LMFDB - Embedded newform 3150.2.bf.b.1601.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1151,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("3150.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$25.1528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.b.1151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.63896 + 0.189469i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.63896 + 0.189469i) q^{7} -1.00000i q^{8} +(-4.67303 + 2.69798i) q^{11} -2.51764i q^{13} +(-2.19067 - 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.24969 - 3.89658i) q^{17} +(-2.48004 - 1.43185i) q^{19} +5.39595 q^{22} +(-0.232051 - 0.133975i) q^{23} +(-1.25882 + 2.18034i) q^{26} +(1.15539 + 2.38014i) q^{28} +8.89898i q^{29} +(4.18154 - 2.41421i) q^{31} +(0.866025 - 0.500000i) q^{32} +4.49938i q^{34} +(-3.25882 + 5.64444i) q^{37} +(1.43185 + 2.48004i) q^{38} +0.760279 q^{41} +5.86370 q^{43} +(-4.67303 - 2.69798i) q^{44} +(0.133975 + 0.232051i) q^{46} +(-3.99768 + 6.92418i) q^{47} +(6.92820 + 1.00000i) q^{49} +(2.18034 - 1.25882i) q^{52} +(7.27319 - 4.19918i) q^{53} +(0.189469 - 2.63896i) q^{56} +(4.44949 - 7.70674i) q^{58} +(6.33573 + 10.9738i) q^{59} +(-2.27035 - 1.31079i) q^{61} -4.82843 q^{62} -1.00000 q^{64} +(4.91119 + 8.50643i) q^{67} +(2.24969 - 3.89658i) q^{68} +4.76268i q^{71} +(-10.0951 + 5.82843i) q^{73} +(5.64444 - 3.25882i) q^{74} -2.86370i q^{76} +(-12.8431 + 6.23445i) q^{77} +(-4.29618 + 7.44120i) q^{79} +(-0.658421 - 0.380139i) q^{82} -9.45001 q^{83} +(-5.07812 - 2.93185i) q^{86} +(2.69798 + 4.67303i) q^{88} +(-3.98502 + 6.90226i) q^{89} +(0.477014 - 6.64394i) q^{91} -0.267949i q^{92} +(6.92418 - 3.99768i) q^{94} -6.16353i q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 24 q^{11} - 4 q^{16} + 12 q^{23} - 8 q^{26} - 24 q^{37} - 4 q^{38} - 32 q^{41} + 16 q^{43} - 24 q^{44} + 8 q^{46} - 8 q^{47} + 24 q^{53} + 16 q^{58} + 24 q^{59} - 16 q^{62} - 8 q^{64} + 24 q^{67} - 16 q^{77} - 24 q^{79} - 16 q^{83} + 16 q^{89} - 20 q^{91} - 12 q^{94} - 44 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 - 24 * q^11 - 4 * q^16 + 12 * q^23 - 8 * q^26 - 24 * q^37 - 4 * q^38 - 32 * q^41 + 16 * q^43 - 24 * q^44 + 8 * q^46 - 8 * q^47 + 24 * q^53 + 16 * q^58 + 24 * q^59 - 16 * q^62 - 8 * q^64 + 24 * q^67 - 16 * q^77 - 24 * q^79 - 16 * q^83 + 16 * q^89 - 20 * q^91 - 12 * q^94 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$2801$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$		0			0
$11$	−4.67303	+	2.69798i	−1.40897	+	0.813471i	−0.995289	−	0.0969504i	$-0.969091\pi$
$11$	−4.67303	+	2.69798i	−1.40897	+	0.813471i	−0.413683	+	0.910421i	$0.635758\pi$
$12$		0			0
$13$		−	2.51764i		−	0.698267i	−0.937073	−	0.349134i	$-0.886476\pi$
$13$		−	2.51764i		−	0.698267i	0.937073	−	0.349134i	$-0.113524\pi$
$14$	−2.19067	−	1.48356i	−0.585481	−	0.396499i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.24969	−	3.89658i	−0.545630	−	0.945058i	−0.998567	−	0.0535160i	$-0.982957\pi$
$17$	−2.24969	−	3.89658i	−0.545630	−	0.945058i	0.452937	−	0.891542i	$-0.350376\pi$
$18$		0			0
$19$	−2.48004	−	1.43185i	−0.568960	−	0.328489i	0.187774	−	0.982212i	$-0.439873\pi$
$19$	−2.48004	−	1.43185i	−0.568960	−	0.328489i	−0.756734	+	0.653723i	$0.773206\pi$
$20$		0			0
$21$		0			0
$22$	5.39595			1.15042
$23$	−0.232051	−	0.133975i	−0.0483859	−	0.0279356i	0.475612	−	0.879655i	$-0.342227\pi$
$23$	−0.232051	−	0.133975i	−0.0483859	−	0.0279356i	−0.523998	+	0.851720i	$0.675560\pi$
$24$		0			0
$25$		0			0
$26$	−1.25882	+	2.18034i	−0.246875	+	0.427600i
$27$		0			0
$28$	1.15539	+	2.38014i	0.218349	+	0.449804i
$29$			8.89898i			1.65250i	0.563304	+	0.826250i	$0.309530\pi$
$29$			8.89898i			1.65250i	−0.563304	+	0.826250i	$0.690470\pi$
$30$		0			0
$31$	4.18154	−	2.41421i	0.751027	−	0.433606i	−0.0750380	−	0.997181i	$-0.523908\pi$
$31$	4.18154	−	2.41421i	0.751027	−	0.433606i	0.826065	+	0.563575i	$0.190574\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			4.49938i			0.771637i
$35$		0			0
$36$		0			0
$37$	−3.25882	+	5.64444i	−0.535747	+	0.927940i	0.463380	+	0.886160i	$0.346636\pi$
$37$	−3.25882	+	5.64444i	−0.535747	+	0.927940i	−0.999127	+	0.0417807i	$0.986697\pi$
$38$	1.43185	+	2.48004i	0.232277	+	0.402316i
$39$		0			0
$40$		0			0
$41$	0.760279			0.118736			0.0593678	−	0.998236i	$-0.481092\pi$
$41$	0.760279			0.118736			0.0593678	+	0.998236i	$0.481092\pi$
$42$		0			0
$43$	5.86370			0.894206			0.447103	−	0.894482i	$-0.352456\pi$
$43$	5.86370			0.894206			0.447103	+	0.894482i	$0.352456\pi$
$44$	−4.67303	−	2.69798i	−0.704486	−	0.406735i
$45$		0			0
$46$	0.133975	+	0.232051i	0.0197535	+	0.0342140i
$47$	−3.99768	+	6.92418i	−0.583121	+	1.01000i	0.411986	+	0.911190i	$0.364835\pi$
$47$	−3.99768	+	6.92418i	−0.583121	+	1.01000i	−0.995107	+	0.0988053i	$0.968498\pi$
$48$		0			0
$49$	6.92820	+	1.00000i	0.989743	+	0.142857i
$50$		0			0
$51$		0			0
$52$	2.18034	−	1.25882i	0.302359	−	0.174567i
$53$	7.27319	−	4.19918i	0.999050	−	0.576802i	0.0910826	−	0.995843i	$-0.470967\pi$
$53$	7.27319	−	4.19918i	0.999050	−	0.576802i	0.907967	+	0.419042i	$0.137634\pi$
$54$		0			0
$55$		0			0
$56$	0.189469	−	2.63896i	0.0253188	−	0.352646i
$57$		0			0
$58$	4.44949	−	7.70674i	0.584247	−	1.01194i
$59$	6.33573	+	10.9738i	0.824842	+	1.42867i	0.902040	+	0.431653i	$0.142069\pi$
$59$	6.33573	+	10.9738i	0.824842	+	1.42867i	−0.0771977	+	0.997016i	$0.524597\pi$
$60$		0			0
$61$	−2.27035	−	1.31079i	−0.290689	−	0.167829i	0.347564	−	0.937656i	$-0.387009\pi$
$61$	−2.27035	−	1.31079i	−0.290689	−	0.167829i	−0.638253	+	0.769827i	$0.720342\pi$
$62$	−4.82843			−0.613211
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	4.91119	+	8.50643i	0.599997	+	1.03923i	0.992821	+	0.119612i	$0.0381649\pi$
$67$	4.91119	+	8.50643i	0.599997	+	1.03923i	−0.392824	+	0.919614i	$0.628502\pi$
$68$	2.24969	−	3.89658i	0.272815	−	0.472529i
$69$		0			0
$70$		0			0
$71$			4.76268i			0.565226i	0.959234	+	0.282613i	$0.0912013\pi$
$71$			4.76268i			0.565226i	−0.959234	+	0.282613i	$0.908799\pi$
$72$		0			0
$73$	−10.0951	+	5.82843i	−1.18155	+	0.682166i	−0.956372	−	0.292153i	$-0.905628\pi$
$73$	−10.0951	+	5.82843i	−1.18155	+	0.682166i	−0.225174	+	0.974319i	$0.572295\pi$
$74$	5.64444	−	3.25882i	0.656153	−	0.378830i
$75$		0			0
$76$		−	2.86370i		−	0.328489i
$77$	−12.8431	+	6.23445i	−1.46361	+	0.710482i
$78$		0			0
$79$	−4.29618	+	7.44120i	−0.483358	+	0.837200i	−0.999817	−	0.0191114i	$-0.993916\pi$
$79$	−4.29618	+	7.44120i	−0.483358	+	0.837200i	0.516460	+	0.856312i	$0.327250\pi$
$80$		0			0
$81$		0			0
$82$	−0.658421	−	0.380139i	−0.0727104	−	0.0419794i
$83$	−9.45001			−1.03727			−0.518636	−	0.854995i	$-0.673560\pi$
$83$	−9.45001			−1.03727			−0.518636	+	0.854995i	$0.673560\pi$
$84$		0			0
$85$		0			0
$86$	−5.07812	−	2.93185i	−0.547587	−	0.316150i
$87$		0			0
$88$	2.69798	+	4.67303i	0.287605	+	0.498147i
$89$	−3.98502	+	6.90226i	−0.422412	+	0.731638i	−0.996175	−	0.0873828i	$-0.972150\pi$
$89$	−3.98502	+	6.90226i	−0.422412	+	0.731638i	0.573763	+	0.819021i	$0.305483\pi$
$90$		0			0
$91$	0.477014	−	6.64394i	0.0500046	−	0.696474i
$92$		−	0.267949i		−	0.0279356i
$93$		0			0
$94$	6.92418	−	3.99768i	0.714175	−	0.412329i
$95$		0			0
$96$		0			0
$97$		−	6.16353i		−	0.625812i	−0.949784	−	0.312906i	$-0.898698\pi$
$97$		−	6.16353i		−	0.625812i	0.949784	−	0.312906i	$-0.101302\pi$
$98$	−5.50000	−	4.33013i	−0.555584	−	0.437409i
$99$		0			0
$100$		0			0
$101$	−7.02458	−	12.1669i	−0.698972	−	1.21065i	−0.968823	−	0.247753i	$-0.920308\pi$
$101$	−7.02458	−	12.1669i	−0.698972	−	1.21065i	0.269852	−	0.962902i	$-0.413025\pi$
$102$		0			0
$103$	−12.2776	−	7.08845i	−1.20974	−	0.698446i	−0.247040	−	0.969005i	$-0.579458\pi$
$103$	−12.2776	−	7.08845i	−1.20974	−	0.698446i	−0.962703	+	0.270560i	$0.912791\pi$
$104$	−2.51764			−0.246875
$105$		0			0
$106$	−8.39836			−0.815721
$107$	1.42178	+	0.820863i	0.137448	+	0.0793559i	0.567147	−	0.823616i	$-0.308047\pi$
$107$	1.42178	+	0.820863i	0.137448	+	0.0793559i	−0.429699	+	0.902972i	$0.641380\pi$
$108$		0			0
$109$	9.94887	+	17.2319i	0.952929	+	1.65052i	0.739039	+	0.673663i	$0.235280\pi$
$109$	9.94887	+	17.2319i	0.952929	+	1.65052i	0.213890	+	0.976858i	$0.431387\pi$
$110$		0			0
$111$		0			0
$112$	−1.48356	+	2.19067i	−0.140184	+	0.206999i
$113$			5.95867i			0.560545i	0.959921	+	0.280272i	$0.0904248\pi$
$113$			5.95867i			0.560545i	−0.959921	+	0.280272i	$0.909575\pi$
$114$		0			0
$115$		0			0
$116$	−7.70674	+	4.44949i	−0.715553	+	0.413125i
$117$		0			0
$118$		−	12.6715i		−	1.16650i
$119$	−5.19856	−	10.7091i	−0.476551	−	0.981706i
$120$		0			0
$121$	9.05816	−	15.6892i	0.823469	−	1.42629i
$122$	1.31079	+	2.27035i	0.118673	+	0.205548i
$123$		0			0
$124$	4.18154	+	2.41421i	0.375513	+	0.216803i
$125$		0			0
$126$		0			0
$127$	14.5103			1.28758			0.643792	−	0.765200i	$-0.277360\pi$
$127$	14.5103			1.28758			0.643792	+	0.765200i	$0.277360\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$		0			0
$131$	7.73325	−	13.3944i	0.675657	−	1.17027i	−0.300619	−	0.953744i	$-0.597193\pi$
$131$	7.73325	−	13.3944i	0.675657	−	1.17027i	0.976276	−	0.216529i	$-0.0694735\pi$
$132$		0			0
$133$	−6.27343	−	4.24849i	−0.543975	−	0.368391i
$134$		−	9.82237i		−	0.848524i
$135$		0			0
$136$	−3.89658	+	2.24969i	−0.334129	+	0.192909i
$137$	−7.46651	+	4.31079i	−0.637907	+	0.368296i	−0.783808	−	0.621004i	$-0.786725\pi$
$137$	−7.46651	+	4.31079i	−0.637907	+	0.368296i	0.145901	+	0.989299i	$0.453392\pi$
$138$		0			0
$139$			10.2512i			0.869495i	0.900552	+	0.434748i	$0.143162\pi$
$139$			10.2512i			0.869495i	−0.900552	+	0.434748i	$0.856838\pi$
$140$		0			0
$141$		0			0
$142$	2.38134	−	4.12460i	0.199838	−	0.346129i
$143$	6.79253	+	11.7650i	0.568020	+	0.983839i
$144$		0			0
$145$		0			0
$146$	11.6569			0.964728
$147$		0			0
$148$	−6.51764			−0.535747
$149$	−7.96640	−	4.59940i	−0.652633	−	0.376798i	0.136831	−	0.990594i	$-0.456308\pi$
$149$	−7.96640	−	4.59940i	−0.652633	−	0.376798i	−0.789464	+	0.613797i	$0.789641\pi$
$150$		0			0
$151$	6.37429	+	11.0406i	0.518733	+	0.898471i	0.999763	+	0.0217674i	$0.00692931\pi$
$151$	6.37429	+	11.0406i	0.518733	+	0.898471i	−0.481030	+	0.876704i	$0.659737\pi$
$152$	−1.43185	+	2.48004i	−0.116139	+	0.201158i
$153$		0			0
$154$	14.2397	+	1.02236i	1.14747	+	0.0823845i
$155$		0			0
$156$		0			0
$157$	−11.9899	+	6.92236i	−0.956896	+	0.552464i	−0.895216	−	0.445632i	$-0.852979\pi$
$157$	−11.9899	+	6.92236i	−0.956896	+	0.552464i	−0.0616798	+	0.998096i	$0.519646\pi$
$158$	7.44120	−	4.29618i	0.591990	−	0.341786i
$159$		0			0
$160$		0			0
$161$	−0.586988	−	0.397520i	−0.0462612	−	0.0313289i
$162$		0			0
$163$	−10.3025	+	17.8444i	−0.806954	+	1.39768i	0.108010	+	0.994150i	$0.465552\pi$
$163$	−10.3025	+	17.8444i	−0.806954	+	1.39768i	−0.914964	+	0.403535i	$0.867781\pi$
$164$	0.380139	+	0.658421i	0.0296839	+	0.0514140i
$165$		0			0
$166$	8.18394	+	4.72500i	0.635197	+	0.366731i
$167$	−6.84961			−0.530038			−0.265019	−	0.964243i	$-0.585378\pi$
$167$	−6.84961			−0.530038			−0.265019	+	0.964243i	$0.585378\pi$
$168$		0			0
$169$	6.66150			0.512423
$170$		0			0
$171$		0			0
$172$	2.93185	+	5.07812i	0.223552	+	0.387203i
$173$	6.37902	−	11.0488i	0.484988	−	0.840024i	−0.514863	−	0.857272i	$-0.672157\pi$
$173$	6.37902	−	11.0488i	0.484988	−	0.840024i	0.999851	+	0.0172486i	$0.00549068\pi$
$174$		0			0
$175$		0			0
$176$		−	5.39595i		−	0.406735i
$177$		0			0
$178$	6.90226	−	3.98502i	0.517347	−	0.298690i
$179$	−16.3390	+	9.43331i	−1.22123	+	0.705079i	−0.965181	−	0.261584i	$-0.915755\pi$
$179$	−16.3390	+	9.43331i	−1.22123	+	0.705079i	−0.256052	+	0.966663i	$0.582422\pi$
$180$		0			0
$181$			25.5498i			1.89910i	0.313615	+	0.949550i	$0.398460\pi$
$181$			25.5498i			1.89910i	−0.313615	+	0.949550i	$0.601540\pi$
$182$	−3.73508	+	5.51532i	−0.276862	+	0.408822i
$183$		0			0
$184$	−0.133975	+	0.232051i	−0.00987674	+	0.0171070i
$185$		0			0
$186$		0			0
$187$	21.0257	+	12.1392i	1.53755	+	0.887707i
$188$	−7.99536			−0.583121
$189$		0			0
$190$		0			0
$191$	−7.00657	−	4.04524i	−0.506977	−	0.292704i	0.224613	−	0.974448i	$-0.427888\pi$
$191$	−7.00657	−	4.04524i	−0.506977	−	0.292704i	−0.731590	+	0.681745i	$0.761222\pi$
$192$		0			0
$193$	−7.06350	−	12.2343i	−0.508442	−	0.880648i	−0.999952	−	0.00977575i	$-0.996888\pi$
$193$	−7.06350	−	12.2343i	−0.508442	−	0.880648i	0.491510	−	0.870872i	$-0.336445\pi$
$194$	−3.08176	+	5.33777i	−0.221258	+	0.383230i
$195$		0			0
$196$	2.59808	+	6.50000i	0.185577	+	0.464286i
$197$		−	14.2738i		−	1.01697i	−0.861072	−	0.508483i	$-0.830207\pi$
$197$		−	14.2738i		−	1.01697i	0.861072	−	0.508483i	$-0.169793\pi$
$198$		0			0
$199$	3.06742	−	1.77098i	0.217444	−	0.125541i	−0.387322	−	0.921944i	$-0.626600\pi$
$199$	3.06742	−	1.77098i	0.217444	−	0.125541i	0.604766	+	0.796403i	$0.293267\pi$
$200$		0			0
$201$		0			0
$202$			14.0492i			0.988495i
$203$	−1.68608	+	23.4840i	−0.118339	+	1.64826i
$204$		0			0
$205$		0			0
$206$	7.08845	+	12.2776i	0.493876	+	0.855418i
$207$		0			0
$208$	2.18034	+	1.25882i	0.151179	+	0.0872834i
$209$	15.4524			1.06887
$210$		0			0
$211$	−3.92340			−0.270098			−0.135049	−	0.990839i	$-0.543119\pi$
$211$	−3.92340			−0.270098			−0.135049	+	0.990839i	$0.543119\pi$
$212$	7.27319	+	4.19918i	0.499525	+	0.288401i
$213$		0			0
$214$	−0.820863	−	1.42178i	−0.0561131	−	0.0971907i
$215$		0			0
$216$		0			0
$217$	11.4923	−	5.57874i	0.780150	−	0.378709i
$218$		−	19.8977i		−	1.34764i
$219$		0			0
$220$		0			0
$221$	−9.81017	+	5.66390i	−0.659903	+	0.380995i
$222$		0			0
$223$		−	14.6904i		−	0.983740i	−0.870669	−	0.491870i	$-0.836314\pi$
$223$		−	14.6904i		−	0.983740i	0.870669	−	0.491870i	$-0.163686\pi$
$224$	2.38014	−	1.15539i	0.159030	−	0.0771980i
$225$		0			0
$226$	2.97934	−	5.16036i	0.198182	−	0.343262i
$227$	11.3913	+	19.7303i	0.756068	+	1.30955i	0.944842	+	0.327527i	$0.106215\pi$
$227$	11.3913	+	19.7303i	0.756068	+	1.30955i	−0.188774	+	0.982021i	$0.560451\pi$
$228$		0			0
$229$	−17.5089	−	10.1087i	−1.15702	−	0.668005i	−0.206431	−	0.978461i	$-0.566185\pi$
$229$	−17.5089	−	10.1087i	−1.15702	−	0.668005i	−0.950588	+	0.310456i	$0.899518\pi$
$230$		0			0
$231$		0			0
$232$	8.89898			0.584247
$233$	−2.27840	−	1.31543i	−0.149263	−	0.0861769i	0.423509	−	0.905892i	$-0.360798\pi$
$233$	−2.27840	−	1.31543i	−0.149263	−	0.0861769i	−0.572771	+	0.819715i	$0.694132\pi$
$234$		0			0
$235$		0			0
$236$	−6.33573	+	10.9738i	−0.412421	+	0.714334i
$237$		0			0
$238$	−0.852491	+	11.8737i	−0.0552588	+	0.769656i
$239$			16.8766i			1.09165i	0.837898	+	0.545827i	$0.183784\pi$
$239$			16.8766i			1.09165i	−0.837898	+	0.545827i	$0.816216\pi$
$240$		0			0
$241$	−12.5793	+	7.26268i	−0.810306	+	0.467831i	−0.847062	−	0.531494i	$-0.821631\pi$
$241$	−12.5793	+	7.26268i	−0.810306	+	0.467831i	0.0367560	+	0.999324i	$0.488298\pi$
$242$	−15.6892	+	9.05816i	−1.00854	+	0.582280i
$243$		0			0
$244$		−	2.62158i		−	0.167829i
$245$		0			0
$246$		0			0
$247$	−3.60488	+	6.24384i	−0.229373	+	0.397286i
$248$	−2.41421	−	4.18154i	−0.153303	−	0.265528i
$249$		0			0
$250$		0			0
$251$	15.7243			0.992507			0.496254	−	0.868178i	$-0.334709\pi$
$251$	15.7243			0.992507			0.496254	+	0.868178i	$0.334709\pi$
$252$		0			0
$253$	1.44584			0.0908993
$254$	−12.5663	−	7.25517i	−0.788481	−	0.455230i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.83083	+	17.0275i	−0.613230	+	1.06215i	0.377462	+	0.926025i	$0.376797\pi$
$257$	−9.83083	+	17.0275i	−0.613230	+	1.06215i	−0.990692	+	0.136121i	$0.956536\pi$
$258$		0			0
$259$	−9.66933	+	14.2780i	−0.600823	+	0.887192i
$260$		0			0
$261$		0			0
$262$	−13.3944	+	7.73325i	−0.827508	+	0.477762i
$263$	3.74275	−	2.16088i	0.230788	−	0.133245i	−0.380148	−	0.924926i	$-0.624127\pi$
$263$	3.74275	−	2.16088i	0.230788	−	0.133245i	0.610935	+	0.791680i	$0.290794\pi$
$264$		0			0
$265$		0			0
$266$	3.30871	+	6.81601i	0.202870	+	0.417917i
$267$		0			0
$268$	−4.91119	+	8.50643i	−0.299999	+	0.519613i
$269$	8.79895	+	15.2402i	0.536482	+	0.929214i	0.999090	+	0.0426509i	$0.0135803\pi$
$269$	8.79895	+	15.2402i	0.536482	+	0.929214i	−0.462608	+	0.886563i	$0.653086\pi$
$270$		0			0
$271$	−9.12436	−	5.26795i	−0.554265	−	0.320005i	0.196575	−	0.980489i	$-0.437018\pi$
$271$	−9.12436	−	5.26795i	−0.554265	−	0.320005i	−0.750840	+	0.660484i	$0.770351\pi$
$272$	4.49938			0.272815
$273$		0			0
$274$	8.62158			0.520849
$275$		0			0
$276$		0			0
$277$	1.50971	+	2.61489i	0.0907097	+	0.157114i	0.907810	−	0.419382i	$-0.137753\pi$
$277$	1.50971	+	2.61489i	0.0907097	+	0.157114i	−0.817100	+	0.576496i	$0.804420\pi$
$278$	5.12560	−	8.87780i	0.307413	−	0.532455i
$279$		0			0
$280$		0			0
$281$			10.6880i			0.637591i	0.947824	+	0.318795i	$0.103278\pi$
$281$			10.6880i			0.637591i	−0.947824	+	0.318795i	$0.896722\pi$
$282$		0			0
$283$	15.2149	−	8.78434i	0.904434	−	0.522175i	0.0257976	−	0.999667i	$-0.491787\pi$
$283$	15.2149	−	8.78434i	0.904434	−	0.522175i	0.878636	+	0.477492i	$0.158454\pi$
$284$	−4.12460	+	2.38134i	−0.244750	+	0.141307i
$285$		0			0
$286$		−	13.5851i		−	0.803301i
$287$	2.00634	+	0.144049i	0.118431	+	0.00850295i
$288$		0			0
$289$	−1.62220	+	2.80973i	−0.0954235	+	0.165278i
$290$		0			0
$291$		0			0
$292$	−10.0951	−	5.82843i	−0.590773	−	0.341083i
$293$	14.6710			0.857086			0.428543	−	0.903521i	$-0.359027\pi$
$293$	14.6710			0.857086			0.428543	+	0.903521i	$0.359027\pi$
$294$		0			0
$295$		0			0
$296$	5.64444	+	3.25882i	0.328076	+	0.189415i
$297$		0			0
$298$	4.59940	+	7.96640i	0.266436	+	0.461481i
$299$	−0.337300	+	0.584220i	−0.0195065	+	0.0337863i
$300$		0			0
$301$	15.4741	+	1.11099i	0.891911	+	0.0640363i
$302$		−	12.7486i		−	0.733599i
$303$		0			0
$304$	2.48004	−	1.43185i	0.142240	−	0.0821223i
$305$		0			0
$306$		0			0
$307$			21.2772i			1.21435i	0.794567	+	0.607177i	$0.207698\pi$
$307$			21.2772i			1.21435i	−0.794567	+	0.607177i	$0.792302\pi$
$308$	−11.8208	−	8.00524i	−0.673550	−	0.456141i
$309$		0			0
$310$		0			0
$311$	−5.91724	−	10.2490i	−0.335536	−	0.581165i	0.648052	−	0.761596i	$-0.275584\pi$
$311$	−5.91724	−	10.2490i	−0.335536	−	0.581165i	−0.983588	+	0.180431i	$0.942251\pi$
$312$		0			0
$313$	3.90551	+	2.25485i	0.220753	+	0.127452i	0.606299	−	0.795237i	$-0.292654\pi$
$313$	3.90551	+	2.25485i	0.220753	+	0.127452i	−0.385546	+	0.922689i	$0.625987\pi$
$314$	13.8447			0.781302
$315$		0			0
$316$	−8.59235			−0.483358
$317$	15.9202	+	9.19151i	0.894165	+	0.516247i	0.875303	−	0.483576i	$-0.160662\pi$
$317$	15.9202	+	9.19151i	0.894165	+	0.516247i	0.0188626	+	0.999822i	$0.493995\pi$
$318$		0			0
$319$	−24.0092	−	41.5852i	−1.34426	−	2.32833i
$320$		0			0
$321$		0			0
$322$	0.309587	+	0.637756i	0.0172526	+	0.0355408i
$323$			12.8849i			0.716934i
$324$		0			0
$325$		0			0
$326$	17.8444	−	10.3025i	0.988313	−	0.570603i
$327$		0			0
$328$		−	0.760279i		−	0.0419794i
$329$	−11.8616	+	17.5152i	−0.653952	+	0.965644i
$330$		0			0
$331$	−3.98066	+	6.89471i	−0.218797	+	0.378967i	−0.954440	−	0.298401i	$-0.903547\pi$
$331$	−3.98066	+	6.89471i	−0.218797	+	0.378967i	0.735643	+	0.677369i	$0.236880\pi$
$332$	−4.72500	−	8.18394i	−0.259318	−	0.449152i
$333$		0			0
$334$	5.93193	+	3.42480i	0.324581	+	0.187397i
$335$		0			0
$336$		0			0
$337$	6.89417			0.375549			0.187775	−	0.982212i	$-0.439873\pi$
$337$	6.89417			0.375549			0.187775	+	0.982212i	$0.439873\pi$
$338$	−5.76903	−	3.33075i	−0.313794	−	0.181169i
$339$		0			0
$340$		0			0
$341$	−13.0270	+	22.5634i	−0.705451	+	1.22188i
$342$		0			0
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$		−	5.86370i		−	0.316150i
$345$		0			0
$346$	−11.0488	+	6.37902i	−0.593986	+	0.342938i
$347$	14.1645	−	8.17789i	0.760392	−	0.439012i	−0.0690448	−	0.997614i	$-0.521995\pi$
$347$	14.1645	−	8.17789i	0.760392	−	0.439012i	0.829436	+	0.558601i	$0.188662\pi$
$348$		0			0
$349$			24.5851i			1.31601i	0.753014	+	0.658004i	$0.228599\pi$
$349$			24.5851i			1.31601i	−0.753014	+	0.658004i	$0.771401\pi$
$350$		0			0
$351$		0			0
$352$	−2.69798	+	4.67303i	−0.143803	+	0.249073i
$353$	−6.85906	−	11.8802i	−0.365071	−	0.632321i	0.623717	−	0.781651i	$-0.285622\pi$
$353$	−6.85906	−	11.8802i	−0.365071	−	0.632321i	−0.988788	+	0.149329i	$0.952289\pi$
$354$		0			0
$355$		0			0
$356$	−7.97005			−0.422412
$357$		0			0
$358$	18.8666			0.997132
$359$	−10.3059	−	5.95011i	−0.543924	−	0.314035i	0.202744	−	0.979232i	$-0.435014\pi$
$359$	−10.3059	−	5.95011i	−0.543924	−	0.314035i	−0.746668	+	0.665197i	$0.768348\pi$
$360$		0			0
$361$	−5.39960	−	9.35238i	−0.284190	−	0.492231i
$362$	12.7749	−	22.1268i	0.671433	−	1.16296i
$363$		0			0
$364$	5.99233	−	2.90887i	0.314083	−	0.152466i
$365$		0			0
$366$		0			0
$367$	10.9026	−	6.29461i	0.569110	−	0.328576i	−0.187684	−	0.982230i	$-0.560098\pi$
$367$	10.9026	−	6.29461i	0.569110	−	0.328576i	0.756794	+	0.653654i	$0.226765\pi$
$368$	0.232051	−	0.133975i	0.0120965	−	0.00698391i
$369$		0			0
$370$		0			0
$371$	19.9893	−	9.70342i	1.03779	−	0.503776i
$372$		0			0
$373$	−13.5868	+	23.5331i	−0.703499	+	1.21850i	0.263731	+	0.964596i	$0.415047\pi$
$373$	−13.5868	+	23.5331i	−0.703499	+	1.21850i	−0.967230	+	0.253900i	$0.918286\pi$
$374$	−12.1392	−	21.0257i	−0.627704	−	1.08722i
$375$		0			0
$376$	6.92418	+	3.99768i	0.357087	+	0.206164i
$377$	22.4044			1.15389
$378$		0			0
$379$	15.7335			0.808174			0.404087	−	0.914721i	$-0.367589\pi$
$379$	15.7335			0.808174			0.404087	+	0.914721i	$0.367589\pi$
$380$		0			0
$381$		0			0
$382$	4.04524	+	7.00657i	0.206973	+	0.358487i
$383$	7.89060	−	13.6669i	0.403191	−	0.698347i	−0.590918	−	0.806732i	$-0.701234\pi$
$383$	7.89060	−	13.6669i	0.403191	−	0.698347i	0.994109	+	0.108384i	$0.0345677\pi$
$384$		0			0
$385$		0			0
$386$			14.1270i			0.719046i
$387$		0			0
$388$	5.33777	−	3.08176i	0.270984	−	0.156453i
$389$	−13.7556	+	7.94182i	−0.697438	+	0.402666i	−0.806393	−	0.591381i	$-0.798583\pi$
$389$	−13.7556	+	7.94182i	−0.697438	+	0.402666i	0.108954	+	0.994047i	$0.465250\pi$
$390$		0			0
$391$			1.20560i			0.0609700i
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$		0			0
$394$	−7.13689	+	12.3615i	−0.359552	+	0.622762i
$395$		0			0
$396$		0			0
$397$	−32.3557	−	18.6806i	−1.62388	−	0.937550i	−0.985867	−	0.167528i	$-0.946422\pi$
$397$	−32.3557	−	18.6806i	−1.62388	−	0.937550i	−0.638017	−	0.770022i	$-0.720245\pi$
$398$	−3.54195			−0.177542
$399$		0			0
$400$		0			0
$401$	24.4856	+	14.1368i	1.22275	+	0.705957i	0.965504	−	0.260389i	$-0.0838507\pi$
$401$	24.4856	+	14.1368i	1.22275	+	0.705957i	0.257249	+	0.966345i	$0.417184\pi$
$402$		0			0
$403$	−6.07812	−	10.5276i	−0.302773	−	0.524417i
$404$	7.02458	−	12.1669i	0.349486	−	0.605327i
$405$		0			0
$406$	13.2022	−	19.4947i	0.655214	−	0.967507i
$407$		−	35.1689i		−	1.74326i
$408$		0			0
$409$	13.8647	−	8.00481i	0.685567	−	0.395812i	−0.116382	−	0.993204i	$-0.537130\pi$
$409$	13.8647	−	8.00481i	0.685567	−	0.395812i	0.801949	+	0.597392i	$0.203796\pi$
$410$		0			0
$411$		0			0
$412$		−	14.1769i		−	0.698446i
$413$	14.6405	+	30.1599i	0.720414	+	1.48407i
$414$		0			0
$415$		0			0
$416$	−1.25882	−	2.18034i	−0.0617187	−	0.106900i
$417$		0			0
$418$	−13.3822	−	7.72620i	−0.654544	−	0.377901i
$419$	29.5137			1.44184			0.720919	−	0.693020i	$-0.243720\pi$
$419$	29.5137			1.44184			0.720919	+	0.693020i	$0.243720\pi$
$420$		0			0
$421$	0.309114			0.0150653			0.00753265	−	0.999972i	$-0.497602\pi$
$421$	0.309114			0.0150653			0.00753265	+	0.999972i	$0.497602\pi$
$422$	3.39776	+	1.96170i	0.165400	+	0.0954939i
$423$		0			0
$424$	−4.19918	−	7.27319i	−0.203930	−	0.353217i
$425$		0			0
$426$		0			0
$427$	−5.74301	−	3.88928i	−0.277924	−	0.188215i
$428$			1.64173i			0.0793559i
$429$		0			0
$430$		0			0
$431$	7.63843	−	4.41005i	0.367930	−	0.212425i	−0.304624	−	0.952473i	$-0.598531\pi$
$431$	7.63843	−	4.41005i	0.367930	−	0.212425i	0.672554	+	0.740048i	$0.265197\pi$
$432$		0			0
$433$			9.56388i			0.459611i	0.973237	+	0.229805i	$0.0738089\pi$
$433$			9.56388i			0.459611i	−0.973237	+	0.229805i	$0.926191\pi$
$434$	−12.7420	−	0.914836i	−0.611636	−	0.0439135i
$435$		0			0
$436$	−9.94887	+	17.2319i	−0.476464	+	0.825260i
$437$	0.383663	+	0.664525i	0.0183531	+	0.0317885i
$438$		0			0
$439$	−31.3336	−	18.0905i	−1.49547	−	0.863412i	−0.495487	−	0.868615i	$-0.665010\pi$
$439$	−31.3336	−	18.0905i	−1.49547	−	0.863412i	−0.999986	+	0.00520362i	$0.998344\pi$
$440$		0			0
$441$		0			0
$442$	11.3278			0.538809
$443$	3.53830	+	2.04284i	0.168110	+	0.0970582i	0.581694	−	0.813408i	$-0.302390\pi$
$443$	3.53830	+	2.04284i	0.168110	+	0.0970582i	−0.413584	+	0.910466i	$0.635723\pi$
$444$		0			0
$445$		0			0
$446$	−7.34519	+	12.7222i	−0.347805	+	0.602415i
$447$		0			0
$448$	−2.63896	−	0.189469i	−0.124679	−	0.00895155i
$449$		−	19.9377i		−	0.940918i	−0.882422	−	0.470459i	$-0.844088\pi$
$449$		−	19.9377i		−	0.940918i	0.882422	−	0.470459i	$-0.155912\pi$
$450$		0			0
$451$	−3.55281	+	2.05121i	−0.167295	+	0.0965879i
$452$	−5.16036	+	2.97934i	−0.242723	+	0.140136i
$453$		0			0
$454$		−	22.7826i		−	1.06924i
$455$		0			0
$456$		0			0
$457$	−10.0623	+	17.4283i	−0.470693	+	0.815264i	−0.999438	−	0.0335168i	$-0.989329\pi$
$457$	−10.0623	+	17.4283i	−0.470693	+	0.815264i	0.528745	+	0.848780i	$0.322663\pi$
$458$	10.1087	+	17.5089i	0.472351	+	0.818136i
$459$		0			0
$460$		0			0
$461$	−0.909299			−0.0423503			−0.0211751	−	0.999776i	$-0.506741\pi$
$461$	−0.909299			−0.0423503			−0.0211751	+	0.999776i	$0.506741\pi$
$462$		0			0
$463$	−21.4280			−0.995843			−0.497922	−	0.867222i	$-0.665903\pi$
$463$	−21.4280			−0.995843			−0.497922	+	0.867222i	$0.665903\pi$
$464$	−7.70674	−	4.44949i	−0.357777	−	0.206562i
$465$		0			0
$466$	1.31543	+	2.27840i	0.0609363	+	0.105545i
$467$	6.34607	−	10.9917i	0.293661	−	0.508636i	−0.681012	−	0.732273i	$-0.738460\pi$
$467$	6.34607	−	10.9917i	0.293661	−	0.508636i	0.974672	+	0.223637i	$0.0717930\pi$
$468$		0			0
$469$	11.3487	+	23.3786i	0.524035	+	1.07952i
$470$		0			0
$471$		0			0
$472$	10.9738	−	6.33573i	0.505111	−	0.291626i
$473$	−27.4013	+	15.8201i	−1.25991	+	0.727411i
$474$		0			0
$475$		0			0
$476$	6.67511	−	9.85666i	0.305953	−	0.451779i
$477$		0			0
$478$	8.43828	−	14.6155i	0.385958	−	0.668499i
$479$	6.43828	+	11.1514i	0.294172	+	0.509522i	0.974792	−	0.223115i	$-0.0716227\pi$
$479$	6.43828	+	11.1514i	0.294172	+	0.509522i	−0.680620	+	0.732637i	$0.738289\pi$
$480$		0			0
$481$	14.2107	+	8.20453i	0.647950	+	0.374094i
$482$	14.5254			0.661612
$483$		0			0
$484$	18.1163			0.823469
$485$		0			0
$486$		0			0
$487$	−10.4097	−	18.0301i	−0.471708	−	0.817022i	0.527768	−	0.849388i	$-0.323029\pi$
$487$	−10.4097	−	18.0301i	−0.471708	−	0.817022i	−0.999476	+	0.0323665i	$0.989696\pi$
$488$	−1.31079	+	2.27035i	−0.0593366	+	0.102774i
$489$		0			0
$490$		0			0
$491$		−	27.3271i		−	1.23325i	−0.787256	−	0.616627i	$-0.788499\pi$
$491$		−	27.3271i		−	1.23325i	0.787256	−	0.616627i	$-0.211501\pi$
$492$		0			0
$493$	34.6755	−	20.0199i	1.56171	−	0.901653i
$494$	6.24384	−	3.60488i	0.280924	−	0.162191i
$495$		0			0
$496$			4.82843i			0.216803i
$497$	−0.902379	+	12.5685i	−0.0404772	+	0.563775i
$498$		0			0
$499$	−16.6802	+	28.8909i	−0.746708	+	1.29334i	0.202685	+	0.979244i	$0.435033\pi$
$499$	−16.6802	+	28.8909i	−0.746708	+	1.29334i	−0.949393	+	0.314092i	$0.898300\pi$
$500$		0			0
$501$		0			0
$502$	−13.6176	−	7.86214i	−0.607784	−	0.350904i
$503$	16.2936			0.726494			0.363247	−	0.931693i	$-0.381668\pi$
$503$	16.2936			0.726494			0.363247	+	0.931693i	$0.381668\pi$
$504$		0			0
$505$		0			0
$506$	−1.25214	−	0.722921i	−0.0556642	−	0.0321377i
$507$		0			0
$508$	7.25517	+	12.5663i	0.321896	+	0.557540i
$509$	12.3400	−	21.3735i	0.546961	−	0.947365i	−0.451519	−	0.892261i	$-0.649118\pi$
$509$	12.3400	−	21.3735i	0.546961	−	0.947365i	0.998481	−	0.0551036i	$-0.0175489\pi$
$510$		0			0
$511$	−27.7449	+	13.4683i	−1.22736	+	0.595801i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	17.0275	−	9.83083i	0.751051	−	0.433619i
$515$		0			0
$516$		0			0
$517$		−	43.1426i		−	1.89741i
$518$	15.5129	−	7.53044i	0.681597	−	0.330869i
$519$		0			0
$520$		0			0
$521$	0.141663	+	0.245367i	0.00620635	+	0.0107497i	0.869112	−	0.494616i	$-0.164691\pi$
$521$	0.141663	+	0.245367i	0.00620635	+	0.0107497i	−0.862906	+	0.505365i	$0.831358\pi$
$522$		0			0
$523$	9.77021	+	5.64083i	0.427222	+	0.246656i	0.698162	−	0.715940i	$-0.254001\pi$
$523$	9.77021	+	5.64083i	0.427222	+	0.246656i	−0.270941	+	0.962596i	$0.587335\pi$
$524$	15.4665			0.675657
$525$		0			0
$526$	−4.32175			−0.188437
$527$	−18.8143	−	10.8625i	−0.819565	−	0.473176i
$528$		0			0
$529$	−11.4641	−	19.8564i	−0.498439	−	0.863322i
$530$		0			0
$531$		0			0
$532$	0.542582	−	7.55719i	0.0235239	−	0.327646i
$533$		−	1.91411i		−	0.0829092i
$534$		0			0
$535$		0			0
$536$	8.50643	−	4.91119i	0.367422	−	0.212131i
$537$		0			0
$538$		−	17.5979i		−	0.758700i
$539$	−35.0737	+	14.0191i	−1.51073	+	0.603845i
$540$		0			0
$541$	17.4125	−	30.1593i	0.748621	−	1.29665i	−0.199862	−	0.979824i	$-0.564049\pi$
$541$	17.4125	−	30.1593i	0.748621	−	1.29665i	0.948484	−	0.316826i	$-0.102617\pi$
$542$	5.26795	+	9.12436i	0.226278	+	0.391925i
$543$		0			0
$544$	−3.89658	−	2.24969i	−0.167064	−	0.0964546i
$545$		0			0
$546$		0			0
$547$	−35.4261			−1.51471			−0.757356	−	0.653002i	$-0.773509\pi$
$547$	−35.4261			−1.51471			−0.757356	+	0.653002i	$0.773509\pi$
$548$	−7.46651	−	4.31079i	−0.318953	−	0.184148i
$549$		0			0
$550$		0			0
$551$	12.7420	−	22.0698i	0.542828	−	0.940206i
$552$		0			0
$553$	−12.7473	+	18.8230i	−0.542071	+	0.800436i
$554$		−	3.01942i		−	0.128283i
$555$		0			0
$556$	−8.87780	+	5.12560i	−0.376503	+	0.217374i
$557$	−7.05105	+	4.07093i	−0.298763	+	0.172491i	−0.641887	−	0.766799i	$-0.721848\pi$
$557$	−7.05105	+	4.07093i	−0.298763	+	0.172491i	0.343124	+	0.939290i	$0.388515\pi$
$558$		0			0
$559$		−	14.7627i		−	0.624395i
$560$		0			0
$561$		0			0
$562$	5.34398	−	9.25605i	0.225422	−	0.390443i
$563$	−10.2088	−	17.6821i	−0.430248	−	0.745212i	0.566646	−	0.823961i	$-0.308241\pi$
$563$	−10.2088	−	17.6821i	−0.430248	−	0.745212i	−0.996894	+	0.0787491i	$0.974907\pi$
$564$		0			0
$565$		0			0
$566$	−17.5687			−0.738467
$567$		0			0
$568$	4.76268			0.199838
$569$	22.5542	+	13.0217i	0.945520	+	0.545896i	0.891686	−	0.452654i	$-0.149523\pi$
$569$	22.5542	+	13.0217i	0.945520	+	0.545896i	0.0538334	+	0.998550i	$0.482856\pi$
$570$		0			0
$571$	6.18811	+	10.7181i	0.258964	+	0.448539i	0.965965	−	0.258674i	$-0.0832855\pi$
$571$	6.18811	+	10.7181i	0.258964	+	0.448539i	−0.707000	+	0.707213i	$0.749952\pi$
$572$	−6.79253	+	11.7650i	−0.284010	+	0.491920i
$573$		0			0
$574$	−1.66552	−	1.12792i	−0.0695175	−	0.0470786i
$575$		0			0
$576$		0			0
$577$	−23.3399	+	13.4753i	−0.971654	+	0.560985i	−0.899740	−	0.436426i	$-0.856244\pi$
$577$	−23.3399	+	13.4753i	−0.971654	+	0.560985i	−0.0719139	+	0.997411i	$0.522911\pi$
$578$	2.80973	−	1.62220i	0.116869	−	0.0674746i
$579$		0			0
$580$		0			0
$581$	−24.9382	−	1.79048i	−1.03461	−	0.0742816i
$582$		0			0
$583$	−22.6586	+	39.2458i	−0.938422	+	1.62539i
$584$	5.82843	+	10.0951i	0.241182	+	0.417740i
$585$		0			0
$586$	−12.7054	−	7.33548i	−0.524856	−	0.303026i
$587$	35.3511			1.45910			0.729548	−	0.683930i	$-0.239731\pi$
$587$	35.3511			1.45910			0.729548	+	0.683930i	$0.239731\pi$
$588$		0			0
$589$	−13.8272			−0.569739
$590$		0			0
$591$		0			0
$592$	−3.25882	−	5.64444i	−0.133937	−	0.231985i
$593$	−14.7057	+	25.4711i	−0.603893	+	1.04597i	0.388333	+	0.921519i	$0.373051\pi$
$593$	−14.7057	+	25.4711i	−0.603893	+	1.04597i	−0.992225	+	0.124454i	$0.960282\pi$
$594$		0			0
$595$		0			0
$596$		−	9.19881i		−	0.376798i
$597$		0			0
$598$	0.584220	−	0.337300i	0.0238905	−	0.0137932i
$599$	26.5494	−	15.3283i	1.08478	−	0.626298i	0.152598	−	0.988288i	$-0.451236\pi$
$599$	26.5494	−	15.3283i	1.08478	−	0.626298i	0.932182	+	0.361990i	$0.117903\pi$
$600$		0			0
$601$		−	34.3407i		−	1.40078i	−0.713758	−	0.700392i	$-0.753008\pi$
$601$		−	34.3407i		−	1.40078i	0.713758	−	0.700392i	$-0.246992\pi$
$602$	−12.8454	−	8.69918i	−0.523541	−	0.354552i
$603$		0			0
$604$	−6.37429	+	11.0406i	−0.259366	+	0.449236i
$605$		0			0
$606$		0			0
$607$	−28.2475	−	16.3087i	−1.14653	−	0.661950i	−0.198492	−	0.980103i	$-0.563604\pi$
$607$	−28.2475	−	16.3087i	−1.14653	−	0.661950i	−0.948040	+	0.318153i	$0.896938\pi$
$608$	−2.86370			−0.116139
$609$		0			0
$610$		0			0
$611$	17.4326	+	10.0647i	0.705247	+	0.407174i
$612$		0			0
$613$	−7.99843	−	13.8537i	−0.323054	−	0.559545i	0.658063	−	0.752963i	$-0.271376\pi$
$613$	−7.99843	−	13.8537i	−0.323054	−	0.559545i	−0.981117	+	0.193418i	$0.938043\pi$
$614$	10.6386	−	18.4266i	0.429339	−	0.743636i
$615$		0			0
$616$	6.23445	+	12.8431i	0.251193	+	0.517464i
$617$			25.1429i			1.01221i	0.862471	+	0.506107i	$0.168916\pi$
$617$			25.1429i			1.01221i	−0.862471	+	0.506107i	$0.831084\pi$
$618$		0			0
$619$	32.3379	−	18.6703i	1.29977	−	0.750423i	0.319406	−	0.947618i	$-0.396517\pi$
$619$	32.3379	−	18.6703i	1.29977	−	0.750423i	0.980364	+	0.197195i	$0.0631832\pi$
$620$		0			0
$621$		0			0
$622$			11.8345i			0.474519i
$623$	−11.8241	+	17.4597i	−0.473722	+	0.699510i
$624$		0			0
$625$		0			0
$626$	−2.25485	−	3.90551i	−0.0901219	−	0.156096i
$627$		0			0
$628$	−11.9899	−	6.92236i	−0.478448	−	0.276232i
$629$	29.3253			1.16928
$630$		0			0
$631$	49.5015			1.97062			0.985311	−	0.170767i	$-0.0546245\pi$
$631$	49.5015			1.97062			0.985311	+	0.170767i	$0.0546245\pi$
$632$	7.44120	+	4.29618i	0.295995	+	0.170893i
$633$		0			0
$634$	−9.19151	−	15.9202i	−0.365041	−	0.632270i
$635$		0			0
$636$		0			0
$637$	2.51764	−	17.4427i	0.0997525	−	0.691105i
$638$			48.0185i			1.90107i
$639$		0			0
$640$		0			0
$641$	−31.4439	+	18.1542i	−1.24196	+	0.717046i	−0.969493	−	0.245119i	$-0.921173\pi$
$641$	−31.4439	+	18.1542i	−1.24196	+	0.717046i	−0.272467	+	0.962165i	$0.587840\pi$
$642$		0			0
$643$			10.2653i			0.404824i	0.979300	+	0.202412i	$0.0648780\pi$
$643$			10.2653i			0.404824i	−0.979300	+	0.202412i	$0.935122\pi$
$644$	0.0507680	−	0.707107i	0.00200054	−	0.0278639i
$645$		0			0
$646$	6.44244	−	11.1586i	0.253474	−	0.439031i
$647$	10.9108	+	18.8980i	0.428946	+	0.742956i	0.996780	−	0.0801869i	$-0.0255517\pi$
$647$	10.9108	+	18.8980i	0.428946	+	0.742956i	−0.567834	+	0.823143i	$0.692218\pi$
$648$		0			0
$649$	−59.2142	−	34.1873i	−2.32436	−	1.34197i
$650$		0			0
$651$		0			0
$652$	−20.6050			−0.806954
$653$	−40.9556	−	23.6457i	−1.60272	−	0.925329i	−0.990941	−	0.134297i	$-0.957122\pi$
$653$	−40.9556	−	23.6457i	−1.60272	−	0.925329i	−0.611775	−	0.791032i	$-0.709544\pi$
$654$		0			0
$655$		0			0
$656$	−0.380139	+	0.658421i	−0.0148419	+	0.0257070i
$657$		0			0
$658$	19.0301	−	9.23779i	0.741869	−	0.360127i
$659$		−	3.58255i		−	0.139556i	−0.997563	−	0.0697782i	$-0.977771\pi$
$659$		−	3.58255i		−	0.139556i	0.997563	−	0.0697782i	$-0.0222291\pi$
$660$		0			0
$661$	−1.41761	+	0.818459i	−0.0551388	+	0.0318344i	−0.527316	−	0.849669i	$-0.676802\pi$
$661$	−1.41761	+	0.818459i	−0.0551388	+	0.0318344i	0.472177	+	0.881504i	$0.343468\pi$
$662$	6.89471	−	3.98066i	0.267970	−	0.154713i
$663$		0			0
$664$			9.45001i			0.366731i
$665$		0			0
$666$		0			0
$667$	1.19224	−	2.06502i	0.0461636	−	0.0799577i
$668$	−3.42480	−	5.93193i	−0.132510	−	0.229513i
$669$		0			0
$670$		0			0
$671$	14.1459			0.546097
$672$		0			0
$673$	2.02242			0.0779587			0.0389794	−	0.999240i	$-0.487589\pi$
$673$	2.02242			0.0779587			0.0389794	+	0.999240i	$0.487589\pi$
$674$	−5.97053	−	3.44709i	−0.229976	−	0.132777i
$675$		0			0
$676$	3.33075	+	5.76903i	0.128106	+	0.221886i
$677$	−11.4413	+	19.8169i	−0.439725	+	0.761626i	−0.997668	−	0.0682532i	$-0.978257\pi$
$677$	−11.4413	+	19.8169i	−0.439725	+	0.761626i	0.557943	+	0.829879i	$0.311591\pi$
$678$		0			0
$679$	1.16780	−	16.2653i	0.0448159	−	0.624205i
$680$		0			0
$681$		0			0
$682$	22.5634	−	13.0270i	0.863997	−	0.498829i
$683$	−27.1977	+	15.7026i	−1.04069	+	0.600844i	−0.920029	−	0.391850i	$-0.871835\pi$
$683$	−27.1977	+	15.7026i	−1.04069	+	0.600844i	−0.120663	+	0.992694i	$0.538502\pi$
$684$		0			0
$685$		0			0
$686$	−13.6938	−	12.4691i	−0.522834	−	0.476073i
$687$		0			0
$688$	−2.93185	+	5.07812i	−0.111776	+	0.193601i
$689$	−10.5720	−	18.3113i	−0.402762	−	0.697604i
$690$		0			0
$691$	29.3677	+	16.9554i	1.11720	+	0.645015i	0.940684	−	0.339283i	$-0.110184\pi$
$691$	29.3677	+	16.9554i	1.11720	+	0.645015i	0.176515	+	0.984298i	$0.443518\pi$
$692$	12.7580			0.484988
$693$		0			0
$694$	−16.3558			−0.620857
$695$		0			0
$696$		0			0
$697$	−1.71039	−	2.96248i	−0.0647857	−	0.112212i
$698$	12.2925	−	21.2913i	0.465279	−	0.805887i
$699$		0			0
$700$		0			0
$701$			10.5296i			0.397699i	0.980030	+	0.198849i	$0.0637205\pi$
$701$			10.5296i			0.397699i	−0.980030	+	0.198849i	$0.936280\pi$
$702$		0			0
$703$	16.1640	−	9.33229i	0.609637	−	0.351974i
$704$	4.67303	−	2.69798i	0.176122	−	0.101684i
$705$		0			0
$706$			13.7181i			0.516288i
$707$	−16.2323	−	33.4390i	−0.610479	−	1.25760i
$708$		0			0
$709$	−7.52572	+	13.0349i	−0.282634	+	0.489537i	−0.972033	−	0.234845i	$-0.924542\pi$
$709$	−7.52572	+	13.0349i	−0.282634	+	0.489537i	0.689398	+	0.724382i	$0.257875\pi$
$710$		0			0
$711$		0			0
$712$	6.90226	+	3.98502i	0.258673	+	0.149345i
$713$	−1.29377			−0.0484522
$714$		0			0
$715$		0			0
$716$	−16.3390	−	9.43331i	−0.610616	−	0.352539i
$717$		0			0
$718$	5.95011	+	10.3059i	0.222056	+	0.384613i
$719$	12.2137	−	21.1547i	0.455494	−	0.788938i	−0.543223	−	0.839589i	$-0.682796\pi$
$719$	12.2137	−	21.1547i	0.455494	−	0.788938i	0.998716	+	0.0506506i	$0.0161295\pi$
$720$		0			0
$721$	−31.0569	−	21.0323i	−1.15662	−	0.783285i
$722$			10.7992i			0.401905i
$723$		0			0
$724$	−22.1268	+	12.7749i	−0.822335	+	0.474775i
$725$		0			0
$726$		0			0
$727$			43.7349i			1.62204i	0.585020	+	0.811019i	$0.301087\pi$
$727$			43.7349i			1.62204i	−0.585020	+	0.811019i	$0.698913\pi$
$728$	−6.64394	−	0.477014i	−0.246241	−	0.0176793i
$729$		0			0
$730$		0			0
$731$	−13.1915	−	22.8484i	−0.487906	−	0.845077i
$732$		0			0
$733$	−38.7280	−	22.3596i	−1.43045	−	0.825872i	−0.433297	−	0.901251i	$-0.642650\pi$
$733$	−38.7280	−	22.3596i	−1.43045	−	0.825872i	−0.997155	+	0.0753789i	$0.975983\pi$
$734$	−12.5892			−0.464677
$735$		0			0
$736$	−0.267949			−0.00987674
$737$	−45.9003	−	26.5005i	−1.69076	−	0.976160i
$738$		0			0
$739$	10.7360	+	18.5954i	0.394932	+	0.684042i	0.993092	−	0.117334i	$-0.0374348\pi$
$739$	10.7360	+	18.5954i	0.394932	+	0.684042i	−0.598161	+	0.801376i	$0.704102\pi$
$740$		0			0
$741$		0			0
$742$	−22.1629	−	1.59123i	−0.813626	−	0.0584157i
$743$		−	29.5637i		−	1.08459i	−0.840190	−	0.542293i	$-0.817556\pi$
$743$		−	29.5637i		−	1.08459i	0.840190	−	0.542293i	$-0.182444\pi$
$744$		0			0
$745$		0			0
$746$	23.5331	−	13.5868i	0.861607	−	0.497449i
$747$		0			0
$748$			24.2784i			0.887707i
$749$	3.59648	+	2.43561i	0.131413	+	0.0889951i
$750$		0			0
$751$	−0.596750	+	1.03360i	−0.0217757	+	0.0377166i	−0.876708	−	0.481023i	$-0.840265\pi$
$751$	−0.596750	+	1.03360i	−0.0217757	+	0.0377166i	0.854932	+	0.518740i	$0.173599\pi$
$752$	−3.99768	−	6.92418i	−0.145780	−	0.252499i
$753$		0			0
$754$	−19.4028	−	11.2022i	−0.706608	−	0.407960i
$755$		0			0
$756$		0			0
$757$	26.8915			0.977386			0.488693	−	0.872456i	$-0.337474\pi$
$757$	26.8915			0.977386			0.488693	+	0.872456i	$0.337474\pi$
$758$	−13.6256	−	7.86673i	−0.494903	−	0.285732i
$759$		0			0
$760$		0			0
$761$	−0.939574	+	1.62739i	−0.0340595	+	0.0589928i	−0.882553	−	0.470213i	$-0.844177\pi$
$761$	−0.939574	+	1.62739i	−0.0340595	+	0.0589928i	0.848493	+	0.529206i	$0.177510\pi$
$762$		0			0
$763$	22.9897	+	47.3594i	0.832284	+	1.71452i
$764$		−	8.09049i		−	0.292704i
$765$		0			0
$766$	−13.6669	+	7.89060i	−0.493806	+	0.285099i
$767$	27.6281	−	15.9511i	0.997592	−	0.575960i
$768$		0			0
$769$		−	50.6544i		−	1.82664i	−0.407239	−	0.913322i	$-0.633508\pi$
$769$		−	50.6544i		−	1.82664i	0.407239	−	0.913322i	$-0.366492\pi$
$770$		0			0
$771$		0			0
$772$	7.06350	−	12.2343i	0.254221	−	0.440324i
$773$	24.3353	+	42.1499i	0.875279	+	1.51603i	0.856466	+	0.516204i	$0.172655\pi$
$773$	24.3353	+	42.1499i	0.875279	+	1.51603i	0.0188128	+	0.999823i	$0.494011\pi$
$774$		0			0
$775$		0			0
$776$	−6.16353			−0.221258
$777$		0			0
$778$	15.8836			0.569456
$779$	−1.88552	−	1.08861i	−0.0675558	−	0.0390034i
$780$		0			0
$781$	−12.8496	−	22.2562i	−0.459795	−	0.796388i
$782$	0.602802	−	1.04408i	0.0215562	−	0.0373364i
$783$		0			0
$784$	−4.33013	+	5.50000i	−0.154647	+	0.196429i
$785$		0			0
$786$		0			0
$787$	12.9437	−	7.47307i	0.461395	−	0.266386i	−0.251236	−	0.967926i	$-0.580837\pi$
$787$	12.9437	−	7.47307i	0.461395	−	0.266386i	0.712630	+	0.701540i	$0.247504\pi$
$788$	12.3615	−	7.13689i	0.440359	−	0.254241i
$789$		0			0
$790$		0			0
$791$	−1.12898	+	15.7247i	−0.0401420	+	0.559105i
$792$		0			0
$793$	−3.30009	+	5.71593i	−0.117190	+	0.202979i
$794$	18.6806	+	32.3557i	0.662948	+	1.14826i
$795$		0			0
$796$	3.06742	+	1.77098i	0.108722	+	0.0627706i
$797$	15.0557			0.533301			0.266650	−	0.963793i	$-0.414083\pi$
$797$	15.0557			0.533301			0.266650	+	0.963793i	$0.414083\pi$
$798$		0			0
$799$	35.9741			1.27267
$800$		0			0
$801$		0			0
$802$	−14.1368	−	24.4856i	−0.499187	−	0.864617i
$803$	31.4499	−	54.4729i	1.10984	−	1.92231i
$804$		0			0
$805$		0			0
$806$			12.1562i			0.428185i
$807$		0			0
$808$	−12.1669	+	7.02458i	−0.428031	+	0.247124i
$809$	30.7426	−	17.7493i	1.08085	−	0.624031i	0.149727	−	0.988727i	$-0.452160\pi$
$809$	30.7426	−	17.7493i	1.08085	−	0.624031i	0.931127	+	0.364696i	$0.118827\pi$
$810$		0			0
$811$			24.5935i			0.863594i	0.901971	+	0.431797i	$0.142120\pi$
$811$			24.5935i			0.863594i	−0.901971	+	0.431797i	$0.857880\pi$
$812$	−21.1808	+	10.2818i	−0.743301	+	0.360822i
$813$		0			0
$814$	−17.5844	+	30.4571i	−0.616334	+	1.06752i
$815$		0			0
$816$		0			0
$817$	−14.5422	−	8.39595i	−0.508768	−	0.293737i
$818$	−16.0096			−0.559763
$819$		0			0
$820$		0			0
$821$	−12.3035	−	7.10342i	−0.429395	−	0.247911i	0.269694	−	0.962946i	$-0.413077\pi$
$821$	−12.3035	−	7.10342i	−0.429395	−	0.247911i	−0.699089	+	0.715035i	$0.746411\pi$
$822$		0			0
$823$	0.945584	+	1.63780i	0.0329610	+	0.0570901i	0.882035	−	0.471183i	$-0.156173\pi$
$823$	0.945584	+	1.63780i	0.0329610	+	0.0570901i	−0.849074	+	0.528273i	$0.822840\pi$
$824$	−7.08845	+	12.2776i	−0.246938	+	0.427709i
$825$		0			0
$826$	2.40085	−	33.4395i	0.0835361	−	1.16351i
$827$		−	31.9280i		−	1.11024i	−0.831769	−	0.555122i	$-0.812671\pi$
$827$		−	31.9280i		−	1.11024i	0.831769	−	0.555122i	$-0.187329\pi$
$828$		0			0
$829$	3.38864	−	1.95643i	0.117692	−	0.0679497i	−0.439998	−	0.897999i	$-0.645021\pi$
$829$	3.38864	−	1.95643i	0.117692	−	0.0679497i	0.557691	+	0.830049i	$0.311688\pi$
$830$		0			0
$831$		0			0
$832$			2.51764i			0.0872834i
$833$	−11.6897	−	29.2460i	−0.405025	−	1.01331i
$834$		0			0
$835$		0			0
$836$	7.72620	+	13.3822i	0.267216	+	0.462832i
$837$		0			0
$838$	−25.5596	−	14.7568i	−0.882941	−	0.509766i
$839$	−15.3513			−0.529984			−0.264992	−	0.964251i	$-0.585369\pi$
$839$	−15.3513			−0.529984			−0.264992	+	0.964251i	$0.585369\pi$
$840$		0			0
$841$	−50.1918			−1.73075
$842$	−0.267701	−	0.154557i	−0.00922557	−	0.00532639i
$843$		0			0
$844$	−1.96170	−	3.39776i	−0.0675244	−	0.116956i
$845$		0			0
$846$		0			0
$847$	26.8767	−	39.6869i	0.923495	−	1.36366i
$848$			8.39836i			0.288401i
$849$		0			0
$850$		0			0
$851$	1.51242	−	0.873198i	0.0518452	−	0.0299328i
$852$		0			0
$853$		−	22.2302i		−	0.761148i	−0.924750	−	0.380574i	$-0.875726\pi$
$853$		−	22.2302i		−	0.761148i	0.924750	−	0.380574i	$-0.124274\pi$
$854$	3.02896	+	6.23972i	0.103649	+	0.213519i
$855$		0			0
$856$	0.820863	−	1.42178i	0.0280565	−	0.0485953i
$857$	−26.4098	−	45.7432i	−0.902143	−	1.56256i	−0.824707	−	0.565560i	$-0.808660\pi$
$857$	−26.4098	−	45.7432i	−0.902143	−	1.56256i	−0.0774356	−	0.996997i	$-0.524673\pi$
$858$		0			0
$859$	−15.2916	−	8.82859i	−0.521742	−	0.301228i	0.215905	−	0.976414i	$-0.430730\pi$
$859$	−15.2916	−	8.82859i	−0.521742	−	0.301228i	−0.737647	+	0.675187i	$0.764063\pi$
$860$		0			0
$861$		0			0
$862$	−8.82010			−0.300414
$863$	14.2452	+	8.22446i	0.484912	+	0.279964i	0.722461	−	0.691412i	$-0.243011\pi$
$863$	14.2452	+	8.22446i	0.484912	+	0.279964i	−0.237549	+	0.971375i	$0.576344\pi$
$864$		0			0
$865$		0			0
$866$	4.78194	−	8.28256i	0.162497	−	0.281453i
$867$		0			0
$868$	10.5775	+	7.16328i	0.359024	+	0.243138i
$869$		−	46.3639i		−	1.57279i
$870$		0			0
$871$	21.4161	−	12.3646i	0.725657	−	0.418958i
$872$	17.2319	−	9.94887i	0.583547	−	0.336911i
$873$		0			0
$874$		−	0.767327i		−	0.0259552i
$875$		0			0
$876$		0			0
$877$	27.1078	−	46.9521i	0.915366	−	1.58546i	0.109001	−	0.994042i	$-0.465235\pi$
$877$	27.1078	−	46.9521i	0.915366	−	1.58546i	0.806365	−	0.591418i	$-0.201432\pi$
$878$	18.0905	+	31.3336i	0.610524	+	1.05746i
$879$		0			0
$880$		0			0
$881$	−50.1647			−1.69009			−0.845046	−	0.534694i	$-0.820427\pi$
$881$	−50.1647			−1.69009			−0.845046	+	0.534694i	$0.820427\pi$
$882$		0			0
$883$	0.841563			0.0283208			0.0141604	−	0.999900i	$-0.495492\pi$
$883$	0.841563			0.0283208			0.0141604	+	0.999900i	$0.495492\pi$
$884$	−9.81017	−	5.66390i	−0.329952	−	0.190498i
$885$		0			0
$886$	−2.04284	−	3.53830i	−0.0686305	−	0.118872i
$887$	20.0492	−	34.7262i	0.673185	−	1.16599i	−0.303811	−	0.952732i	$-0.598259\pi$
$887$	20.0492	−	34.7262i	0.673185	−	1.16599i	0.976996	−	0.213258i	$-0.0684075\pi$
$888$		0			0
$889$	38.2922	+	2.74926i	1.28428	+	0.0922071i
$890$		0			0
$891$		0			0
$892$	12.7222	−	7.34519i	0.425972	−	0.245935i
$893$	19.8288	−	11.4482i	0.663546	−	0.383098i
$894$		0			0
$895$		0			0
$896$	2.19067	+	1.48356i	0.0731852	+	0.0495624i
$897$		0			0
$898$	−9.96885	+	17.2665i	−0.332665	+	0.576192i
$899$	21.4840	+	37.2114i	0.716533	+	1.24107i
$900$		0			0
$901$	−32.7248	−	18.8937i	−1.09022	−	0.629440i
$902$	4.10243			0.136596
$903$		0			0
$904$	5.95867			0.198182
$905$		0			0
$906$		0			0
$907$	−22.5945	−	39.1348i	−0.750238	−	1.29945i	−0.947707	−	0.319142i	$-0.896605\pi$
$907$	−22.5945	−	39.1348i	−0.750238	−	1.29945i	0.197469	−	0.980309i	$-0.436728\pi$
$908$	−11.3913	+	19.7303i	−0.378034	+	0.654774i
$909$		0			0
$910$		0			0
$911$		−	58.2281i		−	1.92918i	−0.263746	−	0.964592i	$-0.584958\pi$
$911$		−	58.2281i		−	1.92918i	0.263746	−	0.964592i	$-0.415042\pi$
$912$		0			0
$913$	44.1602	−	25.4959i	1.46149	−	0.843791i
$914$	17.4283	−	10.0623i	0.576478	−	0.332830i
$915$		0			0
$916$		−	20.2175i		−	0.668005i
$917$	22.9455	−	33.8820i	0.757729	−	1.11888i
$918$		0			0
$919$	−6.61745	+	11.4618i	−0.218290	+	0.378089i	−0.954285	−	0.298898i	$-0.903381\pi$
$919$	−6.61745	+	11.4618i	−0.218290	+	0.378089i	0.735996	+	0.676986i	$0.236714\pi$
$920$		0			0
$921$		0			0
$922$	0.787476	+	0.454649i	0.0259341	+	0.0149731i
$923$	11.9907			0.394679
$924$		0			0
$925$		0			0
$926$	18.5572	+	10.7140i	0.609827	+	0.352084i
$927$		0			0
$928$	4.44949	+	7.70674i	0.146062	+	0.252986i
$929$	10.4434	−	18.0885i	0.342637	−	0.593464i	−0.642285	−	0.766466i	$-0.722013\pi$
$929$	10.4434	−	18.0885i	0.342637	−	0.593464i	0.984921	+	0.173002i	$0.0553467\pi$
$930$		0			0
$931$	−15.7504	−	12.4002i	−0.516197	−	0.406400i
$932$		−	2.63087i		−	0.0861769i
$933$		0			0
$934$	−10.9917	+	6.34607i	−0.359660	+	0.207650i
$935$		0			0
$936$		0			0
$937$		−	23.2465i		−	0.759430i	−0.925103	−	0.379715i	$-0.876022\pi$
$937$		−	23.2465i		−	0.759430i	0.925103	−	0.379715i	$-0.123978\pi$
$938$	1.86103	−	25.9208i	0.0607649	−	0.846345i
$939$		0			0
$940$		0			0
$941$	0.752551	+	1.30346i	0.0245325	+	0.0424915i	0.878031	−	0.478604i	$-0.158857\pi$
$941$	0.752551	+	1.30346i	0.0245325	+	0.0424915i	−0.853499	+	0.521095i	$0.825524\pi$
$942$		0			0
$943$	−0.176423	−	0.101858i	−0.00574513	−	0.00331695i
$944$	−12.6715			−0.412421
$945$		0			0
$946$	31.6403			1.02871
$947$	21.0122	+	12.1314i	0.682805	+	0.394218i	0.800911	−	0.598783i	$-0.204349\pi$
$947$	21.0122	+	12.1314i	0.682805	+	0.394218i	−0.118106	+	0.993001i	$0.537682\pi$
$948$		0			0
$949$	14.6739	+	25.4159i	0.476334	+	0.825035i
$950$		0			0
$951$		0			0
$952$	−10.7091	+	5.19856i	−0.347085	+	0.168486i
$953$			56.7061i			1.83689i	0.395547	+	0.918446i	$0.370555\pi$
$953$			56.7061i			1.83689i	−0.395547	+	0.918446i	$0.629445\pi$
$954$		0			0
$955$		0			0
$956$	−14.6155	+	8.43828i	−0.472700	+	0.272913i
$957$		0			0
$958$		−	12.8766i		−	0.416023i
$959$	−20.5206	+	9.96132i	−0.662643	+	0.321668i
$960$		0			0
$961$	−3.84315	+	6.65652i	−0.123972	+	0.214727i
$962$	−8.20453	−	14.2107i	−0.264525	−	0.458170i
$963$		0			0
$964$	−12.5793	−	7.26268i	−0.405153	−	0.233915i
$965$		0			0
$966$		0			0
$967$	−7.23556			−0.232680			−0.116340	−	0.993209i	$-0.537116\pi$
$967$	−7.23556			−0.232680			−0.116340	+	0.993209i	$0.537116\pi$
$968$	−15.6892	−	9.05816i	−0.504270	−	0.291140i
$969$		0			0
$970$		0			0
$971$	−19.3560	+	33.5256i	−0.621163	+	1.07589i	0.368106	+	0.929784i	$0.380006\pi$
$971$	−19.3560	+	33.5256i	−0.621163	+	1.07589i	−0.989269	+	0.146103i	$0.953327\pi$
$972$		0			0
$973$	−1.94228	+	27.0525i	−0.0622667	+	0.867263i
$974$			20.8194i			0.667096i
$975$		0			0
$976$	2.27035	−	1.31079i	0.0726722	−	0.0419573i
$977$	−15.7279	+	9.08052i	−0.503181	+	0.290512i	−0.730026	−	0.683419i	$-0.760492\pi$
$977$	−15.7279	+	9.08052i	−0.503181	+	0.290512i	0.226845	+	0.973931i	$0.427159\pi$
$978$		0			0
$979$		−	43.0060i		−	1.37448i
$980$		0			0
$981$		0			0
$982$	−13.6635	+	23.6659i	−0.436021	+	0.755211i
$983$	−8.19988	−	14.2026i	−0.261536	−	0.452993i	0.705115	−	0.709093i	$-0.250896\pi$
$983$	−8.19988	−	14.2026i	−0.261536	−	0.452993i	−0.966650	+	0.256100i	$0.917562\pi$
$984$		0			0
$985$		0			0
$986$	−40.0399			−1.27513
$987$		0			0
$988$	−7.20977			−0.229373
$989$	−1.36068	−	0.785587i	−0.0432670	−	0.0249802i
$990$		0			0
$991$	5.44584	+	9.43247i	0.172993	+	0.299632i	0.939465	−	0.342645i	$-0.111323\pi$
$991$	5.44584	+	9.43247i	0.172993	+	0.299632i	−0.766472	+	0.642278i	$0.777990\pi$
$992$	2.41421	−	4.18154i	0.0766514	−	0.132764i
$993$		0			0
$994$	7.06574	−	10.4335i	0.224112	−	0.330930i
$995$		0			0
$996$		0			0
$997$	−30.7856	+	17.7740i	−0.974988	+	0.562910i	−0.900753	−	0.434331i	$-0.856985\pi$
$997$	−30.7856	+	17.7740i	−0.974988	+	0.562910i	−0.0742349	+	0.997241i	$0.523651\pi$
$998$	28.8909	−	16.6802i	0.914527	−	0.528002i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.b.1601.2		8
3.2	odd	2		3150.2.bf.c.1601.4		8
5.2	odd	4		3150.2.bp.d.1349.2		8
5.3	odd	4		3150.2.bp.a.1349.3		8
5.4	even	2		630.2.be.a.341.3	✓	8
7.3	odd	6		3150.2.bf.c.1151.4		8
15.2	even	4		3150.2.bp.c.1349.2		8
15.8	even	4		3150.2.bp.f.1349.3		8
15.14	odd	2		630.2.be.b.341.1	yes	8
21.17	even	6	inner	3150.2.bf.b.1151.2		8
35.3	even	12		3150.2.bp.c.899.2		8
35.9	even	6		4410.2.b.e.881.1		8
35.17	even	12		3150.2.bp.f.899.3		8
35.19	odd	6		4410.2.b.b.881.1		8
35.24	odd	6		630.2.be.b.521.1	yes	8
105.17	odd	12		3150.2.bp.a.899.3		8
105.38	odd	12		3150.2.bp.d.899.2		8
105.44	odd	6		4410.2.b.b.881.8		8
105.59	even	6		630.2.be.a.521.3	yes	8
105.89	even	6		4410.2.b.e.881.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.be.a.341.3	✓	8	5.4	even	2
630.2.be.a.521.3	yes	8	105.59	even	6
630.2.be.b.341.1	yes	8	15.14	odd	2
630.2.be.b.521.1	yes	8	35.24	odd	6
3150.2.bf.b.1151.2		8	21.17	even	6	inner
3150.2.bf.b.1601.2		8	1.1	even	1	trivial
3150.2.bf.c.1151.4		8	7.3	odd	6
3150.2.bf.c.1601.4		8	3.2	odd	2
3150.2.bp.a.899.3		8	105.17	odd	12
3150.2.bp.a.1349.3		8	5.3	odd	4
3150.2.bp.c.899.2		8	35.3	even	12
3150.2.bp.c.1349.2		8	15.2	even	4
3150.2.bp.d.899.2		8	105.38	odd	12
3150.2.bp.d.1349.2		8	5.2	odd	4
3150.2.bp.f.899.3		8	35.17	even	12
3150.2.bp.f.1349.3		8	15.8	even	4
4410.2.b.b.881.1		8	35.19	odd	6
4410.2.b.b.881.8		8	105.44	odd	6
4410.2.b.e.881.1		8	35.9	even	6
4410.2.b.e.881.8		8	105.89	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.63896 + 0.189469i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.63896 + 0.189469i) q^{7} -1.00000i q^{8} +(-4.67303 + 2.69798i) q^{11} -2.51764i q^{13} +(-2.19067 - 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.24969 - 3.89658i) q^{17} +(-2.48004 - 1.43185i) q^{19} +5.39595 q^{22} +(-0.232051 - 0.133975i) q^{23} +(-1.25882 + 2.18034i) q^{26} +(1.15539 + 2.38014i) q^{28} +8.89898i q^{29} +(4.18154 - 2.41421i) q^{31} +(0.866025 - 0.500000i) q^{32} +4.49938i q^{34} +(-3.25882 + 5.64444i) q^{37} +(1.43185 + 2.48004i) q^{38} +0.760279 q^{41} +5.86370 q^{43} +(-4.67303 - 2.69798i) q^{44} +(0.133975 + 0.232051i) q^{46} +(-3.99768 + 6.92418i) q^{47} +(6.92820 + 1.00000i) q^{49} +(2.18034 - 1.25882i) q^{52} +(7.27319 - 4.19918i) q^{53} +(0.189469 - 2.63896i) q^{56} +(4.44949 - 7.70674i) q^{58} +(6.33573 + 10.9738i) q^{59} +(-2.27035 - 1.31079i) q^{61} -4.82843 q^{62} -1.00000 q^{64} +(4.91119 + 8.50643i) q^{67} +(2.24969 - 3.89658i) q^{68} +4.76268i q^{71} +(-10.0951 + 5.82843i) q^{73} +(5.64444 - 3.25882i) q^{74} -2.86370i q^{76} +(-12.8431 + 6.23445i) q^{77} +(-4.29618 + 7.44120i) q^{79} +(-0.658421 - 0.380139i) q^{82} -9.45001 q^{83} +(-5.07812 - 2.93185i) q^{86} +(2.69798 + 4.67303i) q^{88} +(-3.98502 + 6.90226i) q^{89} +(0.477014 - 6.64394i) q^{91} -0.267949i q^{92} +(6.92418 - 3.99768i) q^{94} -6.16353i q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 24 q^{11} - 4 q^{16} + 12 q^{23} - 8 q^{26} - 24 q^{37} - 4 q^{38} - 32 q^{41} + 16 q^{43} - 24 q^{44} + 8 q^{46} - 8 q^{47} + 24 q^{53} + 16 q^{58} + 24 q^{59} - 16 q^{62} - 8 q^{64} + 24 q^{67} - 16 q^{77} - 24 q^{79} - 16 q^{83} + 16 q^{89} - 20 q^{91} - 12 q^{94} - 44 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 - 24 * q^11 - 4 * q^16 + 12 * q^23 - 8 * q^26 - 24 * q^37 - 4 * q^38 - 32 * q^41 + 16 * q^43 - 24 * q^44 + 8 * q^46 - 8 * q^47 + 24 * q^53 + 16 * q^58 + 24 * q^59 - 16 * q^62 - 8 * q^64 + 24 * q^67 - 16 * q^77 - 24 * q^79 - 16 * q^83 + 16 * q^89 - 20 * q^91 - 12 * q^94 - 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more