LMFDB - Embedded newform 930.2.n.e.901.1

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 16 x^{10} - 6 x^{9} + 161 x^{8} - 180 x^{7} + 1725 x^{6} - 2255 x^{5} + 17635 x^{4} + \cdots + 25 $ x^12 - x^11 + 16x^10 - 6x^9 + 161x^8 - 180x^7 + 1725x^6 - 2255x^5 + 17635x^4 - 18375x^3 + 60975x^2 + 2000x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.1
Root			$2.41709 - 1.75612i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.e.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.23226 - 3.79252i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.23226 - 3.79252i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.732264 - 2.25368i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(1.55840 - 1.13224i) q^{13} +(1.23226 - 3.79252i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.485923 - 1.49552i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-4.47549 - 3.25164i) q^{19} +(0.309017 + 0.951057i) q^{20} +(3.22611 + 2.34391i) q^{21} +(0.732264 - 2.25368i) q^{22} +(1.18483 - 3.64653i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +1.92629 q^{26} +(0.309017 + 0.951057i) q^{27} +(3.22611 - 2.34391i) q^{28} +(-0.786239 - 0.571236i) q^{29} -1.00000 q^{30} +(-1.29494 - 5.41508i) q^{31} -1.00000 q^{32} +(1.91709 + 1.39285i) q^{33} +(1.27216 - 0.924280i) q^{34} +(-1.23226 - 3.79252i) q^{35} +1.00000 q^{36} -1.72598 q^{37} +(-1.70949 - 5.26126i) q^{38} +(-0.595256 + 1.83201i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(9.22818 + 6.70467i) q^{41} +(1.23226 + 3.79252i) q^{42} +(4.55225 + 3.30740i) q^{43} +(1.91709 - 1.39285i) q^{44} +(0.309017 - 0.951057i) q^{45} +(3.10192 - 2.25368i) q^{46} +(3.24323 - 2.35634i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-7.20160 + 5.23227i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.485923 + 1.49552i) q^{51} +(1.55840 + 1.13224i) q^{52} +(0.978605 - 3.01184i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-0.732264 - 2.25368i) q^{55} +3.98769 q^{56} +5.53201 q^{57} +(-0.300317 - 0.924280i) q^{58} +(-1.77578 + 1.29018i) q^{59} +(-0.809017 - 0.587785i) q^{60} -5.27402 q^{61} +(2.13528 - 5.14204i) q^{62} -3.98769 q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.55840 - 1.13224i) q^{65} +(0.732264 + 2.25368i) q^{66} +11.8088 q^{67} +1.57248 q^{68} +(1.18483 + 3.64653i) q^{69} +(1.23226 - 3.79252i) q^{70} +(-1.36818 + 4.21082i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.05186 + 3.23730i) q^{73} +(-1.39635 - 1.01451i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(1.70949 - 5.26126i) q^{76} +(-7.64477 + 5.55425i) q^{77} +(-1.55840 + 1.13224i) q^{78} +(-1.87836 + 5.78099i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.52485 + 10.8484i) q^{82} +(-6.51982 - 4.73692i) q^{83} +(-1.23226 + 3.79252i) q^{84} +(0.485923 - 1.49552i) q^{85} +(1.73880 + 5.35149i) q^{86} +0.971845 q^{87} +2.36966 q^{88} +(2.02504 + 6.23244i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-6.21442 - 4.51504i) q^{91} +3.83418 q^{92} +(4.23053 + 3.61975i) q^{93} +4.00885 q^{94} +(-4.47549 - 3.25164i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-1.61145 - 4.95952i) q^{97} -8.90167 q^{98} -2.36966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 - 5 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^24 + 12 * q^25 + 10 * q^26 - 3 * q^27 + 4 * q^28 + q^29 - 12 * q^30 - 6 * q^31 - 12 * q^32 - 5 * q^33 + 2 * q^34 - q^35 + 12 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 3 * q^40 + 15 * q^41 + q^42 + 10 * q^43 - 5 * q^44 - 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 5 * q^52 - 13 * q^53 + 3 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 + 4 * q^58 + 11 * q^59 - 3 * q^60 - 70 * q^61 - 19 * q^62 - 6 * q^63 - 3 * q^64 - 5 * q^65 - 5 * q^66 + 38 * q^67 - 2 * q^68 + q^70 + 21 * q^71 + 3 * q^72 - 14 * q^73 - 11 * q^74 - 3 * q^75 + 3 * q^76 - 14 * q^77 + 5 * q^78 + 5 * q^79 - 3 * q^80 - 3 * q^81 - 15 * q^82 - q^84 + 3 * q^85 + 10 * q^86 + 6 * q^87 + 3 * q^89 + 3 * q^90 + 16 * q^91 - 10 * q^92 - 11 * q^93 - 6 * q^94 - 2 * q^95 + 3 * q^96 - 35 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000			−0.408248
$7$	−1.23226	−	3.79252i	−0.465752	−	1.43344i	−0.858034	−	0.513592i	$-0.828314\pi$
$7$	−1.23226	−	3.79252i	−0.465752	−	1.43344i	0.392282	−	0.919845i	$-0.371686\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	−0.732264	−	2.25368i	−0.220786	−	0.679509i	−0.998692	−	0.0511286i	$-0.983718\pi$
$11$	−0.732264	−	2.25368i	−0.220786	−	0.679509i	0.777906	−	0.628380i	$-0.216282\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	1.55840	−	1.13224i	0.432223	−	0.314028i	−0.350314	−	0.936632i	$-0.613925\pi$
$13$	1.55840	−	1.13224i	0.432223	−	0.314028i	0.782537	+	0.622604i	$0.213925\pi$
$14$	1.23226	−	3.79252i	0.329336	−	1.01359i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.485923	−	1.49552i	0.117854	−	0.362716i	−0.874678	−	0.484705i	$-0.838927\pi$
$17$	0.485923	−	1.49552i	0.117854	−	0.362716i	0.992531	+	0.121989i	$0.0389271\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	−4.47549	−	3.25164i	−1.02675	−	0.745976i	−0.0590932	−	0.998252i	$-0.518821\pi$
$19$	−4.47549	−	3.25164i	−1.02675	−	0.745976i	−0.967655	+	0.252276i	$0.918821\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	3.22611	+	2.34391i	0.703995	+	0.511482i
$22$	0.732264	−	2.25368i	0.156119	−	0.480485i
$23$	1.18483	−	3.64653i	0.247054	−	0.760353i	−0.748238	−	0.663430i	$-0.769100\pi$
$23$	1.18483	−	3.64653i	0.247054	−	0.760353i	0.995292	−	0.0969229i	$-0.0309000\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	1.92629			0.377776
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	3.22611	−	2.34391i	0.609677	−	0.442956i
$29$	−0.786239	−	0.571236i	−0.146001	−	0.106076i	0.512387	−	0.858755i	$-0.328761\pi$
$29$	−0.786239	−	0.571236i	−0.146001	−	0.106076i	−0.658388	+	0.752679i	$0.728761\pi$
$30$	−1.00000			−0.182574
$31$	−1.29494	−	5.41508i	−0.232578	−	0.972578i
$31$	−1.29494	−	5.41508i	−0.232578	−	0.972578i
$32$	−1.00000			−0.176777
$33$	1.91709	+	1.39285i	0.333723	+	0.242464i
$34$	1.27216	−	0.924280i	0.218174	−	0.158513i
$35$	−1.23226	−	3.79252i	−0.208291	−	0.641053i
$36$	1.00000			0.166667
$37$	−1.72598			−0.283750			−0.141875	−	0.989885i	$-0.545313\pi$
$37$	−1.72598			−0.283750			−0.141875	+	0.989885i	$0.545313\pi$
$38$	−1.70949	−	5.26126i	−0.277315	−	0.853489i
$39$	−0.595256	+	1.83201i	−0.0953173	+	0.293356i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	9.22818	+	6.70467i	1.44120	+	1.04709i	0.987790	+	0.155791i	$0.0497927\pi$
$41$	9.22818	+	6.70467i	1.44120	+	1.04709i	0.453410	+	0.891302i	$0.350207\pi$
$42$	1.23226	+	3.79252i	0.190142	+	0.585198i
$43$	4.55225	+	3.30740i	0.694211	+	0.504374i	0.878042	−	0.478584i	$-0.158850\pi$
$43$	4.55225	+	3.30740i	0.694211	+	0.504374i	−0.183831	+	0.982958i	$0.558850\pi$
$44$	1.91709	−	1.39285i	0.289012	−	0.209980i
$45$	0.309017	−	0.951057i	0.0460655	−	0.141775i
$46$	3.10192	−	2.25368i	0.457353	−	0.332286i
$47$	3.24323	−	2.35634i	0.473074	−	0.343708i	−0.325564	−	0.945520i	$-0.605554\pi$
$47$	3.24323	−	2.35634i	0.473074	−	0.343708i	0.798638	+	0.601812i	$0.205554\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−7.20160	+	5.23227i	−1.02880	+	0.747467i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	0.485923	+	1.49552i	0.0680428	+	0.209414i
$52$	1.55840	+	1.13224i	0.216111	+	0.157014i
$53$	0.978605	−	3.01184i	0.134422	−	0.413708i	−0.861078	−	0.508473i	$-0.830210\pi$
$53$	0.978605	−	3.01184i	0.134422	−	0.413708i	0.995500	+	0.0947655i	$0.0302101\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−0.732264	−	2.25368i	−0.0987384	−	0.303886i
$56$	3.98769			0.532877
$57$	5.53201			0.732733
$58$	−0.300317	−	0.924280i	−0.0394335	−	0.121364i
$59$	−1.77578	+	1.29018i	−0.231187	+	0.167967i	−0.697348	−	0.716733i	$-0.745637\pi$
$59$	−1.77578	+	1.29018i	−0.231187	+	0.167967i	0.466161	+	0.884700i	$0.345637\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	−5.27402			−0.675268			−0.337634	−	0.941277i	$-0.609627\pi$
$61$	−5.27402			−0.675268			−0.337634	+	0.941277i	$0.609627\pi$
$62$	2.13528	−	5.14204i	0.271181	−	0.653040i
$63$	−3.98769			−0.502402
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.55840	−	1.13224i	0.193296	−	0.140438i
$66$	0.732264	+	2.25368i	0.0901355	+	0.277408i
$67$	11.8088			1.44267			0.721337	−	0.692584i	$-0.243528\pi$
$67$	11.8088			1.44267			0.721337	+	0.692584i	$0.243528\pi$
$68$	1.57248			0.190691
$69$	1.18483	+	3.64653i	0.142637	+	0.438990i
$70$	1.23226	−	3.79252i	0.147284	−	0.453293i
$71$	−1.36818	+	4.21082i	−0.162373	+	0.499733i	−0.998833	−	0.0482951i	$-0.984621\pi$
$71$	−1.36818	+	4.21082i	−0.162373	+	0.499733i	0.836460	+	0.548028i	$0.184621\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	1.05186	+	3.23730i	0.123111	+	0.378897i	0.993552	−	0.113376i	$-0.0361663\pi$
$73$	1.05186	+	3.23730i	0.123111	+	0.378897i	−0.870441	+	0.492273i	$0.836166\pi$
$74$	−1.39635	−	1.01451i	−0.162323	−	0.117934i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	1.70949	−	5.26126i	0.196092	−	0.603508i
$77$	−7.64477	+	5.55425i	−0.871202	+	0.632965i
$78$	−1.55840	+	1.13224i	−0.176454	+	0.128201i
$79$	−1.87836	+	5.78099i	−0.211332	+	0.650412i	0.788062	+	0.615596i	$0.211085\pi$
$79$	−1.87836	+	5.78099i	−0.211332	+	0.650412i	−0.999394	+	0.0348160i	$0.988915\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	3.52485	+	10.8484i	0.389255	+	1.19800i
$83$	−6.51982	−	4.73692i	−0.715643	−	0.519945i	0.169346	−	0.985557i	$-0.445834\pi$
$83$	−6.51982	−	4.73692i	−0.715643	−	0.519945i	−0.884989	+	0.465612i	$0.845834\pi$
$84$	−1.23226	+	3.79252i	−0.134451	+	0.413798i
$85$	0.485923	−	1.49552i	0.0527057	−	0.162211i
$86$	1.73880	+	5.35149i	0.187500	+	0.577066i
$87$	0.971845			0.104193
$88$	2.36966			0.252606
$89$	2.02504	+	6.23244i	0.214654	+	0.660637i	0.999178	+	0.0405387i	$0.0129074\pi$
$89$	2.02504	+	6.23244i	0.214654	+	0.660637i	−0.784524	+	0.620099i	$0.787093\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	−6.21442	−	4.51504i	−0.651448	−	0.473305i
$92$	3.83418			0.399741
$93$	4.23053	+	3.61975i	0.438686	+	0.375350i
$94$	4.00885			0.413481
$95$	−4.47549	−	3.25164i	−0.459176	−	0.333611i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−1.61145	−	4.95952i	−0.163618	−	0.503563i	0.835314	−	0.549773i	$-0.185286\pi$
$97$	−1.61145	−	4.95952i	−0.163618	−	0.503563i	−0.998932	+	0.0462096i	$0.985286\pi$
$98$	−8.90167			−0.899204
$99$	−2.36966			−0.238159
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	5.10270	−	15.7045i	0.507737	−	1.56266i	−0.288382	−	0.957515i	$-0.593117\pi$
$101$	5.10270	−	15.7045i	0.507737	−	1.56266i	0.796119	−	0.605140i	$-0.206883\pi$
$102$	−0.485923	+	1.49552i	−0.0481135	+	0.148078i
$103$	9.82263	+	7.13656i	0.967853	+	0.703186i	0.954961	−	0.296731i	$-0.0958963\pi$
$103$	9.82263	+	7.13656i	0.967853	+	0.703186i	0.0128917	+	0.999917i	$0.495896\pi$
$104$	0.595256	+	1.83201i	0.0583697	+	0.179643i
$105$	3.22611	+	2.34391i	0.314836	+	0.228742i
$106$	2.56202	−	1.86142i	0.248846	−	0.180797i
$107$	4.16978	−	12.8333i	0.403108	−	1.24064i	−0.519357	−	0.854558i	$-0.673828\pi$
$107$	4.16978	−	12.8333i	0.403108	−	1.24064i	0.922465	−	0.386081i	$-0.126172\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−14.4292	+	10.4834i	−1.38207	+	1.00413i	−0.385386	+	0.922756i	$0.625932\pi$
$109$	−14.4292	+	10.4834i	−1.38207	+	1.00413i	−0.996683	+	0.0813763i	$0.974068\pi$
$110$	0.732264	−	2.25368i	0.0698186	−	0.214880i
$111$	1.39635	−	1.01451i	0.132536	−	0.0962929i
$112$	3.22611	+	2.34391i	0.304839	+	0.221478i
$113$	−1.21819	−	3.74919i	−0.114597	−	0.352694i	0.877265	−	0.480005i	$-0.159365\pi$
$113$	−1.21819	−	3.74919i	−0.114597	−	0.352694i	−0.991863	+	0.127311i	$0.959365\pi$
$114$	4.47549	+	3.25164i	0.419168	+	0.304544i
$115$	1.18483	−	3.64653i	0.110486	−	0.340040i
$116$	0.300317	−	0.924280i	0.0278837	−	0.0858172i
$117$	−0.595256	−	1.83201i	−0.0550315	−	0.169369i
$118$	−2.19499			−0.202065
$119$	−6.27056			−0.574821
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	4.35634	−	3.16507i	0.396031	−	0.287733i
$122$	−4.26677	−	3.09999i	−0.386295	−	0.280660i
$123$	−11.4067			−1.02850
$124$	4.74989	−	2.90491i	0.426553	−	0.260869i
$125$	1.00000			0.0894427
$126$	−3.22611	−	2.34391i	−0.287405	−	0.208812i
$127$	−7.97911	+	5.79717i	−0.708032	+	0.514415i	−0.882538	−	0.470241i	$-0.844167\pi$
$127$	−7.97911	+	5.79717i	−0.708032	+	0.514415i	0.174506	+	0.984656i	$0.444167\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−5.62689			−0.495420
$130$	1.92629			0.168947
$131$	−2.69657	−	8.29919i	−0.235601	−	0.725104i	−0.997041	−	0.0768692i	$-0.975508\pi$
$131$	−2.69657	−	8.29919i	−0.235601	−	0.725104i	0.761441	−	0.648235i	$-0.224492\pi$
$132$	−0.732264	+	2.25368i	−0.0637354	+	0.196157i
$133$	−6.81690	+	20.9803i	−0.591100	+	1.81922i
$134$	9.55352	+	6.94104i	0.825298	+	0.599614i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	1.27216	+	0.924280i	0.109087	+	0.0792563i
$137$	5.70022	−	4.14145i	0.487003	−	0.353828i	−0.317028	−	0.948416i	$-0.602685\pi$
$137$	5.70022	−	4.14145i	0.487003	−	0.353828i	0.804030	+	0.594588i	$0.202685\pi$
$138$	−1.18483	+	3.64653i	−0.100859	+	0.310413i
$139$	−10.0551	+	7.30549i	−0.852866	+	0.619643i	−0.925935	−	0.377683i	$-0.876721\pi$
$139$	−10.0551	+	7.30549i	−0.852866	+	0.619643i	0.0730687	+	0.997327i	$0.476721\pi$
$140$	3.22611	−	2.34391i	0.272656	−	0.198096i
$141$	−1.23880	+	3.81264i	−0.104326	+	0.321083i
$142$	−3.58194	+	2.60243i	−0.300590	+	0.218391i
$143$	−3.69287	−	2.68303i	−0.308814	−	0.224366i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	−0.786239	−	0.571236i	−0.0652936	−	0.0474386i
$146$	−1.05186	+	3.23730i	−0.0870527	+	0.267921i
$147$	2.75077	−	8.46599i	0.226879	−	0.698263i
$148$	−0.533359	−	1.64151i	−0.0438418	−	0.134931i
$149$	−8.01770			−0.656836			−0.328418	−	0.944533i	$-0.606515\pi$
$149$	−8.01770			−0.656836			−0.328418	+	0.944533i	$0.606515\pi$
$150$	−1.00000			−0.0816497
$151$	−4.71700	−	14.5174i	−0.383864	−	1.18141i	−0.937301	−	0.348521i	$-0.886684\pi$
$151$	−4.71700	−	14.5174i	−0.383864	−	1.18141i	0.553437	−	0.832891i	$-0.313316\pi$
$152$	4.47549	−	3.25164i	0.363010	−	0.263742i
$153$	−1.27216	−	0.924280i	−0.102848	−	0.0747236i
$154$	−9.44945			−0.761459
$155$	−1.29494	−	5.41508i	−0.104012	−	0.434950i
$156$	−1.92629			−0.154227
$157$	1.35410	+	0.983813i	0.108069	+	0.0785168i	0.640507	−	0.767952i	$-0.278724\pi$
$157$	1.35410	+	0.983813i	0.108069	+	0.0785168i	−0.532438	+	0.846469i	$0.678724\pi$
$158$	−4.91760	+	3.57285i	−0.391223	+	0.284240i
$159$	0.978605	+	3.01184i	0.0776084	+	0.238854i
$160$	−1.00000			−0.0790569
$161$	−15.2895			−1.20498
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−2.94194	+	9.05437i	−0.230431	+	0.709193i	0.767264	+	0.641332i	$0.221618\pi$
$163$	−2.94194	+	9.05437i	−0.230431	+	0.709193i	−0.997695	+	0.0678617i	$0.978382\pi$
$164$	−3.52485	+	10.8484i	−0.275245	+	0.847116i
$165$	1.91709	+	1.39285i	0.149245	+	0.108433i
$166$	−2.49035	−	7.66450i	−0.193289	−	0.594881i
$167$	10.9383	+	7.94716i	0.846433	+	0.614969i	0.924160	−	0.382005i	$-0.124766\pi$
$167$	10.9383	+	7.94716i	0.846433	+	0.614969i	−0.0777273	+	0.996975i	$0.524766\pi$
$168$	−3.22611	+	2.34391i	−0.248900	+	0.180836i
$169$	−2.87058	+	8.83475i	−0.220814	+	0.679596i
$170$	1.27216	−	0.924280i	0.0975704	−	0.0708890i
$171$	−4.47549	+	3.25164i	−0.342249	+	0.248659i
$172$	−1.73880	+	5.35149i	−0.132583	+	0.408047i
$173$	12.9464	−	9.40611i	0.984296	−	0.715133i	0.0256317	−	0.999671i	$-0.491840\pi$
$173$	12.9464	−	9.40611i	0.984296	−	0.715133i	0.958665	+	0.284538i	$0.0918403\pi$
$174$	0.786239	+	0.571236i	0.0596046	+	0.0433053i
$175$	−1.23226	−	3.79252i	−0.0931504	−	0.286687i
$176$	1.91709	+	1.39285i	0.144506	+	0.104990i
$177$	0.678289	−	2.08756i	0.0509833	−	0.156910i
$178$	−2.02504	+	6.23244i	−0.151783	+	0.467141i
$179$	−2.00635	−	6.17491i	−0.149962	−	0.461534i	0.847654	−	0.530549i	$-0.178014\pi$
$179$	−2.00635	−	6.17491i	−0.149962	−	0.461534i	−0.997616	+	0.0690151i	$0.978014\pi$
$180$	1.00000			0.0745356
$181$	−20.7709			−1.54389			−0.771945	−	0.635689i	$-0.780716\pi$
$181$	−20.7709			−1.54389			−0.771945	+	0.635689i	$0.780716\pi$
$182$	−2.37370	−	7.30549i	−0.175950	−	0.541519i
$183$	4.26677	−	3.09999i	0.315409	−	0.229158i
$184$	3.10192	+	2.25368i	0.228677	+	0.166143i
$185$	−1.72598			−0.126897
$186$	1.29494	+	5.41508i	0.0949496	+	0.397053i
$187$	−3.72623			−0.272489
$188$	3.24323	+	2.35634i	0.236537	+	0.171854i
$189$	3.22611	−	2.34391i	0.234665	−	0.170494i
$190$	−1.70949	−	5.26126i	−0.124019	−	0.381692i
$191$	0.842019			0.0609263			0.0304632	−	0.999536i	$-0.490302\pi$
$191$	0.842019			0.0609263			0.0304632	+	0.999536i	$0.490302\pi$
$192$	1.00000			0.0721688
$193$	5.22942	+	16.0945i	0.376422	+	1.15851i	0.942514	+	0.334166i	$0.108455\pi$
$193$	5.22942	+	16.0945i	0.376422	+	1.15851i	−0.566092	+	0.824342i	$0.691545\pi$
$194$	1.61145	−	4.95952i	0.115695	−	0.356073i
$195$	−0.595256	+	1.83201i	−0.0426272	+	0.131193i
$196$	−7.20160	−	5.23227i	−0.514400	−	0.373734i
$197$	7.82857	+	24.0939i	0.557762	+	1.71662i	0.688534	+	0.725204i	$0.258254\pi$
$197$	7.82857	+	24.0939i	0.557762	+	1.71662i	−0.130772	+	0.991412i	$0.541746\pi$
$198$	−1.91709	−	1.39285i	−0.136242	−	0.0989854i
$199$	−12.3422	+	8.96712i	−0.874914	+	0.635663i	−0.931901	−	0.362712i	$-0.881851\pi$
$199$	−12.3422	+	8.96712i	−0.874914	+	0.635663i	0.0569867	+	0.998375i	$0.481851\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	−9.55352	+	6.94104i	−0.673853	+	0.489583i
$202$	13.3590	−	9.70591i	0.939938	−	0.682905i
$203$	−1.19757	+	3.68574i	−0.0840529	+	0.258688i
$204$	−1.27216	+	0.924280i	−0.0890691	+	0.0647125i
$205$	9.22818	+	6.70467i	0.644524	+	0.468274i
$206$	3.75191	+	11.5472i	0.261408	+	0.804531i
$207$	−3.10192	−	2.25368i	−0.215598	−	0.156641i
$208$	−0.595256	+	1.83201i	−0.0412736	+	0.127027i
$209$	−4.05089	+	12.4674i	−0.280206	+	0.862386i
$210$	1.23226	+	3.79252i	0.0850343	+	0.261709i
$211$	12.2482			0.843201			0.421601	−	0.906782i	$-0.361468\pi$
$211$	12.2482			0.843201			0.421601	+	0.906782i	$0.361468\pi$
$212$	3.16683			0.217499
$213$	−1.36818	−	4.21082i	−0.0937461	−	0.288521i
$214$	10.9166	−	7.93140i	0.746246	−	0.542179i
$215$	4.55225	+	3.30740i	0.310461	+	0.225563i
$216$	−1.00000			−0.0680414
$217$	−18.9411	+	11.5839i	−1.28581	+	0.786366i
$218$	−17.8355			−1.20797
$219$	−2.75381	−	2.00076i	−0.186085	−	0.135199i
$220$	1.91709	−	1.39285i	0.129250	−	0.0939058i
$221$	−0.936028	−	2.88080i	−0.0629640	−	0.193783i
$222$	1.72598			0.115841
$223$	0.264851			0.0177357			0.00886787	−	0.999961i	$-0.497177\pi$
$223$	0.264851			0.0177357			0.00886787	+	0.999961i	$0.497177\pi$
$224$	1.23226	+	3.79252i	0.0823341	+	0.253398i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	1.21819	−	3.74919i	0.0810326	−	0.249393i
$227$	13.9174	+	10.1116i	0.923729	+	0.671128i	0.944449	−	0.328657i	$-0.106596\pi$
$227$	13.9174	+	10.1116i	0.923729	+	0.671128i	−0.0207206	+	0.999785i	$0.506596\pi$
$228$	1.70949	+	5.26126i	0.113213	+	0.348435i
$229$	−19.4070	−	14.1000i	−1.28245	−	0.931755i	−0.282827	−	0.959171i	$-0.591272\pi$
$229$	−19.4070	−	14.1000i	−1.28245	−	0.931755i	−0.999624	+	0.0274156i	$0.991272\pi$
$230$	3.10192	−	2.25368i	0.204535	−	0.148603i
$231$	2.92004	−	8.98696i	0.192125	−	0.591299i
$232$	0.786239	−	0.571236i	0.0516191	−	0.0375035i
$233$	11.6293	−	8.44916i	0.761859	−	0.553523i	−0.137621	−	0.990485i	$-0.543946\pi$
$233$	11.6293	−	8.44916i	0.761859	−	0.553523i	0.899480	+	0.436962i	$0.143946\pi$
$234$	0.595256	−	1.83201i	0.0389131	−	0.119762i
$235$	3.24323	−	2.35634i	0.211565	−	0.153711i
$236$	−1.77578	−	1.29018i	−0.115594	−	0.0839837i
$237$	−1.87836	−	5.78099i	−0.122012	−	0.375515i
$238$	−5.07299	−	3.68574i	−0.328833	−	0.238911i
$239$	2.11238	−	6.50123i	0.136638	−	0.420529i	−0.859203	−	0.511635i	$-0.829040\pi$
$239$	2.11238	−	6.50123i	0.136638	−	0.420529i	0.995841	+	0.0911055i	$0.0290401\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	9.08178	+	27.9509i	0.585009	+	1.80047i	0.599234	+	0.800574i	$0.295472\pi$
$241$	9.08178	+	27.9509i	0.585009	+	1.80047i	−0.0142247	+	0.999899i	$0.504528\pi$
$242$	5.38473			0.346144
$243$	1.00000			0.0641500
$244$	−1.62976	−	5.01589i	−0.104335	−	0.321109i
$245$	−7.20160	+	5.23227i	−0.460093	+	0.334277i
$246$	−9.22818	−	6.70467i	−0.588367	−	0.427474i
$247$	−10.6563			−0.678042
$248$	5.55021	+	0.441792i	0.352439	+	0.0280538i
$249$	8.05894			0.510714
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	0.0529801	−	0.0384923i	0.00334407	−	0.00242961i	−0.586112	−	0.810230i	$-0.699342\pi$
$251$	0.0529801	−	0.0384923i	0.00334407	−	0.00242961i	0.589456	+	0.807800i	$0.299342\pi$
$252$	−1.23226	−	3.79252i	−0.0776253	−	0.238906i
$253$	−9.08569			−0.571213
$254$	−9.86273			−0.618843
$255$	0.485923	+	1.49552i	0.0304297	+	0.0936528i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	2.09148	−	6.43690i	0.130463	−	0.401523i	−0.864394	−	0.502815i	$-0.832298\pi$
$257$	2.09148	−	6.43690i	0.130463	−	0.401523i	0.994857	+	0.101292i	$0.0322977\pi$
$258$	−4.55225	−	3.30740i	−0.283410	−	0.205910i
$259$	2.12687	+	6.54583i	0.132157	+	0.406738i
$260$	1.55840	+	1.13224i	0.0966479	+	0.0702188i
$261$	−0.786239	+	0.571236i	−0.0486670	+	0.0353586i
$262$	2.69657	−	8.29919i	0.166595	−	0.512726i
$263$	−6.89481	+	5.00937i	−0.425152	+	0.308891i	−0.779707	−	0.626144i	$-0.784632\pi$
$263$	−6.89481	+	5.00937i	−0.425152	+	0.308891i	0.354556	+	0.935035i	$0.384632\pi$
$264$	−1.91709	+	1.39285i	−0.117989	+	0.0857239i
$265$	0.978605	−	3.01184i	0.0601152	−	0.185016i
$266$	−17.8469	+	12.9665i	−1.09426	+	0.795028i
$267$	−5.30163	−	3.85186i	−0.324454	−	0.235730i
$268$	3.64912	+	11.2308i	0.222905	+	0.686032i
$269$	0.466614	+	0.339015i	0.0284500	+	0.0206701i	0.601919	−	0.798557i	$-0.294403\pi$
$269$	0.466614	+	0.339015i	0.0284500	+	0.0206701i	−0.573469	+	0.819227i	$0.694403\pi$
$270$	−0.309017	+	0.951057i	−0.0188062	+	0.0578795i
$271$	3.32144	−	10.2223i	0.201763	−	0.620963i	−0.798068	−	0.602568i	$-0.794144\pi$
$271$	3.32144	−	10.2223i	0.201763	−	0.620963i	0.999831	−	0.0183954i	$-0.00585575\pi$
$272$	0.485923	+	1.49552i	0.0294634	+	0.0906790i
$273$	7.68145			0.464902
$274$	7.04586			0.425656
$275$	−0.732264	−	2.25368i	−0.0441572	−	0.135902i
$276$	−3.10192	+	2.25368i	−0.186714	+	0.135655i
$277$	23.1956	+	16.8526i	1.39369	+	1.01257i	0.995449	+	0.0952930i	$0.0303788\pi$
$277$	23.1956	+	16.8526i	1.39369	+	1.01257i	0.398240	+	0.917281i	$0.369621\pi$
$278$	−12.4288			−0.745432
$279$	−5.55021	−	0.441792i	−0.332282	−	0.0264494i
$280$	3.98769			0.238310
$281$	1.30606	+	0.948905i	0.0779128	+	0.0566069i	0.626060	−	0.779775i	$-0.284667\pi$
$281$	1.30606	+	0.948905i	0.0779128	+	0.0566069i	−0.548147	+	0.836382i	$0.684667\pi$
$282$	−3.24323	+	2.35634i	−0.193131	+	0.140318i
$283$	−5.71376	−	17.5851i	−0.339648	−	1.04533i	−0.964387	−	0.264495i	$-0.914795\pi$
$283$	−5.71376	−	17.5851i	−0.339648	−	1.04533i	0.624739	−	0.780833i	$-0.285205\pi$
$284$	−4.42752			−0.262725
$285$	5.53201			0.327688
$286$	−1.41055	−	4.34123i	−0.0834077	−	0.256703i
$287$	14.0560	−	43.2600i	0.829700	−	2.55356i
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	11.7528	+	8.53894i	0.691344	+	0.502291i
$290$	−0.300317	−	0.924280i	−0.0176352	−	0.0542756i
$291$	4.21882	+	3.06515i	0.247312	+	0.179683i
$292$	−2.75381	+	2.00076i	−0.161155	+	0.117086i
$293$	3.70628	−	11.4068i	0.216523	−	0.666390i	−0.782519	−	0.622627i	$-0.786065\pi$
$293$	3.70628	−	11.4068i	0.216523	−	0.666390i	0.999042	−	0.0437629i	$-0.0139346\pi$
$294$	7.20160	−	5.23227i	0.420006	−	0.305152i
$295$	−1.77578	+	1.29018i	−0.103390	+	0.0751173i
$296$	0.533359	−	1.64151i	0.0310008	−	0.0954108i
$297$	1.91709	−	1.39285i	0.111241	−	0.0808213i
$298$	−6.48646	−	4.71269i	−0.375750	−	0.272999i
$299$	−2.28232	−	7.02426i	−0.131990	−	0.406224i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	6.93381	−	21.3401i	0.399658	−	1.23002i
$302$	4.71700	−	14.5174i	0.271433	−	0.835384i
$303$	5.10270	+	15.7045i	0.293142	+	0.902199i
$304$	5.53201			0.317283
$305$	−5.27402			−0.301989
$306$	−0.485923	−	1.49552i	−0.0277783	−	0.0854930i
$307$	12.1638	−	8.83750i	0.694223	−	0.504383i	−0.183822	−	0.982959i	$-0.558847\pi$
$307$	12.1638	−	8.83750i	0.694223	−	0.504383i	0.878046	+	0.478577i	$0.158847\pi$
$308$	−7.64477	−	5.55425i	−0.435601	−	0.316483i
$309$	−12.1414			−0.690703
$310$	2.13528	−	5.14204i	0.121276	−	0.292048i
$311$	28.1086			1.59389			0.796946	−	0.604051i	$-0.206448\pi$
$311$	28.1086			1.59389			0.796946	+	0.604051i	$0.206448\pi$
$312$	−1.55840	−	1.13224i	−0.0882271	−	0.0641007i
$313$	3.32610	−	2.41656i	0.188003	−	0.136592i	−0.489803	−	0.871833i	$-0.662931\pi$
$313$	3.32610	−	2.41656i	0.188003	−	0.136592i	0.677805	+	0.735241i	$0.262931\pi$
$314$	0.517221	+	1.59184i	0.0291885	+	0.0898329i
$315$	−3.98769			−0.224681
$316$	−6.07849			−0.341942
$317$	−6.12446	−	18.8491i	−0.343984	−	1.05867i	−0.962125	−	0.272607i	$-0.912114\pi$
$317$	−6.12446	−	18.8491i	−0.343984	−	1.05867i	0.618142	−	0.786067i	$-0.287886\pi$
$318$	−0.978605	+	3.01184i	−0.0548775	+	0.168895i
$319$	−0.711647	+	2.19022i	−0.0398446	+	0.122629i
$320$	−0.809017	−	0.587785i	−0.0452254	−	0.0328582i
$321$	4.16978	+	12.8333i	0.232735	+	0.716283i
$322$	−12.3695	−	8.98696i	−0.689325	−	0.500824i
$323$	−7.03762	+	5.11313i	−0.391583	+	0.284502i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	1.55840	−	1.13224i	0.0864445	−	0.0628056i
$326$	−7.70211	+	5.59591i	−0.426580	+	0.309929i
$327$	5.51147	−	16.9626i	0.304785	−	0.938032i
$328$	−9.22818	+	6.70467i	−0.509541	+	0.370203i
$329$	−12.9330	−	9.39637i	−0.713019	−	0.518039i
$330$	0.732264	+	2.25368i	0.0403098	+	0.124061i
$331$	22.1696	+	16.1072i	1.21855	+	0.885329i	0.995979	−	0.0895870i	$-0.0285547\pi$
$331$	22.1696	+	16.1072i	1.21855	+	0.885329i	0.222572	+	0.974916i	$0.428555\pi$
$332$	2.49035	−	7.66450i	0.136676	−	0.420644i
$333$	−0.533359	+	1.64151i	−0.0292279	+	0.0899541i
$334$	4.17807	+	12.8588i	0.228614	+	0.703601i
$335$	11.8088			0.645183
$336$	−3.98769			−0.217546
$337$	−1.43367	−	4.41237i	−0.0780968	−	0.240357i	0.904384	−	0.426719i	$-0.140331\pi$
$337$	−1.43367	−	4.41237i	−0.0780968	−	0.240357i	−0.982481	+	0.186361i	$0.940331\pi$
$338$	−7.51529	+	5.46018i	−0.408778	+	0.296994i
$339$	3.18925	+	2.31713i	0.173216	+	0.125849i
$340$	1.57248			0.0852796
$341$	−11.2556	+	6.88365i	−0.609525	+	0.372770i
$342$	−5.53201			−0.299137
$343$	6.13499	+	4.45733i	0.331258	+	0.240673i
$344$	−4.55225	+	3.30740i	−0.245441	+	0.178323i
$345$	1.18483	+	3.64653i	0.0637890	+	0.196322i
$346$	16.0026			0.860307
$347$	−20.7000			−1.11124			−0.555618	−	0.831438i	$-0.687518\pi$
$347$	−20.7000			−1.11124			−0.555618	+	0.831438i	$0.687518\pi$
$348$	0.300317	+	0.924280i	0.0160987	+	0.0495466i
$349$	3.97421	−	12.2314i	0.212734	−	0.654729i	−0.786572	−	0.617498i	$-0.788146\pi$
$349$	3.97421	−	12.2314i	0.212734	−	0.654729i	0.999307	−	0.0372310i	$-0.0118537\pi$
$350$	1.23226	−	3.79252i	0.0658673	−	0.202719i
$351$	1.55840	+	1.13224i	0.0831813	+	0.0604348i
$352$	0.732264	+	2.25368i	0.0390298	+	0.120121i
$353$	20.3797	+	14.8067i	1.08470	+	0.788081i	0.978497	−	0.206263i	$-0.0661302\pi$
$353$	20.3797	+	14.8067i	1.08470	+	0.788081i	0.106204	+	0.994344i	$0.466130\pi$
$354$	1.77578	−	1.29018i	0.0943818	−	0.0685724i
$355$	−1.36818	+	4.21082i	−0.0726154	+	0.223487i
$356$	−5.30163	+	3.85186i	−0.280986	+	0.204148i
$357$	5.07299	−	3.68574i	0.268491	−	0.195070i
$358$	2.00635	−	6.17491i	0.106039	−	0.326354i
$359$	−4.09631	+	2.97615i	−0.216195	+	0.157075i	−0.690612	−	0.723225i	$-0.742659\pi$
$359$	−4.09631	+	2.97615i	−0.216195	+	0.157075i	0.474417	+	0.880300i	$0.342659\pi$
$360$	0.809017	+	0.587785i	0.0426389	+	0.0309790i
$361$	3.58558	+	11.0353i	0.188715	+	0.580804i
$362$	−16.8040	−	12.2088i	−0.883200	−	0.641682i
$363$	−1.66397	+	5.12118i	−0.0873360	+	0.268792i
$364$	2.37370	−	7.30549i	0.124416	−	0.382912i
$365$	1.05186	+	3.23730i	0.0550570	+	0.169448i
$366$	5.27402			0.275677
$367$	23.1771			1.20983			0.604916	−	0.796289i	$-0.293207\pi$
$367$	23.1771			1.20983			0.604916	+	0.796289i	$0.293207\pi$
$368$	1.18483	+	3.64653i	0.0617634	+	0.190088i
$369$	9.22818	−	6.70467i	0.480400	−	0.349031i
$370$	−1.39635	−	1.01451i	−0.0725928	−	0.0527418i
$371$	−12.6283			−0.655631
$372$	−2.13528	+	5.14204i	−0.110709	+	0.266602i
$373$	22.0764			1.14307			0.571536	−	0.820577i	$-0.306348\pi$
$373$	22.0764			1.14307			0.571536	+	0.820577i	$0.306348\pi$
$374$	−3.01459	−	2.19022i	−0.155881	−	0.113254i
$375$	−0.809017	+	0.587785i	−0.0417775	+	0.0303531i
$376$	1.23880	+	3.81264i	0.0638864	+	0.196622i
$377$	−1.87206			−0.0964158
$378$	3.98769			0.205105
$379$	7.99701	+	24.6123i	0.410779	+	1.26425i	0.915972	+	0.401241i	$0.131421\pi$
$379$	7.99701	+	24.6123i	0.410779	+	1.26425i	−0.505193	+	0.863006i	$0.668579\pi$
$380$	1.70949	−	5.26126i	0.0876948	−	0.269897i
$381$	3.04775	−	9.38001i	0.156141	−	0.480552i
$382$	0.681207	+	0.494926i	0.0348536	+	0.0253226i
$383$	−7.95037	−	24.4687i	−0.406245	−	1.25029i	−0.919851	−	0.392267i	$-0.871691\pi$
$383$	−7.95037	−	24.4687i	−0.406245	−	1.25029i	0.513606	−	0.858026i	$-0.328309\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	−7.64477	+	5.55425i	−0.389613	+	0.283071i
$386$	−5.22942	+	16.0945i	−0.266171	+	0.819189i
$387$	4.55225	−	3.30740i	0.231404	−	0.168125i
$388$	4.21882	−	3.06515i	0.214178	−	0.155610i
$389$	−1.68719	+	5.19263i	−0.0855439	+	0.263277i	−0.984674	−	0.174404i	$-0.944200\pi$
$389$	−1.68719	+	5.19263i	−0.0855439	+	0.263277i	0.899130	+	0.437681i	$0.144200\pi$
$390$	−1.55840	+	1.13224i	−0.0789127	+	0.0573334i
$391$	−4.87770	−	3.54386i	−0.246676	−	0.179221i
$392$	−2.75077	−	8.46599i	−0.138935	−	0.427597i
$393$	7.05971	+	5.12918i	0.356115	+	0.258733i
$394$	−7.82857	+	24.0939i	−0.394398	+	1.21383i
$395$	−1.87836	+	5.78099i	−0.0945103	+	0.290873i
$396$	−0.732264	−	2.25368i	−0.0367976	−	0.113252i
$397$	−10.3275			−0.518322			−0.259161	−	0.965834i	$-0.583446\pi$
$397$	−10.3275			−0.518322			−0.259161	+	0.965834i	$0.583446\pi$
$398$	−15.2558			−0.764703
$399$	−6.81690	−	20.9803i	−0.341272	−	1.05033i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	25.3541	+	18.4208i	1.26612	+	0.919892i	0.999041	−	0.0437825i	$-0.0139409\pi$
$401$	25.3541	+	18.4208i	1.26612	+	0.919892i	0.267081	+	0.963674i	$0.413941\pi$
$402$	−11.8088			−0.588969
$403$	−8.14924	−	6.97268i	−0.405942	−	0.347334i
$404$	16.5127			0.821536
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	−3.13528	+	2.27791i	−0.155601	+	0.113051i
$407$	1.26388	+	3.88981i	0.0626480	+	0.192811i
$408$	−1.57248			−0.0778493
$409$	−0.820443			−0.0405683			−0.0202841	−	0.999794i	$-0.506457\pi$
$409$	−0.820443			−0.0405683			−0.0202841	+	0.999794i	$0.506457\pi$
$410$	3.52485	+	10.8484i	0.174080	+	0.535763i
$411$	−2.17729	+	6.70101i	−0.107398	+	0.330536i
$412$	−3.75191	+	11.5472i	−0.184843	+	0.568890i
$413$	7.08127	+	5.14484i	0.348446	+	0.253161i
$414$	−1.18483	−	3.64653i	−0.0582311	−	0.179217i
$415$	−6.51982	−	4.73692i	−0.320045	−	0.232526i
$416$	−1.55840	+	1.13224i	−0.0764069	+	0.0555129i
$417$	3.84072	−	11.8205i	0.188081	−	0.578854i
$418$	−10.6054	+	7.70526i	−0.518726	+	0.376876i
$419$	7.29651	−	5.30122i	0.356458	−	0.258982i	−0.395115	−	0.918631i	$-0.629295\pi$
$419$	7.29651	−	5.30122i	0.356458	−	0.258982i	0.751573	+	0.659650i	$0.229295\pi$
$420$	−1.23226	+	3.79252i	−0.0601283	+	0.185056i
$421$	5.77485	−	4.19568i	0.281449	−	0.204485i	−0.438100	−	0.898926i	$-0.644348\pi$
$421$	5.77485	−	4.19568i	0.281449	−	0.204485i	0.719549	+	0.694441i	$0.244348\pi$
$422$	9.90901	+	7.19931i	0.482363	+	0.350457i
$423$	−1.23880	−	3.81264i	−0.0602327	−	0.185377i
$424$	2.56202	+	1.86142i	0.124423	+	0.0903984i
$425$	0.485923	−	1.49552i	0.0235707	−	0.0725432i
$426$	1.36818	−	4.21082i	0.0662885	−	0.204015i
$427$	6.49898	+	20.0018i	0.314508	+	0.967955i
$428$	13.4937			0.652243
$429$	4.56464			0.220383
$430$	1.73880	+	5.35149i	0.0838525	+	0.258072i
$431$	−22.7816	+	16.5518i	−1.09735	+	0.797273i	−0.980626	−	0.195891i	$-0.937240\pi$
$431$	−22.7816	+	16.5518i	−1.09735	+	0.797273i	−0.116726	+	0.993164i	$0.537240\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−21.6103			−1.03852			−0.519261	−	0.854616i	$-0.673793\pi$
$433$	−21.6103			−1.03852			−0.519261	+	0.854616i	$0.673793\pi$
$434$	−22.1325	−	1.76173i	−1.06239	−	0.0845657i
$435$	0.971845			0.0465964
$436$	−14.4292	−	10.4834i	−0.691035	−	0.502066i
$437$	−17.1599	+	12.4674i	−0.820867	+	0.596395i
$438$	−1.05186	−	3.23730i	−0.0502599	−	0.154684i
$439$	17.9892			0.858577			0.429289	−	0.903167i	$-0.358764\pi$
$439$	17.9892			0.858577			0.429289	+	0.903167i	$0.358764\pi$
$440$	2.36966			0.112969
$441$	2.75077	+	8.46599i	0.130989	+	0.403142i
$442$	0.936028	−	2.88080i	0.0445223	−	0.137026i
$443$	−8.95142	+	27.5496i	−0.425295	+	1.30892i	0.477417	+	0.878677i	$0.341573\pi$
$443$	−8.95142	+	27.5496i	−0.425295	+	1.30892i	−0.902712	+	0.430246i	$0.858427\pi$
$444$	1.39635	+	1.01451i	0.0662679	+	0.0481464i
$445$	2.02504	+	6.23244i	0.0959962	+	0.295446i
$446$	0.214269	+	0.155675i	0.0101459	+	0.00737145i
$447$	6.48646	−	4.71269i	0.306799	−	0.222902i
$448$	−1.23226	+	3.79252i	−0.0582190	+	0.179180i
$449$	23.7140	−	17.2293i	1.11913	−	0.813099i	0.135057	−	0.990838i	$-0.456878\pi$
$449$	23.7140	−	17.2293i	1.11913	−	0.813099i	0.984078	+	0.177739i	$0.0568783\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	8.35269	−	25.7069i	0.393313	−	1.21049i
$452$	3.18925	−	2.31713i	0.150010	−	0.108989i
$453$	12.3493	+	8.97226i	0.580219	+	0.421554i
$454$	5.31596	+	16.3609i	0.249491	+	0.767853i
$455$	−6.21442	−	4.51504i	−0.291337	−	0.211668i
$456$	−1.70949	+	5.26126i	−0.0800540	+	0.246381i
$457$	7.89556	−	24.3000i	0.369339	−	1.13671i	−0.577880	−	0.816121i	$-0.696120\pi$
$457$	7.89556	−	24.3000i	0.369339	−	1.13671i	0.947219	−	0.320587i	$-0.103880\pi$
$458$	−7.41282	−	22.8143i	−0.346378	−	1.06604i
$459$	1.57248			0.0733970
$460$	3.83418			0.178770
$461$	11.0777	+	34.0937i	0.515940	+	1.58790i	0.781565	+	0.623823i	$0.214422\pi$
$461$	11.0777	+	34.0937i	0.515940	+	1.58790i	−0.265625	+	0.964076i	$0.585578\pi$
$462$	7.64477	−	5.55425i	0.355667	−	0.258407i
$463$	−8.01228	−	5.82126i	−0.372362	−	0.270537i	0.385828	−	0.922571i	$-0.373916\pi$
$463$	−8.01228	−	5.82126i	−0.372362	−	0.270537i	−0.758190	+	0.652034i	$0.773916\pi$
$464$	0.971845			0.0451168
$465$	4.23053	+	3.61975i	0.196186	+	0.167862i
$466$	14.3746			0.665889
$467$	16.5030	+	11.9901i	0.763668	+	0.554837i	0.900033	−	0.435822i	$-0.143542\pi$
$467$	16.5030	+	11.9901i	0.763668	+	0.554837i	−0.136365	+	0.990659i	$0.543542\pi$
$468$	1.55840	−	1.13224i	0.0720371	−	0.0523380i
$469$	−14.5516	−	44.7851i	−0.671928	−	2.06798i
$470$	4.00885			0.184915
$471$	−1.67376			−0.0771229
$472$	−0.678289	−	2.08756i	−0.0312208	−	0.0960876i
$473$	4.12037	−	12.6812i	0.189455	−	0.583081i
$474$	1.87836	−	5.78099i	0.0862757	−	0.265529i
$475$	−4.47549	−	3.25164i	−0.205350	−	0.149195i
$476$	−1.93771	−	5.96365i	−0.0888147	−	0.273344i
$477$	−2.56202	−	1.86142i	−0.117307	−	0.0852285i
$478$	5.53027	−	4.01798i	0.252949	−	0.183778i
$479$	5.39362	−	16.5999i	0.246441	−	0.758467i	−0.748955	−	0.662620i	$-0.769444\pi$
$479$	5.39362	−	16.5999i	0.246441	−	0.758467i	0.995396	−	0.0958463i	$-0.0305557\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	−2.68978	+	1.95424i	−0.122643	+	0.0891055i
$482$	−9.08178	+	27.9509i	−0.413664	+	1.27313i
$483$	12.3695	−	8.98696i	0.562831	−	0.408921i
$484$	4.35634	+	3.16507i	0.198015	+	0.143867i
$485$	−1.61145	−	4.95952i	−0.0731721	−	0.225200i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−5.39415	+	16.6015i	−0.244432	+	0.752285i	0.751297	+	0.659964i	$0.229428\pi$
$487$	−5.39415	+	16.6015i	−0.244432	+	0.752285i	−0.995729	+	0.0923207i	$0.970572\pi$
$488$	1.62976	−	5.01589i	0.0737758	−	0.227059i
$489$	−2.94194	−	9.05437i	−0.133039	−	0.409453i
$490$	−8.90167			−0.402136
$491$	−31.7750			−1.43399			−0.716993	−	0.697080i	$-0.754482\pi$
$491$	−31.7750			−1.43399			−0.716993	+	0.697080i	$0.754482\pi$
$492$	−3.52485	−	10.8484i	−0.158913	−	0.489083i
$493$	−1.23634	+	0.898257i	−0.0556821	+	0.0404554i
$494$	−8.62110	−	6.26359i	−0.387881	−	0.281812i
$495$	−2.36966			−0.106508
$496$	4.23053	+	3.61975i	0.189957	+	0.162531i
$497$	17.6556			0.791961
$498$	6.51982	+	4.73692i	0.292160	+	0.212267i
$499$	−15.4482	+	11.2238i	−0.691555	+	0.502444i	−0.877171	−	0.480178i	$-0.840572\pi$
$499$	−15.4482	+	11.2238i	−0.691555	+	0.502444i	0.185616	+	0.982622i	$0.440572\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−13.5205			−0.604052
$502$	0.0654870			0.00292283
$503$	3.56903	+	10.9843i	0.159135	+	0.489768i	0.998556	−	0.0537137i	$-0.0171058\pi$
$503$	3.56903	+	10.9843i	0.159135	+	0.489768i	−0.839421	+	0.543481i	$0.817106\pi$
$504$	1.23226	−	3.79252i	0.0548894	−	0.168932i
$505$	5.10270	−	15.7045i	0.227067	−	0.698841i
$506$	−7.35048	−	5.34044i	−0.326769	−	0.237411i
$507$	−2.87058	−	8.83475i	−0.127487	−	0.392365i
$508$	−7.97911	−	5.79717i	−0.354016	−	0.257208i
$509$	17.2315	−	12.5194i	0.763774	−	0.554915i	−0.136291	−	0.990669i	$-0.543518\pi$
$509$	17.2315	−	12.5194i	0.763774	−	0.554915i	0.900066	+	0.435754i	$0.143518\pi$
$510$	−0.485923	+	1.49552i	−0.0215170	+	0.0662226i
$511$	10.9813	−	7.97841i	0.485786	−	0.352944i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	1.70949	−	5.26126i	0.0754757	−	0.232290i
$514$	5.47555	−	3.97822i	0.241516	−	0.175472i
$515$	9.82263	+	7.13656i	0.432837	+	0.314474i
$516$	−1.73880	−	5.35149i	−0.0765465	−	0.235586i
$517$	−7.68534	−	5.58372i	−0.338001	−	0.245572i
$518$	−2.12687	+	6.54583i	−0.0934492	+	0.287607i
$519$	−4.94508	+	15.2194i	−0.217065	+	0.668058i
$520$	0.595256	+	1.83201i	0.0261037	+	0.0803390i
$521$	15.2854			0.669667			0.334833	−	0.942277i	$-0.391320\pi$
$521$	15.2854			0.669667			0.334833	+	0.942277i	$0.391320\pi$
$522$	−0.971845			−0.0425365
$523$	−9.49286	−	29.2160i	−0.415094	−	1.27753i	−0.912167	−	0.409819i	$-0.865592\pi$
$523$	−9.49286	−	29.2160i	−0.415094	−	1.27753i	0.497073	−	0.867709i	$-0.334408\pi$
$524$	7.05971	−	5.12918i	0.308405	−	0.224069i
$525$	3.22611	+	2.34391i	0.140799	+	0.102296i
$526$	−8.52245			−0.371596
$527$	−8.72758	−	0.694709i	−0.380180	−	0.0302620i
$528$	−2.36966			−0.103126
$529$	6.71406	+	4.87805i	0.291916	+	0.212089i
$530$	2.56202	−	1.86142i	0.111287	−	0.0808548i
$531$	0.678289	+	2.08756i	0.0294352	+	0.0905923i
$532$	−22.0600			−0.956420
$533$	21.9725			0.951736
$534$	−2.02504	−	6.23244i	−0.0876322	−	0.269704i
$535$	4.16978	−	12.8333i	0.180275	−	0.554831i
$536$	−3.64912	+	11.2308i	−0.157618	+	0.485098i
$537$	5.25269	+	3.81630i	0.226670	+	0.164686i
$538$	0.178231	+	0.548538i	0.00768407	+	0.0236491i
$539$	17.0653	+	12.3987i	0.735055	+	0.534049i
$540$	−0.809017	+	0.587785i	−0.0348145	+	0.0252942i
$541$	3.31413	−	10.1999i	0.142486	−	0.438526i	−0.854193	−	0.519956i	$-0.825949\pi$
$541$	3.31413	−	10.1999i	0.142486	−	0.438526i	0.996679	+	0.0814294i	$0.0259485\pi$
$542$	8.69565	−	6.31776i	0.373510	−	0.271371i
$543$	16.8040	−	12.2088i	0.721130	−	0.523932i
$544$	−0.485923	+	1.49552i	−0.0208338	+	0.0641197i
$545$	−14.4292	+	10.4834i	−0.618080	+	0.449061i
$546$	6.21442	+	4.51504i	0.265953	+	0.193226i
$547$	4.69708	+	14.4561i	0.200832	+	0.618099i	0.999859	+	0.0168027i	$0.00534872\pi$
$547$	4.69708	+	14.4561i	0.200832	+	0.618099i	−0.799026	+	0.601296i	$0.794651\pi$
$548$	5.70022	+	4.14145i	0.243501	+	0.176914i
$549$	−1.62976	+	5.01589i	−0.0695565	+	0.214073i
$550$	0.732264	−	2.25368i	0.0312238	−	0.0960971i
$551$	1.66136	+	5.11313i	0.0707761	+	0.217827i
$552$	−3.83418			−0.163194
$553$	24.2391			1.03075
$554$	8.85993	+	27.2681i	0.376423	+	1.15851i
$555$	1.39635	−	1.01451i	0.0592718	−	0.0430635i
$556$	−10.0551	−	7.30549i	−0.426433	−	0.309822i
$557$	16.2233			0.687402			0.343701	−	0.939079i	$-0.388319\pi$
$557$	16.2233			0.687402			0.343701	+	0.939079i	$0.388319\pi$
$558$	−4.23053	−	3.61975i	−0.179093	−	0.153236i
$559$	10.8390			0.458441
$560$	3.22611	+	2.34391i	0.136328	+	0.0990481i
$561$	3.01459	−	2.19022i	0.127276	−	0.0924714i
$562$	0.498869	+	1.53536i	0.0210435	+	0.0647653i
$563$	−34.2000			−1.44136			−0.720678	−	0.693270i	$-0.756170\pi$
$563$	−34.2000			−1.44136			−0.720678	+	0.693270i	$0.756170\pi$
$564$	−4.00885			−0.168803
$565$	−1.21819	−	3.74919i	−0.0512495	−	0.157730i
$566$	5.71376	−	17.5851i	0.240167	−	0.739159i
$567$	−1.23226	+	3.79252i	−0.0517502	+	0.159271i
$568$	−3.58194	−	2.60243i	−0.150295	−	0.109196i
$569$	10.5183	+	32.3721i	0.440951	+	1.35711i	0.886863	+	0.462032i	$0.152879\pi$
$569$	10.5183	+	32.3721i	0.440951	+	1.35711i	−0.445912	+	0.895077i	$0.647121\pi$
$570$	4.47549	+	3.25164i	0.187458	+	0.136196i
$571$	7.52561	−	5.46768i	0.314937	−	0.228815i	−0.419075	−	0.907952i	$-0.637646\pi$
$571$	7.52561	−	5.46768i	0.314937	−	0.228815i	0.734012	+	0.679136i	$0.237646\pi$
$572$	1.41055	−	4.34123i	0.0589782	−	0.181516i
$573$	−0.681207	+	0.494926i	−0.0284578	+	0.0206758i
$574$	36.7991	−	26.7361i	1.53597	−	1.11594i
$575$	1.18483	−	3.64653i	0.0494107	−	0.152071i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	8.04567	+	5.84552i	0.334946	+	0.243352i	0.742526	−	0.669817i	$-0.233627\pi$
$577$	8.04567	+	5.84552i	0.334946	+	0.243352i	−0.407581	+	0.913169i	$0.633627\pi$
$578$	4.48919	+	13.8163i	0.186726	+	0.574682i
$579$	−13.6908	−	9.94695i	−0.568970	−	0.413381i
$580$	0.300317	−	0.924280i	0.0124700	−	0.0383786i
$581$	−9.93074	+	30.5637i	−0.411996	+	1.26799i
$582$	1.61145	+	4.95952i	0.0667966	+	0.205579i
$583$	−7.50430			−0.310797
$584$	−3.40390			−0.140854
$585$	−0.595256	−	1.83201i	−0.0246108	−	0.0757443i
$586$	9.70317	−	7.04976i	0.400834	−	0.291223i
$587$	−23.6886	−	17.2108i	−0.977732	−	0.710364i	−0.0205313	−	0.999789i	$-0.506536\pi$
$587$	−23.6886	−	17.2108i	−0.977732	−	0.710364i	−0.957201	+	0.289425i	$0.906536\pi$
$588$	8.90167			0.367099
$589$	−11.8124	+	28.4458i	−0.486721	+	1.17209i
$590$	−2.19499			−0.0903662
$591$	−20.4955	−	14.8908i	−0.843071	−	0.612527i
$592$	1.39635	−	1.01451i	0.0573897	−	0.0416960i
$593$	−11.4394	−	35.2069i	−0.469760	−	1.44577i	−0.852896	−	0.522081i	$-0.825156\pi$
$593$	−11.4394	−	35.2069i	−0.469760	−	1.44577i	0.383136	−	0.923692i	$-0.374844\pi$
$594$	2.36966			0.0972282
$595$	−6.27056			−0.257068
$596$	−2.47761	−	7.62529i	−0.101487	−	0.312344i
$597$	4.71430	−	14.5091i	0.192943	−	0.593818i
$598$	2.28232	−	7.02426i	0.0933311	−	0.287244i
$599$	−2.29187	−	1.66514i	−0.0936433	−	0.0680359i	0.539978	−	0.841679i	$-0.318432\pi$
$599$	−2.29187	−	1.66514i	−0.0936433	−	0.0680359i	−0.633622	+	0.773643i	$0.718432\pi$
$600$	−0.309017	−	0.951057i	−0.0126156	−	0.0388267i
$601$	0.443279	+	0.322061i	0.0180817	+	0.0131371i	0.596789	−	0.802398i	$-0.296443\pi$
$601$	0.443279	+	0.322061i	0.0180817	+	0.0131371i	−0.578708	+	0.815535i	$0.696443\pi$
$602$	18.1529	−	13.1889i	0.739859	−	0.537539i
$603$	3.64912	−	11.2308i	0.148604	−	0.457355i
$604$	12.3493	−	8.97226i	0.502484	−	0.365076i
$605$	4.35634	−	3.16507i	0.177110	−	0.128678i
$606$	−5.10270	+	15.7045i	−0.207283	+	0.637951i
$607$	30.6648	−	22.2793i	1.24465	−	0.904289i	0.246748	−	0.969080i	$-0.420638\pi$
$607$	30.6648	−	22.2793i	1.24465	−	0.904289i	0.997899	+	0.0647909i	$0.0206381\pi$
$608$	4.47549	+	3.25164i	0.181505	+	0.131871i
$609$	−1.19757	−	3.68574i	−0.0485280	−	0.149354i
$610$	−4.26677	−	3.09999i	−0.172756	−	0.125515i
$611$	2.38629	−	7.34426i	0.0965391	−	0.297117i
$612$	0.485923	−	1.49552i	0.0196423	−	0.0604526i
$613$	−11.5976	−	35.6938i	−0.468424	−	1.44166i	−0.854625	−	0.519246i	$-0.826213\pi$
$613$	−11.5976	−	35.6938i	−0.468424	−	1.44166i	0.386201	−	0.922415i	$-0.373787\pi$
$614$	15.0353			0.606774
$615$	−11.4067			−0.459961
$616$	−2.92004	−	8.98696i	−0.117652	−	0.362095i
$617$	−4.31488	+	3.13494i	−0.173710	+	0.126208i	−0.671243	−	0.741237i	$-0.734239\pi$
$617$	−4.31488	+	3.13494i	−0.173710	+	0.126208i	0.497533	+	0.867445i	$0.334239\pi$
$618$	−9.82263	−	7.13656i	−0.395124	−	0.287075i
$619$	−48.5852			−1.95280			−0.976401	−	0.215964i	$-0.930710\pi$
$619$	−48.5852			−1.95280			−0.976401	+	0.215964i	$0.930710\pi$
$620$	4.74989	−	2.90491i	0.190760	−	0.116664i
$621$	3.83418			0.153860
$622$	22.7403	+	16.5218i	0.911804	+	0.662464i
$623$	21.1413	−	15.3600i	0.847007	−	0.615386i
$624$	−0.595256	−	1.83201i	−0.0238293	−	0.0733391i
$625$	1.00000			0.0400000
$626$	4.11129			0.164320
$627$	−4.05089	−	12.4674i	−0.161777	−	0.497899i
$628$	−0.517221	+	1.59184i	−0.0206394	+	0.0635214i
$629$	−0.838695	+	2.58124i	−0.0334410	+	0.102921i
$630$	−3.22611	−	2.34391i	−0.128531	−	0.0933834i
$631$	−6.73238	−	20.7201i	−0.268012	−	0.824855i	−0.990984	−	0.133979i	$-0.957225\pi$
$631$	−6.73238	−	20.7201i	−0.268012	−	0.824855i	0.722972	−	0.690877i	$-0.242775\pi$
$632$	−4.91760	−	3.57285i	−0.195612	−	0.142120i
$633$	−9.90901	+	7.19931i	−0.393848	+	0.286147i
$634$	6.12446	−	18.8491i	0.243233	−	0.748595i
$635$	−7.97911	+	5.79717i	−0.316641	+	0.230053i
$636$	−2.56202	+	1.86142i	−0.101591	+	0.0738100i
$637$	−5.29877	+	16.3080i	−0.209945	+	0.646145i
$638$	−1.86312	+	1.35363i	−0.0737615	+	0.0535909i
$639$	3.58194	+	2.60243i	0.141699	+	0.102951i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	28.6760	+	20.8343i	1.13263	+	0.822905i	0.986076	−	0.166297i	$-0.0531810\pi$
$641$	28.6760	+	20.8343i	1.13263	+	0.822905i	0.146556	+	0.989202i	$0.453181\pi$
$642$	−4.16978	+	12.8333i	−0.164568	+	0.506489i
$643$	−8.13252	+	25.0293i	−0.320715	+	0.987060i	0.652622	+	0.757683i	$0.273669\pi$
$643$	−8.13252	+	25.0293i	−0.320715	+	0.987060i	−0.973338	+	0.229377i	$0.926331\pi$
$644$	−4.72473	−	14.5412i	−0.186180	−	0.573004i
$645$	−5.62689			−0.221558
$646$	−8.69897			−0.342256
$647$	11.4957	+	35.3802i	0.451943	+	1.39094i	0.874687	+	0.484689i	$0.161067\pi$
$647$	11.4957	+	35.3802i	0.451943	+	1.39094i	−0.422744	+	0.906249i	$0.638933\pi$
$648$	0.809017	−	0.587785i	0.0317812	−	0.0230904i
$649$	4.20799	+	3.05729i	0.165178	+	0.120009i
$650$	1.92629			0.0755553
$651$	8.51483	−	20.5049i	0.333722	−	0.803649i
$652$	−9.52033			−0.372845
$653$	22.5181	+	16.3604i	0.881202	+	0.640231i	0.933569	−	0.358397i	$-0.116677\pi$
$653$	22.5181	+	16.3604i	0.881202	+	0.640231i	−0.0523672	+	0.998628i	$0.516677\pi$
$654$	14.4292	−	10.4834i	0.564227	−	0.409935i
$655$	−2.69657	−	8.29919i	−0.105364	−	0.324276i
$656$	−11.4067			−0.445355
$657$	3.40390			0.132799
$658$	−4.93996	−	15.2036i	−0.192580	−	0.592700i
$659$	−5.20634	+	16.0235i	−0.202810	+	0.624186i	0.796986	+	0.603998i	$0.206426\pi$
$659$	−5.20634	+	16.0235i	−0.202810	+	0.624186i	−0.999796	+	0.0201880i	$0.993574\pi$
$660$	−0.732264	+	2.25368i	−0.0285033	+	0.0877242i
$661$	−6.37440	−	4.63127i	−0.247935	−	0.180136i	0.456876	−	0.889530i	$-0.348968\pi$
$661$	−6.37440	−	4.63127i	−0.247935	−	0.180136i	−0.704811	+	0.709395i	$0.748968\pi$
$662$	8.46803	+	26.0619i	0.329119	+	1.01293i
$663$	2.45055	+	1.78043i	0.0951716	+	0.0691462i
$664$	6.51982	−	4.73692i	0.253018	−	0.183828i
$665$	−6.81690	+	20.9803i	−0.264348	+	0.813580i
$666$	−1.39635	+	1.01451i	−0.0541075	+	0.0393114i
$667$	−3.01459	+	2.19022i	−0.116725	+	0.0848058i
$668$	−4.17807	+	12.8588i	−0.161654	+	0.497521i
$669$	−0.214269	+	0.155675i	−0.00828411	+	0.00601876i
$670$	9.55352	+	6.94104i	0.369085	+	0.268156i
$671$	3.86197	+	11.8859i	0.149090	+	0.458851i
$672$	−3.22611	−	2.34391i	−0.124450	−	0.0904181i
$673$	−4.20344	+	12.9369i	−0.162031	+	0.498679i	−0.998805	−	0.0488683i	$-0.984439\pi$
$673$	−4.20344	+	12.9369i	−0.162031	+	0.498679i	0.836774	+	0.547548i	$0.184439\pi$
$674$	1.43367	−	4.41237i	0.0552228	−	0.169958i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	−9.28941			−0.357285
$677$	14.2847			0.549004			0.274502	−	0.961586i	$-0.411487\pi$
$677$	14.2847			0.549004			0.274502	+	0.961586i	$0.411487\pi$
$678$	1.21819	+	3.74919i	0.0467842	+	0.143987i
$679$	−16.8234	+	12.2229i	−0.645621	+	0.469071i
$680$	1.27216	+	0.924280i	0.0487852	+	0.0354445i
$681$	−17.2028			−0.659214
$682$	−13.1521	−	1.04690i	−0.503619	−	0.0400877i
$683$	40.3109			1.54245			0.771226	−	0.636561i	$-0.219644\pi$
$683$	40.3109			1.54245			0.771226	+	0.636561i	$0.219644\pi$
$684$	−4.47549	−	3.25164i	−0.171125	−	0.124329i
$685$	5.70022	−	4.14145i	0.217794	−	0.158237i
$686$	2.34336	+	7.21211i	0.0894698	+	0.275360i
$687$	23.9884			0.915214
$688$	−5.62689			−0.214523
$689$	−1.88508	−	5.80167i	−0.0718157	−	0.221026i
$690$	−1.18483	+	3.64653i	−0.0451056	+	0.138821i
$691$	1.56364	−	4.81239i	0.0594837	−	0.183072i	−0.916899	−	0.399118i	$-0.869316\pi$
$691$	1.56364	−	4.81239i	0.0594837	−	0.183072i	0.976383	+	0.216046i	$0.0693162\pi$
$692$	12.9464	+	9.40611i	0.492148	+	0.357567i
$693$	2.92004	+	8.98696i	0.110923	+	0.341386i
$694$	−16.7467	−	12.1672i	−0.635696	−	0.461860i
$695$	−10.0551	+	7.30549i	−0.381413	+	0.277113i
$696$	−0.300317	+	0.924280i	−0.0113835	+	0.0350347i
$697$	14.5111	−	10.5429i	0.549648	−	0.399343i
$698$	10.4046	−	7.55939i	0.393820	−	0.286127i
$699$	−4.44199	+	13.6710i	−0.168011	+	0.517086i
$700$	3.22611	−	2.34391i	0.121935	−	0.0885913i
$701$	35.4691	+	25.7698i	1.33965	+	0.973313i	0.999457	+	0.0329581i	$0.0104928\pi$
$701$	35.4691	+	25.7698i	1.33965	+	0.973313i	0.340194	+	0.940355i	$0.389507\pi$
$702$	0.595256	+	1.83201i	0.0224665	+	0.0691448i
$703$	7.72463	+	5.61227i	0.291340	+	0.211671i
$704$	−0.732264	+	2.25368i	−0.0275982	+	0.0849386i
$705$	−1.23880	+	3.81264i	−0.0466560	+	0.143592i
$706$	7.78435	+	23.9578i	0.292968	+	0.901662i
$707$	−65.8474			−2.47645
$708$	2.19499			0.0824927
$709$	−5.05004	−	15.5424i	−0.189658	−	0.583708i	0.810339	−	0.585961i	$-0.199283\pi$
$709$	−5.05004	−	15.5424i	−0.189658	−	0.583708i	−0.999997	+	0.00225311i	$0.999283\pi$
$710$	−3.58194	+	2.60243i	−0.134428	+	0.0976675i
$711$	4.91760	+	3.57285i	0.184424	+	0.133992i
$712$	−6.55318			−0.245591
$713$	−21.2805	−	1.69391i	−0.796962	−	0.0634375i
$714$	6.27056			0.234670
$715$	−3.69287	−	2.68303i	−0.138106	−	0.100340i
$716$	5.25269	−	3.81630i	0.196302	−	0.142622i
$717$	2.11238	+	6.50123i	0.0788881	+	0.242793i
$718$	−5.06332			−0.188962
$719$	36.7036			1.36881			0.684406	−	0.729101i	$-0.260062\pi$
$719$	36.7036			1.36881			0.684406	+	0.729101i	$0.260062\pi$
$720$	0.309017	+	0.951057i	0.0115164	+	0.0354438i
$721$	14.9615	−	46.0466i	0.557194	−	1.71487i
$722$	−3.58558	+	11.0353i	−0.133441	+	0.410690i
$723$	−23.7764	−	17.2746i	−0.884255	−	0.642449i
$724$	−6.41857	−	19.7543i	−0.238544	−	0.734164i
$725$	−0.786239	−	0.571236i	−0.0292002	−	0.0212152i
$726$	−4.35634	+	3.16507i	−0.161679	+	0.117467i
$727$	−6.38069	+	19.6377i	−0.236647	+	0.728323i	0.760252	+	0.649628i	$0.225075\pi$
$727$	−6.38069	+	19.6377i	−0.236647	+	0.728323i	−0.996899	+	0.0786953i	$0.974925\pi$
$728$	6.21442	−	4.51504i	0.230322	−	0.167339i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.05186	+	3.23730i	−0.0389312	+	0.119818i
$731$	7.15831	−	5.20082i	0.264760	−	0.192359i
$732$	4.26677	+	3.09999i	0.157704	+	0.114579i
$733$	−11.1559	−	34.3344i	−0.412054	−	1.26817i	−0.914860	−	0.403772i	$-0.867699\pi$
$733$	−11.1559	−	34.3344i	−0.412054	−	1.26817i	0.502806	−	0.864399i	$-0.332301\pi$
$734$	18.7506	+	13.6231i	0.692098	+	0.502839i
$735$	2.75077	−	8.46599i	0.101464	−	0.312273i
$736$	−1.18483	+	3.64653i	−0.0436733	+	0.134413i
$737$	−8.64715	−	26.6132i	−0.318522	−	0.980310i
$738$	11.4067			0.419885
$739$	39.4637			1.45170			0.725848	−	0.687855i	$-0.241447\pi$
$739$	39.4637			1.45170			0.725848	+	0.687855i	$0.241447\pi$
$740$	−0.533359	−	1.64151i	−0.0196067	−	0.0603431i
$741$	8.62110	−	6.26359i	0.316704	−	0.230099i
$742$	−10.2165	−	7.42276i	−0.375061	−	0.272498i
$743$	1.20723			0.0442891			0.0221445	−	0.999755i	$-0.492951\pi$
$743$	1.20723			0.0442891			0.0221445	+	0.999755i	$0.492951\pi$
$744$	−4.74989	+	2.90491i	−0.174140	+	0.106499i
$745$	−8.01770			−0.293746
$746$	17.8602	+	12.9762i	0.653908	+	0.475092i
$747$	−6.51982	+	4.73692i	−0.238548	+	0.173315i
$748$	−1.15147	−	3.54386i	−0.0421019	−	0.129576i
$749$	−53.8087			−1.96613
$750$	−1.00000			−0.0365148
$751$	−5.10951	−	15.7255i	−0.186449	−	0.573830i	0.813522	−	0.581535i	$-0.197548\pi$
$751$	−5.10951	−	15.7255i	−0.186449	−	0.573830i	−0.999970	+	0.00770450i	$0.997548\pi$
$752$	−1.23880	+	3.81264i	−0.0451745	+	0.139033i
$753$	−0.0202366	+	0.0622818i	−0.000737462	+	0.00226967i
$754$	−1.51452	−	1.10037i	−0.0551557	−	0.0400730i
$755$	−4.71700	−	14.5174i	−0.171669	−	0.528343i
$756$	3.22611	+	2.34391i	0.117332	+	0.0852470i
$757$	−6.27628	+	4.55998i	−0.228115	+	0.165735i	−0.695972	−	0.718069i	$-0.745026\pi$
$757$	−6.27628	+	4.55998i	−0.228115	+	0.165735i	0.467857	+	0.883804i	$0.345026\pi$
$758$	−7.99701	+	24.6123i	−0.290465	+	0.893958i
$759$	7.35048	−	5.34044i	0.266806	−	0.193846i
$760$	4.47549	−	3.25164i	0.162343	−	0.117949i
$761$	8.78468	−	27.0365i	0.318445	−	0.980071i	−0.655869	−	0.754875i	$-0.727698\pi$
$761$	8.78468	−	27.0365i	0.318445	−	0.980071i	0.974313	−	0.225197i	$-0.0723024\pi$
$762$	7.97911	−	5.79717i	0.289053	−	0.210009i
$763$	57.5393	+	41.8047i	2.08306	+	1.51343i
$764$	0.260198	+	0.800807i	0.00941364	+	0.0289722i
$765$	−1.27216	−	0.924280i	−0.0459951	−	0.0334174i
$766$	7.95037	−	24.4687i	0.287259	−	0.884091i
$767$	−1.30658	+	4.02124i	−0.0471779	+	0.145199i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	−31.8616			−1.14896			−0.574479	−	0.818520i	$-0.694795\pi$
$769$	−31.8616			−1.14896			−0.574479	+	0.818520i	$0.694795\pi$
$770$	−9.44945			−0.340535
$771$	2.09148	+	6.43690i	0.0753226	+	0.231819i
$772$	−13.6908	+	9.94695i	−0.492743	+	0.357999i
$773$	−29.4212	−	21.3758i	−1.05821	−	0.768833i	−0.0844517	−	0.996428i	$-0.526914\pi$
$773$	−29.4212	−	21.3758i	−1.05821	−	0.768833i	−0.973756	+	0.227595i	$0.926914\pi$
$774$	5.62689			0.202254
$775$	−1.29494	−	5.41508i	−0.0465156	−	0.194516i
$776$	5.21475			0.187199
$777$	−5.56821	−	4.04554i	−0.199759	−	0.145133i
$778$	−4.41712	+	3.20922i	−0.158361	+	0.115056i
$779$	−19.4995	−	60.0134i	−0.698643	−	2.15020i
$780$	−1.92629			−0.0689722
$781$	10.4917			0.375423
$782$	−1.86312	−	5.73408i	−0.0666249	−	0.205050i
$783$	0.300317	−	0.924280i	0.0107324	−	0.0330311i
$784$	2.75077	−	8.46599i	0.0982417	−	0.302357i
$785$	1.35410	+	0.983813i	0.0483300	+	0.0351138i
$786$	2.69657	+	8.29919i	0.0961835	+	0.296022i
$787$	19.4737	+	14.1484i	0.694161	+	0.504338i	0.878025	−	0.478614i	$-0.158861\pi$
$787$	19.4737	+	14.1484i	0.694161	+	0.504338i	−0.183864	+	0.982952i	$0.558861\pi$
$788$	−20.4955	+	14.8908i	−0.730121	+	0.530464i
$789$	2.63358	−	8.10533i	0.0937580	−	0.288557i
$790$	−4.91760	+	3.57285i	−0.174960	+	0.127116i
$791$	−12.7178	+	9.23999i	−0.452191	+	0.328536i
$792$	0.732264	−	2.25368i	0.0260199	−	0.0800809i
$793$	−8.21903	+	5.97148i	−0.291866	+	0.212053i
$794$	−8.35512	−	6.07035i	−0.296512	−	0.215429i
$795$	0.978605	+	3.01184i	0.0347075	+	0.106819i
$796$	−12.3422	−	8.96712i	−0.437457	−	0.317831i
$797$	−15.2444	+	46.9176i	−0.539986	+	1.66191i	0.192636	+	0.981270i	$0.438296\pi$
$797$	−15.2444	+	46.9176i	−0.539986	+	1.66191i	−0.732622	+	0.680636i	$0.761704\pi$
$798$	6.81690	−	20.9803i	0.241316	−	0.742693i
$799$	−1.94799	−	5.99530i	−0.0689150	−	0.212099i
$800$	−1.00000			−0.0353553
$801$	6.55318			0.231545
$802$	9.68440	+	29.8055i	0.341968	+	1.05247i
$803$	6.52558	−	4.74111i	0.230283	−	0.167310i
$804$	−9.55352	−	6.94104i	−0.336927	−	0.244791i
$805$	−15.2895			−0.538885
$806$	−2.49443	−	10.4310i	−0.0878625	−	0.367417i
$807$	−0.576767			−0.0203032
$808$	13.3590	+	9.70591i	0.469969	+	0.341453i
$809$	−44.6183	+	32.4171i	−1.56870	+	1.13973i	−0.640307	+	0.768119i	$0.721193\pi$
$809$	−44.6183	+	32.4171i	−1.56870	+	1.13973i	−0.928390	+	0.371606i	$0.878807\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−32.0776			−1.12640			−0.563199	−	0.826322i	$-0.690429\pi$
$811$	−32.0776			−1.12640			−0.563199	+	0.826322i	$0.690429\pi$
$812$	−3.87542			−0.136000
$813$	3.32144	+	10.2223i	0.116488	+	0.358513i
$814$	−1.26388	+	3.88981i	−0.0442988	+	0.136338i
$815$	−2.94194	+	9.05437i	−0.103052	+	0.317161i
$816$	−1.27216	−	0.924280i	−0.0445346	−	0.0323563i
$817$	−9.61908	−	29.6045i	−0.336529	−	1.03573i
$818$	−0.663752	−	0.482244i	−0.0232076	−	0.0168613i
$819$	−6.21442	+	4.51504i	−0.217149	+	0.157768i
$820$	−3.52485	+	10.8484i	−0.123093	+	0.378842i
$821$	−43.9728	+	31.9481i	−1.53466	+	1.11500i	−0.581084	+	0.813843i	$0.697371\pi$
$821$	−43.9728	+	31.9481i	−1.53466	+	1.11500i	−0.953576	+	0.301153i	$0.902629\pi$
$822$	−5.70022	+	4.14145i	−0.198818	+	0.144450i
$823$	3.86904	−	11.9077i	0.134866	−	0.415076i	−0.860703	−	0.509108i	$-0.829976\pi$
$823$	3.86904	−	11.9077i	0.134866	−	0.415076i	0.995569	+	0.0940318i	$0.0299755\pi$
$824$	−9.82263	+	7.13656i	−0.342188	+	0.248614i
$825$	1.91709	+	1.39285i	0.0667446	+	0.0484928i
$826$	2.70480	+	8.32453i	0.0941122	+	0.289647i
$827$	−9.48428	−	6.89074i	−0.329801	−	0.239614i	0.410545	−	0.911840i	$-0.365338\pi$
$827$	−9.48428	−	6.89074i	−0.329801	−	0.239614i	−0.740346	+	0.672226i	$0.765338\pi$
$828$	1.18483	−	3.64653i	0.0411756	−	0.126726i
$829$	11.9844	−	36.8843i	0.416237	−	1.28104i	−0.494903	−	0.868948i	$-0.664797\pi$
$829$	11.9844	−	36.8843i	0.416237	−	1.28104i	0.911140	−	0.412097i	$-0.135203\pi$
$830$	−2.49035	−	7.66450i	−0.0864413	−	0.266039i
$831$	−28.6713			−0.994598
$832$	−1.92629			−0.0667821
$833$	4.32552	+	13.3126i	0.149870	+	0.461254i
$834$	10.0551	−	7.30549i	0.348181	−	0.252968i
$835$	10.9383	+	7.94716i	0.378536	+	0.275023i
$836$	−13.1090			−0.453383
$837$	4.74989	−	2.90491i	0.164180	−	0.100409i
$838$	9.01898			0.311555
$839$	−14.4485	−	10.4975i	−0.498818	−	0.362412i	0.309747	−	0.950819i	$-0.399756\pi$
$839$	−14.4485	−	10.4975i	−0.498818	−	0.362412i	−0.808565	+	0.588406i	$0.799756\pi$
$840$	−3.22611	+	2.34391i	−0.111311	+	0.0808724i
$841$	−8.66963	−	26.6824i	−0.298953	−	0.920082i
$842$	7.13811			0.245996
$843$	−1.61437			−0.0556020
$844$	3.78490	+	11.6487i	0.130282	+	0.400966i
$845$	−2.87058	+	8.83475i	−0.0987511	+	0.303925i
$846$	1.23880	−	3.81264i	0.0425909	−	0.131081i
$847$	−17.3717	−	12.6213i	−0.596900	−	0.433673i
$848$	0.978605	+	3.01184i	0.0336054	+	0.103427i
$849$	14.9588	+	10.8682i	0.513385	+	0.372996i
$850$	1.27216	−	0.924280i	0.0436348	−	0.0317025i
$851$	−2.04499	+	6.29385i	−0.0701015	+	0.215750i
$852$	3.58194	−	2.60243i	0.122715	−	0.0891578i
$853$	−3.28653	+	2.38780i	−0.112529	+	0.0817568i	−0.642626	−	0.766180i	$-0.722155\pi$
$853$	−3.28653	+	2.38780i	−0.112529	+	0.0817568i	0.530098	+	0.847937i	$0.322155\pi$
$854$	−6.49898	+	20.0018i	−0.222390	+	0.684447i
$855$	−4.47549	+	3.25164i	−0.153059	+	0.111204i
$856$	10.9166	+	7.93140i	0.373123	+	0.271090i
$857$	−11.1344	−	34.2681i	−0.380343	−	1.17057i	−0.939803	−	0.341717i	$-0.888991\pi$
$857$	−11.1344	−	34.2681i	−0.380343	−	1.17057i	0.559460	−	0.828857i	$-0.311009\pi$
$858$	3.69287	+	2.68303i	0.126073	+	0.0915971i
$859$	−14.2232	+	43.7744i	−0.485288	+	1.49356i	0.346275	+	0.938133i	$0.387446\pi$
$859$	−14.2232	+	43.7744i	−0.485288	+	1.49356i	−0.831563	+	0.555430i	$0.812554\pi$
$860$	−1.73880	+	5.35149i	−0.0592927	+	0.182484i
$861$	14.0560	+	43.2600i	0.479028	+	1.47430i
$862$	−28.1596			−0.959121
$863$	11.5864			0.394406			0.197203	−	0.980363i	$-0.436814\pi$
$863$	11.5864			0.394406			0.197203	+	0.980363i	$0.436814\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	12.9464	−	9.40611i	0.440191	−	0.319817i
$866$	−17.4831	−	12.7022i	−0.594099	−	0.431638i
$867$	−14.5273			−0.493373
$868$	−16.8701	−	14.4344i	−0.572607	−	0.489937i
$869$	14.4039			0.488620
$870$	0.786239	+	0.571236i	0.0266560	+	0.0193667i
$871$	18.4028	−	13.3704i	0.623556	−	0.453040i
$872$	−5.51147	−	16.9626i	−0.186642	−	0.574425i
$873$	−5.21475			−0.176493
$874$	−21.2108			−0.717464
$875$	−1.23226	−	3.79252i	−0.0416581	−	0.128211i
$876$	1.05186	−	3.23730i	0.0355391	−	0.109378i
$877$	−14.5519	+	44.7861i	−0.491382	+	1.51232i	0.331139	+	0.943582i	$0.392567\pi$
$877$	−14.5519	+	44.7861i	−0.491382	+	1.51232i	−0.822520	+	0.568736i	$0.807433\pi$
$878$	14.5536	+	10.5738i	0.491159	+	0.356848i
$879$	3.70628	+	11.4068i	0.125010	+	0.384740i
$880$	1.91709	+	1.39285i	0.0646251	+	0.0469529i
$881$	−7.77009	+	5.64530i	−0.261781	+	0.190195i	−0.710932	−	0.703261i	$-0.751727\pi$
$881$	−7.77009	+	5.64530i	−0.261781	+	0.190195i	0.449151	+	0.893456i	$0.351727\pi$
$882$	−2.75077	+	8.46599i	−0.0926231	+	0.285065i
$883$	−2.69008	+	1.95445i	−0.0905283	+	0.0657726i	−0.632129	−	0.774863i	$-0.717819\pi$
$883$	−2.69008	+	1.95445i	−0.0905283	+	0.0657726i	0.541600	+	0.840636i	$0.317819\pi$
$884$	2.45055	−	1.78043i	0.0824210	−	0.0598824i
$885$	0.678289	−	2.08756i	0.0228004	−	0.0701725i
$886$	−23.4351	+	17.0266i	−0.787318	+	0.572020i
$887$	−23.6358	−	17.1724i	−0.793612	−	0.576593i	0.115421	−	0.993317i	$-0.463178\pi$
$887$	−23.6358	−	17.1724i	−0.793612	−	0.576593i	−0.909033	+	0.416724i	$0.863178\pi$
$888$	0.533359	+	1.64151i	0.0178983	+	0.0550854i
$889$	31.8182	+	23.1173i	1.06715	+	0.775329i
$890$	−2.02504	+	6.23244i	−0.0678796	+	0.208912i
$891$	−0.732264	+	2.25368i	−0.0245318	+	0.0755010i
$892$	0.0818434	+	0.251888i	0.00274032	+	0.00843384i
$893$	−22.1770			−0.742126
$894$	8.01770			0.268152
$895$	−2.00635	−	6.17491i	−0.0670649	−	0.206404i
$896$	−3.22611	+	2.34391i	−0.107777	+	0.0783044i
$897$	5.97520	+	4.34123i	0.199506	+	0.144950i
$898$	29.3122			0.978159
$899$	−2.07516	+	4.99727i	−0.0692105	+	0.166668i
$900$	1.00000			0.0333333
$901$	−4.02872	−	2.92704i	−0.134216	−	0.0975138i
$902$	21.8676	−	15.8878i	0.728112	−	0.529004i
$903$	6.93381	+	21.3401i	0.230743	+	0.710153i
$904$	3.94213			0.131113
$905$	−20.7709			−0.690449
$906$	4.71700	+	14.5174i	0.156712	+	0.482309i
$907$	−15.0977	+	46.4659i	−0.501310	+	1.54287i	0.305576	+	0.952168i	$0.401151\pi$
$907$	−15.0977	+	46.4659i	−0.501310	+	1.54287i	−0.806886	+	0.590707i	$0.798849\pi$
$908$	−5.31596	+	16.3609i	−0.176416	+	0.542954i
$909$	−13.3590	−	9.70591i	−0.443091	−	0.321925i
$910$	−2.37370	−	7.30549i	−0.0786873	−	0.242175i
$911$	30.7302	+	22.3268i	1.01814	+	0.739719i	0.965900	−	0.258916i	$-0.0833652\pi$
$911$	30.7302	+	22.3268i	1.01814	+	0.739719i	0.0522359	+	0.998635i	$0.483365\pi$
$912$	−4.47549	+	3.25164i	−0.148198	+	0.107672i
$913$	−5.90127	+	18.1622i	−0.195303	+	0.601082i
$914$	20.6709	−	15.0183i	0.683731	−	0.496760i
$915$	4.26677	−	3.09999i	0.141055	−	0.102482i
$916$	7.41282	−	22.8143i	0.244926	−	0.753806i
$917$	−28.1520	+	20.4536i	−0.929659	+	0.675437i
$918$	1.27216	+	0.924280i	0.0419876	+	0.0305058i
$919$	6.07964	+	18.7112i	0.200549	+	0.617225i	0.999867	+	0.0163173i	$0.00519420\pi$
$919$	6.07964	+	18.7112i	0.200549	+	0.617225i	−0.799318	+	0.600908i	$0.794806\pi$
$920$	3.10192	+	2.25368i	0.102267	+	0.0743015i
$921$	−4.64615	+	14.2994i	−0.153096	+	0.471181i
$922$	−11.0777	+	34.0937i	−0.364825	+	1.12281i
$923$	2.63551	+	8.11127i	0.0867489	+	0.266986i
$924$	9.44945			0.310864
$925$	−1.72598			−0.0567500
$926$	−3.06042	−	9.41900i	−0.100572	−	0.309527i
$927$	9.82263	−	7.13656i	0.322618	−	0.234395i
$928$	0.786239	+	0.571236i	0.0258096	+	0.0187517i
$929$	25.0883			0.823121			0.411560	−	0.911383i	$-0.364984\pi$
$929$	25.0883			0.823121			0.411560	+	0.911383i	$0.364984\pi$
$930$	1.29494	+	5.41508i	0.0424627	+	0.177568i
$931$	49.2442			1.61391
$932$	11.6293	+	8.44916i	0.380930	+	0.276762i
$933$	−22.7403	+	16.5218i	−0.744485	+	0.540900i
$934$	6.30358	+	19.4004i	0.206260	+	0.634802i
$935$	−3.72623			−0.121861
$936$	1.92629			0.0629627
$937$	−12.2553	−	37.7180i	−0.400363	−	1.23219i	−0.924705	−	0.380684i	$-0.875689\pi$
$937$	−12.2553	−	37.7180i	−0.400363	−	1.23219i	0.524342	−	0.851508i	$-0.324311\pi$
$938$	14.5516	−	44.7851i	0.475125	−	1.46228i
$939$	−1.27046	+	3.91007i	−0.0414599	+	0.127600i
$940$	3.24323	+	2.35634i	0.105782	+	0.0768555i
$941$	1.40040	+	4.30998i	0.0456517	+	0.140501i	0.971284	−	0.237922i	$-0.0764663\pi$
$941$	1.40040	+	4.30998i	0.0456517	+	0.140501i	−0.925633	+	0.378424i	$0.876466\pi$
$942$	−1.35410	−	0.983813i	−0.0441190	−	0.0320543i
$943$	35.3825	−	25.7069i	1.15221	−	0.837133i
$944$	0.678289	−	2.08756i	0.0220764	−	0.0679442i
$945$	3.22611	−	2.34391i	0.104945	−	0.0762472i
$946$	10.7873	−	7.83740i	0.350724	−	0.254816i
$947$	−12.0175	+	36.9862i	−0.390517	+	1.20189i	0.541881	+	0.840455i	$0.317712\pi$
$947$	−12.0175	+	36.9862i	−0.390517	+	1.20189i	−0.932398	+	0.361433i	$0.882288\pi$
$948$	4.91760	−	3.57285i	0.159716	−	0.116041i
$949$	5.30464	+	3.85404i	0.172196	+	0.125108i
$950$	−1.70949	−	5.26126i	−0.0554631	−	0.170698i
$951$	16.0340	+	11.6494i	0.519940	+	0.377758i
$952$	1.93771	−	5.96365i	0.0628015	−	0.193283i
$953$	5.24965	−	16.1568i	0.170053	−	0.523369i	−0.829320	−	0.558774i	$-0.811272\pi$
$953$	5.24965	−	16.1568i	0.170053	−	0.523369i	0.999373	+	0.0354047i	$0.0112720\pi$
$954$	−0.978605	−	3.01184i	−0.0316835	−	0.0975118i
$955$	0.842019			0.0272471
$956$	6.83579			0.221085
$957$	−0.711647	−	2.19022i	−0.0230043	−	0.0707999i
$958$	14.1207	−	10.2593i	0.456218	−	0.331462i
$959$	−22.7307	−	16.5148i	−0.734013	−	0.533291i
$960$	1.00000			0.0322749
$961$	−27.6463	+	14.0244i	−0.891815	+	0.452400i
$962$	−3.32475			−0.107194
$963$	−10.9166	−	7.93140i	−0.351784	−	0.255586i
$964$	−23.7764	+	17.2746i	−0.765787	+	0.556377i
$965$	5.22942	+	16.0945i	0.168341	+	0.518101i
$966$	15.2895			0.491933
$967$	−59.2768			−1.90621			−0.953107	−	0.302634i	$-0.902134\pi$
$967$	−59.2768			−1.90621			−0.953107	+	0.302634i	$0.902134\pi$
$968$	1.66397	+	5.12118i	0.0534821	+	0.164601i
$969$	2.68813	−	8.27321i	0.0863552	−	0.265774i
$970$	1.61145	−	4.95952i	0.0517405	−	0.159241i
$971$	8.80009	+	6.39364i	0.282408	+	0.205182i	0.719967	−	0.694008i	$-0.244157\pi$
$971$	8.80009	+	6.39364i	0.282408	+	0.205182i	−0.437559	+	0.899190i	$0.644157\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	40.0968	+	29.1320i	1.28544	+	0.933930i
$974$	−14.1221	+	10.2603i	−0.452500	+	0.328760i
$975$	−0.595256	+	1.83201i	−0.0190635	+	0.0586713i
$976$	4.26677	−	3.09999i	0.136576	−	0.0992282i
$977$	−1.80683	+	1.31274i	−0.0578056	+	0.0419982i	−0.616313	−	0.787501i	$-0.711374\pi$
$977$	−1.80683	+	1.31274i	−0.0578056	+	0.0419982i	0.558507	+	0.829500i	$0.311374\pi$
$978$	2.94194	−	9.05437i	0.0940730	−	0.289527i
$979$	12.5630	−	9.12758i	0.401516	−	0.291719i
$980$	−7.20160	−	5.23227i	−0.230047	−	0.167139i
$981$	5.51147	+	16.9626i	0.175968	+	0.541573i
$982$	−25.7065	−	18.6769i	−0.820328	−	0.596003i
$983$	−7.95972	+	24.4975i	−0.253876	+	0.781349i	0.740174	+	0.672416i	$0.234743\pi$
$983$	−7.95972	+	24.4975i	−0.253876	+	0.781349i	−0.994049	+	0.108933i	$0.965257\pi$
$984$	3.52485	−	10.8484i	0.112368	−	0.345834i
$985$	7.82857	+	24.0939i	0.249439	+	0.767694i
$986$	−1.52821			−0.0486680
$987$	15.9861			0.508842
$988$	−3.29297	−	10.1347i	−0.104763	−	0.322428i
$989$	17.4541	−	12.6812i	0.555010	−	0.403238i
$990$	−1.91709	−	1.39285i	−0.0609292	−	0.0442676i
$991$	−32.9447			−1.04652			−0.523261	−	0.852172i	$-0.675285\pi$
$991$	−32.9447			−1.04652			−0.523261	+	0.852172i	$0.675285\pi$
$992$	1.29494	+	5.41508i	0.0411144	+	0.171929i
$993$	−27.4031			−0.869612
$994$	14.2837	+	10.3777i	0.453050	+	0.329160i
$995$	−12.3422	+	8.96712i	−0.391274	+	0.284277i
$996$	2.49035	+	7.66450i	0.0789097	+	0.242859i
$997$	5.16406			0.163547			0.0817737	−	0.996651i	$-0.473942\pi$
$997$	5.16406			0.163547			0.0817737	+	0.996651i	$0.473942\pi$
$998$	−19.0950			−0.604441
$999$	−0.533359	−	1.64151i	−0.0168747	−	0.0519350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.e.901.1	yes	12
31.16	even	5	inner	930.2.n.e.481.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.e.481.1	✓	12	31.16	even	5	inner
930.2.n.e.901.1	yes	12	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.23226 - 3.79252i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-1.23226 - 3.79252i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.732264 - 2.25368i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(1.55840 - 1.13224i) q^{13} +(1.23226 - 3.79252i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.485923 - 1.49552i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-4.47549 - 3.25164i) q^{19} +(0.309017 + 0.951057i) q^{20} +(3.22611 + 2.34391i) q^{21} +(0.732264 - 2.25368i) q^{22} +(1.18483 - 3.64653i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +1.92629 q^{26} +(0.309017 + 0.951057i) q^{27} +(3.22611 - 2.34391i) q^{28} +(-0.786239 - 0.571236i) q^{29} -1.00000 q^{30} +(-1.29494 - 5.41508i) q^{31} -1.00000 q^{32} +(1.91709 + 1.39285i) q^{33} +(1.27216 - 0.924280i) q^{34} +(-1.23226 - 3.79252i) q^{35} +1.00000 q^{36} -1.72598 q^{37} +(-1.70949 - 5.26126i) q^{38} +(-0.595256 + 1.83201i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(9.22818 + 6.70467i) q^{41} +(1.23226 + 3.79252i) q^{42} +(4.55225 + 3.30740i) q^{43} +(1.91709 - 1.39285i) q^{44} +(0.309017 - 0.951057i) q^{45} +(3.10192 - 2.25368i) q^{46} +(3.24323 - 2.35634i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-7.20160 + 5.23227i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.485923 + 1.49552i) q^{51} +(1.55840 + 1.13224i) q^{52} +(0.978605 - 3.01184i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-0.732264 - 2.25368i) q^{55} +3.98769 q^{56} +5.53201 q^{57} +(-0.300317 - 0.924280i) q^{58} +(-1.77578 + 1.29018i) q^{59} +(-0.809017 - 0.587785i) q^{60} -5.27402 q^{61} +(2.13528 - 5.14204i) q^{62} -3.98769 q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.55840 - 1.13224i) q^{65} +(0.732264 + 2.25368i) q^{66} +11.8088 q^{67} +1.57248 q^{68} +(1.18483 + 3.64653i) q^{69} +(1.23226 - 3.79252i) q^{70} +(-1.36818 + 4.21082i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.05186 + 3.23730i) q^{73} +(-1.39635 - 1.01451i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(1.70949 - 5.26126i) q^{76} +(-7.64477 + 5.55425i) q^{77} +(-1.55840 + 1.13224i) q^{78} +(-1.87836 + 5.78099i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(3.52485 + 10.8484i) q^{82} +(-6.51982 - 4.73692i) q^{83} +(-1.23226 + 3.79252i) q^{84} +(0.485923 - 1.49552i) q^{85} +(1.73880 + 5.35149i) q^{86} +0.971845 q^{87} +2.36966 q^{88} +(2.02504 + 6.23244i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-6.21442 - 4.51504i) q^{91} +3.83418 q^{92} +(4.23053 + 3.61975i) q^{93} +4.00885 q^{94} +(-4.47549 - 3.25164i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-1.61145 - 4.95952i) q^{97} -8.90167 q^{98} -2.36966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 - 5 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^24 + 12 * q^25 + 10 * q^26 - 3 * q^27 + 4 * q^28 + q^29 - 12 * q^30 - 6 * q^31 - 12 * q^32 - 5 * q^33 + 2 * q^34 - q^35 + 12 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 3 * q^40 + 15 * q^41 + q^42 + 10 * q^43 - 5 * q^44 - 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 5 * q^52 - 13 * q^53 + 3 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 + 4 * q^58 + 11 * q^59 - 3 * q^60 - 70 * q^61 - 19 * q^62 - 6 * q^63 - 3 * q^64 - 5 * q^65 - 5 * q^66 + 38 * q^67 - 2 * q^68 + q^70 + 21 * q^71 + 3 * q^72 - 14 * q^73 - 11 * q^74 - 3 * q^75 + 3 * q^76 - 14 * q^77 + 5 * q^78 + 5 * q^79 - 3 * q^80 - 3 * q^81 - 15 * q^82 - q^84 + 3 * q^85 + 10 * q^86 + 6 * q^87 + 3 * q^89 + 3 * q^90 + 16 * q^91 - 10 * q^92 - 11 * q^93 - 6 * q^94 - 2 * q^95 + 3 * q^96 - 35 * q^97 - 10 * q^98

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