$
$432$		0			0
$433$			17.0844i			0.821023i	0.911855	+	0.410512i	$0.134650\pi$
$433$			17.0844i			0.821023i	−0.911855	+	0.410512i	$0.865350\pi$
$434$		0			0
$435$	−2.58178	−	15.2397i	−0.123787	−	0.730686i
$436$		0			0
$437$	−16.0199	+	9.24909i	−0.766335	+	0.442444i
$438$		0			0
$439$	−4.78572	+	8.28910i	−0.228410	+	0.395617i	−0.957337	−	0.288974i	$-0.906686\pi$
$439$	−4.78572	+	8.28910i	−0.228410	+	0.395617i	0.728927	+	0.684591i	$0.240019\pi$
$440$		0			0
$441$	−18.1253	+	12.7217i	−0.863110	+	0.605797i
$442$		0			0
$443$	0.803150	+	0.463699i	0.0381588	+	0.0220310i	0.518958	−	0.854800i	$-0.326320\pi$
$443$	0.803150	+	0.463699i	0.0381588	+	0.0220310i	−0.480799	+	0.876831i	$0.659653\pi$
$444$		0			0
$445$	−2.76271	+	19.8670i	−0.130965	+	0.941788i
$446$		0			0
$447$	−2.85305	+	12.9034i	−0.134944	+	0.610312i
$448$		0			0
$449$	−26.0869			−1.23112			−0.615558	−	0.788092i	$-0.711069\pi$
$449$	−26.0869			−1.23112			−0.615558	+	0.788092i	$0.711069\pi$
$450$		0			0
$451$	21.8616			1.02942
$452$		0			0
$453$	9.90341	−	3.12863i	0.465303	−	0.146996i
$454$		0			0
$455$	1.48289	−	10.6637i	0.0695190	−	0.499922i
$456$		0			0
$457$	22.9713	+	13.2625i	1.07455	+	0.620392i	0.929421	−	0.369021i	$-0.120307\pi$
$457$	22.9713	+	13.2625i	1.07455	+	0.620392i	0.145129	+	0.989413i	$0.453640\pi$
$458$		0			0
$459$	−4.01662	−	3.07136i	−0.187480	−	0.143359i
$460$		0			0
$461$	2.04128	−	3.53560i	0.0950718	−	0.164669i	−0.814567	−	0.580070i	$-0.803025\pi$
$461$	2.04128	−	3.53560i	0.0950718	−	0.164669i	0.909639	+	0.415401i	$0.136359\pi$
$462$		0			0
$463$	6.74462	−	3.89401i	0.313449	−	0.180970i	−0.335020	−	0.942211i	$-0.608743\pi$
$463$	6.74462	−	3.89401i	0.313449	−	0.180970i	0.648469	+	0.761241i	$0.275410\pi$
$464$		0			0
$465$	38.9261	+	14.4647i	1.80516	+	0.670783i
$466$		0			0
$467$			30.1413i			1.39477i	0.716695	+	0.697387i	$0.245654\pi$
$467$			30.1413i			1.39477i	−0.716695	+	0.697387i	$0.754346\pi$
$468$		0			0
$469$	−4.34923			−0.200829
$470$		0			0
$471$	−20.0921	−	4.44250i	−0.925793	−	0.204700i
$472$		0			0
$473$	−18.4874	+	10.6737i	−0.850053	+	0.490778i
$474$		0			0
$475$	−13.2021	−	3.74416i	−0.605753	−	0.171794i
$476$		0			0
$477$	−30.2594	+	2.68149i	−1.38548	+	0.122777i
$478$		0			0
$479$	−4.64266	+	8.04133i	−0.212129	+	0.367418i	−0.952381	−	0.304912i	$-0.901373\pi$
$479$	−4.64266	+	8.04133i	−0.212129	+	0.367418i	0.740252	+	0.672330i	$0.234706\pi$
$480$		0			0
$481$	4.82153	+	8.35113i	0.219843	+	0.380779i
$482$		0			0
$483$	−32.6568	−	29.8908i	−1.48594	−	1.36008i
$484$		0			0
$485$	−8.82519	+	11.3296i	−0.400731	+	0.514452i
$486$		0			0
$487$			11.7910i			0.534300i	0.963655	+	0.267150i	$0.0860818\pi$
$487$			11.7910i			0.534300i	−0.963655	+	0.267150i	$0.913918\pi$
$488$		0			0
$489$	−9.89121	+	10.8065i	−0.447296	+	0.488687i
$490$		0			0
$491$	−5.74759	−	9.95512i	−0.259385	−	0.449268i	0.706692	−	0.707521i	$-0.250187\pi$
$491$	−5.74759	−	9.95512i	−0.259385	−	0.449268i	−0.966077	+	0.258253i	$0.916853\pi$
$492$		0			0
$493$	3.36324	+	1.94177i	0.151473	+	0.0874529i
$494$		0			0
$495$	−13.5782	+	21.0268i	−0.610294	+	0.945083i
$496$		0			0
$497$	−30.2263	−	17.4512i	−1.35583	−	0.782791i
$498$		0			0
$499$	−7.00545	−	12.1338i	−0.313607	−	0.543183i	0.665533	−	0.746368i	$-0.268204\pi$
$499$	−7.00545	−	12.1338i	−0.313607	−	0.543183i	−0.979140	+	0.203185i	$0.934871\pi$
$500$		0			0
$501$	6.80074	+	1.50370i	0.303835	+	0.0671802i
$502$		0			0
$503$		−	18.3416i		−	0.817811i	−0.912577	−	0.408905i	$-0.865911\pi$
$503$		−	18.3416i		−	0.817811i	0.912577	−	0.408905i	$-0.134089\pi$
$504$		0			0
$505$	−16.1492	−	12.5794i	−0.718631	−	0.559777i
$506$		0			0
$507$	18.8084	−	5.94184i	0.835309	−	0.263886i
$508$		0			0
$509$	−4.88475	−	8.46063i	−0.216513	−	0.375011i	0.737227	−	0.675645i	$-0.236135\pi$
$509$	−4.88475	−	8.46063i	−0.216513	−	0.375011i	−0.953739	+	0.300634i	$0.902802\pi$
$510$		0			0
$511$	1.87895	−	3.25443i	0.0831197	−	0.143968i
$512$		0			0
$513$	8.66259	−	11.3286i	0.382463	−	0.500172i
$514$		0			0
$515$	3.97661	+	9.80143i	0.175230	+	0.431903i
$516$		0			0
$517$	15.6094	−	9.01207i	0.686499	−	0.396350i
$518$		0			0
$519$	2.50152	+	7.91835i	0.109804	+	0.347577i
$520$		0			0
$521$	−31.0391			−1.35985			−0.679923	−	0.733284i	$-0.737987\pi$
$521$	−31.0391			−1.35985			−0.679923	+	0.733284i	$0.737987\pi$
$522$		0			0
$523$		−	37.8139i		−	1.65349i	−0.562579	−	0.826744i	$-0.690191\pi$
$523$		−	37.8139i		−	1.65349i	0.562579	−	0.826744i	$-0.309809\pi$
$524$		0			0
$525$	−0.973464	−	32.8277i	−0.0424854	−	1.43272i
$526$		0			0
$527$	−9.03580	+	5.21682i	−0.393606	+	0.227248i
$528$		0			0
$529$	11.2136	−	19.4226i	0.487549	−	0.844459i
$530$		0			0
$531$	19.5945	−	13.7529i	0.850328	−	0.596826i
$532$		0			0
$533$	6.44232	+	3.71948i	0.279048	+	0.161108i
$534$		0			0
$535$	21.9755	+	3.05591i	0.950086	+	0.132119i
$536$		0			0
$537$	−14.4072	−	13.1869i	−0.621716	−	0.569058i
$538$		0			0
$539$	−27.5418			−1.18631
$540$		0			0
$541$	15.5060			0.666656			0.333328	−	0.942811i	$-0.391828\pi$
$541$	15.5060			0.666656			0.333328	+	0.942811i	$0.391828\pi$
$542$		0			0
$543$	27.1339	+	24.8357i	1.16443	+	1.06580i
$544$		0			0
$545$	−5.18129	+	37.2594i	−0.221942	+	1.59602i
$546$		0			0
$547$	−32.2535	−	18.6215i	−1.37906	−	0.796200i	−0.387012	−	0.922075i	$-0.626493\pi$
$547$	−32.2535	−	18.6215i	−1.37906	−	0.796200i	−0.992046	+	0.125875i	$0.959826\pi$
$548$		0			0
$549$	23.3852	+	10.8728i	0.998055	+	0.464041i
$550$		0			0
$551$	−5.47665	+	9.48584i	−0.233313	+	0.404110i
$552$		0			0
$553$	−51.4618	+	29.7115i	−2.18838	+	1.26346i
$554$		0			0
$555$	18.7563	+	22.6602i	0.796162	+	0.961872i
$556$		0			0
$557$		−	4.54570i		−	0.192608i	−0.995352	−	0.0963038i	$-0.969298\pi$
$557$		−	4.54570i		−	0.192608i	0.995352	−	0.0963038i	$-0.0307020\pi$
$558$		0			0
$559$	−7.26398			−0.307234
$560$		0			0
$561$	−1.89443	−	5.99665i	−0.0799828	−	0.253179i
$562$		0			0
$563$	−19.0016	+	10.9706i	−0.800820	+	0.462354i	−0.843758	−	0.536724i	$-0.819662\pi$
$563$	−19.0016	+	10.9706i	−0.800820	+	0.462354i	0.0429376	+	0.999078i	$0.486328\pi$
$564$		0			0
$565$	−10.8228	−	26.6756i	−0.455317	−	1.12225i
$566$		0			0
$567$	32.0983	+	11.6015i	1.34800	+	0.487217i
$568$		0			0
$569$	1.06022	−	1.83635i	0.0444466	−	0.0769838i	−0.842946	−	0.537998i	$-0.819181\pi$
$569$	1.06022	−	1.83635i	0.0444466	−	0.0769838i	0.887393	+	0.461014i	$0.152514\pi$
$570$		0			0
$571$	−0.0869292	−	0.150566i	−0.00363788	−	0.00630099i	0.864201	−	0.503147i	$-0.167825\pi$
$571$	−0.0869292	−	0.150566i	−0.00363788	−	0.00630099i	−0.867839	+	0.496846i	$0.834491\pi$
$572$		0			0
$573$	−7.71646	+	2.43774i	−0.322360	+	0.101838i
$574$		0			0
$575$	32.6750	−	8.24770i	1.36264	−	0.343953i
$576$		0			0
$577$		−	7.84498i		−	0.326591i	−0.986577	−	0.163295i	$-0.947788\pi$
$577$		−	7.84498i		−	0.326591i	0.986577	−	0.163295i	$-0.0522123\pi$
$578$		0			0
$579$	17.9831	+	3.97619i	0.747351	+	0.165245i
$580$		0			0
$581$	−2.37184	−	4.10815i	−0.0984007	−	0.170435i
$582$		0			0
$583$	−32.7205	−	18.8912i	−1.35514	−	0.782392i
$584$		0			0
$585$	−7.57874	+	3.88615i	−0.313342	+	0.160672i
$586$		0			0
$587$	13.8070	+	7.97146i	0.569874	+	0.329017i	0.757099	−	0.653300i	$-0.226616\pi$
$587$	13.8070	+	7.97146i	0.569874	+	0.329017i	−0.187225	+	0.982317i	$0.559949\pi$
$588$		0			0
$589$	−14.7137	−	25.4849i	−0.606269	−	1.05009i
$590$		0			0
$591$	−22.7263	+	24.8293i	−0.934834	+	1.02134i
$592$		0			0
$593$		−	17.7893i		−	0.730517i	−0.930906	−	0.365259i	$-0.880981\pi$
$593$		−	17.7893i		−	0.730517i	0.930906	−	0.365259i	$-0.119019\pi$
$594$		0			0
$595$	6.50975	+	5.07076i	0.266874	+	0.207881i
$596$		0			0
$597$	−0.994477	−	0.910247i	−0.0407012	−	0.0372539i
$598$		0			0
$599$	4.73972	+	8.20944i	0.193660	+	0.335429i	0.946460	−	0.322820i	$-0.104631\pi$
$599$	4.73972	+	8.20944i	0.193660	+	0.335429i	−0.752801	+	0.658249i	$0.771298\pi$
$600$		0			0
$601$	16.2642	−	28.1705i	0.663431	−	1.14910i	−0.316277	−	0.948667i	$-0.602433\pi$
$601$	16.2642	−	28.1705i	0.663431	−	1.14910i	0.979708	−	0.200430i	$-0.0642338\pi$
$602$		0			0
$603$	1.97659	+	2.81615i	0.0804930	+	0.114683i
$604$		0			0
$605$	−6.05458	+	2.45645i	−0.246154	+	0.0998688i
$606$		0			0
$607$	−2.65327	+	1.53187i	−0.107693	+	0.0621766i	−0.552879	−	0.833261i	$-0.686471\pi$
$607$	−2.65327	+	1.53187i	−0.107693	+	0.0621766i	0.445186	+	0.895438i	$0.353138\pi$
$608$		0			0
$609$	−25.5959	−	5.65946i	−1.03720	−	0.229333i
$610$		0			0
$611$	6.13315			0.248121
$612$		0			0
$613$		−	48.3053i		−	1.95103i	−0.219930	−	0.975516i	$-0.570583\pi$
$613$		−	48.3053i		−	1.95103i	0.219930	−	0.975516i	$-0.429417\pi$
$614$		0			0
$615$	21.2711	+	7.90419i	0.857734	+	0.318728i
$616$		0			0
$617$	2.43835	−	1.40778i	0.0981641	−	0.0566751i	−0.450114	−	0.892971i	$-0.648617\pi$
$617$	2.43835	−	1.40778i	0.0981641	−	0.0566751i	0.548278	+	0.836296i	$0.315283\pi$
$618$		0			0
$619$	−9.63476	+	16.6879i	−0.387254	+	0.670743i	−0.992079	−	0.125615i	$-0.959910\pi$
$619$	−9.63476	+	16.6879i	−0.387254	+	0.670743i	0.604825	+	0.796358i	$0.293243\pi$
$620$		0			0
$621$	−4.51297	+	34.7299i	−0.181099	+	1.39366i
$622$		0			0
$623$	29.4604	+	17.0090i	1.18031	+	0.681451i
$624$		0			0
$625$	21.2778	+	13.1246i	0.851113	+	0.524983i
$626$		0			0
$627$	16.9132	−	5.34312i	0.675448	−	0.213384i
$628$		0			0
$629$	−7.39073			−0.294688
$630$		0			0
$631$	−47.6172			−1.89561			−0.947805	−	0.318851i	$-0.896703\pi$
$631$	−47.6172			−1.89561			−0.947805	+	0.318851i	$0.896703\pi$
$632$		0			0
$633$	−7.94561	+	35.9355i	−0.315810	+	1.42831i
$634$		0			0
$635$	−17.5271	−	2.43732i	−0.695542	−	0.0967220i
$636$		0			0
$637$	−8.11618	−	4.68588i	−0.321575	−	0.185661i
$638$		0			0
$639$	2.43720	+	27.5027i	0.0964143	+	1.08799i
$640$		0			0
$641$	0.339505	−	0.588039i	0.0134096	−	0.0232262i	−0.859243	−	0.511568i	$-0.829065\pi$
$641$	0.339505	−	0.588039i	0.0134096	−	0.0232262i	0.872652	+	0.488342i	$0.162398\pi$
$642$		0			0
$643$	−19.4381	+	11.2226i	−0.766563	+	0.442575i	−0.831647	−	0.555305i	$-0.812602\pi$
$643$	−19.4381	+	11.2226i	−0.766563	+	0.442575i	0.0650844	+	0.997880i	$0.479268\pi$
$644$		0			0
$645$	−21.8472	+	3.70117i	−0.860231	+	0.145734i
$646$		0			0
$647$		−	22.0230i		−	0.865815i	−0.901438	−	0.432907i	$-0.857488\pi$
$647$		−	22.0230i		−	0.865815i	0.901438	−	0.432907i	$-0.142512\pi$
$648$		0			0
$649$	29.7742			1.16874
$650$		0			0
$651$	47.5512	−	51.9514i	1.86368	−	2.03614i
$652$		0			0
$653$	−26.3221	+	15.1971i	−1.03006	+	0.594708i	−0.917003	−	0.398880i	$-0.869399\pi$
$653$	−26.3221	+	15.1971i	−1.03006	+	0.594708i	−0.113062	+	0.993588i	$0.536066\pi$
$654$		0			0
$655$	44.3741	−	18.0033i	1.73384	−	0.703449i
$656$		0			0
$657$	−2.96119	+	0.262411i	−0.115527	+	0.0102376i
$658$		0			0
$659$	−5.95605	+	10.3162i	−0.232015	+	0.401862i	−0.958401	−	0.285425i	$-0.907865\pi$
$659$	−5.95605	+	10.3162i	−0.232015	+	0.401862i	0.726386	+	0.687287i	$0.241198\pi$
$660$		0			0
$661$	3.76736	+	6.52526i	0.146533	+	0.253803i	0.929944	−	0.367701i	$-0.119855\pi$
$661$	3.76736	+	6.52526i	0.146533	+	0.253803i	−0.783411	+	0.621505i	$0.786522\pi$
$662$		0			0
$663$	0.461991	−	2.08944i	0.0179423	−	0.0811472i
$664$		0			0
$665$	−14.3018	+	18.3604i	−0.554599	+	0.711984i
$666$		0			0
$667$		−	26.8988i		−	1.04152i
$668$		0			0
$669$	−14.5123	−	45.9374i	−0.561078	−	1.77604i
$670$		0			0
$671$	16.0376	+	27.7779i	0.619124	+	1.07235i
$672$		0			0
$673$	16.3568	+	9.44361i	0.630509	+	0.364025i	0.780949	−	0.624595i	$-0.214736\pi$
$673$	16.3568	+	9.44361i	0.630509	+	0.364025i	−0.150440	+	0.988619i	$0.548069\pi$
$674$		0			0
$675$	−20.8137	+	15.5495i	−0.801121	+	0.598502i
$676$		0			0
$677$	16.1944	+	9.34982i	0.622400	+	0.359343i	0.777803	−	0.628508i	$-0.216334\pi$
$677$	16.1944	+	9.34982i	0.622400	+	0.359343i	−0.155403	+	0.987851i	$0.549668\pi$
$678$		0			0
$679$	12.1780	+	21.0930i	0.467350	+	0.809474i
$680$		0			0
$681$	2.70502	+	8.56251i	0.103657	+	0.328116i
$682$		0			0
$683$		−	37.6717i		−	1.44147i	−0.693212	−	0.720734i	$-0.743805\pi$
$683$		−	37.6717i		−	1.44147i	0.693212	−	0.720734i	$-0.256195\pi$
$684$		0			0
$685$	−22.5413	+	28.9381i	−0.861258	+	1.10567i
$686$		0			0
$687$	9.35011	−	42.2876i	0.356729	−	1.61337i
$688$		0			0
$689$	−6.42818	−	11.1339i	−0.244894	−	0.424169i
$690$		0			0
$691$	3.67544	−	6.36605i	0.139820	−	0.242176i	−0.787608	−	0.616176i	$-0.788681\pi$
$691$	3.67544	−	6.36605i	0.139820	−	0.242176i	0.927429	+	0.374000i	$0.122014\pi$
$692$		0			0
$693$	24.3870	+	34.7454i	0.926387	+	1.31987i
$694$		0			0
$695$	11.0436	−	4.48057i	0.418907	−	0.169958i
$696$		0			0
$697$	−4.93759	+	2.85072i	−0.187025	+	0.107979i
$698$		0			0
$699$	−1.88318	+	2.05744i	−0.0712283	+	0.0778195i
$700$		0			0
$701$	−31.4837			−1.18912			−0.594561	−	0.804051i	$-0.702674\pi$
$701$	−31.4837			−1.18912			−0.594561	+	0.804051i	$0.702674\pi$
$702$		0			0
$703$		−	20.8451i		−	0.786189i
$704$		0			0
$705$	18.4461	−	3.12499i	0.694720	−	0.117694i
$706$		0			0
$707$	−30.0659	+	17.3586i	−1.13074	+	0.652836i
$708$		0			0
$709$	14.9738	−	25.9353i	0.562351	−	0.974021i	−0.434940	−	0.900460i	$-0.643230\pi$
$709$	14.9738	−	25.9353i	0.562351	−	0.974021i	0.997291	−	0.0735610i	$-0.0234363\pi$
$710$		0			0
$711$	42.6262	+	19.8189i	1.59861	+	0.743265i
$712$		0			0
$713$	62.5851	+	36.1335i	2.34383	+	1.35321i
$714$		0			0
$715$	−10.4920	−	1.45902i	−0.392379	−	0.0545641i
$716$		0			0
$717$	−0.954947	+	4.31893i	−0.0356631	+	0.161293i
$718$		0			0
$719$	5.61533			0.209416			0.104708	−	0.994503i	$-0.466609\pi$
$719$	5.61533			0.209416			0.104708	+	0.994503i	$0.466609\pi$
$720$		0			0
$721$	17.9389			0.668079
$722$		0			0
$723$	−26.7998	+	8.46643i	−0.996694	+	0.314870i
$724$		0			0
$725$	14.3138	−	13.9033i	0.531603	−	0.516356i
$726$		0			0
$727$	−3.38153	−	1.95233i	−0.125414	−	0.0724078i	0.435981	−	0.899956i	$-0.356402\pi$
$727$	−3.38153	−	1.95233i	−0.125414	−	0.0724078i	−0.561395	+	0.827548i	$0.689735\pi$
$728$		0			0
$729$	−7.07566	−	26.0564i	−0.262062	−	0.965051i
$730$		0			0
$731$	2.78367	−	4.82146i	0.102958	−	0.178328i
$732$		0			0
$733$	2.31071	−	1.33409i	0.0853480	−	0.0492757i	−0.456719	−	0.889611i	$-0.650975\pi$
$733$	2.31071	−	1.33409i	0.0853480	−	0.0492757i	0.542067	+	0.840336i	$0.317642\pi$
$734$		0			0
$735$	−26.7978	−	9.95788i	−0.988453	−	0.367302i
$736$		0			0
$737$			4.27920i			0.157626i
$738$		0			0
$739$	−9.48405			−0.348876			−0.174438	−	0.984668i	$-0.555811\pi$
$739$	−9.48405			−0.348876			−0.174438	+	0.984668i	$0.555811\pi$
$740$		0			0
$741$	5.89315	+	1.30302i	0.216490	+	0.0478676i
$742$		0			0
$743$	32.5459	−	18.7904i	1.19399	−	0.689353i	0.234784	−	0.972047i	$-0.424562\pi$
$743$	32.5459	−	18.7904i	1.19399	−	0.689353i	0.959210	+	0.282694i	$0.0912282\pi$
$744$		0			0
$745$	−15.8090	+	6.41399i	−0.579198	+	0.234990i
$746$		0			0
$747$	−1.58212	+	3.40282i	−0.0578869	+	0.124502i
$748$		0			0
$749$	18.8142	−	32.5871i	0.687454	−	1.19071i
$750$		0			0
$751$	5.53509	+	9.58706i	0.201978	+	0.349837i	0.949166	−	0.314777i	$-0.101930\pi$
$751$	5.53509	+	9.58706i	0.201978	+	0.349837i	−0.747187	+	0.664613i	$0.768596\pi$
$752$		0			0
$753$	−20.0960	−	18.3939i	−0.732338	−	0.670310i
$754$		0			0
$755$	10.5777	+	8.23948i	0.384961	+	0.299865i
$756$		0			0
$757$			37.8369i			1.37521i	0.726087	+	0.687603i	$0.241337\pi$
$757$			37.8369i			1.37521i	−0.726087	+	0.687603i	$0.758663\pi$
$758$		0			0
$759$	−29.4096	+	32.1310i	−1.06750	+	1.16628i
$760$		0			0
$761$	−24.4427	−	42.3361i	−0.886049	−	1.53468i	−0.844507	−	0.535545i	$-0.820106\pi$
$761$	−24.4427	−	42.3361i	−0.886049	−	1.53468i	−0.0415422	−	0.999137i	$-0.513227\pi$
$762$		0			0
$763$	55.2512	+	31.8993i	2.00023	+	1.15483i
$764$		0			0
$765$	0.324865	−	6.51961i	0.0117455	−	0.235717i
$766$		0			0
$767$	8.77405	+	5.06570i	0.316812	+	0.182912i
$768$		0			0
$769$	−4.59389	−	7.95684i	−0.165660	−	0.286931i	0.771230	−	0.636557i	$-0.219642\pi$
$769$	−4.59389	−	7.95684i	−0.165660	−	0.286931i	−0.936889	+	0.349626i	$0.886309\pi$
$770$		0			0
$771$	−2.13794	−	0.472715i	−0.0769961	−	0.0170244i
$772$		0			0
$773$			0.238387i			0.00857419i	0.999991	+	0.00428710i	$0.00136463\pi$
$773$			0.238387i			0.00857419i	−0.999991	+	0.00428710i	$0.998635\pi$
$774$		0			0
$775$	13.1207	+	51.9804i	0.471310	+	1.86719i
$776$		0			0
$777$	47.5706	−	15.0282i	1.70658	−	0.539135i
$778$		0			0
$779$	−8.04029	−	13.9262i	−0.288073	−	0.498958i
$780$		0			0
$781$	−17.1702	+	29.7396i	−0.614397	+	1.06417i
$782$		0			0
$783$	7.96805	+	19.1456i	0.284755	+	0.684207i
$784$		0			0
$785$	−9.98727	−	24.6164i	−0.356461	−	0.878595i
$786$		0			0
$787$	44.6401	−	25.7730i	1.59125	−	0.918707i	0.598154	−	0.801381i	$-0.295901\pi$
$787$	44.6401	−	25.7730i	1.59125	−	0.918707i	0.993094	−	0.117326i	$-0.0374321\pi$
$788$		0			0
$789$	3.81164	+	12.0654i	0.135698	+	0.429541i
$790$		0			0
$791$	−48.8226			−1.73593
$792$		0			0
$793$			10.9144i			0.387580i
$794$		0			0
$795$	−25.0064	−	30.2111i	−0.886886	−	1.07148i
$796$		0			0
$797$	8.00605	−	4.62229i	0.283589	−	0.163730i	−0.351458	−	0.936204i	$-0.614314\pi$
$797$	8.00605	−	4.62229i	0.283589	−	0.163730i	0.635047	+	0.772474i	$0.280981\pi$
$798$		0			0
$799$	−2.35032	+	4.07087i	−0.0831483	+	0.144017i
$800$		0			0
$801$	−2.37545	−	26.8059i	−0.0839324	−	0.947139i
$802$		0			0
$803$	−3.20203	−	1.84869i	−0.112997	−	0.0652390i
$804$		0			0
$805$	7.87203	−	56.6090i	0.277453	−	1.99520i
$806$		0			0
$807$	−12.5960	−	11.5292i	−0.443402	−	0.405847i
$808$		0			0
$809$	41.3473			1.45369			0.726847	−	0.686799i	$-0.240985\pi$
$809$	41.3473			1.45369			0.726847	+	0.686799i	$0.240985\pi$
$810$		0			0
$811$	40.5079			1.42242			0.711212	−	0.702977i	$-0.248146\pi$
$811$	40.5079			1.42242			0.711212	+	0.702977i	$0.248146\pi$
$812$		0			0
$813$	10.2195	+	9.35396i	0.358415	+	0.328058i
$814$		0			0
$815$	−18.7326	−	2.60494i	−0.656173	−	0.0912472i
$816$		0			0
$817$	13.5986	+	7.85118i	0.475756	+	0.274678i
$818$		0			0
$819$	1.27503	+	14.3881i	0.0445532	+	0.502762i
$820$		0			0
$821$	−13.0294	+	22.5676i	−0.454729	+	0.787615i	−0.998673	−	0.0515075i	$-0.983597\pi$
$821$	−13.0294	+	22.5676i	−0.454729	+	0.787615i	0.543943	+	0.839122i	$0.316931\pi$
$822$		0			0
$823$	−27.5143	+	15.8854i	−0.959089	+	0.553730i	−0.895892	−	0.444271i	$-0.853463\pi$
$823$	−27.5143	+	15.8854i	−0.959089	+	0.553730i	−0.0631963	+	0.998001i	$0.520129\pi$
$824$		0			0
$825$	−32.2992	+	0.957791i	−1.12451	+	0.0333460i
$826$		0			0
$827$		−	28.9806i		−	1.00776i	−0.863775	−	0.503878i	$-0.831906\pi$
$827$		−	28.9806i		−	1.00776i	0.863775	−	0.503878i	$-0.168094\pi$
$828$		0			0
$829$	−13.2492			−0.460165			−0.230082	−	0.973171i	$-0.573900\pi$
$829$	−13.2492			−0.460165			−0.230082	+	0.973171i	$0.573900\pi$
$830$		0			0
$831$	−8.61956	−	27.2845i	−0.299009	−	0.946489i
$832$		0			0
$833$	6.22049	−	3.59140i	0.215527	−	0.124435i
$834$		0			0
$835$	3.38049	+	8.33213i	0.116987	+	0.288345i
$836$		0			0
$837$	−55.2495	−	7.17937i	−1.90970	−	0.248155i
$838$		0			0
$839$	0.720616	−	1.24814i	0.0248784	−	0.0430907i	−0.853318	−	0.521391i	$-0.825413\pi$
$839$	0.720616	−	1.24814i	0.0248784	−	0.0430907i	0.878197	+	0.478300i	$0.158747\pi$
$840$		0			0
$841$	6.53623	+	11.3211i	0.225387	+	0.390382i
$842$		0			0
$843$	38.5226	−	12.1698i	1.32679	−	0.419151i
$844$		0			0
$845$	20.0890	+	15.6483i	0.691081	+	0.538317i
$846$		0			0
$847$			11.0813i			0.380757i
$848$		0			0
$849$	35.9805	+	7.95555i	1.23485	+	0.273034i
$850$		0			0
$851$	25.5954	+	44.3326i	0.877399	+	1.51970i
$852$		0			0
$853$	−16.2785	−	9.39837i	−0.557364	−	0.321794i	0.194723	−	0.980858i	$-0.437619\pi$
$853$	−16.2785	−	9.39837i	−0.557364	−	0.321794i	−0.752087	+	0.659064i	$0.770953\pi$
$854$		0			0
$855$	18.3882	+	0.916263i	0.628862	+	0.0313355i
$856$		0			0
$857$	−26.0576	−	15.0444i	−0.890111	−	0.513906i	−0.0161324	−	0.999870i	$-0.505135\pi$
$857$	−26.0576	−	15.0444i	−0.890111	−	0.513906i	−0.873979	+	0.485964i	$0.838469\pi$
$858$		0			0
$859$	−5.39690	−	9.34770i	−0.184140	−	0.318940i	0.759146	−	0.650920i	$-0.225617\pi$
$859$	−5.39690	−	9.34770i	−0.184140	−	0.318940i	−0.943286	+	0.331980i	$0.892283\pi$
$860$		0			0
$861$	25.9843	−	28.3887i	0.885542	−	0.967486i
$862$		0			0
$863$			28.5284i			0.971117i	0.874204	+	0.485559i	$0.161384\pi$
$863$			28.5284i			0.971117i	−0.874204	+	0.485559i	$0.838616\pi$
$864$		0			0
$865$	−6.58794	+	8.45747i	−0.223997	+	0.287563i
$866$		0			0
$867$	−20.5103	−	18.7732i	−0.696568	−	0.637570i
$868$		0			0
$869$	29.2331	+	50.6332i	0.991665	+	1.71761i
$870$		0			0
$871$	−0.728051	+	1.26102i	−0.0246691	+	0.0427281i
$872$		0			0
$873$	8.12328	−	17.4715i	0.274931	−	0.591320i
$874$		0			0
$875$	34.1926	−	25.0708i	1.15592	−	0.847547i
$876$		0			0
$877$	3.43095	−	1.98086i	0.115855	−	0.0668889i	−0.440953	−	0.897530i	$-0.645359\pi$
$877$	3.43095	−	1.98086i	0.115855	−	0.0668889i	0.556808	+	0.830641i	$0.312026\pi$
$878$		0			0
$879$	−4.19955	−	0.928551i	−0.141647	−	0.0313193i
$880$		0			0
$881$	18.2264			0.614062			0.307031	−	0.951700i	$-0.400665\pi$
$881$	18.2264			0.614062			0.307031	+	0.951700i	$0.400665\pi$
$882$		0			0
$883$			5.15578i			0.173506i	0.996230	+	0.0867529i	$0.0276491\pi$
$883$			5.15578i			0.173506i	−0.996230	+	0.0867529i	$0.972351\pi$
$884$		0			0
$885$	28.9699	+	10.7650i	0.973814	+	0.361862i
$886$		0			0
$887$	−10.4111	+	6.01083i	−0.349570	+	0.201824i	−0.664496	−	0.747292i	$-0.731354\pi$
$887$	−10.4111	+	6.01083i	−0.349570	+	0.201824i	0.314926	+	0.949116i	$0.398020\pi$
$888$		0			0
$889$	−15.0057	+	25.9906i	−0.503274	+	0.871697i
$890$		0			0
$891$	11.4147	−	31.5815i	0.382407	−	1.05802i
$892$		0			0
$893$	−11.4817	−	6.62893i	−0.384219	−	0.221829i
$894$		0			0
$895$	3.47290	−	24.9742i	0.116086	−	0.834795i
$896$		0			0
$897$	−14.1333	+	4.46490i	−0.471896	+	0.149079i
$898$		0			0
$899$	42.7914			1.42717
$900$		0			0
$901$	9.85350			0.328268
$902$		0			0
$903$	−8.11324	+	36.6937i	−0.269992	+	1.22109i
$904$		0			0
$905$	−6.54071	+	47.0353i	−0.217421	+	1.56351i
$906$		0			0
$907$	−15.7789	−	9.10998i	−0.523931	−	0.302492i	0.214610	−	0.976700i	$-0.431152\pi$
$907$	−15.7789	−	9.10998i	−0.523931	−	0.302492i	−0.738542	+	0.674208i	$0.764485\pi$
$908$		0			0
$909$	24.9038	+	11.5789i	0.826007	+	0.384048i
$910$		0			0
$911$	17.6827	−	30.6273i	0.585853	−	1.01473i	−0.408915	−	0.912572i	$-0.634093\pi$
$911$	17.6827	−	30.6273i	0.585853	−	1.01473i	0.994768	−	0.102155i	$-0.0325738\pi$
$912$		0			0
$913$	−4.04201	+	2.33366i	−0.133771	+	0.0772327i
$914$		0			0
$915$	5.56113	+	32.8260i	0.183845	+	1.08520i
$916$		0			0
$917$		−	81.2149i		−	2.68195i
$918$		0			0
$919$	13.7063			0.452129			0.226065	−	0.974112i	$-0.427414\pi$
$919$	13.7063			0.452129			0.226065	+	0.974112i	$0.427414\pi$
$920$		0			0
$921$	−12.5596	+	13.7218i	−0.413853	+	0.452150i
$922$		0			0
$923$	−10.1196	+	5.84257i	−0.333092	+	0.192310i
$924$		0			0
$925$	−10.3614	+	36.5347i	−0.340680	+	1.20125i
$926$		0			0
$927$	−8.15268	−	11.6155i	−0.267769	−	0.381504i
$928$		0			0
$929$	21.0101	−	36.3906i	0.689319	−	1.19394i	−0.282740	−	0.959197i	$-0.591243\pi$
$929$	21.0101	−	36.3906i	0.689319	−	1.19394i	0.972059	−	0.234739i	$-0.0754234\pi$
$930$		0			0
$931$	10.1293	+	17.5445i	0.331976	+	0.574999i
$932$		0			0
$933$	−1.80817	+	8.17777i	−0.0591967	+	0.267728i
$934$		0			0
$935$	4.98912	−	6.40493i	0.163162	−	0.209464i
$936$		0			0
$937$		−	41.2829i		−	1.34865i	−0.738433	−	0.674326i	$-0.764434\pi$
$937$		−	41.2829i		−	1.34865i	0.738433	−	0.674326i	$-0.235566\pi$
$938$		0			0
$939$	−9.76158	−	30.8994i	−0.318557	−	1.00837i
$940$		0			0
$941$	−18.2029	−	31.5283i	−0.593397	−	1.02779i	−0.993771	−	0.111442i	$-0.964453\pi$
$941$	−18.2029	−	31.5283i	−0.593397	−	1.02779i	0.400374	−	0.916352i	$-0.368880\pi$
$942$		0			0
$943$	34.1995	+	19.7451i	1.11369	+	0.642989i
$944$		0			0
$945$	11.1659	+	42.6241i	0.363226	+	1.38656i
$946$		0			0
$947$	−1.39203	−	0.803687i	−0.0452348	−	0.0261163i	0.477212	−	0.878788i	$-0.341647\pi$
$947$	−1.39203	−	0.803687i	−0.0452348	−	0.0261163i	−0.522447	+	0.852672i	$0.674981\pi$
$948$		0			0
$949$	−0.629063	−	1.08957i	−0.0204202	−	0.0353689i
$950$		0			0
$951$	−15.8161	−	50.0646i	−0.512873	−	1.62346i
$952$		0			0
$953$		−	46.0152i		−	1.49058i	−0.666742	−	0.745289i	$-0.732312\pi$
$953$		−	46.0152i		−	1.49058i	0.666742	−	0.745289i	$-0.267688\pi$
$954$		0			0
$955$	−8.24184	−	6.41997i	−0.266700	−	0.207745i
$956$		0			0
$957$	−5.56834	+	25.1838i	−0.179999	+	0.814078i
$958$		0			0
$959$	31.1051	+	53.8756i	1.00444	+	1.73973i
$960$		0			0
$961$	−41.9823	+	72.7155i	−1.35427	+	2.34566i
$962$		0			0
$963$	−29.6508	+	2.62756i	−0.955484	+	0.0846719i
$964$		0			0
$965$	8.93895	+	22.0325i	0.287755	+	0.709251i
$966$		0			0
$967$	42.8357	−	24.7312i	1.37750	−	0.795301i	0.385644	−	0.922648i	$-0.373979\pi$
$967$	42.8357	−	24.7312i	1.37750	−	0.795301i	0.991858	+	0.127347i	$0.0406461\pi$
$968$		0			0
$969$	−3.12322	+	3.41223i	−0.100332	+	0.109617i
$970$		0			0
$971$	−36.3398			−1.16620			−0.583100	−	0.812401i	$-0.698160\pi$
$971$	−36.3398			−1.16620			−0.583100	+	0.812401i	$0.698160\pi$
$972$		0			0
$973$		−	20.2123i		−	0.647976i
$974$		0			0
$975$	−9.68107	−	5.21304i	−0.310042	−	0.166951i
$976$		0			0
$977$	49.4177	−	28.5313i	1.58101	−	0.912797i	0.586299	−	0.810095i	$-0.300584\pi$
$977$	49.4177	−	28.5313i	1.58101	−	0.912797i	0.994712	−	0.102702i	$-0.0327488\pi$
$978$		0			0
$979$	16.7351	−	28.9861i	0.534857	−	0.926400i
$980$		0			0
$981$	−4.45501	−	50.2728i	−0.142238	−	1.60509i
$982$		0			0
$983$	−41.1642	−	23.7662i	−1.31293	−	0.758023i	−0.330353	−	0.943858i	$-0.607168\pi$
$983$	−41.1642	−	23.7662i	−1.31293	−	0.758023i	−0.982581	+	0.185835i	$0.940501\pi$
$984$		0			0
$985$	−43.0403	−	5.98518i	−1.37138	−	0.190704i
$986$		0			0
$987$	6.85020	−	30.9813i	0.218044	−	0.986146i
$988$		0			0
$989$	−38.5614			−1.22618
$990$		0			0
$991$	−47.2512			−1.50098			−0.750492	−	0.660879i	$-0.770184\pi$
$991$	−47.2512			−1.50098			−0.750492	+	0.660879i	$0.770184\pi$
$992$		0			0
$993$	−13.7860	+	4.35519i	−0.437485	+	0.138208i
$994$		0			0
$995$	0.239722	−	1.72388i	0.00759970	−	0.0546506i
$996$		0			0
$997$	−24.3221	−	14.0423i	−0.770287	−	0.444726i	0.0626897	−	0.998033i	$-0.480032\pi$
$997$	−24.3221	−	14.0423i	−0.770287	−	0.444726i	−0.832977	+	0.553307i	$0.813365\pi$
$998$		0			0
$999$	−31.3503	−	23.9724i	−0.991878	−	0.758452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.b.169.4	yes	32
3.2	odd	2		1080.2.bi.b.289.9		32
4.3	odd	2		720.2.by.f.529.13		32
5.4	even	2	inner	360.2.bi.b.169.13	yes	32
9.2	odd	6		3240.2.f.i.649.3		16
9.4	even	3	inner	360.2.bi.b.49.13	yes	32
9.5	odd	6		1080.2.bi.b.1009.13		32
9.7	even	3		3240.2.f.k.649.14		16
12.11	even	2		2160.2.by.f.289.9		32
15.14	odd	2		1080.2.bi.b.289.13		32
20.19	odd	2		720.2.by.f.529.4		32
36.23	even	6		2160.2.by.f.1009.13		32
36.31	odd	6		720.2.by.f.49.4		32
45.4	even	6	inner	360.2.bi.b.49.4	✓	32
45.14	odd	6		1080.2.bi.b.1009.9		32
45.29	odd	6		3240.2.f.i.649.4		16
45.34	even	6		3240.2.f.k.649.13		16
60.59	even	2		2160.2.by.f.289.13		32
180.59	even	6		2160.2.by.f.1009.9		32
180.139	odd	6		720.2.by.f.49.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.b.49.4	✓	32	45.4	even	6	inner
360.2.bi.b.49.13	yes	32	9.4	even	3	inner
360.2.bi.b.169.4	yes	32	1.1	even	1	trivial
360.2.bi.b.169.13	yes	32	5.4	even	2	inner
720.2.by.f.49.4		32	36.31	odd	6
720.2.by.f.49.13		32	180.139	odd	6
720.2.by.f.529.4		32	20.19	odd	2
720.2.by.f.529.13		32	4.3	odd	2
1080.2.bi.b.289.9		32	3.2	odd	2
1080.2.bi.b.289.13		32	15.14	odd	2
1080.2.bi.b.1009.9		32	45.14	odd	6
1080.2.bi.b.1009.13		32	9.5	odd	6
2160.2.by.f.289.9		32	12.11	even	2
2160.2.by.f.289.13		32	60.59	even	2
2160.2.by.f.1009.9		32	180.59	even	6
2160.2.by.f.1009.13		32	36.23	even	6
3240.2.f.i.649.3		16	9.2	odd	6
3240.2.f.i.649.4		16	45.29	odd	6
3240.2.f.k.649.13		16	45.34	even	6
3240.2.f.k.649.14		16	9.7	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)

\(f(q)\)	\(=\)	\(q+(-1.27766 - 1.16944i) q^{3} +(0.307984 - 2.21476i) q^{5} +(-3.28422 - 1.89614i) q^{7} +(0.264813 + 2.98829i) q^{9} +O(q^{10})\)	\(q+(-1.27766 - 1.16944i) q^{3} +(0.307984 - 2.21476i) q^{5} +(-3.28422 - 1.89614i) q^{7} +(0.264813 + 2.98829i) q^{9} +(-1.86561 + 3.23134i) q^{11} +(-1.09954 + 0.634820i) q^{13} +(-2.98353 + 2.46953i) q^{15} -0.973091i q^{17} +2.74455 q^{19} +(1.97867 + 6.26332i) q^{21} +(-5.83699 + 3.36999i) q^{23} +(-4.81029 - 1.36422i) q^{25} +(3.15629 - 4.12769i) q^{27} +(-1.99547 + 3.45625i) q^{29} +(-5.36108 - 9.28566i) q^{31} +(6.16247 - 1.94681i) q^{33} +(-5.21098 + 6.68976i) q^{35} -7.59511i q^{37} +(2.14722 + 0.474767i) q^{39} +(-2.92955 - 5.07413i) q^{41} +(4.95478 + 2.86065i) q^{43} +(6.69989 + 0.333848i) q^{45} +(-4.18344 - 2.41531i) q^{47} +(3.69072 + 6.39251i) q^{49} +(-1.13797 + 1.24328i) q^{51} +10.1260i q^{53} +(6.58205 + 5.12708i) q^{55} +(-3.50659 - 3.20959i) q^{57} +(-3.98987 - 6.91066i) q^{59} +(4.29821 - 7.44471i) q^{61} +(4.79652 - 10.3163i) q^{63} +(1.06733 + 2.63073i) q^{65} +(0.993211 - 0.573431i) q^{67} +(11.3987 + 2.52033i) q^{69} +9.20350 q^{71} +0.990931i q^{73} +(4.55053 + 7.36836i) q^{75} +(12.2542 - 7.07494i) q^{77} +(7.83472 - 13.5701i) q^{79} +(-8.85975 + 1.58267i) q^{81} +(1.08329 + 0.625439i) q^{83} +(-2.15516 - 0.299696i) q^{85} +(6.59140 - 2.08232i) q^{87} -8.97031 q^{89} +4.81484 q^{91} +(-4.00942 + 18.1334i) q^{93} +(0.845275 - 6.07851i) q^{95} +(-5.56207 - 3.21126i) q^{97} +(-10.1502 - 4.71929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 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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Representations

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Database

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