LMFDB - Embedded newform 765.2.be.b.586.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(406,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("765.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.be (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			586.4
Character	$\chi$	$=$	765.586
Dual form			765.2.be.b.406.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.254738 - 0.254738i) q^{2} +1.87022i q^{4} +(-0.923880 - 0.382683i) q^{5} +(0.275980 - 0.114315i) q^{7} +(0.985893 + 0.985893i) q^{8} +O(q^{10})$	\(q+(0.254738 - 0.254738i) q^{2} +1.87022i q^{4} +(-0.923880 - 0.382683i) q^{5} +(0.275980 - 0.114315i) q^{7} +(0.985893 + 0.985893i) q^{8} +(-0.332832 + 0.137863i) q^{10} +(1.05900 + 2.55665i) q^{11} -1.97956i q^{13} +(0.0411823 - 0.0994229i) q^{14} -3.23814 q^{16} +(1.21202 + 3.94094i) q^{17} +(-1.99331 + 1.99331i) q^{19} +(0.715701 - 1.72785i) q^{20} +(0.921046 + 0.381510i) q^{22} +(2.57919 + 6.22672i) q^{23} +(0.707107 + 0.707107i) q^{25} +(-0.504269 - 0.504269i) q^{26} +(0.213793 + 0.516142i) q^{28} +(-4.36632 - 1.80859i) q^{29} +(1.15808 - 2.79584i) q^{31} +(-2.79667 + 2.79667i) q^{32} +(1.31266 + 0.695159i) q^{34} -0.298718 q^{35} +(-3.60537 + 8.70414i) q^{37} +1.01554i q^{38} +(-0.533561 - 1.28813i) q^{40} +(-2.87301 + 1.19004i) q^{41} +(5.78771 + 5.78771i) q^{43} +(-4.78150 + 1.98056i) q^{44} +(2.24320 + 0.929166i) q^{46} -1.08341i q^{47} +(-4.88665 + 4.88665i) q^{49} +0.360254 q^{50} +3.70220 q^{52} +(1.89858 - 1.89858i) q^{53} -2.76730i q^{55} +(0.384788 + 0.159384i) q^{56} +(-1.57299 + 0.651553i) q^{58} +(6.47310 + 6.47310i) q^{59} +(10.3418 - 4.28372i) q^{61} +(-0.417202 - 1.00722i) q^{62} -5.05145i q^{64} +(-0.757544 + 1.82887i) q^{65} -12.5585 q^{67} +(-7.37041 + 2.26675i) q^{68} +(-0.0760950 + 0.0760950i) q^{70} +(2.25315 - 5.43960i) q^{71} +(-0.200173 - 0.0829144i) q^{73} +(1.29885 + 3.13570i) q^{74} +(-3.72792 - 3.72792i) q^{76} +(0.584525 + 0.584525i) q^{77} +(-4.07771 - 9.84447i) q^{79} +(2.99165 + 1.23918i) q^{80} +(-0.428717 + 1.03501i) q^{82} +(11.0129 - 11.0129i) q^{83} +(0.388367 - 4.10477i) q^{85} +2.94870 q^{86} +(-1.47653 + 3.56465i) q^{88} +1.55264i q^{89} +(-0.226292 - 0.546318i) q^{91} +(-11.6453 + 4.82365i) q^{92} +(-0.275986 - 0.275986i) q^{94} +(2.60438 - 1.07877i) q^{95} +(8.28752 + 3.43280i) q^{97} +2.48963i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	0.254738	−	0.254738i	0.180127	−	0.180127i	−0.611284	−	0.791411i	$-0.709347\pi$
$2$	0.254738	−	0.254738i	0.180127	−	0.180127i	0.791411	+	0.611284i	$0.209347\pi$
$3$		0			0
$3$		0			0
$4$			1.87022i			0.935108i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$6$		0			0
$7$	0.275980	−	0.114315i	0.104310	−	0.0432068i	−0.329918	−	0.944010i	$-0.607021\pi$
$7$	0.275980	−	0.114315i	0.104310	−	0.0432068i	0.434228	+	0.900803i	$0.357021\pi$
$8$	0.985893	+	0.985893i	0.348566	+	0.348566i
$9$		0			0
$10$	−0.332832	+	0.137863i	−0.105251	+	0.0435962i
$11$	1.05900	+	2.55665i	0.319301	+	0.770860i	0.999291	+	0.0376394i	$0.0119838\pi$
$11$	1.05900	+	2.55665i	0.319301	+	0.770860i	−0.679991	+	0.733221i	$0.738016\pi$
$12$		0			0
$13$		−	1.97956i		−	0.549030i	−0.961583	−	0.274515i	$-0.911483\pi$
$13$		−	1.97956i		−	0.549030i	0.961583	−	0.274515i	$-0.0885174\pi$
$14$	0.0411823	−	0.0994229i	0.0110064	−	0.0265719i
$15$		0			0
$16$	−3.23814			−0.809536
$17$	1.21202	+	3.94094i	0.293959	+	0.955818i
$17$	1.21202	+	3.94094i	0.293959	+	0.955818i
$18$		0			0
$19$	−1.99331	+	1.99331i	−0.457296	+	0.457296i	−0.897767	−	0.440471i	$-0.854812\pi$
$19$	−1.99331	+	1.99331i	−0.457296	+	0.457296i	0.440471	+	0.897767i	$0.354812\pi$
$20$	0.715701	−	1.72785i	0.160036	−	0.386360i
$21$		0			0
$22$	0.921046	+	0.381510i	0.196368	+	0.0813382i
$23$	2.57919	+	6.22672i	0.537799	+	1.29836i	0.926256	+	0.376895i	$0.123008\pi$
$23$	2.57919	+	6.22672i	0.537799	+	1.29836i	−0.388457	+	0.921467i	$0.626992\pi$
$24$		0			0
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	−0.504269	−	0.504269i	−0.0988953	−	0.0988953i
$27$		0			0
$28$	0.213793	+	0.516142i	0.0404031	+	0.0975416i
$29$	−4.36632	−	1.80859i	−0.810806	−	0.335847i	−0.0615305	−	0.998105i	$-0.519598\pi$
$29$	−4.36632	−	1.80859i	−0.810806	−	0.335847i	−0.749276	+	0.662258i	$0.769598\pi$
$30$		0			0
$31$	1.15808	−	2.79584i	0.207997	−	0.502148i	−0.785111	−	0.619355i	$-0.787394\pi$
$31$	1.15808	−	2.79584i	0.207997	−	0.502148i	0.993108	+	0.117207i	$0.0373941\pi$
$32$	−2.79667	+	2.79667i	−0.494385	+	0.494385i
$33$		0			0
$34$	1.31266	+	0.695159i	0.225119	+	0.119219i
$35$	−0.298718			−0.0504926
$36$		0			0
$37$	−3.60537	+	8.70414i	−0.592719	+	1.43095i	0.288147	+	0.957586i	$0.406961\pi$
$37$	−3.60537	+	8.70414i	−0.592719	+	1.43095i	−0.880866	+	0.473365i	$0.843039\pi$
$38$			1.01554i			0.164743i
$39$		0			0
$40$	−0.533561	−	1.28813i	−0.0843635	−	0.203671i
$41$	−2.87301	+	1.19004i	−0.448688	+	0.185853i	−0.595574	−	0.803301i	$-0.703075\pi$
$41$	−2.87301	+	1.19004i	−0.448688	+	0.185853i	0.146885	+	0.989154i	$0.453075\pi$
$42$		0			0
$43$	5.78771	+	5.78771i	0.882617	+	0.882617i	0.993800	−	0.111183i	$-0.0354638\pi$
$43$	5.78771	+	5.78771i	0.882617	+	0.882617i	−0.111183	+	0.993800i	$0.535464\pi$
$44$	−4.78150	+	1.98056i	−0.720838	+	0.298581i
$45$		0			0
$46$	2.24320	+	0.929166i	0.330742	+	0.136998i
$47$		−	1.08341i		−	0.158032i	−0.996873	−	0.0790159i	$-0.974822\pi$
$47$		−	1.08341i		−	0.158032i	0.996873	−	0.0790159i	$-0.0251778\pi$
$48$		0			0
$49$	−4.88665	+	4.88665i	−0.698093	+	0.698093i
$50$	0.360254			0.0509477
$51$		0			0
$52$	3.70220			0.513403
$53$	1.89858	−	1.89858i	0.260790	−	0.260790i	−0.564585	−	0.825375i	$-0.690964\pi$
$53$	1.89858	−	1.89858i	0.260790	−	0.260790i	0.825375	+	0.564585i	$0.190964\pi$
$54$		0			0
$55$		−	2.76730i		−	0.373143i
$56$	0.384788	+	0.159384i	0.0514195	+	0.0212986i
$57$		0			0
$58$	−1.57299	+	0.651553i	−0.206543	+	0.0855531i
$59$	6.47310	+	6.47310i	0.842726	+	0.842726i	0.989213	−	0.146487i	$-0.0467966\pi$
$59$	6.47310	+	6.47310i	0.842726	+	0.842726i	−0.146487	+	0.989213i	$0.546797\pi$
$60$		0			0
$61$	10.3418	−	4.28372i	1.32413	−	0.548474i	0.395158	−	0.918613i	$-0.370690\pi$
$61$	10.3418	−	4.28372i	1.32413	−	0.548474i	0.928976	+	0.370139i	$0.120690\pi$
$62$	−0.417202	−	1.00722i	−0.0529847	−	0.127916i
$63$		0			0
$64$		−	5.05145i		−	0.631432i
$65$	−0.757544	+	1.82887i	−0.0939617	+	0.226844i
$66$		0			0
$67$	−12.5585			−1.53427			−0.767133	−	0.641488i	$-0.778317\pi$
$67$	−12.5585			−1.53427			−0.767133	+	0.641488i	$0.778317\pi$
$68$	−7.37041	+	2.26675i	−0.893793	+	0.274884i
$69$		0			0
$70$	−0.0760950	+	0.0760950i	−0.00909509	+	0.00909509i
$71$	2.25315	−	5.43960i	0.267400	−	0.645561i	−0.731959	−	0.681348i	$-0.761394\pi$
$71$	2.25315	−	5.43960i	0.267400	−	0.645561i	0.999359	+	0.0357872i	$0.0113939\pi$
$72$		0			0
$73$	−0.200173	−	0.0829144i	−0.0234285	−	0.00970440i	0.370938	−	0.928657i	$-0.379036\pi$
$73$	−0.200173	−	0.0829144i	−0.0234285	−	0.00970440i	−0.394367	+	0.918953i	$0.629036\pi$
$74$	1.29885	+	3.13570i	0.150988	+	0.364518i
$75$		0			0
$76$	−3.72792	−	3.72792i	−0.427622	−	0.427622i
$77$	0.584525	+	0.584525i	0.0666128	+	0.0666128i
$78$		0			0
$79$	−4.07771	−	9.84447i	−0.458779	−	1.10759i	−0.968892	−	0.247482i	$-0.920397\pi$
$79$	−4.07771	−	9.84447i	−0.458779	−	1.10759i	0.510114	−	0.860107i	$-0.329603\pi$
$80$	2.99165	+	1.23918i	0.334477	+	0.138545i
$81$		0			0
$82$	−0.428717	+	1.03501i	−0.0473438	+	0.114298i
$83$	11.0129	−	11.0129i	1.20883	−	1.20883i	0.237421	−	0.971407i	$-0.423698\pi$
$83$	11.0129	−	11.0129i	1.20883	−	1.20883i	0.971407	−	0.237421i	$-0.0763020\pi$
$84$		0			0
$85$	0.388367	−	4.10477i	0.0421243	−	0.445225i
$86$	2.94870			0.317967
$87$		0			0
$88$	−1.47653	+	3.56465i	−0.157398	+	0.379993i
$89$			1.55264i			0.164579i	0.996608	+	0.0822897i	$0.0262233\pi$
$89$			1.55264i			0.164579i	−0.996608	+	0.0822897i	$0.973777\pi$
$90$		0			0
$91$	−0.226292	−	0.546318i	−0.0237219	−	0.0572696i
$92$	−11.6453	+	4.82365i	−1.21411	+	0.502900i
$93$		0			0
$94$	−0.275986	−	0.275986i	−0.0284658	−	0.0284658i
$95$	2.60438	−	1.07877i	0.267204	−	0.110680i
$96$		0			0
$97$	8.28752	+	3.43280i	0.841471	+	0.348549i	0.761433	−	0.648243i	$-0.224496\pi$
$97$	8.28752	+	3.43280i	0.841471	+	0.348549i	0.0800373	+	0.996792i	$0.474496\pi$
$98$			2.48963i			0.251491i
$99$		0			0
$100$	−1.32244	+	1.32244i	−0.132244	+	0.132244i
$101$	6.92132			0.688697			0.344349	−	0.938842i	$-0.388100\pi$
$101$	6.92132			0.688697			0.344349	+	0.938842i	$0.388100\pi$
$102$		0			0
$103$	12.9642			1.27740			0.638699	−	0.769457i	$-0.279473\pi$
$103$	12.9642			1.27740			0.638699	+	0.769457i	$0.279473\pi$
$104$	1.95163	−	1.95163i	0.191373	−	0.191373i
$105$		0			0
$106$		−	0.967283i		−	0.0939508i
$107$	3.34779	+	1.38670i	0.323643	+	0.134058i	0.538589	−	0.842568i	$-0.318957\pi$
$107$	3.34779	+	1.38670i	0.323643	+	0.134058i	−0.214946	+	0.976626i	$0.568957\pi$
$108$		0			0
$109$	−4.75832	+	1.97096i	−0.455764	+	0.188784i	−0.598742	−	0.800942i	$-0.704332\pi$
$109$	−4.75832	+	1.97096i	−0.455764	+	0.188784i	0.142977	+	0.989726i	$0.454332\pi$
$110$	−0.704938	−	0.704938i	−0.0672132	−	0.0672132i
$111$		0			0
$112$	−0.893662	+	0.370167i	−0.0844431	+	0.0349775i
$113$	−4.21202	−	10.1687i	−0.396234	−	0.956593i	−0.988551	−	0.150888i	$-0.951787\pi$
$113$	−4.21202	−	10.1687i	−0.396234	−	0.956593i	0.592317	−	0.805705i	$-0.298213\pi$
$114$		0			0
$115$		−	6.73975i		−	0.628485i
$116$	3.38246	−	8.16597i	0.314053	−	0.758192i
$117$		0			0
$118$	3.29789			0.303596
$119$	0.785001	+	0.949067i	0.0719609	+	0.0870008i
$120$		0			0
$121$	2.36318	−	2.36318i	0.214834	−	0.214834i
$122$	1.54323	−	3.72569i	0.139717	−	0.337308i
$123$		0			0
$124$	5.22883	+	2.16585i	0.469563	+	0.194499i
$125$	−0.382683	−	0.923880i	−0.0342282	−	0.0826343i
$126$		0			0
$127$	5.18472	+	5.18472i	0.460070	+	0.460070i	0.898678	−	0.438608i	$-0.144528\pi$
$127$	5.18472	+	5.18472i	0.460070	+	0.460070i	−0.438608	+	0.898678i	$0.644528\pi$
$128$	−6.88013	−	6.88013i	−0.608123	−	0.608123i
$129$		0			0
$130$	0.272909	+	0.658860i	0.0239357	+	0.0577858i
$131$	−16.0035	−	6.62885i	−1.39823	−	0.579166i	−0.448938	−	0.893563i	$-0.648198\pi$
$131$	−16.0035	−	6.62885i	−1.39823	−	0.579166i	−0.949291	+	0.314397i	$0.898198\pi$
$132$		0			0
$133$	−0.322249	+	0.777977i	−0.0279425	+	0.0674592i
$134$	−3.19913	+	3.19913i	−0.276363	+	0.276363i
$135$		0			0
$136$	−2.69042	+	5.08027i	−0.230701	+	0.435629i
$137$	13.9745			1.19392			0.596959	−	0.802272i	$-0.296375\pi$
$137$	13.9745			1.19392			0.596959	+	0.802272i	$0.296375\pi$
$138$		0			0
$139$	−1.38555	+	3.34501i	−0.117521	+	0.283720i	−0.971684	−	0.236285i	$-0.924070\pi$
$139$	−1.38555	+	3.34501i	−0.117521	+	0.283720i	0.854163	+	0.520005i	$0.174070\pi$
$140$		−	0.558668i		−	0.0472160i
$141$		0			0
$142$	−0.811709	−	1.95964i	−0.0681171	−	0.164449i
$143$	5.06104	−	2.09635i	0.423226	−	0.175306i
$144$		0			0
$145$	3.34184	+	3.34184i	0.277525	+	0.277525i
$146$	−0.0721133	+	0.0298703i	−0.00596814	+	0.00247208i
$147$		0			0
$148$	−16.2786	−	6.74283i	−1.33809	−	0.554257i
$149$		−	12.8580i		−	1.05336i	−0.850062	−	0.526682i	$-0.823436\pi$
$149$		−	12.8580i		−	1.05336i	0.850062	−	0.526682i	$-0.176564\pi$
$150$		0			0
$151$	13.5511	−	13.5511i	1.10277	−	1.10277i	0.108700	−	0.994075i	$-0.465331\pi$
$151$	13.5511	−	13.5511i	1.10277	−	1.10277i	0.994075	−	0.108700i	$-0.0346687\pi$
$152$	−3.93038			−0.318796
$153$		0			0
$154$	0.297802			0.0239976
$155$	−2.13985	+	2.13985i	−0.171877	+	0.171877i
$156$		0			0
$157$			2.70222i			0.215661i	0.994169	+	0.107830i	$0.0343903\pi$
$157$			2.70222i			0.215661i	−0.994169	+	0.107830i	$0.965610\pi$
$158$	−3.54651	−	1.46901i	−0.282146	−	0.116868i
$159$		0			0
$160$	3.65402	−	1.51354i	0.288876	−	0.119656i
$161$	1.42361	+	1.42361i	0.112196	+	0.112196i
$162$		0			0
$163$	−15.8036	+	6.54609i	−1.23784	+	0.512729i	−0.903038	−	0.429561i	$-0.858668\pi$
$163$	−15.8036	+	6.54609i	−1.23784	+	0.512729i	−0.334799	+	0.942290i	$0.608668\pi$
$164$	−2.22563	−	5.37315i	−0.173792	−	0.419572i
$165$		0			0
$166$		−	5.61084i		−	0.435486i
$167$	−3.38773	+	8.17871i	−0.262151	+	0.632887i	−0.999071	−	0.0430919i	$-0.986279\pi$
$167$	−3.38773	+	8.17871i	−0.262151	+	0.632887i	0.736921	+	0.675979i	$0.236279\pi$
$168$		0			0
$169$	9.08135			0.698566
$170$	−0.946712	−	1.14458i	−0.0726095	−	0.0877849i
$171$		0			0
$172$	−10.8243	+	10.8243i	−0.825343	+	0.825343i
$173$	−7.34175	+	17.7246i	−0.558183	+	1.34757i	0.353020	+	0.935616i	$0.385155\pi$
$173$	−7.34175	+	17.7246i	−0.558183	+	1.34757i	−0.911203	+	0.411957i	$0.864845\pi$
$174$		0			0
$175$	0.275980	+	0.114315i	0.0208621	+	0.00864136i
$176$	−3.42920	−	8.27881i	−0.258485	−	0.624039i
$177$		0			0
$178$	0.395517	+	0.395517i	0.0296452	+	0.0296452i
$179$	3.06554	+	3.06554i	0.229129	+	0.229129i	0.812329	−	0.583200i	$-0.198199\pi$
$179$	3.06554	+	3.06554i	0.229129	+	0.229129i	−0.583200	+	0.812329i	$0.698199\pi$
$180$		0			0
$181$	−9.09958	−	21.9683i	−0.676366	−	1.63289i	−0.770582	−	0.637341i	$-0.780034\pi$
$181$	−9.09958	−	21.9683i	−0.676366	−	1.63289i	0.0942155	−	0.995552i	$-0.469966\pi$
$182$	−0.196813	−	0.0815228i	−0.0145888	−	0.00604287i
$183$		0			0
$184$	−3.59607	+	8.68169i	−0.265106	+	0.640022i
$185$	6.66186	−	6.66186i	0.489790	−	0.489790i
$186$		0			0
$187$	−8.79208	+	7.27219i	−0.642941	+	0.531795i
$188$	2.02621			0.147777
$189$		0			0
$190$	0.388632	−	0.938241i	0.0281943	−	0.0680672i
$191$		−	7.27055i		−	0.526079i	−0.964785	−	0.263039i	$-0.915275\pi$
$191$		−	7.27055i		−	0.526079i	0.964785	−	0.263039i	$-0.0847249\pi$
$192$		0			0
$193$	−8.49528	−	20.5094i	−0.611504	−	1.47630i	−0.861348	−	0.508015i	$-0.830380\pi$
$193$	−8.49528	−	20.5094i	−0.611504	−	1.47630i	0.249845	−	0.968286i	$-0.419620\pi$
$194$	2.98562	−	1.23668i	0.214355	−	0.0887887i
$195$		0			0
$196$	−9.13910	−	9.13910i	−0.652793	−	0.652793i
$197$	−4.14027	+	1.71496i	−0.294982	+	0.122186i	−0.525267	−	0.850938i	$-0.676034\pi$
$197$	−4.14027	+	1.71496i	−0.294982	+	0.122186i	0.230284	+	0.973123i	$0.426034\pi$
$198$		0			0
$199$	−0.368987	−	0.152839i	−0.0261568	−	0.0108345i	0.369567	−	0.929204i	$-0.379506\pi$
$199$	−0.368987	−	0.152839i	−0.0261568	−	0.0108345i	−0.395723	+	0.918370i	$0.629506\pi$
$200$			1.39426i			0.0985893i
$201$		0			0
$202$	1.76313	−	1.76313i	0.124053	−	0.124053i
$203$	−1.41176			−0.0990865
$204$		0			0
$205$	3.10972			0.217192
$206$	3.30247	−	3.30247i	0.230094	−	0.230094i
$207$		0			0
$208$			6.41009i			0.444460i
$209$	−7.20712	−	2.98529i	−0.498527	−	0.206497i
$210$		0			0
$211$	−1.80171	+	0.746294i	−0.124035	+	0.0513770i	−0.443838	−	0.896107i	$-0.646383\pi$
$211$	−1.80171	+	0.746294i	−0.124035	+	0.0513770i	0.319803	+	0.947484i	$0.396383\pi$
$212$	3.55076	+	3.55076i	0.243867	+	0.243867i
$213$		0			0
$214$	1.20606	−	0.499566i	0.0824444	−	0.0341496i
$215$	−3.13229	−	7.56201i	−0.213620	−	0.515725i
$216$		0			0
$217$		−	0.903981i		−	0.0613662i
$218$	−0.710047	+	1.71421i	−0.0480905	+	0.116101i
$219$		0			0
$220$	5.17546			0.348929
$221$	7.80131	−	2.39927i	0.524773	−	0.161393i
$222$		0			0
$223$	16.7800	−	16.7800i	1.12367	−	1.12367i	0.132491	−	0.991184i	$-0.457703\pi$
$223$	16.7800	−	16.7800i	1.12367	−	1.12367i	0.991184	−	0.132491i	$-0.0422974\pi$
$224$	−0.452123	+	1.09152i	−0.0302088	+	0.0729304i
$225$		0			0
$226$	−3.66333	−	1.51740i	−0.243681	−	0.100936i
$227$	−7.86790	−	18.9948i	−0.522211	−	1.26073i	−0.936527	−	0.350595i	$-0.885979\pi$
$227$	−7.86790	−	18.9948i	−0.522211	−	1.26073i	0.414316	−	0.910133i	$-0.364021\pi$
$228$		0			0
$229$	18.8066	+	18.8066i	1.24277	+	1.24277i	0.958846	+	0.283928i	$0.0916375\pi$
$229$	18.8066	+	18.8066i	1.24277	+	1.24277i	0.283928	+	0.958846i	$0.408362\pi$
$230$	−1.71687	−	1.71687i	−0.113207	−	0.113207i
$231$		0			0
$232$	−2.52165	−	6.08780i	−0.165554	−	0.399684i
$233$	21.7104	+	8.99275i	1.42230	+	0.589135i	0.955437	−	0.295196i	$-0.0953851\pi$
$233$	21.7104	+	8.99275i	1.42230	+	0.589135i	0.466860	+	0.884331i	$0.345385\pi$
$234$		0			0
$235$	−0.414604	+	1.00094i	−0.0270458	+	0.0652942i
$236$	−12.1061	+	12.1061i	−0.788040	+	0.788040i
$237$		0			0
$238$	0.441734	+	0.0417939i	0.0286333	+	0.00270910i
$239$	−5.25737			−0.340071			−0.170036	−	0.985438i	$-0.554388\pi$
$239$	−5.25737			−0.340071			−0.170036	+	0.985438i	$0.554388\pi$
$240$		0			0
$241$	2.08146	−	5.02509i	0.134079	−	0.323694i	−0.842553	−	0.538613i	$-0.818949\pi$
$241$	2.08146	−	5.02509i	0.134079	−	0.323694i	0.976632	+	0.214918i	$0.0689486\pi$
$242$		−	1.20398i		−	0.0773950i
$243$		0			0
$244$	8.01149	+	19.3414i	0.512883	+	1.23821i
$245$	6.38472	−	2.64464i	0.407905	−	0.168960i
$246$		0			0
$247$	3.94587	+	3.94587i	0.251070	+	0.251070i
$248$	3.89814	−	1.61466i	0.247532	−	0.102531i
$249$		0			0
$250$	−0.332832	−	0.137863i	−0.0210501	−	0.00871925i
$251$		−	26.3864i		−	1.66550i	−0.553652	−	0.832748i	$-0.686766\pi$
$251$		−	26.3864i		−	1.66550i	0.553652	−	0.832748i	$-0.313234\pi$
$252$		0			0
$253$	−13.1882	+	13.1882i	−0.829135	+	0.829135i
$254$	2.64150			0.165742
$255$		0			0
$256$	6.59764			0.412352
$257$	−13.2589	+	13.2589i	−0.827065	+	0.827065i	−0.987110	−	0.160045i	$-0.948836\pi$
$257$	−13.2589	+	13.2589i	−0.827065	+	0.827065i	0.160045	+	0.987110i	$0.448836\pi$
$258$		0			0
$259$			2.81431i			0.174873i
$260$	−3.42039	−	1.41677i	−0.212123	−	0.0878644i
$261$		0			0
$262$	−5.76532	+	2.38807i	−0.356183	+	0.147536i
$263$	−11.3145	−	11.3145i	−0.697680	−	0.697680i	0.266230	−	0.963910i	$-0.414222\pi$
$263$	−11.3145	−	11.3145i	−0.697680	−	0.697680i	−0.963910	+	0.266230i	$0.914222\pi$
$264$		0			0
$265$	−2.48062	+	1.02750i	−0.152383	+	0.0631191i
$266$	0.116091	+	0.280270i	0.00711803	+	0.0171844i
$267$		0			0
$268$		−	23.4871i		−	1.43470i
$269$	−0.457836	+	1.10531i	−0.0279147	+	0.0673922i	−0.937222	−	0.348733i	$-0.886612\pi$
$269$	−0.457836	+	1.10531i	−0.0279147	+	0.0673922i	0.909307	+	0.416125i	$0.136612\pi$
$270$		0			0
$271$	−0.888590			−0.0539780			−0.0269890	−	0.999636i	$-0.508592\pi$
$271$	−0.888590			−0.0539780			−0.0269890	+	0.999636i	$0.508592\pi$
$272$	−3.92471	−	12.7613i	−0.237971	−	0.773769i
$273$		0			0
$274$	3.55983	−	3.55983i	0.215057	−	0.215057i
$275$	−1.05900	+	2.55665i	−0.0638602	+	0.154172i
$276$		0			0
$277$	−5.70841	−	2.36450i	−0.342985	−	0.142069i	0.204540	−	0.978858i	$-0.434430\pi$
$277$	−5.70841	−	2.36450i	−0.342985	−	0.142069i	−0.547525	+	0.836789i	$0.684430\pi$
$278$	0.499150	+	1.20505i	0.0299370	+	0.0722744i
$279$		0			0
$280$	−0.294504	−	0.294504i	−0.0176000	−	0.0176000i
$281$	19.7250	+	19.7250i	1.17670	+	1.17670i	0.980581	+	0.196117i	$0.0628332\pi$
$281$	19.7250	+	19.7250i	1.17670	+	1.17670i	0.196117	+	0.980581i	$0.437167\pi$
$282$		0			0
$283$	11.3703	+	27.4503i	0.675893	+	1.63175i	0.771422	+	0.636324i	$0.219546\pi$
$283$	11.3703	+	27.4503i	0.675893	+	1.63175i	−0.0955282	+	0.995427i	$0.530454\pi$
$284$	10.1732	+	4.21389i	0.603670	+	0.250048i
$285$		0			0
$286$	0.755221	−	1.82326i	0.0446571	−	0.107812i
$287$	−0.656853	+	0.656853i	−0.0387728	+	0.0387728i
$288$		0			0
$289$	−14.0620	+	9.55303i	−0.827176	+	0.561943i
$290$	1.70259			0.0999795
$291$		0			0
$292$	0.155068	−	0.374367i	0.00907466	−	0.0219082i
$293$			22.4626i			1.31228i	0.754639	+	0.656140i	$0.227812\pi$
$293$			22.4626i			1.31228i	−0.754639	+	0.656140i	$0.772188\pi$
$294$		0			0
$295$	−3.50322	−	8.45751i	−0.203965	−	0.492415i
$296$	−12.1359	+	5.02684i	−0.705382	+	0.292179i
$297$		0			0
$298$	−3.27542	−	3.27542i	−0.189740	−	0.189740i
$299$	12.3262	−	5.10566i	0.712840	−	0.295268i
$300$		0			0
$301$	2.25891	+	0.935671i	0.130201	+	0.0539312i
$302$		−	6.90398i		−	0.397279i
$303$		0			0
$304$	6.45462	−	6.45462i	0.370198	−	0.370198i
$305$	−11.1939			−0.640961
$306$		0			0
$307$	5.53854			0.316101			0.158050	−	0.987431i	$-0.449479\pi$
$307$	5.53854			0.316101			0.158050	+	0.987431i	$0.449479\pi$
$308$	−1.09319	+	1.09319i	−0.0622902	+	0.0622902i
$309$		0			0
$310$			1.09020i			0.0619193i
$311$	20.8510	+	8.63675i	1.18235	+	0.489745i	0.885256	−	0.465104i	$-0.153983\pi$
$311$	20.8510	+	8.63675i	1.18235	+	0.489745i	0.297093	+	0.954849i	$0.403983\pi$
$312$		0			0
$313$	−11.2581	+	4.66325i	−0.636345	+	0.263583i	−0.677446	−	0.735572i	$-0.736913\pi$
$313$	−11.2581	+	4.66325i	−0.636345	+	0.263583i	0.0411013	+	0.999155i	$0.486913\pi$
$314$	0.688359	+	0.688359i	0.0388463	+	0.0388463i
$315$		0			0
$316$	18.4113	−	7.62621i	1.03572	−	0.429008i
$317$	8.41030	+	20.3043i	0.472370	+	1.14040i	0.963113	+	0.269097i	$0.0867253\pi$
$317$	8.41030	+	20.3043i	0.472370	+	1.14040i	−0.490743	+	0.871304i	$0.663275\pi$
$318$		0			0
$319$		−	13.0785i		−	0.732254i
$320$	−1.93311	+	4.66693i	−0.108064	+	0.260889i
$321$		0			0
$322$	0.725296			0.0404192
$323$	−10.2714	−	5.43957i	−0.571519	−	0.302666i
$324$		0			0
$325$	1.39976	−	1.39976i	0.0776446	−	0.0776446i
$326$	−2.35826	+	5.69333i	−0.130612	+	0.315325i
$327$		0			0
$328$	−4.00573	−	1.65923i	−0.221179	−	0.0916155i
$329$	−0.123850	−	0.298999i	−0.00682805	−	0.0164844i
$330$		0			0
$331$	10.2262	+	10.2262i	0.562083	+	0.562083i	0.929899	−	0.367816i	$-0.119894\pi$
$331$	10.2262	+	10.2262i	0.562083	+	0.562083i	−0.367816	+	0.929899i	$0.619894\pi$
$332$	20.5966	+	20.5966i	1.13038	+	1.13038i
$333$		0			0
$334$	1.22045	+	2.94642i	0.0667798	+	0.161221i
$335$	11.6025	+	4.80593i	0.633915	+	0.262576i
$336$		0			0
$337$	−9.27853	+	22.4004i	−0.505434	+	1.22023i	0.441052	+	0.897481i	$0.354605\pi$
$337$	−9.27853	+	22.4004i	−0.505434	+	1.22023i	−0.946486	+	0.322744i	$0.895395\pi$
$338$	2.31337	−	2.31337i	0.125831	−	0.125831i
$339$		0			0
$340$	7.67682	+	0.726330i	0.416334	+	0.0393908i
$341$	8.37441			0.453500
$342$		0			0
$343$	−1.59020	+	3.83909i	−0.0858629	+	0.207291i
$344$			11.4121i			0.615300i
$345$		0			0
$346$	2.64490	+	6.38535i	0.142191	+	0.343279i
$347$	19.8599	−	8.22624i	1.06614	−	0.441608i	0.220510	−	0.975385i	$-0.429228\pi$
$347$	19.8599	−	8.22624i	1.06614	−	0.441608i	0.845625	+	0.533777i	$0.179228\pi$
$348$		0			0
$349$	−17.0669	−	17.0669i	−0.913570	−	0.913570i	0.0829813	−	0.996551i	$-0.473556\pi$
$349$	−17.0669	−	17.0669i	−0.913570	−	0.913570i	−0.996551	+	0.0829813i	$0.973556\pi$
$350$	0.0994229	−	0.0411823i	0.00531438	−	0.00220129i
$351$		0			0
$352$	−10.1118	−	4.18843i	−0.538959	−	0.223244i
$353$			7.24444i			0.385583i	0.981240	+	0.192791i	$0.0617541\pi$
$353$			7.24444i			0.385583i	−0.981240	+	0.192791i	$0.938246\pi$
$354$		0			0
$355$	−4.16329	+	4.16329i	−0.220964	+	0.220964i
$356$	−2.90377			−0.153900
$357$		0			0
$358$	1.56182			0.0825449
$359$	−12.2079	+	12.2079i	−0.644308	+	0.644308i	−0.951612	−	0.307303i	$-0.900573\pi$
$359$	−12.2079	+	12.2079i	−0.644308	+	0.644308i	0.307303	+	0.951612i	$0.400573\pi$
$360$		0			0
$361$			11.0534i			0.581760i
$362$	−7.91419	−	3.27816i	−0.415960	−	0.172296i
$363$		0			0
$364$	1.02173	−	0.423215i	0.0535533	−	0.0221825i
$365$	0.153206	+	0.153206i	0.00801916	+	0.00801916i
$366$		0			0
$367$	34.5930	−	14.3289i	1.80574	−	0.747963i	0.821726	−	0.569883i	$-0.193011\pi$
$367$	34.5930	−	14.3289i	1.80574	−	0.747963i	0.984016	−	0.178080i	$-0.0569886\pi$
$368$	−8.35180	−	20.1630i	−0.435368	−	1.05107i
$369$		0			0
$370$		−	3.39406i		−	0.176449i
$371$	0.306934	−	0.741005i	0.0159352	−	0.0384711i
$372$		0			0
$373$	29.8887			1.54758			0.773789	−	0.633443i	$-0.218359\pi$
$373$	29.8887			1.54758			0.773789	+	0.633443i	$0.218359\pi$
$374$	−0.387176	+	4.09219i	−0.0200204	+	0.211602i
$375$		0			0
$376$	1.06813	−	1.06813i	0.0550845	−	0.0550845i
$377$	−3.58021	+	8.64339i	−0.184390	+	0.445157i
$378$		0			0
$379$	−27.7353	−	11.4883i	−1.42467	−	0.590116i	−0.468637	−	0.883391i	$-0.655255\pi$
$379$	−27.7353	−	11.4883i	−1.42467	−	0.590116i	−0.956028	+	0.293275i	$0.905255\pi$
$380$	2.01754	+	4.87076i	0.103497	+	0.249865i
$381$		0			0
$382$	−1.85209	−	1.85209i	−0.0947611	−	0.0947611i
$383$	−13.9465	−	13.9465i	−0.712634	−	0.712634i	0.254451	−	0.967086i	$-0.418105\pi$
$383$	−13.9465	−	13.9465i	−0.712634	−	0.712634i	−0.967086	+	0.254451i	$0.918105\pi$
$384$		0			0
$385$	−0.316343	−	0.763719i	−0.0161223	−	0.0389227i
$386$	−7.38861	−	3.06046i	−0.376070	−	0.155773i
$387$		0			0
$388$	−6.42009	+	15.4995i	−0.325931	+	0.786866i
$389$	−2.62699	+	2.62699i	−0.133194	+	0.133194i	−0.770561	−	0.637367i	$-0.780024\pi$
$389$	−2.62699	+	2.62699i	−0.133194	+	0.133194i	0.637367	+	0.770561i	$0.280024\pi$
$390$		0			0
$391$	−21.4131	+	17.7114i	−1.08291	+	0.895703i
$392$	−9.63543			−0.486663
$393$		0			0
$394$	−0.617821	+	1.49155i	−0.0311254	+	0.0751433i
$395$			10.6556i			0.536140i
$396$		0			0
$397$	−1.97916	−	4.77812i	−0.0993314	−	0.239807i	0.866400	−	0.499350i	$-0.166428\pi$
$397$	−1.97916	−	4.77812i	−0.0993314	−	0.239807i	−0.965731	+	0.259543i	$0.916428\pi$
$398$	−0.132929	+	0.0550610i	−0.00666313	+	0.00275996i
$399$		0			0
$400$	−2.28971	−	2.28971i	−0.114486	−	0.114486i
$401$	−0.364698	+	0.151063i	−0.0182122	+	0.00754372i	−0.391771	−	0.920063i	$-0.628137\pi$
$401$	−0.364698	+	0.151063i	−0.0182122	+	0.00754372i	0.373559	+	0.927607i	$0.378137\pi$
$402$		0			0
$403$	−5.53453	−	2.29248i	−0.275695	−	0.114196i
$404$			12.9444i			0.644007i
$405$		0			0
$406$	−0.359631	+	0.359631i	−0.0178482	+	0.0178482i
$407$	−26.0716			−1.29232
$408$		0			0
$409$	0.521080			0.0257657			0.0128829	−	0.999917i	$-0.495899\pi$
$409$	0.521080			0.0257657			0.0128829	+	0.999917i	$0.495899\pi$
$410$	0.792165	−	0.792165i	0.0391222	−	0.0391222i
$411$		0			0
$412$			24.2458i			1.19451i
$413$	2.52641	+	1.04647i	0.124317	+	0.0514936i
$414$		0			0
$415$	−14.3891	+	5.96016i	−0.706333	+	0.292573i
$416$	5.53616	+	5.53616i	0.271433	+	0.271433i
$417$		0			0
$418$	−2.59640	+	1.07546i	−0.126994	+	0.0526026i
$419$	−1.74972	−	4.22419i	−0.0854793	−	0.206365i	0.875360	−	0.483472i	$-0.160624\pi$
$419$	−1.74972	−	4.22419i	−0.0854793	−	0.206365i	−0.960839	+	0.277107i	$0.910624\pi$
$420$		0			0
$421$			7.55233i			0.368078i	0.982919	+	0.184039i	$0.0589173\pi$
$421$			7.55233i			0.368078i	−0.982919	+	0.184039i	$0.941083\pi$
$422$	−0.268856	+	0.649075i	−0.0130877	+	0.0315965i
$423$		0			0
$424$	3.74359			0.181805
$425$	−1.92963	+	3.64370i	−0.0936010	+	0.176745i
$426$		0			0
$427$	2.36444	−	2.36444i	0.114423	−	0.114423i
$428$	−2.59343	+	6.26110i	−0.125358	+	0.302642i
$429$		0			0
$430$	−2.72425	−	1.12842i	−0.131375	−	0.0544172i
$431$	−7.99371	−	19.2985i	−0.385043	−	0.929577i	−0.990973	−	0.134059i	$-0.957199\pi$
$431$	−7.99371	−	19.2985i	−0.385043	−	0.929577i	0.605930	−	0.795518i	$-0.292801\pi$
$432$		0			0
$433$	23.2292	+	23.2292i	1.11632	+	1.11632i	0.992277	+	0.124045i	$0.0395868\pi$
$433$	23.2292	+	23.2292i	1.11632	+	1.11632i	0.124045	+	0.992277i	$0.460413\pi$
$434$	−0.230279	−	0.230279i	−0.0110537	−	0.0110537i
$435$		0			0
$436$	−3.68612	−	8.89909i	−0.176533	−	0.426189i
$437$	−17.5529	−	7.27065i	−0.839670	−	0.347803i
$438$		0			0
$439$	9.19069	−	22.1883i	0.438648	−	1.05899i	−0.537769	−	0.843093i	$-0.680733\pi$
$439$	9.19069	−	22.1883i	0.438648	−	1.05899i	0.976416	−	0.215897i	$-0.0692674\pi$
$440$	2.72826	−	2.72826i	0.130065	−	0.130065i
$441$		0			0
$442$	1.37611	−	2.59848i	0.0654547	−	0.123597i
$443$	−8.36893			−0.397620			−0.198810	−	0.980038i	$-0.563708\pi$
$443$	−8.36893			−0.397620			−0.198810	+	0.980038i	$0.563708\pi$
$444$		0			0
$445$	0.594169	−	1.43445i	0.0281663	−	0.0679995i
$446$		−	8.54904i		−	0.404809i
$447$		0			0
$448$	−0.577454	−	1.39410i	−0.0272821	−	0.0658649i
$449$	−22.7241	+	9.41265i	−1.07242	+	0.444210i	−0.847844	−	0.530246i	$-0.822099\pi$
$449$	−22.7241	+	9.41265i	−1.07242	+	0.444210i	−0.224575	+	0.974457i	$0.572099\pi$
$450$		0			0
$451$	−6.08503	−	6.08503i	−0.286533	−	0.286533i
$452$	19.0177	−	7.87740i	0.894518	−	0.370522i
$453$		0			0
$454$	−6.84296	−	2.83444i	−0.321156	−	0.133027i
$455$			0.591330i			0.0277220i
$456$		0			0
$457$	5.38146	−	5.38146i	0.251734	−	0.251734i	−0.569947	−	0.821681i	$-0.693036\pi$
$457$	5.38146	−	5.38146i	0.251734	−	0.251734i	0.821681	+	0.569947i	$0.193036\pi$
$458$	9.58151			0.447715
$459$		0			0
$460$	12.6048			0.587702
$461$	−5.10577	+	5.10577i	−0.237800	+	0.237800i	−0.815938	−	0.578139i	$-0.803779\pi$
$461$	−5.10577	+	5.10577i	−0.237800	+	0.237800i	0.578139	+	0.815938i	$0.303779\pi$
$462$		0			0
$463$			23.0362i			1.07058i	0.844667	+	0.535292i	$0.179798\pi$
$463$			23.0362i			1.07058i	−0.844667	+	0.535292i	$0.820202\pi$
$464$	14.1388	+	5.85648i	0.656377	+	0.271880i
$465$		0			0
$466$	7.82128	−	3.23968i	0.362314	−	0.150075i
$467$	21.1457	+	21.1457i	0.978506	+	0.978506i	0.999774	−	0.0212676i	$-0.00677021\pi$
$467$	21.1457	+	21.1457i	0.978506	+	0.978506i	−0.0212676	+	0.999774i	$0.506770\pi$
$468$		0			0
$469$	−3.46589	+	1.43562i	−0.160040	+	0.0662907i
$470$	0.149363	+	0.360594i	0.00688959	+	0.0166329i
$471$		0			0
$472$			12.7636i			0.587491i
$473$	−8.66798	+	20.9264i	−0.398554	+	0.962195i
$474$		0			0
$475$	−2.81896			−0.129343
$476$	−1.77496	+	1.46812i	−0.0813552	+	0.0672912i
$477$		0			0
$478$	−1.33925	+	1.33925i	−0.0612561	+	0.0612561i
$479$	−3.69569	+	8.92218i	−0.168860	+	0.407665i	−0.985544	−	0.169421i	$-0.945810\pi$
$479$	−3.69569	+	8.92218i	−0.168860	+	0.407665i	0.816684	+	0.577086i	$0.195810\pi$
$480$		0			0
$481$	17.2303	+	7.13704i	0.785636	+	0.325421i
$482$	−0.749855	−	1.81031i	−0.0341550	−	0.0824574i
$483$		0			0
$484$	4.41965	+	4.41965i	0.200893	+	0.200893i
$485$	−6.34300	−	6.34300i	−0.288021	−	0.288021i
$486$		0			0
$487$	−1.84840	−	4.46244i	−0.0837591	−	0.202212i	0.876451	−	0.481491i	$-0.159905\pi$
$487$	−1.84840	−	4.46244i	−0.0837591	−	0.202212i	−0.960210	+	0.279279i	$0.909905\pi$
$488$	14.4192	+	5.97263i	0.652727	+	0.270368i
$489$		0			0
$490$	0.952742	−	2.30012i	0.0430405	−	0.103909i
$491$	−15.1849	+	15.1849i	−0.685287	+	0.685287i	−0.961186	−	0.275900i	$-0.911024\pi$
$491$	−15.1849	+	15.1849i	−0.685287	+	0.685287i	0.275900	+	0.961186i	$0.411024\pi$
$492$		0			0
$493$	1.83545	−	19.3995i	0.0826646	−	0.873708i
$494$	2.01033			0.0904490
$495$		0			0
$496$	−3.75002	+	9.05334i	−0.168381	+	0.406507i
$497$		−	1.75879i		−	0.0788923i
$498$		0			0
$499$	−7.13250	−	17.2194i	−0.319295	−	0.770845i	−0.999292	−	0.0376305i	$-0.988019\pi$
$499$	−7.13250	−	17.2194i	−0.319295	−	0.770845i	0.679997	−	0.733215i	$-0.261981\pi$
$500$	1.72785	−	0.715701i	0.0772720	−	0.0320071i
$501$		0			0
$502$	−6.72164	−	6.72164i	−0.300001	−	0.300001i
$503$	17.1646	−	7.10981i	0.765332	−	0.317011i	0.0343519	−	0.999410i	$-0.489063\pi$
$503$	17.1646	−	7.10981i	0.765332	−	0.317011i	0.730980	+	0.682399i	$0.239063\pi$
$504$		0			0
$505$	−6.39447	−	2.64868i	−0.284550	−	0.117865i
$506$			6.71908i			0.298700i
$507$		0			0
$508$	−9.69656	+	9.69656i	−0.430215	+	0.430215i
$509$	28.4343			1.26033			0.630163	−	0.776463i	$-0.282988\pi$
$509$	28.4343			1.26033			0.630163	+	0.776463i	$0.282988\pi$
$510$		0			0
$511$	−0.0647220			−0.00286313
$512$	15.4409	−	15.4409i	0.682399	−	0.682399i
$513$		0			0
$514$			6.75508i			0.297954i
$515$	−11.9773	−	4.96117i	−0.527784	−	0.218615i
$516$		0			0
$517$	2.76991	−	1.14733i	0.121820	−	0.0504597i
$518$	0.716913	+	0.716913i	0.0314993	+	0.0314993i
$519$		0			0
$520$	−2.54993	+	1.05622i	−0.111822	+	0.0463181i
$521$	7.26078	+	17.5291i	0.318100	+	0.767962i	0.999355	+	0.0359155i	$0.0114347\pi$
$521$	7.26078	+	17.5291i	0.318100	+	0.767962i	−0.681254	+	0.732047i	$0.738565\pi$
$522$		0			0
$523$		−	24.4504i		−	1.06914i	−0.845124	−	0.534571i	$-0.820473\pi$
$523$		−	24.4504i		−	1.06914i	0.845124	−	0.534571i	$-0.179527\pi$
$524$	12.3974	−	29.9299i	0.541583	−	1.30750i
$525$		0			0
$526$	−5.76445			−0.251342
$527$	12.4219	+	1.17528i	0.541105	+	0.0511958i
$528$		0			0
$529$	−15.8564	+	15.8564i	−0.689407	+	0.689407i
$530$	−0.370163	+	0.893653i	−0.0160789	+	0.0388178i
$531$		0			0
$532$	−1.45499	−	0.602675i	−0.0630816	−	0.0261293i
$533$	2.35575	+	5.68728i	0.102039	+	0.246344i
$534$		0			0
$535$	−2.56229	−	2.56229i	−0.110777	−	0.110777i
$536$	−12.3813	−	12.3813i	−0.534792	−	0.534792i
$537$		0			0
$538$	0.164937	+	0.398194i	0.00711096	+	0.0171674i
$539$	−17.6684	−	7.31851i	−0.761034	−	0.315230i
$540$		0			0
$541$	−4.13701	+	9.98762i	−0.177864	+	0.429401i	−0.987518	−	0.157506i	$-0.949655\pi$
$541$	−4.13701	+	9.98762i	−0.177864	+	0.429401i	0.809654	+	0.586907i	$0.199655\pi$
$542$	−0.226358	+	0.226358i	−0.00972291	+	0.00972291i
$543$		0			0
$544$	−14.4111	−	7.63186i	−0.617871	−	0.327213i
$545$	5.15037			0.220618
$546$		0			0
$547$	−2.78305	+	6.71889i	−0.118995	+	0.287279i	−0.972143	−	0.234391i	$-0.924691\pi$
$547$	−2.78305	+	6.71889i	−0.118995	+	0.287279i	0.853148	+	0.521669i	$0.174691\pi$
$548$			26.1353i			1.11644i
$549$		0			0
$550$	0.381510	+	0.921046i	0.0162676	+	0.0392735i
$551$	12.3085	−	5.09835i	0.524360	−	0.217197i
$552$		0			0
$553$	−2.25073	−	2.25073i	−0.0957108	−	0.0957108i
$554$	−2.05648	+	0.851821i	−0.0873714	+	0.0361904i
$555$		0			0
$556$	−6.25589	−	2.59128i	−0.265309	−	0.109895i
$557$			18.3930i			0.779335i	0.920956	+	0.389667i	$0.127410\pi$
$557$			18.3930i			0.779335i	−0.920956	+	0.389667i	$0.872590\pi$
$558$		0			0
$559$	11.4571	−	11.4571i	0.484584	−	0.484584i
$560$	0.967293			0.0408756
$561$		0			0
$562$	10.0495			0.423911
$563$	−0.317586	+	0.317586i	−0.0133847	+	0.0133847i	−0.713767	−	0.700383i	$-0.753013\pi$
$563$	−0.317586	+	0.317586i	−0.0133847	+	0.0133847i	0.700383	+	0.713767i	$0.253013\pi$
$564$		0			0
$565$			11.0065i			0.463049i
$566$	9.88909	+	4.09620i	0.415670	+	0.172176i
$567$		0			0
$568$	7.58423	−	3.14149i	0.318227	−	0.131814i
$569$	−10.1299	−	10.1299i	−0.424669	−	0.424669i	0.462138	−	0.886808i	$-0.347082\pi$
$569$	−10.1299	−	10.1299i	−0.424669	−	0.424669i	−0.886808	+	0.462138i	$0.847082\pi$
$570$		0			0
$571$	25.8617	−	10.7123i	1.08228	−	0.448294i	0.230970	−	0.972961i	$-0.425810\pi$
$571$	25.8617	−	10.7123i	1.08228	−	0.448294i	0.851307	+	0.524667i	$0.175810\pi$
$572$	3.92063	+	9.46525i	0.163930	+	0.395762i
$573$		0			0
$574$			0.334651i			0.0139681i
$575$	−2.57919	+	6.22672i	−0.107560	+	0.259672i
$576$		0			0
$577$	−6.76924			−0.281807			−0.140904	−	0.990023i	$-0.545001\pi$
$577$	−6.76924			−0.281807			−0.140904	+	0.990023i	$0.545001\pi$
$578$	−1.14861	+	6.01565i	−0.0477757	+	0.250218i
$579$		0			0
$580$	−6.24996	+	6.24996i	−0.259516	+	0.259516i
$581$	1.78041	−	4.29829i	0.0738638	−	0.178323i
$582$		0			0
$583$	6.86461	+	2.84342i	0.284303	+	0.117762i
$584$	−0.115605	−	0.279094i	−0.00478375	−	0.0115490i
$585$		0			0
$586$	5.72209	+	5.72209i	0.236377	+	0.236377i
$587$	−17.4713	−	17.4713i	−0.721117	−	0.721117i	0.247715	−	0.968833i	$-0.420320\pi$
$587$	−17.4713	−	17.4713i	−0.721117	−	0.721117i	−0.968833	+	0.247715i	$0.920320\pi$
$588$		0			0
$589$	3.26458	+	7.88139i	0.134515	+	0.324747i
$590$	−3.04686	−	1.26205i	−0.125437	−	0.0519577i
$591$		0			0
$592$	11.6747	−	28.1852i	0.479828	−	1.15841i
$593$	15.8749	−	15.8749i	0.651905	−	0.651905i	−0.301547	−	0.953451i	$-0.597503\pi$
$593$	15.8749	−	15.8749i	0.651905	−	0.651905i	0.953451	+	0.301547i	$0.0975029\pi$
$594$		0			0
$595$	−0.362054	−	1.17723i	−0.0148428	−	0.0482617i
$596$	24.0472			0.985010
$597$		0			0
$598$	1.83934	−	4.44055i	0.0752161	−	0.181588i
$599$		−	19.1639i		−	0.783018i	−0.920174	−	0.391509i	$-0.871953\pi$
$599$		−	19.1639i		−	0.783018i	0.920174	−	0.391509i	$-0.128047\pi$
$600$		0			0
$601$	−8.87947	−	21.4369i	−0.362201	−	0.874431i	−0.994978	−	0.100096i	$-0.968085\pi$
$601$	−8.87947	−	21.4369i	−0.362201	−	0.874431i	0.632777	−	0.774334i	$-0.281915\pi$
$602$	0.813782	−	0.337080i	0.0331673	−	0.0137383i
$603$		0			0
$604$	25.3435	+	25.3435i	1.03121	+	1.03121i
$605$	−3.08764	+	1.27894i	−0.125530	+	0.0519964i
$606$		0			0
$607$	1.72244	+	0.713459i	0.0699118	+	0.0289584i	0.417365	−	0.908739i	$-0.362954\pi$
$607$	1.72244	+	0.713459i	0.0699118	+	0.0289584i	−0.347454	+	0.937697i	$0.612954\pi$
$608$		−	11.1492i		−	0.452161i
$609$		0			0
$610$	−2.85152	+	2.85152i	−0.115455	+	0.115455i
$611$	−2.14468			−0.0867643
$612$		0			0
$613$	−0.383092			−0.0154729			−0.00773647	−	0.999970i	$-0.502463\pi$
$613$	−0.383092			−0.0154729			−0.00773647	+	0.999970i	$0.502463\pi$
$614$	1.41088	−	1.41088i	0.0569384	−	0.0569384i
$615$		0			0
$616$			1.15256i			0.0464379i
$617$	−10.7794	−	4.46499i	−0.433964	−	0.179754i	0.154997	−	0.987915i	$-0.450463\pi$
$617$	−10.7794	−	4.46499i	−0.433964	−	0.179754i	−0.588962	+	0.808161i	$0.700463\pi$
$618$		0			0
$619$	−12.4590	+	5.16070i	−0.500771	+	0.207426i	−0.618747	−	0.785590i	$-0.712359\pi$
$619$	−12.4590	+	5.16070i	−0.500771	+	0.207426i	0.117976	+	0.993016i	$0.462359\pi$
$620$	−4.00198	−	4.00198i	−0.160723	−	0.160723i
$621$		0			0
$622$	7.51165	−	3.11143i	0.301190	−	0.124757i
$623$	0.177489	+	0.428497i	0.00711096	+	0.0171674i
$624$		0			0
$625$			1.00000i			0.0400000i
$626$	−1.67996	+	4.05578i	−0.0671446	+	0.162101i
$627$		0			0
$628$	−5.05373			−0.201666
$629$	−38.6723	−	3.65892i	−1.54196	−	0.145891i
$630$		0			0
$631$	−33.1913	+	33.1913i	−1.32132	+	1.32132i	−0.408617	+	0.912706i	$0.633989\pi$
$631$	−33.1913	+	33.1913i	−1.32132	+	1.32132i	−0.912706	+	0.408617i	$0.866011\pi$
$632$	5.68540	−	13.7258i	0.226153	−	0.545982i
$633$		0			0
$634$	7.31470	+	3.02985i	0.290504	+	0.120331i
$635$	−2.80595	−	6.77417i	−0.111351	−	0.268825i
$636$		0			0
$637$	9.67341	+	9.67341i	0.383274	+	0.383274i
$638$	−3.33159	−	3.33159i	−0.131899	−	0.131899i
$639$		0			0
$640$	3.72350	+	8.98932i	0.147184	+	0.355334i
$641$	−36.5657	−	15.1460i	−1.44426	−	0.598232i	−0.483433	−	0.875382i	$-0.660610\pi$
$641$	−36.5657	−	15.1460i	−1.44426	−	0.598232i	−0.960827	+	0.277150i	$0.910610\pi$
$642$		0			0
$643$	6.78010	−	16.3686i	0.267381	−	0.645515i	−0.731978	−	0.681329i	$-0.761402\pi$
$643$	6.78010	−	16.3686i	0.267381	−	0.645515i	0.999358	+	0.0358141i	$0.0114024\pi$
$644$	−2.66246	+	2.66246i	−0.104916	+	0.104916i
$645$		0			0
$646$	−4.00220	+	1.23087i	−0.157464	+	0.0484278i
$647$	14.8304			0.583045			0.291522	−	0.956564i	$-0.405838\pi$
$647$	14.8304			0.583045			0.291522	+	0.956564i	$0.405838\pi$
$648$		0			0
$649$	−9.69446	+	23.4045i	−0.380541	+	0.918707i
$650$		−	0.713144i		−	0.0279718i
$651$		0			0
$652$	−12.2426	−	29.5562i	−0.479457	−	1.15751i
$653$	−9.42227	+	3.90283i	−0.368722	+	0.152730i	−0.559348	−	0.828933i	$-0.688948\pi$
$653$	−9.42227	+	3.90283i	−0.368722	+	0.152730i	0.190626	+	0.981663i	$0.438948\pi$
$654$		0			0
$655$	12.2485	+	12.2485i	0.478589	+	0.478589i
$656$	9.30321	−	3.85352i	0.363229	−	0.150455i
$657$		0			0
$658$	−0.107716	−	0.0446174i	−0.00419920	−	0.00173937i
$659$		−	45.4453i		−	1.77030i	−0.465309	−	0.885148i	$-0.654057\pi$
$659$		−	45.4453i		−	1.77030i	0.465309	−	0.885148i	$-0.345943\pi$
$660$		0			0
$661$	−5.62214	+	5.62214i	−0.218676	+	0.218676i	−0.807940	−	0.589264i	$-0.799418\pi$
$661$	−5.62214	+	5.62214i	−0.218676	+	0.218676i	0.589264	+	0.807940i	$0.299418\pi$
$662$	5.21001			0.202493
$663$		0			0
$664$	21.7152			0.842712
$665$	0.595438	−	0.595438i	0.0230901	−	0.0230901i
$666$		0			0
$667$		−	31.8526i		−	1.23334i
$668$	−15.2960	−	6.33579i	−0.591818	−	0.245139i
$669$		0			0
$670$	4.17987	−	1.73136i	0.161482	−	0.0668882i
$671$	21.9040	+	21.9040i	0.845594	+	0.845594i
$672$		0			0
$673$	20.3139	−	8.41428i	0.783042	−	0.324347i	0.0448994	−	0.998992i	$-0.485703\pi$
$673$	20.3139	−	8.41428i	0.783042	−	0.324347i	0.738142	+	0.674645i	$0.235703\pi$
$674$	3.34263	+	8.06983i	0.128753	+	0.310838i
$675$		0			0
$676$			16.9841i			0.653234i
$677$	6.97899	−	16.8488i	0.268224	−	0.647551i	−0.731176	−	0.682189i	$-0.761028\pi$
$677$	6.97899	−	16.8488i	0.268224	−	0.647551i	0.999400	+	0.0346387i	$0.0110280\pi$
$678$		0			0
$679$	2.67961			0.102834
$680$	4.42976	−	3.66398i	0.169873	−	0.140507i
$681$		0			0
$682$	2.13328	−	2.13328i	0.0816876	−	0.0816876i
$683$	6.96604	−	16.8175i	0.266548	−	0.643504i	−0.732768	−	0.680478i	$-0.761772\pi$
$683$	6.96604	−	16.8175i	0.266548	−	0.643504i	0.999316	+	0.0369746i	$0.0117721\pi$
$684$		0			0
$685$	−12.9107	−	5.34779i	−0.493293	−	0.204329i
$686$	0.572878	+	1.38305i	0.0218726	+	0.0528051i
$687$		0			0
$688$	−18.7414	−	18.7414i	−0.714511	−	0.714511i
$689$	−3.75835	−	3.75835i	−0.143182	−	0.143182i
$690$		0			0
$691$	5.95556	+	14.3780i	0.226560	+	0.546965i	0.995754	−	0.0920503i	$-0.0293421\pi$
$691$	5.95556	+	14.3780i	0.226560	+	0.546965i	−0.769194	+	0.639015i	$0.779342\pi$
$692$	−33.1488	−	13.7307i	−1.26013	−	0.521962i
$693$		0			0
$694$	2.96354	−	7.15462i	0.112494	−	0.271586i
$695$	2.56016	−	2.56016i	0.0971124	−	0.0971124i
$696$		0			0
$697$	−8.17202	−	9.87999i	−0.309537	−	0.374231i
$698$	−8.69519			−0.329118
$699$		0			0
$700$	−0.213793	+	0.516142i	−0.00808061	+	0.0195083i
$701$			8.07561i			0.305011i	0.988303	+	0.152506i	$0.0487342\pi$
$701$			8.07561i			0.305011i	−0.988303	+	0.152506i	$0.951266\pi$
$702$		0			0
$703$	−10.1634	−	24.5367i	−0.383320	−	0.925417i
$704$	12.9148	−	5.34949i	0.486745	−	0.201617i
$705$		0			0
$706$	1.84544	+	1.84544i	0.0694540	+	0.0694540i
$707$	1.91014	−	0.791208i	0.0718384	−	0.0297564i
$708$		0			0
$709$	−4.88749	−	2.02447i	−0.183554	−	0.0760304i	0.289014	−	0.957325i	$-0.406673\pi$
$709$	−4.88749	−	2.02447i	−0.183554	−	0.0760304i	−0.472567	+	0.881295i	$0.656673\pi$
$710$			2.12110i			0.0796034i
$711$		0			0
$712$	−1.53074	+	1.53074i	−0.0573668	+	0.0573668i
$713$	20.3958			0.763830
$714$		0			0
$715$	−5.47803			−0.204867
$716$	−5.73323	+	5.73323i	−0.214261	+	0.214261i
$717$		0			0
$718$			6.21964i			0.232115i
$719$	8.27731	+	3.42857i	0.308691	+	0.127864i	0.531651	−	0.846964i	$-0.321572\pi$
$719$	8.27731	+	3.42857i	0.308691	+	0.127864i	−0.222960	+	0.974828i	$0.571572\pi$
$720$		0			0
$721$	3.57785	−	1.48199i	0.133246	−	0.0551923i
$722$	2.81573	+	2.81573i	0.104791	+	0.104791i
$723$		0			0
$724$	41.0855	−	17.0182i	1.52693	−	0.632476i
$725$	−1.80859	−	4.36632i	−0.0671694	−	0.162161i
$726$		0			0
$727$		−	29.9868i		−	1.11215i	−0.831133	−	0.556074i	$-0.812307\pi$
$727$		−	29.9868i		−	1.11215i	0.831133	−	0.556074i	$-0.187693\pi$
$728$	0.315511	−	0.761710i	0.0116936	−	0.0282309i
$729$		0			0
$730$	0.0780548			0.00288894
$731$	−15.7942	+	29.8239i	−0.584168	+	1.10308i
$732$		0			0
$733$	−19.0696	+	19.0696i	−0.704352	+	0.704352i	−0.965342	−	0.260990i	$-0.915951\pi$
$733$	−19.0696	+	19.0696i	−0.704352	+	0.704352i	0.260990	+	0.965342i	$0.415951\pi$
$734$	5.16205	−	12.4623i	0.190535	−	0.459992i
$735$		0			0
$736$	−24.6272	−	10.2009i	−0.907770	−	0.376011i
$737$	−13.2995	−	32.1078i	−0.489892	−	1.18270i
$738$		0			0
$739$	−24.6401	−	24.6401i	−0.906400	−	0.906400i	0.0895798	−	0.995980i	$-0.471448\pi$
$739$	−24.6401	−	24.6401i	−0.906400	−	0.906400i	−0.995980	+	0.0895798i	$0.971448\pi$
$740$	12.4591	+	12.4591i	0.458006	+	0.458006i
$741$		0			0
$742$	−0.110574	−	0.266950i	−0.00405932	−	0.00980006i
$743$	15.7918	+	6.54116i	0.579344	+	0.239972i	0.653059	−	0.757307i	$-0.273486\pi$
$743$	15.7918	+	6.54116i	0.579344	+	0.239972i	−0.0737150	+	0.997279i	$0.523486\pi$
$744$		0			0
$745$	−4.92053	+	11.8792i	−0.180274	+	0.435220i
$746$	7.61380	−	7.61380i	0.278761	−	0.278761i
$747$		0			0
$748$	−13.6006	−	16.4431i	−0.497286	−	0.601219i
$749$	1.08244			0.0395516
$750$		0			0
$751$	−12.5831	+	30.3783i	−0.459165	+	1.10852i	0.509572	+	0.860428i	$0.329804\pi$
$751$	−12.5831	+	30.3783i	−0.459165	+	1.10852i	−0.968736	+	0.248093i	$0.920196\pi$
$752$			3.50824i			0.127932i
$753$		0			0
$754$	1.28979	+	3.11382i	0.0469713	+	0.113399i
$755$	−17.7054	+	7.33381i	−0.644365	+	0.266905i
$756$		0			0
$757$	12.3728	+	12.3728i	0.449698	+	0.449698i	0.895254	−	0.445556i	$-0.146994\pi$
$757$	12.3728	+	12.3728i	0.449698	+	0.449698i	−0.445556	+	0.895254i	$0.646994\pi$
$758$	−9.99176	+	4.13872i	−0.362917	+	0.150325i
$759$		0			0
$760$	3.63120	+	1.50409i	0.131717	+	0.0545591i
$761$			10.8439i			0.393092i	0.980495	+	0.196546i	$0.0629724\pi$
$761$			10.8439i			0.393092i	−0.980495	+	0.196546i	$0.937028\pi$
$762$		0			0
$763$	−1.08789	+	1.08789i	−0.0393843	+	0.0393843i
$764$	13.5975			0.491941
$765$		0			0
$766$	−7.10543			−0.256730
$767$	12.8139	−	12.8139i	0.462682	−	0.462682i
$768$		0			0
$769$		−	14.8775i		−	0.536497i	−0.963350	−	0.268248i	$-0.913555\pi$
$769$		−	14.8775i		−	0.536497i	0.963350	−	0.268248i	$-0.0864448\pi$
$770$	−0.275133	−	0.113964i	−0.00991511	−	0.00410697i
$771$		0			0
$772$	38.3571	−	15.8880i	1.38050	−	0.571822i
$773$	−5.45537	−	5.45537i	−0.196216	−	0.196216i	0.602160	−	0.798376i	$-0.294307\pi$
$773$	−5.45537	−	5.45537i	−0.196216	−	0.196216i	−0.798376	+	0.602160i	$0.794307\pi$
$774$		0			0
$775$	2.79584	−	1.15808i	0.100430	−	0.0415993i
$776$	4.78623	+	11.5550i	0.171816	+	0.414800i
$777$		0			0
$778$			1.33839i			0.0479836i
$779$	3.35468	−	8.09891i	0.120194	−	0.290173i
$780$		0			0
$781$	16.2933			0.583019
$782$	−0.942965	+	9.96650i	−0.0337204	+	0.356401i
$783$		0			0
$784$	15.8237	−	15.8237i	0.565131	−	0.565131i
$785$	1.03409	−	2.49652i	0.0369084	−	0.0891048i
$786$		0			0
$787$	−35.3404	−	14.6385i	−1.25975	−	0.521805i	−0.349917	−	0.936781i	$-0.613790\pi$
$787$	−35.3404	−	14.6385i	−1.25975	−	0.521805i	−0.909833	+	0.414975i	$0.863790\pi$
$788$	−3.20734	−	7.74321i	−0.114257	−	0.275840i
$789$		0			0
$790$	2.71438	+	2.71438i	0.0965735	+	0.0965735i
$791$	−2.32487	−	2.32487i	−0.0826627	−	0.0826627i
$792$		0			0
$793$	−8.47987	−	20.4722i	−0.301129	−	0.726990i
$794$	−1.72134	−	0.713003i	−0.0610881	−	0.0253035i
$795$		0			0
$796$	0.285843	−	0.690085i	0.0101314	−	0.0244594i
$797$	18.8205	−	18.8205i	0.666657	−	0.666657i	−0.290284	−	0.956941i	$-0.593750\pi$
$797$	18.8205	−	18.8205i	0.666657	−	0.666657i	0.956941	+	0.290284i	$0.0937496\pi$
$798$		0			0
$799$	4.26966	−	1.31312i	0.151050	−	0.0464549i
$800$	−3.95508			−0.139833
$801$		0			0
$802$	−0.0544211	+	0.131384i	−0.00192168	+	0.00463934i
$803$		−	0.599580i		−	0.0211587i
$804$		0			0
$805$	−0.770452	−	1.86004i	−0.0271549	−	0.0655576i
$806$	−1.99384	+	0.825876i	−0.0702300	+	0.0290902i
$807$		0			0
$808$	6.82368	+	6.82368i	0.240056	+	0.240056i
$809$	−15.1856	+	6.29009i	−0.533898	+	0.221148i	−0.633309	−	0.773899i	$-0.718304\pi$
$809$	−15.1856	+	6.29009i	−0.533898	+	0.221148i	0.0994117	+	0.995046i	$0.468304\pi$
$810$		0			0
$811$	−3.36428	−	1.39353i	−0.118136	−	0.0489335i	0.322833	−	0.946456i	$-0.395365\pi$
$811$	−3.36428	−	1.39353i	−0.118136	−	0.0489335i	−0.440968	+	0.897523i	$0.645365\pi$
$812$		−	2.64031i		−	0.0926566i
$813$		0			0
$814$	−6.64143	+	6.64143i	−0.232782	+	0.232782i
$815$	17.1057			0.599188
$816$		0			0
$817$	−23.0734			−0.807236
$818$	0.132739	−	0.132739i	0.00464111	−	0.00464111i
$819$		0			0
$820$			5.81585i			0.203098i
$821$	−32.8228	−	13.5957i	−1.14552	−	0.474492i	−0.272494	−	0.962158i	$-0.587848\pi$
$821$	−32.8228	−	13.5957i	−1.14552	−	0.474492i	−0.873030	+	0.487666i	$0.837848\pi$
$822$		0			0
$823$	4.63438	−	1.91962i	0.161544	−	0.0669138i	−0.300446	−	0.953799i	$-0.597136\pi$
$823$	4.63438	−	1.91962i	0.161544	−	0.0669138i	0.461990	+	0.886885i	$0.347136\pi$
$824$	12.7813	+	12.7813i	0.445257	+	0.445257i
$825$		0			0
$826$	0.910152	−	0.376997i	0.0316682	−	0.0131174i
$827$	−14.9585	−	36.1131i	−0.520159	−	1.25578i	−0.937804	−	0.347165i	$-0.887144\pi$
$827$	−14.9585	−	36.1131i	−0.520159	−	1.25578i	0.417645	−	0.908610i	$-0.362856\pi$
$828$		0			0
$829$		−	16.3998i		−	0.569587i	−0.958589	−	0.284794i	$-0.908075\pi$
$829$		−	16.3998i		−	0.569587i	0.958589	−	0.284794i	$-0.0919250\pi$
$830$	−2.14718	+	5.18374i	−0.0745295	+	0.179930i
$831$		0			0
$832$	−9.99964			−0.346675
$833$	−25.1807	−	13.3352i	−0.872461	−	0.462039i
$834$		0			0
$835$	6.25971	−	6.25971i	0.216626	−	0.216626i
$836$	5.58313	−	13.4789i	0.193097	−	0.466177i
$837$		0			0
$838$	−1.52178	−	0.630344i	−0.0525692	−	0.0217749i
$839$	11.4471	+	27.6357i	0.395197	+	0.954090i	0.988788	+	0.149324i	$0.0477096\pi$
$839$	11.4471	+	27.6357i	0.395197	+	0.954090i	−0.593591	+	0.804767i	$0.702290\pi$
$840$		0			0
$841$	−4.71231	−	4.71231i	−0.162493	−	0.162493i
$842$	1.92387	+	1.92387i	0.0663009	+	0.0663009i
$843$		0			0
$844$	−1.39573	−	3.36959i	−0.0480431	−	0.115986i
$845$	−8.39008	−	3.47528i	−0.288627	−	0.119553i
$846$		0			0
$847$	0.382043	−	0.922334i	0.0131272	−	0.0316918i
$848$	−6.14788	+	6.14788i	−0.211119	+	0.211119i
$849$		0			0
$850$	0.436637	+	1.41974i	0.0149765	+	0.0486967i
$851$	−63.4972			−2.17666
$852$		0			0
$853$	−13.7430	+	33.1784i	−0.470550	+	1.13601i	0.493371	+	0.869819i	$0.335765\pi$
$853$	−13.7430	+	33.1784i	−0.470550	+	1.13601i	−0.963921	+	0.266189i	$0.914235\pi$
$854$		−	1.20463i		−	0.0412215i
$855$		0			0
$856$	1.93343	+	4.66771i	0.0660832	+	0.159539i
$857$	−19.4676	+	8.06374i	−0.665000	+	0.275452i	−0.689541	−	0.724247i	$-0.742188\pi$
$857$	−19.4676	+	8.06374i	−0.665000	+	0.275452i	0.0245406	+	0.999699i	$0.492188\pi$
$858$		0			0
$859$	−11.2104	−	11.2104i	−0.382494	−	0.382494i	0.489506	−	0.872000i	$-0.337177\pi$
$859$	−11.2104	−	11.2104i	−0.382494	−	0.382494i	−0.872000	+	0.489506i	$0.837177\pi$
$860$	14.1426	−	5.85805i	0.482258	−	0.199758i
$861$		0			0
$862$	−6.95238	−	2.87977i	−0.236799	−	0.0980853i
$863$		−	23.8125i		−	0.810587i	−0.914187	−	0.405294i	$-0.867169\pi$
$863$		−	23.8125i		−	0.810587i	0.914187	−	0.405294i	$-0.132831\pi$
$864$		0			0
$865$	13.5658	−	13.5658i	0.461251	−	0.461251i
$866$	11.8347			0.402160
$867$		0			0
$868$	1.69064			0.0573841
$869$	20.8506	−	20.8506i	0.707308	−	0.707308i
$870$		0			0
$871$			24.8603i			0.842359i
$872$	−6.63435	−	2.74804i	−0.224667	−	0.0930603i
$873$		0			0
$874$	−6.32351	+	2.61929i	−0.213896	+	0.0885987i
$875$	−0.211226	−	0.211226i	−0.00714073	−	0.00714073i
$876$		0			0
$877$	16.5557	−	6.85759i	0.559046	−	0.231564i	−0.0852252	−	0.996362i	$-0.527161\pi$
$877$	16.5557	−	6.85759i	0.559046	−	0.231564i	0.644271	+	0.764797i	$0.277161\pi$
$878$	−3.31099	−	7.99343i	−0.111740	−	0.269765i
$879$		0			0
$880$			8.96092i			0.302073i
$881$	12.9301	−	31.2159i	0.435625	−	1.05169i	−0.541819	−	0.840495i	$-0.682264\pi$
$881$	12.9301	−	31.2159i	0.435625	−	1.05169i	0.977444	−	0.211196i	$-0.0677358\pi$
$882$		0			0
$883$	26.0211			0.875680			0.437840	−	0.899053i	$-0.355744\pi$
$883$	26.0211			0.875680			0.437840	+	0.899053i	$0.355744\pi$
$884$	4.48716	+	14.5901i	0.150920	+	0.490720i
$885$		0			0
$886$	−2.13189	+	2.13189i	−0.0716222	+	0.0716222i
$887$	11.3477	−	27.3959i	0.381020	−	0.919863i	−0.610749	−	0.791824i	$-0.709132\pi$
$887$	11.3477	−	27.3959i	0.381020	−	0.919863i	0.991769	−	0.128039i	$-0.0408683\pi$
$888$		0			0
$889$	2.02357	+	0.838189i	0.0678683	+	0.0281120i
$890$	−0.214052	−	0.516768i	−0.00717505	−	0.0173221i
$891$		0			0
$892$	31.3823	+	31.3823i	1.05076	+	1.05076i
$893$	2.15957	+	2.15957i	0.0722674	+	0.0722674i
$894$		0			0
$895$	−1.65906	−	4.00532i	−0.0554562	−	0.133883i
$896$	−2.68527	−	1.11228i	−0.0897087	−	0.0371586i
$897$		0			0
$898$	−3.39095	+	8.18648i	−0.113157	+	0.273186i
$899$	−10.1131	+	10.1131i	−0.337290	+	0.337290i
$900$		0			0
$901$	9.78332	+	5.18106i	0.325930	+	0.172606i
$902$	−3.10018			−0.103225
$903$		0			0
$904$	5.87267	−	14.1779i	0.195322	−	0.471549i
$905$			23.7783i			0.790419i
$906$		0			0
$907$	−2.30095	−	5.55499i	−0.0764018	−	0.184450i	0.881064	−	0.472997i	$-0.156828\pi$
$907$	−2.30095	−	5.55499i	−0.0764018	−	0.184450i	−0.957466	+	0.288547i	$0.906828\pi$
$908$	35.5244	−	14.7147i	1.17892	−	0.488324i
$909$		0			0
$910$	0.150634	+	0.150634i	0.00499348	+	0.00499348i
$911$	33.5802	−	13.9094i	1.11256	−	0.460839i	0.250744	−	0.968054i	$-0.419325\pi$
$911$	33.5802	−	13.9094i	1.11256	−	0.460839i	0.861820	+	0.507215i	$0.169325\pi$
$912$		0			0
$913$	39.8190	+	16.4936i	1.31782	+	0.545858i
$914$		−	2.74173i		−	0.0906883i
$915$		0			0
$916$	−35.1724	+	35.1724i	−1.16213	+	1.16213i
$917$	−5.17440			−0.170874
$918$		0			0
$919$	31.4827			1.03852			0.519259	−	0.854617i	$-0.326208\pi$
$919$	31.4827			1.03852			0.519259	+	0.854617i	$0.326208\pi$
$920$	6.64468	−	6.64468i	0.219068	−	0.219068i
$921$		0			0
$922$			2.60127i			0.0856684i
$923$	−10.7680	−	4.46025i	−0.354433	−	0.146811i
$924$		0			0
$925$	−8.70414	+	3.60537i	−0.286190	+	0.118544i
$926$	5.86821	+	5.86821i	0.192841	+	0.192841i
$927$		0			0
$928$	17.2692	−	7.15312i	0.566888	−	0.234813i
$929$	16.5321	+	39.9121i	0.542402	+	1.30947i	0.923024	+	0.384743i	$0.125710\pi$
$929$	16.5321	+	39.9121i	0.542402	+	1.30947i	−0.380622	+	0.924731i	$0.624290\pi$
$930$		0			0
$931$		−	19.4812i		−	0.638471i
$932$	−16.8184	+	40.6032i	−0.550905	+	1.33000i
$933$		0			0
$934$	10.7732			0.352511
$935$	10.9058	−	3.35404i	0.356657	−	0.109689i
$936$		0			0
$937$	8.15745	−	8.15745i	0.266492	−	0.266492i	−0.561193	−	0.827685i	$-0.689657\pi$
$937$	8.15745	−	8.15745i	0.266492	−	0.266492i	0.827685	+	0.561193i	$0.189657\pi$
$938$	−0.517188	+	1.24860i	−0.0168868	+	0.0407683i
$939$		0			0
$940$	−1.87198	−	0.775399i	−0.0610572	−	0.0252907i
$941$	10.4367	+	25.1965i	0.340227	+	0.821382i	0.997692	+	0.0678965i	$0.0216288\pi$
$941$	10.4367	+	25.1965i	0.340227	+	0.821382i	−0.657465	+	0.753485i	$0.728371\pi$
$942$		0			0
$943$	−14.8201	−	14.8201i	−0.482608	−	0.482608i
$944$	−20.9608	−	20.9608i	−0.682217	−	0.682217i
$945$		0			0
$946$	3.12268	+	7.53882i	0.101527	+	0.245108i
$947$	21.0575	+	8.72231i	0.684278	+	0.283437i	0.697614	−	0.716474i	$-0.254245\pi$
$947$	21.0575	+	8.72231i	0.684278	+	0.283437i	−0.0133362	+	0.999911i	$0.504245\pi$
$948$		0			0
$949$	−0.164134	+	0.396254i	−0.00532801	+	0.0128630i
$950$	−0.718099	+	0.718099i	−0.0232982	+	0.0232982i
$951$		0			0
$952$	−0.161752	+	1.70960i	−0.00524240	+	0.0554086i
$953$	28.9548			0.937938			0.468969	−	0.883215i	$-0.344626\pi$
$953$	28.9548			0.937938			0.468969	+	0.883215i	$0.344626\pi$
$954$		0			0
$955$	−2.78232	+	6.71712i	−0.0900338	+	0.217361i
$956$		−	9.83243i		−	0.318003i
$957$		0			0
$958$	1.33139	+	3.21425i	0.0430152	+	0.103848i
$959$	3.85667	−	1.59748i	0.124538	−	0.0515854i
$960$		0			0
$961$	15.4447	+	15.4447i	0.498216	+	0.498216i
$962$	6.20731	−	2.57115i	0.200132	−	0.0828972i
$963$		0			0
$964$	9.39800	+	3.89278i	0.302689	+	0.125378i
$965$			22.1992i			0.714619i
$966$		0			0
$967$	35.7870	−	35.7870i	1.15083	−	1.15083i	0.164447	−	0.986386i	$-0.447416\pi$
$967$	35.7870	−	35.7870i	1.15083	−	1.15083i	0.986386	−	0.164447i	$-0.0525841\pi$
$968$	4.65968			0.149768
$969$		0			0
$970$	−3.23161			−0.103761
$971$	−23.2222	+	23.2222i	−0.745236	+	0.745236i	−0.973580	−	0.228344i	$-0.926669\pi$
$971$	−23.2222	+	23.2222i	−0.745236	+	0.745236i	0.228344	+	0.973580i	$0.426669\pi$
$972$		0			0
$973$			1.08154i			0.0346727i
$974$	−1.60761	−	0.665895i	−0.0515112	−	0.0213366i
$975$		0			0
$976$	−33.4883	+	13.8713i	−1.07193	+	0.444010i
$977$	15.2966	+	15.2966i	0.489381	+	0.489381i	0.908111	−	0.418730i	$-0.137525\pi$
$977$	15.2966	+	15.2966i	0.489381	+	0.489381i	−0.418730	+	0.908111i	$0.637525\pi$
$978$		0			0
$979$	−3.96956	+	1.64425i	−0.126868	+	0.0525503i
$980$	4.94604	+	11.9408i	0.157996	+	0.381435i
$981$		0			0
$982$			7.73637i			0.246878i
$983$	−1.95570	+	4.72148i	−0.0623771	+	0.150592i	−0.951995	−	0.306115i	$-0.900971\pi$
$983$	−1.95570	+	4.72148i	−0.0623771	+	0.150592i	0.889618	+	0.456706i	$0.150971\pi$
$984$		0			0
$985$	4.48140			0.142789
$986$	−4.47423	−	5.40935i	−0.142489	−	0.172269i
$987$		0			0
$988$	−7.37963	+	7.37963i	−0.234777	+	0.234777i
$989$	−21.1108	+	50.9661i	−0.671286	+	1.62063i
$990$		0			0
$991$	2.32187	+	0.961750i	0.0737566	+	0.0305510i	0.419257	−	0.907868i	$-0.362291\pi$
$991$	2.32187	+	0.961750i	0.0737566	+	0.0305510i	−0.345500	+	0.938419i	$0.612291\pi$
$992$	4.58029	+	11.0578i	0.145424	+	0.351085i
$993$		0			0
$994$	−0.448030	−	0.448030i	−0.0142107	−	0.0142107i
$995$	0.282410	+	0.282410i	0.00895300	+	0.00895300i
$996$		0			0
$997$	13.7947	+	33.3033i	0.436882	+	1.05473i	0.977020	+	0.213149i	$0.0683720\pi$
$997$	13.7947	+	33.3033i	0.436882	+	1.05473i	−0.540138	+	0.841576i	$0.681628\pi$
$998$	−6.20336	−	2.56951i	−0.196364	−	0.0813366i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.be.b.586.4		24
3.2	odd	2		85.2.l.a.76.3	yes	24
15.2	even	4		425.2.n.f.399.3		24
15.8	even	4		425.2.n.c.399.4		24
15.14	odd	2		425.2.m.b.76.4		24
17.15	even	8	inner	765.2.be.b.406.4		24
51.11	even	16		1445.2.d.j.866.10		24
51.23	even	16		1445.2.d.j.866.9		24
51.32	odd	8		85.2.l.a.66.3	✓	24
51.41	even	16		1445.2.a.q.1.8		12
51.44	even	16		1445.2.a.p.1.8		12
255.32	even	8		425.2.n.c.49.4		24
255.44	even	16		7225.2.a.bs.1.5		12
255.83	even	8		425.2.n.f.49.3		24
255.134	odd	8		425.2.m.b.151.4		24
255.194	even	16		7225.2.a.bq.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.3	✓	24	51.32	odd	8
85.2.l.a.76.3	yes	24	3.2	odd	2
425.2.m.b.76.4		24	15.14	odd	2
425.2.m.b.151.4		24	255.134	odd	8
425.2.n.c.49.4		24	255.32	even	8
425.2.n.c.399.4		24	15.8	even	4
425.2.n.f.49.3		24	255.83	even	8
425.2.n.f.399.3		24	15.2	even	4
765.2.be.b.406.4		24	17.15	even	8	inner
765.2.be.b.586.4		24	1.1	even	1	trivial
1445.2.a.p.1.8		12	51.44	even	16
1445.2.a.q.1.8		12	51.41	even	16
1445.2.d.j.866.9		24	51.23	even	16
1445.2.d.j.866.10		24	51.11	even	16
7225.2.a.bq.1.5		12	255.194	even	16
7225.2.a.bs.1.5		12	255.44	even	16

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.be (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.254738 - 0.254738i) q^{2} +1.87022i q^{4} +(-0.923880 - 0.382683i) q^{5} +(0.275980 - 0.114315i) q^{7} +(0.985893 + 0.985893i) q^{8} +O(q^{10})\)	\(q+(0.254738 - 0.254738i) q^{2} +1.87022i q^{4} +(-0.923880 - 0.382683i) q^{5} +(0.275980 - 0.114315i) q^{7} +(0.985893 + 0.985893i) q^{8} +(-0.332832 + 0.137863i) q^{10} +(1.05900 + 2.55665i) q^{11} -1.97956i q^{13} +(0.0411823 - 0.0994229i) q^{14} -3.23814 q^{16} +(1.21202 + 3.94094i) q^{17} +(-1.99331 + 1.99331i) q^{19} +(0.715701 - 1.72785i) q^{20} +(0.921046 + 0.381510i) q^{22} +(2.57919 + 6.22672i) q^{23} +(0.707107 + 0.707107i) q^{25} +(-0.504269 - 0.504269i) q^{26} +(0.213793 + 0.516142i) q^{28} +(-4.36632 - 1.80859i) q^{29} +(1.15808 - 2.79584i) q^{31} +(-2.79667 + 2.79667i) q^{32} +(1.31266 + 0.695159i) q^{34} -0.298718 q^{35} +(-3.60537 + 8.70414i) q^{37} +1.01554i q^{38} +(-0.533561 - 1.28813i) q^{40} +(-2.87301 + 1.19004i) q^{41} +(5.78771 + 5.78771i) q^{43} +(-4.78150 + 1.98056i) q^{44} +(2.24320 + 0.929166i) q^{46} -1.08341i q^{47} +(-4.88665 + 4.88665i) q^{49} +0.360254 q^{50} +3.70220 q^{52} +(1.89858 - 1.89858i) q^{53} -2.76730i q^{55} +(0.384788 + 0.159384i) q^{56} +(-1.57299 + 0.651553i) q^{58} +(6.47310 + 6.47310i) q^{59} +(10.3418 - 4.28372i) q^{61} +(-0.417202 - 1.00722i) q^{62} -5.05145i q^{64} +(-0.757544 + 1.82887i) q^{65} -12.5585 q^{67} +(-7.37041 + 2.26675i) q^{68} +(-0.0760950 + 0.0760950i) q^{70} +(2.25315 - 5.43960i) q^{71} +(-0.200173 - 0.0829144i) q^{73} +(1.29885 + 3.13570i) q^{74} +(-3.72792 - 3.72792i) q^{76} +(0.584525 + 0.584525i) q^{77} +(-4.07771 - 9.84447i) q^{79} +(2.99165 + 1.23918i) q^{80} +(-0.428717 + 1.03501i) q^{82} +(11.0129 - 11.0129i) q^{83} +(0.388367 - 4.10477i) q^{85} +2.94870 q^{86} +(-1.47653 + 3.56465i) q^{88} +1.55264i q^{89} +(-0.226292 - 0.546318i) q^{91} +(-11.6453 + 4.82365i) q^{92} +(-0.275986 - 0.275986i) q^{94} +(2.60438 - 1.07877i) q^{95} +(8.28752 + 3.43280i) q^{97} +2.48963i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

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