LMFDB - Embedded newform 315.2.k.b.256.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

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([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, 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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			256.3
Character	$\chi$	$=$	315.256
Dual form			315.2.k.b.16.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08176 + 1.87367i) q^{2} +(-1.55999 - 0.752618i) q^{3} +(-1.34041 - 2.32167i) q^{4} -1.00000 q^{5} +(3.09769 - 2.10874i) q^{6} +(2.14928 - 1.54292i) q^{7} +1.47299 q^{8} +(1.86713 + 2.34815i) q^{9} +O(q^{10})$	\(q+(-1.08176 + 1.87367i) q^{2} +(-1.55999 - 0.752618i) q^{3} +(-1.34041 - 2.32167i) q^{4} -1.00000 q^{5} +(3.09769 - 2.10874i) q^{6} +(2.14928 - 1.54292i) q^{7} +1.47299 q^{8} +(1.86713 + 2.34815i) q^{9} +(1.08176 - 1.87367i) q^{10} +2.52066 q^{11} +(0.343705 + 4.63059i) q^{12} +(-0.542414 + 0.939489i) q^{13} +(0.565917 + 5.69610i) q^{14} +(1.55999 + 0.752618i) q^{15} +(1.08741 - 1.88345i) q^{16} +(-2.85163 + 4.93917i) q^{17} +(-6.41944 + 0.958242i) q^{18} +(1.75436 + 3.03863i) q^{19} +(1.34041 + 2.32167i) q^{20} +(-4.51408 + 0.789359i) q^{21} +(-2.72676 + 4.72288i) q^{22} -0.273308 q^{23} +(-2.29785 - 1.10860i) q^{24} +1.00000 q^{25} +(-1.17352 - 2.03260i) q^{26} +(-1.14545 - 5.06833i) q^{27} +(-6.46307 - 2.92175i) q^{28} +(4.63947 + 8.03580i) q^{29} +(-3.09769 + 2.10874i) q^{30} +(0.884081 + 1.53127i) q^{31} +(3.82562 + 6.62617i) q^{32} +(-3.93221 - 1.89710i) q^{33} +(-6.16956 - 10.6860i) q^{34} +(-2.14928 + 1.54292i) q^{35} +(2.94889 - 7.48235i) q^{36} +(1.14456 + 1.98243i) q^{37} -7.59118 q^{38} +(1.55324 - 1.05736i) q^{39} -1.47299 q^{40} +(2.65518 - 4.59891i) q^{41} +(3.40416 - 9.31177i) q^{42} +(3.14508 + 5.44743i) q^{43} +(-3.37874 - 5.85214i) q^{44} +(-1.86713 - 2.34815i) q^{45} +(0.295654 - 0.512088i) q^{46} +(-2.34203 + 4.05652i) q^{47} +(-3.11386 + 2.11975i) q^{48} +(2.23878 - 6.63234i) q^{49} +(-1.08176 + 1.87367i) q^{50} +(8.16582 - 5.55886i) q^{51} +2.90824 q^{52} +(4.86938 - 8.43401i) q^{53} +(10.7354 + 3.33654i) q^{54} -2.52066 q^{55} +(3.16586 - 2.27271i) q^{56} +(-0.449846 - 6.06060i) q^{57} -20.0752 q^{58} +(1.68373 + 2.91631i) q^{59} +(-0.343705 - 4.63059i) q^{60} +(-2.47366 + 4.28451i) q^{61} -3.82546 q^{62} +(7.63600 + 2.16599i) q^{63} -12.2040 q^{64} +(0.542414 - 0.939489i) q^{65} +(7.80824 - 5.31544i) q^{66} +(6.42542 + 11.1292i) q^{67} +15.2895 q^{68} +(0.426358 + 0.205697i) q^{69} +(-0.565917 - 5.69610i) q^{70} +10.9734 q^{71} +(2.75026 + 3.45880i) q^{72} +(-0.107878 + 0.186850i) q^{73} -4.95255 q^{74} +(-1.55999 - 0.752618i) q^{75} +(4.70313 - 8.14606i) q^{76} +(5.41761 - 3.88919i) q^{77} +(0.300911 + 4.05406i) q^{78} +(1.95176 - 3.38055i) q^{79} +(-1.08741 + 1.88345i) q^{80} +(-2.02763 + 8.76862i) q^{81} +(5.74454 + 9.94984i) q^{82} +(5.18081 + 8.97342i) q^{83} +(7.88336 + 9.42212i) q^{84} +(2.85163 - 4.93917i) q^{85} -13.6089 q^{86} +(-1.18964 - 16.0275i) q^{87} +3.71291 q^{88} +(-6.78158 - 11.7460i) q^{89} +(6.41944 - 0.958242i) q^{90} +(0.283761 + 2.85612i) q^{91} +(0.366346 + 0.634530i) q^{92} +(-0.226693 - 3.05415i) q^{93} +(-5.06704 - 8.77636i) q^{94} +(-1.75436 - 3.03863i) q^{95} +(-0.980952 - 13.2160i) q^{96} +(-6.91171 - 11.9714i) q^{97} +(10.0050 + 11.3693i) q^{98} +(4.70642 + 5.91890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - 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 $

$2$	−1.08176	+	1.87367i	−0.764921	+	1.32488i	0.175368	+	0.984503i	$0.443889\pi$
$2$	−1.08176	+	1.87367i	−0.764921	+	1.32488i	−0.940289	+	0.340378i	$0.889445\pi$
$3$	−1.55999	−	0.752618i	−0.900660	−	0.434524i
$3$	−1.55999	−	0.752618i	−0.900660	−	0.434524i
$4$	−1.34041	−	2.32167i	−0.670207	−	1.16083i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	3.09769	−	2.10874i	1.26463	−	0.860891i
$7$	2.14928	−	1.54292i	0.812350	−	0.583170i
$7$	2.14928	−	1.54292i	0.812350	−	0.583170i
$8$	1.47299			0.520780
$9$	1.86713	+	2.34815i	0.622377	+	0.782717i
$10$	1.08176	−	1.87367i	0.342083	−	0.592505i
$11$	2.52066			0.760009			0.380005	−	0.924985i	$-0.375922\pi$
$11$	2.52066			0.760009			0.380005	+	0.924985i	$0.375922\pi$
$12$	0.343705	+	4.63059i	0.0992190	+	1.33674i
$13$	−0.542414	+	0.939489i	−0.150439	+	0.260567i	−0.931389	−	0.364026i	$-0.881402\pi$
$13$	−0.542414	+	0.939489i	−0.150439	+	0.260567i	0.780950	+	0.624593i	$0.214735\pi$
$14$	0.565917	+	5.69610i	0.151248	+	1.52235i
$15$	1.55999	+	0.752618i	0.402787	+	0.194325i
$16$	1.08741	−	1.88345i	0.271852	−	0.470861i
$17$	−2.85163	+	4.93917i	−0.691622	+	1.19792i	0.279684	+	0.960092i	$0.409770\pi$
$17$	−2.85163	+	4.93917i	−0.691622	+	1.19792i	−0.971306	+	0.237832i	$0.923563\pi$
$18$	−6.41944	+	0.958242i	−1.51308	+	0.225860i
$19$	1.75436	+	3.03863i	0.402477	+	0.697111i	0.994024	−	0.109160i	$-0.0348160\pi$
$19$	1.75436	+	3.03863i	0.402477	+	0.697111i	−0.591547	+	0.806270i	$0.701483\pi$
$20$	1.34041	+	2.32167i	0.299726	+	0.519140i
$21$	−4.51408	+	0.789359i	−0.985053	+	0.172252i
$22$	−2.72676	+	4.72288i	−0.581347	+	1.00692i
$23$	−0.273308			−0.0569887			−0.0284943	−	0.999594i	$-0.509071\pi$
$23$	−0.273308			−0.0569887			−0.0284943	+	0.999594i	$0.509071\pi$
$24$	−2.29785	−	1.10860i	−0.469046	−	0.226291i
$25$	1.00000			0.200000
$26$	−1.17352	−	2.03260i	−0.230147	−	0.398627i
$27$	−1.14545	−	5.06833i	−0.220441	−	0.975400i
$28$	−6.46307	−	2.92175i	−1.22141	−	0.552158i
$29$	4.63947	+	8.03580i	0.861528	+	1.49221i	0.870454	+	0.492250i	$0.163825\pi$
$29$	4.63947	+	8.03580i	0.861528	+	1.49221i	−0.00892568	+	0.999960i	$0.502841\pi$
$30$	−3.09769	+	2.10874i	−0.565558	+	0.385002i
$31$	0.884081	+	1.53127i	0.158786	+	0.275025i	0.934431	−	0.356144i	$-0.115909\pi$
$31$	0.884081	+	1.53127i	0.158786	+	0.275025i	−0.775645	+	0.631169i	$0.782575\pi$
$32$	3.82562	+	6.62617i	0.676280	+	1.17135i
$33$	−3.93221	−	1.89710i	−0.684510	−	0.330242i
$34$	−6.16956	−	10.6860i	−1.05807	−	1.83263i
$35$	−2.14928	+	1.54292i	−0.363294	+	0.260802i
$36$	2.94889	−	7.48235i	0.491482	−	1.24706i
$37$	1.14456	+	1.98243i	0.188164	+	0.325909i	0.944638	−	0.328114i	$-0.106413\pi$
$37$	1.14456	+	1.98243i	0.188164	+	0.325909i	−0.756474	+	0.654024i	$0.773080\pi$
$38$	−7.59118			−1.23145
$39$	1.55324	−	1.05736i	0.248717	−	0.169313i
$40$	−1.47299			−0.232900
$41$	2.65518	−	4.59891i	0.414670	−	0.718229i	−0.580724	−	0.814100i	$-0.697231\pi$
$41$	2.65518	−	4.59891i	0.414670	−	0.718229i	0.995394	+	0.0958717i	$0.0305639\pi$
$42$	3.40416	−	9.31177i	0.525274	−	1.43684i
$43$	3.14508	+	5.44743i	0.479620	+	0.830726i	0.999727	−	0.0233755i	$-0.00744132\pi$
$43$	3.14508	+	5.44743i	0.479620	+	0.830726i	−0.520107	+	0.854101i	$0.674108\pi$
$44$	−3.37874	−	5.85214i	−0.509364	−	0.882243i
$45$	−1.86713	−	2.34815i	−0.278336	−	0.350042i
$46$	0.295654	−	0.512088i	0.0435918	−	0.0755032i
$47$	−2.34203	+	4.05652i	−0.341620	+	0.591704i	−0.984734	−	0.174067i	$-0.944309\pi$
$47$	−2.34203	+	4.05652i	−0.341620	+	0.591704i	0.643113	+	0.765771i	$0.277642\pi$
$48$	−3.11386	+	2.11975i	−0.449447	+	0.305960i
$49$	2.23878	−	6.63234i	0.319826	−	0.947476i
$50$	−1.08176	+	1.87367i	−0.152984	+	0.264976i
$51$	8.16582	−	5.55886i	1.14344	−	0.778396i
$52$	2.90824			0.403300
$53$	4.86938	−	8.43401i	0.668861	−	1.15850i	−0.309362	−	0.950944i	$-0.600116\pi$
$53$	4.86938	−	8.43401i	0.668861	−	1.15850i	0.978223	−	0.207557i	$-0.0665511\pi$
$54$	10.7354	+	3.33654i	1.46091	+	0.454046i
$55$	−2.52066			−0.339886
$56$	3.16586	−	2.27271i	0.423056	−	0.303703i
$57$	−0.449846	−	6.06060i	−0.0595836	−	0.802746i
$58$	−20.0752			−2.63600
$59$	1.68373	+	2.91631i	0.219203	+	0.379671i	0.954565	−	0.298004i	$-0.0963208\pi$
$59$	1.68373	+	2.91631i	0.219203	+	0.379671i	−0.735361	+	0.677675i	$0.762988\pi$
$60$	−0.343705	−	4.63059i	−0.0443721	−	0.597807i
$61$	−2.47366	+	4.28451i	−0.316720	+	0.548575i	−0.979802	−	0.199972i	$-0.935915\pi$
$61$	−2.47366	+	4.28451i	−0.316720	+	0.548575i	0.663081	+	0.748547i	$0.269248\pi$
$62$	−3.82546			−0.485834
$63$	7.63600	+	2.16599i	0.962046	+	0.272889i
$64$	−12.2040			−1.52550
$65$	0.542414	−	0.939489i	0.0672782	−	0.116529i
$66$	7.80824	−	5.31544i	0.961128	−	0.654285i
$67$	6.42542	+	11.1292i	0.784990	+	1.35964i	0.929005	+	0.370068i	$0.120665\pi$
$67$	6.42542	+	11.1292i	0.784990	+	1.35964i	−0.144015	+	0.989576i	$0.546001\pi$
$68$	15.2895			1.85412
$69$	0.426358	+	0.205697i	0.0513274	+	0.0247630i
$70$	−0.565917	−	5.69610i	−0.0676400	−	0.680814i
$71$	10.9734			1.30230			0.651149	−	0.758950i	$-0.274287\pi$
$71$	10.9734			1.30230			0.651149	+	0.758950i	$0.274287\pi$
$72$	2.75026	+	3.45880i	0.324122	+	0.407623i
$73$	−0.107878	+	0.186850i	−0.0126262	+	0.0218692i	−0.872269	−	0.489026i	$-0.837352\pi$
$73$	−0.107878	+	0.186850i	−0.0126262	+	0.0218692i	0.859643	+	0.510895i	$0.170686\pi$
$74$	−4.95255			−0.575722
$75$	−1.55999	−	0.752618i	−0.180132	−	0.0869048i
$76$	4.70313	−	8.14606i	0.539486	−	0.934417i
$77$	5.41761	−	3.88919i	0.617393	−	0.443214i
$78$	0.300911	+	4.05406i	0.0340715	+	0.459032i
$79$	1.95176	−	3.38055i	0.219590	−	0.380342i	−0.735092	−	0.677967i	$-0.762861\pi$
$79$	1.95176	−	3.38055i	0.219590	−	0.380342i	0.954683	+	0.297625i	$0.0961946\pi$
$80$	−1.08741	+	1.88345i	−0.121576	+	0.210576i
$81$	−2.02763	+	8.76862i	−0.225293	+	0.974291i
$82$	5.74454	+	9.94984i	0.634379	+	1.09878i
$83$	5.18081	+	8.97342i	0.568667	+	0.984961i	0.996698	+	0.0811964i	$0.0258741\pi$
$83$	5.18081	+	8.97342i	0.568667	+	0.984961i	−0.428031	+	0.903764i	$0.640793\pi$
$84$	7.88336	+	9.42212i	0.860146	+	1.02804i
$85$	2.85163	−	4.93917i	0.309303	−	0.535728i
$86$	−13.6089			−1.46748
$87$	−1.18964	−	16.0275i	−0.127543	−	1.71833i
$88$	3.71291			0.395797
$89$	−6.78158	−	11.7460i	−0.718846	−	1.24508i	−0.961457	−	0.274954i	$-0.911338\pi$
$89$	−6.78158	−	11.7460i	−0.718846	−	1.24508i	0.242612	−	0.970123i	$-0.421996\pi$
$90$	6.41944	−	0.958242i	0.676669	−	0.101008i
$91$	0.283761	+	2.85612i	0.0297462	+	0.299403i
$92$	0.366346	+	0.634530i	0.0381942	+	0.0661543i
$93$	−0.226693	−	3.05415i	−0.0235070	−	0.316700i
$94$	−5.06704	−	8.77636i	−0.522625	−	0.905213i
$95$	−1.75436	−	3.03863i	−0.179993	−	0.311757i
$96$	−0.980952	−	13.2160i	−0.100118	−	1.34885i
$97$	−6.91171	−	11.9714i	−0.701778	−	1.21552i	−0.967842	−	0.251560i	$-0.919056\pi$
$97$	−6.91171	−	11.9714i	−0.701778	−	1.21552i	0.266064	−	0.963955i	$-0.414277\pi$
$98$	10.0050	+	11.3693i	1.01065	+	1.14848i
$99$	4.70642	+	5.91890i	0.473013	+	0.594872i
$100$	−1.34041	−	2.32167i	−0.134041	−	0.232167i
$101$	−10.2886			−1.02376			−0.511878	−	0.859058i	$-0.671050\pi$
$101$	−10.2886			−1.02376			−0.511878	+	0.859058i	$0.671050\pi$
$102$	1.58198	+	21.3134i	0.156639	+	2.11034i
$103$	18.3697			1.81002			0.905008	−	0.425395i	$-0.139865\pi$
$103$	18.3697			1.81002			0.905008	+	0.425395i	$0.139865\pi$
$104$	−0.798969	+	1.38386i	−0.0783454	+	0.135698i
$105$	4.51408	−	0.789359i	0.440529	−	0.0770335i
$106$	10.5350	+	18.2472i	1.02325	+	1.77232i
$107$	−7.21802	−	12.5020i	−0.697793	−	1.20861i	−0.969230	−	0.246156i	$-0.920832\pi$
$107$	−7.21802	−	12.5020i	−0.697793	−	1.20861i	0.271437	−	0.962456i	$-0.412501\pi$
$108$	−10.2316	+	9.45300i	−0.984536	+	0.909615i
$109$	−10.0219	+	17.3584i	−0.959924	+	1.66264i	−0.237249	+	0.971449i	$0.576246\pi$
$109$	−10.0219	+	17.3584i	−0.959924	+	1.66264i	−0.722675	+	0.691188i	$0.757088\pi$
$110$	2.72676	−	4.72288i	0.259986	−	0.450309i
$111$	−0.293483	−	3.95398i	−0.0278562	−	0.375295i
$112$	−0.568871	−	5.72583i	−0.0537533	−	0.541040i
$113$	9.36733	−	16.2247i	0.881204	−	1.52629i	0.0312006	−	0.999513i	$-0.490067\pi$
$113$	9.36733	−	16.2247i	0.881204	−	1.52629i	0.850003	−	0.526777i	$-0.176600\pi$
$114$	11.8422	+	5.71326i	1.10912	+	0.535096i
$115$	0.273308			0.0254861
$116$	12.4376	−	21.5426i	1.15480	−	2.00018i
$117$	−3.21882	+	0.480479i	−0.297580	+	0.0444203i
$118$	−7.28559			−0.670693
$119$	1.49181	+	15.0155i	0.136754	+	1.37647i
$120$	2.29785	+	1.10860i	0.209764	+	0.101201i
$121$	−4.64625			−0.422386
$122$	−5.35183	−	9.26963i	−0.484532	−	0.839233i
$123$	−7.60327	+	5.17591i	−0.685564	+	0.466696i
$124$	2.37007	−	4.10508i	0.212839	−	0.368647i
$125$	−1.00000			−0.0894427
$126$	−12.3187	+	11.9642i	−1.09743	+	1.06586i
$127$	−10.6444			−0.944539			−0.472269	−	0.881454i	$-0.656565\pi$
$127$	−10.6444			−0.944539			−0.472269	+	0.881454i	$0.656565\pi$
$128$	5.55057	−	9.61386i	0.490605	−	0.849753i
$129$	−0.806450	−	10.8650i	−0.0710040	−	0.956608i
$130$	1.17352	+	2.03260i	0.102925	+	0.178271i
$131$	−19.8935			−1.73810			−0.869052	−	0.494722i	$-0.835270\pi$
$131$	−19.8935			−1.73810			−0.869052	+	0.494722i	$0.835270\pi$
$132$	0.866364	+	11.6722i	0.0754073	+	1.01593i
$133$	8.45898	+	3.82403i	0.733486	+	0.331585i
$134$	−27.8031			−2.40182
$135$	1.14545	+	5.06833i	0.0985842	+	0.436212i
$136$	−4.20042	+	7.27533i	−0.360183	+	0.623855i
$137$	−13.5567			−1.15823			−0.579113	−	0.815247i	$-0.696601\pi$
$137$	−13.5567			−1.15823			−0.579113	+	0.815247i	$0.696601\pi$
$138$	−0.846623	+	0.576337i	−0.0720694	+	0.0490610i
$139$	5.37133	−	9.30342i	0.455590	−	0.789105i	−0.543132	−	0.839648i	$-0.682762\pi$
$139$	5.37133	−	9.30342i	0.455590	−	0.789105i	0.998722	+	0.0505421i	$0.0160949\pi$
$140$	6.46307	+	2.92175i	0.546229	+	0.246933i
$141$	6.70655	−	4.56547i	0.564793	−	0.384482i
$142$	−11.8705	+	20.5604i	−0.996154	+	1.72539i
$143$	−1.36724	+	2.36814i	−0.114335	+	0.198033i
$144$	6.45295	−	0.963244i	0.537746	−	0.0802703i
$145$	−4.63947	−	8.03580i	−0.385287	−	0.667337i
$146$	−0.233397	−	0.404255i	−0.0193161	−	0.0334564i
$147$	−8.48408	+	8.66143i	−0.699756	+	0.714382i
$148$	3.06836	−	5.31456i	0.252218	−	0.436854i
$149$	−11.9813			−0.981543			−0.490772	−	0.871288i	$-0.663285\pi$
$149$	−11.9813			−0.981543			−0.490772	+	0.871288i	$0.663285\pi$
$150$	3.09769	−	2.10874i	0.252925	−	0.172178i
$151$	5.76381			0.469052			0.234526	−	0.972110i	$-0.424646\pi$
$151$	5.76381			0.469052			0.234526	+	0.972110i	$0.424646\pi$
$152$	2.58415	+	4.47587i	0.209602	+	0.363041i
$153$	−16.9223	+	2.52602i	−1.36809	+	0.204217i
$154$	1.42649	+	14.3580i	0.114950	+	1.15700i
$155$	−0.884081	−	1.53127i	−0.0710111	−	0.122995i
$156$	−4.53682	−	2.18879i	−0.363236	−	0.175244i
$157$	5.56990	+	9.64735i	0.444527	+	0.769943i	0.998019	−	0.0629115i	$-0.0200386\pi$
$157$	5.56990	+	9.64735i	0.444527	+	0.769943i	−0.553493	+	0.832854i	$0.686705\pi$
$158$	4.22268	+	7.31390i	0.335939	+	0.581863i
$159$	−13.9438	+	9.49219i	−1.10581	+	0.752779i
$160$	−3.82562	−	6.62617i	−0.302442	−	0.523844i
$161$	−0.587415	+	0.421693i	−0.0462947	+	0.0332341i
$162$	−14.2360	−	13.2847i	−1.11849	−	1.04374i
$163$	−0.636575	−	1.10258i	−0.0498604	−	0.0863607i	0.840018	−	0.542558i	$-0.182544\pi$
$163$	−0.636575	−	1.10258i	−0.0498604	−	0.0863607i	−0.889878	+	0.456198i	$0.849211\pi$
$164$	−14.2362			−1.11166
$165$	3.93221	+	1.89710i	0.306122	+	0.147689i
$166$	−22.4176			−1.73994
$167$	−0.472660	+	0.818671i	−0.0365755	+	0.0633506i	−0.883734	−	0.467990i	$-0.844978\pi$
$167$	−0.472660	+	0.818671i	−0.0365755	+	0.0633506i	0.847158	+	0.531341i	$0.178312\pi$
$168$	−6.64918	+	1.16272i	−0.512996	+	0.0897055i
$169$	5.91157	+	10.2391i	0.454736	+	0.787627i
$170$	6.16956	+	10.6860i	0.473184	+	0.819579i
$171$	−3.85956	+	9.79303i	−0.295148	+	0.748892i
$172$	8.43141	−	14.6036i	0.642889	−	1.11352i
$173$	3.52039	−	6.09749i	0.267650	−	0.463584i	−0.700604	−	0.713550i	$-0.747086\pi$
$173$	3.52039	−	6.09749i	0.267650	−	0.463584i	0.968255	+	0.249966i	$0.0804196\pi$
$174$	31.3171	+	15.1090i	2.37414	+	1.14541i
$175$	2.14928	−	1.54292i	0.162470	−	0.116634i
$176$	2.74099	−	4.74753i	0.206610	−	0.357859i
$177$	−0.431737	−	5.81662i	−0.0324514	−	0.437204i
$178$	29.3442			2.19944
$179$	−3.95249	+	6.84590i	−0.295423	+	0.511687i	−0.975083	−	0.221840i	$-0.928794\pi$
$179$	−3.95249	+	6.84590i	−0.295423	+	0.511687i	0.679661	+	0.733527i	$0.262127\pi$
$180$	−2.94889	+	7.48235i	−0.219797	+	0.557702i
$181$	13.2016			0.981268			0.490634	−	0.871366i	$-0.336765\pi$
$181$	13.2016			0.981268			0.490634	+	0.871366i	$0.336765\pi$
$182$	−5.65838	−	2.55797i	−0.419427	−	0.189609i
$183$	7.08349	−	4.82207i	0.523627	−	0.356457i
$184$	−0.402579			−0.0296785
$185$	−1.14456	−	1.98243i	−0.0841495	−	0.145751i
$186$	5.96768	+	2.87911i	0.437571	+	0.211107i
$187$	−7.18800	+	12.4500i	−0.525639	+	0.910433i
$188$	12.5572			0.915826
$189$	−10.2819	−	9.12591i	−0.747900	−	0.663812i
$190$	7.59118			0.550722
$191$	3.46679	−	6.00466i	0.250848	−	0.434482i	−0.712911	−	0.701254i	$-0.752624\pi$
$191$	3.46679	−	6.00466i	0.250848	−	0.434482i	0.963760	+	0.266772i	$0.0859571\pi$
$192$	19.0381	+	9.18494i	1.37396	+	0.662866i
$193$	−4.91963	−	8.52105i	−0.354123	−	0.613359i	0.632845	−	0.774279i	$-0.281887\pi$
$193$	−4.91963	−	8.52105i	−0.354123	−	0.613359i	−0.986967	+	0.160920i	$0.948554\pi$
$194$	29.9073			2.14722
$195$	−1.55324	+	1.05736i	−0.111230	+	0.0757192i
$196$	−18.3990	+	3.69238i	−1.31421	+	0.263742i
$197$	4.92577			0.350947			0.175473	−	0.984484i	$-0.443854\pi$
$197$	4.92577			0.350947			0.175473	+	0.984484i	$0.443854\pi$
$198$	−16.1813	+	2.41541i	−1.14995	+	0.171655i
$199$	2.96416	−	5.13407i	0.210123	−	0.363945i	−0.741630	−	0.670810i	$-0.765947\pi$
$199$	2.96416	−	5.13407i	0.210123	−	0.363945i	0.951753	+	0.306865i	$0.0992801\pi$
$200$	1.47299			0.104156
$201$	−1.64759	−	22.1973i	−0.116212	−	1.56567i
$202$	11.1298	−	19.2774i	0.783092	−	1.35635i
$203$	22.3701	+	10.1128i	1.57007	+	0.709780i
$204$	−23.8514	−	11.5071i	−1.66993	−	0.805660i
$205$	−2.65518	+	4.59891i	−0.185446	+	0.321202i
$206$	−19.8716	+	34.4186i	−1.38452	+	2.39806i
$207$	−0.510302	−	0.641769i	−0.0354685	−	0.0446060i
$208$	1.17965	+	2.04321i	0.0817940	+	0.141671i
$209$	4.42214	+	7.65938i	0.305886	+	0.529810i
$210$	−3.40416	+	9.31177i	−0.234909	+	0.642573i
$211$	1.57045	−	2.72010i	0.108114	−	0.187260i	−0.806892	−	0.590699i	$-0.798852\pi$
$211$	1.57045	−	2.72010i	0.108114	−	0.187260i	0.915006	+	0.403439i	$0.132185\pi$
$212$	−26.1079			−1.79310
$213$	−17.1183	−	8.25874i	−1.17293	−	0.565880i
$214$	31.2327			2.13502
$215$	−3.14508	−	5.44743i	−0.214492	−	0.371512i
$216$	−1.68723	−	7.46559i	−0.114801	−	0.507969i
$217$	4.26277	+	1.92706i	0.289376	+	0.130817i
$218$	−21.6826	−	37.5554i	−1.46853	−	2.54357i
$219$	0.308916	−	0.210294i	0.0208746	−	0.0142103i
$220$	3.37874	+	5.85214i	0.227794	+	0.394551i
$221$	−3.09353	−	5.35815i	−0.208093	−	0.360428i
$222$	7.72592	+	3.72738i	0.518530	+	0.250165i
$223$	−1.24047	−	2.14855i	−0.0830679	−	0.143878i	0.821498	−	0.570211i	$-0.193138\pi$
$223$	−1.24047	−	2.14855i	−0.0830679	−	0.143878i	−0.904566	+	0.426333i	$0.859805\pi$
$224$	18.4460	+	8.33883i	1.23247	+	0.557161i
$225$	1.86713	+	2.34815i	0.124475	+	0.156543i
$226$	20.2664	+	35.1025i	1.34810	+	2.33498i
$227$	26.5203			1.76021			0.880106	−	0.474778i	$-0.157472\pi$
$227$	26.5203			1.76021			0.880106	+	0.474778i	$0.157472\pi$
$228$	−13.4677	+	9.16810i	−0.891920	+	0.607173i
$229$	−20.4619			−1.35216			−0.676079	−	0.736829i	$-0.736322\pi$
$229$	−20.4619			−1.35216			−0.676079	+	0.736829i	$0.736322\pi$
$230$	−0.295654	+	0.512088i	−0.0194948	+	0.0337661i
$231$	−11.3785	+	1.98971i	−0.748649	+	0.130913i
$232$	6.83388	+	11.8366i	0.448666	+	0.777113i
$233$	10.3634	+	17.9499i	0.678929	+	1.17594i	0.975304	+	0.220868i	$0.0708891\pi$
$233$	10.3634	+	17.9499i	0.678929	+	1.17594i	−0.296374	+	0.955072i	$0.595778\pi$
$234$	2.58174	−	6.55076i	0.168773	−	0.428236i
$235$	2.34203	−	4.05652i	0.152777	−	0.264618i
$236$	4.51380	−	7.81813i	0.293823	−	0.508917i
$237$	−5.58899	+	3.80469i	−0.363044	+	0.247141i
$238$	−29.7478	−	13.4480i	−1.92826	−	0.871705i
$239$	−1.88457	+	3.26418i	−0.121903	+	0.211142i	−0.920518	−	0.390700i	$-0.872233\pi$
$239$	−1.88457	+	3.26418i	−0.121903	+	0.211142i	0.798615	+	0.601842i	$0.205566\pi$
$240$	3.11386	−	2.11975i	0.200999	−	0.136829i
$241$	7.18908			0.463089			0.231545	−	0.972824i	$-0.425622\pi$
$241$	7.18908			0.463089			0.231545	+	0.972824i	$0.425622\pi$
$242$	5.02613	−	8.70551i	0.323092	−	0.559612i
$243$	9.76251	−	12.1529i	0.626265	−	0.779610i
$244$	13.2629			0.849072
$245$	−2.23878	+	6.63234i	−0.143030	+	0.423724i
$246$	−1.47300	−	19.8451i	−0.0939148	−	1.26528i
$247$	−3.80635			−0.242192
$248$	1.30224	+	2.25555i	0.0826924	+	0.143227i
$249$	−1.32844	−	17.8976i	−0.0841868	−	1.13421i
$250$	1.08176	−	1.87367i	0.0684166	−	0.118501i
$251$	−12.3897			−0.782031			−0.391016	−	0.920384i	$-0.627876\pi$
$251$	−12.3897			−0.782031			−0.391016	+	0.920384i	$0.627876\pi$
$252$	−5.20671	−	20.6316i	−0.327992	−	1.29967i
$253$	−0.688918			−0.0433119
$254$	11.5147	−	19.9441i	0.722497	−	1.25140i
$255$	−8.16582	+	5.55886i	−0.511363	+	0.348109i
$256$	−0.195217	−	0.338126i	−0.0122011	−	0.0211329i
$257$	24.4919			1.52776			0.763880	−	0.645358i	$-0.223292\pi$
$257$	24.4919			1.52776			0.763880	+	0.645358i	$0.223292\pi$
$258$	21.2297	+	10.2423i	1.32170	+	0.637657i
$259$	5.51870	+	2.49483i	0.342916	+	0.155021i
$260$	−2.90824			−0.180361
$261$	−10.2068	+	25.8981i	−0.631783	+	1.60305i
$262$	21.5200	−	37.2738i	1.32951	−	2.30278i
$263$	8.08761			0.498703			0.249352	−	0.968413i	$-0.419783\pi$
$263$	8.08761			0.498703			0.249352	+	0.968413i	$0.419783\pi$
$264$	−5.79210	−	2.79440i	−0.356479	−	0.171984i
$265$	−4.86938	+	8.43401i	−0.299124	+	0.518097i
$266$	−16.3155	+	11.7126i	−1.00037	+	0.718146i
$267$	1.73891	+	23.4276i	0.106419	+	1.43375i
$268$	17.2255	−	29.8354i	1.05221	−	1.82249i
$269$	−2.38892	+	4.13774i	−0.145655	+	0.252282i	−0.929617	−	0.368527i	$-0.879862\pi$
$269$	−2.38892	+	4.13774i	−0.145655	+	0.252282i	0.783962	+	0.620809i	$0.213196\pi$
$270$	−10.7354	−	3.33654i	−0.653339	−	0.203055i
$271$	0.249128	+	0.431503i	0.0151335	+	0.0262119i	0.873493	−	0.486837i	$-0.161849\pi$
$271$	0.249128	+	0.431503i	0.0151335	+	0.0262119i	−0.858359	+	0.513049i	$0.828516\pi$
$272$	6.20177	+	10.7418i	0.376037	+	0.651316i
$273$	1.70691	−	4.66909i	0.103307	−	0.282586i
$274$	14.6651	−	25.4007i	0.885951	−	1.53451i
$275$	2.52066			0.152002
$276$	−0.0939372	−	1.26558i	−0.00565436	−	0.0761789i
$277$	−27.8993			−1.67630			−0.838152	−	0.545437i	$-0.816364\pi$
$277$	−27.8993			−1.67630			−0.838152	+	0.545437i	$0.816364\pi$
$278$	11.6210	+	20.1281i	0.696981	+	1.20721i
$279$	−1.94497	+	4.93505i	−0.116442	+	0.295454i
$280$	−3.16586	+	2.27271i	−0.189196	+	0.135820i
$281$	−2.67023	−	4.62498i	−0.159293	−	0.275903i	0.775321	−	0.631567i	$-0.217588\pi$
$281$	−2.67023	−	4.62498i	−0.159293	−	0.275903i	−0.934614	+	0.355664i	$0.884255\pi$
$282$	1.29927	+	17.5046i	0.0773706	+	1.04238i
$283$	15.8455	+	27.4453i	0.941920	+	1.63145i	0.761804	+	0.647808i	$0.224314\pi$
$283$	15.8455	+	27.4453i	0.941920	+	1.63145i	0.180116	+	0.983645i	$0.442353\pi$
$284$	−14.7088	−	25.4765i	−0.872809	−	1.51175i
$285$	0.449846	+	6.06060i	0.0266466	+	0.358999i
$286$	−2.95806	−	5.12352i	−0.174914	−	0.302960i
$287$	−1.38904	−	13.9811i	−0.0819926	−	0.825276i
$288$	−8.41631	+	21.3551i	−0.495936	+	1.25836i
$289$	−7.76359	−	13.4469i	−0.456682	−	0.790996i
$290$	20.0752			1.17886
$291$	1.77228	+	23.8772i	0.103893	+	1.39971i
$292$	0.578406			0.0338486
$293$	−2.45898	+	4.25908i	−0.143655	+	0.248818i	−0.928870	−	0.370405i	$-0.879219\pi$
$293$	−2.45898	+	4.25908i	−0.143655	+	0.248818i	0.785215	+	0.619223i	$0.212552\pi$
$294$	−7.05086	−	25.2659i	−0.411215	−	1.47354i
$295$	−1.68373	−	2.91631i	−0.0980307	−	0.169794i
$296$	1.68592	+	2.92010i	0.0979920	+	0.169727i
$297$	−2.88728	−	12.7756i	−0.167537	−	0.741313i
$298$	12.9609	−	22.4489i	0.750803	−	1.30043i
$299$	0.148246	−	0.256770i	0.00857329	−	0.0148494i
$300$	0.343705	+	4.63059i	0.0198438	+	0.267347i
$301$	15.1646	+	6.85543i	0.874073	+	0.395140i
$302$	−6.23506	+	10.7994i	−0.358788	+	0.621438i
$303$	16.0501	+	7.74340i	0.922056	+	0.444847i
$304$	7.63080			0.437657
$305$	2.47366	−	4.28451i	0.141642	−	0.245330i
$306$	13.5730	−	34.4393i	0.775914	−	1.96876i
$307$	−13.9386			−0.795519			−0.397760	−	0.917490i	$-0.630212\pi$
$307$	−13.9386			−0.795519			−0.397760	+	0.917490i	$0.630212\pi$
$308$	−16.2912	−	7.36474i	−0.928279	−	0.419645i
$309$	−28.6565	−	13.8253i	−1.63021	−	0.786495i
$310$	3.82546			0.217272
$311$	−1.34331	−	2.32668i	−0.0761722	−	0.131934i	0.825423	−	0.564514i	$-0.190937\pi$
$311$	−1.34331	−	2.32668i	−0.0761722	−	0.131934i	−0.901595	+	0.432580i	$0.857603\pi$
$312$	2.28790	−	1.55748i	0.129527	−	0.0881750i
$313$	0.832722	−	1.44232i	0.0470682	−	0.0815245i	−0.841531	−	0.540208i	$-0.818346\pi$
$313$	0.832722	−	1.44232i	0.0470682	−	0.0815245i	0.888600	+	0.458684i	$0.151679\pi$
$314$	−24.1012			−1.36011
$315$	−7.63600	−	2.16599i	−0.430240	−	0.122039i
$316$	−10.4647			−0.588684
$317$	14.4913	−	25.0996i	0.813910	−	1.40973i	−0.0961980	−	0.995362i	$-0.530668\pi$
$317$	14.4913	−	25.0996i	0.813910	−	1.40973i	0.910108	−	0.414371i	$-0.135998\pi$
$318$	−2.70135	−	36.3942i	−0.151484	−	2.04089i
$319$	11.6946	+	20.2556i	0.654769	+	1.13409i
$320$	12.2040			0.682224
$321$	1.85082	+	24.9354i	0.103303	+	1.39176i
$322$	−0.154670	−	1.55679i	−0.00861940	−	0.0867565i
$323$	−20.0111			−1.11345
$324$	23.0757	−	7.04610i	1.28198	−	0.391450i
$325$	−0.542414	+	0.939489i	−0.0300877	+	0.0521135i
$326$	2.75449			0.152557
$327$	28.6983	−	19.5363i	1.58702	−	1.08036i
$328$	3.91105	−	6.77414i	0.215952	−	0.374039i
$329$	1.22522	+	12.3321i	0.0675486	+	0.679893i
$330$	−7.80824	+	5.31544i	−0.429829	+	0.292605i
$331$	12.5999	−	21.8237i	0.692555	−	1.19954i	−0.278443	−	0.960453i	$-0.589818\pi$
$331$	12.5999	−	21.8237i	0.692555	−	1.19954i	0.970998	−	0.239088i	$-0.0768485\pi$
$332$	13.8889	−	24.0562i	0.762250	−	1.32026i
$333$	−2.51801	+	6.38905i	−0.137986	+	0.350118i
$334$	−1.02261	−	1.77121i	−0.0559547	−	0.0969164i
$335$	−6.42542	−	11.1292i	−0.351058	−	0.608051i
$336$	−3.42193	+	9.36038i	−0.186682	+	0.510650i
$337$	−8.11842	+	14.0615i	−0.442238	+	0.765979i	−0.997855	−	0.0654591i	$-0.979149\pi$
$337$	−8.11842	+	14.0615i	−0.442238	+	0.765979i	0.555617	+	0.831438i	$0.312482\pi$
$338$	−25.5796			−1.39135
$339$	−26.8239	+	18.2603i	−1.45688	+	0.991764i
$340$	−15.2895			−0.829188
$341$	2.22847	+	3.85983i	0.120679	+	0.209021i
$342$	−14.1737	−	17.8252i	−0.766428	−	0.963879i
$343$	−5.42143	−	17.7090i	−0.292730	−	0.956195i
$344$	4.63266	+	8.02400i	0.249776	+	0.432625i
$345$	−0.426358	−	0.205697i	−0.0229543	−	0.0110743i
$346$	7.61644	+	13.1921i	0.409462	+	0.709209i
$347$	−5.16058	−	8.93839i	−0.277035	−	0.479838i	0.693612	−	0.720349i	$-0.256018\pi$
$347$	−5.16058	−	8.93839i	−0.277035	−	0.479838i	−0.970646	+	0.240511i	$0.922685\pi$
$348$	−35.6159	+	24.2454i	−1.90921	+	1.29969i
$349$	1.88276	+	3.26103i	0.100782	+	0.174559i	0.912007	−	0.410175i	$-0.134532\pi$
$349$	1.88276	+	3.26103i	0.100782	+	0.174559i	−0.811225	+	0.584734i	$0.801199\pi$
$350$	0.565917	+	5.69610i	0.0302495	+	0.304469i
$351$	5.38294	+	1.67300i	0.287320	+	0.0892981i
$352$	9.64310	+	16.7023i	0.513979	+	0.890238i
$353$	14.9957			0.798140			0.399070	−	0.916921i	$-0.369333\pi$
$353$	14.9957			0.798140			0.399070	+	0.916921i	$0.369333\pi$
$354$	11.3654	+	5.48326i	0.604066	+	0.291432i
$355$	−10.9734			−0.582405
$356$	−18.1802	+	31.4891i	−0.963551	+	1.66892i
$357$	8.97371	−	24.5468i	0.474939	−	1.29915i
$358$	−8.55129	−	14.8113i	−0.451950	−	0.782800i
$359$	−3.80747	−	6.59474i	−0.200951	−	0.348057i	0.747884	−	0.663829i	$-0.231070\pi$
$359$	−3.80747	−	6.59474i	−0.200951	−	0.348057i	−0.948835	+	0.315772i	$0.897736\pi$
$360$	−2.75026	−	3.45880i	−0.144952	−	0.182295i
$361$	3.34447	−	5.79279i	0.176025	−	0.304883i
$362$	−14.2810	+	24.7354i	−0.750592	+	1.30006i
$363$	7.24810	+	3.49685i	0.380426	+	0.183537i
$364$	6.25061	−	4.48719i	0.327621	−	0.235192i
$365$	0.107878	−	0.186850i	0.00564660	−	0.00978020i
$366$	1.37230	+	18.4884i	0.0717311	+	0.966405i
$367$	−10.1947			−0.532160			−0.266080	−	0.963951i	$-0.585728\pi$
$367$	−10.1947			−0.532160			−0.266080	+	0.963951i	$0.585728\pi$
$368$	−0.297197	+	0.514761i	−0.0154925	+	0.0268338i
$369$	15.7565	−	2.35200i	0.820251	−	0.122440i
$370$	4.95255			0.257471
$371$	−2.54739	−	25.6401i	−0.132254	−	1.33117i
$372$	−6.78684	+	4.62013i	−0.351881	+	0.239542i
$373$	−20.1884			−1.04531			−0.522657	−	0.852543i	$-0.675059\pi$
$373$	−20.1884			−1.04531			−0.522657	+	0.852543i	$0.675059\pi$
$374$	−15.5514	−	26.9358i	−0.804144	−	1.39282i
$375$	1.55999	+	0.752618i	0.0805575	+	0.0388650i
$376$	−3.44978	+	5.97520i	−0.177909	+	0.308147i
$377$	−10.0661			−0.518428
$378$	28.2215	−	9.39282i	1.45156	−	0.483115i
$379$	−15.9413			−0.818852			−0.409426	−	0.912343i	$-0.634271\pi$
$379$	−15.9413			−0.818852			−0.409426	+	0.912343i	$0.634271\pi$
$380$	−4.70313	+	8.14606i	−0.241265	+	0.417884i
$381$	16.6052	+	8.01118i	0.850709	+	0.410425i
$382$	7.50048	+	12.9912i	0.383758	+	0.664688i
$383$	−29.6997			−1.51758			−0.758792	−	0.651333i	$-0.774210\pi$
$383$	−29.6997			−1.51758			−0.758792	+	0.651333i	$0.774210\pi$
$384$	−15.8944	+	10.8201i	−0.811107	+	0.552159i
$385$	−5.41761	+	3.88919i	−0.276107	+	0.198212i
$386$	21.2875			1.08350
$387$	−6.91912	+	17.5562i	−0.351719	+	0.892431i
$388$	−18.5291	+	32.0934i	−0.940673	+	1.62929i
$389$	0.947100			0.0480199			0.0240099	−	0.999712i	$-0.492357\pi$
$389$	0.947100			0.0480199			0.0240099	+	0.999712i	$0.492357\pi$
$390$	−0.300911	−	4.05406i	−0.0152372	−	0.205285i
$391$	0.779373	−	1.34991i	0.0394146	−	0.0682681i
$392$	3.29769	−	9.76935i	0.166559	−	0.493427i
$393$	31.0336	+	14.9722i	1.56544	+	0.755248i
$394$	−5.32851	+	9.22925i	−0.268446	+	0.464963i
$395$	−1.95176	+	3.38055i	−0.0982038	+	0.170094i
$396$	7.43317	−	18.8605i	0.373531	−	0.947776i
$397$	5.41011	+	9.37059i	0.271526	+	0.470297i	0.969253	−	0.246067i	$-0.0791384\pi$
$397$	5.41011	+	9.37059i	0.271526	+	0.470297i	−0.697727	+	0.716364i	$0.745805\pi$
$398$	6.41302	+	11.1077i	0.321456	+	0.556777i
$399$	−10.3179	−	12.3318i	−0.516540	−	0.617363i
$400$	1.08741	−	1.88345i	0.0543704	−	0.0941723i
$401$	−3.26387			−0.162990			−0.0814950	−	0.996674i	$-0.525969\pi$
$401$	−3.26387			−0.162990			−0.0814950	+	0.996674i	$0.525969\pi$
$402$	43.3725	+	20.9251i	2.16322	+	1.04365i
$403$	−1.91815			−0.0955500
$404$	13.7910	+	23.8867i	0.686128	+	1.18841i
$405$	2.02763	−	8.76862i	0.100754	−	0.435716i
$406$	−43.1471	+	30.9745i	−2.14136	+	1.53724i
$407$	2.88504	+	4.99704i	0.143006	+	0.247694i
$408$	12.0282	−	8.18813i	0.595482	−	0.405373i
$409$	−16.4987	−	28.5765i	−0.815807	−	1.41302i	−0.908747	−	0.417348i	$-0.862960\pi$
$409$	−16.4987	−	28.5765i	−0.815807	−	1.41302i	0.0929397	−	0.995672i	$-0.470374\pi$
$410$	−5.74454	−	9.94984i	−0.283703	−	0.491388i
$411$	21.1483	+	10.2030i	1.04317	+	0.503277i
$412$	−24.6229	−	42.6482i	−1.21309	−	2.10113i
$413$	8.11845	+	3.67009i	0.399483	+	0.180593i
$414$	1.75448	−	0.261895i	0.0862282	−	0.0128714i
$415$	−5.18081	−	8.97342i	−0.254316	−	0.440488i
$416$	−8.30028			−0.406955
$417$	−15.3811	+	10.4707i	−0.753217	+	0.512751i
$418$	−19.1348			−0.935915
$419$	17.0245	−	29.4874i	0.831703	−	1.44055i	−0.0649832	−	0.997886i	$-0.520699\pi$
$419$	17.0245	−	29.4874i	0.831703	−	1.44055i	0.896687	−	0.442666i	$-0.145967\pi$
$420$	−7.88336	−	9.42212i	−0.384669	−	0.459752i
$421$	8.49807	+	14.7191i	0.414171	+	0.717364i	0.995341	−	0.0964175i	$-0.0307384\pi$
$421$	8.49807	+	14.7191i	0.414171	+	0.717364i	−0.581170	+	0.813782i	$0.697405\pi$
$422$	3.39771	+	5.88500i	0.165398	+	0.286478i
$423$	−13.8982	+	2.07461i	−0.675754	+	0.100871i
$424$	7.17254	−	12.4232i	0.348329	−	0.603324i
$425$	−2.85163	+	4.93917i	−0.138324	+	0.239585i
$426$	33.9920	−	23.1400i	1.64692	−	1.12114i
$427$	1.29408	+	13.0253i	0.0626251	+	0.630337i
$428$	−19.3503	+	33.5157i	−0.935331	+	1.62004i
$429$	3.91519	−	2.66525i	0.189027	−	0.128680i
$430$	13.6089			0.656279
$431$	−1.15916	+	2.00773i	−0.0558349	+	0.0967090i	−0.892592	−	0.450866i	$-0.851115\pi$
$431$	−1.15916	+	2.00773i	−0.0558349	+	0.0967090i	0.836757	+	0.547574i	$0.184449\pi$
$432$	−10.7915	−	3.35396i	−0.519206	−	0.161367i
$433$	−21.8516			−1.05012			−0.525062	−	0.851064i	$-0.675958\pi$
$433$	−21.8516			−1.05012			−0.525062	+	0.851064i	$0.675958\pi$
$434$	−8.22197	+	5.90239i	−0.394667	+	0.283324i
$435$	1.18964	+	16.0275i	0.0570388	+	0.768460i
$436$	53.7340			2.57339
$437$	−0.479480	−	0.830483i	−0.0229366	−	0.0397274i
$438$	0.0598468	+	0.806292i	0.00285959	+	0.0385261i
$439$	−8.39926	+	14.5479i	−0.400875	+	0.694335i	−0.993832	−	0.110899i	$-0.964627\pi$
$439$	−8.39926	+	14.5479i	−0.400875	+	0.694335i	0.592957	+	0.805234i	$0.297960\pi$
$440$	−3.71291			−0.177006
$441$	19.7538	−	7.12646i	0.940658	−	0.339355i
$442$	13.3858			0.636699
$443$	−8.17378	+	14.1574i	−0.388348	+	0.672639i	−0.992228	−	0.124437i	$-0.960288\pi$
$443$	−8.17378	+	14.1574i	−0.388348	+	0.672639i	0.603879	+	0.797076i	$0.293621\pi$
$444$	−8.78644	+	5.98135i	−0.416986	+	0.283862i
$445$	6.78158	+	11.7460i	0.321478	+	0.556815i
$446$	5.36756			0.254161
$447$	18.6906	+	9.01731i	0.884037	+	0.426504i
$448$	−26.2298	+	18.8298i	−1.23924	+	0.889625i
$449$	24.9939			1.17953			0.589767	−	0.807574i	$-0.299220\pi$
$449$	24.9939			1.17953			0.589767	+	0.807574i	$0.299220\pi$
$450$	−6.41944	+	0.958242i	−0.302615	+	0.0451720i
$451$	6.69282	−	11.5923i	0.315153	−	0.545860i
$452$	−50.2244			−2.36236
$453$	−8.99148	−	4.33795i	−0.422457	−	0.203814i
$454$	−28.6886	+	49.6901i	−1.34642	+	2.33207i
$455$	−0.283761	−	2.85612i	−0.0133029	−	0.133897i
$456$	−0.662618	−	8.92719i	−0.0310299	−	0.418054i
$457$	2.47421	−	4.28546i	0.115739	−	0.200465i	−0.802336	−	0.596873i	$-0.796410\pi$
$457$	2.47421	−	4.28546i	0.115739	−	0.200465i	0.918075	+	0.396407i	$0.129743\pi$
$458$	22.1349	−	38.3387i	1.03429	−	1.79145i
$459$	28.2997	+	8.79545i	1.32092	+	0.410537i
$460$	−0.366346	−	0.634530i	−0.0170810	−	0.0295851i
$461$	6.77101	+	11.7277i	0.315358	+	0.546215i	0.979513	−	0.201379i	$-0.0645422\pi$
$461$	6.77101	+	11.7277i	0.315358	+	0.546215i	−0.664156	+	0.747594i	$0.731209\pi$
$462$	8.58075	−	23.4719i	0.399213	−	1.09201i
$463$	14.7612	−	25.5672i	0.686012	−	1.18821i	−0.287106	−	0.957899i	$-0.592693\pi$
$463$	14.7612	−	25.5672i	0.686012	−	1.18821i	0.973118	−	0.230308i	$-0.0739734\pi$
$464$	20.1800			0.936832
$465$	0.226693	+	3.05415i	0.0105126	+	0.141633i
$466$	−44.8429			−2.07731
$467$	5.21574	+	9.03393i	0.241356	+	0.418040i	0.961101	−	0.276198i	$-0.0890746\pi$
$467$	5.21574	+	9.03393i	0.241356	+	0.418040i	−0.719745	+	0.694239i	$0.755741\pi$
$468$	5.43007	+	6.82898i	0.251005	+	0.315670i
$469$	30.9814	+	14.0057i	1.43059	+	0.646723i
$470$	5.06704	+	8.77636i	0.233725	+	0.404824i
$471$	−1.42822	−	19.2418i	−0.0658087	−	0.886614i
$472$	2.48012	+	4.29569i	0.114157	+	0.197725i
$473$	7.92768	+	13.7312i	0.364515	+	0.631359i
$474$	−1.08277	−	14.5877i	−0.0497331	−	0.670034i
$475$	1.75436	+	3.03863i	0.0804954	+	0.139422i
$476$	32.8613	−	23.5905i	1.50619	−	1.08127i
$477$	28.8961	−	4.31338i	1.32306	−	0.197496i
$478$	−4.07732	−	7.06212i	−0.186492	−	0.323014i
$479$	30.2584			1.38254			0.691270	−	0.722597i	$-0.257052\pi$
$479$	30.2584			1.38254			0.691270	+	0.722597i	$0.257052\pi$
$480$	0.980952	+	13.2160i	0.0447741	+	0.603224i
$481$	−2.48329			−0.113228
$482$	−7.77687	+	13.4699i	−0.354227	+	0.613538i
$483$	1.23373	−	0.215738i	0.0561368	−	0.00981642i
$484$	6.22790	+	10.7870i	0.283086	+	0.490320i
$485$	6.91171	+	11.9714i	0.313845	+	0.543595i
$486$	12.2098	+	31.4382i	0.553848	+	1.42607i
$487$	6.50566	−	11.2681i	0.294799	−	0.510608i	−0.680139	−	0.733083i	$-0.738080\pi$
$487$	6.50566	−	11.2681i	0.294799	−	0.510608i	0.974938	+	0.222476i	$0.0714138\pi$
$488$	−3.64368	+	6.31103i	−0.164941	+	0.285687i
$489$	0.163228	+	2.19911i	0.00738144	+	0.0994472i
$490$	−10.0050	−	11.3693i	−0.451978	−	0.513614i
$491$	4.60953	−	7.98393i	0.208025	−	0.360310i	−0.743067	−	0.669217i	$-0.766630\pi$
$491$	4.60953	−	7.98393i	0.208025	−	0.360310i	0.951092	+	0.308907i	$0.0999631\pi$
$492$	22.2083	+	10.7144i	1.00123	+	0.483042i
$493$	−52.9202			−2.38341
$494$	4.11756	−	7.13183i	0.185258	−	0.320876i
$495$	−4.70642	−	5.91890i	−0.211538	−	0.266035i
$496$	3.84543			0.172665
$497$	23.5848	−	16.9310i	1.05792	−	0.759461i
$498$	34.9712	+	16.8719i	1.56710	+	0.756047i
$499$	22.3488			1.00047			0.500235	−	0.865890i	$-0.333247\pi$
$499$	22.3488			1.00047			0.500235	+	0.865890i	$0.333247\pi$
$500$	1.34041	+	2.32167i	0.0599452	+	0.103828i
$501$	1.35349	−	0.921385i	0.0604695	−	0.0411645i
$502$	13.4027	−	23.2142i	0.598192	−	1.03610i
$503$	−16.6128			−0.740728			−0.370364	−	0.928887i	$-0.620767\pi$
$503$	−16.6128			−0.740728			−0.370364	+	0.928887i	$0.620767\pi$
$504$	11.2477	+	3.19047i	0.501014	+	0.142115i
$505$	10.2886			0.457837
$506$	0.745245	−	1.29080i	0.0331302	−	0.0573831i
$507$	−1.51583	−	20.4221i	−0.0673202	−	0.906978i
$508$	14.2679	+	24.7128i	0.633037	+	1.09645i
$509$	−16.2874			−0.721928			−0.360964	−	0.932580i	$-0.617552\pi$
$509$	−16.2874			−0.721928			−0.360964	+	0.932580i	$0.617552\pi$
$510$	−1.58198	−	21.3134i	−0.0700512	−	0.943772i
$511$	0.0564358	+	0.568041i	0.00249657	+	0.0251286i
$512$	23.0470			1.01854
$513$	13.3913	−	12.3722i	0.591239	−	0.546248i
$514$	−26.4943	+	45.8895i	−1.16862	+	2.02410i
$515$	−18.3697			−0.809464
$516$	−24.1439	+	16.4359i	−1.06287	+	0.723549i
$517$	−5.90348	+	10.2251i	−0.259635	+	0.449700i
$518$	−10.6444	+	7.64140i	−0.467688	+	0.335744i
$519$	−10.0808	+	6.86251i	−0.442500	+	0.301231i
$520$	0.798969	−	1.38386i	0.0350371	−	0.0606861i
$521$	−8.40287	+	14.5542i	−0.368136	+	0.637631i	−0.989274	−	0.146071i	$-0.953337\pi$
$521$	−8.40287	+	14.5542i	−0.368136	+	0.637631i	0.621138	+	0.783701i	$0.286671\pi$
$522$	−37.4830	−	47.1396i	−1.64059	−	2.06324i
$523$	4.58284	+	7.93771i	0.200394	+	0.347092i	0.948655	−	0.316312i	$-0.102445\pi$
$523$	4.58284	+	7.93771i	0.200394	+	0.347092i	−0.748262	+	0.663404i	$0.769111\pi$
$524$	26.6655	+	46.1861i	1.16489	+	2.01765i
$525$	−4.51408	+	0.789359i	−0.197011	+	0.0344504i
$526$	−8.74886	+	15.1535i	−0.381468	+	0.660723i
$527$	−10.0843			−0.439279
$528$	−7.84899	+	5.34318i	−0.341584	+	0.232532i
$529$	−22.9253			−0.996752
$530$	−10.5350	−	18.2472i	−0.457612	−	0.792607i
$531$	−3.70419	+	9.39880i	−0.160748	+	0.407873i
$532$	−2.46041	−	24.7647i	−0.106673	−	1.07369i
$533$	2.88041	+	4.98902i	0.124765	+	0.216099i
$534$	−45.7766	−	22.0850i	−1.98095	−	0.955710i
$535$	7.21802	+	12.5020i	0.312062	+	0.540508i
$536$	9.46457	+	16.3931i	0.408807	+	0.708075i
$537$	11.3182	−	7.70483i	0.488416	−	0.332488i
$538$	−5.16849	−	8.95209i	−0.222829	−	0.385952i
$539$	5.64321	−	16.7179i	0.243070	−	0.720091i
$540$	10.2316	−	9.45300i	0.440298	−	0.406792i
$541$	−11.0257	−	19.0970i	−0.474030	−	0.821044i	0.525528	−	0.850776i	$-0.323868\pi$
$541$	−11.0257	−	19.0970i	−0.474030	−	0.821044i	−0.999558	+	0.0297324i	$0.990534\pi$
$542$	−1.07799			−0.0463036
$543$	−20.5944	−	9.93577i	−0.883789	−	0.426385i
$544$	−43.6370			−1.87092
$545$	10.0219	−	17.3584i	0.429291	−	0.743554i
$546$	6.90184	+	8.24901i	0.295371	+	0.353025i
$547$	1.95281	+	3.38236i	0.0834960	+	0.144619i	0.904749	−	0.425944i	$-0.140058\pi$
$547$	1.95281	+	3.38236i	0.0834960	+	0.144619i	−0.821253	+	0.570564i	$0.806725\pi$
$548$	18.1716	+	31.4741i	0.776251	+	1.34451i
$549$	−14.6793	+	2.19121i	−0.626499	+	0.0935187i
$550$	−2.72676	+	4.72288i	−0.116269	+	0.201384i
$551$	−16.2786	+	28.1953i	−0.693490	+	1.20116i
$552$	0.628020	+	0.302988i	0.0267303	+	0.0128960i
$553$	−1.02105	−	10.2772i	−0.0434196	−	0.437029i
$554$	30.1803	−	52.2739i	1.28224	−	2.22090i
$555$	0.293483	+	3.95398i	0.0124577	+	0.167837i
$556$	−28.7992			−1.22136
$557$	0.621333	−	1.07618i	0.0263267	−	0.0455992i	−0.852562	−	0.522626i	$-0.824952\pi$
$557$	0.621333	−	1.07618i	0.0263267	−	0.0455992i	0.878889	+	0.477027i	$0.158286\pi$
$558$	−7.14264	−	8.98276i	−0.302372	−	0.380271i
$559$	−6.82373			−0.288613
$560$	0.568871	+	5.72583i	0.0240392	+	0.241960i
$561$	20.5833	−	14.0120i	0.869027	−	0.591588i
$562$	11.5542			0.487385
$563$	−2.06788	−	3.58167i	−0.0871506	−	0.150949i	0.819155	−	0.573572i	$-0.194443\pi$
$563$	−2.06788	−	3.58167i	−0.0871506	−	0.150949i	−0.906306	+	0.422623i	$0.861109\pi$
$564$	−19.5890	−	9.45075i	−0.824848	−	0.397948i
$565$	−9.36733	+	16.2247i	−0.394086	+	0.682578i
$566$	−68.5644			−2.88198
$567$	9.17136	+	21.9747i	0.385161	+	0.922849i
$568$	16.1636			0.678210
$569$	5.64630	−	9.77967i	0.236705	−	0.409985i	−0.723062	−	0.690783i	$-0.757266\pi$
$569$	5.64630	−	9.77967i	0.236705	−	0.409985i	0.959767	+	0.280798i	$0.0905992\pi$
$570$	−11.8422	−	5.71326i	−0.496013	−	0.239302i
$571$	−20.6379	−	35.7459i	−0.863670	−	1.49592i	−0.868361	−	0.495932i	$-0.834827\pi$
$571$	−20.6379	−	35.7459i	−0.863670	−	1.49592i	0.00469093	−	0.999989i	$-0.498507\pi$
$572$	7.33069			0.306512
$573$	−9.92737	+	6.75804i	−0.414722	+	0.282321i
$574$	27.6984	+	12.5216i	1.15611	+	0.522640i
$575$	−0.273308			−0.0113977
$576$	−22.7865	−	28.6568i	−0.949436	−	1.19403i
$577$	4.01893	−	6.96099i	0.167310	−	0.289790i	−0.770163	−	0.637847i	$-0.779825\pi$
$577$	4.01893	−	6.96099i	0.167310	−	0.289790i	0.937473	+	0.348057i	$0.113159\pi$
$578$	33.5934			1.39730
$579$	1.26148	+	16.9954i	0.0524251	+	0.706303i
$580$	−12.4376	+	21.5426i	−0.516444	+	0.894508i
$581$	24.9803	+	11.2928i	1.03636	+	0.468503i
$582$	−46.6550	−	22.5088i	−1.93391	−	0.933018i
$583$	12.2741	−	21.2593i	0.508340	−	0.880471i
$584$	−0.158903	+	0.275228i	−0.00657546	+	0.0113890i
$585$	3.21882	−	0.480479i	0.133082	−	0.0198654i
$586$	−5.32006	−	9.21462i	−0.219770	−	0.380652i
$587$	−9.64751	−	16.7100i	−0.398195	−	0.689695i	0.595308	−	0.803498i	$-0.297030\pi$
$587$	−9.64751	−	16.7100i	−0.398195	−	0.689695i	−0.993503	+	0.113803i	$0.963697\pi$
$588$	31.4811	+	8.08731i	1.29826	+	0.333515i
$589$	−3.10199	+	5.37280i	−0.127815	+	0.221382i
$590$	7.28559			0.299943
$591$	−7.68415	−	3.70722i	−0.316084	−	0.152495i
$592$	4.97840			0.204611
$593$	−14.8846	−	25.7809i	−0.611237	−	1.05869i	−0.991032	−	0.133623i	$-0.957339\pi$
$593$	−14.8846	−	25.7809i	−0.611237	−	1.05869i	0.379795	−	0.925071i	$-0.375995\pi$
$594$	27.0605	+	8.41030i	1.11030	+	0.345079i
$595$	−1.49181	−	15.0155i	−0.0611584	−	0.615575i
$596$	16.0599	+	27.8165i	0.657837	+	1.13941i
$597$	−8.48804	+	5.77822i	−0.347393	+	0.236487i
$598$	0.320734	+	0.555527i	0.0131158	+	0.0227172i
$599$	−5.02705	−	8.70711i	−0.205400	−	0.355763i	0.744860	−	0.667220i	$-0.232516\pi$
$599$	−5.02705	−	8.70711i	−0.205400	−	0.355763i	−0.950260	+	0.311458i	$0.899183\pi$
$600$	−2.29785	−	1.10860i	−0.0938091	−	0.0452583i
$601$	4.59732	+	7.96278i	0.187528	+	0.324809i	0.944426	−	0.328725i	$-0.106619\pi$
$601$	4.59732	+	7.96278i	0.187528	+	0.324809i	−0.756897	+	0.653534i	$0.773286\pi$
$602$	−29.2493	+	20.9975i	−1.19211	+	0.855793i
$603$	−14.1358	+	35.8675i	−0.575656	+	1.46064i
$604$	−7.72589	−	13.3816i	−0.314362	−	0.544491i
$605$	4.64625			0.188897
$606$	−31.8709	+	21.6961i	−1.29467	+	0.881342i
$607$	−0.368646			−0.0149629			−0.00748145	−	0.999972i	$-0.502381\pi$
$607$	−0.368646			−0.0149629			−0.00748145	+	0.999972i	$0.502381\pi$
$608$	−13.4230	+	23.2493i	−0.544374	+	0.942884i
$609$	−27.2861	−	32.6120i	−1.10569	−	1.32151i
$610$	5.35183	+	9.26963i	0.216689	+	0.375317i
$611$	−2.54070	−	4.40062i	−0.102786	−	0.178030i
$612$	28.5475	+	35.9020i	1.15396	+	1.45125i
$613$	7.89766	−	13.6791i	0.318983	−	0.552496i	−0.661293	−	0.750128i	$-0.729992\pi$
$613$	7.89766	−	13.6791i	0.318983	−	0.552496i	0.980276	+	0.197632i	$0.0633252\pi$
$614$	15.0783	−	26.1163i	0.608509	−	1.05397i
$615$	7.60327	−	5.17591i	0.306594	−	0.208713i
$616$	7.98007	−	5.72873i	0.321526	−	0.230817i
$617$	−6.94086	+	12.0219i	−0.279428	+	0.483984i	−0.971243	−	0.238091i	$-0.923478\pi$
$617$	−6.94086	+	12.0219i	−0.279428	+	0.483984i	0.691814	+	0.722075i	$0.256812\pi$
$618$	56.9035	−	38.7369i	2.28899	−	1.55823i
$619$	2.56086			0.102930			0.0514648	−	0.998675i	$-0.483611\pi$
$619$	2.56086			0.102930			0.0514648	+	0.998675i	$0.483611\pi$
$620$	−2.37007	+	4.10508i	−0.0951843	+	0.164864i
$621$	0.313059	+	1.38521i	0.0125626	+	0.0555868i
$622$	5.81257			0.233063
$623$	−32.6987	−	14.7820i	−1.31005	−	0.592229i
$624$	−0.302482	−	4.07522i	−0.0121090	−	0.163139i
$625$	1.00000			0.0400000
$626$	1.80161	+	3.12048i	0.0720069	+	0.124720i
$627$	−1.13391	−	15.2767i	−0.0452841	−	0.610094i
$628$	14.9320	−	25.8629i	0.595850	−	1.03204i
$629$	−13.0554			−0.520553
$630$	12.3187	−	11.9642i	0.490787	−	0.476666i
$631$	−42.1192			−1.67674			−0.838370	−	0.545102i	$-0.816491\pi$
$631$	−42.1192			−1.67674			−0.838370	+	0.545102i	$0.816491\pi$
$632$	2.87492	−	4.97951i	0.114358	−	0.198074i
$633$	−4.49709	+	3.06138i	−0.178743	+	0.121679i
$634$	31.3522	+	54.3035i	1.24515	+	2.15667i
$635$	10.6444			0.422411
$636$	40.7281	+	19.6493i	1.61497	+	0.779146i
$637$	5.01666	+	5.70078i	0.198767	+	0.225873i
$638$	−50.6028			−2.00339
$639$	20.4887	+	25.7671i	0.810521	+	1.01933i
$640$	−5.55057	+	9.61386i	−0.219405	+	0.380021i
$641$	−26.7464			−1.05642			−0.528209	−	0.849114i	$-0.677136\pi$
$641$	−26.7464			−1.05642			−0.528209	+	0.849114i	$0.677136\pi$
$642$	−48.7227	−	23.5063i	−1.92293	−	0.927720i
$643$	21.5988	−	37.4102i	0.851773	−	1.47531i	−0.0278342	−	0.999613i	$-0.508861\pi$
$643$	21.5988	−	37.4102i	0.851773	−	1.47531i	0.879607	−	0.475701i	$-0.157806\pi$
$644$	1.76641	+	0.798537i	0.0696063	+	0.0314667i
$645$	0.806450	+	10.8650i	0.0317539	+	0.427808i
$646$	21.6472	−	37.4941i	0.851699	−	1.47519i
$647$	−11.1554	+	19.3217i	−0.438564	+	0.759616i	−0.997579	−	0.0695419i	$-0.977846\pi$
$647$	−11.1554	+	19.3217i	−0.438564	+	0.759616i	0.559015	+	0.829158i	$0.311180\pi$
$648$	−2.98668	+	12.9161i	−0.117328	+	0.507391i
$649$	4.24413	+	7.35104i	0.166597	+	0.288554i
$650$	−1.17352	−	2.03260i	−0.0460294	−	0.0797253i
$651$	−5.19954	−	6.21443i	−0.203786	−	0.243563i
$652$	−1.70655	+	2.95583i	−0.0668336	+	0.115759i
$653$	22.1446			0.866584			0.433292	−	0.901254i	$-0.357352\pi$
$653$	22.1446			0.866584			0.433292	+	0.901254i	$0.357352\pi$
$654$	5.55978	+	74.9047i	0.217405	+	2.92900i
$655$	19.8935			0.777303
$656$	−5.77453	−	10.0018i	−0.225457	−	0.390504i
$657$	−0.640176	+	0.0955602i	−0.0249756	+	0.00372816i
$658$	−24.4317	−	11.0448i	−0.952447	−	0.430571i
$659$	19.3173	+	33.4585i	0.752494	+	1.30336i	0.946610	+	0.322380i	$0.104483\pi$
$659$	19.3173	+	33.4585i	0.752494	+	1.30336i	−0.194116	+	0.980979i	$0.562184\pi$
$660$	−0.866364	−	11.6722i	−0.0337232	−	0.454339i
$661$	−23.2242	−	40.2255i	−0.903318	−	1.56459i	−0.823159	−	0.567810i	$-0.807791\pi$
$661$	−23.2242	−	40.2255i	−0.903318	−	1.56459i	−0.0801584	−	0.996782i	$-0.525543\pi$
$662$	27.2602	+	47.2161i	1.05950	+	1.83511i
$663$	0.793232	+	10.6869i	0.0308066	+	0.415045i
$664$	7.63126	+	13.2177i	0.296150	+	0.512948i
$665$	−8.45898	−	3.82403i	−0.328025	−	0.148289i
$666$	−9.24706	−	11.6293i	−0.358316	−	0.450627i
$667$	−1.26800	−	2.19625i	−0.0490973	−	0.0850391i
$668$	2.53424			0.0980527
$669$	0.318077	+	4.28532i	0.0122976	+	0.165680i
$670$	27.8031			1.07413
$671$	−6.23528	+	10.7998i	−0.240710	+	0.416922i
$672$	−22.4996	−	26.8913i	−0.867940	−	1.03735i
$673$	−13.5441	−	23.4590i	−0.522086	−	0.904280i	−0.999670	−	0.0256936i	$-0.991821\pi$
$673$	−13.5441	−	23.4590i	−0.522086	−	0.904280i	0.477584	−	0.878586i	$-0.341513\pi$
$674$	−17.5644	−	30.4224i	−0.676555	−	1.17183i
$675$	−1.14545	−	5.06833i	−0.0440882	−	0.195080i
$676$	15.8479	−	27.4494i	0.609535	−	1.05575i
$677$	−11.8568	+	20.5365i	−0.455693	+	0.789283i	−0.998728	−	0.0504268i	$-0.983942\pi$
$677$	−11.8568	+	20.5365i	−0.455693	+	0.789283i	0.543035	+	0.839710i	$0.317275\pi$
$678$	−5.19665	−	70.0124i	−0.199576	−	2.68881i
$679$	−33.3262	−	15.0657i	−1.27894	−	0.578168i
$680$	4.20042	−	7.27533i	0.161079	−	0.278996i
$681$	−41.3713	−	19.9596i	−1.58535	−	0.764854i
$682$	−9.64270			−0.369238
$683$	11.9778	−	20.7462i	0.458319	−	0.793831i	−0.540554	−	0.841310i	$-0.681785\pi$
$683$	11.9778	−	20.7462i	0.458319	−	0.793831i	0.998872	+	0.0474784i	$0.0151185\pi$
$684$	27.9095	−	4.16611i	1.06715	−	0.159295i
$685$	13.5567			0.517974
$686$	39.0454	+	8.99895i	1.49076	+	0.343582i
$687$	31.9203	+	15.4000i	1.21784	+	0.587546i
$688$	13.6799			0.521542
$689$	5.28244	+	9.14945i	0.201245	+	0.348566i
$690$	0.846623	−	0.576337i	0.0322304	−	0.0219408i
$691$	5.46854	−	9.47179i	0.208033	−	0.360324i	−0.743062	−	0.669223i	$-0.766627\pi$
$691$	5.46854	−	9.47179i	0.208033	−	0.360324i	0.951095	+	0.308899i	$0.0999605\pi$
$692$	−18.8751			−0.717524
$693$	19.2478	+	5.45972i	0.731163	+	0.207398i
$694$	22.3301			0.847638
$695$	−5.37133	+	9.30342i	−0.203746	+	0.352899i
$696$	−1.75232	−	23.6083i	−0.0664216	−	0.894871i
$697$	15.1432	+	26.2288i	0.573589	+	0.993485i
$698$	−8.14678			−0.308360
$699$	−2.65735	−	35.8014i	−0.100510	−	1.35413i
$700$	−6.46307	−	2.92175i	−0.244281	−	0.110432i
$701$	39.4789			1.49110			0.745550	−	0.666450i	$-0.232187\pi$
$701$	39.4789			1.49110			0.745550	+	0.666450i	$0.232187\pi$
$702$	−8.95770	+	8.27605i	−0.338087	+	0.312359i
$703$	−4.01592	+	6.95578i	−0.151463	+	0.262342i
$704$	−30.7622			−1.15939
$705$	−6.70655	+	4.56547i	−0.252583	+	0.171945i
$706$	−16.2217	+	28.0969i	−0.610513	+	1.05744i
$707$	−22.1131	+	15.8745i	−0.831648	+	0.597024i
$708$	−12.9255	+	8.79903i	−0.485772	+	0.330688i
$709$	3.91439	−	6.77992i	0.147008	−	0.254625i	−0.783112	−	0.621880i	$-0.786369\pi$
$709$	3.91439	−	6.77992i	0.147008	−	0.254625i	0.930120	+	0.367255i	$0.119702\pi$
$710$	11.8705	−	20.5604i	0.445494	−	0.771618i
$711$	11.5822	−	1.72890i	0.434368	−	0.0648390i
$712$	−9.98918	−	17.3018i	−0.374360	−	0.648411i
$713$	−0.241627	−	0.418509i	−0.00904899	−	0.0156733i
$714$	36.2850	+	43.3675i	1.35793	+	1.62299i
$715$	1.36724	−	2.36814i	0.0511320	−	0.0885633i
$716$	21.1919			0.791977
$717$	5.39659	−	3.67372i	0.201540	−	0.137198i
$718$	16.4751			0.614845
$719$	10.3821	+	17.9824i	0.387188	+	0.670629i	0.992070	−	0.125686i	$-0.0401131\pi$
$719$	10.3821	+	17.9824i	0.387188	+	0.670629i	−0.604882	+	0.796315i	$0.706780\pi$
$720$	−6.45295	+	0.963244i	−0.240487	+	0.0358980i
$721$	39.4815	−	28.3430i	1.47037	−	1.05555i
$722$	7.23583	+	12.5328i	0.269290	+	0.466423i
$723$	−11.2149	−	5.41063i	−0.417086	−	0.201223i
$724$	−17.6956	−	30.6497i	−0.657653	−	1.13909i
$725$	4.63947	+	8.03580i	0.172306	+	0.298442i
$726$	−14.3926	+	9.79775i	−0.534161	+	0.363629i
$727$	16.9614	+	29.3780i	0.629063	+	1.08957i	0.987740	+	0.156108i	$0.0498947\pi$
$727$	16.9614	+	29.3780i	0.629063	+	1.08957i	−0.358677	+	0.933462i	$0.616772\pi$
$728$	0.417976	+	4.20704i	0.0154912	+	0.155923i
$729$	−24.3759	+	11.6110i	−0.902811	+	0.430037i
$730$	0.233397	+	0.404255i	0.00863840	+	0.0149622i
$731$	−35.8744			−1.32686
$732$	−20.6900	−	9.98192i	−0.764726	−	0.368943i
$733$	48.3519			1.78592			0.892960	−	0.450136i	$-0.148625\pi$
$733$	48.3519			1.78592			0.892960	+	0.450136i	$0.148625\pi$
$734$	11.0282	−	19.1015i	0.407060	−	0.705048i
$735$	8.48408	−	8.66143i	0.312940	−	0.319482i
$736$	−1.04557	−	1.81098i	−0.0385403	−	0.0667538i
$737$	16.1963	+	28.0529i	0.596600	+	1.03334i
$738$	−12.6379	+	32.0667i	−0.465208	+	1.18039i
$739$	20.2749	−	35.1172i	0.745825	−	1.29181i	−0.203983	−	0.978974i	$-0.565389\pi$
$739$	20.2749	−	35.1172i	0.745825	−	1.29181i	0.949808	−	0.312832i	$-0.101278\pi$
$740$	−3.06836	+	5.31456i	−0.112795	+	0.195367i
$741$	5.93787	+	2.86473i	0.218133	+	0.105238i
$742$	50.7966	+	22.9635i	1.86480	+	0.843017i
$743$	−10.6501	+	18.4465i	−0.390714	+	0.676736i	−0.992544	−	0.121888i	$-0.961105\pi$
$743$	−10.6501	+	18.4465i	−0.390714	+	0.676736i	0.601830	+	0.798624i	$0.294438\pi$
$744$	−0.333916	−	4.49872i	−0.0122420	−	0.164931i
$745$	11.9813			0.438960
$746$	21.8390	−	37.8262i	0.799582	−	1.38492i
$747$	−11.3977	+	28.9199i	−0.417020	+	1.05812i
$748$	38.5396			1.40915
$749$	−34.8031	−	15.7334i	−1.27168	−	0.574885i
$750$	−3.09769	+	2.10874i	−0.113112	+	0.0770005i
$751$	28.8893			1.05418			0.527092	−	0.849808i	$-0.323282\pi$
$751$	28.8893			1.05418			0.527092	+	0.849808i	$0.323282\pi$
$752$	5.09348	+	8.82217i	0.185740	+	0.321712i
$753$	19.3278	+	9.32472i	0.704345	+	0.339812i
$754$	10.8891	−	18.8604i	0.396556	−	0.686856i
$755$	−5.76381			−0.209766
$756$	−7.40527	+	36.1037i	−0.269327	+	1.31308i
$757$	−42.7548			−1.55395			−0.776975	−	0.629531i	$-0.783247\pi$
$757$	−42.7548			−1.55395			−0.776975	+	0.629531i	$0.783247\pi$
$758$	17.2447	−	29.8687i	0.626357	−	1.08488i
$759$	1.07470	+	0.518492i	0.0390093	+	0.0188201i
$760$	−2.58415	−	4.47587i	−0.0937368	−	0.162357i
$761$	16.8231			0.609837			0.304918	−	0.952379i	$-0.401371\pi$
$761$	16.8231			0.609837			0.304918	+	0.952379i	$0.401371\pi$
$762$	−32.9731	+	22.4463i	−1.19449	+	0.813145i
$763$	5.24290	+	52.7711i	0.189806	+	1.91044i
$764$	−18.5878			−0.672481
$765$	16.9223	−	2.52602i	0.611827	−	0.0913285i
$766$	32.1280	−	55.6473i	1.16083	−	2.01062i
$767$	−3.65312			−0.131907
$768$	0.0500569	+	0.674396i	0.00180627	+	0.0243352i
$769$	10.7497	−	18.6190i	0.387643	−	0.671417i	−0.604489	−	0.796613i	$-0.706623\pi$
$769$	10.7497	−	18.6190i	0.387643	−	0.671417i	0.992132	+	0.125197i	$0.0399561\pi$
$770$	−1.42649	−	14.3580i	−0.0514070	−	0.517425i
$771$	−38.2070	−	18.4330i	−1.37599	−	0.663849i
$772$	−13.1887	+	22.8435i	−0.474671	+	0.822155i
$773$	2.71661	−	4.70531i	0.0977098	−	0.169238i	−0.813027	−	0.582227i	$-0.802182\pi$
$773$	2.71661	−	4.70531i	0.0977098	−	0.169238i	0.910736	+	0.412988i	$0.135515\pi$
$774$	−25.4096	−	31.9557i	−0.913329	−	1.14862i
$775$	0.884081	+	1.53127i	0.0317571	+	0.0550050i
$776$	−10.1809	−	17.6338i	−0.365472	−	0.633016i
$777$	−6.73147	−	8.04538i	−0.241490	−	0.288626i
$778$	−1.02454	+	1.77455i	−0.0367314	+	0.0636207i
$779$	18.6325			0.667580
$780$	4.53682	+	2.18879i	0.162444	+	0.0783713i
$781$	27.6601			0.989758
$782$	1.68619	+	2.92057i	0.0602981	+	0.104439i
$783$	35.4138	−	32.7189i	1.26559	−	1.16928i
$784$	−10.0572	−	11.4287i	−0.359185	−	0.408167i
$785$	−5.56990	−	9.64735i	−0.198798	−	0.344329i
$786$	−61.6239	+	41.9503i	−2.19805	+	1.49632i
$787$	−13.2465	−	22.9436i	−0.472187	−	0.817852i	0.527307	−	0.849675i	$-0.323202\pi$
$787$	−13.2465	−	22.9436i	−0.472187	−	0.817852i	−0.999494	+	0.0318233i	$0.989869\pi$
$788$	−6.60257	−	11.4360i	−0.235207	−	0.407390i
$789$	−12.6166	−	6.08688i	−0.449162	−	0.216699i
$790$	−4.22268	−	7.31390i	−0.150236	−	0.260217i
$791$	−4.90046	−	49.3244i	−0.174240	−	1.75377i
$792$	6.93249	+	8.71847i	0.246335	+	0.309797i
$793$	−2.68350	−	4.64796i	−0.0952939	−	0.165054i
$794$	−23.4098			−0.830783
$795$	13.9438	−	9.49219i	0.494535	−	0.336653i
$796$	−15.8928			−0.563305
$797$	18.9194	−	32.7694i	0.670160	−	1.16075i	−0.307698	−	0.951484i	$-0.599559\pi$
$797$	18.9194	−	32.7694i	0.670160	−	1.16075i	0.977858	−	0.209268i	$-0.0671080\pi$
$798$	34.2672	−	5.99216i	1.21305	−	0.212120i
$799$	−13.3572	−	23.1354i	−0.472544	−	0.818471i
$800$	3.82562	+	6.62617i	0.135256	+	0.234270i
$801$	14.9194	−	37.8556i	0.527150	−	1.33756i
$802$	3.53073	−	6.11540i	0.124674	−	0.215942i
$803$	−0.271925	+	0.470987i	−0.00959601	+	0.0166208i
$804$	−49.3262	+	33.5787i	−1.73960	+	1.18423i
$805$	0.587415	−	0.421693i	0.0207036	−	0.0148627i
$806$	2.07498	−	3.59398i	0.0730882	−	0.126592i
$807$	6.84083	−	4.65688i	0.240809	−	0.163930i
$808$	−15.1550			−0.533151
$809$	−17.1655	+	29.7315i	−0.603506	+	1.04530i	0.388780	+	0.921331i	$0.372897\pi$
$809$	−17.1655	+	29.7315i	−0.603506	+	1.04530i	−0.992286	+	0.123972i	$0.960437\pi$
$810$	14.2360	+	13.2847i	0.500204	+	0.466775i
$811$	25.0033			0.877983			0.438992	−	0.898491i	$-0.355336\pi$
$811$	25.0033			0.877983			0.438992	+	0.898491i	$0.355336\pi$
$812$	−6.50667	−	65.4913i	−0.228339	−	2.29829i
$813$	−0.0638806	−	0.860638i	−0.00224039	−	0.0301839i
$814$	−12.4837			−0.437554
$815$	0.636575	+	1.10258i	0.0222982	+	0.0386217i
$816$	−1.59024	−	21.4246i	−0.0556694	−	0.750012i
$817$	−11.0352	+	19.1135i	−0.386072	+	0.668696i
$818$	71.3905			2.49611
$819$	−6.17679	+	5.99907i	−0.215835	+	0.209625i
$820$	14.2362			0.497149
$821$	−21.8766	+	37.8914i	−0.763499	+	1.32242i	0.177537	+	0.984114i	$0.443187\pi$
$821$	−21.8766	+	37.8914i	−0.763499	+	1.32242i	−0.941037	+	0.338305i	$0.890146\pi$
$822$	−41.9944	+	28.5876i	−1.46472	+	0.997107i
$823$	1.09251	+	1.89229i	0.0380826	+	0.0659610i	0.884438	−	0.466657i	$-0.154542\pi$
$823$	1.09251	+	1.89229i	0.0380826	+	0.0659610i	−0.846356	+	0.532618i	$0.821208\pi$
$824$	27.0583			0.942620
$825$	−3.93221	−	1.89710i	−0.136902	−	0.0660485i
$826$	−15.6587	+	11.2411i	−0.544837	+	0.391128i
$827$	30.4431			1.05861			0.529305	−	0.848432i	$-0.322453\pi$
$827$	30.4431			1.05861			0.529305	+	0.848432i	$0.322453\pi$
$828$	−0.805956	+	2.04499i	−0.0280089	+	0.0710682i
$829$	−15.0073	+	25.9934i	−0.521225	+	0.902789i	0.478470	+	0.878104i	$0.341192\pi$
$829$	−15.0073	+	25.9934i	−0.521225	+	0.902789i	−0.999695	+	0.0246849i	$0.992142\pi$
$830$	22.4176			0.778125
$831$	43.5225	+	20.9975i	1.50978	+	0.728395i
$832$	6.61962	−	11.4655i	0.229494	−	0.397495i
$833$	26.3741	+	29.9707i	0.913807	+	1.03842i
$834$	−2.97982	−	40.1459i	−0.103183	−	1.39014i
$835$	0.472660	−	0.818671i	0.0163571	−	0.0283313i
$836$	11.8550	−	20.5335i	0.410014	−	0.710165i
$837$	6.74833	−	6.23481i	0.233257	−	0.215506i
$838$	36.8330	+	63.7966i	1.27237	+	2.20382i
$839$	−2.88789	−	5.00197i	−0.0997009	−	0.172687i	0.811860	−	0.583852i	$-0.198455\pi$
$839$	−2.88789	−	5.00197i	−0.0997009	−	0.172687i	−0.911561	+	0.411165i	$0.865122\pi$
$840$	6.64918	−	1.16272i	0.229419	−	0.0401175i
$841$	−28.5494	+	49.4490i	−0.984461	+	1.70514i
$842$	−36.7715			−1.26723
$843$	0.684692	+	9.22458i	0.0235821	+	0.317712i
$844$	−8.42023			−0.289836
$845$	−5.91157	−	10.2391i	−0.203364	−	0.352237i
$846$	11.1474	−	28.2848i	0.383256	−	0.972452i
$847$	−9.98607	+	7.16880i	−0.343125	+	0.246323i
$848$	−10.5900	−	18.3424i	−0.363662	−	0.629881i
$849$	−4.06306	−	54.7400i	−0.139444	−	1.87867i
$850$	−6.16956	−	10.6860i	−0.211614	−	0.366527i
$851$	−0.312816	−	0.541814i	−0.0107232	−	0.0185731i
$852$	3.77159	+	50.8131i	0.129213	+	1.74083i
$853$	22.8381	+	39.5568i	0.781962	+	1.35440i	0.930797	+	0.365536i	$0.119114\pi$
$853$	22.8381	+	39.5568i	0.781962	+	1.35440i	−0.148835	+	0.988862i	$0.547552\pi$
$854$	−25.8049	−	11.6656i	−0.883025	−	0.399187i
$855$	3.85956	−	9.79303i	0.131994	−	0.334915i
$856$	−10.6321	−	18.4153i	−0.363396	−	0.629421i
$857$	33.7447			1.15270			0.576348	−	0.817204i	$-0.304477\pi$
$857$	33.7447			1.15270			0.576348	+	0.817204i	$0.304477\pi$
$858$	0.758497	+	10.2189i	0.0258946	+	0.348868i
$859$	51.2677			1.74923			0.874615	−	0.484818i	$-0.161114\pi$
$859$	51.2677			1.74923			0.874615	+	0.484818i	$0.161114\pi$
$860$	−8.43141	+	14.6036i	−0.287509	+	0.497980i
$861$	−8.35551	+	22.8557i	−0.284755	+	0.778921i
$862$	−2.50788	−	4.34377i	−0.0854186	−	0.147949i
$863$	8.50532	+	14.7316i	0.289524	+	0.501471i	0.973696	−	0.227850i	$-0.0731695\pi$
$863$	8.50532	+	14.7316i	0.289524	+	0.501471i	−0.684172	+	0.729321i	$0.739836\pi$
$864$	29.2015	−	26.9794i	0.993457	−	0.917858i
$865$	−3.52039	+	6.09749i	−0.119697	+	0.207321i
$866$	23.6383	−	40.9427i	0.803261	−	1.39129i
$867$	1.99071	+	26.8201i	0.0676082	+	0.910858i
$868$	−1.23989	−	12.4798i	−0.0420846	−	0.423592i
$869$	4.91974	−	8.52124i	0.166891	−	0.289063i
$870$	−31.3171	−	15.1090i	−1.06175	−	0.512241i
$871$	−13.9410			−0.472371
$872$	−14.7621	+	25.5688i	−0.499909	+	0.865868i
$873$	15.2057	−	38.5820i	0.514634	−	1.30580i
$874$	2.07473			0.0701788
$875$	−2.14928	+	1.54292i	−0.0726588	+	0.0521603i
$876$	−0.902307	−	0.435318i	−0.0304861	−	0.0147080i
$877$	−35.0553			−1.18373			−0.591867	−	0.806036i	$-0.701609\pi$
$877$	−35.0553			−1.18373			−0.591867	+	0.806036i	$0.701609\pi$
$878$	−18.1720	−	31.4748i	−0.613275	−	1.06222i
$879$	7.04145	−	4.79345i	0.237502	−	0.161679i
$880$	−2.74099	+	4.74753i	−0.0923988	+	0.160039i
$881$	−25.6988			−0.865813			−0.432907	−	0.901439i	$-0.642512\pi$
$881$	−25.6988			−0.865813			−0.432907	+	0.901439i	$0.642512\pi$
$882$	−8.01633	+	44.7212i	−0.269924	+	1.50584i
$883$	28.5262			0.959985			0.479992	−	0.877273i	$-0.340639\pi$
$883$	28.5262			0.959985			0.479992	+	0.877273i	$0.340639\pi$
$884$	−8.29322	+	14.3643i	−0.278931	+	0.483123i
$885$	0.431737	+	5.81662i	0.0145127	+	0.195524i
$886$	−17.6842	−	30.6299i	−0.594111	−	1.02903i
$887$	17.8373			0.598919			0.299460	−	0.954109i	$-0.403194\pi$
$887$	17.8373			0.598919			0.299460	+	0.954109i	$0.403194\pi$
$888$	−0.432297	−	5.82417i	−0.0145070	−	0.195446i
$889$	−22.8778	+	16.4235i	−0.767296	+	0.550827i
$890$	−29.3442			−0.983619
$891$	−5.11098	+	22.1028i	−0.171224	+	0.740470i
$892$	−3.32548	+	5.75990i	−0.111345	+	0.192856i
$893$	−16.4350			−0.549977
$894$	−37.1142	+	25.2654i	−1.24129	+	0.845002i
$895$	3.95249	−	6.84590i	0.132117	−	0.228833i
$896$	−2.90375	−	29.2269i	−0.0970074	−	0.976404i
$897$	−0.424512	+	0.288985i	−0.0141740	+	0.00964894i
$898$	−27.0374	+	46.8301i	−0.902249	+	1.56274i
$899$	−8.20334	+	14.2086i	−0.273597	+	0.473883i
$900$	2.94889	−	7.48235i	0.0982964	−	0.249412i
$901$	27.7713	+	48.1014i	0.925197	+	1.60249i
$902$	14.4801	+	25.0802i	0.482133	+	0.835080i
$903$	−18.4971	−	22.1075i	−0.615545	−	0.735693i
$904$	13.7980	−	23.8988i	0.458913	−	0.794861i
$905$	−13.2016			−0.438837
$906$	17.8545	−	12.1544i	0.593176	−	0.403803i
$907$	23.9137			0.794043			0.397021	−	0.917809i	$-0.370044\pi$
$907$	23.9137			0.794043			0.397021	+	0.917809i	$0.370044\pi$
$908$	−35.5481	−	61.5712i	−1.17971	−	2.04331i
$909$	−19.2102	−	24.1592i	−0.637162	−	0.801311i
$910$	5.65838	+	2.55797i	0.187574	+	0.0847959i
$911$	−8.81756	−	15.2725i	−0.292139	−	0.505999i	0.682176	−	0.731188i	$-0.261034\pi$
$911$	−8.81756	−	15.2725i	−0.292139	−	0.505999i	−0.974315	+	0.225188i	$0.927700\pi$
$912$	−11.9040	−	5.74308i	−0.394180	−	0.190172i
$913$	13.0591	+	22.6190i	0.432192	+	0.748579i
$914$	5.35301	+	9.27169i	0.177062	+	0.306680i
$915$	−7.08349	+	4.82207i	−0.234173	+	0.159413i
$916$	27.4274	+	47.5056i	0.906226	+	1.56963i
$917$	−42.7566	+	30.6941i	−1.41195	+	1.01361i
$918$	−47.0933	+	43.5096i	−1.55431	+	1.43603i
$919$	−0.708010	−	1.22631i	−0.0233551	−	0.0404522i	0.854112	−	0.520090i	$-0.174101\pi$
$919$	−0.708010	−	1.22631i	−0.0233551	−	0.0404522i	−0.877467	+	0.479638i	$0.840768\pi$
$920$	0.402579			0.0132727
$921$	21.7441	+	10.4905i	0.716493	+	0.345672i
$922$	−29.2985			−0.964894
$923$	−5.95210	+	10.3093i	−0.195916	+	0.339336i
$924$	19.8713	+	23.7500i	0.653718	+	0.781318i
$925$	1.14456	+	1.98243i	0.0376328	+	0.0651819i
$926$	31.9362	+	55.3151i	1.04949	+	1.81777i
$927$	34.2986	+	43.1347i	1.12651	+	1.41673i
$928$	−35.4977	+	61.4838i	−1.16527	+	2.01830i
$929$	9.67639	−	16.7600i	0.317472	−	0.549878i	−0.662488	−	0.749073i	$-0.730499\pi$
$929$	9.67639	−	16.7600i	0.317472	−	0.549878i	0.979960	+	0.199195i	$0.0638327\pi$
$930$	−5.96768	−	2.87911i	−0.195688	−	0.0944097i
$931$	24.0809	−	4.83265i	0.789218	−	0.158384i
$932$	27.7825	−	48.1207i	0.910047	−	1.57625i
$933$	0.344447	+	4.64060i	0.0112767	+	0.151926i
$934$	−22.5687			−0.738472
$935$	7.18800	−	12.4500i	0.235073	−	0.407158i
$936$	−4.74128	+	0.707740i	−0.154974	+	0.0231332i
$937$	9.34357			0.305241			0.152621	−	0.988285i	$-0.451229\pi$
$937$	9.34357			0.305241			0.152621	+	0.988285i	$0.451229\pi$
$938$	−59.7565	+	42.8980i	−1.95112	+	1.40067i
$939$	−2.38455	+	1.62328i	−0.0778168	+	0.0529736i
$940$	−12.5572			−0.409570
$941$	16.3696	+	28.3530i	0.533634	+	0.924281i	0.999228	+	0.0392827i	$0.0125073\pi$
$941$	16.3696	+	28.3530i	0.533634	+	0.924281i	−0.465594	+	0.884998i	$0.654159\pi$
$942$	37.5976	+	18.1390i	1.22500	+	0.591001i
$943$	−0.725682	+	1.25692i	−0.0236315	+	0.0409309i
$944$	7.32362			0.238363
$945$	10.2819	+	9.12591i	0.334471	+	0.296866i
$946$	−34.3034			−1.11530
$947$	−9.85492	+	17.0692i	−0.320242	+	0.554675i	−0.980538	−	0.196330i	$-0.937097\pi$
$947$	−9.85492	+	17.0692i	−0.320242	+	0.554675i	0.660296	+	0.751005i	$0.270431\pi$
$948$	16.3248	+	7.87591i	0.530205	+	0.255798i
$949$	−0.117029	−	0.202701i	−0.00379893	−	0.00657994i
$950$	−7.59118			−0.246290
$951$	−41.4966	+	28.2487i	−1.34562	+	0.916027i
$952$	2.19742	+	22.1176i	0.0712189	+	0.716836i
$953$	10.9242			0.353870			0.176935	−	0.984223i	$-0.443382\pi$
$953$	10.9242			0.353870			0.176935	+	0.984223i	$0.443382\pi$
$954$	−23.1769	+	58.8077i	−0.750379	+	1.90397i
$955$	−3.46679	+	6.00466i	−0.112183	+	0.194306i
$956$	10.1044			0.326801
$957$	−2.99868	−	40.4000i	−0.0969335	−	1.30595i
$958$	−32.7323	+	56.6940i	−1.05753	+	1.83170i
$959$	−29.1371	+	20.9169i	−0.940885	+	0.675443i
$960$	−19.0381	−	9.18494i	−0.614452	−	0.296443i
$961$	13.9368	−	24.1392i	0.449574	−	0.778685i
$962$	2.68633	−	4.65286i	0.0866108	−	0.150014i
$963$	15.8796	−	40.2919i	0.511711	−	1.29839i
$964$	−9.63634	−	16.6906i	−0.310366	−	0.537569i
$965$	4.91963	+	8.52105i	0.158369	+	0.274302i
$966$	−0.930385	+	2.54498i	−0.0299346	+	0.0818834i
$967$	3.26247	−	5.65076i	0.104914	−	0.181716i	−0.808789	−	0.588099i	$-0.799877\pi$
$967$	3.26247	−	5.65076i	0.104914	−	0.181716i	0.913703	+	0.406383i	$0.133210\pi$
$968$	−6.84387			−0.219970
$969$	31.2171	+	15.0607i	1.00284	+	0.483820i
$970$	−29.9073			−0.960265
$971$	12.6674	+	21.9406i	0.406516	+	0.704107i	0.994497	−	0.104768i	$-0.0334101\pi$
$971$	12.6674	+	21.9406i	0.406516	+	0.704107i	−0.587980	+	0.808875i	$0.700077\pi$
$972$	−41.3008	−	6.37533i	−1.32472	−	0.204489i
$973$	−2.80998	−	28.2832i	−0.0900838	−	0.906716i
$974$	14.0751	+	24.3788i	0.450996	+	0.781149i
$975$	1.55324	−	1.05736i	0.0497434	−	0.0338627i
$976$	5.37976	+	9.31802i	0.172202	+	0.298263i
$977$	−12.6098	−	21.8408i	−0.403423	−	0.698749i	0.590713	−	0.806881i	$-0.298846\pi$
$977$	−12.6098	−	21.8408i	−0.403423	−	0.698749i	−0.994137	+	0.108132i	$0.965513\pi$
$978$	−4.29697	−	2.07308i	−0.137402	−	0.0662897i
$979$	−17.0941	−	29.6078i	−0.546329	−	0.946270i
$980$	18.3990	−	3.69238i	0.587733	−	0.117949i
$981$	−59.4725	+	8.87756i	−1.89881	+	0.283439i
$982$	9.97281	+	17.2734i	0.318245	+	0.551217i
$983$	22.8298			0.728159			0.364079	−	0.931368i	$-0.381384\pi$
$983$	22.8298			0.728159			0.364079	+	0.931368i	$0.381384\pi$
$984$	−11.1995	+	7.62405i	−0.357028	+	0.243046i
$985$	−4.92577			−0.156948
$986$	57.2470	−	99.1548i	1.82312	−	3.15773i
$987$	7.37007	−	20.1601i	0.234592	−	0.641704i
$988$	5.10209	+	8.83707i	0.162319	+	0.281145i
$989$	−0.859575	−	1.48883i	−0.0273329	−	0.0473419i
$990$	16.1813	−	2.41541i	0.514274	−	0.0767667i
$991$	−9.84990	+	17.0605i	−0.312892	+	0.541946i	−0.978987	−	0.203921i	$-0.934631\pi$
$991$	−9.84990	+	17.0605i	−0.312892	+	0.541946i	0.666095	+	0.745867i	$0.267965\pi$
$992$	−6.76432	+	11.7161i	−0.214767	+	0.371988i
$993$	−36.0807	+	24.5618i	−1.14499	+	0.779447i
$994$	6.21001	+	62.5053i	0.196969	+	1.98255i
$995$	−2.96416	+	5.13407i	−0.0939701	+	0.162761i
$996$	−39.7716	+	27.0744i	−1.26021	+	0.857885i
$997$	−6.93585			−0.219660			−0.109830	−	0.993950i	$-0.535031\pi$
$997$	−6.93585			−0.219660			−0.109830	+	0.993950i	$0.535031\pi$
$998$	−24.1760	+	41.8741i	−0.765279	+	1.32550i
$999$	8.73658	−	8.07175i	0.276413	−	0.255379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.b.256.3	yes	24
3.2	odd	2		945.2.k.b.361.10		24
7.2	even	3		315.2.l.b.121.10	yes	24
9.2	odd	6		945.2.l.b.46.3		24
9.7	even	3		315.2.l.b.151.10	yes	24
21.2	odd	6		945.2.l.b.226.3		24
63.2	odd	6		945.2.k.b.856.10		24
63.16	even	3	inner	315.2.k.b.16.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.3	✓	24	63.16	even	3	inner
315.2.k.b.256.3	yes	24	1.1	even	1	trivial
315.2.l.b.121.10	yes	24	7.2	even	3
315.2.l.b.151.10	yes	24	9.7	even	3
945.2.k.b.361.10		24	3.2	odd	2
945.2.k.b.856.10		24	63.2	odd	6
945.2.l.b.46.3		24	9.2	odd	6
945.2.l.b.226.3		24	21.2	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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08176 + 1.87367i) q^{2} +(-1.55999 - 0.752618i) q^{3} +(-1.34041 - 2.32167i) q^{4} -1.00000 q^{5} +(3.09769 - 2.10874i) q^{6} +(2.14928 - 1.54292i) q^{7} +1.47299 q^{8} +(1.86713 + 2.34815i) q^{9} +O(q^{10})\)	\(q+(-1.08176 + 1.87367i) q^{2} +(-1.55999 - 0.752618i) q^{3} +(-1.34041 - 2.32167i) q^{4} -1.00000 q^{5} +(3.09769 - 2.10874i) q^{6} +(2.14928 - 1.54292i) q^{7} +1.47299 q^{8} +(1.86713 + 2.34815i) q^{9} +(1.08176 - 1.87367i) q^{10} +2.52066 q^{11} +(0.343705 + 4.63059i) q^{12} +(-0.542414 + 0.939489i) q^{13} +(0.565917 + 5.69610i) q^{14} +(1.55999 + 0.752618i) q^{15} +(1.08741 - 1.88345i) q^{16} +(-2.85163 + 4.93917i) q^{17} +(-6.41944 + 0.958242i) q^{18} +(1.75436 + 3.03863i) q^{19} +(1.34041 + 2.32167i) q^{20} +(-4.51408 + 0.789359i) q^{21} +(-2.72676 + 4.72288i) q^{22} -0.273308 q^{23} +(-2.29785 - 1.10860i) q^{24} +1.00000 q^{25} +(-1.17352 - 2.03260i) q^{26} +(-1.14545 - 5.06833i) q^{27} +(-6.46307 - 2.92175i) q^{28} +(4.63947 + 8.03580i) q^{29} +(-3.09769 + 2.10874i) q^{30} +(0.884081 + 1.53127i) q^{31} +(3.82562 + 6.62617i) q^{32} +(-3.93221 - 1.89710i) q^{33} +(-6.16956 - 10.6860i) q^{34} +(-2.14928 + 1.54292i) q^{35} +(2.94889 - 7.48235i) q^{36} +(1.14456 + 1.98243i) q^{37} -7.59118 q^{38} +(1.55324 - 1.05736i) q^{39} -1.47299 q^{40} +(2.65518 - 4.59891i) q^{41} +(3.40416 - 9.31177i) q^{42} +(3.14508 + 5.44743i) q^{43} +(-3.37874 - 5.85214i) q^{44} +(-1.86713 - 2.34815i) q^{45} +(0.295654 - 0.512088i) q^{46} +(-2.34203 + 4.05652i) q^{47} +(-3.11386 + 2.11975i) q^{48} +(2.23878 - 6.63234i) q^{49} +(-1.08176 + 1.87367i) q^{50} +(8.16582 - 5.55886i) q^{51} +2.90824 q^{52} +(4.86938 - 8.43401i) q^{53} +(10.7354 + 3.33654i) q^{54} -2.52066 q^{55} +(3.16586 - 2.27271i) q^{56} +(-0.449846 - 6.06060i) q^{57} -20.0752 q^{58} +(1.68373 + 2.91631i) q^{59} +(-0.343705 - 4.63059i) q^{60} +(-2.47366 + 4.28451i) q^{61} -3.82546 q^{62} +(7.63600 + 2.16599i) q^{63} -12.2040 q^{64} +(0.542414 - 0.939489i) q^{65} +(7.80824 - 5.31544i) q^{66} +(6.42542 + 11.1292i) q^{67} +15.2895 q^{68} +(0.426358 + 0.205697i) q^{69} +(-0.565917 - 5.69610i) q^{70} +10.9734 q^{71} +(2.75026 + 3.45880i) q^{72} +(-0.107878 + 0.186850i) q^{73} -4.95255 q^{74} +(-1.55999 - 0.752618i) q^{75} +(4.70313 - 8.14606i) q^{76} +(5.41761 - 3.88919i) q^{77} +(0.300911 + 4.05406i) q^{78} +(1.95176 - 3.38055i) q^{79} +(-1.08741 + 1.88345i) q^{80} +(-2.02763 + 8.76862i) q^{81} +(5.74454 + 9.94984i) q^{82} +(5.18081 + 8.97342i) q^{83} +(7.88336 + 9.42212i) q^{84} +(2.85163 - 4.93917i) q^{85} -13.6089 q^{86} +(-1.18964 - 16.0275i) q^{87} +3.71291 q^{88} +(-6.78158 - 11.7460i) q^{89} +(6.41944 - 0.958242i) q^{90} +(0.283761 + 2.85612i) q^{91} +(0.366346 + 0.634530i) q^{92} +(-0.226693 - 3.05415i) q^{93} +(-5.06704 - 8.77636i) q^{94} +(-1.75436 - 3.03863i) q^{95} +(-0.980952 - 13.2160i) q^{96} +(-6.91171 - 11.9714i) q^{97} +(10.0050 + 11.3693i) q^{98} +(4.70642 + 5.91890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

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