LMFDB - Embedded newform 3150.2.bf.e.1601.8

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.8
Character	$\chi$	$=$	3150.1601
Dual form			3150.2.bf.e.1151.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.43194 + 1.04195i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.43194 + 1.04195i) q^{7} +1.00000i q^{8} +(1.38605 - 0.800236i) q^{11} -0.770726i q^{13} +(1.58515 + 2.11833i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.76107 + 3.05027i) q^{17} +(3.06818 + 1.77141i) q^{19} +1.60047 q^{22} +(-2.79527 - 1.61385i) q^{23} +(0.385363 - 0.667468i) q^{26} +(0.313613 + 2.62710i) q^{28} +0.700774i q^{29} +(1.13725 - 0.656589i) q^{31} +(-0.866025 + 0.500000i) q^{32} +3.52215i q^{34} +(0.457320 - 0.792101i) q^{37} +(1.77141 + 3.06818i) q^{38} +4.88167 q^{41} +9.26963 q^{43} +(1.38605 + 0.800236i) q^{44} +(-1.61385 - 2.79527i) q^{46} +(-1.33635 + 2.31462i) q^{47} +(4.82867 + 5.06793i) q^{49} +(0.667468 - 0.385363i) q^{52} +(-8.04572 + 4.64520i) q^{53} +(-1.04195 + 2.43194i) q^{56} +(-0.350387 + 0.606888i) q^{58} +(1.56198 + 2.70542i) q^{59} +(-9.43214 - 5.44565i) q^{61} +1.31318 q^{62} -1.00000 q^{64} +(3.40818 + 5.90314i) q^{67} +(-1.76107 + 3.05027i) q^{68} -6.47930i q^{71} +(9.55835 - 5.51852i) q^{73} +(0.792101 - 0.457320i) q^{74} +3.54282i q^{76} +(4.20460 - 0.501930i) q^{77} +(-1.45086 + 2.51296i) q^{79} +(4.22765 + 2.44083i) q^{82} -11.9777 q^{83} +(8.02773 + 4.63481i) q^{86} +(0.800236 + 1.38605i) q^{88} +(4.40369 - 7.62742i) q^{89} +(0.803059 - 1.87436i) q^{91} -3.22770i q^{92} +(-2.31462 + 1.33635i) q^{94} +5.31224i q^{97} +(1.64779 + 6.80329i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 4 q^{7}+O(q^{10}) $ 24 * q + 12 * q^4 + 4 * q^7	$ 24 q + 12 q^{4} + 4 q^{7} - 12 q^{16} + 12 q^{19} - 4 q^{28} - 28 q^{37} - 96 q^{43} - 8 q^{46} - 52 q^{49} + 12 q^{52} - 8 q^{58} - 12 q^{61} - 24 q^{64} + 4 q^{67} + 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) $ 24 * q + 12 * q^4 + 4 * q^7 - 12 * q^16 + 12 * q^19 - 4 * q^28 - 28 * q^37 - 96 * q^43 - 8 * q^46 - 52 * q^49 + 12 * q^52 - 8 * q^58 - 12 * q^61 - 24 * q^64 + 4 * q^67 + 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

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
$7$	2.43194	+	1.04195i	0.919187	+	0.393821i
$7$	2.43194	+	1.04195i	0.919187	+	0.393821i
$8$			1.00000i			0.353553i
$9$		0			0
$10$		0			0
$11$	1.38605	−	0.800236i	0.417910	−	0.241280i	−0.276273	−	0.961079i	$-0.589099\pi$
$11$	1.38605	−	0.800236i	0.417910	−	0.241280i	0.694183	+	0.719799i	$0.255766\pi$
$12$		0			0
$13$		−	0.770726i		−	0.213761i	−0.994272	−	0.106880i	$-0.965914\pi$
$13$		−	0.770726i		−	0.213761i	0.994272	−	0.106880i	$-0.0340862\pi$
$14$	1.58515	+	2.11833i	0.423648	+	0.566147i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.76107	+	3.05027i	0.427123	+	0.739799i	0.996616	−	0.0821974i	$-0.0261938\pi$
$17$	1.76107	+	3.05027i	0.427123	+	0.739799i	−0.569493	+	0.821996i	$0.692860\pi$
$18$		0			0
$19$	3.06818	+	1.77141i	0.703888	+	0.406390i	0.808794	−	0.588092i	$-0.200121\pi$
$19$	3.06818	+	1.77141i	0.703888	+	0.406390i	−0.104906	+	0.994482i	$0.533454\pi$
$20$		0			0
$21$		0			0
$22$	1.60047			0.341222
$23$	−2.79527	−	1.61385i	−0.582854	−	0.336511i	0.179413	−	0.983774i	$-0.442580\pi$
$23$	−2.79527	−	1.61385i	−0.582854	−	0.336511i	−0.762267	+	0.647263i	$0.775914\pi$
$24$		0			0
$25$		0			0
$26$	0.385363	−	0.667468i	0.0755759	−	0.130901i
$27$		0			0
$28$	0.313613	+	2.62710i	0.0592674	+	0.496475i
$29$			0.700774i			0.130131i	0.997881	+	0.0650653i	$0.0207256\pi$
$29$			0.700774i			0.130131i	−0.997881	+	0.0650653i	$0.979274\pi$
$30$		0			0
$31$	1.13725	−	0.656589i	0.204255	−	0.117927i	−0.394383	−	0.918946i	$-0.629042\pi$
$31$	1.13725	−	0.656589i	0.204255	−	0.117927i	0.598639	+	0.801019i	$0.295708\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			3.52215i			0.604043i
$35$		0			0
$36$		0			0
$37$	0.457320	−	0.792101i	0.0751829	−	0.130221i	−0.825983	−	0.563695i	$-0.809379\pi$
$37$	0.457320	−	0.792101i	0.0751829	−	0.130221i	0.901166	+	0.433475i	$0.142713\pi$
$38$	1.77141	+	3.06818i	0.287361	+	0.497724i
$39$		0			0
$40$		0			0
$41$	4.88167			0.762388			0.381194	−	0.924495i	$-0.375513\pi$
$41$	4.88167			0.762388			0.381194	+	0.924495i	$0.375513\pi$
$42$		0			0
$43$	9.26963			1.41361			0.706803	−	0.707411i	$-0.250137\pi$
$43$	9.26963			1.41361			0.706803	+	0.707411i	$0.250137\pi$
$44$	1.38605	+	0.800236i	0.208955	+	0.120640i
$45$		0			0
$46$	−1.61385	−	2.79527i	−0.237949	−	0.412140i
$47$	−1.33635	+	2.31462i	−0.194926	+	0.337623i	−0.946876	−	0.321598i	$-0.895780\pi$
$47$	−1.33635	+	2.31462i	−0.194926	+	0.337623i	0.751950	+	0.659220i	$0.229113\pi$
$48$		0			0
$49$	4.82867	+	5.06793i	0.689810	+	0.723990i
$50$		0			0
$51$		0			0
$52$	0.667468	−	0.385363i	0.0925612	−	0.0534402i
$53$	−8.04572	+	4.64520i	−1.10516	+	0.638067i	−0.937573	−	0.347789i	$-0.886932\pi$
$53$	−8.04572	+	4.64520i	−1.10516	+	0.638067i	−0.167592	+	0.985856i	$0.553599\pi$
$54$		0			0
$55$		0			0
$56$	−1.04195	+	2.43194i	−0.139237	+	0.324982i
$57$		0			0
$58$	−0.350387	+	0.606888i	−0.0460081	+	0.0796883i
$59$	1.56198	+	2.70542i	0.203352	+	0.352216i	0.949606	−	0.313445i	$-0.101483\pi$
$59$	1.56198	+	2.70542i	0.203352	+	0.352216i	−0.746254	+	0.665661i	$0.768150\pi$
$60$		0			0
$61$	−9.43214	−	5.44565i	−1.20766	−	0.697244i	−0.245414	−	0.969418i	$-0.578924\pi$
$61$	−9.43214	−	5.44565i	−1.20766	−	0.697244i	−0.962248	+	0.272175i	$0.912257\pi$
$62$	1.31318			0.166774
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	3.40818	+	5.90314i	0.416375	+	0.721183i	0.995572	−	0.0940048i	$-0.0299669\pi$
$67$	3.40818	+	5.90314i	0.416375	+	0.721183i	−0.579196	+	0.815188i	$0.696634\pi$
$68$	−1.76107	+	3.05027i	−0.213561	+	0.369899i
$69$		0			0
$70$		0			0
$71$		−	6.47930i		−	0.768951i	−0.923135	−	0.384475i	$-0.874382\pi$
$71$		−	6.47930i		−	0.768951i	0.923135	−	0.384475i	$-0.125618\pi$
$72$		0			0
$73$	9.55835	−	5.51852i	1.11872	−	0.645894i	0.177647	−	0.984094i	$-0.443152\pi$
$73$	9.55835	−	5.51852i	1.11872	−	0.645894i	0.941074	+	0.338201i	$0.109818\pi$
$74$	0.792101	−	0.457320i	0.0920799	−	0.0531623i
$75$		0			0
$76$			3.54282i			0.406390i
$77$	4.20460	−	0.501930i	0.479158	−	0.0572002i
$78$		0			0
$79$	−1.45086	+	2.51296i	−0.163234	+	0.282730i	−0.936027	−	0.351928i	$-0.885526\pi$
$79$	−1.45086	+	2.51296i	−0.163234	+	0.282730i	0.772792	+	0.634659i	$0.218859\pi$
$80$		0			0
$81$		0			0
$82$	4.22765	+	2.44083i	0.466865	+	0.269545i
$83$	−11.9777			−1.31472			−0.657361	−	0.753576i	$-0.728327\pi$
$83$	−11.9777			−1.31472			−0.657361	+	0.753576i	$0.728327\pi$
$84$		0			0
$85$		0			0
$86$	8.02773	+	4.63481i	0.865653	+	0.499785i
$87$		0			0
$88$	0.800236	+	1.38605i	0.0853055	+	0.147753i
$89$	4.40369	−	7.62742i	0.466791	−	0.808505i	−0.532490	−	0.846437i	$-0.678743\pi$
$89$	4.40369	−	7.62742i	0.466791	−	0.808505i	0.999280	+	0.0379313i	$0.0120768\pi$
$90$		0			0
$91$	0.803059	−	1.87436i	0.0841835	−	0.196486i
$92$		−	3.22770i		−	0.336511i
$93$		0			0
$94$	−2.31462	+	1.33635i	−0.238735	+	0.137834i
$95$		0			0
$96$		0			0
$97$			5.31224i			0.539376i	0.962948	+	0.269688i	$0.0869206\pi$
$97$			5.31224i			0.539376i	−0.962948	+	0.269688i	$0.913079\pi$
$98$	1.64779	+	6.80329i	0.166452	+	0.687236i
$99$		0			0
$100$		0			0
$101$	−4.62663	−	8.01356i	−0.460367	−	0.797379i	0.538612	−	0.842554i	$-0.318949\pi$
$101$	−4.62663	−	8.01356i	−0.460367	−	0.797379i	−0.998979	+	0.0451749i	$0.985615\pi$
$102$		0			0
$103$	13.7055	+	7.91290i	1.35045	+	0.779681i	0.988312	−	0.152444i	$-0.0487144\pi$
$103$	13.7055	+	7.91290i	1.35045	+	0.779681i	0.362136	+	0.932125i	$0.382048\pi$
$104$	0.770726			0.0755759
$105$		0			0
$106$	−9.29040			−0.902363
$107$	10.7514	+	6.20735i	1.03938	+	0.600087i	0.919658	−	0.392720i	$-0.128466\pi$
$107$	10.7514	+	6.20735i	1.03938	+	0.600087i	0.119724	+	0.992807i	$0.461799\pi$
$108$		0			0
$109$	5.51750	+	9.55659i	0.528480	+	0.915355i	0.999449	+	0.0332048i	$0.0105713\pi$
$109$	5.51750	+	9.55659i	0.528480	+	0.915355i	−0.470968	+	0.882150i	$0.656095\pi$
$110$		0			0
$111$		0			0
$112$	−2.11833	+	1.58515i	−0.200163	+	0.149782i
$113$			15.0301i			1.41391i	0.707256	+	0.706957i	$0.249933\pi$
$113$			15.0301i			1.41391i	−0.707256	+	0.706957i	$0.750067\pi$
$114$		0			0
$115$		0			0
$116$	−0.606888	+	0.350387i	−0.0563482	+	0.0325326i
$117$		0			0
$118$			3.12395i			0.287583i
$119$	1.10459	+	9.25303i	0.101258	+	0.848223i
$120$		0			0
$121$	−4.21924	+	7.30795i	−0.383568	+	0.664359i
$122$	−5.44565	−	9.43214i	−0.493026	−	0.853946i
$123$		0			0
$124$	1.13725	+	0.656589i	0.102128	+	0.0589634i
$125$		0			0
$126$		0			0
$127$	−2.66506			−0.236486			−0.118243	−	0.992985i	$-0.537726\pi$
$127$	−2.66506			−0.236486			−0.118243	+	0.992985i	$0.537726\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	7.10987	−	12.3147i	0.621192	−	1.07594i	−0.368071	−	0.929797i	$-0.619982\pi$
$131$	7.10987	−	12.3147i	0.621192	−	1.07594i	0.989264	−	0.146139i	$-0.0466848\pi$
$132$		0			0
$133$	5.61590	+	7.50486i	0.486960	+	0.650754i
$134$			6.81636i			0.588844i
$135$		0			0
$136$	−3.05027	+	1.76107i	−0.261558	+	0.151011i
$137$	−0.112698	+	0.0650662i	−0.00962843	+	0.00555898i	−0.504806	−	0.863233i	$-0.668436\pi$
$137$	−0.112698	+	0.0650662i	−0.00962843	+	0.00555898i	0.495178	+	0.868792i	$0.335103\pi$
$138$		0			0
$139$		−	3.63572i		−	0.308378i	−0.988041	−	0.154189i	$-0.950724\pi$
$139$		−	3.63572i		−	0.308378i	0.988041	−	0.154189i	$-0.0492765\pi$
$140$		0			0
$141$		0			0
$142$	3.23965	−	5.61123i	0.271865	−	0.470884i
$143$	−0.616762	−	1.06826i	−0.0515763	−	0.0893327i
$144$		0			0
$145$		0			0
$146$	11.0370			0.913432
$147$		0			0
$148$	0.914639			0.0751829
$149$	−2.53957	−	1.46622i	−0.208049	−	0.120117i	0.392355	−	0.919814i	$-0.371660\pi$
$149$	−2.53957	−	1.46622i	−0.208049	−	0.120117i	−0.600405	+	0.799696i	$0.704994\pi$
$150$		0			0
$151$	−3.56919	−	6.18201i	−0.290456	−	0.503085i	0.683461	−	0.729987i	$-0.260474\pi$
$151$	−3.56919	−	6.18201i	−0.290456	−	0.503085i	−0.973918	+	0.226902i	$0.927140\pi$
$152$	−1.77141	+	3.06818i	−0.143681	+	0.248862i
$153$		0			0
$154$	3.89225	+	1.66762i	0.313647	+	0.134380i
$155$		0			0
$156$		0			0
$157$	−12.3963	+	7.15702i	−0.989334	+	0.571192i	−0.905075	−	0.425252i	$-0.860186\pi$
$157$	−12.3963	+	7.15702i	−0.989334	+	0.571192i	−0.0842589	+	0.996444i	$0.526852\pi$
$158$	−2.51296	+	1.45086i	−0.199921	+	0.115424i
$159$		0			0
$160$		0			0
$161$	−5.11638	−	6.83732i	−0.403227	−	0.538857i
$162$		0			0
$163$	−3.60448	+	6.24313i	−0.282324	+	0.489000i	−0.971957	−	0.235159i	$-0.924439\pi$
$163$	−3.60448	+	6.24313i	−0.282324	+	0.489000i	0.689632	+	0.724160i	$0.257772\pi$
$164$	2.44083	+	4.22765i	0.190597	+	0.330124i
$165$		0			0
$166$	−10.3730	−	5.98884i	−0.805099	−	0.464824i
$167$	−13.8952			−1.07524			−0.537620	−	0.843187i	$-0.680677\pi$
$167$	−13.8952			−1.07524			−0.537620	+	0.843187i	$0.680677\pi$
$168$		0			0
$169$	12.4060			0.954306
$170$		0			0
$171$		0			0
$172$	4.63481	+	8.02773i	0.353401	+	0.612109i
$173$	1.18370	−	2.05023i	0.0899951	−	0.155876i	−0.817514	−	0.575909i	$-0.804648\pi$
$173$	1.18370	−	2.05023i	0.0899951	−	0.155876i	0.907509	+	0.420033i	$0.137982\pi$
$174$		0			0
$175$		0			0
$176$			1.60047i			0.120640i
$177$		0			0
$178$	7.62742	−	4.40369i	0.571700	−	0.330071i
$179$	−15.4837	+	8.93953i	−1.15731	+	0.668172i	−0.950657	−	0.310243i	$-0.899590\pi$
$179$	−15.4837	+	8.93953i	−1.15731	+	0.668172i	−0.206650	+	0.978415i	$0.566256\pi$
$180$		0			0
$181$		−	16.6673i		−	1.23887i	−0.785049	−	0.619434i	$-0.787362\pi$
$181$		−	16.6673i		−	1.23887i	0.785049	−	0.619434i	$-0.212638\pi$
$182$	1.63265	−	1.22171i	0.121020	−	0.0905594i
$183$		0			0
$184$	1.61385	−	2.79527i	0.118975	−	0.206070i
$185$		0			0
$186$		0			0
$187$	4.88187	+	2.81855i	0.356998	+	0.206113i
$188$	−2.67270			−0.194926
$189$		0			0
$190$		0			0
$191$	−21.4359	−	12.3760i	−1.55104	−	0.895496i	−0.998057	−	0.0623063i	$-0.980154\pi$
$191$	−21.4359	−	12.3760i	−1.55104	−	0.895496i	−0.552987	−	0.833190i	$-0.686512\pi$
$192$		0			0
$193$	6.28835	+	10.8917i	0.452645	+	0.784005i	0.998549	−	0.0538428i	$-0.0171470\pi$
$193$	6.28835	+	10.8917i	0.452645	+	0.784005i	−0.545904	+	0.837848i	$0.683814\pi$
$194$	−2.65612	+	4.60054i	−0.190698	+	0.330299i
$195$		0			0
$196$	−1.97462	+	6.71572i	−0.141044	+	0.479694i
$197$			19.7360i			1.40613i	0.711125	+	0.703066i	$0.248186\pi$
$197$			19.7360i			1.40613i	−0.711125	+	0.703066i	$0.751814\pi$
$198$		0			0
$199$	9.82275	−	5.67117i	0.696316	−	0.402018i	−0.109658	−	0.993969i	$-0.534975\pi$
$199$	9.82275	−	5.67117i	0.696316	−	0.402018i	0.805974	+	0.591951i	$0.201642\pi$
$200$		0			0
$201$		0			0
$202$		−	9.25326i		−	0.651057i
$203$	−0.730173	+	1.70424i	−0.0512481	+	0.119614i
$204$		0			0
$205$		0			0
$206$	7.91290	+	13.7055i	0.551318	+	0.954911i
$207$		0			0
$208$	0.667468	+	0.385363i	0.0462806	+	0.0267201i
$209$	5.67019			0.392215
$210$		0			0
$211$	16.0647			1.10594			0.552970	−	0.833201i	$-0.313494\pi$
$211$	16.0647			1.10594			0.552970	+	0.833201i	$0.313494\pi$
$212$	−8.04572	−	4.64520i	−0.552582	−	0.319034i
$213$		0			0
$214$	6.20735	+	10.7514i	0.424326	+	0.734954i
$215$		0			0
$216$		0			0
$217$	3.44985	−	0.411830i	0.234191	−	0.0279569i
$218$			11.0350i			0.747384i
$219$		0			0
$220$		0			0
$221$	2.35092	−	1.35730i	0.158140	−	0.0913022i
$222$		0			0
$223$		−	2.00917i		−	0.134544i	−0.997735	−	0.0672720i	$-0.978570\pi$
$223$		−	2.00917i		−	0.134544i	0.997735	−	0.0672720i	$-0.0214295\pi$
$224$	−2.62710	+	0.313613i	−0.175530	+	0.0209542i
$225$		0			0
$226$	−7.51506	+	13.0165i	−0.499894	+	0.865842i
$227$	−1.95288	−	3.38249i	−0.129617	−	0.224504i	0.793911	−	0.608034i	$-0.208042\pi$
$227$	−1.95288	−	3.38249i	−0.129617	−	0.224504i	−0.923528	+	0.383530i	$0.874708\pi$
$228$		0			0
$229$	11.5904	+	6.69174i	0.765918	+	0.442203i	0.831416	−	0.555650i	$-0.187530\pi$
$229$	11.5904	+	6.69174i	0.765918	+	0.442203i	−0.0654987	+	0.997853i	$0.520864\pi$
$230$		0			0
$231$		0			0
$232$	−0.700774			−0.0460081
$233$	−8.91673	−	5.14808i	−0.584154	−	0.337262i	0.178628	−	0.983917i	$-0.442834\pi$
$233$	−8.91673	−	5.14808i	−0.584154	−	0.337262i	−0.762783	+	0.646655i	$0.776167\pi$
$234$		0			0
$235$		0			0
$236$	−1.56198	+	2.70542i	−0.101676	+	0.176108i
$237$		0			0
$238$	−3.66991	+	8.56565i	−0.237885	+	0.555229i
$239$			17.5460i			1.13495i	0.823389	+	0.567477i	$0.192080\pi$
$239$			17.5460i			1.13495i	−0.823389	+	0.567477i	$0.807920\pi$
$240$		0			0
$241$	8.66068	−	5.00024i	0.557883	−	0.322094i	−0.194412	−	0.980920i	$-0.562280\pi$
$241$	8.66068	−	5.00024i	0.557883	−	0.322094i	0.752295	+	0.658826i	$0.228947\pi$
$242$	−7.30795	+	4.21924i	−0.469773	+	0.271223i
$243$		0			0
$244$		−	10.8913i		−	0.697244i
$245$		0			0
$246$		0			0
$247$	1.36527	−	2.36472i	0.0868702	−	0.150464i
$248$	0.656589	+	1.13725i	0.0416935	+	0.0722152i
$249$		0			0
$250$		0			0
$251$	3.55412			0.224334			0.112167	−	0.993689i	$-0.464221\pi$
$251$	3.55412			0.224334			0.112167	+	0.993689i	$0.464221\pi$
$252$		0			0
$253$	−5.16584			−0.324774
$254$	−2.30801	−	1.33253i	−0.144818	−	0.0836105i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.55507	+	6.15756i	−0.221759	+	0.384098i	−0.955342	−	0.295502i	$-0.904513\pi$
$257$	−3.55507	+	6.15756i	−0.221759	+	0.384098i	0.733583	+	0.679600i	$0.237847\pi$
$258$		0			0
$259$	1.93751	−	1.44984i	0.120391	−	0.0900885i
$260$		0			0
$261$		0			0
$262$	12.3147	−	7.10987i	0.760802	−	0.439249i
$263$	24.7253	−	14.2752i	1.52463	−	0.880245i	0.525054	−	0.851069i	$-0.324045\pi$
$263$	24.7253	−	14.2752i	1.52463	−	0.880245i	0.999574	−	0.0291760i	$-0.00928833\pi$
$264$		0			0
$265$		0			0
$266$	1.11108	+	9.30735i	0.0681245	+	0.570670i
$267$		0			0
$268$	−3.40818	+	5.90314i	−0.208188	+	0.360592i
$269$	−12.9628	−	22.4523i	−0.790359	−	1.36894i	−0.925745	−	0.378149i	$-0.876561\pi$
$269$	−12.9628	−	22.4523i	−0.790359	−	1.36894i	0.135386	−	0.990793i	$-0.456772\pi$
$270$		0			0
$271$	−24.1643	−	13.9513i	−1.46788	−	0.847479i	−0.468523	−	0.883451i	$-0.655214\pi$
$271$	−24.1643	−	13.9513i	−1.46788	−	0.847479i	−0.999353	+	0.0359726i	$0.988547\pi$
$272$	−3.52215			−0.213561
$273$		0			0
$274$	−0.130132			−0.00786158
$275$		0			0
$276$		0			0
$277$	5.18485	+	8.98042i	0.311527	+	0.539581i	0.978693	−	0.205328i	$-0.0658261\pi$
$277$	5.18485	+	8.98042i	0.311527	+	0.539581i	−0.667166	+	0.744909i	$0.732493\pi$
$278$	1.81786	−	3.14863i	0.109028	−	0.188842i
$279$		0			0
$280$		0			0
$281$		−	21.0412i		−	1.25521i	−0.778530	−	0.627607i	$-0.784035\pi$
$281$		−	21.0412i		−	1.25521i	0.778530	−	0.627607i	$-0.215965\pi$
$282$		0			0
$283$	23.7046	−	13.6859i	1.40909	−	0.813541i	0.413794	−	0.910371i	$-0.364203\pi$
$283$	23.7046	−	13.6859i	1.40909	−	0.813541i	0.995301	+	0.0968293i	$0.0308701\pi$
$284$	5.61123	−	3.23965i	0.332965	−	0.192238i
$285$		0			0
$286$		−	1.23352i		−	0.0729399i
$287$	11.8719	+	5.08646i	0.700777	+	0.300244i
$288$		0			0
$289$	2.29724	−	3.97894i	0.135132	−	0.234055i
$290$		0			0
$291$		0			0
$292$	9.55835	+	5.51852i	0.559360	+	0.322947i
$293$	−16.9059			−0.987654			−0.493827	−	0.869560i	$-0.664402\pi$
$293$	−16.9059			−0.987654			−0.493827	+	0.869560i	$0.664402\pi$
$294$		0			0
$295$		0			0
$296$	0.792101	+	0.457320i	0.0460399	+	0.0265812i
$297$		0			0
$298$	−1.46622	−	2.53957i	−0.0849358	−	0.147113i
$299$	−1.24384	+	2.15439i	−0.0719328	+	0.124591i
$300$		0			0
$301$	22.5432	+	9.65851i	1.29937	+	0.556707i
$302$		−	7.13837i		−	0.410767i
$303$		0			0
$304$	−3.06818	+	1.77141i	−0.175972	+	0.101597i
$305$		0			0
$306$		0			0
$307$		−	14.0139i		−	0.799813i	−0.916556	−	0.399906i	$-0.869043\pi$
$307$		−	14.0139i		−	0.799813i	0.916556	−	0.399906i	$-0.130957\pi$
$308$	2.53698	+	3.39032i	0.144558	+	0.193182i
$309$		0			0
$310$		0			0
$311$	6.72211	+	11.6430i	0.381176	+	0.660216i	0.991231	−	0.132143i	$-0.0421859\pi$
$311$	6.72211	+	11.6430i	0.381176	+	0.660216i	−0.610055	+	0.792359i	$0.708853\pi$
$312$		0			0
$313$	−3.68760	−	2.12904i	−0.208436	−	0.120340i	0.392149	−	0.919902i	$-0.371732\pi$
$313$	−3.68760	−	2.12904i	−0.208436	−	0.120340i	−0.600584	+	0.799562i	$0.705065\pi$
$314$	−14.3140			−0.807788
$315$		0			0
$316$	−2.90172			−0.163234
$317$	0.171111	+	0.0987910i	0.00961055	+	0.00554866i	0.504798	−	0.863238i	$-0.331567\pi$
$317$	0.171111	+	0.0987910i	0.00961055	+	0.00554866i	−0.495187	+	0.868786i	$0.664900\pi$
$318$		0			0
$319$	0.560785	+	0.971308i	0.0313979	+	0.0543828i
$320$		0			0
$321$		0			0
$322$	−1.01225	−	8.47948i	−0.0564105	−	0.472543i
$323$			12.4783i			0.694314i
$324$		0			0
$325$		0			0
$326$	−6.24313	+	3.60448i	−0.345775	+	0.199633i
$327$		0			0
$328$			4.88167i			0.269545i
$329$	−5.66165	+	4.23662i	−0.312137	+	0.233572i
$330$		0			0
$331$	−2.29740	+	3.97922i	−0.126277	+	0.218718i	−0.922231	−	0.386639i	$-0.873636\pi$
$331$	−2.29740	+	3.97922i	−0.126277	+	0.218718i	0.795955	+	0.605356i	$0.206969\pi$
$332$	−5.98884	−	10.3730i	−0.328680	−	0.569291i
$333$		0			0
$334$	−12.0336	−	6.94758i	−0.658447	−	0.380155i
$335$		0			0
$336$		0			0
$337$	−6.05076			−0.329606			−0.164803	−	0.986327i	$-0.552699\pi$
$337$	−6.05076			−0.329606			−0.164803	+	0.986327i	$0.552699\pi$
$338$	10.7439	+	6.20299i	0.584391	+	0.337398i
$339$		0			0
$340$		0			0
$341$	1.05085	−	1.82013i	0.0569069	−	0.0985656i
$342$		0			0
$343$	6.46250	+	17.3562i	0.348942	+	0.937144i
$344$			9.26963i			0.499785i
$345$		0			0
$346$	2.05023	−	1.18370i	0.110221	−	0.0636362i
$347$	−2.75573	+	1.59102i	−0.147935	+	0.0854104i	−0.572140	−	0.820156i	$-0.693887\pi$
$347$	−2.75573	+	1.59102i	−0.147935	+	0.0854104i	0.424205	+	0.905566i	$0.360553\pi$
$348$		0			0
$349$		−	29.0573i		−	1.55540i	−0.628636	−	0.777700i	$-0.716386\pi$
$349$		−	29.0573i		−	1.55540i	0.628636	−	0.777700i	$-0.283614\pi$
$350$		0			0
$351$		0			0
$352$	−0.800236	+	1.38605i	−0.0426527	+	0.0738767i
$353$	3.83327	+	6.63942i	0.204025	+	0.353381i	0.949822	−	0.312792i	$-0.101264\pi$
$353$	3.83327	+	6.63942i	0.204025	+	0.353381i	−0.745797	+	0.666173i	$0.767931\pi$
$354$		0			0
$355$		0			0
$356$	8.80739			0.466791
$357$		0			0
$358$	−17.8791			−0.944938
$359$	−19.6694	−	11.3561i	−1.03811	−	0.599353i	−0.118812	−	0.992917i	$-0.537909\pi$
$359$	−19.6694	−	11.3561i	−1.03811	−	0.599353i	−0.919297	+	0.393564i	$0.871242\pi$
$360$		0			0
$361$	−3.22420	−	5.58447i	−0.169695	−	0.293920i
$362$	8.33363	−	14.4343i	0.438006	−	0.758649i
$363$		0			0
$364$	2.02477	−	0.241710i	0.106127	−	0.0126690i
$365$		0			0
$366$		0			0
$367$	−16.2368	+	9.37433i	−0.847555	+	0.489336i	−0.859825	−	0.510589i	$-0.829427\pi$
$367$	−16.2368	+	9.37433i	−0.847555	+	0.489336i	0.0122703	+	0.999925i	$0.496094\pi$
$368$	2.79527	−	1.61385i	0.145713	−	0.0841277i
$369$		0			0
$370$		0			0
$371$	−24.4068	+	2.91359i	−1.26714	+	0.151266i
$372$		0			0
$373$	−1.42057	+	2.46050i	−0.0735545	+	0.127400i	−0.900457	−	0.434946i	$-0.856768\pi$
$373$	−1.42057	+	2.46050i	−0.0735545	+	0.127400i	0.826902	+	0.562346i	$0.190101\pi$
$374$	2.81855	+	4.88187i	0.145744	+	0.252435i
$375$		0			0
$376$	−2.31462	−	1.33635i	−0.119368	−	0.0689169i
$377$	0.540105			0.0278168
$378$		0			0
$379$	−27.2750			−1.40102			−0.700510	−	0.713642i	$-0.747044\pi$
$379$	−27.2750			−1.40102			−0.700510	+	0.713642i	$0.747044\pi$
$380$		0			0
$381$		0			0
$382$	−12.3760	−	21.4359i	−0.633211	−	1.09675i
$383$	15.1175	−	26.1843i	0.772469	−	1.33796i	−0.163737	−	0.986504i	$-0.552355\pi$
$383$	15.1175	−	26.1843i	0.772469	−	1.33796i	0.936206	−	0.351451i	$-0.114312\pi$
$384$		0			0
$385$		0			0
$386$			12.5767i			0.640137i
$387$		0			0
$388$	−4.60054	+	2.65612i	−0.233557	+	0.134844i
$389$	4.29588	−	2.48023i	0.217810	−	0.125752i	−0.387126	−	0.922027i	$-0.626532\pi$
$389$	4.29588	−	2.48023i	0.217810	−	0.125752i	0.604936	+	0.796274i	$0.293199\pi$
$390$		0			0
$391$		−	11.3684i		−	0.574926i
$392$	−5.06793	+	4.82867i	−0.255969	+	0.243885i
$393$		0			0
$394$	−9.86800	+	17.0919i	−0.497143	+	0.861077i
$395$		0			0
$396$		0			0
$397$	12.6477	+	7.30213i	0.634768	+	0.366483i	0.782596	−	0.622530i	$-0.213895\pi$
$397$	12.6477	+	7.30213i	0.634768	+	0.366483i	−0.147828	+	0.989013i	$0.547228\pi$
$398$	11.3423			0.568540
$399$		0			0
$400$		0			0
$401$	−17.5622	−	10.1395i	−0.877014	−	0.506345i	−0.00734158	−	0.999973i	$-0.502337\pi$
$401$	−17.5622	−	10.1395i	−0.877014	−	0.506345i	−0.869673	+	0.493629i	$0.835670\pi$
$402$		0			0
$403$	−0.506050	−	0.876505i	−0.0252082	−	0.0436618i
$404$	4.62663	−	8.01356i	0.230183	−	0.398689i
$405$		0			0
$406$	−1.48447	+	1.11083i	−0.0736730	+	0.0551296i
$407$		−	1.46385i		−	0.0725606i
$408$		0			0
$409$	4.26877	−	2.46458i	0.211077	−	0.121865i	−0.390735	−	0.920503i	$-0.627779\pi$
$409$	4.26877	−	2.46458i	0.211077	−	0.121865i	0.601812	+	0.798638i	$0.294446\pi$
$410$		0			0
$411$		0			0
$412$			15.8258i			0.779681i
$413$	0.979714	+	8.20693i	0.0482086	+	0.403837i
$414$		0			0
$415$		0			0
$416$	0.385363	+	0.667468i	0.0188940	+	0.0327253i
$417$		0			0
$418$	4.91053	+	2.83510i	0.240182	+	0.138669i
$419$	−24.0686			−1.17583			−0.587913	−	0.808924i	$-0.700050\pi$
$419$	−24.0686			−1.17583			−0.587913	+	0.808924i	$0.700050\pi$
$420$		0			0
$421$	16.0657			0.782995			0.391498	−	0.920179i	$-0.371957\pi$
$421$	16.0657			0.782995			0.391498	+	0.920179i	$0.371957\pi$
$422$	13.9125	+	8.03236i	0.677248	+	0.391009i
$423$		0			0
$424$	−4.64520	−	8.04572i	−0.225591	−	0.390735i
$425$		0			0
$426$		0			0
$427$	−17.2643	−	23.0713i	−0.835478	−	1.11650i
$428$			12.4147i			0.600087i
$429$		0			0
$430$		0			0
$431$	−0.373691	+	0.215751i	−0.0180001	+	0.0103923i	−0.508973	−	0.860782i	$-0.669975\pi$
$431$	−0.373691	+	0.215751i	−0.0180001	+	0.0103923i	0.490973	+	0.871175i	$0.336641\pi$
$432$		0			0
$433$		−	30.5287i		−	1.46711i	−0.679628	−	0.733557i	$-0.737859\pi$
$433$		−	30.5287i		−	1.46711i	0.679628	−	0.733557i	$-0.262141\pi$
$434$	3.19357	+	1.36827i	0.153296	+	0.0656790i
$435$		0			0
$436$	−5.51750	+	9.55659i	−0.264240	+	0.457677i
$437$	−5.71759	−	9.90315i	−0.273509	−	0.473732i
$438$		0			0
$439$	−32.9059	−	18.9982i	−1.57051	−	0.906735i	−0.996106	−	0.0881648i	$-0.971900\pi$
$439$	−32.9059	−	18.9982i	−1.57051	−	0.906735i	−0.574406	−	0.818571i	$-0.694767\pi$
$440$		0			0
$441$		0			0
$442$	2.71461			0.129121
$443$	−20.1789	−	11.6503i	−0.958728	−	0.553522i	−0.0629464	−	0.998017i	$-0.520050\pi$
$443$	−20.1789	−	11.6503i	−0.958728	−	0.553522i	−0.895781	+	0.444495i	$0.853383\pi$
$444$		0			0
$445$		0			0
$446$	1.00459	−	1.73999i	0.0475685	−	0.0823911i
$447$		0			0
$448$	−2.43194	−	1.04195i	−0.114898	−	0.0492276i
$449$		−	21.9119i		−	1.03409i	−0.855960	−	0.517043i	$-0.827033\pi$
$449$		−	21.9119i		−	1.03409i	0.855960	−	0.517043i	$-0.172967\pi$
$450$		0			0
$451$	6.76623	−	3.90648i	0.318609	−	0.183949i
$452$	−13.0165	+	7.51506i	−0.612243	+	0.353479i
$453$		0			0
$454$		−	3.90576i		−	0.183306i
$455$		0			0
$456$		0			0
$457$	19.6821	−	34.0904i	0.920691	−	1.59468i	0.122341	−	0.992488i	$-0.460960\pi$
$457$	19.6821	−	34.0904i	0.920691	−	1.59468i	0.798349	−	0.602195i	$-0.205707\pi$
$458$	6.69174	+	11.5904i	0.312685	+	0.541586i
$459$		0			0
$460$		0			0
$461$	2.35282			0.109582			0.0547909	−	0.998498i	$-0.482551\pi$
$461$	2.35282			0.109582			0.0547909	+	0.998498i	$0.482551\pi$
$462$		0			0
$463$	2.24550			0.104357			0.0521787	−	0.998638i	$-0.483383\pi$
$463$	2.24550			0.104357			0.0521787	+	0.998638i	$0.483383\pi$
$464$	−0.606888	−	0.350387i	−0.0281741	−	0.0162663i
$465$		0			0
$466$	−5.14808	−	8.91673i	−0.238480	−	0.413059i
$467$	−16.0931	+	27.8740i	−0.744699	+	1.28986i	0.205636	+	0.978628i	$0.434074\pi$
$467$	−16.0931	+	27.8740i	−0.744699	+	1.28986i	−0.950335	+	0.311228i	$0.899260\pi$
$468$		0			0
$469$	2.13770	+	17.9072i	0.0987099	+	0.826880i
$470$		0			0
$471$		0			0
$472$	−2.70542	+	1.56198i	−0.124527	+	0.0718958i
$473$	12.8482	−	7.41789i	0.590759	−	0.341075i
$474$		0			0
$475$		0			0
$476$	−7.46106	+	5.58312i	−0.341977	+	0.255902i
$477$		0			0
$478$	−8.77298	+	15.1952i	−0.401267	+	0.695014i
$479$	−3.30556	−	5.72539i	−0.151035	−	0.261600i	0.780573	−	0.625064i	$-0.214927\pi$
$479$	−3.30556	−	5.72539i	−0.151035	−	0.261600i	−0.931608	+	0.363464i	$0.881594\pi$
$480$		0			0
$481$	−0.610493	−	0.352468i	−0.0278361	−	0.0160712i
$482$	10.0005			0.455510
$483$		0			0
$484$	−8.43849			−0.383568
$485$		0			0
$486$		0			0
$487$	2.88167	+	4.99120i	0.130581	+	0.226173i	0.923901	−	0.382632i	$-0.124982\pi$
$487$	2.88167	+	4.99120i	0.130581	+	0.226173i	−0.793320	+	0.608805i	$0.791649\pi$
$488$	5.44565	−	9.43214i	0.246513	−	0.426973i
$489$		0			0
$490$		0			0
$491$			2.90529i			0.131114i	0.997849	+	0.0655570i	$0.0208824\pi$
$491$			2.90529i			0.131114i	−0.997849	+	0.0655570i	$0.979118\pi$
$492$		0			0
$493$	−2.13755	+	1.23411i	−0.0962704	+	0.0555817i
$494$	2.36472	−	1.36527i	0.106394	−	0.0614265i
$495$		0			0
$496$			1.31318i			0.0589634i
$497$	6.75111	−	15.7573i	0.302829	−	0.706810i
$498$		0			0
$499$	−1.14104	+	1.97634i	−0.0510800	+	0.0884732i	−0.890435	−	0.455111i	$-0.849600\pi$
$499$	−1.14104	+	1.97634i	−0.0510800	+	0.0884732i	0.839355	+	0.543584i	$0.182933\pi$
$500$		0			0
$501$		0			0
$502$	3.07796	+	1.77706i	0.137376	+	0.0793141i
$503$	−1.32664			−0.0591520			−0.0295760	−	0.999563i	$-0.509416\pi$
$503$	−1.32664			−0.0591520			−0.0295760	+	0.999563i	$0.509416\pi$
$504$		0			0
$505$		0			0
$506$	−4.47375	−	2.58292i	−0.198882	−	0.114825i
$507$		0			0
$508$	−1.33253	−	2.30801i	−0.0591215	−	0.102402i
$509$	21.5053	−	37.2483i	0.953207	−	1.65100i	0.214788	−	0.976661i	$-0.431094\pi$
$509$	21.5053	−	37.2483i	0.953207	−	1.65100i	0.738419	−	0.674342i	$-0.235573\pi$
$510$		0			0
$511$	28.9954	−	3.46136i	1.28268	−	0.153122i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−6.15756	+	3.55507i	−0.271598	+	0.156807i
$515$		0			0
$516$		0			0
$517$			4.27758i			0.188128i
$518$	2.40285	−	0.286843i	0.105575	−	0.0126032i
$519$		0			0
$520$		0			0
$521$	19.8838	+	34.4397i	0.871124	+	1.50883i	0.860835	+	0.508884i	$0.169942\pi$
$521$	19.8838	+	34.4397i	0.871124	+	1.50883i	0.0102890	+	0.999947i	$0.496725\pi$
$522$		0			0
$523$	−34.4338	−	19.8804i	−1.50568	−	0.869307i	−0.999978	−	0.00660128i	$-0.997899\pi$
$523$	−34.4338	−	19.8804i	−1.50568	−	0.869307i	−0.505706	−	0.862706i	$-0.668768\pi$
$524$	14.2197			0.621192
$525$		0			0
$526$	28.5503			1.24485
$527$	4.00555	+	2.31260i	0.174484	+	0.100739i
$528$		0			0
$529$	−6.29098	−	10.8963i	−0.273521	−	0.473752i
$530$		0			0
$531$		0			0
$532$	−3.69145	+	8.61594i	−0.160045	+	0.373548i
$533$		−	3.76242i		−	0.162969i
$534$		0			0
$535$		0			0
$536$	−5.90314	+	3.40818i	−0.254977	+	0.147211i
$537$		0			0
$538$		−	25.9257i		−	1.11774i
$539$	10.7483	+	3.16033i	0.462963	+	0.136125i
$540$		0			0
$541$	−10.1006	+	17.4947i	−0.434258	+	0.752157i	−0.997235	−	0.0743161i	$-0.976323\pi$
$541$	−10.1006	+	17.4947i	−0.434258	+	0.752157i	0.562977	+	0.826473i	$0.309656\pi$
$542$	−13.9513	−	24.1643i	−0.599258	−	1.03795i
$543$		0			0
$544$	−3.05027	−	1.76107i	−0.130779	−	0.0755054i
$545$		0			0
$546$		0			0
$547$	−34.5631			−1.47781			−0.738905	−	0.673810i	$-0.764657\pi$
$547$	−34.5631			−1.47781			−0.738905	+	0.673810i	$0.764657\pi$
$548$	−0.112698	−	0.0650662i	−0.00481422	−	0.00277949i
$549$		0			0
$550$		0			0
$551$	−1.24136	+	2.15010i	−0.0528837	+	0.0915973i
$552$		0			0
$553$	−6.14679	+	4.59965i	−0.261388	+	0.195597i
$554$			10.3697i			0.440566i
$555$		0			0
$556$	3.14863	−	1.81786i	0.133532	−	0.0770945i
$557$	28.1278	−	16.2396i	1.19181	−	0.688094i	0.233096	−	0.972454i	$-0.425114\pi$
$557$	28.1278	−	16.2396i	1.19181	−	0.688094i	0.958718	+	0.284360i	$0.0917811\pi$
$558$		0			0
$559$		−	7.14434i		−	0.302173i
$560$		0			0
$561$		0			0
$562$	10.5206	−	18.2222i	0.443785	−	0.768658i
$563$	−7.19395	−	12.4603i	−0.303189	−	0.525139i	0.673668	−	0.739035i	$-0.264718\pi$
$563$	−7.19395	−	12.4603i	−0.303189	−	0.525139i	−0.976856	+	0.213896i	$0.931385\pi$
$564$		0			0
$565$		0			0
$566$	27.3718			1.15052
$567$		0			0
$568$	6.47930			0.271865
$569$	6.84504	+	3.95199i	0.286959	+	0.165676i	0.636570	−	0.771219i	$-0.280353\pi$
$569$	6.84504	+	3.95199i	0.286959	+	0.165676i	−0.349611	+	0.936895i	$0.613686\pi$
$570$		0			0
$571$	18.3198	+	31.7309i	0.766661	+	1.32789i	0.939364	+	0.342921i	$0.111416\pi$
$571$	18.3198	+	31.7309i	0.766661	+	1.32789i	−0.172704	+	0.984974i	$0.555250\pi$
$572$	0.616762	−	1.06826i	0.0257881	−	0.0446664i
$573$		0			0
$574$	7.73815	+	10.3410i	0.322984	+	0.431624i
$575$		0			0
$576$		0			0
$577$	−20.2583	+	11.6961i	−0.843363	+	0.486916i	−0.858406	−	0.512971i	$-0.828545\pi$
$577$	−20.2583	+	11.6961i	−0.843363	+	0.486916i	0.0150431	+	0.999887i	$0.495211\pi$
$578$	3.97894	−	2.29724i	0.165502	−	0.0955527i
$579$		0			0
$580$		0			0
$581$	−29.1290	−	12.4802i	−1.20848	−	0.517765i
$582$		0			0
$583$	−7.43451	+	12.8770i	−0.307906	+	0.533309i
$584$	5.51852	+	9.55835i	0.228358	+	0.395527i
$585$		0			0
$586$	−14.6409	−	8.45295i	−0.604812	−	0.349188i
$587$	−23.7776			−0.981407			−0.490704	−	0.871327i	$-0.663260\pi$
$587$	−23.7776			−0.981407			−0.490704	+	0.871327i	$0.663260\pi$
$588$		0			0
$589$	4.65236			0.191697
$590$		0			0
$591$		0			0
$592$	0.457320	+	0.792101i	0.0187957	+	0.0325551i
$593$	19.4555	−	33.6979i	0.798942	−	1.38381i	−0.121364	−	0.992608i	$-0.538727\pi$
$593$	19.4555	−	33.6979i	0.798942	−	1.38381i	0.920306	−	0.391200i	$-0.127940\pi$
$594$		0			0
$595$		0			0
$596$		−	2.93244i		−	0.120117i
$597$		0			0
$598$	−2.15439	+	1.24384i	−0.0880994	+	0.0508642i
$599$	3.09380	−	1.78621i	0.126409	−	0.0729824i	−0.435462	−	0.900207i	$-0.643415\pi$
$599$	3.09380	−	1.78621i	0.126409	−	0.0729824i	0.561871	+	0.827225i	$0.310082\pi$
$600$		0			0
$601$			21.3183i			0.869591i	0.900529	+	0.434795i	$0.143179\pi$
$601$			21.3183i			0.869591i	−0.900529	+	0.434795i	$0.856821\pi$
$602$	14.6937	+	19.6361i	0.598871	+	0.800308i
$603$		0			0
$604$	3.56919	−	6.18201i	0.145228	−	0.251543i
$605$		0			0
$606$		0			0
$607$	0.494331	+	0.285402i	0.0200643	+	0.0115841i	0.509999	−	0.860175i	$-0.329646\pi$
$607$	0.494331	+	0.285402i	0.0200643	+	0.0115841i	−0.489934	+	0.871759i	$0.662979\pi$
$608$	−3.54282			−0.143681
$609$		0			0
$610$		0			0
$611$	1.78394	+	1.02996i	0.0721705	+	0.0416676i
$612$		0			0
$613$	−17.0869	−	29.5954i	−0.690134	−	1.19535i	−0.971794	−	0.235833i	$-0.924218\pi$
$613$	−17.0869	−	29.5954i	−0.690134	−	1.19535i	0.281659	−	0.959514i	$-0.409115\pi$
$614$	7.00693	−	12.1364i	0.282777	−	0.489783i
$615$		0			0
$616$	0.501930	+	4.20460i	0.0202233	+	0.169408i
$617$		−	20.1713i		−	0.812066i	−0.913858	−	0.406033i	$-0.866912\pi$
$617$		−	20.1713i		−	0.812066i	0.913858	−	0.406033i	$-0.133088\pi$
$618$		0			0
$619$	13.9621	−	8.06104i	0.561186	−	0.324001i	−0.192436	−	0.981310i	$-0.561639\pi$
$619$	13.9621	−	8.06104i	0.561186	−	0.324001i	0.753621	+	0.657309i	$0.228305\pi$
$620$		0			0
$621$		0			0
$622$			13.4442i			0.539064i
$623$	18.6569	−	13.9610i	0.747474	−	0.559336i
$624$		0			0
$625$		0			0
$626$	−2.12904	−	3.68760i	−0.0850935	−	0.147386i
$627$		0			0
$628$	−12.3963	−	7.15702i	−0.494667	−	0.285596i
$629$	3.22149			0.128449
$630$		0			0
$631$	3.10655			0.123670			0.0618350	−	0.998086i	$-0.480305\pi$
$631$	3.10655			0.123670			0.0618350	+	0.998086i	$0.480305\pi$
$632$	−2.51296	−	1.45086i	−0.0999603	−	0.0577121i
$633$		0			0
$634$	0.0987910	+	0.171111i	0.00392349	+	0.00679569i
$635$		0			0
$636$		0			0
$637$	3.90598	−	3.72158i	0.154761	−	0.147454i
$638$			1.12157i			0.0444034i
$639$		0			0
$640$		0			0
$641$	18.9248	−	10.9262i	0.747483	−	0.431559i	−0.0773008	−	0.997008i	$-0.524630\pi$
$641$	18.9248	−	10.9262i	0.747483	−	0.431559i	0.824784	+	0.565448i	$0.191297\pi$
$642$		0			0
$643$		−	25.4873i		−	1.00512i	−0.864542	−	0.502560i	$-0.832391\pi$
$643$		−	25.4873i		−	1.00512i	0.864542	−	0.502560i	$-0.167609\pi$
$644$	3.36311	−	7.84957i	0.132525	−	0.309317i
$645$		0			0
$646$	−6.23917	+	10.8066i	−0.245477	+	0.425179i
$647$	24.0030	+	41.5745i	0.943657	+	1.63446i	0.758418	+	0.651768i	$0.225973\pi$
$647$	24.0030	+	41.5745i	0.943657	+	1.63446i	0.185239	+	0.982694i	$0.440694\pi$
$648$		0			0
$649$	4.32995	+	2.49990i	0.169966	+	0.0981296i
$650$		0			0
$651$		0			0
$652$	−7.20895			−0.282324
$653$	−39.8741	−	23.0213i	−1.56039	−	0.900894i	−0.997217	−	0.0745575i	$-0.976246\pi$
$653$	−39.8741	−	23.0213i	−1.56039	−	0.900894i	−0.563177	−	0.826336i	$-0.690421\pi$
$654$		0			0
$655$		0			0
$656$	−2.44083	+	4.22765i	−0.0952985	+	0.165062i
$657$		0			0
$658$	−7.02144	+	0.838194i	−0.273724	+	0.0326762i
$659$			14.8751i			0.579453i	0.957109	+	0.289727i	$0.0935644\pi$
$659$			14.8751i			0.579453i	−0.957109	+	0.289727i	$0.906436\pi$
$660$		0			0
$661$	36.7957	−	21.2440i	1.43119	−	0.826296i	0.433974	−	0.900925i	$-0.357111\pi$
$661$	36.7957	−	21.2440i	1.43119	−	0.826296i	0.997211	+	0.0746297i	$0.0237775\pi$
$662$	−3.97922	+	2.29740i	−0.154657	+	0.0892911i
$663$		0			0
$664$		−	11.9777i		−	0.464824i
$665$		0			0
$666$		0			0
$667$	1.13094	−	1.95885i	0.0437903	−	0.0758471i
$668$	−6.94758	−	12.0336i	−0.268810	−	0.465593i
$669$		0			0
$670$		0			0
$671$	−17.4312			−0.672925
$672$		0			0
$673$	−50.6101			−1.95088			−0.975439	−	0.220270i	$-0.929306\pi$
$673$	−50.6101			−1.95088			−0.975439	+	0.220270i	$0.929306\pi$
$674$	−5.24011	−	3.02538i	−0.201841	−	0.116533i
$675$		0			0
$676$	6.20299	+	10.7439i	0.238577	+	0.413227i
$677$	17.2777	−	29.9259i	0.664037	−	1.15015i	−0.315508	−	0.948923i	$-0.602175\pi$
$677$	17.2777	−	29.9259i	0.664037	−	1.15015i	0.979545	−	0.201223i	$-0.0644916\pi$
$678$		0			0
$679$	−5.53510	+	12.9191i	−0.212418	+	0.495788i
$680$		0			0
$681$		0			0
$682$	1.82013	−	1.05085i	0.0696964	−	0.0402392i
$683$	14.8563	−	8.57731i	0.568462	−	0.328202i	−0.188073	−	0.982155i	$-0.560224\pi$
$683$	14.8563	−	8.57731i	0.568462	−	0.328202i	0.756535	+	0.653953i	$0.226891\pi$
$684$		0			0
$685$		0			0
$686$	−3.08138	+	18.2621i	−0.117648	+	0.697251i
$687$		0			0
$688$	−4.63481	+	8.02773i	−0.176701	+	0.306055i
$689$	3.58017	+	6.20104i	0.136394	+	0.236241i
$690$		0			0
$691$	−30.8635	−	17.8190i	−1.17410	−	0.677869i	−0.219460	−	0.975622i	$-0.570429\pi$
$691$	−30.8635	−	17.8190i	−1.17410	−	0.677869i	−0.954643	+	0.297753i	$0.903763\pi$
$692$	2.36740			0.0899951
$693$		0			0
$694$	−3.18204			−0.120788
$695$		0			0
$696$		0			0
$697$	8.59697	+	14.8904i	0.325633	+	0.564014i
$698$	14.5286	−	25.1643i	0.549917	−	0.952484i
$699$		0			0
$700$		0			0
$701$			23.0808i			0.871751i	0.900007	+	0.435876i	$0.143561\pi$
$701$			23.0808i			0.871751i	−0.900007	+	0.435876i	$0.856439\pi$
$702$		0			0
$703$	2.80627	−	1.62020i	0.105841	−	0.0611071i
$704$	−1.38605	+	0.800236i	−0.0522387	+	0.0301600i
$705$		0			0
$706$			7.66655i			0.288534i
$707$	−2.90195	−	24.3092i	−0.109139	−	0.914243i
$708$		0			0
$709$	−4.08362	+	7.07303i	−0.153363	+	0.265633i	−0.932462	−	0.361268i	$-0.882344\pi$
$709$	−4.08362	+	7.07303i	−0.153363	+	0.265633i	0.779098	+	0.626902i	$0.215677\pi$
$710$		0			0
$711$		0			0
$712$	7.62742	+	4.40369i	0.285850	+	0.165035i
$713$	−4.23854			−0.158735
$714$		0			0
$715$		0			0
$716$	−15.4837	−	8.93953i	−0.578654	−	0.334086i
$717$		0			0
$718$	−11.3561	−	19.6694i	−0.423806	−	0.734054i
$719$	0.377499	−	0.653847i	0.0140783	−	0.0243844i	−0.858900	−	0.512143i	$-0.828852\pi$
$719$	0.377499	−	0.653847i	0.0140783	−	0.0243844i	0.872979	+	0.487758i	$0.162185\pi$
$720$		0			0
$721$	25.0862	+	33.5242i	0.934260	+	1.24851i
$722$		−	6.44839i		−	0.239984i
$723$		0			0
$724$	14.4343	−	8.33363i	0.536446	−	0.309717i
$725$		0			0
$726$		0			0
$727$		−	4.27807i		−	0.158665i	−0.996848	−	0.0793325i	$-0.974721\pi$
$727$		−	4.27807i		−	0.158665i	0.996848	−	0.0793325i	$-0.0252789\pi$
$728$	1.87436	+	0.803059i	0.0694684	+	0.0297634i
$729$		0			0
$730$		0			0
$731$	16.3245	+	28.2749i	0.603783	+	1.04578i
$732$		0			0
$733$	−29.0656	−	16.7810i	−1.07356	−	0.619822i	−0.144410	−	0.989518i	$-0.546129\pi$
$733$	−29.0656	−	16.7810i	−1.07356	−	0.619822i	−0.929153	+	0.369696i	$0.879462\pi$
$734$	−18.7487			−0.692026
$735$		0			0
$736$	3.22770			0.118975
$737$	9.44781	+	5.45470i	0.348015	+	0.200926i
$738$		0			0
$739$	−17.3726	−	30.0902i	−0.639060	−	1.10688i	−0.985639	−	0.168864i	$-0.945990\pi$
$739$	−17.3726	−	30.0902i	−0.639060	−	1.10688i	0.346579	−	0.938021i	$-0.387343\pi$
$740$		0			0
$741$		0			0
$742$	−22.5937	−	9.68015i	−0.829441	−	0.355369i
$743$		−	14.3040i		−	0.524762i	−0.964964	−	0.262381i	$-0.915492\pi$
$743$		−	14.3040i		−	0.524762i	0.964964	−	0.262381i	$-0.0845077\pi$
$744$		0			0
$745$		0			0
$746$	−2.46050	+	1.42057i	−0.0900854	+	0.0520109i
$747$		0			0
$748$			5.63710i			0.206113i
$749$	19.6791	+	26.2984i	0.719060	+	0.960923i
$750$		0			0
$751$	−21.3172	+	36.9224i	−0.777874	+	1.34732i	0.155290	+	0.987869i	$0.450369\pi$
$751$	−21.3172	+	36.9224i	−0.777874	+	1.34732i	−0.933165	+	0.359449i	$0.882965\pi$
$752$	−1.33635	−	2.31462i	−0.0487316	−	0.0844056i
$753$		0			0
$754$	0.467744	+	0.270052i	0.0170342	+	0.00983473i
$755$		0			0
$756$		0			0
$757$	−2.92253			−0.106221			−0.0531107	−	0.998589i	$-0.516914\pi$
$757$	−2.92253			−0.106221			−0.0531107	+	0.998589i	$0.516914\pi$
$758$	−23.6208	−	13.6375i	−0.857946	−	0.495336i
$759$		0			0
$760$		0			0
$761$	15.2447	−	26.4046i	0.552621	−	0.957167i	−0.445464	−	0.895300i	$-0.646961\pi$
$761$	15.2447	−	26.4046i	0.552621	−	0.957167i	0.998084	−	0.0618669i	$-0.0197054\pi$
$762$		0			0
$763$	3.46072	+	28.9900i	0.125287	+	1.04951i
$764$		−	24.7520i		−	0.895496i
$765$		0			0
$766$	26.1843	−	15.1175i	0.946077	−	0.546218i
$767$	2.08514	−	1.20386i	0.0752900	−	0.0434687i
$768$		0			0
$769$			42.7989i			1.54337i	0.636005	+	0.771685i	$0.280586\pi$
$769$			42.7989i			1.54337i	−0.636005	+	0.771685i	$0.719414\pi$
$770$		0			0
$771$		0			0
$772$	−6.28835	+	10.8917i	−0.226323	+	0.392002i
$773$	20.1996	+	34.9867i	0.726529	+	1.25838i	0.958342	+	0.285624i	$0.0922010\pi$
$773$	20.1996	+	34.9867i	0.726529	+	1.25838i	−0.231813	+	0.972760i	$0.574466\pi$
$774$		0			0
$775$		0			0
$776$	−5.31224			−0.190698
$777$		0			0
$778$	4.96045			0.177841
$779$	14.9778	+	8.64744i	0.536636	+	0.309827i
$780$		0			0
$781$	−5.18497	−	8.98062i	−0.185533	−	0.321352i
$782$	5.68421	−	9.84535i	0.203267	−	0.352069i
$783$		0			0
$784$	−6.80329	+	1.64779i	−0.242975	+	0.0588495i
$785$		0			0
$786$		0			0
$787$	−27.5015	+	15.8780i	−0.980323	+	0.565990i	−0.902368	−	0.430967i	$-0.858173\pi$
$787$	−27.5015	+	15.8780i	−0.980323	+	0.565990i	−0.0779556	+	0.996957i	$0.524839\pi$
$788$	−17.0919	+	9.86800i	−0.608873	+	0.351533i
$789$		0			0
$790$		0			0
$791$	−15.6607	+	36.5524i	−0.556829	+	1.29965i
$792$		0			0
$793$	−4.19710	+	7.26959i	−0.149043	+	0.258151i
$794$	7.30213	+	12.6477i	0.259143	+	0.448849i
$795$		0			0
$796$	9.82275	+	5.67117i	0.348158	+	0.201009i
$797$	2.25420			0.0798477			0.0399239	−	0.999203i	$-0.487288\pi$
$797$	2.25420			0.0798477			0.0399239	+	0.999203i	$0.487288\pi$
$798$		0			0
$799$	−9.41363			−0.333030
$800$		0			0
$801$		0			0
$802$	−10.1395	−	17.5622i	−0.358040	−	0.620143i
$803$	8.83223	−	15.2979i	0.311683	−	0.539850i
$804$		0			0
$805$		0			0
$806$		−	1.01210i		−	0.0356497i
$807$		0			0
$808$	8.01356	−	4.62663i	0.281916	−	0.162764i
$809$	43.6911	−	25.2251i	1.53610	−	0.886867i	0.537037	−	0.843559i	$-0.319544\pi$
$809$	43.6911	−	25.2251i	1.53610	−	0.886867i	0.999062	−	0.0433083i	$-0.0137898\pi$
$810$		0			0
$811$		−	12.2828i		−	0.431308i	−0.976470	−	0.215654i	$-0.930812\pi$
$811$		−	12.2828i		−	0.431308i	0.976470	−	0.215654i	$-0.0691883\pi$
$812$	−1.84100	+	0.219772i	−0.0646065	+	0.00771250i
$813$		0			0
$814$	0.731927	−	1.26774i	0.0256540	−	0.0444341i
$815$		0			0
$816$		0			0
$817$	28.4409	+	16.4203i	0.995020	+	0.574475i
$818$	4.92915			0.172344
$819$		0			0
$820$		0			0
$821$	−31.8702	−	18.4003i	−1.11228	−	0.642174i	−0.172859	−	0.984947i	$-0.555301\pi$
$821$	−31.8702	−	18.4003i	−1.11228	−	0.642174i	−0.939418	+	0.342773i	$0.888634\pi$
$822$		0			0
$823$	−8.06030	−	13.9608i	−0.280964	−	0.486644i	0.690658	−	0.723181i	$-0.257321\pi$
$823$	−8.06030	−	13.9608i	−0.280964	−	0.486644i	−0.971622	+	0.236537i	$0.923988\pi$
$824$	−7.91290	+	13.7055i	−0.275659	+	0.477455i
$825$		0			0
$826$	−3.25501	+	7.59727i	−0.113256	+	0.264343i
$827$			35.1713i			1.22302i	0.791235	+	0.611512i	$0.209438\pi$
$827$			35.1713i			1.22302i	−0.791235	+	0.611512i	$0.790562\pi$
$828$		0			0
$829$	3.89744	−	2.25019i	0.135364	−	0.0781522i	−0.430789	−	0.902453i	$-0.641765\pi$
$829$	3.89744	−	2.25019i	0.135364	−	0.0781522i	0.566152	+	0.824301i	$0.308431\pi$
$830$		0			0
$831$		0			0
$832$			0.770726i			0.0267201i
$833$	−6.95490	+	23.6537i	−0.240973	+	0.819554i
$834$		0			0
$835$		0			0
$836$	2.83510	+	4.91053i	0.0980539	+	0.169834i
$837$		0			0
$838$	−20.8440	−	12.0343i	−0.720044	−	0.415718i
$839$	37.7067			1.30178			0.650891	−	0.759172i	$-0.274396\pi$
$839$	37.7067			1.30178			0.650891	+	0.759172i	$0.274396\pi$
$840$		0			0
$841$	28.5089			0.983066
$842$	13.9133	+	8.03286i	0.479485	+	0.276831i
$843$		0			0
$844$	8.03236	+	13.9125i	0.276485	+	0.478886i
$845$		0			0
$846$		0			0
$847$	−17.8755	+	13.3762i	−0.614209	+	0.459613i
$848$		−	9.29040i		−	0.319034i
$849$		0			0
$850$		0			0
$851$	−2.55666	+	1.47609i	−0.0876413	+	0.0505997i
$852$		0			0
$853$		−	33.4928i		−	1.14677i	−0.819285	−	0.573386i	$-0.805629\pi$
$853$		−	33.4928i		−	1.14677i	0.819285	−	0.573386i	$-0.194371\pi$
$854$	−3.41566	−	28.6125i	−0.116881	−	0.979100i
$855$		0			0
$856$	−6.20735	+	10.7514i	−0.212163	+	0.367477i
$857$	−22.3650	−	38.7373i	−0.763973	−	1.32324i	−0.940788	−	0.338996i	$-0.889913\pi$
$857$	−22.3650	−	38.7373i	−0.763973	−	1.32324i	0.176815	−	0.984244i	$-0.443421\pi$
$858$		0			0
$859$	−26.4154	−	15.2509i	−0.901281	−	0.520355i	−0.0236654	−	0.999720i	$-0.507534\pi$
$859$	−26.4154	−	15.2509i	−0.901281	−	0.520355i	−0.877616	+	0.479365i	$0.840867\pi$
$860$		0			0
$861$		0			0
$862$	−0.431501			−0.0146970
$863$	20.5715	+	11.8770i	0.700262	+	0.404297i	0.807445	−	0.589943i	$-0.200850\pi$
$863$	20.5715	+	11.8770i	0.700262	+	0.404297i	−0.107183	+	0.994239i	$0.534183\pi$
$864$		0			0
$865$		0			0
$866$	15.2643	−	26.4386i	0.518703	−	0.898420i
$867$		0			0
$868$	2.08158	+	2.78174i	0.0706534	+	0.0944185i
$869$			4.64412i			0.157541i
$870$		0			0
$871$	4.54970	−	2.62677i	0.154161	−	0.0890047i
$872$	−9.55659	+	5.51750i	−0.323627	+	0.186846i
$873$		0			0
$874$		−	11.4352i		−	0.386800i
$875$		0			0
$876$		0			0
$877$	6.86700	−	11.8940i	0.231882	−	0.401632i	−0.726480	−	0.687188i	$-0.758845\pi$
$877$	6.86700	−	11.8940i	0.231882	−	0.401632i	0.958362	+	0.285556i	$0.0921783\pi$
$878$	−18.9982	−	32.9059i	−0.641159	−	1.11052i
$879$		0			0
$880$		0			0
$881$	45.0753			1.51863			0.759313	−	0.650726i	$-0.225535\pi$
$881$	45.0753			1.51863			0.759313	+	0.650726i	$0.225535\pi$
$882$		0			0
$883$	−5.61116			−0.188831			−0.0944153	−	0.995533i	$-0.530098\pi$
$883$	−5.61116			−0.188831			−0.0944153	+	0.995533i	$0.530098\pi$
$884$	2.35092	+	1.35730i	0.0790700	+	0.0456511i
$885$		0			0
$886$	−11.6503	−	20.1789i	−0.391399	−	0.677923i
$887$	−6.87285	+	11.9041i	−0.230768	+	0.399701i	−0.958034	−	0.286654i	$-0.907457\pi$
$887$	−6.87285	+	11.9041i	−0.230768	+	0.399701i	0.727267	+	0.686355i	$0.240790\pi$
$888$		0			0
$889$	−6.48128	−	2.77687i	−0.217375	−	0.0931332i
$890$		0			0
$891$		0			0
$892$	1.73999	−	1.00459i	0.0582593	−	0.0336360i
$893$	−8.20031	+	4.73445i	−0.274413	+	0.158432i
$894$		0			0
$895$		0			0
$896$	−1.58515	−	2.11833i	−0.0529560	−	0.0707683i
$897$		0			0
$898$	10.9559	−	18.9762i	0.365604	−	0.633245i
$899$	0.460121	+	0.796953i	0.0153459	+	0.0265799i
$900$		0			0
$901$	−28.3382	−	16.3611i	−0.944083	−	0.545066i
$902$	7.81297			0.260143
$903$		0			0
$904$	−15.0301			−0.499894
$905$		0			0
$906$		0			0
$907$	−2.89624	−	5.01644i	−0.0961681	−	0.166568i	0.813927	−	0.580967i	$-0.197325\pi$
$907$	−2.89624	−	5.01644i	−0.0961681	−	0.166568i	−0.910096	+	0.414399i	$0.863992\pi$
$908$	1.95288	−	3.38249i	0.0648086	−	0.112252i
$909$		0			0
$910$		0			0
$911$			14.9139i			0.494120i	0.969000	+	0.247060i	$0.0794645\pi$
$911$			14.9139i			0.494120i	−0.969000	+	0.247060i	$0.920535\pi$
$912$		0			0
$913$	−16.6017	+	9.58497i	−0.549435	+	0.317216i
$914$	34.0904	−	19.6821i	1.12761	−	0.651027i
$915$		0			0
$916$			13.3835i			0.442203i
$917$	30.1221	−	22.5404i	0.994719	−	0.744349i
$918$		0			0
$919$	−27.3387	+	47.3520i	−0.901821	+	1.56200i	−0.0766921	+	0.997055i	$0.524436\pi$
$919$	−27.3387	+	47.3520i	−0.901821	+	1.56200i	−0.825129	+	0.564945i	$0.808897\pi$
$920$		0			0
$921$		0			0
$922$	2.03760	+	1.17641i	0.0671049	+	0.0387430i
$923$	−4.99376			−0.164372
$924$		0			0
$925$		0			0
$926$	1.94466	+	1.12275i	0.0639056	+	0.0368959i
$927$		0			0
$928$	−0.350387	−	0.606888i	−0.0115020	−	0.0199221i
$929$	24.6920	−	42.7678i	0.810118	−	1.40317i	−0.102663	−	0.994716i	$-0.532736\pi$
$929$	24.6920	−	42.7678i	0.810118	−	1.40317i	0.912781	−	0.408449i	$-0.133930\pi$
$930$		0			0
$931$	5.83782	+	24.1029i	0.191327	+	0.789940i
$932$		−	10.2962i		−	0.337262i
$933$		0			0
$934$	−27.8740	+	16.0931i	−0.912066	+	0.526582i
$935$		0			0
$936$		0			0
$937$		−	12.4762i		−	0.407578i	−0.979015	−	0.203789i	$-0.934674\pi$
$937$		−	12.4762i		−	0.407578i	0.979015	−	0.203789i	$-0.0653257\pi$
$938$	−7.10232	+	16.5770i	−0.231899	+	0.541258i
$939$		0			0
$940$		0			0
$941$	6.11387	+	10.5895i	0.199307	+	0.345209i	0.948304	−	0.317364i	$-0.102798\pi$
$941$	6.11387	+	10.5895i	0.199307	+	0.345209i	−0.748997	+	0.662573i	$0.769464\pi$
$942$		0			0
$943$	−13.6456	−	7.87827i	−0.444361	−	0.256552i
$944$	−3.12395			−0.101676
$945$		0			0
$946$	14.8358			0.482353
$947$	−1.58651	−	0.915974i	−0.0515548	−	0.0297652i	0.474001	−	0.880524i	$-0.342809\pi$
$947$	−1.58651	−	0.915974i	−0.0515548	−	0.0297652i	−0.525556	+	0.850759i	$0.676143\pi$
$948$		0			0
$949$	−4.25326	−	7.36687i	−0.138067	−	0.239139i
$950$		0			0
$951$		0			0
$952$	−9.25303	+	1.10459i	−0.299892	+	0.0358001i
$953$			42.7813i			1.38582i	0.721023	+	0.692911i	$0.243672\pi$
$953$			42.7813i			1.38582i	−0.721023	+	0.692911i	$0.756328\pi$
$954$		0			0
$955$		0			0
$956$	−15.1952	+	8.77298i	−0.491449	+	0.283738i
$957$		0			0
$958$		−	6.61111i		−	0.213595i
$959$	−0.341870	+	0.0408113i	−0.0110396	+	0.00131786i
$960$		0			0
$961$	−14.6378	+	25.3534i	−0.472186	+	0.817851i
$962$	−0.352468	−	0.610493i	−0.0113640	−	0.0196831i
$963$		0			0
$964$	8.66068	+	5.00024i	0.278942	+	0.161047i
$965$		0			0
$966$		0			0
$967$	−24.5160			−0.788380			−0.394190	−	0.919029i	$-0.628975\pi$
$967$	−24.5160			−0.788380			−0.394190	+	0.919029i	$0.628975\pi$
$968$	−7.30795	−	4.21924i	−0.234886	−	0.135612i
$969$		0			0
$970$		0			0
$971$	−11.5704	+	20.0405i	−0.371312	+	0.643131i	−0.989768	−	0.142688i	$-0.954425\pi$
$971$	−11.5704	+	20.0405i	−0.371312	+	0.643131i	0.618456	+	0.785820i	$0.287759\pi$
$972$		0			0
$973$	3.78825	−	8.84186i	0.121446	−	0.283457i
$974$			5.76335i			0.184669i
$975$		0			0
$976$	9.43214	−	5.44565i	0.301915	−	0.174311i
$977$	40.4007	−	23.3254i	1.29253	−	0.746244i	0.313430	−	0.949611i	$-0.398522\pi$
$977$	40.4007	−	23.3254i	1.29253	−	0.746244i	0.979103	+	0.203367i	$0.0651884\pi$
$978$		0			0
$979$		−	14.0960i		−	0.450510i
$980$		0			0
$981$		0			0
$982$	−1.45265	+	2.51606i	−0.0463558	+	0.0802906i
$983$	−2.46490	−	4.26934i	−0.0786182	−	0.136171i	0.824036	−	0.566538i	$-0.191717\pi$
$983$	−2.46490	−	4.26934i	−0.0786182	−	0.136171i	−0.902654	+	0.430367i	$0.858384\pi$
$984$		0			0
$985$		0			0
$986$	−2.46823			−0.0786044
$987$		0			0
$988$	2.73055			0.0868702
$989$	−25.9111	−	14.9598i	−0.823925	−	0.475694i
$990$		0			0
$991$	−11.0708	−	19.1752i	−0.351676	−	0.609121i	0.634867	−	0.772621i	$-0.281055\pi$
$991$	−11.0708	−	19.1752i	−0.351676	−	0.609121i	−0.986543	+	0.163500i	$0.947722\pi$
$992$	−0.656589	+	1.13725i	−0.0208467	+	0.0361076i
$993$		0			0
$994$	13.7253	−	10.2706i	0.435339	−	0.325765i
$995$		0			0
$996$		0			0
$997$	−12.0289	+	6.94487i	−0.380958	+	0.219946i	−0.678235	−	0.734845i	$-0.737255\pi$
$997$	−12.0289	+	6.94487i	−0.380958	+	0.219946i	0.297277	+	0.954791i	$0.403922\pi$
$998$	−1.97634	+	1.14104i	−0.0625600	+	0.0361190i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.bf.e.1601.8	yes	24
3.2	odd	2	inner	3150.2.bf.e.1601.5	yes	24
5.2	odd	4		3150.2.bp.g.1349.6		24
5.3	odd	4		3150.2.bp.h.1349.7		24
5.4	even	2		3150.2.bf.d.1601.5	yes	24
7.3	odd	6	inner	3150.2.bf.e.1151.5	yes	24
15.2	even	4		3150.2.bp.h.1349.6		24
15.8	even	4		3150.2.bp.g.1349.7		24
15.14	odd	2		3150.2.bf.d.1601.8	yes	24
21.17	even	6	inner	3150.2.bf.e.1151.8	yes	24
35.3	even	12		3150.2.bp.h.899.6		24
35.17	even	12		3150.2.bp.g.899.7		24
35.24	odd	6		3150.2.bf.d.1151.8	yes	24
105.17	odd	12		3150.2.bp.h.899.7		24
105.38	odd	12		3150.2.bp.g.899.6		24
105.59	even	6		3150.2.bf.d.1151.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.5	✓	24	105.59	even	6
3150.2.bf.d.1151.8	yes	24	35.24	odd	6
3150.2.bf.d.1601.5	yes	24	5.4	even	2
3150.2.bf.d.1601.8	yes	24	15.14	odd	2
3150.2.bf.e.1151.5	yes	24	7.3	odd	6	inner
3150.2.bf.e.1151.8	yes	24	21.17	even	6	inner
3150.2.bf.e.1601.5	yes	24	3.2	odd	2	inner
3150.2.bf.e.1601.8	yes	24	1.1	even	1	trivial
3150.2.bp.g.899.6		24	105.38	odd	12
3150.2.bp.g.899.7		24	35.17	even	12
3150.2.bp.g.1349.6		24	5.2	odd	4
3150.2.bp.g.1349.7		24	15.8	even	4
3150.2.bp.h.899.6		24	35.3	even	12
3150.2.bp.h.899.7		24	105.17	odd	12
3150.2.bp.h.1349.6		24	15.2	even	4
3150.2.bp.h.1349.7		24	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.43194 + 1.04195i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.43194 + 1.04195i) q^{7} +1.00000i q^{8} +(1.38605 - 0.800236i) q^{11} -0.770726i q^{13} +(1.58515 + 2.11833i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.76107 + 3.05027i) q^{17} +(3.06818 + 1.77141i) q^{19} +1.60047 q^{22} +(-2.79527 - 1.61385i) q^{23} +(0.385363 - 0.667468i) q^{26} +(0.313613 + 2.62710i) q^{28} +0.700774i q^{29} +(1.13725 - 0.656589i) q^{31} +(-0.866025 + 0.500000i) q^{32} +3.52215i q^{34} +(0.457320 - 0.792101i) q^{37} +(1.77141 + 3.06818i) q^{38} +4.88167 q^{41} +9.26963 q^{43} +(1.38605 + 0.800236i) q^{44} +(-1.61385 - 2.79527i) q^{46} +(-1.33635 + 2.31462i) q^{47} +(4.82867 + 5.06793i) q^{49} +(0.667468 - 0.385363i) q^{52} +(-8.04572 + 4.64520i) q^{53} +(-1.04195 + 2.43194i) q^{56} +(-0.350387 + 0.606888i) q^{58} +(1.56198 + 2.70542i) q^{59} +(-9.43214 - 5.44565i) q^{61} +1.31318 q^{62} -1.00000 q^{64} +(3.40818 + 5.90314i) q^{67} +(-1.76107 + 3.05027i) q^{68} -6.47930i q^{71} +(9.55835 - 5.51852i) q^{73} +(0.792101 - 0.457320i) q^{74} +3.54282i q^{76} +(4.20460 - 0.501930i) q^{77} +(-1.45086 + 2.51296i) q^{79} +(4.22765 + 2.44083i) q^{82} -11.9777 q^{83} +(8.02773 + 4.63481i) q^{86} +(0.800236 + 1.38605i) q^{88} +(4.40369 - 7.62742i) q^{89} +(0.803059 - 1.87436i) q^{91} -3.22770i q^{92} +(-2.31462 + 1.33635i) q^{94} +5.31224i q^{97} +(1.64779 + 6.80329i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 4 q^{7}+O(q^{10}) \) 24 * q + 12 * q^4 + 4 * q^7	\( 24 q + 12 q^{4} + 4 q^{7} - 12 q^{16} + 12 q^{19} - 4 q^{28} - 28 q^{37} - 96 q^{43} - 8 q^{46} - 52 q^{49} + 12 q^{52} - 8 q^{58} - 12 q^{61} - 24 q^{64} + 4 q^{67} + 12 q^{73} + 4 q^{79} + 68 q^{91} - 24 q^{94}+O(q^{100}) \) 24 * q + 12 * q^4 + 4 * q^7 - 12 * q^16 + 12 * q^19 - 4 * q^28 - 28 * q^37 - 96 * q^43 - 8 * q^46 - 52 * q^49 + 12 * q^52 - 8 * q^58 - 12 * q^61 - 24 * q^64 + 4 * q^67 + 12 * q^73 + 4 * q^79 + 68 * q^91 - 24 * q^94

Introduction

L-functions

Modular forms

Varieties

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Database

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