LMFDB - Embedded newform 315.2.l.c.121.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([2, 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("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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			121.13
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.50060 q^{2} +(-1.11516 - 1.32530i) q^{3} +0.251799 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.67341 - 1.98874i) q^{6} +(0.0793460 - 2.64456i) q^{7} -2.62335 q^{8} +(-0.512840 + 2.95584i) q^{9} +O(q^{10})$	\(q+1.50060 q^{2} +(-1.11516 - 1.32530i) q^{3} +0.251799 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.67341 - 1.98874i) q^{6} +(0.0793460 - 2.64456i) q^{7} -2.62335 q^{8} +(-0.512840 + 2.95584i) q^{9} +(-0.750300 - 1.29956i) q^{10} +(1.41600 - 2.45259i) q^{11} +(-0.280796 - 0.333710i) q^{12} +(0.0336366 - 0.0582603i) q^{13} +(0.119067 - 3.96843i) q^{14} +(-0.590164 + 1.62841i) q^{15} -4.44020 q^{16} +(-3.48110 - 6.02944i) q^{17} +(-0.769568 + 4.43553i) q^{18} +(0.667810 - 1.15668i) q^{19} +(-0.125900 - 0.218065i) q^{20} +(-3.59332 + 2.84395i) q^{21} +(2.12485 - 3.68035i) q^{22} +(1.61091 + 2.79017i) q^{23} +(2.92545 + 3.47673i) q^{24} +(-0.500000 + 0.866025i) 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} +(-0.885600 + 2.44359i) q^{30} +9.47250 q^{31} -1.41626 q^{32} +(-4.82948 + 0.858398i) 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} +(1.00212 - 1.73571i) q^{38} +(-0.114723 + 0.0203909i) q^{39} +(1.31167 + 2.27189i) q^{40} +(2.36194 - 4.09100i) q^{41} +(-5.39214 + 4.26763i) q^{42} +(3.96429 + 6.86635i) q^{43} +(0.356548 - 0.617560i) q^{44} +(2.81625 - 1.03379i) q^{45} +(2.41733 + 4.18693i) q^{46} +1.73415 q^{47} +(4.95152 + 5.88459i) q^{48} +(-6.98741 - 0.419671i) q^{49} +(-0.750300 + 1.29956i) q^{50} +(-4.10884 + 11.3373i) q^{51} +(0.00846968 - 0.0146699i) q^{52} +(-6.77377 - 11.7325i) q^{53} +(6.73660 - 3.92642i) q^{54} -2.83201 q^{55} +(-0.208152 + 6.93761i) q^{56} +(-2.27766 + 0.404834i) q^{57} +(6.77000 + 11.7260i) q^{58} -6.87084 q^{59} +(-0.148603 + 0.410031i) q^{60} +3.79648 q^{61} +14.2144 q^{62} +(7.77621 + 1.59077i) q^{63} +6.75516 q^{64} -0.0672732 q^{65} +(-7.24712 + 1.28811i) q^{66} +3.65033 q^{67} +(-0.876539 - 1.51821i) q^{68} +(1.90140 - 5.24642i) q^{69} +(-3.49629 + 1.88110i) q^{70} -8.89186 q^{71} +(1.34536 - 7.75420i) q^{72} +(2.58047 + 4.46951i) q^{73} +(2.06798 - 3.58185i) q^{74} +(1.70532 - 0.303106i) q^{75} +(0.168154 - 0.291251i) q^{76} +(-6.37367 - 3.93931i) q^{77} +(-0.172153 + 0.0305986i) q^{78} +11.4666 q^{79} +(2.22010 + 3.84532i) q^{80} +(-8.47399 - 3.03175i) q^{81} +(3.54433 - 6.13895i) q^{82} +(-5.40726 - 9.36564i) q^{83} +(-0.904795 + 0.716104i) q^{84} +(-3.48110 + 6.02944i) q^{85} +(5.94881 + 10.3036i) q^{86} +(5.32509 - 14.6932i) q^{87} +(-3.71467 + 6.43400i) 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} +(-10.5633 - 12.5539i) q^{93} +2.60226 q^{94} -1.33562 q^{95} +(1.57935 + 1.87697i) 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} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.50060			1.06108			0.530542	−	0.847659i	$-0.321988\pi$
$2$	1.50060			1.06108			0.530542	+	0.847659i	$0.321988\pi$
$3$	−1.11516	−	1.32530i	−0.643837	−	0.765162i
$3$	−1.11516	−	1.32530i	−0.643837	−	0.765162i
$4$	0.251799			0.125900
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.67341	−	1.98874i	−0.683166	−	0.811902i
$7$	0.0793460	−	2.64456i	0.0299900	−	0.999550i
$7$	0.0793460	−	2.64456i	0.0299900	−	0.999550i
$8$	−2.62335			−0.927494
$9$	−0.512840	+	2.95584i	−0.170947	+	0.985280i
$10$	−0.750300	−	1.29956i	−0.237266	−	0.410956i
$11$	1.41600	−	2.45259i	0.426941	−	0.739483i	−0.569659	−	0.821881i	$-0.692925\pi$
$11$	1.41600	−	2.45259i	0.426941	−	0.739483i	0.996599	+	0.0823981i	$0.0262579\pi$
$12$	−0.280796	−	0.333710i	−0.0810589	−	0.0963337i
$13$	0.0336366	−	0.0582603i	0.00932912	−	0.0161585i	−0.861323	−	0.508057i	$-0.830364\pi$
$13$	0.0336366	−	0.0582603i	0.00932912	−	0.0161585i	0.870652	+	0.491899i	$0.163697\pi$
$14$	0.119067	−	3.96843i	0.0318219	−	1.06061i
$15$	−0.590164	+	1.62841i	−0.152380	+	0.420453i
$16$	−4.44020			−1.11005
$17$	−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	$-0.486645\pi$
$18$	−0.769568	+	4.43553i	−0.181389	+	1.04547i
$19$	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
$21$	−3.59332	+	2.84395i	−0.784127	+	0.620601i
$22$	2.12485	−	3.68035i	0.453020	−	0.784654i
$23$	1.61091	+	2.79017i	0.335898	+	0.581792i	0.983657	−	0.180053i	$-0.0576271\pi$
$23$	1.61091	+	2.79017i	0.335898	+	0.581792i	−0.647759	+	0.761845i	$0.724294\pi$
$24$	2.92545	+	3.47673i	0.597155	+	0.709684i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	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	0.891755	+	0.452519i	$0.149475\pi$
$29$	4.51153	+	7.81420i	0.837770	+	1.45106i	−0.0539845	+	0.998542i	$0.517192\pi$
$30$	−0.885600	+	2.44359i	−0.161688	+	0.446136i
$31$	9.47250			1.70131			0.850656	−	0.525723i	$-0.176205\pi$
$31$	9.47250			1.70131			0.850656	+	0.525723i	$0.176205\pi$
$32$	−1.41626			−0.250361
$33$	−4.82948	+	0.858398i	−0.840705	+	0.149428i
$34$	−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	$0.0939192\pi$
$38$	1.00212	−	1.73571i	0.162565	−	0.281570i
$39$	−0.114723	+	0.0203909i	−0.0183703	+	0.00326516i
$40$	1.31167	+	2.27189i	0.207394	+	0.359217i
$41$	2.36194	−	4.09100i	0.368873	−	0.638907i	−0.620516	−	0.784193i	$-0.713077\pi$
$41$	2.36194	−	4.09100i	0.368873	−	0.638907i	0.989390	+	0.145286i	$0.0464103\pi$
$42$	−5.39214	+	4.26763i	−0.832025	+	0.658509i
$43$	3.96429	+	6.86635i	0.604549	+	1.04711i	0.992123	+	0.125271i	$0.0399799\pi$
$43$	3.96429	+	6.86635i	0.604549	+	1.04711i	−0.387574	+	0.921839i	$0.626687\pi$
$44$	0.356548	−	0.617560i	0.0537517	−	0.0931007i
$45$	2.81625	−	1.03379i	0.419822	−	0.154108i
$46$	2.41733	+	4.18693i	0.356416	+	0.617330i
$47$	1.73415			0.252951			0.126476	−	0.991970i	$-0.459633\pi$
$47$	1.73415			0.252951			0.126476	+	0.991970i	$0.459633\pi$
$48$	4.95152	+	5.88459i	0.714691	+	0.849368i
$49$	−6.98741	−	0.419671i	−0.998201	−	0.0599530i
$50$	−0.750300	+	1.29956i	−0.106108	+	0.183785i
$51$	−4.10884	+	11.3373i	−0.575353	+	1.58754i
$52$	0.00846968	−	0.0146699i	0.00117453	−	0.00203435i
$53$	−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	$-0.547249\pi$
$54$	6.73660	−	3.92642i	0.916736	−	0.534318i
$55$	−2.83201			−0.381868
$56$	−0.208152	+	6.93761i	−0.0278155	+	0.927077i
$57$	−2.27766	+	0.404834i	−0.301684	+	0.0536216i
$58$	6.77000	+	11.7260i	0.888945	+	1.53970i
$59$	−6.87084			−0.894507			−0.447253	−	0.894407i	$-0.647598\pi$
$59$	−6.87084			−0.894507			−0.447253	+	0.894407i	$0.647598\pi$
$60$	−0.148603	+	0.410031i	−0.0191845	+	0.0529348i
$61$	3.79648			0.486089			0.243045	−	0.970015i	$-0.421854\pi$
$61$	3.79648			0.486089			0.243045	+	0.970015i	$0.421854\pi$
$62$	14.2144			1.80523
$63$	7.77621	+	1.59077i	0.979710	+	0.200418i
$64$	6.75516			0.844395
$65$	−0.0672732			−0.00834422
$66$	−7.24712	+	1.28811i	−0.892059	+	0.158556i
$67$	3.65033			0.445959			0.222980	−	0.974823i	$-0.428422\pi$
$67$	3.65033			0.445959			0.222980	+	0.974823i	$0.428422\pi$
$68$	−0.876539	−	1.51821i	−0.106296	−	0.184110i
$69$	1.90140	−	5.24642i	0.228902	−	0.631595i
$70$	−3.49629	+	1.88110i	−0.417887	+	0.224834i
$71$	−8.89186			−1.05527			−0.527635	−	0.849471i	$-0.676921\pi$
$71$	−8.89186			−1.05527			−0.527635	+	0.849471i	$0.676921\pi$
$72$	1.34536	−	7.75420i	0.158552	−	0.913842i
$73$	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	$0.735672\pi$
$74$	2.06798	−	3.58185i	0.240398	−	0.416381i
$75$	1.70532	−	0.303106i	0.196914	−	0.0349997i
$76$	0.168154	−	0.291251i	0.0192886	−	0.0334088i
$77$	−6.37367	−	3.93931i	−0.726347	−	0.448926i
$78$	−0.172153	+	0.0305986i	−0.0194925	+	0.00346461i
$79$	11.4666			1.29010			0.645048	−	0.764142i	$-0.276837\pi$
$79$	11.4666			1.29010			0.645048	+	0.764142i	$0.276837\pi$
$80$	2.22010	+	3.84532i	0.248214	+	0.429920i
$81$	−8.47399	−	3.03175i	−0.941554	−	0.336861i
$82$	3.54433	−	6.13895i	0.391405	−	0.677934i
$83$	−5.40726	−	9.36564i	−0.593524	−	1.02801i	−0.993753	−	0.111598i	$-0.964403\pi$
$83$	−5.40726	−	9.36564i	−0.593524	−	1.02801i	0.400230	−	0.916415i	$-0.368930\pi$
$84$	−0.904795	+	0.716104i	−0.0987213	+	0.0781334i
$85$	−3.48110	+	6.02944i	−0.377578	+	0.653985i
$86$	5.94881	+	10.3036i	0.641477	+	1.11107i
$87$	5.32509	−	14.6932i	0.570909	−	1.57528i
$88$	−3.71467	+	6.43400i	−0.395985	+	0.685866i
$89$	−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
$93$	−10.5633	−	12.5539i	−1.09537	−	1.30178i
$94$	2.60226			0.268403
$95$	−1.33562			−0.137032
$96$	1.57935	+	1.87697i	0.161192	+	0.191567i
$97$	1.45661	+	2.52293i	0.147897	+	0.256164i	0.930450	−	0.366419i	$-0.119416\pi$
$97$	1.45661	+	2.52293i	0.147897	+	0.256164i	−0.782553	+	0.622584i	$0.786083\pi$
$98$	−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
$101$	−4.50391	+	7.80101i	−0.448156	+	0.776229i	−0.998266	−	0.0588629i	$-0.981253\pi$
$101$	−4.50391	+	7.80101i	−0.448156	+	0.776229i	0.550110	+	0.835092i	$0.314586\pi$
$102$	−6.16573	+	17.0127i	−0.610498	+	1.68451i
$103$	0.304456	+	0.527333i	0.0299989	+	0.0519596i	0.880635	−	0.473795i	$-0.157116\pi$
$103$	0.304456	+	0.527333i	0.0299989	+	0.0519596i	−0.850636	+	0.525755i	$0.823783\pi$
$104$	−0.0882406	+	0.152837i	−0.00865270	+	0.0149869i
$105$	4.25959	+	1.68993i	0.415694	+	0.164921i
$106$	−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	$0.276203\pi$
$108$	1.13040	−	0.658849i	0.108772	−	0.0633978i
$109$	−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	$-0.497230\pi$
$110$	−4.24971			−0.405194
$111$	−4.70022	+	0.835422i	−0.446125	+	0.0792948i
$112$	−0.352312	+	11.7424i	−0.0332903	+	1.10955i
$113$	8.13028	−	14.0821i	0.764833	−	1.32473i	−0.175502	−	0.984479i	$-0.556155\pi$
$113$	8.13028	−	14.0821i	0.764833	−	1.32473i	0.940335	−	0.340250i	$-0.110512\pi$
$114$	−3.41786	+	0.607494i	−0.320112	+	0.0568971i
$115$	1.61091	−	2.79017i	0.150218	−	0.260185i
$116$	1.13600	+	1.96761i	0.105475	+	0.182688i
$117$	0.154958	+	0.129303i	0.0143259	+	0.0119540i
$118$	−10.3104			−0.949147
$119$	−16.2214	+	8.72757i	−1.48702	+	0.800055i
$120$	1.54821	−	4.27188i	0.141331	−	0.389967i
$121$	1.48987	+	2.58053i	0.135443	+	0.234594i
$122$	5.69700			0.515782
$123$	−8.05574	+	1.43184i	−0.726362	+	0.129104i
$124$	2.38517			0.214194
$125$	1.00000			0.0894427
$126$	11.6690	+	2.38711i	1.03956	+	0.212661i
$127$	15.7379			1.39652			0.698258	−	0.715846i	$-0.253959\pi$
$127$	15.7379			1.39652			0.698258	+	0.715846i	$0.253959\pi$
$128$	12.9693			1.14633
$129$	4.67916	−	12.9110i	0.411977	−	1.13675i
$130$	−0.100950			−0.00885392
$131$	−2.53794	−	4.39585i	−0.221741	−	0.384067i	0.733596	−	0.679586i	$-0.237841\pi$
$131$	−2.53794	−	4.39585i	−0.221741	−	0.384067i	−0.955337	+	0.295519i	$0.904507\pi$
$132$	−1.21606	+	0.216144i	−0.105844	+	0.0188129i
$133$	−3.00593	−	1.85784i	−0.260647	−	0.161095i
$134$	5.47769			0.473200
$135$	−4.51065	−	2.57954i	−0.388215	−	0.222012i
$136$	9.13215	+	15.8173i	0.783075	+	1.35633i
$137$	1.18084	−	2.04527i	0.100886	−	0.174740i	−0.811164	−	0.584819i	$-0.801166\pi$
$137$	1.18084	−	2.04527i	0.100886	−	0.174740i	0.912050	+	0.410079i	$0.134499\pi$
$138$	2.85324	−	7.87278i	0.242884	−	0.670176i
$139$	−3.45961	+	5.99223i	−0.293441	+	0.508254i	−0.974621	−	0.223862i	$-0.928134\pi$
$139$	−3.45961	+	5.99223i	−0.293441	+	0.508254i	0.681180	+	0.732116i	$0.261467\pi$
$140$	−0.586675	+	0.315647i	−0.0495831	+	0.0266770i
$141$	−1.93385	−	2.29826i	−0.162860	−	0.193549i
$142$	−13.3431			−1.11973
$143$	−0.0952591	−	0.164994i	−0.00796597	−	0.0137975i
$144$	2.27711	−	13.1245i	0.189759	−	1.09371i
$145$	4.51153	−	7.81420i	0.374662	−	0.648934i
$146$	3.87225	+	6.70694i	0.320470	+	0.555070i
$147$	7.23588	+	9.72841i	0.596805	+	0.802386i
$148$	0.347005	−	0.601031i	0.0285236	−	0.0494044i
$149$	−0.997645	−	1.72797i	−0.0817303	−	0.141561i	0.822263	−	0.569108i	$-0.192711\pi$
$149$	−0.997645	−	1.72797i	−0.0817303	−	0.141561i	−0.903993	+	0.427547i	$0.859378\pi$
$150$	2.55901	−	0.454841i	0.208942	−	0.0371376i
$151$	−2.53595	+	4.39239i	−0.206372	+	0.357447i	−0.950569	−	0.310513i	$-0.899499\pi$
$151$	−2.53595	+	4.39239i	−0.206372	+	0.357447i	0.744197	+	0.667960i	$0.232832\pi$
$152$	−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
$156$	−0.0288871	+	0.00513442i	−0.00231282	+	0.000411083i
$157$	10.1019			0.806216			0.403108	−	0.915152i	$-0.367930\pi$
$157$	10.1019			0.806216			0.403108	+	0.915152i	$0.367930\pi$
$158$	17.2068			1.36890
$159$	−7.99527	+	22.0609i	−0.634066	+	1.74954i
$160$	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	$0.134147\pi$
$164$	0.594735	−	1.03011i	0.0464410	−	0.0804382i
$165$	3.15814	+	3.75326i	0.245861	+	0.292191i
$166$	−8.11413	−	14.0541i	−0.629778	−	1.09081i
$167$	−4.13083	+	7.15481i	−0.319653	+	0.553656i	−0.980416	−	0.196939i	$-0.936900\pi$
$167$	−4.13083	+	7.15481i	−0.319653	+	0.553656i	0.660762	+	0.750595i	$0.270233\pi$
$168$	9.42654	−	7.46067i	0.727273	−	0.575603i
$169$	6.49774	+	11.2544i	0.499826	+	0.865724i
$170$	−5.22374	+	9.04778i	−0.400643	+	0.693933i
$171$	3.07648	+	2.56713i	0.235265	+	0.196314i
$172$	0.998206	+	1.72894i	0.0761125	+	0.131831i
$173$	−16.1027			−1.22427			−0.612133	−	0.790755i	$-0.709688\pi$
$173$	−16.1027			−1.22427			−0.612133	+	0.790755i	$0.709688\pi$
$174$	7.99082	−	22.0486i	0.605783	−	1.67150i
$175$	2.25058	+	1.39100i	0.170128	+	0.105149i
$176$	−6.28733	+	10.8900i	−0.473925	+	0.820863i
$177$	7.66208	+	9.10592i	0.575917	+	0.684443i
$178$	−5.14047	+	8.90356i	−0.385295	+	0.667350i
$179$	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	$0.693947\pi$
$180$	0.709131	−	0.260307i	0.0528555	−	0.0194021i
$181$	−19.6274			−1.45890			−0.729448	−	0.684037i	$-0.760223\pi$
$181$	−19.6274			−1.45890			−0.729448	+	0.684037i	$0.760223\pi$
$182$	−0.227197	−	0.140421i	−0.0168410	−	0.0104087i
$183$	−4.23368	−	5.03147i	−0.312963	−	0.371937i
$184$	−4.22597	−	7.31960i	−0.311543	−	0.539608i
$185$	−2.75620			−0.202640
$186$	−15.8513	−	18.8384i	−1.16228	−	1.38130i
$187$	−19.7170			−1.44185
$188$	0.436657			0.0318465
$189$	−6.56346	−	12.0798i	−0.477422	−	0.878674i
$190$	−2.00423			−0.145402
$191$	19.0907			1.38135			0.690676	−	0.723164i	$-0.257313\pi$
$191$	19.0907			1.38135			0.690676	+	0.723164i	$0.257313\pi$
$192$	−7.53307	−	8.95261i	−0.543653	−	0.646099i
$193$	2.23778			0.161079			0.0805393	−	0.996751i	$-0.474336\pi$
$193$	2.23778			0.161079			0.0805393	+	0.996751i	$0.474336\pi$
$194$	2.18579	+	3.78590i	0.156931	+	0.271812i
$195$	0.0750204	+	0.0891572i	0.00537232	+	0.00638468i
$196$	−1.75942	−	0.105673i	−0.125673	−	0.00754806i
$197$	11.5499			0.822898			0.411449	−	0.911433i	$-0.365023\pi$
$197$	11.5499			0.822898			0.411449	+	0.911433i	$0.365023\pi$
$198$	9.78883	+	8.16816i	0.695662	+	0.580486i
$199$	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	$0.760360\pi$
$200$	1.31167	−	2.27189i	0.0927494	−	0.160647i
$201$	−4.07070	−	4.83779i	−0.287125	−	0.341231i
$202$	−6.75857	+	11.7062i	−0.475532	+	0.823645i
$203$	21.0231	−	11.3110i	1.47553	−	0.793876i
$204$	−1.03460	+	2.85472i	−0.0724367	+	0.199871i
$205$	−4.72388			−0.329930
$206$	0.456866	+	0.791315i	0.0318314	+	0.0551335i
$207$	−9.07345	+	3.33067i	−0.630648	+	0.231498i
$208$	−0.149353	+	0.258687i	−0.0103558	+	0.0179367i
$209$	−1.89124	−	3.27573i	−0.130820	−	0.226587i
$210$	6.39194	+	2.53591i	0.441086	+	0.174995i
$211$	0.698417	−	1.20969i	0.0480810	−	0.0832788i	−0.840983	−	0.541061i	$-0.818023\pi$
$211$	0.698417	−	1.20969i	0.0480810	−	0.0832788i	0.889064	+	0.457782i	$0.151356\pi$
$212$	−1.70563	−	2.95424i	−0.117143	−	0.202898i
$213$	9.91584	+	11.7844i	0.679422	+	0.807453i
$214$	−5.23671	+	9.07025i	−0.357974	+	0.620030i
$215$	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
$219$	3.04580	−	8.40411i	0.205816	−	0.567897i
$220$	−0.713097			−0.0480770
$221$	−0.468370			−0.0315060
$222$	−7.05315	+	1.25363i	−0.473376	+	0.0841384i
$223$	0.738934	+	1.27987i	0.0494827	+	0.0857065i	0.889706	−	0.456534i	$-0.150909\pi$
$223$	0.738934	+	1.27987i	0.0494827	+	0.0857065i	−0.840223	+	0.542241i	$0.817576\pi$
$224$	−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
$227$	2.34258	−	4.05747i	0.155483	−	0.269304i	−0.777752	−	0.628571i	$-0.783640\pi$
$227$	2.34258	−	4.05747i	0.155483	−	0.269304i	0.933235	+	0.359267i	$0.116973\pi$
$228$	−0.573514	+	0.101937i	−0.0379819	+	0.00675094i
$229$	−10.9218	−	18.9171i	−0.721732	−	1.25008i	−0.960305	−	0.278952i	$-0.910013\pi$
$229$	−10.9218	−	18.9171i	−0.721732	−	1.25008i	0.238573	−	0.971125i	$-0.423320\pi$
$230$	2.41733	−	4.18693i	0.159394	−	0.276078i
$231$	1.88689	+	12.8400i	0.124148	+	0.844809i
$232$	−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	$0.0991768\pi$
$234$	0.232530	+	0.194032i	0.0152010	+	0.0126842i
$235$	−0.867073	−	1.50182i	−0.0565616	−	0.0979676i
$236$	−1.73007			−0.112618
$237$	−12.7871	−	15.1967i	−0.830612	−	0.987133i
$238$	−24.3419	+	13.0966i	−1.57785	+	0.848926i
$239$	−7.02033	+	12.1596i	−0.454107	+	0.786537i	−0.998636	−	0.0522051i	$-0.983375\pi$
$239$	−7.02033	+	12.1596i	−0.454107	+	0.786537i	0.544529	+	0.838742i	$0.316708\pi$
$240$	2.62044	−	7.23044i	0.169149	−	0.466723i
$241$	−5.45436	+	9.44722i	−0.351346	+	0.608549i	−0.986486	−	0.163848i	$-0.947609\pi$
$241$	−5.45436	+	9.44722i	−0.351346	+	0.608549i	0.635140	+	0.772397i	$0.280943\pi$
$242$	2.23570	+	3.87235i	0.143716	+	0.248924i
$243$	5.43187	+	14.6115i	0.348454	+	0.937326i
$244$	0.955951			0.0611985
$245$	3.13026	+	6.26111i	0.199985	+	0.400008i
$246$	−12.0884	+	2.14861i	−0.770731	+	0.136991i
$247$	−0.0449257	−	0.0778137i	−0.00285856	−	0.00495116i
$248$	−24.8497			−1.57796
$249$	−6.38234	+	17.6104i	−0.404464	+	1.11601i
$250$	1.50060			0.0949063
$251$	26.5729			1.67727			0.838633	−	0.544698i	$-0.183356\pi$
$251$	26.5729			1.67727			0.838633	+	0.544698i	$0.183356\pi$
$252$	1.95804	+	0.400555i	0.123345	+	0.0252326i
$253$	9.12420			0.573634
$254$	23.6163			1.48182
$255$	11.8728	−	2.11029i	0.743504	−	0.132151i
$256$	5.95141			0.371963
$257$	8.02773	+	13.9044i	0.500756	+	0.867335i	1.00000		0.000873427i	$0.000278020\pi$
$257$	8.02773	+	13.9044i	0.500756	+	0.867335i	−0.499243	+	0.866462i	$0.666389\pi$
$258$	7.02155	−	19.3742i	0.437143	−	1.20618i
$259$	−6.20307	−	3.83387i	−0.385440	−	0.238225i
$260$	−0.0169394			−0.00105053
$261$	−25.4112	+	9.32793i	−1.57292	+	0.577384i
$262$	−3.80844	−	6.59641i	−0.235286	−	0.407527i
$263$	0.257265	−	0.445597i	0.0158637	−	0.0274767i	−0.857985	−	0.513675i	$-0.828284\pi$
$263$	0.257265	−	0.445597i	0.0158637	−	0.0274767i	0.873848	+	0.486199i	$0.161617\pi$
$264$	12.6694	−	2.25188i	0.779749	−	0.138594i
$265$	−6.77377	+	11.7325i	−0.416109	+	0.720723i
$266$	−4.51069	−	2.78788i	−0.276568	−	0.170936i
$267$	11.6836	−	2.07665i	0.715022	−	0.127089i
$268$	0.919151			0.0561461
$269$	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	$0.639098\pi$
$270$	−6.76868	−	3.87086i	−0.411929	−	0.235573i
$271$	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
$273$	0.0448223	+	0.305009i	0.00271277	+	0.0184600i
$274$	1.77197	−	3.06914i	0.107048	−	0.185413i
$275$	1.41600	+	2.45259i	0.0853882	+	0.147897i
$276$	0.478771	−	1.32105i	0.0288186	−	0.0795176i
$277$	−7.61425	+	13.1883i	−0.457496	+	0.792406i	−0.998828	−	0.0484031i	$-0.984587\pi$
$277$	−7.61425	+	13.1883i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$278$	−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	0.999402	−	0.0345807i	$-0.0110096\pi$
$281$	7.87450	+	13.6390i	0.469753	+	0.813636i	−0.529649	+	0.848217i	$0.677676\pi$
$282$	−2.90193	−	3.44878i	−0.172808	−	0.205372i
$283$	−12.3715			−0.735410			−0.367705	−	0.929943i	$-0.619856\pi$
$283$	−12.3715			−0.735410			−0.367705	+	0.929943i	$0.619856\pi$
$284$	−2.23896			−0.132858
$285$	1.48943	+	1.77010i	0.0882261	+	0.104852i
$286$	−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
$290$	6.77000	−	11.7260i	0.397548	−	0.688574i
$291$	1.71928	−	4.74391i	0.100786	−	0.278093i
$292$	0.649760	+	1.12542i	0.0380244	+	0.0658601i
$293$	−8.80515	+	15.2510i	−0.514403	+	0.890971i	0.485458	+	0.874260i	$0.338653\pi$
$293$	−8.80515	+	15.2510i	−0.514403	+	0.890971i	−0.999860	+	0.0167112i	$0.994680\pi$
$294$	10.8582	+	14.5985i	0.633261	+	0.851399i
$295$	3.43542	+	5.95032i	0.200018	+	0.346441i
$296$	−3.61524	+	6.26179i	−0.210132	+	0.363959i
$297$	−0.0605327	−	14.7154i	−0.00351246	−	0.853875i
$298$	−1.49707	−	2.59299i	−0.0867227	−	0.150208i
$299$	0.216742			0.0125345
$300$	0.429399	−	0.0763219i	0.0247914	−	0.00440645i
$301$	18.4730	−	9.93899i	1.06477	−	0.572874i
$302$	−3.80544	+	6.59121i	−0.218978	+	0.379282i
$303$	15.3613	−	2.73033i	0.882481	−	0.156853i
$304$	−2.96521	+	5.13589i	−0.170066	+	0.294563i
$305$	−1.89824	−	3.28785i	−0.108693	−	0.188262i
$306$	29.4228	−	10.8005i	1.68199	−	0.617422i
$307$	6.14034			0.350448			0.175224	−	0.984529i	$-0.443935\pi$
$307$	6.14034			0.350448			0.175224	+	0.984529i	$0.443935\pi$
$308$	−1.60488	−	0.991915i	−0.0914468	−	0.0565196i
$309$	0.359357	−	0.991555i	0.0204431	−	0.0564076i
$310$	−7.10721	−	12.3101i	−0.403663	−	0.699164i
$311$	24.8011			1.40634			0.703170	−	0.711022i	$-0.251767\pi$
$311$	24.8011			1.40634			0.703170	+	0.711022i	$0.251767\pi$
$312$	0.300957	−	0.0534925i	0.0170384	−	0.00302842i
$313$	25.7761			1.45695			0.728476	−	0.685072i	$-0.240229\pi$
$313$	25.7761			1.45695			0.728476	+	0.685072i	$0.240229\pi$
$314$	15.1588			0.855463
$315$	−2.51046	−	7.52978i	−0.141448	−	0.424255i
$316$	2.88729			0.162423
$317$	−9.38024			−0.526847			−0.263423	−	0.964680i	$-0.584852\pi$
$317$	−9.38024			−0.526847			−0.263423	+	0.964680i	$0.584852\pi$
$318$	−11.9977	+	33.1046i	−0.672798	+	1.85641i
$319$	25.5534			1.43071
$320$	−3.37758	−	5.85014i	−0.188812	−	0.327033i
$321$	11.9023	−	2.11553i	0.664321	−	0.118077i
$322$	11.2644	−	6.06056i	0.627741	−	0.337742i
$323$	−9.29886			−0.517402
$324$	−2.13374	−	0.763392i	−0.118541	−	0.0424107i
$325$	0.0336366	+	0.0582603i	0.00186582	+	0.00323170i
$326$	1.95389	−	3.38424i	0.108216	−	0.187436i
$327$	−10.6180	+	29.2977i	−0.587177	+	1.62016i
$328$	−6.19620	+	10.7321i	−0.342128	+	0.592583i
$329$	0.137598	−	4.58606i	0.00758600	−	0.252838i
$330$	4.73910	+	5.63214i	0.260879	+	0.310039i
$331$	29.2059			1.60530			0.802651	−	0.596448i	$-0.203422\pi$
$331$	29.2059			1.60530			0.802651	+	0.596448i	$0.203422\pi$
$332$	−1.36154	−	2.35826i	−0.0747244	−	0.129426i
$333$	6.34868	+	5.29757i	0.347905	+	0.290305i
$334$	−6.19873	+	10.7365i	−0.339179	+	0.587476i
$335$	−1.82517	−	3.16128i	−0.0997195	−	0.172719i
$336$	15.9550	−	12.6277i	0.870419	−	0.688897i
$337$	−2.22121	+	3.84725i	−0.120997	+	0.209573i	−0.920161	−	0.391540i	$-0.871943\pi$
$337$	−2.22121	+	3.84725i	−0.120997	+	0.209573i	0.799164	+	0.601113i	$0.205276\pi$
$338$	9.75050	+	16.8884i	0.530357	+	0.918606i
$339$	−27.7295	+	4.92868i	−1.50606	+	0.267689i
$340$	−0.876539	+	1.51821i	−0.0475370	+	0.0823365i
$341$	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
$345$	−5.49424	+	0.976552i	−0.295800	+	0.0525758i
$346$	−24.1637			−1.29905
$347$	7.32919			0.393452			0.196726	−	0.980459i	$-0.436969\pi$
$347$	7.32919			0.393452			0.196726	+	0.980459i	$0.436969\pi$
$348$	1.34085	−	3.69974i	0.0718773	−	0.198327i
$349$	−10.9927	−	19.0399i	−0.588424	−	1.01918i	−0.994439	−	0.105314i	$-0.966415\pi$
$349$	−10.9927	−	19.0399i	−0.588424	−	1.01918i	0.406015	−	0.913866i	$-0.366918\pi$
$350$	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
$353$	−12.8938	+	22.3326i	−0.686265	+	1.18865i	0.286772	+	0.957999i	$0.407418\pi$
$353$	−12.8938	+	22.3326i	−0.686265	+	1.18865i	−0.973037	+	0.230647i	$0.925916\pi$
$354$	11.4977	+	13.6643i	0.611096	+	0.726252i
$355$	4.44593	+	7.70058i	0.235966	+	0.408704i
$356$	−0.862567	+	1.49401i	−0.0457159	+	0.0791823i
$357$	29.6561	+	11.7657i	1.56957	+	0.622704i
$358$	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	$0.148972\pi$
$360$	−7.38802	+	2.71199i	−0.389383	+	0.142934i
$361$	8.60806	+	14.9096i	0.453056	+	0.784716i
$362$	−29.4529			−1.54801
$363$	1.75854	−	4.85223i	0.0922993	−	0.254676i
$364$	−0.0381234	−	0.0235626i	−0.00199821	−	0.00123501i
$365$	2.58047	−	4.46951i	0.135068	−	0.233945i
$366$	−6.35306	−	7.55023i	−0.332080	−	0.394657i
$367$	−2.79479	+	4.84072i	−0.145887	+	0.252683i	−0.929703	−	0.368309i	$-0.879937\pi$
$367$	−2.79479	+	4.84072i	−0.145887	+	0.252683i	0.783817	+	0.620992i	$0.213270\pi$
$368$	−7.15275	−	12.3889i	−0.372863	−	0.645817i
$369$	10.8810	+	9.07955i	0.566445	+	0.472663i
$370$	−4.13596			−0.215018
$371$	−31.5648	+	16.9827i	−1.63876	+	0.881699i
$372$	−2.65984	−	3.16106i	−0.137906	−	0.163894i
$373$	−2.52496	−	4.37337i	−0.130738	−	0.226444i	0.793223	−	0.608931i	$-0.208401\pi$
$373$	−2.52496	−	4.37337i	−0.130738	−	0.226444i	−0.923961	+	0.382486i	$0.875068\pi$
$374$	−29.5873			−1.52992
$375$	−1.11516	−	1.32530i	−0.0575866	−	0.0684382i
$376$	−4.54927			−0.234611
$377$	0.607011			0.0312626
$378$	−9.84913	−	18.1269i	−0.506584	−	0.932348i
$379$	−0.343947			−0.0176674			−0.00883369	−	0.999961i	$-0.502812\pi$
$379$	−0.343947			−0.0176674			−0.00883369	+	0.999961i	$0.502812\pi$
$380$	−0.336308			−0.0172522
$381$	−17.5503	−	20.8575i	−0.899129	−	1.06856i
$382$	28.6475			1.46573
$383$	0.899383	+	1.55778i	0.0459563	+	0.0795987i	0.888089	−	0.459672i	$-0.152033\pi$
$383$	0.899383	+	1.55778i	0.0459563	+	0.0795987i	−0.842132	+	0.539271i	$0.818700\pi$
$384$	−14.4628	−	17.1882i	−0.738053	−	0.877132i
$385$	−0.224708	+	7.48941i	−0.0114522	+	0.381696i
$386$	3.35800			0.170918
$387$	−22.3289	+	8.19647i	−1.13504	+	0.416650i
$388$	0.366774	+	0.635271i	0.0186201	+	0.0322510i
$389$	13.9240	−	24.1170i	0.705973	−	1.22278i	−0.260366	−	0.965510i	$-0.583843\pi$
$389$	13.9240	−	24.1170i	0.705973	−	1.22278i	0.966339	−	0.257271i	$-0.0828235\pi$
$390$	0.112576	+	0.133789i	0.00570048	+	0.00677468i
$391$	11.2155	−	19.4258i	0.567191	−	0.982403i
$392$	18.3304	+	1.10094i	0.925826	+	0.0556060i
$393$	−2.99561	+	8.26561i	−0.151108	+	0.416945i
$394$	17.3318			0.873164
$395$	−5.73331	−	9.93039i	−0.288474	−	0.499652i
$396$	1.64256	+	1.37061i	0.0825416	+	0.0688758i
$397$	−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
$399$	0.889886	+	6.05554i	0.0445500	+	0.303156i
$400$	2.22010	−	3.84532i	0.111005	−	0.192266i
$401$	−13.1641	−	22.8009i	−0.657384	−	1.13862i	−0.981290	−	0.192533i	$-0.938330\pi$
$401$	−13.1641	−	22.8009i	−0.657384	−	1.13862i	0.323906	−	0.946089i	$-0.395004\pi$
$402$	−6.10850	−	7.25958i	−0.304664	−	0.362075i
$403$	0.318623	−	0.551871i	0.0158717	−	0.0274907i
$404$	−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
$408$	10.7789	−	29.7417i	0.533636	−	1.47243i
$409$	−5.03178			−0.248806			−0.124403	−	0.992232i	$-0.539702\pi$
$409$	−5.03178			−0.248806			−0.124403	+	0.992232i	$0.539702\pi$
$410$	−7.08865			−0.350084
$411$	−4.02743	+	0.715839i	−0.198658	+	0.0353097i
$412$	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
$416$	−0.0476381	+	0.0825116i	−0.00233565	+	0.00404546i
$417$	11.7995	−	2.09726i	0.577825	−	0.102703i
$418$	−2.83800	−	4.91555i	−0.138811	−	0.240428i
$419$	−10.3206	+	17.8758i	−0.504195	+	0.873291i	0.495793	+	0.868441i	$0.334877\pi$
$419$	−10.3206	+	17.8758i	−0.504195	+	0.873291i	−0.999988	+	0.00485063i	$0.998456\pi$
$420$	1.07256	+	0.425524i	0.0523357	+	0.0207634i
$421$	−12.2741	−	21.2594i	−0.598204	−	1.03612i	−0.993086	−	0.117388i	$-0.962548\pi$
$421$	−12.2741	−	21.2594i	−0.598204	−	1.03612i	0.394882	−	0.918732i	$-0.370785\pi$
$422$	1.04804	−	1.81527i	0.0510180	−	0.0883658i
$423$	−0.889341	+	5.12586i	−0.0432412	+	0.249228i
$424$	17.7700	+	30.7785i	0.862986	+	1.49474i
$425$	6.96220			0.337716
$426$	14.8797	+	17.6836i	0.720924	+	0.856776i
$427$	0.301236	−	10.0400i	0.0145778	−	0.485871i
$428$	−0.878715	+	1.52198i	−0.0424743	+	0.0735677i
$429$	−0.112437	+	0.310241i	−0.00542851	+	0.0149786i
$430$	5.94881	−	10.3036i	0.286877	−	0.496886i
$431$	−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	$-0.489223\pi$
$432$	−19.9333	+	11.6181i	−0.959039	+	0.558974i
$433$	−41.2488			−1.98229			−0.991146	−	0.132775i	$-0.957611\pi$
$433$	−41.2488			−1.98229			−0.991146	+	0.132775i	$0.957611\pi$
$434$	1.12786	−	37.5909i	0.0541389	−	1.80442i
$435$	−15.3872	+	2.73494i	−0.737761	+	0.131131i
$436$	−2.26514	−	3.92333i	−0.108480	−	0.187894i
$437$	4.30312			0.205846
$438$	4.57053	−	12.6112i	0.218388	−	0.602586i
$439$	32.4000			1.54637			0.773183	−	0.634183i	$-0.218663\pi$
$439$	32.4000			1.54637			0.773183	+	0.634183i	$0.218663\pi$
$440$	7.42934			0.354180
$441$	4.82391	−	20.4384i	0.229710	−	0.973259i
$442$	−0.702836			−0.0334305
$443$	−15.2371			−0.723936			−0.361968	−	0.932190i	$-0.617895\pi$
$443$	−15.2371			−0.723936			−0.361968	+	0.932190i	$0.617895\pi$
$444$	−1.18351	+	0.210359i	−0.0561670	+	0.00998318i
$445$	6.85123			0.324779
$446$	1.10884	+	1.92057i	0.0525053	+	0.0909418i
$447$	−1.17755	+	3.24914i	−0.0556961	+	0.153679i
$448$	0.535995	−	17.8644i	0.0253234	−	0.844015i
$449$	7.30992			0.344976			0.172488	−	0.985012i	$-0.444819\pi$
$449$	7.30992			0.344976			0.172488	+	0.985012i	$0.444819\pi$
$450$	−3.45650	−	2.88423i	−0.162941	−	0.135964i
$451$	−6.68903	−	11.5857i	−0.314974	−	0.545551i
$452$	2.04720	−	3.54585i	0.0962921	−	0.166783i
$453$	8.64921	−	1.53732i	0.406376	−	0.0722296i
$454$	3.51528	−	6.08864i	0.164980	−	0.285754i
$455$	−0.00533786	+	0.177908i	−0.000250243	+	0.00834047i
$456$	5.97511	−	1.06202i	0.279810	−	0.0497338i
$457$	−30.3898			−1.42157			−0.710787	−	0.703407i	$-0.751661\pi$
$457$	−30.3898			−1.42157			−0.710787	+	0.703407i	$0.751661\pi$
$458$	−16.3892	−	28.3870i	−0.765819	−	1.32644i
$459$	−31.4041	−	17.9593i	−1.46582	−	0.838269i
$460$	0.405625	−	0.702564i	0.0189124	−	0.0327572i
$461$	−10.0136	−	17.3440i	−0.466379	−	0.807793i	0.532883	−	0.846189i	$-0.321108\pi$
$461$	−10.0136	−	17.3440i	−0.466379	−	0.807793i	−0.999263	+	0.0383961i	$0.987775\pi$
$462$	2.83146	+	19.2677i	0.131731	+	0.896413i
$463$	−18.8943	+	32.7259i	−0.878092	+	1.52090i	−0.0246600	+	0.999696i	$0.507850\pi$
$463$	−18.8943	+	32.7259i	−0.878092	+	1.52090i	−0.853432	+	0.521204i	$0.825483\pi$
$464$	−20.0321	−	34.6966i	−0.929966	−	1.61075i
$465$	−5.59033	+	15.4251i	−0.259245	+	0.715321i
$466$	4.82028	−	8.34897i	0.223295	−	0.386758i
$467$	−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
$471$	−11.2652	−	13.3880i	−0.519072	−	0.616886i
$472$	18.0246			0.829650
$473$	22.4538			1.03243
$474$	−19.1883	−	22.8042i	−0.881349	−	1.04743i
$475$	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
$479$	13.8539	−	23.9957i	0.633001	−	1.09639i	−0.353934	−	0.935270i	$-0.615156\pi$
$479$	13.8539	−	23.9957i	0.633001	−	1.09639i	0.986935	−	0.161119i	$-0.0515104\pi$
$480$	0.835824	−	2.30624i	0.0381500	−	0.105265i
$481$	−0.0927094	−	0.160577i	−0.00422719	−	0.00732170i
$482$	−8.18480	+	14.1765i	−0.372808	+	0.645722i
$483$	−13.7236	−	5.44465i	−0.624446	−	0.247740i
$484$	0.375149	+	0.649776i	0.0170522	+	0.0295353i
$485$	1.45661	−	2.52293i	0.0661413	−	0.114560i
$486$	8.15106	+	21.9260i	0.369740	+	0.994581i
$487$	−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	$0.935983\pi$
$488$	−9.95949			−0.450845
$489$	−4.44091	+	0.789333i	−0.200825	+	0.0356949i
$490$	4.69726	+	9.39542i	0.212201	+	0.424442i
$491$	−4.04649	+	7.00872i	−0.182615	+	0.316299i	−0.942770	−	0.333443i	$-0.891790\pi$
$491$	−4.04649	+	7.00872i	−0.182615	+	0.316299i	0.760155	+	0.649742i	$0.225123\pi$
$492$	−2.02843	+	0.360535i	−0.0914487	+	0.0162542i
$493$	31.4102	−	54.4041i	1.41464	−	2.45024i
$494$	−0.0674155	−	0.116767i	−0.00303317	−	0.00525360i
$495$	1.45237	−	8.37096i	0.0652791	−	0.376247i
$496$	−42.0597			−1.88854
$497$	−0.705534	+	23.5151i	−0.0316475	+	1.05480i
$498$	−9.57733	+	26.4262i	−0.429170	+	1.18419i
$499$	0.973828	+	1.68672i	0.0435945	+	0.0755079i	0.886999	−	0.461771i	$-0.152786\pi$
$499$	0.973828	+	1.68672i	0.0435945	+	0.0755079i	−0.843405	+	0.537279i	$0.819452\pi$
$500$	0.251799			0.0112608
$501$	14.0888	−	2.50416i	0.629442	−	0.111878i
$502$	39.8752			1.77972
$503$	3.94050			0.175698			0.0878491	−	0.996134i	$-0.472001\pi$
$503$	3.94050			0.175698			0.0878491	+	0.996134i	$0.472001\pi$
$504$	−20.3997	−	4.17315i	−0.908676	−	0.185887i
$505$	9.00783			0.400843
$506$	13.6918			0.608674
$507$	7.66946	−	21.1619i	0.340613	−	0.939833i
$508$	3.96280			0.175821
$509$	−0.928982	−	1.60904i	−0.0411764	−	0.0713196i	0.844703	−	0.535236i	$-0.179777\pi$
$509$	−0.928982	−	1.60904i	−0.0411764	−	0.0713196i	−0.885879	+	0.463916i	$0.846444\pi$
$510$	17.8163	−	3.16669i	0.788920	−	0.140224i
$511$	12.0246	−	6.46957i	0.531938	−	0.286197i
$512$	−17.0079			−0.751651
$513$	−0.0285482	−	6.94003i	−0.00126043	−	0.306410i
$514$	12.0464	+	20.8650i	0.531344	+	0.920316i
$515$	0.304456	−	0.527333i	0.0134159	−	0.0232370i
$516$	1.17821	−	3.25097i	0.0518678	−	0.143116i
$517$	2.45556	−	4.25315i	0.107995	−	0.187053i
$518$	−9.30833	−	5.75310i	−0.408984	−	0.252777i
$519$	17.9571	+	21.3409i	0.788228	+	0.936762i
$520$	0.176481			0.00773921
$521$	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	$0.666339\pi$
$522$	−38.1321	+	13.9975i	−1.66900	+	0.612653i
$523$	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
$525$	−0.666272	−	4.53388i	−0.0290785	−	0.197875i
$526$	0.386052	−	0.668662i	0.0168327	−	0.0291551i
$527$	−32.9747	−	57.1139i	−1.43640	−	2.48792i
$528$	21.4439	−	3.81146i	0.933224	−	0.165872i
$529$	6.30995	−	10.9292i	0.274346	−	0.475181i
$530$	−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
$534$	17.5323	−	3.11622i	0.758698	−	0.134852i
$535$	6.97949			0.301750
$536$	−9.57610			−0.413625
$537$	6.69623	−	18.4765i	0.288964	−	0.797321i
$538$	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	$0.194071\pi$
$542$	12.9639	−	22.4542i	0.556848	−	0.964489i
$543$	21.8877	+	26.0122i	0.939292	+	1.11629i
$544$	4.93014	+	8.53924i	0.211378	+	0.366117i
$545$	−8.99581	+	15.5812i	−0.385338	+	0.667425i
$546$	0.0672603	+	0.457696i	0.00287847	+	0.0195876i
$547$	6.16681	+	10.6812i	0.263674	+	0.456696i	0.967215	−	0.253958i	$-0.0817325\pi$
$547$	6.16681	+	10.6812i	0.263674	+	0.456696i	−0.703542	+	0.710654i	$0.748399\pi$
$548$	0.297335	−	0.514998i	0.0127015	−	0.0219996i
$549$	−1.94699	+	11.2218i	−0.0830954	+	0.478934i
$550$	2.12485	+	3.68035i	0.0906041	+	0.156931i
$551$	12.0514			0.513406
$552$	−4.98804	+	13.7632i	−0.212305	+	0.585801i
$553$	0.909831	−	30.3242i	0.0386900	−	1.28952i
$554$	−11.4259	+	19.7903i	−0.485441	+	0.840809i
$555$	3.07361	+	3.65280i	0.130467	+	0.155053i
$556$	−0.871128	+	1.50884i	−0.0369441	+	0.0639890i
$557$	−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	$0.973067\pi$
$558$	−7.28973	+	42.0156i	−0.308599	+	1.77866i
$559$	0.533381			0.0225596
$560$	10.3453	−	5.56607i	0.437171	−	0.235210i
$561$	21.9876	+	26.1309i	0.928317	+	1.10325i
$562$	11.8165	+	20.4667i	0.498448	+	0.863337i
$563$	−3.70504			−0.156149			−0.0780743	−	0.996948i	$-0.524877\pi$
$563$	−3.70504			−0.156149			−0.0780743	+	0.996948i	$0.524877\pi$
$564$	−0.486942	−	0.578701i	−0.0205040	−	0.0243677i
$565$	−16.2606			−0.684087
$566$	−18.5647			−0.780332
$567$	−8.69003	+	22.1694i	−0.364947	+	0.931028i
$568$	23.3265			0.978757
$569$	24.9245			1.04489			0.522445	−	0.852673i	$-0.325020\pi$
$569$	24.9245			1.04489			0.522445	+	0.852673i	$0.325020\pi$
$570$	2.23504	+	2.65621i	0.0936154	+	0.111256i
$571$	24.7070			1.03395			0.516977	−	0.855999i	$-0.327057\pi$
$571$	24.7070			1.03395			0.516977	+	0.855999i	$0.327057\pi$
$572$	−0.0239862	−	0.0415453i	−0.00100291	−	0.00173709i
$573$	−21.2891	−	25.3009i	−0.889367	−	1.05696i
$574$	−15.9536	−	9.86029i	−0.665891	−	0.411561i
$575$	−3.22182			−0.134359
$576$	−3.46432	+	19.9672i	−0.144347	+	0.831965i
$577$	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	$0.806846\pi$
$578$	−23.6136	+	40.9000i	−0.982198	+	1.70122i
$579$	−2.49548	−	2.96572i	−0.103708	−	0.123251i
$580$	1.13600	−	1.96761i	0.0471698	−	0.0817006i
$581$	−25.1971	+	13.5567i	−1.04535	+	0.562426i
$582$	2.57995	−	7.11871i	0.106942	−	0.295080i
$583$	−38.3667			−1.58899
$584$	−6.76947	−	11.7251i	−0.280123	−	0.485187i
$585$	0.0345004	−	0.198849i	0.00142642	−	0.00822139i
$586$	−13.2130	+	22.8856i	−0.545824	+	0.945396i
$587$	5.98200	+	10.3611i	0.246904	+	0.427649i	0.962665	−	0.270695i	$-0.0872536\pi$
$587$	5.98200	+	10.3611i	0.246904	+	0.427649i	−0.715762	+	0.698345i	$0.753920\pi$
$588$	1.82199	+	2.44961i	0.0751376	+	0.101020i
$589$	6.32583	−	10.9567i	0.260651	−	0.451461i
$590$	5.15519	+	8.92905i	0.212236	+	0.367603i
$591$	−12.8800	−	15.3071i	−0.529812	−	0.629651i
$592$	−6.11904	+	10.5985i	−0.251491	+	0.435595i
$593$	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
$597$	3.78385	−	10.4406i	0.154863	−	0.427304i
$598$	0.325243			0.0133002
$599$	31.5591			1.28947			0.644734	−	0.764407i	$-0.276968\pi$
$599$	31.5591			1.28947			0.644734	+	0.764407i	$0.276968\pi$
$600$	−4.47366	+	0.795153i	−0.182636	+	0.0324620i
$601$	17.2897	+	29.9467i	0.705262	+	1.22155i	0.966597	+	0.256301i	$0.0825039\pi$
$601$	17.2897	+	29.9467i	0.705262	+	1.22155i	−0.261335	+	0.965248i	$0.584163\pi$
$602$	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
$605$	1.48987	−	2.58053i	0.0605719	−	0.104914i
$606$	23.0511	−	4.09713i	0.936387	−	0.166434i
$607$	−16.5863	−	28.7283i	−0.673217	−	1.16605i	−0.976987	−	0.213301i	$-0.931578\pi$
$607$	−16.5863	−	28.7283i	−0.673217	−	1.16605i	0.303769	−	0.952746i	$-0.401755\pi$
$608$	−0.945791	+	1.63816i	−0.0383569	+	0.0664361i
$609$	−38.4346	−	15.2484i	−1.55745	−	0.617895i
$610$	−2.84850	−	4.93374i	−0.115332	−	0.199761i
$611$	0.0583308	−	0.101032i	0.00235981	−	0.00408732i
$612$	4.93711	−	1.81231i	0.199571	−	0.0732583i
$613$	−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	$0.945625\pi$
$614$	9.21420			0.371855
$615$	5.26788	+	6.26056i	0.212421	+	0.252450i
$616$	16.7204	+	10.3342i	0.673682	+	0.416376i
$617$	1.83717	−	3.18206i	0.0739615	−	0.128105i	−0.826673	−	0.562683i	$-0.809769\pi$
$617$	1.83717	−	3.18206i	0.0739615	−	0.128105i	0.900634	+	0.434578i	$0.143102\pi$
$618$	0.539252	−	1.48793i	0.0216919	−	0.0598532i
$619$	−17.3735	+	30.0917i	−0.698299	+	1.20949i	0.270757	+	0.962648i	$0.412726\pi$
$619$	−17.3735	+	30.0917i	−0.698299	+	1.20949i	−0.969056	+	0.246841i	$0.920607\pi$
$620$	−1.19258	−	2.06562i	−0.0478953	−	0.0829571i
$621$	14.5325	+	8.31081i	0.583168	+	0.333501i
$622$	37.2165			1.49225
$623$	15.4193	+	9.53003i	0.617760	+	0.381813i
$624$	0.509391	−	0.0905397i	0.0203920	−	0.00362449i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	38.6796			1.54595
$627$	−2.23229	+	6.15942i	−0.0891489	+	0.245984i
$628$	2.54364			0.101502
$629$	−19.1893			−0.765126
$630$	−3.76719	−	11.2992i	−0.150088	−	0.450170i
$631$	−31.6609			−1.26040			−0.630201	−	0.776432i	$-0.717027\pi$
$631$	−31.6609			−1.26040			−0.630201	+	0.776432i	$0.717027\pi$
$632$	−30.0810			−1.19656
$633$	−2.38205	+	0.423389i	−0.0946781	+	0.0168282i
$634$	−14.0760			−0.559029
$635$	−7.86897	−	13.6294i	−0.312270	−	0.540868i
$636$	−2.01320	+	5.55492i	−0.0798287	+	0.220267i
$637$	−0.259483	+	0.392972i	−0.0102811	+	0.0155701i
$638$	38.3454			1.51811
$639$	4.56011	−	26.2829i	0.180395	−	1.03974i
$640$	−6.48465	−	11.2317i	−0.256328	−	0.443974i
$641$	−20.6089	+	35.6956i	−0.814001	+	1.40989i	0.0960419	+	0.995377i	$0.469382\pi$
$641$	−20.6089	+	35.6956i	−0.814001	+	1.40989i	−0.910043	+	0.414514i	$0.863952\pi$
$642$	17.8606	−	3.17456i	0.704900	−	0.125290i
$643$	24.5575	−	42.5348i	0.968452	−	1.67741i	0.268413	−	0.963304i	$-0.413501\pi$
$643$	24.5575	−	42.5348i	0.968452	−	1.67741i	0.700039	−	0.714105i	$-0.253166\pi$
$644$	1.89016	−	1.01696i	0.0744827	−	0.0400737i
$645$	−13.5208	+	2.40320i	−0.532381	+	0.0946260i
$646$	−13.9539			−0.549007
$647$	−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	$0.861045\pi$
$648$	22.2302	+	7.95334i	0.873286	+	0.312437i
$649$	−9.72913	+	16.8513i	−0.381902	+	0.661473i
$650$	0.0504751	+	0.0874254i	0.00197980	+	0.00342911i
$651$	−34.0377	+	26.9393i	−1.33404	+	1.05583i
$652$	0.327861	−	0.567872i	0.0128400	−	0.0222396i
$653$	5.85460	+	10.1405i	0.229108	+	0.396827i	0.957544	−	0.288287i	$-0.0930856\pi$
$653$	5.85460	+	10.1405i	0.229108	+	0.396827i	−0.728436	+	0.685114i	$0.759752\pi$
$654$	−15.9334	+	43.9641i	−0.623044	+	1.71913i
$655$	−2.53794	+	4.39585i	−0.0991657	+	0.171760i
$656$	−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	0.914739	−	0.404046i	$-0.132396\pi$
$659$	2.75850	+	4.77786i	0.107456	+	0.186119i	−0.807283	+	0.590164i	$0.799063\pi$
$660$	0.795216	+	0.945067i	0.0309538	+	0.0367867i
$661$	−30.0223			−1.16773			−0.583865	−	0.811850i	$-0.698460\pi$
$661$	−30.0223			−1.16773			−0.583865	+	0.811850i	$0.698460\pi$
$662$	43.8264			1.70336
$663$	0.522307	+	0.620731i	0.0202847	+	0.0241072i
$664$	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
$668$	−1.04014	+	1.80158i	−0.0402443	+	0.0697051i
$669$	0.872184	−	2.40657i	0.0337206	−	0.0930433i
$670$	−2.73884	−	4.74382i	−0.105811	−	0.183270i
$671$	5.37583	−	9.31120i	0.207531	−	0.359455i
$672$	5.08907	−	4.02776i	0.196315	−	0.155374i
$673$	11.1215	+	19.2630i	0.428703	+	0.742535i	0.996758	−	0.0804552i	$-0.0256374\pi$
$673$	11.1215	+	19.2630i	0.428703	+	0.742535i	−0.568055	+	0.822990i	$0.692304\pi$
$674$	−3.33315	+	5.77319i	−0.128388	+	0.222375i
$675$	0.0213745	+	5.19611i	0.000822705	+	0.199998i
$676$	1.63613	+	2.83385i	0.0629279	+	0.108994i
$677$	33.0519			1.27029			0.635144	−	0.772394i	$-0.280941\pi$
$677$	33.0519			1.27029			0.635144	+	0.772394i	$0.280941\pi$
$678$	−41.6109	+	7.39597i	−1.59806	+	0.284040i
$679$	6.78761	−	3.65192i	0.260484	−	0.140148i
$680$	9.13215	−	15.8173i	0.350202	−	0.606567i
$681$	−7.98972	+	1.42010i	−0.306167	+	0.0544184i
$682$	20.1277	−	34.8622i	0.770728	−	1.33494i
$683$	−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	$-0.343889\pi$
$684$	0.774656	+	0.646402i	0.0296197	+	0.0247158i
$685$	−2.36168			−0.0902351
$686$	−2.49740	+	27.6791i	−0.0953512	+	1.05679i
$687$	−12.8913	+	35.5702i	−0.491834	+	1.35709i
$688$	−17.6022	−	30.4880i	−0.671079	−	1.16234i
$689$	−0.911387			−0.0347211
$690$	−8.24465	+	1.46541i	−0.313868	+	0.0557873i
$691$	1.90577			0.0724989			0.0362494	−	0.999343i	$-0.488459\pi$
$691$	1.90577			0.0724989			0.0362494	+	0.999343i	$0.488459\pi$
$692$	−4.05465			−0.154135
$693$	14.9126	−	16.8193i	0.566485	−	0.638913i
$694$	10.9982			0.417485
$695$	6.91923			0.262461
$696$	−13.9696	+	38.5454i	−0.529515	+	1.46106i
$697$	−32.8886			−1.24575
$698$	−16.4956	−	28.5712i	−0.624367	−	1.08144i
$699$	−10.9558	+	1.94730i	−0.414386	+	0.0736535i
$700$	0.566695	+	0.350252i	0.0214191	+	0.0132383i
$701$	10.3758			0.391887			0.195944	−	0.980615i	$-0.437223\pi$
$701$	10.3758			0.391887			0.195944	+	0.980615i	$0.437223\pi$
$702$	−0.00215776	−	0.524548i	−8.14394e−5	−	0.0197978i
$703$	−1.84062	−	3.18805i	−0.0694203	−	0.120240i
$704$	9.56532	−	16.5676i	0.360507	−	0.624416i
$705$	−1.02343	+	2.82390i	−0.0385446	+	0.106354i
$706$	−19.3484	+	33.5123i	−0.728185	+	1.26125i
$707$	20.2729	+	12.5299i	0.762440	+	0.471234i
$708$	1.92931	+	2.29286i	0.0725077	+	0.0861711i
$709$	40.7128			1.52900			0.764501	−	0.644622i	$-0.222985\pi$
$709$	40.7128			1.52900			0.764501	+	0.644622i	$0.222985\pi$
$710$	6.67156	+	11.5555i	0.250379	+	0.433670i
$711$	−5.88055	+	33.8935i	−0.220538	+	1.27111i
$712$	8.98658	−	15.5652i	0.336786	−	0.583331i
$713$	15.2593	+	26.4299i	0.571466	+	0.989808i
$714$	44.5020	+	17.6555i	1.66545	+	0.660742i
$715$	−0.0952591	+	0.164994i	−0.00356249	+	0.00617041i
$716$	1.42851	+	2.47424i	0.0533858	+	0.0924669i
$717$	23.9439	−	4.25581i	0.894200	−	0.158936i
$718$	1.57974	−	2.73620i	0.0589555	−	0.102114i
$719$	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
$723$	18.6029	−	3.30650i	0.691848	−	0.122970i
$724$	−4.94217			−0.183674
$725$	−9.02306			−0.335108
$726$	2.63886	−	7.28126i	0.0979373	−	0.270233i
$727$	10.5553	+	18.2823i	0.391473	+	0.678052i	0.992644	−	0.121069i	$-0.0386322\pi$
$727$	10.5553	+	18.2823i	0.391473	+	0.678052i	−0.601171	+	0.799121i	$0.705299\pi$
$728$	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
$731$	27.6002	−	47.8050i	1.02083	−	1.76813i
$732$	−1.06604	−	1.26692i	−0.0394019	−	0.0468268i
$733$	−1.90259	−	3.29538i	−0.0702738	−	0.121718i	0.828747	−	0.559623i	$-0.189054\pi$
$733$	−1.90259	−	3.29538i	−0.0702738	−	0.121718i	−0.899021	+	0.437905i	$0.855721\pi$
$734$	−4.19386	+	7.26398i	−0.154798	+	0.268118i
$735$	4.80711	−	11.1307i	0.177313	−	0.410561i
$736$	−2.28146	−	3.95160i	−0.0840957	−	0.145658i
$737$	5.16888	−	8.95277i	0.190398	−	0.329779i
$738$	16.3281	+	13.6248i	0.601046	+	0.501535i
$739$	−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	$0.868413\pi$
$740$	−0.694010			−0.0255123
$741$	−0.0530271	+	0.146315i	−0.00194800	+	0.00537500i
$742$	−47.3662	+	25.4843i	−1.73887	+	0.935557i
$743$	21.7701	−	37.7069i	0.798667	−	1.38333i	−0.121818	−	0.992552i	$-0.538872\pi$
$743$	21.7701	−	37.7069i	0.798667	−	1.38333i	0.920485	−	0.390779i	$-0.127794\pi$
$744$	27.7113	+	32.9333i	1.01595	+	1.20739i
$745$	−0.997645	+	1.72797i	−0.0365509	+	0.0633080i
$746$	−3.78896	−	6.56267i	−0.138724	−	0.240277i
$747$	30.4564	−	11.1799i	1.11434	−	0.409051i
$748$	−4.96473			−0.181528
$749$	15.7079	+	9.70845i	0.573955	+	0.354739i
$750$	−1.67341	−	1.98874i	−0.0611042	−	0.0726187i
$751$	−15.4964	−	26.8405i	−0.565471	−	0.979425i	−0.997006	−	0.0773286i	$-0.975361\pi$
$751$	−15.4964	−	26.8405i	−0.565471	−	0.979425i	0.431534	−	0.902097i	$-0.357972\pi$
$752$	−7.69995			−0.280788
$753$	−29.6330	−	35.2170i	−1.07989	−	1.28338i
$754$	0.910880			0.0331723
$755$	5.07189			0.184585
$756$	−1.65267	−	3.04168i	−0.0601072	−	0.110625i
$757$	−20.4941			−0.744870			−0.372435	−	0.928058i	$-0.621477\pi$
$757$	−20.4941			−0.744870			−0.372435	+	0.928058i	$0.621477\pi$
$758$	−0.516127			−0.0187466
$759$	−10.1749	−	12.0923i	−0.369327	−	0.438923i
$760$	3.50380			0.127096
$761$	20.7102	+	35.8711i	0.750744	+	1.30033i	0.947463	+	0.319866i	$0.103638\pi$
$761$	20.7102	+	35.8711i	0.750744	+	1.30033i	−0.196719	+	0.980460i	$0.563029\pi$
$762$	−26.3360	−	31.2987i	−0.954052	−	1.13383i
$763$	−41.9192	+	22.5537i	−1.51758	+	0.816497i
$764$	4.80702			0.173912
$765$	−16.0368	−	13.3817i	−0.579813	−	0.483817i
$766$	1.34961	+	2.33760i	0.0487635	+	0.0844609i
$767$	−0.231112	+	0.400297i	−0.00834496	+	0.0144539i
$768$	−6.63677	−	7.88741i	−0.239484	−	0.284612i
$769$	4.59954	−	7.96663i	0.165864	−	0.287284i	−0.771098	−	0.636716i	$-0.780292\pi$
$769$	4.59954	−	7.96663i	0.165864	−	0.287284i	0.936962	+	0.349432i	$0.113626\pi$
$770$	−0.337197	+	11.2386i	−0.0121517	+	0.405011i
$771$	9.47536	−	26.1448i	0.341247	−	0.941583i
$772$	0.563470			0.0202797
$773$	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	$0.576424\pi$
$774$	−33.5067	+	12.2996i	−1.20437	+	0.442101i
$775$	−4.73625	+	8.20342i	−0.170131	+	0.294676i
$776$	−3.82120	−	6.61852i	−0.137173	−	0.237591i
$777$	1.83638	+	12.4963i	0.0658798	+	0.448302i
$778$	20.8943	−	36.1900i	0.749097	−	1.29747i
$779$	−3.15466	−	5.46402i	−0.113027	−	0.195769i
$780$	0.0188901	+	0.0224497i	0.000676373	+	0.000803829i
$781$	−12.5909	+	21.8081i	−0.450538	+	0.780355i
$782$	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
$786$	−4.49521	+	12.4034i	−0.160339	+	0.442414i
$787$	−30.6403			−1.09221			−0.546104	−	0.837718i	$-0.683890\pi$
$787$	−30.6403			−1.09221			−0.546104	+	0.837718i	$0.683890\pi$
$788$	2.90826			0.103603
$789$	−0.877441	+	0.155957i	−0.0312377	+	0.00555223i
$790$	−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
$794$	−22.9991	+	39.8356i	−0.816207	+	1.41371i
$795$	23.1029	−	4.10634i	0.819377	−	0.145637i
$796$	0.807208	+	1.39813i	0.0286107	+	0.0495553i
$797$	−20.3117	+	35.1808i	−0.719476	+	1.24617i	0.241731	+	0.970343i	$0.422285\pi$
$797$	−20.3117	+	35.1808i	−0.719476	+	1.24617i	−0.961208	+	0.275826i	$0.911049\pi$
$798$	1.33536	+	9.08695i	0.0472713	+	0.321674i
$799$	−6.03674	−	10.4559i	−0.213565	−	0.369905i
$800$	0.708129	−	1.22651i	0.0250361	−	0.0433638i
$801$	−15.7812	−	13.1684i	−0.557601	−	0.465283i
$802$	−19.7541	−	34.2150i	−0.697540	−	1.20817i
$803$	14.6158			0.515781
$804$	−1.02500	−	1.21815i	−0.0361490	−	0.0429609i
$805$	−7.25097	−	4.48153i	−0.255563	−	0.157953i
$806$	0.478125	−	0.828137i	0.0168412	−	0.0291699i
$807$	11.0933	−	30.6092i	0.390504	−	1.07750i
$808$	11.8153	−	20.4648i	0.415662	−	0.719948i
$809$	−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	$0.895237\pi$
$810$	2.41810	+	13.2872i	0.0849634	+	0.466863i
$811$	−1.78517			−0.0626857			−0.0313428	−	0.999509i	$-0.509978\pi$
$811$	−1.78517			−0.0626857			−0.0313428	+	0.999509i	$0.509978\pi$
$812$	5.29360	−	2.84810i	0.185769	−	0.0999487i
$813$	−29.4651	+	5.23716i	−1.03339	+	0.183675i
$814$	−5.85653	−	10.1438i	−0.205271	−	0.355540i
$815$	−2.60415			−0.0912193
$816$	18.2441	−	50.3398i	0.638670	−	1.76225i
$817$	10.5896			0.370482
$818$	−7.55069			−0.264004
$819$	0.354244	−	0.399536i	0.0123783	−	0.0139609i
$820$	−1.18947			−0.0415381
$821$	−24.6305			−0.859609			−0.429805	−	0.902922i	$-0.641418\pi$
$821$	−24.6305			−0.859609			−0.429805	+	0.902922i	$0.641418\pi$
$822$	−6.04355	+	1.07419i	−0.210793	+	0.0374666i
$823$	40.9102			1.42604			0.713020	−	0.701144i	$-0.247327\pi$
$823$	40.9102			1.42604			0.713020	+	0.701144i	$0.247327\pi$
$824$	−0.798693	−	1.38338i	−0.0278238	−	0.0481922i
$825$	1.67135	−	4.61166i	0.0581889	−	0.160557i
$826$	−0.818087	+	27.2664i	−0.0284649	+	0.948720i
$827$	−45.5340			−1.58337			−0.791686	−	0.610928i	$-0.790797\pi$
$827$	−45.5340			−1.58337			−0.791686	+	0.610928i	$0.790797\pi$
$828$	−2.28469	+	0.838661i	−0.0793984	+	0.0291455i
$829$	−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	$-0.373071\pi$
$830$	−8.11413	+	14.0541i	−0.281645	+	0.487824i
$831$	25.9695	−	4.61585i	0.900872	−	0.160122i
$832$	0.227221	−	0.393558i	0.00787746	−	0.0136442i
$833$	21.7935	+	43.5911i	0.755100	+	1.51034i
$834$	17.7063	−	3.14715i	0.613121	−	0.108977i
$835$	8.26167			0.285907
$836$	−0.476213	−	0.824826i	−0.0164702	−	0.0285272i
$837$	42.5247	−	24.7854i	1.46987	−	0.856709i
$838$	−15.4871	+	26.8245i	−0.534993	+	0.926635i
$839$	−10.8976	−	18.8751i	−0.376226	−	0.651642i	0.614284	−	0.789085i	$-0.289445\pi$
$839$	−10.8976	−	18.8751i	−0.376226	−	0.651642i	−0.990510	+	0.137443i	$0.956112\pi$
$840$	−11.1744	−	4.43328i	−0.385553	−	0.152963i
$841$	−26.2078	+	45.3933i	−0.903718	+	1.56529i
$842$	−18.4185	−	31.9019i	−0.634745	−	1.09941i
$843$	9.29449	−	25.6458i	0.320119	−	0.883287i
$844$	0.175861	−	0.304600i	0.00605338	−	0.0104848i
$845$	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
$849$	13.7962	+	16.3960i	0.473484	+	0.562708i
$850$	10.4475			0.358346
$851$	8.87998			0.304402
$852$	2.49680	+	2.96730i	0.0855390	+	0.101658i
$853$	−18.3064	−	31.7076i	−0.626800	−	1.08565i	−0.988190	−	0.153234i	$-0.951031\pi$
$853$	−18.3064	−	31.7076i	−0.626800	−	1.08565i	0.361390	−	0.932415i	$-0.382302\pi$
$854$	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
$857$	9.29661	−	16.1022i	0.317566	−	0.550041i	−0.662413	−	0.749138i	$-0.730468\pi$
$857$	9.29661	−	16.1022i	0.317566	−	0.550041i	0.979980	+	0.199098i	$0.0638011\pi$
$858$	−0.168723	+	0.465548i	−0.00576010	+	0.0158935i
$859$	−20.1855	−	34.9623i	−0.688720	−	1.19290i	−0.972252	−	0.233936i	$-0.924840\pi$
$859$	−20.1855	−	34.9623i	−0.688720	−	1.19290i	0.283532	−	0.958963i	$-0.408494\pi$
$860$	0.998206	−	1.72894i	0.0340385	−	0.0589565i
$861$	3.14739	+	21.4175i	0.107263	+	0.729907i
$862$	−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	$0.188004\pi$
$864$	−6.35797	+	3.70573i	−0.216302	+	0.126071i
$865$	8.05135	+	13.9453i	0.273754	+	0.474156i
$866$	−61.8980			−2.10338
$867$	53.6704	−	9.53944i	1.82274	−	0.323976i
$868$	0.189254	−	6.30772i	0.00642369	−	0.214098i
$869$	16.2368	−	28.1229i	0.550795	−	0.954005i
$870$	−23.0901	+	4.10406i	−0.782827	+	0.139141i
$871$	0.122785	−	0.212670i	0.00416041	−	0.00720604i
$872$	23.5992	+	40.8749i	0.799168	+	1.38420i
$873$	−8.20438	+	3.01165i	−0.277676	+	0.101929i
$874$	6.45726			0.218420
$875$	0.0793460	−	2.64456i	0.00268239	−	0.0894025i
$876$	0.766930	−	2.11615i	0.0259122	−	0.0714980i
$877$	20.0285	+	34.6904i	0.676314	+	1.17141i	0.976083	+	0.217399i	$0.0697572\pi$
$877$	20.0285	+	34.6904i	0.676314	+	1.17141i	−0.299768	+	0.954012i	$0.596909\pi$
$878$	48.6194			1.64082
$879$	30.0313	−	5.33779i	1.01293	−	0.180039i
$880$	12.5747			0.423892
$881$	−11.5557			−0.389322			−0.194661	−	0.980871i	$-0.562361\pi$
$881$	−11.5557			−0.389322			−0.194661	+	0.980871i	$0.562361\pi$
$882$	7.23875	−	30.6699i	0.243741	−	1.03271i
$883$	2.50842			0.0844149			0.0422075	−	0.999109i	$-0.486561\pi$
$883$	2.50842			0.0844149			0.0422075	+	0.999109i	$0.486561\pi$
$884$	−0.117935			−0.00396659
$885$	4.05492	−	11.1885i	0.136305	−	0.376098i
$886$	−22.8648			−0.768157
$887$	−7.79813	−	13.5068i	−0.261836	−	0.453513i	0.704894	−	0.709313i	$-0.250994\pi$
$887$	−7.79813	−	13.5068i	−0.261836	−	0.453513i	−0.966730	+	0.255800i	$0.917661\pi$
$888$	12.3303	−	2.19160i	0.413778	−	0.0735454i
$889$	1.24874	−	41.6199i	0.0418815	−	1.39589i
$890$	10.2809			0.344618
$891$	−19.4348	+	16.4902i	−0.651091	+	0.552444i
$892$	0.186063	+	0.322270i	0.00622985	+	0.0107904i
$893$	1.15808	−	2.00585i	0.0387537	−	0.0671234i
$894$	−1.76703	+	4.87566i	−0.0590983	+	0.163067i
$895$	5.67319	−	9.82626i	0.189634	−	0.328456i
$896$	1.02906	−	34.2981i	0.0343786	−	1.14582i
$897$	−0.241702	−	0.287248i	−0.00807019	−	0.00959094i
$898$	10.9693			0.366049
$899$	42.7355	+	74.0200i	1.42531	+	2.46871i
$900$	−0.579998	−	0.483972i	−0.0193333	−	0.0161324i
$901$	−47.1604	+	81.6842i	−1.57114	+	2.72129i
$902$	−10.0376	−	17.3856i	−0.334214	−	0.578876i
$903$	−33.7725	−	13.3988i	−1.12388	−	0.445883i
$904$	−21.3286	+	36.9422i	−0.709378	+	1.22868i
$905$	9.81372	+	16.9979i	0.326219	+	0.565028i
$906$	12.9790	−	2.30690i	0.431199	−	0.0766417i
$907$	−28.0845	+	48.6439i	−0.932532	+	1.61519i	−0.153555	+	0.988140i	$0.549072\pi$
$907$	−28.0845	+	48.6439i	−0.932532	+	1.61519i	−0.778977	+	0.627053i	$0.784261\pi$
$908$	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	0.753871	−	0.657022i	$-0.228184\pi$
$911$	−5.79696	−	10.0406i	−0.192062	−	0.332661i	−0.945933	+	0.324361i	$0.894851\pi$
$912$	10.1133	−	1.79754i	0.334884	−	0.0595226i
$913$	−30.6268			−1.01360
$914$	−45.6029			−1.50841
$915$	−2.24055	+	6.18221i	−0.0740701	+	0.204378i
$916$	−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	$0.272500\pi$
$920$	−4.22597	+	7.31960i	−0.139326	+	0.241320i
$921$	−6.84746	−	8.13780i	−0.225631	−	0.268150i
$922$	−15.0264	−	26.0265i	−0.494868	−	0.857136i
$923$	−0.299092	+	0.518043i	−0.00984474	+	0.0170516i
$924$	0.475116	+	3.23310i	0.0156302	+	0.106361i
$925$	1.37810	+	2.38694i	0.0453117	+	0.0784822i
$926$	−28.3528	+	49.1084i	−0.931730	+	1.61380i
$927$	−1.71485	+	0.629485i	−0.0563230	+	0.0206750i
$928$	−6.38949	−	11.0669i	−0.209745	−	0.363289i
$929$	3.87177			0.127029			0.0635143	−	0.997981i	$-0.479769\pi$
$929$	3.87177			0.127029			0.0635143	+	0.997981i	$0.479769\pi$
$930$	−8.38884	+	23.1469i	−0.275081	+	0.759016i
$931$	−5.15169	+	7.80194i	−0.168840	+	0.255698i
$932$	0.808838	−	1.40095i	0.0264944	−	0.0458896i
$933$	−27.6572	−	32.8689i	−0.905454	−	1.07608i
$934$	−19.4935	+	33.7638i	−0.637847	+	1.10478i
$935$	9.85850	+	17.0754i	0.322407	+	0.558426i
$936$	−0.406509	−	0.339206i	−0.0132872	−	0.0110873i
$937$	39.5281			1.29133			0.645663	−	0.763623i	$-0.276581\pi$
$937$	39.5281			1.29133			0.645663	+	0.763623i	$0.276581\pi$
$938$	0.434633	−	14.4861i	0.0141913	−	0.472987i
$939$	−28.7445	−	34.1611i	−0.938040	−	1.11480i
$940$	−0.218328	−	0.378156i	−0.00712109	−	0.0123341i
$941$	−1.99861			−0.0651528			−0.0325764	−	0.999469i	$-0.510371\pi$
$941$	−1.99861			−0.0651528			−0.0325764	+	0.999469i	$0.510371\pi$
$942$	−16.9045	−	20.0900i	−0.550779	−	0.654568i
$943$	15.2195			0.495614
$944$	30.5079			0.992946
$945$	−7.17966	+	11.7240i	−0.233554	+	0.381382i
$946$	33.6942			1.09549
$947$	−3.87615			−0.125958			−0.0629790	−	0.998015i	$-0.520060\pi$
$947$	−3.87615			−0.125958			−0.0629790	+	0.998015i	$0.520060\pi$
$948$	−3.21979	−	3.82652i	−0.104574	−	0.124280i
$949$	0.347193			0.0112704
$950$	1.00212	+	1.73571i	0.0325129	+	0.0563140i
$951$	10.4605	+	12.4316i	0.339204	+	0.403123i
$952$	42.5545	−	22.8955i	1.37920	−	0.742047i
$953$	−10.7772			−0.349108			−0.174554	−	0.984648i	$-0.555848\pi$
$953$	−10.7772			−0.349108			−0.174554	+	0.984648i	$0.555848\pi$
$954$	57.2528	−	21.0163i	1.85363	−	0.680428i
$955$	−9.54534	−	16.5330i	−0.308880	−	0.534996i
$956$	−1.76771	+	3.06177i	−0.0571719	+	0.0990247i
$957$	−28.4961	−	33.8659i	−0.921147	−	1.09473i
$958$	20.7892	−	36.0079i	0.671667	−	1.16336i
$959$	−5.31516	−	3.28509i	−0.171635	−	0.106081i
$960$	−3.98665	+	11.0001i	−0.128669	+	0.355028i
$961$	58.7282			1.89446
$962$	−0.139120	−	0.240962i	−0.00448540	−	0.00776894i
$963$	−16.0767	−	13.4150i	−0.518063	−	0.432291i
$964$	−1.37340	+	2.37880i	−0.0442343	+	0.0766161i
$965$	−1.11889	−	1.93797i	−0.0360183	−	0.0623855i
$966$	−20.5937	−	8.17024i	−0.662590	−	0.262873i
$967$	17.7351	−	30.7180i	0.570321	−	0.987826i	−0.426211	−	0.904624i	$-0.640152\pi$
$967$	17.7351	−	30.7180i	0.570321	−	0.987826i	0.996533	−	0.0832021i	$-0.0265147\pi$
$968$	−3.90845	−	6.76964i	−0.125622	−	0.217585i
$969$	10.3697	+	12.3238i	0.333123	+	0.395897i
$970$	2.18579	−	3.78590i	0.0701815	−	0.121558i
$971$	−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
$975$	0.0397022	−	0.109548i	0.00127149	−	0.00350835i
$976$	−16.8571			−0.539583
$977$	−12.9989			−0.415871			−0.207936	−	0.978143i	$-0.566674\pi$
$977$	−12.9989			−0.415871			−0.207936	+	0.978143i	$0.566674\pi$
$978$	−6.66403	+	1.18447i	−0.213092	+	0.0378752i
$979$	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
$983$	−26.8398	+	46.4880i	−0.856058	+	1.48274i	0.0196026	+	0.999808i	$0.493760\pi$
$983$	−26.8398	+	46.4880i	−0.856058	+	1.48274i	−0.875660	+	0.482928i	$0.839573\pi$
$984$	21.1330	−	3.75621i	0.673696	−	0.119744i
$985$	−5.77496	−	10.0025i	−0.184006	−	0.318707i
$986$	47.1341	−	81.6387i	1.50106	−	2.59991i
$987$	−6.23135	+	4.93183i	−0.198346	+	0.156982i
$988$	−0.0113123	−	0.0195934i	−0.000359891	−	0.000623350i
$989$	−12.7722	+	22.1221i	−0.406133	+	0.703443i
$990$	2.17942	−	12.5615i	0.0692666	−	0.399229i
$991$	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	$0.745876\pi$
$992$	−13.4155			−0.425942
$993$	−32.5693	−	38.7066i	−1.03355	−	1.22832i
$994$	−1.05872	+	35.2867i	−0.0335807	+	1.11923i
$995$	3.20576	−	5.55254i	0.101629	−	0.176027i
$996$	−1.60707	+	4.43429i	−0.0509219	+	0.140506i
$997$	−5.12930	+	8.88421i	−0.162447	+	0.281366i	−0.935746	−	0.352676i	$-0.885272\pi$
$997$	−5.12930	+	8.88421i	−0.162447	+	0.281366i	0.773299	+	0.634042i	$0.218605\pi$
$998$	1.46133	+	2.53109i	0.0462575	+	0.0801203i
$999$	−0.0589125	−	14.3215i	−0.00186391	−	0.453113i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.6	✓	36	9.7	even	3
315.2.k.c.256.6	yes	36	7.4	even	3
315.2.l.c.121.13	yes	36	1.1	even	1	trivial
315.2.l.c.151.13	yes	36	63.25	even	3	inner
945.2.k.c.361.13		36	21.11	odd	6
945.2.k.c.856.13		36	9.2	odd	6
945.2.l.c.46.6		36	63.11	odd	6
945.2.l.c.226.6		36	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.50060 q^{2} +(-1.11516 - 1.32530i) q^{3} +0.251799 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.67341 - 1.98874i) q^{6} +(0.0793460 - 2.64456i) q^{7} -2.62335 q^{8} +(-0.512840 + 2.95584i) q^{9} +O(q^{10})\)	\(q+1.50060 q^{2} +(-1.11516 - 1.32530i) q^{3} +0.251799 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.67341 - 1.98874i) q^{6} +(0.0793460 - 2.64456i) q^{7} -2.62335 q^{8} +(-0.512840 + 2.95584i) q^{9} +(-0.750300 - 1.29956i) q^{10} +(1.41600 - 2.45259i) q^{11} +(-0.280796 - 0.333710i) q^{12} +(0.0336366 - 0.0582603i) q^{13} +(0.119067 - 3.96843i) q^{14} +(-0.590164 + 1.62841i) q^{15} -4.44020 q^{16} +(-3.48110 - 6.02944i) q^{17} +(-0.769568 + 4.43553i) q^{18} +(0.667810 - 1.15668i) q^{19} +(-0.125900 - 0.218065i) q^{20} +(-3.59332 + 2.84395i) q^{21} +(2.12485 - 3.68035i) q^{22} +(1.61091 + 2.79017i) q^{23} +(2.92545 + 3.47673i) q^{24} +(-0.500000 + 0.866025i) 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} +(-0.885600 + 2.44359i) q^{30} +9.47250 q^{31} -1.41626 q^{32} +(-4.82948 + 0.858398i) 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} +(1.00212 - 1.73571i) q^{38} +(-0.114723 + 0.0203909i) q^{39} +(1.31167 + 2.27189i) q^{40} +(2.36194 - 4.09100i) q^{41} +(-5.39214 + 4.26763i) q^{42} +(3.96429 + 6.86635i) q^{43} +(0.356548 - 0.617560i) q^{44} +(2.81625 - 1.03379i) q^{45} +(2.41733 + 4.18693i) q^{46} +1.73415 q^{47} +(4.95152 + 5.88459i) q^{48} +(-6.98741 - 0.419671i) q^{49} +(-0.750300 + 1.29956i) q^{50} +(-4.10884 + 11.3373i) q^{51} +(0.00846968 - 0.0146699i) q^{52} +(-6.77377 - 11.7325i) q^{53} +(6.73660 - 3.92642i) q^{54} -2.83201 q^{55} +(-0.208152 + 6.93761i) q^{56} +(-2.27766 + 0.404834i) q^{57} +(6.77000 + 11.7260i) q^{58} -6.87084 q^{59} +(-0.148603 + 0.410031i) q^{60} +3.79648 q^{61} +14.2144 q^{62} +(7.77621 + 1.59077i) q^{63} +6.75516 q^{64} -0.0672732 q^{65} +(-7.24712 + 1.28811i) q^{66} +3.65033 q^{67} +(-0.876539 - 1.51821i) q^{68} +(1.90140 - 5.24642i) q^{69} +(-3.49629 + 1.88110i) q^{70} -8.89186 q^{71} +(1.34536 - 7.75420i) q^{72} +(2.58047 + 4.46951i) q^{73} +(2.06798 - 3.58185i) q^{74} +(1.70532 - 0.303106i) q^{75} +(0.168154 - 0.291251i) q^{76} +(-6.37367 - 3.93931i) q^{77} +(-0.172153 + 0.0305986i) q^{78} +11.4666 q^{79} +(2.22010 + 3.84532i) q^{80} +(-8.47399 - 3.03175i) q^{81} +(3.54433 - 6.13895i) q^{82} +(-5.40726 - 9.36564i) q^{83} +(-0.904795 + 0.716104i) q^{84} +(-3.48110 + 6.02944i) q^{85} +(5.94881 + 10.3036i) q^{86} +(5.32509 - 14.6932i) q^{87} +(-3.71467 + 6.43400i) 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} +(-10.5633 - 12.5539i) q^{93} +2.60226 q^{94} -1.33562 q^{95} +(1.57935 + 1.87697i) q^{96} +(1.45661 + 2.52293i) q^{97} +(-10.4853 - 0.629758i) q^{98} +(6.52328 + 5.44327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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