LMFDB - Embedded newform 370.2.q.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (of order $12$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.97
Dual form			370.2.q.b.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.633975 - 2.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.366025 - 1.36603i) q^{7} +1.00000 q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.633975 - 2.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.366025 - 1.36603i) q^{7} +1.00000 q^{8} +(-2.59808 - 1.50000i) q^{9} +(-1.00000 - 2.00000i) q^{10} -6.46410i q^{11} +(-2.36603 + 0.633975i) q^{12} +(0.133975 + 0.232051i) q^{13} +(1.00000 + 1.00000i) q^{14} +(3.63397 + 4.09808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.36603 - 1.36603i) q^{17} +(2.59808 - 1.50000i) q^{18} +(1.86603 + 0.500000i) q^{19} +(2.23205 + 0.133975i) q^{20} +(-3.00000 - 1.73205i) q^{21} +(5.59808 + 3.23205i) q^{22} -3.73205 q^{23} +(0.633975 - 2.36603i) q^{24} +(-1.96410 - 4.59808i) q^{25} -0.267949 q^{26} +(-1.36603 + 0.366025i) q^{28} +(-5.46410 - 5.46410i) q^{29} +(-5.36603 + 1.09808i) q^{30} +(4.19615 - 4.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-15.2942 - 4.09808i) q^{33} +(2.36603 - 1.36603i) q^{34} +(2.09808 + 2.36603i) q^{35} +3.00000i q^{36} +(0.500000 + 6.06218i) q^{37} +(-1.36603 + 1.36603i) q^{38} +(0.633975 - 0.169873i) q^{39} +(-1.23205 + 1.86603i) q^{40} +(2.19615 - 1.26795i) q^{41} +(3.00000 - 1.73205i) q^{42} +4.00000 q^{43} +(-5.59808 + 3.23205i) q^{44} +(6.00000 - 3.00000i) q^{45} +(1.86603 - 3.23205i) q^{46} +(-3.09808 - 3.09808i) q^{47} +(1.73205 + 1.73205i) q^{48} +(4.33013 + 2.50000i) q^{49} +(4.96410 + 0.598076i) q^{50} +(-4.73205 + 4.73205i) q^{51} +(0.133975 - 0.232051i) q^{52} +(3.56218 + 13.2942i) q^{53} +(12.0622 + 7.96410i) q^{55} +(0.366025 - 1.36603i) q^{56} +(2.36603 - 4.09808i) q^{57} +(7.46410 - 2.00000i) q^{58} +(0.598076 + 2.23205i) q^{59} +(1.73205 - 5.19615i) q^{60} +(11.5622 + 3.09808i) q^{61} +(1.53590 + 5.73205i) q^{62} +(-3.00000 + 3.00000i) q^{63} +1.00000 q^{64} +(-0.598076 - 0.0358984i) q^{65} +(11.1962 - 11.1962i) q^{66} +(-5.83013 - 1.56218i) q^{67} +2.73205i q^{68} +(-2.36603 + 8.83013i) q^{69} +(-3.09808 + 0.633975i) q^{70} +(3.00000 + 5.19615i) q^{71} +(-2.59808 - 1.50000i) q^{72} +(-7.92820 - 7.92820i) q^{73} +(-5.50000 - 2.59808i) q^{74} +(-12.1244 + 1.73205i) q^{75} +(-0.500000 - 1.86603i) q^{76} +(-8.83013 - 2.36603i) q^{77} +(-0.169873 + 0.633975i) q^{78} +(12.9282 + 3.46410i) q^{79} +(-1.00000 - 2.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +2.53590i q^{82} +(1.46410 + 5.46410i) q^{83} +3.46410i q^{84} +(5.46410 - 2.73205i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-16.3923 + 9.46410i) q^{87} -6.46410i q^{88} +(11.7942 - 3.16025i) q^{89} +(-0.401924 + 6.69615i) q^{90} +(0.366025 - 0.0980762i) q^{91} +(1.86603 + 3.23205i) q^{92} +(-7.26795 - 12.5885i) q^{93} +(4.23205 - 1.13397i) q^{94} +(-3.23205 + 2.86603i) q^{95} +(-2.36603 + 0.633975i) q^{96} +2.53590i q^{97} +(-4.33013 + 2.50000i) q^{98} +(-9.69615 + 16.7942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8} - 4 q^{10} - 6 q^{12} + 4 q^{13} + 4 q^{14} + 18 q^{15} - 2 q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{20} - 12 q^{21} + 12 q^{22} - 8 q^{23} + 6 q^{24} + 6 q^{25} - 8 q^{26} - 2 q^{28} - 8 q^{29} - 18 q^{30} - 4 q^{31} - 2 q^{32} - 30 q^{33} + 6 q^{34} - 2 q^{35} + 2 q^{37} - 2 q^{38} + 6 q^{39} + 2 q^{40} - 12 q^{41} + 12 q^{42} + 16 q^{43} - 12 q^{44} + 24 q^{45} + 4 q^{46} - 2 q^{47} + 6 q^{50} - 12 q^{51} + 4 q^{52} - 10 q^{53} + 24 q^{55} - 2 q^{56} + 6 q^{57} + 16 q^{58} - 8 q^{59} + 22 q^{61} + 20 q^{62} - 12 q^{63} + 4 q^{64} + 8 q^{65} + 24 q^{66} - 6 q^{67} - 6 q^{69} - 2 q^{70} + 12 q^{71} - 4 q^{73} - 22 q^{74} - 2 q^{76} - 18 q^{77} - 18 q^{78} + 24 q^{79} - 4 q^{80} - 18 q^{81} - 8 q^{83} + 8 q^{85} - 8 q^{86} - 24 q^{87} + 16 q^{89} - 12 q^{90} - 2 q^{91} + 4 q^{92} - 36 q^{93} + 10 q^{94} - 6 q^{95} - 6 q^{96} - 18 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8 - 4 * q^10 - 6 * q^12 + 4 * q^13 + 4 * q^14 + 18 * q^15 - 2 * q^16 - 6 * q^17 + 4 * q^19 + 2 * q^20 - 12 * q^21 + 12 * q^22 - 8 * q^23 + 6 * q^24 + 6 * q^25 - 8 * q^26 - 2 * q^28 - 8 * q^29 - 18 * q^30 - 4 * q^31 - 2 * q^32 - 30 * q^33 + 6 * q^34 - 2 * q^35 + 2 * q^37 - 2 * q^38 + 6 * q^39 + 2 * q^40 - 12 * q^41 + 12 * q^42 + 16 * q^43 - 12 * q^44 + 24 * q^45 + 4 * q^46 - 2 * q^47 + 6 * q^50 - 12 * q^51 + 4 * q^52 - 10 * q^53 + 24 * q^55 - 2 * q^56 + 6 * q^57 + 16 * q^58 - 8 * q^59 + 22 * q^61 + 20 * q^62 - 12 * q^63 + 4 * q^64 + 8 * q^65 + 24 * q^66 - 6 * q^67 - 6 * q^69 - 2 * q^70 + 12 * q^71 - 4 * q^73 - 22 * q^74 - 2 * q^76 - 18 * q^77 - 18 * q^78 + 24 * q^79 - 4 * q^80 - 18 * q^81 - 8 * q^83 + 8 * q^85 - 8 * q^86 - 24 * q^87 + 16 * q^89 - 12 * q^90 - 2 * q^91 + 4 * q^92 - 36 * q^93 + 10 * q^94 - 6 * q^95 - 6 * q^96 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.633975	−	2.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.633975	−	2.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$6$	1.73205	+	1.73205i	0.707107	+	0.707107i
$7$	0.366025	−	1.36603i	0.138345	−	0.516309i	−0.861617	−	0.507559i	$-0.830548\pi$
$7$	0.366025	−	1.36603i	0.138345	−	0.516309i	0.999962	−	0.00875026i	$-0.00278533\pi$
$8$	1.00000			0.353553
$9$	−2.59808	−	1.50000i	−0.866025	−	0.500000i
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$		−	6.46410i		−	1.94900i	−0.224388	−	0.974500i	$-0.572038\pi$
$11$		−	6.46410i		−	1.94900i	0.224388	−	0.974500i	$-0.427962\pi$
$12$	−2.36603	+	0.633975i	−0.683013	+	0.183013i
$13$	0.133975	+	0.232051i	0.0371579	+	0.0643593i	0.884006	−	0.467475i	$-0.154836\pi$
$13$	0.133975	+	0.232051i	0.0371579	+	0.0643593i	−0.846848	+	0.531834i	$0.821503\pi$
$14$	1.00000	+	1.00000i	0.267261	+	0.267261i
$15$	3.63397	+	4.09808i	0.938288	+	1.05812i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.36603	−	1.36603i	−0.573845	−	0.331310i	0.184838	−	0.982769i	$-0.440824\pi$
$17$	−2.36603	−	1.36603i	−0.573845	−	0.331310i	−0.758684	+	0.651459i	$0.774157\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	1.86603	+	0.500000i	0.428096	+	0.114708i	0.466432	−	0.884557i	$-0.345539\pi$
$19$	1.86603	+	0.500000i	0.428096	+	0.114708i	−0.0383365	+	0.999265i	$0.512206\pi$
$20$	2.23205	+	0.133975i	0.499102	+	0.0299576i
$21$	−3.00000	−	1.73205i	−0.654654	−	0.377964i
$22$	5.59808	+	3.23205i	1.19351	+	0.689076i
$23$	−3.73205			−0.778186			−0.389093	−	0.921198i	$-0.627212\pi$
$23$	−3.73205			−0.778186			−0.389093	+	0.921198i	$0.627212\pi$
$24$	0.633975	−	2.36603i	0.129410	−	0.482963i
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$	−0.267949			−0.0525492
$27$		0			0
$28$	−1.36603	+	0.366025i	−0.258155	+	0.0691723i
$29$	−5.46410	−	5.46410i	−1.01466	−	1.01466i	−0.999891	−	0.0147672i	$-0.995299\pi$
$29$	−5.46410	−	5.46410i	−1.01466	−	1.01466i	−0.0147672	−	0.999891i	$-0.504701\pi$
$30$	−5.36603	+	1.09808i	−0.979698	+	0.200480i
$31$	4.19615	−	4.19615i	0.753651	−	0.753651i	−0.221507	−	0.975159i	$-0.571098\pi$
$31$	4.19615	−	4.19615i	0.753651	−	0.753651i	0.975159	+	0.221507i	$0.0710977\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−15.2942	−	4.09808i	−2.66238	−	0.713384i
$34$	2.36603	−	1.36603i	0.405770	−	0.234271i
$35$	2.09808	+	2.36603i	0.354640	+	0.399931i
$36$			3.00000i			0.500000i
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$38$	−1.36603	+	1.36603i	−0.221599	+	0.221599i
$39$	0.633975	−	0.169873i	0.101517	−	0.0272014i
$40$	−1.23205	+	1.86603i	−0.194804	+	0.295045i
$41$	2.19615	−	1.26795i	0.342981	−	0.198020i	−0.318608	−	0.947886i	$-0.603215\pi$
$41$	2.19615	−	1.26795i	0.342981	−	0.198020i	0.661590	+	0.749866i	$0.269882\pi$
$42$	3.00000	−	1.73205i	0.462910	−	0.267261i
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−5.59808	+	3.23205i	−0.843942	+	0.487250i
$45$	6.00000	−	3.00000i	0.894427	−	0.447214i
$46$	1.86603	−	3.23205i	0.275130	−	0.476540i
$47$	−3.09808	−	3.09808i	−0.451901	−	0.451901i	0.444084	−	0.895985i	$-0.353529\pi$
$47$	−3.09808	−	3.09808i	−0.451901	−	0.451901i	−0.895985	+	0.444084i	$0.853529\pi$
$48$	1.73205	+	1.73205i	0.250000	+	0.250000i
$49$	4.33013	+	2.50000i	0.618590	+	0.357143i
$50$	4.96410	+	0.598076i	0.702030	+	0.0845807i
$51$	−4.73205	+	4.73205i	−0.662620	+	0.662620i
$52$	0.133975	−	0.232051i	0.0185789	−	0.0321797i
$53$	3.56218	+	13.2942i	0.489303	+	1.82610i	0.559850	+	0.828594i	$0.310859\pi$
$53$	3.56218	+	13.2942i	0.489303	+	1.82610i	−0.0705468	+	0.997508i	$0.522474\pi$
$54$		0			0
$55$	12.0622	+	7.96410i	1.62646	+	1.07388i
$56$	0.366025	−	1.36603i	0.0489122	−	0.182543i
$57$	2.36603	−	4.09808i	0.313388	−	0.542803i
$58$	7.46410	−	2.00000i	0.980085	−	0.262613i
$59$	0.598076	+	2.23205i	0.0778629	+	0.290588i	0.993867	−	0.110580i	$-0.0352709\pi$
$59$	0.598076	+	2.23205i	0.0778629	+	0.290588i	−0.916004	+	0.401168i	$0.868604\pi$
$60$	1.73205	−	5.19615i	0.223607	−	0.670820i
$61$	11.5622	+	3.09808i	1.48039	+	0.396668i	0.906478	−	0.422253i	$-0.138760\pi$
$61$	11.5622	+	3.09808i	1.48039	+	0.396668i	0.573907	+	0.818921i	$0.305427\pi$
$62$	1.53590	+	5.73205i	0.195059	+	0.727971i
$63$	−3.00000	+	3.00000i	−0.377964	+	0.377964i
$64$	1.00000			0.125000
$65$	−0.598076	−	0.0358984i	−0.0741822	−	0.00445265i
$66$	11.1962	−	11.1962i	1.37815	−	1.37815i
$67$	−5.83013	−	1.56218i	−0.712263	−	0.190850i	−0.115546	−	0.993302i	$-0.536862\pi$
$67$	−5.83013	−	1.56218i	−0.712263	−	0.190850i	−0.596717	+	0.802452i	$0.703529\pi$
$68$			2.73205i			0.331310i
$69$	−2.36603	+	8.83013i	−0.284836	+	1.06302i
$70$	−3.09808	+	0.633975i	−0.370291	+	0.0757745i
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	−7.92820	−	7.92820i	−0.927926	−	0.927926i	0.0696458	−	0.997572i	$-0.477813\pi$
$73$	−7.92820	−	7.92820i	−0.927926	−	0.927926i	−0.997572	+	0.0696458i	$0.977813\pi$
$74$	−5.50000	−	2.59808i	−0.639362	−	0.302020i
$75$	−12.1244	+	1.73205i	−1.40000	+	0.200000i
$76$	−0.500000	−	1.86603i	−0.0573539	−	0.214048i
$77$	−8.83013	−	2.36603i	−1.00629	−	0.269634i
$78$	−0.169873	+	0.633975i	−0.0192343	+	0.0717835i
$79$	12.9282	+	3.46410i	1.45454	+	0.389742i	0.897599	−	0.440813i	$-0.145310\pi$
$79$	12.9282	+	3.46410i	1.45454	+	0.389742i	0.556937	+	0.830555i	$0.311976\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$			2.53590i			0.280043i
$83$	1.46410	+	5.46410i	0.160706	+	0.599763i	0.998549	+	0.0538517i	$0.0171498\pi$
$83$	1.46410	+	5.46410i	0.160706	+	0.599763i	−0.837843	+	0.545911i	$0.816184\pi$
$84$			3.46410i			0.377964i
$85$	5.46410	−	2.73205i	0.592665	−	0.296333i
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$	−16.3923	+	9.46410i	−1.75744	+	1.01466i
$88$		−	6.46410i		−	0.689076i
$89$	11.7942	−	3.16025i	1.25019	−	0.334986i	0.427778	−	0.903884i	$-0.359297\pi$
$89$	11.7942	−	3.16025i	1.25019	−	0.334986i	0.822408	+	0.568898i	$0.192630\pi$
$90$	−0.401924	+	6.69615i	−0.0423665	+	0.705836i
$91$	0.366025	−	0.0980762i	0.0383699	−	0.0102812i
$92$	1.86603	+	3.23205i	0.194547	+	0.336965i
$93$	−7.26795	−	12.5885i	−0.753651	−	1.30536i
$94$	4.23205	−	1.13397i	0.436503	−	0.116961i
$95$	−3.23205	+	2.86603i	−0.331601	+	0.294048i
$96$	−2.36603	+	0.633975i	−0.241481	+	0.0647048i
$97$			2.53590i			0.257481i	0.991678	+	0.128741i	$0.0410935\pi$
$97$			2.53590i			0.257481i	−0.991678	+	0.128741i	$0.958906\pi$
$98$	−4.33013	+	2.50000i	−0.437409	+	0.252538i
$99$	−9.69615	+	16.7942i	−0.974500	+	1.68788i
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$			8.39230i			0.835066i	0.908662	+	0.417533i	$0.137105\pi$
$101$			8.39230i			0.835066i	−0.908662	+	0.417533i	$0.862895\pi$
$102$	−1.73205	−	6.46410i	−0.171499	−	0.640041i
$103$		−	3.39230i		−	0.334254i	−0.985935	−	0.167127i	$-0.946551\pi$
$103$		−	3.39230i		−	0.334254i	0.985935	−	0.167127i	$-0.0534489\pi$
$104$	0.133975	+	0.232051i	0.0131373	+	0.0227545i
$105$	6.92820	−	3.46410i	0.676123	−	0.338062i
$106$	−13.2942	−	3.56218i	−1.29125	−	0.345989i
$107$	−0.196152	+	0.732051i	−0.0189628	+	0.0707700i	−0.974759	−	0.223260i	$-0.928330\pi$
$107$	−0.196152	+	0.732051i	−0.0189628	+	0.0707700i	0.955796	+	0.294030i	$0.0949967\pi$
$108$		0			0
$109$	2.83013	+	10.5622i	0.271077	+	1.01167i	0.958425	+	0.285345i	$0.0921081\pi$
$109$	2.83013	+	10.5622i	0.271077	+	1.01167i	−0.687348	+	0.726328i	$0.741225\pi$
$110$	−12.9282	+	6.46410i	−1.23266	+	0.616328i
$111$	14.6603	+	2.66025i	1.39149	+	0.252500i
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	3.63397	+	2.09808i	0.341856	+	0.197370i	0.661092	−	0.750305i	$-0.270093\pi$
$113$	3.63397	+	2.09808i	0.341856	+	0.197370i	−0.319237	+	0.947675i	$0.603427\pi$
$114$	2.36603	+	4.09808i	0.221599	+	0.383820i
$115$	4.59808	−	6.96410i	0.428773	−	0.649406i
$116$	−2.00000	+	7.46410i	−0.185695	+	0.693024i
$117$		−	0.803848i		−	0.0743157i
$118$	−2.23205	−	0.598076i	−0.205477	−	0.0550574i
$119$	−2.73205	+	2.73205i	−0.250447	+	0.250447i
$120$	3.63397	+	4.09808i	0.331735	+	0.374101i
$121$	−30.7846			−2.79860
$122$	−8.46410	+	8.46410i	−0.766304	+	0.766304i
$123$	−1.60770	−	6.00000i	−0.144961	−	0.541002i
$124$	−5.73205	−	1.53590i	−0.514753	−	0.137928i
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$	−1.09808	−	4.09808i	−0.0978244	−	0.365086i
$127$	−5.86603	+	1.57180i	−0.520526	+	0.139474i	−0.509510	−	0.860465i	$-0.670173\pi$
$127$	−5.86603	+	1.57180i	−0.520526	+	0.139474i	−0.0110159	+	0.999939i	$0.503507\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.53590	−	9.46410i	0.223273	−	0.833268i
$130$	0.330127	−	0.500000i	0.0289541	−	0.0438529i
$131$	−3.63397	−	13.5622i	−0.317502	−	1.18493i	−0.921638	−	0.388052i	$-0.873148\pi$
$131$	−3.63397	−	13.5622i	−0.317502	−	1.18493i	0.604136	−	0.796881i	$-0.293518\pi$
$132$	4.09808	+	15.2942i	0.356692	+	1.33119i
$133$	1.36603	−	2.36603i	0.118449	−	0.205160i
$134$	4.26795	−	4.26795i	0.368695	−	0.368695i
$135$		0			0
$136$	−2.36603	−	1.36603i	−0.202885	−	0.117136i
$137$	4.19615	+	4.19615i	0.358501	+	0.358501i	0.863260	−	0.504759i	$-0.168419\pi$
$137$	4.19615	+	4.19615i	0.358501	+	0.358501i	−0.504759	+	0.863260i	$0.668419\pi$
$138$	−6.46410	−	6.46410i	−0.550261	−	0.550261i
$139$	−5.86603	+	10.1603i	−0.497550	+	0.861781i	−0.999996	−	0.00282696i	$-0.999100\pi$
$139$	−5.86603	+	10.1603i	−0.497550	+	0.861781i	0.502446	+	0.864608i	$0.332433\pi$
$140$	1.00000	−	3.00000i	0.0845154	−	0.253546i
$141$	−9.29423	+	5.36603i	−0.782715	+	0.451901i
$142$	−6.00000			−0.503509
$143$	1.50000	−	0.866025i	0.125436	−	0.0724207i
$144$	2.59808	−	1.50000i	0.216506	−	0.125000i
$145$	16.9282	−	3.46410i	1.40581	−	0.287678i
$146$	10.8301	−	2.90192i	0.896308	−	0.240165i
$147$	8.66025	−	8.66025i	0.714286	−	0.714286i
$148$	5.00000	−	3.46410i	0.410997	−	0.284747i
$149$		−	21.4641i		−	1.75841i	−0.476446	−	0.879204i	$-0.658075\pi$
$149$		−	21.4641i		−	1.75841i	0.476446	−	0.879204i	$-0.341925\pi$
$150$	4.56218	−	11.3660i	0.372500	−	0.928032i
$151$	2.83013	−	1.63397i	0.230312	−	0.132971i	−0.380404	−	0.924821i	$-0.624215\pi$
$151$	2.83013	−	1.63397i	0.230312	−	0.132971i	0.610716	+	0.791850i	$0.290882\pi$
$152$	1.86603	+	0.500000i	0.151355	+	0.0405554i
$153$	4.09808	+	7.09808i	0.331310	+	0.573845i
$154$	6.46410	−	6.46410i	0.520892	−	0.520892i
$155$	2.66025	+	13.0000i	0.213677	+	1.04419i
$156$	−0.464102	−	0.464102i	−0.0371579	−	0.0371579i
$157$	1.76795	−	0.473721i	0.141098	−	0.0378070i	−0.187579	−	0.982250i	$-0.560064\pi$
$157$	1.76795	−	0.473721i	0.141098	−	0.0378070i	0.328677	+	0.944443i	$0.393397\pi$
$158$	−9.46410	+	9.46410i	−0.752923	+	0.752923i
$159$	33.7128			2.67360
$160$	2.23205	+	0.133975i	0.176459	+	0.0105916i
$161$	−1.36603	+	5.09808i	−0.107658	+	0.401785i
$162$	9.00000			0.707107
$163$	−1.09808	−	0.633975i	−0.0860080	−	0.0496567i	0.456379	−	0.889785i	$-0.349146\pi$
$163$	−1.09808	−	0.633975i	−0.0860080	−	0.0496567i	−0.542387	+	0.840129i	$0.682479\pi$
$164$	−2.19615	−	1.26795i	−0.171491	−	0.0990102i
$165$	26.4904	−	23.4904i	2.06227	−	1.82872i
$166$	−5.46410	−	1.46410i	−0.424097	−	0.113636i
$167$	−13.8564	+	8.00000i	−1.07224	+	0.619059i	−0.928793	−	0.370599i	$-0.879152\pi$
$167$	−13.8564	+	8.00000i	−1.07224	+	0.619059i	−0.143448	+	0.989658i	$0.545819\pi$
$168$	−3.00000	−	1.73205i	−0.231455	−	0.133631i
$169$	6.46410	−	11.1962i	0.497239	−	0.861242i
$170$	−0.366025	+	6.09808i	−0.0280729	+	0.467701i
$171$	−4.09808	−	4.09808i	−0.313388	−	0.313388i
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	23.1603	−	6.20577i	1.76084	−	0.471816i	0.773956	−	0.633239i	$-0.218275\pi$
$173$	23.1603	−	6.20577i	1.76084	−	0.471816i	0.986885	+	0.161423i	$0.0516084\pi$
$174$		−	18.9282i		−	1.43494i
$175$	−7.00000	+	1.00000i	−0.529150	+	0.0755929i
$176$	5.59808	+	3.23205i	0.421971	+	0.243625i
$177$	5.66025			0.425451
$178$	−3.16025	+	11.7942i	−0.236871	+	0.884015i
$179$	0.437822	+	0.437822i	0.0327244	+	0.0327244i	0.723280	−	0.690555i	$-0.242634\pi$
$179$	0.437822	+	0.437822i	0.0327244	+	0.0327244i	−0.690555	+	0.723280i	$0.742634\pi$
$180$	−5.59808	−	3.69615i	−0.417256	−	0.275495i
$181$	−13.0263	−	22.5622i	−0.968236	−	1.67703i	−0.700658	−	0.713497i	$-0.747110\pi$
$181$	−13.0263	−	22.5622i	−0.968236	−	1.67703i	−0.267578	−	0.963536i	$-0.586223\pi$
$182$	−0.0980762	+	0.366025i	−0.00726989	+	0.0271316i
$183$	14.6603	−	25.3923i	1.08372	−	1.87705i
$184$	−3.73205			−0.275130
$185$	−11.9282	−	6.53590i	−0.876979	−	0.480529i
$186$	14.5359			1.06582
$187$	−8.83013	+	15.2942i	−0.645723	+	1.11842i
$188$	−1.13397	+	4.23205i	−0.0827036	+	0.308654i
$189$		0			0
$190$	−0.866025	−	4.23205i	−0.0628281	−	0.307025i
$191$	−5.80385	−	5.80385i	−0.419952	−	0.419952i	0.465235	−	0.885187i	$-0.345970\pi$
$191$	−5.80385	−	5.80385i	−0.419952	−	0.419952i	−0.885187	+	0.465235i	$0.845970\pi$
$192$	0.633975	−	2.36603i	0.0457532	−	0.170753i
$193$	11.8038			0.849660			0.424830	−	0.905273i	$-0.360334\pi$
$193$	11.8038			0.849660			0.424830	+	0.905273i	$0.360334\pi$
$194$	−2.19615	−	1.26795i	−0.157675	−	0.0910334i
$195$	−0.464102	+	1.39230i	−0.0332350	+	0.0997050i
$196$		−	5.00000i		−	0.357143i
$197$	−7.56218	+	2.02628i	−0.538783	+	0.144366i	−0.517941	−	0.855416i	$-0.673301\pi$
$197$	−7.56218	+	2.02628i	−0.538783	+	0.144366i	−0.0208419	+	0.999783i	$0.506635\pi$
$198$	−9.69615	−	16.7942i	−0.689076	−	1.19351i
$199$	−2.92820	−	2.92820i	−0.207575	−	0.207575i	0.595661	−	0.803236i	$-0.296890\pi$
$199$	−2.92820	−	2.92820i	−0.207575	−	0.207575i	−0.803236	+	0.595661i	$0.796890\pi$
$200$	−1.96410	−	4.59808i	−0.138883	−	0.325133i
$201$	−7.39230	+	12.8038i	−0.521413	+	0.903114i
$202$	−7.26795	−	4.19615i	−0.511371	−	0.295240i
$203$	−9.46410	+	5.46410i	−0.664250	+	0.383505i
$204$	6.46410	+	1.73205i	0.452578	+	0.121268i
$205$	−0.339746	+	5.66025i	−0.0237289	+	0.395329i
$206$	2.93782	+	1.69615i	0.204688	+	0.118177i
$207$	9.69615	+	5.59808i	0.673929	+	0.389093i
$208$	−0.267949			−0.0185789
$209$	3.23205	−	12.0622i	0.223566	−	0.834358i
$210$	−0.464102	+	7.73205i	−0.0320261	+	0.533562i
$211$	26.8564			1.84887			0.924436	−	0.381338i	$-0.124537\pi$
$211$	26.8564			1.84887			0.924436	+	0.381338i	$0.124537\pi$
$212$	9.73205	−	9.73205i	0.668400	−	0.668400i
$213$	14.1962	−	3.80385i	0.972704	−	0.260635i
$214$	−0.535898	−	0.535898i	−0.0366333	−	0.0366333i
$215$	−4.92820	+	7.46410i	−0.336101	+	0.509048i
$216$		0			0
$217$	−4.19615	−	7.26795i	−0.284853	−	0.493381i
$218$	−10.5622	−	2.83013i	−0.715361	−	0.191680i
$219$	−23.7846	+	13.7321i	−1.60721	+	0.927926i
$220$	0.866025	−	14.4282i	0.0583874	−	0.972749i
$221$		−	0.732051i		−	0.0492431i
$222$	−9.63397	+	11.3660i	−0.646590	+	0.762838i
$223$	9.63397	−	9.63397i	0.645139	−	0.645139i	−0.306675	−	0.951814i	$-0.599217\pi$
$223$	9.63397	−	9.63397i	0.645139	−	0.645139i	0.951814	+	0.306675i	$0.0992166\pi$
$224$	−1.36603	+	0.366025i	−0.0912714	+	0.0244561i
$225$	−1.79423	+	14.8923i	−0.119615	+	0.992820i
$226$	−3.63397	+	2.09808i	−0.241728	+	0.139562i
$227$	−19.9019	+	11.4904i	−1.32094	+	0.762643i	−0.983878	−	0.178840i	$-0.942765\pi$
$227$	−19.9019	+	11.4904i	−1.32094	+	0.762643i	−0.337059	+	0.941484i	$0.609432\pi$
$228$	−4.73205			−0.313388
$229$	−16.8564	+	9.73205i	−1.11390	+	0.643112i	−0.939837	−	0.341622i	$-0.889024\pi$
$229$	−16.8564	+	9.73205i	−1.11390	+	0.643112i	−0.174065	+	0.984734i	$0.555690\pi$
$230$	3.73205	+	7.46410i	0.246084	+	0.492168i
$231$	−11.1962	+	19.3923i	−0.736653	+	1.27592i
$232$	−5.46410	−	5.46410i	−0.358736	−	0.358736i
$233$	7.19615	+	7.19615i	0.471436	+	0.471436i	0.902379	−	0.430943i	$-0.141819\pi$
$233$	7.19615	+	7.19615i	0.471436	+	0.471436i	−0.430943	+	0.902379i	$0.641819\pi$
$234$	0.696152	+	0.401924i	0.0455089	+	0.0262746i
$235$	9.59808	−	1.96410i	0.626109	−	0.128124i
$236$	1.63397	−	1.63397i	0.106363	−	0.106363i
$237$	16.3923	−	28.3923i	1.06479	−	1.84428i
$238$	−1.00000	−	3.73205i	−0.0648204	−	0.241913i
$239$	1.49038	+	5.56218i	0.0964047	+	0.359787i	0.997229	−	0.0743971i	$-0.0237032\pi$
$239$	1.49038	+	5.56218i	0.0964047	+	0.359787i	−0.900824	+	0.434185i	$0.857037\pi$
$240$	−5.36603	+	1.09808i	−0.346375	+	0.0708805i
$241$	−2.03590	+	7.59808i	−0.131144	+	0.489435i	−0.999984	−	0.00565742i	$-0.998199\pi$
$241$	−2.03590	+	7.59808i	−0.131144	+	0.489435i	0.868840	+	0.495093i	$0.164866\pi$
$242$	15.3923	−	26.6603i	0.989455	−	1.71379i
$243$	−21.2942	+	5.70577i	−1.36603	+	0.366025i
$244$	−3.09808	−	11.5622i	−0.198334	−	0.740193i
$245$	−10.0000	+	5.00000i	−0.638877	+	0.319438i
$246$	6.00000	+	1.60770i	0.382546	+	0.102503i
$247$	0.133975	+	0.500000i	0.00852460	+	0.0318142i
$248$	4.19615	−	4.19615i	0.266456	−	0.266456i
$249$	13.8564			0.878114
$250$	−7.23205	+	8.52628i	−0.457395	+	0.539249i
$251$	−6.90192	+	6.90192i	−0.435646	+	0.435646i	−0.890544	−	0.454898i	$-0.849676\pi$
$251$	−6.90192	+	6.90192i	−0.435646	+	0.435646i	0.454898	+	0.890544i	$0.349676\pi$
$252$	4.09808	+	1.09808i	0.258155	+	0.0691723i
$253$			24.1244i			1.51669i
$254$	1.57180	−	5.86603i	0.0986233	−	0.368067i
$255$	−3.00000	−	14.6603i	−0.187867	−	0.918061i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.90192	+	4.56218i	0.492908	+	0.284581i	0.725780	−	0.687927i	$-0.241479\pi$
$257$	7.90192	+	4.56218i	0.492908	+	0.284581i	−0.232872	+	0.972507i	$0.574812\pi$
$258$	6.92820	+	6.92820i	0.431331	+	0.431331i
$259$	8.46410	+	1.53590i	0.525934	+	0.0954361i
$260$	0.267949	+	0.535898i	0.0166175	+	0.0332350i
$261$	6.00000	+	22.3923i	0.371391	+	1.38605i
$262$	13.5622	+	3.63397i	0.837874	+	0.224508i
$263$	2.50000	−	9.33013i	0.154157	−	0.575320i	−0.845019	−	0.534735i	$-0.820411\pi$
$263$	2.50000	−	9.33013i	0.154157	−	0.575320i	0.999176	−	0.0405848i	$-0.0129221\pi$
$264$	−15.2942	−	4.09808i	−0.941295	−	0.252219i
$265$	−29.1962	−	9.73205i	−1.79351	−	0.597835i
$266$	1.36603	+	2.36603i	0.0837564	+	0.145070i
$267$		−	29.9090i		−	1.83040i
$268$	1.56218	+	5.83013i	0.0954252	+	0.356132i
$269$			12.7321i			0.776287i	0.921599	+	0.388143i	$0.126883\pi$
$269$			12.7321i			0.776287i	−0.921599	+	0.388143i	$0.873117\pi$
$270$		0			0
$271$	12.8564	−	22.2679i	0.780971	−	1.35268i	−0.150406	−	0.988624i	$-0.548058\pi$
$271$	12.8564	−	22.2679i	0.780971	−	1.35268i	0.931377	−	0.364057i	$-0.118609\pi$
$272$	2.36603	−	1.36603i	0.143461	−	0.0828275i
$273$		−	0.928203i		−	0.0561774i
$274$	−5.73205	+	1.53590i	−0.346286	+	0.0927870i
$275$	−29.7224	+	12.6962i	−1.79233	+	0.765607i
$276$	8.83013	−	2.36603i	0.531511	−	0.142418i
$277$	10.7321	+	18.5885i	0.644826	+	1.11687i	0.984342	+	0.176272i	$0.0564037\pi$
$277$	10.7321	+	18.5885i	0.644826	+	1.11687i	−0.339515	+	0.940601i	$0.610263\pi$
$278$	−5.86603	−	10.1603i	−0.351821	−	0.609372i
$279$	−17.1962	+	4.60770i	−1.02951	+	0.275855i
$280$	2.09808	+	2.36603i	0.125384	+	0.141397i
$281$	−6.50000	+	1.74167i	−0.387757	+	0.103899i	−0.447431	−	0.894319i	$-0.647661\pi$
$281$	−6.50000	+	1.74167i	−0.387757	+	0.103899i	0.0596731	+	0.998218i	$0.480994\pi$
$282$		−	10.7321i		−	0.639084i
$283$	−3.29423	+	1.90192i	−0.195822	+	0.113058i	−0.594705	−	0.803944i	$-0.702731\pi$
$283$	−3.29423	+	1.90192i	−0.195822	+	0.113058i	0.398883	+	0.917002i	$0.369398\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	4.73205	+	9.46410i	0.280302	+	0.560605i
$286$			1.73205i			0.102418i
$287$	−0.928203	−	3.46410i	−0.0547901	−	0.204479i
$288$			3.00000i			0.176777i
$289$	−4.76795	−	8.25833i	−0.280468	−	0.485784i
$290$	−5.46410	+	16.3923i	−0.320863	+	0.962589i
$291$	6.00000	+	1.60770i	0.351726	+	0.0942448i
$292$	−2.90192	+	10.8301i	−0.169822	+	0.633785i
$293$	−9.06218	−	2.42820i	−0.529418	−	0.141857i	−0.0157985	−	0.999875i	$-0.505029\pi$
$293$	−9.06218	−	2.42820i	−0.529418	−	0.141857i	−0.513620	+	0.858018i	$0.671696\pi$
$294$	3.16987	+	11.8301i	0.184871	+	0.689947i
$295$	−4.90192	−	1.63397i	−0.285401	−	0.0951337i
$296$	0.500000	+	6.06218i	0.0290619	+	0.352357i
$297$		0			0
$298$	18.5885	+	10.7321i	1.07680	+	0.621691i
$299$	−0.500000	−	0.866025i	−0.0289157	−	0.0500835i
$300$	7.56218	+	9.63397i	0.436603	+	0.556218i
$301$	1.46410	−	5.46410i	0.0843894	−	0.314946i
$302$			3.26795i			0.188049i
$303$	19.8564	+	5.32051i	1.14072	+	0.305655i
$304$	−1.36603	+	1.36603i	−0.0783469	+	0.0783469i
$305$	−20.0263	+	17.7583i	−1.14670	+	1.01684i
$306$	−8.19615			−0.468543
$307$	−1.73205	+	1.73205i	−0.0988534	+	0.0988534i	−0.754804	−	0.655951i	$-0.772268\pi$
$307$	−1.73205	+	1.73205i	−0.0988534	+	0.0988534i	0.655951	+	0.754804i	$0.272268\pi$
$308$	2.36603	+	8.83013i	0.134817	+	0.503143i
$309$	−8.02628	−	2.15064i	−0.456599	−	0.122345i
$310$	−12.5885	−	4.19615i	−0.714976	−	0.238325i
$311$	1.36603	+	5.09808i	0.0774602	+	0.289085i	0.993780	−	0.111362i	$-0.0355213\pi$
$311$	1.36603	+	5.09808i	0.0774602	+	0.289085i	−0.916320	+	0.400448i	$0.868855\pi$
$312$	0.633975	−	0.169873i	0.0358917	−	0.00961716i
$313$	13.9282	−	24.1244i	0.787269	−	1.36359i	−0.140366	−	0.990100i	$-0.544828\pi$
$313$	13.9282	−	24.1244i	0.787269	−	1.36359i	0.927634	−	0.373489i	$-0.121839\pi$
$314$	−0.473721	+	1.76795i	−0.0267336	+	0.0997711i
$315$	−1.90192	−	9.29423i	−0.107161	−	0.523670i
$316$	−3.46410	−	12.9282i	−0.194871	−	0.727268i
$317$	−3.47372	−	12.9641i	−0.195104	−	0.728136i	−0.992240	−	0.124337i	$-0.960320\pi$
$317$	−3.47372	−	12.9641i	−0.195104	−	0.728136i	0.797136	−	0.603799i	$-0.206347\pi$
$318$	−16.8564	+	29.1962i	−0.945260	+	1.63724i
$319$	−35.3205	+	35.3205i	−1.97757	+	1.97757i
$320$	−1.23205	+	1.86603i	−0.0688737	+	0.104314i
$321$	1.60770	+	0.928203i	0.0897328	+	0.0518073i
$322$	−3.73205	−	3.73205i	−0.207979	−	0.207979i
$323$	−3.73205	−	3.73205i	−0.207657	−	0.207657i
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	0.803848	−	1.07180i	0.0445894	−	0.0594526i
$326$	1.09808	−	0.633975i	0.0608168	−	0.0351126i
$327$	26.7846			1.48119
$328$	2.19615	−	1.26795i	0.121262	−	0.0700108i
$329$	−5.36603	+	3.09808i	−0.295839	+	0.170802i
$330$	7.09808	+	34.6865i	0.390736	+	1.90943i
$331$	−7.33013	+	1.96410i	−0.402900	+	0.107957i	−0.454578	−	0.890707i	$-0.650210\pi$
$331$	−7.33013	+	1.96410i	−0.402900	+	0.107957i	0.0516776	+	0.998664i	$0.483543\pi$
$332$	4.00000	−	4.00000i	0.219529	−	0.219529i
$333$	7.79423	−	16.5000i	0.427121	−	0.904194i
$334$		−	16.0000i		−	0.875481i
$335$	10.0981	−	8.95448i	0.551717	−	0.489236i
$336$	3.00000	−	1.73205i	0.163663	−	0.0944911i
$337$	35.3205	+	9.46410i	1.92403	+	0.515542i	0.985281	+	0.170943i	$0.0546813\pi$
$337$	35.3205	+	9.46410i	1.92403	+	0.515542i	0.938750	+	0.344600i	$0.111985\pi$
$338$	6.46410	+	11.1962i	0.351601	+	0.608990i
$339$	7.26795	−	7.26795i	0.394741	−	0.394741i
$340$	−5.09808	−	3.36603i	−0.276482	−	0.182548i
$341$	−27.1244	−	27.1244i	−1.46887	−	1.46887i
$342$	5.59808	−	1.50000i	0.302709	−	0.0811107i
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	4.00000			0.215666
$345$	−13.5622	−	15.2942i	−0.730163	−	0.823414i
$346$	−6.20577	+	23.1603i	−0.333624	+	1.24510i
$347$	15.1244			0.811918			0.405959	−	0.913891i	$-0.366938\pi$
$347$	15.1244			0.811918			0.405959	+	0.913891i	$0.366938\pi$
$348$	16.3923	+	9.46410i	0.878720	+	0.507329i
$349$	2.07180	+	1.19615i	0.110901	+	0.0640286i	0.554424	−	0.832234i	$-0.312938\pi$
$349$	2.07180	+	1.19615i	0.110901	+	0.0640286i	−0.443524	+	0.896263i	$0.646272\pi$
$350$	2.63397	−	6.56218i	0.140792	−	0.350763i
$351$		0			0
$352$	−5.59808	+	3.23205i	−0.298378	+	0.172269i
$353$	−14.4904	−	8.36603i	−0.771245	−	0.445279i	0.0620735	−	0.998072i	$-0.480229\pi$
$353$	−14.4904	−	8.36603i	−0.771245	−	0.445279i	−0.833319	+	0.552793i	$0.813562\pi$
$354$	−2.83013	+	4.90192i	−0.150420	+	0.260534i
$355$	−13.3923	−	0.803848i	−0.710790	−	0.0426638i
$356$	−8.63397	−	8.63397i	−0.457600	−	0.457600i
$357$	4.73205	+	8.19615i	0.250447	+	0.433786i
$358$	−0.598076	+	0.160254i	−0.0316093	+	0.00846969i
$359$		−	21.1244i		−	1.11490i	−0.830210	−	0.557450i	$-0.811780\pi$
$359$		−	21.1244i		−	1.11490i	0.830210	−	0.557450i	$-0.188220\pi$
$360$	6.00000	−	3.00000i	0.316228	−	0.158114i
$361$	−13.2224	−	7.63397i	−0.695917	−	0.401788i
$362$	26.0526			1.36929
$363$	−19.5167	+	72.8372i	−1.02436	+	3.82296i
$364$	−0.267949	−	0.267949i	−0.0140444	−	0.0140444i
$365$	24.5622	−	5.02628i	1.28564	−	0.263087i
$366$	14.6603	+	25.3923i	0.766304	+	1.32728i
$367$	8.25833	−	30.8205i	0.431081	−	1.60882i	−0.319192	−	0.947690i	$-0.603412\pi$
$367$	8.25833	−	30.8205i	0.431081	−	1.60882i	0.750274	−	0.661127i	$-0.229922\pi$
$368$	1.86603	−	3.23205i	0.0972733	−	0.168482i
$369$	−7.60770			−0.396041
$370$	11.6244	−	7.06218i	0.604321	−	0.367145i
$371$	19.4641			1.01053
$372$	−7.26795	+	12.5885i	−0.376826	+	0.652681i
$373$	−5.23205	+	19.5263i	−0.270905	+	1.01103i	0.687631	+	0.726061i	$0.258651\pi$
$373$	−5.23205	+	19.5263i	−0.270905	+	1.01103i	−0.958536	+	0.284972i	$0.908016\pi$
$374$	−8.83013	−	15.2942i	−0.456595	−	0.790846i
$375$	11.7058	−	24.7583i	0.604483	−	1.27851i
$376$	−3.09808	−	3.09808i	−0.159771	−	0.159771i
$377$	0.535898	−	2.00000i	0.0276002	−	0.103005i
$378$		0			0
$379$	33.1244	+	19.1244i	1.70148	+	0.982352i	0.944262	+	0.329194i	$0.106777\pi$
$379$	33.1244	+	19.1244i	1.70148	+	0.982352i	0.757222	+	0.653158i	$0.226556\pi$
$380$	4.09808	+	1.36603i	0.210227	+	0.0700756i
$381$			14.8756i			0.762102i
$382$	7.92820	−	2.12436i	0.405642	−	0.108691i
$383$	1.66987	+	2.89230i	0.0853265	+	0.147790i	0.905530	−	0.424282i	$-0.139473\pi$
$383$	1.66987	+	2.89230i	0.0853265	+	0.147790i	−0.820204	+	0.572071i	$0.806140\pi$
$384$	1.73205	+	1.73205i	0.0883883	+	0.0883883i
$385$	15.2942	−	13.5622i	0.779466	−	0.691193i
$386$	−5.90192	+	10.2224i	−0.300400	+	0.520308i
$387$	−10.3923	−	6.00000i	−0.528271	−	0.304997i
$388$	2.19615	−	1.26795i	0.111493	−	0.0643704i
$389$	4.00000	+	1.07180i	0.202808	+	0.0543423i	0.358793	−	0.933417i	$-0.383188\pi$
$389$	4.00000	+	1.07180i	0.202808	+	0.0543423i	−0.155985	+	0.987759i	$0.549855\pi$
$390$	−0.973721	−	1.09808i	−0.0493063	−	0.0556033i
$391$	8.83013	+	5.09808i	0.446559	+	0.257821i
$392$	4.33013	+	2.50000i	0.218704	+	0.126269i
$393$	−34.3923			−1.73486
$394$	2.02628	−	7.56218i	0.102082	−	0.380977i
$395$	−22.3923	+	19.8564i	−1.12668	+	0.999084i
$396$	19.3923			0.974500
$397$	−17.0981	+	17.0981i	−0.858128	+	0.858128i	−0.991117	−	0.132990i	$-0.957542\pi$
$397$	−17.0981	+	17.0981i	−0.858128	+	0.858128i	0.132990	+	0.991117i	$0.457542\pi$
$398$	4.00000	−	1.07180i	0.200502	−	0.0537243i
$399$	−4.73205	−	4.73205i	−0.236899	−	0.236899i
$400$	4.96410	+	0.598076i	0.248205	+	0.0299038i
$401$	2.43782	−	2.43782i	0.121739	−	0.121739i	−0.643612	−	0.765352i	$-0.722565\pi$
$401$	2.43782	−	2.43782i	0.121739	−	0.121739i	0.765352	+	0.643612i	$0.222565\pi$
$402$	−7.39230	−	12.8038i	−0.368695	−	0.638598i
$403$	1.53590	+	0.411543i	0.0765085	+	0.0205004i
$404$	7.26795	−	4.19615i	0.361594	−	0.208766i
$405$	20.0885	+	1.20577i	0.998203	+	0.0599153i
$406$		−	10.9282i		−	0.542358i
$407$	39.1865	−	3.23205i	1.94240	−	0.160207i
$408$	−4.73205	+	4.73205i	−0.234271	+	0.234271i
$409$	−14.5622	+	3.90192i	−0.720053	+	0.192938i	−0.600195	−	0.799853i	$-0.704911\pi$
$409$	−14.5622	+	3.90192i	−0.720053	+	0.192938i	−0.119858	+	0.992791i	$0.538244\pi$
$410$	−4.73205	−	3.12436i	−0.233699	−	0.154301i
$411$	12.5885	−	7.26795i	0.620943	−	0.358501i
$412$	−2.93782	+	1.69615i	−0.144736	+	0.0835634i
$413$	3.26795			0.160805
$414$	−9.69615	+	5.59808i	−0.476540	+	0.275130i
$415$	−12.0000	−	4.00000i	−0.589057	−	0.196352i
$416$	0.133975	−	0.232051i	0.00656865	−	0.0113772i
$417$	20.3205	+	20.3205i	0.995100	+	0.995100i
$418$	8.83013	+	8.83013i	0.431896	+	0.431896i
$419$	−8.08846	−	4.66987i	−0.395147	−	0.228138i	0.289241	−	0.957256i	$-0.406597\pi$
$419$	−8.08846	−	4.66987i	−0.395147	−	0.228138i	−0.684388	+	0.729118i	$0.739930\pi$
$420$	−6.46410	−	4.26795i	−0.315416	−	0.208255i
$421$	−15.3205	+	15.3205i	−0.746676	+	0.746676i	−0.973853	−	0.227177i	$-0.927050\pi$
$421$	−15.3205	+	15.3205i	−0.746676	+	0.746676i	0.227177	+	0.973853i	$0.427050\pi$
$422$	−13.4282	+	23.2583i	−0.653675	+	1.13220i
$423$	3.40192	+	12.6962i	0.165407	+	0.617308i
$424$	3.56218	+	13.2942i	0.172995	+	0.645625i
$425$	−1.63397	+	13.5622i	−0.0792594	+	0.657862i
$426$	−3.80385	+	14.1962i	−0.184297	+	0.687806i
$427$	8.46410	−	14.6603i	0.409607	−	0.709459i
$428$	0.732051	−	0.196152i	0.0353850	−	0.00948139i
$429$	−1.09808	−	4.09808i	−0.0530156	−	0.197857i
$430$	−4.00000	−	8.00000i	−0.192897	−	0.385794i
$431$	29.7583	+	7.97372i	1.43341	+	0.384081i	0.890220	−	0.455530i	$-0.150550\pi$
$431$	29.7583	+	7.97372i	1.43341	+	0.384081i	0.543188	+	0.839611i	$0.317217\pi$
$432$		0			0
$433$	−16.5167	+	16.5167i	−0.793740	+	0.793740i	−0.982100	−	0.188360i	$-0.939683\pi$
$433$	−16.5167	+	16.5167i	−0.793740	+	0.793740i	0.188360	+	0.982100i	$0.439683\pi$
$434$	8.39230			0.402844
$435$	2.53590	−	42.2487i	0.121587	−	2.02567i
$436$	7.73205	−	7.73205i	0.370298	−	0.370298i
$437$	−6.96410	−	1.86603i	−0.333138	−	0.0892641i
$438$		−	27.4641i		−	1.31229i
$439$	4.63397	−	17.2942i	0.221168	−	0.825408i	−0.762736	−	0.646710i	$-0.776145\pi$
$439$	4.63397	−	17.2942i	0.221168	−	0.825408i	0.983904	−	0.178699i	$-0.0571888\pi$
$440$	12.0622	+	7.96410i	0.575042	+	0.379674i
$441$	−7.50000	−	12.9904i	−0.357143	−	0.618590i
$442$	0.633975	+	0.366025i	0.0301551	+	0.0174101i
$443$	17.8564	+	17.8564i	0.848383	+	0.848383i	0.989931	−	0.141548i	$-0.0452079\pi$
$443$	17.8564	+	17.8564i	0.848383	+	0.848383i	−0.141548	+	0.989931i	$0.545208\pi$
$444$	−5.02628	−	14.0263i	−0.238537	−	0.665658i
$445$	−8.63397	+	25.9019i	−0.409290	+	1.22787i
$446$	3.52628	+	13.1603i	0.166974	+	0.623156i
$447$	−50.7846	−	13.6077i	−2.40203	−	0.643622i
$448$	0.366025	−	1.36603i	0.0172931	−	0.0645386i
$449$	−26.2224	−	7.02628i	−1.23751	−	0.331591i	−0.420012	−	0.907518i	$-0.637974\pi$
$449$	−26.2224	−	7.02628i	−1.23751	−	0.331591i	−0.817501	+	0.575928i	$0.804641\pi$
$450$	−12.0000	−	9.00000i	−0.565685	−	0.424264i
$451$	−8.19615	−	14.1962i	−0.385942	−	0.668471i
$452$		−	4.19615i		−	0.197370i
$453$	−2.07180	−	7.73205i	−0.0973415	−	0.363283i
$454$		−	22.9808i		−	1.07854i
$455$	−0.267949	+	0.803848i	−0.0125617	+	0.0376850i
$456$	2.36603	−	4.09808i	0.110799	−	0.191910i
$457$	−4.73205	+	2.73205i	−0.221356	+	0.127800i	−0.606578	−	0.795024i	$-0.707458\pi$
$457$	−4.73205	+	2.73205i	−0.221356	+	0.127800i	0.385222	+	0.922824i	$0.374125\pi$
$458$		−	19.4641i		−	0.909498i
$459$		0			0
$460$	−8.33013	−	0.500000i	−0.388394	−	0.0233126i
$461$	−11.0981	+	2.97372i	−0.516889	+	0.138500i	−0.507827	−	0.861459i	$-0.669551\pi$
$461$	−11.0981	+	2.97372i	−0.516889	+	0.138500i	−0.00906176	+	0.999959i	$0.502884\pi$
$462$	−11.1962	−	19.3923i	−0.520892	−	0.902212i
$463$	2.39230	+	4.14359i	0.111180	+	0.192569i	0.916246	−	0.400616i	$-0.131204\pi$
$463$	2.39230	+	4.14359i	0.111180	+	0.192569i	−0.805066	+	0.593185i	$0.797870\pi$
$464$	7.46410	−	2.00000i	0.346512	−	0.0928477i
$465$	32.4449	+	1.94744i	1.50459	+	0.0903104i
$466$	−9.83013	+	2.63397i	−0.455372	+	0.122017i
$467$		−	27.6603i		−	1.27996i	−0.768390	−	0.639982i	$-0.778942\pi$
$467$		−	27.6603i		−	1.27996i	0.768390	−	0.639982i	$-0.221058\pi$
$468$	−0.696152	+	0.401924i	−0.0321797	+	0.0185789i
$469$	−4.26795	+	7.39230i	−0.197076	+	0.341345i
$470$	−3.09808	+	9.29423i	−0.142904	+	0.428711i
$471$		−	4.48334i		−	0.206581i
$472$	0.598076	+	2.23205i	0.0275287	+	0.102738i
$473$		−	25.8564i		−	1.18888i
$474$	16.3923	+	28.3923i	0.752923	+	1.30410i
$475$	−1.36603	−	9.56218i	−0.0626775	−	0.438743i
$476$	3.73205	+	1.00000i	0.171058	+	0.0458349i
$477$	10.6865	−	39.8827i	0.489303	−	1.82610i
$478$	−5.56218	−	1.49038i	−0.254408	−	0.0681684i
$479$	4.92820	+	18.3923i	0.225175	+	0.840366i	0.982334	+	0.187135i	$0.0599202\pi$
$479$	4.92820	+	18.3923i	0.225175	+	0.840366i	−0.757159	+	0.653231i	$0.773413\pi$
$480$	1.73205	−	5.19615i	0.0790569	−	0.237171i
$481$	−1.33975	+	0.928203i	−0.0610872	+	0.0423224i
$482$	−5.56218	−	5.56218i	−0.253350	−	0.253350i
$483$	11.1962	+	6.46410i	0.509443	+	0.294127i
$484$	15.3923	+	26.6603i	0.699650	+	1.21183i
$485$	−4.73205	−	3.12436i	−0.214871	−	0.141870i
$486$	5.70577	−	21.2942i	0.258819	−	0.965926i
$487$			30.7846i			1.39498i	0.716593	+	0.697492i	$0.245701\pi$
$487$			30.7846i			1.39498i	−0.716593	+	0.697492i	$0.754299\pi$
$488$	11.5622	+	3.09808i	0.523395	+	0.140243i
$489$	−2.19615	+	2.19615i	−0.0993134	+	0.0993134i
$490$	0.669873	−	11.1603i	0.0302618	−	0.504169i
$491$	23.3923			1.05568			0.527840	−	0.849344i	$-0.323002\pi$
$491$	23.3923			1.05568			0.527840	+	0.849344i	$0.323002\pi$
$492$	−4.39230	+	4.39230i	−0.198020	+	0.198020i
$493$	5.46410	+	20.3923i	0.246091	+	0.918423i
$494$	−0.500000	−	0.133975i	−0.0224961	−	0.00602780i
$495$	−19.3923	−	38.7846i	−0.871619	−	1.74324i
$496$	1.53590	+	5.73205i	0.0689639	+	0.257377i
$497$	8.19615	−	2.19615i	0.367648	−	0.0985109i
$498$	−6.92820	+	12.0000i	−0.310460	+	0.537733i
$499$	−8.22243	+	30.6865i	−0.368087	+	1.37372i	0.495101	+	0.868835i	$0.335131\pi$
$499$	−8.22243	+	30.6865i	−0.368087	+	1.37372i	−0.863188	+	0.504883i	$0.831536\pi$
$500$	−3.76795	−	10.5263i	−0.168508	−	0.470750i
$501$	10.1436	+	37.8564i	0.453182	+	1.69130i
$502$	−2.52628	−	9.42820i	−0.112753	−	0.420801i
$503$	−6.66025	+	11.5359i	−0.296966	+	0.514360i	−0.975440	−	0.220264i	$-0.929308\pi$
$503$	−6.66025	+	11.5359i	−0.296966	+	0.514360i	0.678474	+	0.734624i	$0.262641\pi$
$504$	−3.00000	+	3.00000i	−0.133631	+	0.133631i
$505$	−15.6603	−	10.3397i	−0.696872	−	0.460113i
$506$	−20.8923	−	12.0622i	−0.928776	−	0.536229i
$507$	−22.3923	−	22.3923i	−0.994477	−	0.994477i
$508$	4.29423	+	4.29423i	0.190526	+	0.190526i
$509$	−13.2679	+	22.9808i	−0.588092	+	1.01860i	0.406391	+	0.913699i	$0.366787\pi$
$509$	−13.2679	+	22.9808i	−0.588092	+	1.01860i	−0.994482	+	0.104905i	$0.966546\pi$
$510$	14.1962	+	4.73205i	0.628616	+	0.209539i
$511$	−13.7321	+	7.92820i	−0.607470	+	0.350723i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−7.90192	+	4.56218i	−0.348539	+	0.201229i
$515$	6.33013	+	4.17949i	0.278939	+	0.184170i
$516$	−9.46410	+	2.53590i	−0.416634	+	0.111637i
$517$	−20.0263	+	20.0263i	−0.880755	+	0.880755i
$518$	−5.56218	+	6.56218i	−0.244388	+	0.288326i
$519$		−	58.7321i		−	2.57805i
$520$	−0.598076	−	0.0358984i	−0.0262274	−	0.00157425i
$521$	17.1340	−	9.89230i	0.750653	−	0.433390i	−0.0752768	−	0.997163i	$-0.523984\pi$
$521$	17.1340	−	9.89230i	0.750653	−	0.433390i	0.825930	+	0.563773i	$0.190651\pi$
$522$	−22.3923	−	6.00000i	−0.980085	−	0.262613i
$523$	−20.9545	−	36.2942i	−0.916276	−	1.58704i	−0.805023	−	0.593244i	$-0.797847\pi$
$523$	−20.9545	−	36.2942i	−0.916276	−	1.58704i	−0.111253	−	0.993792i	$-0.535486\pi$
$524$	−9.92820	+	9.92820i	−0.433716	+	0.433716i
$525$	−2.07180	+	17.1962i	−0.0904206	+	0.750502i
$526$	6.83013	+	6.83013i	0.297808	+	0.297808i
$527$	−15.6603	+	4.19615i	−0.682171	+	0.182787i
$528$	11.1962	−	11.1962i	0.487250	−	0.487250i
$529$	−9.07180			−0.394426
$530$	23.0263	−	20.4186i	1.00020	−	0.886927i
$531$	1.79423	−	6.69615i	0.0778629	−	0.290588i
$532$	−2.73205			−0.118449
$533$	0.588457	+	0.339746i	0.0254889	+	0.0147160i
$534$	25.9019	+	14.9545i	1.12089	+	0.647144i
$535$	−1.12436	−	1.26795i	−0.0486101	−	0.0548182i
$536$	−5.83013	−	1.56218i	−0.251823	−	0.0674758i
$537$	1.31347	−	0.758330i	0.0566803	−	0.0327244i
$538$	−11.0263	−	6.36603i	−0.475377	−	0.274459i
$539$	16.1603	−	27.9904i	0.696071	−	1.20563i
$540$		0			0
$541$	14.9282	+	14.9282i	0.641814	+	0.641814i	0.951001	−	0.309188i	$-0.100057\pi$
$541$	14.9282	+	14.9282i	0.641814	+	0.641814i	−0.309188	+	0.951001i	$0.600057\pi$
$542$	12.8564	+	22.2679i	0.552230	+	0.956490i
$543$	−61.6410	+	16.5167i	−2.64527	+	0.708798i
$544$			2.73205i			0.117136i
$545$	−23.1962	−	7.73205i	−0.993614	−	0.331205i
$546$	0.803848	+	0.464102i	0.0344015	+	0.0198617i
$547$	−7.46410			−0.319142			−0.159571	−	0.987186i	$-0.551011\pi$
$547$	−7.46410			−0.319142			−0.159571	+	0.987186i	$0.551011\pi$
$548$	1.53590	−	5.73205i	0.0656103	−	0.244861i
$549$	−25.3923	−	25.3923i	−1.08372	−	1.08372i
$550$	3.86603	−	32.0885i	0.164848	−	1.36826i
$551$	−7.46410	−	12.9282i	−0.317981	−	0.550760i
$552$	−2.36603	+	8.83013i	−0.100705	+	0.375835i
$553$	9.46410	−	16.3923i	0.402455	−	0.697072i
$554$	−21.4641			−0.911922
$555$	−23.0263	+	24.0788i	−0.977411	+	1.02209i
$556$	11.7321			0.497550
$557$	8.59808	−	14.8923i	0.364312	−	0.631007i	−0.624353	−	0.781142i	$-0.714637\pi$
$557$	8.59808	−	14.8923i	0.364312	−	0.631007i	0.988666	+	0.150135i	$0.0479708\pi$
$558$	4.60770	−	17.1962i	0.195059	−	0.727971i
$559$	0.535898	+	0.928203i	0.0226661	+	0.0392588i
$560$	−3.09808	+	0.633975i	−0.130918	+	0.0267903i
$561$	30.5885	+	30.5885i	1.29145	+	1.29145i
$562$	1.74167	−	6.50000i	0.0734679	−	0.274186i
$563$	8.87564			0.374064			0.187032	−	0.982354i	$-0.440113\pi$
$563$	8.87564			0.374064			0.187032	+	0.982354i	$0.440113\pi$
$564$	9.29423	+	5.36603i	0.391358	+	0.225950i
$565$	−8.39230	+	4.19615i	−0.353067	+	0.176533i
$566$		−	3.80385i		−	0.159888i
$567$	−12.2942	+	3.29423i	−0.516309	+	0.138345i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	28.3468	+	28.3468i	1.18836	+	1.18836i	0.977521	+	0.210838i	$0.0676193\pi$
$569$	28.3468	+	28.3468i	1.18836	+	1.18836i	0.210838	+	0.977521i	$0.432381\pi$
$570$	−10.5622	−	0.633975i	−0.442401	−	0.0265543i
$571$	−8.72243	+	15.1077i	−0.365022	+	0.632237i	−0.988780	−	0.149381i	$-0.952272\pi$
$571$	−8.72243	+	15.1077i	−0.365022	+	0.632237i	0.623757	+	0.781618i	$0.285605\pi$
$572$	−1.50000	−	0.866025i	−0.0627182	−	0.0362103i
$573$	−17.4115	+	10.0526i	−0.727378	+	0.419952i
$574$	3.46410	+	0.928203i	0.144589	+	0.0387425i
$575$	7.33013	+	17.1603i	0.305687	+	0.715632i
$576$	−2.59808	−	1.50000i	−0.108253	−	0.0625000i
$577$	25.1769	+	14.5359i	1.04813	+	0.605137i	0.922125	−	0.386892i	$-0.126452\pi$
$577$	25.1769	+	14.5359i	1.04813	+	0.605137i	0.126004	+	0.992030i	$0.459785\pi$
$578$	9.53590			0.396641
$579$	7.48334	−	27.9282i	0.310997	−	1.16066i
$580$	−11.4641	−	12.9282i	−0.476021	−	0.536814i
$581$	8.00000			0.331896
$582$	−4.39230	+	4.39230i	−0.182067	+	0.182067i
$583$	85.9352	−	23.0263i	3.55907	−	0.953651i
$584$	−7.92820	−	7.92820i	−0.328071	−	0.328071i
$585$	1.50000	+	0.990381i	0.0620174	+	0.0409472i
$586$	6.63397	−	6.63397i	0.274047	−	0.274047i
$587$	18.8301	+	32.6147i	0.777203	+	1.34615i	0.933548	+	0.358452i	$0.116695\pi$
$587$	18.8301	+	32.6147i	0.777203	+	1.34615i	−0.156346	+	0.987702i	$0.549971\pi$
$588$	−11.8301	−	3.16987i	−0.487866	−	0.130723i
$589$	9.92820	−	5.73205i	0.409084	−	0.236185i
$590$	3.86603	−	3.42820i	0.159162	−	0.141137i
$591$			19.1769i			0.788833i
$592$	−5.50000	−	2.59808i	−0.226049	−	0.106780i
$593$	10.7846	−	10.7846i	0.442871	−	0.442871i	−0.450105	−	0.892976i	$-0.648613\pi$
$593$	10.7846	−	10.7846i	0.442871	−	0.442871i	0.892976	+	0.450105i	$0.148613\pi$
$594$		0			0
$595$	−1.73205	−	8.46410i	−0.0710072	−	0.346994i
$596$	−18.5885	+	10.7321i	−0.761413	+	0.439602i
$597$	−8.78461	+	5.07180i	−0.359530	+	0.207575i
$598$	1.00000			0.0408930
$599$	24.5885	−	14.1962i	1.00466	−	0.580039i	0.0950342	−	0.995474i	$-0.469704\pi$
$599$	24.5885	−	14.1962i	1.00466	−	0.580039i	0.909623	+	0.415435i	$0.136371\pi$
$600$	−12.1244	+	1.73205i	−0.494975	+	0.0707107i
$601$	−10.6962	+	18.5263i	−0.436305	+	0.755703i	−0.997401	−	0.0720480i	$-0.977047\pi$
$601$	−10.6962	+	18.5263i	−0.436305	+	0.755703i	0.561096	+	0.827751i	$0.310380\pi$
$602$	4.00000	+	4.00000i	0.163028	+	0.163028i
$603$	12.8038	+	12.8038i	0.521413	+	0.521413i
$604$	−2.83013	−	1.63397i	−0.115156	−	0.0664855i
$605$	37.9282	−	57.4449i	1.54200	−	2.33547i
$606$	−14.5359	+	14.5359i	−0.590481	+	0.590481i
$607$	−1.73205	+	3.00000i	−0.0703018	+	0.121766i	−0.899034	−	0.437880i	$-0.855730\pi$
$607$	−1.73205	+	3.00000i	−0.0703018	+	0.121766i	0.828732	+	0.559646i	$0.189063\pi$
$608$	−0.500000	−	1.86603i	−0.0202777	−	0.0756773i
$609$	6.92820	+	25.8564i	0.280745	+	1.04775i
$610$	−5.36603	−	26.2224i	−0.217264	−	1.06172i
$611$	0.303848	−	1.13397i	0.0122924	−	0.0458757i
$612$	4.09808	−	7.09808i	0.165655	−	0.286923i
$613$	−3.13397	+	0.839746i	−0.126580	+	0.0339170i	−0.321553	−	0.946892i	$-0.604205\pi$
$613$	−3.13397	+	0.839746i	−0.126580	+	0.0339170i	0.194973	+	0.980809i	$0.437538\pi$
$614$	−0.633975	−	2.36603i	−0.0255851	−	0.0954850i
$615$	13.1769	+	4.39230i	0.531344	+	0.177115i
$616$	−8.83013	−	2.36603i	−0.355776	−	0.0953299i
$617$	−9.46410	−	35.3205i	−0.381010	−	1.42195i	−0.844361	−	0.535775i	$-0.820020\pi$
$617$	−9.46410	−	35.3205i	−0.381010	−	1.42195i	0.463350	−	0.886175i	$-0.346647\pi$
$618$	5.87564	−	5.87564i	0.236353	−	0.236353i
$619$	−6.67949			−0.268471			−0.134236	−	0.990949i	$-0.542858\pi$
$619$	−6.67949			−0.268471			−0.134236	+	0.990949i	$0.542858\pi$
$620$	9.92820	−	8.80385i	0.398726	−	0.353571i
$621$		0			0
$622$	−5.09808	−	1.36603i	−0.204414	−	0.0547726i
$623$		−	17.2679i		−	0.691826i
$624$	−0.169873	+	0.633975i	−0.00680036	+	0.0253793i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	13.9282	+	24.1244i	0.556683	+	0.964203i
$627$	−26.4904	−	15.2942i	−1.05792	−	0.610793i
$628$	−1.29423	−	1.29423i	−0.0516453	−	0.0516453i
$629$	7.09808	−	15.0263i	0.283019	−	0.599137i
$630$	9.00000	+	3.00000i	0.358569	+	0.119523i
$631$	7.16987	+	26.7583i	0.285428	+	1.06523i	0.948526	+	0.316700i	$0.102575\pi$
$631$	7.16987	+	26.7583i	0.285428	+	1.06523i	−0.663098	+	0.748533i	$0.730759\pi$
$632$	12.9282	+	3.46410i	0.514256	+	0.137795i
$633$	17.0263	−	63.5429i	0.676734	−	2.52561i
$634$	12.9641	+	3.47372i	0.514870	+	0.137959i
$635$	4.29423	−	12.8827i	0.170411	−	0.511234i
$636$	−16.8564	−	29.1962i	−0.668400	−	1.15770i
$637$			1.33975i			0.0530827i
$638$	−12.9282	−	48.2487i	−0.511832	−	1.91018i
$639$		−	18.0000i		−	0.712069i
$640$	−1.00000	−	2.00000i	−0.0395285	−	0.0790569i
$641$	−1.16025	+	2.00962i	−0.0458273	+	0.0793752i	−0.888029	−	0.459787i	$-0.847926\pi$
$641$	−1.16025	+	2.00962i	−0.0458273	+	0.0793752i	0.842202	+	0.539162i	$0.181259\pi$
$642$	−1.60770	+	0.928203i	−0.0634507	+	0.0366333i
$643$		−	2.24871i		−	0.0886805i	−0.999016	−	0.0443403i	$-0.985881\pi$
$643$		−	2.24871i		−	0.0886805i	0.999016	−	0.0443403i	$-0.0141186\pi$
$644$	5.09808	−	1.36603i	0.200892	−	0.0538289i
$645$	14.5359	+	16.3923i	0.572350	+	0.645446i
$646$	5.09808	−	1.36603i	0.200581	−	0.0537456i
$647$	−22.0885	−	38.2583i	−0.868387	−	1.50409i	−0.863644	−	0.504101i	$-0.831824\pi$
$647$	−22.0885	−	38.2583i	−0.868387	−	1.50409i	−0.00474239	−	0.999989i	$-0.501510\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	14.4282	−	3.86603i	0.566357	−	0.151755i
$650$	0.526279	+	1.23205i	0.0206424	+	0.0483250i
$651$	−19.8564	+	5.32051i	−0.778234	+	0.208527i
$652$			1.26795i			0.0496567i
$653$	−31.4545	+	18.1603i	−1.23091	+	0.710666i	−0.967219	−	0.253942i	$-0.918273\pi$
$653$	−31.4545	+	18.1603i	−1.23091	+	0.710666i	−0.263690	+	0.964608i	$0.584939\pi$
$654$	−13.3923	+	23.1962i	−0.523681	+	0.907041i
$655$	29.7846	+	9.92820i	1.16378	+	0.387927i
$656$			2.53590i			0.0990102i
$657$	8.70577	+	32.4904i	0.339644	+	1.26757i
$658$		−	6.19615i		−	0.241551i
$659$	9.79423	+	16.9641i	0.381529	+	0.660828i	0.991281	−	0.131765i	$-0.0420643\pi$
$659$	9.79423	+	16.9641i	0.381529	+	0.660828i	−0.609752	+	0.792592i	$0.708731\pi$
$660$	−33.5885	−	11.1962i	−1.30743	−	0.435810i
$661$	−6.29423	−	1.68653i	−0.244817	−	0.0655985i	0.134324	−	0.990937i	$-0.457114\pi$
$661$	−6.29423	−	1.68653i	−0.244817	−	0.0655985i	−0.379141	+	0.925339i	$0.623780\pi$
$662$	1.96410	−	7.33013i	0.0763370	−	0.284893i
$663$	−1.73205	−	0.464102i	−0.0672673	−	0.0180242i
$664$	1.46410	+	5.46410i	0.0568182	+	0.212048i
$665$	2.73205	+	5.46410i	0.105944	+	0.211889i
$666$	10.3923	+	15.0000i	0.402694	+	0.581238i
$667$	20.3923	+	20.3923i	0.789593	+	0.789593i
$668$	13.8564	+	8.00000i	0.536120	+	0.309529i
$669$	−16.6865	−	28.9019i	−0.645139	−	1.11741i
$670$	2.70577	+	13.2224i	0.104533	+	0.510827i
$671$	20.0263	−	74.7391i	0.773106	−	2.88527i
$672$			3.46410i			0.133631i
$673$	−21.9282	−	5.87564i	−0.845270	−	0.226489i	−0.189906	−	0.981802i	$-0.560818\pi$
$673$	−21.9282	−	5.87564i	−0.845270	−	0.226489i	−0.655364	+	0.755313i	$0.727485\pi$
$674$	−25.8564	+	25.8564i	−0.995952	+	0.995952i
$675$		0			0
$676$	−12.9282			−0.497239
$677$	26.5622	−	26.5622i	1.02087	−	1.02087i	0.0210898	−	0.999778i	$-0.493286\pi$
$677$	26.5622	−	26.5622i	1.02087	−	1.02087i	0.999778	−	0.0210898i	$-0.00671360\pi$
$678$	2.66025	+	9.92820i	0.102166	+	0.381290i
$679$	3.46410	+	0.928203i	0.132940	+	0.0356212i
$680$	5.46410	−	2.73205i	0.209539	−	0.104769i
$681$	14.5692	+	54.3731i	0.558294	+	2.08358i
$682$	37.0526	−	9.92820i	1.41882	−	0.380171i
$683$	−11.1962	+	19.3923i	−0.428409	+	0.742026i	−0.996732	−	0.0807795i	$-0.974259\pi$
$683$	−11.1962	+	19.3923i	−0.428409	+	0.742026i	0.568323	+	0.822805i	$0.307592\pi$
$684$	−1.50000	+	5.59808i	−0.0573539	+	0.214048i
$685$	−13.0000	+	2.66025i	−0.496704	+	0.101643i
$686$	4.39230	+	16.3923i	0.167699	+	0.625861i
$687$	12.3397	+	46.0526i	0.470791	+	1.75701i
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	−2.60770	+	2.60770i	−0.0993453	+	0.0993453i
$690$	20.0263	−	4.09808i	0.762387	−	0.156011i
$691$	−24.3397	−	14.0526i	−0.925928	−	0.534585i	−0.0404063	−	0.999183i	$-0.512865\pi$
$691$	−24.3397	−	14.0526i	−0.925928	−	0.534585i	−0.885521	+	0.464599i	$0.846199\pi$
$692$	−16.9545	−	16.9545i	−0.644513	−	0.644513i
$693$	19.3923	+	19.3923i	0.736653	+	0.736653i
$694$	−7.56218	+	13.0981i	−0.287056	+	0.497196i
$695$	−11.7321	−	23.4641i	−0.445022	−	0.890044i
$696$	−16.3923	+	9.46410i	−0.621349	+	0.358736i
$697$	−6.92820			−0.262424
$698$	−2.07180	+	1.19615i	−0.0784187	+	0.0452750i
$699$	21.5885	−	12.4641i	0.816550	−	0.471436i
$700$	4.36603	+	5.56218i	0.165020	+	0.210231i
$701$	32.6865	−	8.75833i	1.23455	−	0.330798i	0.418202	−	0.908354i	$-0.362660\pi$
$701$	32.6865	−	8.75833i	1.23455	−	0.330798i	0.816351	+	0.577556i	$0.195994\pi$
$702$		0			0
$703$	−2.09808	+	11.5622i	−0.0791304	+	0.436076i
$704$		−	6.46410i		−	0.243625i
$705$	1.43782	−	23.9545i	0.0541515	−	0.902178i
$706$	14.4904	−	8.36603i	0.545353	−	0.314860i
$707$	11.4641	+	3.07180i	0.431152	+	0.115527i
$708$	−2.83013	−	4.90192i	−0.106363	−	0.184226i
$709$	−9.80385	+	9.80385i	−0.368191	+	0.368191i	−0.866817	−	0.498626i	$-0.833838\pi$
$709$	−9.80385	+	9.80385i	−0.368191	+	0.368191i	0.498626	+	0.866817i	$0.333838\pi$
$710$	7.39230	−	11.1962i	0.277428	−	0.420184i
$711$	−28.3923	−	28.3923i	−1.06479	−	1.06479i
$712$	11.7942	−	3.16025i	0.442007	−	0.118436i
$713$	−15.6603	+	15.6603i	−0.586481	+	0.586481i
$714$	−9.46410			−0.354185
$715$	−0.232051	+	3.86603i	−0.00867821	+	0.144581i
$716$	0.160254	−	0.598076i	0.00598897	−	0.0223512i
$717$	14.1051			0.526765
$718$	18.2942	+	10.5622i	0.682735	+	0.394177i
$719$	13.7321	+	7.92820i	0.512119	+	0.295672i	0.733704	−	0.679469i	$-0.237790\pi$
$719$	13.7321	+	7.92820i	0.512119	+	0.295672i	−0.221585	+	0.975141i	$0.571123\pi$
$720$	−0.401924	+	6.69615i	−0.0149788	+	0.249551i
$721$	−4.63397	−	1.24167i	−0.172578	−	0.0462422i
$722$	13.2224	−	7.63397i	0.492088	−	0.284107i
$723$	16.6865	+	9.63397i	0.620579	+	0.358291i
$724$	−13.0263	+	22.5622i	−0.484118	+	0.838517i
$725$	−14.3923	+	35.8564i	−0.534517	+	1.33167i
$726$	−53.3205	−	53.3205i	−1.97891	−	1.97891i
$727$	−6.79423	−	11.7679i	−0.251984	−	0.436449i	0.712088	−	0.702090i	$-0.247750\pi$
$727$	−6.79423	−	11.7679i	−0.251984	−	0.436449i	−0.964072	+	0.265641i	$0.914416\pi$
$728$	0.366025	−	0.0980762i	0.0135658	−	0.00363495i
$729$			27.0000i			1.00000i
$730$	−7.92820	+	23.7846i	−0.293436	+	0.880308i
$731$	−9.46410	−	5.46410i	−0.350042	−	0.202097i
$732$	−29.3205			−1.08372
$733$	−2.30385	+	8.59808i	−0.0850946	+	0.317577i	−0.995332	−	0.0965093i	$-0.969232\pi$
$733$	−2.30385	+	8.59808i	−0.0850946	+	0.317577i	0.910238	+	0.414087i	$0.135899\pi$
$734$	22.5622	+	22.5622i	0.832785	+	0.832785i
$735$	5.49038	+	26.8301i	0.202516	+	0.989644i
$736$	1.86603	+	3.23205i	0.0687826	+	0.119135i
$737$	−10.0981	+	37.6865i	−0.371967	+	1.38820i
$738$	3.80385	−	6.58846i	0.140022	−	0.242524i
$739$	44.2679			1.62842			0.814211	−	0.580568i	$-0.197170\pi$
$739$	44.2679			1.62842			0.814211	+	0.580568i	$0.197170\pi$
$740$	0.303848	+	13.5981i	0.0111697	+	0.499875i
$741$	1.26795			0.0465793
$742$	−9.73205	+	16.8564i	−0.357275	+	0.618818i
$743$	−7.57180	+	28.2583i	−0.277782	+	1.03670i	0.676172	+	0.736744i	$0.263638\pi$
$743$	−7.57180	+	28.2583i	−0.277782	+	1.03670i	−0.953954	+	0.299953i	$0.903029\pi$
$744$	−7.26795	−	12.5885i	−0.266456	−	0.461515i
$745$	40.0526	+	26.4449i	1.46741	+	0.968865i
$746$	−14.2942	−	14.2942i	−0.523349	−	0.523349i
$747$	4.39230	−	16.3923i	0.160706	−	0.599763i
$748$	17.6603			0.645723
$749$	0.928203	+	0.535898i	0.0339158	+	0.0195813i
$750$	15.5885	+	22.5167i	0.569210	+	0.822192i
$751$			17.1769i			0.626795i	0.949622	+	0.313397i	$0.101467\pi$
$751$			17.1769i			0.626795i	−0.949622	+	0.313397i	$0.898533\pi$
$752$	4.23205	−	1.13397i	0.154327	−	0.0413518i
$753$	11.9545	+	20.7058i	0.435646	+	0.754560i
$754$	1.46410	+	1.46410i	0.0533194	+	0.0533194i
$755$	−0.437822	+	7.29423i	−0.0159340	+	0.265464i
$756$		0			0
$757$	−29.0429	−	16.7679i	−1.05558	−	0.609441i	−0.131376	−	0.991333i	$-0.541940\pi$
$757$	−29.0429	−	16.7679i	−1.05558	−	0.609441i	−0.924207	+	0.381891i	$0.875273\pi$
$758$	−33.1244	+	19.1244i	−1.20313	+	0.694628i
$759$	57.0788	+	15.2942i	2.07183	+	0.555145i
$760$	−3.23205	+	2.86603i	−0.117239	+	0.103962i
$761$	7.50000	+	4.33013i	0.271875	+	0.156967i	0.629739	−	0.776807i	$-0.283162\pi$
$761$	7.50000	+	4.33013i	0.271875	+	0.156967i	−0.357865	+	0.933774i	$0.616495\pi$
$762$	−12.8827	−	7.43782i	−0.466690	−	0.269444i
$763$	15.4641			0.559838
$764$	−2.12436	+	7.92820i	−0.0768565	+	0.286832i
$765$	−18.2942	−	1.09808i	−0.661429	−	0.0397010i
$766$	−3.33975			−0.120670
$767$	−0.437822	+	0.437822i	−0.0158088	+	0.0158088i
$768$	−2.36603	+	0.633975i	−0.0853766	+	0.0228766i
$769$	−27.5885	−	27.5885i	−0.994865	−	0.994865i	0.00512167	−	0.999987i	$-0.498370\pi$
$769$	−27.5885	−	27.5885i	−0.994865	−	0.994865i	−0.999987	+	0.00512167i	$0.998370\pi$
$770$	4.09808	+	20.0263i	0.147684	+	0.721697i
$771$	15.8038	−	15.8038i	0.569162	−	0.569162i
$772$	−5.90192	−	10.2224i	−0.212415	−	0.367913i
$773$	−29.5526	−	7.91858i	−1.06293	−	0.284812i	−0.315346	−	0.948977i	$-0.602120\pi$
$773$	−29.5526	−	7.91858i	−1.06293	−	0.284812i	−0.747586	+	0.664165i	$0.768787\pi$
$774$	10.3923	−	6.00000i	0.373544	−	0.215666i
$775$	−27.5359	−	11.0526i	−0.989119	−	0.397020i
$776$			2.53590i			0.0910334i
$777$	9.00000	−	19.0526i	0.322873	−	0.683507i
$778$	−2.92820	+	2.92820i	−0.104981	+	0.104981i
$779$	4.73205	−	1.26795i	0.169543	−	0.0454290i
$780$	1.43782	−	0.294229i	0.0514823	−	0.0105351i
$781$	33.5885	−	19.3923i	1.20189	−	0.693911i
$782$	−8.83013	+	5.09808i	−0.315765	+	0.182307i
$783$		0			0
$784$	−4.33013	+	2.50000i	−0.154647	+	0.0892857i
$785$	−1.29423	+	3.88269i	−0.0461930	+	0.138579i
$786$	17.1962	−	29.7846i	0.613366	−	1.06238i
$787$	8.07180	+	8.07180i	0.287728	+	0.287728i	0.836181	−	0.548453i	$-0.184783\pi$
$787$	8.07180	+	8.07180i	0.287728	+	0.287728i	−0.548453	+	0.836181i	$0.684783\pi$
$788$	5.53590	+	5.53590i	0.197208	+	0.197208i
$789$	−20.4904	−	11.8301i	−0.729477	−	0.421164i
$790$	−6.00000	−	29.3205i	−0.213470	−	1.04318i
$791$	4.19615	−	4.19615i	0.149198	−	0.149198i
$792$	−9.69615	+	16.7942i	−0.344538	+	0.596757i
$793$	0.830127	+	3.09808i	0.0294787	+	0.110016i
$794$	−6.25833	−	23.3564i	−0.222100	−	0.828888i
$795$	−41.5359	+	62.9090i	−1.47313	+	2.23115i
$796$	−1.07180	+	4.00000i	−0.0379888	+	0.141776i
$797$	−14.6962	+	25.4545i	−0.520564	+	0.901644i	0.479150	+	0.877733i	$0.340945\pi$
$797$	−14.6962	+	25.4545i	−0.520564	+	0.901644i	−0.999714	+	0.0239108i	$0.992388\pi$
$798$	6.46410	−	1.73205i	0.228827	−	0.0613139i
$799$	3.09808	+	11.5622i	0.109602	+	0.409040i
$800$	−3.00000	+	4.00000i	−0.106066	+	0.141421i
$801$	−35.3827	−	9.48076i	−1.25019	−	0.334986i
$802$	0.892305	+	3.33013i	0.0315084	+	0.117591i
$803$	−51.2487	+	51.2487i	−1.80853	+	1.80853i
$804$	14.7846			0.521413
$805$	−7.83013	−	8.83013i	−0.275976	−	0.311221i
$806$	−1.12436	+	1.12436i	−0.0396037	+	0.0396037i
$807$	30.1244	+	8.07180i	1.06043	+	0.284141i
$808$			8.39230i			0.295240i
$809$	7.74167	−	28.8923i	0.272183	−	1.01580i	−0.685523	−	0.728051i	$-0.740427\pi$
$809$	7.74167	−	28.8923i	0.272183	−	1.01580i	0.957706	−	0.287749i	$-0.0929068\pi$
$810$	−11.0885	+	16.7942i	−0.389609	+	0.590089i
$811$	−27.0622	−	46.8731i	−0.950282	−	1.64594i	−0.744814	−	0.667272i	$-0.767462\pi$
$811$	−27.0622	−	46.8731i	−0.950282	−	1.64594i	−0.205468	−	0.978664i	$-0.565871\pi$
$812$	9.46410	+	5.46410i	0.332125	+	0.191752i
$813$	−44.5359	−	44.5359i	−1.56194	−	1.56194i
$814$	−16.7942	+	35.5526i	−0.588637	+	1.24612i
$815$	2.53590	−	1.26795i	0.0888286	−	0.0444143i
$816$	−1.73205	−	6.46410i	−0.0606339	−	0.226289i
$817$	7.46410	+	2.00000i	0.261136	+	0.0699711i
$818$	3.90192	−	14.5622i	0.136428	−	0.509155i
$819$	−1.09808	−	0.294229i	−0.0383699	−	0.0102812i
$820$	5.07180	−	2.53590i	0.177115	−	0.0885574i
$821$	2.66025	+	4.60770i	0.0928435	+	0.160810i	0.908707	−	0.417436i	$-0.137071\pi$
$821$	2.66025	+	4.60770i	0.0928435	+	0.160810i	−0.815863	+	0.578245i	$0.803738\pi$
$822$			14.5359i			0.506998i
$823$	−14.0981	−	52.6147i	−0.491428	−	1.83403i	−0.549181	−	0.835704i	$-0.685060\pi$
$823$	−14.0981	−	52.6147i	−0.491428	−	1.83403i	0.0577528	−	0.998331i	$-0.481606\pi$
$824$		−	3.39230i		−	0.118177i
$825$	11.1962	+	78.3731i	0.389800	+	2.72860i
$826$	−1.63397	+	2.83013i	−0.0568532	+	0.0984727i
$827$	−12.1699	+	7.02628i	−0.423188	+	0.244328i	−0.696440	−	0.717615i	$-0.745234\pi$
$827$	−12.1699	+	7.02628i	−0.423188	+	0.244328i	0.273252	+	0.961942i	$0.411901\pi$
$828$		−	11.1962i		−	0.389093i
$829$	−2.16987	+	0.581416i	−0.0753628	+	0.0201934i	−0.296303	−	0.955094i	$-0.595754\pi$
$829$	−2.16987	+	0.581416i	−0.0753628	+	0.0201934i	0.220941	+	0.975287i	$0.429087\pi$
$830$	9.46410	−	8.39230i	0.328504	−	0.291301i
$831$	50.7846	−	13.6077i	1.76170	−	0.472046i
$832$	0.133975	+	0.232051i	0.00464473	+	0.00804491i
$833$	−6.83013	−	11.8301i	−0.236650	−	0.409890i
$834$	−27.7583	+	7.43782i	−0.961192	+	0.257551i
$835$	2.14359	−	35.7128i	0.0741821	−	1.23589i
$836$	−12.0622	+	3.23205i	−0.417179	+	0.111783i
$837$		0			0
$838$	8.08846	−	4.66987i	0.279411	−	0.161318i
$839$	3.16987	−	5.49038i	0.109436	−	0.189549i	−0.806106	−	0.591771i	$-0.798429\pi$
$839$	3.16987	−	5.49038i	0.109436	−	0.189549i	0.915542	+	0.402222i	$0.131762\pi$
$840$	6.92820	−	3.46410i	0.239046	−	0.119523i
$841$			30.7128i			1.05906i
$842$	−5.60770	−	20.9282i	−0.193254	−	0.721234i
$843$			16.4833i			0.567716i
$844$	−13.4282	−	23.2583i	−0.462218	−	0.800585i
$845$	12.9282	+	25.8564i	0.444744	+	0.889487i
$846$	−12.6962	−	3.40192i	−0.436503	−	0.116961i
$847$	−11.2679	+	42.0526i	−0.387171	+	1.44494i
$848$	−13.2942	−	3.56218i	−0.456526	−	0.122326i
$849$	2.41154	+	9.00000i	0.0827639	+	0.308879i
$850$	−10.9282	−	8.19615i	−0.374834	−	0.281126i
$851$	−1.86603	−	22.6244i	−0.0639665	−	0.775553i
$852$	−10.3923	−	10.3923i	−0.356034	−	0.356034i
$853$	25.4545	+	14.6962i	0.871545	+	0.503187i	0.867861	−	0.496807i	$-0.165494\pi$
$853$	25.4545	+	14.6962i	0.871545	+	0.503187i	0.00368357	+	0.999993i	$0.498827\pi$
$854$	8.46410	+	14.6603i	0.289636	+	0.501664i
$855$	12.6962	−	2.59808i	0.434199	−	0.0888523i
$856$	−0.196152	+	0.732051i	−0.00670435	+	0.0250210i
$857$			36.9282i			1.26144i	0.776009	+	0.630722i	$0.217241\pi$
$857$			36.9282i			1.26144i	−0.776009	+	0.630722i	$0.782759\pi$
$858$	4.09808	+	1.09808i	0.139906	+	0.0374877i
$859$	−37.6865	+	37.6865i	−1.28585	+	1.28585i	−0.348562	+	0.937286i	$0.613330\pi$
$859$	−37.6865	+	37.6865i	−1.28585	+	1.28585i	−0.937286	+	0.348562i	$0.886670\pi$
$860$	8.92820	+	0.535898i	0.304449	+	0.0182740i
$861$	−8.78461			−0.299379
$862$	−21.7846	+	21.7846i	−0.741987	+	0.741987i
$863$	−0.251289	−	0.937822i	−0.00855397	−	0.0319238i	0.961517	−	0.274746i	$-0.0885936\pi$
$863$	−0.251289	−	0.937822i	−0.00855397	−	0.0319238i	−0.970071	+	0.242822i	$0.921927\pi$
$864$		0			0
$865$	−16.9545	+	50.8634i	−0.576470	+	1.72941i
$866$	−6.04552	−	22.5622i	−0.205435	−	0.766694i
$867$	−22.5622	+	6.04552i	−0.766252	+	0.205317i
$868$	−4.19615	+	7.26795i	−0.142427	+	0.246690i
$869$	22.3923	−	83.5692i	0.759607	−	2.83489i
$870$	35.3205	+	23.3205i	1.19748	+	0.790639i
$871$	−0.418584	−	1.56218i	−0.0141832	−	0.0529324i
$872$	2.83013	+	10.5622i	0.0958402	+	0.357680i
$873$	3.80385	−	6.58846i	0.128741	−	0.222985i
$874$	5.09808	−	5.09808i	0.172445	−	0.172445i
$875$	6.75833	−	14.2942i	0.228473	−	0.483233i
$876$	23.7846	+	13.7321i	0.803607	+	0.463963i
$877$	−17.2224	−	17.2224i	−0.581560	−	0.581560i	0.353772	−	0.935332i	$-0.384899\pi$
$877$	−17.2224	−	17.2224i	−0.581560	−	0.581560i	−0.935332	+	0.353772i	$0.884899\pi$
$878$	12.6603	+	12.6603i	0.427263	+	0.427263i
$879$	−11.4904	+	19.9019i	−0.387561	+	0.671275i
$880$	−12.9282	+	6.46410i	−0.435810	+	0.217905i
$881$	25.5788	−	14.7679i	0.861773	−	0.497545i	−0.00283265	−	0.999996i	$-0.500902\pi$
$881$	25.5788	−	14.7679i	0.861773	−	0.497545i	0.864606	+	0.502451i	$0.167568\pi$
$882$	15.0000			0.505076
$883$	40.9808	−	23.6603i	1.37911	−	0.796231i	0.387060	−	0.922055i	$-0.373491\pi$
$883$	40.9808	−	23.6603i	1.37911	−	0.796231i	0.992053	+	0.125824i	$0.0401574\pi$
$884$	−0.633975	+	0.366025i	−0.0213229	+	0.0123108i
$885$	−6.97372	+	10.5622i	−0.234419	+	0.355044i
$886$	−24.3923	+	6.53590i	−0.819476	+	0.219578i
$887$	22.8038	−	22.8038i	0.765678	−	0.765678i	−0.211664	−	0.977342i	$-0.567888\pi$
$887$	22.8038	−	22.8038i	0.765678	−	0.765678i	0.977342	+	0.211664i	$0.0678883\pi$
$888$	14.6603	+	2.66025i	0.491966	+	0.0892723i
$889$			8.58846i			0.288048i
$890$	−18.1147	−	20.4282i	−0.607207	−	0.684755i
$891$	−50.3827	+	29.0885i	−1.68788	+	0.974500i
$892$	−13.1603	−	3.52628i	−0.440638	−	0.118069i
$893$	−4.23205	−	7.33013i	−0.141620	−	0.245293i
$894$	37.1769	−	37.1769i	1.24338	−	1.24338i
$895$	−1.35641	+	0.277568i	−0.0453397	+	0.00927808i
$896$	1.00000	+	1.00000i	0.0334077	+	0.0334077i
$897$	−2.36603	+	0.633975i	−0.0789993	+	0.0211678i
$898$	19.1962	−	19.1962i	0.640584	−	0.640584i
$899$	−45.8564			−1.52940
$900$	13.7942	−	5.89230i	0.459808	−	0.196410i
$901$	9.73205	−	36.3205i	0.324222	−	1.21001i
$902$	16.3923			0.545804
$903$	−12.0000	−	6.92820i	−0.399335	−	0.230556i
$904$	3.63397	+	2.09808i	0.120864	+	0.0697810i
$905$	58.1506	+	3.49038i	1.93299	+	0.116024i
$906$	7.73205	+	2.07180i	0.256880	+	0.0688308i
$907$	44.6147	−	25.7583i	1.48141	−	0.855291i	0.481630	−	0.876374i	$-0.340045\pi$
$907$	44.6147	−	25.7583i	1.48141	−	0.855291i	0.999778	+	0.0210832i	$0.00671148\pi$
$908$	19.9019	+	11.4904i	0.660469	+	0.381322i
$909$	12.5885	−	21.8038i	0.417533	−	0.723188i
$910$	−0.562178	−	0.633975i	−0.0186360	−	0.0210161i
$911$	22.4641	+	22.4641i	0.744269	+	0.744269i	0.973396	−	0.229128i	$-0.0735873\pi$
$911$	22.4641	+	22.4641i	0.744269	+	0.744269i	−0.229128	+	0.973396i	$0.573587\pi$
$912$	2.36603	+	4.09808i	0.0783469	+	0.135701i
$913$	35.3205	−	9.46410i	1.16894	−	0.313216i
$914$		−	5.46410i		−	0.180736i
$915$	29.3205	+	58.6410i	0.969306	+	1.93861i
$916$	16.8564	+	9.73205i	0.556951	+	0.321556i
$917$	−19.8564			−0.655716
$918$		0			0
$919$	−24.6603	−	24.6603i	−0.813467	−	0.813467i	0.171685	−	0.985152i	$-0.445079\pi$
$919$	−24.6603	−	24.6603i	−0.813467	−	0.813467i	−0.985152	+	0.171685i	$0.945079\pi$
$920$	4.59808	−	6.96410i	0.151594	−	0.229600i
$921$	3.00000	+	5.19615i	0.0988534	+	0.171219i
$922$	2.97372	−	11.0981i	0.0979343	−	0.365496i
$923$	−0.803848	+	1.39230i	−0.0264590	+	0.0458283i
$924$	22.3923			0.736653
$925$	26.8923	−	14.2058i	0.884214	−	0.467083i
$926$	−4.78461			−0.157232
$927$	−5.08846	+	8.81347i	−0.167127	+	0.289472i
$928$	−2.00000	+	7.46410i	−0.0656532	+	0.245021i
$929$	27.4545	+	47.5526i	0.900752	+	1.56015i	0.826520	+	0.562908i	$0.190317\pi$
$929$	27.4545	+	47.5526i	0.900752	+	1.56015i	0.0742327	+	0.997241i	$0.476349\pi$
$930$	−17.9090	+	27.1244i	−0.587258	+	0.889443i
$931$	6.83013	+	6.83013i	0.223848	+	0.223848i
$932$	2.63397	−	9.83013i	0.0862787	−	0.321997i
$933$	12.9282			0.423250
$934$	23.9545	+	13.8301i	0.783815	+	0.452536i
$935$	−17.6603	−	35.3205i	−0.577552	−	1.15510i
$936$		−	0.803848i		−	0.0262746i
$937$	−27.0263	+	7.24167i	−0.882910	+	0.236575i	−0.671662	−	0.740857i	$-0.734419\pi$
$937$	−27.0263	+	7.24167i	−0.882910	+	0.236575i	−0.211248	+	0.977433i	$0.567753\pi$
$938$	−4.26795	−	7.39230i	−0.139353	−	0.241367i
$939$	−48.2487	−	48.2487i	−1.57454	−	1.57454i
$940$	−6.50000	−	7.33013i	−0.212007	−	0.239082i
$941$	7.33975	−	12.7128i	0.239269	−	0.414426i	−0.721236	−	0.692690i	$-0.756426\pi$
$941$	7.33975	−	12.7128i	0.239269	−	0.414426i	0.960505	+	0.278264i	$0.0897589\pi$
$942$	3.88269	+	2.24167i	0.126505	+	0.0730375i
$943$	−8.19615	+	4.73205i	−0.266903	+	0.154097i
$944$	−2.23205	−	0.598076i	−0.0726471	−	0.0194657i
$945$		0			0
$946$	22.3923	+	12.9282i	0.728037	+	0.420332i
$947$	5.02628	+	2.90192i	0.163332	+	0.0942999i	0.579438	−	0.815016i	$-0.303272\pi$
$947$	5.02628	+	2.90192i	0.163332	+	0.0942999i	−0.416106	+	0.909316i	$0.636605\pi$
$948$	−32.7846			−1.06479
$949$	0.777568	−	2.90192i	0.0252409	−	0.0942004i
$950$	8.96410	+	3.59808i	0.290834	+	0.116737i
$951$	−32.8756			−1.06607
$952$	−2.73205	+	2.73205i	−0.0885463	+	0.0885463i
$953$	22.3923	−	6.00000i	0.725358	−	0.194359i	0.122797	−	0.992432i	$-0.460814\pi$
$953$	22.3923	−	6.00000i	0.725358	−	0.194359i	0.602561	+	0.798073i	$0.294147\pi$
$954$	29.1962	+	29.1962i	0.945260	+	0.945260i
$955$	17.9808	−	3.67949i	0.581844	−	0.119066i
$956$	4.07180	−	4.07180i	0.131691	−	0.131691i
$957$	61.1769	+	105.962i	1.97757	+	3.42525i
$958$	−18.3923	−	4.92820i	−0.594228	−	0.159223i
$959$	7.26795	−	4.19615i	0.234694	−	0.135501i
$960$	3.63397	+	4.09808i	0.117286	+	0.132265i
$961$		−	4.21539i		−	0.135980i
$962$	−0.133975	−	1.62436i	−0.00431951	−	0.0523713i
$963$	1.60770	−	1.60770i	0.0518073	−	0.0518073i
$964$	7.59808	−	2.03590i	0.244718	−	0.0655719i
$965$	−14.5429	+	22.0263i	−0.468154	+	0.709051i
$966$	−11.1962	+	6.46410i	−0.360230	+	0.207979i
$967$	−3.91154	+	2.25833i	−0.125787	+	0.0726230i	−0.561573	−	0.827427i	$-0.689804\pi$
$967$	−3.91154	+	2.25833i	−0.125787	+	0.0726230i	0.435786	+	0.900050i	$0.356470\pi$
$968$	−30.7846			−0.989455
$969$	−11.1962	+	6.46410i	−0.359672	+	0.207657i
$970$	5.07180	−	2.53590i	0.162846	−	0.0814228i
$971$	11.0359	−	19.1147i	0.354159	−	0.613421i	−0.632815	−	0.774303i	$-0.718101\pi$
$971$	11.0359	−	19.1147i	0.354159	−	0.613421i	0.986974	+	0.160882i	$0.0514339\pi$
$972$	15.5885	+	15.5885i	0.500000	+	0.500000i
$973$	11.7321	+	11.7321i	0.376112	+	0.376112i
$974$	−26.6603	−	15.3923i	−0.854250	−	0.493201i
$975$	−2.02628	−	2.58142i	−0.0648929	−	0.0826715i
$976$	−8.46410	+	8.46410i	−0.270929	+	0.270929i
$977$	−19.9019	+	34.4711i	−0.636719	+	1.10283i	0.349429	+	0.936963i	$0.386376\pi$
$977$	−19.9019	+	34.4711i	−0.636719	+	1.10283i	−0.986148	+	0.165867i	$0.946958\pi$
$978$	−0.803848	−	3.00000i	−0.0257042	−	0.0959294i
$979$	−20.4282	−	76.2391i	−0.652888	−	2.43661i
$980$	9.33013	+	6.16025i	0.298040	+	0.196782i
$981$	8.49038	−	31.6865i	0.271077	−	1.01167i
$982$	−11.6962	+	20.2583i	−0.373239	+	0.646469i
$983$	7.03590	−	1.88526i	0.224410	−	0.0601306i	−0.144862	−	0.989452i	$-0.546274\pi$
$983$	7.03590	−	1.88526i	0.224410	−	0.0601306i	0.369272	+	0.929321i	$0.379607\pi$
$984$	−1.60770	−	6.00000i	−0.0512514	−	0.191273i
$985$	5.53590	−	16.6077i	0.176388	−	0.529165i
$986$	−20.3923	−	5.46410i	−0.649423	−	0.174012i
$987$	3.92820	+	14.6603i	0.125036	+	0.466641i
$988$	0.366025	−	0.366025i	0.0116448	−	0.0116448i
$989$	−14.9282			−0.474689
$990$	43.2846	+	2.59808i	1.37568	+	0.0825723i
$991$	−25.4641	+	25.4641i	−0.808894	+	0.808894i	−0.984466	−	0.175573i	$-0.943822\pi$
$991$	−25.4641	+	25.4641i	−0.808894	+	0.808894i	0.175573	+	0.984466i	$0.443822\pi$
$992$	−5.73205	−	1.53590i	−0.181993	−	0.0487648i
$993$			18.5885i			0.589887i
$994$	−2.19615	+	8.19615i	−0.0696577	+	0.259966i
$995$	9.07180	−	1.85641i	0.287595	−	0.0588520i
$996$	−6.92820	−	12.0000i	−0.219529	−	0.380235i
$997$	16.1147	+	9.30385i	0.510359	+	0.294656i	0.732981	−	0.680249i	$-0.238128\pi$
$997$	16.1147	+	9.30385i	0.510359	+	0.294656i	−0.222622	+	0.974905i	$0.571462\pi$
$998$	−22.4641	−	22.4641i	−0.711089	−	0.711089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.b.97.1	✓	4
5.3	odd	4		370.2.r.b.23.1	yes	4
37.29	odd	12		370.2.r.b.177.1	yes	4
185.103	even	12	inner	370.2.q.b.103.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.b.97.1	✓	4	1.1	even	1	trivial
370.2.q.b.103.1	yes	4	185.103	even	12	inner
370.2.r.b.23.1	yes	4	5.3	odd	4
370.2.r.b.177.1	yes	4	37.29	odd	12

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.633975 - 2.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.366025 - 1.36603i) q^{7} +1.00000 q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.633975 - 2.36603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.23205 + 1.86603i) q^{5} +(1.73205 + 1.73205i) q^{6} +(0.366025 - 1.36603i) q^{7} +1.00000 q^{8} +(-2.59808 - 1.50000i) q^{9} +(-1.00000 - 2.00000i) q^{10} -6.46410i q^{11} +(-2.36603 + 0.633975i) q^{12} +(0.133975 + 0.232051i) q^{13} +(1.00000 + 1.00000i) q^{14} +(3.63397 + 4.09808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.36603 - 1.36603i) q^{17} +(2.59808 - 1.50000i) q^{18} +(1.86603 + 0.500000i) q^{19} +(2.23205 + 0.133975i) q^{20} +(-3.00000 - 1.73205i) q^{21} +(5.59808 + 3.23205i) q^{22} -3.73205 q^{23} +(0.633975 - 2.36603i) q^{24} +(-1.96410 - 4.59808i) q^{25} -0.267949 q^{26} +(-1.36603 + 0.366025i) q^{28} +(-5.46410 - 5.46410i) q^{29} +(-5.36603 + 1.09808i) q^{30} +(4.19615 - 4.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-15.2942 - 4.09808i) q^{33} +(2.36603 - 1.36603i) q^{34} +(2.09808 + 2.36603i) q^{35} +3.00000i q^{36} +(0.500000 + 6.06218i) q^{37} +(-1.36603 + 1.36603i) q^{38} +(0.633975 - 0.169873i) q^{39} +(-1.23205 + 1.86603i) q^{40} +(2.19615 - 1.26795i) q^{41} +(3.00000 - 1.73205i) q^{42} +4.00000 q^{43} +(-5.59808 + 3.23205i) q^{44} +(6.00000 - 3.00000i) q^{45} +(1.86603 - 3.23205i) q^{46} +(-3.09808 - 3.09808i) q^{47} +(1.73205 + 1.73205i) q^{48} +(4.33013 + 2.50000i) q^{49} +(4.96410 + 0.598076i) q^{50} +(-4.73205 + 4.73205i) q^{51} +(0.133975 - 0.232051i) q^{52} +(3.56218 + 13.2942i) q^{53} +(12.0622 + 7.96410i) q^{55} +(0.366025 - 1.36603i) q^{56} +(2.36603 - 4.09808i) q^{57} +(7.46410 - 2.00000i) q^{58} +(0.598076 + 2.23205i) q^{59} +(1.73205 - 5.19615i) q^{60} +(11.5622 + 3.09808i) q^{61} +(1.53590 + 5.73205i) q^{62} +(-3.00000 + 3.00000i) q^{63} +1.00000 q^{64} +(-0.598076 - 0.0358984i) q^{65} +(11.1962 - 11.1962i) q^{66} +(-5.83013 - 1.56218i) q^{67} +2.73205i q^{68} +(-2.36603 + 8.83013i) q^{69} +(-3.09808 + 0.633975i) q^{70} +(3.00000 + 5.19615i) q^{71} +(-2.59808 - 1.50000i) q^{72} +(-7.92820 - 7.92820i) q^{73} +(-5.50000 - 2.59808i) q^{74} +(-12.1244 + 1.73205i) q^{75} +(-0.500000 - 1.86603i) q^{76} +(-8.83013 - 2.36603i) q^{77} +(-0.169873 + 0.633975i) q^{78} +(12.9282 + 3.46410i) q^{79} +(-1.00000 - 2.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +2.53590i q^{82} +(1.46410 + 5.46410i) q^{83} +3.46410i q^{84} +(5.46410 - 2.73205i) q^{85} +(-2.00000 + 3.46410i) q^{86} +(-16.3923 + 9.46410i) q^{87} -6.46410i q^{88} +(11.7942 - 3.16025i) q^{89} +(-0.401924 + 6.69615i) q^{90} +(0.366025 - 0.0980762i) q^{91} +(1.86603 + 3.23205i) q^{92} +(-7.26795 - 12.5885i) q^{93} +(4.23205 - 1.13397i) q^{94} +(-3.23205 + 2.86603i) q^{95} +(-2.36603 + 0.633975i) q^{96} +2.53590i q^{97} +(-4.33013 + 2.50000i) q^{98} +(-9.69615 + 16.7942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{7} + 4 q^{8} - 4 q^{10} - 6 q^{12} + 4 q^{13} + 4 q^{14} + 18 q^{15} - 2 q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{20} - 12 q^{21} + 12 q^{22} - 8 q^{23} + 6 q^{24} + 6 q^{25} - 8 q^{26} - 2 q^{28} - 8 q^{29} - 18 q^{30} - 4 q^{31} - 2 q^{32} - 30 q^{33} + 6 q^{34} - 2 q^{35} + 2 q^{37} - 2 q^{38} + 6 q^{39} + 2 q^{40} - 12 q^{41} + 12 q^{42} + 16 q^{43} - 12 q^{44} + 24 q^{45} + 4 q^{46} - 2 q^{47} + 6 q^{50} - 12 q^{51} + 4 q^{52} - 10 q^{53} + 24 q^{55} - 2 q^{56} + 6 q^{57} + 16 q^{58} - 8 q^{59} + 22 q^{61} + 20 q^{62} - 12 q^{63} + 4 q^{64} + 8 q^{65} + 24 q^{66} - 6 q^{67} - 6 q^{69} - 2 q^{70} + 12 q^{71} - 4 q^{73} - 22 q^{74} - 2 q^{76} - 18 q^{77} - 18 q^{78} + 24 q^{79} - 4 q^{80} - 18 q^{81} - 8 q^{83} + 8 q^{85} - 8 q^{86} - 24 q^{87} + 16 q^{89} - 12 q^{90} - 2 q^{91} + 4 q^{92} - 36 q^{93} + 10 q^{94} - 6 q^{95} - 6 q^{96} - 18 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^7 + 4 * q^8 - 4 * q^10 - 6 * q^12 + 4 * q^13 + 4 * q^14 + 18 * q^15 - 2 * q^16 - 6 * q^17 + 4 * q^19 + 2 * q^20 - 12 * q^21 + 12 * q^22 - 8 * q^23 + 6 * q^24 + 6 * q^25 - 8 * q^26 - 2 * q^28 - 8 * q^29 - 18 * q^30 - 4 * q^31 - 2 * q^32 - 30 * q^33 + 6 * q^34 - 2 * q^35 + 2 * q^37 - 2 * q^38 + 6 * q^39 + 2 * q^40 - 12 * q^41 + 12 * q^42 + 16 * q^43 - 12 * q^44 + 24 * q^45 + 4 * q^46 - 2 * q^47 + 6 * q^50 - 12 * q^51 + 4 * q^52 - 10 * q^53 + 24 * q^55 - 2 * q^56 + 6 * q^57 + 16 * q^58 - 8 * q^59 + 22 * q^61 + 20 * q^62 - 12 * q^63 + 4 * q^64 + 8 * q^65 + 24 * q^66 - 6 * q^67 - 6 * q^69 - 2 * q^70 + 12 * q^71 - 4 * q^73 - 22 * q^74 - 2 * q^76 - 18 * q^77 - 18 * q^78 + 24 * q^79 - 4 * q^80 - 18 * q^81 - 8 * q^83 + 8 * q^85 - 8 * q^86 - 24 * q^87 + 16 * q^89 - 12 * q^90 - 2 * q^91 + 4 * q^92 - 36 * q^93 + 10 * q^94 - 6 * q^95 - 6 * q^96 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more