LMFDB - Embedded newform 273.2.bf.b.185.18

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			185.18
Character	$\chi$	$=$	273.185
Dual form			273.2.bf.b.152.18

$q$-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} +(-0.0643970 - 0.943866i) 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} +(-1.29652 + 2.64688i) q^{12} +(-1.89716 - 3.06607i) q^{13} +(1.40585 + 0.334664i) q^{14} +(1.91480 - 3.90911i) q^{15} +(-1.14947 + 1.99095i) q^{16} +(0.323651 + 0.560581i) q^{17} +(-1.29466 + 1.00446i) q^{18} -2.29555i q^{19} +(2.13825 - 3.70356i) q^{20} +(-3.53668 - 2.91408i) 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} +(5.05766 - 0.693365i) q^{36} +(1.97766 - 3.42541i) q^{37} +(0.626924 - 1.08587i) q^{38} +(-2.57482 + 5.68949i) q^{39} +(4.40050 - 2.54063i) q^{40} +(4.48689 + 7.77153i) q^{41} +(-0.877112 - 2.34433i) q^{42} +(-4.09951 + 7.10056i) q^{43} +(-8.88279 + 5.12848i) q^{44} +(-7.46955 + 1.02402i) q^{45} +(0.282202 + 0.488787i) q^{46} +(2.09646 + 3.63118i) q^{47} +(3.97266 - 0.271042i) q^{48} +(5.85603 - 3.83496i) q^{49} +(-0.622448 + 0.359370i) q^{50} +(0.493189 - 1.00686i) q^{51} +(-2.90425 + 5.40450i) q^{52} +(0.0406517 + 0.0234703i) q^{53} +(2.69478 + 0.890735i) 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} +(-7.38994 + 0.504192i) q^{60} +3.59276i q^{61} +(2.91937 + 5.05650i) q^{62} +(-0.772338 + 7.89959i) q^{63} +1.70329 q^{64} +(4.28922 - 7.98179i) q^{65} +(-5.68928 + 0.388162i) q^{66} +1.52251 q^{67} +(0.550743 - 0.953916i) q^{68} +(-0.121826 - 1.78560i) 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} +(2.27387 - 0.155139i) q^{75} +(-3.38290 + 1.95312i) q^{76} +(-4.55868 - 15.2822i) q^{77} +(-2.77179 + 1.98811i) 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} +(-1.28530 + 7.69132i) q^{84} +(-0.813381 + 1.40882i) q^{85} +(-3.87838 + 2.23919i) q^{86} +(8.01520 + 3.92608i) 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} +(-1.26028 - 18.4720i) q^{93} +2.29021i q^{94} +(4.99614 - 2.88452i) q^{95} +(8.24314 + 4.03773i) 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	0.657830	−	0.753167i	$-0.271475\pi$
$2$	0.473030	+	0.273104i	0.334483	+	0.193114i	−0.323347	+	0.946281i	$0.604808\pi$
$3$	−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	$0.0232840\pi$
$5$	1.25657	+	2.17644i	0.561955	+	0.973335i	−0.435371	+	0.900251i	$0.643383\pi$
$6$	−0.0643970	−	0.943866i	−0.0262900	−	0.385332i
$7$	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	$-0.637076\pi$
$11$		−	6.02763i		−	1.81740i	0.417450	−	0.908700i	$-0.362924\pi$
$12$	−1.29652	+	2.64688i	−0.374272	+	0.764087i
$13$	−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
$15$	1.91480	−	3.90911i	0.494398	−	1.00933i
$16$	−1.14947	+	1.99095i	−0.287369	+	0.497737i
$17$	0.323651	+	0.560581i	0.0784970	+	0.135961i	0.902602	−	0.430477i	$-0.141655\pi$
$17$	0.323651	+	0.560581i	0.0784970	+	0.135961i	−0.824105	+	0.566438i	$0.808321\pi$
$18$	−1.29466	+	1.00446i	−0.305154	+	0.236754i
$19$		−	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
$21$	−3.53668	−	2.91408i	−0.771768	−	0.635904i
$22$	1.64617	−	2.85125i	0.350965	−	0.607889i
$23$	0.894874	+	0.516656i	0.186594	+	0.107730i	0.590387	−	0.807120i	$-0.298975\pi$
$23$	0.894874	+	0.516656i	0.186594	+	0.107730i	−0.403793	+	0.914850i	$0.632308\pi$
$24$	−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	−0.853399	−	0.521258i	$-0.825463\pi$
$29$	−4.46255	+	2.57646i	−0.828676	+	0.478436i	0.0247234	+	0.999694i	$0.492129\pi$
$30$	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
$36$	5.05766	−	0.693365i	0.842944	−	0.115561i
$37$	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
$39$	−2.57482	+	5.68949i	−0.412301	+	0.911048i
$40$	4.40050	−	2.54063i	0.695780	−	0.401709i
$41$	4.48689	+	7.77153i	0.700735	+	1.21371i	0.968209	+	0.250143i	$0.0804778\pi$
$41$	4.48689	+	7.77153i	0.700735	+	1.21371i	−0.267474	+	0.963565i	$0.586189\pi$
$42$	−0.877112	−	2.34433i	−0.135341	−	0.361738i
$43$	−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
$45$	−7.46955	+	1.02402i	−1.11350	+	0.152651i
$46$	0.282202	+	0.488787i	0.0416084	+	0.0720678i
$47$	2.09646	+	3.63118i	0.305800	+	0.529662i	0.977439	−	0.211217i	$-0.0677426\pi$
$47$	2.09646	+	3.63118i	0.305800	+	0.529662i	−0.671639	+	0.740879i	$0.734409\pi$
$48$	3.97266	−	0.271042i	0.573404	−	0.0391216i
$49$	5.85603	−	3.83496i	0.836576	−	0.547851i
$50$	−0.622448	+	0.359370i	−0.0880274	+	0.0508226i
$51$	0.493189	−	1.00686i	0.0690603	−	0.140989i
$52$	−2.90425	+	5.40450i	−0.402747	+	0.749469i
$53$	0.0406517	+	0.0234703i	0.00558394	+	0.00322389i	0.502789	−	0.864409i	$-0.332307\pi$
$53$	0.0406517	+	0.0234703i	0.00558394	+	0.00322389i	−0.497205	+	0.867633i	$0.665640\pi$
$54$	2.69478	+	0.890735i	0.366714	+	0.121214i
$55$	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	0.915044	−	0.403355i	$-0.132156\pi$
$59$	0.831148	+	1.43959i	0.108206	+	0.187419i	−0.806837	+	0.590774i	$0.798823\pi$
$60$	−7.38994	+	0.504192i	−0.954037	+	0.0650909i
$61$			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
$63$	−0.772338	+	7.89959i	−0.0973054	+	0.995255i
$64$	1.70329			0.212911
$65$	4.28922	−	7.98179i	0.532013	−	0.990019i
$66$	−5.68928	+	0.388162i	−0.700302	+	0.0477794i
$67$	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
$69$	−0.121826	−	1.78560i	−0.0146661	−	0.214961i
$70$	1.03817	+	3.48027i	0.124085	+	0.415972i
$71$	−11.4729	−	6.62389i	−1.36158	−	0.786111i	−0.371749	−	0.928333i	$-0.621242\pi$
$71$	−11.4729	−	6.62389i	−1.36158	−	0.786111i	−0.989835	+	0.142222i	$0.954575\pi$
$72$	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
$75$	2.27387	−	0.155139i	0.262564	−	0.0179139i
$76$	−3.38290	+	1.95312i	−0.388046	+	0.224038i
$77$	−4.55868	−	15.2822i	−0.519509	−	1.74157i
$78$	−2.77179	+	1.98811i	−0.313844	+	0.225109i
$79$	−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	$-0.726106\pi$
$83$	−11.8816			−1.30417			−0.652085	+	0.758146i	$0.726106\pi$
$84$	−1.28530	+	7.69132i	−0.140238	+	0.839191i
$85$	−0.813381	+	1.40882i	−0.0882236	+	0.152808i
$86$	−3.87838	+	2.23919i	−0.418217	+	0.241458i
$87$	8.01520	+	3.92608i	0.859320	+	0.420920i
$88$	−12.1871			−1.29915
$89$	−0.507769	+	0.879481i	−0.0538234	+	0.0932248i	−0.891682	−	0.452663i	$-0.850474\pi$
$89$	−0.507769	+	0.879481i	−0.0538234	+	0.0932248i	0.837858	+	0.545888i	$0.183807\pi$
$90$	−3.81299	−	1.55558i	−0.401924	−	0.163972i
$91$	−7.12882	−	6.33877i	−0.747303	−	0.664483i
$92$		−	1.75834i		−	0.183320i
$93$	−1.26028	−	18.4720i	−0.130685	−	1.91545i
$94$			2.29021i			0.236217i
$95$	4.99614	−	2.88452i	0.512593	−	0.295946i
$96$	8.24314	+	4.03773i	0.841312	+	0.412099i
$97$	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	$-0.585222\pi$
$101$	−5.31728			−0.529089			−0.264545	+	0.964373i	$0.585222\pi$
$102$	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
$105$	1.89824	−	11.3591i	0.185249	−	1.10854i
$106$	0.0128197	+	0.0222043i	0.00124515	+	0.00215667i
$107$	16.6485	+	9.61203i	1.60947	+	0.929230i	0.989488	+	0.144617i	$0.0461949\pi$
$107$	16.6485	+	9.61203i	1.60947	+	0.929230i	0.619986	+	0.784613i	$0.287138\pi$
$108$	−5.88307	−	6.60088i	−0.566099	−	0.635170i
$109$	−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
$111$	−6.83493	+	0.466326i	−0.648743	+	0.0442617i
$112$	−1.40858	+	5.91710i	−0.133098	+	0.559113i
$113$	7.42599	+	4.28740i	0.698578	+	0.403324i	0.806818	−	0.590800i	$-0.201188\pi$
$113$	7.42599	+	4.28740i	0.698578	+	0.403324i	−0.108239	+	0.994125i	$0.534521\pi$
$114$	−2.16669	+	0.147827i	−0.202929	+	0.0138452i
$115$			2.59686i			0.242158i
$116$	7.59374	+	4.38425i	0.705061	+	0.407067i
$117$	10.6666	−	1.79524i	0.986131	−	0.165970i
$118$			0.907960i			0.0835845i
$119$	1.24454	+	1.17649i	0.114086	+	0.107849i
$120$	−7.90374	−	3.87148i	−0.721510	−	0.353416i
$121$	−25.3324			−2.30294
$122$	−0.981198	+	1.69949i	−0.0888335	+	0.153864i
$123$	6.83725	−	13.9585i	0.616494	−	1.25859i
$124$		−	18.1900i		−	1.63351i
$125$	9.25873			0.828126
$126$	−2.52275	+	3.52582i	−0.224744	+	0.314105i
$127$	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
$129$	14.1682	−	0.966650i	1.24744	−	0.0851088i
$130$	4.20879	−	2.60422i	0.369135	−	0.228405i
$131$	−1.65182	−	2.86103i	−0.144320	−	0.249969i	0.784799	−	0.619750i	$-0.212766\pi$
$131$	−1.65182	−	2.86103i	−0.144320	−	0.249969i	−0.929119	+	0.369781i	$0.879433\pi$
$132$	15.9544	+	7.81492i	1.38865	+	0.680202i
$133$	−1.73612	−	5.82003i	−0.150540	−	0.504661i
$134$	0.720192	+	0.415803i	0.0622151	+	0.0359199i
$135$	8.68858	+	9.74870i	0.747794	+	0.839035i
$136$	1.13342	−	0.654383i	0.0971903	−	0.0561129i
$137$	−7.14564	+	4.12554i	−0.610493	+	0.352468i	−0.773158	−	0.634213i	$-0.781324\pi$
$137$	−7.14564	+	4.12554i	−0.610493	+	0.352468i	0.162665	+	0.986681i	$0.447991\pi$
$138$	0.430027	−	0.877912i	0.0366063	−	0.0747329i
$139$	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
$141$	3.19465	−	6.52197i	0.269038	−	0.549249i
$142$	−3.61802	−	6.26660i	−0.303618	−	0.525881i
$143$	−18.4812	+	11.4354i	−1.54547	+	0.956273i
$144$	−4.22771	−	5.44912i	−0.352309	−	0.454094i
$145$	−11.2150	−	6.47500i	−0.931357	−	0.537719i
$146$	1.50371	+	2.60451i	0.124448	+	0.215551i
$147$	−11.1707	−	4.71344i	−0.921340	−	0.388758i
$148$	−6.73060			−0.553252
$149$		−	13.8118i		−	1.13151i	−0.824574	−	0.565753i	$-0.808585\pi$
$149$		−	13.8118i		−	1.13151i	0.824574	−	0.565753i	$-0.191415\pi$
$150$	1.11798	+	0.547619i	0.0912827	+	0.0447129i
$151$	−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
$153$	−1.92391	+	0.263753i	−0.155539	+	0.0213232i
$154$	2.01723	−	8.47393i	0.162553	−	0.682848i
$155$			26.8644i			2.15780i
$156$	10.5752	−	1.04632i	0.846694	−	0.0837730i
$157$	−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
$159$	−0.00553421	−	0.0811148i	−0.000438891	−	0.00643282i
$160$	−11.5340	−	6.65914i	−0.911840	−	0.526451i
$161$	2.65957	+	0.633115i	0.209603	+	0.0498964i
$162$	−1.32299	−	4.73450i	−0.103944	−	0.371978i
$163$	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
$165$	−23.5627	−	11.5417i	−1.83435	−	0.898519i
$166$	−5.62034	−	3.24490i	−0.436223	−	0.251853i
$167$	−6.71323	−	11.6277i	−0.519486	−	0.899775i	−0.999743	−	0.0226481i	$-0.992790\pi$
$167$	−6.71323	−	11.6277i	−0.519486	−	0.899775i	0.480258	−	0.877127i	$-0.340543\pi$
$168$	−5.89191	+	7.15074i	−0.454570	+	0.551691i
$169$	−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	$-0.604058\pi$
$173$	−8.44726			−0.642233			−0.321116	+	0.947040i	$0.604058\pi$
$174$	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
$177$	1.26653	−	2.58565i	0.0951980	−	0.194350i
$178$	−0.480380	+	0.277347i	−0.0360060	+	0.0207881i
$179$		−	12.9185i		−	0.965577i	−0.875737	−	0.482788i	$-0.839624\pi$
$179$		−	12.9185i		−	0.965577i	0.875737	−	0.482788i	$-0.160376\pi$
$180$	7.86438	+	10.1365i	0.586176	+	0.755527i
$181$			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
$186$	4.44862	−	9.08199i	0.326188	−	0.665924i
$187$	3.37897	−	1.95085i	0.247095	−	0.142660i
$188$	3.56746	−	6.17902i	0.260184	−	0.450651i
$189$	12.1024	−	6.52166i	0.880320	−	0.474381i
$190$	3.15110			0.228605
$191$		−	10.3102i		−	0.746020i	−0.927827	−	0.373010i	$-0.878326\pi$
$191$		−	10.3102i		−	0.746020i	0.927827	−	0.373010i	$-0.121674\pi$
$192$	−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
$195$	−15.6183	+	1.54529i	−1.11845	+	0.110661i
$196$	−10.6340	−	5.36702i	−0.759569	−	0.383358i
$197$	11.8813	−	6.85965i	0.846505	−	0.488730i	−0.0129653	−	0.999916i	$-0.504127\pi$
$197$	11.8813	−	6.85965i	0.846505	−	0.488730i	0.859470	+	0.511186i	$0.170794\pi$
$198$	6.05453	+	7.80374i	0.430277	+	0.554587i
$199$	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
$204$	−1.90341	+	0.129863i	−0.133265	+	0.00909226i
$205$	−11.2762	+	19.5309i	−0.787563	+	1.36410i
$206$	1.52277			0.106096
$207$	−2.44923	+	1.90023i	−0.170233	+	0.132075i
$208$	8.28512	−	0.252766i	0.574470	−	0.0175262i
$209$	−13.8367			−0.957107
$210$	4.00015	−	4.85480i	0.276037	−	0.335013i
$211$	−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
$213$	1.56189	+	22.8926i	0.107019	+	1.56858i
$214$	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
$219$	−0.649150	−	9.51457i	−0.0438655	−	0.642935i
$220$	−22.3237	−	12.8886i	−1.50506	−	0.868949i
$221$	1.10476	−	2.05585i	0.0743145	−	0.138291i
$222$	−3.36049	−	1.64606i	−0.225541	−	0.110476i
$223$	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
$225$	−2.41986	−	3.11897i	−0.161324	−	0.207931i
$226$	2.34181	+	4.05614i	0.155775	+	0.269810i
$227$	11.3923	+	19.7320i	0.756132	+	1.30966i	0.944809	+	0.327620i	$0.106247\pi$
$227$	11.3923	+	19.7320i	0.756132	+	1.30966i	−0.188677	+	0.982039i	$0.560420\pi$
$228$	6.07604	+	2.97622i	0.402396	+	0.197105i
$229$	−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
$231$	−17.5650	+	21.3178i	−1.15569	+	1.40261i
$232$	5.20928	+	9.02273i	0.342006	+	0.592371i
$233$	−1.62211	+	0.936526i	−0.106268	+	0.0613538i	−0.552192	−	0.833717i	$-0.686208\pi$
$233$	−1.62211	+	0.936526i	−0.106268	+	0.0613538i	0.445924	+	0.895071i	$0.352875\pi$
$234$	5.53593	+	2.06390i	0.361895	+	0.134921i
$235$	−5.26870	+	9.12566i	−0.343692	+	0.595292i
$236$	1.41433	−	2.44969i	0.0920650	−	0.159461i
$237$	−3.27312	+	6.68218i	−0.212612	+	0.434054i
$238$	0.267398	+	0.896405i	0.0173328	+	0.0581053i
$239$		−	23.7791i		−	1.53814i	−0.639164	−	0.769071i	$-0.720719\pi$
$239$		−	23.7791i		−	1.53814i	0.639164	−	0.769071i	$-0.279281\pi$
$240$	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	$-0.611673\pi$
$251$	10.1622	−	17.6015i	0.641433	−	1.11100i	0.985113	−	0.171908i	$-0.0549932\pi$
$252$	12.2986	−	5.58302i	0.774737	−	0.351697i
$253$	3.11421	−	5.39397i	0.195789	−	0.339116i
$254$			1.74360i			0.109403i
$255$	2.81110	−	0.191793i	0.176038	−	0.0120105i
$256$	1.44540	+	2.50350i	0.0903374	+	0.156469i
$257$	−11.9462	+	20.6914i	−0.745183	+	1.29069i	0.204926	+	0.978777i	$0.434304\pi$
$257$	−11.9462	+	20.6914i	−0.745183	+	1.29069i	−0.950109	+	0.311917i	$0.899029\pi$
$258$	6.96597	+	3.41213i	0.433683	+	0.212430i
$259$	2.42345	−	10.1803i	0.150586	−	0.632575i
$260$	−15.4120	+	0.470195i	−0.955810	+	0.0291603i
$261$	−2.09963	−	15.3155i	−0.129964	−	0.948005i
$262$		−	1.80447i		−	0.111481i
$263$			1.61574i			0.0996308i	0.998758	+	0.0498154i	$0.0158633\pi$
$263$			1.61574i			0.0996308i	−0.998758	+	0.0498154i	$0.984137\pi$
$264$	11.7742	+	17.5199i	0.724653	+	1.07827i
$265$			0.117968i			0.00724672i
$266$	0.768239	−	3.22719i	0.0471038	−	0.197872i
$267$	1.75488	−	0.119730i	0.107397	−	0.00732736i
$268$	−1.29539	−	2.24369i	−0.0791287	−	0.137055i
$269$	−8.22623	−	14.2482i	−0.501562	−	0.868731i	−0.999998	−	0.00180469i	$-0.999426\pi$
$269$	−8.22623	−	14.2482i	−0.501562	−	0.868731i	0.498436	−	0.866926i	$-0.333908\pi$
$270$	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
$273$	−2.22514	+	16.3722i	−0.134672	+	0.990890i
$274$	−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
$279$	−25.3372	+	19.6579i	−1.51690	+	1.17689i
$280$	9.23535	−	9.76947i	0.551918	−	0.583837i
$281$		−	4.25154i		−	0.253625i	−0.991927	−	0.126813i	$-0.959525\pi$
$281$		−	4.25154i		−	0.253625i	0.991927	−	0.126813i	$-0.0404747\pi$
$282$	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
$285$	−8.97357	−	4.39551i	−0.531549	−	0.260368i
$286$	−11.8652	+	0.361988i	−0.701603	+	0.0214048i
$287$	17.2534	+	16.3101i	1.01844	+	0.962757i
$288$	−2.15934	−	15.7510i	−0.127240	−	0.928139i
$289$	8.29050	−	14.3596i	0.487676	−	0.844680i
$290$	−3.53670	−	6.12574i	−0.207682	−	0.359716i
$291$	−1.16826	−	17.1231i	−0.0684845	−	1.00378i
$292$		−	9.36934i		−	0.548299i
$293$	6.93842	−	12.0177i	0.405347	−	0.702081i	−0.589015	−	0.808122i	$-0.700484\pi$
$293$	6.93842	−	12.0177i	0.405347	−	0.702081i	0.994362	+	0.106041i	$0.0338174\pi$
$294$	−3.99680	−	5.28035i	−0.233098	−	0.307956i
$295$	−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
$309$	−4.33649	−	2.12414i	−0.246694	−	0.120838i
$310$	−7.33679	+	12.7077i	−0.416702	+	0.721748i
$311$	−1.31104	+	2.27079i	−0.0743423	+	0.128765i	−0.900800	−	0.434234i	$-0.857019\pi$
$311$	−1.31104	+	2.27079i	−0.0743423	+	0.128765i	0.826458	+	0.562999i	$0.190352\pi$
$312$	11.5034	+	5.20597i	0.651254	+	0.294730i
$313$	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
$315$	−18.1635	+	8.24544i	−1.02340	+	0.464578i
$316$	−3.65509	+	6.33081i	−0.205615	+	0.356136i
$317$	−14.6674	+	8.46825i	−0.823805	+	0.475624i	−0.851727	−	0.523986i	$-0.824444\pi$
$317$	−14.6674	+	8.46825i	−0.823805	+	0.475624i	0.0279217	+	0.999610i	$0.491111\pi$
$318$	0.0195349	−	0.0398812i	0.00109546	−	0.00223642i
$319$	15.5299	+	26.8986i	0.869510	+	1.50603i
$320$	2.14030	+	3.70711i	0.119647	+	0.207234i
$321$	−2.26648	−	33.2198i	−0.126503	−	1.85415i
$322$	1.08515	+	1.02582i	0.0604730	+	0.0571668i
$323$	1.28684	−	0.742958i	0.0716018	−	0.0413393i
$324$	−3.80549	+	14.8346i	−0.211416	+	0.824143i
$325$	4.74224	−	0.144678i	0.263052	−	0.00802531i
$326$	5.94905	+	3.43469i	0.329488	+	0.190230i
$327$	10.4559	−	0.713372i	0.578211	−	0.0394496i
$328$	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
$333$	7.27374	+	9.37518i	0.398599	+	0.513757i
$334$		−	7.33365i		−	0.401279i
$335$	1.91314	+	3.31365i	0.104526	+	0.181044i
$336$	9.86711	−	3.69169i	0.538295	−	0.201398i
$337$	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
$339$	−1.01095	−	14.8175i	−0.0549075	−	0.804778i
$340$	2.76819			0.150126
$341$	32.2165	−	55.8005i	1.74462	−	3.02177i
$342$	2.30580	+	2.97196i	0.124683	+	0.160705i
$343$	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	−0.313698	−	0.949523i	$-0.601568\pi$
$347$	6.55263	−	3.78316i	0.351763	−	0.203091i	0.665462	+	0.746432i	$0.268235\pi$
$348$	−1.03379	−	15.1522i	−0.0554170	−	0.812246i
$349$	−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
$351$	−12.8860	−	13.5996i	−0.687806	−	0.725895i
$352$	15.9716	+	27.6636i	0.851288	+	1.47447i
$353$	−12.8501			−0.683940			−0.341970	−	0.939711i	$-0.611094\pi$
$353$	−12.8501			−0.683940			−0.341970	+	0.939711i	$0.611094\pi$
$354$	1.30526	−	0.877198i	0.0693737	−	0.0466226i
$355$		−	33.2935i		−	1.76704i
$356$	1.72810			0.0915889
$357$	0.488924	−	2.92574i	0.0258766	−	0.154847i
$358$	3.52811	−	6.11086i	0.186466	−	0.322969i
$359$	−14.4330	+	8.33290i	−0.761745	+	0.439794i	−0.829922	−	0.557880i	$-0.811615\pi$
$359$	−14.4330	+	8.33290i	−0.761745	+	0.439794i	0.0681770	+	0.997673i	$0.478282\pi$
$360$	2.07043	+	15.1025i	0.109121	+	0.795972i
$361$	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
$366$	3.39109	−	0.231363i	0.177255	−	0.0120936i
$367$		−	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
$369$	−26.6719	+	3.65650i	−1.38848	+	0.190350i
$370$	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
$378$	7.50589	+	0.220273i	0.386061	+	0.0113296i
$379$	−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
$381$	2.43217	−	4.96535i	0.124604	−	0.254383i
$382$	2.81576	−	4.87703i	0.144067	−	0.249531i
$383$	−8.52108			−0.435407			−0.217703	−	0.976015i	$-0.569857\pi$
$383$	−8.52108			−0.435407			−0.217703	+	0.976015i	$0.569857\pi$
$384$	−1.35928	−	19.9230i	−0.0693655	−	1.01669i
$385$	27.5325	−	29.1248i	1.40319	−	1.48434i
$386$	1.53244	+	0.884754i	0.0779991	+	0.0450328i
$387$	−15.0778	−	19.4339i	−0.766447	−	0.987879i
$388$		−	16.8618i		−	0.856027i
$389$	−11.0480	−	6.37855i	−0.560155	−	0.323406i	0.193053	−	0.981188i	$-0.438161\pi$
$389$	−11.0480	−	6.37855i	−0.560155	−	0.323406i	−0.753208	+	0.657783i	$0.771494\pi$
$390$	−7.80995	−	3.53445i	−0.395472	−	0.178974i
$391$			0.668865i			0.0338260i
$392$	−7.75380	−	11.8402i	−0.391626	−	0.598019i
$393$	−2.51708	+	5.13870i	−0.126970	+	0.259213i
$394$	7.49359			0.377522
$395$	5.39813	−	9.34983i	0.271609	−	0.470441i
$396$	−4.17935	−	30.4857i	−0.210020	−	1.53197i
$397$			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
$399$	−6.68942	+	8.11864i	−0.334890	+	0.406440i
$400$	−1.51256	−	2.61983i	−0.0756281	−	0.130992i
$401$	−19.1034	−	11.0293i	−0.953977	−	0.550779i	−0.0596628	−	0.998219i	$-0.519003\pi$
$401$	−19.1034	−	11.0293i	−0.953977	−	0.550779i	−0.894314	+	0.447440i	$0.852336\pi$
$402$	−0.0980450	−	1.43704i	−0.00489004	−	0.0716732i
$403$	−1.17530	−	38.5239i	−0.0585461	−	1.91901i
$404$	4.52409	+	7.83596i	0.225082	+	0.389854i
$405$	5.62025	−	21.9089i	0.279272	−	1.08866i
$406$	−7.13591	+	2.12864i	−0.354150	+	0.105643i
$407$	−20.6471	−	11.9206i	−1.02344	−	0.590883i
$408$	−2.03575	−	0.997167i	−0.100784	−	0.0493671i
$409$	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
$411$	12.8343	+	6.28661i	0.633069	+	0.310096i
$412$	−4.10846	−	2.37202i	−0.202409	−	0.116861i
$413$	3.19601	+	3.02128i	0.157265	+	0.148667i
$414$	−1.67752	+	0.229974i	−0.0824456	+	0.0113026i
$415$	−14.9300	−	25.8595i	−0.732886	−	1.26940i
$416$	16.8312	+	9.04468i	0.825217	+	0.443452i
$417$	−1.02154	−	14.9726i	−0.0500248	−	0.733213i
$418$	−6.54520	−	3.77887i	−0.320136	−	0.184831i
$419$	12.5477	+	21.7332i	0.612994	+	1.06174i	0.990733	+	0.135825i	$0.0433684\pi$
$419$	12.5477	+	21.7332i	0.612994	+	1.06174i	−0.377739	+	0.925912i	$0.623298\pi$
$420$	−18.3548	+	6.86729i	−0.895622	+	0.335089i
$421$	−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
$423$	−12.4622	+	1.70847i	−0.605933	+	0.0830685i
$424$	0.0474539	−	0.0821926i	0.00230457	−	0.00399163i
$425$	−0.851768			−0.0413168
$426$	−5.51324	+	11.2555i	−0.267117	+	0.545328i
$427$	2.71719	+	9.10892i	0.131494	+	0.440812i
$428$		−	32.7127i		−	1.58123i
$429$	34.2942	+	15.5201i	1.65574	+	0.749316i
$430$	−9.74692	−	5.62739i	−0.470038	−	0.271377i
$431$			28.8820i			1.39119i	0.718432	+	0.695597i	$0.244860\pi$
$431$			28.8820i			1.39119i	−0.718432	+	0.695597i	$0.755140\pi$
$432$	−3.74904	+	11.3421i	−0.180376	+	0.545699i
$433$	−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
$435$	1.52678	+	22.3780i	0.0732036	+	1.07294i
$436$	10.2963			0.493102
$437$	1.18601	−	2.05423i	0.0567345	−	0.0982671i
$438$	2.29140	−	4.67797i	0.109487	−	0.223522i
$439$	−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
$441$	4.01628	+	20.6124i	0.191251	+	0.981541i
$442$	1.08405	−	0.670762i	0.0515629	−	0.0319049i
$443$	26.2992	−	15.1839i	1.24951	−	0.721407i	0.278501	−	0.960436i	$-0.410162\pi$
$443$	26.2992	−	15.1839i	1.24951	−	0.721407i	0.971012	+	0.239029i	$0.0768291\pi$
$444$	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	0.876381	−	0.481618i	$-0.159951\pi$
$449$	19.0172	+	10.9796i	0.897478	+	0.518159i	0.0210967	+	0.999777i	$0.493284\pi$
$450$	−0.292861	−	2.13624i	−0.0138056	−	0.100703i
$451$	46.8439	−	27.0453i	2.20579	−	1.27352i
$452$		−	14.5914i		−	0.686320i
$453$	13.5083	−	0.921631i	0.634676	−	0.0433020i
$454$			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
$459$	2.23789	+	2.51095i	0.104456	+	0.117201i
$460$	3.82693	−	2.20948i	0.178431	−	0.103017i
$461$	−4.57076	+	7.91680i	−0.212882	+	0.368722i	−0.952615	−	0.304178i	$-0.901618\pi$
$461$	−4.57076	+	7.91680i	−0.212882	+	0.368722i	0.739734	+	0.672900i	$0.234952\pi$
$462$	−14.1308	+	5.28691i	−0.657423	+	0.245969i
$463$	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	0.873243	−	0.487285i	$-0.162013\pi$
$467$	0.315959	+	0.547257i	0.0146208	+	0.0253240i	−0.858622	+	0.512609i	$0.828679\pi$
$468$	−11.7211	−	14.1917i	−0.541807	−	0.656014i
$469$	3.86009	−	1.15147i	0.178243	−	0.0531698i
$470$	−4.98451	+	2.87781i	−0.229918	+	0.132743i
$471$	1.03999	+	15.2431i	0.0479201	+	0.702364i
$472$	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
$477$	−0.111262	+	0.0863224i	−0.00509432	+	0.00395243i
$478$	6.49417	−	11.2482i	0.297036	−	0.514482i
$479$	22.3302			1.02029			0.510146	−	0.860088i	$-0.329591\pi$
$479$	22.3302			1.02029			0.510146	+	0.860088i	$0.329591\pi$
$480$	1.57020	+	23.0144i	0.0716696	+	1.05046i
$481$	−14.2545	+	0.434882i	−0.649949	+	0.0198289i
$482$	−11.4098			−0.519704
$483$	−1.65931	−	4.43498i	−0.0755013	−	0.201799i
$484$	21.5535	+	37.3317i	0.979704	+	1.69690i
$485$			24.9028i			1.13078i
$486$	−5.52802	+	6.47599i	−0.250756	+	0.293757i
$487$	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	−0.643612	−	0.765352i	$-0.722565\pi$
$491$	−6.70526	+	3.87128i	−0.302604	+	0.174709i	0.341008	+	0.940060i	$0.389232\pi$
$492$	−26.3876	+	1.80034i	−1.18964	+	0.0811657i
$493$	−2.88862	−	1.66775i	−0.130097	−	0.0751116i
$494$	−4.51871	+	0.137859i	−0.203307	+	0.00620256i
$495$	6.17239	+	45.0237i	0.277428	+	2.02367i
$496$	−21.2824	+	12.2874i	−0.955608	+	0.551721i
$497$	−34.0975	−	8.11698i	−1.52948	−	0.364096i
$498$	0.765137	+	11.2146i	0.0342866	+	0.502538i
$499$	−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
$501$	−10.2298	+	20.8845i	−0.457034	+	0.933049i
$502$	9.61407	−	5.55069i	0.429097	−	0.247739i
$503$	−14.9743	+	25.9362i	−0.667671	+	1.15644i	0.310883	+	0.950448i	$0.399375\pi$
$503$	−14.9743	+	25.9362i	−0.667671	+	1.15644i	−0.978554	+	0.205992i	$0.933958\pi$
$504$	15.9720	+	1.56157i	0.711449	+	0.0695579i
$505$	−6.68154	−	11.5728i	−0.297325	−	0.514981i
$506$	2.94623	−	1.70101i	0.130976	−	0.0756190i
$507$	22.3292	−	2.89926i	0.991676	−	0.128761i
$508$	2.71600	−	4.70426i	0.120503	−	0.208718i
$509$	3.30037	−	5.71641i	0.146286	−	0.253376i	−0.783566	−	0.621309i	$-0.786601\pi$
$509$	3.30037	−	5.71641i	0.146286	−	0.253376i	0.929852	+	0.367933i	$0.119935\pi$
$510$	1.38211	+	0.676999i	0.0612011	+	0.0299780i
$511$	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	−0.999881	−	0.0154387i	$-0.995086\pi$
$521$	−11.1062	+	19.2365i	−0.486570	+	0.842764i	0.513311	+	0.858203i	$0.328419\pi$
$522$	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
$525$	5.64774	−	2.11305i	0.246488	−	0.0922212i
$526$	−0.441265	+	0.764294i	−0.0192401	+	0.0333248i
$527$			6.91940i			0.301414i
$528$	−1.63374	−	23.9457i	−0.0710995	−	1.04210i
$529$	−10.9661	−	18.9939i	−0.476788	−	0.825822i
$530$	−0.0322176	+	0.0558025i	−0.00139944	+	0.00242390i
$531$	−4.94068	+	0.677327i	−0.214407	+	0.0293935i
$532$	−7.09972	+	7.51033i	−0.307812	+	0.325614i
$533$	15.3157	−	28.5009i	0.663398	−	1.23451i
$534$	0.862811	+	0.422630i	0.0373375	+	0.0182890i
$535$			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
$540$	6.97395	−	21.0986i	0.300111	−	0.907941i
$541$	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
$546$	−5.52387	+	7.13685i	−0.236400	+	0.305429i
$547$	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
$552$	−3.61025	+	0.246316i	−0.153663	+	0.0104839i
$553$	−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	$0.149833\pi$
$557$			21.4071i			0.907046i	−0.891245	+	0.453523i	$0.850167\pi$
$558$	−17.3539	+	2.37908i	−0.734649	+	0.100714i
$559$	29.5482	−	0.901470i	1.24976	−	0.0381281i
$560$	−14.6482	+	4.36956i	−0.619000	+	0.184648i
$561$	−6.06898	−	2.97276i	−0.256233	−	0.125510i
$562$	1.16111	−	2.01111i	0.0489786	−	0.0848334i
$563$	14.7814	+	25.6022i	0.622963	+	1.07900i	0.988931	+	0.148376i	$0.0474045\pi$
$563$	14.7814	+	25.6022i	0.622963	+	1.07900i	−0.365969	+	0.930627i	$0.619262\pi$
$564$	−12.3294	+	0.841195i	−0.519160	+	0.0354207i
$565$			21.5497i			0.906601i
$566$	−3.67778	+	6.37011i	−0.154589	+	0.267756i
$567$	−21.0677	−	11.0974i	−0.884761	−	0.466045i
$568$	−13.3927	+	23.1968i	−0.561944	+	0.973316i
$569$	23.8838	+	13.7893i	1.00126	+	0.578078i	0.908621	−	0.417622i	$-0.137136\pi$
$569$	23.8838	+	13.7893i	1.00126	+	0.578078i	0.0926389	+	0.995700i	$0.470470\pi$
$570$	−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
$582$	4.12378	−	8.41882i	0.170936	−	0.348971i
$583$	0.141470	−	0.245033i	0.00585909	−	0.0101482i
$584$	5.56624	−	9.64100i	0.230332	−	0.398948i
$585$	17.3106	+	20.9595i	0.715706	+	0.866568i
$586$	6.56417	−	3.78982i	0.271163	−	0.156556i
$587$	−12.6832	−	21.9680i	−0.523493	−	0.906717i	−0.999626	−	0.0273434i	$-0.991295\pi$
$587$	−12.6832	−	21.9680i	−0.523493	−	0.906717i	0.476133	−	0.879373i	$-0.342038\pi$
$588$	2.55822	+	20.4723i	0.105499	+	0.844262i
$589$	12.2692	−	21.2510i	0.505546	−	0.875631i
$590$	−1.97612	+	1.14092i	−0.0813557	+	0.0469707i
$591$	−21.3400	−	10.4529i	−0.877808	−	0.429976i
$592$	4.54654	+	7.87484i	0.186862	+	0.323654i
$593$	−5.88143	−	10.1869i	−0.241521	−	0.418327i	0.719627	−	0.694361i	$-0.244313\pi$
$593$	−5.88143	−	10.1869i	−0.241521	−	0.418327i	−0.961148	+	0.276034i	$0.910980\pi$
$594$	5.36903	−	16.2432i	0.220294	−	0.666465i
$595$	−0.996725	+	4.18701i	−0.0408618	+	0.171651i
$596$	−20.3541	+	11.7515i	−0.833738	+	0.481359i
$597$	−5.18002	−	2.53732i	−0.212004	−	0.103846i
$598$	0.963278	−	1.79256i	0.0393913	−	0.0733031i
$599$	−39.8531	−	23.0092i	−1.62835	−	0.940131i	−0.984584	−	0.174911i	$-0.944036\pi$
$599$	−39.8531	−	23.0092i	−1.62835	−	0.940131i	−0.643770	−	0.765219i	$-0.722631\pi$
$600$	−0.313672	−	4.59749i	−0.0128056	−	0.187692i
$601$	−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
$606$	0.342417	+	5.01880i	0.0139097	+	0.203875i
$607$			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
$609$	23.2907	+	3.89212i	0.943785	+	0.157717i
$610$	−4.93178			−0.199682
$611$	7.15614	−	13.3168i	0.289507	−	0.538741i
$612$	2.02561	+	2.61082i	0.0818803	+	0.105536i
$613$	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
$615$	38.9713	−	2.65889i	1.57147	−	0.107217i
$616$	−30.8987	+	9.21707i	−1.24494	+	0.371367i
$617$	6.51889	+	3.76368i	0.262441	+	0.151520i	0.625447	−	0.780266i	$-0.284916\pi$
$617$	6.51889	+	3.76368i	0.262441	+	0.151520i	−0.363007	+	0.931786i	$0.618250\pi$
$618$	−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
$621$	5.09797	+	1.68508i	0.204574	+	0.0676201i
$622$	−1.24032	+	0.716101i	−0.0497325	+	0.0287130i
$623$	−0.622225	+	2.61382i	−0.0249289	+	0.104720i
$624$	−8.36779	−	11.6663i	−0.334980	−	0.467024i
$625$	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
$630$	−10.8437	−	1.06019i	−0.432025	−	0.0422388i
$631$	−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
$633$	−7.12056	+	14.5368i	−0.283017	+	0.577788i
$634$	−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
$639$	31.4008	−	24.3623i	1.24220	−	0.963759i
$640$			28.9746i			1.14532i
$641$	−0.799986	+	0.461872i	−0.0315975	+	0.0182428i	−0.515716	−	0.856760i	$-0.672474\pi$
$641$	−0.799986	+	0.461872i	−0.0315975	+	0.0182428i	0.484118	+	0.875003i	$0.339141\pi$
$642$	8.00035	−	16.3330i	0.315749	−	0.644611i
$643$	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	$-0.342075\pi$
$647$	24.2168			0.952061			0.476030	+	0.879429i	$0.342075\pi$
$648$	−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
$651$	−17.1655	−	45.8798i	−0.672771	−	1.79817i
$652$	−10.7004	−	18.5337i	−0.419061	−	0.725835i
$653$	−31.2511	−	18.0428i	−1.22295	−	0.706070i	−0.257404	−	0.966304i	$-0.582867\pi$
$653$	−31.2511	−	18.0428i	−1.22295	−	0.706070i	−0.965546	+	0.260234i	$0.916200\pi$
$654$	5.14077	+	2.51810i	0.201020	+	0.0984654i
$655$	4.15124	−	7.19017i	0.162203	−	0.280943i
$656$	−20.6303			−0.805477
$657$	−13.0507	+	10.1254i	−0.509157	+	0.395030i
$658$	1.73208	+	5.80649i	0.0675234	+	0.226361i
$659$	10.7491	+	6.20598i	0.418724	+	0.241751i	0.694531	−	0.719462i	$-0.255612\pi$
$659$	10.7491	+	6.20598i	0.418724	+	0.241751i	−0.275807	+	0.961213i	$0.588945\pi$
$660$	3.03909	+	44.5438i	0.118296	+	1.73387i
$661$			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
$663$	−4.02276	+	0.398017i	−0.156231	+	0.0154577i
$664$			24.0230i			0.932275i
$665$	10.4854	−	11.0918i	0.406607	−	0.430123i
$666$	0.880299	+	6.42123i	0.0341109	+	0.248818i
$667$	−5.32456			−0.206168
$668$	−11.4236	+	19.7863i	−0.441993	+	0.765554i
$669$	−8.49036	−	4.15882i	−0.328256	−	0.160789i
$670$			2.08994i			0.0807415i
$671$	21.6559			0.836015
$672$	23.9530	+	4.00281i	0.924007	+	0.154412i
$673$	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
$675$	−2.14588	+	6.49202i	−0.0825948	+	0.249878i
$676$	22.0804	−	1.34853i	0.849246	−	0.0518666i
$677$	6.45592	+	11.1820i	0.248121	+	0.429758i	0.963004	−	0.269485i	$-0.0868536\pi$
$677$	6.45592	+	11.1820i	0.248121	+	0.429758i	−0.714883	+	0.699244i	$0.753520\pi$
$678$	3.56852	−	7.28524i	0.137048	−	0.279788i
$679$	25.5041	+	6.07131i	0.978759	+	0.232996i
$680$	2.84845	+	1.64456i	0.109233	+	0.0630658i
$681$	17.3599	−	35.4407i	0.665232	−	1.35809i
$682$	30.4787	−	17.5969i	1.16709	−	0.673820i
$683$	7.62396	−	4.40170i	0.291723	−	0.168426i	−0.346996	−	0.937867i	$-0.612798\pi$
$683$	7.62396	−	4.40170i	0.291723	−	0.168426i	0.638719	+	0.769440i	$0.279465\pi$
$684$	−1.59165	−	11.6101i	−0.0608584	−	0.443924i
$685$	−17.9580	−	10.3681i	−0.686140	−	0.396143i
$686$	9.51610	−	3.43155i	0.363327	−	0.131017i
$687$	27.1330	+	13.2905i	1.03519	+	0.507066i
$688$	−9.42456	−	16.3238i	−0.359308	−	0.622340i
$689$	−0.00516104	−	0.169168i	−0.000196620	−	0.00644478i
$690$	2.45108	−	0.167230i	0.0933112	−	0.00636633i
$691$	−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
$693$	47.6158	+	4.65537i	1.80878	+	0.176843i
$694$	4.13279			0.156878
$695$			21.7752i			0.825982i
$696$	7.93804	−	16.2057i	0.300891	−	0.614277i
$697$	−2.90438	+	5.03053i	−0.110011	+	0.190545i
$698$	−14.6537			−0.554652
$699$	2.91348	+	1.42710i	0.110198	+	0.0539780i
$700$	5.67707	−	1.69347i	0.214573	−	0.0640072i
$701$			39.6954i			1.49927i	0.661849	+	0.749637i	$0.269772\pi$
$701$			39.6954i			1.49927i	−0.661849	+	0.749637i	$0.730228\pi$
$702$	−2.38137	−	9.95227i	−0.0898789	−	0.375624i
$703$	−7.86321	−	4.53982i	−0.296566	−	0.171223i
$704$		−	10.2668i		−	0.386945i
$705$	18.2090	−	1.24234i	0.685790	−	0.0467893i
$706$	−6.07847	−	3.50941i	−0.228766	−	0.132078i
$707$	−13.4812	+	4.02144i	−0.507012	+	0.151242i
$708$	−4.88802	+	0.333494i	−0.183703	+	0.0125335i
$709$	−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
$711$	12.7683	−	1.75044i	0.478850	−	0.0656465i
$712$	1.77820	+	1.02664i	0.0666409	+	0.0384751i
$713$	5.52284	+	9.56583i	0.206832	+	0.358243i
$714$	1.03031	−	1.25044i	0.0385583	−	0.0467965i
$715$	−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	$-0.434700\pi$
$719$	10.9246			0.407418			0.203709	+	0.979032i	$0.434700\pi$
$720$	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
$723$	32.4925	+	15.9157i	1.20841	+	0.591913i
$724$	2.00582	−	1.15806i	0.0745458	−	0.0430390i
$725$		−	6.78058i		−	0.251824i
$726$	1.63133	+	23.9104i	0.0605443	+	0.887397i
$727$		−	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
$732$	−9.50960	−	4.65807i	−0.351485	−	0.172167i
$733$	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
$735$	−3.77817	−	30.2351i	−0.139360	−	1.11524i
$736$	−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
$741$	13.0605	+	5.91063i	0.479790	+	0.217132i
$742$	0.0492954	+	0.0466003i	0.00180969	+	0.00171075i
$743$	−6.39543	+	3.69241i	−0.234626	+	0.135461i	−0.612704	−	0.790312i	$-0.709918\pi$
$743$	−6.39543	+	3.69241i	−0.234626	+	0.135461i	0.378078	+	0.925774i	$0.376585\pi$
$744$	−37.3480	+	2.54814i	−1.36924	+	0.0934193i
$745$	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
$750$	−0.596235	−	8.73900i	−0.0217714	−	0.319103i
$751$	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
$753$	−35.1213	+	2.39622i	−1.27989	+	0.0873230i
$754$	5.33967	+	8.62966i	0.194459	+	0.314274i
$755$	−19.6456			−0.714978
$756$	−19.9079	−	12.2862i	−0.724043	−	0.446846i
$757$	−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
$759$	−10.7629	+	0.734320i	−0.390669	+	0.0266541i
$760$	−5.83214	−	10.1016i	−0.211554	−	0.366422i
$761$	−7.97685			−0.289161			−0.144580	−	0.989493i	$-0.546183\pi$
$761$	−7.97685			−0.289161			−0.144580	+	0.989493i	$0.546183\pi$
$762$	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
$765$	−2.99157	−	3.85586i	−0.108161	−	0.139409i
$766$	−4.03073	−	2.32714i	−0.145636	−	0.0840830i
$767$	2.83707	−	5.27949i	0.102441	−	0.190631i
$768$	2.20254	−	4.49655i	0.0794773	−	0.162255i
$769$	−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
$771$	41.2868	−	2.81687i	1.48691	−	0.101447i
$772$	−2.75636	−	4.77416i	−0.0992036	−	0.171826i
$773$	8.69927	+	15.0676i	0.312891	+	0.541943i	0.978987	−	0.203923i	$-0.0653692\pi$
$773$	8.69927	+	15.0676i	0.312891	+	0.541943i	−0.666096	+	0.745866i	$0.732036\pi$
$774$	−1.82478	−	13.3106i	−0.0655903	−	0.478440i
$775$	−12.1816	+	7.03307i	−0.437577	+	0.252635i
$776$	10.0174	−	17.3507i	0.359604	−	0.622853i
$777$	−16.9763	+	6.35153i	−0.609021	+	0.227860i
$778$	−3.48402	−	6.03450i	−0.124908	−	0.216347i
$779$	17.8399	−	10.2999i	0.639182	−	0.369032i
$780$	15.5658	+	21.7016i	0.557343	+	0.777040i
$781$	−39.9264	+	69.1545i	−1.42868	+	2.47454i
$782$	−0.182670	+	0.316393i	−0.00653226	+	0.0113142i
$783$	−19.9886	+	17.8150i	−0.714335	+	0.636655i
$784$	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	−0.970731	−	0.240168i	$-0.922798\pi$
$797$	−7.83061	+	13.5630i	−0.277374	+	0.480426i	0.693357	+	0.720594i	$0.256131\pi$
$798$	−5.38153	+	2.01345i	−0.190504	+	0.0712755i
$799$	−1.35705	+	2.35047i	−0.0480088	+	0.0831537i
$800$		−	6.97341i		−	0.246547i
$801$	−1.86755	−	2.40710i	−0.0659865	−	0.0850505i
$802$	−6.02431	−	10.4344i	−0.212726	−	0.368452i
$803$	16.5941	−	28.7418i	0.585593	−	1.01428i
$804$	−1.97395	+	4.02989i	−0.0696160	+	0.142123i
$805$	1.96399	+	6.58395i	0.0692216	+	0.232054i
$806$	9.96509	−	18.5440i	0.351005	−	0.653183i
$807$	−12.5354	+	25.5913i	−0.441265	+	0.900857i
$808$			10.7509i			0.378215i
$809$		−	7.94208i		−	0.279229i	−0.990206	−	0.139614i	$-0.955414\pi$
$809$		−	7.94208i		−	0.279229i	0.990206	−	0.139614i	$-0.0445863\pi$
$810$	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
$813$	0.0724190	+	1.06144i	0.00253984	+	0.0372265i
$814$	−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
$819$	25.6860	−	12.6187i	0.897540	−	0.440933i
$820$	38.3764			1.34016
$821$	−18.3241	−	10.5794i	−0.639515	−	0.369224i	0.144912	−	0.989444i	$-0.453710\pi$
$821$	−18.3241	−	10.5794i	−0.639515	−	0.369224i	−0.784428	+	0.620220i	$0.787043\pi$
$822$	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
$825$	−0.935122	−	13.7061i	−0.0325568	−	0.477184i
$826$	0.686687	+	2.30200i	0.0238929	+	0.0800968i
$827$		−	19.8390i		−	0.689871i	−0.938626	−	0.344935i	$-0.887901\pi$
$827$		−	19.8390i		−	0.689871i	0.938626	−	0.344935i	$-0.112099\pi$
$828$	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
$831$	7.36568	−	15.0373i	0.255513	−	0.521637i
$832$	−3.23141	−	5.22241i	−0.112029	−	0.181054i
$833$	4.04511	+	2.04159i	0.140155	+	0.0707369i
$834$	3.60587	−	7.36150i	0.124861	−	0.254908i
$835$	16.8713	−	29.2219i	0.583855	−	1.01127i
$836$	11.7727	+	20.3909i	0.407167	+	0.705234i
$837$	52.7384	+	17.4322i	1.82290	+	0.602544i
$838$			13.7073i			0.473510i
$839$	3.02970	−	5.24760i	0.104597	−	0.181167i	−0.808977	−	0.587841i	$-0.799978\pi$
$839$	3.02970	−	5.24760i	0.104597	−	0.181167i	0.913573	+	0.406674i	$0.133311\pi$
$840$	−22.9668	−	3.83800i	−0.792429	−	0.132423i
$841$	−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
$855$	2.35068	+	17.1467i	0.0803915	+	0.586406i
$856$	19.4343	−	33.6612i	0.664252	−	1.15052i
$857$	4.19504	−	7.26603i	0.143300	−	0.248203i	−0.785437	−	0.618941i	$-0.787562\pi$
$857$	4.19504	−	7.26603i	0.143300	−	0.248203i	0.928737	+	0.370738i	$0.120895\pi$
$858$	11.9836	+	16.7073i	0.409113	+	0.570379i
$859$	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
$861$	6.77812	−	40.5606i	0.230998	−	1.38230i
$862$	−7.88778	+	13.6620i	−0.268659	+	0.465331i
$863$	16.9737	−	9.79980i	0.577793	−	0.333589i	−0.182463	−	0.983213i	$-0.558407\pi$
$863$	16.9737	−	9.79980i	0.577793	−	0.333589i	0.760256	+	0.649624i	$0.225074\pi$
$864$	−20.5571	+	18.3216i	−0.699366	+	0.623313i
$865$	−10.6146	−	18.3850i	−0.360906	−	0.625108i
$866$	−2.04443	−	3.54106i	−0.0694727	−	0.120330i
$867$	−28.6525	+	1.95487i	−0.973091	+	0.0663909i
$868$	−13.7570	−	46.1181i	−0.466944	−	1.56535i
$869$	−22.4251	+	12.9471i	−0.760719	+	0.439201i
$870$	−5.38932	+	11.0025i	−0.182715	+	0.373018i
$871$	−2.88843	−	4.66812i	−0.0978708	−	0.158173i
$872$	10.5948	+	6.11692i	0.358786	+	0.207145i
$873$	−23.4871	+	18.2225i	−0.794917	+	0.616737i
$874$	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
$879$	−23.9797	+	1.63606i	−0.808814	+	0.0551828i
$880$			34.8251i			1.17395i
$881$	−22.1811	−	38.4188i	−0.747300	−	1.29436i	−0.949113	−	0.314937i	$-0.898017\pi$
$881$	−22.1811	−	38.4188i	−0.747300	−	1.29436i	0.201813	−	0.979424i	$-0.435317\pi$
$882$	−3.72950	+	10.8471i	−0.125579	+	0.365242i
$883$	−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
$885$	7.21901	−	0.492530i	0.242664	−	0.0165562i
$886$	16.5871			0.557254
$887$	−20.8583	+	36.1277i	−0.700354	+	1.21305i	0.267989	+	0.963422i	$0.413641\pi$
$887$	−20.8583	+	36.1277i	−0.700354	+	1.21305i	−0.968342	+	0.249626i	$0.919692\pi$
$888$	0.942853	+	13.8194i	0.0316401	+	0.463748i
$889$	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
$894$	−13.0365	+	0.889439i	−0.436006	+	0.0297473i
$895$	28.1165	−	16.2330i	0.939829	−	0.542611i
$896$	29.6743	+	7.06403i	0.991350	+	0.235993i
$897$	−5.24365	+	3.76108i	−0.175080	+	0.125579i
$898$	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
$903$	35.1903	−	13.1661i	1.17106	−	0.438142i
$904$	8.66858	−	15.0144i	0.288313	−	0.499372i
$905$	−2.96235	+	1.71032i	−0.0984720	+	0.0568528i
$906$	6.64155	+	3.25322i	0.220651	+	0.108081i
$907$	−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	$-0.755330\pi$
$911$		−	41.9642i		−	1.39034i	0.718847	−	0.695168i	$-0.244670\pi$
$912$	−0.622191	−	9.11944i	−0.0206028	−	0.301975i
$913$			71.6177i			2.37020i
$914$	−17.0561	+	9.84732i	−0.564164	+	0.325720i
$915$	14.0445	+	6.87941i	0.464297	+	0.227426i
$916$	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
$924$	46.3604	+	7.74733i	1.52515	+	0.254869i
$925$	2.60235	+	4.50741i	0.0855648	+	0.148203i
$926$	10.4716	+	6.04576i	0.344117	+	0.198676i
$927$	1.13597	+	8.28618i	0.0373101	+	0.272154i
$928$	13.6538	−	23.6491i	0.448209	−	0.776320i
$929$	31.6451			1.03824			0.519121	−	0.854701i	$-0.326259\pi$
$929$	31.6451			1.03824			0.519121	+	0.854701i	$0.326259\pi$
$930$	25.3564	−	1.72999i	0.831470	−	0.0567286i
$931$	−8.80334	−	13.4428i	−0.288518	−	0.440571i
$932$	2.76027	+	1.59364i	0.0904158	+	0.0522016i
$933$	4.53105	−	0.309139i	0.148340	−	0.0101208i
$934$			0.345159i			0.0112939i
$935$	8.49184	+	4.90276i	0.277713	+	0.160338i
$936$	−3.62975	−	21.5666i	−0.118642	−	0.704927i
$937$		−	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
$939$	−5.66213	−	2.77347i	−0.184777	−	0.0905089i
$940$	17.9310			0.584846
$941$	0.833591	−	1.44382i	0.0271743	−	0.0470672i	−0.852118	−	0.523349i	$-0.824682\pi$
$941$	0.833591	−	1.44382i	0.0271743	−	0.0470672i	0.879293	+	0.476282i	$0.158016\pi$
$942$	−3.67100	+	7.49447i	−0.119608	+	0.244183i
$943$			9.27271i			0.301961i
$944$	−3.82153			−0.124380
$945$	29.4015	+	18.1453i	0.956432	+	0.590265i
$946$	13.4970	+	23.3775i	0.438825	+	0.760067i
$947$	−17.3559	−	10.0204i	−0.563991	−	0.325620i	0.190755	−	0.981638i	$-0.438906\pi$
$947$	−17.3559	−	10.0204i	−0.563991	−	0.325620i	−0.754746	+	0.656017i	$0.772240\pi$
$948$	12.6322	−	0.861858i	0.410276	−	0.0279919i
$949$	−0.605378	−	19.8430i	−0.0196514	−	0.644130i
$950$	0.824953	+	1.42886i	0.0267650	+	0.0463584i
$951$	26.3442	+	12.9042i	0.854270	+	0.418446i
$952$	2.37872	−	2.51630i	0.0770949	−	0.0815536i
$953$	6.14947	+	3.55040i	0.199201	+	0.115009i	0.596283	−	0.802774i	$-0.296644\pi$
$953$	6.14947	+	3.55040i	0.199201	+	0.115009i	−0.397082	+	0.917783i	$0.629977\pi$
$954$	−0.0762051	+	0.0104471i	−0.00246723	+	0.000338237i
$955$	22.4396	−	12.9555i	0.726127	−	0.419230i
$956$	−35.0427	+	20.2319i	−1.13336	+	0.654347i
$957$	23.6649	−	48.3127i	0.764979	−	1.56173i
$958$	10.5628	+	6.09846i	0.341270	+	0.197032i
$959$	−14.9966	+	15.8639i	−0.484265	+	0.512273i
$960$	3.26145	−	6.65835i	0.105263	−	0.214897i
$961$	41.6336	+	72.1116i	1.34302	+	2.32618i
$962$	−6.86157	−	3.68725i	−0.221226	−	0.118882i
$963$	−45.5662	+	35.3526i	−1.46835	+	1.13922i
$964$	30.7839	+	17.7731i	0.991483	+	0.572433i
$965$	4.07081	+	7.05085i	0.131044	+	0.226975i
$966$	0.426308	−	2.55105i	0.0137162	−	0.0820785i
$967$	−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
$969$	−2.31130	−	1.13214i	−0.0742496	−	0.0363696i
$970$	−6.80105	+	11.7798i	−0.218369	+	0.378226i
$971$	2.08912			0.0670431			0.0335216	−	0.999438i	$-0.489328\pi$
$971$	2.08912			0.0670431			0.0335216	+	0.999438i	$0.489328\pi$
$972$	25.0023	−	8.86131i	0.801950	−	0.284227i
$973$	22.3011	+	5.30881i	0.714940	+	0.170193i
$974$			22.0058i			0.705111i
$975$	−4.78956	−	6.67754i	−0.153389	−	0.213852i
$976$	−7.15300	−	4.12979i	−0.228962	−	0.132191i
$977$			21.3475i			0.682968i	0.939888	+	0.341484i	$0.110929\pi$
$977$			21.3475i			0.682968i	−0.939888	+	0.341484i	$0.889071\pi$
$978$	−0.809888	−	11.8705i	−0.0258974	−	0.379577i
$979$	5.30119	+	3.06064i	0.169427	+	0.0978186i
$980$	−1.68132	−	29.8883i	−0.0537078	−	0.954745i
$981$	−11.1272	−	14.3419i	−0.355263	−	0.457901i
$982$	−4.22905			−0.134955
$983$	−26.2192	+	45.4129i	−0.836261	+	1.44845i	0.0567381	+	0.998389i	$0.481930\pi$
$983$	−26.2192	+	45.4129i	−0.836261	+	1.44845i	−0.892999	+	0.450058i	$0.851403\pi$
$984$	−28.2223	−	13.8241i	−0.899693	−	0.440695i
$985$	29.8593	+	17.2393i	0.951395	+	0.549288i
$986$	−0.910938	−	1.57779i	−0.0290102	−	0.0502471i
$987$	3.16702	−	18.9516i	0.100807	−	0.603236i
$988$	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
$996$	15.4046	−	31.4490i	0.488114	−	0.996500i
$997$	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
$999$	6.45019	−	19.5141i	0.204075	−	0.617398i

Twists

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

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

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} +(-0.0643970 - 0.943866i) 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} +(-1.29652 + 2.64688i) q^{12} +(-1.89716 - 3.06607i) q^{13} +(1.40585 + 0.334664i) q^{14} +(1.91480 - 3.90911i) q^{15} +(-1.14947 + 1.99095i) q^{16} +(0.323651 + 0.560581i) q^{17} +(-1.29466 + 1.00446i) q^{18} -2.29555i q^{19} +(2.13825 - 3.70356i) q^{20} +(-3.53668 - 2.91408i) 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} +(5.05766 - 0.693365i) q^{36} +(1.97766 - 3.42541i) q^{37} +(0.626924 - 1.08587i) q^{38} +(-2.57482 + 5.68949i) q^{39} +(4.40050 - 2.54063i) q^{40} +(4.48689 + 7.77153i) q^{41} +(-0.877112 - 2.34433i) q^{42} +(-4.09951 + 7.10056i) q^{43} +(-8.88279 + 5.12848i) q^{44} +(-7.46955 + 1.02402i) q^{45} +(0.282202 + 0.488787i) q^{46} +(2.09646 + 3.63118i) q^{47} +(3.97266 - 0.271042i) q^{48} +(5.85603 - 3.83496i) q^{49} +(-0.622448 + 0.359370i) q^{50} +(0.493189 - 1.00686i) q^{51} +(-2.90425 + 5.40450i) q^{52} +(0.0406517 + 0.0234703i) q^{53} +(2.69478 + 0.890735i) 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} +(-7.38994 + 0.504192i) q^{60} +3.59276i q^{61} +(2.91937 + 5.05650i) q^{62} +(-0.772338 + 7.89959i) q^{63} +1.70329 q^{64} +(4.28922 - 7.98179i) q^{65} +(-5.68928 + 0.388162i) q^{66} +1.52251 q^{67} +(0.550743 - 0.953916i) q^{68} +(-0.121826 - 1.78560i) 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} +(2.27387 - 0.155139i) q^{75} +(-3.38290 + 1.95312i) q^{76} +(-4.55868 - 15.2822i) q^{77} +(-2.77179 + 1.98811i) 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} +(-1.28530 + 7.69132i) q^{84} +(-0.813381 + 1.40882i) q^{85} +(-3.87838 + 2.23919i) q^{86} +(8.01520 + 3.92608i) 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} +(-1.26028 - 18.4720i) q^{93} +2.29021i q^{94} +(4.99614 - 2.88452i) q^{95} +(8.24314 + 4.03773i) 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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