LMFDB - Embedded newform 930.2.r.b.119.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(119,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("930.119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.r (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			119.14
Character	$\chi$	$=$	930.119
Dual form			930.2.r.b.719.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.392310 + 1.68704i) q^{3} +1.00000 q^{4} +(0.381329 + 2.20331i) q^{5} +(-0.392310 + 1.68704i) q^{6} +(-2.96938 - 1.71437i) q^{7} +1.00000 q^{8} +(-2.69219 - 1.32368i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.392310 + 1.68704i) q^{3} +1.00000 q^{4} +(0.381329 + 2.20331i) q^{5} +(-0.392310 + 1.68704i) q^{6} +(-2.96938 - 1.71437i) q^{7} +1.00000 q^{8} +(-2.69219 - 1.32368i) q^{9} +(0.381329 + 2.20331i) q^{10} +(3.19099 + 5.52696i) q^{11} +(-0.392310 + 1.68704i) q^{12} +(-0.452539 - 0.783821i) q^{13} +(-2.96938 - 1.71437i) q^{14} +(-3.86667 - 0.221066i) q^{15} +1.00000 q^{16} +(-2.93950 - 1.69712i) q^{17} +(-2.69219 - 1.32368i) q^{18} +(-3.28949 + 5.69756i) q^{19} +(0.381329 + 2.20331i) q^{20} +(4.05713 - 4.33689i) q^{21} +(3.19099 + 5.52696i) q^{22} -1.28143i q^{23} +(-0.392310 + 1.68704i) q^{24} +(-4.70918 + 1.68037i) q^{25} +(-0.452539 - 0.783821i) q^{26} +(3.28927 - 4.02252i) q^{27} +(-2.96938 - 1.71437i) q^{28} -2.03276 q^{29} +(-3.86667 - 0.221066i) q^{30} +(1.79672 + 5.26989i) q^{31} +1.00000 q^{32} +(-10.5760 + 3.21504i) q^{33} +(-2.93950 - 1.69712i) q^{34} +(2.64499 - 7.19621i) q^{35} +(-2.69219 - 1.32368i) q^{36} +(-2.47900 + 4.29376i) q^{37} +(-3.28949 + 5.69756i) q^{38} +(1.49987 - 0.455949i) q^{39} +(0.381329 + 2.20331i) q^{40} +(1.87833 - 1.08446i) q^{41} +(4.05713 - 4.33689i) q^{42} +(4.12891 - 7.15148i) q^{43} +(3.19099 + 5.52696i) q^{44} +(1.88988 - 6.43649i) q^{45} -1.28143i q^{46} +1.78914 q^{47} +(-0.392310 + 1.68704i) q^{48} +(2.37814 + 4.11906i) q^{49} +(-4.70918 + 1.68037i) q^{50} +(4.01630 - 4.29325i) q^{51} +(-0.452539 - 0.783821i) q^{52} +(-7.60886 + 4.39298i) q^{53} +(3.28927 - 4.02252i) q^{54} +(-10.9608 + 9.13834i) q^{55} +(-2.96938 - 1.71437i) q^{56} +(-8.32150 - 7.78470i) q^{57} -2.03276 q^{58} +(-2.39397 - 1.38216i) q^{59} +(-3.86667 - 0.221066i) q^{60} -4.65692i q^{61} +(1.79672 + 5.26989i) q^{62} +(5.72483 + 8.54593i) q^{63} +1.00000 q^{64} +(1.55444 - 1.29598i) q^{65} +(-10.5760 + 3.21504i) q^{66} +(0.0466974 - 0.0269608i) q^{67} +(-2.93950 - 1.69712i) q^{68} +(2.16183 + 0.502719i) q^{69} +(2.64499 - 7.19621i) q^{70} +(9.80635 - 5.66170i) q^{71} +(-2.69219 - 1.32368i) q^{72} +(5.91441 + 10.2441i) q^{73} +(-2.47900 + 4.29376i) q^{74} +(-0.987394 - 8.60378i) q^{75} +(-3.28949 + 5.69756i) q^{76} -21.8822i q^{77} +(1.49987 - 0.455949i) q^{78} +(3.12853 + 1.80626i) q^{79} +(0.381329 + 2.20331i) q^{80} +(5.49573 + 7.12720i) q^{81} +(1.87833 - 1.08446i) q^{82} +(11.9468 - 6.89749i) q^{83} +(4.05713 - 4.33689i) q^{84} +(2.61837 - 7.12380i) q^{85} +(4.12891 - 7.15148i) q^{86} +(0.797471 - 3.42934i) q^{87} +(3.19099 + 5.52696i) q^{88} +5.15412 q^{89} +(1.88988 - 6.43649i) q^{90} +3.10328i q^{91} -1.28143i q^{92} +(-9.59538 + 0.963701i) q^{93} +1.78914 q^{94} +(-13.8079 - 5.07513i) q^{95} +(-0.392310 + 1.68704i) q^{96} +14.7656i q^{97} +(2.37814 + 4.11906i) q^{98} +(-1.27480 - 19.1035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	$ 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) $ 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.392310	+	1.68704i	−0.226500	+	0.974011i
$3$	−0.392310	+	1.68704i	−0.226500	+	0.974011i
$4$	1.00000			0.500000
$5$	0.381329	+	2.20331i	0.170535	+	0.985352i
$5$	0.381329	+	2.20331i	0.170535	+	0.985352i
$6$	−0.392310	+	1.68704i	−0.160160	+	0.688730i
$7$	−2.96938	−	1.71437i	−1.12232	−	0.647972i	−0.180328	−	0.983607i	$-0.557716\pi$
$7$	−2.96938	−	1.71437i	−1.12232	−	0.647972i	−0.941992	+	0.335635i	$0.891049\pi$
$8$	1.00000			0.353553
$9$	−2.69219	−	1.32368i	−0.897395	−	0.441228i
$10$	0.381329	+	2.20331i	0.120587	+	0.696749i
$11$	3.19099	+	5.52696i	0.962120	+	1.66644i	0.717162	+	0.696906i	$0.245441\pi$
$11$	3.19099	+	5.52696i	0.962120	+	1.66644i	0.244958	+	0.969534i	$0.421226\pi$
$12$	−0.392310	+	1.68704i	−0.113250	+	0.487006i
$13$	−0.452539	−	0.783821i	−0.125512	−	0.217393i	0.796421	−	0.604742i	$-0.206724\pi$
$13$	−0.452539	−	0.783821i	−0.125512	−	0.217393i	−0.921933	+	0.387350i	$0.873391\pi$
$14$	−2.96938	−	1.71437i	−0.793600	−	0.458185i
$15$	−3.86667	−	0.221066i	−0.998370	−	0.0570791i
$16$	1.00000			0.250000
$17$	−2.93950	−	1.69712i	−0.712934	−	0.411612i	0.0992126	−	0.995066i	$-0.468368\pi$
$17$	−2.93950	−	1.69712i	−0.712934	−	0.411612i	−0.812146	+	0.583454i	$0.801701\pi$
$18$	−2.69219	−	1.32368i	−0.634554	−	0.311995i
$19$	−3.28949	+	5.69756i	−0.754661	+	1.30711i	0.190882	+	0.981613i	$0.438865\pi$
$19$	−3.28949	+	5.69756i	−0.754661	+	1.30711i	−0.945543	+	0.325498i	$0.894468\pi$
$20$	0.381329	+	2.20331i	0.0852677	+	0.492676i
$21$	4.05713	−	4.33689i	0.885338	−	0.946386i
$22$	3.19099	+	5.52696i	0.680321	+	1.17835i
$23$		−	1.28143i		−	0.267197i	−0.991036	−	0.133599i	$-0.957347\pi$
$23$		−	1.28143i		−	0.267197i	0.991036	−	0.133599i	$-0.0426533\pi$
$24$	−0.392310	+	1.68704i	−0.0800800	+	0.344365i
$25$	−4.70918	+	1.68037i	−0.941835	+	0.336075i
$26$	−0.452539	−	0.783821i	−0.0887502	−	0.153720i
$27$	3.28927	−	4.02252i	0.633021	−	0.774135i
$28$	−2.96938	−	1.71437i	−0.561160	−	0.323986i
$29$	−2.03276			−0.377473			−0.188737	−	0.982028i	$-0.560439\pi$
$29$	−2.03276			−0.377473			−0.188737	+	0.982028i	$0.560439\pi$
$30$	−3.86667	−	0.221066i	−0.705954	−	0.0403610i
$31$	1.79672	+	5.26989i	0.322701	+	0.946501i
$31$	1.79672	+	5.26989i	0.322701	+	0.946501i
$32$	1.00000			0.176777
$33$	−10.5760	+	3.21504i	−1.84105	+	0.559666i
$34$	−2.93950	−	1.69712i	−0.504120	−	0.291054i
$35$	2.64499	−	7.19621i	0.447085	−	1.21638i
$36$	−2.69219	−	1.32368i	−0.448698	−	0.220614i
$37$	−2.47900	+	4.29376i	−0.407546	+	0.705890i	−0.994614	−	0.103647i	$-0.966949\pi$
$37$	−2.47900	+	4.29376i	−0.407546	+	0.705890i	0.587068	+	0.809537i	$0.300282\pi$
$38$	−3.28949	+	5.69756i	−0.533626	+	0.924267i
$39$	1.49987	−	0.455949i	0.240171	−	0.0730103i
$40$	0.381329	+	2.20331i	0.0602934	+	0.348374i
$41$	1.87833	−	1.08446i	0.293347	−	0.169364i	−0.346104	−	0.938196i	$-0.612495\pi$
$41$	1.87833	−	1.08446i	0.293347	−	0.169364i	0.639450	+	0.768833i	$0.279162\pi$
$42$	4.05713	−	4.33689i	0.626028	−	0.669196i
$43$	4.12891	−	7.15148i	0.629653	−	1.09059i	−0.357968	−	0.933734i	$-0.616530\pi$
$43$	4.12891	−	7.15148i	0.629653	−	1.09059i	0.987621	−	0.156857i	$-0.0501363\pi$
$44$	3.19099	+	5.52696i	0.481060	+	0.833220i
$45$	1.88988	−	6.43649i	0.281727	−	0.959495i
$46$		−	1.28143i		−	0.188937i
$47$	1.78914			0.260974			0.130487	−	0.991450i	$-0.458346\pi$
$47$	1.78914			0.260974			0.130487	+	0.991450i	$0.458346\pi$
$48$	−0.392310	+	1.68704i	−0.0566251	+	0.243503i
$49$	2.37814	+	4.11906i	0.339735	+	0.588438i
$50$	−4.70918	+	1.68037i	−0.665978	+	0.237641i
$51$	4.01630	−	4.29325i	0.562395	−	0.601175i
$52$	−0.452539	−	0.783821i	−0.0627559	−	0.108696i
$53$	−7.60886	+	4.39298i	−1.04516	+	0.603422i	−0.921290	−	0.388877i	$-0.872863\pi$
$53$	−7.60886	+	4.39298i	−1.04516	+	0.603422i	−0.123868	+	0.992299i	$0.539530\pi$
$54$	3.28927	−	4.02252i	0.447613	−	0.547396i
$55$	−10.9608	+	9.13834i	−1.47795	+	1.23221i
$56$	−2.96938	−	1.71437i	−0.396800	−	0.229093i
$57$	−8.32150	−	7.78470i	−1.10221	−	1.03111i
$58$	−2.03276			−0.266914
$59$	−2.39397	−	1.38216i	−0.311668	−	0.179942i	0.336005	−	0.941860i	$-0.390924\pi$
$59$	−2.39397	−	1.38216i	−0.311668	−	0.179942i	−0.647673	+	0.761919i	$0.724258\pi$
$60$	−3.86667	−	0.221066i	−0.499185	−	0.0285396i
$61$		−	4.65692i		−	0.596258i	−0.954526	−	0.298129i	$-0.903637\pi$
$61$		−	4.65692i		−	0.596258i	0.954526	−	0.298129i	$-0.0963625\pi$
$62$	1.79672	+	5.26989i	0.228184	+	0.669277i
$63$	5.72483	+	8.54593i	0.721261	+	1.07669i
$64$	1.00000			0.125000
$65$	1.55444	−	1.29598i	0.192804	−	0.160746i
$66$	−10.5760	+	3.21504i	−1.30182	+	0.395744i
$67$	0.0466974	−	0.0269608i	0.00570499	−	0.00329378i	−0.497145	−	0.867668i	$-0.665618\pi$
$67$	0.0466974	−	0.0269608i	0.00570499	−	0.00329378i	0.502850	+	0.864374i	$0.332285\pi$
$68$	−2.93950	−	1.69712i	−0.356467	−	0.205806i
$69$	2.16183	+	0.502719i	0.260253	+	0.0605203i
$70$	2.64499	−	7.19621i	0.316137	−	0.860112i
$71$	9.80635	−	5.66170i	1.16380	−	0.671920i	0.211588	−	0.977359i	$-0.432136\pi$
$71$	9.80635	−	5.66170i	1.16380	−	0.671920i	0.952212	+	0.305439i	$0.0988032\pi$
$72$	−2.69219	−	1.32368i	−0.317277	−	0.155998i
$73$	5.91441	+	10.2441i	0.692229	+	1.19898i	0.971106	+	0.238649i	$0.0767046\pi$
$73$	5.91441	+	10.2441i	0.692229	+	1.19898i	−0.278877	+	0.960327i	$0.589962\pi$
$74$	−2.47900	+	4.29376i	−0.288178	+	0.499140i
$75$	−0.987394	−	8.60378i	−0.114014	−	0.993479i
$76$	−3.28949	+	5.69756i	−0.377330	+	0.653555i
$77$		−	21.8822i		−	2.49371i
$78$	1.49987	−	0.455949i	0.169827	−	0.0516261i
$79$	3.12853	+	1.80626i	0.351987	+	0.203220i	0.665560	−	0.746344i	$-0.268193\pi$
$79$	3.12853	+	1.80626i	0.351987	+	0.203220i	−0.313573	+	0.949564i	$0.601526\pi$
$80$	0.381329	+	2.20331i	0.0426339	+	0.246338i
$81$	5.49573	+	7.12720i	0.610636	+	0.791911i
$82$	1.87833	−	1.08446i	0.207427	−	0.119758i
$83$	11.9468	−	6.89749i	1.31133	−	0.757098i	0.329015	−	0.944325i	$-0.393283\pi$
$83$	11.9468	−	6.89749i	1.31133	−	0.757098i	0.982317	+	0.187227i	$0.0599499\pi$
$84$	4.05713	−	4.33689i	0.442669	−	0.473193i
$85$	2.61837	−	7.12380i	0.284003	−	0.772685i
$86$	4.12891	−	7.15148i	0.445232	−	0.771164i
$87$	0.797471	−	3.42934i	0.0854979	−	0.367663i
$88$	3.19099	+	5.52696i	0.340161	+	0.589176i
$89$	5.15412			0.546336			0.273168	−	0.961966i	$-0.411929\pi$
$89$	5.15412			0.546336			0.273168	+	0.961966i	$0.411929\pi$
$90$	1.88988	−	6.43649i	0.199211	−	0.678465i
$91$			3.10328i			0.325312i
$92$		−	1.28143i		−	0.133599i
$93$	−9.59538	+	0.963701i	−0.994994	+	0.0999312i
$94$	1.78914			0.184536
$95$	−13.8079	−	5.07513i	−1.41666	−	0.520697i
$96$	−0.392310	+	1.68704i	−0.0400400	+	0.172182i
$97$			14.7656i			1.49922i	0.661879	+	0.749611i	$0.269759\pi$
$97$			14.7656i			1.49922i	−0.661879	+	0.749611i	$0.730241\pi$
$98$	2.37814	+	4.11906i	0.240229	+	0.416088i
$99$	−1.27480	−	19.1035i	−0.128122	−	1.91997i
$100$	−4.70918	+	1.68037i	−0.470918	+	0.168037i
$101$			12.2575i			1.21966i	0.792531	+	0.609832i	$0.208763\pi$
$101$			12.2575i			1.21966i	−0.792531	+	0.609832i	$0.791237\pi$
$102$	4.01630	−	4.29325i	0.397673	−	0.425095i
$103$	−4.90895	+	2.83419i	−0.483694	+	0.279261i	−0.721954	−	0.691941i	$-0.756756\pi$
$103$	−4.90895	+	2.83419i	−0.483694	+	0.279261i	0.238261	+	0.971201i	$0.423423\pi$
$104$	−0.452539	−	0.783821i	−0.0443751	−	0.0768599i
$105$	11.1026	+	7.28534i	1.08350	+	0.710976i
$106$	−7.60886	+	4.39298i	−0.739038	+	0.426684i
$107$	−0.900033	+	1.55890i	−0.0870095	+	0.150705i	−0.906246	−	0.422751i	$-0.861064\pi$
$107$	−0.900033	+	1.55890i	−0.0870095	+	0.150705i	0.819236	+	0.573456i	$0.194398\pi$
$108$	3.28927	−	4.02252i	0.316511	−	0.387067i
$109$	11.9427			1.14390			0.571951	−	0.820288i	$-0.306187\pi$
$109$	11.9427			1.14390			0.571951	+	0.820288i	$0.306187\pi$
$110$	−10.9608	+	9.13834i	−1.04507	+	0.871306i
$111$	−6.27120	−	5.86666i	−0.595235	−	0.556839i
$112$	−2.96938	−	1.71437i	−0.280580	−	0.161993i
$113$	8.34722	+	14.4578i	0.785240	+	1.36008i	0.928856	+	0.370442i	$0.120794\pi$
$113$	8.34722	+	14.4578i	0.785240	+	1.36008i	−0.143615	+	0.989634i	$0.545873\pi$
$114$	−8.32150	−	7.78470i	−0.779380	−	0.729104i
$115$	2.82340	−	0.488647i	0.263283	−	0.0455666i
$116$	−2.03276			−0.188737
$117$	0.180789	+	2.70921i	0.0167139	+	0.250466i
$118$	−2.39397	−	1.38216i	−0.220383	−	0.127238i
$119$	5.81900	+	10.0788i	0.533426	+	0.923922i
$120$	−3.86667	−	0.221066i	−0.352977	−	0.0201805i
$121$	−14.8648	+	25.7466i	−1.35135	+	2.34060i
$122$		−	4.65692i		−	0.421618i
$123$	1.09263	+	3.59426i	0.0985190	+	0.324084i
$124$	1.79672	+	5.26989i	0.161350	+	0.473251i
$125$	−5.49813	−	9.73502i	−0.491768	−	0.870726i
$126$	5.72483	+	8.54593i	0.510009	+	0.761332i
$127$	5.17437	−	8.96227i	0.459151	−	0.795273i	−0.539765	−	0.841816i	$-0.681487\pi$
$127$	5.17437	−	8.96227i	0.459151	−	0.795273i	0.998916	+	0.0465425i	$0.0148203\pi$
$128$	1.00000			0.0883883
$129$	10.4450	+	9.77122i	0.919631	+	0.860308i
$130$	1.55444	−	1.29598i	0.136333	−	0.113665i
$131$	14.6750	+	8.47260i	1.28216	+	0.740254i	0.977242	−	0.212125i	$-0.0680385\pi$
$131$	14.6750	+	8.47260i	1.28216	+	0.740254i	0.304915	+	0.952379i	$0.401372\pi$
$132$	−10.5760	+	3.21504i	−0.920526	+	0.279833i
$133$	19.5355	−	11.2788i	1.69394	−	0.977998i
$134$	0.0466974	−	0.0269608i	0.00403404	−	0.00232905i
$135$	10.1172	+	5.71340i	0.870747	+	0.491731i
$136$	−2.93950	−	1.69712i	−0.252060	−	0.145527i
$137$	−7.94537	+	4.58726i	−0.678819	+	0.391916i	−0.799410	−	0.600786i	$-0.794854\pi$
$137$	−7.94537	+	4.58726i	−0.678819	+	0.391916i	0.120591	+	0.992702i	$0.461521\pi$
$138$	2.16183	+	0.502719i	0.184027	+	0.0427943i
$139$			18.2894i			1.55128i	0.631173	+	0.775642i	$0.282574\pi$
$139$			18.2894i			1.55128i	−0.631173	+	0.775642i	$0.717426\pi$
$140$	2.64499	−	7.19621i	0.223542	−	0.608191i
$141$	−0.701899	+	3.01835i	−0.0591106	+	0.254191i
$142$	9.80635	−	5.66170i	0.822931	−	0.475119i
$143$	2.88810	−	5.00233i	0.241515	−	0.418316i
$144$	−2.69219	−	1.32368i	−0.224349	−	0.110307i
$145$	−0.775149	−	4.47880i	−0.0643726	−	0.371944i
$146$	5.91441	+	10.2441i	0.489480	+	0.847804i
$147$	−7.88198	+	2.39606i	−0.650095	+	0.197624i
$148$	−2.47900	+	4.29376i	−0.203773	+	0.352945i
$149$	−13.6580	−	7.88548i	−1.11891	−	0.646003i	−0.177788	−	0.984069i	$-0.556894\pi$
$149$	−13.6580	−	7.88548i	−1.11891	−	0.646003i	−0.941123	+	0.338065i	$0.890227\pi$
$150$	−0.987394	−	8.60378i	−0.0806204	−	0.702496i
$151$			1.96141i			0.159617i	0.996810	+	0.0798087i	$0.0254309\pi$
$151$			1.96141i			0.159617i	−0.996810	+	0.0798087i	$0.974569\pi$
$152$	−3.28949	+	5.69756i	−0.266813	+	0.462133i
$153$	5.66723	+	8.45993i	0.458168	+	0.683945i
$154$		−	21.8822i		−	1.76332i
$155$	−10.9261	+	5.96830i	−0.877604	+	0.479386i
$156$	1.49987	−	0.455949i	0.120086	−	0.0365052i
$157$		−	6.06530i		−	0.484064i	−0.970268	−	0.242032i	$-0.922186\pi$
$157$		−	6.06530i		−	0.484064i	0.970268	−	0.242032i	$-0.0778139\pi$
$158$	3.12853	+	1.80626i	0.248892	+	0.143698i
$159$	−4.42608	−	14.5598i	−0.351011	−	1.15467i
$160$	0.381329	+	2.20331i	0.0301467	+	0.174187i
$161$	−2.19685	+	3.80506i	−0.173136	+	0.299881i
$162$	5.49573	+	7.12720i	0.431785	+	0.559966i
$163$			1.25379i			0.0982044i	0.998794	+	0.0491022i	$0.0156360\pi$
$163$			1.25379i			0.0982044i	−0.998794	+	0.0491022i	$0.984364\pi$
$164$	1.87833	−	1.08446i	0.146673	−	0.0846819i
$165$	−11.1167	−	22.0763i	−0.865432	−	1.71864i
$166$	11.9468	−	6.89749i	0.927252	−	0.535349i
$167$	10.2810	+	5.93575i	0.795569	+	0.459322i	0.841919	−	0.539603i	$-0.181426\pi$
$167$	10.2810	+	5.93575i	0.795569	+	0.459322i	−0.0463505	+	0.998925i	$0.514759\pi$
$168$	4.05713	−	4.33689i	0.313014	−	0.334598i
$169$	6.09042	−	10.5489i	0.468494	−	0.811455i
$170$	2.61837	−	7.12380i	0.200820	−	0.546371i
$171$	16.3977	−	10.9847i	1.25396	−	0.840018i
$172$	4.12891	−	7.15148i	0.314827	−	0.545296i
$173$	−11.6604	−	20.1964i	−0.886523	−	1.53550i	−0.843958	−	0.536409i	$-0.819780\pi$
$173$	−11.6604	−	20.1964i	−0.886523	−	1.53550i	−0.0425649	−	0.999094i	$-0.513553\pi$
$174$	0.797471	−	3.42934i	0.0604561	−	0.259977i
$175$	16.8641	+	3.08361i	1.27481	+	0.233099i
$176$	3.19099	+	5.52696i	0.240530	+	0.416610i
$177$	3.27093	−	3.49648i	0.245858	−	0.262811i
$178$	5.15412			0.386318
$179$	5.70902	−	9.88831i	0.426712	−	0.739087i	−0.569867	−	0.821737i	$-0.693005\pi$
$179$	5.70902	−	9.88831i	0.426712	−	0.739087i	0.996579	+	0.0826503i	$0.0263384\pi$
$180$	1.88988	−	6.43649i	0.140863	−	0.479747i
$181$	0.120326	−	0.0694702i	0.00894376	−	0.00516368i	−0.495521	−	0.868596i	$-0.665023\pi$
$181$	0.120326	−	0.0694702i	0.00894376	−	0.00516368i	0.504465	+	0.863432i	$0.331690\pi$
$182$			3.10328i			0.230031i
$183$	7.85640	+	1.82696i	0.580762	+	0.135053i
$184$		−	1.28143i		−	0.0944685i
$185$	−10.4058	−	3.82469i	−0.765051	−	0.281197i
$186$	−9.59538	+	0.963701i	−0.703567	+	0.0706620i
$187$		−	21.6620i		−	1.58408i
$188$	1.78914			0.130487
$189$	−16.6632	+	6.30535i	−1.21207	+	0.458647i
$190$	−13.8079	−	5.07513i	−1.00173	−	0.368189i
$191$	11.0681	−	6.39017i	0.800859	−	0.462376i	−0.0429124	−	0.999079i	$-0.513664\pi$
$191$	11.0681	−	6.39017i	0.800859	−	0.462376i	0.843771	+	0.536703i	$0.180330\pi$
$192$	−0.392310	+	1.68704i	−0.0283125	+	0.121751i
$193$	9.22586	+	5.32655i	0.664092	+	0.383414i	0.793834	−	0.608134i	$-0.208082\pi$
$193$	9.22586	+	5.32655i	0.664092	+	0.383414i	−0.129742	+	0.991548i	$0.541415\pi$
$194$			14.7656i			1.06011i
$195$	1.57654	+	3.13082i	0.112899	+	0.224202i
$196$	2.37814	+	4.11906i	0.169867	+	0.294219i
$197$	21.2751	−	12.2832i	1.51579	−	0.875140i	0.515958	−	0.856614i	$-0.327436\pi$
$197$	21.2751	−	12.2832i	1.51579	−	0.875140i	0.999828	−	0.0185255i	$-0.00589719\pi$
$198$	−1.27480	−	19.1035i	−0.0905959	−	1.35762i
$199$	−1.07789	+	0.622319i	−0.0764095	+	0.0441150i	−0.537718	−	0.843125i	$-0.680713\pi$
$199$	−1.07789	+	0.622319i	−0.0764095	+	0.0441150i	0.461308	+	0.887240i	$0.347380\pi$
$200$	−4.70918	+	1.68037i	−0.332989	+	0.118820i
$201$	0.0271639	+	0.0893572i	0.00191600	+	0.00630277i
$202$			12.2575i			0.862432i
$203$	6.03603	+	3.48490i	0.423646	+	0.244592i
$204$	4.01630	−	4.29325i	0.281197	−	0.300587i
$205$	3.10566	+	3.72502i	0.216909	+	0.260167i
$206$	−4.90895	+	2.83419i	−0.342023	+	0.197467i
$207$	−1.69621	+	3.44986i	−0.117895	+	0.239782i
$208$	−0.452539	−	0.783821i	−0.0313779	−	0.0543482i
$209$	−41.9869			−2.90430
$210$	11.1026	+	7.28534i	0.766153	+	0.502736i
$211$	13.9957	−	24.2412i	0.963501	−	1.66883i	0.249912	−	0.968268i	$-0.419598\pi$
$211$	13.9957	−	24.2412i	0.963501	−	1.66883i	0.713589	−	0.700565i	$-0.247068\pi$
$212$	−7.60886	+	4.39298i	−0.522579	+	0.301711i
$213$	5.70436	+	18.7648i	0.390857	+	1.28574i
$214$	−0.900033	+	1.55890i	−0.0615250	+	0.106564i
$215$	17.3314	+	6.37022i	1.18199	+	0.434445i
$216$	3.28927	−	4.02252i	0.223807	−	0.273698i
$217$	3.69941	−	18.7286i	0.251133	−	1.27138i
$218$	11.9427			0.808861
$219$	−19.6024	+	5.95898i	−1.32461	+	0.402670i
$220$	−10.9608	+	9.13834i	−0.738977	+	0.616107i
$221$			3.07206i			0.206649i
$222$	−6.27120	−	5.86666i	−0.420895	−	0.393744i
$223$	0.843359	−	1.46074i	0.0564755	−	0.0978184i	−0.836405	−	0.548111i	$-0.815347\pi$
$223$	0.843359	−	1.46074i	0.0564755	−	0.0978184i	0.892881	+	0.450293i	$0.148680\pi$
$224$	−2.96938	−	1.71437i	−0.198400	−	0.114546i
$225$	14.9023	+	1.70958i	0.993484	+	0.113972i
$226$	8.34722	+	14.4578i	0.555249	+	0.961719i
$227$	4.42782	+	7.66921i	0.293885	+	0.509024i	0.974725	−	0.223409i	$-0.0717184\pi$
$227$	4.42782	+	7.66921i	0.293885	+	0.509024i	−0.680840	+	0.732432i	$0.738385\pi$
$228$	−8.32150	−	7.78470i	−0.551105	−	0.515555i
$229$	−15.4179	−	8.90151i	−1.01884	−	0.588228i	−0.105073	−	0.994465i	$-0.533508\pi$
$229$	−15.4179	−	8.90151i	−1.01884	−	0.588228i	−0.913768	+	0.406236i	$0.866841\pi$
$230$	2.82340	−	0.488647i	0.186169	−	0.0322205i
$231$	36.9160	+	8.58460i	2.42890	+	0.564825i
$232$	−2.03276			−0.133457
$233$	−0.695815			−0.0455844			−0.0227922	−	0.999740i	$-0.507256\pi$
$233$	−0.695815			−0.0455844			−0.0227922	+	0.999740i	$0.507256\pi$
$234$	0.180789	+	2.70921i	0.0118185	+	0.177107i
$235$	0.682252	+	3.94205i	0.0445052	+	0.257151i
$236$	−2.39397	−	1.38216i	−0.155834	−	0.0899708i
$237$	−4.27457	+	4.56933i	−0.277663	+	0.296810i
$238$	5.81900	+	10.0788i	0.377189	+	0.653311i
$239$	−2.71108	−	4.69573i	−0.175365	−	0.303741i	0.764922	−	0.644122i	$-0.222777\pi$
$239$	−2.71108	−	4.69573i	−0.175365	−	0.303741i	−0.940288	+	0.340381i	$0.889444\pi$
$240$	−3.86667	−	0.221066i	−0.249592	−	0.0142698i
$241$	−19.9045	−	11.4919i	−1.28216	−	0.740257i	−0.304919	−	0.952378i	$-0.598629\pi$
$241$	−19.9045	−	11.4919i	−1.28216	−	0.740257i	−0.977243	+	0.212122i	$0.931963\pi$
$242$	−14.8648	+	25.7466i	−0.955548	+	1.65506i
$243$	−14.1799	+	6.47542i	−0.909640	+	0.415398i
$244$		−	4.65692i		−	0.298129i
$245$	−8.16873	+	6.81051i	−0.521881	+	0.435108i
$246$	1.09263	+	3.59426i	0.0696635	+	0.229162i
$247$	5.95449			0.378875
$248$	1.79672	+	5.26989i	0.114092	+	0.334639i
$249$	6.94947	+	22.8607i	0.440405	+	1.44873i
$250$	−5.49813	−	9.73502i	−0.347732	−	0.615696i
$251$	−3.90398	+	6.76189i	−0.246417	+	0.426806i	−0.962529	−	0.271179i	$-0.912587\pi$
$251$	−3.90398	+	6.76189i	−0.246417	+	0.426806i	0.716112	+	0.697985i	$0.245920\pi$
$252$	5.72483	+	8.54593i	0.360631	+	0.538343i
$253$	7.08243	−	4.08904i	0.445268	−	0.257076i
$254$	5.17437	−	8.96227i	0.324669	−	0.562343i
$255$	10.9909	+	7.21203i	0.688277	+	0.451635i
$256$	1.00000			0.0625000
$257$	6.11433	+	10.5903i	0.381401	+	0.660606i	0.991263	−	0.131902i	$-0.0421083\pi$
$257$	6.11433	+	10.5903i	0.381401	+	0.660606i	−0.609862	+	0.792508i	$0.708775\pi$
$258$	10.4450	+	9.77122i	0.650277	+	0.608330i
$259$	14.7222	−	8.49987i	0.914794	−	0.528156i
$260$	1.55444	−	1.29598i	0.0964020	−	0.0803732i
$261$	5.47256	+	2.69073i	0.338743	+	0.166552i
$262$	14.6750	+	8.47260i	0.906623	+	0.523439i
$263$		−	11.4714i		−	0.707359i	−0.935367	−	0.353679i	$-0.884930\pi$
$263$		−	11.4714i		−	0.707359i	0.935367	−	0.353679i	$-0.115070\pi$
$264$	−10.5760	+	3.21504i	−0.650910	+	0.197872i
$265$	−12.5806	−	15.0895i	−0.772819	−	0.926943i
$266$	19.5355	−	11.2788i	1.19780	−	0.691549i
$267$	−2.02201	+	8.69519i	−0.123745	+	0.532137i
$268$	0.0466974	−	0.0269608i	0.00285250	−	0.00164689i
$269$	−3.40220	−	5.89278i	−0.207436	−	0.359289i	0.743470	−	0.668769i	$-0.233178\pi$
$269$	−3.40220	−	5.89278i	−0.207436	−	0.359289i	−0.950906	+	0.309480i	$0.899845\pi$
$270$	10.1172	+	5.71340i	0.615711	+	0.347706i
$271$			31.7105i			1.92628i	0.269005	+	0.963139i	$0.413305\pi$
$271$			31.7105i			1.92628i	−0.269005	+	0.963139i	$0.586695\pi$
$272$	−2.93950	−	1.69712i	−0.178233	−	0.102903i
$273$	−5.23535	−	1.21745i	−0.316858	−	0.0736833i
$274$	−7.94537	+	4.58726i	−0.479997	+	0.277127i
$275$	−24.3143	−	20.6654i	−1.46621	−	1.24617i
$276$	2.16183	+	0.502719i	0.130127	+	0.0302601i
$277$	−28.8854			−1.73555			−0.867777	−	0.496954i	$-0.834452\pi$
$277$	−28.8854			−1.73555			−0.867777	+	0.496954i	$0.834452\pi$
$278$			18.2894i			1.09692i
$279$	2.13856	−	16.5658i	0.128033	−	0.991770i
$280$	2.64499	−	7.19621i	0.158068	−	0.430056i
$281$		−	7.77372i		−	0.463741i	−0.972747	−	0.231871i	$-0.925515\pi$
$281$		−	7.77372i		−	0.463741i	0.972747	−	0.231871i	$-0.0744846\pi$
$282$	−0.701899	+	3.01835i	−0.0417975	+	0.179740i
$283$			17.5057i			1.04060i	0.853982	+	0.520302i	$0.174181\pi$
$283$			17.5057i			1.04060i	−0.853982	+	0.520302i	$0.825819\pi$
$284$	9.80635	−	5.66170i	0.581900	−	0.335960i
$285$	13.9789	−	21.3034i	0.828039	−	1.26190i
$286$	2.88810	−	5.00233i	0.170777	−	0.295794i
$287$	−7.43665			−0.438972
$288$	−2.69219	−	1.32368i	−0.158639	−	0.0779988i
$289$	−2.73956	−	4.74505i	−0.161150	−	0.279121i
$290$	−0.775149	−	4.47880i	−0.0455183	−	0.263004i
$291$	−24.9102	−	5.79270i	−1.46026	−	0.339574i
$292$	5.91441	+	10.2441i	0.346115	+	0.599488i
$293$	8.96242	−	15.5234i	0.523590	−	0.906885i	−0.476033	−	0.879427i	$-0.657926\pi$
$293$	8.96242	−	15.5234i	0.523590	−	0.906885i	0.999623	−	0.0274571i	$-0.00874097\pi$
$294$	−7.88198	+	2.39606i	−0.459687	+	0.139741i
$295$	2.13244	−	5.80172i	0.124155	−	0.337789i
$296$	−2.47900	+	4.29376i	−0.144089	+	0.249570i
$297$	32.7283	+	5.34385i	1.89909	+	0.310082i
$298$	−13.6580	−	7.88548i	−0.791189	−	0.456793i
$299$	−1.00441	+	0.579899i	−0.0580868	+	0.0335364i
$300$	−0.987394	−	8.60378i	−0.0570072	−	0.496740i
$301$	−24.5206	+	14.1570i	−1.41334	+	0.815995i
$302$			1.96141i			0.112867i
$303$	−20.6788	−	4.80873i	−1.18797	−	0.276254i
$304$	−3.28949	+	5.69756i	−0.188665	+	0.326778i
$305$	10.2607	−	1.77582i	0.587524	−	0.101683i
$306$	5.66723	+	8.45993i	0.323974	+	0.483622i
$307$	6.41230	+	3.70214i	0.365969	+	0.211292i	0.671696	−	0.740827i	$-0.265566\pi$
$307$	6.41230	+	3.70214i	0.365969	+	0.211292i	−0.305727	+	0.952119i	$0.598899\pi$
$308$		−	21.8822i		−	1.24685i
$309$	−2.85554	−	9.39347i	−0.162446	−	0.534376i
$310$	−10.9261	+	5.96830i	−0.620560	+	0.338977i
$311$			7.06882i			0.400836i	0.979710	+	0.200418i	$0.0642300\pi$
$311$			7.06882i			0.400836i	−0.979710	+	0.200418i	$0.935770\pi$
$312$	1.49987	−	0.455949i	0.0849134	−	0.0258130i
$313$	−9.11672	+	15.7906i	−0.515308	+	0.892539i	0.484535	+	0.874772i	$0.338989\pi$
$313$	−9.11672	+	15.7906i	−0.515308	+	0.892539i	−0.999842	+	0.0177668i	$0.994344\pi$
$314$		−	6.06530i		−	0.342285i
$315$	−16.6463	+	15.8724i	−0.937913	+	0.894309i
$316$	3.12853	+	1.80626i	0.175993	+	0.101610i
$317$	4.15118	−	7.19006i	0.233154	−	0.403834i	−0.725581	−	0.688137i	$-0.758429\pi$
$317$	4.15118	−	7.19006i	0.233154	−	0.403834i	0.958734	+	0.284303i	$0.0917622\pi$
$318$	−4.42608	−	14.5598i	−0.248202	−	0.816475i
$319$	−6.48651	−	11.2350i	−0.363175	−	0.629037i
$320$	0.381329	+	2.20331i	0.0213169	+	0.123169i
$321$	−2.27683	−	2.12996i	−0.127080	−	0.118883i
$322$	−2.19685	+	3.80506i	−0.122426	+	0.212048i
$323$	19.3389	−	11.1653i	1.07605	−	0.621256i
$324$	5.49573	+	7.12720i	0.305318	+	0.395956i
$325$	3.44820	+	2.93072i	0.191272	+	0.162567i
$326$			1.25379i			0.0694410i
$327$	−4.68524	+	20.1477i	−0.259094	+	1.11417i
$328$	1.87833	−	1.08446i	0.103714	−	0.0598791i
$329$	−5.31265	−	3.06726i	−0.292896	−	0.169103i
$330$	−11.1167	−	22.0763i	−0.611953	−	1.21526i
$331$	−14.6191	+	8.44036i	−0.803540	+	0.463924i	−0.844708	−	0.535228i	$-0.820226\pi$
$331$	−14.6191	+	8.44036i	−0.803540	+	0.463924i	0.0411672	+	0.999152i	$0.486892\pi$
$332$	11.9468	−	6.89749i	0.655666	−	0.378549i
$333$	12.3575	−	8.27819i	0.677188	−	0.453642i
$334$	10.2810	+	5.93575i	0.562552	+	0.324790i
$335$	0.0772100	+	0.0926081i	0.00421844	+	0.00505972i
$336$	4.05713	−	4.33689i	0.221334	−	0.236597i
$337$	−26.7132			−1.45516			−0.727580	−	0.686023i	$-0.759355\pi$
$337$	−26.7132			−1.45516			−0.727580	+	0.686023i	$0.759355\pi$
$338$	6.09042	−	10.5489i	0.331275	−	0.573785i
$339$	−27.6655	+	8.41012i	−1.50259	+	0.456775i
$340$	2.61837	−	7.12380i	0.142001	−	0.386342i
$341$	−23.3932	+	26.7466i	−1.26681	+	1.44841i
$342$	16.3977	−	10.9847i	0.886685	−	0.593982i
$343$			7.69312i			0.415390i
$344$	4.12891	−	7.15148i	0.222616	−	0.385582i
$345$	−0.283282	+	4.95488i	−0.0152514	+	0.266762i
$346$	−11.6604	−	20.1964i	−0.626866	−	1.08576i
$347$	−17.9299	−	10.3518i	−0.962526	−	0.555714i	−0.0655762	−	0.997848i	$-0.520889\pi$
$347$	−17.9299	−	10.3518i	−0.962526	−	0.555714i	−0.896949	+	0.442133i	$0.854222\pi$
$348$	0.797471	−	3.42934i	0.0427489	−	0.183832i
$349$	29.0198			1.55339			0.776697	−	0.629875i	$-0.216894\pi$
$349$	29.0198			1.55339			0.776697	+	0.629875i	$0.216894\pi$
$350$	16.8641	+	3.08361i	0.901425	+	0.164826i
$351$	−4.64146	−	0.757853i	−0.247743	−	0.0404512i
$352$	3.19099	+	5.52696i	0.170080	+	0.294588i
$353$	−13.3349	−	7.69893i	−0.709747	−	0.409773i	0.101220	−	0.994864i	$-0.467725\pi$
$353$	−13.3349	−	7.69893i	−0.709747	−	0.409773i	−0.810967	+	0.585091i	$0.801059\pi$
$354$	3.27093	−	3.49648i	0.173848	−	0.185836i
$355$	16.2139	+	19.4475i	0.860547	+	1.03217i
$356$	5.15412			0.273168
$357$	−19.2862	+	5.86285i	−1.02073	+	0.310295i
$358$	5.70902	−	9.88831i	0.301731	−	0.522613i
$359$	11.0965	−	6.40655i	0.585649	−	0.338125i	−0.177726	−	0.984080i	$-0.556874\pi$
$359$	11.0965	−	6.40655i	0.585649	−	0.338125i	0.763375	+	0.645955i	$0.223541\pi$
$360$	1.88988	−	6.43649i	0.0996055	−	0.339233i
$361$	−12.1415	−	21.0297i	−0.639026	−	1.10683i
$362$	0.120326	−	0.0694702i	0.00632419	−	0.00365127i
$363$	−37.6039	−	35.1782i	−1.97369	−	1.84638i
$364$			3.10328i			0.162656i
$365$	−20.3155	+	16.9376i	−1.06336	+	0.886557i
$366$	7.85640	+	1.82696i	0.410661	+	0.0954966i
$367$	0.284663	+	0.493050i	0.0148593	+	0.0257370i	0.873359	−	0.487076i	$-0.161937\pi$
$367$	0.284663	+	0.493050i	0.0148593	+	0.0257370i	−0.858500	+	0.512813i	$0.828603\pi$
$368$		−	1.28143i		−	0.0667993i
$369$	−6.49230	+	0.433239i	−0.337976	+	0.0225535i
$370$	−10.4058	−	3.82469i	−0.540973	−	0.198836i
$371$	30.1248			1.56400
$372$	−9.59538	+	0.963701i	−0.497497	+	0.0499656i
$373$		−	26.2391i		−	1.35861i	−0.733855	−	0.679306i	$-0.762281\pi$
$373$		−	26.2391i		−	1.35861i	0.733855	−	0.679306i	$-0.237719\pi$
$374$		−	21.6620i		−	1.12012i
$375$	18.5803	−	5.45641i	0.959483	−	0.281768i
$376$	1.78914			0.0922681
$377$	0.919902	+	1.59332i	0.0473774	+	0.0820600i
$378$	−16.6632	+	6.30535i	−0.857063	+	0.324312i
$379$	7.36256	−	12.7523i	0.378189	−	0.655043i	−0.612609	−	0.790386i	$-0.709880\pi$
$379$	7.36256	−	12.7523i	0.378189	−	0.655043i	0.990799	+	0.135343i	$0.0432135\pi$
$380$	−13.8079	−	5.07513i	−0.708330	−	0.260349i
$381$	13.0897	+	12.2453i	0.670607	+	0.627348i
$382$	11.0681	−	6.39017i	0.566293	−	0.326949i
$383$	−15.9925	+	9.23329i	−0.817180	+	0.471799i	−0.849443	−	0.527681i	$-0.823062\pi$
$383$	−15.9925	+	9.23329i	−0.817180	+	0.471799i	0.0322633	+	0.999479i	$0.489728\pi$
$384$	−0.392310	+	1.68704i	−0.0200200	+	0.0860912i
$385$	48.2133	−	8.34430i	2.45718	−	0.425265i
$386$	9.22586	+	5.32655i	0.469584	+	0.271114i
$387$	−20.5821	+	13.7878i	−1.04625	+	0.700871i
$388$			14.7656i			0.749611i
$389$	7.48029	−	12.9562i	0.379266	−	0.656907i	−0.611690	−	0.791098i	$-0.709510\pi$
$389$	7.48029	−	12.9562i	0.379266	−	0.656907i	0.990956	+	0.134190i	$0.0428433\pi$
$390$	1.57654	+	3.13082i	0.0798313	+	0.158535i
$391$	−2.17475	+	3.76677i	−0.109982	+	0.190494i
$392$	2.37814	+	4.11906i	0.120114	+	0.208044i
$393$	−20.0507	+	21.4333i	−1.01143	+	1.08117i
$394$	21.2751	−	12.2832i	1.07182	−	0.618817i
$395$	−2.78675	+	7.58191i	−0.140217	+	0.381487i
$396$	−1.27480	−	19.1035i	−0.0640610	−	0.959985i
$397$	9.37611	+	5.41330i	0.470574	+	0.271686i	0.716480	−	0.697608i	$-0.245752\pi$
$397$	9.37611	+	5.41330i	0.470574	+	0.271686i	−0.245906	+	0.969294i	$0.579086\pi$
$398$	−1.07789	+	0.622319i	−0.0540297	+	0.0311940i
$399$	11.3638	+	37.3819i	0.568902	+	1.87143i
$400$	−4.70918	+	1.68037i	−0.235459	+	0.0840187i
$401$	15.2743			0.762762			0.381381	−	0.924418i	$-0.375449\pi$
$401$	15.2743			0.762762			0.381381	+	0.924418i	$0.375449\pi$
$402$	0.0271639	+	0.0893572i	0.00135481	+	0.00445673i
$403$	3.31757	−	3.79314i	0.165260	−	0.188950i
$404$			12.2575i			0.609832i
$405$	−13.6078	+	14.8266i	−0.676176	+	0.736740i
$406$	6.03603	+	3.48490i	0.299563	+	0.172953i
$407$	−31.6419			−1.56843
$408$	4.01630	−	4.29325i	0.198837	−	0.212547i
$409$	8.93038	+	5.15596i	0.441579	+	0.254946i	0.704267	−	0.709935i	$-0.251276\pi$
$409$	8.93038	+	5.15596i	0.441579	+	0.254946i	−0.262688	+	0.964881i	$0.584609\pi$
$410$	3.10566	+	3.72502i	0.153378	+	0.183966i
$411$	−4.62183	−	15.2038i	−0.227978	−	0.749946i
$412$	−4.90895	+	2.83419i	−0.241847	+	0.139630i
$413$	4.73906	+	8.20830i	0.233194	+	0.403904i
$414$	−1.69621	+	3.44986i	−0.0833643	+	0.169551i
$415$	19.7530	+	23.6923i	0.969636	+	1.16301i
$416$	−0.452539	−	0.783821i	−0.0221876	−	0.0384300i
$417$	−30.8548	−	7.17511i	−1.51097	−	0.351366i
$418$	−41.9869			−2.05365
$419$			21.4031i			1.04561i	0.852452	+	0.522806i	$0.175115\pi$
$419$			21.4031i			1.04561i	−0.852452	+	0.522806i	$0.824885\pi$
$420$	11.1026	+	7.28534i	0.541752	+	0.355488i
$421$	9.22392	+	15.9763i	0.449546	+	0.778637i	0.998356	−	0.0573100i	$-0.0182524\pi$
$421$	9.22392	+	15.9763i	0.449546	+	0.778637i	−0.548810	+	0.835947i	$0.684919\pi$
$422$	13.9957	−	24.2412i	0.681298	−	1.18004i
$423$	−4.81671	−	2.36826i	−0.234196	−	0.115149i
$424$	−7.60886	+	4.39298i	−0.369519	+	0.213342i
$425$	16.6944	+	3.05259i	0.809799	+	0.148072i
$426$	5.70436	+	18.7648i	0.276377	+	0.909158i
$427$	−7.98370	+	13.8282i	−0.386358	+	0.669192i
$428$	−0.900033	+	1.55890i	−0.0435047	+	0.0753524i
$429$	7.30608	+	6.83479i	0.352741	+	0.329987i
$430$	17.3314	+	6.37022i	0.835796	+	0.307199i
$431$	−10.6515	−	6.14966i	−0.513066	−	0.296219i	0.221027	−	0.975268i	$-0.429059\pi$
$431$	−10.6515	−	6.14966i	−0.513066	−	0.296219i	−0.734093	+	0.679049i	$0.762392\pi$
$432$	3.28927	−	4.02252i	0.158255	−	0.193534i
$433$	−34.2578			−1.64632			−0.823162	−	0.567807i	$-0.807792\pi$
$433$	−34.2578			−1.64632			−0.823162	+	0.567807i	$0.807792\pi$
$434$	3.69941	−	18.7286i	0.177578	−	0.899000i
$435$	7.86000	+	0.449374i	0.376858	+	0.0215458i
$436$	11.9427			0.571951
$437$	7.30105	+	4.21526i	0.349257	+	0.201643i
$438$	−19.6024	+	5.95898i	−0.936638	+	0.284731i
$439$	8.21787	+	14.2338i	0.392218	+	0.679341i	0.992742	−	0.120266i	$-0.0383747\pi$
$439$	8.21787	+	14.2338i	0.392218	+	0.679341i	−0.600524	+	0.799607i	$0.705041\pi$
$440$	−10.9608	+	9.13834i	−0.522536	+	0.435653i
$441$	−0.950066	−	14.2372i	−0.0452412	−	0.677962i
$442$			3.07206i			0.146123i
$443$	3.14960	+	5.45527i	0.149642	+	0.259188i	0.931095	−	0.364776i	$-0.118854\pi$
$443$	3.14960	+	5.45527i	0.149642	+	0.259188i	−0.781453	+	0.623964i	$0.785521\pi$
$444$	−6.27120	−	5.86666i	−0.297618	−	0.278419i
$445$	1.96541	+	11.3561i	0.0931696	+	0.538333i
$446$	0.843359	−	1.46074i	0.0399342	−	0.0691680i
$447$	18.6613	−	19.9481i	0.882648	−	0.943511i
$448$	−2.96938	−	1.71437i	−0.140290	−	0.0809965i
$449$	26.3801			1.24495			0.622476	−	0.782639i	$-0.286127\pi$
$449$	26.3801			1.24495			0.622476	+	0.782639i	$0.286127\pi$
$450$	14.9023	+	1.70958i	0.702499	+	0.0805904i
$451$	11.9875	+	6.92098i	0.564469	+	0.325896i
$452$	8.34722	+	14.4578i	0.392620	+	0.680038i
$453$	−3.30897	−	0.769482i	−0.155469	−	0.0361534i
$454$	4.42782	+	7.66921i	0.207808	+	0.359934i
$455$	−6.83750	+	1.18337i	−0.320547	+	0.0554773i
$456$	−8.32150	−	7.78470i	−0.389690	−	0.364552i
$457$	−39.1752			−1.83254			−0.916270	−	0.400561i	$-0.868815\pi$
$457$	−39.1752			−1.83254			−0.916270	+	0.400561i	$0.868815\pi$
$458$	−15.4179	−	8.90151i	−0.720430	−	0.415940i
$459$	−16.4955	+	6.24191i	−0.769945	+	0.291347i
$460$	2.82340	−	0.488647i	0.131642	−	0.0227833i
$461$	0.0357305			0.00166413			0.000832067	−	1.00000i	$-0.499735\pi$
$461$	0.0357305			0.00166413			0.000832067		1.00000i	$0.499735\pi$
$462$	36.9160	+	8.58460i	1.71749	+	0.399392i
$463$	−8.82365			−0.410070			−0.205035	−	0.978755i	$-0.565731\pi$
$463$	−8.82365			−0.410070			−0.205035	+	0.978755i	$0.565731\pi$
$464$	−2.03276			−0.0943684
$465$	−5.78233	−	20.7741i	−0.268149	−	0.963377i
$466$	−0.695815			−0.0322330
$467$	−5.63272			−0.260651			−0.130326	−	0.991471i	$-0.541602\pi$
$467$	−5.63272			−0.260651			−0.130326	+	0.991471i	$0.541602\pi$
$468$	0.180789	+	2.70921i	0.00835697	+	0.125233i
$469$	−0.184883			−0.00853711
$470$	0.682252	+	3.94205i	0.0314699	+	0.181833i
$471$	10.2324	+	2.37948i	0.471484	+	0.109641i
$472$	−2.39397	−	1.38216i	−0.110191	−	0.0636190i
$473$	52.7013			2.42321
$474$	−4.27457	+	4.56933i	−0.196338	+	0.209876i
$475$	5.91676	−	32.3584i	0.271479	−	1.48471i
$476$	5.81900	+	10.0788i	0.266713	+	0.461961i
$477$	26.2994	−	1.75499i	1.20417	−	0.0803555i
$478$	−2.71108	−	4.69573i	−0.124002	−	0.214778i
$479$	−16.0091	−	9.24288i	−0.731476	−	0.422318i	0.0874856	−	0.996166i	$-0.472117\pi$
$479$	−16.0091	−	9.24288i	−0.731476	−	0.422318i	−0.818962	+	0.573848i	$0.805450\pi$
$480$	−3.86667	−	0.221066i	−0.176488	−	0.0100903i
$481$	4.48739			0.204607
$482$	−19.9045	−	11.4919i	−0.906626	−	0.523441i
$483$	−5.55743	−	5.19894i	−0.252872	−	0.236560i
$484$	−14.8648	+	25.7466i	−0.675674	+	1.17030i
$485$	−32.5333	+	5.63056i	−1.47726	+	0.255670i
$486$	−14.1799	+	6.47542i	−0.643212	+	0.293731i
$487$	−4.58796	−	7.94657i	−0.207900	−	0.360094i	0.743153	−	0.669122i	$-0.233330\pi$
$487$	−4.58796	−	7.94657i	−0.207900	−	0.360094i	−0.951053	+	0.309028i	$0.899996\pi$
$488$		−	4.65692i		−	0.210809i
$489$	−2.11519	−	0.491874i	−0.0956522	−	0.0222433i
$490$	−8.16873	+	6.81051i	−0.369026	+	0.307668i
$491$	−1.65595	−	2.86819i	−0.0747321	−	0.129440i	0.826238	−	0.563322i	$-0.190477\pi$
$491$	−1.65595	−	2.86819i	−0.0747321	−	0.129440i	−0.900970	+	0.433882i	$0.857143\pi$
$492$	1.09263	+	3.59426i	0.0492595	+	0.162042i
$493$	5.97529	+	3.44984i	0.269114	+	0.155373i
$494$	5.95449			0.267905
$495$	41.6048	−	10.0935i	1.87000	−	0.453668i
$496$	1.79672	+	5.26989i	0.0806752	+	0.236625i
$497$	−38.8250			−1.74154
$498$	6.94947	+	22.8607i	0.311413	+	1.02441i
$499$	−18.6560	−	10.7710i	−0.835156	−	0.482177i	0.0204589	−	0.999791i	$-0.493487\pi$
$499$	−18.6560	−	10.7710i	−0.835156	−	0.482177i	−0.855615	+	0.517613i	$0.826821\pi$
$500$	−5.49813	−	9.73502i	−0.245884	−	0.435363i
$501$	−14.0472	+	15.0158i	−0.627581	+	0.670856i
$502$	−3.90398	+	6.76189i	−0.174243	+	0.301798i
$503$	17.3799	−	30.1028i	0.774930	−	1.34222i	−0.159904	−	0.987133i	$-0.551119\pi$
$503$	17.3799	−	30.1028i	0.774930	−	1.34222i	0.934834	−	0.355085i	$-0.115548\pi$
$504$	5.72483	+	8.54593i	0.255004	+	0.380666i
$505$	−27.0070	+	4.67412i	−1.20180	+	0.207996i
$506$	7.08243	−	4.08904i	0.314852	−	0.181780i
$507$	15.4071	+	14.4132i	0.684252	+	0.640113i
$508$	5.17437	−	8.96227i	0.229576	−	0.397637i
$509$	9.19595	+	15.9279i	0.407603	+	0.705990i	0.994621	−	0.103585i	$-0.0330313\pi$
$509$	9.19595	+	15.9279i	0.407603	+	0.705990i	−0.587017	+	0.809574i	$0.699698\pi$
$510$	10.9909	+	7.21203i	0.486685	+	0.319354i
$511$		−	40.5580i		−	1.79418i
$512$	1.00000			0.0441942
$513$	12.0985	+	31.9729i	0.534164	+	1.41164i
$514$	6.11433	+	10.5903i	0.269691	+	0.467119i
$515$	−8.11653	−	9.73521i	−0.357657	−	0.428984i
$516$	10.4450	+	9.77122i	0.459816	+	0.430154i
$517$	5.70914	+	9.88852i	0.251088	+	0.434897i
$518$	14.7222	−	8.49987i	0.646857	−	0.373463i
$519$	38.6465	−	11.7483i	1.69639	−	0.515691i
$520$	1.55444	−	1.29598i	0.0681665	−	0.0568324i
$521$	−33.3768	−	19.2701i	−1.46226	−	0.844238i	−0.463148	−	0.886281i	$-0.653280\pi$
$521$	−33.3768	−	19.2701i	−1.46226	−	0.844238i	−0.999116	+	0.0420428i	$0.986613\pi$
$522$	5.47256	+	2.69073i	0.239527	+	0.117770i
$523$	37.8881			1.65673			0.828365	−	0.560189i	$-0.189271\pi$
$523$	37.8881			1.65673			0.828365	+	0.560189i	$0.189271\pi$
$524$	14.6750	+	8.47260i	0.641079	+	0.370127i
$525$	−11.8181	+	27.2407i	−0.515786	+	1.18888i
$526$		−	11.4714i		−	0.500178i
$527$	3.66219	−	18.5401i	0.159527	−	0.807620i
$528$	−10.5760	+	3.21504i	−0.460263	+	0.139916i
$529$	21.3579			0.928606
$530$	−12.5806	−	15.0895i	−0.546466	−	0.655447i
$531$	4.61546	+	6.88988i	0.200294	+	0.298995i
$532$	19.5355	−	11.2788i	0.846971	−	0.488999i
$533$	−1.70004	−	0.981518i	−0.0736369	−	0.0425143i
$534$	−2.02201	+	8.69519i	−0.0875011	+	0.376278i
$535$	−3.77796	−	1.38860i	−0.163335	−	0.0600344i
$536$	0.0466974	−	0.0269608i	0.00201702	−	0.00116453i
$537$	14.4422	+	13.5106i	0.623228	+	0.583026i
$538$	−3.40220	−	5.89278i	−0.146679	−	0.254056i
$539$	−15.1773	+	26.2878i	−0.653731	+	1.13230i
$540$	10.1172	+	5.71340i	0.435374	+	0.245865i
$541$	7.72420	−	13.3787i	0.332089	−	0.575196i	−0.650832	−	0.759222i	$-0.725580\pi$
$541$	7.72420	−	13.3787i	0.332089	−	0.575196i	0.982921	+	0.184026i	$0.0589131\pi$
$542$			31.7105i			1.36208i
$543$	0.0699937	+	0.230248i	0.00300372	+	0.00988089i
$544$	−2.93950	−	1.69712i	−0.126030	−	0.0727635i
$545$	4.55409	+	26.3135i	0.195076	+	1.12715i
$546$	−5.23535	−	1.21745i	−0.224052	−	0.0521020i
$547$	−0.0188280	+	0.0108704i	−0.000805029	+	0.000464784i	−0.500402	−	0.865793i	$-0.666815\pi$
$547$	−0.0188280	+	0.0108704i	−0.000805029	+	0.000464784i	0.499597	+	0.866258i	$0.333481\pi$
$548$	−7.94537	+	4.58726i	−0.339409	+	0.195958i
$549$	−6.16429	+	12.5373i	−0.263086	+	0.535079i
$550$	−24.3143	−	20.6654i	−1.03676	−	0.881174i
$551$	6.68673	−	11.5818i	0.284864	−	0.493400i
$552$	2.16183	+	0.502719i	0.0920134	+	0.0213972i
$553$	−6.19319	−	10.7269i	−0.263361	−	0.456155i
$554$	−28.8854			−1.22722
$555$	10.5347	−	16.0545i	0.447173	−	0.681477i
$556$			18.2894i			0.775642i
$557$			6.44159i			0.272939i	0.990644	+	0.136469i	$0.0435755\pi$
$557$			6.44159i			0.272939i	−0.990644	+	0.136469i	$0.956424\pi$
$558$	2.13856	−	16.5658i	0.0905327	−	0.701287i
$559$	−7.47397			−0.316115
$560$	2.64499	−	7.19621i	0.111771	−	0.304095i
$561$	36.5446	+	8.49822i	1.54291	+	0.358795i
$562$		−	7.77372i		−	0.327915i
$563$	−0.125330	−	0.217078i	−0.00528203	−	0.00914874i	0.863372	−	0.504567i	$-0.168348\pi$
$563$	−0.125330	−	0.217078i	−0.00528203	−	0.00914874i	−0.868654	+	0.495419i	$0.835015\pi$
$564$	−0.701899	+	3.01835i	−0.0295553	+	0.127096i
$565$	−28.6720	+	23.9047i	−1.20624	+	1.00568i
$566$			17.5057i			0.735818i
$567$	−4.10022	−	30.5851i	−0.172193	−	1.28445i
$568$	9.80635	−	5.66170i	0.411465	−	0.237560i
$569$	0.964911	+	1.67127i	0.0404512	+	0.0700635i	0.885542	−	0.464559i	$-0.153787\pi$
$569$	0.964911	+	1.67127i	0.0404512	+	0.0700635i	−0.845091	+	0.534622i	$0.820454\pi$
$570$	13.9789	−	21.3034i	0.585512	−	0.892301i
$571$	−28.1429	+	16.2483i	−1.17774	+	0.679970i	−0.955491	−	0.295020i	$-0.904674\pi$
$571$	−28.1429	+	16.2483i	−1.17774	+	0.679970i	−0.222251	+	0.974990i	$0.571340\pi$
$572$	2.88810	−	5.00233i	0.120757	−	0.209158i
$573$	6.43832	+	21.1792i	0.268965	+	0.884774i
$574$	−7.43665			−0.310400
$575$	2.15329	+	6.03450i	0.0897983	+	0.251656i
$576$	−2.69219	−	1.32368i	−0.112174	−	0.0551535i
$577$	−8.97782	−	5.18335i	−0.373752	−	0.215786i	0.301345	−	0.953515i	$-0.402565\pi$
$577$	−8.97782	−	5.18335i	−0.373752	−	0.215786i	−0.675096	+	0.737730i	$0.735898\pi$
$578$	−2.73956	−	4.74505i	−0.113951	−	0.197368i
$579$	−12.6055	+	13.4747i	−0.523866	+	0.559989i
$580$	−0.775149	−	4.47880i	−0.0321863	−	0.185972i
$581$	−47.2995			−1.96231
$582$	−24.9102	−	5.79270i	−1.03256	−	0.240115i
$583$	−48.5596	−	28.0359i	−2.01113	−	1.16113i
$584$	5.91441	+	10.2441i	0.244740	+	0.423902i
$585$	−5.90030	+	1.43143i	−0.243947	+	0.0591825i
$586$	8.96242	−	15.5234i	0.370234	−	0.641264i
$587$			34.7319i			1.43354i	0.697310	+	0.716770i	$0.254380\pi$
$587$			34.7319i			1.43354i	−0.697310	+	0.716770i	$0.745620\pi$
$588$	−7.88198	+	2.39606i	−0.325047	+	0.0988120i
$589$	−35.9359	−	7.09833i	−1.48071	−	0.292482i
$590$	2.13244	−	5.80172i	0.0877911	−	0.238853i
$591$	12.3757	+	40.7106i	0.509069	+	1.67461i
$592$	−2.47900	+	4.29376i	−0.101886	+	0.176473i
$593$	34.6846			1.42432			0.712162	−	0.702015i	$-0.247716\pi$
$593$	34.6846			1.42432			0.712162	+	0.702015i	$0.247716\pi$
$594$	32.7283	+	5.34385i	1.34286	+	0.219261i
$595$	−19.9878	+	16.6644i	−0.819420	+	0.683174i
$596$	−13.6580	−	7.88548i	−0.559455	−	0.323002i
$597$	−0.627009	−	2.06258i	−0.0256618	−	0.0844158i
$598$	−1.00441	+	0.579899i	−0.0410735	+	0.0237138i
$599$	15.6420	−	9.03093i	0.639116	−	0.368994i	−0.145158	−	0.989409i	$-0.546369\pi$
$599$	15.6420	−	9.03093i	0.639116	−	0.368994i	0.784274	+	0.620415i	$0.213036\pi$
$600$	−0.987394	−	8.60378i	−0.0403102	−	0.351248i
$601$	−30.2679	−	17.4752i	−1.23465	−	0.712826i	−0.266656	−	0.963792i	$-0.585919\pi$
$601$	−30.2679	−	17.4752i	−1.23465	−	0.712826i	−0.967996	+	0.250965i	$0.919252\pi$
$602$	−24.5206	+	14.1570i	−0.999385	+	0.576995i
$603$	−0.161406	+	0.0107708i	−0.00657294	+	0.000438621i
$604$			1.96141i			0.0798087i
$605$	−62.3963	−	22.9339i	−2.53677	−	0.932398i
$606$	−20.6788	−	4.80873i	−0.840018	−	0.195341i
$607$	−28.2525	+	16.3116i	−1.14674	+	0.662068i	−0.948090	−	0.318004i	$-0.896988\pi$
$607$	−28.2525	+	16.3116i	−1.14674	+	0.662068i	−0.198646	+	0.980071i	$0.563654\pi$
$608$	−3.28949	+	5.69756i	−0.133406	+	0.231067i
$609$	−8.24715	+	8.81584i	−0.334191	+	0.357236i
$610$	10.2607	−	1.77582i	0.415442	−	0.0719008i
$611$	−0.809658	−	1.40237i	−0.0327552	−	0.0567338i
$612$	5.66723	+	8.45993i	0.229084	+	0.341973i
$613$	−10.9824	+	19.0221i	−0.443576	+	0.768296i	−0.997952	−	0.0639701i	$-0.979624\pi$
$613$	−10.9824	+	19.0221i	−0.443576	+	0.768296i	0.554376	+	0.832267i	$0.312957\pi$
$614$	6.41230	+	3.70214i	0.258779	+	0.149406i
$615$	−7.50264	+	3.77800i	−0.302535	+	0.152344i
$616$		−	21.8822i		−	0.881658i
$617$	1.14669	−	1.98612i	0.0461639	−	0.0799581i	−0.842020	−	0.539446i	$-0.818634\pi$
$617$	1.14669	−	1.98612i	0.0461639	−	0.0799581i	0.888184	+	0.459488i	$0.151967\pi$
$618$	−2.85554	−	9.39347i	−0.114867	−	0.377861i
$619$		−	16.1427i		−	0.648830i	−0.945915	−	0.324415i	$-0.894833\pi$
$619$		−	16.1427i		−	0.648830i	0.945915	−	0.324415i	$-0.105167\pi$
$620$	−10.9261	+	5.96830i	−0.438802	+	0.239693i
$621$	−5.15459	−	4.21499i	−0.206847	−	0.169142i
$622$			7.06882i			0.283434i
$623$	−15.3045	−	8.83608i	−0.613163	−	0.354010i
$624$	1.49987	−	0.455949i	0.0600428	−	0.0182526i
$625$	19.3527	−	15.8263i	0.774108	−	0.633054i
$626$	−9.11672	+	15.7906i	−0.364377	+	0.631120i
$627$	16.4719	−	70.8335i	0.657824	−	2.82882i
$628$		−	6.06530i		−	0.242032i
$629$	14.5741	−	8.41434i	0.581106	−	0.335502i
$630$	−16.6463	+	15.8724i	−0.663205	+	0.632372i
$631$	31.2769	−	18.0577i	1.24511	−	0.718866i	0.274982	−	0.961449i	$-0.411328\pi$
$631$	31.2769	−	18.0577i	1.24511	−	0.718866i	0.970131	+	0.242583i	$0.0779948\pi$
$632$	3.12853	+	1.80626i	0.124446	+	0.0718490i
$633$	35.4052	+	33.1213i	1.40723	+	1.31645i
$634$	4.15118	−	7.19006i	0.164865	−	0.285554i
$635$	21.7198	+	7.98319i	0.861925	+	0.316803i
$636$	−4.42608	−	14.5598i	−0.175506	−	0.577335i
$637$	2.15241	−	3.72807i	0.0852814	−	0.147712i
$638$	−6.48651	−	11.2350i	−0.256803	−	0.444796i
$639$	−33.8948	+	2.26184i	−1.34086	+	0.0894771i
$640$	0.381329	+	2.20331i	0.0150733	+	0.0870936i
$641$	8.80615	+	15.2527i	0.347822	+	0.602445i	0.985862	−	0.167558i	$-0.0535880\pi$
$641$	8.80615	+	15.2527i	0.347822	+	0.602445i	−0.638040	+	0.770003i	$0.720255\pi$
$642$	−2.27683	−	2.12996i	−0.0898595	−	0.0840629i
$643$	−8.78010			−0.346253			−0.173127	−	0.984900i	$-0.555387\pi$
$643$	−8.78010			−0.346253			−0.173127	+	0.984900i	$0.555387\pi$
$644$	−2.19685	+	3.80506i	−0.0865682	+	0.149940i
$645$	−17.5461	+	26.7397i	−0.690876	+	1.05287i
$646$	19.3389	−	11.1653i	0.760880	−	0.439294i
$647$			34.8674i			1.37078i	0.728177	+	0.685389i	$0.240368\pi$
$647$			34.8674i			1.37078i	−0.728177	+	0.685389i	$0.759632\pi$
$648$	5.49573	+	7.12720i	0.215892	+	0.279983i
$649$		−	17.6418i		−	0.692501i
$650$	3.44820	+	2.93072i	0.135249	+	0.114952i
$651$	30.1445	+	13.5885i	1.18145	+	0.532573i
$652$			1.25379i			0.0491022i
$653$	16.8526			0.659492			0.329746	−	0.944070i	$-0.393037\pi$
$653$	16.8526			0.659492			0.329746	+	0.944070i	$0.393037\pi$
$654$	−4.68524	+	20.1477i	−0.183207	+	0.787839i
$655$	−13.0718	+	35.5644i	−0.510757	+	1.38962i
$656$	1.87833	−	1.08446i	0.0733367	−	0.0423409i
$657$	−2.36280	−	35.4077i	−0.0921816	−	1.38139i
$658$	−5.31265	−	3.06726i	−0.207109	−	0.119574i
$659$			9.17901i			0.357563i	0.983889	+	0.178782i	$0.0572156\pi$
$659$			9.17901i			0.357563i	−0.983889	+	0.178782i	$0.942784\pi$
$660$	−11.1167	−	22.0763i	−0.432716	−	0.859320i
$661$	16.5167	+	28.6077i	0.642425	+	1.11271i	0.984890	+	0.173182i	$0.0554048\pi$
$661$	16.5167	+	28.6077i	0.642425	+	1.11271i	−0.342465	+	0.939530i	$0.611262\pi$
$662$	−14.6191	+	8.44036i	−0.568189	+	0.328044i
$663$	−5.18267	−	1.20520i	−0.201278	−	0.0468060i
$664$	11.9468	−	6.89749i	0.463626	−	0.267675i
$665$	32.3002	+	38.7419i	1.25255	+	1.50234i
$666$	12.3575	−	8.27819i	0.478844	−	0.320773i
$667$			2.60484i			0.100860i
$668$	10.2810	+	5.93575i	0.397784	+	0.229661i
$669$	2.13346	+	1.99584i	0.0824845	+	0.0771636i
$670$	0.0772100	+	0.0926081i	0.00298288	+	0.00357776i
$671$	25.7386	−	14.8602i	0.993628	−	0.573671i
$672$	4.05713	−	4.33689i	0.156507	−	0.167299i
$673$	12.9425	+	22.4170i	0.498896	+	0.864113i	0.999999	−	0.00127433i	$-0.000405630\pi$
$673$	12.9425	+	22.4170i	0.498896	+	0.864113i	−0.501103	+	0.865388i	$0.667072\pi$
$674$	−26.7132			−1.02895
$675$	−8.73043	+	24.4700i	−0.336035	+	0.941850i
$676$	6.09042	−	10.5489i	0.234247	−	0.405727i
$677$	23.3498	−	13.4810i	0.897405	−	0.518117i	0.0210477	−	0.999778i	$-0.493300\pi$
$677$	23.3498	−	13.4810i	0.897405	−	0.518117i	0.876357	+	0.481661i	$0.159966\pi$
$678$	−27.6655	+	8.41012i	−1.06249	+	0.322989i
$679$	25.3138	−	43.8447i	0.971454	−	1.68261i
$680$	2.61837	−	7.12380i	0.100410	−	0.273185i
$681$	−14.6753	+	4.46119i	−0.562360	+	0.170953i
$682$	−23.3932	+	26.7466i	−0.895771	+	1.02418i
$683$	23.6261			0.904026			0.452013	−	0.892011i	$-0.350706\pi$
$683$	23.6261			0.904026			0.452013	+	0.892011i	$0.350706\pi$
$684$	16.3977	−	10.9847i	0.626981	−	0.420009i
$685$	−13.1370	−	15.7569i	−0.501938	−	0.602039i
$686$			7.69312i			0.293725i
$687$	21.0658	−	22.5184i	0.803709	−	0.859129i
$688$	4.12891	−	7.15148i	0.157413	−	0.272648i
$689$	6.88661	+	3.97599i	0.262359	+	0.151473i
$690$	−0.283282	+	4.95488i	−0.0107844	+	0.188629i
$691$	−21.2560	−	36.8165i	−0.808616	−	1.40056i	−0.913822	−	0.406114i	$-0.866884\pi$
$691$	−21.2560	−	36.8165i	−0.808616	−	1.40056i	0.105206	−	0.994450i	$-0.466450\pi$
$692$	−11.6604	−	20.1964i	−0.443261	−	0.767751i
$693$	−28.9651	+	58.9109i	−1.10029	+	2.23784i
$694$	−17.9299	−	10.3518i	−0.680608	−	0.392949i
$695$	−40.2972	+	6.97426i	−1.52856	+	0.264549i
$696$	0.797471	−	3.42934i	0.0302281	−	0.129989i
$697$	−7.36182			−0.278849
$698$	29.0198			1.09842
$699$	0.272975	−	1.17387i	0.0103249	−	0.0443997i
$700$	16.8641	+	3.08361i	0.637404	+	0.116550i
$701$	−30.3007	−	17.4941i	−1.14444	−	0.660744i	−0.196916	−	0.980420i	$-0.563093\pi$
$701$	−30.3007	−	17.4941i	−1.14444	−	0.660744i	−0.947527	+	0.319676i	$0.896426\pi$
$702$	−4.64146	−	0.757853i	−0.175181	−	0.0286033i
$703$	−16.3093	−	28.2486i	−0.615118	−	1.06542i
$704$	3.19099	+	5.52696i	0.120265	+	0.208305i
$705$	−6.91803	−	0.395520i	−0.260548	−	0.0148961i
$706$	−13.3349	−	7.69893i	−0.501867	−	0.289753i
$707$	21.0138	−	36.3971i	0.790307	−	1.36885i
$708$	3.27093	−	3.49648i	0.122929	−	0.131406i
$709$		−	22.0190i		−	0.826941i	−0.910517	−	0.413471i	$-0.864316\pi$
$709$		−	22.0190i		−	0.826941i	0.910517	−	0.413471i	$-0.135684\pi$
$710$	16.2139	+	19.4475i	0.608498	+	0.729851i
$711$	−6.03167	−	9.00396i	−0.226205	−	0.337675i
$712$	5.15412			0.193159
$713$	6.75302	−	2.30238i	0.252903	−	0.0862248i
$714$	−19.2862	+	5.86285i	−0.721766	+	0.219411i
$715$	12.1230	+	4.45585i	0.453375	+	0.166639i
$716$	5.70902	−	9.88831i	0.213356	−	0.369543i
$717$	8.98545	−	2.73151i	0.335568	−	0.102010i
$718$	11.0965	−	6.40655i	0.414116	−	0.239090i
$719$	25.1655	−	43.5879i	0.938515	−	1.62556i	0.170271	−	0.985397i	$-0.445536\pi$
$719$	25.1655	−	43.5879i	0.938515	−	1.62556i	0.768243	−	0.640158i	$-0.221131\pi$
$720$	1.88988	−	6.43649i	0.0704317	−	0.239874i
$721$	19.4354			0.723812
$722$	−12.1415	−	21.0297i	−0.451859	−	0.782644i
$723$	27.1960	−	29.0713i	1.01143	−	1.08117i
$724$	0.120326	−	0.0694702i	0.00447188	−	0.00258184i
$725$	9.57261	−	3.41579i	0.355518	−	0.126859i
$726$	−37.6039	−	35.1782i	−1.39561	−	1.30559i
$727$	12.0318	+	6.94655i	0.446234	+	0.257633i	0.706238	−	0.707974i	$-0.250391\pi$
$727$	12.0318	+	6.94655i	0.446234	+	0.257633i	−0.260004	+	0.965607i	$0.583724\pi$
$728$			3.10328i			0.115015i
$729$	−5.36136	−	26.4623i	−0.198569	−	0.980087i
$730$	−20.3155	+	16.9376i	−0.751912	+	0.626891i
$731$	−24.2739	+	14.0145i	−0.897802	+	0.518346i
$732$	7.85640	+	1.82696i	0.290381	+	0.0675263i
$733$	19.0114	−	10.9762i	0.702201	−	0.405416i	−0.105966	−	0.994370i	$-0.533793\pi$
$733$	19.0114	−	10.9762i	0.702201	−	0.405416i	0.808167	+	0.588954i	$0.200460\pi$
$734$	0.284663	+	0.493050i	0.0105071	+	0.0181988i
$735$	−8.28490	−	16.4528i	−0.305593	−	0.606870i
$736$		−	1.28143i		−	0.0472343i
$737$	0.298022	+	0.172063i	0.0109778	+	0.00633802i
$738$	−6.49230	+	0.433239i	−0.238985	+	0.0159478i
$739$	21.5748	−	12.4562i	0.793643	−	0.458210i	−0.0476007	−	0.998866i	$-0.515158\pi$
$739$	21.5748	−	12.4562i	0.793643	−	0.458210i	0.841243	+	0.540657i	$0.181824\pi$
$740$	−10.4058	−	3.82469i	−0.382525	−	0.140598i
$741$	−2.33601	+	10.0454i	−0.0858154	+	0.369029i
$742$	30.1248			1.10592
$743$			23.7503i			0.871315i	0.900112	+	0.435658i	$0.143484\pi$
$743$			23.7503i			0.871315i	−0.900112	+	0.435658i	$0.856516\pi$
$744$	−9.59538	+	0.963701i	−0.351784	+	0.0353310i
$745$	12.1660	−	33.0999i	0.445727	−	1.21269i
$746$		−	26.2391i		−	0.960683i
$747$	−41.2931	+	2.75554i	−1.51084	+	0.100820i
$748$		−	21.6620i		−	0.792041i
$749$	5.34508	−	3.08598i	0.195305	−	0.112759i
$750$	18.5803	−	5.45641i	0.678457	−	0.199240i
$751$	−16.4353	+	28.4669i	−0.599734	+	1.03877i	0.393126	+	0.919485i	$0.371394\pi$
$751$	−16.4353	+	28.4669i	−0.599734	+	1.03877i	−0.992860	+	0.119286i	$0.961940\pi$
$752$	1.78914			0.0652434
$753$	−9.87598	−	9.23891i	−0.359901	−	0.336685i
$754$	0.919902	+	1.59332i	0.0335009	+	0.0580252i
$755$	−4.32160	+	0.747943i	−0.157279	+	0.0272204i
$756$	−16.6632	+	6.30535i	−0.606035	+	0.229323i
$757$	−10.9423	−	18.9527i	−0.397706	−	0.688848i	0.595736	−	0.803180i	$-0.296860\pi$
$757$	−10.9423	−	18.9527i	−0.397706	−	0.688848i	−0.993443	+	0.114333i	$0.963527\pi$
$758$	7.36256	−	12.7523i	0.267420	−	0.463185i
$759$	4.11985	+	13.5525i	0.149541	+	0.491924i
$760$	−13.8079	−	5.07513i	−0.500865	−	0.184094i
$761$	−8.15330	+	14.1219i	−0.295557	+	0.511919i	−0.975114	−	0.221703i	$-0.928838\pi$
$761$	−8.15330	+	14.1219i	−0.295557	+	0.511919i	0.679557	+	0.733622i	$0.262172\pi$
$762$	13.0897	+	12.2453i	0.474191	+	0.443602i
$763$	−35.4624	−	20.4742i	−1.28382	−	0.741216i
$764$	11.0681	−	6.39017i	0.400430	−	0.231188i
$765$	−16.4788	+	15.7127i	−0.595792	+	0.568094i
$766$	−15.9925	+	9.23329i	−0.577833	+	0.333612i
$767$			2.50192i			0.0903391i
$768$	−0.392310	+	1.68704i	−0.0141563	+	0.0608757i
$769$	−15.5847	+	26.9935i	−0.562000	+	0.973412i	0.435322	+	0.900275i	$0.356634\pi$
$769$	−15.5847	+	26.9935i	−0.562000	+	0.973412i	−0.997322	+	0.0731373i	$0.976699\pi$
$770$	48.2133	−	8.34430i	1.73749	−	0.300708i
$771$	−20.2650	+	6.16040i	−0.729825	+	0.221861i
$772$	9.22586	+	5.32655i	0.332046	+	0.191707i
$773$		−	3.32319i		−	0.119527i	−0.998213	−	0.0597635i	$-0.980965\pi$
$773$		−	3.32319i		−	0.119527i	0.998213	−	0.0597635i	$-0.0190346\pi$
$774$	−20.5821	+	13.7878i	−0.739808	+	0.495590i
$775$	−17.3165	−	21.7977i	−0.622026	−	0.782997i
$776$			14.7656i			0.530055i
$777$	8.56392	+	28.1715i	0.307229	+	1.01065i
$778$	7.48029	−	12.9562i	0.268181	−	0.464504i
$779$			14.2692i			0.511249i
$780$	1.57654	+	3.13082i	0.0564493	+	0.112101i
$781$	62.5839	+	36.1329i	2.23943	+	1.29294i
$782$	−2.17475	+	3.76677i	−0.0777688	+	0.134700i
$783$	−6.68629	+	8.17681i	−0.238949	+	0.292215i
$784$	2.37814	+	4.11906i	0.0849337	+	0.147109i
$785$	13.3638	−	2.31287i	0.476973	−	0.0825500i
$786$	−20.0507	+	21.4333i	−0.715185	+	0.764501i
$787$	7.97092	−	13.8060i	0.284133	−	0.492132i	−0.688266	−	0.725459i	$-0.741628\pi$
$787$	7.97092	−	13.8060i	0.284133	−	0.492132i	0.972398	+	0.233326i	$0.0749611\pi$
$788$	21.2751	−	12.2832i	0.757893	−	0.437570i
$789$	19.3527	+	4.50036i	0.688975	+	0.160217i
$790$	−2.78675	+	7.58191i	−0.0991482	+	0.269752i
$791$		−	57.2409i		−	2.03525i
$792$	−1.27480	−	19.1035i	−0.0452979	−	0.678812i
$793$	−3.65019	+	2.10744i	−0.129622	+	0.0748374i
$794$	9.37611	+	5.41330i	0.332746	+	0.192111i
$795$	30.3921	−	15.3041i	1.07790	−	0.542781i
$796$	−1.07789	+	0.622319i	−0.0382048	+	0.0220575i
$797$	−4.62644	+	2.67108i	−0.163877	+	0.0946144i	−0.579695	−	0.814833i	$-0.696828\pi$
$797$	−4.62644	+	2.67108i	−0.163877	+	0.0946144i	0.415819	+	0.909448i	$0.363495\pi$
$798$	11.3638	+	37.3819i	0.402275	+	1.32330i
$799$	−5.25919	−	3.03640i	−0.186057	−	0.107420i
$800$	−4.70918	+	1.68037i	−0.166495	+	0.0594102i
$801$	−13.8758	−	6.82242i	−0.490279	−	0.241058i
$802$	15.2743			0.539354
$803$	−37.7456	+	65.3774i	−1.33201	+	2.30712i
$804$	0.0271639	+	0.0893572i	0.000957998	+	0.00315139i
$805$	−9.22147	−	3.38938i	−0.325014	−	0.119460i
$806$	3.31757	−	3.79314i	0.116856	−	0.133608i
$807$	11.2760	−	3.42783i	0.396936	−	0.120665i
$808$			12.2575i			0.431216i
$809$	−3.07180	+	5.32052i	−0.107999	+	0.187059i	−0.914959	−	0.403546i	$-0.867778\pi$
$809$	−3.07180	+	5.32052i	−0.107999	+	0.187059i	0.806961	+	0.590605i	$0.201111\pi$
$810$	−13.6078	+	14.8266i	−0.478129	+	0.520954i
$811$	−20.9582	−	36.3006i	−0.735941	−	1.27469i	−0.954309	−	0.298821i	$-0.903407\pi$
$811$	−20.9582	−	36.3006i	−0.735941	−	1.27469i	0.218368	−	0.975866i	$-0.429927\pi$
$812$	6.03603	+	3.48490i	0.211823	+	0.122296i
$813$	−53.4968	−	12.4404i	−1.87622	−	0.436303i
$814$	−31.6419			−1.10905
$815$	−2.76249	+	0.478106i	−0.0967659	+	0.0167473i
$816$	4.01630	−	4.29325i	0.140599	−	0.150294i
$817$	27.1640	+	47.0495i	0.950349	+	1.64605i
$818$	8.93038	+	5.15596i	0.312243	+	0.180274i
$819$	4.10776	−	8.35461i	0.143537	−	0.291934i
$820$	3.10566	+	3.72502i	0.108454	+	0.130084i
$821$	41.5376			1.44967			0.724836	−	0.688921i	$-0.241915\pi$
$821$	41.5376			1.44967			0.724836	+	0.688921i	$0.241915\pi$
$822$	−4.62183	−	15.2038i	−0.161205	−	0.530292i
$823$	1.28219	−	2.22082i	0.0446945	−	0.0774131i	−0.842813	−	0.538207i	$-0.819102\pi$
$823$	1.28219	−	2.22082i	0.0446945	−	0.0774131i	0.887507	+	0.460794i	$0.152435\pi$
$824$	−4.90895	+	2.83419i	−0.171012	+	0.0987336i
$825$	44.4020	−	32.9119i	1.54588	−	1.14584i
$826$	4.73906	+	8.20830i	0.164893	+	0.285603i
$827$	4.32024	−	2.49429i	0.150230	−	0.0867350i	−0.423001	−	0.906129i	$-0.639023\pi$
$827$	4.32024	−	2.49429i	0.150230	−	0.0867350i	0.573230	+	0.819394i	$0.305690\pi$
$828$	−1.69621	+	3.44986i	−0.0589474	+	0.119891i
$829$		−	15.3259i		−	0.532292i	−0.963933	−	0.266146i	$-0.914250\pi$
$829$		−	15.3259i		−	0.532292i	0.963933	−	0.266146i	$-0.0857503\pi$
$830$	19.7530	+	23.6923i	0.685636	+	0.822373i
$831$	11.3320	−	48.7307i	0.393104	−	1.69045i
$832$	−0.452539	−	0.783821i	−0.0156890	−	0.0271741i
$833$		−	16.1440i		−	0.559356i
$834$	−30.8548	−	7.17511i	−1.06842	−	0.248454i
$835$	−9.15786	+	24.9158i	−0.316921	+	0.862246i
$836$	−41.9869			−1.45215
$837$	27.1082	+	10.1068i	0.936996	+	0.349341i
$838$			21.4031i			0.739359i
$839$			52.0333i			1.79639i	0.439598	+	0.898195i	$0.355121\pi$
$839$			52.0333i			1.79639i	−0.439598	+	0.898195i	$0.644879\pi$
$840$	11.1026	+	7.28534i	0.383077	+	0.251368i
$841$	−24.8679			−0.857514
$842$	9.22392	+	15.9763i	0.317877	+	0.550579i
$843$	13.1146	+	3.04971i	0.451689	+	0.105038i
$844$	13.9957	−	24.2412i	0.481751	−	0.834417i
$845$	25.5650	+	9.39649i	0.879463	+	0.323249i
$846$	−4.81671	−	2.36826i	−0.165602	−	0.0814225i
$847$	88.2787	−	50.9677i	3.03329	−	1.75127i
$848$	−7.60886	+	4.39298i	−0.261289	+	0.150855i
$849$	−29.5327	−	6.86765i	−1.01356	−	0.235697i
$850$	16.6944	+	3.05259i	0.572614	+	0.104703i
$851$	5.50217	+	3.17668i	0.188612	+	0.108895i
$852$	5.70436	+	18.7648i	0.195428	+	0.642872i
$853$			52.5513i			1.79932i	0.436588	+	0.899661i	$0.356187\pi$
$853$			52.5513i			1.79932i	−0.436588	+	0.899661i	$0.643813\pi$
$854$	−7.98370	+	13.8282i	−0.273197	+	0.473190i
$855$	30.4555	+	31.9405i	1.04156	+	1.09234i
$856$	−0.900033	+	1.55890i	−0.0307625	+	0.0532822i
$857$	6.10310	+	10.5709i	0.208478	+	0.361094i	0.951235	−	0.308466i	$-0.0998158\pi$
$857$	6.10310	+	10.5709i	0.208478	+	0.361094i	−0.742757	+	0.669561i	$0.766482\pi$
$858$	7.30608	+	6.83479i	0.249426	+	0.233336i
$859$	18.3031	−	10.5673i	0.624494	−	0.360552i	−0.154122	−	0.988052i	$-0.549255\pi$
$859$	18.3031	−	10.5673i	0.624494	−	0.360552i	0.778617	+	0.627500i	$0.215922\pi$
$860$	17.3314	+	6.37022i	0.590997	+	0.217223i
$861$	2.91747	−	12.5459i	0.0994272	−	0.427563i
$862$	−10.6515	−	6.14966i	−0.362792	−	0.209458i
$863$	−13.5233	+	7.80768i	−0.460339	+	0.265777i	−0.712187	−	0.701990i	$-0.752295\pi$
$863$	−13.5233	+	7.80768i	−0.460339	+	0.265777i	0.251848	+	0.967767i	$0.418962\pi$
$864$	3.28927	−	4.02252i	0.111903	−	0.136849i
$865$	40.0525	−	33.3930i	1.36183	−	1.13539i
$866$	−34.2578			−1.16413
$867$	9.07983	−	2.76020i	0.308367	−	0.0937413i
$868$	3.69941	−	18.7286i	0.125566	−	0.635689i
$869$			23.0550i			0.782087i
$870$	7.86000	+	0.449374i	0.266479	+	0.0152352i
$871$	−0.0422648	−	0.0244016i	−0.00143209	−	0.000826816i
$872$	11.9427			0.404430
$873$	19.5450	−	39.7518i	0.661498	−	1.34539i
$874$	7.30105	+	4.21526i	0.246962	+	0.142583i
$875$	−0.363395	+	38.3328i	−0.0122850	+	1.29589i
$876$	−19.6024	+	5.95898i	−0.662303	+	0.201335i
$877$	25.3816	−	14.6541i	0.857076	−	0.494833i	−0.00595583	−	0.999982i	$-0.501896\pi$
$877$	25.3816	−	14.6541i	0.857076	−	0.494833i	0.863032	+	0.505149i	$0.168562\pi$
$878$	8.21787	+	14.2338i	0.277340	+	0.480366i
$879$	22.6724	+	21.2099i	0.764722	+	0.715392i
$880$	−10.9608	+	9.13834i	−0.369488	+	0.308053i
$881$	−1.89020	−	3.27392i	−0.0636825	−	0.110301i	0.832426	−	0.554136i	$-0.186951\pi$
$881$	−1.89020	−	3.27392i	−0.0636825	−	0.110301i	−0.896109	+	0.443834i	$0.853618\pi$
$882$	−0.950066	−	14.2372i	−0.0319904	−	0.479391i
$883$	−23.4774			−0.790078			−0.395039	−	0.918664i	$-0.629269\pi$
$883$	−23.4774			−0.790078			−0.395039	+	0.918664i	$0.629269\pi$
$884$			3.07206i			0.103324i
$885$	8.95113	+	5.87357i	0.300889	+	0.197438i
$886$	3.14960	+	5.45527i	0.105813	+	0.183273i
$887$	−15.3302	+	26.5527i	−0.514738	+	0.891553i	0.485115	+	0.874450i	$0.338778\pi$
$887$	−15.3302	+	26.5527i	−0.514738	+	0.891553i	−0.999854	+	0.0171029i	$0.994556\pi$
$888$	−6.27120	−	5.86666i	−0.210448	−	0.196872i
$889$	−30.7293	+	17.7416i	−1.03063	+	0.595034i
$890$	1.96541	+	11.3561i	0.0658808	+	0.380659i
$891$	−21.8549	+	53.1175i	−0.732168	+	1.77950i
$892$	0.843359	−	1.46074i	0.0282377	−	0.0489092i
$893$	−5.88537	+	10.1938i	−0.196946	+	0.341121i
$894$	18.6613	−	19.9481i	0.624126	−	0.667163i
$895$	23.9641	+	8.80806i	0.801030	+	0.294421i
$896$	−2.96938	−	1.71437i	−0.0992000	−	0.0572731i
$897$	−0.584269	−	1.92198i	−0.0195082	−	0.0641732i
$898$	26.3801			0.880314
$899$	−3.65230	−	10.7124i	−0.121811	−	0.357279i
$900$	14.9023	+	1.70958i	0.496742	+	0.0569860i
$901$	29.8217			0.993504
$902$	11.9875	+	6.92098i	0.399140	+	0.230444i
$903$	−14.2637	−	46.9211i	−0.474665	−	1.56144i
$904$	8.34722	+	14.4578i	0.277624	+	0.480859i
$905$	0.198948	+	0.238625i	0.00661327	+	0.00793215i
$906$	−3.30897	−	0.769482i	−0.109933	−	0.0255643i
$907$		−	25.5776i		−	0.849291i	−0.905360	−	0.424646i	$-0.860399\pi$
$907$		−	25.5776i		−	0.849291i	0.905360	−	0.424646i	$-0.139601\pi$
$908$	4.42782	+	7.66921i	0.146942	+	0.254512i
$909$	16.2250	−	32.9994i	0.538149	−	1.09452i
$910$	−6.83750	+	1.18337i	−0.226661	+	0.0392283i
$911$	16.7161	−	28.9532i	0.553830	−	0.959261i	−0.444164	−	0.895946i	$-0.646499\pi$
$911$	16.7161	−	28.9532i	0.553830	−	0.959261i	0.997994	−	0.0633155i	$-0.0201674\pi$
$912$	−8.32150	−	7.78470i	−0.275552	−	0.257777i
$913$	76.2443	+	44.0196i	2.52332	+	1.45684i
$914$	−39.1752			−1.29580
$915$	−1.02949	+	18.0068i	−0.0340339	+	0.595286i
$916$	−15.4179	−	8.90151i	−0.509421	−	0.294114i
$917$	−29.0504	−	50.3167i	−0.959328	−	1.66160i
$918$	−16.4955	+	6.24191i	−0.544434	+	0.206014i
$919$	24.3439	+	42.1649i	0.803032	+	1.39089i	0.917612	+	0.397477i	$0.130114\pi$
$919$	24.3439	+	42.1649i	0.803032	+	1.39089i	−0.114580	+	0.993414i	$0.536552\pi$
$920$	2.82340	−	0.488647i	0.0930847	−	0.0161102i
$921$	−8.76126	+	9.36539i	−0.288693	+	0.308600i
$922$	0.0357305			0.00117672
$923$	−8.87551	−	5.12428i	−0.292141	−	0.168668i
$924$	36.9160	+	8.58460i	1.21445	+	0.282413i
$925$	4.45895	−	24.3857i	0.146609	−	0.801798i
$926$	−8.82365			−0.289963
$927$	16.9674	−	1.13225i	0.557282	−	0.0371881i
$928$	−2.03276			−0.0667285
$929$	48.3243			1.58547			0.792734	−	0.609567i	$-0.208657\pi$
$929$	48.3243			1.58547			0.792734	+	0.609567i	$0.208657\pi$
$930$	−5.78233	−	20.7741i	−0.189610	−	0.681211i
$931$	−31.2915			−1.02554
$932$	−0.695815			−0.0227922
$933$	−11.9254	−	2.77317i	−0.390419	−	0.0907895i
$934$	−5.63272			−0.184308
$935$	47.7282	−	8.26034i	1.56088	−	0.270142i
$936$	0.180789	+	2.70921i	0.00590927	+	0.0885533i
$937$	−3.74078	−	2.15974i	−0.122206	−	0.0705557i	0.437651	−	0.899145i	$-0.355811\pi$
$937$	−3.74078	−	2.15974i	−0.122206	−	0.0705557i	−0.559857	+	0.828589i	$0.689144\pi$
$938$	−0.184883			−0.00603665
$939$	−23.0628	−	21.5751i	−0.752625	−	0.704076i
$940$	0.682252	+	3.94205i	0.0222526	+	0.128575i
$941$	−22.1895	−	38.4333i	−0.723356	−	1.25289i	−0.959647	−	0.281207i	$-0.909265\pi$
$941$	−22.1895	−	38.4333i	−0.723356	−	1.25289i	0.236291	−	0.971682i	$-0.424068\pi$
$942$	10.2324	+	2.37948i	0.333389	+	0.0775277i
$943$	−1.38966	−	2.40696i	−0.0452535	−	0.0783814i
$944$	−2.39397	−	1.38216i	−0.0779170	−	0.0449854i
$945$	−20.2468	−	34.3098i	−0.658629	−	1.11610i
$946$	52.7013			1.71347
$947$	37.2751	+	21.5208i	1.21128	+	0.699332i	0.963038	−	0.269367i	$-0.0868143\pi$
$947$	37.2751	+	21.5208i	1.21128	+	0.699332i	0.248241	+	0.968698i	$0.420148\pi$
$948$	−4.27457	+	4.56933i	−0.138832	+	0.148405i
$949$	5.35300	−	9.27167i	0.173766	−	0.300971i
$950$	5.91676	−	32.3584i	0.191965	−	1.04985i
$951$	10.5013	+	9.82393i	0.340529	+	0.318563i
$952$	5.81900	+	10.0788i	0.188595	+	0.326656i
$953$		−	46.5489i		−	1.50787i	−0.656951	−	0.753933i	$-0.728154\pi$
$953$		−	46.5489i		−	1.50787i	0.656951	−	0.753933i	$-0.271846\pi$
$954$	26.2994	−	1.75499i	0.851474	−	0.0568199i
$955$	18.3001	+	21.9497i	0.592178	+	0.710276i
$956$	−2.71108	−	4.69573i	−0.0876826	−	0.151871i
$957$	21.4985	−	6.53539i	0.694948	−	0.211259i
$958$	−16.0091	−	9.24288i	−0.517232	−	0.298624i
$959$	31.4571			1.01580
$960$	−3.86667	−	0.221066i	−0.124796	−	0.00713489i
$961$	−24.5436	+	18.9371i	−0.791729	+	0.610873i
$962$	4.48739			0.144679
$963$	4.48655	−	3.00550i	0.144577	−	0.0968508i
$964$	−19.9045	−	11.4919i	−0.641081	−	0.370128i
$965$	−8.21798	+	22.3586i	−0.264546	+	0.719750i
$966$	−5.55743	−	5.19894i	−0.178807	−	0.167273i
$967$	−13.6964	+	23.7228i	−0.440446	+	0.762875i	−0.997723	−	0.0674518i	$-0.978513\pi$
$967$	−13.6964	+	23.7228i	−0.440446	+	0.762875i	0.557276	+	0.830327i	$0.311846\pi$
$968$	−14.8648	+	25.7466i	−0.477774	+	0.827529i
$969$	11.2495	+	37.0057i	0.361385	+	1.18880i
$970$	−32.5333	+	5.63056i	−1.04458	+	0.180786i
$971$	−27.9798	+	16.1541i	−0.897914	+	0.518411i	−0.876523	−	0.481360i	$-0.840143\pi$
$971$	−27.9798	+	16.1541i	−0.897914	+	0.518411i	−0.0213914	+	0.999771i	$0.506810\pi$
$972$	−14.1799	+	6.47542i	−0.454820	+	0.207699i
$973$	31.3548	−	54.3081i	1.00519	−	1.74104i
$974$	−4.58796	−	7.94657i	−0.147008	−	0.254625i
$975$	−6.29699	+	4.66749i	−0.201665	+	0.149479i
$976$		−	4.65692i		−	0.149064i
$977$	−10.8353			−0.346652			−0.173326	−	0.984865i	$-0.555451\pi$
$977$	−10.8353			−0.346652			−0.173326	+	0.984865i	$0.555451\pi$
$978$	−2.11519	−	0.491874i	−0.0676363	−	0.0157284i
$979$	16.4467	+	28.4866i	0.525640	+	0.910436i
$980$	−8.16873	+	6.81051i	−0.260941	+	0.217554i
$981$	−32.1519	−	15.8083i	−1.02653	−	0.504721i
$982$	−1.65595	−	2.86819i	−0.0528436	−	0.0915277i
$983$	5.28856	−	3.05335i	0.168679	−	0.0973867i	−0.413284	−	0.910602i	$-0.635618\pi$
$983$	5.28856	−	3.05335i	0.168679	−	0.0973867i	0.581963	+	0.813216i	$0.302285\pi$
$984$	1.09263	+	3.59426i	0.0348317	+	0.114581i
$985$	35.1765	+	42.1917i	1.12082	+	1.34434i
$986$	5.97529	+	3.44984i	0.190292	+	0.109865i
$987$	7.25878	−	7.75932i	0.231050	−	0.246982i
$988$	5.95449			0.189438
$989$	−9.16415	−	5.29092i	−0.291403	−	0.168242i
$990$	41.6048	−	10.0935i	1.32229	−	0.320792i
$991$		−	2.90080i		−	0.0921468i	−0.998938	−	0.0460734i	$-0.985329\pi$
$991$		−	2.90080i		−	0.0921468i	0.998938	−	0.0460734i	$-0.0146708\pi$
$992$	1.79672	+	5.26989i	0.0570460	+	0.167319i
$993$	−8.50397	−	27.9743i	−0.269865	−	0.887736i
$994$	−38.8250			−1.23146
$995$	−1.78219	−	2.13762i	−0.0564994	−	0.0677670i
$996$	6.94947	+	22.8607i	0.220202	+	0.724367i
$997$	20.5183	−	11.8463i	0.649821	−	0.375175i	−0.138566	−	0.990353i	$-0.544249\pi$
$997$	20.5183	−	11.8463i	0.649821	−	0.375175i	0.788388	+	0.615179i	$0.210916\pi$
$998$	−18.6560	−	10.7710i	−0.590544	−	0.340951i
$999$	9.11762	+	24.0952i	0.288469	+	0.762339i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.r.b.119.14	yes	64
3.2	odd	2		930.2.r.a.119.8	✓	64
5.4	even	2		930.2.r.a.119.19	yes	64
15.14	odd	2	inner	930.2.r.b.119.25	yes	64
31.6	odd	6	inner	930.2.r.b.719.25	yes	64
93.68	even	6		930.2.r.a.719.19	yes	64
155.99	odd	6		930.2.r.a.719.8	yes	64
465.254	even	6	inner	930.2.r.b.719.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.8	✓	64	3.2	odd	2
930.2.r.a.119.19	yes	64	5.4	even	2
930.2.r.a.719.8	yes	64	155.99	odd	6
930.2.r.a.719.19	yes	64	93.68	even	6
930.2.r.b.119.14	yes	64	1.1	even	1	trivial
930.2.r.b.119.25	yes	64	15.14	odd	2	inner
930.2.r.b.719.14	yes	64	465.254	even	6	inner
930.2.r.b.719.25	yes	64	31.6	odd	6	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.392310 + 1.68704i) q^{3} +1.00000 q^{4} +(0.381329 + 2.20331i) q^{5} +(-0.392310 + 1.68704i) q^{6} +(-2.96938 - 1.71437i) q^{7} +1.00000 q^{8} +(-2.69219 - 1.32368i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.392310 + 1.68704i) q^{3} +1.00000 q^{4} +(0.381329 + 2.20331i) q^{5} +(-0.392310 + 1.68704i) q^{6} +(-2.96938 - 1.71437i) q^{7} +1.00000 q^{8} +(-2.69219 - 1.32368i) q^{9} +(0.381329 + 2.20331i) q^{10} +(3.19099 + 5.52696i) q^{11} +(-0.392310 + 1.68704i) q^{12} +(-0.452539 - 0.783821i) q^{13} +(-2.96938 - 1.71437i) q^{14} +(-3.86667 - 0.221066i) q^{15} +1.00000 q^{16} +(-2.93950 - 1.69712i) q^{17} +(-2.69219 - 1.32368i) q^{18} +(-3.28949 + 5.69756i) q^{19} +(0.381329 + 2.20331i) q^{20} +(4.05713 - 4.33689i) q^{21} +(3.19099 + 5.52696i) q^{22} -1.28143i q^{23} +(-0.392310 + 1.68704i) q^{24} +(-4.70918 + 1.68037i) q^{25} +(-0.452539 - 0.783821i) q^{26} +(3.28927 - 4.02252i) q^{27} +(-2.96938 - 1.71437i) q^{28} -2.03276 q^{29} +(-3.86667 - 0.221066i) q^{30} +(1.79672 + 5.26989i) q^{31} +1.00000 q^{32} +(-10.5760 + 3.21504i) q^{33} +(-2.93950 - 1.69712i) q^{34} +(2.64499 - 7.19621i) q^{35} +(-2.69219 - 1.32368i) q^{36} +(-2.47900 + 4.29376i) q^{37} +(-3.28949 + 5.69756i) q^{38} +(1.49987 - 0.455949i) q^{39} +(0.381329 + 2.20331i) q^{40} +(1.87833 - 1.08446i) q^{41} +(4.05713 - 4.33689i) q^{42} +(4.12891 - 7.15148i) q^{43} +(3.19099 + 5.52696i) q^{44} +(1.88988 - 6.43649i) q^{45} -1.28143i q^{46} +1.78914 q^{47} +(-0.392310 + 1.68704i) q^{48} +(2.37814 + 4.11906i) q^{49} +(-4.70918 + 1.68037i) q^{50} +(4.01630 - 4.29325i) q^{51} +(-0.452539 - 0.783821i) q^{52} +(-7.60886 + 4.39298i) q^{53} +(3.28927 - 4.02252i) q^{54} +(-10.9608 + 9.13834i) q^{55} +(-2.96938 - 1.71437i) q^{56} +(-8.32150 - 7.78470i) q^{57} -2.03276 q^{58} +(-2.39397 - 1.38216i) q^{59} +(-3.86667 - 0.221066i) q^{60} -4.65692i q^{61} +(1.79672 + 5.26989i) q^{62} +(5.72483 + 8.54593i) q^{63} +1.00000 q^{64} +(1.55444 - 1.29598i) q^{65} +(-10.5760 + 3.21504i) q^{66} +(0.0466974 - 0.0269608i) q^{67} +(-2.93950 - 1.69712i) q^{68} +(2.16183 + 0.502719i) q^{69} +(2.64499 - 7.19621i) q^{70} +(9.80635 - 5.66170i) q^{71} +(-2.69219 - 1.32368i) q^{72} +(5.91441 + 10.2441i) q^{73} +(-2.47900 + 4.29376i) q^{74} +(-0.987394 - 8.60378i) q^{75} +(-3.28949 + 5.69756i) q^{76} -21.8822i q^{77} +(1.49987 - 0.455949i) q^{78} +(3.12853 + 1.80626i) q^{79} +(0.381329 + 2.20331i) q^{80} +(5.49573 + 7.12720i) q^{81} +(1.87833 - 1.08446i) q^{82} +(11.9468 - 6.89749i) q^{83} +(4.05713 - 4.33689i) q^{84} +(2.61837 - 7.12380i) q^{85} +(4.12891 - 7.15148i) q^{86} +(0.797471 - 3.42934i) q^{87} +(3.19099 + 5.52696i) q^{88} +5.15412 q^{89} +(1.88988 - 6.43649i) q^{90} +3.10328i q^{91} -1.28143i q^{92} +(-9.59538 + 0.963701i) q^{93} +1.78914 q^{94} +(-13.8079 - 5.07513i) q^{95} +(-0.392310 + 1.68704i) q^{96} +14.7656i q^{97} +(2.37814 + 4.11906i) q^{98} +(-1.27480 - 19.1035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9}+O(q^{10}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9	\( 64 q + 64 q^{2} + 64 q^{4} + 2 q^{5} + 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{20} + 2 q^{25} + 18 q^{31} + 64 q^{32} - 8 q^{33} + 6 q^{34} + 16 q^{35} - 4 q^{36} + 4 q^{38} - 8 q^{39} + 2 q^{40} + 9 q^{45} - 4 q^{47} + 30 q^{49} + 2 q^{50} - 8 q^{51} - 6 q^{53} + 6 q^{57} + 18 q^{62} + 12 q^{63} + 64 q^{64} - 8 q^{66} + 6 q^{68} - 10 q^{69} + 16 q^{70} - 4 q^{72} - 63 q^{75} + 4 q^{76} - 8 q^{78} - 30 q^{79} + 2 q^{80} - 12 q^{81} - 54 q^{83} - 16 q^{87} + 9 q^{90} - 18 q^{93} - 4 q^{94} - 56 q^{95} + 30 q^{98} - 102 q^{99}+O(q^{100}) \) 64 * q + 64 * q^2 + 64 * q^4 + 2 * q^5 + 64 * q^8 - 4 * q^9 + 2 * q^10 + 64 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^20 + 2 * q^25 + 18 * q^31 + 64 * q^32 - 8 * q^33 + 6 * q^34 + 16 * q^35 - 4 * q^36 + 4 * q^38 - 8 * q^39 + 2 * q^40 + 9 * q^45 - 4 * q^47 + 30 * q^49 + 2 * q^50 - 8 * q^51 - 6 * q^53 + 6 * q^57 + 18 * q^62 + 12 * q^63 + 64 * q^64 - 8 * q^66 + 6 * q^68 - 10 * q^69 + 16 * q^70 - 4 * q^72 - 63 * q^75 + 4 * q^76 - 8 * q^78 - 30 * q^79 + 2 * q^80 - 12 * q^81 - 54 * q^83 - 16 * q^87 + 9 * q^90 - 18 * q^93 - 4 * q^94 - 56 * q^95 + 30 * q^98 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more