LMFDB - Embedded newform 315.2.k.c.16.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 0, 2]))

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

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

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.15
Character	$\chi$	$=$	315.16
Dual form			315.2.k.c.256.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.845194 + 1.46392i) q^{2} +(0.216636 - 1.71845i) q^{3} +(-0.428706 + 0.742540i) q^{4} +1.00000 q^{5} +(2.69877 - 1.13529i) q^{6} +(-2.15586 - 1.53371i) q^{7} +1.93142 q^{8} +(-2.90614 - 0.744556i) q^{9} +O(q^{10})$	\(q+(0.845194 + 1.46392i) q^{2} +(0.216636 - 1.71845i) q^{3} +(-0.428706 + 0.742540i) q^{4} +1.00000 q^{5} +(2.69877 - 1.13529i) q^{6} +(-2.15586 - 1.53371i) q^{7} +1.93142 q^{8} +(-2.90614 - 0.744556i) q^{9} +(0.845194 + 1.46392i) q^{10} +4.54491 q^{11} +(1.18314 + 0.897570i) q^{12} +(1.58483 + 2.74501i) q^{13} +(0.423107 - 4.45229i) q^{14} +(0.216636 - 1.71845i) q^{15} +(2.48983 + 4.31252i) q^{16} +(-2.83608 - 4.91224i) q^{17} +(-1.36628 - 4.88364i) q^{18} +(1.70155 - 2.94717i) q^{19} +(-0.428706 + 0.742540i) q^{20} +(-3.10264 + 3.37248i) q^{21} +(3.84133 + 6.65338i) q^{22} -0.0233324 q^{23} +(0.418415 - 3.31905i) q^{24} +1.00000 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} +(2.69877 - 1.13529i) q^{30} +(-0.859563 + 1.48881i) q^{31} +(-2.27737 + 3.94452i) q^{32} +(0.984591 - 7.81020i) 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} +5.75256 q^{38} +(5.06050 - 2.12879i) q^{39} +1.93142 q^{40} +(-3.45798 - 5.98939i) q^{41} +(-7.55937 - 1.69161i) q^{42} +(-4.52050 + 7.82973i) q^{43} +(-1.94843 + 3.37478i) q^{44} +(-2.90614 - 0.744556i) q^{45} +(-0.0197204 - 0.0341567i) q^{46} +(0.619810 + 1.07354i) q^{47} +(7.95023 - 3.34441i) q^{48} +(2.29547 + 6.61293i) q^{49} +(0.845194 + 1.46392i) q^{50} +(-9.05584 + 3.80950i) q^{51} -2.71771 q^{52} +(-5.10622 - 8.84423i) q^{53} +(-8.68828 + 1.28991i) q^{54} +4.54491 q^{55} +(-4.16387 - 2.96224i) q^{56} +(-4.69595 - 3.56249i) q^{57} -17.4802 q^{58} +(-4.64378 + 8.04327i) q^{59} +(1.18314 + 0.897570i) q^{60} +(4.28926 + 7.42921i) q^{61} -2.90599 q^{62} +(5.12329 + 6.06233i) q^{63} +2.26007 q^{64} +(1.58483 + 2.74501i) q^{65} +(12.2657 - 5.15977i) q^{66} +(0.751275 - 1.30125i) q^{67} +4.86338 q^{68} +(-0.00505463 + 0.0400955i) q^{69} +(0.423107 - 4.45229i) q^{70} +9.66372 q^{71} +(-5.61297 - 1.43805i) q^{72} +(-5.85704 - 10.1447i) q^{73} -11.9114 q^{74} +(0.216636 - 1.71845i) q^{75} +(1.45893 + 2.52694i) q^{76} +(-9.79819 - 6.97058i) q^{77} +(7.39347 + 5.60892i) q^{78} +(1.08269 + 1.87527i) q^{79} +(2.48983 + 4.31252i) q^{80} +(7.89127 + 4.32756i) q^{81} +(5.84532 - 10.1244i) q^{82} +(3.75755 - 6.50826i) q^{83} +(-1.17408 - 3.74963i) q^{84} +(-2.83608 - 4.91224i) q^{85} -15.2828 q^{86} +(14.2695 + 10.8253i) q^{87} +8.77812 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} +(2.37223 + 1.79965i) q^{93} +(-1.04772 + 1.81470i) q^{94} +(1.70155 - 2.94717i) q^{95} +(6.28509 + 4.76806i) 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} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) $ 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.845194	+	1.46392i	0.597642	+	1.03515i	0.993168	+	0.116692i	$0.0372291\pi$
$2$	0.845194	+	1.46392i	0.597642	+	1.03515i	−0.395526	+	0.918455i	$0.629438\pi$
$3$	0.216636	−	1.71845i	0.125075	−	0.992147i
$3$	0.216636	−	1.71845i	0.125075	−	0.992147i
$4$	−0.428706	+	0.742540i	−0.214353	+	0.371270i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	2.69877	−	1.13529i	1.10177	−	0.463478i
$7$	−2.15586	−	1.53371i	−0.814839	−	0.579688i
$7$	−2.15586	−	1.53371i	−0.814839	−	0.579688i
$8$	1.93142			0.682860
$9$	−2.90614	−	0.744556i	−0.968713	−	0.248185i
$10$	0.845194	+	1.46392i	0.267274	+	0.462932i
$11$	4.54491			1.37034			0.685171	−	0.728382i	$-0.259727\pi$
$11$	4.54491			1.37034			0.685171	+	0.728382i	$0.259727\pi$
$12$	1.18314	+	0.897570i	0.341544	+	0.259106i
$13$	1.58483	+	2.74501i	0.439554	+	0.761329i	0.997655	−	0.0684435i	$-0.0218033\pi$
$13$	1.58483	+	2.74501i	0.439554	+	0.761329i	−0.558101	+	0.829773i	$0.688470\pi$
$14$	0.423107	−	4.45229i	0.113080	−	1.18992i
$15$	0.216636	−	1.71845i	0.0559352	−	0.443702i
$16$	2.48983	+	4.31252i	0.622459	+	1.07813i
$17$	−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	$-0.408113\pi$
$18$	−1.36628	−	4.88364i	−0.322035	−	1.15109i
$19$	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
$21$	−3.10264	+	3.37248i	−0.677052	+	0.735935i
$22$	3.84133	+	6.65338i	0.818974	+	1.41851i
$23$	−0.0233324			−0.00486514			−0.00243257	−	0.999997i	$-0.500774\pi$
$23$	−0.0233324			−0.00486514			−0.00243257	+	0.999997i	$0.500774\pi$
$24$	0.418415	−	3.31905i	0.0854085	−	0.677497i
$25$	1.00000			0.200000
$26$	−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	−0.237979	+	0.971270i	$0.576485\pi$
$29$	−5.17048	+	8.95554i	−0.960134	+	1.66300i	−0.722155	+	0.691731i	$0.756848\pi$
$30$	2.69877	−	1.13529i	0.492726	−	0.207274i
$31$	−0.859563	+	1.48881i	−0.154382	+	0.267398i	−0.932834	−	0.360307i	$-0.882672\pi$
$31$	−0.859563	+	1.48881i	−0.154382	+	0.267398i	0.778452	+	0.627704i	$0.216005\pi$
$32$	−2.27737	+	3.94452i	−0.402585	+	0.697298i
$33$	0.984591	−	7.81020i	0.171395	−	1.35958i
$34$	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	$0.970024\pi$
$38$	5.75256			0.933188
$39$	5.06050	−	2.12879i	0.810328	−	0.340879i
$40$	1.93142			0.305384
$41$	−3.45798	−	5.98939i	−0.540045	−	0.935386i	−0.998901	−	0.0468747i	$-0.985074\pi$
$41$	−3.45798	−	5.98939i	−0.540045	−	0.935386i	0.458856	−	0.888511i	$-0.348259\pi$
$42$	−7.55937	−	1.69161i	−1.16644	−	0.261022i
$43$	−4.52050	+	7.82973i	−0.689369	+	1.19402i	0.282673	+	0.959216i	$0.408779\pi$
$43$	−4.52050	+	7.82973i	−0.689369	+	1.19402i	−0.972042	+	0.234806i	$0.924554\pi$
$44$	−1.94843	+	3.37478i	−0.293737	+	0.508767i
$45$	−2.90614	−	0.744556i	−0.433221	−	0.110992i
$46$	−0.0197204	−	0.0341567i	−0.00290761	−	0.00503613i
$47$	0.619810	+	1.07354i	0.0904085	+	0.156592i	0.907683	−	0.419656i	$-0.137849\pi$
$47$	0.619810	+	1.07354i	0.0904085	+	0.156592i	−0.817275	+	0.576248i	$0.804516\pi$
$48$	7.95023	−	3.34441i	1.14752	−	0.482724i
$49$	2.29547	+	6.61293i	0.327924	+	0.944704i
$50$	0.845194	+	1.46392i	0.119528	+	0.207029i
$51$	−9.05584	+	3.80950i	−1.26807	+	0.533437i
$52$	−2.71771			−0.376878
$53$	−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	$-0.414105\pi$
$54$	−8.68828	+	1.28991i	−1.18233	+	0.175535i
$55$	4.54491			0.612836
$56$	−4.16387	−	2.96224i	−0.556420	−	0.395845i
$57$	−4.69595	−	3.56249i	−0.621993	−	0.471863i
$58$	−17.4802			−2.29527
$59$	−4.64378	+	8.04327i	−0.604569	+	1.04714i	0.387550	+	0.921848i	$0.373321\pi$
$59$	−4.64378	+	8.04327i	−0.604569	+	1.04714i	−0.992119	+	0.125296i	$0.960012\pi$
$60$	1.18314	+	0.897570i	0.152743	+	0.115876i
$61$	4.28926	+	7.42921i	0.549183	+	0.951213i	0.998331	+	0.0577554i	$0.0183943\pi$
$61$	4.28926	+	7.42921i	0.549183	+	0.951213i	−0.449148	+	0.893457i	$0.648272\pi$
$62$	−2.90599			−0.369061
$63$	5.12329	+	6.06233i	0.645474	+	0.763782i
$64$	2.26007			0.282509
$65$	1.58483	+	2.74501i	0.196574	+	0.340477i
$66$	12.2657	−	5.15977i	1.50980	−	0.635124i
$67$	0.751275	−	1.30125i	0.0917828	−	0.158973i	−0.816479	−	0.577376i	$-0.804077\pi$
$67$	0.751275	−	1.30125i	0.0917828	−	0.158973i	0.908261	+	0.418403i	$0.137410\pi$
$68$	4.86338			0.589772
$69$	−0.00505463	+	0.0400955i	−0.000608506	+	0.00482693i
$70$	0.423107	−	4.45229i	0.0505710	−	0.532150i
$71$	9.66372			1.14687			0.573436	−	0.819250i	$-0.305610\pi$
$71$	9.66372			1.14687			0.573436	+	0.819250i	$0.305610\pi$
$72$	−5.61297	−	1.43805i	−0.661495	−	0.169476i
$73$	−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	$-0.407090\pi$
$74$	−11.9114			−1.38467
$75$	0.216636	−	1.71845i	0.0250150	−	0.198429i
$76$	1.45893	+	2.52694i	0.167350	+	0.289860i
$77$	−9.79819	−	6.97058i	−1.11661	−	0.794371i
$78$	7.39347	+	5.60892i	0.837146	+	0.635085i
$79$	1.08269	+	1.87527i	0.121812	+	0.210985i	0.920482	−	0.390784i	$-0.127796\pi$
$79$	1.08269	+	1.87527i	0.121812	+	0.210985i	−0.798670	+	0.601769i	$0.794463\pi$
$80$	2.48983	+	4.31252i	0.278372	+	0.482154i
$81$	7.89127	+	4.32756i	0.876808	+	0.480840i
$82$	5.84532	−	10.1244i	0.645508	−	1.11805i
$83$	3.75755	−	6.50826i	0.412444	−	0.714374i	−0.582712	−	0.812679i	$-0.698008\pi$
$83$	3.75755	−	6.50826i	0.412444	−	0.714374i	0.995156	+	0.0983042i	$0.0313418\pi$
$84$	−1.17408	−	3.74963i	−0.128103	−	0.409119i
$85$	−2.83608	−	4.91224i	−0.307617	−	0.532808i
$86$	−15.2828			−1.64799
$87$	14.2695	+	10.8253i	1.52985	+	1.16059i
$88$	8.77812			0.935751
$89$	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
$93$	2.37223	+	1.79965i	0.245989	+	0.186615i
$94$	−1.04772	+	1.81470i	−0.108064	+	0.187172i
$95$	1.70155	−	2.94717i	0.174575	−	0.302373i
$96$	6.28509	+	4.76806i	0.641469	+	0.486638i
$97$	−0.533838	+	0.924635i	−0.0542030	+	0.0938824i	−0.891854	−	0.452324i	$-0.850595\pi$
$97$	−0.533838	+	0.924635i	−0.0542030	+	0.0938824i	0.837651	+	0.546206i	$0.183928\pi$
$98$	−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
$101$	−2.78241			−0.276861			−0.138430	−	0.990372i	$-0.544206\pi$
$101$	−2.78241			−0.276861			−0.138430	+	0.990372i	$0.544206\pi$
$102$	−13.2307	−	10.0372i	−1.31004	−	0.993836i
$103$	−3.91721			−0.385975			−0.192987	−	0.981201i	$-0.561818\pi$
$103$	−3.91721			−0.385975			−0.192987	+	0.981201i	$0.561818\pi$
$104$	3.06098	+	5.30177i	0.300153	+	0.519881i
$105$	−3.10264	+	3.37248i	−0.302787	+	0.329120i
$106$	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	$-0.0415981\pi$
$108$	−2.77009	−	3.48938i	−0.266552	−	0.335766i
$109$	−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	$0.836128\pi$
$110$	3.84133	+	6.65338i	0.366257	+	0.634375i
$111$	9.72351	+	7.37656i	0.922915	+	0.700152i
$112$	1.24642	−	13.1159i	0.117776	−	1.23933i
$113$	−1.24821	−	2.16197i	−0.117422	−	0.203381i	0.801323	−	0.598231i	$-0.204130\pi$
$113$	−1.24821	−	2.16197i	−0.117422	−	0.203381i	−0.918745	+	0.394851i	$0.870796\pi$
$114$	1.24621	−	9.88548i	0.116718	−	0.925860i
$115$	−0.0233324			−0.00217576
$116$	−4.43323	−	7.67858i	−0.411615	−	0.712938i
$117$	−2.56193	−	9.15738i	−0.236850	−	0.846600i
$118$	−15.6996			−1.44526
$119$	−1.41976	+	14.9398i	−0.130149	+	1.36953i
$120$	0.418415	−	3.31905i	0.0381959	−	0.302986i
$121$	9.65621			0.877837
$122$	−7.25051	+	12.5582i	−0.656430	+	1.13697i
$123$	−11.0416	+	4.64484i	−0.995586	+	0.418811i
$124$	−0.736999	−	1.27652i	−0.0661845	−	0.114635i
$125$	1.00000			0.0894427
$126$	−4.54458	+	12.6239i	−0.404864	+	1.12463i
$127$	−0.0467625			−0.00414950			−0.00207475	−	0.999998i	$-0.500660\pi$
$127$	−0.0467625			−0.00414950			−0.00207475	+	0.999998i	$0.500660\pi$
$128$	6.46493	+	11.1976i	0.571425	+	0.989736i
$129$	12.4757	+	9.46445i	1.09842	+	0.833298i
$130$	−2.67898	+	4.64013i	−0.234962	+	0.406967i
$131$	10.1498			0.886794			0.443397	−	0.896325i	$-0.353773\pi$
$131$	10.1498			0.886794			0.443397	+	0.896325i	$0.353773\pi$
$132$	5.37728	+	4.07937i	0.468032	+	0.355064i
$133$	−8.18841	+	3.74400i	−0.710025	+	0.324646i
$134$	2.53989			0.219413
$135$	−1.90906	+	4.83275i	−0.164305	+	0.415937i
$136$	−5.47767	−	9.48760i	−0.469706	−	0.813555i
$137$	−15.5890			−1.33186			−0.665930	−	0.746014i	$-0.731965\pi$
$137$	−15.5890			−1.33186			−0.665930	+	0.746014i	$0.731965\pi$
$138$	−0.0629687	+	0.0264889i	−0.00536025	+	0.00225489i
$139$	7.81319	+	13.5328i	0.662706	+	1.14784i	0.979902	+	0.199481i	$0.0639255\pi$
$139$	7.81319	+	13.5328i	0.662706	+	1.14784i	−0.317195	+	0.948360i	$0.602741\pi$
$140$	2.06307	−	0.943302i	0.174361	−	0.0797235i
$141$	1.97910	−	0.832544i	0.166670	−	0.0701128i
$142$	8.16772	+	14.1469i	0.685420	+	1.18718i
$143$	7.20293	+	12.4758i	0.602339	+	1.04328i
$144$	−4.02489	−	14.3866i	−0.335407	−	1.19888i
$145$	−5.17048	+	8.95554i	−0.429385	+	0.743717i
$146$	9.90067	−	17.1485i	0.819385	−	1.41922i
$147$	11.8613	−	2.51204i	0.978301	−	0.207190i
$148$	−3.02088	−	5.23232i	−0.248315	−	0.430094i
$149$	7.19090			0.589102			0.294551	−	0.955636i	$-0.404830\pi$
$149$	7.19090			0.589102			0.294551	+	0.955636i	$0.404830\pi$
$150$	2.69877	−	1.13529i	0.220354	−	0.0926957i
$151$	14.0262			1.14143			0.570717	−	0.821147i	$-0.306665\pi$
$151$	14.0262			1.14143			0.570717	+	0.821147i	$0.306665\pi$
$152$	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
$156$	−0.588753	+	4.67024i	−0.0471380	+	0.373919i
$157$	−0.839922	+	1.45479i	−0.0670331	+	0.116105i	−0.897594	−	0.440823i	$-0.854687\pi$
$157$	−0.839922	+	1.45479i	−0.0670331	+	0.116105i	0.830561	+	0.556928i	$0.188020\pi$
$158$	−1.83017	+	3.16994i	−0.145600	+	0.252187i
$159$	−16.3046	+	6.85880i	−1.29304	+	0.543938i
$160$	−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	$0.741421\pi$
$164$	5.92981			0.463041
$165$	0.984591	−	7.81020i	0.0766503	−	0.608023i
$166$	12.7034			0.985977
$167$	−6.89385	−	11.9405i	−0.533462	−	0.923983i	−0.999236	−	0.0390794i	$-0.987557\pi$
$167$	−6.89385	−	11.9405i	−0.533462	−	0.923983i	0.465774	−	0.884904i	$-0.345776\pi$
$168$	−5.99250	+	6.51367i	−0.462331	+	0.502541i
$169$	1.47661	−	2.55756i	0.113585	−	0.196735i
$170$	4.79408	−	8.30360i	0.367689	−	0.636857i
$171$	−7.13927	+	7.29799i	−0.545954	+	0.558091i
$172$	−3.87592	−	6.71330i	−0.295536	−	0.511884i
$173$	0.0888908	+	0.153963i	0.00675825	+	0.0117056i	0.869385	−	0.494136i	$-0.164515\pi$
$173$	0.0888908	+	0.153963i	0.00675825	+	0.0117056i	−0.862627	+	0.505841i	$0.831182\pi$
$174$	−3.78685	+	30.0389i	−0.287080	+	2.27724i
$175$	−2.15586	−	1.53371i	−0.162968	−	0.115938i
$176$	11.3161	+	19.6000i	0.852981	+	1.47741i
$177$	12.8159	+	9.72257i	0.963305	+	0.730793i
$178$	14.4645			1.08416
$179$	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	$0.712989\pi$
$180$	1.79874	−	1.83873i	0.134070	−	0.137051i
$181$	−11.8350			−0.879692			−0.439846	−	0.898073i	$-0.644967\pi$
$181$	−11.8350			−0.879692			−0.439846	+	0.898073i	$0.644967\pi$
$182$	12.8921	−	5.89470i	0.955629	−	0.436944i
$183$	13.6959	−	5.76144i	1.01243	−	0.425898i
$184$	−0.0450646			−0.00332221
$185$	−3.52326	+	6.10247i	−0.259035	+	0.448662i
$186$	−0.629542	+	4.99380i	−0.0461603	+	0.366163i
$187$	−12.8898	−	22.3257i	−0.942592	−	1.63262i
$188$	−1.06286			−0.0775173
$189$	11.5277	−	7.49080i	0.838517	−	0.544876i
$190$	5.75256			0.417334
$191$	−9.09336	−	15.7502i	−0.657973	−	1.13964i	−0.981140	−	0.193300i	$-0.938081\pi$
$191$	−9.09336	−	15.7502i	−0.657973	−	1.13964i	0.323167	−	0.946342i	$-0.395252\pi$
$192$	0.489612	−	3.88382i	0.0353347	−	0.280290i
$193$	−3.84670	+	6.66268i	−0.276892	+	0.479590i	−0.970611	−	0.240655i	$-0.922638\pi$
$193$	−3.84670	+	6.66268i	−0.276892	+	0.479590i	0.693719	+	0.720246i	$0.255971\pi$
$194$	−1.80479			−0.129576
$195$	5.06050	−	2.12879i	0.362390	−	0.152446i
$196$	−5.89444	−	1.13052i	−0.421032	−	0.0807518i
$197$	3.01874			0.215077			0.107538	−	0.994201i	$-0.465703\pi$
$197$	3.01874			0.215077			0.107538	+	0.994201i	$0.465703\pi$
$198$	−6.20962	−	22.1957i	−0.441299	−	1.57738i
$199$	−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	$0.856109\pi$
$200$	1.93142			0.136572
$201$	−2.07337	−	1.57292i	−0.146244	−	0.110946i
$202$	−2.35168	−	4.07323i	−0.165464	−	0.286591i
$203$	24.8820	−	11.3769i	1.74638	−	0.798499i
$204$	1.05358	−	8.35747i	0.0737656	−	0.585140i
$205$	−3.45798	−	5.98939i	−0.241516	−	0.418317i
$206$	−3.31081	−	5.73448i	−0.230675	−	0.399540i
$207$	0.0678071	+	0.0173723i	0.00471292	+	0.00120746i
$208$	−7.89194	+	13.6692i	−0.547208	+	0.947792i
$209$	7.73339	−	13.3946i	0.534930	−	0.926526i
$210$	−7.55937	−	1.69161i	−0.521646	−	0.116732i
$211$	−2.69724	−	4.67175i	−0.185686	−	0.321617i	0.758122	−	0.652113i	$-0.226117\pi$
$211$	−2.69724	−	4.67175i	−0.185686	−	0.321617i	−0.943807	+	0.330496i	$0.892784\pi$
$212$	8.75626			0.601382
$213$	2.09351	−	16.6066i	0.143445	−	1.13787i
$214$	21.2830			1.45488
$215$	−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
$219$	−18.7020	+	7.86733i	−1.26376	+	0.531625i
$220$	−1.94843	+	3.37478i	−0.131363	+	0.227527i
$221$	8.98944	−	15.5702i	0.604695	−	1.04736i
$222$	−2.58043	+	20.4691i	−0.173187	+	1.37379i
$223$	8.93044	−	15.4680i	0.598026	−	1.03581i	−0.395086	−	0.918644i	$-0.629285\pi$
$223$	8.93044	−	15.4680i	0.598026	−	1.03581i	0.993112	−	0.117168i	$-0.0373816\pi$
$224$	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
$227$	1.60590			0.106587			0.0532936	−	0.998579i	$-0.483028\pi$
$227$	1.60590			0.106587			0.0532936	+	0.998579i	$0.483028\pi$
$228$	4.65847	−	1.95967i	0.308515	−	0.129782i
$229$	−17.0481			−1.12657			−0.563285	−	0.826263i	$-0.690463\pi$
$229$	−17.0481			−1.12657			−0.563285	+	0.826263i	$0.690463\pi$
$230$	−0.0197204	−	0.0341567i	−0.00130032	−	0.00225223i
$231$	−14.1012	+	15.3276i	−0.927792	+	1.00848i
$232$	−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	$0.0142752\pi$
$234$	11.2403	−	11.4902i	0.734804	−	0.751139i
$235$	0.619810	+	1.07354i	0.0404319	+	0.0700301i
$236$	−3.98163	−	6.89639i	−0.259182	−	0.448916i
$237$	3.45711	−	1.45430i	0.224564	−	0.0944667i
$238$	−23.0707	+	10.5487i	−1.49545	+	0.683768i
$239$	−13.9148	−	24.1011i	−0.900072	−	1.55897i	−0.827400	−	0.561614i	$-0.810181\pi$
$239$	−13.9148	−	24.1011i	−0.900072	−	1.55897i	−0.0726720	−	0.997356i	$-0.523153\pi$
$240$	7.95023	−	3.34441i	0.513185	−	0.215881i
$241$	−22.8514			−1.47199			−0.735993	−	0.676989i	$-0.763284\pi$
$241$	−22.8514			−1.47199			−0.735993	+	0.676989i	$0.763284\pi$
$242$	8.16137	+	14.1359i	0.524633	+	0.908691i
$243$	9.14623	−	12.6232i	0.586731	−	0.809782i
$244$	−7.35531			−0.470876
$245$	2.29547	+	6.61293i	0.146652	+	0.422485i
$246$	−16.1319	−	12.2382i	−1.02854	−	0.780279i
$247$	10.7867			0.686341
$248$	−1.66018	+	2.87551i	−0.105421	+	0.182595i
$249$	−10.3701	−	7.86708i	−0.657178	−	0.498556i
$250$	0.845194	+	1.46392i	0.0534548	+	0.0925864i
$251$	−0.248772			−0.0157023			−0.00785116	−	0.999969i	$-0.502499\pi$
$251$	−0.248772			−0.0157023			−0.00785116	+	0.999969i	$0.502499\pi$
$252$	−6.69791	+	1.20529i	−0.421928	+	0.0759264i
$253$	−0.106044			−0.00666690
$254$	−0.0395234	−	0.0684566i	−0.00247992	−	0.00429535i
$255$	−9.05584	+	3.80950i	−0.567099	+	0.238560i
$256$	−8.66817	+	15.0137i	−0.541761	+	0.938357i
$257$	7.98390			0.498022			0.249011	−	0.968501i	$-0.419894\pi$
$257$	7.98390			0.498022			0.249011	+	0.968501i	$0.419894\pi$
$258$	−3.31080	+	26.2627i	−0.206121	+	1.63504i
$259$	16.9551	−	7.75240i	1.05354	−	0.481711i
$260$	−2.71771			−0.168545
$261$	21.6940	−	22.1763i	1.34283	−	1.37268i
$262$	8.57857	+	14.8585i	0.529986	+	0.917962i
$263$	10.8865			0.671288			0.335644	−	0.941989i	$-0.391046\pi$
$263$	10.8865			0.671288			0.335644	+	0.941989i	$0.391046\pi$
$264$	1.90166	−	15.0848i	0.117039	−	0.928403i
$265$	−5.10622	−	8.84423i	−0.313673	−	0.543297i
$266$	−12.4017	−	8.82276i	−0.760398	−	0.540958i
$267$	−11.8077	−	8.95770i	−0.722621	−	0.548203i
$268$	0.644151	+	1.11570i	0.0393478	+	0.0681524i
$269$	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	$0.782180\pi$
$270$	−8.68828	+	1.28991i	−0.528752	+	0.0785015i
$271$	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
$273$	−14.1747	−	3.17197i	−0.857890	−	0.191976i
$274$	−13.1757	−	22.8211i	−0.795976	−	1.37867i
$275$	4.54491			0.274068
$276$	−0.0276056	−	0.0209424i	−0.00166166	−	0.00126059i
$277$	8.64216			0.519257			0.259629	−	0.965709i	$-0.416400\pi$
$277$	8.64216			0.519257			0.259629	+	0.965709i	$0.416400\pi$
$278$	−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	0.127812	−	0.991798i	$-0.459205\pi$
$281$	15.4694	−	26.7938i	0.922829	−	1.59839i	0.795017	−	0.606588i	$-0.207462\pi$
$282$	2.89150	+	2.19358i	0.172186	+	0.130626i
$283$	−2.82865	+	4.89937i	−0.168146	+	0.291237i	−0.937768	−	0.347262i	$-0.887111\pi$
$283$	−2.82865	+	4.89937i	−0.168146	+	0.291237i	0.769622	+	0.638500i	$0.220445\pi$
$284$	−4.14289	+	7.17570i	−0.245835	+	0.425799i
$285$	−4.69595	−	3.56249i	−0.278164	−	0.211024i
$286$	−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
$290$	−17.4802			−1.02647
$291$	1.47329	+	1.11768i	0.0863658	+	0.0655197i
$292$	10.0438			0.587768
$293$	7.09988	+	12.2974i	0.414779	+	0.718419i	0.995405	−	0.0957516i	$-0.0305254\pi$
$293$	7.09988	+	12.2974i	0.414779	+	0.718419i	−0.580626	+	0.814170i	$0.697192\pi$
$294$	13.7025	+	15.2408i	0.799146	+	0.888860i
$295$	−4.64378	+	8.04327i	−0.270371	+	0.468297i
$296$	−6.80489	+	11.7864i	−0.395526	+	0.685071i
$297$	−8.67649	+	21.9644i	−0.503461	+	1.27451i
$298$	6.07771	+	10.5269i	0.352072	+	0.609807i
$299$	−0.0369779	−	0.0640477i	−0.00213849	−	0.00370397i
$300$	1.18314	+	0.897570i	0.0683089	+	0.0518212i
$301$	21.7541	−	9.94667i	1.25389	−	0.573317i
$302$	11.8548	+	20.5332i	0.682169	+	1.18155i
$303$	−0.602771	+	4.78144i	−0.0346283	+	0.274687i
$304$	16.9463			0.971937
$305$	4.28926	+	7.42921i	0.245602	+	0.425395i
$306$	−20.1148	+	20.5619i	−1.14988	+	1.17545i
$307$	10.5235			0.600606			0.300303	−	0.953844i	$-0.402912\pi$
$307$	10.5235			0.600606			0.300303	+	0.953844i	$0.402912\pi$
$308$	9.37647	−	4.28722i	0.534274	−	0.244287i
$309$	−0.848609	+	6.73153i	−0.0482757	+	0.382944i
$310$	−2.90599			−0.165049
$311$	−13.9474	+	24.1575i	−0.790882	+	1.36985i	0.134540	+	0.990908i	$0.457044\pi$
$311$	−13.9474	+	24.1575i	−0.790882	+	1.36985i	−0.925421	+	0.378939i	$0.876289\pi$
$312$	9.77394	−	4.11158i	0.553340	−	0.232772i
$313$	−14.7928	−	25.6218i	−0.836137	−	1.44823i	−0.893102	−	0.449855i	$-0.851476\pi$
$313$	−14.7928	−	25.6218i	−0.836137	−	1.44823i	0.0569648	−	0.998376i	$-0.481858\pi$
$314$	−2.83959			−0.160247
$315$	5.12329	+	6.06233i	0.288665	+	0.341574i
$316$	−1.85662			−0.104443
$317$	2.75375	+	4.76964i	0.154666	+	0.267890i	0.932937	−	0.360039i	$-0.117236\pi$
$317$	2.75375	+	4.76964i	0.154666	+	0.267890i	−0.778271	+	0.627928i	$0.783903\pi$
$318$	−23.8212	−	18.0715i	−1.33583	−	1.01340i
$319$	−23.4994	+	40.7021i	−1.31571	+	2.27888i
$320$	2.26007			0.126342
$321$	−17.3738	−	13.1803i	−0.969713	−	0.735654i
$322$	−0.00987210	+	0.103882i	−0.000550151	+	0.00578914i
$323$	−19.3030			−1.07405
$324$	−6.59642	+	4.00433i	−0.366468	+	0.222463i
$325$	1.58483	+	2.74501i	0.0879107	+	0.152266i
$326$	−41.9780			−2.32495
$327$	−0.292699	+	0.123129i	−0.0161863	+	0.00680904i
$328$	−6.67880	−	11.5680i	−0.368775	−	0.638737i
$329$	0.310279	−	3.26501i	0.0171062	−	0.180006i
$330$	12.2657	−	5.15977i	0.675203	−	0.284036i
$331$	−4.52586	−	7.83902i	−0.248764	−	0.430872i	0.714419	−	0.699718i	$-0.246691\pi$
$331$	−4.52586	−	7.83902i	−0.248764	−	0.430872i	−0.963183	+	0.268846i	$0.913358\pi$
$332$	3.22176	+	5.58025i	0.176817	+	0.306256i
$333$	14.7827	−	15.1113i	0.810087	−	0.828096i
$334$	11.6533	−	20.1841i	0.637639	−	1.10442i
$335$	0.751275	−	1.30125i	0.0410465	−	0.0710947i
$336$	−22.2689	−	4.98328i	−1.21487	−	0.271860i
$337$	−4.96159	−	8.59372i	−0.270275	−	0.468130i	0.698657	−	0.715456i	$-0.253781\pi$
$337$	−4.96159	−	8.59372i	−0.270275	−	0.468130i	−0.968932	+	0.247327i	$0.920448\pi$
$338$	4.99207			0.271533
$339$	−3.98564	+	1.67663i	−0.216470	+	0.0910621i
$340$	4.86338			0.263754
$341$	−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
$345$	−0.00505463	+	0.0400955i	−0.000272132	+	0.00215867i
$346$	−0.150260	+	0.260258i	−0.00807803	+	0.0139916i
$347$	5.59737	−	9.69494i	0.300483	−	0.520451i	−0.675763	−	0.737119i	$-0.736186\pi$
$347$	5.59737	−	9.69494i	0.300483	−	0.520451i	0.976245	+	0.216668i	$0.0695189\pi$
$348$	−14.1556	+	5.95482i	−0.758822	+	0.319212i
$349$	−14.1414	+	24.4937i	−0.756974	+	1.31112i	0.187413	+	0.982281i	$0.439990\pi$
$349$	−14.1414	+	24.4937i	−0.756974	+	1.31112i	−0.944387	+	0.328836i	$0.893344\pi$
$350$	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
$353$	−7.35756			−0.391603			−0.195802	−	0.980644i	$-0.562731\pi$
$353$	−7.35756			−0.391603			−0.195802	+	0.980644i	$0.562731\pi$
$354$	−3.40109	+	26.9789i	−0.180766	+	1.43391i
$355$	9.66372			0.512897
$356$	3.66840	+	6.35385i	0.194425	+	0.336754i
$357$	25.3658	+	5.67628i	1.34250	+	0.300421i
$358$	−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	$-0.0303212\pi$
$360$	−5.61297	−	1.43805i	−0.295829	−	0.0757918i
$361$	3.70946	+	6.42497i	0.195235	+	0.338156i
$362$	−10.0029	−	17.3255i	−0.525741	−	0.910611i
$363$	2.09188	−	16.5937i	0.109795	−	0.870944i
$364$	5.85900	+	4.16818i	0.307095	+	0.218472i
$365$	−5.85704	−	10.1447i	−0.306572	−	0.530998i
$366$	20.0100	+	15.1802i	1.04594	+	0.793482i
$367$	−21.2211			−1.10773			−0.553866	−	0.832606i	$-0.686848\pi$
$367$	−21.2211			−1.10773			−0.553866	+	0.832606i	$0.686848\pi$
$368$	−0.0580938	−	0.100621i	−0.00302835	−	0.00524525i
$369$	5.58992	+	19.9806i	0.291000	+	1.04015i
$370$	−11.9114			−0.619242
$371$	−2.55619	+	26.8984i	−0.132711	+	1.39649i
$372$	−2.35330	+	0.989956i	−0.122013	+	0.0513268i
$373$	7.20176			0.372893			0.186446	−	0.982465i	$-0.440303\pi$
$373$	7.20176			0.372893			0.186446	+	0.982465i	$0.440303\pi$
$374$	21.7887	−	37.7391i	1.12667	−	1.95144i
$375$	0.216636	−	1.71845i	0.0111870	−	0.0887404i
$376$	1.19711	+	2.07346i	0.0617363	+	0.106930i
$377$	−32.7774			−1.68812
$378$	20.7091	+	10.5444i	1.06516	+	0.542347i
$379$	−4.15827			−0.213596			−0.106798	−	0.994281i	$-0.534060\pi$
$379$	−4.15827			−0.213596			−0.106798	+	0.994281i	$0.534060\pi$
$380$	1.45893	+	2.52694i	0.0748414	+	0.129629i
$381$	−0.0101304	+	0.0803591i	−0.000518999	+	0.00411692i
$382$	15.3713	−	26.6239i	0.786464	−	1.36220i
$383$	28.8560			1.47447			0.737237	−	0.675634i	$-0.236130\pi$
$383$	28.8560			1.47447			0.737237	+	0.675634i	$0.236130\pi$
$384$	20.6430	−	8.68386i	1.05344	−	0.443146i
$385$	−9.79819	−	6.97058i	−0.499362	−	0.355253i
$386$	−13.0048			−0.661928
$387$	18.9669	−	19.3885i	0.964140	−	0.985574i
$388$	−0.457719	−	0.792792i	−0.0232371	−	0.0402479i
$389$	−11.3953			−0.577766			−0.288883	−	0.957364i	$-0.593284\pi$
$389$	−11.3953			−0.577766			−0.288883	+	0.957364i	$0.593284\pi$
$390$	7.39347	+	5.60892i	0.374383	+	0.284019i
$391$	0.0661726	+	0.114614i	0.00334649	+	0.00579630i
$392$	4.43350	+	12.7723i	0.223926	+	0.645100i
$393$	2.19882	−	17.4420i	0.110916	−	0.879831i
$394$	2.55142	+	4.41920i	0.128539	+	0.222636i
$395$	1.08269	+	1.87527i	0.0544761	+	0.0943553i
$396$	8.17511	−	8.35685i	0.410815	−	0.419948i
$397$	−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
$399$	4.65998	+	14.8825i	0.233291	+	0.745055i
$400$	2.48983	+	4.31252i	0.124492	+	0.215626i
$401$	−34.9888			−1.74726			−0.873629	−	0.486593i	$-0.838239\pi$
$401$	−34.9888			−1.74726			−0.873629	+	0.486593i	$0.838239\pi$
$402$	0.550232	−	4.36468i	0.0274431	−	0.217690i
$403$	−5.44906			−0.271437
$404$	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
$408$	−17.4906	+	7.35774i	−0.865914	+	0.364262i
$409$	19.6361	−	34.0107i	0.970941	−	1.68172i	0.278214	−	0.960519i	$-0.410258\pi$
$409$	19.6361	−	34.0107i	0.970941	−	1.68172i	0.692727	−	0.721200i	$-0.256409\pi$
$410$	5.84532	−	10.1244i	0.288680	−	0.500008i
$411$	−3.37714	+	26.7889i	−0.166582	+	1.32140i
$412$	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
$416$	−14.4370			−0.707832
$417$	24.9481	−	10.4949i	1.22172	−	0.513936i
$418$	26.1449			1.27879
$419$	−5.62364	−	9.74043i	−0.274733	−	0.475851i	0.695335	−	0.718686i	$-0.255256\pi$
$419$	−5.62364	−	9.74043i	−0.274733	−	0.475851i	−0.970068	+	0.242835i	$0.921923\pi$
$420$	−1.17408	−	3.74963i	−0.0572893	−	0.182963i
$421$	8.87270	−	15.3680i	0.432429	−	0.748989i	−0.564653	−	0.825328i	$-0.690990\pi$
$421$	8.87270	−	15.3680i	0.432429	−	0.748989i	0.997082	+	0.0763395i	$0.0243233\pi$
$422$	4.55938	−	7.89707i	0.221947	−	0.384424i
$423$	−1.00194	−	3.58134i	−0.0487160	−	0.174131i
$424$	−9.86225	−	17.0819i	−0.478953	−	0.829571i
$425$	−2.83608	−	4.91224i	−0.137570	−	0.238279i
$426$	26.0802	−	10.9711i	1.26359	−	0.531551i
$427$	2.14722	−	22.5948i	0.103911	−	1.09344i
$428$	5.39767	+	9.34903i	0.260906	+	0.451903i
$429$	22.9995	−	9.67515i	1.11043	−	0.467121i
$430$	−15.2828			−0.737002
$431$	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	$0.760119\pi$
$432$	−25.5946	+	3.79992i	−1.23142	+	0.182824i
$433$	5.88453			0.282793			0.141396	−	0.989953i	$-0.454841\pi$
$433$	5.88453			0.282793			0.141396	+	0.989953i	$0.454841\pi$
$434$	6.26491	+	4.45695i	0.300725	+	0.213940i
$435$	14.2695	+	10.8253i	0.684171	+	0.519034i
$436$	0.157192			0.00752812
$437$	−0.0397012	+	0.0687645i	−0.00189917	+	0.00328945i
$438$	−27.3239	−	20.7288i	−1.30559	−	0.990459i
$439$	6.45010	+	11.1719i	0.307847	+	0.533206i	0.977891	−	0.209115i	$-0.0670583\pi$
$439$	6.45010	+	11.1719i	0.307847	+	0.533206i	−0.670044	+	0.742321i	$0.733725\pi$
$440$	8.77812			0.418481
$441$	−1.74724	−	20.9272i	−0.0832021	−	0.996533i
$442$	30.3913			1.44557
$443$	6.59467	+	11.4223i	0.313322	+	0.542690i	0.979079	−	0.203478i	$-0.0652247\pi$
$443$	6.59467	+	11.4223i	0.313322	+	0.542690i	−0.665757	+	0.746168i	$0.731891\pi$
$444$	−9.64591	+	4.05772i	−0.457775	+	0.192571i
$445$	4.27846	−	7.41051i	0.202819	−	0.351292i
$446$	30.1918			1.42962
$447$	1.55781	−	12.3572i	0.0736818	−	0.584476i
$448$	−4.87240	−	3.46629i	−0.230199	−	0.163767i
$449$	−0.602445			−0.0284311			−0.0142156	−	0.999899i	$-0.504525\pi$
$449$	−0.602445			−0.0284311			−0.0142156	+	0.999899i	$0.504525\pi$
$450$	−1.36628	−	4.88364i	−0.0644071	−	0.230217i
$451$	−15.7162	−	27.2212i	−0.740047	−	1.28180i
$452$	2.14046			0.100679
$453$	3.03857	−	24.1033i	0.142765	−	1.13247i
$454$	1.35729	+	2.35090i	0.0637010	+	0.110333i
$455$	0.793374	−	8.34854i	0.0371939	−	0.391385i
$456$	−9.06984	−	6.88066i	−0.424734	−	0.322216i
$457$	2.74108	+	4.74770i	0.128222	+	0.222088i	0.922988	−	0.384829i	$-0.125740\pi$
$457$	2.74108	+	4.74770i	0.128222	+	0.222088i	−0.794765	+	0.606917i	$0.792406\pi$
$458$	−14.4089	−	24.9570i	−0.673286	−	1.16616i
$459$	29.1539	−	4.32835i	1.36079	−	0.202030i
$460$	0.0100027	−	0.0173252i	0.000466379	−	0.000807793i
$461$	−3.76201	+	6.51599i	−0.175214	+	0.303480i	−0.940235	−	0.340525i	$-0.889395\pi$
$461$	−3.76201	+	6.51599i	−0.175214	+	0.303480i	0.765021	+	0.644005i	$0.222728\pi$
$462$	−34.3567	−	7.68824i	−1.59842	−	0.357689i
$463$	17.5231	+	30.3509i	0.814368	+	1.41053i	0.909781	+	0.415089i	$0.136250\pi$
$463$	17.5231	+	30.3509i	0.814368	+	1.41053i	−0.0954126	+	0.995438i	$0.530417\pi$
$464$	−51.4946			−2.39058
$465$	2.37223	+	1.79965i	0.110009	+	0.0834565i
$466$	23.7731			1.10127
$467$	−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
$471$	2.31802	+	1.75852i	0.106809	+	0.0810285i
$472$	−8.96909	+	15.5349i	−0.412836	+	0.715052i
$473$	−20.5453	+	35.5854i	−0.944672	+	1.63622i
$474$	5.05090	+	3.83177i	0.231996	+	0.175999i
$475$	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
$479$	2.36409			0.108018			0.0540089	−	0.998540i	$-0.482800\pi$
$479$	2.36409			0.108018			0.0540089	+	0.998540i	$0.482800\pi$
$480$	6.28509	+	4.76806i	0.286874	+	0.217631i
$481$	−22.3351			−1.01839
$482$	−19.3138	−	33.4525i	−0.879721	−	1.52372i
$483$	0.0723920	−	0.0786880i	0.00329395	−	0.00358043i
$484$	−4.13967	+	7.17012i	−0.188167	+	0.325915i
$485$	−0.533838	+	0.924635i	−0.0242403	+	0.0419855i
$486$	26.2098	+	2.72025i	1.18890	+	0.123393i
$487$	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	$0.602826\pi$
$488$	8.28435	+	14.3489i	0.375015	+	0.649545i
$489$	34.2676	+	25.9965i	1.54964	+	1.17560i
$490$	−7.74068	+	8.94958i	−0.349688	+	0.404301i
$491$	12.0023	+	20.7885i	0.541655	+	0.938174i	0.998809	+	0.0487865i	$0.0155354\pi$
$491$	12.0023	+	20.7885i	0.541655	+	0.938174i	−0.457154	+	0.889387i	$0.651131\pi$
$492$	1.28461	−	10.1901i	0.0579147	−	0.459404i
$493$	58.6557			2.64172
$494$	9.11685	+	15.7908i	0.410186	+	0.710464i
$495$	−13.2081	−	3.38394i	−0.593662	−	0.152097i
$496$	−8.56068			−0.384386
$497$	−20.8336	−	14.8214i	−0.934516	−	0.664828i
$498$	2.75202	−	21.8302i	0.123321	−	0.978234i
$499$	0.0639743			0.00286388			0.00143194	−	0.999999i	$-0.499544\pi$
$499$	0.0639743			0.00286388			0.00143194	+	0.999999i	$0.499544\pi$
$500$	−0.428706	+	0.742540i	−0.0191723	+	0.0332074i
$501$	−22.0126	+	9.25999i	−0.983450	+	0.413706i
$502$	−0.210260	−	0.364181i	−0.00938437	−	0.0162542i
$503$	−33.9925			−1.51565			−0.757825	−	0.652458i	$-0.773738\pi$
$503$	−33.9925			−1.51565			−0.757825	+	0.652458i	$0.773738\pi$
$504$	9.89522	+	11.7089i	0.440768	+	0.521556i
$505$	−2.78241			−0.123816
$506$	−0.0896274	−	0.155239i	−0.00398442	−	0.00690122i
$507$	−4.07515	−	3.09153i	−0.180984	−	0.137300i
$508$	0.0200474	−	0.0347230i	0.000889458	−	0.00154059i
$509$	−20.5770			−0.912060			−0.456030	−	0.889964i	$-0.650729\pi$
$509$	−20.5770			−0.912060			−0.456030	+	0.889964i	$0.650729\pi$
$510$	−13.2307	−	10.0372i	−0.585867	−	0.444457i
$511$	−2.93206	+	30.8535i	−0.129707	+	1.36488i
$512$	−3.44542			−0.152267
$513$	10.9946	+	13.8495i	0.485423	+	0.611470i
$514$	6.74794	+	11.6878i	0.297639	+	0.515526i
$515$	−3.91721			−0.172613
$516$	−12.3761	+	5.20624i	−0.544829	+	0.229192i
$517$	2.81698	+	4.87915i	0.123891	+	0.214585i
$518$	25.6792	+	18.2686i	1.12828	+	0.802675i
$519$	0.283835	−	0.119400i	0.0124590	−	0.00524110i
$520$	3.06098	+	5.30177i	0.134233	+	0.232498i
$521$	−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	$-0.377060\pi$
$522$	50.8000	+	13.0150i	2.22345	+	0.569652i
$523$	−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
$525$	−3.10264	+	3.37248i	−0.135410	+	0.147187i
$526$	9.20117	+	15.9369i	0.401190	+	0.694881i
$527$	9.75118			0.424768
$528$	36.1331	−	15.2000i	1.57249	−	0.661497i
$529$	−22.9995			−0.999976
$530$	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
$534$	3.13353	−	24.8565i	0.135601	−	1.07565i
$535$	6.29531	−	10.9038i	0.272170	−	0.471412i
$536$	1.45103	−	2.51325i	0.0626748	−	0.108556i
$537$	15.7694	−	6.63370i	0.680502	−	0.286265i
$538$	−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	$-0.00578502\pi$
$542$	23.1789			0.995617
$543$	−2.56390	+	20.3379i	−0.110027	+	0.872784i
$544$	25.8352			1.10768
$545$	−0.0916666	−	0.158771i	−0.00392656	−	0.00680101i
$546$	−7.33684	−	23.4315i	−0.313988	−	1.00278i
$547$	15.1076	−	26.1671i	0.645954	−	1.11883i	−0.338126	−	0.941101i	$-0.609793\pi$
$547$	15.1076	−	26.1671i	0.645954	−	1.11883i	0.984080	−	0.177724i	$-0.0568736\pi$
$548$	6.68310	−	11.5755i	0.285488	−	0.494480i
$549$	−6.93371	−	24.7839i	−0.295923	−	1.05775i
$550$	3.84133	+	6.65338i	0.163795	+	0.283701i
$551$	17.5957	+	30.4766i	0.749600	+	1.29835i
$552$	−0.00976261	+	0.0774412i	−0.000415524	+	0.00329612i
$553$	0.541999	−	5.70336i	0.0230481	−	0.242532i
$554$	7.30430	+	12.6514i	0.310330	+	0.537507i
$555$	9.72351	+	7.37656i	0.412740	+	0.313117i
$556$	−13.3982			−0.568212
$557$	−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	$0.902107\pi$
$558$	8.44521	+	2.16367i	0.357514	+	0.0915956i
$559$	−28.6569			−1.21206
$560$	1.24642	−	13.1159i	0.0526709	−	0.554247i
$561$	−41.1580	+	17.3138i	−1.73769	+	0.730991i
$562$	52.2987			2.20609
$563$	−10.3601	+	17.9442i	−0.436625	+	0.756256i	−0.997427	−	0.0716938i	$-0.977160\pi$
$563$	−10.3601	+	17.9442i	−0.436625	+	0.756256i	0.560802	+	0.827950i	$0.310493\pi$
$564$	−0.230254	+	1.82648i	−0.00969546	+	0.0769085i
$565$	−1.24821	−	2.16197i	−0.0525127	−	0.0909547i
$566$	−9.56304			−0.401965
$567$	−10.3753	−	21.4325i	−0.435720	−	0.900082i
$568$	18.6647			0.783153
$569$	0.0784820	+	0.135935i	0.00329014	+	0.00569868i	0.867666	−	0.497148i	$-0.165619\pi$
$569$	0.0784820	+	0.135935i	0.00329014	+	0.00569868i	−0.864376	+	0.502847i	$0.832286\pi$
$570$	1.24621	−	9.88548i	0.0521980	−	0.414057i
$571$	1.65930	−	2.87399i	0.0694395	−	0.120273i	−0.829215	−	0.558929i	$-0.811212\pi$
$571$	1.65930	−	2.87399i	0.0694395	−	0.120273i	0.898655	+	0.438657i	$0.144546\pi$
$572$	−12.3517			−0.516452
$573$	−29.0358	+	12.2144i	−1.21299	+	0.510265i
$574$	−28.1296	+	12.8617i	−1.17411	+	0.536839i
$575$	−0.0233324			−0.000973028
$576$	−6.56808	−	1.68275i	−0.273670	−	0.0701145i
$577$	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	$0.474327\pi$
$578$	−25.6491			−1.06686
$579$	10.6161	+	8.05374i	0.441192	+	0.334702i
$580$	−4.43323	−	7.67858i	−0.184080	−	0.318835i
$581$	−18.0825	+	8.26791i	−0.750190	+	0.343011i
$582$	−0.390982	+	3.10143i	−0.0162067	+	0.128559i
$583$	−23.2073	−	40.1962i	−0.961149	−	1.66476i
$584$	−11.3124	−	19.5936i	−0.468110	−	0.810791i
$585$	−2.56193	−	9.15738i	−0.105923	−	0.378611i
$586$	−12.0015	+	20.7873i	−0.495779	+	0.858715i
$587$	−4.12605	+	7.14652i	−0.170300	+	0.294969i	−0.938525	−	0.345212i	$-0.887807\pi$
$587$	−4.12605	+	7.14652i	−0.170300	+	0.294969i	0.768225	+	0.640180i	$0.221140\pi$
$588$	−3.21970	+	9.88439i	−0.132778	+	0.407625i
$589$	2.92518	+	5.06656i	0.120530	+	0.208764i
$590$	−15.6996			−0.646342
$591$	0.653969	−	5.18756i	0.0269007	−	0.213388i
$592$	−35.0893			−1.44216
$593$	−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
$597$	−3.22023	+	1.35465i	−0.131795	+	0.0554420i
$598$	0.0625071	−	0.108265i	0.00255610	−	0.00442730i
$599$	2.94689	−	5.10417i	0.120407	−	0.208551i	−0.799521	−	0.600638i	$-0.794913\pi$
$599$	2.94689	−	5.10417i	0.120407	−	0.208551i	0.919928	+	0.392087i	$0.128247\pi$
$600$	0.418415	−	3.31905i	0.0170817	−	0.135499i
$601$	−8.73192	+	15.1241i	−0.356182	+	0.616926i	−0.987320	−	0.158745i	$-0.949255\pi$
$601$	−8.73192	+	15.1241i	−0.356182	+	0.616926i	0.631137	+	0.775671i	$0.282588\pi$
$602$	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
$605$	9.65621			0.392581
$606$	−7.50910	+	3.15884i	−0.305036	+	0.128319i
$607$	0.258987			0.0105120			0.00525599	−	0.999986i	$-0.498327\pi$
$607$	0.258987			0.0105120			0.00525599	+	0.999986i	$0.498327\pi$
$608$	7.75011	+	13.4236i	0.314308	+	0.544398i
$609$	−14.1602	−	45.2232i	−0.573801	−	1.83253i
$610$	−7.25051	+	12.5582i	−0.293564	+	0.508469i
$611$	−1.96459	+	3.40277i	−0.0794788	+	0.137661i
$612$	−14.1337	−	3.62106i	−0.571319	−	0.146373i
$613$	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	$0.723349\pi$
$614$	8.89437	+	15.4055i	0.358948	+	0.621716i
$615$	−11.0416	+	4.64484i	−0.445240	+	0.187298i
$616$	−18.9244	−	13.4631i	−0.762486	−	0.542444i
$617$	−3.88360	−	6.72659i	−0.156348	−	0.270802i	0.777201	−	0.629252i	$-0.216639\pi$
$617$	−3.88360	−	6.72659i	−0.156348	−	0.270802i	−0.933549	+	0.358450i	$0.883305\pi$
$618$	−10.5717	+	4.44716i	−0.425254	+	0.178891i
$619$	−17.4818			−0.702652			−0.351326	−	0.936253i	$-0.614269\pi$
$619$	−17.4818			−0.702652			−0.351326	+	0.936253i	$0.614269\pi$
$620$	−0.736999	−	1.27652i	−0.0295986	−	0.0512663i
$621$	0.0445428	−	0.112760i	0.00178744	−	0.00452489i
$622$	−47.1529			−1.89066
$623$	−20.5893	+	9.41411i	−0.824895	+	0.377168i
$624$	21.7802	+	16.5232i	0.871907	+	0.661456i
$625$	1.00000			0.0400000
$626$	25.0055	−	43.3108i	0.999421	−	1.73105i
$627$	−21.3427	−	16.1912i	−0.852344	−	0.646614i
$628$	−0.720159	−	1.24735i	−0.0287375	−	0.0497747i
$629$	39.9691			1.59367
$630$	−4.54458	+	12.6239i	−0.181061	+	0.502949i
$631$	34.0347			1.35490			0.677451	−	0.735568i	$-0.263085\pi$
$631$	34.0347			1.35490			0.677451	+	0.735568i	$0.263085\pi$
$632$	2.09113	+	3.62194i	0.0831806	+	0.144073i
$633$	−8.61249	+	3.62300i	−0.342316	+	0.144001i
$634$	−4.65491	+	8.06254i	−0.184870	+	0.320204i
$635$	−0.0467625			−0.00185571
$636$	1.89692	−	15.0472i	0.0752178	−	0.596660i
$637$	−14.5146	+	16.7815i	−0.575091	+	0.664906i
$638$	−79.4461			−3.14530
$639$	−28.0841	−	7.19518i	−1.11099	−	0.284637i
$640$	6.46493	+	11.1976i	0.255549	+	0.442624i
$641$	24.4012			0.963789			0.481895	−	0.876229i	$-0.339949\pi$
$641$	24.4012			0.963789			0.481895	+	0.876229i	$0.339949\pi$
$642$	4.61067	−	36.5738i	0.181969	−	1.44345i
$643$	−2.75458	−	4.77107i	−0.108630	−	0.188153i	0.806586	−	0.591117i	$-0.201313\pi$
$643$	−2.75458	−	4.77107i	−0.108630	−	0.188153i	−0.915215	+	0.402965i	$0.867980\pi$
$644$	−0.0481363	+	0.0220095i	−0.00189684	+	0.000867295i
$645$	12.4757	+	9.46445i	0.491230	+	0.372662i
$646$	−16.3147	−	28.2580i	−0.641895	−	1.11179i
$647$	−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	$-0.406261\pi$
$648$	15.2414	+	8.35834i	0.598737	+	0.328347i
$649$	−21.1056	+	36.5559i	−0.828466	+	1.43495i
$650$	−2.67898	+	4.64013i	−0.105078	+	0.182001i
$651$	−2.35406	−	7.51809i	−0.0922628	−	0.294657i
$652$	−10.6462	−	18.4398i	−0.416937	−	0.722157i
$653$	−6.50001			−0.254365			−0.127182	−	0.991879i	$-0.540593\pi$
$653$	−6.50001			−0.254365			−0.127182	+	0.991879i	$0.540593\pi$
$654$	−0.427638	−	0.324419i	−0.0167220	−	0.0126858i
$655$	10.1498			0.396587
$656$	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	0.117147	−	0.993115i	$-0.462625\pi$
$659$	23.5823	−	40.8457i	0.918636	−	1.59112i	0.801489	−	0.598010i	$-0.204042\pi$
$660$	5.37728	+	4.07937i	0.209310	+	0.158789i
$661$	−0.413867	+	0.716838i	−0.0160975	+	0.0278818i	−0.873962	−	0.485994i	$-0.838458\pi$
$661$	−0.413867	+	0.716838i	−0.0160975	+	0.0278818i	0.857864	+	0.513876i	$0.171791\pi$
$662$	7.65046	−	13.2510i	0.297344	−	0.515014i
$663$	−24.8091	−	18.8210i	−0.963506	−	0.730946i
$664$	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
$668$	11.8217			0.457396
$669$	−24.6463	−	18.6974i	−0.952880	−	0.722884i
$670$	2.53989			0.0981246
$671$	19.4943	+	33.7651i	0.752569	+	1.30349i
$672$	−6.23695	−	19.9188i	−0.240595	−	0.768384i
$673$	−13.8314	+	23.9566i	−0.533160	+	0.923460i	0.466090	+	0.884737i	$0.345662\pi$
$673$	−13.8314	+	23.9566i	−0.533160	+	0.923460i	−0.999250	+	0.0387229i	$0.987671\pi$
$674$	8.38700	−	14.5267i	0.323055	−	0.559548i
$675$	−1.90906	+	4.83275i	−0.0734796	+	0.186013i
$676$	1.26606	+	2.19288i	0.0486945	+	0.0843414i
$677$	12.2771	+	21.2646i	0.471848	+	0.817265i	0.999481	−	0.0322072i	$-0.0102537\pi$
$677$	12.2771	+	21.2646i	0.471848	+	0.817265i	−0.527633	+	0.849473i	$0.676920\pi$
$678$	−5.82309	−	4.41758i	−0.223634	−	0.169656i
$679$	2.56900	−	1.17463i	0.0985892	−	0.0450782i
$680$	−5.47767	−	9.48760i	−0.210059	−	0.363833i
$681$	0.347895	−	2.75965i	0.0133314	−	0.105750i
$682$	−13.2075			−0.505740
$683$	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	$0.789346\pi$
$684$	−2.35840	−	8.42988i	−0.0901756	−	0.322324i
$685$	−15.5890			−0.595626
$686$	30.4139	−	7.42209i	1.16121	−	0.283377i
$687$	−3.69323	+	29.2963i	−0.140905	+	1.11772i
$688$	−45.0212			−1.71642
$689$	16.1850	−	28.0333i	0.616600	−	1.06798i
$690$	−0.0629687	+	0.0264889i	−0.00239718	+	0.00100842i
$691$	−23.0542	−	39.9311i	−0.877023	−	1.51905i	−0.854592	−	0.519301i	$-0.826192\pi$
$691$	−23.0542	−	39.9311i	−0.877023	−	1.51905i	−0.0224318	−	0.999748i	$-0.507141\pi$
$692$	−0.152432			−0.00579459
$693$	23.2849	+	27.5528i	0.884521	+	1.04664i
$694$	18.9235			0.718325
$695$	7.81319	+	13.5328i	0.296371	+	0.513330i
$696$	27.5604	+	20.9082i	1.04468	+	0.792523i
$697$	−19.6142	+	33.9728i	−0.742942	+	1.28681i
$698$	−47.8090			−1.80960
$699$	−19.4065	−	14.7224i	−0.734023	−	0.556852i
$700$	2.06307	−	0.943302i	0.0779767	−	0.0356535i
$701$	26.1712			0.988473			0.494236	−	0.869328i	$-0.335448\pi$
$701$	26.1712			0.988473			0.494236	+	0.869328i	$0.335448\pi$
$702$	−17.3103	−	21.8051i	−0.653335	−	0.822982i
$703$	11.9900	+	20.7673i	0.452212	+	0.783253i
$704$	10.2718			0.387134
$705$	1.97910	−	0.832544i	0.0745372	−	0.0313554i
$706$	−6.21856	−	10.7709i	−0.234039	−	0.405367i
$707$	5.99850	+	4.26742i	0.225597	+	0.160493i
$708$	−12.7137	+	5.34823i	−0.477808	+	0.200999i
$709$	5.44311	+	9.42774i	0.204420	+	0.354066i	0.949948	−	0.312408i	$-0.101136\pi$
$709$	5.44311	+	9.42774i	0.204420	+	0.354066i	−0.745528	+	0.666475i	$0.767802\pi$
$710$	8.16772	+	14.1469i	0.306529	+	0.530924i
$711$	−1.75020	−	6.25593i	−0.0656376	−	0.234616i
$712$	8.26350	−	14.3128i	0.309688	−	0.536395i
$713$	0.0200557	−	0.0347374i	0.000751090	−	0.00130093i
$714$	13.1294	+	41.9310i	0.491355	+	1.56923i
$715$	7.20293	+	12.4758i	0.269374	+	0.466570i
$716$	−8.46888			−0.316497
$717$	−44.4309	+	18.6907i	−1.65930	+	0.698016i
$718$	37.1594			1.38678
$719$	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
$723$	−4.95043	+	39.2689i	−0.184108	+	1.46043i
$724$	5.07375	−	8.78799i	0.188564	−	0.326603i
$725$	−5.17048	+	8.95554i	−0.192027	+	0.332600i
$726$	26.0599	−	10.9626i	0.967173	−	0.406859i
$727$	14.1401	−	24.4914i	0.524429	−	0.908337i	−0.475167	−	0.879896i	$-0.657612\pi$
$727$	14.1401	−	24.4914i	0.524429	−	0.908337i	0.999595	−	0.0284413i	$-0.00905435\pi$
$728$	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
$731$	51.2821			1.89674
$732$	−1.59342	+	12.6397i	−0.0588947	+	0.467178i
$733$	34.6534			1.27995			0.639976	−	0.768395i	$-0.278944\pi$
$733$	34.6534			1.27995			0.639976	+	0.768395i	$0.278944\pi$
$734$	−17.9359	−	31.0659i	−0.662027	−	1.14666i
$735$	11.8613	−	2.51204i	0.437509	−	0.0926581i
$736$	0.0531364	−	0.0920349i	0.00195863	−	0.00339245i
$737$	3.41448	−	5.91405i	0.125774	−	0.217847i
$738$	−24.5255	+	25.0707i	−0.902795	+	0.922866i
$739$	−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	$-0.510016\pi$
$740$	−3.02088	−	5.23232i	−0.111050	−	0.192344i
$741$	2.33679	−	18.5364i	0.0858440	−	0.680951i
$742$	−41.5375	+	18.9923i	−1.52489	+	0.697229i
$743$	−16.5756	−	28.7098i	−0.608100	−	1.05326i	−0.991553	−	0.129700i	$-0.958598\pi$
$743$	−16.5756	−	28.7098i	−0.608100	−	1.05326i	0.383453	−	0.923560i	$-0.374735\pi$
$744$	4.58176	+	3.47587i	0.167976	+	0.127432i
$745$	7.19090			0.263454
$746$	6.08688	+	10.5428i	0.222857	+	0.385999i
$747$	−15.7657	+	16.1162i	−0.576837	+	0.589661i
$748$	22.1036			0.808189
$749$	−30.2951	+	13.8519i	−1.10696	+	0.506137i
$750$	2.69877	−	1.13529i	0.0985451	−	0.0414548i
$751$	25.4347			0.928126			0.464063	−	0.885802i	$-0.346391\pi$
$751$	25.4347			0.928126			0.464063	+	0.885802i	$0.346391\pi$
$752$	−3.08645	+	5.34588i	−0.112551	+	0.194944i
$753$	−0.0538929	+	0.427501i	−0.00196396	+	0.0155790i
$754$	−27.7033	−	47.9835i	−1.00889	−	1.74745i
$755$	14.0262			0.510465
$756$	0.620229	+	11.7711i	0.0225575	+	0.428112i
$757$	13.9500			0.507020			0.253510	−	0.967333i	$-0.418415\pi$
$757$	13.9500			0.507020			0.253510	+	0.967333i	$0.418415\pi$
$758$	−3.51454	−	6.08737i	−0.127654	−	0.221103i
$759$	−0.0229729	+	0.182231i	−0.000833862	+	0.00661455i
$760$	3.28640	−	5.69222i	0.119210	−	0.206479i
$761$	−10.6457			−0.385907			−0.192953	−	0.981208i	$-0.561807\pi$
$761$	−10.6457			−0.385907			−0.192953	+	0.981208i	$0.561807\pi$
$762$	−0.126201	+	0.0530888i	−0.00457179	+	0.00192321i
$763$	−0.0458887	+	0.482878i	−0.00166128	+	0.0174814i
$764$	15.5935			0.564153
$765$	4.58461	+	16.3873i	0.165757	+	0.592483i
$766$	24.3889	+	42.2429i	0.881208	+	1.52630i
$767$	−29.4385			−1.06296
$768$	23.9225	+	18.1483i	0.863228	+	0.654871i
$769$	14.8500	+	25.7209i	0.535504	+	0.927520i	0.999139	+	0.0414934i	$0.0132116\pi$
$769$	14.8500	+	25.7209i	0.535504	+	0.927520i	−0.463635	+	0.886026i	$0.653455\pi$
$770$	1.92299	−	20.2352i	0.0692996	−	0.729228i
$771$	1.72960	−	13.7199i	0.0622900	−	0.494111i
$772$	−3.29820	−	5.71266i	−0.118705	−	0.205603i
$773$	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	$0.591800\pi$
$774$	44.4139	+	11.3789i	1.59642	+	0.409006i
$775$	−0.859563	+	1.48881i	−0.0308764	+	0.0534795i
$776$	−1.03106	+	1.78586i	−0.0370131	+	0.0641085i
$777$	−9.64903	−	30.8159i	−0.346157	−	1.10551i
$778$	−9.63125	−	16.6818i	−0.345297	−	0.598072i
$779$	−23.5357			−0.843253
$780$	−0.588753	+	4.67024i	−0.0210807	+	0.167222i
$781$	43.9208			1.57161
$782$	−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
$786$	27.3920	−	11.5230i	0.977042	−	0.411010i
$787$	10.2825	−	17.8098i	0.366532	−	0.634852i	−0.622489	−	0.782629i	$-0.713878\pi$
$787$	10.2825	−	17.8098i	0.366532	−	0.634852i	0.989021	+	0.147777i	$0.0472117\pi$
$788$	−1.29415	+	2.24154i	−0.0461023	+	0.0798515i
$789$	2.35840	−	18.7078i	0.0839612	−	0.666016i
$790$	−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
$794$	−6.63263			−0.235383
$795$	−16.3046	+	6.85880i	−0.578263	+	0.243257i
$796$	1.72940			0.0612970
$797$	12.3509	+	21.3924i	0.437491	+	0.757756i	0.997495	−	0.0707333i	$-0.0225339\pi$
$797$	12.3509	+	21.3924i	0.437491	+	0.757756i	−0.560004	+	0.828490i	$0.689201\pi$
$798$	−17.8481	+	19.4004i	−0.631817	+	0.686766i
$799$	3.51567	−	6.08931i	0.124375	−	0.215424i
$800$	−2.27737	+	3.94452i	−0.0805171	+	0.139460i
$801$	−17.9513	+	18.3504i	−0.634279	+	0.648380i
$802$	−29.5723	−	51.2208i	−1.04423	−	1.80867i
$803$	−26.6197	−	46.1067i	−0.939390	−	1.62707i
$804$	2.05683	−	0.865240i	0.0725386	−	0.0305147i
$805$	0.0503014	+	0.0357851i	0.00177289	+	0.00126126i
$806$	−4.60551	−	7.97698i	−0.162222	−	0.280977i
$807$	8.37992	−	3.52516i	0.294987	−	0.124092i
$808$	−5.37401			−0.189057
$809$	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	$0.822596\pi$
$810$	0.334453	+	15.2098i	0.0117515	+	0.534418i
$811$	−23.8796			−0.838526			−0.419263	−	0.907865i	$-0.637711\pi$
$811$	−23.8796			−0.838526			−0.419263	+	0.907865i	$0.637711\pi$
$812$	−2.21929	+	23.3532i	−0.0778819	+	0.819537i
$813$	−18.9214	−	14.3544i	−0.663604	−	0.503431i
$814$	−54.1360			−1.89747
$815$	−12.4167	+	21.5063i	−0.434937	+	0.753334i
$816$	−38.9761	−	29.5685i	−1.36444	−	1.03510i
$817$	15.3837	+	26.6454i	0.538208	+	0.932203i
$818$	66.3851			2.32110
$819$	−8.52161	+	23.6713i	−0.297769	+	0.827142i
$820$	5.92981			0.207078
$821$	−3.19084	−	5.52669i	−0.111361	−	0.192883i	0.804958	−	0.593331i	$-0.202188\pi$
$821$	−3.19084	−	5.52669i	−0.111361	−	0.192883i	−0.916319	+	0.400449i	$0.868854\pi$
$822$	−42.0712	+	17.6980i	−1.46740	+	0.617288i
$823$	17.4753	−	30.2681i	0.609151	−	1.05508i	−0.382230	−	0.924067i	$-0.624844\pi$
$823$	17.4753	−	30.2681i	0.609151	−	1.05508i	0.991381	−	0.131013i	$-0.0418228\pi$
$824$	−7.56578			−0.263566
$825$	0.984591	−	7.81020i	0.0342791	−	0.271916i
$826$	33.8461	+	24.0786i	1.17766	+	0.837802i
$827$	40.0335			1.39210			0.696051	−	0.717992i	$-0.254939\pi$
$827$	40.0335			1.39210			0.696051	+	0.717992i	$0.254939\pi$
$828$	−0.0419689	+	0.0429019i	−0.00145852	+	0.00149094i
$829$	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	$0.655467\pi$
$830$	12.7034			0.440942
$831$	1.87220	−	14.8511i	0.0649460	−	0.515180i
$832$	3.58183	+	6.20392i	0.124178	+	0.215082i
$833$	25.9742	−	30.0307i	0.899952	−	1.04050i
$834$	36.4497	+	27.6518i	1.26215	+	0.957505i
$835$	−6.89385	−	11.9405i	−0.238571	−	0.413218i
$836$	6.63070	+	11.4847i	0.229327	+	0.397207i
$837$	−5.55408	−	6.99627i	−0.191977	−	0.241827i
$838$	9.50613	−	16.4651i	0.328384	−	0.568778i
$839$	−6.96724	+	12.0676i	−0.240536	+	0.416621i	−0.960867	−	0.277010i	$-0.910657\pi$
$839$	−6.96724	+	12.0676i	−0.240536	+	0.416621i	0.720331	+	0.693630i	$0.243990\pi$
$840$	−5.99250	+	6.51367i	−0.206761	+	0.224743i
$841$	−38.9677	−	67.4941i	−1.34372	−	2.32738i
$842$	29.9966			1.03375
$843$	−42.6926	−	32.3879i	−1.47041	−	1.11550i
$844$	4.62528			0.159209
$845$	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
$849$	7.80654	+	5.92228i	0.267920	+	0.203252i
$850$	4.79408	−	8.30360i	0.164436	−	0.284811i
$851$	0.0822060	−	0.142385i	0.00281799	−	0.00488090i
$852$	11.4336	+	8.67386i	0.391708	+	0.297162i
$853$	−26.8533	+	46.5112i	−0.919439	+	1.59251i	−0.119169	+	0.992874i	$0.538023\pi$
$853$	−26.8533	+	46.5112i	−0.919439	+	1.59251i	−0.800270	+	0.599640i	$0.795310\pi$
$854$	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
$857$	−13.4891			−0.460779			−0.230390	−	0.973098i	$-0.574000\pi$
$857$	−13.4891			−0.460779			−0.230390	+	0.973098i	$0.574000\pi$
$858$	33.6027	+	25.4920i	1.14718	+	0.870283i
$859$	6.57647			0.224386			0.112193	−	0.993686i	$-0.464212\pi$
$859$	6.57647			0.224386			0.112193	+	0.993686i	$0.464212\pi$
$860$	−3.87592	−	6.71330i	−0.132168	−	0.228922i
$861$	30.9280	+	6.92097i	1.05402	+	0.235866i
$862$	−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	$0.102529\pi$
$864$	−14.7152	−	18.5363i	−0.500623	−	0.630616i
$865$	0.0888908	+	0.153963i	0.00302238	+	0.00523491i
$866$	4.97357	+	8.61448i	0.169009	+	0.292732i
$867$	20.9380	+	15.8842i	0.711091	+	0.539455i
$868$	−0.368945	+	3.88234i	−0.0125228	+	0.131775i
$869$	4.92073	+	8.52295i	0.166924	+	0.289121i
$870$	−3.78685	+	30.0389i	−0.128386	+	1.01841i
$871$	4.76258			0.161374
$872$	−0.177047	−	0.306654i	−0.00599555	−	0.0103846i
$873$	2.23985	−	2.28964i	0.0758074	−	0.0774927i
$874$	−0.134221			−0.00454009
$875$	−2.15586	−	1.53371i	−0.0728814	−	0.0518489i
$876$	2.17584	−	17.2597i	0.0735150	−	0.583152i
$877$	−19.6473			−0.663442			−0.331721	−	0.943378i	$-0.607629\pi$
$877$	−19.6473			−0.663442			−0.331721	+	0.943378i	$0.607629\pi$
$878$	−10.9032	+	18.8849i	−0.367964	+	0.637333i
$879$	22.6705	−	9.53674i	0.764656	−	0.321666i
$880$	11.3161	+	19.6000i	0.381465	+	0.660716i
$881$	6.87969			0.231783			0.115891	−	0.993262i	$-0.463028\pi$
$881$	6.87969			0.231783			0.115891	+	0.993262i	$0.463028\pi$
$882$	29.1589	−	20.2454i	0.981833	−	0.681697i
$883$	−28.2458			−0.950546			−0.475273	−	0.879838i	$-0.657651\pi$
$883$	−28.2458			−0.950546			−0.475273	+	0.879838i	$0.657651\pi$
$884$	7.70765	+	13.3500i	0.259236	+	0.449010i
$885$	12.8159	+	9.72257i	0.430803	+	0.326821i
$886$	−11.1475	+	19.3081i	−0.374509	+	0.648669i
$887$	25.6968			0.862815			0.431407	−	0.902157i	$-0.358017\pi$
$887$	25.6968			0.862815			0.431407	+	0.902157i	$0.358017\pi$
$888$	18.7802	+	14.2472i	0.630221	+	0.478105i
$889$	0.100813	+	0.0717202i	0.00338118	+	0.00240542i
$890$	14.4645			0.484852
$891$	35.8651	+	19.6684i	1.20153	+	0.658916i
$892$	7.65706	+	13.2624i	0.256377	+	0.444058i
$893$	4.21855			0.141168
$894$	19.4066	−	8.16373i	0.649053	−	0.273036i
$895$	4.93863	+	8.55396i	0.165080	+	0.285927i
$896$	3.23637	−	34.0558i	0.108120	−	1.13772i
$897$	−0.118073	+	0.0496697i	−0.00394236	+	0.00165842i
$898$	−0.509182	−	0.881930i	−0.0169916	−	0.0294304i
$899$	−8.88871	−	15.3957i	−0.296455	−	0.513475i
$900$	1.79874	−	1.83873i	0.0599580	−	0.0612909i
$901$	−28.9633	+	50.1660i	−0.964909	+	1.67127i
$902$	26.5665	−	46.0145i	0.884566	−	1.53211i
$903$	−12.3801	−	39.5381i	−0.411985	−	1.31575i
$904$	−2.41082	−	4.17567i	−0.0801827	−	0.138881i
$905$	−11.8350			−0.393410
$906$	37.8534	−	15.9237i	1.25760	−	0.529030i
$907$	−9.48091			−0.314808			−0.157404	−	0.987534i	$-0.550313\pi$
$907$	−9.48091			−0.314808			−0.157404	+	0.987534i	$0.550313\pi$
$908$	−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	−0.0226277	+	0.999744i	$0.507203\pi$
$911$	−26.4738	+	45.8540i	−0.877118	+	1.51921i	−0.854490	+	0.519468i	$0.826130\pi$
$912$	3.67118	−	29.1214i	0.121565	−	0.964305i
$913$	17.0777	−	29.5795i	0.565190	−	0.978937i
$914$	−4.63349	+	8.02545i	−0.153262	+	0.265458i
$915$	13.6959	−	5.76144i	0.452773	−	0.190467i
$916$	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	$0.0293636\pi$
$920$	−0.0450646			−0.00148574
$921$	2.27976	−	18.0841i	0.0751207	−	0.595890i
$922$	−12.7185			−0.418862
$923$	15.3154	+	26.5270i	0.504112	+	0.873148i
$924$	−5.33609	−	17.0418i	−0.175545	−	0.560633i
$925$	−3.52326	+	6.10247i	−0.115844	+	0.200648i
$926$	−29.6209	+	51.3048i	−0.973402	+	1.68598i
$927$	11.3840	+	2.91658i	0.373898	+	0.0957932i
$928$	−23.5502	−	40.7901i	−0.773072	−	1.33900i
$929$	2.72382	+	4.71780i	0.0893657	+	0.154786i	0.907243	−	0.420606i	$-0.138183\pi$
$929$	2.72382	+	4.71780i	0.0893657	+	0.154786i	−0.817877	+	0.575392i	$0.804849\pi$
$930$	−0.629542	+	4.99380i	−0.0206435	+	0.163753i
$931$	23.3953	+	4.48710i	0.766749	+	0.147059i
$932$	6.02918	+	10.4429i	0.197492	+	0.342067i
$933$	38.4920	+	29.2012i	1.26017	+	0.956005i
$934$	−23.1191			−0.756479
$935$	−12.8898	−	22.3257i	−0.421540	−	0.730129i
$936$	−4.94816	−	17.6867i	−0.161736	−	0.578109i
$937$	30.3887			0.992754			0.496377	−	0.868107i	$-0.334663\pi$
$937$	30.3887			0.992754			0.496377	+	0.868107i	$0.334663\pi$
$938$	−5.47565	−	3.89546i	−0.178786	−	0.127191i
$939$	−47.2345	+	19.8700i	−1.54144	+	0.648434i
$940$	−1.06286			−0.0346668
$941$	14.7975	−	25.6300i	0.482384	−	0.835513i	−0.517412	−	0.855736i	$-0.673104\pi$
$941$	14.7975	−	25.6300i	0.482384	−	0.835513i	0.999795	+	0.0202236i	$0.00643782\pi$
$942$	−0.615157	+	4.87969i	−0.0200429	+	0.158989i
$943$	0.0806828	+	0.139747i	0.00262739	+	0.00455078i
$944$	−46.2490			−1.50528
$945$	11.5277	−	7.49080i	0.374996	−	0.243676i
$946$	−69.4589			−2.25830
$947$	4.27832	+	7.41027i	0.139027	+	0.240801i	0.927128	−	0.374744i	$-0.122269\pi$
$947$	4.27832	+	7.41027i	0.139027	+	0.240801i	−0.788102	+	0.615545i	$0.788936\pi$
$948$	−0.402211	+	3.19051i	−0.0130632	+	0.103623i
$949$	18.5649	−	32.1553i	0.602641	−	1.04381i
$950$	5.75256			0.186638
$951$	8.79294	−	3.69891i	0.285131	−	0.119945i
$952$	−2.74214	+	28.8551i	−0.0888733	+	0.935199i
$953$	25.0758			0.812284			0.406142	−	0.913810i	$-0.366874\pi$
$953$	25.0758			0.812284			0.406142	+	0.913810i	$0.366874\pi$
$954$	−36.2155	+	37.0207i	−1.17252	+	1.19859i
$955$	−9.09336	−	15.7502i	−0.294254	−	0.509663i
$956$	23.8614			0.771731
$957$	64.8537	+	49.2000i	2.09642	+	1.59041i
$958$	1.99811	+	3.46083i	0.0645560	+	0.111814i
$959$	33.6078	+	23.9090i	1.08525	+	0.772063i
$960$	0.489612	−	3.88382i	0.0158022	−	0.125350i
$961$	14.0223	+	24.2873i	0.452332	+	0.783463i
$962$	−18.8775	−	32.6968i	−0.608635	−	1.05419i
$963$	−26.4135	+	27.0007i	−0.851164	+	0.870086i
$964$	9.79651	−	16.9680i	0.315524	−	0.546504i
$965$	−3.84670	+	6.66268i	−0.123830	+	0.214479i
$966$	0.176378	+	0.0394694i	0.00567487	+	0.00126991i
$967$	−15.1149	−	26.1798i	−0.486063	−	0.841886i	0.513808	−	0.857905i	$-0.328234\pi$
$967$	−15.1149	−	26.1798i	−0.486063	−	0.841886i	−0.999872	+	0.0160186i	$0.994901\pi$
$968$	18.6502			0.599440
$969$	−4.18171	+	33.1712i	−0.134336	+	1.06561i
$970$	−1.80479			−0.0579482
$971$	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
$975$	5.06050	−	2.12879i	0.162066	−	0.0681758i
$976$	−21.3591	+	36.9950i	−0.683687	+	1.18418i
$977$	−22.1698	+	38.3993i	−0.709276	+	1.22850i	0.255850	+	0.966717i	$0.417645\pi$
$977$	−22.1698	+	38.3993i	−0.709276	+	1.22850i	−0.965126	+	0.261786i	$0.915689\pi$
$978$	−9.09395	+	72.1371i	−0.290792	+	2.30669i
$979$	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
$983$	31.6792			1.01041			0.505204	−	0.863000i	$-0.331417\pi$
$983$	31.6792			1.01041			0.505204	+	0.863000i	$0.331417\pi$
$984$	−21.3259	+	8.97113i	−0.679846	+	0.285989i
$985$	3.01874			0.0961852
$986$	49.5754	+	85.8672i	1.57880	+	2.73457i
$987$	−5.54354	−	1.24052i	−0.176453	−	0.0394861i
$988$	−4.62431	+	8.00955i	−0.147119	+	0.254818i
$989$	0.105474	−	0.182686i	0.00335388	−	0.00580909i
$990$	−6.20962	−	22.1957i	−0.197355	−	0.705426i
$991$	−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	$0.861270\pi$
$992$	−3.91508	−	6.78112i	−0.124304	−	0.215301i
$993$	−14.4514	+	6.07925i	−0.458602	+	0.192919i
$994$	4.08879	−	43.0257i	0.129689	−	1.36469i
$995$	−1.00850	−	1.74678i	−0.0319717	−	0.0553766i
$996$	10.2873	−	4.32755i	0.325967	−	0.137124i
$997$	−15.3886			−0.487361			−0.243680	−	0.969856i	$-0.578355\pi$
$997$	−15.3886			−0.487361			−0.243680	+	0.969856i	$0.578355\pi$
$998$	0.0540707	+	0.0936531i	0.00171158	+	0.00296454i
$999$	−22.7656	−	28.6770i	−0.720272	−	0.907300i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.15	✓	36	1.1	even	1	trivial
315.2.k.c.256.15	yes	36	63.4	even	3	inner
315.2.l.c.121.4	yes	36	9.4	even	3
315.2.l.c.151.4	yes	36	7.4	even	3
945.2.k.c.361.4		36	63.32	odd	6
945.2.k.c.856.4		36	3.2	odd	2
945.2.l.c.46.15		36	21.11	odd	6
945.2.l.c.226.15		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.845194 + 1.46392i) q^{2} +(0.216636 - 1.71845i) q^{3} +(-0.428706 + 0.742540i) q^{4} +1.00000 q^{5} +(2.69877 - 1.13529i) q^{6} +(-2.15586 - 1.53371i) q^{7} +1.93142 q^{8} +(-2.90614 - 0.744556i) q^{9} +O(q^{10})\)	\(q+(0.845194 + 1.46392i) q^{2} +(0.216636 - 1.71845i) q^{3} +(-0.428706 + 0.742540i) q^{4} +1.00000 q^{5} +(2.69877 - 1.13529i) q^{6} +(-2.15586 - 1.53371i) q^{7} +1.93142 q^{8} +(-2.90614 - 0.744556i) q^{9} +(0.845194 + 1.46392i) q^{10} +4.54491 q^{11} +(1.18314 + 0.897570i) q^{12} +(1.58483 + 2.74501i) q^{13} +(0.423107 - 4.45229i) q^{14} +(0.216636 - 1.71845i) q^{15} +(2.48983 + 4.31252i) q^{16} +(-2.83608 - 4.91224i) q^{17} +(-1.36628 - 4.88364i) q^{18} +(1.70155 - 2.94717i) q^{19} +(-0.428706 + 0.742540i) q^{20} +(-3.10264 + 3.37248i) q^{21} +(3.84133 + 6.65338i) q^{22} -0.0233324 q^{23} +(0.418415 - 3.31905i) q^{24} +1.00000 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} +(2.69877 - 1.13529i) q^{30} +(-0.859563 + 1.48881i) q^{31} +(-2.27737 + 3.94452i) q^{32} +(0.984591 - 7.81020i) 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} +5.75256 q^{38} +(5.06050 - 2.12879i) q^{39} +1.93142 q^{40} +(-3.45798 - 5.98939i) q^{41} +(-7.55937 - 1.69161i) q^{42} +(-4.52050 + 7.82973i) q^{43} +(-1.94843 + 3.37478i) q^{44} +(-2.90614 - 0.744556i) q^{45} +(-0.0197204 - 0.0341567i) q^{46} +(0.619810 + 1.07354i) q^{47} +(7.95023 - 3.34441i) q^{48} +(2.29547 + 6.61293i) q^{49} +(0.845194 + 1.46392i) q^{50} +(-9.05584 + 3.80950i) q^{51} -2.71771 q^{52} +(-5.10622 - 8.84423i) q^{53} +(-8.68828 + 1.28991i) q^{54} +4.54491 q^{55} +(-4.16387 - 2.96224i) q^{56} +(-4.69595 - 3.56249i) q^{57} -17.4802 q^{58} +(-4.64378 + 8.04327i) q^{59} +(1.18314 + 0.897570i) q^{60} +(4.28926 + 7.42921i) q^{61} -2.90599 q^{62} +(5.12329 + 6.06233i) q^{63} +2.26007 q^{64} +(1.58483 + 2.74501i) q^{65} +(12.2657 - 5.15977i) q^{66} +(0.751275 - 1.30125i) q^{67} +4.86338 q^{68} +(-0.00505463 + 0.0400955i) q^{69} +(0.423107 - 4.45229i) q^{70} +9.66372 q^{71} +(-5.61297 - 1.43805i) q^{72} +(-5.85704 - 10.1447i) q^{73} -11.9114 q^{74} +(0.216636 - 1.71845i) q^{75} +(1.45893 + 2.52694i) q^{76} +(-9.79819 - 6.97058i) q^{77} +(7.39347 + 5.60892i) q^{78} +(1.08269 + 1.87527i) q^{79} +(2.48983 + 4.31252i) q^{80} +(7.89127 + 4.32756i) q^{81} +(5.84532 - 10.1244i) q^{82} +(3.75755 - 6.50826i) q^{83} +(-1.17408 - 3.74963i) q^{84} +(-2.83608 - 4.91224i) q^{85} -15.2828 q^{86} +(14.2695 + 10.8253i) q^{87} +8.77812 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} +(2.37223 + 1.79965i) q^{93} +(-1.04772 + 1.81470i) q^{94} +(1.70155 - 2.94717i) q^{95} +(6.28509 + 4.76806i) q^{96} +(-0.533838 + 0.924635i) q^{97} +(-7.74068 + 8.94958i) q^{98} +(-13.2081 - 3.38394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9}+O(q^{10}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9	\( 36 q - q^{3} - 22 q^{4} + 36 q^{5} - 4 q^{6} - q^{7} + 3 q^{9} - 2 q^{11} + 5 q^{12} + 2 q^{13} - 6 q^{14} - q^{15} - 30 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} - 22 q^{20} - 11 q^{21} - 19 q^{22} + 6 q^{23} + 16 q^{24} + 36 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} - 4 q^{30} + 10 q^{32} - 5 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} + 44 q^{38} - 8 q^{39} - 4 q^{41} - 30 q^{42} - 29 q^{43} - 7 q^{44} + 3 q^{45} - 24 q^{46} - 23 q^{47} - 19 q^{48} - 7 q^{49} - 21 q^{51} + 14 q^{52} - 2 q^{55} + 33 q^{56} + 21 q^{57} + 40 q^{58} - 5 q^{59} + 5 q^{60} - 3 q^{61} - 12 q^{62} + 11 q^{63} + 128 q^{64} + 2 q^{65} - 30 q^{66} - 35 q^{67} + 34 q^{68} - 50 q^{69} - 6 q^{70} + 24 q^{71} + 5 q^{72} - 10 q^{73} - 44 q^{74} - q^{75} + 10 q^{76} + 5 q^{77} + 66 q^{78} - 28 q^{79} - 30 q^{80} + 47 q^{81} - 8 q^{82} - 22 q^{83} - 2 q^{84} - 5 q^{85} - 38 q^{86} + 45 q^{87} + 100 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - 28 q^{93} - 2 q^{94} - 2 q^{95} + 79 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 - 22 * q^4 + 36 * q^5 - 4 * q^6 - q^7 + 3 * q^9 - 2 * q^11 + 5 * q^12 + 2 * q^13 - 6 * q^14 - q^15 - 30 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 - 22 * q^20 - 11 * q^21 - 19 * q^22 + 6 * q^23 + 16 * q^24 + 36 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 - 4 * q^30 + 10 * q^32 - 5 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 + 44 * q^38 - 8 * q^39 - 4 * q^41 - 30 * q^42 - 29 * q^43 - 7 * q^44 + 3 * q^45 - 24 * q^46 - 23 * q^47 - 19 * q^48 - 7 * q^49 - 21 * q^51 + 14 * q^52 - 2 * q^55 + 33 * q^56 + 21 * q^57 + 40 * q^58 - 5 * q^59 + 5 * q^60 - 3 * q^61 - 12 * q^62 + 11 * q^63 + 128 * q^64 + 2 * q^65 - 30 * q^66 - 35 * q^67 + 34 * q^68 - 50 * q^69 - 6 * q^70 + 24 * q^71 + 5 * q^72 - 10 * q^73 - 44 * q^74 - q^75 + 10 * q^76 + 5 * q^77 + 66 * q^78 - 28 * q^79 - 30 * q^80 + 47 * q^81 - 8 * q^82 - 22 * q^83 - 2 * q^84 - 5 * q^85 - 38 * q^86 + 45 * q^87 + 100 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - 28 * q^93 - 2 * q^94 - 2 * q^95 + 79 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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