LMFDB - Embedded newform 288.2.i.f.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(97,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("288.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.i (of order $3$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			97.3
Root			$0.774115 + 1.18353i$ of defining polynomial
Character	$\chi$	$=$	288.97
Dual form			288.2.i.f.193.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.637910 + 1.61030i) q^{3} +(1.68614 + 2.92048i) q^{5} +(2.35143 - 4.07279i) q^{7} +(-2.18614 + 2.05446i) q^{9} +O(q^{10})$	\(q+(0.637910 + 1.61030i) q^{3} +(1.68614 + 2.92048i) q^{5} +(2.35143 - 4.07279i) q^{7} +(-2.18614 + 2.05446i) q^{9} +(0.437696 - 0.758112i) q^{11} +(0.686141 + 1.18843i) q^{13} +(-3.62725 + 4.57820i) q^{15} -2.37228 q^{17} -5.57825 q^{19} +(8.05842 + 1.18843i) q^{21} +(2.35143 + 4.07279i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(-4.70285 - 2.20979i) q^{27} +(2.68614 - 4.65253i) q^{29} +(-3.22682 - 5.58902i) q^{31} +(1.50000 + 0.221215i) q^{33} +15.8593 q^{35} +4.00000 q^{37} +(-1.47603 + 1.86301i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(-0.437696 + 0.758112i) q^{43} +(-9.68614 - 2.92048i) q^{45} +(2.35143 - 4.07279i) q^{47} +(-7.55842 - 13.0916i) q^{49} +(-1.51330 - 3.82009i) q^{51} -4.00000 q^{53} +2.95207 q^{55} +(-3.55842 - 8.98266i) q^{57} +(4.26516 + 7.38747i) q^{59} +(1.05842 - 1.83324i) q^{61} +(3.22682 + 13.7346i) q^{63} +(-2.31386 + 4.00772i) q^{65} +(-4.26516 - 7.38747i) q^{67} +(-5.05842 + 6.38458i) q^{69} -9.40571 q^{71} +10.3723 q^{73} +(-10.9190 - 1.61030i) q^{75} +(-2.05842 - 3.56529i) q^{77} +(3.22682 - 5.58902i) q^{79} +(0.558422 - 8.98266i) q^{81} +(-1.47603 + 2.55657i) q^{83} +(-4.00000 - 6.92820i) q^{85} +(9.20550 + 1.35760i) q^{87} +12.7446 q^{89} +6.45364 q^{91} +(6.94158 - 8.76144i) q^{93} +(-9.40571 - 16.2912i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(0.600642 + 2.55657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 8 * q + 2 * q^5 - 6 * q^9	$ 8 q + 2 q^{5} - 6 q^{9} - 6 q^{13} + 4 q^{17} + 30 q^{21} - 14 q^{25} + 10 q^{29} + 12 q^{33} + 32 q^{37} - 4 q^{41} - 66 q^{45} - 26 q^{49} - 32 q^{53} + 6 q^{57} - 26 q^{61} - 30 q^{65} - 6 q^{69} + 60 q^{73} + 18 q^{77} - 30 q^{81} - 32 q^{85} + 56 q^{89} + 90 q^{93} - 36 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 - 6 * q^9 - 6 * q^13 + 4 * q^17 + 30 * q^21 - 14 * q^25 + 10 * q^29 + 12 * q^33 + 32 * q^37 - 4 * q^41 - 66 * q^45 - 26 * q^49 - 32 * q^53 + 6 * q^57 - 26 * q^61 - 30 * q^65 - 6 * q^69 + 60 * q^73 + 18 * q^77 - 30 * q^81 - 32 * q^85 + 56 * q^89 + 90 * q^93 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.637910	+	1.61030i	0.368298	+	0.929708i
$3$	0.637910	+	1.61030i	0.368298	+	0.929708i
$4$		0			0
$5$	1.68614	+	2.92048i	0.754065	+	1.30608i	0.945838	+	0.324640i	$0.105243\pi$
$5$	1.68614	+	2.92048i	0.754065	+	1.30608i	−0.191773	+	0.981439i	$0.561424\pi$
$6$		0			0
$7$	2.35143	−	4.07279i	0.888756	−	1.53937i	0.0474088	−	0.998876i	$-0.484904\pi$
$7$	2.35143	−	4.07279i	0.888756	−	1.53937i	0.841347	−	0.540495i	$-0.181763\pi$
$8$		0			0
$9$	−2.18614	+	2.05446i	−0.728714	+	0.684819i
$10$		0			0
$11$	0.437696	−	0.758112i	0.131970	−	0.228579i	−0.792466	−	0.609917i	$-0.791203\pi$
$11$	0.437696	−	0.758112i	0.131970	−	0.228579i	0.924436	+	0.381337i	$0.124536\pi$
$12$		0			0
$13$	0.686141	+	1.18843i	0.190301	+	0.329611i	0.945350	−	0.326057i	$-0.105720\pi$
$13$	0.686141	+	1.18843i	0.190301	+	0.329611i	−0.755049	+	0.655669i	$0.772387\pi$
$14$		0			0
$15$	−3.62725	+	4.57820i	−0.936551	+	1.18209i
$16$		0			0
$17$	−2.37228			−0.575363			−0.287681	−	0.957726i	$-0.592884\pi$
$17$	−2.37228			−0.575363			−0.287681	+	0.957726i	$0.592884\pi$
$18$		0			0
$19$	−5.57825			−1.27974			−0.639869	−	0.768484i	$-0.721011\pi$
$19$	−5.57825			−1.27974			−0.639869	+	0.768484i	$0.721011\pi$
$20$		0			0
$21$	8.05842	+	1.18843i	1.75849	+	0.259337i
$22$		0			0
$23$	2.35143	+	4.07279i	0.490307	+	0.849236i	0.999938	−	0.0111571i	$-0.00355150\pi$
$23$	2.35143	+	4.07279i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$24$		0			0
$25$	−3.18614	+	5.51856i	−0.637228	+	1.10371i
$26$		0			0
$27$	−4.70285	−	2.20979i	−0.905065	−	0.425274i
$28$		0			0
$29$	2.68614	−	4.65253i	0.498804	−	0.863954i	−0.501195	−	0.865334i	$-0.667106\pi$
$29$	2.68614	−	4.65253i	0.498804	−	0.863954i	0.999999	+	0.00138070i	$0.000439492\pi$
$30$		0			0
$31$	−3.22682	−	5.58902i	−0.579554	−	1.00382i	−0.995530	−	0.0944415i	$-0.969893\pi$
$31$	−3.22682	−	5.58902i	−0.579554	−	1.00382i	0.415976	−	0.909375i	$-0.363440\pi$
$32$		0			0
$33$	1.50000	+	0.221215i	0.261116	+	0.0385086i
$34$		0			0
$35$	15.8593			2.68072
$36$		0			0
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$		0			0
$39$	−1.47603	+	1.86301i	−0.236355	+	0.298320i
$40$		0			0
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	0.824338	−	0.566099i	$-0.191548\pi$
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	−0.902424	+	0.430848i	$0.858214\pi$
$42$		0			0
$43$	−0.437696	+	0.758112i	−0.0667481	+	0.115611i	−0.897468	−	0.441079i	$-0.854596\pi$
$43$	−0.437696	+	0.758112i	−0.0667481	+	0.115611i	0.830720	+	0.556690i	$0.187929\pi$
$44$		0			0
$45$	−9.68614	−	2.92048i	−1.44392	−	0.435360i
$46$		0			0
$47$	2.35143	−	4.07279i	0.342991	−	0.594078i	−0.641996	−	0.766708i	$-0.721893\pi$
$47$	2.35143	−	4.07279i	0.342991	−	0.594078i	0.984987	+	0.172630i	$0.0552266\pi$
$48$		0			0
$49$	−7.55842	−	13.0916i	−1.07977	−	1.87022i
$50$		0			0
$51$	−1.51330	−	3.82009i	−0.211905	−	0.534919i
$52$		0			0
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$	2.95207			0.398057
$56$		0			0
$57$	−3.55842	−	8.98266i	−0.471325	−	1.18978i
$58$		0			0
$59$	4.26516	+	7.38747i	0.555276	+	0.961767i	0.997882	+	0.0650505i	$0.0207208\pi$
$59$	4.26516	+	7.38747i	0.555276	+	0.961767i	−0.442606	+	0.896716i	$0.645946\pi$
$60$		0			0
$61$	1.05842	−	1.83324i	0.135517	−	0.234722i	−0.790278	−	0.612749i	$-0.790064\pi$
$61$	1.05842	−	1.83324i	0.135517	−	0.234722i	0.925795	+	0.378026i	$0.123397\pi$
$62$		0			0
$63$	3.22682	+	13.7346i	0.406541	+	1.73040i
$64$		0			0
$65$	−2.31386	+	4.00772i	−0.286999	+	0.497097i
$66$		0			0
$67$	−4.26516	−	7.38747i	−0.521072	−	0.902523i	−0.999700	−	0.0245053i	$-0.992199\pi$
$67$	−4.26516	−	7.38747i	−0.521072	−	0.902523i	0.478628	−	0.878018i	$-0.341134\pi$
$68$		0			0
$69$	−5.05842	+	6.38458i	−0.608962	+	0.768613i
$70$		0			0
$71$	−9.40571			−1.11625			−0.558126	−	0.829756i	$-0.688480\pi$
$71$	−9.40571			−1.11625			−0.558126	+	0.829756i	$0.688480\pi$
$72$		0			0
$73$	10.3723			1.21398			0.606992	−	0.794708i	$-0.292376\pi$
$73$	10.3723			1.21398			0.606992	+	0.794708i	$0.292376\pi$
$74$		0			0
$75$	−10.9190	−	1.61030i	−1.26082	−	0.185942i
$76$		0			0
$77$	−2.05842	−	3.56529i	−0.234579	−	0.406303i
$78$		0			0
$79$	3.22682	−	5.58902i	0.363046	−	0.628813i	−0.625415	−	0.780292i	$-0.715070\pi$
$79$	3.22682	−	5.58902i	0.363046	−	0.628813i	0.988460	+	0.151479i	$0.0484036\pi$
$80$		0			0
$81$	0.558422	−	8.98266i	0.0620469	−	0.998073i
$82$		0			0
$83$	−1.47603	+	2.55657i	−0.162016	+	0.280620i	−0.935592	−	0.353084i	$-0.885133\pi$
$83$	−1.47603	+	2.55657i	−0.162016	+	0.280620i	0.773576	+	0.633704i	$0.218466\pi$
$84$		0			0
$85$	−4.00000	−	6.92820i	−0.433861	−	0.751469i
$86$		0			0
$87$	9.20550	+	1.35760i	0.986933	+	0.145550i
$88$		0			0
$89$	12.7446			1.35092			0.675460	−	0.737396i	$-0.263945\pi$
$89$	12.7446			1.35092			0.675460	+	0.737396i	$0.263945\pi$
$90$		0			0
$91$	6.45364			0.676525
$92$		0			0
$93$	6.94158	−	8.76144i	0.719808	−	0.908519i
$94$		0			0
$95$	−9.40571	−	16.2912i	−0.965005	−	1.67144i
$96$		0			0
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	−0.998796	−	0.0490655i	$-0.984376\pi$
$97$	−4.50000	+	7.79423i	−0.456906	+	0.791384i	0.541890	+	0.840450i	$0.317709\pi$
$98$		0			0
$99$	0.600642	+	2.55657i	0.0603668	+	0.256945i
$100$		0			0
$101$	−1.05842	+	1.83324i	−0.105317	+	0.182414i	−0.913868	−	0.406012i	$-0.866919\pi$
$101$	−1.05842	+	1.83324i	−0.105317	+	0.182414i	0.808551	+	0.588426i	$0.200252\pi$
$102$		0			0
$103$	−2.35143	−	4.07279i	−0.231693	−	0.401304i	0.726613	−	0.687047i	$-0.241093\pi$
$103$	−2.35143	−	4.07279i	−0.231693	−	0.401304i	−0.958306	+	0.285742i	$0.907760\pi$
$104$		0			0
$105$	10.1168	+	25.5383i	0.987303	+	2.49229i
$106$		0			0
$107$	−5.57825			−0.539270			−0.269635	−	0.962963i	$-0.586903\pi$
$107$	−5.57825			−0.539270			−0.269635	+	0.962963i	$0.586903\pi$
$108$		0			0
$109$	−5.48913			−0.525763			−0.262881	−	0.964828i	$-0.584673\pi$
$109$	−5.48913			−0.525763			−0.262881	+	0.964828i	$0.584673\pi$
$110$		0			0
$111$	2.55164	+	6.44121i	0.242191	+	0.611372i
$112$		0			0
$113$	−8.68614	−	15.0448i	−0.817123	−	1.41530i	−0.907793	−	0.419418i	$-0.862234\pi$
$113$	−8.68614	−	15.0448i	−0.817123	−	1.41530i	0.0906698	−	0.995881i	$-0.471099\pi$
$114$		0			0
$115$	−7.92967	+	13.7346i	−0.739446	+	1.28076i
$116$		0			0
$117$	−3.94158	−	1.18843i	−0.364399	−	0.109870i
$118$		0			0
$119$	−5.57825	+	9.66181i	−0.511357	+	0.885696i
$120$		0			0
$121$	5.11684	+	8.86263i	0.465168	+	0.805694i
$122$		0			0
$123$	1.07561	−	1.35760i	0.0969842	−	0.122410i
$124$		0			0
$125$	−4.62772			−0.413916
$126$		0			0
$127$	11.1565			0.989979			0.494989	−	0.868899i	$-0.335172\pi$
$127$	11.1565			0.989979			0.494989	+	0.868899i	$0.335172\pi$
$128$		0			0
$129$	−1.50000	−	0.221215i	−0.132068	−	0.0194769i
$130$		0			0
$131$	3.22682	+	5.58902i	0.281929	+	0.488315i	0.971860	−	0.235560i	$-0.0756925\pi$
$131$	3.22682	+	5.58902i	0.281929	+	0.488315i	−0.689931	+	0.723875i	$0.742359\pi$
$132$		0			0
$133$	−13.1168	+	22.7190i	−1.13737	+	1.96999i
$134$		0			0
$135$	−1.47603	−	17.4606i	−0.127037	−	1.50277i
$136$		0			0
$137$	−5.24456	+	9.08385i	−0.448073	+	0.776086i	−0.998261	−	0.0589556i	$-0.981223\pi$
$137$	−5.24456	+	9.08385i	−0.448073	+	0.776086i	0.550187	+	0.835041i	$0.314556\pi$
$138$		0			0
$139$	9.84341	+	17.0493i	0.834907	+	1.44610i	0.894106	+	0.447855i	$0.147812\pi$
$139$	9.84341	+	17.0493i	0.834907	+	1.44610i	−0.0591995	+	0.998246i	$0.518855\pi$
$140$		0			0
$141$	8.05842	+	1.18843i	0.678642	+	0.100084i
$142$		0			0
$143$	1.20128			0.100456
$144$		0			0
$145$	18.1168			1.50452
$146$		0			0
$147$	16.2598	−	20.5226i	1.34108	−	1.69267i
$148$		0			0
$149$	8.68614	+	15.0448i	0.711596	+	1.23252i	0.964258	+	0.264966i	$0.0853608\pi$
$149$	8.68614	+	15.0448i	0.711596	+	1.23252i	−0.252661	+	0.967555i	$0.581306\pi$
$150$		0			0
$151$	−2.35143	+	4.07279i	−0.191356	+	0.331439i	−0.945700	−	0.325041i	$-0.894622\pi$
$151$	−2.35143	+	4.07279i	−0.191356	+	0.331439i	0.754344	+	0.656480i	$0.227955\pi$
$152$		0			0
$153$	5.18614	−	4.87375i	0.419275	−	0.394019i
$154$		0			0
$155$	10.8817	−	18.8477i	0.874043	−	1.51389i
$156$		0			0
$157$	−7.05842	−	12.2255i	−0.563323	−	0.975705i	−0.997203	−	0.0747341i	$-0.976189\pi$
$157$	−7.05842	−	12.2255i	−0.563323	−	0.975705i	0.433880	−	0.900971i	$-0.357144\pi$
$158$		0			0
$159$	−2.55164	−	6.44121i	−0.202358	−	0.510821i
$160$		0			0
$161$	22.1168			1.74305
$162$		0			0
$163$	−18.8114			−1.47342			−0.736712	−	0.676207i	$-0.763623\pi$
$163$	−18.8114			−1.47342			−0.736712	+	0.676207i	$0.763623\pi$
$164$		0			0
$165$	1.88316	+	4.75372i	0.146603	+	0.370077i
$166$		0			0
$167$	3.22682	+	5.58902i	0.249699	+	0.432491i	0.963442	−	0.267916i	$-0.0863351\pi$
$167$	3.22682	+	5.58902i	0.249699	+	0.432491i	−0.713743	+	0.700407i	$0.753002\pi$
$168$		0			0
$169$	5.55842	−	9.62747i	0.427571	−	0.740575i
$170$		0			0
$171$	12.1948	−	11.4603i	0.932562	−	0.876388i
$172$		0			0
$173$	−2.68614	+	4.65253i	−0.204223	+	0.353725i	−0.949885	−	0.312599i	$-0.898800\pi$
$173$	−2.68614	+	4.65253i	−0.204223	+	0.353725i	0.745662	+	0.666325i	$0.232134\pi$
$174$		0			0
$175$	14.9840	+	25.9530i	1.13268	+	1.96186i
$176$		0			0
$177$	−9.17527	+	11.5807i	−0.689655	+	0.870461i
$178$		0			0
$179$	−18.8114			−1.40603			−0.703016	−	0.711174i	$-0.748164\pi$
$179$	−18.8114			−1.40603			−0.703016	+	0.711174i	$0.748164\pi$
$180$		0			0
$181$	26.2337			1.94993			0.974967	−	0.222348i	$-0.0713722\pi$
$181$	26.2337			1.94993			0.974967	+	0.222348i	$0.0713722\pi$
$182$		0			0
$183$	3.62725	+	0.534935i	0.268134	+	0.0395435i
$184$		0			0
$185$	6.74456	+	11.6819i	0.495870	+	0.858872i
$186$		0			0
$187$	−1.03834	+	1.79846i	−0.0759308	+	0.131516i
$188$		0			0
$189$	−20.0584	+	13.9576i	−1.45904	+	1.01527i
$190$		0			0
$191$	−8.80507	+	15.2508i	−0.637112	+	1.10351i	0.348951	+	0.937141i	$0.386538\pi$
$191$	−8.80507	+	15.2508i	−0.637112	+	1.10351i	−0.986063	+	0.166370i	$0.946795\pi$
$192$		0			0
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	0.847469	−	0.530845i	$-0.178125\pi$
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	−0.883460	+	0.468507i	$0.844792\pi$
$194$		0			0
$195$	−7.92967	−	1.16944i	−0.567856	−	0.0837456i
$196$		0			0
$197$	−10.7446			−0.765518			−0.382759	−	0.923848i	$-0.625026\pi$
$197$	−10.7446			−0.765518			−0.382759	+	0.923848i	$0.625026\pi$
$198$		0			0
$199$	−17.0606			−1.20940			−0.604698	−	0.796455i	$-0.706706\pi$
$199$	−17.0606			−1.20940			−0.604698	+	0.796455i	$0.706706\pi$
$200$		0			0
$201$	9.17527	−	11.5807i	0.647173	−	0.816842i
$202$		0			0
$203$	−12.6325	−	21.8802i	−0.886630	−	1.53569i
$204$		0			0
$205$	1.68614	−	2.92048i	0.117765	−	0.203975i
$206$		0			0
$207$	−13.5079	−	4.07279i	−0.938865	−	0.283079i
$208$		0			0
$209$	−2.44158	+	4.22894i	−0.168887	+	0.292522i
$210$		0			0
$211$	7.92967	+	13.7346i	0.545901	+	0.945529i	0.998550	+	0.0538397i	$0.0171460\pi$
$211$	7.92967	+	13.7346i	0.545901	+	0.945529i	−0.452648	+	0.891689i	$0.649521\pi$
$212$		0			0
$213$	−6.00000	−	15.1460i	−0.411113	−	1.03779i
$214$		0			0
$215$	−2.95207			−0.201329
$216$		0			0
$217$	−30.3505			−2.06033
$218$		0			0
$219$	6.61659	+	16.7025i	0.447107	+	1.12865i
$220$		0			0
$221$	−1.62772	−	2.81929i	−0.109492	−	0.189646i
$222$		0			0
$223$	2.35143	−	4.07279i	0.157463	−	0.272734i	−0.776490	−	0.630130i	$-0.783002\pi$
$223$	2.35143	−	4.07279i	0.157463	−	0.272734i	0.933953	+	0.357395i	$0.116335\pi$
$224$		0			0
$225$	−4.37228	−	18.6101i	−0.291485	−	1.24068i
$226$		0			0
$227$	−10.7188	+	18.5655i	−0.711432	+	1.23224i	0.252888	+	0.967496i	$0.418620\pi$
$227$	−10.7188	+	18.5655i	−0.711432	+	1.23224i	−0.964320	+	0.264740i	$0.914714\pi$
$228$		0			0
$229$	−0.686141	−	1.18843i	−0.0453415	−	0.0785337i	0.842464	−	0.538753i	$-0.181104\pi$
$229$	−0.686141	−	1.18843i	−0.0453415	−	0.0785337i	−0.887805	+	0.460219i	$0.847771\pi$
$230$		0			0
$231$	4.42810	−	5.58902i	0.291348	−	0.367730i
$232$		0			0
$233$	−25.8614			−1.69424			−0.847119	−	0.531404i	$-0.821665\pi$
$233$	−25.8614			−1.69424			−0.847119	+	0.531404i	$0.821665\pi$
$234$		0			0
$235$	15.8593			1.03455
$236$		0			0
$237$	11.0584	+	1.63086i	0.718322	+	0.105936i
$238$		0			0
$239$	−8.80507	−	15.2508i	−0.569552	−	0.986494i	−0.996610	−	0.0822694i	$-0.973783\pi$
$239$	−8.80507	−	15.2508i	−0.569552	−	0.986494i	0.427058	−	0.904224i	$-0.359550\pi$
$240$		0			0
$241$	−5.87228	+	10.1711i	−0.378267	+	0.655177i	−0.990810	−	0.135260i	$-0.956813\pi$
$241$	−5.87228	+	10.1711i	−0.378267	+	0.655177i	0.612543	+	0.790437i	$0.290147\pi$
$242$		0			0
$243$	14.8210	−	4.83090i	0.950768	−	0.309903i
$244$		0			0
$245$	25.4891	−	44.1485i	1.62844	−	2.82054i
$246$		0			0
$247$	−3.82746	−	6.62936i	−0.243536	−	0.421816i
$248$		0			0
$249$	−5.05842	−	0.746000i	−0.320564	−	0.0472758i
$250$		0			0
$251$	−16.7347			−1.05629			−0.528144	−	0.849155i	$-0.677112\pi$
$251$	−16.7347			−1.05629			−0.528144	+	0.849155i	$0.677112\pi$
$252$		0			0
$253$	4.11684			0.258824
$254$		0			0
$255$	8.60485	−	10.8608i	0.538857	−	0.680128i
$256$		0			0
$257$	−8.24456	−	14.2800i	−0.514282	−	0.890762i	−0.999863	−	0.0165703i	$-0.994725\pi$
$257$	−8.24456	−	14.2800i	−0.514282	−	0.890762i	0.485581	−	0.874192i	$-0.338608\pi$
$258$		0			0
$259$	9.40571	−	16.2912i	0.584442	−	1.01228i
$260$		0			0
$261$	3.68614	+	15.6896i	0.228166	+	0.971165i
$262$		0			0
$263$	8.80507	−	15.2508i	0.542944	−	0.940406i	−0.455790	−	0.890088i	$-0.650643\pi$
$263$	8.80507	−	15.2508i	0.542944	−	0.940406i	0.998733	−	0.0503185i	$-0.0160236\pi$
$264$		0			0
$265$	−6.74456	−	11.6819i	−0.414315	−	0.717615i
$266$		0			0
$267$	8.12989	+	20.5226i	0.497541	+	1.25596i
$268$		0			0
$269$	−13.4891			−0.822446			−0.411223	−	0.911535i	$-0.634898\pi$
$269$	−13.4891			−0.822446			−0.411223	+	0.911535i	$0.634898\pi$
$270$		0			0
$271$	22.3130			1.35542			0.677709	−	0.735330i	$-0.262973\pi$
$271$	22.3130			1.35542			0.677709	+	0.735330i	$0.262973\pi$
$272$		0			0
$273$	4.11684	+	10.3923i	0.249163	+	0.628971i
$274$		0			0
$275$	2.78912	+	4.83090i	0.168190	+	0.291314i
$276$		0			0
$277$	2.05842	−	3.56529i	0.123679	−	0.214218i	−0.797537	−	0.603270i	$-0.793864\pi$
$277$	2.05842	−	3.56529i	0.123679	−	0.214218i	0.921216	+	0.389052i	$0.127197\pi$
$278$		0			0
$279$	18.5367	+	5.58902i	1.10976	+	0.334606i
$280$		0			0
$281$	1.43070	−	2.47805i	0.0853486	−	0.147828i	−0.820191	−	0.572090i	$-0.806133\pi$
$281$	1.43070	−	2.47805i	0.0853486	−	0.147828i	0.905540	+	0.424262i	$0.139466\pi$
$282$		0			0
$283$	−7.92967	−	13.7346i	−0.471370	−	0.816437i	0.528093	−	0.849186i	$-0.322907\pi$
$283$	−7.92967	−	13.7346i	−0.471370	−	0.816437i	−0.999464	+	0.0327491i	$0.989574\pi$
$284$		0			0
$285$	20.2337	−	25.5383i	1.19854	−	1.51276i
$286$		0			0
$287$	−4.70285			−0.277601
$288$		0			0
$289$	−11.3723			−0.668958
$290$		0			0
$291$	−15.4217	−	2.27434i	−0.904033	−	0.133324i
$292$		0			0
$293$	7.31386	+	12.6680i	0.427280	+	0.740071i	0.996630	−	0.0820241i	$-0.0261384\pi$
$293$	7.31386	+	12.6680i	0.427280	+	0.740071i	−0.569350	+	0.822095i	$0.692805\pi$
$294$		0			0
$295$	−14.3833	+	24.9126i	−0.837429	+	1.45047i
$296$		0			0
$297$	−3.73369	+	2.59808i	−0.216651	+	0.150756i
$298$		0			0
$299$	−3.22682	+	5.58902i	−0.186612	+	0.323221i
$300$		0			0
$301$	2.05842	+	3.56529i	0.118645	+	0.205500i
$302$		0			0
$303$	−3.62725	−	0.534935i	−0.208380	−	0.0307312i
$304$		0			0
$305$	7.13859			0.408755
$306$		0			0
$307$	20.8881			1.19215			0.596073	−	0.802930i	$-0.296727\pi$
$307$	20.8881			1.19215			0.596073	+	0.802930i	$0.296727\pi$
$308$		0			0
$309$	5.05842	−	6.38458i	0.287764	−	0.363206i
$310$		0			0
$311$	13.5079	+	23.3964i	0.765964	+	1.32669i	0.939735	+	0.341903i	$0.111071\pi$
$311$	13.5079	+	23.3964i	0.765964	+	1.32669i	−0.173771	+	0.984786i	$0.555595\pi$
$312$		0			0
$313$	7.61684	−	13.1928i	0.430529	−	0.745699i	−0.566389	−	0.824138i	$-0.691660\pi$
$313$	7.61684	−	13.1928i	0.430529	−	0.745699i	0.996919	+	0.0784388i	$0.0249935\pi$
$314$		0			0
$315$	−34.6708	+	32.5823i	−1.95348	+	1.83581i
$316$		0			0
$317$	−1.31386	+	2.27567i	−0.0737937	+	0.127814i	−0.900561	−	0.434730i	$-0.856844\pi$
$317$	−1.31386	+	2.27567i	−0.0737937	+	0.127814i	0.826767	+	0.562544i	$0.190177\pi$
$318$		0			0
$319$	−2.35143	−	4.07279i	−0.131655	−	0.228033i
$320$		0			0
$321$	−3.55842	−	8.98266i	−0.198612	−	0.501363i
$322$		0			0
$323$	13.2332			0.736313
$324$		0			0
$325$	−8.74456			−0.485061
$326$		0			0
$327$	−3.50157	−	8.83915i	−0.193637	−	0.488806i
$328$		0			0
$329$	−11.0584	−	19.1537i	−0.609671	−	1.05598i
$330$		0			0
$331$	4.97760	−	8.62146i	0.273594	−	0.473879i	−0.696186	−	0.717862i	$-0.745121\pi$
$331$	4.97760	−	8.62146i	0.273594	−	0.473879i	0.969779	+	0.243983i	$0.0784542\pi$
$332$		0			0
$333$	−8.74456	+	8.21782i	−0.479199	+	0.450334i
$334$		0			0
$335$	14.3833	−	24.9126i	0.785844	−	1.36112i
$336$		0			0
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	0.962168	−	0.272456i	$-0.0878358\pi$
$337$	4.50000	+	7.79423i	0.245131	+	0.424579i	−0.717038	+	0.697034i	$0.754502\pi$
$338$		0			0
$339$	18.6857	−	23.5846i	1.01487	−	1.28094i
$340$		0			0
$341$	−5.64947			−0.305936
$342$		0			0
$343$	−38.1723			−2.06111
$344$		0			0
$345$	−27.1753	−	4.00772i	−1.46307	−	0.215768i
$346$		0			0
$347$	−4.26516	−	7.38747i	−0.228966	−	0.396580i	0.728536	−	0.685007i	$-0.240201\pi$
$347$	−4.26516	−	7.38747i	−0.228966	−	0.396580i	−0.957502	+	0.288427i	$0.906868\pi$
$348$		0			0
$349$	2.94158	−	5.09496i	0.157459	−	0.272727i	−0.776493	−	0.630126i	$-0.783003\pi$
$349$	2.94158	−	5.09496i	0.157459	−	0.272727i	0.933952	+	0.357399i	$0.116336\pi$
$350$		0			0
$351$	−0.600642	−	7.10524i	−0.0320599	−	0.379250i
$352$		0			0
$353$	−7.61684	+	13.1928i	−0.405404	+	0.702180i	−0.994368	−	0.105979i	$-0.966202\pi$
$353$	−7.61684	+	13.1928i	−0.405404	+	0.702180i	0.588965	+	0.808159i	$0.299536\pi$
$354$		0			0
$355$	−15.8593	−	27.4692i	−0.841727	−	1.45791i
$356$		0			0
$357$	−19.1168	−	2.81929i	−1.01177	−	0.149213i
$358$		0			0
$359$	33.4695			1.76645			0.883226	−	0.468948i	$-0.155367\pi$
$359$	33.4695			1.76645			0.883226	+	0.468948i	$0.155367\pi$
$360$		0			0
$361$	12.1168			0.637729
$362$		0			0
$363$	−11.0074	+	13.8932i	−0.577740	+	0.729205i
$364$		0			0
$365$	17.4891	+	30.2921i	0.915423	+	1.58556i
$366$		0			0
$367$	−15.5846	+	26.9933i	−0.813509	+	1.40904i	0.0968838	+	0.995296i	$0.469112\pi$
$367$	−15.5846	+	26.9933i	−0.813509	+	1.40904i	−0.910393	+	0.413744i	$0.864221\pi$
$368$		0			0
$369$	2.87228	+	0.866025i	0.149525	+	0.0450835i
$370$		0			0
$371$	−9.40571	+	16.2912i	−0.488320	+	0.845795i
$372$		0			0
$373$	−0.0584220	−	0.101190i	−0.00302498	−	0.00523941i	0.864509	−	0.502617i	$-0.167630\pi$
$373$	−0.0584220	−	0.101190i	−0.00302498	−	0.00523941i	−0.867534	+	0.497378i	$0.834296\pi$
$374$		0			0
$375$	−2.95207	−	7.45202i	−0.152444	−	0.384821i
$376$		0			0
$377$	7.37228			0.379692
$378$		0			0
$379$	3.82746			0.196604			0.0983018	−	0.995157i	$-0.468659\pi$
$379$	3.82746			0.196604			0.0983018	+	0.995157i	$0.468659\pi$
$380$		0			0
$381$	7.11684	+	17.9653i	0.364607	+	0.920391i
$382$		0			0
$383$	10.8817	+	18.8477i	0.556031	+	0.963074i	0.997823	+	0.0659564i	$0.0210098\pi$
$383$	10.8817	+	18.8477i	0.556031	+	0.963074i	−0.441791	+	0.897118i	$0.645657\pi$
$384$		0			0
$385$	6.94158	−	12.0232i	0.353776	−	0.612757i
$386$		0			0
$387$	−0.600642	−	2.55657i	−0.0305324	−	0.129958i
$388$		0			0
$389$	−16.1753	+	28.0164i	−0.820119	+	1.42049i	0.0854750	+	0.996340i	$0.472759\pi$
$389$	−16.1753	+	28.0164i	−0.820119	+	1.42049i	−0.905594	+	0.424147i	$0.860574\pi$
$390$		0			0
$391$	−5.57825	−	9.66181i	−0.282104	−	0.488619i
$392$		0			0
$393$	−6.94158	+	8.76144i	−0.350156	+	0.441956i
$394$		0			0
$395$	21.7635			1.09504
$396$		0			0
$397$	−4.00000			−0.200754			−0.100377	−	0.994949i	$-0.532005\pi$
$397$	−4.00000			−0.200754			−0.100377	+	0.994949i	$0.532005\pi$
$398$		0			0
$399$	−44.9519	−	6.62936i	−2.25041	−	0.331883i
$400$		0			0
$401$	8.98913	+	15.5696i	0.448895	+	0.777510i	0.998314	−	0.0580372i	$-0.0184842\pi$
$401$	8.98913	+	15.5696i	0.448895	+	0.777510i	−0.549419	+	0.835547i	$0.685151\pi$
$402$		0			0
$403$	4.42810	−	7.66970i	0.220580	−	0.382055i
$404$		0			0
$405$	27.1753	−	13.5152i	1.35035	−	0.671574i
$406$		0			0
$407$	1.75079	−	3.03245i	0.0867832	−	0.150313i
$408$		0			0
$409$	14.8723	+	25.7595i	0.735387	+	1.27373i	0.954553	+	0.298040i	$0.0963329\pi$
$409$	14.8723	+	25.7595i	0.735387	+	1.27373i	−0.219166	+	0.975688i	$0.570334\pi$
$410$		0			0
$411$	−17.9733	−	2.65064i	−0.886557	−	0.130747i
$412$		0			0
$413$	40.1168			1.97402
$414$		0			0
$415$	−9.95521			−0.488682
$416$		0			0
$417$	−21.1753	+	26.7268i	−1.03696	+	1.30882i
$418$		0			0
$419$	7.92967	+	13.7346i	0.387390	+	0.670979i	0.992098	−	0.125468i	$-0.0400434\pi$
$419$	7.92967	+	13.7346i	0.387390	+	0.670979i	−0.604708	+	0.796448i	$0.706710\pi$
$420$		0			0
$421$	8.31386	−	14.4000i	0.405193	−	0.701814i	−0.589151	−	0.808023i	$-0.700538\pi$
$421$	8.31386	−	14.4000i	0.405193	−	0.701814i	0.994344	+	0.106208i	$0.0338711\pi$
$422$		0			0
$423$	3.22682	+	13.7346i	0.156893	+	0.667799i
$424$		0			0
$425$	7.55842	−	13.0916i	0.366637	−	0.635034i
$426$		0			0
$427$	−4.97760	−	8.62146i	−0.240883	−	0.417222i
$428$		0			0
$429$	0.766312	+	1.93443i	0.0369979	+	0.0933952i
$430$		0			0
$431$	11.1565			0.537389			0.268695	−	0.963225i	$-0.413408\pi$
$431$	11.1565			0.537389			0.268695	+	0.963225i	$0.413408\pi$
$432$		0			0
$433$	−0.883156			−0.0424418			−0.0212209	−	0.999775i	$-0.506755\pi$
$433$	−0.883156			−0.0424418			−0.0212209	+	0.999775i	$0.506755\pi$
$434$		0			0
$435$	11.5569	+	29.1736i	0.554112	+	1.39877i
$436$		0			0
$437$	−13.1168	−	22.7190i	−0.627464	−	1.08680i
$438$		0			0
$439$	10.8817	−	18.8477i	0.519357	−	0.899553i	−0.480390	−	0.877055i	$-0.659505\pi$
$439$	10.8817	−	18.8477i	0.519357	−	0.899553i	0.999747	−	0.0224981i	$-0.00716196\pi$
$440$		0			0
$441$	43.4198	+	13.0916i	2.06761	+	0.623408i
$442$		0			0
$443$	10.7188	−	18.5655i	0.509265	−	0.882074i	−0.490677	−	0.871342i	$-0.663250\pi$
$443$	10.7188	−	18.5655i	0.509265	−	0.882074i	0.999942	−	0.0107321i	$-0.00341620\pi$
$444$		0			0
$445$	21.4891	+	37.2203i	1.01868	+	1.76441i
$446$		0			0
$447$	−18.6857	+	23.5846i	−0.883805	+	1.11551i
$448$		0			0
$449$	−0.883156			−0.0416787			−0.0208394	−	0.999783i	$-0.506634\pi$
$449$	−0.883156			−0.0416787			−0.0208394	+	0.999783i	$0.506634\pi$
$450$		0			0
$451$	−0.875393			−0.0412206
$452$		0			0
$453$	−8.05842	−	1.18843i	−0.378618	−	0.0558373i
$454$		0			0
$455$	10.8817	+	18.8477i	0.510144	+	0.883595i
$456$		0			0
$457$	−9.98913	+	17.3017i	−0.467272	+	0.809338i	−0.999301	−	0.0373879i	$-0.988096\pi$
$457$	−9.98913	+	17.3017i	−0.467272	+	0.809338i	0.532029	+	0.846726i	$0.321430\pi$
$458$		0			0
$459$	11.1565	+	5.24224i	0.520741	+	0.244687i
$460$		0			0
$461$	5.94158	−	10.2911i	0.276727	−	0.479305i	−0.693842	−	0.720127i	$-0.744084\pi$
$461$	5.94158	−	10.2911i	0.276727	−	0.479305i	0.970569	+	0.240822i	$0.0774169\pi$
$462$		0			0
$463$	0.274750	+	0.475881i	0.0127687	+	0.0221161i	0.872339	−	0.488901i	$-0.162602\pi$
$463$	0.274750	+	0.475881i	0.0127687	+	0.0221161i	−0.859570	+	0.511017i	$0.829269\pi$
$464$		0			0
$465$	37.2921	+	5.49972i	1.72938	+	0.255043i
$466$		0			0
$467$	−9.73160			−0.450325			−0.225162	−	0.974321i	$-0.572291\pi$
$467$	−9.73160			−0.450325			−0.225162	+	0.974321i	$0.572291\pi$
$468$		0			0
$469$	−40.1168			−1.85242
$470$		0			0
$471$	15.1842	−	19.1650i	0.699650	−	0.883076i
$472$		0			0
$473$	0.383156	+	0.663646i	0.0176175	+	0.0305145i
$474$		0			0
$475$	17.7731	−	30.7839i	0.815485	−	1.41246i
$476$		0			0
$477$	8.74456	−	8.21782i	0.400386	−	0.376268i
$478$		0			0
$479$	−2.35143	+	4.07279i	−0.107439	+	0.186091i	−0.914732	−	0.404061i	$-0.867599\pi$
$479$	−2.35143	+	4.07279i	−0.107439	+	0.186091i	0.807293	+	0.590151i	$0.200932\pi$
$480$		0			0
$481$	2.74456	+	4.75372i	0.125141	+	0.216751i
$482$		0			0
$483$	14.1086	+	35.6148i	0.641962	+	1.62053i
$484$		0			0
$485$	−30.3505			−1.37815
$486$		0			0
$487$	11.1565			0.505549			0.252775	−	0.967525i	$-0.418657\pi$
$487$	11.1565			0.505549			0.252775	+	0.967525i	$0.418657\pi$
$488$		0			0
$489$	−12.0000	−	30.2921i	−0.542659	−	1.36985i
$490$		0			0
$491$	−20.1245	−	34.8567i	−0.908206	−	1.57306i	−0.816554	−	0.577268i	$-0.804119\pi$
$491$	−20.1245	−	34.8567i	−0.908206	−	1.57306i	−0.0916519	−	0.995791i	$-0.529215\pi$
$492$		0			0
$493$	−6.37228	+	11.0371i	−0.286993	+	0.497087i
$494$		0			0
$495$	−6.45364	+	6.06490i	−0.290070	+	0.272597i
$496$		0			0
$497$	−22.1168	+	38.3075i	−0.992076	+	1.71833i
$498$		0			0
$499$	−6.89134	−	11.9361i	−0.308499	−	0.534335i	0.669536	−	0.742780i	$-0.266493\pi$
$499$	−6.89134	−	11.9361i	−0.308499	−	0.534335i	−0.978034	+	0.208445i	$0.933160\pi$
$500$		0			0
$501$	−6.94158	+	8.76144i	−0.310127	+	0.391432i
$502$		0			0
$503$	31.7187			1.41427			0.707133	−	0.707080i	$-0.249988\pi$
$503$	31.7187			1.41427			0.707133	+	0.707080i	$0.249988\pi$
$504$		0			0
$505$	−7.13859			−0.317663
$506$		0			0
$507$	19.0489	+	2.80927i	0.845991	+	0.124764i
$508$		0			0
$509$	−19.1753	−	33.2125i	−0.849929	−	1.47212i	−0.881271	−	0.472611i	$-0.843312\pi$
$509$	−19.1753	−	33.2125i	−0.849929	−	1.47212i	0.0313424	−	0.999509i	$-0.490022\pi$
$510$		0			0
$511$	24.3897	−	42.2441i	1.07894	−	1.86877i
$512$		0			0
$513$	26.2337	+	12.3267i	1.15825	+	0.544239i
$514$		0			0
$515$	7.92967	−	13.7346i	0.349423	−	0.605219i
$516$		0			0
$517$	−2.05842	−	3.56529i	−0.0905293	−	0.156801i
$518$		0			0
$519$	−9.20550	−	1.35760i	−0.404076	−	0.0595919i
$520$		0			0
$521$	35.3505			1.54873			0.774367	−	0.632736i	$-0.218068\pi$
$521$	35.3505			1.54873			0.774367	+	0.632736i	$0.218068\pi$
$522$		0			0
$523$	−12.9073			−0.564396			−0.282198	−	0.959356i	$-0.591064\pi$
$523$	−12.9073			−0.564396			−0.282198	+	0.959356i	$0.591064\pi$
$524$		0			0
$525$	−32.2337	+	40.6844i	−1.40679	+	1.77561i
$526$		0			0
$527$	7.65492	+	13.2587i	0.333454	+	0.577559i
$528$		0			0
$529$	0.441578	−	0.764836i	0.0191990	−	0.0332537i
$530$		0			0
$531$	−24.5015	−	7.38747i	−1.06327	−	0.320589i
$532$		0			0
$533$	0.686141	−	1.18843i	0.0297201	−	0.0514766i
$534$		0			0
$535$	−9.40571	−	16.2912i	−0.406644	−	0.704329i
$536$		0			0
$537$	−12.0000	−	30.2921i	−0.517838	−	1.30720i
$538$		0			0
$539$	−13.2332			−0.569993
$540$		0			0
$541$	−2.74456			−0.117998			−0.0589990	−	0.998258i	$-0.518791\pi$
$541$	−2.74456			−0.117998			−0.0589990	+	0.998258i	$0.518791\pi$
$542$		0			0
$543$	16.7347	+	42.2441i	0.718157	+	1.81287i
$544$		0			0
$545$	−9.25544	−	16.0309i	−0.396459	−	0.686688i
$546$		0			0
$547$	−5.14055	+	8.90370i	−0.219794	+	0.380695i	−0.954745	−	0.297426i	$-0.903872\pi$
$547$	−5.14055	+	8.90370i	−0.219794	+	0.380695i	0.734951	+	0.678120i	$0.237205\pi$
$548$		0			0
$549$	1.45245	+	6.18220i	0.0619892	+	0.263850i
$550$		0			0
$551$	−14.9840	+	25.9530i	−0.638338	+	1.10563i
$552$		0			0
$553$	−15.1753	−	26.2843i	−0.645318	−	1.11772i
$554$		0			0
$555$	−14.5090	+	18.3128i	−0.615872	+	0.777335i
$556$		0			0
$557$	−7.25544			−0.307423			−0.153711	−	0.988116i	$-0.549123\pi$
$557$	−7.25544			−0.307423			−0.153711	+	0.988116i	$0.549123\pi$
$558$		0			0
$559$	−1.20128			−0.0508089
$560$		0			0
$561$	−3.55842	−	0.524785i	−0.150237	−	0.0221564i
$562$		0			0
$563$	3.38977	+	5.87125i	0.142862	+	0.247444i	0.928573	−	0.371150i	$-0.121036\pi$
$563$	3.38977	+	5.87125i	0.142862	+	0.247444i	−0.785711	+	0.618593i	$0.787703\pi$
$564$		0			0
$565$	29.2921	−	50.7354i	1.23233	−	2.13446i
$566$		0			0
$567$	−35.2714	−	23.3964i	−1.48126	−	0.982557i
$568$		0			0
$569$	14.1277	−	24.4699i	0.592265	−	1.02583i	−0.401662	−	0.915788i	$-0.631567\pi$
$569$	14.1277	−	24.4699i	0.592265	−	1.02583i	0.993927	−	0.110045i	$-0.0350994\pi$
$570$		0			0
$571$	20.1245	+	34.8567i	0.842184	+	1.45871i	0.888044	+	0.459758i	$0.152064\pi$
$571$	20.1245	+	34.8567i	0.842184	+	1.45871i	−0.0458596	+	0.998948i	$0.514603\pi$
$572$		0			0
$573$	−30.1753	−	4.45015i	−1.26059	−	0.185908i
$574$		0			0
$575$	−29.9679			−1.24975
$576$		0			0
$577$	0.883156			0.0367663			0.0183831	−	0.999831i	$-0.494148\pi$
$577$	0.883156			0.0367663			0.0183831	+	0.999831i	$0.494148\pi$
$578$		0			0
$579$	1.07561	−	1.35760i	0.0447007	−	0.0564198i
$580$		0			0
$581$	6.94158	+	12.0232i	0.287985	+	0.498805i
$582$		0			0
$583$	−1.75079	+	3.03245i	−0.0725101	+	0.125591i
$584$		0			0
$585$	−3.17527	−	13.5152i	−0.131281	−	0.558783i
$586$		0			0
$587$	−19.2491	+	33.3404i	−0.794496	+	1.37611i	0.128663	+	0.991688i	$0.458932\pi$
$587$	−19.2491	+	33.3404i	−0.794496	+	1.37611i	−0.923159	+	0.384419i	$0.874402\pi$
$588$		0			0
$589$	18.0000	+	31.1769i	0.741677	+	1.28462i
$590$		0			0
$591$	−6.85407	−	17.3020i	−0.281939	−	0.711708i
$592$		0			0
$593$	39.7228			1.63122			0.815610	−	0.578602i	$-0.196401\pi$
$593$	39.7228			1.63122			0.815610	+	0.578602i	$0.196401\pi$
$594$		0			0
$595$	−37.6228			−1.54239
$596$		0			0
$597$	−10.8832	−	27.4728i	−0.445418	−	1.12439i
$598$		0			0
$599$	−15.5846	−	26.9933i	−0.636769	−	1.10292i	−0.986137	−	0.165931i	$-0.946937\pi$
$599$	−15.5846	−	26.9933i	−0.636769	−	1.10292i	0.349368	−	0.936986i	$-0.386396\pi$
$600$		0			0
$601$	18.6168	−	32.2453i	0.759397	−	1.31531i	−0.183762	−	0.982971i	$-0.558827\pi$
$601$	18.6168	−	32.2453i	0.759397	−	1.31531i	0.943159	−	0.332343i	$-0.107839\pi$
$602$		0			0
$603$	24.5015	+	7.38747i	0.997777	+	0.300841i
$604$		0			0
$605$	−17.2554	+	29.8873i	−0.701533	+	1.21509i
$606$		0			0
$607$	−0.274750	−	0.475881i	−0.0111518	−	0.0193154i	0.860396	−	0.509627i	$-0.170216\pi$
$607$	−0.274750	−	0.475881i	−0.0111518	−	0.0193154i	−0.871547	+	0.490311i	$0.836883\pi$
$608$		0			0
$609$	27.1753	−	34.2998i	1.10120	−	1.38990i
$610$		0			0
$611$	6.45364			0.261086
$612$		0			0
$613$	−32.4674			−1.31134			−0.655672	−	0.755045i	$-0.727615\pi$
$613$	−32.4674			−1.31134			−0.655672	+	0.755045i	$0.727615\pi$
$614$		0			0
$615$	5.77846	+	0.852189i	0.233010	+	0.0343636i
$616$		0			0
$617$	13.1277	+	22.7379i	0.528502	+	0.915392i	0.999448	+	0.0332302i	$0.0105794\pi$
$617$	13.1277	+	22.7379i	0.528502	+	0.915392i	−0.470946	+	0.882162i	$0.656087\pi$
$618$		0			0
$619$	−5.14055	+	8.90370i	−0.206616	+	0.357870i	−0.950646	−	0.310276i	$-0.899578\pi$
$619$	−5.14055	+	8.90370i	−0.206616	+	0.357870i	0.744030	+	0.668146i	$0.232912\pi$
$620$		0			0
$621$	−2.05842	−	24.3499i	−0.0826016	−	0.977128i
$622$		0			0
$623$	29.9679	−	51.9060i	1.20064	−	2.07957i
$624$		0			0
$625$	8.12772	+	14.0776i	0.325109	+	0.563105i
$626$		0			0
$627$	−8.36737	−	1.23399i	−0.334161	−	0.0492809i
$628$		0			0
$629$	−9.48913			−0.378356
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$	−17.0584	+	21.5306i	−0.678011	+	0.855765i
$634$		0			0
$635$	18.8114	+	32.5823i	0.746508	+	1.29299i
$636$		0			0
$637$	10.3723	−	17.9653i	0.410965	−	0.711812i
$638$		0			0
$639$	20.5622	−	19.3236i	0.813428	−	0.764430i
$640$		0			0
$641$	−1.12772	+	1.95327i	−0.0445422	+	0.0771494i	−0.887437	−	0.460929i	$-0.847516\pi$
$641$	−1.12772	+	1.95327i	−0.0445422	+	0.0771494i	0.842895	+	0.538078i	$0.180850\pi$
$642$		0			0
$643$	1.31309	+	2.27434i	0.0517832	+	0.0896911i	0.890755	−	0.454484i	$-0.150176\pi$
$643$	1.31309	+	2.27434i	0.0517832	+	0.0896911i	−0.838972	+	0.544175i	$0.816843\pi$
$644$		0			0
$645$	−1.88316	−	4.75372i	−0.0741492	−	0.187178i
$646$		0			0
$647$	4.15335			0.163285			0.0816426	−	0.996662i	$-0.473983\pi$
$647$	4.15335			0.163285			0.0816426	+	0.996662i	$0.473983\pi$
$648$		0			0
$649$	7.46738			0.293120
$650$		0			0
$651$	−19.3609	−	48.8735i	−0.758814	−	1.91550i
$652$		0			0
$653$	−11.9416	−	20.6834i	−0.467310	−	0.809405i	0.531992	−	0.846749i	$-0.321443\pi$
$653$	−11.9416	−	20.6834i	−0.467310	−	0.809405i	−0.999302	+	0.0373444i	$0.988110\pi$
$654$		0			0
$655$	−10.8817	+	18.8477i	−0.425185	+	0.736442i
$656$		0			0
$657$	−22.6753	+	21.3094i	−0.884646	+	0.831359i
$658$		0			0
$659$	20.2875	−	35.1389i	0.790287	−	1.36882i	−0.135502	−	0.990777i	$-0.543265\pi$
$659$	20.2875	−	35.1389i	0.790287	−	1.36882i	0.925789	−	0.378040i	$-0.123402\pi$
$660$		0			0
$661$	−7.05842	−	12.2255i	−0.274541	−	0.475519i	0.695478	−	0.718547i	$-0.255193\pi$
$661$	−7.05842	−	12.2255i	−0.274541	−	0.475519i	−0.970019	+	0.243028i	$0.921859\pi$
$662$		0			0
$663$	3.50157	−	4.41957i	0.135990	−	0.171642i
$664$		0			0
$665$	−88.4674			−3.43062
$666$		0			0
$667$	25.2651			0.978267
$668$		0			0
$669$	8.05842	+	1.18843i	0.311557	+	0.0459474i
$670$		0			0
$671$	−0.926535	−	1.60481i	−0.0357685	−	0.0619528i
$672$		0			0
$673$	14.1753	−	24.5523i	0.546416	−	0.946421i	−0.452100	−	0.891967i	$-0.649325\pi$
$673$	14.1753	−	24.5523i	0.546416	−	0.946421i	0.998516	−	0.0544536i	$-0.0173417\pi$
$674$		0			0
$675$	27.1788	−	18.9123i	1.04611	−	0.727934i
$676$		0			0
$677$	25.1753	−	43.6048i	0.967564	−	1.67587i	0.265002	−	0.964248i	$-0.414627\pi$
$677$	25.1753	−	43.6048i	0.967564	−	1.67587i	0.702562	−	0.711622i	$-0.252039\pi$
$678$		0			0
$679$	21.1628	+	36.6551i	0.812156	+	1.40669i
$680$		0			0
$681$	−36.7337	−	5.41737i	−1.40764	−	0.207594i
$682$		0			0
$683$	9.73160			0.372369			0.186185	−	0.982515i	$-0.440388\pi$
$683$	9.73160			0.372369			0.186185	+	0.982515i	$0.440388\pi$
$684$		0			0
$685$	−35.3723			−1.35151
$686$		0			0
$687$	1.47603	−	1.86301i	0.0563142	−	0.0710781i
$688$		0			0
$689$	−2.74456	−	4.75372i	−0.104560	−	0.181102i
$690$		0			0
$691$	−9.13096	+	15.8153i	−0.347358	+	0.601642i	−0.985779	−	0.168045i	$-0.946254\pi$
$691$	−9.13096	+	15.8153i	−0.347358	+	0.601642i	0.638421	+	0.769687i	$0.279588\pi$
$692$		0			0
$693$	11.8247	+	3.56529i	0.449185	+	0.135434i
$694$		0			0
$695$	−33.1947	+	57.4950i	−1.25915	+	2.18091i
$696$		0			0
$697$	1.18614	+	2.05446i	0.0449283	+	0.0778181i
$698$		0			0
$699$	−16.4973	−	41.6447i	−0.623984	−	1.57515i
$700$		0			0
$701$	23.2554			0.878346			0.439173	−	0.898403i	$-0.355272\pi$
$701$	23.2554			0.878346			0.439173	+	0.898403i	$0.355272\pi$
$702$		0			0
$703$	−22.3130			−0.841550
$704$		0			0
$705$	10.1168	+	25.5383i	0.381022	+	0.961829i
$706$		0			0
$707$	4.97760	+	8.62146i	0.187202	+	0.324244i
$708$		0			0
$709$	−13.8030	+	23.9075i	−0.518382	+	0.897864i	0.481390	+	0.876507i	$0.340132\pi$
$709$	−13.8030	+	23.9075i	−0.518382	+	0.897864i	−0.999772	+	0.0213574i	$0.993201\pi$
$710$		0			0
$711$	4.42810	+	18.8477i	0.166067	+	0.706845i
$712$		0			0
$713$	15.1753	−	26.2843i	0.568318	−	0.984356i
$714$		0			0
$715$	2.02554	+	3.50833i	0.0757507	+	0.131204i
$716$		0			0
$717$	18.9416	−	23.9075i	0.707386	−	0.892841i
$718$		0			0
$719$	15.3098			0.570961			0.285481	−	0.958385i	$-0.407847\pi$
$719$	15.3098			0.570961			0.285481	+	0.958385i	$0.407847\pi$
$720$		0			0
$721$	−22.1168			−0.823674
$722$		0			0
$723$	−20.1245	−	2.96790i	−0.748439	−	0.110377i
$724$		0			0
$725$	17.1168	+	29.6472i	0.635704	+	1.10107i
$726$		0			0
$727$	−10.0064	+	17.3315i	−0.371115	+	0.642790i	−0.989737	−	0.142898i	$-0.954358\pi$
$727$	−10.0064	+	17.3315i	−0.371115	+	0.642790i	0.618622	+	0.785689i	$0.287691\pi$
$728$		0			0
$729$	17.2337	+	20.7846i	0.638285	+	0.769800i
$730$		0			0
$731$	1.03834	−	1.79846i	0.0384043	−	0.0665183i
$732$		0			0
$733$	−20.0584	−	34.7422i	−0.740875	−	1.28323i	−0.952097	−	0.305795i	$-0.901078\pi$
$733$	−20.0584	−	34.7422i	−0.740875	−	1.28323i	0.211223	−	0.977438i	$-0.432255\pi$
$734$		0			0
$735$	87.3521	+	12.8824i	3.22203	+	0.475175i
$736$		0			0
$737$	−7.46738			−0.275064
$738$		0			0
$739$	7.32903			0.269603			0.134801	−	0.990873i	$-0.456960\pi$
$739$	7.32903			0.269603			0.134801	+	0.990873i	$0.456960\pi$
$740$		0			0
$741$	8.23369	−	10.3923i	0.302472	−	0.381771i
$742$		0			0
$743$	−24.6644	−	42.7200i	−0.904850	−	1.56725i	−0.821119	−	0.570757i	$-0.806650\pi$
$743$	−24.6644	−	42.7200i	−0.904850	−	1.56725i	−0.0837309	−	0.996488i	$-0.526684\pi$
$744$		0			0
$745$	−29.2921	+	50.7354i	−1.07318	+	1.85880i
$746$		0			0
$747$	−2.02554	−	8.62146i	−0.0741105	−	0.315443i
$748$		0			0
$749$	−13.1168	+	22.7190i	−0.479279	+	0.830136i
$750$		0			0
$751$	10.8817	+	18.8477i	0.397081	+	0.687764i	0.993364	−	0.115010i	$-0.0366900\pi$
$751$	10.8817	+	18.8477i	0.397081	+	0.687764i	−0.596284	+	0.802774i	$0.703357\pi$
$752$		0			0
$753$	−10.6753	−	26.9480i	−0.389028	−	0.982039i
$754$		0			0
$755$	−15.8593			−0.577181
$756$		0			0
$757$	34.4674			1.25274			0.626369	−	0.779527i	$-0.284540\pi$
$757$	34.4674			1.25274			0.626369	+	0.779527i	$0.284540\pi$
$758$		0			0
$759$	2.62618	+	6.62936i	0.0953242	+	0.240630i
$760$		0			0
$761$	−7.31386	−	12.6680i	−0.265127	−	0.459214i	0.702470	−	0.711714i	$-0.252081\pi$
$761$	−7.31386	−	12.6680i	−0.265127	−	0.459214i	−0.967597	+	0.252500i	$0.918747\pi$
$762$		0			0
$763$	−12.9073	+	22.3561i	−0.467275	+	0.809344i
$764$		0			0
$765$	22.9783	+	6.92820i	0.830780	+	0.250490i
$766$		0			0
$767$	−5.85300	+	10.1377i	−0.211339	+	0.366051i
$768$		0			0
$769$	16.0584	+	27.8140i	0.579082	+	1.00300i	0.995585	+	0.0938645i	$0.0299220\pi$
$769$	16.0584	+	27.8140i	0.579082	+	1.00300i	−0.416503	+	0.909134i	$0.636745\pi$
$770$		0			0
$771$	17.7358	−	22.3856i	0.638740	−	0.806197i
$772$		0			0
$773$	−7.25544			−0.260960			−0.130480	−	0.991451i	$-0.541652\pi$
$773$	−7.25544			−0.260960			−0.130480	+	0.991451i	$0.541652\pi$
$774$		0			0
$775$	41.1244			1.47723
$776$		0			0
$777$	32.2337	+	4.75372i	1.15638	+	0.170539i
$778$		0			0
$779$	2.78912	+	4.83090i	0.0999307	+	0.173085i
$780$		0			0
$781$	−4.11684	+	7.13058i	−0.147312	+	0.255152i
$782$		0			0
$783$	−22.9136	+	15.9444i	−0.818866	+	0.569806i
$784$		0			0
$785$	23.8030	−	41.2280i	0.849565	−	1.47149i
$786$		0			0
$787$	−4.42810	−	7.66970i	−0.157845	−	0.273395i	0.776246	−	0.630430i	$-0.217121\pi$
$787$	−4.42810	−	7.66970i	−0.157845	−	0.273395i	−0.934091	+	0.357034i	$0.883788\pi$
$788$		0			0
$789$	30.1753	+	4.45015i	1.07427	+	0.158430i
$790$		0			0
$791$	−81.6993			−2.90489
$792$		0			0
$793$	2.90491			0.103156
$794$		0			0
$795$	14.5090	−	18.3128i	0.514581	−	0.649488i
$796$		0			0
$797$	8.54755	+	14.8048i	0.302770	+	0.524412i	0.976762	−	0.214326i	$-0.0687554\pi$
$797$	8.54755	+	14.8048i	0.302770	+	0.524412i	−0.673993	+	0.738738i	$0.735422\pi$
$798$		0			0
$799$	−5.57825	+	9.66181i	−0.197344	+	0.341810i
$800$		0			0
$801$	−27.8614	+	26.1831i	−0.984434	+	0.925136i
$802$		0			0
$803$	4.53991	−	7.86335i	0.160210	−	0.277492i
$804$		0			0
$805$	37.2921	+	64.5918i	1.31437	+	2.27656i
$806$		0			0
$807$	−8.60485	−	21.7216i	−0.302905	−	0.764635i
$808$		0			0
$809$	−18.3723			−0.645935			−0.322968	−	0.946410i	$-0.604680\pi$
$809$	−18.3723			−0.645935			−0.322968	+	0.946410i	$0.604680\pi$
$810$		0			0
$811$	50.2042			1.76291			0.881454	−	0.472269i	$-0.156565\pi$
$811$	50.2042			1.76291			0.881454	+	0.472269i	$0.156565\pi$
$812$		0			0
$813$	14.2337	+	35.9306i	0.499197	+	1.26014i
$814$		0			0
$815$	−31.7187	−	54.9384i	−1.11106	−	1.92441i
$816$		0			0
$817$	2.44158	−	4.22894i	0.0854200	−	0.147952i
$818$		0			0
$819$	−14.1086	+	13.2587i	−0.492993	+	0.463297i
$820$		0			0
$821$	−1.31386	+	2.27567i	−0.0458540	+	0.0794215i	−0.888041	−	0.459763i	$-0.847934\pi$
$821$	−1.31386	+	2.27567i	−0.0458540	+	0.0794215i	0.842187	+	0.539185i	$0.181268\pi$
$822$		0			0
$823$	−10.8817	−	18.8477i	−0.379314	−	0.656991i	0.611649	−	0.791129i	$-0.290507\pi$
$823$	−10.8817	−	18.8477i	−0.379314	−	0.656991i	−0.990963	+	0.134139i	$0.957173\pi$
$824$		0			0
$825$	−6.00000	+	7.57301i	−0.208893	+	0.263658i
$826$		0			0
$827$	−18.8114			−0.654137			−0.327069	−	0.945001i	$-0.606061\pi$
$827$	−18.8114			−0.654137			−0.327069	+	0.945001i	$0.606061\pi$
$828$		0			0
$829$	26.2337			0.911134			0.455567	−	0.890202i	$-0.349437\pi$
$829$	26.2337			0.911134			0.455567	+	0.890202i	$0.349437\pi$
$830$		0			0
$831$	7.05428	+	1.04034i	0.244710	+	0.0360891i
$832$		0			0
$833$	17.9307	+	31.0569i	0.621262	+	1.07606i
$834$		0			0
$835$	−10.8817	+	18.8477i	−0.376578	+	0.652253i
$836$		0			0
$837$	2.82473	+	33.4149i	0.0976371	+	1.15499i
$838$		0			0
$839$	−3.22682	+	5.58902i	−0.111402	+	0.192954i	−0.916336	−	0.400411i	$-0.868868\pi$
$839$	−3.22682	+	5.58902i	−0.111402	+	0.192954i	0.804934	+	0.593365i	$0.202201\pi$
$840$		0			0
$841$	0.0692967	+	0.120025i	0.00238954	+	0.00413881i
$842$		0			0
$843$	4.90307	+	0.723089i	0.168871	+	0.0249045i
$844$		0			0
$845$	37.4891			1.28967
$846$		0			0
$847$	48.1275			1.65368
$848$		0			0
$849$	17.0584	−	21.5306i	0.585444	−	0.738929i
$850$		0			0
$851$	9.40571	+	16.2912i	0.322424	+	0.558454i
$852$		0			0
$853$	1.94158	−	3.36291i	0.0664784	−	0.115144i	−0.830870	−	0.556466i	$-0.812157\pi$
$853$	1.94158	−	3.36291i	0.0664784	−	0.115144i	0.897349	+	0.441322i	$0.145490\pi$
$854$		0			0
$855$	54.0317	+	16.2912i	1.84784	+	0.557146i
$856$		0			0
$857$	−9.54755	+	16.5368i	−0.326138	+	0.564888i	−0.981742	−	0.190217i	$-0.939081\pi$
$857$	−9.54755	+	16.5368i	−0.326138	+	0.564888i	0.655604	+	0.755105i	$0.272414\pi$
$858$		0			0
$859$	1.31309	+	2.27434i	0.0448020	+	0.0775994i	0.887557	−	0.460698i	$-0.152401\pi$
$859$	1.31309	+	2.27434i	0.0448020	+	0.0775994i	−0.842755	+	0.538298i	$0.819068\pi$
$860$		0			0
$861$	−3.00000	−	7.57301i	−0.102240	−	0.258088i
$862$		0			0
$863$	−37.6228			−1.28070			−0.640348	−	0.768085i	$-0.721210\pi$
$863$	−37.6228			−1.28070			−0.640348	+	0.768085i	$0.721210\pi$
$864$		0			0
$865$	−18.1168			−0.615991
$866$		0			0
$867$	−7.25450	−	18.3128i	−0.246376	−	0.621935i
$868$		0			0
$869$	−2.82473	−	4.89258i	−0.0958225	−	0.165970i
$870$		0			0
$871$	5.85300	−	10.1377i	0.198321	−	0.343502i
$872$		0			0
$873$	−6.17527	−	26.2843i	−0.209001	−	0.889590i
$874$		0			0
$875$	−10.8817	+	18.8477i	−0.367870	+	0.637170i
$876$		0			0
$877$	−19.1753	−	33.2125i	−0.647503	−	1.12151i	−0.983717	−	0.179722i	$-0.942480\pi$
$877$	−19.1753	−	33.2125i	−0.647503	−	1.12151i	0.336215	−	0.941785i	$-0.390853\pi$
$878$		0			0
$879$	−15.7337	+	19.8586i	−0.530684	+	0.669812i
$880$		0			0
$881$	−30.2337			−1.01860			−0.509299	−	0.860589i	$-0.670095\pi$
$881$	−30.2337			−1.01860			−0.509299	+	0.860589i	$0.670095\pi$
$882$		0			0
$883$	−32.0446			−1.07839			−0.539193	−	0.842182i	$-0.681271\pi$
$883$	−32.0446			−1.07839			−0.539193	+	0.842182i	$0.681271\pi$
$884$		0			0
$885$	−49.2921	−	7.26944i	−1.65694	−	0.244360i
$886$		0			0
$887$	−10.8817	−	18.8477i	−0.365373	−	0.632845i	0.623463	−	0.781853i	$-0.285725\pi$
$887$	−10.8817	−	18.8477i	−0.365373	−	0.632845i	−0.988836	+	0.149008i	$0.952392\pi$
$888$		0			0
$889$	26.2337	−	45.4381i	0.879850	−	1.52394i
$890$		0			0
$891$	−6.56544	−	4.35502i	−0.219951	−	0.145899i
$892$		0			0
$893$	−13.1168	+	22.7190i	−0.438938	+	0.760264i
$894$		0			0
$895$	−31.7187	−	54.9384i	−1.06024	−	1.83639i
$896$		0			0
$897$	−11.0584	−	1.63086i	−0.369230	−	0.0544529i
$898$		0			0
$899$	−34.6708			−1.15633
$900$		0			0
$901$	9.48913			0.316129
$902$		0			0
$903$	−4.42810	+	5.58902i	−0.147358	+	0.185991i
$904$		0			0
$905$	44.2337	+	76.6150i	1.47038	+	2.54677i
$906$		0			0
$907$	−17.1724	+	29.7435i	−0.570201	+	0.987618i	0.426343	+	0.904561i	$0.359802\pi$
$907$	−17.1724	+	29.7435i	−0.570201	+	0.987618i	−0.996545	+	0.0830565i	$0.973532\pi$
$908$		0			0
$909$	−1.45245	−	6.18220i	−0.0481748	−	0.205051i
$910$		0			0
$911$	−11.4312	+	19.7995i	−0.378734	+	0.655987i	−0.990878	−	0.134759i	$-0.956974\pi$
$911$	−11.4312	+	19.7995i	−0.378734	+	0.655987i	0.612144	+	0.790746i	$0.290307\pi$
$912$		0			0
$913$	1.29211	+	2.23800i	0.0427626	+	0.0740670i
$914$		0			0
$915$	4.55378	+	11.4953i	0.150543	+	0.380022i
$916$		0			0
$917$	30.3505			1.00226
$918$		0			0
$919$	26.4663			0.873044			0.436522	−	0.899694i	$-0.356210\pi$
$919$	26.4663			0.873044			0.436522	+	0.899694i	$0.356210\pi$
$920$		0			0
$921$	13.3247	+	33.6361i	0.439065	+	1.10835i
$922$		0			0
$923$	−6.45364	−	11.1780i	−0.212424	−	0.367929i
$924$		0			0
$925$	−12.7446	+	22.0742i	−0.419039	+	0.725796i
$926$		0			0
$927$	13.5079	+	4.07279i	0.443658	+	0.133768i
$928$		0			0
$929$	−15.3139	+	26.5244i	−0.502431	+	0.870237i	0.497565	+	0.867427i	$0.334228\pi$
$929$	−15.3139	+	26.5244i	−0.502431	+	0.870237i	−0.999996	+	0.00280985i	$0.999106\pi$
$930$		0			0
$931$	42.1627	+	73.0280i	1.38183	+	2.39340i
$932$		0			0
$933$	−29.0584	+	36.6766i	−0.951330	+	1.20074i
$934$		0			0
$935$	−7.00314			−0.229027
$936$		0			0
$937$	−22.2337			−0.726343			−0.363171	−	0.931722i	$-0.618306\pi$
$937$	−22.2337			−0.726343			−0.363171	+	0.931722i	$0.618306\pi$
$938$		0			0
$939$	26.1032	+	3.84961i	0.851845	+	0.125627i
$940$		0			0
$941$	−8.54755	−	14.8048i	−0.278642	−	0.482622i	0.692405	−	0.721509i	$-0.256551\pi$
$941$	−8.54755	−	14.8048i	−0.278642	−	0.482622i	−0.971048	+	0.238886i	$0.923218\pi$
$942$		0			0
$943$	2.35143	−	4.07279i	0.0765730	−	0.132628i
$944$		0			0
$945$	−74.5842	−	35.0458i	−2.42622	−	1.14004i
$946$		0			0
$947$	2.51437	−	4.35502i	0.0817062	−	0.141519i	−0.822277	−	0.569088i	$-0.807296\pi$
$947$	2.51437	−	4.35502i	0.0817062	−	0.141519i	0.903983	+	0.427569i	$0.140630\pi$
$948$		0			0
$949$	7.11684	+	12.3267i	0.231023	+	0.400143i
$950$		0			0
$951$	−4.50264	−	0.664035i	−0.146008	−	0.0215328i
$952$		0			0
$953$	8.60597			0.278775			0.139387	−	0.990238i	$-0.455487\pi$
$953$	8.60597			0.278775			0.139387	+	0.990238i	$0.455487\pi$
$954$		0			0
$955$	−59.3863			−1.92170
$956$		0			0
$957$	5.05842	−	6.38458i	0.163516	−	0.206384i
$958$		0			0
$959$	24.6644	+	42.7200i	0.796456	+	1.37950i
$960$		0			0
$961$	−5.32473	+	9.22271i	−0.171766	+	0.297507i
$962$		0			0
$963$	12.1948	−	11.4603i	0.392973	−	0.369302i
$964$		0			0
$965$	1.68614	−	2.92048i	0.0542788	−	0.0940136i
$966$		0			0
$967$	24.6644	+	42.7200i	0.793154	+	1.37378i	0.924005	+	0.382381i	$0.124896\pi$
$967$	24.6644	+	42.7200i	0.793154	+	1.37378i	−0.130850	+	0.991402i	$0.541771\pi$
$968$		0			0
$969$	8.44158	+	21.3094i	0.271183	+	0.684556i
$970$		0			0
$971$	57.5333			1.84633			0.923165	−	0.384404i	$-0.125593\pi$
$971$	57.5333			1.84633			0.923165	+	0.384404i	$0.125593\pi$
$972$		0			0
$973$	92.5842			2.96811
$974$		0			0
$975$	−5.57825	−	14.0814i	−0.178647	−	0.450965i
$976$		0			0
$977$	−22.6168	−	39.1735i	−0.723577	−	1.25327i	−0.959557	−	0.281514i	$-0.909163\pi$
$977$	−22.6168	−	39.1735i	−0.723577	−	1.25327i	0.235980	−	0.971758i	$-0.424170\pi$
$978$		0			0
$979$	5.57825	−	9.66181i	0.178282	−	0.308793i
$980$		0			0
$981$	12.0000	−	11.2772i	0.383131	−	0.360052i
$982$		0			0
$983$	29.6932	−	51.4301i	0.947065	−	1.64036i	0.195502	−	0.980703i	$-0.437367\pi$
$983$	29.6932	−	51.4301i	0.947065	−	1.64036i	0.751563	−	0.659661i	$-0.229300\pi$
$984$		0			0
$985$	−18.1168	−	31.3793i	−0.577251	−	0.999827i
$986$		0			0
$987$	23.7890	−	30.0258i	0.757213	−	0.955731i
$988$		0			0
$989$	−4.11684			−0.130908
$990$		0			0
$991$	−7.00314			−0.222462			−0.111231	−	0.993795i	$-0.535479\pi$
$991$	−7.00314			−0.222462			−0.111231	+	0.993795i	$0.535479\pi$
$992$		0			0
$993$	17.0584	+	2.51572i	0.541333	+	0.0798340i
$994$		0			0
$995$	−28.7666	−	49.8253i	−0.911963	−	1.57957i
$996$		0			0
$997$	5.17527	−	8.96382i	0.163902	−	0.283887i	−0.772363	−	0.635182i	$-0.780925\pi$
$997$	5.17527	−	8.96382i	0.163902	−	0.283887i	0.936265	+	0.351295i	$0.114258\pi$
$998$		0			0
$999$	−18.8114	−	8.83915i	−0.595167	−	0.279658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.i.f.97.3	yes	8
3.2	odd	2		864.2.i.f.289.2		8
4.3	odd	2	inner	288.2.i.f.97.2	✓	8
8.3	odd	2		576.2.i.n.385.3		8
8.5	even	2		576.2.i.n.385.2		8
9.2	odd	6		2592.2.a.x.1.3		4
9.4	even	3	inner	288.2.i.f.193.3	yes	8
9.5	odd	6		864.2.i.f.577.2		8
9.7	even	3		2592.2.a.u.1.1		4
12.11	even	2		864.2.i.f.289.1		8
24.5	odd	2		1728.2.i.n.1153.4		8
24.11	even	2		1728.2.i.n.1153.3		8
36.7	odd	6		2592.2.a.u.1.2		4
36.11	even	6		2592.2.a.x.1.4		4
36.23	even	6		864.2.i.f.577.1		8
36.31	odd	6	inner	288.2.i.f.193.2	yes	8
72.5	odd	6		1728.2.i.n.577.4		8
72.11	even	6		5184.2.a.cc.1.2		4
72.13	even	6		576.2.i.n.193.2		8
72.29	odd	6		5184.2.a.cc.1.1		4
72.43	odd	6		5184.2.a.cf.1.4		4
72.59	even	6		1728.2.i.n.577.3		8
72.61	even	6		5184.2.a.cf.1.3		4
72.67	odd	6		576.2.i.n.193.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.i.f.97.2	✓	8	4.3	odd	2	inner
288.2.i.f.97.3	yes	8	1.1	even	1	trivial
288.2.i.f.193.2	yes	8	36.31	odd	6	inner
288.2.i.f.193.3	yes	8	9.4	even	3	inner
576.2.i.n.193.2		8	72.13	even	6
576.2.i.n.193.3		8	72.67	odd	6
576.2.i.n.385.2		8	8.5	even	2
576.2.i.n.385.3		8	8.3	odd	2
864.2.i.f.289.1		8	12.11	even	2
864.2.i.f.289.2		8	3.2	odd	2
864.2.i.f.577.1		8	36.23	even	6
864.2.i.f.577.2		8	9.5	odd	6
1728.2.i.n.577.3		8	72.59	even	6
1728.2.i.n.577.4		8	72.5	odd	6
1728.2.i.n.1153.3		8	24.11	even	2
1728.2.i.n.1153.4		8	24.5	odd	2
2592.2.a.u.1.1		4	9.7	even	3
2592.2.a.u.1.2		4	36.7	odd	6
2592.2.a.x.1.3		4	9.2	odd	6
2592.2.a.x.1.4		4	36.11	even	6
5184.2.a.cc.1.1		4	72.29	odd	6
5184.2.a.cc.1.2		4	72.11	even	6
5184.2.a.cf.1.3		4	72.61	even	6
5184.2.a.cf.1.4		4	72.43	odd	6

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.637910 + 1.61030i) q^{3} +(1.68614 + 2.92048i) q^{5} +(2.35143 - 4.07279i) q^{7} +(-2.18614 + 2.05446i) q^{9} +O(q^{10})\)	\(q+(0.637910 + 1.61030i) q^{3} +(1.68614 + 2.92048i) q^{5} +(2.35143 - 4.07279i) q^{7} +(-2.18614 + 2.05446i) q^{9} +(0.437696 - 0.758112i) q^{11} +(0.686141 + 1.18843i) q^{13} +(-3.62725 + 4.57820i) q^{15} -2.37228 q^{17} -5.57825 q^{19} +(8.05842 + 1.18843i) q^{21} +(2.35143 + 4.07279i) q^{23} +(-3.18614 + 5.51856i) q^{25} +(-4.70285 - 2.20979i) q^{27} +(2.68614 - 4.65253i) q^{29} +(-3.22682 - 5.58902i) q^{31} +(1.50000 + 0.221215i) q^{33} +15.8593 q^{35} +4.00000 q^{37} +(-1.47603 + 1.86301i) q^{39} +(-0.500000 - 0.866025i) q^{41} +(-0.437696 + 0.758112i) q^{43} +(-9.68614 - 2.92048i) q^{45} +(2.35143 - 4.07279i) q^{47} +(-7.55842 - 13.0916i) q^{49} +(-1.51330 - 3.82009i) q^{51} -4.00000 q^{53} +2.95207 q^{55} +(-3.55842 - 8.98266i) q^{57} +(4.26516 + 7.38747i) q^{59} +(1.05842 - 1.83324i) q^{61} +(3.22682 + 13.7346i) q^{63} +(-2.31386 + 4.00772i) q^{65} +(-4.26516 - 7.38747i) q^{67} +(-5.05842 + 6.38458i) q^{69} -9.40571 q^{71} +10.3723 q^{73} +(-10.9190 - 1.61030i) q^{75} +(-2.05842 - 3.56529i) q^{77} +(3.22682 - 5.58902i) q^{79} +(0.558422 - 8.98266i) q^{81} +(-1.47603 + 2.55657i) q^{83} +(-4.00000 - 6.92820i) q^{85} +(9.20550 + 1.35760i) q^{87} +12.7446 q^{89} +6.45364 q^{91} +(6.94158 - 8.76144i) q^{93} +(-9.40571 - 16.2912i) q^{95} +(-4.50000 + 7.79423i) q^{97} +(0.600642 + 2.55657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 8 * q + 2 * q^5 - 6 * q^9	\( 8 q + 2 q^{5} - 6 q^{9} - 6 q^{13} + 4 q^{17} + 30 q^{21} - 14 q^{25} + 10 q^{29} + 12 q^{33} + 32 q^{37} - 4 q^{41} - 66 q^{45} - 26 q^{49} - 32 q^{53} + 6 q^{57} - 26 q^{61} - 30 q^{65} - 6 q^{69} + 60 q^{73} + 18 q^{77} - 30 q^{81} - 32 q^{85} + 56 q^{89} + 90 q^{93} - 36 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 - 6 * q^9 - 6 * q^13 + 4 * q^17 + 30 * q^21 - 14 * q^25 + 10 * q^29 + 12 * q^33 + 32 * q^37 - 4 * q^41 - 66 * q^45 - 26 * q^49 - 32 * q^53 + 6 * q^57 - 26 * q^61 - 30 * q^65 - 6 * q^69 + 60 * q^73 + 18 * q^77 - 30 * q^81 - 32 * q^85 + 56 * q^89 + 90 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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