LMFDB - Embedded newform 630.2.t.b.551.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.5
Character	$\chi$	$=$	630.551
Dual form			630.2.t.b.311.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.16177 - 1.28464i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.363801 + 1.69341i) q^{6} +(-1.57438 + 2.12634i) q^{7} +1.00000i q^{8} +(-0.300592 - 2.98490i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.16177 - 1.28464i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.363801 + 1.69341i) q^{6} +(-1.57438 + 2.12634i) q^{7} +1.00000i q^{8} +(-0.300592 - 2.98490i) q^{9} +(0.866025 - 0.500000i) q^{10} +5.66323i q^{11} +(-0.531646 - 1.64844i) q^{12} +(2.43404 - 1.40529i) q^{13} +(0.300277 - 2.62866i) q^{14} +(-1.16177 + 1.28464i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.51050 + 6.08036i) q^{17} +(1.75277 + 2.43471i) q^{18} +(3.76339 + 2.17279i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.902526 + 4.49282i) q^{21} +(-2.83161 - 4.90450i) q^{22} -4.07471i q^{23} +(1.28464 + 1.16177i) q^{24} +1.00000 q^{25} +(-1.40529 + 2.43404i) q^{26} +(-4.18374 - 3.08161i) q^{27} +(1.05428 + 2.42662i) q^{28} +(5.28540 + 3.05152i) q^{29} +(0.363801 - 1.69341i) q^{30} +(0.319228 + 0.184307i) q^{31} +(0.866025 + 0.500000i) q^{32} +(7.27520 + 6.57936i) q^{33} +(-6.08036 - 3.51050i) q^{34} +(1.57438 - 2.12634i) q^{35} +(-2.73530 - 1.23213i) q^{36} +(0.783876 - 1.35771i) q^{37} -4.34559 q^{38} +(1.02249 - 4.75948i) q^{39} -1.00000i q^{40} +(1.39596 + 2.41787i) q^{41} +(-3.02802 - 3.43963i) q^{42} +(3.18170 - 5.51086i) q^{43} +(4.90450 + 2.83161i) q^{44} +(0.300592 + 2.98490i) q^{45} +(2.03736 + 3.52880i) q^{46} +(-2.59337 - 4.49185i) q^{47} +(-1.69341 - 0.363801i) q^{48} +(-2.04268 - 6.69533i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(11.8894 + 2.55424i) q^{51} -2.81058i q^{52} +(-3.02705 + 1.74767i) q^{53} +(5.16403 + 0.576883i) q^{54} -5.66323i q^{55} +(-2.12634 - 1.57438i) q^{56} +(7.16344 - 2.31031i) q^{57} -6.10305 q^{58} +(-5.32873 + 9.22962i) q^{59} +(0.531646 + 1.64844i) q^{60} +(12.6860 - 7.32427i) q^{61} -0.368613 q^{62} +(6.82018 + 4.06020i) q^{63} -1.00000 q^{64} +(-2.43404 + 1.40529i) q^{65} +(-9.59019 - 2.06029i) q^{66} +(-1.36579 + 2.36562i) q^{67} +7.02099 q^{68} +(-5.23453 - 4.73387i) q^{69} +(-0.300277 + 2.62866i) q^{70} +9.06430i q^{71} +(2.98490 - 0.300592i) q^{72} +(-14.3736 + 8.29858i) q^{73} +1.56775i q^{74} +(1.16177 - 1.28464i) q^{75} +(3.76339 - 2.17279i) q^{76} +(-12.0420 - 8.91605i) q^{77} +(1.49423 + 4.63307i) q^{78} +(4.37159 + 7.57182i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-8.81929 + 1.79448i) q^{81} +(-2.41787 - 1.39596i) q^{82} +(-8.34157 + 14.4480i) q^{83} +(4.34216 + 1.46480i) q^{84} +(-3.51050 - 6.08036i) q^{85} +6.36340i q^{86} +(10.0605 - 3.24466i) q^{87} -5.66323 q^{88} +(-0.332109 + 0.575230i) q^{89} +(-1.75277 - 2.43471i) q^{90} +(-0.843953 + 7.38805i) q^{91} +(-3.52880 - 2.03736i) q^{92} +(0.607637 - 0.195972i) q^{93} +(4.49185 + 2.59337i) q^{94} +(-3.76339 - 2.17279i) q^{95} +(1.64844 - 0.531646i) q^{96} +(1.68214 + 0.971182i) q^{97} +(5.11668 + 4.77698i) q^{98} +(16.9042 - 1.70232i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.16177	−	1.28464i	0.670747	−	0.741686i
$3$	1.16177	−	1.28464i	0.670747	−	0.741686i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.363801	+	1.69341i	−0.148521	+	0.691333i
$7$	−1.57438	+	2.12634i	−0.595058	+	0.803683i
$7$	−1.57438	+	2.12634i	−0.595058	+	0.803683i
$8$			1.00000i			0.353553i
$9$	−0.300592	−	2.98490i	−0.100197	−	0.994968i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$			5.66323i			1.70753i	0.520660	+	0.853764i	$0.325686\pi$
$11$			5.66323i			1.70753i	−0.520660	+	0.853764i	$0.674314\pi$
$12$	−0.531646	−	1.64844i	−0.153473	−	0.475863i
$13$	2.43404	−	1.40529i	0.675080	−	0.389758i	−0.122919	−	0.992417i	$-0.539225\pi$
$13$	2.43404	−	1.40529i	0.675080	−	0.389758i	0.797999	+	0.602659i	$0.205892\pi$
$14$	0.300277	−	2.62866i	0.0802524	−	0.702538i
$15$	−1.16177	+	1.28464i	−0.299967	+	0.331692i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.51050	+	6.08036i	0.851420	+	1.47470i	0.879927	+	0.475109i	$0.157591\pi$
$17$	3.51050	+	6.08036i	0.851420	+	1.47470i	−0.0285066	+	0.999594i	$0.509075\pi$
$18$	1.75277	+	2.43471i	0.413132	+	0.573866i
$19$	3.76339	+	2.17279i	0.863381	+	0.498473i	0.865143	−	0.501525i	$-0.167228\pi$
$19$	3.76339	+	2.17279i	0.863381	+	0.498473i	−0.00176228	+	0.999998i	$0.500561\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.902526	+	4.49282i	0.196947	+	0.980414i
$22$	−2.83161	−	4.90450i	−0.603702	−	1.04564i
$23$		−	4.07471i		−	0.849636i	−0.905279	−	0.424818i	$-0.860338\pi$
$23$		−	4.07471i		−	0.849636i	0.905279	−	0.424818i	$-0.139662\pi$
$24$	1.28464	+	1.16177i	0.262226	+	0.237145i
$25$	1.00000			0.200000
$26$	−1.40529	+	2.43404i	−0.275600	+	0.477354i
$27$	−4.18374	−	3.08161i	−0.805161	−	0.593056i
$28$	1.05428	+	2.42662i	0.199240	+	0.458588i
$29$	5.28540	+	3.05152i	0.981473	+	0.566654i	0.902715	−	0.430240i	$-0.141571\pi$
$29$	5.28540	+	3.05152i	0.981473	+	0.566654i	0.0787587	+	0.996894i	$0.474904\pi$
$30$	0.363801	−	1.69341i	0.0664207	−	0.309174i
$31$	0.319228	+	0.184307i	0.0573351	+	0.0331024i	0.528394	−	0.849000i	$-0.322795\pi$
$31$	0.319228	+	0.184307i	0.0573351	+	0.0331024i	−0.471058	+	0.882102i	$0.656128\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	7.27520	+	6.57936i	1.26645	+	1.14532i
$34$	−6.08036	−	3.51050i	−1.04277	−	0.602045i
$35$	1.57438	−	2.12634i	0.266118	−	0.359418i
$36$	−2.73530	−	1.23213i	−0.455883	−	0.205355i
$37$	0.783876	−	1.35771i	0.128868	−	0.223207i	−0.794370	−	0.607434i	$-0.792199\pi$
$37$	0.783876	−	1.35771i	0.128868	−	0.223207i	0.923238	+	0.384227i	$0.125532\pi$
$38$	−4.34559			−0.704947
$39$	1.02249	−	4.75948i	0.163730	−	0.762126i
$40$		−	1.00000i		−	0.158114i
$41$	1.39596	+	2.41787i	0.218012	+	0.377609i	0.954200	−	0.299169i	$-0.0967093\pi$
$41$	1.39596	+	2.41787i	0.218012	+	0.377609i	−0.736188	+	0.676777i	$0.763376\pi$
$42$	−3.02802	−	3.43963i	−0.467234	−	0.530747i
$43$	3.18170	−	5.51086i	0.485204	−	0.840399i	−0.514651	−	0.857400i	$-0.672079\pi$
$43$	3.18170	−	5.51086i	0.485204	−	0.840399i	0.999855	+	0.0170011i	$0.00541188\pi$
$44$	4.90450	+	2.83161i	0.739381	+	0.426882i
$45$	0.300592	+	2.98490i	0.0448097	+	0.444963i
$46$	2.03736	+	3.52880i	0.300392	+	0.520294i
$47$	−2.59337	−	4.49185i	−0.378282	−	0.655204i	0.612530	−	0.790447i	$-0.290152\pi$
$47$	−2.59337	−	4.49185i	−0.378282	−	0.655204i	−0.990812	+	0.135243i	$0.956818\pi$
$48$	−1.69341	−	0.363801i	−0.244423	−	0.0525101i
$49$	−2.04268	−	6.69533i	−0.291812	−	0.956476i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	11.8894	+	2.55424i	1.66485	+	0.357666i
$52$		−	2.81058i		−	0.389758i
$53$	−3.02705	+	1.74767i	−0.415797	+	0.240060i	−0.693277	−	0.720671i	$-0.743834\pi$
$53$	−3.02705	+	1.74767i	−0.415797	+	0.240060i	0.277481	+	0.960731i	$0.410501\pi$
$54$	5.16403	+	0.576883i	0.702735	+	0.0785038i
$55$		−	5.66323i		−	0.763630i
$56$	−2.12634	−	1.57438i	−0.284145	−	0.210385i
$57$	7.16344	−	2.31031i	0.948820	−	0.306008i
$58$	−6.10305			−0.801370
$59$	−5.32873	+	9.22962i	−0.693741	+	1.20159i	0.276862	+	0.960910i	$0.410705\pi$
$59$	−5.32873	+	9.22962i	−0.693741	+	1.20159i	−0.970603	+	0.240685i	$0.922628\pi$
$60$	0.531646	+	1.64844i	0.0686352	+	0.212813i
$61$	12.6860	−	7.32427i	1.62428	−	0.937777i	0.638519	−	0.769606i	$-0.279547\pi$
$61$	12.6860	−	7.32427i	1.62428	−	0.937777i	0.985758	−	0.168171i	$-0.0537861\pi$
$62$	−0.368613			−0.0468139
$63$	6.82018	+	4.06020i	0.859262	+	0.511537i
$64$	−1.00000			−0.125000
$65$	−2.43404	+	1.40529i	−0.301905	+	0.174305i
$66$	−9.59019	−	2.06029i	−1.18047	−	0.253604i
$67$	−1.36579	+	2.36562i	−0.166858	+	0.289007i	−0.937314	−	0.348487i	$-0.886696\pi$
$67$	−1.36579	+	2.36562i	−0.166858	+	0.289007i	0.770455	+	0.637494i	$0.220029\pi$
$68$	7.02099			0.851420
$69$	−5.23453	−	4.73387i	−0.630164	−	0.569891i
$70$	−0.300277	+	2.62866i	−0.0358900	+	0.314185i
$71$			9.06430i			1.07573i	0.843030	+	0.537867i	$0.180770\pi$
$71$			9.06430i			1.07573i	−0.843030	+	0.537867i	$0.819230\pi$
$72$	2.98490	−	0.300592i	0.351774	−	0.0354252i
$73$	−14.3736	+	8.29858i	−1.68230	+	0.971275i	−0.722169	+	0.691716i	$0.756855\pi$
$73$	−14.3736	+	8.29858i	−1.68230	+	0.971275i	−0.960129	+	0.279559i	$0.909812\pi$
$74$			1.56775i			0.182248i
$75$	1.16177	−	1.28464i	0.134149	−	0.148337i
$76$	3.76339	−	2.17279i	0.431690	−	0.249237i
$77$	−12.0420	−	8.91605i	−1.37231	−	1.01608i
$78$	1.49423	+	4.63307i	0.169189	+	0.524592i
$79$	4.37159	+	7.57182i	0.491842	+	0.851896i	0.999956	−	0.00939423i	$-0.00299032\pi$
$79$	4.37159	+	7.57182i	0.491842	+	0.851896i	−0.508114	+	0.861290i	$0.669657\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−8.81929	+	1.79448i	−0.979921	+	0.199386i
$82$	−2.41787	−	1.39596i	−0.267010	−	0.154158i
$83$	−8.34157	+	14.4480i	−0.915606	+	1.58588i	−0.109595	+	0.993976i	$0.534956\pi$
$83$	−8.34157	+	14.4480i	−0.915606	+	1.58588i	−0.806011	+	0.591901i	$0.798378\pi$
$84$	4.34216	+	1.46480i	0.473769	+	0.159823i
$85$	−3.51050	−	6.08036i	−0.380767	−	0.659507i
$86$			6.36340i			0.686183i
$87$	10.0605	−	3.24466i	1.07860	−	0.347864i
$88$	−5.66323			−0.603702
$89$	−0.332109	+	0.575230i	−0.0352035	+	0.0609742i	−0.883090	−	0.469203i	$-0.844541\pi$
$89$	−0.332109	+	0.575230i	−0.0352035	+	0.0609742i	0.847887	+	0.530177i	$0.177875\pi$
$90$	−1.75277	−	2.43471i	−0.184758	−	0.256640i
$91$	−0.843953	+	7.38805i	−0.0884703	+	0.774479i
$92$	−3.52880	−	2.03736i	−0.367903	−	0.212409i
$93$	0.607637	−	0.195972i	0.0630090	−	0.0203213i
$94$	4.49185	+	2.59337i	0.463299	+	0.267486i
$95$	−3.76339	−	2.17279i	−0.386116	−	0.222924i
$96$	1.64844	−	0.531646i	0.168243	−	0.0542609i
$97$	1.68214	+	0.971182i	0.170795	+	0.0986085i	0.582961	−	0.812500i	$-0.301894\pi$
$97$	1.68214	+	0.971182i	0.170795	+	0.0986085i	−0.412166	+	0.911109i	$0.635227\pi$
$98$	5.11668	+	4.77698i	0.516863	+	0.482548i
$99$	16.9042	−	1.70232i	1.69893	−	0.171090i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	6.28513			0.625393			0.312697	−	0.949853i	$-0.398768\pi$
$101$	6.28513			0.625393			0.312697	+	0.949853i	$0.398768\pi$
$102$	−11.5737	+	3.73268i	−1.14596	+	0.369590i
$103$		−	5.60402i		−	0.552181i	−0.961132	−	0.276090i	$-0.910961\pi$
$103$		−	5.60402i		−	0.552181i	0.961132	−	0.276090i	$-0.0890389\pi$
$104$	1.40529	+	2.43404i	0.137800	+	0.238677i
$105$	−0.902526	−	4.49282i	−0.0880775	−	0.438455i
$106$	1.74767	−	3.02705i	0.169748	−	0.294013i
$107$	−1.38444	−	0.799307i	−0.133839	−	0.0772720i	0.431586	−	0.902072i	$-0.357954\pi$
$107$	−1.38444	−	0.799307i	−0.133839	−	0.0772720i	−0.565425	+	0.824800i	$0.691288\pi$
$108$	−4.76062	+	2.08242i	−0.458091	+	0.200381i
$109$	2.63446	+	4.56303i	0.252336	+	0.437059i	0.964169	−	0.265290i	$-0.0854679\pi$
$109$	2.63446	+	4.56303i	0.252336	+	0.437059i	−0.711833	+	0.702349i	$0.752135\pi$
$110$	2.83161	+	4.90450i	0.269984	+	0.467626i
$111$	−0.833489	−	2.58435i	−0.0791113	−	0.245295i
$112$	2.62866	+	0.300277i	0.248385	+	0.0283735i
$113$	13.0916	−	7.55846i	1.23156	−	0.711040i	0.264203	−	0.964467i	$-0.414891\pi$
$113$	13.0916	−	7.55846i	1.23156	−	0.711040i	0.967355	+	0.253427i	$0.0815576\pi$
$114$	−5.04856	+	5.58251i	−0.472841	+	0.522850i
$115$			4.07471i			0.379969i
$116$	5.28540	−	3.05152i	0.490737	−	0.283327i
$117$	−4.92631	−	6.84294i	−0.455437	−	0.632630i
$118$		−	10.6575i		−	0.981098i
$119$	−18.4558	−	2.10824i	−1.69184	−	0.193262i
$120$	−1.28464	−	1.16177i	−0.117271	−	0.106054i
$121$	−21.0722			−1.91565
$122$	−7.32427	+	12.6860i	−0.663108	+	1.14854i
$123$	4.72788	+	1.01570i	0.426298	+	0.0915829i
$124$	0.319228	−	0.184307i	0.0286676	−	0.0165512i
$125$	−1.00000			−0.0894427
$126$	−7.93654	−	0.106144i	−0.707044	−	0.00945602i
$127$	−4.63451			−0.411247			−0.205623	−	0.978631i	$-0.565922\pi$
$127$	−4.63451			−0.411247			−0.205623	+	0.978631i	$0.565922\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.38307	−	10.4897i	−0.297863	−	0.923564i
$130$	1.40529	−	2.43404i	0.123252	−	0.213479i
$131$	−3.71505			−0.324585			−0.162293	−	0.986743i	$-0.551889\pi$
$131$	−3.71505			−0.324585			−0.162293	+	0.986743i	$0.551889\pi$
$132$	9.33549	−	3.01083i	0.812550	−	0.262059i
$133$	−10.5451	+	4.58147i	−0.914376	+	0.397264i
$134$		−	2.73159i		−	0.235973i
$135$	4.18374	+	3.08161i	0.360079	+	0.265223i
$136$	−6.08036	+	3.51050i	−0.521386	+	0.301022i
$137$		−	21.0639i		−	1.79961i	−0.436294	−	0.899804i	$-0.643709\pi$
$137$		−	21.0639i		−	1.79961i	0.436294	−	0.899804i	$-0.356291\pi$
$138$	6.90017	+	1.48238i	0.587382	+	0.126189i
$139$	−7.81740	+	4.51338i	−0.663063	+	0.382820i	−0.793443	−	0.608645i	$-0.791714\pi$
$139$	−7.81740	+	4.51338i	−0.663063	+	0.382820i	0.130380	+	0.991464i	$0.458380\pi$
$140$	−1.05428	−	2.42662i	−0.0891030	−	0.205087i
$141$	−8.78330	−	1.88694i	−0.739688	−	0.158909i
$142$	−4.53215	−	7.84991i	−0.380329	−	0.658750i
$143$	7.95849	+	13.7845i	0.665522	+	1.15272i
$144$	−2.43471	+	1.75277i	−0.202892	+	0.146064i
$145$	−5.28540	−	3.05152i	−0.438928	−	0.253415i
$146$	8.29858	−	14.3736i	0.686795	−	1.18956i
$147$	−10.9742	−	5.15431i	−0.905137	−	0.425120i
$148$	−0.783876	−	1.35771i	−0.0644342	−	0.111603i
$149$		−	8.86835i		−	0.726524i	−0.931687	−	0.363262i	$-0.881663\pi$
$149$		−	8.86835i		−	0.726524i	0.931687	−	0.363262i	$-0.118337\pi$
$150$	−0.363801	+	1.69341i	−0.0297042	+	0.138267i
$151$	13.4954			1.09824			0.549122	−	0.835742i	$-0.314962\pi$
$151$	13.4954			1.09824			0.549122	+	0.835742i	$0.314962\pi$
$152$	−2.17279	+	3.76339i	−0.176237	+	0.305251i
$153$	17.0940	−	12.3062i	1.38197	−	0.994897i
$154$	14.8867	+	1.70054i	1.19960	+	0.137033i
$155$	−0.319228	−	0.184307i	−0.0256410	−	0.0148039i
$156$	−3.61058	−	3.26524i	−0.289078	−	0.261429i
$157$	−2.88573	−	1.66608i	−0.230306	−	0.132967i	0.380407	−	0.924819i	$-0.375784\pi$
$157$	−2.88573	−	1.66608i	−0.230306	−	0.132967i	−0.610713	+	0.791852i	$0.709117\pi$
$158$	−7.57182	−	4.37159i	−0.602381	−	0.347785i
$159$	−1.27161	+	5.91904i	−0.100845	+	0.469411i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	8.66424	+	6.41513i	0.682838	+	0.505583i
$162$	6.74049	−	5.96371i	0.529583	−	0.468553i
$163$	7.01305	−	12.1470i	0.549304	−	0.951423i	−0.449018	−	0.893523i	$-0.648226\pi$
$163$	7.01305	−	12.1470i	0.549304	−	0.951423i	0.998322	−	0.0579002i	$-0.0184405\pi$
$164$	2.79192			0.218012
$165$	−7.27520	−	6.57936i	−0.566374	−	0.512202i
$166$		−	16.6831i		−	1.29486i
$167$	−9.43447	−	16.3410i	−0.730061	−	1.26450i	−0.956857	−	0.290560i	$-0.906158\pi$
$167$	−9.43447	−	16.3410i	−0.730061	−	1.26450i	0.226796	−	0.973942i	$-0.427175\pi$
$168$	−4.49282	+	0.902526i	−0.346629	+	0.0696314i
$169$	−2.55031	+	4.41727i	−0.196178	+	0.339790i
$170$	6.08036	+	3.51050i	0.466342	+	0.269243i
$171$	5.35433	−	11.8865i	0.409456	−	0.908981i
$172$	−3.18170	−	5.51086i	−0.242602	−	0.420199i
$173$	−4.54360	−	7.86975i	−0.345444	−	0.598326i	0.639991	−	0.768383i	$-0.278938\pi$
$173$	−4.54360	−	7.86975i	−0.345444	−	0.598326i	−0.985434	+	0.170057i	$0.945605\pi$
$174$	−7.09032	+	7.84021i	−0.537516	+	0.594365i
$175$	−1.57438	+	2.12634i	−0.119012	+	0.160737i
$176$	4.90450	−	2.83161i	0.369691	−	0.213441i
$177$	5.66599	+	17.5682i	0.425882	+	1.32050i
$178$		−	0.664218i		−	0.0497853i
$179$	12.1711	−	7.02701i	0.909714	−	0.525224i	0.0293749	−	0.999568i	$-0.490648\pi$
$179$	12.1711	−	7.02701i	0.909714	−	0.525224i	0.880339	+	0.474345i	$0.157315\pi$
$180$	2.73530	+	1.23213i	0.203877	+	0.0918376i
$181$		−	3.34540i		−	0.248662i	−0.992241	−	0.124331i	$-0.960322\pi$
$181$		−	3.34540i		−	0.248662i	0.992241	−	0.124331i	$-0.0396784\pi$
$182$	−2.96314	−	6.82022i	−0.219643	−	0.505548i
$183$	5.32915	−	24.8060i	0.393942	−	1.83372i
$184$	4.07471			0.300392
$185$	−0.783876	+	1.35771i	−0.0576317	+	0.0998211i
$186$	−0.428243	+	0.473535i	−0.0314003	+	0.0347213i
$187$	−34.4345	+	19.8807i	−2.51810	+	1.45382i
$188$	−5.18675			−0.378282
$189$	13.1393	−	4.04446i	0.955747	−	0.294191i
$190$	4.34559			0.315262
$191$	5.35829	−	3.09361i	0.387713	−	0.223846i	−0.293456	−	0.955973i	$-0.594805\pi$
$191$	5.35829	−	3.09361i	0.387713	−	0.223846i	0.681169	+	0.732127i	$0.261472\pi$
$192$	−1.16177	+	1.28464i	−0.0838433	+	0.0927108i
$193$	−1.04267	+	1.80595i	−0.0750528	+	0.129995i	−0.901109	−	0.433592i	$-0.857246\pi$
$193$	−1.04267	+	1.80595i	−0.0750528	+	0.129995i	0.826056	+	0.563587i	$0.190579\pi$
$194$	−1.94236			−0.139454
$195$	−1.02249	+	4.75948i	−0.0732222	+	0.340833i
$196$	−6.81967	−	1.57865i	−0.487119	−	0.112761i
$197$		−	24.7197i		−	1.76121i	−0.473853	−	0.880604i	$-0.657137\pi$
$197$		−	24.7197i		−	1.76121i	0.473853	−	0.880604i	$-0.342863\pi$
$198$	−13.7883	+	9.92635i	−0.979891	+	0.705435i
$199$	5.60009	−	3.23321i	0.396980	−	0.229196i	−0.288200	−	0.957570i	$-0.593057\pi$
$199$	5.60009	−	3.23321i	0.396980	−	0.229196i	0.685180	+	0.728374i	$0.259724\pi$
$200$			1.00000i			0.0707107i
$201$	1.45224	+	4.50286i	0.102433	+	0.317607i
$202$	−5.44308	+	3.14256i	−0.382974	+	0.221110i
$203$	−14.8098	+	6.43433i	−1.03944	+	0.451601i
$204$	8.15676	−	9.01943i	0.571087	−	0.631487i
$205$	−1.39596	−	2.41787i	−0.0974981	−	0.168872i
$206$	2.80201	+	4.85323i	0.195225	+	0.338140i
$207$	−12.1626	+	1.22483i	−0.845361	+	0.0851314i
$208$	−2.43404	−	1.40529i	−0.168770	−	0.0974394i
$209$	−12.3050	+	21.3129i	−0.851157	+	1.47425i
$210$	3.02802	+	3.43963i	0.208953	+	0.237357i
$211$	0.607035	+	1.05142i	0.0417900	+	0.0723824i	0.886164	−	0.463372i	$-0.153361\pi$
$211$	0.607035	+	1.05142i	0.0417900	+	0.0723824i	−0.844374	+	0.535754i	$0.820027\pi$
$212$			3.49533i			0.240060i
$213$	11.6443	+	10.5306i	0.797857	+	0.721545i
$214$	1.59861			0.109279
$215$	−3.18170	+	5.51086i	−0.216990	+	0.375838i
$216$	3.08161	−	4.18374i	0.209677	−	0.284667i
$217$	−0.894485	+	0.388622i	−0.0607216	+	0.0263814i
$218$	−4.56303	−	2.63446i	−0.309047	−	0.178428i
$219$	−6.03806	+	28.1058i	−0.408014	+	1.89922i
$220$	−4.90450	−	2.83161i	−0.330661	−	0.190907i
$221$	17.0893	+	9.86653i	1.14955	+	0.663695i
$222$	2.01400	+	1.82136i	0.135171	+	0.122242i
$223$	1.79024	+	1.03360i	0.119884	+	0.0692148i	0.558743	−	0.829341i	$-0.311284\pi$
$223$	1.79024	+	1.03360i	0.119884	+	0.0692148i	−0.438859	+	0.898556i	$0.644617\pi$
$224$	−2.42662	+	1.05428i	−0.162135	+	0.0704421i
$225$	−0.300592	−	2.98490i	−0.0200395	−	0.198994i
$226$	−7.55846	+	13.0916i	−0.502781	+	0.870843i
$227$	−19.5582			−1.29813			−0.649063	−	0.760735i	$-0.724839\pi$
$227$	−19.5582			−1.29813			−0.649063	+	0.760735i	$0.724839\pi$
$228$	1.58093	−	7.35888i	0.104700	−	0.487353i
$229$		−	13.3285i		−	0.880775i	−0.897808	−	0.440388i	$-0.854841\pi$
$229$		−	13.3285i		−	0.880775i	0.897808	−	0.440388i	$-0.145159\pi$
$230$	−2.03736	−	3.52880i	−0.134339	−	0.232682i
$231$	−25.4439	+	5.11121i	−1.67408	+	0.336293i
$232$	−3.05152	+	5.28540i	−0.200342	+	0.347003i
$233$	−15.4047	−	8.89393i	−1.00920	−	0.582661i	−0.0982415	−	0.995163i	$-0.531322\pi$
$233$	−15.4047	−	8.89393i	−1.00920	−	0.582661i	−0.910957	+	0.412502i	$0.864655\pi$
$234$	7.68778	+	3.46300i	0.502566	+	0.226384i
$235$	2.59337	+	4.49185i	0.169173	+	0.293016i
$236$	5.32873	+	9.22962i	0.346871	+	0.600797i
$237$	14.8058	+	3.18078i	0.961741	+	0.206614i
$238$	17.0373	−	7.40209i	1.10436	−	0.479806i
$239$	−3.40145	+	1.96383i	−0.220021	+	0.127029i	−0.605960	−	0.795495i	$-0.707211\pi$
$239$	−3.40145	+	1.96383i	−0.220021	+	0.127029i	0.385939	+	0.922524i	$0.373878\pi$
$240$	1.69341	+	0.363801i	0.109309	+	0.0234832i
$241$		−	11.1448i		−	0.717903i	−0.933356	−	0.358951i	$-0.883134\pi$
$241$		−	11.1448i		−	0.717903i	0.933356	−	0.358951i	$-0.116866\pi$
$242$	18.2490	−	10.5361i	1.17309	−	0.677285i
$243$	−7.94071	+	13.4144i	−0.509397	+	0.860532i
$244$		−	14.6485i		−	0.937777i
$245$	2.04268	+	6.69533i	0.130502	+	0.427749i
$246$	−4.60231	+	1.48431i	−0.293433	+	0.0946363i
$247$	12.2136			0.777135
$248$	−0.184307	+	0.319228i	−0.0117035	+	0.0202710i
$249$	8.86952	+	27.5012i	0.562083	+	1.74281i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	−20.9221			−1.32059			−0.660295	−	0.751006i	$-0.729569\pi$
$251$	−20.9221			−1.32059			−0.660295	+	0.751006i	$0.729569\pi$
$252$	6.92632	−	3.87635i	0.436317	−	0.244187i
$253$	23.0760			1.45078
$254$	4.01361	−	2.31726i	0.251836	−	0.145398i
$255$	−11.8894	−	2.55424i	−0.744546	−	0.159953i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	29.1778			1.82006			0.910030	−	0.414541i	$-0.136058\pi$
$257$	29.1778			1.82006			0.910030	+	0.414541i	$0.136058\pi$
$258$	8.17466	+	7.39279i	0.508932	+	0.460255i
$259$	1.65285	+	3.80434i	0.102703	+	0.236390i
$260$			2.81058i			0.174305i
$261$	7.51975	−	16.6937i	0.465461	−	1.03331i
$262$	3.21733	−	1.85752i	0.198767	−	0.114758i
$263$		−	0.627322i		−	0.0386824i	−0.999813	−	0.0193412i	$-0.993843\pi$
$263$		−	0.627322i		−	0.0386824i	0.999813	−	0.0193412i	$-0.00615687\pi$
$264$	−6.57936	+	7.27520i	−0.404931	+	0.447758i
$265$	3.02705	−	1.74767i	0.185950	−	0.107358i
$266$	6.84159	−	9.24022i	0.419485	−	0.566554i
$267$	0.353129	+	1.09492i	0.0216111	+	0.0670082i
$268$	1.36579	+	2.36562i	0.0834291	+	0.144504i
$269$	1.72988	+	2.99624i	0.105472	+	0.182684i	0.913931	−	0.405869i	$-0.133031\pi$
$269$	1.72988	+	2.99624i	0.105472	+	0.182684i	−0.808459	+	0.588553i	$0.799698\pi$
$270$	−5.16403	−	0.576883i	−0.314273	−	0.0351080i
$271$	−3.95501	−	2.28343i	−0.240250	−	0.138708i	0.375042	−	0.927008i	$-0.377628\pi$
$271$	−3.95501	−	2.28343i	−0.240250	−	0.138708i	−0.615292	+	0.788300i	$0.710962\pi$
$272$	3.51050	−	6.08036i	0.212855	−	0.368676i
$273$	8.51050	+	9.66738i	0.515079	+	0.585096i
$274$	10.5319	+	18.2419i	0.636258	+	1.10203i
$275$			5.66323i			0.341506i
$276$	−6.71692	+	2.16630i	−0.404311	+	0.130396i
$277$	30.6143			1.83943			0.919717	−	0.392582i	$-0.128418\pi$
$277$	30.6143			1.83943			0.919717	+	0.392582i	$0.128418\pi$
$278$	4.51338	−	7.81740i	0.270694	−	0.468856i
$279$	0.454180	−	1.00827i	0.0271910	−	0.0603634i
$280$	2.12634	+	1.57438i	0.127073	+	0.0940869i
$281$	8.79291	+	5.07659i	0.524541	+	0.302844i	0.738791	−	0.673935i	$-0.235397\pi$
$281$	8.79291	+	5.07659i	0.524541	+	0.302844i	−0.214250	+	0.976779i	$0.568731\pi$
$282$	8.55004	−	2.75751i	0.509147	−	0.164207i
$283$	7.55807	+	4.36365i	0.449280	+	0.259392i	0.707526	−	0.706687i	$-0.249811\pi$
$283$	7.55807	+	4.36365i	0.449280	+	0.259392i	−0.258246	+	0.966079i	$0.583144\pi$
$284$	7.84991	+	4.53215i	0.465806	+	0.268933i
$285$	−7.16344	+	2.31031i	−0.424325	+	0.136851i
$286$	−13.7845	−	7.95849i	−0.815095	−	0.470595i
$287$	−7.33900	−	0.838350i	−0.433207	−	0.0494862i
$288$	1.23213	−	2.73530i	0.0726040	−	0.161179i
$289$	−16.1472	+	27.9677i	−0.949833	+	1.64516i
$290$	6.10305			0.358383
$291$	3.20187	−	1.03265i	0.187697	−	0.0605350i
$292$			16.5972i			0.971275i
$293$	−8.72722	−	15.1160i	−0.509849	−	0.883085i	−0.999935	−	0.0114108i	$-0.996368\pi$
$293$	−8.72722	−	15.1160i	−0.509849	−	0.883085i	0.490085	−	0.871674i	$-0.336966\pi$
$294$	12.0811	−	1.02334i	0.704584	−	0.0596823i
$295$	5.32873	−	9.22962i	0.310250	−	0.537369i
$296$	1.35771	+	0.783876i	0.0789155	+	0.0455619i
$297$	17.4519	−	23.6935i	1.01266	−	1.37484i
$298$	4.43418	+	7.68022i	0.256865	+	0.444903i
$299$	−5.72616	−	9.91800i	−0.331152	−	0.573572i
$300$	−0.531646	−	1.64844i	−0.0306946	−	0.0951727i
$301$	6.70880	+	15.4416i	0.386689	+	0.890036i
$302$	−11.6874	+	6.74772i	−0.672534	+	0.388288i
$303$	7.30186	−	8.07412i	0.419481	−	0.463846i
$304$		−	4.34559i		−	0.249237i
$305$	−12.6860	+	7.32427i	−0.726399	+	0.419387i
$306$	−8.65078	+	19.2045i	−0.494532	+	1.09785i
$307$		−	3.26532i		−	0.186362i	−0.995649	−	0.0931808i	$-0.970297\pi$
$307$		−	3.26532i		−	0.186362i	0.995649	−	0.0931808i	$-0.0297035\pi$
$308$	−13.7425	+	5.97063i	−0.783052	+	0.340208i
$309$	−7.19914	−	6.51057i	−0.409545	−	0.370373i
$310$	0.368613			0.0209358
$311$	13.2864	−	23.0127i	0.753403	−	1.30493i	−0.192761	−	0.981246i	$-0.561744\pi$
$311$	13.2864	−	23.0127i	0.753403	−	1.30493i	0.946164	−	0.323687i	$-0.104923\pi$
$312$	4.75948	+	1.02249i	0.269452	+	0.0578872i
$313$	4.19978	−	2.42475i	0.237386	−	0.137055i	−0.376589	−	0.926380i	$-0.622903\pi$
$313$	4.19978	−	2.42475i	0.237386	−	0.137055i	0.613975	+	0.789326i	$0.289570\pi$
$314$	3.33216			0.188044
$315$	−6.82018	−	4.06020i	−0.384273	−	0.228766i
$316$	8.74318			0.491842
$317$	−19.6462	+	11.3428i	−1.10344	+	0.637073i	−0.937123	−	0.348999i	$-0.886522\pi$
$317$	−19.6462	+	11.3428i	−1.10344	+	0.637073i	−0.166319	+	0.986072i	$0.553188\pi$
$318$	−1.85828	−	5.76185i	−0.104207	−	0.323108i
$319$	−17.2815	+	29.9324i	−0.967577	+	1.67589i
$320$	1.00000			0.0559017
$321$	−2.63522	+	0.849897i	−0.147084	+	0.0474366i
$322$	−10.7110	−	1.22354i	−0.596902	−	0.0681854i
$323$			30.5103i			1.69764i
$324$	−2.85558	+	8.53497i	−0.158643	+	0.474165i
$325$	2.43404	−	1.40529i	0.135016	−	0.0779515i
$326$			14.0261i			0.776834i
$327$	8.92248	+	1.91684i	0.493414	+	0.106002i
$328$	−2.41787	+	1.39596i	−0.133505	+	0.0770790i
$329$	13.6342	+	1.55746i	0.751676	+	0.0858656i
$330$	9.59019	+	2.06029i	0.527923	+	0.113415i
$331$	5.18322	+	8.97760i	0.284895	+	0.493453i	0.972584	−	0.232553i	$-0.0747078\pi$
$331$	5.18322	+	8.97760i	0.284895	+	0.493453i	−0.687688	+	0.726006i	$0.741374\pi$
$332$	8.34157	+	14.4480i	0.457803	+	0.792938i
$333$	−4.28827	−	1.93168i	−0.234996	−	0.105855i
$334$	16.3410	+	9.43447i	0.894138	+	0.516231i
$335$	1.36579	−	2.36562i	0.0746213	−	0.129248i
$336$	3.43963	−	3.02802i	0.187647	−	0.165192i
$337$	13.0605	+	22.6214i	0.711449	+	1.23227i	0.964313	+	0.264765i	$0.0852942\pi$
$337$	13.0605	+	22.6214i	0.711449	+	1.23227i	−0.252864	+	0.967502i	$0.581372\pi$
$338$		−	5.10063i		−	0.277438i
$339$	5.49955	−	25.5992i	0.298695	−	1.39036i
$340$	−7.02099			−0.380767
$341$	−1.04377	+	1.80786i	−0.0565233	+	0.0979013i
$342$	1.30625	+	12.9712i	0.0706339	+	0.701400i
$343$	17.4525	+	6.19752i	0.942348	+	0.334635i
$344$	5.51086	+	3.18170i	0.297126	+	0.171546i
$345$	5.23453	+	4.73387i	0.281818	+	0.254863i
$346$	7.86975	+	4.54360i	0.423080	+	0.244266i
$347$	−5.80811	−	3.35332i	−0.311796	−	0.180015i	0.335934	−	0.941886i	$-0.390948\pi$
$347$	−5.80811	−	3.35332i	−0.311796	−	0.180015i	−0.647730	+	0.761870i	$0.724281\pi$
$348$	2.22029	−	10.3350i	0.119020	−	0.554013i
$349$	−18.6240	−	10.7526i	−0.996920	−	0.575572i	−0.0895843	−	0.995979i	$-0.528554\pi$
$349$	−18.6240	−	10.7526i	−0.996920	−	0.575572i	−0.907335	+	0.420407i	$0.861887\pi$
$350$	0.300277	−	2.62866i	0.0160505	−	0.140508i
$351$	−14.5139	−	1.62138i	−0.774696	−	0.0865427i
$352$	−2.83161	+	4.90450i	−0.150926	+	0.261411i
$353$	7.03656			0.374518			0.187259	−	0.982311i	$-0.440040\pi$
$353$	7.03656			0.374518			0.187259	+	0.982311i	$0.440040\pi$
$354$	−13.6910	−	12.3815i	−0.727667	−	0.658068i
$355$		−	9.06430i		−	0.481083i
$356$	0.332109	+	0.575230i	0.0176017	+	0.0304871i
$357$	−24.1496	+	21.2597i	−1.27813	+	1.12518i
$358$	−7.02701	+	12.1711i	−0.371389	+	0.643265i
$359$	5.90962	+	3.41192i	0.311898	+	0.180074i	0.647775	−	0.761831i	$-0.275699\pi$
$359$	5.90962	+	3.41192i	0.311898	+	0.180074i	−0.335878	+	0.941906i	$0.609033\pi$
$360$	−2.98490	+	0.300592i	−0.157318	+	0.0158426i
$361$	−0.0579356	−	0.100347i	−0.00304924	−	0.00528144i
$362$	1.67270	+	2.89720i	0.0879152	+	0.152274i
$363$	−24.4810	+	27.0701i	−1.28492	+	1.42081i
$364$	5.97627	+	4.42491i	0.313241	+	0.231928i
$365$	14.3736	−	8.29858i	0.752346	−	0.434367i
$366$	7.78784	+	24.1472i	0.407077	+	1.26220i
$367$			35.3498i			1.84525i	0.385703	+	0.922623i	$0.373959\pi$
$367$			35.3498i			1.84525i	−0.385703	+	0.922623i	$0.626041\pi$
$368$	−3.52880	+	2.03736i	−0.183952	+	0.106205i
$369$	6.79750	−	4.89360i	0.353864	−	0.254751i
$370$		−	1.56775i		−	0.0815036i
$371$	1.04957	−	9.18803i	0.0544909	−	0.477019i
$372$	0.134102	−	0.624215i	0.00695286	−	0.0323640i
$373$	−17.4842			−0.905300			−0.452650	−	0.891688i	$-0.649521\pi$
$373$	−17.4842			−0.905300			−0.452650	+	0.891688i	$0.649521\pi$
$374$	19.8807	−	34.4345i	1.02801	−	1.78056i
$375$	−1.16177	+	1.28464i	−0.0599934	+	0.0663384i
$376$	4.49185	−	2.59337i	0.231650	−	0.133743i
$377$	17.1531			0.883431
$378$	−9.35678	+	10.0723i	−0.481261	+	0.518062i
$379$	−11.0373			−0.566948			−0.283474	−	0.958980i	$-0.591487\pi$
$379$	−11.0373			−0.566948			−0.283474	+	0.958980i	$0.591487\pi$
$380$	−3.76339	+	2.17279i	−0.193058	+	0.111462i
$381$	−5.38423	+	5.95368i	−0.275842	+	0.305016i
$382$	−3.09361	+	5.35829i	−0.158283	+	0.274154i
$383$	27.9589			1.42864			0.714318	−	0.699822i	$-0.246737\pi$
$383$	27.9589			1.42864			0.714318	+	0.699822i	$0.246737\pi$
$384$	0.363801	−	1.69341i	0.0185651	−	0.0864166i
$385$	12.0420	+	8.91605i	0.613716	+	0.454404i
$386$		−	2.08533i		−	0.106141i
$387$	−17.4058	−	7.84053i	−0.884786	−	0.398557i
$388$	1.68214	−	0.971182i	0.0853975	−	0.0493043i
$389$		−	13.7967i		−	0.699523i	−0.936839	−	0.349761i	$-0.886263\pi$
$389$		−	13.7967i		−	0.699523i	0.936839	−	0.349761i	$-0.113737\pi$
$390$	−1.49423	−	4.63307i	−0.0756635	−	0.234605i
$391$	24.7757	−	14.3043i	1.25296	−	0.723398i
$392$	6.69533	−	2.04268i	0.338165	−	0.103171i
$393$	−4.31602	+	4.77249i	−0.217714	+	0.240740i
$394$	12.3599	+	21.4079i	0.622681	+	1.07851i
$395$	−4.37159	−	7.57182i	−0.219959	−	0.380979i
$396$	6.97784	−	15.4906i	0.350650	−	0.778433i
$397$	−18.2602	−	10.5425i	−0.916453	−	0.529114i	−0.0339514	−	0.999423i	$-0.510809\pi$
$397$	−18.2602	−	10.5425i	−0.916453	−	0.529114i	−0.882502	+	0.470309i	$0.844142\pi$
$398$	−3.23321	+	5.60009i	−0.162066	+	0.280707i
$399$	−6.36542	+	18.8692i	−0.318670	+	0.944643i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$		−	20.6070i		−	1.02907i	−0.857471	−	0.514533i	$-0.827965\pi$
$401$		−	20.6070i		−	1.02907i	0.857471	−	0.514533i	$-0.172035\pi$
$402$	−3.50910	−	3.17347i	−0.175018	−	0.158278i
$403$	1.03602			0.0516077
$404$	3.14256	−	5.44308i	0.156348	−	0.270803i
$405$	8.81929	−	1.79448i	0.438234	−	0.0891683i
$406$	9.60849	−	12.9772i	0.476861	−	0.644047i
$407$	7.68904	+	4.43927i	0.381132	+	0.220047i
$408$	−2.55424	+	11.8894i	−0.126454	+	0.588615i
$409$	−20.1815	−	11.6518i	−0.997909	−	0.576143i	−0.0902803	−	0.995916i	$-0.528776\pi$
$409$	−20.1815	−	11.6518i	−0.997909	−	0.576143i	−0.907629	+	0.419773i	$0.862110\pi$
$410$	2.41787	+	1.39596i	0.119410	+	0.0689416i
$411$	−27.0595	−	24.4713i	−1.33475	−	1.20708i
$412$	−4.85323	−	2.80201i	−0.239101	−	0.138045i
$413$	−11.2359	−	25.8616i	−0.552885	−	1.27257i
$414$	9.92073	−	7.14204i	0.487577	−	0.351012i
$415$	8.34157	−	14.4480i	0.409472	−	0.709226i
$416$	2.81058			0.137800
$417$	−3.28394	+	15.2860i	−0.160815	+	0.748560i
$418$		−	24.6101i		−	1.20372i
$419$	−6.50968	−	11.2751i	−0.318019	−	0.550824i	0.662056	−	0.749454i	$-0.269684\pi$
$419$	−6.50968	−	11.2751i	−0.318019	−	0.550824i	−0.980075	+	0.198630i	$0.936351\pi$
$420$	−4.34216	−	1.46480i	−0.211876	−	0.0714750i
$421$	16.4495	−	28.4914i	0.801701	−	1.38859i	−0.116795	−	0.993156i	$-0.537262\pi$
$421$	16.4495	−	28.4914i	0.801701	−	1.38859i	0.918496	−	0.395431i	$-0.129405\pi$
$422$	−1.05142	−	0.607035i	−0.0511821	−	0.0295500i
$423$	−12.6282	+	9.09118i	−0.614004	+	0.442028i
$424$	−1.74767	−	3.02705i	−0.0848742	−	0.147006i
$425$	3.51050	+	6.08036i	0.170284	+	0.294941i
$426$	−15.3496	−	3.29760i	−0.743691	−	0.159769i
$427$	−4.39862	+	38.5060i	−0.212864	+	1.86344i
$428$	−1.38444	+	0.799307i	−0.0669195	+	0.0386360i
$429$	26.9540	+	5.79061i	1.30135	+	0.279573i
$430$		−	6.36340i		−	0.306870i
$431$	22.8306	−	13.1813i	1.09971	−	0.634919i	0.163567	−	0.986532i	$-0.447700\pi$
$431$	22.8306	−	13.1813i	1.09971	−	0.634919i	0.936146	+	0.351613i	$0.114367\pi$
$432$	−0.576883	+	5.16403i	−0.0277553	+	0.248455i
$433$		−	29.2742i		−	1.40683i	−0.710780	−	0.703415i	$-0.751658\pi$
$433$		−	29.2742i		−	1.40683i	0.710780	−	0.703415i	$-0.248342\pi$
$434$	0.580336	−	0.783799i	0.0278570	−	0.0376235i
$435$	−10.0605	+	3.24466i	−0.482364	+	0.155570i
$436$	5.26893			0.252336
$437$	8.85351	−	15.3347i	0.423521	−	0.733560i
$438$	−8.82381	−	27.3594i	−0.421618	−	1.30728i
$439$	−11.0785	+	6.39616i	−0.528747	+	0.305272i	−0.740506	−	0.672050i	$-0.765414\pi$
$439$	−11.0785	+	6.39616i	−0.528747	+	0.305272i	0.211759	+	0.977322i	$0.432081\pi$
$440$	5.66323			0.269984
$441$	−19.3709	+	8.10977i	−0.922424	+	0.386180i
$442$	−19.7331			−0.938606
$443$	19.0694	−	11.0097i	0.906014	−	0.523087i	0.0268674	−	0.999639i	$-0.491447\pi$
$443$	19.0694	−	11.0097i	0.906014	−	0.523087i	0.879146	+	0.476552i	$0.158113\pi$
$444$	−2.65485	−	0.570350i	−0.125994	−	0.0270676i
$445$	0.332109	−	0.575230i	0.0157435	−	0.0272685i
$446$	−2.06719			−0.0978845
$447$	−11.3926	−	10.3030i	−0.538853	−	0.487313i
$448$	1.57438	−	2.12634i	0.0743823	−	0.100460i
$449$		−	15.8715i		−	0.749025i	−0.927222	−	0.374512i	$-0.877810\pi$
$449$		−	15.8715i		−	0.749025i	0.927222	−	0.374512i	$-0.122190\pi$
$450$	1.75277	+	2.43471i	0.0826265	+	0.114773i
$451$	−13.6930	+	7.90564i	−0.644777	+	0.372262i
$452$		−	15.1169i		−	0.711040i
$453$	15.6786	−	17.3368i	0.736643	−	0.814552i
$454$	16.9379	−	9.77912i	0.794936	−	0.458957i
$455$	0.843953	−	7.38805i	0.0395651	−	0.346357i
$456$	2.31031	+	7.16344i	0.108190	+	0.335459i
$457$	10.6090	+	18.3754i	0.496270	+	0.859565i	0.999991	−	0.00430150i	$-0.00136921\pi$
$457$	10.6090	+	18.3754i	0.496270	+	0.859565i	−0.503721	+	0.863867i	$0.668036\pi$
$458$	6.66427	+	11.5429i	0.311401	+	0.539363i
$459$	4.05029	−	36.2566i	0.189051	−	1.69231i
$460$	3.52880	+	2.03736i	0.164531	+	0.0949922i
$461$	−13.3910	+	23.1938i	−0.623679	+	1.08024i	0.365115	+	0.930962i	$0.381030\pi$
$461$	−13.3910	+	23.1938i	−0.623679	+	1.08024i	−0.988795	+	0.149282i	$0.952304\pi$
$462$	19.4794	−	17.1484i	0.906266	−	0.797815i
$463$	7.79895	+	13.5082i	0.362448	+	0.627778i	0.988363	−	0.152113i	$-0.0486077\pi$
$463$	7.79895	+	13.5082i	0.362448	+	0.627778i	−0.625915	+	0.779891i	$0.715274\pi$
$464$		−	6.10305i		−	0.283327i
$465$	−0.607637	+	0.195972i	−0.0281785	+	0.00908797i
$466$	17.7879			0.824007
$467$	−11.6318	+	20.1469i	−0.538256	+	0.932288i	0.460742	+	0.887534i	$0.347583\pi$
$467$	−11.6318	+	20.1469i	−0.538256	+	0.932288i	−0.998998	+	0.0447533i	$0.985750\pi$
$468$	−8.38931	+	0.844840i	−0.387796	+	0.0390527i
$469$	−2.87986	−	6.62853i	−0.132980	−	0.306077i
$470$	−4.49185	−	2.59337i	−0.207194	−	0.119623i
$471$	−5.49286	+	1.77153i	−0.253097	+	0.0816276i
$472$	−9.22962	−	5.32873i	−0.424828	−	0.245274i
$473$	31.2093	+	18.0187i	1.43500	+	0.828500i
$474$	−14.4126	+	4.64828i	−0.661993	+	0.213502i
$475$	3.76339	+	2.17279i	0.172676	+	0.0996946i
$476$	−11.0537	+	14.9290i	−0.506644	+	0.684272i
$477$	6.12652	+	8.51011i	0.280514	+	0.389651i
$478$	1.96383	−	3.40145i	0.0898233	−	0.155579i
$479$	−18.9385			−0.865320			−0.432660	−	0.901557i	$-0.642425\pi$
$479$	−18.9385			−0.865320			−0.432660	+	0.901557i	$0.642425\pi$
$480$	−1.64844	+	0.531646i	−0.0752406	+	0.0242662i
$481$		−	4.40630i		−	0.200910i
$482$	5.57242	+	9.65172i	0.253817	+	0.439624i
$483$	18.3070	−	3.67753i	0.832995	−	0.167334i
$484$	−10.5361	+	18.2490i	−0.478913	+	0.829502i
$485$	−1.68214	−	0.971182i	−0.0763819	−	0.0440991i
$486$	0.169672	−	15.5875i	0.00769646	−	0.707065i
$487$	14.3962	+	24.9350i	0.652355	+	1.12991i	0.982550	+	0.185999i	$0.0595521\pi$
$487$	14.3962	+	24.9350i	0.652355	+	1.12991i	−0.330195	+	0.943913i	$0.607115\pi$
$488$	7.32427	+	12.6860i	0.331554	+	0.574269i
$489$	−7.45692	−	23.1212i	−0.337213	−	1.04558i
$490$	−5.11668	−	4.77698i	−0.231148	−	0.215802i
$491$	−2.36612	+	1.36608i	−0.106782	+	0.0616504i	−0.552440	−	0.833553i	$-0.686303\pi$
$491$	−2.36612	+	1.36608i	−0.106782	+	0.0616504i	0.445658	+	0.895203i	$0.352970\pi$
$492$	3.24356	−	3.58661i	0.146231	−	0.161697i
$493$			42.8494i			1.92984i
$494$	−10.5773	+	6.10681i	−0.475896	+	0.274759i
$495$	−16.9042	+	1.70232i	−0.759787	+	0.0765138i
$496$		−	0.368613i		−	0.0165512i
$497$	−19.2738	−	14.2706i	−0.864549	−	0.640124i
$498$	−21.4318	−	19.3819i	−0.960382	−	0.868525i
$499$	24.1713			1.08205			0.541027	−	0.841005i	$-0.318036\pi$
$499$	24.1713			1.08205			0.541027	+	0.841005i	$0.318036\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−31.9529	−	6.86454i	−1.42755	−	0.306685i
$502$	18.1191	−	10.4610i	0.808693	−	0.466899i
$503$	−14.6533			−0.653358			−0.326679	−	0.945135i	$-0.605930\pi$
$503$	−14.6533			−0.653358			−0.326679	+	0.945135i	$0.605930\pi$
$504$	−4.06020	+	6.82018i	−0.180855	+	0.303795i
$505$	−6.28513			−0.279684
$506$	−19.9844	+	11.5380i	−0.888416	+	0.512927i
$507$	2.71173	+	8.40808i	0.120432	+	0.373416i
$508$	−2.31726	+	4.01361i	−0.102812	+	0.178075i
$509$	−38.5161			−1.70720			−0.853598	−	0.520932i	$-0.825585\pi$
$509$	−38.5161			−1.70720			−0.853598	+	0.520932i	$0.825585\pi$
$510$	11.5737	−	3.73268i	0.512491	−	0.165286i
$511$	4.98374	−	43.6282i	0.220468	−	1.93000i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.04934	−	20.6877i	−0.399538	−	0.913384i
$514$	−25.2687	+	14.5889i	−1.11456	+	0.643489i
$515$			5.60402i			0.246943i
$516$	−10.7759	−	2.31501i	−0.474381	−	0.101913i
$517$	25.4384	−	14.6869i	1.11878	−	0.645928i
$518$	−3.33358	−	2.46823i	−0.146469	−	0.108448i
$519$	−15.3884	−	3.30593i	−0.675476	−	0.145114i
$520$	−1.40529	−	2.43404i	−0.0616261	−	0.106740i
$521$	12.7686	+	22.1158i	0.559401	+	0.968911i	0.997547	+	0.0700066i	$0.0223020\pi$
$521$	12.7686	+	22.1158i	0.559401	+	0.968911i	−0.438146	+	0.898904i	$0.644365\pi$
$522$	1.83453	+	18.2170i	0.0802952	+	0.797337i
$523$	−10.7847	−	6.22654i	−0.471581	−	0.272268i	0.245320	−	0.969442i	$-0.421107\pi$
$523$	−10.7847	−	6.22654i	−0.471581	−	0.272268i	−0.716901	+	0.697175i	$0.754440\pi$
$524$	−1.85752	+	3.21733i	−0.0811463	+	0.140550i
$525$	0.902526	+	4.49282i	0.0393895	+	0.196083i
$526$	0.313661	+	0.543277i	0.0136763	+	0.0236880i
$527$			2.58803i			0.112736i
$528$	2.06029	−	9.59019i	0.0896625	−	0.417359i
$529$	6.39672			0.278118
$530$	−1.74767	+	3.02705i	−0.0759138	+	0.131487i
$531$	29.1513	+	13.1314i	1.26506	+	0.569853i
$532$	−1.30488	+	11.4231i	−0.0565737	+	0.495252i
$533$	6.79563	+	3.92346i	0.294352	+	0.169944i
$534$	−0.853280	−	0.771667i	−0.0369250	−	0.0333933i
$535$	1.38444	+	0.799307i	0.0598546	+	0.0345571i
$536$	−2.36562	−	1.36579i	−0.102179	−	0.0589933i
$537$	5.11287	−	23.7993i	0.220637	−	1.02701i
$538$	−2.99624	−	1.72988i	−0.129177	−	0.0745803i
$539$	37.9172	−	11.5682i	1.63321	−	0.498277i
$540$	4.76062	−	2.08242i	0.204865	−	0.0896131i
$541$	8.36504	−	14.4887i	0.359641	−	0.622916i	−0.628260	−	0.778004i	$-0.716232\pi$
$541$	8.36504	−	14.4887i	0.359641	−	0.622916i	0.987901	+	0.155087i	$0.0495658\pi$
$542$	4.56686			0.196163
$543$	−4.29763	−	3.88658i	−0.184429	−	0.166789i
$544$			7.02099i			0.301022i
$545$	−2.63446	−	4.56303i	−0.112848	−	0.195459i
$546$	−12.2040	−	4.11694i	−0.522283	−	0.176189i
$547$	16.1409	−	27.9569i	0.690137	−	1.19535i	−0.281656	−	0.959515i	$-0.590884\pi$
$547$	16.1409	−	27.9569i	0.690137	−	1.19535i	0.971793	−	0.235836i	$-0.0757829\pi$
$548$	−18.2419	−	10.5319i	−0.779253	−	0.449902i
$549$	−25.6756	−	35.6649i	−1.09581	−	1.52214i
$550$	−2.83161	−	4.90450i	−0.120740	−	0.209129i
$551$	13.2607	+	22.9681i	0.564923	+	0.978476i
$552$	4.73387	−	5.23453i	0.201487	−	0.222797i
$553$	−22.9828	−	2.62538i	−0.977329	−	0.111642i
$554$	−26.5128	+	15.3071i	−1.12642	+	0.650338i
$555$	0.833489	+	2.58435i	0.0353796	+	0.109699i
$556$			9.02675i			0.382820i
$557$	26.6920	−	15.4106i	1.13097	−	0.652969i	0.186795	−	0.982399i	$-0.440190\pi$
$557$	26.6920	−	15.4106i	1.13097	−	0.652969i	0.944180	+	0.329430i	$0.106857\pi$
$558$	0.110802	+	1.10027i	0.00469064	+	0.0465783i
$559$		−	17.8848i		−	0.756448i
$560$	−2.62866	−	0.300277i	−0.111081	−	0.0126890i
$561$	−14.4653	+	67.3326i	−0.610724	+	2.84279i
$562$	−10.1532			−0.428286
$563$	−20.5084	+	35.5216i	−0.864325	+	1.49705i	0.00339066	+	0.999994i	$0.498921\pi$
$563$	−20.5084	+	35.5216i	−0.864325	+	1.49705i	−0.867716	+	0.497061i	$0.834413\pi$
$564$	−6.02579	+	6.66309i	−0.253732	+	0.280567i
$565$	−13.0916	+	7.55846i	−0.550769	+	0.317987i
$566$	−8.72730			−0.366836
$567$	10.0692	−	21.5780i	0.422866	−	0.906192i
$568$	−9.06430			−0.380329
$569$	14.1078	−	8.14517i	0.591432	−	0.341463i	−0.174232	−	0.984705i	$-0.555744\pi$
$569$	14.1078	−	8.14517i	0.591432	−	0.341463i	0.765663	+	0.643241i	$0.222411\pi$
$570$	5.04856	−	5.58251i	0.211461	−	0.233826i
$571$	−5.84580	+	10.1252i	−0.244639	+	0.423727i	−0.962030	−	0.272944i	$-0.912003\pi$
$571$	−5.84580	+	10.1252i	−0.244639	+	0.423727i	0.717391	+	0.696671i	$0.245336\pi$
$572$	15.9170			0.665522
$573$	2.25092	−	10.4775i	0.0940334	−	0.437705i
$574$	6.77494	−	2.94347i	0.282780	−	0.122858i
$575$		−	4.07471i		−	0.169927i
$576$	0.300592	+	2.98490i	0.0125247	+	0.124371i
$577$	30.4481	−	17.5792i	1.26757	−	0.731833i	0.293044	−	0.956099i	$-0.405332\pi$
$577$	30.4481	−	17.5792i	1.26757	−	0.731833i	0.974528	+	0.224266i	$0.0719984\pi$
$578$		−	32.2943i		−	1.34327i
$579$	1.10866	+	3.43754i	0.0460743	+	0.142859i
$580$	−5.28540	+	3.05152i	−0.219464	+	0.126708i
$581$	−17.5887	−	40.4837i	−0.729703	−	1.67955i
$582$	−2.25657	+	2.49523i	−0.0935380	+	0.103431i
$583$	−9.89744	−	17.1429i	−0.409910	−	0.709985i
$584$	−8.29858	−	14.3736i	−0.343398	−	0.594782i
$585$	4.92631	+	6.84294i	0.203678	+	0.282921i
$586$	15.1160	+	8.72722i	0.624436	+	0.360518i
$587$	−3.93572	+	6.81686i	−0.162444	+	0.281362i	−0.935745	−	0.352678i	$-0.885271\pi$
$587$	−3.93572	+	6.81686i	−0.162444	+	0.281362i	0.773300	+	0.634040i	$0.218605\pi$
$588$	−9.95086	+	6.92678i	−0.410367	+	0.285656i
$589$	0.800920	+	1.38723i	0.0330014	+	0.0571600i
$590$			10.6575i			0.438760i
$591$	−31.7559	−	28.7186i	−1.30626	−	1.18132i
$592$	−1.56775			−0.0644342
$593$	−3.43635	+	5.95193i	−0.141114	+	0.244416i	−0.927916	−	0.372788i	$-0.878402\pi$
$593$	−3.43635	+	5.95193i	−0.141114	+	0.244416i	0.786802	+	0.617205i	$0.211735\pi$
$594$	−3.26702	+	29.2451i	−0.134048	+	1.19994i
$595$	18.4558	+	2.10824i	0.756613	+	0.0864295i
$596$	−7.68022	−	4.43418i	−0.314594	−	0.181631i
$597$	2.35249	−	10.9503i	0.0962811	−	0.448167i
$598$	9.91800	+	5.72616i	0.405577	+	0.234160i
$599$	−28.1842	−	16.2722i	−1.15157	−	0.664862i	−0.202304	−	0.979323i	$-0.564843\pi$
$599$	−28.1842	−	16.2722i	−1.15157	−	0.664862i	−0.949271	+	0.314461i	$0.898176\pi$
$600$	1.28464	+	1.16177i	0.0524451	+	0.0474290i
$601$	28.7087	+	16.5750i	1.17105	+	0.676107i	0.953927	−	0.300038i	$-0.0969992\pi$
$601$	28.7087	+	16.5750i	1.17105	+	0.676107i	0.217124	+	0.976144i	$0.430333\pi$
$602$	−13.5308	−	10.0184i	−0.551473	−	0.408318i
$603$	7.47171	+	3.36567i	0.304271	+	0.137061i
$604$	6.74772	−	11.6874i	0.274561	−	0.475553i
$605$	21.0722			0.856705
$606$	−2.28653	+	10.6433i	−0.0928841	+	0.432355i
$607$			26.2617i			1.06593i	0.846138	+	0.532964i	$0.178922\pi$
$607$			26.2617i			1.06593i	−0.846138	+	0.532964i	$0.821078\pi$
$608$	2.17279	+	3.76339i	0.0881184	+	0.152626i
$609$	−8.93975	+	26.5004i	−0.362257	+	1.07385i
$610$	7.32427	−	12.6860i	0.296551	−	0.513642i
$611$	−12.6247	−	7.28889i	−0.510742	−	0.294877i
$612$	−2.11046	−	20.9570i	−0.0853101	−	0.847135i
$613$	9.71301	+	16.8234i	0.392305	+	0.679492i	0.992753	−	0.120172i	$-0.0383445\pi$
$613$	9.71301	+	16.8234i	0.392305	+	0.679492i	−0.600448	+	0.799664i	$0.705011\pi$
$614$	1.63266	+	2.82785i	0.0658888	+	0.114123i
$615$	−4.72788	−	1.01570i	−0.190646	−	0.0409571i
$616$	8.91605	−	12.0420i	0.359238	−	0.485185i
$617$	15.6130	−	9.01417i	0.628556	−	0.362897i	−0.151637	−	0.988436i	$-0.548454\pi$
$617$	15.6130	−	9.01417i	0.628556	−	0.362897i	0.780192	+	0.625540i	$0.215121\pi$
$618$	9.48993	+	2.03875i	0.381741	+	0.0820105i
$619$		−	15.9835i		−	0.642432i	−0.947006	−	0.321216i	$-0.895908\pi$
$619$		−	15.9835i		−	0.642432i	0.947006	−	0.321216i	$-0.104092\pi$
$620$	−0.319228	+	0.184307i	−0.0128205	+	0.00740193i
$621$	−12.5567	+	17.0475i	−0.503882	+	0.684094i
$622$			26.5728i			1.06547i
$623$	−0.700272	−	1.61181i	−0.0280558	−	0.0645757i
$624$	−4.63307	+	1.49423i	−0.185471	+	0.0598172i
$625$	1.00000			0.0400000
$626$	−2.42475	+	4.19978i	−0.0969123	+	0.167857i
$627$	13.0838	+	40.5682i	0.522518	+	1.62014i
$628$	−2.88573	+	1.66608i	−0.115153	+	0.0664837i
$629$	11.0072			0.438885
$630$	7.93654	+	0.106144i	0.316199	+	0.00422886i
$631$	−43.0538			−1.71395			−0.856973	−	0.515362i	$-0.827657\pi$
$631$	−43.0538			−1.71395			−0.856973	+	0.515362i	$0.827657\pi$
$632$	−7.57182	+	4.37159i	−0.301191	+	0.173893i
$633$	2.05592	+	0.441680i	0.0817155	+	0.0175552i
$634$	11.3428	−	19.6462i	0.450478	−	0.780251i
$635$	4.63451			0.183915
$636$	4.49024	+	4.06076i	0.178050	+	0.161020i
$637$	−14.3808	−	13.4261i	−0.569790	−	0.531962i
$638$		−	34.5630i		−	1.36836i
$639$	27.0560	−	2.72466i	1.07032	−	0.107786i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$			8.31902i			0.328582i	0.986412	+	0.164291i	$0.0525335\pi$
$641$			8.31902i			0.328582i	−0.986412	+	0.164291i	$0.947466\pi$
$642$	1.85722	−	2.05364i	0.0732986	−	0.0810508i
$643$	11.2945	−	6.52086i	0.445410	−	0.257158i	−0.260480	−	0.965479i	$-0.583881\pi$
$643$	11.2945	−	6.52086i	0.445410	−	0.257158i	0.705890	+	0.708322i	$0.250547\pi$
$644$	9.88779	−	4.29589i	0.389633	−	0.169282i
$645$	3.38307	+	10.4897i	0.133208	+	0.413030i
$646$	−15.2552	−	26.4227i	−0.600206	−	1.03959i
$647$	−3.58732	−	6.21343i	−0.141032	−	0.244275i	0.786853	−	0.617140i	$-0.211709\pi$
$647$	−3.58732	−	6.21343i	−0.141032	−	0.244275i	−0.927886	+	0.372865i	$0.878375\pi$
$648$	−1.79448	−	8.81929i	−0.0704938	−	0.346454i
$649$	−52.2695	−	30.1778i	−2.05176	−	1.18458i
$650$	−1.40529	+	2.43404i	−0.0551200	+	0.0954707i
$651$	−0.539945	+	1.60058i	−0.0211621	+	0.0627316i
$652$	−7.01305	−	12.1470i	−0.274652	−	0.475711i
$653$			21.2930i			0.833261i	0.909076	+	0.416631i	$0.136789\pi$
$653$			21.2930i			0.833261i	−0.909076	+	0.416631i	$0.863211\pi$
$654$	−8.68551	+	2.80120i	−0.339630	+	0.109536i
$655$	3.71505			0.145159
$656$	1.39596	−	2.41787i	0.0545031	−	0.0944021i
$657$	29.0910	+	40.4092i	1.13495	+	1.57651i
$658$	−12.5863	+	5.46829i	−0.490664	+	0.213176i
$659$	7.91663	+	4.57067i	0.308388	+	0.178048i	0.646205	−	0.763164i	$-0.276355\pi$
$659$	7.91663	+	4.57067i	0.308388	+	0.178048i	−0.337817	+	0.941212i	$0.609688\pi$
$660$	−9.33549	+	3.01083i	−0.363383	+	0.117196i
$661$	−18.5903	−	10.7331i	−0.723078	−	0.417469i	0.0928066	−	0.995684i	$-0.470416\pi$
$661$	−18.5903	−	10.7331i	−0.723078	−	0.417469i	−0.815884	+	0.578215i	$0.803749\pi$
$662$	−8.97760	−	5.18322i	−0.348924	−	0.201451i
$663$	32.5288	−	10.4910i	1.26331	−	0.407437i
$664$	−14.4480	−	8.34157i	−0.560692	−	0.323716i
$665$	10.5451	−	4.58147i	0.408921	−	0.177662i
$666$	4.67959	−	0.471255i	0.181330	−	0.0182607i
$667$	12.4341	−	21.5365i	0.481450	−	0.833895i
$668$	−18.8689			−0.730061
$669$	3.40765	−	1.09902i	0.131747	−	0.0424904i
$670$			2.73159i			0.105530i
$671$	41.4790	+	71.8438i	1.60128	+	2.77350i
$672$	−1.46480	+	4.34216i	−0.0565059	+	0.167502i
$673$	−17.7533	+	30.7497i	−0.684341	+	1.18531i	0.289302	+	0.957238i	$0.406577\pi$
$673$	−17.7533	+	30.7497i	−0.684341	+	1.18531i	−0.973643	+	0.228076i	$0.926757\pi$
$674$	−22.6214	−	13.0605i	−0.871344	−	0.503071i
$675$	−4.18374	−	3.08161i	−0.161032	−	0.118611i
$676$	2.55031	+	4.41727i	0.0980890	+	0.169895i
$677$	−6.78337	−	11.7491i	−0.260706	−	0.451556i	0.705724	−	0.708487i	$-0.250622\pi$
$677$	−6.78337	−	11.7491i	−0.260706	−	0.451556i	−0.966430	+	0.256931i	$0.917289\pi$
$678$	8.03685	+	24.9193i	0.308653	+	0.957021i
$679$	−4.71338	+	2.04780i	−0.180883	+	0.0785872i
$680$	6.08036	−	3.51050i	0.233171	−	0.134621i
$681$	−22.7221	+	25.1253i	−0.870714	+	0.962802i
$682$		−	2.08754i		−	0.0799361i
$683$	17.5340	−	10.1233i	0.670922	−	0.387357i	−0.125504	−	0.992093i	$-0.540055\pi$
$683$	17.5340	−	10.1233i	0.670922	−	0.387357i	0.796426	+	0.604736i	$0.206721\pi$
$684$	−7.61682	−	10.5802i	−0.291237	−	0.404545i
$685$			21.0639i			0.804809i
$686$	−18.2131	+	3.35906i	−0.695379	+	0.128249i
$687$	−17.1224	−	15.4847i	−0.653259	−	0.590777i
$688$	−6.36340			−0.242602
$689$	−4.91196	+	8.50776i	−0.187131	+	0.324120i
$690$	−6.90017	−	1.48238i	−0.262685	−	0.0564334i
$691$	25.4972	−	14.7208i	0.969958	−	0.560006i	0.0707348	−	0.997495i	$-0.477466\pi$
$691$	25.4972	−	14.7208i	0.969958	−	0.560006i	0.899224	+	0.437489i	$0.144132\pi$
$692$	−9.08721			−0.345444
$693$	−22.9938	+	38.6242i	−0.873463	+	1.46721i
$694$	6.70663			0.254580
$695$	7.81740	−	4.51338i	0.296531	−	0.171202i
$696$	3.24466	+	10.0605i	0.122989	+	0.381343i
$697$	−9.80102	+	16.9759i	−0.371240	+	0.643007i
$698$	21.5051			0.813982
$699$	−29.3222	+	9.45685i	−1.10907	+	0.357691i
$700$	1.05428	+	2.42662i	0.0398481	+	0.0917177i
$701$			41.6152i			1.57178i	0.618364	+	0.785892i	$0.287796\pi$
$701$			41.6152i			1.57178i	−0.618364	+	0.785892i	$0.712204\pi$
$702$	13.3801	−	5.85281i	0.505000	−	0.220900i
$703$	5.90006	−	3.40640i	0.222525	−	0.128475i
$704$		−	5.66323i		−	0.213441i
$705$	8.78330	+	1.88694i	0.330798	+	0.0710664i
$706$	−6.09384	+	3.51828i	−0.229345	+	0.132412i
$707$	−9.89515	+	13.3643i	−0.372145	+	0.502618i
$708$	18.0475	+	3.87719i	0.678266	+	0.145714i
$709$	−11.1912	−	19.3838i	−0.420296	−	0.727973i	0.575673	−	0.817680i	$-0.304740\pi$
$709$	−11.1912	−	19.3838i	−0.420296	−	0.727973i	−0.995968	+	0.0897069i	$0.971407\pi$
$710$	4.53215	+	7.84991i	0.170088	+	0.294602i
$711$	21.2871	−	15.3248i	0.798327	−	0.574725i
$712$	−0.575230	−	0.332109i	−0.0215576	−	0.0124463i
$713$	0.750996	−	1.30076i	0.0281250	−	0.0487140i
$714$	10.2844	−	30.4863i	0.384882	−	1.14092i
$715$	−7.95849	−	13.7845i	−0.297630	−	0.515511i
$716$		−	14.0540i		−	0.525224i
$717$	−1.42888	+	6.65114i	−0.0533626	+	0.248391i
$718$	−6.82384			−0.254664
$719$	−13.3750	+	23.1661i	−0.498802	+	0.863951i	−0.999999	−	0.00138257i	$-0.999560\pi$
$719$	−13.3750	+	23.1661i	−0.498802	+	0.863951i	0.501197	+	0.865333i	$0.332893\pi$
$720$	2.43471	−	1.75277i	0.0907361	−	0.0653220i
$721$	11.9161	+	8.82284i	0.443778	+	0.328580i
$722$	0.100347	+	0.0579356i	0.00373454	+	0.00215614i
$723$	−14.3171	−	12.9477i	−0.532459	−	0.481531i
$724$	−2.89720	−	1.67270i	−0.107674	−	0.0621655i
$725$	5.28540	+	3.05152i	0.196295	+	0.113331i
$726$	7.66607	−	35.6839i	0.284515	−	1.32435i
$727$	−9.55141	−	5.51451i	−0.354242	−	0.204522i	0.312310	−	0.949980i	$-0.398897\pi$
$727$	−9.55141	−	5.51451i	−0.354242	−	0.204522i	−0.666552	+	0.745458i	$0.732231\pi$
$728$	−7.38805	−	0.843953i	−0.273820	−	0.0312790i
$729$	8.00735	+	25.7853i	0.296569	+	0.955012i
$730$	−8.29858	+	14.3736i	−0.307144	+	0.531989i
$731$	44.6773			1.65245
$732$	−18.8181	−	17.0182i	−0.695536	−	0.629011i
$733$			4.89952i			0.180968i	0.995898	+	0.0904839i	$0.0288414\pi$
$733$			4.89952i			0.180968i	−0.995898	+	0.0904839i	$0.971159\pi$
$734$	−17.6749	−	30.6139i	−0.652393	−	1.12998i
$735$	10.9742	+	5.15431i	0.404790	+	0.190120i
$736$	2.03736	−	3.52880i	0.0750980	−	0.130073i
$737$	−13.3971	−	7.73481i	−0.493488	−	0.284915i
$738$	−3.44001	+	7.63673i	−0.126629	+	0.281112i
$739$	−5.60509	−	9.70830i	−0.206187	−	0.357126i	0.744324	−	0.667819i	$-0.232772\pi$
$739$	−5.60509	−	9.70830i	−0.206187	−	0.357126i	−0.950510	+	0.310693i	$0.899439\pi$
$740$	0.783876	+	1.35771i	0.0288159	+	0.0499105i
$741$	14.1894	−	15.6901i	0.521261	−	0.576390i
$742$	3.68506	+	8.48185i	0.135283	+	0.311379i
$743$	−33.4349	+	19.3036i	−1.22661	+	0.708182i	−0.966318	−	0.257349i	$-0.917151\pi$
$743$	−33.4349	+	19.3036i	−1.22661	+	0.708182i	−0.260288	+	0.965531i	$0.583818\pi$
$744$	0.195972	+	0.607637i	0.00718467	+	0.0222770i
$745$			8.86835i			0.324911i
$746$	15.1418	−	8.74212i	0.554381	−	0.320072i
$747$	45.6334	+	20.5558i	1.66964	+	0.752098i
$748$			39.7615i			1.45382i
$749$	3.87923	−	1.68539i	0.141744	−	0.0615828i
$750$	0.363801	−	1.69341i	0.0132841	−	0.0618347i
$751$	39.0281			1.42416			0.712078	−	0.702100i	$-0.247754\pi$
$751$	39.0281			1.42416			0.712078	+	0.702100i	$0.247754\pi$
$752$	−2.59337	+	4.49185i	−0.0945706	+	0.163801i
$753$	−24.3066	+	26.8773i	−0.885782	+	0.979464i
$754$	−14.8550	+	8.57656i	−0.540989	+	0.312340i
$755$	−13.4954			−0.491149
$756$	3.06707	−	13.4012i	0.111548	−	0.487398i
$757$	−51.3343			−1.86578			−0.932889	−	0.360163i	$-0.882721\pi$
$757$	−51.3343			−1.86578			−0.932889	+	0.360163i	$0.882721\pi$
$758$	9.55858	−	5.51865i	0.347183	−	0.200446i
$759$	26.8090	−	29.6444i	0.973105	−	1.07602i
$760$	2.17279	−	3.76339i	0.0788155	−	0.136512i
$761$	3.20178			0.116064			0.0580321	−	0.998315i	$-0.481517\pi$
$761$	3.20178			0.116064			0.0580321	+	0.998315i	$0.481517\pi$
$762$	1.68604	−	7.84815i	0.0610788	−	0.284308i
$763$	−13.8502	−	1.58214i	−0.501411	−	0.0572773i
$764$		−	6.18722i		−	0.223846i
$765$	−17.0940	+	12.3062i	−0.618036	+	0.444931i
$766$	−24.2132	+	13.9795i	−0.874857	+	0.505099i
$767$			29.9536i			1.08156i
$768$	0.531646	+	1.64844i	0.0191841	+	0.0594829i
$769$	26.4700	−	15.2825i	0.954533	−	0.551100i	0.0600465	−	0.998196i	$-0.480875\pi$
$769$	26.4700	−	15.2825i	0.954533	−	0.551100i	0.894486	+	0.447096i	$0.147542\pi$
$770$	−14.8867	−	1.70054i	−0.536479	−	0.0612831i
$771$	33.8978	−	37.4829i	1.22080	−	1.34991i
$772$	1.04267	+	1.80595i	0.0375264	+	0.0649976i
$773$	8.73288	+	15.1258i	0.314100	+	0.544037i	0.979246	−	0.202676i	$-0.0649639\pi$
$773$	8.73288	+	15.1258i	0.314100	+	0.544037i	−0.665146	+	0.746714i	$0.731631\pi$
$774$	18.9941	−	1.91279i	0.682729	−	0.0687538i
$775$	0.319228	+	0.184307i	0.0114670	+	0.00662049i
$776$	−0.971182	+	1.68214i	−0.0348634	+	0.0603852i
$777$	6.80743	+	2.29645i	0.244215	+	0.0823845i
$778$	6.89837	+	11.9483i	0.247319	+	0.428368i
$779$			12.1325i			0.434693i
$780$	3.61058	+	3.26524i	0.129280	+	0.116914i
$781$	−51.3332			−1.83685
$782$	−14.3043	+	24.7757i	−0.511519	+	0.885977i
$783$	−12.7091	−	29.0543i	−0.454187	−	1.03832i
$784$	−4.77698	+	5.11668i	−0.170607	+	0.182739i
$785$	2.88573	+	1.66608i	0.102996	+	0.0594649i
$786$	1.35154	−	6.29111i	0.0482077	−	0.224396i
$787$	17.4903	+	10.0980i	0.623461	+	0.359956i	0.778215	−	0.627997i	$-0.216125\pi$
$787$	17.4903	+	10.0980i	0.623461	+	0.359956i	−0.154754	+	0.987953i	$0.549459\pi$
$788$	−21.4079	−	12.3599i	−0.762625	−	0.440302i
$789$	−0.805883	−	0.728803i	−0.0286902	−	0.0259461i
$790$	7.57182	+	4.37159i	0.269393	+	0.155534i
$791$	−4.53927	+	39.7372i	−0.161398	+	1.41289i
$792$	1.70232	+	16.9042i	0.0604894	+	0.600664i
$793$	20.5855	−	35.6551i	0.731011	−	1.26615i
$794$	21.0851			0.748281
$795$	1.27161	−	5.91904i	0.0450992	−	0.209927i
$796$		−	6.46643i		−	0.229196i
$797$	−12.9050	−	22.3521i	−0.457118	−	0.791752i	0.541689	−	0.840579i	$-0.317785\pi$
$797$	−12.9050	−	22.3521i	−0.457118	−	0.791752i	−0.998807	+	0.0488273i	$0.984452\pi$
$798$	−3.92200	−	19.5239i	−0.138837	−	0.691140i
$799$	18.2080	−	31.5373i	0.644154	−	1.11571i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$	1.81683	+	0.818404i	0.0641947	+	0.0289169i
$802$	10.3035	+	17.8462i	0.363830	+	0.630172i
$803$	−46.9968	−	81.4008i	−1.65848	−	2.87257i
$804$	4.62571	+	0.993754i	0.163136	+	0.0350470i
$805$	−8.66424	−	6.41513i	−0.305374	−	0.226104i
$806$	−0.897218	+	0.518009i	−0.0316031	+	0.0182461i
$807$	5.85879	+	1.25866i	0.206239	+	0.0443070i
$808$			6.28513i			0.221110i
$809$	32.1130	−	18.5405i	1.12903	−	0.651848i	0.185342	−	0.982674i	$-0.440661\pi$
$809$	32.1130	−	18.5405i	1.12903	−	0.651848i	0.943692	+	0.330827i	$0.107328\pi$
$810$	−6.74049	+	5.96371i	−0.236837	+	0.209543i
$811$			8.95559i			0.314473i	0.987561	+	0.157237i	$0.0502585\pi$
$811$			8.95559i			0.314473i	−0.987561	+	0.157237i	$0.949741\pi$
$812$	−1.83261	+	16.0428i	−0.0643118	+	0.562993i
$813$	−7.52819	+	2.42795i	−0.264025	+	0.0851519i
$814$	−8.87854			−0.311193
$815$	−7.01305	+	12.1470i	−0.245656	+	0.425489i
$816$	−3.73268	−	11.5737i	−0.130670	−	0.405160i
$817$	23.9479	−	13.8263i	0.837832	−	0.483723i
$818$	23.3036			0.814790
$819$	22.3063	+	0.298325i	0.779446	+	0.0104243i
$820$	−2.79192			−0.0974981
$821$	26.4839	−	15.2905i	0.924294	−	0.533641i	0.0392915	−	0.999228i	$-0.487490\pi$
$821$	26.4839	−	15.2905i	0.924294	−	0.533641i	0.885002	+	0.465586i	$0.154157\pi$
$822$	35.6698	+	7.66306i	1.24413	+	0.267280i
$823$	8.50650	−	14.7337i	0.296518	−	0.513584i	−0.678819	−	0.734306i	$-0.737508\pi$
$823$	8.50650	−	14.7337i	0.296518	−	0.513584i	0.975337	+	0.220721i	$0.0708412\pi$
$824$	5.60402			0.195225
$825$	7.27520	+	6.57936i	0.253290	+	0.229064i
$826$	22.6614	+	16.7788i	0.788491	+	0.583810i
$827$		−	41.4119i		−	1.44003i	−0.693956	−	0.720017i	$-0.744134\pi$
$827$		−	41.4119i		−	1.44003i	0.693956	−	0.720017i	$-0.255866\pi$
$828$	−5.02058	+	11.1456i	−0.174477	+	0.387335i
$829$	5.80702	−	3.35269i	0.201686	−	0.116444i	−0.395756	−	0.918356i	$-0.629517\pi$
$829$	5.80702	−	3.35269i	0.201686	−	0.116444i	0.597442	+	0.801912i	$0.296184\pi$
$830$			16.6831i			0.579080i
$831$	35.5667	−	39.3283i	1.23379	−	1.36428i
$832$	−2.43404	+	1.40529i	−0.0843850	+	0.0487197i
$833$	33.5392	−	35.9242i	1.16206	−	1.24470i
$834$	−4.79904	−	14.8801i	−0.166177	−	0.515254i
$835$	9.43447	+	16.3410i	0.326493	+	0.565503i
$836$	12.3050	+	21.3129i	0.425578	+	0.737123i
$837$	−0.767607	−	1.75483i	−0.0265324	−	0.0606557i
$838$	11.2751	+	6.50968i	0.389492	+	0.224873i
$839$	−20.6497	+	35.7663i	−0.712906	+	1.23479i	0.250856	+	0.968025i	$0.419288\pi$
$839$	−20.6497	+	35.7663i	−0.712906	+	1.23479i	−0.963762	+	0.266765i	$0.914045\pi$
$840$	4.49282	−	0.902526i	0.155017	−	0.0311401i
$841$	4.12360	+	7.14229i	0.142193	+	0.246286i
$842$			32.8991i			1.13378i
$843$	16.7369	−	5.39789i	0.576449	−	0.185913i
$844$	1.21407			0.0417900
$845$	2.55031	−	4.41727i	0.0877335	−	0.151959i
$846$	6.39075	−	14.1873i	0.219718	−	0.487769i
$847$	33.1755	−	44.8067i	1.13992	−	1.53958i
$848$	3.02705	+	1.74767i	0.103949	+	0.0600151i
$849$	14.3864	−	4.63983i	0.493741	−	0.159239i
$850$	−6.08036	−	3.51050i	−0.208554	−	0.120409i
$851$	−5.53229	−	3.19407i	−0.189645	−	0.109491i
$852$	14.9419	−	4.81900i	0.511903	−	0.165096i
$853$	26.9412	+	15.5545i	0.922449	+	0.532576i	0.884415	−	0.466701i	$-0.154557\pi$
$853$	26.9412	+	15.5545i	0.922449	+	0.532576i	0.0380332	+	0.999276i	$0.487891\pi$
$854$	−15.4437	−	35.5465i	−0.528472	−	1.21638i
$855$	−5.35433	+	11.8865i	−0.183114	+	0.406509i
$856$	0.799307	−	1.38444i	0.0273198	−	0.0473192i
$857$	−24.4533			−0.835309			−0.417654	−	0.908606i	$-0.637148\pi$
$857$	−24.4533			−0.835309			−0.417654	+	0.908606i	$0.637148\pi$
$858$	−26.2382	+	8.46219i	−0.895756	+	0.288894i
$859$			34.7993i			1.18734i	0.804710	+	0.593668i	$0.202321\pi$
$859$			34.7993i			1.18734i	−0.804710	+	0.593668i	$0.797679\pi$
$860$	3.18170	+	5.51086i	0.108495	+	0.187919i
$861$	−9.60319	+	8.45399i	−0.327276	+	0.288111i
$862$	−13.1813	+	22.8306i	−0.448956	+	0.777614i
$863$	−7.18913	−	4.15065i	−0.244721	−	0.141290i	0.372624	−	0.927983i	$-0.378458\pi$
$863$	−7.18913	−	4.15065i	−0.244721	−	0.141290i	−0.617345	+	0.786693i	$0.711792\pi$
$864$	−2.08242	−	4.76062i	−0.0708454	−	0.161960i
$865$	4.54360	+	7.86975i	0.154487	+	0.267580i
$866$	14.6371	+	25.3522i	0.497389	+	0.861503i
$867$	17.1691	+	53.2352i	0.583094	+	1.80796i
$868$	−0.110686	+	0.968957i	−0.00375693	+	0.0328886i
$869$	−42.8809	+	24.7573i	−1.45464	+	0.839834i
$870$	7.09032	−	7.84021i	0.240385	−	0.265808i
$871$			7.67735i			0.260137i
$872$	−4.56303	+	2.63446i	−0.154524	+	0.0892142i
$873$	2.39325	−	5.31294i	0.0809991	−	0.179816i
$874$			17.7070i			0.598949i
$875$	1.57438	−	2.12634i	0.0532236	−	0.0718836i
$876$	21.3213	+	19.2820i	0.720382	+	0.651480i
$877$	15.2655			0.515480			0.257740	−	0.966214i	$-0.417022\pi$
$877$	15.2655			0.515480			0.257740	+	0.966214i	$0.417022\pi$
$878$	6.39616	−	11.0785i	0.215860	−	0.373881i
$879$	−29.5576	−	6.34994i	−0.996952	−	0.214178i
$880$	−4.90450	+	2.83161i	−0.165331	+	0.0954537i
$881$	−18.8162			−0.633933			−0.316967	−	0.948437i	$-0.602664\pi$
$881$	−18.8162			−0.633933			−0.316967	+	0.948437i	$0.602664\pi$
$882$	12.7208	−	16.7087i	0.428332	−	0.562612i
$883$	−13.6066			−0.457899			−0.228949	−	0.973438i	$-0.573529\pi$
$883$	−13.6066			−0.457899			−0.228949	+	0.973438i	$0.573529\pi$
$884$	17.0893	−	9.86653i	0.574777	−	0.331847i
$885$	−5.66599	−	17.5682i	−0.190460	−	0.590547i
$886$	−11.0097	+	19.0694i	−0.369879	+	0.640649i
$887$	−10.4409			−0.350571			−0.175285	−	0.984518i	$-0.556085\pi$
$887$	−10.4409			−0.350571			−0.175285	+	0.984518i	$0.556085\pi$
$888$	2.58435	−	0.833489i	0.0867250	−	0.0279701i
$889$	7.29647	−	9.85457i	0.244716	−	0.330512i
$890$			0.664218i			0.0222646i
$891$	−10.1625	−	49.9457i	−0.340458	−	1.67324i
$892$	1.79024	−	1.03360i	0.0599418	−	0.0346074i
$893$		−	22.5395i		−	0.754254i
$894$	15.0178	+	3.22631i	0.502270	+	0.107904i
$895$	−12.1711	+	7.02701i	−0.406836	+	0.234887i
$896$	−0.300277	+	2.62866i	−0.0100316	+	0.0878172i
$897$	−19.3935	−	4.16636i	−0.647530	−	0.139111i
$898$	7.93577	+	13.7452i	0.264820	+	0.458682i
$899$	1.12483	+	1.94827i	0.0375153	+	0.0649783i
$900$	−2.73530	−	1.23213i	−0.0911766	−	0.0410710i
$901$	−21.2529	−	12.2704i	−0.708036	−	0.408785i
$902$	7.90564	−	13.6930i	0.263229	−	0.455926i
$903$	27.6309	+	9.32111i	0.919498	+	0.310187i
$904$	7.55846	+	13.0916i	0.251391	+	0.435422i
$905$			3.34540i			0.111205i
$906$	−4.90965	+	22.8534i	−0.163112	+	0.759252i
$907$	−34.3521			−1.14064			−0.570321	−	0.821422i	$-0.693181\pi$
$907$	−34.3521			−1.14064			−0.570321	+	0.821422i	$0.693181\pi$
$908$	−9.77912	+	16.9379i	−0.324531	+	0.562105i
$909$	−1.88926	−	18.7605i	−0.0626628	−	0.622246i
$910$	2.96314	+	6.82022i	0.0982272	+	0.226088i
$911$	−26.3197	−	15.1957i	−0.872010	−	0.503455i	−0.00399406	−	0.999992i	$-0.501271\pi$
$911$	−26.3197	−	15.1957i	−0.872010	−	0.503455i	−0.868016	+	0.496537i	$0.834605\pi$
$912$	−5.58251	−	5.04856i	−0.184855	−	0.167175i
$913$	−81.8225	−	47.2402i	−2.70793	−	1.56342i
$914$	−18.3754	−	10.6090i	−0.607804	−	0.350916i
$915$	−5.32915	+	24.8060i	−0.176176	+	0.820062i
$916$	−11.5429	−	6.66427i	−0.381387	−	0.220194i
$917$	5.84888	−	7.89947i	0.193147	−	0.260864i
$918$	14.6206	+	33.4243i	0.482553	+	1.10317i
$919$	−11.9867	+	20.7616i	−0.395406	+	0.684862i	−0.993153	−	0.116822i	$-0.962729\pi$
$919$	−11.9867	+	20.7616i	−0.395406	+	0.684862i	0.597747	+	0.801685i	$0.296063\pi$
$920$	−4.07471			−0.134339
$921$	−4.19476	−	3.79354i	−0.138222	−	0.125001i
$922$		−	26.7819i		−	0.882016i
$923$	12.7380	+	22.0628i	0.419276	+	0.726206i
$924$	−8.29550	+	24.5907i	−0.272902	+	0.808973i
$925$	0.783876	−	1.35771i	0.0257737	−	0.0446413i
$926$	−13.5082	−	7.79895i	−0.443906	−	0.256289i
$927$	−16.7275	+	1.68453i	−0.549402	+	0.0553271i
$928$	3.05152	+	5.28540i	0.100171	+	0.173502i
$929$	15.9915	+	27.6981i	0.524665	+	0.908746i	0.999588	+	0.0287187i	$0.00914271\pi$
$929$	15.9915	+	27.6981i	0.524665	+	0.908746i	−0.474923	+	0.880028i	$0.657524\pi$
$930$	0.428243	−	0.473535i	0.0140426	−	0.0155278i
$931$	6.86016	−	29.6355i	0.224833	−	0.971263i
$932$	−15.4047	+	8.89393i	−0.504599	+	0.291330i
$933$	−14.1273	−	43.8037i	−0.462508	−	1.43407i
$934$		−	23.2636i		−	0.761210i
$935$	34.4345	−	19.8807i	1.12613	−	0.650170i
$936$	6.84294	−	4.92631i	0.223668	−	0.161021i
$937$			19.4842i			0.636522i	0.948003	+	0.318261i	$0.103099\pi$
$937$			19.4842i			0.636522i	−0.948003	+	0.318261i	$0.896901\pi$
$938$	5.80830	+	4.30055i	0.189648	+	0.140418i
$939$	1.76425	−	8.21219i	0.0575741	−	0.267995i
$940$	5.18675			0.169173
$941$	−4.96490	+	8.59946i	−0.161851	+	0.280334i	−0.935533	−	0.353240i	$-0.885080\pi$
$941$	−4.96490	+	8.59946i	−0.161851	+	0.280334i	0.773681	+	0.633575i	$0.218413\pi$
$942$	3.87119	−	4.28062i	0.126130	−	0.139470i
$943$	9.85214	−	5.68814i	0.320830	−	0.185231i
$944$	10.6575			0.346871
$945$	−13.1393	+	4.04446i	−0.427423	+	0.131566i
$946$	−36.0374			−1.17168
$947$	41.6103	−	24.0237i	1.35215	−	0.780665i	0.363601	−	0.931555i	$-0.381547\pi$
$947$	41.6103	−	24.0237i	1.35215	−	0.780665i	0.988551	+	0.150890i	$0.0482138\pi$
$948$	10.1575	−	11.2318i	0.329902	−	0.364793i
$949$	−23.3238	+	40.3981i	−0.757124	+	1.31138i
$950$	−4.34559			−0.140989
$951$	−8.25301	+	38.4159i	−0.267622	+	1.24572i
$952$	2.10824	−	18.4558i	0.0683285	−	0.598155i
$953$			43.5664i			1.41126i	0.708583	+	0.705628i	$0.249335\pi$
$953$			43.5664i			1.41126i	−0.708583	+	0.705628i	$0.750665\pi$
$954$	−9.56078	−	4.30671i	−0.309542	−	0.139435i
$955$	−5.35829	+	3.09361i	−0.173390	+	0.100107i
$956$			3.92765i			0.127029i
$957$	18.3753	+	56.9750i	0.593988	+	1.84174i
$958$	16.4012	−	9.46923i	0.529898	−	0.305937i
$959$	44.7891	+	33.1625i	1.44631	+	1.07087i
$960$	1.16177	−	1.28464i	0.0374959	−	0.0414615i
$961$	−15.4321	−	26.7291i	−0.497808	−	0.862230i
$962$	2.20315	+	3.81597i	0.0710324	+	0.123032i
$963$	−1.96970	+	4.37269i	−0.0634728	+	0.140908i
$964$	−9.65172	−	5.57242i	−0.310861	−	0.179476i
$965$	1.04267	−	1.80595i	0.0335646	−	0.0581356i
$966$	−14.0155	+	12.3383i	−0.450942	+	0.396979i
$967$	1.35974	+	2.35513i	0.0437261	+	0.0757359i	0.887060	−	0.461654i	$-0.152744\pi$
$967$	1.35974	+	2.35513i	0.0437261	+	0.0757359i	−0.843334	+	0.537390i	$0.819410\pi$
$968$		−	21.0722i		−	0.677285i
$969$	39.1947	+	35.4459i	1.25912	+	1.13869i
$970$	1.94236			0.0623655
$971$	5.40380	−	9.35966i	0.173416	−	0.300366i	−0.766196	−	0.642607i	$-0.777853\pi$
$971$	5.40380	−	9.35966i	0.173416	−	0.300366i	0.939612	+	0.342241i	$0.111186\pi$
$972$	7.64683	+	13.5840i	0.245272	+	0.435708i
$973$	2.71053	−	23.7282i	0.0868955	−	0.760692i
$974$	−24.9350	−	14.3962i	−0.798968	−	0.461284i
$975$	1.02249	−	4.75948i	0.0327460	−	0.152425i
$976$	−12.6860	−	7.32427i	−0.406069	−	0.234444i
$977$	−16.0175	−	9.24772i	−0.512446	−	0.295861i	0.221393	−	0.975185i	$-0.428940\pi$
$977$	−16.0175	−	9.24772i	−0.512446	−	0.295861i	−0.733839	+	0.679324i	$0.762273\pi$
$978$	18.0185	+	16.2951i	0.576167	+	0.521059i
$979$	−3.25766	−	1.88081i	−0.104115	−	0.0601109i
$980$	6.81967	+	1.57865i	0.217846	+	0.0504281i
$981$	12.8283	−	9.23523i	0.409576	−	0.294858i
$982$	1.36608	−	2.36612i	0.0435934	−	0.0755061i
$983$	41.8397			1.33448			0.667239	−	0.744844i	$-0.267476\pi$
$983$	41.8397			1.33448			0.667239	+	0.744844i	$0.267476\pi$
$984$	−1.01570	+	4.72788i	−0.0323794	+	0.150719i
$985$			24.7197i			0.787636i
$986$	−21.4247	−	37.1087i	−0.682302	−	1.18178i
$987$	17.8405	−	15.7056i	0.567870	−	0.499914i
$988$	6.10681	−	10.5773i	0.194284	−	0.336509i
$989$	−22.4552	−	12.9645i	−0.714033	−	0.412247i
$990$	13.7883	−	9.92635i	0.438221	−	0.315480i
$991$	−6.08551	−	10.5404i	−0.193313	−	0.334827i	0.753034	−	0.657982i	$-0.228590\pi$
$991$	−6.08551	−	10.5404i	−0.193313	−	0.334827i	−0.946346	+	0.323155i	$0.895256\pi$
$992$	0.184307	+	0.319228i	0.00585174	+	0.0101355i
$993$	17.5547	+	3.77132i	0.557080	+	0.119679i
$994$	23.8269	+	2.72180i	0.755744	+	0.0863302i
$995$	−5.60009	+	3.23321i	−0.177535	+	0.102500i
$996$	28.2515	+	6.06934i	0.895182	+	0.192314i
$997$		−	7.33233i		−	0.232217i	−0.993237	−	0.116109i	$-0.962958\pi$
$997$		−	7.33233i		−	0.232217i	0.993237	−	0.116109i	$-0.0370420\pi$
$998$	−20.9329	+	12.0856i	−0.662620	+	0.382564i
$999$	−7.46348	+	3.26472i	−0.236134	+	0.103291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.551.5	yes	28
3.2	odd	2		1890.2.t.b.1601.8		28
7.3	odd	6		630.2.bk.b.101.7	yes	28
9.4	even	3		1890.2.bk.b.341.14		28
9.5	odd	6		630.2.bk.b.131.14	yes	28
21.17	even	6		1890.2.bk.b.521.14		28
63.31	odd	6		1890.2.t.b.1151.8		28
63.59	even	6	inner	630.2.t.b.311.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.5	✓	28	63.59	even	6	inner
630.2.t.b.551.5	yes	28	1.1	even	1	trivial
630.2.bk.b.101.7	yes	28	7.3	odd	6
630.2.bk.b.131.14	yes	28	9.5	odd	6
1890.2.t.b.1151.8		28	63.31	odd	6
1890.2.t.b.1601.8		28	3.2	odd	2
1890.2.bk.b.341.14		28	9.4	even	3
1890.2.bk.b.521.14		28	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.16177 - 1.28464i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.363801 + 1.69341i) q^{6} +(-1.57438 + 2.12634i) q^{7} +1.00000i q^{8} +(-0.300592 - 2.98490i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.16177 - 1.28464i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(-0.363801 + 1.69341i) q^{6} +(-1.57438 + 2.12634i) q^{7} +1.00000i q^{8} +(-0.300592 - 2.98490i) q^{9} +(0.866025 - 0.500000i) q^{10} +5.66323i q^{11} +(-0.531646 - 1.64844i) q^{12} +(2.43404 - 1.40529i) q^{13} +(0.300277 - 2.62866i) q^{14} +(-1.16177 + 1.28464i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.51050 + 6.08036i) q^{17} +(1.75277 + 2.43471i) q^{18} +(3.76339 + 2.17279i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.902526 + 4.49282i) q^{21} +(-2.83161 - 4.90450i) q^{22} -4.07471i q^{23} +(1.28464 + 1.16177i) q^{24} +1.00000 q^{25} +(-1.40529 + 2.43404i) q^{26} +(-4.18374 - 3.08161i) q^{27} +(1.05428 + 2.42662i) q^{28} +(5.28540 + 3.05152i) q^{29} +(0.363801 - 1.69341i) q^{30} +(0.319228 + 0.184307i) q^{31} +(0.866025 + 0.500000i) q^{32} +(7.27520 + 6.57936i) q^{33} +(-6.08036 - 3.51050i) q^{34} +(1.57438 - 2.12634i) q^{35} +(-2.73530 - 1.23213i) q^{36} +(0.783876 - 1.35771i) q^{37} -4.34559 q^{38} +(1.02249 - 4.75948i) q^{39} -1.00000i q^{40} +(1.39596 + 2.41787i) q^{41} +(-3.02802 - 3.43963i) q^{42} +(3.18170 - 5.51086i) q^{43} +(4.90450 + 2.83161i) q^{44} +(0.300592 + 2.98490i) q^{45} +(2.03736 + 3.52880i) q^{46} +(-2.59337 - 4.49185i) q^{47} +(-1.69341 - 0.363801i) q^{48} +(-2.04268 - 6.69533i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(11.8894 + 2.55424i) q^{51} -2.81058i q^{52} +(-3.02705 + 1.74767i) q^{53} +(5.16403 + 0.576883i) q^{54} -5.66323i q^{55} +(-2.12634 - 1.57438i) q^{56} +(7.16344 - 2.31031i) q^{57} -6.10305 q^{58} +(-5.32873 + 9.22962i) q^{59} +(0.531646 + 1.64844i) q^{60} +(12.6860 - 7.32427i) q^{61} -0.368613 q^{62} +(6.82018 + 4.06020i) q^{63} -1.00000 q^{64} +(-2.43404 + 1.40529i) q^{65} +(-9.59019 - 2.06029i) q^{66} +(-1.36579 + 2.36562i) q^{67} +7.02099 q^{68} +(-5.23453 - 4.73387i) q^{69} +(-0.300277 + 2.62866i) q^{70} +9.06430i q^{71} +(2.98490 - 0.300592i) q^{72} +(-14.3736 + 8.29858i) q^{73} +1.56775i q^{74} +(1.16177 - 1.28464i) q^{75} +(3.76339 - 2.17279i) q^{76} +(-12.0420 - 8.91605i) q^{77} +(1.49423 + 4.63307i) q^{78} +(4.37159 + 7.57182i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-8.81929 + 1.79448i) q^{81} +(-2.41787 - 1.39596i) q^{82} +(-8.34157 + 14.4480i) q^{83} +(4.34216 + 1.46480i) q^{84} +(-3.51050 - 6.08036i) q^{85} +6.36340i q^{86} +(10.0605 - 3.24466i) q^{87} -5.66323 q^{88} +(-0.332109 + 0.575230i) q^{89} +(-1.75277 - 2.43471i) q^{90} +(-0.843953 + 7.38805i) q^{91} +(-3.52880 - 2.03736i) q^{92} +(0.607637 - 0.195972i) q^{93} +(4.49185 + 2.59337i) q^{94} +(-3.76339 - 2.17279i) q^{95} +(1.64844 - 0.531646i) q^{96} +(1.68214 + 0.971182i) q^{97} +(5.11668 + 4.77698i) q^{98} +(16.9042 - 1.70232i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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