LMFDB - Embedded newform 315.2.l.c.121.4

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			121.4
Character	$\chi$	$=$	315.121
Dual form			315.2.l.c.151.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69039 q^{2} +(-1.59654 - 0.671613i) q^{3} +0.857411 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.69877 + 1.13529i) q^{6} +(2.40616 - 1.10017i) q^{7} +1.93142 q^{8} +(2.09787 + 2.14451i) q^{9} +O(q^{10})$	\(q-1.69039 q^{2} +(-1.59654 - 0.671613i) q^{3} +0.857411 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.69877 + 1.13529i) q^{6} +(2.40616 - 1.10017i) q^{7} +1.93142 q^{8} +(2.09787 + 2.14451i) q^{9} +(0.845194 + 1.46392i) q^{10} +(-2.27246 + 3.93601i) q^{11} +(-1.36889 - 0.575848i) q^{12} +(1.58483 - 2.74501i) q^{13} +(-4.06735 + 1.85972i) q^{14} +(0.216636 + 1.71845i) q^{15} -4.97967 q^{16} +(-2.83608 - 4.91224i) q^{17} +(-3.54622 - 3.62506i) q^{18} +(1.70155 - 2.94717i) q^{19} +(-0.428706 - 0.742540i) q^{20} +(-4.58042 + 0.140463i) q^{21} +(3.84133 - 6.65338i) q^{22} +(0.0116662 + 0.0202064i) q^{23} +(-3.08358 - 1.29716i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.67898 + 4.64013i) q^{26} +(-1.90906 - 4.83275i) q^{27} +(2.06307 - 0.943302i) q^{28} +(-5.17048 - 8.95554i) q^{29} +(-0.366199 - 2.90485i) q^{30} +1.71913 q^{31} +4.55473 q^{32} +(6.27154 - 4.75778i) q^{33} +(4.79408 + 8.30360i) q^{34} +(-2.15586 - 1.53371i) q^{35} +(1.79874 + 1.83873i) q^{36} +(-3.52326 + 6.10247i) q^{37} +(-2.87628 + 4.98186i) q^{38} +(-4.37383 + 3.31812i) q^{39} +(-0.965709 - 1.67266i) q^{40} +(-3.45798 + 5.98939i) q^{41} +(7.74269 - 0.237437i) q^{42} +(-4.52050 - 7.82973i) q^{43} +(-1.94843 + 3.37478i) q^{44} +(0.808265 - 2.88907i) q^{45} +(-0.0197204 - 0.0341567i) q^{46} -1.23962 q^{47} +(7.95023 + 3.34441i) q^{48} +(4.57923 - 5.29440i) q^{49} +(0.845194 - 1.46392i) q^{50} +(1.22880 + 9.74734i) q^{51} +(1.35885 - 2.35360i) q^{52} +(-5.10622 - 8.84423i) q^{53} +(3.22704 + 8.16923i) q^{54} +4.54491 q^{55} +(4.64731 - 2.12490i) q^{56} +(-4.69595 + 3.56249i) q^{57} +(8.74012 + 15.1383i) q^{58} +9.28756 q^{59} +(0.185746 + 1.47342i) q^{60} -8.57851 q^{61} -2.90599 q^{62} +(7.40716 + 2.85201i) q^{63} +2.26007 q^{64} -3.16967 q^{65} +(-10.6013 + 8.04249i) q^{66} -1.50255 q^{67} +(-2.43169 - 4.21181i) q^{68} +(-0.00505463 - 0.0400955i) q^{69} +(3.64424 + 2.59257i) q^{70} +9.66372 q^{71} +(4.05187 + 4.14195i) q^{72} +(-5.85704 - 10.1447i) q^{73} +(5.95568 - 10.3155i) q^{74} +(1.37990 - 1.04684i) q^{75} +(1.45893 - 2.52694i) q^{76} +(-1.13760 + 11.9708i) q^{77} +(7.39347 - 5.60892i) q^{78} -2.16538 q^{79} +(2.48983 + 4.31252i) q^{80} +(-0.197856 + 8.99782i) q^{81} +(5.84532 - 10.1244i) q^{82} +(3.75755 + 6.50826i) q^{83} +(-3.92730 + 0.120434i) q^{84} +(-2.83608 + 4.91224i) q^{85} +(7.64139 + 13.2353i) q^{86} +(2.24022 + 17.7704i) q^{87} +(-4.38906 + 7.60208i) q^{88} +(4.27846 - 7.41051i) q^{89} +(-1.36628 + 4.88364i) q^{90} +(0.793374 - 8.34854i) q^{91} +(0.0100027 + 0.0173252i) q^{92} +(-2.74465 - 1.15459i) q^{93} +2.09544 q^{94} -3.40310 q^{95} +(-7.27181 - 3.05902i) q^{96} +(-0.533838 - 0.924635i) q^{97} +(-7.74068 + 8.94958i) q^{98} +(-13.2081 + 3.38394i) 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 $

$2$	−1.69039			−1.19528			−0.597642	−	0.801763i	$-0.703896\pi$
$2$	−1.69039			−1.19528			−0.597642	+	0.801763i	$0.703896\pi$
$3$	−1.59654	−	0.671613i	−0.921762	−	0.387756i
$3$	−1.59654	−	0.671613i	−0.921762	−	0.387756i
$4$	0.857411			0.428706
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.69877	+	1.13529i	1.10177	+	0.463478i
$7$	2.40616	−	1.10017i	0.909444	−	0.415827i
$7$	2.40616	−	1.10017i	0.909444	−	0.415827i
$8$	1.93142			0.682860
$9$	2.09787	+	2.14451i	0.699291	+	0.714837i
$10$	0.845194	+	1.46392i	0.267274	+	0.462932i
$11$	−2.27246	+	3.93601i	−0.685171	+	1.18675i	0.288212	+	0.957567i	$0.406939\pi$
$11$	−2.27246	+	3.93601i	−0.685171	+	1.18675i	−0.973383	+	0.229184i	$0.926394\pi$
$12$	−1.36889	−	0.575848i	−0.395165	−	0.166233i
$13$	1.58483	−	2.74501i	0.439554	−	0.761329i	−0.558101	−	0.829773i	$-0.688470\pi$
$13$	1.58483	−	2.74501i	0.439554	−	0.761329i	0.997655	+	0.0684435i	$0.0218033\pi$
$14$	−4.06735	+	1.85972i	−1.08704	+	0.497031i
$15$	0.216636	+	1.71845i	0.0559352	+	0.443702i
$16$	−4.97967			−1.24492
$17$	−2.83608	−	4.91224i	−0.687852	−	1.19139i	−0.972532	−	0.232771i	$-0.925221\pi$
$17$	−2.83608	−	4.91224i	−0.687852	−	1.19139i	0.284680	−	0.958623i	$-0.408113\pi$
$18$	−3.54622	−	3.62506i	−0.835852	−	0.854434i
$19$	1.70155	−	2.94717i	0.390362	−	0.676127i	−0.602135	−	0.798394i	$-0.705683\pi$
$19$	1.70155	−	2.94717i	0.390362	−	0.676127i	0.992497	+	0.122267i	$0.0390164\pi$
$20$	−0.428706	−	0.742540i	−0.0958615	−	0.166037i
$21$	−4.58042	+	0.140463i	−0.999530	+	0.0306515i
$22$	3.84133	−	6.65338i	0.818974	−	1.41851i
$23$	0.0116662	+	0.0202064i	0.00243257	+	0.00421333i	0.867239	−	0.497892i	$-0.165892\pi$
$23$	0.0116662	+	0.0202064i	0.00243257	+	0.00421333i	−0.864807	+	0.502105i	$0.832559\pi$
$24$	−3.08358	−	1.29716i	−0.629434	−	0.264783i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.67898	+	4.64013i	−0.525392	+	0.910005i
$27$	−1.90906	−	4.83275i	−0.367398	−	0.930064i
$28$	2.06307	−	0.943302i	0.389884	−	0.178267i
$29$	−5.17048	−	8.95554i	−0.960134	−	1.66300i	−0.722155	−	0.691731i	$-0.756848\pi$
$29$	−5.17048	−	8.95554i	−0.960134	−	1.66300i	−0.237979	−	0.971270i	$-0.576485\pi$
$30$	−0.366199	−	2.90485i	−0.0668584	−	0.530350i
$31$	1.71913			0.308764			0.154382	−	0.988011i	$-0.450661\pi$
$31$	1.71913			0.308764			0.154382	+	0.988011i	$0.450661\pi$
$32$	4.55473			0.805171
$33$	6.27154	−	4.75778i	1.09173	−	0.828223i
$34$	4.79408	+	8.30360i	0.822178	+	1.42405i
$35$	−2.15586	−	1.53371i	−0.364407	−	0.259244i
$36$	1.79874	+	1.83873i	0.299790	+	0.306455i
$37$	−3.52326	+	6.10247i	−0.579220	+	1.00324i	0.416349	+	0.909205i	$0.363310\pi$
$37$	−3.52326	+	6.10247i	−0.579220	+	1.00324i	−0.995569	+	0.0940340i	$0.970024\pi$
$38$	−2.87628	+	4.98186i	−0.466594	+	0.808165i
$39$	−4.37383	+	3.31812i	−0.700374	+	0.531325i
$40$	−0.965709	−	1.67266i	−0.152692	−	0.264470i
$41$	−3.45798	+	5.98939i	−0.540045	+	0.935386i	0.458856	+	0.888511i	$0.348259\pi$
$41$	−3.45798	+	5.98939i	−0.540045	+	0.935386i	−0.998901	+	0.0468747i	$0.985074\pi$
$42$	7.74269	−	0.237437i	1.19472	−	0.0366373i
$43$	−4.52050	−	7.82973i	−0.689369	−	1.19402i	−0.972042	−	0.234806i	$-0.924554\pi$
$43$	−4.52050	−	7.82973i	−0.689369	−	1.19402i	0.282673	−	0.959216i	$-0.408779\pi$
$44$	−1.94843	+	3.37478i	−0.293737	+	0.508767i
$45$	0.808265	−	2.88907i	0.120489	−	0.430677i
$46$	−0.0197204	−	0.0341567i	−0.00290761	−	0.00503613i
$47$	−1.23962			−0.180817			−0.0904085	−	0.995905i	$-0.528817\pi$
$47$	−1.23962			−0.180817			−0.0904085	+	0.995905i	$0.528817\pi$
$48$	7.95023	+	3.34441i	1.14752	+	0.482724i
$49$	4.57923	−	5.29440i	0.654176	−	0.756342i
$50$	0.845194	−	1.46392i	0.119528	−	0.207029i
$51$	1.22880	+	9.74734i	0.172066	+	1.36490i
$52$	1.35885	−	2.35360i	0.188439	−	0.326386i
$53$	−5.10622	−	8.84423i	−0.701393	−	1.21485i	−0.967977	−	0.251037i	$-0.919228\pi$
$53$	−5.10622	−	8.84423i	−0.701393	−	1.21485i	0.266584	−	0.963812i	$-0.414105\pi$
$54$	3.22704	+	8.16923i	0.439145	+	1.11169i
$55$	4.54491			0.612836
$56$	4.64731	−	2.12490i	0.621022	−	0.283951i
$57$	−4.69595	+	3.56249i	−0.621993	+	0.471863i
$58$	8.74012	+	15.1383i	1.14763	+	1.98776i
$59$	9.28756			1.20914			0.604569	−	0.796553i	$-0.293345\pi$
$59$	9.28756			1.20914			0.604569	+	0.796553i	$0.293345\pi$
$60$	0.185746	+	1.47342i	0.0239797	+	0.190217i
$61$	−8.57851			−1.09837			−0.549183	−	0.835702i	$-0.685061\pi$
$61$	−8.57851			−1.09837			−0.549183	+	0.835702i	$0.685061\pi$
$62$	−2.90599			−0.369061
$63$	7.40716	+	2.85201i	0.933214	+	0.359320i
$64$	2.26007			0.282509
$65$	−3.16967			−0.393149
$66$	−10.6013	+	8.04249i	−1.30493	+	0.989963i
$67$	−1.50255			−0.183566			−0.0917828	−	0.995779i	$-0.529257\pi$
$67$	−1.50255			−0.183566			−0.0917828	+	0.995779i	$0.529257\pi$
$68$	−2.43169	−	4.21181i	−0.294886	−	0.510757i
$69$	−0.00505463	−	0.0400955i	−0.000608506	−	0.00482693i
$70$	3.64424	+	2.59257i	0.435570	+	0.309871i
$71$	9.66372			1.14687			0.573436	−	0.819250i	$-0.305610\pi$
$71$	9.66372			1.14687			0.573436	+	0.819250i	$0.305610\pi$
$72$	4.05187	+	4.14195i	0.477518	+	0.488133i
$73$	−5.85704	−	10.1447i	−0.685515	−	1.18735i	−0.973275	−	0.229644i	$-0.926244\pi$
$73$	−5.85704	−	10.1447i	−0.685515	−	1.18735i	0.287760	−	0.957703i	$-0.407090\pi$
$74$	5.95568	−	10.3155i	0.692333	−	1.19916i
$75$	1.37990	−	1.04684i	0.159337	−	0.120878i
$76$	1.45893	−	2.52694i	0.167350	−	0.289860i
$77$	−1.13760	+	11.9708i	−0.129642	+	1.36420i
$78$	7.39347	−	5.60892i	0.837146	−	0.635085i
$79$	−2.16538			−0.243624			−0.121812	−	0.992553i	$-0.538871\pi$
$79$	−2.16538			−0.243624			−0.121812	+	0.992553i	$0.538871\pi$
$80$	2.48983	+	4.31252i	0.278372	+	0.482154i
$81$	−0.197856	+	8.99782i	−0.0219840	+	0.999758i
$82$	5.84532	−	10.1244i	0.645508	−	1.11805i
$83$	3.75755	+	6.50826i	0.412444	+	0.714374i	0.995156	−	0.0983042i	$-0.0313418\pi$
$83$	3.75755	+	6.50826i	0.412444	+	0.714374i	−0.582712	+	0.812679i	$0.698008\pi$
$84$	−3.92730	+	0.120434i	−0.428504	+	0.0131405i
$85$	−2.83608	+	4.91224i	−0.307617	+	0.532808i
$86$	7.64139	+	13.2353i	0.823993	+	1.42720i
$87$	2.24022	+	17.7704i	0.240177	+	1.90519i
$88$	−4.38906	+	7.60208i	−0.467876	+	0.810384i
$89$	4.27846	−	7.41051i	0.453516	−	0.785513i	−0.545086	−	0.838380i	$-0.683503\pi$
$89$	4.27846	−	7.41051i	0.453516	−	0.785513i	0.998602	+	0.0528677i	$0.0168362\pi$
$90$	−1.36628	+	4.88364i	−0.144019	+	0.514781i
$91$	0.793374	−	8.34854i	0.0831682	−	0.875165i
$92$	0.0100027	+	0.0173252i	0.00104286	+	0.00180628i
$93$	−2.74465	−	1.15459i	−0.284607	−	0.119725i
$94$	2.09544			0.216128
$95$	−3.40310			−0.349151
$96$	−7.27181	−	3.05902i	−0.742176	−	0.312210i
$97$	−0.533838	−	0.924635i	−0.0542030	−	0.0938824i	0.837651	−	0.546206i	$-0.183928\pi$
$97$	−0.533838	−	0.924635i	−0.0542030	−	0.0938824i	−0.891854	+	0.452324i	$0.850595\pi$
$98$	−7.74068	+	8.94958i	−0.781927	+	0.904044i
$99$	−13.2081	+	3.38394i	−1.32747	+	0.340099i
$100$	−0.428706	+	0.742540i	−0.0428706	+	0.0742540i
$101$	1.39121	−	2.40964i	0.138430	−	0.239768i	−0.788472	−	0.615070i	$-0.789128\pi$
$101$	1.39121	−	2.40964i	0.138430	−	0.239768i	0.926903	+	0.375302i	$0.122461\pi$
$102$	−2.07714	−	16.4768i	−0.205668	−	1.63144i
$103$	1.95861	+	3.39241i	0.192987	+	0.334264i	0.946239	−	0.323469i	$-0.104849\pi$
$103$	1.95861	+	3.39241i	0.192987	+	0.334264i	−0.753252	+	0.657732i	$0.771516\pi$
$104$	3.06098	−	5.30177i	0.300153	−	0.519881i
$105$	2.41186	+	3.89653i	0.235373	+	0.380262i
$106$	8.63149	+	14.9502i	0.838365	+	1.45209i
$107$	6.29531	−	10.9038i	0.608591	−	1.05411i	−0.382882	−	0.923797i	$-0.625069\pi$
$107$	6.29531	−	10.9038i	0.608591	−	1.05411i	0.991473	−	0.130313i	$-0.0415981\pi$
$108$	−1.63685	−	4.14366i	−0.157506	−	0.398723i
$109$	−0.0916666	−	0.158771i	−0.00878007	−	0.0152075i	0.861602	−	0.507584i	$-0.169461\pi$
$109$	−0.0916666	−	0.158771i	−0.00878007	−	0.0152075i	−0.870382	+	0.492377i	$0.836128\pi$
$110$	−7.68266			−0.732513
$111$	9.72351	−	7.37656i	0.922915	−	0.700152i
$112$	−11.9819	+	5.47850i	−1.13218	+	0.517670i
$113$	−1.24821	+	2.16197i	−0.117422	+	0.203381i	−0.918745	−	0.394851i	$-0.870796\pi$
$113$	−1.24821	+	2.16197i	−0.117422	+	0.203381i	0.801323	+	0.598231i	$0.204130\pi$
$114$	7.93797	−	6.02199i	0.743459	−	0.564011i
$115$	0.0116662	−	0.0202064i	0.00108788	−	0.00188426i
$116$	−4.43323	−	7.67858i	−0.411615	−	0.712938i
$117$	9.21149	−	2.35999i	0.851602	−	0.218182i
$118$	−15.6996			−1.44526
$119$	−12.2284	−	8.69946i	−1.12098	−	0.797479i
$120$	0.418415	+	3.31905i	0.0381959	+	0.302986i
$121$	−4.82811	−	8.36252i	−0.438919	−	0.760230i
$122$	14.5010			1.31286
$123$	9.54334	−	7.23987i	0.860494	−	0.652797i
$124$	1.47400			0.132369
$125$	1.00000			0.0894427
$126$	−12.5210	−	4.82101i	−1.11546	−	0.429490i
$127$	−0.0467625			−0.00414950			−0.00207475	−	0.999998i	$-0.500660\pi$
$127$	−0.0467625			−0.00414950			−0.00207475	+	0.999998i	$0.500660\pi$
$128$	−12.9299			−1.14285
$129$	1.95860	+	15.5365i	0.172446	+	1.36791i
$130$	5.35797			0.469925
$131$	−5.07491	−	8.79001i	−0.443397	−	0.767986i	0.554542	−	0.832156i	$-0.312894\pi$
$131$	−5.07491	−	8.79001i	−0.443397	−	0.767986i	−0.997939	+	0.0641694i	$0.979560\pi$
$132$	5.37728	−	4.07937i	0.468032	−	0.355064i
$133$	0.851803	−	8.96337i	0.0738607	−	0.777223i
$134$	2.53989			0.219413
$135$	−3.23076	+	4.06967i	−0.278059	+	0.350261i
$136$	−5.47767	−	9.48760i	−0.469706	−	0.813555i
$137$	7.79451	−	13.5005i	0.665930	−	1.15342i	−0.313102	−	0.949719i	$-0.601368\pi$
$137$	7.79451	−	13.5005i	0.665930	−	1.15342i	0.979032	−	0.203705i	$-0.0652984\pi$
$138$	0.00854429	+	0.0677770i	0.000727338	+	0.00576956i
$139$	7.81319	−	13.5328i	0.662706	−	1.14784i	−0.317195	−	0.948360i	$-0.602741\pi$
$139$	7.81319	−	13.5328i	0.662706	−	1.14784i	0.979902	−	0.199481i	$-0.0639255\pi$
$140$	−1.84846	−	1.31502i	−0.156223	−	0.111139i
$141$	1.97910	+	0.832544i	0.166670	+	0.0701128i
$142$	−16.3354			−1.37084
$143$	7.20293	+	12.4758i	0.602339	+	1.04328i
$144$	−10.4467	−	10.6790i	−0.870559	−	0.889913i
$145$	−5.17048	+	8.95554i	−0.429385	+	0.743717i
$146$	9.90067	+	17.1485i	0.819385	+	1.41922i
$147$	−10.8667	+	5.37724i	−0.896271	+	0.443507i
$148$	−3.02088	+	5.23232i	−0.248315	+	0.430094i
$149$	−3.59545	−	6.22750i	−0.294551	−	0.510177i	0.680329	−	0.732906i	$-0.261837\pi$
$149$	−3.59545	−	6.22750i	−0.294551	−	0.510177i	−0.974880	+	0.222729i	$0.928503\pi$
$150$	−2.33257	+	1.76956i	−0.190454	+	0.144484i
$151$	−7.01309	+	12.1470i	−0.570717	+	0.988511i	0.425776	+	0.904829i	$0.360001\pi$
$151$	−7.01309	+	12.1470i	−0.570717	+	0.988511i	−0.996493	+	0.0836819i	$0.973332\pi$
$152$	3.28640	−	5.69222i	0.266563	−	0.461700i
$153$	4.58461	−	16.3873i	0.370644	−	1.32483i
$154$	1.92299	−	20.2352i	0.154959	−	1.63060i
$155$	−0.859563	−	1.48881i	−0.0690418	−	0.119584i
$156$	−3.75017	+	2.84500i	−0.300254	+	0.227782i
$157$	1.67984			0.134066			0.0670331	−	0.997751i	$-0.478647\pi$
$157$	1.67984			0.134066			0.0670331	+	0.997751i	$0.478647\pi$
$158$	3.66033			0.291200
$159$	2.21238	+	17.5496i	0.175453	+	1.39177i
$160$	−2.27737	−	3.94452i	−0.180042	−	0.311841i
$161$	0.0503014	+	0.0357851i	0.00396430	+	0.00282026i
$162$	0.334453	−	15.2098i	0.0262771	−	1.19500i
$163$	−12.4167	+	21.5063i	−0.972550	+	1.68451i	−0.284755	+	0.958600i	$0.591912\pi$
$163$	−12.4167	+	21.5063i	−0.972550	+	1.68451i	−0.687795	+	0.725905i	$0.741421\pi$
$164$	−2.96491	+	5.13537i	−0.231520	+	0.401005i
$165$	−7.25613	−	3.05242i	−0.564889	−	0.237630i
$166$	−6.35171	−	11.0015i	−0.492988	−	0.853881i
$167$	−6.89385	+	11.9405i	−0.533462	+	0.923983i	0.465774	+	0.884904i	$0.345776\pi$
$167$	−6.89385	+	11.9405i	−0.533462	+	0.923983i	−0.999236	+	0.0390794i	$0.987557\pi$
$168$	−8.84671	+	0.271292i	−0.682539	+	0.0209307i
$169$	1.47661	+	2.55756i	0.113585	+	0.196735i
$170$	4.79408	−	8.30360i	0.367689	−	0.636857i
$171$	9.88988	−	2.53380i	0.756298	−	0.193764i
$172$	−3.87592	−	6.71330i	−0.295536	−	0.511884i
$173$	−0.177782			−0.0135165			−0.00675825	−	0.999977i	$-0.502151\pi$
$173$	−0.177782			−0.0135165			−0.00675825	+	0.999977i	$0.502151\pi$
$174$	−3.78685	−	30.0389i	−0.287080	−	2.27724i
$175$	−0.250302	+	2.63388i	−0.0189211	+	0.199103i
$176$	11.3161	−	19.6000i	0.852981	−	1.47741i
$177$	−14.8280	−	6.23765i	−1.11454	−	0.468850i
$178$	−7.23226	+	12.5266i	−0.542081	+	0.938911i
$179$	4.93863	+	8.55396i	0.369131	+	0.639353i	0.989430	−	0.145012i	$-0.0463221\pi$
$179$	4.93863	+	8.55396i	0.369131	+	0.639353i	−0.620299	+	0.784365i	$0.712989\pi$
$180$	0.693015	−	2.47712i	0.0516543	−	0.184633i
$181$	−11.8350			−0.879692			−0.439846	−	0.898073i	$-0.644967\pi$
$181$	−11.8350			−0.879692			−0.439846	+	0.898073i	$0.644967\pi$
$182$	−1.34111	+	14.1123i	−0.0994097	+	1.04607i
$183$	13.6959	+	5.76144i	1.01243	+	0.425898i
$184$	0.0225323	+	0.0390271i	0.00166110	+	0.00287711i
$185$	7.04652			0.518070
$186$	4.63953	+	1.95170i	0.340187	+	0.143106i
$187$	25.7795			1.88518
$188$	−1.06286			−0.0775173
$189$	−9.91037	−	9.52809i	−0.720873	−	0.693067i
$190$	5.75256			0.417334
$191$	18.1867			1.31595			0.657973	−	0.753042i	$-0.271414\pi$
$191$	18.1867			1.31595			0.657973	+	0.753042i	$0.271414\pi$
$192$	−3.60829	−	1.51789i	−0.260406	−	0.109544i
$193$	7.69340			0.553783			0.276892	−	0.960901i	$-0.410696\pi$
$193$	7.69340			0.553783			0.276892	+	0.960901i	$0.410696\pi$
$194$	0.902393	+	1.56299i	0.0647881	+	0.112216i
$195$	5.06050	+	2.12879i	0.362390	+	0.152446i
$196$	3.92628	−	4.53947i	0.280449	−	0.324248i
$197$	3.01874			0.215077			0.107538	−	0.994201i	$-0.465703\pi$
$197$	3.01874			0.215077			0.107538	+	0.994201i	$0.465703\pi$
$198$	22.3269	−	5.72017i	1.58670	−	0.406515i
$199$	−1.00850	−	1.74678i	−0.0714908	−	0.123826i	0.828064	−	0.560634i	$-0.189442\pi$
$199$	−1.00850	−	1.74678i	−0.0714908	−	0.123826i	−0.899555	+	0.436808i	$0.856109\pi$
$200$	−0.965709	+	1.67266i	−0.0682860	+	0.118275i
$201$	2.39888	+	1.00913i	0.169204	+	0.0711786i
$202$	−2.35168	+	4.07323i	−0.165464	+	0.286591i
$203$	−22.2937	−	15.8600i	−1.56471	−	1.11316i
$204$	1.05358	+	8.35747i	0.0737656	+	0.585140i
$205$	6.91595			0.483031
$206$	−3.31081	−	5.73448i	−0.230675	−	0.399540i
$207$	−0.0188587	+	0.0674088i	−0.00131077	+	0.00468524i
$208$	−7.89194	+	13.6692i	−0.547208	+	0.947792i
$209$	7.73339	+	13.3946i	0.534930	+	0.926526i
$210$	−4.07697	−	6.58665i	−0.281338	−	0.454522i
$211$	−2.69724	+	4.67175i	−0.185686	+	0.321617i	−0.943807	−	0.330496i	$-0.892784\pi$
$211$	−2.69724	+	4.67175i	−0.185686	+	0.321617i	0.758122	+	0.652113i	$0.226117\pi$
$212$	−4.37813	−	7.58314i	−0.300691	−	0.520812i
$213$	−15.4285	−	6.49028i	−1.05714	−	0.444706i
$214$	−10.6415	+	18.4316i	−0.727439	+	1.25996i
$215$	−4.52050	+	7.82973i	−0.308295	+	0.533983i
$216$	−3.68719	−	9.33407i	−0.250881	−	0.635103i
$217$	4.13650	−	1.89134i	0.280804	−	0.128392i
$218$	0.154952	+	0.268385i	0.0104947	+	0.0181773i
$219$	2.53769	+	20.1301i	0.171481	+	1.36026i
$220$	3.89686			0.262726
$221$	−17.9789			−1.20939
$222$	−16.4365	+	12.4692i	−1.10315	+	0.836881i
$223$	8.93044	+	15.4680i	0.598026	+	1.03581i	0.993112	+	0.117168i	$0.0373816\pi$
$223$	8.93044	+	15.4680i	0.598026	+	1.03581i	−0.395086	+	0.918644i	$0.629285\pi$
$224$	10.9594	−	5.01100i	0.732258	−	0.334812i
$225$	−2.90614	+	0.744556i	−0.193743	+	0.0496371i
$226$	2.10996	−	3.65456i	0.140353	−	0.243098i
$227$	−0.802948	+	1.39075i	−0.0532936	+	0.0923071i	−0.891441	−	0.453136i	$-0.850305\pi$
$227$	−0.802948	+	1.39075i	−0.0532936	+	0.0923071i	0.838148	+	0.545443i	$0.183639\pi$
$228$	−4.02636	+	3.05452i	−0.266652	+	0.202290i
$229$	8.52404	+	14.7641i	0.563285	+	0.975638i	0.997207	+	0.0746875i	$0.0237959\pi$
$229$	8.52404	+	14.7641i	0.563285	+	0.975638i	−0.433922	+	0.900950i	$0.642871\pi$
$230$	−0.0197204	+	0.0341567i	−0.00130032	+	0.00225223i
$231$	9.85594	−	18.3478i	0.648473	−	1.20719i
$232$	−9.98636	−	17.2969i	−0.655637	−	1.13560i
$233$	7.03185	−	12.1795i	0.460672	−	0.797907i	−0.538323	−	0.842739i	$-0.680942\pi$
$233$	7.03185	−	12.1795i	0.460672	−	0.797907i	0.998995	+	0.0448319i	$0.0142752\pi$
$234$	−15.5710	+	3.98931i	−1.01791	+	0.260789i
$235$	0.619810	+	1.07354i	0.0404319	+	0.0700301i
$236$	7.96326			0.518364
$237$	3.45711	+	1.45430i	0.224564	+	0.0944667i
$238$	20.6707	+	14.7055i	1.33989	+	0.953214i
$239$	−13.9148	+	24.1011i	−0.900072	+	1.55897i	−0.0726720	+	0.997356i	$0.523153\pi$
$239$	−13.9148	+	24.1011i	−0.900072	+	1.55897i	−0.827400	+	0.561614i	$0.810181\pi$
$240$	−1.07878	−	8.55731i	−0.0696346	−	0.552372i
$241$	11.4257	−	19.7899i	0.735993	−	1.27478i	−0.218293	−	0.975883i	$-0.570049\pi$
$241$	11.4257	−	19.7899i	0.735993	−	1.27478i	0.954286	−	0.298894i	$-0.0966177\pi$
$242$	8.16137	+	14.1359i	0.524633	+	0.908691i
$243$	6.35894	−	14.2325i	0.407926	−	0.913015i
$244$	−7.35531			−0.470876
$245$	−6.87470	−	1.31853i	−0.439208	−	0.0842380i
$246$	−16.1319	+	12.2382i	−1.02854	+	0.780279i
$247$	−5.39335	−	9.34155i	−0.343170	−	0.594389i
$248$	3.32035			0.210843
$249$	−1.62804	−	12.9143i	−0.103173	−	0.818411i
$250$	−1.69039			−0.106910
$251$	−0.248772			−0.0157023			−0.00785116	−	0.999969i	$-0.502499\pi$
$251$	−0.248772			−0.0157023			−0.00785116	+	0.999969i	$0.502499\pi$
$252$	6.35098	+	2.44535i	0.400074	+	0.154043i
$253$	−0.106044			−0.00666690
$254$	0.0790468			0.00495984
$255$	7.82704	−	5.93784i	0.490148	−	0.371842i
$256$	17.3363			1.08352
$257$	−3.99195	−	6.91426i	−0.249011	−	0.431300i	0.714241	−	0.699900i	$-0.246772\pi$
$257$	−3.99195	−	6.91426i	−0.249011	−	0.431300i	−0.963252	+	0.268600i	$0.913439\pi$
$258$	−3.31080	−	26.2627i	−0.206121	−	1.63504i
$259$	−1.76376	+	18.5597i	−0.109595	+	1.15324i
$260$	−2.71771			−0.168545
$261$	8.35823	−	29.8757i	0.517362	−	1.84926i
$262$	8.57857	+	14.8585i	0.529986	+	0.917962i
$263$	−5.44323	+	9.42795i	−0.335644	+	0.581352i	−0.983608	−	0.180318i	$-0.942287\pi$
$263$	−5.44323	+	9.42795i	−0.335644	+	0.581352i	0.647964	+	0.761671i	$0.275621\pi$
$264$	12.1130	−	9.18927i	0.745501	−	0.565560i
$265$	−5.10622	+	8.84423i	−0.313673	+	0.543297i
$266$	−1.43988	+	15.1516i	−0.0882845	+	0.929003i
$267$	−11.8077	+	8.95770i	−0.722621	+	0.548203i
$268$	−1.28830			−0.0786956
$269$	2.62440	+	4.54560i	0.160013	+	0.277150i	0.934873	−	0.354982i	$-0.115513\pi$
$269$	2.62440	+	4.54560i	0.160013	+	0.277150i	−0.774860	+	0.632133i	$0.782180\pi$
$270$	5.46124	−	6.87932i	0.332360	−	0.418662i
$271$	6.85608	−	11.8751i	0.416477	−	0.721359i	−0.579105	−	0.815253i	$-0.696598\pi$
$271$	6.85608	−	11.8751i	0.416477	−	0.721359i	0.995582	+	0.0938934i	$0.0299313\pi$
$272$	14.1228	+	24.4613i	0.856318	+	1.48319i
$273$	−6.87363	+	12.7959i	−0.416011	+	0.774445i
$274$	−13.1757	+	22.8211i	−0.795976	+	1.37867i
$275$	−2.27246	−	3.93601i	−0.137034	−	0.237350i
$276$	−0.00433390	−	0.0343783i	−0.000260870	−	0.00206933i
$277$	−4.32108	+	7.48433i	−0.259629	+	0.449690i	−0.966142	−	0.258009i	$-0.916933\pi$
$277$	−4.32108	+	7.48433i	−0.259629	+	0.449690i	0.706514	+	0.707699i	$0.250267\pi$
$278$	−13.2073	+	22.8758i	−0.792123	+	1.37200i
$279$	3.60651	+	3.68669i	0.215916	+	0.220716i
$280$	−4.16387	−	2.96224i	−0.248839	−	0.177027i
$281$	15.4694	+	26.7938i	0.922829	+	1.59839i	0.795017	+	0.606588i	$0.207462\pi$
$281$	15.4694	+	26.7938i	0.922829	+	1.59839i	0.127812	+	0.991798i	$0.459205\pi$
$282$	−3.34545	−	1.40732i	−0.199218	−	0.0838048i
$283$	5.65731			0.336292			0.168146	−	0.985762i	$-0.446222\pi$
$283$	5.65731			0.336292			0.168146	+	0.985762i	$0.446222\pi$
$284$	8.28578			0.491671
$285$	5.43318	+	2.28556i	0.321834	+	0.135385i
$286$	−12.1757	−	21.0890i	−0.719967	−	1.24702i
$287$	−1.73108	+	18.2158i	−0.102182	+	1.07525i
$288$	9.55525	+	9.76768i	0.563049	+	0.575566i
$289$	−7.58675	+	13.1406i	−0.446280	+	0.772979i
$290$	8.74012	−	15.1383i	0.513237	−	0.888953i
$291$	0.231297	+	1.83475i	0.0135589	+	0.107555i
$292$	−5.02189	−	8.69817i	−0.293884	−	0.509022i
$293$	7.09988	−	12.2974i	0.414779	−	0.718419i	−0.580626	−	0.814170i	$-0.697192\pi$
$293$	7.09988	−	12.2974i	0.414779	−	0.718419i	0.995405	+	0.0957516i	$0.0305254\pi$
$294$	18.3689	−	9.08962i	1.07130	−	0.530117i
$295$	−4.64378	−	8.04327i	−0.270371	−	0.468297i
$296$	−6.80489	+	11.7864i	−0.395526	+	0.685071i
$297$	23.3600	+	3.46816i	1.35548	+	0.201243i
$298$	6.07771	+	10.5269i	0.352072	+	0.609807i
$299$	0.0739559			0.00427698
$300$	1.18314	−	0.897570i	0.0683089	−	0.0518212i
$301$	−19.4911	−	13.8663i	−1.12345	−	0.799238i
$302$	11.8548	−	20.5332i	0.682169	−	1.18155i
$303$	−3.83946	+	2.91273i	−0.220571	+	0.167332i
$304$	−8.47315	+	14.6759i	−0.485969	+	0.841722i
$305$	4.28926	+	7.42921i	0.245602	+	0.425395i
$306$	−7.74977	+	27.7009i	−0.443025	+	1.58355i
$307$	10.5235			0.600606			0.300303	−	0.953844i	$-0.402912\pi$
$307$	10.5235			0.600606			0.300303	+	0.953844i	$0.402912\pi$
$308$	−0.975391	+	10.2639i	−0.0555781	+	0.584838i
$309$	−0.848609	−	6.73153i	−0.0482757	−	0.382944i
$310$	1.45300	+	2.51666i	0.0825246	+	0.142937i
$311$	27.8947			1.58176			0.790882	−	0.611969i	$-0.209622\pi$
$311$	27.8947			1.58176			0.790882	+	0.611969i	$0.209622\pi$
$312$	−8.44770	+	6.40869i	−0.478257	+	0.362820i
$313$	29.5855			1.67227			0.836137	−	0.548521i	$-0.184809\pi$
$313$	29.5855			1.67227			0.836137	+	0.548521i	$0.184809\pi$
$314$	−2.83959			−0.160247
$315$	−1.23366	−	7.84080i	−0.0695090	−	0.441779i
$316$	−1.85662			−0.104443
$317$	−5.50750			−0.309332			−0.154666	−	0.987967i	$-0.549430\pi$
$317$	−5.50750			−0.309332			−0.154666	+	0.987967i	$0.549430\pi$
$318$	−3.73978	−	29.6656i	−0.209717	−	1.66356i
$319$	46.9987			2.63142
$320$	−1.13004	−	1.95728i	−0.0631709	−	0.109415i
$321$	−17.3738	+	13.1803i	−0.969713	+	0.735654i
$322$	−0.0850288	−	0.0604907i	−0.00473847	−	0.00337102i
$323$	−19.3030			−1.07405
$324$	−0.169644	+	7.71483i	−0.00942466	+	0.428602i
$325$	1.58483	+	2.74501i	0.0879107	+	0.152266i
$326$	20.9890	−	36.3540i	1.16247	−	2.01346i
$327$	0.0397166	+	0.315049i	0.00219633	+	0.0174222i
$328$	−6.67880	+	11.5680i	−0.368775	+	0.638737i
$329$	−2.98272	+	1.36380i	−0.164443	+	0.0751886i
$330$	12.2657	+	5.15977i	0.675203	+	0.284036i
$331$	9.05172			0.497528			0.248764	−	0.968564i	$-0.419976\pi$
$331$	9.05172			0.497528			0.248764	+	0.968564i	$0.419976\pi$
$332$	3.22176	+	5.58025i	0.176817	+	0.306256i
$333$	−20.4782	+	5.24653i	−1.12220	+	0.287508i
$334$	11.6533	−	20.1841i	0.637639	−	1.10442i
$335$	0.751275	+	1.30125i	0.0410465	+	0.0710947i
$336$	22.8090	−	0.699458i	1.24433	−	0.0381586i
$337$	−4.96159	+	8.59372i	−0.270275	+	0.468130i	−0.968932	−	0.247327i	$-0.920448\pi$
$337$	−4.96159	+	8.59372i	−0.270275	+	0.468130i	0.698657	+	0.715456i	$0.253781\pi$
$338$	−2.49604	−	4.32326i	−0.135766	−	0.235154i
$339$	3.44483	−	2.61335i	0.187097	−	0.141938i
$340$	−2.43169	+	4.21181i	−0.131877	+	0.228418i
$341$	−3.90664	+	6.76650i	−0.211556	+	0.366426i
$342$	−16.7177	+	4.28310i	−0.903991	+	0.231604i
$343$	5.19362	−	17.7771i	0.280429	−	0.959875i
$344$	−8.73097	−	15.1225i	−0.470743	−	0.815350i
$345$	−0.0321964	+	0.0244252i	−0.00173340	+	0.00131501i
$346$	0.300520			0.0161561
$347$	−11.1947			−0.600966			−0.300483	−	0.953787i	$-0.597148\pi$
$347$	−11.1947			−0.600966			−0.300483	+	0.953787i	$0.597148\pi$
$348$	1.92079	+	15.2366i	0.102965	+	0.816765i
$349$	−14.1414	−	24.4937i	−0.756974	−	1.31112i	−0.944387	−	0.328836i	$-0.893344\pi$
$349$	−14.1414	−	24.4937i	−0.756974	−	1.31112i	0.187413	−	0.982281i	$-0.439990\pi$
$350$	0.423107	−	4.45229i	0.0226160	−	0.237985i
$351$	−16.2915	−	2.41873i	−0.869576	−	0.129102i
$352$	−10.3504	+	17.9275i	−0.551680	+	0.955537i
$353$	3.67878	−	6.37183i	0.195802	−	0.339138i	−0.751361	−	0.659891i	$-0.770602\pi$
$353$	3.67878	−	6.37183i	0.195802	−	0.339138i	0.947163	+	0.320753i	$0.103936\pi$
$354$	25.0650	+	10.5440i	1.33219	+	0.560409i
$355$	−4.83186	−	8.36903i	−0.256449	−	0.444182i
$356$	3.66840	−	6.35385i	0.194425	−	0.336754i
$357$	13.6805	+	22.1018i	0.724046	+	1.16975i
$358$	−8.34821	−	14.4595i	−0.441216	−	0.764209i
$359$	10.9914	−	19.0376i	0.580103	−	1.00477i	−0.415363	−	0.909656i	$-0.636345\pi$
$359$	10.9914	−	19.0376i	0.580103	−	1.00477i	0.995467	−	0.0951128i	$-0.0303212\pi$
$360$	1.56110	−	5.58000i	0.0822770	−	0.294092i
$361$	3.70946	+	6.42497i	0.195235	+	0.338156i
$362$	20.0058			1.05148
$363$	2.09188	+	16.5937i	0.109795	+	0.870944i
$364$	0.680248	−	7.15813i	0.0356547	−	0.375188i
$365$	−5.85704	+	10.1447i	−0.306572	+	0.530998i
$366$	−23.1514	−	9.73906i	−1.21014	−	0.509069i
$367$	10.6105	−	18.3780i	0.553866	−	0.959324i	−0.444125	−	0.895965i	$-0.646485\pi$
$367$	10.6105	−	18.3780i	0.553866	−	0.959324i	0.997991	−	0.0633588i	$-0.0201813\pi$
$368$	−0.0580938	−	0.100621i	−0.00302835	−	0.00524525i
$369$	−20.0987	+	5.14931i	−1.04630	+	0.268063i
$370$	−11.9114			−0.619242
$371$	−22.0166	−	15.6629i	−1.14304	−	0.813178i
$372$	−2.35330	−	0.989956i	−0.122013	−	0.0513268i
$373$	−3.60088	−	6.23691i	−0.186446	−	0.322935i	0.757617	−	0.652700i	$-0.226364\pi$
$373$	−3.60088	−	6.23691i	−0.186446	−	0.322935i	−0.944063	+	0.329765i	$0.893030\pi$
$374$	−43.5774			−2.25333
$375$	−1.59654	−	0.671613i	−0.0824449	−	0.0346819i
$376$	−2.39422			−0.123473
$377$	−32.7774			−1.68812
$378$	16.7524	+	16.1062i	0.861649	+	0.828412i
$379$	−4.15827			−0.213596			−0.106798	−	0.994281i	$-0.534060\pi$
$379$	−4.15827			−0.213596			−0.106798	+	0.994281i	$0.534060\pi$
$380$	−2.91786			−0.149683
$381$	0.0746582	+	0.0314063i	0.00382486	+	0.00160899i
$382$	−30.7426			−1.57293
$383$	−14.4280	−	24.9900i	−0.737237	−	1.27693i	−0.953735	−	0.300649i	$-0.902797\pi$
$383$	−14.4280	−	24.9900i	−0.737237	−	1.27693i	0.216498	−	0.976283i	$-0.430537\pi$
$384$	20.6430	+	8.68386i	1.05344	+	0.443146i
$385$	10.9358	−	5.00019i	0.557340	−	0.254834i
$386$	−13.0048			−0.661928
$387$	7.30752	−	26.1200i	0.371462	−	1.32776i
$388$	−0.457719	−	0.792792i	−0.0232371	−	0.0402479i
$389$	5.69766	−	9.86863i	0.288883	−	0.500360i	−0.684661	−	0.728862i	$-0.740050\pi$
$389$	5.69766	−	9.86863i	0.288883	−	0.500360i	0.973543	+	0.228502i	$0.0733829\pi$
$390$	−8.55420	−	3.59848i	−0.433159	−	0.182216i
$391$	0.0661726	−	0.114614i	0.00334649	−	0.00579630i
$392$	8.84441	−	10.2257i	0.446710	−	0.516476i
$393$	2.19882	+	17.4420i	0.110916	+	0.879831i
$394$	−5.10285			−0.257078
$395$	1.08269	+	1.87527i	0.0544761	+	0.0943553i
$396$	−11.3248	+	2.90143i	−0.569093	+	0.145802i
$397$	−1.96186	+	3.39805i	−0.0984632	+	0.170543i	−0.911049	−	0.412299i	$-0.864726\pi$
$397$	−1.96186	+	3.39805i	−0.0984632	+	0.170543i	0.812586	+	0.582842i	$0.198059\pi$
$398$	1.70476	+	2.95273i	0.0854519	+	0.148007i
$399$	−7.37985	+	13.7383i	−0.369455	+	0.687775i
$400$	2.48983	−	4.31252i	0.124492	−	0.215626i
$401$	17.4944	+	30.3012i	0.873629	+	1.51317i	0.858217	+	0.513288i	$0.171573\pi$
$401$	17.4944	+	30.3012i	0.873629	+	1.51317i	0.0154120	+	0.999881i	$0.495094\pi$
$402$	−4.05504	−	1.70582i	−0.202247	−	0.0850787i
$403$	2.72453	−	4.71902i	0.135718	−	0.235071i
$404$	1.19284	−	2.06605i	0.0593458	−	0.102790i
$405$	7.89127	−	4.32756i	0.392121	−	0.215038i
$406$	37.6849	+	26.8096i	1.87027	+	1.33054i
$407$	−16.0129	−	27.7352i	−0.793730	−	1.37478i
$408$	2.37332	+	18.8262i	0.117497	+	0.932035i
$409$	−39.2721			−1.94188			−0.970941	−	0.239319i	$-0.923076\pi$
$409$	−39.2721			−1.94188			−0.970941	+	0.239319i	$0.923076\pi$
$410$	−11.6906			−0.577360
$411$	−21.5113	+	16.3192i	−1.06108	+	0.804965i
$412$	1.67933	+	2.90869i	0.0827347	+	0.143301i
$413$	22.3474	−	10.2179i	1.09964	−	0.502792i
$414$	0.0318786	−	0.113947i	0.00156675	−	0.00560019i
$415$	3.75755	−	6.50826i	0.184451	−	0.319478i
$416$	7.21849	−	12.5028i	0.353916	−	0.613000i
$417$	−21.5629	+	16.3583i	−1.05594	+	0.801068i
$418$	−13.0724	−	22.6421i	−0.639394	−	1.10746i
$419$	−5.62364	+	9.74043i	−0.274733	+	0.475851i	−0.970068	−	0.242835i	$-0.921923\pi$
$419$	−5.62364	+	9.74043i	−0.274733	+	0.475851i	0.695335	+	0.718686i	$0.255256\pi$
$420$	2.06795	+	3.34093i	0.100906	+	0.163021i
$421$	8.87270	+	15.3680i	0.432429	+	0.748989i	0.997082	−	0.0763395i	$-0.0243233\pi$
$421$	8.87270	+	15.3680i	0.432429	+	0.748989i	−0.564653	+	0.825328i	$0.690990\pi$
$422$	4.55938	−	7.89707i	0.221947	−	0.384424i
$423$	−2.60056	−	2.65838i	−0.126444	−	0.129255i
$424$	−9.86225	−	17.0819i	−0.478953	−	0.829571i
$425$	5.67217			0.275141
$426$	26.0802	+	10.9711i	1.26359	+	0.531551i
$427$	−20.6413	+	9.43786i	−0.998902	+	0.456730i
$428$	5.39767	−	9.34903i	0.260906	−	0.451903i
$429$	−3.12083	−	24.7557i	−0.150675	−	1.19522i
$430$	7.64139	−	13.2353i	0.368501	−	0.638262i
$431$	4.73316	+	8.19807i	0.227988	+	0.394887i	0.957212	−	0.289388i	$-0.0934519\pi$
$431$	4.73316	+	8.19807i	0.227988	+	0.394887i	−0.729223	+	0.684276i	$0.760119\pi$
$432$	9.50646	+	24.0655i	0.457380	+	1.15785i
$433$	5.88453			0.282793			0.141396	−	0.989953i	$-0.454841\pi$
$433$	5.88453			0.282793			0.141396	+	0.989953i	$0.454841\pi$
$434$	−6.99228	+	3.19710i	−0.335640	+	0.153466i
$435$	14.2695	−	10.8253i	0.684171	−	0.519034i
$436$	−0.0785959	−	0.136132i	−0.00376406	−	0.00651955i
$437$	0.0794024			0.00379833
$438$	−4.28968	−	34.0276i	−0.204969	−	1.62590i
$439$	−12.9002			−0.615693			−0.307847	−	0.951436i	$-0.599608\pi$
$439$	−12.9002			−0.615693			−0.307847	+	0.951436i	$0.599608\pi$
$440$	8.77812			0.418481
$441$	20.9605	−	1.28676i	0.998121	−	0.0612742i
$442$	30.3913			1.44557
$443$	−13.1893			−0.626644			−0.313322	−	0.949647i	$-0.601442\pi$
$443$	−13.1893			−0.626644			−0.313322	+	0.949647i	$0.601442\pi$
$444$	8.33705	−	6.32474i	0.395659	−	0.300159i
$445$	−8.55692			−0.405637
$446$	−15.0959	−	26.1469i	−0.714812	−	1.23809i
$447$	1.55781	+	12.3572i	0.0736818	+	0.584476i
$448$	5.43810	−	2.48647i	0.256926	−	0.117475i
$449$	−0.602445			−0.0284311			−0.0142156	−	0.999899i	$-0.504525\pi$
$449$	−0.602445			−0.0284311			−0.0142156	+	0.999899i	$0.504525\pi$
$450$	4.91250	−	1.25859i	0.231577	−	0.0593304i
$451$	−15.7162	−	27.2212i	−0.740047	−	1.28180i
$452$	−1.07023	+	1.85370i	−0.0503395	+	0.0871905i
$453$	19.3548	−	14.6831i	0.909366	−	0.689873i
$454$	1.35729	−	2.35090i	0.0637010	−	0.110333i
$455$	−7.62673	+	3.48719i	−0.357547	+	0.163482i
$456$	−9.06984	+	6.88066i	−0.424734	+	0.322216i
$457$	−5.48217			−0.256445			−0.128222	−	0.991745i	$-0.540927\pi$
$457$	−5.48217			−0.256445			−0.128222	+	0.991745i	$0.540927\pi$
$458$	−14.4089	−	24.9570i	−0.673286	−	1.16616i
$459$	−18.3254	+	23.0838i	−0.855357	+	1.07746i
$460$	0.0100027	−	0.0173252i	0.000466379	−	0.000807793i
$461$	−3.76201	−	6.51599i	−0.175214	−	0.303480i	0.765021	−	0.644005i	$-0.222728\pi$
$461$	−3.76201	−	6.51599i	−0.175214	−	0.303480i	−0.940235	+	0.340525i	$0.889395\pi$
$462$	−16.6604	+	31.0149i	−0.775110	+	1.44294i
$463$	17.5231	−	30.3509i	0.814368	−	1.41053i	−0.0954126	−	0.995438i	$-0.530417\pi$
$463$	17.5231	−	30.3509i	0.814368	−	1.41053i	0.909781	−	0.415089i	$-0.136250\pi$
$464$	25.7473	+	44.5956i	1.19529	+	2.07030i
$465$	0.372425	+	2.95423i	0.0172708	+	0.136999i
$466$	−11.8865	+	20.5881i	−0.550634	+	0.953726i
$467$	−6.83839	+	11.8444i	−0.316443	+	0.548095i	−0.979743	−	0.200258i	$-0.935822\pi$
$467$	−6.83839	+	11.8444i	−0.316443	+	0.548095i	0.663300	+	0.748353i	$0.269155\pi$
$468$	7.89803	−	2.02349i	0.365087	−	0.0935356i
$469$	−3.61538	+	1.65307i	−0.166943	+	0.0763315i
$470$	−1.04772	−	1.81470i	−0.0483277	−	0.0837060i
$471$	−2.68194	−	1.12820i	−0.123577	−	0.0519849i
$472$	17.9382			0.825671
$473$	41.0905			1.88934
$474$	−5.84386	−	2.45833i	−0.268418	−	0.112915i
$475$	1.70155	+	2.94717i	0.0780725	+	0.135225i
$476$	−10.4848	−	7.45902i	−0.480569	−	0.341883i
$477$	8.25435	−	29.5044i	0.377941	−	1.35091i
$478$	23.5214	−	40.7402i	1.07584	−	1.86341i
$479$	−1.18204	+	2.04736i	−0.0540089	+	0.0935462i	−0.891766	−	0.452497i	$-0.850533\pi$
$479$	−1.18204	+	2.04736i	−0.0540089	+	0.0935462i	0.837757	+	0.546043i	$0.183867\pi$
$480$	0.986719	+	7.82708i	0.0450374	+	0.357256i
$481$	11.1676	+	19.3428i	0.509197	+	0.881955i
$482$	−19.3138	+	33.4525i	−0.879721	+	1.52372i
$483$	−0.0562743	−	0.0909153i	−0.00256057	−	0.00413679i
$484$	−4.13967	−	7.17012i	−0.188167	−	0.325915i
$485$	−0.533838	+	0.924635i	−0.0242403	+	0.0419855i
$486$	−10.7491	+	24.0584i	−0.487588	+	1.09131i
$487$	14.6202	+	25.3230i	0.662506	+	1.14749i	0.979955	+	0.199219i	$0.0638404\pi$
$487$	14.6202	+	25.3230i	0.662506	+	1.14749i	−0.317449	+	0.948275i	$0.602826\pi$
$488$	−16.5687			−0.750030
$489$	34.2676	−	25.9965i	1.54964	−	1.17560i
$490$	11.6209	+	2.22883i	0.524979	+	0.100688i
$491$	12.0023	−	20.7885i	0.541655	−	0.938174i	−0.457154	−	0.889387i	$-0.651131\pi$
$491$	12.0023	−	20.7885i	0.541655	−	0.938174i	0.998809	−	0.0487865i	$-0.0155354\pi$
$492$	8.18257	−	6.20755i	0.368899	−	0.279858i
$493$	−29.3278	+	50.7973i	−1.32086	+	2.28780i
$494$	9.11685	+	15.7908i	0.410186	+	0.710464i
$495$	9.53465	+	9.74661i	0.428550	+	0.438078i
$496$	−8.56068			−0.384386
$497$	23.2525	−	10.6318i	1.04302	−	0.476901i
$498$	2.75202	+	21.8302i	0.123321	+	0.978234i
$499$	−0.0319871	−	0.0554034i	−0.00143194	−	0.00248019i	0.865309	−	0.501240i	$-0.167122\pi$
$499$	−0.0319871	−	0.0554034i	−0.00143194	−	0.00248019i	−0.866740	+	0.498759i	$0.833789\pi$
$500$	0.857411			0.0383446
$501$	19.0257	−	14.4335i	0.850005	−	0.644840i
$502$	0.420520			0.0187687
$503$	−33.9925			−1.51565			−0.757825	−	0.652458i	$-0.773738\pi$
$503$	−33.9925			−1.51565			−0.757825	+	0.652458i	$0.773738\pi$
$504$	14.3063	+	5.50843i	0.637254	+	0.245365i
$505$	−2.78241			−0.123816
$506$	0.179255			0.00796885
$507$	−0.639772	−	5.07495i	−0.0284133	−	0.225386i
$508$	−0.0400947			−0.00177892
$509$	10.2885	+	17.8202i	0.456030	+	0.789867i	0.998747	−	0.0500485i	$-0.0159376\pi$
$509$	10.2885	+	17.8202i	0.456030	+	0.789867i	−0.542717	+	0.839916i	$0.682604\pi$
$510$	−13.2307	+	10.0372i	−0.585867	+	0.444457i
$511$	−25.2539	−	17.9660i	−1.11717	−	0.794769i
$512$	−3.44542			−0.152267
$513$	−17.4913	−	2.59686i	−0.772260	−	0.114654i
$514$	6.74794	+	11.6878i	0.297639	+	0.515526i
$515$	1.95861	−	3.39241i	0.0863065	−	0.149487i
$516$	1.67933	+	13.3212i	0.0739283	+	0.586431i
$517$	2.81698	−	4.87915i	0.123891	−	0.214585i
$518$	2.98143	−	31.3731i	0.130997	−	1.37846i
$519$	0.283835	+	0.119400i	0.0124590	+	0.00524110i
$520$	−6.12195			−0.268465
$521$	−14.0122	−	24.2698i	−0.613884	−	1.06328i	−0.990579	−	0.136941i	$-0.956273\pi$
$521$	−14.0122	−	24.2698i	−0.613884	−	1.06328i	0.376695	−	0.926337i	$-0.377060\pi$
$522$	−14.1287	+	50.5016i	−0.618394	+	2.21039i
$523$	−6.72521	+	11.6484i	−0.294073	+	0.509349i	−0.974769	−	0.223217i	$-0.928344\pi$
$523$	−6.72521	+	11.6484i	−0.294073	+	0.509349i	0.680696	+	0.732566i	$0.261678\pi$
$524$	−4.35129	−	7.53665i	−0.190087	−	0.329240i
$525$	2.16857	−	4.03699i	0.0946440	−	0.176189i
$526$	9.20117	−	15.9369i	0.401190	−	0.694881i
$527$	−4.87559	−	8.44477i	−0.212384	−	0.367860i
$528$	−31.2302	+	23.6922i	−1.35912	+	1.03107i
$529$	11.4997	−	19.9181i	0.499988	−	0.866005i
$530$	8.63149	−	14.9502i	0.374928	−	0.649394i
$531$	19.4841	+	19.9173i	0.845539	+	0.864337i
$532$	0.730345	−	7.68529i	0.0316645	−	0.333200i
$533$	10.9606	+	18.9844i	0.474758	+	0.822304i
$534$	19.9596	−	15.1420i	0.863738	−	0.655258i
$535$	−12.5906			−0.544340
$536$	−2.90205			−0.125350
$537$	−2.13977	−	16.9736i	−0.0923379	−	0.732464i
$538$	−4.43626	−	7.68383i	−0.191261	−	0.331273i
$539$	10.4327	+	30.0552i	0.449368	+	1.29457i
$540$	−2.77009	+	3.48938i	−0.119206	+	0.150159i
$541$	11.9938	−	20.7740i	0.515656	−	0.893142i	−0.484179	−	0.874969i	$-0.660882\pi$
$541$	11.9938	−	20.7740i	0.515656	−	0.893142i	0.999835	−	0.0181732i	$-0.00578502\pi$
$542$	−11.5894	+	20.0735i	−0.497809	+	0.862230i
$543$	18.8951	+	7.94857i	0.810867	+	0.341106i
$544$	−12.9176	−	22.3740i	−0.553838	−	0.959276i
$545$	−0.0916666	+	0.158771i	−0.00392656	+	0.00680101i
$546$	11.6191	−	21.6301i	0.497252	−	0.925682i
$547$	15.1076	+	26.1671i	0.645954	+	1.11883i	0.984080	+	0.177724i	$0.0568736\pi$
$547$	15.1076	+	26.1671i	0.645954	+	1.11883i	−0.338126	+	0.941101i	$0.609793\pi$
$548$	6.68310	−	11.5755i	0.285488	−	0.494480i
$549$	−17.9966	−	18.3967i	−0.768078	−	0.785153i
$550$	3.84133	+	6.65338i	0.163795	+	0.283701i
$551$	−35.1913			−1.49920
$552$	−0.00976261	−	0.0774412i	−0.000415524	−	0.00329612i
$553$	−5.21026	+	2.38230i	−0.221563	+	0.101306i
$554$	7.30430	−	12.6514i	0.310330	−	0.537507i
$555$	−11.2500	−	4.73253i	−0.477538	−	0.200885i
$556$	6.69912	−	11.6032i	0.284106	−	0.492086i
$557$	−5.05961	−	8.76349i	−0.214382	−	0.371321i	0.738699	−	0.674035i	$-0.235441\pi$
$557$	−5.05961	−	8.76349i	−0.214382	−	0.371321i	−0.953081	+	0.302714i	$0.902107\pi$
$558$	−6.09640	−	6.23193i	−0.258081	−	0.263819i
$559$	−28.6569			−1.21206
$560$	10.7355	+	7.63737i	0.453656	+	0.322738i
$561$	−41.1580	−	17.3138i	−1.73769	−	0.730991i
$562$	−26.1493	−	45.2920i	−1.10304	−	1.91053i
$563$	20.7201			0.873249			0.436625	−	0.899644i	$-0.356174\pi$
$563$	20.7201			0.873249			0.436625	+	0.899644i	$0.356174\pi$
$564$	1.69690	+	0.713832i	0.0714525	+	0.0300578i
$565$	2.49643			0.105025
$566$	−9.56304			−0.401965
$567$	9.42310	+	21.8679i	0.395733	+	0.918366i
$568$	18.6647			0.783153
$569$	−0.156964			−0.00658027			−0.00329014	−	0.999995i	$-0.501047\pi$
$569$	−0.156964			−0.00658027			−0.00329014	+	0.999995i	$0.501047\pi$
$570$	−9.18418	−	3.86349i	−0.384683	−	0.161824i
$571$	−3.31860			−0.138879			−0.0694395	−	0.997586i	$-0.522121\pi$
$571$	−3.31860			−0.138879			−0.0694395	+	0.997586i	$0.522121\pi$
$572$	6.17587	+	10.6969i	0.258226	+	0.447261i
$573$	−29.0358	−	12.2144i	−1.21299	−	0.510265i
$574$	2.92619	−	30.7918i	0.122137	−	1.28522i
$575$	−0.0233324			−0.000973028
$576$	4.74134	+	4.84675i	0.197556	+	0.201948i
$577$	21.7027	+	37.5901i	0.903494	+	1.56490i	0.822926	+	0.568148i	$0.192340\pi$
$577$	21.7027	+	37.5901i	0.903494	+	1.56490i	0.0805674	+	0.996749i	$0.474327\pi$
$578$	12.8246	−	22.2128i	0.533431	−	0.923930i
$579$	−12.2828	−	5.16698i	−0.510456	−	0.214733i
$580$	−4.43323	+	7.67858i	−0.184080	+	0.318835i
$581$	16.2015	+	11.5260i	0.672151	+	0.478178i
$582$	−0.390982	−	3.10143i	−0.0162067	−	0.128559i
$583$	46.4146			1.92230
$584$	−11.3124	−	19.5936i	−0.468110	−	0.810791i
$585$	−6.64956	−	6.79739i	−0.274925	−	0.281037i
$586$	−12.0015	+	20.7873i	−0.495779	+	0.858715i
$587$	−4.12605	−	7.14652i	−0.170300	−	0.294969i	0.768225	−	0.640180i	$-0.221140\pi$
$587$	−4.12605	−	7.14652i	−0.170300	−	0.294969i	−0.938525	+	0.345212i	$0.887807\pi$
$588$	−9.31723	+	4.61051i	−0.384236	+	0.190134i
$589$	2.92518	−	5.06656i	0.120530	−	0.208764i
$590$	7.84979	+	13.5962i	0.323171	+	0.559748i
$591$	−4.81954	−	2.02743i	−0.198250	−	0.0833972i
$592$	17.5447	−	30.3883i	0.721081	−	1.24895i
$593$	−11.2473	+	19.4809i	−0.461871	+	0.799984i	−0.999054	−	0.0434819i	$-0.986155\pi$
$593$	−11.2473	+	19.4809i	−0.461871	+	0.799984i	0.537184	+	0.843465i	$0.319488\pi$
$594$	−39.4875	−	5.86253i	−1.62019	−	0.240543i
$595$	−1.41976	+	14.9398i	−0.0582043	+	0.612474i
$596$	−3.08278	−	5.33953i	−0.126276	−	0.218716i
$597$	0.436956	+	3.46612i	0.0178834	+	0.141859i
$598$	−0.125014			−0.00511221
$599$	−5.89379			−0.240814			−0.120407	−	0.992725i	$-0.538420\pi$
$599$	−5.89379			−0.240814			−0.120407	+	0.992725i	$0.538420\pi$
$600$	2.66517	−	2.02188i	0.108805	−	0.0825429i
$601$	−8.73192	−	15.1241i	−0.356182	−	0.616926i	0.631137	−	0.775671i	$-0.282588\pi$
$601$	−8.73192	−	15.1241i	−0.356182	−	0.616926i	−0.987320	+	0.158745i	$0.949255\pi$
$602$	32.9476	+	23.4394i	1.34284	+	0.955317i
$603$	−3.15216	−	3.22223i	−0.128366	−	0.131220i
$604$	−6.01310	+	10.4150i	−0.244669	+	0.423780i
$605$	−4.82811	+	8.36252i	−0.196290	+	0.339985i
$606$	6.49018	−	4.92365i	0.263646	−	0.200010i
$607$	−0.129494	−	0.224290i	−0.00525599	−	0.00910364i	0.863385	−	0.504545i	$-0.168340\pi$
$607$	−0.129494	−	0.224290i	−0.00525599	−	0.00910364i	−0.868641	+	0.495441i	$0.835006\pi$
$608$	7.75011	−	13.4236i	0.314308	−	0.544398i
$609$	24.9409	+	40.2939i	1.01066	+	1.63279i
$610$	−7.25051	−	12.5582i	−0.293564	−	0.508469i
$611$	−1.96459	+	3.40277i	−0.0794788	+	0.137661i
$612$	3.93090	−	14.0506i	0.158897	−	0.567963i
$613$	8.38558	+	14.5243i	0.338690	+	0.586629i	0.984187	−	0.177134i	$-0.0566827\pi$
$613$	8.38558	+	14.5243i	0.338690	+	0.586629i	−0.645496	+	0.763763i	$0.723349\pi$
$614$	−17.7887			−0.717896
$615$	−11.0416	−	4.64484i	−0.445240	−	0.187298i
$616$	−2.19718	+	23.1206i	−0.0885270	+	0.931554i
$617$	−3.88360	+	6.72659i	−0.156348	+	0.270802i	−0.933549	−	0.358450i	$-0.883305\pi$
$617$	−3.88360	+	6.72659i	−0.156348	+	0.270802i	0.777201	+	0.629252i	$0.216639\pi$
$618$	1.43448	+	11.3789i	0.0577032	+	0.457727i
$619$	8.74089	−	15.1397i	0.351326	−	0.608514i	−0.635156	−	0.772384i	$-0.719064\pi$
$619$	8.74089	−	15.1397i	0.351326	−	0.608514i	0.986482	+	0.163870i	$0.0523976\pi$
$620$	−0.736999	−	1.27652i	−0.0295986	−	0.0512663i
$621$	0.0753813	−	0.0949550i	0.00302495	−	0.00381041i
$622$	−47.1529			−1.89066
$623$	2.14181	−	22.5379i	0.0858100	−	0.902964i
$624$	21.7802	−	16.5232i	0.871907	−	0.661456i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−50.0110			−1.99884
$627$	−3.35066	−	26.5789i	−0.133813	−	1.06146i
$628$	1.44032			0.0574749
$629$	39.9691			1.59367
$630$	2.08537	+	13.2540i	0.0830830	+	0.528051i
$631$	34.0347			1.35490			0.677451	−	0.735568i	$-0.263085\pi$
$631$	34.0347			1.35490			0.677451	+	0.735568i	$0.263085\pi$
$632$	−4.18226			−0.166361
$633$	7.44385	−	5.64714i	0.295867	−	0.224454i
$634$	9.30982			0.369740
$635$	0.0233813	+	0.0404975i	0.000927857	+	0.00160710i
$636$	1.89692	+	15.0472i	0.0752178	+	0.596660i
$637$	−7.27586	−	20.9608i	−0.288280	−	0.830496i
$638$	−79.4461			−3.14530
$639$	20.2733	+	20.7240i	0.801998	+	0.819827i
$640$	6.46493	+	11.1976i	0.255549	+	0.442624i
$641$	−12.2006	+	21.1321i	−0.481895	+	0.834666i	−0.999784	−	0.0207816i	$-0.993385\pi$
$641$	−12.2006	+	21.1321i	−0.481895	+	0.834666i	0.517889	+	0.855448i	$0.326718\pi$
$642$	29.3685	−	22.2799i	1.15908	−	0.879316i
$643$	−2.75458	+	4.77107i	−0.108630	+	0.188153i	−0.915215	−	0.402965i	$-0.867980\pi$
$643$	−2.75458	+	4.77107i	−0.108630	+	0.188153i	0.806586	+	0.591117i	$0.201313\pi$
$644$	0.0431289	+	0.0306826i	0.00169952	+	0.00120906i
$645$	12.4757	−	9.46445i	0.491230	−	0.372662i
$646$	32.6295			1.28379
$647$	−17.3886	−	30.1180i	−0.683617	−	1.18406i	−0.973869	−	0.227110i	$-0.927072\pi$
$647$	−17.3886	−	30.1180i	−0.683617	−	1.18406i	0.290252	−	0.956950i	$-0.406261\pi$
$648$	−0.382143	+	17.3786i	−0.0150120	+	0.682695i
$649$	−21.1056	+	36.5559i	−0.828466	+	1.43495i
$650$	−2.67898	−	4.64013i	−0.105078	−	0.182001i
$651$	−7.87433	+	0.241473i	−0.308619	+	0.00946408i
$652$	−10.6462	+	18.4398i	−0.416937	+	0.722157i
$653$	3.25000	+	5.62917i	0.127182	+	0.220287i	0.922584	−	0.385796i	$-0.126073\pi$
$653$	3.25000	+	5.62917i	0.127182	+	0.220287i	−0.795401	+	0.606083i	$0.792740\pi$
$654$	−0.0671364	−	0.532555i	−0.00262524	−	0.0208245i
$655$	−5.07491	+	8.79001i	−0.198293	+	0.343454i
$656$	17.2196	−	29.8252i	0.672311	−	1.16448i
$657$	9.46808	−	33.8428i	0.369385	−	1.32033i
$658$	5.04196	−	2.30535i	0.196556	−	0.0898718i
$659$	23.5823	+	40.8457i	0.918636	+	1.59112i	0.801489	+	0.598010i	$0.204042\pi$
$659$	23.5823	+	40.8457i	0.918636	+	1.59112i	0.117147	+	0.993115i	$0.462625\pi$
$660$	−6.22148	−	2.61718i	−0.242171	−	0.101873i
$661$	0.827733			0.0321951			0.0160975	−	0.999870i	$-0.494876\pi$
$661$	0.827733			0.0321951			0.0160975	+	0.999870i	$0.494876\pi$
$662$	−15.3009			−0.594687
$663$	28.7040	+	12.0748i	1.11477	+	0.468948i
$664$	7.25739	+	12.5702i	0.281641	+	0.487817i
$665$	−8.18841	+	3.74400i	−0.317533	+	0.145186i
$666$	34.6160	−	8.86867i	1.34134	−	0.343654i
$667$	0.120640	−	0.208954i	0.00467119	−	0.00809073i
$668$	−5.91086	+	10.2379i	−0.228698	+	0.396117i
$669$	−3.86931	−	30.6930i	−0.149596	−	1.18666i
$670$	−1.26995	−	2.19961i	−0.0490623	−	0.0849784i
$671$	19.4943	−	33.7651i	0.752569	−	1.30349i
$672$	−20.8626	+	0.639771i	−0.804792	+	0.0246797i
$673$	−13.8314	−	23.9566i	−0.533160	−	0.923460i	−0.999250	−	0.0387229i	$-0.987671\pi$
$673$	−13.8314	−	23.9566i	−0.533160	−	0.923460i	0.466090	−	0.884737i	$-0.345662\pi$
$674$	8.38700	−	14.5267i	0.323055	−	0.559548i
$675$	5.13982	+	0.763086i	0.197832	+	0.0293712i
$676$	1.26606	+	2.19288i	0.0486945	+	0.0843414i
$677$	−24.5543			−0.943697			−0.471848	−	0.881680i	$-0.656413\pi$
$677$	−24.5543			−0.943697			−0.471848	+	0.881680i	$0.656413\pi$
$678$	−5.82309	+	4.41758i	−0.223634	+	0.169656i
$679$	−2.30176	−	1.63751i	−0.0883335	−	0.0628417i
$680$	−5.47767	+	9.48760i	−0.210059	+	0.363833i
$681$	2.21598	−	1.68111i	0.0849166	−	0.0644204i
$682$	6.60373	−	11.4380i	0.252870	−	0.437984i
$683$	3.60001	+	6.23539i	0.137750	+	0.238591i	0.926645	−	0.375938i	$-0.122679\pi$
$683$	3.60001	+	6.23539i	0.137750	+	0.238591i	−0.788894	+	0.614529i	$0.789346\pi$
$684$	8.47969	−	2.17251i	0.324229	−	0.0830679i
$685$	−15.5890			−0.595626
$686$	−8.77922	+	30.0502i	−0.335192	+	1.14732i
$687$	−3.69323	−	29.2963i	−0.140905	−	1.11772i
$688$	22.5106	+	38.9895i	0.858208	+	1.48646i
$689$	−32.3700			−1.23320
$690$	0.0544244	−	0.0412881i	0.00207190	−	0.00157181i
$691$	46.1084			1.75405			0.877023	−	0.480448i	$-0.159526\pi$
$691$	46.1084			1.75405			0.877023	+	0.480448i	$0.159526\pi$
$692$	−0.152432			−0.00579459
$693$	−28.0580	+	22.6736i	−1.06583	+	0.861297i
$694$	18.9235			0.718325
$695$	−15.6264			−0.592743
$696$	4.32681	+	34.3221i	0.164007	+	1.30098i
$697$	39.2284			1.48588
$698$	23.9045	+	41.4038i	0.904799	+	1.56716i
$699$	−19.4065	+	14.7224i	−0.734023	+	0.556852i
$700$	−0.214612	+	2.25832i	−0.00811156	+	0.0853565i
$701$	26.1712			0.988473			0.494236	−	0.869328i	$-0.335448\pi$
$701$	26.1712			0.988473			0.494236	+	0.869328i	$0.335448\pi$
$702$	27.5390	+	4.08859i	1.03939	+	0.154314i
$703$	11.9900	+	20.7673i	0.452212	+	0.783253i
$704$	−5.13591	+	8.89565i	−0.193567	+	0.335268i
$705$	−0.268546	−	2.13022i	−0.0101140	−	0.0802288i
$706$	−6.21856	+	10.7709i	−0.234039	+	0.405367i
$707$	0.696444	−	7.32856i	0.0261925	−	0.275619i
$708$	−12.7137	−	5.34823i	−0.477808	−	0.200999i
$709$	−10.8862			−0.408841			−0.204420	−	0.978883i	$-0.565531\pi$
$709$	−10.8862			−0.408841			−0.204420	+	0.978883i	$0.565531\pi$
$710$	8.16772	+	14.1469i	0.306529	+	0.530924i
$711$	−4.54269	−	4.64368i	−0.170364	−	0.174152i
$712$	8.26350	−	14.3128i	0.309688	−	0.536395i
$713$	0.0200557	+	0.0347374i	0.000751090	+	0.00130093i
$714$	−23.1253	−	37.3606i	−0.865442	−	1.39818i
$715$	7.20293	−	12.4758i	0.269374	−	0.466570i
$716$	4.23444	+	7.33426i	0.158248	+	0.274094i
$717$	38.4021	−	29.1330i	1.43415	−	1.08799i
$718$	−18.5797	+	32.1810i	−0.693389	+	1.20098i
$719$	2.36774	−	4.10105i	0.0883019	−	0.152943i	−0.818492	−	0.574519i	$-0.805189\pi$
$719$	2.36774	−	4.10105i	0.0883019	−	0.152943i	0.906793	+	0.421575i	$0.138523\pi$
$720$	−4.02489	+	14.3866i	−0.149999	+	0.536157i
$721$	8.44496	+	6.00787i	0.314507	+	0.223745i
$722$	−6.27042	−	10.8607i	−0.233361	−	0.404193i
$723$	−31.5327	+	23.9217i	−1.17271	+	0.889656i
$724$	−10.1475			−0.377129
$725$	10.3410			0.384054
$726$	−3.53609	−	28.0498i	−0.131237	−	1.04103i
$727$	14.1401	+	24.4914i	0.524429	+	0.908337i	0.999595	+	0.0284413i	$0.00905435\pi$
$727$	14.1401	+	24.4914i	0.524429	+	0.908337i	−0.475167	+	0.879896i	$0.657612\pi$
$728$	1.53234	−	16.1245i	0.0567922	−	0.597614i
$729$	−19.7110	+	18.4520i	−0.730038	+	0.683407i
$730$	9.90067	−	17.1485i	0.366440	−	0.634693i
$731$	−25.6410	+	44.4116i	−0.948368	+	1.64262i
$732$	11.7430	+	4.93992i	0.434035	+	0.182585i
$733$	−17.3267	−	30.0107i	−0.639976	−	1.10847i	−0.985438	−	0.170038i	$-0.945611\pi$
$733$	−17.3267	−	30.0107i	−0.639976	−	1.10847i	0.345462	−	0.938433i	$-0.387722\pi$
$734$	−17.9359	+	31.0659i	−0.662027	+	1.14666i
$735$	10.0902	+	6.72222i	0.372182	+	0.247953i
$736$	0.0531364	+	0.0920349i	0.00195863	+	0.00339245i
$737$	3.41448	−	5.91405i	0.125774	−	0.217847i
$738$	33.9746	−	8.70434i	1.25062	−	0.320411i
$739$	−23.9585	−	41.4973i	−0.881328	−	1.52650i	−0.849865	−	0.527000i	$-0.823317\pi$
$739$	−23.9585	−	41.4973i	−0.881328	−	1.52650i	−0.0314624	−	0.999505i	$-0.510016\pi$
$740$	6.04176			0.222100
$741$	2.33679	+	18.5364i	0.0858440	+	0.680951i
$742$	37.2166	+	26.4764i	1.36626	+	0.971980i
$743$	−16.5756	+	28.7098i	−0.608100	+	1.05326i	0.383453	+	0.923560i	$0.374735\pi$
$743$	−16.5756	+	28.7098i	−0.608100	+	1.05326i	−0.991553	+	0.129700i	$0.958598\pi$
$744$	−5.30107	−	2.22999i	−0.194347	−	0.0817554i
$745$	−3.59545	+	6.22750i	−0.131727	+	0.228158i
$746$	6.08688	+	10.5428i	0.222857	+	0.385999i
$747$	−6.07418	+	21.7116i	−0.222243	+	0.794386i
$748$	22.1036			0.808189
$749$	3.15146	−	33.1622i	0.115152	−	1.21172i
$750$	2.69877	+	1.13529i	0.0985451	+	0.0414548i
$751$	−12.7174	−	22.0271i	−0.464063	−	0.803781i	0.535096	−	0.844791i	$-0.320276\pi$
$751$	−12.7174	−	22.0271i	−0.464063	−	0.803781i	−0.999159	+	0.0410107i	$0.986942\pi$
$752$	6.17289			0.225102
$753$	0.397173	+	0.167078i	0.0144738	+	0.00608866i
$754$	55.4065			2.01779
$755$	14.0262			0.510465
$756$	−8.49726	−	8.16949i	−0.309042	−	0.297122i
$757$	13.9500			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$757$	13.9500			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$758$	7.02909			0.255308
$759$	0.169303	+	0.0712202i	0.00614530	+	0.00258513i
$760$	−6.57281			−0.238421
$761$	5.32285	+	9.21945i	0.192953	+	0.334205i	0.946228	−	0.323502i	$-0.104860\pi$
$761$	5.32285	+	9.21945i	0.192953	+	0.334205i	−0.753274	+	0.657706i	$0.771527\pi$
$762$	−0.126201	−	0.0530888i	−0.00457179	−	0.00192321i
$763$	−0.395241	−	0.281180i	−0.0143087	−	0.0101794i
$764$	15.5935			0.564153
$765$	−16.4841	+	4.22325i	−0.595984	+	0.152692i
$766$	24.3889	+	42.2429i	0.881208	+	1.52630i
$767$	14.7192	−	25.4945i	0.531481	−	0.920552i
$768$	−27.6781	−	11.6433i	−0.998749	−	0.420142i
$769$	14.8500	−	25.7209i	0.535504	−	0.927520i	−0.463635	−	0.886026i	$-0.653455\pi$
$769$	14.8500	−	25.7209i	0.535504	−	0.927520i	0.999139	−	0.0414934i	$-0.0132116\pi$
$770$	−18.4857	+	8.45227i	−0.666179	+	0.304599i
$771$	1.72960	+	13.7199i	0.0622900	+	0.494111i
$772$	6.59641			0.237410
$773$	19.1298	+	33.1338i	0.688051	+	1.19174i	0.972467	+	0.233039i	$0.0748668\pi$
$773$	19.1298	+	33.1338i	0.688051	+	1.19174i	−0.284416	+	0.958701i	$0.591800\pi$
$774$	−12.3525	+	44.1530i	−0.444003	+	1.58705i
$775$	−0.859563	+	1.48881i	−0.0308764	+	0.0534795i
$776$	−1.03106	−	1.78586i	−0.0370131	−	0.0641085i
$777$	15.2808	−	28.4468i	0.548197	−	1.02052i
$778$	−9.63125	+	16.6818i	−0.345297	+	0.598072i
$779$	11.7678	+	20.3825i	0.421626	+	0.730279i
$780$	4.33893	+	1.82525i	0.155358	+	0.0653543i
$781$	−21.9604	+	38.0365i	−0.785804	+	1.36105i
$782$	−0.111857	+	0.193743i	−0.00400001	+	0.00692822i
$783$	−33.4092	+	42.0843i	−1.19395	+	1.50397i
$784$	−22.8031	+	26.3643i	−0.814395	+	0.941584i
$785$	−0.839922	−	1.45479i	−0.0299781	−	0.0519236i
$786$	−3.71685	−	29.4837i	−0.132576	−	1.05165i
$787$	−20.5650			−0.733064			−0.366532	−	0.930405i	$-0.619455\pi$
$787$	−20.5650			−0.733064			−0.366532	+	0.930405i	$0.619455\pi$
$788$	2.58831			0.0922046
$789$	15.0223	−	11.3963i	0.534806	−	0.405721i
$790$	−1.83017	−	3.16994i	−0.0651144	−	0.112781i
$791$	−0.624860	+	6.57530i	−0.0222175	+	0.233791i
$792$	−25.5104	+	6.53580i	−0.906474	+	0.232240i
$793$	−13.5955	+	23.5481i	−0.482791	+	0.836218i
$794$	3.31631	−	5.74402i	0.117692	−	0.203848i
$795$	14.0922	−	10.6908i	0.499798	−	0.379162i
$796$	−0.864701	−	1.49771i	−0.0306485	−	0.0530848i
$797$	12.3509	−	21.3924i	0.437491	−	0.757756i	−0.560004	−	0.828490i	$-0.689201\pi$
$797$	12.3509	−	21.3924i	0.437491	−	0.757756i	0.997495	+	0.0707333i	$0.0225339\pi$
$798$	12.4748	−	23.2230i	0.441603	−	0.822087i
$799$	3.51567	+	6.08931i	0.124375	+	0.215424i
$800$	−2.27737	+	3.94452i	−0.0805171	+	0.139460i
$801$	24.8676	−	6.37111i	0.878653	−	0.225112i
$802$	−29.5723	−	51.2208i	−1.04423	−	1.80867i
$803$	53.2395			1.87878
$804$	2.05683	+	0.865240i	0.0725386	+	0.0305147i
$805$	0.00584014	−	0.0614548i	0.000205838	−	0.00216600i
$806$	−4.60551	+	7.97698i	−0.162222	+	0.280977i
$807$	−1.13708	−	9.01981i	−0.0400271	−	0.317512i
$808$	2.68700	−	4.65403i	0.0945285	−	0.163728i
$809$	0.959234	+	1.66144i	0.0337249	+	0.0584132i	0.882395	−	0.470509i	$-0.155930\pi$
$809$	0.959234	+	1.66144i	0.0337249	+	0.0584132i	−0.848670	+	0.528922i	$0.822596\pi$
$810$	−13.3393	+	7.31526i	−0.468696	+	0.257032i
$811$	−23.8796			−0.838526			−0.419263	−	0.907865i	$-0.637711\pi$
$811$	−23.8796			−0.838526			−0.419263	+	0.907865i	$0.637711\pi$
$812$	−19.1148	−	13.5986i	−0.670799	−	0.477216i
$813$	−18.9214	+	14.3544i	−0.663604	+	0.503431i
$814$	27.0680	+	46.8832i	0.948733	+	1.64325i
$815$	24.8334			0.869875
$816$	−6.11900	−	48.5385i	−0.214208	−	1.69919i
$817$	−30.7674			−1.07642
$818$	66.3851			2.32110
$819$	19.5679	−	15.8128i	0.683759	−	0.552543i
$820$	5.92981			0.207078
$821$	6.38168			0.222722			0.111361	−	0.993780i	$-0.464479\pi$
$821$	6.38168			0.222722			0.111361	+	0.993780i	$0.464479\pi$
$822$	36.3625	−	27.5857i	1.26829	−	0.962162i
$823$	−34.9506			−1.21830			−0.609151	−	0.793055i	$-0.708489\pi$
$823$	−34.9506			−1.21830			−0.609151	+	0.793055i	$0.708489\pi$
$824$	3.78289	+	6.55216i	0.131783	+	0.228255i
$825$	0.984591	+	7.81020i	0.0342791	+	0.271916i
$826$	−37.7758	+	17.2723i	−1.31439	+	0.600980i
$827$	40.0335			1.39210			0.696051	−	0.717992i	$-0.254939\pi$
$827$	40.0335			1.39210			0.696051	+	0.717992i	$0.254939\pi$
$828$	−0.0161697	+	0.0577971i	−0.000561936	+	0.00200859i
$829$	15.2644	+	26.4388i	0.530155	+	0.918256i	0.999381	+	0.0351777i	$0.0111997\pi$
$829$	15.2644	+	26.4388i	0.530155	+	0.918256i	−0.469226	+	0.883078i	$0.655467\pi$
$830$	−6.35171	+	11.0015i	−0.220471	+	0.381867i
$831$	11.9253	−	9.04694i	0.413686	−	0.313835i
$832$	3.58183	−	6.20392i	0.124178	−	0.215082i
$833$	−38.9944	−	7.47894i	−1.35108	−	0.259130i
$834$	36.4497	−	27.6518i	1.26215	−	0.957505i
$835$	13.7877			0.477143
$836$	6.63070	+	11.4847i	0.229327	+	0.397207i
$837$	−3.28191	−	8.30811i	−0.113439	−	0.287170i
$838$	9.50613	−	16.4651i	0.328384	−	0.568778i
$839$	−6.96724	−	12.0676i	−0.240536	−	0.416621i	0.720331	−	0.693630i	$-0.243990\pi$
$839$	−6.96724	−	12.0676i	−0.240536	−	0.416621i	−0.960867	+	0.277010i	$0.910657\pi$
$840$	4.65830	+	7.52583i	0.160727	+	0.259666i
$841$	−38.9677	+	67.4941i	−1.34372	+	2.32738i
$842$	−14.9983	−	25.9778i	−0.516876	−	0.895255i
$843$	−6.70247	−	53.1669i	−0.230845	−	1.83116i
$844$	−2.31264	+	4.00561i	−0.0796044	+	0.137879i
$845$	1.47661	−	2.55756i	0.0507968	−	0.0879826i
$846$	4.39596	+	4.49369i	0.151136	+	0.154496i
$847$	−20.8174	−	14.8098i	−0.715296	−	0.508872i
$848$	25.4273	+	44.0413i	0.873176	+	1.51239i
$849$	−9.03211	−	3.79952i	−0.309981	−	0.130399i
$850$	−9.58817			−0.328871
$851$	−0.164412			−0.00563597
$852$	−13.2286	−	5.56484i	−0.453203	−	0.190648i
$853$	−26.8533	−	46.5112i	−0.919439	−	1.59251i	−0.800270	−	0.599640i	$-0.795310\pi$
$853$	−26.8533	−	46.5112i	−0.919439	−	1.59251i	−0.119169	−	0.992874i	$-0.538023\pi$
$854$	34.8918	−	15.9536i	1.19397	−	0.545922i
$855$	−7.13927	−	7.29799i	−0.244158	−	0.249586i
$856$	12.1589	−	21.0598i	0.415582	−	0.719809i
$857$	6.74456	−	11.6819i	0.230390	−	0.399047i	−0.727533	−	0.686073i	$-0.759333\pi$
$857$	6.74456	−	11.6819i	0.230390	−	0.399047i	0.957923	+	0.287026i	$0.0926666\pi$
$858$	5.27541	+	41.8468i	0.180099	+	1.42863i
$859$	−3.28824	−	5.69539i	−0.112193	−	0.194324i	0.804461	−	0.594005i	$-0.202454\pi$
$859$	−3.28824	−	5.69539i	−0.112193	−	0.194324i	−0.916654	+	0.399681i	$0.869121\pi$
$860$	−3.87592	+	6.71330i	−0.132168	+	0.228922i
$861$	14.9977	−	27.9197i	0.511120	−	0.951499i
$862$	−8.00088	−	13.8579i	−0.272511	−	0.472003i
$863$	5.87933	−	10.1833i	0.200135	−	0.346644i	−0.748437	−	0.663206i	$-0.769195\pi$
$863$	5.87933	−	10.1833i	0.200135	−	0.346644i	0.948572	+	0.316562i	$0.102529\pi$
$864$	−8.69524	−	22.0119i	−0.295818	−	0.748860i
$865$	0.0888908	+	0.153963i	0.00302238	+	0.00523491i
$866$	−9.94714			−0.338018
$867$	20.9380	−	15.8842i	0.711091	−	0.539455i
$868$	3.54668	−	1.62165i	0.120382	−	0.0550426i
$869$	4.92073	−	8.52295i	0.166924	−	0.289121i
$870$	−24.1210	+	18.2990i	−0.817780	+	0.620393i
$871$	−2.38129	+	4.12452i	−0.0806870	+	0.139754i
$872$	−0.177047	−	0.306654i	−0.00599555	−	0.0103846i
$873$	0.862965	−	3.08459i	0.0292069	−	0.104397i
$874$	−0.134221			−0.00454009
$875$	2.40616	−	1.10017i	0.0813431	−	0.0371927i
$876$	2.17584	+	17.2597i	0.0735150	+	0.583152i
$877$	9.82365	+	17.0151i	0.331721	+	0.574558i	0.982849	−	0.184410i	$-0.0590374\pi$
$877$	9.82365	+	17.0151i	0.331721	+	0.574558i	−0.651128	+	0.758968i	$0.725704\pi$
$878$	21.8064			0.735929
$879$	−19.5943	+	14.8648i	−0.660899	+	0.501378i
$880$	−22.6321			−0.762930
$881$	6.87969			0.231783			0.115891	−	0.993262i	$-0.463028\pi$
$881$	6.87969			0.231783			0.115891	+	0.993262i	$0.463028\pi$
$882$	−35.4314	+	2.17512i	−1.19304	+	0.0732401i
$883$	−28.2458			−0.950546			−0.475273	−	0.879838i	$-0.657651\pi$
$883$	−28.2458			−0.950546			−0.475273	+	0.879838i	$0.657651\pi$
$884$	−15.4153			−0.518473
$885$	2.01202	+	15.9602i	0.0676333	+	0.536497i
$886$	22.2951			0.749018
$887$	−12.8484	−	22.2541i	−0.431407	−	0.747219i	0.565587	−	0.824688i	$-0.308649\pi$
$887$	−12.8484	−	22.2541i	−0.431407	−	0.747219i	−0.996995	+	0.0774689i	$0.975316\pi$
$888$	18.7802	−	14.2472i	0.630221	−	0.478105i
$889$	−0.112518	+	0.0514470i	−0.00377374	+	0.00172548i
$890$	14.4645			0.484852
$891$	−34.9659	−	21.2259i	−1.17140	−	0.711095i
$892$	7.65706	+	13.2624i	0.256377	+	0.444058i
$893$	−2.10927	+	3.65337i	−0.0705842	+	0.122255i
$894$	−2.63330	−	20.8885i	−0.0880707	−	0.698615i
$895$	4.93863	−	8.55396i	0.165080	−	0.285927i
$896$	−31.1113	+	14.2251i	−1.03936	+	0.475227i
$897$	−0.118073	−	0.0496697i	−0.00394236	−	0.00165842i
$898$	1.01836			0.0339833
$899$	−8.88871	−	15.3957i	−0.296455	−	0.513475i
$900$	−2.49175	+	0.638390i	−0.0830585	+	0.0212797i
$901$	−28.9633	+	50.1660i	−0.964909	+	1.67127i
$902$	26.5665	+	46.0145i	0.884566	+	1.53211i
$903$	21.8056	+	35.2285i	0.725644	+	1.17233i
$904$	−2.41082	+	4.17567i	−0.0801827	+	0.138881i
$905$	5.91752	+	10.2495i	0.196705	+	0.340703i
$906$	−32.7170	+	24.8202i	−1.08695	+	0.824595i
$907$	4.74046	−	8.21071i	0.157404	−	0.272632i	−0.776528	−	0.630083i	$-0.783021\pi$
$907$	4.74046	−	8.21071i	0.157404	−	0.272632i	0.933932	+	0.357451i	$0.116354\pi$
$908$	−0.688457	+	1.19244i	−0.0228472	+	0.0395726i
$909$	8.08608	−	2.07166i	0.268198	−	0.0687127i
$910$	12.8921	−	5.89470i	0.427370	−	0.195407i
$911$	−26.4738	−	45.8540i	−0.877118	−	1.51921i	−0.854490	−	0.519468i	$-0.826130\pi$
$911$	−26.4738	−	45.8540i	−0.877118	−	1.51921i	−0.0226277	−	0.999744i	$-0.507203\pi$
$912$	23.3843	−	17.7400i	0.774330	−	0.587431i
$913$	−34.1554			−1.13038
$914$	9.26699			0.306525
$915$	−1.85841	−	14.7417i	−0.0614373	−	0.487347i
$916$	7.30861	+	12.6589i	0.241483	+	0.418261i
$917$	−21.8816	−	15.5669i	−0.722594	−	0.514064i
$918$	30.9771	−	39.0206i	1.02240	−	1.28787i
$919$	12.6746	−	21.9531i	0.418098	−	0.724167i	−0.577650	−	0.816284i	$-0.696030\pi$
$919$	12.6746	−	21.9531i	0.418098	−	0.724167i	0.995748	+	0.0921177i	$0.0293636\pi$
$920$	0.0225323	−	0.0390271i	0.000742868	−	0.00128668i
$921$	−16.8011	−	7.06770i	−0.553616	−	0.232888i
$922$	6.35926	+	11.0146i	0.209431	+	0.362745i
$923$	15.3154	−	26.5270i	0.504112	−	0.873148i
$924$	8.45059	−	15.7316i	0.278004	−	0.517531i
$925$	−3.52326	−	6.10247i	−0.115844	−	0.200648i
$926$	−29.6209	+	51.3048i	−0.973402	+	1.68598i
$927$	−3.16614	+	11.3171i	−0.103990	+	0.371702i
$928$	−23.5502	−	40.7901i	−0.773072	−	1.33900i
$929$	−5.44765			−0.178731			−0.0893657	−	0.995999i	$-0.528484\pi$
$929$	−5.44765			−0.178731			−0.0893657	+	0.995999i	$0.528484\pi$
$930$	−0.629542	−	4.99380i	−0.0206435	−	0.163753i
$931$	−7.81170	−	22.5045i	−0.256018	−	0.737554i
$932$	6.02918	−	10.4429i	0.197492	−	0.342067i
$933$	−44.5350	−	18.7344i	−1.45801	−	0.613338i
$934$	11.5595	−	20.0217i	0.378240	−	0.655130i
$935$	−12.8898	−	22.3257i	−0.421540	−	0.730129i
$936$	17.7912	−	4.55814i	0.581525	−	0.148987i
$937$	30.3887			0.992754			0.496377	−	0.868107i	$-0.334663\pi$
$937$	30.3887			0.992754			0.496377	+	0.868107i	$0.334663\pi$
$938$	6.11139	−	2.79432i	0.199544	−	0.0912379i
$939$	−47.2345	−	19.8700i	−1.54144	−	0.648434i
$940$	0.531432	+	0.920467i	0.0173334	+	0.0300223i
$941$	−29.5949			−0.964767			−0.482384	−	0.875960i	$-0.660229\pi$
$941$	−29.5949			−0.964767			−0.482384	+	0.875960i	$0.660229\pi$
$942$	4.53351	+	1.90710i	0.147710	+	0.0621368i
$943$	−0.161366			−0.00525479
$944$	−46.2490			−1.50528
$945$	−3.29639	+	13.3467i	−0.107231	+	0.434167i
$946$	−69.4589			−2.25830
$947$	−8.55664			−0.278053			−0.139027	−	0.990289i	$-0.544397\pi$
$947$	−8.55664			−0.278053			−0.139027	+	0.990289i	$0.544397\pi$
$948$	2.96417	+	1.24693i	0.0962717	+	0.0404984i
$949$	−37.1297			−1.20528
$950$	−2.87628	−	4.98186i	−0.0933188	−	0.161633i
$951$	8.79294	+	3.69891i	0.285131	+	0.119945i
$952$	−23.6182	−	16.8023i	−0.765469	−	0.544566i
$953$	25.0758			0.812284			0.406142	−	0.913810i	$-0.366874\pi$
$953$	25.0758			0.812284			0.406142	+	0.913810i	$0.366874\pi$
$954$	−13.9531	+	49.8739i	−0.451747	+	1.61473i
$955$	−9.09336	−	15.7502i	−0.294254	−	0.509663i
$956$	−11.9307	+	20.6645i	−0.385866	+	0.668339i
$957$	−75.0353	−	31.5649i	−2.42555	−	1.02035i
$958$	1.99811	−	3.46083i	0.0645560	−	0.111814i
$959$	3.90196	−	41.0597i	0.126001	−	1.32589i
$960$	0.489612	+	3.88382i	0.0158022	+	0.125350i
$961$	−28.0446			−0.904665
$962$	−18.8775	−	32.6968i	−0.608635	−	1.05419i
$963$	36.5901	−	9.37442i	1.17910	−	0.302086i
$964$	9.79651	−	16.9680i	0.315524	−	0.546504i
$965$	−3.84670	−	6.66268i	−0.123830	−	0.214479i
$966$	0.0951255	+	0.153682i	0.00306061	+	0.00494464i
$967$	−15.1149	+	26.1798i	−0.486063	+	0.841886i	−0.999872	−	0.0160186i	$-0.994901\pi$
$967$	−15.1149	+	26.1798i	−0.486063	+	0.841886i	0.513808	+	0.857905i	$0.328234\pi$
$968$	−9.32509	−	16.1515i	−0.299720	−	0.519130i
$969$	30.8179	+	12.9641i	0.990014	+	0.416467i
$970$	0.902393	−	1.56299i	0.0289741	−	0.0501846i
$971$	14.0133	−	24.2717i	0.449708	−	0.778916i	−0.548659	−	0.836046i	$-0.684862\pi$
$971$	14.0133	−	24.2717i	0.449708	−	0.778916i	0.998367	+	0.0571298i	$0.0181949\pi$
$972$	5.45222	−	12.2031i	0.174880	−	0.391415i
$973$	3.91131	−	41.1581i	0.125391	−	1.31947i
$974$	−24.7139	−	42.8057i	−0.791883	−	1.37158i
$975$	−0.686664	−	5.44691i	−0.0219908	−	0.174441i
$976$	42.7181			1.36737
$977$	44.3397			1.41855			0.709276	−	0.704931i	$-0.249022\pi$
$977$	44.3397			1.41855			0.709276	+	0.704931i	$0.249022\pi$
$978$	−57.9256	+	43.9442i	−1.85226	+	1.40518i
$979$	19.4452	+	33.6801i	0.621472	+	1.07642i
$980$	−5.89444	−	1.13052i	−0.188291	−	0.0361133i
$981$	0.148182	−	0.529662i	0.00473108	−	0.0169108i
$982$	−20.2885	+	35.1407i	−0.647432	+	1.12138i
$983$	−15.8396	+	27.4350i	−0.505204	+	0.875040i	0.494777	+	0.869020i	$0.335250\pi$
$983$	−15.8396	+	27.4350i	−0.505204	+	0.875040i	−0.999982	+	0.00602002i	$0.998084\pi$
$984$	18.4322	−	13.9832i	0.587597	−	0.445769i
$985$	−1.50937	−	2.61431i	−0.0480926	−	0.0832988i
$986$	49.5754	−	85.8672i	1.57880	−	2.73457i
$987$	5.67798	−	0.174120i	0.180732	−	0.00554231i
$988$	−4.62431	−	8.00955i	−0.147119	−	0.254818i
$989$	0.105474	−	0.182686i	0.00335388	−	0.00580909i
$990$	−16.1172	−	16.4756i	−0.512240	−	0.523627i
$991$	−2.75931	−	4.77927i	−0.0876525	−	0.151819i	0.818866	−	0.573985i	$-0.194603\pi$
$991$	−2.75931	−	4.77927i	−0.0876525	−	0.151819i	−0.906518	+	0.422166i	$0.861270\pi$
$992$	7.83016			0.248608
$993$	−14.4514	−	6.07925i	−0.458602	−	0.192919i
$994$	−39.3057	+	17.9718i	−1.24670	+	0.570032i
$995$	−1.00850	+	1.74678i	−0.0319717	+	0.0553766i
$996$	−1.39590	−	11.0729i	−0.0442307	−	0.350857i
$997$	7.69429	−	13.3269i	0.243680	−	0.422067i	−0.718079	−	0.695961i	$-0.754979\pi$
$997$	7.69429	−	13.3269i	0.243680	−	0.422067i	0.961760	+	0.273894i	$0.0883118\pi$
$998$	0.0540707	+	0.0936531i	0.00171158	+	0.00296454i
$999$	36.2178	+	5.37710i	1.14588	+	0.170124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.121.4	yes	36
3.2	odd	2		945.2.l.c.226.15		36
7.4	even	3		315.2.k.c.256.15	yes	36
9.2	odd	6		945.2.k.c.856.4		36
9.7	even	3		315.2.k.c.16.15	✓	36
21.11	odd	6		945.2.k.c.361.4		36
63.11	odd	6		945.2.l.c.46.15		36
63.25	even	3	inner	315.2.l.c.151.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.15	✓	36	9.7	even	3
315.2.k.c.256.15	yes	36	7.4	even	3
315.2.l.c.121.4	yes	36	1.1	even	1	trivial
315.2.l.c.151.4	yes	36	63.25	even	3	inner
945.2.k.c.361.4		36	21.11	odd	6
945.2.k.c.856.4		36	9.2	odd	6
945.2.l.c.46.15		36	63.11	odd	6
945.2.l.c.226.15		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)

\(f(q)\)	\(=\)	\(q-1.69039 q^{2} +(-1.59654 - 0.671613i) q^{3} +0.857411 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.69877 + 1.13529i) q^{6} +(2.40616 - 1.10017i) q^{7} +1.93142 q^{8} +(2.09787 + 2.14451i) q^{9} +O(q^{10})\)	\(q-1.69039 q^{2} +(-1.59654 - 0.671613i) q^{3} +0.857411 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.69877 + 1.13529i) q^{6} +(2.40616 - 1.10017i) q^{7} +1.93142 q^{8} +(2.09787 + 2.14451i) q^{9} +(0.845194 + 1.46392i) q^{10} +(-2.27246 + 3.93601i) q^{11} +(-1.36889 - 0.575848i) q^{12} +(1.58483 - 2.74501i) q^{13} +(-4.06735 + 1.85972i) q^{14} +(0.216636 + 1.71845i) q^{15} -4.97967 q^{16} +(-2.83608 - 4.91224i) q^{17} +(-3.54622 - 3.62506i) q^{18} +(1.70155 - 2.94717i) q^{19} +(-0.428706 - 0.742540i) q^{20} +(-4.58042 + 0.140463i) q^{21} +(3.84133 - 6.65338i) q^{22} +(0.0116662 + 0.0202064i) q^{23} +(-3.08358 - 1.29716i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.67898 + 4.64013i) q^{26} +(-1.90906 - 4.83275i) q^{27} +(2.06307 - 0.943302i) q^{28} +(-5.17048 - 8.95554i) q^{29} +(-0.366199 - 2.90485i) q^{30} +1.71913 q^{31} +4.55473 q^{32} +(6.27154 - 4.75778i) q^{33} +(4.79408 + 8.30360i) q^{34} +(-2.15586 - 1.53371i) q^{35} +(1.79874 + 1.83873i) q^{36} +(-3.52326 + 6.10247i) q^{37} +(-2.87628 + 4.98186i) q^{38} +(-4.37383 + 3.31812i) q^{39} +(-0.965709 - 1.67266i) q^{40} +(-3.45798 + 5.98939i) q^{41} +(7.74269 - 0.237437i) q^{42} +(-4.52050 - 7.82973i) q^{43} +(-1.94843 + 3.37478i) q^{44} +(0.808265 - 2.88907i) q^{45} +(-0.0197204 - 0.0341567i) q^{46} -1.23962 q^{47} +(7.95023 + 3.34441i) q^{48} +(4.57923 - 5.29440i) q^{49} +(0.845194 - 1.46392i) q^{50} +(1.22880 + 9.74734i) q^{51} +(1.35885 - 2.35360i) q^{52} +(-5.10622 - 8.84423i) q^{53} +(3.22704 + 8.16923i) q^{54} +4.54491 q^{55} +(4.64731 - 2.12490i) q^{56} +(-4.69595 + 3.56249i) q^{57} +(8.74012 + 15.1383i) q^{58} +9.28756 q^{59} +(0.185746 + 1.47342i) q^{60} -8.57851 q^{61} -2.90599 q^{62} +(7.40716 + 2.85201i) q^{63} +2.26007 q^{64} -3.16967 q^{65} +(-10.6013 + 8.04249i) q^{66} -1.50255 q^{67} +(-2.43169 - 4.21181i) q^{68} +(-0.00505463 - 0.0400955i) q^{69} +(3.64424 + 2.59257i) q^{70} +9.66372 q^{71} +(4.05187 + 4.14195i) q^{72} +(-5.85704 - 10.1447i) q^{73} +(5.95568 - 10.3155i) q^{74} +(1.37990 - 1.04684i) q^{75} +(1.45893 - 2.52694i) q^{76} +(-1.13760 + 11.9708i) q^{77} +(7.39347 - 5.60892i) q^{78} -2.16538 q^{79} +(2.48983 + 4.31252i) q^{80} +(-0.197856 + 8.99782i) q^{81} +(5.84532 - 10.1244i) q^{82} +(3.75755 + 6.50826i) q^{83} +(-3.92730 + 0.120434i) q^{84} +(-2.83608 + 4.91224i) q^{85} +(7.64139 + 13.2353i) q^{86} +(2.24022 + 17.7704i) q^{87} +(-4.38906 + 7.60208i) q^{88} +(4.27846 - 7.41051i) q^{89} +(-1.36628 + 4.88364i) q^{90} +(0.793374 - 8.34854i) q^{91} +(0.0100027 + 0.0173252i) q^{92} +(-2.74465 - 1.15459i) q^{93} +2.09544 q^{94} -3.40310 q^{95} +(-7.27181 - 3.05902i) q^{96} +(-0.533838 - 0.924635i) q^{97} +(-7.74068 + 8.94958i) q^{98} +(-13.2081 + 3.38394i) 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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