LMFDB - Embedded newform 756.2.ck.a.5.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.19
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26963 + 1.17815i) q^{3} +(0.263400 - 1.49382i) q^{5} +(0.0912000 + 2.64418i) q^{7} +(0.223916 + 2.99163i) q^{9} +O(q^{10})$	\(q+(1.26963 + 1.17815i) q^{3} +(0.263400 - 1.49382i) q^{5} +(0.0912000 + 2.64418i) q^{7} +(0.223916 + 2.99163i) q^{9} +(6.22570 - 1.09776i) q^{11} +(0.407322 - 0.485427i) q^{13} +(2.09436 - 1.58627i) q^{15} -6.93398 q^{17} +2.05921i q^{19} +(-2.99945 + 3.46457i) q^{21} +(2.16096 - 2.57533i) q^{23} +(2.53635 + 0.923157i) q^{25} +(-3.24031 + 4.06207i) q^{27} +(2.79770 + 3.33417i) q^{29} +(-1.20541 - 3.31183i) q^{31} +(9.19765 + 5.94107i) q^{33} +(3.97394 + 0.560241i) q^{35} +(3.88922 + 6.73632i) q^{37} +(1.08905 - 0.136425i) q^{39} +(0.418271 + 0.350971i) q^{41} +(-9.16836 - 3.33701i) q^{43} +(4.52793 + 0.453508i) q^{45} +(9.33615 + 3.39808i) q^{47} +(-6.98337 + 0.482298i) q^{49} +(-8.80358 - 8.16928i) q^{51} +(7.54846 - 4.35811i) q^{53} -9.58920i q^{55} +(-2.42606 + 2.61443i) q^{57} +(1.80096 + 1.51118i) q^{59} +(0.539493 - 1.48225i) q^{61} +(-7.88999 + 0.864910i) q^{63} +(-0.617851 - 0.736326i) q^{65} +(-1.21605 + 6.89658i) q^{67} +(5.77774 - 0.723775i) q^{69} +(-8.41776 - 4.85999i) q^{71} +(-12.7696 - 7.37256i) q^{73} +(2.13261 + 4.16028i) q^{75} +(3.47045 + 16.3617i) q^{77} +(-1.34555 - 7.63097i) q^{79} +(-8.89972 + 1.33975i) q^{81} +(2.58568 - 2.16964i) q^{83} +(-1.82641 + 10.3581i) q^{85} +(-0.376117 + 7.52927i) q^{87} -4.90235 q^{89} +(1.32070 + 1.03276i) q^{91} +(2.37142 - 5.62495i) q^{93} +(3.07608 + 0.542397i) q^{95} +(2.07416 - 5.69871i) q^{97} +(4.67812 + 18.3792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	1.26963	+	1.17815i	0.733021	+	0.680206i
$3$	1.26963	+	1.17815i	0.733021	+	0.680206i
$4$		0			0
$5$	0.263400	−	1.49382i	0.117796	−	0.668055i	−0.867531	−	0.497382i	$-0.834295\pi$
$5$	0.263400	−	1.49382i	0.117796	−	0.668055i	0.985328	−	0.170673i	$-0.0545942\pi$
$6$		0			0
$7$	0.0912000	+	2.64418i	0.0344704	+	0.999406i
$7$	0.0912000	+	2.64418i	0.0344704	+	0.999406i
$8$		0			0
$9$	0.223916	+	2.99163i	0.0746386	+	0.997211i
$10$		0			0
$11$	6.22570	−	1.09776i	1.87712	−	0.330986i	0.885969	−	0.463744i	$-0.153494\pi$
$11$	6.22570	−	1.09776i	1.87712	−	0.330986i	0.991149	+	0.132758i	$0.0423832\pi$
$12$		0			0
$13$	0.407322	−	0.485427i	0.112971	−	0.134633i	−0.706596	−	0.707618i	$-0.749770\pi$
$13$	0.407322	−	0.485427i	0.112971	−	0.134633i	0.819566	+	0.572984i	$0.194214\pi$
$14$		0			0
$15$	2.09436	−	1.58627i	0.540763	−	0.409573i
$16$		0			0
$17$	−6.93398			−1.68174			−0.840868	−	0.541240i	$-0.817955\pi$
$17$	−6.93398			−1.68174			−0.840868	+	0.541240i	$0.817955\pi$
$18$		0			0
$19$			2.05921i			0.472415i	0.971703	+	0.236208i	$0.0759046\pi$
$19$			2.05921i			0.472415i	−0.971703	+	0.236208i	$0.924095\pi$
$20$		0			0
$21$	−2.99945	+	3.46457i	−0.654535	+	0.756032i
$22$		0			0
$23$	2.16096	−	2.57533i	0.450590	−	0.536993i	−0.492154	−	0.870508i	$-0.663790\pi$
$23$	2.16096	−	2.57533i	0.450590	−	0.536993i	0.942745	+	0.333515i	$0.108235\pi$
$24$		0			0
$25$	2.53635	+	0.923157i	0.507270	+	0.184631i
$26$		0			0
$27$	−3.24031	+	4.06207i	−0.623597	+	0.781746i
$28$		0			0
$29$	2.79770	+	3.33417i	0.519520	+	0.619140i	0.960467	−	0.278393i	$-0.0898019\pi$
$29$	2.79770	+	3.33417i	0.519520	+	0.619140i	−0.440947	+	0.897533i	$0.645357\pi$
$30$		0			0
$31$	−1.20541	−	3.31183i	−0.216497	−	0.594822i	0.783137	−	0.621849i	$-0.213618\pi$
$31$	−1.20541	−	3.31183i	−0.216497	−	0.594822i	−0.999635	+	0.0270270i	$0.991396\pi$
$32$		0			0
$33$	9.19765	+	5.94107i	1.60111	+	1.03421i
$34$		0			0
$35$	3.97394	+	0.560241i	0.671719	+	0.0946981i
$36$		0			0
$37$	3.88922	+	6.73632i	0.639383	+	1.10744i	0.985568	+	0.169278i	$0.0541437\pi$
$37$	3.88922	+	6.73632i	0.639383	+	1.10744i	−0.346185	+	0.938166i	$0.612523\pi$
$38$		0			0
$39$	1.08905	−	0.136425i	0.174388	−	0.0218456i
$40$		0			0
$41$	0.418271	+	0.350971i	0.0653230	+	0.0548125i	0.674865	−	0.737942i	$-0.264202\pi$
$41$	0.418271	+	0.350971i	0.0653230	+	0.0548125i	−0.609542	+	0.792754i	$0.708646\pi$
$42$		0			0
$43$	−9.16836	−	3.33701i	−1.39816	−	0.508889i	−0.470529	−	0.882384i	$-0.655937\pi$
$43$	−9.16836	−	3.33701i	−1.39816	−	0.508889i	−0.927632	+	0.373495i	$0.878159\pi$
$44$		0			0
$45$	4.52793	+	0.453508i	0.674984	+	0.0676049i
$46$		0			0
$47$	9.33615	+	3.39808i	1.36182	+	0.495661i	0.916616	−	0.399770i	$-0.130910\pi$
$47$	9.33615	+	3.39808i	1.36182	+	0.495661i	0.445201	+	0.895430i	$0.353132\pi$
$48$		0			0
$49$	−6.98337	+	0.482298i	−0.997624	+	0.0688997i
$50$		0			0
$51$	−8.80358	−	8.16928i	−1.23275	−	1.14393i
$52$		0			0
$53$	7.54846	−	4.35811i	1.03686	−	0.598632i	0.117919	−	0.993023i	$-0.462378\pi$
$53$	7.54846	−	4.35811i	1.03686	−	0.598632i	0.918943	+	0.394391i	$0.129044\pi$
$54$		0			0
$55$		−	9.58920i		−	1.29301i
$56$		0			0
$57$	−2.42606	+	2.61443i	−0.321340	+	0.346290i
$58$		0			0
$59$	1.80096	+	1.51118i	0.234465	+	0.196740i	0.752448	−	0.658651i	$-0.228873\pi$
$59$	1.80096	+	1.51118i	0.234465	+	0.196740i	−0.517983	+	0.855391i	$0.673317\pi$
$60$		0			0
$61$	0.539493	−	1.48225i	0.0690750	−	0.189782i	−0.900352	−	0.435163i	$-0.856691\pi$
$61$	0.539493	−	1.48225i	0.0690750	−	0.189782i	0.969427	+	0.245381i	$0.0789130\pi$
$62$		0			0
$63$	−7.88999	+	0.864910i	−0.994045	+	0.108968i
$64$		0			0
$65$	−0.617851	−	0.736326i	−0.0766350	−	0.0913300i
$66$		0			0
$67$	−1.21605	+	6.89658i	−0.148565	+	0.842552i	0.815871	+	0.578234i	$0.196258\pi$
$67$	−1.21605	+	6.89658i	−0.148565	+	0.842552i	−0.964436	+	0.264318i	$0.914853\pi$
$68$		0			0
$69$	5.77774	−	0.723775i	0.695558	−	0.0871323i
$70$		0			0
$71$	−8.41776	−	4.85999i	−0.999004	−	0.576775i	−0.0910504	−	0.995846i	$-0.529022\pi$
$71$	−8.41776	−	4.85999i	−0.999004	−	0.576775i	−0.907953	+	0.419071i	$0.862356\pi$
$72$		0			0
$73$	−12.7696	−	7.37256i	−1.49457	−	0.862892i	−0.494593	−	0.869125i	$-0.664683\pi$
$73$	−12.7696	−	7.37256i	−1.49457	−	0.862892i	−0.999981	+	0.00623244i	$0.998016\pi$
$74$		0			0
$75$	2.13261	+	4.16028i	0.246252	+	0.480387i
$76$		0			0
$77$	3.47045	+	16.3617i	0.395495	+	1.86459i
$78$		0			0
$79$	−1.34555	−	7.63097i	−0.151386	−	0.858551i	−0.962016	−	0.272993i	$-0.911986\pi$
$79$	−1.34555	−	7.63097i	−0.151386	−	0.858551i	0.810630	−	0.585558i	$-0.199125\pi$
$80$		0			0
$81$	−8.89972	+	1.33975i	−0.988858	+	0.148861i
$82$		0			0
$83$	2.58568	−	2.16964i	0.283815	−	0.238149i	−0.489755	−	0.871860i	$-0.662914\pi$
$83$	2.58568	−	2.16964i	0.283815	−	0.238149i	0.773570	+	0.633711i	$0.218469\pi$
$84$		0			0
$85$	−1.82641	+	10.3581i	−0.198102	+	1.12349i
$86$		0			0
$87$	−0.376117	+	7.52927i	−0.0403240	+	0.807223i
$88$		0			0
$89$	−4.90235			−0.519649			−0.259824	−	0.965656i	$-0.583665\pi$
$89$	−4.90235			−0.519649			−0.259824	+	0.965656i	$0.583665\pi$
$90$		0			0
$91$	1.32070	+	1.03276i	0.138447	+	0.108263i
$92$		0			0
$93$	2.37142	−	5.62495i	0.245905	−	0.583280i
$94$		0			0
$95$	3.07608	+	0.542397i	0.315600	+	0.0556487i
$96$		0			0
$97$	2.07416	−	5.69871i	0.210599	−	0.578616i	−0.788749	−	0.614715i	$-0.789271\pi$
$97$	2.07416	−	5.69871i	0.210599	−	0.578616i	0.999348	+	0.0360992i	$0.0114932\pi$
$98$		0			0
$99$	4.67812	+	18.3792i	0.470169	+	1.84718i
$100$		0			0
$101$	2.40939	−	2.02171i	0.239743	−	0.201168i	−0.514998	−	0.857192i	$-0.672207\pi$
$101$	2.40939	−	2.02171i	0.239743	−	0.201168i	0.754740	+	0.656023i	$0.227763\pi$
$102$		0			0
$103$	2.24328	+	0.395550i	0.221036	+	0.0389747i	0.283069	−	0.959099i	$-0.408647\pi$
$103$	2.24328	+	0.395550i	0.221036	+	0.0389747i	−0.0620330	+	0.998074i	$0.519758\pi$
$104$		0			0
$105$	4.38538	+	5.39321i	0.427970	+	0.526323i
$106$		0			0
$107$	2.62949	+	1.51814i	0.254203	+	0.146764i	0.621687	−	0.783266i	$-0.286448\pi$
$107$	2.62949	+	1.51814i	0.254203	+	0.146764i	−0.367484	+	0.930030i	$0.619781\pi$
$108$		0			0
$109$	−8.34749	−	14.4583i	−0.799544	−	1.38485i	−0.919913	−	0.392122i	$-0.871741\pi$
$109$	−8.34749	−	14.4583i	−0.799544	−	1.38485i	0.120369	−	0.992729i	$-0.461592\pi$
$110$		0			0
$111$	−2.99855	+	13.1347i	−0.284610	+	1.24669i
$112$		0			0
$113$	2.01570	+	5.53809i	0.189621	+	0.520980i	0.997677	−	0.0681266i	$-0.0217022\pi$
$113$	2.01570	+	5.53809i	0.189621	+	0.520980i	−0.808056	+	0.589106i	$0.799480\pi$
$114$		0			0
$115$	−3.27787	−	3.90641i	−0.305663	−	0.364275i
$116$		0			0
$117$	1.54342	+	1.10986i	0.142690	+	0.102607i
$118$		0			0
$119$	−0.632379	−	18.3347i	−0.0579701	−	1.68074i
$120$		0			0
$121$	27.2176	−	9.90639i	2.47433	−	0.900581i
$122$		0			0
$123$	0.117552	+	0.938390i	0.0105993	+	0.0846118i
$124$		0			0
$125$	5.83926	−	10.1139i	0.522279	−	0.904614i
$126$		0			0
$127$	−4.41291	−	7.64339i	−0.391583	−	0.678241i	0.601076	−	0.799192i	$-0.294739\pi$
$127$	−4.41291	−	7.64339i	−0.391583	−	0.678241i	−0.992658	+	0.120951i	$0.961406\pi$
$128$		0			0
$129$	−7.70891	−	15.0385i	−0.678732	−	1.32406i
$130$		0			0
$131$	−16.8235	−	14.1166i	−1.46987	−	1.23337i	−0.916252	−	0.400602i	$-0.868801\pi$
$131$	−16.8235	−	14.1166i	−1.46987	−	1.23337i	−0.553622	−	0.832768i	$-0.686755\pi$
$132$		0			0
$133$	−5.44492	+	0.187800i	−0.472135	+	0.0162843i
$134$		0			0
$135$	5.21449	+	5.91038i	0.448792	+	0.508684i
$136$		0			0
$137$	1.59677	−	4.38708i	0.136421	−	0.374813i	−0.852605	−	0.522556i	$-0.824979\pi$
$137$	1.59677	−	4.38708i	0.136421	−	0.374813i	0.989026	+	0.147743i	$0.0472008\pi$
$138$		0			0
$139$	−4.40567	−	0.776839i	−0.373684	−	0.0658906i	−0.0163478	−	0.999866i	$-0.505204\pi$
$139$	−4.40567	−	0.776839i	−0.373684	−	0.0658906i	−0.357336	+	0.933976i	$0.616315\pi$
$140$		0			0
$141$	7.84999	+	15.3137i	0.661088	+	1.28965i
$142$		0			0
$143$	2.00298	−	3.46926i	0.167498	−	0.290114i
$144$		0			0
$145$	5.71756	−	3.30103i	0.474817	−	0.274136i
$146$		0			0
$147$	−9.43450	−	7.61513i	−0.778145	−	0.628085i
$148$		0			0
$149$	0.383613	+	1.05397i	0.0314268	+	0.0863444i	0.954414	−	0.298487i	$-0.0964819\pi$
$149$	0.383613	+	1.05397i	0.0314268	+	0.0863444i	−0.922987	+	0.384831i	$0.874260\pi$
$150$		0			0
$151$	−3.00716	−	17.0544i	−0.244719	−	1.38787i	−0.821144	−	0.570720i	$-0.806664\pi$
$151$	−3.00716	−	17.0544i	−0.244719	−	1.38787i	0.576426	−	0.817150i	$-0.304447\pi$
$152$		0			0
$153$	−1.55263	−	20.7439i	−0.125522	−	1.67705i
$154$		0			0
$155$	−5.26477	+	0.928321i	−0.422877	+	0.0745645i
$156$		0			0
$157$	−7.28158	+	8.67784i	−0.581133	+	0.692567i	−0.973876	−	0.227081i	$-0.927082\pi$
$157$	−7.28158	+	8.67784i	−0.581133	+	0.692567i	0.392743	+	0.919648i	$0.371526\pi$
$158$		0			0
$159$	14.7183	+	3.36006i	1.16723	+	0.266470i
$160$		0			0
$161$	7.00670	+	5.47908i	0.552206	+	0.431812i
$162$		0			0
$163$	−8.25148	+	14.2920i	−0.646306	+	1.11943i	0.337692	+	0.941257i	$0.390354\pi$
$163$	−8.25148	+	14.2920i	−0.646306	+	1.11943i	−0.983998	+	0.178178i	$0.942980\pi$
$164$		0			0
$165$	11.2975	−	12.1747i	0.879512	−	0.947801i
$166$		0			0
$167$	−2.71714	+	0.988957i	−0.210258	+	0.0765278i	−0.445002	−	0.895529i	$-0.646797\pi$
$167$	−2.71714	+	0.988957i	−0.210258	+	0.0765278i	0.234744	+	0.972057i	$0.424575\pi$
$168$		0			0
$169$	2.18770	+	12.4071i	0.168284	+	0.954389i
$170$		0			0
$171$	−6.16040	+	0.461090i	−0.471098	+	0.0352604i
$172$		0			0
$173$	15.4607	−	12.9730i	1.17545	−	0.986322i	0.175454	−	0.984488i	$-0.443861\pi$
$173$	15.4607	−	12.9730i	1.17545	−	0.986322i	0.999998	−	0.00183404i	$-0.000583793\pi$
$174$		0			0
$175$	−2.20968	+	6.79076i	−0.167036	+	0.513333i
$176$		0			0
$177$	0.506146	+	4.04045i	0.0380442	+	0.303699i
$178$		0			0
$179$		−	12.0748i		−	0.902515i	−0.892394	−	0.451257i	$-0.850976\pi$
$179$		−	12.0748i		−	0.902515i	0.892394	−	0.451257i	$-0.149024\pi$
$180$		0			0
$181$	−6.40684	+	3.69899i	−0.476217	+	0.274944i	−0.718839	−	0.695177i	$-0.755326\pi$
$181$	−6.40684	+	3.69899i	−0.476217	+	0.274944i	0.242622	+	0.970121i	$0.421993\pi$
$182$		0			0
$183$	2.43127	−	1.24630i	0.179724	−	0.0921289i
$184$		0			0
$185$	11.0873	−	4.03543i	0.815151	−	0.296691i
$186$		0			0
$187$	−43.1688	+	7.61183i	−3.15682	+	0.556632i
$188$		0			0
$189$	−11.0364	−	8.19749i	−0.802777	−	0.596280i
$190$		0			0
$191$	5.55972	−	0.980328i	0.402287	−	0.0709341i	0.0311560	−	0.999515i	$-0.490081\pi$
$191$	5.55972	−	0.980328i	0.402287	−	0.0709341i	0.371131	+	0.928580i	$0.378970\pi$
$192$		0			0
$193$	−14.2418	+	5.18360i	−1.02515	+	0.373123i	−0.799232	−	0.601023i	$-0.794760\pi$
$193$	−14.2418	+	5.18360i	−1.02515	+	0.373123i	−0.225917	+	0.974147i	$0.572538\pi$
$194$		0			0
$195$	0.0830625	−	1.66278i	0.00594823	−	0.119074i
$196$		0			0
$197$	0.934577	−	0.539578i	0.0665858	−	0.0384433i	−0.466337	−	0.884607i	$-0.654427\pi$
$197$	0.934577	−	0.539578i	0.0665858	−	0.0384433i	0.532923	+	0.846164i	$0.321093\pi$
$198$		0			0
$199$		−	17.7092i		−	1.25537i	−0.778467	−	0.627686i	$-0.784002\pi$
$199$		−	17.7092i		−	1.25537i	0.778467	−	0.627686i	$-0.215998\pi$
$200$		0			0
$201$	−9.66916	+	7.32341i	−0.682010	+	0.516553i
$202$		0			0
$203$	−8.56099	+	7.70170i	−0.600864	+	0.540553i
$204$		0			0
$205$	0.634460	−	0.532375i	0.0443126	−	0.0371827i
$206$		0			0
$207$	8.18830	+	5.88813i	0.569126	+	0.409253i
$208$		0			0
$209$	2.26051	+	12.8200i	0.156363	+	0.886779i
$210$		0			0
$211$	19.0790	−	6.94420i	1.31346	−	0.478059i	0.412100	−	0.911139i	$-0.364796\pi$
$211$	19.0790	−	6.94420i	1.31346	−	0.478059i	0.901355	+	0.433080i	$0.142573\pi$
$212$		0			0
$213$	−4.96162	−	16.0878i	−0.339964	−	1.10232i
$214$		0			0
$215$	−7.39983	+	12.8169i	−0.504664	+	0.874104i
$216$		0			0
$217$	8.64713	−	3.48935i	0.587006	−	0.236873i
$218$		0			0
$219$	−7.52672	−	24.4050i	−0.508608	−	1.64914i
$220$		0			0
$221$	−2.82436	+	3.36594i	−0.189987	+	0.226418i
$222$		0			0
$223$	−17.2647	+	3.04424i	−1.15613	+	0.203857i	−0.718652	−	0.695370i	$-0.755240\pi$
$223$	−17.2647	+	3.04424i	−1.15613	+	0.203857i	−0.437481	+	0.899228i	$0.644129\pi$
$224$		0			0
$225$	−2.19382	+	7.79454i	−0.146254	+	0.519636i
$226$		0			0
$227$	−2.10666	−	11.9475i	−0.139824	−	0.792982i	−0.971378	−	0.237538i	$-0.923659\pi$
$227$	−2.10666	−	11.9475i	−0.139824	−	0.792982i	0.831554	−	0.555444i	$-0.187452\pi$
$228$		0			0
$229$	4.71675	+	12.9592i	0.311692	+	0.856366i	0.992316	+	0.123733i	$0.0394866\pi$
$229$	4.71675	+	12.9592i	0.311692	+	0.856366i	−0.680624	+	0.732633i	$0.738291\pi$
$230$		0			0
$231$	−14.8704	+	24.8621i	−0.978402	+	1.63580i
$232$		0			0
$233$	−23.1239	+	13.3506i	−1.51490	+	0.874626i	−0.515049	+	0.857161i	$0.672226\pi$
$233$	−23.1239	+	13.3506i	−1.51490	+	0.874626i	−0.999847	+	0.0174651i	$0.994440\pi$
$234$		0			0
$235$	7.53526	−	13.0514i	0.491546	−	0.851382i
$236$		0			0
$237$	7.28210	−	11.2738i	0.473023	−	0.732309i
$238$		0			0
$239$	20.1454	+	3.55218i	1.30310	+	0.229772i	0.781761	−	0.623579i	$-0.214322\pi$
$239$	20.1454	+	3.55218i	1.30310	+	0.229772i	0.521338	+	0.853350i	$0.325433\pi$
$240$		0			0
$241$	−8.95643	+	24.6076i	−0.576935	+	1.58511i	0.216384	+	0.976308i	$0.430574\pi$
$241$	−8.95643	+	24.6076i	−0.576935	+	1.58511i	−0.793319	+	0.608806i	$0.791649\pi$
$242$		0			0
$243$	−12.8778	−	8.78425i	−0.826109	−	0.563510i
$244$		0			0
$245$	−1.11896	+	10.5589i	−0.0714874	+	0.674584i
$246$		0			0
$247$	0.999597	+	0.838761i	0.0636028	+	0.0533691i
$248$		0			0
$249$	5.83902	+	0.291682i	0.370033	+	0.0184846i
$250$		0			0
$251$	−5.28712	−	9.15756i	−0.333720	−	0.578020i	0.649518	−	0.760346i	$-0.274971\pi$
$251$	−5.28712	−	9.15756i	−0.333720	−	0.578020i	−0.983238	+	0.182326i	$0.941637\pi$
$252$		0			0
$253$	10.6264	−	18.4054i	0.668074	−	1.15714i
$254$		0			0
$255$	−14.5223	+	10.9992i	−0.909420	+	0.688794i
$256$		0			0
$257$	−5.48984	+	1.99814i	−0.342447	+	0.124640i	−0.507518	−	0.861641i	$-0.669437\pi$
$257$	−5.48984	+	1.99814i	−0.342447	+	0.124640i	0.165071	+	0.986282i	$0.447215\pi$
$258$		0			0
$259$	−17.4573	+	10.8981i	−1.08475	+	0.677177i
$260$		0			0
$261$	−9.34816	+	9.11626i	−0.578636	+	0.564282i
$262$		0			0
$263$	−14.7457	−	17.5733i	−0.909261	−	1.08362i	−0.996173	−	0.0873993i	$-0.972144\pi$
$263$	−14.7457	−	17.5733i	−0.909261	−	1.08362i	0.0869122	−	0.996216i	$-0.472300\pi$
$264$		0			0
$265$	−4.52195	−	12.4240i	−0.277781	−	0.763197i
$266$		0			0
$267$	−6.22417	−	5.77572i	−0.380913	−	0.353468i
$268$		0			0
$269$	−8.18503	−	14.1769i	−0.499050	−	0.864380i	0.500949	−	0.865477i	$-0.332984\pi$
$269$	−8.18503	−	14.1769i	−0.499050	−	0.864380i	−0.999999	+	0.00109664i	$0.999651\pi$
$270$		0			0
$271$	19.5804	+	11.3048i	1.18943	+	0.686716i	0.958177	−	0.286178i	$-0.0923848\pi$
$271$	19.5804	+	11.3048i	1.18943	+	0.686716i	0.231251	+	0.972894i	$0.425718\pi$
$272$		0			0
$273$	0.460055	+	2.86721i	0.0278438	+	0.173532i
$274$		0			0
$275$	16.8040	+	2.96299i	1.01332	+	0.178675i
$276$		0			0
$277$	21.0898	−	17.6964i	1.26716	−	1.06328i	0.272282	−	0.962217i	$-0.412222\pi$
$277$	21.0898	−	17.6964i	1.26716	−	1.06328i	0.994880	−	0.101058i	$-0.0322229\pi$
$278$		0			0
$279$	9.63786	−	4.34770i	0.577004	−	0.260290i
$280$		0			0
$281$	4.96511	−	13.6415i	0.296194	−	0.813785i	−0.698934	−	0.715186i	$-0.746342\pi$
$281$	4.96511	−	13.6415i	0.296194	−	0.813785i	0.995127	−	0.0985987i	$-0.0314360\pi$
$282$		0			0
$283$	−3.61091	−	0.636701i	−0.214646	−	0.0378479i	0.0652908	−	0.997866i	$-0.479203\pi$
$283$	−3.61091	−	0.636701i	−0.214646	−	0.0378479i	−0.279937	+	0.960018i	$0.590314\pi$
$284$		0			0
$285$	3.26646	+	4.31274i	0.193488	+	0.255465i
$286$		0			0
$287$	−0.889884	+	1.13799i	−0.0525282	+	0.0671736i
$288$		0			0
$289$	31.0801			1.82824
$290$		0			0
$291$	9.34735	−	4.79157i	0.547952	−	0.280887i
$292$		0			0
$293$	−1.04313	+	5.91589i	−0.0609404	+	0.345610i	0.939058	+	0.343759i	$0.111700\pi$
$293$	−1.04313	+	5.91589i	−0.0609404	+	0.345610i	−0.999998	+	0.00185105i	$0.999411\pi$
$294$		0			0
$295$	2.73181	−	2.29226i	0.159052	−	0.133460i
$296$		0			0
$297$	−15.7140	+	28.8463i	−0.911819	+	1.67383i
$298$		0			0
$299$	−0.369929	−	2.09797i	−0.0213936	−	0.121329i
$300$		0			0
$301$	7.98750	−	24.5471i	0.460392	−	1.41487i
$302$		0			0
$303$	5.44091	+	0.271795i	0.312572	+	0.0156142i
$304$		0			0
$305$	−2.07210	−	1.19633i	−0.118648	−	0.0685015i
$306$		0			0
$307$	−4.71419	−	2.72174i	−0.269053	−	0.155338i	0.359404	−	0.933182i	$-0.382980\pi$
$307$	−4.71419	−	2.72174i	−0.269053	−	0.155338i	−0.628457	+	0.777844i	$0.716313\pi$
$308$		0			0
$309$	2.38211	+	3.14512i	0.135513	+	0.178920i
$310$		0			0
$311$	2.49922	−	14.1738i	0.141718	−	0.803720i	−0.828227	−	0.560393i	$-0.810650\pi$
$311$	2.49922	−	14.1738i	0.141718	−	0.803720i	0.969944	−	0.243327i	$-0.0782389\pi$
$312$		0			0
$313$	14.2007	+	16.9237i	0.802670	+	0.956585i	0.999717	−	0.0238095i	$-0.00757950\pi$
$313$	14.2007	+	16.9237i	0.802670	+	0.956585i	−0.197047	+	0.980394i	$0.563135\pi$
$314$		0			0
$315$	−0.786208	+	12.0140i	−0.0442978	+	0.676913i
$316$		0			0
$317$	−10.0640	+	27.6507i	−0.565252	+	1.55302i	0.246578	+	0.969123i	$0.420694\pi$
$317$	−10.0640	+	27.6507i	−0.565252	+	1.55302i	−0.811830	+	0.583894i	$0.801528\pi$
$318$		0			0
$319$	21.0777	+	17.6863i	1.18013	+	0.990244i
$320$		0			0
$321$	1.54988	+	5.02542i	0.0865061	+	0.280492i
$322$		0			0
$323$		−	14.2785i		−	0.794478i
$324$		0			0
$325$	1.48124	−	0.855192i	0.0821642	−	0.0474375i
$326$		0			0
$327$	6.43583	−	28.1913i	0.355902	−	1.55898i
$328$		0			0
$329$	−8.13368	+	24.9964i	−0.448424	+	1.37809i
$330$		0			0
$331$	1.07765	+	0.392234i	0.0592332	+	0.0215591i	0.371467	−	0.928446i	$-0.378855\pi$
$331$	1.07765	+	0.392234i	0.0592332	+	0.0215591i	−0.312234	+	0.950005i	$0.601077\pi$
$332$		0			0
$333$	−19.2817	+	13.1435i	−1.05663	+	0.720258i
$334$		0			0
$335$	9.98193	+	3.63313i	0.545371	+	0.198499i
$336$		0			0
$337$	15.6459	+	13.1285i	0.852288	+	0.715155i	0.960292	−	0.278996i	$-0.0900015\pi$
$337$	15.6459	+	13.1285i	0.852288	+	0.715155i	−0.108004	+	0.994150i	$0.534446\pi$
$338$		0			0
$339$	−3.96552	+	9.40612i	−0.215378	+	0.510870i
$340$		0			0
$341$	−11.1401	−	19.2952i	−0.603269	−	1.04489i
$342$		0			0
$343$	−1.91217	−	18.4213i	−0.103247	−	0.994656i
$344$		0			0
$345$	0.440670	−	8.82153i	0.0237249	−	0.474935i
$346$		0			0
$347$	1.62544	+	4.46586i	0.0872581	+	0.239740i	0.975645	−	0.219356i	$-0.0703957\pi$
$347$	1.62544	+	4.46586i	0.0872581	+	0.239740i	−0.888387	+	0.459096i	$0.848173\pi$
$348$		0			0
$349$	13.4726	+	16.0561i	0.721174	+	0.859462i	0.994744	−	0.102390i	$-0.0326491\pi$
$349$	13.4726	+	16.0561i	0.721174	+	0.859462i	−0.273570	+	0.961852i	$0.588205\pi$
$350$		0			0
$351$	0.651991	+	3.22750i	0.0348007	+	0.172271i
$352$		0			0
$353$	15.1977	+	5.53151i	0.808892	+	0.294413i	0.713166	−	0.700995i	$-0.247260\pi$
$353$	15.1977	+	5.53151i	0.808892	+	0.294413i	0.0957261	+	0.995408i	$0.469483\pi$
$354$		0			0
$355$	−9.47718	+	11.2945i	−0.502997	+	0.599448i
$356$		0			0
$357$	20.7982	−	24.0233i	1.10076	−	1.27145i
$358$		0			0
$359$			11.1992i			0.591070i	0.955332	+	0.295535i	$0.0954979\pi$
$359$			11.1992i			0.591070i	−0.955332	+	0.295535i	$0.904502\pi$
$360$		0			0
$361$	14.7597			0.776824
$362$		0			0
$363$	46.2275	+	19.4890i	2.42631	+	1.02291i
$364$		0			0
$365$	−14.3768	+	17.1336i	−0.752515	+	0.896812i
$366$		0			0
$367$	−2.06813	+	0.364668i	−0.107956	+	0.0190355i	−0.227365	−	0.973810i	$-0.573011\pi$
$367$	−2.06813	+	0.364668i	−0.107956	+	0.0190355i	0.119409	+	0.992845i	$0.461900\pi$
$368$		0			0
$369$	−0.956319	+	1.32990i	−0.0497840	+	0.0692319i
$370$		0			0
$371$	12.2120	+	19.5620i	0.634017	+	1.01561i
$372$		0			0
$373$	−2.45162	+	13.9038i	−0.126940	+	0.719914i	0.853196	+	0.521590i	$0.174661\pi$
$373$	−2.45162	+	13.9038i	−0.126940	+	0.719914i	−0.980137	+	0.198324i	$0.936450\pi$
$374$		0			0
$375$	19.3294	−	5.96136i	0.998166	−	0.307843i
$376$		0			0
$377$	2.75806			0.142047
$378$		0			0
$379$	8.32020			0.427380			0.213690	−	0.976902i	$-0.431452\pi$
$379$	8.32020			0.427380			0.213690	+	0.976902i	$0.431452\pi$
$380$		0			0
$381$	3.40231	−	14.9033i	0.174306	−	0.763522i
$382$		0			0
$383$	−4.35077	+	24.6744i	−0.222314	+	1.26081i	0.645440	+	0.763811i	$0.276674\pi$
$383$	−4.35077	+	24.6744i	−0.222314	+	1.26081i	−0.867754	+	0.496994i	$0.834437\pi$
$384$		0			0
$385$	25.3556	−	0.874535i	1.29224	−	0.0445704i
$386$		0			0
$387$	7.93016	−	28.1756i	0.403113	−	1.43224i
$388$		0			0
$389$	−4.66730	+	0.822971i	−0.236642	+	0.0417263i	−0.290711	−	0.956811i	$-0.593892\pi$
$389$	−4.66730	+	0.822971i	−0.236642	+	0.0417263i	0.0540696	+	0.998537i	$0.482781\pi$
$390$		0			0
$391$	−14.9840	+	17.8573i	−0.757774	+	0.903080i
$392$		0			0
$393$	−4.72810	−	37.7434i	−0.238501	−	1.90390i
$394$		0			0
$395$	−11.7537			−0.591392
$396$		0			0
$397$			1.53121i			0.0768491i	0.999262	+	0.0384246i	$0.0122339\pi$
$397$			1.53121i			0.0768491i	−0.999262	+	0.0384246i	$0.987766\pi$
$398$		0			0
$399$	−7.13429	−	6.17651i	−0.357161	−	0.309212i
$400$		0			0
$401$	0.484566	−	0.577483i	0.0241980	−	0.0288381i	−0.753810	−	0.657093i	$-0.771786\pi$
$401$	0.484566	−	0.577483i	0.0241980	−	0.0288381i	0.778008	+	0.628255i	$0.216230\pi$
$402$		0			0
$403$	−2.09864	−	0.763842i	−0.104541	−	0.0380497i
$404$		0			0
$405$	−0.342853	+	13.6475i	−0.0170365	+	0.678147i
$406$		0			0
$407$	31.6079	+	37.6689i	1.56675	+	1.86718i
$408$		0			0
$409$	−9.58927	−	26.3463i	−0.474159	−	1.30274i	−0.914382	−	0.404852i	$-0.867323\pi$
$409$	−9.58927	−	26.3463i	−0.474159	−	1.30274i	0.440223	−	0.897888i	$-0.354899\pi$
$410$		0			0
$411$	7.19594	−	3.68873i	0.354950	−	0.181951i
$412$		0			0
$413$	−3.83160	+	4.89988i	−0.188541	+	0.241107i
$414$		0			0
$415$	−2.55998	−	4.43401i	−0.125664	−	0.217657i
$416$		0			0
$417$	−4.67833	−	6.17685i	−0.229099	−	0.302481i
$418$		0			0
$419$	17.1375	+	14.3801i	0.837221	+	0.702512i	0.956937	−	0.290296i	$-0.0937538\pi$
$419$	17.1375	+	14.3801i	0.837221	+	0.702512i	−0.119716	+	0.992808i	$0.538198\pi$
$420$		0			0
$421$	−28.8426	−	10.4978i	−1.40570	−	0.511634i	−0.475837	−	0.879534i	$-0.657855\pi$
$421$	−28.8426	−	10.4978i	−1.40570	−	0.511634i	−0.929865	+	0.367900i	$0.880077\pi$
$422$		0			0
$423$	−8.07529	+	28.6912i	−0.392634	+	1.39501i
$424$		0			0
$425$	−17.5870	−	6.40115i	−0.853095	−	0.310501i
$426$		0			0
$427$	3.96852	+	1.29134i	0.192050	+	0.0624921i
$428$		0			0
$429$	6.63036	−	2.04486i	0.320117	−	0.0987268i
$430$		0			0
$431$	11.9074	−	6.87475i	0.573560	−	0.331145i	−0.185010	−	0.982737i	$-0.559232\pi$
$431$	11.9074	−	6.87475i	0.573560	−	0.331145i	0.758570	+	0.651592i	$0.225898\pi$
$432$		0			0
$433$			33.2402i			1.59742i	0.601714	+	0.798712i	$0.294485\pi$
$433$			33.2402i			1.59742i	−0.601714	+	0.798712i	$0.705515\pi$
$434$		0			0
$435$	11.1483	+	2.54506i	0.534520	+	0.122026i
$436$		0			0
$437$	5.30314	+	4.44986i	0.253684	+	0.212866i
$438$		0			0
$439$	−7.54885	+	20.7403i	−0.360287	+	0.989880i	0.618641	+	0.785674i	$0.287684\pi$
$439$	−7.54885	+	20.7403i	−0.360287	+	0.989880i	−0.978928	+	0.204206i	$0.934539\pi$
$440$		0			0
$441$	−3.00654	−	20.7837i	−0.143169	−	0.989698i
$442$		0			0
$443$	−16.3668	−	19.5052i	−0.777610	−	0.926720i	0.221212	−	0.975226i	$-0.428999\pi$
$443$	−16.3668	−	19.5052i	−0.777610	−	0.926720i	−0.998823	+	0.0485056i	$0.984554\pi$
$444$		0			0
$445$	−1.29128	+	7.32322i	−0.0612126	+	0.347154i
$446$		0			0
$447$	−0.754688	+	1.79010i	−0.0356955	+	0.0846689i
$448$		0			0
$449$	24.3369	+	14.0509i	1.14853	+	0.663105i	0.948529	−	0.316691i	$-0.102572\pi$
$449$	24.3369	+	14.0509i	1.14853	+	0.663105i	0.200002	+	0.979795i	$0.435905\pi$
$450$		0			0
$451$	2.98931	+	1.72588i	0.140761	+	0.0812685i
$452$		0			0
$453$	16.2747	−	25.1957i	0.764654	−	1.18380i
$454$		0			0
$455$	1.89063	−	1.70086i	0.0886341	−	0.0797376i
$456$		0			0
$457$	2.33654	+	13.2512i	0.109299	+	0.619863i	0.989416	+	0.145107i	$0.0463527\pi$
$457$	2.33654	+	13.2512i	0.109299	+	0.619863i	−0.880117	+	0.474756i	$0.842536\pi$
$458$		0			0
$459$	22.4682	−	28.1663i	1.04873	−	1.31469i
$460$		0			0
$461$	−1.38658	+	1.16348i	−0.0645797	+	0.0541888i	−0.674506	−	0.738269i	$-0.735643\pi$
$461$	−1.38658	+	1.16348i	−0.0645797	+	0.0541888i	0.609926	+	0.792458i	$0.291199\pi$
$462$		0			0
$463$	−5.72241	+	32.4534i	−0.265943	+	1.50824i	0.500394	+	0.865798i	$0.333188\pi$
$463$	−5.72241	+	32.4534i	−0.265943	+	1.50824i	−0.766337	+	0.642439i	$0.777923\pi$
$464$		0			0
$465$	−7.77801	−	5.02408i	−0.360697	−	0.232986i
$466$		0			0
$467$	−35.0137			−1.62024			−0.810122	−	0.586262i	$-0.800599\pi$
$467$	−35.0137			−1.62024			−0.810122	+	0.586262i	$0.800599\pi$
$468$		0			0
$469$	−18.3467	−	2.58650i	−0.847172	−	0.119433i
$470$		0			0
$471$	−19.4687	+	2.43884i	−0.897071	+	0.112376i
$472$		0			0
$473$	−60.7426	−	10.7106i	−2.79295	−	0.492472i
$474$		0			0
$475$	−1.90097	+	5.22288i	−0.0872227	+	0.239642i
$476$		0			0
$477$	14.7281	+	21.6064i	0.674352	+	0.989288i
$478$		0			0
$479$	7.07435	−	5.93608i	0.323235	−	0.271226i	−0.466702	−	0.884415i	$-0.654558\pi$
$479$	7.07435	−	5.93608i	0.323235	−	0.271226i	0.789937	+	0.613188i	$0.210113\pi$
$480$		0			0
$481$	4.85416	+	0.855919i	0.221330	+	0.0390265i
$482$		0			0
$483$	2.44072	+	15.2114i	0.111057	+	0.692141i
$484$		0			0
$485$	−7.96649	−	4.59946i	−0.361740	−	0.208851i
$486$		0			0
$487$	10.1326	+	17.5502i	0.459154	+	0.795278i	0.998916	−	0.0465396i	$-0.0148194\pi$
$487$	10.1326	+	17.5502i	0.459154	+	0.795278i	−0.539763	+	0.841817i	$0.681486\pi$
$488$		0			0
$489$	−27.3145	+	8.42402i	−1.23520	+	0.380947i
$490$		0			0
$491$	3.70113	+	10.1688i	0.167030	+	0.458910i	0.994763	−	0.102212i	$-0.0325921\pi$
$491$	3.70113	+	10.1688i	0.167030	+	0.458910i	−0.827733	+	0.561122i	$0.810370\pi$
$492$		0			0
$493$	−19.3992	−	23.1191i	−0.873696	−	1.04123i
$494$		0			0
$495$	28.6874	−	2.14717i	1.28940	−	0.0965082i
$496$		0			0
$497$	12.0830	−	22.7013i	0.541996	−	1.01829i
$498$		0			0
$499$	−0.882124	+	0.321067i	−0.0394893	+	0.0143729i	−0.361689	−	0.932299i	$-0.617800\pi$
$499$	−0.882124	+	0.321067i	−0.0394893	+	0.0143729i	0.322200	+	0.946672i	$0.395578\pi$
$500$		0			0
$501$	−4.61490	−	1.94559i	−0.206179	−	0.0869227i
$502$		0			0
$503$	9.08797	−	15.7408i	0.405212	−	0.701849i	−0.589134	−	0.808036i	$-0.700531\pi$
$503$	9.08797	−	15.7408i	0.405212	−	0.701849i	0.994346	+	0.106187i	$0.0338642\pi$
$504$		0			0
$505$	−2.38544	−	4.13170i	−0.106151	−	0.183858i
$506$		0			0
$507$	−11.8398	+	18.3298i	−0.525825	+	0.814055i
$508$		0			0
$509$	1.86161	+	1.56208i	0.0825145	+	0.0692379i	0.683112	−	0.730314i	$-0.260626\pi$
$509$	1.86161	+	1.56208i	0.0825145	+	0.0692379i	−0.600597	+	0.799552i	$0.705071\pi$
$510$		0			0
$511$	18.3298	−	34.4376i	0.810861	−	1.52343i
$512$		0			0
$513$	−8.36466	−	6.67248i	−0.369309	−	0.294597i
$514$		0			0
$515$	1.18176	−	3.24686i	0.0520745	−	0.143074i
$516$		0			0
$517$	61.8543	+	10.9066i	2.72035	+	0.479671i
$518$		0			0
$519$	34.9135	+	1.74407i	1.53253	+	0.0765561i
$520$		0			0
$521$	−19.7138	+	34.1453i	−0.863676	+	1.49593i	0.00467898	+	0.999989i	$0.498511\pi$
$521$	−19.7138	+	34.1453i	−0.863676	+	1.49593i	−0.868355	+	0.495942i	$0.834823\pi$
$522$		0			0
$523$	12.3537	−	7.13242i	0.540191	−	0.311879i	−0.204966	−	0.978769i	$-0.565708\pi$
$523$	12.3537	−	7.13242i	0.540191	−	0.311879i	0.745156	+	0.666890i	$0.232375\pi$
$524$		0			0
$525$	−10.8060	+	6.01841i	−0.471613	+	0.262665i
$526$		0			0
$527$	8.35826	+	22.9641i	0.364092	+	1.00033i
$528$		0			0
$529$	2.03133	+	11.5202i	0.0883187	+	0.500880i
$530$		0			0
$531$	−4.11765	+	5.72619i	−0.178691	+	0.248495i
$532$		0			0
$533$	0.340742	−	0.0600820i	0.0147592	−	0.00260244i
$534$		0			0
$535$	2.96043	−	3.52811i	0.127991	−	0.152533i
$536$		0			0
$537$	14.2260	−	15.3305i	0.613896	−	0.661562i
$538$		0			0
$539$	−42.9469	+	10.6687i	−1.84985	+	0.459533i
$540$		0			0
$541$	−4.91219	+	8.50816i	−0.211192	+	0.365795i	−0.952088	−	0.305825i	$-0.901068\pi$
$541$	−4.91219	+	8.50816i	−0.211192	+	0.365795i	0.740896	+	0.671620i	$0.234401\pi$
$542$		0			0
$543$	−12.4923	−	2.85189i	−0.536095	−	0.122386i
$544$		0			0
$545$	−23.7968	+	8.66131i	−1.01934	+	0.371010i
$546$		0			0
$547$	1.86365	+	10.5693i	0.0796841	+	0.451911i	0.998378	+	0.0569398i	$0.0181343\pi$
$547$	1.86365	+	10.5693i	0.0796841	+	0.451911i	−0.918694	+	0.394971i	$0.870755\pi$
$548$		0			0
$549$	4.55513	+	1.28207i	0.194408	+	0.0547173i
$550$		0			0
$551$	−6.86576	+	5.76105i	−0.292491	+	0.245429i
$552$		0			0
$553$	20.0549	−	4.25381i	0.852822	−	0.180890i
$554$		0			0
$555$	18.8311	+	7.93897i	0.799334	+	0.336991i
$556$		0			0
$557$			0.870040i			0.0368648i	0.999830	+	0.0184324i	$0.00586755\pi$
$557$			0.870040i			0.0368648i	−0.999830	+	0.0184324i	$0.994132\pi$
$558$		0			0
$559$	−5.35435	+	3.09133i	−0.226465	+	0.130749i
$560$		0			0
$561$	−63.7763	−	41.1952i	−2.69264	−	1.73926i
$562$		0			0
$563$	−3.44766	+	1.25485i	−0.145302	+	0.0528854i	−0.413647	−	0.910437i	$-0.635745\pi$
$563$	−3.44766	+	1.25485i	−0.145302	+	0.0528854i	0.268346	+	0.963323i	$0.413523\pi$
$564$		0			0
$565$	8.80383	−	1.55235i	0.370380	−	0.0653080i
$566$		0			0
$567$	−4.35418	−	23.4103i	−0.182859	−	0.983139i
$568$		0			0
$569$	−20.4503	+	3.60594i	−0.857321	+	0.151169i	−0.584996	−	0.811036i	$-0.698904\pi$
$569$	−20.4503	+	3.60594i	−0.857321	+	0.151169i	−0.272326	+	0.962205i	$0.587793\pi$
$570$		0			0
$571$	−10.3410	+	3.76383i	−0.432759	+	0.157512i	−0.549209	−	0.835685i	$-0.685071\pi$
$571$	−10.3410	+	3.76383i	−0.432759	+	0.157512i	0.116450	+	0.993197i	$0.462849\pi$
$572$		0			0
$573$	8.21376	+	5.30554i	0.343135	+	0.221642i
$574$		0			0
$575$	7.85837	−	4.53703i	0.327717	−	0.189207i
$576$		0			0
$577$			3.34129i			0.139100i	0.997578	+	0.0695498i	$0.0221563\pi$
$577$			3.34129i			0.139100i	−0.997578	+	0.0695498i	$0.977844\pi$
$578$		0			0
$579$	−24.1889	−	10.1978i	−1.00526	−	0.423805i
$580$		0			0
$581$	5.97273	+	6.63912i	0.247791	+	0.275437i
$582$		0			0
$583$	42.2103	−	35.4186i	1.74817	−	1.46689i
$584$		0			0
$585$	2.06447	−	2.01326i	0.0853553	−	0.0832379i
$586$		0			0
$587$	−4.74616	−	26.9168i	−0.195895	−	1.11098i	−0.911138	−	0.412101i	$-0.864795\pi$
$587$	−4.74616	−	26.9168i	−0.195895	−	1.11098i	0.715243	−	0.698876i	$-0.246316\pi$
$588$		0			0
$589$	6.81975	−	2.48219i	0.281003	−	0.102277i
$590$		0			0
$591$	1.82227	+	0.416009i	0.0749582	+	0.0171123i
$592$		0			0
$593$	19.5789	−	33.9116i	0.804008	−	1.39258i	−0.112951	−	0.993601i	$-0.536030\pi$
$593$	19.5789	−	33.9116i	0.804008	−	1.39258i	0.916959	−	0.398982i	$-0.130636\pi$
$594$		0			0
$595$	−27.5552	−	3.88470i	−1.12965	−	0.159257i
$596$		0			0
$597$	20.8641	−	22.4841i	0.853911	−	0.920213i
$598$		0			0
$599$	12.9498	−	15.4330i	0.529116	−	0.630576i	−0.433595	−	0.901108i	$-0.642755\pi$
$599$	12.9498	−	15.4330i	0.529116	−	0.630576i	0.962711	+	0.270532i	$0.0871995\pi$
$600$		0			0
$601$	−39.6988	+	6.99996i	−1.61935	+	0.285534i	−0.908523	−	0.417836i	$-0.862789\pi$
$601$	−39.6988	+	6.99996i	−1.61935	+	0.285534i	−0.710824	+	0.703370i	$0.751678\pi$
$602$		0			0
$603$	−20.9043	−	2.09373i	−0.851290	−	0.0852634i
$604$		0			0
$605$	−7.62922	−	43.2675i	−0.310172	−	1.75907i
$606$		0			0
$607$	4.18499	+	11.4982i	0.169863	+	0.466696i	0.995190	−	0.0979593i	$-0.0312315\pi$
$607$	4.18499	+	11.4982i	0.169863	+	0.466696i	−0.825327	+	0.564655i	$0.809009\pi$
$608$		0			0
$609$	−19.9430	−	0.307851i	−0.808133	−	0.0124747i
$610$		0			0
$611$	5.45234	−	3.14791i	0.220578	−	0.127351i
$612$		0			0
$613$	−8.74896	+	15.1536i	−0.353367	+	0.612050i	−0.986837	−	0.161717i	$-0.948297\pi$
$613$	−8.74896	+	15.1536i	−0.353367	+	0.612050i	0.633470	+	0.773767i	$0.281630\pi$
$614$		0			0
$615$	1.43275	+	0.0715713i	0.0577739	+	0.00288603i
$616$		0			0
$617$	−43.7766	−	7.71900i	−1.76238	−	0.310755i	−0.803656	−	0.595094i	$-0.797115\pi$
$617$	−43.7766	−	7.71900i	−1.76238	−	0.310755i	−0.958724	+	0.284338i	$0.908226\pi$
$618$		0			0
$619$	8.66126	−	23.7966i	0.348125	−	0.956467i	−0.634835	−	0.772648i	$-0.718932\pi$
$619$	8.66126	−	23.7966i	0.348125	−	0.956467i	0.982960	−	0.183819i	$-0.0588460\pi$
$620$		0			0
$621$	3.45900	+	17.1228i	0.138805	+	0.687114i
$622$		0			0
$623$	−0.447095	−	12.9627i	−0.0179125	−	0.519340i
$624$		0			0
$625$	−3.23198	−	2.71195i	−0.129279	−	0.108478i
$626$		0			0
$627$	−12.2339	+	18.9399i	−0.488575	+	0.756387i
$628$		0			0
$629$	−26.9678	−	46.7095i	−1.07527	−	1.86243i
$630$		0			0
$631$	14.7613	−	25.5674i	0.587640	−	1.01782i	−0.406901	−	0.913472i	$-0.633391\pi$
$631$	14.7613	−	25.5674i	0.587640	−	1.01782i	0.994541	−	0.104350i	$-0.0332761\pi$
$632$		0			0
$633$	32.4046	+	13.6614i	1.28797	+	0.542994i
$634$		0			0
$635$	−12.5802	+	4.57881i	−0.499230	+	0.181705i
$636$		0			0
$637$	−2.61036	+	3.58637i	−0.103426	+	0.142097i
$638$		0			0
$639$	12.6544	−	26.2711i	0.500602	−	1.03927i
$640$		0			0
$641$	20.0445	+	23.8881i	0.791711	+	0.943525i	0.999399	−	0.0346706i	$-0.0110382\pi$
$641$	20.0445	+	23.8881i	0.791711	+	0.943525i	−0.207688	+	0.978195i	$0.566594\pi$
$642$		0			0
$643$	−7.08263	−	19.4594i	−0.279311	−	0.767402i	−0.997441	−	0.0714926i	$-0.977224\pi$
$643$	−7.08263	−	19.4594i	−0.279311	−	0.767402i	0.718130	−	0.695909i	$-0.244998\pi$
$644$		0			0
$645$	−24.4953	+	7.55456i	−0.964501	+	0.297461i
$646$		0			0
$647$	16.1677	+	28.0032i	0.635616	+	1.10092i	0.986384	+	0.164457i	$0.0525871\pi$
$647$	16.1677	+	28.0032i	0.635616	+	1.10092i	−0.350768	+	0.936462i	$0.614080\pi$
$648$		0			0
$649$	12.8711	+	7.43116i	0.505237	+	0.291698i
$650$		0			0
$651$	15.0896	+	5.75746i	0.591409	+	0.225653i
$652$		0			0
$653$	−20.0864	−	3.54177i	−0.786040	−	0.138600i	−0.233800	−	0.972285i	$-0.575116\pi$
$653$	−20.0864	−	3.54177i	−0.786040	−	0.138600i	−0.552241	+	0.833685i	$0.686227\pi$
$654$		0			0
$655$	−25.5189	+	21.4129i	−0.997105	+	0.836671i
$656$		0			0
$657$	19.1966	−	39.8529i	0.748933	−	1.55481i
$658$		0			0
$659$	4.08387	−	11.2203i	0.159085	−	0.437083i	−0.834384	−	0.551183i	$-0.814176\pi$
$659$	4.08387	−	11.2203i	0.159085	−	0.437083i	0.993469	+	0.114101i	$0.0363987\pi$
$660$		0			0
$661$	−16.7908	−	2.96067i	−0.653087	−	0.115157i	−0.162719	−	0.986672i	$-0.552026\pi$
$661$	−16.7908	−	2.96067i	−0.653087	−	0.115157i	−0.490368	+	0.871516i	$0.663138\pi$
$662$		0			0
$663$	−7.55148	+	0.945971i	−0.293275	+	0.0367385i
$664$		0			0
$665$	−1.15366	+	8.18319i	−0.0447368	+	0.317330i
$666$		0			0
$667$	14.6323			0.566564
$668$		0			0
$669$	−25.5064	−	16.4754i	−0.986134	−	0.636977i
$670$		0			0
$671$	1.73157	−	9.82024i	0.0668466	−	0.379106i
$672$		0			0
$673$	15.6186	−	13.1055i	0.602051	−	0.505181i	−0.290053	−	0.957011i	$-0.593673\pi$
$673$	15.6186	−	13.1055i	0.602051	−	0.505181i	0.892104	+	0.451830i	$0.149229\pi$
$674$		0			0
$675$	−11.9685	+	7.31153i	−0.460667	+	0.281421i
$676$		0			0
$677$	7.05294	+	39.9992i	0.271067	+	1.53730i	0.751185	+	0.660092i	$0.229483\pi$
$677$	7.05294	+	39.9992i	0.271067	+	1.53730i	−0.480118	+	0.877204i	$0.659406\pi$
$678$		0			0
$679$	15.2576	+	4.96473i	0.585531	+	0.190529i
$680$		0			0
$681$	11.4013	−	17.6508i	0.436898	−	0.676382i
$682$		0			0
$683$	16.5906	+	9.57856i	0.634820	+	0.366514i	0.782616	−	0.622504i	$-0.213885\pi$
$683$	16.5906	+	9.57856i	0.634820	+	0.366514i	−0.147796	+	0.989018i	$0.547218\pi$
$684$		0			0
$685$	−6.13290	−	3.54083i	−0.234326	−	0.135288i
$686$		0			0
$687$	−9.27934	+	22.0104i	−0.354029	+	0.839748i
$688$		0			0
$689$	0.959110	−	5.43938i	0.0365392	−	0.207224i
$690$		0			0
$691$	5.45867	+	6.50539i	0.207657	+	0.247477i	0.859813	−	0.510608i	$-0.170580\pi$
$691$	5.45867	+	6.50539i	0.207657	+	0.247477i	−0.652156	+	0.758085i	$0.726135\pi$
$692$		0			0
$693$	−48.1712	+	14.0460i	−1.82987	+	0.533562i
$694$		0			0
$695$	−2.32091	+	6.37665i	−0.0880371	+	0.241880i
$696$		0			0
$697$	−2.90028	−	2.43363i	−0.109856	−	0.0921802i
$698$		0			0
$699$	−45.0878	−	10.2932i	−1.70538	−	0.389323i
$700$		0			0
$701$			18.4875i			0.698262i	0.937074	+	0.349131i	$0.113523\pi$
$701$			18.4875i			0.698262i	−0.937074	+	0.349131i	$0.886477\pi$
$702$		0			0
$703$	−13.8715	+	8.00872i	−0.523174	+	0.302055i
$704$		0			0
$705$	24.9436	−	7.69282i	0.939429	−	0.289728i
$706$		0			0
$707$	5.56551	+	6.18647i	0.209313	+	0.232666i
$708$		0			0
$709$	34.5513	+	12.5756i	1.29760	+	0.472288i	0.896215	−	0.443620i	$-0.146306\pi$
$709$	34.5513	+	12.5756i	1.29760	+	0.472288i	0.401387	+	0.915909i	$0.368528\pi$
$710$		0			0
$711$	22.5278	−	5.73407i	0.844857	−	0.215044i
$712$		0			0
$713$	−11.1339	−	4.05240i	−0.416967	−	0.151763i
$714$		0			0
$715$	−4.65486	−	3.90589i	−0.174082	−	0.146072i
$716$		0			0
$717$	21.3922	+	28.2443i	0.798906	+	1.05480i
$718$		0			0
$719$	−9.09840	−	15.7589i	−0.339313	−	0.587707i	0.644991	−	0.764190i	$-0.276861\pi$
$719$	−9.09840	−	15.7589i	−0.339313	−	0.587707i	−0.984304	+	0.176483i	$0.943528\pi$
$720$		0			0
$721$	−0.841318	+	5.96770i	−0.0313323	+	0.222249i
$722$		0			0
$723$	−40.3628	+	20.6905i	−1.50111	+	0.769487i
$724$		0			0
$725$	4.01799	+	11.0393i	0.149224	+	0.409991i
$726$		0			0
$727$	25.4362	+	30.3136i	0.943375	+	1.12427i	0.992099	+	0.125458i	$0.0400401\pi$
$727$	25.4362	+	30.3136i	0.943375	+	1.12427i	−0.0487239	+	0.998812i	$0.515515\pi$
$728$		0			0
$729$	−6.00082	−	26.3247i	−0.222252	−	0.974989i
$730$		0			0
$731$	63.5732	+	23.1388i	2.35134	+	0.855818i
$732$		0			0
$733$	−28.7216	+	34.2291i	−1.06086	+	1.26428i	−0.0977361	+	0.995212i	$0.531160\pi$
$733$	−28.7216	+	34.2291i	−1.06086	+	1.26428i	−0.963121	+	0.269068i	$0.913284\pi$
$734$		0			0
$735$	−13.8607	+	12.0876i	−0.511258	+	0.445858i
$736$		0			0
$737$			44.2710i			1.63074i
$738$		0			0
$739$	8.51550			0.313248			0.156624	−	0.987658i	$-0.449939\pi$
$739$	8.51550			0.313248			0.156624	+	0.987658i	$0.449939\pi$
$740$		0			0
$741$	0.280929	+	2.24259i	0.0103202	+	0.0823837i
$742$		0			0
$743$	33.0132	−	39.3436i	1.21114	−	1.44338i	0.348685	−	0.937240i	$-0.386628\pi$
$743$	33.0132	−	39.3436i	1.21114	−	1.44338i	0.862453	−	0.506138i	$-0.168927\pi$
$744$		0			0
$745$	1.67548	−	0.295432i	0.0613848	−	0.0108238i
$746$		0			0
$747$	7.06974	+	7.24958i	0.258668	+	0.265248i
$748$		0			0
$749$	−3.77442	+	7.09131i	−0.137914	+	0.259111i
$750$		0			0
$751$	−0.658428	+	3.73413i	−0.0240264	+	0.136260i	−0.994461	−	0.105102i	$-0.966483\pi$
$751$	−0.658428	+	3.73413i	−0.0240264	+	0.136260i	0.970435	+	0.241362i	$0.0775942\pi$
$752$		0			0
$753$	4.07632	−	17.8557i	0.148549	−	0.650699i
$754$		0			0
$755$	−26.2683			−0.956001
$756$		0			0
$757$	0.263430			0.00957452			0.00478726	−	0.999989i	$-0.498476\pi$
$757$	0.263430			0.00957452			0.00478726	+	0.999989i	$0.498476\pi$
$758$		0			0
$759$	35.1759	−	10.8486i	1.27680	−	0.393778i
$760$		0			0
$761$	3.38374	−	19.1902i	0.122661	−	0.695643i	−0.860009	−	0.510279i	$-0.829542\pi$
$761$	3.38374	−	19.1902i	0.122661	−	0.695643i	0.982670	−	0.185365i	$-0.0593466\pi$
$762$		0			0
$763$	37.4690	−	23.3909i	1.35647	−	0.846806i
$764$		0			0
$765$	−31.3966	−	3.14461i	−1.13515	−	0.113694i
$766$		0			0
$767$	1.46714	−	0.258696i	0.0529754	−	0.00934099i
$768$		0			0
$769$	27.2853	−	32.5174i	0.983935	−	1.17261i	−0.00105564	−	0.999999i	$-0.500336\pi$
$769$	27.2853	−	32.5174i	0.983935	−	1.17261i	0.984991	−	0.172608i	$-0.0552195\pi$
$770$		0			0
$771$	−9.32417	−	3.93097i	−0.335802	−	0.141570i
$772$		0			0
$773$	31.9866			1.15048			0.575239	−	0.817985i	$-0.304909\pi$
$773$	31.9866			1.15048			0.575239	+	0.817985i	$0.304909\pi$
$774$		0			0
$775$		−	9.51274i		−	0.341708i
$776$		0			0
$777$	−35.0040	−	6.73081i	−1.25576	−	0.241467i
$778$		0			0
$779$	−0.722723	+	0.861308i	−0.0258943	+	0.0308596i
$780$		0			0
$781$	−57.7415	−	21.0162i	−2.06615	−	0.752018i
$782$		0			0
$783$	−22.6090	+	0.560719i	−0.807981	+	0.0200385i
$784$		0			0
$785$	11.0451	+	13.1631i	0.394218	+	0.469811i
$786$		0			0
$787$	−0.625383	−	1.71823i	−0.0222925	−	0.0612482i	0.928047	−	0.372463i	$-0.121486\pi$
$787$	−0.625383	−	1.71823i	−0.0222925	−	0.0612482i	−0.950340	+	0.311214i	$0.899264\pi$
$788$		0			0
$789$	1.98239	−	39.6843i	0.0705748	−	1.41280i
$790$		0			0
$791$	−14.4599	+	5.83494i	−0.514134	+	0.207467i
$792$		0			0
$793$	−0.499775	−	0.865635i	−0.0177475	−	0.0307396i
$794$		0			0
$795$	8.89611	−	21.1014i	0.315512	−	0.748388i
$796$		0			0
$797$	−32.7872	−	27.5117i	−1.16138	−	0.974515i	−0.161458	−	0.986880i	$-0.551620\pi$
$797$	−32.7872	−	27.5117i	−1.16138	−	0.974515i	−0.999924	+	0.0123651i	$0.996064\pi$
$798$		0			0
$799$	−64.7366	−	23.5622i	−2.29022	−	0.833571i
$800$		0			0
$801$	−1.09771	−	14.6660i	−0.0387858	−	0.518199i
$802$		0			0
$803$	−87.5932	−	31.8813i	−3.09110	−	1.12507i
$804$		0			0
$805$	10.0303	−	9.02354i	0.353522	−	0.318038i
$806$		0			0
$807$	6.31058	−	27.6426i	0.222143	−	0.973065i
$808$		0			0
$809$	−10.9332	+	6.31229i	−0.384391	+	0.221928i	−0.679727	−	0.733465i	$-0.737902\pi$
$809$	−10.9332	+	6.31229i	−0.384391	+	0.221928i	0.295336	+	0.955393i	$0.404568\pi$
$810$		0			0
$811$		−	54.6907i		−	1.92045i	−0.279228	−	0.960225i	$-0.590078\pi$
$811$		−	54.6907i		−	1.92045i	0.279228	−	0.960225i	$-0.409922\pi$
$812$		0			0
$813$	11.5412	+	37.4216i	0.404766	+	1.31243i
$814$		0			0
$815$	19.1762	+	16.0907i	0.671712	+	0.563633i
$816$		0			0
$817$	6.87161	−	18.8796i	0.240407	−	0.660513i
$818$		0			0
$819$	−2.79391	+	4.18231i	−0.0976272	+	0.146142i
$820$		0			0
$821$	−5.26259	−	6.27171i	−0.183666	−	0.218884i	0.666354	−	0.745636i	$-0.267854\pi$
$821$	−5.26259	−	6.27171i	−0.183666	−	0.218884i	−0.850019	+	0.526752i	$0.823410\pi$
$822$		0			0
$823$	−3.74658	+	21.2479i	−0.130597	+	0.740655i	0.847227	+	0.531230i	$0.178270\pi$
$823$	−3.74658	+	21.2479i	−0.130597	+	0.740655i	−0.977825	+	0.209425i	$0.932841\pi$
$824$		0			0
$825$	17.8439	+	23.5595i	0.621246	+	0.820237i
$826$		0			0
$827$	−0.396212	−	0.228753i	−0.0137776	−	0.00795452i	0.493095	−	0.869975i	$-0.335865\pi$
$827$	−0.396212	−	0.228753i	−0.0137776	−	0.00795452i	−0.506873	+	0.862021i	$0.669199\pi$
$828$		0			0
$829$	−29.4449	−	17.0000i	−1.02266	−	0.590436i	−0.107790	−	0.994174i	$-0.534377\pi$
$829$	−29.4449	−	17.0000i	−1.02266	−	0.590436i	−0.914875	+	0.403738i	$0.867711\pi$
$830$		0			0
$831$	47.6253	+	2.37907i	1.65210	+	0.0825291i
$832$		0			0
$833$	48.4225	−	3.34424i	1.67774	−	0.115871i
$834$		0			0
$835$	0.761627	+	4.31940i	0.0263572	+	0.149479i
$836$		0			0
$837$	17.3588	+	5.83489i	0.600007	+	0.201683i
$838$		0			0
$839$	38.9288	−	32.6651i	1.34397	−	1.12773i	0.363384	−	0.931639i	$-0.381621\pi$
$839$	38.9288	−	32.6651i	1.34397	−	1.12773i	0.980587	−	0.196086i	$-0.0628233\pi$
$840$		0			0
$841$	1.74624	−	9.90341i	0.0602151	−	0.341497i
$842$		0			0
$843$	22.3756	−	11.4700i	0.770658	−	0.395049i
$844$		0			0
$845$	19.1101			0.657408
$846$		0			0
$847$	28.6765	+	71.0647i	0.985337	+	2.44181i
$848$		0			0
$849$	−3.83439	−	5.06258i	−0.131596	−	0.173747i
$850$		0			0
$851$	25.7527	+	4.54089i	0.882790	+	0.155660i
$852$		0			0
$853$	−4.52864	+	12.4423i	−0.155058	+	0.426018i	−0.992761	−	0.120108i	$-0.961676\pi$
$853$	−4.52864	+	12.4423i	−0.155058	+	0.426018i	0.837703	+	0.546126i	$0.183898\pi$
$854$		0			0
$855$	−0.933868	+	9.32396i	−0.0319376	+	0.318873i
$856$		0			0
$857$	−31.0609	+	26.0632i	−1.06102	+	0.890302i	−0.994209	−	0.107464i	$-0.965727\pi$
$857$	−31.0609	+	26.0632i	−1.06102	+	0.890302i	−0.0668115	+	0.997766i	$0.521283\pi$
$858$		0			0
$859$	12.1501	+	2.14238i	0.414555	+	0.0730972i	0.377036	−	0.926199i	$-0.376943\pi$
$859$	12.1501	+	2.14238i	0.414555	+	0.0730972i	0.0375190	+	0.999296i	$0.488055\pi$
$860$		0			0
$861$	−2.47055	+	0.396409i	−0.0841961	+	0.0135096i
$862$		0			0
$863$	−17.7203	−	10.2308i	−0.603206	−	0.348261i	0.167096	−	0.985941i	$-0.446561\pi$
$863$	−17.7203	−	10.2308i	−0.603206	−	0.348261i	−0.770302	+	0.637679i	$0.779894\pi$
$864$		0			0
$865$	−15.3070	−	26.5125i	−0.520454	−	0.901452i
$866$		0			0
$867$	39.4601	+	36.6170i	1.34014	+	1.24358i
$868$		0			0
$869$	−16.7539	−	46.0310i	−0.568338	−	1.56149i
$870$		0			0
$871$	2.85246	+	3.39943i	0.0966521	+	0.115185i
$872$		0			0
$873$	17.5129	+	4.92909i	0.592721	+	0.166824i
$874$		0			0
$875$	27.2755	+	14.5177i	0.922080	+	0.490786i
$876$		0			0
$877$	−46.5207	+	16.9321i	−1.57089	+	0.571758i	−0.973198	−	0.229967i	$-0.926138\pi$
$877$	−46.5207	+	16.9321i	−1.57089	+	0.571758i	−0.597693	+	0.801725i	$0.703916\pi$
$878$		0			0
$879$	−8.29421	+	6.28202i	−0.279757	+	0.211887i
$880$		0			0
$881$	14.3510	−	24.8567i	0.483499	−	0.837445i	−0.516321	−	0.856395i	$-0.672699\pi$
$881$	14.3510	−	24.8567i	0.483499	−	0.837445i	0.999820	+	0.0189501i	$0.00603236\pi$
$882$		0			0
$883$	−4.53046	−	7.84698i	−0.152462	−	0.264072i	0.779670	−	0.626191i	$-0.215387\pi$
$883$	−4.53046	−	7.84698i	−0.152462	−	0.264072i	−0.932132	+	0.362119i	$0.882054\pi$
$884$		0			0
$885$	6.16901	+	0.308166i	0.207369	+	0.0103589i
$886$		0			0
$887$	5.38583	+	4.51925i	0.180838	+	0.151741i	0.728713	−	0.684819i	$-0.240119\pi$
$887$	5.38583	+	4.51925i	0.180838	+	0.151741i	−0.547875	+	0.836560i	$0.684563\pi$
$888$		0			0
$889$	19.8080	−	12.3656i	0.664340	−	0.414729i
$890$		0			0
$891$	−53.9362	+	18.1106i	−1.80693	+	0.606728i
$892$		0			0
$893$	−6.99736	+	19.2251i	−0.234158	+	0.643343i
$894$		0			0
$895$	−18.0376	−	3.18051i	−0.602930	−	0.106313i
$896$		0			0
$897$	2.00206	−	3.09948i	0.0668468	−	0.103489i
$898$		0			0
$899$	7.66983	−	13.2845i	0.255803	−	0.443064i
$900$		0			0
$901$	−52.3409	+	30.2190i	−1.74373	+	1.00674i
$902$		0			0
$903$	39.0614	−	21.7552i	1.29988	−	0.723969i
$904$		0			0
$905$	3.83805	+	10.5450i	0.127581	+	0.350527i
$906$		0			0
$907$	4.27219	+	24.2288i	0.141856	+	0.804503i	0.969838	+	0.243749i	$0.0783774\pi$
$907$	4.27219	+	24.2288i	0.141856	+	0.804503i	−0.827983	+	0.560754i	$0.810511\pi$
$908$		0			0
$909$	6.58772	+	6.75530i	0.218501	+	0.224059i
$910$		0			0
$911$	−44.6394	+	7.87113i	−1.47897	+	0.260782i	−0.854166	−	0.520000i	$-0.825932\pi$
$911$	−44.6394	+	7.87113i	−1.47897	+	0.260782i	−0.624803	+	0.780782i	$0.714821\pi$
$912$		0			0
$913$	13.7159	−	16.3460i	0.453930	−	0.540973i
$914$		0			0
$915$	−1.22134	−	3.96014i	−0.0403764	−	0.130918i
$916$		0			0
$917$	35.7924	−	45.7717i	1.18197	−	1.51151i
$918$		0			0
$919$	24.8679	−	43.0724i	0.820315	−	1.42083i	−0.0851319	−	0.996370i	$-0.527131\pi$
$919$	24.8679	−	43.0724i	0.820315	−	1.42083i	0.905447	−	0.424458i	$-0.139535\pi$
$920$		0			0
$921$	−2.77865	−	9.00963i	−0.0915596	−	0.296877i
$922$		0			0
$923$	−5.78791	+	2.10663i	−0.190511	+	0.0693404i
$924$		0			0
$925$	3.64574	+	20.6760i	0.119871	+	0.679824i
$926$		0			0
$927$	−0.681035	+	6.79962i	−0.0223681	+	0.223329i
$928$		0			0
$929$	−8.23824	+	6.91270i	−0.270288	+	0.226798i	−0.767850	−	0.640630i	$-0.778673\pi$
$929$	−8.23824	+	6.91270i	−0.270288	+	0.226798i	0.497562	+	0.867429i	$0.334229\pi$
$930$		0			0
$931$	−0.993153	−	14.3802i	−0.0325493	−	0.471293i
$932$		0			0
$933$	19.8719	−	15.0510i	0.650578	−	0.492746i
$934$		0			0
$935$			66.4913i			2.17450i
$936$		0			0
$937$	−27.2033	+	15.7058i	−0.888692	+	0.513086i	−0.873514	−	0.486798i	$-0.838165\pi$
$937$	−27.2033	+	15.7058i	−0.888692	+	0.513086i	−0.0151775	+	0.999885i	$0.504831\pi$
$938$		0			0
$939$	−1.90911	+	38.2174i	−0.0623014	+	1.24718i
$940$		0			0
$941$	10.5403	−	3.83634i	0.343603	−	0.125061i	−0.164454	−	0.986385i	$-0.552586\pi$
$941$	10.5403	−	3.83634i	0.343603	−	0.125061i	0.508057	+	0.861324i	$0.330364\pi$
$942$		0			0
$943$	1.80773	−	0.318752i	0.0588678	−	0.0103800i
$944$		0			0
$945$	−15.1525	+	14.3271i	−0.492912	+	0.466060i
$946$		0			0
$947$	−17.0971	+	3.01467i	−0.555580	+	0.0979637i	−0.444387	−	0.895835i	$-0.646578\pi$
$947$	−17.0971	+	3.01467i	−0.555580	+	0.0979637i	−0.111193	+	0.993799i	$0.535467\pi$
$948$		0			0
$949$	−8.78019	+	3.19573i	−0.285017	+	0.103738i
$950$		0			0
$951$	−45.3543	+	23.2492i	−1.47071	+	0.753905i
$952$		0			0
$953$	16.0540	−	9.26877i	0.520039	−	0.300245i	−0.216911	−	0.976191i	$-0.569598\pi$
$953$	16.0540	−	9.26877i	0.520039	−	0.300245i	0.736951	+	0.675946i	$0.236265\pi$
$954$		0			0
$955$		−	8.56342i		−	0.277106i
$956$		0			0
$957$	5.92373	+	47.2878i	0.191487	+	1.52860i
$958$		0			0
$959$	11.7458	+	3.82203i	0.379293	+	0.123420i
$960$		0			0
$961$	14.2322	−	11.9422i	0.459103	−	0.385233i
$962$		0			0
$963$	−3.95293	+	8.20642i	−0.127381	+	0.264448i
$964$		0			0
$965$	3.99205	+	22.6400i	0.128509	+	0.728808i
$966$		0			0
$967$	−8.67991	+	3.15923i	−0.279127	+	0.101594i	−0.477790	−	0.878474i	$-0.658562\pi$
$967$	−8.67991	+	3.15923i	−0.279127	+	0.101594i	0.198663	+	0.980068i	$0.436340\pi$
$968$		0			0
$969$	16.8223	−	18.1284i	0.540409	−	0.582369i
$970$		0			0
$971$	1.58026	−	2.73709i	0.0507130	−	0.0878375i	−0.839555	−	0.543275i	$-0.817184\pi$
$971$	1.58026	−	2.73709i	0.0507130	−	0.0878375i	0.890268	+	0.455438i	$0.150517\pi$
$972$		0			0
$973$	1.65230	−	11.7202i	0.0529704	−	0.375733i
$974$		0			0
$975$	2.88817	+	0.659345i	0.0924954	+	0.0211159i
$976$		0			0
$977$	19.5961	−	23.3537i	0.626934	−	0.747151i	−0.355312	−	0.934748i	$-0.615625\pi$
$977$	19.5961	−	23.3537i	0.626934	−	0.747151i	0.982246	+	0.187597i	$0.0600698\pi$
$978$		0			0
$979$	−30.5206	+	5.38160i	−0.975442	+	0.171997i
$980$		0			0
$981$	41.3847	−	28.2101i	1.32131	−	0.900678i
$982$		0			0
$983$	−6.43962	−	36.5209i	−0.205392	−	1.16484i	−0.896822	−	0.442392i	$-0.854130\pi$
$983$	−6.43962	−	36.5209i	−0.205392	−	1.16484i	0.691429	−	0.722444i	$-0.256981\pi$
$984$		0			0
$985$	−0.559863	−	1.53821i	−0.0178387	−	0.0490115i
$986$		0			0
$987$	−39.7763	+	22.1534i	−1.26609	+	0.705150i
$988$		0			0
$989$	−28.4063	+	16.4004i	−0.903268	+	0.521502i
$990$		0			0
$991$	−21.4890	+	37.2200i	−0.682619	+	1.18233i	0.291560	+	0.956553i	$0.405826\pi$
$991$	−21.4890	+	37.2200i	−0.682619	+	1.18233i	−0.974179	+	0.225778i	$0.927508\pi$
$992$		0			0
$993$	0.906110	+	1.76763i	0.0287545	+	0.0560941i
$994$		0			0
$995$	−26.4543	−	4.66461i	−0.838658	−	0.147878i
$996$		0			0
$997$	−8.43136	+	23.1650i	−0.267024	+	0.733642i	0.731627	+	0.681706i	$0.238762\pi$
$997$	−8.43136	+	23.1650i	−0.267024	+	0.733642i	−0.998650	+	0.0519363i	$0.983461\pi$
$998$		0			0
$999$	−39.9657	−	6.02948i	−1.26446	−	0.190764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.19	yes	144
7.3	odd	6		756.2.ca.a.437.11	yes	144
27.11	odd	18		756.2.ca.a.173.11	✓	144
189.38	even	18	inner	756.2.ck.a.605.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.11	✓	144	27.11	odd	18
756.2.ca.a.437.11	yes	144	7.3	odd	6
756.2.ck.a.5.19	yes	144	1.1	even	1	trivial
756.2.ck.a.605.19	yes	144	189.38	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26963 + 1.17815i) q^{3} +(0.263400 - 1.49382i) q^{5} +(0.0912000 + 2.64418i) q^{7} +(0.223916 + 2.99163i) q^{9} +O(q^{10})\)	\(q+(1.26963 + 1.17815i) q^{3} +(0.263400 - 1.49382i) q^{5} +(0.0912000 + 2.64418i) q^{7} +(0.223916 + 2.99163i) q^{9} +(6.22570 - 1.09776i) q^{11} +(0.407322 - 0.485427i) q^{13} +(2.09436 - 1.58627i) q^{15} -6.93398 q^{17} +2.05921i q^{19} +(-2.99945 + 3.46457i) q^{21} +(2.16096 - 2.57533i) q^{23} +(2.53635 + 0.923157i) q^{25} +(-3.24031 + 4.06207i) q^{27} +(2.79770 + 3.33417i) q^{29} +(-1.20541 - 3.31183i) q^{31} +(9.19765 + 5.94107i) q^{33} +(3.97394 + 0.560241i) q^{35} +(3.88922 + 6.73632i) q^{37} +(1.08905 - 0.136425i) q^{39} +(0.418271 + 0.350971i) q^{41} +(-9.16836 - 3.33701i) q^{43} +(4.52793 + 0.453508i) q^{45} +(9.33615 + 3.39808i) q^{47} +(-6.98337 + 0.482298i) q^{49} +(-8.80358 - 8.16928i) q^{51} +(7.54846 - 4.35811i) q^{53} -9.58920i q^{55} +(-2.42606 + 2.61443i) q^{57} +(1.80096 + 1.51118i) q^{59} +(0.539493 - 1.48225i) q^{61} +(-7.88999 + 0.864910i) q^{63} +(-0.617851 - 0.736326i) q^{65} +(-1.21605 + 6.89658i) q^{67} +(5.77774 - 0.723775i) q^{69} +(-8.41776 - 4.85999i) q^{71} +(-12.7696 - 7.37256i) q^{73} +(2.13261 + 4.16028i) q^{75} +(3.47045 + 16.3617i) q^{77} +(-1.34555 - 7.63097i) q^{79} +(-8.89972 + 1.33975i) q^{81} +(2.58568 - 2.16964i) q^{83} +(-1.82641 + 10.3581i) q^{85} +(-0.376117 + 7.52927i) q^{87} -4.90235 q^{89} +(1.32070 + 1.03276i) q^{91} +(2.37142 - 5.62495i) q^{93} +(3.07608 + 0.542397i) q^{95} +(2.07416 - 5.69871i) q^{97} +(4.67812 + 18.3792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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