LMFDB - Embedded newform 315.2.bo.b.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(4,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

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

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

chi := DirichletCharacter("315.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bo (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	315.4
Dual form			315.2.bo.b.79.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56714 - 0.904786i) q^{2} +(1.72657 + 0.137634i) q^{3} +(0.637277 + 1.10380i) q^{4} +(-0.0315838 + 2.23584i) q^{5} +(-2.58125 - 1.77787i) q^{6} +(-2.37354 - 1.16889i) q^{7} +1.31275i q^{8} +(2.96211 + 0.475270i) q^{9} +O(q^{10})$	\(q+(-1.56714 - 0.904786i) q^{2} +(1.72657 + 0.137634i) q^{3} +(0.637277 + 1.10380i) q^{4} +(-0.0315838 + 2.23584i) q^{5} +(-2.58125 - 1.77787i) q^{6} +(-2.37354 - 1.16889i) q^{7} +1.31275i q^{8} +(2.96211 + 0.475270i) q^{9} +(2.07246 - 3.47530i) q^{10} +3.80862 q^{11} +(0.948385 + 1.99349i) q^{12} +(0.0893763 + 0.0516014i) q^{13} +(2.66207 + 3.97935i) q^{14} +(-0.362259 + 3.85600i) q^{15} +(2.46231 - 4.26485i) q^{16} +(3.29140 + 1.90029i) q^{17} +(-4.21202 - 3.42489i) q^{18} +(2.57787 + 4.46499i) q^{19} +(-2.48804 + 1.38999i) q^{20} +(-3.93722 - 2.34485i) q^{21} +(-5.96863 - 3.44599i) q^{22} +2.88075i q^{23} +(-0.180679 + 2.26656i) q^{24} +(-4.99800 - 0.141233i) q^{25} +(-0.0933765 - 0.161733i) q^{26} +(5.04890 + 1.22827i) q^{27} +(-0.222393 - 3.36481i) q^{28} +(2.69377 + 4.66574i) q^{29} +(4.05657 - 5.71511i) q^{30} +(-3.45985 - 5.99264i) q^{31} +(-5.44380 + 3.14298i) q^{32} +(6.57587 + 0.524195i) q^{33} +(-3.43871 - 5.95602i) q^{34} +(2.68841 - 5.26996i) q^{35} +(1.36309 + 3.57245i) q^{36} +(9.48307 - 5.47505i) q^{37} -9.32967i q^{38} +(0.147213 + 0.101395i) q^{39} +(-2.93510 - 0.0414616i) q^{40} +(-0.753474 + 1.30506i) q^{41} +(4.04857 + 7.23703i) q^{42} +(1.50478 - 0.868787i) q^{43} +(2.42715 + 4.20394i) q^{44} +(-1.15618 + 6.60782i) q^{45} +(2.60646 - 4.51453i) q^{46} +(-9.31264 - 5.37666i) q^{47} +(4.83835 - 7.02468i) q^{48} +(4.26741 + 5.54880i) q^{49} +(7.70477 + 4.74346i) q^{50} +(5.42129 + 3.73399i) q^{51} +0.131538i q^{52} +(-0.391152 - 0.225832i) q^{53} +(-6.80098 - 6.49304i) q^{54} +(-0.120291 + 8.51549i) q^{55} +(1.53445 - 3.11587i) q^{56} +(3.83634 + 8.06394i) q^{57} -9.74913i q^{58} +(-5.69321 - 9.86092i) q^{59} +(-4.48710 + 2.05748i) q^{60} +(-5.08990 + 8.81596i) q^{61} +12.5217i q^{62} +(-6.47517 - 4.59044i) q^{63} +1.52566 q^{64} +(-0.118196 + 0.198202i) q^{65} +(-9.83100 - 6.77124i) q^{66} +(5.13882 - 2.96690i) q^{67} +4.84404i q^{68} +(-0.396489 + 4.97383i) q^{69} +(-8.98129 + 5.82630i) q^{70} -6.43418 q^{71} +(-0.623910 + 3.88851i) q^{72} +(-13.6186 - 7.86273i) q^{73} -19.8150 q^{74} +(-8.60999 - 0.931743i) q^{75} +(-3.28563 + 5.69087i) q^{76} +(-9.03993 - 4.45184i) q^{77} +(-0.138962 - 0.292096i) q^{78} +(-1.64428 + 2.84798i) q^{79} +(9.45777 + 5.64004i) q^{80} +(8.54824 + 2.81561i) q^{81} +(2.36159 - 1.36347i) q^{82} +(-1.21389 + 0.700839i) q^{83} +(0.0791327 - 5.84020i) q^{84} +(-4.35270 + 7.29903i) q^{85} -3.14427 q^{86} +(4.00882 + 8.42650i) q^{87} +4.99977i q^{88} +(1.89392 + 3.28036i) q^{89} +(7.79056 - 9.30925i) q^{90} +(-0.151822 - 0.226949i) q^{91} +(-3.17976 + 1.83584i) q^{92} +(-5.14890 - 10.8229i) q^{93} +(9.72945 + 16.8519i) q^{94} +(-10.0645 + 5.62269i) q^{95} +(-9.83171 + 4.67734i) q^{96} +(5.26915 - 3.04215i) q^{97} +(-1.66714 - 12.5568i) q^{98} +(11.2816 + 1.81012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	$ 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.56714	−	0.904786i	−1.10813	−	0.639781i	−0.169787	−	0.985481i	$-0.554308\pi$
$2$	−1.56714	−	0.904786i	−1.10813	−	0.639781i	−0.938345	+	0.345700i	$0.887641\pi$
$3$	1.72657	+	0.137634i	0.996838	+	0.0794629i
$3$	1.72657	+	0.137634i	0.996838	+	0.0794629i
$4$	0.637277	+	1.10380i	0.318638	+	0.551898i
$5$	−0.0315838	+	2.23584i	−0.0141247	+	0.999900i
$5$	−0.0315838	+	2.23584i	−0.0141247	+	0.999900i
$6$	−2.58125	−	1.77787i	−1.05379	−	0.725813i
$7$	−2.37354	−	1.16889i	−0.897115	−	0.441797i
$7$	−2.37354	−	1.16889i	−0.897115	−	0.441797i
$8$			1.31275i			0.464127i
$9$	2.96211	+	0.475270i	0.987371	+	0.158423i
$10$	2.07246	−	3.47530i	0.655369	−	1.09899i
$11$	3.80862			1.14834			0.574172	−	0.818735i	$-0.305324\pi$
$11$	3.80862			1.14834			0.574172	+	0.818735i	$0.305324\pi$
$12$	0.948385	+	1.99349i	0.273775	+	0.575472i
$13$	0.0893763	+	0.0516014i	0.0247885	+	0.0143117i	0.512343	−	0.858781i	$-0.328778\pi$
$13$	0.0893763	+	0.0516014i	0.0247885	+	0.0143117i	−0.487555	+	0.873093i	$0.662111\pi$
$14$	2.66207	+	3.97935i	0.711469	+	1.06353i
$15$	−0.362259	+	3.85600i	−0.0935350	+	0.995616i
$16$	2.46231	−	4.26485i	0.615578	−	1.06621i
$17$	3.29140	+	1.90029i	0.798281	+	0.460888i	0.842870	−	0.538118i	$-0.180864\pi$
$17$	3.29140	+	1.90029i	0.798281	+	0.460888i	−0.0445890	+	0.999005i	$0.514198\pi$
$18$	−4.21202	−	3.42489i	−0.992782	−	0.807255i
$19$	2.57787	+	4.46499i	0.591403	+	1.02434i	0.994044	+	0.108982i	$0.0347591\pi$
$19$	2.57787	+	4.46499i	0.591403	+	1.02434i	−0.402641	+	0.915358i	$0.631908\pi$
$20$	−2.48804	+	1.38999i	−0.556343	+	0.310811i
$21$	−3.93722	−	2.34485i	−0.859172	−	0.511687i
$22$	−5.96863	−	3.44599i	−1.27252	−	0.734688i
$23$			2.88075i			0.600678i	0.953832	+	0.300339i	$0.0970999\pi$
$23$			2.88075i			0.600678i	−0.953832	+	0.300339i	$0.902900\pi$
$24$	−0.180679	+	2.26656i	−0.0368809	+	0.462659i
$25$	−4.99800	−	0.141233i	−0.999601	−	0.0282466i
$26$	−0.0933765	−	0.161733i	−0.0183126	−	0.0317184i
$27$	5.04890	+	1.22827i	0.971660	+	0.236382i
$28$	−0.222393	−	3.36481i	−0.0420284	−	0.635889i
$29$	2.69377	+	4.66574i	0.500220	+	0.866406i	1.00000		0.000253817i	$8.07925e-5\pi$
$29$	2.69377	+	4.66574i	0.500220	+	0.866406i	−0.499780	+	0.866152i	$0.666586\pi$
$30$	4.05657	−	5.71511i	0.740625	−	1.04343i
$31$	−3.45985	−	5.99264i	−0.621408	−	1.07631i	−0.989224	−	0.146412i	$-0.953228\pi$
$31$	−3.45985	−	5.99264i	−0.621408	−	1.07631i	0.367816	−	0.929899i	$-0.380106\pi$
$32$	−5.44380	+	3.14298i	−0.962337	+	0.555606i
$33$	6.57587	+	0.524195i	1.14471	+	0.0912507i
$34$	−3.43871	−	5.95602i	−0.589734	−	1.02145i
$35$	2.68841	−	5.26996i	0.454425	−	0.890785i
$36$	1.36309	+	3.57245i	0.227181	+	0.595408i
$37$	9.48307	−	5.47505i	1.55901	−	0.900093i	0.561654	−	0.827372i	$-0.310165\pi$
$37$	9.48307	−	5.47505i	1.55901	−	0.900093i	0.997352	−	0.0727209i	$-0.0231682\pi$
$38$		−	9.32967i		−	1.51347i
$39$	0.147213	+	0.101395i	0.0235729	+	0.0162362i
$40$	−2.93510	−	0.0414616i	−0.464081	−	0.00655566i
$41$	−0.753474	+	1.30506i	−0.117673	+	0.203815i	−0.918845	−	0.394619i	$-0.870877\pi$
$41$	−0.753474	+	1.30506i	−0.117673	+	0.203815i	0.801172	+	0.598434i	$0.204210\pi$
$42$	4.04857	+	7.23703i	0.624708	+	1.11670i
$43$	1.50478	−	0.868787i	0.229477	−	0.132489i	−0.380854	−	0.924635i	$-0.624370\pi$
$43$	1.50478	−	0.868787i	0.229477	−	0.132489i	0.610331	+	0.792147i	$0.291036\pi$
$44$	2.42715	+	4.20394i	0.365906	+	0.633768i
$45$	−1.15618	+	6.60782i	−0.172354	+	0.985035i
$46$	2.60646	−	4.51453i	0.384302	−	0.665631i
$47$	−9.31264	−	5.37666i	−1.35839	−	0.784266i	−0.368982	−	0.929437i	$-0.620294\pi$
$47$	−9.31264	−	5.37666i	−1.35839	−	0.784266i	−0.989407	+	0.145171i	$0.953627\pi$
$48$	4.83835	−	7.02468i	0.698355	−	1.01392i
$49$	4.26741	+	5.54880i	0.609631	+	0.792686i
$50$	7.70477	+	4.74346i	1.08962	+	0.670826i
$51$	5.42129	+	3.73399i	0.759133	+	0.522864i
$52$			0.131538i			0.0182410i
$53$	−0.391152	−	0.225832i	−0.0537288	−	0.0310204i	0.472895	−	0.881119i	$-0.343209\pi$
$53$	−0.391152	−	0.225832i	−0.0537288	−	0.0310204i	−0.526624	+	0.850098i	$0.676542\pi$
$54$	−6.80098	−	6.49304i	−0.925496	−	0.883591i
$55$	−0.120291	+	8.51549i	−0.0162200	+	1.14823i
$56$	1.53445	−	3.11587i	0.205050	−	0.416375i
$57$	3.83634	+	8.06394i	0.508136	+	1.06810i
$58$		−	9.74913i		−	1.28012i
$59$	−5.69321	−	9.86092i	−0.741192	−	1.28378i	−0.951953	−	0.306245i	$-0.900927\pi$
$59$	−5.69321	−	9.86092i	−0.741192	−	1.28378i	0.210760	−	0.977538i	$-0.432406\pi$
$60$	−4.48710	+	2.05748i	−0.579282	+	0.265620i
$61$	−5.08990	+	8.81596i	−0.651694	+	1.12877i	0.331017	+	0.943625i	$0.392608\pi$
$61$	−5.08990	+	8.81596i	−0.651694	+	1.12877i	−0.982712	+	0.185143i	$0.940725\pi$
$62$			12.5217i			1.59026i
$63$	−6.47517	−	4.59044i	−0.815795	−	0.578342i
$64$	1.52566			0.190708
$65$	−0.118196	+	0.198202i	−0.0146604	+	0.0245839i
$66$	−9.83100	−	6.77124i	−1.21011	−	0.833482i
$67$	5.13882	−	2.96690i	0.627806	−	0.362464i	−0.152096	−	0.988366i	$-0.548602\pi$
$67$	5.13882	−	2.96690i	0.627806	−	0.362464i	0.779902	+	0.625902i	$0.215269\pi$
$68$			4.84404i			0.587426i
$69$	−0.396489	+	4.97383i	−0.0477316	+	0.598779i
$70$	−8.98129	+	5.82630i	−1.07347	+	0.696376i
$71$	−6.43418			−0.763596			−0.381798	−	0.924246i	$-0.624695\pi$
$71$	−6.43418			−0.763596			−0.381798	+	0.924246i	$0.624695\pi$
$72$	−0.623910	+	3.88851i	−0.0735285	+	0.458266i
$73$	−13.6186	−	7.86273i	−1.59394	−	0.920263i	−0.992621	−	0.121255i	$-0.961308\pi$
$73$	−13.6186	−	7.86273i	−1.59394	−	0.920263i	−0.601321	−	0.799008i	$-0.705359\pi$
$74$	−19.8150			−2.30345
$75$	−8.60999	−	0.931743i	−0.994196	−	0.107588i
$76$	−3.28563	+	5.69087i	−0.376887	+	0.652788i
$77$	−9.03993	−	4.45184i	−1.03020	−	0.507335i
$78$	−0.138962	−	0.292096i	−0.0157343	−	0.0330733i
$79$	−1.64428	+	2.84798i	−0.184996	+	0.320423i	−0.943575	−	0.331158i	$-0.892561\pi$
$79$	−1.64428	+	2.84798i	−0.184996	+	0.320423i	0.758579	+	0.651581i	$0.225894\pi$
$80$	9.45777	+	5.64004i	1.05741	+	0.630576i
$81$	8.54824	+	2.81561i	0.949804	+	0.312845i
$82$	2.36159	−	1.36347i	0.260794	−	0.150570i
$83$	−1.21389	+	0.700839i	−0.133242	+	0.0769271i	−0.565139	−	0.824996i	$-0.691178\pi$
$83$	−1.21389	+	0.700839i	−0.133242	+	0.0769271i	0.431898	+	0.901923i	$0.357844\pi$
$84$	0.0791327	−	5.84020i	0.00863409	−	0.637218i
$85$	−4.35270	+	7.29903i	−0.472117	+	0.791691i
$86$	−3.14427			−0.339055
$87$	4.00882	+	8.42650i	0.429791	+	0.903415i
$88$			4.99977i			0.532977i
$89$	1.89392	+	3.28036i	0.200755	+	0.347717i	0.948772	−	0.315962i	$-0.102327\pi$
$89$	1.89392	+	3.28036i	0.200755	+	0.347717i	−0.748017	+	0.663679i	$0.768994\pi$
$90$	7.79056	−	9.30925i	0.821197	−	0.981281i
$91$	−0.151822	−	0.226949i	−0.0159153	−	0.0237907i
$92$	−3.17976	+	1.83584i	−0.331513	+	0.191399i
$93$	−5.14890	−	10.8229i	−0.533916	−	1.12229i
$94$	9.72945	+	16.8519i	1.00352	+	1.73814i
$95$	−10.0645	+	5.62269i	−1.03259	+	0.576875i
$96$	−9.83171	+	4.67734i	−1.00344	+	0.477379i
$97$	5.26915	−	3.04215i	0.535002	−	0.308883i	−0.208049	−	0.978118i	$-0.566711\pi$
$97$	5.26915	−	3.04215i	0.535002	−	0.308883i	0.743051	+	0.669235i	$0.233378\pi$
$98$	−1.66714	−	12.5568i	−0.168407	−	1.26843i
$99$	11.2816	+	1.81012i	1.13384	+	0.181924i
$100$	−3.02922	−	5.60678i	−0.302922	−	0.560678i
$101$	−6.84505			−0.681108			−0.340554	−	0.940225i	$-0.610615\pi$
$101$	−6.84505			−0.681108			−0.340554	+	0.940225i	$0.610615\pi$
$102$	−5.11744	−	10.7568i	−0.506702	−	1.06508i
$103$			2.99895i			0.295495i	0.989025	+	0.147747i	$0.0472023\pi$
$103$			2.99895i			0.295495i	−0.989025	+	0.147747i	$0.952798\pi$
$104$	−0.0677397	+	0.117329i	−0.00664243	+	0.0115050i
$105$	5.36706	−	8.72895i	0.523772	−	0.851859i
$106$	0.408659	+	0.707818i	0.0396925	+	0.0687493i
$107$	−4.04654	+	2.33627i	−0.391194	+	0.225856i	−0.682677	−	0.730720i	$-0.739184\pi$
$107$	−4.04654	+	2.33627i	−0.391194	+	0.225856i	0.291483	+	0.956576i	$0.405851\pi$
$108$	1.86178	+	6.35570i	0.179150	+	0.611577i
$109$	4.25733	−	7.37392i	0.407779	−	0.706293i	−0.586862	−	0.809687i	$-0.699637\pi$
$109$	4.25733	−	7.37392i	0.407779	−	0.706293i	0.994640	+	0.103394i	$0.0329702\pi$
$110$	7.89321	−	13.2361i	0.752588	−	1.26201i
$111$	17.1268	−	8.14789i	1.62560	−	0.773364i
$112$	−10.8295	+	7.24464i	−1.02329	+	0.684554i
$113$	3.29067	+	1.89987i	0.309560	+	0.178724i	0.646729	−	0.762719i	$-0.276136\pi$
$113$	3.29067	+	1.89987i	0.309560	+	0.178724i	−0.337170	+	0.941444i	$0.609470\pi$
$114$	1.28408	−	16.1084i	0.120265	−	1.50869i
$115$	−6.44091	−	0.0909851i	−0.600618	−	0.00848441i
$116$	−3.43335	+	5.94673i	−0.318778	+	0.552140i
$117$	0.240218	+	0.195327i	0.0222082	+	0.0180580i
$118$			20.6045i			1.89680i
$119$	−5.59105	−	8.35768i	−0.512531	−	0.766147i
$120$	−5.06197	−	0.475556i	−0.462092	−	0.0434121i
$121$	3.50562			0.318693
$122$	15.9531	−	9.21054i	1.44433	−	0.833883i
$123$	−1.48055	+	2.14957i	−0.133497	+	0.193820i
$124$	4.40977	−	7.63794i	0.396009	−	0.685907i
$125$	0.473631	−	11.1703i	0.0423629	−	0.999102i
$126$	5.99410	+	13.0525i	0.533997	+	1.16281i
$127$		−	14.2403i		−	1.26362i	−0.775123	−	0.631811i	$-0.782312\pi$
$127$		−	14.2403i		−	1.26362i	0.775123	−	0.631811i	$-0.217688\pi$
$128$	8.49669	+	4.90556i	0.751008	+	0.433595i
$129$	2.71769	−	1.29292i	0.239280	−	0.113835i
$130$	0.364559	−	0.203667i	0.0319739	−	0.0178628i
$131$	11.4463			1.00007			0.500036	−	0.866005i	$-0.333320\pi$
$131$	11.4463			1.00007			0.500036	+	0.866005i	$0.333320\pi$
$132$	3.61204	+	7.59247i	0.314388	+	0.660840i
$133$	−0.899610	−	13.6111i	−0.0780061	−	1.18023i
$134$	−10.7376			−0.927590
$135$	−2.90570	+	11.2498i	−0.250082	+	0.968225i
$136$	−2.49460	+	4.32078i	−0.213910	+	0.370503i
$137$			6.52118i			0.557142i	0.960416	+	0.278571i	$0.0898607\pi$
$137$			6.52118i			0.557142i	−0.960416	+	0.278571i	$0.910139\pi$
$138$	5.12161	−	7.43593i	0.435980	−	0.632988i
$139$	−4.38424	+	7.59373i	−0.371867	+	0.644092i	−0.989853	−	0.142097i	$-0.954615\pi$
$139$	−4.38424	+	7.59373i	−0.371867	+	0.644092i	0.617986	+	0.786189i	$0.287949\pi$
$140$	7.53021	−	0.390963i	0.636419	−	0.0330424i
$141$	−15.3390	−	10.5649i	−1.29177	−	0.889727i
$142$	10.0832	+	5.82155i	0.846166	+	0.488534i
$143$	0.340401	+	0.196530i	0.0284657	+	0.0164347i
$144$	9.32060	−	11.4627i	0.776716	−	0.955225i
$145$	−10.5169	+	5.87548i	−0.873385	+	0.487932i
$146$	14.2282	+	24.6439i	1.17753	+	2.03955i
$147$	6.60430	+	10.1678i	0.544714	+	0.838622i
$148$	12.0867	+	6.97824i	0.993518	+	0.573608i
$149$	−11.1332			−0.912066			−0.456033	−	0.889963i	$-0.650730\pi$
$149$	−11.1332			−0.912066			−0.456033	+	0.889963i	$0.650730\pi$
$150$	12.6500	+	9.25037i	1.03287	+	0.755289i
$151$	9.28735			0.755794			0.377897	−	0.925848i	$-0.376647\pi$
$151$	9.28735			0.755794			0.377897	+	0.925848i	$0.376647\pi$
$152$	−5.86142	+	3.38409i	−0.475424	+	0.274486i
$153$	8.84634	+	7.19317i	0.715184	+	0.581533i
$154$	10.1388	+	15.1559i	0.817011	+	1.22129i
$155$	13.5079	−	7.54643i	1.08498	−	0.606143i
$156$	−0.0181040	+	0.227109i	−0.00144948	+	0.0181833i
$157$	6.83155	−	3.94420i	0.545217	−	0.314781i	−0.201974	−	0.979391i	$-0.564736\pi$
$157$	6.83155	−	3.94420i	0.545217	−	0.314781i	0.747191	+	0.664610i	$0.231402\pi$
$158$	5.15363	−	2.97545i	0.410001	−	0.236714i
$159$	−0.644271	−	0.443751i	−0.0510940	−	0.0351917i
$160$	−6.85528	−	12.2708i	−0.541958	−	0.970089i
$161$	3.36727	−	6.83759i	0.265378	−	0.538878i
$162$	−10.8487	−	12.1468i	−0.852357	−	0.954340i
$163$	10.7692	−	6.21761i	0.843510	−	0.487001i	−0.0149459	−	0.999888i	$-0.504758\pi$
$163$	10.7692	−	6.21761i	0.843510	−	0.487001i	0.858456	+	0.512888i	$0.171424\pi$
$164$	−1.92068			−0.149980
$165$	−1.37971	+	14.6861i	−0.107410	+	1.14331i
$166$	2.53644			0.196866
$167$	−15.9568	−	9.21266i	−1.23477	−	0.712897i	−0.266753	−	0.963765i	$-0.585951\pi$
$167$	−15.9568	−	9.21266i	−1.23477	−	0.712897i	−0.968021	+	0.250868i	$0.919284\pi$
$168$	3.07819	−	5.16858i	0.237488	−	0.398765i
$169$	−6.49467	−	11.2491i	−0.499590	−	0.865316i
$170$	13.4253	−	7.50031i	1.02968	−	0.575247i
$171$	5.51386	+	14.4510i	0.421655	+	1.10510i
$172$	1.91793	+	1.10732i	0.146241	+	0.0844320i
$173$	16.2126	+	9.36032i	1.23262	+	0.711652i	0.967575	−	0.252584i	$-0.0812805\pi$
$173$	16.2126	+	9.36032i	1.23262	+	0.711652i	0.265043	+	0.964237i	$0.414614\pi$
$174$	1.34181	−	16.8326i	0.101722	−	1.27608i
$175$	11.6979	+	6.17732i	0.884278	+	0.466961i
$176$	9.37801	−	16.2432i	0.706894	−	1.22438i
$177$	−8.47255	−	17.8092i	−0.636836	−	1.33862i
$178$		−	6.85435i		−	0.513756i
$179$	4.80576	−	8.32382i	0.359199	−	0.622152i	−0.628628	−	0.777706i	$-0.716383\pi$
$179$	4.80576	−	8.32382i	0.359199	−	0.622152i	0.987827	+	0.155555i	$0.0497165\pi$
$180$	−8.03049	+	2.93482i	−0.598557	+	0.218748i
$181$	−14.1492			−1.05170			−0.525851	−	0.850577i	$-0.676253\pi$
$181$	−14.1492			−1.05170			−0.525851	+	0.850577i	$0.676253\pi$
$182$	0.0325860	+	0.493027i	0.00241544	+	0.0365456i
$183$	−10.0015	+	14.5209i	−0.739329	+	1.07341i
$184$	−3.78170			−0.278791
$185$	11.9419	+	21.3756i	0.877983	+	1.57156i
$186$	−1.72341	+	21.6197i	−0.126367	+	1.58523i
$187$	12.5357	+	7.23748i	0.916700	+	0.529257i
$188$		−	13.7057i		−	0.999588i
$189$	−10.5481	−	8.81694i	−0.767258	−	0.641338i
$190$	20.8597	+	0.294667i	1.51332	+	0.0213774i
$191$	9.12718	−	15.8087i	0.660420	−	1.14388i	−0.320086	−	0.947388i	$-0.603712\pi$
$191$	9.12718	−	15.8087i	0.660420	−	1.14388i	0.980506	−	0.196492i	$-0.0629549\pi$
$192$	2.63417	+	0.209982i	0.190105	+	0.0151542i
$193$	−16.2617	+	9.38868i	−1.17054	+	0.675812i	−0.953807	−	0.300419i	$-0.902874\pi$
$193$	−16.2617	+	9.38868i	−1.17054	+	0.675812i	−0.216733	+	0.976231i	$0.569540\pi$
$194$	−11.0100			−0.790470
$195$	−0.231353	+	0.325942i	−0.0165675	+	0.0233412i
$196$	−3.40522	+	8.24647i	−0.243230	+	0.589034i
$197$		−	5.62033i		−	0.400432i	−0.979752	−	0.200216i	$-0.935836\pi$
$197$		−	5.62033i		−	0.400432i	0.979752	−	0.200216i	$-0.0641644\pi$
$198$	−16.0420	−	13.0441i	−1.14005	−	0.927006i
$199$	8.68092	−	15.0358i	0.615374	−	1.06586i	−0.374945	−	0.927047i	$-0.622338\pi$
$199$	8.68092	−	15.0358i	0.615374	−	1.06586i	0.990319	−	0.138812i	$-0.0443283\pi$
$200$	0.185404	−	6.56113i	0.0131100	−	0.463942i
$201$	9.28089	−	4.41529i	0.654624	−	0.311431i
$202$	10.7271	+	6.19331i	0.754758	+	0.435760i
$203$	−0.940056	−	14.2230i	−0.0659790	−	0.998262i
$204$	−0.666703	+	8.36358i	−0.0466785	+	0.585568i
$205$	−2.89410	−	1.72587i	−0.202133	−	0.120540i
$206$	2.71340	−	4.69975i	0.189052	−	0.327447i
$207$	−1.36913	+	8.53312i	−0.0951614	+	0.593093i
$208$	0.440144	−	0.254117i	0.0305185	−	0.0176199i
$209$	9.81812	+	17.0055i	0.679134	+	1.17629i
$210$	−16.3088	+	8.82341i	−1.12541	+	0.608873i
$211$	5.30209	−	9.18350i	0.365011	−	0.632218i	−0.623767	−	0.781611i	$-0.714398\pi$
$211$	5.30209	−	9.18350i	0.365011	−	0.632218i	0.988778	+	0.149393i	$0.0477318\pi$
$212$		−	0.575669i		−	0.0395371i
$213$	−11.1091	−	0.885559i	−0.761181	−	0.0606775i
$214$	8.45530			0.577993
$215$	1.89495	+	3.39190i	0.129234	+	0.231326i
$216$	−1.61242	+	6.62793i	−0.109711	+	0.450974i
$217$	1.20740	+	18.2680i	0.0819637	+	1.24011i
$218$	−13.3436	+	7.70395i	−0.903745	+	0.521778i
$219$	−22.4314	−	15.4500i	−1.51578	−	1.04401i
$220$	−9.47602	+	5.29395i	−0.638873	+	0.356918i
$221$	0.196115	+	0.339681i	0.0131921	+	0.0228494i
$222$	−34.2121	−	2.72721i	−2.29616	−	0.183039i
$223$	−15.0973	+	8.71644i	−1.01099	+	0.583696i	−0.911482	−	0.411341i	$-0.865061\pi$
$223$	−15.0973	+	8.71644i	−1.01099	+	0.583696i	−0.0995091	+	0.995037i	$0.531727\pi$
$224$	16.5949	−	1.09682i	1.10879	−	0.0732844i
$225$	−14.7375	−	2.79375i	−0.982502	−	0.186250i
$226$	−3.43795	−	5.95470i	−0.228689	−	0.396101i
$227$		−	2.84098i		−	0.188562i	−0.995546	−	0.0942811i	$-0.969945\pi$
$227$		−	2.84098i		−	0.188562i	0.995546	−	0.0942811i	$-0.0300552\pi$
$228$	−6.45613	+	9.37350i	−0.427568	+	0.620775i
$229$	18.9276			1.25077			0.625384	−	0.780317i	$-0.284942\pi$
$229$	18.9276			1.25077			0.625384	+	0.780317i	$0.284942\pi$
$230$	10.0115	+	5.97024i	0.660137	+	0.393666i
$231$	−14.9954	−	8.93064i	−0.986624	−	0.587593i
$232$	−6.12495	+	3.53624i	−0.402122	+	0.232165i
$233$	−12.0455	+	6.95446i	−0.789126	+	0.455602i	−0.839655	−	0.543121i	$-0.817243\pi$
$233$	−12.0455	+	6.95446i	−0.789126	+	0.455602i	0.0505291	+	0.998723i	$0.483909\pi$
$234$	−0.199725	−	0.523450i	−0.0130564	−	0.0342190i
$235$	12.3155	−	20.6518i	0.803375	−	1.34718i
$236$	7.25629	−	12.5683i	0.472345	−	0.818125i
$237$	−3.23096	+	4.69095i	−0.209873	+	0.304710i
$238$	1.20002	+	18.1563i	0.0777859	+	1.17690i
$239$	−0.688457	+	1.19244i	−0.0445326	+	0.0771327i	−0.887433	−	0.460938i	$-0.847513\pi$
$239$	−0.688457	+	1.19244i	−0.0445326	+	0.0771327i	0.842900	+	0.538070i	$0.180847\pi$
$240$	15.5533	+	11.0397i	1.00396	+	0.712607i
$241$	−8.12006			−0.523059			−0.261530	−	0.965195i	$-0.584227\pi$
$241$	−8.12006			−0.523059			−0.261530	+	0.965195i	$0.584227\pi$
$242$	−5.49378	−	3.17184i	−0.353154	−	0.203893i
$243$	14.3716	+	6.03788i	0.921941	+	0.387330i
$244$	−12.9747			−0.830619
$245$	−12.5410	+	9.36603i	−0.801217	+	0.598373i
$246$	4.26512	−	2.02909i	0.271934	−	0.129370i
$247$			0.532086i			0.0338558i
$248$	7.86684	−	4.54192i	0.499545	−	0.288412i
$249$	−2.19233	+	1.04298i	−0.138933	+	0.0660961i
$250$	−10.8490	+	17.0768i	−0.686150	+	1.08003i
$251$	0.219929			0.0138818			0.00694089	−	0.999976i	$-0.497791\pi$
$251$	0.219929			0.0138818			0.00694089	+	0.999976i	$0.497791\pi$
$252$	0.940437	−	10.0726i	0.0592420	−	0.634517i
$253$			10.9717i			0.689785i
$254$	−12.8844	+	22.3165i	−0.808441	+	1.40026i
$255$	−8.51986	+	12.0032i	−0.533534	+	0.751672i
$256$	−10.4026	−	18.0179i	−0.650165	−	1.12612i
$257$		−	4.14861i		−	0.258783i	−0.991594	−	0.129391i	$-0.958698\pi$
$257$		−	4.14861i		−	0.258783i	0.991594	−	0.129391i	$-0.0413024\pi$
$258$	−5.42881	−	0.432757i	−0.337983	−	0.0269423i
$259$	−28.9082	+	1.91065i	−1.79627	+	0.118722i
$260$	−0.294098	−	0.00415446i	−0.0182392	−	0.000257649i
$261$	5.76176	+	15.1007i	0.356644	+	0.934711i
$262$	−17.9380	−	10.3565i	−1.10821	−	0.639826i
$263$			0.126344i			0.00779069i	0.999992	+	0.00389535i	$0.00123993\pi$
$263$			0.126344i			0.00779069i	−0.999992	+	0.00389535i	$0.998760\pi$
$264$	−0.688137	+	8.63247i	−0.0423519	+	0.531292i
$265$	0.517279	−	0.867422i	0.0317762	−	0.0532853i
$266$	−10.9053	+	22.1444i	−0.668648	+	1.35776i
$267$	2.81850	+	5.92445i	0.172489	+	0.362570i
$268$	6.54969	+	3.78147i	0.400086	+	0.230990i
$269$	−7.56255	+	13.0987i	−0.461097	+	0.798643i	−0.999016	−	0.0443537i	$-0.985877\pi$
$269$	−7.56255	+	13.0987i	−0.461097	+	0.798643i	0.537919	+	0.842996i	$0.319210\pi$
$270$	14.7322	−	15.0009i	0.896576	−	0.912923i
$271$	1.27405	+	2.20671i	0.0773928	+	0.134048i	0.902124	−	0.431476i	$-0.142007\pi$
$271$	1.27405	+	2.20671i	0.0773928	+	0.134048i	−0.824732	+	0.565524i	$0.808674\pi$
$272$	16.2089	−	9.35820i	0.982807	−	0.567424i
$273$	−0.230897	−	0.412740i	−0.0139745	−	0.0249802i
$274$	5.90027	−	10.2196i	0.356448	−	0.617387i
$275$	−19.0355	−	0.537904i	−1.14789	−	0.0324368i
$276$	−5.74276	+	2.73206i	−0.345674	+	0.164451i
$277$		−	25.0622i		−	1.50584i	−0.658110	−	0.752922i	$-0.728644\pi$
$277$		−	25.0622i		−	1.50584i	0.658110	−	0.752922i	$-0.271356\pi$
$278$	13.7414	−	7.93361i	0.824155	−	0.475826i
$279$	−7.40036	−	19.3953i	−0.443048	−	1.16116i
$280$	6.91813	+	3.52921i	0.413437	+	0.210911i
$281$	−9.06472	−	15.7006i	−0.540756	−	0.936617i	−0.998861	−	0.0477187i	$-0.984805\pi$
$281$	−9.06472	−	15.7006i	−0.540756	−	0.936617i	0.458105	−	0.888898i	$-0.348528\pi$
$282$	14.4792	+	30.4352i	0.862225	+	1.81239i
$283$	8.58750	−	4.95799i	0.510474	−	0.294722i	−0.222555	−	0.974920i	$-0.571440\pi$
$283$	8.58750	−	4.95799i	0.510474	−	0.294722i	0.733028	+	0.680198i	$0.238106\pi$
$284$	−4.10035	−	7.10201i	−0.243311	−	0.421427i
$285$	−18.1509	+	8.32277i	−1.07517	+	0.492999i
$286$	−0.355636	−	0.615980i	−0.0210292	−	0.0364237i
$287$	3.31386	−	2.21688i	0.195611	−	0.130858i
$288$	−17.6189	+	6.72259i	−1.03821	+	0.396133i
$289$	−1.27781	−	2.21324i	−0.0751654	−	0.130190i
$290$	21.7975	+	0.307915i	1.28000	+	0.0180814i
$291$	9.51629	−	4.52728i	0.557855	−	0.265394i
$292$		−	20.0429i		−	1.17292i
$293$	−5.08585	−	2.93631i	−0.297118	−	0.171541i	0.344029	−	0.938959i	$-0.388208\pi$
$293$	−5.08585	−	2.93631i	−0.297118	−	0.171541i	−0.641148	+	0.767418i	$0.721541\pi$
$294$	−1.15020	−	21.9097i	−0.0670810	−	1.27780i
$295$	22.2273	−	12.4177i	1.29412	−	0.722985i
$296$	7.18737	+	12.4489i	0.417757	+	0.723577i
$297$	19.2293	+	4.67804i	1.11580	+	0.271447i
$298$	17.4472	+	10.0732i	1.01069	+	0.583522i
$299$	−0.148651	+	0.257471i	−0.00859671	+	0.0148899i
$300$	−4.45849	−	10.0974i	−0.257411	−	0.582976i
$301$	−4.58718	+	0.303185i	−0.264401	+	0.0174753i
$302$	−14.5545	−	8.40307i	−0.837520	−	0.483542i
$303$	−11.8185	−	0.942110i	−0.678955	−	0.0541228i
$304$	25.3900			1.45622
$305$	−19.5504	−	11.6587i	−1.11945	−	0.667573i
$306$	−7.35513	−	19.2767i	−0.420465	−	1.10198i
$307$		−	3.17751i		−	0.181350i	−0.995881	−	0.0906751i	$-0.971098\pi$
$307$		−	3.17751i		−	0.181350i	0.995881	−	0.0906751i	$-0.0289025\pi$
$308$	−0.847013	−	12.8153i	−0.0482630	−	0.730219i
$309$	−0.412756	+	5.17790i	−0.0234809	+	0.294560i
$310$	−27.9966	−	0.395483i	−1.59010	−	0.0224620i
$311$	−2.89710	−	5.01793i	−0.164280	−	0.284541i	0.772120	−	0.635477i	$-0.219197\pi$
$311$	−2.89710	−	5.01793i	−0.164280	−	0.284541i	−0.936399	+	0.350937i	$0.885863\pi$
$312$	−0.133106	+	0.193253i	−0.00753564	+	0.0109408i
$313$	14.2647	+	8.23575i	0.806291	+	0.465512i	0.845666	−	0.533712i	$-0.179203\pi$
$313$	14.2647	+	8.23575i	0.806291	+	0.465512i	−0.0393753	+	0.999224i	$0.512537\pi$
$314$	−14.2746			−0.805563
$315$	10.4680	−	14.3325i	0.589807	−	0.807544i
$316$	−4.19146			−0.235788
$317$	22.6478	+	13.0757i	1.27203	+	0.734406i	0.975369	−	0.220577i	$-0.0707942\pi$
$317$	22.6478	+	13.0757i	1.27203	+	0.734406i	0.296659	+	0.954983i	$0.404128\pi$
$318$	0.608160	+	1.27834i	0.0341039	+	0.0716860i
$319$	10.2595	+	17.7700i	0.574424	+	0.994932i
$320$	−0.0481862	+	3.41114i	−0.00269369	+	0.190689i
$321$	−7.30820	+	3.47680i	−0.407904	+	0.194056i
$322$	−11.4635	+	7.66877i	−0.638837	+	0.427364i
$323$			19.5947i			1.09028i
$324$	2.33974	+	11.2298i	0.129986	+	0.623879i
$325$	−0.439415	−	0.270527i	−0.0243744	−	0.0150061i
$326$	−22.5024			−1.24629
$327$	8.36550	−	12.1457i	0.462613	−	0.671656i
$328$	−1.71321	−	0.989122i	−0.0945962	−	0.0546151i
$329$	15.8193	+	23.6471i	0.872144	+	1.30371i
$330$	15.4499	−	21.7667i	0.850492	−	1.19822i
$331$	7.76263	−	13.4453i	0.426673	−	0.739019i	−0.569902	−	0.821712i	$-0.693019\pi$
$331$	7.76263	−	13.4453i	0.426673	−	0.739019i	0.996575	+	0.0826937i	$0.0263523\pi$
$332$	−1.54717	−	0.893257i	−0.0849118	−	0.0490238i
$333$	30.6921	−	11.7107i	1.68191	−	0.641743i
$334$	16.6710	+	28.8750i	0.912196	+	1.57997i
$335$	6.47122	+	11.5833i	0.353560	+	0.632863i
$336$	−19.6951	+	11.0179i	−1.07445	+	0.601076i
$337$	10.6550	+	6.15165i	0.580413	+	0.335102i	0.761298	−	0.648403i	$-0.224563\pi$
$337$	10.6550	+	6.15165i	0.580413	+	0.335102i	−0.180884	+	0.983504i	$0.557896\pi$
$338$			23.5052i			1.27851i
$339$	5.42009	+	3.73317i	0.294379	+	0.202758i
$340$	−10.8305	−	0.152993i	−0.587367	−	0.00829722i
$341$	−13.1773	−	22.8237i	−0.713590	−	1.23597i
$342$	4.43411	−	27.6355i	0.239769	−	1.49436i
$343$	−3.64298	−	18.1584i	−0.196703	−	0.980463i
$344$	1.14050	+	1.97540i	0.0614916	+	0.106507i
$345$	−11.1082	−	1.04358i	−0.598045	−	0.0561844i
$346$	−16.9382	−	29.3378i	−0.910603	−	1.57721i
$347$	25.4834	−	14.7128i	1.36802	−	0.789826i	0.377344	−	0.926073i	$-0.376837\pi$
$347$	25.4834	−	14.7128i	1.36802	−	0.789826i	0.990675	+	0.136247i	$0.0435040\pi$
$348$	−6.74640	+	9.79493i	−0.361645	+	0.525063i
$349$	3.85104	+	6.67020i	0.206142	+	0.357048i	0.950496	−	0.310737i	$-0.100576\pi$
$349$	3.85104	+	6.67020i	0.206142	+	0.357048i	−0.744354	+	0.667785i	$0.767243\pi$
$350$	−12.7430	−	20.2648i	−0.681144	−	1.08320i
$351$	0.387871	+	0.370309i	0.0207030	+	0.0197656i
$352$	−20.7334	+	11.9704i	−1.10509	+	0.638026i
$353$			28.5248i			1.51822i	0.650961	+	0.759111i	$0.274366\pi$
$353$			28.5248i			1.51822i	−0.650961	+	0.759111i	$0.725634\pi$
$354$	−2.83588	+	35.5753i	−0.150725	+	1.89080i
$355$	0.203216	−	14.3858i	0.0107856	−	0.763520i
$356$	−2.41390	+	4.18099i	−0.127936	+	0.221592i
$357$	−8.50306	−	15.1997i	−0.450030	−	0.804452i
$358$	−15.0626	+	8.69637i	−0.796081	+	0.459618i
$359$	15.2317	+	26.3821i	0.803898	+	1.39239i	0.917032	+	0.398813i	$0.130578\pi$
$359$	15.2317	+	26.3821i	0.803898	+	1.39239i	−0.113134	+	0.993580i	$0.536089\pi$
$360$	−8.67440	−	1.51778i	−0.457181	−	0.0799940i
$361$	−3.79078	+	6.56583i	−0.199515	+	0.345570i
$362$	22.1737	+	12.8020i	1.16542	+	0.672858i
$363$	6.05271	+	0.482491i	0.317685	+	0.0253242i
$364$	0.153752	−	0.312210i	0.00805881	−	0.0163643i
$365$	18.0100	−	30.2008i	0.942685	−	1.58078i
$366$	28.8119	−	13.7070i	1.50602	−	0.716476i
$367$			17.9387i			0.936391i	0.883625	+	0.468196i	$0.155096\pi$
$367$			17.9387i			0.936391i	−0.883625	+	0.468196i	$0.844904\pi$
$368$	12.2860	+	7.09331i	0.640450	+	0.369764i
$369$	−2.85213	+	3.50762i	−0.148476	+	0.182599i
$370$	0.625834	−	44.3033i	0.0325355	−	2.30322i
$371$	0.664445	+	0.993233i	0.0344962	+	0.0515661i
$372$	8.66503	−	12.5805i	0.449261	−	0.652270i
$373$			7.72893i			0.400189i	0.979777	+	0.200094i	$0.0641249\pi$
$373$			7.72893i			0.400189i	−0.979777	+	0.200094i	$0.935875\pi$
$374$	−13.0968	−	22.6842i	−0.677217	−	1.17297i
$375$	2.35517	−	19.2212i	0.121620	−	0.992577i
$376$	7.05820	−	12.2252i	0.363999	−	0.630465i
$377$			0.556009i			0.0286359i
$378$	8.55279	+	23.3611i	0.439908	+	1.20156i
$379$	−3.74284			−0.192257			−0.0961284	−	0.995369i	$-0.530646\pi$
$379$	−3.74284			−0.192257			−0.0961284	+	0.995369i	$0.530646\pi$
$380$	−12.6201	−	7.52589i	−0.647399	−	0.386070i
$381$	1.95994	−	24.5869i	0.100411	−	1.25963i
$382$	−28.6071	+	16.5163i	−1.46366	+	0.845047i
$383$		−	15.1541i		−	0.774338i	−0.922009	−	0.387169i	$-0.873453\pi$
$383$		−	15.1541i		−	0.774338i	0.922009	−	0.387169i	$-0.126547\pi$
$384$	13.9950	+	9.63925i	0.714178	+	0.491901i
$385$	10.2391	−	20.0713i	0.521835	−	1.02293i
$386$	33.9790			1.72949
$387$	4.87025	−	1.85827i	0.247569	−	0.0944611i
$388$	6.71582	+	3.87738i	0.340944	+	0.196844i
$389$	−29.2328			−1.48216			−0.741081	−	0.671415i	$-0.765687\pi$
$389$	−29.2328			−1.48216			−0.741081	+	0.671415i	$0.765687\pi$
$390$	0.657469	−	0.301471i	0.0332923	−	0.0152656i
$391$	−5.47426	+	9.48169i	−0.276845	+	0.479510i
$392$	−7.28418	+	5.60204i	−0.367907	+	0.282946i
$393$	19.7630	+	1.57540i	0.996909	+	0.0794685i
$394$	−5.08520	+	8.80783i	−0.256189	+	0.443732i
$395$	−6.31572	−	3.76632i	−0.317778	−	0.189504i
$396$	5.19148	+	13.6061i	0.260882	+	0.683732i
$397$	−15.7263	+	9.07960i	−0.789282	+	0.455692i	−0.839710	−	0.543036i	$-0.817275\pi$
$397$	−15.7263	+	9.07960i	−0.789282	+	0.455692i	0.0504279	+	0.998728i	$0.483941\pi$
$398$	−27.2084	+	15.7088i	−1.36383	+	0.787409i
$399$	0.320102	−	23.6244i	0.0160251	−	1.18270i
$400$	−12.9090	+	20.9680i	−0.645449	+	1.04840i
$401$	−18.9091			−0.944274			−0.472137	−	0.881525i	$-0.656517\pi$
$401$	−18.9091			−0.944274			−0.472137	+	0.881525i	$0.656517\pi$
$402$	−18.5393	−	1.47786i	−0.924657	−	0.0737090i
$403$		−	0.714134i		−	0.0355735i
$404$	−4.36219	−	7.55554i	−0.217027	−	0.375902i
$405$	−6.56524	+	19.0236i	−0.326230	+	0.945291i
$406$	−11.3956	+	23.1400i	−0.565555	+	1.14842i
$407$	36.1174	−	20.8524i	1.79028	−	1.03362i
$408$	−4.90180	+	7.11680i	−0.242675	+	0.352334i
$409$	11.7452	+	20.3433i	0.580765	+	1.00591i	0.995389	+	0.0959211i	$0.0305797\pi$
$409$	11.7452	+	20.3433i	0.580765	+	1.00591i	−0.414624	+	0.909993i	$0.636087\pi$
$410$	2.97391	+	5.32322i	0.146871	+	0.262895i
$411$	−0.897534	+	11.2593i	−0.0442721	+	0.555380i
$412$	−3.31022	+	1.91116i	−0.163083	+	0.0941560i
$413$	1.98678	+	30.0600i	0.0977633	+	1.47916i
$414$	9.86626	−	12.1338i	0.484900	−	0.596343i
$415$	−1.52863	−	2.73620i	−0.0750374	−	0.134315i
$416$	−0.648729			−0.0318066
$417$	−8.61487	+	12.5077i	−0.421872	+	0.612506i
$418$		−	35.5332i		−	1.73799i
$419$	14.0462	−	24.3287i	0.686202	−	1.18854i	−0.286855	−	0.957974i	$-0.592610\pi$
$419$	14.0462	−	24.3287i	0.686202	−	1.18854i	0.973057	−	0.230563i	$-0.0740568\pi$
$420$	13.0553	+	0.361384i	0.637032	+	0.0176337i
$421$	16.7130	+	28.9477i	0.814540	+	1.41082i	0.909658	+	0.415359i	$0.136344\pi$
$421$	16.7130	+	28.9477i	0.814540	+	1.41082i	−0.0951179	+	0.995466i	$0.530323\pi$
$422$	−16.6182	+	9.59452i	−0.808961	+	0.467054i
$423$	−25.0297	−	20.3523i	−1.21699	−	0.989562i
$424$	0.296460	−	0.513484i	0.0143974	−	0.0249370i
$425$	−16.1820	−	9.96250i	−0.784944	−	0.483252i
$426$	16.6082	+	11.4391i	0.804670	+	0.554228i
$427$	22.3859	−	14.9756i	1.08333	−	0.724718i
$428$	−5.15753	−	2.97770i	−0.249299	−	0.143933i
$429$	0.560678	+	0.386175i	0.0270698	+	0.0186447i
$430$	0.0993080	−	7.03009i	0.00478905	−	0.339021i
$431$	1.30398	−	2.25856i	0.0628105	−	0.108791i	−0.832910	−	0.553408i	$-0.813327\pi$
$431$	1.30398	−	2.25856i	0.0628105	−	0.108791i	0.895721	+	0.444617i	$0.146660\pi$
$432$	17.6703	−	18.5084i	0.850165	−	0.890484i
$433$		−	0.0636994i		−	0.00306120i	−0.999999	−	0.00153060i	$-0.999513\pi$
$433$		−	0.0636994i		−	0.00306120i	0.999999	−	0.00153060i	$-0.000487205\pi$
$434$	14.6364	−	29.7208i	0.702572	−	1.42665i
$435$	−18.9670	+	8.69696i	−0.909396	+	0.416988i
$436$	10.8524			0.519735
$437$	−12.8625	+	7.42619i	−0.615299	+	0.355243i
$438$	21.1742	+	44.5078i	1.01174	+	2.12667i
$439$	7.70129	−	13.3390i	0.367562	−	0.636637i	−0.621622	−	0.783318i	$-0.713526\pi$
$439$	7.70129	−	13.3390i	0.367562	−	0.636637i	0.989184	+	0.146681i	$0.0468591\pi$
$440$	−11.1787	−	0.157912i	−0.532924	−	0.00752815i
$441$	10.0034	+	18.4643i	0.476352	+	0.879255i
$442$		−	0.709769i		−	0.0337603i
$443$	−25.6472	−	14.8074i	−1.21853	−	0.703521i	−0.253929	−	0.967223i	$-0.581723\pi$
$443$	−25.6472	−	14.8074i	−1.21853	−	0.703521i	−0.964604	+	0.263702i	$0.915056\pi$
$444$	19.9081	+	13.7120i	0.944796	+	0.650742i
$445$	−7.39419	+	4.13089i	−0.350518	+	0.195823i
$446$	31.5460			1.49375
$447$	−19.2223	−	1.53230i	−0.909182	−	0.0724754i
$448$	−3.62122	−	1.78332i	−0.171087	−	0.0842541i
$449$	−39.1113			−1.84578			−0.922888	−	0.385069i	$-0.874178\pi$
$449$	−39.1113			−1.84578			−0.922888	+	0.385069i	$0.874178\pi$
$450$	20.5680	+	17.7125i	0.969584	+	0.834975i
$451$	−2.86970	+	4.97046i	−0.135129	+	0.234050i
$452$			4.84296i			0.227794i
$453$	16.0353	+	1.27825i	0.753404	+	0.0600575i
$454$	−2.57048	+	4.45219i	−0.120638	+	0.208952i
$455$	0.512218	−	0.332283i	0.0240131	−	0.0155777i
$456$	−10.5859	+	5.03615i	−0.495732	+	0.235840i
$457$	−24.6157	−	14.2119i	−1.15147	−	0.664803i	−0.202227	−	0.979339i	$-0.564818\pi$
$457$	−24.6157	−	14.2119i	−1.15147	−	0.664803i	−0.949246	+	0.314535i	$0.898151\pi$
$458$	−29.6621	−	17.1254i	−1.38602	−	0.800217i
$459$	14.2838	+	13.6371i	0.666712	+	0.636525i
$460$	−4.00421	−	7.16743i	−0.186697	−	0.334183i
$461$	7.25489	+	12.5658i	0.337894	+	0.585249i	0.984036	−	0.177967i	$-0.0569522\pi$
$461$	7.25489	+	12.5658i	0.337894	+	0.585249i	−0.646142	+	0.763217i	$0.723619\pi$
$462$	15.4195	+	27.5631i	0.717380	+	1.28235i
$463$	−29.2347	−	16.8786i	−1.35865	−	0.784417i	−0.369208	−	0.929347i	$-0.620371\pi$
$463$	−29.2347	−	16.8786i	−1.35865	−	0.784417i	−0.989442	+	0.144930i	$0.953704\pi$
$464$	26.5316			1.23170
$465$	24.3610	−	11.1703i	1.12972	−	0.518011i
$466$	25.1692			1.16594
$467$	−34.3450	+	19.8291i	−1.58930	+	0.917581i	−0.595874	+	0.803078i	$0.703194\pi$
$467$	−34.3450	+	19.8291i	−1.58930	+	0.917581i	−0.993423	+	0.114503i	$0.963472\pi$
$468$	−0.0625158	+	0.389629i	−0.00288979	+	0.0180106i
$469$	−15.6652	+	1.03537i	−0.723350	+	0.0478090i
$470$	−37.9855	+	21.2213i	−1.75214	+	0.978865i
$471$	12.3380	−	5.86969i	0.568506	−	0.270461i
$472$	12.9449	−	7.47375i	0.595838	−	0.344007i
$473$	5.73115	−	3.30888i	0.263519	−	0.152143i
$474$	9.30765	−	4.42802i	0.427515	−	0.203386i
$475$	−12.2536	−	22.6801i	−0.562233	−	1.04064i
$476$	5.66212	−	11.4975i	0.259523	−	0.526988i
$477$	−1.05131	−	0.854842i	−0.0481360	−	0.0391405i
$478$	2.15781	−	1.24581i	0.0986960	−	0.0569822i
$479$	−15.7751			−0.720781			−0.360390	−	0.932802i	$-0.617356\pi$
$479$	−15.7751			−0.720781			−0.360390	+	0.932802i	$0.617356\pi$
$480$	−10.1473	−	22.1299i	−0.463158	−	1.01009i
$481$	1.13008			0.0515273
$482$	12.7252	+	7.34692i	0.579619	+	0.334643i
$483$	6.75492	−	11.3422i	0.307360	−	0.516086i
$484$	2.23405	+	3.86949i	0.101548	+	0.175886i
$485$	6.63535	+	11.8771i	0.301296	+	0.539311i
$486$	−17.0593	−	22.4654i	−0.773827	−	1.01905i
$487$	33.3922	+	19.2790i	1.51315	+	0.873615i	0.999882	+	0.0153837i	$0.00489698\pi$
$487$	33.3922	+	19.2790i	1.51315	+	0.873615i	0.513264	+	0.858231i	$0.328436\pi$
$488$	−11.5731	−	6.68176i	−0.523892	−	0.302469i
$489$	19.4496	−	9.25295i	0.879541	−	0.418433i
$490$	28.1278	−	3.33088i	1.27068	−	0.150474i
$491$	−4.66790	+	8.08504i	−0.210659	+	0.364873i	−0.951921	−	0.306343i	$-0.900894\pi$
$491$	−4.66790	+	8.08504i	−0.210659	+	0.364873i	0.741262	+	0.671216i	$0.234228\pi$
$492$	−3.31620	−	0.264351i	−0.149506	−	0.0119179i
$493$			20.4757i			0.922180i
$494$	0.481424	−	0.833852i	0.0216603	−	0.0375168i
$495$	−4.40347	+	25.1667i	−0.197921	+	1.13116i
$496$	−34.0769			−1.53010
$497$	15.2718	+	7.52081i	0.685034	+	0.337355i
$498$	4.37935	+	0.349100i	0.196243	+	0.0156435i
$499$	13.8462			0.619840			0.309920	−	0.950763i	$-0.399698\pi$
$499$	13.8462			0.619840			0.309920	+	0.950763i	$0.399698\pi$
$500$	12.6316	−	6.59578i	0.564901	−	0.294972i
$501$	−26.2826	−	18.1025i	−1.17422	−	0.808762i
$502$	−0.344658	−	0.198988i	−0.0153828	−	0.00888129i
$503$			5.02665i			0.224127i	0.993701	+	0.112064i	$0.0357461\pi$
$503$			5.02665i			0.224127i	−0.993701	+	0.112064i	$0.964254\pi$
$504$	6.02610	−	8.50027i	0.268424	−	0.378632i
$505$	0.216193	−	15.3045i	0.00962046	−	0.681040i
$506$	9.92705	−	17.1941i	0.441311	−	0.764373i
$507$	−9.66528	−	20.3163i	−0.429250	−	0.902278i
$508$	15.7184	−	9.07500i	0.697390	−	0.402638i
$509$	−16.8393			−0.746391			−0.373195	−	0.927753i	$-0.621738\pi$
$509$	−16.8393			−0.746391			−0.373195	+	0.927753i	$0.621738\pi$
$510$	24.2121	−	11.1021i	1.07213	−	0.491607i
$511$	23.1338	+	34.5812i	1.02338	+	1.52978i
$512$			18.0264i			0.796661i
$513$	7.53113	+	25.7096i	0.332508	+	1.13511i
$514$	−3.75360	+	6.50143i	−0.165564	+	0.286766i
$515$	−6.70518	−	0.0947181i	−0.295465	−	0.00417378i
$516$	3.15904	+	2.17583i	0.139069	+	0.0957857i
$517$	−35.4684	−	20.4777i	−1.55990	−	0.900607i
$518$	47.0318	+	23.1615i	2.06646	+	1.01766i
$519$	26.7039	+	18.3927i	1.17217	+	0.807349i
$520$	−0.260189	−	0.155161i	−0.0114101	−	0.00680427i
$521$	−13.4928	+	23.3701i	−0.591128	+	1.02386i	0.402953	+	0.915221i	$0.367984\pi$
$521$	−13.4928	+	23.3701i	−0.591128	+	1.02386i	−0.994081	+	0.108643i	$0.965349\pi$
$522$	4.63346	−	28.8780i	0.202801	−	1.26396i
$523$	−6.44322	+	3.71999i	−0.281742	+	0.162664i	−0.634212	−	0.773159i	$-0.718675\pi$
$523$	−6.44322	+	3.71999i	−0.281742	+	0.162664i	0.352470	+	0.935823i	$0.385342\pi$
$524$	7.29448	+	12.6344i	0.318661	+	0.551937i
$525$	19.3471	+	12.2756i	0.844375	+	0.535752i
$526$	0.114314	−	0.197998i	0.00498433	−	0.00863312i
$527$		−	26.2989i		−	1.14560i
$528$	18.4274	−	26.7543i	0.801952	−	1.16433i
$529$	14.7013			0.639186
$530$	−1.59548	+	0.891342i	−0.0693031	+	0.0387174i
$531$	−12.1773	−	31.9150i	−0.528451	−	1.38499i
$532$	14.4506	−	9.66701i	0.626511	−	0.419118i
$533$	−0.134685	+	0.0777607i	−0.00583387	+	0.00336819i
$534$	0.943390	−	11.8345i	0.0408245	−	0.512131i
$535$	−5.09573	−	9.12122i	−0.220308	−	0.394345i
$536$	3.89479	+	6.74598i	0.168229	+	0.291382i
$537$	9.44314	−	13.7103i	0.407502	−	0.591641i
$538$	23.7031	−	13.6850i	1.02191	−	0.590001i
$539$	16.2530	+	21.1333i	0.700065	+	0.910275i
$540$	−14.2692	+	3.96191i	−0.614047	+	0.170493i
$541$	−3.00421	−	5.20345i	−0.129161	−	0.223714i	0.794191	−	0.607669i	$-0.207895\pi$
$541$	−3.00421	−	5.20345i	−0.129161	−	0.223714i	−0.923352	+	0.383955i	$0.874562\pi$
$542$		−	4.61096i		−	0.198058i
$543$	−24.4296	−	1.94741i	−1.04838	−	0.0835712i
$544$	−23.8903			−1.02429
$545$	16.3525	+	9.75163i	0.700463	+	0.417714i
$546$	−0.0115949	+	0.855732i	−0.000496215	+	0.0366219i
$547$	−21.5061	+	12.4166i	−0.919536	+	0.530894i	−0.883487	−	0.468456i	$-0.844810\pi$
$547$	−21.5061	+	12.4166i	−0.919536	+	0.530894i	−0.0360487	+	0.999350i	$0.511477\pi$
$548$	−7.19804	+	4.15579i	−0.307485	+	0.177527i
$549$	−19.2668	+	23.6948i	−0.822287	+	1.01127i
$550$	29.3446	+	18.0660i	1.25126	+	0.770339i
$551$	−13.8883	+	24.0553i	−0.591663	+	1.02479i
$552$	−6.52939	−	0.520490i	−0.277909	−	0.0221535i
$553$	7.23175	−	4.83783i	0.307525	−	0.205726i
$554$	−22.6760	+	39.2759i	−0.963409	+	1.66867i
$555$	17.6765	+	38.5501i	0.750325	+	1.63636i
$556$	−11.1759			−0.473964
$557$	18.8530	+	10.8848i	0.798829	+	0.461204i	0.843062	−	0.537817i	$-0.180751\pi$
$557$	18.8530	+	10.8848i	0.798829	+	0.461204i	−0.0442323	+	0.999021i	$0.514084\pi$
$558$	−5.95119	+	37.0907i	−0.251934	+	1.57018i
$559$	0.179323			0.00758454
$560$	−15.8559	−	24.4419i	−0.670032	−	1.03286i
$561$	20.6477	+	14.2214i	0.871745	+	0.600427i
$562$			32.8065i			1.38386i
$563$	−34.5549	+	19.9503i	−1.45632	+	0.840804i	−0.998827	−	0.0484116i	$-0.984584\pi$
$563$	−34.5549	+	19.9503i	−1.45632	+	0.840804i	−0.457488	+	0.889216i	$0.651251\pi$
$564$	1.88636	−	23.6638i	0.0794302	−	0.996428i
$565$	−4.35174	+	7.29741i	−0.183079	+	0.307005i
$566$	−17.9437			−0.754230
$567$	−16.9985	−	16.6749i	−0.713870	−	0.700279i
$568$		−	8.44646i		−	0.354405i
$569$	21.4570	−	37.1646i	0.899525	−	1.55802i	0.0714217	−	0.997446i	$-0.477246\pi$
$569$	21.4570	−	37.1646i	0.899525	−	1.55802i	0.828103	−	0.560576i	$-0.189420\pi$
$570$	35.9752	+	3.37976i	1.50684	+	0.141563i
$571$	−2.58213	−	4.47238i	−0.108059	−	0.187163i	0.806925	−	0.590654i	$-0.201130\pi$
$571$	−2.58213	−	4.47238i	−0.108059	−	0.187163i	−0.914984	+	0.403491i	$0.867797\pi$
$572$			0.500977i			0.0209469i
$573$	17.9346	−	26.0387i	0.749227	−	1.08778i
$574$	−7.19908	+	0.475815i	−0.300484	+	0.0198601i
$575$	0.406857	−	14.3980i	0.0169671	−	0.600439i
$576$	4.51918	+	0.725100i	0.188299	+	0.0302125i
$577$	−6.42548	−	3.70975i	−0.267496	−	0.154439i	0.360253	−	0.932855i	$-0.382690\pi$
$577$	−6.42548	−	3.70975i	−0.267496	−	0.154439i	−0.627749	+	0.778416i	$0.716024\pi$
$578$			4.62459i			0.192357i
$579$	−29.3692	+	13.9721i	−1.22054	+	0.580660i
$580$	−13.1875	−	7.86425i	−0.547583	−	0.326545i
$581$	3.70042	−	0.244575i	0.153519	−	0.0101467i
$582$	−19.0095	−	1.51534i	−0.787971	−	0.0628130i
$583$	−1.48975	−	0.860108i	−0.0616992	−	0.0356220i
$584$	10.3218	−	17.8779i	0.427119	−	0.739791i
$585$	−0.444308	+	0.530922i	−0.0183699	+	0.0219509i
$586$	5.31347	+	9.20321i	0.219498	+	0.380181i
$587$	9.68643	−	5.59247i	0.399802	−	0.230826i	−0.286597	−	0.958051i	$-0.592524\pi$
$587$	9.68643	−	5.59247i	0.399802	−	0.230826i	0.686399	+	0.727226i	$0.259191\pi$
$588$	−7.01435	+	13.7695i	−0.289267	+	0.567843i
$589$	17.8381	−	30.8965i	0.735005	−	1.27307i
$590$	−46.0686	−	0.650770i	−1.89661	−	0.0267918i
$591$	0.773548	−	9.70392i	0.0318195	−	0.399166i
$592$		−	53.9251i		−	2.21631i
$593$	22.2978	−	12.8737i	0.915663	−	0.528658i	0.0334140	−	0.999442i	$-0.489362\pi$
$593$	22.2978	−	12.8737i	0.915663	−	0.528658i	0.882249	+	0.470783i	$0.156029\pi$
$594$	−25.9024	−	24.7296i	−1.06279	−	1.01467i
$595$	18.8631	−	12.2368i	0.773310	−	0.501658i
$596$	−7.09492	−	12.2888i	−0.290619	−	0.503367i
$597$	17.0577	−	24.7656i	0.698124	−	1.01359i
$598$	0.465912	−	0.268995i	0.0190526	−	0.0110000i
$599$	−0.628601	−	1.08877i	−0.0256840	−	0.0444859i	0.852898	−	0.522078i	$-0.174843\pi$
$599$	−0.628601	−	1.08877i	−0.0256840	−	0.0444859i	−0.878582	+	0.477592i	$0.841510\pi$
$600$	1.22315	−	11.3028i	0.0499347	−	0.461433i
$601$	10.5538	+	18.2797i	0.430498	+	0.745645i	0.996916	−	0.0784732i	$-0.0250045\pi$
$601$	10.5538	+	18.2797i	0.430498	+	0.745645i	−0.566418	+	0.824118i	$0.691671\pi$
$602$	7.46305	+	3.67529i	0.304171	+	0.149794i
$603$	16.6318	−	6.34596i	0.677301	−	0.258428i
$604$	5.91861	+	10.2513i	0.240825	+	0.417121i
$605$	−0.110721	+	7.83802i	−0.00450144	+	0.318661i
$606$	17.6688	+	12.1696i	0.717745	+	0.494357i
$607$			32.8539i			1.33350i	0.745283	+	0.666748i	$0.232314\pi$
$607$			32.8539i			1.33350i	−0.745283	+	0.666748i	$0.767686\pi$
$608$	−28.0668	−	16.2044i	−1.13826	−	0.657174i
$609$	0.334494	−	24.6865i	0.0135544	−	1.00035i
$610$	20.0895	+	35.9596i	0.813399	+	1.45596i
$611$	−0.554886	−	0.961091i	−0.0224483	−	0.0388816i
$612$	−2.30222	+	14.3486i	−0.0930618	+	0.580007i
$613$	−36.4927	−	21.0691i	−1.47393	−	0.850973i	−0.474359	−	0.880332i	$-0.657320\pi$
$613$	−36.4927	−	21.0691i	−1.47393	−	0.850973i	−0.999569	+	0.0293591i	$0.990653\pi$
$614$	−2.87497	+	4.97959i	−0.116024	+	0.200960i
$615$	−4.75934	−	3.37817i	−0.191915	−	0.136221i
$616$	5.84415	−	11.8672i	0.235468	−	0.478142i
$617$	−1.25040	−	0.721921i	−0.0503394	−	0.0290635i	0.474619	−	0.880191i	$-0.342586\pi$
$617$	−1.25040	−	0.721921i	−0.0503394	−	0.0290635i	−0.524958	+	0.851128i	$0.675919\pi$
$618$	5.33174	−	7.74102i	0.214474	−	0.311389i
$619$	−1.42461			−0.0572600			−0.0286300	−	0.999590i	$-0.509114\pi$
$619$	−1.42461			−0.0572600			−0.0286300	+	0.999590i	$0.509114\pi$
$620$	16.9380	+	10.1008i	0.680245	+	0.405657i
$621$	−3.53835	+	14.5446i	−0.141989	+	0.583655i
$622$			10.4850i			0.420411i
$623$	−0.660928	−	9.99984i	−0.0264795	−	0.400635i
$624$	0.794917	−	0.378174i	0.0318221	−	0.0151391i
$625$	24.9601	+	1.41177i	0.998404	+	0.0564707i
$626$	−14.9032	−	25.8131i	−0.595651	−	1.03170i
$627$	14.6112	+	30.7125i	0.583514	+	1.22654i
$628$	8.70717	+	5.02709i	0.347454	+	0.200603i
$629$	41.6167			1.65937
$630$	−29.3727	+	12.9896i	−1.17024	+	0.517519i
$631$	18.5591			0.738825			0.369412	−	0.929266i	$-0.379559\pi$
$631$	18.5591			0.738825			0.369412	+	0.929266i	$0.379559\pi$
$632$	−3.73869	−	2.15853i	−0.148717	−	0.0858618i
$633$	10.4184	−	15.1262i	0.414095	−	0.601214i
$634$	−23.6615	−	40.9829i	−0.939717	−	1.62764i
$635$	31.8391	+	0.449763i	1.26350	+	0.0178483i
$636$	0.0792314	−	0.993935i	0.00314173	−	0.0394121i
$637$	0.0950798	+	0.716136i	0.00376720	+	0.0283743i
$638$		−	37.1308i		−	1.47002i
$639$	−19.0588	−	3.05797i	−0.753953	−	0.120971i
$640$	−11.2364	+	18.8423i	−0.444159	+	0.744809i
$641$	10.5932			0.418405			0.209202	−	0.977872i	$-0.432913\pi$
$641$	10.5932			0.418405			0.209202	+	0.977872i	$0.432913\pi$
$642$	14.5987	+	1.16373i	0.576165	+	0.0459290i
$643$	−14.0744	−	8.12587i	−0.555041	−	0.320453i	0.196112	−	0.980582i	$-0.437168\pi$
$643$	−14.0744	−	8.12587i	−0.555041	−	0.320453i	−0.751153	+	0.660129i	$0.770502\pi$
$644$	9.69318	−	0.640660i	0.381965	−	0.0252455i
$645$	2.80492	+	6.11718i	0.110444	+	0.240864i
$646$	17.7291	−	30.7076i	0.697541	−	1.20818i
$647$	−7.69286	−	4.44147i	−0.302437	−	0.174612i	0.341100	−	0.940027i	$-0.389201\pi$
$647$	−7.69286	−	4.44147i	−0.302437	−	0.174612i	−0.643537	+	0.765415i	$0.722534\pi$
$648$	−3.69618	+	11.2217i	−0.145200	+	0.440830i
$649$	−21.6833	−	37.5566i	−0.851143	−	1.47422i
$650$	0.443854	+	0.821530i	0.0174094	+	0.0322230i
$651$	−0.429621	+	31.7072i	−0.0168382	+	1.24270i
$652$	13.7259	+	7.92467i	0.537549	+	0.310354i
$653$			29.8024i			1.16626i	0.812379	+	0.583130i	$0.198172\pi$
$653$			29.8024i			1.16626i	−0.812379	+	0.583130i	$0.801828\pi$
$654$	−24.0991	+	11.4649i	−0.942349	+	0.448313i
$655$	−0.361519	+	25.5922i	−0.0141257	+	0.999972i
$656$	3.71057	+	6.42690i	0.144874	+	0.250928i
$657$	−36.6031	−	29.7628i	−1.42802	−	1.16116i
$658$	−3.39533	−	51.3713i	−0.132364	−	2.00266i
$659$	24.8107	+	42.9733i	0.966486	+	1.67400i	0.705568	+	0.708642i	$0.250692\pi$
$659$	24.8107	+	42.9733i	0.966486	+	1.67400i	0.260918	+	0.965361i	$0.415975\pi$
$660$	−17.0897	+	7.83617i	−0.665215	+	0.305023i
$661$	−17.4238	−	30.1789i	−0.677708	−	1.17382i	−0.975669	−	0.219247i	$-0.929640\pi$
$661$	−17.4238	−	30.1789i	−0.677708	−	1.17382i	0.297961	−	0.954578i	$-0.403693\pi$
$662$	−24.3302	+	14.0470i	−0.945620	+	0.545954i
$663$	0.291856	+	0.613477i	0.0113347	+	0.0238255i
$664$	−0.920026	−	1.59353i	−0.0357039	−	0.0618410i
$665$	30.4607	−	1.58150i	1.18121	−	0.0613279i
$666$	−58.6943	−	9.41747i	−2.27436	−	0.364920i
$667$	−13.4408	+	7.76007i	−0.520431	+	0.300471i
$668$		−	23.4841i		−	0.908625i
$669$	−27.2663	+	12.9717i	−1.05418	+	0.501514i
$670$	0.339135	−	24.0077i	0.0131019	−	0.927497i
$671$	−19.3855	+	33.5767i	−0.748369	+	1.29621i
$672$	28.8032	+	0.390274i	1.11111	+	0.0150552i
$673$	−15.4334	+	8.91050i	−0.594915	+	0.343475i	−0.767039	−	0.641601i	$-0.778271\pi$
$673$	−15.4334	+	8.91050i	−0.594915	+	0.343475i	0.172123	+	0.985075i	$0.444937\pi$
$674$	−11.1319	−	19.2809i	−0.428783	−	0.742674i
$675$	−25.0609	−	6.85199i	−0.964596	−	0.263733i
$676$	8.27781	−	14.3376i	0.318377	−	0.551445i
$677$	−0.959427	−	0.553925i	−0.0368738	−	0.0212891i	0.481450	−	0.876474i	$-0.340110\pi$
$677$	−0.959427	−	0.553925i	−0.0368738	−	0.0212891i	−0.518324	+	0.855185i	$0.673444\pi$
$678$	−5.11630	−	10.7544i	−0.196490	−	0.413020i
$679$	−16.0625	+	1.06163i	−0.616422	+	0.0407417i
$680$	−9.58180	−	5.71401i	−0.367445	−	0.219122i
$681$	0.391014	−	4.90515i	0.0149837	−	0.187966i
$682$			47.6905i			1.82616i
$683$	11.2902	+	6.51838i	0.432006	+	0.249419i	0.700201	−	0.713946i	$-0.253094\pi$
$683$	11.2902	+	6.51838i	0.432006	+	0.249419i	−0.268195	+	0.963365i	$0.586427\pi$
$684$	−12.4371	+	15.2955i	−0.475544	+	0.584836i
$685$	−14.5803	−	0.205964i	−0.557086	−	0.00786947i
$686$	−10.7205	+	31.7529i	−0.409309	+	1.21233i
$687$	32.6798	+	2.60507i	1.24681	+	0.0993897i
$688$		−	8.55689i		−	0.326229i
$689$	−0.0233065	−	0.0403680i	−0.000887906	−	0.00153790i
$690$	16.4638	+	11.6860i	0.626767	+	0.444877i
$691$	−18.3351	+	31.7574i	−0.697502	+	1.20811i	0.271829	+	0.962346i	$0.412372\pi$
$691$	−18.3351	+	31.7574i	−0.697502	+	1.20811i	−0.969330	+	0.245762i	$0.920962\pi$
$692$			23.8605i			0.907039i
$693$	−24.6615	−	17.4833i	−0.936812	−	0.664135i
$694$	−53.2479			−2.02126
$695$	−16.8399	−	10.0423i	−0.638775	−	0.380927i
$696$	−11.0619	+	5.26258i	−0.419299	+	0.199478i
$697$	−4.95996	+	2.86363i	−0.187872	+	0.108468i
$698$		−	13.9375i		−	0.527542i
$699$	−21.7546	+	10.3495i	−0.822834	+	0.391455i
$700$	0.636301	+	16.8487i	0.0240499	+	0.636823i
$701$	−12.4808			−0.471393			−0.235696	−	0.971827i	$-0.575737\pi$
$701$	−12.4808			−0.471393			−0.235696	+	0.971827i	$0.575737\pi$
$702$	−0.272796	−	0.931265i	−0.0102960	−	0.0351483i
$703$	48.8922	+	28.2279i	1.84400	+	1.06464i
$704$	5.81067			0.218998
$705$	24.1060	−	33.9618i	0.907885	−	1.27908i
$706$	25.8089	−	44.7022i	0.971329	−	1.68239i
$707$	16.2470	+	8.00108i	0.611032	+	0.300912i
$708$	14.2583	−	20.7013i	0.535861	−	0.778004i
$709$	−24.2584	+	42.0168i	−0.911043	+	1.57797i	−0.0984498	+	0.995142i	$0.531388\pi$
$709$	−24.2584	+	42.0168i	−0.911043	+	1.57797i	−0.812593	+	0.582831i	$0.801945\pi$
$710$	−13.3346	+	22.3607i	−0.500437	+	0.839181i
$711$	−6.22412	+	7.65458i	−0.233423	+	0.287069i
$712$	−4.30629	+	2.48624i	−0.161385	+	0.0931756i
$713$	17.2633	−	9.96698i	0.646516	−	0.373266i
$714$	−0.426996	+	31.5134i	−0.0159799	+	1.17936i
$715$	−0.450163	+	0.754876i	−0.0168351	+	0.0282308i
$716$	12.2504			0.457819
$717$	−1.35279	+	1.96409i	−0.0505210	+	0.0733501i
$718$		−	55.1257i		−	2.05727i
$719$	−19.6093	−	33.9643i	−0.731302	−	1.26665i	−0.956327	−	0.292300i	$-0.905580\pi$
$719$	−19.6093	−	33.9643i	−0.731302	−	1.26665i	0.225024	−	0.974353i	$-0.427754\pi$
$720$	25.3344	+	21.2014i	0.944159	+	0.790131i
$721$	3.50542	−	7.11813i	0.130549	−	0.265093i
$722$	11.8813	−	6.85970i	0.442178	−	0.255292i
$723$	−14.0199	−	1.11759i	−0.521405	−	0.0415638i
$724$	−9.01695	−	15.6178i	−0.335112	−	0.580431i
$725$	−12.8045	−	23.6998i	−0.475547	−	0.880190i
$726$	−9.04887	−	6.23254i	−0.335835	−	0.231311i
$727$	34.0419	−	19.6541i	1.26254	−	0.728930i	0.288977	−	0.957336i	$-0.406685\pi$
$727$	34.0419	−	19.6541i	1.26254	−	0.728930i	0.973566	+	0.228406i	$0.0733515\pi$
$728$	0.297927	−	0.199305i	0.0110419	−	0.00738672i
$729$	23.9827	+	12.4029i	0.888247	+	0.459365i
$730$	−55.5494	+	31.0337i	−2.05598	+	1.14861i
$731$	6.60378			0.244250
$732$	−22.4018	−	1.78575i	−0.827993	−	0.0660034i
$733$			28.1107i			1.03829i	0.854686	+	0.519145i	$0.173750\pi$
$733$			28.1107i			1.03829i	−0.854686	+	0.519145i	$0.826250\pi$
$734$	16.2307	−	28.1123i	0.599085	−	1.03765i
$735$	−22.9421	+	14.4451i	−0.846232	+	0.532814i
$736$	−9.05415	−	15.6822i	−0.333740	−	0.578055i
$737$	19.5718	−	11.2998i	0.720937	−	0.416233i
$738$	7.64332	−	2.91635i	0.281354	−	0.107352i
$739$	2.39190	−	4.14289i	0.0879875	−	0.152399i	−0.818673	−	0.574260i	$-0.805290\pi$
$739$	2.39190	−	4.14289i	0.0879875	−	0.152399i	0.906660	+	0.421861i	$0.138623\pi$
$740$	−15.9840	+	26.8035i	−0.587584	+	0.985317i
$741$	−0.0732330	+	0.918686i	−0.00269028	+	0.0337488i
$742$	−0.142612	−	2.15771i	−0.00523543	−	0.0792121i
$743$	10.0985	+	5.83037i	0.370478	+	0.213895i	0.673667	−	0.739035i	$-0.264718\pi$
$743$	10.0985	+	5.83037i	0.370478	+	0.213895i	−0.303189	+	0.952930i	$0.598052\pi$
$744$	14.2078	−	6.75922i	0.520883	−	0.247805i
$745$	0.351628	−	24.8921i	0.0128827	−	0.911975i
$746$	6.99303	−	12.1123i	0.256033	−	0.443462i
$747$	−3.92877	+	1.49904i	−0.143746	+	0.0548471i
$748$			18.4491i			0.674566i
$749$	12.3355	−	0.815299i	0.450728	−	0.0297904i
$750$	−21.0819	+	27.9913i	−0.769803	+	1.02210i
$751$	14.1321			0.515686			0.257843	−	0.966187i	$-0.416988\pi$
$751$	14.1321			0.515686			0.257843	+	0.966187i	$0.416988\pi$
$752$	−45.8612	+	26.4780i	−1.67239	+	0.965553i
$753$	0.379723	+	0.0302696i	0.0138379	+	0.00110309i
$754$	0.503069	−	0.871341i	0.0183207	−	0.0317324i
$755$	−0.293330	+	20.7651i	−0.0106754	+	0.755718i
$756$	3.01007	−	17.2617i	0.109475	−	0.627803i
$757$			16.7658i			0.609365i	0.952454	+	0.304682i	$0.0985503\pi$
$757$			16.7658i			0.609365i	−0.952454	+	0.304682i	$0.901450\pi$
$758$	5.86554	+	3.38647i	0.213046	+	0.123002i
$759$	−1.51008	+	18.9435i	−0.0548123	+	0.687604i
$760$	−7.38118	−	13.2121i	−0.267743	−	0.479253i
$761$	19.8247			0.718643			0.359322	−	0.933214i	$-0.383008\pi$
$761$	19.8247			0.718643			0.359322	+	0.933214i	$0.383008\pi$
$762$	−25.3174	+	36.7577i	−0.917153	+	1.33159i
$763$	−18.7242	+	12.5260i	−0.677863	+	0.453471i
$764$	23.2661			0.841740
$765$	−16.3622	+	19.5519i	−0.591577	+	0.706899i
$766$	−13.7112	+	23.7485i	−0.495407	+	0.858069i
$767$		−	1.17511i		−	0.0424308i
$768$	−15.4810	−	32.5410i	−0.558624	−	1.17422i
$769$	10.3063	−	17.8511i	0.371656	−	0.643728i	−0.618164	−	0.786049i	$-0.712123\pi$
$769$	10.3063	−	17.8511i	0.371656	−	0.643728i	0.989821	+	0.142321i	$0.0454566\pi$
$770$	−34.2064	+	22.1902i	−1.23271	+	0.799679i
$771$	0.570988	−	7.16287i	0.0205636	−	0.257965i
$772$	−20.7264	−	11.9664i	−0.745958	−	0.430679i
$773$	29.0993	+	16.8005i	1.04663	+	0.604272i	0.921704	−	0.387894i	$-0.126797\pi$
$773$	29.0993	+	16.8005i	1.04663	+	0.604272i	0.124926	+	0.992166i	$0.460131\pi$
$774$	−9.31368	−	1.49437i	−0.334773	−	0.0537142i
$775$	16.4460	+	30.4399i	0.590758	+	1.09343i
$776$	3.99358	+	6.91708i	0.143361	+	0.248309i
$777$	−50.1751	−	0.679855i	−1.80002	−	0.0243897i
$778$	45.8118	+	26.4494i	1.64243	+	0.948259i
$779$	−7.76942			−0.278368
$780$	−0.507209	−	0.0476507i	−0.0181610	−	0.00170617i
$781$	−24.5054			−0.876871
$782$	17.1578	−	9.90607i	0.613562	−	0.354240i
$783$	7.86973	+	26.8655i	0.281241	+	0.960095i
$784$	34.1725	−	4.53700i	1.22045	−	0.162036i
$785$	8.60284	+	15.3989i	0.307049	+	0.549609i
$786$	−29.5458	−	20.3501i	−1.05386	−	0.725865i
$787$	3.15703	−	1.82271i	0.112536	−	0.0649727i	−0.442676	−	0.896682i	$-0.645971\pi$
$787$	3.15703	−	1.82271i	0.112536	−	0.0649727i	0.555212	+	0.831709i	$0.312637\pi$
$788$	6.20370	−	3.58171i	0.220998	−	0.127593i
$789$	−0.0173892	+	0.218142i	−0.000619071	+	0.00776606i
$790$	6.48988	+	11.6167i	0.230900	+	0.413304i
$791$	−5.58981	−	8.35583i	−0.198751	−	0.297099i
$792$	−2.37624	+	14.8099i	−0.0844359	+	0.526246i
$793$	−0.909832	+	0.525292i	−0.0323091	+	0.0186537i
$794$	32.8604			1.16617
$795$	1.01251	−	1.42647i	0.0359099	−	0.0505918i
$796$	22.1286			0.784327
$797$	27.9090	+	16.1133i	0.988587	+	0.570761i	0.904852	−	0.425727i	$-0.139982\pi$
$797$	27.9090	+	16.1133i	0.988587	+	0.570761i	0.0837354	+	0.996488i	$0.473315\pi$
$798$	−21.8766	+	36.7330i	−0.774425	+	1.30033i
$799$	−20.4344	−	35.3934i	−0.722917	−	1.25213i
$800$	27.6520	−	14.9398i	0.977647	−	0.528201i
$801$	4.05094	+	10.6169i	0.143133	+	0.375130i
$802$	29.6331	+	17.1087i	1.04638	+	0.604128i
$803$	−51.8683	−	29.9462i	−1.83039	−	1.05678i
$804$	10.7881	+	7.43044i	0.380466	+	0.262051i
$805$	15.1814	+	7.74465i	0.535075	+	0.272963i
$806$	−0.646138	+	1.11914i	−0.0227593	+	0.0394202i
$807$	−14.8601	+	21.5750i	−0.523101	+	0.759477i
$808$		−	8.98584i		−	0.316121i
$809$	9.02975	−	15.6400i	0.317469	−	0.549873i	−0.662490	−	0.749071i	$-0.730500\pi$
$809$	9.02975	−	15.6400i	0.317469	−	0.549873i	0.979959	+	0.199198i	$0.0638337\pi$
$810$	27.5009	−	23.8724i	0.966284	−	0.838792i
$811$	2.51554			0.0883326			0.0441663	−	0.999024i	$-0.485937\pi$
$811$	2.51554			0.0883326			0.0441663	+	0.999024i	$0.485937\pi$
$812$	15.1002	−	10.1016i	0.529915	−	0.354498i
$813$	1.89602	+	3.98540i	0.0664962	+	0.139774i
$814$	−75.4679			−2.64515
$815$	13.5615	+	24.2747i	0.475038	+	0.850304i
$816$	29.2738	−	13.9267i	1.02479	−	0.487533i
$817$	7.75826	+	4.47923i	0.271427	+	0.156709i
$818$		−	42.5077i		−	1.48625i
$819$	−0.341853	−	0.744405i	−0.0119453	−	0.0260116i
$820$	0.0606626	−	4.29435i	0.00211843	−	0.149965i
$821$	3.84573	−	6.66100i	0.134217	−	0.232470i	−0.791081	−	0.611711i	$-0.790481\pi$
$821$	3.84573	−	6.66100i	0.134217	−	0.232470i	0.925298	+	0.379241i	$0.123815\pi$
$822$	11.5938	−	16.8328i	0.404381	−	0.587110i
$823$	−11.0345	+	6.37075i	−0.384637	+	0.222070i	−0.679834	−	0.733366i	$-0.737948\pi$
$823$	−11.0345	+	6.37075i	−0.384637	+	0.222070i	0.295197	+	0.955436i	$0.404615\pi$
$824$	−3.93686			−0.137147
$825$	−32.7922	−	3.54866i	−1.14168	−	0.123548i
$826$	24.0843	−	48.9058i	0.838002	−	1.70165i
$827$			5.86058i			0.203792i	0.994795	+	0.101896i	$0.0324910\pi$
$827$			5.86058i			0.203792i	−0.994795	+	0.101896i	$0.967509\pi$
$828$	−10.2913	+	3.92671i	−0.357648	+	0.136463i
$829$	17.8395	−	30.8989i	0.619592	−	1.07316i	−0.369968	−	0.929044i	$-0.620632\pi$
$829$	17.8395	−	30.8989i	0.619592	−	1.07316i	0.989560	−	0.144120i	$-0.0460352\pi$
$830$	−0.0801104	+	5.67109i	−0.00278067	+	0.196846i
$831$	3.44941	−	43.2718i	0.119659	−	1.50108i
$832$	0.136358	+	0.0787263i	0.00472736	+	0.00272934i
$833$	3.50143	+	26.3726i	0.121317	+	0.913757i
$834$	24.8175	−	11.8067i	0.859359	−	0.408832i
$835$	21.1021	−	35.3860i	0.730267	−	1.22458i
$836$	−12.5137	+	21.6744i	−0.432796	+	0.749625i
$837$	−10.1078	−	34.5059i	−0.349378	−	1.19270i
$838$	−44.0246	+	25.4176i	−1.52081	+	0.878037i
$839$	−10.0753	−	17.4509i	−0.347837	−	0.602472i	0.638028	−	0.770013i	$-0.279750\pi$
$839$	−10.0753	−	17.4509i	−0.347837	−	0.602472i	−0.985865	+	0.167542i	$0.946417\pi$
$840$	11.4589	+	7.04561i	0.395370	+	0.243097i
$841$	−0.0127510	+	0.0220853i	−0.000439688	+	0.000761563i
$842$		−	60.4866i		−	2.08451i
$843$	−13.4900	−	28.3558i	−0.464620	−	0.976625i
$844$	13.5156			0.465226
$845$	25.3564	−	14.1658i	0.872286	−	0.487318i
$846$	20.8105	+	54.5414i	0.715481	+	1.87517i
$847$	−8.32074	−	4.09767i	−0.285904	−	0.140797i
$848$	−1.92627	+	1.11214i	−0.0661485	+	0.0381909i
$849$	15.5093	−	7.37841i	0.532279	−	0.253226i
$850$	16.3455	+	30.2539i	0.560646	+	1.03770i
$851$	15.7723	+	27.3184i	0.540666	+	0.936461i
$852$	−6.10208	−	12.8265i	−0.209054	−	0.439428i
$853$	15.5699	−	8.98930i	0.533104	−	0.307788i	−0.209175	−	0.977878i	$-0.567078\pi$
$853$	15.5699	−	8.98930i	0.533104	−	0.307788i	0.742280	+	0.670090i	$0.233745\pi$
$854$	−48.6315	+	3.21424i	−1.66413	+	0.109989i
$855$	−32.4844	+	11.8717i	−1.11094	+	0.406004i
$856$	−3.06694	−	5.31209i	−0.104826	−	0.181564i
$857$			14.3518i			0.490249i	0.969492	+	0.245124i	$0.0788288\pi$
$857$			14.3518i			0.490249i	−0.969492	+	0.245124i	$0.921171\pi$
$858$	−0.529252	−	1.11248i	−0.0180684	−	0.0379795i
$859$	−5.96261			−0.203442			−0.101721	−	0.994813i	$-0.532435\pi$
$859$	−5.96261			−0.203442			−0.101721	+	0.994813i	$0.532435\pi$
$860$	−2.53636	+	4.25321i	−0.0864892	+	0.145033i
$861$	6.02675	−	3.37151i	0.205391	−	0.114901i
$862$	−4.08703	+	2.35965i	−0.139205	+	0.0803699i
$863$	42.3854	−	24.4712i	1.44281	−	0.833010i	0.444778	−	0.895641i	$-0.353283\pi$
$863$	42.3854	−	24.4712i	1.44281	−	0.833010i	0.998037	+	0.0626312i	$0.0199492\pi$
$864$	−31.3456	+	9.18209i	−1.06640	+	0.312381i
$865$	−21.4403	+	35.9531i	−0.728992	+	1.22244i
$866$	−0.0576343	+	0.0998256i	−0.00195849	+	0.00339221i
$867$	−1.90162	−	3.99718i	−0.0645824	−	0.135751i
$868$	−19.3946	+	12.9745i	−0.658297	+	0.440382i
$869$	−6.26246	+	10.8469i	−0.212439	+	0.367956i
$870$	37.5927	+	3.53171i	1.27451	+	0.119736i
$871$	0.612385			0.0207499
$872$	9.68010	+	5.58881i	0.327810	+	0.189261i
$873$	17.0537	−	6.50692i	0.577180	−	0.220226i
$874$	26.8765			0.909110
$875$	−14.1810	+	25.9596i	−0.479405	+	0.877594i
$876$	2.75858	−	34.6056i	0.0932039	−	1.16921i
$877$			2.93061i			0.0989595i	0.998775	+	0.0494798i	$0.0157563\pi$
$877$			2.93061i			0.0989595i	−0.998775	+	0.0494798i	$0.984244\pi$
$878$	−24.1379	+	13.9360i	−0.814615	+	0.470318i
$879$	−8.37695	−	5.76975i	−0.282548	−	0.194609i
$880$	36.0211	+	21.4808i	1.21427	+	0.724118i
$881$	−0.475996			−0.0160367			−0.00801835	−	0.999968i	$-0.502552\pi$
$881$	−0.475996			−0.0160367			−0.00801835	+	0.999968i	$0.502552\pi$
$882$	1.02961	−	37.9871i	0.0346689	−	1.27909i
$883$		−	25.7817i		−	0.867622i	−0.901004	−	0.433811i	$-0.857169\pi$
$883$		−	25.7817i		−	0.867622i	0.901004	−	0.433811i	$-0.142831\pi$
$884$	−0.249959	+	0.432942i	−0.00840704	+	0.0145614i
$885$	40.0862	−	18.3808i	1.34748	−	0.617864i
$886$	26.7951	+	46.4104i	0.900198	+	1.55919i
$887$		−	6.59384i		−	0.221399i	−0.993854	−	0.110700i	$-0.964691\pi$
$887$		−	6.59384i		−	0.221399i	0.993854	−	0.110700i	$-0.0353092\pi$
$888$	10.6961	+	22.4831i	0.358939	+	0.754485i
$889$	−16.6453	+	33.8000i	−0.558264	+	1.13361i
$890$	15.3253	+	0.216487i	0.513704	+	0.00725665i
$891$	32.5570	+	10.7236i	1.09070	+	0.359254i
$892$	−19.2423	−	11.1096i	−0.644281	−	0.371976i
$893$		−	55.4412i		−	1.85527i
$894$	28.7375	+	19.7934i	0.961125	+	0.661989i
$895$	18.4590	+	11.0078i	0.617016	+	0.367951i
$896$	−14.4332	−	21.5752i	−0.482180	−	0.720777i
$897$	−0.292094	+	0.424083i	−0.00975272	+	0.0141597i
$898$	61.2927	+	35.3874i	2.04536	+	1.18089i
$899$	18.6401	−	32.2856i	0.621681	−	1.07678i
$900$	−6.30816	−	18.0476i	−0.210272	−	0.601587i
$901$	−0.858290	−	1.48660i	−0.0285938	−	0.0495259i
$902$	8.99442	−	5.19293i	0.299481	−	0.172906i
$903$	−7.96184	−	0.107880i	−0.264953	−	0.00359003i
$904$	−2.49405	+	4.31982i	−0.0829508	+	0.143675i
$905$	0.446886	−	31.6354i	0.0148550	−	1.05160i
$906$	−23.9729	−	16.5117i	−0.796448	−	0.548565i
$907$			50.9178i			1.69070i	0.534214	+	0.845350i	$0.320608\pi$
$907$			50.9178i			1.69070i	−0.534214	+	0.845350i	$0.679392\pi$
$908$	3.13586	−	1.81049i	0.104067	−	0.0600831i
$909$	−20.2758	−	3.25325i	−0.672507	−	0.107903i
$910$	−1.10336	+	0.0572857i	−0.0365760	+	0.00189900i
$911$	−22.9879	−	39.8163i	−0.761625	−	1.31917i	−0.942013	−	0.335577i	$-0.891069\pi$
$911$	−22.9879	−	39.8163i	−0.761625	−	1.31917i	0.180388	−	0.983596i	$-0.442265\pi$
$912$	43.8377	+	3.49452i	1.45161	+	0.115715i
$913$	−4.62325	+	2.66923i	−0.153007	+	0.0883388i
$914$	25.7174	+	44.5439i	0.850656	+	1.47338i
$915$	−32.1505	−	22.8203i	−1.06286	−	0.754417i
$916$	12.0621	+	20.8922i	0.398543	+	0.690296i
$917$	−27.1684	−	13.3795i	−0.897179	−	0.441829i
$918$	−10.0461	−	34.2950i	−0.331569	−	1.13190i
$919$	−1.65257	−	2.86233i	−0.0545132	−	0.0944196i	0.837481	−	0.546466i	$-0.184027\pi$
$919$	−1.65257	−	2.86233i	−0.0545132	−	0.0944196i	−0.891994	+	0.452047i	$0.850694\pi$
$920$	0.119441	−	8.45530i	0.00393784	−	0.278763i
$921$	0.437333	−	5.48621i	0.0144106	−	0.180777i
$922$		−	26.2565i		−	0.864712i
$923$	−0.575063	−	0.332013i	−0.0189284	−	0.0109283i
$924$	0.301387	−	22.2431i	0.00991490	−	0.731745i
$925$	−48.1697	+	26.0250i	−1.58381	+	0.855697i
$926$	30.5431	+	52.9022i	1.00371	+	1.73847i
$927$	−1.42531	+	8.88322i	−0.0468132	+	0.291763i
$928$	−29.3287	−	16.9329i	−0.962760	−	0.555850i
$929$	12.2782	−	21.2665i	0.402836	−	0.697732i	−0.591231	−	0.806502i	$-0.701358\pi$
$929$	12.2782	−	21.2665i	0.402836	−	0.697732i	0.994067	+	0.108770i	$0.0346912\pi$
$930$	−48.2838	−	4.53611i	−1.58329	−	0.148745i
$931$	−13.7745	+	33.3580i	−0.451442	+	1.09327i
$932$	−15.3526	−	8.86383i	−0.502891	−	0.290344i
$933$	−4.31142	−	9.06256i	−0.141150	−	0.296695i
$934$	71.7644			2.34820
$935$	−16.5778	+	27.7993i	−0.542152	+	0.909133i
$936$	−0.256416	+	0.315346i	−0.00838120	+	0.0103074i
$937$		−	4.74809i		−	0.155113i	−0.996988	−	0.0775566i	$-0.975288\pi$
$937$		−	4.74809i		−	0.155113i	0.996988	−	0.0775566i	$-0.0247119\pi$
$938$	25.4862	+	12.5511i	0.832155	+	0.409807i
$939$	23.4956	+	16.1829i	0.766750	+	0.528110i
$940$	30.6437	+	0.432877i	0.999489	+	0.0141189i
$941$	−14.1107	−	24.4404i	−0.459995	−	0.796735i	0.538965	−	0.842328i	$-0.318815\pi$
$941$	−14.1107	−	24.4404i	−0.459995	−	0.796735i	−0.998960	+	0.0455934i	$0.985482\pi$
$942$	−24.6462	−	1.96467i	−0.803016	−	0.0640124i
$943$	−3.75954	−	2.17057i	−0.122427	−	0.0706835i
$944$	−56.0738			−1.82505
$945$	20.0465	−	23.3053i	0.652111	−	0.758123i
$946$	−11.9753			−0.389352
$947$	−9.74942	−	5.62883i	−0.316814	−	0.182912i	0.333158	−	0.942871i	$-0.391886\pi$
$947$	−9.74942	−	5.62883i	−0.316814	−	0.182912i	−0.649971	+	0.759959i	$0.725219\pi$
$948$	−7.23686	−	0.576886i	−0.235042	−	0.0187364i
$949$	−0.811456	−	1.40548i	−0.0263410	−	0.0456239i
$950$	−1.31766	+	46.6297i	−0.0427505	+	1.51287i
$951$	37.3035	+	25.6933i	1.20965	+	0.833163i
$952$	10.9715	−	7.33965i	0.355589	−	0.237879i
$953$		−	36.1169i		−	1.16994i	−0.811055	−	0.584970i	$-0.801106\pi$
$953$		−	36.1169i		−	1.16994i	0.811055	−	0.584970i	$-0.198894\pi$
$954$	0.874090	+	2.29086i	0.0282997	+	0.0741693i
$955$	35.0576	+	20.9063i	1.13444	+	0.676511i
$956$	−1.75495			−0.0567592
$957$	15.2681	+	32.0934i	0.493548	+	1.03743i
$958$	24.7217	+	14.2731i	0.798720	+	0.461141i
$959$	7.62251	−	15.4783i	0.246144	−	0.499820i
$960$	−0.552685	+	5.88295i	−0.0178378	+	0.189872i
$961$	−8.44117	+	14.6205i	−0.272296	+	0.471630i
$962$	−1.77099	−	1.02248i	−0.0570991	−	0.0329662i
$963$	−13.0967	+	4.99710i	−0.422034	+	0.161029i
$964$	−5.17472	−	8.96288i	−0.166667	−	0.288675i
$965$	−20.4780	−	36.6551i	−0.659211	−	1.17997i
$966$	−20.8481	+	11.6629i	−0.670777	+	0.375249i
$967$	48.7009	+	28.1175i	1.56612	+	0.904198i	0.996615	+	0.0822077i	$0.0261971\pi$
$967$	48.7009	+	28.1175i	1.56612	+	0.904198i	0.569502	+	0.821990i	$0.307136\pi$
$968$			4.60200i			0.147914i
$969$	−2.69690	+	33.8318i	−0.0866369	+	1.08683i
$970$	0.347737	−	24.6166i	0.0111652	−	0.790391i
$971$	−12.1224	−	20.9966i	−0.389027	−	0.673814i	0.603292	−	0.797520i	$-0.293855\pi$
$971$	−12.1224	−	20.9966i	−0.389027	−	0.673814i	−0.992319	+	0.123706i	$0.960522\pi$
$972$	2.49413	+	19.7111i	0.0799993	+	0.632235i
$973$	19.2824	−	12.8994i	0.618165	−	0.413535i
$974$	−34.8867	−	60.4256i	−1.11784	−	1.93616i
$975$	−0.721449	−	0.527563i	−0.0231049	−	0.0168956i
$976$	25.0658	+	43.4153i	0.802337	+	1.38969i
$977$	−13.9482	+	8.05303i	−0.446244	+	0.257639i	−0.706243	−	0.707970i	$-0.749611\pi$
$977$	−13.9482	+	8.05303i	−0.446244	+	0.257639i	0.259999	+	0.965609i	$0.416278\pi$
$978$	−38.8521	−	3.09709i	−1.24235	−	0.0990341i
$979$	7.21321	+	12.4936i	0.230535	+	0.399299i
$980$	−18.3303	−	7.87399i	−0.585539	−	0.251525i
$981$	16.1153	−	19.8190i	0.514522	−	0.632772i
$982$	14.6305	−	8.44691i	0.466877	−	0.269552i
$983$		−	14.6728i		−	0.467990i	−0.972238	−	0.233995i	$-0.924820\pi$
$983$		−	14.6728i		−	0.467990i	0.972238	−	0.233995i	$-0.0751799\pi$
$984$	−2.82185	−	1.94359i	−0.0899572	−	0.0619593i
$985$	12.5662	+	0.177512i	0.400392	+	0.00565599i
$986$	18.5262	−	32.0882i	0.589993	−	1.02190i
$987$	24.0585	+	43.0058i	0.765790	+	1.36889i
$988$	−0.587314	+	0.339086i	−0.0186850	+	0.0107878i
$989$	2.50276	+	4.33491i	0.0795831	+	0.137842i
$990$	29.6713	−	35.4554i	0.943016	−	1.12685i
$991$	−23.4659	+	40.6441i	−0.745419	+	1.29110i	0.204580	+	0.978850i	$0.434417\pi$
$991$	−23.4659	+	40.6441i	−0.745419	+	1.29110i	−0.949999	+	0.312253i	$0.898916\pi$
$992$	37.6695	+	21.7485i	1.19601	+	0.690516i
$993$	15.2533	−	22.1458i	0.484048	−	0.702777i
$994$	−17.1282	−	25.6038i	−0.543275	−	0.812105i
$995$	33.3435	+	19.8841i	1.05706	+	0.630367i
$996$	−2.54835	−	1.75522i	−0.0807477	−	0.0556162i
$997$			10.3854i			0.328908i	0.986385	+	0.164454i	$0.0525863\pi$
$997$			10.3854i			0.328908i	−0.986385	+	0.164454i	$0.947414\pi$
$998$	−21.6989	−	12.5278i	−0.686865	−	0.396562i
$999$	54.6039	−	15.9951i	1.72759	−	0.506064i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bo.b.4.9	yes	84
3.2	odd	2		945.2.bo.b.739.34		84
5.4	even	2	inner	315.2.bo.b.4.34	yes	84
7.2	even	3		315.2.r.b.184.34	yes	84
9.2	odd	6		945.2.r.b.424.9		84
9.7	even	3		315.2.r.b.214.34	yes	84
15.14	odd	2		945.2.bo.b.739.9		84
21.2	odd	6		945.2.r.b.604.9		84
35.9	even	6		315.2.r.b.184.9	✓	84
45.29	odd	6		945.2.r.b.424.34		84
45.34	even	6		315.2.r.b.214.9	yes	84
63.2	odd	6		945.2.bo.b.289.9		84
63.16	even	3	inner	315.2.bo.b.79.34	yes	84
105.44	odd	6		945.2.r.b.604.34		84
315.79	even	6	inner	315.2.bo.b.79.9	yes	84
315.254	odd	6		945.2.bo.b.289.34		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.9	✓	84	35.9	even	6
315.2.r.b.184.34	yes	84	7.2	even	3
315.2.r.b.214.9	yes	84	45.34	even	6
315.2.r.b.214.34	yes	84	9.7	even	3
315.2.bo.b.4.9	yes	84	1.1	even	1	trivial
315.2.bo.b.4.34	yes	84	5.4	even	2	inner
315.2.bo.b.79.9	yes	84	315.79	even	6	inner
315.2.bo.b.79.34	yes	84	63.16	even	3	inner
945.2.r.b.424.9		84	9.2	odd	6
945.2.r.b.424.34		84	45.29	odd	6
945.2.r.b.604.9		84	21.2	odd	6
945.2.r.b.604.34		84	105.44	odd	6
945.2.bo.b.289.9		84	63.2	odd	6
945.2.bo.b.289.34		84	315.254	odd	6
945.2.bo.b.739.9		84	15.14	odd	2
945.2.bo.b.739.34		84	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56714 - 0.904786i) q^{2} +(1.72657 + 0.137634i) q^{3} +(0.637277 + 1.10380i) q^{4} +(-0.0315838 + 2.23584i) q^{5} +(-2.58125 - 1.77787i) q^{6} +(-2.37354 - 1.16889i) q^{7} +1.31275i q^{8} +(2.96211 + 0.475270i) q^{9} +O(q^{10})\)	\(q+(-1.56714 - 0.904786i) q^{2} +(1.72657 + 0.137634i) q^{3} +(0.637277 + 1.10380i) q^{4} +(-0.0315838 + 2.23584i) q^{5} +(-2.58125 - 1.77787i) q^{6} +(-2.37354 - 1.16889i) q^{7} +1.31275i q^{8} +(2.96211 + 0.475270i) q^{9} +(2.07246 - 3.47530i) q^{10} +3.80862 q^{11} +(0.948385 + 1.99349i) q^{12} +(0.0893763 + 0.0516014i) q^{13} +(2.66207 + 3.97935i) q^{14} +(-0.362259 + 3.85600i) q^{15} +(2.46231 - 4.26485i) q^{16} +(3.29140 + 1.90029i) q^{17} +(-4.21202 - 3.42489i) q^{18} +(2.57787 + 4.46499i) q^{19} +(-2.48804 + 1.38999i) q^{20} +(-3.93722 - 2.34485i) q^{21} +(-5.96863 - 3.44599i) q^{22} +2.88075i q^{23} +(-0.180679 + 2.26656i) q^{24} +(-4.99800 - 0.141233i) q^{25} +(-0.0933765 - 0.161733i) q^{26} +(5.04890 + 1.22827i) q^{27} +(-0.222393 - 3.36481i) q^{28} +(2.69377 + 4.66574i) q^{29} +(4.05657 - 5.71511i) q^{30} +(-3.45985 - 5.99264i) q^{31} +(-5.44380 + 3.14298i) q^{32} +(6.57587 + 0.524195i) q^{33} +(-3.43871 - 5.95602i) q^{34} +(2.68841 - 5.26996i) q^{35} +(1.36309 + 3.57245i) q^{36} +(9.48307 - 5.47505i) q^{37} -9.32967i q^{38} +(0.147213 + 0.101395i) q^{39} +(-2.93510 - 0.0414616i) q^{40} +(-0.753474 + 1.30506i) q^{41} +(4.04857 + 7.23703i) q^{42} +(1.50478 - 0.868787i) q^{43} +(2.42715 + 4.20394i) q^{44} +(-1.15618 + 6.60782i) q^{45} +(2.60646 - 4.51453i) q^{46} +(-9.31264 - 5.37666i) q^{47} +(4.83835 - 7.02468i) q^{48} +(4.26741 + 5.54880i) q^{49} +(7.70477 + 4.74346i) q^{50} +(5.42129 + 3.73399i) q^{51} +0.131538i q^{52} +(-0.391152 - 0.225832i) q^{53} +(-6.80098 - 6.49304i) q^{54} +(-0.120291 + 8.51549i) q^{55} +(1.53445 - 3.11587i) q^{56} +(3.83634 + 8.06394i) q^{57} -9.74913i q^{58} +(-5.69321 - 9.86092i) q^{59} +(-4.48710 + 2.05748i) q^{60} +(-5.08990 + 8.81596i) q^{61} +12.5217i q^{62} +(-6.47517 - 4.59044i) q^{63} +1.52566 q^{64} +(-0.118196 + 0.198202i) q^{65} +(-9.83100 - 6.77124i) q^{66} +(5.13882 - 2.96690i) q^{67} +4.84404i q^{68} +(-0.396489 + 4.97383i) q^{69} +(-8.98129 + 5.82630i) q^{70} -6.43418 q^{71} +(-0.623910 + 3.88851i) q^{72} +(-13.6186 - 7.86273i) q^{73} -19.8150 q^{74} +(-8.60999 - 0.931743i) q^{75} +(-3.28563 + 5.69087i) q^{76} +(-9.03993 - 4.45184i) q^{77} +(-0.138962 - 0.292096i) q^{78} +(-1.64428 + 2.84798i) q^{79} +(9.45777 + 5.64004i) q^{80} +(8.54824 + 2.81561i) q^{81} +(2.36159 - 1.36347i) q^{82} +(-1.21389 + 0.700839i) q^{83} +(0.0791327 - 5.84020i) q^{84} +(-4.35270 + 7.29903i) q^{85} -3.14427 q^{86} +(4.00882 + 8.42650i) q^{87} +4.99977i q^{88} +(1.89392 + 3.28036i) q^{89} +(7.79056 - 9.30925i) q^{90} +(-0.151822 - 0.226949i) q^{91} +(-3.17976 + 1.83584i) q^{92} +(-5.14890 - 10.8229i) q^{93} +(9.72945 + 16.8519i) q^{94} +(-10.0645 + 5.62269i) q^{95} +(-9.83171 + 4.67734i) q^{96} +(5.26915 - 3.04215i) q^{97} +(-1.66714 - 12.5568i) q^{98} +(11.2816 + 1.81012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9}+O(q^{10}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9	\( 84 q + 44 q^{4} - 6 q^{5} + 6 q^{6} - 14 q^{9} + 6 q^{10} - 24 q^{11} - 10 q^{14} + 4 q^{15} - 36 q^{16} + 8 q^{19} - 10 q^{20} - 14 q^{21} + 18 q^{24} + 10 q^{25} - 40 q^{26} - 10 q^{29} - 28 q^{30} - 6 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} + 4 q^{39} - 8 q^{40} - 30 q^{41} - 4 q^{44} - 30 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} + 14 q^{51} + 18 q^{54} - 54 q^{55} + 48 q^{56} + 42 q^{59} + 66 q^{60} + 22 q^{61} - 28 q^{64} + 8 q^{65} - 38 q^{66} - 32 q^{69} - 26 q^{70} - 4 q^{71} - 108 q^{74} + 6 q^{75} + 24 q^{76} + 24 q^{79} - 9 q^{80} - 106 q^{81} - 64 q^{84} + q^{85} - 92 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} - 8 q^{94} - 25 q^{95} + 54 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q + 44 * q^4 - 6 * q^5 + 6 * q^6 - 14 * q^9 + 6 * q^10 - 24 * q^11 - 10 * q^14 + 4 * q^15 - 36 * q^16 + 8 * q^19 - 10 * q^20 - 14 * q^21 + 18 * q^24 + 10 * q^25 - 40 * q^26 - 10 * q^29 - 28 * q^30 - 6 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 + 4 * q^39 - 8 * q^40 - 30 * q^41 - 4 * q^44 - 30 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 + 14 * q^51 + 18 * q^54 - 54 * q^55 + 48 * q^56 + 42 * q^59 + 66 * q^60 + 22 * q^61 - 28 * q^64 + 8 * q^65 - 38 * q^66 - 32 * q^69 - 26 * q^70 - 4 * q^71 - 108 * q^74 + 6 * q^75 + 24 * q^76 + 24 * q^79 - 9 * q^80 - 106 * q^81 - 64 * q^84 + q^85 - 92 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 - 8 * q^94 - 25 * q^95 + 54 * q^96 - 102 * q^99

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