LMFDB - Embedded newform 425.2.m.b.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (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:	$3.39364208590$
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			151.4
Character	$\chi$	$=$	425.151
Dual form			425.2.m.b.76.4

$q$-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} +(-0.0207557 - 0.0501087i) q^{3} -1.87022i q^{4} +(0.00747733 - 0.0180519i) q^{6} +(-0.275980 - 0.114315i) q^{7} +(0.985893 - 0.985893i) q^{8} +(2.11924 - 2.11924i) q^{9} +(-1.05900 + 2.55665i) q^{11} +(-0.0937141 + 0.0388177i) q^{12} -1.97956i q^{13} +(-0.0411823 - 0.0994229i) q^{14} -3.23814 q^{16} +(1.21202 - 3.94094i) q^{17} +1.07970 q^{18} +(-1.99331 - 1.99331i) q^{19} +0.0162017i q^{21} +(-0.921046 + 0.381510i) q^{22} +(2.57919 - 6.22672i) q^{23} +(-0.0698647 - 0.0289389i) q^{24} +(0.504269 - 0.504269i) q^{26} +(-0.300505 - 0.124473i) q^{27} +(-0.213793 + 0.516142i) q^{28} +(4.36632 - 1.80859i) q^{29} +(1.15808 + 2.79584i) q^{31} +(-2.79667 - 2.79667i) q^{32} +0.150091 q^{33} +(1.31266 - 0.695159i) q^{34} +(-3.96344 - 3.96344i) q^{36} +(3.60537 + 8.70414i) q^{37} -1.01554i q^{38} +(-0.0991930 + 0.0410871i) q^{39} +(2.87301 + 1.19004i) q^{41} +(-0.00412718 + 0.00412718i) q^{42} +(-5.78771 + 5.78771i) q^{43} +(4.78150 + 1.98056i) q^{44} +(2.24320 - 0.929166i) q^{46} +1.08341i q^{47} +(0.0672100 + 0.162259i) q^{48} +(-4.88665 - 4.88665i) q^{49} +(-0.222632 + 0.0210640i) q^{51} -3.70220 q^{52} +(1.89858 + 1.89858i) q^{53} +(-0.0448420 - 0.108258i) q^{54} +(-0.384788 + 0.159384i) q^{56} +(-0.0585096 + 0.141255i) q^{57} +(1.57299 + 0.651553i) q^{58} +(-6.47310 + 6.47310i) q^{59} +(10.3418 + 4.28372i) q^{61} +(-0.417202 + 1.00722i) q^{62} +(-0.827127 + 0.342607i) q^{63} +5.05145i q^{64} +(0.0382339 + 0.0382339i) q^{66} +12.5585 q^{67} +(-7.37041 - 2.26675i) q^{68} -0.365546 q^{69} +(-2.25315 - 5.43960i) q^{71} -4.17869i q^{72} +(0.200173 - 0.0829144i) q^{73} +(-1.29885 + 3.13570i) q^{74} +(-3.72792 + 3.72792i) q^{76} +(0.584525 - 0.584525i) q^{77} +(-0.0357347 - 0.0148018i) q^{78} +(-4.07771 + 9.84447i) q^{79} -8.97353i q^{81} +(0.428717 + 1.03501i) q^{82} +(11.0129 + 11.0129i) q^{83} +0.0303006 q^{84} -2.94870 q^{86} +(-0.181252 - 0.181252i) q^{87} +(1.47653 + 3.56465i) q^{88} +1.55264i q^{89} +(-0.226292 + 0.546318i) q^{91} +(-11.6453 - 4.82365i) q^{92} +(0.116059 - 0.116059i) q^{93} +(-0.275986 + 0.275986i) q^{94} +(-0.0820905 + 0.198184i) q^{96} +(-8.28752 + 3.43280i) q^{97} -2.48963i q^{98} +(3.17389 + 7.66244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} - 24 q^{12} - 24 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 32 q^{22} + 16 q^{23} - 8 q^{24} + 16 q^{26} - 24 q^{27} - 48 q^{28} - 8 q^{29} + 16 q^{34} - 24 q^{36} - 24 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 - 24 * q^12 - 24 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 32 * q^22 + 16 * q^23 - 8 * q^24 + 16 * q^26 - 24 * q^27 - 48 * q^28 - 8 * q^29 + 16 * q^34 - 24 * q^36 - 24 * q^37 + 8 * q^39 + 16 * q^41 + 24 * q^42 - 8 * q^43 + 16 * q^44 + 8 * q^46 - 80 * q^48 - 56 * q^51 + 48 * q^52 - 24 * q^53 - 32 * q^54 + 64 * q^56 - 32 * q^57 + 64 * q^58 + 32 * q^59 + 32 * q^61 + 32 * q^62 + 56 * q^63 + 96 * q^66 - 16 * q^67 + 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^76 - 24 * q^77 + 112 * q^78 + 80 * q^82 + 96 * q^83 - 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 - 80 * q^92 - 64 * q^93 + 56 * q^94 - 168 * q^96 + 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	0.254738	+	0.254738i	0.180127	+	0.180127i	0.791411	−	0.611284i	$-0.209347\pi$
$2$	0.254738	+	0.254738i	0.180127	+	0.180127i	−0.611284	+	0.791411i	$0.709347\pi$
$3$	−0.0207557	−	0.0501087i	−0.0119833	−	0.0289303i	0.917775	−	0.397102i	$-0.129984\pi$
$3$	−0.0207557	−	0.0501087i	−0.0119833	−	0.0289303i	−0.929758	+	0.368171i	$0.879984\pi$
$4$		−	1.87022i		−	0.935108i
$5$		0			0
$5$		0			0
$6$	0.00747733	−	0.0180519i	0.00305261	−	0.00736965i
$7$	−0.275980	−	0.114315i	−0.104310	−	0.0432068i	0.329918	−	0.944010i	$-0.392979\pi$
$7$	−0.275980	−	0.114315i	−0.104310	−	0.0432068i	−0.434228	+	0.900803i	$0.642979\pi$
$8$	0.985893	−	0.985893i	0.348566	−	0.348566i
$9$	2.11924	−	2.11924i	0.706413	−	0.706413i
$10$		0			0
$11$	−1.05900	+	2.55665i	−0.319301	+	0.770860i	0.679991	+	0.733221i	$0.261984\pi$
$11$	−1.05900	+	2.55665i	−0.319301	+	0.770860i	−0.999291	+	0.0376394i	$0.988016\pi$
$12$	−0.0937141	+	0.0388177i	−0.0270529	+	0.0112057i
$13$		−	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
$18$	1.07970			0.254489
$19$	−1.99331	−	1.99331i	−0.457296	−	0.457296i	0.440471	−	0.897767i	$-0.354812\pi$
$19$	−1.99331	−	1.99331i	−0.457296	−	0.457296i	−0.897767	+	0.440471i	$0.854812\pi$
$20$		0			0
$21$			0.0162017i			0.00353549i
$22$	−0.921046	+	0.381510i	−0.196368	+	0.0813382i
$23$	2.57919	−	6.22672i	0.537799	−	1.29836i	−0.388457	−	0.921467i	$-0.626992\pi$
$23$	2.57919	−	6.22672i	0.537799	−	1.29836i	0.926256	−	0.376895i	$-0.123008\pi$
$24$	−0.0698647	−	0.0289389i	−0.0142611	−	0.00590713i
$25$		0			0
$26$	0.504269	−	0.504269i	0.0988953	−	0.0988953i
$27$	−0.300505	−	0.124473i	−0.0578322	−	0.0239549i
$28$	−0.213793	+	0.516142i	−0.0404031	+	0.0975416i
$29$	4.36632	−	1.80859i	0.810806	−	0.335847i	0.0615305	−	0.998105i	$-0.480402\pi$
$29$	4.36632	−	1.80859i	0.810806	−	0.335847i	0.749276	+	0.662258i	$0.230402\pi$
$30$		0			0
$31$	1.15808	+	2.79584i	0.207997	+	0.502148i	0.993108	−	0.117207i	$-0.0373941\pi$
$31$	1.15808	+	2.79584i	0.207997	+	0.502148i	−0.785111	+	0.619355i	$0.787394\pi$
$32$	−2.79667	−	2.79667i	−0.494385	−	0.494385i
$33$	0.150091			0.0261275
$34$	1.31266	−	0.695159i	0.225119	−	0.119219i
$35$		0			0
$36$	−3.96344	−	3.96344i	−0.660573	−	0.660573i
$37$	3.60537	+	8.70414i	0.592719	+	1.43095i	0.880866	+	0.473365i	$0.156961\pi$
$37$	3.60537	+	8.70414i	0.592719	+	1.43095i	−0.288147	+	0.957586i	$0.593039\pi$
$38$		−	1.01554i		−	0.164743i
$39$	−0.0991930	+	0.0410871i	−0.0158836	+	0.00657920i
$40$		0			0
$41$	2.87301	+	1.19004i	0.448688	+	0.185853i	0.595574	−	0.803301i	$-0.296925\pi$
$41$	2.87301	+	1.19004i	0.448688	+	0.185853i	−0.146885	+	0.989154i	$0.546925\pi$
$42$	−0.00412718	+	0.00412718i	−0.000636838	+	0.000636838i
$43$	−5.78771	+	5.78771i	−0.882617	+	0.882617i	−0.993800	−	0.111183i	$-0.964536\pi$
$43$	−5.78771	+	5.78771i	−0.882617	+	0.882617i	0.111183	+	0.993800i	$0.464536\pi$
$44$	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	$0.0251778\pi$
$47$			1.08341i			0.158032i	−0.996873	+	0.0790159i	$0.974822\pi$
$48$	0.0672100	+	0.162259i	0.00970092	+	0.0234201i
$49$	−4.88665	−	4.88665i	−0.698093	−	0.698093i
$50$		0			0
$51$	−0.222632	+	0.0210640i	−0.0311747	+	0.00294954i
$52$	−3.70220			−0.513403
$53$	1.89858	+	1.89858i	0.260790	+	0.260790i	0.825375	−	0.564585i	$-0.190964\pi$
$53$	1.89858	+	1.89858i	0.260790	+	0.260790i	−0.564585	+	0.825375i	$0.690964\pi$
$54$	−0.0448420	−	0.108258i	−0.00610222	−	0.0147321i
$55$		0			0
$56$	−0.384788	+	0.159384i	−0.0514195	+	0.0212986i
$57$	−0.0585096	+	0.141255i	−0.00774979	+	0.0187096i
$58$	1.57299	+	0.651553i	0.206543	+	0.0855531i
$59$	−6.47310	+	6.47310i	−0.842726	+	0.842726i	−0.989213	−	0.146487i	$-0.953203\pi$
$59$	−6.47310	+	6.47310i	−0.842726	+	0.842726i	0.146487	+	0.989213i	$0.453203\pi$
$60$		0			0
$61$	10.3418	+	4.28372i	1.32413	+	0.548474i	0.928976	−	0.370139i	$-0.120690\pi$
$61$	10.3418	+	4.28372i	1.32413	+	0.548474i	0.395158	+	0.918613i	$0.370690\pi$
$62$	−0.417202	+	1.00722i	−0.0529847	+	0.127916i
$63$	−0.827127	+	0.342607i	−0.104208	+	0.0431645i
$64$			5.05145i			0.631432i
$65$		0			0
$66$	0.0382339	+	0.0382339i	0.00470627	+	0.00470627i
$67$	12.5585			1.53427			0.767133	−	0.641488i	$-0.221683\pi$
$67$	12.5585			1.53427			0.767133	+	0.641488i	$0.221683\pi$
$68$	−7.37041	−	2.26675i	−0.893793	−	0.274884i
$69$	−0.365546			−0.0440066
$70$		0			0
$71$	−2.25315	−	5.43960i	−0.267400	−	0.645561i	0.731959	−	0.681348i	$-0.238606\pi$
$71$	−2.25315	−	5.43960i	−0.267400	−	0.645561i	−0.999359	+	0.0357872i	$0.988606\pi$
$72$		−	4.17869i		−	0.492463i
$73$	0.200173	−	0.0829144i	0.0234285	−	0.00970440i	−0.370938	−	0.928657i	$-0.620964\pi$
$73$	0.200173	−	0.0829144i	0.0234285	−	0.00970440i	0.394367	+	0.918953i	$0.370964\pi$
$74$	−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
$78$	−0.0357347	−	0.0148018i	−0.00404616	−	0.00167598i
$79$	−4.07771	+	9.84447i	−0.458779	+	1.10759i	0.510114	+	0.860107i	$0.329603\pi$
$79$	−4.07771	+	9.84447i	−0.458779	+	1.10759i	−0.968892	+	0.247482i	$0.920397\pi$
$80$		0			0
$81$		−	8.97353i		−	0.997059i
$82$	0.428717	+	1.03501i	0.0473438	+	0.114298i
$83$	11.0129	+	11.0129i	1.20883	+	1.20883i	0.971407	+	0.237421i	$0.0763020\pi$
$83$	11.0129	+	11.0129i	1.20883	+	1.20883i	0.237421	+	0.971407i	$0.423698\pi$
$84$	0.0303006			0.00330607
$85$		0			0
$86$	−2.94870			−0.317967
$87$	−0.181252	−	0.181252i	−0.0194323	−	0.0194323i
$88$	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
$93$	0.116059	−	0.116059i	0.0120348	−	0.0120348i
$94$	−0.275986	+	0.275986i	−0.0284658	+	0.0284658i
$95$		0			0
$96$	−0.0820905	+	0.198184i	−0.00837833	+	0.0202271i
$97$	−8.28752	+	3.43280i	−0.841471	+	0.348549i	−0.761433	−	0.648243i	$-0.775504\pi$
$97$	−8.28752	+	3.43280i	−0.841471	+	0.348549i	−0.0800373	+	0.996792i	$0.525504\pi$
$98$		−	2.48963i		−	0.251491i
$99$	3.17389	+	7.66244i	0.318988	+	0.770104i
$100$		0			0
$101$	−6.92132			−0.688697			−0.344349	−	0.938842i	$-0.611900\pi$
$101$	−6.92132			−0.688697			−0.344349	+	0.938842i	$0.611900\pi$
$102$	−0.0620786	−	0.0513470i	−0.00614670	−	0.00508412i
$103$	−12.9642			−1.27740			−0.638699	−	0.769457i	$-0.720527\pi$
$103$	−12.9642			−1.27740			−0.638699	+	0.769457i	$0.720527\pi$
$104$	−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	−0.214946	−	0.976626i	$-0.568957\pi$
$107$	3.34779	−	1.38670i	0.323643	−	0.134058i	0.538589	+	0.842568i	$0.318957\pi$
$108$	−0.232792	+	0.562009i	−0.0224004	+	0.0540793i
$109$	−4.75832	−	1.97096i	−0.455764	−	0.188784i	0.142977	−	0.989726i	$-0.454332\pi$
$109$	−4.75832	−	1.97096i	−0.455764	−	0.188784i	−0.598742	+	0.800942i	$0.704332\pi$
$110$		0			0
$111$	0.361321	−	0.361321i	0.0342951	−	0.0342951i
$112$	0.893662	+	0.370167i	0.0844431	+	0.0349775i
$113$	−4.21202	+	10.1687i	−0.396234	+	0.956593i	0.592317	+	0.805705i	$0.298213\pi$
$113$	−4.21202	+	10.1687i	−0.396234	+	0.956593i	−0.988551	+	0.150888i	$0.951787\pi$
$114$	−0.0508876	+	0.0210783i	−0.00476606	+	0.00197417i
$115$		0			0
$116$	−3.38246	−	8.16597i	−0.314053	−	0.758192i
$117$	−4.19516	−	4.19516i	−0.387842	−	0.387842i
$118$	−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
$123$		−	0.168663i		−	0.0152078i
$124$	5.22883	−	2.16585i	0.469563	−	0.194499i
$125$		0			0
$126$	−0.297976	−	0.123426i	−0.0265458	−	0.0109956i
$127$	−5.18472	+	5.18472i	−0.460070	+	0.460070i	−0.898678	−	0.438608i	$-0.855472\pi$
$127$	−5.18472	+	5.18472i	−0.460070	+	0.460070i	0.438608	+	0.898678i	$0.355472\pi$
$128$	−6.88013	+	6.88013i	−0.608123	+	0.608123i
$129$	0.410143	+	0.169887i	0.0361110	+	0.0149577i
$130$		0			0
$131$	16.0035	−	6.62885i	1.39823	−	0.579166i	0.448938	−	0.893563i	$-0.351802\pi$
$131$	16.0035	−	6.62885i	1.39823	−	0.579166i	0.949291	+	0.314397i	$0.101802\pi$
$132$		−	0.280703i		−	0.0244320i
$133$	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	$0.296375\pi$
$138$	−0.0931186	−	0.0931186i	−0.00792678	−	0.00792678i
$139$	−1.38555	−	3.34501i	−0.117521	−	0.283720i	0.854163	−	0.520005i	$-0.174070\pi$
$139$	−1.38555	−	3.34501i	−0.117521	−	0.283720i	−0.971684	+	0.236285i	$0.924070\pi$
$140$		0			0
$141$	0.0542883	−	0.0224870i	0.00457190	−	0.00189374i
$142$	0.811709	−	1.95964i	0.0681171	−	0.164449i
$143$	5.06104	+	2.09635i	0.423226	+	0.175306i
$144$	−6.86241	+	6.86241i	−0.571867	+	0.571867i
$145$		0			0
$146$	0.0721133	+	0.0298703i	0.00596814	+	0.00247208i
$147$	−0.143438	+	0.346290i	−0.0118306	+	0.0285615i
$148$	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	0.994075	+	0.108700i	$0.0346687\pi$
$151$	13.5511	+	13.5511i	1.10277	+	1.10277i	0.108700	+	0.994075i	$0.465331\pi$
$152$	−3.93038			−0.318796
$153$	−5.78322	−	10.9204i	−0.467546	−	0.882859i
$154$	0.297802			0.0239976
$155$		0			0
$156$	0.0768418	+	0.185512i	0.00615227	+	0.0148529i
$157$			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
$159$	0.0557290	−	0.134542i	0.00441960	−	0.0106699i
$160$		0			0
$161$	−1.42361	+	1.42361i	−0.112196	+	0.112196i
$162$	2.28590	−	2.28590i	0.179598	−	0.179598i
$163$	15.8036	+	6.54609i	1.23784	+	0.512729i	0.903038	−	0.429561i	$-0.141332\pi$
$163$	15.8036	+	6.54609i	1.23784	+	0.512729i	0.334799	+	0.942290i	$0.391332\pi$
$164$	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	0.736921	−	0.675979i	$-0.236279\pi$
$167$	−3.38773	−	8.17871i	−0.262151	−	0.632887i	−0.999071	+	0.0430919i	$0.986279\pi$
$168$	0.0159731	+	0.0159731i	0.00123235	+	0.00123235i
$169$	9.08135			0.698566
$170$		0			0
$171$	−8.44860			−0.646081
$172$	10.8243	+	10.8243i	0.825343	+	0.825343i
$173$	−7.34175	−	17.7246i	−0.558183	−	1.34757i	−0.911203	−	0.411957i	$-0.864845\pi$
$173$	−7.34175	−	17.7246i	−0.558183	−	1.34757i	0.353020	−	0.935616i	$-0.385155\pi$
$174$		−	0.0923438i		−	0.00700057i
$175$		0			0
$176$	3.42920	−	8.27881i	0.258485	−	0.624039i
$177$	0.458712	+	0.190005i	0.0344789	+	0.0142816i
$178$	−0.395517	+	0.395517i	−0.0296452	+	0.0296452i
$179$	−3.06554	+	3.06554i	−0.229129	+	0.229129i	−0.812329	−	0.583200i	$-0.801801\pi$
$179$	−3.06554	+	3.06554i	−0.229129	+	0.229129i	0.583200	+	0.812329i	$0.301801\pi$
$180$		0			0
$181$	−9.09958	+	21.9683i	−0.676366	+	1.63289i	0.0942155	+	0.995552i	$0.469966\pi$
$181$	−9.09958	+	21.9683i	−0.676366	+	1.63289i	−0.770582	+	0.637341i	$0.780034\pi$
$182$	−0.196813	+	0.0815228i	−0.0145888	+	0.00604287i
$183$		−	0.607127i		−	0.0448801i
$184$	−3.59607	−	8.68169i	−0.265106	−	0.640022i
$185$		0			0
$186$	0.0591296			0.00433559
$187$	8.79208	+	7.27219i	0.642941	+	0.531795i
$188$	2.02621			0.147777
$189$	0.0687041	+	0.0687041i	0.00499749	+	0.00499749i
$190$		0			0
$191$		−	7.27055i		−	0.526079i	−0.964785	−	0.263039i	$-0.915275\pi$
$191$		−	7.27055i		−	0.526079i	0.964785	−	0.263039i	$-0.0847249\pi$
$192$	0.253122	−	0.104846i	0.0182675	−	0.00756664i
$193$	8.49528	−	20.5094i	0.611504	−	1.47630i	−0.249845	−	0.968286i	$-0.580380\pi$
$193$	8.49528	−	20.5094i	0.611504	−	1.47630i	0.861348	−	0.508015i	$-0.169620\pi$
$194$	−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	0.230284	−	0.973123i	$-0.426034\pi$
$197$	−4.14027	−	1.71496i	−0.294982	−	0.122186i	−0.525267	+	0.850938i	$0.676034\pi$
$198$	−1.14341	+	2.76043i	−0.0812584	+	0.196175i
$199$	−0.368987	+	0.152839i	−0.0261568	+	0.0108345i	−0.395723	−	0.918370i	$-0.629506\pi$
$199$	−0.368987	+	0.152839i	−0.0261568	+	0.0108345i	0.369567	+	0.929204i	$0.379506\pi$
$200$		0			0
$201$	−0.260661	−	0.629290i	−0.0183856	−	0.0443867i
$202$	−1.76313	−	1.76313i	−0.124053	−	0.124053i
$203$	−1.41176			−0.0990865
$204$	0.0393942	+	0.416370i	0.00275814	+	0.0291517i
$205$		0			0
$206$	−3.30247	−	3.30247i	−0.230094	−	0.230094i
$207$	−7.72999	−	18.6618i	−0.537271	−	1.29709i
$208$			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	0.319803	−	0.947484i	$-0.396383\pi$
$211$	−1.80171	−	0.746294i	−0.124035	−	0.0513770i	−0.443838	+	0.896107i	$0.646383\pi$
$212$	3.55076	−	3.55076i	0.243867	−	0.243867i
$213$	−0.225805	+	0.225805i	−0.0154719	+	0.0154719i
$214$	1.20606	+	0.499566i	0.0824444	+	0.0341496i
$215$		0			0
$216$	−0.418983	+	0.173548i	−0.0285082	+	0.0118085i
$217$		−	0.903981i		−	0.0613662i
$218$	−0.710047	−	1.71421i	−0.0480905	−	0.116101i
$219$	−0.00830947	−	0.00830947i	−0.000561502	−	0.000561502i
$220$		0			0
$221$	−7.80131	−	2.39927i	−0.524773	−	0.161393i
$222$	0.184085			0.0123550
$223$	−16.7800	−	16.7800i	−1.12367	−	1.12367i	−0.991184	−	0.132491i	$-0.957703\pi$
$223$	−16.7800	−	16.7800i	−1.12367	−	1.12367i	−0.132491	−	0.991184i	$-0.542297\pi$
$224$	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	0.414316	+	0.910133i	$0.364021\pi$
$227$	−7.86790	+	18.9948i	−0.522211	+	1.26073i	−0.936527	+	0.350595i	$0.885979\pi$
$228$	0.264177	+	0.109426i	0.0174955	+	0.00724689i
$229$	18.8066	−	18.8066i	1.24277	−	1.24277i	0.283928	−	0.958846i	$-0.408362\pi$
$229$	18.8066	−	18.8066i	1.24277	−	1.24277i	0.958846	−	0.283928i	$-0.0916375\pi$
$230$		0			0
$231$	−0.0414220	−	0.0171576i	−0.00272537	−	0.00112889i
$232$	2.52165	−	6.08780i	0.165554	−	0.399684i
$233$	21.7104	−	8.99275i	1.42230	−	0.589135i	0.466860	−	0.884331i	$-0.345385\pi$
$233$	21.7104	−	8.99275i	1.42230	−	0.589135i	0.955437	+	0.295196i	$0.0953851\pi$
$234$		−	2.13734i		−	0.139722i
$235$		0			0
$236$	12.1061	+	12.1061i	0.788040	+	0.788040i
$237$	0.577929			0.0375405
$238$	−0.441734	+	0.0417939i	−0.0286333	+	0.00270910i
$239$	5.25737			0.340071			0.170036	−	0.985438i	$-0.445612\pi$
$239$	5.25737			0.340071			0.170036	+	0.985438i	$0.445612\pi$
$240$		0			0
$241$	2.08146	+	5.02509i	0.134079	+	0.323694i	0.976632	−	0.214918i	$-0.0689486\pi$
$241$	2.08146	+	5.02509i	0.134079	+	0.323694i	−0.842553	+	0.538613i	$0.818949\pi$
$242$			1.20398i			0.0773950i
$243$	−1.35117	+	0.559671i	−0.0866774	+	0.0359029i
$244$	8.01149	−	19.3414i	0.512883	−	1.23821i
$245$		0			0
$246$	0.0429649	−	0.0429649i	0.00273934	−	0.00273934i
$247$	−3.94587	+	3.94587i	−0.251070	+	0.251070i
$248$	3.89814	+	1.61466i	0.247532	+	0.102531i
$249$	0.323263	−	0.780426i	0.0204860	−	0.0494575i
$250$		0			0
$251$		−	26.3864i		−	1.66550i	−0.553652	−	0.832748i	$-0.686766\pi$
$251$		−	26.3864i		−	1.66550i	0.553652	−	0.832748i	$-0.313234\pi$
$252$	0.640750	+	1.54691i	0.0403634	+	0.0974460i
$253$	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	0.160045	−	0.987110i	$-0.448836\pi$
$257$	−13.2589	−	13.2589i	−0.827065	−	0.827065i	−0.987110	+	0.160045i	$0.948836\pi$
$258$	0.0612024	+	0.147756i	0.00381030	+	0.00919887i
$259$		−	2.81431i		−	0.174873i
$260$		0			0
$261$	5.42045	−	13.0861i	0.335518	−	0.810011i
$262$	5.76532	+	2.38807i	0.356183	+	0.147536i
$263$	−11.3145	+	11.3145i	−0.697680	+	0.697680i	−0.963910	−	0.266230i	$-0.914222\pi$
$263$	−11.3145	+	11.3145i	−0.697680	+	0.697680i	0.266230	+	0.963910i	$0.414222\pi$
$264$	0.147974	−	0.147974i	0.00910714	−	0.00910714i
$265$		0			0
$266$	−0.116091	+	0.280270i	−0.00711803	+	0.0171844i
$267$	0.0778007	−	0.0322261i	0.00476133	−	0.00197221i
$268$		−	23.4871i		−	1.43470i
$269$	0.457836	+	1.10531i	0.0279147	+	0.0673922i	0.937222	−	0.348733i	$-0.113388\pi$
$269$	0.457836	+	1.10531i	0.0279147	+	0.0673922i	−0.909307	+	0.416125i	$0.863388\pi$
$270$		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
$273$	0.0320721			0.00194109
$274$	3.55983	+	3.55983i	0.215057	+	0.215057i
$275$		0			0
$276$			0.683650i			0.0411509i
$277$	5.70841	−	2.36450i	0.342985	−	0.142069i	−0.204540	−	0.978858i	$-0.565570\pi$
$277$	5.70841	−	2.36450i	0.342985	−	0.142069i	0.547525	+	0.836789i	$0.315570\pi$
$278$	0.499150	−	1.20505i	0.0299370	−	0.0722744i
$279$	8.37931	+	3.47082i	0.501656	+	0.207793i
$280$		0			0
$281$	−19.7250	+	19.7250i	−1.17670	+	1.17670i	−0.196117	+	0.980581i	$0.562833\pi$
$281$	−19.7250	+	19.7250i	−1.17670	+	1.17670i	−0.980581	+	0.196117i	$0.937167\pi$
$282$	0.0195576	+	0.00810103i	0.00116464	+	0.000482409i
$283$	−11.3703	+	27.4503i	−0.675893	+	1.63175i	0.0955282	+	0.995427i	$0.469546\pi$
$283$	−11.3703	+	27.4503i	−0.675893	+	1.63175i	−0.771422	+	0.636324i	$0.780454\pi$
$284$	−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
$288$	−11.8536			−0.698481
$289$	−14.0620	−	9.55303i	−0.827176	−	0.561943i
$290$		0			0
$291$	0.344027	+	0.344027i	0.0201672	+	0.0201672i
$292$	−0.155068	−	0.374367i	−0.00907466	−	0.0219082i
$293$		−	22.4626i		−	1.31228i	−0.754639	−	0.656140i	$-0.772188\pi$
$293$		−	22.4626i		−	1.31228i	0.754639	−	0.656140i	$-0.227812\pi$
$294$	−0.124752	+	0.0516741i	−0.00727571	+	0.00301370i
$295$		0			0
$296$	12.1359	+	5.02684i	0.705382	+	0.292179i
$297$	0.636470	−	0.636470i	0.0369317	−	0.0369317i
$298$	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
$303$	0.143657	+	0.346818i	0.00825287	+	0.0199242i
$304$	6.45462	+	6.45462i	0.370198	+	0.370198i
$305$		0			0
$306$	1.30863	−	4.25505i	0.0748093	−	0.243245i
$307$	−5.53854			−0.316101			−0.158050	−	0.987431i	$-0.550521\pi$
$307$	−5.53854			−0.316101			−0.158050	+	0.987431i	$0.550521\pi$
$308$	−1.09319	−	1.09319i	−0.0622902	−	0.0622902i
$309$	0.269080	+	0.649618i	0.0153075	+	0.0369555i
$310$		0			0
$311$	−20.8510	+	8.63675i	−1.18235	+	0.489745i	−0.885256	−	0.465104i	$-0.846017\pi$
$311$	−20.8510	+	8.63675i	−1.18235	+	0.489745i	−0.297093	+	0.954849i	$0.596017\pi$
$312$	−0.0572862	+	0.138301i	−0.00324319	+	0.00782976i
$313$	11.2581	+	4.66325i	0.636345	+	0.263583i	0.677446	−	0.735572i	$-0.263087\pi$
$313$	11.2581	+	4.66325i	0.636345	+	0.263583i	−0.0411013	+	0.999155i	$0.513087\pi$
$314$	−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	−0.490743	−	0.871304i	$-0.663275\pi$
$317$	8.41030	−	20.3043i	0.472370	−	1.14040i	0.963113	−	0.269097i	$-0.0867253\pi$
$318$	0.0484693	−	0.0200766i	0.00271802	−	0.00112584i
$319$			13.0785i			0.732254i
$320$		0			0
$321$	−0.138972	−	0.138972i	−0.00775664	−	0.00775664i
$322$	−0.725296			−0.0404192
$323$	−10.2714	+	5.43957i	−0.571519	+	0.302666i
$324$	−16.7825			−0.932358
$325$		0			0
$326$	2.35826	+	5.69333i	0.130612	+	0.315325i
$327$			0.279342i			0.0154476i
$328$	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	−0.367816	−	0.929899i	$-0.619894\pi$
$331$	10.2262	−	10.2262i	0.562083	−	0.562083i	0.929899	+	0.367816i	$0.119894\pi$
$332$	20.5966	−	20.5966i	1.13038	−	1.13038i
$333$	26.0868	+	10.8055i	1.42955	+	0.592138i
$334$	1.22045	−	2.94642i	0.0667798	−	0.161221i
$335$		0			0
$336$		−	0.0524633i		−	0.00286211i
$337$	9.27853	+	22.4004i	0.505434	+	1.22023i	0.946486	+	0.322744i	$0.104605\pi$
$337$	9.27853	+	22.4004i	0.505434	+	1.22023i	−0.441052	+	0.897481i	$0.645395\pi$
$338$	2.31337	+	2.31337i	0.125831	+	0.125831i
$339$	0.596965			0.0324227
$340$		0			0
$341$	−8.37441			−0.453500
$342$	−2.15218	−	2.15218i	−0.116377	−	0.116377i
$343$	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	0.845625	−	0.533777i	$-0.179228\pi$
$347$	19.8599	+	8.22624i	1.06614	+	0.441608i	0.220510	+	0.975385i	$0.429228\pi$
$348$	−0.338981	+	0.338981i	−0.0181713	+	0.0181713i
$349$	−17.0669	+	17.0669i	−0.913570	+	0.913570i	−0.996551	−	0.0829813i	$-0.973556\pi$
$349$	−17.0669	+	17.0669i	−0.913570	+	0.913570i	0.0829813	+	0.996551i	$0.473556\pi$
$350$		0			0
$351$	−0.246402	+	0.594866i	−0.0131520	+	0.0317516i
$352$	10.1118	−	4.18843i	0.538959	−	0.223244i
$353$		−	7.24444i		−	0.385583i	−0.981240	−	0.192791i	$-0.938246\pi$
$353$		−	7.24444i		−	0.385583i	0.981240	−	0.192791i	$-0.0617541\pi$
$354$	0.0684501	+	0.165253i	0.00363808	+	0.00878311i
$355$		0			0
$356$	2.90377			0.153900
$357$	0.0638497	+	0.0196368i	0.00337929	+	0.00103929i
$358$	−1.56182			−0.0825449
$359$	12.2079	+	12.2079i	0.644308	+	0.644308i	0.951612	−	0.307303i	$-0.0994266\pi$
$359$	12.2079	+	12.2079i	0.644308	+	0.644308i	−0.307303	+	0.951612i	$0.599427\pi$
$360$		0			0
$361$		−	11.0534i		−	0.581760i
$362$	−7.91419	+	3.27816i	−0.415960	+	0.172296i
$363$	0.0693663	−	0.167465i	0.00364079	−	0.00878964i
$364$	1.02173	+	0.423215i	0.0535533	+	0.0221825i
$365$		0			0
$366$	0.154658	−	0.154658i	0.00808413	−	0.00808413i
$367$	−34.5930	−	14.3289i	−1.80574	−	0.747963i	−0.984016	−	0.178080i	$-0.943011\pi$
$367$	−34.5930	−	14.3289i	−1.80574	−	0.747963i	−0.821726	−	0.569883i	$-0.806989\pi$
$368$	−8.35180	+	20.1630i	−0.435368	+	1.05107i
$369$	8.61057	−	3.56661i	0.448248	−	0.185671i
$370$		0			0
$371$	−0.306934	−	0.741005i	−0.0159352	−	0.0384711i
$372$	−0.217056	−	0.217056i	−0.0112538	−	0.0112538i
$373$	−29.8887			−1.54758			−0.773789	−	0.633443i	$-0.781641\pi$
$373$	−29.8887			−1.54758			−0.773789	+	0.633443i	$0.781641\pi$
$374$	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
$378$			0.0350031i			0.00180037i
$379$	−27.7353	+	11.4883i	−1.42467	+	0.590116i	−0.956028	−	0.293275i	$-0.905255\pi$
$379$	−27.7353	+	11.4883i	−1.42467	+	0.590116i	−0.468637	+	0.883391i	$0.655255\pi$
$380$		0			0
$381$	0.367412	+	0.152187i	0.0188231	+	0.00779679i
$382$	1.85209	−	1.85209i	0.0947611	−	0.0947611i
$383$	−13.9465	+	13.9465i	−0.712634	+	0.712634i	−0.967086	−	0.254451i	$-0.918105\pi$
$383$	−13.9465	+	13.9465i	−0.712634	+	0.712634i	0.254451	+	0.967086i	$0.418105\pi$
$384$	0.487556	+	0.201952i	0.0248805	+	0.0103058i
$385$		0			0
$386$	7.38861	−	3.06046i	0.376070	−	0.155773i
$387$			24.5311i			1.24699i
$388$	6.42009	+	15.4995i	0.325931	+	0.786866i
$389$	2.62699	+	2.62699i	0.133194	+	0.133194i	0.770561	−	0.637367i	$-0.219976\pi$
$389$	2.62699	+	2.62699i	0.133194	+	0.133194i	−0.637367	+	0.770561i	$0.719976\pi$
$390$		0			0
$391$	−21.4131	−	17.7114i	−1.08291	−	0.895703i
$392$	−9.63543			−0.486663
$393$	−0.664326	−	0.664326i	−0.0335108	−	0.0335108i
$394$	−0.617821	−	1.49155i	−0.0311254	−	0.0751433i
$395$		0			0
$396$	14.3304	−	5.93586i	0.720131	−	0.298288i
$397$	1.97916	−	4.77812i	0.0993314	−	0.239807i	−0.866400	−	0.499350i	$-0.833572\pi$
$397$	1.97916	−	4.77812i	0.0993314	−	0.239807i	0.965731	+	0.259543i	$0.0835720\pi$
$398$	−0.132929	−	0.0550610i	−0.00666313	−	0.00275996i
$399$	0.0322949	−	0.0322949i	0.00161677	−	0.00161677i
$400$		0			0
$401$	0.364698	+	0.151063i	0.0182122	+	0.00754372i	0.391771	−	0.920063i	$-0.371863\pi$
$401$	0.364698	+	0.151063i	0.0182122	+	0.00754372i	−0.373559	+	0.927607i	$0.621863\pi$
$402$	0.0939042	−	0.226705i	0.00468351	−	0.0113070i
$403$	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
$408$	−0.198724	+	0.240258i	−0.00983831	+	0.0118945i
$409$	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			0
$411$	−0.290050	−	0.700242i	−0.0143071	−	0.0345404i
$412$			24.2458i			1.19451i
$413$	2.52641	−	1.04647i	0.124317	−	0.0514936i
$414$	2.78476	−	6.72301i	0.136864	−	0.330418i
$415$		0			0
$416$	−5.53616	+	5.53616i	−0.271433	+	0.271433i
$417$	−0.138856	+	0.138856i	−0.00679981	+	0.00679981i
$418$	2.59640	+	1.07546i	0.126994	+	0.0526026i
$419$	1.74972	−	4.22419i	0.0854793	−	0.206365i	−0.875360	−	0.483472i	$-0.839376\pi$
$419$	1.74972	−	4.22419i	0.0854793	−	0.206365i	0.960839	+	0.277107i	$0.0893755\pi$
$420$		0			0
$421$		−	7.55233i		−	0.368078i	−0.982919	−	0.184039i	$-0.941083\pi$
$421$		−	7.55233i		−	0.368078i	0.982919	−	0.184039i	$-0.0589173\pi$
$422$	−0.268856	−	0.649075i	−0.0130877	−	0.0315965i
$423$	2.29601	+	2.29601i	0.111636	+	0.111636i
$424$	3.74359			0.181805
$425$		0			0
$426$	−0.115043			−0.00557383
$427$	−2.36444	−	2.36444i	−0.114423	−	0.114423i
$428$	−2.59343	−	6.26110i	−0.125358	−	0.302642i
$429$		−	0.297114i		−	0.0143448i
$430$		0			0
$431$	7.99371	−	19.2985i	0.385043	−	0.929577i	−0.605930	−	0.795518i	$-0.707199\pi$
$431$	7.99371	−	19.2985i	0.385043	−	0.929577i	0.990973	−	0.134059i	$-0.0428011\pi$
$432$	0.973078	+	0.403062i	0.0468172	+	0.0193923i
$433$	−23.2292	+	23.2292i	−1.11632	+	1.11632i	−0.124045	+	0.992277i	$0.539587\pi$
$433$	−23.2292	+	23.2292i	−1.11632	+	1.11632i	−0.992277	+	0.124045i	$0.960413\pi$
$434$	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
$438$		−	0.00423348i		−	0.000202284i
$439$	9.19069	+	22.1883i	0.438648	+	1.05899i	0.976416	+	0.215897i	$0.0692674\pi$
$439$	9.19069	+	22.1883i	0.438648	+	1.05899i	−0.537769	+	0.843093i	$0.680733\pi$
$440$		0			0
$441$	−20.7120			−0.986284
$442$	−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	$0.563708\pi$
$444$	−0.675748	−	0.675748i	−0.0320696	−	0.0320696i
$445$		0			0
$446$		−	8.54904i		−	0.404809i
$447$	−0.644296	+	0.266876i	−0.0304741	+	0.0126228i
$448$	0.577454	−	1.39410i	0.0272821	−	0.0658649i
$449$	22.7241	+	9.41265i	1.07242	+	0.444210i	0.847844	−	0.530246i	$-0.177901\pi$
$449$	22.7241	+	9.41265i	1.07242	+	0.444210i	0.224575	+	0.974457i	$0.427901\pi$
$450$		0			0
$451$	−6.08503	+	6.08503i	−0.286533	+	0.286533i
$452$	19.0177	+	7.87740i	0.894518	+	0.370522i
$453$	0.397766	−	0.960292i	0.0186887	−	0.0451184i
$454$	−6.84296	+	2.83444i	−0.321156	+	0.133027i
$455$		0			0
$456$	0.0815778	+	0.196946i	0.00382023	+	0.00922285i
$457$	−5.38146	−	5.38146i	−0.251734	−	0.251734i	0.569947	−	0.821681i	$-0.306964\pi$
$457$	−5.38146	−	5.38146i	−0.251734	−	0.251734i	−0.821681	+	0.569947i	$0.806964\pi$
$458$	9.58151			0.447715
$459$	−0.854760	+	1.03341i	−0.0398968	+	0.0482353i
$460$		0			0
$461$	5.10577	+	5.10577i	0.237800	+	0.237800i	0.815938	−	0.578139i	$-0.196221\pi$
$461$	5.10577	+	5.10577i	0.237800	+	0.237800i	−0.578139	+	0.815938i	$0.696221\pi$
$462$	−0.00618109	−	0.0149225i	−0.000287570	−	0.000694256i
$463$			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	−0.0212676	−	0.999774i	$-0.506770\pi$
$467$	21.1457	−	21.1457i	0.978506	−	0.978506i	0.999774	+	0.0212676i	$0.00677021\pi$
$468$	−7.84585	+	7.84585i	−0.362675	+	0.362675i
$469$	−3.46589	−	1.43562i	−0.160040	−	0.0662907i
$470$		0			0
$471$	0.135405	−	0.0560865i	0.00623912	−	0.00258433i
$472$			12.7636i			0.587491i
$473$	−8.66798	−	20.9264i	−0.398554	−	0.962195i
$474$	0.147221	+	0.147221i	0.00676207	+	0.00676207i
$475$		0			0
$476$	1.77496	+	1.46812i	0.0813552	+	0.0672912i
$477$	8.04710			0.368451
$478$	1.33925	+	1.33925i	0.0612561	+	0.0612561i
$479$	3.69569	+	8.92218i	0.168860	+	0.407665i	0.985544	−	0.169421i	$-0.0541898\pi$
$479$	3.69569	+	8.92218i	0.168860	+	0.407665i	−0.816684	+	0.577086i	$0.804190\pi$
$480$		0			0
$481$	17.2303	−	7.13704i	0.785636	−	0.325421i
$482$	−0.749855	+	1.81031i	−0.0341550	+	0.0824574i
$483$	0.100883	+	0.0417872i	0.00459035	+	0.00190138i
$484$	4.41965	−	4.41965i	0.200893	−	0.200893i
$485$		0			0
$486$	−0.486764	−	0.201624i	−0.0220801	−	0.00914586i
$487$	1.84840	−	4.46244i	0.0837591	−	0.202212i	−0.876451	−	0.481491i	$-0.840095\pi$
$487$	1.84840	−	4.46244i	0.0837591	−	0.202212i	0.960210	+	0.279279i	$0.0900954\pi$
$488$	14.4192	−	5.97263i	0.652727	−	0.270368i
$489$		−	0.927769i		−	0.0419552i
$490$		0			0
$491$	15.1849	+	15.1849i	0.685287	+	0.685287i	0.961186	−	0.275900i	$-0.0889758\pi$
$491$	15.1849	+	15.1849i	0.685287	+	0.685287i	−0.275900	+	0.961186i	$0.588976\pi$
$492$	−0.315436			−0.0142209
$493$	−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
$498$	0.281152	−	0.116457i	0.0125987	−	0.00521856i
$499$	−7.13250	+	17.2194i	−0.319295	+	0.770845i	0.679997	+	0.733215i	$0.261981\pi$
$499$	−7.13250	+	17.2194i	−0.319295	+	0.770845i	−0.999292	+	0.0376305i	$0.988019\pi$
$500$		0			0
$501$	−0.339510	+	0.339510i	−0.0151682	+	0.0151682i
$502$	6.72164	−	6.72164i	0.300001	−	0.300001i
$503$	17.1646	+	7.10981i	0.765332	+	0.317011i	0.730980	−	0.682399i	$-0.239063\pi$
$503$	17.1646	+	7.10981i	0.765332	+	0.317011i	0.0343519	+	0.999410i	$0.489063\pi$
$504$	−0.477685	+	1.15323i	−0.0212778	+	0.0513691i
$505$		0			0
$506$			6.71908i			0.298700i
$507$	−0.188490	−	0.455055i	−0.00837113	−	0.0202097i
$508$	9.69656	+	9.69656i	0.430215	+	0.430215i
$509$	−28.4343			−1.26033			−0.630163	−	0.776463i	$-0.717012\pi$
$509$	−28.4343			−1.26033			−0.630163	+	0.776463i	$0.717012\pi$
$510$		0			0
$511$	−0.0647220			−0.00286313
$512$	15.4409	+	15.4409i	0.682399	+	0.682399i
$513$	0.350885	+	0.847112i	0.0154920	+	0.0374009i
$514$		−	6.75508i		−	0.297954i
$515$		0			0
$516$	0.317725	−	0.767056i	0.0139871	−	0.0337677i
$517$	−2.76991	−	1.14733i	−0.121820	−	0.0504597i
$518$	0.716913	−	0.716913i	0.0314993	−	0.0314993i
$519$	−0.735771	+	0.735771i	−0.0322968	+	0.0322968i
$520$		0			0
$521$	−7.26078	+	17.5291i	−0.318100	+	0.767962i	0.681254	+	0.732047i	$0.261435\pi$
$521$	−7.26078	+	17.5291i	−0.318100	+	0.767962i	−0.999355	+	0.0359155i	$0.988565\pi$
$522$	4.71434	−	1.95274i	0.206341	−	0.0854692i
$523$		−	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
$528$	−0.486016			−0.0211511
$529$	−15.8564	−	15.8564i	−0.689407	−	0.689407i
$530$		0			0
$531$			27.4361i			1.19063i
$532$	1.45499	−	0.602675i	0.0630816	−	0.0261293i
$533$	2.35575	−	5.68728i	0.102039	−	0.246344i
$534$	0.0280281	+	0.0116096i	0.00121289	+	0.000502397i
$535$		0			0
$536$	12.3813	−	12.3813i	0.534792	−	0.534792i
$537$	0.217238	+	0.0899828i	0.00937450	+	0.00388305i
$538$	−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	0.809654	−	0.586907i	$-0.199655\pi$
$541$	−4.13701	−	9.98762i	−0.177864	−	0.429401i	−0.987518	+	0.157506i	$0.949655\pi$
$542$	−0.226358	−	0.226358i	−0.00972291	−	0.00972291i
$543$	1.28967			0.0553451
$544$	−14.4111	+	7.63186i	−0.617871	+	0.327213i
$545$		0			0
$546$	0.00817000	+	0.00817000i	0.000349644	+	0.000349644i
$547$	2.78305	+	6.71889i	0.118995	+	0.287279i	0.972143	−	0.234391i	$-0.0753094\pi$
$547$	2.78305	+	6.71889i	0.118995	+	0.287279i	−0.853148	+	0.521669i	$0.825309\pi$
$548$		−	26.1353i		−	1.11644i
$549$	30.9950	−	12.8386i	1.32284	−	0.547937i
$550$		0			0
$551$	−12.3085	−	5.09835i	−0.524360	−	0.217197i
$552$	−0.360389	+	0.360389i	−0.0153392	+	0.0153392i
$553$	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	$-0.872590\pi$
$557$		−	18.3930i		−	0.779335i	0.920956	−	0.389667i	$-0.127410\pi$
$558$	1.25038	+	3.01868i	0.0529328	+	0.127791i
$559$	11.4571	+	11.4571i	0.484584	+	0.484584i
$560$		0			0
$561$	0.181914	−	0.591499i	0.00768041	−	0.0249731i
$562$	−10.0495			−0.423911
$563$	−0.317586	−	0.317586i	−0.0133847	−	0.0133847i	0.700383	−	0.713767i	$-0.253013\pi$
$563$	−0.317586	−	0.317586i	−0.0133847	−	0.0133847i	−0.713767	+	0.700383i	$0.753013\pi$
$564$	−0.0420555	−	0.101531i	−0.00177086	−	0.00427522i
$565$		0			0
$566$	−9.88909	+	4.09620i	−0.415670	+	0.172176i
$567$	−1.02581	+	2.47651i	−0.0430798	+	0.104004i
$568$	−7.58423	−	3.14149i	−0.318227	−	0.131814i
$569$	10.1299	−	10.1299i	0.424669	−	0.424669i	−0.462138	−	0.886808i	$-0.652918\pi$
$569$	10.1299	−	10.1299i	0.424669	−	0.424669i	0.886808	+	0.462138i	$0.152918\pi$
$570$		0			0
$571$	25.8617	+	10.7123i	1.08228	+	0.448294i	0.851307	−	0.524667i	$-0.175810\pi$
$571$	25.8617	+	10.7123i	1.08228	+	0.448294i	0.230970	+	0.972961i	$0.425810\pi$
$572$	3.92063	−	9.46525i	0.163930	−	0.395762i
$573$	−0.364318	+	0.150905i	−0.0152196	+	0.00630417i
$574$		−	0.334651i		−	0.0139681i
$575$		0			0
$576$	10.7052	+	10.7052i	0.446052	+	0.446052i
$577$	6.76924			0.281807			0.140904	−	0.990023i	$-0.454999\pi$
$577$	6.76924			0.281807			0.140904	+	0.990023i	$0.454999\pi$
$578$	−1.14861	−	6.01565i	−0.0477757	−	0.250218i
$579$	−1.20403			−0.0500376
$580$		0			0
$581$	−1.78041	−	4.29829i	−0.0738638	−	0.178323i
$582$			0.175274i			0.00726533i
$583$	−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	−0.968833	−	0.247715i	$-0.920320\pi$
$587$	−17.4713	+	17.4713i	−0.721117	+	0.721117i	0.247715	+	0.968833i	$0.420320\pi$
$588$	0.647637	+	0.268260i	0.0267081	+	0.0110628i
$589$	3.26458	−	7.88139i	0.134515	−	0.324747i
$590$		0			0
$591$			0.243059i			0.00999810i
$592$	−11.6747	−	28.1852i	−0.479828	−	1.15841i
$593$	15.8749	+	15.8749i	0.651905	+	0.651905i	0.953451	−	0.301547i	$-0.0975029\pi$
$593$	15.8749	+	15.8749i	0.651905	+	0.651905i	−0.301547	+	0.953451i	$0.597503\pi$
$594$	0.324266			0.0133048
$595$		0			0
$596$	−24.0472			−0.985010
$597$	0.0153172	+	0.0153172i	0.000626889	+	0.000626889i
$598$	−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	0.632777	+	0.774334i	$0.281915\pi$
$601$	−8.87947	+	21.4369i	−0.362201	+	0.874431i	−0.994978	+	0.100096i	$0.968085\pi$
$602$	0.813782	+	0.337080i	0.0331673	+	0.0137383i
$603$	26.6145	−	26.6145i	1.08383	−	1.08383i
$604$	25.3435	−	25.3435i	1.03121	−	1.03121i
$605$		0			0
$606$	−0.0517530	+	0.124943i	−0.00210232	+	0.00507546i
$607$	−1.72244	+	0.713459i	−0.0699118	+	0.0289584i	−0.417365	−	0.908739i	$-0.637046\pi$
$607$	−1.72244	+	0.713459i	−0.0699118	+	0.0289584i	0.347454	+	0.937697i	$0.387046\pi$
$608$			11.1492i			0.452161i
$609$	0.0293022	+	0.0707417i	0.00118738	+	0.00286660i
$610$		0			0
$611$	2.14468			0.0867643
$612$	−20.4235	+	10.8159i	−0.825569	+	0.437206i
$613$	0.383092			0.0154729			0.00773647	−	0.999970i	$-0.497537\pi$
$613$	0.383092			0.0154729			0.00773647	+	0.999970i	$0.497537\pi$
$614$	−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	−0.588962	−	0.808161i	$-0.700463\pi$
$617$	−10.7794	+	4.46499i	−0.433964	+	0.179754i	0.154997	+	0.987915i	$0.450463\pi$
$618$	−0.0969375	+	0.234028i	−0.00389940	+	0.00941398i
$619$	−12.4590	−	5.16070i	−0.500771	−	0.207426i	0.117976	−	0.993016i	$-0.462359\pi$
$619$	−12.4590	−	5.16070i	−0.500771	−	0.207426i	−0.618747	+	0.785590i	$0.712359\pi$
$620$		0			0
$621$	−1.55012	+	1.55012i	−0.0622041	+	0.0622041i
$622$	−7.51165	−	3.11143i	−0.301190	−	0.124757i
$623$	0.177489	−	0.428497i	0.00711096	−	0.0171674i
$624$	0.321201	−	0.133046i	0.0128583	−	0.00532610i
$625$		0			0
$626$	1.67996	+	4.05578i	0.0671446	+	0.162101i
$627$	−0.299178	−	0.299178i	−0.0119480	−	0.0119480i
$628$	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	−0.912706	−	0.408617i	$-0.866011\pi$
$631$	−33.1913	−	33.1913i	−1.32132	−	1.32132i	−0.408617	−	0.912706i	$-0.633989\pi$
$632$	5.68540	+	13.7258i	0.226153	+	0.545982i
$633$			0.105771i			0.00420403i
$634$	7.31470	−	3.02985i	0.290504	−	0.120331i
$635$		0			0
$636$	−0.251622	−	0.104225i	−0.00997747	−	0.00413280i
$637$	−9.67341	+	9.67341i	−0.383274	+	0.383274i
$638$	−3.33159	+	3.33159i	−0.131899	+	0.131899i
$639$	−16.3028	−	6.75284i	−0.644928	−	0.267138i
$640$		0			0
$641$	36.5657	−	15.1460i	1.44426	−	0.598232i	0.483433	−	0.875382i	$-0.339390\pi$
$641$	36.5657	−	15.1460i	1.44426	−	0.598232i	0.960827	+	0.277150i	$0.0893898\pi$
$642$		−	0.0708028i		−	0.00279436i
$643$	−6.78010	−	16.3686i	−0.267381	−	0.645515i	0.731978	−	0.681329i	$-0.238598\pi$
$643$	−6.78010	−	16.3686i	−0.267381	−	0.645515i	−0.999358	+	0.0358141i	$0.988598\pi$
$644$	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	$0.405838\pi$
$648$	−8.84694	−	8.84694i	−0.347541	−	0.347541i
$649$	−9.69446	−	23.4045i	−0.380541	−	0.918707i
$650$		0			0
$651$	−0.0452973	+	0.0187628i	−0.00177534	+	0.000735370i
$652$	12.2426	−	29.5562i	0.479457	−	1.15751i
$653$	−9.42227	−	3.90283i	−0.368722	−	0.152730i	0.190626	−	0.981663i	$-0.438948\pi$
$653$	−9.42227	−	3.90283i	−0.368722	−	0.152730i	−0.559348	+	0.828933i	$0.688948\pi$
$654$	−0.0711591	+	0.0711591i	−0.00278254	+	0.00278254i
$655$		0			0
$656$	−9.30321	−	3.85352i	−0.363229	−	0.150455i
$657$	0.248499	−	0.599931i	0.00969488	−	0.0234055i
$658$	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	0.589264	−	0.807940i	$-0.299418\pi$
$661$	−5.62214	−	5.62214i	−0.218676	−	0.218676i	−0.807940	+	0.589264i	$0.799418\pi$
$662$	5.21001			0.202493
$663$	0.0416973	+	0.440712i	0.00161939	+	0.0171158i
$664$	21.7152			0.842712
$665$		0			0
$666$	3.89273	+	9.39789i	0.150840	+	0.364161i
$667$		−	31.8526i		−	1.23334i
$668$	−15.2960	+	6.33579i	−0.591818	+	0.245139i
$669$	−0.492545	+	1.18911i	−0.0190429	+	0.0459736i
$670$		0			0
$671$	−21.9040	+	21.9040i	−0.845594	+	0.845594i
$672$	0.0453106	−	0.0453106i	0.00174789	−	0.00174789i
$673$	−20.3139	−	8.41428i	−0.783042	−	0.324347i	−0.0448994	−	0.998992i	$-0.514297\pi$
$673$	−20.3139	−	8.41428i	−0.783042	−	0.324347i	−0.738142	+	0.674645i	$0.764297\pi$
$674$	−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	0.999400	−	0.0346387i	$-0.0110280\pi$
$677$	6.97899	+	16.8488i	0.268224	+	0.647551i	−0.731176	+	0.682189i	$0.761028\pi$
$678$	0.152070	+	0.152070i	0.00584021	+	0.00584021i
$679$	2.67961			0.102834
$680$		0			0
$681$	1.11511			0.0427310
$682$	−2.13328	−	2.13328i	−0.0816876	−	0.0816876i
$683$	6.96604	+	16.8175i	0.266548	+	0.643504i	0.999316	−	0.0369746i	$-0.0117721\pi$
$683$	6.96604	+	16.8175i	0.266548	+	0.643504i	−0.732768	+	0.680478i	$0.761772\pi$
$684$			15.8007i			0.604156i
$685$		0			0
$686$	−0.572878	+	1.38305i	−0.0218726	+	0.0528051i
$687$	−1.33272	−	0.552029i	−0.0508463	−	0.0210612i
$688$	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	−0.769194	−	0.639015i	$-0.779342\pi$
$691$	5.95556	−	14.3780i	0.226560	−	0.546965i	0.995754	+	0.0920503i	$0.0293421\pi$
$692$	−33.1488	+	13.7307i	−1.26013	+	0.521962i
$693$		−	2.47750i		−	0.0941124i
$694$	2.96354	+	7.15462i	0.112494	+	0.271586i
$695$		0			0
$696$	−0.357391			−0.0135469
$697$	8.17202	−	9.87999i	0.309537	−	0.374231i
$698$	−8.69519			−0.329118
$699$	−0.901230	−	0.901230i	−0.0340876	−	0.0340876i
$700$		0			0
$701$			8.07561i			0.305011i	0.988303	+	0.152506i	$0.0487342\pi$
$701$			8.07561i			0.305011i	−0.988303	+	0.152506i	$0.951266\pi$
$702$	−0.214303	+	0.0887673i	−0.00808836	+	0.00335031i
$703$	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
$708$	0.355350	−	0.857891i	0.0133549	−	0.0322415i
$709$	−4.88749	+	2.02447i	−0.183554	+	0.0760304i	−0.472567	−	0.881295i	$-0.656673\pi$
$709$	−4.88749	+	2.02447i	−0.183554	+	0.0760304i	0.289014	+	0.957325i	$0.406673\pi$
$710$		0			0
$711$	12.2211	+	29.5044i	0.458329	+	1.10650i
$712$	1.53074	+	1.53074i	0.0573668	+	0.0573668i
$713$	20.3958			0.763830
$714$	0.0112627	+	0.0212672i	0.000421497	+	0.000795906i
$715$		0			0
$716$	5.73323	+	5.73323i	0.214261	+	0.214261i
$717$	−0.109120	−	0.263440i	−0.00407518	−	0.00983835i
$718$			6.21964i			0.232115i
$719$	−8.27731	+	3.42857i	−0.308691	+	0.127864i	−0.531651	−	0.846964i	$-0.678428\pi$
$719$	−8.27731	+	3.42857i	−0.308691	+	0.127864i	0.222960	+	0.974828i	$0.428428\pi$
$720$		0			0
$721$	3.57785	+	1.48199i	0.133246	+	0.0551923i
$722$	2.81573	−	2.81573i	0.104791	−	0.104791i
$723$	0.208598	−	0.208598i	0.00775786	−	0.00775786i
$724$	41.0855	+	17.0182i	1.52693	+	0.632476i
$725$		0			0
$726$	0.0603301	−	0.0249895i	0.00223906	−	0.000927449i
$727$		−	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
$729$	−18.9797	−	18.9797i	−0.702950	−	0.702950i
$730$		0			0
$731$	15.7942	+	29.8239i	0.584168	+	1.10308i
$732$	−1.13546			−0.0419678
$733$	19.0696	+	19.0696i	0.704352	+	0.704352i	0.965342	−	0.260990i	$-0.0840488\pi$
$733$	19.0696	+	19.0696i	0.704352	+	0.704352i	−0.260990	+	0.965342i	$0.584049\pi$
$734$	−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
$738$	3.10200	+	1.28489i	0.114186	+	0.0472974i
$739$	−24.6401	+	24.6401i	−0.906400	+	0.906400i	−0.995980	−	0.0895798i	$-0.971448\pi$
$739$	−24.6401	+	24.6401i	−0.906400	+	0.906400i	0.0895798	+	0.995980i	$0.471448\pi$
$740$		0			0
$741$	0.279622	+	0.115823i	0.0102722	+	0.00425487i
$742$	0.110574	−	0.266950i	0.00405932	−	0.00980006i
$743$	15.7918	−	6.54116i	0.579344	−	0.239972i	−0.0737150	−	0.997279i	$-0.523486\pi$
$743$	15.7918	−	6.54116i	0.579344	−	0.239972i	0.653059	+	0.757307i	$0.273486\pi$
$744$		−	0.228844i		−	0.00838984i
$745$		0			0
$746$	−7.61380	−	7.61380i	−0.278761	−	0.278761i
$747$	46.6781			1.70786
$748$	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	−0.968736	−	0.248093i	$-0.920196\pi$
$751$	−12.5831	−	30.3783i	−0.459165	−	1.10852i	0.509572	−	0.860428i	$-0.329804\pi$
$752$		−	3.50824i		−	0.127932i
$753$	−1.32219	+	0.547669i	−0.0481833	+	0.0199582i
$754$	1.28979	−	3.11382i	0.0469713	−	0.113399i
$755$		0			0
$756$	0.128492	−	0.128492i	0.00467319	−	0.00467319i
$757$	−12.3728	+	12.3728i	−0.449698	+	0.449698i	−0.895254	−	0.445556i	$-0.853006\pi$
$757$	−12.3728	+	12.3728i	−0.449698	+	0.449698i	0.445556	+	0.895254i	$0.353006\pi$
$758$	−9.99176	−	4.13872i	−0.362917	−	0.150325i
$759$	0.387113	−	0.934574i	0.0140513	−	0.0339229i
$760$		0			0
$761$			10.8439i			0.393092i	0.980495	+	0.196546i	$0.0629724\pi$
$761$			10.8439i			0.393092i	−0.980495	+	0.196546i	$0.937028\pi$
$762$	0.0548261	+	0.132362i	0.00198614	+	0.00479497i
$763$	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
$768$	−0.136939	−	0.330599i	−0.00494135	−	0.0119295i
$769$			14.8775i			0.536497i	0.963350	+	0.268248i	$0.0864448\pi$
$769$			14.8775i			0.536497i	−0.963350	+	0.268248i	$0.913555\pi$
$770$		0			0
$771$	−0.389187	+	0.939581i	−0.0140162	+	0.0338382i
$772$	−38.3571	−	15.8880i	−1.38050	−	0.571822i
$773$	−5.45537	+	5.45537i	−0.196216	+	0.196216i	−0.798376	−	0.602160i	$-0.794307\pi$
$773$	−5.45537	+	5.45537i	−0.196216	+	0.196216i	0.602160	+	0.798376i	$0.294307\pi$
$774$	−6.24901	+	6.24901i	−0.224616	+	0.224616i
$775$		0			0
$776$	−4.78623	+	11.5550i	−0.171816	+	0.414800i
$777$	−0.141021	+	0.0584130i	−0.00505912	+	0.00209555i
$778$			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
$783$	−1.53722			−0.0549358
$784$	15.8237	+	15.8237i	0.565131	+	0.565131i
$785$		0			0
$786$		−	0.338459i		−	0.0120724i
$787$	35.3404	−	14.6385i	1.25975	−	0.521805i	0.349917	−	0.936781i	$-0.386210\pi$
$787$	35.3404	−	14.6385i	1.25975	−	0.521805i	0.909833	+	0.414975i	$0.136210\pi$
$788$	−3.20734	+	7.74321i	−0.114257	+	0.275840i
$789$	0.801792	+	0.332113i	0.0285446	+	0.0118235i
$790$		0			0
$791$	2.32487	−	2.32487i	0.0826627	−	0.0826627i
$792$	10.6835	+	4.42523i	0.379620	+	0.157244i
$793$	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	0.956941	−	0.290284i	$-0.0937496\pi$
$797$	18.8205	+	18.8205i	0.666657	+	0.666657i	−0.290284	+	0.956941i	$0.593750\pi$
$798$	0.0164535			0.000582448
$799$	4.26966	+	1.31312i	0.151050	+	0.0464549i
$800$		0			0
$801$	3.29042	+	3.29042i	0.116261	+	0.116261i
$802$	0.0544211	+	0.131384i	0.00192168	+	0.00463934i
$803$			0.599580i			0.0211587i
$804$	−1.17691	+	0.487492i	−0.0415064	+	0.0171925i
$805$		0			0
$806$	1.99384	+	0.825876i	0.0702300	+	0.0290902i
$807$	0.0458831	−	0.0458831i	0.00161516	−	0.00161516i
$808$	−6.82368	+	6.82368i	−0.240056	+	0.240056i
$809$	15.1856	+	6.29009i	0.533898	+	0.221148i	0.633309	−	0.773899i	$-0.281696\pi$
$809$	15.1856	+	6.29009i	0.533898	+	0.221148i	−0.0994117	+	0.995046i	$0.531696\pi$
$810$		0			0
$811$	−3.36428	+	1.39353i	−0.118136	+	0.0489335i	−0.440968	−	0.897523i	$-0.645365\pi$
$811$	−3.36428	+	1.39353i	−0.118136	+	0.0489335i	0.322833	+	0.946456i	$0.395365\pi$
$812$			2.64031i			0.0926566i
$813$	0.0184433	+	0.0445261i	0.000646835	+	0.00156160i
$814$	−6.64143	−	6.64143i	−0.232782	−	0.232782i
$815$		0			0
$816$	0.720914	−	0.0682081i	0.0252370	−	0.00238776i
$817$	23.0734			0.807236
$818$	0.132739	+	0.132739i	0.00464111	+	0.00464111i
$819$	0.678211	+	1.63735i	0.0236986	+	0.0572135i
$820$		0			0
$821$	32.8228	−	13.5957i	1.14552	−	0.474492i	0.272494	−	0.962158i	$-0.412152\pi$
$821$	32.8228	−	13.5957i	1.14552	−	0.474492i	0.873030	+	0.487666i	$0.162152\pi$
$822$	0.104492	−	0.252265i	0.00364457	−	0.00879876i
$823$	−4.63438	−	1.91962i	−0.161544	−	0.0669138i	0.300446	−	0.953799i	$-0.402864\pi$
$823$	−4.63438	−	1.91962i	−0.161544	−	0.0669138i	−0.461990	+	0.886885i	$0.652864\pi$
$824$	−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	0.417645	+	0.908610i	$0.362856\pi$
$827$	−14.9585	+	36.1131i	−0.520159	+	1.25578i	−0.937804	+	0.347165i	$0.887144\pi$
$828$	−34.9017	+	14.4568i	−1.21292	+	0.502407i
$829$			16.3998i			0.569587i	0.958589	+	0.284794i	$0.0919250\pi$
$829$			16.3998i			0.569587i	−0.958589	+	0.284794i	$0.908075\pi$
$830$		0			0
$831$	−0.236964	−	0.236964i	−0.00822019	−	0.00822019i
$832$	9.99964			0.346675
$833$	−25.1807	+	13.3352i	−0.872461	+	0.462039i
$834$	−0.0707439			−0.00244966
$835$		0			0
$836$	−5.58313	−	13.4789i	−0.193097	−	0.466177i
$837$		−	0.984314i		−	0.0340229i
$838$	1.52178	−	0.630344i	0.0525692	−	0.0217749i
$839$	−11.4471	+	27.6357i	−0.395197	+	0.954090i	0.593591	+	0.804767i	$0.297710\pi$
$839$	−11.4471	+	27.6357i	−0.395197	+	0.954090i	−0.988788	+	0.149324i	$0.952290\pi$
$840$		0			0
$841$	−4.71231	+	4.71231i	−0.162493	+	0.162493i
$842$	1.92387	−	1.92387i	0.0663009	−	0.0663009i
$843$	1.39780	+	0.578989i	0.0481429	+	0.0199414i
$844$	−1.39573	+	3.36959i	−0.0480431	+	0.115986i
$845$		0			0
$846$			1.16976i			0.0402173i
$847$	−0.382043	−	0.922334i	−0.0131272	−	0.0316918i
$848$	−6.14788	−	6.14788i	−0.211119	−	0.211119i
$849$	1.61150			0.0553064
$850$		0			0
$851$	63.4972			2.17666
$852$	0.422305	+	0.422305i	0.0144679	+	0.0144679i
$853$	13.7430	+	33.1784i	0.470550	+	1.13601i	0.963921	+	0.266189i	$0.0857646\pi$
$853$	13.7430	+	33.1784i	0.470550	+	1.13601i	−0.493371	+	0.869819i	$0.664235\pi$
$854$		−	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	0.0245406	−	0.999699i	$-0.492188\pi$
$857$	−19.4676	−	8.06374i	−0.665000	−	0.275452i	−0.689541	+	0.724247i	$0.742188\pi$
$858$	0.0756862	−	0.0756862i	0.00258389	−	0.00258389i
$859$	−11.2104	+	11.2104i	−0.382494	+	0.382494i	−0.872000	−	0.489506i	$-0.837177\pi$
$859$	−11.2104	+	11.2104i	−0.382494	+	0.382494i	0.489506	+	0.872000i	$0.337177\pi$
$860$		0			0
$861$	−0.0192806	+	0.0465475i	−0.000657081	+	0.00158633i
$862$	6.95238	−	2.87977i	0.236799	−	0.0980853i
$863$			23.8125i			0.810587i	0.914187	+	0.405294i	$0.132831\pi$
$863$			23.8125i			0.810587i	−0.914187	+	0.405294i	$0.867169\pi$
$864$	0.492301	+	1.18852i	0.0167484	+	0.0404343i
$865$		0			0
$866$	−11.8347			−0.402160
$867$	−0.186823	+	0.902908i	−0.00634486	+	0.0306644i
$868$	−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
$873$	−10.2883	+	24.8382i	−0.348207	+	0.840645i
$874$	−6.32351	−	2.61929i	−0.213896	−	0.0885987i
$875$		0			0
$876$	−0.0155405	+	0.0155405i	−0.000525065	+	0.000525065i
$877$	−16.5557	−	6.85759i	−0.559046	−	0.231564i	0.0852252	−	0.996362i	$-0.472839\pi$
$877$	−16.5557	−	6.85759i	−0.559046	−	0.231564i	−0.644271	+	0.764797i	$0.722839\pi$
$878$	−3.31099	+	7.99343i	−0.111740	+	0.269765i
$879$	−1.12557	+	0.466228i	−0.0379646	+	0.0157255i
$880$		0			0
$881$	−12.9301	−	31.2159i	−0.435625	−	1.05169i	−0.977444	−	0.211196i	$-0.932264\pi$
$881$	−12.9301	−	31.2159i	−0.435625	−	1.05169i	0.541819	−	0.840495i	$-0.317736\pi$
$882$	−5.27613	−	5.27613i	−0.177657	−	0.177657i
$883$	−26.0211			−0.875680			−0.437840	−	0.899053i	$-0.644256\pi$
$883$	−26.0211			−0.875680			−0.437840	+	0.899053i	$0.644256\pi$
$884$	−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	0.991769	+	0.128039i	$0.0408683\pi$
$887$	11.3477	+	27.3959i	0.381020	+	0.919863i	−0.610749	+	0.791824i	$0.709132\pi$
$888$		−	0.712447i		−	0.0239082i
$889$	2.02357	−	0.838189i	0.0678683	−	0.0281120i
$890$		0			0
$891$	22.9422	+	9.50298i	0.768593	+	0.318362i
$892$	−31.3823	+	31.3823i	−1.05076	+	1.05076i
$893$	2.15957	−	2.15957i	0.0722674	−	0.0722674i
$894$	−0.232110	−	0.0961433i	−0.00776293	−	0.00321551i
$895$		0			0
$896$	2.68527	−	1.11228i	0.0897087	−	0.0371586i
$897$			0.723619i			0.0241609i
$898$	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
$903$	−0.0937705	−	0.0937705i	−0.00312049	−	0.00312049i
$904$	5.87267	+	14.1779i	0.195322	+	0.471549i
$905$		0			0
$906$	0.345949	−	0.143297i	0.0114934	−	0.00476072i
$907$	2.30095	−	5.55499i	0.0764018	−	0.184450i	−0.881064	−	0.472997i	$-0.843172\pi$
$907$	2.30095	−	5.55499i	0.0764018	−	0.184450i	0.957466	+	0.288547i	$0.0931721\pi$
$908$	35.5244	+	14.7147i	1.17892	+	0.488324i
$909$	−14.6679	+	14.6679i	−0.486505	+	0.486505i
$910$		0			0
$911$	−33.5802	−	13.9094i	−1.11256	−	0.460839i	−0.250744	−	0.968054i	$-0.580675\pi$
$911$	−33.5802	−	13.9094i	−1.11256	−	0.460839i	−0.861820	+	0.507215i	$0.830675\pi$
$912$	0.189462	−	0.457403i	0.00627373	−	0.0151461i
$913$	−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
$918$	−0.480989	+	0.0455080i	−0.0158750	+	0.00150199i
$919$	31.4827			1.03852			0.519259	−	0.854617i	$-0.326208\pi$
$919$	31.4827			1.03852			0.519259	+	0.854617i	$0.326208\pi$
$920$		0			0
$921$	0.114956	+	0.277529i	0.00378794	+	0.00914489i
$922$			2.60127i			0.0856684i
$923$	−10.7680	+	4.46025i	−0.354433	+	0.146811i
$924$	−0.0320884	+	0.0774682i	−0.00105563	+	0.00254852i
$925$		0			0
$926$	−5.86821	+	5.86821i	−0.192841	+	0.192841i
$927$	−27.4742	+	27.4742i	−0.902371	+	0.902371i
$928$	−17.2692	−	7.15312i	−0.566888	−	0.234813i
$929$	−16.5321	+	39.9121i	−0.542402	+	1.30947i	0.380622	+	0.924731i	$0.375710\pi$
$929$	−16.5321	+	39.9121i	−0.542402	+	1.30947i	−0.923024	+	0.384743i	$0.874290\pi$
$930$		0			0
$931$			19.4812i			0.638471i
$932$	−16.8184	−	40.6032i	−0.550905	−	1.33000i
$933$	0.865552	+	0.865552i	0.0283369	+	0.0283369i
$934$	10.7732			0.352511
$935$		0			0
$936$	−8.27195			−0.270377
$937$	−8.15745	−	8.15745i	−0.266492	−	0.266492i	0.561193	−	0.827685i	$-0.310343\pi$
$937$	−8.15745	−	8.15745i	−0.266492	−	0.266492i	−0.827685	+	0.561193i	$0.810343\pi$
$938$	−0.517188	−	1.24860i	−0.0168868	−	0.0407683i
$939$		−	0.660917i		−	0.0215682i
$940$		0			0
$941$	−10.4367	+	25.1965i	−0.340227	+	0.821382i	0.657465	+	0.753485i	$0.271629\pi$
$941$	−10.4367	+	25.1965i	−0.340227	+	0.821382i	−0.997692	+	0.0678965i	$0.978371\pi$
$942$	0.0487801	+	0.0202054i	0.00158934	+	0.000658327i
$943$	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	−0.0133362	−	0.999911i	$-0.504245\pi$
$947$	21.0575	−	8.72231i	0.684278	−	0.283437i	0.697614	+	0.716474i	$0.254245\pi$
$948$		−	1.08085i		−	0.0351045i
$949$	−0.164134	−	0.396254i	−0.00532801	−	0.0128630i
$950$		0			0
$951$	−1.19198			−0.0386527
$952$	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	$0.344626\pi$
$954$	2.04990	+	2.04990i	0.0663681	+	0.0663681i
$955$		0			0
$956$		−	9.83243i		−	0.318003i
$957$	0.655346	−	0.271453i	0.0211843	−	0.00877483i
$958$	−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
$963$	4.15603	−	10.0335i	0.133926	−	0.323326i
$964$	9.39800	−	3.89278i	0.302689	−	0.125378i
$965$		0			0
$966$	0.0150540	+	0.0363436i	0.000484355	+	0.00116934i
$967$	−35.7870	−	35.7870i	−1.15083	−	1.15083i	−0.986386	−	0.164447i	$-0.947416\pi$
$967$	−35.7870	−	35.7870i	−1.15083	−	1.15083i	−0.164447	−	0.986386i	$-0.552584\pi$
$968$	4.65968			0.149768
$969$	0.485761	+	0.401787i	0.0156049	+	0.0129073i
$970$		0			0
$971$	23.2222	+	23.2222i	0.745236	+	0.745236i	0.973580	−	0.228344i	$-0.0733312\pi$
$971$	23.2222	+	23.2222i	0.745236	+	0.745236i	−0.228344	+	0.973580i	$0.573331\pi$
$972$	1.04671	+	2.52697i	0.0335731	+	0.0810527i
$973$			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	−0.418730	−	0.908111i	$-0.637525\pi$
$977$	15.2966	−	15.2966i	0.489381	−	0.489381i	0.908111	+	0.418730i	$0.137525\pi$
$978$	0.236338	−	0.236338i	0.00755727	−	0.00755727i
$979$	−3.96956	−	1.64425i	−0.126868	−	0.0525503i
$980$		0			0
$981$	−14.2610	+	5.90708i	−0.455317	+	0.188599i
$982$			7.73637i			0.246878i
$983$	−1.95570	−	4.72148i	−0.0623771	−	0.150592i	0.889618	−	0.456706i	$-0.150971\pi$
$983$	−1.95570	−	4.72148i	−0.0623771	−	0.150592i	−0.951995	+	0.306115i	$0.900971\pi$
$984$	−0.166283	−	0.166283i	−0.00530092	−	0.00530092i
$985$		0			0
$986$	4.47423	−	5.40935i	0.142489	−	0.172269i
$987$	−0.0175531			−0.000558720
$988$	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	−0.345500	−	0.938419i	$-0.612291\pi$
$991$	2.32187	−	0.961750i	0.0737566	−	0.0305510i	0.419257	+	0.907868i	$0.362291\pi$
$992$	4.58029	−	11.0578i	0.145424	−	0.351085i
$993$	−0.724673	−	0.300170i	−0.0229968	−	0.00952559i
$994$	−0.448030	+	0.448030i	−0.0142107	+	0.0142107i
$995$		0			0
$996$	−1.45957	−	0.604572i	−0.0462481	−	0.0191566i
$997$	−13.7947	+	33.3033i	−0.436882	+	1.05473i	0.540138	+	0.841576i	$0.318372\pi$
$997$	−13.7947	+	33.3033i	−0.436882	+	1.05473i	−0.977020	+	0.213149i	$0.931628\pi$
$998$	−6.20336	+	2.56951i	−0.196364	+	0.0813366i
$999$		−	3.06441i		−	0.0969535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.b.151.4		24
5.2	odd	4		425.2.n.f.49.3		24
5.3	odd	4		425.2.n.c.49.4		24
5.4	even	2		85.2.l.a.66.3	✓	24
15.14	odd	2		765.2.be.b.406.4		24
17.5	odd	16		7225.2.a.bq.1.5		12
17.8	even	8	inner	425.2.m.b.76.4		24
17.12	odd	16		7225.2.a.bs.1.5		12
85.8	odd	8		425.2.n.f.399.3		24
85.14	odd	16		1445.2.d.j.866.9		24
85.29	odd	16		1445.2.a.p.1.8		12
85.39	odd	16		1445.2.a.q.1.8		12
85.42	odd	8		425.2.n.c.399.4		24
85.54	odd	16		1445.2.d.j.866.10		24
85.59	even	8		85.2.l.a.76.3	yes	24
255.59	odd	8		765.2.be.b.586.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.3	✓	24	5.4	even	2
85.2.l.a.76.3	yes	24	85.59	even	8
425.2.m.b.76.4		24	17.8	even	8	inner
425.2.m.b.151.4		24	1.1	even	1	trivial
425.2.n.c.49.4		24	5.3	odd	4
425.2.n.c.399.4		24	85.42	odd	8
425.2.n.f.49.3		24	5.2	odd	4
425.2.n.f.399.3		24	85.8	odd	8
765.2.be.b.406.4		24	15.14	odd	2
765.2.be.b.586.4		24	255.59	odd	8
1445.2.a.p.1.8		12	85.29	odd	16
1445.2.a.q.1.8		12	85.39	odd	16
1445.2.d.j.866.9		24	85.14	odd	16
1445.2.d.j.866.10		24	85.54	odd	16
7225.2.a.bq.1.5		12	17.5	odd	16
7225.2.a.bs.1.5		12	17.12	odd	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.254738 + 0.254738i) q^{2} +(-0.0207557 - 0.0501087i) q^{3} -1.87022i q^{4} +(0.00747733 - 0.0180519i) q^{6} +(-0.275980 - 0.114315i) q^{7} +(0.985893 - 0.985893i) q^{8} +(2.11924 - 2.11924i) q^{9} +(-1.05900 + 2.55665i) q^{11} +(-0.0937141 + 0.0388177i) q^{12} -1.97956i q^{13} +(-0.0411823 - 0.0994229i) q^{14} -3.23814 q^{16} +(1.21202 - 3.94094i) q^{17} +1.07970 q^{18} +(-1.99331 - 1.99331i) q^{19} +0.0162017i q^{21} +(-0.921046 + 0.381510i) q^{22} +(2.57919 - 6.22672i) q^{23} +(-0.0698647 - 0.0289389i) q^{24} +(0.504269 - 0.504269i) q^{26} +(-0.300505 - 0.124473i) q^{27} +(-0.213793 + 0.516142i) q^{28} +(4.36632 - 1.80859i) q^{29} +(1.15808 + 2.79584i) q^{31} +(-2.79667 - 2.79667i) q^{32} +0.150091 q^{33} +(1.31266 - 0.695159i) q^{34} +(-3.96344 - 3.96344i) q^{36} +(3.60537 + 8.70414i) q^{37} -1.01554i q^{38} +(-0.0991930 + 0.0410871i) q^{39} +(2.87301 + 1.19004i) q^{41} +(-0.00412718 + 0.00412718i) q^{42} +(-5.78771 + 5.78771i) q^{43} +(4.78150 + 1.98056i) q^{44} +(2.24320 - 0.929166i) q^{46} +1.08341i q^{47} +(0.0672100 + 0.162259i) q^{48} +(-4.88665 - 4.88665i) q^{49} +(-0.222632 + 0.0210640i) q^{51} -3.70220 q^{52} +(1.89858 + 1.89858i) q^{53} +(-0.0448420 - 0.108258i) q^{54} +(-0.384788 + 0.159384i) q^{56} +(-0.0585096 + 0.141255i) q^{57} +(1.57299 + 0.651553i) q^{58} +(-6.47310 + 6.47310i) q^{59} +(10.3418 + 4.28372i) q^{61} +(-0.417202 + 1.00722i) q^{62} +(-0.827127 + 0.342607i) q^{63} +5.05145i q^{64} +(0.0382339 + 0.0382339i) q^{66} +12.5585 q^{67} +(-7.37041 - 2.26675i) q^{68} -0.365546 q^{69} +(-2.25315 - 5.43960i) q^{71} -4.17869i q^{72} +(0.200173 - 0.0829144i) q^{73} +(-1.29885 + 3.13570i) q^{74} +(-3.72792 + 3.72792i) q^{76} +(0.584525 - 0.584525i) q^{77} +(-0.0357347 - 0.0148018i) q^{78} +(-4.07771 + 9.84447i) q^{79} -8.97353i q^{81} +(0.428717 + 1.03501i) q^{82} +(11.0129 + 11.0129i) q^{83} +0.0303006 q^{84} -2.94870 q^{86} +(-0.181252 - 0.181252i) q^{87} +(1.47653 + 3.56465i) q^{88} +1.55264i q^{89} +(-0.226292 + 0.546318i) q^{91} +(-11.6453 - 4.82365i) q^{92} +(0.116059 - 0.116059i) q^{93} +(-0.275986 + 0.275986i) q^{94} +(-0.0820905 + 0.198184i) q^{96} +(-8.28752 + 3.43280i) q^{97} -2.48963i q^{98} +(3.17389 + 7.66244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} - 24 q^{12} - 24 q^{16} + 8 q^{17} - 8 q^{18} - 8 q^{19} + 32 q^{22} + 16 q^{23} - 8 q^{24} + 16 q^{26} - 24 q^{27} - 48 q^{28} - 8 q^{29} + 16 q^{34} - 24 q^{36} - 24 q^{37}+ \cdots - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 - 24 * q^12 - 24 * q^16 + 8 * q^17 - 8 * q^18 - 8 * q^19 + 32 * q^22 + 16 * q^23 - 8 * q^24 + 16 * q^26 - 24 * q^27 - 48 * q^28 - 8 * q^29 + 16 * q^34 - 24 * q^36 - 24 * q^37 + 8 * q^39 + 16 * q^41 + 24 * q^42 - 8 * q^43 + 16 * q^44 + 8 * q^46 - 80 * q^48 - 56 * q^51 + 48 * q^52 - 24 * q^53 - 32 * q^54 + 64 * q^56 - 32 * q^57 + 64 * q^58 + 32 * q^59 + 32 * q^61 + 32 * q^62 + 56 * q^63 + 96 * q^66 - 16 * q^67 + 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^76 - 24 * q^77 + 112 * q^78 + 80 * q^82 + 96 * q^83 - 64 * q^84 - 16 * q^86 + 48 * q^87 + 8 * q^88 - 24 * q^91 - 80 * q^92 - 64 * q^93 + 56 * q^94 - 168 * q^96 + 40 * q^97 - 8 * q^99

Introduction

L-functions

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