LMFDB - Embedded newform 315.2.k.c.16.6

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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.750300 - 1.29956i) q^{2} +(-0.590164 - 1.62841i) q^{3} +(-0.125900 + 0.218065i) q^{4} +1.00000 q^{5} +(-1.67341 + 1.98874i) q^{6} +(-2.32993 + 1.25356i) q^{7} -2.62335 q^{8} +(-2.30341 + 1.92205i) q^{9} +O(q^{10})$	\(q+(-0.750300 - 1.29956i) q^{2} +(-0.590164 - 1.62841i) q^{3} +(-0.125900 + 0.218065i) q^{4} +1.00000 q^{5} +(-1.67341 + 1.98874i) q^{6} +(-2.32993 + 1.25356i) q^{7} -2.62335 q^{8} +(-2.30341 + 1.92205i) q^{9} +(-0.750300 - 1.29956i) q^{10} -2.83201 q^{11} +(0.429399 + 0.0763219i) q^{12} +(0.0336366 + 0.0582603i) q^{13} +(3.37723 + 2.08733i) q^{14} +(-0.590164 - 1.62841i) q^{15} +(2.22010 + 3.84532i) q^{16} +(-3.48110 - 6.02944i) q^{17} +(4.22607 + 1.55130i) q^{18} +(0.667810 - 1.15668i) q^{19} +(-0.125900 + 0.218065i) q^{20} +(3.41635 + 3.05426i) q^{21} +(2.12485 + 3.68035i) q^{22} -3.22182 q^{23} +(1.54821 + 4.27188i) q^{24} +1.00000 q^{25} +(0.0504751 - 0.0874254i) q^{26} +(4.48927 + 2.61657i) q^{27} +(0.0199793 - 0.665899i) q^{28} +(4.51153 - 7.81420i) q^{29} +(-1.67341 + 1.98874i) q^{30} +(-4.73625 + 8.20342i) q^{31} +(0.708129 - 1.22651i) q^{32} +(1.67135 + 4.61166i) q^{33} +(-5.22374 + 9.04778i) q^{34} +(-2.32993 + 1.25356i) q^{35} +(-0.129133 - 0.744278i) q^{36} +(1.37810 - 2.38694i) q^{37} -2.00423 q^{38} +(0.0750204 - 0.0891572i) q^{39} -2.62335 q^{40} +(2.36194 + 4.09100i) q^{41} +(1.40590 - 6.73136i) q^{42} +(3.96429 - 6.86635i) q^{43} +(0.356548 - 0.617560i) q^{44} +(-2.30341 + 1.92205i) q^{45} +(2.41733 + 4.18693i) q^{46} +(-0.867073 - 1.50182i) q^{47} +(4.95152 - 5.88459i) q^{48} +(3.85715 - 5.84144i) q^{49} +(-0.750300 - 1.29956i) q^{50} +(-7.76396 + 9.22701i) q^{51} -0.0169394 q^{52} +(-6.77377 - 11.7325i) q^{53} +(0.0320746 - 7.79728i) q^{54} -2.83201 q^{55} +(6.11222 - 3.28854i) q^{56} +(-2.27766 - 0.404834i) q^{57} -13.5400 q^{58} +(3.43542 - 5.95032i) q^{59} +(0.429399 + 0.0763219i) q^{60} +(-1.89824 - 3.28785i) q^{61} +14.2144 q^{62} +(2.95737 - 7.36573i) q^{63} +6.75516 q^{64} +(0.0336366 + 0.0582603i) q^{65} +(4.73910 - 5.63214i) q^{66} +(-1.82517 + 3.16128i) q^{67} +1.75308 q^{68} +(1.90140 + 5.24642i) q^{69} +(3.37723 + 2.08733i) q^{70} -8.89186 q^{71} +(6.04266 - 5.04222i) q^{72} +(2.58047 + 4.46951i) q^{73} -4.13596 q^{74} +(-0.590164 - 1.62841i) q^{75} +(0.168154 + 0.291251i) q^{76} +(6.59838 - 3.55010i) q^{77} +(-0.172153 - 0.0305986i) q^{78} +(-5.73331 - 9.93039i) q^{79} +(2.22010 + 3.84532i) q^{80} +(1.61142 - 8.85456i) q^{81} +(3.54433 - 6.13895i) q^{82} +(-5.40726 + 9.36564i) q^{83} +(-1.09614 + 0.360455i) q^{84} +(-3.48110 - 6.02944i) q^{85} -11.8976 q^{86} +(-15.3872 - 2.73494i) q^{87} +7.42934 q^{88} +(-3.42561 + 5.93334i) q^{89} +(4.22607 + 1.55130i) q^{90} +(-0.151404 - 0.0935768i) q^{91} +(0.405625 - 0.702564i) q^{92} +(16.1537 + 2.87117i) q^{93} +(-1.30113 + 2.25362i) q^{94} +(0.667810 - 1.15668i) q^{95} +(-2.41518 - 0.429276i) q^{96} +(1.45661 - 2.52293i) q^{97} +(-10.4853 - 0.629758i) q^{98} +(6.52328 - 5.44327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.750300	−	1.29956i	−0.530542	−	0.918926i	−0.999365	−	0.0356336i	$-0.988655\pi$
$2$	−0.750300	−	1.29956i	−0.530542	−	0.918926i	0.468823	−	0.883292i	$-0.344678\pi$
$3$	−0.590164	−	1.62841i	−0.340731	−	0.940161i
$3$	−0.590164	−	1.62841i	−0.340731	−	0.940161i
$4$	−0.125900	+	0.218065i	−0.0629498	+	0.109032i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.67341	+	1.98874i	−0.683166	+	0.811902i
$7$	−2.32993	+	1.25356i	−0.880631	+	0.473803i
$7$	−2.32993	+	1.25356i	−0.880631	+	0.473803i
$8$	−2.62335			−0.927494
$9$	−2.30341	+	1.92205i	−0.767804	+	0.640684i
$10$	−0.750300	−	1.29956i	−0.237266	−	0.410956i
$11$	−2.83201			−0.853882			−0.426941	−	0.904280i	$-0.640409\pi$
$11$	−2.83201			−0.853882			−0.426941	+	0.904280i	$0.640409\pi$
$12$	0.429399	+	0.0763219i	0.123957	+	0.0220322i
$13$	0.0336366	+	0.0582603i	0.00932912	+	0.0161585i	0.870652	−	0.491899i	$-0.163697\pi$
$13$	0.0336366	+	0.0582603i	0.00932912	+	0.0161585i	−0.861323	+	0.508057i	$0.830364\pi$
$14$	3.37723	+	2.08733i	0.902602	+	0.557862i
$15$	−0.590164	−	1.62841i	−0.152380	−	0.420453i
$16$	2.22010	+	3.84532i	0.555024	+	0.961331i
$17$	−3.48110	−	6.02944i	−0.844291	−	1.46236i	−0.886235	−	0.463235i	$-0.846689\pi$
$17$	−3.48110	−	6.02944i	−0.844291	−	1.46236i	0.0419442	−	0.999120i	$-0.486645\pi$
$18$	4.22607	+	1.55130i	0.996094	+	0.365645i
$19$	0.667810	−	1.15668i	0.153206	−	0.265361i	−0.779198	−	0.626778i	$-0.784373\pi$
$19$	0.667810	−	1.15668i	0.153206	−	0.265361i	0.932404	+	0.361417i	$0.117707\pi$
$20$	−0.125900	+	0.218065i	−0.0281520	+	0.0487607i
$21$	3.41635	+	3.05426i	0.745510	+	0.666495i
$22$	2.12485	+	3.68035i	0.453020	+	0.784654i
$23$	−3.22182			−0.671795			−0.335898	−	0.941899i	$-0.609040\pi$
$23$	−3.22182			−0.671795			−0.335898	+	0.941899i	$0.609040\pi$
$24$	1.54821	+	4.27188i	0.316026	+	0.871993i
$25$	1.00000			0.200000
$26$	0.0504751	−	0.0874254i	0.00989898	−	0.0171455i
$27$	4.48927	+	2.61657i	0.863961	+	0.503558i
$28$	0.0199793	−	0.665899i	0.00377573	−	0.125843i
$29$	4.51153	−	7.81420i	0.837770	−	1.45106i	−0.0539845	−	0.998542i	$-0.517192\pi$
$29$	4.51153	−	7.81420i	0.837770	−	1.45106i	0.891755	−	0.452519i	$-0.149475\pi$
$30$	−1.67341	+	1.98874i	−0.305521	+	0.363093i
$31$	−4.73625	+	8.20342i	−0.850656	+	1.47338i	0.0299621	+	0.999551i	$0.490461\pi$
$31$	−4.73625	+	8.20342i	−0.850656	+	1.47338i	−0.880618	+	0.473828i	$0.842872\pi$
$32$	0.708129	−	1.22651i	0.125181	−	0.216819i
$33$	1.67135	+	4.61166i	0.290944	+	0.802786i
$34$	−5.22374	+	9.04778i	−0.895864	+	1.55168i
$35$	−2.32993	+	1.25356i	−0.393830	+	0.211891i
$36$	−0.129133	−	0.744278i	−0.0215221	−	0.124046i
$37$	1.37810	−	2.38694i	0.226559	−	0.392411i	−0.730227	−	0.683204i	$-0.760586\pi$
$37$	1.37810	−	2.38694i	0.226559	−	0.392411i	0.956786	+	0.290793i	$0.0939192\pi$
$38$	−2.00423			−0.325129
$39$	0.0750204	−	0.0891572i	0.0120129	−	0.0142766i
$40$	−2.62335			−0.414788
$41$	2.36194	+	4.09100i	0.368873	+	0.638907i	0.989390	−	0.145286i	$-0.0464103\pi$
$41$	2.36194	+	4.09100i	0.368873	+	0.638907i	−0.620516	+	0.784193i	$0.713077\pi$
$42$	1.40590	−	6.73136i	0.216935	−	1.03867i
$43$	3.96429	−	6.86635i	0.604549	−	1.04711i	−0.387574	−	0.921839i	$-0.626687\pi$
$43$	3.96429	−	6.86635i	0.604549	−	1.04711i	0.992123	−	0.125271i	$-0.0399799\pi$
$44$	0.356548	−	0.617560i	0.0537517	−	0.0931007i
$45$	−2.30341	+	1.92205i	−0.343373	+	0.286523i
$46$	2.41733	+	4.18693i	0.356416	+	0.617330i
$47$	−0.867073	−	1.50182i	−0.126476	−	0.219062i	0.795833	−	0.605516i	$-0.207033\pi$
$47$	−0.867073	−	1.50182i	−0.126476	−	0.219062i	−0.922309	+	0.386454i	$0.873700\pi$
$48$	4.95152	−	5.88459i	0.714691	−	0.849368i
$49$	3.85715	−	5.84144i	0.551021	−	0.834491i
$50$	−0.750300	−	1.29956i	−0.106108	−	0.183785i
$51$	−7.76396	+	9.22701i	−1.08717	+	1.29204i
$52$	−0.0169394			−0.00234907
$53$	−6.77377	−	11.7325i	−0.930449	−	1.61158i	−0.782555	−	0.622582i	$-0.786084\pi$
$53$	−6.77377	−	11.7325i	−0.930449	−	1.61158i	−0.147894	−	0.989003i	$-0.547249\pi$
$54$	0.0320746	−	7.79728i	0.00436480	−	1.06108i
$55$	−2.83201			−0.381868
$56$	6.11222	−	3.28854i	0.816780	−	0.439449i
$57$	−2.27766	−	0.404834i	−0.301684	−	0.0536216i
$58$	−13.5400			−1.77789
$59$	3.43542	−	5.95032i	0.447253	−	0.774666i	−0.550953	−	0.834536i	$-0.685736\pi$
$59$	3.43542	−	5.95032i	0.447253	−	0.774666i	0.998206	+	0.0598708i	$0.0190689\pi$
$60$	0.429399	+	0.0763219i	0.0554352	+	0.00985311i
$61$	−1.89824	−	3.28785i	−0.243045	−	0.420966i	0.718535	−	0.695490i	$-0.244813\pi$
$61$	−1.89824	−	3.28785i	−0.243045	−	0.420966i	−0.961580	+	0.274525i	$0.911479\pi$
$62$	14.2144			1.80523
$63$	2.95737	−	7.36573i	0.372594	−	0.927994i
$64$	6.75516			0.844395
$65$	0.0336366	+	0.0582603i	0.00417211	+	0.00722630i
$66$	4.73910	−	5.63214i	0.583343	−	0.693268i
$67$	−1.82517	+	3.16128i	−0.222980	+	0.386212i	−0.955711	−	0.294306i	$-0.904912\pi$
$67$	−1.82517	+	3.16128i	−0.222980	+	0.386212i	0.732732	+	0.680518i	$0.238245\pi$
$68$	1.75308			0.212592
$69$	1.90140	+	5.24642i	0.228902	+	0.631595i
$70$	3.37723	+	2.08733i	0.403656	+	0.249483i
$71$	−8.89186			−1.05527			−0.527635	−	0.849471i	$-0.676921\pi$
$71$	−8.89186			−1.05527			−0.527635	+	0.849471i	$0.676921\pi$
$72$	6.04266	−	5.04222i	0.712134	−	0.594231i
$73$	2.58047	+	4.46951i	0.302021	+	0.523116i	0.976594	−	0.215093i	$-0.0690053\pi$
$73$	2.58047	+	4.46951i	0.302021	+	0.523116i	−0.674572	+	0.738209i	$0.735672\pi$
$74$	−4.13596			−0.480796
$75$	−0.590164	−	1.62841i	−0.0681463	−	0.188032i
$76$	0.168154	+	0.291251i	0.0192886	+	0.0334088i
$77$	6.59838	−	3.55010i	0.751955	−	0.404572i
$78$	−0.172153	−	0.0305986i	−0.0194925	−	0.00346461i
$79$	−5.73331	−	9.93039i	−0.645048	−	1.11726i	−0.984290	−	0.176557i	$-0.943504\pi$
$79$	−5.73331	−	9.93039i	−0.645048	−	1.11726i	0.339242	−	0.940699i	$-0.389829\pi$
$80$	2.22010	+	3.84532i	0.248214	+	0.429920i
$81$	1.61142	−	8.85456i	0.179047	−	0.983841i
$82$	3.54433	−	6.13895i	0.391405	−	0.677934i
$83$	−5.40726	+	9.36564i	−0.593524	+	1.02801i	0.400230	+	0.916415i	$0.368930\pi$
$83$	−5.40726	+	9.36564i	−0.593524	+	1.02801i	−0.993753	+	0.111598i	$0.964403\pi$
$84$	−1.09614	+	0.360455i	−0.119599	+	0.0393289i
$85$	−3.48110	−	6.02944i	−0.377578	−	0.653985i
$86$	−11.8976			−1.28295
$87$	−15.3872	−	2.73494i	−1.64968	−	0.293217i
$88$	7.42934			0.791970
$89$	−3.42561	+	5.93334i	−0.363114	+	0.628932i	−0.988472	−	0.151406i	$-0.951620\pi$
$89$	−3.42561	+	5.93334i	−0.363114	+	0.628932i	0.625357	+	0.780338i	$0.284953\pi$
$90$	4.22607	+	1.55130i	0.445467	+	0.163521i
$91$	−0.151404	−	0.0935768i	−0.0158715	−	0.00980952i
$92$	0.405625	−	0.702564i	0.0422894	−	0.0732473i
$93$	16.1537	+	2.87117i	1.67506	+	0.297727i
$94$	−1.30113	+	2.25362i	−0.134201	+	0.232443i
$95$	0.667810	−	1.15668i	0.0685159	−	0.118673i
$96$	−2.41518	−	0.429276i	−0.246498	−	0.0438128i
$97$	1.45661	−	2.52293i	0.147897	−	0.256164i	−0.782553	−	0.622584i	$-0.786083\pi$
$97$	1.45661	−	2.52293i	0.147897	−	0.256164i	0.930450	+	0.366419i	$0.119416\pi$
$98$	−10.4853	−	0.629758i	−1.05918	−	0.0636152i
$99$	6.52328	−	5.44327i	0.655614	−	0.547069i
$100$	−0.125900	+	0.218065i	−0.0125900	+	0.0218065i
$101$	9.00783			0.896313			0.448156	−	0.893955i	$-0.352081\pi$
$101$	9.00783			0.896313			0.448156	+	0.893955i	$0.352081\pi$
$102$	17.8163	+	3.16669i	1.76408	+	0.313549i
$103$	−0.608911			−0.0599978			−0.0299989	−	0.999550i	$-0.509550\pi$
$103$	−0.608911			−0.0599978			−0.0299989	+	0.999550i	$0.509550\pi$
$104$	−0.0882406	−	0.152837i	−0.00865270	−	0.0149869i
$105$	3.41635	+	3.05426i	0.333402	+	0.298066i
$106$	−10.1647	+	17.6058i	−0.987285	+	1.71003i
$107$	−3.48975	+	6.04442i	−0.337366	+	0.584336i	−0.983937	−	0.178519i	$-0.942869\pi$
$107$	−3.48975	+	6.04442i	−0.337366	+	0.584336i	0.646570	+	0.762855i	$0.276203\pi$
$108$	−1.13578	+	0.649527i	−0.109290	+	0.0625008i
$109$	−8.99581	−	15.5812i	−0.861642	−	1.49241i	−0.870343	−	0.492446i	$-0.836103\pi$
$109$	−8.99581	−	15.5812i	−0.861642	−	1.49241i	0.00870077	−	0.999962i	$-0.497230\pi$
$110$	2.12485	+	3.68035i	0.202597	+	0.350908i
$111$	−4.70022	−	0.835422i	−0.446125	−	0.0792948i
$112$	−9.99303	−	6.17630i	−0.944253	−	0.583605i
$113$	8.13028	+	14.0821i	0.764833	+	1.32473i	0.940335	+	0.340250i	$0.110512\pi$
$113$	8.13028	+	14.0821i	0.764833	+	1.32473i	−0.175502	+	0.984479i	$0.556155\pi$
$114$	1.18282	+	3.26370i	0.110782	+	0.305674i
$115$	−3.22182			−0.300436
$116$	1.13600	+	1.96761i	0.105475	+	0.182688i
$117$	−0.189458	−	0.0695462i	−0.0175154	−	0.00642955i
$118$	−10.3104			−0.949147
$119$	15.6690	+	9.68440i	1.43638	+	0.887767i
$120$	1.54821	+	4.27188i	0.141331	+	0.389967i
$121$	−2.97974			−0.270886
$122$	−2.84850	+	4.93374i	−0.257891	+	0.446680i
$123$	5.26788	−	6.26056i	0.474989	−	0.564496i
$124$	−1.19258	−	2.06562i	−0.107097	−	0.185498i
$125$	1.00000			0.0894427
$126$	−11.7911	+	1.68323i	−1.05043	+	0.149954i
$127$	15.7379			1.39652			0.698258	−	0.715846i	$-0.253959\pi$
$127$	15.7379			1.39652			0.698258	+	0.715846i	$0.253959\pi$
$128$	−6.48465	−	11.2317i	−0.573167	−	0.992755i
$129$	−13.5208	−	2.40320i	−1.19044	−	0.211590i
$130$	0.0504751	−	0.0874254i	0.00442696	−	0.00766772i
$131$	5.07589			0.443482			0.221741	−	0.975106i	$-0.428826\pi$
$131$	5.07589			0.443482			0.221741	+	0.975106i	$0.428826\pi$
$132$	−1.21606	−	0.216144i	−0.105844	−	0.0188129i
$133$	−0.105976	+	3.53213i	−0.00918930	+	0.306274i
$134$	5.47769			0.473200
$135$	4.48927	+	2.61657i	0.386375	+	0.225198i
$136$	9.13215	+	15.8173i	0.783075	+	1.35633i
$137$	−2.36168			−0.201772			−0.100886	−	0.994898i	$-0.532168\pi$
$137$	−2.36168			−0.201772			−0.100886	+	0.994898i	$0.532168\pi$
$138$	5.39141	−	6.40737i	0.458947	−	0.545432i
$139$	−3.45961	−	5.99223i	−0.293441	−	0.508254i	0.681180	−	0.732116i	$-0.261467\pi$
$139$	−3.45961	−	5.99223i	−0.293441	−	0.508254i	−0.974621	+	0.223862i	$0.928134\pi$
$140$	0.0199793	−	0.665899i	0.00168856	−	0.0562787i
$141$	−1.93385	+	2.29826i	−0.162860	+	0.193549i
$142$	6.67156	+	11.5555i	0.559865	+	0.969715i
$143$	−0.0952591	−	0.164994i	−0.00796597	−	0.0137975i
$144$	−12.5047	−	4.59022i	−1.04206	−	0.382518i
$145$	4.51153	−	7.81420i	0.374662	−	0.648934i
$146$	3.87225	−	6.70694i	0.320470	−	0.555070i
$147$	−11.7886	−	2.83360i	−0.972306	−	0.233711i
$148$	0.347005	+	0.601031i	0.0285236	+	0.0494044i
$149$	1.99529			0.163461			0.0817303	−	0.996654i	$-0.473955\pi$
$149$	1.99529			0.163461			0.0817303	+	0.996654i	$0.473955\pi$
$150$	−1.67341	+	1.98874i	−0.136633	+	0.162380i
$151$	5.07189			0.412745			0.206372	−	0.978474i	$-0.433834\pi$
$151$	5.07189			0.412745			0.206372	+	0.978474i	$0.433834\pi$
$152$	−1.75190	+	3.03438i	−0.142098	+	0.246121i
$153$	19.6073	+	7.19744i	1.58516	+	0.581878i
$154$	−9.56432	−	5.91133i	−0.770715	−	0.476348i
$155$	−4.73625	+	8.20342i	−0.380425	+	0.658915i
$156$	0.00999699	+	0.0275841i	0.000800400	+	0.00220850i
$157$	−5.05093	+	8.74847i	−0.403108	+	0.698204i	−0.994099	−	0.108474i	$-0.965403\pi$
$157$	−5.05093	+	8.74847i	−0.403108	+	0.698204i	0.590991	+	0.806678i	$0.298737\pi$
$158$	−8.60341	+	14.9015i	−0.684450	+	1.18550i
$159$	−15.1077	+	17.9546i	−1.19812	+	1.42389i
$160$	0.708129	−	1.22651i	0.0559825	−	0.0969645i
$161$	7.50661	−	4.03876i	0.591603	−	0.318299i
$162$	−12.7161	+	4.54944i	−0.999068	+	0.357438i
$163$	1.30207	−	2.25526i	0.101986	−	0.176645i	−0.810517	−	0.585716i	$-0.800814\pi$
$163$	1.30207	−	2.25526i	0.101986	−	0.176645i	0.912503	+	0.409070i	$0.134147\pi$
$164$	−1.18947			−0.0928820
$165$	1.67135	+	4.61166i	0.130114	+	0.359017i
$166$	16.2283			1.25956
$167$	−4.13083	−	7.15481i	−0.319653	−	0.553656i	0.660762	−	0.750595i	$-0.270233\pi$
$167$	−4.13083	−	7.15481i	−0.319653	−	0.553656i	−0.980416	+	0.196939i	$0.936900\pi$
$168$	−8.96229	−	8.01240i	−0.691456	−	0.618170i
$169$	6.49774	−	11.2544i	0.499826	−	0.865724i
$170$	−5.22374	+	9.04778i	−0.400643	+	0.693933i
$171$	0.684960	+	3.94788i	0.0523802	+	0.301902i
$172$	0.998206	+	1.72894i	0.0761125	+	0.131831i
$173$	8.05135	+	13.9453i	0.612133	+	1.06025i	0.990880	+	0.134745i	$0.0430216\pi$
$173$	8.05135	+	13.9453i	0.612133	+	1.06025i	−0.378747	+	0.925500i	$0.623645\pi$
$174$	7.99082	+	22.0486i	0.605783	+	1.67150i
$175$	−2.32993	+	1.25356i	−0.176126	+	0.0947606i
$176$	−6.28733	−	10.8900i	−0.473925	−	0.820863i
$177$	−11.7170	−	2.08259i	−0.880703	−	0.156537i
$178$	10.2809			0.770590
$179$	5.67319	+	9.82626i	0.424034	+	0.734449i	0.996330	−	0.0855985i	$-0.0272802\pi$
$179$	5.67319	+	9.82626i	0.424034	+	0.734449i	−0.572295	+	0.820048i	$0.693947\pi$
$180$	−0.129133	−	0.744278i	−0.00962499	−	0.0554752i
$181$	−19.6274			−1.45890			−0.729448	−	0.684037i	$-0.760223\pi$
$181$	−19.6274			−1.45890			−0.729448	+	0.684037i	$0.760223\pi$
$182$	−0.00801000	+	0.266969i	−0.000593740	+	0.0197891i
$183$	−4.23368	+	5.03147i	−0.312963	+	0.371937i
$184$	8.45195			0.623086
$185$	1.37810	−	2.38694i	0.101320	−	0.175492i
$186$	−8.38884	−	23.1469i	−0.615100	−	1.69721i
$187$	9.85850	+	17.0754i	0.720925	+	1.24868i
$188$	0.436657			0.0318465
$189$	−13.7397	−	0.468817i	−0.999418	−	0.0341014i
$190$	−2.00423			−0.145402
$191$	−9.54534	−	16.5330i	−0.690676	−	1.19629i	−0.971617	−	0.236561i	$-0.923980\pi$
$191$	−9.54534	−	16.5330i	−0.690676	−	1.19629i	0.280940	−	0.959725i	$-0.409354\pi$
$192$	−3.98665	−	11.0001i	−0.287712	−	0.793867i
$193$	−1.11889	+	1.93797i	−0.0805393	+	0.139498i	−0.903482	−	0.428627i	$-0.858998\pi$
$193$	−1.11889	+	1.93797i	−0.0805393	+	0.139498i	0.822942	+	0.568125i	$0.192331\pi$
$194$	−4.37158			−0.313861
$195$	0.0750204	−	0.0891572i	0.00537232	−	0.00638468i
$196$	0.788197	+	1.57654i	0.0562998	+	0.112610i
$197$	11.5499			0.822898			0.411449	−	0.911433i	$-0.365023\pi$
$197$	11.5499			0.822898			0.411449	+	0.911433i	$0.365023\pi$
$198$	−11.9683	−	4.39329i	−0.850547	−	0.312218i
$199$	3.20576	+	5.55254i	0.227250	+	0.393609i	0.956992	−	0.290114i	$-0.0936931\pi$
$199$	3.20576	+	5.55254i	0.227250	+	0.393609i	−0.729742	+	0.683723i	$0.760360\pi$
$200$	−2.62335			−0.185499
$201$	6.22500	+	1.10644i	0.439078	+	0.0780421i
$202$	−6.75857	−	11.7062i	−0.475532	−	0.823645i
$203$	−0.715944	+	23.8620i	−0.0502494	+	1.67479i
$204$	−1.03460	−	2.85472i	−0.0724367	−	0.199871i
$205$	2.36194	+	4.09100i	0.164965	+	0.285728i
$206$	0.456866	+	0.791315i	0.0318314	+	0.0551335i
$207$	7.42117	−	6.19250i	0.515807	−	0.430409i
$208$	−0.149353	+	0.258687i	−0.0103558	+	0.0179367i
$209$	−1.89124	+	3.27573i	−0.130820	+	0.226587i
$210$	1.40590	−	6.73136i	0.0970164	−	0.464508i
$211$	0.698417	+	1.20969i	0.0480810	+	0.0832788i	0.889064	−	0.457782i	$-0.151356\pi$
$211$	0.698417	+	1.20969i	0.0480810	+	0.0832788i	−0.840983	+	0.541061i	$0.818023\pi$
$212$	3.41126			0.234286
$213$	5.24766	+	14.4796i	0.359564	+	0.992123i
$214$	10.4734			0.715948
$215$	3.96429	−	6.86635i	0.270362	−	0.468282i
$216$	−11.7769	−	6.86416i	−0.801319	−	0.467047i
$217$	0.751605	−	25.0506i	0.0510223	−	1.70055i
$218$	−13.4991	+	23.3811i	−0.914275	+	1.58357i
$219$	5.75527	−	6.83979i	0.388905	−	0.462190i
$220$	0.356548	−	0.617560i	0.0240385	−	0.0416359i
$221$	0.234185	−	0.405620i	0.0157530	−	0.0272850i
$222$	2.44089	+	6.73502i	0.163822	+	0.452025i
$223$	0.738934	−	1.27987i	0.0494827	−	0.0857065i	−0.840223	−	0.542241i	$-0.817576\pi$
$223$	0.738934	−	1.27987i	0.0494827	−	0.0857065i	0.889706	+	0.456534i	$0.150909\pi$
$224$	−0.112374	+	3.74538i	−0.00750833	+	0.250249i
$225$	−2.30341	+	1.92205i	−0.153561	+	0.128137i
$226$	12.2003	−	21.1315i	0.811552	−	1.40565i
$227$	−4.68517			−0.310965			−0.155483	−	0.987839i	$-0.549693\pi$
$227$	−4.68517			−0.310965			−0.155483	+	0.987839i	$0.549693\pi$
$228$	0.375037	−	0.445709i	0.0248374	−	0.0295178i
$229$	21.8436			1.44346			0.721732	−	0.692172i	$-0.243346\pi$
$229$	21.8436			1.44346			0.721732	+	0.692172i	$0.243346\pi$
$230$	2.41733	+	4.18693i	0.159394	+	0.276078i
$231$	−9.67513	−	8.64969i	−0.636577	−	0.569108i
$232$	−11.8353	+	20.4994i	−0.777027	+	1.34585i
$233$	3.21224	−	5.56375i	0.210441	−	0.364494i	−0.741412	−	0.671050i	$-0.765844\pi$
$233$	3.21224	−	5.56375i	0.210441	−	0.364494i	0.951852	+	0.306556i	$0.0991768\pi$
$234$	0.0517713	+	0.298393i	0.00338440	+	0.0195065i
$235$	−0.867073	−	1.50182i	−0.0565616	−	0.0979676i
$236$	0.865036	+	1.49829i	0.0563090	+	0.0975301i
$237$	−12.7871	+	15.1967i	−0.830612	+	0.987133i
$238$	0.828966	−	27.6290i	0.0537339	−	1.79092i
$239$	−7.02033	−	12.1596i	−0.454107	−	0.786537i	0.544529	−	0.838742i	$-0.316708\pi$
$239$	−7.02033	−	12.1596i	−0.454107	−	0.786537i	−0.998636	+	0.0522051i	$0.983375\pi$
$240$	4.95152	−	5.88459i	0.319620	−	0.379849i
$241$	10.9087			0.702692			0.351346	−	0.936246i	$-0.385724\pi$
$241$	10.9087			0.702692			0.351346	+	0.936246i	$0.385724\pi$
$242$	2.23570	+	3.87235i	0.143716	+	0.248924i
$243$	−15.3698	+	2.60160i	−0.985975	+	0.166892i
$244$	0.955951			0.0611985
$245$	3.85715	−	5.84144i	0.246424	−	0.373196i
$246$	−12.0884	−	2.14861i	−0.770731	−	0.136991i
$247$	0.0898515			0.00571711
$248$	12.4248	−	21.5204i	0.788978	−	1.36655i
$249$	18.4422	+	3.27794i	1.16873	+	0.207731i
$250$	−0.750300	−	1.29956i	−0.0474531	−	0.0821912i
$251$	26.5729			1.67727			0.838633	−	0.544698i	$-0.183356\pi$
$251$	26.5729			1.67727			0.838633	+	0.544698i	$0.183356\pi$
$252$	1.23387	+	1.57224i	0.0777266	+	0.0990418i
$253$	9.12420			0.573634
$254$	−11.8082	−	20.4523i	−0.740910	−	1.28329i
$255$	−7.76396	+	9.22701i	−0.486198	+	0.577818i
$256$	−2.97571	+	5.15408i	−0.185982	+	0.322130i
$257$	−16.0555			−1.00151			−0.500756	−	0.865588i	$-0.666945\pi$
$257$	−16.0555			−1.00151			−0.500756	+	0.865588i	$0.666945\pi$
$258$	7.02155	+	19.3742i	0.437143	+	1.20618i
$259$	−0.218694	+	7.28895i	−0.0135890	+	0.452913i
$260$	−0.0169394			−0.00105053
$261$	4.62739	+	26.6707i	0.286428	+	1.65088i
$262$	−3.80844	−	6.59641i	−0.235286	−	0.407527i
$263$	−0.514531			−0.0317273			−0.0158637	−	0.999874i	$-0.505050\pi$
$263$	−0.514531			−0.0317273			−0.0158637	+	0.999874i	$0.505050\pi$
$264$	−4.38453	−	12.0980i	−0.269849	−	0.744579i
$265$	−6.77377	−	11.7325i	−0.416109	−	0.720723i
$266$	4.66972	−	2.51243i	0.286319	−	0.154047i
$267$	11.6836	+	2.07665i	0.715022	+	0.127089i
$268$	−0.459576	−	0.796008i	−0.0280731	−	0.0486240i
$269$	9.39853	+	16.2787i	0.573038	+	0.992531i	0.996252	+	0.0865015i	$0.0275687\pi$
$269$	9.39853	+	16.2787i	0.573038	+	0.992531i	−0.423213	+	0.906030i	$0.639098\pi$
$270$	0.0320746	−	7.79728i	0.00195200	−	0.474527i
$271$	8.63916	−	14.9635i	0.524792	−	0.908966i	−0.474792	−	0.880098i	$-0.657477\pi$
$271$	8.63916	−	14.9635i	0.524792	−	0.908966i	0.999583	−	0.0288675i	$-0.00919007\pi$
$272$	15.4568	−	26.7719i	0.937204	−	1.62329i
$273$	−0.0630278	+	0.301773i	−0.00381462	+	0.0182641i
$274$	1.77197	+	3.06914i	0.107048	+	0.185413i
$275$	−2.83201			−0.170776
$276$	−1.38344	−	0.245895i	−0.0832736	−	0.0148011i
$277$	15.2285			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$277$	15.2285			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$278$	−5.19149	+	8.99193i	−0.311365	+	0.539300i
$279$	−4.85788	−	27.9992i	−0.290834	−	1.67627i
$280$	6.11222	−	3.28854i	0.365275	−	0.196528i
$281$	7.87450	−	13.6390i	0.469753	−	0.813636i	−0.529649	−	0.848217i	$-0.677676\pi$
$281$	7.87450	−	13.6390i	0.469753	−	0.813636i	0.999402	+	0.0345807i	$0.0110096\pi$
$282$	4.43769	+	0.788761i	0.264261	+	0.0469700i
$283$	6.18575	−	10.7140i	0.367705	−	0.636883i	−0.621501	−	0.783413i	$-0.713477\pi$
$283$	6.18575	−	10.7140i	0.367705	−	0.636883i	0.989206	+	0.146530i	$0.0468103\pi$
$284$	1.11948	−	1.93900i	0.0664291	−	0.115058i
$285$	−2.27766	−	0.404834i	−0.134917	−	0.0239803i
$286$	−0.142946	+	0.247589i	−0.00845256	+	0.0146403i
$287$	−10.6315	−	6.57090i	−0.627557	−	0.387868i
$288$	0.726314	+	4.18623i	0.0427985	+	0.246676i
$289$	−15.7361	+	27.2558i	−0.925655	+	1.60328i
$290$	−13.5400			−0.795096
$291$	−4.96799	−	0.883016i	−0.291229	−	0.0517633i
$292$	−1.29952			−0.0760487
$293$	−8.80515	−	15.2510i	−0.514403	−	0.890971i	−0.999860	−	0.0167112i	$-0.994680\pi$
$293$	−8.80515	−	15.2510i	−0.514403	−	0.890971i	0.485458	−	0.874260i	$-0.338653\pi$
$294$	5.16255	+	17.4460i	0.301086	+	1.01747i
$295$	3.43542	−	5.95032i	0.200018	−	0.346441i
$296$	−3.61524	+	6.26179i	−0.210132	+	0.363959i
$297$	−12.7137	−	7.41013i	−0.737721	−	0.429979i
$298$	−1.49707	−	2.59299i	−0.0867227	−	0.150208i
$299$	−0.108371	−	0.187704i	−0.00626726	−	0.0108552i
$300$	0.429399	+	0.0763219i	0.0247914	+	0.00440645i
$301$	−0.629102	+	20.9676i	−0.0362608	+	1.20855i
$302$	−3.80544	−	6.59121i	−0.218978	−	0.379282i
$303$	−5.31610	−	14.6684i	−0.305402	−	0.842678i
$304$	5.93041			0.340133
$305$	−1.89824	−	3.28785i	−0.108693	−	0.188262i
$306$	−5.35789	−	30.8811i	−0.306290	−	1.76535i
$307$	6.14034			0.350448			0.175224	−	0.984529i	$-0.443935\pi$
$307$	6.14034			0.350448			0.175224	+	0.984529i	$0.443935\pi$
$308$	−0.0565814	+	1.88583i	−0.00322402	+	0.107455i
$309$	0.359357	+	0.991555i	0.0204431	+	0.0564076i
$310$	14.2144			0.807325
$311$	−12.4005	+	21.4784i	−0.703170	+	1.21793i	0.264178	+	0.964474i	$0.414899\pi$
$311$	−12.4005	+	21.4784i	−0.703170	+	1.21793i	−0.967348	+	0.253452i	$0.918434\pi$
$312$	−0.196805	+	0.233891i	−0.0111419	+	0.0132414i
$313$	−12.8881	−	22.3228i	−0.728476	−	1.26176i	−0.957527	−	0.288343i	$-0.906896\pi$
$313$	−12.8881	−	22.3228i	−0.728476	−	1.26176i	0.229052	−	0.973414i	$-0.426438\pi$
$314$	15.1588			0.855463
$315$	2.95737	−	7.36573i	0.166629	−	0.415012i
$316$	2.88729			0.162423
$317$	4.69012	+	8.12352i	0.263423	+	0.456263i	0.967149	−	0.254209i	$-0.0818151\pi$
$317$	4.69012	+	8.12352i	0.263423	+	0.456263i	−0.703726	+	0.710471i	$0.748482\pi$
$318$	34.6683	+	6.16197i	1.94410	+	0.345546i
$319$	−12.7767	+	22.1299i	−0.715357	+	1.23903i
$320$	6.75516			0.377625
$321$	11.9023	+	2.11553i	0.664321	+	0.118077i
$322$	−10.8808	−	6.72499i	−0.606363	−	0.374769i
$323$	−9.29886			−0.517402
$324$	1.72799	+	1.46618i	0.0959994	+	0.0814545i
$325$	0.0336366	+	0.0582603i	0.00186582	+	0.00323170i
$326$	−3.90778			−0.216432
$327$	−20.0635	+	23.8443i	−1.10951	+	1.31859i
$328$	−6.19620	−	10.7321i	−0.342128	−	0.592583i
$329$	3.90284	+	2.41219i	0.215171	+	0.132988i
$330$	4.73910	−	5.63214i	0.260879	−	0.310039i
$331$	−14.6030	−	25.2931i	−0.802651	−	1.39023i	−0.917865	−	0.396892i	$-0.870089\pi$
$331$	−14.6030	−	25.2931i	−0.802651	−	1.39023i	0.115214	−	0.993341i	$-0.463245\pi$
$332$	−1.36154	−	2.35826i	−0.0747244	−	0.129426i
$333$	1.41349	+	8.14690i	0.0774590	+	0.446447i
$334$	−6.19873	+	10.7365i	−0.339179	+	0.587476i
$335$	−1.82517	+	3.16128i	−0.0997195	+	0.172719i
$336$	−4.15999	+	19.9177i	−0.226946	+	1.08660i
$337$	−2.22121	−	3.84725i	−0.120997	−	0.209573i	0.799164	−	0.601113i	$-0.205276\pi$
$337$	−2.22121	−	3.84725i	−0.120997	−	0.209573i	−0.920161	+	0.391540i	$0.871943\pi$
$338$	−19.5010			−1.06071
$339$	18.1331	−	21.5501i	0.984856	−	1.17044i
$340$	1.75308			0.0950740
$341$	13.4131	−	23.2321i	0.726359	−	1.25809i
$342$	4.61657	−	3.85224i	0.249636	−	0.208305i
$343$	−1.66427	+	18.4453i	−0.0898620	+	0.995954i
$344$	−10.3997	+	18.0128i	−0.560715	+	0.971188i
$345$	1.90140	+	5.24642i	0.102368	+	0.282458i
$346$	12.0819	−	20.9264i	0.649524	−	1.12501i
$347$	−3.66460	+	6.34727i	−0.196726	+	0.340739i	−0.947465	−	0.319860i	$-0.896364\pi$
$347$	−3.66460	+	6.34727i	−0.196726	+	0.340739i	0.750739	+	0.660599i	$0.229698\pi$
$348$	2.53364	−	3.01108i	0.135817	−	0.161411i
$349$	−10.9927	+	19.0399i	−0.588424	+	1.01918i	0.406015	+	0.913866i	$0.366918\pi$
$349$	−10.9927	+	19.0399i	−0.588424	+	1.01918i	−0.994439	+	0.105314i	$0.966415\pi$
$350$	3.37723	+	2.08733i	0.180520	+	0.111572i
$351$	−0.00143793	+	0.349559i	−7.67511e−5	+	0.0186581i
$352$	−2.00542	+	3.47350i	−0.106889	+	0.185138i
$353$	25.7875			1.37253			0.686265	−	0.727351i	$-0.259249\pi$
$353$	25.7875			1.37253			0.686265	+	0.727351i	$0.259249\pi$
$354$	6.08481	+	16.7895i	0.323404	+	0.892351i
$355$	−8.89186			−0.471931
$356$	−0.862567	−	1.49401i	−0.0457159	−	0.0791823i
$357$	6.52284	−	31.2309i	0.345225	−	1.65292i
$358$	8.51319	−	14.7453i	0.449936	−	0.779312i
$359$	1.05274	−	1.82340i	0.0555616	−	0.0962355i	−0.836907	−	0.547345i	$-0.815638\pi$
$359$	1.05274	−	1.82340i	0.0555616	−	0.0962355i	0.892468	+	0.451110i	$0.148972\pi$
$360$	6.04266	−	5.04222i	0.318476	−	0.265748i
$361$	8.60806	+	14.9096i	0.453056	+	0.784716i
$362$	14.7265	+	25.5070i	0.774005	+	1.34062i
$363$	1.75854	+	4.85223i	0.0922993	+	0.254676i
$364$	0.0394675	−	0.0212346i	0.00206866	−	0.00111299i
$365$	2.58047	+	4.46951i	0.135068	+	0.233945i
$366$	9.71522	+	1.72679i	0.507823	+	0.0902610i
$367$	5.58958			0.291774			0.145887	−	0.989301i	$-0.453396\pi$
$367$	5.58958			0.291774			0.145887	+	0.989301i	$0.453396\pi$
$368$	−7.15275	−	12.3889i	−0.372863	−	0.645817i
$369$	−13.3036	−	4.88349i	−0.692560	−	0.254224i
$370$	−4.13596			−0.215018
$371$	30.4899	+	18.8446i	1.58296	+	0.978362i
$372$	−2.65984	+	3.16106i	−0.137906	+	0.163894i
$373$	5.04993			0.261475			0.130738	−	0.991417i	$-0.458265\pi$
$373$	5.04993			0.261475			0.130738	+	0.991417i	$0.458265\pi$
$374$	14.7937	−	25.6234i	0.764962	−	1.32495i
$375$	−0.590164	−	1.62841i	−0.0304759	−	0.0840905i
$376$	2.27464	+	3.93979i	0.117305	+	0.203179i
$377$	0.607011			0.0312626
$378$	9.69966	+	18.2073i	0.498897	+	0.936484i
$379$	−0.343947			−0.0176674			−0.00883369	−	0.999961i	$-0.502812\pi$
$379$	−0.343947			−0.0176674			−0.00883369	+	0.999961i	$0.502812\pi$
$380$	0.168154	+	0.291251i	0.00862612	+	0.0149409i
$381$	−9.28796	−	25.6277i	−0.475837	−	1.31295i
$382$	−14.3237	+	24.8094i	−0.732866	+	1.26936i
$383$	−1.79877			−0.0919126			−0.0459563	−	0.998943i	$-0.514633\pi$
$383$	−1.79877			−0.0919126			−0.0459563	+	0.998943i	$0.514633\pi$
$384$	−14.4628	+	17.1882i	−0.738053	+	0.877132i
$385$	6.59838	−	3.55010i	0.336284	−	0.180930i
$386$	3.35800			0.170918
$387$	4.06610	+	23.4356i	0.206691	+	1.19130i
$388$	0.366774	+	0.635271i	0.0186201	+	0.0322510i
$389$	−27.8479			−1.41195			−0.705973	−	0.708239i	$-0.749490\pi$
$389$	−27.8479			−1.41195			−0.705973	+	0.708239i	$0.749490\pi$
$390$	−0.172153	−	0.0305986i	−0.00871729	−	0.00154942i
$391$	11.2155	+	19.4258i	0.567191	+	0.982403i
$392$	−10.1187	+	15.3241i	−0.511069	+	0.773986i
$393$	−2.99561	−	8.26561i	−0.151108	−	0.416945i
$394$	−8.66591	−	15.0098i	−0.436582	−	0.756182i
$395$	−5.73331	−	9.93039i	−0.288474	−	0.499652i
$396$	0.365705	+	2.10780i	0.0183774	+	0.105921i
$397$	−15.3266	+	26.5465i	−0.769220	+	1.33233i	0.168766	+	0.985656i	$0.446022\pi$
$397$	−15.3266	+	26.5465i	−0.769220	+	1.33233i	−0.937986	+	0.346672i	$0.887312\pi$
$398$	4.81056	−	8.33214i	0.241132	−	0.417653i
$399$	5.81428	−	1.91196i	0.291078	−	0.0957179i
$400$	2.22010	+	3.84532i	0.111005	+	0.192266i
$401$	26.3282			1.31477			0.657384	−	0.753556i	$-0.271663\pi$
$401$	26.3282			1.31477			0.657384	+	0.753556i	$0.271663\pi$
$402$	−3.23274	−	8.91990i	−0.161234	−	0.444884i
$403$	−0.637246			−0.0317435
$404$	−1.13408	+	1.96429i	−0.0564227	+	0.0977270i
$405$	1.61142	−	8.85456i	0.0800722	−	0.439987i
$406$	31.5473	−	16.9733i	1.56566	−	0.842369i
$407$	−3.90279	+	6.75984i	−0.193454	+	0.335073i
$408$	20.3676	−	24.2057i	1.00835	−	1.19836i
$409$	2.51589	−	4.35765i	0.124403	−	0.215472i	−0.797097	−	0.603852i	$-0.793632\pi$
$409$	2.51589	−	4.35765i	0.124403	−	0.215472i	0.921499	+	0.388380i	$0.126965\pi$
$410$	3.54433	−	6.13895i	0.175042	−	0.303181i
$411$	1.39378	+	3.84577i	0.0687500	+	0.189698i
$412$	0.0766617	−	0.132782i	0.00377685	−	0.00654170i
$413$	−0.545174	+	18.1704i	−0.0268262	+	0.894104i
$414$	−13.6156	−	4.99801i	−0.669171	−	0.245639i
$415$	−5.40726	+	9.36564i	−0.265432	+	0.459741i
$416$	0.0952762			0.00467130
$417$	−7.71604	+	9.17005i	−0.377856	+	0.449059i
$418$	5.67599			0.277622
$419$	−10.3206	−	17.8758i	−0.504195	−	0.873291i	−0.999988	−	0.00485063i	$-0.998456\pi$
$419$	−10.3206	−	17.8758i	−0.504195	−	0.873291i	0.495793	−	0.868441i	$-0.334877\pi$
$420$	−1.09614	+	0.360455i	−0.0534864	+	0.0175884i
$421$	−12.2741	+	21.2594i	−0.598204	+	1.03612i	0.394882	+	0.918732i	$0.370785\pi$
$421$	−12.2741	+	21.2594i	−0.598204	+	1.03612i	−0.993086	+	0.117388i	$0.962548\pi$
$422$	1.04804	−	1.81527i	0.0510180	−	0.0883658i
$423$	4.88380	+	1.79274i	0.237458	+	0.0871660i
$424$	17.7700	+	30.7785i	0.862986	+	1.49474i
$425$	−3.48110	−	6.02944i	−0.168858	−	0.292471i
$426$	14.8797	−	17.6836i	0.720924	−	0.856776i
$427$	8.54430	+	5.28089i	0.413487	+	0.255560i
$428$	−0.878715	−	1.52198i	−0.0424743	−	0.0735677i
$429$	−0.212458	+	0.252494i	−0.0102576	+	0.0121905i
$430$	−11.8976			−0.573755
$431$	−17.6175	−	30.5144i	−0.848604	−	1.46982i	−0.882455	−	0.470398i	$-0.844110\pi$
$431$	−17.6175	−	30.5144i	−0.848604	−	1.46982i	0.0338510	−	0.999427i	$-0.489223\pi$
$432$	−0.0949070	+	23.0717i	−0.00456621	+	1.11004i
$433$	−41.2488			−1.98229			−0.991146	−	0.132775i	$-0.957611\pi$
$433$	−41.2488			−1.98229			−0.991146	+	0.132775i	$0.957611\pi$
$434$	−33.1186	+	17.8187i	−1.58975	+	0.855325i
$435$	−15.3872	−	2.73494i	−0.737761	−	0.131131i
$436$	4.53028			0.216961
$437$	−2.15156	+	3.72661i	−0.102923	+	0.178268i
$438$	−13.2069	−	2.34741i	−0.631049	−	0.112163i
$439$	−16.2000	−	28.0592i	−0.773183	−	1.33919i	−0.935810	−	0.352504i	$-0.885330\pi$
$439$	−16.2000	−	28.0592i	−0.773183	−	1.33919i	0.162627	−	0.986688i	$-0.448003\pi$
$440$	7.42934			0.354180
$441$	2.34295	+	20.8689i	0.111569	+	0.993757i
$442$	−0.702836			−0.0334305
$443$	7.61855	+	13.1957i	0.361968	+	0.626947i	0.988285	−	0.152622i	$-0.0487716\pi$
$443$	7.61855	+	13.1957i	0.361968	+	0.626947i	−0.626317	+	0.779569i	$0.715438\pi$
$444$	0.773932	−	0.919772i	0.0367292	−	0.0436504i
$445$	−3.42561	+	5.93334i	−0.162390	+	0.281267i
$446$	−2.21769			−0.105011
$447$	−1.17755	−	3.24914i	−0.0556961	−	0.153679i
$448$	−15.7390	+	8.46803i	−0.743600	+	0.400077i
$449$	7.30992			0.344976			0.172488	−	0.985012i	$-0.444819\pi$
$449$	7.30992			0.344976			0.172488	+	0.985012i	$0.444819\pi$
$450$	4.22607	+	1.55130i	0.199219	+	0.0731290i
$451$	−6.68903	−	11.5857i	−0.314974	−	0.545551i
$452$	−4.09440			−0.192584
$453$	−2.99325	−	8.25910i	−0.140635	−	0.388046i
$454$	3.51528	+	6.08864i	0.164980	+	0.285754i
$455$	−0.151404	−	0.0935768i	−0.00709793	−	0.00438695i
$456$	5.97511	+	1.06202i	0.279810	+	0.0497338i
$457$	15.1949	+	26.3183i	0.710787	+	1.23112i	0.964562	+	0.263856i	$0.0849944\pi$
$457$	15.1949	+	26.3183i	0.710787	+	1.23112i	−0.253775	+	0.967263i	$0.581672\pi$
$458$	−16.3892	−	28.3870i	−0.765819	−	1.32644i
$459$	0.148814	−	36.1764i	0.00694603	−	1.68857i
$460$	0.405625	−	0.702564i	0.0189124	−	0.0327572i
$461$	−10.0136	+	17.3440i	−0.466379	+	0.807793i	−0.999263	−	0.0383961i	$-0.987775\pi$
$461$	−10.0136	+	17.3440i	−0.466379	+	0.807793i	0.532883	+	0.846189i	$0.321108\pi$
$462$	−3.98152	+	19.0633i	−0.185237	+	0.886903i
$463$	−18.8943	−	32.7259i	−0.878092	−	1.52090i	−0.853432	−	0.521204i	$-0.825483\pi$
$463$	−18.8943	−	32.7259i	−0.878092	−	1.52090i	−0.0246600	−	0.999696i	$-0.507850\pi$
$464$	40.0642			1.85993
$465$	16.1537	+	2.87117i	0.749109	+	0.133147i
$466$	−9.64056			−0.446590
$467$	−12.9905	+	22.5002i	−0.601128	+	1.04118i	0.391523	+	0.920168i	$0.371948\pi$
$467$	−12.9905	+	22.5002i	−0.601128	+	1.04118i	−0.992651	+	0.121016i	$0.961385\pi$
$468$	0.0390183	−	0.0325583i	0.00180362	−	0.00150501i
$469$	0.289639	−	9.65353i	0.0133743	−	0.445759i
$470$	−1.30113	+	2.25362i	−0.0600167	+	0.103952i
$471$	17.2269	+	3.06194i	0.793775	+	0.141087i
$472$	−9.01230	+	15.6098i	−0.414825	+	0.718498i
$473$	−11.2269	+	19.4456i	−0.516213	+	0.894108i
$474$	29.3432	+	5.21549i	1.34778	+	0.239555i
$475$	0.667810	−	1.15668i	0.0306412	−	0.0530722i
$476$	−4.08455	+	2.19760i	−0.187215	+	0.100727i
$477$	38.1533	+	14.0053i	1.74692	+	0.641258i
$478$	−10.5347	+	18.2466i	−0.481846	+	0.834582i
$479$	−27.7078			−1.26600			−0.633001	−	0.774151i	$-0.718177\pi$
$479$	−27.7078			−1.26600			−0.633001	+	0.774151i	$0.718177\pi$
$480$	−2.41518	−	0.429276i	−0.110237	−	0.0195937i
$481$	0.185419			0.00845437
$482$	−8.18480	−	14.1765i	−0.372808	−	0.645722i
$483$	−11.0069	−	9.84028i	−0.500830	−	0.447748i
$484$	0.375149	−	0.649776i	0.0170522	−	0.0295353i
$485$	1.45661	−	2.52293i	0.0661413	−	0.114560i
$486$	14.9129	+	18.0220i	0.676463	+	0.817495i
$487$	−6.99385	−	12.1137i	−0.316922	−	0.548925i	0.662922	−	0.748688i	$-0.269316\pi$
$487$	−6.99385	−	12.1137i	−0.316922	−	0.548925i	−0.979844	+	0.199763i	$0.935983\pi$
$488$	4.97975	+	8.62517i	0.225422	+	0.390443i
$489$	−4.44091	−	0.789333i	−0.200825	−	0.0356949i
$490$	−10.4853	−	0.629758i	−0.473678	−	0.0284496i
$491$	−4.04649	−	7.00872i	−0.182615	−	0.316299i	0.760155	−	0.649742i	$-0.225123\pi$
$491$	−4.04649	−	7.00872i	−0.182615	−	0.316299i	−0.942770	+	0.333443i	$0.891790\pi$
$492$	0.701982	+	1.93694i	0.0316478	+	0.0873240i
$493$	−62.8204			−2.82929
$494$	−0.0674155	−	0.116767i	−0.00303317	−	0.00525360i
$495$	6.52328	−	5.44327i	0.293200	−	0.244657i
$496$	−42.0597			−1.88854
$497$	20.7174	−	11.1465i	0.929303	−	0.499990i
$498$	−9.57733	−	26.4262i	−0.429170	−	1.18419i
$499$	−1.94766			−0.0871891			−0.0435945	−	0.999049i	$-0.513881\pi$
$499$	−1.94766			−0.0871891			−0.0435945	+	0.999049i	$0.513881\pi$
$500$	−0.125900	+	0.218065i	−0.00563040	+	0.00975214i
$501$	−9.21307	+	10.9492i	−0.411610	+	0.489174i
$502$	−19.9376	−	34.5330i	−0.889860	−	1.54128i
$503$	3.94050			0.175698			0.0878491	−	0.996134i	$-0.472001\pi$
$503$	3.94050			0.175698			0.0878491	+	0.996134i	$0.472001\pi$
$504$	−7.75822	+	19.3229i	−0.345579	+	0.860709i
$505$	9.00783			0.400843
$506$	−6.84589	−	11.8574i	−0.304337	−	0.527127i
$507$	−22.1615	−	3.93901i	−0.984226	−	0.174937i
$508$	−1.98140	+	3.43189i	−0.0879104	+	0.152265i
$509$	1.85796			0.0823528			0.0411764	−	0.999152i	$-0.486889\pi$
$509$	1.85796			0.0823528			0.0411764	+	0.999152i	$0.486889\pi$
$510$	17.8163	+	3.16669i	0.788920	+	0.140224i
$511$	−11.6151	−	7.17885i	−0.513823	−	0.317574i
$512$	−17.0079			−0.751651
$513$	6.02451	−	3.44529i	0.265989	−	0.152113i
$514$	12.0464	+	20.8650i	0.531344	+	0.920316i
$515$	−0.608911			−0.0268318
$516$	2.22632	−	2.64584i	0.0980081	−	0.116477i
$517$	2.45556	+	4.25315i	0.107995	+	0.187053i
$518$	9.63650	−	5.18469i	0.423403	−	0.227802i
$519$	17.9571	−	21.3409i	0.788228	−	0.936762i
$520$	−0.0882406	−	0.152837i	−0.00386961	−	0.00670236i
$521$	11.4331	+	19.8027i	0.500892	+	0.867571i	0.999999	+	0.00103053i	$0.000328027\pi$
$521$	11.4331	+	19.8027i	0.500892	+	0.867571i	−0.499107	+	0.866540i	$0.666339\pi$
$522$	31.1882	−	26.0246i	1.36507	−	1.13907i
$523$	13.3034	−	23.0422i	0.581718	−	1.00756i	−0.413558	−	0.910478i	$-0.635714\pi$
$523$	13.3034	−	23.0422i	0.581718	−	1.00756i	0.995276	−	0.0970867i	$-0.0309524\pi$
$524$	−0.639052	+	1.10687i	−0.0279171	+	0.0483539i
$525$	3.41635	+	3.05426i	0.149102	+	0.133299i
$526$	0.386052	+	0.668662i	0.0168327	+	0.0291551i
$527$	65.9495			2.87280
$528$	−14.0227	+	16.6652i	−0.610262	+	0.725260i
$529$	−12.6199			−0.548691
$530$	−10.1647	+	17.6058i	−0.441527	+	0.764747i
$531$	3.52364	+	20.3091i	0.152913	+	0.881340i
$532$	−0.756890	−	0.467803i	−0.0328153	−	0.0202818i
$533$	−0.158895	+	0.275215i	−0.00688252	+	0.0119209i
$534$	−6.06744	−	16.7416i	−0.262564	−	0.724478i
$535$	−3.48975	+	6.04442i	−0.150875	+	0.261323i
$536$	4.78805	−	8.29315i	0.206812	−	0.358209i
$537$	12.6530	−	15.0374i	0.546018	−	0.648910i
$538$	14.1034	−	24.4279i	0.608042	−	1.05316i
$539$	−10.9235	+	16.5430i	−0.470507	+	0.712557i
$540$	−1.13578	+	0.649527i	−0.0488761	+	0.0279512i
$541$	−2.00002	+	3.46414i	−0.0859878	+	0.148935i	−0.905812	−	0.423681i	$-0.860738\pi$
$541$	−2.00002	+	3.46414i	−0.0859878	+	0.148935i	0.819824	+	0.572616i	$0.194071\pi$
$542$	−25.9278			−1.11370
$543$	11.5834	+	31.9614i	0.497091	+	1.37160i
$544$	−9.86027			−0.422756
$545$	−8.99581	−	15.5812i	−0.385338	−	0.667425i
$546$	0.439461	−	0.144512i	0.0188072	−	0.00618454i
$547$	6.16681	−	10.6812i	0.263674	−	0.456696i	−0.703542	−	0.710654i	$-0.748399\pi$
$547$	6.16681	−	10.6812i	0.263674	−	0.456696i	0.967215	+	0.253958i	$0.0817325\pi$
$548$	0.297335	−	0.514998i	0.0127015	−	0.0219996i
$549$	10.6918	+	3.92475i	0.456317	+	0.167504i
$550$	2.12485	+	3.68035i	0.0906041	+	0.156931i
$551$	−6.02569	−	10.4368i	−0.256703	−	0.444623i
$552$	−4.98804	−	13.7632i	−0.212305	−	0.585801i
$553$	25.8066	+	15.9500i	1.09741	+	0.678264i
$554$	−11.4259	−	19.7903i	−0.485441	−	0.840809i
$555$	−4.70022	−	0.835422i	−0.199513	−	0.0354617i
$556$	1.74226			0.0738881
$557$	−10.0309	−	17.3739i	−0.425021	−	0.736158i	0.571402	−	0.820671i	$-0.306400\pi$
$557$	−10.0309	−	17.3739i	−0.425021	−	0.736158i	−0.996422	+	0.0845130i	$0.973067\pi$
$558$	−32.7417	+	27.3209i	−1.38607	+	1.15659i
$559$	0.533381			0.0225596
$560$	−9.99303	−	6.17630i	−0.422283	−	0.260996i
$561$	21.9876	−	26.1309i	0.928317	−	1.10325i
$562$	−23.6329			−0.996895
$563$	1.85252	−	3.20865i	0.0780743	−	0.135229i	−0.824345	−	0.566088i	$-0.808456\pi$
$563$	1.85252	−	3.20865i	0.0780743	−	0.135229i	0.902419	+	0.430859i	$0.141790\pi$
$564$	−0.257699	−	0.711055i	−0.0108511	−	0.0299408i
$565$	8.13028	+	14.0821i	0.342044	+	0.592437i
$566$	−18.5647			−0.780332
$567$	7.34527	+	22.6505i	0.308472	+	0.951233i
$568$	23.3265			0.978757
$569$	−12.4623	−	21.5853i	−0.522445	−	0.904901i	−0.999659	−	0.0261142i	$-0.991687\pi$
$569$	−12.4623	−	21.5853i	−0.522445	−	0.904901i	0.477214	−	0.878787i	$-0.341647\pi$
$570$	1.18282	+	3.26370i	0.0495431	+	0.136701i
$571$	−12.3535	+	21.3969i	−0.516977	+	0.895430i	0.482829	+	0.875715i	$0.339609\pi$
$571$	−12.3535	+	21.3969i	−0.516977	+	0.895430i	−0.999806	+	0.0197156i	$0.993724\pi$
$572$	0.0479723			0.00200582
$573$	−21.2891	+	25.3009i	−0.889367	+	1.05696i
$574$	−0.562457	+	18.7464i	−0.0234765	+	0.782459i
$575$	−3.22182			−0.134359
$576$	−15.5599	+	12.9838i	−0.648330	+	0.540990i
$577$	1.99653	+	3.45809i	0.0831165	+	0.143962i	0.904587	−	0.426289i	$-0.140179\pi$
$577$	1.99653	+	3.45809i	0.0831165	+	0.143962i	−0.821471	+	0.570251i	$0.806846\pi$
$578$	47.2273			1.96440
$579$	3.81613	+	0.678283i	0.158593	+	0.0281885i
$580$	1.13600	+	1.96761i	0.0471698	+	0.0817006i
$581$	0.858089	−	28.5996i	0.0355995	−	1.18651i
$582$	2.57995	+	7.11871i	0.106942	+	0.295080i
$583$	19.1834	+	33.2265i	0.794493	+	1.37610i
$584$	−6.76947	−	11.7251i	−0.280123	−	0.485187i
$585$	−0.189458	−	0.0695462i	−0.00783314	−	0.00287538i
$586$	−13.2130	+	22.8856i	−0.545824	+	0.945396i
$587$	5.98200	−	10.3611i	0.246904	−	0.427649i	−0.715762	−	0.698345i	$-0.753920\pi$
$587$	5.98200	−	10.3611i	0.246904	−	0.427649i	0.962665	+	0.270695i	$0.0872536\pi$
$588$	2.10209	−	2.21392i	0.0866886	−	0.0913006i
$589$	6.32583	+	10.9567i	0.260651	+	0.451461i
$590$	−10.3104			−0.424471
$591$	−6.81635	−	18.8080i	−0.280387	−	0.773656i
$592$	12.2381			0.502982
$593$	8.42545	−	14.5933i	0.345992	−	0.599275i	−0.639542	−	0.768756i	$-0.720876\pi$
$593$	8.42545	−	14.5933i	0.345992	−	0.599275i	0.985533	+	0.169481i	$0.0542091\pi$
$594$	−0.0908354	+	22.0819i	−0.00372702	+	0.906033i
$595$	15.6690	+	9.68440i	0.642367	+	0.397022i
$596$	−0.251206	+	0.435102i	−0.0102898	+	0.0178225i
$597$	7.14987	−	8.49719i	0.292625	−	0.347767i
$598$	−0.162621	+	0.281669i	−0.00665009	+	0.0115183i
$599$	−15.7795	+	27.3310i	−0.644734	+	1.11671i	0.339628	+	0.940560i	$0.389699\pi$
$599$	−15.7795	+	27.3310i	−0.644734	+	1.11671i	−0.984363	+	0.176153i	$0.943635\pi$
$600$	1.54821	+	4.27188i	0.0632053	+	0.174399i
$601$	17.2897	−	29.9467i	0.705262	−	1.22155i	−0.261335	−	0.965248i	$-0.584163\pi$
$601$	17.2897	−	29.9467i	0.705262	−	1.22155i	0.966597	−	0.256301i	$-0.0825039\pi$
$602$	27.7206	−	14.9145i	1.12981	−	0.607868i
$603$	−1.87204	−	10.7898i	−0.0762353	−	0.439395i
$604$	−0.638549	+	1.10600i	−0.0259822	+	0.0450025i
$605$	−2.97974			−0.121144
$606$	−15.0738	+	17.9143i	−0.612330	+	0.727718i
$607$	33.1726			1.34643			0.673217	−	0.739445i	$-0.264912\pi$
$607$	33.1726			1.34643			0.673217	+	0.739445i	$0.264912\pi$
$608$	−0.945791	−	1.63816i	−0.0383569	−	0.0664361i
$609$	39.2796	−	12.9167i	1.59169	−	0.523410i
$610$	−2.84850	+	4.93374i	−0.115332	+	0.199761i
$611$	0.0583308	−	0.101032i	0.00235981	−	0.00408732i
$612$	−4.03806	+	3.36951i	−0.163229	+	0.136204i
$613$	−8.55424	−	14.8164i	−0.345502	−	0.598428i	0.639942	−	0.768423i	$-0.278958\pi$
$613$	−8.55424	−	14.8164i	−0.345502	−	0.598428i	−0.985445	+	0.169995i	$0.945625\pi$
$614$	−4.60710	−	7.97973i	−0.185927	−	0.322036i
$615$	5.26788	−	6.26056i	0.212421	−	0.252450i
$616$	−17.3098	+	9.31316i	−0.697434	+	0.375238i
$617$	1.83717	+	3.18206i	0.0739615	+	0.128105i	0.900634	−	0.434578i	$-0.143102\pi$
$617$	1.83717	+	3.18206i	0.0739615	+	0.128105i	−0.826673	+	0.562683i	$0.809769\pi$
$618$	1.01896	−	1.21097i	0.0409884	−	0.0487123i
$619$	34.7469			1.39660			0.698299	−	0.715806i	$-0.253941\pi$
$619$	34.7469			1.39660			0.698299	+	0.715806i	$0.253941\pi$
$620$	−1.19258	−	2.06562i	−0.0478953	−	0.0829571i
$621$	−14.4636	−	8.43009i	−0.580405	−	0.338288i
$622$	37.2165			1.49225
$623$	0.543618	−	18.1185i	0.0217796	−	0.725902i
$624$	0.509391	+	0.0905397i	0.0203920	+	0.00362449i
$625$	1.00000			0.0400000
$626$	−19.3398	+	33.4975i	−0.772974	+	1.33883i
$627$	6.45036	+	1.14649i	0.257602	+	0.0457865i
$628$	−1.27182	−	2.20286i	−0.0507512	−	0.0879036i
$629$	−19.1893			−0.765126
$630$	−11.7911	+	1.68323i	−0.469769	+	0.0670614i
$631$	−31.6609			−1.26040			−0.630201	−	0.776432i	$-0.717027\pi$
$631$	−31.6609			−1.26040			−0.630201	+	0.776432i	$0.717027\pi$
$632$	15.0405	+	26.0509i	0.598278	+	1.03625i
$633$	1.55769	−	1.85122i	0.0619127	−	0.0735796i
$634$	7.03799	−	12.1902i	0.279514	−	0.484133i
$635$	15.7379			0.624541
$636$	−2.01320	−	5.55492i	−0.0798287	−	0.220267i
$637$	0.470066	+	0.0282326i	0.0186247	+	0.00111862i
$638$	38.3454			1.51811
$639$	20.4816	−	17.0906i	0.810241	−	0.676095i
$640$	−6.48465	−	11.2317i	−0.256328	−	0.443974i
$641$	41.2177			1.62800			0.814001	−	0.580863i	$-0.197285\pi$
$641$	41.2177			1.62800			0.814001	+	0.580863i	$0.197285\pi$
$642$	−6.18104	−	17.0550i	−0.243946	−	0.673107i
$643$	24.5575	+	42.5348i	0.968452	+	1.67741i	0.700039	+	0.714105i	$0.253166\pi$
$643$	24.5575	+	42.5348i	0.968452	+	1.67741i	0.268413	+	0.963304i	$0.413501\pi$
$644$	−0.0643695	+	2.14540i	−0.00253651	+	0.0845407i
$645$	−13.5208	−	2.40320i	−0.532381	−	0.0946260i
$646$	6.97693	+	12.0844i	0.274504	+	0.475454i
$647$	−2.21162	−	3.83064i	−0.0869479	−	0.150598i	0.819272	−	0.573405i	$-0.194378\pi$
$647$	−2.21162	−	3.83064i	−0.0869479	−	0.150598i	−0.906220	+	0.422807i	$0.861045\pi$
$648$	−4.22732	+	23.2286i	−0.166065	+	0.912506i
$649$	−9.72913	+	16.8513i	−0.381902	+	0.661473i
$650$	0.0504751	−	0.0874254i	0.00197980	−	0.00342911i
$651$	−41.2361	+	13.5600i	−1.61617	+	0.531460i
$652$	0.327861	+	0.567872i	0.0128400	+	0.0222396i
$653$	−11.7092			−0.458217			−0.229108	−	0.973401i	$-0.573581\pi$
$653$	−11.7092			−0.458217			−0.229108	+	0.973401i	$0.573581\pi$
$654$	46.0407	+	8.18332i	1.80033	+	0.319993i
$655$	5.07589			0.198331
$656$	−10.4875	+	18.1648i	−0.409467	+	0.709218i
$657$	−14.5345	−	5.33532i	−0.567045	−	0.208150i
$658$	0.206479	−	6.88184i	0.00804939	−	0.268282i
$659$	2.75850	−	4.77786i	0.107456	−	0.186119i	−0.807283	−	0.590164i	$-0.799063\pi$
$659$	2.75850	−	4.77786i	0.107456	−	0.186119i	0.914739	+	0.404046i	$0.132396\pi$
$660$	−1.21606	−	0.216144i	−0.0473351	−	0.00841339i
$661$	15.0111	−	26.0000i	0.583865	−	1.01128i	−0.411150	−	0.911567i	$-0.634873\pi$
$661$	15.0111	−	26.0000i	0.583865	−	1.01128i	0.995016	−	0.0997170i	$-0.0317937\pi$
$662$	−21.9132	+	37.9548i	−0.851681	+	1.47515i
$663$	−0.798722	−	0.141966i	−0.0310198	−	0.00551349i
$664$	14.1851	−	24.5694i	0.550490	−	0.953476i
$665$	−0.105976	+	3.53213i	−0.00410958	+	0.136970i
$666$	9.52682	−	7.94954i	0.369157	−	0.308038i
$667$	−14.5353	+	25.1759i	−0.562810	+	0.974815i
$668$	2.08028			0.0804885
$669$	−2.52024	−	0.447951i	−0.0974382	−	0.0173188i
$670$	5.47769			0.211622
$671$	5.37583	+	9.31120i	0.207531	+	0.359455i
$672$	6.16532	−	2.02740i	0.237832	−	0.0782085i
$673$	11.1215	−	19.2630i	0.428703	−	0.742535i	−0.568055	−	0.822990i	$-0.692304\pi$
$673$	11.1215	−	19.2630i	0.428703	−	0.742535i	0.996758	+	0.0804552i	$0.0256374\pi$
$674$	−3.33315	+	5.77319i	−0.128388	+	0.222375i
$675$	4.48927	+	2.61657i	0.172792	+	0.100712i
$676$	1.63613	+	2.83385i	0.0629279	+	0.108994i
$677$	−16.5260	−	28.6238i	−0.635144	−	1.10010i	−0.986485	−	0.163854i	$-0.947607\pi$
$677$	−16.5260	−	28.6238i	−0.635144	−	1.10010i	0.351341	−	0.936248i	$-0.385726\pi$
$678$	−41.6109	−	7.39597i	−1.59806	−	0.284040i
$679$	−0.231153	+	7.70420i	−0.00887083	+	0.295660i
$680$	9.13215	+	15.8173i	0.350202	+	0.606567i
$681$	2.76502	+	7.62935i	0.105956	+	0.292357i
$682$	−40.2553			−1.54146
$683$	−13.8104	−	23.9203i	−0.528439	−	0.915283i	−0.999450	−	0.0331560i	$-0.989444\pi$
$683$	−13.8104	−	23.9203i	−0.528439	−	0.915283i	0.471011	−	0.882127i	$-0.343889\pi$
$684$	−0.947129	−	0.347671i	−0.0362144	−	0.0132935i
$685$	−2.36168			−0.0902351
$686$	25.2195	−	11.6767i	0.962884	−	0.445819i
$687$	−12.8913	−	35.5702i	−0.491834	−	1.35709i
$688$	35.2045			1.34216
$689$	0.455693	−	0.789284i	0.0173605	−	0.0300693i
$690$	5.39141	−	6.40737i	0.205247	−	0.243924i
$691$	−0.952884	−	1.65044i	−0.0362494	−	0.0627859i	0.847332	−	0.531064i	$-0.178208\pi$
$691$	−0.952884	−	1.65044i	−0.0362494	−	0.0627859i	−0.883581	+	0.468278i	$0.844874\pi$
$692$	−4.05465			−0.154135
$693$	−8.37530	+	20.8598i	−0.318151	+	0.792398i
$694$	10.9982			0.417485
$695$	−3.45961	−	5.99223i	−0.131231	−	0.227298i
$696$	40.3661	+	7.17472i	1.53007	+	0.271957i
$697$	16.4443	−	28.4824i	0.622873	−	1.07885i
$698$	32.9912			1.24873
$699$	−10.9558	−	1.94730i	−0.414386	−	0.0736535i
$700$	0.0199793	−	0.665899i	0.000755145	−	0.0251686i
$701$	10.3758			0.391887			0.195944	−	0.980615i	$-0.437223\pi$
$701$	10.3758			0.391887			0.195944	+	0.980615i	$0.437223\pi$
$702$	0.455351	−	0.260405i	0.0171861	−	0.00982837i
$703$	−1.84062	−	3.18805i	−0.0694203	−	0.120240i
$704$	−19.1306			−0.721013
$705$	−1.93385	+	2.29826i	−0.0728330	+	0.0865577i
$706$	−19.3484	−	33.5123i	−0.728185	−	1.26125i
$707$	−20.9876	+	11.2919i	−0.789320	+	0.424676i
$708$	1.92931	−	2.29286i	0.0725077	−	0.0861711i
$709$	−20.3564	−	35.2583i	−0.764501	−	1.32416i	−0.940510	−	0.339766i	$-0.889652\pi$
$709$	−20.3564	−	35.2583i	−0.764501	−	1.32416i	0.176009	−	0.984389i	$-0.443681\pi$
$710$	6.67156	+	11.5555i	0.250379	+	0.433670i
$711$	32.2929	+	11.8541i	1.21108	+	0.444562i
$712$	8.98658	−	15.5652i	0.336786	−	0.583331i
$713$	15.2593	−	26.4299i	0.571466	−	0.989808i
$714$	−45.4805	+	14.9557i	−1.70206	+	0.559705i
$715$	−0.0952591	−	0.164994i	−0.00356249	−	0.00617041i
$716$	−2.85701			−0.106772
$717$	−15.6576	+	18.6081i	−0.584742	+	0.694932i
$718$	−3.15949			−0.117911
$719$	2.94866	−	5.10723i	0.109967	−	0.190468i	−0.805790	−	0.592201i	$-0.798259\pi$
$719$	2.94866	−	5.10723i	0.109967	−	0.190468i	0.915756	+	0.401734i	$0.131592\pi$
$720$	−12.5047	−	4.59022i	−0.466023	−	0.171067i
$721$	1.41872	−	0.763310i	0.0528359	−	0.0284271i
$722$	12.9173	−	22.3733i	0.480730	−	0.832649i
$723$	−6.43793	−	17.7638i	−0.239429	−	0.660643i
$724$	2.47109	−	4.28005i	0.0918372	−	0.159067i
$725$	4.51153	−	7.81420i	0.167554	−	0.290212i
$726$	4.98633	−	5.92595i	0.185060	−	0.219933i
$727$	10.5553	−	18.2823i	0.391473	−	0.678052i	−0.601171	−	0.799121i	$-0.705299\pi$
$727$	10.5553	−	18.2823i	0.391473	−	0.678052i	0.992644	+	0.121069i	$0.0386322\pi$
$728$	0.397186	+	0.245485i	0.0147207	+	0.00909827i
$729$	13.3072	+	23.4930i	0.492858	+	0.870110i
$730$	3.87225	−	6.70694i	0.143318	−	0.248235i
$731$	−55.2004			−2.04166
$732$	−0.564168	−	1.55668i	−0.0208522	−	0.0575364i
$733$	3.80518			0.140548			0.0702738	−	0.997528i	$-0.477613\pi$
$733$	3.80518			0.140548			0.0702738	+	0.997528i	$0.477613\pi$
$734$	−4.19386	−	7.26398i	−0.154798	−	0.268118i
$735$	−11.7886	−	2.83360i	−0.434828	−	0.104519i
$736$	−2.28146	+	3.95160i	−0.0840957	+	0.145658i
$737$	5.16888	−	8.95277i	0.190398	−	0.329779i
$738$	3.63535	+	20.9529i	0.133819	+	0.771288i
$739$	−2.98981	−	5.17850i	−0.109982	−	0.190494i	0.805781	−	0.592214i	$-0.201746\pi$
$739$	−2.98981	−	5.17850i	−0.109982	−	0.190494i	−0.915763	+	0.401720i	$0.868413\pi$
$740$	0.347005	+	0.601031i	0.0127562	+	0.0220943i
$741$	−0.0530271	−	0.146315i	−0.00194800	−	0.00537500i
$742$	1.61306	−	53.7624i	0.0592173	−	1.97368i
$743$	21.7701	+	37.7069i	0.798667	+	1.38333i	0.920485	+	0.390779i	$0.127794\pi$
$743$	21.7701	+	37.7069i	0.798667	+	1.38333i	−0.121818	+	0.992552i	$0.538872\pi$
$744$	−42.3767	−	7.53209i	−1.55361	−	0.276140i
$745$	1.99529			0.0731018
$746$	−3.78896	−	6.56267i	−0.138724	−	0.240277i
$747$	−5.54612	−	31.9660i	−0.202922	−	1.16957i
$748$	−4.96473			−0.181528
$749$	0.553795	−	18.4577i	0.0202352	−	0.674429i
$750$	−1.67341	+	1.98874i	−0.0611042	+	0.0726187i
$751$	30.9928			1.13094			0.565471	−	0.824768i	$-0.308694\pi$
$751$	30.9928			1.13094			0.565471	+	0.824768i	$0.308694\pi$
$752$	3.84998	−	6.66835i	0.140394	−	0.243170i
$753$	−15.6824	−	43.2714i	−0.571497	−	1.57690i
$754$	−0.455440	−	0.788845i	−0.0165861	−	0.0287280i
$755$	5.07189			0.184585
$756$	1.83206	−	2.93712i	0.0666314	−	0.106822i
$757$	−20.4941			−0.744870			−0.372435	−	0.928058i	$-0.621477\pi$
$757$	−20.4941			−0.744870			−0.372435	+	0.928058i	$0.621477\pi$
$758$	0.258064	+	0.446979i	0.00937329	+	0.0162350i
$759$	−5.38477	−	14.8579i	−0.195455	−	0.539308i
$760$	−1.75190	+	3.03438i	−0.0635481	+	0.110068i
$761$	−41.4204			−1.50149			−0.750744	−	0.660594i	$-0.770305\pi$
$761$	−41.4204			−1.50149			−0.750744	+	0.660594i	$0.770305\pi$
$762$	−26.3360	+	31.2987i	−0.954052	+	1.13383i
$763$	40.4917	+	25.0263i	1.46590	+	0.906012i
$764$	4.80702			0.173912
$765$	19.6073	+	7.19744i	0.708904	+	0.260224i
$766$	1.34961	+	2.33760i	0.0487635	+	0.0844609i
$767$	0.462223			0.0166899
$768$	10.1491	+	1.80391i	0.366223	+	0.0650930i
$769$	4.59954	+	7.96663i	0.165864	+	0.287284i	0.936962	−	0.349432i	$-0.113626\pi$
$769$	4.59954	+	7.96663i	0.165864	+	0.287284i	−0.771098	+	0.636716i	$0.780292\pi$
$770$	−9.56432	−	5.91133i	−0.344674	−	0.213029i
$771$	9.47536	+	26.1448i	0.341247	+	0.941583i
$772$	−0.281735	−	0.487979i	−0.0101399	−	0.0175628i
$773$	20.0817	+	34.7825i	0.722288	+	1.25104i	0.960081	+	0.279723i	$0.0902426\pi$
$773$	20.0817	+	34.7825i	0.722288	+	1.25104i	−0.237793	+	0.971316i	$0.576424\pi$
$774$	27.4052	−	22.8679i	0.985058	−	0.821969i
$775$	−4.73625	+	8.20342i	−0.170131	+	0.294676i
$776$	−3.82120	+	6.61852i	−0.137173	+	0.237591i
$777$	11.9984	−	3.94555i	0.430442	−	0.141546i
$778$	20.8943	+	36.1900i	0.749097	+	1.29747i
$779$	6.30931			0.226054
$780$	0.00999699	+	0.0275841i	0.000357950	+	0.000987671i
$781$	25.1818			0.901076
$782$	16.8299	−	29.1503i	0.601837	−	1.04241i
$783$	40.6999	−	23.2754i	1.45449	−	0.831794i
$784$	31.0255	+	1.86342i	1.10805	+	0.0665507i
$785$	−5.05093	+	8.74847i	−0.180275	+	0.312246i
$786$	−8.49403	+	10.0946i	−0.302972	+	0.360064i
$787$	15.3201	−	26.5352i	0.546104	−	0.945879i	−0.452433	−	0.891798i	$-0.649444\pi$
$787$	15.3201	−	26.5352i	0.546104	−	0.945879i	0.998537	−	0.0540808i	$-0.0172228\pi$
$788$	−1.45413	+	2.51863i	−0.0518013	+	0.0897224i
$789$	0.303657	+	0.837865i	0.0108105	+	0.0298288i
$790$	−8.60341	+	14.9015i	−0.306096	+	0.530173i
$791$	−36.5958	−	22.6184i	−1.30120	−	0.804217i
$792$	−17.1128	+	14.2796i	−0.608078	+	0.507403i
$793$	0.127701	−	0.221184i	0.00453479	−	0.00785448i
$794$	45.9982			1.63241
$795$	−15.1077	+	17.9546i	−0.535814	+	0.636783i
$796$	−1.61442			−0.0572215
$797$	−20.3117	−	35.1808i	−0.719476	−	1.24617i	−0.961208	−	0.275826i	$-0.911049\pi$
$797$	−20.3117	−	35.1808i	−0.719476	−	1.24617i	0.241731	−	0.970343i	$-0.422285\pi$
$798$	−6.84716	−	6.12145i	−0.242387	−	0.216697i
$799$	−6.03674	+	10.4559i	−0.213565	+	0.369905i
$800$	0.708129	−	1.22651i	0.0250361	−	0.0433638i
$801$	−3.51359	−	20.2511i	−0.124146	−	0.715539i
$802$	−19.7541	−	34.2150i	−0.697540	−	1.20817i
$803$	−7.30791	−	12.6577i	−0.257890	−	0.446679i
$804$	−1.02500	+	1.21815i	−0.0361490	+	0.0429609i
$805$	7.50661	−	4.03876i	0.264573	−	0.142347i
$806$	0.478125	+	0.828137i	0.0168412	+	0.0291699i
$807$	20.9617	−	24.9117i	0.737887	−	0.876935i
$808$	−23.6307			−0.831325
$809$	−5.49671	−	9.52058i	−0.193254	−	0.334726i	0.753073	−	0.657937i	$-0.228571\pi$
$809$	−5.49671	−	9.52058i	−0.193254	−	0.334726i	−0.946327	+	0.323212i	$0.895237\pi$
$810$	−12.7161	+	4.54944i	−0.446797	+	0.159851i
$811$	−1.78517			−0.0626857			−0.0313428	−	0.999509i	$-0.509978\pi$
$811$	−1.78517			−0.0626857			−0.0313428	+	0.999509i	$0.509978\pi$
$812$	−5.11333	−	3.16034i	−0.179443	−	0.110906i
$813$	−29.4651	−	5.23716i	−1.03339	−	0.183675i
$814$	11.7131			0.410543
$815$	1.30207	−	2.25526i	0.0456096	−	0.0789982i
$816$	−52.7176	−	9.37008i	−1.84548	−	0.328018i
$817$	−5.29479	−	9.17084i	−0.185241	−	0.320847i
$818$	−7.55069			−0.264004
$819$	0.528606	−	0.0754607i	0.0184710	−	0.00263681i
$820$	−1.18947			−0.0415381
$821$	12.3152	+	21.3306i	0.429805	+	0.744443i	0.996856	−	0.0792393i	$-0.0252491\pi$
$821$	12.3152	+	21.3306i	0.429805	+	0.744443i	−0.567051	+	0.823683i	$0.691916\pi$
$822$	3.95205	−	4.69678i	0.137844	−	0.163819i
$823$	−20.4551	+	35.4293i	−0.713020	+	1.23499i	0.250699	+	0.968065i	$0.419340\pi$
$823$	−20.4551	+	35.4293i	−0.713020	+	1.23499i	−0.963718	+	0.266921i	$0.913994\pi$
$824$	1.59739			0.0556476
$825$	1.67135	+	4.61166i	0.0581889	+	0.160557i
$826$	24.0225	−	12.9247i	0.835848	−	0.449709i
$827$	−45.5340			−1.58337			−0.791686	−	0.610928i	$-0.790797\pi$
$827$	−45.5340			−1.58337			−0.791686	+	0.610928i	$0.790797\pi$
$828$	0.416042	+	2.39793i	0.0144585	+	0.0833338i
$829$	−17.3889	−	30.1185i	−0.603942	−	1.04606i	−0.992218	−	0.124514i	$-0.960263\pi$
$829$	−17.3889	−	30.1185i	−0.603942	−	1.04606i	0.388276	−	0.921543i	$-0.373071\pi$
$830$	16.2283			0.563291
$831$	−8.98731	−	24.7982i	−0.311766	−	0.860239i
$832$	0.227221	+	0.393558i	0.00787746	+	0.0136442i
$833$	−48.6478	−	2.92183i	−1.68554	−	0.101236i
$834$	17.7063	+	3.14715i	0.613121	+	0.108977i
$835$	−4.13083	−	7.15481i	−0.142953	−	0.247603i
$836$	−0.476213	−	0.824826i	−0.0164702	−	0.0285272i
$837$	−42.7271	+	24.4347i	−1.47687	+	0.844588i
$838$	−15.4871	+	26.8245i	−0.534993	+	0.926635i
$839$	−10.8976	+	18.8751i	−0.376226	+	0.651642i	−0.990510	−	0.137443i	$-0.956112\pi$
$839$	−10.8976	+	18.8751i	−0.376226	+	0.651642i	0.614284	+	0.789085i	$0.289445\pi$
$840$	−8.96229	−	8.01240i	−0.309228	−	0.276454i
$841$	−26.2078	−	45.3933i	−0.903718	−	1.56529i
$842$	36.8371			1.26949
$843$	−26.8571	−	4.77362i	−0.925009	−	0.164412i
$844$	−0.351722			−0.0121068
$845$	6.49774	−	11.2544i	0.223529	−	0.387164i
$846$	−1.33454	−	7.69187i	−0.0458826	−	0.264452i
$847$	6.94260	−	3.73530i	0.238550	−	0.128347i
$848$	30.0769	−	52.0947i	1.03284	−	1.78894i
$849$	−21.0974	−	3.74988i	−0.724061	−	0.128695i
$850$	−5.22374	+	9.04778i	−0.179173	+	0.310336i
$851$	−4.43999	+	7.69029i	−0.152201	+	0.263620i
$852$	−3.81816	−	0.678644i	−0.130808	−	0.0232500i
$853$	−18.3064	+	31.7076i	−0.626800	+	1.08565i	0.361390	+	0.932415i	$0.382302\pi$
$853$	−18.3064	+	31.7076i	−0.626800	+	1.08565i	−0.988190	+	0.153234i	$0.951031\pi$
$854$	0.452034	−	15.0661i	0.0154683	−	0.515550i
$855$	0.684960	+	3.94788i	0.0234251	+	0.135015i
$856$	9.15482	−	15.8566i	0.312905	−	0.541968i
$857$	−18.5932			−0.635132			−0.317566	−	0.948236i	$-0.602866\pi$
$857$	−18.5932			−0.635132			−0.317566	+	0.948236i	$0.602866\pi$
$858$	0.487537	+	0.0866555i	0.0166443	+	0.00295837i
$859$	40.3710			1.37744			0.688720	−	0.725027i	$-0.258173\pi$
$859$	40.3710			1.37744			0.688720	+	0.725027i	$0.258173\pi$
$860$	0.998206	+	1.72894i	0.0340385	+	0.0589565i
$861$	−4.42577	+	21.1903i	−0.150830	+	0.722163i
$862$	−26.4368	+	45.7898i	−0.900440	+	1.55961i
$863$	−1.96773	+	3.40822i	−0.0669825	+	0.116017i	−0.897572	−	0.440869i	$-0.854670\pi$
$863$	−1.96773	+	3.40822i	−0.0669825	+	0.116017i	0.830589	+	0.556886i	$0.188004\pi$
$864$	6.38824	−	3.65330i	0.217332	−	0.124288i
$865$	8.05135	+	13.9453i	0.273754	+	0.474156i
$866$	30.9490	+	53.6052i	1.05169	+	1.82158i
$867$	53.6704	+	9.53944i	1.82274	+	0.323976i
$868$	5.36802	+	3.31776i	0.182203	+	0.112612i
$869$	16.2368	+	28.1229i	0.550795	+	0.954005i
$870$	7.99082	+	22.0486i	0.270914	+	0.747518i
$871$	−0.245570			−0.00832081
$872$	23.5992	+	40.8749i	0.799168	+	1.38420i
$873$	1.49402	+	8.61103i	0.0505649	+	0.291439i
$874$	6.45726			0.218420
$875$	−2.32993	+	1.25356i	−0.0787660	+	0.0423782i
$876$	0.766930	+	2.11615i	0.0259122	+	0.0714980i
$877$	−40.0570			−1.35263			−0.676314	−	0.736613i	$-0.736424\pi$
$877$	−40.0570			−1.35263			−0.676314	+	0.736613i	$0.736424\pi$
$878$	−24.3097	+	42.1056i	−0.820412	+	1.42100i
$879$	−19.6383	+	23.3389i	−0.662383	+	0.787203i
$880$	−6.28733	−	10.8900i	−0.211946	−	0.367101i
$881$	−11.5557			−0.389322			−0.194661	−	0.980871i	$-0.562361\pi$
$881$	−11.5557			−0.389322			−0.194661	+	0.980871i	$0.562361\pi$
$882$	25.3624	−	18.7027i	0.853997	−	0.629753i
$883$	2.50842			0.0844149			0.0422075	−	0.999109i	$-0.486561\pi$
$883$	2.50842			0.0844149			0.0422075	+	0.999109i	$0.486561\pi$
$884$	0.0589676	+	0.102135i	0.00198330	+	0.00343517i
$885$	−11.7170	−	2.08259i	−0.393863	−	0.0700056i
$886$	11.4324	−	19.8015i	0.384079	−	0.665244i
$887$	15.5963			0.523671			0.261836	−	0.965112i	$-0.415672\pi$
$887$	15.5963			0.523671			0.261836	+	0.965112i	$0.415672\pi$
$888$	12.3303	+	2.19160i	0.413778	+	0.0735454i
$889$	−36.6683	+	19.7285i	−1.22981	+	0.661673i
$890$	10.2809			0.344618
$891$	−4.56356	+	25.0762i	−0.152885	+	0.840084i
$892$	0.186063	+	0.322270i	0.00622985	+	0.0107904i
$893$	−2.31616			−0.0775074
$894$	−3.33893	+	3.96812i	−0.111671	+	0.132714i
$895$	5.67319	+	9.82626i	0.189634	+	0.328456i
$896$	29.1885	+	18.0402i	0.975119	+	0.602682i
$897$	−0.241702	+	0.287248i	−0.00807019	+	0.00959094i
$898$	−5.48463	−	9.49966i	−0.183024	−	0.317008i
$899$	42.7355	+	74.0200i	1.42531	+	2.46871i
$900$	−0.129133	−	0.744278i	−0.00430443	−	0.0248093i
$901$	−47.1604	+	81.6842i	−1.57114	+	2.72129i
$902$	−10.0376	+	17.3856i	−0.334214	+	0.578876i
$903$	34.5151	−	11.3499i	1.14859	−	0.377701i
$904$	−21.3286	−	36.9422i	−0.709378	−	1.22868i
$905$	−19.6274			−0.652438
$906$	−8.48734	+	10.0867i	−0.281973	+	0.335108i
$907$	56.1691			1.86506			0.932532	−	0.361087i	$-0.117594\pi$
$907$	56.1691			1.86506			0.932532	+	0.361087i	$0.117594\pi$
$908$	0.589861	−	1.02167i	0.0195752	−	0.0339053i
$909$	−20.7488	+	17.3135i	−0.688193	+	0.574254i
$910$	−0.00801000	+	0.266969i	−0.000265529	+	0.00884994i
$911$	−5.79696	+	10.0406i	−0.192062	+	0.332661i	−0.945933	−	0.324361i	$-0.894851\pi$
$911$	−5.79696	+	10.0406i	−0.192062	+	0.332661i	0.753871	+	0.657022i	$0.228184\pi$
$912$	−3.49992	−	9.65712i	−0.115894	−	0.319779i
$913$	15.3134	−	26.5236i	0.506799	−	0.877802i
$914$	22.8015	−	39.4933i	0.754205	−	1.30632i
$915$	−4.23368	+	5.03147i	−0.139961	+	0.166335i
$916$	−2.75010	+	4.76331i	−0.0908658	+	0.157384i
$917$	−11.8265	+	6.36296i	−0.390544	+	0.210123i
$918$	−47.1249	+	26.9497i	−1.55535	+	0.889474i
$919$	−9.89463	+	17.1380i	−0.326394	+	0.565330i	−0.981793	−	0.189952i	$-0.939167\pi$
$919$	−9.89463	+	17.1380i	−0.326394	+	0.565330i	0.655400	+	0.755282i	$0.272500\pi$
$920$	8.45195			0.278653
$921$	−3.62381	−	9.99897i	−0.119409	−	0.329477i
$922$	30.0528			0.989735
$923$	−0.299092	−	0.518043i	−0.00984474	−	0.0170516i
$924$	3.10429	−	1.02081i	0.102124	−	0.0335822i
$925$	1.37810	−	2.38694i	0.0453117	−	0.0784822i
$926$	−28.3528	+	49.1084i	−0.931730	+	1.61380i
$927$	1.40257	−	1.17036i	0.0460666	−	0.0384397i
$928$	−6.38949	−	11.0669i	−0.209745	−	0.363289i
$929$	−1.93589	−	3.35305i	−0.0635143	−	0.110010i	0.832520	−	0.553995i	$-0.186898\pi$
$929$	−1.93589	−	3.35305i	−0.0635143	−	0.110010i	−0.896034	+	0.443985i	$0.853564\pi$
$930$	−8.38884	−	23.1469i	−0.275081	−	0.759016i
$931$	−4.18084	−	8.36246i	−0.137021	−	0.274069i
$932$	0.808838	+	1.40095i	0.0264944	+	0.0458896i
$933$	42.2939	+	7.51736i	1.38464	+	0.246107i
$934$	38.9870			1.27569
$935$	9.85850	+	17.0754i	0.322407	+	0.558426i
$936$	0.497016	+	0.182444i	0.0162455	+	0.00596337i
$937$	39.5281			1.29133			0.645663	−	0.763623i	$-0.276581\pi$
$937$	39.5281			1.29133			0.645663	+	0.763623i	$0.276581\pi$
$938$	−12.7626	+	6.86664i	−0.416715	+	0.224204i
$939$	−28.7445	+	34.1611i	−0.938040	+	1.11480i
$940$	0.436657			0.0142422
$941$	0.999305	−	1.73085i	0.0325764	−	0.0564240i	−0.849278	−	0.527947i	$-0.822962\pi$
$941$	0.999305	−	1.73085i	0.0325764	−	0.0564240i	0.881854	+	0.471523i	$0.156295\pi$
$942$	−8.94621	−	24.6848i	−0.291483	−	0.804273i
$943$	−7.60974	−	13.1805i	−0.247807	−	0.429215i
$944$	30.5079			0.992946
$945$	−13.7397	−	0.468817i	−0.446953	−	0.0152506i
$946$	33.6942			1.09549
$947$	1.93807	+	3.35684i	0.0629790	+	0.109083i	0.895796	−	0.444466i	$-0.146607\pi$
$947$	1.93807	+	3.35684i	0.0629790	+	0.109083i	−0.832817	+	0.553549i	$0.813273\pi$
$948$	−1.70397	−	4.70168i	−0.0553425	−	0.152703i
$949$	−0.173597	+	0.300678i	−0.00563518	+	0.00976042i
$950$	−2.00423			−0.0650258
$951$	10.4605	−	12.4316i	0.339204	−	0.403123i
$952$	−41.1053	−	25.4056i	−1.33223	−	0.823399i
$953$	−10.7772			−0.349108			−0.174554	−	0.984648i	$-0.555848\pi$
$953$	−10.7772			−0.349108			−0.174554	+	0.984648i	$0.555848\pi$
$954$	−10.4258	−	60.0906i	−0.337546	−	1.94550i
$955$	−9.54534	−	16.5330i	−0.308880	−	0.534996i
$956$	3.53543			0.114344
$957$	43.5767	+	7.74538i	1.40864	+	0.250373i
$958$	20.7892	+	36.0079i	0.671667	+	1.16336i
$959$	5.50255	−	2.96052i	0.177687	−	0.0956001i
$960$	−3.98665	−	11.0001i	−0.128669	−	0.355028i
$961$	−29.3641	−	50.8601i	−0.947230	−	1.64065i
$962$	−0.139120	−	0.240962i	−0.00448540	−	0.00776894i
$963$	−3.57937	−	20.6303i	−0.115343	−	0.664801i
$964$	−1.37340	+	2.37880i	−0.0442343	+	0.0766161i
$965$	−1.11889	+	1.93797i	−0.0360183	+	0.0623855i
$966$	−4.52956	+	21.6872i	−0.145736	+	0.697774i
$967$	17.7351	+	30.7180i	0.570321	+	0.987826i	0.996533	+	0.0832021i	$0.0265147\pi$
$967$	17.7351	+	30.7180i	0.570321	+	0.987826i	−0.426211	+	0.904624i	$0.640152\pi$
$968$	7.81691			0.251245
$969$	5.48785	+	15.1423i	0.176295	+	0.486441i
$970$	−4.37158			−0.140363
$971$	−9.70446	+	16.8086i	−0.311431	+	0.539414i	−0.978672	−	0.205427i	$-0.934142\pi$
$971$	−9.70446	+	16.8086i	−0.311431	+	0.539414i	0.667241	+	0.744842i	$0.267475\pi$
$972$	1.36774	−	3.67916i	0.0438703	−	0.118009i
$973$	15.5723	+	9.62462i	0.499225	+	0.308551i
$974$	−10.4950	+	18.1778i	−0.336281	+	0.582455i
$975$	0.0750204	−	0.0891572i	0.00240257	−	0.00285532i
$976$	8.42856	−	14.5987i	0.269791	−	0.467293i
$977$	6.49944	−	11.2574i	0.207936	−	0.360155i	−0.743129	−	0.669149i	$-0.766659\pi$
$977$	6.49944	−	11.2574i	0.207936	−	0.360155i	0.951064	+	0.308994i	$0.0999922\pi$
$978$	2.30623	+	6.36346i	0.0737452	+	0.203481i
$979$	9.70136	−	16.8032i	0.310057	−	0.537034i
$980$	0.788197	+	1.57654i	0.0251780	+	0.0503608i
$981$	50.6690	+	18.5995i	1.61774	+	0.593837i
$982$	−6.07216	+	10.5173i	−0.193770	+	0.335620i
$983$	53.6797			1.71212			0.856058	−	0.516880i	$-0.172907\pi$
$983$	53.6797			1.71212			0.856058	+	0.516880i	$0.172907\pi$
$984$	−13.8195	+	16.4236i	−0.440549	+	0.523566i
$985$	11.5499			0.368011
$986$	47.1341	+	81.6387i	1.50106	+	2.59991i
$987$	1.62471	−	7.77900i	0.0517151	−	0.247608i
$988$	−0.0113123	+	0.0195934i	−0.000359891	+	0.000623350i
$989$	−12.7722	+	22.1221i	−0.406133	+	0.703443i
$990$	−11.9683	−	4.39329i	−0.380376	−	0.139628i
$991$	8.54095	+	14.7934i	0.271312	+	0.469927i	0.969198	−	0.246282i	$-0.0792091\pi$
$991$	8.54095	+	14.7934i	0.271312	+	0.469927i	−0.697886	+	0.716209i	$0.745876\pi$
$992$	6.70775	+	11.6182i	0.212971	+	0.368877i
$993$	−32.5693	+	38.7066i	−1.03355	+	1.22832i
$994$	−30.0298	−	18.5602i	−0.952488	−	0.588695i
$995$	3.20576	+	5.55254i	0.101629	+	0.176027i
$996$	−3.03667	+	3.60891i	−0.0962207	+	0.114353i
$997$	10.2586			0.324893			0.162447	−	0.986717i	$-0.448061\pi$
$997$	10.2586			0.324893			0.162447	+	0.986717i	$0.448061\pi$
$998$	1.46133	+	2.53109i	0.0462575	+	0.0801203i
$999$	12.4323	−	7.10975i	0.393340	−	0.224943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.c.16.6	✓	36
3.2	odd	2		945.2.k.c.856.13		36
7.4	even	3		315.2.l.c.151.13	yes	36
9.4	even	3		315.2.l.c.121.13	yes	36
9.5	odd	6		945.2.l.c.226.6		36
21.11	odd	6		945.2.l.c.46.6		36
63.4	even	3	inner	315.2.k.c.256.6	yes	36
63.32	odd	6		945.2.k.c.361.13		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.6	✓	36	1.1	even	1	trivial
315.2.k.c.256.6	yes	36	63.4	even	3	inner
315.2.l.c.121.13	yes	36	9.4	even	3
315.2.l.c.151.13	yes	36	7.4	even	3
945.2.k.c.361.13		36	63.32	odd	6
945.2.k.c.856.13		36	3.2	odd	2
945.2.l.c.46.6		36	21.11	odd	6
945.2.l.c.226.6		36	9.5	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)

\(f(q)\)	\(=\)	\(q+(-0.750300 - 1.29956i) q^{2} +(-0.590164 - 1.62841i) q^{3} +(-0.125900 + 0.218065i) q^{4} +1.00000 q^{5} +(-1.67341 + 1.98874i) q^{6} +(-2.32993 + 1.25356i) q^{7} -2.62335 q^{8} +(-2.30341 + 1.92205i) q^{9} +O(q^{10})\)	\(q+(-0.750300 - 1.29956i) q^{2} +(-0.590164 - 1.62841i) q^{3} +(-0.125900 + 0.218065i) q^{4} +1.00000 q^{5} +(-1.67341 + 1.98874i) q^{6} +(-2.32993 + 1.25356i) q^{7} -2.62335 q^{8} +(-2.30341 + 1.92205i) q^{9} +(-0.750300 - 1.29956i) q^{10} -2.83201 q^{11} +(0.429399 + 0.0763219i) q^{12} +(0.0336366 + 0.0582603i) q^{13} +(3.37723 + 2.08733i) q^{14} +(-0.590164 - 1.62841i) q^{15} +(2.22010 + 3.84532i) q^{16} +(-3.48110 - 6.02944i) q^{17} +(4.22607 + 1.55130i) q^{18} +(0.667810 - 1.15668i) q^{19} +(-0.125900 + 0.218065i) q^{20} +(3.41635 + 3.05426i) q^{21} +(2.12485 + 3.68035i) q^{22} -3.22182 q^{23} +(1.54821 + 4.27188i) q^{24} +1.00000 q^{25} +(0.0504751 - 0.0874254i) q^{26} +(4.48927 + 2.61657i) q^{27} +(0.0199793 - 0.665899i) q^{28} +(4.51153 - 7.81420i) q^{29} +(-1.67341 + 1.98874i) q^{30} +(-4.73625 + 8.20342i) q^{31} +(0.708129 - 1.22651i) q^{32} +(1.67135 + 4.61166i) q^{33} +(-5.22374 + 9.04778i) q^{34} +(-2.32993 + 1.25356i) q^{35} +(-0.129133 - 0.744278i) q^{36} +(1.37810 - 2.38694i) q^{37} -2.00423 q^{38} +(0.0750204 - 0.0891572i) q^{39} -2.62335 q^{40} +(2.36194 + 4.09100i) q^{41} +(1.40590 - 6.73136i) q^{42} +(3.96429 - 6.86635i) q^{43} +(0.356548 - 0.617560i) q^{44} +(-2.30341 + 1.92205i) q^{45} +(2.41733 + 4.18693i) q^{46} +(-0.867073 - 1.50182i) q^{47} +(4.95152 - 5.88459i) q^{48} +(3.85715 - 5.84144i) q^{49} +(-0.750300 - 1.29956i) q^{50} +(-7.76396 + 9.22701i) q^{51} -0.0169394 q^{52} +(-6.77377 - 11.7325i) q^{53} +(0.0320746 - 7.79728i) q^{54} -2.83201 q^{55} +(6.11222 - 3.28854i) q^{56} +(-2.27766 - 0.404834i) q^{57} -13.5400 q^{58} +(3.43542 - 5.95032i) q^{59} +(0.429399 + 0.0763219i) q^{60} +(-1.89824 - 3.28785i) q^{61} +14.2144 q^{62} +(2.95737 - 7.36573i) q^{63} +6.75516 q^{64} +(0.0336366 + 0.0582603i) q^{65} +(4.73910 - 5.63214i) q^{66} +(-1.82517 + 3.16128i) q^{67} +1.75308 q^{68} +(1.90140 + 5.24642i) q^{69} +(3.37723 + 2.08733i) q^{70} -8.89186 q^{71} +(6.04266 - 5.04222i) q^{72} +(2.58047 + 4.46951i) q^{73} -4.13596 q^{74} +(-0.590164 - 1.62841i) q^{75} +(0.168154 + 0.291251i) q^{76} +(6.59838 - 3.55010i) q^{77} +(-0.172153 - 0.0305986i) q^{78} +(-5.73331 - 9.93039i) q^{79} +(2.22010 + 3.84532i) q^{80} +(1.61142 - 8.85456i) q^{81} +(3.54433 - 6.13895i) q^{82} +(-5.40726 + 9.36564i) q^{83} +(-1.09614 + 0.360455i) q^{84} +(-3.48110 - 6.02944i) q^{85} -11.8976 q^{86} +(-15.3872 - 2.73494i) q^{87} +7.42934 q^{88} +(-3.42561 + 5.93334i) q^{89} +(4.22607 + 1.55130i) q^{90} +(-0.151404 - 0.0935768i) q^{91} +(0.405625 - 0.702564i) q^{92} +(16.1537 + 2.87117i) q^{93} +(-1.30113 + 2.25362i) q^{94} +(0.667810 - 1.15668i) q^{95} +(-2.41518 - 0.429276i) q^{96} +(1.45661 - 2.52293i) q^{97} +(-10.4853 - 0.629758i) q^{98} +(6.52328 - 5.44327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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