LMFDB - Embedded newform 1071.2.i.g.919.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,2,Mod(613,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1071.613");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.i (of order $3$, 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:	$8.55197805648$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.5743021975227.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 2x^{8} + 10x^{7} - 8x^{6} - 12x^{5} - 24x^{4} + 90x^{3} + 54x^{2} - 324x + 243 $ x^10 - 4x^9 + 2x^8 + 10x^7 - 8x^6 - 12x^5 - 24x^4 + 90x^3 + 54x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.5
Root			$-1.68232 + 0.412079i$ of defining polynomial
Character	$\chi$	$=$	1071.919
Dual form			1071.2.i.g.613.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19803 - 2.07505i) q^{2} +(-1.87055 - 3.23989i) q^{4} +(2.18232 - 3.77988i) q^{5} +(-2.64467 + 0.0756600i) q^{7} -4.17178 q^{8} +O(q^{10})$	\(q+(1.19803 - 2.07505i) q^{2} +(-1.87055 - 3.23989i) q^{4} +(2.18232 - 3.77988i) q^{5} +(-2.64467 + 0.0756600i) q^{7} -4.17178 q^{8} +(-5.22896 - 9.05683i) q^{10} +(-1.09643 - 1.89907i) q^{11} +4.97572 q^{13} +(-3.01139 + 5.57846i) q^{14} +(-1.25681 + 2.17686i) q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.28983 + 2.23406i) q^{19} -16.3285 q^{20} -5.25422 q^{22} +(-2.98429 + 5.16894i) q^{23} +(-7.02502 - 12.1677i) q^{25} +(5.96106 - 10.3249i) q^{26} +(5.19211 + 8.42690i) q^{28} +8.59607 q^{29} +(1.62736 + 2.81867i) q^{31} +(-1.16038 - 2.00984i) q^{32} +2.39606 q^{34} +(-5.48552 + 10.1617i) q^{35} +(-3.41799 + 5.92014i) q^{37} +(3.09051 + 5.35293i) q^{38} +(-9.10414 + 15.7688i) q^{40} +2.32076 q^{41} +3.15824 q^{43} +(-4.10185 + 7.10461i) q^{44} +(7.15053 + 12.3851i) q^{46} +(0.0918028 - 0.159007i) q^{47} +(6.98855 - 0.400192i) q^{49} -33.6647 q^{50} +(-9.30734 - 16.1208i) q^{52} +(-1.42933 - 2.47567i) q^{53} -9.57103 q^{55} +(11.0330 - 0.315637i) q^{56} +(10.2983 - 17.8372i) q^{58} +(-3.78034 - 6.54775i) q^{59} +(-2.96235 + 5.13094i) q^{61} +7.79850 q^{62} -10.5879 q^{64} +(10.8586 - 18.8077i) q^{65} +(-0.801720 - 1.38862i) q^{67} +(1.87055 - 3.23989i) q^{68} +(14.5141 + 23.5567i) q^{70} +10.8783 q^{71} +(-4.18694 - 7.25200i) q^{73} +(8.18972 + 14.1850i) q^{74} +9.65078 q^{76} +(3.04338 + 4.93946i) q^{77} +(-3.55446 + 6.15651i) q^{79} +(5.48552 + 9.50120i) q^{80} +(2.78034 - 4.81570i) q^{82} +0.625125 q^{83} +4.36463 q^{85} +(3.78367 - 6.55350i) q^{86} +(4.57406 + 7.92250i) q^{88} +(0.479661 - 0.830797i) q^{89} +(-13.1591 + 0.376463i) q^{91} +22.3290 q^{92} +(-0.219965 - 0.380990i) q^{94} +(5.62965 + 9.75083i) q^{95} -6.43415 q^{97} +(7.54207 - 14.9810i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7}+O(q^{10}) $ 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7	$ 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7} - 13 q^{10} - 11 q^{11} + 14 q^{13} - 3 q^{14} + 2 q^{16} + 5 q^{17} - 9 q^{19} - 24 q^{20} + 10 q^{22} - 23 q^{23} - 14 q^{25} + 18 q^{26} + 7 q^{28} + 36 q^{29} - 9 q^{31} + 3 q^{32} - 4 q^{34} + 5 q^{35} - 31 q^{40} - 6 q^{41} + 24 q^{43} - 33 q^{44} - 13 q^{46} + 11 q^{47} + 3 q^{49} - 48 q^{50} - 5 q^{52} - 3 q^{53} - 20 q^{55} + 27 q^{56} + 34 q^{58} - 14 q^{59} - 29 q^{61} + 10 q^{62} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 18 q^{70} + 38 q^{71} - 11 q^{73} + 45 q^{74} + 18 q^{76} - 21 q^{77} - q^{79} - 5 q^{80} + 4 q^{82} - 10 q^{83} + 2 q^{85} - 3 q^{86} - 37 q^{88} + 8 q^{89} - 33 q^{91} + 96 q^{92} + 18 q^{94} - 21 q^{95} + 38 q^{97} + 17 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7 - 13 * q^10 - 11 * q^11 + 14 * q^13 - 3 * q^14 + 2 * q^16 + 5 * q^17 - 9 * q^19 - 24 * q^20 + 10 * q^22 - 23 * q^23 - 14 * q^25 + 18 * q^26 + 7 * q^28 + 36 * q^29 - 9 * q^31 + 3 * q^32 - 4 * q^34 + 5 * q^35 - 31 * q^40 - 6 * q^41 + 24 * q^43 - 33 * q^44 - 13 * q^46 + 11 * q^47 + 3 * q^49 - 48 * q^50 - 5 * q^52 - 3 * q^53 - 20 * q^55 + 27 * q^56 + 34 * q^58 - 14 * q^59 - 29 * q^61 + 10 * q^62 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 18 * q^70 + 38 * q^71 - 11 * q^73 + 45 * q^74 + 18 * q^76 - 21 * q^77 - q^79 - 5 * q^80 + 4 * q^82 - 10 * q^83 + 2 * q^85 - 3 * q^86 - 37 * q^88 + 8 * q^89 - 33 * q^91 + 96 * q^92 + 18 * q^94 - 21 * q^95 + 38 * q^97 + 17 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.19803	−	2.07505i	0.847135	−	1.46728i	−0.0366195	−	0.999329i	$-0.511659\pi$
$2$	1.19803	−	2.07505i	0.847135	−	1.46728i	0.883754	−	0.467951i	$-0.155008\pi$
$3$		0			0
$3$		0			0
$4$	−1.87055	−	3.23989i	−0.935275	−	1.61994i
$5$	2.18232	−	3.77988i	0.975962	−	1.69042i	0.299238	−	0.954178i	$-0.403267\pi$
$5$	2.18232	−	3.77988i	0.975962	−	1.69042i	0.676724	−	0.736237i	$-0.263399\pi$
$6$		0			0
$7$	−2.64467	+	0.0756600i	−0.999591	+	0.0285968i
$7$	−2.64467	+	0.0756600i	−0.999591	+	0.0285968i
$8$	−4.17178			−1.47495
$9$		0			0
$10$	−5.22896	−	9.05683i	−1.65354	−	2.86402i
$11$	−1.09643	−	1.89907i	−0.330586	−	0.572592i	0.652041	−	0.758184i	$-0.273913\pi$
$11$	−1.09643	−	1.89907i	−0.330586	−	0.572592i	−0.982627	+	0.185592i	$0.940580\pi$
$12$		0			0
$13$	4.97572			1.38002			0.690009	−	0.723801i	$-0.257607\pi$
$13$	4.97572			1.38002			0.690009	+	0.723801i	$0.257607\pi$
$14$	−3.01139	+	5.57846i	−0.804829	+	1.49091i
$15$		0			0
$16$	−1.25681	+	2.17686i	−0.314203	+	0.544215i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$		0			0
$19$	−1.28983	+	2.23406i	−0.295908	+	0.512527i	−0.975196	−	0.221345i	$-0.928955\pi$
$19$	−1.28983	+	2.23406i	−0.295908	+	0.512527i	0.679288	+	0.733872i	$0.262289\pi$
$20$	−16.3285			−3.65117
$21$		0			0
$22$	−5.25422			−1.12020
$23$	−2.98429	+	5.16894i	−0.622267	+	1.07780i	0.366796	+	0.930302i	$0.380455\pi$
$23$	−2.98429	+	5.16894i	−0.622267	+	1.07780i	−0.989063	+	0.147496i	$0.952878\pi$
$24$		0			0
$25$	−7.02502	−	12.1677i	−1.40500	−	2.43354i
$26$	5.96106	−	10.3249i	1.16906	−	2.02487i
$27$		0			0
$28$	5.19211	+	8.42690i	0.981217	+	1.59253i
$29$	8.59607			1.59625			0.798125	−	0.602492i	$-0.205826\pi$
$29$	8.59607			1.59625			0.798125	+	0.602492i	$0.205826\pi$
$30$		0			0
$31$	1.62736	+	2.81867i	0.292283	+	0.506248i	0.974349	−	0.225042i	$-0.0722519\pi$
$31$	1.62736	+	2.81867i	0.292283	+	0.506248i	−0.682067	+	0.731290i	$0.738919\pi$
$32$	−1.16038	−	2.00984i	−0.205128	−	0.355293i
$33$		0			0
$34$	2.39606			0.410921
$35$	−5.48552	+	10.1617i	−0.927222	+	1.71763i
$36$		0			0
$37$	−3.41799	+	5.92014i	−0.561915	+	0.973265i	0.435415	+	0.900230i	$0.356602\pi$
$37$	−3.41799	+	5.92014i	−0.561915	+	0.973265i	−0.997329	+	0.0730350i	$0.976732\pi$
$38$	3.09051	+	5.35293i	0.501348	+	0.868360i
$39$		0			0
$40$	−9.10414	+	15.7688i	−1.43949	+	2.49327i
$41$	2.32076			0.362442			0.181221	−	0.983442i	$-0.441995\pi$
$41$	2.32076			0.362442			0.181221	+	0.983442i	$0.441995\pi$
$42$		0			0
$43$	3.15824			0.481627			0.240814	−	0.970571i	$-0.422586\pi$
$43$	3.15824			0.481627			0.240814	+	0.970571i	$0.422586\pi$
$44$	−4.10185	+	7.10461i	−0.618377	+	1.07106i
$45$		0			0
$46$	7.15053	+	12.3851i	1.05429	+	1.82608i
$47$	0.0918028	−	0.159007i	0.0133908	−	0.0231936i	−0.859252	−	0.511552i	$-0.829071\pi$
$47$	0.0918028	−	0.159007i	0.0133908	−	0.0231936i	0.872643	+	0.488358i	$0.162404\pi$
$48$		0			0
$49$	6.98855	−	0.400192i	0.998364	−	0.0571702i
$50$	−33.6647			−4.76091
$51$		0			0
$52$	−9.30734	−	16.1208i	−1.29070	−	2.23555i
$53$	−1.42933	−	2.47567i	−0.196334	−	0.340060i	0.751003	−	0.660299i	$-0.229570\pi$
$53$	−1.42933	−	2.47567i	−0.196334	−	0.340060i	−0.947337	+	0.320239i	$0.896237\pi$
$54$		0			0
$55$	−9.57103			−1.29056
$56$	11.0330	−	0.315637i	1.47434	−	0.0421787i
$57$		0			0
$58$	10.2983	−	17.8372i	1.35224	−	2.34215i
$59$	−3.78034	−	6.54775i	−0.492159	−	0.852444i	0.507800	−	0.861475i	$-0.330459\pi$
$59$	−3.78034	−	6.54775i	−0.492159	−	0.852444i	−0.999959	+	0.00903077i	$0.997125\pi$
$60$		0			0
$61$	−2.96235	+	5.13094i	−0.379290	+	0.656950i	−0.990959	−	0.134164i	$-0.957165\pi$
$61$	−2.96235	+	5.13094i	−0.379290	+	0.656950i	0.611669	+	0.791114i	$0.290499\pi$
$62$	7.79850			0.990411
$63$		0			0
$64$	−10.5879			−1.32349
$65$	10.8586	−	18.8077i	1.34684	−	2.33280i
$66$		0			0
$67$	−0.801720	−	1.38862i	−0.0979456	−	0.169647i	0.812889	−	0.582419i	$-0.197894\pi$
$67$	−0.801720	−	1.38862i	−0.0979456	−	0.169647i	−0.910834	+	0.412772i	$0.864560\pi$
$68$	1.87055	−	3.23989i	0.226837	−	0.392894i
$69$		0			0
$70$	14.5141	+	23.5567i	1.73477	+	2.81556i
$71$	10.8783			1.29101			0.645506	−	0.763755i	$-0.276647\pi$
$71$	10.8783			1.29101			0.645506	+	0.763755i	$0.276647\pi$
$72$		0			0
$73$	−4.18694	−	7.25200i	−0.490045	−	0.848782i	0.509890	−	0.860240i	$-0.329686\pi$
$73$	−4.18694	−	7.25200i	−0.490045	−	0.848782i	−0.999934	+	0.0114575i	$0.996353\pi$
$74$	8.18972	+	14.1850i	0.952035	+	1.64897i
$75$		0			0
$76$	9.65078			1.10702
$77$	3.04338	+	4.93946i	0.346825	+	0.562904i
$78$		0			0
$79$	−3.55446	+	6.15651i	−0.399908	+	0.692662i	−0.993714	−	0.111947i	$-0.964291\pi$
$79$	−3.55446	+	6.15651i	−0.399908	+	0.692662i	0.593806	+	0.804608i	$0.297625\pi$
$80$	5.48552	+	9.50120i	0.613300	+	1.06227i
$81$		0			0
$82$	2.78034	−	4.81570i	0.307038	−	0.531805i
$83$	0.625125			0.0686164			0.0343082	−	0.999411i	$-0.489077\pi$
$83$	0.625125			0.0686164			0.0343082	+	0.999411i	$0.489077\pi$
$84$		0			0
$85$	4.36463			0.473411
$86$	3.78367	−	6.55350i	0.408003	−	0.706682i
$87$		0			0
$88$	4.57406	+	7.92250i	0.487596	+	0.844541i
$89$	0.479661	−	0.830797i	0.0508440	−	0.0880643i	−0.839483	−	0.543385i	$-0.817142\pi$
$89$	0.479661	−	0.830797i	0.0508440	−	0.0880643i	0.890327	+	0.455321i	$0.150476\pi$
$90$		0			0
$91$	−13.1591	+	0.376463i	−1.37945	+	0.0394641i
$92$	22.3290			2.32796
$93$		0			0
$94$	−0.219965	−	0.380990i	−0.0226877	−	0.0392962i
$95$	5.62965	+	9.75083i	0.577590	+	1.00041i
$96$		0			0
$97$	−6.43415			−0.653289			−0.326644	−	0.945147i	$-0.605918\pi$
$97$	−6.43415			−0.653289			−0.326644	+	0.945147i	$0.605918\pi$
$98$	7.54207	−	14.9810i	0.761865	−	1.51331i
$99$		0			0
$100$	−26.2813	+	45.5205i	−2.62813	+	4.55205i
$101$	−5.25964	−	9.10997i	−0.523354	−	0.906475i	−0.999631	−	0.0271800i	$-0.991347\pi$
$101$	−5.25964	−	9.10997i	−0.523354	−	0.906475i	0.476277	−	0.879295i	$-0.341986\pi$
$102$		0			0
$103$	1.08614	−	1.88125i	0.107020	−	0.185365i	−0.807541	−	0.589811i	$-0.799202\pi$
$103$	1.08614	−	1.88125i	0.107020	−	0.185365i	0.914562	+	0.404446i	$0.132536\pi$
$104$	−20.7576			−2.03545
$105$		0			0
$106$	−6.84952			−0.665284
$107$	1.59803	−	2.76786i	0.154487	−	0.267579i	−0.778385	−	0.627787i	$-0.783961\pi$
$107$	1.59803	−	2.76786i	0.154487	−	0.267579i	0.932872	+	0.360208i	$0.117294\pi$
$108$		0			0
$109$	5.59519	+	9.69116i	0.535922	+	0.928244i	0.999118	+	0.0419885i	$0.0133693\pi$
$109$	5.59519	+	9.69116i	0.535922	+	0.928244i	−0.463196	+	0.886256i	$0.653297\pi$
$110$	−11.4664	+	19.8603i	−1.09328	+	1.89361i
$111$		0			0
$112$	3.15915	−	5.85217i	0.298511	−	0.552978i
$113$	13.7644			1.29484			0.647422	−	0.762131i	$-0.275847\pi$
$113$	13.7644			1.29484			0.647422	+	0.762131i	$0.275847\pi$
$114$		0			0
$115$	13.0253	+	22.5605i	1.21462	+	2.10378i
$116$	−16.0794	−	27.8503i	−1.49293	−	2.58583i
$117$		0			0
$118$	−18.1158			−1.66770
$119$	−1.38786	−	2.25252i	−0.127225	−	0.206488i
$120$		0			0
$121$	3.09568	−	5.36188i	0.281426	−	0.487444i
$122$	7.09797	+	12.2940i	0.642620	+	1.11305i
$123$		0			0
$124$	6.08812	−	10.5449i	0.546729	−	0.946962i
$125$	−39.5001			−3.53299
$126$		0			0
$127$	4.37337			0.388074			0.194037	−	0.980994i	$-0.437842\pi$
$127$	4.37337			0.388074			0.194037	+	0.980994i	$0.437842\pi$
$128$	−10.3639	+	17.9508i	−0.916047	+	1.58664i
$129$		0			0
$130$	−26.0179	−	45.0643i	−2.28192	−	3.95240i
$131$	−3.57782	+	6.19696i	−0.312595	+	0.541431i	−0.978923	−	0.204228i	$-0.934532\pi$
$131$	−3.57782	+	6.19696i	−0.312595	+	0.541431i	0.666328	+	0.745659i	$0.267865\pi$
$132$		0			0
$133$	3.24215	−	6.00593i	0.281130	−	0.520780i
$134$	−3.84194			−0.331893
$135$		0			0
$136$	−2.08589	−	3.61286i	−0.178863	−	0.309800i
$137$	9.04381	+	15.6643i	0.772665	+	1.33829i	0.936098	+	0.351740i	$0.114410\pi$
$137$	9.04381	+	15.6643i	0.772665	+	1.33829i	−0.163433	+	0.986554i	$0.552257\pi$
$138$		0			0
$139$	17.3458			1.47125			0.735624	−	0.677390i	$-0.236889\pi$
$139$	17.3458			1.47125			0.735624	+	0.677390i	$0.236889\pi$
$140$	43.1836	−	1.23542i	3.64968	−	0.104412i
$141$		0			0
$142$	13.0325	−	22.5729i	1.09366	−	1.89428i
$143$	−5.45553	−	9.44926i	−0.456214	−	0.790186i
$144$		0			0
$145$	18.7593	−	32.4921i	1.55788	−	2.69832i
$146$	−20.0643			−1.66054
$147$		0			0
$148$	25.5741			2.10218
$149$	6.42817	−	11.1339i	0.526616	−	0.912126i	−0.472903	−	0.881115i	$-0.656794\pi$
$149$	6.42817	−	11.1339i	0.526616	−	0.912126i	0.999519	−	0.0310117i	$-0.00987292\pi$
$150$		0			0
$151$	3.40505	+	5.89773i	0.277099	+	0.479950i	0.970663	−	0.240445i	$-0.0772935\pi$
$151$	3.40505	+	5.89773i	0.277099	+	0.479950i	−0.693563	+	0.720396i	$0.743960\pi$
$152$	5.38089	−	9.31998i	0.436448	−	0.755950i
$153$		0			0
$154$	13.8957	−	0.397534i	1.11975	−	0.0320342i
$155$	14.2057			1.14103
$156$		0			0
$157$	−3.63055	−	6.28830i	−0.289750	−	0.501861i	0.684000	−	0.729482i	$-0.260239\pi$
$157$	−3.63055	−	6.28830i	−0.289750	−	0.501861i	−0.973750	+	0.227621i	$0.926905\pi$
$158$	8.51670	+	14.7514i	0.677552	+	1.17356i
$159$		0			0
$160$	−10.1293			−0.800790
$161$	7.50137	−	13.8959i	0.591191	−	1.09515i
$162$		0			0
$163$	1.56698	−	2.71409i	0.122736	−	0.212584i	−0.798110	−	0.602512i	$-0.794167\pi$
$163$	1.56698	−	2.71409i	0.122736	−	0.212584i	0.920846	+	0.389928i	$0.127500\pi$
$164$	−4.34110	−	7.51901i	−0.338983	−	0.587136i
$165$		0			0
$166$	0.748918	−	1.29716i	0.0581273	−	0.100679i
$167$	−21.3606			−1.65293			−0.826465	−	0.562988i	$-0.809652\pi$
$167$	−21.3606			−1.65293			−0.826465	+	0.562988i	$0.809652\pi$
$168$		0			0
$169$	11.7578			0.904448
$170$	5.22896	−	9.05683i	0.401043	−	0.694627i
$171$		0			0
$172$	−5.90765	−	10.2323i	−0.450454	−	0.780209i
$173$	4.07001	−	7.04947i	0.309437	−	0.535961i	−0.668802	−	0.743441i	$-0.733193\pi$
$173$	4.07001	−	7.04947i	0.309437	−	0.535961i	0.978239	+	0.207479i	$0.0665260\pi$
$174$		0			0
$175$	19.4995	+	31.6480i	1.47402	+	2.39236i
$176$	5.51202			0.415484
$177$		0			0
$178$	−1.14930	−	1.99064i	−0.0861434	−	0.149205i
$179$	−7.36309	−	12.7532i	−0.550343	−	0.953222i	−0.998250	−	0.0591417i	$-0.981164\pi$
$179$	−7.36309	−	12.7532i	−0.550343	−	0.953222i	0.447907	−	0.894080i	$-0.352170\pi$
$180$		0			0
$181$	−20.6446			−1.53450			−0.767251	−	0.641347i	$-0.778376\pi$
$181$	−20.6446			−1.53450			−0.767251	+	0.641347i	$0.778376\pi$
$182$	−14.9839	+	27.7569i	−1.11068	+	2.05748i
$183$		0			0
$184$	12.4498	−	21.5636i	0.917810	−	1.58969i
$185$	14.9183	+	25.8392i	1.09681	+	1.89974i
$186$		0			0
$187$	1.09643	−	1.89907i	0.0801789	−	0.138874i
$188$	−0.686887			−0.0500964
$189$		0			0
$190$	26.9779			1.95718
$191$	8.66754	−	15.0126i	0.627162	−	1.08628i	−0.360957	−	0.932582i	$-0.617550\pi$
$191$	8.66754	−	15.0126i	0.627162	−	1.08628i	0.988119	−	0.153693i	$-0.0491167\pi$
$192$		0			0
$193$	0.280724	+	0.486229i	0.0202070	+	0.0349995i	0.875952	−	0.482398i	$-0.160234\pi$
$193$	0.280724	+	0.486229i	0.0202070	+	0.0349995i	−0.855745	+	0.517398i	$0.826901\pi$
$194$	−7.70830	+	13.3512i	−0.553423	+	0.958558i
$195$		0			0
$196$	−14.3690	−	21.8935i	−1.02636	−	1.56382i
$197$	1.87318			0.133459			0.0667294	−	0.997771i	$-0.478744\pi$
$197$	1.87318			0.133459			0.0667294	+	0.997771i	$0.478744\pi$
$198$		0			0
$199$	3.40899	+	5.90455i	0.241657	+	0.418562i	0.961186	−	0.275900i	$-0.0889758\pi$
$199$	3.40899	+	5.90455i	0.241657	+	0.418562i	−0.719529	+	0.694462i	$0.755642\pi$
$200$	29.3068	+	50.7608i	2.07230	+	3.58933i
$201$		0			0
$202$	−25.2048			−1.77340
$203$	−22.7338	+	0.650379i	−1.59560	+	0.0456476i
$204$		0			0
$205$	5.06464	−	8.77222i	0.353730	−	0.612678i
$206$	−2.60245	−	4.50758i	−0.181321	−	0.314058i
$207$		0			0
$208$	−6.25354	+	10.8315i	−0.433605	+	0.751026i
$209$	5.65684			0.391292
$210$		0			0
$211$	2.55589			0.175955			0.0879774	−	0.996122i	$-0.471960\pi$
$211$	2.55589			0.175955			0.0879774	+	0.996122i	$0.471960\pi$
$212$	−5.34727	+	9.26174i	−0.367252	+	0.636099i
$213$		0			0
$214$	−3.82896	−	6.63196i	−0.261743	−	0.453351i
$215$	6.89228	−	11.9378i	0.470050	−	0.814150i
$216$		0			0
$217$	−4.51709	−	7.33133i	−0.306640	−	0.497683i
$218$	26.8128			1.81599
$219$		0			0
$220$	17.9031	+	31.0090i	1.20703	+	2.09063i
$221$	2.48786	+	4.30910i	0.167352	+	0.289862i
$222$		0			0
$223$	19.1692			1.28366			0.641832	−	0.766845i	$-0.278175\pi$
$223$	19.1692			1.28366			0.641832	+	0.766845i	$0.278175\pi$
$224$	3.22089	+	5.22757i	0.215205	+	0.349282i
$225$		0			0
$226$	16.4901	−	28.5618i	1.09691	−	1.89990i
$227$	−0.938026	−	1.62471i	−0.0622589	−	0.107836i	0.833216	−	0.552948i	$-0.186497\pi$
$227$	−0.938026	−	1.62471i	−0.0622589	−	0.107836i	−0.895475	+	0.445112i	$0.853164\pi$
$228$		0			0
$229$	−2.89889	+	5.02103i	−0.191564	+	0.331799i	−0.945769	−	0.324840i	$-0.894689\pi$
$229$	−2.89889	+	5.02103i	−0.191564	+	0.331799i	0.754205	+	0.656640i	$0.228023\pi$
$230$	62.4189			4.11578
$231$		0			0
$232$	−35.8609			−2.35438
$233$	−1.15626	+	2.00271i	−0.0757493	+	0.131202i	−0.901412	−	0.432963i	$-0.857468\pi$
$233$	−1.15626	+	2.00271i	−0.0757493	+	0.131202i	0.825663	+	0.564164i	$0.190802\pi$
$234$		0			0
$235$	−0.400686	−	0.694008i	−0.0261379	−	0.0452721i
$236$	−14.1426	+	24.4958i	−0.920607	+	1.59454i
$237$		0			0
$238$	−6.33678	+	0.181286i	−0.410753	+	0.0117510i
$239$	19.1330			1.23761			0.618805	−	0.785545i	$-0.287617\pi$
$239$	19.1330			1.23761			0.618805	+	0.785545i	$0.287617\pi$
$240$		0			0
$241$	6.40283	+	11.0900i	0.412442	+	0.714371i	0.995156	−	0.0983064i	$-0.0313425\pi$
$241$	6.40283	+	11.0900i	0.412442	+	0.714371i	−0.582714	+	0.812677i	$0.698009\pi$
$242$	−7.41744	−	12.8474i	−0.476811	−	0.825861i
$243$		0			0
$244$	22.1649			1.41896
$245$	13.7386	−	27.2893i	0.877724	−	1.74345i
$246$		0			0
$247$	−6.41785	+	11.1160i	−0.408358	+	0.707297i
$248$	−6.78898	−	11.7589i	−0.431101	−	0.746689i
$249$		0			0
$250$	−47.3223	+	81.9646i	−2.99292	+	5.18389i
$251$	−21.7013			−1.36977			−0.684887	−	0.728649i	$-0.740148\pi$
$251$	−21.7013			−1.36977			−0.684887	+	0.728649i	$0.740148\pi$
$252$		0			0
$253$	13.0882			0.822851
$254$	5.23943	−	9.07496i	0.328751	−	0.569413i
$255$		0			0
$256$	14.2446	+	24.6723i	0.890285	+	1.54202i
$257$	−8.34036	+	14.4459i	−0.520257	+	0.901112i	0.479465	+	0.877561i	$0.340831\pi$
$257$	−8.34036	+	14.4459i	−0.520257	+	0.901112i	−0.999723	+	0.0235512i	$0.992503\pi$
$258$		0			0
$259$	8.59155	−	15.9154i	0.533853	−	0.988936i
$260$	−81.2462			−5.03868
$261$		0			0
$262$	8.57266	+	14.8483i	0.529621	+	0.917330i
$263$	−4.82913	−	8.36429i	−0.297777	−	0.515764i	0.677850	−	0.735200i	$-0.262912\pi$
$263$	−4.82913	−	8.36429i	−0.297777	−	0.515764i	−0.975627	+	0.219436i	$0.929578\pi$
$264$		0			0
$265$	−12.4770			−0.766457
$266$	−8.57839	−	13.9229i	−0.525975	−	0.853667i
$267$		0			0
$268$	−2.99931	+	5.19496i	−0.183212	+	0.317333i
$269$	−0.722251	−	1.25097i	−0.0440364	−	0.0762733i	0.843167	−	0.537652i	$-0.180688\pi$
$269$	−0.722251	−	1.25097i	−0.0440364	−	0.0762733i	−0.887203	+	0.461378i	$0.847355\pi$
$270$		0			0
$271$	1.38122	−	2.39235i	0.0839032	−	0.145325i	−0.821020	−	0.570899i	$-0.806595\pi$
$271$	1.38122	−	2.39235i	0.0839032	−	0.145325i	0.904923	+	0.425575i	$0.139928\pi$
$272$	−2.51362			−0.152411
$273$		0			0
$274$	43.3390			2.61820
$275$	−15.4049	+	26.6820i	−0.928949	+	1.60899i
$276$		0			0
$277$	5.17139	+	8.95712i	0.310719	+	0.538181i	0.978518	−	0.206160i	$-0.0660969\pi$
$277$	5.17139	+	8.95712i	0.310719	+	0.538181i	−0.667799	+	0.744341i	$0.732764\pi$
$278$	20.7807	−	35.9933i	1.24635	−	2.15873i
$279$		0			0
$280$	22.8844	−	42.3922i	1.36760	−	2.53342i
$281$	−1.78040			−0.106210			−0.0531048	−	0.998589i	$-0.516912\pi$
$281$	−1.78040			−0.106210			−0.0531048	+	0.998589i	$0.516912\pi$
$282$		0			0
$283$	6.43481	+	11.1454i	0.382510	+	0.662526i	0.991420	−	0.130713i	$-0.0417265\pi$
$283$	6.43481	+	11.1454i	0.382510	+	0.662526i	−0.608911	+	0.793239i	$0.708393\pi$
$284$	−20.3483	−	35.2443i	−1.20745	−	2.09137i
$285$		0			0
$286$	−26.1435			−1.54590
$287$	−6.13765	+	0.175589i	−0.362294	+	0.0103647i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−44.9485	−	77.8531i	−2.63947	−	4.57169i
$291$		0			0
$292$	−15.6638	+	27.1304i	−0.916653	+	1.58769i
$293$	21.5809			1.26077			0.630384	−	0.776283i	$-0.282897\pi$
$293$	21.5809			1.26077			0.630384	+	0.776283i	$0.282897\pi$
$294$		0			0
$295$	−32.9996			−1.92131
$296$	14.2591	−	24.6975i	0.828794	−	1.43551i
$297$		0			0
$298$	−15.4023	−	26.6775i	−0.892230	−	1.54539i
$299$	−14.8490	+	25.7192i	−0.858739	+	1.48738i
$300$		0			0
$301$	−8.35250	+	0.238953i	−0.481430	+	0.0137730i
$302$	16.3174			0.938962
$303$		0			0
$304$	−3.24215	−	5.61557i	−0.185950	−	0.322075i
$305$	12.9296	+	22.3947i	0.740346	+	1.28232i
$306$		0			0
$307$	−24.3141			−1.38768			−0.693840	−	0.720129i	$-0.744083\pi$
$307$	−24.3141			−1.38768			−0.693840	+	0.720129i	$0.744083\pi$
$308$	10.3105	−	19.0997i	0.587495	−	1.08831i
$309$		0			0
$310$	17.0188	−	29.4774i	0.966603	−	1.67421i
$311$	−7.40974	−	12.8340i	−0.420168	−	0.727752i	0.575788	−	0.817599i	$-0.304695\pi$
$311$	−7.40974	−	12.8340i	−0.420168	−	0.727752i	−0.995956	+	0.0898473i	$0.971362\pi$
$312$		0			0
$313$	4.81325	−	8.33680i	0.272061	−	0.471224i	−0.697328	−	0.716752i	$-0.745628\pi$
$313$	4.81325	−	8.33680i	0.272061	−	0.471224i	0.969389	+	0.245528i	$0.0789614\pi$
$314$	−17.3980			−0.981828
$315$		0			0
$316$	26.5952			1.49610
$317$	−11.4779	+	19.8803i	−0.644663	+	1.11659i	0.339716	+	0.940528i	$0.389669\pi$
$317$	−11.4779	+	19.8803i	−0.644663	+	1.11659i	−0.984379	+	0.176061i	$0.943664\pi$
$318$		0			0
$319$	−9.42498	−	16.3245i	−0.527698	−	0.913999i
$320$	−23.1062	+	40.0211i	−1.29168	+	2.23725i
$321$		0			0
$322$	−19.8478	−	32.2134i	−1.10608	−	1.79518i
$323$	−2.57966			−0.143536
$324$		0			0
$325$	−34.9545	−	60.5430i	−1.93893	−	3.35832i
$326$	−3.75458	−	6.50313i	−0.207947	−	0.360175i
$327$		0			0
$328$	−9.68170			−0.534583
$329$	−0.230758	+	0.427467i	−0.0127221	+	0.0235670i
$330$		0			0
$331$	−6.92669	+	11.9974i	−0.380725	+	0.659435i	−0.991166	−	0.132626i	$-0.957659\pi$
$331$	−6.92669	+	11.9974i	−0.380725	+	0.659435i	0.610441	+	0.792062i	$0.290992\pi$
$332$	−1.16933	−	2.02533i	−0.0641752	−	0.111155i
$333$		0			0
$334$	−25.5906	+	44.3242i	−1.40025	+	2.42531i
$335$	−6.99843			−0.382365
$336$		0			0
$337$	24.5717			1.33850			0.669252	−	0.743035i	$-0.266615\pi$
$337$	24.5717			1.33850			0.669252	+	0.743035i	$0.266615\pi$
$338$	14.0862	−	24.3981i	0.766189	−	1.32708i
$339$		0			0
$340$	−8.16426	−	14.1409i	−0.442769	−	0.766899i
$341$	3.56857	−	6.18095i	0.193249	−	0.334717i
$342$		0			0
$343$	−18.4521	+	1.58713i	−0.996321	+	0.0856969i
$344$	−13.1755			−0.710374
$345$		0			0
$346$	−9.75199	−	16.8909i	−0.524270	−	0.908063i
$347$	−11.5530	−	20.0104i	−0.620197	−	1.07421i	−0.989449	−	0.144884i	$-0.953719\pi$
$347$	−11.5530	−	20.0104i	−0.620197	−	1.07421i	0.369251	−	0.929330i	$-0.379614\pi$
$348$		0			0
$349$	20.4788			1.09621			0.548104	−	0.836410i	$-0.315350\pi$
$349$	20.4788			1.09621			0.548104	+	0.836410i	$0.315350\pi$
$350$	89.0320	−	2.54707i	4.75896	−	0.136147i
$351$		0			0
$352$	−2.54455	+	4.40730i	−0.135625	+	0.234910i
$353$	−1.03754	−	1.79706i	−0.0552224	−	0.0956481i	0.837093	−	0.547061i	$-0.184253\pi$
$353$	−1.03754	−	1.79706i	−0.0552224	−	0.0956481i	−0.892315	+	0.451413i	$0.850920\pi$
$354$		0			0
$355$	23.7398	−	41.1185i	1.25998	−	2.18235i
$356$	−3.58892			−0.190212
$357$		0			0
$358$	−35.2848			−1.86486
$359$	4.22642	−	7.32038i	0.223062	−	0.386355i	−0.732674	−	0.680580i	$-0.761728\pi$
$359$	4.22642	−	7.32038i	0.223062	−	0.386355i	0.955736	+	0.294225i	$0.0950614\pi$
$360$		0			0
$361$	6.17267	+	10.6914i	0.324877	+	0.562704i
$362$	−24.7329	+	42.8386i	−1.29993	+	2.25154i
$363$		0			0
$364$	25.8345	+	41.9299i	1.35410	+	2.19773i
$365$	−36.5490			−1.91306
$366$		0			0
$367$	12.8169	+	22.1995i	0.669035	+	1.15880i	0.978174	+	0.207787i	$0.0666259\pi$
$367$	12.8169	+	22.1995i	0.669035	+	1.15880i	−0.309139	+	0.951017i	$0.600041\pi$
$368$	−7.50137	−	12.9928i	−0.391036	−	0.677294i
$369$		0			0
$370$	71.4902			3.71660
$371$	3.96742	+	6.43920i	0.205978	+	0.334306i
$372$		0			0
$373$	−3.38282	+	5.85921i	−0.175156	+	0.303379i	−0.940215	−	0.340581i	$-0.889376\pi$
$373$	−3.38282	+	5.85921i	−0.175156	+	0.303379i	0.765059	+	0.643960i	$0.222710\pi$
$374$	−2.62711	−	4.55029i	−0.135845	−	0.235290i
$375$		0			0
$376$	−0.382981	+	0.663342i	−0.0197507	+	0.0342093i
$377$	42.7717			2.20285
$378$		0			0
$379$	−20.6501			−1.06072			−0.530361	−	0.847772i	$-0.677944\pi$
$379$	−20.6501			−1.06072			−0.530361	+	0.847772i	$0.677944\pi$
$380$	21.0611	−	36.4788i	1.08041	−	1.87132i
$381$		0			0
$382$	−20.7679	−	35.9711i	−1.06258	−	1.84044i
$383$	8.24800	−	14.2859i	0.421453	−	0.729978i	−0.574629	−	0.818414i	$-0.694854\pi$
$383$	8.24800	−	14.2859i	0.421453	−	0.729978i	0.996082	+	0.0884362i	$0.0281869\pi$
$384$		0			0
$385$	25.3122	−	0.724144i	1.29003	−	0.0369058i
$386$	1.34526			0.0684722
$387$		0			0
$388$	12.0354	+	20.8459i	0.611004	+	1.05829i
$389$	15.1210	+	26.1903i	0.766665	+	1.32790i	0.939362	+	0.342928i	$0.111419\pi$
$389$	15.1210	+	26.1903i	0.766665	+	1.32790i	−0.172696	+	0.984975i	$0.555248\pi$
$390$		0			0
$391$	−5.96858			−0.301844
$392$	−29.1547	+	1.66951i	−1.47253	+	0.0843229i
$393$		0			0
$394$	2.24413	−	3.88695i	0.113058	−	0.195821i
$395$	15.5139	+	26.8709i	0.780591	+	1.35202i
$396$		0			0
$397$	−7.73265	+	13.3933i	−0.388090	+	0.672192i	−0.992193	−	0.124714i	$-0.960199\pi$
$397$	−7.73265	+	13.3933i	−0.388090	+	0.672192i	0.604102	+	0.796907i	$0.293532\pi$
$398$	16.3363			0.818864
$399$		0			0
$400$	35.3165			1.76582
$401$	−9.61275	+	16.6498i	−0.480038	+	0.831450i	−0.999738	−	0.0228989i	$-0.992710\pi$
$401$	−9.61275	+	16.6498i	−0.480038	+	0.831450i	0.519700	+	0.854349i	$0.326044\pi$
$402$		0			0
$403$	8.09730	+	14.0249i	0.403355	+	0.698631i
$404$	−19.6768	+	34.0813i	−0.978959	+	1.69561i
$405$		0			0
$406$	−25.8861	+	47.9528i	−1.28471	+	2.37986i
$407$	14.9904			0.743045
$408$		0			0
$409$	14.3357	+	24.8302i	0.708857	+	1.22778i	0.965281	+	0.261212i	$0.0841222\pi$
$409$	14.3357	+	24.8302i	0.708857	+	1.22778i	−0.256424	+	0.966564i	$0.582544\pi$
$410$	−12.1352	−	21.0187i	−0.599314	−	1.03804i
$411$		0			0
$412$	−8.12670			−0.400374
$413$	10.4932	+	17.0306i	0.516335	+	0.838021i
$414$		0			0
$415$	1.36422	−	2.36290i	0.0669670	−	0.115990i
$416$	−5.77374	−	10.0004i	−0.283081	−	0.490310i
$417$		0			0
$418$	6.77706	−	11.7382i	0.331477	−	0.574135i
$419$	−20.2899			−0.991228			−0.495614	−	0.868543i	$-0.665057\pi$
$419$	−20.2899			−0.991228			−0.495614	+	0.868543i	$0.665057\pi$
$420$		0			0
$421$	−38.1649			−1.86004			−0.930022	−	0.367505i	$-0.880212\pi$
$421$	−38.1649			−1.86004			−0.930022	+	0.367505i	$0.880212\pi$
$422$	3.06203	−	5.30359i	0.149057	−	0.258175i
$423$		0			0
$424$	5.96285	+	10.3280i	0.289581	+	0.501570i
$425$	7.02502	−	12.1677i	0.340763	−	0.590219i
$426$		0			0
$427$	7.44623	−	13.7938i	0.360349	−	0.667528i
$428$	−11.9567			−0.577951
$429$		0			0
$430$	−16.5143	−	28.6036i	−0.796391	−	1.37939i
$431$	16.3906	+	28.3894i	0.789509	+	1.36747i	0.926268	+	0.376865i	$0.122998\pi$
$431$	16.3906	+	28.3894i	0.789509	+	1.36747i	−0.136760	+	0.990604i	$0.543669\pi$
$432$		0			0
$433$	4.92769			0.236809			0.118405	−	0.992965i	$-0.462222\pi$
$433$	4.92769			0.236809			0.118405	+	0.992965i	$0.462222\pi$
$434$	−20.6245	+	0.590035i	−0.990006	+	0.0283226i
$435$		0			0
$436$	20.9322	−	36.2556i	1.00247	−	1.73633i
$437$	−7.69846	−	13.3341i	−0.368267	−	0.637858i
$438$		0			0
$439$	−20.3065	+	35.1719i	−0.969177	+	1.67866i	−0.271229	+	0.962515i	$0.587430\pi$
$439$	−20.3065	+	35.1719i	−0.969177	+	1.67866i	−0.697947	+	0.716149i	$0.745903\pi$
$440$	39.9282			1.90350
$441$		0			0
$442$	11.9221			0.567078
$443$	−16.5925	+	28.7390i	−0.788333	+	1.36543i	0.138655	+	0.990341i	$0.455722\pi$
$443$	−16.5925	+	28.7390i	−0.788333	+	1.36543i	−0.926988	+	0.375092i	$0.877611\pi$
$444$		0			0
$445$	−2.09354	−	3.62613i	−0.0992435	−	0.171895i
$446$	22.9652	−	39.7770i	1.08744	−	1.88349i
$447$		0			0
$448$	28.0016	−	0.801083i	1.32295	−	0.0378476i
$449$	1.65248			0.0779855			0.0389928	−	0.999239i	$-0.487585\pi$
$449$	1.65248			0.0779855			0.0389928	+	0.999239i	$0.487585\pi$
$450$		0			0
$451$	−2.54455	−	4.40730i	−0.119818	−	0.207531i
$452$	−25.7470	−	44.5951i	−1.21104	−	2.09757i
$453$		0			0
$454$	−4.49513			−0.210967
$455$	−27.2944	+	50.5616i	−1.27958	+	2.37036i
$456$		0			0
$457$	−16.8113	+	29.1180i	−0.786400	+	1.36208i	0.141759	+	0.989901i	$0.454724\pi$
$457$	−16.8113	+	29.1180i	−0.786400	+	1.36208i	−0.928159	+	0.372183i	$0.878609\pi$
$458$	6.94592	+	12.0307i	0.324562	+	0.562157i
$459$		0			0
$460$	48.7290	−	84.4011i	2.27200	−	3.93522i
$461$	−2.06554			−0.0962018			−0.0481009	−	0.998842i	$-0.515317\pi$
$461$	−2.06554			−0.0962018			−0.0481009	+	0.998842i	$0.515317\pi$
$462$		0			0
$463$	20.3132			0.944034			0.472017	−	0.881590i	$-0.343526\pi$
$463$	20.3132			0.944034			0.472017	+	0.881590i	$0.343526\pi$
$464$	−10.8036	+	18.7124i	−0.501546	+	0.868703i
$465$		0			0
$466$	2.77048	+	4.79860i	0.128340	+	0.222291i
$467$	6.02188	−	10.4302i	0.278659	−	0.482652i	−0.692392	−	0.721521i	$-0.743443\pi$
$467$	6.02188	−	10.4302i	0.278659	−	0.482652i	0.971052	+	0.238869i	$0.0767766\pi$
$468$		0			0
$469$	2.22535	+	3.61178i	0.102757	+	0.166777i
$470$	−1.92013			−0.0885691
$471$		0			0
$472$	15.7707	+	27.3157i	0.725907	+	1.25731i
$473$	−3.46279	−	5.99773i	−0.159219	−	0.275776i
$474$		0			0
$475$	36.2444			1.66301
$476$	−4.70185	+	8.70995i	−0.215509	+	0.399220i
$477$		0			0
$478$	22.9219	−	39.7019i	1.04842	−	1.81592i
$479$	0.106277	+	0.184077i	0.00485591	+	0.00841069i	0.868443	−	0.495789i	$-0.165121\pi$
$479$	0.106277	+	0.184077i	0.00485591	+	0.00841069i	−0.863587	+	0.504199i	$0.831788\pi$
$480$		0			0
$481$	−17.0070	+	29.4570i	−0.775452	+	1.34312i
$482$	30.6831			1.39758
$483$		0			0
$484$	−23.1625			−1.05284
$485$	−14.0413	+	24.3203i	−0.637585	+	1.10433i
$486$		0			0
$487$	17.3209	+	30.0006i	0.784883	+	1.35946i	0.929069	+	0.369906i	$0.120610\pi$
$487$	17.3209	+	30.0006i	0.784883	+	1.35946i	−0.144186	+	0.989551i	$0.546056\pi$
$488$	12.3583	−	21.4051i	0.559432	−	0.968965i
$489$		0			0
$490$	−40.1673	−	61.2015i	−1.81457	−	2.76480i
$491$	26.4747			1.19479			0.597394	−	0.801948i	$-0.296203\pi$
$491$	26.4747			1.19479			0.597394	+	0.801948i	$0.296203\pi$
$492$		0			0
$493$	4.29803	+	7.44441i	0.193574	+	0.335279i
$494$	15.3775	+	26.6347i	0.691868	+	1.19835i
$495$		0			0
$496$	−8.18114			−0.367344
$497$	−28.7694	+	0.823049i	−1.29048	+	0.0369188i
$498$		0			0
$499$	14.7664	−	25.5762i	0.661036	−	1.14495i	−0.319308	−	0.947651i	$-0.603451\pi$
$499$	14.7664	−	25.5762i	0.661036	−	1.14495i	0.980344	−	0.197296i	$-0.0632161\pi$
$500$	73.8868	+	127.976i	3.30432	+	5.72325i
$501$		0			0
$502$	−25.9988	+	45.0312i	−1.16038	+	2.00984i
$503$	−36.7527			−1.63872			−0.819361	−	0.573277i	$-0.805672\pi$
$503$	−36.7527			−1.63872			−0.819361	+	0.573277i	$0.805672\pi$
$504$		0			0
$505$	−45.9128			−2.04309
$506$	15.6801	−	27.1587i	0.697066	−	1.20735i
$507$		0			0
$508$	−8.18061	−	14.1692i	−0.362956	−	0.628658i
$509$	0.494132	−	0.855862i	0.0219020	−	0.0379354i	−0.854867	−	0.518848i	$-0.826361\pi$
$509$	0.494132	−	0.855862i	0.0219020	−	0.0379354i	0.876769	+	0.480912i	$0.159694\pi$
$510$		0			0
$511$	11.6218	+	18.8624i	0.514117	+	0.834421i
$512$	26.8061			1.18467
$513$		0			0
$514$	19.9840	+	34.6133i	0.881456	+	1.52673i
$515$	−4.74060	−	8.21096i	−0.208896	−	0.361818i
$516$		0			0
$517$	−0.402621			−0.0177073
$518$	−22.7323	−	36.8950i	−0.998801	−	1.62107i
$519$		0			0
$520$	−45.2997	+	78.4613i	−1.98652	+	3.44076i
$521$	15.8889	+	27.5204i	0.696107	+	1.20569i	0.969806	+	0.243877i	$0.0784193\pi$
$521$	15.8889	+	27.5204i	0.696107	+	1.20569i	−0.273700	+	0.961815i	$0.588247\pi$
$522$		0			0
$523$	−18.2958	+	31.6892i	−0.800018	+	1.38567i	0.119586	+	0.992824i	$0.461843\pi$
$523$	−18.2958	+	31.6892i	−0.800018	+	1.38567i	−0.919604	+	0.392847i	$0.871490\pi$
$524$	26.7699			1.16945
$525$		0			0
$526$	−23.1417			−1.00903
$527$	−1.62736	+	2.81867i	−0.0708889	+	0.122783i
$528$		0			0
$529$	−6.31194	−	10.9326i	−0.274432	−	0.475331i
$530$	−14.9478	+	25.8904i	−0.649292	+	1.12461i
$531$		0			0
$532$	−25.5231	+	0.730178i	−1.10657	+	0.0316572i
$533$	11.5475			0.500177
$534$		0			0
$535$	−6.97480	−	12.0807i	−0.301547	−	0.522294i
$536$	3.34459	+	5.79301i	0.144464	+	0.250220i
$537$		0			0
$538$	−3.46111			−0.149219
$539$	−8.42245	−	12.8330i	−0.362780	−	0.552755i
$540$		0			0
$541$	11.1998	−	19.3987i	0.481518	−	0.834014i	−0.518257	−	0.855225i	$-0.673419\pi$
$541$	11.1998	−	19.3987i	0.481518	−	0.834014i	0.999775	+	0.0212110i	$0.00675217\pi$
$542$	−3.30949	−	5.73220i	−0.142155	−	0.246219i
$543$		0			0
$544$	1.16038	−	2.00984i	0.0497510	−	0.0861712i
$545$	48.8419			2.09216
$546$		0			0
$547$	−7.71216			−0.329748			−0.164874	−	0.986315i	$-0.552722\pi$
$547$	−7.71216			−0.329748			−0.164874	+	0.986315i	$0.552722\pi$
$548$	33.8338	−	58.6018i	1.44531	−	2.50335i
$549$		0			0
$550$	36.9110	+	63.9317i	1.57389	+	2.72606i
$551$	−11.0875	+	19.2041i	−0.472343	+	0.818122i
$552$		0			0
$553$	8.93458	−	16.5509i	0.379937	−	0.703814i
$554$	24.7819			1.05288
$555$		0			0
$556$	−32.4461	−	56.1983i	−1.37602	−	2.38334i
$557$	−16.6240	−	28.7937i	−0.704383	−	1.22003i	−0.966914	−	0.255104i	$-0.917890\pi$
$557$	−16.6240	−	28.7937i	−0.704383	−	1.22003i	0.262531	−	0.964924i	$-0.415443\pi$
$558$		0			0
$559$	15.7145			0.664654
$560$	−15.2262	−	24.7125i	−0.643426	−	1.04429i
$561$		0			0
$562$	−2.13297	+	3.69441i	−0.0899739	+	0.155839i
$563$	10.6025	+	18.3640i	0.446841	+	0.773952i	0.998178	−	0.0603305i	$-0.0192155\pi$
$563$	10.6025	+	18.3640i	0.446841	+	0.773952i	−0.551337	+	0.834283i	$0.685882\pi$
$564$		0			0
$565$	30.0383	−	52.0278i	1.26372	−	2.18883i
$566$	30.8364			1.29615
$567$		0			0
$568$	−45.3816			−1.90417
$569$	−10.7030	+	18.5381i	−0.448691	+	0.777156i	−0.998301	−	0.0582653i	$-0.981443\pi$
$569$	−10.7030	+	18.5381i	−0.448691	+	0.777156i	0.549610	+	0.835421i	$0.314776\pi$
$570$		0			0
$571$	−1.25694	−	2.17709i	−0.0526014	−	0.0911083i	0.838526	−	0.544862i	$-0.183418\pi$
$571$	−1.25694	−	2.17709i	−0.0526014	−	0.0911083i	−0.891127	+	0.453754i	$0.850085\pi$
$572$	−20.4097	+	35.3506i	−0.853371	+	1.47808i
$573$		0			0
$574$	−6.98873	+	12.9463i	−0.291704	+	0.540367i
$575$	83.8587			3.49715
$576$		0			0
$577$	−12.7436	−	22.0726i	−0.530523	−	0.918893i	−0.999366	−	0.0356110i	$-0.988662\pi$
$577$	−12.7436	−	22.0726i	−0.530523	−	0.918893i	0.468843	−	0.883282i	$-0.344671\pi$
$578$	1.19803	+	2.07505i	0.0498315	+	0.0863106i
$579$		0			0
$580$	−140.361			−5.82818
$581$	−1.65325	+	0.0472970i	−0.0685883	+	0.00196221i
$582$		0			0
$583$	−3.13432	+	5.42880i	−0.129810	+	0.224838i
$584$	17.4670	+	30.2537i	0.722789	+	1.25191i
$585$		0			0
$586$	25.8545	−	44.7814i	1.06804	−	1.84990i
$587$	6.39447			0.263928			0.131964	−	0.991255i	$-0.457872\pi$
$587$	6.39447			0.263928			0.131964	+	0.991255i	$0.457872\pi$
$588$		0			0
$589$	−8.39609			−0.345955
$590$	−39.5345	+	68.4758i	−1.62761	+	2.81910i
$591$		0			0
$592$	−8.59155	−	14.8810i	−0.353110	−	0.611605i
$593$	−5.98440	+	10.3653i	−0.245750	+	0.425651i	−0.962342	−	0.271841i	$-0.912368\pi$
$593$	−5.98440	+	10.3653i	−0.245750	+	0.425651i	0.716592	+	0.697492i	$0.245701\pi$
$594$		0			0
$595$	−11.5430	+	0.330228i	−0.473217	+	0.0135380i
$596$	−48.0969			−1.97012
$597$		0			0
$598$	35.5791	+	61.6247i	1.45494	+	2.52002i
$599$	−1.76721	−	3.06089i	−0.0722061	−	0.125065i	0.827662	−	0.561227i	$-0.189671\pi$
$599$	−1.76721	−	3.06089i	−0.0722061	−	0.125065i	−0.899868	+	0.436163i	$0.856337\pi$
$600$		0			0
$601$	−42.9126			−1.75044			−0.875222	−	0.483722i	$-0.839284\pi$
$601$	−42.9126			−1.75044			−0.875222	+	0.483722i	$0.839284\pi$
$602$	−9.51071	+	17.6181i	−0.387628	+	0.718061i
$603$		0			0
$604$	12.7386	−	22.0640i	0.518328	−	0.897771i
$605$	−13.5115	−	23.4027i	−0.549322	−	0.951453i
$606$		0			0
$607$	13.4819	−	23.3513i	0.547213	−	0.947801i	−0.451251	−	0.892397i	$-0.649022\pi$
$607$	13.4819	−	23.3513i	0.547213	−	0.947801i	0.998464	−	0.0554040i	$-0.0176447\pi$
$608$	5.98679			0.242796
$609$		0			0
$610$	61.9601			2.50869
$611$	0.456785	−	0.791175i	0.0184796	−	0.0320075i
$612$		0			0
$613$	−5.29975	−	9.17944i	−0.214055	−	0.370754i	0.738925	−	0.673788i	$-0.235334\pi$
$613$	−5.29975	−	9.17944i	−0.214055	−	0.370754i	−0.952980	+	0.303034i	$0.902000\pi$
$614$	−29.1290	+	50.4530i	−1.17555	+	2.03612i
$615$		0			0
$616$	−12.6963	−	20.6063i	−0.511548	−	0.830252i
$617$	−23.5671			−0.948775			−0.474388	−	0.880316i	$-0.657330\pi$
$617$	−23.5671			−0.948775			−0.474388	+	0.880316i	$0.657330\pi$
$618$		0			0
$619$	4.84300	+	8.38832i	0.194657	+	0.337155i	0.946788	−	0.321858i	$-0.104307\pi$
$619$	4.84300	+	8.38832i	0.194657	+	0.337155i	−0.752131	+	0.659013i	$0.770974\pi$
$620$	−26.5724	−	46.0247i	−1.06717	−	1.84840i
$621$		0			0
$622$	−35.5083			−1.42375
$623$	−1.20569	+	2.23347i	−0.0483048	+	0.0894823i
$624$		0			0
$625$	−51.0766	+	88.4673i	−2.04306	+	3.53869i
$626$	−11.5328	−	19.9755i	−0.460945	−	0.798380i
$627$		0			0
$628$	−13.5823	+	23.5252i	−0.541991	+	0.938756i
$629$	−6.83599			−0.272569
$630$		0			0
$631$	43.5486			1.73364			0.866822	−	0.498618i	$-0.166159\pi$
$631$	43.5486			1.73364			0.866822	+	0.498618i	$0.166159\pi$
$632$	14.8284	−	25.6836i	0.589843	−	1.02164i
$633$		0			0
$634$	27.5017	+	47.6344i	1.09223	+	1.89180i
$635$	9.54408	−	16.5308i	0.378745	−	0.656006i
$636$		0			0
$637$	34.7731	−	1.99124i	1.37776	−	0.0788959i
$638$	−45.1656			−1.78812
$639$		0			0
$640$	45.2346	+	78.3486i	1.78805	+	3.09700i
$641$	2.92920	+	5.07352i	0.115696	+	0.200392i	0.918058	−	0.396446i	$-0.129757\pi$
$641$	2.92920	+	5.07352i	0.115696	+	0.200392i	−0.802361	+	0.596838i	$0.796423\pi$
$642$		0			0
$643$	23.5636			0.929257			0.464629	−	0.885506i	$-0.346188\pi$
$643$	23.5636			0.929257			0.464629	+	0.885506i	$0.346188\pi$
$644$	−59.0529	+	1.68941i	−2.32701	+	0.0665723i
$645$		0			0
$646$	−3.09051	+	5.35293i	−0.121595	+	0.210608i
$647$	−6.14288	−	10.6398i	−0.241502	−	0.418293i	0.719641	−	0.694347i	$-0.244307\pi$
$647$	−6.14288	−	10.6398i	−0.241502	−	0.418293i	−0.961142	+	0.276054i	$0.910973\pi$
$648$		0			0
$649$	−8.28976	+	14.3583i	−0.325401	+	0.563612i
$650$	−167.506			−6.57014
$651$		0			0
$652$	−11.7245			−0.459166
$653$	−9.69477	+	16.7918i	−0.379386	+	0.657116i	−0.990973	−	0.134061i	$-0.957198\pi$
$653$	−9.69477	+	16.7918i	−0.379386	+	0.657116i	0.611587	+	0.791177i	$0.290531\pi$
$654$		0			0
$655$	15.6159	+	27.0475i	0.610162	+	1.05683i
$656$	−2.91676	+	5.05198i	−0.113880	+	0.197247i
$657$		0			0
$658$	0.610560	+	0.990951i	0.0238021	+	0.0386313i
$659$	−3.43238			−0.133707			−0.0668533	−	0.997763i	$-0.521296\pi$
$659$	−3.43238			−0.133707			−0.0668533	+	0.997763i	$0.521296\pi$
$660$		0			0
$661$	−6.29680	−	10.9064i	−0.244917	−	0.424209i	0.717191	−	0.696876i	$-0.245427\pi$
$661$	−6.29680	−	10.9064i	−0.244917	−	0.424209i	−0.962108	+	0.272668i	$0.912094\pi$
$662$	16.5968	+	28.7464i	0.645051	+	1.11726i
$663$		0			0
$664$	−2.60788			−0.101205
$665$	−15.6263	−	25.3618i	−0.605962	−	0.983488i
$666$		0			0
$667$	−25.6531	+	44.4325i	−0.993293	+	1.72043i
$668$	39.9560	+	69.2058i	1.54594	+	2.67765i
$669$		0			0
$670$	−8.38432	+	14.5221i	−0.323915	+	0.561037i
$671$	12.9920			0.501552
$672$		0			0
$673$	26.6163			1.02598			0.512992	−	0.858393i	$-0.328537\pi$
$673$	26.6163			1.02598			0.512992	+	0.858393i	$0.328537\pi$
$674$	29.4376	−	50.9874i	1.13389	−	1.96396i
$675$		0			0
$676$	−21.9936	−	38.0940i	−0.845907	−	1.46515i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$		0			0
$679$	17.0162	−	0.486808i	0.653021	−	0.0186820i
$680$	−18.2083			−0.698255
$681$		0			0
$682$	−8.55051	−	14.8099i	−0.327416	−	0.567101i
$683$	18.7560	+	32.4863i	0.717678	+	1.24305i	0.961918	+	0.273340i	$0.0881283\pi$
$683$	18.7560	+	32.4863i	0.717678	+	1.24305i	−0.244240	+	0.969715i	$0.578538\pi$
$684$		0			0
$685$	78.9458			3.01637
$686$	−18.8128	+	40.1905i	−0.718277	+	1.53448i
$687$		0			0
$688$	−3.96931	+	6.87505i	−0.151329	+	0.262109i
$689$	−7.11196	−	12.3183i	−0.270944	−	0.469289i
$690$		0			0
$691$	12.5446	−	21.7279i	0.477219	−	0.826567i	−0.522441	−	0.852676i	$-0.674978\pi$
$691$	12.5446	−	21.7279i	0.477219	−	0.826567i	0.999659	+	0.0261090i	$0.00831169\pi$
$692$	−30.4526			−1.15764
$693$		0			0
$694$	−55.3633			−2.10156
$695$	37.8539	−	65.5649i	1.43588	−	2.48702i
$696$		0			0
$697$	1.16038	+	2.00984i	0.0439526	+	0.0761281i
$698$	24.5343	−	42.4946i	0.928635	−	1.60844i
$699$		0			0
$700$	66.0612	−	122.375i	2.49688	−	4.62535i
$701$	8.29504			0.313300			0.156650	−	0.987654i	$-0.449931\pi$
$701$	8.29504			0.313300			0.156650	+	0.987654i	$0.449931\pi$
$702$		0			0
$703$	−8.81728	−	15.2720i	−0.332550	−	0.575993i
$704$	11.6089	+	20.1072i	0.437528	+	0.757820i
$705$		0			0
$706$	−4.97199			−0.187123
$707$	14.5993	+	23.6949i	0.549062	+	0.891138i
$708$		0			0
$709$	9.63068	−	16.6808i	0.361688	−	0.626462i	−0.626551	−	0.779381i	$-0.715534\pi$
$709$	9.63068	−	16.6808i	0.361688	−	0.626462i	0.988239	+	0.152919i	$0.0488673\pi$
$710$	−56.8820	−	98.5225i	−2.13474	−	3.69748i
$711$		0			0
$712$	−2.00104	+	3.46590i	−0.0749921	+	0.129890i
$713$	−19.4260			−0.727511
$714$		0			0
$715$	−47.6228			−1.78099
$716$	−27.5460	+	47.7111i	−1.02944	+	1.78305i
$717$		0			0
$718$	−10.1268	−	17.5401i	−0.377927	−	0.654589i
$719$	21.7489	−	37.6702i	0.811098	−	1.40486i	−0.100998	−	0.994887i	$-0.532204\pi$
$719$	21.7489	−	37.6702i	0.811098	−	1.40486i	0.912096	−	0.409976i	$-0.134463\pi$
$720$		0			0
$721$	−2.73014	+	5.05745i	−0.101676	+	0.188349i
$722$	29.5801			1.10086
$723$		0			0
$724$	38.6168	+	66.8862i	1.43518	+	2.48581i
$725$	−60.3875	−	104.594i	−2.24274	−	3.88453i
$726$		0			0
$727$	9.10836			0.337810			0.168905	−	0.985632i	$-0.445977\pi$
$727$	9.10836			0.337810			0.168905	+	0.985632i	$0.445977\pi$
$728$	54.8970	−	1.57052i	2.03462	−	0.0582074i
$729$		0			0
$730$	−43.7867	+	75.8408i	−1.62062	+	2.80700i
$731$	1.57912	+	2.73512i	0.0584059	+	0.101162i
$732$		0			0
$733$	−15.9462	+	27.6197i	−0.588987	+	1.02016i	0.405378	+	0.914149i	$0.367140\pi$
$733$	−15.9462	+	27.6197i	−0.588987	+	1.02016i	−0.994365	+	0.106007i	$0.966194\pi$
$734$	61.4200			2.26705
$735$		0			0
$736$	13.8517			0.510579
$737$	−1.75806	+	3.04505i	−0.0647589	+	0.112166i
$738$		0			0
$739$	−23.8982	−	41.3928i	−0.879108	−	1.52266i	−0.852321	−	0.523019i	$-0.824806\pi$
$739$	−23.8982	−	41.3928i	−0.879108	−	1.52266i	−0.0267867	−	0.999641i	$-0.508527\pi$
$740$	55.8108	−	96.6672i	2.05165	−	3.55356i
$741$		0			0
$742$	18.1147	−	0.518235i	0.665012	−	0.0190250i
$743$	−9.63256			−0.353385			−0.176692	−	0.984266i	$-0.556540\pi$
$743$	−9.63256			−0.353385			−0.176692	+	0.984266i	$0.556540\pi$
$744$		0			0
$745$	−28.0566	−	48.5955i	−1.02792	−	1.78040i
$746$	8.10543	+	14.0390i	0.296761	+	0.514005i
$747$		0			0
$748$	−8.20370			−0.299957
$749$	−4.01683	+	7.44099i	−0.146772	+	0.271888i
$750$		0			0
$751$	−6.83617	+	11.8406i	−0.249455	+	0.432069i	−0.963375	−	0.268159i	$-0.913585\pi$
$751$	−6.83617	+	11.8406i	−0.249455	+	0.432069i	0.713919	+	0.700228i	$0.246918\pi$
$752$	0.230758	+	0.399684i	0.00841486	+	0.0145750i
$753$		0			0
$754$	51.2417	−	88.7532i	1.86611	−	3.23220i
$755$	29.7236			1.08175
$756$		0			0
$757$	−6.75888			−0.245656			−0.122828	−	0.992428i	$-0.539196\pi$
$757$	−6.75888			−0.245656			−0.122828	+	0.992428i	$0.539196\pi$
$758$	−24.7394	+	42.8499i	−0.898575	+	1.55638i
$759$		0			0
$760$	−23.4856	−	40.6783i	−0.851913	−	1.47556i
$761$	24.3809	−	42.2289i	0.883805	−	1.53080i	0.0367281	−	0.999325i	$-0.488306\pi$
$761$	24.3809	−	42.2289i	0.883805	−	1.53080i	0.847077	−	0.531470i	$-0.178360\pi$
$762$		0			0
$763$	−15.5307	−	25.2066i	−0.562248	−	0.912539i
$764$	−64.8523			−2.34627
$765$		0			0
$766$	−19.7627	−	34.2300i	−0.714055	−	1.23678i
$767$	−18.8099	−	32.5798i	−0.679188	−	1.17639i
$768$		0			0
$769$	−5.85163			−0.211015			−0.105508	−	0.994419i	$-0.533647\pi$
$769$	−5.85163			−0.211015			−0.105508	+	0.994419i	$0.533647\pi$
$770$	28.8221	−	53.3916i	1.03868	−	1.92410i
$771$		0			0
$772$	1.05022	−	1.81903i	0.0377982	−	0.0654683i
$773$	4.54763	+	7.87672i	0.163567	+	0.283306i	0.936145	−	0.351613i	$-0.114367\pi$
$773$	4.54763	+	7.87672i	0.163567	+	0.283306i	−0.772579	+	0.634919i	$0.781033\pi$
$774$		0			0
$775$	22.8645	−	39.6024i	0.821316	−	1.42256i
$776$	26.8418			0.963565
$777$		0			0
$778$	72.4616			2.59788
$779$	−2.99340	+	5.18471i	−0.107250	+	0.185762i
$780$		0			0
$781$	−11.9272	−	20.6586i	−0.426790	−	0.739222i
$782$	−7.15053	+	12.3851i	−0.255702	+	0.442890i
$783$		0			0
$784$	−7.91213	+	15.7161i	−0.282576	+	0.561288i
$785$	−31.6921			−1.13114
$786$		0			0
$787$	−3.76255	−	6.51693i	−0.134120	−	0.232303i	0.791141	−	0.611634i	$-0.209488\pi$
$787$	−3.76255	−	6.51693i	−0.134120	−	0.232303i	−0.925261	+	0.379331i	$0.876154\pi$
$788$	−3.50388	−	6.06890i	−0.124821	−	0.216196i
$789$		0			0
$790$	74.3446			2.64506
$791$	−36.4023	+	1.04141i	−1.29432	+	0.0370284i
$792$		0			0
$793$	−14.7398	+	25.5302i	−0.523427	+	0.906603i
$794$	18.5279	+	32.0912i	0.657530	+	1.13888i
$795$		0			0
$796$	12.7534	−	22.0895i	0.452031	−	0.782941i
$797$	−26.6126			−0.942666			−0.471333	−	0.881955i	$-0.656227\pi$
$797$	−26.6126			−0.942666			−0.471333	+	0.881955i	$0.656227\pi$
$798$		0			0
$799$	0.183606			0.00649550
$800$	−16.3034	+	28.2383i	−0.576412	+	0.998375i
$801$		0			0
$802$	23.0327	+	39.8938i	0.813314	+	1.40870i
$803$	−9.18138	+	15.9026i	−0.324004	+	0.561191i
$804$		0			0
$805$	−36.1546	−	58.6796i	−1.27428	−	2.06819i
$806$	38.8032			1.36678
$807$		0			0
$808$	21.9420	+	38.0047i	0.771918	+	1.33700i
$809$	−3.17606	−	5.50109i	−0.111664	−	0.193408i	0.804777	−	0.593577i	$-0.202285\pi$
$809$	−3.17606	−	5.50109i	−0.111664	−	0.193408i	−0.916441	+	0.400169i	$0.868951\pi$
$810$		0			0
$811$	7.80208			0.273968			0.136984	−	0.990573i	$-0.456259\pi$
$811$	7.80208			0.273968			0.136984	+	0.990573i	$0.456259\pi$
$812$	44.6318	+	72.4382i	1.56627	+	2.54208i
$813$		0			0
$814$	17.9589	−	31.1057i	0.629459	−	1.09025i
$815$	−6.83931	−	11.8460i	−0.239570	−	0.414948i
$816$		0			0
$817$	−4.07360	+	7.05569i	−0.142517	+	0.246847i
$818$	68.6986			2.40199
$819$		0			0
$820$	−37.8946			−1.32334
$821$	25.5601	−	44.2713i	0.892053	−	1.54508i	0.0546419	−	0.998506i	$-0.482598\pi$
$821$	25.5601	−	44.2713i	0.892053	−	1.54508i	0.837411	−	0.546574i	$-0.184068\pi$
$822$		0			0
$823$	−26.6959	−	46.2386i	−0.930560	−	1.61178i	−0.782366	−	0.622819i	$-0.785987\pi$
$823$	−26.6959	−	46.2386i	−0.930560	−	1.61178i	−0.148194	−	0.988958i	$-0.547346\pi$
$824$	−4.53113	+	7.84814i	−0.157849	+	0.273403i
$825$		0			0
$826$	47.9104	−	1.37065i	1.66702	−	0.0476909i
$827$	−31.7470			−1.10395			−0.551976	−	0.833860i	$-0.686126\pi$
$827$	−31.7470			−1.10395			−0.551976	+	0.833860i	$0.686126\pi$
$828$		0			0
$829$	−12.4345	−	21.5372i	−0.431869	−	0.748018i	0.565166	−	0.824977i	$-0.308812\pi$
$829$	−12.4345	−	21.5372i	−0.431869	−	0.748018i	−0.997034	+	0.0769591i	$0.975479\pi$
$830$	−3.26875	−	5.66165i	−0.113460	−	0.196519i
$831$		0			0
$832$	−52.6826			−1.82644
$833$	3.84085	+	5.85217i	0.133078	+	0.202766i
$834$		0			0
$835$	−46.6155	+	80.7405i	−1.61320	+	2.79414i
$836$	−10.5814	−	18.3275i	−0.365965	−	0.633871i
$837$		0			0
$838$	−24.3079	+	42.1026i	−0.839704	+	1.45441i
$839$	10.8963			0.376184			0.188092	−	0.982151i	$-0.439770\pi$
$839$	10.8963			0.376184			0.188092	+	0.982151i	$0.439770\pi$
$840$		0			0
$841$	44.8924			1.54801
$842$	−45.7227	+	79.1940i	−1.57571	+	2.72920i
$843$		0			0
$844$	−4.78092	−	8.28079i	−0.164566	−	0.285037i
$845$	25.6593	−	44.4432i	0.882707	−	1.52889i
$846$		0			0
$847$	−7.78138	+	14.4146i	−0.267371	+	0.495292i
$848$	7.18560			0.246754
$849$		0			0
$850$	−16.8324	−	29.1545i	−0.577345	−	0.999991i
$851$	−20.4006	−	35.3348i	−0.699322	−	1.21126i
$852$		0			0
$853$	−12.7086			−0.435134			−0.217567	−	0.976045i	$-0.569812\pi$
$853$	−12.7086			−0.435134			−0.217567	+	0.976045i	$0.569812\pi$
$854$	−19.7020	−	31.9767i	−0.674187	−	1.09422i
$855$		0			0
$856$	−6.66660	+	11.5469i	−0.227860	+	0.394665i
$857$	−9.21088	−	15.9537i	−0.314638	−	0.544969i	0.664723	−	0.747090i	$-0.268550\pi$
$857$	−9.21088	−	15.9537i	−0.314638	−	0.544969i	−0.979360	+	0.202122i	$0.935216\pi$
$858$		0			0
$859$	−15.3763	+	26.6325i	−0.524632	+	0.908689i	0.474957	+	0.880009i	$0.342464\pi$
$859$	−15.3763	+	26.6325i	−0.524632	+	0.908689i	−0.999589	+	0.0286799i	$0.990870\pi$
$860$	−51.5694			−1.75850
$861$		0			0
$862$	78.5458			2.67528
$863$	−25.1654	+	43.5878i	−0.856641	+	1.48375i	0.0184737	+	0.999829i	$0.494119\pi$
$863$	−25.1654	+	43.5878i	−0.856641	+	1.48375i	−0.875114	+	0.483916i	$0.839214\pi$
$864$		0			0
$865$	−17.7641	−	30.7684i	−0.603998	−	1.04616i
$866$	5.90351	−	10.2252i	0.200610	−	0.347466i
$867$		0			0
$868$	−15.3032	+	28.3485i	−0.519425	+	0.962210i
$869$	15.5889			0.528816
$870$		0			0
$871$	−3.98914	−	6.90939i	−0.135167	−	0.234116i
$872$	−23.3419	−	40.4293i	−0.790456	−	1.36911i
$873$		0			0
$874$	−36.8919			−1.24789
$875$	104.465	−	2.98858i	3.53155	−	0.101032i
$876$		0			0
$877$	−27.0243	+	46.8075i	−0.912546	+	1.58058i	−0.102091	+	0.994775i	$0.532553\pi$
$877$	−27.0243	+	46.8075i	−0.912546	+	1.58058i	−0.810455	+	0.585801i	$0.800780\pi$
$878$	48.6556	+	84.2740i	1.64205	+	2.84411i
$879$		0			0
$880$	12.0290	−	20.8348i	0.405497	−	0.702341i
$881$	−54.8806			−1.84898			−0.924488	−	0.381212i	$-0.875507\pi$
$881$	−54.8806			−1.84898			−0.924488	+	0.381212i	$0.875507\pi$
$882$		0			0
$883$	2.87978			0.0969124			0.0484562	−	0.998825i	$-0.484570\pi$
$883$	2.87978			0.0969124			0.0484562	+	0.998825i	$0.484570\pi$
$884$	9.30734	−	16.1208i	0.313040	−	0.542201i
$885$		0			0
$886$	39.7566	+	68.8604i	1.33565	+	2.31341i
$887$	−14.9536	+	25.9004i	−0.502093	+	0.869650i	0.497904	+	0.867232i	$0.334103\pi$
$887$	−14.9536	+	25.9004i	−0.502093	+	0.869650i	−0.999997	+	0.00241828i	$0.999230\pi$
$888$		0			0
$889$	−11.5661	+	0.330889i	−0.387915	+	0.0110977i
$890$	−10.0325			−0.336291
$891$		0			0
$892$	−35.8569	−	62.1060i	−1.20058	−	2.07946i
$893$	0.236820	+	0.410185i	0.00792489	+	0.0137263i
$894$		0			0
$895$	−64.2744			−2.14846
$896$	26.0509	−	48.2580i	0.870300	−	1.61219i
$897$		0			0
$898$	1.97972	−	3.42898i	0.0660642	−	0.114427i
$899$	13.9889	+	24.2295i	0.466556	+	0.808099i
$900$		0			0
$901$	1.42933	−	2.47567i	0.0476179	−	0.0824767i
$902$	−12.1938			−0.406009
$903$		0			0
$904$	−57.4219			−1.90983
$905$	−45.0531	+	78.0342i	−1.49762	+	2.59395i
$906$		0			0
$907$	13.5091	+	23.3984i	0.448561	+	0.776931i	0.998293	−	0.0584105i	$-0.0186032\pi$
$907$	13.5091	+	23.3984i	0.448561	+	0.776931i	−0.549731	+	0.835342i	$0.685270\pi$
$908$	−3.50925	+	6.07819i	−0.116458	+	0.201712i
$909$		0			0
$910$	72.2182	+	117.212i	2.39401	+	3.88553i
$911$	−5.30202			−0.175664			−0.0878318	−	0.996135i	$-0.527994\pi$
$911$	−5.30202			−0.175664			−0.0878318	+	0.996135i	$0.527994\pi$
$912$		0			0
$913$	−0.685405	−	1.18716i	−0.0226836	−	0.0392892i
$914$	40.2809	+	69.7685i	1.33237	+	2.30774i
$915$		0			0
$916$	21.6901			0.716661
$917$	8.99328	−	16.6596i	0.296984	−	0.550149i
$918$		0			0
$919$	12.5494	−	21.7361i	0.413965	−	0.717009i	−0.581354	−	0.813651i	$-0.697477\pi$
$919$	12.5494	−	21.7361i	0.413965	−	0.717009i	0.995319	+	0.0966420i	$0.0308102\pi$
$920$	−54.3387	−	94.1174i	−1.79149	−	3.10296i
$921$		0			0
$922$	−2.47458	+	4.28610i	−0.0814959	+	0.141155i
$923$	54.1272			1.78162
$924$		0			0
$925$	96.0459			3.15797
$926$	24.3358	−	42.1508i	0.799724	−	1.38516i
$927$		0			0
$928$	−9.97472	−	17.2767i	−0.327436	−	0.567136i
$929$	8.14447	−	14.1066i	0.267212	−	0.462824i	−0.700929	−	0.713231i	$-0.747231\pi$
$929$	8.14447	−	14.1066i	0.267212	−	0.462824i	0.968141	+	0.250407i	$0.0805644\pi$
$930$		0			0
$931$	−8.12001	+	16.1290i	−0.266123	+	0.528606i
$932$	8.65139			0.283386
$933$		0			0
$934$	−14.4288	−	24.9914i	−0.472124	−	0.817743i
$935$	−4.78551	−	8.28875i	−0.156503	−	0.271071i
$936$		0			0
$937$	9.08956			0.296943			0.148471	−	0.988917i	$-0.452565\pi$
$937$	9.08956			0.296943			0.148471	+	0.988917i	$0.452565\pi$
$938$	10.1606	−	0.290681i	0.331757	−	0.00949107i
$939$		0			0
$940$	−1.49900	+	2.59635i	−0.0488921	+	0.0846837i
$941$	−27.8005	−	48.1519i	−0.906271	−	1.56971i	−0.819202	−	0.573505i	$-0.805583\pi$
$941$	−27.8005	−	48.1519i	−0.906271	−	1.56971i	−0.0870689	−	0.996202i	$-0.527750\pi$
$942$		0			0
$943$	−6.92583	+	11.9959i	−0.225536	+	0.390640i
$944$	19.0047			0.618551
$945$		0			0
$946$	−16.5941			−0.539520
$947$	2.65557	−	4.59959i	0.0862946	−	0.149467i	−0.819648	−	0.572868i	$-0.805831\pi$
$947$	2.65557	−	4.59959i	0.0862946	−	0.149467i	0.905942	+	0.423402i	$0.139164\pi$
$948$		0			0
$949$	−20.8331	−	36.0839i	−0.676270	−	1.17133i
$950$	43.4218	−	75.2088i	1.40879	−	2.44010i
$951$		0			0
$952$	5.78983	+	9.39701i	0.187650	+	0.304559i
$953$	−40.9327			−1.32594			−0.662971	−	0.748645i	$-0.730705\pi$
$953$	−40.9327			−1.32594			−0.662971	+	0.748645i	$0.730705\pi$
$954$		0			0
$955$	−37.8307	−	65.5246i	−1.22417	−	2.12033i
$956$	−35.7892	−	61.9887i	−1.15751	−	2.00486i
$957$		0			0
$958$	0.509291			0.0164545
$959$	−25.1030	−	40.7427i	−0.810620	−	1.31565i
$960$		0			0
$961$	10.2034	−	17.6728i	0.329142	−	0.570090i
$962$	40.7498	+	70.5807i	1.31383	+	2.27561i
$963$		0			0
$964$	23.9536	−	41.4889i	0.771494	−	1.33627i
$965$	2.45052			0.0788850
$966$		0			0
$967$	52.0112			1.67257			0.836284	−	0.548296i	$-0.184723\pi$
$967$	52.0112			1.67257			0.836284	+	0.548296i	$0.184723\pi$
$968$	−12.9145	+	22.3686i	−0.415088	+	0.718953i
$969$		0			0
$970$	33.6439	+	58.2729i	1.08024	+	1.87103i
$971$	9.32140	−	16.1451i	0.299138	−	0.518122i	−0.676801	−	0.736166i	$-0.736634\pi$
$971$	9.32140	−	16.1451i	0.299138	−	0.518122i	0.975939	+	0.218044i	$0.0699675\pi$
$972$		0			0
$973$	−45.8738	+	1.31238i	−1.47065	+	0.0420730i
$974$	83.0036			2.65961
$975$		0			0
$976$	−7.44623	−	12.8973i	−0.238348	−	0.412831i
$977$	9.24492	+	16.0127i	0.295771	+	0.512291i	0.975164	−	0.221484i	$-0.0710901\pi$
$977$	9.24492	+	16.0127i	0.295771	+	0.512291i	−0.679393	+	0.733775i	$0.737757\pi$
$978$		0			0
$979$	−2.10366			−0.0672332
$980$	−114.113	+	6.53454i	−3.64520	+	0.208738i
$981$		0			0
$982$	31.7175	−	54.9363i	1.01215	−	1.75309i
$983$	12.4403	+	21.5472i	0.396784	+	0.687249i	0.993327	−	0.115331i	$-0.0367930\pi$
$983$	12.4403	+	21.5472i	0.396784	+	0.687249i	−0.596544	+	0.802581i	$0.703460\pi$
$984$		0			0
$985$	4.08788	−	7.08042i	0.130251	−	0.225601i
$986$	20.5967			0.655932
$987$		0			0
$988$	48.0196			1.52771
$989$	−9.42510	+	16.3248i	−0.299701	+	0.519097i
$990$		0			0
$991$	8.08189	+	13.9982i	0.256730	+	0.444669i	0.965364	−	0.260907i	$-0.0840216\pi$
$991$	8.08189	+	13.9982i	0.256730	+	0.444669i	−0.708634	+	0.705576i	$0.750688\pi$
$992$	3.77672	−	6.54147i	0.119911	−	0.207692i
$993$		0			0
$994$	−32.7587	+	60.6839i	−1.03904	+	1.92478i
$995$	29.7580			0.943392
$996$		0			0
$997$	−9.16220	−	15.8694i	−0.290170	−	0.502589i	0.683680	−	0.729782i	$-0.260378\pi$
$997$	−9.16220	−	15.8694i	−0.290170	−	0.502589i	−0.973850	+	0.227193i	$0.927045\pi$
$998$	−35.3812	−	61.2820i	−1.11997	−	1.93985i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.i.g.919.5		10
3.2	odd	2		357.2.i.f.205.1	✓	10
7.2	even	3		7497.2.a.bv.1.1		5
7.4	even	3	inner	1071.2.i.g.613.5		10
7.5	odd	6		7497.2.a.bw.1.1		5
21.2	odd	6		2499.2.a.ba.1.5		5
21.5	even	6		2499.2.a.bb.1.5		5
21.11	odd	6		357.2.i.f.256.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.f.205.1	✓	10	3.2	odd	2
357.2.i.f.256.1	yes	10	21.11	odd	6
1071.2.i.g.613.5		10	7.4	even	3	inner
1071.2.i.g.919.5		10	1.1	even	1	trivial
2499.2.a.ba.1.5		5	21.2	odd	6
2499.2.a.bb.1.5		5	21.5	even	6
7497.2.a.bv.1.1		5	7.2	even	3
7497.2.a.bw.1.1		5	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19803 - 2.07505i) q^{2} +(-1.87055 - 3.23989i) q^{4} +(2.18232 - 3.77988i) q^{5} +(-2.64467 + 0.0756600i) q^{7} -4.17178 q^{8} +O(q^{10})\)	\(q+(1.19803 - 2.07505i) q^{2} +(-1.87055 - 3.23989i) q^{4} +(2.18232 - 3.77988i) q^{5} +(-2.64467 + 0.0756600i) q^{7} -4.17178 q^{8} +(-5.22896 - 9.05683i) q^{10} +(-1.09643 - 1.89907i) q^{11} +4.97572 q^{13} +(-3.01139 + 5.57846i) q^{14} +(-1.25681 + 2.17686i) q^{16} +(0.500000 + 0.866025i) q^{17} +(-1.28983 + 2.23406i) q^{19} -16.3285 q^{20} -5.25422 q^{22} +(-2.98429 + 5.16894i) q^{23} +(-7.02502 - 12.1677i) q^{25} +(5.96106 - 10.3249i) q^{26} +(5.19211 + 8.42690i) q^{28} +8.59607 q^{29} +(1.62736 + 2.81867i) q^{31} +(-1.16038 - 2.00984i) q^{32} +2.39606 q^{34} +(-5.48552 + 10.1617i) q^{35} +(-3.41799 + 5.92014i) q^{37} +(3.09051 + 5.35293i) q^{38} +(-9.10414 + 15.7688i) q^{40} +2.32076 q^{41} +3.15824 q^{43} +(-4.10185 + 7.10461i) q^{44} +(7.15053 + 12.3851i) q^{46} +(0.0918028 - 0.159007i) q^{47} +(6.98855 - 0.400192i) q^{49} -33.6647 q^{50} +(-9.30734 - 16.1208i) q^{52} +(-1.42933 - 2.47567i) q^{53} -9.57103 q^{55} +(11.0330 - 0.315637i) q^{56} +(10.2983 - 17.8372i) q^{58} +(-3.78034 - 6.54775i) q^{59} +(-2.96235 + 5.13094i) q^{61} +7.79850 q^{62} -10.5879 q^{64} +(10.8586 - 18.8077i) q^{65} +(-0.801720 - 1.38862i) q^{67} +(1.87055 - 3.23989i) q^{68} +(14.5141 + 23.5567i) q^{70} +10.8783 q^{71} +(-4.18694 - 7.25200i) q^{73} +(8.18972 + 14.1850i) q^{74} +9.65078 q^{76} +(3.04338 + 4.93946i) q^{77} +(-3.55446 + 6.15651i) q^{79} +(5.48552 + 9.50120i) q^{80} +(2.78034 - 4.81570i) q^{82} +0.625125 q^{83} +4.36463 q^{85} +(3.78367 - 6.55350i) q^{86} +(4.57406 + 7.92250i) q^{88} +(0.479661 - 0.830797i) q^{89} +(-13.1591 + 0.376463i) q^{91} +22.3290 q^{92} +(-0.219965 - 0.380990i) q^{94} +(5.62965 + 9.75083i) q^{95} -6.43415 q^{97} +(7.54207 - 14.9810i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7}+O(q^{10}) \) 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7	\( 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7} - 13 q^{10} - 11 q^{11} + 14 q^{13} - 3 q^{14} + 2 q^{16} + 5 q^{17} - 9 q^{19} - 24 q^{20} + 10 q^{22} - 23 q^{23} - 14 q^{25} + 18 q^{26} + 7 q^{28} + 36 q^{29} - 9 q^{31} + 3 q^{32} - 4 q^{34} + 5 q^{35} - 31 q^{40} - 6 q^{41} + 24 q^{43} - 33 q^{44} - 13 q^{46} + 11 q^{47} + 3 q^{49} - 48 q^{50} - 5 q^{52} - 3 q^{53} - 20 q^{55} + 27 q^{56} + 34 q^{58} - 14 q^{59} - 29 q^{61} + 10 q^{62} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 18 q^{70} + 38 q^{71} - 11 q^{73} + 45 q^{74} + 18 q^{76} - 21 q^{77} - q^{79} - 5 q^{80} + 4 q^{82} - 10 q^{83} + 2 q^{85} - 3 q^{86} - 37 q^{88} + 8 q^{89} - 33 q^{91} + 96 q^{92} + 18 q^{94} - 21 q^{95} + 38 q^{97} + 17 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7 - 13 * q^10 - 11 * q^11 + 14 * q^13 - 3 * q^14 + 2 * q^16 + 5 * q^17 - 9 * q^19 - 24 * q^20 + 10 * q^22 - 23 * q^23 - 14 * q^25 + 18 * q^26 + 7 * q^28 + 36 * q^29 - 9 * q^31 + 3 * q^32 - 4 * q^34 + 5 * q^35 - 31 * q^40 - 6 * q^41 + 24 * q^43 - 33 * q^44 - 13 * q^46 + 11 * q^47 + 3 * q^49 - 48 * q^50 - 5 * q^52 - 3 * q^53 - 20 * q^55 + 27 * q^56 + 34 * q^58 - 14 * q^59 - 29 * q^61 + 10 * q^62 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 18 * q^70 + 38 * q^71 - 11 * q^73 + 45 * q^74 + 18 * q^76 - 21 * q^77 - q^79 - 5 * q^80 + 4 * q^82 - 10 * q^83 + 2 * q^85 - 3 * q^86 - 37 * q^88 + 8 * q^89 - 33 * q^91 + 96 * q^92 + 18 * q^94 - 21 * q^95 + 38 * q^97 + 17 * q^98

Introduction

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