LMFDB - Embedded newform 633.2.k.a.23.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(23,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("633.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.k (of order $10$, 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:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.19
Character	$\chi$	$=$	633.23
Dual form			633.2.k.a.578.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.489132 + 1.50539i) q^{2} +(0.372318 - 1.69156i) q^{3} +(-0.408927 - 0.297103i) q^{4} +(0.626907 - 0.862864i) q^{5} +(2.36435 + 1.38788i) q^{6} +(-2.01574 + 0.654954i) q^{7} +(-1.91385 + 1.39050i) q^{8} +(-2.72276 - 1.25960i) q^{9} +O(q^{10})$	\(q+(-0.489132 + 1.50539i) q^{2} +(0.372318 - 1.69156i) q^{3} +(-0.408927 - 0.297103i) q^{4} +(0.626907 - 0.862864i) q^{5} +(2.36435 + 1.38788i) q^{6} +(-2.01574 + 0.654954i) q^{7} +(-1.91385 + 1.39050i) q^{8} +(-2.72276 - 1.25960i) q^{9} +(0.992309 + 1.36580i) q^{10} +(-3.35816 + 4.62212i) q^{11} +(-0.654818 + 0.581108i) q^{12} +(1.22664 + 3.77520i) q^{13} -3.35484i q^{14} +(-1.22618 - 1.38171i) q^{15} +(-1.46951 - 4.52268i) q^{16} +(-0.173195 - 0.533040i) q^{17} +(3.22798 - 3.48272i) q^{18} +(-0.903759 - 2.78148i) q^{19} +(-0.512718 + 0.166592i) q^{20} +(0.357399 + 3.65360i) q^{21} +(-5.31552 - 7.31619i) q^{22} +(-1.71625 + 5.28206i) q^{23} +(1.63955 + 3.75511i) q^{24} +(1.19356 + 3.67341i) q^{25} -6.28316 q^{26} +(-3.14442 + 4.13674i) q^{27} +(1.01888 + 0.331054i) q^{28} +(3.00993 + 9.26360i) q^{29} +(2.67978 - 1.17004i) q^{30} -4.04459i q^{31} +2.79590 q^{32} +(6.56829 + 7.40144i) q^{33} +0.887150 q^{34} +(-0.698547 + 2.14991i) q^{35} +(0.739179 + 1.32402i) q^{36} +(4.55281 - 3.30781i) q^{37} +4.62929 q^{38} +(6.84269 - 0.669358i) q^{39} +2.52311i q^{40} +(2.95023 + 2.14346i) q^{41} +(-5.67492 - 1.24907i) q^{42} +5.34174 q^{43} +(2.74649 - 0.892387i) q^{44} +(-2.79378 + 1.55972i) q^{45} +(-7.11211 - 5.16725i) q^{46} +(-6.66478 + 2.16552i) q^{47} +(-8.19752 + 0.801889i) q^{48} +(-2.02887 + 1.47406i) q^{49} -6.11374 q^{50} +(-0.966153 + 0.0945100i) q^{51} +(0.620018 - 1.90822i) q^{52} +(-5.11997 - 7.04704i) q^{53} +(-4.68939 - 6.75700i) q^{54} +(1.88300 + 5.79528i) q^{55} +(2.94712 - 4.05637i) q^{56} +(-5.04154 + 0.493168i) q^{57} -15.4176 q^{58} +(1.01215 - 1.39310i) q^{59} +(0.0909069 + 0.929319i) q^{60} +(-2.74266 - 3.77495i) q^{61} +(6.08870 + 1.97834i) q^{62} +(6.31336 + 0.755739i) q^{63} +(1.57145 - 4.83644i) q^{64} +(4.02648 + 1.30828i) q^{65} +(-14.3548 + 6.26758i) q^{66} -0.264195i q^{67} +(-0.0875434 + 0.269431i) q^{68} +(8.29594 + 4.86974i) q^{69} +(-2.89477 - 2.10318i) q^{70} +(-8.83341 - 12.1582i) q^{71} +(6.96243 - 1.37530i) q^{72} -4.80651 q^{73} +(2.75263 + 8.47173i) q^{74} +(6.65819 - 0.651310i) q^{75} +(-0.456815 + 1.40593i) q^{76} +(3.74192 - 11.5164i) q^{77} +(-2.33933 + 10.6283i) q^{78} +(0.561323 + 0.407825i) q^{79} +(-4.82371 - 1.56732i) q^{80} +(5.82683 + 6.85916i) q^{81} +(-4.66981 + 3.39281i) q^{82} +(-3.03351 + 4.17527i) q^{83} +(0.939345 - 1.60024i) q^{84} +(-0.568518 - 0.184723i) q^{85} +(-2.61281 + 8.04142i) q^{86} +(16.7906 - 1.64247i) q^{87} -13.5156i q^{88} +(-0.449681 - 1.38397i) q^{89} +(-0.981467 - 4.96864i) q^{90} +(-4.94517 - 6.80644i) q^{91} +(2.27113 - 1.65007i) q^{92} +(-6.84167 - 1.50587i) q^{93} -11.0923i q^{94} +(-2.96662 - 0.963912i) q^{95} +(1.04096 - 4.72943i) q^{96} +(2.66510 + 3.66820i) q^{97} +(-1.22666 - 3.77526i) q^{98} +(14.9655 - 8.35498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9}+O(q^{10}) $ 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9	$ 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9} - 20 q^{10} + 6 q^{13} - 46 q^{16} - 20 q^{18} + 6 q^{19} - 3 q^{21} - 10 q^{22} + 23 q^{24} + 50 q^{25} - 40 q^{27} + 80 q^{28} - q^{30} + 12 q^{34} + 13 q^{36} - 42 q^{37} + 25 q^{39} - 10 q^{42} + 40 q^{43} - 23 q^{45} - 2 q^{46} - 15 q^{48} + 30 q^{49} - 11 q^{51} - 34 q^{52} + 128 q^{54} + 14 q^{55} + 20 q^{57} + 60 q^{58} + 30 q^{60} - 10 q^{61} - 108 q^{64} - 73 q^{66} + 40 q^{69} + 70 q^{70} - 105 q^{72} - 20 q^{73} - 10 q^{75} - 12 q^{76} - 82 q^{78} - 30 q^{79} - 42 q^{81} - 106 q^{82} + 121 q^{84} - 110 q^{85} - 11 q^{87} + 60 q^{90} - 40 q^{91} - 45 q^{93} - 114 q^{96} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9 - 20 * q^10 + 6 * q^13 - 46 * q^16 - 20 * q^18 + 6 * q^19 - 3 * q^21 - 10 * q^22 + 23 * q^24 + 50 * q^25 - 40 * q^27 + 80 * q^28 - q^30 + 12 * q^34 + 13 * q^36 - 42 * q^37 + 25 * q^39 - 10 * q^42 + 40 * q^43 - 23 * q^45 - 2 * q^46 - 15 * q^48 + 30 * q^49 - 11 * q^51 - 34 * q^52 + 128 * q^54 + 14 * q^55 + 20 * q^57 + 60 * q^58 + 30 * q^60 - 10 * q^61 - 108 * q^64 - 73 * q^66 + 40 * q^69 + 70 * q^70 - 105 * q^72 - 20 * q^73 - 10 * q^75 - 12 * q^76 - 82 * q^78 - 30 * q^79 - 42 * q^81 - 106 * q^82 + 121 * q^84 - 110 * q^85 - 11 * q^87 + 60 * q^90 - 40 * q^91 - 45 * q^93 - 114 * q^96 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$.

$n$	$212$	$424$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.489132	+	1.50539i	−0.345869	+	1.06447i	0.615248	+	0.788333i	$0.289056\pi$
$2$	−0.489132	+	1.50539i	−0.345869	+	1.06447i	−0.961117	+	0.276141i	$0.910944\pi$
$3$	0.372318	−	1.69156i	0.214958	−	0.976623i
$3$	0.372318	−	1.69156i	0.214958	−	0.976623i
$4$	−0.408927	−	0.297103i	−0.204463	−	0.148551i
$5$	0.626907	−	0.862864i	0.280361	−	0.385884i	−0.645492	−	0.763767i	$-0.723348\pi$
$5$	0.626907	−	0.862864i	0.280361	−	0.385884i	0.925854	+	0.377883i	$0.123348\pi$
$6$	2.36435	+	1.38788i	0.965243	+	0.566600i
$7$	−2.01574	+	0.654954i	−0.761879	+	0.247549i	−0.664085	−	0.747657i	$-0.731179\pi$
$7$	−2.01574	+	0.654954i	−0.761879	+	0.247549i	−0.0977939	+	0.995207i	$0.531179\pi$
$8$	−1.91385	+	1.39050i	−0.676649	+	0.491615i
$9$	−2.72276	−	1.25960i	−0.907586	−	0.419865i
$10$	0.992309	+	1.36580i	0.313796	+	0.431903i
$11$	−3.35816	+	4.62212i	−1.01252	+	1.39362i	−0.0952104	+	0.995457i	$0.530352\pi$
$11$	−3.35816	+	4.62212i	−1.01252	+	1.39362i	−0.917314	+	0.398164i	$0.869648\pi$
$12$	−0.654818	+	0.581108i	−0.189030	+	0.167751i
$13$	1.22664	+	3.77520i	0.340208	+	1.04705i	0.964099	+	0.265542i	$0.0855509\pi$
$13$	1.22664	+	3.77520i	0.340208	+	1.04705i	−0.623891	+	0.781511i	$0.714449\pi$
$14$		−	3.35484i		−	0.896620i
$15$	−1.22618	−	1.38171i	−0.316598	−	0.356756i
$16$	−1.46951	−	4.52268i	−0.367377	−	1.13067i
$17$	−0.173195	−	0.533040i	−0.0420060	−	0.129281i	0.927854	−	0.372943i	$-0.121651\pi$
$17$	−0.173195	−	0.533040i	−0.0420060	−	0.129281i	−0.969860	+	0.243662i	$0.921651\pi$
$18$	3.22798	−	3.48272i	0.760842	−	0.820884i
$19$	−0.903759	−	2.78148i	−0.207337	−	0.638116i	−0.999609	−	0.0279493i	$-0.991102\pi$
$19$	−0.903759	−	2.78148i	−0.207337	−	0.638116i	0.792273	−	0.610167i	$-0.208898\pi$
$20$	−0.512718	+	0.166592i	−0.114647	+	0.0372512i
$21$	0.357399	+	3.65360i	0.0779908	+	0.797281i
$22$	−5.31552	−	7.31619i	−1.13327	−	1.55982i
$23$	−1.71625	+	5.28206i	−0.357862	+	1.10139i	0.596469	+	0.802636i	$0.296570\pi$
$23$	−1.71625	+	5.28206i	−0.357862	+	1.10139i	−0.954331	+	0.298750i	$0.903430\pi$
$24$	1.63955	+	3.75511i	0.334671	+	0.766508i
$25$	1.19356	+	3.67341i	0.238713	+	0.734682i
$26$	−6.28316			−1.23223
$27$	−3.14442	+	4.13674i	−0.605143	+	0.796117i
$28$	1.01888	+	0.331054i	0.192550	+	0.0625633i
$29$	3.00993	+	9.26360i	0.558929	+	1.72021i	0.685334	+	0.728229i	$0.259656\pi$
$29$	3.00993	+	9.26360i	0.558929	+	1.72021i	−0.126405	+	0.991979i	$0.540344\pi$
$30$	2.67978	−	1.17004i	0.489259	−	0.213619i
$31$		−	4.04459i		−	0.726430i	−0.931705	−	0.363215i	$-0.881679\pi$
$31$		−	4.04459i		−	0.726430i	0.931705	−	0.363215i	$-0.118321\pi$
$32$	2.79590			0.494250
$33$	6.56829	+	7.40144i	1.14339	+	1.28842i
$34$	0.887150			0.152145
$35$	−0.698547	+	2.14991i	−0.118076	+	0.363400i
$36$	0.739179	+	1.32402i	0.123197	+	0.220670i
$37$	4.55281	−	3.30781i	0.748478	−	0.543801i	−0.146877	−	0.989155i	$-0.546922\pi$
$37$	4.55281	−	3.30781i	0.748478	−	0.543801i	0.895355	+	0.445354i	$0.146922\pi$
$38$	4.62929			0.750970
$39$	6.84269	−	0.669358i	1.09571	−	0.107183i
$40$			2.52311i			0.398938i
$41$	2.95023	+	2.14346i	0.460748	+	0.334753i	0.793825	−	0.608147i	$-0.208087\pi$
$41$	2.95023	+	2.14346i	0.460748	+	0.334753i	−0.333077	+	0.942900i	$0.608087\pi$
$42$	−5.67492	−	1.24907i	−0.875660	−	0.192735i
$43$	5.34174			0.814607			0.407304	−	0.913293i	$-0.366469\pi$
$43$	5.34174			0.814607			0.407304	+	0.913293i	$0.366469\pi$
$44$	2.74649	−	0.892387i	0.414048	−	0.134532i
$45$	−2.79378	+	1.55972i	−0.416472	+	0.232509i
$46$	−7.11211	−	5.16725i	−1.04862	−	0.761870i
$47$	−6.66478	+	2.16552i	−0.972157	+	0.315873i	−0.751687	−	0.659520i	$-0.770759\pi$
$47$	−6.66478	+	2.16552i	−0.972157	+	0.315873i	−0.220471	+	0.975394i	$0.570759\pi$
$48$	−8.19752	+	0.801889i	−1.18321	+	0.115743i
$49$	−2.02887	+	1.47406i	−0.289839	+	0.210580i
$50$	−6.11374			−0.864614
$51$	−0.966153	+	0.0945100i	−0.135288	+	0.0132340i
$52$	0.620018	−	1.90822i	0.0859810	−	0.264622i
$53$	−5.11997	−	7.04704i	−0.703282	−	0.967985i	−0.999916	−	0.0129935i	$-0.995864\pi$
$53$	−5.11997	−	7.04704i	−0.703282	−	0.967985i	0.296633	−	0.954991i	$-0.404136\pi$
$54$	−4.68939	−	6.75700i	−0.638146	−	0.919511i
$55$	1.88300	+	5.79528i	0.253904	+	0.781435i
$56$	2.94712	−	4.05637i	0.393826	−	0.542055i
$57$	−5.04154	+	0.493168i	−0.667768	+	0.0653217i
$58$	−15.4176			−2.02443
$59$	1.01215	−	1.39310i	0.131770	−	0.181366i	−0.738034	−	0.674764i	$-0.764245\pi$
$59$	1.01215	−	1.39310i	0.131770	−	0.181366i	0.869804	+	0.493398i	$0.164245\pi$
$60$	0.0909069	+	0.929319i	0.0117360	+	0.119975i
$61$	−2.74266	−	3.77495i	−0.351162	−	0.483333i	0.596498	−	0.802615i	$-0.296558\pi$
$61$	−2.74266	−	3.77495i	−0.351162	−	0.483333i	−0.947660	+	0.319282i	$0.896558\pi$
$62$	6.08870	+	1.97834i	0.773266	+	0.251249i
$63$	6.31336	+	0.755739i	0.795408	+	0.0952141i
$64$	1.57145	−	4.83644i	0.196432	−	0.604555i
$65$	4.02648	+	1.30828i	0.499423	+	0.162272i
$66$	−14.3548	+	6.26758i	−1.76696	+	0.771486i
$67$		−	0.264195i		−	0.0322766i	−0.999870	−	0.0161383i	$-0.994863\pi$
$67$		−	0.264195i		−	0.0322766i	0.999870	−	0.0161383i	$-0.00513720\pi$
$68$	−0.0875434	+	0.269431i	−0.0106162	+	0.0326733i
$69$	8.29594	+	4.86974i	0.998714	+	0.586248i
$70$	−2.89477	−	2.10318i	−0.345992	−	0.251378i
$71$	−8.83341	−	12.1582i	−1.04833	−	1.44291i	−0.890245	−	0.455482i	$-0.849467\pi$
$71$	−8.83341	−	12.1582i	−1.04833	−	1.44291i	−0.158089	−	0.987425i	$-0.550533\pi$
$72$	6.96243	−	1.37530i	0.820530	−	0.162081i
$73$	−4.80651			−0.562560			−0.281280	−	0.959626i	$-0.590759\pi$
$73$	−4.80651			−0.562560			−0.281280	+	0.959626i	$0.590759\pi$
$74$	2.75263	+	8.47173i	0.319987	+	0.984819i
$75$	6.65819	−	0.651310i	0.768821	−	0.0752068i
$76$	−0.456815	+	1.40593i	−0.0524003	+	0.161272i
$77$	3.74192	−	11.5164i	0.426431	−	1.31242i
$78$	−2.33933	+	10.6283i	−0.264877	+	1.20342i
$79$	0.561323	+	0.407825i	0.0631538	+	0.0458839i	0.618914	−	0.785459i	$-0.287573\pi$
$79$	0.561323	+	0.407825i	0.0631538	+	0.0458839i	−0.555760	+	0.831342i	$0.687573\pi$
$80$	−4.82371	−	1.56732i	−0.539307	−	0.175231i
$81$	5.82683	+	6.85916i	0.647426	+	0.762128i
$82$	−4.66981	+	3.39281i	−0.515694	+	0.374674i
$83$	−3.03351	+	4.17527i	−0.332971	+	0.458295i	−0.942372	−	0.334567i	$-0.891410\pi$
$83$	−3.03351	+	4.17527i	−0.332971	+	0.458295i	0.609401	+	0.792862i	$0.291410\pi$
$84$	0.939345	−	1.60024i	0.102491	−	0.174600i
$85$	−0.568518	−	0.184723i	−0.0616644	−	0.0200360i
$86$	−2.61281	+	8.04142i	−0.281747	+	0.867128i
$87$	16.7906	−	1.64247i	1.80014	−	0.176092i
$88$		−	13.5156i		−	1.44076i
$89$	−0.449681	−	1.38397i	−0.0476661	−	0.146701i	0.924391	−	0.381447i	$-0.124574\pi$
$89$	−0.449681	−	1.38397i	−0.0476661	−	0.146701i	−0.972057	+	0.234746i	$0.924574\pi$
$90$	−0.981467	−	4.96864i	−0.103456	−	0.523741i
$91$	−4.94517	−	6.80644i	−0.518395	−	0.713509i
$92$	2.27113	−	1.65007i	0.236782	−	0.172032i
$93$	−6.84167	−	1.50587i	−0.709448	−	0.156152i
$94$		−	11.0923i		−	1.14409i
$95$	−2.96662	−	0.963912i	−0.304368	−	0.0988953i
$96$	1.04096	−	4.72943i	0.106243	−	0.482696i
$97$	2.66510	+	3.66820i	0.270600	+	0.372449i	0.922592	−	0.385777i	$-0.126066\pi$
$97$	2.66510	+	3.66820i	0.270600	+	0.372449i	−0.651992	+	0.758226i	$0.726066\pi$
$98$	−1.22666	−	3.77526i	−0.123911	−	0.381359i
$99$	14.9655	−	8.35498i	1.50409	−	0.839707i
$100$	0.603300	−	1.85677i	0.0603300	−	0.185677i
$101$			11.1175i			1.10623i	0.833104	+	0.553117i	$0.186562\pi$
$101$			11.1175i			1.10623i	−0.833104	+	0.553117i	$0.813438\pi$
$102$	0.330302	−	1.50067i	0.0327047	−	0.148588i
$103$	−0.877290	+	2.70002i	−0.0864419	+	0.266041i	−0.984929	−	0.172959i	$-0.944667\pi$
$103$	−0.877290	+	2.70002i	−0.0864419	+	0.266041i	0.898487	+	0.439000i	$0.144667\pi$
$104$	−7.59701	−	5.51955i	−0.744948	−	0.541237i
$105$	3.37662	+	1.98208i	0.329524	+	0.193431i
$106$	13.1129	−	4.26064i	1.27364	−	0.413830i
$107$	3.82247	−	5.26118i	0.369532	−	0.508617i	−0.583241	−	0.812299i	$-0.698216\pi$
$107$	3.82247	−	5.26118i	0.369532	−	0.508617i	0.952774	+	0.303681i	$0.0982159\pi$
$108$	2.51487	−	0.757411i	0.241994	−	0.0728819i
$109$	0.721057	−	0.523879i	0.0690648	−	0.0501785i	−0.552717	−	0.833369i	$-0.686409\pi$
$109$	0.721057	−	0.523879i	0.0690648	−	0.0501785i	0.621782	+	0.783190i	$0.286409\pi$
$110$	−9.64521			−0.919635
$111$	−3.90027	−	8.93292i	−0.370198	−	0.847875i
$112$	5.92430	+	8.15410i	0.559794	+	0.770490i
$113$	−11.9053	+	3.86828i	−1.11996	+	0.363897i	−0.809752	−	0.586772i	$-0.800399\pi$
$113$	−11.9053	+	3.86828i	−1.11996	+	0.363897i	−0.310207	+	0.950669i	$0.600399\pi$
$114$	1.72357	−	7.83072i	0.161427	−	0.733415i
$115$	3.48177	+	4.79225i	0.324677	+	0.446880i
$116$	1.52140	−	4.68239i	0.141259	−	0.434749i
$117$	1.41539	−	11.8240i	0.130853	−	1.09313i
$118$	1.60209	+	2.20509i	0.147484	+	0.202995i
$119$	0.698233	+	0.961035i	0.0640069	+	0.0880979i
$120$	4.26799	+	0.939397i	0.389612	+	0.0857549i
$121$	−6.68751	−	20.5820i	−0.607956	−	1.87109i
$122$	7.02431	−	2.28234i	0.635951	−	0.206633i
$123$	4.72422	−	4.19244i	0.425969	−	0.378019i
$124$	−1.20166	+	1.65394i	−0.107912	+	0.148528i
$125$	8.98969	+	2.92093i	0.804063	+	0.261256i
$126$	−4.22575	+	9.13443i	−0.376460	+	0.813760i
$127$	−1.04940	+	0.340970i	−0.0931190	+	0.0302562i	−0.355206	−	0.934788i	$-0.615589\pi$
$127$	−1.04940	+	0.340970i	−0.0931190	+	0.0302562i	0.262087	+	0.965044i	$0.415589\pi$
$128$	11.0360	+	8.01809i	0.975450	+	0.708706i
$129$	1.98882	−	9.03587i	0.175106	−	0.795564i
$130$	−3.93896	+	5.42151i	−0.345469	+	0.475498i
$131$	2.94208	−	9.05479i	0.257051	−	0.791121i	−0.736368	−	0.676581i	$-0.763461\pi$
$131$	2.94208	−	9.05479i	0.257051	−	0.791121i	0.993419	−	0.114540i	$-0.0365393\pi$
$132$	−0.486963	−	4.97810i	−0.0423847	−	0.433288i
$133$	3.64349	+	5.01483i	0.315931	+	0.434841i
$134$	0.397718	+	0.129226i	0.0343576	+	0.0111635i
$135$	1.59819	+	5.30656i	0.137550	+	0.456716i
$136$	1.07266	+	0.779333i	0.0919798	+	0.0668272i
$137$	18.9489	−	6.15688i	1.61892	−	0.526018i	0.647230	−	0.762295i	$-0.275927\pi$
$137$	18.9489	−	6.15688i	1.61892	−	0.526018i	0.971686	+	0.236277i	$0.0759274\pi$
$138$	−11.3887	+	10.1067i	−0.969470	+	0.860341i
$139$	6.70405	+	20.6329i	0.568630	+	1.75006i	0.656911	+	0.753968i	$0.271863\pi$
$139$	6.70405	+	20.6329i	0.568630	+	1.75006i	−0.0882808	+	0.996096i	$0.528137\pi$
$140$	0.924397	−	0.671614i	0.0781258	−	0.0567617i
$141$	1.18169	+	12.0801i	0.0995163	+	1.01733i
$142$	22.6235	−	7.35083i	1.89852	−	0.616868i
$143$	−21.5687	−	7.00809i	−1.80366	−	0.586046i
$144$	−1.69564	+	14.1652i	−0.141303	+	1.18043i
$145$	9.88017	+	3.21026i	0.820504	+	0.266598i
$146$	2.35102	−	7.23569i	0.194572	−	0.598830i
$147$	1.73808	+	3.98078i	0.143354	+	0.328329i
$148$	−2.84453			−0.233819
$149$	3.81811	−	11.7509i	0.312792	−	0.962674i	−0.663862	−	0.747855i	$-0.731084\pi$
$149$	3.81811	−	11.7509i	0.312792	−	0.962674i	0.976654	−	0.214819i	$-0.0689162\pi$
$150$	−2.27625	+	10.3418i	−0.185855	+	0.844402i
$151$	−12.4770	−	9.06508i	−1.01537	−	0.737706i	−0.0500377	−	0.998747i	$-0.515934\pi$
$151$	−12.4770	−	9.06508i	−1.01537	−	0.737706i	−0.965328	+	0.261041i	$0.915934\pi$
$152$	5.59731	+	4.06668i	0.454001	+	0.329851i
$153$	−0.199846	+	1.66949i	−0.0161566	+	0.134971i
$154$	15.5065	+	11.2661i	1.24955	+	0.907850i
$155$	−3.48993	−	2.53558i	−0.280318	−	0.203663i
$156$	−2.99703	−	1.75926i	−0.239954	−	0.140854i
$157$			15.9488i			1.27286i	0.771336	+	0.636428i	$0.219589\pi$
$157$			15.9488i			1.27286i	−0.771336	+	0.636428i	$0.780411\pi$
$158$	−0.888499	+	0.645532i	−0.0706851	+	0.0513558i
$159$	−13.8268	+	6.03701i	−1.09653	+	0.478766i
$160$	1.75277	−	2.41248i	0.138569	−	0.190723i
$161$		−	11.7713i		−	0.927711i
$162$	−13.1758	+	5.41665i	−1.03519	+	0.425572i
$163$	17.3548	+	12.6090i	1.35934	+	0.987615i	0.998487	+	0.0549909i	$0.0175130\pi$
$163$	17.3548	+	12.6090i	1.35934	+	0.987615i	0.360849	+	0.932624i	$0.382487\pi$
$164$	−0.569597	−	1.75304i	−0.0444781	−	0.136889i
$165$	10.5041	−	1.02753i	0.817746	−	0.0799927i
$166$	−4.80164	−	6.60888i	−0.372679	−	0.512949i
$167$	5.88328	+	18.1069i	0.455262	+	1.40115i	0.870827	+	0.491589i	$0.163584\pi$
$167$	5.88328	+	18.1069i	0.455262	+	1.40115i	−0.415565	+	0.909563i	$0.636416\pi$
$168$	−5.76433	−	6.49550i	−0.444727	−	0.501138i
$169$	−2.23031	+	1.62041i	−0.171562	+	0.124647i
$170$	0.556161	−	0.765489i	0.0426556	−	0.0587104i
$171$	−1.04283	+	8.71168i	−0.0797472	+	0.666199i
$172$	−2.18438	−	1.58704i	−0.166557	−	0.121011i
$173$			9.80409i			0.745391i	0.927954	+	0.372695i	$0.121566\pi$
$173$			9.80409i			0.745391i	−0.927954	+	0.372695i	$0.878434\pi$
$174$	−5.74025	+	26.0799i	−0.435167	+	1.97711i
$175$	−4.81183	−	6.62292i	−0.363740	−	0.500646i
$176$	25.8392	+	8.39567i	1.94771	+	0.632848i
$177$	−1.97967	−	2.23078i	−0.148801	−	0.167676i
$178$	2.30338			0.172646
$179$			1.46320i			0.109364i	0.998504	+	0.0546822i	$0.0174146\pi$
$179$			1.46320i			0.109364i	−0.998504	+	0.0546822i	$0.982585\pi$
$180$	1.60585	+	0.192227i	0.119693	+	0.0143278i
$181$	−0.902371	−	0.293198i	−0.0670727	−	0.0217932i	0.275288	−	0.961362i	$-0.411227\pi$
$181$	−0.902371	−	0.293198i	−0.0670727	−	0.0217932i	−0.342361	+	0.939568i	$0.611227\pi$
$182$	12.6652	−	4.11518i	0.938809	−	0.305037i
$183$	−7.40670	+	3.23390i	−0.547519	+	0.239057i
$184$	−4.06004	−	12.4955i	−0.299310	−	0.921182i
$185$		−	6.00215i		−	0.441287i
$186$	5.61341	−	9.56284i	0.411595	−	0.701182i
$187$	3.04539	+	0.989507i	0.222701	+	0.0723599i
$188$	3.36878	+	1.09458i	0.245694	+	0.0798308i
$189$	3.62895	−	10.3981i	0.263967	−	0.756347i
$190$	2.90213	−	3.99444i	0.210543	−	0.289787i
$191$	0.0998928	+	0.307438i	0.00722799	+	0.0222455i	0.954605	−	0.297873i	$-0.0962772\pi$
$191$	0.0998928	+	0.307438i	0.00722799	+	0.0222455i	−0.947377	+	0.320119i	$0.896277\pi$
$192$	−7.59605	−	4.45890i	−0.548198	−	0.321794i
$193$	14.0701	+	10.2225i	1.01279	+	0.735832i	0.964791	−	0.263016i	$-0.0847172\pi$
$193$	14.0701	+	10.2225i	1.01279	+	0.735832i	0.0479939	+	0.998848i	$0.484717\pi$
$194$	−6.82567	+	2.21779i	−0.490055	+	0.159228i
$195$	3.71217	−	6.32393i	0.265834	−	0.452866i
$196$	1.26761			0.0905433
$197$	20.5983			1.46757			0.733785	−	0.679382i	$-0.237752\pi$
$197$	20.5983			1.46757			0.733785	+	0.679382i	$0.237752\pi$
$198$	5.25744	+	26.6156i	0.373630	+	1.89149i
$199$	−20.0082			−1.41835			−0.709173	−	0.705034i	$-0.750932\pi$
$199$	−20.0082			−1.41835			−0.709173	+	0.705034i	$0.750932\pi$
$200$	−7.39217	−	5.37073i	−0.522705	−	0.379768i
$201$	−0.446902	−	0.0983646i	−0.0315221	−	0.00693810i
$202$	−16.7362	−	5.43793i	−1.17756	−	0.382612i
$203$	−12.1345	−	16.7017i	−0.851673	−	1.17223i
$204$	0.423165	+	0.248399i	0.0296275	+	0.0173914i
$205$	3.69904	−	1.20189i	0.258352	−	0.0839436i
$206$	−3.63548	−	2.64133i	−0.253296	−	0.184030i
$207$	11.3262	−	12.2200i	0.787225	−	0.849349i
$208$	15.2715	−	11.0954i	1.05889	−	0.769327i
$209$	15.8913	+	5.16340i	1.09923	+	0.357160i
$210$	−4.63543	+	4.11364i	−0.319875	+	0.283868i
$211$	−9.84341	−	10.6821i	−0.677648	−	0.735386i
$211$	−9.84341	−	10.6821i	−0.677648	−	0.735386i
$212$			4.40288i			0.302391i
$213$	−23.8551	+	10.4156i	−1.63452	+	0.713663i
$214$	6.05045	+	8.32774i	0.413601	+	0.569272i
$215$	3.34877	−	4.60919i	0.228384	−	0.314344i
$216$	0.265826	−	12.2894i	0.0180872	−	0.836189i
$217$	2.64902	+	8.15285i	0.179827	+	0.553451i
$218$	0.435952	+	1.34172i	0.0295264	+	0.0908728i
$219$	−1.78955	+	8.13051i	−0.120927	+	0.549409i
$220$	0.951783	−	2.92929i	0.0641692	−	0.197493i
$221$	1.79989	−	1.30769i	0.121073	−	0.0879650i
$222$	15.3553	−	1.50207i	1.03058	−	0.100812i
$223$			16.1680i			1.08269i	0.840802	+	0.541343i	$0.182084\pi$
$223$			16.1680i			1.08269i	−0.840802	+	0.541343i	$0.817916\pi$
$224$	−5.63581	+	1.83119i	−0.376558	+	0.122351i
$225$	1.37723	−	11.5052i	0.0918153	−	0.767015i
$226$		−	19.8143i		−	1.31803i
$227$	−19.7225	+	6.40823i	−1.30903	+	0.425329i	−0.878714	−	0.477349i	$-0.841598\pi$
$227$	−19.7225	+	6.40823i	−1.30903	+	0.425329i	−0.430315	+	0.902679i	$0.641598\pi$
$228$	2.20814	+	1.29618i	0.146238	+	0.0858419i
$229$	13.2357	−	18.2174i	0.874641	−	1.20384i	−0.103236	−	0.994657i	$-0.532920\pi$
$229$	13.2357	−	18.2174i	0.874641	−	1.20384i	0.977877	−	0.209183i	$-0.0670804\pi$
$230$	−8.91727	+	2.89740i	−0.587987	+	0.191049i
$231$	−18.0876	−	10.6175i	−1.19008	−	0.698577i
$232$	−18.6416	−	13.5439i	−1.22388	−	0.889200i
$233$	3.67861	−	2.67267i	0.240994	−	0.175092i	−0.460732	−	0.887539i	$-0.652413\pi$
$233$	3.67861	−	2.67267i	0.240994	−	0.175092i	0.701726	+	0.712447i	$0.252413\pi$
$234$	17.1075	+	7.91424i	1.11835	+	0.517370i
$235$	−2.30965	+	7.10837i	−0.150665	+	0.463699i
$236$	−0.827786	+	0.268964i	−0.0538843	+	0.0175081i
$237$	0.898852	−	0.797672i	0.0583867	−	0.0518144i
$238$	−1.78826	+	0.581042i	−0.115916	+	0.0376634i
$239$	3.92311	−	12.0741i	0.253765	−	0.781007i	−0.740306	−	0.672270i	$-0.765319\pi$
$239$	3.92311	−	12.0741i	0.253765	−	0.781007i	0.994071	−	0.108737i	$-0.0346807\pi$
$240$	−4.44716	+	7.57605i	−0.287063	+	0.489032i
$241$	−6.36469	+	19.5885i	−0.409986	+	1.26181i	0.506674	+	0.862137i	$0.330875\pi$
$241$	−6.36469	+	19.5885i	−0.409986	+	1.26181i	−0.916660	+	0.399668i	$0.869125\pi$
$242$	34.2552			2.20201
$243$	13.7721	−	7.30266i	0.883482	−	0.468466i
$244$			2.35853i			0.150989i
$245$			2.67474i			0.170883i
$246$	4.00050	+	9.16247i	0.255063	+	0.584178i
$247$	9.39209	−	6.82375i	0.597604	−	0.434185i
$248$	5.62399	+	7.74075i	0.357124	+	0.491538i
$249$	5.93329	+	6.68589i	0.376007	+	0.423701i
$250$	−8.79430	+	12.1043i	−0.556200	+	0.765544i
$251$	−10.4580			−0.660104			−0.330052	−	0.943963i	$-0.607066\pi$
$251$	−10.4580			−0.660104			−0.330052	+	0.943963i	$0.607066\pi$
$252$	−2.35717	−	2.18476i	−0.148488	−	0.137627i
$253$	−18.6509	−	25.6707i	−1.17257	−	1.61390i
$254$		−	1.74654i		−	0.109587i
$255$	−0.524139	+	0.892907i	−0.0328228	+	0.0559160i
$256$	−9.24019	+	6.71339i	−0.577512	+	0.419587i
$257$	6.62077	−	9.11270i	0.412992	−	0.568435i	−0.550953	−	0.834536i	$-0.685736\pi$
$257$	6.62077	−	9.11270i	0.412992	−	0.568435i	0.963945	+	0.266102i	$0.0857357\pi$
$258$	12.6298	+	7.41370i	0.786294	+	0.461557i
$259$	−7.01083	+	9.64958i	−0.435632	+	0.599596i
$260$	−1.25784	−	1.73127i	−0.0780079	−	0.107369i
$261$	3.47309	−	29.0138i	0.214979	−	1.79591i
$262$	12.1920	+	8.85798i	0.753222	+	0.547248i
$263$	28.7749	+	9.34954i	1.77434	+	0.576517i	0.998517	−	0.0544362i	$-0.0173361\pi$
$263$	28.7749	+	9.34954i	1.77434	+	0.576517i	0.775821	+	0.630953i	$0.217336\pi$
$264$	−22.8624	−	5.03209i	−1.40708	−	0.309703i
$265$	−9.29038			−0.570703
$266$	−9.33145	+	3.03197i	−0.572148	+	0.185902i
$267$	−2.50850	+	0.245384i	−0.153518	+	0.0150173i
$268$	−0.0784931	+	0.108036i	−0.00479473	+	0.00659938i
$269$			11.4375i			0.697359i	0.937242	+	0.348679i	$0.113370\pi$
$269$			11.4375i			0.697359i	−0.937242	+	0.348679i	$0.886630\pi$
$270$	−8.77018	−	0.189703i	−0.533736	−	0.0115450i
$271$	6.11911	−	8.42224i	0.371710	−	0.511615i	−0.581655	−	0.813436i	$-0.697595\pi$
$271$	6.11911	−	8.42224i	0.371710	−	0.511615i	0.953365	+	0.301821i	$0.0975945\pi$
$272$	−2.15626	+	1.56661i	−0.130742	+	0.0949899i
$273$	−13.3547	+	5.83090i	−0.808263	+	0.352902i
$274$			31.5371i			1.90523i
$275$	−20.9871	−	6.81913i	−1.26557	−	0.411209i
$276$	−1.94562	−	4.45611i	−0.117113	−	0.268226i
$277$	−7.66008	+	23.5753i	−0.460249	+	1.41650i	0.404611	+	0.914489i	$0.367407\pi$
$277$	−7.66008	+	23.5753i	−0.460249	+	1.41650i	−0.864860	+	0.502013i	$0.832593\pi$
$278$	−34.3399			−2.05957
$279$	−5.09455	+	11.0124i	−0.305003	+	0.659298i
$280$	−1.65252	−	5.08593i	−0.0987569	−	0.303943i
$281$	8.08165	−	11.1234i	0.482111	−	0.663569i	−0.496798	−	0.867866i	$-0.665491\pi$
$281$	8.08165	−	11.1234i	0.482111	−	0.663569i	0.978909	+	0.204297i	$0.0654910\pi$
$282$	−18.7634	−	4.12987i	−1.11734	−	0.245930i
$283$	14.2285	−	4.62311i	0.845794	−	0.274815i	0.146111	−	0.989268i	$-0.453324\pi$
$283$	14.2285	−	4.62311i	0.845794	−	0.274815i	0.699683	+	0.714453i	$0.253324\pi$
$284$			7.59622i			0.450753i
$285$	−2.73504	+	4.65933i	−0.162010	+	0.275995i
$286$	21.0999	−	29.0415i	1.24766	−	1.71726i
$287$	−7.35076	−	2.38841i	−0.433902	−	0.140983i
$288$	−7.61256	−	3.52170i	−0.448574	−	0.207518i
$289$	13.4992	−	9.80771i	0.794068	−	0.576924i
$290$	−9.66542	+	13.3033i	−0.567573	+	0.781197i
$291$	7.19725	−	3.14245i	0.421910	−	0.184214i
$292$	1.96551	+	1.42803i	0.115023	+	0.0835690i
$293$	−5.63830	−	7.76046i	−0.329393	−	0.453371i	0.611913	−	0.790925i	$-0.290400\pi$
$293$	−5.63830	−	7.76046i	−0.329393	−	0.453371i	−0.941306	+	0.337554i	$0.890400\pi$
$294$	−6.84279	+	0.669368i	−0.399079	+	0.0390383i
$295$	−0.567533	−	1.74669i	−0.0330430	−	0.101696i
$296$	−4.11392	+	12.6613i	−0.239117	+	0.735925i
$297$	−8.56105	−	28.4257i	−0.496762	−	1.64943i
$298$	15.8222	+	11.4955i	0.916557	+	0.665918i
$299$	−22.0461			−1.27496
$300$	−2.91622	−	1.71183i	−0.168368	−	0.0988323i
$301$	−10.7676	+	3.49859i	−0.620632	+	0.201655i
$302$	19.7494	−	14.3488i	1.13645	−	0.825681i
$303$	18.8060	+	4.13925i	1.08037	+	0.237794i
$304$	−11.2517	+	8.17483i	−0.645329	+	0.468859i
$305$	−4.97666			−0.284963
$306$	−2.41549	−	1.11745i	−0.138085	−	0.0638804i
$307$	−4.80914	+	3.49405i	−0.274472	+	0.199416i	−0.716503	−	0.697584i	$-0.754258\pi$
$307$	−4.80914	+	3.49405i	−0.274472	+	0.199416i	0.442031	+	0.897000i	$0.354258\pi$
$308$	−4.95173	+	3.59765i	−0.282151	+	0.204995i
$309$	4.24062	+	2.48926i	0.241240	+	0.141609i
$310$	5.52409	−	4.01348i	0.313747	−	0.227951i
$311$	32.3918	+	10.5247i	1.83677	+	0.596802i	0.998685	+	0.0512588i	$0.0163233\pi$
$311$	32.3918	+	10.5247i	1.83677	+	0.596802i	0.838083	+	0.545543i	$0.183677\pi$
$312$	−12.1652	+	10.7958i	−0.688717	+	0.611191i
$313$	2.42972	+	3.34422i	0.137336	+	0.189027i	0.872145	−	0.489247i	$-0.162728\pi$
$313$	2.42972	+	3.34422i	0.137336	+	0.189027i	−0.734809	+	0.678274i	$0.762728\pi$
$314$	−24.0093	−	7.80108i	−1.35492	−	0.440241i
$315$	4.60999	−	4.97379i	0.259743	−	0.280241i
$316$	−0.108374	−	0.333541i	−0.00609652	−	0.0187632i
$317$	−8.37783	−	25.7843i	−0.470546	−	1.44819i	−0.851872	−	0.523750i	$-0.824533\pi$
$317$	−8.37783	−	25.7843i	−0.470546	−	1.44819i	0.381326	−	0.924441i	$-0.375467\pi$
$318$	−2.32497	−	23.7676i	−0.130378	−	1.33282i
$319$	−52.9253	−	17.1965i	−2.96325	−	0.962817i
$320$	−3.18803	−	4.38795i	−0.178216	−	0.245294i
$321$	−7.47643	−	8.42477i	−0.417294	−	0.470225i
$322$	17.7205	+	5.75774i	0.987525	+	0.320866i
$323$	−1.32611	+	0.963479i	−0.0737870	+	0.0536094i
$324$	−0.344875	−	4.53606i	−0.0191597	−	0.252003i
$325$	−12.4038	+	9.01189i	−0.688039	+	0.499890i
$326$	−27.4704	+	19.9584i	−1.52144	+	1.10539i
$327$	−0.617711	−	1.41476i	−0.0341595	−	0.0782365i
$328$	−8.62678			−0.476334
$329$	12.0162	−	8.73024i	0.662472	−	0.481314i
$330$	−3.59108	+	16.3155i	−0.197683	+	0.898137i
$331$	−9.20209	+	6.68571i	−0.505793	+	0.367480i	−0.811225	−	0.584734i	$-0.801199\pi$
$331$	−9.20209	+	6.68571i	−0.505793	+	0.367480i	0.305432	+	0.952214i	$0.401199\pi$
$332$	2.48097	−	0.806115i	0.136161	−	0.0442413i
$333$	−16.5627	+	3.27167i	−0.907632	+	0.179286i
$334$	−30.1357			−1.64895
$335$	−0.227965	−	0.165626i	−0.0124550	−	0.00904911i
$336$	15.9989	−	6.98540i	0.872811	−	0.381085i
$337$	−6.87513	+	21.1595i	−0.374512	+	1.15263i	0.569295	+	0.822133i	$0.307216\pi$
$337$	−6.87513	+	21.1595i	−0.374512	+	1.15263i	−0.943807	+	0.330497i	$0.892784\pi$
$338$	−1.34844	−	4.15008i	−0.0733457	−	0.225735i
$339$	2.11086	+	21.5788i	0.114646	+	1.17200i
$340$	0.177600	+	0.244446i	0.00963174	+	0.0132569i
$341$	18.6946	+	13.5824i	1.01237	+	0.735528i
$342$	−12.6044	−	5.83103i	−0.681570	−	0.315306i
$343$	11.8448	−	16.3030i	0.639560	−	0.880279i
$344$	−10.2233	+	7.42766i	−0.551203	+	0.400473i
$345$	9.40271	−	4.10539i	0.506225	−	0.221027i
$346$	−14.7590	−	4.79549i	−0.793449	−	0.257807i
$347$	10.2398	−	14.0939i	0.549701	−	0.756598i	−0.440271	−	0.897865i	$-0.645118\pi$
$347$	10.2398	−	14.0939i	0.549701	−	0.756598i	0.989972	+	0.141267i	$0.0451176\pi$
$348$	−7.35411	−	4.31688i	−0.394221	−	0.231409i
$349$			13.8176i			0.739638i	0.929104	+	0.369819i	$0.120580\pi$
$349$			13.8176i			0.739638i	−0.929104	+	0.369819i	$0.879420\pi$
$350$	12.3237	−	4.00422i	0.658731	−	0.214035i
$351$	−19.4741	−	6.79652i	−1.03945	−	0.362772i
$352$	−9.38909	+	12.9230i	−0.500440	+	0.688797i
$353$	0.609344	+	1.87537i	0.0324321	+	0.0998158i	0.965962	−	0.258683i	$-0.0832886\pi$
$353$	0.609344	+	1.87537i	0.0324321	+	0.0998158i	−0.933530	+	0.358499i	$0.883289\pi$
$354$	4.32652	−	1.88904i	0.229952	−	0.100401i
$355$	−16.0286			−0.850708
$356$	−0.227296	+	0.699545i	−0.0120467	+	0.0370758i
$357$	1.88561	−	0.823293i	0.0997973	−	0.0435733i
$358$	−2.20269	−	0.715696i	−0.116416	−	0.0378257i
$359$		−	14.8863i		−	0.785671i	−0.919609	−	0.392836i	$-0.871494\pi$
$359$		−	14.8863i		−	0.785671i	0.919609	−	0.392836i	$-0.128506\pi$
$360$	3.17810	−	6.86981i	0.167500	−	0.362071i
$361$	8.45145	−	6.14033i	0.444813	−	0.323176i
$362$	0.882757	−	1.21501i	0.0463967	−	0.0638596i
$363$	−37.3057	+	3.64928i	−1.95804	+	0.191537i
$364$			4.25256i			0.222895i
$365$	−3.01324	+	4.14737i	−0.157720	+	0.217083i
$366$	−1.24544	−	12.7318i	−0.0651001	−	0.665502i
$367$	−30.3411	+	9.85842i	−1.58379	+	0.514605i	−0.963030	−	0.269394i	$-0.913177\pi$
$367$	−30.3411	+	9.85842i	−1.58379	+	0.514605i	−0.620762	+	0.783999i	$0.713177\pi$
$368$	26.4111			1.37678
$369$	−5.33285	−	9.55223i	−0.277617	−	0.497269i
$370$	9.03560	+	2.93584i	0.469738	+	0.152627i
$371$	14.9360	+	10.8517i	0.775440	+	0.563390i
$372$	2.35034	+	2.64847i	0.121860	+	0.137317i
$373$	8.48674	+	11.6810i	0.439427	+	0.604819i	0.970085	−	0.242767i	$-0.0780550\pi$
$373$	8.48674	+	11.6810i	0.439427	+	0.604819i	−0.530658	+	0.847586i	$0.678055\pi$
$374$	−2.97919	+	4.10051i	−0.154051	+	0.212032i
$375$	8.28795	−	14.1191i	0.427988	−	0.729107i
$376$	9.74426	−	13.4118i	0.502522	−	0.691662i
$377$	−31.2799	+	22.7262i	−1.61100	+	1.17046i
$378$	13.8781	+	10.5490i	0.713814	+	0.542583i
$379$		−	16.2891i		−	0.836715i	−0.908282	−	0.418358i	$-0.862606\pi$
$379$		−	16.2891i		−	0.836715i	0.908282	−	0.418358i	$-0.137394\pi$
$380$	0.926747	+	1.27556i	0.0475411	+	0.0654348i
$381$	0.186062	+	1.90207i	0.00953226	+	0.0974460i
$382$	−0.511677			−0.0261797
$383$	−20.0870	+	27.6474i	−1.02640	+	1.41272i	−0.118782	+	0.992920i	$0.537899\pi$
$383$	−20.0870	+	27.6474i	−1.02640	+	1.41272i	−0.907618	+	0.419798i	$0.862101\pi$
$384$	17.6720	−	15.6827i	0.901819	−	0.800305i
$385$	−7.59128	−	10.4485i	−0.386888	−	0.532505i
$386$	−22.2710	+	16.1808i	−1.13356	+	0.823583i
$387$	−14.5443	−	6.72843i	−0.739326	−	0.342025i
$388$		−	2.29183i		−	0.116350i
$389$			20.3301i			1.03078i	0.856957	+	0.515388i	$0.172352\pi$
$389$			20.3301i			1.03078i	−0.856957	+	0.515388i	$0.827648\pi$
$390$	7.70427	+	8.68151i	0.390121	+	0.439605i
$391$	3.11279			0.157421
$392$	1.83328	−	5.64227i	0.0925949	−	0.284978i
$393$	−14.2213	−	8.34797i	−0.717372	−	0.421099i
$394$	−10.0753	+	31.0086i	−0.507586	+	1.56219i
$395$	0.703795	−	0.228677i	0.0354118	−	0.0115060i
$396$	−8.60207	−	1.02971i	−0.432270	−	0.0517448i
$397$	31.9021	−	10.3656i	1.60112	−	0.520236i	0.633737	−	0.773548i	$-0.281520\pi$
$397$	31.9021	−	10.3656i	1.60112	−	0.520236i	0.967385	+	0.253312i	$0.0815201\pi$
$398$	9.78667	−	30.1203i	0.490561	−	1.50979i
$399$	9.83943	−	4.29608i	0.492588	−	0.215073i
$400$	14.8597	−	10.7962i	0.742986	−	0.539811i
$401$	−11.5540	−	8.39445i	−0.576978	−	0.419199i	0.260656	−	0.965432i	$-0.416061\pi$
$401$	−11.5540	−	8.39445i	−0.576978	−	0.419199i	−0.837633	+	0.546233i	$0.816061\pi$
$402$	0.366672	−	0.624651i	0.0182879	−	0.0311548i
$403$	15.2692	−	4.96125i	0.760611	−	0.247137i
$404$	3.30304	−	4.54625i	0.164332	−	0.226184i
$405$	9.57140	−	0.727710i	0.475607	−	0.0361602i
$406$	31.0779	−	10.0978i	1.54237	−	0.501147i
$407$			32.1518i			1.59371i
$408$	1.71766	−	1.52431i	0.0850368	−	0.0754646i
$409$	18.1470	−	5.89632i	0.897311	−	0.291554i	0.176185	−	0.984357i	$-0.443624\pi$
$409$	18.1470	−	5.89632i	0.897311	−	0.291554i	0.721127	+	0.692803i	$0.243624\pi$
$410$			6.15639i			0.304042i
$411$	−3.35972	−	34.3456i	−0.165723	−	1.69414i
$412$	1.16093	−	0.843465i	0.0571949	−	0.0415546i
$413$	−1.12781	+	3.47103i	−0.0554958	+	0.170798i
$414$	12.8559	+	23.0276i	0.631834	+	1.13174i
$415$	1.70096	+	5.23501i	0.0834968	+	0.256977i
$416$	3.42956	+	10.5551i	0.168148	+	0.517506i
$417$	37.3979	−	3.65830i	1.83138	−	0.179148i
$418$	−15.5459	+	21.3971i	−0.760375	+	1.04657i
$419$	1.37290	+	1.88963i	0.0670705	+	0.0923147i	0.841234	−	0.540670i	$-0.181829\pi$
$419$	1.37290	+	1.88963i	0.0670705	+	0.0923147i	−0.774164	+	0.632985i	$0.781829\pi$
$420$	−0.791906	−	1.81373i	−0.0386411	−	0.0885009i
$421$			9.34873i			0.455629i	0.973705	+	0.227815i	$0.0731580\pi$
$421$			9.34873i			0.455629i	−0.973705	+	0.227815i	$0.926842\pi$
$422$	20.8955	−	9.59326i	1.01718	−	0.466992i
$423$	20.8743	+	2.49875i	1.01494	+	0.121493i
$424$	19.5978	+	6.36770i	0.951751	+	0.309243i
$425$	1.75135	−	1.27243i	0.0849532	−	0.0617221i
$426$	−4.01124	−	41.0059i	−0.194345	−	1.98674i
$427$	8.00092	+	5.81301i	0.387191	+	0.281311i
$428$	−3.12622	+	1.01577i	−0.151112	+	0.0490991i
$429$	−19.8850	+	33.8755i	−0.960058	+	1.63553i
$430$	5.30065	+	7.29573i	0.255620	+	0.351831i
$431$	17.3192	+	5.62735i	0.834236	+	0.271060i	0.694829	−	0.719175i	$-0.255480\pi$
$431$	17.3192	+	5.62735i	0.834236	+	0.271060i	0.139408	+	0.990235i	$0.455480\pi$
$432$	23.3299	+	8.14222i	1.12246	+	0.391743i
$433$	27.8982	+	20.2692i	1.34070	+	0.974077i	0.999418	+	0.0341172i	$0.0108619\pi$
$433$	27.8982	+	20.2692i	1.34070	+	0.974077i	0.341284	+	0.939960i	$0.389138\pi$
$434$	−13.5690			−0.651331
$435$	9.10892	−	15.5177i	0.436739	−	0.744016i
$436$	−0.450505			−0.0215753
$437$	16.2430			0.777010
$438$	−11.3643	−	6.67087i	−0.543007	−	0.318747i
$439$	19.2415	−	6.25193i	0.918345	−	0.298388i	0.188557	−	0.982062i	$-0.439619\pi$
$439$	19.2415	−	6.25193i	0.918345	−	0.298388i	0.729788	+	0.683674i	$0.239619\pi$
$440$	−11.6621	−	8.47301i	−0.555969	−	0.403935i
$441$	7.38084	−	1.45795i	0.351469	−	0.0694264i
$442$	1.08821	+	3.34917i	0.0517610	+	0.159304i
$443$	−9.09767	+	12.5219i	−0.432244	+	0.594932i	−0.968466	−	0.249144i	$-0.919851\pi$
$443$	−9.09767	+	12.5219i	−0.432244	+	0.594932i	0.536223	+	0.844076i	$0.319851\pi$
$444$	−1.05907	+	4.81169i	−0.0502611	+	0.228353i
$445$	−1.47609	−	0.479611i	−0.0699734	−	0.0227357i
$446$	−24.3391	−	7.90827i	−1.15249	−	0.374467i
$447$	−18.4559	−	10.8337i	−0.872933	−	0.512414i
$448$			10.7782i			0.509224i
$449$	4.04724	+	12.4561i	0.191001	+	0.587841i	1.00000		3.06037e-5i	$9.74146e-6\pi$
$449$	4.04724	+	12.4561i	0.191001	+	0.587841i	−0.808999	+	0.587810i	$0.799990\pi$
$450$	16.6462	+	7.70085i	0.784712	+	0.363021i
$451$	−19.8147	+	6.43818i	−0.933037	+	0.303162i
$452$	6.01768	+	1.95526i	0.283048	+	0.0919679i
$453$	−19.9796	+	17.7306i	−0.938722	+	0.833054i
$454$		−	32.8246i		−	1.54054i
$455$	−8.97320			−0.420670
$456$	8.96302	−	7.95409i	0.419732	−	0.372484i
$457$	−27.4950	−	8.93367i	−1.28616	−	0.417899i	−0.415416	−	0.909632i	$-0.636364\pi$
$457$	−27.4950	−	8.93367i	−1.28616	−	0.417899i	−0.870746	+	0.491732i	$0.836364\pi$
$458$	20.9504	+	28.8357i	0.978946	+	1.34740i
$459$	2.74965	+	0.959634i	0.128342	+	0.0447919i
$460$		−	2.99412i		−	0.139602i
$461$	−31.2395	−	22.6968i	−1.45497	−	1.05710i	−0.984639	−	0.174604i	$-0.944136\pi$
$461$	−31.2395	−	22.6968i	−1.45497	−	1.05710i	−0.470328	−	0.882492i	$-0.655864\pi$
$462$	24.8307	−	22.0356i	1.15523	−	1.02519i
$463$	−23.2655	+	32.0222i	−1.08124	+	1.48820i	−0.223088	+	0.974798i	$0.571614\pi$
$463$	−23.2655	+	32.0222i	−1.08124	+	1.48820i	−0.858150	+	0.513399i	$0.828386\pi$
$464$	37.4732	−	27.2259i	1.73965	−	1.26393i
$465$	−5.58846	+	4.95939i	−0.259158	+	0.229986i
$466$	2.22409	+	6.84505i	0.103029	+	0.317091i
$467$	7.61555	+	10.4819i	0.352406	+	0.485045i	0.948013	−	0.318231i	$-0.103089\pi$
$467$	7.61555	+	10.4819i	0.352406	+	0.485045i	−0.595608	+	0.803275i	$0.703089\pi$
$468$	−4.09175	+	4.41465i	−0.189141	+	0.204067i
$469$	0.173036	+	0.532549i	0.00799005	+	0.0245908i
$470$	−9.57117	−	6.95387i	−0.441485	−	0.320758i
$471$	26.9784	+	5.93803i	1.24310	+	0.273610i
$472$			4.07357i			0.187501i
$473$	−17.9384	+	24.6901i	−0.824810	+	1.13525i
$474$	0.761153	+	1.74329i	0.0349609	+	0.0800721i
$475$	9.13884	−	6.63976i	0.419319	−	0.304653i
$476$		−	0.600440i		−	0.0275211i
$477$	5.06403	+	25.6365i	0.231866	+	1.17381i
$478$	16.2573	+	11.8116i	0.743593	+	0.540252i
$479$	−10.4102	−	7.56349i	−0.475656	−	0.345585i	0.323985	−	0.946062i	$-0.394977\pi$
$479$	−10.4102	−	7.56349i	−0.475656	−	0.345585i	−0.799642	+	0.600478i	$0.794977\pi$
$480$	−3.42827	−	3.86313i	−0.156478	−	0.176327i
$481$	18.0723	+	13.1303i	0.824027	+	0.598691i
$482$	−26.3752	−	19.1627i	−1.20136	−	0.872838i
$483$	−19.9119	−	4.38268i	−0.906024	−	0.199419i
$484$	−3.38028	+	10.4034i	−0.153649	+	0.472883i
$485$	4.83593			0.219588
$486$	4.25700	+	24.3044i	0.193101	+	1.10247i
$487$	−1.14166	+	3.51368i	−0.0517338	+	0.159220i	−0.973586	−	0.228322i	$-0.926676\pi$
$487$	−1.14166	+	3.51368i	−0.0517338	+	0.159220i	0.921852	+	0.387543i	$0.126676\pi$
$488$	10.4981	+	3.41104i	0.475227	+	0.154411i
$489$	27.7905	−	24.6622i	1.25673	−	1.11526i
$490$	−4.02653	−	1.30830i	−0.181900	−	0.0591030i
$491$	−38.9476	+	12.6548i	−1.75768	+	0.571105i	−0.996956	−	0.0779690i	$-0.975156\pi$
$491$	−38.9476	+	12.6548i	−1.75768	+	0.571105i	−0.760725	+	0.649074i	$0.775156\pi$
$492$	−3.17744	+	0.310821i	−0.143250	+	0.0140129i
$493$	4.41656	−	3.20882i	0.198912	−	0.144518i
$494$	5.67846	+	17.4765i	0.255486	+	0.786305i
$495$	2.17276	−	18.1510i	0.0976581	−	0.815825i
$496$	−18.2924	+	5.94356i	−0.821353	+	0.266874i
$497$	25.7689	+	18.7222i	1.15589	+	0.839806i
$498$	−12.9671	+	5.66166i	−0.581068	+	0.253705i
$499$	−0.381686	−	0.124017i	−0.0170866	−	0.00555177i	0.300461	−	0.953794i	$-0.402859\pi$
$499$	−0.381686	−	0.124017i	−0.0170866	−	0.00555177i	−0.317548	+	0.948242i	$0.602859\pi$
$500$	−2.80831	−	3.86531i	−0.125591	−	0.172862i
$501$	32.8193	−	3.21042i	1.46626	−	0.143431i
$502$	5.11535	−	15.7434i	0.228309	−	0.702663i
$503$	−5.19831	+	7.15485i	−0.231781	+	0.319019i	−0.909027	−	0.416738i	$-0.863173\pi$
$503$	−5.19831	+	7.15485i	−0.231781	+	0.319019i	0.677246	+	0.735757i	$0.263173\pi$
$504$	−13.1337	+	7.33232i	−0.585021	+	0.326608i
$505$	9.59290	+	6.96965i	0.426878	+	0.310145i
$506$	47.7673	−	15.5205i	2.12352	−	0.689972i
$507$	1.91064	+	4.37601i	0.0848546	+	0.194345i
$508$	0.530430	+	0.172347i	0.0235340	+	0.00764667i
$509$	−12.1048	+	16.6608i	−0.536534	+	0.738476i	−0.988109	−	0.153757i	$-0.950863\pi$
$509$	−12.1048	+	16.6608i	−0.536534	+	0.738476i	0.451574	+	0.892234i	$0.350863\pi$
$510$	−1.08780	−	1.22578i	−0.0481688	−	0.0542787i
$511$	9.68869	−	3.14804i	0.428602	−	0.139261i
$512$	2.84410	+	8.75323i	0.125693	+	0.386842i
$513$	14.3481	+	5.00753i	0.633483	+	0.221088i
$514$	10.4798	+	14.4242i	0.462243	+	0.636223i
$515$	1.77977	+	2.44964i	0.0784261	+	0.107944i
$516$	−3.49786	+	3.10412i	−0.153985	+	0.136651i
$517$	12.3721	−	38.0775i	0.544126	−	1.67465i
$518$	−11.0972	−	15.2740i	−0.487583	−	0.671100i
$519$	16.5842	+	3.65023i	0.727966	+	0.160228i
$520$	−9.52524	+	3.09494i	−0.417710	+	0.135722i
$521$	−8.60738	−	11.8470i	−0.377096	−	0.519029i	0.577716	−	0.816238i	$-0.303944\pi$
$521$	−8.60738	−	11.8470i	−0.377096	−	0.519029i	−0.954812	+	0.297209i	$0.903944\pi$
$522$	41.9785	+	19.4200i	1.83735	+	0.849989i
$523$	−8.29999			−0.362933			−0.181467	−	0.983397i	$-0.558084\pi$
$523$	−8.29999			−0.362933			−0.181467	+	0.983397i	$0.558084\pi$
$524$	−3.89330	+	2.82865i	−0.170079	+	0.123570i
$525$	−12.9946	+	5.67368i	−0.567131	+	0.247620i
$526$	−28.1495	+	38.7444i	−1.22738	+	1.68934i
$527$	−2.15593	+	0.700503i	−0.0939136	+	0.0305144i
$528$	23.8222	−	40.5828i	1.03673	−	1.76614i
$529$	−6.34729	−	4.61158i	−0.275969	−	0.200503i
$530$	4.54422	−	13.9857i	0.197388	−	0.607499i
$531$	−4.51057	+	2.51818i	−0.195742	+	0.109280i
$532$		−	3.13319i		−	0.135841i
$533$	−4.47316	+	13.7670i	−0.193754	+	0.596313i
$534$	0.857589	−	3.89631i	0.0371115	−	0.168610i
$535$	−2.14335	−	6.59654i	−0.0926649	−	0.285193i
$536$	0.367362	+	0.505631i	0.0158676	+	0.0218399i
$537$	2.47509	+	0.544774i	0.106808	+	0.0235087i
$538$	−17.2180	−	5.59446i	−0.742320	−	0.241194i
$539$		−	14.3278i		−	0.617143i
$540$	0.923050	−	2.64482i	0.0397217	−	0.113815i
$541$	−15.5794	+	11.3191i	−0.669812	+	0.486647i	−0.869962	−	0.493118i	$-0.835857\pi$
$541$	−15.5794	+	11.3191i	−0.669812	+	0.486647i	0.200150	+	0.979765i	$0.435857\pi$
$542$	9.68573	+	13.3313i	0.416038	+	0.572627i
$543$	−0.831931	+	1.41725i	−0.0357016	+	0.0608201i
$544$	−0.484236	−	1.49032i	−0.0207614	−	0.0638971i
$545$		−	0.950598i		−	0.0407191i
$546$	−2.24559	−	22.9562i	−0.0961025	−	0.982433i
$547$	11.8203	−	36.3791i	0.505399	−	1.55546i	−0.294699	−	0.955590i	$-0.595219\pi$
$547$	11.8203	−	36.3791i	0.505399	−	1.55546i	0.800098	−	0.599869i	$-0.204781\pi$
$548$	−9.57794	−	3.11206i	−0.409149	−	0.132941i
$549$	2.71269	+	13.7329i	0.115775	+	0.586107i
$550$	20.5310	−	28.2584i	0.875443	−	1.20494i
$551$	23.0463	−	16.7441i	0.981806	−	0.713324i
$552$	−22.6486	+	2.21551i	−0.963987	+	0.0942982i
$553$	−1.39859	−	0.454429i	−0.0594741	−	0.0193243i
$554$	−31.7433	−	23.0629i	−1.34864	−	0.979847i
$555$	−10.1530	−	2.23471i	−0.430971	−	0.0948580i
$556$	3.38864	−	10.4292i	0.143710	−	0.442295i
$557$	−0.331298	+	1.01963i	−0.0140376	+	0.0432032i	−0.957830	−	0.287336i	$-0.907230\pi$
$557$	−0.331298	+	1.01963i	−0.0140376	+	0.0432032i	0.943792	+	0.330539i	$0.107230\pi$
$558$	−14.0862	−	13.0558i	−0.596315	−	0.552698i
$559$	6.55238	+	20.1661i	0.277136	+	0.852937i
$560$	10.7499			0.454265
$561$	2.80766	−	4.78305i	0.118540	−	0.201941i
$562$	12.7922	+	17.6069i	0.539605	+	0.742702i
$563$	1.30707	+	0.949645i	0.0550866	+	0.0400228i	0.614988	−	0.788537i	$-0.289161\pi$
$563$	1.30707	+	0.949645i	0.0550866	+	0.0400228i	−0.559901	+	0.828559i	$0.689161\pi$
$564$	3.10582	−	5.29097i	0.130778	−	0.222790i
$565$	−4.12574	+	12.6977i	−0.173571	+	0.534198i
$566$			23.6807i			0.995376i
$567$	−16.2378	−	10.0100i	−0.681924	−	0.420379i
$568$	33.8117	+	10.9861i	1.41871	+	0.460966i
$569$	0.352568	−	1.08509i	0.0147804	−	0.0454895i	−0.943394	−	0.331673i	$-0.892387\pi$
$569$	0.352568	−	1.08509i	0.0147804	−	0.0454895i	0.958175	+	0.286184i	$0.0923868\pi$
$570$	−5.67633	−	6.39634i	−0.237755	−	0.267913i
$571$	18.3790	+	5.97171i	0.769138	+	0.249908i	0.667196	−	0.744882i	$-0.267494\pi$
$571$	18.3790	+	5.97171i	0.769138	+	0.249908i	0.101942	+	0.994790i	$0.467494\pi$
$572$	6.73789	+	9.27391i	0.281725	+	0.387762i
$573$	0.557243	−	0.0545100i	0.0232791	−	0.00227719i
$574$	7.19099	−	9.89755i	0.300146	−	0.413116i
$575$	−21.4516			−0.894595
$576$	−10.3707	+	11.1891i	−0.432110	+	0.466211i
$577$	−14.9086	+	20.5200i	−0.620655	+	0.854258i	−0.997400	−	0.0720584i	$-0.977043\pi$
$577$	−14.9086	+	20.5200i	−0.620655	+	0.854258i	0.376745	+	0.926317i	$0.377043\pi$
$578$	8.16160	+	25.1188i	0.339478	+	1.04480i
$579$	22.5305	−	19.9944i	0.936336	−	0.830937i
$580$	−3.08649	−	4.24819i	−0.128159	−	0.176396i
$581$	3.38016	−	10.4031i	0.140233	−	0.431592i
$582$	1.21022	+	12.3718i	0.0501651	+	0.512826i
$583$	49.7659			2.06109
$584$	9.19896	−	6.68344i	0.380656	−	0.276563i
$585$	−9.31522	−	8.63387i	−0.385137	−	0.356967i
$586$	14.4404	−	4.69198i	0.596528	−	0.193824i
$587$	−18.3356	−	13.3216i	−0.756789	−	0.549840i	0.141135	−	0.989990i	$-0.454925\pi$
$587$	−18.3356	−	13.3216i	−0.756789	−	0.549840i	−0.897924	+	0.440151i	$0.854925\pi$
$588$	0.471952	−	2.14423i	0.0194630	−	0.0884267i
$589$	−11.2500	+	3.65534i	−0.463547	+	0.150615i
$590$	2.90705			0.119681
$591$	7.66912	−	34.8433i	0.315465	−	1.43326i
$592$	−21.6506	−	15.7301i	−0.889834	−	0.646502i
$593$		−	1.65769i		−	0.0680730i	−0.999421	−	0.0340365i	$-0.989164\pi$
$593$		−	1.65769i		−	0.0680730i	0.999421	−	0.0340365i	$-0.0108362\pi$
$594$	46.9794	+	1.01619i	1.92759	+	0.0416947i
$595$	1.26697			0.0519407
$596$	−5.05256	+	3.67090i	−0.206961	+	0.150366i
$597$	−7.44942	+	33.8452i	−0.304884	+	1.38519i
$598$	10.7834	−	33.1880i	0.440968	−	1.35716i
$599$	33.9667			1.38784			0.693920	−	0.720052i	$-0.255882\pi$
$599$	33.9667			1.38784			0.693920	+	0.720052i	$0.255882\pi$
$600$	−11.8371	+	10.5047i	−0.483250	+	0.428852i
$601$	27.4715			1.12059			0.560293	−	0.828295i	$-0.310689\pi$
$601$	27.4715			1.12059			0.560293	+	0.828295i	$0.310689\pi$
$602$		−	17.9207i		−	0.730393i
$603$	−0.332779	+	0.719340i	−0.0135518	+	0.0292938i
$604$	2.40893	+	7.41391i	0.0980178	+	0.301668i
$605$	−21.9519	−	7.13262i	−0.892474	−	0.289982i
$606$	−15.4298	+	26.2857i	−0.626793	+	1.06778i
$607$	−6.47484			−0.262806			−0.131403	−	0.991329i	$-0.541948\pi$
$607$	−6.47484			−0.262806			−0.131403	+	0.991329i	$0.541948\pi$
$608$	−2.52682	−	7.77675i	−0.102476	−	0.315389i
$609$	−32.7698	+	14.3079i	−1.32790	+	0.579784i
$610$	2.43425	−	7.49184i	0.0985597	−	0.303336i
$611$	−16.3505	−	22.5046i	−0.661472	−	0.910438i
$612$	0.577733	−	0.623326i	0.0233535	−	0.0251964i
$613$	−17.8107	+	5.78705i	−0.719368	+	0.233737i	−0.645749	−	0.763550i	$-0.723455\pi$
$613$	−17.8107	+	5.78705i	−0.719368	+	0.233737i	−0.0736186	+	0.997286i	$0.523455\pi$
$614$	−2.90761	−	8.94870i	−0.117342	−	0.361140i
$615$	−0.655853	−	6.70463i	−0.0264466	−	0.270357i
$616$	8.85208	+	27.2439i	0.356660	+	1.09769i
$617$	−7.03024	−	21.6368i	−0.283027	−	0.871067i	−0.986983	−	0.160823i	$-0.948585\pi$
$617$	−7.03024	−	21.6368i	−0.283027	−	0.871067i	0.703957	−	0.710243i	$-0.251415\pi$
$618$	−5.82153	+	5.16623i	−0.234176	+	0.207816i
$619$		−	25.9212i		−	1.04186i	−0.853599	−	0.520931i	$-0.825585\pi$
$619$		−	25.9212i		−	1.04186i	0.853599	−	0.520931i	$-0.174415\pi$
$620$	0.673797	+	2.07373i	0.0270603	+	0.0832832i
$621$	−16.4539	−	23.7087i	−0.660274	−	0.951396i
$622$	−31.6877	+	43.6144i	−1.27056	+	1.74878i
$623$	1.81288	+	2.49522i	0.0726315	+	0.0999687i
$624$	−13.0827	−	29.9637i	−0.523727	−	1.19951i
$625$	−7.46789	+	5.42574i	−0.298715	+	0.217029i
$626$	−6.22282	+	2.02192i	−0.248714	+	0.0808121i
$627$	14.6508	−	24.9587i	0.585098	−	0.996755i
$628$	4.73844	−	6.52190i	0.189084	−	0.260252i
$629$	−2.55172	−	1.85393i	−0.101744	−	0.0739211i
$630$	5.23262	+	9.37269i	0.208472	+	0.373417i
$631$	−4.00442	+	12.3243i	−0.159413	+	0.490624i	−0.998581	−	0.0532486i	$-0.983042\pi$
$631$	−4.00442	+	12.3243i	−0.159413	+	0.490624i	0.839168	+	0.543872i	$0.183042\pi$
$632$	−1.64137			−0.0652902
$633$	−21.7343	+	12.6736i	−0.863861	+	0.503730i
$634$	42.9134			1.70431
$635$	−0.363664	+	1.11924i	−0.0144316	+	0.0444158i
$636$	7.44774	+	1.63927i	0.295322	+	0.0650013i
$637$	−8.05357	−	5.85126i	−0.319094	−	0.231835i
$638$	51.7749	−	71.2621i	2.04979	−	2.82129i
$639$	8.73689	+	44.2303i	0.345626	+	1.74972i
$640$	13.8370	−	4.49593i	0.546957	−	0.177717i
$641$	−6.78829	+	4.93198i	−0.268121	+	0.194802i	−0.713720	−	0.700431i	$-0.752991\pi$
$641$	−6.78829	+	4.93198i	−0.268121	+	0.194802i	0.445598	+	0.895233i	$0.352991\pi$
$642$	16.3396	−	7.13415i	0.644871	−	0.281562i
$643$	−15.8477	−	21.8124i	−0.624971	−	0.860199i	0.372732	−	0.927939i	$-0.378421\pi$
$643$	−15.8477	−	21.8124i	−0.624971	−	0.860199i	−0.997703	+	0.0677402i	$0.978421\pi$
$644$	−3.49729	+	4.81361i	−0.137813	+	0.189683i
$645$	−6.54992	−	7.38074i	−0.257903	−	0.290616i
$646$	−0.801770	−	2.46759i	−0.0315452	−	0.0970862i
$647$		−	6.72025i		−	0.264200i	−0.991236	−	0.132100i	$-0.957828\pi$
$647$		−	6.72025i		−	0.264200i	0.991236	−	0.132100i	$-0.0421720\pi$
$648$	−20.6893	−	5.02523i	−0.812754	−	0.197410i
$649$	3.04011	+	9.35651i	0.119335	+	0.367275i
$650$	−7.49935	−	23.0806i	−0.294149	−	0.905297i
$651$	14.7773	−	1.44553i	0.579169	−	0.0566549i
$652$	−3.35068	−	10.3123i	−0.131223	−	0.403862i
$653$	−5.34923	+	1.73807i	−0.209331	+	0.0680159i	−0.411806	−	0.911272i	$-0.635102\pi$
$653$	−5.34923	+	1.73807i	−0.209331	+	0.0680159i	0.202474	+	0.979288i	$0.435102\pi$
$654$	2.43192	−	0.237892i	0.0950954	−	0.00930233i
$655$	−5.96864	−	8.21513i	−0.233214	−	0.320992i
$656$	5.35883	−	16.4928i	0.209227	−	0.643935i
$657$	13.0870	+	6.05427i	0.510571	+	0.236199i
$658$	7.26497	+	22.3593i	0.283218	+	0.871656i
$659$	−15.2966			−0.595873			−0.297936	−	0.954586i	$-0.596298\pi$
$659$	−15.2966			−0.595873			−0.297936	+	0.954586i	$0.596298\pi$
$660$	−4.60070	−	2.70063i	−0.179082	−	0.105122i
$661$	−15.3650	−	4.99238i	−0.597627	−	0.194181i	−0.00544542	−	0.999985i	$-0.501733\pi$
$661$	−15.3650	−	4.99238i	−0.597627	−	0.194181i	−0.592182	+	0.805804i	$0.701733\pi$
$662$	−5.56359	−	17.1230i	−0.216235	−	0.665503i
$663$	−1.54191	−	3.53149i	−0.0598830	−	0.137152i
$664$		−	12.2089i		−	0.473799i
$665$	6.61125			0.256373
$666$	3.17621	−	26.5337i	0.123076	−	1.02816i
$667$	−54.0967			−2.09463
$668$	2.97377	−	9.15232i	0.115059	−	0.354114i
$669$	27.3491	+	6.01962i	1.05738	+	0.232732i
$670$	0.360837	−	0.262163i	0.0139404	−	0.0101283i
$671$	26.6586			1.02914
$672$	0.999251	+	10.2151i	0.0385469	+	0.394056i
$673$		−	1.62326i		−	0.0625720i	−0.999510	−	0.0312860i	$-0.990040\pi$
$673$		−	1.62326i		−	0.0625720i	0.999510	−	0.0312860i	$-0.00996027\pi$
$674$	−28.4905	−	20.6996i	−1.09741	−	0.797317i
$675$	−18.9490	−	6.61327i	−0.729348	−	0.254545i
$676$	1.39346			0.0535946
$677$	9.93287	−	3.22738i	0.381751	−	0.124038i	−0.111854	−	0.993725i	$-0.535679\pi$
$677$	9.93287	−	3.22738i	0.381751	−	0.124038i	0.493605	+	0.869686i	$0.335679\pi$
$678$	−33.5171	−	7.37722i	−1.28722	−	0.283320i
$679$	−7.77466	−	5.64862i	−0.298364	−	0.216774i
$680$	1.34492	−	0.436990i	0.0515752	−	0.0167578i
$681$	3.49688	+	35.7477i	0.134001	+	1.36986i
$682$	−29.5910	+	21.4991i	−1.13310	+	0.823243i
$683$	−12.9892			−0.497018			−0.248509	−	0.968630i	$-0.579940\pi$
$683$	−12.9892			−0.497018			−0.248509	+	0.968630i	$0.579940\pi$
$684$	3.01471	−	3.25261i	0.115270	−	0.124367i
$685$	6.56667	−	20.2101i	0.250900	−	0.772189i
$686$	18.7487	+	25.8054i	0.715830	+	0.985256i
$687$	−25.8880	−	29.1717i	−0.987687	−	1.11297i
$688$	−7.84973	−	24.1590i	−0.299268	−	0.921053i
$689$	20.3236	−	27.9731i	0.774269	−	1.06569i
$690$	1.58107	+	16.1629i	0.0601902	+	0.615310i
$691$	43.3044			1.64738			0.823689	−	0.567043i	$-0.191913\pi$
$691$	43.3044			1.64738			0.823689	+	0.567043i	$0.191913\pi$
$692$	2.91282	−	4.00915i	0.110729	−	0.152405i
$693$	−24.6944	+	26.6432i	−0.938063	+	1.01209i
$694$	16.2082	+	22.3087i	0.615255	+	0.846826i
$695$	22.0062	+	7.15026i	0.834744	+	0.271225i
$696$	−29.8509	+	26.4907i	−1.13150	+	1.00413i
$697$	0.631587	−	1.94382i	0.0239231	−	0.0736276i
$698$	−20.8009	−	6.75863i	−0.787326	−	0.255818i
$699$	−3.15137	−	7.21768i	−0.119196	−	0.272998i
$700$			4.13790i			0.156398i
$701$	5.31231	−	16.3496i	0.200643	−	0.617516i	−0.799221	−	0.601037i	$-0.794754\pi$
$701$	5.31231	−	16.3496i	0.200643	−	0.617516i	0.999864	−	0.0164791i	$-0.00524568\pi$
$702$	19.7569	−	25.9918i	0.745675	−	0.980998i
$703$	−13.3153	−	9.67411i	−0.502195	−	0.364866i
$704$	17.0774	+	23.5050i	0.643628	+	0.885878i
$705$	11.1643	+	6.55349i	0.420473	+	0.246819i
$706$	−3.12122			−0.117469
$707$	−7.28146	−	22.4100i	−0.273848	−	0.842816i
$708$	0.146770	+	1.50039i	0.00551594	+	0.0563882i
$709$	−2.13555	+	6.57254i	−0.0802021	+	0.246837i	−0.983116	−	0.182986i	$-0.941424\pi$
$709$	−2.13555	+	6.57254i	−0.0802021	+	0.246837i	0.902913	+	0.429822i	$0.141424\pi$
$710$	7.84008	−	24.1293i	0.294233	−	0.905556i
$711$	−1.01465	−	1.81745i	−0.0380524	−	0.0681597i
$712$	2.78503	+	2.02345i	0.104374	+	0.0758318i
$713$	21.3638	+	6.94151i	0.800080	+	0.259962i
$714$	0.317066	+	3.24129i	0.0118659	+	0.121302i
$715$	−19.5686	+	14.2174i	−0.731824	+	0.531701i
$716$	0.434719	−	0.598340i	0.0162462	−	0.0223610i
$717$	−18.9634	−	11.1316i	−0.708201	−	0.415716i
$718$	22.4098	+	7.28139i	0.836327	+	0.271739i
$719$	−9.64671	+	29.6895i	−0.359762	+	1.10723i	0.593435	+	0.804882i	$0.297771\pi$
$719$	−9.64671	+	29.6895i	−0.359762	+	1.10723i	−0.953197	+	0.302351i	$0.902229\pi$
$720$	11.1596	+	10.3433i	0.415894	+	0.385474i
$721$		−	6.01713i		−	0.224090i
$722$	5.10975	+	15.7262i	0.190165	+	0.585268i
$723$	30.7654	+	18.0594i	1.14418	+	0.671636i
$724$	0.281894	+	0.387993i	0.0104765	+	0.0144197i
$725$	−30.4365	+	22.1134i	−1.13038	+	0.821271i
$726$	12.7538	−	57.9447i	0.473338	−	2.15053i
$727$			32.7576i			1.21491i	0.794354	+	0.607456i	$0.207810\pi$
$727$			32.7576i			1.21491i	−0.794354	+	0.607456i	$0.792190\pi$
$728$	18.9287	+	6.15030i	0.701543	+	0.227945i
$729$	−7.22530	−	26.0153i	−0.267604	−	0.963529i
$730$	−4.76955	−	6.56472i	−0.176529	−	0.242971i
$731$	−0.925162	−	2.84736i	−0.0342184	−	0.105313i
$732$	3.98960	+	0.878122i	0.147460	+	0.0324563i
$733$	−11.9722	+	36.8466i	−0.442203	+	1.36096i	0.443320	+	0.896363i	$0.353801\pi$
$733$	−11.9722	+	36.8466i	−0.442203	+	1.36096i	−0.885523	+	0.464596i	$0.846199\pi$
$734$		−	50.4974i		−	1.86389i
$735$	4.52448	+	0.995852i	0.166888	+	0.0367326i
$736$	−4.79845	+	14.7681i	−0.176873	+	0.544360i
$737$	1.22114	+	0.887211i	0.0449813	+	0.0326808i
$738$	16.9883	−	3.35574i	0.625349	−	0.123527i
$739$	6.14342	−	1.99612i	0.225989	−	0.0734284i	−0.193834	−	0.981034i	$-0.562092\pi$
$739$	6.14342	−	1.99612i	0.225989	−	0.0734284i	0.419823	+	0.907606i	$0.362092\pi$
$740$	−1.78325	+	2.45444i	−0.0655537	+	0.0902270i
$741$	−8.04595	−	18.4279i	−0.295575	−	0.676966i
$742$	−23.6417	+	17.1767i	−0.867914	+	0.630577i
$743$	−16.6812			−0.611975			−0.305988	−	0.952036i	$-0.598987\pi$
$743$	−16.6812			−0.611975			−0.305988	+	0.952036i	$0.598987\pi$
$744$	15.1879	−	6.63130i	0.556814	−	0.243115i
$745$	−7.74586	−	10.6613i	−0.283786	−	0.390598i
$746$	−21.7356	+	7.06234i	−0.795799	+	0.258571i
$747$	13.5187	−	7.54725i	0.494622	−	0.276139i
$748$	−0.951356	−	1.30943i	−0.0347850	−	0.0478774i
$749$	−4.25928	+	13.1087i	−0.155631	+	0.478982i
$750$	17.2009	+	19.3827i	0.628088	+	0.707758i
$751$	−2.76343	−	3.80354i	−0.100839	−	0.138793i	0.755616	−	0.655015i	$-0.227338\pi$
$751$	−2.76343	−	3.80354i	−0.100839	−	0.138793i	−0.856455	+	0.516222i	$0.827338\pi$
$752$	19.5879	+	26.9604i	0.714297	+	0.983146i
$753$	−3.89370	+	17.6904i	−0.141894	+	0.644673i
$754$	−18.9118	−	58.2047i	−0.688729	−	2.11969i
$755$	−15.6439	+	5.08300i	−0.569339	+	0.184989i
$756$	−4.57326	+	3.17387i	−0.166328	+	0.115433i
$757$	−11.4735	+	15.7919i	−0.417012	+	0.573967i	−0.964911	−	0.262577i	$-0.915428\pi$
$757$	−11.4735	+	15.7919i	−0.417012	+	0.573967i	0.547899	+	0.836544i	$0.315428\pi$
$758$	24.5215	+	7.96752i	0.890662	+	0.289394i
$759$	−50.3677	+	21.9914i	−1.82823	+	0.798238i
$760$	7.01798	−	2.28028i	0.254569	−	0.0827145i
$761$	3.86511	+	2.80817i	0.140110	+	0.101796i	0.655632	−	0.755080i	$-0.272402\pi$
$761$	3.86511	+	2.80817i	0.140110	+	0.101796i	−0.515522	+	0.856876i	$0.672402\pi$
$762$	−2.95437	−	0.650267i	−0.107026	−	0.0235567i
$763$	−1.11035	+	1.52826i	−0.0401973	+	0.0553269i
$764$	0.0504919	−	0.155398i	0.00182673	−	0.00562211i
$765$	1.31526	+	1.21906i	0.0475534	+	0.0440751i
$766$	−31.7951	−	43.7622i	−1.14880	−	1.58119i
$767$	6.50077	+	2.11223i	0.234729	+	0.0762681i
$768$	7.91582	+	18.1299i	0.285638	+	0.654205i
$769$	−21.3233	−	15.4923i	−0.768938	−	0.558666i	0.132700	−	0.991156i	$-0.457635\pi$
$769$	−21.3233	−	15.4923i	−0.768938	−	0.558666i	−0.901639	+	0.432490i	$0.857635\pi$
$770$	19.4423	−	6.31717i	0.700650	−	0.227655i
$771$	−12.9497	−	14.5923i	−0.466371	−	0.525527i
$772$	−2.71649	−	8.36051i	−0.0977687	−	0.300901i
$773$	−7.76995	+	5.64520i	−0.279466	+	0.203044i	−0.718684	−	0.695337i	$-0.755255\pi$
$773$	−7.76995	+	5.64520i	−0.279466	+	0.203044i	0.439219	+	0.898380i	$0.355255\pi$
$774$	17.2430	−	18.6037i	0.619787	−	0.668698i
$775$	14.8574	−	4.82748i	0.533695	−	0.173408i
$776$	−10.2012	−	3.31458i	−0.366203	−	0.118987i
$777$	13.7126	+	15.4520i	0.491937	+	0.554336i
$778$	−30.6048	−	9.94410i	−1.09724	−	0.356513i
$779$	3.29572	−	10.1432i	0.118081	−	0.363417i
$780$	−3.39686	+	1.48313i	−0.121627	+	0.0531046i
$781$	85.8605			3.07233
$782$	−1.52257	+	4.68598i	−0.0544469	+	0.167570i
$783$	−47.7856	−	16.6773i	−1.70772	−	0.595999i
$784$	9.64815	+	7.00979i	0.344577	+	0.250350i
$785$	13.7617	+	9.99844i	0.491175	+	0.356859i
$786$	19.5231	−	17.3255i	0.696366	−	0.617979i
$787$	−28.1168	−	20.4281i	−1.00226	−	0.728182i	−0.0396858	−	0.999212i	$-0.512636\pi$
$787$	−28.1168	−	20.4281i	−1.00226	−	0.728182i	−0.962571	+	0.271030i	$0.912636\pi$
$788$	−8.42320	−	6.11981i	−0.300064	−	0.218009i
$789$	26.5287	−	45.1936i	0.944448	−	1.60893i
$790$			1.17134i			0.0416745i
$791$	21.4645	−	15.5949i	0.763191	−	0.554491i
$792$	−17.0242	+	36.7996i	−0.604927	+	1.30762i
$793$	10.8870	−	14.9846i	0.386607	−	0.532119i
$794$			53.0954i			1.88429i
$795$	−3.45897	+	15.7152i	−0.122677	+	0.557362i
$796$	8.18190	+	5.94450i	0.290000	+	0.210697i
$797$	12.7722	+	39.3088i	0.452415	+	1.39239i	0.874144	+	0.485667i	$0.161423\pi$
$797$	12.7722	+	39.3088i	0.452415	+	1.39239i	−0.421729	+	0.906722i	$0.638577\pi$
$798$	1.65450	+	16.9136i	0.0585687	+	0.598734i
$799$	2.30861	+	3.17753i	0.0816728	+	0.112413i
$800$	3.33708	+	10.2705i	0.117984	+	0.363117i
$801$	−0.518878	+	4.33465i	−0.0183336	+	0.153157i
$802$	18.2884	−	13.2873i	0.645785	−	0.469190i
$803$	16.1411	−	22.2163i	0.569606	−	0.783995i
$804$	0.153526	+	0.173000i	0.00541444	+	0.00610123i
$805$	−10.1571	−	7.37953i	−0.357989	−	0.260094i
$806$			25.4128i			0.895128i
$807$	19.3473	+	4.25840i	0.681057	+	0.149903i
$808$	−15.4589	−	21.2773i	−0.543841	−	0.748532i
$809$	−3.50272	−	1.13810i	−0.123149	−	0.0400135i	0.246794	−	0.969068i	$-0.420623\pi$
$809$	−3.50272	−	1.13810i	−0.123149	−	0.0400135i	−0.369943	+	0.929054i	$0.620623\pi$
$810$	−3.58619	+	14.7647i	−0.126006	+	0.518778i
$811$	30.1275			1.05792			0.528959	−	0.848647i	$-0.322582\pi$
$811$	30.1275			1.05792			0.528959	+	0.848647i	$0.322582\pi$
$812$			10.4349i			0.366194i
$813$	−11.9685	−	13.4866i	−0.419753	−	0.472996i
$814$	−48.4011	−	15.7265i	−1.69646	−	0.551213i
$815$	21.7597	−	7.07017i	0.762211	−	0.247657i
$816$	1.84721	+	4.23072i	0.0646652	+	0.148105i
$817$	−4.82764	−	14.8580i	−0.168898	−	0.519814i
$818$			30.2025i			1.05600i
$819$	4.89114	+	24.7612i	0.170910	+	0.865227i
$820$	−1.86972	−	0.607508i	−0.0652934	−	0.0212151i
$821$	−40.9204	−	13.2958i	−1.42813	−	0.464028i	−0.509955	−	0.860201i	$-0.670338\pi$
$821$	−40.9204	−	13.2958i	−1.42813	−	0.464028i	−0.918176	+	0.396173i	$0.870338\pi$
$822$	53.3470	+	11.7418i	1.86069	+	0.409543i
$823$	12.2125	−	16.8091i	0.425701	−	0.585927i	−0.541259	−	0.840856i	$-0.682052\pi$
$823$	12.2125	−	16.8091i	0.425701	−	0.585927i	0.966960	+	0.254929i	$0.0820522\pi$
$824$	−2.07536	−	6.38731i	−0.0722987	−	0.222513i
$825$	−19.3489	+	32.9621i	−0.673641	+	1.14759i
$826$	−4.67363	−	3.39559i	−0.162616	−	0.118148i
$827$	4.96864	−	1.61441i	0.172776	−	0.0561385i	−0.221351	−	0.975194i	$-0.571047\pi$
$827$	4.96864	−	1.61441i	0.172776	−	0.0561385i	0.394128	+	0.919056i	$0.371047\pi$
$828$	−8.26218	+	1.63204i	−0.287130	+	0.0567175i
$829$	0.170666			0.00592746			0.00296373	−	0.999996i	$-0.499057\pi$
$829$	0.170666			0.00592746			0.00296373	+	0.999996i	$0.499057\pi$
$830$	−8.71275			−0.302424
$831$	37.0271	+	21.7350i	1.28445	+	0.753978i
$832$	20.1861			0.699829
$833$	1.13712	+	0.826168i	0.0393990	+	0.0286250i
$834$	−12.7853	+	58.0880i	−0.442720	+	2.01142i
$835$	19.3120	+	6.27486i	0.668321	+	0.217151i
$836$	−4.96432	−	6.83281i	−0.171695	−	0.236318i
$837$	16.7314	+	12.7179i	0.578323	+	0.439594i
$838$	−3.51617	+	1.14247i	−0.121464	+	0.0394661i
$839$	19.1267	+	13.8964i	0.660328	+	0.479757i	0.866774	−	0.498702i	$-0.166190\pi$
$839$	19.1267	+	13.8964i	0.660328	+	0.479757i	−0.206446	+	0.978458i	$0.566190\pi$
$840$	−9.21843	+	0.901755i	−0.318066	+	0.0311135i
$841$	−53.2932	+	38.7197i	−1.83770	+	1.33516i
$842$	−14.0735	−	4.57276i	−0.485006	−	0.157588i
$843$	−15.8070	−	17.8121i	−0.544423	−	0.613480i
$844$	0.851554	+	7.29270i	0.0293117	+	0.251025i
$845$			2.94030i			0.101149i
$846$	−13.9719	+	30.2018i	−0.480363	+	1.03836i
$847$	26.9606	+	37.1081i	0.926377	+	1.27505i
$848$	−24.3477	+	33.5117i	−0.836103	+	1.15080i
$849$	−2.52276	−	25.7896i	−0.0865809	−	0.885096i
$850$	1.05887	+	3.25887i	0.0363189	+	0.111778i
$851$	9.65832	+	29.7253i	0.331083	+	1.01897i
$852$	12.8495	+	2.82821i	0.440216	+	0.0968928i
$853$	2.68597	−	8.26658i	0.0919660	−	0.283042i	−0.894485	−	0.447098i	$-0.852458\pi$
$853$	2.68597	−	8.26658i	0.0919660	−	0.283042i	0.986451	+	0.164056i	$0.0524576\pi$
$854$	−12.6644	+	9.20120i	−0.433366	+	0.314859i
$855$	6.86324	+	6.36124i	0.234718	+	0.217550i
$856$			15.3843i			0.525823i
$857$	16.3973	−	5.32781i	0.560122	−	0.181995i	−0.0152543	−	0.999884i	$-0.504856\pi$
$857$	16.3973	−	5.32781i	0.560122	−	0.181995i	0.575376	+	0.817889i	$0.304856\pi$
$858$	−41.2696	−	46.5044i	−1.40892	−	1.58763i
$859$			58.4533i			1.99440i	0.0747857	+	0.997200i	$0.476173\pi$
$859$			58.4533i			1.99440i	−0.0747857	+	0.997200i	$0.523827\pi$
$860$	−2.73880	+	0.889892i	−0.0933925	+	0.0303451i
$861$	−6.77696	+	11.5450i	−0.230958	+	0.393453i
$862$	−16.9428	+	23.3197i	−0.577072	+	0.794272i
$863$	10.3630	−	3.36714i	0.352760	−	0.114619i	−0.127276	−	0.991867i	$-0.540624\pi$
$863$	10.3630	−	3.36714i	0.352760	−	0.114619i	0.480036	+	0.877249i	$0.340624\pi$
$864$	−8.79147	+	11.5659i	−0.299092	+	0.393481i
$865$	8.45959	+	6.14625i	0.287635	+	0.208979i
$866$	−44.1591	+	32.0835i	−1.50059	+	1.09024i
$867$	−11.5644	−	26.4862i	−0.392747	−	0.899520i
$868$	1.33898	−	4.12095i	0.0454478	−	0.139874i
$869$	−3.77003	+	1.22496i	−0.127890	+	0.0415538i
$870$	18.9048	+	21.3027i	0.640931	+	0.722229i
$871$	0.997391	−	0.324072i	0.0337953	−	0.0109808i
$872$	−0.651547	+	2.00525i	−0.0220642	+	0.0679065i
$873$	−2.63598	−	13.3446i	−0.0892144	−	0.451645i
$874$	−7.94500	+	24.4522i	−0.268744	+	0.827108i
$875$	−20.0340			−0.677272
$876$	3.14739	−	2.79310i	0.106340	−	0.0943702i
$877$			22.4955i			0.759621i	0.925064	+	0.379810i	$0.124011\pi$
$877$			22.4955i			0.759621i	−0.925064	+	0.379810i	$0.875989\pi$
$878$			32.0240i			1.08076i
$879$	−15.2265	+	6.64818i	−0.513578	+	0.224238i
$880$	23.4431	−	17.0324i	0.790268	−	0.574163i
$881$	15.3960	+	21.1908i	0.518704	+	0.713935i	0.985357	−	0.170506i	$-0.0545401\pi$
$881$	15.3960	+	21.1908i	0.518704	+	0.713935i	−0.466653	+	0.884441i	$0.654540\pi$
$882$	−1.41541	+	11.8242i	−0.0476595	+	0.398142i
$883$	6.89651	−	9.49224i	0.232086	−	0.319439i	−0.677051	−	0.735936i	$-0.736742\pi$
$883$	6.89651	−	9.49224i	0.232086	−	0.319439i	0.909137	+	0.416497i	$0.136742\pi$
$884$	−1.12454			−0.0378224
$885$	−3.16593	+	0.309694i	−0.106422	+	0.0104103i
$886$	−14.4004	−	19.8204i	−0.483790	−	0.665880i
$887$			19.6243i			0.658920i	0.944170	+	0.329460i	$0.106867\pi$
$887$			19.6243i			0.658920i	−0.944170	+	0.329460i	$0.893133\pi$
$888$	19.8857	+	11.6730i	0.667322	+	0.391720i
$889$	1.89200	−	1.37462i	0.0634555	−	0.0461031i
$890$	1.44401	−	1.98750i	0.0484032	−	0.0666213i
$891$	−51.2713	+	3.89814i	−1.71765	+	0.130592i
$892$	4.80354	−	6.61151i	0.160834	−	0.221370i
$893$	12.0467	+	16.5809i	0.403128	+	0.554858i
$894$	25.3363	−	22.4843i	0.847372	−	0.751987i
$895$	1.26254	+	0.917288i	0.0422020	+	0.0306616i
$896$	−27.4971	−	8.93436i	−0.918614	−	0.298476i
$897$	−8.20814	+	37.2923i	−0.274062	+	1.24515i
$898$	−20.7310			−0.691802
$899$	37.4675	−	12.1739i	1.24961	−	0.406023i
$900$	−3.98142	+	4.29561i	−0.132714	+	0.143187i
$901$	−2.86960	+	3.94966i	−0.0956001	+	0.131582i
$902$		−	32.9780i		−	1.09805i
$903$	1.90913	+	19.5166i	0.0635319	+	0.649471i
$904$	17.4062	−	23.9576i	0.578923	−	0.796819i
$905$	−0.818693	+	0.594815i	−0.0272143	+	0.0197723i
$906$	−16.9188	−	38.7497i	−0.562090	−	1.28737i
$907$		−	39.5952i		−	1.31474i	−0.753569	−	0.657369i	$-0.771669\pi$
$907$		−	39.5952i		−	1.31474i	0.753569	−	0.657369i	$-0.228331\pi$
$908$	9.96896	+	3.23911i	0.330832	+	0.107494i
$909$	14.0036	−	30.2703i	0.464469	−	1.00400i
$910$	4.38908	−	13.5082i	0.145497	−	0.447792i
$911$	−26.7424			−0.886015			−0.443007	−	0.896518i	$-0.646088\pi$
$911$	−26.7424			−0.886015			−0.443007	+	0.896518i	$0.646088\pi$
$912$	9.63903	+	22.0766i	0.319180	+	0.731028i
$913$	−9.11155	−	28.0425i	−0.301548	−	0.928070i
$914$	26.8974	−	37.0211i	0.889686	−	1.22455i
$915$	−1.85290	+	8.41833i	−0.0612550	+	0.278301i
$916$	−10.8249	+	3.51722i	−0.357664	+	0.116212i
$917$			20.1790i			0.666371i
$918$	−2.78957	+	3.66991i	−0.0920695	+	0.121125i
$919$	33.7110	−	46.3992i	1.11202	−	1.53057i	0.293622	−	0.955922i	$-0.405139\pi$
$919$	33.7110	−	46.3992i	1.11202	−	1.53057i	0.818402	−	0.574647i	$-0.194861\pi$
$920$	−13.3272	−	4.33027i	−0.439385	−	0.142765i
$921$	4.11987	+	9.43586i	0.135754	+	0.310922i
$922$	49.4479	−	35.9260i	1.62848	−	1.18316i
$923$	35.0641	−	48.2616i	1.15415	−	1.58855i
$924$	4.24202	+	9.71563i	0.139552	+	0.319621i
$925$	17.5850	+	12.7763i	0.578192	+	0.420081i
$926$	−36.8261	−	50.6868i	−1.21018	−	1.66567i
$927$	5.78959	−	6.24647i	0.190155	−	0.205161i
$928$	8.41545	+	25.9001i	0.276251	+	0.850212i
$929$	4.77628	−	14.6999i	0.156705	−	0.482288i	−0.841625	−	0.540063i	$-0.818401\pi$
$929$	4.77628	−	14.6999i	0.156705	−	0.482288i	0.998330	+	0.0577749i	$0.0184006\pi$
$930$	−4.73234	−	10.8386i	−0.155180	−	0.355413i
$931$	5.93369	+	4.31108i	0.194469	+	0.141290i
$932$	−2.29834			−0.0752846
$933$	29.8632	−	50.8741i	0.977678	−	1.66554i
$934$	−19.5044	+	6.33736i	−0.638204	+	0.207365i
$935$	2.76299	−	2.00743i	0.0903593	−	0.0656499i
$936$	13.7324	+	24.5976i	0.448858	+	0.803997i
$937$	47.0788	−	34.2047i	1.53800	−	1.11742i	0.586420	−	0.810007i	$-0.300537\pi$
$937$	47.0788	−	34.2047i	1.53800	−	1.11742i	0.951576	−	0.307413i	$-0.0994633\pi$
$938$	−0.886334			−0.0289398
$939$	6.56158	−	2.86491i	0.214129	−	0.0934927i
$940$	3.05639	−	2.22060i	0.0996885	−	0.0724280i
$941$	7.78949	−	5.65940i	0.253930	−	0.184491i	−0.453537	−	0.891238i	$-0.649838\pi$
$941$	7.78949	−	5.65940i	0.253930	−	0.184491i	0.707467	+	0.706747i	$0.249838\pi$
$942$	−22.1351	+	37.7087i	−0.721200	+	1.22861i
$943$	−16.3852	+	11.9046i	−0.533576	+	0.387666i
$944$	−7.78790	−	2.53044i	−0.253475	−	0.0823589i
$945$	−6.69709	−	9.64991i	−0.217856	−	0.313912i
$946$	−28.3941	−	39.0811i	−0.923172	−	1.27064i
$947$	−25.4271	−	8.26177i	−0.826271	−	0.268472i	−0.134797	−	0.990873i	$-0.543038\pi$
$947$	−25.4271	−	8.26177i	−0.826271	−	0.268472i	−0.691474	+	0.722402i	$0.743038\pi$
$948$	−0.604555	+	0.0591381i	−0.0196350	+	0.00192072i
$949$	−5.89585	−	18.1456i	−0.191387	−	0.589030i
$950$	5.52535	+	17.0053i	0.179266	+	0.551724i
$951$	−46.7349	+	4.57166i	−1.51548	+	0.148246i
$952$	−2.67263	−	0.868390i	−0.0866205	−	0.0281447i
$953$	11.7832	+	16.2182i	0.381696	+	0.525359i	0.956033	−	0.293260i	$-0.0947401\pi$
$953$	11.7832	+	16.2182i	0.381696	+	0.525359i	−0.574337	+	0.818619i	$0.694740\pi$
$954$	−41.0700	−	4.91627i	−1.32969	−	0.159170i
$955$	0.327901	+	0.106541i	0.0106106	+	0.00344760i
$956$	−5.19150	+	3.77185i	−0.167905	+	0.121990i
$957$	−48.7939	+	83.1238i	−1.57728	+	2.68701i
$958$	16.4780	−	11.9720i	0.532380	−	0.386797i
$959$	−34.1637	+	24.8213i	−1.10320	+	0.801523i
$960$	−8.60945	+	3.75904i	−0.277869	+	0.121322i
$961$	14.6413			0.472300
$962$	−28.6060	+	20.7835i	−0.922296	+	0.670087i
$963$	−17.0346	+	9.51015i	−0.548933	+	0.306460i
$964$	8.42248	−	6.11929i	0.271270	−	0.197089i
$965$	17.6412	−	5.73199i	0.567892	−	0.184519i
$966$	16.3372	−	27.8316i	0.525641	−	0.895467i
$967$	−44.2251			−1.42218			−0.711092	−	0.703099i	$-0.751799\pi$
$967$	−44.2251			−1.42218			−0.711092	+	0.703099i	$0.751799\pi$
$968$	41.4182	+	30.0921i	1.33123	+	0.967195i
$969$	1.13605	+	2.60192i	0.0364951	+	0.0835859i
$970$	−2.36541	+	7.27998i	−0.0759487	+	0.233746i
$971$	−15.5547	−	47.8725i	−0.499175	−	1.53630i	−0.810348	−	0.585950i	$-0.800722\pi$
$971$	−15.5547	−	47.8725i	−0.499175	−	1.53630i	0.311172	−	0.950353i	$-0.399278\pi$
$972$	−7.80142	−	1.10548i	−0.250231	−	0.0354582i
$973$	−27.0273	−	37.1998i	−0.866454	−	1.19257i
$974$	−4.73105	−	3.43731i	−0.151593	−	0.110138i
$975$	10.6260	+	24.3371i	0.340305	+	0.779411i
$976$	−13.0425	+	17.9515i	−0.417482	+	0.574614i
$977$	29.8982	−	21.7223i	0.956530	−	0.694959i	0.00418746	−	0.999991i	$-0.498667\pi$
$977$	29.8982	−	21.7223i	0.956530	−	0.694959i	0.952342	+	0.305032i	$0.0986671\pi$
$978$	23.5331	+	53.8987i	0.752507	+	1.72349i
$979$	7.90700	+	2.56914i	0.252709	+	0.0821100i
$980$	0.794671	−	1.09377i	0.0253848	−	0.0349392i
$981$	−2.62314	+	0.518154i	−0.0837504	+	0.0165434i
$982$		−	64.8214i		−	2.06853i
$983$	45.1232	−	14.6614i	1.43921	−	0.467627i	0.517557	−	0.855649i	$-0.326841\pi$
$983$	45.1232	−	14.6614i	1.43921	−	0.467627i	0.921650	+	0.388022i	$0.126841\pi$
$984$	−3.21190	+	14.5927i	−0.102392	+	0.465199i
$985$	12.9132	−	17.7735i	0.411450	−	0.566312i
$986$	2.67026	+	8.21820i	0.0850383	+	0.261721i
$987$	−10.2939	−	23.5765i	−0.327659	−	0.750448i
$988$	−5.86803			−0.186687
$989$	−9.16773	+	28.2154i	−0.291517	+	0.897197i
$990$	26.2616	+	12.1491i	0.834648	+	0.386123i
$991$	−34.9064	−	11.3418i	−1.10884	−	0.360284i	−0.303341	−	0.952882i	$-0.598102\pi$
$991$	−34.9064	−	11.3418i	−1.10884	−	0.360284i	−0.805498	+	0.592598i	$0.798102\pi$
$992$		−	11.3083i		−	0.359038i
$993$	7.88319	+	18.0551i	0.250165	+	0.572962i
$994$	−40.7887	+	29.6347i	−1.29374	+	0.939957i
$995$	−12.5433	+	17.2644i	−0.397650	+	0.547318i
$996$	−0.439885	−	4.49684i	−0.0139383	−	0.142488i
$997$			54.2987i			1.71966i	0.510583	+	0.859829i	$0.329430\pi$
$997$			54.2987i			1.71966i	−0.510583	+	0.859829i	$0.670570\pi$
$998$	0.373389	−	0.513926i	0.0118194	−	0.0162681i
$999$	−0.632366	+	29.2350i	−0.0200072	+	0.924953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.k.a.23.19	✓	272
3.2	odd	2	inner	633.2.k.a.23.50	yes	272
211.156	odd	10	inner	633.2.k.a.578.50	yes	272
633.578	even	10	inner	633.2.k.a.578.19	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.k.a.23.19	✓	272	1.1	even	1	trivial
633.2.k.a.23.50	yes	272	3.2	odd	2	inner
633.2.k.a.578.19	yes	272	633.578	even	10	inner
633.2.k.a.578.50	yes	272	211.156	odd	10	inner

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:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.489132 + 1.50539i) q^{2} +(0.372318 - 1.69156i) q^{3} +(-0.408927 - 0.297103i) q^{4} +(0.626907 - 0.862864i) q^{5} +(2.36435 + 1.38788i) q^{6} +(-2.01574 + 0.654954i) q^{7} +(-1.91385 + 1.39050i) q^{8} +(-2.72276 - 1.25960i) q^{9} +O(q^{10})\)	\(q+(-0.489132 + 1.50539i) q^{2} +(0.372318 - 1.69156i) q^{3} +(-0.408927 - 0.297103i) q^{4} +(0.626907 - 0.862864i) q^{5} +(2.36435 + 1.38788i) q^{6} +(-2.01574 + 0.654954i) q^{7} +(-1.91385 + 1.39050i) q^{8} +(-2.72276 - 1.25960i) q^{9} +(0.992309 + 1.36580i) q^{10} +(-3.35816 + 4.62212i) q^{11} +(-0.654818 + 0.581108i) q^{12} +(1.22664 + 3.77520i) q^{13} -3.35484i q^{14} +(-1.22618 - 1.38171i) q^{15} +(-1.46951 - 4.52268i) q^{16} +(-0.173195 - 0.533040i) q^{17} +(3.22798 - 3.48272i) q^{18} +(-0.903759 - 2.78148i) q^{19} +(-0.512718 + 0.166592i) q^{20} +(0.357399 + 3.65360i) q^{21} +(-5.31552 - 7.31619i) q^{22} +(-1.71625 + 5.28206i) q^{23} +(1.63955 + 3.75511i) q^{24} +(1.19356 + 3.67341i) q^{25} -6.28316 q^{26} +(-3.14442 + 4.13674i) q^{27} +(1.01888 + 0.331054i) q^{28} +(3.00993 + 9.26360i) q^{29} +(2.67978 - 1.17004i) q^{30} -4.04459i q^{31} +2.79590 q^{32} +(6.56829 + 7.40144i) q^{33} +0.887150 q^{34} +(-0.698547 + 2.14991i) q^{35} +(0.739179 + 1.32402i) q^{36} +(4.55281 - 3.30781i) q^{37} +4.62929 q^{38} +(6.84269 - 0.669358i) q^{39} +2.52311i q^{40} +(2.95023 + 2.14346i) q^{41} +(-5.67492 - 1.24907i) q^{42} +5.34174 q^{43} +(2.74649 - 0.892387i) q^{44} +(-2.79378 + 1.55972i) q^{45} +(-7.11211 - 5.16725i) q^{46} +(-6.66478 + 2.16552i) q^{47} +(-8.19752 + 0.801889i) q^{48} +(-2.02887 + 1.47406i) q^{49} -6.11374 q^{50} +(-0.966153 + 0.0945100i) q^{51} +(0.620018 - 1.90822i) q^{52} +(-5.11997 - 7.04704i) q^{53} +(-4.68939 - 6.75700i) q^{54} +(1.88300 + 5.79528i) q^{55} +(2.94712 - 4.05637i) q^{56} +(-5.04154 + 0.493168i) q^{57} -15.4176 q^{58} +(1.01215 - 1.39310i) q^{59} +(0.0909069 + 0.929319i) q^{60} +(-2.74266 - 3.77495i) q^{61} +(6.08870 + 1.97834i) q^{62} +(6.31336 + 0.755739i) q^{63} +(1.57145 - 4.83644i) q^{64} +(4.02648 + 1.30828i) q^{65} +(-14.3548 + 6.26758i) q^{66} -0.264195i q^{67} +(-0.0875434 + 0.269431i) q^{68} +(8.29594 + 4.86974i) q^{69} +(-2.89477 - 2.10318i) q^{70} +(-8.83341 - 12.1582i) q^{71} +(6.96243 - 1.37530i) q^{72} -4.80651 q^{73} +(2.75263 + 8.47173i) q^{74} +(6.65819 - 0.651310i) q^{75} +(-0.456815 + 1.40593i) q^{76} +(3.74192 - 11.5164i) q^{77} +(-2.33933 + 10.6283i) q^{78} +(0.561323 + 0.407825i) q^{79} +(-4.82371 - 1.56732i) q^{80} +(5.82683 + 6.85916i) q^{81} +(-4.66981 + 3.39281i) q^{82} +(-3.03351 + 4.17527i) q^{83} +(0.939345 - 1.60024i) q^{84} +(-0.568518 - 0.184723i) q^{85} +(-2.61281 + 8.04142i) q^{86} +(16.7906 - 1.64247i) q^{87} -13.5156i q^{88} +(-0.449681 - 1.38397i) q^{89} +(-0.981467 - 4.96864i) q^{90} +(-4.94517 - 6.80644i) q^{91} +(2.27113 - 1.65007i) q^{92} +(-6.84167 - 1.50587i) q^{93} -11.0923i q^{94} +(-2.96662 - 0.963912i) q^{95} +(1.04096 - 4.72943i) q^{96} +(2.66510 + 3.66820i) q^{97} +(-1.22666 - 3.77526i) q^{98} +(14.9655 - 8.35498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9}+O(q^{10}) \) 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9	\( 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9} - 20 q^{10} + 6 q^{13} - 46 q^{16} - 20 q^{18} + 6 q^{19} - 3 q^{21} - 10 q^{22} + 23 q^{24} + 50 q^{25} - 40 q^{27} + 80 q^{28} - q^{30} + 12 q^{34} + 13 q^{36} - 42 q^{37} + 25 q^{39} - 10 q^{42} + 40 q^{43} - 23 q^{45} - 2 q^{46} - 15 q^{48} + 30 q^{49} - 11 q^{51} - 34 q^{52} + 128 q^{54} + 14 q^{55} + 20 q^{57} + 60 q^{58} + 30 q^{60} - 10 q^{61} - 108 q^{64} - 73 q^{66} + 40 q^{69} + 70 q^{70} - 105 q^{72} - 20 q^{73} - 10 q^{75} - 12 q^{76} - 82 q^{78} - 30 q^{79} - 42 q^{81} - 106 q^{82} + 121 q^{84} - 110 q^{85} - 11 q^{87} + 60 q^{90} - 40 q^{91} - 45 q^{93} - 114 q^{96} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9 - 20 * q^10 + 6 * q^13 - 46 * q^16 - 20 * q^18 + 6 * q^19 - 3 * q^21 - 10 * q^22 + 23 * q^24 + 50 * q^25 - 40 * q^27 + 80 * q^28 - q^30 + 12 * q^34 + 13 * q^36 - 42 * q^37 + 25 * q^39 - 10 * q^42 + 40 * q^43 - 23 * q^45 - 2 * q^46 - 15 * q^48 + 30 * q^49 - 11 * q^51 - 34 * q^52 + 128 * q^54 + 14 * q^55 + 20 * q^57 + 60 * q^58 + 30 * q^60 - 10 * q^61 - 108 * q^64 - 73 * q^66 + 40 * q^69 + 70 * q^70 - 105 * q^72 - 20 * q^73 - 10 * q^75 - 12 * q^76 - 82 * q^78 - 30 * q^79 - 42 * q^81 - 106 * q^82 + 121 * q^84 - 110 * q^85 - 11 * q^87 + 60 * q^90 - 40 * q^91 - 45 * q^93 - 114 * q^96 - 80 * q^97 - 18 * q^99

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