LMFDB - Embedded newform 315.2.m.a.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(8,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("315.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 $ x^12 + 18x^10 + 107x^8 + 240x^6 + 151x^4 + 30*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.3
Root			$2.15459i$ of defining polynomial
Character	$\chi$	$=$	315.197
Dual form			315.2.m.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0241053 + 0.0241053i) q^{2} +1.99884i q^{4} +(2.20653 - 0.362277i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.0963933 - 0.0963933i) q^{8} +O(q^{10})$	\(q+(-0.0241053 + 0.0241053i) q^{2} +1.99884i q^{4} +(2.20653 - 0.362277i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.0963933 - 0.0963933i) q^{8} +(-0.0444562 + 0.0619218i) q^{10} +0.390676i q^{11} +(-2.20280 + 2.20280i) q^{13} -0.0340901 q^{14} -3.99303 q^{16} +(4.78742 - 4.78742i) q^{17} +5.50477i q^{19} +(0.724132 + 4.41049i) q^{20} +(-0.00941736 - 0.00941736i) q^{22} +(2.18868 + 2.18868i) q^{23} +(4.73751 - 1.59874i) q^{25} -0.106198i q^{26} +(-1.41339 + 1.41339i) q^{28} -7.17089 q^{29} +5.38951 q^{31} +(0.289040 - 0.289040i) q^{32} +0.230805i q^{34} +(1.81642 + 1.30408i) q^{35} +(-2.75668 - 2.75668i) q^{37} +(-0.132694 - 0.132694i) q^{38} +(-0.247615 - 0.177773i) q^{40} -2.54112i q^{41} +(6.99884 - 6.99884i) q^{43} -0.780897 q^{44} -0.105518 q^{46} +(0.537576 - 0.537576i) q^{47} +1.00000i q^{49} +(-0.0756610 + 0.152737i) q^{50} +(-4.40304 - 4.40304i) q^{52} +(-5.19225 - 5.19225i) q^{53} +(0.141533 + 0.862036i) q^{55} -0.136321i q^{56} +(0.172857 - 0.172857i) q^{58} -10.3092 q^{59} -8.12574 q^{61} +(-0.129916 + 0.129916i) q^{62} -7.97212i q^{64} +(-4.06251 + 5.65856i) q^{65} +(-3.76141 - 3.76141i) q^{67} +(9.56928 + 9.56928i) q^{68} +(-0.0752206 + 0.0123500i) q^{70} -16.0785i q^{71} +(7.17580 - 7.17580i) q^{73} +0.132901 q^{74} -11.0031 q^{76} +(-0.276249 + 0.276249i) q^{77} +7.35036i q^{79} +(-8.81072 + 1.44658i) q^{80} +(0.0612544 + 0.0612544i) q^{82} +(6.29085 + 6.29085i) q^{83} +(8.82920 - 12.2979i) q^{85} +0.337418i q^{86} +(0.0376585 - 0.0376585i) q^{88} -9.94088 q^{89} -3.11523 q^{91} +(-4.37481 + 4.37481i) q^{92} +0.0259169i q^{94} +(1.99425 + 12.1464i) q^{95} +(2.17456 + 2.17456i) q^{97} +(-0.0241053 - 0.0241053i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{5} + 24 q^{8}+O(q^{10}) $ 12 * q - 4 * q^5 + 24 * q^8	$ 12 q - 4 q^{5} + 24 q^{8} + 16 q^{10} - 4 q^{13} - 4 q^{14} - 20 q^{16} + 8 q^{17} - 12 q^{20} - 8 q^{22} + 8 q^{23} - 8 q^{25} - 32 q^{29} + 48 q^{32} + 8 q^{35} + 4 q^{37} + 24 q^{38} - 28 q^{40} + 40 q^{43} - 64 q^{44} + 16 q^{46} + 24 q^{47} - 16 q^{50} + 36 q^{52} - 40 q^{53} - 16 q^{55} - 28 q^{58} - 80 q^{59} - 32 q^{61} + 16 q^{62} + 48 q^{65} - 48 q^{67} + 32 q^{68} + 8 q^{70} - 20 q^{73} - 64 q^{74} + 16 q^{76} + 36 q^{80} + 20 q^{82} + 24 q^{83} - 56 q^{89} + 8 q^{92} + 56 q^{95} + 12 q^{97}+O(q^{100}) $ 12 * q - 4 * q^5 + 24 * q^8 + 16 * q^10 - 4 * q^13 - 4 * q^14 - 20 * q^16 + 8 * q^17 - 12 * q^20 - 8 * q^22 + 8 * q^23 - 8 * q^25 - 32 * q^29 + 48 * q^32 + 8 * q^35 + 4 * q^37 + 24 * q^38 - 28 * q^40 + 40 * q^43 - 64 * q^44 + 16 * q^46 + 24 * q^47 - 16 * q^50 + 36 * q^52 - 40 * q^53 - 16 * q^55 - 28 * q^58 - 80 * q^59 - 32 * q^61 + 16 * q^62 + 48 * q^65 - 48 * q^67 + 32 * q^68 + 8 * q^70 - 20 * q^73 - 64 * q^74 + 16 * q^76 + 36 * q^80 + 20 * q^82 + 24 * q^83 - 56 * q^89 + 8 * q^92 + 56 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0241053	+	0.0241053i	−0.0170450	+	0.0170450i	−0.715578	−	0.698533i	$-0.753837\pi$
$2$	−0.0241053	+	0.0241053i	−0.0170450	+	0.0170450i	0.698533	+	0.715578i	$0.253837\pi$
$3$		0			0
$3$		0			0
$4$			1.99884i			0.999419i
$5$	2.20653	−	0.362277i	0.986788	−	0.162015i
$5$	2.20653	−	0.362277i	0.986788	−	0.162015i
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−0.0963933	−	0.0963933i	−0.0340802	−	0.0340802i
$9$		0			0
$10$	−0.0444562	+	0.0619218i	−0.0140583	+	0.0195814i
$11$			0.390676i			0.117793i	0.998264	+	0.0588966i	$0.0187582\pi$
$11$			0.390676i			0.117793i	−0.998264	+	0.0588966i	$0.981242\pi$
$12$		0			0
$13$	−2.20280	+	2.20280i	−0.610947	+	0.610947i	−0.943193	−	0.332246i	$-0.892194\pi$
$13$	−2.20280	+	2.20280i	−0.610947	+	0.610947i	0.332246	+	0.943193i	$0.392194\pi$
$14$	−0.0340901			−0.00911095
$15$		0			0
$16$	−3.99303			−0.998257
$17$	4.78742	−	4.78742i	1.16112	−	1.16112i	0.176890	−	0.984231i	$-0.443396\pi$
$17$	4.78742	−	4.78742i	1.16112	−	1.16112i	0.984231	−	0.176890i	$-0.0566037\pi$
$18$		0			0
$19$			5.50477i			1.26288i	0.775424	+	0.631440i	$0.217536\pi$
$19$			5.50477i			1.26288i	−0.775424	+	0.631440i	$0.782464\pi$
$20$	0.724132	+	4.41049i	0.161921	+	0.986215i
$21$		0			0
$22$	−0.00941736	−	0.00941736i	−0.00200779	−	0.00200779i
$23$	2.18868	+	2.18868i	0.456371	+	0.456371i	0.897462	−	0.441091i	$-0.145408\pi$
$23$	2.18868	+	2.18868i	0.456371	+	0.456371i	−0.441091	+	0.897462i	$0.645408\pi$
$24$		0			0
$25$	4.73751	−	1.59874i	0.947502	−	0.319749i
$26$		−	0.106198i		−	0.0208272i
$27$		0			0
$28$	−1.41339	+	1.41339i	−0.267106	+	0.267106i
$29$	−7.17089			−1.33160			−0.665801	−	0.746130i	$-0.731910\pi$
$29$	−7.17089			−1.33160			−0.665801	+	0.746130i	$0.731910\pi$
$30$		0			0
$31$	5.38951			0.967985			0.483993	−	0.875072i	$-0.339186\pi$
$31$	5.38951			0.967985			0.483993	+	0.875072i	$0.339186\pi$
$32$	0.289040	−	0.289040i	0.0510955	−	0.0510955i
$33$		0			0
$34$			0.230805i			0.0395827i
$35$	1.81642	+	1.30408i	0.307031	+	0.220430i
$36$		0			0
$37$	−2.75668	−	2.75668i	−0.453195	−	0.453195i	0.443218	−	0.896414i	$-0.353837\pi$
$37$	−2.75668	−	2.75668i	−0.453195	−	0.453195i	−0.896414	+	0.443218i	$0.853837\pi$
$38$	−0.132694	−	0.132694i	−0.0215258	−	0.0215258i
$39$		0			0
$40$	−0.247615	−	0.177773i	−0.0391514	−	0.0281084i
$41$		−	2.54112i		−	0.396856i	−0.980115	−	0.198428i	$-0.936416\pi$
$41$		−	2.54112i		−	0.396856i	0.980115	−	0.198428i	$-0.0635836\pi$
$42$		0			0
$43$	6.99884	−	6.99884i	1.06731	−	1.06731i	0.0697481	−	0.997565i	$-0.477780\pi$
$43$	6.99884	−	6.99884i	1.06731	−	1.06731i	0.997565	−	0.0697481i	$-0.0222196\pi$
$44$	−0.780897			−0.117725
$45$		0			0
$46$	−0.105518			−0.0155577
$47$	0.537576	−	0.537576i	0.0784135	−	0.0784135i	−0.666812	−	0.745226i	$-0.732342\pi$
$47$	0.537576	−	0.537576i	0.0784135	−	0.0784135i	0.745226	+	0.666812i	$0.232342\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	−0.0756610	+	0.152737i	−0.0107001	+	0.0216003i
$51$		0			0
$52$	−4.40304	−	4.40304i	−0.610592	−	0.610592i
$53$	−5.19225	−	5.19225i	−0.713210	−	0.713210i	0.253995	−	0.967205i	$-0.418255\pi$
$53$	−5.19225	−	5.19225i	−0.713210	−	0.713210i	−0.967205	+	0.253995i	$0.918255\pi$
$54$		0			0
$55$	0.141533	+	0.862036i	0.0190843	+	0.116237i
$56$		−	0.136321i		−	0.0182166i
$57$		0			0
$58$	0.172857	−	0.172857i	0.0226972	−	0.0226972i
$59$	−10.3092			−1.34214			−0.671070	−	0.741394i	$-0.734165\pi$
$59$	−10.3092			−1.34214			−0.671070	+	0.741394i	$0.734165\pi$
$60$		0			0
$61$	−8.12574			−1.04039			−0.520197	−	0.854046i	$-0.674142\pi$
$61$	−8.12574			−1.04039			−0.520197	+	0.854046i	$0.674142\pi$
$62$	−0.129916	+	0.129916i	−0.0164993	+	0.0164993i
$63$		0			0
$64$		−	7.97212i		−	0.996515i
$65$	−4.06251	+	5.65856i	−0.503892	+	0.701857i
$66$		0			0
$67$	−3.76141	−	3.76141i	−0.459529	−	0.459529i	0.438972	−	0.898501i	$-0.355343\pi$
$67$	−3.76141	−	3.76141i	−0.459529	−	0.459529i	−0.898501	+	0.438972i	$0.855343\pi$
$68$	9.56928	+	9.56928i	1.16045	+	1.16045i
$69$		0			0
$70$	−0.0752206	+	0.0123500i	−0.00899058	+	0.00147611i
$71$		−	16.0785i		−	1.90816i	−0.299550	−	0.954081i	$-0.596836\pi$
$71$		−	16.0785i		−	1.90816i	0.299550	−	0.954081i	$-0.403164\pi$
$72$		0			0
$73$	7.17580	−	7.17580i	0.839864	−	0.839864i	−0.148977	−	0.988841i	$-0.547598\pi$
$73$	7.17580	−	7.17580i	0.839864	−	0.839864i	0.988841	+	0.148977i	$0.0475979\pi$
$74$	0.132901			0.0154495
$75$		0			0
$76$	−11.0031			−1.26215
$77$	−0.276249	+	0.276249i	−0.0314815	+	0.0314815i
$78$		0			0
$79$			7.35036i			0.826980i	0.910509	+	0.413490i	$0.135690\pi$
$79$			7.35036i			0.826980i	−0.910509	+	0.413490i	$0.864310\pi$
$80$	−8.81072	+	1.44658i	−0.985068	+	0.161733i
$81$		0			0
$82$	0.0612544	+	0.0612544i	0.00676442	+	0.00676442i
$83$	6.29085	+	6.29085i	0.690511	+	0.690511i	0.962344	−	0.271834i	$-0.0876300\pi$
$83$	6.29085	+	6.29085i	0.690511	+	0.690511i	−0.271834	+	0.962344i	$0.587630\pi$
$84$		0			0
$85$	8.82920	−	12.2979i	0.957661	−	1.33390i
$86$			0.337418i			0.0363848i
$87$		0			0
$88$	0.0376585	−	0.0376585i	0.00401441	−	0.00401441i
$89$	−9.94088			−1.05373			−0.526865	−	0.849949i	$-0.676633\pi$
$89$	−9.94088			−1.05373			−0.526865	+	0.849949i	$0.676633\pi$
$90$		0			0
$91$	−3.11523			−0.326565
$92$	−4.37481	+	4.37481i	−0.456106	+	0.456106i
$93$		0			0
$94$			0.0259169i			0.00267312i
$95$	1.99425	+	12.1464i	0.204606	+	1.24620i
$96$		0			0
$97$	2.17456	+	2.17456i	0.220793	+	0.220793i	0.808832	−	0.588039i	$-0.200100\pi$
$97$	2.17456	+	2.17456i	0.220793	+	0.220793i	−0.588039	+	0.808832i	$0.700100\pi$
$98$	−0.0241053	−	0.0241053i	−0.00243501	−	0.00243501i
$99$		0			0
$100$	3.19563	+	9.46952i	0.319563	+	0.946952i
$101$			5.24052i			0.521451i	0.965413	+	0.260725i	$0.0839617\pi$
$101$			5.24052i			0.521451i	−0.965413	+	0.260725i	$0.916038\pi$
$102$		0			0
$103$	−1.29201	+	1.29201i	−0.127306	+	0.127306i	−0.767889	−	0.640583i	$-0.778693\pi$
$103$	−1.29201	+	1.29201i	−0.127306	+	0.127306i	0.640583	+	0.767889i	$0.278693\pi$
$104$	0.424670			0.0416423
$105$		0			0
$106$	0.250322			0.0243134
$107$	10.0523	−	10.0523i	0.971794	−	0.971794i	−0.0278187	−	0.999613i	$-0.508856\pi$
$107$	10.0523	−	10.0523i	0.971794	−	0.971794i	0.999613	+	0.0278187i	$0.00885610\pi$
$108$		0			0
$109$		−	13.9522i		−	1.33638i	−0.743991	−	0.668189i	$-0.767070\pi$
$109$		−	13.9522i		−	1.33638i	0.743991	−	0.668189i	$-0.232930\pi$
$110$	−0.0241913	−	0.0173680i	−0.00230655	−	0.00165597i
$111$		0			0
$112$	−2.82350	−	2.82350i	−0.266795	−	0.266795i
$113$	−8.80038	−	8.80038i	−0.827870	−	0.827870i	0.159352	−	0.987222i	$-0.449060\pi$
$113$	−8.80038	−	8.80038i	−0.827870	−	0.827870i	−0.987222	+	0.159352i	$0.949060\pi$
$114$		0			0
$115$	5.62228	+	4.03647i	0.524281	+	0.376403i
$116$		−	14.3335i		−	1.33083i
$117$		0			0
$118$	0.248506	−	0.248506i	0.0228768	−	0.0228768i
$119$	6.77044			0.620645
$120$		0			0
$121$	10.8474			0.986125
$122$	0.195874	−	0.195874i	0.0177336	−	0.0177336i
$123$		0			0
$124$			10.7728i			0.967423i
$125$	9.87425	−	5.24396i	0.883180	−	0.469034i
$126$		0			0
$127$	4.61675	+	4.61675i	0.409670	+	0.409670i	0.881624	−	0.471953i	$-0.156451\pi$
$127$	4.61675	+	4.61675i	0.409670	+	0.409670i	−0.471953	+	0.881624i	$0.656451\pi$
$128$	0.770250	+	0.770250i	0.0680811	+	0.0680811i
$129$		0			0
$130$	−0.0384732	−	0.234329i	−0.00337432	−	0.0205521i
$131$			3.44081i			0.300625i	0.988639	+	0.150313i	$0.0480280\pi$
$131$			3.44081i			0.300625i	−0.988639	+	0.150313i	$0.951972\pi$
$132$		0			0
$133$	−3.89246	+	3.89246i	−0.337519	+	0.337519i
$134$	0.181340			0.0156654
$135$		0			0
$136$	−0.922951			−0.0791424
$137$	1.07863	−	1.07863i	0.0921540	−	0.0921540i	−0.659527	−	0.751681i	$-0.729243\pi$
$137$	1.07863	−	1.07863i	0.0921540	−	0.0921540i	0.751681	+	0.659527i	$0.229243\pi$
$138$		0			0
$139$			21.5355i			1.82662i	0.407268	+	0.913309i	$0.366481\pi$
$139$			21.5355i			1.82662i	−0.407268	+	0.913309i	$0.633519\pi$
$140$	−2.60665	+	3.63072i	−0.220302	+	0.306852i
$141$		0			0
$142$	0.387576	+	0.387576i	0.0325247	+	0.0325247i
$143$	−0.860580	−	0.860580i	−0.0719653	−	0.0719653i
$144$		0			0
$145$	−15.8228	+	2.59785i	−1.31401	+	0.215739i
$146$			0.345950i			0.0286310i
$147$		0			0
$148$	5.51015	−	5.51015i	0.452932	−	0.452932i
$149$	6.48256			0.531072			0.265536	−	0.964101i	$-0.414451\pi$
$149$	6.48256			0.531072			0.265536	+	0.964101i	$0.414451\pi$
$150$		0			0
$151$	−1.76882			−0.143945			−0.0719724	−	0.997407i	$-0.522929\pi$
$151$	−1.76882			−0.143945			−0.0719724	+	0.997407i	$0.522929\pi$
$152$	0.530623	−	0.530623i	0.0430392	−	0.0430392i
$153$		0			0
$154$		−	0.0133182i		−	0.00107321i
$155$	11.8921	−	1.95249i	0.955196	−	0.156828i
$156$		0			0
$157$	−7.49249	−	7.49249i	−0.597966	−	0.597966i	0.341805	−	0.939771i	$-0.388962\pi$
$157$	−7.49249	−	7.49249i	−0.597966	−	0.597966i	−0.939771	+	0.341805i	$0.888962\pi$
$158$	−0.177183	−	0.177183i	−0.0140959	−	0.0140959i
$159$		0			0
$160$	0.533061	−	0.742486i	0.0421422	−	0.0586987i
$161$			3.09526i			0.243941i
$162$		0			0
$163$	−13.9311	+	13.9311i	−1.09117	+	1.09117i	−0.0957639	+	0.995404i	$0.530529\pi$
$163$	−13.9311	+	13.9311i	−1.09117	+	1.09117i	−0.995404	+	0.0957639i	$0.969471\pi$
$164$	5.07928			0.396625
$165$		0			0
$166$	−0.303286			−0.0235396
$167$	−0.477182	+	0.477182i	−0.0369254	+	0.0369254i	−0.725328	−	0.688403i	$-0.758312\pi$
$167$	−0.477182	+	0.477182i	−0.0369254	+	0.0369254i	0.688403	+	0.725328i	$0.258312\pi$
$168$		0			0
$169$			3.29535i			0.253488i
$170$	0.0836151	+	0.509277i	0.00641299	+	0.0390597i
$171$		0			0
$172$	13.9895	+	13.9895i	1.06669	+	1.06669i
$173$	14.6395	+	14.6395i	1.11302	+	1.11302i	0.992740	+	0.120278i	$0.0383786\pi$
$173$	14.6395	+	14.6395i	1.11302	+	1.11302i	0.120278	+	0.992740i	$0.461621\pi$
$174$		0			0
$175$	4.48041	+	2.21944i	0.338687	+	0.167774i
$176$		−	1.55998i		−	0.117588i
$177$		0			0
$178$	0.239628	−	0.239628i	0.0179609	−	0.0179609i
$179$	−3.04789			−0.227810			−0.113905	−	0.993492i	$-0.536336\pi$
$179$	−3.04789			−0.227810			−0.113905	+	0.993492i	$0.536336\pi$
$180$		0			0
$181$	4.12967			0.306956			0.153478	−	0.988152i	$-0.450953\pi$
$181$	4.12967			0.306956			0.153478	+	0.988152i	$0.450953\pi$
$182$	0.0750936	−	0.0750936i	0.00556631	−	0.00556631i
$183$		0			0
$184$		−	0.421948i		−	0.0311064i
$185$	−7.08136	−	5.08400i	−0.520632	−	0.373783i
$186$		0			0
$187$	1.87033	+	1.87033i	0.136772	+	0.136772i
$188$	1.07453	+	1.07453i	0.0783679	+	0.0783679i
$189$		0			0
$190$	−0.340865	−	0.244721i	−0.0247290	−	0.0177539i
$191$			21.4943i			1.55527i	0.628714	+	0.777637i	$0.283582\pi$
$191$			21.4943i			1.55527i	−0.628714	+	0.777637i	$0.716418\pi$
$192$		0			0
$193$	−9.04475	+	9.04475i	−0.651055	+	0.651055i	−0.953247	−	0.302192i	$-0.902282\pi$
$193$	−9.04475	+	9.04475i	−0.651055	+	0.651055i	0.302192	+	0.953247i	$0.402282\pi$
$194$	−0.104837			−0.00752685
$195$		0			0
$196$	−1.99884			−0.142774
$197$	−8.80038	+	8.80038i	−0.627001	+	0.627001i	−0.947312	−	0.320311i	$-0.896213\pi$
$197$	−8.80038	+	8.80038i	−0.627001	+	0.627001i	0.320311	+	0.947312i	$0.396213\pi$
$198$		0			0
$199$		−	0.816553i		−	0.0578839i	−0.999581	−	0.0289419i	$-0.990786\pi$
$199$		−	0.816553i		−	0.0578839i	0.999581	−	0.0289419i	$-0.00921379\pi$
$200$	−0.610772	−	0.302556i	−0.0431881	−	0.0213939i
$201$		0			0
$202$	−0.126324	−	0.126324i	−0.00888815	−	0.00888815i
$203$	−5.07059	−	5.07059i	−0.355885	−	0.355885i
$204$		0			0
$205$	−0.920587	−	5.60704i	−0.0642966	−	0.391613i
$206$		−	0.0622888i		−	0.00433987i
$207$		0			0
$208$	8.79584	−	8.79584i	0.609882	−	0.609882i
$209$	−2.15058			−0.148759
$210$		0			0
$211$	5.93663			0.408695			0.204347	−	0.978898i	$-0.434493\pi$
$211$	5.93663			0.408695			0.204347	+	0.978898i	$0.434493\pi$
$212$	10.3785	−	10.3785i	0.712796	−	0.712796i
$213$		0			0
$214$			0.484629i			0.0331285i
$215$	12.9076	−	17.9786i	0.880291	−	1.22613i
$216$		0			0
$217$	3.81096	+	3.81096i	0.258705	+	0.258705i
$218$	0.336322	+	0.336322i	0.0227786	+	0.0227786i
$219$		0			0
$220$	−1.72307	+	0.282901i	−0.116169	+	0.0190732i
$221$			21.0915i			1.41877i
$222$		0			0
$223$	−2.17086	+	2.17086i	−0.145372	+	0.145372i	−0.776047	−	0.630675i	$-0.782778\pi$
$223$	−2.17086	+	2.17086i	−0.145372	+	0.145372i	0.630675	+	0.776047i	$0.282778\pi$
$224$	0.408764			0.0273117
$225$		0			0
$226$	0.424272			0.0282222
$227$	17.8822	−	17.8822i	1.18688	−	1.18688i	0.208960	−	0.977924i	$-0.432992\pi$
$227$	17.8822	−	17.8822i	1.18688	−	1.18688i	0.977924	−	0.208960i	$-0.0670077\pi$
$228$		0			0
$229$			2.42623i			0.160330i	0.996782	+	0.0801649i	$0.0255447\pi$
$229$			2.42623i			0.160330i	−0.996782	+	0.0801649i	$0.974455\pi$
$230$	−0.232827	+	0.0382266i	−0.0153522	+	0.00252058i
$231$		0			0
$232$	0.691226	+	0.691226i	0.0453812	+	0.0453812i
$233$	−16.9725	−	16.9725i	−1.11191	−	1.11191i	−0.992893	−	0.119014i	$-0.962027\pi$
$233$	−16.9725	−	16.9725i	−1.11191	−	1.11191i	−0.119014	−	0.992893i	$-0.537973\pi$
$234$		0			0
$235$	0.991424	−	1.38093i	0.0646734	−	0.0900817i
$236$		−	20.6064i		−	1.34136i
$237$		0			0
$238$	−0.163204	+	0.163204i	−0.0105789	+	0.0105789i
$239$	−8.48710			−0.548985			−0.274492	−	0.961589i	$-0.588510\pi$
$239$	−8.48710			−0.548985			−0.274492	+	0.961589i	$0.588510\pi$
$240$		0			0
$241$	12.5268			0.806924			0.403462	−	0.914996i	$-0.367807\pi$
$241$	12.5268			0.806924			0.403462	+	0.914996i	$0.367807\pi$
$242$	−0.261479	+	0.261479i	−0.0168085	+	0.0168085i
$243$		0			0
$244$		−	16.2420i		−	1.03979i
$245$	0.362277	+	2.20653i	0.0231450	+	0.140970i
$246$		0			0
$247$	−12.1259	−	12.1259i	−0.771553	−	0.771553i
$248$	−0.519513	−	0.519513i	−0.0329891	−	0.0329891i
$249$		0			0
$250$	−0.111615	+	0.364429i	−0.00705913	+	0.0230485i
$251$			6.60853i			0.417127i	0.978009	+	0.208563i	$0.0668788\pi$
$251$			6.60853i			0.417127i	−0.978009	+	0.208563i	$0.933121\pi$
$252$		0			0
$253$	−0.855063	+	0.855063i	−0.0537574	+	0.0537574i
$254$	−0.222576			−0.0139657
$255$		0			0
$256$	15.9071			0.994194
$257$	−20.9703	+	20.9703i	−1.30809	+	1.30809i	−0.385296	+	0.922793i	$0.625901\pi$
$257$	−20.9703	+	20.9703i	−1.30809	+	1.30809i	−0.922793	+	0.385296i	$0.874099\pi$
$258$		0			0
$259$		−	3.89853i		−	0.242243i
$260$	−11.3105	−	8.12030i	−0.701450	−	0.503600i
$261$		0			0
$262$	−0.0829419	−	0.0829419i	−0.00512417	−	0.00512417i
$263$	−16.8546	−	16.8546i	−1.03930	−	1.03930i	−0.999196	−	0.0401013i	$-0.987232\pi$
$263$	−16.8546	−	16.8546i	−1.03930	−	1.03930i	−0.0401013	−	0.999196i	$-0.512768\pi$
$264$		0			0
$265$	−13.3379	−	9.57580i	−0.819338	−	0.588237i
$266$		−	0.187658i		−	0.0115060i
$267$		0			0
$268$	7.51845	−	7.51845i	0.459262	−	0.459262i
$269$	15.6271			0.952798			0.476399	−	0.879229i	$-0.341942\pi$
$269$	15.6271			0.952798			0.476399	+	0.879229i	$0.341942\pi$
$270$		0			0
$271$	−5.42718			−0.329678			−0.164839	−	0.986320i	$-0.552710\pi$
$271$	−5.42718			−0.329678			−0.164839	+	0.986320i	$0.552710\pi$
$272$	−19.1163	+	19.1163i	−1.15910	+	1.15910i
$273$		0			0
$274$			0.0520017i			0.00314154i
$275$	0.624591	+	1.85083i	0.0376642	+	0.111609i
$276$		0			0
$277$	−19.7465	−	19.7465i	−1.18645	−	1.18645i	−0.978041	−	0.208411i	$-0.933171\pi$
$277$	−19.7465	−	19.7465i	−1.18645	−	1.18645i	−0.208411	−	0.978041i	$-0.566829\pi$
$278$	−0.519120	−	0.519120i	−0.0311348	−	0.0311348i
$279$		0			0
$280$	−0.0493858	−	0.300795i	−0.00295136	−	0.0179759i
$281$			14.3252i			0.854572i	0.904117	+	0.427286i	$0.140530\pi$
$281$			14.3252i			0.854572i	−0.904117	+	0.427286i	$0.859470\pi$
$282$		0			0
$283$	−11.4260	+	11.4260i	−0.679208	+	0.679208i	−0.959821	−	0.280613i	$-0.909462\pi$
$283$	−11.4260	+	11.4260i	−0.679208	+	0.679208i	0.280613	+	0.959821i	$0.409462\pi$
$284$	32.1382			1.90705
$285$		0			0
$286$	0.0414891			0.00245330
$287$	1.79684	−	1.79684i	0.106064	−	0.106064i
$288$		0			0
$289$		−	28.8388i		−	1.69640i
$290$	0.318791	−	0.444035i	0.0187200	−	0.0260746i
$291$		0			0
$292$	14.3433	+	14.3433i	0.839376	+	0.839376i
$293$	−6.46919	−	6.46919i	−0.377934	−	0.377934i	0.492422	−	0.870356i	$-0.336112\pi$
$293$	−6.46919	−	6.46919i	−0.377934	−	0.377934i	−0.870356	+	0.492422i	$0.836112\pi$
$294$		0			0
$295$	−22.7475	+	3.73477i	−1.32441	+	0.217447i
$296$			0.531451i			0.0308899i
$297$		0			0
$298$	−0.156264	+	0.156264i	−0.00905214	+	0.00905214i
$299$	−9.64244			−0.557637
$300$		0			0
$301$	9.89785			0.570503
$302$	0.0426381	−	0.0426381i	0.00245354	−	0.00245354i
$303$		0			0
$304$		−	21.9807i		−	1.26068i
$305$	−17.9297	+	2.94377i	−1.02665	+	0.168560i
$306$		0			0
$307$	8.46817	+	8.46817i	0.483304	+	0.483304i	0.906185	−	0.422881i	$-0.138981\pi$
$307$	8.46817	+	8.46817i	0.483304	+	0.483304i	−0.422881	+	0.906185i	$0.638981\pi$
$308$	−0.552178	−	0.552178i	−0.0314632	−	0.0314632i
$309$		0			0
$310$	−0.239597	+	0.333728i	−0.0136082	+	0.0189545i
$311$			10.3241i			0.585425i	0.956200	+	0.292713i	$0.0945579\pi$
$311$			10.3241i			0.585425i	−0.956200	+	0.292713i	$0.905442\pi$
$312$		0			0
$313$	18.2107	−	18.2107i	1.02933	−	1.02933i	0.0297710	−	0.999557i	$-0.490522\pi$
$313$	18.2107	−	18.2107i	1.02933	−	1.02933i	0.999557	−	0.0297710i	$-0.00947782\pi$
$314$	0.361218			0.0203847
$315$		0			0
$316$	−14.6922			−0.826500
$317$	−24.6528	+	24.6528i	−1.38464	+	1.38464i	−0.548467	+	0.836172i	$0.684788\pi$
$317$	−24.6528	+	24.6528i	−1.38464	+	1.38464i	−0.836172	+	0.548467i	$0.815212\pi$
$318$		0			0
$319$		−	2.80149i		−	0.156853i
$320$	−2.88811	−	17.5907i	−0.161450	−	0.983350i
$321$		0			0
$322$	−0.0746122	−	0.0746122i	−0.00415798	−	0.00415798i
$323$	26.3537	+	26.3537i	1.46636	+	1.46636i
$324$		0			0
$325$	−6.91407	+	13.9575i	−0.383524	+	0.774223i
$326$		−	0.671627i		−	0.0371980i
$327$		0			0
$328$	−0.244947	+	0.244947i	−0.0135249	+	0.0135249i
$329$	0.760247			0.0419138
$330$		0			0
$331$	−13.0815			−0.719025			−0.359513	−	0.933140i	$-0.617057\pi$
$331$	−13.0815			−0.719025			−0.359513	+	0.933140i	$0.617057\pi$
$332$	−12.5744	+	12.5744i	−0.690109	+	0.690109i
$333$		0			0
$334$		−	0.0230052i		−	0.00125879i
$335$	−9.66232	−	6.93698i	−0.527909	−	0.379007i
$336$		0			0
$337$	6.38566	+	6.38566i	0.347849	+	0.347849i	0.859308	−	0.511459i	$-0.170895\pi$
$337$	6.38566	+	6.38566i	0.347849	+	0.347849i	−0.511459	+	0.859308i	$0.670895\pi$
$338$	−0.0794355	−	0.0794355i	−0.00432072	−	0.00432072i
$339$		0			0
$340$	24.5816	+	17.6481i	1.33312	+	0.957105i
$341$			2.10555i			0.114022i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−1.34928			−0.0727484
$345$		0			0
$346$	−0.705778			−0.0379429
$347$	1.89442	−	1.89442i	0.101698	−	0.101698i	−0.654427	−	0.756125i	$-0.727090\pi$
$347$	1.89442	−	1.89442i	0.101698	−	0.101698i	0.756125	+	0.654427i	$0.227090\pi$
$348$		0			0
$349$		−	27.5744i		−	1.47602i	−0.674789	−	0.738011i	$-0.735765\pi$
$349$		−	27.5744i		−	1.47602i	0.674789	−	0.738011i	$-0.264235\pi$
$350$	−0.161502	+	0.0545013i	−0.00863265	+	0.00291322i
$351$		0			0
$352$	0.112921	+	0.112921i	0.00601870	+	0.00601870i
$353$	−10.9194	−	10.9194i	−0.581181	−	0.581181i	0.354047	−	0.935228i	$-0.384805\pi$
$353$	−10.9194	−	10.9194i	−0.581181	−	0.581181i	−0.935228	+	0.354047i	$0.884805\pi$
$354$		0			0
$355$	−5.82485	−	35.4775i	−0.309151	−	1.88295i
$356$		−	19.8702i		−	1.05312i
$357$		0			0
$358$	0.0734704	−	0.0734704i	0.00388303	−	0.00388303i
$359$	17.0586			0.900318			0.450159	−	0.892948i	$-0.351367\pi$
$359$	17.0586			0.900318			0.450159	+	0.892948i	$0.351367\pi$
$360$		0			0
$361$	−11.3025			−0.594868
$362$	−0.0995470	+	0.0995470i	−0.00523208	+	0.00523208i
$363$		0			0
$364$		−	6.22684i		−	0.326375i
$365$	13.2340	−	18.4332i	0.692698	−	0.964839i
$366$		0			0
$367$	15.2807	+	15.2807i	0.797645	+	0.797645i	0.982724	−	0.185079i	$-0.0592541\pi$
$367$	15.2807	+	15.2807i	0.797645	+	0.797645i	−0.185079	+	0.982724i	$0.559254\pi$
$368$	−8.73946	−	8.73946i	−0.455576	−	0.455576i
$369$		0			0
$370$	0.293250	−	0.0481470i	0.0152453	−	0.00250304i
$371$		−	7.34295i		−	0.381227i
$372$		0			0
$373$	−4.83636	+	4.83636i	−0.250417	+	0.250417i	−0.821142	−	0.570724i	$-0.806662\pi$
$373$	−4.83636	+	4.83636i	−0.250417	+	0.250417i	0.570724	+	0.821142i	$0.306662\pi$
$374$	−0.0901698			−0.00466257
$375$		0			0
$376$	−0.103637			−0.00534469
$377$	15.7960	−	15.7960i	0.813537	−	0.813537i
$378$		0			0
$379$			15.5588i			0.799203i	0.916689	+	0.399602i	$0.130852\pi$
$379$			15.5588i			0.799203i	−0.916689	+	0.399602i	$0.869148\pi$
$380$	−24.2787	+	3.98618i	−1.24547	+	0.204487i
$381$		0			0
$382$	−0.518127	−	0.518127i	−0.0265097	−	0.0265097i
$383$	10.6615	+	10.6615i	0.544777	+	0.544777i	0.924926	−	0.380148i	$-0.124127\pi$
$383$	10.6615	+	10.6615i	0.544777	+	0.544777i	−0.380148	+	0.924926i	$0.624127\pi$
$384$		0			0
$385$	−0.509473	+	0.709630i	−0.0259651	+	0.0361661i
$386$		−	0.436053i		−	0.0221945i
$387$		0			0
$388$	−4.34659	+	4.34659i	−0.220665	+	0.220665i
$389$	22.6658			1.14920			0.574602	−	0.818433i	$-0.305157\pi$
$389$	22.6658			1.14920			0.574602	+	0.818433i	$0.305157\pi$
$390$		0			0
$391$	20.9563			1.05980
$392$	0.0963933	−	0.0963933i	0.00486860	−	0.00486860i
$393$		0			0
$394$		−	0.424272i		−	0.0213745i
$395$	2.66286	+	16.2188i	0.133983	+	0.816054i
$396$		0			0
$397$	8.59588	+	8.59588i	0.431415	+	0.431415i	0.889109	−	0.457695i	$-0.151325\pi$
$397$	8.59588	+	8.59588i	0.431415	+	0.431415i	−0.457695	+	0.889109i	$0.651325\pi$
$398$	0.0196833	+	0.0196833i	0.000986633	+	0.000986633i
$399$		0			0
$400$	−18.9170	+	6.38383i	−0.945851	+	0.319192i
$401$		−	17.9764i		−	0.897697i	−0.893608	−	0.448848i	$-0.851834\pi$
$401$		−	17.9764i		−	0.897697i	0.893608	−	0.448848i	$-0.148166\pi$
$402$		0			0
$403$	−11.8720	+	11.8720i	−0.591387	+	0.591387i
$404$	−10.4749			−0.521148
$405$		0			0
$406$	0.244456			0.0121322
$407$	1.07697	−	1.07697i	0.0533833	−	0.0533833i
$408$		0			0
$409$			19.3321i			0.955908i	0.878385	+	0.477954i	$0.158622\pi$
$409$			19.3321i			0.955908i	−0.878385	+	0.477954i	$0.841378\pi$
$410$	0.157351	+	0.112968i	0.00777099	+	0.00557911i
$411$		0			0
$412$	−2.58253	−	2.58253i	−0.127232	−	0.127232i
$413$	−7.28969	−	7.28969i	−0.358702	−	0.358702i
$414$		0			0
$415$	16.1600	+	11.6019i	0.793261	+	0.569515i
$416$			1.27339i			0.0624332i
$417$		0			0
$418$	0.0518404	−	0.0518404i	0.00253560	−	0.00253560i
$419$	−0.694391			−0.0339232			−0.0169616	−	0.999856i	$-0.505399\pi$
$419$	−0.694391			−0.0339232			−0.0169616	+	0.999856i	$0.505399\pi$
$420$		0			0
$421$	−13.9451			−0.679641			−0.339821	−	0.940490i	$-0.610366\pi$
$421$	−13.9451			−0.679641			−0.339821	+	0.940490i	$0.610366\pi$
$422$	−0.143104	+	0.143104i	−0.00696621	+	0.00696621i
$423$		0			0
$424$			1.00100i			0.0486126i
$425$	15.0266	−	30.3343i	0.728897	−	1.47143i
$426$		0			0
$427$	−5.74577	−	5.74577i	−0.278057	−	0.278057i
$428$	20.0930	+	20.0930i	0.971230	+	0.971230i
$429$		0			0
$430$	0.122239	+	0.744523i	0.00589488	+	0.0359041i
$431$			31.4909i			1.51686i	0.651754	+	0.758431i	$0.274034\pi$
$431$			31.4909i			1.51686i	−0.651754	+	0.758431i	$0.725966\pi$
$432$		0			0
$433$	21.7296	−	21.7296i	1.04426	−	1.04426i	0.0452816	−	0.998974i	$-0.485581\pi$
$433$	21.7296	−	21.7296i	1.04426	−	1.04426i	0.998974	−	0.0452816i	$-0.0144185\pi$
$434$	−0.183729			−0.00881927
$435$		0			0
$436$	27.8882			1.33560
$437$	−12.0482	+	12.0482i	−0.576342	+	0.576342i
$438$		0			0
$439$			5.11682i			0.244212i	0.992517	+	0.122106i	$0.0389648\pi$
$439$			5.11682i			0.244212i	−0.992517	+	0.122106i	$0.961035\pi$
$440$	0.0694517	−	0.0967372i	0.00331098	−	0.00461177i
$441$		0			0
$442$	−0.508417	−	0.508417i	−0.0241829	−	0.0241829i
$443$	−16.0066	−	16.0066i	−0.760498	−	0.760498i	0.215914	−	0.976412i	$-0.430727\pi$
$443$	−16.0066	−	16.0066i	−0.760498	−	0.760498i	−0.976412	+	0.215914i	$0.930727\pi$
$444$		0			0
$445$	−21.9348	+	3.60135i	−1.03981	+	0.170720i
$446$		−	0.104659i		−	0.00495574i
$447$		0			0
$448$	5.63714	−	5.63714i	0.266330	−	0.266330i
$449$	28.5938			1.34943			0.674713	−	0.738080i	$-0.264267\pi$
$449$	28.5938			1.34943			0.674713	+	0.738080i	$0.264267\pi$
$450$		0			0
$451$	0.992752			0.0467469
$452$	17.5905	−	17.5905i	0.827389	−	0.827389i
$453$		0			0
$454$			0.862113i			0.0404610i
$455$	−6.87383	+	1.12857i	−0.322250	+	0.0529084i
$456$		0			0
$457$	20.1448	+	20.1448i	0.942336	+	0.942336i	0.998426	−	0.0560895i	$-0.0178632\pi$
$457$	20.1448	+	20.1448i	0.942336	+	0.942336i	−0.0560895	+	0.998426i	$0.517863\pi$
$458$	−0.0584851	−	0.0584851i	−0.00273283	−	0.00273283i
$459$		0			0
$460$	−8.06825	+	11.2380i	−0.376184	+	0.523976i
$461$			8.52903i			0.397236i	0.980077	+	0.198618i	$0.0636454\pi$
$461$			8.52903i			0.397236i	−0.980077	+	0.198618i	$0.936355\pi$
$462$		0			0
$463$	−23.3379	+	23.3379i	−1.08461	+	1.08461i	−0.0885330	+	0.996073i	$0.528218\pi$
$463$	−23.3379	+	23.3379i	−1.08461	+	1.08461i	−0.996073	+	0.0885330i	$0.971782\pi$
$464$	28.6336			1.32928
$465$		0			0
$466$	0.818256			0.0379050
$467$	−26.1758	+	26.1758i	−1.21127	+	1.21127i	−0.240660	+	0.970609i	$0.577364\pi$
$467$	−26.1758	+	26.1758i	−1.21127	+	1.21127i	−0.970609	+	0.240660i	$0.922636\pi$
$468$		0			0
$469$		−	5.31944i		−	0.245629i
$470$	0.00938907	+	0.0571862i	0.000433086	+	0.00263780i
$471$		0			0
$472$	0.993735	+	0.993735i	0.0457404	+	0.0457404i
$473$	2.73428	+	2.73428i	0.125722	+	0.125722i
$474$		0			0
$475$	8.80072	+	26.0789i	0.403805	+	1.19658i
$476$			13.5330i			0.620285i
$477$		0			0
$478$	0.204584	−	0.204584i	0.00935746	−	0.00935746i
$479$	29.9325			1.36765			0.683826	−	0.729645i	$-0.260315\pi$
$479$	29.9325			1.36765			0.683826	+	0.729645i	$0.260315\pi$
$480$		0			0
$481$	12.1448			0.553756
$482$	−0.301963	+	0.301963i	−0.0137540	+	0.0137540i
$483$		0			0
$484$			21.6821i			0.985552i
$485$	5.58601	+	4.01043i	0.253648	+	0.182104i
$486$		0			0
$487$	−9.20330	−	9.20330i	−0.417041	−	0.417041i	0.467141	−	0.884183i	$-0.345284\pi$
$487$	−9.20330	−	9.20330i	−0.417041	−	0.417041i	−0.884183	+	0.467141i	$0.845284\pi$
$488$	0.783267	+	0.783267i	0.0354568	+	0.0354568i
$489$		0			0
$490$	−0.0619218	−	0.0444562i	−0.00279734	−	0.00200833i
$491$			0.109662i			0.00494898i	0.999997	+	0.00247449i	$0.000787655\pi$
$491$			0.109662i			0.00494898i	−0.999997	+	0.00247449i	$0.999212\pi$
$492$		0			0
$493$	−34.3301	+	34.3301i	−1.54615	+	1.54615i
$494$	0.584598			0.0263023
$495$		0			0
$496$	−21.5205			−0.966298
$497$	11.3692	−	11.3692i	0.509978	−	0.509978i
$498$		0			0
$499$		−	4.07430i		−	0.182391i	−0.995833	−	0.0911953i	$-0.970931\pi$
$499$		−	4.07430i		−	0.182391i	0.995833	−	0.0911953i	$-0.0290688\pi$
$500$	10.4818	+	19.7370i	0.468762	+	0.882667i
$501$		0			0
$502$	−0.159301	−	0.159301i	−0.00710994	−	0.00710994i
$503$	5.34928	+	5.34928i	0.238513	+	0.238513i	0.816234	−	0.577721i	$-0.196058\pi$
$503$	5.34928	+	5.34928i	0.238513	+	0.238513i	−0.577721	+	0.816234i	$0.696058\pi$
$504$		0			0
$505$	1.89852	+	11.5633i	0.0844828	+	0.514562i
$506$		−	0.0412232i		−	0.00183259i
$507$		0			0
$508$	−9.22813	+	9.22813i	−0.409432	+	0.409432i
$509$	−38.2954			−1.69742			−0.848708	−	0.528862i	$-0.822619\pi$
$509$	−38.2954			−1.69742			−0.848708	+	0.528862i	$0.822619\pi$
$510$		0			0
$511$	10.1481			0.448926
$512$	−1.92395	+	1.92395i	−0.0850272	+	0.0850272i
$513$		0			0
$514$		−	1.01099i		−	0.0445928i
$515$	−2.38279	+	3.31893i	−0.104998	+	0.146249i
$516$		0			0
$517$	0.210018	+	0.210018i	0.00923657	+	0.00923657i
$518$	0.0939754	+	0.0939754i	0.00412904	+	0.00412904i
$519$		0			0
$520$	0.937045	−	0.153848i	0.0410922	−	0.00674668i
$521$			13.9501i			0.611167i	0.952165	+	0.305583i	$0.0988514\pi$
$521$			13.9501i			0.611167i	−0.952165	+	0.305583i	$0.901149\pi$
$522$		0			0
$523$	30.1757	−	30.1757i	1.31949	−	1.31949i	0.405312	−	0.914179i	$-0.367163\pi$
$523$	30.1757	−	30.1757i	1.31949	−	1.31949i	0.914179	−	0.405312i	$-0.132837\pi$
$524$	−6.87762			−0.300450
$525$		0			0
$526$	0.812569			0.0354297
$527$	25.8019	−	25.8019i	1.12395	−	1.12395i
$528$		0			0
$529$		−	13.4194i		−	0.583451i
$530$	0.552341	−	0.0906856i	0.0239922	−	0.00393913i
$531$		0			0
$532$	−7.78040	−	7.78040i	−0.337323	−	0.337323i
$533$	5.59757	+	5.59757i	0.242458	+	0.242458i
$534$		0			0
$535$	18.5390	−	25.8224i	0.801510	−	1.11640i
$536$			0.725149i			0.0313217i
$537$		0			0
$538$	−0.376695	+	0.376695i	−0.0162405	+	0.0162405i
$539$	−0.390676			−0.0168276
$540$		0			0
$541$	7.24202			0.311359			0.155679	−	0.987808i	$-0.450243\pi$
$541$	7.24202			0.311359			0.155679	+	0.987808i	$0.450243\pi$
$542$	0.130824	−	0.130824i	0.00561937	−	0.00561937i
$543$		0			0
$544$		−	2.76751i		−	0.118656i
$545$	−5.05456	−	30.7859i	−0.216513	−	1.31872i
$546$		0			0
$547$	12.9323	+	12.9323i	0.552944	+	0.552944i	0.927289	−	0.374346i	$-0.122133\pi$
$547$	12.9323	+	12.9323i	0.552944	+	0.552944i	−0.374346	+	0.927289i	$0.622133\pi$
$548$	2.15602	+	2.15602i	0.0921004	+	0.0921004i
$549$		0			0
$550$	−0.0596708	−	0.0295589i	−0.00254437	−	0.00126040i
$551$		−	39.4741i		−	1.68165i
$552$		0			0
$553$	−5.19749	+	5.19749i	−0.221020	+	0.221020i
$554$	0.951992			0.0404462
$555$		0			0
$556$	−43.0460			−1.82556
$557$	7.14290	−	7.14290i	0.302654	−	0.302654i	−0.539397	−	0.842052i	$-0.681348\pi$
$557$	7.14290	−	7.14290i	0.302654	−	0.302654i	0.842052	+	0.539397i	$0.181348\pi$
$558$		0			0
$559$			30.8341i			1.30414i
$560$	−7.25301	−	5.20723i	−0.306495	−	0.220046i
$561$		0			0
$562$	−0.345314	−	0.345314i	−0.0145662	−	0.0145662i
$563$	−23.3269	−	23.3269i	−0.983111	−	0.983111i	0.0167491	−	0.999860i	$-0.494668\pi$
$563$	−23.3269	−	23.3269i	−0.983111	−	0.983111i	−0.999860	+	0.0167491i	$0.994668\pi$
$564$		0			0
$565$	−22.6064	−	16.2301i	−0.951060	−	0.682805i
$566$		−	0.550857i		−	0.0231543i
$567$		0			0
$568$	−1.54985	+	1.54985i	−0.0650305	+	0.0650305i
$569$	−20.2162			−0.847506			−0.423753	−	0.905778i	$-0.639288\pi$
$569$	−20.2162			−0.847506			−0.423753	+	0.905778i	$0.639288\pi$
$570$		0			0
$571$	26.7908			1.12116			0.560581	−	0.828100i	$-0.310578\pi$
$571$	26.7908			1.12116			0.560581	+	0.828100i	$0.310578\pi$
$572$	1.72016	−	1.72016i	0.0719235	−	0.0719235i
$573$		0			0
$574$			0.0866269i			0.00361574i
$575$	13.8680	+	6.86975i	0.578337	+	0.286488i
$576$		0			0
$577$	−8.31514	−	8.31514i	−0.346164	−	0.346164i	0.512515	−	0.858678i	$-0.328714\pi$
$577$	−8.31514	−	8.31514i	−0.346164	−	0.346164i	−0.858678	+	0.512515i	$0.828714\pi$
$578$	0.695170	+	0.695170i	0.0289152	+	0.0289152i
$579$		0			0
$580$	−5.19267	−	31.6271i	−0.215614	−	1.31324i
$581$			8.89661i			0.369093i
$582$		0			0
$583$	2.02848	−	2.02848i	0.0840112	−	0.0840112i
$584$	−1.38340			−0.0572454
$585$		0			0
$586$	0.311884			0.0128838
$587$	8.18891	−	8.18891i	0.337993	−	0.337993i	−0.517619	−	0.855611i	$-0.673181\pi$
$587$	8.18891	−	8.18891i	0.337993	−	0.337993i	0.855611	+	0.517619i	$0.173181\pi$
$588$		0			0
$589$			29.6680i			1.22245i
$590$	0.458307	−	0.638363i	0.0188682	−	0.0262810i
$591$		0			0
$592$	11.0075	+	11.0075i	0.452405	+	0.452405i
$593$	17.0635	+	17.0635i	0.700714	+	0.700714i	0.964564	−	0.263850i	$-0.0849924\pi$
$593$	17.0635	+	17.0635i	0.700714	+	0.700714i	−0.263850	+	0.964564i	$0.584992\pi$
$594$		0			0
$595$	14.9391	−	2.45277i	0.612445	−	0.100554i
$596$			12.9576i			0.530763i
$597$		0			0
$598$	0.232434	−	0.232434i	0.00950494	−	0.00950494i
$599$	−46.8508			−1.91427			−0.957136	−	0.289640i	$-0.906464\pi$
$599$	−46.8508			−1.91427			−0.957136	+	0.289640i	$0.906464\pi$
$600$		0			0
$601$	34.9943			1.42745			0.713723	−	0.700428i	$-0.247008\pi$
$601$	34.9943			1.42745			0.713723	+	0.700428i	$0.247008\pi$
$602$	−0.238591	+	0.238591i	−0.00972424	+	0.00972424i
$603$		0			0
$604$		−	3.53559i		−	0.143861i
$605$	23.9350	−	3.92975i	0.973096	−	0.159767i
$606$		0			0
$607$	−6.68444	−	6.68444i	−0.271313	−	0.271313i	0.558316	−	0.829629i	$-0.311448\pi$
$607$	−6.68444	−	6.68444i	−0.271313	−	0.271313i	−0.829629	+	0.558316i	$0.811448\pi$
$608$	1.59110	+	1.59110i	0.0645275	+	0.0645275i
$609$		0			0
$610$	0.361240	−	0.503161i	0.0146262	−	0.0203724i
$611$			2.36834i			0.0958129i
$612$		0			0
$613$	−10.0152	+	10.0152i	−0.404510	+	0.404510i	−0.879819	−	0.475309i	$-0.842336\pi$
$613$	−10.0152	+	10.0152i	−0.404510	+	0.404510i	0.475309	+	0.879819i	$0.342336\pi$
$614$	−0.408256			−0.0164759
$615$		0			0
$616$	0.0532572			0.00214579
$617$	−2.25298	+	2.25298i	−0.0907017	+	0.0907017i	−0.751002	−	0.660300i	$-0.770429\pi$
$617$	−2.25298	+	2.25298i	−0.0907017	+	0.0907017i	0.660300	+	0.751002i	$0.270429\pi$
$618$		0			0
$619$		−	18.8285i		−	0.756781i	−0.925646	−	0.378390i	$-0.876478\pi$
$619$		−	18.8285i		−	0.756781i	0.925646	−	0.378390i	$-0.123522\pi$
$620$	3.90272	+	23.7704i	0.156737	+	0.954641i
$621$		0			0
$622$	−0.248865	−	0.248865i	−0.00997859	−	0.00997859i
$623$	−7.02926	−	7.02926i	−0.281621	−	0.281621i
$624$		0			0
$625$	19.8880	−	15.1481i	0.795521	−	0.605926i
$626$			0.877948i			0.0350899i
$627$		0			0
$628$	14.9763	−	14.9763i	0.597618	−	0.597618i
$629$	−26.3948			−1.05243
$630$		0			0
$631$	−18.6473			−0.742338			−0.371169	−	0.928565i	$-0.621043\pi$
$631$	−18.6473			−0.742338			−0.371169	+	0.928565i	$0.621043\pi$
$632$	0.708525	−	0.708525i	0.0281836	−	0.0281836i
$633$		0			0
$634$		−	1.18853i		−	0.0472025i
$635$	11.8595	+	8.51444i	0.470631	+	0.337885i
$636$		0			0
$637$	−2.20280	−	2.20280i	−0.0872781	−	0.0872781i
$638$	0.0675309	+	0.0675309i	0.00267357	+	0.00267357i
$639$		0			0
$640$	1.97862	+	1.42053i	0.0782118	+	0.0561515i
$641$		−	1.94420i		−	0.0767912i	−0.999263	−	0.0383956i	$-0.987775\pi$
$641$		−	1.94420i		−	0.0767912i	0.999263	−	0.0383956i	$-0.0122247\pi$
$642$		0			0
$643$	29.8737	−	29.8737i	1.17810	−	1.17810i	0.197878	−	0.980227i	$-0.436595\pi$
$643$	29.8737	−	29.8737i	1.17810	−	1.17810i	0.980227	−	0.197878i	$-0.0634051\pi$
$644$	−6.18692			−0.243799
$645$		0			0
$646$	−1.27053			−0.0499882
$647$	−5.84909	+	5.84909i	−0.229952	+	0.229952i	−0.812672	−	0.582721i	$-0.801988\pi$
$647$	−5.84909	+	5.84909i	−0.229952	+	0.229952i	0.582721	+	0.812672i	$0.301988\pi$
$648$		0			0
$649$		−	4.02754i		−	0.158095i
$650$	−0.169784	−	0.503116i	−0.00665948	−	0.0197338i
$651$		0			0
$652$	−27.8460	−	27.8460i	−1.09053	−	1.09053i
$653$	−34.0909	−	34.0909i	−1.33408	−	1.33408i	−0.901684	−	0.432396i	$-0.857668\pi$
$653$	−34.0909	−	34.0909i	−1.33408	−	1.33408i	−0.432396	−	0.901684i	$-0.642332\pi$
$654$		0			0
$655$	1.24653	+	7.59224i	0.0487058	+	0.296653i
$656$			10.1468i			0.396164i
$657$		0			0
$658$	−0.0183260	+	0.0183260i	−0.000714422	+	0.000714422i
$659$	−24.0596			−0.937229			−0.468614	−	0.883403i	$-0.655247\pi$
$659$	−24.0596			−0.937229			−0.468614	+	0.883403i	$0.655247\pi$
$660$		0			0
$661$	−2.95088			−0.114776			−0.0573880	−	0.998352i	$-0.518277\pi$
$661$	−2.95088			−0.114776			−0.0573880	+	0.998352i	$0.518277\pi$
$662$	0.315334	−	0.315334i	0.0122558	−	0.0122558i
$663$		0			0
$664$		−	1.21279i		−	0.0470654i
$665$	−7.17867	+	9.99896i	−0.278377	+	0.387743i
$666$		0			0
$667$	−15.6948	−	15.6948i	−0.607704	−	0.607704i
$668$	−0.953809	−	0.953809i	−0.0369040	−	0.0369040i
$669$		0			0
$670$	0.400131	−	0.0656952i	0.0154584	−	0.00253803i
$671$		−	3.17453i		−	0.122551i
$672$		0			0
$673$	18.8062	−	18.8062i	0.724925	−	0.724925i	−0.244679	−	0.969604i	$-0.578683\pi$
$673$	18.8062	−	18.8062i	0.724925	−	0.724925i	0.969604	+	0.244679i	$0.0786825\pi$
$674$	−0.307857			−0.0118582
$675$		0			0
$676$	−6.58687			−0.253341
$677$	4.99857	−	4.99857i	0.192111	−	0.192111i	−0.604497	−	0.796608i	$-0.706626\pi$
$677$	4.99857	−	4.99857i	0.192111	−	0.192111i	0.796608	+	0.604497i	$0.206626\pi$
$678$		0			0
$679$			3.07529i			0.118019i
$680$	−2.03651	+	0.334363i	−0.0780968	+	0.0128223i
$681$		0			0
$682$	−0.0507550	−	0.0507550i	−0.00194351	−	0.00194351i
$683$	10.0092	+	10.0092i	0.382990	+	0.382990i	0.872178	−	0.489188i	$-0.162707\pi$
$683$	10.0092	+	10.0092i	0.382990	+	0.382990i	−0.489188	+	0.872178i	$0.662707\pi$
$684$		0			0
$685$	1.98927	−	2.77080i	0.0760061	−	0.105867i
$686$		−	0.0340901i		−	0.00130156i
$687$		0			0
$688$	−27.9466	+	27.9466i	−1.06545	+	1.06545i
$689$	22.8750			0.871466
$690$		0			0
$691$	−19.5494			−0.743696			−0.371848	−	0.928294i	$-0.621276\pi$
$691$	−19.5494			−0.743696			−0.371848	+	0.928294i	$0.621276\pi$
$692$	−29.2619	+	29.2619i	−1.11237	+	1.11237i
$693$		0			0
$694$			0.0913314i			0.00346689i
$695$	7.80181	+	47.5186i	0.295939	+	1.80248i
$696$		0			0
$697$	−12.1654	−	12.1654i	−0.460797	−	0.460797i
$698$	0.664689	+	0.664689i	0.0251589	+	0.0251589i
$699$		0			0
$700$	−4.43631	+	8.95561i	−0.167677	+	0.338490i
$701$			11.8659i			0.448171i	0.974570	+	0.224085i	$0.0719394\pi$
$701$			11.8659i			0.448171i	−0.974570	+	0.224085i	$0.928061\pi$
$702$		0			0
$703$	15.1749	−	15.1749i	0.572331	−	0.572331i
$704$	3.11451			0.117383
$705$		0			0
$706$	0.526431			0.0198125
$707$	−3.70560	+	3.70560i	−0.139364	+	0.139364i
$708$		0			0
$709$		−	29.1357i		−	1.09421i	−0.837063	−	0.547107i	$-0.815729\pi$
$709$		−	29.1357i		−	1.09421i	0.837063	−	0.547107i	$-0.184271\pi$
$710$	0.995607	+	0.714787i	0.0373645	+	0.0268255i
$711$		0			0
$712$	0.958234	+	0.958234i	0.0359113	+	0.0359113i
$713$	11.7959	+	11.7959i	0.441760	+	0.441760i
$714$		0			0
$715$	−2.21066	−	1.58712i	−0.0826740	−	0.0593551i
$716$		−	6.09224i		−	0.227678i
$717$		0			0
$718$	−0.411203	+	0.411203i	−0.0153460	+	0.0153460i
$719$	−33.8893			−1.26386			−0.631928	−	0.775027i	$-0.717736\pi$
$719$	−33.8893			−1.26386			−0.631928	+	0.775027i	$0.717736\pi$
$720$		0			0
$721$	−1.82718			−0.0680478
$722$	0.272450	−	0.272450i	0.0101395	−	0.0101395i
$723$		0			0
$724$			8.25454i			0.306778i
$725$	−33.9722	+	11.4644i	−1.26170	+	0.425778i
$726$		0			0
$727$	−26.7239	−	26.7239i	−0.991135	−	0.991135i	0.00882647	−	0.999961i	$-0.497190\pi$
$727$	−26.7239	−	26.7239i	−0.991135	−	0.991135i	−0.999961	+	0.00882647i	$0.997190\pi$
$728$	0.300287	+	0.300287i	0.0111294	+	0.0111294i
$729$		0			0
$730$	0.125330	+	0.763348i	0.00463866	+	0.0282528i
$731$		−	67.0128i		−	2.47856i
$732$		0			0
$733$	−12.2852	+	12.2852i	−0.453763	+	0.453763i	−0.896601	−	0.442838i	$-0.853972\pi$
$733$	−12.2852	+	12.2852i	−0.453763	+	0.453763i	0.442838	+	0.896601i	$0.353972\pi$
$734$	−0.736691			−0.0271918
$735$		0			0
$736$	1.26523			0.0466370
$737$	1.46949	−	1.46949i	0.0541294	−	0.0541294i
$738$		0			0
$739$		−	3.61431i		−	0.132955i	−0.997788	−	0.0664774i	$-0.978824\pi$
$739$		−	3.61431i		−	0.132955i	0.997788	−	0.0664774i	$-0.0211760\pi$
$740$	10.1621	−	14.1545i	0.373566	−	0.520330i
$741$		0			0
$742$	0.177004	+	0.177004i	0.00649802	+	0.00649802i
$743$	9.96922	+	9.96922i	0.365735	+	0.365735i	0.865919	−	0.500184i	$-0.166734\pi$
$743$	9.96922	+	9.96922i	0.365735	+	0.365735i	−0.500184	+	0.865919i	$0.666734\pi$
$744$		0			0
$745$	14.3039	−	2.34848i	0.524056	−	0.0860416i
$746$		−	0.233164i		−	0.00853674i
$747$		0			0
$748$	−3.73849	+	3.73849i	−0.136693	+	0.136693i
$749$	14.2161			0.519446
$750$		0			0
$751$	−20.7823			−0.758359			−0.379179	−	0.925323i	$-0.623794\pi$
$751$	−20.7823			−0.758359			−0.379179	+	0.925323i	$0.623794\pi$
$752$	−2.14656	+	2.14656i	−0.0782768	+	0.0782768i
$753$		0			0
$754$			0.761537i			0.0277335i
$755$	−3.90295	+	0.640803i	−0.142043	+	0.0233212i
$756$		0			0
$757$	5.61667	+	5.61667i	0.204141	+	0.204141i	0.801772	−	0.597630i	$-0.203891\pi$
$757$	5.61667	+	5.61667i	0.204141	+	0.204141i	−0.597630	+	0.801772i	$0.703891\pi$
$758$	−0.375051	−	0.375051i	−0.0136224	−	0.0136224i
$759$		0			0
$760$	0.978601	−	1.36306i	0.0354976	−	0.0494436i
$761$		−	27.7154i		−	1.00468i	−0.864670	−	0.502341i	$-0.832472\pi$
$761$		−	27.7154i		−	1.00468i	0.864670	−	0.502341i	$-0.167528\pi$
$762$		0			0
$763$	9.86570	−	9.86570i	0.357162	−	0.357162i
$764$	−42.9636			−1.55437
$765$		0			0
$766$	−0.513998			−0.0185715
$767$	22.7090	−	22.7090i	0.819976	−	0.819976i
$768$		0			0
$769$			16.1150i			0.581123i	0.956856	+	0.290561i	$0.0938421\pi$
$769$			16.1150i			0.581123i	−0.956856	+	0.290561i	$0.906158\pi$
$770$	−0.00482486	−	0.0293869i	−0.000173876	−	0.00105903i
$771$		0			0
$772$	−18.0790	−	18.0790i	−0.650677	−	0.650677i
$773$	15.2927	+	15.2927i	0.550041	+	0.550041i	0.926452	−	0.376412i	$-0.122842\pi$
$773$	15.2927	+	15.2927i	0.550041	+	0.550041i	−0.376412	+	0.926452i	$0.622842\pi$
$774$		0			0
$775$	25.5329	−	8.61646i	0.917168	−	0.309512i
$776$		−	0.419226i		−	0.0150493i
$777$		0			0
$778$	−0.546367	+	0.546367i	−0.0195882	+	0.0195882i
$779$	13.9883			0.501182
$780$		0			0
$781$	6.28146			0.224768
$782$	−0.505157	+	0.505157i	−0.0180644	+	0.0180644i
$783$		0			0
$784$		−	3.99303i		−	0.142608i
$785$	−19.2467	−	13.8180i	−0.686945	−	0.493186i
$786$		0			0
$787$	5.60346	+	5.60346i	0.199742	+	0.199742i	0.799889	−	0.600148i	$-0.204891\pi$
$787$	5.60346	+	5.60346i	0.199742	+	0.199742i	−0.600148	+	0.799889i	$0.704891\pi$
$788$	−17.5905	−	17.5905i	−0.626637	−	0.626637i
$789$		0			0
$790$	−0.455148	−	0.326769i	−0.0161934	−	0.0116259i
$791$		−	12.4456i		−	0.442515i
$792$		0			0
$793$	17.8994	−	17.8994i	0.635626	−	0.635626i
$794$	−0.414413			−0.0147070
$795$		0			0
$796$	1.63216			0.0578502
$797$	20.1318	−	20.1318i	0.713105	−	0.713105i	−0.254079	−	0.967184i	$-0.581772\pi$
$797$	20.1318	−	20.1318i	0.713105	−	0.713105i	0.967184	+	0.254079i	$0.0817722\pi$
$798$		0			0
$799$		−	5.14721i		−	0.182095i
$800$	0.907228	−	1.83143i	0.0320754	−	0.0647508i
$801$		0			0
$802$	0.433326	+	0.433326i	0.0153013	+	0.0153013i
$803$	2.80341	+	2.80341i	0.0989302	+	0.0989302i
$804$		0			0
$805$	1.12134	+	6.82977i	0.0395220	+	0.240718i
$806$		−	0.572358i		−	0.0201604i
$807$		0			0
$808$	0.505150	−	0.505150i	0.0177711	−	0.0177711i
$809$	39.2478			1.37988			0.689939	−	0.723868i	$-0.257637\pi$
$809$	39.2478			1.37988			0.689939	+	0.723868i	$0.257637\pi$
$810$		0			0
$811$	−50.5122			−1.77372			−0.886861	−	0.462036i	$-0.847119\pi$
$811$	−50.5122			−1.77372			−0.886861	+	0.462036i	$0.847119\pi$
$812$	10.1353	−	10.1353i	0.355679	−	0.355679i
$813$		0			0
$814$			0.0519213i			0.00181984i
$815$	−25.6924	+	35.7862i	−0.899966	+	1.25354i
$816$		0			0
$817$	38.5270	+	38.5270i	1.34789	+	1.34789i
$818$	−0.466005	−	0.466005i	−0.0162935	−	0.0162935i
$819$		0			0
$820$	11.2076	−	1.84010i	0.391385	−	0.0642592i
$821$			22.3236i			0.779097i	0.921006	+	0.389549i	$0.127369\pi$
$821$			22.3236i			0.779097i	−0.921006	+	0.389549i	$0.872631\pi$
$822$		0			0
$823$	23.8490	−	23.8490i	0.831323	−	0.831323i	−0.156375	−	0.987698i	$-0.549981\pi$
$823$	23.8490	−	23.8490i	0.831323	−	0.831323i	0.987698	+	0.156375i	$0.0499807\pi$
$824$	0.249083			0.00867721
$825$		0			0
$826$	0.351441			0.0122282
$827$	17.6588	−	17.6588i	0.614057	−	0.614057i	−0.329944	−	0.944001i	$-0.607030\pi$
$827$	17.6588	−	17.6588i	0.614057	−	0.614057i	0.944001	+	0.329944i	$0.107030\pi$
$828$		0			0
$829$			17.1138i			0.594388i	0.954817	+	0.297194i	$0.0960509\pi$
$829$			17.1138i			0.594388i	−0.954817	+	0.297194i	$0.903949\pi$
$830$	−0.669208	+	0.109873i	−0.0232286	+	0.00381376i
$831$		0			0
$832$	17.5610	+	17.5610i	0.608818	+	0.608818i
$833$	4.78742	+	4.78742i	0.165874	+	0.165874i
$834$		0			0
$835$	−0.880042	+	1.22579i	−0.0304551	+	0.0424201i
$836$		−	4.29866i		−	0.148672i
$837$		0			0
$838$	0.0167385	−	0.0167385i	0.000578223	−	0.000578223i
$839$	−43.4377			−1.49964			−0.749818	−	0.661644i	$-0.769859\pi$
$839$	−43.4377			−1.49964			−0.749818	+	0.661644i	$0.769859\pi$
$840$		0			0
$841$	22.4217			0.773162
$842$	0.336150	−	0.336150i	0.0115845	−	0.0115845i
$843$		0			0
$844$			11.8664i			0.408457i
$845$	1.19383	+	7.27128i	0.0410689	+	0.250139i
$846$		0			0
$847$	7.67025	+	7.67025i	0.263553	+	0.263553i
$848$	20.7328	+	20.7328i	0.711967	+	0.711967i
$849$		0			0
$850$	0.368998	+	1.09344i	0.0126565	+	0.0375047i
$851$		−	12.0670i		−	0.413650i
$852$		0			0
$853$	−27.5983	+	27.5983i	−0.944949	+	0.944949i	−0.998562	−	0.0536129i	$-0.982926\pi$
$853$	−27.5983	+	27.5983i	−0.944949	+	0.944949i	0.0536129	+	0.998562i	$0.482926\pi$
$854$	0.277007			0.00947899
$855$		0			0
$856$	−1.93795			−0.0662378
$857$	19.1806	−	19.1806i	0.655198	−	0.655198i	−0.299042	−	0.954240i	$-0.596667\pi$
$857$	19.1806	−	19.1806i	0.655198	−	0.655198i	0.954240	+	0.299042i	$0.0966670\pi$
$858$		0			0
$859$			37.8659i			1.29197i	0.763351	+	0.645984i	$0.223553\pi$
$859$			37.8659i			1.29197i	−0.763351	+	0.645984i	$0.776447\pi$
$860$	35.9364	+	25.8002i	1.22542	+	0.879780i
$861$		0			0
$862$	−0.759097	−	0.759097i	−0.0258550	−	0.0258550i
$863$	14.5099	+	14.5099i	0.493924	+	0.493924i	0.909540	−	0.415616i	$-0.136434\pi$
$863$	14.5099	+	14.5099i	0.493924	+	0.493924i	−0.415616	+	0.909540i	$0.636434\pi$
$864$		0			0
$865$	37.6059	+	26.9988i	1.27864	+	0.917988i
$866$			1.04760i			0.0355988i
$867$		0			0
$868$	−7.61749	+	7.61749i	−0.258555	+	0.258555i
$869$	−2.87161			−0.0974126
$870$		0			0
$871$	16.5713			0.561496
$872$	−1.34490	+	1.34490i	−0.0455440	+	0.0455440i
$873$		0			0
$874$		−	0.580850i		−	0.0196475i
$875$	10.6902	+	3.27411i	0.361394	+	0.110685i
$876$		0			0
$877$	−2.22943	−	2.22943i	−0.0752826	−	0.0752826i	0.668463	−	0.743745i	$-0.266953\pi$
$877$	−2.22943	−	2.22943i	−0.0752826	−	0.0752826i	−0.743745	+	0.668463i	$0.766953\pi$
$878$	−0.123343	−	0.123343i	−0.00416261	−	0.00416261i
$879$		0			0
$880$	−0.565144	−	3.44213i	−0.0190510	−	0.116034i
$881$		−	13.5419i		−	0.456238i	−0.973633	−	0.228119i	$-0.926742\pi$
$881$		−	13.5419i		−	0.456238i	0.973633	−	0.228119i	$-0.0732575\pi$
$882$		0			0
$883$	23.3601	−	23.3601i	0.786129	−	0.786129i	−0.194728	−	0.980857i	$-0.562383\pi$
$883$	23.3601	−	23.3601i	0.786129	−	0.786129i	0.980857	+	0.194728i	$0.0623826\pi$
$884$	−42.1584			−1.41794
$885$		0			0
$886$	0.771690			0.0259254
$887$	−12.4892	+	12.4892i	−0.419346	+	0.419346i	−0.884978	−	0.465632i	$-0.845827\pi$
$887$	−12.4892	+	12.4892i	−0.419346	+	0.419346i	0.465632	+	0.884978i	$0.345827\pi$
$888$		0			0
$889$			6.52907i			0.218978i
$890$	0.441934	−	0.615557i	0.0148137	−	0.0206335i
$891$		0			0
$892$	−4.33921	−	4.33921i	−0.145287	−	0.145287i
$893$	2.95923	+	2.95923i	0.0990269	+	0.0990269i
$894$		0			0
$895$	−6.72525	+	1.10418i	−0.224800	+	0.0369086i
$896$			1.08930i			0.0363909i
$897$		0			0
$898$	−0.689263	+	0.689263i	−0.0230010	+	0.0230010i
$899$	−38.6476			−1.28897
$900$		0			0
$901$	−49.7150			−1.65625
$902$	−0.0239306	+	0.0239306i	−0.000796802	+	0.000796802i
$903$		0			0
$904$			1.69660i			0.0564279i
$905$	9.11222	−	1.49608i	0.302901	−	0.0497315i
$906$		0			0
$907$	−30.6351	−	30.6351i	−1.01722	−	1.01722i	−0.999849	−	0.0173730i	$-0.994470\pi$
$907$	−30.6351	−	30.6351i	−1.01722	−	1.01722i	−0.0173730	−	0.999849i	$-0.505530\pi$
$908$	35.7436	+	35.7436i	1.18619	+	1.18619i
$909$		0			0
$910$	0.138491	−	0.192901i	0.00459094	−	0.00639459i
$911$		−	39.0547i		−	1.29394i	−0.762516	−	0.646969i	$-0.776036\pi$
$911$		−	39.0547i		−	1.29394i	0.762516	−	0.646969i	$-0.223964\pi$
$912$		0			0
$913$	−2.45768	+	2.45768i	−0.0813374	+	0.0813374i
$914$	−0.971196			−0.0321243
$915$		0			0
$916$	−4.84964			−0.160237
$917$	−2.43302	+	2.43302i	−0.0803454	+	0.0803454i
$918$		0			0
$919$			44.2050i			1.45819i	0.684413	+	0.729095i	$0.260059\pi$
$919$			44.2050i			1.45819i	−0.684413	+	0.729095i	$0.739941\pi$
$920$	−0.152862	−	0.931039i	−0.00503970	−	0.0306954i
$921$		0			0
$922$	−0.205595	−	0.205595i	−0.00677091	−	0.00677091i
$923$	35.4176	+	35.4176i	1.16578	+	1.16578i
$924$		0			0
$925$	−17.4670	−	8.65257i	−0.574312	−	0.284495i
$926$		−	1.12514i		−	0.0369743i
$927$		0			0
$928$	−2.07267	+	2.07267i	−0.0680388	+	0.0680388i
$929$	44.4925			1.45975			0.729875	−	0.683580i	$-0.239578\pi$
$929$	44.4925			1.45975			0.729875	+	0.683580i	$0.239578\pi$
$930$		0			0
$931$	−5.50477			−0.180412
$932$	33.9253	−	33.9253i	1.11126	−	1.11126i
$933$		0			0
$934$		−	1.26195i		−	0.0412923i
$935$	4.80451	+	3.44935i	0.157124	+	0.112806i
$936$		0			0
$937$	7.24786	+	7.24786i	0.236777	+	0.236777i	0.815514	−	0.578737i	$-0.196454\pi$
$937$	7.24786	+	7.24786i	0.236777	+	0.236777i	−0.578737	+	0.815514i	$0.696454\pi$
$938$	0.128227	+	0.128227i	0.00418675	+	0.00418675i
$939$		0			0
$940$	2.76025	+	1.98170i	0.0900293	+	0.0646358i
$941$			29.6137i			0.965380i	0.875791	+	0.482690i	$0.160340\pi$
$941$			29.6137i			0.965380i	−0.875791	+	0.482690i	$0.839660\pi$
$942$		0			0
$943$	5.56169	−	5.56169i	0.181113	−	0.181113i
$944$	41.1648			1.33980
$945$		0			0
$946$	−0.131821			−0.00428588
$947$	−35.1629	+	35.1629i	−1.14264	+	1.14264i	−0.154676	+	0.987965i	$0.549433\pi$
$947$	−35.1629	+	35.1629i	−1.14264	+	1.14264i	−0.987965	+	0.154676i	$0.950567\pi$
$948$		0			0
$949$			31.6137i			1.02622i
$950$	−0.840785	−	0.416496i	−0.0272787	−	0.0135129i
$951$		0			0
$952$	−0.652625	−	0.652625i	−0.0211517	−	0.0211517i
$953$	−23.2547	−	23.2547i	−0.753295	−	0.753295i	0.221798	−	0.975093i	$-0.428808\pi$
$953$	−23.2547	−	23.2547i	−0.753295	−	0.753295i	−0.975093	+	0.221798i	$0.928808\pi$
$954$		0			0
$955$	7.78688	+	47.4278i	0.251978	+	1.53473i
$956$		−	16.9643i		−	0.548666i
$957$		0			0
$958$	−0.721533	+	0.721533i	−0.0233117	+	0.0233117i
$959$	1.52542			0.0492584
$960$		0			0
$961$	−1.95314			−0.0630047
$962$	−0.292755	+	0.292755i	−0.00943879	+	0.00943879i
$963$		0			0
$964$			25.0391i			0.806455i
$965$	−16.6808	+	23.2342i	−0.536973	+	0.747935i
$966$		0			0
$967$	−9.48404	−	9.48404i	−0.304986	−	0.304986i	0.537975	−	0.842961i	$-0.319190\pi$
$967$	−9.48404	−	9.48404i	−0.304986	−	0.304986i	−0.842961	+	0.537975i	$0.819190\pi$
$968$	−1.04561	−	1.04561i	−0.0336073	−	0.0336073i
$969$		0			0
$970$	−0.231325	+	0.0379799i	−0.00742740	+	0.00121946i
$971$		−	27.4171i		−	0.879858i	−0.898033	−	0.439929i	$-0.855004\pi$
$971$		−	27.4171i		−	0.879858i	0.898033	−	0.439929i	$-0.144996\pi$
$972$		0			0
$973$	−15.2279	+	15.2279i	−0.488184	+	0.488184i
$974$	0.443697			0.0142170
$975$		0			0
$976$	32.4463			1.03858
$977$	0.810961	−	0.810961i	0.0259449	−	0.0259449i	−0.694015	−	0.719960i	$-0.744160\pi$
$977$	0.810961	−	0.810961i	0.0259449	−	0.0259449i	0.719960	+	0.694015i	$0.244160\pi$
$978$		0			0
$979$		−	3.88366i		−	0.124122i
$980$	−4.41049	+	0.724132i	−0.140888	+	0.0231315i
$981$		0			0
$982$	−0.00264344	−	0.00264344i	−8.43555e−5	−	8.43555e-5i
$983$	−1.20950	−	1.20950i	−0.0385771	−	0.0385771i	0.687555	−	0.726132i	$-0.258684\pi$
$983$	−1.20950	−	1.20950i	−0.0385771	−	0.0385771i	−0.726132	+	0.687555i	$0.758684\pi$
$984$		0			0
$985$	−16.2301	+	22.6064i	−0.517134	+	0.720301i
$986$		−	1.65508i		−	0.0527084i
$987$		0			0
$988$	24.2377	−	24.2377i	0.771104	−	0.771104i
$989$	30.6364			0.974181
$990$		0			0
$991$	−28.2009			−0.895832			−0.447916	−	0.894076i	$-0.647834\pi$
$991$	−28.2009			−0.895832			−0.447916	+	0.894076i	$0.647834\pi$
$992$	1.55778	−	1.55778i	0.0494597	−	0.0494597i
$993$		0			0
$994$			0.548116i			0.0173852i
$995$	−0.295818	−	1.80174i	−0.00937805	−	0.0571191i
$996$		0			0
$997$	23.4397	+	23.4397i	0.742342	+	0.742342i	0.973028	−	0.230687i	$-0.0740972\pi$
$997$	23.4397	+	23.4397i	0.742342	+	0.742342i	−0.230687	+	0.973028i	$0.574097\pi$
$998$	0.0982123	+	0.0982123i	0.00310886	+	0.00310886i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.m.a.197.3	yes	12
3.2	odd	2		315.2.m.b.197.4	yes	12
5.2	odd	4		1575.2.m.d.1268.3		12
5.3	odd	4		315.2.m.b.8.4	yes	12
5.4	even	2		1575.2.m.c.1457.4		12
15.2	even	4		1575.2.m.c.1268.4		12
15.8	even	4	inner	315.2.m.a.8.3	✓	12
15.14	odd	2		1575.2.m.d.1457.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.3	✓	12	15.8	even	4	inner
315.2.m.a.197.3	yes	12	1.1	even	1	trivial
315.2.m.b.8.4	yes	12	5.3	odd	4
315.2.m.b.197.4	yes	12	3.2	odd	2
1575.2.m.c.1268.4		12	15.2	even	4
1575.2.m.c.1457.4		12	5.4	even	2
1575.2.m.d.1268.3		12	5.2	odd	4
1575.2.m.d.1457.3		12	15.14	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0241053 + 0.0241053i) q^{2} +1.99884i q^{4} +(2.20653 - 0.362277i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.0963933 - 0.0963933i) q^{8} +O(q^{10})\)	\(q+(-0.0241053 + 0.0241053i) q^{2} +1.99884i q^{4} +(2.20653 - 0.362277i) q^{5} +(0.707107 + 0.707107i) q^{7} +(-0.0963933 - 0.0963933i) q^{8} +(-0.0444562 + 0.0619218i) q^{10} +0.390676i q^{11} +(-2.20280 + 2.20280i) q^{13} -0.0340901 q^{14} -3.99303 q^{16} +(4.78742 - 4.78742i) q^{17} +5.50477i q^{19} +(0.724132 + 4.41049i) q^{20} +(-0.00941736 - 0.00941736i) q^{22} +(2.18868 + 2.18868i) q^{23} +(4.73751 - 1.59874i) q^{25} -0.106198i q^{26} +(-1.41339 + 1.41339i) q^{28} -7.17089 q^{29} +5.38951 q^{31} +(0.289040 - 0.289040i) q^{32} +0.230805i q^{34} +(1.81642 + 1.30408i) q^{35} +(-2.75668 - 2.75668i) q^{37} +(-0.132694 - 0.132694i) q^{38} +(-0.247615 - 0.177773i) q^{40} -2.54112i q^{41} +(6.99884 - 6.99884i) q^{43} -0.780897 q^{44} -0.105518 q^{46} +(0.537576 - 0.537576i) q^{47} +1.00000i q^{49} +(-0.0756610 + 0.152737i) q^{50} +(-4.40304 - 4.40304i) q^{52} +(-5.19225 - 5.19225i) q^{53} +(0.141533 + 0.862036i) q^{55} -0.136321i q^{56} +(0.172857 - 0.172857i) q^{58} -10.3092 q^{59} -8.12574 q^{61} +(-0.129916 + 0.129916i) q^{62} -7.97212i q^{64} +(-4.06251 + 5.65856i) q^{65} +(-3.76141 - 3.76141i) q^{67} +(9.56928 + 9.56928i) q^{68} +(-0.0752206 + 0.0123500i) q^{70} -16.0785i q^{71} +(7.17580 - 7.17580i) q^{73} +0.132901 q^{74} -11.0031 q^{76} +(-0.276249 + 0.276249i) q^{77} +7.35036i q^{79} +(-8.81072 + 1.44658i) q^{80} +(0.0612544 + 0.0612544i) q^{82} +(6.29085 + 6.29085i) q^{83} +(8.82920 - 12.2979i) q^{85} +0.337418i q^{86} +(0.0376585 - 0.0376585i) q^{88} -9.94088 q^{89} -3.11523 q^{91} +(-4.37481 + 4.37481i) q^{92} +0.0259169i q^{94} +(1.99425 + 12.1464i) q^{95} +(2.17456 + 2.17456i) q^{97} +(-0.0241053 - 0.0241053i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{5} + 24 q^{8}+O(q^{10}) \) 12 * q - 4 * q^5 + 24 * q^8	\( 12 q - 4 q^{5} + 24 q^{8} + 16 q^{10} - 4 q^{13} - 4 q^{14} - 20 q^{16} + 8 q^{17} - 12 q^{20} - 8 q^{22} + 8 q^{23} - 8 q^{25} - 32 q^{29} + 48 q^{32} + 8 q^{35} + 4 q^{37} + 24 q^{38} - 28 q^{40} + 40 q^{43} - 64 q^{44} + 16 q^{46} + 24 q^{47} - 16 q^{50} + 36 q^{52} - 40 q^{53} - 16 q^{55} - 28 q^{58} - 80 q^{59} - 32 q^{61} + 16 q^{62} + 48 q^{65} - 48 q^{67} + 32 q^{68} + 8 q^{70} - 20 q^{73} - 64 q^{74} + 16 q^{76} + 36 q^{80} + 20 q^{82} + 24 q^{83} - 56 q^{89} + 8 q^{92} + 56 q^{95} + 12 q^{97}+O(q^{100}) \) 12 * q - 4 * q^5 + 24 * q^8 + 16 * q^10 - 4 * q^13 - 4 * q^14 - 20 * q^16 + 8 * q^17 - 12 * q^20 - 8 * q^22 + 8 * q^23 - 8 * q^25 - 32 * q^29 + 48 * q^32 + 8 * q^35 + 4 * q^37 + 24 * q^38 - 28 * q^40 + 40 * q^43 - 64 * q^44 + 16 * q^46 + 24 * q^47 - 16 * q^50 + 36 * q^52 - 40 * q^53 - 16 * q^55 - 28 * q^58 - 80 * q^59 - 32 * q^61 + 16 * q^62 + 48 * q^65 - 48 * q^67 + 32 * q^68 + 8 * q^70 - 20 * q^73 - 64 * q^74 + 16 * q^76 + 36 * q^80 + 20 * q^82 + 24 * q^83 - 56 * q^89 + 8 * q^92 + 56 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more