LMFDB - Embedded newform 930.2.r.a.119.8

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			119.8
Character	$\chi$	$=$	930.119
Dual form			930.2.r.a.719.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.26486 + 1.18327i) q^{3} +1.00000 q^{4} +(-0.381329 - 2.20331i) q^{5} +(1.26486 - 1.18327i) q^{6} +(-2.96938 - 1.71437i) q^{7} -1.00000 q^{8} +(0.199749 - 2.99334i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.26486 + 1.18327i) q^{3} +1.00000 q^{4} +(-0.381329 - 2.20331i) q^{5} +(1.26486 - 1.18327i) q^{6} +(-2.96938 - 1.71437i) q^{7} -1.00000 q^{8} +(0.199749 - 2.99334i) q^{9} +(0.381329 + 2.20331i) q^{10} +(-3.19099 - 5.52696i) q^{11} +(-1.26486 + 1.18327i) q^{12} +(-0.452539 - 0.783821i) q^{13} +(2.96938 + 1.71437i) q^{14} +(3.08944 + 2.33567i) q^{15} +1.00000 q^{16} +(2.93950 + 1.69712i) q^{17} +(-0.199749 + 2.99334i) q^{18} +(-3.28949 + 5.69756i) q^{19} +(-0.381329 - 2.20331i) q^{20} +(5.78442 - 1.34513i) q^{21} +(3.19099 + 5.52696i) q^{22} +1.28143i q^{23} +(1.26486 - 1.18327i) 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} +(-3.08944 - 2.33567i) 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} +(0.199749 - 2.99334i) 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} +(-5.78442 + 1.34513i) q^{42} +(4.12891 - 7.15148i) q^{43} +(-3.19099 - 5.52696i) q^{44} +(-6.67144 + 0.701337i) q^{45} -1.28143i q^{46} -1.78914 q^{47} +(-1.26486 + 1.18327i) q^{48} +(2.37814 + 4.11906i) q^{49} +(4.70918 - 1.68037i) q^{50} +(-5.72621 + 1.33160i) 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} +(-2.58100 - 11.0990i) q^{57} -2.03276 q^{58} +(2.39397 + 1.38216i) q^{59} +(3.08944 + 2.33567i) 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} +(-1.51628 - 1.62084i) q^{69} +(2.64499 - 7.19621i) q^{70} +(-9.80635 + 5.66170i) q^{71} +(-0.199749 + 2.99334i) q^{72} +(5.91441 + 10.2441i) q^{73} +(2.47900 - 4.29376i) q^{74} +(3.96812 - 7.69766i) 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} +(-8.92020 - 1.19584i) q^{81} +(1.87833 - 1.08446i) q^{82} +(-11.9468 + 6.89749i) q^{83} +(5.78442 - 1.34513i) q^{84} +(2.61837 - 7.12380i) q^{85} +(-4.12891 + 7.15148i) q^{86} +(-2.57116 + 2.40530i) q^{87} +(3.19099 + 5.52696i) q^{88} -5.15412 q^{89} +(6.67144 - 0.701337i) q^{90} +3.10328i q^{91} +1.28143i q^{92} +(-8.50831 - 4.53968i) q^{93} +1.78914 q^{94} +(13.8079 + 5.07513i) q^{95} +(1.26486 - 1.18327i) q^{96} +14.7656i q^{97} +(-2.37814 - 4.11906i) q^{98} +(-17.1815 + 8.44772i) 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} + 5 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} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 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 + 5 * 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 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * 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
$3$	−1.26486	+	1.18327i	−0.730268	+	0.683161i
$3$	−1.26486	+	1.18327i	−0.730268	+	0.683161i
$4$	1.00000			0.500000
$5$	−0.381329	−	2.20331i	−0.170535	−	0.985352i
$5$	−0.381329	−	2.20331i	−0.170535	−	0.985352i
$6$	1.26486	−	1.18327i	0.516378	−	0.483068i
$7$	−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
$9$	0.199749	−	2.99334i	0.0665832	−	0.997781i
$10$	0.381329	+	2.20331i	0.120587	+	0.696749i
$11$	−3.19099	−	5.52696i	−0.962120	−	1.66644i	−0.717162	−	0.696906i	$-0.754559\pi$
$11$	−3.19099	−	5.52696i	−0.962120	−	1.66644i	−0.244958	−	0.969534i	$-0.578774\pi$
$12$	−1.26486	+	1.18327i	−0.365134	+	0.341580i
$13$	−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
$15$	3.08944	+	2.33567i	0.797690	+	0.603068i
$16$	1.00000			0.250000
$17$	2.93950	+	1.69712i	0.712934	+	0.411612i	0.812146	−	0.583454i	$-0.198299\pi$
$17$	2.93950	+	1.69712i	0.712934	+	0.411612i	−0.0992126	+	0.995066i	$0.531632\pi$
$18$	−0.199749	+	2.99334i	−0.0470814	+	0.705538i
$19$	−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
$21$	5.78442	−	1.34513i	1.26226	−	0.293532i
$22$	3.19099	+	5.52696i	0.680321	+	1.17835i
$23$			1.28143i			0.267197i	0.991036	+	0.133599i	$0.0426533\pi$
$23$			1.28143i			0.267197i	−0.991036	+	0.133599i	$0.957347\pi$
$24$	1.26486	−	1.18327i	0.258189	−	0.241534i
$25$	−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	$-0.439561\pi$
$29$	2.03276			0.377473			0.188737	+	0.982028i	$0.439561\pi$
$30$	−3.08944	−	2.33567i	−0.564052	−	0.426433i
$31$	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
$36$	0.199749	−	2.99334i	0.0332916	−	0.498890i
$37$	−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	−0.639450	−	0.768833i	$-0.720838\pi$
$41$	−1.87833	+	1.08446i	−0.293347	+	0.169364i	0.346104	+	0.938196i	$0.387505\pi$
$42$	−5.78442	+	1.34513i	−0.892555	+	0.207558i
$43$	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
$45$	−6.67144	+	0.701337i	−0.994520	+	0.104549i
$46$		−	1.28143i		−	0.188937i
$47$	−1.78914			−0.260974			−0.130487	−	0.991450i	$-0.541654\pi$
$47$	−1.78914			−0.260974			−0.130487	+	0.991450i	$0.541654\pi$
$48$	−1.26486	+	1.18327i	−0.182567	+	0.170790i
$49$	2.37814	+	4.11906i	0.339735	+	0.588438i
$50$	4.70918	−	1.68037i	0.665978	−	0.237641i
$51$	−5.72621	+	1.33160i	−0.801830	+	0.186461i
$52$	−0.452539	−	0.783821i	−0.0627559	−	0.108696i
$53$	7.60886	−	4.39298i	1.04516	−	0.603422i	0.123868	−	0.992299i	$-0.460470\pi$
$53$	7.60886	−	4.39298i	1.04516	−	0.603422i	0.921290	+	0.388877i	$0.127137\pi$
$54$	−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
$57$	−2.58100	−	11.0990i	−0.341862	−	1.47010i
$58$	−2.03276			−0.266914
$59$	2.39397	+	1.38216i	0.311668	+	0.179942i	0.647673	−	0.761919i	$-0.275742\pi$
$59$	2.39397	+	1.38216i	0.311668	+	0.179942i	−0.336005	+	0.941860i	$0.609076\pi$
$60$	3.08944	+	2.33567i	0.398845	+	0.301534i
$61$		−	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
$69$	−1.51628	−	1.62084i	−0.182539	−	0.195126i
$70$	2.64499	−	7.19621i	0.316137	−	0.860112i
$71$	−9.80635	+	5.66170i	−1.16380	+	0.671920i	−0.952212	−	0.305439i	$-0.901197\pi$
$71$	−9.80635	+	5.66170i	−1.16380	+	0.671920i	−0.211588	+	0.977359i	$0.567864\pi$
$72$	−0.199749	+	2.99334i	−0.0235407	+	0.352769i
$73$	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
$75$	3.96812	−	7.69766i	0.458199	−	0.888849i
$76$	−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
$81$	−8.92020	−	1.19584i	−0.991133	−	0.132871i
$82$	1.87833	−	1.08446i	0.207427	−	0.119758i
$83$	−11.9468	+	6.89749i	−1.31133	+	0.757098i	−0.982317	−	0.187227i	$-0.940050\pi$
$83$	−11.9468	+	6.89749i	−1.31133	+	0.757098i	−0.329015	+	0.944325i	$0.606717\pi$
$84$	5.78442	−	1.34513i	0.631132	−	0.146766i
$85$	2.61837	−	7.12380i	0.284003	−	0.772685i
$86$	−4.12891	+	7.15148i	−0.445232	+	0.771164i
$87$	−2.57116	+	2.40530i	−0.275657	+	0.257875i
$88$	3.19099	+	5.52696i	0.340161	+	0.589176i
$89$	−5.15412			−0.546336			−0.273168	−	0.961966i	$-0.588071\pi$
$89$	−5.15412			−0.546336			−0.273168	+	0.961966i	$0.588071\pi$
$90$	6.67144	−	0.701337i	0.703232	−	0.0739274i
$91$			3.10328i			0.325312i
$92$			1.28143i			0.133599i
$93$	−8.50831	−	4.53968i	−0.882270	−	0.470743i
$94$	1.78914			0.184536
$95$	13.8079	+	5.07513i	1.41666	+	0.520697i
$96$	1.26486	−	1.18327i	0.129094	−	0.120767i
$97$			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
$99$	−17.1815	+	8.44772i	−1.72680	+	0.849028i
$100$	−4.70918	+	1.68037i	−0.470918	+	0.168037i
$101$		−	12.2575i		−	1.21966i	−0.792531	−	0.609832i	$-0.791237\pi$
$101$		−	12.2575i		−	1.21966i	0.792531	−	0.609832i	$-0.208763\pi$
$102$	5.72621	−	1.33160i	0.566980	−	0.131848i
$103$	−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
$105$	−5.16951	−	12.2319i	−0.504492	−	1.19372i
$106$	−7.60886	+	4.39298i	−0.739038	+	0.426684i
$107$	0.900033	−	1.55890i	0.0870095	−	0.150705i	−0.819236	−	0.573456i	$-0.805602\pi$
$107$	0.900033	−	1.55890i	0.0870095	−	0.150705i	0.906246	+	0.422751i	$0.138936\pi$
$108$	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
$111$	−1.94508	−	8.36434i	−0.184619	−	0.793908i
$112$	−2.96938	−	1.71437i	−0.280580	−	0.161993i
$113$	−8.34722	−	14.4578i	−0.785240	−	1.36008i	−0.928856	−	0.370442i	$-0.879206\pi$
$113$	−8.34722	−	14.4578i	−0.785240	−	1.36008i	0.143615	−	0.989634i	$-0.454127\pi$
$114$	2.58100	+	11.0990i	0.241733	+	1.03951i
$115$	2.82340	−	0.488647i	0.263283	−	0.0455666i
$116$	2.03276			0.188737
$117$	−2.43664	+	1.19804i	−0.225267	+	0.110759i
$118$	−2.39397	−	1.38216i	−0.220383	−	0.127238i
$119$	−5.81900	−	10.0788i	−0.533426	−	0.923922i
$120$	−3.08944	−	2.33567i	−0.282026	−	0.213217i
$121$	−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
$129$	3.23963	+	13.9312i	0.285233	+	1.22658i
$130$	1.55444	−	1.29598i	0.136333	−	0.113665i
$131$	−14.6750	−	8.47260i	−1.28216	−	0.740254i	−0.304915	−	0.952379i	$-0.598628\pi$
$131$	−14.6750	−	8.47260i	−1.28216	−	0.740254i	−0.977242	+	0.212125i	$0.931962\pi$
$132$	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
$135$	7.60858	−	8.78120i	0.654842	−	0.755766i
$136$	−2.93950	−	1.69712i	−0.252060	−	0.145527i
$137$	7.94537	−	4.58726i	0.678819	−	0.391916i	−0.120591	−	0.992702i	$-0.538479\pi$
$137$	7.94537	−	4.58726i	0.678819	−	0.391916i	0.799410	+	0.600786i	$0.205146\pi$
$138$	1.51628	+	1.62084i	0.129074	+	0.137975i
$139$			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
$141$	2.26302	−	2.11704i	0.190581	−	0.178287i
$142$	9.80635	−	5.66170i	0.822931	−	0.475119i
$143$	−2.88810	+	5.00233i	−0.241515	+	0.418316i
$144$	0.199749	−	2.99334i	0.0166458	−	0.249445i
$145$	−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	0.941123	−	0.338065i	$-0.109773\pi$
$149$	13.6580	+	7.88548i	1.11891	+	0.646003i	0.177788	+	0.984069i	$0.443106\pi$
$150$	−3.96812	+	7.69766i	−0.323996	+	0.628511i
$151$			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
$162$	8.92020	+	1.19584i	0.700837	+	0.0939538i
$163$			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
$165$	3.05078	−	24.5283i	0.237503	−	1.90953i
$166$	11.9468	−	6.89749i	0.927252	−	0.535349i
$167$	−10.2810	−	5.93575i	−0.795569	−	0.459322i	0.0463505	−	0.998925i	$-0.485241\pi$
$167$	−10.2810	−	5.93575i	−0.795569	−	0.459322i	−0.841919	+	0.539603i	$0.818574\pi$
$168$	−5.78442	+	1.34513i	−0.446277	+	0.103779i
$169$	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	$0.180220\pi$
$173$	11.6604	+	20.1964i	0.886523	+	1.53550i	0.0425649	+	0.999094i	$0.486447\pi$
$174$	2.57116	−	2.40530i	0.194919	−	0.182345i
$175$	16.8641	+	3.08361i	1.27481	+	0.233099i
$176$	−3.19099	−	5.52696i	−0.240530	−	0.416610i
$177$	−4.66350	+	1.08447i	−0.350530	+	0.0815137i
$178$	5.15412			0.386318
$179$	−5.70902	+	9.88831i	−0.426712	+	0.739087i	−0.996579	−	0.0826503i	$-0.973662\pi$
$179$	−5.70902	+	9.88831i	−0.426712	+	0.739087i	0.569867	+	0.821737i	$0.306995\pi$
$180$	−6.67144	+	0.701337i	−0.497260	+	0.0522746i
$181$	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
$183$	5.51039	+	5.89036i	0.407340	+	0.435428i
$184$		−	1.28143i		−	0.0944685i
$185$	10.4058	+	3.82469i	0.765051	+	0.281197i
$186$	8.50831	+	4.53968i	0.623859	+	0.332866i
$187$		−	21.6620i		−	1.58408i
$188$	−1.78914			−0.130487
$189$	−2.87100	−	17.5834i	−0.208835	−	1.27901i
$190$	−13.8079	−	5.07513i	−1.00173	−	0.368189i
$191$	−11.0681	+	6.39017i	−0.800859	+	0.462376i	−0.843771	−	0.536703i	$-0.819670\pi$
$191$	−11.0681	+	6.39017i	−0.800859	+	0.462376i	0.0429124	+	0.999079i	$0.486336\pi$
$192$	−1.26486	+	1.18327i	−0.0912835	+	0.0853951i
$193$	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
$195$	0.432655	−	3.47855i	0.0309831	−	0.249104i
$196$	2.37814	+	4.11906i	0.169867	+	0.294219i
$197$	−21.2751	+	12.2832i	−1.51579	+	0.875140i	−0.515958	+	0.856614i	$0.672564\pi$
$197$	−21.2751	+	12.2832i	−1.51579	+	0.875140i	−0.999828	+	0.0185255i	$0.994103\pi$
$198$	17.1815	−	8.44772i	1.22103	−	0.600353i
$199$	−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
$204$	−5.72621	+	1.33160i	−0.400915	+	0.0932304i
$205$	3.10566	+	3.72502i	0.216909	+	0.260167i
$206$	4.90895	−	2.83419i	0.342023	−	0.197467i
$207$	3.83577	+	0.255966i	0.266604	+	0.0177908i
$208$	−0.452539	−	0.783821i	−0.0313779	−	0.0543482i
$209$	41.9869			2.90430
$210$	5.16951	+	12.2319i	0.356730	+	0.844084i
$211$	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
$222$	1.94508	+	8.36434i	0.130545	+	0.561378i
$223$	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
$225$	4.08928	+	14.4318i	0.272619	+	0.962122i
$226$	8.34722	+	14.4578i	0.555249	+	0.961719i
$227$	−4.42782	−	7.66921i	−0.293885	−	0.509024i	0.680840	−	0.732432i	$-0.261615\pi$
$227$	−4.42782	−	7.66921i	−0.293885	−	0.509024i	−0.974725	+	0.223409i	$0.928282\pi$
$228$	−2.58100	−	11.0990i	−0.170931	−	0.735048i
$229$	−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
$231$	−25.8925	−	27.6779i	−1.70360	−	1.82107i
$232$	−2.03276			−0.133457
$233$	0.695815			0.0455844			0.0227922	−	0.999740i	$-0.492744\pi$
$233$	0.695815			0.0455844			0.0227922	+	0.999740i	$0.492744\pi$
$234$	2.43664	−	1.19804i	0.159288	−	0.0783181i
$235$	0.682252	+	3.94205i	0.0445052	+	0.257151i
$236$	2.39397	+	1.38216i	0.155834	+	0.0899708i
$237$	−6.09444	+	1.41723i	−0.395877	+	0.0920587i
$238$	5.81900	+	10.0788i	0.377189	+	0.653311i
$239$	2.71108	+	4.69573i	0.175365	+	0.303741i	0.940288	−	0.340381i	$-0.110556\pi$
$239$	2.71108	+	4.69573i	0.175365	+	0.303741i	−0.764922	+	0.644122i	$0.777223\pi$
$240$	3.08944	+	2.33567i	0.199422	+	0.150767i
$241$	−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
$243$	12.6978	−	9.04243i	0.814565	−	0.580072i
$244$		−	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	−0.716112	−	0.697985i	$-0.754080\pi$
$251$	3.90398	−	6.76189i	0.246417	−	0.426806i	0.962529	+	0.271179i	$0.0874134\pi$
$252$	−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
$255$	5.11749	+	12.1089i	0.320470	+	0.758286i
$256$	1.00000			0.0625000
$257$	−6.11433	−	10.5903i	−0.381401	−	0.660606i	0.609862	−	0.792508i	$-0.291225\pi$
$257$	−6.11433	−	10.5903i	−0.381401	−	0.660606i	−0.991263	+	0.131902i	$0.957892\pi$
$258$	−3.23963	−	13.9312i	−0.201690	−	0.867322i
$259$	14.7222	−	8.49987i	0.914794	−	0.528156i
$260$	−1.55444	+	1.29598i	−0.0964020	+	0.0803732i
$261$	0.406042	−	6.08474i	0.0251334	−	0.376636i
$262$	14.6750	+	8.47260i	0.906623	+	0.523439i
$263$			11.4714i			0.707359i	0.935367	+	0.353679i	$0.115070\pi$
$263$			11.4714i			0.707359i	−0.935367	+	0.353679i	$0.884930\pi$
$264$	−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
$267$	6.51925	−	6.09871i	0.398972	−	0.373235i
$268$	0.0466974	−	0.0269608i	0.00285250	−	0.00164689i
$269$	3.40220	+	5.89278i	0.207436	+	0.359289i	0.950906	−	0.309480i	$-0.100155\pi$
$269$	3.40220	+	5.89278i	0.207436	+	0.359289i	−0.743470	+	0.668769i	$0.766822\pi$
$270$	−7.60858	+	8.78120i	−0.463043	+	0.534407i
$271$			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
$273$	−3.67202	−	3.92522i	−0.222241	−	0.237565i
$274$	−7.94537	+	4.58726i	−0.479997	+	0.277127i
$275$	24.3143	+	20.6654i	1.46621	+	1.24617i
$276$	−1.51628	−	1.62084i	−0.0912693	−	0.0975629i
$277$	−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
$279$	16.1335	−	4.32554i	0.965887	−	0.258964i
$280$	2.64499	−	7.19621i	0.158068	−	0.430056i
$281$			7.77372i			0.463741i	0.972747	+	0.231871i	$0.0744846\pi$
$281$			7.77372i			0.463741i	−0.972747	+	0.231871i	$0.925515\pi$
$282$	−2.26302	+	2.11704i	−0.134761	+	0.126068i
$283$			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
$285$	−23.4703	+	9.91911i	−1.39026	+	0.587558i
$286$	2.88810	−	5.00233i	0.170777	−	0.295794i
$287$	7.43665			0.438972
$288$	−0.199749	+	2.99334i	−0.0117704	+	0.176384i
$289$	−2.73956	−	4.74505i	−0.161150	−	0.279121i
$290$	0.775149	+	4.47880i	0.0455183	+	0.263004i
$291$	−17.4717	−	18.6765i	−1.02421	−	1.09483i
$292$	5.91441	+	10.2441i	0.346115	+	0.599488i
$293$	−8.96242	+	15.5234i	−0.523590	+	0.906885i	0.476033	+	0.879427i	$0.342074\pi$
$293$	−8.96242	+	15.5234i	−0.523590	+	0.906885i	−0.999623	+	0.0274571i	$0.991259\pi$
$294$	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
$297$	11.7363	−	31.0155i	0.681007	−	1.79970i
$298$	−13.6580	−	7.88548i	−0.791189	−	0.456793i
$299$	1.00441	−	0.579899i	0.0580868	−	0.0335364i
$300$	3.96812	−	7.69766i	0.229100	−	0.444425i
$301$	−24.5206	+	14.1570i	−1.41334	+	0.815995i
$302$		−	1.96141i		−	0.112867i
$303$	14.5039	+	15.5040i	0.833226	+	0.890681i
$304$	−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	$-0.935770\pi$
$311$		−	7.06882i		−	0.400836i	0.979710	−	0.200418i	$-0.0642300\pi$
$312$	−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
$315$	21.0124	+	9.35480i	1.18391	+	0.527083i
$316$	3.12853	+	1.80626i	0.175993	+	0.101610i
$317$	−4.15118	+	7.19006i	−0.233154	+	0.403834i	−0.958734	−	0.284303i	$-0.908238\pi$
$317$	−4.15118	+	7.19006i	−0.233154	+	0.403834i	0.725581	+	0.688137i	$0.241571\pi$
$318$	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
$321$	0.706184	+	3.03678i	0.0394154	+	0.169496i
$322$	−2.19685	+	3.80506i	−0.122426	+	0.212048i
$323$	−19.3389	+	11.1653i	−1.07605	+	0.621256i
$324$	−8.92020	−	1.19584i	−0.495567	−	0.0664354i
$325$	3.44820	+	2.93072i	0.191272	+	0.162567i
$326$		−	1.25379i		−	0.0694410i
$327$	−15.1058	+	14.1314i	−0.835355	+	0.781469i
$328$	1.87833	−	1.08446i	0.103714	−	0.0598791i
$329$	5.31265	+	3.06726i	0.292896	+	0.169103i
$330$	−3.05078	+	24.5283i	−0.167940	+	1.35024i
$331$	−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
$336$	5.78442	−	1.34513i	0.315566	−	0.0733829i
$337$	−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
$345$	−2.99301	+	3.95891i	−0.161138	+	0.213141i
$346$	−11.6604	−	20.1964i	−0.626866	−	1.08576i
$347$	17.9299	+	10.3518i	0.962526	+	0.555714i	0.896949	−	0.442133i	$-0.145778\pi$
$347$	17.9299	+	10.3518i	0.962526	+	0.555714i	0.0655762	+	0.997848i	$0.479111\pi$
$348$	−2.57116	+	2.40530i	−0.137828	+	0.128938i
$349$	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
$351$	1.66441	−	4.39855i	0.0888397	−	0.234777i
$352$	3.19099	+	5.52696i	0.170080	+	0.294588i
$353$	13.3349	+	7.69893i	0.709747	+	0.409773i	0.810967	−	0.585091i	$-0.198941\pi$
$353$	13.3349	+	7.69893i	0.709747	+	0.409773i	−0.101220	+	0.994864i	$0.532275\pi$
$354$	4.66350	−	1.08447i	0.247862	−	0.0576389i
$355$	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	−0.763375	−	0.645955i	$-0.776459\pi$
$359$	−11.0965	+	6.40655i	−0.585649	+	0.338125i	0.177726	+	0.984080i	$0.443126\pi$
$360$	6.67144	−	0.701337i	0.351616	−	0.0369637i
$361$	−12.1415	−	21.0297i	−0.639026	−	1.10683i
$362$	−0.120326	+	0.0694702i	−0.00632419	+	0.00365127i
$363$	−11.6633	−	50.1550i	−0.612162	−	2.63246i
$364$			3.10328i			0.162656i
$365$	20.3155	−	16.9376i	1.06336	−	0.886557i
$366$	−5.51039	−	5.89036i	−0.288033	−	0.307894i
$367$	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
$369$	2.87096	+	5.83912i	0.149456	+	0.303972i
$370$	−10.4058	−	3.82469i	−0.540973	−	0.198836i
$371$	−30.1248			−1.56400
$372$	−8.50831	−	4.53968i	−0.441135	−	0.235372i
$373$		−	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
$375$	−18.4735	−	5.80768i	−0.953968	−	0.299907i
$376$	1.78914			0.0922681
$377$	−0.919902	−	1.59332i	−0.0473774	−	0.0820600i
$378$	2.87100	+	17.5834i	0.147669	+	0.904394i
$379$	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
$381$	4.05992	+	17.4587i	0.207996	+	0.894437i
$382$	11.0681	−	6.39017i	0.566293	−	0.326949i
$383$	15.9925	−	9.23329i	0.817180	−	0.471799i	−0.0322633	−	0.999479i	$-0.510272\pi$
$383$	15.9925	−	9.23329i	0.817180	−	0.471799i	0.849443	+	0.527681i	$0.176938\pi$
$384$	1.26486	−	1.18327i	0.0645472	−	0.0603834i
$385$	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	−0.990956	−	0.134190i	$-0.957157\pi$
$389$	−7.48029	+	12.9562i	−0.379266	+	0.656907i	0.611690	+	0.791098i	$0.290490\pi$
$390$	−0.432655	+	3.47855i	−0.0219084	+	0.176143i
$391$	−2.17475	+	3.76677i	−0.109982	+	0.190494i
$392$	−2.37814	−	4.11906i	−0.120114	−	0.208044i
$393$	28.5872	−	6.64777i	1.44203	−	0.335336i
$394$	21.2751	−	12.2832i	1.07182	−	0.618817i
$395$	2.78675	−	7.58191i	0.140217	−	0.381487i
$396$	−17.1815	+	8.44772i	−0.863402	+	0.424514i
$397$	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	$-0.624551\pi$
$401$	−15.2743			−0.762762			−0.381381	+	0.924418i	$0.624551\pi$
$402$	0.0271639	−	0.0893572i	0.00135481	−	0.00445673i
$403$	3.31757	−	3.79314i	0.165260	−	0.188950i
$404$		−	12.2575i		−	0.609832i
$405$	0.766725	+	20.1100i	0.0380989	+	0.999274i
$406$	6.03603	+	3.48490i	0.299563	+	0.172953i
$407$	31.6419			1.56843
$408$	5.72621	−	1.33160i	0.283490	−	0.0659238i
$409$	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
$414$	−3.83577	−	0.255966i	−0.188518	−	0.0125800i
$415$	19.7530	+	23.6923i	0.969636	+	1.16301i
$416$	0.452539	+	0.783821i	0.0221876	+	0.0384300i
$417$	−21.6412	−	23.1335i	−1.05978	−	1.13285i
$418$	−41.9869			−2.05365
$419$		−	21.4031i		−	1.04561i	−0.852452	−	0.522806i	$-0.824885\pi$
$419$		−	21.4031i		−	1.04561i	0.852452	−	0.522806i	$-0.175115\pi$
$420$	−5.16951	−	12.2319i	−0.252246	−	0.596858i
$421$	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
$423$	−0.357381	+	5.35552i	−0.0173764	+	0.260394i
$424$	−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
$429$	−2.26606	−	9.74465i	−0.109406	−	0.470476i
$430$	17.3314	+	6.37022i	0.835796	+	0.307199i
$431$	10.6515	+	6.14966i	0.513066	+	0.296219i	0.734093	−	0.679049i	$-0.237608\pi$
$431$	10.6515	+	6.14966i	0.513066	+	0.296219i	−0.221027	+	0.975268i	$0.570941\pi$
$432$	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
$435$	6.28008	+	4.74785i	0.301107	+	0.227642i
$436$	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
$441$	12.8048	−	6.29582i	0.609753	−	0.299801i
$442$			3.07206i			0.146123i
$443$	−3.14960	−	5.45527i	−0.149642	−	0.259188i	0.781453	−	0.623964i	$-0.214479\pi$
$443$	−3.14960	−	5.45527i	−0.149642	−	0.259188i	−0.931095	+	0.364776i	$0.881146\pi$
$444$	−1.94508	−	8.36434i	−0.0923093	−	0.396954i
$445$	1.96541	+	11.3561i	0.0931696	+	0.538333i
$446$	−0.843359	+	1.46074i	−0.0399342	+	0.0691680i
$447$	−26.6062	+	6.18710i	−1.25843	+	0.292640i
$448$	−2.96938	−	1.71437i	−0.140290	−	0.0809965i
$449$	−26.3801			−1.24495			−0.622476	−	0.782639i	$-0.713873\pi$
$449$	−26.3801			−1.24495			−0.622476	+	0.782639i	$0.713873\pi$
$450$	−4.08928	−	14.4318i	−0.192770	−	0.680323i
$451$	11.9875	+	6.92098i	0.564469	+	0.325896i
$452$	−8.34722	−	14.4578i	−0.392620	−	0.680038i
$453$	−2.32088	−	2.48091i	−0.109044	−	0.116563i
$454$	4.42782	+	7.66921i	0.207808	+	0.359934i
$455$	6.83750	−	1.18337i	0.320547	−	0.0554773i
$456$	2.58100	+	11.0990i	0.120866	+	0.519757i
$457$	−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
$459$	2.84212	+	17.4065i	0.132659	+	0.812466i
$460$	2.82340	−	0.488647i	0.131642	−	0.0227833i
$461$	−0.0357305			−0.00166413			−0.000832067	−	1.00000i	$-0.500265\pi$
$461$	−0.0357305			−0.00166413			−0.000832067		1.00000i	$0.500265\pi$
$462$	25.8925	+	27.6779i	1.20463	+	1.28769i
$463$	−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
$465$	−6.75788	+	20.4776i	−0.313389	+	0.949625i
$466$	−0.695815			−0.0322330
$467$	5.63272			0.260651			0.130326	−	0.991471i	$-0.458398\pi$
$467$	5.63272			0.260651			0.130326	+	0.991471i	$0.458398\pi$
$468$	−2.43664	+	1.19804i	−0.112634	+	0.0553793i
$469$	−0.184883			−0.00853711
$470$	−0.682252	−	3.94205i	−0.0314699	−	0.181833i
$471$	7.17689	+	7.67177i	0.330693	+	0.353496i
$472$	−2.39397	−	1.38216i	−0.110191	−	0.0636190i
$473$	−52.7013			−2.42321
$474$	6.09444	−	1.41723i	0.279927	−	0.0650953i
$475$	5.91676	−	32.3584i	0.271479	−	1.48471i
$476$	−5.81900	−	10.0788i	−0.266713	−	0.461961i
$477$	−11.6298	−	23.6534i	−0.532493	−	1.08302i
$478$	−2.71108	−	4.69573i	−0.124002	−	0.214778i
$479$	16.0091	+	9.24288i	0.731476	+	0.422318i	0.818962	−	0.573848i	$-0.194550\pi$
$479$	16.0091	+	9.24288i	0.731476	+	0.422318i	−0.0874856	+	0.996166i	$0.527883\pi$
$480$	−3.08944	−	2.33567i	−0.141013	−	0.106608i
$481$	4.48739			0.204607
$482$	19.9045	+	11.4919i	0.906626	+	0.523441i
$483$	1.72370	+	7.41235i	0.0784309	+	0.337273i
$484$	−14.8648	+	25.7466i	−0.675674	+	1.17030i
$485$	32.5333	−	5.63056i	1.47726	−	0.255670i
$486$	−12.6978	+	9.04243i	−0.575985	+	0.410173i
$487$	−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
$489$	−1.48357	−	1.58587i	−0.0670894	−	0.0717155i
$490$	−8.16873	+	6.81051i	−0.369026	+	0.307668i
$491$	1.65595	+	2.86819i	0.0747321	+	0.129440i	0.900970	−	0.433882i	$-0.142857\pi$
$491$	1.65595	+	2.86819i	0.0747321	+	0.129440i	−0.826238	+	0.563322i	$0.809523\pi$
$492$	1.09263	−	3.59426i	0.0492595	−	0.162042i
$493$	5.97529	+	3.44984i	0.269114	+	0.155373i
$494$	−5.95449			−0.267905
$495$	25.1648	+	34.6348i	1.13107	+	1.55672i
$496$	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
$501$	20.0276	−	4.65731i	0.894769	−	0.208073i
$502$	−3.90398	+	6.76189i	−0.174243	+	0.301798i
$503$	−17.3799	+	30.1028i	−0.774930	+	1.34222i	0.159904	+	0.987133i	$0.448881\pi$
$503$	−17.3799	+	30.1028i	−0.774930	+	1.34222i	−0.934834	+	0.355085i	$0.884452\pi$
$504$	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
$507$	4.77866	+	20.5495i	0.212228	+	0.912636i
$508$	5.17437	−	8.96227i	0.229576	−	0.397637i
$509$	−9.19595	−	15.9279i	−0.407603	−	0.705990i	0.587017	−	0.809574i	$-0.300302\pi$
$509$	−9.19595	−	15.9279i	−0.407603	−	0.705990i	−0.994621	+	0.103585i	$0.966969\pi$
$510$	−5.11749	−	12.1089i	−0.226606	−	0.536190i
$511$		−	40.5580i		−	1.79418i
$512$	−1.00000			−0.0441942
$513$	−33.7386	+	5.50880i	−1.48960	+	0.243220i
$514$	6.11433	+	10.5903i	0.269691	+	0.467119i
$515$	8.11653	+	9.73521i	0.357657	+	0.428984i
$516$	3.23963	+	13.9312i	0.142617	+	0.613289i
$517$	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	0.999116	−	0.0420428i	$-0.0133866\pi$
$521$	33.3768	+	19.2701i	1.46226	+	0.844238i	0.463148	+	0.886281i	$0.346720\pi$
$522$	−0.406042	+	6.08474i	−0.0177720	+	0.266322i
$523$	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
$525$	−24.9795	+	16.0544i	−1.09020	+	0.700673i
$526$		−	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
$534$	−6.51925	+	6.09871i	−0.282115	+	0.263917i
$535$	−3.77796	−	1.38860i	−0.163335	−	0.0600344i
$536$	−0.0466974	+	0.0269608i	−0.00201702	+	0.00116453i
$537$	−4.47941	−	19.2626i	−0.193301	−	0.831245i
$538$	−3.40220	−	5.89278i	−0.146679	−	0.254056i
$539$	15.1773	−	26.2878i	0.653731	−	1.13230i
$540$	7.60858	−	8.78120i	0.327421	−	0.377883i
$541$	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
$546$	3.67202	+	3.92522i	0.157148	+	0.167984i
$547$	−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
$549$	−13.9398	−	0.930218i	−0.594935	−	0.0397007i
$550$	−24.3143	−	20.6654i	−1.03676	−	0.881174i
$551$	−6.68673	+	11.5818i	−0.284864	+	0.493400i
$552$	1.51628	+	1.62084i	0.0645372	+	0.0689874i
$553$	−6.19319	−	10.7269i	−0.263361	−	0.456155i
$554$	28.8854			1.22722
$555$	−17.6876	+	7.47518i	−0.750795	+	0.317304i
$556$			18.2894i			0.775642i
$557$		−	6.44159i		−	0.272939i	−0.990644	−	0.136469i	$-0.956424\pi$
$557$		−	6.44159i		−	0.272939i	0.990644	−	0.136469i	$-0.0435755\pi$
$558$	−16.1335	+	4.32554i	−0.682985	+	0.183115i
$559$	−7.47397			−0.316115
$560$	−2.64499	+	7.19621i	−0.111771	+	0.304095i
$561$	25.6320	+	27.3994i	1.08218	+	1.15680i
$562$		−	7.77372i		−	0.327915i
$563$	0.125330	+	0.217078i	0.00528203	+	0.00914874i	0.868654	−	0.495419i	$-0.164985\pi$
$563$	0.125330	+	0.217078i	0.00528203	+	0.00914874i	−0.863372	+	0.504567i	$0.831652\pi$
$564$	2.26302	−	2.11704i	0.0952903	−	0.0891434i
$565$	−28.6720	+	23.9047i	−1.20624	+	1.00568i
$566$		−	17.5057i		−	0.735818i
$567$	24.4373	+	18.8434i	1.02627	+	0.791350i
$568$	9.80635	−	5.66170i	0.411465	−	0.237560i
$569$	−0.964911	−	1.67127i	−0.0404512	−	0.0700635i	0.845091	−	0.534622i	$-0.179546\pi$
$569$	−0.964911	−	1.67127i	−0.0404512	−	0.0700635i	−0.885542	+	0.464559i	$0.846213\pi$
$570$	23.4703	−	9.91911i	0.983064	−	0.415466i
$571$	−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
$576$	0.199749	−	2.99334i	0.00832289	−	0.124723i
$577$	−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
$579$	−17.9722	+	4.17932i	−0.746898	+	0.173687i
$580$	−0.775149	−	4.47880i	−0.0321863	−	0.185972i
$581$	47.2995			1.96231
$582$	17.4717	+	18.6765i	0.724225	+	0.774165i
$583$	−48.5596	−	28.0359i	−2.01113	−	1.16113i
$584$	−5.91441	−	10.2441i	−0.244740	−	0.423902i
$585$	3.56881	+	4.91183i	0.147552	+	0.203079i
$586$	8.96242	−	15.5234i	0.370234	−	0.641264i
$587$		−	34.7319i		−	1.43354i	−0.697310	−	0.716770i	$-0.745620\pi$
$587$		−	34.7319i		−	1.43354i	0.697310	−	0.716770i	$-0.254380\pi$
$588$	−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	$-0.752284\pi$
$593$	−34.6846			−1.42432			−0.712162	+	0.702015i	$0.752284\pi$
$594$	−11.7363	+	31.0155i	−0.481545	+	1.27258i
$595$	−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	−0.784274	−	0.620415i	$-0.786964\pi$
$599$	−15.6420	+	9.03093i	−0.639116	+	0.368994i	0.145158	+	0.989409i	$0.453631\pi$
$600$	−3.96812	+	7.69766i	−0.161998	+	0.314256i
$601$	−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
$603$	−0.0713750	−	0.145167i	−0.00290661	−	0.00591165i
$604$			1.96141i			0.0798087i
$605$	62.3963	+	22.9339i	2.53677	+	0.932398i
$606$	−14.5039	−	15.5040i	−0.589180	−	0.629807i
$607$	−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
$609$	11.7583	−	2.73432i	0.476471	−	0.110800i
$610$	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
$615$	−8.33594	−	1.03681i	−0.336137	−	0.0418081i
$616$		−	21.8822i		−	0.881658i
$617$	−1.14669	+	1.98612i	−0.0461639	+	0.0799581i	−0.888184	−	0.459488i	$-0.848033\pi$
$617$	−1.14669	+	1.98612i	−0.0461639	+	0.0799581i	0.842020	+	0.539446i	$0.181366\pi$
$618$	−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
$627$	−53.1076	+	49.6818i	−2.12091	+	1.98410i
$628$		−	6.06530i		−	0.242032i
$629$	−14.5741	+	8.41434i	−0.581106	+	0.335502i
$630$	−21.0124	−	9.35480i	−0.837154	−	0.372704i
$631$	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
$633$	10.9813	+	47.2224i	0.436467	+	1.87692i
$634$	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
$639$	14.9886	+	30.4847i	0.592940	+	1.20596i
$640$	0.381329	+	2.20331i	0.0150733	+	0.0870936i
$641$	−8.80615	−	15.2527i	−0.347822	−	0.602445i	0.638040	−	0.770003i	$-0.279745\pi$
$641$	−8.80615	−	15.2527i	−0.347822	−	0.602445i	−0.985862	+	0.167558i	$0.946412\pi$
$642$	−0.706184	−	3.03678i	−0.0278709	−	0.119852i
$643$	−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
$645$	29.4595	−	12.4503i	1.15997	−	0.490230i
$646$	19.3389	−	11.1653i	0.760880	−	0.439294i
$647$		−	34.8674i		−	1.37078i	−0.728177	−	0.685389i	$-0.759632\pi$
$647$		−	34.8674i		−	1.37078i	0.728177	−	0.685389i	$-0.240368\pi$
$648$	8.92020	+	1.19584i	0.350419	+	0.0469769i
$649$		−	17.6418i		−	0.692501i
$650$	−3.44820	−	2.93072i	−0.135249	−	0.114952i
$651$	17.4817	+	28.0664i	0.685161	+	1.10001i
$652$			1.25379i			0.0491022i
$653$	−16.8526			−0.659492			−0.329746	−	0.944070i	$-0.606963\pi$
$653$	−16.8526			−0.659492			−0.329746	+	0.944070i	$0.606963\pi$
$654$	15.1058	−	14.1314i	0.590685	−	0.552582i
$655$	−13.0718	+	35.5644i	−0.510757	+	1.38962i
$656$	−1.87833	+	1.08446i	−0.0733367	+	0.0423409i
$657$	31.8454	−	15.6576i	1.24241	−	0.610862i
$658$	−5.31265	−	3.06726i	−0.207109	−	0.119574i
$659$		−	9.17901i		−	0.357563i	−0.983889	−	0.178782i	$-0.942784\pi$
$659$		−	9.17901i		−	0.357563i	0.983889	−	0.178782i	$-0.0572156\pi$
$660$	3.05078	−	24.5283i	0.118752	−	0.954763i
$661$	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
$663$	3.63507	+	3.88572i	0.141174	+	0.150909i
$664$	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
$669$	0.661716	+	2.84555i	0.0255834	+	0.110015i
$670$	0.0772100	+	0.0926081i	0.00298288	+	0.00357776i
$671$	−25.7386	+	14.8602i	−0.993628	+	0.573671i
$672$	−5.78442	+	1.34513i	−0.223139	+	0.0518896i
$673$	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
$675$	−22.2491	−	13.4156i	−0.856369	−	0.516365i
$676$	6.09042	−	10.5489i	0.234247	−	0.405727i
$677$	−23.3498	+	13.4810i	−0.897405	+	0.518117i	−0.876357	−	0.481661i	$-0.840034\pi$
$677$	−23.3498	+	13.4810i	−0.897405	+	0.518117i	−0.0210477	+	0.999778i	$0.506700\pi$
$678$	−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	$-0.649294\pi$
$683$	−23.6261			−0.904026			−0.452013	+	0.892011i	$0.649294\pi$
$684$	16.3977	+	10.9847i	0.626981	+	0.420009i
$685$	−13.1370	−	15.7569i	−0.501938	−	0.602039i
$686$		−	7.69312i		−	0.293725i
$687$	30.0343	−	6.98430i	1.14588	−	0.266468i
$688$	4.12891	−	7.15148i	0.157413	−	0.272648i
$689$	−6.88661	−	3.97599i	−0.262359	−	0.151473i
$690$	2.99301	−	3.95891i	0.113942	−	0.150713i
$691$	−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
$693$	65.5009	+	4.37095i	2.48817	+	0.166039i
$694$	−17.9299	−	10.3518i	−0.680608	−	0.392949i
$695$	40.2972	−	6.97426i	1.52856	−	0.264549i
$696$	2.57116	−	2.40530i	0.0974594	−	0.0911726i
$697$	−7.36182			−0.278849
$698$	−29.0198			−1.09842
$699$	−0.880110	+	0.823337i	−0.0332888	+	0.0311415i
$700$	16.8641	+	3.08361i	0.637404	+	0.116550i
$701$	30.3007	+	17.4941i	1.14444	+	0.660744i	0.947527	−	0.319676i	$-0.103574\pi$
$701$	30.3007	+	17.4941i	1.14444	+	0.660744i	0.196916	+	0.980420i	$0.436907\pi$
$702$	−1.66441	+	4.39855i	−0.0628191	+	0.166013i
$703$	−16.3093	−	28.2486i	−0.615118	−	1.06542i
$704$	−3.19099	−	5.52696i	−0.120265	−	0.208305i
$705$	−5.52745	−	4.17885i	−0.208176	−	0.157385i
$706$	−13.3349	−	7.69893i	−0.501867	−	0.289753i
$707$	−21.0138	+	36.3971i	−0.790307	+	1.36885i
$708$	−4.66350	+	1.08447i	−0.175265	+	0.0407568i
$709$		−	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	$0.554464\pi$
$719$	−25.1655	+	43.5879i	−0.938515	+	1.62556i	−0.768243	+	0.640158i	$0.778869\pi$
$720$	−6.67144	+	0.701337i	−0.248630	+	0.0261373i
$721$	19.4354			0.723812
$722$	12.1415	+	21.0297i	0.451859	+	0.782644i
$723$	38.7744	−	9.01676i	1.44204	−	0.335337i
$724$	0.120326	−	0.0694702i	0.00447188	−	0.00258184i
$725$	−9.57261	+	3.41579i	−0.355518	+	0.126859i
$726$	11.6633	+	50.1550i	0.432864	+	1.86143i
$727$	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
$732$	5.51039	+	5.89036i	0.203670	+	0.217714i
$733$	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
$735$	−2.27365	+	18.2802i	−0.0838649	+	0.674274i
$736$		−	1.28143i		−	0.0472343i
$737$	−0.298022	−	0.172063i	−0.0109778	−	0.00633802i
$738$	−2.87096	−	5.83912i	−0.105681	−	0.214941i
$739$	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
$741$	−7.53161	+	7.04576i	−0.276680	+	0.258833i
$742$	30.1248			1.10592
$743$		−	23.7503i		−	0.871315i	−0.900112	−	0.435658i	$-0.856516\pi$
$743$		−	23.7503i		−	0.871315i	0.900112	−	0.435658i	$-0.143484\pi$
$744$	8.50831	+	4.53968i	0.311930	+	0.166433i
$745$	12.1660	−	33.0999i	0.445727	−	1.21269i
$746$			26.2391i			0.960683i
$747$	18.2602	+	37.1386i	0.668105	+	1.35883i
$748$		−	21.6620i		−	0.792041i
$749$	−5.34508	+	3.08598i	−0.195305	+	0.112759i
$750$	18.4735	+	5.80768i	0.674558	+	0.212066i
$751$	−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
$753$	3.06314	+	13.1723i	0.111627	+	0.480025i
$754$	0.919902	+	1.59332i	0.0335009	+	0.0580252i
$755$	4.32160	−	0.747943i	0.157279	−	0.0272204i
$756$	−2.87100	−	17.5834i	−0.104417	−	0.639503i
$757$	−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	−0.679557	−	0.733622i	$-0.737828\pi$
$761$	8.15330	−	14.1219i	0.295557	−	0.511919i	0.975114	+	0.221703i	$0.0711615\pi$
$762$	−4.05992	−	17.4587i	−0.147075	−	0.632462i
$763$	−35.4624	−	20.4742i	−1.28382	−	0.741216i
$764$	−11.0681	+	6.39017i	−0.400430	+	0.231188i
$765$	−20.8010	−	9.26067i	−0.752060	−	0.334820i
$766$	−15.9925	+	9.23329i	−0.577833	+	0.333612i
$767$		−	2.50192i		−	0.0903391i
$768$	−1.26486	+	1.18327i	−0.0456418	+	0.0426975i
$769$	−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	$0.0190346\pi$
$773$			3.32319i			0.119527i	−0.998213	+	0.0597635i	$0.980965\pi$
$774$	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
$780$	0.432655	−	3.47855i	0.0154915	−	0.124552i
$781$	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
$786$	−28.5872	+	6.64777i	−1.01967	+	0.237118i
$787$	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
$789$	−13.5738	−	14.5098i	−0.483240	−	0.516562i
$790$	−2.78675	+	7.58191i	−0.0991482	+	0.269752i
$791$			57.2409i			2.03525i
$792$	17.1815	−	8.44772i	0.610517	−	0.300177i
$793$	−3.65019	+	2.10744i	−0.129622	+	0.0748374i
$794$	−9.37611	−	5.41330i	−0.332746	−	0.192111i
$795$	33.7677	+	4.19996i	1.19762	+	0.148957i
$796$	−1.07789	+	0.622319i	−0.0382048	+	0.0220575i
$797$	4.62644	−	2.67108i	0.163877	−	0.0946144i	−0.415819	−	0.909448i	$-0.636505\pi$
$797$	4.62644	−	2.67108i	0.163877	−	0.0946144i	0.579695	+	0.814833i	$0.303172\pi$
$798$	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
$801$	−1.02953	+	15.4280i	−0.0363768	+	0.545123i
$802$	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	−0.806961	−	0.590605i	$-0.798889\pi$
$809$	3.07180	−	5.32052i	0.107999	−	0.187059i	0.914959	+	0.403546i	$0.132222\pi$
$810$	−0.766725	−	20.1100i	−0.0269400	−	0.706593i
$811$	−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
$813$	−37.5221	−	40.1094i	−1.31596	−	1.40670i
$814$	−31.6419			−1.10905
$815$	2.76249	−	0.478106i	0.0967659	−	0.0167473i
$816$	−5.72621	+	1.33160i	−0.200458	+	0.0466152i
$817$	27.1640	+	47.0495i	0.950349	+	1.64605i
$818$	−8.93038	−	5.15596i	−0.312243	−	0.180274i
$819$	9.28918	+	0.619879i	0.324590	+	0.0216603i
$820$	3.10566	+	3.72502i	0.108454	+	0.130084i
$821$	−41.5376			−1.44967			−0.724836	−	0.688921i	$-0.758085\pi$
$821$	−41.5376			−1.44967			−0.724836	+	0.688921i	$0.758085\pi$
$822$	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
$825$	−55.2069	+	2.63152i	−1.92206	+	0.0916177i
$826$	4.73906	+	8.20830i	0.164893	+	0.285603i
$827$	−4.32024	+	2.49429i	−0.150230	+	0.0867350i	−0.573230	−	0.819394i	$-0.694310\pi$
$827$	−4.32024	+	2.49429i	−0.150230	+	0.0867350i	0.423001	+	0.906129i	$0.360977\pi$
$828$	3.83577	+	0.255966i	0.133302	+	0.00889542i
$829$		−	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
$831$	36.5360	−	34.1792i	1.26742	−	1.18566i
$832$	−0.452539	−	0.783821i	−0.0156890	−	0.0271741i
$833$			16.1440i			0.559356i
$834$	21.6412	+	23.1335i	0.749375	+	0.801048i
$835$	−9.15786	+	24.9158i	−0.316921	+	0.862246i
$836$	41.9869			1.45215
$837$	−15.2884	+	24.5615i	−0.528443	+	0.848969i
$838$			21.4031i			0.739359i
$839$		−	52.0333i		−	1.79639i	−0.439598	−	0.898195i	$-0.644879\pi$
$839$		−	52.0333i		−	1.79639i	0.439598	−	0.898195i	$-0.355121\pi$
$840$	5.16951	+	12.2319i	0.178365	+	0.422042i
$841$	−24.8679			−0.857514
$842$	−9.22392	−	15.9763i	−0.317877	−	0.550579i
$843$	−9.19840	−	9.83268i	−0.316810	−	0.338656i
$844$	13.9957	−	24.2412i	0.481751	−	0.834417i
$845$	−25.5650	−	9.39649i	−0.879463	−	0.323249i
$846$	0.357381	−	5.35552i	0.0122870	−	0.184127i
$847$	88.2787	−	50.9677i	3.03329	−	1.75127i
$848$	7.60886	−	4.39298i	0.261289	−	0.150855i
$849$	−20.7139	−	22.1422i	−0.710900	−	0.759920i
$850$	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
$855$	17.9497	−	40.3180i	0.613868	−	1.37885i
$856$	−0.900033	+	1.55890i	−0.0307625	+	0.0532822i
$857$	−6.10310	−	10.5709i	−0.208478	−	0.361094i	0.742757	−	0.669561i	$-0.233518\pi$
$857$	−6.10310	−	10.5709i	−0.208478	−	0.361094i	−0.951235	+	0.308466i	$0.900184\pi$
$858$	2.26606	+	9.74465i	0.0773620	+	0.332677i
$859$	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
$861$	−9.40633	+	8.79956i	−0.320567	+	0.299888i
$862$	−10.6515	−	6.14966i	−0.362792	−	0.209458i
$863$	13.5233	−	7.80768i	0.460339	−	0.265777i	−0.251848	−	0.967767i	$-0.581038\pi$
$863$	13.5233	−	7.80768i	0.460339	−	0.265777i	0.712187	+	0.701990i	$0.247705\pi$
$864$	−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
$870$	−6.28008	−	4.74785i	−0.212915	−	0.160967i
$871$	−0.0422648	−	0.0244016i	−0.00143209	−	0.000826816i
$872$	−11.9427			−0.404430
$873$	44.1986	+	2.94943i	1.49590	+	0.0998229i
$874$	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
$879$	−7.03210	−	30.2399i	−0.237187	−	1.01997i
$880$	−10.9608	+	9.13834i	−0.369488	+	0.308053i
$881$	1.89020	+	3.27392i	0.0636825	+	0.110301i	0.896109	−	0.443834i	$-0.146382\pi$
$881$	1.89020	+	3.27392i	0.0636825	+	0.110301i	−0.832426	+	0.554136i	$0.813049\pi$
$882$	−12.8048	+	6.29582i	−0.431160	+	0.211991i
$883$	−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
$885$	4.16775	+	9.86161i	0.140097	+	0.331495i
$886$	3.14960	+	5.45527i	0.105813	+	0.183273i
$887$	15.3302	−	26.5527i	0.514738	−	0.891553i	−0.485115	−	0.874450i	$-0.661222\pi$
$887$	15.3302	−	26.5527i	0.514738	−	0.891553i	0.999854	−	0.0171029i	$-0.00544429\pi$
$888$	1.94508	+	8.36434i	0.0652725	+	0.280689i
$889$	−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
$894$	26.6062	−	6.18710i	0.889844	−	0.206928i
$895$	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
$900$	4.08928	+	14.4318i	0.136309	+	0.481061i
$901$	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
$906$	2.32088	+	2.48091i	0.0771060	+	0.0824228i
$907$		−	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
$909$	−36.6908	−	2.44842i	−1.21696	−	0.0812090i
$910$	−6.83750	+	1.18337i	−0.226661	+	0.0392283i
$911$	−16.7161	+	28.9532i	−0.553830	+	0.959261i	0.444164	+	0.895946i	$0.353501\pi$
$911$	−16.7161	+	28.9532i	−0.553830	+	0.959261i	−0.997994	+	0.0633155i	$0.979833\pi$
$912$	−2.58100	−	11.0990i	−0.0854655	−	0.367524i
$913$	76.2443	+	44.0196i	2.52332	+	1.45684i
$914$	39.1752			1.29580
$915$	10.8770	−	14.3873i	0.359584	−	0.475629i
$916$	−15.4179	−	8.90151i	−0.509421	−	0.294114i
$917$	29.0504	+	50.3167i	0.959328	+	1.66160i
$918$	−2.84212	−	17.4065i	−0.0938038	−	0.574500i
$919$	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
$921$	−12.4913	+	2.90478i	−0.411602	+	0.0957156i
$922$	0.0357305			0.00117672
$923$	8.87551	+	5.12428i	0.292141	+	0.168668i
$924$	−25.8925	−	27.6779i	−0.851801	−	0.910537i
$925$	4.45895	−	24.3857i	0.146609	−	0.801798i
$926$	8.82365			0.289963
$927$	7.50313	+	15.2603i	0.246435	+	0.501214i
$928$	−2.03276			−0.0667285
$929$	−48.3243			−1.58547			−0.792734	−	0.609567i	$-0.791343\pi$
$929$	−48.3243			−1.58547			−0.792734	+	0.609567i	$0.791343\pi$
$930$	6.75788	−	20.4776i	0.221600	−	0.671486i
$931$	−31.2915			−1.02554
$932$	0.695815			0.0227922
$933$	8.36431	+	8.94108i	0.273835	+	0.292718i
$934$	−5.63272			−0.184308
$935$	−47.7282	+	8.26034i	−1.56088	+	0.270142i
$936$	2.43664	−	1.19804i	0.0796440	−	0.0391591i
$937$	−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
$939$	−7.15316	−	30.7605i	−0.233435	−	1.00383i
$940$	0.682252	+	3.94205i	0.0222526	+	0.128575i
$941$	22.1895	+	38.4333i	0.723356	+	1.25289i	0.959647	+	0.281207i	$0.0907349\pi$
$941$	22.1895	+	38.4333i	0.723356	+	1.25289i	−0.236291	+	0.971682i	$0.575932\pi$
$942$	−7.17689	−	7.67177i	−0.233836	−	0.249960i
$943$	−1.38966	−	2.40696i	−0.0452535	−	0.0783814i
$944$	2.39397	+	1.38216i	0.0779170	+	0.0449854i
$945$	−37.6470	+	13.0308i	−1.22466	+	0.423892i
$946$	52.7013			1.71347
$947$	−37.2751	−	21.5208i	−1.21128	−	0.699332i	−0.248241	−	0.968698i	$-0.579852\pi$
$947$	−37.2751	−	21.5208i	−1.21128	−	0.699332i	−0.963038	+	0.269367i	$0.913186\pi$
$948$	−6.09444	+	1.41723i	−0.197938	+	0.0460293i
$949$	5.35300	−	9.27167i	0.173766	−	0.300971i
$950$	−5.91676	+	32.3584i	−0.191965	+	1.04985i
$951$	−3.25710	−	14.0064i	−0.105619	−	0.454188i
$952$	5.81900	+	10.0788i	0.188595	+	0.326656i
$953$			46.5489i			1.50787i	0.656951	+	0.753933i	$0.271846\pi$
$953$			46.5489i			1.50787i	−0.656951	+	0.753933i	$0.728154\pi$
$954$	11.6298	+	23.6534i	0.376529	+	0.765808i
$955$	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
$960$	3.08944	+	2.33567i	0.0997112	+	0.0753835i
$961$	−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
$966$	−1.72370	−	7.41235i	−0.0554590	−	0.238488i
$967$	−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	0.0213914	−	0.999771i	$-0.493190\pi$
$971$	27.9798	−	16.1541i	0.897914	−	0.518411i	0.876523	+	0.481360i	$0.159857\pi$
$972$	12.6978	−	9.04243i	0.407283	−	0.290036i
$973$	31.3548	−	54.3081i	1.00519	−	1.74104i
$974$	4.58796	+	7.94657i	0.147008	+	0.254625i
$975$	−7.82932	+	0.373196i	−0.250739	+	0.0119518i
$976$		−	4.65692i		−	0.149064i
$977$	10.8353			0.346652			0.173326	−	0.984865i	$-0.444549\pi$
$977$	10.8353			0.346652			0.173326	+	0.984865i	$0.444549\pi$
$978$	1.48357	+	1.58587i	0.0474394	+	0.0507105i
$979$	16.4467	+	28.4866i	0.525640	+	0.910436i
$980$	8.16873	−	6.81051i	0.260941	−	0.217554i
$981$	2.38554	−	35.7485i	0.0761646	−	1.14136i
$982$	−1.65595	−	2.86819i	−0.0528436	−	0.0915277i
$983$	−5.28856	+	3.05335i	−0.168679	+	0.0973867i	−0.581963	−	0.813216i	$-0.697715\pi$
$983$	−5.28856	+	3.05335i	−0.168679	+	0.0973867i	0.413284	+	0.910602i	$0.364382\pi$
$984$	−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
$987$	−10.3492	+	2.40663i	−0.329417	+	0.0766040i
$988$	5.95449			0.189438
$989$	9.16415	+	5.29092i	0.291403	+	0.168242i
$990$	−25.1648	−	34.6348i	−0.799789	−	1.10077i
$991$		−	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
$999$	−25.4259	+	4.15151i	−0.804439	+	0.131348i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.r.a.119.8	✓	64	1.1	even	1	trivial
930.2.r.a.119.19	yes	64	15.14	odd	2	inner
930.2.r.a.719.8	yes	64	465.254	even	6	inner
930.2.r.a.719.19	yes	64	31.6	odd	6	inner
930.2.r.b.119.14	yes	64	3.2	odd	2
930.2.r.b.119.25	yes	64	5.4	even	2
930.2.r.b.719.14	yes	64	155.99	odd	6
930.2.r.b.719.25	yes	64	93.68	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.26486 + 1.18327i) q^{3} +1.00000 q^{4} +(-0.381329 - 2.20331i) q^{5} +(1.26486 - 1.18327i) q^{6} +(-2.96938 - 1.71437i) q^{7} -1.00000 q^{8} +(0.199749 - 2.99334i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.26486 + 1.18327i) q^{3} +1.00000 q^{4} +(-0.381329 - 2.20331i) q^{5} +(1.26486 - 1.18327i) q^{6} +(-2.96938 - 1.71437i) q^{7} -1.00000 q^{8} +(0.199749 - 2.99334i) q^{9} +(0.381329 + 2.20331i) q^{10} +(-3.19099 - 5.52696i) q^{11} +(-1.26486 + 1.18327i) q^{12} +(-0.452539 - 0.783821i) q^{13} +(2.96938 + 1.71437i) q^{14} +(3.08944 + 2.33567i) q^{15} +1.00000 q^{16} +(2.93950 + 1.69712i) q^{17} +(-0.199749 + 2.99334i) q^{18} +(-3.28949 + 5.69756i) q^{19} +(-0.381329 - 2.20331i) q^{20} +(5.78442 - 1.34513i) q^{21} +(3.19099 + 5.52696i) q^{22} +1.28143i q^{23} +(1.26486 - 1.18327i) 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} +(-3.08944 - 2.33567i) 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} +(0.199749 - 2.99334i) 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} +(-5.78442 + 1.34513i) q^{42} +(4.12891 - 7.15148i) q^{43} +(-3.19099 - 5.52696i) q^{44} +(-6.67144 + 0.701337i) q^{45} -1.28143i q^{46} -1.78914 q^{47} +(-1.26486 + 1.18327i) q^{48} +(2.37814 + 4.11906i) q^{49} +(4.70918 - 1.68037i) q^{50} +(-5.72621 + 1.33160i) 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} +(-2.58100 - 11.0990i) q^{57} -2.03276 q^{58} +(2.39397 + 1.38216i) q^{59} +(3.08944 + 2.33567i) 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} +(-1.51628 - 1.62084i) q^{69} +(2.64499 - 7.19621i) q^{70} +(-9.80635 + 5.66170i) q^{71} +(-0.199749 + 2.99334i) q^{72} +(5.91441 + 10.2441i) q^{73} +(2.47900 - 4.29376i) q^{74} +(3.96812 - 7.69766i) 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} +(-8.92020 - 1.19584i) q^{81} +(1.87833 - 1.08446i) q^{82} +(-11.9468 + 6.89749i) q^{83} +(5.78442 - 1.34513i) q^{84} +(2.61837 - 7.12380i) q^{85} +(-4.12891 + 7.15148i) q^{86} +(-2.57116 + 2.40530i) q^{87} +(3.19099 + 5.52696i) q^{88} -5.15412 q^{89} +(6.67144 - 0.701337i) q^{90} +3.10328i q^{91} +1.28143i q^{92} +(-8.50831 - 4.53968i) q^{93} +1.78914 q^{94} +(13.8079 + 5.07513i) q^{95} +(1.26486 - 1.18327i) q^{96} +14.7656i q^{97} +(-2.37814 - 4.11906i) q^{98} +(-17.1815 + 8.44772i) 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	\( 64 q - 64 q^{2} + 64 q^{4} - 2 q^{5} - 64 q^{8} - 4 q^{9} + 2 q^{10} + 64 q^{16} - 6 q^{17} + 4 q^{18} + 4 q^{19} - 2 q^{20} + 2 q^{25} + 18 q^{31} - 64 q^{32} + 8 q^{33} + 6 q^{34} - 16 q^{35} - 4 q^{36} - 4 q^{38} - 8 q^{39} + 2 q^{40} + 5 q^{45} + 4 q^{47} + 30 q^{49} - 2 q^{50} - 8 q^{51} + 6 q^{53} - 6 q^{57} - 18 q^{62} - 12 q^{63} + 64 q^{64} - 8 q^{66} - 6 q^{68} - 10 q^{69} + 16 q^{70} + 4 q^{72} + 15 q^{75} + 4 q^{76} + 8 q^{78} - 30 q^{79} - 2 q^{80} - 12 q^{81} + 54 q^{83} + 16 q^{87} - 5 q^{90} + 18 q^{93} - 4 q^{94} + 56 q^{95} - 30 q^{98} - 102 q^{99}+O(q^{100}) \) 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 + 5 * 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 + 15 * q^75 + 4 * q^76 + 8 * q^78 - 30 * q^79 - 2 * q^80 - 12 * q^81 + 54 * q^83 + 16 * q^87 - 5 * q^90 + 18 * q^93 - 4 * q^94 + 56 * q^95 - 30 * q^98 - 102 * q^99

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