LMFDB - Embedded newform 930.2.n.d.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} - 2 x^{11} + 13 x^{10} - 9 x^{9} + 60 x^{8} + x^{7} + 263 x^{6} + 823 x^{5} + 1931 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 13x^10 - 9x^9 + 60x^8 + x^7 + 263x^6 + 823x^5 + 1931x^4 + 1170x^3 + 1340x^2 + 1000x + 400
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			$-0.781164 - 2.40418i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.d.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-0.482786 - 1.48586i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(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} +(-0.482786 - 1.48586i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.945865 + 2.91107i) q^{11} +(0.809017 + 0.587785i) q^{12} +(-5.04097 + 3.66248i) q^{13} +(-0.482786 + 1.48586i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.20421 + 6.78386i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(5.71245 + 4.15034i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(-1.26395 - 0.918314i) q^{21} +(0.945865 - 2.91107i) q^{22} +(0.457949 - 1.40942i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +6.23099 q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.26395 - 0.918314i) q^{28} +(-6.07561 - 4.41419i) q^{29} +1.00000 q^{30} +(5.34781 - 1.54950i) q^{31} +1.00000 q^{32} +(2.47631 + 1.79914i) q^{33} +(5.77070 - 4.19266i) q^{34} +(0.482786 + 1.48586i) q^{35} +1.00000 q^{36} -0.145898 q^{37} +(-2.18196 - 6.71539i) q^{38} +(-1.92548 + 5.92602i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(0.510889 + 0.371183i) q^{41} +(0.482786 + 1.48586i) q^{42} +(7.05602 + 5.12650i) q^{43} +(-2.47631 + 1.79914i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-1.19893 + 0.871071i) q^{46} +(-6.97476 + 5.06746i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(3.68841 - 2.67979i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(2.20421 + 6.78386i) q^{51} +(-5.04097 - 3.66248i) q^{52} +(-3.67237 + 11.3024i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-0.945865 - 2.91107i) q^{55} -1.56233 q^{56} +7.06098 q^{57} +(2.32067 + 7.14230i) q^{58} +(-2.94172 + 2.13729i) q^{59} +(-0.809017 - 0.587785i) q^{60} +11.2548 q^{61} +(-5.23724 - 1.88979i) q^{62} -1.56233 q^{63} +(-0.809017 - 0.587785i) q^{64} +(5.04097 - 3.66248i) q^{65} +(-0.945865 - 2.91107i) q^{66} -6.16263 q^{67} -7.13298 q^{68} +(-0.457949 - 1.40942i) q^{69} +(0.482786 - 1.48586i) q^{70} +(-1.16864 + 3.59670i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(4.45246 + 13.7033i) q^{73} +(0.118034 + 0.0857567i) q^{74} +(0.809017 - 0.587785i) q^{75} +(-2.18196 + 6.71539i) q^{76} +(3.86881 - 2.81085i) q^{77} +(5.04097 - 3.66248i) q^{78} +(1.21142 - 3.72835i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.195142 - 0.600586i) q^{82} +(2.65416 + 1.92836i) q^{83} +(0.482786 - 1.48586i) q^{84} +(2.20421 - 6.78386i) q^{85} +(-2.69516 - 8.29485i) q^{86} -7.50986 q^{87} +3.06088 q^{88} +(-1.97058 - 6.06481i) q^{89} +(0.809017 - 0.587785i) q^{90} +(7.87566 + 5.72200i) q^{91} +1.48195 q^{92} +(3.41569 - 4.39694i) q^{93} +8.62127 q^{94} +(-5.71245 - 4.15034i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-4.33487 - 13.3414i) q^{97} -4.55913 q^{98} +3.06088 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	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 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 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	−0.482786	−	1.48586i	−0.182476	−	0.561603i	0.817420	−	0.576043i	$-0.195404\pi$
$7$	−0.482786	−	1.48586i	−0.182476	−	0.561603i	−0.999896	+	0.0144391i	$0.995404\pi$
$8$	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
$11$	0.945865	+	2.91107i	0.285189	+	0.877722i	0.986342	+	0.164711i	$0.0526690\pi$
$11$	0.945865	+	2.91107i	0.285189	+	0.877722i	−0.701153	+	0.713011i	$0.747331\pi$
$12$	0.809017	+	0.587785i	0.233543	+	0.169679i
$13$	−5.04097	+	3.66248i	−1.39811	+	1.01579i	−0.403195	+	0.915114i	$0.632101\pi$
$13$	−5.04097	+	3.66248i	−1.39811	+	1.01579i	−0.994919	+	0.100676i	$0.967899\pi$
$14$	−0.482786	+	1.48586i	−0.129030	+	0.397114i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.20421	+	6.78386i	−0.534600	+	1.64533i	0.209913	+	0.977720i	$0.432682\pi$
$17$	−2.20421	+	6.78386i	−0.534600	+	1.64533i	−0.744513	+	0.667608i	$0.767318\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	5.71245	+	4.15034i	1.31053	+	0.952153i	0.999999	+	0.00158911i	$0.000505829\pi$
$19$	5.71245	+	4.15034i	1.31053	+	0.952153i	0.310528	+	0.950564i	$0.399494\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	−1.26395	−	0.918314i	−0.275817	−	0.200393i
$22$	0.945865	−	2.91107i	0.201659	−	0.620643i
$23$	0.457949	−	1.40942i	0.0954890	−	0.293885i	−0.891892	−	0.452249i	$-0.850622\pi$
$23$	0.457949	−	1.40942i	0.0954890	−	0.293885i	0.987381	+	0.158364i	$0.0506219\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	6.23099			1.22200
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	1.26395	−	0.918314i	0.238864	−	0.173545i
$29$	−6.07561	−	4.41419i	−1.12821	−	0.819694i	−0.142778	−	0.989755i	$-0.545604\pi$
$29$	−6.07561	−	4.41419i	−1.12821	−	0.819694i	−0.985434	+	0.170061i	$0.945604\pi$
$30$	1.00000			0.182574
$31$	5.34781	−	1.54950i	0.960495	−	0.278299i
$31$	5.34781	−	1.54950i	0.960495	−	0.278299i
$32$	1.00000			0.176777
$33$	2.47631	+	1.79914i	0.431070	+	0.313190i
$34$	5.77070	−	4.19266i	0.989667	−	0.719035i
$35$	0.482786	+	1.48586i	0.0816058	+	0.251157i
$36$	1.00000			0.166667
$37$	−0.145898			−0.0239855			−0.0119927	−	0.999928i	$-0.503818\pi$
$37$	−0.145898			−0.0239855			−0.0119927	+	0.999928i	$0.503818\pi$
$38$	−2.18196	−	6.71539i	−0.353961	−	1.08938i
$39$	−1.92548	+	5.92602i	−0.308324	+	0.948923i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	0.510889	+	0.371183i	0.0797875	+	0.0579690i	0.626964	−	0.779048i	$-0.284297\pi$
$41$	0.510889	+	0.371183i	0.0797875	+	0.0579690i	−0.547176	+	0.837017i	$0.684297\pi$
$42$	0.482786	+	1.48586i	0.0744955	+	0.229274i
$43$	7.05602	+	5.12650i	1.07603	+	0.781784i	0.976987	−	0.213299i	$-0.0684208\pi$
$43$	7.05602	+	5.12650i	1.07603	+	0.781784i	0.0990464	+	0.995083i	$0.468421\pi$
$44$	−2.47631	+	1.79914i	−0.373317	+	0.271231i
$45$	−0.309017	+	0.951057i	−0.0460655	+	0.141775i
$46$	−1.19893	+	0.871071i	−0.176772	+	0.128432i
$47$	−6.97476	+	5.06746i	−1.01737	+	0.739164i	−0.965743	−	0.259502i	$-0.916442\pi$
$47$	−6.97476	+	5.06746i	−1.01737	+	0.739164i	−0.0516300	+	0.998666i	$0.516442\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	3.68841	−	2.67979i	0.526916	−	0.382827i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	2.20421	+	6.78386i	0.308651	+	0.949931i
$52$	−5.04097	−	3.66248i	−0.699057	−	0.507895i
$53$	−3.67237	+	11.3024i	−0.504439	+	1.55250i	0.297272	+	0.954793i	$0.403923\pi$
$53$	−3.67237	+	11.3024i	−0.504439	+	1.55250i	−0.801711	+	0.597711i	$0.796077\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−0.945865	−	2.91107i	−0.127540	−	0.392529i
$56$	−1.56233			−0.208775
$57$	7.06098			0.935250
$58$	2.32067	+	7.14230i	0.304720	+	0.937830i
$59$	−2.94172	+	2.13729i	−0.382980	+	0.278251i	−0.762573	−	0.646902i	$-0.776064\pi$
$59$	−2.94172	+	2.13729i	−0.382980	+	0.278251i	0.379593	+	0.925154i	$0.376064\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	11.2548			1.44103			0.720515	−	0.693439i	$-0.243905\pi$
$61$	11.2548			1.44103			0.720515	+	0.693439i	$0.243905\pi$
$62$	−5.23724	−	1.88979i	−0.665130	−	0.240003i
$63$	−1.56233			−0.196835
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	5.04097	−	3.66248i	0.625256	−	0.454275i
$66$	−0.945865	−	2.91107i	−0.116428	−	0.358328i
$67$	−6.16263			−0.752885			−0.376443	−	0.926440i	$-0.622853\pi$
$67$	−6.16263			−0.752885			−0.376443	+	0.926440i	$0.622853\pi$
$68$	−7.13298			−0.865000
$69$	−0.457949	−	1.40942i	−0.0551306	−	0.169675i
$70$	0.482786	−	1.48586i	0.0577040	−	0.177595i
$71$	−1.16864	+	3.59670i	−0.138692	+	0.426850i	−0.996146	−	0.0877105i	$-0.972045\pi$
$71$	−1.16864	+	3.59670i	−0.138692	+	0.426850i	0.857454	+	0.514561i	$0.172045\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	4.45246	+	13.7033i	0.521121	+	1.60385i	0.771861	+	0.635791i	$0.219326\pi$
$73$	4.45246	+	13.7033i	0.521121	+	1.60385i	−0.250741	+	0.968054i	$0.580674\pi$
$74$	0.118034	+	0.0857567i	0.0137212	+	0.00996902i
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$	−2.18196	+	6.71539i	−0.250288	+	0.770308i
$77$	3.86881	−	2.81085i	0.440891	−	0.320326i
$78$	5.04097	−	3.66248i	0.570778	−	0.414694i
$79$	1.21142	−	3.72835i	0.136295	−	0.419473i	−0.859494	−	0.511145i	$-0.829221\pi$
$79$	1.21142	−	3.72835i	0.136295	−	0.419473i	0.995789	+	0.0916728i	$0.0292214\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.195142	−	0.600586i	−0.0215499	−	0.0663236i
$83$	2.65416	+	1.92836i	0.291332	+	0.211665i	0.723845	−	0.689963i	$-0.242373\pi$
$83$	2.65416	+	1.92836i	0.291332	+	0.211665i	−0.432513	+	0.901628i	$0.642373\pi$
$84$	0.482786	−	1.48586i	0.0526763	−	0.162121i
$85$	2.20421	−	6.78386i	0.239080	−	0.735813i
$86$	−2.69516	−	8.29485i	−0.290627	−	0.894457i
$87$	−7.50986			−0.805142
$88$	3.06088			0.326291
$89$	−1.97058	−	6.06481i	−0.208881	−	0.642869i	−0.999532	−	0.0306017i	$-0.990258\pi$
$89$	−1.97058	−	6.06481i	−0.208881	−	0.642869i	0.790651	−	0.612267i	$-0.209742\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	7.87566	+	5.72200i	0.825593	+	0.599829i
$92$	1.48195			0.154504
$93$	3.41569	−	4.39694i	0.354191	−	0.455941i
$94$	8.62127			0.889216
$95$	−5.71245	−	4.15034i	−0.586085	−	0.425816i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−4.33487	−	13.3414i	−0.440140	−	1.35461i	−0.887727	−	0.460370i	$-0.847717\pi$
$97$	−4.33487	−	13.3414i	−0.440140	−	1.35461i	0.447587	−	0.894240i	$-0.352283\pi$
$98$	−4.55913			−0.460542
$99$	3.06088			0.307630
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−1.26139	+	3.88216i	−0.125513	+	0.386290i	−0.993994	−	0.109433i	$-0.965097\pi$
$101$	−1.26139	+	3.88216i	−0.125513	+	0.386290i	0.868481	+	0.495722i	$0.165097\pi$
$102$	2.20421	−	6.78386i	0.218249	−	0.671703i
$103$	−8.40457	−	6.10628i	−0.828127	−	0.601670i	0.0909018	−	0.995860i	$-0.471025\pi$
$103$	−8.40457	−	6.10628i	−0.828127	−	0.601670i	−0.919029	+	0.394190i	$0.871025\pi$
$104$	1.92548	+	5.92602i	0.188809	+	0.581094i
$105$	1.26395	+	0.918314i	0.123349	+	0.0896183i
$106$	9.61440	−	6.98527i	0.933833	−	0.678469i
$107$	3.15650	−	9.71470i	0.305150	−	0.939155i	−0.674471	−	0.738301i	$-0.735628\pi$
$107$	3.15650	−	9.71470i	0.305150	−	0.939155i	0.979621	−	0.200854i	$-0.0643717\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−11.8925	+	8.64043i	−1.13910	+	0.827603i	−0.986993	−	0.160761i	$-0.948605\pi$
$109$	−11.8925	+	8.64043i	−1.13910	+	0.827603i	−0.152105	+	0.988364i	$0.548605\pi$
$110$	−0.945865	+	2.91107i	−0.0901847	+	0.277560i
$111$	−0.118034	+	0.0857567i	−0.0112033	+	0.00813967i
$112$	1.26395	+	0.918314i	0.119432	+	0.0867725i
$113$	4.25391	+	13.0922i	0.400174	+	1.23161i	0.924858	+	0.380313i	$0.124184\pi$
$113$	4.25391	+	13.0922i	0.400174	+	1.23161i	−0.524684	+	0.851297i	$0.675816\pi$
$114$	−5.71245	−	4.15034i	−0.535020	−	0.388715i
$115$	−0.457949	+	1.40942i	−0.0427040	+	0.131429i
$116$	2.32067	−	7.14230i	0.215469	−	0.663146i
$117$	1.92548	+	5.92602i	0.178011	+	0.547861i
$118$	3.63617			0.334737
$119$	11.1441			1.02157
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	1.31950	−	0.958674i	0.119955	−	0.0871521i
$122$	−9.10533	−	6.61541i	−0.824358	−	0.598931i
$123$	0.631494			0.0569399
$124$	3.12623	+	4.60724i	0.280744	+	0.413743i
$125$	−1.00000			−0.0894427
$126$	1.26395	+	0.918314i	0.112602	+	0.0818099i
$127$	6.67485	−	4.84956i	0.592297	−	0.430329i	−0.250839	−	0.968029i	$-0.580707\pi$
$127$	6.67485	−	4.84956i	0.592297	−	0.430329i	0.843136	+	0.537700i	$0.180707\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	8.72172			0.767905
$130$	−6.23099			−0.546494
$131$	4.00580	+	12.3286i	0.349988	+	1.07715i	0.958859	+	0.283883i	$0.0916228\pi$
$131$	4.00580	+	12.3286i	0.349988	+	1.07715i	−0.608871	+	0.793269i	$0.708377\pi$
$132$	−0.945865	+	2.91107i	−0.0823270	+	0.253376i
$133$	3.40894	−	10.4917i	0.295593	−	0.909741i
$134$	4.98567	+	3.62230i	0.430697	+	0.312919i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	5.77070	+	4.19266i	0.494833	+	0.359517i
$137$	0.318811	−	0.231630i	0.0272379	−	0.0197895i	−0.574083	−	0.818797i	$-0.694641\pi$
$137$	0.318811	−	0.231630i	0.0272379	−	0.0197895i	0.601321	+	0.799008i	$0.294641\pi$
$138$	−0.457949	+	1.40942i	−0.0389832	+	0.119978i
$139$	−13.2441	+	9.62242i	−1.12335	+	0.816163i	−0.984714	−	0.174180i	$-0.944273\pi$
$139$	−13.2441	+	9.62242i	−1.12335	+	0.816163i	−0.138638	+	0.990343i	$0.544273\pi$
$140$	−1.26395	+	0.918314i	−0.106823	+	0.0776117i
$141$	−2.66412	+	8.19932i	−0.224359	+	0.690507i
$142$	3.05954	−	2.22288i	0.256751	−	0.186540i
$143$	−15.4298	−	11.2104i	−1.29031	−	0.937463i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	6.07561	+	4.41419i	0.504552	+	0.366578i
$146$	4.45246	−	13.7033i	0.368488	−	1.13409i
$147$	1.40885	−	4.33599i	0.116200	−	0.357626i
$148$	−0.0450850	−	0.138757i	−0.00370596	−	0.0114058i
$149$	8.72415			0.714710			0.357355	−	0.933969i	$-0.383679\pi$
$149$	8.72415			0.714710			0.357355	+	0.933969i	$0.383679\pi$
$150$	−1.00000			−0.0816497
$151$	5.43249	+	16.7195i	0.442090	+	1.36061i	0.885644	+	0.464365i	$0.153718\pi$
$151$	5.43249	+	16.7195i	0.442090	+	1.36061i	−0.443554	+	0.896248i	$0.646282\pi$
$152$	5.71245	−	4.15034i	0.463341	−	0.336637i
$153$	5.77070	+	4.19266i	0.466533	+	0.338956i
$154$	−4.78211			−0.385353
$155$	−5.34781	+	1.54950i	−0.429546	+	0.124459i
$156$	−6.23099			−0.498878
$157$	−7.39870	−	5.37547i	−0.590480	−	0.429009i	0.252007	−	0.967725i	$-0.418909\pi$
$157$	−7.39870	−	5.37547i	−0.590480	−	0.429009i	−0.842487	+	0.538716i	$0.818909\pi$
$158$	−3.17153	+	2.30425i	−0.252313	+	0.183316i
$159$	3.67237	+	11.3024i	0.291238	+	0.896339i
$160$	−1.00000			−0.0790569
$161$	−2.31530			−0.182471
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−1.30056	+	4.00271i	−0.101868	+	0.313517i	−0.988983	−	0.148032i	$-0.952706\pi$
$163$	−1.30056	+	4.00271i	−0.101868	+	0.313517i	0.887115	+	0.461549i	$0.152706\pi$
$164$	−0.195142	+	0.600586i	−0.0152380	+	0.0468979i
$165$	−2.47631	−	1.79914i	−0.192780	−	0.140063i
$166$	−1.01380	−	3.12015i	−0.0786860	−	0.242171i
$167$	−0.584088	−	0.424365i	−0.0451981	−	0.0328383i	0.564957	−	0.825120i	$-0.308893\pi$
$167$	−0.584088	−	0.424365i	−0.0451981	−	0.0328383i	−0.610155	+	0.792282i	$0.708893\pi$
$168$	−1.26395	+	0.918314i	−0.0975159	+	0.0708495i
$169$	7.98043	−	24.5612i	0.613879	−	1.88932i
$170$	−5.77070	+	4.19266i	−0.442592	+	0.321562i
$171$	5.71245	−	4.15034i	0.436842	−	0.317384i
$172$	−2.69516	+	8.29485i	−0.205504	+	0.632477i
$173$	1.62481	−	1.18050i	0.123532	−	0.0897514i	−0.524304	−	0.851531i	$-0.675674\pi$
$173$	1.62481	−	1.18050i	0.123532	−	0.0897514i	0.647836	+	0.761780i	$0.275674\pi$
$174$	6.07561	+	4.41419i	0.460590	+	0.334639i
$175$	−0.482786	−	1.48586i	−0.0364952	−	0.112321i
$176$	−2.47631	−	1.79914i	−0.186659	−	0.135615i
$177$	−1.12364	+	3.45820i	−0.0844579	+	0.259935i
$178$	−1.97058	+	6.06481i	−0.147701	+	0.454577i
$179$	−2.42434	−	7.46134i	−0.181203	−	0.557687i	0.818659	−	0.574280i	$-0.194718\pi$
$179$	−2.42434	−	7.46134i	−0.181203	−	0.557687i	−0.999862	+	0.0165932i	$0.994718\pi$
$180$	−1.00000			−0.0745356
$181$	−18.1308			−1.34765			−0.673827	−	0.738889i	$-0.735351\pi$
$181$	−18.1308			−1.34765			−0.673827	+	0.738889i	$0.735351\pi$
$182$	−3.00823	−	9.25839i	−0.222985	−	0.686278i
$183$	9.10533	−	6.61541i	0.673085	−	0.489025i
$184$	−1.19893	−	0.871071i	−0.0883860	−	0.0642162i
$185$	0.145898			0.0107266
$186$	−5.34781	+	1.54950i	−0.392120	+	0.113615i
$187$	−21.8332			−1.59660
$188$	−6.97476	−	5.06746i	−0.508686	−	0.369582i
$189$	−1.26395	+	0.918314i	−0.0919389	+	0.0667975i
$190$	2.18196	+	6.71539i	0.158296	+	0.487186i
$191$	−19.8009			−1.43274			−0.716371	−	0.697720i	$-0.754198\pi$
$191$	−19.8009			−1.43274			−0.716371	+	0.697720i	$0.754198\pi$
$192$	−1.00000			−0.0721688
$193$	−6.52687	−	20.0877i	−0.469815	−	1.44594i	−0.852825	−	0.522197i	$-0.825113\pi$
$193$	−6.52687	−	20.0877i	−0.469815	−	1.44594i	0.383010	−	0.923744i	$-0.374887\pi$
$194$	−4.33487	+	13.3414i	−0.311226	+	0.957854i
$195$	1.92548	−	5.92602i	0.137887	−	0.424371i
$196$	3.68841	+	2.67979i	0.263458	+	0.191413i
$197$	−7.02740	−	21.6281i	−0.500681	−	1.54094i	−0.807912	−	0.589304i	$-0.799402\pi$
$197$	−7.02740	−	21.6281i	−0.500681	−	1.54094i	0.307230	−	0.951635i	$-0.400598\pi$
$198$	−2.47631	−	1.79914i	−0.175983	−	0.127859i
$199$	−5.99062	+	4.35244i	−0.424664	+	0.308536i	−0.779512	−	0.626388i	$-0.784533\pi$
$199$	−5.99062	+	4.35244i	−0.424664	+	0.308536i	0.354848	+	0.934924i	$0.384533\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	−4.98567	+	3.62230i	−0.351662	+	0.255498i
$202$	3.30237	−	2.39931i	0.232354	−	0.168815i
$203$	−3.62566	+	11.1586i	−0.254471	+	0.783182i
$204$	−5.77070	+	4.19266i	−0.404030	+	0.293545i
$205$	−0.510889	−	0.371183i	−0.0356820	−	0.0259245i
$206$	3.21026	+	9.88017i	0.223669	+	0.688384i
$207$	−1.19893	−	0.871071i	−0.0833312	−	0.0605436i
$208$	1.92548	−	5.92602i	0.133508	−	0.410896i
$209$	−6.67873	+	20.5550i	−0.461978	+	1.42182i
$210$	−0.482786	−	1.48586i	−0.0333154	−	0.102534i
$211$	−4.07178			−0.280313			−0.140157	−	0.990129i	$-0.544761\pi$
$211$	−4.07178			−0.280313			−0.140157	+	0.990129i	$0.544761\pi$
$212$	−11.8840			−0.816200
$213$	1.16864	+	3.59670i	0.0800739	+	0.246442i
$214$	−8.26381	+	6.00401i	−0.564903	+	0.410426i
$215$	−7.05602	−	5.12650i	−0.481217	−	0.349624i
$216$	−1.00000			−0.0680414
$217$	−4.88420	−	7.19803i	−0.331561	−	0.488634i
$218$	14.7000			0.995608
$219$	11.6567	+	8.46908i	0.787686	+	0.572287i
$220$	2.47631	−	1.79914i	0.166953	−	0.121298i
$221$	−13.7344	−	42.2702i	−0.923876	−	2.84340i
$222$	0.145898			0.00979203
$223$	19.6521			1.31600			0.658000	−	0.753018i	$-0.271403\pi$
$223$	19.6521			1.31600			0.658000	+	0.753018i	$0.271403\pi$
$224$	−0.482786	−	1.48586i	−0.0322575	−	0.0992784i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	4.25391	−	13.0922i	0.282966	−	0.870880i
$227$	−19.6412	−	14.2702i	−1.30363	−	0.947145i	−0.303649	−	0.952784i	$-0.598205\pi$
$227$	−19.6412	−	14.2702i	−1.30363	−	0.947145i	−0.999984	+	0.00563890i	$0.998205\pi$
$228$	2.18196	+	6.71539i	0.144504	+	0.444738i
$229$	20.3631	+	14.7946i	1.34563	+	0.977657i	0.999217	+	0.0395751i	$0.0126004\pi$
$229$	20.3631	+	14.7946i	1.34563	+	0.977657i	0.346413	+	0.938082i	$0.387400\pi$
$230$	1.19893	−	0.871071i	0.0790549	−	0.0574367i
$231$	1.47775	−	4.54805i	0.0972290	−	0.299240i
$232$	−6.07561	+	4.41419i	−0.398883	+	0.289805i
$233$	−2.27586	+	1.65351i	−0.149096	+	0.108325i	−0.659833	−	0.751413i	$-0.729373\pi$
$233$	−2.27586	+	1.65351i	−0.149096	+	0.108325i	0.510736	+	0.859737i	$0.329373\pi$
$234$	1.92548	−	5.92602i	0.125873	−	0.387396i
$235$	6.97476	−	5.06746i	0.454983	−	0.330564i
$236$	−2.94172	−	2.13729i	−0.191490	−	0.139126i
$237$	−1.21142	−	3.72835i	−0.0786899	−	0.242183i
$238$	−9.01573	−	6.55031i	−0.584403	−	0.424594i
$239$	6.50773	−	20.0287i	0.420950	−	1.29555i	−0.485870	−	0.874031i	$-0.661497\pi$
$239$	6.50773	−	20.0287i	0.420950	−	1.29555i	0.906820	−	0.421519i	$-0.138503\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	0.00164170	+	0.00505264i	0.000105751	+	0.000325469i	0.951109	−	0.308854i	$-0.0999455\pi$
$241$	0.00164170	+	0.00505264i	0.000105751	+	0.000325469i	−0.951004	+	0.309180i	$0.899946\pi$
$242$	−1.63099			−0.104844
$243$	−1.00000			−0.0641500
$244$	3.47793	+	10.7040i	0.222651	+	0.685250i
$245$	−3.68841	+	2.67979i	−0.235644	+	0.171205i
$246$	−0.510889	−	0.371183i	−0.0325731	−	0.0236657i
$247$	−43.9969			−2.79945
$248$	0.178899	−	5.56489i	0.0113601	−	0.353371i
$249$	3.28072			0.207907
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	4.38998	−	3.18950i	0.277093	−	0.201320i	−0.440556	−	0.897725i	$-0.645219\pi$
$251$	4.38998	−	3.18950i	0.277093	−	0.201320i	0.717648	+	0.696406i	$0.245219\pi$
$252$	−0.482786	−	1.48586i	−0.0304127	−	0.0936006i
$253$	4.53609			0.285182
$254$	−8.25056			−0.517686
$255$	−2.20421	−	6.78386i	−0.138033	−	0.424822i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.93485	+	9.03252i	−0.183071	+	0.563433i	−0.999910	−	0.0134321i	$-0.995724\pi$
$257$	−2.93485	+	9.03252i	−0.183071	+	0.563433i	0.816839	+	0.576865i	$0.195724\pi$
$258$	−7.05602	−	5.12650i	−0.439289	−	0.319162i
$259$	0.0704376	+	0.216784i	0.00437678	+	0.0134703i
$260$	5.04097	+	3.66248i	0.312628	+	0.227138i
$261$	−6.07561	+	4.41419i	−0.376071	+	0.273231i
$262$	4.00580	−	12.3286i	0.247479	−	0.761662i
$263$	21.7705	−	15.8172i	1.34243	−	0.975330i	0.343076	−	0.939308i	$-0.388531\pi$
$263$	21.7705	−	15.8172i	1.34243	−	0.975330i	0.999351	−	0.0360226i	$-0.0114688\pi$
$264$	2.47631	−	1.79914i	0.152406	−	0.110730i
$265$	3.67237	−	11.3024i	0.225592	−	0.694301i
$266$	−8.92473	+	6.48420i	−0.547210	+	0.397572i
$267$	−5.15904	−	3.74826i	−0.315728	−	0.229390i
$268$	−1.90436	−	5.86101i	−0.116327	−	0.358018i
$269$	7.49025	+	5.44198i	0.456688	+	0.331804i	0.792231	−	0.610222i	$-0.208920\pi$
$269$	7.49025	+	5.44198i	0.456688	+	0.331804i	−0.335542	+	0.942025i	$0.608920\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	−0.620319	+	1.90915i	−0.0376817	+	0.115972i	−0.968128	−	0.250456i	$-0.919419\pi$
$271$	−0.620319	+	1.90915i	−0.0376817	+	0.115972i	0.930446	+	0.366428i	$0.119419\pi$
$272$	−2.20421	−	6.78386i	−0.133650	−	0.411332i
$273$	9.73485			0.589180
$274$	−0.394072			−0.0238068
$275$	0.945865	+	2.91107i	0.0570378	+	0.175544i
$276$	1.19893	−	0.871071i	0.0721669	−	0.0524323i
$277$	22.6245	+	16.4377i	1.35938	+	0.987645i	0.998484	+	0.0550378i	$0.0175279\pi$
$277$	22.6245	+	16.4377i	1.35938	+	0.987645i	0.360893	+	0.932607i	$0.382472\pi$
$278$	16.3706			0.981846
$279$	0.178899	−	5.56489i	0.0107104	−	0.333161i
$280$	1.56233			0.0933670
$281$	15.4684	+	11.2385i	0.922769	+	0.670431i	0.944212	−	0.329339i	$-0.106826\pi$
$281$	15.4684	+	11.2385i	0.922769	+	0.670431i	−0.0214429	+	0.999770i	$0.506826\pi$
$282$	6.97476	−	5.06746i	0.415341	−	0.301763i
$283$	8.26050	+	25.4232i	0.491036	+	1.51125i	0.823045	+	0.567976i	$0.192273\pi$
$283$	8.26050	+	25.4232i	0.491036	+	1.51125i	−0.332009	+	0.943276i	$0.607727\pi$
$284$	−3.78180			−0.224408
$285$	−7.06098			−0.418256
$286$	5.89367	+	18.1389i	0.348500	+	1.07257i
$287$	0.304876	−	0.938313i	0.0179963	−	0.0553869i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−27.4090	−	19.9138i	−1.61229	−	1.17140i
$290$	−2.32067	−	7.14230i	−0.136275	−	0.419410i
$291$	−11.3488	−	8.24542i	−0.665281	−	0.483355i
$292$	−11.6567	+	8.46908i	−0.682156	+	0.495615i
$293$	3.58864	−	11.0447i	0.209651	−	0.645238i	−0.789840	−	0.613313i	$-0.789836\pi$
$293$	3.58864	−	11.0447i	0.209651	−	0.645238i	0.999490	−	0.0319248i	$-0.0101637\pi$
$294$	−3.68841	+	2.67979i	−0.215113	+	0.156288i
$295$	2.94172	−	2.13729i	0.171274	−	0.124438i
$296$	−0.0450850	+	0.138757i	−0.00262051	+	0.00806510i
$297$	2.47631	−	1.79914i	0.143690	−	0.104397i
$298$	−7.05799	−	5.12793i	−0.408858	−	0.297053i
$299$	2.85348	+	8.78209i	0.165021	+	0.507882i
$300$	0.809017	+	0.587785i	0.0467086	+	0.0339358i
$301$	4.21073	−	12.9593i	0.242702	−	0.746961i
$302$	5.43249	−	16.7195i	0.312605	−	0.962099i
$303$	1.26139	+	3.88216i	0.0724651	+	0.223024i
$304$	−7.06098			−0.404975
$305$	−11.2548			−0.644448
$306$	−2.20421	−	6.78386i	−0.126006	−	0.387808i
$307$	−13.3480	+	9.69790i	−0.761812	+	0.553489i	−0.899465	−	0.436992i	$-0.856044\pi$
$307$	−13.3480	+	9.69790i	−0.761812	+	0.553489i	0.137654	+	0.990480i	$0.456044\pi$
$308$	3.86881	+	2.81085i	0.220446	+	0.160163i
$309$	−10.3886			−0.590988
$310$	5.23724	+	1.88979i	0.297455	+	0.107333i
$311$	3.47195			0.196876			0.0984380	−	0.995143i	$-0.468615\pi$
$311$	3.47195			0.196876			0.0984380	+	0.995143i	$0.468615\pi$
$312$	5.04097	+	3.66248i	0.285389	+	0.207347i
$313$	−6.74389	+	4.89972i	−0.381187	+	0.276949i	−0.761835	−	0.647772i	$-0.775701\pi$
$313$	−6.74389	+	4.89972i	−0.381187	+	0.276949i	0.380648	+	0.924720i	$0.375701\pi$
$314$	2.82605	+	8.69769i	0.159483	+	0.490839i
$315$	1.56233			0.0880273
$316$	3.92022			0.220530
$317$	2.99288	+	9.21114i	0.168097	+	0.517349i	0.999251	−	0.0386928i	$-0.0123194\pi$
$317$	2.99288	+	9.21114i	0.168097	+	0.517349i	−0.831154	+	0.556042i	$0.812319\pi$
$318$	3.67237	−	11.3024i	0.205936	−	0.633807i
$319$	7.10331	−	21.8618i	0.397709	−	1.22402i
$320$	0.809017	+	0.587785i	0.0452254	+	0.0328582i
$321$	−3.15650	−	9.71470i	−0.176178	−	0.542221i
$322$	1.87312	+	1.36090i	0.104385	+	0.0758400i
$323$	−40.7468	+	29.6043i	−2.26721	+	1.64723i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−5.04097	+	3.66248i	−0.279623	+	0.203158i
$326$	3.40491	−	2.47381i	0.188580	−	0.137012i
$327$	−4.54254	+	13.9805i	−0.251203	+	0.773124i
$328$	0.510889	−	0.371183i	0.0282091	−	0.0204951i
$329$	10.8969	+	7.91703i	0.600763	+	0.436480i
$330$	0.945865	+	2.91107i	0.0520682	+	0.160249i
$331$	−15.8268	−	11.4989i	−0.869921	−	0.632035i	0.0606446	−	0.998159i	$-0.480684\pi$
$331$	−15.8268	−	11.4989i	−0.869921	−	0.632035i	−0.930566	+	0.366125i	$0.880684\pi$
$332$	−1.01380	+	3.12015i	−0.0556394	+	0.171241i
$333$	−0.0450850	+	0.138757i	−0.00247064	+	0.00760385i
$334$	0.223102	+	0.686637i	0.0122076	+	0.0375711i
$335$	6.16263			0.336701
$336$	1.56233			0.0852320
$337$	−7.91353	−	24.3554i	−0.431078	−	1.32672i	−0.897053	−	0.441923i	$-0.854296\pi$
$337$	−7.91353	−	24.3554i	−0.431078	−	1.32672i	0.465975	−	0.884798i	$-0.345704\pi$
$338$	−20.8930	+	15.1797i	−1.13643	+	0.825665i
$339$	11.1369	+	8.09142i	0.604873	+	0.439466i
$340$	7.13298			0.386840
$341$	9.56902	+	14.1022i	0.518191	+	0.763679i
$342$	−7.06098			−0.381814
$343$	−14.6102	−	10.6149i	−0.788875	−	0.573151i
$344$	7.05602	−	5.12650i	0.380435	−	0.276402i
$345$	0.457949	+	1.40942i	0.0246552	+	0.0758808i
$346$	−2.00838			−0.107971
$347$	24.2157			1.29997			0.649984	−	0.759947i	$-0.274775\pi$
$347$	24.2157			1.29997			0.649984	+	0.759947i	$0.274775\pi$
$348$	−2.32067	−	7.14230i	−0.124401	−	0.382868i
$349$	7.39056	−	22.7458i	0.395608	−	1.21756i	−0.532879	−	0.846191i	$-0.678890\pi$
$349$	7.39056	−	22.7458i	0.395608	−	1.21756i	0.928487	−	0.371364i	$-0.121110\pi$
$350$	−0.482786	+	1.48586i	−0.0258060	+	0.0794227i
$351$	5.04097	+	3.66248i	0.269067	+	0.195489i
$352$	0.945865	+	2.91107i	0.0504148	+	0.155161i
$353$	0.558968	+	0.406114i	0.0297509	+	0.0216153i	0.602561	−	0.798073i	$-0.294147\pi$
$353$	0.558968	+	0.406114i	0.0297509	+	0.0216153i	−0.572810	+	0.819688i	$0.694147\pi$
$354$	2.94172	−	2.13729i	0.156351	−	0.113596i
$355$	1.16864	−	3.59670i	0.0620249	−	0.190893i
$356$	5.15904	−	3.74826i	0.273428	−	0.198657i
$357$	9.01573	−	6.55031i	0.477163	−	0.346679i
$358$	−2.42434	+	7.46134i	−0.128130	+	0.394344i
$359$	−3.09155	+	2.24614i	−0.163166	+	0.118547i	−0.666372	−	0.745620i	$-0.732154\pi$
$359$	−3.09155	+	2.24614i	−0.163166	+	0.118547i	0.503206	+	0.864166i	$0.332154\pi$
$360$	0.809017	+	0.587785i	0.0426389	+	0.0309790i
$361$	9.53548	+	29.3472i	0.501867	+	1.54459i
$362$	14.6681	+	10.6570i	0.770941	+	0.560121i
$363$	0.504005	−	1.55117i	0.0264534	−	0.0814151i
$364$	−3.00823	+	9.25839i	−0.157674	+	0.485272i
$365$	−4.45246	−	13.7033i	−0.233052	−	0.717261i
$366$	−11.2548			−0.588298
$367$	−27.3527			−1.42780			−0.713900	−	0.700247i	$-0.753073\pi$
$367$	−27.3527			−1.42780			−0.713900	+	0.700247i	$0.753073\pi$
$368$	0.457949	+	1.40942i	0.0238723	+	0.0734712i
$369$	0.510889	−	0.371183i	0.0265958	−	0.0193230i
$370$	−0.118034	−	0.0857567i	−0.00613629	−	0.00445828i
$371$	18.5668			0.963940
$372$	5.23724	+	1.88979i	0.271538	+	0.0979810i
$373$	6.21206			0.321648			0.160824	−	0.986983i	$-0.448585\pi$
$373$	6.21206			0.321648			0.160824	+	0.986983i	$0.448585\pi$
$374$	17.6634	+	12.8332i	0.913355	+	0.663591i
$375$	−0.809017	+	0.587785i	−0.0417775	+	0.0303531i
$376$	2.66412	+	8.19932i	0.137391	+	0.422847i
$377$	46.7938			2.41001
$378$	1.56233			0.0803575
$379$	−0.189287	−	0.582564i	−0.00972300	−	0.0299243i	0.946077	−	0.323941i	$-0.105008\pi$
$379$	−0.189287	−	0.582564i	−0.00972300	−	0.0299243i	−0.955800	+	0.294017i	$0.905008\pi$
$380$	2.18196	−	6.71539i	0.111932	−	0.344492i
$381$	2.54956	−	7.84675i	0.130618	−	0.402001i
$382$	16.0192	+	11.6387i	0.819616	+	0.595486i
$383$	−6.06165	−	18.6558i	−0.309736	−	0.953268i	−0.977867	−	0.209225i	$-0.932906\pi$
$383$	−6.06165	−	18.6558i	−0.309736	−	0.953268i	0.668132	−	0.744043i	$-0.267094\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	−3.86881	+	2.81085i	−0.197173	+	0.143254i
$386$	−6.52687	+	20.0877i	−0.332209	+	1.02243i
$387$	7.05602	−	5.12650i	0.358678	−	0.260595i
$388$	11.3488	−	8.24542i	0.576150	−	0.418598i
$389$	−1.07478	+	3.30783i	−0.0544935	+	0.167714i	−0.974599	−	0.223957i	$-0.928103\pi$
$389$	−1.07478	+	3.30783i	−0.0544935	+	0.167714i	0.920106	+	0.391670i	$0.128103\pi$
$390$	−5.04097	+	3.66248i	−0.255260	+	0.185457i
$391$	8.55191	+	6.21333i	0.432489	+	0.314222i
$392$	−1.40885	−	4.33599i	−0.0711576	−	0.219001i
$393$	10.4873	+	7.61948i	0.529015	+	0.384352i
$394$	−7.02740	+	21.6281i	−0.354035	+	1.08961i
$395$	−1.21142	+	3.72835i	−0.0609529	+	0.187594i
$396$	0.945865	+	2.91107i	0.0475315	+	0.146287i
$397$	27.8724			1.39888			0.699438	−	0.714693i	$-0.253434\pi$
$397$	27.8724			1.39888			0.699438	+	0.714693i	$0.253434\pi$
$398$	7.40481			0.371170
$399$	−3.40894	−	10.4917i	−0.170661	−	0.525239i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	1.69825	+	1.23385i	0.0848065	+	0.0616155i	0.629381	−	0.777097i	$-0.283309\pi$
$401$	1.69825	+	1.23385i	0.0848065	+	0.0616155i	−0.544574	+	0.838713i	$0.683309\pi$
$402$	6.16263			0.307364
$403$	−21.2831	+	27.3973i	−1.06019	+	1.36475i
$404$	−4.08195			−0.203085
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	9.49209	−	6.89641i	0.471085	−	0.342263i
$407$	−0.138000	−	0.424720i	−0.00684040	−	0.0210526i
$408$	7.13298			0.353135
$409$	30.2260			1.49458			0.747291	−	0.664497i	$-0.231354\pi$
$409$	30.2260			1.49458			0.747291	+	0.664497i	$0.231354\pi$
$410$	0.195142	+	0.600586i	0.00963739	+	0.0296608i
$411$	0.121775	−	0.374785i	0.00600672	−	0.0184868i
$412$	3.21026	−	9.88017i	0.158158	−	0.486761i
$413$	4.59594	+	3.33915i	0.226151	+	0.164309i
$414$	0.457949	+	1.40942i	0.0225070	+	0.0692693i
$415$	−2.65416	−	1.92836i	−0.130288	−	0.0946594i
$416$	−5.04097	+	3.66248i	−0.247154	+	0.179568i
$417$	−5.05881	+	15.5694i	−0.247731	+	0.762437i
$418$	17.4852	−	12.7037i	0.855227	−	0.621359i
$419$	−2.20176	+	1.59967i	−0.107563	+	0.0781490i	−0.640266	−	0.768153i	$-0.721176\pi$
$419$	−2.20176	+	1.59967i	−0.107563	+	0.0781490i	0.532704	+	0.846302i	$0.321176\pi$
$420$	−0.482786	+	1.48586i	−0.0235576	+	0.0725027i
$421$	6.32078	−	4.59232i	0.308056	−	0.223816i	−0.423006	−	0.906127i	$-0.639025\pi$
$421$	6.32078	−	4.59232i	0.308056	−	0.223816i	0.731062	+	0.682311i	$0.239025\pi$
$422$	3.29414	+	2.39333i	0.160356	+	0.116506i
$423$	2.66412	+	8.19932i	0.129534	+	0.398664i
$424$	9.61440	+	6.98527i	0.466916	+	0.339235i
$425$	−2.20421	+	6.78386i	−0.106920	+	0.329066i
$426$	1.16864	−	3.59670i	0.0566208	−	0.174261i
$427$	−5.43366	−	16.7231i	−0.262953	−	0.809287i
$428$	10.2146			0.493743
$429$	−19.0723			−0.920821
$430$	2.69516	+	8.29485i	0.129972	+	0.400013i
$431$	−22.9440	+	16.6698i	−1.10517	+	0.802954i	−0.981897	−	0.189418i	$-0.939340\pi$
$431$	−22.9440	+	16.6698i	−1.10517	+	0.802954i	−0.123275	+	0.992372i	$0.539340\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−12.6166			−0.606316			−0.303158	−	0.952940i	$-0.598041\pi$
$433$	−12.6166			−0.606316			−0.303158	+	0.952940i	$0.598041\pi$
$434$	−0.279499	+	8.69419i	−0.0134164	+	0.417334i
$435$	7.50986			0.360070
$436$	−11.8925	−	8.64043i	−0.569549	−	0.413802i
$437$	8.46560	−	6.15062i	0.404964	−	0.294224i
$438$	−4.45246	−	13.7033i	−0.212747	−	0.654767i
$439$	−16.8449			−0.803961			−0.401981	−	0.915648i	$-0.631678\pi$
$439$	−16.8449			−0.803961			−0.401981	+	0.915648i	$0.631678\pi$
$440$	−3.06088			−0.145922
$441$	−1.40885	−	4.33599i	−0.0670880	−	0.206476i
$442$	−13.7344	+	42.2702i	−0.653279	+	2.01059i
$443$	5.89639	−	18.1472i	0.280146	−	0.862201i	−0.707666	−	0.706548i	$-0.750252\pi$
$443$	5.89639	−	18.1472i	0.280146	−	0.862201i	0.987812	−	0.155654i	$-0.0497484\pi$
$444$	−0.118034	−	0.0857567i	−0.00560165	−	0.00406983i
$445$	1.97058	+	6.06481i	0.0934143	+	0.287500i
$446$	−15.8989	−	11.5512i	−0.752833	−	0.546965i
$447$	7.05799	−	5.12793i	0.333831	−	0.242543i
$448$	−0.482786	+	1.48586i	−0.0228095	+	0.0702004i
$449$	−22.4111	+	16.2826i	−1.05765	+	0.768424i	−0.973651	−	0.228042i	$-0.926768\pi$
$449$	−22.4111	+	16.2826i	−1.05765	+	0.768424i	−0.0839942	+	0.996466i	$0.526768\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	−0.597308	+	1.83832i	−0.0281261	+	0.0865633i
$452$	−11.1369	+	8.09142i	−0.523835	+	0.380588i
$453$	14.2225	+	10.3332i	0.668229	+	0.485497i
$454$	7.50228	+	23.0896i	0.352099	+	1.08365i
$455$	−7.87566	−	5.72200i	−0.369217	−	0.268252i
$456$	2.18196	−	6.71539i	0.102180	−	0.314477i
$457$	8.33575	−	25.6548i	0.389930	−	1.20008i	−0.542910	−	0.839791i	$-0.682678\pi$
$457$	8.33575	−	25.6548i	0.389930	−	1.20008i	0.932840	−	0.360290i	$-0.117322\pi$
$458$	−7.77800	−	23.9382i	−0.363442	−	1.11856i
$459$	7.13298			0.332939
$460$	−1.48195			−0.0690965
$461$	5.32443	+	16.3869i	0.247984	+	0.763215i	0.995131	+	0.0985571i	$0.0314227\pi$
$461$	5.32443	+	16.3869i	0.247984	+	0.763215i	−0.747148	+	0.664658i	$0.768577\pi$
$462$	−3.86881	+	2.81085i	−0.179993	+	0.130773i
$463$	25.4248	+	18.4722i	1.18159	+	0.858475i	0.992350	−	0.123455i	$-0.0393976\pi$
$463$	25.4248	+	18.4722i	1.18159	+	0.858475i	0.189240	+	0.981931i	$0.439398\pi$
$464$	7.50986			0.348637
$465$	−3.41569	+	4.39694i	−0.158399	+	0.203903i
$466$	2.81312			0.130315
$467$	20.1650	+	14.6507i	0.933124	+	0.677955i	0.946756	−	0.321952i	$-0.104339\pi$
$467$	20.1650	+	14.6507i	0.933124	+	0.677955i	−0.0136314	+	0.999907i	$0.504339\pi$
$468$	−5.04097	+	3.66248i	−0.233019	+	0.169298i
$469$	2.97523	+	9.15683i	0.137384	+	0.422823i
$470$	−8.62127			−0.397670
$471$	−9.14529			−0.421393
$472$	1.12364	+	3.45820i	0.0517197	+	0.159177i
$473$	−8.24957	+	25.3896i	−0.379316	+	1.16741i
$474$	−1.21142	+	3.72835i	−0.0556422	+	0.171249i
$475$	5.71245	+	4.15034i	0.262105	+	0.190431i
$476$	3.44370	+	10.5986i	0.157842	+	0.485787i
$477$	9.61440	+	6.98527i	0.440213	+	0.319833i
$478$	−17.0374	+	12.3784i	−0.779275	+	0.566176i
$479$	10.5601	−	32.5006i	0.482503	−	1.48499i	−0.353061	−	0.935600i	$-0.614859\pi$
$479$	10.5601	−	32.5006i	0.482503	−	1.48499i	0.835565	−	0.549392i	$-0.185141\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	0.735468	−	0.534349i	0.0335345	−	0.0243642i
$482$	0.00164170	−	0.00505264i	7.47775e−5	−	0.000230142i
$483$	−1.87312	+	1.36090i	−0.0852298	+	0.0619231i
$484$	1.31950	+	0.958674i	0.0599773	+	0.0435761i
$485$	4.33487	+	13.3414i	0.196836	+	0.605800i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−1.81438	+	5.58409i	−0.0822174	+	0.253039i	−0.983712	−	0.179751i	$-0.942471\pi$
$487$	−1.81438	+	5.58409i	−0.0822174	+	0.253039i	0.901495	+	0.432790i	$0.142471\pi$
$488$	3.47793	−	10.7040i	0.157438	−	0.484545i
$489$	1.30056	+	4.00271i	0.0588133	+	0.181009i
$490$	4.55913			0.205960
$491$	−3.40548			−0.153687			−0.0768435	−	0.997043i	$-0.524484\pi$
$491$	−3.40548			−0.153687			−0.0768435	+	0.997043i	$0.524484\pi$
$492$	0.195142	+	0.600586i	0.00879769	+	0.0270765i
$493$	43.3371	−	31.4863i	1.95181	−	1.41807i
$494$	35.5942	+	25.8607i	1.60146	+	1.16353i
$495$	−3.06088			−0.137576
$496$	−3.41569	+	4.39694i	−0.153369	+	0.197428i
$497$	5.90841			0.265028
$498$	−2.65416	−	1.92836i	−0.118936	−	0.0864119i
$499$	−27.5699	+	20.0307i	−1.23420	+	0.896696i	−0.997198	−	0.0748139i	$-0.976164\pi$
$499$	−27.5699	+	20.0307i	−1.23420	+	0.896696i	−0.236999	+	0.971510i	$0.576164\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−0.721973			−0.0322554
$502$	−5.42631			−0.242188
$503$	10.0442	+	30.9129i	0.447849	+	1.37834i	0.879329	+	0.476215i	$0.157992\pi$
$503$	10.0442	+	30.9129i	0.447849	+	1.37834i	−0.431479	+	0.902123i	$0.642008\pi$
$504$	−0.482786	+	1.48586i	−0.0215050	+	0.0661856i
$505$	1.26139	−	3.88216i	0.0561312	−	0.172754i
$506$	−3.66977	−	2.66625i	−0.163141	−	0.118529i
$507$	−7.98043	−	24.5612i	−0.354423	−	1.09080i
$508$	6.67485	+	4.84956i	0.296148	+	0.215164i
$509$	22.8756	−	16.6201i	1.01394	−	0.736674i	0.0489120	−	0.998803i	$-0.484425\pi$
$509$	22.8756	−	16.6201i	1.01394	−	0.736674i	0.965033	+	0.262129i	$0.0844246\pi$
$510$	−2.20421	+	6.78386i	−0.0976041	+	0.300395i
$511$	18.2116	−	13.2315i	0.805633	−	0.585327i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	2.18196	−	6.71539i	0.0963360	−	0.296492i
$514$	7.68352	−	5.58241i	0.338906	−	0.246229i
$515$	8.40457	+	6.10628i	0.370350	+	0.269075i
$516$	2.69516	+	8.29485i	0.118648	+	0.365161i
$517$	−21.3489	−	15.5109i	−0.938924	−	0.682168i
$518$	0.0704376	−	0.216784i	0.00309485	−	0.00952496i
$519$	0.620623	−	1.91008i	0.0272423	−	0.0838433i
$520$	−1.92548	−	5.92602i	−0.0844379	−	0.259873i
$521$	29.1228			1.27589			0.637946	−	0.770081i	$-0.279784\pi$
$521$	29.1228			1.27589			0.637946	+	0.770081i	$0.279784\pi$
$522$	7.50986			0.328698
$523$	0.961645	+	2.95964i	0.0420498	+	0.129416i	0.969878	−	0.243593i	$-0.0783261\pi$
$523$	0.961645	+	2.95964i	0.0420498	+	0.129416i	−0.927828	+	0.373009i	$0.878326\pi$
$524$	−10.4873	+	7.61948i	−0.458140	+	0.332858i
$525$	−1.26395	−	0.918314i	−0.0551633	−	0.0400785i
$526$	−26.9098			−1.17332
$527$	−1.27608	+	39.6942i	−0.0555870	+	1.72911i
$528$	−3.06088			−0.133208
$529$	16.8306	+	12.2282i	0.731767	+	0.531660i
$530$	−9.61440	+	6.98527i	−0.417623	+	0.303421i
$531$	1.12364	+	3.45820i	0.0487618	+	0.150073i
$532$	11.0316			0.478279
$533$	−3.93483			−0.170436
$534$	1.97058	+	6.06481i	0.0852752	+	0.262450i
$535$	−3.15650	+	9.71470i	−0.136467	+	0.420003i
$536$	−1.90436	+	5.86101i	−0.0822557	+	0.253157i
$537$	−6.34700	−	4.61136i	−0.273893	−	0.198995i
$538$	−2.86102	−	8.80531i	−0.123347	−	0.379624i
$539$	11.2898	+	8.20252i	0.486286	+	0.353308i
$540$	−0.809017	+	0.587785i	−0.0348145	+	0.0252942i
$541$	−2.51474	+	7.73959i	−0.108117	+	0.332751i	−0.990449	−	0.137876i	$-0.955972\pi$
$541$	−2.51474	+	7.73959i	−0.108117	+	0.332751i	0.882332	+	0.470627i	$0.155972\pi$
$542$	1.62402	−	1.17992i	0.0697575	−	0.0506818i
$543$	−14.6681	+	10.6570i	−0.629470	+	0.457337i
$544$	−2.20421	+	6.78386i	−0.0945048	+	0.290856i
$545$	11.8925	−	8.64043i	0.509420	−	0.370115i
$546$	−7.87566	−	5.72200i	−0.337047	−	0.244879i
$547$	−6.96745	−	21.4436i	−0.297907	−	0.916862i	−0.982230	−	0.187683i	$-0.939902\pi$
$547$	−6.96745	−	21.4436i	−0.297907	−	0.916862i	0.684323	−	0.729179i	$-0.260098\pi$
$548$	0.318811	+	0.231630i	0.0136189	+	0.00989473i
$549$	3.47793	−	10.7040i	0.148434	−	0.456834i
$550$	0.945865	−	2.91107i	0.0403318	−	0.124129i
$551$	−16.3862	−	50.4317i	−0.698077	−	2.14846i
$552$	−1.48195			−0.0630762
$553$	−6.12468			−0.260448
$554$	−8.64181	−	26.5967i	−0.367155	−	1.12999i
$555$	0.118034	−	0.0857567i	0.00501026	−	0.00364017i
$556$	−13.2441	−	9.62242i	−0.561676	−	0.408082i
$557$	31.2385			1.32362			0.661808	−	0.749673i	$-0.269789\pi$
$557$	31.2385			1.32362			0.661808	+	0.749673i	$0.269789\pi$
$558$	−3.41569	+	4.39694i	−0.144598	+	0.186137i
$559$	−54.3449			−2.29855
$560$	−1.26395	−	0.918314i	−0.0534117	−	0.0388058i
$561$	−17.6634	+	12.8332i	−0.745751	+	0.541820i
$562$	−5.90841	−	18.1842i	−0.249231	−	0.767055i
$563$	21.2403			0.895173			0.447586	−	0.894241i	$-0.352284\pi$
$563$	21.2403			0.895173			0.447586	+	0.894241i	$0.352284\pi$
$564$	−8.62127			−0.363021
$565$	−4.25391	−	13.0922i	−0.178963	−	0.550793i
$566$	8.26050	−	25.4232i	0.347215	−	1.06862i
$567$	−0.482786	+	1.48586i	−0.0202751	+	0.0624004i
$568$	3.05954	+	2.22288i	0.128375	+	0.0932702i
$569$	−2.70936	−	8.33855i	−0.113582	−	0.349570i	0.878066	−	0.478539i	$-0.158833\pi$
$569$	−2.70936	−	8.33855i	−0.113582	−	0.349570i	−0.991649	+	0.128968i	$0.958833\pi$
$570$	5.71245	+	4.15034i	0.239268	+	0.173839i
$571$	7.23696	−	5.25796i	0.302857	−	0.220039i	−0.425968	−	0.904738i	$-0.640066\pi$
$571$	7.23696	−	5.25796i	0.302857	−	0.220039i	0.728826	+	0.684699i	$0.240066\pi$
$572$	5.89367	−	18.1389i	0.246427	−	0.758424i
$573$	−16.0192	+	11.6387i	−0.669214	+	0.486212i
$574$	−0.798177	+	0.579909i	−0.0333152	+	0.0242049i
$575$	0.457949	−	1.40942i	0.0190978	−	0.0587770i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−4.11770	−	2.99168i	−0.171422	−	0.124545i	0.498766	−	0.866737i	$-0.333787\pi$
$577$	−4.11770	−	2.99168i	−0.171422	−	0.124545i	−0.670188	+	0.742191i	$0.733787\pi$
$578$	10.4693	+	32.2212i	0.435465	+	1.34022i
$579$	−17.0876	−	12.4149i	−0.710136	−	0.515944i
$580$	−2.32067	+	7.14230i	−0.0963608	+	0.296568i
$581$	1.58389	−	4.87470i	0.0657107	−	0.202237i
$582$	4.33487	+	13.3414i	0.179686	+	0.553017i
$583$	−36.3757			−1.50653
$584$	14.4085			0.596226
$585$	−1.92548	−	5.92602i	−0.0796088	−	0.245011i
$586$	−9.39518	+	6.82600i	−0.388111	+	0.281979i
$587$	37.2730	+	27.0804i	1.53842	+	1.11773i	0.951317	+	0.308215i	$0.0997317\pi$
$587$	37.2730	+	27.0804i	1.53842	+	1.11773i	0.587103	+	0.809512i	$0.300268\pi$
$588$	4.55913			0.188015
$589$	36.9801	+	13.3438i	1.52374	+	0.549820i
$590$	−3.63617			−0.149699
$591$	−18.3980	−	13.3669i	−0.756791	−	0.549841i
$592$	0.118034	−	0.0857567i	0.00485117	−	0.00352458i
$593$	−0.0141339	−	0.0434996i	−0.000580409	−	0.00178632i	0.950766	−	0.309910i	$-0.100299\pi$
$593$	−0.0141339	−	0.0434996i	−0.000580409	−	0.00178632i	−0.951346	+	0.308124i	$0.900299\pi$
$594$	−3.06088			−0.125590
$595$	−11.1441			−0.456862
$596$	2.69591	+	8.29716i	0.110429	+	0.339865i
$597$	−2.28821	+	7.04239i	−0.0936503	+	0.288226i
$598$	2.85348	−	8.78209i	0.116687	−	0.359127i
$599$	18.9543	+	13.7711i	0.774454	+	0.562673i	0.903309	−	0.428990i	$-0.141130\pi$
$599$	18.9543	+	13.7711i	0.774454	+	0.562673i	−0.128856	+	0.991663i	$0.541130\pi$
$600$	−0.309017	−	0.951057i	−0.0126156	−	0.0388267i
$601$	2.63758	+	1.91631i	0.107589	+	0.0781680i	0.640279	−	0.768143i	$-0.278819\pi$
$601$	2.63758	+	1.91631i	0.107589	+	0.0781680i	−0.532690	+	0.846311i	$0.678819\pi$
$602$	−11.0238	+	8.00928i	−0.449298	+	0.326434i
$603$	−1.90436	+	5.86101i	−0.0775515	+	0.238679i
$604$	−14.2225	+	10.3332i	−0.578703	+	0.420453i
$605$	−1.31950	+	0.958674i	−0.0536453	+	0.0389756i
$606$	1.26139	−	3.88216i	0.0512405	−	0.157702i
$607$	−7.05094	+	5.12281i	−0.286189	+	0.207928i	−0.721612	−	0.692297i	$-0.756599\pi$
$607$	−7.05094	+	5.12281i	−0.286189	+	0.207928i	0.435423	+	0.900226i	$0.356599\pi$
$608$	5.71245	+	4.15034i	0.231671	+	0.168319i
$609$	3.62566	+	11.1586i	0.146919	+	0.452170i
$610$	9.10533	+	6.61541i	0.368664	+	0.267850i
$611$	16.6001	−	51.0898i	0.671568	−	2.06687i
$612$	−2.20421	+	6.78386i	−0.0890999	+	0.274221i
$613$	−1.36100	−	4.18872i	−0.0549702	−	0.169181i	0.919802	−	0.392383i	$-0.128349\pi$
$613$	−1.36100	−	4.18872i	−0.0549702	−	0.169181i	−0.974772	+	0.223202i	$0.928349\pi$
$614$	16.4991			0.665848
$615$	−0.631494			−0.0254643
$616$	−1.47775	−	4.54805i	−0.0595403	−	0.183246i
$617$	−5.36453	+	3.89756i	−0.215968	+	0.156910i	−0.690510	−	0.723323i	$-0.742614\pi$
$617$	−5.36453	+	3.89756i	−0.215968	+	0.156910i	0.474542	+	0.880233i	$0.342614\pi$
$618$	8.40457	+	6.10628i	0.338081	+	0.245631i
$619$	6.96062			0.279771			0.139885	−	0.990168i	$-0.455327\pi$
$619$	6.96062			0.279771			0.139885	+	0.990168i	$0.455327\pi$
$620$	−3.12623	−	4.60724i	−0.125552	−	0.185031i
$621$	−1.48195			−0.0594688
$622$	−2.80886	−	2.04076i	−0.112625	−	0.0818270i
$623$	−8.06011	+	5.85602i	−0.322922	+	0.234616i
$624$	−1.92548	−	5.92602i	−0.0770809	−	0.237231i
$625$	1.00000			0.0400000
$626$	8.33590			0.333170
$627$	6.67873	+	20.5550i	0.266723	+	0.820889i
$628$	2.82605	−	8.69769i	0.112772	−	0.347076i
$629$	0.321590	−	0.989752i	0.0128226	−	0.0394640i
$630$	−1.26395	−	0.918314i	−0.0503570	−	0.0365865i
$631$	4.27325	+	13.1517i	0.170115	+	0.523561i	0.999377	−	0.0352998i	$-0.0112386\pi$
$631$	4.27325	+	13.1517i	0.170115	+	0.523561i	−0.829261	+	0.558861i	$0.811239\pi$
$632$	−3.17153	−	2.30425i	−0.126157	−	0.0916581i
$633$	−3.29414	+	2.39333i	−0.130930	+	0.0951265i
$634$	2.99288	−	9.21114i	0.118862	−	0.365821i
$635$	−6.67485	+	4.84956i	−0.264883	+	0.192449i
$636$	−9.61440	+	6.98527i	−0.381236	+	0.276984i
$637$	−8.77851	+	27.0175i	−0.347817	+	1.07047i
$638$	−18.5967	+	13.5113i	−0.736251	+	0.534918i
$639$	3.05954	+	2.22288i	0.121033	+	0.0879360i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−33.9221	−	24.6458i	−1.33984	−	0.973452i	−0.999450	−	0.0331681i	$-0.989440\pi$
$641$	−33.9221	−	24.6458i	−1.33984	−	0.973452i	−0.340392	−	0.940284i	$-0.610560\pi$
$642$	−3.15650	+	9.71470i	−0.124577	+	0.383408i
$643$	10.6518	−	32.7830i	0.420068	−	1.29284i	−0.487571	−	0.873083i	$-0.662117\pi$
$643$	10.6518	−	32.7830i	0.420068	−	1.29284i	0.907639	−	0.419752i	$-0.137883\pi$
$644$	−0.715467	−	2.20198i	−0.0281934	−	0.0867702i
$645$	−8.72172			−0.343418
$646$	50.3658			1.98162
$647$	13.9599	+	42.9643i	0.548822	+	1.68910i	0.711726	+	0.702458i	$0.247914\pi$
$647$	13.9599	+	42.9643i	0.548822	+	1.68910i	−0.162904	+	0.986642i	$0.552086\pi$
$648$	−0.809017	+	0.587785i	−0.0317812	+	0.0230904i
$649$	−9.00428	−	6.54199i	−0.353449	−	0.256796i
$650$	6.23099			0.244399
$651$	−8.18229	−	2.95247i	−0.320689	−	0.115716i
$652$	−4.20870			−0.164825
$653$	−31.7816	−	23.0907i	−1.24371	−	0.903607i	−0.245869	−	0.969303i	$-0.579073\pi$
$653$	−31.7816	−	23.0907i	−1.24371	−	0.903607i	−0.997840	+	0.0656961i	$0.979073\pi$
$654$	11.8925	−	8.64043i	0.465035	−	0.337868i
$655$	−4.00580	−	12.3286i	−0.156519	−	0.481717i
$656$	−0.631494			−0.0246557
$657$	14.4085			0.562128
$658$	−4.16223	−	12.8100i	−0.162261	−	0.499387i
$659$	2.41976	−	7.44725i	0.0942603	−	0.290104i	−0.892800	−	0.450454i	$-0.851262\pi$
$659$	2.41976	−	7.44725i	0.0942603	−	0.290104i	0.987060	+	0.160350i	$0.0512623\pi$
$660$	0.945865	−	2.91107i	0.0368177	−	0.113313i
$661$	34.8377	+	25.3111i	1.35503	+	0.984487i	0.998744	+	0.0501095i	$0.0159570\pi$
$661$	34.8377	+	25.3111i	1.35503	+	0.984487i	0.356286	+	0.934377i	$0.384043\pi$
$662$	6.04531	+	18.6056i	0.234958	+	0.723125i
$663$	−35.9572	−	26.1244i	−1.39646	−	1.01459i
$664$	2.65416	−	1.92836i	0.103001	−	0.0748349i
$665$	−3.40894	+	10.4917i	−0.132193	+	0.406849i
$666$	0.118034	−	0.0857567i	0.00457372	−	0.00332301i
$667$	−9.00377	+	6.54162i	−0.348627	+	0.253293i
$668$	0.223102	−	0.686637i	0.00863207	−	0.0265668i
$669$	15.8989	−	11.5512i	0.614685	−	0.446595i
$670$	−4.98567	−	3.62230i	−0.192613	−	0.139942i
$671$	10.6455	+	32.7636i	0.410966	+	1.26482i
$672$	−1.26395	−	0.918314i	−0.0487580	−	0.0354247i
$673$	6.98740	−	21.5050i	0.269345	−	0.828958i	−0.721316	−	0.692606i	$-0.756462\pi$
$673$	6.98740	−	21.5050i	0.269345	−	0.828958i	0.990661	−	0.136351i	$-0.0435376\pi$
$674$	−7.91353	+	24.3554i	−0.304818	+	0.938133i
$675$	−0.309017	−	0.951057i	−0.0118941	−	0.0366062i
$676$	25.8252			0.993277
$677$	−1.18096			−0.0453882			−0.0226941	−	0.999742i	$-0.507224\pi$
$677$	−1.18096			−0.0453882			−0.0226941	+	0.999742i	$0.507224\pi$
$678$	−4.25391	−	13.0922i	−0.163370	−	0.502803i
$679$	−17.7306	+	12.8821i	−0.680439	+	0.494368i
$680$	−5.77070	−	4.19266i	−0.221296	−	0.160781i
$681$	−24.2779			−0.930330
$682$	0.547588	−	17.0335i	0.0209682	−	0.652246i
$683$	40.4963			1.54955			0.774774	−	0.632239i	$-0.217864\pi$
$683$	40.4963			1.54955			0.774774	+	0.632239i	$0.217864\pi$
$684$	5.71245	+	4.15034i	0.218421	+	0.158692i
$685$	−0.318811	+	0.231630i	−0.0121811	+	0.00885012i
$686$	5.58059	+	17.1753i	0.213068	+	0.655755i
$687$	25.1701			0.960301
$688$	−8.72172			−0.332513
$689$	−22.8825	−	70.4251i	−0.871754	−	2.68298i
$690$	0.457949	−	1.40942i	0.0174338	−	0.0536558i
$691$	−0.0881680	+	0.271353i	−0.00335407	+	0.0103228i	−0.952720	−	0.303851i	$-0.901727\pi$
$691$	−0.0881680	+	0.271353i	−0.00335407	+	0.0103228i	0.949365	+	0.314174i	$0.101727\pi$
$692$	1.62481	+	1.18050i	0.0617661	+	0.0448757i
$693$	−1.47775	−	4.54805i	−0.0561352	−	0.172766i
$694$	−19.5909	−	14.2337i	−0.743662	−	0.540302i
$695$	13.2441	−	9.62242i	0.502378	−	0.364999i
$696$	−2.32067	+	7.14230i	−0.0879649	+	0.270728i
$697$	−3.64416	+	2.64764i	−0.138032	+	0.100286i
$698$	−19.3487	+	14.0577i	−0.732361	+	0.532091i
$699$	−0.869301	+	2.67543i	−0.0328800	+	0.101194i
$700$	1.26395	−	0.918314i	0.0477728	−	0.0347090i
$701$	−4.54407	−	3.30146i	−0.171627	−	0.124694i	0.498656	−	0.866800i	$-0.333827\pi$
$701$	−4.54407	−	3.30146i	−0.171627	−	0.124694i	−0.670283	+	0.742106i	$0.733827\pi$
$702$	−1.92548	−	5.92602i	−0.0726726	−	0.223663i
$703$	−0.833436	−	0.605526i	−0.0314336	−	0.0228379i
$704$	0.945865	−	2.91107i	0.0356486	−	0.109715i
$705$	2.66412	−	8.19932i	0.100337	−	0.308804i
$706$	−0.213507	−	0.657106i	−0.00803543	−	0.0247305i
$707$	6.37735			0.239845
$708$	−3.63617			−0.136656
$709$	−13.3828	−	41.1881i	−0.502602	−	1.54685i	−0.804765	−	0.593594i	$-0.797709\pi$
$709$	−13.3828	−	41.1881i	−0.502602	−	1.54685i	0.302163	−	0.953256i	$-0.402291\pi$
$710$	−3.05954	+	2.22288i	−0.114822	+	0.0834234i
$711$	−3.17153	−	2.30425i	−0.118942	−	0.0864161i
$712$	−6.37692			−0.238985
$713$	0.265120	−	8.24691i	0.00992882	−	0.308849i
$714$	−11.1441			−0.417056
$715$	15.4298	+	11.2104i	0.577043	+	0.419246i
$716$	6.34700	−	4.61136i	0.237198	−	0.172335i
$717$	−6.50773	−	20.0287i	−0.243035	−	0.747986i
$718$	3.82137			0.142612
$719$	−15.4612			−0.576604			−0.288302	−	0.957539i	$-0.593091\pi$
$719$	−15.4612			−0.576604			−0.288302	+	0.957539i	$0.593091\pi$
$720$	−0.309017	−	0.951057i	−0.0115164	−	0.0354438i
$721$	−5.01548	+	15.4361i	−0.186786	+	0.574869i
$722$	9.53548	−	29.3472i	0.354874	−	1.09219i
$723$	0.00429803	+	0.00312270i	0.000159846	+	0.000116135i
$724$	−5.60273	−	17.2434i	−0.208224	−	0.640847i
$725$	−6.07561	−	4.41419i	−0.225642	−	0.163939i
$726$	−1.31950	+	0.958674i	−0.0489713	+	0.0355797i
$727$	2.11091	−	6.49672i	0.0782894	−	0.240950i	−0.904250	−	0.427003i	$-0.859569\pi$
$727$	2.11091	−	6.49672i	0.0782894	−	0.240950i	0.982540	+	0.186053i	$0.0595695\pi$
$728$	7.87566	−	5.72200i	0.291891	−	0.212071i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−4.45246	+	13.7033i	−0.164793	+	0.507180i
$731$	−50.3304	+	36.5672i	−1.86154	+	1.35249i
$732$	9.10533	+	6.61541i	0.336543	+	0.244512i
$733$	1.36450	+	4.19949i	0.0503989	+	0.155112i	0.973088	−	0.230432i	$-0.0740139\pi$
$733$	1.36450	+	4.19949i	0.0503989	+	0.155112i	−0.922690	+	0.385544i	$0.874014\pi$
$734$	22.1288	+	16.0775i	0.816790	+	0.593433i
$735$	−1.40885	+	4.33599i	−0.0519661	+	0.159935i
$736$	0.457949	−	1.40942i	0.0168802	−	0.0519520i
$737$	−5.82902	−	17.9399i	−0.214715	−	0.660824i
$738$	−0.631494			−0.0232456
$739$	45.1243			1.65992			0.829962	−	0.557820i	$-0.188362\pi$
$739$	45.1243			1.65992			0.829962	+	0.557820i	$0.188362\pi$
$740$	0.0450850	+	0.138757i	0.00165736	+	0.00510082i
$741$	−35.5942	+	25.8607i	−1.30759	+	0.950017i
$742$	−15.0208	−	10.9133i	−0.551433	−	0.400639i
$743$	−8.89623			−0.326371			−0.163185	−	0.986595i	$-0.552177\pi$
$743$	−8.89623			−0.326371			−0.163185	+	0.986595i	$0.552177\pi$
$744$	−3.12623	−	4.60724i	−0.114613	−	0.168910i
$745$	−8.72415			−0.319628
$746$	−5.02566	−	3.65136i	−0.184002	−	0.133686i
$747$	2.65416	−	1.92836i	0.0971106	−	0.0705550i
$748$	−6.74683	−	20.7646i	−0.246689	−	0.759230i
$749$	−15.9586			−0.583115
$750$	1.00000			0.0365148
$751$	−0.633678	−	1.95026i	−0.0231233	−	0.0711661i	0.938829	−	0.344384i	$-0.111912\pi$
$751$	−0.633678	−	1.95026i	−0.0231233	−	0.0711661i	−0.961952	+	0.273218i	$0.911912\pi$
$752$	2.66412	−	8.19932i	0.0971504	−	0.298998i
$753$	1.67682	−	5.16073i	0.0611068	−	0.188067i
$754$	−37.8570	−	27.5047i	−1.37867	−	1.00166i
$755$	−5.43249	−	16.7195i	−0.197709	−	0.608485i
$756$	−1.26395	−	0.918314i	−0.0459694	−	0.0333988i
$757$	−1.08133	+	0.785632i	−0.0393016	+	0.0285543i	−0.607263	−	0.794501i	$-0.707732\pi$
$757$	−1.08133	+	0.785632i	−0.0393016	+	0.0285543i	0.567961	+	0.823055i	$0.307732\pi$
$758$	−0.189287	+	0.582564i	−0.00687520	+	0.0211597i
$759$	3.66977	−	2.66625i	0.133204	−	0.0967786i
$760$	−5.71245	+	4.15034i	−0.207212	+	0.150549i
$761$	11.0687	−	34.0660i	0.401241	−	1.23489i	−0.522753	−	0.852484i	$-0.675095\pi$
$761$	11.0687	−	34.0660i	0.401241	−	1.23489i	0.923994	−	0.382408i	$-0.124905\pi$
$762$	−6.67485	+	4.84956i	−0.241804	+	0.175681i
$763$	18.5801	+	13.4992i	0.672643	+	0.488704i
$764$	−6.11881	−	18.8318i	−0.221371	−	0.681309i
$765$	−5.77070	−	4.19266i	−0.208640	−	0.151586i
$766$	−6.06165	+	18.6558i	−0.219016	+	0.674062i
$767$	7.00138	−	21.5480i	0.252805	−	0.778054i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	11.5483			0.416441			0.208220	−	0.978082i	$-0.433233\pi$
$769$	11.5483			0.416441			0.208220	+	0.978082i	$0.433233\pi$
$770$	4.78211			0.172335
$771$	2.93485	+	9.03252i	0.105696	+	0.325298i
$772$	17.0876	−	12.4149i	0.614995	−	0.446820i
$773$	28.4794	+	20.6915i	1.02433	+	0.744222i	0.967167	−	0.254143i	$-0.0817933\pi$
$773$	28.4794	+	20.6915i	1.02433	+	0.744222i	0.0571668	+	0.998365i	$0.481793\pi$
$774$	−8.72172			−0.313496
$775$	5.34781	−	1.54950i	0.192099	−	0.0556598i
$776$	−14.0279			−0.503574
$777$	0.184408	+	0.133980i	0.00661560	+	0.00480651i
$778$	2.81381	−	2.04435i	0.100880	−	0.0732936i
$779$	1.37790	+	4.24073i	0.0493682	+	0.151940i
$780$	6.23099			0.223105
$781$	−11.5756			−0.414209
$782$	−3.26654	−	10.0534i	−0.116811	−	0.359508i
$783$	−2.32067	+	7.14230i	−0.0829341	+	0.255245i
$784$	−1.40885	+	4.33599i	−0.0503160	+	0.154857i
$785$	7.39870	+	5.37547i	0.264071	+	0.191859i
$786$	−4.00580	−	12.3286i	−0.142882	−	0.439746i
$787$	−7.22037	−	5.24590i	−0.257378	−	0.186996i	0.451612	−	0.892214i	$-0.350849\pi$
$787$	−7.22037	−	5.24590i	−0.257378	−	0.186996i	−0.708990	+	0.705218i	$0.750849\pi$
$788$	18.3980	−	13.3669i	0.655400	−	0.476176i
$789$	8.31559	−	25.5928i	0.296043	−	0.911127i
$790$	3.17153	−	2.30425i	0.112838	−	0.0819815i
$791$	17.3995	−	12.6415i	0.618654	−	0.449479i
$792$	0.945865	−	2.91107i	0.0336098	−	0.103440i
$793$	−56.7352	+	41.2205i	−2.01473	+	1.46378i
$794$	−22.5493	−	16.3830i	−0.800243	−	0.581411i
$795$	−3.67237	−	11.3024i	−0.130246	−	0.400855i
$796$	−5.99062	−	4.35244i	−0.212332	−	0.154268i
$797$	−0.156744	+	0.482410i	−0.00555217	+	0.0170878i	−0.953794	−	0.300461i	$-0.902860\pi$
$797$	−0.156744	+	0.482410i	−0.00555217	+	0.0170878i	0.948242	+	0.317548i	$0.102860\pi$
$798$	−3.40894	+	10.4917i	−0.120675	+	0.371400i
$799$	−19.0031	−	58.4855i	−0.672281	−	2.06907i
$800$	1.00000			0.0353553
$801$	−6.37692			−0.225317
$802$	−0.648673	−	1.99641i	−0.0229054	−	0.0704957i
$803$	−35.6798	+	25.9229i	−1.25911	+	0.914798i
$804$	−4.98567	−	3.62230i	−0.175831	−	0.127749i
$805$	2.31530			0.0816036
$806$	33.3221	−	9.65493i	1.17372	−	0.340080i
$807$	9.25845			0.325913
$808$	3.30237	+	2.39931i	0.116177	+	0.0844074i
$809$	5.26480	−	3.82510i	0.185101	−	0.134483i	−0.491376	−	0.870947i	$-0.663506\pi$
$809$	5.26480	−	3.82510i	0.185101	−	0.134483i	0.676477	+	0.736464i	$0.263506\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	14.6774			0.515394			0.257697	−	0.966226i	$-0.417036\pi$
$811$	14.6774			0.515394			0.257697	+	0.966226i	$0.417036\pi$
$812$	−11.7329			−0.411743
$813$	0.620319	+	1.90915i	0.0217555	+	0.0669567i
$814$	−0.138000	+	0.424720i	−0.00483689	+	0.0148864i
$815$	1.30056	−	4.00271i	0.0455566	−	0.140209i
$816$	−5.77070	−	4.19266i	−0.202015	−	0.146772i
$817$	19.0305	+	58.5698i	0.665792	+	2.04910i
$818$	−24.4534	−	17.7664i	−0.854993	−	0.621188i
$819$	7.87566	−	5.72200i	0.275198	−	0.199943i
$820$	0.195142	−	0.600586i	0.00681466	−	0.0209734i
$821$	−40.2749	+	29.2614i	−1.40560	+	1.02123i	−0.411659	+	0.911338i	$0.635051\pi$
$821$	−40.2749	+	29.2614i	−1.40560	+	1.02123i	−0.993943	+	0.109892i	$0.964949\pi$
$822$	−0.318811	+	0.231630i	−0.0111198	+	0.00807902i
$823$	−9.95968	+	30.6527i	−0.347173	+	1.06849i	0.613238	+	0.789898i	$0.289867\pi$
$823$	−9.95968	+	30.6527i	−0.347173	+	1.06849i	−0.960410	+	0.278589i	$0.910133\pi$
$824$	−8.40457	+	6.10628i	−0.292787	+	0.212722i
$825$	2.47631	+	1.79914i	0.0862139	+	0.0626381i
$826$	−1.75549	−	5.40285i	−0.0610814	−	0.187989i
$827$	7.63332	+	5.54593i	0.265436	+	0.192851i	0.712540	−	0.701631i	$-0.247545\pi$
$827$	7.63332	+	5.54593i	0.265436	+	0.192851i	−0.447104	+	0.894482i	$0.647545\pi$
$828$	0.457949	−	1.40942i	0.0159148	−	0.0489808i
$829$	−0.840238	+	2.58599i	−0.0291827	+	0.0898151i	−0.964587	−	0.263765i	$-0.915036\pi$
$829$	−0.840238	+	2.58599i	−0.0291827	+	0.0898151i	0.935404	+	0.353580i	$0.115036\pi$
$830$	1.01380	+	3.12015i	0.0351895	+	0.108302i
$831$	27.9655			0.970111
$832$	6.23099			0.216021
$833$	10.0493	+	30.9285i	0.348187	+	1.07161i
$834$	13.2441	−	9.62242i	0.458607	−	0.333197i
$835$	0.584088	+	0.424365i	0.0202132	+	0.0146858i
$836$	−21.6128			−0.747496
$837$	−3.12623	−	4.60724i	−0.108058	−	0.159250i
$838$	2.72152			0.0940134
$839$	−44.7163	−	32.4883i	−1.54378	−	1.12162i	−0.947910	−	0.318539i	$-0.896808\pi$
$839$	−44.7163	−	32.4883i	−1.54378	−	1.12162i	−0.595869	−	0.803082i	$-0.703192\pi$
$840$	1.26395	−	0.918314i	0.0436104	−	0.0316848i
$841$	8.46645	+	26.0571i	0.291947	+	0.898519i
$842$	−7.81292			−0.269251
$843$	19.1200			0.658528
$844$	−1.25825	−	3.87250i	−0.0433108	−	0.133297i
$845$	−7.98043	+	24.5612i	−0.274535	+	0.844932i
$846$	2.66412	−	8.19932i	0.0915943	−	0.281898i
$847$	−2.06149	−	1.49776i	−0.0708338	−	0.0514638i
$848$	−3.67237	−	11.3024i	−0.126110	−	0.388126i
$849$	21.6263	+	15.7124i	0.742211	+	0.539248i
$850$	5.77070	−	4.19266i	0.197933	−	0.143807i
$851$	−0.0668139	+	0.205632i	−0.00229035	+	0.00704897i
$852$	−3.05954	+	2.22288i	−0.104818	+	0.0761548i
$853$	45.8536	−	33.3146i	1.57000	−	1.14067i	0.642841	−	0.765999i	$-0.277755\pi$
$853$	45.8536	−	33.3146i	1.57000	−	1.14067i	0.927158	−	0.374672i	$-0.122245\pi$
$854$	−5.43366	+	16.7231i	−0.185936	+	0.572253i
$855$	−5.71245	+	4.15034i	−0.195362	+	0.141939i
$856$	−8.26381	−	6.00401i	−0.282451	−	0.205213i
$857$	5.09114	+	15.6689i	0.173910	+	0.535240i	0.999582	−	0.0289105i	$-0.00920377\pi$
$857$	5.09114	+	15.6689i	0.173910	+	0.535240i	−0.825672	+	0.564151i	$0.809204\pi$
$858$	15.4298	+	11.2104i	0.526766	+	0.382718i
$859$	−13.2398	+	40.7480i	−0.451737	+	1.39030i	0.423187	+	0.906042i	$0.360911\pi$
$859$	−13.2398	+	40.7480i	−0.451737	+	1.39030i	−0.874924	+	0.484260i	$0.839089\pi$
$860$	2.69516	−	8.29485i	0.0919042	−	0.282852i
$861$	−0.304876	−	0.938313i	−0.0103902	−	0.0319776i
$862$	28.3603			0.965956
$863$	21.4906			0.731547			0.365774	−	0.930704i	$-0.380804\pi$
$863$	21.4906			0.731547			0.365774	+	0.930704i	$0.380804\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−1.62481	+	1.18050i	−0.0552453	+	0.0401380i
$866$	10.2071	+	7.41586i	0.346850	+	0.252001i
$867$	−33.8793			−1.15060
$868$	5.33643	−	6.86946i	0.181130	−	0.233165i
$869$	11.9993			0.407050
$870$	−6.07561	−	4.41419i	−0.205982	−	0.149655i
$871$	31.0657	−	22.5705i	1.05262	−	0.764773i
$872$	4.54254	+	13.9805i	0.153830	+	0.473440i
$873$	−14.0279			−0.474774
$874$	−10.4641			−0.353952
$875$	0.482786	+	1.48586i	0.0163212	+	0.0502313i
$876$	−4.45246	+	13.7033i	−0.150435	+	0.462990i
$877$	0.979968	−	3.01603i	0.0330912	−	0.101844i	−0.933147	−	0.359496i	$-0.882949\pi$
$877$	0.979968	−	3.01603i	0.0330912	−	0.101844i	0.966238	+	0.257652i	$0.0829487\pi$
$878$	13.6278	+	9.90116i	0.459915	+	0.334148i
$879$	−3.58864	−	11.0447i	−0.121042	−	0.372528i
$880$	2.47631	+	1.79914i	0.0834763	+	0.0606491i
$881$	−7.83413	+	5.69183i	−0.263939	+	0.191763i	−0.711882	−	0.702299i	$-0.752157\pi$
$881$	−7.83413	+	5.69183i	−0.263939	+	0.191763i	0.447943	+	0.894062i	$0.352157\pi$
$882$	−1.40885	+	4.33599i	−0.0474384	+	0.146000i
$883$	−26.1095	+	18.9696i	−0.878654	+	0.638379i	−0.932895	−	0.360148i	$-0.882726\pi$
$883$	−26.1095	+	18.9696i	−0.878654	+	0.638379i	0.0542411	+	0.998528i	$0.482726\pi$
$884$	35.9572	−	26.1244i	1.20937	−	0.878659i
$885$	1.12364	−	3.45820i	0.0377707	−	0.116246i
$886$	−15.4370	+	11.2156i	−0.518615	+	0.376796i
$887$	−25.8740	−	18.7986i	−0.868766	−	0.631195i	0.0614899	−	0.998108i	$-0.480415\pi$
$887$	−25.8740	−	18.7986i	−0.868766	−	0.631195i	−0.930255	+	0.366913i	$0.880415\pi$
$888$	0.0450850	+	0.138757i	0.00151295	+	0.00465639i
$889$	−10.4283	−	7.57661i	−0.349754	−	0.254111i
$890$	1.97058	−	6.06481i	0.0660539	−	0.203293i
$891$	0.945865	−	2.91107i	0.0316877	−	0.0975246i
$892$	6.07282	+	18.6902i	0.203333	+	0.625795i
$893$	−60.8746			−2.03709
$894$	−8.72415			−0.291779
$895$	2.42434	+	7.46134i	0.0810367	+	0.249405i
$896$	1.26395	−	0.918314i	0.0422256	−	0.0306787i
$897$	7.47050	+	5.42763i	0.249433	+	0.181223i
$898$	27.7017			0.924416
$899$	−39.3310	−	14.1920i	−1.31176	−	0.473331i
$900$	1.00000			0.0333333
$901$	−68.5793	−	49.8257i	−2.28471	−	1.65994i
$902$	1.56377	−	1.13615i	0.0520679	−	0.0378295i
$903$	−4.21073	−	12.9593i	−0.140124	−	0.431258i
$904$	13.7659			0.457849
$905$	18.1308			0.602689
$906$	−5.43249	−	16.7195i	−0.180482	−	0.555468i
$907$	−7.38312	+	22.7229i	−0.245152	+	0.754501i	0.750459	+	0.660917i	$0.229832\pi$
$907$	−7.38312	+	22.7229i	−0.245152	+	0.754501i	−0.995611	+	0.0935844i	$0.970168\pi$
$908$	7.50228	−	23.0896i	0.248972	−	0.766256i
$909$	3.30237	+	2.39931i	0.109533	+	0.0795801i
$910$	3.00823	+	9.25839i	0.0997220	+	0.306913i
$911$	12.0984	+	8.79000i	0.400838	+	0.291226i	0.769882	−	0.638186i	$-0.220315\pi$
$911$	12.0984	+	8.79000i	0.400838	+	0.291226i	−0.369044	+	0.929412i	$0.620315\pi$
$912$	−5.71245	+	4.15034i	−0.189158	+	0.137432i
$913$	−3.10312	+	9.55042i	−0.102698	+	0.316073i
$914$	−21.8233	+	15.8555i	−0.721850	+	0.524455i
$915$	−9.10533	+	6.61541i	−0.301013	+	0.218699i
$916$	−7.77800	+	23.9382i	−0.256992	+	0.790941i
$917$	16.3846	−	11.9041i	0.541068	−	0.393109i
$918$	−5.77070	−	4.19266i	−0.190461	−	0.138378i
$919$	5.03837	+	15.5065i	0.166201	+	0.511513i	0.999123	−	0.0418773i	$-0.0133339\pi$
$919$	5.03837	+	15.5065i	0.166201	+	0.511513i	−0.832922	+	0.553390i	$0.813334\pi$
$920$	1.19893	+	0.871071i	0.0395274	+	0.0287184i
$921$	−5.09849	+	15.6915i	−0.168001	+	0.517054i
$922$	5.32443	−	16.3869i	0.175351	−	0.539674i
$923$	−7.28178	−	22.4110i	−0.239683	−	0.737667i
$924$	4.78211			0.157320
$925$	−0.145898			−0.00479710
$926$	−9.71140	−	29.8886i	−0.319137	−	0.982201i
$927$	−8.40457	+	6.10628i	−0.276042	+	0.200557i
$928$	−6.07561	−	4.41419i	−0.199442	−	0.144903i
$929$	46.0922			1.51224			0.756119	−	0.654435i	$-0.227093\pi$
$929$	46.0922			1.51224			0.756119	+	0.654435i	$0.227093\pi$
$930$	5.34781	−	1.54950i	0.175362	−	0.0508102i
$931$	32.1919			1.05505
$932$	−2.27586	−	1.65351i	−0.0745482	−	0.0541625i
$933$	2.80886	−	2.04076i	0.0919581	−	0.0668115i
$934$	−7.70234	−	23.7054i	−0.252028	−	0.775663i
$935$	21.8332			0.714022
$936$	6.23099			0.203666
$937$	−4.54937	−	14.0015i	−0.148622	−	0.457410i	0.848837	−	0.528654i	$-0.177303\pi$
$937$	−4.54937	−	14.0015i	−0.148622	−	0.457410i	−0.997459	+	0.0712440i	$0.977303\pi$
$938$	2.97523	−	9.15683i	0.0971448	−	0.298981i
$939$	−2.57594	+	7.92792i	−0.0840625	+	0.258718i
$940$	6.97476	+	5.06746i	0.227491	+	0.165282i
$941$	5.55287	+	17.0900i	0.181018	+	0.557117i	0.999857	−	0.0169063i	$-0.00538171\pi$
$941$	5.55287	+	17.0900i	0.181018	+	0.557117i	−0.818839	+	0.574024i	$0.805382\pi$
$942$	7.39870	+	5.37547i	0.241063	+	0.175142i
$943$	0.757114	−	0.550076i	0.0246550	−	0.0179129i
$944$	1.12364	−	3.45820i	0.0365713	−	0.112555i
$945$	1.26395	−	0.918314i	0.0411163	−	0.0298728i
$946$	21.5977	−	15.6916i	0.702201	−	0.510179i
$947$	−8.34377	+	25.6795i	−0.271136	+	0.834471i	0.719080	+	0.694927i	$0.244563\pi$
$947$	−8.34377	+	25.6795i	−0.271136	+	0.834471i	−0.990216	+	0.139543i	$0.955437\pi$
$948$	3.17153	−	2.30425i	0.103006	−	0.0748386i
$949$	−72.6327	−	52.7707i	−2.35776	−	1.71301i
$950$	−2.18196	−	6.71539i	−0.0707922	−	0.217876i
$951$	7.83546	+	5.69280i	0.254082	+	0.184602i
$952$	3.44370	−	10.5986i	0.111611	−	0.343503i
$953$	−8.32380	+	25.6180i	−0.269634	+	0.829849i	0.720955	+	0.692982i	$0.243703\pi$
$953$	−8.32380	+	25.6180i	−0.269634	+	0.829849i	−0.990589	+	0.136867i	$0.956297\pi$
$954$	−3.67237	−	11.3024i	−0.118897	−	0.365929i
$955$	19.8009			0.640741
$956$	21.0594			0.681111
$957$	−7.10331	−	21.8618i	−0.229618	−	0.706690i
$958$	−27.6467	+	20.0865i	−0.893224	+	0.648965i
$959$	−0.498088	−	0.361882i	−0.0160841	−	0.0116858i
$960$	1.00000			0.0322749
$961$	26.1981	−	16.5729i	0.845099	−	0.534609i
$962$	−0.909089			−0.0293102
$963$	−8.26381	−	6.00401i	−0.266298	−	0.193477i
$964$	−0.00429803	+	0.00312270i	−0.000138430	+	0.000100576i
$965$	6.52687	+	20.0877i	0.210108	+	0.646645i
$966$	2.31530			0.0744936
$967$	4.33890			0.139530			0.0697648	−	0.997563i	$-0.477775\pi$
$967$	4.33890			0.139530			0.0697648	+	0.997563i	$0.477775\pi$
$968$	−0.504005	−	1.55117i	−0.0161993	−	0.0498564i
$969$	−15.5639	+	47.9007i	−0.499984	+	1.53879i
$970$	4.33487	−	13.3414i	0.139184	−	0.428365i
$971$	10.4141	+	7.56628i	0.334204	+	0.242813i	0.742212	−	0.670165i	$-0.233777\pi$
$971$	10.4141	+	7.56628i	0.334204	+	0.242813i	−0.408008	+	0.912978i	$0.633777\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	20.6917	+	15.0334i	0.663345	+	0.481948i
$974$	4.75011	−	3.45115i	0.152203	−	0.110582i
$975$	−1.92548	+	5.92602i	−0.0616647	+	0.189785i
$976$	−9.10533	+	6.61541i	−0.291454	+	0.211754i
$977$	−8.67888	+	6.30557i	−0.277662	+	0.201733i	−0.717897	−	0.696149i	$-0.754895\pi$
$977$	−8.67888	+	6.30557i	−0.277662	+	0.201733i	0.440235	+	0.897883i	$0.354895\pi$
$978$	1.30056	−	4.00271i	0.0415873	−	0.127993i
$979$	15.7912	−	11.4730i	0.504689	−	0.366678i
$980$	−3.68841	−	2.67979i	−0.117822	−	0.0856027i
$981$	4.54254	+	13.9805i	0.145032	+	0.446363i
$982$	2.75509	+	2.00169i	0.0879184	+	0.0638764i
$983$	7.95923	−	24.4960i	0.253860	−	0.781301i	−0.740192	−	0.672395i	$-0.765265\pi$
$983$	7.95923	−	24.4960i	0.253860	−	0.781301i	0.994052	−	0.108905i	$-0.0347345\pi$
$984$	0.195142	−	0.600586i	0.00622091	−	0.0191460i
$985$	7.02740	+	21.6281i	0.223912	+	0.689129i
$986$	−53.5677			−1.70594
$987$	13.4693			0.428731
$988$	−13.5958	−	41.8435i	−0.432539	−	1.33122i
$989$	10.4567	−	7.59724i	0.332504	−	0.241578i
$990$	2.47631	+	1.79914i	0.0787022	+	0.0571805i
$991$	37.5355			1.19235			0.596177	−	0.802853i	$-0.296686\pi$
$991$	37.5355			1.19235			0.596177	+	0.802853i	$0.296686\pi$
$992$	5.34781	−	1.54950i	0.169793	−	0.0491968i
$993$	−19.5630			−0.620814
$994$	−4.78000	−	3.47288i	−0.151613	−	0.110153i
$995$	5.99062	−	4.35244i	0.189915	−	0.137982i
$996$	1.01380	+	3.12015i	0.0321234	+	0.0988658i
$997$	22.3831			0.708880			0.354440	−	0.935079i	$-0.384671\pi$
$997$	22.3831			0.708880			0.354440	+	0.935079i	$0.384671\pi$
$998$	34.0782			1.07873
$999$	0.0450850	+	0.138757i	0.00142643	+	0.00439009i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.d.481.1	✓	12	31.16	even	5	inner
930.2.n.d.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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-0.482786 - 1.48586i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(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} +(-0.482786 - 1.48586i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.945865 + 2.91107i) q^{11} +(0.809017 + 0.587785i) q^{12} +(-5.04097 + 3.66248i) q^{13} +(-0.482786 + 1.48586i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.20421 + 6.78386i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(5.71245 + 4.15034i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(-1.26395 - 0.918314i) q^{21} +(0.945865 - 2.91107i) q^{22} +(0.457949 - 1.40942i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +6.23099 q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.26395 - 0.918314i) q^{28} +(-6.07561 - 4.41419i) q^{29} +1.00000 q^{30} +(5.34781 - 1.54950i) q^{31} +1.00000 q^{32} +(2.47631 + 1.79914i) q^{33} +(5.77070 - 4.19266i) q^{34} +(0.482786 + 1.48586i) q^{35} +1.00000 q^{36} -0.145898 q^{37} +(-2.18196 - 6.71539i) q^{38} +(-1.92548 + 5.92602i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(0.510889 + 0.371183i) q^{41} +(0.482786 + 1.48586i) q^{42} +(7.05602 + 5.12650i) q^{43} +(-2.47631 + 1.79914i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-1.19893 + 0.871071i) q^{46} +(-6.97476 + 5.06746i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(3.68841 - 2.67979i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(2.20421 + 6.78386i) q^{51} +(-5.04097 - 3.66248i) q^{52} +(-3.67237 + 11.3024i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-0.945865 - 2.91107i) q^{55} -1.56233 q^{56} +7.06098 q^{57} +(2.32067 + 7.14230i) q^{58} +(-2.94172 + 2.13729i) q^{59} +(-0.809017 - 0.587785i) q^{60} +11.2548 q^{61} +(-5.23724 - 1.88979i) q^{62} -1.56233 q^{63} +(-0.809017 - 0.587785i) q^{64} +(5.04097 - 3.66248i) q^{65} +(-0.945865 - 2.91107i) q^{66} -6.16263 q^{67} -7.13298 q^{68} +(-0.457949 - 1.40942i) q^{69} +(0.482786 - 1.48586i) q^{70} +(-1.16864 + 3.59670i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(4.45246 + 13.7033i) q^{73} +(0.118034 + 0.0857567i) q^{74} +(0.809017 - 0.587785i) q^{75} +(-2.18196 + 6.71539i) q^{76} +(3.86881 - 2.81085i) q^{77} +(5.04097 - 3.66248i) q^{78} +(1.21142 - 3.72835i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.195142 - 0.600586i) q^{82} +(2.65416 + 1.92836i) q^{83} +(0.482786 - 1.48586i) q^{84} +(2.20421 - 6.78386i) q^{85} +(-2.69516 - 8.29485i) q^{86} -7.50986 q^{87} +3.06088 q^{88} +(-1.97058 - 6.06481i) q^{89} +(0.809017 - 0.587785i) q^{90} +(7.87566 + 5.72200i) q^{91} +1.48195 q^{92} +(3.41569 - 4.39694i) q^{93} +8.62127 q^{94} +(-5.71245 - 4.15034i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-4.33487 - 13.3414i) q^{97} -4.55913 q^{98} +3.06088 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	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 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 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

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