LMFDB - Embedded newform 1530.2.m.h.647.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(647,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1530.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.m (of order $4$, 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:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.17364600040304039428096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 20 x^{14} - 40 x^{13} + 104 x^{12} - 180 x^{11} + 242 x^{10} - 132 x^{9} - 302 x^{8} + \cdots + 1 $ x^16 - 4x^15 + 20x^14 - 40x^13 + 104x^12 - 180x^11 + 242x^10 - 132x^9 - 302x^8 + 416x^7 + 296x^6 - 416x^5 + 2x^4 + 32x^3 + 46x^2 + 12*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.7
Root			$-0.143668 - 0.0595092i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.h.953.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.24148 + 1.85976i) q^{5} +(-1.28734 - 1.28734i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.24148 + 1.85976i) q^{5} +(-1.28734 - 1.28734i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.19291 + 0.437190i) q^{10} -1.23656i q^{11} +(3.04306 - 3.04306i) q^{13} -1.82057 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} -3.83488i q^{19} +(1.85976 - 1.24148i) q^{20} +(-0.874380 - 0.874380i) q^{22} +(0.795934 + 0.795934i) q^{23} +(-1.91744 + 4.61773i) q^{25} -4.30353i q^{26} +(-1.28734 + 1.28734i) q^{28} +0.0783908 q^{29} +3.53517 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.00000i q^{34} +(0.795934 - 3.99235i) q^{35} +(-2.05543 - 2.05543i) q^{37} +(-2.71167 - 2.71167i) q^{38} +(0.437190 - 2.19291i) q^{40} -1.35332i q^{41} +(3.16868 - 3.16868i) q^{43} -1.23656 q^{44} +1.12562 q^{46} +(8.91416 - 8.91416i) q^{47} -3.68553i q^{49} +(1.90939 + 4.62106i) q^{50} +(-3.04306 - 3.04306i) q^{52} +(5.71775 + 5.71775i) q^{53} +(2.29971 - 1.53517i) q^{55} +1.82057i q^{56} +(0.0554307 - 0.0554307i) q^{58} +11.6867 q^{59} -11.6213 q^{61} +(2.49974 - 2.49974i) q^{62} +1.00000i q^{64} +(9.43727 + 1.88146i) q^{65} +(-2.64247 - 2.64247i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(-2.26020 - 3.38582i) q^{70} -14.9165i q^{71} +(-1.34277 + 1.34277i) q^{73} -2.90682 q^{74} -3.83488 q^{76} +(-1.59187 + 1.59187i) q^{77} +3.30867i q^{79} +(-1.24148 - 1.85976i) q^{80} +(-0.956942 - 0.956942i) q^{82} +(10.0213 + 10.0213i) q^{83} +(2.19291 + 0.437190i) q^{85} -4.48119i q^{86} +(-0.874380 + 0.874380i) q^{88} -9.24212 q^{89} -7.83488 q^{91} +(0.795934 - 0.795934i) q^{92} -12.6065i q^{94} +(7.13196 - 4.76094i) q^{95} +(-6.16868 - 6.16868i) q^{97} +(-2.60607 - 2.60607i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^7	$ 16 q - 8 q^{7} + 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{22} + 16 q^{25} - 8 q^{28} - 56 q^{31} - 24 q^{37} + 4 q^{40} + 16 q^{43} + 24 q^{46} - 8 q^{52} + 56 q^{55} - 8 q^{58} + 8 q^{61} - 40 q^{67} + 32 q^{70} + 32 q^{76} - 56 q^{82} + 4 q^{85} - 8 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) $ 16 * q - 8 * q^7 + 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^22 + 16 * q^25 - 8 * q^28 - 56 * q^31 - 24 * q^37 + 4 * q^40 + 16 * q^43 + 24 * q^46 - 8 * q^52 + 56 * q^55 - 8 * q^58 + 8 * q^61 - 40 * q^67 + 32 * q^70 + 32 * q^76 - 56 * q^82 + 4 * q^85 - 8 * q^88 - 32 * q^91 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.24148	+	1.85976i	0.555208	+	0.831711i
$5$	1.24148	+	1.85976i	0.555208	+	0.831711i
$6$		0			0
$7$	−1.28734	−	1.28734i	−0.486567	−	0.486567i	0.420654	−	0.907221i	$-0.361801\pi$
$7$	−1.28734	−	1.28734i	−0.486567	−	0.486567i	−0.907221	+	0.420654i	$0.861801\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.19291	+	0.437190i	0.693460	+	0.138252i
$11$		−	1.23656i		−	0.372837i	−0.982470	−	0.186418i	$-0.940312\pi$
$11$		−	1.23656i		−	0.372837i	0.982470	−	0.186418i	$-0.0596880\pi$
$12$		0			0
$13$	3.04306	−	3.04306i	0.843993	−	0.843993i	−0.145383	−	0.989375i	$-0.546441\pi$
$13$	3.04306	−	3.04306i	0.843993	−	0.843993i	0.989375	+	0.145383i	$0.0464414\pi$
$14$	−1.82057			−0.486567
$15$		0			0
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$		0			0
$19$		−	3.83488i		−	0.879781i	−0.898051	−	0.439890i	$-0.855017\pi$
$19$		−	3.83488i		−	0.879781i	0.898051	−	0.439890i	$-0.144983\pi$
$20$	1.85976	−	1.24148i	0.415856	−	0.277604i
$21$		0			0
$22$	−0.874380	−	0.874380i	−0.186418	−	0.186418i
$23$	0.795934	+	0.795934i	0.165964	+	0.165964i	0.785203	−	0.619239i	$-0.212559\pi$
$23$	0.795934	+	0.795934i	0.165964	+	0.165964i	−0.619239	+	0.785203i	$0.712559\pi$
$24$		0			0
$25$	−1.91744	+	4.61773i	−0.383488	+	0.923546i
$26$		−	4.30353i		−	0.843993i
$27$		0			0
$28$	−1.28734	+	1.28734i	−0.243284	+	0.243284i
$29$	0.0783908			0.0145568			0.00727840	−	0.999974i	$-0.497683\pi$
$29$	0.0783908			0.0145568			0.00727840	+	0.999974i	$0.497683\pi$
$30$		0			0
$31$	3.53517			0.634935			0.317467	−	0.948269i	$-0.397168\pi$
$31$	3.53517			0.634935			0.317467	+	0.948269i	$0.397168\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$		−	1.00000i		−	0.171499i
$35$	0.795934	−	3.99235i	0.134537	−	0.674830i
$36$		0			0
$37$	−2.05543	−	2.05543i	−0.337911	−	0.337911i	0.517670	−	0.855581i	$-0.326800\pi$
$37$	−2.05543	−	2.05543i	−0.337911	−	0.337911i	−0.855581	+	0.517670i	$0.826800\pi$
$38$	−2.71167	−	2.71167i	−0.439890	−	0.439890i
$39$		0			0
$40$	0.437190	−	2.19291i	0.0691258	−	0.346730i
$41$		−	1.35332i		−	0.211353i	−0.994401	−	0.105677i	$-0.966299\pi$
$41$		−	1.35332i		−	0.211353i	0.994401	−	0.105677i	$-0.0337008\pi$
$42$		0			0
$43$	3.16868	−	3.16868i	0.483219	−	0.483219i	−0.422939	−	0.906158i	$-0.639002\pi$
$43$	3.16868	−	3.16868i	0.483219	−	0.483219i	0.906158	+	0.422939i	$0.139002\pi$
$44$	−1.23656			−0.186418
$45$		0			0
$46$	1.12562			0.165964
$47$	8.91416	−	8.91416i	1.30026	−	1.30026i	0.372052	−	0.928212i	$-0.378654\pi$
$47$	8.91416	−	8.91416i	1.30026	−	1.30026i	0.928212	−	0.372052i	$-0.121346\pi$
$48$		0			0
$49$		−	3.68553i		−	0.526505i
$50$	1.90939	+	4.62106i	0.270029	+	0.653517i
$51$		0			0
$52$	−3.04306	−	3.04306i	−0.421996	−	0.421996i
$53$	5.71775	+	5.71775i	0.785393	+	0.785393i	0.980735	−	0.195342i	$-0.0625817\pi$
$53$	5.71775	+	5.71775i	0.785393	+	0.785393i	−0.195342	+	0.980735i	$0.562582\pi$
$54$		0			0
$55$	2.29971	−	1.53517i	0.310093	−	0.207002i
$56$			1.82057i			0.243284i
$57$		0			0
$58$	0.0554307	−	0.0554307i	0.00727840	−	0.00727840i
$59$	11.6867			1.52148			0.760741	−	0.649056i	$-0.224836\pi$
$59$	11.6867			1.52148			0.760741	+	0.649056i	$0.224836\pi$
$60$		0			0
$61$	−11.6213			−1.48795			−0.743977	−	0.668206i	$-0.767063\pi$
$61$	−11.6213			−1.48795			−0.743977	+	0.668206i	$0.767063\pi$
$62$	2.49974	−	2.49974i	0.317467	−	0.317467i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	9.43727	+	1.88146i	1.17055	+	0.233367i
$66$		0			0
$67$	−2.64247	−	2.64247i	−0.322830	−	0.322830i	0.527022	−	0.849852i	$-0.323309\pi$
$67$	−2.64247	−	2.64247i	−0.322830	−	0.322830i	−0.849852	+	0.527022i	$0.823309\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$		0			0
$70$	−2.26020	−	3.38582i	−0.270146	−	0.404683i
$71$		−	14.9165i		−	1.77026i	−0.465344	−	0.885130i	$-0.654069\pi$
$71$		−	14.9165i		−	1.77026i	0.465344	−	0.885130i	$-0.345931\pi$
$72$		0			0
$73$	−1.34277	+	1.34277i	−0.157159	+	0.157159i	−0.781306	−	0.624148i	$-0.785446\pi$
$73$	−1.34277	+	1.34277i	−0.157159	+	0.157159i	0.624148	+	0.781306i	$0.285446\pi$
$74$	−2.90682			−0.337911
$75$		0			0
$76$	−3.83488			−0.439890
$77$	−1.59187	+	1.59187i	−0.181410	+	0.181410i
$78$		0			0
$79$			3.30867i			0.372255i	0.982526	+	0.186127i	$0.0595937\pi$
$79$			3.30867i			0.372255i	−0.982526	+	0.186127i	$0.940406\pi$
$80$	−1.24148	−	1.85976i	−0.138802	−	0.207928i
$81$		0			0
$82$	−0.956942	−	0.956942i	−0.105677	−	0.105677i
$83$	10.0213	+	10.0213i	1.09998	+	1.09998i	0.994412	+	0.105566i	$0.0336656\pi$
$83$	10.0213	+	10.0213i	1.09998	+	1.09998i	0.105566	+	0.994412i	$0.466334\pi$
$84$		0			0
$85$	2.19291	+	0.437190i	0.237855	+	0.0474199i
$86$		−	4.48119i		−	0.483219i
$87$		0			0
$88$	−0.874380	+	0.874380i	−0.0932092	+	0.0932092i
$89$	−9.24212			−0.979663			−0.489832	−	0.871817i	$-0.662942\pi$
$89$	−9.24212			−0.979663			−0.489832	+	0.871817i	$0.662942\pi$
$90$		0			0
$91$	−7.83488			−0.821318
$92$	0.795934	−	0.795934i	0.0829818	−	0.0829818i
$93$		0			0
$94$		−	12.6065i		−	1.30026i
$95$	7.13196	−	4.76094i	0.731724	−	0.488462i
$96$		0			0
$97$	−6.16868	−	6.16868i	−0.626334	−	0.626334i	0.320809	−	0.947144i	$-0.396045\pi$
$97$	−6.16868	−	6.16868i	−0.626334	−	0.626334i	−0.947144	+	0.320809i	$0.896045\pi$
$98$	−2.60607	−	2.60607i	−0.263252	−	0.263252i
$99$		0			0
$100$	4.61773	+	1.91744i	0.461773	+	0.191744i
$101$		−	3.40259i		−	0.338570i	−0.985567	−	0.169285i	$-0.945854\pi$
$101$		−	3.40259i		−	0.338570i	0.985567	−	0.169285i	$-0.0541459\pi$
$102$		0			0
$103$	−8.10984	+	8.10984i	−0.799086	+	0.799086i	−0.982951	−	0.183865i	$-0.941139\pi$
$103$	−8.10984	+	8.10984i	−0.799086	+	0.799086i	0.183865	+	0.982951i	$0.441139\pi$
$104$	−4.30353			−0.421996
$105$		0			0
$106$	8.08612			0.785393
$107$	−2.16603	+	2.16603i	−0.209398	+	0.209398i	−0.804012	−	0.594614i	$-0.797305\pi$
$107$	−2.16603	+	2.16603i	−0.209398	+	0.209398i	0.594614	+	0.804012i	$0.297305\pi$
$108$		0			0
$109$			14.6302i			1.40132i	0.713493	+	0.700662i	$0.247112\pi$
$109$			14.6302i			1.40132i	−0.713493	+	0.700662i	$0.752888\pi$
$110$	0.540611	−	2.71167i	0.0515453	−	0.258547i
$111$		0			0
$112$	1.28734	+	1.28734i	0.121642	+	0.121642i
$113$	14.3934	+	14.3934i	1.35401	+	1.35401i	0.881119	+	0.472894i	$0.156791\pi$
$113$	14.3934	+	14.3934i	1.35401	+	1.35401i	0.472894	+	0.881119i	$0.343209\pi$
$114$		0			0
$115$	−0.492110	+	2.46839i	−0.0458895	+	0.230178i
$116$		−	0.0783908i		−	0.00727840i
$117$		0			0
$118$	8.26376	−	8.26376i	0.760741	−	0.760741i
$119$	−1.82057			−0.166891
$120$		0			0
$121$	9.47092			0.860993
$122$	−8.21749	+	8.21749i	−0.743977	+	0.743977i
$123$		0			0
$124$		−	3.53517i		−	0.317467i
$125$	−10.9684	+	2.16685i	−0.981039	+	0.193809i
$126$		0			0
$127$	−5.95153	−	5.95153i	−0.528113	−	0.528113i	0.391896	−	0.920009i	$-0.371819\pi$
$127$	−5.95153	−	5.95153i	−0.528113	−	0.528113i	−0.920009	+	0.391896i	$0.871819\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	8.00355	−	5.34277i	0.701958	−	0.468592i
$131$		−	3.45080i		−	0.301498i	−0.988572	−	0.150749i	$-0.951831\pi$
$131$		−	3.45080i		−	0.301498i	0.988572	−	0.150749i	$-0.0481686\pi$
$132$		0			0
$133$	−4.93677	+	4.93677i	−0.428073	+	0.428073i
$134$	−3.73702			−0.322830
$135$		0			0
$136$	−1.00000			−0.0857493
$137$	−10.9299	+	10.9299i	−0.933803	+	0.933803i	−0.997941	−	0.0641384i	$-0.979570\pi$
$137$	−10.9299	+	10.9299i	−0.933803	+	0.933803i	0.0641384	+	0.997941i	$0.479570\pi$
$138$		0			0
$139$		−	10.8578i		−	0.920944i	−0.887674	−	0.460472i	$-0.847680\pi$
$139$		−	10.8578i		−	0.920944i	0.887674	−	0.460472i	$-0.152320\pi$
$140$	−3.99235	−	0.795934i	−0.337415	−	0.0672687i
$141$		0			0
$142$	−10.5475	−	10.5475i	−0.885130	−	0.885130i
$143$	−3.76292	−	3.76292i	−0.314671	−	0.314671i
$144$		0			0
$145$	0.0973209	+	0.145788i	0.00808206	+	0.0121071i
$146$			1.89896i			0.157159i
$147$		0			0
$148$	−2.05543	+	2.05543i	−0.168955	+	0.168955i
$149$	1.20804			0.0989663			0.0494832	−	0.998775i	$-0.484243\pi$
$149$	1.20804			0.0989663			0.0494832	+	0.998775i	$0.484243\pi$
$150$		0			0
$151$	−0.212570			−0.0172987			−0.00864934	−	0.999963i	$-0.502753\pi$
$151$	−0.212570			−0.0172987			−0.00864934	+	0.999963i	$0.502753\pi$
$152$	−2.71167	+	2.71167i	−0.219945	+	0.219945i
$153$		0			0
$154$			2.25124i			0.181410i
$155$	4.38885	+	6.57458i	0.352521	+	0.528083i
$156$		0			0
$157$	0.382270	+	0.382270i	0.0305085	+	0.0305085i	0.722196	−	0.691688i	$-0.243133\pi$
$157$	0.382270	+	0.382270i	0.0305085	+	0.0305085i	−0.691688	+	0.722196i	$0.743133\pi$
$158$	2.33958	+	2.33958i	0.186127	+	0.186127i
$159$		0			0
$160$	−2.19291	−	0.437190i	−0.173365	−	0.0345629i
$161$		−	2.04927i		−	0.161505i
$162$		0			0
$163$	−5.02289	+	5.02289i	−0.393423	+	0.393423i	−0.875906	−	0.482482i	$-0.839735\pi$
$163$	−5.02289	+	5.02289i	−0.393423	+	0.393423i	0.482482	+	0.875906i	$0.339735\pi$
$164$	−1.35332			−0.105677
$165$		0			0
$166$	14.1722			1.09998
$167$	0.211926	−	0.211926i	0.0163993	−	0.0163993i	−0.698860	−	0.715259i	$-0.746309\pi$
$167$	0.211926	−	0.211926i	0.0163993	−	0.0163993i	0.715259	+	0.698860i	$0.246309\pi$
$168$		0			0
$169$		−	5.52041i		−	0.424647i
$170$	1.85976	−	1.24148i	0.142637	−	0.0952174i
$171$		0			0
$172$	−3.16868	−	3.16868i	−0.241609	−	0.241609i
$173$	6.35352	+	6.35352i	0.483050	+	0.483050i	0.906104	−	0.423055i	$-0.139042\pi$
$173$	6.35352	+	6.35352i	0.483050	+	0.483050i	−0.423055	+	0.906104i	$0.639042\pi$
$174$		0			0
$175$	8.41296	−	3.47618i	0.635960	−	0.262775i
$176$			1.23656i			0.0932092i
$177$		0			0
$178$	−6.53517	+	6.53517i	−0.489832	+	0.489832i
$179$	−4.54973			−0.340063			−0.170031	−	0.985439i	$-0.554387\pi$
$179$	−4.54973			−0.340063			−0.170031	+	0.985439i	$0.554387\pi$
$180$		0			0
$181$	−15.4019			−1.14481			−0.572407	−	0.819970i	$-0.693990\pi$
$181$	−15.4019			−1.14481			−0.572407	+	0.819970i	$0.693990\pi$
$182$	−5.54009	+	5.54009i	−0.410659	+	0.410659i
$183$		0			0
$184$		−	1.12562i		−	0.0829818i
$185$	1.27083	−	6.37440i	0.0934334	−	0.468655i
$186$		0			0
$187$	−0.874380	−	0.874380i	−0.0639410	−	0.0639410i
$188$	−8.91416	−	8.91416i	−0.650132	−	0.650132i
$189$		0			0
$190$	1.67657	−	8.40955i	0.121631	−	0.610093i
$191$		−	0.690921i		−	0.0499933i	−0.999688	−	0.0249966i	$-0.992042\pi$
$191$		−	0.690921i		−	0.0499933i	0.999688	−	0.0249966i	$-0.00795751\pi$
$192$		0			0
$193$	6.94033	−	6.94033i	0.499576	−	0.499576i	−0.411730	−	0.911306i	$-0.635075\pi$
$193$	6.94033	−	6.94033i	0.499576	−	0.499576i	0.911306	+	0.411730i	$0.135075\pi$
$194$	−8.72383			−0.626334
$195$		0			0
$196$	−3.68553			−0.263252
$197$	−8.33425	+	8.33425i	−0.593791	+	0.593791i	−0.938653	−	0.344863i	$-0.887926\pi$
$197$	−8.33425	+	8.33425i	−0.593791	+	0.593791i	0.344863	+	0.938653i	$0.387926\pi$
$198$		0			0
$199$			16.3068i			1.15596i	0.816051	+	0.577980i	$0.196159\pi$
$199$			16.3068i			1.15596i	−0.816051	+	0.577980i	$0.803841\pi$
$200$	4.62106	−	1.90939i	0.326758	−	0.135015i
$201$		0			0
$202$	−2.40599	−	2.40599i	−0.169285	−	0.169285i
$203$	−0.100915	−	0.100915i	−0.00708286	−	0.00708286i
$204$		0			0
$205$	2.51685	−	1.68012i	0.175785	−	0.117345i
$206$			11.4690i			0.799086i
$207$		0			0
$208$	−3.04306	+	3.04306i	−0.210998	+	0.210998i
$209$	−4.74205			−0.328015
$210$		0			0
$211$	−5.65182			−0.389088			−0.194544	−	0.980894i	$-0.562323\pi$
$211$	−5.65182			−0.389088			−0.194544	+	0.980894i	$0.562323\pi$
$212$	5.71775	−	5.71775i	0.392697	−	0.392697i
$213$		0			0
$214$			3.06323i			0.209398i
$215$	9.82685	+	1.95913i	0.670186	+	0.133612i
$216$		0			0
$217$	−4.55095	−	4.55095i	−0.308939	−	0.308939i
$218$	10.3451	+	10.3451i	0.700662	+	0.700662i
$219$		0			0
$220$	−1.53517	−	2.29971i	−0.103501	−	0.155046i
$221$		−	4.30353i		−	0.289487i
$222$		0			0
$223$	10.4580	−	10.4580i	0.700321	−	0.700321i	−0.264159	−	0.964479i	$-0.585094\pi$
$223$	10.4580	−	10.4580i	0.700321	−	0.700321i	0.964479	+	0.264159i	$0.0850943\pi$
$224$	1.82057			0.121642
$225$		0			0
$226$	20.3553			1.35401
$227$	−6.77665	+	6.77665i	−0.449782	+	0.449782i	−0.895282	−	0.445500i	$-0.853026\pi$
$227$	−6.77665	+	6.77665i	−0.449782	+	0.449782i	0.445500	+	0.895282i	$0.353026\pi$
$228$		0			0
$229$			10.7716i			0.711811i	0.934522	+	0.355905i	$0.115827\pi$
$229$			10.7716i			0.711811i	−0.934522	+	0.355905i	$0.884173\pi$
$230$	1.39744	+	2.09339i	0.0921444	+	0.138034i
$231$		0			0
$232$	−0.0554307	−	0.0554307i	−0.00363920	−	0.00363920i
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	0.899716	−	0.436475i	$-0.143773\pi$
$233$	7.07107	+	7.07107i	0.463241	+	0.463241i	−0.436475	+	0.899716i	$0.643773\pi$
$234$		0			0
$235$	27.6450	+	5.51145i	1.80336	+	0.359527i
$236$		−	11.6867i		−	0.760741i
$237$		0			0
$238$	−1.28734	+	1.28734i	−0.0834456	+	0.0834456i
$239$	−22.6725			−1.46656			−0.733280	−	0.679927i	$-0.762012\pi$
$239$	−22.6725			−1.46656			−0.733280	+	0.679927i	$0.762012\pi$
$240$		0			0
$241$	−10.5025			−0.676524			−0.338262	−	0.941052i	$-0.609839\pi$
$241$	−10.5025			−0.676524			−0.338262	+	0.941052i	$0.609839\pi$
$242$	6.69695	−	6.69695i	0.430496	−	0.430496i
$243$		0			0
$244$			11.6213i			0.743977i
$245$	6.85422	−	4.57553i	0.437900	−	0.292320i
$246$		0			0
$247$	−11.6698	−	11.6698i	−0.742529	−	0.742529i
$248$	−2.49974	−	2.49974i	−0.158734	−	0.158734i
$249$		0			0
$250$	−6.22360	+	9.28799i	−0.393615	+	0.587424i
$251$		−	3.27962i		−	0.207008i	−0.994629	−	0.103504i	$-0.966995\pi$
$251$		−	3.27962i		−	0.207008i	0.994629	−	0.103504i	$-0.0330055\pi$
$252$		0			0
$253$	0.984220	−	0.984220i	0.0618774	−	0.0618774i
$254$	−8.41674			−0.528113
$255$		0			0
$256$	1.00000			0.0625000
$257$	−1.38569	+	1.38569i	−0.0864371	+	0.0864371i	−0.749003	−	0.662566i	$-0.769467\pi$
$257$	−1.38569	+	1.38569i	−0.0864371	+	0.0864371i	0.662566	+	0.749003i	$0.269467\pi$
$258$		0			0
$259$			5.29206i			0.328833i
$260$	1.88146	−	9.43727i	0.116683	−	0.585275i
$261$		0			0
$262$	−2.44009	−	2.44009i	−0.150749	−	0.150749i
$263$	0.512089	+	0.512089i	0.0315768	+	0.0315768i	0.722719	−	0.691142i	$-0.242892\pi$
$263$	0.512089	+	0.512089i	0.0315768	+	0.0315768i	−0.691142	+	0.722719i	$0.742892\pi$
$264$		0			0
$265$	−3.53517	+	17.7321i	−0.217164	+	1.08928i
$266$			6.98165i			0.428073i
$267$		0			0
$268$	−2.64247	+	2.64247i	−0.161415	+	0.161415i
$269$	6.27944			0.382864			0.191432	−	0.981506i	$-0.438687\pi$
$269$	6.27944			0.382864			0.191432	+	0.981506i	$0.438687\pi$
$270$		0			0
$271$	1.58364			0.0961990			0.0480995	−	0.998843i	$-0.484684\pi$
$271$	1.58364			0.0961990			0.0480995	+	0.998843i	$0.484684\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$		0			0
$274$			15.4572i			0.933803i
$275$	5.71010	+	2.37103i	0.344332	+	0.142978i
$276$		0			0
$277$	21.0230	+	21.0230i	1.26315	+	1.26315i	0.949557	+	0.313595i	$0.101533\pi$
$277$	21.0230	+	21.0230i	1.26315	+	1.26315i	0.313595	+	0.949557i	$0.398467\pi$
$278$	−7.67760	−	7.67760i	−0.460472	−	0.460472i
$279$		0			0
$280$	−3.38582	+	2.26020i	−0.202342	+	0.135073i
$281$			22.3030i			1.33049i	0.746626	+	0.665244i	$0.231672\pi$
$281$			22.3030i			1.33049i	−0.746626	+	0.665244i	$0.768328\pi$
$282$		0			0
$283$	−7.42533	+	7.42533i	−0.441390	+	0.441390i	−0.892479	−	0.451089i	$-0.851036\pi$
$283$	−7.42533	+	7.42533i	−0.441390	+	0.441390i	0.451089	+	0.892479i	$0.351036\pi$
$284$	−14.9165			−0.885130
$285$		0			0
$286$	−5.32158			−0.314671
$287$	−1.74218	+	1.74218i	−0.102837	+	0.102837i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	0.171904	+	0.0342717i	0.0100946	+	0.00201250i
$291$		0			0
$292$	1.34277	+	1.34277i	0.0785795	+	0.0785795i
$293$	20.2005	+	20.2005i	1.18013	+	1.18013i	0.979711	+	0.200416i	$0.0642295\pi$
$293$	20.2005	+	20.2005i	1.18013	+	1.18013i	0.200416	+	0.979711i	$0.435770\pi$
$294$		0			0
$295$	14.5089	+	21.7345i	0.844739	+	1.26543i
$296$			2.90682i			0.168955i
$297$		0			0
$298$	0.854212	−	0.854212i	0.0494832	−	0.0494832i
$299$	4.84415			0.280144
$300$		0			0
$301$	−8.15831			−0.470237
$302$	−0.150309	+	0.150309i	−0.00864934	+	0.00864934i
$303$		0			0
$304$			3.83488i			0.219945i
$305$	−14.4276	−	21.6128i	−0.826124	−	1.23755i
$306$		0			0
$307$	10.0264	+	10.0264i	0.572239	+	0.572239i	0.932754	−	0.360514i	$-0.117399\pi$
$307$	10.0264	+	10.0264i	0.572239	+	0.572239i	−0.360514	+	0.932754i	$0.617399\pi$
$308$	1.59187	+	1.59187i	0.0907051	+	0.0907051i
$309$		0			0
$310$	7.75231	+	1.54554i	0.440302	+	0.0877808i
$311$			4.29369i			0.243473i	0.992562	+	0.121736i	$0.0388462\pi$
$311$			4.29369i			0.243473i	−0.992562	+	0.121736i	$0.961154\pi$
$312$		0			0
$313$	−14.7752	+	14.7752i	−0.835144	+	0.835144i	−0.988215	−	0.153071i	$-0.951084\pi$
$313$	−14.7752	+	14.7752i	−0.835144	+	0.835144i	0.153071	+	0.988215i	$0.451084\pi$
$314$	0.540611			0.0305085
$315$		0			0
$316$	3.30867			0.186127
$317$	−6.20659	+	6.20659i	−0.348597	+	0.348597i	−0.859587	−	0.510990i	$-0.829279\pi$
$317$	−6.20659	+	6.20659i	−0.348597	+	0.348597i	0.510990	+	0.859587i	$0.329279\pi$
$318$		0			0
$319$		−	0.0969349i		−	0.00542731i
$320$	−1.85976	+	1.24148i	−0.103964	+	0.0694010i
$321$		0			0
$322$	−1.44905	−	1.44905i	−0.0807525	−	0.0807525i
$323$	−2.71167	−	2.71167i	−0.150881	−	0.150881i
$324$		0			0
$325$	8.21715	+	19.8869i	0.455805	+	1.10313i
$326$			7.10344i			0.393423i
$327$		0			0
$328$	−0.956942	+	0.956942i	−0.0528383	+	0.0528383i
$329$	−22.9510			−1.26533
$330$		0			0
$331$	12.3553			0.679108			0.339554	−	0.940587i	$-0.389724\pi$
$331$	12.3553			0.679108			0.339554	+	0.940587i	$0.389724\pi$
$332$	10.0213	−	10.0213i	0.549989	−	0.549989i
$333$		0			0
$334$		−	0.299708i		−	0.0163993i
$335$	1.63379	−	8.19496i	0.0892634	−	0.447739i
$336$		0			0
$337$	8.02830	+	8.02830i	0.437329	+	0.437329i	0.891112	−	0.453783i	$-0.149926\pi$
$337$	8.02830	+	8.02830i	0.437329	+	0.437329i	−0.453783	+	0.891112i	$0.649926\pi$
$338$	−3.90352	−	3.90352i	−0.212323	−	0.212323i
$339$		0			0
$340$	0.437190	−	2.19291i	0.0237099	−	0.118927i
$341$		−	4.37145i		−	0.236727i
$342$		0			0
$343$	−13.7559	+	13.7559i	−0.742747	+	0.742747i
$344$	−4.48119			−0.241609
$345$		0			0
$346$	8.98524			0.483050
$347$	0.272097	−	0.272097i	0.0146069	−	0.0146069i	−0.699766	−	0.714373i	$-0.746712\pi$
$347$	0.272097	−	0.272097i	0.0146069	−	0.0146069i	0.714373	+	0.699766i	$0.246712\pi$
$348$		0			0
$349$		−	31.7559i		−	1.69985i	−0.526901	−	0.849926i	$-0.676646\pi$
$349$		−	31.7559i		−	1.69985i	0.526901	−	0.849926i	$-0.323354\pi$
$350$	3.49083	−	8.40689i	0.186593	−	0.449367i
$351$		0			0
$352$	0.874380	+	0.874380i	0.0466046	+	0.0466046i
$353$	13.8401	+	13.8401i	0.736633	+	0.736633i	0.971925	−	0.235292i	$-0.0756046\pi$
$353$	13.8401	+	13.8401i	0.736633	+	0.736633i	−0.235292	+	0.971925i	$0.575605\pi$
$354$		0			0
$355$	27.7411	−	18.5186i	1.47235	−	0.982863i
$356$			9.24212i			0.489832i
$357$		0			0
$358$	−3.21715	+	3.21715i	−0.170031	+	0.170031i
$359$	8.49534			0.448367			0.224183	−	0.974547i	$-0.428029\pi$
$359$	8.49534			0.448367			0.224183	+	0.974547i	$0.428029\pi$
$360$		0			0
$361$	4.29372			0.225985
$362$	−10.8908	+	10.8908i	−0.572407	+	0.572407i
$363$		0			0
$364$			7.83488i			0.410659i
$365$	−4.16425	−	0.830205i	−0.217967	−	0.0434549i
$366$		0			0
$367$	22.1630	+	22.1630i	1.15690	+	1.15690i	0.985138	+	0.171762i	$0.0549461\pi$
$367$	22.1630	+	22.1630i	1.15690	+	1.15690i	0.171762	+	0.985138i	$0.445054\pi$
$368$	−0.795934	−	0.795934i	−0.0414909	−	0.0414909i
$369$		0			0
$370$	−3.60877	−	5.40599i	−0.187611	−	0.281044i
$371$		−	14.7213i		−	0.764293i
$372$		0			0
$373$	6.86001	−	6.86001i	0.355198	−	0.355198i	−0.506842	−	0.862039i	$-0.669187\pi$
$373$	6.86001	−	6.86001i	0.355198	−	0.355198i	0.862039	+	0.506842i	$0.169187\pi$
$374$	−1.23656			−0.0639410
$375$		0			0
$376$	−12.6065			−0.650132
$377$	0.238548	−	0.238548i	0.0122858	−	0.0122858i
$378$		0			0
$379$			0.936774i			0.0481188i	0.999711	+	0.0240594i	$0.00765909\pi$
$379$			0.936774i			0.0481188i	−0.999711	+	0.0240594i	$0.992341\pi$
$380$	−4.76094	−	7.13196i	−0.244231	−	0.365862i
$381$		0			0
$382$	−0.488555	−	0.488555i	−0.0249966	−	0.0249966i
$383$	3.60759	+	3.60759i	0.184339	+	0.184339i	0.793244	−	0.608904i	$-0.208391\pi$
$383$	3.60759	+	3.60759i	0.184339	+	0.184339i	−0.608904	+	0.793244i	$0.708391\pi$
$384$		0			0
$385$	−4.93677	−	0.984220i	−0.251601	−	0.0501605i
$386$		−	9.81511i		−	0.499576i
$387$		0			0
$388$	−6.16868	+	6.16868i	−0.313167	+	0.313167i
$389$	−4.21530			−0.213724			−0.106862	−	0.994274i	$-0.534080\pi$
$389$	−4.21530			−0.213724			−0.106862	+	0.994274i	$0.534080\pi$
$390$		0			0
$391$	1.12562			0.0569251
$392$	−2.60607	+	2.60607i	−0.131626	+	0.131626i
$393$		0			0
$394$			11.7864i			0.593791i
$395$	−6.15335	+	4.10766i	−0.309608	+	0.206679i
$396$		0			0
$397$	−12.1405	−	12.1405i	−0.609316	−	0.609316i	0.333452	−	0.942767i	$-0.391787\pi$
$397$	−12.1405	−	12.1405i	−0.609316	−	0.609316i	−0.942767	+	0.333452i	$0.891787\pi$
$398$	11.5307	+	11.5307i	0.577980	+	0.577980i
$399$		0			0
$400$	1.91744	−	4.61773i	0.0958719	−	0.230887i
$401$		−	12.3117i		−	0.614818i	−0.951577	−	0.307409i	$-0.900538\pi$
$401$		−	12.3117i		−	0.614818i	0.951577	−	0.307409i	$-0.0994620\pi$
$402$		0			0
$403$	10.7577	−	10.7577i	0.535880	−	0.535880i
$404$	−3.40259			−0.169285
$405$		0			0
$406$	−0.142716			−0.00708286
$407$	−2.54166	+	2.54166i	−0.125986	+	0.125986i
$408$		0			0
$409$		−	35.2534i		−	1.74317i	−0.490246	−	0.871584i	$-0.663093\pi$
$409$		−	35.2534i		−	1.74317i	0.490246	−	0.871584i	$-0.336907\pi$
$410$	0.591658	−	2.96771i	0.0292199	−	0.146565i
$411$		0			0
$412$	8.10984	+	8.10984i	0.399543	+	0.399543i
$413$	−15.0447	−	15.0447i	−0.740303	−	0.740303i
$414$		0			0
$415$	−6.19596	+	31.0785i	−0.304148	+	1.52558i
$416$			4.30353i			0.210998i
$417$		0			0
$418$	−3.35314	+	3.35314i	−0.164007	+	0.164007i
$419$	−3.41581			−0.166873			−0.0834366	−	0.996513i	$-0.526590\pi$
$419$	−3.41581			−0.166873			−0.0834366	+	0.996513i	$0.526590\pi$
$420$		0			0
$421$	25.1951			1.22794			0.613968	−	0.789331i	$-0.289573\pi$
$421$	25.1951			1.22794			0.613968	+	0.789331i	$0.289573\pi$
$422$	−3.99644	+	3.99644i	−0.194544	+	0.194544i
$423$		0			0
$424$		−	8.08612i		−	0.392697i
$425$	1.90939	+	4.62106i	0.0926192	+	0.224154i
$426$		0			0
$427$	14.9605	+	14.9605i	0.723989	+	0.723989i
$428$	2.16603	+	2.16603i	0.104699	+	0.104699i
$429$		0			0
$430$	8.33395	−	5.56332i	0.401899	−	0.268287i
$431$		−	37.2533i		−	1.79443i	−0.441594	−	0.897215i	$-0.645587\pi$
$431$		−	37.2533i		−	1.79443i	0.441594	−	0.897215i	$-0.354413\pi$
$432$		0			0
$433$	−17.4333	+	17.4333i	−0.837790	+	0.837790i	−0.988568	−	0.150778i	$-0.951822\pi$
$433$	−17.4333	+	17.4333i	−0.837790	+	0.837790i	0.150778	+	0.988568i	$0.451822\pi$
$434$	−6.43601			−0.308939
$435$		0			0
$436$	14.6302			0.700662
$437$	3.05231	−	3.05231i	0.146012	−	0.146012i
$438$		0			0
$439$			30.7255i			1.46645i	0.679987	+	0.733225i	$0.261986\pi$
$439$			30.7255i			1.46645i	−0.679987	+	0.733225i	$0.738014\pi$
$440$	−2.71167	−	0.540611i	−0.129274	−	0.0257726i
$441$		0			0
$442$	−3.04306	−	3.04306i	−0.144744	−	0.144744i
$443$	−23.0887	−	23.0887i	−1.09698	−	1.09698i	−0.994763	−	0.102213i	$-0.967408\pi$
$443$	−23.0887	−	23.0887i	−1.09698	−	1.09698i	−0.102213	−	0.994763i	$-0.532592\pi$
$444$		0			0
$445$	−11.4739	−	17.1882i	−0.543917	−	0.814797i
$446$		−	14.7899i		−	0.700321i
$447$		0			0
$448$	1.28734	−	1.28734i	0.0608209	−	0.0608209i
$449$	−37.6659			−1.77756			−0.888782	−	0.458331i	$-0.848447\pi$
$449$	−37.6659			−1.77756			−0.888782	+	0.458331i	$0.848447\pi$
$450$		0			0
$451$	−1.67346			−0.0788002
$452$	14.3934	−	14.3934i	0.677007	−	0.677007i
$453$		0			0
$454$			9.58364i			0.449782i
$455$	−9.72687	−	14.5710i	−0.456003	−	0.683100i
$456$		0			0
$457$	−7.65499	−	7.65499i	−0.358085	−	0.358085i	0.505021	−	0.863107i	$-0.331485\pi$
$457$	−7.65499	−	7.65499i	−0.358085	−	0.358085i	−0.863107	+	0.505021i	$0.831485\pi$
$458$	7.61671	+	7.61671i	0.355905	+	0.355905i
$459$		0			0
$460$	2.46839	+	0.492110i	0.115089	+	0.0229447i
$461$			30.0298i			1.39863i	0.714816	+	0.699313i	$0.246510\pi$
$461$			30.0298i			1.39863i	−0.714816	+	0.699313i	$0.753490\pi$
$462$		0			0
$463$	−20.4472	+	20.4472i	−0.950262	+	0.950262i	−0.998820	−	0.0485585i	$-0.984537\pi$
$463$	−20.4472	+	20.4472i	−0.950262	+	0.950262i	0.0485585	+	0.998820i	$0.484537\pi$
$464$	−0.0783908			−0.00363920
$465$		0			0
$466$	10.0000			0.463241
$467$	9.81008	−	9.81008i	0.453956	−	0.453956i	−0.442709	−	0.896665i	$-0.645983\pi$
$467$	9.81008	−	9.81008i	0.453956	−	0.453956i	0.896665	+	0.442709i	$0.145983\pi$
$468$		0			0
$469$			6.80350i			0.314157i
$470$	23.4452	−	15.6508i	1.08144	−	0.721917i
$471$		0			0
$472$	−8.26376	−	8.26376i	−0.380370	−	0.380370i
$473$	−3.91826	−	3.91826i	−0.180162	−	0.180162i
$474$		0			0
$475$	17.7084	+	7.35314i	0.812518	+	0.337385i
$476$			1.82057i			0.0834456i
$477$		0			0
$478$	−16.0319	+	16.0319i	−0.733280	+	0.733280i
$479$	16.1645			0.738576			0.369288	−	0.929315i	$-0.379602\pi$
$479$	16.1645			0.738576			0.369288	+	0.929315i	$0.379602\pi$
$480$		0			0
$481$	−12.5096			−0.570388
$482$	−7.42638	+	7.42638i	−0.338262	+	0.338262i
$483$		0			0
$484$		−	9.47092i		−	0.430496i
$485$	3.81397	−	19.1306i	0.173183	−	0.868676i
$486$		0			0
$487$	−20.2797	−	20.2797i	−0.918960	−	0.918960i	0.0779935	−	0.996954i	$-0.475149\pi$
$487$	−20.2797	−	20.2797i	−0.918960	−	0.918960i	−0.996954	+	0.0779935i	$0.975149\pi$
$488$	8.21749	+	8.21749i	0.371988	+	0.371988i
$489$		0			0
$490$	1.61128	−	8.08205i	0.0727901	−	0.365110i
$491$		−	6.46336i		−	0.291687i	−0.989308	−	0.145844i	$-0.953410\pi$
$491$		−	6.46336i		−	0.291687i	0.989308	−	0.145844i	$-0.0465896\pi$
$492$		0			0
$493$	0.0554307	−	0.0554307i	0.00249647	−	0.00249647i
$494$	−16.5035			−0.742529
$495$		0			0
$496$	−3.53517			−0.158734
$497$	−19.2025	+	19.2025i	−0.861350	+	0.861350i
$498$		0			0
$499$		−	42.9618i		−	1.92323i	−0.274394	−	0.961617i	$-0.588477\pi$
$499$		−	42.9618i		−	1.92323i	0.274394	−	0.961617i	$-0.411523\pi$
$500$	2.16685	+	10.9684i	0.0969047	+	0.490520i
$501$		0			0
$502$	−2.31904	−	2.31904i	−0.103504	−	0.103504i
$503$	21.8080	+	21.8080i	0.972370	+	0.972370i	0.999628	−	0.0272583i	$-0.00867765\pi$
$503$	21.8080	+	21.8080i	0.972370	+	0.972370i	−0.0272583	+	0.999628i	$0.508678\pi$
$504$		0			0
$505$	6.32801	−	4.22426i	0.281593	−	0.187977i
$506$		−	1.39190i		−	0.0618774i
$507$		0			0
$508$	−5.95153	+	5.95153i	−0.264057	+	0.264057i
$509$	−23.3684			−1.03579			−0.517893	−	0.855445i	$-0.673284\pi$
$509$	−23.3684			−1.03579			−0.517893	+	0.855445i	$0.673284\pi$
$510$		0			0
$511$	3.45718			0.152937
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			1.95966i			0.0864371i
$515$	−25.1506	−	5.01415i	−1.10827	−	0.220950i
$516$		0			0
$517$	−11.0229	−	11.0229i	−0.484786	−	0.484786i
$518$	3.74205	+	3.74205i	0.164416	+	0.164416i
$519$		0			0
$520$	−5.34277	−	8.00355i	−0.234296	−	0.350979i
$521$		−	9.12799i		−	0.399904i	−0.979806	−	0.199952i	$-0.935921\pi$
$521$		−	9.12799i		−	0.399904i	0.979806	−	0.199952i	$-0.0640787\pi$
$522$		0			0
$523$	19.8850	−	19.8850i	0.869512	−	0.869512i	−0.122906	−	0.992418i	$-0.539221\pi$
$523$	19.8850	−	19.8850i	0.869512	−	0.869512i	0.992418	+	0.122906i	$0.0392214\pi$
$524$	−3.45080			−0.150749
$525$		0			0
$526$	0.724204			0.0315768
$527$	2.49974	−	2.49974i	0.108890	−	0.108890i
$528$		0			0
$529$		−	21.7330i		−	0.944912i
$530$	10.0388	+	15.0383i	0.436057	+	0.653220i
$531$		0			0
$532$	4.93677	+	4.93677i	0.214036	+	0.214036i
$533$	−4.11823	−	4.11823i	−0.178380	−	0.178380i
$534$		0			0
$535$	−6.71739	−	1.33921i	−0.290418	−	0.0578992i
$536$			3.73702i			0.161415i
$537$		0			0
$538$	4.44023	−	4.44023i	0.191432	−	0.191432i
$539$	−4.55738			−0.196300
$540$		0			0
$541$	1.40327			0.0603313			0.0301657	−	0.999545i	$-0.490397\pi$
$541$	1.40327			0.0603313			0.0301657	+	0.999545i	$0.490397\pi$
$542$	1.11980	−	1.11980i	0.0480995	−	0.0480995i
$543$		0			0
$544$			1.00000i			0.0428746i
$545$	−27.2088	+	18.1632i	−1.16550	+	0.778026i
$546$		0			0
$547$	23.9824	+	23.9824i	1.02541	+	1.02541i	0.999669	+	0.0257433i	$0.00819526\pi$
$547$	23.9824	+	23.9824i	1.02541	+	1.02541i	0.0257433	+	0.999669i	$0.491805\pi$
$548$	10.9299	+	10.9299i	0.466901	+	0.466901i
$549$		0			0
$550$	5.71422	−	2.36108i	0.243655	−	0.100677i
$551$		−	0.300619i		−	0.0128068i
$552$		0			0
$553$	4.25937	−	4.25937i	0.181127	−	0.181127i
$554$	29.7311			1.26315
$555$		0			0
$556$	−10.8578			−0.460472
$557$	2.73254	−	2.73254i	0.115781	−	0.115781i	−0.646842	−	0.762624i	$-0.723911\pi$
$557$	2.73254	−	2.73254i	0.115781	−	0.115781i	0.762624	+	0.646842i	$0.223911\pi$
$558$		0			0
$559$		−	19.2849i		−	0.815666i
$560$	−0.795934	+	3.99235i	−0.0336343	+	0.168707i
$561$		0			0
$562$	15.7706	+	15.7706i	0.665244	+	0.665244i
$563$	30.0988	+	30.0988i	1.26851	+	1.26851i	0.946855	+	0.321660i	$0.104241\pi$
$563$	30.0988	+	30.0988i	1.26851	+	1.26851i	0.321660	+	0.946855i	$0.395759\pi$
$564$		0			0
$565$	−8.89912	+	44.6374i	−0.374389	+	1.87791i
$566$			10.5010i			0.441390i
$567$		0			0
$568$	−10.5475	+	10.5475i	−0.442565	+	0.442565i
$569$	33.5635			1.40706			0.703528	−	0.710668i	$-0.251607\pi$
$569$	33.5635			1.40706			0.703528	+	0.710668i	$0.251607\pi$
$570$		0			0
$571$	−7.66264			−0.320672			−0.160336	−	0.987063i	$-0.551258\pi$
$571$	−7.66264			−0.320672			−0.160336	+	0.987063i	$0.551258\pi$
$572$	−3.76292	+	3.76292i	−0.157336	+	0.157336i
$573$		0			0
$574$			2.46381i			0.102837i
$575$	−5.20156	+	2.14925i	−0.216920	+	0.0896301i
$576$		0			0
$577$	−15.6926	−	15.6926i	−0.653293	−	0.653293i	0.300491	−	0.953785i	$-0.402849\pi$
$577$	−15.6926	−	15.6926i	−0.653293	−	0.653293i	−0.953785	+	0.300491i	$0.902849\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$		0			0
$580$	0.145788	−	0.0973209i	0.00605353	−	0.00404103i
$581$		−	25.8015i		−	1.07043i
$582$		0			0
$583$	7.07034	−	7.07034i	0.292823	−	0.292823i
$584$	1.89896			0.0785795
$585$		0			0
$586$	28.5679			1.18013
$587$	−2.88932	+	2.88932i	−0.119255	+	0.119255i	−0.764216	−	0.644961i	$-0.776874\pi$
$587$	−2.88932	+	2.88932i	−0.119255	+	0.119255i	0.644961	+	0.764216i	$0.276874\pi$
$588$		0			0
$589$		−	13.5569i		−	0.558604i
$590$	25.6280	+	5.10932i	1.05509	+	0.210347i
$591$		0			0
$592$	2.05543	+	2.05543i	0.0844777	+	0.0844777i
$593$	−11.2629	−	11.2629i	−0.462511	−	0.462511i	0.436967	−	0.899478i	$-0.356053\pi$
$593$	−11.2629	−	11.2629i	−0.462511	−	0.462511i	−0.899478	+	0.436967i	$0.856053\pi$
$594$		0			0
$595$	−2.26020	−	3.38582i	−0.0926594	−	0.138805i
$596$		−	1.20804i		−	0.0494832i
$597$		0			0
$598$	3.42533	−	3.42533i	0.140072	−	0.140072i
$599$	30.8892			1.26210			0.631050	−	0.775742i	$-0.282624\pi$
$599$	30.8892			1.26210			0.631050	+	0.775742i	$0.282624\pi$
$600$		0			0
$601$	22.3041			0.909804			0.454902	−	0.890541i	$-0.349674\pi$
$601$	22.3041			0.909804			0.454902	+	0.890541i	$0.349674\pi$
$602$	−5.76879	+	5.76879i	−0.235119	+	0.235119i
$603$		0			0
$604$			0.212570i			0.00864934i
$605$	11.7580	+	17.6137i	0.478030	+	0.716097i
$606$		0			0
$607$	19.3429	+	19.3429i	0.785105	+	0.785105i	0.980687	−	0.195583i	$-0.0626598\pi$
$607$	19.3429	+	19.3429i	0.785105	+	0.785105i	−0.195583	+	0.980687i	$0.562660\pi$
$608$	2.71167	+	2.71167i	0.109973	+	0.109973i
$609$		0			0
$610$	−25.4845	−	5.08071i	−1.03184	−	0.205712i
$611$		−	54.2526i		−	2.19483i
$612$		0			0
$613$	27.4302	−	27.4302i	1.10790	−	1.10790i	0.114468	−	0.993427i	$-0.463484\pi$
$613$	27.4302	−	27.4302i	1.10790	−	1.10790i	0.993427	−	0.114468i	$-0.0365165\pi$
$614$	14.1795			0.572239
$615$		0			0
$616$	2.25124			0.0907051
$617$	−14.8908	+	14.8908i	−0.599480	+	0.599480i	−0.940174	−	0.340694i	$-0.889338\pi$
$617$	−14.8908	+	14.8908i	−0.599480	+	0.599480i	0.340694	+	0.940174i	$0.389338\pi$
$618$		0			0
$619$		−	0.0474460i		−	0.00190701i	−1.00000		0.000953507i	$-0.999696\pi$
$619$		−	0.0474460i		−	0.00190701i	1.00000		0.000953507i	$-0.000303511\pi$
$620$	6.57458	−	4.38885i	0.264041	−	0.176261i
$621$		0			0
$622$	3.03610	+	3.03610i	0.121736	+	0.121736i
$623$	11.8977	+	11.8977i	0.476672	+	0.476672i
$624$		0			0
$625$	−17.6469	−	17.7084i	−0.705874	−	0.708337i
$626$			20.8953i			0.835144i
$627$		0			0
$628$	0.382270	−	0.382270i	0.0152542	−	0.0152542i
$629$	−2.90682			−0.115902
$630$		0			0
$631$	−15.4480			−0.614976			−0.307488	−	0.951552i	$-0.599488\pi$
$631$	−15.4480			−0.614976			−0.307488	+	0.951552i	$0.599488\pi$
$632$	2.33958	−	2.33958i	0.0930637	−	0.0930637i
$633$		0			0
$634$			8.77744i			0.348597i
$635$	3.67971	−	18.4572i	0.146025	−	0.732450i
$636$		0			0
$637$	−11.2153	−	11.2153i	−0.444366	−	0.444366i
$638$	−0.0685433	−	0.0685433i	−0.00271366	−	0.00271366i
$639$		0			0
$640$	−0.437190	+	2.19291i	−0.0172814	+	0.0866825i
$641$			27.6669i			1.09278i	0.837532	+	0.546389i	$0.183998\pi$
$641$			27.6669i			1.09278i	−0.837532	+	0.546389i	$0.816002\pi$
$642$		0			0
$643$	−9.61315	+	9.61315i	−0.379106	+	0.379106i	−0.870780	−	0.491674i	$-0.836385\pi$
$643$	−9.61315	+	9.61315i	−0.379106	+	0.379106i	0.491674	+	0.870780i	$0.336385\pi$
$644$	−2.04927			−0.0807525
$645$		0			0
$646$	−3.83488			−0.150881
$647$	−22.5492	+	22.5492i	−0.886502	+	0.886502i	−0.994185	−	0.107683i	$-0.965657\pi$
$647$	−22.5492	+	22.5492i	−0.886502	+	0.886502i	0.107683	+	0.994185i	$0.465657\pi$
$648$		0			0
$649$		−	14.4513i		−	0.567264i
$650$	19.8726	+	8.25176i	0.779466	+	0.323661i
$651$		0			0
$652$	5.02289	+	5.02289i	0.196712	+	0.196712i
$653$	19.5698	+	19.5698i	0.765824	+	0.765824i	0.977368	−	0.211544i	$-0.0678492\pi$
$653$	19.5698	+	19.5698i	0.765824	+	0.765824i	−0.211544	+	0.977368i	$0.567849\pi$
$654$		0			0
$655$	6.41768	−	4.28412i	0.250759	−	0.167394i
$656$			1.35332i			0.0528383i
$657$		0			0
$658$	−16.2288	+	16.2288i	−0.632666	+	0.632666i
$659$	−45.8714			−1.78690			−0.893448	−	0.449166i	$-0.851721\pi$
$659$	−45.8714			−1.78690			−0.893448	+	0.449166i	$0.851721\pi$
$660$		0			0
$661$	−24.5607			−0.955302			−0.477651	−	0.878550i	$-0.658512\pi$
$661$	−24.5607			−0.955302			−0.477651	+	0.878550i	$0.658512\pi$
$662$	8.73651	−	8.73651i	0.339554	−	0.339554i
$663$		0			0
$664$		−	14.1722i		−	0.549989i
$665$	−15.3102	−	3.05231i	−0.593702	−	0.118363i
$666$		0			0
$667$	0.0623939	+	0.0623939i	0.00241590	+	0.00241590i
$668$	−0.211926	−	0.211926i	−0.00819965	−	0.00819965i
$669$		0			0
$670$	−4.63945	−	6.94998i	−0.179238	−	0.268501i
$671$			14.3704i			0.554764i
$672$		0			0
$673$	3.47604	−	3.47604i	0.133991	−	0.133991i	−0.636930	−	0.770922i	$-0.719796\pi$
$673$	3.47604	−	3.47604i	0.133991	−	0.133991i	0.770922	+	0.636930i	$0.219796\pi$
$674$	11.3537			0.437329
$675$		0			0
$676$	−5.52041			−0.212323
$677$	6.69754	−	6.69754i	0.257407	−	0.257407i	−0.566591	−	0.823999i	$-0.691738\pi$
$677$	6.69754	−	6.69754i	0.257407	−	0.257407i	0.823999	+	0.566591i	$0.191738\pi$
$678$		0			0
$679$			15.8823i			0.609508i
$680$	−1.24148	−	1.85976i	−0.0476087	−	0.0713187i
$681$		0			0
$682$	−3.09108	−	3.09108i	−0.118364	−	0.118364i
$683$	−6.59279	−	6.59279i	−0.252266	−	0.252266i	0.569633	−	0.821899i	$-0.307085\pi$
$683$	−6.59279	−	6.59279i	−0.252266	−	0.252266i	−0.821899	+	0.569633i	$0.807085\pi$
$684$		0			0
$685$	−33.8962	−	6.75772i	−1.29511	−	0.258199i
$686$			19.4537i			0.742747i
$687$		0			0
$688$	−3.16868	+	3.16868i	−0.120805	+	0.120805i
$689$	34.7989			1.32573
$690$		0			0
$691$	9.52704			0.362426			0.181213	−	0.983444i	$-0.441998\pi$
$691$	9.52704			0.362426			0.181213	+	0.983444i	$0.441998\pi$
$692$	6.35352	−	6.35352i	0.241525	−	0.241525i
$693$		0			0
$694$		−	0.384803i		−	0.0146069i
$695$	20.1929	−	13.4797i	0.765959	−	0.511316i
$696$		0			0
$697$	−0.956942	−	0.956942i	−0.0362467	−	0.0362467i
$698$	−22.4548	−	22.4548i	−0.849926	−	0.849926i
$699$		0			0
$700$	−3.47618	−	8.41296i	−0.131387	−	0.317980i
$701$		−	7.55581i		−	0.285379i	−0.989767	−	0.142690i	$-0.954425\pi$
$701$		−	7.55581i		−	0.285379i	0.989767	−	0.142690i	$-0.0455751\pi$
$702$		0			0
$703$	−7.88232	+	7.88232i	−0.297287	+	0.297287i
$704$	1.23656			0.0466046
$705$		0			0
$706$	19.5728			0.736633
$707$	−4.38027	+	4.38027i	−0.164737	+	0.164737i
$708$		0			0
$709$		−	6.12981i		−	0.230210i	−0.993353	−	0.115105i	$-0.963280\pi$
$709$		−	6.12981i		−	0.230210i	0.993353	−	0.115105i	$-0.0367204\pi$
$710$	6.52133	−	32.7105i	0.244741	−	1.22760i
$711$		0			0
$712$	6.53517	+	6.53517i	0.244916	+	0.244916i
$713$	2.81376	+	2.81376i	0.105376	+	0.105376i
$714$		0			0
$715$	2.32654	−	11.6698i	0.0870076	−	0.436424i
$716$			4.54973i			0.170031i
$717$		0			0
$718$	6.00711	−	6.00711i	0.224183	−	0.224183i
$719$	−41.7325			−1.55636			−0.778180	−	0.628041i	$-0.783857\pi$
$719$	−41.7325			−1.55636			−0.778180	+	0.628041i	$0.783857\pi$
$720$		0			0
$721$	20.8802			0.777618
$722$	3.03612	−	3.03612i	0.112993	−	0.112993i
$723$		0			0
$724$			15.4019i			0.572407i
$725$	−0.150309	+	0.361988i	−0.00558235	+	0.0134439i
$726$		0			0
$727$	−11.8043	−	11.8043i	−0.437799	−	0.437799i	0.453472	−	0.891271i	$-0.350185\pi$
$727$	−11.8043	−	11.8043i	−0.437799	−	0.437799i	−0.891271	+	0.453472i	$0.850185\pi$
$728$	5.54009	+	5.54009i	0.205330	+	0.205330i
$729$		0			0
$730$	−3.53161	+	2.35753i	−0.130711	+	0.0872559i
$731$		−	4.48119i		−	0.165743i
$732$		0			0
$733$	−19.7357	+	19.7357i	−0.728955	+	0.728955i	−0.970412	−	0.241457i	$-0.922375\pi$
$733$	−19.7357	+	19.7357i	−0.728955	+	0.728955i	0.241457	+	0.970412i	$0.422375\pi$
$734$	31.3433			1.15690
$735$		0			0
$736$	−1.12562			−0.0414909
$737$	−3.26758	+	3.26758i	−0.120363	+	0.120363i
$738$		0			0
$739$		−	21.9668i		−	0.808061i	−0.914746	−	0.404030i	$-0.867609\pi$
$739$		−	21.9668i		−	0.808061i	0.914746	−	0.404030i	$-0.132391\pi$
$740$	−6.37440	−	1.27083i	−0.234328	−	0.0467167i
$741$		0			0
$742$	−10.4095	−	10.4095i	−0.382147	−	0.382147i
$743$	17.8149	+	17.8149i	0.653566	+	0.653566i	0.953850	−	0.300284i	$-0.0970814\pi$
$743$	17.8149	+	17.8149i	0.653566	+	0.653566i	−0.300284	+	0.953850i	$0.597081\pi$
$744$		0			0
$745$	1.49976	+	2.24666i	0.0549469	+	0.0823114i
$746$		−	9.70151i		−	0.355198i
$747$		0			0
$748$	−0.874380	+	0.874380i	−0.0319705	+	0.0319705i
$749$	5.57681			0.203772
$750$		0			0
$751$	−48.5970			−1.77333			−0.886665	−	0.462412i	$-0.846984\pi$
$751$	−48.5970			−1.77333			−0.886665	+	0.462412i	$0.846984\pi$
$752$	−8.91416	+	8.91416i	−0.325066	+	0.325066i
$753$		0			0
$754$		−	0.337357i		−	0.0122858i
$755$	−0.263902	−	0.395329i	−0.00960437	−	0.0143875i
$756$		0			0
$757$	−24.2809	−	24.2809i	−0.882503	−	0.882503i	0.111286	−	0.993788i	$-0.464503\pi$
$757$	−24.2809	−	24.2809i	−0.882503	−	0.882503i	−0.993788	+	0.111286i	$0.964503\pi$
$758$	0.662399	+	0.662399i	0.0240594	+	0.0240594i
$759$		0			0
$760$	−8.40955	−	1.67657i	−0.305046	−	0.0608155i
$761$			24.6558i			0.893773i	0.894591	+	0.446886i	$0.147467\pi$
$761$			24.6558i			0.893773i	−0.894591	+	0.446886i	$0.852533\pi$
$762$		0			0
$763$	18.8340	−	18.8340i	0.681838	−	0.681838i
$764$	−0.690921			−0.0249966
$765$		0			0
$766$	5.10190			0.184339
$767$	35.5634	−	35.5634i	1.28412	−	1.28412i
$768$		0			0
$769$		−	34.4530i		−	1.24241i	−0.783649	−	0.621203i	$-0.786644\pi$
$769$		−	34.4530i		−	1.24241i	0.783649	−	0.621203i	$-0.213356\pi$
$770$	−4.18677	+	2.79488i	−0.150881	+	0.100720i
$771$		0			0
$772$	−6.94033	−	6.94033i	−0.249788	−	0.249788i
$773$	−3.06815	−	3.06815i	−0.110354	−	0.110354i	0.649774	−	0.760128i	$-0.274864\pi$
$773$	−3.06815	−	3.06815i	−0.110354	−	0.110354i	−0.760128	+	0.649774i	$0.774864\pi$
$774$		0			0
$775$	−6.77847	+	16.3245i	−0.243490	+	0.586392i
$776$			8.72383i			0.313167i
$777$		0			0
$778$	−2.98066	+	2.98066i	−0.106862	+	0.106862i
$779$	−5.18981			−0.185944
$780$		0			0
$781$	−18.4451			−0.660018
$782$	0.795934	−	0.795934i	0.0284625	−	0.0284625i
$783$		0			0
$784$			3.68553i			0.131626i
$785$	−0.236350	+	1.18551i	−0.00843569	+	0.0423128i
$786$		0			0
$787$	−22.9757	−	22.9757i	−0.818997	−	0.818997i	0.166966	−	0.985963i	$-0.446603\pi$
$787$	−22.9757	−	22.9757i	−0.818997	−	0.818997i	−0.985963	+	0.166966i	$0.946603\pi$
$788$	8.33425	+	8.33425i	0.296895	+	0.296895i
$789$		0			0
$790$	−1.44652	+	7.25563i	−0.0514648	+	0.258144i
$791$		−	37.0582i		−	1.31764i
$792$		0			0
$793$	−35.3642	+	35.3642i	−1.25582	+	1.25582i
$794$	−17.1693			−0.609316
$795$		0			0
$796$	16.3068			0.577980
$797$	−27.1822	+	27.1822i	−0.962842	+	0.962842i	−0.999334	−	0.0364919i	$-0.988382\pi$
$797$	−27.1822	+	27.1822i	−0.962842	+	0.962842i	0.0364919	+	0.999334i	$0.488382\pi$
$798$		0			0
$799$		−	12.6065i		−	0.445987i
$800$	−1.90939	−	4.62106i	−0.0675073	−	0.163379i
$801$		0			0
$802$	−8.70570	−	8.70570i	−0.307409	−	0.307409i
$803$	1.66041	+	1.66041i	0.0585946	+	0.0585946i
$804$		0			0
$805$	3.81115	−	2.54413i	0.134326	−	0.0896689i
$806$		−	15.2137i		−	0.535880i
$807$		0			0
$808$	−2.40599	+	2.40599i	−0.0846425	+	0.0846425i
$809$	52.9693			1.86230			0.931150	−	0.364635i	$-0.118806\pi$
$809$	52.9693			1.86230			0.931150	+	0.364635i	$0.118806\pi$
$810$		0			0
$811$	33.1727			1.16485			0.582426	−	0.812884i	$-0.302104\pi$
$811$	33.1727			1.16485			0.582426	+	0.812884i	$0.302104\pi$
$812$	−0.100915	+	0.100915i	−0.00354143	+	0.00354143i
$813$		0			0
$814$			3.59445i			0.125986i
$815$	−15.5772	−	3.10555i	−0.545646	−	0.108783i
$816$		0			0
$817$	−12.1515	−	12.1515i	−0.425127	−	0.425127i
$818$	−24.9279	−	24.9279i	−0.871584	−	0.871584i
$819$		0			0
$820$	−1.68012	−	2.51685i	−0.0586725	−	0.0878924i
$821$			19.1400i			0.667989i	0.942575	+	0.333995i	$0.108397\pi$
$821$			19.1400i			0.667989i	−0.942575	+	0.333995i	$0.891603\pi$
$822$		0			0
$823$	36.0888	−	36.0888i	1.25798	−	1.25798i	0.305919	−	0.952058i	$-0.401036\pi$
$823$	36.0888	−	36.0888i	1.25798	−	1.25798i	0.952058	−	0.305919i	$-0.0989636\pi$
$824$	11.4690			0.399543
$825$		0			0
$826$	−21.2765			−0.740303
$827$	2.80493	−	2.80493i	0.0975371	−	0.0975371i	−0.656654	−	0.754192i	$-0.728029\pi$
$827$	2.80493	−	2.80493i	0.0975371	−	0.0975371i	0.754192	+	0.656654i	$0.228029\pi$
$828$		0			0
$829$		−	37.9739i		−	1.31889i	−0.751754	−	0.659444i	$-0.770792\pi$
$829$		−	37.9739i		−	1.31889i	0.751754	−	0.659444i	$-0.229208\pi$
$830$	17.5946	+	26.3570i	0.610717	+	0.914865i
$831$		0			0
$832$	3.04306	+	3.04306i	0.105499	+	0.105499i
$833$	−2.60607	−	2.60607i	−0.0902948	−	0.0902948i
$834$		0			0
$835$	0.657234	+	0.131029i	0.0227445	+	0.00453446i
$836$			4.74205i			0.164007i
$837$		0			0
$838$	−2.41534	+	2.41534i	−0.0834366	+	0.0834366i
$839$	−28.7565			−0.992786			−0.496393	−	0.868098i	$-0.665343\pi$
$839$	−28.7565			−0.992786			−0.496393	+	0.868098i	$0.665343\pi$
$840$		0			0
$841$	−28.9939			−0.999788
$842$	17.8156	−	17.8156i	0.613968	−	0.613968i
$843$		0			0
$844$			5.65182i			0.194544i
$845$	10.2667	−	6.85350i	0.353184	−	0.235767i
$846$		0			0
$847$	−12.1923	−	12.1923i	−0.418931	−	0.418931i
$848$	−5.71775	−	5.71775i	−0.196348	−	0.196348i
$849$		0			0
$850$	4.61773	+	1.91744i	0.158387	+	0.0657676i
$851$		−	3.27197i		−	0.112162i
$852$		0			0
$853$	27.7618	−	27.7618i	0.950546	−	0.950546i	−0.0482872	−	0.998833i	$-0.515376\pi$
$853$	27.7618	−	27.7618i	0.950546	−	0.950546i	0.998833	+	0.0482872i	$0.0153763\pi$
$854$	21.1573			0.723989
$855$		0			0
$856$	3.06323			0.104699
$857$	−4.17410	+	4.17410i	−0.142584	+	0.142584i	−0.774796	−	0.632211i	$-0.782147\pi$
$857$	−4.17410	+	4.17410i	−0.142584	+	0.142584i	0.632211	+	0.774796i	$0.282147\pi$
$858$		0			0
$859$		−	27.2059i		−	0.928255i	−0.885768	−	0.464127i	$-0.846368\pi$
$859$		−	27.2059i		−	0.928255i	0.885768	−	0.464127i	$-0.153632\pi$
$860$	1.95913	−	9.82685i	0.0668058	−	0.335093i
$861$		0			0
$862$	−26.3421	−	26.3421i	−0.897215	−	0.897215i
$863$	−18.2121	−	18.2121i	−0.619949	−	0.619949i	0.325569	−	0.945518i	$-0.394444\pi$
$863$	−18.2121	−	18.2121i	−0.619949	−	0.619949i	−0.945518	+	0.325569i	$0.894444\pi$
$864$		0			0
$865$	−3.92826	+	19.7038i	−0.133565	+	0.669951i
$866$			24.6544i			0.837790i
$867$		0			0
$868$	−4.55095	+	4.55095i	−0.154469	+	0.154469i
$869$	4.09137			0.138790
$870$		0			0
$871$	−16.0824			−0.544932
$872$	10.3451	−	10.3451i	0.350331	−	0.350331i
$873$		0			0
$874$		−	4.31661i		−	0.146012i
$875$	16.9094	+	11.3305i	0.571643	+	0.383040i
$876$		0			0
$877$	9.93746	+	9.93746i	0.335564	+	0.335564i	0.854695	−	0.519131i	$-0.173744\pi$
$877$	9.93746	+	9.93746i	0.335564	+	0.335564i	−0.519131	+	0.854695i	$0.673744\pi$
$878$	21.7262	+	21.7262i	0.733225	+	0.733225i
$879$		0			0
$880$	−2.29971	+	1.53517i	−0.0775231	+	0.0517505i
$881$			12.2197i			0.411692i	0.978584	+	0.205846i	$0.0659945\pi$
$881$			12.2197i			0.411692i	−0.978584	+	0.205846i	$0.934005\pi$
$882$		0			0
$883$	28.3804	−	28.3804i	0.955077	−	0.955077i	−0.0439564	−	0.999033i	$-0.513996\pi$
$883$	28.3804	−	28.3804i	0.955077	−	0.955077i	0.999033	+	0.0439564i	$0.0139963\pi$
$884$	−4.30353			−0.144744
$885$		0			0
$886$	−32.6523			−1.09698
$887$	31.6319	−	31.6319i	1.06210	−	1.06210i	0.0641561	−	0.997940i	$-0.479564\pi$
$887$	31.6319	−	31.6319i	1.06210	−	1.06210i	0.997940	−	0.0641561i	$-0.0204356\pi$
$888$		0			0
$889$			15.3232i			0.513925i
$890$	−20.2672	−	4.04056i	−0.679357	−	0.135440i
$891$		0			0
$892$	−10.4580	−	10.4580i	−0.350160	−	0.350160i
$893$	−34.1847	−	34.1847i	−1.14395	−	1.14395i
$894$		0			0
$895$	−5.64842	−	8.46142i	−0.188806	−	0.282834i
$896$		−	1.82057i		−	0.0608209i
$897$		0			0
$898$	−26.6338	+	26.6338i	−0.888782	+	0.888782i
$899$	0.277125			0.00924262
$900$		0			0
$901$	8.08612			0.269388
$902$	−1.18332	+	1.18332i	−0.0394001	+	0.0394001i
$903$		0			0
$904$		−	20.3553i		−	0.677007i
$905$	−19.1212	−	28.6439i	−0.635610	−	0.952155i
$906$		0			0
$907$	−10.2939	−	10.2939i	−0.341804	−	0.341804i	0.515241	−	0.857045i	$-0.327702\pi$
$907$	−10.2939	−	10.2939i	−0.341804	−	0.341804i	−0.857045	+	0.515241i	$0.827702\pi$
$908$	6.77665	+	6.77665i	0.224891	+	0.224891i
$909$		0			0
$910$	−17.1812	−	3.42533i	−0.569551	−	0.113549i
$911$			43.8447i			1.45264i	0.687357	+	0.726319i	$0.258771\pi$
$911$			43.8447i			1.45264i	−0.687357	+	0.726319i	$0.741229\pi$
$912$		0			0
$913$	12.3919	−	12.3919i	0.410112	−	0.410112i
$914$	−10.8258			−0.358085
$915$		0			0
$916$	10.7716			0.355905
$917$	−4.44234	+	4.44234i	−0.146699	+	0.146699i
$918$		0			0
$919$		−	20.8757i		−	0.688626i	−0.938855	−	0.344313i	$-0.888112\pi$
$919$		−	20.8757i		−	0.688626i	0.938855	−	0.344313i	$-0.111888\pi$
$920$	2.09339	−	1.39744i	0.0690169	−	0.0460722i
$921$		0			0
$922$	21.2342	+	21.2342i	0.699313	+	0.699313i
$923$	−45.3917	−	45.3917i	−1.49409	−	1.49409i
$924$		0			0
$925$	13.4326	−	5.55026i	0.441661	−	0.182492i
$926$			28.9167i			0.950262i
$927$		0			0
$928$	−0.0554307	+	0.0554307i	−0.00181960	+	0.00181960i
$929$	46.0812			1.51187			0.755937	−	0.654644i	$-0.227181\pi$
$929$	46.0812			1.51187			0.755937	+	0.654644i	$0.227181\pi$
$930$		0			0
$931$	−14.1336			−0.463209
$932$	7.07107	−	7.07107i	0.231621	−	0.231621i
$933$		0			0
$934$		−	13.8735i		−	0.453956i
$935$	0.540611	−	2.71167i	0.0176799	−	0.0886810i
$936$		0			0
$937$	25.7008	+	25.7008i	0.839608	+	0.839608i	0.988807	−	0.149199i	$-0.0476696\pi$
$937$	25.7008	+	25.7008i	0.839608	+	0.839608i	−0.149199	+	0.988807i	$0.547670\pi$
$938$	4.81080	+	4.81080i	0.157078	+	0.157078i
$939$		0			0
$940$	5.51145	−	27.6450i	0.179764	−	0.901681i
$941$			8.13018i			0.265036i	0.991181	+	0.132518i	$0.0423063\pi$
$941$			8.13018i			0.265036i	−0.991181	+	0.132518i	$0.957694\pi$
$942$		0			0
$943$	1.07715	−	1.07715i	0.0350769	−	0.0350769i
$944$	−11.6867			−0.380370
$945$		0			0
$946$	−5.54126			−0.180162
$947$	−35.5816	+	35.5816i	−1.15625	+	1.15625i	−0.170971	+	0.985276i	$0.554691\pi$
$947$	−35.5816	+	35.5816i	−1.15625	+	1.15625i	−0.985276	+	0.170971i	$0.945309\pi$
$948$		0			0
$949$			8.17223i			0.265282i
$950$	17.7212	−	7.32229i	0.574952	−	0.237567i
$951$		0			0
$952$	1.28734	+	1.28734i	0.0417228	+	0.0417228i
$953$	−31.3678	−	31.3678i	−1.01610	−	1.01610i	−0.999868	−	0.0162336i	$-0.994832\pi$
$953$	−31.3678	−	31.3678i	−1.01610	−	1.01610i	−0.0162336	−	0.999868i	$-0.505168\pi$
$954$		0			0
$955$	1.28495	−	0.857767i	0.0415800	−	0.0277567i
$956$			22.6725i			0.733280i
$957$		0			0
$958$	11.4301	−	11.4301i	0.369288	−	0.369288i
$959$	28.1408			0.908715
$960$		0			0
$961$	−18.5026			−0.596858
$962$	−8.84562	+	8.84562i	−0.285194	+	0.285194i
$963$		0			0
$964$			10.5025i			0.338262i
$965$	21.5237	+	4.29107i	0.692871	+	0.138134i
$966$		0			0
$967$	27.5850	+	27.5850i	0.887072	+	0.887072i	0.994241	−	0.107169i	$-0.0341785\pi$
$967$	27.5850	+	27.5850i	0.887072	+	0.887072i	−0.107169	+	0.994241i	$0.534178\pi$
$968$	−6.69695	−	6.69695i	−0.215248	−	0.215248i
$969$		0			0
$970$	−10.8305	−	16.2243i	−0.347746	−	0.520929i
$971$		−	52.0207i		−	1.66942i	−0.550688	−	0.834711i	$-0.685634\pi$
$971$		−	52.0207i		−	1.66942i	0.550688	−	0.834711i	$-0.314366\pi$
$972$		0			0
$973$	−13.9776	+	13.9776i	−0.448101	+	0.448101i
$974$	−28.6798			−0.918960
$975$		0			0
$976$	11.6213			0.371988
$977$	11.8447	−	11.8447i	0.378945	−	0.378945i	−0.491777	−	0.870721i	$-0.663652\pi$
$977$	11.8447	−	11.8447i	0.378945	−	0.378945i	0.870721	+	0.491777i	$0.163652\pi$
$978$		0			0
$979$			11.4284i			0.365254i
$980$	−4.57553	−	6.85422i	−0.146160	−	0.218950i
$981$		0			0
$982$	−4.57028	−	4.57028i	−0.145844	−	0.145844i
$983$	11.2351	+	11.2351i	0.358343	+	0.358343i	0.863202	−	0.504859i	$-0.168455\pi$
$983$	11.2351	+	11.2351i	0.358343	+	0.358343i	−0.504859	+	0.863202i	$0.668455\pi$
$984$		0			0
$985$	−25.8466	−	5.15290i	−0.823540	−	0.164185i
$986$		−	0.0783908i		−	0.00249647i
$987$		0			0
$988$	−11.6698	+	11.6698i	−0.371264	+	0.371264i
$989$	5.04412			0.160394
$990$		0			0
$991$	56.1014			1.78212			0.891059	−	0.453887i	$-0.149963\pi$
$991$	56.1014			1.78212			0.891059	+	0.453887i	$0.149963\pi$
$992$	−2.49974	+	2.49974i	−0.0793669	+	0.0793669i
$993$		0			0
$994$			27.1565i			0.861350i
$995$	−30.3268	+	20.2446i	−0.961425	+	0.641798i
$996$		0			0
$997$	25.7808	+	25.7808i	0.816485	+	0.816485i	0.985597	−	0.169112i	$-0.0540899\pi$
$997$	25.7808	+	25.7808i	0.816485	+	0.816485i	−0.169112	+	0.985597i	$0.554090\pi$
$998$	−30.3786	−	30.3786i	−0.961617	−	0.961617i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.h.647.7	yes	16
3.2	odd	2	inner	1530.2.m.h.647.2	✓	16
5.3	odd	4	inner	1530.2.m.h.953.2	yes	16
15.8	even	4	inner	1530.2.m.h.953.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.h.647.2	✓	16	3.2	odd	2	inner
1530.2.m.h.647.7	yes	16	1.1	even	1	trivial
1530.2.m.h.953.2	yes	16	5.3	odd	4	inner
1530.2.m.h.953.7	yes	16	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.24148 + 1.85976i) q^{5} +(-1.28734 - 1.28734i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.24148 + 1.85976i) q^{5} +(-1.28734 - 1.28734i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.19291 + 0.437190i) q^{10} -1.23656i q^{11} +(3.04306 - 3.04306i) q^{13} -1.82057 q^{14} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} -3.83488i q^{19} +(1.85976 - 1.24148i) q^{20} +(-0.874380 - 0.874380i) q^{22} +(0.795934 + 0.795934i) q^{23} +(-1.91744 + 4.61773i) q^{25} -4.30353i q^{26} +(-1.28734 + 1.28734i) q^{28} +0.0783908 q^{29} +3.53517 q^{31} +(-0.707107 + 0.707107i) q^{32} -1.00000i q^{34} +(0.795934 - 3.99235i) q^{35} +(-2.05543 - 2.05543i) q^{37} +(-2.71167 - 2.71167i) q^{38} +(0.437190 - 2.19291i) q^{40} -1.35332i q^{41} +(3.16868 - 3.16868i) q^{43} -1.23656 q^{44} +1.12562 q^{46} +(8.91416 - 8.91416i) q^{47} -3.68553i q^{49} +(1.90939 + 4.62106i) q^{50} +(-3.04306 - 3.04306i) q^{52} +(5.71775 + 5.71775i) q^{53} +(2.29971 - 1.53517i) q^{55} +1.82057i q^{56} +(0.0554307 - 0.0554307i) q^{58} +11.6867 q^{59} -11.6213 q^{61} +(2.49974 - 2.49974i) q^{62} +1.00000i q^{64} +(9.43727 + 1.88146i) q^{65} +(-2.64247 - 2.64247i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(-2.26020 - 3.38582i) q^{70} -14.9165i q^{71} +(-1.34277 + 1.34277i) q^{73} -2.90682 q^{74} -3.83488 q^{76} +(-1.59187 + 1.59187i) q^{77} +3.30867i q^{79} +(-1.24148 - 1.85976i) q^{80} +(-0.956942 - 0.956942i) q^{82} +(10.0213 + 10.0213i) q^{83} +(2.19291 + 0.437190i) q^{85} -4.48119i q^{86} +(-0.874380 + 0.874380i) q^{88} -9.24212 q^{89} -7.83488 q^{91} +(0.795934 - 0.795934i) q^{92} -12.6065i q^{94} +(7.13196 - 4.76094i) q^{95} +(-6.16868 - 6.16868i) q^{97} +(-2.60607 - 2.60607i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^7	\( 16 q - 8 q^{7} + 4 q^{10} + 8 q^{13} - 16 q^{16} - 8 q^{22} + 16 q^{25} - 8 q^{28} - 56 q^{31} - 24 q^{37} + 4 q^{40} + 16 q^{43} + 24 q^{46} - 8 q^{52} + 56 q^{55} - 8 q^{58} + 8 q^{61} - 40 q^{67} + 32 q^{70} + 32 q^{76} - 56 q^{82} + 4 q^{85} - 8 q^{88} - 32 q^{91} - 64 q^{97}+O(q^{100}) \) 16 * q - 8 * q^7 + 4 * q^10 + 8 * q^13 - 16 * q^16 - 8 * q^22 + 16 * q^25 - 8 * q^28 - 56 * q^31 - 24 * q^37 + 4 * q^40 + 16 * q^43 + 24 * q^46 - 8 * q^52 + 56 * q^55 - 8 * q^58 + 8 * q^61 - 40 * q^67 + 32 * q^70 + 32 * q^76 - 56 * q^82 + 4 * q^85 - 8 * q^88 - 32 * q^91 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more