LMFDB - Embedded newform 425.2.n.f.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not 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			49.3
Character	$\chi$	$=$	425.49
Dual form			425.2.n.f.399.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.254738 + 0.254738i) q^{2} +(-0.0501087 + 0.0207557i) q^{3} +1.87022i q^{4} +(0.00747733 - 0.0180519i) q^{6} +(0.114315 - 0.275980i) q^{7} +(-0.985893 - 0.985893i) q^{8} +(-2.11924 + 2.11924i) q^{9} +(-1.05900 + 2.55665i) q^{11} +(-0.0388177 - 0.0937141i) q^{12} -1.97956 q^{13} +(0.0411823 + 0.0994229i) q^{14} -3.23814 q^{16} +(3.94094 + 1.21202i) q^{17} -1.07970i q^{18} +(1.99331 + 1.99331i) q^{19} +0.0162017i q^{21} +(-0.381510 - 0.921046i) q^{22} +(-6.22672 - 2.57919i) q^{23} +(0.0698647 + 0.0289389i) q^{24} +(0.504269 - 0.504269i) q^{26} +(0.124473 - 0.300505i) q^{27} +(0.516142 + 0.213793i) q^{28} +(-4.36632 + 1.80859i) q^{29} +(1.15808 + 2.79584i) q^{31} +(2.79667 - 2.79667i) q^{32} -0.150091i q^{33} +(-1.31266 + 0.695159i) q^{34} +(-3.96344 - 3.96344i) q^{36} +(-8.70414 + 3.60537i) q^{37} -1.01554 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} -1.08341 q^{47} +(0.162259 - 0.0672100i) q^{48} +(4.88665 + 4.88665i) q^{49} +(-0.222632 + 0.0210640i) q^{51} -3.70220i q^{52} +(1.89858 - 1.89858i) q^{53} +(0.0448420 + 0.108258i) q^{54} +(-0.384788 + 0.159384i) q^{56} +(-0.141255 - 0.0585096i) q^{57} +(0.651553 - 1.57299i) q^{58} +(6.47310 - 6.47310i) q^{59} +(10.3418 + 4.28372i) q^{61} +(-1.00722 - 0.417202i) q^{62} +(0.342607 + 0.827127i) q^{63} -5.05145i q^{64} +(0.0382339 + 0.0382339i) q^{66} +12.5585i q^{67} +(-2.26675 + 7.37041i) q^{68} +0.365546 q^{69} +(-2.25315 - 5.43960i) q^{71} +4.17869 q^{72} +(-0.0829144 - 0.200173i) q^{73} +(1.29885 - 3.13570i) q^{74} +(-3.72792 + 3.72792i) q^{76} +(0.584525 + 0.584525i) q^{77} +(-0.0148018 + 0.0357347i) q^{78} +(4.07771 - 9.84447i) q^{79} -8.97353i q^{81} +(-1.03501 + 0.428717i) q^{82} +(11.0129 - 11.0129i) q^{83} -0.0303006 q^{84} -2.94870 q^{86} +(0.181252 - 0.181252i) q^{87} +(3.56465 - 1.47653i) q^{88} -1.55264i q^{89} +(-0.226292 + 0.546318i) q^{91} +(4.82365 - 11.6453i) q^{92} +(-0.116059 - 0.116059i) q^{93} +(0.275986 - 0.275986i) q^{94} +(-0.0820905 + 0.198184i) q^{96} +(-3.43280 - 8.28752i) q^{97} -2.48963 q^{98} +(-3.17389 - 7.66244i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) $ 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 - 40 * q^12 - 16 * q^13 - 24 * q^16 + 8 * q^19 + 24 * q^22 - 8 * q^23 + 8 * q^24 + 16 * q^26 - 16 * q^27 + 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 + 16 * q^41 + 24 * q^42 + 8 * q^43 - 16 * q^44 + 8 * q^46 + 64 * q^47 + 8 * q^48 - 56 * q^51 - 24 * q^53 + 32 * q^54 + 64 * q^56 - 16 * q^57 - 56 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 80 * q^63 + 96 * q^66 - 24 * q^68 - 96 * q^69 - 24 * q^71 + 24 * q^72 + 64 * q^73 + 64 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 16 * q^82 + 96 * q^83 + 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 - 112 * q^92 + 64 * q^93 - 56 * q^94 - 168 * q^96 - 48 * q^97 - 120 * q^98 + 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	$-0.790653\pi$
$2$	−0.254738	+	0.254738i	−0.180127	+	0.180127i	0.611284	+	0.791411i	$0.290653\pi$
$3$	−0.0501087	+	0.0207557i	−0.0289303	+	0.0119833i	−0.397102	−	0.917775i	$-0.629984\pi$
$3$	−0.0501087	+	0.0207557i	−0.0289303	+	0.0119833i	0.368171	+	0.929758i	$0.379984\pi$
$4$			1.87022i			0.935108i
$5$		0			0
$5$		0			0
$6$	0.00747733	−	0.0180519i	0.00305261	−	0.00736965i
$7$	0.114315	−	0.275980i	0.0432068	−	0.104310i	−0.900803	−	0.434228i	$-0.857021\pi$
$7$	0.114315	−	0.275980i	0.0432068	−	0.104310i	0.944010	+	0.329918i	$0.107021\pi$
$8$	−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	$0.988016\pi$
$12$	−0.0388177	−	0.0937141i	−0.0112057	−	0.0270529i
$13$	−1.97956			−0.549030			−0.274515	−	0.961583i	$-0.588517\pi$
$13$	−1.97956			−0.549030			−0.274515	+	0.961583i	$0.588517\pi$
$14$	0.0411823	+	0.0994229i	0.0110064	+	0.0265719i
$15$		0			0
$16$	−3.23814			−0.809536
$17$	3.94094	+	1.21202i	0.955818	+	0.293959i
$17$	3.94094	+	1.21202i	0.955818	+	0.293959i
$18$		−	1.07970i		−	0.254489i
$19$	1.99331	+	1.99331i	0.457296	+	0.457296i	0.897767	−	0.440471i	$-0.145188\pi$
$19$	1.99331	+	1.99331i	0.457296	+	0.457296i	−0.440471	+	0.897767i	$0.645188\pi$
$20$		0			0
$21$			0.0162017i			0.00353549i
$22$	−0.381510	−	0.921046i	−0.0813382	−	0.196368i
$23$	−6.22672	−	2.57919i	−1.29836	−	0.537799i	−0.376895	−	0.926256i	$-0.623008\pi$
$23$	−6.22672	−	2.57919i	−1.29836	−	0.537799i	−0.921467	+	0.388457i	$0.873008\pi$
$24$	0.0698647	+	0.0289389i	0.0142611	+	0.00590713i
$25$		0			0
$26$	0.504269	−	0.504269i	0.0988953	−	0.0988953i
$27$	0.124473	−	0.300505i	0.0239549	−	0.0578322i
$28$	0.516142	+	0.213793i	0.0975416	+	0.0404031i
$29$	−4.36632	+	1.80859i	−0.810806	+	0.335847i	−0.749276	−	0.662258i	$-0.769598\pi$
$29$	−4.36632	+	1.80859i	−0.810806	+	0.335847i	−0.0615305	+	0.998105i	$0.519598\pi$
$30$		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
$33$		−	0.150091i		−	0.0261275i
$34$	−1.31266	+	0.695159i	−0.225119	+	0.119219i
$35$		0			0
$36$	−3.96344	−	3.96344i	−0.660573	−	0.660573i
$37$	−8.70414	+	3.60537i	−1.43095	+	0.592719i	−0.957586	−	0.288147i	$-0.906961\pi$
$37$	−8.70414	+	3.60537i	−1.43095	+	0.592719i	−0.473365	+	0.880866i	$0.656961\pi$
$38$	−1.01554			−0.164743
$39$	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	$-0.0354638\pi$
$43$	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
$47$	−1.08341			−0.158032			−0.0790159	−	0.996873i	$-0.525178\pi$
$47$	−1.08341			−0.158032			−0.0790159	+	0.996873i	$0.525178\pi$
$48$	0.162259	−	0.0672100i	0.0234201	−	0.00970092i
$49$	4.88665	+	4.88665i	0.698093	+	0.698093i
$50$		0			0
$51$	−0.222632	+	0.0210640i	−0.0311747	+	0.00294954i
$52$		−	3.70220i		−	0.513403i
$53$	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	$0.190964\pi$
$54$	0.0448420	+	0.108258i	0.00610222	+	0.0147321i
$55$		0			0
$56$	−0.384788	+	0.159384i	−0.0514195	+	0.0212986i
$57$	−0.141255	−	0.0585096i	−0.0187096	−	0.00774979i
$58$	0.651553	−	1.57299i	0.0855531	−	0.206543i
$59$	6.47310	−	6.47310i	0.842726	−	0.842726i	−0.146487	−	0.989213i	$-0.546797\pi$
$59$	6.47310	−	6.47310i	0.842726	−	0.842726i	0.989213	+	0.146487i	$0.0467966\pi$
$60$		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	$0.370690\pi$
$62$	−1.00722	−	0.417202i	−0.127916	−	0.0529847i
$63$	0.342607	+	0.827127i	0.0431645	+	0.104208i
$64$		−	5.05145i		−	0.631432i
$65$		0			0
$66$	0.0382339	+	0.0382339i	0.00470627	+	0.00470627i
$67$			12.5585i			1.53427i	0.641488	+	0.767133i	$0.278317\pi$
$67$			12.5585i			1.53427i	−0.641488	+	0.767133i	$0.721683\pi$
$68$	−2.26675	+	7.37041i	−0.274884	+	0.893793i
$69$	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	$0.988606\pi$
$72$	4.17869			0.492463
$73$	−0.0829144	−	0.200173i	−0.00970440	−	0.0234285i	0.918953	−	0.394367i	$-0.129036\pi$
$73$	−0.0829144	−	0.200173i	−0.00970440	−	0.0234285i	−0.928657	+	0.370938i	$0.879036\pi$
$74$	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
$78$	−0.0148018	+	0.0357347i	−0.00167598	+	0.00404616i
$79$	4.07771	−	9.84447i	0.458779	−	1.10759i	−0.510114	−	0.860107i	$-0.670397\pi$
$79$	4.07771	−	9.84447i	0.458779	−	1.10759i	0.968892	−	0.247482i	$-0.0796032\pi$
$80$		0			0
$81$		−	8.97353i		−	0.997059i
$82$	−1.03501	+	0.428717i	−0.114298	+	0.0473438i
$83$	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	$-0.0763020\pi$
$84$	−0.0303006			−0.00330607
$85$		0			0
$86$	−2.94870			−0.317967
$87$	0.181252	−	0.181252i	0.0194323	−	0.0194323i
$88$	3.56465	−	1.47653i	0.379993	−	0.157398i
$89$		−	1.55264i		−	0.164579i	−0.996608	−	0.0822897i	$-0.973777\pi$
$89$		−	1.55264i		−	0.164579i	0.996608	−	0.0822897i	$-0.0262233\pi$
$90$		0			0
$91$	−0.226292	+	0.546318i	−0.0237219	+	0.0572696i
$92$	4.82365	−	11.6453i	0.502900	−	1.21411i
$93$	−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
$97$	−3.43280	−	8.28752i	−0.348549	−	0.841471i	−0.996792	−	0.0800373i	$-0.974496\pi$
$97$	−3.43280	−	8.28752i	−0.348549	−	0.841471i	0.648243	−	0.761433i	$-0.275504\pi$
$98$	−2.48963			−0.251491
$99$	−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	$0.611900\pi$
$102$	0.0513470	−	0.0620786i	0.00508412	−	0.00614670i
$103$			12.9642i			1.27740i	0.769457	+	0.638699i	$0.220527\pi$
$103$			12.9642i			1.27740i	−0.769457	+	0.638699i	$0.779473\pi$
$104$	1.95163	+	1.95163i	0.191373	+	0.191373i
$105$		0			0
$106$			0.967283i			0.0939508i
$107$	1.38670	+	3.34779i	0.134058	+	0.323643i	0.976626	−	0.214946i	$-0.0689575\pi$
$107$	1.38670	+	3.34779i	0.134058	+	0.323643i	−0.842568	+	0.538589i	$0.818957\pi$
$108$	0.562009	+	0.232792i	0.0540793	+	0.0224004i
$109$	4.75832	+	1.97096i	0.455764	+	0.188784i	0.598742	−	0.800942i	$-0.295668\pi$
$109$	4.75832	+	1.97096i	0.455764	+	0.188784i	−0.142977	+	0.989726i	$0.545668\pi$
$110$		0			0
$111$	0.361321	−	0.361321i	0.0342951	−	0.0342951i
$112$	−0.370167	+	0.893662i	−0.0349775	+	0.0844431i
$113$	10.1687	+	4.21202i	0.956593	+	0.396234i	0.805705	−	0.592317i	$-0.201787\pi$
$113$	10.1687	+	4.21202i	0.956593	+	0.396234i	0.150888	+	0.988551i	$0.451787\pi$
$114$	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
$118$			3.29789i			0.303596i
$119$	0.785001	−	0.949067i	0.0719609	−	0.0870008i
$120$		0			0
$121$	2.36318	+	2.36318i	0.214834	+	0.214834i
$122$	−3.72569	+	1.54323i	−0.337308	+	0.139717i
$123$	−0.168663			−0.0152078
$124$	−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	0.438608	−	0.898678i	$-0.355472\pi$
$127$	−5.18472	−	5.18472i	−0.460070	−	0.460070i	−0.898678	+	0.438608i	$0.855472\pi$
$128$	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	$0.101802\pi$
$132$	0.280703			0.0244320
$133$	0.777977	−	0.322249i	0.0674592	−	0.0279425i
$134$	−3.19913	−	3.19913i	−0.276363	−	0.276363i
$135$		0			0
$136$	−2.69042	−	5.08027i	−0.230701	−	0.435629i
$137$			13.9745i			1.19392i	0.802272	+	0.596959i	$0.203625\pi$
$137$			13.9745i			1.19392i	−0.802272	+	0.596959i	$0.796375\pi$
$138$	−0.0931186	+	0.0931186i	−0.00792678	+	0.00792678i
$139$	1.38555	+	3.34501i	0.117521	+	0.283720i	0.971684	−	0.236285i	$-0.0759300\pi$
$139$	1.38555	+	3.34501i	0.117521	+	0.283720i	−0.854163	+	0.520005i	$0.825930\pi$
$140$		0			0
$141$	0.0542883	−	0.0224870i	0.00457190	−	0.00189374i
$142$	1.95964	+	0.811709i	0.164449	+	0.0681171i
$143$	2.09635	−	5.06104i	0.175306	−	0.423226i
$144$	6.86241	−	6.86241i	0.571867	−	0.571867i
$145$		0			0
$146$	0.0721133	+	0.0298703i	0.00596814	+	0.00247208i
$147$	−0.346290	−	0.143438i	−0.0285615	−	0.0118306i
$148$	−6.74283	−	16.2786i	−0.554257	−	1.33809i
$149$			12.8580i			1.05336i	0.850062	+	0.526682i	$0.176564\pi$
$149$			12.8580i			1.05336i	−0.850062	+	0.526682i	$0.823436\pi$
$150$		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	$0.465331\pi$
$152$		−	3.93038i		−	0.318796i
$153$	−10.9204	+	5.78322i	−0.882859	+	0.467546i
$154$	−0.297802			−0.0239976
$155$		0			0
$156$	0.0768418	+	0.185512i	0.00615227	+	0.0148529i
$157$	−2.70222			−0.215661			−0.107830	−	0.994169i	$-0.534390\pi$
$157$	−2.70222			−0.215661			−0.107830	+	0.994169i	$0.534390\pi$
$158$	1.46901	+	3.54651i	0.116868	+	0.282146i
$159$	−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
$163$	6.54609	−	15.8036i	0.512729	−	1.23784i	−0.429561	−	0.903038i	$-0.641332\pi$
$163$	6.54609	−	15.8036i	0.512729	−	1.23784i	0.942290	−	0.334799i	$-0.108668\pi$
$164$	−2.22563	+	5.37315i	−0.173792	+	0.419572i
$165$		0			0
$166$			5.61084i			0.435486i
$167$	8.17871	−	3.38773i	0.632887	−	0.262151i	−0.0430919	−	0.999071i	$-0.513721\pi$
$167$	8.17871	−	3.38773i	0.632887	−	0.262151i	0.675979	+	0.736921i	$0.263721\pi$
$168$	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
$173$	−17.7246	+	7.34175i	−1.34757	+	0.558183i	−0.935616	−	0.353020i	$-0.885155\pi$
$173$	−17.7246	+	7.34175i	−1.34757	+	0.558183i	−0.411957	+	0.911203i	$0.635155\pi$
$174$			0.0923438i			0.00700057i
$175$		0			0
$176$	3.42920	−	8.27881i	0.258485	−	0.624039i
$177$	−0.190005	+	0.458712i	−0.0142816	+	0.0344789i
$178$	0.395517	+	0.395517i	0.0296452	+	0.0296452i
$179$	3.06554	−	3.06554i	0.229129	−	0.229129i	−0.583200	−	0.812329i	$-0.698199\pi$
$179$	3.06554	−	3.06554i	0.229129	−	0.229129i	0.812329	+	0.583200i	$0.198199\pi$
$180$		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	$0.780034\pi$
$182$	−0.0815228	−	0.196813i	−0.00604287	−	0.0145888i
$183$	−0.607127			−0.0448801
$184$	3.59607	+	8.68169i	0.265106	+	0.640022i
$185$		0			0
$186$	0.0591296			0.00433559
$187$	−7.27219	+	8.79208i	−0.531795	+	0.642941i
$188$		−	2.02621i		−	0.147777i
$189$	−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	$-0.0847249\pi$
$192$	0.104846	+	0.253122i	0.00756664	+	0.0182675i
$193$	−20.5094	−	8.49528i	−1.47630	−	0.611504i	−0.508015	−	0.861348i	$-0.669620\pi$
$193$	−20.5094	−	8.49528i	−1.47630	−	0.611504i	−0.968286	+	0.249845i	$0.919620\pi$
$194$	2.98562	+	1.23668i	0.214355	+	0.0887887i
$195$		0			0
$196$	−9.13910	+	9.13910i	−0.652793	+	0.652793i
$197$	1.71496	−	4.14027i	0.122186	−	0.294982i	−0.850938	−	0.525267i	$-0.823966\pi$
$197$	1.71496	−	4.14027i	0.122186	−	0.294982i	0.973123	+	0.230284i	$0.0739656\pi$
$198$	2.76043	+	1.14341i	0.196175	+	0.0812584i
$199$	0.368987	−	0.152839i	0.0261568	−	0.0108345i	−0.369567	−	0.929204i	$-0.620494\pi$
$199$	0.368987	−	0.152839i	0.0261568	−	0.0108345i	0.395723	+	0.918370i	$0.370494\pi$
$200$		0			0
$201$	−0.260661	−	0.629290i	−0.0183856	−	0.0443867i
$202$	1.76313	−	1.76313i	0.124053	−	0.124053i
$203$			1.41176i			0.0990865i
$204$	−0.0393942	−	0.416370i	−0.00275814	−	0.0291517i
$205$		0			0
$206$	−3.30247	−	3.30247i	−0.230094	−	0.230094i
$207$	18.6618	−	7.72999i	1.29709	−	0.537271i
$208$	6.41009			0.444460
$209$	−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
$217$	0.903981			0.0613662
$218$	−1.71421	+	0.710047i	−0.116101	+	0.0480905i
$219$	0.00830947	+	0.00830947i	0.000561502	+	0.000561502i
$220$		0			0
$221$	−7.80131	−	2.39927i	−0.524773	−	0.161393i
$222$			0.184085i			0.0123550i
$223$	−16.7800	+	16.7800i	−1.12367	+	1.12367i	−0.132491	+	0.991184i	$0.542297\pi$
$223$	−16.7800	+	16.7800i	−1.12367	+	1.12367i	−0.991184	+	0.132491i	$0.957703\pi$
$224$	−0.452123	−	1.09152i	−0.0302088	−	0.0729304i
$225$		0			0
$226$	−3.66333	+	1.51740i	−0.243681	+	0.100936i
$227$	−18.9948	−	7.86790i	−1.26073	−	0.522211i	−0.350595	−	0.936527i	$-0.614021\pi$
$227$	−18.9948	−	7.86790i	−1.26073	−	0.522211i	−0.910133	+	0.414316i	$0.864021\pi$
$228$	0.109426	−	0.264177i	0.00724689	−	0.0174955i
$229$	−18.8066	+	18.8066i	−1.24277	+	1.24277i	−0.283928	+	0.958846i	$0.591638\pi$
$229$	−18.8066	+	18.8066i	−1.24277	+	1.24277i	−0.958846	+	0.283928i	$0.908362\pi$
$230$		0			0
$231$	−0.0414220	−	0.0171576i	−0.00272537	−	0.00112889i
$232$	6.08780	+	2.52165i	0.399684	+	0.165554i
$233$	−8.99275	−	21.7104i	−0.589135	−	1.42230i	−0.884331	−	0.466860i	$-0.845385\pi$
$233$	−8.99275	−	21.7104i	−0.589135	−	1.42230i	0.295196	−	0.955437i	$-0.404615\pi$
$234$			2.13734i			0.139722i
$235$		0			0
$236$	12.1061	+	12.1061i	0.788040	+	0.788040i
$237$			0.577929i			0.0375405i
$238$	0.0417939	+	0.441734i	0.00270910	+	0.0286333i
$239$	−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	0.976632	−	0.214918i	$-0.0689486\pi$
$241$	2.08146	+	5.02509i	0.134079	+	0.323694i	−0.842553	+	0.538613i	$0.818949\pi$
$242$	−1.20398			−0.0773950
$243$	0.559671	+	1.35117i	0.0359029	+	0.0866774i
$244$	−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
$248$	1.61466	−	3.89814i	0.102531	−	0.247532i
$249$	−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	$-0.313234\pi$
$252$	−1.54691	+	0.640750i	−0.0974460	+	0.0403634i
$253$	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	$-0.551164\pi$
$257$	13.2589	−	13.2589i	0.827065	−	0.827065i	0.987110	+	0.160045i	$0.0511639\pi$
$258$	0.147756	−	0.0612024i	0.00919887	−	0.00381030i
$259$			2.81431i			0.174873i
$260$		0			0
$261$	5.42045	−	13.0861i	0.335518	−	0.810011i
$262$	−2.38807	+	5.76532i	−0.147536	+	0.356183i
$263$	11.3145	+	11.3145i	0.697680	+	0.697680i	0.963910	−	0.266230i	$-0.0857781\pi$
$263$	11.3145	+	11.3145i	0.697680	+	0.697680i	−0.266230	+	0.963910i	$0.585778\pi$
$264$	−0.147974	+	0.147974i	−0.00910714	+	0.00910714i
$265$		0			0
$266$	−0.116091	+	0.280270i	−0.00711803	+	0.0171844i
$267$	0.0322261	+	0.0778007i	0.00197221	+	0.00476133i
$268$	−23.4871			−1.43470
$269$	−0.457836	−	1.10531i	−0.0279147	−	0.0673922i	0.909307	−	0.416125i	$-0.136612\pi$
$269$	−0.457836	−	1.10531i	−0.0279147	−	0.0673922i	−0.937222	+	0.348733i	$0.886612\pi$
$270$		0			0
$271$	−0.888590			−0.0539780			−0.0269890	−	0.999636i	$-0.508592\pi$
$271$	−0.888590			−0.0539780			−0.0269890	+	0.999636i	$0.508592\pi$
$272$	−12.7613	−	3.92471i	−0.773769	−	0.237971i
$273$		−	0.0320721i		−	0.00194109i
$274$	−3.55983	−	3.55983i	−0.215057	−	0.215057i
$275$		0			0
$276$			0.683650i			0.0411509i
$277$	2.36450	+	5.70841i	0.142069	+	0.342985i	0.978858	−	0.204540i	$-0.0655700\pi$
$277$	2.36450	+	5.70841i	0.142069	+	0.342985i	−0.836789	+	0.547525i	$0.815570\pi$
$278$	−1.20505	−	0.499150i	−0.0722744	−	0.0299370i
$279$	−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	$0.937167\pi$
$282$	−0.00810103	+	0.0195576i	−0.000482409	+	0.00116464i
$283$	27.4503	+	11.3703i	1.63175	+	0.675893i	0.995427	−	0.0955282i	$-0.0304540\pi$
$283$	27.4503	+	11.3703i	1.63175	+	0.675893i	0.636324	+	0.771422i	$0.280454\pi$
$284$	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
$288$			11.8536i			0.698481i
$289$	14.0620	+	9.55303i	0.827176	+	0.561943i
$290$		0			0
$291$	0.344027	+	0.344027i	0.0201672	+	0.0201672i
$292$	0.374367	−	0.155068i	0.0219082	−	0.00907466i
$293$	−22.4626			−1.31228			−0.656140	−	0.754639i	$-0.727812\pi$
$293$	−22.4626			−1.31228			−0.656140	+	0.754639i	$0.727812\pi$
$294$	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
$302$	−6.90398			−0.397279
$303$	0.346818	−	0.143657i	0.0199242	−	0.00825287i
$304$	−6.45462	−	6.45462i	−0.370198	−	0.370198i
$305$		0			0
$306$	1.30863	−	4.25505i	0.0748093	−	0.243245i
$307$		−	5.53854i		−	0.316101i	−0.987431	−	0.158050i	$-0.949479\pi$
$307$		−	5.53854i		−	0.316101i	0.987431	−	0.158050i	$-0.0505209\pi$
$308$	−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	$0.596017\pi$
$312$	−0.138301	−	0.0572862i	−0.00782976	−	0.00324319i
$313$	4.66325	−	11.2581i	0.263583	−	0.636345i	−0.735572	−	0.677446i	$-0.763087\pi$
$313$	4.66325	−	11.2581i	0.263583	−	0.636345i	0.999155	+	0.0411013i	$0.0130866\pi$
$314$	0.688359	−	0.688359i	0.0388463	−	0.0388463i
$315$		0			0
$316$	18.4113	+	7.62621i	1.03572	+	0.429008i
$317$	20.3043	+	8.41030i	1.14040	+	0.472370i	0.871304	−	0.490743i	$-0.163275\pi$
$317$	20.3043	+	8.41030i	1.14040	+	0.472370i	0.269097	+	0.963113i	$0.413275\pi$
$318$	−0.0200766	−	0.0484693i	−0.00112584	−	0.00271802i
$319$		−	13.0785i		−	0.732254i
$320$		0			0
$321$	−0.138972	−	0.138972i	−0.00775664	−	0.00775664i
$322$		−	0.725296i		−	0.0404192i
$323$	5.43957	+	10.2714i	0.302666	+	0.571519i
$324$	16.7825			0.932358
$325$		0			0
$326$	2.35826	+	5.69333i	0.130612	+	0.315325i
$327$	−0.279342			−0.0154476
$328$	−1.65923	−	4.00573i	−0.0916155	−	0.221179i
$329$	−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
$333$	10.8055	−	26.0868i	0.592138	−	1.42955i
$334$	−1.22045	+	2.94642i	−0.0667798	+	0.161221i
$335$		0			0
$336$		−	0.0524633i		−	0.00286211i
$337$	−22.4004	+	9.27853i	−1.22023	+	0.505434i	−0.897481	−	0.441052i	$-0.854605\pi$
$337$	−22.4004	+	9.27853i	−1.22023	+	0.505434i	−0.322744	+	0.946486i	$0.604605\pi$
$338$	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
$343$	3.83909	−	1.59020i	0.207291	−	0.0858629i
$344$		−	11.4121i		−	0.615300i
$345$		0			0
$346$	2.64490	−	6.38535i	0.142191	−	0.343279i
$347$	−8.22624	+	19.8599i	−0.441608	+	1.06614i	0.533777	+	0.845625i	$0.320772\pi$
$347$	−8.22624	+	19.8599i	−0.441608	+	1.06614i	−0.975385	+	0.220510i	$0.929228\pi$
$348$	0.338981	+	0.338981i	0.0181713	+	0.0181713i
$349$	17.0669	−	17.0669i	0.913570	−	0.913570i	−0.0829813	−	0.996551i	$-0.526444\pi$
$349$	17.0669	−	17.0669i	0.913570	−	0.913570i	0.996551	+	0.0829813i	$0.0264442\pi$
$350$		0			0
$351$	−0.246402	+	0.594866i	−0.0131520	+	0.0317516i
$352$	4.18843	+	10.1118i	0.223244	+	0.538959i
$353$	−7.24444			−0.385583			−0.192791	−	0.981240i	$-0.561754\pi$
$353$	−7.24444			−0.385583			−0.192791	+	0.981240i	$0.561754\pi$
$354$	−0.0684501	−	0.165253i	−0.00363808	−	0.00878311i
$355$		0			0
$356$	2.90377			0.153900
$357$	−0.0196368	+	0.0638497i	−0.00103929	+	0.00337929i
$358$			1.56182i			0.0825449i
$359$	−12.2079	−	12.2079i	−0.644308	−	0.644308i	0.307303	−	0.951612i	$-0.400573\pi$
$359$	−12.2079	−	12.2079i	−0.644308	−	0.644308i	−0.951612	+	0.307303i	$0.900573\pi$
$360$		0			0
$361$		−	11.0534i		−	0.581760i
$362$	−3.27816	−	7.91419i	−0.172296	−	0.415960i
$363$	−0.167465	−	0.0693663i	−0.00878964	−	0.00364079i
$364$	−1.02173	−	0.423215i	−0.0535533	−	0.0221825i
$365$		0			0
$366$	0.154658	−	0.154658i	0.00808413	−	0.00808413i
$367$	14.3289	−	34.5930i	0.747963	−	1.80574i	0.178080	−	0.984016i	$-0.443011\pi$
$367$	14.3289	−	34.5930i	0.747963	−	1.80574i	0.569883	−	0.821726i	$-0.306989\pi$
$368$	20.1630	+	8.35180i	1.05107	+	0.435368i
$369$	−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
$373$			29.8887i			1.54758i	0.633443	+	0.773789i	$0.281641\pi$
$373$			29.8887i			1.54758i	−0.633443	+	0.773789i	$0.718359\pi$
$374$	−0.387176	−	4.09219i	−0.0200204	−	0.211602i
$375$		0			0
$376$	1.06813	+	1.06813i	0.0550845	+	0.0550845i
$377$	8.64339	−	3.58021i	0.445157	−	0.184390i
$378$	0.0350031			0.00180037
$379$	27.7353	−	11.4883i	1.42467	−	0.590116i	0.468637	−	0.883391i	$-0.344745\pi$
$379$	27.7353	−	11.4883i	1.42467	−	0.590116i	0.956028	+	0.293275i	$0.0947452\pi$
$380$		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	$-0.0818949\pi$
$383$	13.9465	+	13.9465i	0.712634	+	0.712634i	−0.254451	+	0.967086i	$0.581895\pi$
$384$	−0.487556	−	0.201952i	−0.0248805	−	0.0103058i
$385$		0			0
$386$	7.38861	−	3.06046i	0.376070	−	0.155773i
$387$	−24.5311			−1.24699
$388$	15.4995	−	6.42009i	0.786866	−	0.325931i
$389$	−2.62699	−	2.62699i	−0.133194	−	0.133194i	0.637367	−	0.770561i	$-0.280024\pi$
$389$	−2.62699	−	2.62699i	−0.133194	−	0.133194i	−0.770561	+	0.637367i	$0.780024\pi$
$390$		0			0
$391$	−21.4131	−	17.7114i	−1.08291	−	0.895703i
$392$		−	9.63543i		−	0.486663i
$393$	−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
$397$	4.77812	+	1.97916i	0.239807	+	0.0993314i	0.499350	−	0.866400i	$-0.333572\pi$
$397$	4.77812	+	1.97916i	0.239807	+	0.0993314i	−0.259543	+	0.965731i	$0.583572\pi$
$398$	−0.0550610	+	0.132929i	−0.00275996	+	0.00666313i
$399$	−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	$0.621863\pi$
$402$	0.226705	+	0.0939042i	0.0113070	+	0.00468351i
$403$	−2.29248	−	5.53453i	−0.114196	−	0.275695i
$404$		−	12.9444i		−	0.644007i
$405$		0			0
$406$	−0.359631	−	0.359631i	−0.0178482	−	0.0178482i
$407$		−	26.0716i		−	1.29232i
$408$	0.240258	+	0.198724i	0.0118945	+	0.00983831i
$409$	−0.521080			−0.0257657			−0.0128829	−	0.999917i	$-0.504101\pi$
$409$	−0.521080			−0.0257657			−0.0128829	+	0.999917i	$0.504101\pi$
$410$		0			0
$411$	−0.290050	−	0.700242i	−0.0143071	−	0.0345404i
$412$	−24.2458			−1.19451
$413$	−1.04647	−	2.52641i	−0.0514936	−	0.124317i
$414$	−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
$418$	1.07546	−	2.59640i	0.0526026	−	0.126994i
$419$	−1.74972	+	4.22419i	−0.0854793	+	0.206365i	−0.960839	−	0.277107i	$-0.910624\pi$
$419$	−1.74972	+	4.22419i	−0.0854793	+	0.206365i	0.875360	+	0.483472i	$0.160624\pi$
$420$		0			0
$421$		−	7.55233i		−	0.368078i	−0.982919	−	0.184039i	$-0.941083\pi$
$421$		−	7.55233i		−	0.368078i	0.982919	−	0.184039i	$-0.0589173\pi$
$422$	0.649075	−	0.268856i	0.0315965	−	0.0130877i
$423$	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
$428$	−6.26110	+	2.59343i	−0.302642	+	0.125358i
$429$			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	$-0.0428011\pi$
$432$	−0.403062	+	0.973078i	−0.0193923	+	0.0468172i
$433$	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
$437$	−7.27065	−	17.5529i	−0.347803	−	0.839670i
$438$	−0.00423348			−0.000202284
$439$	−9.19069	−	22.1883i	−0.438648	−	1.05899i	−0.976416	−	0.215897i	$-0.930733\pi$
$439$	−9.19069	−	22.1883i	−0.438648	−	1.05899i	0.537769	−	0.843093i	$-0.319267\pi$
$440$		0			0
$441$	−20.7120			−0.986284
$442$	2.59848	−	1.37611i	0.123597	−	0.0654547i
$443$			8.36893i			0.397620i	0.980038	+	0.198810i	$0.0637077\pi$
$443$			8.36893i			0.397620i	−0.980038	+	0.198810i	$0.936292\pi$
$444$	0.675748	+	0.675748i	0.0320696	+	0.0320696i
$445$		0			0
$446$		−	8.54904i		−	0.404809i
$447$	−0.266876	−	0.644296i	−0.0126228	−	0.0304741i
$448$	−1.39410	−	0.577454i	−0.0658649	−	0.0272821i
$449$	−22.7241	−	9.41265i	−1.07242	−	0.444210i	−0.224575	−	0.974457i	$-0.572099\pi$
$449$	−22.7241	−	9.41265i	−1.07242	−	0.444210i	−0.847844	+	0.530246i	$0.822099\pi$
$450$		0			0
$451$	−6.08503	+	6.08503i	−0.286533	+	0.286533i
$452$	−7.87740	+	19.0177i	−0.370522	+	0.894518i
$453$	−0.960292	−	0.397766i	−0.0451184	−	0.0186887i
$454$	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	$-0.693036\pi$
$457$	5.38146	−	5.38146i	0.251734	−	0.251734i	0.821681	+	0.569947i	$0.193036\pi$
$458$		−	9.58151i		−	0.447715i
$459$	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	$0.696221\pi$
$462$	0.0149225	−	0.00618109i	0.000694256	−	0.000287570i
$463$	23.0362			1.07058			0.535292	−	0.844667i	$-0.320202\pi$
$463$	23.0362			1.07058			0.535292	+	0.844667i	$0.320202\pi$
$464$	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	$0.506770\pi$
$468$	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
$472$	−12.7636			−0.587491
$473$	−20.9264	+	8.66798i	−0.962195	+	0.398554i
$474$	−0.147221	−	0.147221i	−0.00676207	−	0.00676207i
$475$		0			0
$476$	1.77496	+	1.46812i	0.0813552	+	0.0672912i
$477$			8.04710i			0.368451i
$478$	1.33925	−	1.33925i	0.0612561	−	0.0612561i
$479$	−3.69569	−	8.92218i	−0.168860	−	0.407665i	0.816684	−	0.577086i	$-0.195810\pi$
$479$	−3.69569	−	8.92218i	−0.168860	−	0.407665i	−0.985544	+	0.169421i	$0.945810\pi$
$480$		0			0
$481$	17.2303	−	7.13704i	0.785636	−	0.325421i
$482$	−1.81031	−	0.749855i	−0.0824574	−	0.0341550i
$483$	0.0417872	−	0.100883i	0.00190138	−	0.00459035i
$484$	−4.41965	+	4.41965i	−0.200893	+	0.200893i
$485$		0			0
$486$	−0.486764	−	0.201624i	−0.0220801	−	0.00914586i
$487$	4.46244	+	1.84840i	0.202212	+	0.0837591i	0.481491	−	0.876451i	$-0.340095\pi$
$487$	4.46244	+	1.84840i	0.202212	+	0.0837591i	−0.279279	+	0.960210i	$0.590095\pi$
$488$	−5.97263	−	14.4192i	−0.270368	−	0.652727i
$489$			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	$0.588976\pi$
$492$		−	0.315436i		−	0.0142209i
$493$	−19.3995	+	1.83545i	−0.873708	+	0.0826646i
$494$	2.01033			0.0904490
$495$		0			0
$496$	−3.75002	−	9.05334i	−0.168381	−	0.406507i
$497$	−1.75879			−0.0788923
$498$	−0.116457	−	0.281152i	−0.00521856	−	0.0125987i
$499$	7.13250	−	17.2194i	0.319295	−	0.770845i	−0.679997	−	0.733215i	$-0.738019\pi$
$499$	7.13250	−	17.2194i	0.319295	−	0.770845i	0.999292	−	0.0376305i	$-0.0119810\pi$
$500$		0			0
$501$	−0.339510	+	0.339510i	−0.0151682	+	0.0151682i
$502$	6.72164	+	6.72164i	0.300001	+	0.300001i
$503$	7.10981	−	17.1646i	0.317011	−	0.765332i	−0.682399	−	0.730980i	$-0.739063\pi$
$503$	7.10981	−	17.1646i	0.317011	−	0.765332i	0.999410	−	0.0343519i	$-0.0109367\pi$
$504$	0.477685	−	1.15323i	0.0212778	−	0.0513691i
$505$		0			0
$506$			6.71908i			0.298700i
$507$	0.455055	−	0.188490i	0.0202097	−	0.00837113i
$508$	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
$513$	0.847112	−	0.350885i	0.0374009	−	0.0154920i
$514$			6.75508i			0.297954i
$515$		0			0
$516$	0.317725	−	0.767056i	0.0139871	−	0.0337677i
$517$	1.14733	−	2.76991i	0.0504597	−	0.121820i
$518$	−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	$0.988565\pi$
$522$	1.95274	+	4.71434i	0.0854692	+	0.206341i
$523$	−24.4504			−1.06914			−0.534571	−	0.845124i	$-0.679527\pi$
$523$	−24.4504			−1.06914			−0.534571	+	0.845124i	$0.679527\pi$
$524$	12.3974	+	29.9299i	0.541583	+	1.30750i
$525$		0			0
$526$	−5.76445			−0.251342
$527$	1.17528	+	12.4219i	0.0511958	+	0.541105i
$528$			0.486016i			0.0211511i
$529$	15.8564	+	15.8564i	0.689407	+	0.689407i
$530$		0			0
$531$			27.4361i			1.19063i
$532$	0.602675	+	1.45499i	0.0261293	+	0.0630816i
$533$	−5.68728	−	2.35575i	−0.246344	−	0.102039i
$534$	−0.0280281	−	0.0116096i	−0.00121289	−	0.000502397i
$535$		0			0
$536$	12.3813	−	12.3813i	0.534792	−	0.534792i
$537$	−0.0899828	+	0.217238i	−0.00388305	+	0.00937450i
$538$	0.398194	+	0.164937i	0.0171674	+	0.00711096i
$539$	−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
$543$		−	1.28967i		−	0.0553451i
$544$	14.4111	−	7.63186i	0.617871	−	0.327213i
$545$		0			0
$546$	0.00817000	+	0.00817000i	0.000349644	+	0.000349644i
$547$	−6.71889	+	2.78305i	−0.287279	+	0.118995i	−0.521669	−	0.853148i	$-0.674691\pi$
$547$	−6.71889	+	2.78305i	−0.287279	+	0.118995i	0.234391	+	0.972143i	$0.424691\pi$
$548$	−26.1353			−1.11644
$549$	−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
$557$	18.3930			0.779335			0.389667	−	0.920956i	$-0.372590\pi$
$557$	18.3930			0.779335			0.389667	+	0.920956i	$0.372590\pi$
$558$	3.01868	−	1.25038i	0.127791	−	0.0529328i
$559$	−11.4571	−	11.4571i	−0.484584	−	0.484584i
$560$		0			0
$561$	0.181914	−	0.591499i	0.00768041	−	0.0249731i
$562$		−	10.0495i		−	0.423911i
$563$	−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	$0.253013\pi$
$564$	0.0420555	+	0.101531i	0.00177086	+	0.00427522i
$565$		0			0
$566$	−9.88909	+	4.09620i	−0.415670	+	0.172176i
$567$	−2.47651	−	1.02581i	−0.104004	−	0.0430798i
$568$	−3.14149	+	7.58423i	−0.131814	+	0.318227i
$569$	−10.1299	+	10.1299i	−0.424669	+	0.424669i	−0.886808	−	0.462138i	$-0.847082\pi$
$569$	−10.1299	+	10.1299i	−0.424669	+	0.424669i	0.462138	+	0.886808i	$0.347082\pi$
$570$		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	$0.425810\pi$
$572$	9.46525	+	3.92063i	0.395762	+	0.163930i
$573$	0.150905	+	0.364318i	0.00630417	+	0.0152196i
$574$			0.334651i			0.0139681i
$575$		0			0
$576$	10.7052	+	10.7052i	0.446052	+	0.446052i
$577$			6.76924i			0.281807i	0.990023	+	0.140904i	$0.0450008\pi$
$577$			6.76924i			0.281807i	−0.990023	+	0.140904i	$0.954999\pi$
$578$	−6.01565	+	1.14861i	−0.250218	+	0.0477757i
$579$	1.20403			0.0500376
$580$		0			0
$581$	−1.78041	−	4.29829i	−0.0738638	−	0.178323i
$582$	−0.175274			−0.00726533
$583$	2.84342	+	6.86461i	0.117762	+	0.284303i
$584$	−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	$0.920320\pi$
$588$	0.268260	−	0.647637i	0.0110628	−	0.0267081i
$589$	−3.26458	+	7.88139i	−0.134515	+	0.324747i
$590$		0			0
$591$			0.243059i			0.00999810i
$592$	28.1852	−	11.6747i	1.15841	−	0.479828i
$593$	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	$0.0975029\pi$
$594$	−0.324266			−0.0133048
$595$		0			0
$596$	−24.0472			−0.985010
$597$	−0.0153172	+	0.0153172i	−0.000626889	+	0.000626889i
$598$	−4.44055	+	1.83934i	−0.181588	+	0.0752161i
$599$			19.1639i			0.783018i	0.920174	+	0.391509i	$0.128047\pi$
$599$			19.1639i			0.783018i	−0.920174	+	0.391509i	$0.871953\pi$
$600$		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	$0.968085\pi$
$602$	−0.337080	+	0.813782i	−0.0137383	+	0.0331673i
$603$	−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
$607$	−0.713459	−	1.72244i	−0.0289584	−	0.0699118i	0.908739	−	0.417365i	$-0.137046\pi$
$607$	−0.713459	−	1.72244i	−0.0289584	−	0.0699118i	−0.937697	+	0.347454i	$0.887046\pi$
$608$	11.1492			0.452161
$609$	−0.0293022	−	0.0707417i	−0.00118738	−	0.00286660i
$610$		0			0
$611$	2.14468			0.0867643
$612$	−10.8159	−	20.4235i	−0.437206	−	0.825569i
$613$		−	0.383092i		−	0.0154729i	−0.999970	−	0.00773647i	$-0.997537\pi$
$613$		−	0.383092i		−	0.0154729i	0.999970	−	0.00773647i	$-0.00246262\pi$
$614$	1.41088	+	1.41088i	0.0569384	+	0.0569384i
$615$		0			0
$616$		−	1.15256i		−	0.0464379i
$617$	−4.46499	−	10.7794i	−0.179754	−	0.433964i	0.808161	−	0.588962i	$-0.200463\pi$
$617$	−4.46499	−	10.7794i	−0.179754	−	0.433964i	−0.987915	+	0.154997i	$0.950463\pi$
$618$	0.234028	+	0.0969375i	0.00941398	+	0.00389940i
$619$	12.4590	+	5.16070i	0.500771	+	0.207426i	0.618747	−	0.785590i	$-0.287641\pi$
$619$	12.4590	+	5.16070i	0.500771	+	0.207426i	−0.117976	+	0.993016i	$0.537641\pi$
$620$		0			0
$621$	−1.55012	+	1.55012i	−0.0622041	+	0.0622041i
$622$	3.11143	−	7.51165i	0.124757	−	0.301190i
$623$	−0.428497	−	0.177489i	−0.0171674	−	0.00711096i
$624$	−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
$628$		−	5.05373i		−	0.201666i
$629$	−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	$-0.633989\pi$
$632$	−13.7258	+	5.68540i	−0.545982	+	0.226153i
$633$	0.105771			0.00420403
$634$	−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	$0.0893898\pi$
$642$	0.0708028			0.00279436
$643$	−16.3686	+	6.78010i	−0.645515	+	0.267381i	−0.681329	−	0.731978i	$-0.738598\pi$
$643$	−16.3686	+	6.78010i	−0.645515	+	0.267381i	0.0358141	+	0.999358i	$0.488598\pi$
$644$	−2.66246	−	2.66246i	−0.104916	−	0.104916i
$645$		0			0
$646$	−4.00220	−	1.23087i	−0.157464	−	0.0484278i
$647$			14.8304i			0.583045i	0.956564	+	0.291522i	$0.0941618\pi$
$647$			14.8304i			0.583045i	−0.956564	+	0.291522i	$0.905838\pi$
$648$	−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
$652$	29.5562	+	12.2426i	1.15751	+	0.479457i
$653$	−3.90283	+	9.42227i	−0.152730	+	0.368722i	−0.981663	−	0.190626i	$-0.938948\pi$
$653$	−3.90283	+	9.42227i	−0.152730	+	0.368722i	0.828933	+	0.559348i	$0.188948\pi$
$654$	0.0711591	−	0.0711591i	0.00278254	−	0.00278254i
$655$		0			0
$656$	−9.30321	−	3.85352i	−0.363229	−	0.150455i
$657$	0.599931	+	0.248499i	0.0234055	+	0.00969488i
$658$	−0.0446174	−	0.107716i	−0.00173937	−	0.00419920i
$659$			45.4453i			1.77030i	0.465309	+	0.885148i	$0.345943\pi$
$659$			45.4453i			1.77030i	−0.465309	+	0.885148i	$0.654057\pi$
$660$		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	$0.799418\pi$
$662$			5.21001i			0.202493i
$663$	0.440712	−	0.0416973i	0.0171158	−	0.00161939i
$664$	−21.7152			−0.842712
$665$		0			0
$666$	3.89273	+	9.39789i	0.150840	+	0.364161i
$667$	31.8526			1.23334
$668$	6.33579	+	15.2960i	0.245139	+	0.591818i
$669$	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
$673$	−8.41428	+	20.3139i	−0.324347	+	0.783042i	0.674645	+	0.738142i	$0.264297\pi$
$673$	−8.41428	+	20.3139i	−0.324347	+	0.783042i	−0.998992	+	0.0448994i	$0.985703\pi$
$674$	3.34263	−	8.06983i	0.128753	−	0.310838i
$675$		0			0
$676$		−	16.9841i		−	0.653234i
$677$	−16.8488	+	6.97899i	−0.647551	+	0.268224i	−0.682189	−	0.731176i	$-0.738972\pi$
$677$	−16.8488	+	6.97899i	−0.647551	+	0.268224i	0.0346387	+	0.999400i	$0.488972\pi$
$678$	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
$683$	16.8175	−	6.96604i	0.643504	−	0.266548i	−0.0369746	−	0.999316i	$-0.511772\pi$
$683$	16.8175	−	6.96604i	0.643504	−	0.266548i	0.680478	+	0.732768i	$0.261772\pi$
$684$		−	15.8007i		−	0.604156i
$685$		0			0
$686$	−0.572878	+	1.38305i	−0.0218726	+	0.0528051i
$687$	0.552029	−	1.33272i	0.0210612	−	0.0508463i
$688$	−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	$0.0293421\pi$
$692$	−13.7307	−	33.1488i	−0.521962	−	1.26013i
$693$	−2.47750			−0.0941124
$694$	−2.96354	−	7.15462i	−0.112494	−	0.271586i
$695$		0			0
$696$	−0.357391			−0.0135469
$697$	9.87999	+	8.17202i	0.374231	+	0.309537i
$698$			8.69519i			0.329118i
$699$	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	$0.951266\pi$
$702$	−0.0887673	−	0.214303i	−0.00335031	−	0.00808836i
$703$	−24.5367	−	10.1634i	−0.925417	−	0.383320i
$704$	12.9148	+	5.34949i	0.486745	+	0.201617i
$705$		0			0
$706$	1.84544	−	1.84544i	0.0694540	−	0.0694540i
$707$	−0.791208	+	1.91014i	−0.0297564	+	0.0718384i
$708$	−0.857891	−	0.355350i	−0.0322415	−	0.0133549i
$709$	4.88749	−	2.02447i	0.183554	−	0.0760304i	−0.289014	−	0.957325i	$-0.593327\pi$
$709$	4.88749	−	2.02447i	0.183554	−	0.0760304i	0.472567	+	0.881295i	$0.343327\pi$
$710$		0			0
$711$	12.2211	+	29.5044i	0.458329	+	1.10650i
$712$	−1.53074	+	1.53074i	−0.0573668	+	0.0573668i
$713$		−	20.3958i		−	0.763830i
$714$	−0.0112627	−	0.0212672i	−0.000421497	−	0.000795906i
$715$		0			0
$716$	5.73323	+	5.73323i	0.214261	+	0.214261i
$717$	0.263440	−	0.109120i	0.00983835	−	0.00407518i
$718$	6.21964			0.232115
$719$	8.27731	−	3.42857i	0.308691	−	0.127864i	−0.222960	−	0.974828i	$-0.571572\pi$
$719$	8.27731	−	3.42857i	0.308691	−	0.127864i	0.531651	+	0.846964i	$0.321572\pi$
$720$		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
$727$	29.9868			1.11215			0.556074	−	0.831133i	$-0.312307\pi$
$727$	29.9868			1.11215			0.556074	+	0.831133i	$0.312307\pi$
$728$	0.761710	−	0.315511i	0.0282309	−	0.0116936i
$729$	18.9797	+	18.9797i	0.702950	+	0.702950i
$730$		0			0
$731$	15.7942	+	29.8239i	0.584168	+	1.10308i
$732$		−	1.13546i		−	0.0419678i
$733$	19.0696	−	19.0696i	0.704352	−	0.704352i	−0.260990	−	0.965342i	$-0.584049\pi$
$733$	19.0696	−	19.0696i	0.704352	−	0.704352i	0.965342	+	0.260990i	$0.0840488\pi$
$734$	5.16205	+	12.4623i	0.190535	+	0.459992i
$735$		0			0
$736$	−24.6272	+	10.2009i	−0.907770	+	0.376011i
$737$	−32.1078	−	13.2995i	−1.18270	−	0.489892i
$738$	1.28489	−	3.10200i	0.0472974	−	0.114186i
$739$	24.6401	−	24.6401i	0.906400	−	0.906400i	−0.0895798	−	0.995980i	$-0.528552\pi$
$739$	24.6401	−	24.6401i	0.906400	−	0.906400i	0.995980	+	0.0895798i	$0.0285524\pi$
$740$		0			0
$741$	0.279622	+	0.115823i	0.0102722	+	0.00425487i
$742$	0.266950	+	0.110574i	0.00980006	+	0.00405932i
$743$	−6.54116	−	15.7918i	−0.239972	−	0.579344i	0.757307	−	0.653059i	$-0.226514\pi$
$743$	−6.54116	−	15.7918i	−0.239972	−	0.579344i	−0.997279	+	0.0737150i	$0.976514\pi$
$744$			0.228844i			0.00838984i
$745$		0			0
$746$	−7.61380	−	7.61380i	−0.278761	−	0.278761i
$747$			46.6781i			1.70786i
$748$	−16.4431	−	13.6006i	−0.601219	−	0.497286i
$749$	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	$-0.329804\pi$
$752$	3.50824			0.127932
$753$	0.547669	+	1.32219i	0.0199582	+	0.0481833i
$754$	−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	0.445556	−	0.895254i	$-0.353006\pi$
$757$	−12.3728	−	12.3728i	−0.449698	−	0.449698i	−0.895254	+	0.445556i	$0.853006\pi$
$758$	−4.13872	+	9.99176i	−0.150325	+	0.362917i
$759$	−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	$0.937028\pi$
$762$	−0.132362	+	0.0548261i	−0.00479497	+	0.00198614i
$763$	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
$768$	−0.330599	+	0.136939i	−0.0119295	+	0.00494135i
$769$		−	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			0
$771$	−0.389187	+	0.939581i	−0.0140162	+	0.0338382i
$772$	15.8880	−	38.3571i	0.571822	−	1.38050i
$773$	5.45537	+	5.45537i	0.196216	+	0.196216i	0.798376	−	0.602160i	$-0.205693\pi$
$773$	5.45537	+	5.45537i	0.196216	+	0.196216i	−0.602160	+	0.798376i	$0.705693\pi$
$774$	6.24901	−	6.24901i	0.224616	−	0.224616i
$775$		0			0
$776$	−4.78623	+	11.5550i	−0.171816	+	0.414800i
$777$	−0.0584130	−	0.141021i	−0.00209555	−	0.00505912i
$778$	1.33839			0.0479836
$779$	3.35468	+	8.09891i	0.120194	+	0.290173i
$780$		0			0
$781$	16.2933			0.583019
$782$	9.96650	−	0.942965i	0.356401	−	0.0337204i
$783$			1.53722i			0.0549358i
$784$	−15.8237	−	15.8237i	−0.565131	−	0.565131i
$785$		0			0
$786$		−	0.338459i		−	0.0120724i
$787$	14.6385	+	35.3404i	0.521805	+	1.25975i	0.936781	+	0.349917i	$0.113790\pi$
$787$	14.6385	+	35.3404i	0.521805	+	1.25975i	−0.414975	+	0.909833i	$0.636210\pi$
$788$	7.74321	+	3.20734i	0.275840	+	0.114257i
$789$	−0.801792	−	0.332113i	−0.0285446	−	0.0118235i
$790$		0			0
$791$	2.32487	−	2.32487i	0.0826627	−	0.0826627i
$792$	−4.42523	+	10.6835i	−0.157244	+	0.379620i
$793$	−20.4722	−	8.47987i	−0.726990	−	0.301129i
$794$	−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	$-0.906250\pi$
$797$	−18.8205	+	18.8205i	−0.666657	+	0.666657i	0.290284	+	0.956941i	$0.406250\pi$
$798$		−	0.0164535i		−	0.000582448i
$799$	−4.26966	−	1.31312i	−0.151050	−	0.0464549i
$800$		0			0
$801$	3.29042	+	3.29042i	0.116261	+	0.116261i
$802$	−0.131384	+	0.0544211i	−0.00463934	+	0.00192168i
$803$	0.599580			0.0211587
$804$	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	0.0994117	−	0.995046i	$-0.468304\pi$
$809$	−15.1856	−	6.29009i	−0.533898	−	0.221148i	−0.633309	+	0.773899i	$0.718304\pi$
$810$		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	$0.395365\pi$
$812$	−2.64031			−0.0926566
$813$	0.0445261	−	0.0184433i	0.00156160	−	0.000646835i
$814$	6.64143	+	6.64143i	0.232782	+	0.232782i
$815$		0			0
$816$	0.720914	−	0.0682081i	0.0252370	−	0.00238776i
$817$			23.0734i			0.807236i
$818$	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	$0.162152\pi$
$822$	0.252265	+	0.104492i	0.00879876	+	0.00364457i
$823$	−1.91962	+	4.63438i	−0.0669138	+	0.161544i	−0.953799	−	0.300446i	$-0.902864\pi$
$823$	−1.91962	+	4.63438i	−0.0669138	+	0.161544i	0.886885	+	0.461990i	$0.152864\pi$
$824$	12.7813	−	12.7813i	0.445257	−	0.445257i
$825$		0			0
$826$	0.910152	+	0.376997i	0.0316682	+	0.0131174i
$827$	−36.1131	−	14.9585i	−1.25578	−	0.520159i	−0.347165	−	0.937804i	$-0.612856\pi$
$827$	−36.1131	−	14.9585i	−1.25578	−	0.520159i	−0.908610	+	0.417645i	$0.862856\pi$
$828$	14.4568	+	34.9017i	0.502407	+	1.21292i
$829$		−	16.3998i		−	0.569587i	−0.958589	−	0.284794i	$-0.908075\pi$
$829$		−	16.3998i		−	0.569587i	0.958589	−	0.284794i	$-0.0919250\pi$
$830$		0			0
$831$	−0.236964	−	0.236964i	−0.00822019	−	0.00822019i
$832$			9.99964i			0.346675i
$833$	13.3352	+	25.1807i	0.462039	+	0.872461i
$834$	0.0707439			0.00244966
$835$		0			0
$836$	−5.58313	−	13.4789i	−0.193097	−	0.466177i
$837$	0.984314			0.0340229
$838$	−0.630344	−	1.52178i	−0.0217749	−	0.0525692i
$839$	11.4471	−	27.6357i	0.395197	−	0.954090i	−0.593591	−	0.804767i	$-0.702290\pi$
$839$	11.4471	−	27.6357i	0.395197	−	0.954090i	0.988788	−	0.149324i	$-0.0477096\pi$
$840$		0			0
$841$	−4.71231	+	4.71231i	−0.162493	+	0.162493i
$842$	1.92387	+	1.92387i	0.0663009	+	0.0663009i
$843$	0.578989	−	1.39780i	0.0199414	−	0.0481429i
$844$	1.39573	−	3.36959i	0.0480431	−	0.115986i
$845$		0			0
$846$			1.16976i			0.0402173i
$847$	0.922334	−	0.382043i	0.0316918	−	0.0131272i
$848$	−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
$853$	33.1784	−	13.7430i	1.13601	−	0.470550i	0.266189	−	0.963921i	$-0.414235\pi$
$853$	33.1784	−	13.7430i	1.13601	−	0.470550i	0.869819	+	0.493371i	$0.164235\pi$
$854$			1.20463i			0.0412215i
$855$		0			0
$856$	1.93343	−	4.66771i	0.0660832	−	0.159539i
$857$	8.06374	−	19.4676i	0.275452	−	0.665000i	−0.724247	−	0.689541i	$-0.757812\pi$
$857$	8.06374	−	19.4676i	0.275452	−	0.665000i	0.999699	+	0.0245406i	$0.00781230\pi$
$858$	−0.0756862	−	0.0756862i	−0.00258389	−	0.00258389i
$859$	11.2104	−	11.2104i	0.382494	−	0.382494i	−0.489506	−	0.872000i	$-0.662823\pi$
$859$	11.2104	−	11.2104i	0.382494	−	0.382494i	0.872000	+	0.489506i	$0.162823\pi$
$860$		0			0
$861$	−0.0192806	+	0.0465475i	−0.000657081	+	0.00158633i
$862$	2.87977	+	6.95238i	0.0980853	+	0.236799i
$863$	23.8125			0.810587			0.405294	−	0.914187i	$-0.367169\pi$
$863$	23.8125			0.810587			0.405294	+	0.914187i	$0.367169\pi$
$864$	−0.492301	−	1.18852i	−0.0167484	−	0.0404343i
$865$		0			0
$866$	−11.8347			−0.402160
$867$	−0.902908	−	0.186823i	−0.0306644	−	0.00634486i
$868$			1.69064i			0.0573841i
$869$	20.8506	+	20.8506i	0.707308	+	0.707308i
$870$		0			0
$871$		−	24.8603i		−	0.842359i
$872$	−2.74804	−	6.63435i	−0.0930603	−	0.224667i
$873$	24.8382	+	10.2883i	0.840645	+	0.348207i
$874$	6.32351	+	2.61929i	0.213896	+	0.0885987i
$875$		0			0
$876$	−0.0155405	+	0.0155405i	−0.000525065	+	0.000525065i
$877$	6.85759	−	16.5557i	0.231564	−	0.559046i	−0.764797	−	0.644271i	$-0.777161\pi$
$877$	6.85759	−	16.5557i	0.231564	−	0.559046i	0.996362	+	0.0852252i	$0.0271610\pi$
$878$	7.99343	+	3.31099i	0.269765	+	0.111740i
$879$	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
$883$			26.0211i			0.875680i	0.899053	+	0.437840i	$0.144256\pi$
$883$			26.0211i			0.875680i	−0.899053	+	0.437840i	$0.855744\pi$
$884$	4.48716	−	14.5901i	0.150920	−	0.490720i
$885$		0			0
$886$	−2.13189	−	2.13189i	−0.0716222	−	0.0716222i
$887$	−27.3959	+	11.3477i	−0.919863	+	0.381020i	−0.791824	−	0.610749i	$-0.790868\pi$
$887$	−27.3959	+	11.3477i	−0.919863	+	0.381020i	−0.128039	+	0.991769i	$0.540868\pi$
$888$	−0.712447			−0.0239082
$889$	−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
$897$	−0.723619			−0.0241609
$898$	8.18648	−	3.39095i	0.273186	−	0.113157i
$899$	−10.1131	−	10.1131i	−0.337290	−	0.337290i
$900$		0			0
$901$	9.78332	−	5.18106i	0.325930	−	0.172606i
$902$		−	3.10018i		−	0.103225i
$903$	−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
$907$	5.55499	+	2.30095i	0.184450	+	0.0764018i	0.472997	−	0.881064i	$-0.343172\pi$
$907$	5.55499	+	2.30095i	0.184450	+	0.0764018i	−0.288547	+	0.957466i	$0.593172\pi$
$908$	14.7147	−	35.5244i	0.488324	−	1.17892i
$909$	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	$0.830675\pi$
$912$	0.457403	+	0.189462i	0.0151461	+	0.00627373i
$913$	16.4936	+	39.8190i	0.545858	+	1.31782i
$914$			2.74173i			0.0906883i
$915$		0			0
$916$	−35.1724	−	35.1724i	−1.16213	−	1.16213i
$917$		−	5.17440i		−	0.170874i
$918$	0.0455080	+	0.480989i	0.00150199	+	0.0158750i
$919$	−31.4827			−1.03852			−0.519259	−	0.854617i	$-0.673792\pi$
$919$	−31.4827			−1.03852			−0.519259	+	0.854617i	$0.673792\pi$
$920$		0			0
$921$	0.114956	+	0.277529i	0.00378794	+	0.00914489i
$922$	−2.60127			−0.0856684
$923$	4.46025	+	10.7680i	0.146811	+	0.354433i
$924$	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
$928$	−7.15312	+	17.2692i	−0.234813	+	0.566888i
$929$	16.5321	−	39.9121i	0.542402	−	1.30947i	−0.380622	−	0.924731i	$-0.624290\pi$
$929$	16.5321	−	39.9121i	0.542402	−	1.30947i	0.923024	−	0.384743i	$-0.125710\pi$
$930$		0			0
$931$			19.4812i			0.638471i
$932$	40.6032	−	16.8184i	1.33000	−	0.550905i
$933$	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	$-0.689657\pi$
$937$	8.15745	−	8.15745i	0.266492	−	0.266492i	0.827685	+	0.561193i	$0.189657\pi$
$938$	−1.24860	+	0.517188i	−0.0407683	+	0.0168868i
$939$			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	$0.978371\pi$
$942$	−0.0202054	+	0.0487801i	−0.000658327	+	0.00158934i
$943$	−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
$947$	8.72231	+	21.0575i	0.283437	+	0.684278i	0.999911	−	0.0133362i	$-0.00424516\pi$
$947$	8.72231	+	21.0575i	0.283437	+	0.684278i	−0.716474	+	0.697614i	$0.754245\pi$
$948$	−1.08085			−0.0351045
$949$	0.164134	+	0.396254i	0.00532801	+	0.0128630i
$950$		0			0
$951$	−1.19198			−0.0386527
$952$	−1.70960	+	0.161752i	−0.0554086	+	0.00524240i
$953$		−	28.9548i		−	0.937938i	−0.883215	−	0.468969i	$-0.844626\pi$
$953$		−	28.9548i		−	0.937938i	0.883215	−	0.468969i	$-0.155374\pi$
$954$	−2.04990	−	2.04990i	−0.0663681	−	0.0663681i
$955$		0			0
$956$		−	9.83243i		−	0.318003i
$957$	0.271453	+	0.655346i	0.00877483	+	0.0211843i
$958$	3.21425	+	1.33139i	0.103848	+	0.0430152i
$959$	3.85667	+	1.59748i	0.124538	+	0.0515854i
$960$		0			0
$961$	15.4447	−	15.4447i	0.498216	−	0.498216i
$962$	−2.57115	+	6.20731i	−0.0828972	+	0.200132i
$963$	−10.0335	−	4.15603i	−0.323326	−	0.133926i
$964$	−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	0.164447	−	0.986386i	$-0.447416\pi$
$967$	35.7870	−	35.7870i	1.15083	−	1.15083i	0.986386	−	0.164447i	$-0.0525841\pi$
$968$		−	4.65968i		−	0.149768i
$969$	−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	$0.573331\pi$
$972$	−2.52697	+	1.04671i	−0.0810527	+	0.0335731i
$973$	1.08154			0.0346727
$974$	−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	$0.637525\pi$
$978$	−0.236338	−	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
$982$	−7.73637			−0.246878
$983$	−4.72148	+	1.95570i	−0.150592	+	0.0623771i	−0.456706	−	0.889618i	$-0.650971\pi$
$983$	−4.72148	+	1.95570i	−0.150592	+	0.0623771i	0.306115	+	0.951995i	$0.400971\pi$
$984$	0.166283	+	0.166283i	0.00530092	+	0.00530092i
$985$		0			0
$986$	4.47423	−	5.40935i	0.142489	−	0.172269i
$987$		−	0.0175531i		−	0.000558720i
$988$	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	$0.362291\pi$
$992$	11.0578	+	4.58029i	0.351085	+	0.145424i
$993$	−0.300170	+	0.724673i	−0.00952559	+	0.0229968i
$994$	0.448030	−	0.448030i	0.0142107	−	0.0142107i
$995$		0			0
$996$	−1.45957	−	0.604572i	−0.0462481	−	0.0191566i
$997$	−33.3033	−	13.7947i	−1.05473	−	0.436882i	−0.213149	−	0.977020i	$-0.568372\pi$
$997$	−33.3033	−	13.7947i	−1.05473	−	0.436882i	−0.841576	+	0.540138i	$0.818372\pi$
$998$	2.56951	+	6.20336i	0.0813366	+	0.196364i
$999$			3.06441i			0.0969535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.f.49.3		24
5.2	odd	4		85.2.l.a.66.3	✓	24
5.3	odd	4		425.2.m.b.151.4		24
5.4	even	2		425.2.n.c.49.4		24
15.2	even	4		765.2.be.b.406.4		24
17.8	even	8		425.2.n.c.399.4		24
85.8	odd	8		425.2.m.b.76.4		24
85.12	even	16		1445.2.a.p.1.8		12
85.22	even	16		1445.2.a.q.1.8		12
85.37	even	16		1445.2.d.j.866.10		24
85.42	odd	8		85.2.l.a.76.3	yes	24
85.59	even	8	inner	425.2.n.f.399.3		24
85.63	even	16		7225.2.a.bs.1.5		12
85.73	even	16		7225.2.a.bq.1.5		12
85.82	even	16		1445.2.d.j.866.9		24
255.212	even	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	5.2	odd	4
85.2.l.a.76.3	yes	24	85.42	odd	8
425.2.m.b.76.4		24	85.8	odd	8
425.2.m.b.151.4		24	5.3	odd	4
425.2.n.c.49.4		24	5.4	even	2
425.2.n.c.399.4		24	17.8	even	8
425.2.n.f.49.3		24	1.1	even	1	trivial
425.2.n.f.399.3		24	85.59	even	8	inner
765.2.be.b.406.4		24	15.2	even	4
765.2.be.b.586.4		24	255.212	even	8
1445.2.a.p.1.8		12	85.12	even	16
1445.2.a.q.1.8		12	85.22	even	16
1445.2.d.j.866.9		24	85.82	even	16
1445.2.d.j.866.10		24	85.37	even	16
7225.2.a.bq.1.5		12	85.73	even	16
7225.2.a.bs.1.5		12	85.63	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.254738 + 0.254738i) q^{2} +(-0.0501087 + 0.0207557i) q^{3} +1.87022i q^{4} +(0.00747733 - 0.0180519i) q^{6} +(0.114315 - 0.275980i) q^{7} +(-0.985893 - 0.985893i) q^{8} +(-2.11924 + 2.11924i) q^{9} +(-1.05900 + 2.55665i) q^{11} +(-0.0388177 - 0.0937141i) q^{12} -1.97956 q^{13} +(0.0411823 + 0.0994229i) q^{14} -3.23814 q^{16} +(3.94094 + 1.21202i) q^{17} -1.07970i q^{18} +(1.99331 + 1.99331i) q^{19} +0.0162017i q^{21} +(-0.381510 - 0.921046i) q^{22} +(-6.22672 - 2.57919i) q^{23} +(0.0698647 + 0.0289389i) q^{24} +(0.504269 - 0.504269i) q^{26} +(0.124473 - 0.300505i) q^{27} +(0.516142 + 0.213793i) q^{28} +(-4.36632 + 1.80859i) q^{29} +(1.15808 + 2.79584i) q^{31} +(2.79667 - 2.79667i) q^{32} -0.150091i q^{33} +(-1.31266 + 0.695159i) q^{34} +(-3.96344 - 3.96344i) q^{36} +(-8.70414 + 3.60537i) q^{37} -1.01554 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} -1.08341 q^{47} +(0.162259 - 0.0672100i) q^{48} +(4.88665 + 4.88665i) q^{49} +(-0.222632 + 0.0210640i) q^{51} -3.70220i q^{52} +(1.89858 - 1.89858i) q^{53} +(0.0448420 + 0.108258i) q^{54} +(-0.384788 + 0.159384i) q^{56} +(-0.141255 - 0.0585096i) q^{57} +(0.651553 - 1.57299i) q^{58} +(6.47310 - 6.47310i) q^{59} +(10.3418 + 4.28372i) q^{61} +(-1.00722 - 0.417202i) q^{62} +(0.342607 + 0.827127i) q^{63} -5.05145i q^{64} +(0.0382339 + 0.0382339i) q^{66} +12.5585i q^{67} +(-2.26675 + 7.37041i) q^{68} +0.365546 q^{69} +(-2.25315 - 5.43960i) q^{71} +4.17869 q^{72} +(-0.0829144 - 0.200173i) q^{73} +(1.29885 - 3.13570i) q^{74} +(-3.72792 + 3.72792i) q^{76} +(0.584525 + 0.584525i) q^{77} +(-0.0148018 + 0.0357347i) q^{78} +(4.07771 - 9.84447i) q^{79} -8.97353i q^{81} +(-1.03501 + 0.428717i) q^{82} +(11.0129 - 11.0129i) q^{83} -0.0303006 q^{84} -2.94870 q^{86} +(0.181252 - 0.181252i) q^{87} +(3.56465 - 1.47653i) q^{88} -1.55264i q^{89} +(-0.226292 + 0.546318i) q^{91} +(4.82365 - 11.6453i) q^{92} +(-0.116059 - 0.116059i) q^{93} +(0.275986 - 0.275986i) q^{94} +(-0.0820905 + 0.198184i) q^{96} +(-3.43280 - 8.28752i) q^{97} -2.48963 q^{98} +(-3.17389 - 7.66244i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 8 q^{6} + 24 q^{9} - 8 q^{11} - 40 q^{12} - 16 q^{13} - 24 q^{16} + 8 q^{19} + 24 q^{22} - 8 q^{23} + 8 q^{24} + 16 q^{26} - 16 q^{27} + 40 q^{28} + 8 q^{29} - 16 q^{34} - 24 q^{36} + 16 q^{37}+ \cdots + 8 q^{99}+O(q^{100}) \) 24 * q + 8 * q^3 - 8 * q^6 + 24 * q^9 - 8 * q^11 - 40 * q^12 - 16 * q^13 - 24 * q^16 + 8 * q^19 + 24 * q^22 - 8 * q^23 + 8 * q^24 + 16 * q^26 - 16 * q^27 + 40 * q^28 + 8 * q^29 - 16 * q^34 - 24 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 + 16 * q^41 + 24 * q^42 + 8 * q^43 - 16 * q^44 + 8 * q^46 + 64 * q^47 + 8 * q^48 - 56 * q^51 - 24 * q^53 + 32 * q^54 + 64 * q^56 - 16 * q^57 - 56 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 80 * q^63 + 96 * q^66 - 24 * q^68 - 96 * q^69 - 24 * q^71 + 24 * q^72 + 64 * q^73 + 64 * q^74 - 8 * q^76 - 24 * q^77 - 8 * q^78 + 16 * q^82 + 96 * q^83 + 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 - 112 * q^92 + 64 * q^93 - 56 * q^94 - 168 * q^96 - 48 * q^97 - 120 * q^98 + 8 * q^99

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