LMFDB - Embedded newform 273.2.bf.b.185.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(152,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

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

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

chi := DirichletCharacter("273.152");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.15
Character	$\chi$	$=$	273.185
Dual form			273.2.bf.b.152.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.473030 - 0.273104i) q^{2} +(0.966120 - 1.43757i) q^{3} +(-0.850828 - 1.47368i) q^{4} +(-1.25657 - 2.17644i) q^{5} +(-0.849611 + 0.416164i) q^{6} +(2.53535 - 0.756296i) q^{7} +2.02188i q^{8} +(-1.13323 - 2.77773i) q^{9} +1.37270i q^{10} +6.02763i q^{11} +(-2.94052 - 0.200622i) q^{12} +(-1.89716 - 3.06607i) q^{13} +(-1.40585 - 0.334664i) q^{14} +(-4.34279 - 0.296295i) q^{15} +(-1.14947 + 1.99095i) q^{16} +(-0.323651 - 0.560581i) q^{17} +(-0.222560 + 1.62344i) q^{18} -2.29555i q^{19} +(-2.13825 + 3.70356i) q^{20} +(1.36222 - 4.37543i) q^{21} +(1.64617 - 2.85125i) q^{22} +(-0.894874 - 0.516656i) q^{23} +(2.90659 + 1.95337i) q^{24} +(-0.657937 + 1.13958i) q^{25} +(0.0600548 + 1.96847i) q^{26} +(-5.08802 - 1.05453i) q^{27} +(-3.27169 - 3.09282i) q^{28} +(4.46255 - 2.57646i) q^{29} +(1.97335 + 1.32619i) q^{30} +(9.25745 + 5.34479i) q^{31} +(4.58946 - 2.64973i) q^{32} +(8.66515 + 5.82341i) q^{33} +0.353562i q^{34} +(-4.83188 - 4.56771i) q^{35} +(-3.12930 + 4.03338i) q^{36} +(1.97766 - 3.42541i) q^{37} +(-0.626924 + 1.08587i) q^{38} +(-6.24058 - 0.234896i) q^{39} +(4.40050 - 2.54063i) q^{40} +(-4.48689 - 7.77153i) q^{41} +(-1.83932 + 1.69768i) q^{42} +(-4.09951 + 7.10056i) q^{43} +(8.88279 - 5.12848i) q^{44} +(-4.62160 + 5.95682i) q^{45} +(0.282202 + 0.488787i) q^{46} +(-2.09646 - 3.63118i) q^{47} +(1.75160 + 3.57594i) q^{48} +(5.85603 - 3.83496i) q^{49} +(0.622448 - 0.359370i) q^{50} +(-1.11856 - 0.0763159i) q^{51} +(-2.90425 + 5.40450i) q^{52} +(-0.0406517 - 0.0234703i) q^{53} +(2.11879 + 1.88838i) q^{54} +(13.1188 - 7.57414i) q^{55} +(1.52914 + 5.12617i) q^{56} +(-3.30002 - 2.21778i) q^{57} -2.81456 q^{58} +(-0.831148 - 1.43959i) q^{59} +(3.25833 + 6.65197i) q^{60} +3.59276i q^{61} +(-2.91937 - 5.05650i) q^{62} +(-4.97392 - 6.18548i) q^{63} +1.70329 q^{64} +(-4.28922 + 7.98179i) q^{65} +(-2.50848 - 5.12114i) q^{66} +1.52251 q^{67} +(-0.550743 + 0.953916i) q^{68} +(-1.60728 + 0.787294i) q^{69} +(1.03817 + 3.48027i) q^{70} +(11.4729 + 6.62389i) q^{71} +(5.61623 - 2.29124i) q^{72} +(4.76835 + 2.75301i) q^{73} +(-1.87099 + 1.08022i) q^{74} +(1.00258 + 2.04680i) q^{75} +(-3.38290 + 1.95312i) q^{76} +(4.55868 + 15.2822i) q^{77} +(2.88783 + 1.81544i) q^{78} +(-2.14796 - 3.72038i) q^{79} +5.77758 q^{80} +(-6.43160 + 6.29559i) q^{81} +4.90156i q^{82} +11.8816 q^{83} +(-7.60699 + 1.71526i) q^{84} +(-0.813381 + 1.40882i) q^{85} +(3.87838 - 2.23919i) q^{86} +(0.607520 - 8.90441i) q^{87} -12.1871 q^{88} +(0.507769 - 0.879481i) q^{89} +(3.81299 - 1.55558i) q^{90} +(-7.12882 - 6.33877i) q^{91} +1.75834i q^{92} +(16.6273 - 8.14455i) q^{93} +2.29021i q^{94} +(-4.99614 + 2.88452i) q^{95} +(0.624797 - 9.15764i) q^{96} +(8.58147 + 4.95452i) q^{97} +(-3.81742 + 0.214744i) q^{98} +(16.7432 - 6.83067i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.473030	−	0.273104i	−0.334483	−	0.193114i	0.323347	−	0.946281i	$-0.395192\pi$
$2$	−0.473030	−	0.273104i	−0.334483	−	0.193114i	−0.657830	+	0.753167i	$0.728525\pi$
$3$	0.966120	−	1.43757i	0.557789	−	0.829982i
$3$	0.966120	−	1.43757i	0.557789	−	0.829982i
$4$	−0.850828	−	1.47368i	−0.425414	−	0.736839i
$5$	−1.25657	−	2.17644i	−0.561955	−	0.973335i	−0.997326	−	0.0730836i	$-0.976716\pi$
$5$	−1.25657	−	2.17644i	−0.561955	−	0.973335i	0.435371	−	0.900251i	$-0.356617\pi$
$6$	−0.849611	+	0.416164i	−0.346852	+	0.169898i
$7$	2.53535	−	0.756296i	0.958273	−	0.285853i
$7$	2.53535	−	0.756296i	0.958273	−	0.285853i
$8$			2.02188i			0.714841i
$9$	−1.13323	−	2.77773i	−0.377742	−	0.925911i
$10$			1.37270i			0.434085i
$11$			6.02763i			1.81740i	0.417450	+	0.908700i	$0.362924\pi$
$11$			6.02763i			1.81740i	−0.417450	+	0.908700i	$0.637076\pi$
$12$	−2.94052	−	0.200622i	−0.848855	−	0.0579147i
$13$	−1.89716	−	3.06607i	−0.526176	−	0.850376i
$13$	−1.89716	−	3.06607i	−0.526176	−	0.850376i
$14$	−1.40585	−	0.334664i	−0.375728	−	0.0894428i
$15$	−4.34279	−	0.296295i	−1.12130	−	0.0765030i
$16$	−1.14947	+	1.99095i	−0.287369	+	0.497737i
$17$	−0.323651	−	0.560581i	−0.0784970	−	0.135961i	0.824105	−	0.566438i	$-0.191679\pi$
$17$	−0.323651	−	0.560581i	−0.0784970	−	0.135961i	−0.902602	+	0.430477i	$0.858345\pi$
$18$	−0.222560	+	1.62344i	−0.0524580	+	0.382649i
$19$		−	2.29555i		−	0.526636i	−0.964709	−	0.263318i	$-0.915183\pi$
$19$		−	2.29555i		−	0.526636i	0.964709	−	0.263318i	$-0.0848168\pi$
$20$	−2.13825	+	3.70356i	−0.478127	+	0.828141i
$21$	1.36222	−	4.37543i	0.297262	−	0.954796i
$22$	1.64617	−	2.85125i	0.350965	−	0.607889i
$23$	−0.894874	−	0.516656i	−0.186594	−	0.107730i	0.403793	−	0.914850i	$-0.367692\pi$
$23$	−0.894874	−	0.516656i	−0.186594	−	0.107730i	−0.590387	+	0.807120i	$0.701025\pi$
$24$	2.90659	+	1.95337i	0.593305	+	0.398731i
$25$	−0.657937	+	1.13958i	−0.131587	+	0.227916i
$26$	0.0600548	+	1.96847i	0.0117777	+	0.386048i
$27$	−5.08802	−	1.05453i	−0.979190	−	0.202944i
$28$	−3.27169	−	3.09282i	−0.618291	−	0.584487i
$29$	4.46255	−	2.57646i	0.828676	−	0.478436i	−0.0247234	−	0.999694i	$-0.507871\pi$
$29$	4.46255	−	2.57646i	0.828676	−	0.478436i	0.853399	+	0.521258i	$0.174537\pi$
$30$	1.97335	+	1.32619i	0.360283	+	0.242128i
$31$	9.25745	+	5.34479i	1.66269	+	0.959953i	0.971424	+	0.237351i	$0.0762792\pi$
$31$	9.25745	+	5.34479i	1.66269	+	0.959953i	0.691264	+	0.722602i	$0.257054\pi$
$32$	4.58946	−	2.64973i	0.811310	−	0.468410i
$33$	8.66515	+	5.82341i	1.50841	+	1.01373i
$34$			0.353562i			0.0606354i
$35$	−4.83188	−	4.56771i	−0.816738	−	0.772084i
$36$	−3.12930	+	4.03338i	−0.521551	+	0.672230i
$37$	1.97766	−	3.42541i	0.325126	−	0.563134i	−0.656412	−	0.754402i	$-0.727927\pi$
$37$	1.97766	−	3.42541i	0.325126	−	0.563134i	0.981538	+	0.191268i	$0.0612601\pi$
$38$	−0.626924	+	1.08587i	−0.101701	+	0.176151i
$39$	−6.24058	−	0.234896i	−0.999292	−	0.0376135i
$40$	4.40050	−	2.54063i	0.695780	−	0.401709i
$41$	−4.48689	−	7.77153i	−0.700735	−	1.21371i	−0.968209	−	0.250143i	$-0.919522\pi$
$41$	−4.48689	−	7.77153i	−0.700735	−	1.21371i	0.267474	−	0.963565i	$-0.413811\pi$
$42$	−1.83932	+	1.69768i	−0.283813	+	0.261958i
$43$	−4.09951	+	7.10056i	−0.625169	+	1.08282i	0.363339	+	0.931657i	$0.381637\pi$
$43$	−4.09951	+	7.10056i	−0.625169	+	1.08282i	−0.988508	+	0.151168i	$0.951697\pi$
$44$	8.88279	−	5.12848i	1.33913	−	0.773147i
$45$	−4.62160	+	5.95682i	−0.688948	+	0.887990i
$46$	0.282202	+	0.488787i	0.0416084	+	0.0720678i
$47$	−2.09646	−	3.63118i	−0.305800	−	0.529662i	0.671639	−	0.740879i	$-0.265591\pi$
$47$	−2.09646	−	3.63118i	−0.305800	−	0.529662i	−0.977439	+	0.211217i	$0.932257\pi$
$48$	1.75160	+	3.57594i	0.252822	+	0.516143i
$49$	5.85603	−	3.83496i	0.836576	−	0.547851i
$50$	0.622448	−	0.359370i	0.0880274	−	0.0508226i
$51$	−1.11856	−	0.0763159i	−0.156630	−	0.0106864i
$52$	−2.90425	+	5.40450i	−0.402747	+	0.749469i
$53$	−0.0406517	−	0.0234703i	−0.00558394	−	0.00322389i	0.497205	−	0.867633i	$-0.334360\pi$
$53$	−0.0406517	−	0.0234703i	−0.00558394	−	0.00322389i	−0.502789	+	0.864409i	$0.667693\pi$
$54$	2.11879	+	1.88838i	0.288331	+	0.256977i
$55$	13.1188	−	7.57414i	1.76894	−	1.02130i
$56$	1.52914	+	5.12617i	0.204339	+	0.685013i
$57$	−3.30002	−	2.21778i	−0.437098	−	0.293752i
$58$	−2.81456			−0.369570
$59$	−0.831148	−	1.43959i	−0.108206	−	0.187419i	0.806837	−	0.590774i	$-0.201177\pi$
$59$	−0.831148	−	1.43959i	−0.108206	−	0.187419i	−0.915044	+	0.403355i	$0.867844\pi$
$60$	3.25833	+	6.65197i	0.420648	+	0.858766i
$61$			3.59276i			0.460006i	0.973190	+	0.230003i	$0.0738736\pi$
$61$			3.59276i			0.460006i	−0.973190	+	0.230003i	$0.926126\pi$
$62$	−2.91937	−	5.05650i	−0.370760	−	0.642176i
$63$	−4.97392	−	6.18548i	−0.626654	−	0.779297i
$64$	1.70329			0.212911
$65$	−4.28922	+	7.98179i	−0.532013	+	0.990019i
$66$	−2.50848	−	5.12114i	−0.308773	−	0.630369i
$67$	1.52251			0.186004			0.0930020	−	0.995666i	$-0.470354\pi$
$67$	1.52251			0.186004			0.0930020	+	0.995666i	$0.470354\pi$
$68$	−0.550743	+	0.953916i	−0.0667875	+	0.115679i
$69$	−1.60728	+	0.787294i	−0.193494	+	0.0947791i
$70$	1.03817	+	3.48027i	0.124085	+	0.415972i
$71$	11.4729	+	6.62389i	1.36158	+	0.786111i	0.989835	−	0.142222i	$-0.0454248\pi$
$71$	11.4729	+	6.62389i	1.36158	+	0.786111i	0.371749	+	0.928333i	$0.378758\pi$
$72$	5.61623	−	2.29124i	0.661879	−	0.270025i
$73$	4.76835	+	2.75301i	0.558093	+	0.322215i	0.752380	−	0.658730i	$-0.228906\pi$
$73$	4.76835	+	2.75301i	0.558093	+	0.322215i	−0.194287	+	0.980945i	$0.562239\pi$
$74$	−1.87099	+	1.08022i	−0.217498	+	0.125572i
$75$	1.00258	+	2.04680i	0.115768	+	0.236344i
$76$	−3.38290	+	1.95312i	−0.388046	+	0.224038i
$77$	4.55868	+	15.2822i	0.519509	+	1.74157i
$78$	2.88783	+	1.81544i	0.326983	+	0.205558i
$79$	−2.14796	−	3.72038i	−0.241665	−	0.418575i	0.719524	−	0.694468i	$-0.244360\pi$
$79$	−2.14796	−	3.72038i	−0.241665	−	0.418575i	−0.961189	+	0.275892i	$0.911027\pi$
$80$	5.77758			0.645953
$81$	−6.43160	+	6.29559i	−0.714622	+	0.699511i
$82$			4.90156i			0.541286i
$83$	11.8816			1.30417			0.652085	−	0.758146i	$-0.273894\pi$
$83$	11.8816			1.30417			0.652085	+	0.758146i	$0.273894\pi$
$84$	−7.60699	+	1.71526i	−0.829990	+	0.187150i
$85$	−0.813381	+	1.40882i	−0.0882236	+	0.152808i
$86$	3.87838	−	2.23919i	0.418217	−	0.241458i
$87$	0.607520	−	8.90441i	0.0651330	−	0.954653i
$88$	−12.1871			−1.29915
$89$	0.507769	−	0.879481i	0.0538234	−	0.0932248i	−0.837858	−	0.545888i	$-0.816193\pi$
$89$	0.507769	−	0.879481i	0.0538234	−	0.0932248i	0.891682	+	0.452663i	$0.149526\pi$
$90$	3.81299	−	1.55558i	0.401924	−	0.163972i
$91$	−7.12882	−	6.33877i	−0.747303	−	0.664483i
$92$			1.75834i			0.183320i
$93$	16.6273	−	8.14455i	1.72417	−	0.844550i
$94$			2.29021i			0.236217i
$95$	−4.99614	+	2.88452i	−0.512593	+	0.295946i
$96$	0.624797	−	9.15764i	0.0637681	−	0.934647i
$97$	8.58147	+	4.95452i	0.871317	+	0.503055i	0.867786	−	0.496939i	$-0.165543\pi$
$97$	8.58147	+	4.95452i	0.871317	+	0.503055i	0.00353111	+	0.999994i	$0.498876\pi$
$98$	−3.81742	+	0.214744i	−0.385618	+	0.0216924i
$99$	16.7432	−	6.83067i	1.68275	−	0.686508i
$100$	2.23916			0.223916
$101$	5.31728			0.529089			0.264545	−	0.964373i	$-0.414778\pi$
$101$	5.31728			0.529089			0.264545	+	0.964373i	$0.414778\pi$
$102$	0.508271	+	0.341583i	0.0503263	+	0.0338218i
$103$	2.41439	−	1.39395i	0.237897	−	0.137350i	−0.376313	−	0.926493i	$-0.622808\pi$
$103$	2.41439	−	1.39395i	0.237897	−	0.137350i	0.614210	+	0.789143i	$0.289475\pi$
$104$	6.19922	−	3.83581i	0.607883	−	0.376132i
$105$	−11.2346	+	2.53322i	−1.09638	+	0.247217i
$106$	0.0128197	+	0.0222043i	0.00124515	+	0.00215667i
$107$	−16.6485	−	9.61203i	−1.60947	−	0.929230i	−0.989488	−	0.144617i	$-0.953805\pi$
$107$	−16.6485	−	9.61203i	−1.60947	−	0.929230i	−0.619986	−	0.784613i	$-0.712862\pi$
$108$	2.77500	+	8.39533i	0.267024	+	0.807841i
$109$	−3.02537	+	5.24009i	−0.289778	+	0.501910i	−0.973757	−	0.227592i	$-0.926915\pi$
$109$	−3.02537	+	5.24009i	−0.289778	+	0.501910i	0.683979	+	0.729502i	$0.260248\pi$
$110$	−8.27412			−0.788906
$111$	−3.01362	−	6.15239i	−0.286040	−	0.583959i
$112$	−1.40858	+	5.91710i	−0.133098	+	0.559113i
$113$	−7.42599	−	4.28740i	−0.698578	−	0.403324i	0.108239	−	0.994125i	$-0.465479\pi$
$113$	−7.42599	−	4.28740i	−0.698578	−	0.403324i	−0.806818	+	0.590800i	$0.798812\pi$
$114$	0.955325	+	1.95032i	0.0894744	+	0.182665i
$115$			2.59686i			0.242158i
$116$	−7.59374	−	4.38425i	−0.705061	−	0.407067i
$117$	−6.36683	+	8.74434i	−0.588613	+	0.808415i
$118$			0.907960i			0.0835845i
$119$	−1.24454	−	1.17649i	−0.114086	−	0.107849i
$120$	0.599072	−	8.78058i	0.0546875	−	0.801554i
$121$	−25.3324			−2.30294
$122$	0.981198	−	1.69949i	0.0888335	−	0.153864i
$123$	−15.5070	−	1.05799i	−1.39822	−	0.0953961i
$124$		−	18.1900i		−	1.63351i
$125$	−9.25873			−0.828126
$126$	0.663532	+	4.28432i	0.0591122	+	0.381677i
$127$	1.59609	+	2.76452i	0.141630	+	0.245311i	0.928111	−	0.372304i	$-0.121432\pi$
$127$	1.59609	+	2.76452i	0.141630	+	0.245311i	−0.786480	+	0.617615i	$0.788099\pi$
$128$	−9.98463	−	5.76463i	−0.882525	−	0.509526i
$129$	6.24695	+	12.7533i	0.550013	+	1.12287i
$130$	4.20879	−	2.60422i	0.369135	−	0.228405i
$131$	1.65182	+	2.86103i	0.144320	+	0.249969i	0.929119	−	0.369781i	$-0.120567\pi$
$131$	1.65182	+	2.86103i	0.144320	+	0.249969i	−0.784799	+	0.619750i	$0.787234\pi$
$132$	1.20928	−	17.7244i	0.105254	−	1.54271i
$133$	−1.73612	−	5.82003i	−0.150540	−	0.504661i
$134$	−0.720192	−	0.415803i	−0.0622151	−	0.0359199i
$135$	4.09833	+	12.3989i	0.352728	+	1.06713i
$136$	1.13342	−	0.654383i	0.0971903	−	0.0561129i
$137$	7.14564	−	4.12554i	0.610493	−	0.352468i	−0.162665	−	0.986681i	$-0.552009\pi$
$137$	7.14564	−	4.12554i	0.610493	−	0.352468i	0.773158	+	0.634213i	$0.218676\pi$
$138$	0.975308	+	0.0665422i	0.0830237	+	0.00566445i
$139$	7.50372	+	4.33228i	0.636457	+	0.367459i	0.783249	−	0.621709i	$-0.213561\pi$
$139$	7.50372	+	4.33228i	0.636457	+	0.367459i	−0.146791	+	0.989168i	$0.546895\pi$
$140$	−2.62023	+	11.0070i	−0.221450	+	0.930260i
$141$	−7.24551	−	0.494339i	−0.610182	−	0.0416308i
$142$	−3.61802	−	6.26660i	−0.303618	−	0.525881i
$143$	18.4812	−	11.4354i	1.54547	−	0.956273i
$144$	6.83293	+	0.936740i	0.569411	+	0.0780616i
$145$	−11.2150	−	6.47500i	−0.931357	−	0.537719i
$146$	−1.50371	−	2.60451i	−0.124448	−	0.215551i
$147$	0.144603	−	12.1235i	0.0119267	−	0.999929i
$148$	−6.73060			−0.553252
$149$			13.8118i			1.13151i	0.824574	+	0.565753i	$0.191415\pi$
$149$			13.8118i			1.13151i	−0.824574	+	0.565753i	$0.808585\pi$
$150$	0.0847383	−	1.24201i	0.00691885	−	0.101410i
$151$	−3.90858	+	6.76986i	−0.318076	+	0.550924i	−0.980087	−	0.198571i	$-0.936370\pi$
$151$	−3.90858	+	6.76986i	−0.318076	+	0.550924i	0.662011	+	0.749494i	$0.269703\pi$
$152$	4.64132			0.376461
$153$	−1.19037	+	1.53428i	−0.0962360	+	0.124039i
$154$	2.01723	−	8.47393i	0.162553	−	0.682848i
$155$		−	26.8644i		−	2.15780i
$156$	4.96350	+	9.39646i	0.397398	+	0.752319i
$157$	−7.63926	−	4.41053i	−0.609679	−	0.351999i	0.163161	−	0.986600i	$-0.447831\pi$
$157$	−7.63926	−	4.41053i	−0.609679	−	0.351999i	−0.772840	+	0.634601i	$0.781164\pi$
$158$			2.34647i			0.186675i
$159$	−0.0730146	+	0.0357646i	−0.00579043	+	0.00283632i
$160$	−11.5340	−	6.65914i	−0.911840	−	0.526451i
$161$	−2.65957	−	0.633115i	−0.209603	−	0.0498964i
$162$	4.76169	−	1.22151i	0.374114	−	0.0959709i
$163$	12.5765			0.985066			0.492533	−	0.870294i	$-0.336071\pi$
$163$	12.5765			0.985066			0.492533	+	0.870294i	$0.336071\pi$
$164$	−7.63515	+	13.2245i	−0.596205	+	1.03266i
$165$	1.78596	−	26.1767i	0.139037	−	2.03786i
$166$	−5.62034	−	3.24490i	−0.436223	−	0.251853i
$167$	6.71323	+	11.6277i	0.519486	+	0.899775i	0.999743	+	0.0226481i	$0.00720973\pi$
$167$	6.71323	+	11.6277i	0.519486	+	0.899775i	−0.480258	+	0.877127i	$0.659457\pi$
$168$	8.84656	+	2.75425i	0.682527	+	0.212495i
$169$	−5.80160	+	11.6336i	−0.446277	+	0.894895i
$170$	0.769508	−	0.444276i	0.0590186	−	0.0340744i
$171$	−6.37643	+	2.60138i	−0.487618	+	0.198932i
$172$	13.9519			1.06382
$173$	8.44726			0.642233			0.321116	−	0.947040i	$-0.395942\pi$
$173$	8.44726			0.642233			0.321116	+	0.947040i	$0.395942\pi$
$174$	−2.71921	+	4.04614i	−0.206142	+	0.306737i
$175$	−0.806242	+	3.38683i	−0.0609462	+	0.256020i
$176$	−12.0007	−	6.92861i	−0.904587	−	0.522263i
$177$	−2.87250	−	0.195982i	−0.215911	−	0.0147309i
$178$	−0.480380	+	0.277347i	−0.0360060	+	0.0207881i
$179$			12.9185i			0.965577i	0.875737	+	0.482788i	$0.160376\pi$
$179$			12.9185i			0.965577i	−0.875737	+	0.482788i	$0.839624\pi$
$180$	12.7106	+	1.74252i	0.947393	+	0.129880i
$181$			1.36110i			0.101170i	0.998720	+	0.0505848i	$0.0161085\pi$
$181$			1.36110i			0.101170i	−0.998720	+	0.0505848i	$0.983891\pi$
$182$	1.64100	+	4.94534i	0.121639	+	0.366573i
$183$	5.16485	+	3.47104i	0.381797	+	0.256587i
$184$	1.04461	−	1.80932i	0.0770099	−	0.133385i
$185$	−9.94028			−0.730824
$186$	−10.0895	−	0.688378i	−0.739801	−	0.0504743i
$187$	3.37897	−	1.95085i	0.247095	−	0.142660i
$188$	−3.56746	+	6.17902i	−0.260184	+	0.450651i
$189$	−13.6975	+	1.17445i	−0.996344	+	0.0854284i
$190$	3.15110			0.228605
$191$			10.3102i			0.746020i	0.927827	+	0.373010i	$0.121674\pi$
$191$			10.3102i			0.746020i	−0.927827	+	0.373010i	$0.878326\pi$
$192$	1.64558	−	2.44860i	0.118760	−	0.176713i
$193$	3.23962			0.233193			0.116597	−	0.993179i	$-0.462802\pi$
$193$	3.23962			0.233193			0.116597	+	0.993179i	$0.462802\pi$
$194$	−2.70620	−	4.68727i	−0.194294	−	0.336527i
$195$	7.33049	+	13.8774i	0.524947	+	0.993783i
$196$	−10.6340	−	5.36702i	−0.759569	−	0.383358i
$197$	−11.8813	+	6.85965i	−0.846505	+	0.488730i	−0.859470	−	0.511186i	$-0.829206\pi$
$197$	−11.8813	+	6.85965i	−0.846505	+	0.488730i	0.0129653	+	0.999916i	$0.495873\pi$
$198$	−9.78550	−	1.34151i	−0.695425	−	0.0953372i
$199$	2.88404	−	1.66510i	0.204444	−	0.118036i	−0.394283	−	0.918989i	$-0.629007\pi$
$199$	2.88404	−	1.66510i	0.204444	−	0.118036i	0.598727	+	0.800953i	$0.295674\pi$
$200$	−2.30409	−	1.33027i	−0.162924	−	0.0940640i
$201$	1.47092	−	2.18871i	0.103751	−	0.154380i
$202$	−2.51524	−	1.45217i	−0.176971	−	0.102174i
$203$	9.36559	−	9.90724i	0.657335	−	0.695352i
$204$	0.839238	+	1.71333i	0.0587584	+	0.119957i
$205$	−11.2762	+	19.5309i	−0.787563	+	1.36410i
$206$	−1.52277			−0.106096
$207$	−0.421038	+	3.07121i	−0.0292641	+	0.213464i
$208$	8.28512	−	0.252766i	0.574470	−	0.0175262i
$209$	13.8367			0.957107
$210$	6.00614	+	1.86992i	0.414463	+	0.129037i
$211$	−4.67281	−	8.09355i	−0.321690	−	0.557183i	0.659147	−	0.752014i	$-0.270917\pi$
$211$	−4.67281	−	8.09355i	−0.321690	−	0.557183i	−0.980837	+	0.194831i	$0.937584\pi$
$212$			0.0798766i			0.00548595i
$213$	20.6065	−	10.0937i	1.41194	−	0.691607i
$214$	5.25017	+	9.09356i	0.358894	+	0.621623i
$215$	20.6053			1.40527
$216$	2.13213	−	10.2873i	0.145073	−	0.699965i
$217$	27.5132	+	6.54956i	1.86772	+	0.444613i
$218$	2.86218	−	1.65248i	0.193851	−	0.111920i
$219$	8.56444	−	4.19511i	0.578731	−	0.283479i
$220$	−22.3237	−	12.8886i	−1.50506	−	0.868949i
$221$	−1.10476	+	2.05585i	−0.0743145	+	0.138291i
$222$	−0.254711	+	3.73330i	−0.0170951	+	0.250562i
$223$	4.72711	−	2.72920i	0.316550	−	0.182760i	−0.333304	−	0.942820i	$-0.608163\pi$
$223$	4.72711	−	2.72920i	0.316550	−	0.182760i	0.649854	+	0.760059i	$0.274830\pi$
$224$	9.63193	−	10.1890i	0.643560	−	0.680780i
$225$	3.91104	+	0.536172i	0.260736	+	0.0357448i
$226$	2.34181	+	4.05614i	0.155775	+	0.269810i
$227$	−11.3923	−	19.7320i	−0.756132	−	1.30966i	−0.944809	−	0.327620i	$-0.893753\pi$
$227$	−11.3923	−	19.7320i	−0.756132	−	1.30966i	0.188677	−	0.982039i	$-0.439580\pi$
$228$	−0.460539	+	6.75011i	−0.0304999	+	0.447037i
$229$	−15.1066	+	8.72181i	−0.998273	+	0.576353i	−0.907737	−	0.419540i	$-0.862191\pi$
$229$	−15.1066	+	8.72181i	−0.998273	+	0.576353i	−0.0905364	+	0.995893i	$0.528858\pi$
$230$	0.709212	−	1.22839i	0.0467641	−	0.0809977i
$231$	26.3735	+	8.21099i	1.73525	+	0.540243i
$232$	5.20928	+	9.02273i	0.342006	+	0.592371i
$233$	1.62211	−	0.936526i	0.106268	−	0.0613538i	−0.445924	−	0.895071i	$-0.647125\pi$
$233$	1.62211	−	0.936526i	0.106268	−	0.0613538i	0.552192	+	0.833717i	$0.313792\pi$
$234$	5.39982	−	2.39753i	0.352997	−	0.156732i
$235$	−5.26870	+	9.12566i	−0.343692	+	0.595292i
$236$	−1.41433	+	2.44969i	−0.0920650	+	0.159461i
$237$	−7.42350	−	0.506482i	−0.482208	−	0.0328995i
$238$	0.267398	+	0.896405i	0.0173328	+	0.0581053i
$239$			23.7791i			1.53814i	0.639164	+	0.769071i	$0.279281\pi$
$239$			23.7791i			1.53814i	−0.639164	+	0.769071i	$0.720719\pi$
$240$	5.58183	−	8.30568i	0.360306	−	0.536130i
$241$	−18.0905	+	10.4446i	−1.16531	+	0.672795i	−0.952572	−	0.304314i	$-0.901573\pi$
$241$	−18.0905	+	10.4446i	−1.16531	+	0.672795i	−0.212743	+	0.977108i	$0.568240\pi$
$242$	11.9830	+	6.91837i	0.770295	+	0.444730i
$243$	2.83667	+	15.3282i	0.181973	+	0.983304i
$244$	5.29457	−	3.05682i	0.338950	−	0.195693i
$245$	−15.7051	−	7.92643i	−1.00336	−	0.506401i
$246$	7.04634	+	4.73549i	0.449258	+	0.301924i
$247$	−7.03833	+	4.35502i	−0.447838	+	0.277103i
$248$	−10.8065	+	18.7174i	−0.686214	+	1.18856i
$249$	11.4790	−	17.0806i	0.727453	−	1.08244i
$250$	4.37966	+	2.52860i	0.276994	+	0.159922i
$251$	−10.1622	+	17.6015i	−0.641433	+	1.11100i	0.343680	+	0.939087i	$0.388327\pi$
$251$	−10.1622	+	17.6015i	−0.641433	+	1.11100i	−0.985113	+	0.171908i	$0.945007\pi$
$252$	−4.88346	+	12.5927i	−0.307629	+	0.793267i
$253$	3.11421	−	5.39397i	0.195789	−	0.339116i
$254$		−	1.74360i		−	0.109403i
$255$	1.23945	+	2.53038i	0.0776175	+	0.158459i
$256$	1.44540	+	2.50350i	0.0903374	+	0.156469i
$257$	11.9462	−	20.6914i	0.745183	−	1.29069i	−0.204926	−	0.978777i	$-0.565696\pi$
$257$	11.9462	−	20.6914i	0.745183	−	1.29069i	0.950109	−	0.311917i	$-0.100971\pi$
$258$	0.527992	−	7.73878i	0.0328714	−	0.481795i
$259$	2.42345	−	10.1803i	0.150586	−	0.632575i
$260$	15.4120	−	0.470195i	0.955810	−	0.0291603i
$261$	−12.2138	−	9.47608i	−0.756015	−	0.586555i
$262$		−	1.80447i		−	0.111481i
$263$		−	1.61574i		−	0.0996308i	−0.998758	−	0.0498154i	$-0.984137\pi$
$263$		−	1.61574i		−	0.0996308i	0.998758	−	0.0498154i	$-0.0158633\pi$
$264$	−11.7742	+	17.5199i	−0.724653	+	1.07827i
$265$			0.117968i			0.00724672i
$266$	−0.768239	+	3.22719i	−0.0471038	+	0.197872i
$267$	−0.773752	−	1.57964i	−0.0473528	−	0.0966723i
$268$	−1.29539	−	2.24369i	−0.0791287	−	0.137055i
$269$	8.22623	+	14.2482i	0.501562	+	0.868731i	0.999998	+	0.00180469i	$0.000574450\pi$
$269$	8.22623	+	14.2482i	0.501562	+	0.868731i	−0.498436	+	0.866926i	$0.666092\pi$
$270$	1.44755	−	6.98432i	0.0880951	−	0.425052i
$271$	−0.531956	−	0.307125i	−0.0323140	−	0.0186565i	0.483756	−	0.875203i	$-0.339272\pi$
$271$	−0.531956	−	0.307125i	−0.0323140	−	0.0186565i	−0.516070	+	0.856546i	$0.672606\pi$
$272$	1.48812			0.0902302
$273$	−15.9997	+	4.12418i	−0.968347	+	0.249607i
$274$	−4.50681			−0.272266
$275$	−6.86897	−	3.96580i	−0.414214	−	0.239147i
$276$	2.52774	+	1.69877i	0.152152	+	0.102254i
$277$	4.83367	+	8.37217i	0.290427	+	0.503035i	0.973911	−	0.226931i	$-0.0728692\pi$
$277$	4.83367	+	8.37217i	0.290427	+	0.503035i	−0.683484	+	0.729966i	$0.739536\pi$
$278$	−2.36633	−	4.09860i	−0.141923	−	0.245817i
$279$	4.35563	−	31.7716i	0.260765	−	1.90212i
$280$	9.23535	−	9.76947i	0.551918	−	0.583837i
$281$			4.25154i			0.253625i	0.991927	+	0.126813i	$0.0404747\pi$
$281$			4.25154i			0.253625i	−0.991927	+	0.126813i	$0.959525\pi$
$282$	3.29234	+	2.21262i	0.196056	+	0.131759i
$283$			13.4666i			0.800506i	0.916405	+	0.400253i	$0.131078\pi$
$283$			13.4666i			0.800506i	−0.916405	+	0.400253i	$0.868922\pi$
$284$		−	22.5432i		−	1.33769i
$285$	−0.680160	+	9.96910i	−0.0402892	+	0.590518i
$286$	−11.8652	+	0.361988i	−0.701603	+	0.0214048i
$287$	−17.2534	−	16.3101i	−1.01844	−	0.962757i
$288$	−12.5611	−	9.74556i	−0.740172	−	0.574263i
$289$	8.29050	−	14.3596i	0.487676	−	0.844680i
$290$	3.53670	+	6.12574i	0.207682	+	0.359716i
$291$	15.4132	−	7.54983i	0.903538	−	0.442579i
$292$		−	9.36934i		−	0.548299i
$293$	−6.93842	+	12.0177i	−0.405347	+	0.702081i	−0.994362	−	0.106041i	$-0.966183\pi$
$293$	−6.93842	+	12.0177i	−0.405347	+	0.702081i	0.589015	+	0.808122i	$0.299516\pi$
$294$	−3.37938	+	5.69529i	−0.197089	+	0.332156i
$295$	−2.08879	+	3.61789i	−0.121614	+	0.210642i
$296$	6.92575	+	3.99859i	0.402551	+	0.232413i
$297$	6.35632	−	30.6687i	0.368831	−	1.77958i
$298$	3.77206	−	6.53340i	0.218510	−	0.378470i
$299$	0.113611	+	3.72392i	0.00657030	+	0.215360i
$300$	2.16330	−	3.21896i	0.124898	−	0.185847i
$301$	−5.02358	+	21.1029i	−0.289554	+	1.21635i
$302$	3.69776	−	2.13490i	0.212782	−	0.122850i
$303$	5.13713	−	7.64397i	0.295120	−	0.439135i
$304$	4.57032	+	2.63868i	0.262126	+	0.151338i
$305$	7.81944	−	4.51456i	0.447740	−	0.258503i
$306$	0.982101	−	0.400666i	0.0561430	−	0.0229045i
$307$			19.0928i			1.08969i	0.838538	+	0.544843i	$0.183411\pi$
$307$			19.0928i			1.08969i	−0.838538	+	0.544843i	$0.816589\pi$
$308$	18.6424	−	19.7205i	1.06225	−	1.12368i
$309$	0.328688	−	4.81758i	0.0186984	−	0.274062i
$310$	−7.33679	+	12.7077i	−0.416702	+	0.721748i
$311$	1.31104	−	2.27079i	0.0743423	−	0.128765i	−0.826458	−	0.562999i	$-0.809648\pi$
$311$	1.31104	−	2.27079i	0.0743423	−	0.128765i	0.900800	+	0.434234i	$0.142981\pi$
$312$	0.474930	−	12.6177i	0.0268876	−	0.714335i
$313$	3.15245	−	1.82007i	0.178187	−	0.102876i	−0.408253	−	0.912869i	$-0.633862\pi$
$313$	3.15245	−	1.82007i	0.178187	−	0.102876i	0.586441	+	0.809992i	$0.300529\pi$
$314$	2.40907	+	4.17263i	0.135952	+	0.235475i
$315$	−7.21227	+	18.5979i	−0.406366	+	1.04787i
$316$	−3.65509	+	6.33081i	−0.205615	+	0.356136i
$317$	14.6674	−	8.46825i	0.823805	−	0.475624i	−0.0279217	−	0.999610i	$-0.508889\pi$
$317$	14.6674	−	8.46825i	0.823805	−	0.475624i	0.851727	+	0.523986i	$0.175556\pi$
$318$	0.0443056	+	0.00302283i	0.00248453	+	0.000169512i
$319$	15.5299	+	26.8986i	0.869510	+	1.50603i
$320$	−2.14030	−	3.70711i	−0.119647	−	0.207234i
$321$	−29.9024	+	14.6471i	−1.66899	+	0.817520i
$322$	1.08515	+	1.02582i	0.0604730	+	0.0571668i
$323$	−1.28684	+	0.742958i	−0.0716018	+	0.0413393i
$324$	14.7499	+	4.12164i	0.819437	+	0.228980i
$325$	4.74224	−	0.144678i	0.263052	−	0.00802531i
$326$	−5.94905	−	3.43469i	−0.329488	−	0.190230i
$327$	4.61014	+	9.41174i	0.254941	+	0.520471i
$328$	15.7131	−	9.07194i	0.867608	−	0.500914i
$329$	−8.06152	−	7.62077i	−0.444446	−	0.420147i
$330$	−7.99379	+	11.8946i	−0.440044	+	0.654778i
$331$	−10.4278			−0.573166			−0.286583	−	0.958055i	$-0.592519\pi$
$331$	−10.4278			−0.573166			−0.286583	+	0.958055i	$0.592519\pi$
$332$	−10.1092	−	17.5096i	−0.554813	−	0.960964i
$333$	−11.7560	−	1.61165i	−0.644226	−	0.0883181i
$334$		−	7.33365i		−	0.401279i
$335$	−1.91314	−	3.31365i	−0.104526	−	0.181044i
$336$	7.14540	+	7.74155i	0.389813	+	0.422336i
$337$	18.5940			1.01288			0.506440	−	0.862275i	$-0.330961\pi$
$337$	18.5940			1.01288			0.506440	+	0.862275i	$0.330961\pi$
$338$	5.92153	−	3.91862i	0.322089	−	0.213145i
$339$	−13.3378	+	6.53326i	−0.724412	+	0.354838i
$340$	2.76819			0.150126
$341$	−32.2165	+	55.8005i	−1.74462	+	3.02177i
$342$	3.72669	+	0.510899i	0.201516	+	0.0276263i
$343$	11.9467	−	14.1519i	0.645064	−	0.764129i
$344$	−14.3564	−	8.28870i	−0.774048	−	0.446897i
$345$	3.73317	+	2.50887i	0.200987	+	0.135073i
$346$	−3.99581	−	2.30698i	−0.214816	−	0.124024i
$347$	−6.55263	+	3.78316i	−0.351763	+	0.203091i	−0.665462	−	0.746432i	$-0.731765\pi$
$347$	−6.55263	+	3.78316i	−0.351763	+	0.203091i	0.313698	+	0.949523i	$0.398432\pi$
$348$	−13.6391	+	6.68083i	−0.731134	+	0.358130i
$349$	−23.2338	+	13.4141i	−1.24368	+	0.718038i	−0.969841	−	0.243738i	$-0.921626\pi$
$349$	−23.2338	+	13.4141i	−1.24368	+	0.718038i	−0.273837	+	0.961776i	$0.588293\pi$
$350$	1.30633	−	1.38189i	0.0698265	−	0.0738649i
$351$	6.41950	+	17.6009i	0.342648	+	0.939464i
$352$	15.9716	+	27.6636i	0.851288	+	1.47447i
$353$	12.8501			0.683940			0.341970	−	0.939711i	$-0.388906\pi$
$353$	12.8501			0.683940			0.341970	+	0.939711i	$0.388906\pi$
$354$	1.30526	+	0.877198i	0.0693737	+	0.0466226i
$355$		−	33.2935i		−	1.76704i
$356$	−1.72810			−0.0915889
$357$	−2.89366	+	0.652476i	−0.153149	+	0.0345327i
$358$	3.52811	−	6.11086i	0.186466	−	0.322969i
$359$	14.4330	−	8.33290i	0.761745	−	0.439794i	−0.0681770	−	0.997673i	$-0.521718\pi$
$359$	14.4330	−	8.33290i	0.761745	−	0.439794i	0.829922	+	0.557880i	$0.188385\pi$
$360$	−12.0439	−	9.34430i	−0.634771	−	0.492488i
$361$	13.7304			0.722655
$362$	0.371722	−	0.643841i	0.0195373	−	0.0338395i
$363$	−24.4741	+	36.4171i	−1.28456	+	1.91140i
$364$	−3.27590	+	15.8988i	−0.171704	+	0.833323i
$365$		−	13.8374i		−	0.724282i
$366$	−1.49518	−	3.05245i	−0.0781542	−	0.159554i
$367$		−	27.1720i		−	1.41837i	−0.705023	−	0.709184i	$-0.749063\pi$
$367$		−	27.1720i		−	1.41837i	0.705023	−	0.709184i	$-0.250937\pi$
$368$	2.05727	−	1.18776i	0.107243	−	0.0619165i
$369$	−16.5026	+	21.2703i	−0.859089	+	1.10729i
$370$	4.70205	+	2.71473i	0.244448	+	0.141132i
$371$	−0.120817	−	0.0287607i	−0.00627250	−	0.00149318i
$372$	−26.1494	−	17.5737i	−1.35579	−	0.911155i
$373$	−17.0879			−0.884780			−0.442390	−	0.896823i	$-0.645869\pi$
$373$	−17.0879			−0.884780			−0.442390	+	0.896823i	$0.645869\pi$
$374$	−2.13114			−0.110199
$375$	−8.94504	+	13.3101i	−0.461920	+	0.687330i
$376$	7.34179	−	4.23879i	0.378624	−	0.218599i
$377$	−16.3658	−	8.79458i	−0.842880	−	0.452944i
$378$	6.80006	+	3.18529i	0.349758	+	0.163833i
$379$	−11.4321	−	19.8010i	−0.587229	−	1.01711i	−0.994594	−	0.103845i	$-0.966886\pi$
$379$	−11.4321	−	19.8010i	−0.587229	−	1.01711i	0.407365	−	0.913266i	$-0.366448\pi$
$380$	8.50171	+	4.90846i	0.436128	+	0.251799i
$381$	5.51621	+	0.376353i	0.282604	+	0.0192812i
$382$	2.81576	−	4.87703i	0.144067	−	0.249531i
$383$	8.52108			0.435407			0.217703	−	0.976015i	$-0.430143\pi$
$383$	8.52108			0.435407			0.217703	+	0.976015i	$0.430143\pi$
$384$	−17.9334	+	8.78430i	−0.915161	+	0.448272i
$385$	27.5325	−	29.1248i	1.40319	−	1.48434i
$386$	−1.53244	−	0.884754i	−0.0779991	−	0.0450328i
$387$	24.3691	+	3.34081i	1.23875	+	0.169823i
$388$		−	16.8618i		−	0.856027i
$389$	11.0480	+	6.37855i	0.560155	+	0.323406i	0.753208	−	0.657783i	$-0.228506\pi$
$389$	11.0480	+	6.37855i	0.560155	+	0.323406i	−0.193053	+	0.981188i	$0.561839\pi$
$390$	0.322441	−	8.56643i	0.0163274	−	0.433778i
$391$			0.668865i			0.0338260i
$392$	7.75380	+	11.8402i	0.391626	+	0.598019i
$393$	5.70879	+	0.389493i	0.287970	+	0.0196473i
$394$	7.49359			0.377522
$395$	−5.39813	+	9.34983i	−0.271609	+	0.470441i
$396$	−24.3118	−	18.8623i	−1.22171	−	0.947866i
$397$			3.89299i			0.195384i	0.995217	+	0.0976918i	$0.0311459\pi$
$397$			3.89299i			0.195384i	−0.995217	+	0.0976918i	$0.968854\pi$
$398$	−1.81898			−0.0911773
$399$	−10.0440	−	3.12706i	−0.502830	−	0.156549i
$400$	−1.51256	−	2.61983i	−0.0756281	−	0.130992i
$401$	19.1034	+	11.0293i	0.953977	+	0.550779i	0.894314	−	0.447440i	$-0.147664\pi$
$401$	19.1034	+	11.0293i	0.953977	+	0.550779i	0.0596628	+	0.998219i	$0.480997\pi$
$402$	−1.29354	+	0.633612i	−0.0645158	+	0.0316017i
$403$	−1.17530	−	38.5239i	−0.0585461	−	1.91901i
$404$	−4.52409	−	7.83596i	−0.225082	−	0.389854i
$405$	21.7838	+	6.08716i	1.08244	+	0.302473i
$406$	−7.13591	+	2.12864i	−0.354150	+	0.105643i
$407$	20.6471	+	11.9206i	1.02344	+	0.590883i
$408$	0.154301	−	2.26159i	0.00763905	−	0.111965i
$409$	7.43125	−	4.29044i	0.367452	−	0.212148i	−0.304893	−	0.952387i	$-0.598621\pi$
$409$	7.43125	−	4.29044i	0.367452	−	0.212148i	0.672345	+	0.740238i	$0.265287\pi$
$410$	10.6680	−	6.15915i	0.526853	−	0.304179i
$411$	0.972788	−	14.2581i	0.0479841	−	0.703302i
$412$	−4.10846	−	2.37202i	−0.202409	−	0.116861i
$413$	−3.19601	−	3.02128i	−0.157265	−	0.148667i
$414$	1.03792	−	1.33779i	0.0510111	−	0.0657486i
$415$	−14.9300	−	25.8595i	−0.732886	−	1.26940i
$416$	−16.8312	−	9.04468i	−0.825217	−	0.443452i
$417$	13.4775	−	6.60164i	0.659994	−	0.323284i
$418$	−6.54520	−	3.77887i	−0.320136	−	0.184831i
$419$	−12.5477	−	21.7332i	−0.612994	−	1.06174i	−0.990733	−	0.135825i	$-0.956632\pi$
$419$	−12.5477	−	21.7332i	−0.612994	−	1.06174i	0.377739	−	0.925912i	$-0.376702\pi$
$420$	13.2919	+	14.4008i	0.648577	+	0.702689i
$421$	−11.9143			−0.580668			−0.290334	−	0.956925i	$-0.593766\pi$
$421$	−11.9143			−0.580668			−0.290334	+	0.956925i	$0.593766\pi$
$422$			5.10466i			0.248491i
$423$	−7.71068	+	9.93836i	−0.374906	+	0.483219i
$424$	0.0474539	−	0.0821926i	0.00230457	−	0.00399163i
$425$	0.851768			0.0413168
$426$	−12.5041	−	0.853118i	−0.605827	−	0.0413337i
$427$	2.71719	+	9.10892i	0.131494	+	0.440812i
$428$			32.7127i			1.58123i
$429$	1.41587	−	37.6159i	0.0683587	−	1.81611i
$430$	−9.74692	−	5.62739i	−0.470038	−	0.271377i
$431$		−	28.8820i		−	1.39119i	−0.718432	−	0.695597i	$-0.755140\pi$
$431$		−	28.8820i		−	1.39119i	0.718432	−	0.695597i	$-0.244860\pi$
$432$	7.94806	−	8.91783i	0.382401	−	0.429059i
$433$	−6.48299	−	3.74296i	−0.311553	−	0.179875i	0.336068	−	0.941838i	$-0.390903\pi$
$433$	−6.48299	−	3.74296i	−0.311553	−	0.179875i	−0.647621	+	0.761963i	$0.724236\pi$
$434$	−11.2258	−	10.6121i	−0.538858	−	0.509397i
$435$	−20.1433	+	9.86678i	−0.965799	+	0.473076i
$436$	10.2963			0.493102
$437$	−1.18601	+	2.05423i	−0.0567345	+	0.0982671i
$438$	−5.19694	−	0.354571i	−0.248319	−	0.0169421i
$439$	−8.85143	−	5.11037i	−0.422456	−	0.243905i	0.273672	−	0.961823i	$-0.411762\pi$
$439$	−8.85143	−	5.11037i	−0.422456	−	0.243905i	−0.696127	+	0.717918i	$0.745095\pi$
$440$	15.3140	+	26.5246i	0.730065	+	1.26451i
$441$	−17.2887	−	11.9206i	−0.823271	−	0.567649i
$442$	1.08405	−	0.670762i	0.0515629	−	0.0319049i
$443$	−26.2992	+	15.1839i	−1.24951	+	0.721407i	−0.971012	−	0.239029i	$-0.923171\pi$
$443$	−26.2992	+	15.1839i	−1.24951	+	0.721407i	−0.278501	+	0.960436i	$0.589838\pi$
$444$	−6.50257	+	9.67572i	−0.308598	+	0.459190i
$445$	−2.55219			−0.120985
$446$	−2.98142			−0.141174
$447$	19.8555	+	13.3439i	0.939131	+	0.631143i
$448$	4.31844	−	1.28819i	0.204027	−	0.0608613i
$449$	−19.0172	−	10.9796i	−0.897478	−	0.518159i	−0.0210967	−	0.999777i	$-0.506716\pi$
$449$	−19.0172	−	10.9796i	−0.897478	−	0.518159i	−0.876381	+	0.481618i	$0.840049\pi$
$450$	−1.70361	−	1.32175i	−0.0803089	−	0.0623077i
$451$	46.8439	−	27.0453i	2.20579	−	1.27352i
$452$			14.5914i			0.686320i
$453$	5.95601	+	12.1594i	0.279838	+	0.571297i
$454$			12.4451i			0.584078i
$455$	−4.83810	+	23.4806i	−0.226814	+	1.10079i
$456$	4.48407	−	6.67223i	0.209986	−	0.312456i
$457$	−18.0285	+	31.2263i	−0.843338	+	1.46070i	0.0437182	+	0.999044i	$0.486080\pi$
$457$	−18.0285	+	31.2263i	−0.843338	+	1.46070i	−0.887057	+	0.461661i	$0.847254\pi$
$458$	9.52785			0.445207
$459$	1.05560	+	3.19355i	0.0492710	+	0.149062i
$460$	3.82693	−	2.20948i	0.178431	−	0.103017i
$461$	4.57076	−	7.91680i	0.212882	−	0.368722i	−0.739734	−	0.672900i	$-0.765048\pi$
$461$	4.57076	−	7.91680i	0.212882	−	0.368722i	0.952615	+	0.304178i	$0.0983818\pi$
$462$	−10.2330	−	11.0867i	−0.476082	−	0.515802i
$463$	22.1372			1.02880			0.514401	−	0.857550i	$-0.328014\pi$
$463$	22.1372			1.02880			0.514401	+	0.857550i	$0.328014\pi$
$464$			11.8463i			0.549950i
$465$	−38.6195	−	25.9543i	−1.79094	−	1.20360i
$466$	−1.02308			−0.0473931
$467$	−0.315959	−	0.547257i	−0.0146208	−	0.0253240i	0.858622	−	0.512609i	$-0.171321\pi$
$467$	−0.315959	−	0.547257i	−0.0146208	−	0.0253240i	−0.873243	+	0.487285i	$0.837987\pi$
$468$	18.3034	+	1.94272i	0.846076	+	0.0898021i
$469$	3.86009	−	1.15147i	0.178243	−	0.0531698i
$470$	4.98451	−	2.87781i	0.229918	−	0.132743i
$471$	−13.7209	+	6.72089i	−0.632225	+	0.309682i
$472$	2.91067	−	1.68048i	0.133975	−	0.0773503i
$473$	−42.7996	−	24.7103i	−1.96793	−	1.13618i
$474$	3.37322	+	2.26697i	0.154937	+	0.104125i
$475$	2.61596	+	1.51033i	0.120029	+	0.0692986i
$476$	−0.674886	+	2.83504i	−0.0309334	+	0.129944i
$477$	−0.0191266	+	0.139517i	−0.000875747	+	0.00638803i
$478$	6.49417	−	11.2482i	0.297036	−	0.514482i
$479$	−22.3302			−1.02029			−0.510146	−	0.860088i	$-0.670409\pi$
$479$	−22.3302			−1.02029			−0.510146	+	0.860088i	$0.670409\pi$
$480$	−20.7162	+	10.1474i	−0.945560	+	0.463162i
$481$	−14.2545	+	0.434882i	−0.649949	+	0.0198289i
$482$	11.4098			0.519704
$483$	−3.47961	+	3.21165i	−0.158328	+	0.146135i
$484$	21.5535	+	37.3317i	0.979704	+	1.69690i
$485$		−	24.9028i		−	1.13078i
$486$	2.84436	−	8.02540i	0.129023	−	0.364040i
$487$	20.1441	+	34.8907i	0.912817	+	1.58105i	0.810066	+	0.586339i	$0.199431\pi$
$487$	20.1441	+	34.8907i	0.912817	+	1.58105i	0.102752	+	0.994707i	$0.467235\pi$
$488$	−7.26412			−0.328831
$489$	12.1504	−	18.0796i	0.549459	−	0.817587i
$490$	5.26424	+	8.03856i	0.237814	+	0.363145i
$491$	6.70526	−	3.87128i	0.302604	−	0.174709i	−0.341008	−	0.940060i	$-0.610768\pi$
$491$	6.70526	−	3.87128i	0.302604	−	0.174709i	0.643612	+	0.765352i	$0.277435\pi$
$492$	11.6347	+	23.7525i	0.524531	+	1.07085i
$493$	−2.88862	−	1.66775i	−0.130097	−	0.0751116i
$494$	4.51871	−	0.137859i	0.203307	−	0.00620256i
$495$	−35.9055	−	27.8573i	−1.61383	−	1.25209i
$496$	−21.2824	+	12.2874i	−0.955608	+	0.551721i
$497$	34.0975	+	8.11698i	1.52948	+	0.364096i
$498$	−10.0947	+	4.94467i	−0.452354	+	0.221576i
$499$	−7.94320	−	13.7580i	−0.355587	−	0.615894i	0.631632	−	0.775269i	$-0.282386\pi$
$499$	−7.94320	−	13.7580i	−0.355587	−	0.615894i	−0.987218	+	0.159375i	$0.949052\pi$
$500$	7.87759	+	13.6444i	0.352296	+	0.610195i
$501$	23.2014	+	1.58296i	1.03656	+	0.0707213i
$502$	9.61407	−	5.55069i	0.429097	−	0.247739i
$503$	14.9743	−	25.9362i	0.667671	−	1.15644i	−0.310883	−	0.950448i	$-0.600625\pi$
$503$	14.9743	−	25.9362i	0.667671	−	1.15644i	0.978554	−	0.205992i	$-0.0660420\pi$
$504$	12.5063	−	10.0566i	0.557074	−	0.447958i
$505$	−6.68154	−	11.5728i	−0.297325	−	0.514981i
$506$	−2.94623	+	1.70101i	−0.130976	+	0.0756190i
$507$	11.1191	+	19.5797i	0.493818	+	0.869565i
$508$	2.71600	−	4.70426i	0.120503	−	0.208718i
$509$	−3.30037	+	5.71641i	−0.146286	+	0.253376i	−0.929852	−	0.367933i	$-0.880065\pi$
$509$	−3.30037	+	5.71641i	−0.146286	+	0.253376i	0.783566	+	0.621309i	$0.213399\pi$
$510$	0.104759	−	1.53545i	0.00463879	−	0.0679907i
$511$	14.1715	+	3.37356i	0.626912	+	0.149238i
$512$			21.4795i			0.949271i
$513$	−2.42073	+	11.6798i	−0.106878	+	0.515676i
$514$	−11.3018	+	6.52511i	−0.498502	+	0.287810i
$515$	−6.06769	−	3.50318i	−0.267375	−	0.154369i
$516$	13.4792	−	20.0569i	0.593389	−	0.882955i
$517$	21.8874	−	12.6367i	0.962607	−	0.555762i
$518$	−3.92665	+	4.15375i	−0.172527	+	0.182505i
$519$	8.16106	−	12.1435i	0.358231	−	0.533042i
$520$	−16.1382	−	8.67228i	−0.707706	−	0.380304i
$521$	11.1062	−	19.2365i	0.486570	−	0.842764i	−0.513311	−	0.858203i	$-0.671581\pi$
$521$	11.1062	−	19.2365i	0.486570	−	0.842764i	0.999881	+	0.0154387i	$0.00491447\pi$
$522$	3.18954	+	7.81811i	0.139602	+	0.342189i
$523$	−22.8268	−	13.1791i	−0.998147	−	0.576280i	−0.0904472	−	0.995901i	$-0.528830\pi$
$523$	−22.8268	−	13.1791i	−0.998147	−	0.576280i	−0.907699	+	0.419621i	$0.862163\pi$
$524$	2.81082	−	4.86849i	0.122791	−	0.212681i
$525$	4.08989	+	4.43112i	0.178497	+	0.193390i
$526$	−0.441265	+	0.764294i	−0.0192401	+	0.0333248i
$527$		−	6.91940i		−	0.301414i
$528$	−21.5545	+	10.5580i	−0.938038	+	0.459478i
$529$	−10.9661	−	18.9939i	−0.476788	−	0.825822i
$530$	0.0322176	−	0.0558025i	0.00139944	−	0.00242390i
$531$	−3.05692	+	3.94009i	−0.132659	+	0.170985i
$532$	−7.09972	+	7.51033i	−0.307812	+	0.325614i
$533$	−15.3157	+	28.5009i	−0.663398	+	1.23451i
$534$	−0.0653976	+	0.958531i	−0.00283003	+	0.0414797i
$535$			48.3127i			2.08874i
$536$			3.07832i			0.132963i
$537$	18.5713	+	12.4809i	0.801412	+	0.538588i
$538$		−	8.98647i		−	0.387434i
$539$	23.1157	+	35.2980i	0.995664	+	1.52039i
$540$	14.7850	−	16.5889i	0.636244	−	0.713874i
$541$	7.27566	+	12.6018i	0.312805	+	0.541794i	0.978968	−	0.204012i	$-0.0653981\pi$
$541$	7.27566	+	12.6018i	0.312805	+	0.541794i	−0.666164	+	0.745806i	$0.732065\pi$
$542$	0.167754	+	0.290559i	0.00720566	+	0.0124806i
$543$	1.95668	+	1.31498i	0.0839691	+	0.0564314i
$544$	−2.97077	−	1.71518i	−0.127371	−	0.0735376i
$545$	15.2064			0.651369
$546$	8.69468	+	2.41873i	0.372098	+	0.103512i
$547$	13.3560			0.571060			0.285530	−	0.958370i	$-0.407830\pi$
$547$	13.3560			0.571060			0.285530	+	0.958370i	$0.407830\pi$
$548$	−12.1594	−	7.02025i	−0.519425	−	0.299890i
$549$	9.97973	−	4.07141i	0.425925	−	0.173764i
$550$	2.16615	+	3.75189i	0.0923651	+	0.159981i
$551$	−5.91439	−	10.2440i	−0.251961	−	0.436410i
$552$	−1.59181	−	3.24973i	−0.0677520	−	0.138318i
$553$	−8.25955	−	7.80798i	−0.351232	−	0.332029i
$554$		−	5.28038i		−	0.224342i
$555$	−9.60350	+	14.2899i	−0.407646	+	0.606571i
$556$		−	14.7441i		−	0.625289i
$557$		−	21.4071i		−	0.907046i	−0.891245	−	0.453523i	$-0.850167\pi$
$557$		−	21.4071i		−	0.907046i	0.891245	−	0.453523i	$-0.149833\pi$
$558$	−10.7373	+	13.8394i	−0.454546	+	0.585868i
$559$	29.5482	−	0.901470i	1.24976	−	0.0381281i
$560$	14.6482	−	4.36956i	0.619000	−	0.184648i
$561$	0.460004	−	6.74227i	0.0194214	−	0.284659i
$562$	1.16111	−	2.01111i	0.0489786	−	0.0848334i
$563$	−14.7814	−	25.6022i	−0.622963	−	1.07900i	−0.988931	−	0.148376i	$-0.952596\pi$
$563$	−14.7814	−	25.6022i	−0.622963	−	1.07900i	0.365969	−	0.930627i	$-0.380738\pi$
$564$	5.43619	+	11.0981i	0.228905	+	0.467316i
$565$			21.5497i			0.906601i
$566$	3.67778	−	6.37011i	0.154589	−	0.267756i
$567$	−11.5450	+	20.8258i	−0.484846	+	0.874599i
$568$	−13.3927	+	23.1968i	−0.561944	+	0.973316i
$569$	−23.8838	−	13.7893i	−1.00126	−	0.578078i	−0.0926389	−	0.995700i	$-0.529530\pi$
$569$	−23.8838	−	13.7893i	−1.00126	−	0.578078i	−0.908621	+	0.417622i	$0.862864\pi$
$570$	3.04434	−	4.52993i	0.127513	−	0.189738i
$571$	17.4312	−	30.1918i	0.729475	−	1.26349i	−0.227630	−	0.973748i	$-0.573098\pi$
$571$	17.4312	−	30.1918i	0.729475	−	1.26349i	0.957105	−	0.289740i	$-0.0935689\pi$
$572$	−32.5763	−	17.5057i	−1.36208	−	0.731952i
$573$	14.8216	+	9.96088i	0.619183	+	0.416122i
$574$	3.70703	+	12.4272i	0.154728	+	0.518700i
$575$	1.17754	−	0.679853i	0.0491068	−	0.0283518i
$576$	−1.93021	−	4.73128i	−0.0804255	−	0.197137i
$577$	−9.56438	−	5.52200i	−0.398170	−	0.229884i	0.287524	−	0.957773i	$-0.407168\pi$
$577$	−9.56438	−	5.52200i	−0.398170	−	0.229884i	−0.685694	+	0.727890i	$0.740501\pi$
$578$	−7.84331	+	4.52834i	−0.326239	+	0.188354i
$579$	3.12986	−	4.65719i	0.130073	−	0.193546i
$580$			22.0364i			0.915014i
$581$	30.1240	−	8.98598i	1.24975	−	0.372801i
$582$	−9.35280	−	0.638112i	−0.387686	−	0.0264506i
$583$	0.141470	−	0.245033i	0.00585909	−	0.0101482i
$584$	−5.56624	+	9.64100i	−0.230332	+	0.398948i
$585$	27.0319	+	2.86916i	1.11763	+	0.118625i
$586$	6.56417	−	3.78982i	0.271163	−	0.156556i
$587$	12.6832	+	21.9680i	0.523493	+	0.906717i	0.999626	+	0.0273434i	$0.00870477\pi$
$587$	12.6832	+	21.9680i	0.523493	+	0.906717i	−0.476133	+	0.879373i	$0.657962\pi$
$588$	−17.9892	+	10.1019i	−0.741860	+	0.416596i
$589$	12.2692	−	21.2510i	0.505546	−	0.875631i
$590$	1.97612	−	1.14092i	0.0813557	−	0.0469707i
$591$	−1.61748	+	23.7074i	−0.0665343	+	0.975192i
$592$	4.54654	+	7.87484i	0.186862	+	0.323654i
$593$	5.88143	+	10.1869i	0.241521	+	0.418327i	0.961148	−	0.276034i	$-0.0890203\pi$
$593$	5.88143	+	10.1869i	0.241521	+	0.418327i	−0.719627	+	0.694361i	$0.755687\pi$
$594$	−11.3825	+	12.7713i	−0.467029	+	0.524013i
$595$	−0.996725	+	4.18701i	−0.0408618	+	0.171651i
$596$	20.3541	−	11.7515i	0.833738	−	0.481359i
$597$	0.392625	−	5.75469i	0.0160691	−	0.235524i
$598$	0.963278	−	1.79256i	0.0393913	−	0.0733031i
$599$	39.8531	+	23.0092i	1.62835	+	0.940131i	0.984584	+	0.174911i	$0.0559639\pi$
$599$	39.8531	+	23.0092i	1.62835	+	0.940131i	0.643770	+	0.765219i	$0.277369\pi$
$600$	−4.13838	+	2.02710i	−0.168949	+	0.0827558i
$601$	−26.1034	+	15.0708i	−1.06478	+	0.614751i	−0.926751	−	0.375677i	$-0.877410\pi$
$601$	−26.1034	+	15.0708i	−1.06478	+	0.614751i	−0.138030	+	0.990428i	$0.544077\pi$
$602$	8.13958	−	8.61033i	0.331745	−	0.350931i
$603$	−1.72534	−	4.22912i	−0.0702614	−	0.172223i
$604$	13.3021			0.541256
$605$	31.8319	+	55.1344i	1.29415	+	2.24153i
$606$	−4.51762	+	2.21286i	−0.183516	+	0.0898913i
$607$			36.2573i			1.47164i	0.677179	+	0.735818i	$0.263202\pi$
$607$			36.2573i			1.47164i	−0.677179	+	0.735818i	$0.736798\pi$
$608$	−6.08259	−	10.5353i	−0.246681	−	0.427265i
$609$	−5.19409	−	23.0353i	−0.210475	−	0.933437i
$610$	−4.93178			−0.199682
$611$	−7.15614	+	13.3168i	−0.289507	+	0.538741i
$612$	3.27384	+	0.448817i	0.132337	+	0.0181423i
$613$	33.6982			1.36106			0.680530	−	0.732721i	$-0.261750\pi$
$613$	33.6982			1.36106			0.680530	+	0.732721i	$0.261750\pi$
$614$	5.21433	−	9.03149i	0.210433	−	0.364481i
$615$	17.1830	+	35.0796i	0.692884	+	1.41454i
$616$	−30.8987	+	9.21707i	−1.24494	+	0.371367i
$617$	−6.51889	−	3.76368i	−0.262441	−	0.151520i	0.363007	−	0.931786i	$-0.381750\pi$
$617$	−6.51889	−	3.76368i	−0.262441	−	0.151520i	−0.625447	+	0.780266i	$0.715084\pi$
$618$	−1.47118	+	2.18909i	−0.0591795	+	0.0880582i
$619$	−39.6473	−	22.8904i	−1.59356	−	0.920043i	−0.992689	−	0.120697i	$-0.961487\pi$
$619$	−39.6473	−	22.8904i	−1.59356	−	0.920043i	−0.600871	−	0.799346i	$-0.705179\pi$
$620$	−39.5895	+	22.8570i	−1.58995	+	0.917960i
$621$	4.00831	+	3.57243i	0.160848	+	0.143357i
$622$	−1.24032	+	0.716101i	−0.0497325	+	0.0287130i
$623$	0.622225	−	2.61382i	0.0249289	−	0.104720i
$624$	7.64105	−	12.1547i	0.305887	−	0.486576i
$625$	14.9239	+	25.8490i	0.596957	+	1.03396i
$626$	−1.98828			−0.0794675
$627$	13.3679	−	19.8913i	0.533864	−	0.794382i
$628$			15.0104i			0.598981i
$629$	−2.56029			−0.102086
$630$	8.49080	−	6.82768i	0.338281	−	0.272021i
$631$	−14.0226	+	24.2878i	−0.558230	+	0.966882i	0.439415	+	0.898284i	$0.355186\pi$
$631$	−14.0226	+	24.2878i	−0.558230	+	0.966882i	−0.997644	+	0.0685980i	$0.978147\pi$
$632$	7.52214	−	4.34291i	0.299215	−	0.172752i
$633$	−16.1496	−	1.10183i	−0.641887	−	0.0437940i
$634$	−9.25085			−0.367398
$635$	4.01121	−	6.94761i	0.159180	−	0.275708i
$636$	0.114828	+	0.0771704i	0.00455324	+	0.00306001i
$637$	−22.8681	−	10.6795i	−0.906065	−	0.423138i
$638$		−	16.9652i		−	0.671657i
$639$	5.39800	−	39.3750i	0.213542	−	1.55765i
$640$			28.9746i			1.14532i
$641$	0.799986	−	0.461872i	0.0315975	−	0.0182428i	−0.484118	−	0.875003i	$-0.660859\pi$
$641$	0.799986	−	0.461872i	0.0315975	−	0.0182428i	0.515716	+	0.856760i	$0.327526\pi$
$642$	18.1449	+	1.23797i	0.716124	+	0.0488589i
$643$	6.72532	+	3.88286i	0.265221	+	0.153125i	0.626714	−	0.779250i	$-0.284400\pi$
$643$	6.72532	+	3.88286i	0.265221	+	0.153125i	−0.361493	+	0.932375i	$0.617733\pi$
$644$	1.32983	+	4.45802i	0.0524025	+	0.175670i
$645$	19.9072	−	29.6216i	0.783844	−	1.16635i
$646$	0.811620			0.0319328
$647$	−24.2168			−0.952061			−0.476030	−	0.879429i	$-0.657925\pi$
$647$	−24.2168			−0.952061			−0.476030	+	0.879429i	$0.657925\pi$
$648$	−12.7289	−	13.0039i	−0.500039	−	0.510841i
$649$	8.67733	−	5.00986i	0.340615	−	0.196654i
$650$	−2.28274	−	1.22669i	−0.0895363	−	0.0481147i
$651$	35.9965	−	33.2245i	1.41081	−	1.30217i
$652$	−10.7004	−	18.5337i	−0.419061	−	0.725835i
$653$	31.2511	+	18.0428i	1.22295	+	0.706070i	0.965546	−	0.260234i	$-0.0837996\pi$
$653$	31.2511	+	18.0428i	1.22295	+	0.706070i	0.257404	+	0.966304i	$0.417133\pi$
$654$	0.389650	−	5.71109i	0.0152365	−	0.223321i
$655$	4.15124	−	7.19017i	0.162203	−	0.280943i
$656$	20.6303			0.805477
$657$	2.24350	−	16.3650i	0.0875275	−	0.638458i
$658$	1.73208	+	5.80649i	0.0675234	+	0.226361i
$659$	−10.7491	−	6.20598i	−0.418724	−	0.241751i	0.275807	−	0.961213i	$-0.411055\pi$
$659$	−10.7491	−	6.20598i	−0.418724	−	0.241751i	−0.694531	+	0.719462i	$0.744388\pi$
$660$	−40.0956	+	19.6400i	−1.56072	+	0.764486i
$661$			28.4702i			1.10736i	0.832728	+	0.553682i	$0.186778\pi$
$661$			28.4702i			1.10736i	−0.832728	+	0.553682i	$0.813222\pi$
$662$	4.93268	+	2.84789i	0.191714	+	0.110686i
$663$	1.88809	+	3.57437i	0.0733275	+	0.138817i
$664$			24.0230i			0.932275i
$665$	−10.4854	+	11.0918i	−0.406607	+	0.430123i
$666$	5.12080	+	3.97298i	0.198427	+	0.153950i
$667$	−5.32456			−0.206168
$668$	11.4236	−	19.7863i	0.441993	−	0.765554i
$669$	0.643535	−	9.43228i	0.0248805	−	0.364673i
$670$			2.08994i			0.0807415i
$671$	−21.6559			−0.836015
$672$	−5.34181	−	23.6904i	−0.206065	−	0.913876i
$673$	5.65042	+	9.78682i	0.217808	+	0.377254i	0.954137	−	0.299369i	$-0.0967761\pi$
$673$	5.65042	+	9.78682i	0.217808	+	0.377254i	−0.736330	+	0.676623i	$0.763443\pi$
$674$	−8.79553	−	5.07810i	−0.338791	−	0.195601i
$675$	4.54932	−	5.10439i	0.175103	−	0.196468i
$676$	22.0804	−	1.34853i	0.849246	−	0.0518666i
$677$	−6.45592	−	11.1820i	−0.248121	−	0.429758i	0.714883	−	0.699244i	$-0.246480\pi$
$677$	−6.45592	−	11.1820i	−0.248121	−	0.429758i	−0.963004	+	0.269485i	$0.913146\pi$
$678$	8.09346	+	0.552191i	0.310827	+	0.0212068i
$679$	25.5041	+	6.07131i	0.978759	+	0.232996i
$680$	−2.84845	−	1.64456i	−0.109233	−	0.0630658i
$681$	−39.3725	−	2.68626i	−1.50876	−	0.102938i
$682$	30.4787	−	17.5969i	1.16709	−	0.673820i
$683$	−7.62396	+	4.40170i	−0.291723	+	0.168426i	−0.638719	−	0.769440i	$-0.720535\pi$
$683$	−7.62396	+	4.40170i	−0.291723	+	0.168426i	0.346996	+	0.937867i	$0.387202\pi$
$684$	9.25884	+	7.18348i	0.354020	+	0.274667i
$685$	−17.9580	−	10.3681i	−0.686140	−	0.396143i
$686$	−9.51610	+	3.43155i	−0.363327	+	0.131017i
$687$	−2.05657	+	30.1432i	−0.0784632	+	1.15003i
$688$	−9.42456	−	16.3238i	−0.359308	−	0.622340i
$689$	0.00516104	+	0.169168i	0.000196620	+	0.00644478i
$690$	−1.08072	−	2.20632i	−0.0411422	−	0.0839930i
$691$	−18.3482	−	10.5934i	−0.698000	−	0.402990i	0.108602	−	0.994085i	$-0.465363\pi$
$691$	−18.3482	−	10.5934i	−0.698000	−	0.402990i	−0.806602	+	0.591095i	$0.798696\pi$
$692$	−7.18716	−	12.4485i	−0.273215	−	0.473222i
$693$	37.2838	−	29.9809i	1.41629	−	1.13888i
$694$	4.13279			0.156878
$695$		−	21.7752i		−	0.825982i
$696$	18.0036	+	1.22833i	0.682425	+	0.0465597i
$697$	−2.90438	+	5.03053i	−0.110011	+	0.190545i
$698$	14.6537			0.554652
$699$	0.220830	−	3.23670i	0.00835254	−	0.122423i
$700$	5.67707	−	1.69347i	0.214573	−	0.0640072i
$701$		−	39.6954i		−	1.49927i	−0.661849	−	0.749637i	$-0.730228\pi$
$701$		−	39.6954i		−	1.49927i	0.661849	−	0.749637i	$-0.269772\pi$
$702$	1.77025	−	10.0789i	0.0668136	−	0.380405i
$703$	−7.86321	−	4.53982i	−0.296566	−	0.171223i
$704$			10.2668i			0.386945i
$705$	8.02860	+	16.3906i	0.302374	+	0.617306i
$706$	−6.07847	−	3.50941i	−0.228766	−	0.132078i
$707$	13.4812	−	4.02144i	0.507012	−	0.151242i
$708$	2.15519	+	4.39989i	0.0809971	+	0.165358i
$709$	−9.11397			−0.342282			−0.171141	−	0.985247i	$-0.554745\pi$
$709$	−9.11397			−0.342282			−0.171141	+	0.985247i	$0.554745\pi$
$710$	−9.09260	+	15.7488i	−0.341239	+	0.591043i
$711$	−7.90009	+	10.1825i	−0.296277	+	0.381873i
$712$	1.77820	+	1.02664i	0.0666409	+	0.0384751i
$713$	−5.52284	−	9.56583i	−0.206832	−	0.358243i
$714$	1.54698	+	0.481631i	0.0578944	+	0.0180246i
$715$	−48.1113	−	25.8539i	−1.79926	−	0.966880i
$716$	19.0378	−	10.9915i	0.711474	−	0.410770i
$717$	34.1841	+	22.9734i	1.27663	+	0.857959i
$718$	−9.10300			−0.339721
$719$	−10.9246			−0.407418			−0.203709	−	0.979032i	$-0.565300\pi$
$719$	−10.9246			−0.407418			−0.203709	+	0.979032i	$0.565300\pi$
$720$	−6.54730	−	16.0486i	−0.244003	−	0.598095i
$721$	5.06709	−	5.36014i	0.188708	−	0.199622i
$722$	−6.49492	−	3.74984i	−0.241716	−	0.139555i
$723$	−2.46280	+	36.0972i	−0.0915924	+	1.34247i
$724$	2.00582	−	1.15806i	0.0745458	−	0.0430390i
$725$			6.78058i			0.251824i
$726$	21.5226	−	10.5424i	0.798780	−	0.391265i
$727$		−	45.7930i		−	1.69837i	−0.528098	−	0.849183i	$-0.677095\pi$
$727$		−	45.7930i		−	1.69837i	0.528098	−	0.849183i	$-0.322905\pi$
$728$	12.8162	−	14.4136i	0.475000	−	0.534203i
$729$	24.7759	+	10.7309i	0.917627	+	0.397442i
$730$	−3.77905	+	6.54550i	−0.139869	+	0.242260i
$731$	5.30725			0.196296
$732$	0.720789	−	10.5646i	0.0266411	−	0.390478i
$733$	17.4750	−	10.0892i	0.645455	−	0.372654i	−0.141258	−	0.989973i	$-0.545115\pi$
$733$	17.4750	−	10.0892i	0.645455	−	0.372654i	0.786713	+	0.617319i	$0.211781\pi$
$734$	−7.42079	+	12.8532i	−0.273906	+	0.474420i
$735$	−26.5678	+	14.9193i	−0.979968	+	0.550307i
$736$	−5.47599			−0.201848
$737$			9.17712i			0.338043i
$738$	13.6152	−	5.55457i	0.501183	−	0.204466i
$739$	−48.5659			−1.78652			−0.893262	−	0.449536i	$-0.851589\pi$
$739$	−48.5659			−1.78652			−0.893262	+	0.449536i	$0.851589\pi$
$740$	8.45747	+	14.6488i	0.310903	+	0.538500i
$741$	−0.539216	+	14.3256i	−0.0198086	+	0.526263i
$742$	0.0492954	+	0.0466003i	0.00180969	+	0.00171075i
$743$	6.39543	−	3.69241i	0.234626	−	0.135461i	−0.378078	−	0.925774i	$-0.623415\pi$
$743$	6.39543	−	3.69241i	0.234626	−	0.135461i	0.612704	+	0.790312i	$0.290082\pi$
$744$	16.4673	+	33.6184i	0.603719	+	1.23251i
$745$	30.0606	−	17.3555i	1.10134	−	0.635856i
$746$	8.08311	+	4.66678i	0.295944	+	0.170863i
$747$	−13.4645	−	33.0038i	−0.492640	−	1.20755i
$748$	−5.74985	−	3.31968i	−0.210235	−	0.121380i
$749$	−49.4794	−	11.7787i	−1.80794	−	0.430383i
$750$	7.86631	−	3.85315i	0.287237	−	0.140697i
$751$	11.5832	−	20.0627i	0.422676	−	0.732097i	−0.573524	−	0.819189i	$-0.694424\pi$
$751$	11.5832	−	20.0627i	0.422676	−	0.732097i	0.996200	+	0.0870918i	$0.0277573\pi$
$752$	9.63931			0.351510
$753$	15.4855	+	31.6140i	0.564322	+	1.15208i
$754$	5.33967	+	8.62966i	0.194459	+	0.314274i
$755$	19.6456			0.714978
$756$	13.3850	+	19.1864i	0.486806	+	0.697803i
$757$	−19.9604	−	34.5725i	−0.725475	−	1.25656i	−0.958778	−	0.284155i	$-0.908287\pi$
$757$	−19.9604	−	34.5725i	−0.725475	−	1.25656i	0.233304	−	0.972404i	$-0.425046\pi$
$758$			12.4886i			0.453608i
$759$	−4.74552	−	9.68812i	−0.172251	−	0.351657i
$760$	−5.83214	−	10.1016i	−0.211554	−	0.366422i
$761$	7.97685			0.289161			0.144580	−	0.989493i	$-0.453817\pi$
$761$	7.97685			0.289161			0.144580	+	0.989493i	$0.453817\pi$
$762$	−2.50655	−	1.68453i	−0.0908027	−	0.0610239i
$763$	−3.70732	+	15.5736i	−0.134214	+	0.563801i
$764$	15.1939	−	8.77221i	0.549696	−	0.317367i
$765$	4.83506	+	0.662848i	0.174812	+	0.0239653i
$766$	−4.03073	−	2.32714i	−0.145636	−	0.0840830i
$767$	−2.83707	+	5.27949i	−0.102441	+	0.190631i
$768$	4.99540	+	0.340820i	0.180256	+	0.0122983i
$769$	−8.79268	+	5.07646i	−0.317072	+	0.183062i	−0.650087	−	0.759860i	$-0.725267\pi$
$769$	−8.79268	+	5.07646i	−0.317072	+	0.183062i	0.333015	+	0.942922i	$0.391934\pi$
$770$	−20.9778	+	6.25768i	−0.755988	+	0.225511i
$771$	−18.2039	−	37.1639i	−0.655599	−	1.33842i
$772$	−2.75636	−	4.77416i	−0.0992036	−	0.171826i
$773$	−8.69927	−	15.0676i	−0.312891	−	0.541943i	0.666096	−	0.745866i	$-0.267964\pi$
$773$	−8.69927	−	15.0676i	−0.312891	−	0.541943i	−0.978987	+	0.203923i	$0.934631\pi$
$774$	−10.6149	−	8.23561i	−0.381546	−	0.296023i
$775$	−12.1816	+	7.03307i	−0.437577	+	0.252635i
$776$	−10.0174	+	17.3507i	−0.359604	+	0.622853i
$777$	−12.2936	−	13.3193i	−0.441031	−	0.477827i
$778$	−3.48402	−	6.03450i	−0.124908	−	0.216347i
$779$	−17.8399	+	10.2999i	−0.639182	+	0.369032i
$780$	14.2139	−	22.6101i	0.508938	−	0.809571i
$781$	−39.9264	+	69.1545i	−1.42868	+	2.47454i
$782$	0.182670	−	0.316393i	0.00653226	−	0.0113142i
$783$	−25.4225	+	8.40317i	−0.908527	+	0.300305i
$784$	0.903839	+	16.0672i	0.0322800	+	0.573830i
$785$			22.1686i			0.791230i
$786$	−2.59406	−	1.74333i	−0.0925269	−	0.0621827i
$787$	−14.0025	+	8.08436i	−0.499136	+	0.288176i	−0.728357	−	0.685198i	$-0.759716\pi$
$787$	−14.0025	+	8.08436i	−0.499136	+	0.288176i	0.229221	+	0.973374i	$0.426382\pi$
$788$	20.2178	+	11.6728i	0.720230	+	0.415825i
$789$	−2.32274	−	1.56100i	−0.0826918	−	0.0555730i
$790$	5.10696	−	2.94850i	0.181697	−	0.104903i
$791$	−22.0701	−	5.25382i	−0.784721	−	0.186804i
$792$	13.8108	+	33.8526i	0.490744	+	1.20290i
$793$	11.0157	−	6.81603i	0.391178	−	0.242044i
$794$	1.06319	−	1.84150i	0.0377313	−	0.0653525i
$795$	0.169588	+	0.113971i	0.00601465	+	0.00404215i
$796$	−4.90764	−	2.83343i	−0.173947	−	0.100428i
$797$	7.83061	−	13.5630i	0.277374	−	0.480426i	−0.693357	−	0.720594i	$-0.743869\pi$
$797$	7.83061	−	13.5630i	0.277374	−	0.480426i	0.970731	+	0.240168i	$0.0772025\pi$
$798$	3.89711	+	4.22225i	0.137956	+	0.149466i
$799$	−1.35705	+	2.35047i	−0.0480088	+	0.0831537i
$800$			6.97341i			0.246547i
$801$	−3.01838	−	0.413795i	−0.106649	−	0.0146207i
$802$	−6.02431	−	10.4344i	−0.212726	−	0.368452i
$803$	−16.5941	+	28.7418i	−0.585593	+	1.01428i
$804$	−4.47696	−	0.305449i	−0.157890	−	0.0107724i
$805$	1.96399	+	6.58395i	0.0692216	+	0.232054i
$806$	−9.96509	+	18.5440i	−0.351005	+	0.653183i
$807$	28.4304	+	1.93972i	1.00080	+	0.0682813i
$808$			10.7509i			0.378215i
$809$			7.94208i			0.279229i	0.990206	+	0.139614i	$0.0445863\pi$
$809$			7.94208i			0.279229i	−0.990206	+	0.139614i	$0.955414\pi$
$810$	−8.64195	−	8.82864i	−0.303647	−	0.310207i
$811$		−	27.8689i		−	0.978608i	−0.872113	−	0.489304i	$-0.837251\pi$
$811$		−	27.8689i		−	0.978608i	0.872113	−	0.489304i	$-0.162749\pi$
$812$	−22.5686	−	5.37250i	−0.792002	−	0.188538i
$813$	−0.955447	+	0.468005i	−0.0335090	+	0.0164137i
$814$	−6.51114	−	11.2776i	−0.228215	−	0.395281i
$815$	−15.8032	−	27.3720i	−0.553563	−	0.958799i
$816$	1.43770	−	2.13927i	0.0503295	−	0.0748895i
$817$	16.2997	+	9.41063i	0.570254	+	0.329236i
$818$	−4.68694			−0.163875
$819$	−9.52884	+	26.9852i	−0.332965	+	0.942939i
$820$	38.3764			1.34016
$821$	18.3241	+	10.5794i	0.639515	+	0.369224i	0.784428	−	0.620220i	$-0.212957\pi$
$821$	18.3241	+	10.5794i	0.639515	+	0.369224i	−0.144912	+	0.989444i	$0.546290\pi$
$822$	−4.35411	+	6.47886i	−0.151867	+	0.225976i
$823$	−23.3711	−	40.4800i	−0.814666	−	1.41104i	−0.909567	−	0.415556i	$-0.863587\pi$
$823$	−23.3711	−	40.4800i	−0.814666	−	1.41104i	0.0949015	−	0.995487i	$-0.469746\pi$
$824$	2.81839	+	4.88159i	0.0981832	+	0.170058i
$825$	−12.3374	+	6.04320i	−0.429532	+	0.210397i
$826$	0.686687	+	2.30200i	0.0238929	+	0.0800968i
$827$			19.8390i			0.689871i	0.938626	+	0.344935i	$0.112099\pi$
$827$			19.8390i			0.689871i	−0.938626	+	0.344935i	$0.887901\pi$
$828$	4.88420	−	1.99260i	0.169738	−	0.0692475i
$829$			22.9829i			0.798231i	0.916901	+	0.399115i	$0.130683\pi$
$829$			22.9829i			0.798231i	−0.916901	+	0.399115i	$0.869317\pi$
$830$			16.3098i			0.566121i
$831$	16.7055	+	1.13976i	0.579507	+	0.0395380i
$832$	−3.23141	−	5.22241i	−0.112029	−	0.181054i
$833$	−4.04511	−	2.04159i	−0.140155	−	0.0707369i
$834$	−8.17818	−	0.557971i	−0.283187	−	0.0193210i
$835$	16.8713	−	29.2219i	0.583855	−	1.01127i
$836$	−11.7727	−	20.3909i	−0.407167	−	0.705234i
$837$	−41.4659	−	36.9567i	−1.43327	−	1.27741i
$838$			13.7073i			0.473510i
$839$	−3.02970	+	5.24760i	−0.104597	+	0.181167i	−0.913573	−	0.406674i	$-0.866689\pi$
$839$	−3.02970	+	5.24760i	−0.104597	+	0.181167i	0.808977	+	0.587841i	$0.200022\pi$
$840$	−5.12186	−	22.7150i	−0.176721	−	0.783740i
$841$	−1.22374	+	2.11958i	−0.0421979	+	0.0730888i
$842$	5.63583	+	3.25385i	0.194224	+	0.112135i
$843$	6.11189	+	4.10749i	0.210505	+	0.141470i
$844$	−7.95152	+	13.7724i	−0.273703	+	0.474067i
$845$	32.6101	−	1.99162i	1.12182	−	0.0685137i
$846$	6.36159	−	2.59532i	0.218716	−	0.0892291i
$847$	−64.2265	+	19.1588i	−2.20685	+	0.658303i
$848$	0.0934561	−	0.0539569i	0.00320930	−	0.00185289i
$849$	19.3592	+	13.0103i	0.664406	+	0.446514i
$850$	−0.402912	−	0.232621i	−0.0138198	−	0.00797885i
$851$	−3.53952	+	2.04354i	−0.121333	+	0.0700517i
$852$	−32.4074	−	21.7794i	−1.11026	−	0.746150i
$853$		−	26.7903i		−	0.917284i	−0.888621	−	0.458642i	$-0.848336\pi$
$853$		−	26.7903i		−	0.917284i	0.888621	−	0.458642i	$-0.151664\pi$
$854$	1.20237	−	5.05087i	0.0411443	−	0.172837i
$855$	13.6742	+	10.6091i	0.467647	+	0.362824i
$856$	19.4343	−	33.6612i	0.664252	−	1.15052i
$857$	−4.19504	+	7.26603i	−0.143300	+	0.248203i	−0.928737	−	0.370738i	$-0.879105\pi$
$857$	−4.19504	+	7.26603i	−0.143300	+	0.248203i	0.785437	+	0.618941i	$0.212438\pi$
$858$	−10.9428	+	17.4068i	−0.373581	+	0.594258i
$859$	10.3636	−	5.98343i	0.353601	−	0.204152i	−0.312669	−	0.949862i	$-0.601223\pi$
$859$	10.3636	−	5.98343i	0.353601	−	0.204152i	0.666270	+	0.745710i	$0.267890\pi$
$860$	−17.5316	−	30.3655i	−0.597821	−	1.03546i
$861$	−40.1159	+	9.04550i	−1.36715	+	0.308270i
$862$	−7.88778	+	13.6620i	−0.268659	+	0.465331i
$863$	−16.9737	+	9.79980i	−0.577793	+	0.333589i	−0.760256	−	0.649624i	$-0.774926\pi$
$863$	−16.9737	+	9.79980i	−0.577793	+	0.333589i	0.182463	+	0.983213i	$0.441593\pi$
$864$	−26.1455	+	8.64215i	−0.889488	+	0.294012i
$865$	−10.6146	−	18.3850i	−0.360906	−	0.625108i
$866$	2.04443	+	3.54106i	0.0694727	+	0.120330i
$867$	−12.6333	−	25.7912i	−0.429049	−	0.875917i
$868$	−13.7570	−	46.1181i	−0.466944	−	1.56535i
$869$	22.4251	−	12.9471i	0.760719	−	0.439201i
$870$	12.2231	+	0.833941i	0.414401	+	0.0282733i
$871$	−2.88843	−	4.66812i	−0.0978708	−	0.158173i
$872$	−10.5948	−	6.11692i	−0.358786	−	0.207145i
$873$	4.03758	−	29.4516i	0.136651	−	0.996787i
$874$	1.12204	−	0.647808i	0.0379535	−	0.0219124i
$875$	−23.4741	+	7.00234i	−0.793571	+	0.236722i
$876$	−13.4691	−	9.05191i	−0.455079	−	0.305836i
$877$	−11.4236			−0.385748			−0.192874	−	0.981224i	$-0.561781\pi$
$877$	−11.4236			−0.385748			−0.192874	+	0.981224i	$0.561781\pi$
$878$	2.79133	+	4.83472i	0.0942028	+	0.163164i
$879$	10.5730	+	21.5850i	0.356617	+	0.728045i
$880$			34.8251i			1.17395i
$881$	22.1811	+	38.4188i	0.747300	+	1.29436i	0.949113	+	0.314937i	$0.101983\pi$
$881$	22.1811	+	38.4188i	0.747300	+	1.29436i	−0.201813	+	0.979424i	$0.564683\pi$
$882$	4.92250	+	10.3604i	0.165749	+	0.348854i
$883$	−12.9921			−0.437220			−0.218610	−	0.975812i	$-0.570152\pi$
$883$	−12.9921			−0.437220			−0.218610	+	0.975812i	$0.570152\pi$
$884$	3.96962	−	0.121107i	0.133513	−	0.00407327i
$885$	3.18296	+	6.49811i	0.106994	+	0.218431i
$886$	16.5871			0.557254
$887$	20.8583	−	36.1277i	0.700354	−	1.21305i	−0.267989	−	0.963422i	$-0.586359\pi$
$887$	20.8583	−	36.1277i	0.700354	−	1.21305i	0.968342	−	0.249626i	$-0.0803077\pi$
$888$	12.4394	−	6.09316i	0.417438	−	0.204473i
$889$	6.13745	+	5.80190i	0.205844	+	0.194590i
$890$	1.20726	+	0.697013i	0.0404675	+	0.0233639i
$891$	−37.9475	−	38.7673i	−1.27129	−	1.29875i
$892$	−8.04391	−	4.64415i	−0.269330	−	0.155498i
$893$	−8.33556	+	4.81254i	−0.278939	+	0.161045i
$894$	−5.74797	−	11.7347i	−0.192241	−	0.392466i
$895$	28.1165	−	16.2330i	0.939829	−	0.542611i
$896$	−29.6743	−	7.06403i	−0.991350	−	0.235993i
$897$	5.46317	+	3.43443i	0.182410	+	0.114672i
$898$	5.99714	+	10.3874i	0.200127	+	0.346631i
$899$	55.0825			1.83711
$900$	−2.53748	−	6.21980i	−0.0845826	−	0.207327i
$901$			0.0303847i			0.00101226i
$902$	−29.5448			−0.983734
$903$	25.4835	+	27.6096i	0.848038	+	0.918792i
$904$	8.66858	−	15.0144i	0.288313	−	0.499372i
$905$	2.96235	−	1.71032i	0.0984720	−	0.0568528i
$906$	0.503402	−	7.37836i	0.0167244	−	0.245130i
$907$	−58.0241			−1.92666			−0.963329	−	0.268324i	$-0.913530\pi$
$907$	−58.0241			−1.92666			−0.963329	+	0.268324i	$0.913530\pi$
$908$	−19.3858	+	33.5771i	−0.643339	+	1.11430i
$909$	−6.02568	−	14.7700i	−0.199859	−	0.489890i
$910$	8.70121	−	9.78571i	0.288442	−	0.324393i
$911$			41.9642i			1.39034i	0.718847	+	0.695168i	$0.244670\pi$
$911$			41.9642i			1.39034i	−0.718847	+	0.695168i	$0.755330\pi$
$912$	8.20876	−	4.02089i	0.271819	−	0.133145i
$913$			71.6177i			2.37020i
$914$	17.0561	−	9.84732i	0.564164	−	0.325720i
$915$	1.06452	−	15.6026i	0.0351919	−	0.515807i
$916$	25.7063	+	14.8415i	0.849359	+	0.490378i
$917$	6.35172	+	6.00446i	0.209752	+	0.198285i
$918$	0.372842	−	1.79893i	0.0123056	−	0.0593736i
$919$	−10.7537			−0.354732			−0.177366	−	0.984145i	$-0.556758\pi$
$919$	−10.7537			−0.354732			−0.177366	+	0.984145i	$0.556758\pi$
$920$	−5.25052			−0.173104
$921$	27.4473	+	18.4460i	0.904420	+	0.607815i
$922$	−4.32422	+	2.49659i	−0.142411	+	0.0822208i
$923$	−1.45657	−	47.7433i	−0.0479437	−	1.57149i
$924$	−10.3389	−	45.8521i	−0.340126	−	1.50842i
$925$	2.60235	+	4.50741i	0.0855648	+	0.148203i
$926$	−10.4716	−	6.04576i	−0.344117	−	0.198676i
$927$	−6.60806	−	5.12687i	−0.217037	−	0.168388i
$928$	13.6538	−	23.6491i	0.448209	−	0.776320i
$929$	−31.6451			−1.03824			−0.519121	−	0.854701i	$-0.673741\pi$
$929$	−31.6451			−1.03824			−0.519121	+	0.854701i	$0.673741\pi$
$930$	11.1800	+	22.8243i	0.366607	+	0.748439i
$931$	−8.80334	−	13.4428i	−0.288518	−	0.440571i
$932$	−2.76027	−	1.59364i	−0.0904158	−	0.0522016i
$933$	−1.99780	−	4.07857i	−0.0654050	−	0.133526i
$934$			0.345159i			0.0112939i
$935$	−8.49184	−	4.90276i	−0.277713	−	0.160338i
$936$	−17.6800	−	12.8729i	−0.577888	−	0.420765i
$937$		−	2.52593i		−	0.0825185i	−0.999148	−	0.0412593i	$-0.986863\pi$
$937$		−	2.52593i		−	0.0825185i	0.999148	−	0.0412593i	$-0.0131370\pi$
$938$	−2.14041	−	0.509529i	−0.0698869	−	0.0166367i
$939$	0.429167	−	6.29029i	0.0140053	−	0.205276i
$940$	17.9310			0.584846
$941$	−0.833591	+	1.44382i	−0.0271743	+	0.0470672i	−0.879293	−	0.476282i	$-0.841984\pi$
$941$	−0.833591	+	1.44382i	−0.0271743	+	0.0470672i	0.852118	+	0.523349i	$0.175318\pi$
$942$	8.32590	+	0.568050i	0.271272	+	0.0185081i
$943$			9.27271i			0.301961i
$944$	3.82153			0.124380
$945$	19.7679	+	28.3360i	0.643051	+	0.921770i
$946$	13.4970	+	23.3775i	0.438825	+	0.760067i
$947$	17.3559	+	10.0204i	0.563991	+	0.325620i	0.754746	−	0.656017i	$-0.227760\pi$
$947$	17.3559	+	10.0204i	0.563991	+	0.325620i	−0.190755	+	0.981638i	$0.561094\pi$
$948$	5.56973	+	11.3708i	0.180896	+	0.369306i
$949$	−0.605378	−	19.8430i	−0.0196514	−	0.644130i
$950$	−0.824953	−	1.42886i	−0.0267650	−	0.0463584i
$951$	1.99678	−	29.2668i	0.0647502	−	0.949042i
$952$	2.37872	−	2.51630i	0.0770949	−	0.0815536i
$953$	−6.14947	−	3.55040i	−0.199201	−	0.115009i	0.397082	−	0.917783i	$-0.370023\pi$
$953$	−6.14947	−	3.55040i	−0.199201	−	0.115009i	−0.596283	+	0.802774i	$0.703356\pi$
$954$	0.0471500	−	0.0607720i	0.00152654	−	0.00196757i
$955$	22.4396	−	12.9555i	0.726127	−	0.419230i
$956$	35.0427	−	20.2319i	1.13336	−	0.654347i
$957$	53.6725	+	3.66191i	1.73499	+	0.118373i
$958$	10.5628	+	6.09846i	0.341270	+	0.197032i
$959$	14.9966	−	15.8639i	0.484265	−	0.512273i
$960$	−7.39703	−	0.504676i	−0.238738	−	0.0162884i
$961$	41.6336	+	72.1116i	1.34302	+	2.32618i
$962$	6.86157	+	3.68725i	0.221226	+	0.118882i
$963$	−7.83312	+	57.1377i	−0.252419	+	1.84124i
$964$	30.7839	+	17.7731i	0.991483	+	0.572433i
$965$	−4.07081	−	7.05085i	−0.131044	−	0.226975i
$966$	2.52307	−	0.568914i	0.0811786	−	0.0183045i
$967$	−57.1582			−1.83808			−0.919041	−	0.394161i	$-0.871035\pi$
$967$	−57.1582			−1.83808			−0.919041	+	0.394161i	$0.871035\pi$
$968$		−	51.2189i		−	1.64624i
$969$	−0.175187	+	2.56771i	−0.00562782	+	0.0824868i
$970$	−6.80105	+	11.7798i	−0.218369	+	0.378226i
$971$	−2.08912			−0.0670431			−0.0335216	−	0.999438i	$-0.510672\pi$
$971$	−2.08912			−0.0670431			−0.0335216	+	0.999438i	$0.510672\pi$
$972$	20.1753	−	17.2220i	0.647123	−	0.552396i
$973$	22.3011	+	5.30881i	0.714940	+	0.170193i
$974$		−	22.0058i		−	0.705111i
$975$	4.37359	−	6.95709i	0.140067	−	0.222805i
$976$	−7.15300	−	4.12979i	−0.228962	−	0.132191i
$977$		−	21.3475i		−	0.682968i	−0.939888	−	0.341484i	$-0.889071\pi$
$977$		−	21.3475i		−	0.682968i	0.939888	−	0.341484i	$-0.110929\pi$
$978$	−10.6851	+	5.23387i	−0.341672	+	0.167361i
$979$	5.30119	+	3.06064i	0.169427	+	0.0978186i
$980$	1.68132	+	29.8883i	0.0537078	+	0.954745i
$981$	17.9840	+	2.46546i	0.574185	+	0.0787161i
$982$	−4.22905			−0.134955
$983$	26.2192	−	45.4129i	0.836261	−	1.44845i	−0.0567381	−	0.998389i	$-0.518070\pi$
$983$	26.2192	−	45.4129i	0.836261	−	1.44845i	0.892999	−	0.450058i	$-0.148597\pi$
$984$	2.13913	−	31.3532i	0.0681931	−	0.999504i
$985$	29.8593	+	17.2393i	0.951395	+	0.549288i
$986$	0.910938	+	1.57779i	0.0290102	+	0.0502471i
$987$	−18.7438	+	4.22643i	−0.596622	+	0.134529i
$988$	12.4063	+	6.66685i	0.394697	+	0.212101i
$989$	7.33709	−	4.23607i	0.233306	−	0.134699i
$990$	9.37644	+	22.9833i	0.298003	+	0.730457i
$991$	−7.60585			−0.241608			−0.120804	−	0.992676i	$-0.538547\pi$
$991$	−7.60585			−0.241608			−0.120804	+	0.992676i	$0.538547\pi$
$992$	56.6490			1.79861
$993$	−10.0745	+	14.9908i	−0.319706	+	0.475718i
$994$	−13.9124	−	13.1517i	−0.441274	−	0.417148i
$995$	−7.24798	−	4.18463i	−0.229777	−	0.132662i
$996$	−34.9380	−	2.38371i	−1.10705	−	0.0755307i
$997$	24.5233	−	14.1586i	0.776662	−	0.448406i	−0.0585841	−	0.998282i	$-0.518659\pi$
$997$	24.5233	−	14.1586i	0.776662	−	0.448406i	0.835246	+	0.549877i	$0.185325\pi$
$998$			8.67729i			0.274675i
$999$	−13.6746	+	15.3431i	−0.432645	+	0.485433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bf.b.185.15	yes	64
3.2	odd	2	inner	273.2.bf.b.185.18	yes	64
7.5	odd	6		273.2.r.b.68.18	yes	64
13.9	even	3		273.2.r.b.269.18	yes	64
21.5	even	6		273.2.r.b.68.15	✓	64
39.35	odd	6		273.2.r.b.269.15	yes	64
91.61	odd	6	inner	273.2.bf.b.152.18	yes	64
273.152	even	6	inner	273.2.bf.b.152.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.15	✓	64	21.5	even	6
273.2.r.b.68.18	yes	64	7.5	odd	6
273.2.r.b.269.15	yes	64	39.35	odd	6
273.2.r.b.269.18	yes	64	13.9	even	3
273.2.bf.b.152.15	yes	64	273.152	even	6	inner
273.2.bf.b.152.18	yes	64	91.61	odd	6	inner
273.2.bf.b.185.15	yes	64	1.1	even	1	trivial
273.2.bf.b.185.18	yes	64	3.2	odd	2	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.473030 - 0.273104i) q^{2} +(0.966120 - 1.43757i) q^{3} +(-0.850828 - 1.47368i) q^{4} +(-1.25657 - 2.17644i) q^{5} +(-0.849611 + 0.416164i) q^{6} +(2.53535 - 0.756296i) q^{7} +2.02188i q^{8} +(-1.13323 - 2.77773i) q^{9} +1.37270i q^{10} +6.02763i q^{11} +(-2.94052 - 0.200622i) q^{12} +(-1.89716 - 3.06607i) q^{13} +(-1.40585 - 0.334664i) q^{14} +(-4.34279 - 0.296295i) q^{15} +(-1.14947 + 1.99095i) q^{16} +(-0.323651 - 0.560581i) q^{17} +(-0.222560 + 1.62344i) q^{18} -2.29555i q^{19} +(-2.13825 + 3.70356i) q^{20} +(1.36222 - 4.37543i) q^{21} +(1.64617 - 2.85125i) q^{22} +(-0.894874 - 0.516656i) q^{23} +(2.90659 + 1.95337i) q^{24} +(-0.657937 + 1.13958i) q^{25} +(0.0600548 + 1.96847i) q^{26} +(-5.08802 - 1.05453i) q^{27} +(-3.27169 - 3.09282i) q^{28} +(4.46255 - 2.57646i) q^{29} +(1.97335 + 1.32619i) q^{30} +(9.25745 + 5.34479i) q^{31} +(4.58946 - 2.64973i) q^{32} +(8.66515 + 5.82341i) q^{33} +0.353562i q^{34} +(-4.83188 - 4.56771i) q^{35} +(-3.12930 + 4.03338i) q^{36} +(1.97766 - 3.42541i) q^{37} +(-0.626924 + 1.08587i) q^{38} +(-6.24058 - 0.234896i) q^{39} +(4.40050 - 2.54063i) q^{40} +(-4.48689 - 7.77153i) q^{41} +(-1.83932 + 1.69768i) q^{42} +(-4.09951 + 7.10056i) q^{43} +(8.88279 - 5.12848i) q^{44} +(-4.62160 + 5.95682i) q^{45} +(0.282202 + 0.488787i) q^{46} +(-2.09646 - 3.63118i) q^{47} +(1.75160 + 3.57594i) q^{48} +(5.85603 - 3.83496i) q^{49} +(0.622448 - 0.359370i) q^{50} +(-1.11856 - 0.0763159i) q^{51} +(-2.90425 + 5.40450i) q^{52} +(-0.0406517 - 0.0234703i) q^{53} +(2.11879 + 1.88838i) q^{54} +(13.1188 - 7.57414i) q^{55} +(1.52914 + 5.12617i) q^{56} +(-3.30002 - 2.21778i) q^{57} -2.81456 q^{58} +(-0.831148 - 1.43959i) q^{59} +(3.25833 + 6.65197i) q^{60} +3.59276i q^{61} +(-2.91937 - 5.05650i) q^{62} +(-4.97392 - 6.18548i) q^{63} +1.70329 q^{64} +(-4.28922 + 7.98179i) q^{65} +(-2.50848 - 5.12114i) q^{66} +1.52251 q^{67} +(-0.550743 + 0.953916i) q^{68} +(-1.60728 + 0.787294i) q^{69} +(1.03817 + 3.48027i) q^{70} +(11.4729 + 6.62389i) q^{71} +(5.61623 - 2.29124i) q^{72} +(4.76835 + 2.75301i) q^{73} +(-1.87099 + 1.08022i) q^{74} +(1.00258 + 2.04680i) q^{75} +(-3.38290 + 1.95312i) q^{76} +(4.55868 + 15.2822i) q^{77} +(2.88783 + 1.81544i) q^{78} +(-2.14796 - 3.72038i) q^{79} +5.77758 q^{80} +(-6.43160 + 6.29559i) q^{81} +4.90156i q^{82} +11.8816 q^{83} +(-7.60699 + 1.71526i) q^{84} +(-0.813381 + 1.40882i) q^{85} +(3.87838 - 2.23919i) q^{86} +(0.607520 - 8.90441i) q^{87} -12.1871 q^{88} +(0.507769 - 0.879481i) q^{89} +(3.81299 - 1.55558i) q^{90} +(-7.12882 - 6.33877i) q^{91} +1.75834i q^{92} +(16.6273 - 8.14455i) q^{93} +2.29021i q^{94} +(-4.99614 + 2.88452i) q^{95} +(0.624797 - 9.15764i) q^{96} +(8.58147 + 4.95452i) q^{97} +(-3.81742 + 0.214744i) q^{98} +(16.7432 - 6.83067i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Introduction

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