LMFDB - Embedded newform 930.2.n.a.721.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.2
Root			$0.418926 - 1.28932i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.a.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(3.89263 + 2.82816i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(3.89263 + 2.82816i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(-5.16165 - 3.75016i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(-0.206673 - 0.636074i) q^{13} +(3.89263 - 2.82816i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.68038 - 3.40050i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-0.409229 + 1.25948i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(1.48685 - 4.57607i) q^{21} +(-5.16165 + 3.75016i) q^{22} +(6.26400 - 4.55106i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -0.668808 q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.48685 - 4.57607i) q^{28} +(0.718501 - 2.21132i) q^{29} -1.00000 q^{30} +(3.04707 - 4.65997i) q^{31} +1.00000 q^{32} +(-1.97158 + 6.06789i) q^{33} +(-1.78775 - 5.50212i) q^{34} +(3.89263 + 2.82816i) q^{35} +1.00000 q^{36} +1.94233 q^{37} +(1.07138 + 0.778401i) q^{38} +(-0.541077 + 0.393115i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(1.23296 - 3.79468i) q^{41} +(-3.89263 - 2.82816i) q^{42} +(1.79085 - 5.51167i) q^{43} +(1.97158 + 6.06789i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(-2.39263 - 7.36377i) q^{46} +(0.567369 + 1.74618i) q^{47} +(0.809017 - 0.587785i) q^{48} +(4.99097 + 15.3606i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-4.68038 - 3.40050i) q^{51} +(-0.206673 + 0.636074i) q^{52} +(-7.03606 + 5.11199i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-5.16165 - 3.75016i) q^{55} -4.81156 q^{56} +1.32429 q^{57} +(-1.88106 - 1.36667i) q^{58} +(-2.09799 - 6.45695i) q^{59} +(-0.309017 + 0.951057i) q^{60} +1.85410 q^{61} +(-3.49030 - 4.33795i) q^{62} -4.81156 q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.206673 - 0.636074i) q^{65} +(5.16165 + 3.75016i) q^{66} -6.44848 q^{67} -5.78527 q^{68} +(-6.26400 - 4.55106i) q^{69} +(3.89263 - 2.82816i) q^{70} +(-8.01800 + 5.82542i) q^{71} +(0.309017 - 0.951057i) q^{72} +(3.92255 + 2.84990i) q^{73} +(0.600212 - 1.84726i) q^{74} +(-0.309017 - 0.951057i) q^{75} +(1.07138 - 0.778401i) q^{76} +(-9.48636 - 29.1960i) q^{77} +(0.206673 + 0.636074i) q^{78} +(-6.90009 + 5.01321i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-3.22794 - 2.34524i) q^{82} +(-4.55175 + 14.0088i) q^{83} +(-3.89263 + 2.82816i) q^{84} +(4.68038 - 3.40050i) q^{85} +(-4.68851 - 3.40640i) q^{86} -2.32512 q^{87} +6.38016 q^{88} +(6.21881 + 4.51823i) q^{89} +(0.309017 + 0.951057i) q^{90} +(0.994419 - 3.06051i) q^{91} -7.74273 q^{92} +(-5.37350 - 1.45792i) q^{93} +1.83604 q^{94} +(-0.409229 + 1.25948i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-10.9616 - 7.96410i) q^{97} +16.1511 q^{98} +6.38016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + q^{13} + 9 q^{14} + 2 q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - q^{22} + 8 q^{23} + 2 q^{24} + 8 q^{25} + 16 q^{26} + 2 q^{27} - q^{28} - q^{29} - 8 q^{30} + 3 q^{31} + 8 q^{32} + q^{33} - 12 q^{34} + 9 q^{35} + 8 q^{36} + 8 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} + 29 q^{41} - 9 q^{42} - 25 q^{43} - q^{44} - 2 q^{45} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 25 q^{49} - 2 q^{50} - 13 q^{51} + q^{52} - 19 q^{53} + 2 q^{54} - q^{55} - 16 q^{56} + 12 q^{57} + 4 q^{58} + 23 q^{59} + 2 q^{60} - 12 q^{61} - 27 q^{62} - 16 q^{63} - 2 q^{64} + q^{65} + q^{66} - 24 q^{67} - 2 q^{68} - 8 q^{69} + 9 q^{70} + 3 q^{71} - 2 q^{72} - 14 q^{73} + 8 q^{74} + 2 q^{75} + 8 q^{76} - 24 q^{77} - q^{78} - 34 q^{79} - 2 q^{80} - 2 q^{81} - 21 q^{82} + 8 q^{83} - 9 q^{84} + 13 q^{85} + 6 q^{87} + 4 q^{88} + 25 q^{89} - 2 q^{90} + 3 q^{91} - 22 q^{92} - 18 q^{93} - 42 q^{94} - 2 q^{95} + 2 q^{96} - 28 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^12 + q^13 + 9 * q^14 + 2 * q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + q^21 - q^22 + 8 * q^23 + 2 * q^24 + 8 * q^25 + 16 * q^26 + 2 * q^27 - q^28 - q^29 - 8 * q^30 + 3 * q^31 + 8 * q^32 + q^33 - 12 * q^34 + 9 * q^35 + 8 * q^36 + 8 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 + 29 * q^41 - 9 * q^42 - 25 * q^43 - q^44 - 2 * q^45 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 25 * q^49 - 2 * q^50 - 13 * q^51 + q^52 - 19 * q^53 + 2 * q^54 - q^55 - 16 * q^56 + 12 * q^57 + 4 * q^58 + 23 * q^59 + 2 * q^60 - 12 * q^61 - 27 * q^62 - 16 * q^63 - 2 * q^64 + q^65 + q^66 - 24 * q^67 - 2 * q^68 - 8 * q^69 + 9 * q^70 + 3 * q^71 - 2 * q^72 - 14 * q^73 + 8 * q^74 + 2 * q^75 + 8 * q^76 - 24 * q^77 - q^78 - 34 * q^79 - 2 * q^80 - 2 * q^81 - 21 * q^82 + 8 * q^83 - 9 * q^84 + 13 * q^85 + 6 * q^87 + 4 * q^88 + 25 * q^89 - 2 * q^90 + 3 * q^91 - 22 * q^92 - 18 * q^93 - 42 * q^94 - 2 * q^95 + 2 * q^96 - 28 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000			−0.408248
$7$	3.89263	+	2.82816i	1.47128	+	1.06895i	0.980241	+	0.197807i	$0.0633819\pi$
$7$	3.89263	+	2.82816i	1.47128	+	1.06895i	0.491037	+	0.871139i	$0.336618\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.309017	−	0.951057i	0.0977198	−	0.300750i
$11$	−5.16165	−	3.75016i	−1.55630	−	1.13072i	−0.938964	−	0.344014i	$-0.888213\pi$
$11$	−5.16165	−	3.75016i	−1.55630	−	1.13072i	−0.617333	−	0.786702i	$-0.711787\pi$
$12$	−0.309017	+	0.951057i	−0.0892055	+	0.274546i
$13$	−0.206673	−	0.636074i	−0.0573208	−	0.176415i	0.918297	−	0.395893i	$-0.129565\pi$
$13$	−0.206673	−	0.636074i	−0.0573208	−	0.176415i	−0.975618	+	0.219477i	$0.929565\pi$
$14$	3.89263	−	2.82816i	1.04035	−	0.755859i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	4.68038	−	3.40050i	1.13516	−	0.824741i	0.148722	−	0.988879i	$-0.452484\pi$
$17$	4.68038	−	3.40050i	1.13516	−	0.824741i	0.986437	+	0.164138i	$0.0524841\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	−0.409229	+	1.25948i	−0.0938837	+	0.288944i	−0.986961	−	0.160959i	$-0.948541\pi$
$19$	−0.409229	+	1.25948i	−0.0938837	+	0.288944i	0.893077	+	0.449903i	$0.148541\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	1.48685	−	4.57607i	0.324458	−	0.998580i
$22$	−5.16165	+	3.75016i	−1.10047	+	0.799537i
$23$	6.26400	−	4.55106i	1.30613	−	0.948962i	0.306139	−	0.951987i	$-0.400963\pi$
$23$	6.26400	−	4.55106i	1.30613	−	0.948962i	0.999995	+	0.00302500i	$0.000962888\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	−0.668808			−0.131164
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.48685	−	4.57607i	−0.280989	−	0.864795i
$29$	0.718501	−	2.21132i	0.133422	−	0.410632i	−0.861919	−	0.507046i	$-0.830737\pi$
$29$	0.718501	−	2.21132i	0.133422	−	0.410632i	0.995341	+	0.0964143i	$0.0307374\pi$
$30$	−1.00000			−0.182574
$31$	3.04707	−	4.65997i	0.547270	−	0.836956i
$31$	3.04707	−	4.65997i	0.547270	−	0.836956i
$32$	1.00000			0.176777
$33$	−1.97158	+	6.06789i	−0.343207	+	1.05628i
$34$	−1.78775	−	5.50212i	−0.306596	−	0.943605i
$35$	3.89263	+	2.82816i	0.657975	+	0.478047i
$36$	1.00000			0.166667
$37$	1.94233			0.319317			0.159658	−	0.987172i	$-0.448961\pi$
$37$	1.94233			0.319317			0.159658	+	0.987172i	$0.448961\pi$
$38$	1.07138	+	0.778401i	0.173800	+	0.126273i
$39$	−0.541077	+	0.393115i	−0.0866416	+	0.0629488i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	1.23296	−	3.79468i	0.192557	−	0.592629i	−0.807440	−	0.589950i	$-0.799147\pi$
$41$	1.23296	−	3.79468i	0.192557	−	0.592629i	0.999996	−	0.00267854i	$-0.000852608\pi$
$42$	−3.89263	−	2.82816i	−0.600647	−	0.436395i
$43$	1.79085	−	5.51167i	0.273102	−	0.840522i	−0.716613	−	0.697471i	$-0.754309\pi$
$43$	1.79085	−	5.51167i	0.273102	−	0.840522i	0.989715	−	0.143051i	$-0.0456913\pi$
$44$	1.97158	+	6.06789i	0.297226	+	0.914769i
$45$	−0.809017	+	0.587785i	−0.120601	+	0.0876219i
$46$	−2.39263	−	7.36377i	−0.352775	−	1.08573i
$47$	0.567369	+	1.74618i	0.0827592	+	0.254707i	0.983871	−	0.178881i	$-0.0572476\pi$
$47$	0.567369	+	1.74618i	0.0827592	+	0.254707i	−0.901112	+	0.433587i	$0.857248\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	4.99097	+	15.3606i	0.712996	+	2.19438i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	−4.68038	−	3.40050i	−0.655384	−	0.476165i
$52$	−0.206673	+	0.636074i	−0.0286604	+	0.0882076i
$53$	−7.03606	+	5.11199i	−0.966477	+	0.702186i	−0.954646	−	0.297744i	$-0.903766\pi$
$53$	−7.03606	+	5.11199i	−0.966477	+	0.702186i	−0.0118307	+	0.999930i	$0.503766\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−5.16165	−	3.75016i	−0.695997	−	0.505672i
$56$	−4.81156			−0.642972
$57$	1.32429			0.175407
$58$	−1.88106	−	1.36667i	−0.246995	−	0.179453i
$59$	−2.09799	−	6.45695i	−0.273135	−	0.840623i	−0.989707	−	0.143110i	$-0.954290\pi$
$59$	−2.09799	−	6.45695i	−0.273135	−	0.840623i	0.716572	−	0.697513i	$-0.245710\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	1.85410			0.237393			0.118697	−	0.992931i	$-0.462128\pi$
$61$	1.85410			0.237393			0.118697	+	0.992931i	$0.462128\pi$
$62$	−3.49030	−	4.33795i	−0.443269	−	0.550920i
$63$	−4.81156			−0.606200
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−0.206673	−	0.636074i	−0.0256346	−	0.0788953i
$66$	5.16165	+	3.75016i	0.635356	+	0.461613i
$67$	−6.44848			−0.787807			−0.393904	−	0.919152i	$-0.628876\pi$
$67$	−6.44848			−0.787807			−0.393904	+	0.919152i	$0.628876\pi$
$68$	−5.78527			−0.701567
$69$	−6.26400	−	4.55106i	−0.754097	−	0.547883i
$70$	3.89263	−	2.82816i	0.465259	−	0.338030i
$71$	−8.01800	+	5.82542i	−0.951561	+	0.691350i	−0.951176	−	0.308650i	$-0.900123\pi$
$71$	−8.01800	+	5.82542i	−0.951561	+	0.691350i	−0.000385546		1.00000i	$0.500123\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	3.92255	+	2.84990i	0.459100	+	0.333556i	0.793178	−	0.608990i	$-0.208425\pi$
$73$	3.92255	+	2.84990i	0.459100	+	0.333556i	−0.334078	+	0.942545i	$0.608425\pi$
$74$	0.600212	−	1.84726i	0.0697733	−	0.214740i
$75$	−0.309017	−	0.951057i	−0.0356822	−	0.109819i
$76$	1.07138	−	0.778401i	0.122895	−	0.0892887i
$77$	−9.48636	−	29.1960i	−1.08107	−	3.32720i
$78$	0.206673	+	0.636074i	0.0234011	+	0.0720212i
$79$	−6.90009	+	5.01321i	−0.776321	+	0.564030i	−0.903873	−	0.427802i	$-0.859288\pi$
$79$	−6.90009	+	5.01321i	−0.776321	+	0.564030i	0.127552	+	0.991832i	$0.459288\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−3.22794	−	2.34524i	−0.356467	−	0.258988i
$83$	−4.55175	+	14.0088i	−0.499619	+	1.53767i	0.310014	+	0.950732i	$0.399666\pi$
$83$	−4.55175	+	14.0088i	−0.499619	+	1.53767i	−0.809633	+	0.586937i	$0.800334\pi$
$84$	−3.89263	+	2.82816i	−0.424721	+	0.308578i
$85$	4.68038	−	3.40050i	0.507659	−	0.368836i
$86$	−4.68851	−	3.40640i	−0.505575	−	0.367321i
$87$	−2.32512			−0.249279
$88$	6.38016			0.680127
$89$	6.21881	+	4.51823i	0.659192	+	0.478931i	0.866390	−	0.499368i	$-0.166434\pi$
$89$	6.21881	+	4.51823i	0.659192	+	0.478931i	−0.207198	+	0.978299i	$0.566434\pi$
$90$	0.309017	+	0.951057i	0.0325733	+	0.100250i
$91$	0.994419	−	3.06051i	0.104243	−	0.320828i
$92$	−7.74273			−0.807235
$93$	−5.37350	−	1.45792i	−0.557206	−	0.151180i
$94$	1.83604			0.189373
$95$	−0.409229	+	1.25948i	−0.0419861	+	0.129220i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−10.9616	−	7.96410i	−1.11299	−	0.808632i	−0.129855	−	0.991533i	$-0.541451\pi$
$97$	−10.9616	−	7.96410i	−1.11299	−	0.808632i	−0.983131	+	0.182901i	$0.941451\pi$
$98$	16.1511			1.63151
$99$	6.38016			0.641230
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	11.6689	−	8.47793i	1.16110	−	0.843586i	0.171180	−	0.985240i	$-0.445242\pi$
$101$	11.6689	−	8.47793i	1.16110	−	0.843586i	0.989916	+	0.141654i	$0.0452420\pi$
$102$	−4.68038	+	3.40050i	−0.463427	+	0.336699i
$103$	−1.13840	+	3.50363i	−0.112170	+	0.345223i	−0.991346	−	0.131273i	$-0.958093\pi$
$103$	−1.13840	+	3.50363i	−0.112170	+	0.345223i	0.879176	+	0.476496i	$0.158093\pi$
$104$	0.541077	+	0.393115i	0.0530569	+	0.0385481i
$105$	1.48685	−	4.57607i	0.145102	−	0.446578i
$106$	2.68753	+	8.27138i	0.261036	+	0.803387i
$107$	−1.05743	+	0.768271i	−0.102226	+	0.0742716i	−0.637724	−	0.770265i	$-0.720124\pi$
$107$	−1.05743	+	0.768271i	−0.102226	+	0.0742716i	0.535498	+	0.844537i	$0.320124\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	3.95711	+	12.1787i	0.379023	+	1.16651i	0.940724	+	0.339172i	$0.110147\pi$
$109$	3.95711	+	12.1787i	0.379023	+	1.16651i	−0.561702	+	0.827340i	$0.689853\pi$
$110$	−5.16165	+	3.75016i	−0.492144	+	0.357564i
$111$	−0.600212	−	1.84726i	−0.0569696	−	0.175335i
$112$	−1.48685	+	4.57607i	−0.140495	+	0.432398i
$113$	7.46007	+	5.42006i	0.701784	+	0.509876i	0.880513	−	0.474022i	$-0.157198\pi$
$113$	7.46007	+	5.42006i	0.701784	+	0.509876i	−0.178729	+	0.983898i	$0.557198\pi$
$114$	0.409229	−	1.25948i	0.0383279	−	0.117961i
$115$	6.26400	−	4.55106i	0.584121	−	0.424389i
$116$	−1.88106	+	1.36667i	−0.174652	+	0.126892i
$117$	0.541077	+	0.393115i	0.0500226	+	0.0363435i
$118$	−6.78924			−0.625000
$119$	27.8362			2.55174
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	9.17978	+	28.2525i	0.834526	+	2.56841i
$122$	0.572949	−	1.76336i	0.0518724	−	0.159647i
$123$	−3.98996			−0.359762
$124$	−5.20420	+	1.97898i	−0.467351	+	0.177717i
$125$	1.00000			0.0894427
$126$	−1.48685	+	4.57607i	−0.132459	+	0.407668i
$127$	−3.24683	−	9.99271i	−0.288109	−	0.886709i	−0.985449	−	0.169969i	$-0.945633\pi$
$127$	−3.24683	−	9.99271i	−0.288109	−	0.886709i	0.697340	−	0.716740i	$-0.254367\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−5.79531			−0.510249
$130$	−0.668808			−0.0586583
$131$	17.5608	+	12.7587i	1.53430	+	1.11473i	0.953788	+	0.300479i	$0.0971466\pi$
$131$	17.5608	+	12.7587i	1.53430	+	1.11473i	0.580509	+	0.814253i	$0.302853\pi$
$132$	5.16165	−	3.75016i	0.449264	−	0.326410i
$133$	−5.15499	+	3.74532i	−0.446995	+	0.324761i
$134$	−1.99269	+	6.13287i	−0.172142	+	0.529799i
$135$	0.809017	+	0.587785i	0.0696291	+	0.0505885i
$136$	−1.78775	+	5.50212i	−0.153298	+	0.471803i
$137$	2.48933	+	7.66137i	0.212678	+	0.654555i	0.999310	+	0.0371337i	$0.0118227\pi$
$137$	2.48933	+	7.66137i	0.212678	+	0.654555i	−0.786632	+	0.617422i	$0.788177\pi$
$138$	−6.26400	+	4.55106i	−0.533227	+	0.387412i
$139$	4.35995	+	13.4185i	0.369806	+	1.13815i	0.946916	+	0.321480i	$0.104180\pi$
$139$	4.35995	+	13.4185i	0.369806	+	1.13815i	−0.577110	+	0.816666i	$0.695820\pi$
$140$	−1.48685	−	4.57607i	−0.125662	−	0.386748i
$141$	1.48539	−	1.07920i	0.125092	−	0.0908850i
$142$	3.06260	+	9.42572i	0.257008	+	0.790989i
$143$	−1.31861	+	4.05825i	−0.110267	+	0.339368i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	0.718501	−	2.21132i	0.0596683	−	0.183640i
$146$	3.92255	−	2.84990i	0.324633	−	0.235859i
$147$	13.0665	−	9.49339i	1.07771	−	0.783002i
$148$	−1.57138	−	1.14167i	−0.129166	−	0.0938449i
$149$	0.178103			0.0145908			0.00729538	−	0.999973i	$-0.497678\pi$
$149$	0.178103			0.0145908			0.00729538	+	0.999973i	$0.497678\pi$
$150$	−1.00000			−0.0816497
$151$	−10.0478	−	7.30016i	−0.817679	−	0.594078i	0.0983679	−	0.995150i	$-0.468638\pi$
$151$	−10.0478	−	7.30016i	−0.817679	−	0.594078i	−0.916047	+	0.401072i	$0.868638\pi$
$152$	−0.409229	−	1.25948i	−0.0331929	−	0.102157i
$153$	−1.78775	+	5.50212i	−0.144531	+	0.444820i
$154$	−30.6985			−2.47376
$155$	3.04707	−	4.65997i	0.244747	−	0.374298i
$156$	0.668808			0.0535475
$157$	−3.95589	+	12.1750i	−0.315714	+	0.971668i	0.659745	+	0.751489i	$0.270664\pi$
$157$	−3.95589	+	12.1750i	−0.315714	+	0.971668i	−0.975459	+	0.220179i	$0.929336\pi$
$158$	2.63560	+	8.11154i	0.209677	+	0.645320i
$159$	7.03606	+	5.11199i	0.557995	+	0.405407i
$160$	1.00000			0.0790569
$161$	37.2546			2.93607
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	1.08149	−	0.785746i	0.0847085	−	0.0615443i	−0.544625	−	0.838680i	$-0.683328\pi$
$163$	1.08149	−	0.785746i	0.0847085	−	0.0615443i	0.629333	+	0.777135i	$0.283328\pi$
$164$	−3.22794	+	2.34524i	−0.252060	+	0.183132i
$165$	−1.97158	+	6.06789i	−0.153487	+	0.472385i
$166$	11.9166	+	8.65793i	0.924909	+	0.671986i
$167$	4.82156	−	14.8392i	0.373104	−	1.14830i	−0.571645	−	0.820501i	$-0.693695\pi$
$167$	4.82156	−	14.8392i	0.373104	−	1.14830i	0.944749	−	0.327794i	$-0.106305\pi$
$168$	1.48685	+	4.57607i	0.114713	+	0.353051i
$169$	10.1553	−	7.37829i	0.781180	−	0.567561i
$170$	−1.78775	−	5.50212i	−0.137114	−	0.421993i
$171$	−0.409229	−	1.25948i	−0.0312946	−	0.0963148i
$172$	−4.68851	+	3.40640i	−0.357495	+	0.259735i
$173$	−6.30369	−	19.4008i	−0.479261	−	1.47501i	−0.840124	−	0.542394i	$-0.817518\pi$
$173$	−6.30369	−	19.4008i	−0.479261	−	1.47501i	0.360863	−	0.932619i	$-0.382482\pi$
$174$	−0.718501	+	2.21132i	−0.0544695	+	0.167640i
$175$	3.89263	+	2.82816i	0.294256	+	0.213789i
$176$	1.97158	−	6.06789i	0.148613	−	0.457384i
$177$	−5.49261	+	3.99061i	−0.412850	+	0.299953i
$178$	6.21881	−	4.51823i	0.466119	−	0.338655i
$179$	−10.4495	−	7.59198i	−0.781030	−	0.567451i	0.124258	−	0.992250i	$-0.460345\pi$
$179$	−10.4495	−	7.59198i	−0.781030	−	0.567451i	−0.905288	+	0.424798i	$0.860345\pi$
$180$	1.00000			0.0745356
$181$	−2.59092			−0.192581			−0.0962907	−	0.995353i	$-0.530698\pi$
$181$	−2.59092			−0.192581			−0.0962907	+	0.995353i	$0.530698\pi$
$182$	−2.60342	−	1.89150i	−0.192979	−	0.140207i
$183$	−0.572949	−	1.76336i	−0.0423536	−	0.130351i
$184$	−2.39263	+	7.36377i	−0.176387	+	0.542865i
$185$	1.94233			0.142803
$186$	−3.04707	+	4.65997i	−0.223422	+	0.341686i
$187$	−36.9109			−2.69919
$188$	0.567369	−	1.74618i	0.0413796	−	0.127353i
$189$	1.48685	+	4.57607i	0.108153	+	0.332860i
$190$	1.07138	+	0.778401i	0.0777258	+	0.0564711i
$191$	−17.5586			−1.27049			−0.635246	−	0.772310i	$-0.719101\pi$
$191$	−17.5586			−1.27049			−0.635246	+	0.772310i	$0.719101\pi$
$192$	−1.00000			−0.0721688
$193$	4.28471	+	3.11302i	0.308420	+	0.224080i	0.731218	−	0.682144i	$-0.238952\pi$
$193$	4.28471	+	3.11302i	0.308420	+	0.224080i	−0.422798	+	0.906224i	$0.638952\pi$
$194$	−10.9616	+	7.96410i	−0.787000	+	0.571789i
$195$	−0.541077	+	0.393115i	−0.0387473	+	0.0281516i
$196$	4.99097	−	15.3606i	0.356498	−	1.09719i
$197$	−7.16183	−	5.20337i	−0.510259	−	0.370725i	0.302663	−	0.953098i	$-0.402124\pi$
$197$	−7.16183	−	5.20337i	−0.510259	−	0.370725i	−0.812922	+	0.582373i	$0.802124\pi$
$198$	1.97158	−	6.06789i	0.140114	−	0.431226i
$199$	3.56153	+	10.9613i	0.252470	+	0.777024i	0.994318	+	0.106455i	$0.0339500\pi$
$199$	3.56153	+	10.9613i	0.252470	+	0.777024i	−0.741847	+	0.670569i	$0.766050\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	1.99269	+	6.13287i	0.140553	+	0.432579i
$202$	−4.45711	−	13.7176i	−0.313601	−	0.965166i
$203$	9.05084	−	6.57582i	0.635244	−	0.461532i
$204$	1.78775	+	5.50212i	0.125167	+	0.385225i
$205$	1.23296	−	3.79468i	0.0861140	−	0.265032i
$206$	2.98037	+	2.16536i	0.207652	+	0.150868i
$207$	−2.39263	+	7.36377i	−0.166300	+	0.511818i
$208$	0.541077	−	0.393115i	0.0375169	−	0.0272576i
$209$	6.83555	−	4.96632i	0.472825	−	0.343527i
$210$	−3.89263	−	2.82816i	−0.268617	−	0.195162i
$211$	−19.2316			−1.32396			−0.661980	−	0.749522i	$-0.730284\pi$
$211$	−19.2316			−1.32396			−0.661980	+	0.749522i	$0.730284\pi$
$212$	8.69704			0.597315
$213$	8.01800	+	5.82542i	0.549384	+	0.399151i
$214$	0.403904	+	1.24309i	0.0276103	+	0.0849758i
$215$	1.79085	−	5.51167i	0.122135	−	0.375893i
$216$	−1.00000			−0.0680414
$217$	25.0403	−	9.52196i	1.69985	−	0.646393i
$218$	12.8055			0.867297
$219$	1.49828	−	4.61123i	0.101244	−	0.311598i
$220$	1.97158	+	6.06789i	0.132924	+	0.409097i
$221$	−3.13027	−	2.27428i	−0.210565	−	0.152984i
$222$	−1.94233			−0.130361
$223$	8.25871			0.553044			0.276522	−	0.961008i	$-0.410818\pi$
$223$	8.25871			0.553044			0.276522	+	0.961008i	$0.410818\pi$
$224$	3.89263	+	2.82816i	0.260088	+	0.188965i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	7.46007	−	5.42006i	0.496236	−	0.360537i
$227$	−2.53950	+	7.81579i	−0.168553	+	0.518752i	−0.999281	−	0.0379267i	$-0.987925\pi$
$227$	−2.53950	+	7.81579i	−0.168553	+	0.518752i	0.830728	+	0.556679i	$0.187925\pi$
$228$	−1.07138	−	0.778401i	−0.0709537	−	0.0515508i
$229$	−4.43989	+	13.6646i	−0.293396	+	0.902981i	0.690359	+	0.723467i	$0.257453\pi$
$229$	−4.43989	+	13.6646i	−0.293396	+	0.902981i	−0.983755	+	0.179514i	$0.942547\pi$
$230$	−2.39263	−	7.36377i	−0.157766	−	0.485553i
$231$	−24.8356	+	18.0441i	−1.63406	+	1.18722i
$232$	0.718501	+	2.21132i	0.0471719	+	0.145180i
$233$	8.14810	+	25.0773i	0.533800	+	1.64287i	0.746229	+	0.665690i	$0.231863\pi$
$233$	8.14810	+	25.0773i	0.533800	+	1.64287i	−0.212429	+	0.977176i	$0.568137\pi$
$234$	0.541077	−	0.393115i	0.0353713	−	0.0256988i
$235$	0.567369	+	1.74618i	0.0370110	+	0.113908i
$236$	−2.09799	+	6.45695i	−0.136568	+	0.420312i
$237$	6.90009	+	5.01321i	0.448209	+	0.325643i
$238$	8.60185	−	26.4738i	0.557575	−	1.71604i
$239$	−11.8431	+	8.60453i	−0.766067	+	0.556581i	−0.900765	−	0.434306i	$-0.856994\pi$
$239$	−11.8431	+	8.60453i	−0.766067	+	0.556581i	0.134698	+	0.990887i	$0.456994\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	22.8029	+	16.5673i	1.46886	+	1.06719i	0.980941	+	0.194306i	$0.0622453\pi$
$241$	22.8029	+	16.5673i	1.46886	+	1.06719i	0.487923	+	0.872887i	$0.337755\pi$
$242$	29.7064			1.90960
$243$	−1.00000			−0.0641500
$244$	−1.50000	−	1.08981i	−0.0960277	−	0.0697682i
$245$	4.99097	+	15.3606i	0.318861	+	0.981355i
$246$	−1.23296	+	3.79468i	−0.0786110	+	0.241940i
$247$	0.885698			0.0563556
$248$	0.273933	+	5.56102i	0.0173948	+	0.353125i
$249$	14.7298			0.933460
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−9.55272	−	29.4002i	−0.602962	−	1.85573i	−0.510235	−	0.860035i	$-0.670441\pi$
$251$	−9.55272	−	29.4002i	−0.602962	−	1.85573i	−0.0927275	−	0.995692i	$-0.529559\pi$
$252$	3.89263	+	2.82816i	0.245213	+	0.178158i
$253$	−49.3998			−3.10574
$254$	−10.5070			−0.659265
$255$	−4.68038	−	3.40050i	−0.293097	−	0.212947i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−4.39675	+	3.19443i	−0.274262	+	0.199263i	−0.716411	−	0.697679i	$-0.754216\pi$
$257$	−4.39675	+	3.19443i	−0.274262	+	0.199263i	0.442149	+	0.896942i	$0.354216\pi$
$258$	−1.79085	+	5.51167i	−0.111493	+	0.343142i
$259$	7.56077	+	5.49322i	0.469804	+	0.341332i
$260$	−0.206673	+	0.636074i	−0.0128173	+	0.0394476i
$261$	0.718501	+	2.21132i	0.0444741	+	0.136877i
$262$	17.5608	−	12.7587i	1.08491	−	0.788235i
$263$	−0.839226	−	2.58287i	−0.0517489	−	0.159267i	0.921842	−	0.387565i	$-0.126684\pi$
$263$	−0.839226	−	2.58287i	−0.0517489	−	0.159267i	−0.973591	+	0.228298i	$0.926684\pi$
$264$	−1.97158	−	6.06789i	−0.121342	−	0.373453i
$265$	−7.03606	+	5.11199i	−0.432221	+	0.314027i
$266$	1.96903	+	6.06006i	0.120729	+	0.371566i
$267$	2.37537	−	7.31064i	0.145370	−	0.447404i
$268$	5.21693	+	3.79032i	0.318675	+	0.231531i
$269$	0.0505188	−	0.155481i	0.00308018	−	0.00947983i	−0.949505	−	0.313753i	$-0.898414\pi$
$269$	0.0505188	−	0.155481i	0.00308018	−	0.00947983i	0.952585	+	0.304273i	$0.0984136\pi$
$270$	0.809017	−	0.587785i	0.0492352	−	0.0357715i
$271$	7.69704	−	5.59223i	0.467562	−	0.339704i	−0.328928	−	0.944355i	$-0.606687\pi$
$271$	7.69704	−	5.59223i	0.467562	−	0.339704i	0.796490	+	0.604651i	$0.206687\pi$
$272$	4.68038	+	3.40050i	0.283790	+	0.206185i
$273$	−3.21801			−0.194763
$274$	8.05565			0.486659
$275$	−5.16165	−	3.75016i	−0.311259	−	0.226143i
$276$	2.39263	+	7.36377i	0.144020	+	0.443247i
$277$	−4.20505	+	12.9418i	−0.252657	+	0.777598i	0.741625	+	0.670814i	$0.234055\pi$
$277$	−4.20505	+	12.9418i	−0.252657	+	0.777598i	−0.994282	+	0.106784i	$0.965945\pi$
$278$	14.1091			0.846207
$279$	0.273933	+	5.56102i	0.0164000	+	0.332930i
$280$	−4.81156			−0.287546
$281$	0.983405	−	3.02661i	0.0586650	−	0.180552i	−0.917430	−	0.397898i	$-0.869740\pi$
$281$	0.983405	−	3.02661i	0.0586650	−	0.180552i	0.976095	+	0.217345i	$0.0697398\pi$
$282$	−0.567369	−	1.74618i	−0.0337863	−	0.103984i
$283$	−5.07127	−	3.68449i	−0.301456	−	0.219020i	0.426766	−	0.904362i	$-0.359653\pi$
$283$	−5.07127	−	3.68449i	−0.301456	−	0.219020i	−0.728222	+	0.685342i	$0.759653\pi$
$284$	9.91079			0.588097
$285$	1.32429			0.0784444
$286$	3.45215	+	2.50814i	0.204130	+	0.148309i
$287$	15.5314	−	11.2843i	0.916792	−	0.666089i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	5.08931	−	15.6633i	0.299371	−	0.921369i
$290$	−1.88106	−	1.36667i	−0.110460	−	0.0802537i
$291$	−4.18697	+	12.8862i	−0.245445	+	0.755401i
$292$	−1.49828	−	4.61123i	−0.0876803	−	0.269852i
$293$	−13.0644	+	9.49184i	−0.763230	+	0.554519i	−0.899899	−	0.436097i	$-0.856360\pi$
$293$	−13.0644	+	9.49184i	−0.763230	+	0.554519i	0.136669	+	0.990617i	$0.456360\pi$
$294$	−4.99097	−	15.3606i	−0.291079	−	0.895850i
$295$	−2.09799	−	6.45695i	−0.122150	−	0.375938i
$296$	−1.57138	+	1.14167i	−0.0913344	+	0.0663583i
$297$	−1.97158	−	6.06789i	−0.114402	−	0.352095i
$298$	0.0550368	−	0.169386i	0.00318820	−	0.00981227i
$299$	−4.18941	−	3.04379i	−0.242280	−	0.176027i
$300$	−0.309017	+	0.951057i	−0.0178411	+	0.0549093i
$301$	22.5590	−	16.3901i	1.30028	−	0.944709i
$302$	−10.0478	+	7.30016i	−0.578186	+	0.420077i
$303$	−11.6689	−	8.47793i	−0.670359	−	0.487045i
$304$	−1.32429			−0.0759535
$305$	1.85410			0.106166
$306$	4.68038	+	3.40050i	0.267560	+	0.194393i
$307$	2.23824	+	6.88860i	0.127743	+	0.393153i	0.994391	−	0.105768i	$-0.0337299\pi$
$307$	2.23824	+	6.88860i	0.127743	+	0.393153i	−0.866648	+	0.498921i	$0.833730\pi$
$308$	−9.48636	+	29.1960i	−0.540536	+	1.66360i
$309$	3.68394			0.209572
$310$	−3.49030	−	4.33795i	−0.198236	−	0.246379i
$311$	−18.2666			−1.03581			−0.517903	−	0.855440i	$-0.673287\pi$
$311$	−18.2666			−1.03581			−0.517903	+	0.855440i	$0.673287\pi$
$312$	0.206673	−	0.636074i	0.0117006	−	0.0360106i
$313$	2.80161	+	8.62247i	0.158356	+	0.487371i	0.998485	−	0.0550157i	$-0.0175209\pi$
$313$	2.80161	+	8.62247i	0.158356	+	0.487371i	−0.840129	+	0.542386i	$0.817521\pi$
$314$	10.3566	+	7.52454i	0.584459	+	0.424635i
$315$	−4.81156			−0.271101
$316$	8.52898			0.479793
$317$	24.2262	+	17.6014i	1.36068	+	0.988591i	0.998401	+	0.0565209i	$0.0180008\pi$
$317$	24.2262	+	17.6014i	1.36068	+	0.988591i	0.362278	+	0.932070i	$0.381999\pi$
$318$	7.03606	−	5.11199i	0.394562	−	0.286666i
$319$	−12.0015	+	8.71957i	−0.671953	+	0.488202i
$320$	0.309017	−	0.951057i	0.0172746	−	0.0531657i
$321$	1.05743	+	0.768271i	0.0590202	+	0.0428807i
$322$	11.5123	−	35.4312i	0.641556	−	1.97451i
$323$	2.36750	+	7.28642i	0.131731	+	0.405427i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−0.206673	−	0.636074i	−0.0114642	−	0.0352830i
$326$	−0.413091	−	1.27136i	−0.0228790	−	0.0704143i
$327$	10.3599	−	7.52688i	0.572901	−	0.416237i
$328$	1.23296	+	3.79468i	0.0680791	+	0.209526i
$329$	−2.72993	+	8.40186i	−0.150506	+	0.463209i
$330$	5.16165	+	3.75016i	0.284140	+	0.206440i
$331$	7.23799	−	22.2762i	0.397836	−	1.22441i	−0.528895	−	0.848687i	$-0.677394\pi$
$331$	7.23799	−	22.2762i	0.397836	−	1.22441i	0.926731	−	0.375725i	$-0.122606\pi$
$332$	11.9166	−	8.65793i	0.654010	−	0.475166i
$333$	−1.57138	+	1.14167i	−0.0861109	+	0.0625632i
$334$	−12.6230	−	9.17116i	−0.690701	−	0.501823i
$335$	−6.44848			−0.352318
$336$	4.81156			0.262492
$337$	−2.74576	−	1.99491i	−0.149571	−	0.108670i	0.510483	−	0.859888i	$-0.329467\pi$
$337$	−2.74576	−	1.99491i	−0.149571	−	0.108670i	−0.660054	+	0.751218i	$0.729467\pi$
$338$	−3.87900	−	11.9383i	−0.210990	−	0.649359i
$339$	2.84949	−	8.76984i	0.154763	−	0.476312i
$340$	−5.78527			−0.313750
$341$	−33.2036	+	12.6262i	−1.79807	+	0.683746i
$342$	−1.32429			−0.0716096
$343$	−13.6064	+	41.8761i	−0.734675	+	2.26110i
$344$	1.79085	+	5.51167i	0.0965562	+	0.297169i
$345$	−6.26400	−	4.55106i	−0.337242	−	0.245021i
$346$	−20.3992			−1.09667
$347$	−26.6128			−1.42865			−0.714325	−	0.699815i	$-0.753266\pi$
$347$	−26.6128			−1.42865			−0.714325	+	0.699815i	$0.753266\pi$
$348$	1.88106	+	1.36667i	0.100835	+	0.0732613i
$349$	20.7604	−	15.0833i	1.11128	−	0.807393i	0.128416	−	0.991720i	$-0.459011\pi$
$349$	20.7604	−	15.0833i	1.11128	−	0.807393i	0.982865	+	0.184327i	$0.0590107\pi$
$350$	3.89263	−	2.82816i	0.208070	−	0.151172i
$351$	0.206673	−	0.636074i	0.0110314	−	0.0339511i
$352$	−5.16165	−	3.75016i	−0.275117	−	0.199884i
$353$	7.66039	−	23.5762i	0.407721	−	1.25484i	−0.510880	−	0.859652i	$-0.670680\pi$
$353$	7.66039	−	23.5762i	0.407721	−	1.25484i	0.918602	−	0.395185i	$-0.129320\pi$
$354$	2.09799	+	6.45695i	0.111507	+	0.343183i
$355$	−8.01800	+	5.82542i	−0.425551	+	0.309181i
$356$	−2.37537	−	7.31064i	−0.125894	−	0.387463i
$357$	−8.60185	−	26.4738i	−0.455258	−	1.40114i
$358$	−10.4495	+	7.59198i	−0.552272	+	0.401249i
$359$	−5.21100	−	16.0378i	−0.275026	−	0.846444i	−0.989212	−	0.146488i	$-0.953203\pi$
$359$	−5.21100	−	16.0378i	−0.275026	−	0.846444i	0.714186	−	0.699956i	$-0.246797\pi$
$360$	0.309017	−	0.951057i	0.0162866	−	0.0501251i
$361$	13.9525	+	10.1371i	0.734342	+	0.533531i
$362$	−0.800637	+	2.46411i	−0.0420806	+	0.129511i
$363$	24.0330	−	17.4610i	1.26140	−	0.916464i
$364$	−2.60342	+	1.89150i	−0.136456	+	0.0991414i
$365$	3.92255	+	2.84990i	0.205316	+	0.149171i
$366$	−1.85410			−0.0969155
$367$	−20.9879			−1.09556			−0.547779	−	0.836623i	$-0.684526\pi$
$367$	−20.9879			−1.09556			−0.547779	+	0.836623i	$0.684526\pi$
$368$	6.26400	+	4.55106i	0.326534	+	0.237240i
$369$	1.23296	+	3.79468i	0.0641856	+	0.197543i
$370$	0.600212	−	1.84726i	0.0312036	−	0.0960347i
$371$	−41.8464			−2.17255
$372$	3.49030	+	4.33795i	0.180964	+	0.224912i
$373$	11.2220			0.581052			0.290526	−	0.956867i	$-0.406170\pi$
$373$	11.2220			0.581052			0.290526	+	0.956867i	$0.406170\pi$
$374$	−11.4061	+	35.1044i	−0.589796	+	1.81520i
$375$	−0.309017	−	0.951057i	−0.0159576	−	0.0491123i
$376$	−1.48539	−	1.07920i	−0.0766031	−	0.0556554i
$377$	−1.55506			−0.0800896
$378$	4.81156			0.247480
$379$	22.1289	+	16.0776i	1.13669	+	0.825852i	0.986654	−	0.162829i	$-0.0520619\pi$
$379$	22.1289	+	16.0776i	1.13669	+	0.825852i	0.150033	+	0.988681i	$0.452062\pi$
$380$	1.07138	−	0.778401i	0.0549605	−	0.0399311i
$381$	−8.50030	+	6.17583i	−0.435484	+	0.316397i
$382$	−5.42589	+	16.6992i	−0.277613	+	0.854404i
$383$	13.1431	+	9.54902i	0.671581	+	0.487932i	0.870554	−	0.492073i	$-0.163761\pi$
$383$	13.1431	+	9.54902i	0.671581	+	0.487932i	−0.198973	+	0.980005i	$0.563761\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−9.48636	−	29.1960i	−0.483470	−	1.48797i
$386$	4.28471	−	3.11302i	0.218086	−	0.158449i
$387$	1.79085	+	5.51167i	0.0910340	+	0.280174i
$388$	4.18697	+	12.8862i	0.212561	+	0.654197i
$389$	−19.1691	+	13.9272i	−0.971913	+	0.706136i	−0.955887	−	0.293736i	$-0.905101\pi$
$389$	−19.1691	+	13.9272i	−0.971913	+	0.706136i	−0.0160261	+	0.999872i	$0.505101\pi$
$390$	0.206673	+	0.636074i	0.0104653	+	0.0322089i
$391$	13.8420	−	42.6014i	0.700022	−	2.15445i
$392$	−13.0665	−	9.49339i	−0.659959	−	0.479489i
$393$	6.70764	−	20.6440i	0.338356	−	1.04135i
$394$	−7.16183	+	5.20337i	−0.360808	+	0.262142i
$395$	−6.90009	+	5.01321i	−0.347181	+	0.252242i
$396$	−5.16165	−	3.75016i	−0.259383	−	0.188453i
$397$	−9.81846			−0.492774			−0.246387	−	0.969171i	$-0.579243\pi$
$397$	−9.81846			−0.492774			−0.246387	+	0.969171i	$0.579243\pi$
$398$	11.5254			0.577714
$399$	5.15499	+	3.74532i	0.258073	+	0.187501i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−2.40968	+	7.41624i	−0.120334	+	0.370349i	−0.993022	−	0.117928i	$-0.962375\pi$
$401$	−2.40968	+	7.41624i	−0.120334	+	0.370349i	0.872688	+	0.488278i	$0.162375\pi$
$402$	6.44848			0.321621
$403$	−3.59384	−	0.975071i	−0.179022	−	0.0485717i
$404$	−14.4235			−0.717597
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	−3.45711	−	10.6399i	−0.171574	−	0.528049i
$407$	−10.0256	−	7.28405i	−0.496952	−	0.361057i
$408$	5.78527			0.286414
$409$	−14.3140			−0.707780			−0.353890	−	0.935287i	$-0.615141\pi$
$409$	−14.3140			−0.707780			−0.353890	+	0.935287i	$0.615141\pi$
$410$	−3.22794	−	2.34524i	−0.159417	−	0.115823i
$411$	6.51715	−	4.73499i	0.321468	−	0.233560i
$412$	2.98037	−	2.16536i	0.146832	−	0.106680i
$413$	10.0946	−	31.0680i	0.496723	−	1.52876i
$414$	6.26400	+	4.55106i	0.307859	+	0.223672i
$415$	−4.55175	+	14.0088i	−0.223436	+	0.687667i
$416$	−0.206673	−	0.636074i	−0.0101330	−	0.0311861i
$417$	11.4145	−	8.29311i	0.558970	−	0.406116i
$418$	−2.61095	−	8.03567i	−0.127706	−	0.393038i
$419$	6.37324	+	19.6148i	0.311353	+	0.958247i	0.977230	+	0.212185i	$0.0680578\pi$
$419$	6.37324	+	19.6148i	0.311353	+	0.958247i	−0.665876	+	0.746062i	$0.731942\pi$
$420$	−3.89263	+	2.82816i	−0.189941	+	0.138000i
$421$	−4.83074	−	14.8675i	−0.235436	−	0.724597i	−0.997063	−	0.0765820i	$-0.975599\pi$
$421$	−4.83074	−	14.8675i	−0.235436	−	0.724597i	0.761627	−	0.648015i	$-0.224401\pi$
$422$	−5.94290	+	18.2904i	−0.289296	+	0.890361i
$423$	−1.48539	−	1.07920i	−0.0722221	−	0.0524725i
$424$	2.68753	−	8.27138i	0.130518	−	0.401694i
$425$	4.68038	−	3.40050i	0.227032	−	0.164948i
$426$	8.01800	−	5.82542i	0.388473	−	0.282242i
$427$	7.21734	+	5.24371i	0.349272	+	0.253761i
$428$	1.30706			0.0631792
$429$	4.26710			0.206017
$430$	−4.68851	−	3.40640i	−0.226100	−	0.164271i
$431$	2.21180	+	6.80723i	0.106539	+	0.327893i	0.990089	−	0.140445i	$-0.0448532\pi$
$431$	2.21180	+	6.80723i	0.106539	+	0.327893i	−0.883550	+	0.468337i	$0.844853\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	4.70626			0.226168			0.113084	−	0.993585i	$-0.463927\pi$
$433$	4.70626			0.226168			0.113084	+	0.993585i	$0.463927\pi$
$434$	−1.31805	−	26.7572i	−0.0632683	−	1.28439i
$435$	−2.32512			−0.111481
$436$	3.95711	−	12.1787i	0.189511	−	0.583256i
$437$	3.16855	+	9.75180i	0.151572	+	0.466492i
$438$	−3.92255	−	2.84990i	−0.187427	−	0.136173i
$439$	−31.0842			−1.48357			−0.741785	−	0.670638i	$-0.766020\pi$
$439$	−31.0842			−1.48357			−0.741785	+	0.670638i	$0.766020\pi$
$440$	6.38016			0.304162
$441$	−13.0665	−	9.49339i	−0.622216	−	0.452066i
$442$	−3.13027	+	2.27428i	−0.148892	+	0.108176i
$443$	17.2458	−	12.5298i	0.819374	−	0.595310i	−0.0971590	−	0.995269i	$-0.530976\pi$
$443$	17.2458	−	12.5298i	0.819374	−	0.595310i	0.916533	+	0.399959i	$0.130976\pi$
$444$	−0.600212	+	1.84726i	−0.0284848	+	0.0876673i
$445$	6.21881	+	4.51823i	0.294800	+	0.214184i
$446$	2.55208	−	7.85450i	0.120845	−	0.371921i
$447$	−0.0550368	−	0.169386i	−0.00260315	−	0.00801168i
$448$	3.89263	−	2.82816i	0.183910	−	0.133618i
$449$	9.42879	+	29.0188i	0.444972	+	1.36948i	0.882514	+	0.470285i	$0.155849\pi$
$449$	9.42879	+	29.0188i	0.444972	+	1.36948i	−0.437542	+	0.899198i	$0.644151\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	−20.5948	+	14.9630i	−0.969770	+	0.704579i
$452$	−2.84949	−	8.76984i	−0.134029	−	0.412498i
$453$	−3.83792	+	11.8119i	−0.180321	+	0.554972i
$454$	6.64851	+	4.83042i	0.312030	+	0.226703i
$455$	0.994419	−	3.06051i	0.0466191	−	0.143479i
$456$	−1.07138	+	0.778401i	−0.0501718	+	0.0364520i
$457$	4.36418	−	3.17076i	0.204148	−	0.148322i	−0.481014	−	0.876713i	$-0.659731\pi$
$457$	4.36418	−	3.17076i	0.204148	−	0.148322i	0.685162	+	0.728391i	$0.259731\pi$
$458$	11.6238	+	8.44518i	0.543144	+	0.394617i
$459$	5.78527			0.270033
$460$	−7.74273			−0.361007
$461$	25.7046	+	18.6755i	1.19718	+	0.869804i	0.994005	−	0.109337i	$-0.0348728\pi$
$461$	25.7046	+	18.6755i	1.19718	+	0.869804i	0.203178	+	0.979142i	$0.434873\pi$
$462$	9.48636	+	29.1960i	0.441345	+	1.35832i
$463$	4.86742	−	14.9804i	0.226208	−	0.696198i	−0.771958	−	0.635673i	$-0.780723\pi$
$463$	4.86742	−	14.9804i	0.226208	−	0.696198i	0.998167	−	0.0605246i	$-0.0192774\pi$
$464$	2.32512			0.107941
$465$	−5.37350	−	1.45792i	−0.249190	−	0.0676096i
$466$	26.3678			1.22146
$467$	−4.27984	+	13.1720i	−0.198047	+	0.609527i	0.801880	+	0.597485i	$0.203833\pi$
$467$	−4.27984	+	13.1720i	−0.198047	+	0.609527i	−0.999927	+	0.0120418i	$0.996167\pi$
$468$	−0.206673	−	0.636074i	−0.00955346	−	0.0294025i
$469$	−25.1016	−	18.2374i	−1.15908	−	0.842123i
$470$	1.83604			0.0846904
$471$	12.8015			0.589863
$472$	5.49261	+	3.99061i	0.252818	+	0.183683i
$473$	−29.9134	+	21.7334i	−1.37542	+	0.999301i
$474$	6.90009	−	5.01321i	0.316932	−	0.230264i
$475$	−0.409229	+	1.25948i	−0.0187767	+	0.0577889i
$476$	−22.5199	−	16.3617i	−1.03220	−	0.749937i
$477$	2.68753	−	8.27138i	0.123054	−	0.378720i
$478$	4.52367	+	13.9224i	0.206908	+	0.636797i
$479$	31.8179	−	23.1171i	1.45380	−	1.05625i	0.468874	−	0.883265i	$-0.344660\pi$
$479$	31.8179	−	23.1171i	1.45380	−	1.05625i	0.984925	−	0.172982i	$-0.0553401\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	−0.401427	−	1.23546i	−0.0183035	−	0.0563323i
$482$	22.8029	−	16.5673i	1.03864	−	0.754619i
$483$	−11.5123	−	35.4312i	−0.523828	−	1.61218i
$484$	9.17978	−	28.2525i	0.417263	−	1.28420i
$485$	−10.9616	−	7.96410i	−0.497743	−	0.361631i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	14.6912	−	10.6738i	0.665723	−	0.483676i	−0.202868	−	0.979206i	$-0.565026\pi$
$487$	14.6912	−	10.6738i	0.665723	−	0.483676i	0.868591	+	0.495530i	$0.165026\pi$
$488$	−1.50000	+	1.08981i	−0.0679018	+	0.0493336i
$489$	−1.08149	−	0.785746i	−0.0489065	−	0.0355326i
$490$	16.1511			0.729633
$491$	−8.04928			−0.363259			−0.181629	−	0.983367i	$-0.558137\pi$
$491$	−8.04928			−0.363259			−0.181629	+	0.983367i	$0.558137\pi$
$492$	3.22794	+	2.34524i	0.145527	+	0.105732i
$493$	−4.15672	−	12.7931i	−0.187209	−	0.576171i
$494$	0.273696	−	0.842349i	0.0123142	−	0.0378991i
$495$	6.38016			0.286767
$496$	5.37350	+	1.45792i	0.241277	+	0.0654627i
$497$	−47.6864			−2.13903
$498$	4.55175	−	14.0088i	0.203969	−	0.627751i
$499$	12.8402	+	39.5181i	0.574807	+	1.76907i	0.636837	+	0.770999i	$0.280243\pi$
$499$	12.8402	+	39.5181i	0.574807	+	1.76907i	−0.0620299	+	0.998074i	$0.519757\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−15.6029			−0.697086
$502$	−30.9132			−1.37973
$503$	−13.1274	−	9.53762i	−0.585322	−	0.425262i	0.255317	−	0.966858i	$-0.417820\pi$
$503$	−13.1274	−	9.53762i	−0.585322	−	0.425262i	−0.840639	+	0.541596i	$0.817820\pi$
$504$	3.89263	−	2.82816i	0.173392	−	0.125976i
$505$	11.6689	−	8.47793i	0.519258	−	0.377263i
$506$	−15.2654	+	46.9820i	−0.678629	+	2.08861i
$507$	−10.1553	−	7.37829i	−0.451015	−	0.327681i
$508$	−3.24683	+	9.99271i	−0.144055	+	0.443355i
$509$	9.04429	+	27.8355i	0.400881	+	1.23378i	0.924286	+	0.381701i	$0.124662\pi$
$509$	9.04429	+	27.8355i	0.400881	+	1.23378i	−0.523405	+	0.852084i	$0.675338\pi$
$510$	−4.68038	+	3.40050i	−0.207251	+	0.150576i
$511$	7.20907	+	22.1872i	0.318910	+	0.981506i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−1.07138	+	0.778401i	−0.0473024	+	0.0343672i
$514$	1.67941	+	5.16869i	0.0740756	+	0.227981i
$515$	−1.13840	+	3.50363i	−0.0501639	+	0.154389i
$516$	4.68851	+	3.40640i	0.206400	+	0.149958i
$517$	3.61990	−	11.1409i	0.159203	−	0.489976i
$518$	7.56077	−	5.49322i	0.332201	−	0.241358i
$519$	−16.5033	+	11.9903i	−0.724414	+	0.526317i
$520$	0.541077	+	0.393115i	0.0237278	+	0.0172392i
$521$	−44.0712			−1.93080			−0.965398	−	0.260782i	$-0.916020\pi$
$521$	−44.0712			−1.93080			−0.965398	+	0.260782i	$0.916020\pi$
$522$	2.32512			0.101768
$523$	−5.86578	−	4.26174i	−0.256493	−	0.186353i	0.452107	−	0.891964i	$-0.350673\pi$
$523$	−5.86578	−	4.26174i	−0.256493	−	0.186353i	−0.708599	+	0.705611i	$0.750673\pi$
$524$	−6.70764	−	20.6440i	−0.293025	−	0.901838i
$525$	1.48685	−	4.57607i	0.0648916	−	0.199716i
$526$	−2.71579			−0.118414
$527$	−1.58478	−	32.1720i	−0.0690340	−	1.40143i
$528$	−6.38016			−0.277661
$529$	11.4181	−	35.1414i	0.496440	−	1.52789i
$530$	2.68753	+	8.27138i	0.116739	+	0.359286i
$531$	5.49261	+	3.99061i	0.238359	+	0.173178i
$532$	6.37192			0.276258
$533$	−2.66851			−0.115586
$534$	−6.21881	−	4.51823i	−0.269114	−	0.195523i
$535$	−1.05743	+	0.768271i	−0.0457169	+	0.0332152i
$536$	5.21693	−	3.79032i	0.225337	−	0.163717i
$537$	−3.99134	+	12.2841i	−0.172239	+	0.530097i
$538$	−0.132260	−	0.0960924i	−0.00570213	−	0.00414284i
$539$	31.8432	−	98.0032i	1.37158	−	4.22130i
$540$	−0.309017	−	0.951057i	−0.0132980	−	0.0409270i
$541$	−5.18661	+	3.76829i	−0.222990	+	0.162012i	−0.693671	−	0.720292i	$-0.744008\pi$
$541$	−5.18661	+	3.76829i	−0.222990	+	0.162012i	0.470682	+	0.882303i	$0.344008\pi$
$542$	−2.94001	−	9.04842i	−0.126284	−	0.388663i
$543$	0.800637	+	2.46411i	0.0343586	+	0.105745i
$544$	4.68038	−	3.40050i	0.200670	−	0.145795i
$545$	3.95711	+	12.1787i	0.169504	+	0.521680i
$546$	−0.994419	+	3.06051i	−0.0425572	+	0.130978i
$547$	0.0247863	+	0.0180083i	0.00105978	+	0.000769979i	0.588315	−	0.808632i	$-0.299792\pi$
$547$	0.0247863	+	0.0180083i	0.00105978	+	0.000769979i	−0.587255	+	0.809402i	$0.699792\pi$
$548$	2.48933	−	7.66137i	0.106339	−	0.327278i
$549$	−1.50000	+	1.08981i	−0.0640184	+	0.0465121i
$550$	−5.16165	+	3.75016i	−0.220094	+	0.159907i
$551$	2.49108	+	1.80987i	0.106124	+	0.0771033i
$552$	7.74273			0.329552
$553$	−41.0377			−1.74510
$554$	11.0090	+	7.99848i	0.467726	+	0.339823i
$555$	−0.600212	−	1.84726i	−0.0254776	−	0.0784120i
$556$	4.35995	−	13.4185i	0.184903	−	0.569073i
$557$	38.3935			1.62678			0.813391	−	0.581717i	$-0.197619\pi$
$557$	38.3935			1.62678			0.813391	+	0.581717i	$0.197619\pi$
$558$	5.37350	+	1.45792i	0.227478	+	0.0617189i
$559$	−3.87595			−0.163935
$560$	−1.48685	+	4.57607i	−0.0628311	+	0.193374i
$561$	11.4061	+	35.1044i	0.481566	+	1.48211i
$562$	−2.57459	−	1.87055i	−0.108602	−	0.0789043i
$563$	0.568379			0.0239543			0.0119772	−	0.999928i	$-0.496187\pi$
$563$	0.568379			0.0239543			0.0119772	+	0.999928i	$0.496187\pi$
$564$	−1.83604			−0.0773114
$565$	7.46007	+	5.42006i	0.313848	+	0.228024i
$566$	−5.07127	+	3.68449i	−0.213161	+	0.154871i
$567$	3.89263	−	2.82816i	0.163475	−	0.118772i
$568$	3.06260	−	9.42572i	0.128504	−	0.395494i
$569$	−30.4069	−	22.0919i	−1.27472	−	0.926141i	−0.275344	−	0.961346i	$-0.588792\pi$
$569$	−30.4069	−	22.0919i	−1.27472	−	0.926141i	−0.999380	+	0.0352044i	$0.988792\pi$
$570$	0.409229	−	1.25948i	0.0171407	−	0.0527538i
$571$	−9.65726	−	29.7220i	−0.404144	−	1.24383i	−0.921608	−	0.388122i	$-0.873124\pi$
$571$	−9.65726	−	29.7220i	−0.404144	−	1.24383i	0.517464	−	0.855705i	$-0.326876\pi$
$572$	3.45215	−	2.50814i	0.144342	−	0.104870i
$573$	5.42589	+	16.6992i	0.226670	+	0.697618i
$574$	−5.93248	−	18.2583i	−0.247617	−	0.762087i
$575$	6.26400	−	4.55106i	0.261227	−	0.189792i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−3.07235	+	9.45572i	−0.127904	+	0.393647i	−0.994419	−	0.105504i	$-0.966354\pi$
$577$	−3.07235	+	9.45572i	−0.127904	+	0.393647i	0.866515	+	0.499150i	$0.166354\pi$
$578$	−13.3240	−	9.68044i	−0.554204	−	0.402653i
$579$	1.63661	−	5.03698i	0.0680153	−	0.209330i
$580$	−1.88106	+	1.36667i	−0.0781068	+	0.0567479i
$581$	−57.3376	+	41.6582i	−2.37876	+	1.72827i
$582$	10.9616	+	7.96410i	0.454375	+	0.330123i
$583$	55.4885			2.29810
$584$	−4.84854			−0.200634
$585$	0.541077	+	0.393115i	0.0223708	+	0.0162533i
$586$	4.99016	+	15.3581i	0.206141	+	0.634438i
$587$	−3.33663	+	10.2691i	−0.137718	+	0.423851i	−0.996003	−	0.0893218i	$-0.971530\pi$
$587$	−3.33663	+	10.2691i	−0.137718	+	0.423851i	0.858285	+	0.513173i	$0.171530\pi$
$588$	−16.1511			−0.666061
$589$	4.62219	+	5.74472i	0.190454	+	0.236707i
$590$	−6.78924			−0.279509
$591$	−2.73558	+	8.41924i	−0.112527	+	0.346321i
$592$	0.600212	+	1.84726i	0.0246686	+	0.0759221i
$593$	−21.5486	−	15.6560i	−0.884895	−	0.642914i	0.0496470	−	0.998767i	$-0.484190\pi$
$593$	−21.5486	−	15.6560i	−0.884895	−	0.642914i	−0.934542	+	0.355853i	$0.884190\pi$
$594$	−6.38016			−0.261781
$595$	27.8362			1.14117
$596$	−0.144088	−	0.104686i	−0.00590209	−	0.00428812i
$597$	9.32421	−	6.77444i	0.381615	−	0.277259i
$598$	−4.18941	+	3.04379i	−0.171318	+	0.124470i
$599$	0.758978	−	2.33589i	0.0310110	−	0.0954420i	−0.934353	−	0.356349i	$-0.884022\pi$
$599$	0.758978	−	2.33589i	0.0310110	−	0.0954420i	0.965364	+	0.260907i	$0.0840215\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	14.3328	−	44.1118i	0.584646	−	1.79936i	−0.0160404	−	0.999871i	$-0.505106\pi$
$601$	14.3328	−	44.1118i	0.584646	−	1.79936i	0.600687	−	0.799485i	$-0.294894\pi$
$602$	−8.61678	−	26.5197i	−0.351194	−	1.08086i
$603$	5.21693	−	3.79032i	0.212450	−	0.154354i
$604$	3.83792	+	11.8119i	0.156163	+	0.480619i
$605$	9.17978	+	28.2525i	0.373211	+	1.14863i
$606$	−11.6689	+	8.47793i	−0.474016	+	0.344393i
$607$	7.48979	+	23.0512i	0.304001	+	0.935619i	0.980048	+	0.198760i	$0.0636916\pi$
$607$	7.48979	+	23.0512i	0.304001	+	0.935619i	−0.676047	+	0.736858i	$0.736308\pi$
$608$	−0.409229	+	1.25948i	−0.0165964	+	0.0510786i
$609$	−9.05084	−	6.57582i	−0.366759	−	0.266466i
$610$	0.572949	−	1.76336i	0.0231980	−	0.0713962i
$611$	0.993440	−	0.721777i	0.0401903	−	0.0292000i
$612$	4.68038	−	3.40050i	0.189193	−	0.137457i
$613$	0.297727	+	0.216311i	0.0120251	+	0.00873673i	0.593782	−	0.804626i	$-0.297634\pi$
$613$	0.297727	+	0.216311i	0.0120251	+	0.00873673i	−0.581756	+	0.813363i	$0.697634\pi$
$614$	7.24310			0.292308
$615$	−3.98996			−0.160891
$616$	24.8356	+	18.0441i	1.00066	+	0.727019i
$617$	−10.7374	−	33.0462i	−0.432270	−	1.33039i	−0.895859	−	0.444339i	$-0.853438\pi$
$617$	−10.7374	−	33.0462i	−0.432270	−	1.33039i	0.463589	−	0.886051i	$-0.346562\pi$
$618$	1.13840	−	3.50363i	0.0457931	−	0.140937i
$619$	−29.9497			−1.20378			−0.601890	−	0.798579i	$-0.705585\pi$
$619$	−29.9497			−1.20378			−0.601890	+	0.798579i	$0.705585\pi$
$620$	−5.20420	+	1.97898i	−0.209006	+	0.0794776i
$621$	7.74273			0.310705
$622$	−5.64470	+	17.3726i	−0.226332	+	0.696577i
$623$	11.4292	+	35.1756i	0.457903	+	1.40928i
$624$	−0.541077	−	0.393115i	−0.0216604	−	0.0157372i
$625$	1.00000			0.0400000
$626$	9.06620			0.362358
$627$	−6.83555	−	4.96632i	−0.272986	−	0.198336i
$628$	10.3566	−	7.52454i	0.413275	−	0.300262i
$629$	9.09084	−	6.60488i	0.362475	−	0.263354i
$630$	−1.48685	+	4.57607i	−0.0592377	+	0.182315i
$631$	22.3245	+	16.2197i	0.888726	+	0.645697i	0.935545	−	0.353206i	$-0.114909\pi$
$631$	22.3245	+	16.2197i	0.888726	+	0.645697i	−0.0468197	+	0.998903i	$0.514909\pi$
$632$	2.63560	−	8.11154i	0.104839	−	0.322660i
$633$	5.94290	+	18.2904i	0.236209	+	0.726977i
$634$	24.2262	−	17.6014i	0.962145	−	0.699040i
$635$	−3.24683	−	9.99271i	−0.128846	−	0.396548i
$636$	−2.68753	−	8.27138i	−0.106568	−	0.327982i
$637$	8.73900	−	6.34925i	0.346252	−	0.251567i
$638$	4.58415	+	14.1086i	0.181488	+	0.558564i
$639$	3.06260	−	9.42572i	0.121155	−	0.372876i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	−4.35298	+	13.3971i	−0.171933	+	0.529154i	−0.999480	−	0.0322417i	$-0.989735\pi$
$641$	−4.35298	+	13.3971i	−0.171933	+	0.529154i	0.827548	+	0.561396i	$0.189735\pi$
$642$	1.05743	−	0.768271i	0.0417336	−	0.0303212i
$643$	−28.5978	+	20.7776i	−1.12779	+	0.819387i	−0.985372	−	0.170420i	$-0.945488\pi$
$643$	−28.5978	+	20.7776i	−1.12779	+	0.819387i	−0.142418	+	0.989807i	$0.545488\pi$
$644$	−30.1396	−	21.8977i	−1.18767	−	0.862891i
$645$	−5.79531			−0.228190
$646$	7.66140			0.301434
$647$	1.57883	+	1.14709i	0.0620704	+	0.0450968i	0.618388	−	0.785873i	$-0.287786\pi$
$647$	1.57883	+	1.14709i	0.0620704	+	0.0450968i	−0.556317	+	0.830970i	$0.687786\pi$
$648$	0.309017	+	0.951057i	0.0121393	+	0.0373610i
$649$	−13.3855	+	41.1964i	−0.525427	+	1.61710i
$650$	−0.668808			−0.0262328
$651$	−16.7938	−	20.8723i	−0.658201	−	0.818050i
$652$	−1.33679			−0.0523528
$653$	8.64085	−	26.5938i	0.338142	−	1.04070i	−0.627011	−	0.779010i	$-0.715722\pi$
$653$	8.64085	−	26.5938i	0.338142	−	1.04070i	0.965153	−	0.261685i	$-0.0842781\pi$
$654$	−3.95711	−	12.1787i	−0.154735	−	0.476227i
$655$	17.5608	+	12.7587i	0.686159	+	0.498524i
$656$	3.98996			0.155782
$657$	−4.84854			−0.189160
$658$	7.14704	+	5.19263i	0.278621	+	0.202430i
$659$	−0.487137	+	0.353926i	−0.0189762	+	0.0137870i	−0.597233	−	0.802068i	$-0.703733\pi$
$659$	−0.487137	+	0.353926i	−0.0189762	+	0.0137870i	0.578257	+	0.815855i	$0.303733\pi$
$660$	5.16165	−	3.75016i	0.200917	−	0.145975i
$661$	−1.05863	+	3.25814i	−0.0411760	+	0.126727i	−0.969531	−	0.244967i	$-0.921223\pi$
$661$	−1.05863	+	3.25814i	−0.0411760	+	0.126727i	0.928355	+	0.371694i	$0.121223\pi$
$662$	−18.9493	−	13.7675i	−0.736485	−	0.535088i
$663$	−1.19566	+	3.67986i	−0.0464355	+	0.142914i
$664$	−4.55175	−	14.0088i	−0.176642	−	0.543648i
$665$	−5.15499	+	3.74532i	−0.199902	+	0.145237i
$666$	0.600212	+	1.84726i	0.0232578	+	0.0715800i
$667$	−5.56316	−	17.1217i	−0.215406	−	0.662953i
$668$	−12.6230	+	9.17116i	−0.488399	+	0.354843i
$669$	−2.55208	−	7.85450i	−0.0986691	−	0.303672i
$670$	−1.99269	+	6.13287i	−0.0769843	+	0.236933i
$671$	−9.57023	−	6.95318i	−0.369455	−	0.268425i
$672$	1.48685	−	4.57607i	0.0573566	−	0.176526i
$673$	21.0670	−	15.3061i	0.812072	−	0.590005i	−0.102358	−	0.994748i	$-0.532639\pi$
$673$	21.0670	−	15.3061i	0.812072	−	0.590005i	0.914431	+	0.404742i	$0.132639\pi$
$674$	−2.74576	+	1.99491i	−0.105763	+	0.0768413i
$675$	0.809017	+	0.587785i	0.0311391	+	0.0226239i
$676$	−12.5527			−0.482796
$677$	23.7591			0.913138			0.456569	−	0.889688i	$-0.349078\pi$
$677$	23.7591			0.913138			0.456569	+	0.889688i	$0.349078\pi$
$678$	−7.46007	−	5.42006i	−0.286502	−	0.208156i
$679$	−20.1459	−	62.0027i	−0.773128	−	2.37944i
$680$	−1.78775	+	5.50212i	−0.0685570	+	0.210997i
$681$	8.21801			0.314915
$682$	1.74774	+	35.4802i	0.0669243	+	1.35861i
$683$	−25.1041			−0.960582			−0.480291	−	0.877109i	$-0.659469\pi$
$683$	−25.1041			−0.960582			−0.480291	+	0.877109i	$0.659469\pi$
$684$	−0.409229	+	1.25948i	−0.0156473	+	0.0481574i
$685$	2.48933	+	7.66137i	0.0951125	+	0.292726i
$686$	35.6220	+	25.8809i	1.36005	+	0.988136i
$687$	14.3678			0.548166
$688$	5.79531			0.220944
$689$	4.70577	+	3.41894i	0.179275	+	0.130251i
$690$	−6.26400	+	4.55106i	−0.238466	+	0.173256i
$691$	−1.90931	+	1.38719i	−0.0726335	+	0.0527714i	−0.623510	−	0.781816i	$-0.714294\pi$
$691$	−1.90931	+	1.38719i	−0.0726335	+	0.0527714i	0.550876	+	0.834587i	$0.314294\pi$
$692$	−6.30369	+	19.4008i	−0.239630	+	0.737507i
$693$	24.8356	+	18.0441i	0.943427	+	0.685440i
$694$	−8.22380	+	25.3103i	−0.312171	+	0.960764i
$695$	4.35995	+	13.4185i	0.165382	+	0.508994i
$696$	1.88106	−	1.36667i	0.0713014	−	0.0518035i
$697$	−7.13303	−	21.9532i	−0.270183	−	0.831537i
$698$	−7.92978	−	24.4054i	−0.300147	−	0.923757i
$699$	21.3320	−	15.4986i	0.806850	−	0.586211i
$700$	−1.48685	−	4.57607i	−0.0561978	−	0.172959i
$701$	4.47382	−	13.7690i	0.168974	−	0.520048i	−0.830333	−	0.557267i	$-0.811850\pi$
$701$	4.47382	−	13.7690i	0.168974	−	0.520048i	0.999307	+	0.0372193i	$0.0118500\pi$
$702$	−0.541077	−	0.393115i	−0.0204216	−	0.0148372i
$703$	−0.794858	+	2.44632i	−0.0299786	+	0.0922648i
$704$	−5.16165	+	3.75016i	−0.194537	+	0.141340i
$705$	1.48539	−	1.07920i	0.0559430	−	0.0406450i
$706$	−20.0552	−	14.5709i	−0.754786	−	0.548384i
$707$	69.3997			2.61004
$708$	6.78924			0.255155
$709$	10.2648	+	7.45781i	0.385502	+	0.280084i	0.763610	−	0.645678i	$-0.223425\pi$
$709$	10.2648	+	7.45781i	0.385502	+	0.280084i	−0.378108	+	0.925762i	$0.623425\pi$
$710$	3.06260	+	9.42572i	0.114937	+	0.353741i
$711$	2.63560	−	8.11154i	0.0988427	−	0.304207i
$712$	−7.68687			−0.288078
$713$	−2.12099	−	43.0575i	−0.0794317	−	1.61252i
$714$	−27.8362			−1.04174
$715$	−1.31861	+	4.05825i	−0.0493131	+	0.151770i
$716$	3.99134	+	12.2841i	0.149163	+	0.459078i
$717$	11.8431	+	8.60453i	0.442289	+	0.321342i
$718$	−16.8632			−0.629328
$719$	−9.30093			−0.346866			−0.173433	−	0.984846i	$-0.555486\pi$
$719$	−9.30093			−0.346866			−0.173433	+	0.984846i	$0.555486\pi$
$720$	−0.809017	−	0.587785i	−0.0301503	−	0.0219055i
$721$	−14.3402	+	10.4188i	−0.534058	+	0.388016i
$722$	13.9525	−	10.1371i	0.519258	−	0.377263i
$723$	8.70993	−	26.8064i	0.323926	−	0.996941i
$724$	2.09610	+	1.52290i	0.0779008	+	0.0565982i
$725$	0.718501	−	2.21132i	0.0266845	−	0.0821264i
$726$	−9.17978	−	28.2525i	−0.340694	−	1.04855i
$727$	−5.04942	+	3.66862i	−0.187273	+	0.136061i	−0.677471	−	0.735549i	$-0.736924\pi$
$727$	−5.04942	+	3.66862i	−0.187273	+	0.136061i	0.490199	+	0.871611i	$0.336924\pi$
$728$	0.994419	+	3.06051i	0.0368556	+	0.113430i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	3.92255	−	2.84990i	0.145180	−	0.105480i
$731$	−10.3605	−	31.8865i	−0.383199	−	1.17936i
$732$	−0.572949	+	1.76336i	−0.0211768	+	0.0651755i
$733$	−27.9406	−	20.3000i	−1.03201	−	0.749798i	−0.0632993	−	0.997995i	$-0.520162\pi$
$733$	−27.9406	−	20.3000i	−1.03201	−	0.749798i	−0.968710	+	0.248196i	$0.920162\pi$
$734$	−6.48560	+	19.9606i	−0.239388	+	0.736761i
$735$	13.0665	−	9.49339i	0.481966	−	0.350169i
$736$	6.26400	−	4.55106i	0.230894	−	0.167754i
$737$	33.2848	+	24.1828i	1.22606	+	0.890786i
$738$	3.98996			0.146872
$739$	39.5583			1.45518			0.727588	−	0.686015i	$-0.240641\pi$
$739$	39.5583			1.45518			0.727588	+	0.686015i	$0.240641\pi$
$740$	−1.57138	−	1.14167i	−0.0577650	−	0.0419687i
$741$	−0.273696	−	0.842349i	−0.0100545	−	0.0309445i
$742$	−12.9312	+	39.7982i	−0.474721	+	1.46104i
$743$	−42.6977			−1.56643			−0.783213	−	0.621753i	$-0.786421\pi$
$743$	−42.6977			−1.56643			−0.783213	+	0.621753i	$0.786421\pi$
$744$	5.20420	−	1.97898i	0.190795	−	0.0725528i
$745$	0.178103			0.00652519
$746$	3.46778	−	10.6727i	0.126965	−	0.390757i
$747$	−4.55175	−	14.0088i	−0.166540	−	0.512556i
$748$	29.8616	+	21.6957i	1.09185	+	0.793273i
$749$	−6.28900			−0.229795
$750$	−1.00000			−0.0365148
$751$	11.8268	+	8.59270i	0.431567	+	0.313552i	0.782275	−	0.622933i	$-0.214059\pi$
$751$	11.8268	+	8.59270i	0.431567	+	0.313552i	−0.350708	+	0.936485i	$0.614059\pi$
$752$	−1.48539	+	1.07920i	−0.0541666	+	0.0393543i
$753$	−25.0093	+	18.1703i	−0.911391	+	0.662164i
$754$	−0.480539	+	1.47895i	−0.0175002	+	0.0538601i
$755$	−10.0478	−	7.30016i	−0.365677	−	0.265680i
$756$	1.48685	−	4.57607i	0.0540764	−	0.166430i
$757$	0.874292	+	2.69080i	0.0317767	+	0.0977986i	0.965687	−	0.259709i	$-0.0836266\pi$
$757$	0.874292	+	2.69080i	0.0317767	+	0.0977986i	−0.933910	+	0.357508i	$0.883627\pi$
$758$	22.1289	−	16.0776i	0.803759	−	0.583965i
$759$	15.2654	+	46.9820i	0.554098	+	1.70534i
$760$	−0.409229	−	1.25948i	−0.0148443	−	0.0456861i
$761$	−11.9209	+	8.66102i	−0.432131	+	0.313962i	−0.782501	−	0.622650i	$-0.786056\pi$
$761$	−11.9209	+	8.66102i	−0.432131	+	0.313962i	0.350369	+	0.936612i	$0.386056\pi$
$762$	3.24683	+	9.99271i	0.117620	+	0.361998i
$763$	−19.0399	+	58.5988i	−0.689290	+	2.12142i
$764$	14.2052	+	10.3207i	0.513925	+	0.373388i
$765$	−1.78775	+	5.50212i	−0.0646361	+	0.198930i
$766$	13.1431	−	9.54902i	0.474880	−	0.345020i
$767$	−3.67350	+	2.66895i	−0.132642	+	0.0963703i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	−11.8701			−0.428046			−0.214023	−	0.976829i	$-0.568657\pi$
$769$	−11.8701			−0.428046			−0.214023	+	0.976829i	$0.568657\pi$
$770$	−30.6985			−1.10630
$771$	4.39675	+	3.19443i	0.158345	+	0.115044i
$772$	−1.63661	−	5.03698i	−0.0589030	−	0.181285i
$773$	−13.9964	+	43.0764i	−0.503414	+	1.54935i	0.300006	+	0.953937i	$0.403011\pi$
$773$	−13.9964	+	43.0764i	−0.503414	+	1.54935i	−0.803420	+	0.595412i	$0.796989\pi$
$774$	5.79531			0.208308
$775$	3.04707	−	4.65997i	0.109454	−	0.167391i
$776$	13.5493			0.486393
$777$	2.88796	−	8.88822i	0.103605	−	0.318863i
$778$	7.32195	+	22.5346i	0.262505	+	0.807906i
$779$	4.27475	+	3.10579i	0.153159	+	0.111276i
$780$	0.668808			0.0239472
$781$	63.2324			2.26263
$782$	−36.2389	−	26.3291i	−1.29590	−	0.941527i
$783$	1.88106	−	1.36667i	0.0672236	−	0.0488408i
$784$	−13.0665	+	9.49339i	−0.466662	+	0.339050i
$785$	−3.95589	+	12.1750i	−0.141192	+	0.434543i
$786$	−17.5608	−	12.7587i	−0.626374	−	0.455088i
$787$	−3.69093	+	11.3595i	−0.131567	+	0.404923i	−0.995040	−	0.0994725i	$-0.968284\pi$
$787$	−3.69093	+	11.3595i	−0.131567	+	0.404923i	0.863473	+	0.504395i	$0.168284\pi$
$788$	2.73558	+	8.41924i	0.0974508	+	0.299923i
$789$	−2.19712	+	1.59630i	−0.0782196	+	0.0568299i
$790$	2.63560	+	8.11154i	0.0937705	+	0.288596i
$791$	13.7105	+	42.1966i	0.487490	+	1.50034i
$792$	−5.16165	+	3.75016i	−0.183411	+	0.133256i
$793$	−0.383193	−	1.17935i	−0.0136076	−	0.0418798i
$794$	−3.03407	+	9.33791i	−0.107675	+	0.331390i
$795$	7.03606	+	5.11199i	0.249543	+	0.181304i
$796$	3.56153	−	10.9613i	0.126235	−	0.388512i
$797$	−7.52284	+	5.46567i	−0.266473	+	0.193604i	−0.712996	−	0.701168i	$-0.752662\pi$
$797$	−7.52284	+	5.46567i	−0.266473	+	0.193604i	0.446523	+	0.894772i	$0.352662\pi$
$798$	5.15499	−	3.74532i	0.182485	−	0.132583i
$799$	8.59338	+	6.24346i	0.304012	+	0.220878i
$800$	1.00000			0.0353553
$801$	−7.68687			−0.271602
$802$	6.30863	+	4.58349i	0.222766	+	0.161849i
$803$	−9.55927	−	29.4204i	−0.337339	−	1.03822i
$804$	1.99269	−	6.13287i	0.0702767	−	0.216290i
$805$	37.2546			1.31305
$806$	−2.03790	+	3.11663i	−0.0717821	+	0.109779i
$807$	−0.163482			−0.00575484
$808$	−4.45711	+	13.7176i	−0.156801	+	0.482583i
$809$	15.0724	+	46.3881i	0.529918	+	1.63092i	0.754381	+	0.656437i	$0.227937\pi$
$809$	15.0724	+	46.3881i	0.529918	+	1.63092i	−0.224463	+	0.974483i	$0.572063\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	24.9100			0.874709			0.437355	−	0.899289i	$-0.355915\pi$
$811$	24.9100			0.874709			0.437355	+	0.899289i	$0.355915\pi$
$812$	−11.1875			−0.392603
$813$	−7.69704	−	5.59223i	−0.269947	−	0.196128i
$814$	−10.0256	+	7.28405i	−0.351398	+	0.255306i
$815$	1.08149	−	0.785746i	0.0378828	−	0.0275235i
$816$	1.78775	−	5.50212i	0.0625836	−	0.192613i
$817$	6.20896	+	4.51108i	0.217224	+	0.157823i
$818$	−4.42326	+	13.6134i	−0.154656	+	0.475981i
$819$	0.994419	+	3.06051i	0.0347478	+	0.106943i
$820$	−3.22794	+	2.34524i	−0.112725	+	0.0818993i
$821$	−9.58397	−	29.4964i	−0.334483	−	1.02943i	−0.966976	−	0.254866i	$-0.917969\pi$
$821$	−9.58397	−	29.4964i	−0.334483	−	1.02943i	0.632494	−	0.774566i	$-0.282031\pi$
$822$	−2.48933	−	7.66137i	−0.0868254	−	0.267221i
$823$	13.4225	−	9.75201i	0.467879	−	0.339934i	−0.328735	−	0.944422i	$-0.606622\pi$
$823$	13.4225	−	9.75201i	0.467879	−	0.339934i	0.796614	+	0.604488i	$0.206622\pi$
$824$	−1.13840	−	3.50363i	−0.0396580	−	0.122055i
$825$	−1.97158	+	6.06789i	−0.0686415	+	0.211257i
$826$	−26.4280	−	19.2011i	−0.919549	−	0.668091i
$827$	−14.3671	+	44.2174i	−0.499593	+	1.53759i	0.310081	+	0.950710i	$0.399644\pi$
$827$	−14.3671	+	44.2174i	−0.499593	+	1.53759i	−0.809674	+	0.586879i	$0.800356\pi$
$828$	6.26400	−	4.55106i	0.217689	−	0.158160i
$829$	−0.618526	+	0.449386i	−0.0214823	+	0.0156078i	−0.598475	−	0.801142i	$-0.704226\pi$
$829$	−0.618526	+	0.449386i	−0.0214823	+	0.0156078i	0.576992	+	0.816750i	$0.304226\pi$
$830$	11.9166	+	8.65793i	0.413632	+	0.300521i
$831$	13.6078			0.472050
$832$	−0.668808			−0.0231867
$833$	75.5934	+	54.9218i	2.61916	+	1.90293i
$834$	−4.35995	−	13.4185i	−0.150973	−	0.464646i
$835$	4.82156	−	14.8392i	0.166857	−	0.513533i
$836$	−8.44921			−0.292222
$837$	5.20420	−	1.97898i	0.179883	−	0.0684034i
$838$	20.6242			0.712453
$839$	−2.35405	+	7.24501i	−0.0812707	+	0.250125i	−0.983433	−	0.181271i	$-0.941979\pi$
$839$	−2.35405	+	7.24501i	−0.0812707	+	0.250125i	0.902163	+	0.431396i	$0.141979\pi$
$840$	1.48685	+	4.57607i	0.0513013	+	0.157889i
$841$	19.0878	+	13.8681i	0.658200	+	0.478210i
$842$	−15.6326			−0.538735
$843$	−3.18237			−0.109607
$844$	15.5587	+	11.3041i	0.535553	+	0.389102i
$845$	10.1553	−	7.37829i	0.349354	−	0.253821i
$846$	−1.48539	+	1.07920i	−0.0510688	+	0.0371036i
$847$	−44.1691	+	135.938i	−1.51767	+	4.67090i
$848$	−7.03606	−	5.11199i	−0.241619	−	0.175547i
$849$	−1.93705	+	5.96163i	−0.0664795	+	0.204603i
$850$	−1.78775	−	5.50212i	−0.0613192	−	0.188721i
$851$	12.1667	−	8.83966i	0.417071	−	0.303020i
$852$	−3.06260	−	9.42572i	−0.104923	−	0.322920i
$853$	−9.37841	−	28.8638i	−0.321111	−	0.988277i	−0.973166	−	0.230105i	$-0.926093\pi$
$853$	−9.37841	−	28.8638i	−0.321111	−	0.988277i	0.652055	−	0.758171i	$-0.273907\pi$
$854$	7.21734	−	5.24371i	0.246972	−	0.179436i
$855$	−0.409229	−	1.25948i	−0.0139954	−	0.0430733i
$856$	0.403904	−	1.24309i	0.0138052	−	0.0424879i
$857$	−0.366338	−	0.266160i	−0.0125139	−	0.00909187i	0.581511	−	0.813539i	$-0.302462\pi$
$857$	−0.366338	−	0.266160i	−0.0125139	−	0.00909187i	−0.594025	+	0.804447i	$0.702462\pi$
$858$	1.31861	−	4.05825i	0.0450165	−	0.138546i
$859$	21.2210	−	15.4180i	0.724052	−	0.526055i	−0.163624	−	0.986523i	$-0.552318\pi$
$859$	21.2210	−	15.4180i	0.724052	−	0.526055i	0.887676	+	0.460468i	$0.152318\pi$
$860$	−4.68851	+	3.40640i	−0.159877	+	0.116157i
$861$	−15.5314	−	11.2843i	−0.529310	−	0.384566i
$862$	7.15754			0.243787
$863$	−43.1445			−1.46866			−0.734328	−	0.678795i	$-0.762503\pi$
$863$	−43.1445			−1.46866			−0.734328	+	0.678795i	$0.762503\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−6.30369	−	19.4008i	−0.214332	−	0.659646i
$866$	1.45431	−	4.47592i	0.0494196	−	0.152098i
$867$	−16.4693			−0.559328
$868$	−25.8549	−	7.01489i	−0.877573	−	0.238101i
$869$	54.4162			1.84594
$870$	−0.718501	+	2.21132i	−0.0243595	+	0.0749708i
$871$	1.33273	+	4.10171i	0.0451577	+	0.138981i
$872$	−10.3599	−	7.52688i	−0.350829	−	0.254892i
$873$	13.5493			0.458576
$874$	10.2537			0.346835
$875$	3.89263	+	2.82816i	0.131595	+	0.0956094i
$876$	−3.92255	+	2.84990i	−0.132531	+	0.0962892i
$877$	−0.0769572	+	0.0559127i	−0.00259866	+	0.00188804i	−0.589084	−	0.808072i	$-0.700511\pi$
$877$	−0.0769572	+	0.0559127i	−0.00259866	+	0.00188804i	0.586485	+	0.809960i	$0.300511\pi$
$878$	−9.60556	+	29.5629i	−0.324172	+	0.997698i
$879$	13.0644	+	9.49184i	0.440651	+	0.320152i
$880$	1.97158	−	6.06789i	0.0664618	−	0.204549i
$881$	3.93612	+	12.1141i	0.132611	+	0.408136i	0.995211	−	0.0977518i	$-0.0311651\pi$
$881$	3.93612	+	12.1141i	0.132611	+	0.408136i	−0.862600	+	0.505887i	$0.831165\pi$
$882$	−13.0665	+	9.49339i	−0.439973	+	0.319659i
$883$	−8.54395	−	26.2956i	−0.287527	−	0.884917i	−0.985630	−	0.168919i	$-0.945972\pi$
$883$	−8.54395	−	26.2956i	−0.287527	−	0.884917i	0.698103	−	0.715997i	$-0.254028\pi$
$884$	1.19566	+	3.67986i	0.0402144	+	0.123767i
$885$	−5.49261	+	3.99061i	−0.184632	+	0.134143i
$886$	−6.58732	−	20.2737i	−0.221305	−	0.681108i
$887$	−16.8816	+	51.9563i	−0.566830	+	1.74452i	0.0956225	+	0.995418i	$0.469516\pi$
$887$	−16.8816	+	51.9563i	−0.566830	+	1.74452i	−0.662452	+	0.749104i	$0.730484\pi$
$888$	1.57138	+	1.14167i	0.0527319	+	0.0383120i
$889$	15.6223	−	48.0805i	0.523955	−	1.61257i
$890$	6.21881	−	4.51823i	0.208455	−	0.151451i
$891$	−5.16165	+	3.75016i	−0.172922	+	0.125635i
$892$	−6.68143	−	4.85435i	−0.223711	−	0.162535i
$893$	−2.43146			−0.0813658
$894$	−0.178103			−0.00595665
$895$	−10.4495	−	7.59198i	−0.349287	−	0.253772i
$896$	−1.48685	−	4.57607i	−0.0496723	−	0.152876i
$897$	−1.60021	+	4.92495i	−0.0534295	+	0.164439i
$898$	30.5122			1.01821
$899$	−8.11537	−	10.0862i	−0.270663	−	0.336395i
$900$	1.00000			0.0333333
$901$	−15.5481	+	47.8522i	−0.517983	+	1.59419i
$902$	7.86651	+	24.2106i	0.261926	+	0.806125i
$903$	−22.5590	−	16.3901i	−0.750718	−	0.545428i
$904$	−9.22115			−0.306691
$905$	−2.59092			−0.0861250
$906$	10.0478	+	7.30016i	0.333816	+	0.242531i
$907$	33.2733	−	24.1745i	1.10482	−	0.802700i	0.122982	−	0.992409i	$-0.460754\pi$
$907$	33.2733	−	24.1745i	1.10482	−	0.802700i	0.981840	+	0.189709i	$0.0607543\pi$
$908$	6.64851	−	4.83042i	0.220639	−	0.160303i
$909$	−4.45711	+	13.7176i	−0.147833	+	0.454984i
$910$	−2.60342	−	1.89150i	−0.0863027	−	0.0627026i
$911$	−2.15449	+	6.63084i	−0.0713815	+	0.219690i	−0.980383	−	0.197104i	$-0.936846\pi$
$911$	−2.15449	+	6.63084i	−0.0713815	+	0.219690i	0.909001	+	0.416794i	$0.136846\pi$
$912$	0.409229	+	1.25948i	0.0135509	+	0.0417055i
$913$	76.0299	−	55.2390i	2.51622	−	1.82814i
$914$	−1.66697	−	5.13040i	−0.0551385	−	0.169699i
$915$	−0.572949	−	1.76336i	−0.0189411	−	0.0582947i
$916$	11.6238	−	8.44518i	0.384061	−	0.279037i
$917$	32.2742	+	99.3299i	1.06579	+	3.28016i
$918$	1.78775	−	5.50212i	0.0590044	−	0.181597i
$919$	37.5513	+	27.2826i	1.23870	+	0.899970i	0.997511	−	0.0705071i	$-0.0224617\pi$
$919$	37.5513	+	27.2826i	1.23870	+	0.899970i	0.241192	+	0.970477i	$0.422462\pi$
$920$	−2.39263	+	7.36377i	−0.0788828	+	0.242776i
$921$	5.85979	−	4.25739i	0.193087	−	0.140286i
$922$	25.7046	−	18.6755i	0.846536	−	0.615045i
$923$	5.36250	+	3.89608i	0.176509	+	0.128241i
$924$	30.6985			1.00991
$925$	1.94233			0.0638634
$926$	−12.7431	−	9.25839i	−0.418764	−	0.304250i
$927$	−1.13840	−	3.50363i	−0.0373899	−	0.115074i
$928$	0.718501	−	2.21132i	0.0235860	−	0.0725901i
$929$	−43.7574			−1.43563			−0.717817	−	0.696232i	$-0.754858\pi$
$929$	−43.7574			−1.43563			−0.717817	+	0.696232i	$0.754858\pi$
$930$	−3.04707	+	4.65997i	−0.0999174	+	0.152807i
$931$	−21.3888			−0.700991
$932$	8.14810	−	25.0773i	0.266900	−	0.821433i
$933$	5.64470	+	17.3726i	0.184799	+	0.568753i
$934$	11.2048	+	8.14073i	0.366631	+	0.266373i
$935$	−36.9109			−1.20712
$936$	−0.668808			−0.0218607
$937$	−23.5873	−	17.1372i	−0.770564	−	0.559848i	0.131568	−	0.991307i	$-0.457999\pi$
$937$	−23.5873	−	17.1372i	−0.770564	−	0.559848i	−0.902132	+	0.431459i	$0.857999\pi$
$938$	−25.1016	+	18.2374i	−0.819595	+	0.595471i
$939$	7.33471	−	5.32898i	0.239359	−	0.173905i
$940$	0.567369	−	1.74618i	0.0185055	−	0.0569541i
$941$	−32.3491	−	23.5030i	−1.05455	−	0.766175i	−0.0814769	−	0.996675i	$-0.525964\pi$
$941$	−32.3491	−	23.5030i	−1.05455	−	0.766175i	−0.973072	+	0.230500i	$0.925964\pi$
$942$	3.95589	−	12.1750i	0.128890	−	0.396682i
$943$	−9.54651	−	29.3811i	−0.310877	−	0.956782i
$944$	5.49261	−	3.99061i	0.178769	−	0.129883i
$945$	1.48685	+	4.57607i	0.0483674	+	0.148859i
$946$	11.4259	+	35.1653i	0.371488	+	1.14332i
$947$	1.48970	−	1.08233i	0.0484088	−	0.0351711i	−0.563318	−	0.826240i	$-0.690475\pi$
$947$	1.48970	−	1.08233i	0.0484088	−	0.0351711i	0.611727	+	0.791069i	$0.290475\pi$
$948$	−2.63560	−	8.11154i	−0.0856003	−	0.263451i
$949$	1.00206	−	3.08403i	0.0325283	−	0.100112i
$950$	1.07138	+	0.778401i	0.0347600	+	0.0252547i
$951$	9.25359	−	28.4796i	0.300068	−	0.923515i
$952$	−22.5199	+	16.3617i	−0.729875	+	0.530286i
$953$	−7.10769	+	5.16404i	−0.230241	+	0.167280i	−0.696924	−	0.717145i	$-0.745449\pi$
$953$	−7.10769	+	5.16404i	−0.230241	+	0.167280i	0.466684	+	0.884424i	$0.345449\pi$
$954$	−7.03606	−	5.11199i	−0.227801	−	0.165507i
$955$	−17.5586			−0.568181
$956$	14.6389			0.473456
$957$	12.0015	+	8.71957i	0.387952	+	0.281864i
$958$	−12.1534	−	37.4042i	−0.392658	−	1.20848i
$959$	−11.9776	+	36.8632i	−0.386776	+	1.19037i
$960$	−1.00000			−0.0322749
$961$	−12.4307	−	28.3985i	−0.400991	−	0.916082i
$962$	−1.29904			−0.0418829
$963$	0.403904	−	1.24309i	0.0130156	−	0.0400580i
$964$	−8.70993	−	26.8064i	−0.280528	−	0.863377i
$965$	4.28471	+	3.11302i	0.137930	+	0.100212i
$966$	−37.2546			−1.19865
$967$	10.6829			0.343539			0.171770	−	0.985137i	$-0.445052\pi$
$967$	10.6829			0.343539			0.171770	+	0.985137i	$0.445052\pi$
$968$	−24.0330	−	17.4610i	−0.772449	−	0.561217i
$969$	6.19820	−	4.50326i	0.199115	−	0.144665i
$970$	−10.9616	+	7.96410i	−0.351957	+	0.255712i
$971$	7.93699	−	24.4275i	0.254710	−	0.783917i	−0.739176	−	0.673512i	$-0.764785\pi$
$971$	7.93699	−	24.4275i	0.254710	−	0.783917i	0.993887	−	0.110406i	$-0.0352150\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	−20.9782	+	64.5641i	−0.672529	+	2.06983i
$974$	−5.61155	−	17.2706i	−0.179806	−	0.553385i
$975$	−0.541077	+	0.393115i	−0.0173283	+	0.0125898i
$976$	0.572949	+	1.76336i	0.0183397	+	0.0564436i
$977$	−15.5101	−	47.7352i	−0.496213	−	1.52719i	−0.815058	−	0.579379i	$-0.803295\pi$
$977$	−15.5101	−	47.7352i	−0.496213	−	1.52719i	0.318846	−	0.947807i	$-0.396705\pi$
$978$	−1.08149	+	0.785746i	−0.0345821	+	0.0251254i
$979$	−15.1552	−	46.6431i	−0.484364	−	1.49072i
$980$	4.99097	−	15.3606i	0.159431	−	0.490677i
$981$	−10.3599	−	7.52688i	−0.330765	−	0.240315i
$982$	−2.48736	+	7.65532i	−0.0793750	+	0.244291i
$983$	10.1056	−	7.34218i	0.322320	−	0.234179i	−0.414845	−	0.909892i	$-0.636164\pi$
$983$	10.1056	−	7.34218i	0.322320	−	0.234179i	0.737165	+	0.675713i	$0.236164\pi$
$984$	3.22794	−	2.34524i	0.102903	−	0.0747635i
$985$	−7.16183	−	5.20337i	−0.228195	−	0.165793i
$986$	−13.4514			−0.428381
$987$	8.83423			0.281197
$988$	−0.716545	−	0.520600i	−0.0227963	−	0.0165625i
$989$	−13.8661	−	42.6754i	−0.440915	−	1.35700i
$990$	1.97158	−	6.06789i	0.0626608	−	0.192850i
$991$	−1.08050			−0.0343233			−0.0171617	−	0.999853i	$-0.505463\pi$
$991$	−1.08050			−0.0343233			−0.0171617	+	0.999853i	$0.505463\pi$
$992$	3.04707	−	4.65997i	0.0967446	−	0.147954i
$993$	−23.4226			−0.743294
$994$	−14.7359	+	45.3524i	−0.467394	+	1.43849i
$995$	3.56153	+	10.9613i	0.112908	+	0.347496i
$996$	−11.9166	−	8.65793i	−0.377593	−	0.274337i
$997$	−22.9823			−0.727855			−0.363928	−	0.931427i	$-0.618564\pi$
$997$	−22.9823			−0.727855			−0.363928	+	0.931427i	$0.618564\pi$
$998$	41.5518			1.31530
$999$	1.57138	+	1.14167i	0.0497162	+	0.0361209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.a.721.2	✓	8
31.4	even	5	inner	930.2.n.a.841.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.a.721.2	✓	8	1.1	even	1	trivial
930.2.n.a.841.2	yes	8	31.4	even	5	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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(3.89263 + 2.82816i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(3.89263 + 2.82816i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(-5.16165 - 3.75016i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(-0.206673 - 0.636074i) q^{13} +(3.89263 - 2.82816i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(4.68038 - 3.40050i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-0.409229 + 1.25948i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(1.48685 - 4.57607i) q^{21} +(-5.16165 + 3.75016i) q^{22} +(6.26400 - 4.55106i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} -0.668808 q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.48685 - 4.57607i) q^{28} +(0.718501 - 2.21132i) q^{29} -1.00000 q^{30} +(3.04707 - 4.65997i) q^{31} +1.00000 q^{32} +(-1.97158 + 6.06789i) q^{33} +(-1.78775 - 5.50212i) q^{34} +(3.89263 + 2.82816i) q^{35} +1.00000 q^{36} +1.94233 q^{37} +(1.07138 + 0.778401i) q^{38} +(-0.541077 + 0.393115i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(1.23296 - 3.79468i) q^{41} +(-3.89263 - 2.82816i) q^{42} +(1.79085 - 5.51167i) q^{43} +(1.97158 + 6.06789i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(-2.39263 - 7.36377i) q^{46} +(0.567369 + 1.74618i) q^{47} +(0.809017 - 0.587785i) q^{48} +(4.99097 + 15.3606i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-4.68038 - 3.40050i) q^{51} +(-0.206673 + 0.636074i) q^{52} +(-7.03606 + 5.11199i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-5.16165 - 3.75016i) q^{55} -4.81156 q^{56} +1.32429 q^{57} +(-1.88106 - 1.36667i) q^{58} +(-2.09799 - 6.45695i) q^{59} +(-0.309017 + 0.951057i) q^{60} +1.85410 q^{61} +(-3.49030 - 4.33795i) q^{62} -4.81156 q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.206673 - 0.636074i) q^{65} +(5.16165 + 3.75016i) q^{66} -6.44848 q^{67} -5.78527 q^{68} +(-6.26400 - 4.55106i) q^{69} +(3.89263 - 2.82816i) q^{70} +(-8.01800 + 5.82542i) q^{71} +(0.309017 - 0.951057i) q^{72} +(3.92255 + 2.84990i) q^{73} +(0.600212 - 1.84726i) q^{74} +(-0.309017 - 0.951057i) q^{75} +(1.07138 - 0.778401i) q^{76} +(-9.48636 - 29.1960i) q^{77} +(0.206673 + 0.636074i) q^{78} +(-6.90009 + 5.01321i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-3.22794 - 2.34524i) q^{82} +(-4.55175 + 14.0088i) q^{83} +(-3.89263 + 2.82816i) q^{84} +(4.68038 - 3.40050i) q^{85} +(-4.68851 - 3.40640i) q^{86} -2.32512 q^{87} +6.38016 q^{88} +(6.21881 + 4.51823i) q^{89} +(0.309017 + 0.951057i) q^{90} +(0.994419 - 3.06051i) q^{91} -7.74273 q^{92} +(-5.37350 - 1.45792i) q^{93} +1.83604 q^{94} +(-0.409229 + 1.25948i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-10.9616 - 7.96410i) q^{97} +16.1511 q^{98} +6.38016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + q^{13} + 9 q^{14} + 2 q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - q^{22} + 8 q^{23} + 2 q^{24} + 8 q^{25} + 16 q^{26} + 2 q^{27} - q^{28} - q^{29} - 8 q^{30} + 3 q^{31} + 8 q^{32} + q^{33} - 12 q^{34} + 9 q^{35} + 8 q^{36} + 8 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} + 29 q^{41} - 9 q^{42} - 25 q^{43} - q^{44} - 2 q^{45} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 25 q^{49} - 2 q^{50} - 13 q^{51} + q^{52} - 19 q^{53} + 2 q^{54} - q^{55} - 16 q^{56} + 12 q^{57} + 4 q^{58} + 23 q^{59} + 2 q^{60} - 12 q^{61} - 27 q^{62} - 16 q^{63} - 2 q^{64} + q^{65} + q^{66} - 24 q^{67} - 2 q^{68} - 8 q^{69} + 9 q^{70} + 3 q^{71} - 2 q^{72} - 14 q^{73} + 8 q^{74} + 2 q^{75} + 8 q^{76} - 24 q^{77} - q^{78} - 34 q^{79} - 2 q^{80} - 2 q^{81} - 21 q^{82} + 8 q^{83} - 9 q^{84} + 13 q^{85} + 6 q^{87} + 4 q^{88} + 25 q^{89} - 2 q^{90} + 3 q^{91} - 22 q^{92} - 18 q^{93} - 42 q^{94} - 2 q^{95} + 2 q^{96} - 28 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^12 + q^13 + 9 * q^14 + 2 * q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + q^21 - q^22 + 8 * q^23 + 2 * q^24 + 8 * q^25 + 16 * q^26 + 2 * q^27 - q^28 - q^29 - 8 * q^30 + 3 * q^31 + 8 * q^32 + q^33 - 12 * q^34 + 9 * q^35 + 8 * q^36 + 8 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 + 29 * q^41 - 9 * q^42 - 25 * q^43 - q^44 - 2 * q^45 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 25 * q^49 - 2 * q^50 - 13 * q^51 + q^52 - 19 * q^53 + 2 * q^54 - q^55 - 16 * q^56 + 12 * q^57 + 4 * q^58 + 23 * q^59 + 2 * q^60 - 12 * q^61 - 27 * q^62 - 16 * q^63 - 2 * q^64 + q^65 + q^66 - 24 * q^67 - 2 * q^68 - 8 * q^69 + 9 * q^70 + 3 * q^71 - 2 * q^72 - 14 * q^73 + 8 * q^74 + 2 * q^75 + 8 * q^76 - 24 * q^77 - q^78 - 34 * q^79 - 2 * q^80 - 2 * q^81 - 21 * q^82 + 8 * q^83 - 9 * q^84 + 13 * q^85 + 6 * q^87 + 4 * q^88 + 25 * q^89 - 2 * q^90 + 3 * q^91 - 22 * q^92 - 18 * q^93 - 42 * q^94 - 2 * q^95 + 2 * q^96 - 28 * q^97 + 4 * q^99

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