LMFDB - Embedded newform 315.2.r.b.184.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(184,315)]

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, 2]))

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

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

chi := DirichletCharacter("315.184");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.r (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			184.9
Character	$\chi$	$=$	315.184
Dual form			315.2.r.b.214.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.80957i q^{2} +(0.982481 - 1.42644i) q^{3} -1.27455 q^{4} +(-1.92051 + 1.14527i) q^{5} +(-2.58125 - 1.77787i) q^{6} +(0.174487 - 2.63999i) q^{7} -1.31275i q^{8} +(-1.06946 - 2.80290i) q^{9} +O(q^{10})$	\(q-1.80957i q^{2} +(0.982481 - 1.42644i) q^{3} -1.27455 q^{4} +(-1.92051 + 1.14527i) q^{5} +(-2.58125 - 1.77787i) q^{6} +(0.174487 - 2.63999i) q^{7} -1.31275i q^{8} +(-1.06946 - 2.80290i) q^{9} +(2.07246 + 3.47530i) q^{10} +(-1.90431 + 3.29837i) q^{11} +(-1.25222 + 1.81807i) q^{12} +(-0.0893763 - 0.0516014i) q^{13} +(-4.77726 - 0.315747i) q^{14} +(-0.253196 + 3.86470i) q^{15} -4.92462 q^{16} +(3.29140 - 1.90029i) q^{17} +(-5.07205 + 1.93527i) q^{18} +(2.57787 - 4.46499i) q^{19} +(2.44779 - 1.45971i) q^{20} +(-3.59436 - 2.84264i) q^{21} +(5.96863 + 3.44599i) q^{22} +(-2.49480 + 1.44038i) q^{23} +(-1.87256 - 1.28975i) q^{24} +(2.37669 - 4.39902i) 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} +(6.99345 + 0.458176i) q^{30} +6.91971 q^{31} +6.28596i q^{32} +(2.83397 + 5.95697i) 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} +(-8.07973 - 4.66484i) q^{38} +(-0.161417 + 0.0767925i) q^{39} +(1.50346 + 2.52114i) q^{40} +(-0.753474 + 1.30506i) q^{41} +(-5.14396 + 6.50425i) q^{42} +(-1.50478 + 0.868787i) q^{43} +(2.42715 - 4.20394i) q^{44} +(5.26400 + 4.15816i) q^{45} +(2.60646 + 4.51453i) q^{46} -10.7533i q^{47} +(-4.83835 + 7.02468i) q^{48} +(-6.93911 - 0.921290i) q^{49} +(-7.96034 - 4.30080i) q^{50} +(0.523087 - 6.56197i) q^{51} +(0.113915 + 0.0657688i) q^{52} +(-0.391152 + 0.225832i) q^{53} +(-2.22265 + 9.13634i) q^{54} +(-0.120291 - 8.51549i) q^{55} +(-3.46565 - 0.229058i) q^{56} +(-3.83634 - 8.06394i) q^{57} +(8.44299 - 4.87457i) q^{58} +11.3864 q^{59} +(0.322712 - 4.92576i) q^{60} +10.1798 q^{61} -12.5217i q^{62} +(-7.58624 + 2.33430i) q^{63} +1.52566 q^{64} +(0.230746 - 0.00325954i) q^{65} +(10.7796 - 5.12827i) q^{66} -5.93379i q^{67} +(-4.19506 + 2.42202i) q^{68} +(-0.396489 + 4.97383i) q^{69} +(9.53637 - 4.86488i) q^{70} -6.43418 q^{71} +(-3.67951 + 1.40393i) q^{72} +(-13.6186 + 7.86273i) q^{73} +(9.90750 - 17.1603i) q^{74} +(-3.93988 - 7.71216i) q^{75} +(-3.28563 + 5.69087i) q^{76} +(8.37538 + 5.60289i) q^{77} +(0.138962 + 0.292096i) q^{78} +3.28857 q^{79} +(9.45777 - 5.64004i) q^{80} +(-6.71250 + 5.99519i) q^{81} +(2.36159 + 1.36347i) q^{82} +(1.21389 - 0.700839i) q^{83} +(4.58120 + 3.62309i) q^{84} +(-4.14479 + 7.41907i) q^{85} +(1.57213 + 2.72302i) q^{86} +(9.30197 + 0.741506i) q^{87} +(4.32993 + 2.49988i) q^{88} +(1.89392 - 3.28036i) q^{89} +(7.52450 - 9.52559i) q^{90} +(-0.151822 + 0.226949i) q^{91} +(3.17976 - 1.83584i) q^{92} +(6.79848 - 9.87055i) q^{93} -19.4589 q^{94} +(0.162838 + 11.5274i) q^{95} +(8.96654 + 6.17584i) 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 - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	$ 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) $ 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	1.80957i		−	1.27956i	−0.768558	−	0.639781i	$-0.779025\pi$
$2$		−	1.80957i		−	1.27956i	0.768558	−	0.639781i	$-0.220975\pi$
$3$	0.982481	−	1.42644i	0.567236	−	0.823555i
$3$	0.982481	−	1.42644i	0.567236	−	0.823555i
$4$	−1.27455			−0.637277
$5$	−1.92051	+	1.14527i	−0.858877	+	0.512182i
$5$	−1.92051	+	1.14527i	−0.858877	+	0.512182i
$6$	−2.58125	−	1.77787i	−1.05379	−	0.725813i
$7$	0.174487	−	2.63999i	0.0659500	−	0.997823i
$7$	0.174487	−	2.63999i	0.0659500	−	0.997823i
$8$		−	1.31275i		−	0.464127i
$9$	−1.06946	−	2.80290i	−0.356487	−	0.934300i
$10$	2.07246	+	3.47530i	0.655369	+	1.09899i
$11$	−1.90431	+	3.29837i	−0.574172	+	0.994495i	0.421959	+	0.906615i	$0.361342\pi$
$11$	−1.90431	+	3.29837i	−0.574172	+	0.994495i	−0.996131	+	0.0878798i	$0.971991\pi$
$12$	−1.25222	+	1.81807i	−0.361486	+	0.524833i
$13$	−0.0893763	−	0.0516014i	−0.0247885	−	0.0143117i	0.487555	−	0.873093i	$-0.337889\pi$
$13$	−0.0893763	−	0.0516014i	−0.0247885	−	0.0143117i	−0.512343	+	0.858781i	$0.671222\pi$
$14$	−4.77726	−	0.315747i	−1.27678	−	0.0843871i
$15$	−0.253196	+	3.86470i	−0.0653749	+	0.997861i
$16$	−4.92462			−1.23116
$17$	3.29140	−	1.90029i	0.798281	−	0.460888i	−0.0445890	−	0.999005i	$-0.514198\pi$
$17$	3.29140	−	1.90029i	0.798281	−	0.460888i	0.842870	+	0.538118i	$0.180864\pi$
$18$	−5.07205	+	1.93527i	−1.19549	+	0.456147i
$19$	2.57787	−	4.46499i	0.591403	−	1.02434i	−0.402641	−	0.915358i	$-0.631908\pi$
$19$	2.57787	−	4.46499i	0.591403	−	1.02434i	0.994044	−	0.108982i	$-0.0347591\pi$
$20$	2.44779	−	1.45971i	0.547342	−	0.326402i
$21$	−3.59436	−	2.84264i	−0.784353	−	0.620314i
$22$	5.96863	+	3.44599i	1.27252	+	0.734688i
$23$	−2.49480	+	1.44038i	−0.520203	+	0.300339i	−0.737018	−	0.675874i	$-0.763767\pi$
$23$	−2.49480	+	1.44038i	−0.520203	+	0.300339i	0.216815	+	0.976213i	$0.430433\pi$
$24$	−1.87256	−	1.28975i	−0.382234	−	0.263269i
$25$	2.37669	−	4.39902i	0.475338	−	0.879803i
$26$	−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	$0.666586\pi$
$30$	6.99345	+	0.458176i	1.27682	+	0.0836512i
$31$	6.91971			1.24282			0.621408	−	0.783487i	$-0.286561\pi$
$31$	6.91971			1.24282			0.621408	+	0.783487i	$0.286561\pi$
$32$			6.28596i			1.11121i
$33$	2.83397	+	5.95697i	0.493331	+	1.03698i
$34$	−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	0.997352	+	0.0727209i	$0.0231682\pi$
$37$	9.48307	+	5.47505i	1.55901	+	0.900093i	0.561654	+	0.827372i	$0.310165\pi$
$38$	−8.07973	−	4.66484i	−1.31071	−	0.756736i
$39$	−0.161417	+	0.0767925i	−0.0258474	+	0.0122966i
$40$	1.50346	+	2.52114i	0.237718	+	0.398628i
$41$	−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	$0.204210\pi$
$42$	−5.14396	+	6.50425i	−0.793730	+	1.00363i
$43$	−1.50478	+	0.868787i	−0.229477	+	0.132489i	−0.610331	−	0.792147i	$-0.708964\pi$
$43$	−1.50478	+	0.868787i	−0.229477	+	0.132489i	0.380854	+	0.924635i	$0.375630\pi$
$44$	2.42715	−	4.20394i	0.365906	−	0.633768i
$45$	5.26400	+	4.15816i	0.784711	+	0.619862i
$46$	2.60646	+	4.51453i	0.384302	+	0.665631i
$47$		−	10.7533i		−	1.56853i	−0.620425	−	0.784266i	$-0.713040\pi$
$47$		−	10.7533i		−	1.56853i	0.620425	−	0.784266i	$-0.286960\pi$
$48$	−4.83835	+	7.02468i	−0.698355	+	1.01392i
$49$	−6.93911	−	0.921290i	−0.991301	−	0.131613i
$50$	−7.96034	−	4.30080i	−1.12576	−	0.608224i
$51$	0.523087	−	6.56197i	0.0732469	−	0.918860i
$52$	0.113915	+	0.0657688i	0.0157971	+	0.00912049i
$53$	−0.391152	+	0.225832i	−0.0537288	+	0.0310204i	−0.526624	−	0.850098i	$-0.676542\pi$
$53$	−0.391152	+	0.225832i	−0.0537288	+	0.0310204i	0.472895	+	0.881119i	$0.343209\pi$
$54$	−2.22265	+	9.13634i	−0.302465	+	1.24330i
$55$	−0.120291	−	8.51549i	−0.0162200	−	1.14823i
$56$	−3.46565	−	0.229058i	−0.463116	−	0.0306092i
$57$	−3.83634	−	8.06394i	−0.508136	−	1.06810i
$58$	8.44299	−	4.87457i	1.10862	−	0.640062i
$59$	11.3864			1.48238			0.741192	−	0.671293i	$-0.234261\pi$
$59$	11.3864			1.48238			0.741192	+	0.671293i	$0.234261\pi$
$60$	0.322712	−	4.92576i	0.0416619	−	0.635913i
$61$	10.1798			1.30339			0.651694	−	0.758482i	$-0.274058\pi$
$61$	10.1798			1.30339			0.651694	+	0.758482i	$0.274058\pi$
$62$		−	12.5217i		−	1.59026i
$63$	−7.58624	+	2.33430i	−0.955777	+	0.294094i
$64$	1.52566			0.190708
$65$	0.230746	−	0.00325954i	0.0286205	−	0.000404296i
$66$	10.7796	−	5.12827i	1.32687	−	0.631247i
$67$		−	5.93379i		−	0.724928i	−0.931998	−	0.362464i	$-0.881936\pi$
$67$		−	5.93379i		−	0.724928i	0.931998	−	0.362464i	$-0.118064\pi$
$68$	−4.19506	+	2.42202i	−0.508725	+	0.293713i
$69$	−0.396489	+	4.97383i	−0.0477316	+	0.598779i
$70$	9.53637	−	4.86488i	1.13981	−	0.581464i
$71$	−6.43418			−0.763596			−0.381798	−	0.924246i	$-0.624695\pi$
$71$	−6.43418			−0.763596			−0.381798	+	0.924246i	$0.624695\pi$
$72$	−3.67951	+	1.40393i	−0.433634	+	0.165455i
$73$	−13.6186	+	7.86273i	−1.59394	+	0.920263i	−0.601321	+	0.799008i	$0.705359\pi$
$73$	−13.6186	+	7.86273i	−1.59394	+	0.920263i	−0.992621	+	0.121255i	$0.961308\pi$
$74$	9.90750	−	17.1603i	1.15172	−	1.99484i
$75$	−3.93988	−	7.71216i	−0.454938	−	0.890523i
$76$	−3.28563	+	5.69087i	−0.376887	+	0.652788i
$77$	8.37538	+	5.60289i	0.954463	+	0.638509i
$78$	0.138962	+	0.292096i	0.0157343	+	0.0330733i
$79$	3.28857			0.369993			0.184996	−	0.982739i	$-0.440773\pi$
$79$	3.28857			0.369993			0.184996	+	0.982739i	$0.440773\pi$
$80$	9.45777	−	5.64004i	1.05741	−	0.630576i
$81$	−6.71250	+	5.99519i	−0.745834	+	0.666132i
$82$	2.36159	+	1.36347i	0.260794	+	0.150570i
$83$	1.21389	−	0.700839i	0.133242	−	0.0769271i	−0.431898	−	0.901923i	$-0.642156\pi$
$83$	1.21389	−	0.700839i	0.133242	−	0.0769271i	0.565139	+	0.824996i	$0.308822\pi$
$84$	4.58120	+	3.62309i	0.499850	+	0.395312i
$85$	−4.14479	+	7.41907i	−0.449566	+	0.804711i
$86$	1.57213	+	2.72302i	0.169528	+	0.293630i
$87$	9.30197	+	0.741506i	0.997276	+	0.0794978i
$88$	4.32993	+	2.49988i	0.461572	+	0.266489i
$89$	1.89392	−	3.28036i	0.200755	−	0.347717i	−0.748017	−	0.663679i	$-0.768994\pi$
$89$	1.89392	−	3.28036i	0.200755	−	0.347717i	0.948772	+	0.315962i	$0.102327\pi$
$90$	7.52450	−	9.52559i	0.793152	−	1.00409i
$91$	−0.151822	+	0.226949i	−0.0159153	+	0.0237907i
$92$	3.17976	−	1.83584i	0.331513	−	0.191399i
$93$	6.79848	−	9.87055i	0.704970	−	1.02353i
$94$	−19.4589			−2.00703
$95$	0.162838	+	11.5274i	0.0167068	+	1.18269i
$96$	8.96654	+	6.17584i	0.915144	+	0.630319i
$97$	−5.26915	+	3.04215i	−0.535002	+	0.308883i	−0.743051	−	0.669235i	$-0.766622\pi$
$97$	−5.26915	+	3.04215i	−0.535002	+	0.308883i	0.208049	+	0.978118i	$0.433289\pi$
$98$	−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
$101$	3.42253	−	5.92799i	0.340554	−	0.589857i	−0.643982	−	0.765041i	$-0.722719\pi$
$101$	3.42253	−	5.92799i	0.340554	−	0.589857i	0.984536	+	0.175184i	$0.0560520\pi$
$102$	−11.8744	−	0.946565i	−1.17574	−	0.0937239i
$103$	−2.59716	+	1.49947i	−0.255906	+	0.147747i	−0.622466	−	0.782647i	$-0.713869\pi$
$103$	−2.59716	+	1.49947i	−0.255906	+	0.147747i	0.366560	+	0.930395i	$0.380536\pi$
$104$	−0.0677397	+	0.117329i	−0.00664243	+	0.0115050i
$105$	10.1586	+	1.34278i	0.991377	+	0.131041i
$106$	0.408659	+	0.707818i	0.0396925	+	0.0687493i
$107$	−4.04654	−	2.33627i	−0.391194	−	0.225856i	0.291483	−	0.956576i	$-0.405851\pi$
$107$	−4.04654	−	2.33627i	−0.391194	−	0.225856i	−0.682677	+	0.730720i	$0.739184\pi$
$108$	6.43508	+	1.56550i	0.619216	+	0.150640i
$109$	4.25733	+	7.37392i	0.407779	+	0.706293i	0.994640	−	0.103394i	$-0.0329702\pi$
$109$	4.25733	+	7.37392i	0.407779	+	0.706293i	−0.586862	+	0.809687i	$0.699637\pi$
$110$	−15.4094	+	0.217675i	−1.46923	+	0.0207545i
$111$	17.1268	−	8.14789i	1.62560	−	0.773364i
$112$	−0.859284	+	13.0010i	−0.0811947	+	1.22847i
$113$	−3.29067	−	1.89987i	−0.309560	−	0.178724i	0.337170	−	0.941444i	$-0.390530\pi$
$113$	−3.29067	−	1.89987i	−0.309560	−	0.178724i	−0.646729	+	0.762719i	$0.723864\pi$
$114$	−14.5923	+	6.94214i	−1.36669	+	0.650191i
$115$	3.14166	−	5.62349i	0.292961	−	0.524393i
$116$	−3.43335	−	5.94673i	−0.318778	−	0.552140i
$117$	−0.0490492	+	0.305699i	−0.00453460	+	0.0282619i
$118$		−	20.6045i		−	1.89680i
$119$	−4.44244	−	9.02083i	−0.407238	−	0.826938i
$120$	5.07338	+	0.332383i	0.463134	+	0.0303422i
$121$	−1.75281	−	3.03595i	−0.159346	−	0.275996i
$122$		−	18.4211i		−	1.66777i
$123$	1.12131	+	2.35698i	0.101105	+	0.212521i
$124$	−8.81953			−0.792018
$125$	0.473631	+	11.1703i	0.0423629	+	0.999102i
$126$	4.22408	+	13.7279i	0.376311	+	1.22297i
$127$			14.2403i			1.26362i	0.775123	+	0.631811i	$0.217688\pi$
$127$			14.2403i			1.26362i	−0.775123	+	0.631811i	$0.782312\pi$
$128$			9.81113i			0.867189i
$129$	−0.239149	+	3.00005i	−0.0210559	+	0.264140i
$130$	−0.00589838	−	0.417551i	−0.000517322	−	0.0366216i
$131$	−5.72317	−	9.91282i	−0.500036	−	0.866087i	−1.00000		4.12152e-5i	$-0.999987\pi$
$131$	−5.72317	−	9.91282i	−0.500036	−	0.866087i	0.499964	−	0.866046i	$-0.333346\pi$
$132$	−3.61204	−	7.59247i	−0.314388	−	0.660840i
$133$	−11.3377	−	7.58463i	−0.983107	−	0.657671i
$134$	−10.7376			−0.927590
$135$	11.1031	−	3.42346i	0.955607	−	0.294645i
$136$	−2.49460	−	4.32078i	−0.213910	−	0.370503i
$137$	5.64750	+	3.26059i	0.482499	+	0.278571i	0.721457	−	0.692459i	$-0.243473\pi$
$137$	5.64750	+	3.26059i	0.482499	+	0.278571i	−0.238958	+	0.971030i	$0.576806\pi$
$138$	9.00051	+	0.717475i	0.766174	+	0.0610755i
$139$	−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	$0.287949\pi$
$140$	−3.42652	−	6.71684i	−0.289594	−	0.567677i
$141$	−15.3390	−	10.5649i	−1.29177	−	0.889727i
$142$			11.6431i			0.977068i
$143$	0.340401	−	0.196530i	0.0284657	−	0.0164347i
$144$	5.26669	+	13.8032i	0.438891	+	1.15027i
$145$	−10.5169	−	5.87548i	−0.873385	−	0.487932i
$146$	14.2282	+	24.6439i	1.17753	+	2.03955i
$147$	−8.13171	+	8.99307i	−0.670692	+	0.741736i
$148$	−12.0867	−	6.97824i	−0.993518	−	0.573608i
$149$	5.56659	+	9.64162i	0.456033	+	0.789872i	0.998747	−	0.0500453i	$-0.0159366\pi$
$149$	5.56659	+	9.64162i	0.456033	+	0.789872i	−0.542714	+	0.839918i	$0.682603\pi$
$150$	−13.9557	+	7.12949i	−1.13948	+	0.582121i
$151$	−4.64367	+	8.04308i	−0.377897	+	0.654537i	−0.990756	−	0.135656i	$-0.956686\pi$
$151$	−4.64367	+	8.04308i	−0.377897	+	0.654537i	0.612859	+	0.790192i	$0.290019\pi$
$152$	−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
$155$	−13.2893	+	7.92497i	−1.06743	+	0.636549i
$156$	0.205734	−	0.0978761i	0.0164719	−	0.00783636i
$157$		−	7.88839i		−	0.629562i	−0.949164	−	0.314781i	$-0.898069\pi$
$157$		−	7.88839i		−	0.629562i	0.949164	−	0.314781i	$-0.101931\pi$
$158$		−	5.95090i		−	0.473429i
$159$	−0.0621641	+	0.779830i	−0.00492993	+	0.0618445i
$160$	−7.19915	−	12.0722i	−0.569143	−	0.954393i
$161$	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	0.858456	−	0.512888i	$-0.171424\pi$
$163$	10.7692	+	6.21761i	0.843510	+	0.487001i	−0.0149459	+	0.999888i	$0.504758\pi$
$164$	0.960342	−	1.66336i	0.0749901	−	0.129887i
$165$	−12.2650	−	8.19472i	−0.954831	−	0.637958i
$166$	−1.26822	−	2.19662i	−0.0984329	−	0.170491i
$167$	15.9568	+	9.21266i	1.23477	+	0.712897i	0.968021	−	0.250868i	$-0.0807159\pi$
$167$	15.9568	+	9.21266i	1.23477	+	0.712897i	0.266753	+	0.963765i	$0.414049\pi$
$168$	−3.73167	+	4.71849i	−0.287905	+	0.364039i
$169$	−6.49467	−	11.2491i	−0.499590	−	0.865316i
$170$	13.4253	+	7.50031i	1.02968	+	0.575247i
$171$	−15.2719	−	2.45036i	−1.16787	−	0.187384i
$172$	1.91793	−	1.10732i	0.146241	−	0.0844320i
$173$			18.7206i			1.42330i	0.702532	+	0.711652i	$0.252053\pi$
$173$			18.7206i			1.42330i	−0.702532	+	0.711652i	$0.747947\pi$
$174$	1.34181	−	16.8326i	0.101722	−	1.27608i
$175$	−11.1987	−	7.04202i	−0.846539	−	0.532326i
$176$	9.37801	−	16.2432i	0.706894	−	1.22438i
$177$	11.1869	−	16.2420i	0.840862	−	1.22083i
$178$	−5.93605	−	3.42718i	−0.444925	−	0.256878i
$179$	4.80576	+	8.32382i	0.359199	+	0.622152i	0.987827	−	0.155555i	$-0.0497165\pi$
$179$	4.80576	+	8.32382i	0.359199	+	0.622152i	−0.628628	+	0.777706i	$0.716383\pi$
$180$	−6.70925	−	5.29980i	−0.500078	−	0.395024i
$181$	−14.1492			−1.05170			−0.525851	−	0.850577i	$-0.676253\pi$
$181$	−14.1492			−1.05170			−0.525851	+	0.850577i	$0.676253\pi$
$182$	0.410680	+	0.274734i	0.0304417	+	0.0203646i
$183$	10.0015	−	14.5209i	0.739329	−	1.07341i
$184$	1.89085	+	3.27505i	0.139395	+	0.241440i
$185$	−24.4827	+	0.345846i	−1.80001	+	0.0254271i
$186$	−17.8615	−	12.3023i	−1.30967	−	0.902052i
$187$			14.4750i			1.05851i
$188$			13.7057i			0.999588i
$189$	−4.12360	+	13.1147i	−0.299948	+	0.953956i
$190$	20.8597	−	0.294667i	1.51332	−	0.0213774i
$191$	−18.2544			−1.32084			−0.660420	−	0.750897i	$-0.729622\pi$
$191$	−18.2544			−1.32084			−0.660420	+	0.750897i	$0.729622\pi$
$192$	1.49893	−	2.17626i	0.108176	−	0.157058i
$193$			18.7774i			1.35162i	0.737074	+	0.675812i	$0.236207\pi$
$193$			18.7774i			1.35162i	−0.737074	+	0.675812i	$0.763793\pi$
$194$	5.50499	+	9.53492i	0.395235	+	0.684567i
$195$	0.222054	−	0.332347i	0.0159016	−	0.0237999i
$196$	8.84426	+	1.17423i	0.631733	+	0.0838738i
$197$			5.62033i			0.400432i	0.979752	+	0.200216i	$0.0641644\pi$
$197$			5.62033i			0.400432i	−0.979752	+	0.200216i	$0.935836\pi$
$198$	3.27555	−	20.4148i	0.232783	−	1.45082i
$199$	8.68092	+	15.0358i	0.615374	+	1.06586i	0.990319	+	0.138812i	$0.0443283\pi$
$199$	8.68092	+	15.0358i	0.615374	+	1.06586i	−0.374945	+	0.927047i	$0.622338\pi$
$200$	−5.77480	−	3.12000i	−0.408340	−	0.220617i
$201$	−8.46420	−	5.82984i	−0.597019	−	0.411205i
$202$	−10.7271	−	6.19331i	−0.754758	−	0.435760i
$203$	12.7875	−	6.29741i	0.897509	−	0.441991i
$204$	−0.666703	+	8.36358i	−0.0466785	+	0.585568i
$205$	−0.0475952	−	3.36930i	−0.00332419	−	0.235322i
$206$	2.71340	+	4.69975i	0.189052	+	0.327447i
$207$	6.70533	+	5.45226i	0.466053	+	0.378958i
$208$	0.440144	+	0.254117i	0.0305185	+	0.0176199i
$209$	9.81812	+	17.0055i	0.679134	+	1.17629i
$210$	2.42985	−	18.3827i	0.167676	−	1.26853i
$211$	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	$0.0477318\pi$
$212$	0.498544	−	0.287834i	0.0342401	−	0.0197685i
$213$	−6.32146	+	9.17796i	−0.433139	+	0.628864i
$214$	−4.22765	+	7.32251i	−0.288996	+	0.500556i
$215$	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
$219$	−2.16435	+	27.1512i	−0.146253	+	1.83471i
$220$	0.153317	+	10.8534i	0.0103366	+	0.731739i
$221$	−0.392230			−0.0263843
$222$	−14.7442	−	30.9921i	−0.989566	−	2.08006i
$223$	15.0973	−	8.71644i	1.01099	−	0.583696i	0.0995091	−	0.995037i	$-0.468273\pi$
$223$	15.0973	−	8.71644i	1.01099	−	0.583696i	0.911482	+	0.411341i	$0.134939\pi$
$224$	16.5949	+	1.09682i	1.10879	+	0.0732844i
$225$	−14.8718	−	1.95705i	−0.991452	−	0.130470i
$226$	−3.43795	+	5.95470i	−0.228689	+	0.396101i
$227$	−2.46036	−	1.42049i	−0.163300	−	0.0942811i	0.416123	−	0.909308i	$-0.363389\pi$
$227$	−2.46036	−	1.42049i	−0.163300	−	0.0942811i	−0.579423	+	0.815027i	$0.696722\pi$
$228$	4.88962	+	10.2779i	0.323823	+	0.680672i
$229$	−9.46378	−	16.3918i	−0.625384	−	1.08320i	−0.988466	−	0.151440i	$-0.951609\pi$
$229$	−9.46378	−	16.3918i	−0.625384	−	1.08320i	0.363082	−	0.931757i	$-0.381724\pi$
$230$	−10.1761	−	5.68507i	−0.670993	−	0.374862i
$231$	16.2208	−	6.44224i	1.06725	−	0.423868i
$232$	6.12495	−	3.53624i	0.402122	−	0.232165i
$233$	−12.0455	−	6.95446i	−0.789126	−	0.455602i	0.0505291	−	0.998723i	$-0.483909\pi$
$233$	−12.0455	−	6.95446i	−0.789126	−	0.455602i	−0.839655	+	0.543121i	$0.817243\pi$
$234$	0.553184	+	0.0887581i	0.0361628	+	0.00580230i
$235$	12.3155	+	20.6518i	0.803375	+	1.34718i
$236$	−14.5126			−0.944689
$237$	3.23096	−	4.69095i	0.209873	−	0.304710i
$238$	−16.3238	+	8.03891i	−1.05812	+	0.521085i
$239$	−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	$0.180847\pi$
$240$	1.24689	−	19.0322i	0.0804866	−	1.22852i
$241$	4.06003	−	7.03218i	0.261530	−	0.452982i	−0.705119	−	0.709089i	$-0.749106\pi$
$241$	4.06003	−	7.03218i	0.261530	−	0.452982i	0.966649	+	0.256107i	$0.0824398\pi$
$242$	−5.49378	+	3.17184i	−0.353154	+	0.203893i
$243$	1.95687	+	15.4651i	0.125533	+	0.992089i
$244$	−12.9747			−0.830619
$245$	14.3817	−	6.17784i	0.918815	−	0.394688i
$246$	4.26512	−	2.02909i	0.271934	−	0.129370i
$247$	−0.460800	+	0.266043i	−0.0293200	+	0.0169279i
$248$		−	9.08384i		−	0.576824i
$249$	0.192918	−	2.42010i	0.0122257	−	0.153368i
$250$	20.2135	−	0.857070i	1.27841	−	0.0542059i
$251$	0.219929			0.0138818			0.00694089	−	0.999976i	$-0.497791\pi$
$251$	0.219929			0.0138818			0.00694089	+	0.999976i	$0.497791\pi$
$252$	9.66907	−	2.97519i	0.609094	−	0.187419i
$253$		−	10.9717i		−	0.689785i
$254$	25.7688			1.61688
$255$	6.51067	+	13.2014i	0.407714	+	0.826703i
$256$	20.8053			1.30033
$257$	3.59280	−	2.07430i	0.224113	−	0.129391i	−0.383740	−	0.923441i	$-0.625364\pi$
$257$	3.59280	−	2.07430i	0.224113	−	0.129391i	0.607853	+	0.794050i	$0.292031\pi$
$258$	5.42881	+	0.432757i	0.337983	+	0.0269423i
$259$	16.1088	−	24.0799i	1.00095	−	1.49625i
$260$	−0.294098	+	0.00415446i	−0.0182392	+	0.000257649i
$261$	10.1967	−	12.5402i	0.631161	−	0.776218i
$262$	−17.9380	+	10.3565i	−1.10821	+	0.639826i
$263$	0.109417	+	0.0631719i	0.00674694	+	0.00389535i	0.503370	−	0.864071i	$-0.332093\pi$
$263$	0.109417	+	0.0631719i	0.00674694	+	0.00389535i	−0.496623	+	0.867967i	$0.665427\pi$
$264$	7.82000	−	3.72029i	0.481288	−	0.228968i
$265$	0.492571	−	0.881688i	0.0302584	−	0.0541616i
$266$	−13.7249	+	20.5165i	−0.841530	+	1.25795i
$267$	−2.81850	−	5.92445i	−0.172489	−	0.362570i
$268$			7.56293i			0.461980i
$269$	−7.56255	−	13.0987i	−0.461097	−	0.798643i	0.537919	−	0.842996i	$-0.319210\pi$
$269$	−7.56255	−	13.0987i	−0.461097	−	0.798643i	−0.999016	+	0.0443537i	$0.985877\pi$
$270$	−6.19500	−	20.0920i	−0.377016	−	1.22276i
$271$	1.27405	−	2.20671i	0.0773928	−	0.134048i	−0.824732	−	0.565524i	$-0.808674\pi$
$271$	1.27405	−	2.20671i	0.0773928	−	0.134048i	0.902124	+	0.431476i	$0.142007\pi$
$272$	−16.2089	+	9.35820i	−0.982807	+	0.567424i
$273$	0.174566	+	0.439538i	0.0105652	+	0.0266021i
$274$	5.90027	−	10.2196i	0.356448	−	0.617387i
$275$	9.98360	+	16.2163i	0.602034	+	0.977879i
$276$	0.505346	−	6.33941i	0.0304182	−	0.381588i
$277$	−21.7045	−	12.5311i	−1.30410	−	0.752922i	−0.322994	−	0.946401i	$-0.604689\pi$
$277$	−21.7045	−	12.5311i	−1.30410	−	0.752922i	−0.981104	+	0.193479i	$0.938023\pi$
$278$	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	$-0.348528\pi$
$282$	−19.1180	+	27.7570i	−1.13846	+	1.65290i
$283$		−	9.91599i		−	0.589444i	−0.955583	−	0.294722i	$-0.904773\pi$
$283$		−	9.91599i		−	0.589444i	0.955583	−	0.294722i	$-0.0952271\pi$
$284$	8.20070			0.486622
$285$	16.6032	+	11.0932i	0.983486	+	0.657104i
$286$	−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
$290$	−10.6321	+	19.0312i	−0.624339	+	1.11755i
$291$	−0.837404	+	10.5050i	−0.0490895	+	0.615813i
$292$	17.3577	−	10.0215i	1.01578	−	0.586462i
$293$	5.08585	+	2.93631i	0.297118	+	0.171541i	0.641148	−	0.767418i	$-0.278459\pi$
$293$	5.08585	+	2.93631i	0.297118	+	0.171541i	−0.344029	+	0.938959i	$0.611792\pi$
$294$	16.2736	+	14.7149i	0.949096	+	0.858191i
$295$	−21.8677	+	13.0406i	−1.27319	+	0.759252i
$296$	7.18737	−	12.4489i	0.417757	−	0.723577i
$297$	13.6660	−	14.3141i	0.792980	−	0.830587i
$298$	17.4472	−	10.0732i	1.01069	−	0.583522i
$299$	0.297302			0.0171934
$300$	5.02158	+	9.82955i	0.289921	+	0.567510i
$301$	2.03102	+	4.12421i	0.117066	+	0.237715i
$302$	14.5545	+	8.40307i	0.837520	+	0.483542i
$303$	−5.09335	−	10.7062i	−0.292606	−	0.615053i
$304$	−12.6950	+	21.9884i	−0.728109	+	1.26112i
$305$	−19.5504	+	11.6587i	−1.11945	+	0.667573i
$306$	−13.0166	+	16.0081i	−0.744107	+	0.915122i
$307$			3.17751i			0.181350i	0.995881	+	0.0906751i	$0.0289025\pi$
$307$			3.17751i			0.181350i	−0.995881	+	0.0906751i	$0.971098\pi$
$308$	−10.6749	−	7.14118i	−0.608257	−	0.406907i
$309$	−0.412756	+	5.17790i	−0.0234809	+	0.294560i
$310$	14.3408	+	24.0480i	0.814503	+	1.36584i
$311$	5.79420			0.328559			0.164280	−	0.986414i	$-0.447470\pi$
$311$	5.79420			0.328559			0.164280	+	0.986414i	$0.447470\pi$
$312$	0.100809	+	0.211900i	0.00570720	+	0.0119965i
$313$			16.4715i			0.931024i	0.885041	+	0.465512i	$0.154130\pi$
$313$			16.4715i			0.931024i	−0.885041	+	0.465512i	$0.845870\pi$
$314$	−14.2746			−0.805563
$315$	11.8960	−	13.1714i	0.670264	−	0.742122i
$316$	−4.19146			−0.235788
$317$			26.1515i			1.46881i	0.678710	+	0.734406i	$0.262539\pi$
$317$			26.1515i			1.46881i	−0.678710	+	0.734406i	$0.737461\pi$
$318$	1.41116	+	0.112490i	0.0791339	+	0.00630815i
$319$	−20.5191			−1.14885
$320$	−2.93004	+	1.74730i	−0.163794	+	0.0976771i
$321$	−7.30820	+	3.47680i	−0.407904	+	0.194056i
$322$	12.3731	−	6.09332i	0.689527	−	0.339567i
$323$		−	19.5947i		−	1.09028i
$324$	8.55544	−	7.64119i	0.475302	−	0.424510i
$325$	−0.439415	+	0.270527i	−0.0243744	+	0.0150061i
$326$	11.2512	−	19.4877i	0.623147	−	1.07932i
$327$	14.7012	+	1.17191i	0.812978	+	0.0648065i
$328$	1.71321	+	0.989122i	0.0945962	+	0.0546151i
$329$	−28.3887	−	1.87632i	−1.56512	−	0.103445i
$330$	−14.8289	+	22.1944i	−0.816307	+	1.22176i
$331$	−15.5253			−0.853345			−0.426673	−	0.904406i	$-0.640314\pi$
$331$	−15.5253			−0.853345			−0.426673	+	0.904406i	$0.640314\pi$
$332$	−1.54717	+	0.893257i	−0.0849118	+	0.0490238i
$333$	5.20425	−	32.4355i	0.285191	−	1.77745i
$334$	16.6710	−	28.8750i	0.912196	−	1.57997i
$335$	6.79582	+	11.3959i	0.371296	+	0.622624i
$336$	17.7009	+	13.9989i	0.965661	+	0.763703i
$337$	−10.6550	−	6.15165i	−0.580413	−	0.335102i	0.180884	−	0.983504i	$-0.442104\pi$
$337$	−10.6550	−	6.15165i	−0.580413	−	0.335102i	−0.761298	+	0.648403i	$0.775437\pi$
$338$	−20.3561	+	11.7526i	−1.10722	+	0.639256i
$339$	−5.94306	+	2.82735i	−0.322783	+	0.153561i
$340$	5.28276	−	9.45599i	0.286498	−	0.512823i
$341$	−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
$345$	−4.93494	−	10.0064i	−0.265688	−	0.538724i
$346$	33.8764			1.82121
$347$		−	29.4257i		−	1.57965i	−0.613331	−	0.789826i	$-0.710171\pi$
$347$		−	29.4257i		−	1.57965i	0.613331	−	0.789826i	$-0.289829\pi$
$348$	−11.8559	−	0.945089i	−0.635541	−	0.0506621i
$349$	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
$353$	24.7032	+	14.2624i	1.31482	+	0.759111i	0.982890	−	0.184193i	$-0.0589673\pi$
$353$	24.7032	+	14.2624i	1.31482	+	0.759111i	0.331929	+	0.943304i	$0.392301\pi$
$354$	−29.3911	−	20.2436i	−1.56212	−	1.07593i
$355$	12.3569	−	7.36890i	0.655835	−	0.391101i
$356$	−2.41390	+	4.18099i	−0.127936	+	0.221592i
$357$	−17.2323	−	2.52593i	−0.912029	−	0.133686i
$358$	15.0626	−	8.69637i	0.796081	−	0.459618i
$359$	15.2317	−	26.3821i	0.803898	−	1.39239i	−0.113134	−	0.993580i	$-0.536089\pi$
$359$	15.2317	−	26.3821i	0.803898	−	1.39239i	0.917032	−	0.398813i	$-0.130578\pi$
$360$	5.45862	−	6.91031i	0.287695	−	0.364205i
$361$	−3.79078	−	6.56583i	−0.199515	−	0.345570i
$362$			25.6040i			1.34572i
$363$	−6.05271	−	0.482491i	−0.317685	−	0.0253242i
$364$	0.193506	−	0.289258i	0.0101425	−	0.0151613i
$365$	17.1497	−	30.6975i	0.897657	−	1.60678i
$366$	−26.2766	−	18.0984i	−1.37350	−	0.946016i
$367$	15.5354	+	8.96934i	0.810939	+	0.468196i	0.847282	−	0.531144i	$-0.178238\pi$
$367$	15.5354	+	8.96934i	0.810939	+	0.468196i	−0.0363431	+	0.999339i	$0.511571\pi$
$368$	12.2860	−	7.09331i	0.640450	−	0.369764i
$369$	4.46375	+	0.716206i	0.232374	+	0.0372842i
$370$	0.625834	+	44.3033i	0.0325355	+	2.30322i
$371$	0.527943	+	1.07204i	0.0274094	+	0.0556577i
$372$	−8.66503	+	12.5805i	−0.449261	+	0.652270i
$373$	−6.69345	+	3.86446i	−0.346574	+	0.200094i	−0.663175	−	0.748464i	$-0.730792\pi$
$373$	−6.69345	+	3.86446i	−0.346574	+	0.200094i	0.316601	+	0.948559i	$0.397458\pi$
$374$	26.1935			1.35443
$375$	16.3991	+	10.2990i	0.846846	+	0.531838i
$376$	−14.1164			−0.727998
$377$		−	0.556009i		−	0.0286359i
$378$	23.7320	+	7.46196i	1.22064	+	0.383802i
$379$	−3.74284			−0.192257			−0.0961284	−	0.995369i	$-0.530646\pi$
$379$	−3.74284			−0.192257			−0.0961284	+	0.995369i	$0.530646\pi$
$380$	−0.207545	−	14.6923i	−0.0106468	−	0.753699i
$381$	20.3129	+	13.9908i	1.04066	+	0.716771i
$382$			33.0326i			1.69009i
$383$	13.1238	−	7.57705i	0.670597	−	0.387169i	−0.125706	−	0.992068i	$-0.540120\pi$
$383$	13.1238	−	7.57705i	0.670597	−	0.387169i	0.796303	+	0.604898i	$0.206786\pi$
$384$	13.9950	+	9.63925i	0.714178	+	0.491901i
$385$	−22.5018	−	1.16828i	−1.14680	−	0.0595410i
$386$	33.9790			1.72949
$387$	4.04443	+	3.28862i	0.205590	+	0.167170i
$388$	6.71582	−	3.87738i	0.340944	−	0.196844i
$389$	14.6164	−	25.3164i	0.741081	−	1.28359i	−0.210922	−	0.977503i	$-0.567647\pi$
$389$	14.6164	−	25.3164i	0.741081	−	1.28359i	0.952003	−	0.306087i	$-0.0990200\pi$
$390$	−0.601406	−	0.401822i	−0.0304534	−	0.0203471i
$391$	−5.47426	+	9.48169i	−0.276845	+	0.479510i
$392$	−1.20942	+	9.10931i	−0.0610851	+	0.460090i
$393$	−19.7630	−	1.57540i	−0.996909	−	0.0794685i
$394$	10.1704			0.512377
$395$	−6.31572	+	3.76632i	−0.317778	+	0.189504i
$396$	−14.3790	−	2.30710i	−0.722570	−	0.115936i
$397$	−15.7263	−	9.07960i	−0.789282	−	0.455692i	0.0504279	−	0.998728i	$-0.483941\pi$
$397$	−15.7263	−	9.07960i	−0.789282	−	0.455692i	−0.839710	+	0.543036i	$0.817275\pi$
$398$	27.2084	−	15.7088i	1.36383	−	0.787409i
$399$	−21.9581	+	8.72085i	−1.09928	+	0.436589i
$400$	−11.7043	+	21.6635i	−0.585215	+	1.08317i
$401$	9.45454	+	16.3757i	0.472137	+	0.817766i	0.999492	−	0.0318798i	$-0.0101494\pi$
$401$	9.45454	+	16.3757i	0.472137	+	0.817766i	−0.527355	+	0.849645i	$0.676816\pi$
$402$	−10.5495	+	15.3166i	−0.526162	+	0.763922i
$403$	−0.618458	−	0.357067i	−0.0308076	−	0.0177868i
$404$	−4.36219	+	7.55554i	−0.217027	+	0.375902i
$405$	6.02527	−	19.2015i	0.299398	−	0.954128i
$406$	−11.3956	−	23.1400i	−0.565555	−	1.14842i
$407$	−36.1174	+	20.8524i	−1.79028	+	1.03362i
$408$	−8.61423	−	0.686682i	−0.426468	−	0.0339958i
$409$	−23.4905			−1.16153			−0.580765	−	0.814072i	$-0.697246\pi$
$409$	−23.4905			−1.16153			−0.580765	+	0.814072i	$0.697246\pi$
$410$	−6.09700	+	0.0861269i	−0.301109	+	0.00425350i
$411$	10.1996	−	4.85236i	0.503109	−	0.239349i
$412$	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
$416$	0.324365	−	0.561816i	0.0159033	−	0.0275453i
$417$	6.52457	+	13.7146i	0.319509	+	0.671605i
$418$	30.7727	−	17.7666i	1.50514	−	0.868993i
$419$	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	$-0.0740568\pi$
$420$	−12.9477	−	1.71144i	−0.631781	−	0.0835097i
$421$	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
$423$	−30.1405	+	11.5003i	−1.46548	+	0.559161i
$424$	0.296460	+	0.513484i	0.0143974	+	0.0249370i
$425$	−0.536767	−	18.9953i	−0.0260370	−	0.921407i
$426$	16.6082	+	11.4391i	0.804670	+	0.554228i
$427$	1.77624	−	26.8746i	0.0859585	−	1.30055i
$428$	5.15753	+	2.97770i	0.249299	+	0.143933i
$429$	0.0540984	−	0.678649i	0.00261190	−	0.0327655i
$430$	−6.13789	−	3.42904i	−0.295995	−	0.165363i
$431$	1.30398	+	2.25856i	0.0628105	+	0.108791i	0.895721	−	0.444617i	$-0.146660\pi$
$431$	1.30398	+	2.25856i	0.0628105	+	0.108791i	−0.832910	+	0.553408i	$0.813327\pi$
$432$	24.8639	+	6.04879i	1.19626	+	0.291022i
$433$			0.0636994i			0.00306120i	0.999999	+	0.00153060i	$0.000487205\pi$
$433$			0.0636994i			0.00306120i	−0.999999	+	0.00153060i	$0.999513\pi$
$434$	−33.0572	−	2.18488i	−1.58680	−	0.104878i
$435$	−18.7137	+	9.22925i	−0.897254	+	0.442509i
$436$	−5.42620	−	9.39845i	−0.259868	−	0.450104i
$437$			14.8524i			0.710486i
$438$	49.1320	+	3.91655i	2.34762	+	0.187140i
$439$	−15.4026			−0.735125			−0.367562	−	0.929999i	$-0.619808\pi$
$439$	−15.4026			−0.735125			−0.367562	+	0.929999i	$0.619808\pi$
$440$	−11.1787	+	0.157912i	−0.532924	+	0.00752815i
$441$	4.83882	+	20.4349i	0.230420	+	0.973091i
$442$			0.709769i			0.0337603i
$443$		−	29.6148i		−	1.40704i	−0.710675	−	0.703521i	$-0.751610\pi$
$443$		−	29.6148i		−	1.40704i	0.710675	−	0.703521i	$-0.248390\pi$
$444$	−21.8290	+	10.3849i	−1.03596	+	0.492846i
$445$	0.119634	+	8.46900i	0.00567120	+	0.401469i
$446$	−15.7730	−	27.3197i	−0.746874	−	1.29362i
$447$	19.2223	+	1.53230i	0.909182	+	0.0724754i
$448$	0.266208	−	4.02773i	0.0125772	−	0.190292i
$449$	−39.1113			−1.84578			−0.922888	−	0.385069i	$-0.874178\pi$
$449$	−39.1113			−1.84578			−0.922888	+	0.385069i	$0.874178\pi$
$450$	−3.54143	+	26.9116i	−0.166944	+	1.26862i
$451$	−2.86970	−	4.97046i	−0.135129	−	0.234050i
$452$	4.19413	+	2.42148i	0.197275	+	0.113897i
$453$	6.91065	+	14.5261i	0.324691	+	0.682496i
$454$	−2.57048	+	4.45219i	−0.120638	+	0.208952i
$455$	0.0316570	−	0.609735i	0.00148410	−	0.0285848i
$456$	−10.5859	+	5.03615i	−0.495732	+	0.235840i
$457$		−	28.4237i		−	1.32961i	−0.747018	−	0.664803i	$-0.768515\pi$
$457$		−	28.4237i		−	1.32961i	0.747018	−	0.664803i	$-0.231485\pi$
$458$	−29.6621	+	17.1254i	−1.38602	+	0.800217i
$459$	−18.9520	+	5.55162i	−0.884603	+	0.259127i
$460$	−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	$0.723619\pi$
$462$	−11.6577	−	29.3528i	−0.542365	−	1.36562i
$463$	29.2347	+	16.8786i	1.35865	+	0.784417i	0.989442	−	0.144930i	$-0.0462958\pi$
$463$	29.2347	+	16.8786i	1.35865	+	0.784417i	0.369208	+	0.929347i	$0.379629\pi$
$464$	−13.2658	−	22.9770i	−0.615848	−	1.06668i
$465$	−1.75204	+	26.7426i	−0.0812490	+	1.24016i
$466$	−12.5846	+	21.7972i	−0.582970	+	1.00973i
$467$	−34.3450	−	19.8291i	−1.58930	−	0.917581i	−0.993423	−	0.114503i	$-0.963472\pi$
$467$	−34.3450	−	19.8291i	−1.58930	−	0.917581i	−0.595874	−	0.803078i	$-0.703194\pi$
$468$	0.0625158	−	0.389629i	0.00288979	−	0.0180106i
$469$	−15.6652	−	1.03537i	−0.723350	−	0.0478090i
$470$	37.3709	−	22.2858i	1.72379	−	1.02797i
$471$	−11.2523	−	7.75020i	−0.518479	−	0.357110i
$472$		−	14.9475i		−	0.688015i
$473$		−	6.61777i		−	0.304285i
$474$	−8.48861	−	5.84665i	−0.389895	−	0.268546i
$475$	−13.5148	−	21.9520i	−0.620101	−	1.00723i
$476$	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
$479$	7.88753	−	13.6616i	0.360390	−	0.624214i	−0.627635	−	0.778508i	$-0.715977\pi$
$479$	7.88753	−	13.6616i	0.360390	−	0.624214i	0.988025	+	0.154294i	$0.0493102\pi$
$480$	−24.2933	−	1.59158i	−1.10883	−	0.0726453i
$481$	−0.565041	−	0.978680i	−0.0257637	−	0.0446240i
$482$	−12.7252	−	7.34692i	−0.579619	−	0.334643i
$483$	13.0617	+	1.91460i	0.594327	+	0.0871172i
$484$	2.23405	+	3.86949i	0.101548	+	0.175886i
$485$	6.63535	−	11.8771i	0.301296	−	0.539311i
$486$	27.9853	−	3.54109i	1.26944	−	0.160627i
$487$	33.3922	−	19.2790i	1.51315	−	0.873615i	0.513264	−	0.858231i	$-0.328436\pi$
$487$	33.3922	−	19.2790i	1.51315	−	0.873615i	0.999882	−	0.0153837i	$-0.00489698\pi$
$488$		−	13.3635i		−	0.604938i
$489$	19.4496	−	9.25295i	0.879541	−	0.418433i
$490$	−11.1793	−	26.0248i	−0.505027	−	1.17568i
$491$	−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	$0.234228\pi$
$492$	−1.42917	−	3.00409i	−0.0644318	−	0.135435i
$493$	17.7325	+	10.2379i	0.798631	+	0.461090i
$494$	0.481424	+	0.833852i	0.0216603	+	0.0375168i
$495$	−23.7394	+	9.44416i	−1.06701	+	0.424483i
$496$	−34.0769			−1.53010
$497$	−1.12268	+	16.9862i	−0.0503592	+	0.761934i
$498$	−4.37935	−	0.349100i	−0.196243	−	0.0156435i
$499$	−6.92309	−	11.9911i	−0.309920	−	0.536797i	0.668424	−	0.743780i	$-0.266969\pi$
$499$	−6.92309	−	11.9911i	−0.309920	−	0.536797i	−0.978345	+	0.206983i	$0.933636\pi$
$500$	−0.603668	−	14.2371i	−0.0269969	−	0.636704i
$501$	28.8186	−	13.7102i	1.28752	−	0.612524i
$502$		−	0.397977i		−	0.0177626i
$503$		−	5.02665i		−	0.224127i	−0.993701	−	0.112064i	$-0.964254\pi$
$503$		−	5.02665i		−	0.224127i	0.993701	−	0.112064i	$-0.0357461\pi$
$504$	3.06435	+	9.95883i	0.136497	+	0.443602i
$505$	0.216193	+	15.3045i	0.00962046	+	0.681040i
$506$	−19.8541			−0.882622
$507$	−22.4271	−	1.78777i	−0.996021	−	0.0793978i
$508$		−	18.1500i		−	0.805276i
$509$	8.41967	+	14.5833i	0.373195	+	0.646393i	0.990055	−	0.140680i	$-0.0449288\pi$
$509$	8.41967	+	14.5833i	0.373195	+	0.646393i	−0.616860	+	0.787073i	$0.711595\pi$
$510$	23.8889	−	11.7815i	1.05782	−	0.521695i
$511$	18.3813	+	37.3251i	0.813139	+	1.65116i
$512$		−	18.0264i		−	0.796661i
$513$	−18.4996	+	19.3770i	−0.816778	+	0.855514i
$514$	−3.75360	−	6.50143i	−0.165564	−	0.286766i
$515$	3.27056	−	5.85421i	0.144118	−	0.257967i
$516$	0.304808	−	3.82372i	0.0134184	−	0.168330i
$517$	35.4684	+	20.4777i	1.55990	+	0.900607i
$518$	−43.5743	−	29.1500i	−1.91455	−	1.28078i
$519$	26.7039	+	18.3927i	1.17217	+	0.807349i
$520$	−0.00427896	−	0.302911i	−0.000187645	−	0.0132835i
$521$	−13.4928	−	23.3701i	−0.591128	−	1.02386i	−0.994081	−	0.108643i	$-0.965349\pi$
$521$	−13.4928	−	23.3701i	−0.591128	−	1.02386i	0.402953	−	0.915221i	$-0.367984\pi$
$522$	−22.6924	−	18.4517i	−0.993218	−	0.807610i
$523$	−6.44322	−	3.71999i	−0.281742	−	0.162664i	0.352470	−	0.935823i	$-0.385342\pi$
$523$	−6.44322	−	3.71999i	−0.281742	−	0.162664i	−0.634212	+	0.773159i	$0.718675\pi$
$524$	7.29448	+	12.6344i	0.318661	+	0.551937i
$525$	−21.0475	+	9.05557i	−0.918588	+	0.395217i
$526$	0.114314	−	0.197998i	0.00498433	−	0.00863312i
$527$	22.7755	−	13.1494i	0.992116	−	0.572798i
$528$	−13.9562	−	29.3358i	−0.607367	−	1.27668i
$529$	−7.35063	+	12.7317i	−0.319593	+	0.553551i
$530$	−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
$534$	−10.7207	+	5.10027i	−0.463931	+	0.220710i
$535$	10.4471	−	0.147577i	0.451667	−	0.00638030i
$536$	−7.78958			−0.336459
$537$	16.5950	+	1.32287i	0.716127	+	0.0570860i
$538$	−23.7031	+	13.6850i	−1.02191	+	0.590001i
$539$	16.2530	−	21.1333i	0.700065	−	0.910275i
$540$	−14.1516	+	4.36338i	−0.608986	+	0.187770i
$541$	−3.00421	+	5.20345i	−0.129161	+	0.223714i	−0.923352	−	0.383955i	$-0.874562\pi$
$541$	−3.00421	+	5.20345i	−0.129161	+	0.223714i	0.794191	+	0.607669i	$0.207895\pi$
$542$	−3.99321	−	2.30548i	−0.171523	−	0.0990288i
$543$	−13.9013	+	20.1830i	−0.596563	+	0.866134i
$544$	11.9451	+	20.6896i	0.512143	+	0.887058i
$545$	−16.6214	−	9.28584i	−0.711982	−	0.397762i
$546$	0.795377	−	0.315890i	0.0340390	−	0.0135189i
$547$	21.5061	−	12.4166i	0.919536	−	0.530894i	0.0360487	−	0.999350i	$-0.488523\pi$
$547$	21.5061	−	12.4166i	0.919536	−	0.530894i	0.883487	+	0.468456i	$0.155190\pi$
$548$	−7.19804	−	4.15579i	−0.307485	−	0.177527i
$549$	−10.8869	−	28.5329i	−0.464641	−	1.21776i
$550$	29.3446	−	18.0660i	1.25126	−	0.770339i
$551$	27.7767			1.18333
$552$	6.52939	+	0.520490i	0.277909	+	0.0221535i
$553$	0.573814	−	8.68179i	0.0244010	−	0.369187i
$554$	−22.6760	+	39.2759i	−0.963409	+	1.66867i
$555$	−23.5605	+	35.2629i	−1.00009	+	1.49683i
$556$	5.58795	−	9.67861i	0.236982	−	0.410465i
$557$	18.8530	−	10.8848i	0.798829	−	0.461204i	−0.0442323	−	0.999021i	$-0.514084\pi$
$557$	18.8530	−	10.8848i	0.798829	−	0.461204i	0.843062	+	0.537817i	$0.180751\pi$
$558$	−35.0971	+	13.3915i	−1.48578	+	0.566907i
$559$	0.179323			0.00758454
$560$	−13.2394	−	25.9525i	−0.559467	−	1.09669i
$561$	20.6477	+	14.2214i	0.871745	+	0.600427i
$562$	−28.4113	+	16.4033i	−1.19846	+	0.691930i
$563$			39.9006i			1.68161i	0.541339	+	0.840804i	$0.317917\pi$
$563$			39.9006i			1.68161i	−0.541339	+	0.840804i	$0.682083\pi$
$564$	19.5503	+	13.4656i	0.823217	+	0.567002i
$565$	8.49562	−	0.120010i	0.357413	−	0.00504886i
$566$	−17.9437			−0.754230
$567$	14.6560	+	18.7670i	0.615494	+	0.788142i
$568$			8.44646i			0.354405i
$569$	−42.9140			−1.79905			−0.899525	−	0.436870i	$-0.856087\pi$
$569$	−42.9140			−1.79905			−0.899525	+	0.436870i	$0.856087\pi$
$570$	20.0739	−	30.0446i	0.840805	−	1.25843i
$571$	5.16426			0.216118			0.108059	−	0.994145i	$-0.465537\pi$
$571$	5.16426			0.216118			0.108059	+	0.994145i	$0.465537\pi$
$572$	−0.433859	+	0.250489i	−0.0181405	+	0.0104735i
$573$	−17.9346	+	26.0387i	−0.749227	+	1.08778i
$574$	4.01161	−	5.99667i	0.167441	−	0.250296i
$575$	0.406857	+	14.3980i	0.0169671	+	0.600439i
$576$	−1.63164	−	4.27628i	−0.0679848	−	0.178178i
$577$	−6.42548	+	3.70975i	−0.267496	+	0.154439i	−0.627749	−	0.778416i	$-0.716024\pi$
$577$	−6.42548	+	3.70975i	−0.267496	+	0.154439i	0.360253	+	0.932855i	$0.382690\pi$
$578$	4.00501	+	2.31229i	0.166586	+	0.0961787i
$579$	26.7848	+	18.4484i	1.11314	+	0.766689i
$580$	13.4044	+	7.48861i	0.556588	+	0.310948i
$581$	−1.63840	−	3.32695i	−0.0679724	−	0.138025i
$582$	19.0095	+	1.51534i	0.787971	+	0.0628130i
$583$		−	1.72022i		−	0.0712441i
$584$	10.3218	+	17.8779i	0.427119	+	0.739791i
$585$	−0.255910	−	0.643271i	−0.0105806	−	0.0265960i
$586$	5.31347	−	9.20321i	0.219498	−	0.380181i
$587$	−9.68643	+	5.59247i	−0.399802	+	0.230826i	−0.686399	−	0.727226i	$-0.740809\pi$
$587$	−9.68643	+	5.59247i	−0.399802	+	0.230826i	0.286597	+	0.958051i	$0.407476\pi$
$588$	10.3643	−	11.4621i	0.427416	−	0.472691i
$589$	17.8381	−	30.8965i	0.735005	−	1.27307i
$590$	23.5979	+	39.5712i	0.971509	+	1.62912i
$591$	8.01707	+	5.52187i	0.329778	+	0.227139i
$592$	−46.7005	−	26.9626i	−1.91938	−	1.10815i
$593$	22.2978	+	12.8737i	0.915663	+	0.528658i	0.882249	−	0.470783i	$-0.156029\pi$
$593$	22.2978	+	12.8737i	0.915663	+	0.528658i	0.0334140	+	0.999442i	$0.489362\pi$
$594$	−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
$597$	29.9765	+	2.38957i	1.22686	+	0.0977988i
$598$		−	0.537989i		−	0.0220000i
$599$	1.25720			0.0513679			0.0256840	−	0.999670i	$-0.491824\pi$
$599$	1.25720			0.0513679			0.0256840	+	0.999670i	$0.491824\pi$
$600$	−10.1241	+	5.17207i	−0.413316	+	0.211149i
$601$	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
$605$	6.84328	+	3.82312i	0.278219	+	0.155432i
$606$	−19.3736	+	9.21679i	−0.786998	+	0.374407i
$607$	−28.4523	+	16.4269i	−1.15484	+	0.666748i	−0.950063	−	0.312060i	$-0.898981\pi$
$607$	−28.4523	+	16.4269i	−1.15484	+	0.666748i	−0.204780	+	0.978808i	$0.565648\pi$
$608$	28.0668	+	16.2044i	1.13826	+	0.657174i
$609$	3.58065	−	24.4277i	0.145095	−	0.989862i
$610$	21.0972	+	35.3778i	0.854200	+	1.43241i
$611$	−0.554886	+	0.961091i	−0.0224483	+	0.0388816i
$612$	11.2751	+	9.16808i	0.455770	+	0.370597i
$613$	−36.4927	+	21.0691i	−1.47393	+	0.850973i	−0.999569	−	0.0293591i	$-0.990653\pi$
$613$	−36.4927	+	21.0691i	−1.47393	+	0.850973i	−0.474359	+	0.880332i	$0.657320\pi$
$614$	5.74994			0.232049
$615$	−4.85287	−	3.24238i	−0.195687	−	0.130746i
$616$	7.35519	−	10.9948i	0.296349	−	0.442992i
$617$	1.25040	+	0.721921i	0.0503394	+	0.0290635i	0.524958	−	0.851128i	$-0.324081\pi$
$617$	1.25040	+	0.721921i	0.0503394	+	0.0290635i	−0.474619	+	0.880191i	$0.657414\pi$
$618$	9.36979	+	0.746912i	0.376908	+	0.0300452i
$619$	0.712307	−	1.23375i	0.0286300	−	0.0495887i	−0.851355	−	0.524589i	$-0.824219\pi$
$619$	0.712307	−	1.23375i	0.0286300	−	0.0495887i	0.879985	+	0.475001i	$0.157552\pi$
$620$	16.9380	−	10.1008i	0.680245	−	0.405657i
$621$	14.3652	−	4.20800i	0.576455	−	0.168861i
$622$		−	10.4850i		−	0.420411i
$623$	−8.32965	−	5.57230i	−0.333720	−	0.223250i
$624$	0.794917	−	0.378174i	0.0318221	−	0.0151391i
$625$	−13.7027	−	20.9102i	−0.548107	−	0.836408i
$626$	29.8064			1.19130
$627$	33.9034	+	2.70261i	1.35397	+	0.107932i
$628$			10.0542i			0.401205i
$629$	41.6167			1.65937
$630$	−23.8345	−	21.5267i	−0.949591	−	0.857644i
$631$	18.5591			0.738825			0.369412	−	0.929266i	$-0.379559\pi$
$631$	18.5591			0.738825			0.369412	+	0.929266i	$0.379559\pi$
$632$		−	4.31707i		−	0.171724i
$633$	−7.89050	−	16.5857i	−0.313619	−	0.659224i
$634$	47.3230			1.87943
$635$	−16.3090	−	27.3486i	−0.647205	−	1.08530i
$636$	0.0792314	−	0.993935i	0.00314173	−	0.0394121i
$637$	0.572652	+	0.440409i	0.0226893	+	0.0174497i
$638$			37.1308i			1.47002i
$639$	6.88110	+	18.0344i	0.272212	+	0.713428i
$640$	−11.2364	−	18.8423i	−0.444159	−	0.744809i
$641$	−5.29658	+	9.17394i	−0.209202	+	0.362349i	−0.951463	−	0.307762i	$-0.900420\pi$
$641$	−5.29658	+	9.17394i	−0.209202	+	0.362349i	0.742261	+	0.670111i	$0.233753\pi$
$642$	6.29153	+	13.2247i	0.248307	+	0.521938i
$643$	14.0744	+	8.12587i	0.555041	+	0.320453i	0.751153	−	0.660129i	$-0.229498\pi$
$643$	14.0744	+	8.12587i	0.555041	+	0.320453i	−0.196112	+	0.980582i	$0.562832\pi$
$644$	−4.29176	−	8.71487i	−0.169119	−	0.343414i
$645$	−2.97660	−	6.03551i	−0.117203	−	0.237648i
$646$	−35.4581			−1.39508
$647$	−7.69286	+	4.44147i	−0.302437	+	0.174612i	−0.643537	−	0.765415i	$-0.722534\pi$
$647$	−7.69286	+	4.44147i	−0.302437	+	0.174612i	0.341100	+	0.940027i	$0.389201\pi$
$648$	7.87018	+	8.81183i	0.309170	+	0.346162i
$649$	−21.6833	+	37.5566i	−0.851143	+	1.47422i
$650$	0.489538	+	0.795154i	0.0192013	+	0.0311885i
$651$	−24.8719	−	19.6702i	−0.974807	−	0.770937i
$652$	−13.7259	−	7.92467i	−0.537549	−	0.310354i
$653$	−25.8097	+	14.9012i	−1.01001	+	0.583130i	−0.911195	−	0.411976i	$-0.864839\pi$
$653$	−25.8097	+	14.9012i	−1.01001	+	0.583130i	−0.0988158	+	0.995106i	$0.531505\pi$
$654$	2.12065	−	26.6029i	0.0829239	−	1.04026i
$655$	22.3443	+	12.4830i	0.873064	+	0.487753i
$656$	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	$0.415975\pi$
$660$	15.6324	+	10.4446i	0.608491	+	0.406556i
$661$	34.8476			1.35542			0.677708	−	0.735331i	$-0.262973\pi$
$661$	34.8476			1.35542			0.677708	+	0.735331i	$0.262973\pi$
$662$			28.0941i			1.09191i
$663$	−0.385359	+	0.559493i	−0.0149661	+	0.0217289i
$664$	−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
$668$	−20.3378	−	11.7420i	−0.786893	−	0.454313i
$669$	2.39935	−	30.0991i	0.0927643	−	1.16370i
$670$	20.6217	−	12.2975i	0.796685	−	0.475095i
$671$	−19.3855	+	33.5767i	−0.748369	+	1.29621i
$672$	17.8687	−	22.5940i	0.689300	−	0.871582i
$673$	15.4334	−	8.91050i	0.594915	−	0.343475i	−0.172123	−	0.985075i	$-0.555063\pi$
$673$	15.4334	−	8.91050i	0.594915	−	0.343475i	0.767039	+	0.641601i	$0.221729\pi$
$674$	−11.1319	+	19.2809i	−0.428783	+	0.742674i
$675$	−17.4029	+	19.2909i	−0.669837	+	0.742509i
$676$	8.27781	+	14.3376i	0.318377	+	0.551445i
$677$		−	1.10785i		−	0.0425782i	−0.999773	−	0.0212891i	$-0.993223\pi$
$677$		−	1.10785i		−	0.0425782i	0.999773	−	0.0212891i	$-0.00677704\pi$
$678$	5.11630	+	10.7544i	0.196490	+	0.413020i
$679$	7.11184	+	14.4413i	0.272928	+	0.554208i
$680$	9.73937	+	5.44107i	0.373488	+	0.208656i
$681$	−4.44349	+	2.11395i	−0.170275	+	0.0810067i
$682$	41.3012	+	23.8452i	1.58150	+	0.913082i
$683$	11.2902	−	6.51838i	0.432006	−	0.249419i	−0.268195	−	0.963365i	$-0.586427\pi$
$683$	11.2902	−	6.51838i	0.432006	−	0.249419i	0.700201	+	0.713946i	$0.253094\pi$
$684$	19.4648	+	3.12312i	0.744255	+	0.119415i
$685$	−14.5803	+	0.205964i	−0.557086	+	0.00786947i
$686$	32.8590	+	6.59224i	1.25456	+	0.251693i
$687$	−32.6798	−	2.60507i	−1.24681	−	0.0993897i
$688$	7.41049	−	4.27845i	0.282522	−	0.163114i
$689$	0.0466130			0.00177581
$690$	−18.1072	+	8.93014i	−0.689331	+	0.339965i
$691$	36.6703			1.39500			0.697502	−	0.716583i	$-0.254295\pi$
$691$	36.6703			1.39500			0.697502	+	0.716583i	$0.254295\pi$
$692$		−	23.8605i		−	0.907039i
$693$	6.74720	−	29.4674i	0.256305	−	1.11937i
$694$	−53.2479			−2.02126
$695$	−0.276942	−	19.6050i	−0.0105050	−	0.743659i
$696$	0.973411	−	12.2112i	0.0368971	−	0.462863i
$697$			5.72727i			0.216936i
$698$	12.0702	−	6.96874i	0.456865	−	0.263771i
$699$	−21.7546	+	10.3495i	−0.822834	+	0.391455i
$700$	14.2733	+	8.97542i	0.539480	+	0.339239i
$701$	−12.4808			−0.471393			−0.235696	−	0.971827i	$-0.575737\pi$
$701$	−12.4808			−0.471393			−0.235696	+	0.971827i	$0.575737\pi$
$702$	0.670101	−	0.701880i	0.0252913	−	0.0264908i
$703$	48.8922	−	28.2279i	1.84400	−	1.06464i
$704$	−2.90533	+	5.03219i	−0.109499	+	0.189658i
$705$	41.5583	+	2.72269i	1.56518	+	0.102543i
$706$	25.8089	−	44.7022i	0.971329	−	1.68239i
$707$	−15.0527	−	10.0698i	−0.566113	−	0.378714i
$708$	−14.2583	+	20.7013i	−0.535861	+	0.778004i
$709$	48.5168			1.82209			0.911043	−	0.412311i	$-0.135278\pi$
$709$	48.5168			1.82209			0.911043	+	0.412311i	$0.135278\pi$
$710$	−13.3346	−	22.3607i	−0.500437	−	0.839181i
$711$	−3.51700	−	9.21753i	−0.131898	−	0.345684i
$712$	−4.30629	−	2.48624i	−0.161385	−	0.0931756i
$713$	−17.2633	+	9.96698i	−0.646516	+	0.373266i
$714$	−4.57085	+	31.1831i	−0.171060	+	1.16700i
$715$	−0.428661	+	0.767291i	−0.0160310	+	0.0286950i
$716$	−6.12520	−	10.6092i	−0.228909	−	0.396483i
$717$	1.02455	+	2.15360i	0.0382626	+	0.0804275i
$718$	−47.7403	−	27.5629i	−1.78165	−	1.02864i
$719$	−19.6093	+	33.9643i	−0.731302	+	1.26665i	0.225024	+	0.974353i	$0.427754\pi$
$719$	−19.6093	+	33.9643i	−0.731302	+	1.26665i	−0.956327	+	0.292300i	$0.905580\pi$
$720$	−25.9232	−	20.4774i	−0.966101	−	0.763147i
$721$	3.50542	+	7.11813i	0.130549	+	0.265093i
$722$	−11.8813	+	6.85970i	−0.442178	+	0.255292i
$723$	−6.04208	−	12.7004i	−0.224707	−	0.472332i
$724$	18.0339			0.670224
$725$	26.9269	−	0.760898i	1.00004	−	0.0282590i
$726$	−0.873103	+	10.9528i	−0.0324039	+	0.406497i
$727$	−34.0419	+	19.6541i	−1.26254	+	0.728930i	−0.973566	−	0.228406i	$-0.926648\pi$
$727$	−34.0419	+	19.6541i	−1.26254	+	0.728930i	−0.288977	+	0.957336i	$0.593315\pi$
$728$	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
$731$	−3.30189	+	5.71904i	−0.122125	+	0.211526i
$732$	−12.7474	+	18.5076i	−0.471157	+	0.684061i
$733$	−24.3445	+	14.0553i	−0.899186	+	0.519145i	−0.876936	−	0.480607i	$-0.840416\pi$
$733$	−24.3445	+	14.0553i	−0.899186	+	0.519145i	−0.0222501	+	0.999752i	$0.507083\pi$
$734$	16.2307	−	28.1123i	0.599085	−	1.03765i
$735$	5.31746	−	26.5843i	0.196138	−	0.980576i
$736$	−9.05415	−	15.6822i	−0.333740	−	0.578055i
$737$	19.5718	+	11.2998i	0.720937	+	0.416233i
$738$	1.29603	−	8.07748i	0.0477074	−	0.297336i
$739$	2.39190	+	4.14289i	0.0879875	+	0.152399i	0.906660	−	0.421861i	$-0.138623\pi$
$739$	2.39190	+	4.14289i	0.0879875	+	0.152399i	−0.818673	+	0.574260i	$0.805290\pi$
$740$	31.2045	−	0.440799i	1.14710	−	0.0162041i
$741$	−0.0732330	+	0.918686i	−0.00269028	+	0.0337488i
$742$	1.93994	−	0.955350i	0.0712174	−	0.0350720i
$743$	−10.0985	−	5.83037i	−0.370478	−	0.213895i	0.303189	−	0.952930i	$-0.401948\pi$
$743$	−10.0985	−	5.83037i	−0.370478	−	0.213895i	−0.673667	+	0.739035i	$0.735282\pi$
$744$	−12.9576	−	8.92470i	−0.475047	−	0.327195i
$745$	−21.7330	−	12.1415i	−0.796235	−	0.444831i
$746$	6.99303	+	12.1123i	0.256033	+	0.443462i
$747$	−3.26259	−	2.65289i	−0.119372	−	0.0970642i
$748$		−	18.4491i		−	0.674566i
$749$	−6.87380	+	10.2752i	−0.251163	+	0.375447i
$750$	18.6368	−	29.6754i	0.680520	−	1.08359i
$751$	−7.06603	−	12.2387i	−0.257843	−	0.446597i	0.707821	−	0.706392i	$-0.249678\pi$
$751$	−7.06603	−	12.2387i	−0.257843	−	0.446597i	−0.965664	+	0.259795i	$0.916345\pi$
$752$			52.9560i			1.93111i
$753$	0.216076	−	0.313715i	0.00787424	−	0.0114324i
$754$	−1.00614			−0.0366414
$755$	−0.293330	−	20.7651i	−0.0106754	−	0.755718i
$756$	5.25575	−	16.7154i	0.191150	−	0.607933i
$757$		−	16.7658i		−	0.609365i	−0.952454	−	0.304682i	$-0.901450\pi$
$757$		−	16.7658i		−	0.609365i	0.952454	−	0.304682i	$-0.0985503\pi$
$758$			6.77294i			0.246004i
$759$	−15.6505	−	10.7795i	−0.568076	−	0.391271i
$760$	15.1326	−	0.213765i	0.548917	−	0.00775407i
$761$	−9.91233	−	17.1687i	−0.359322	−	0.622363i	0.628526	−	0.777789i	$-0.283659\pi$
$761$	−9.91233	−	17.1687i	−0.359322	−	0.622363i	−0.987848	+	0.155425i	$0.950325\pi$
$762$	25.3174	−	36.7577i	0.917153	−	1.33159i
$763$	20.2099	−	9.95267i	0.731649	−	0.360311i
$764$	23.2661			0.841740
$765$	25.2276	+	3.68304i	0.912106	+	0.133161i
$766$	−13.7112	−	23.7485i	−0.495407	−	0.858069i
$767$	−1.01768	−	0.587555i	−0.0367461	−	0.0212154i
$768$	20.4408	−	29.6775i	0.737593	−	1.07089i
$769$	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	$0.0454566\pi$
$770$	−2.11408	+	40.7187i	−0.0761863	+	1.46740i
$771$	0.570988	−	7.16287i	0.0205636	−	0.257965i
$772$		−	23.9327i		−	0.861358i
$773$	29.0993	−	16.8005i	1.04663	−	0.604272i	0.124926	−	0.992166i	$-0.460131\pi$
$773$	29.0993	−	16.8005i	1.04663	−	0.604272i	0.921704	+	0.387894i	$0.126797\pi$
$774$	5.95100	−	7.31869i	0.213904	−	0.263065i
$775$	16.4460	−	30.4399i	0.590758	−	1.09343i
$776$	3.99358	+	6.91708i	0.143361	+	0.248309i
$777$	−18.5220	−	46.6362i	−0.664471	−	1.67307i
$778$	−45.8118	−	26.4494i	−1.64243	−	0.948259i
$779$	3.88471	+	6.72851i	0.139184	+	0.241074i
$780$	−0.283019	+	0.423594i	−0.0101337	+	0.0151671i
$781$	12.2527	−	21.2223i	0.438435	−	0.759392i
$782$	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
$785$	9.03438	+	15.1497i	0.322451	+	0.540716i
$786$	−2.85081	+	35.7625i	−0.101685	+	1.27561i
$787$		−	3.64543i		−	0.129945i	−0.997887	−	0.0649727i	$-0.979304\pi$
$787$		−	3.64543i		−	0.129945i	0.997887	−	0.0649727i	$-0.0206960\pi$
$788$		−	7.16341i		−	0.255186i
$789$	0.197611	−	0.0940115i	0.00703514	−	0.00334690i
$790$	6.81542	+	11.4288i	0.242482	+	0.406617i
$791$	−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
$794$	−16.4302	+	28.4579i	−0.583086	+	1.00993i
$795$	−0.773733	−	1.56886i	−0.0274415	−	0.0556419i
$796$	−11.0643	−	19.1639i	−0.392163	−	0.679247i
$797$	−27.9090	−	16.1133i	−0.988587	−	0.570761i	−0.0837354	−	0.996488i	$-0.526685\pi$
$797$	−27.9090	−	16.1133i	−0.988587	−	0.570761i	−0.904852	+	0.425727i	$0.860018\pi$
$798$	15.7810	+	39.7348i	0.558642	+	1.40660i
$799$	−20.4344	−	35.3934i	−0.722917	−	1.25213i
$800$	27.6520	+	14.9398i	0.977647	+	0.528201i
$801$	−11.2200	−	1.80024i	−0.396439	−	0.0636084i
$802$	29.6331	−	17.1087i	1.04638	−	0.604128i
$803$		−	59.8924i		−	2.11356i
$804$	10.7881	+	7.43044i	0.380466	+	0.262051i
$805$	−14.2978	−	9.27519i	−0.503931	−	0.326907i
$806$	−0.646138	+	1.11914i	−0.0227593	+	0.0394202i
$807$	−26.1146	−	2.08172i	−0.919277	−	0.0732801i
$808$	−7.78196	−	4.49292i	−0.273769	−	0.158060i
$809$	9.02975	+	15.6400i	0.317469	+	0.549873i	0.979959	−	0.199198i	$-0.0638337\pi$
$809$	9.02975	+	15.6400i	0.317469	+	0.549873i	−0.662490	+	0.749071i	$0.730500\pi$
$810$	−34.7464	−	10.9032i	−1.22087	−	0.383098i
$811$	2.51554			0.0883326			0.0441663	−	0.999024i	$-0.485937\pi$
$811$	2.51554			0.0883326			0.0441663	+	0.999024i	$0.485937\pi$
$812$	−16.2984	+	8.02638i	−0.571962	+	0.281671i
$813$	−1.89602	−	3.98540i	−0.0664962	−	0.139774i
$814$	37.7340	+	65.3571i	1.32257	+	2.29077i
$815$	−27.8032	+	0.392752i	−0.973904	+	0.0137575i
$816$	−2.57601	+	32.3152i	−0.0901783	+	1.13126i
$817$			8.95847i			0.313417i
$818$			42.5077i			1.48625i
$819$	0.798483	+	0.182830i	0.0279013	+	0.00638860i
$820$	0.0606626	+	4.29435i	0.00211843	+	0.149965i
$821$	−7.69146			−0.268434			−0.134217	−	0.990952i	$-0.542852\pi$
$821$	−7.69146			−0.268434			−0.134217	+	0.990952i	$0.542852\pi$
$822$	−8.78070	−	18.4569i	−0.306262	−	0.643759i
$823$			12.7415i			0.444141i	0.975031	+	0.222070i	$0.0712814\pi$
$823$			12.7415i			0.444141i	−0.975031	+	0.222070i	$0.928719\pi$
$824$	1.96843	+	3.40942i	0.0685735	+	0.118773i
$825$	32.9403	+	1.69120i	1.14683	+	0.0588800i
$826$	−54.3958	−	3.59523i	−1.89267	−	0.125094i
$827$		−	5.86058i		−	0.203792i	−0.994795	−	0.101896i	$-0.967509\pi$
$827$		−	5.86058i		−	0.203792i	0.994795	−	0.101896i	$-0.0324910\pi$
$828$	−8.54630	−	6.94920i	−0.297004	−	0.241501i
$829$	17.8395	+	30.8989i	0.619592	+	1.07316i	0.989560	+	0.144120i	$0.0460352\pi$
$829$	17.8395	+	30.8989i	0.619592	+	1.07316i	−0.369968	+	0.929044i	$0.620632\pi$
$830$	4.95136	+	2.76617i	0.171864	+	0.0960150i
$831$	−39.1992	+	18.6486i	−1.35980	+	0.646913i
$832$	−0.136358	−	0.0787263i	−0.00472736	−	0.00272934i
$833$	−24.5901	+	10.1540i	−0.851995	+	0.351814i
$834$	24.8175	−	11.8067i	0.859359	−	0.408832i
$835$	−41.1962	+	0.581942i	−1.42565	+	0.0201389i
$836$	−12.5137	−	21.6744i	−0.432796	−	0.749625i
$837$	−34.9369	−	8.49930i	−1.20760	−	0.293779i
$838$	−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	$0.946417\pi$
$840$	1.76273	−	13.3357i	0.0608199	−	0.460125i
$841$	−0.0127510	+	0.0220853i	−0.000439688	+	0.000761563i
$842$	52.3830	−	30.2433i	1.80524	−	1.04225i
$843$	−31.3018	−	2.49522i	−1.07809	−	0.0859400i
$844$	−6.75780	+	11.7049i	−0.232613	+	0.402898i
$845$	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
$849$	−14.1446	−	9.74227i	−0.485440	−	0.334354i
$850$	−34.3734	+	0.971319i	−1.17900	+	0.0333160i
$851$	−31.5445			−1.08133
$852$	8.05703	−	11.6978i	0.276029	−	0.400760i
$853$	−15.5699	+	8.98930i	−0.533104	+	0.307788i	−0.742280	−	0.670090i	$-0.766255\pi$
$853$	−15.5699	+	8.98930i	−0.533104	+	0.307788i	0.209175	+	0.977878i	$0.432922\pi$
$854$	−48.6315	−	3.21424i	−1.66413	−	0.109989i
$855$	32.1361	−	12.7845i	1.09903	−	0.437222i
$856$	−3.06694	+	5.31209i	−0.104826	+	0.181564i
$857$	12.4290	+	7.17591i	0.424568	+	0.245124i	0.697030	−	0.717042i	$-0.254505\pi$
$857$	12.4290	+	7.17591i	0.424568	+	0.245124i	−0.272462	+	0.962167i	$0.587838\pi$
$858$	−1.22806	−	0.0978951i	−0.0419254	−	0.00334208i
$859$	2.98130	+	5.16377i	0.101721	+	0.176186i	0.912394	−	0.409314i	$-0.134232\pi$
$859$	2.98130	+	5.16377i	0.101721	+	0.176186i	−0.810673	+	0.585499i	$0.800899\pi$
$860$	−2.41521	+	4.32316i	−0.0823580	+	0.147419i
$861$	6.41805	−	2.54898i	0.218727	−	0.0868691i
$862$	4.08703	−	2.35965i	0.139205	−	0.0803699i
$863$	42.3854	+	24.4712i	1.44281	+	0.833010i	0.998037	−	0.0626312i	$-0.0199492\pi$
$863$	42.3854	+	24.4712i	1.44281	+	0.833010i	0.444778	+	0.895641i	$0.353283\pi$
$864$	7.72089	−	31.7372i	0.262670	−	1.07972i
$865$	−21.4403	−	35.9531i	−0.728992	−	1.22244i
$866$	0.115269			0.00391699
$867$	1.90162	+	3.99718i	0.0645824	+	0.135751i
$868$	−1.53890	+	23.2835i	−0.0522336	+	0.790293i
$869$	−6.26246	+	10.8469i	−0.212439	+	0.367956i
$870$	16.7010	+	33.8638i	0.566217	+	1.14809i
$871$	−0.306192	+	0.530341i	−0.0103749	+	0.0179699i
$872$	9.68010	−	5.58881i	0.327810	−	0.189261i
$873$	14.1620	+	11.5155i	0.479311	+	0.389739i
$874$	26.8765			0.909110
$875$	29.5721	+	0.698694i	0.999721	+	0.0236202i
$876$	2.75858	−	34.6056i	0.0932039	−	1.16921i
$877$	−2.53798	+	1.46530i	−0.0857015	+	0.0494798i	−0.542238	−	0.840225i	$-0.682423\pi$
$877$	−2.53798	+	1.46530i	−0.0857015	+	0.0494798i	0.456537	+	0.889705i	$0.349090\pi$
$878$			27.8721i			0.940637i
$879$	9.18523	−	4.36978i	0.309810	−	0.147389i
$880$	0.592387	+	41.9356i	0.0199694	+	1.41365i
$881$	−0.475996			−0.0160367			−0.00801835	−	0.999968i	$-0.502552\pi$
$881$	−0.475996			−0.0160367			−0.00801835	+	0.999968i	$0.502552\pi$
$882$	36.9785	−	8.75620i	1.24513	−	0.294837i
$883$			25.7817i			0.867622i	0.901004	+	0.433811i	$0.142831\pi$
$883$			25.7817i			0.867622i	−0.901004	+	0.433811i	$0.857169\pi$
$884$	0.499918			0.0168141
$885$	−2.88299	+	44.0051i	−0.0969108	+	1.47921i
$886$	−53.5901			−1.80040
$887$	5.71043	−	3.29692i	0.191738	−	0.110700i	−0.401058	−	0.916053i	$-0.631357\pi$
$887$	5.71043	−	3.29692i	0.191738	−	0.110700i	0.592796	+	0.805353i	$0.298024\pi$
$888$	−10.6961	−	22.4831i	−0.358939	−	0.754485i
$889$	37.5942	+	2.48475i	1.26087	+	0.0833359i
$890$	15.3253	−	0.216487i	0.513704	−	0.00725665i
$891$	−6.99162	−	33.5570i	−0.234228	−	1.12420i
$892$	−19.2423	+	11.1096i	−0.644281	+	0.371976i
$893$	−48.0135	−	27.7206i	−1.60671	−	0.927634i
$894$	2.77281	−	34.7841i	0.0927367	−	1.16335i
$895$	−18.7626	−	10.4820i	−0.627163	−	0.350376i
$896$	25.9013	+	1.71192i	0.865301	+	0.0571911i
$897$	0.292094	−	0.424083i	0.00975272	−	0.0141597i
$898$			70.7747i			2.36178i
$899$	18.6401	+	32.2856i	0.621681	+	1.07678i
$900$	18.9549	+	2.49437i	0.631829	+	0.0831455i
$901$	−0.858290	+	1.48660i	−0.0285938	+	0.0495259i
$902$	−8.99442	+	5.19293i	−0.299481	+	0.172906i
$903$	7.87838	+	1.15482i	0.262176	+	0.0384301i
$904$	−2.49405	+	4.31982i	−0.0829508	+	0.143675i
$905$	27.1736	−	16.2047i	0.903282	−	0.538663i
$906$	26.2860	−	12.5053i	0.873295	−	0.415461i
$907$	44.0961	+	25.4589i	1.46419	+	0.845350i	0.999201	−	0.0399677i	$-0.0127255\pi$
$907$	44.0961	+	25.4589i	1.46419	+	0.845350i	0.464987	+	0.885317i	$0.346059\pi$
$908$	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	$-0.442265\pi$
$912$	18.8925	+	39.7119i	0.625594	+	1.31499i
$913$			5.33847i			0.176678i
$914$	−51.4348			−1.70131
$915$	−2.57748	+	39.3418i	−0.0852089	+	1.30060i
$916$	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	−0.891994	−	0.452047i	$-0.850694\pi$
$919$	−1.65257	+	2.86233i	−0.0545132	+	0.0944196i	0.837481	+	0.546466i	$0.184027\pi$
$920$	−7.38223	−	4.12421i	−0.243385	−	0.135971i
$921$	4.53253	+	3.12185i	0.149352	+	0.102868i
$922$	22.7388	−	13.1283i	0.748862	−	0.432356i
$923$	0.575063	+	0.332013i	0.0189284	+	0.0109283i
$924$	−20.6743	+	8.21097i	−0.680135	+	0.270121i
$925$	46.6232	−	28.7037i	1.53296	−	0.943770i
$926$	30.5431	−	52.9022i	1.00371	−	1.73847i
$927$	6.98044	+	5.67596i	0.229268	+	0.186423i
$928$	−29.3287	+	16.9329i	−0.962760	+	0.555850i
$929$	−24.5565			−0.805672			−0.402836	−	0.915272i	$-0.631976\pi$
$929$	−24.5565			−0.805672			−0.402836	+	0.915272i	$0.631976\pi$
$930$	48.3926	+	3.17045i	1.58686	+	0.103963i
$931$	−22.0016	+	28.6081i	−0.721075	+	0.937593i
$932$	15.3526	+	8.86383i	0.502891	+	0.290344i
$933$	5.69270	−	8.26508i	0.186370	−	0.270587i
$934$	−35.8822	+	62.1498i	−1.17410	+	2.03360i
$935$	−16.5778	−	27.7993i	−0.542152	−	0.909133i
$936$	0.401306	+	0.0643893i	0.0131171	+	0.00210463i
$937$			4.74809i			0.155113i	0.996988	+	0.0775566i	$0.0247119\pi$
$937$			4.74809i			0.155113i	−0.996988	+	0.0775566i	$0.975288\pi$
$938$	−1.87358	+	28.3473i	−0.0611746	+	0.925571i
$939$	23.4956	+	16.1829i	0.766750	+	0.528110i
$940$	−15.6968	−	26.3218i	−0.511972	−	0.858523i
$941$	28.2214			0.919990			0.459995	−	0.887922i	$-0.347851\pi$
$941$	28.2214			0.919990			0.459995	+	0.887922i	$0.347851\pi$
$942$	−14.0245	+	20.3619i	−0.456944	+	0.663426i
$943$		−	4.34114i		−	0.141367i
$944$	−56.0738			−1.82505
$945$	−7.10055	−	29.9096i	−0.230981	−	0.972958i
$946$	−11.9753			−0.389352
$947$		−	11.2577i		−	0.365825i	−0.983129	−	0.182912i	$-0.941448\pi$
$947$		−	11.2577i		−	0.365825i	0.983129	−	0.182912i	$-0.0585525\pi$
$948$	−4.11803	+	5.97886i	−0.133747	+	0.194184i
$949$	1.62291			0.0526820
$950$	−39.7237	+	24.4560i	−1.28881	+	0.793457i
$951$	37.3035	+	25.6933i	1.20965	+	0.833163i
$952$	−11.8421	+	5.83180i	−0.383804	+	0.189010i
$953$			36.1169i			1.16994i	0.811055	+	0.584970i	$0.198894\pi$
$953$			36.1169i			1.16994i	−0.811055	+	0.584970i	$0.801106\pi$
$954$	1.54690	−	1.90241i	0.0500827	−	0.0615929i
$955$	35.0576	−	20.9063i	1.13444	−	0.676511i
$956$	0.877475	−	1.51983i	0.0283796	−	0.0491549i
$957$	−20.1596	+	29.2692i	−0.651668	+	0.946140i
$958$	−24.7217	−	14.2731i	−0.798720	−	0.461141i
$959$	9.59334	−	14.3404i	0.309785	−	0.463077i
$960$	−0.386291	+	5.89622i	−0.0124675	+	0.190300i
$961$	16.8823			0.544592
$962$	−1.77099	+	1.02248i	−0.0570991	+	0.0329662i
$963$	−2.22072	+	13.8406i	−0.0715616	+	0.446007i
$964$	−5.17472	+	8.96288i	−0.166667	+	0.288675i
$965$	−21.5052	−	36.0620i	−0.692278	−	1.16088i
$966$	3.46460	−	23.6361i	0.111472	−	0.760478i
$967$	−48.7009	−	28.1175i	−1.56612	−	0.904198i	−0.996615	−	0.0822077i	$-0.973803\pi$
$967$	−48.7009	−	28.1175i	−1.56612	−	0.904198i	−0.569502	−	0.821990i	$-0.692864\pi$
$968$	−3.98545	+	2.30100i	−0.128097	+	0.0739569i
$969$	−27.9507	−	19.2515i	−0.897907	−	0.618446i
$970$	−21.4925	−	12.0071i	−0.690082	−	0.385526i
$971$	−12.1224	+	20.9966i	−0.389027	+	0.673814i	−0.992319	−	0.123706i	$-0.960522\pi$
$971$	−12.1224	+	20.9966i	−0.389027	+	0.673814i	0.603292	+	0.797520i	$0.293855\pi$
$972$	−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
$975$	−0.0458267	+	0.892587i	−0.00146763	+	0.0285857i
$976$	−50.1316			−1.60467
$977$			16.1061i			0.515278i	0.966241	+	0.257639i	$0.0829446\pi$
$977$			16.1061i			0.515278i	−0.966241	+	0.257639i	$0.917055\pi$
$978$	−16.7439	−	35.1954i	−0.535410	−	1.12543i
$979$	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
$983$	−12.7070	−	7.33641i	−0.405291	−	0.233995i	0.283473	−	0.958980i	$-0.408513\pi$
$983$	−12.7070	−	7.33641i	−0.405291	−	0.233995i	−0.688765	+	0.724985i	$0.741847\pi$
$984$	3.09412	−	1.47200i	0.0986369	−	0.0469255i
$985$	−6.43683	−	10.7939i	−0.205094	−	0.343922i
$986$	18.5262	−	32.0882i	0.589993	−	1.02190i
$987$	−30.5678	+	38.6513i	−0.972983	+	1.23028i
$988$	0.587314	−	0.339086i	0.0186850	−	0.0107878i
$989$	2.50276	−	4.33491i	0.0795831	−	0.137842i
$990$	17.0899	+	42.9582i	0.543152	+	1.36530i
$991$	−23.4659	−	40.6441i	−0.745419	−	1.29110i	−0.949999	−	0.312253i	$-0.898916\pi$
$991$	−23.4659	−	40.6441i	−0.745419	−	1.29110i	0.204580	−	0.978850i	$-0.434417\pi$
$992$			43.4970i			1.38103i
$993$	−15.2533	+	22.1458i	−0.484048	+	0.702777i
$994$	30.7377	+	2.03157i	0.974941	+	0.0644376i
$995$	−33.8919	−	18.9343i	−1.07444	−	0.600258i
$996$	−0.245885	+	3.08455i	−0.00779115	+	0.0977376i
$997$	8.99400	+	5.19269i	0.284843	+	0.164454i	0.635614	−	0.772007i	$-0.280747\pi$
$997$	8.99400	+	5.19269i	0.284843	+	0.164454i	−0.350771	+	0.936461i	$0.614080\pi$
$998$	−21.6989	+	12.5278i	−0.686865	+	0.396562i
$999$	−41.1541	−	39.2908i	−1.30206	−	1.24311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.r.b.184.9	✓	84
3.2	odd	2		945.2.r.b.604.34		84
5.4	even	2	inner	315.2.r.b.184.34	yes	84
7.4	even	3		315.2.bo.b.4.34	yes	84
9.2	odd	6		945.2.bo.b.289.34		84
9.7	even	3		315.2.bo.b.79.9	yes	84
15.14	odd	2		945.2.r.b.604.9		84
21.11	odd	6		945.2.bo.b.739.9		84
35.4	even	6		315.2.bo.b.4.9	yes	84
45.29	odd	6		945.2.bo.b.289.9		84
45.34	even	6		315.2.bo.b.79.34	yes	84
63.11	odd	6		945.2.r.b.424.34		84
63.25	even	3	inner	315.2.r.b.214.9	yes	84
105.74	odd	6		945.2.bo.b.739.34		84
315.74	odd	6		945.2.r.b.424.9		84
315.214	even	6	inner	315.2.r.b.214.34	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.r.b.184.9	✓	84	1.1	even	1	trivial
315.2.r.b.184.34	yes	84	5.4	even	2	inner
315.2.r.b.214.9	yes	84	63.25	even	3	inner
315.2.r.b.214.34	yes	84	315.214	even	6	inner
315.2.bo.b.4.9	yes	84	35.4	even	6
315.2.bo.b.4.34	yes	84	7.4	even	3
315.2.bo.b.79.9	yes	84	9.7	even	3
315.2.bo.b.79.34	yes	84	45.34	even	6
945.2.r.b.424.9		84	315.74	odd	6
945.2.r.b.424.34		84	63.11	odd	6
945.2.r.b.604.9		84	15.14	odd	2
945.2.r.b.604.34		84	3.2	odd	2
945.2.bo.b.289.9		84	45.29	odd	6
945.2.bo.b.289.34		84	9.2	odd	6
945.2.bo.b.739.9		84	21.11	odd	6
945.2.bo.b.739.34		84	105.74	odd	6

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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.80957i q^{2} +(0.982481 - 1.42644i) q^{3} -1.27455 q^{4} +(-1.92051 + 1.14527i) q^{5} +(-2.58125 - 1.77787i) q^{6} +(0.174487 - 2.63999i) q^{7} -1.31275i q^{8} +(-1.06946 - 2.80290i) q^{9} +O(q^{10})\)	\(q-1.80957i q^{2} +(0.982481 - 1.42644i) q^{3} -1.27455 q^{4} +(-1.92051 + 1.14527i) q^{5} +(-2.58125 - 1.77787i) q^{6} +(0.174487 - 2.63999i) q^{7} -1.31275i q^{8} +(-1.06946 - 2.80290i) q^{9} +(2.07246 + 3.47530i) q^{10} +(-1.90431 + 3.29837i) q^{11} +(-1.25222 + 1.81807i) q^{12} +(-0.0893763 - 0.0516014i) q^{13} +(-4.77726 - 0.315747i) q^{14} +(-0.253196 + 3.86470i) q^{15} -4.92462 q^{16} +(3.29140 - 1.90029i) q^{17} +(-5.07205 + 1.93527i) q^{18} +(2.57787 - 4.46499i) q^{19} +(2.44779 - 1.45971i) q^{20} +(-3.59436 - 2.84264i) q^{21} +(5.96863 + 3.44599i) q^{22} +(-2.49480 + 1.44038i) q^{23} +(-1.87256 - 1.28975i) q^{24} +(2.37669 - 4.39902i) 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} +(6.99345 + 0.458176i) q^{30} +6.91971 q^{31} +6.28596i q^{32} +(2.83397 + 5.95697i) 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} +(-8.07973 - 4.66484i) q^{38} +(-0.161417 + 0.0767925i) q^{39} +(1.50346 + 2.52114i) q^{40} +(-0.753474 + 1.30506i) q^{41} +(-5.14396 + 6.50425i) q^{42} +(-1.50478 + 0.868787i) q^{43} +(2.42715 - 4.20394i) q^{44} +(5.26400 + 4.15816i) q^{45} +(2.60646 + 4.51453i) q^{46} -10.7533i q^{47} +(-4.83835 + 7.02468i) q^{48} +(-6.93911 - 0.921290i) q^{49} +(-7.96034 - 4.30080i) q^{50} +(0.523087 - 6.56197i) q^{51} +(0.113915 + 0.0657688i) q^{52} +(-0.391152 + 0.225832i) q^{53} +(-2.22265 + 9.13634i) q^{54} +(-0.120291 - 8.51549i) q^{55} +(-3.46565 - 0.229058i) q^{56} +(-3.83634 - 8.06394i) q^{57} +(8.44299 - 4.87457i) q^{58} +11.3864 q^{59} +(0.322712 - 4.92576i) q^{60} +10.1798 q^{61} -12.5217i q^{62} +(-7.58624 + 2.33430i) q^{63} +1.52566 q^{64} +(0.230746 - 0.00325954i) q^{65} +(10.7796 - 5.12827i) q^{66} -5.93379i q^{67} +(-4.19506 + 2.42202i) q^{68} +(-0.396489 + 4.97383i) q^{69} +(9.53637 - 4.86488i) q^{70} -6.43418 q^{71} +(-3.67951 + 1.40393i) q^{72} +(-13.6186 + 7.86273i) q^{73} +(9.90750 - 17.1603i) q^{74} +(-3.93988 - 7.71216i) q^{75} +(-3.28563 + 5.69087i) q^{76} +(8.37538 + 5.60289i) q^{77} +(0.138962 + 0.292096i) q^{78} +3.28857 q^{79} +(9.45777 - 5.64004i) q^{80} +(-6.71250 + 5.99519i) q^{81} +(2.36159 + 1.36347i) q^{82} +(1.21389 - 0.700839i) q^{83} +(4.58120 + 3.62309i) q^{84} +(-4.14479 + 7.41907i) q^{85} +(1.57213 + 2.72302i) q^{86} +(9.30197 + 0.741506i) q^{87} +(4.32993 + 2.49988i) q^{88} +(1.89392 - 3.28036i) q^{89} +(7.52450 - 9.52559i) q^{90} +(-0.151822 + 0.226949i) q^{91} +(3.17976 - 1.83584i) q^{92} +(6.79848 - 9.87055i) q^{93} -19.4589 q^{94} +(0.162838 + 11.5274i) q^{95} +(8.96654 + 6.17584i) q^{96} +(-5.26915 + 3.04215i) q^{97} +(-1.66714 + 12.5568i) q^{98} +(11.2816 + 1.81012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9	\( 84 q - 88 q^{4} + 3 q^{5} + 6 q^{6} - 2 q^{9} + 6 q^{10} + 12 q^{11} + 8 q^{14} + 4 q^{15} + 72 q^{16} + 8 q^{19} - 10 q^{20} - 26 q^{21} + 18 q^{24} - 5 q^{25} - 40 q^{26} - 10 q^{29} + 5 q^{30} + 12 q^{31} - 12 q^{34} + 4 q^{35} - 6 q^{36} - 56 q^{39} + 4 q^{40} - 30 q^{41} - 4 q^{44} + 33 q^{45} + 4 q^{46} + 8 q^{49} + 42 q^{50} - 52 q^{51} + 24 q^{54} - 54 q^{55} - 18 q^{56} - 84 q^{59} - 21 q^{60} - 44 q^{61} - 28 q^{64} - 16 q^{65} + 4 q^{66} - 32 q^{69} + q^{70} - 4 q^{71} + 54 q^{74} + 66 q^{75} + 24 q^{76} - 48 q^{79} - 9 q^{80} + 38 q^{81} + 56 q^{84} + q^{85} + 46 q^{86} + 46 q^{89} + 17 q^{90} - 44 q^{91} + 16 q^{94} + 50 q^{95} + 78 q^{96} - 102 q^{99}+O(q^{100}) \) 84 * q - 88 * q^4 + 3 * q^5 + 6 * q^6 - 2 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^14 + 4 * q^15 + 72 * q^16 + 8 * q^19 - 10 * q^20 - 26 * q^21 + 18 * q^24 - 5 * q^25 - 40 * q^26 - 10 * q^29 + 5 * q^30 + 12 * q^31 - 12 * q^34 + 4 * q^35 - 6 * q^36 - 56 * q^39 + 4 * q^40 - 30 * q^41 - 4 * q^44 + 33 * q^45 + 4 * q^46 + 8 * q^49 + 42 * q^50 - 52 * q^51 + 24 * q^54 - 54 * q^55 - 18 * q^56 - 84 * q^59 - 21 * q^60 - 44 * q^61 - 28 * q^64 - 16 * q^65 + 4 * q^66 - 32 * q^69 + q^70 - 4 * q^71 + 54 * q^74 + 66 * q^75 + 24 * q^76 - 48 * q^79 - 9 * q^80 + 38 * q^81 + 56 * q^84 + q^85 + 46 * q^86 + 46 * q^89 + 17 * q^90 - 44 * q^91 + 16 * q^94 + 50 * q^95 + 78 * q^96 - 102 * q^99

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