LMFDB - Embedded newform 315.2.t.b.101.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, 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:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.15
Character	$\chi$	$=$	315.101
Dual form			315.2.t.b.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.72808i q^{2} +(-1.55907 - 0.754526i) q^{3} -5.44243 q^{4} +(0.500000 - 0.866025i) q^{5} +(2.05841 - 4.25326i) q^{6} +(-2.63818 - 0.200022i) q^{7} -9.39122i q^{8} +(1.86138 + 2.35271i) q^{9} +O(q^{10})$	\(q+2.72808i q^{2} +(-1.55907 - 0.754526i) q^{3} -5.44243 q^{4} +(0.500000 - 0.866025i) q^{5} +(2.05841 - 4.25326i) q^{6} +(-2.63818 - 0.200022i) q^{7} -9.39122i q^{8} +(1.86138 + 2.35271i) q^{9} +(2.36259 + 1.36404i) q^{10} +(0.246087 - 0.142079i) q^{11} +(8.48511 + 4.10646i) q^{12} +(2.89807 - 1.67320i) q^{13} +(0.545675 - 7.19717i) q^{14} +(-1.43297 + 0.972928i) q^{15} +14.7352 q^{16} +(2.65611 - 4.60051i) q^{17} +(-6.41840 + 5.07799i) q^{18} +(0.743281 - 0.429133i) q^{19} +(-2.72121 + 4.71328i) q^{20} +(3.96218 + 2.30242i) q^{21} +(0.387602 + 0.671346i) q^{22} +(-6.85136 - 3.95563i) q^{23} +(-7.08592 + 14.6415i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(4.56463 + 7.90618i) q^{26} +(-1.12683 - 5.07250i) q^{27} +(14.3581 + 1.08860i) q^{28} +(-1.98489 - 1.14598i) q^{29} +(-2.65423 - 3.90927i) q^{30} +1.14550i q^{31} +21.4163i q^{32} +(-0.490868 + 0.0358306i) q^{33} +(12.5506 + 7.24607i) q^{34} +(-1.49231 + 2.18472i) q^{35} +(-10.1304 - 12.8045i) q^{36} +(-4.53064 - 7.84730i) q^{37} +(1.17071 + 2.02773i) q^{38} +(-5.78077 + 0.421963i) q^{39} +(-8.13303 - 4.69561i) q^{40} +(-3.15733 - 5.46865i) q^{41} +(-6.28120 + 10.8091i) q^{42} +(0.223973 - 0.387932i) q^{43} +(-1.33931 + 0.773252i) q^{44} +(2.96820 - 0.435645i) q^{45} +(10.7913 - 18.6911i) q^{46} -6.01964 q^{47} +(-22.9731 - 11.1181i) q^{48} +(6.91998 + 1.05539i) q^{49} +(2.36259 - 1.36404i) q^{50} +(-7.61226 + 5.16840i) q^{51} +(-15.7726 + 9.10629i) q^{52} +(-0.483757 - 0.279297i) q^{53} +(13.8382 - 3.07408i) q^{54} -0.284157i q^{55} +(-1.87845 + 24.7757i) q^{56} +(-1.48262 + 0.108223i) q^{57} +(3.12632 - 5.41494i) q^{58} +9.19616 q^{59} +(7.79885 - 5.29509i) q^{60} +8.04297i q^{61} -3.12502 q^{62} +(-4.44006 - 6.57920i) q^{63} -28.9550 q^{64} -3.34641i q^{65} +(-0.0977488 - 1.33913i) q^{66} +1.60576 q^{67} +(-14.4557 + 25.0379i) q^{68} +(7.69710 + 11.3366i) q^{69} +(-5.96009 - 4.07115i) q^{70} -8.30424i q^{71} +(22.0949 - 17.4806i) q^{72} +(3.55813 + 2.05429i) q^{73} +(21.4081 - 12.3599i) q^{74} +(0.126094 + 1.72745i) q^{75} +(-4.04525 + 2.33553i) q^{76} +(-0.677641 + 0.325606i) q^{77} +(-1.15115 - 15.7704i) q^{78} +4.58911 q^{79} +(7.36758 - 12.7610i) q^{80} +(-2.07053 + 8.75859i) q^{81} +(14.9189 - 8.61345i) q^{82} +(-2.29623 + 3.97719i) q^{83} +(-21.5639 - 12.5308i) q^{84} +(-2.65611 - 4.60051i) q^{85} +(1.05831 + 0.611016i) q^{86} +(2.22991 + 3.28431i) q^{87} +(-1.33429 - 2.31106i) q^{88} +(-5.97567 - 10.3502i) q^{89} +(1.18847 + 8.09749i) q^{90} +(-7.98031 + 3.83453i) q^{91} +(37.2880 + 21.5282i) q^{92} +(0.864310 - 1.78591i) q^{93} -16.4221i q^{94} -0.858267i q^{95} +(16.1591 - 33.3894i) q^{96} +(3.69117 + 2.13110i) q^{97} +(-2.87918 + 18.8783i) q^{98} +(0.792332 + 0.314511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			2.72808i			1.92904i	0.264001	+	0.964522i	$0.414958\pi$
$2$			2.72808i			1.92904i	−0.264001	+	0.964522i	$0.585042\pi$
$3$	−1.55907	−	0.754526i	−0.900128	−	0.435626i
$3$	−1.55907	−	0.754526i	−0.900128	−	0.435626i
$4$	−5.44243			−2.72121
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	2.05841	−	4.25326i	0.840342	−	1.73639i
$7$	−2.63818	−	0.200022i	−0.997138	−	0.0756011i
$7$	−2.63818	−	0.200022i	−0.997138	−	0.0756011i
$8$		−	9.39122i		−	3.32030i
$9$	1.86138	+	2.35271i	0.620460	+	0.784238i
$10$	2.36259	+	1.36404i	0.747116	+	0.431348i
$11$	0.246087	−	0.142079i	0.0741981	−	0.0428383i	−0.462442	−	0.886650i	$-0.653027\pi$
$11$	0.246087	−	0.142079i	0.0741981	−	0.0428383i	0.536640	+	0.843811i	$0.319693\pi$
$12$	8.48511	+	4.10646i	2.44944	+	1.18543i
$13$	2.89807	−	1.67320i	0.803781	−	0.464063i	−0.0410106	−	0.999159i	$-0.513058\pi$
$13$	2.89807	−	1.67320i	0.803781	−	0.464063i	0.844792	+	0.535096i	$0.179724\pi$
$14$	0.545675	−	7.19717i	0.145838	−	1.92352i
$15$	−1.43297	+	0.972928i	−0.369992	+	0.251209i
$16$	14.7352			3.68379
$17$	2.65611	−	4.60051i	0.644200	−	1.11579i	−0.340285	−	0.940322i	$-0.610524\pi$
$17$	2.65611	−	4.60051i	0.644200	−	1.11579i	0.984486	−	0.175466i	$-0.0561431\pi$
$18$	−6.41840	+	5.07799i	−1.51283	+	1.19689i
$19$	0.743281	−	0.429133i	0.170520	−	0.0984499i	−0.412311	−	0.911043i	$-0.635278\pi$
$19$	0.743281	−	0.429133i	0.170520	−	0.0984499i	0.582831	+	0.812593i	$0.301945\pi$
$20$	−2.72121	+	4.71328i	−0.608482	+	1.05392i
$21$	3.96218	+	2.30242i	0.864618	+	0.502430i
$22$	0.387602	+	0.671346i	0.0826370	+	0.143131i
$23$	−6.85136	−	3.95563i	−1.42861	−	0.824807i	−0.431596	−	0.902067i	$-0.642049\pi$
$23$	−6.85136	−	3.95563i	−1.42861	−	0.824807i	−0.997011	+	0.0772602i	$0.975383\pi$
$24$	−7.08592	+	14.6415i	−1.44641	+	2.98869i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.56463	+	7.90618i	0.895198	+	1.55053i
$27$	−1.12683	−	5.07250i	−0.216858	−	0.976203i
$28$	14.3581	+	1.08860i	2.71343	+	0.205727i
$29$	−1.98489	−	1.14598i	−0.368585	−	0.212803i	0.304255	−	0.952591i	$-0.401592\pi$
$29$	−1.98489	−	1.14598i	−0.368585	−	0.212803i	−0.672840	+	0.739788i	$0.734926\pi$
$30$	−2.65423	−	3.90927i	−0.484593	−	0.713731i
$31$			1.14550i			0.205738i	0.994695	+	0.102869i	$0.0328022\pi$
$31$			1.14550i			0.205738i	−0.994695	+	0.102869i	$0.967198\pi$
$32$			21.4163i			3.78590i
$33$	−0.490868	+	0.0358306i	−0.0854492	+	0.00623731i
$34$	12.5506	+	7.24607i	2.15240	+	1.24269i
$35$	−1.49231	+	2.18472i	−0.252247	+	0.369285i
$36$	−10.1304	−	12.8045i	−1.68840	−	2.13408i
$37$	−4.53064	−	7.84730i	−0.744832	−	1.29009i	−0.950273	−	0.311418i	$-0.899196\pi$
$37$	−4.53064	−	7.84730i	−0.744832	−	1.29009i	0.205441	−	0.978670i	$-0.434137\pi$
$38$	1.17071	+	2.02773i	0.189914	+	0.328941i
$39$	−5.78077	+	0.421963i	−0.925663	+	0.0675682i
$40$	−8.13303	−	4.69561i	−1.28595	−	0.742441i
$41$	−3.15733	−	5.46865i	−0.493092	−	0.854060i	0.506877	−	0.862019i	$-0.330800\pi$
$41$	−3.15733	−	5.46865i	−0.493092	−	0.854060i	−0.999968	+	0.00795875i	$0.997467\pi$
$42$	−6.28120	+	10.8091i	−0.969210	+	1.66789i
$43$	0.223973	−	0.387932i	0.0341555	−	0.0591591i	−0.848442	−	0.529288i	$-0.822459\pi$
$43$	0.223973	−	0.387932i	0.0341555	−	0.0591591i	0.882598	+	0.470129i	$0.155793\pi$
$44$	−1.33931	+	0.773252i	−0.201909	+	0.116572i
$45$	2.96820	−	0.435645i	0.442473	−	0.0649421i
$46$	10.7913	−	18.6911i	1.59109	−	2.75585i
$47$	−6.01964			−0.878055			−0.439027	−	0.898474i	$-0.644677\pi$
$47$	−6.01964			−0.878055			−0.439027	+	0.898474i	$0.644677\pi$
$48$	−22.9731	−	11.1181i	−3.31588	−	1.60475i
$49$	6.91998	+	1.05539i	0.988569	+	0.150769i
$50$	2.36259	−	1.36404i	0.334120	−	0.192904i
$51$	−7.61226	+	5.16840i	−1.06593	+	0.723721i
$52$	−15.7726	+	9.10629i	−2.18726	+	1.26281i
$53$	−0.483757	−	0.279297i	−0.0664491	−	0.0383644i	0.466407	−	0.884570i	$-0.345548\pi$
$53$	−0.483757	−	0.279297i	−0.0664491	−	0.0383644i	−0.532856	+	0.846206i	$0.678881\pi$
$54$	13.8382	−	3.07408i	1.88314	−	0.418330i
$55$		−	0.284157i		−	0.0383157i
$56$	−1.87845	+	24.7757i	−0.251018	+	3.31080i
$57$	−1.48262	+	0.108223i	−0.196377	+	0.0143344i
$58$	3.12632	−	5.41494i	0.410506	−	0.711017i
$59$	9.19616			1.19724			0.598619	−	0.801034i	$-0.295716\pi$
$59$	9.19616			1.19724			0.598619	+	0.801034i	$0.295716\pi$
$60$	7.79885	−	5.29509i	1.00683	−	0.683593i
$61$			8.04297i			1.02980i	0.857251	+	0.514899i	$0.172170\pi$
$61$			8.04297i			1.02980i	−0.857251	+	0.514899i	$0.827830\pi$
$62$	−3.12502			−0.396877
$63$	−4.44006	−	6.57920i	−0.559395	−	0.828901i
$64$	−28.9550			−3.61937
$65$		−	3.34641i		−	0.415071i
$66$	−0.0977488	−	1.33913i	−0.0120320	−	0.164835i
$67$	1.60576			0.196175			0.0980875	−	0.995178i	$-0.468727\pi$
$67$	1.60576			0.196175			0.0980875	+	0.995178i	$0.468727\pi$
$68$	−14.4557	+	25.0379i	−1.75301	+	3.03630i
$69$	7.69710	+	11.3366i	0.926622	+	1.36477i
$70$	−5.96009	−	4.07115i	−0.712367	−	0.486596i
$71$		−	8.30424i		−	0.985532i	−0.870162	−	0.492766i	$-0.835986\pi$
$71$		−	8.30424i		−	0.985532i	0.870162	−	0.492766i	$-0.164014\pi$
$72$	22.0949	−	17.4806i	2.60390	−	2.06011i
$73$	3.55813	+	2.05429i	0.416448	+	0.240436i	0.693556	−	0.720402i	$-0.256043\pi$
$73$	3.55813	+	2.05429i	0.416448	+	0.240436i	−0.277109	+	0.960839i	$0.589376\pi$
$74$	21.4081	−	12.3599i	2.48864	−	1.43681i
$75$	0.126094	+	1.72745i	0.0145601	+	0.199469i
$76$	−4.04525	+	2.33553i	−0.464022	+	0.267903i
$77$	−0.677641	+	0.325606i	−0.0772244	+	0.0371062i
$78$	−1.15115	−	15.7704i	−0.130342	−	1.78565i
$79$	4.58911			0.516316			0.258158	−	0.966103i	$-0.416885\pi$
$79$	4.58911			0.516316			0.258158	+	0.966103i	$0.416885\pi$
$80$	7.36758	−	12.7610i	0.823720	−	1.42673i
$81$	−2.07053	+	8.75859i	−0.230059	+	0.973177i
$82$	14.9189	−	8.61345i	1.64752	−	0.951196i
$83$	−2.29623	+	3.97719i	−0.252044	+	0.436553i	−0.964088	−	0.265581i	$-0.914436\pi$
$83$	−2.29623	+	3.97719i	−0.252044	+	0.436553i	0.712044	+	0.702134i	$0.247769\pi$
$84$	−21.5639	−	12.5308i	−2.35281	−	1.36722i
$85$	−2.65611	−	4.60051i	−0.288095	−	0.498996i
$86$	1.05831	+	0.611016i	0.114121	+	0.0658875i
$87$	2.22991	+	3.28431i	0.239071	+	0.352115i
$88$	−1.33429	−	2.31106i	−0.142236	−	0.246360i
$89$	−5.97567	−	10.3502i	−0.633419	−	1.09711i	−0.986848	−	0.161653i	$-0.948317\pi$
$89$	−5.97567	−	10.3502i	−0.633419	−	1.09711i	0.353428	−	0.935462i	$-0.385016\pi$
$90$	1.18847	+	8.09749i	0.125276	+	0.853551i
$91$	−7.98031	+	3.83453i	−0.836564	+	0.401968i
$92$	37.2880	+	21.5282i	3.88754	+	2.24448i
$93$	0.864310	−	1.78591i	0.0896248	−	0.185190i
$94$		−	16.4221i		−	1.69381i
$95$		−	0.858267i		−	0.0880563i
$96$	16.1591	−	33.3894i	1.64923	−	3.40779i
$97$	3.69117	+	2.13110i	0.374781	+	0.216380i	0.675545	−	0.737319i	$-0.263908\pi$
$97$	3.69117	+	2.13110i	0.374781	+	0.216380i	−0.300764	+	0.953699i	$0.597242\pi$
$98$	−2.87918	+	18.8783i	−0.290841	+	1.90699i
$99$	0.792332	+	0.314511i	0.0796324	+	0.0316095i
$100$	2.72121	+	4.71328i	0.272121	+	0.471328i
$101$	−8.72700	−	15.1156i	−0.868369	−	1.50406i	−0.863663	−	0.504070i	$-0.831835\pi$
$101$	−8.72700	−	15.1156i	−0.868369	−	1.50406i	−0.00470633	−	0.999989i	$-0.501498\pi$
$102$	−14.0998	−	20.7669i	−1.39609	−	2.05622i
$103$	5.23103	+	3.02014i	0.515429	+	0.297583i	0.735062	−	0.677999i	$-0.237153\pi$
$103$	5.23103	+	3.02014i	0.515429	+	0.297583i	−0.219634	+	0.975582i	$0.570486\pi$
$104$	−15.7134	−	27.2164i	−1.54083	−	2.66879i
$105$	3.97505	−	2.28013i	0.387925	−	0.222518i
$106$	0.761945	−	1.31973i	0.0740066	−	0.128183i
$107$	−16.6602	+	9.61880i	−1.61061	+	0.929884i	−0.621377	+	0.783512i	$0.713426\pi$
$107$	−16.6602	+	9.61880i	−1.61061	+	0.929884i	−0.989230	+	0.146372i	$0.953240\pi$
$108$	6.13269	+	27.6067i	0.590118	+	2.65646i
$109$	−9.81002	+	16.9915i	−0.939630	+	1.62749i	−0.173467	+	0.984840i	$0.555497\pi$
$109$	−9.81002	+	16.9915i	−0.939630	+	1.62749i	−0.766163	+	0.642647i	$0.777836\pi$
$110$	0.775203			0.0739127
$111$	1.14258	+	15.6529i	0.108449	+	1.48571i
$112$	−38.8740	−	2.94735i	−3.67325	−	0.278498i
$113$	15.1511	−	8.74750i	1.42530	−	0.822895i	0.428552	−	0.903517i	$-0.359024\pi$
$113$	15.1511	−	8.74750i	1.42530	−	0.822895i	0.996745	+	0.0806222i	$0.0256907\pi$
$114$	−0.295240	−	4.04470i	−0.0276518	−	0.378821i
$115$	−6.85136	+	3.95563i	−0.638893	+	0.368865i
$116$	10.8026	+	6.23689i	1.00300	+	0.579081i
$117$	9.33098	+	3.70387i	0.862650	+	0.342423i
$118$			25.0879i			2.30953i
$119$	−7.92749	+	11.6057i	−0.726712	+	1.06389i
$120$	9.13698	+	13.4574i	0.834089	+	1.22848i
$121$	−5.45963	+	9.45635i	−0.496330	+	0.859668i
$122$	−21.9419			−1.98653
$123$	0.796242	+	10.9083i	0.0717948	+	0.983567i
$124$		−	6.23430i		−	0.559857i
$125$	−1.00000			−0.0894427
$126$	17.9486	−	12.1128i	1.59899	−	1.07910i
$127$	−2.11951			−0.188076			−0.0940381	−	0.995569i	$-0.529978\pi$
$127$	−2.11951			−0.188076			−0.0940381	+	0.995569i	$0.529978\pi$
$128$		−	36.1590i		−	3.19604i
$129$	−0.641894	+	0.435819i	−0.0565156	+	0.0383717i
$130$	9.12927			0.800690
$131$	7.04929	−	12.2097i	0.615900	−	1.06677i	−0.374326	−	0.927297i	$-0.622126\pi$
$131$	7.04929	−	12.2097i	0.615900	−	1.06677i	0.990226	−	0.139472i	$-0.0445406\pi$
$132$	2.67152	−	0.195005i	0.232526	−	0.0169730i
$133$	−2.04674	+	0.983458i	−0.177475	+	0.0852767i
$134$			4.38065i			0.378430i
$135$	−4.95633	−	1.56039i	−0.426573	−	0.134297i
$136$	−43.2044	−	24.9441i	−3.70475	−	2.13894i
$137$	−4.94165	+	2.85306i	−0.422194	+	0.243754i	−0.696015	−	0.718027i	$-0.745045\pi$
$137$	−4.94165	+	2.85306i	−0.422194	+	0.243754i	0.273822	+	0.961780i	$0.411712\pi$
$138$	−30.9272	+	20.9983i	−2.63270	+	1.78749i
$139$	5.63256	−	3.25196i	0.477747	−	0.275828i	−0.241730	−	0.970344i	$-0.577715\pi$
$139$	5.63256	−	3.25196i	0.477747	−	0.275828i	0.719477	+	0.694516i	$0.244381\pi$
$140$	8.12181	−	11.8902i	0.686418	−	1.00490i
$141$	9.38502	+	4.54198i	0.790361	+	0.382504i
$142$	22.6546			1.90113
$143$	0.475453	−	0.823508i	0.0397593	−	0.0688652i
$144$	27.4277	+	34.6676i	2.28564	+	2.88897i
$145$	−1.98489	+	1.14598i	−0.164836	+	0.0951682i
$146$	−5.60427	+	9.70687i	−0.463812	+	0.803347i
$147$	−9.99240	−	6.86673i	−0.824159	−	0.566358i
$148$	24.6577	+	42.7083i	2.02685	+	3.51060i
$149$	8.49734	+	4.90594i	0.696129	+	0.401911i	0.805904	−	0.592046i	$-0.201680\pi$
$149$	8.49734	+	4.90594i	0.696129	+	0.401911i	−0.109775	+	0.993956i	$0.535013\pi$
$150$	−4.71264	+	0.343996i	−0.384785	+	0.0280871i
$151$	−4.86219	−	8.42156i	−0.395680	−	0.685337i	0.597508	−	0.801863i	$-0.296158\pi$
$151$	−4.86219	−	8.42156i	−0.395680	−	0.685337i	−0.993188	+	0.116526i	$0.962824\pi$
$152$	−4.03008	−	6.98031i	−0.326883	−	0.566178i
$153$	15.7677	−	2.31424i	1.27474	−	0.187095i
$154$	−0.888279	−	1.84866i	−0.0715796	−	0.148969i
$155$	0.992032	+	0.572750i	0.0796819	+	0.0460044i
$156$	31.4614	−	2.29650i	2.51893	−	0.183867i
$157$			6.28096i			0.501275i	0.968081	+	0.250637i	$0.0806402\pi$
$157$			6.28096i			0.501275i	−0.968081	+	0.250637i	$0.919360\pi$
$158$			12.5195i			0.995996i
$159$	0.543472	+	0.800450i	0.0431001	+	0.0634798i
$160$	18.5470	+	10.7081i	1.46627	+	0.846552i
$161$	17.2839	+	11.8061i	1.36216	+	0.930450i
$162$	−23.8941	−	5.64858i	−1.87730	−	0.443794i
$163$	−9.14675	−	15.8426i	−0.716429	−	1.24089i	−0.962406	−	0.271615i	$-0.912442\pi$
$163$	−9.14675	−	15.8426i	−0.716429	−	1.24089i	0.245977	−	0.969276i	$-0.420891\pi$
$164$	17.1835	+	29.7627i	1.34181	+	2.32408i
$165$	−0.214404	+	0.443020i	−0.0166913	+	0.0344890i
$166$	−10.8501	−	6.26430i	−0.842131	−	0.486204i
$167$	3.77161	+	6.53262i	0.291856	+	0.505510i	0.974249	−	0.225476i	$-0.0723938\pi$
$167$	3.77161	+	6.53262i	0.291856	+	0.505510i	−0.682393	+	0.730986i	$0.739061\pi$
$168$	21.6226	−	37.2097i	1.66822	−	2.87079i
$169$	−0.900781	+	1.56020i	−0.0692908	+	0.120015i
$170$	12.5506	−	7.24607i	0.962585	−	0.555749i
$171$	2.39316	+	0.949947i	0.183009	+	0.0726443i
$172$	−1.21896	+	2.11129i	−0.0929445	+	0.160985i
$173$	−2.46870			−0.187692			−0.0938458	−	0.995587i	$-0.529916\pi$
$173$	−2.46870			−0.187692			−0.0938458	+	0.995587i	$0.529916\pi$
$174$	−8.95986	+	6.08337i	−0.679245	+	0.461179i
$175$	1.14587	+	2.38474i	0.0866193	+	0.180269i
$176$	3.62613	−	2.09355i	0.273330	−	0.157807i
$177$	−14.3374	−	6.93875i	−1.07767	−	0.521548i
$178$	28.2361	−	16.3021i	2.11638	−	1.22189i
$179$	0.894686	+	0.516547i	0.0668720	+	0.0386085i	0.533063	−	0.846075i	$-0.321041\pi$
$179$	0.894686	+	0.516547i	0.0668720	+	0.0386085i	−0.466191	+	0.884684i	$0.654374\pi$
$180$	−16.1542	+	2.37096i	−1.20406	+	0.176721i
$181$		−	4.90430i		−	0.364534i	−0.983249	−	0.182267i	$-0.941656\pi$
$181$		−	4.90430i		−	0.364534i	0.983249	−	0.182267i	$-0.0583435\pi$
$182$	−10.4609	−	21.7709i	−0.775415	−	1.61377i
$183$	6.06864	−	12.5395i	0.448607	−	0.926949i
$184$	−37.1482	+	64.3426i	−2.73860	+	4.74340i
$185$	−9.06128			−0.666198
$186$	4.87211	+	2.35791i	0.357240	+	0.172890i
$187$		−	1.50950i		−	0.110386i
$188$	32.7615			2.38937
$189$	1.95817	+	13.6076i	0.142436	+	0.989804i
$190$	2.34142			0.169865
$191$			1.88932i			0.136707i	0.997661	+	0.0683533i	$0.0217745\pi$
$191$			1.88932i			0.136707i	−0.997661	+	0.0683533i	$0.978225\pi$
$192$	45.1428	+	21.8473i	3.25790	+	1.57669i
$193$	12.3826			0.891318			0.445659	−	0.895203i	$-0.352969\pi$
$193$	12.3826			0.891318			0.445659	+	0.895203i	$0.352969\pi$
$194$	−5.81380	+	10.0698i	−0.417407	+	0.722969i
$195$	−2.52495	+	5.21727i	−0.180816	+	0.373617i
$196$	−37.6615	−	5.74386i	−2.69011	−	0.410276i
$197$		−	2.13992i		−	0.152463i	−0.997090	−	0.0762316i	$-0.975711\pi$
$197$		−	2.13992i		−	0.152463i	0.997090	−	0.0762316i	$-0.0242888\pi$
$198$	−0.858011	+	2.16155i	−0.0609762	+	0.153614i
$199$	2.61298	+	1.50861i	0.185230	+	0.106942i	0.589747	−	0.807588i	$-0.299227\pi$
$199$	2.61298	+	1.50861i	0.185230	+	0.106942i	−0.404518	+	0.914530i	$0.632561\pi$
$200$	−8.13303	+	4.69561i	−0.575092	+	0.332030i
$201$	−2.50349	−	1.21159i	−0.176583	−	0.0854590i
$202$	41.2366	−	23.8080i	2.90140	−	1.67512i
$203$	5.00728	+	3.42031i	0.351442	+	0.240059i
$204$	41.4291	−	28.1287i	2.90062	−	1.96940i
$205$	−6.31465			−0.441035
$206$	−8.23918	+	14.2707i	−0.574051	+	0.994285i
$207$	−3.44650	−	23.4822i	−0.239548	−	1.63213i
$208$	42.7036	−	24.6549i	2.96096	−	1.70951i
$209$	0.121941	−	0.211208i	0.00843485	−	0.0146096i
$210$	6.22039	+	10.8442i	0.429248	+	0.748324i
$211$	2.43826	+	4.22319i	0.167857	+	0.290736i	0.937666	−	0.347538i	$-0.112982\pi$
$211$	2.43826	+	4.22319i	0.167857	+	0.290736i	−0.769809	+	0.638274i	$0.779649\pi$
$212$	2.63281	+	1.52005i	0.180822	+	0.104398i
$213$	−6.26577	+	12.9469i	−0.429323	+	0.887104i
$214$	−26.2409	−	45.4505i	−1.79379	−	3.10693i
$215$	−0.223973	−	0.387932i	−0.0152748	−	0.0264568i
$216$	−47.6370	+	10.5823i	−3.24128	+	0.720035i
$217$	0.229125	−	3.02203i	0.0155540	−	0.205149i
$218$	−46.3541	−	26.7625i	−3.13949	−	1.81259i
$219$	−3.99735	−	5.88748i	−0.270116	−	0.397839i
$220$			1.54650i			0.104265i
$221$		−	17.7768i		−	1.19580i
$222$	−42.7025	+	3.11704i	−2.86600	+	0.209202i
$223$	3.25079	+	1.87684i	0.217689	+	0.125683i	0.604880	−	0.796317i	$-0.293221\pi$
$223$	3.25079	+	1.87684i	0.217689	+	0.125683i	−0.387191	+	0.922000i	$0.626555\pi$
$224$	4.28372	−	56.4999i	0.286218	−	3.77506i
$225$	1.10682	−	2.78836i	0.0737881	−	0.185891i
$226$	23.8639	+	41.3334i	1.58740	+	2.74946i
$227$	−4.28622	−	7.42396i	−0.284487	−	0.492745i	0.687998	−	0.725713i	$-0.258490\pi$
$227$	−4.28622	−	7.42396i	−0.284487	−	0.492745i	−0.972485	+	0.232967i	$0.925156\pi$
$228$	8.06903	−	0.588993i	0.534385	−	0.0390070i
$229$	−1.23993	−	0.715874i	−0.0819369	−	0.0473063i	0.458472	−	0.888709i	$-0.348397\pi$
$229$	−1.23993	−	0.715874i	−0.0819369	−	0.0473063i	−0.540409	+	0.841403i	$0.681730\pi$
$230$	−10.7913	−	18.6911i	−0.711557	−	1.23245i
$231$	1.30217	+	0.00365675i	0.0856762	+	0.000240596i
$232$	−10.7621	+	18.6405i	−0.706568	+	1.22381i
$233$	2.40835	−	1.39046i	0.157777	−	0.0910923i	−0.419033	−	0.907971i	$-0.637631\pi$
$233$	2.40835	−	1.39046i	0.157777	−	0.0910923i	0.576809	+	0.816879i	$0.304298\pi$
$234$	−10.1045	+	25.4557i	−0.660550	+	1.66409i
$235$	−3.00982	+	5.21316i	−0.196339	+	0.340069i
$236$	−50.0495			−3.25794
$237$	−7.15474	−	3.46261i	−0.464750	−	0.224921i
$238$	−31.6613	−	21.6268i	−2.05230	−	1.40186i
$239$	−6.19653	+	3.57757i	−0.400820	+	0.231414i	−0.686838	−	0.726811i	$-0.741002\pi$
$239$	−6.19653	+	3.57757i	−0.400820	+	0.231414i	0.286018	+	0.958224i	$0.407668\pi$
$240$	−21.1151	+	14.3362i	−1.36297	+	0.925401i
$241$	23.1673	−	13.3757i	1.49234	−	0.861602i	0.492376	−	0.870382i	$-0.336128\pi$
$241$	23.1673	−	13.3757i	1.49234	−	0.861602i	0.999961	+	0.00878061i	$0.00279499\pi$
$242$	−25.7977	−	14.8943i	−1.65834	−	0.957442i
$243$	9.83669	−	12.0930i	0.631024	−	0.775764i
$244$		−	43.7733i		−	2.80230i
$245$	4.37398	−	5.46519i	0.279443	−	0.349158i
$246$	−29.7587	+	2.17221i	−1.89734	+	0.138495i
$247$	1.43605	−	2.48732i	0.0913740	−	0.158264i
$248$	10.7576			0.683111
$249$	6.58087	−	4.46814i	0.417046	−	0.283157i
$250$		−	2.72808i		−	0.172539i
$251$	9.60803			0.606453			0.303227	−	0.952918i	$-0.401936\pi$
$251$	9.60803			0.606453			0.303227	+	0.952918i	$0.401936\pi$
$252$	24.1647	+	35.8068i	1.52223	+	2.25562i
$253$	−2.24804			−0.141333
$254$		−	5.78220i		−	0.362807i
$255$	0.669840	+	9.17661i	0.0419470	+	0.574662i
$256$	40.7348			2.54592
$257$	4.98129	−	8.62785i	0.310725	−	0.538191i	−0.667795	−	0.744345i	$-0.732762\pi$
$257$	4.98129	−	8.62785i	0.310725	−	0.538191i	0.978519	+	0.206155i	$0.0660950\pi$
$258$	−1.18895	−	1.75114i	−0.0740207	−	0.109021i
$259$	10.3830	+	21.6088i	0.645169	+	1.34271i
$260$			18.2126i			1.12950i
$261$	−0.998477	−	6.80298i	−0.0618042	−	0.421094i
$262$	33.3091	+	19.2310i	2.05785	+	1.18810i
$263$	11.8871	−	6.86305i	0.732993	−	0.423194i	−0.0865232	−	0.996250i	$-0.527576\pi$
$263$	11.8871	−	6.86305i	0.732993	−	0.423194i	0.819516	+	0.573056i	$0.194242\pi$
$264$	0.336493	+	4.60985i	0.0207097	+	0.283717i
$265$	−0.483757	+	0.279297i	−0.0297169	+	0.0171571i
$266$	−2.68295	−	5.58368i	−0.164502	−	0.342358i
$267$	1.50700	+	20.6454i	0.0922266	+	1.26348i
$268$	−8.73924			−0.533834
$269$	−4.29238	+	7.43463i	−0.261711	+	0.453297i	−0.966697	−	0.255925i	$-0.917620\pi$
$269$	−4.29238	+	7.43463i	−0.261711	+	0.453297i	0.704986	+	0.709222i	$0.250953\pi$
$270$	4.25686	−	13.5213i	0.259064	−	0.822878i
$271$	25.7871	−	14.8882i	1.56645	−	0.904393i	0.569877	−	0.821730i	$-0.306991\pi$
$271$	25.7871	−	14.8882i	1.56645	−	0.904393i	0.996578	−	0.0826626i	$-0.0263424\pi$
$272$	39.1381	−	67.7893i	2.37310	−	4.11033i
$273$	15.3351	+	0.0430641i	0.928123	+	0.00260636i
$274$	−7.78339	−	13.4812i	−0.470212	−	0.814431i
$275$	−0.246087	−	0.142079i	−0.0148396	−	0.00856766i
$276$	−41.8909	−	61.6988i	−2.52154	−	3.71383i
$277$	9.92696	+	17.1940i	0.596453	+	1.03309i	0.993340	+	0.115220i	$0.0367572\pi$
$277$	9.92696	+	17.1940i	0.596453	+	1.03309i	−0.396887	+	0.917868i	$0.629909\pi$
$278$	8.87161	+	15.3661i	0.532084	+	0.921596i
$279$	−2.69503	+	2.13221i	−0.161347	+	0.127652i
$280$	20.5172	+	14.0146i	1.22614	+	0.837535i
$281$	8.54068	+	4.93096i	0.509494	+	0.294157i	0.732626	−	0.680632i	$-0.238295\pi$
$281$	8.54068	+	4.93096i	0.509494	+	0.294157i	−0.223132	+	0.974788i	$0.571628\pi$
$282$	−12.3909	+	25.6031i	−0.737866	+	1.52464i
$283$			10.5552i			0.627441i	0.949515	+	0.313720i	$0.101575\pi$
$283$			10.5552i			0.627441i	−0.949515	+	0.313720i	$0.898425\pi$
$284$			45.1952i			2.68184i
$285$	−0.647585	+	1.33810i	−0.0383596	+	0.0792619i
$286$	2.24660	+	1.29707i	0.132844	+	0.0766975i
$287$	7.23575	+	15.0588i	0.427113	+	0.888894i
$288$	−50.3863	+	39.8638i	−2.96904	+	2.34900i
$289$	−5.60981	−	9.71647i	−0.329989	−	0.571557i
$290$	−3.12632	−	5.41494i	−0.183584	−	0.317976i
$291$	−4.14681	−	6.10760i	−0.243090	−	0.358034i
$292$	−19.3649	−	11.1803i	−1.13324	−	0.654278i
$293$	4.31392	+	7.47192i	0.252022	+	0.436514i	0.964082	−	0.265604i	$-0.0855713\pi$
$293$	4.31392	+	7.47192i	0.252022	+	0.436514i	−0.712061	+	0.702118i	$0.752238\pi$
$294$	18.7330	−	27.2601i	1.09253	−	1.58984i
$295$	4.59808	−	7.96411i	0.267711	−	0.463689i
$296$	−73.6957	+	42.5482i	−4.28347	+	2.47307i
$297$	−0.997992	−	1.08818i	−0.0579093	−	0.0631426i
$298$	−13.3838	+	23.1814i	−0.775303	+	1.34286i
$299$	−26.4743			−1.53105
$300$	−0.686259	−	9.40155i	−0.0396212	−	0.542799i
$301$	−0.668475	+	0.978635i	−0.0385303	+	0.0564076i
$302$	22.9747	−	13.2645i	1.32205	−	0.763284i
$303$	2.20085	+	30.1510i	0.126436	+	1.73213i
$304$	10.9524	−	6.32335i	0.628161	−	0.362669i
$305$	6.96542	+	4.02149i	0.398839	+	0.230270i
$306$	6.31343	+	43.0156i	0.360915	+	2.45904i
$307$		−	11.5914i		−	0.661558i	−0.943708	−	0.330779i	$-0.892689\pi$
$307$		−	11.5914i		−	0.661558i	0.943708	−	0.330779i	$-0.107311\pi$
$308$	3.68801	−	1.77209i	0.210144	−	0.100974i
$309$	−5.87675	−	8.65555i	−0.334317	−	0.492397i
$310$	−1.56251	+	2.70634i	−0.0887445	+	0.153710i
$311$	−4.97187			−0.281929			−0.140964	−	0.990015i	$-0.545020\pi$
$311$	−4.97187			−0.281929			−0.140964	+	0.990015i	$0.545020\pi$
$312$	3.96275	+	54.2884i	0.224346	+	3.07348i
$313$		−	19.5824i		−	1.10686i	−0.832896	−	0.553430i	$-0.813319\pi$
$313$		−	19.5824i		−	1.10686i	0.832896	−	0.553430i	$-0.186681\pi$
$314$	−17.1350			−0.966982
$315$	−7.91778	+	0.555604i	−0.446117	+	0.0313048i
$316$	−24.9759			−1.40500
$317$			1.17626i			0.0660655i	0.999454	+	0.0330327i	$0.0105166\pi$
$317$			1.17626i			0.0660655i	−0.999454	+	0.0330327i	$0.989483\pi$
$318$	−2.18369	+	1.48264i	−0.122455	+	0.0831421i
$319$	−0.651275			−0.0364644
$320$	−14.4775	+	25.0758i	−0.809316	+	1.40178i
$321$	33.2321	−	2.42575i	1.85483	−	0.135392i
$322$	−32.2080	+	47.1519i	−1.79488	+	2.62767i
$323$		−	4.55930i		−	0.253686i
$324$	11.2687	−	47.6680i	0.626040	−	2.64822i
$325$	−2.89807	−	1.67320i	−0.160756	−	0.0928126i
$326$	43.2200	−	24.9531i	2.39373	−	1.38202i
$327$	28.1150	−	19.0889i	1.55476	−	1.05562i
$328$	−51.3573	+	29.6512i	−2.83573	+	1.63721i
$329$	15.8809	+	1.20406i	0.875542	+	0.0663819i
$330$	−1.20859	−	0.584912i	−0.0665309	−	0.0321983i
$331$	−31.3141			−1.72118			−0.860590	−	0.509298i	$-0.829905\pi$
$331$	−31.3141			−1.72118			−0.860590	+	0.509298i	$0.829905\pi$
$332$	12.4971	−	21.6456i	0.685866	−	1.18795i
$333$	10.0292	−	25.2661i	0.549597	−	1.38457i
$334$	−17.8215	+	10.2893i	−0.975150	+	0.563003i
$335$	0.802881	−	1.39063i	0.0438661	−	0.0759783i
$336$	58.3833	+	33.9266i	3.18507	+	1.85085i
$337$	−12.2086	−	21.1459i	−0.665043	−	1.15189i	−0.979274	−	0.202542i	$-0.935080\pi$
$337$	−12.2086	−	21.1459i	−0.665043	−	1.15189i	0.314230	−	0.949347i	$-0.398254\pi$
$338$	−4.25635	−	2.45740i	−0.231515	−	0.133665i
$339$	−30.2218	+	2.20602i	−1.64142	+	0.119815i
$340$	14.4557	+	25.0379i	0.783969	+	1.35787i
$341$	0.162751	+	0.281893i	0.00881346	+	0.0152654i
$342$	−2.59153	+	6.52872i	−0.140134	+	0.353033i
$343$	−18.0451	−	4.16844i	−0.974341	−	0.225075i
$344$	−3.64316	−	2.10338i	−0.196426	−	0.113406i
$345$	13.6664	−	0.997566i	0.735772	−	0.0537072i
$346$		−	6.73480i		−	0.362065i
$347$			18.0152i			0.967108i	0.875314	+	0.483554i	$0.160654\pi$
$347$			18.0152i			0.967108i	−0.875314	+	0.483554i	$0.839346\pi$
$348$	−12.1361	−	17.8746i	−0.650563	−	0.958179i
$349$	−11.6741	−	6.74005i	−0.624901	−	0.360787i	0.153874	−	0.988091i	$-0.450825\pi$
$349$	−11.6741	−	6.74005i	−0.624901	−	0.360787i	−0.778775	+	0.627304i	$0.784158\pi$
$350$	−6.50577	+	3.12602i	−0.347748	+	0.167093i
$351$	−11.7530	−	12.8151i	−0.627327	−	0.684017i
$352$	3.04279	+	5.27027i	0.162181	+	0.280906i
$353$	1.61937	+	2.80483i	0.0861903	+	0.149286i	0.905898	−	0.423496i	$-0.139197\pi$
$353$	1.61937	+	2.80483i	0.0861903	+	0.149286i	−0.819708	+	0.572782i	$0.805864\pi$
$354$	18.9295	−	39.1137i	1.00609	−	2.07887i
$355$	−7.19168	−	4.15212i	−0.381695	−	0.220372i
$356$	32.5221	+	56.3300i	1.72367	+	2.98548i
$357$	21.1163	−	12.1126i	1.11759	−	0.641065i
$358$	−1.40918	+	2.44078i	−0.0744776	+	0.128999i
$359$	25.9750	−	14.9967i	1.37091	−	0.791494i	0.379865	−	0.925042i	$-0.375970\pi$
$359$	25.9750	−	14.9967i	1.37091	−	0.791494i	0.991042	+	0.133548i	$0.0426371\pi$
$360$	−4.09123	−	27.8750i	−0.215627	−	1.46914i
$361$	−9.13169	+	15.8165i	−0.480615	+	0.832450i
$362$	13.3793			0.703202
$363$	15.6470	−	10.6237i	0.821254	−	0.557597i
$364$	43.4323	−	20.8692i	2.27647	−	1.09384i
$365$	3.55813	−	2.05429i	0.186241	−	0.107526i
$366$	34.2089	+	16.5557i	1.78813	+	0.865382i
$367$	−1.08151	+	0.624408i	−0.0564542	+	0.0325938i	−0.527961	−	0.849268i	$-0.677043\pi$
$367$	−1.08151	+	0.624408i	−0.0564542	+	0.0325938i	0.471507	+	0.881862i	$0.343710\pi$
$368$	−100.956	−	58.2869i	−5.26269	−	3.03841i
$369$	6.98919	−	17.6075i	0.363843	−	0.916611i
$370$		−	24.7199i		−	1.28513i
$371$	1.22037	+	0.833598i	0.0633585	+	0.0432782i
$372$	−4.70394	+	9.71969i	−0.243888	+	0.503942i
$373$	−5.05481	+	8.75519i	−0.261728	+	0.453327i	−0.966701	−	0.255907i	$-0.917626\pi$
$373$	−5.05481	+	8.75519i	−0.261728	+	0.453327i	0.704973	+	0.709234i	$0.250959\pi$
$374$	4.11805			0.212939
$375$	1.55907	+	0.754526i	0.0805099	+	0.0389636i
$376$			56.5318i			2.91540i
$377$	−7.66981			−0.395015
$378$	−37.1225	+	5.34205i	−1.90938	+	0.274765i
$379$	15.8027			0.811729			0.405865	−	0.913933i	$-0.366970\pi$
$379$	15.8027			0.811729			0.405865	+	0.913933i	$0.366970\pi$
$380$			4.67105i			0.239620i
$381$	3.30446	+	1.59923i	0.169293	+	0.0819309i
$382$	−5.15422			−0.263713
$383$	2.95231	−	5.11355i	0.150856	−	0.261290i	−0.780686	−	0.624923i	$-0.785130\pi$
$383$	2.95231	−	5.11355i	0.150856	−	0.261290i	0.931542	+	0.363633i	$0.118464\pi$
$384$	−27.2829	+	56.3743i	−1.39228	+	2.87684i
$385$	−0.0568376	+	0.749657i	−0.00289671	+	0.0382061i
$386$			33.7807i			1.71939i
$387$	1.32959	−	0.195145i	0.0675870	−	0.00991978i
$388$	−20.0889	−	11.5983i	−1.01986	−	0.588816i
$389$	−4.86627	+	2.80954i	−0.246730	+	0.142450i	−0.618266	−	0.785969i	$-0.712165\pi$
$389$	−4.86627	+	2.80954i	−0.246730	+	0.142450i	0.371536	+	0.928419i	$0.378831\pi$
$390$	−14.2331	−	6.88828i	−0.720723	−	0.348801i
$391$	−36.3959	+	21.0132i	−1.84062	+	1.06268i
$392$	9.91136	−	64.9871i	0.500599	−	3.28234i
$393$	−20.2029	+	13.7169i	−1.01910	+	0.691927i
$394$	5.83788			0.294108
$395$	2.29456	−	3.97429i	0.115452	−	0.199968i
$396$	−4.31221	−	1.71170i	−0.216697	−	0.0860163i
$397$	−16.4935	+	9.52254i	−0.827786	+	0.477923i	−0.853094	−	0.521757i	$-0.825277\pi$
$397$	−16.4935	+	9.52254i	−0.827786	+	0.477923i	0.0253078	+	0.999680i	$0.491943\pi$
$398$	−4.11560	+	7.12843i	−0.206297	+	0.357316i
$399$	3.93306	+	0.0110448i	0.196899	+	0.000552933i
$400$	−7.36758	−	12.7610i	−0.368379	−	0.638051i
$401$	−18.9650	−	10.9494i	−0.947067	−	0.546789i	−0.0548981	−	0.998492i	$-0.517483\pi$
$401$	−18.9650	−	10.9494i	−0.947067	−	0.546789i	−0.892168	+	0.451703i	$0.850817\pi$
$402$	3.30532	−	6.82973i	0.164854	−	0.340636i
$403$	1.91665	+	3.31974i	0.0954753	+	0.165368i
$404$	47.4961	+	82.2656i	2.36302	+	4.09287i
$405$	6.54990	+	6.17243i	0.325467	+	0.306710i
$406$	−9.33089	+	13.6603i	−0.463084	+	0.677947i
$407$	−2.22986	−	1.28741i	−0.110530	−	0.0638147i
$408$	48.5376	+	71.4884i	2.40297	+	3.53920i
$409$			36.6522i			1.81234i	0.422918	+	0.906168i	$0.361006\pi$
$409$			36.6522i			1.81234i	−0.422918	+	0.906168i	$0.638994\pi$
$410$		−	17.2269i		−	0.850775i
$411$	9.85708	−	0.719510i	0.486214	−	0.0354908i
$412$	−28.4695	−	16.4369i	−1.40259	−	0.809787i
$413$	−24.2611	−	1.83943i	−1.19381	−	0.0905125i
$414$	64.0614	−	9.40234i	3.14845	−	0.462100i
$415$	2.29623	+	3.97719i	0.112718	+	0.195232i
$416$	35.8338	+	62.0659i	1.75689	+	3.04303i
$417$	−11.2352	+	0.820107i	−0.550191	+	0.0401608i
$418$	0.576194	+	0.332666i	0.0281826	+	0.0162712i
$419$	−6.55229	−	11.3489i	−0.320100	−	0.554430i	0.660408	−	0.750907i	$-0.270383\pi$
$419$	−6.55229	−	11.3489i	−0.320100	−	0.554430i	−0.980508	+	0.196477i	$0.937050\pi$
$420$	−21.6339	+	12.4095i	−1.05563	+	0.605520i
$421$	1.47281	−	2.55098i	0.0717803	−	0.124327i	−0.827901	−	0.560874i	$-0.810465\pi$
$421$	1.47281	−	2.55098i	0.0717803	−	0.124327i	0.899682	+	0.436547i	$0.143799\pi$
$422$	−11.5212	+	6.65176i	−0.560843	+	0.323803i
$423$	−11.2048	−	14.1625i	−0.544798	−	0.688604i
$424$	−2.62294	+	4.54307i	−0.127381	+	0.220631i
$425$	−5.31221			−0.257680
$426$	−35.3201	−	17.0935i	−1.71126	−	0.828184i
$427$	1.60877	−	21.2188i	0.0778538	−	1.02685i
$428$	90.6721	−	52.3496i	4.38280	−	2.53041i
$429$	−1.36262	+	0.925162i	−0.0657880	+	0.0446673i
$430$	1.05831	−	0.611016i	0.0510363	−	0.0294658i
$431$	15.9680	+	9.21911i	0.769150	+	0.444069i	0.832571	−	0.553918i	$-0.186868\pi$
$431$	15.9680	+	9.21911i	0.769150	+	0.444069i	−0.0634211	+	0.997987i	$0.520201\pi$
$432$	−16.6040	−	74.7441i	−0.798861	−	3.59613i
$433$			5.22327i			0.251014i	0.992093	+	0.125507i	$0.0400558\pi$
$433$			5.22327i			0.251014i	−0.992093	+	0.125507i	$0.959944\pi$
$434$	8.24435	+	0.625071i	0.395742	+	0.0300044i
$435$	3.95925	−	0.289002i	0.189831	−	0.0138566i
$436$	53.3903	−	92.4748i	2.55693	−	4.42874i
$437$	−6.78998			−0.324809
$438$	16.0615	−	10.9051i	0.767449	−	0.521066i
$439$		−	15.6324i		−	0.746095i	−0.927812	−	0.373048i	$-0.878313\pi$
$439$		−	15.6324i		−	0.746095i	0.927812	−	0.373048i	$-0.121687\pi$
$440$	−2.66858			−0.127220
$441$	10.3977	+	18.2452i	0.495128	+	0.868820i
$442$	48.4966			2.30675
$443$			6.13137i			0.291310i	0.989335	+	0.145655i	$0.0465290\pi$
$443$			6.13137i			0.291310i	−0.989335	+	0.145655i	$0.953471\pi$
$444$	−6.21839	−	85.1900i	−0.295112	−	4.04294i
$445$	−11.9513			−0.566548
$446$	−5.12018	+	8.86842i	−0.242448	+	0.419932i
$447$	−9.54626	−	14.0602i	−0.451523	−	0.665023i
$448$	76.3884	+	5.79162i	3.60901	+	0.273628i
$449$			40.6165i			1.91681i	0.285407	+	0.958407i	$0.407871\pi$
$449$			40.6165i			1.91681i	−0.285407	+	0.958407i	$0.592129\pi$
$450$	7.60687	+	3.01950i	0.358591	+	0.142340i
$451$	−1.55396	−	0.897177i	−0.0731729	−	0.0422464i
$452$	−82.4588	+	47.6076i	−3.87854	+	2.23927i
$453$	1.22619	+	16.7984i	0.0576114	+	0.789259i
$454$	20.2532	−	11.6932i	0.950528	−	0.548787i
$455$	−0.669354	+	8.82842i	−0.0313798	+	0.413883i
$456$	1.01634	+	13.9236i	0.0475946	+	0.652031i
$457$	21.9279			1.02574			0.512872	−	0.858465i	$-0.328582\pi$
$457$	21.9279			1.02574			0.512872	+	0.858465i	$0.328582\pi$
$458$	1.95296	−	3.38263i	0.0912560	−	0.158060i
$459$	−26.3291	−	8.28911i	−1.22894	−	0.386902i
$460$	37.2880	−	21.5282i	1.73856	−	1.00376i
$461$	14.8897	−	25.7897i	0.693483	−	1.20115i	−0.277206	−	0.960810i	$-0.589409\pi$
$461$	14.8897	−	25.7897i	0.693483	−	1.20115i	0.970689	−	0.240338i	$-0.0772581\pi$
$462$	−0.00997591	+	3.55241i	−0.000464121	+	0.165273i
$463$	1.64857	+	2.85540i	0.0766153	+	0.132702i	0.901788	−	0.432180i	$-0.142255\pi$
$463$	1.64857	+	2.85540i	0.0766153	+	0.132702i	−0.825172	+	0.564881i	$0.808922\pi$
$464$	−29.2477	−	16.8861i	−1.35779	−	0.783920i
$465$	−1.11449	−	1.64147i	−0.0516832	−	0.0761213i
$466$	3.79330	+	6.57018i	0.175721	+	0.304358i
$467$	16.5766	+	28.7116i	0.767075	+	1.32861i	0.939142	+	0.343528i	$0.111622\pi$
$467$	16.5766	+	28.7116i	0.767075	+	1.32861i	−0.172067	+	0.985085i	$0.555045\pi$
$468$	−50.7832	−	20.1581i	−2.34745	−	0.931807i
$469$	−4.23629	−	0.321187i	−0.195614	−	0.0148310i
$470$	−14.2219	−	8.21103i	−0.656009	−	0.378747i
$471$	4.73915	−	9.79243i	0.218368	−	0.451212i
$472$		−	86.3632i		−	3.97519i
$473$		−	0.127287i		−	0.00585266i
$474$	9.44627	−	19.5187i	0.433882	−	0.896523i
$475$	−0.743281	−	0.429133i	−0.0341041	−	0.0196900i
$476$	43.1448	−	63.1632i	1.97754	−	2.89508i
$477$	−0.243349	−	1.65802i	−0.0111422	−	0.0759155i
$478$	−9.75990	−	16.9046i	−0.446407	−	0.773200i
$479$	−11.1312	−	19.2799i	−0.508599	−	0.880919i	−0.999950	−	0.00995768i	$-0.996830\pi$
$479$	−11.1312	−	19.2799i	−0.508599	−	0.880919i	0.491352	−	0.870961i	$-0.336503\pi$
$480$	−20.8365	−	30.6889i	−0.951051	−	1.40075i
$481$	−26.2602	−	15.1614i	−1.19736	−	0.691298i
$482$	36.4899	+	63.2023i	1.66207	+	2.87879i
$483$	−18.0388	−	31.4477i	−0.820792	−	1.43092i
$484$	29.7136	−	51.4655i	1.35062	−	2.33934i
$485$	3.69117	−	2.13110i	0.167607	−	0.0967681i
$486$	32.9906	+	26.8353i	1.49648	+	1.21727i
$487$	−3.44182	+	5.96141i	−0.155964	+	0.270137i	−0.933410	−	0.358813i	$-0.883182\pi$
$487$	−3.44182	+	5.96141i	−0.155964	+	0.270137i	0.777446	+	0.628950i	$0.216515\pi$
$488$	75.5333			3.41923
$489$	2.30671	+	31.6012i	0.104313	+	1.42906i
$490$	14.9095	+	11.9326i	0.673541	+	0.539059i
$491$	−10.3634	+	5.98332i	−0.467694	+	0.270023i	−0.715274	−	0.698844i	$-0.753698\pi$
$491$	−10.3634	+	5.98332i	−0.467694	+	0.270023i	0.247580	+	0.968868i	$0.420365\pi$
$492$	−4.33349	−	59.3675i	−0.195369	−	2.67649i
$493$	−10.5442	+	6.08767i	−0.474885	+	0.274175i
$494$	6.78561	+	3.91767i	0.305299	+	0.176264i
$495$	0.668540	−	0.528924i	0.0300487	−	0.0237734i
$496$			16.8791i			0.757895i
$497$	−1.66103	+	21.9081i	−0.0745072	+	0.982711i
$498$	12.1894	+	17.9532i	0.546222	+	0.804500i
$499$	10.6028	−	18.3645i	0.474645	−	0.822110i	−0.524933	−	0.851144i	$-0.675910\pi$
$499$	10.6028	−	18.3645i	0.474645	−	0.822110i	0.999578	+	0.0290335i	$0.00924296\pi$
$500$	5.44243			0.243393
$501$	−0.951158	−	13.0306i	−0.0424946	−	0.582163i
$502$			26.2115i			1.16988i
$503$	10.5680			0.471203			0.235601	−	0.971850i	$-0.424294\pi$
$503$	10.5680			0.471203			0.235601	+	0.971850i	$0.424294\pi$
$504$	−61.7867	+	41.6976i	−2.75220	+	1.85736i
$505$	−17.4540			−0.776693
$506$		−	6.13284i		−	0.272638i
$507$	2.58159	−	1.75279i	0.114652	−	0.0778442i
$508$	11.5353			0.511796
$509$	10.7774	−	18.6671i	0.477702	−	0.827403i	−0.521972	−	0.852963i	$-0.674803\pi$
$509$	10.7774	−	18.6671i	0.477702	−	0.827403i	0.999673	+	0.0255594i	$0.00813670\pi$
$510$	−25.0345	+	1.82738i	−1.10855	+	0.0809177i
$511$	−8.97609	−	6.13129i	−0.397079	−	0.271232i
$512$			38.8098i			1.71517i
$513$	−3.01433	−	3.28673i	−0.133086	−	0.145113i
$514$	23.5375	+	13.5894i	1.03819	+	0.599401i
$515$	5.23103	−	3.02014i	0.230507	−	0.133083i
$516$	3.49346	−	2.37191i	0.153791	−	0.104418i
$517$	−1.48136	+	0.855262i	−0.0651500	+	0.0376144i
$518$	−58.9506	+	28.3257i	−2.59014	+	1.24456i
$519$	3.84886	+	1.86270i	0.168946	+	0.0817633i
$520$	−31.4268			−1.37816
$521$	17.9132	−	31.0265i	0.784791	−	1.35930i	−0.144333	−	0.989529i	$-0.546104\pi$
$521$	17.9132	−	31.0265i	0.784791	−	1.35930i	0.929124	−	0.369768i	$-0.120563\pi$
$522$	18.5591	−	2.72393i	0.812309	−	0.119223i
$523$	5.63357	−	3.25254i	0.246339	−	0.142224i	−0.371748	−	0.928334i	$-0.621241\pi$
$523$	5.63357	−	3.25254i	0.246339	−	0.142224i	0.618087	+	0.786110i	$0.287908\pi$
$524$	−38.3653	+	66.4506i	−1.67599	+	2.90291i
$525$	0.0128688	−	4.58256i	0.000561639	−	0.199999i
$526$	18.7230	+	32.4291i	0.816359	+	1.41398i
$527$	5.26989	+	3.04257i	0.229560	+	0.132536i
$528$	−7.23302	+	0.527969i	−0.314777	+	0.0229769i
$529$	19.7941	+	34.2844i	0.860612	+	1.49062i
$530$	−0.761945	−	1.31973i	−0.0330968	−	0.0573253i
$531$	17.1176	+	21.6360i	0.742838	+	0.938920i
$532$	11.1393	−	5.35240i	0.482948	−	0.232056i
$533$	−18.3003	−	10.5657i	−0.792675	−	0.457651i
$534$	−56.3223	+	4.11121i	−2.43730	+	0.177909i
$535$			19.2376i			0.831714i
$536$		−	15.0801i		−	0.651360i
$537$	−1.00513	−	1.48040i	−0.0433744	−	0.0638838i
$538$	−20.2823	−	11.7100i	−0.874430	−	0.504853i
$539$	1.85287	−	0.723464i	0.0798086	−	0.0311618i
$540$	26.9745	+	8.49229i	1.16080	+	0.365450i
$541$	−17.8864	−	30.9801i	−0.768994	−	1.33194i	−0.938109	−	0.346341i	$-0.887424\pi$
$541$	−17.8864	−	30.9801i	−0.768994	−	1.33194i	0.169114	−	0.985596i	$-0.445909\pi$
$542$	40.6162	+	70.3493i	1.74461	+	3.02176i
$543$	−3.70043	+	7.64614i	−0.158801	+	0.328127i
$544$	98.5258	+	56.8839i	4.22426	+	2.43888i
$545$	9.81002	+	16.9915i	0.420215	+	0.727834i
$546$	−0.117482	+	41.8354i	−0.00502778	+	1.79039i
$547$	5.55863	−	9.62783i	0.237670	−	0.411656i	−0.722375	−	0.691501i	$-0.756950\pi$
$547$	5.55863	−	9.62783i	0.237670	−	0.411656i	0.960045	+	0.279845i	$0.0902831\pi$
$548$	26.8946	−	15.5276i	1.14888	−	0.663306i
$549$	−18.9228	+	14.9710i	−0.807606	+	0.638948i
$550$	0.387602	−	0.671346i	0.0165274	−	0.0286263i
$551$	−1.96711			−0.0838016
$552$	106.465	−	72.2851i	4.53144	−	3.07666i
$553$	−12.1069	−	0.917922i	−0.514838	−	0.0390340i
$554$	−46.9066	+	27.0816i	−1.99287	+	1.15058i
$555$	14.1271	+	6.83697i	0.599664	+	0.290213i
$556$	−30.6548	+	17.6985i	−1.30005	+	0.750586i
$557$	26.1440	+	15.0942i	1.10776	+	0.639564i	0.938247	−	0.345965i	$-0.112448\pi$
$557$	26.1440	+	15.0942i	1.10776	+	0.639564i	0.169509	+	0.985529i	$0.445782\pi$
$558$	−5.81684	−	7.35227i	−0.246247	−	0.311247i
$559$		−	1.49901i		−	0.0634013i
$560$	−21.9895	+	32.1922i	−0.929225	+	1.36037i
$561$	−1.13896	+	2.35342i	−0.0480869	+	0.0993613i
$562$	−13.4521	+	23.2997i	−0.567441	+	0.982837i
$563$	−21.6988			−0.914497			−0.457248	−	0.889339i	$-0.651165\pi$
$563$	−21.6988			−0.914497			−0.457248	+	0.889339i	$0.651165\pi$
$564$	−51.0773	−	24.7194i	−2.15074	−	1.04087i
$565$		−	17.4950i		−	0.736020i
$566$	−28.7954			−1.21036
$567$	7.21434	−	22.6926i	0.302974	−	0.952999i
$568$	−77.9869			−3.27226
$569$			21.6412i			0.907247i	0.891193	+	0.453624i	$0.149869\pi$
$569$			21.6412i			0.907247i	−0.891193	+	0.453624i	$0.850131\pi$
$570$	−3.65043	−	1.76666i	−0.152900	−	0.0739974i
$571$	−17.4113			−0.728640			−0.364320	−	0.931274i	$-0.618699\pi$
$571$	−17.4113			−0.728640			−0.364320	+	0.931274i	$0.618699\pi$
$572$	−2.58762	+	4.48188i	−0.108194	+	0.187397i
$573$	1.42554	−	2.94558i	0.0595529	−	0.123053i
$574$	−41.0817	+	19.7397i	−1.71472	+	0.823919i
$575$			7.91127i			0.329923i
$576$	−53.8962	−	68.1228i	−2.24568	−	2.83845i
$577$	31.1294	+	17.9726i	1.29593	+	0.748207i	0.979699	−	0.200474i	$-0.0642482\pi$
$577$	31.1294	+	17.9726i	1.29593	+	0.748207i	0.316234	+	0.948681i	$0.397582\pi$
$578$	26.5073	−	15.3040i	1.10256	−	0.636563i
$579$	−19.3053	−	9.34299i	−0.802300	−	0.388281i
$580$	10.8026	−	6.23689i	0.448554	−	0.258973i
$581$	6.85339	−	10.0332i	0.284327	−	0.416249i
$582$	16.6620	−	11.3128i	0.690664	−	0.468932i
$583$	−0.158728			−0.00657386
$584$	19.2923	−	33.4152i	0.798320	−	1.38273i
$585$	7.87314	−	6.22893i	0.325514	−	0.257535i
$586$	−20.3840	+	11.7687i	−0.842055	+	0.486161i
$587$	−21.2857	+	36.8680i	−0.878556	+	1.52170i	−0.0256305	+	0.999671i	$0.508159\pi$
$587$	−21.2857	+	36.8680i	−0.878556	+	1.52170i	−0.852926	+	0.522032i	$0.825174\pi$
$588$	54.3829	+	37.3717i	2.24271	+	1.54118i
$589$	0.491572	+	0.851428i	0.0202549	+	0.0350825i
$590$	21.7267	+	12.5439i	0.894476	+	0.516426i
$591$	−1.61463	+	3.33628i	−0.0664170	+	0.137236i
$592$	−66.7597	−	115.631i	−2.74381	−	4.75241i
$593$	12.0906	+	20.9416i	0.496503	+	0.859968i	0.999992	−	0.00403339i	$-0.00128387\pi$
$593$	12.0906	+	20.9416i	0.496503	+	0.859968i	−0.503489	+	0.864002i	$0.667951\pi$
$594$	2.96864	−	2.72260i	0.121805	−	0.111710i
$595$	6.08708	+	12.6683i	0.249546	+	0.519348i
$596$	−46.2462	−	26.7002i	−1.89432	−	1.09368i
$597$	−2.93553	−	4.32359i	−0.120143	−	0.176953i
$598$		−	72.2241i		−	2.95346i
$599$			20.1681i			0.824045i	0.911174	+	0.412023i	$0.135178\pi$
$599$			20.1681i			0.824045i	−0.911174	+	0.412023i	$0.864822\pi$
$600$	16.2229	−	1.18418i	0.662297	−	0.0483439i
$601$	−5.59991	−	3.23311i	−0.228425	−	0.131881i	0.381420	−	0.924402i	$-0.375435\pi$
$601$	−5.59991	−	3.23311i	−0.228425	−	0.131881i	−0.609845	+	0.792520i	$0.708768\pi$
$602$	−2.66980	−	1.82365i	−0.108813	−	0.0743266i
$603$	2.98893	+	3.77790i	0.121719	+	0.153848i
$604$	26.4621	+	45.8337i	1.07673	+	1.86495i
$605$	5.45963	+	9.45635i	0.221965	+	0.384455i
$606$	−82.2544	+	6.00410i	−3.34136	+	0.243900i
$607$	26.7099	+	15.4210i	1.08412	+	0.625918i	0.932005	−	0.362445i	$-0.118058\pi$
$607$	26.7099	+	15.4210i	1.08412	+	0.625918i	0.152116	+	0.988363i	$0.451391\pi$
$608$	9.19043	+	15.9183i	0.372721	+	0.645572i
$609$	−5.22596	−	9.11062i	−0.211767	−	0.369181i
$610$	−10.9709	+	19.0022i	−0.444201	+	0.769378i
$611$	−17.4454	+	10.0721i	−0.705764	+	0.407473i
$612$	−85.8146	+	12.5951i	−3.46885	+	0.509125i
$613$	−19.4865	+	33.7516i	−0.787052	+	1.36321i	0.140713	+	0.990050i	$0.455061\pi$
$613$	−19.4865	+	33.7516i	−0.787052	+	1.36321i	−0.927765	+	0.373164i	$0.878273\pi$
$614$	31.6223			1.27617
$615$	9.84497	+	4.76457i	0.396987	+	0.192126i
$616$	3.05784	+	6.36388i	0.123204	+	0.256408i
$617$	−6.83491	+	3.94614i	−0.275163	+	0.158866i	−0.631232	−	0.775594i	$-0.717450\pi$
$617$	−6.83491	+	3.94614i	−0.275163	+	0.158866i	0.356068	+	0.934460i	$0.384117\pi$
$618$	23.6130	−	16.0323i	0.949856	−	0.644912i
$619$	26.6228	−	15.3707i	1.07006	−	0.617799i	0.141862	−	0.989886i	$-0.454691\pi$
$619$	26.6228	−	15.3707i	1.07006	−	0.617799i	0.928198	+	0.372087i	$0.121358\pi$
$620$	−5.39906	−	3.11715i	−0.216832	−	0.125188i
$621$	−12.3446	+	39.2108i	−0.495373	+	1.57348i
$622$		−	13.5637i		−	0.543853i
$623$	13.6946	+	28.5008i	0.548664	+	1.14186i
$624$	−85.1805	+	6.21769i	−3.40995	+	0.248907i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	53.4223			2.13518
$627$	−0.349477	+	0.237280i	−0.0139568	+	0.00947606i
$628$		−	34.1837i		−	1.36408i
$629$	−48.1354			−1.91929
$630$	−1.51573	−	21.6004i	−0.0603883	−	0.860579i
$631$	23.5241			0.936478			0.468239	−	0.883602i	$-0.344889\pi$
$631$	23.5241			0.936478			0.468239	+	0.883602i	$0.344889\pi$
$632$		−	43.0974i		−	1.71432i
$633$	−0.614901	−	8.42396i	−0.0244401	−	0.334822i
$634$	−3.20894			−0.127443
$635$	−1.05976	+	1.83555i	−0.0420551	+	0.0728416i
$636$	−2.95781	−	4.35639i	−0.117285	−	0.172742i
$637$	21.8205	−	8.51995i	0.864559	−	0.337573i
$638$		−	1.77673i		−	0.0703414i
$639$	19.5375	−	15.4573i	0.772892	−	0.611483i
$640$	−31.3146	−	18.0795i	−1.23782	−	0.714656i
$641$	26.6157	−	15.3666i	1.05126	−	0.606943i	0.128255	−	0.991741i	$-0.459062\pi$
$641$	26.6157	−	15.3666i	1.05126	−	0.606943i	0.923001	+	0.384798i	$0.125729\pi$
$642$	6.61765	+	90.6598i	0.261178	+	3.57806i
$643$	17.2128	−	9.93780i	0.678806	−	0.391909i	−0.120599	−	0.992701i	$-0.538482\pi$
$643$	17.2128	−	9.93780i	0.678806	−	0.391909i	0.799405	+	0.600793i	$0.205148\pi$
$644$	−94.0664	−	64.2538i	−3.70673	−	2.53195i
$645$	0.0564834	+	0.773806i	0.00222403	+	0.0304686i
$646$	12.4381			0.489372
$647$	11.7226	−	20.3041i	0.460861	−	0.798235i	−0.538143	−	0.842854i	$-0.680874\pi$
$647$	11.7226	−	20.3041i	0.460861	−	0.798235i	0.999004	+	0.0446187i	$0.0142073\pi$
$648$	82.2538	+	19.4448i	3.23124	+	0.763865i
$649$	2.26306	−	1.30658i	0.0888328	−	0.0512876i
$650$	4.56463	−	7.90618i	0.179040	−	0.310106i
$651$	−2.63743	+	4.53867i	−0.103369	+	0.177885i
$652$	49.7805	+	86.2224i	1.94956	+	3.37673i
$653$	−13.9889	−	8.07647i	−0.547426	−	0.316057i	0.200657	−	0.979662i	$-0.435692\pi$
$653$	−13.9889	−	8.07647i	−0.547426	−	0.316057i	−0.748083	+	0.663605i	$0.769026\pi$
$654$	52.0761	+	76.7000i	2.03634	+	2.99921i
$655$	−7.04929	−	12.2097i	−0.275439	−	0.477074i
$656$	−46.5237	−	80.5814i	−1.81645	−	3.14618i
$657$	1.78988	+	12.1951i	0.0698299	+	0.475775i
$658$	−3.28477	+	43.3244i	−0.128054	+	1.68896i
$659$	−4.06154	−	2.34493i	−0.158215	−	0.0913455i	0.418802	−	0.908078i	$-0.362450\pi$
$659$	−4.06154	−	2.34493i	−0.158215	−	0.0913455i	−0.577017	+	0.816732i	$0.695783\pi$
$660$	1.16688	−	2.41110i	0.0454207	−	0.0938521i
$661$			18.9083i			0.735448i	0.929935	+	0.367724i	$0.119863\pi$
$661$			18.9083i			0.735448i	−0.929935	+	0.367724i	$0.880137\pi$
$662$		−	85.4275i		−	3.32023i
$663$	−13.4131	+	27.7153i	−0.520921	+	1.07637i
$664$	37.3506	+	21.5644i	1.44949	+	0.836861i
$665$	−0.171672	+	2.26426i	−0.00665715	+	0.0878043i
$666$	68.9280	+	27.3605i	2.67090	+	1.06020i
$667$	9.06613	+	15.7030i	0.351042	+	0.608022i
$668$	−20.5267	−	35.5533i	−0.794203	−	1.37560i
$669$	−3.65207	−	5.37893i	−0.141197	−	0.207962i
$670$	3.79375	+	2.19032i	0.146565	+	0.0846196i
$671$	1.14273	+	1.97927i	0.0441148	+	0.0764090i
$672$	−49.3093	+	84.8550i	−1.90215	+	3.27335i
$673$	13.1728	−	22.8160i	0.507775	−	0.879492i	−0.492185	−	0.870491i	$-0.663802\pi$
$673$	13.1728	−	22.8160i	0.507775	−	0.879492i	0.999959	−	0.00900082i	$-0.00286509\pi$
$674$	57.6876	−	33.3060i	2.22204	−	1.28290i
$675$	−3.82950	+	3.51211i	−0.147397	+	0.135181i
$676$	4.90243	−	8.49126i	0.188555	−	0.326587i
$677$	−44.1773			−1.69787			−0.848936	−	0.528496i	$-0.822756\pi$
$677$	−44.1773			−1.69787			−0.848936	+	0.528496i	$0.822756\pi$
$678$	−6.01820	−	82.4475i	−0.231128	−	3.16638i
$679$	−9.31169	−	6.36053i	−0.357350	−	0.244095i
$680$	−43.2044	+	24.9441i	−1.65681	+	0.956562i
$681$	1.08094	+	14.8085i	0.0414216	+	0.567463i
$682$	−0.769027	+	0.443998i	−0.0294476	+	0.0170016i
$683$	−10.2520	−	5.91898i	−0.392281	−	0.226484i	0.290867	−	0.956764i	$-0.406056\pi$
$683$	−10.2520	−	5.91898i	−0.392281	−	0.226484i	−0.683148	+	0.730280i	$0.739390\pi$
$684$	−13.0246	−	5.17002i	−0.498007	−	0.197681i
$685$			5.70613i			0.218020i
$686$	11.3719	−	49.2284i	0.434179	−	1.87955i
$687$	1.39299	+	2.05166i	0.0531458	+	0.0782756i
$688$	3.30027	−	5.71624i	0.125822	−	0.217930i
$689$	−1.86928			−0.0712140
$690$	2.72144	+	37.2829i	0.103604	+	1.41934i
$691$			40.4090i			1.53723i	0.639710	+	0.768616i	$0.279054\pi$
$691$			40.4090i			1.53723i	−0.639710	+	0.768616i	$0.720946\pi$
$692$	13.4357			0.510749
$693$	−2.02740	−	0.988220i	−0.0770147	−	0.0375394i
$694$	−49.1470			−1.86560
$695$		−	6.50392i		−	0.246708i
$696$	30.8436	−	20.9415i	1.16913	−	0.793787i
$697$	−33.5448			−1.27060
$698$	18.3874	−	31.8479i	0.695974	−	1.20546i
$699$	−4.80393	+	0.350659i	−0.181701	+	0.0132632i
$700$	−6.23629	−	12.9788i	−0.235710	−	0.490552i
$701$		−	30.0434i		−	1.13472i	−0.823468	−	0.567362i	$-0.807964\pi$
$701$		−	30.0434i		−	1.13472i	0.823468	−	0.567362i	$-0.192036\pi$
$702$	34.9605	−	32.0630i	1.31950	−	1.21014i
$703$	−6.73507	−	3.88850i	−0.254018	−	0.146657i
$704$	−7.12545	+	4.11388i	−0.268551	+	0.155048i
$705$	8.62598	−	5.85668i	0.324873	−	0.220575i
$706$	−7.65180	+	4.41777i	−0.287979	+	0.166265i
$707$	19.9999	+	41.6233i	0.752175	+	1.56540i
$708$	78.0304	+	37.7636i	2.93256	+	1.41924i
$709$	1.80261			0.0676985			0.0338492	−	0.999427i	$-0.489223\pi$
$709$	1.80261			0.0676985			0.0338492	+	0.999427i	$0.489223\pi$
$710$	11.3273	−	19.6195i	0.425107	−	0.736306i
$711$	8.54208	+	10.7969i	0.320353	+	0.404914i
$712$	−97.2006	+	56.1188i	−3.64275	+	2.10314i
$713$	4.53118	−	7.84823i	0.169694	−	0.293919i
$714$	33.0440	+	57.6070i	1.23664	+	2.15589i
$715$	−0.475453	−	0.823508i	−0.0177809	−	0.0307974i
$716$	−4.86926	−	2.81127i	−0.181973	−	0.105062i
$717$	12.3602	−	0.902223i	0.461599	−	0.0336941i
$718$	40.9121	+	70.8619i	1.52683	+	2.64454i
$719$	−13.5692	−	23.5026i	−0.506047	−	0.876499i	−0.999976	−	0.00699644i	$-0.997773\pi$
$719$	−13.5692	−	23.5026i	−0.506047	−	0.876499i	0.493929	−	0.869502i	$-0.335560\pi$
$720$	43.7369	−	6.41929i	1.62998	−	0.239233i
$721$	−13.1963	−	9.01398i	−0.491456	−	0.335698i
$722$	−43.1488	−	24.9120i	−1.60583	−	0.927128i
$723$	−46.2117	+	3.37319i	−1.71863	+	0.125450i
$724$			26.6913i			0.991975i
$725$			2.29195i			0.0851210i
$726$	28.9822	+	42.6863i	1.07563	+	1.58424i
$727$	−9.18421	−	5.30251i	−0.340624	−	0.196659i	0.319924	−	0.947443i	$-0.396343\pi$
$727$	−9.18421	−	5.30251i	−0.340624	−	0.196659i	−0.660548	+	0.750784i	$0.729676\pi$
$728$	36.0109	+	74.9449i	1.33465	+	2.77764i
$729$	−24.4605	+	11.4317i	−0.905945	+	0.423396i
$730$	5.60427	+	9.70687i	0.207423	+	0.359268i
$731$	−1.18979	−	2.06078i	−0.0440060	−	0.0762206i
$732$	−33.0281	+	68.2455i	−1.22075	+	2.52243i
$733$	38.4369	+	22.1915i	1.41970	+	0.819663i	0.996272	−	0.0862671i	$-0.0274938\pi$
$733$	38.4369	+	22.1915i	1.41970	+	0.819663i	0.423427	+	0.905930i	$0.360827\pi$
$734$	−1.70344	−	2.95044i	−0.0628750	−	0.108903i
$735$	−10.9430	+	5.22031i	−0.403637	+	0.192554i
$736$	84.7149	−	146.730i	3.12263	−	5.40856i
$737$	0.395158	−	0.228144i	0.0145558	−	0.00840380i
$738$	48.0348	+	19.0671i	1.76818	+	0.701869i
$739$	21.2312	−	36.7736i	0.781004	−	1.35274i	−0.150354	−	0.988632i	$-0.548041\pi$
$739$	21.2312	−	36.7736i	0.781004	−	1.35274i	0.931358	−	0.364106i	$-0.118625\pi$
$740$	49.3153			1.81287
$741$	−4.11565	+	2.79436i	−0.151192	+	0.102653i
$742$	−2.27412	+	3.32927i	−0.0834856	+	0.122221i
$743$	−8.84967	+	5.10936i	−0.324663	+	0.187444i	−0.653469	−	0.756953i	$-0.726687\pi$
$743$	−8.84967	+	5.10936i	−0.324663	+	0.187444i	0.328806	+	0.944397i	$0.393354\pi$
$744$	−16.7719	−	8.11692i	−0.614887	−	0.297581i
$745$	8.49734	−	4.90594i	0.311319	−	0.179740i
$746$	−23.8849	−	13.7899i	−0.874488	−	0.504886i
$747$	−13.6313	+	2.00068i	−0.498745	+	0.0732011i
$748$			8.21536i			0.300383i
$749$	45.8767	−	22.0437i	1.67630	−	0.805459i
$750$	−2.05841	+	4.25326i	−0.0751625	+	0.155307i
$751$	−14.9923	+	25.9674i	−0.547076	+	0.947564i	0.451397	+	0.892323i	$0.350926\pi$
$751$	−14.9923	+	25.9674i	−0.547076	+	0.947564i	−0.998473	+	0.0552407i	$0.982407\pi$
$752$	−88.7003			−3.23457
$753$	−14.9796	−	7.24951i	−0.545886	−	0.264187i
$754$		−	20.9239i		−	0.762002i
$755$	−9.72438			−0.353907
$756$	−10.6572	−	74.0581i	−0.387598	−	2.69347i
$757$	−39.0362			−1.41879			−0.709397	−	0.704809i	$-0.751033\pi$
$757$	−39.0362			−1.41879			−0.709397	+	0.704809i	$0.751033\pi$
$758$			43.1110i			1.56586i
$759$	3.50485	+	1.69621i	0.127218	+	0.0615684i
$760$	−8.06017			−0.292373
$761$	4.83864	−	8.38078i	0.175401	−	0.303803i	−0.764899	−	0.644150i	$-0.777211\pi$
$761$	4.83864	−	8.38078i	0.175401	−	0.303803i	0.940300	+	0.340347i	$0.110545\pi$
$762$	−4.36282	+	9.01484i	−0.158048	+	0.326573i
$763$	29.2793	−	42.8643i	1.05998	−	1.55179i
$764$		−	10.2825i		−	0.372008i
$765$	5.87967	−	14.8124i	0.212580	−	0.535542i
$766$	13.9502	+	8.05414i	0.504040	+	0.291008i
$767$	26.6512	−	15.3871i	0.962318	−	0.555594i
$768$	−63.5083	−	30.7355i	−2.29166	−	1.10907i
$769$	−4.16188	+	2.40286i	−0.150081	+	0.0866494i	−0.573160	−	0.819443i	$-0.694283\pi$
$769$	−4.16188	+	2.40286i	−0.150081	+	0.0866494i	0.423079	+	0.906093i	$0.360949\pi$
$770$	−2.04513	−	0.155057i	−0.0737012	−	0.00558788i
$771$	−14.2761	+	9.69288i	−0.514142	+	0.349081i
$772$	−67.3913			−2.42547
$773$	7.44040	−	12.8872i	0.267613	−	0.463519i	−0.700632	−	0.713523i	$-0.747099\pi$
$773$	7.44040	−	12.8872i	0.267613	−	0.463519i	0.968245	+	0.250004i	$0.0804319\pi$
$774$	0.532372	+	3.62723i	0.0191357	+	0.130378i
$775$	0.992032	−	0.572750i	0.0356348	−	0.0205738i
$776$	20.0136	−	34.6645i	0.718446	−	1.24438i
$777$	0.116607	−	41.5238i	0.00418327	−	1.48966i
$778$	−7.66467	−	13.2756i	−0.274792	−	0.475953i
$779$	−4.69356	−	2.70983i	−0.168164	−	0.0970897i
$780$	13.7419	−	28.3946i	0.492038	−	1.01669i
$781$	−1.17985	−	2.04357i	−0.0422185	−	0.0731246i
$782$	−57.3256	−	99.2909i	−2.04996	−	3.55064i
$783$	−3.57633	+	11.3597i	−0.127808	+	0.405962i
$784$	101.967	+	15.5513i	3.64168	+	0.555403i
$785$	5.43947	+	3.14048i	0.194143	+	0.112088i
$786$	−37.4208	−	55.1151i	−1.33476	−	1.96589i
$787$		−	47.2423i		−	1.68400i	−0.539474	−	0.842002i	$-0.681377\pi$
$787$		−	47.2423i		−	1.68400i	0.539474	−	0.842002i	$-0.318623\pi$
$788$			11.6464i			0.414885i
$789$	−23.7112	+	1.73078i	−0.844141	+	0.0616175i
$790$	10.8422	+	6.25974i	0.385748	+	0.222711i
$791$	−41.7210	+	20.0469i	−1.48343	+	0.712786i
$792$	2.95364	−	7.44096i	0.104953	−	0.264403i
$793$	13.4575	+	23.3091i	0.477891	+	0.827731i
$794$	−25.9783	−	44.9957i	−0.921934	−	1.59684i
$795$	0.964946	−	0.0704356i	0.0342231	−	0.00249809i
$796$	−14.2210	−	8.21049i	−0.504049	−	0.291013i
$797$	1.11087	+	1.92408i	0.0393489	+	0.0681543i	0.885029	−	0.465536i	$-0.154138\pi$
$797$	1.11087	+	1.92408i	0.0393489	+	0.0681543i	−0.845680	+	0.533690i	$0.820805\pi$
$798$	−0.0301312	+	10.7297i	−0.00106663	+	0.379827i
$799$	−15.9888	+	27.6934i	−0.565643	+	0.979723i
$800$	18.5470	−	10.7081i	0.655736	−	0.378590i
$801$	13.2280	−	33.3246i	0.467388	−	1.17747i
$802$	29.8710	−	51.7380i	1.05478	−	1.82693i
$803$	1.16748			0.0411995
$804$	13.6251	+	6.59399i	0.480519	+	0.232552i
$805$	18.8663	−	9.06525i	0.664951	−	0.319508i
$806$	−9.05653	+	5.22879i	−0.319003	+	0.184176i
$807$	12.3017	−	8.35236i	0.433042	−	0.294017i
$808$	−141.954	+	81.9572i	−4.99392	+	2.88324i
$809$	−33.7187	−	19.4675i	−1.18549	−	0.684442i	−0.228210	−	0.973612i	$-0.573287\pi$
$809$	−33.7187	−	19.4675i	−1.18549	−	0.684442i	−0.957278	+	0.289170i	$0.906621\pi$
$810$	−16.8389	+	17.8686i	−0.591658	+	0.627840i
$811$		−	36.6692i		−	1.28763i	−0.765181	−	0.643815i	$-0.777351\pi$
$811$		−	36.6692i		−	1.28763i	0.765181	−	0.643815i	$-0.222649\pi$
$812$	−27.2517	−	18.6148i	−0.956348	−	0.653252i
$813$	−51.4373	+	3.75463i	−1.80399	+	0.131681i
$814$	3.51217	−	6.08325i	0.123101	−	0.213218i
$815$	−18.2935			−0.640793
$816$	−112.168	+	76.1572i	−3.92666	+	2.66604i
$817$		−	0.384457i		−	0.0134504i
$818$	−99.9902			−3.49608
$819$	−23.8760	−	11.6379i	−0.834293	−	0.406660i
$820$	34.3670			1.20015
$821$			4.97972i			0.173793i	0.996217	+	0.0868966i	$0.0276950\pi$
$821$			4.97972i			0.173793i	−0.996217	+	0.0868966i	$0.972305\pi$
$822$	1.96288	+	26.8909i	0.0684634	+	0.937928i
$823$	47.2586			1.64733			0.823666	−	0.567075i	$-0.191925\pi$
$823$	47.2586			1.64733			0.823666	+	0.567075i	$0.191925\pi$
$824$	28.3628	−	49.1258i	0.988064	−	1.71138i
$825$	0.276464	+	0.407189i	0.00962526	+	0.0141765i
$826$	5.01812	−	66.1863i	0.174603	−	2.30292i
$827$			11.6675i			0.405720i	0.979208	+	0.202860i	$0.0650236\pi$
$827$			11.6675i			0.405720i	−0.979208	+	0.202860i	$0.934976\pi$
$828$	18.7573	+	127.800i	0.651862	+	4.44137i
$829$	−32.9245	−	19.0090i	−1.14352	−	0.660209i	−0.196217	−	0.980560i	$-0.562866\pi$
$829$	−32.9245	−	19.0090i	−1.14352	−	0.660209i	−0.947299	+	0.320351i	$0.896199\pi$
$830$	−10.8501	+	6.26430i	−0.376612	+	0.217437i
$831$	−2.50347	−	34.2967i	−0.0868443	−	1.18974i
$832$	−83.9137	+	48.4476i	−2.90918	+	1.67962i
$833$	23.2355	−	29.0322i	0.805063	−	1.00591i
$834$	−2.23732	−	30.6506i	−0.0774720	−	1.06134i
$835$	7.54322			0.261044
$836$	−0.663656	+	1.14949i	−0.0229530	+	0.0397558i
$837$	5.81055	−	1.29078i	0.200842	−	0.0446160i
$838$	30.9607	−	17.8752i	1.06952	−	0.617488i
$839$	−0.674120	+	1.16761i	−0.0232732	+	0.0403104i	−0.877427	−	0.479709i	$-0.840742\pi$
$839$	−0.674120	+	1.16761i	−0.0232732	+	0.0403104i	0.854154	+	0.520020i	$0.174075\pi$
$840$	−21.4132	−	37.3305i	−0.738827	−	1.28803i
$841$	−11.8735	−	20.5655i	−0.409430	−	0.709154i
$842$	6.95928	+	4.01794i	0.239833	+	0.138467i
$843$	−9.59495	−	14.1319i	−0.330468	−	0.486727i
$844$	−13.2700	−	22.9844i	−0.456774	−	0.791155i
$845$	0.900781	+	1.56020i	0.0309878	+	0.0536725i
$846$	38.6364	−	30.5677i	1.32835	−	1.05094i
$847$	16.2950	−	23.8555i	0.559901	−	0.819685i
$848$	−7.12823	−	4.11549i	−0.244784	−	0.141326i
$849$	7.96417	−	16.4562i	0.273330	−	0.564777i
$850$		−	14.4921i		−	0.497077i
$851$			71.6862i			2.45737i
$852$	34.1010	−	70.4623i	1.16828	−	2.41400i
$853$	−40.1559	−	23.1840i	−1.37491	−	0.793805i	−0.383369	−	0.923595i	$-0.625236\pi$
$853$	−40.1559	−	23.1840i	−1.37491	−	0.793805i	−0.991541	+	0.129790i	$0.958570\pi$
$854$	57.8866	+	4.38885i	1.98084	+	0.150183i
$855$	2.01926	−	1.59756i	0.0690571	−	0.0546354i
$856$	90.3322	+	156.460i	3.08749	+	5.34769i
$857$	14.3587	+	24.8700i	0.490483	+	0.849541i	0.999940	−	0.0109547i	$-0.00348706\pi$
$857$	14.3587	+	24.8700i	0.490483	+	0.849541i	−0.509457	+	0.860496i	$0.670154\pi$
$858$	−2.52392	−	3.71734i	−0.0861651	−	0.126908i
$859$	39.3716	+	22.7312i	1.34334	+	0.775579i	0.987296	−	0.158889i	$-0.0507912\pi$
$859$	39.3716	+	22.7312i	1.34334	+	0.775579i	0.356046	+	0.934468i	$0.384125\pi$
$860$	1.21896	+	2.11129i	0.0415660	+	0.0719945i
$861$	0.0812618	−	28.9373i	0.00276939	−	0.986179i
$862$	−25.1505	+	43.5619i	−0.856629	+	1.48373i
$863$	9.01372	−	5.20407i	0.306831	−	0.177149i	−0.338677	−	0.940903i	$-0.609979\pi$
$863$	9.01372	−	5.20407i	0.306831	−	0.177149i	0.645507	+	0.763754i	$0.276646\pi$
$864$	108.634	−	24.1325i	3.69580	−	0.821004i
$865$	−1.23435	+	2.13795i	−0.0419691	+	0.0726926i
$866$	−14.2495			−0.484218
$867$	1.41473	+	19.3814i	0.0480467	+	0.658226i
$868$	−1.24699	+	16.4472i	−0.0423258	+	0.558254i
$869$	1.12932	−	0.652014i	0.0383096	−	0.0221181i
$870$	0.788422	+	10.8011i	0.0267300	+	0.366193i
$871$	4.65362	−	2.68677i	0.157682	−	0.0910376i
$872$	159.571	+	92.1281i	5.40374	+	3.11985i
$873$	1.85680	+	12.6510i	0.0628432	+	0.428173i
$874$		−	18.5236i		−	0.626570i
$875$	2.63818	+	0.200022i	0.0891867	+	0.00676197i
$876$	21.7553	+	32.0422i	0.735043	+	1.08260i
$877$	−21.3437	+	36.9684i	−0.720726	+	1.24833i	0.239983	+	0.970777i	$0.422858\pi$
$877$	−21.3437	+	36.9684i	−0.720726	+	1.24833i	−0.960709	+	0.277557i	$0.910475\pi$
$878$	42.6465			1.43925
$879$	−1.08792	−	14.9042i	−0.0366947	−	0.502706i
$880$		−	4.18710i		−	0.141147i
$881$	5.57362			0.187780			0.0938900	−	0.995583i	$-0.470070\pi$
$881$	5.57362			0.187780			0.0938900	+	0.995583i	$0.470070\pi$
$882$	−49.7744	+	28.3657i	−1.67599	+	0.955124i
$883$	41.3715			1.39226			0.696131	−	0.717915i	$-0.254903\pi$
$883$	41.3715			1.39226			0.696131	+	0.717915i	$0.254903\pi$
$884$			96.7491i			3.25402i
$885$	−13.1779	+	8.94721i	−0.442969	+	0.300757i
$886$	−16.7269			−0.561950
$887$	5.96178	−	10.3261i	0.200177	−	0.346716i	−0.748408	−	0.663238i	$-0.769182\pi$
$887$	5.96178	−	10.3261i	0.200177	−	0.346716i	0.948585	+	0.316522i	$0.102515\pi$
$888$	147.000	−	10.7302i	4.93301	−	0.360081i
$889$	5.59165	+	0.423948i	0.187538	+	0.0142188i
$890$		−	32.6042i		−	1.09290i
$891$	0.734876	+	2.44956i	0.0246193	+	0.0820632i
$892$	−17.6922	−	10.2146i	−0.592378	−	0.342010i
$893$	−4.47428	+	2.58323i	−0.149726	+	0.0864444i
$894$	38.3573	−	26.0430i	1.28286	−	0.871007i
$895$	0.894686	−	0.516547i	0.0299060	−	0.0172663i
$896$	−7.23259	+	95.3940i	−0.241624	+	3.18689i
$897$	41.2752	+	19.9756i	1.37814	+	0.666965i
$898$	−110.805			−3.69762
$899$	1.31272	−	2.27369i	0.0437815	−	0.0758319i
$900$	−6.02379	+	15.1754i	−0.200793	+	0.505848i
$901$	−2.56982	+	1.48369i	−0.0856131	+	0.0494287i
$902$	2.44757	−	4.23932i	0.0814952	−	0.141154i
$903$	1.78060	−	1.02138i	0.0592548	−	0.0339893i
$904$	−82.1497	−	142.287i	−2.73226	−	4.73241i
$905$	−4.24725	−	2.45215i	−0.141183	−	0.0815123i
$906$	−45.8275	+	3.34515i	−1.52252	+	0.111135i
$907$	21.7069	+	37.5975i	0.720766	+	1.24840i	0.960693	+	0.277612i	$0.0895430\pi$
$907$	21.7069	+	37.5975i	0.720766	+	1.24840i	−0.239927	+	0.970791i	$0.577124\pi$
$908$	23.3275	+	40.4043i	0.774149	+	1.34086i
$909$	19.3185	−	48.6680i	0.640753	−	1.61422i
$910$	−24.0847	−	1.82605i	−0.798398	−	0.0605330i
$911$	44.9154	+	25.9319i	1.48811	+	0.859163i	0.999908	−	0.0135658i	$-0.00431825\pi$
$911$	44.9154	+	25.9319i	1.48811	+	0.859163i	0.488206	+	0.872729i	$0.337652\pi$
$912$	−21.8466	+	1.59468i	−0.723413	+	0.0528050i
$913$			1.30498i			0.0431885i
$914$			59.8210i			1.97870i
$915$	−7.82524	−	11.5254i	−0.258694	−	0.381017i
$916$	6.74823	+	3.89609i	0.222968	+	0.128731i
$917$	−21.0395	+	30.8015i	−0.694786	+	1.01715i
$918$	22.6134	−	71.8279i	0.746352	−	2.37067i
$919$	−20.6435	−	35.7555i	−0.680965	−	1.17947i	−0.974687	−	0.223575i	$-0.928227\pi$
$919$	−20.6435	−	35.7555i	−0.680965	−	1.17947i	0.293721	−	0.955891i	$-0.405106\pi$
$920$	37.1482	+	64.3426i	1.22474	+	2.12131i
$921$	−8.74604	+	18.0718i	−0.288192	+	0.595486i
$922$	70.3565	+	40.6203i	2.31707	+	1.33776i
$923$	−13.8947	−	24.0663i	−0.457349	−	0.792152i
$924$	−7.08694	−	0.0199016i	−0.233143	−	0.000654714i
$925$	−4.53064	+	7.84730i	−0.148966	+	0.258018i
$926$	−7.78976	+	4.49742i	−0.255987	+	0.147794i
$927$	2.63141	+	17.9287i	0.0864269	+	0.588857i
$928$	24.5425	−	42.5089i	0.805648	−	1.39542i
$929$	−37.5748			−1.23279			−0.616395	−	0.787437i	$-0.711407\pi$
$929$	−37.5748			−1.23279			−0.616395	+	0.787437i	$0.711407\pi$
$930$	4.47806	−	3.04042i	0.146841	−	0.0996992i
$931$	5.59639	−	2.18515i	0.183414	−	0.0716153i
$932$	−13.1073	+	7.56750i	−0.429344	+	0.247882i
$933$	7.75147	+	3.75141i	0.253772	+	0.122816i
$934$	−78.3275	+	45.2224i	−2.56295	+	1.47972i
$935$	−1.30727	−	0.754751i	−0.0427522	−	0.0246830i
$936$	34.7839	−	87.6293i	1.13695	−	2.86425i
$937$		−	27.8462i		−	0.909695i	−0.890569	−	0.454848i	$-0.849694\pi$
$937$		−	27.8462i		−	0.909695i	0.890569	−	0.454848i	$-0.150306\pi$
$938$	0.876225	−	11.5569i	0.0286098	−	0.377347i
$939$	−14.7754	+	30.5302i	−0.482177	+	0.996316i
$940$	16.3807	−	28.3723i	0.534280	−	0.925401i
$941$	−37.9782			−1.23805			−0.619026	−	0.785370i	$-0.712473\pi$
$941$	−37.9782			−1.23805			−0.619026	+	0.785370i	$0.712473\pi$
$942$	26.7146	+	12.9288i	0.870407	+	0.421242i
$943$			49.9569i			1.62682i
$944$	135.507			4.41037
$945$	12.7636	+	5.10795i	0.415199	+	0.166162i
$946$	0.347249			0.0112900
$947$		−	3.02848i		−	0.0984125i	−0.998789	−	0.0492063i	$-0.984331\pi$
$947$		−	3.02848i		−	0.0984125i	0.998789	−	0.0492063i	$-0.0156692\pi$
$948$	38.9391	+	18.8450i	1.26468	+	0.612057i
$949$	13.7490			0.446310
$950$	1.17071	−	2.02773i	0.0379829	−	0.0657882i
$951$	0.887521	−	1.83387i	0.0287799	−	0.0594674i
$952$	108.992	+	74.4488i	3.53244	+	2.41290i
$953$		−	7.98502i		−	0.258660i	−0.991602	−	0.129330i	$-0.958717\pi$
$953$		−	7.98502i		−	0.258660i	0.991602	−	0.129330i	$-0.0412827\pi$
$954$	4.52321	−	0.663875i	0.146444	−	0.0214937i
$955$	1.63620	+	0.944661i	0.0529462	+	0.0305685i
$956$	33.7242	−	19.4707i	1.09072	−	0.629726i
$957$	1.01538	+	0.491404i	0.0328226	+	0.0158848i
$958$	52.5970	−	30.3669i	1.69933	−	0.981110i
$959$	13.6076	−	6.53846i	0.439413	−	0.211138i
$960$	41.4917	−	28.1711i	1.33914	−	0.909219i
$961$	29.6878			0.957672
$962$	41.3614	−	71.6401i	1.33355	−	2.30977i
$963$	−53.6413	−	21.2926i	−1.72857	−	0.686143i
$964$	−126.086	+	72.7960i	−4.06097	+	2.34460i
$965$	6.19129	−	10.7236i	0.199305	−	0.345206i
$966$	85.7917	−	49.2112i	2.76030	−	1.58334i
$967$	−12.9808	−	22.4834i	−0.417435	−	0.723018i	0.578246	−	0.815863i	$-0.303737\pi$
$967$	−12.9808	−	22.4834i	−0.417435	−	0.723018i	−0.995681	+	0.0928442i	$0.970404\pi$
$968$	88.8067	+	51.2726i	2.85435	+	1.64796i
$969$	−3.44011	+	7.10825i	−0.110512	+	0.228350i
$970$	5.81380	+	10.0698i	0.186670	+	0.323322i
$971$	2.20423	+	3.81784i	0.0707372	+	0.122520i	0.899225	−	0.437487i	$-0.144132\pi$
$971$	2.20423	+	3.81784i	0.0707372	+	0.122520i	−0.828487	+	0.560008i	$0.810798\pi$
$972$	−53.5354	+	65.8150i	−1.71715	+	2.11102i
$973$	−15.5102	+	7.45262i	−0.497233	+	0.238920i
$974$	−16.2632	−	9.38957i	−0.521107	−	0.300861i
$975$	3.25581	+	4.79531i	0.104269	+	0.153573i
$976$			118.514i			3.79356i
$977$		−	30.8147i		−	0.985851i	−0.870072	−	0.492925i	$-0.835928\pi$
$977$		−	30.8147i		−	0.985851i	0.870072	−	0.492925i	$-0.164072\pi$
$978$	−86.2106	+	6.29289i	−2.75671	+	0.201224i
$979$	−2.94107	−	1.69803i	−0.0939970	−	0.0542692i
$980$	−23.8051	+	29.7439i	−0.760425	+	0.950134i
$981$	−58.2362	+	8.54737i	−1.85934	+	0.272896i
$982$	−16.3230	−	28.2722i	−0.520887	−	0.902203i
$983$	−24.9299	−	43.1799i	−0.795140	−	1.37722i	−0.922750	−	0.385399i	$-0.874064\pi$
$983$	−24.9299	−	43.1799i	−0.795140	−	1.37722i	0.127610	−	0.991824i	$-0.459270\pi$
$984$	102.442	−	7.47769i	3.26573	−	0.238380i
$985$	−1.85323	−	1.06996i	−0.0590488	−	0.0340918i
$986$	−16.6077	−	28.7653i	−0.528896	−	0.916075i
$987$	−23.8509	−	13.8598i	−0.759182	−	0.441161i
$988$	−7.81562	+	13.5371i	−0.248648	+	0.430671i
$989$	−3.06904	+	1.77191i	−0.0975896	+	0.0563434i
$990$	1.44295	+	1.82383i	0.0458599	+	0.0579652i
$991$	14.3732	−	24.8951i	0.456579	−	0.790818i	−0.542198	−	0.840251i	$-0.682408\pi$
$991$	14.3732	−	24.8951i	0.456579	−	0.790818i	0.998777	+	0.0494322i	$0.0157412\pi$
$992$	−24.5323			−0.778902
$993$	48.8208	+	23.6273i	1.54928	+	0.749791i
$994$	−59.7670	−	4.53142i	−1.89569	−	0.143728i
$995$	2.61298	−	1.50861i	0.0828372	−	0.0478261i
$996$	−35.8159	+	24.3175i	−1.13487	+	0.770530i
$997$	36.7868	−	21.2389i	1.16505	−	0.672642i	0.212540	−	0.977152i	$-0.431826\pi$
$997$	36.7868	−	21.2389i	1.16505	−	0.672642i	0.952509	+	0.304511i	$0.0984929\pi$
$998$	50.1000	+	28.9252i	1.58589	+	0.915612i
$999$	−34.7002	+	31.8242i	−1.09786	+	1.00687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.b.101.15	✓	30
3.2	odd	2		945.2.t.b.521.1		30
7.5	odd	6		315.2.be.b.236.15	yes	30
9.4	even	3		945.2.be.b.206.1		30
9.5	odd	6		315.2.be.b.311.15	yes	30
21.5	even	6		945.2.be.b.656.1		30
63.5	even	6	inner	315.2.t.b.131.1	yes	30
63.40	odd	6		945.2.t.b.341.15		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.15	✓	30	1.1	even	1	trivial
315.2.t.b.131.1	yes	30	63.5	even	6	inner
315.2.be.b.236.15	yes	30	7.5	odd	6
315.2.be.b.311.15	yes	30	9.5	odd	6
945.2.t.b.341.15		30	63.40	odd	6
945.2.t.b.521.1		30	3.2	odd	2
945.2.be.b.206.1		30	9.4	even	3
945.2.be.b.656.1		30	21.5	even	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.72808i q^{2} +(-1.55907 - 0.754526i) q^{3} -5.44243 q^{4} +(0.500000 - 0.866025i) q^{5} +(2.05841 - 4.25326i) q^{6} +(-2.63818 - 0.200022i) q^{7} -9.39122i q^{8} +(1.86138 + 2.35271i) q^{9} +O(q^{10})\)	\(q+2.72808i q^{2} +(-1.55907 - 0.754526i) q^{3} -5.44243 q^{4} +(0.500000 - 0.866025i) q^{5} +(2.05841 - 4.25326i) q^{6} +(-2.63818 - 0.200022i) q^{7} -9.39122i q^{8} +(1.86138 + 2.35271i) q^{9} +(2.36259 + 1.36404i) q^{10} +(0.246087 - 0.142079i) q^{11} +(8.48511 + 4.10646i) q^{12} +(2.89807 - 1.67320i) q^{13} +(0.545675 - 7.19717i) q^{14} +(-1.43297 + 0.972928i) q^{15} +14.7352 q^{16} +(2.65611 - 4.60051i) q^{17} +(-6.41840 + 5.07799i) q^{18} +(0.743281 - 0.429133i) q^{19} +(-2.72121 + 4.71328i) q^{20} +(3.96218 + 2.30242i) q^{21} +(0.387602 + 0.671346i) q^{22} +(-6.85136 - 3.95563i) q^{23} +(-7.08592 + 14.6415i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(4.56463 + 7.90618i) q^{26} +(-1.12683 - 5.07250i) q^{27} +(14.3581 + 1.08860i) q^{28} +(-1.98489 - 1.14598i) q^{29} +(-2.65423 - 3.90927i) q^{30} +1.14550i q^{31} +21.4163i q^{32} +(-0.490868 + 0.0358306i) q^{33} +(12.5506 + 7.24607i) q^{34} +(-1.49231 + 2.18472i) q^{35} +(-10.1304 - 12.8045i) q^{36} +(-4.53064 - 7.84730i) q^{37} +(1.17071 + 2.02773i) q^{38} +(-5.78077 + 0.421963i) q^{39} +(-8.13303 - 4.69561i) q^{40} +(-3.15733 - 5.46865i) q^{41} +(-6.28120 + 10.8091i) q^{42} +(0.223973 - 0.387932i) q^{43} +(-1.33931 + 0.773252i) q^{44} +(2.96820 - 0.435645i) q^{45} +(10.7913 - 18.6911i) q^{46} -6.01964 q^{47} +(-22.9731 - 11.1181i) q^{48} +(6.91998 + 1.05539i) q^{49} +(2.36259 - 1.36404i) q^{50} +(-7.61226 + 5.16840i) q^{51} +(-15.7726 + 9.10629i) q^{52} +(-0.483757 - 0.279297i) q^{53} +(13.8382 - 3.07408i) q^{54} -0.284157i q^{55} +(-1.87845 + 24.7757i) q^{56} +(-1.48262 + 0.108223i) q^{57} +(3.12632 - 5.41494i) q^{58} +9.19616 q^{59} +(7.79885 - 5.29509i) q^{60} +8.04297i q^{61} -3.12502 q^{62} +(-4.44006 - 6.57920i) q^{63} -28.9550 q^{64} -3.34641i q^{65} +(-0.0977488 - 1.33913i) q^{66} +1.60576 q^{67} +(-14.4557 + 25.0379i) q^{68} +(7.69710 + 11.3366i) q^{69} +(-5.96009 - 4.07115i) q^{70} -8.30424i q^{71} +(22.0949 - 17.4806i) q^{72} +(3.55813 + 2.05429i) q^{73} +(21.4081 - 12.3599i) q^{74} +(0.126094 + 1.72745i) q^{75} +(-4.04525 + 2.33553i) q^{76} +(-0.677641 + 0.325606i) q^{77} +(-1.15115 - 15.7704i) q^{78} +4.58911 q^{79} +(7.36758 - 12.7610i) q^{80} +(-2.07053 + 8.75859i) q^{81} +(14.9189 - 8.61345i) q^{82} +(-2.29623 + 3.97719i) q^{83} +(-21.5639 - 12.5308i) q^{84} +(-2.65611 - 4.60051i) q^{85} +(1.05831 + 0.611016i) q^{86} +(2.22991 + 3.28431i) q^{87} +(-1.33429 - 2.31106i) q^{88} +(-5.97567 - 10.3502i) q^{89} +(1.18847 + 8.09749i) q^{90} +(-7.98031 + 3.83453i) q^{91} +(37.2880 + 21.5282i) q^{92} +(0.864310 - 1.78591i) q^{93} -16.4221i q^{94} -0.858267i q^{95} +(16.1591 - 33.3894i) q^{96} +(3.69117 + 2.13110i) q^{97} +(-2.87918 + 18.8783i) q^{98} +(0.792332 + 0.314511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more