LMFDB - Embedded newform 1520.2.bq.q.1471.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1520,2,Mod(31,1520)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1520.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1520, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,-6,0,0,0,-4,0,0,0,18,0,0,0,18,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 8x^{10} + 53x^{8} + 86x^{6} + 113x^{4} + 11x^{2} + 1 $ x^12 + 8x^10 + 53x^8 + 86x^6 + 113x^4 + 11*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1471.3
Root			$1.25214 - 2.16877i$ of defining polynomial
Character	$\chi$	$=$	1520.1471
Dual form			1520.2.bq.q.31.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.199658 + 0.345817i) q^{3} +(-0.500000 + 0.866025i) q^{5} +4.49947i q^{7} +(1.42027 + 2.45999i) q^{9} -1.01548i q^{11} +(5.20234 - 3.00357i) q^{13} +(-0.199658 - 0.345817i) q^{15} +(-0.351169 + 0.608243i) q^{17} +(3.21688 + 2.94137i) q^{19} +(-1.55599 - 0.898354i) q^{21} +(0.140227 - 0.0809603i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.33222 q^{27} +(-3.40716 + 1.96713i) q^{29} +0.0532027 q^{31} +(0.351169 + 0.202748i) q^{33} +(-3.89665 - 2.24973i) q^{35} -4.61593i q^{37} +2.39875i q^{39} +(6.40716 + 3.69918i) q^{41} +(2.21760 + 1.28033i) q^{43} -2.84055 q^{45} +(-9.93111 + 5.73373i) q^{47} -13.2452 q^{49} +(-0.140227 - 0.242881i) q^{51} +(0.351169 - 0.202748i) q^{53} +(0.879428 + 0.507738i) q^{55} +(-1.65945 + 0.525187i) q^{57} +(-7.19957 + 12.4700i) q^{59} +(-5.04289 - 8.73453i) q^{61} +(-11.0686 + 6.39048i) q^{63} +6.00714i q^{65} +(4.60925 + 7.98346i) q^{67} +0.0646574i q^{69} +(-6.14709 + 10.6471i) q^{71} +(6.69172 - 11.5904i) q^{73} +0.399316 q^{75} +4.56910 q^{77} +(4.66246 - 8.07561i) q^{79} +(-3.79517 + 6.57343i) q^{81} -13.7043i q^{83} +(-0.351169 - 0.608243i) q^{85} -1.57101i q^{87} +(-3.00000 + 1.73205i) q^{89} +(13.5145 + 23.4078i) q^{91} +(-0.0106223 + 0.0183984i) q^{93} +(-4.15574 + 1.31522i) q^{95} +(1.79517 + 1.03644i) q^{97} +(2.49806 - 1.44225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{5} - 4 q^{9} + 18 q^{13} + 18 q^{17} + 24 q^{21} - 6 q^{25} + 24 q^{29} - 18 q^{33} + 12 q^{41} + 8 q^{45} - 28 q^{49} - 18 q^{53} - 62 q^{57} + 26 q^{61} + 16 q^{73} + 56 q^{77} - 66 q^{81}+ \cdots + 42 q^{97}+O(q^{100}) $ 12 * q - 6 * q^5 - 4 * q^9 + 18 * q^13 + 18 * q^17 + 24 * q^21 - 6 * q^25 + 24 * q^29 - 18 * q^33 + 12 * q^41 + 8 * q^45 - 28 * q^49 - 18 * q^53 - 62 * q^57 + 26 * q^61 + 16 * q^73 + 56 * q^77 - 66 * q^81 + 18 * q^85 - 36 * q^89 - 20 * q^93 + 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−0.199658	+	0.345817i	−0.115272	+	0.199658i	−0.917889	−	0.396838i	$-0.870107\pi$
$3$	−0.199658	+	0.345817i	−0.115272	+	0.199658i	0.802616	+	0.596496i	$0.203441\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$			4.49947i			1.70064i	0.526266	+	0.850320i	$0.323591\pi$
$7$			4.49947i			1.70064i	−0.526266	+	0.850320i	$0.676409\pi$
$8$		0			0
$9$	1.42027	+	2.45999i	0.473425	+	0.819995i
$10$		0			0
$11$		−	1.01548i		−	0.306178i	−0.988212	−	0.153089i	$-0.951078\pi$
$11$		−	1.01548i		−	0.306178i	0.988212	−	0.153089i	$-0.0489221\pi$
$12$		0			0
$13$	5.20234	−	3.00357i	1.44287	−	0.833041i	0.444829	−	0.895616i	$-0.353264\pi$
$13$	5.20234	−	3.00357i	1.44287	−	0.833041i	0.998040	+	0.0625747i	$0.0199312\pi$
$14$		0			0
$15$	−0.199658	−	0.345817i	−0.0515514	−	0.0892897i
$16$		0			0
$17$	−0.351169	+	0.608243i	−0.0851711	+	0.147521i	−0.905464	−	0.424423i	$-0.860477\pi$
$17$	−0.351169	+	0.608243i	−0.0851711	+	0.147521i	0.820293	+	0.571943i	$0.193810\pi$
$18$		0			0
$19$	3.21688	+	2.94137i	0.738004	+	0.674796i
$19$	3.21688	+	2.94137i	0.738004	+	0.674796i
$20$		0			0
$21$	−1.55599	−	0.898354i	−0.339546	−	0.196037i
$22$		0			0
$23$	0.140227	−	0.0809603i	0.0292394	−	0.0168814i	−0.485309	−	0.874343i	$-0.661293\pi$
$23$	0.140227	−	0.0809603i	0.0292394	−	0.0168814i	0.514548	+	0.857461i	$0.327960\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−2.33222			−0.448836
$28$		0			0
$29$	−3.40716	+	1.96713i	−0.632695	+	0.365286i	−0.781795	−	0.623536i	$-0.785696\pi$
$29$	−3.40716	+	1.96713i	−0.632695	+	0.365286i	0.149100	+	0.988822i	$0.452362\pi$
$30$		0			0
$31$	0.0532027			0.00955548			0.00477774	−	0.999989i	$-0.498479\pi$
$31$	0.0532027			0.00955548			0.00477774	+	0.999989i	$0.498479\pi$
$32$		0			0
$33$	0.351169	+	0.202748i	0.0611307	+	0.0352939i
$34$		0			0
$35$	−3.89665	−	2.24973i	−0.658655	−	0.380275i
$36$		0			0
$37$		−	4.61593i		−	0.758854i	−0.925222	−	0.379427i	$-0.876121\pi$
$37$		−	4.61593i		−	0.758854i	0.925222	−	0.379427i	$-0.123879\pi$
$38$		0			0
$39$			2.39875i			0.384107i
$40$		0			0
$41$	6.40716	+	3.69918i	1.00063	+	0.577715i	0.908435	−	0.418026i	$-0.137278\pi$
$41$	6.40716	+	3.69918i	1.00063	+	0.577715i	0.0921960	+	0.995741i	$0.470611\pi$
$42$		0			0
$43$	2.21760	+	1.28033i	0.338181	+	0.195249i	0.659467	−	0.751733i	$-0.270782\pi$
$43$	2.21760	+	1.28033i	0.338181	+	0.195249i	−0.321286	+	0.946982i	$0.604115\pi$
$44$		0			0
$45$	−2.84055			−0.423444
$46$		0			0
$47$	−9.93111	+	5.73373i	−1.44860	+	0.836350i	−0.998398	−	0.0565762i	$-0.981982\pi$
$47$	−9.93111	+	5.73373i	−1.44860	+	0.836350i	−0.450203	+	0.892926i	$0.648648\pi$
$48$		0			0
$49$	−13.2452			−1.89217
$50$		0			0
$51$	−0.140227	−	0.242881i	−0.0196358	−	0.0340101i
$52$		0			0
$53$	0.351169	−	0.202748i	0.0482368	−	0.0278495i	−0.475688	−	0.879614i	$-0.657801\pi$
$53$	0.351169	−	0.202748i	0.0482368	−	0.0278495i	0.523924	+	0.851765i	$0.324467\pi$
$54$		0			0
$55$	0.879428	+	0.507738i	0.118582	+	0.0684634i
$56$		0			0
$57$	−1.65945	+	0.525187i	−0.219800	+	0.0695628i
$58$		0			0
$59$	−7.19957	+	12.4700i	−0.937304	+	1.62346i	−0.166832	+	0.985985i	$0.553354\pi$
$59$	−7.19957	+	12.4700i	−0.937304	+	1.62346i	−0.770472	+	0.637473i	$0.779980\pi$
$60$		0			0
$61$	−5.04289	−	8.73453i	−0.645675	−	1.11834i	−0.984145	−	0.177365i	$-0.943243\pi$
$61$	−5.04289	−	8.73453i	−0.645675	−	1.11834i	0.338470	−	0.940977i	$-0.390091\pi$
$62$		0			0
$63$	−11.0686	+	6.39048i	−1.39452	+	0.805124i
$64$		0			0
$65$			6.00714i			0.745094i
$66$		0			0
$67$	4.60925	+	7.98346i	0.563110	+	0.975335i	0.997223	+	0.0744766i	$0.0237286\pi$
$67$	4.60925	+	7.98346i	0.563110	+	0.975335i	−0.434113	+	0.900859i	$0.642938\pi$
$68$		0			0
$69$			0.0646574i			0.00778384i
$70$		0			0
$71$	−6.14709	+	10.6471i	−0.729525	+	1.26357i	0.227559	+	0.973764i	$0.426925\pi$
$71$	−6.14709	+	10.6471i	−0.729525	+	1.26357i	−0.957084	+	0.289810i	$0.906408\pi$
$72$		0			0
$73$	6.69172	−	11.5904i	0.783206	−	1.35655i	−0.146859	−	0.989157i	$-0.546916\pi$
$73$	6.69172	−	11.5904i	0.783206	−	1.35655i	0.930065	−	0.367395i	$-0.119750\pi$
$74$		0			0
$75$	0.399316			0.0461090
$76$		0			0
$77$	4.56910			0.520698
$78$		0			0
$79$	4.66246	−	8.07561i	0.524567	−	0.908577i	−0.475023	−	0.879973i	$-0.657560\pi$
$79$	4.66246	−	8.07561i	0.524567	−	0.908577i	0.999591	−	0.0286042i	$-0.00910625\pi$
$80$		0			0
$81$	−3.79517	+	6.57343i	−0.421686	+	0.730382i
$82$		0			0
$83$		−	13.7043i		−	1.50424i	−0.659026	−	0.752120i	$-0.729031\pi$
$83$		−	13.7043i		−	1.50424i	0.659026	−	0.752120i	$-0.270969\pi$
$84$		0			0
$85$	−0.351169	−	0.608243i	−0.0380897	−	0.0659732i
$86$		0			0
$87$		−	1.57101i		−	0.168430i
$88$		0			0
$89$	−3.00000	+	1.73205i	−0.317999	+	0.183597i	−0.650500	−	0.759506i	$-0.725441\pi$
$89$	−3.00000	+	1.73205i	−0.317999	+	0.183597i	0.332501	+	0.943103i	$0.392107\pi$
$90$		0			0
$91$	13.5145	+	23.4078i	1.41670	+	2.45380i
$92$		0			0
$93$	−0.0106223	+	0.0183984i	−0.00110148	+	0.00190783i
$94$		0			0
$95$	−4.15574	+	1.31522i	−0.426370	+	0.134939i
$96$		0			0
$97$	1.79517	+	1.03644i	0.182272	+	0.105235i	0.588360	−	0.808599i	$-0.299774\pi$
$97$	1.79517	+	1.03644i	0.182272	+	0.105235i	−0.406088	+	0.913834i	$0.633107\pi$
$98$		0			0
$99$	2.49806	−	1.44225i	0.251064	−	0.144952i
$100$		0			0
$101$	1.78207	+	3.08663i	0.177322	+	0.307131i	0.940962	−	0.338511i	$-0.109923\pi$
$101$	1.78207	+	3.08663i	0.177322	+	0.307131i	−0.763640	+	0.645642i	$0.776590\pi$
$102$		0			0
$103$	−13.2544			−1.30599			−0.652997	−	0.757360i	$-0.726489\pi$
$103$	−13.2544			−1.30599			−0.652997	+	0.757360i	$0.726489\pi$
$104$		0			0
$105$	1.55599	−	0.898354i	0.151850	−	0.0876704i
$106$		0			0
$107$	11.6571			1.12694			0.563469	−	0.826137i	$-0.309466\pi$
$107$	11.6571			1.12694			0.563469	+	0.826137i	$0.309466\pi$
$108$		0			0
$109$	10.4607	+	6.03947i	1.00195	+	0.578477i	0.908825	−	0.417178i	$-0.136981\pi$
$109$	10.4607	+	6.03947i	1.00195	+	0.578477i	0.0931258	+	0.995654i	$0.470314\pi$
$110$		0			0
$111$	1.59627	+	0.921607i	0.151511	+	0.0874750i
$112$		0			0
$113$			4.17364i			0.392623i	0.980542	+	0.196311i	$0.0628964\pi$
$113$			4.17364i			0.392623i	−0.980542	+	0.196311i	$0.937104\pi$
$114$		0			0
$115$			0.161921i			0.0150992i
$116$		0			0
$117$	14.7775	+	8.53179i	1.36618	+	0.788764i
$118$		0			0
$119$	−2.73677	−	1.58008i	−0.250879	−	0.144845i
$120$		0			0
$121$	9.96881			0.906255
$122$		0			0
$123$	−2.55848	+	1.47714i	−0.230690	+	0.133189i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−2.55749	−	4.42970i	−0.226940	−	0.393072i	0.729959	−	0.683490i	$-0.239539\pi$
$127$	−2.55749	−	4.42970i	−0.226940	−	0.393072i	−0.956900	+	0.290418i	$0.906206\pi$
$128$		0			0
$129$	−0.885523	+	0.511257i	−0.0779660	+	0.0450137i
$130$		0			0
$131$	9.93111	+	5.73373i	0.867685	+	0.500958i	0.866578	−	0.499041i	$-0.166314\pi$
$131$	9.93111	+	5.73373i	0.867685	+	0.500958i	0.00110670	+	0.999999i	$0.499648\pi$
$132$		0			0
$133$	−13.2346	+	14.4743i	−1.14759	+	1.25508i
$134$		0			0
$135$	1.16611	−	2.01976i	0.100363	−	0.173834i
$136$		0			0
$137$	−9.05599	−	15.6854i	−0.773706	−	1.34010i	−0.935519	−	0.353276i	$-0.885068\pi$
$137$	−9.05599	−	15.6854i	−0.773706	−	1.34010i	0.161813	−	0.986821i	$-0.448266\pi$
$138$		0			0
$139$	−0.340878	+	0.196806i	−0.0289129	+	0.0166929i	−0.514387	−	0.857558i	$-0.671980\pi$
$139$	−0.340878	+	0.196806i	−0.0289129	+	0.0166929i	0.485474	+	0.874251i	$0.338647\pi$
$140$		0			0
$141$		−	4.57913i		−	0.385633i
$142$		0			0
$143$	−3.05006	−	5.28285i	−0.255058	−	0.441774i
$144$		0			0
$145$		−	3.93425i		−	0.326722i
$146$		0			0
$147$	2.64451	−	4.58043i	0.218116	−	0.377787i
$148$		0			0
$149$	0.420274	−	0.727935i	0.0344301	−	0.0596348i	−0.848297	−	0.529521i	$-0.822372\pi$
$149$	0.420274	−	0.727935i	0.0344301	−	0.0596348i	0.882727	+	0.469886i	$0.155705\pi$
$150$		0			0
$151$	−5.79673			−0.471731			−0.235866	−	0.971786i	$-0.575793\pi$
$151$	−5.79673			−0.471731			−0.235866	+	0.971786i	$0.575793\pi$
$152$		0			0
$153$	−1.99503			−0.161288
$154$		0			0
$155$	−0.0266013	+	0.0460749i	−0.00213667	+	0.00370082i
$156$		0			0
$157$	−2.71545	+	4.70329i	−0.216716	+	0.375364i	−0.953802	−	0.300435i	$-0.902868\pi$
$157$	−2.71545	+	4.70329i	−0.216716	+	0.375364i	0.737086	+	0.675799i	$0.236201\pi$
$158$		0			0
$159$			0.161921i			0.0128411i
$160$		0			0
$161$	0.364279	+	0.630949i	0.0287092	+	0.0497257i
$162$		0			0
$163$		−	12.3210i		−	0.965056i	−0.875881	−	0.482528i	$-0.839719\pi$
$163$		−	12.3210i		−	0.965056i	0.875881	−	0.482528i	$-0.160281\pi$
$164$		0			0
$165$	−0.351169	+	0.202748i	−0.0273385	+	0.0157839i
$166$		0			0
$167$	1.16512	+	2.01804i	0.0901595	+	0.156161i	0.907578	−	0.419883i	$-0.137929\pi$
$167$	1.16512	+	2.01804i	0.0901595	+	0.156161i	−0.817419	+	0.576044i	$0.804596\pi$
$168$		0			0
$169$	11.5429	−	19.9929i	0.887914	−	1.53791i
$170$		0			0
$171$	−2.66687	+	12.0910i	−0.203941	+	0.924625i
$172$		0			0
$173$	9.29517	+	5.36657i	0.706699	+	0.408013i	0.809838	−	0.586654i	$-0.199555\pi$
$173$	9.29517	+	5.36657i	0.706699	+	0.408013i	−0.103139	+	0.994667i	$0.532889\pi$
$174$		0			0
$175$	3.89665	−	2.24973i	0.294559	−	0.170064i
$176$		0			0
$177$	−2.87490	−	4.97947i	−0.216091	−	0.374280i
$178$		0			0
$179$	−12.2180			−0.913220			−0.456610	−	0.889667i	$-0.650936\pi$
$179$	−12.2180			−0.913220			−0.456610	+	0.889667i	$0.650936\pi$
$180$		0			0
$181$	−19.7240	+	11.3876i	−1.46607	+	0.846437i	−0.999280	−	0.0379304i	$-0.987923\pi$
$181$	−19.7240	+	11.3876i	−1.46607	+	0.846437i	−0.466792	+	0.884367i	$0.654590\pi$
$182$		0			0
$183$	4.02741			0.297714
$184$		0			0
$185$	3.99751	+	2.30797i	0.293903	+	0.169685i
$186$		0			0
$187$	0.617657	+	0.356604i	0.0451675	+	0.0260775i
$188$		0			0
$189$		−	10.4938i		−	0.763309i
$190$		0			0
$191$			7.29183i			0.527618i	0.964575	+	0.263809i	$0.0849789\pi$
$191$			7.29183i			0.527618i	−0.964575	+	0.263809i	$0.915021\pi$
$192$		0			0
$193$	−16.8678	−	9.73865i	−1.21417	−	0.701003i	−0.250508	−	0.968115i	$-0.580598\pi$
$193$	−16.8678	−	9.73865i	−1.21417	−	0.701003i	−0.963666	+	0.267111i	$0.913931\pi$
$194$		0			0
$195$	−2.07737	−	1.19937i	−0.148764	−	0.0858889i
$196$		0			0
$197$	−18.7619			−1.33673			−0.668365	−	0.743834i	$-0.733005\pi$
$197$	−18.7619			−1.33673			−0.668365	+	0.743834i	$0.733005\pi$
$198$		0			0
$199$	−7.61502	+	4.39653i	−0.539814	+	0.311662i	−0.745004	−	0.667060i	$-0.767552\pi$
$199$	−7.61502	+	4.39653i	−0.539814	+	0.311662i	0.205189	+	0.978722i	$0.434219\pi$
$200$		0			0
$201$	−3.68109			−0.259644
$202$		0			0
$203$	−8.85103	−	15.3304i	−0.621220	−	1.07599i
$204$		0			0
$205$	−6.40716	+	3.69918i	−0.447496	+	0.258362i
$206$		0			0
$207$	0.398323	+	0.229972i	0.0276853	+	0.0159841i
$208$		0			0
$209$	2.98689	−	3.26667i	0.206608	−	0.225960i
$210$		0			0
$211$	6.36811	−	11.0299i	0.438399	−	0.759329i	−0.559167	−	0.829055i	$-0.688879\pi$
$211$	6.36811	−	11.0299i	0.438399	−	0.759329i	0.997566	+	0.0697258i	$0.0222124\pi$
$212$		0			0
$213$	−2.45463	−	4.25154i	−0.168188	−	0.291311i
$214$		0			0
$215$	−2.21760	+	1.28033i	−0.151239	+	0.0873180i
$216$		0			0
$217$			0.239384i			0.0162504i
$218$		0			0
$219$	2.67211	+	4.62822i	0.180564	+	0.312746i
$220$		0			0
$221$			4.21905i			0.283804i
$222$		0			0
$223$	6.23411	−	10.7978i	0.417467	−	0.723074i	−0.578217	−	0.815883i	$-0.696251\pi$
$223$	6.23411	−	10.7978i	0.417467	−	0.723074i	0.995684	+	0.0928091i	$0.0295846\pi$
$224$		0			0
$225$	1.42027	−	2.45999i	0.0946849	−	0.163999i
$226$		0			0
$227$	21.0497			1.39712			0.698559	−	0.715553i	$-0.253825\pi$
$227$	21.0497			1.39712			0.698559	+	0.715553i	$0.253825\pi$
$228$		0			0
$229$	16.1332			1.06611			0.533057	−	0.846079i	$-0.321043\pi$
$229$	16.1332			1.06611			0.533057	+	0.846079i	$0.321043\pi$
$230$		0			0
$231$	−0.912257	+	1.58008i	−0.0600221	+	0.103961i
$232$		0			0
$233$	−9.09888	+	15.7597i	−0.596088	+	1.03245i	0.397305	+	0.917687i	$0.369946\pi$
$233$	−9.09888	+	15.7597i	−0.596088	+	1.03245i	−0.993392	+	0.114767i	$0.963388\pi$
$234$		0			0
$235$		−	11.4675i		−	0.748054i
$236$		0			0
$237$	1.86179	+	3.22472i	0.120936	+	0.209468i
$238$		0			0
$239$		−	10.6139i		−	0.686556i	−0.939234	−	0.343278i	$-0.888463\pi$
$239$		−	10.6139i		−	0.686556i	0.939234	−	0.343278i	$-0.111537\pi$
$240$		0			0
$241$	4.59532	−	2.65311i	0.296011	−	0.170902i	−0.344639	−	0.938735i	$-0.611999\pi$
$241$	4.59532	−	2.65311i	0.296011	−	0.170902i	0.640649	+	0.767834i	$0.278665\pi$
$242$		0			0
$243$	−5.01380	−	8.68416i	−0.321636	−	0.557089i
$244$		0			0
$245$	6.62261	−	11.4707i	0.423103	−	0.732836i
$246$		0			0
$247$	25.5699	+	5.63986i	1.62698	+	0.358856i
$248$		0			0
$249$	4.73918	+	2.73617i	0.300333	+	0.173398i
$250$		0			0
$251$	21.8187	−	12.5971i	1.37719	−	0.795119i	0.385367	−	0.922763i	$-0.374075\pi$
$251$	21.8187	−	12.5971i	1.37719	−	0.795119i	0.991820	+	0.127644i	$0.0407416\pi$
$252$		0			0
$253$	−0.0822133	−	0.142398i	−0.00516871	−	0.00895246i
$254$		0			0
$255$	0.280455			0.0175628
$256$		0			0
$257$	−6.61448	+	3.81887i	−0.412600	+	0.238215i	−0.691906	−	0.721987i	$-0.743229\pi$
$257$	−6.61448	+	3.81887i	−0.412600	+	0.238215i	0.279306	+	0.960202i	$0.409895\pi$
$258$		0			0
$259$	20.7692			1.29054
$260$		0			0
$261$	−9.67821	−	5.58772i	−0.599066	−	0.345871i
$262$		0			0
$263$	−21.0602	−	12.1591i	−1.29863	−	0.749762i	−0.318459	−	0.947937i	$-0.603165\pi$
$263$	−21.0602	−	12.1591i	−1.29863	−	0.749762i	−0.980167	+	0.198175i	$0.936499\pi$
$264$		0			0
$265$			0.405495i			0.0249094i
$266$		0			0
$267$		−	1.38327i		−	0.0846547i
$268$		0			0
$269$	11.9047	+	6.87317i	0.725841	+	0.419064i	0.816899	−	0.576781i	$-0.195691\pi$
$269$	11.9047	+	6.87317i	0.725841	+	0.419064i	−0.0910577	+	0.995846i	$0.529025\pi$
$270$		0			0
$271$	17.3261	+	10.0032i	1.05249	+	0.607653i	0.923344	−	0.383974i	$-0.125445\pi$
$271$	17.3261	+	10.0032i	1.05249	+	0.607653i	0.129141	+	0.991626i	$0.458778\pi$
$272$		0			0
$273$	−10.7931			−0.653227
$274$		0			0
$275$	−0.879428	+	0.507738i	−0.0530315	+	0.0306178i
$276$		0			0
$277$	15.6811			0.942186			0.471093	−	0.882084i	$-0.343860\pi$
$277$	15.6811			0.942186			0.471093	+	0.882084i	$0.343860\pi$
$278$		0			0
$279$	0.0755623	+	0.130878i	0.00452380	+	0.00783545i
$280$		0			0
$281$	16.0776	−	9.28243i	0.959111	−	0.553743i	0.0632119	−	0.998000i	$-0.479866\pi$
$281$	16.0776	−	9.28243i	0.959111	−	0.553743i	0.895899	+	0.444257i	$0.146532\pi$
$282$		0			0
$283$	−13.3086	−	7.68372i	−0.791114	−	0.456750i	0.0492407	−	0.998787i	$-0.484320\pi$
$283$	−13.3086	−	7.68372i	−0.791114	−	0.456750i	−0.840354	+	0.542037i	$0.817653\pi$
$284$		0			0
$285$	0.374901	−	1.69972i	0.0222072	−	0.100683i
$286$		0			0
$287$	−16.6443	+	28.8288i	−0.982484	+	1.70171i
$288$		0			0
$289$	8.25336	+	14.2952i	0.485492	+	0.840896i
$290$		0			0
$291$	−0.716841	+	0.413868i	−0.0420220	+	0.0242614i
$292$		0			0
$293$			0.515564i			0.0301196i	0.999887	+	0.0150598i	$0.00479386\pi$
$293$			0.515564i			0.0301196i	−0.999887	+	0.0150598i	$0.995206\pi$
$294$		0			0
$295$	−7.19957	−	12.4700i	−0.419175	−	0.726033i
$296$		0			0
$297$			2.36832i			0.137424i
$298$		0			0
$299$	0.486340	−	0.842366i	0.0281258	−	0.0487153i
$300$		0			0
$301$	−5.76082	+	9.97803i	−0.332048	+	0.575124i
$302$		0			0
$303$	−1.42321			−0.0817614
$304$		0			0
$305$	10.0858			0.577510
$306$		0			0
$307$	10.7350	−	18.5935i	0.612677	−	1.06119i	−0.378110	−	0.925761i	$-0.623426\pi$
$307$	10.7350	−	18.5935i	0.612677	−	1.06119i	0.990787	−	0.135428i	$-0.0432408\pi$
$308$		0			0
$309$	2.64634	−	4.58360i	0.150545	−	0.260752i
$310$		0			0
$311$		−	26.2354i		−	1.48767i	−0.668361	−	0.743837i	$-0.733004\pi$
$311$		−	26.2354i		−	1.48767i	0.668361	−	0.743837i	$-0.266996\pi$
$312$		0			0
$313$	12.8037	+	22.1767i	0.723708	+	1.25350i	0.959503	+	0.281697i	$0.0908972\pi$
$313$	12.8037	+	22.1767i	0.723708	+	1.25350i	−0.235795	+	0.971803i	$0.575769\pi$
$314$		0			0
$315$		−	12.7810i		−	0.720125i
$316$		0			0
$317$	14.2750	−	8.24168i	0.801764	−	0.462899i	−0.0423236	−	0.999104i	$-0.513476\pi$
$317$	14.2750	−	8.24168i	0.801764	−	0.462899i	0.844088	+	0.536205i	$0.180143\pi$
$318$		0			0
$319$	1.99757	+	3.45989i	0.111843	+	0.193717i
$320$		0			0
$321$	−2.32744	+	4.03124i	−0.129905	+	0.225002i
$322$		0			0
$323$	−2.91874	+	0.923729i	−0.162403	+	0.0513977i
$324$		0			0
$325$	−5.20234	−	3.00357i	−0.288574	−	0.166608i
$326$		0			0
$327$	−4.17711	+	2.41166i	−0.230995	+	0.133365i
$328$		0			0
$329$	−25.7987	−	44.6847i	−1.42233	−	2.46355i
$330$		0			0
$331$	9.85555			0.541710			0.270855	−	0.962620i	$-0.412694\pi$
$331$	9.85555			0.541710			0.270855	+	0.962620i	$0.412694\pi$
$332$		0			0
$333$	11.3551	−	6.55588i	0.622257	−	0.359260i
$334$		0			0
$335$	−9.21851			−0.503661
$336$		0			0
$337$	3.89298	+	2.24762i	0.212064	+	0.122435i	0.602270	−	0.798292i	$-0.294263\pi$
$337$	3.89298	+	2.24762i	0.212064	+	0.122435i	−0.390206	+	0.920728i	$0.627596\pi$
$338$		0			0
$339$	−1.44332	−	0.833299i	−0.0783902	−	0.0452586i
$340$		0			0
$341$		−	0.0540260i		−	0.00292567i
$342$		0			0
$343$		−	28.1002i		−	1.51727i
$344$		0			0
$345$	−0.0559950	−	0.0323287i	−0.00301467	−	0.00174052i
$346$		0			0
$347$	−9.37387	−	5.41201i	−0.503216	−	0.290532i	0.226825	−	0.973936i	$-0.427166\pi$
$347$	−9.37387	−	5.41201i	−0.503216	−	0.290532i	−0.730041	+	0.683404i	$0.760499\pi$
$348$		0			0
$349$	11.3884			0.609607			0.304804	−	0.952415i	$-0.401409\pi$
$349$	11.3884			0.609607			0.304804	+	0.952415i	$0.401409\pi$
$350$		0			0
$351$	−12.1330	+	7.00499i	−0.647612	+	0.373899i
$352$		0			0
$353$	19.8306			1.05548			0.527738	−	0.849407i	$-0.323040\pi$
$353$	19.8306			1.05548			0.527738	+	0.849407i	$0.323040\pi$
$354$		0			0
$355$	−6.14709	−	10.6471i	−0.326253	−	0.565088i
$356$		0			0
$357$	1.09284	−	0.630949i	0.0578390	−	0.0333934i
$358$		0			0
$359$	1.67905	+	0.969401i	0.0886170	+	0.0511630i	0.543654	−	0.839310i	$-0.317041\pi$
$359$	1.67905	+	0.969401i	0.0886170	+	0.0511630i	−0.455037	+	0.890473i	$0.650374\pi$
$360$		0			0
$361$	1.69669	+	18.9241i	0.0892995	+	0.996005i
$362$		0			0
$363$	−1.99035	+	3.44739i	−0.104466	+	0.180941i
$364$		0			0
$365$	6.69172	+	11.5904i	0.350260	+	0.606669i
$366$		0			0
$367$	−20.0822	+	11.5945i	−1.04828	+	0.605227i	−0.922169	−	0.386788i	$-0.873585\pi$
$367$	−20.0822	+	11.5945i	−1.04828	+	0.605227i	−0.126116	+	0.992015i	$0.540251\pi$
$368$		0			0
$369$			21.0154i			1.09402i
$370$		0			0
$371$	0.912257	+	1.58008i	0.0473620	+	0.0820335i
$372$		0			0
$373$			4.21044i			0.218008i	0.994041	+	0.109004i	$0.0347661\pi$
$373$			4.21044i			0.218008i	−0.994041	+	0.109004i	$0.965234\pi$
$374$		0			0
$375$	−0.199658	+	0.345817i	−0.0103103	+	0.0178579i
$376$		0			0
$377$	−11.8168	+	20.4673i	−0.608597	+	1.05412i
$378$		0			0
$379$	26.2835			1.35009			0.675047	−	0.737775i	$-0.264123\pi$
$379$	26.2835			1.35009			0.675047	+	0.737775i	$0.264123\pi$
$380$		0			0
$381$	2.04249			0.104640
$382$		0			0
$383$	17.8699	−	30.9515i	0.913108	−	1.58155i	0.103461	−	0.994634i	$-0.467008\pi$
$383$	17.8699	−	30.9515i	0.913108	−	1.58155i	0.809648	−	0.586916i	$-0.199658\pi$
$384$		0			0
$385$	−2.28455	+	3.95696i	−0.116432	+	0.201665i
$386$		0			0
$387$			7.27369i			0.369743i
$388$		0			0
$389$	−8.74771	−	15.1515i	−0.443527	−	0.768211i	0.554422	−	0.832236i	$-0.312939\pi$
$389$	−8.74771	−	15.1515i	−0.443527	−	0.768211i	−0.997948	+	0.0640253i	$0.979606\pi$
$390$		0			0
$391$			0.113723i			0.00575123i
$392$		0			0
$393$	−3.96565	+	2.28957i	−0.200040	+	0.115493i
$394$		0			0
$395$	4.66246	+	8.07561i	0.234594	+	0.406328i
$396$		0			0
$397$	−0.592836	+	1.02682i	−0.0297536	+	0.0515347i	−0.880519	−	0.474011i	$-0.842806\pi$
$397$	−0.592836	+	1.02682i	−0.0297536	+	0.0515347i	0.850765	+	0.525546i	$0.176139\pi$
$398$		0			0
$399$	−2.36306	−	7.46666i	−0.118301	−	0.373800i
$400$		0			0
$401$	21.7583	+	12.5622i	1.08656	+	0.627325i	0.932658	−	0.360761i	$-0.117483\pi$
$401$	21.7583	+	12.5622i	1.08656	+	0.627325i	0.153901	+	0.988086i	$0.450816\pi$
$402$		0			0
$403$	0.276778	−	0.159798i	0.0137873	−	0.00796011i
$404$		0			0
$405$	−3.79517	−	6.57343i	−0.188584	−	0.326637i
$406$		0			0
$407$	−4.68737			−0.232344
$408$		0			0
$409$	−13.0368	+	7.52682i	−0.644630	+	0.372177i	−0.786396	−	0.617723i	$-0.788055\pi$
$409$	−13.0368	+	7.52682i	−0.644630	+	0.372177i	0.141766	+	0.989900i	$0.454722\pi$
$410$		0			0
$411$	7.23240			0.356748
$412$		0			0
$413$	−56.1085	−	32.3942i	−2.76092	−	1.59402i
$414$		0			0
$415$	11.8683	+	6.85214i	0.582590	+	0.336358i
$416$		0			0
$417$		−	0.157176i		−	0.00769692i
$418$		0			0
$419$		−	18.4139i		−	0.899576i	−0.893135	−	0.449788i	$-0.851499\pi$
$419$		−	18.4139i		−	0.899576i	0.893135	−	0.449788i	$-0.148501\pi$
$420$		0			0
$421$	−14.1949	−	8.19542i	−0.691816	−	0.399420i	0.112476	−	0.993654i	$-0.464122\pi$
$421$	−14.1949	−	8.19542i	−0.691816	−	0.399420i	−0.804292	+	0.594234i	$0.797455\pi$
$422$		0			0
$423$	−28.2098	−	16.2869i	−1.37161	−	0.791897i
$424$		0			0
$425$	0.702339			0.0340684
$426$		0			0
$427$	39.3008	−	22.6903i	1.90190	−	1.09806i
$428$		0			0
$429$	2.43587			0.117605
$430$		0			0
$431$	11.0634	+	19.1624i	0.532905	+	0.923019i	0.999262	+	0.0384218i	$0.0122331\pi$
$431$	11.0634	+	19.1624i	0.532905	+	0.923019i	−0.466357	+	0.884597i	$0.654434\pi$
$432$		0			0
$433$	23.8972	−	13.7971i	1.14843	−	0.663045i	0.199924	−	0.979812i	$-0.435931\pi$
$433$	23.8972	−	13.7971i	1.14843	−	0.663045i	0.948503	+	0.316767i	$0.102597\pi$
$434$		0			0
$435$	1.36053	+	0.785505i	0.0652326	+	0.0376621i
$436$		0			0
$437$	0.689230	+	0.152021i	0.0329703	+	0.00727213i
$438$		0			0
$439$	13.4009	−	23.2110i	0.639588	−	1.10780i	−0.345935	−	0.938258i	$-0.612438\pi$
$439$	13.4009	−	23.2110i	0.639588	−	1.10780i	0.985523	−	0.169540i	$-0.0542283\pi$
$440$		0			0
$441$	−18.8118	−	32.5831i	−0.895802	−	1.55157i
$442$		0			0
$443$	26.6395	−	15.3803i	1.26568	−	0.730742i	0.291515	−	0.956566i	$-0.405841\pi$
$443$	26.6395	−	15.3803i	1.26568	−	0.730742i	0.974168	+	0.225824i	$0.0725074\pi$
$444$		0			0
$445$		−	3.46410i		−	0.164214i
$446$		0			0
$447$	0.167822	+	0.290676i	0.00793770	+	0.0137485i
$448$		0			0
$449$			31.4723i			1.48527i	0.669695	+	0.742636i	$0.266425\pi$
$449$			31.4723i			1.48527i	−0.669695	+	0.742636i	$0.733575\pi$
$450$		0			0
$451$	3.75643	−	6.50632i	0.176883	−	0.306371i
$452$		0			0
$453$	1.15736	−	2.00461i	0.0543776	−	0.0941848i
$454$		0			0
$455$	−27.0290			−1.26714
$456$		0			0
$457$	15.2977			0.715594			0.357797	−	0.933799i	$-0.383528\pi$
$457$	15.2977			0.715594			0.357797	+	0.933799i	$0.383528\pi$
$458$		0			0
$459$	0.819005	−	1.41856i	0.0382279	−	0.0662126i
$460$		0			0
$461$	12.3809	−	21.4444i	0.576638	−	0.998767i	−0.419223	−	0.907883i	$-0.637698\pi$
$461$	12.3809	−	21.4444i	0.576638	−	0.998767i	0.995862	−	0.0908835i	$-0.0289691\pi$
$462$		0			0
$463$			7.77759i			0.361455i	0.983533	+	0.180728i	$0.0578452\pi$
$463$			7.77759i			0.361455i	−0.983533	+	0.180728i	$0.942155\pi$
$464$		0			0
$465$	−0.0106223	−	0.0183984i	−0.000492599	−	0.000853206i
$466$		0			0
$467$			13.8662i			0.641651i	0.947138	+	0.320826i	$0.103960\pi$
$467$			13.8662i			0.641651i	−0.947138	+	0.320826i	$0.896040\pi$
$468$		0			0
$469$	−35.9213	+	20.7392i	−1.65869	+	0.957647i
$470$		0			0
$471$	−1.08432	−	1.87810i	−0.0499629	−	0.0865382i
$472$		0			0
$473$	1.30015	−	2.25192i	0.0597809	−	0.103544i
$474$		0			0
$475$	0.938859	−	4.25659i	0.0430778	−	0.195306i
$476$		0			0
$477$	0.997513	+	0.575915i	0.0456730	+	0.0263693i
$478$		0			0
$479$	−15.8641	+	9.15914i	−0.724849	+	0.418492i	−0.816535	−	0.577296i	$-0.804108\pi$
$479$	−15.8641	+	9.15914i	−0.724849	+	0.418492i	0.0916858	+	0.995788i	$0.470774\pi$
$480$		0			0
$481$	−13.8643	−	24.0136i	−0.632157	−	1.09493i
$482$		0			0
$483$	−0.290924			−0.0132375
$484$		0			0
$485$	−1.79517	+	1.03644i	−0.0815147	+	0.0470625i
$486$		0			0
$487$	−6.42131			−0.290977			−0.145489	−	0.989360i	$-0.546475\pi$
$487$	−6.42131			−0.290977			−0.145489	+	0.989360i	$0.546475\pi$
$488$		0			0
$489$	4.26082	+	2.45999i	0.192681	+	0.111244i
$490$		0			0
$491$	36.7870	+	21.2390i	1.66017	+	0.958502i	0.972630	+	0.232360i	$0.0746448\pi$
$491$	36.7870	+	21.2390i	1.66017	+	0.958502i	0.687545	+	0.726142i	$0.258689\pi$
$492$		0			0
$493$		−	2.76318i		−	0.124447i
$494$		0			0
$495$			2.88451i			0.129649i
$496$		0			0
$497$	−47.9061	−	27.6586i	−2.14888	−	1.24066i
$498$		0			0
$499$	12.9677	+	7.48691i	0.580515	+	0.335160i	0.761338	−	0.648355i	$-0.224543\pi$
$499$	12.9677	+	7.48691i	0.580515	+	0.335160i	−0.180823	+	0.983516i	$0.557876\pi$
$500$		0			0
$501$	−0.930499			−0.0415716
$502$		0			0
$503$	−4.39714	+	2.53869i	−0.196059	+	0.113195i	−0.594816	−	0.803862i	$-0.702775\pi$
$503$	−4.39714	+	2.53869i	−0.196059	+	0.113195i	0.398757	+	0.917057i	$0.369442\pi$
$504$		0			0
$505$	−3.56413			−0.158602
$506$		0			0
$507$	4.60925	+	7.98346i	0.204704	+	0.354558i
$508$		0			0
$509$	−32.6822	+	18.8691i	−1.44861	+	0.836356i	−0.998399	−	0.0565651i	$-0.981985\pi$
$509$	−32.6822	+	18.8691i	−1.44861	+	0.836356i	−0.450213	+	0.892921i	$0.648652\pi$
$510$		0			0
$511$	52.1506	+	30.1092i	2.30701	+	1.33195i
$512$		0			0
$513$	−7.50249	−	6.85993i	−0.331243	−	0.302873i
$514$		0			0
$515$	6.62720	−	11.4786i	0.292029	−	0.505810i
$516$		0			0
$517$	5.82246	+	10.0848i	0.256072	+	0.443529i
$518$		0			0
$519$	−3.71171	+	2.14296i	−0.162926	+	0.0940653i
$520$		0			0
$521$			25.6224i			1.12254i	0.827634	+	0.561268i	$0.189686\pi$
$521$			25.6224i			1.12254i	−0.827634	+	0.561268i	$0.810314\pi$
$522$		0			0
$523$	−1.33195	−	2.30700i	−0.0582420	−	0.100878i	0.835434	−	0.549590i	$-0.185216\pi$
$523$	−1.33195	−	2.30700i	−0.0582420	−	0.100878i	−0.893676	+	0.448712i	$0.851883\pi$
$524$		0			0
$525$			1.79671i			0.0784148i
$526$		0			0
$527$	−0.0186831	+	0.0323602i	−0.000813851	+	0.00140963i
$528$		0			0
$529$	−11.4869	+	19.8959i	−0.499430	+	0.865038i
$530$		0			0
$531$	−40.9014			−1.77497
$532$		0			0
$533$	44.4430			1.92504
$534$		0			0
$535$	−5.82857	+	10.0954i	−0.251991	+	0.436461i
$536$		0			0
$537$	2.43943	−	4.22521i	0.105269	−	0.182331i
$538$		0			0
$539$			13.4502i			0.579342i
$540$		0			0
$541$	−4.46565	−	7.73473i	−0.191993	−	0.332542i	0.753918	−	0.656969i	$-0.228162\pi$
$541$	−4.46565	−	7.73473i	−0.191993	−	0.332542i	−0.945911	+	0.324427i	$0.894828\pi$
$542$		0			0
$543$		−	9.09453i		−	0.390284i
$544$		0			0
$545$	−10.4607	+	6.03947i	−0.448086	+	0.258703i
$546$		0			0
$547$	−6.23312	−	10.7961i	−0.266509	−	0.461607i	0.701449	−	0.712720i	$-0.252537\pi$
$547$	−6.23312	−	10.7961i	−0.266509	−	0.461607i	−0.967958	+	0.251113i	$0.919203\pi$
$548$		0			0
$549$	14.3246	−	24.8109i	0.611357	−	1.05890i
$550$		0			0
$551$	−16.7465	−	3.69371i	−0.713425	−	0.157357i
$552$		0			0
$553$	36.3360	+	20.9786i	1.54516	+	0.892100i
$554$		0			0
$555$	−1.59627	+	0.921607i	−0.0677579	+	0.0391200i
$556$		0			0
$557$	−5.35366	−	9.27280i	−0.226842	−	0.392901i	0.730029	−	0.683416i	$-0.239507\pi$
$557$	−5.35366	−	9.27280i	−0.226842	−	0.392901i	−0.956870	+	0.290515i	$0.906173\pi$
$558$		0			0
$559$	15.3823			0.650602
$560$		0			0
$561$	−0.246640	+	0.142398i	−0.0104131	+	0.00601203i
$562$		0			0
$563$	−34.8327			−1.46802			−0.734012	−	0.679136i	$-0.762355\pi$
$563$	−34.8327			−1.46802			−0.734012	+	0.679136i	$0.762355\pi$
$564$		0			0
$565$	−3.61448	−	2.08682i	−0.152062	−	0.0877931i
$566$		0			0
$567$	−29.5770	−	17.0763i	−1.24212	−	0.717136i
$568$		0			0
$569$		−	10.8711i		−	0.455739i	−0.973692	−	0.227870i	$-0.926824\pi$
$569$		−	10.8711i		−	0.455739i	0.973692	−	0.227870i	$-0.0731760\pi$
$570$		0			0
$571$			37.8605i			1.58441i	0.610252	+	0.792207i	$0.291068\pi$
$571$			37.8605i			1.58441i	−0.610252	+	0.792207i	$0.708932\pi$
$572$		0			0
$573$	−2.52164	−	1.45587i	−0.105343	−	0.0608199i
$574$		0			0
$575$	−0.140227	−	0.0809603i	−0.00584789	−	0.00337628i
$576$		0			0
$577$	32.0121			1.33268			0.666340	−	0.745648i	$-0.267860\pi$
$577$	32.0121			1.33268			0.666340	+	0.745648i	$0.267860\pi$
$578$		0			0
$579$	6.73559	−	3.88879i	0.279922	−	0.161613i
$580$		0			0
$581$	61.6620			2.55817
$582$		0			0
$583$	−0.205886	−	0.356604i	−0.00852691	−	0.0147690i
$584$		0			0
$585$	−14.7775	+	8.53179i	−0.610974	+	0.352746i
$586$		0			0
$587$	−38.7278	−	22.3595i	−1.59847	−	0.922876i	−0.991783	−	0.127935i	$-0.959165\pi$
$587$	−38.7278	−	22.3595i	−1.59847	−	0.922876i	−0.606686	−	0.794941i	$-0.707502\pi$
$588$		0			0
$589$	0.171147	+	0.156489i	0.00705198	+	0.00644800i
$590$		0			0
$591$	3.74596	−	6.48819i	0.154088	−	0.266888i
$592$		0			0
$593$	−13.2665	−	22.9782i	−0.544789	−	0.943602i	−0.998620	−	0.0525141i	$-0.983277\pi$
$593$	−13.2665	−	22.9782i	−0.544789	−	0.943602i	0.453832	−	0.891087i	$-0.350057\pi$
$594$		0			0
$595$	2.73677	−	1.58008i	0.112197	−	0.0647768i
$596$		0			0
$597$		−	3.51121i		−	0.143704i
$598$		0			0
$599$	−5.13267	−	8.89004i	−0.209715	−	0.363237i	0.741910	−	0.670500i	$-0.233920\pi$
$599$	−5.13267	−	8.89004i	−0.209715	−	0.363237i	−0.951625	+	0.307263i	$0.900587\pi$
$600$		0			0
$601$			9.71063i			0.396105i	0.980191	+	0.198052i	$0.0634616\pi$
$601$			9.71063i			0.396105i	−0.980191	+	0.198052i	$0.936538\pi$
$602$		0			0
$603$	−13.0928	+	22.6774i	−0.533180	+	0.923495i
$604$		0			0
$605$	−4.98440	+	8.63324i	−0.202645	+	0.350991i
$606$		0			0
$607$	43.7354			1.77517			0.887583	−	0.460648i	$-0.152383\pi$
$607$	43.7354			1.77517			0.887583	+	0.460648i	$0.152383\pi$
$608$		0			0
$609$	7.06871			0.286438
$610$		0			0
$611$	−34.4433	+	59.6576i	−1.39343	+	2.41349i
$612$		0			0
$613$	−6.26082	+	10.8441i	−0.252872	+	0.437987i	−0.964315	−	0.264756i	$-0.914709\pi$
$613$	−6.26082	+	10.8441i	−0.252872	+	0.437987i	0.711443	+	0.702744i	$0.248042\pi$
$614$		0			0
$615$		−	2.95428i		−	0.119128i
$616$		0			0
$617$	12.2821	+	21.2732i	0.494457	+	0.856425i	0.999980	−	0.00638834i	$-0.00203349\pi$
$617$	12.2821	+	21.2732i	0.494457	+	0.856425i	−0.505522	+	0.862814i	$0.668700\pi$
$618$		0			0
$619$			42.2721i			1.69906i	0.527541	+	0.849530i	$0.323114\pi$
$619$			42.2721i			1.69906i	−0.527541	+	0.849530i	$0.676886\pi$
$620$		0			0
$621$	−0.327041	+	0.188817i	−0.0131237	+	0.00757698i
$622$		0			0
$623$	−7.79331	−	13.4984i	−0.312232	−	0.540802i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	0.533315	+	1.68513i	0.0212986	+	0.0672978i
$628$		0			0
$629$	2.80761	+	1.62097i	0.111947	+	0.0646324i
$630$		0			0
$631$	0.356582	−	0.205873i	0.0141953	−	0.00819567i	−0.492886	−	0.870094i	$-0.664058\pi$
$631$	0.356582	−	0.205873i	0.0141953	−	0.00819567i	0.507081	+	0.861898i	$0.330725\pi$
$632$		0			0
$633$	2.54289	+	4.40441i	0.101071	+	0.175059i
$634$		0			0
$635$	5.11498			0.202982
$636$		0			0
$637$	−68.9061	+	39.7830i	−2.73016	+	1.57626i
$638$		0			0
$639$	−34.9222			−1.38150
$640$		0			0
$641$	14.7942	+	8.54141i	0.584334	+	0.337365i	0.762854	−	0.646571i	$-0.223798\pi$
$641$	14.7942	+	8.54141i	0.584334	+	0.337365i	−0.178520	+	0.983936i	$0.557131\pi$
$642$		0			0
$643$	20.0442	+	11.5725i	0.790465	+	0.456375i	0.840126	−	0.542391i	$-0.182481\pi$
$643$	20.0442	+	11.5725i	0.790465	+	0.456375i	−0.0496609	+	0.998766i	$0.515814\pi$
$644$		0			0
$645$		−	1.02251i		−	0.0402615i
$646$		0			0
$647$			12.4795i			0.490619i	0.969445	+	0.245310i	$0.0788897\pi$
$647$			12.4795i			0.490619i	−0.969445	+	0.245310i	$0.921110\pi$
$648$		0			0
$649$	12.6630	+	7.31099i	0.497067	+	0.286982i
$650$		0			0
$651$	−0.0827831	−	0.0477948i	−0.00324452	−	0.00187323i
$652$		0			0
$653$	23.7718			0.930264			0.465132	−	0.885241i	$-0.346007\pi$
$653$	23.7718			0.930264			0.465132	+	0.885241i	$0.346007\pi$
$654$		0			0
$655$	−9.93111	+	5.73373i	−0.388040	+	0.224035i
$656$		0			0
$657$	38.0163			1.48316
$658$		0			0
$659$	−6.18515	−	10.7130i	−0.240939	−	0.417319i	0.720043	−	0.693930i	$-0.244122\pi$
$659$	−6.18515	−	10.7130i	−0.240939	−	0.417319i	−0.960982	+	0.276611i	$0.910789\pi$
$660$		0			0
$661$	15.2952	−	8.83067i	0.594913	−	0.343473i	−0.172125	−	0.985075i	$-0.555063\pi$
$661$	15.2952	−	8.83067i	0.594913	−	0.343473i	0.767038	+	0.641602i	$0.221730\pi$
$662$		0			0
$663$	−1.45902	−	0.842366i	−0.0566637	−	0.0327148i
$664$		0			0
$665$	−5.91779	−	18.6986i	−0.229482	−	0.725102i
$666$		0			0
$667$	−0.318519	+	0.551690i	−0.0123331	+	0.0213615i
$668$		0			0
$669$	2.48938	+	4.31173i	0.0962449	+	0.166701i
$670$		0			0
$671$	−8.86971	+	5.12093i	−0.342411	+	0.197691i
$672$		0			0
$673$		−	13.7377i		−	0.529550i	−0.964310	−	0.264775i	$-0.914702\pi$
$673$		−	13.7377i		−	0.529550i	0.964310	−	0.264775i	$-0.0852977\pi$
$674$		0			0
$675$	1.16611	+	2.01976i	0.0448836	+	0.0777407i
$676$		0			0
$677$		−	18.1962i		−	0.699335i	−0.936874	−	0.349668i	$-0.886295\pi$
$677$		−	18.1962i		−	0.699335i	0.936874	−	0.349668i	$-0.113705\pi$
$678$		0			0
$679$	−4.66345	+	8.07733i	−0.178967	+	0.309980i
$680$		0			0
$681$	−4.20274	+	7.27935i	−0.161049	+	0.278945i
$682$		0			0
$683$	−15.2122			−0.582079			−0.291040	−	0.956711i	$-0.594001\pi$
$683$	−15.2122			−0.582079			−0.291040	+	0.956711i	$0.594001\pi$
$684$		0			0
$685$	18.1120			0.692024
$686$		0			0
$687$	−3.22113	+	5.57915i	−0.122894	+	0.212858i
$688$		0			0
$689$	1.21793	−	2.10952i	0.0463996	−	0.0803665i
$690$		0			0
$691$		−	39.0603i		−	1.48592i	−0.669333	−	0.742962i	$-0.733420\pi$
$691$		−	39.0603i		−	1.48592i	0.669333	−	0.742962i	$-0.266580\pi$
$692$		0			0
$693$	6.48938	+	11.2399i	0.246511	+	0.426970i
$694$		0			0
$695$		−	0.393612i		−	0.0149306i
$696$		0			0
$697$	−4.50000	+	2.59808i	−0.170450	+	0.0984092i
$698$		0			0
$699$	−3.63332	−	6.29310i	−0.137425	−	0.238027i
$700$		0			0
$701$	−5.01915	+	8.69343i	−0.189571	+	0.328346i	−0.945107	−	0.326760i	$-0.894043\pi$
$701$	−5.01915	+	8.69343i	−0.189571	+	0.328346i	0.755536	+	0.655107i	$0.227376\pi$
$702$		0			0
$703$	13.5772	−	14.8489i	0.512072	−	0.560037i
$704$		0			0
$705$	3.96565	+	2.28957i	0.149355	+	0.0862301i
$706$		0			0
$707$	−13.8882	+	8.01835i	−0.522319	+	0.301561i
$708$		0			0
$709$	−9.95005	−	17.2340i	−0.373682	−	0.647236i	0.616447	−	0.787397i	$-0.288572\pi$
$709$	−9.95005	−	17.2340i	−0.373682	−	0.647236i	−0.990129	+	0.140160i	$0.955238\pi$
$710$		0			0
$711$	26.4879			0.993372
$712$		0			0
$713$	0.00746047	−	0.00430731i	0.000279397	−	0.000161310i
$714$		0			0
$715$	6.10011			0.228131
$716$		0			0
$717$	3.67047	+	2.11915i	0.137076	+	0.0791410i
$718$		0			0
$719$	14.9653	+	8.64021i	0.558111	+	0.322226i	0.752387	−	0.658721i	$-0.228902\pi$
$719$	14.9653	+	8.64021i	0.558111	+	0.322226i	−0.194276	+	0.980947i	$0.562236\pi$
$720$		0			0
$721$		−	59.6378i		−	2.22103i
$722$		0			0
$723$			2.11886i			0.0788011i
$724$		0			0
$725$	3.40716	+	1.96713i	0.126539	+	0.0730573i
$726$		0			0
$727$	19.1230	+	11.0407i	0.709233	+	0.409476i	0.810777	−	0.585355i	$-0.199045\pi$
$727$	19.1230	+	11.0407i	0.709233	+	0.409476i	−0.101544	+	0.994831i	$0.532378\pi$
$728$		0			0
$729$	−18.7669			−0.695069
$730$		0			0
$731$	−1.55751	+	0.899228i	−0.0576065	+	0.0332591i
$732$		0			0
$733$	18.6861			0.690186			0.345093	−	0.938569i	$-0.387847\pi$
$733$	18.6861			0.690186			0.345093	+	0.938569i	$0.387847\pi$
$734$		0			0
$735$	2.64451	+	4.58043i	0.0975443	+	0.168952i
$736$		0			0
$737$	8.10702	−	4.68059i	0.298626	−	0.172412i
$738$		0			0
$739$	−39.2433	−	22.6571i	−1.44359	−	0.833457i	−0.445502	−	0.895281i	$-0.646975\pi$
$739$	−39.2433	−	22.6571i	−1.44359	−	0.833457i	−0.998087	+	0.0618244i	$0.980308\pi$
$740$		0			0
$741$	−7.05560	+	7.71649i	−0.259194	+	0.283472i
$742$		0			0
$743$	−3.75119	+	6.49726i	−0.137618	+	0.238361i	−0.926594	−	0.376062i	$-0.877278\pi$
$743$	−3.75119	+	6.49726i	−0.137618	+	0.238361i	0.788977	+	0.614423i	$0.210611\pi$
$744$		0			0
$745$	0.420274	+	0.727935i	0.0153976	+	0.0266695i
$746$		0			0
$747$	33.7123	−	19.4638i	1.23347	−	0.712144i
$748$		0			0
$749$			52.4509i			1.91652i
$750$		0			0
$751$	−8.44025	−	14.6189i	−0.307989	−	0.533453i	0.669933	−	0.742421i	$-0.266323\pi$
$751$	−8.44025	−	14.6189i	−0.307989	−	0.533453i	−0.977922	+	0.208969i	$0.932989\pi$
$752$		0			0
$753$			10.0604i			0.366621i
$754$		0			0
$755$	2.89837	−	5.02012i	0.105482	−	0.182701i
$756$		0			0
$757$	10.9047	−	18.8875i	0.396337	−	0.686476i	−0.596934	−	0.802291i	$-0.703614\pi$
$757$	10.9047	−	18.8875i	0.396337	−	0.686476i	0.993271	+	0.115814i	$0.0369478\pi$
$758$		0			0
$759$	0.0656581			0.00238324
$760$		0			0
$761$	−27.1453			−0.984017			−0.492009	−	0.870590i	$-0.663737\pi$
$761$	−27.1453			−0.984017			−0.492009	+	0.870590i	$0.663737\pi$
$762$		0			0
$763$	−27.1744	+	47.0675i	−0.983780	+	1.70396i
$764$		0			0
$765$	0.997513	−	1.72774i	0.0360652	−	0.0624667i
$766$		0			0
$767$			86.4977i			3.12325i
$768$		0			0
$769$	−4.51062	−	7.81263i	−0.162657	−	0.281731i	0.773164	−	0.634207i	$-0.218673\pi$
$769$	−4.51062	−	7.81263i	−0.162657	−	0.281731i	−0.935821	+	0.352476i	$0.885340\pi$
$770$		0			0
$771$		−	3.04987i		−	0.109838i
$772$		0			0
$773$	−13.9706	+	8.06594i	−0.502488	+	0.290112i	−0.729741	−	0.683724i	$-0.760359\pi$
$773$	−13.9706	+	8.06594i	−0.502488	+	0.290112i	0.227252	+	0.973836i	$0.427026\pi$
$774$		0			0
$775$	−0.0266013	−	0.0460749i	−0.000955548	−	0.00165506i
$776$		0			0
$777$	−4.14674	+	7.18236i	−0.148763	+	0.257666i
$778$		0			0
$779$	9.73046	+	30.7457i	0.348630	+	1.10158i
$780$		0			0
$781$	10.8118	+	6.24222i	0.386878	+	0.223364i
$782$		0			0
$783$	7.94626	−	4.58778i	0.283976	−	0.163954i
$784$		0			0
$785$	−2.71545	−	4.70329i	−0.0969185	−	0.167868i
$786$		0			0
$787$	15.0789			0.537505			0.268753	−	0.963209i	$-0.413389\pi$
$787$	15.0789			0.537505			0.268753	+	0.963209i	$0.413389\pi$
$788$		0			0
$789$	8.40965	−	4.85531i	0.299392	−	0.172854i
$790$		0			0
$791$	−18.7792			−0.667710
$792$		0			0
$793$	−52.4696	−	30.2933i	−1.86325	−	1.07575i
$794$		0			0
$795$	−0.140227	−	0.0809603i	−0.00497335	−	0.00287137i
$796$		0			0
$797$		−	46.2044i		−	1.63664i	−0.574760	−	0.818322i	$-0.694905\pi$
$797$		−	46.2044i		−	1.63664i	0.574760	−	0.818322i	$-0.305095\pi$
$798$		0			0
$799$		−	8.05404i		−	0.284931i
$800$		0			0
$801$	−8.52164	−	4.91997i	−0.301097	−	0.173839i
$802$		0			0
$803$	−11.7698	−	6.79528i	−0.415346	−	0.239800i
$804$		0			0
$805$	−0.728557			−0.0256783
$806$		0			0
$807$	−4.75372	+	2.74456i	−0.167339	+	0.0966132i
$808$		0			0
$809$	−3.61657			−0.127152			−0.0635759	−	0.997977i	$-0.520250\pi$
$809$	−3.61657			−0.127152			−0.0635759	+	0.997977i	$0.520250\pi$
$810$		0			0
$811$	−6.65380	−	11.5247i	−0.233647	−	0.404688i	0.725232	−	0.688505i	$-0.241733\pi$
$811$	−6.65380	−	11.5247i	−0.233647	−	0.404688i	−0.958878	+	0.283817i	$0.908399\pi$
$812$		0			0
$813$	−6.91858	+	3.99444i	−0.242645	+	0.140091i
$814$		0			0
$815$	10.6703	+	6.16051i	0.373765	+	0.215793i
$816$		0			0
$817$	3.36784	+	10.6415i	0.117826	+	0.372298i
$818$		0			0
$819$	−38.3885	+	66.4909i	−1.34140	+	2.32338i
$820$		0			0
$821$	5.14634	+	8.91373i	0.179609	+	0.311091i	0.941747	−	0.336323i	$-0.109184\pi$
$821$	5.14634	+	8.91373i	0.179609	+	0.311091i	−0.762138	+	0.647415i	$0.775850\pi$
$822$		0			0
$823$	−18.9447	+	10.9377i	−0.660372	+	0.381266i	−0.792419	−	0.609978i	$-0.791178\pi$
$823$	−18.9447	+	10.9377i	−0.660372	+	0.381266i	0.132047	+	0.991243i	$0.457845\pi$
$824$		0			0
$825$		−	0.405495i		−	0.0141175i
$826$		0			0
$827$	10.7225	+	18.5719i	0.372858	+	0.645810i	0.990004	−	0.141039i	$-0.0450444\pi$
$827$	10.7225	+	18.5719i	0.372858	+	0.645810i	−0.617146	+	0.786849i	$0.711711\pi$
$828$		0			0
$829$			7.34231i			0.255009i	0.991838	+	0.127505i	$0.0406967\pi$
$829$			7.34231i			0.255009i	−0.991838	+	0.127505i	$0.959303\pi$
$830$		0			0
$831$	−3.13085	+	5.42280i	−0.108608	+	0.188115i
$832$		0			0
$833$	4.65132	−	8.05632i	0.161159	−	0.279135i
$834$		0			0
$835$	−2.33024			−0.0806411
$836$		0			0
$837$	−0.124080			−0.00428885
$838$		0			0
$839$	15.5173	−	26.8767i	0.535716	−	0.927888i	−0.463412	−	0.886143i	$-0.653375\pi$
$839$	15.5173	−	26.8767i	0.535716	−	0.927888i	0.999128	−	0.0417447i	$-0.0132916\pi$
$840$		0			0
$841$	−6.76082	+	11.7101i	−0.233132	+	0.403796i
$842$		0			0
$843$			7.41324i			0.255325i
$844$		0			0
$845$	11.5429	+	19.9929i	0.397087	+	0.687775i
$846$		0			0
$847$			44.8543i			1.54121i
$848$		0			0
$849$	5.31433	−	3.06823i	0.182387	−	0.105301i
$850$		0			0
$851$	−0.373707	−	0.647280i	−0.0128105	−	0.0221885i
$852$		0			0
$853$	−8.82495	+	15.2853i	−0.302161	+	0.523357i	−0.976625	−	0.214950i	$-0.931041\pi$
$853$	−8.82495	+	15.2853i	−0.302161	+	0.523357i	0.674465	+	0.738307i	$0.264375\pi$
$854$		0			0
$855$	−9.13771	−	8.35510i	−0.312503	−	0.285738i
$856$		0			0
$857$	14.5291	+	8.38838i	0.496305	+	0.286542i	0.727186	−	0.686440i	$-0.240828\pi$
$857$	14.5291	+	8.38838i	0.496305	+	0.286542i	−0.230882	+	0.972982i	$0.574161\pi$
$858$		0			0
$859$	−34.6649	+	20.0138i	−1.18275	+	0.682862i	−0.956650	−	0.291242i	$-0.905932\pi$
$859$	−34.6649	+	20.0138i	−1.18275	+	0.682862i	−0.226102	+	0.974104i	$0.572598\pi$
$860$		0			0
$861$	−6.64634	−	11.5118i	−0.226507	−	0.392321i
$862$		0			0
$863$	2.28100			0.0776463			0.0388232	−	0.999246i	$-0.487639\pi$
$863$	2.28100			0.0776463			0.0388232	+	0.999246i	$0.487639\pi$
$864$		0			0
$865$	−9.29517	+	5.36657i	−0.316045	+	0.182469i
$866$		0			0
$867$	−6.59139			−0.223855
$868$		0			0
$869$	−8.20059	−	4.73461i	−0.278186	−	0.160611i
$870$		0			0
$871$	47.9578	+	27.6885i	1.62499	+	0.938187i
$872$		0			0
$873$			5.88814i			0.199283i
$874$		0			0
$875$			4.49947i			0.152110i
$876$		0			0
$877$	25.9238	+	14.9671i	0.875386	+	0.505404i	0.869134	−	0.494576i	$-0.164677\pi$
$877$	25.9238	+	14.9671i	0.875386	+	0.505404i	0.00625142	+	0.999980i	$0.498010\pi$
$878$		0			0
$879$	−0.178291	−	0.102936i	−0.00601361	−	0.00347196i
$880$		0			0
$881$	−3.99005			−0.134428			−0.0672141	−	0.997739i	$-0.521411\pi$
$881$	−3.99005			−0.134428			−0.0672141	+	0.997739i	$0.521411\pi$
$882$		0			0
$883$	30.9949	−	17.8949i	1.04306	−	0.602213i	0.122364	−	0.992485i	$-0.460953\pi$
$883$	30.9949	−	17.8949i	1.04306	−	0.602213i	0.920699	+	0.390273i	$0.127619\pi$
$884$		0			0
$885$	5.74980			0.193277
$886$		0			0
$887$	13.3743	+	23.1649i	0.449063	+	0.777801i	0.998325	−	0.0578496i	$-0.0184244\pi$
$887$	13.3743	+	23.1649i	0.449063	+	0.777801i	−0.549262	+	0.835650i	$0.685091\pi$
$888$		0			0
$889$	19.9313	−	11.5073i	0.668474	−	0.385944i
$890$		0			0
$891$	6.67517	+	3.85391i	0.223627	+	0.129111i
$892$		0			0
$893$	−48.8122	−	10.7663i	−1.63344	−	0.360281i
$894$		0			0
$895$	6.10902	−	10.5811i	0.204202	−	0.353688i
$896$		0			0
$897$	0.194203	+	0.336370i	0.00648426	+	0.0112311i
$898$		0			0
$899$	−0.181270	+	0.104656i	−0.00604570	+	0.00349049i
$900$		0			0
$901$			0.284795i			0.00948790i
$902$		0			0
$903$	−2.30039	−	3.98438i	−0.0765520	−	0.132592i
$904$		0			0
$905$		−	22.7753i		−	0.757076i
$906$		0			0
$907$	8.24781	−	14.2856i	0.273864	−	0.474347i	−0.695984	−	0.718058i	$-0.745031\pi$
$907$	8.24781	−	14.2856i	0.273864	−	0.474347i	0.969848	+	0.243711i	$0.0783648\pi$
$908$		0			0
$909$	−5.06204	+	8.76771i	−0.167897	+	0.290807i
$910$		0			0
$911$	−46.6599			−1.54591			−0.772957	−	0.634459i	$-0.781223\pi$
$911$	−46.6599			−1.54591			−0.772957	+	0.634459i	$0.781223\pi$
$912$		0			0
$913$	−13.9164			−0.460565
$914$		0			0
$915$	−2.01370	+	3.48784i	−0.0665710	+	0.115304i
$916$		0			0
$917$	−25.7987	+	44.6847i	−0.851949	+	1.47562i
$918$		0			0
$919$			42.1283i			1.38969i	0.719162	+	0.694843i	$0.244526\pi$
$919$			42.1283i			1.38969i	−0.719162	+	0.694843i	$0.755474\pi$
$920$		0			0
$921$	4.28664	+	7.42468i	0.141250	+	0.244652i
$922$		0			0
$923$			73.8529i			2.43090i
$924$		0			0
$925$	−3.99751	+	2.30797i	−0.131437	+	0.0758854i
$926$		0			0
$927$	−18.8249	−	32.6056i	−0.618290	−	1.07091i
$928$		0			0
$929$	27.2538	−	47.2049i	0.894167	−	1.54874i	0.0593343	−	0.998238i	$-0.481102\pi$
$929$	27.2538	−	47.2049i	0.894167	−	1.54874i	0.834832	−	0.550504i	$-0.185564\pi$
$930$		0			0
$931$	−42.6084	−	38.9591i	−1.39643	−	1.27683i
$932$		0			0
$933$	9.07266	+	5.23810i	0.297026	+	0.171488i
$934$		0			0
$935$	−0.617657	+	0.356604i	−0.0201995	+	0.0116622i
$936$		0			0
$937$	−28.8274	−	49.9306i	−0.941751	−	1.63116i	−0.762129	−	0.647426i	$-0.775846\pi$
$937$	−28.8274	−	49.9306i	−0.941751	−	1.63116i	−0.179623	−	0.983736i	$-0.557488\pi$
$938$		0			0
$939$	−10.2254			−0.333695
$940$		0			0
$941$	−35.0433	+	20.2322i	−1.14238	+	0.659552i	−0.947018	−	0.321179i	$-0.895921\pi$
$941$	−35.0433	+	20.2322i	−1.14238	+	0.659552i	−0.195360	+	0.980732i	$0.562587\pi$
$942$		0			0
$943$	1.19795			0.0390105
$944$		0			0
$945$	9.08786	+	5.24688i	0.295628	+	0.170681i
$946$		0			0
$947$	−26.9767	−	15.5750i	−0.876627	−	0.506121i	−0.00708189	−	0.999975i	$-0.502254\pi$
$947$	−26.9767	−	15.5750i	−0.876627	−	0.506121i	−0.869545	+	0.493854i	$0.835588\pi$
$948$		0			0
$949$		−	80.3962i		−	2.60977i
$950$		0			0
$951$			6.58206i			0.213438i
$952$		0			0
$953$	26.7548	+	15.4469i	0.866674	+	0.500374i	0.866242	−	0.499625i	$-0.166529\pi$
$953$	26.7548	+	15.4469i	0.866674	+	0.500374i	0.000432383		1.00000i	$0.499862\pi$
$954$		0			0
$955$	−6.31491	−	3.64591i	−0.204346	−	0.117979i
$956$		0			0
$957$	−1.59532			−0.0515695
$958$		0			0
$959$	70.5762	−	40.7472i	2.27902	−	1.31579i
$960$		0			0
$961$	−30.9972			−0.999909
$962$		0			0
$963$	16.5563	+	28.6764i	0.533520	+	0.924084i
$964$		0			0
$965$	16.8678	−	9.73865i	0.542995	−	0.313498i
$966$		0			0
$967$	−16.1475	−	9.32278i	−0.519270	−	0.299800i	0.217366	−	0.976090i	$-0.430253\pi$
$967$	−16.1475	−	9.32278i	−0.519270	−	0.299800i	−0.736636	+	0.676290i	$0.763587\pi$
$968$		0			0
$969$	0.263307	−	1.19378i	0.00845865	−	0.0383498i
$970$		0			0
$971$	23.2725	−	40.3092i	0.746851	−	1.29358i	−0.202474	−	0.979288i	$-0.564898\pi$
$971$	23.2725	−	40.3092i	0.746851	−	1.29358i	0.949325	−	0.314296i	$-0.101769\pi$
$972$		0			0
$973$	−0.885523	−	1.53377i	−0.0283886	−	0.0491704i
$974$		0			0
$975$	2.07737	−	1.19937i	0.0665292	−	0.0384107i
$976$		0			0
$977$			54.1376i			1.73201i	0.500032	+	0.866007i	$0.333322\pi$
$977$			54.1376i			1.73201i	−0.500032	+	0.866007i	$0.666678\pi$
$978$		0			0
$979$	1.75886	+	3.04643i	0.0562133	+	0.0973643i
$980$		0			0
$981$			34.3108i			1.09546i
$982$		0			0
$983$	0.804859	−	1.39406i	0.0256710	−	0.0444635i	−0.852904	−	0.522067i	$-0.825161\pi$
$983$	0.804859	−	1.39406i	0.0256710	−	0.0444635i	0.878576	+	0.477603i	$0.158494\pi$
$984$		0			0
$985$	9.38095	−	16.2483i	0.298902	−	0.517713i
$986$		0			0
$987$	20.6037			0.655822
$988$		0			0
$989$	0.414625			0.0131843
$990$		0			0
$991$	−3.58536	+	6.21002i	−0.113893	+	0.197268i	−0.917337	−	0.398113i	$-0.869665\pi$
$991$	−3.58536	+	6.21002i	−0.113893	+	0.197268i	0.803444	+	0.595380i	$0.202999\pi$
$992$		0			0
$993$	−1.96774	+	3.40822i	−0.0624442	+	0.108157i
$994$		0			0
$995$		−	8.79307i		−	0.278759i
$996$		0			0
$997$	−5.71901	−	9.90561i	−0.181123	−	0.313714i	0.761140	−	0.648587i	$-0.224640\pi$
$997$	−5.71901	−	9.90561i	−0.181123	−	0.313714i	−0.942263	+	0.334873i	$0.891306\pi$
$998$		0			0
$999$			10.7654i			0.340601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.bq.q.1471.3	yes	12
4.3	odd	2	inner	1520.2.bq.q.1471.4	yes	12
19.12	odd	6	inner	1520.2.bq.q.31.4	yes	12
76.31	even	6	inner	1520.2.bq.q.31.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1520.2.bq.q.31.3	✓	12	76.31	even	6	inner
1520.2.bq.q.31.4	yes	12	19.12	odd	6	inner
1520.2.bq.q.1471.3	yes	12	1.1	even	1	trivial
1520.2.bq.q.1471.4	yes	12	4.3	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.199658 + 0.345817i) q^{3} +(-0.500000 + 0.866025i) q^{5} +4.49947i q^{7} +(1.42027 + 2.45999i) q^{9} -1.01548i q^{11} +(5.20234 - 3.00357i) q^{13} +(-0.199658 - 0.345817i) q^{15} +(-0.351169 + 0.608243i) q^{17} +(3.21688 + 2.94137i) q^{19} +(-1.55599 - 0.898354i) q^{21} +(0.140227 - 0.0809603i) q^{23} +(-0.500000 - 0.866025i) q^{25} -2.33222 q^{27} +(-3.40716 + 1.96713i) q^{29} +0.0532027 q^{31} +(0.351169 + 0.202748i) q^{33} +(-3.89665 - 2.24973i) q^{35} -4.61593i q^{37} +2.39875i q^{39} +(6.40716 + 3.69918i) q^{41} +(2.21760 + 1.28033i) q^{43} -2.84055 q^{45} +(-9.93111 + 5.73373i) q^{47} -13.2452 q^{49} +(-0.140227 - 0.242881i) q^{51} +(0.351169 - 0.202748i) q^{53} +(0.879428 + 0.507738i) q^{55} +(-1.65945 + 0.525187i) q^{57} +(-7.19957 + 12.4700i) q^{59} +(-5.04289 - 8.73453i) q^{61} +(-11.0686 + 6.39048i) q^{63} +6.00714i q^{65} +(4.60925 + 7.98346i) q^{67} +0.0646574i q^{69} +(-6.14709 + 10.6471i) q^{71} +(6.69172 - 11.5904i) q^{73} +0.399316 q^{75} +4.56910 q^{77} +(4.66246 - 8.07561i) q^{79} +(-3.79517 + 6.57343i) q^{81} -13.7043i q^{83} +(-0.351169 - 0.608243i) q^{85} -1.57101i q^{87} +(-3.00000 + 1.73205i) q^{89} +(13.5145 + 23.4078i) q^{91} +(-0.0106223 + 0.0183984i) q^{93} +(-4.15574 + 1.31522i) q^{95} +(1.79517 + 1.03644i) q^{97} +(2.49806 - 1.44225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{5} - 4 q^{9} + 18 q^{13} + 18 q^{17} + 24 q^{21} - 6 q^{25} + 24 q^{29} - 18 q^{33} + 12 q^{41} + 8 q^{45} - 28 q^{49} - 18 q^{53} - 62 q^{57} + 26 q^{61} + 16 q^{73} + 56 q^{77} - 66 q^{81}+ \cdots + 42 q^{97}+O(q^{100}) \) 12 * q - 6 * q^5 - 4 * q^9 + 18 * q^13 + 18 * q^17 + 24 * q^21 - 6 * q^25 + 24 * q^29 - 18 * q^33 + 12 * q^41 + 8 * q^45 - 28 * q^49 - 18 * q^53 - 62 * q^57 + 26 * q^61 + 16 * q^73 + 56 * q^77 - 66 * q^81 + 18 * q^85 - 36 * q^89 - 20 * q^93 + 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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