LMFDB - Embedded newform 3150.2.bp.g.1349.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(899,3150)]

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, 3, 1]))

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

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

chi := DirichletCharacter("3150.899");

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.bp (of order $6$, degree $2$, not 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			1349.7
Character	$\chi$	$=$	3150.1349
Dual form			3150.2.bp.g.899.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.04195 - 2.43194i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.04195 - 2.43194i) q^{7} +1.00000 q^{8} +(-1.38605 + 0.800236i) q^{11} +0.770726 q^{13} +(1.58515 + 2.11833i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.05027 + 1.76107i) q^{17} +(-3.06818 - 1.77141i) q^{19} -1.60047i q^{22} +(-1.61385 + 2.79527i) q^{23} +(-0.385363 + 0.667468i) q^{26} +(-2.62710 + 0.313613i) q^{28} +0.700774i q^{29} +(1.13725 - 0.656589i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.52215i q^{34} +(-0.792101 - 0.457320i) q^{37} +(3.06818 - 1.77141i) q^{38} -4.88167 q^{41} +9.26963i q^{43} +(1.38605 + 0.800236i) q^{44} +(-1.61385 - 2.79527i) q^{46} +(-2.31462 - 1.33635i) q^{47} +(-4.82867 - 5.06793i) q^{49} +(-0.385363 - 0.667468i) q^{52} +(4.64520 + 8.04572i) q^{53} +(1.04195 - 2.43194i) q^{56} +(-0.606888 - 0.350387i) q^{58} +(1.56198 + 2.70542i) q^{59} +(-9.43214 - 5.44565i) q^{61} +1.31318i q^{62} +1.00000 q^{64} +(5.90314 - 3.40818i) q^{67} +(3.05027 + 1.76107i) q^{68} +6.47930i q^{71} +(5.51852 + 9.55835i) q^{73} +(0.792101 - 0.457320i) q^{74} +3.54282i q^{76} +(0.501930 + 4.20460i) q^{77} +(1.45086 - 2.51296i) q^{79} +(2.44083 - 4.22765i) q^{82} +11.9777i q^{83} +(-8.02773 - 4.63481i) q^{86} +(-1.38605 + 0.800236i) q^{88} +(4.40369 - 7.62742i) q^{89} +(0.803059 - 1.87436i) q^{91} +3.22770 q^{92} +(2.31462 - 1.33635i) q^{94} +5.31224 q^{97} +(6.80329 - 1.64779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.04195	−	2.43194i	0.393821	−	0.919187i
$7$	1.04195	−	2.43194i	0.393821	−	0.919187i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	−1.38605	+	0.800236i	−0.417910	+	0.241280i	−0.694183	−	0.719799i	$-0.744234\pi$
$11$	−1.38605	+	0.800236i	−0.417910	+	0.241280i	0.276273	+	0.961079i	$0.410901\pi$
$12$		0			0
$13$	0.770726			0.213761			0.106880	−	0.994272i	$-0.465914\pi$
$13$	0.770726			0.213761			0.106880	+	0.994272i	$0.465914\pi$
$14$	1.58515	+	2.11833i	0.423648	+	0.566147i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.05027	+	1.76107i	−0.739799	+	0.427123i	−0.821996	−	0.569493i	$-0.807140\pi$
$17$	−3.05027	+	1.76107i	−0.739799	+	0.427123i	0.0821974	+	0.996616i	$0.473806\pi$
$18$		0			0
$19$	−3.06818	−	1.77141i	−0.703888	−	0.406390i	0.104906	−	0.994482i	$-0.466546\pi$
$19$	−3.06818	−	1.77141i	−0.703888	−	0.406390i	−0.808794	+	0.588092i	$0.799879\pi$
$20$		0			0
$21$		0			0
$22$		−	1.60047i		−	0.341222i
$23$	−1.61385	+	2.79527i	−0.336511	+	0.582854i	−0.983774	−	0.179413i	$-0.942580\pi$
$23$	−1.61385	+	2.79527i	−0.336511	+	0.582854i	0.647263	+	0.762267i	$0.275914\pi$
$24$		0			0
$25$		0			0
$26$	−0.385363	+	0.667468i	−0.0755759	+	0.130901i
$27$		0			0
$28$	−2.62710	+	0.313613i	−0.496475	+	0.0592674i
$29$			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	$0.295708\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$		−	3.52215i		−	0.604043i
$35$		0			0
$36$		0			0
$37$	−0.792101	−	0.457320i	−0.130221	−	0.0751829i	0.433475	−	0.901166i	$-0.357287\pi$
$37$	−0.792101	−	0.457320i	−0.130221	−	0.0751829i	−0.563695	+	0.825983i	$0.690621\pi$
$38$	3.06818	−	1.77141i	0.497724	−	0.287361i
$39$		0			0
$40$		0			0
$41$	−4.88167			−0.762388			−0.381194	−	0.924495i	$-0.624487\pi$
$41$	−4.88167			−0.762388			−0.381194	+	0.924495i	$0.624487\pi$
$42$		0			0
$43$			9.26963i			1.41361i	0.707411	+	0.706803i	$0.249863\pi$
$43$			9.26963i			1.41361i	−0.707411	+	0.706803i	$0.750137\pi$
$44$	1.38605	+	0.800236i	0.208955	+	0.120640i
$45$		0			0
$46$	−1.61385	−	2.79527i	−0.237949	−	0.412140i
$47$	−2.31462	−	1.33635i	−0.337623	−	0.194926i	0.321598	−	0.946876i	$-0.395780\pi$
$47$	−2.31462	−	1.33635i	−0.337623	−	0.194926i	−0.659220	+	0.751950i	$0.729113\pi$
$48$		0			0
$49$	−4.82867	−	5.06793i	−0.689810	−	0.723990i
$50$		0			0
$51$		0			0
$52$	−0.385363	−	0.667468i	−0.0534402	−	0.0925612i
$53$	4.64520	+	8.04572i	0.638067	+	1.10516i	0.985856	+	0.167592i	$0.0535991\pi$
$53$	4.64520	+	8.04572i	0.638067	+	1.10516i	−0.347789	+	0.937573i	$0.613068\pi$
$54$		0			0
$55$		0			0
$56$	1.04195	−	2.43194i	0.139237	−	0.324982i
$57$		0			0
$58$	−0.606888	−	0.350387i	−0.0796883	−	0.0460081i
$59$	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	$0.912257\pi$
$62$			1.31318i			0.166774i
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	5.90314	−	3.40818i	0.721183	−	0.416375i	−0.0940048	−	0.995572i	$-0.529967\pi$
$67$	5.90314	−	3.40818i	0.721183	−	0.416375i	0.815188	+	0.579196i	$0.196634\pi$
$68$	3.05027	+	1.76107i	0.369899	+	0.213561i
$69$		0			0
$70$		0			0
$71$			6.47930i			0.768951i	0.923135	+	0.384475i	$0.125618\pi$
$71$			6.47930i			0.768951i	−0.923135	+	0.384475i	$0.874382\pi$
$72$		0			0
$73$	5.51852	+	9.55835i	0.645894	+	1.11872i	0.984094	+	0.177647i	$0.0568484\pi$
$73$	5.51852	+	9.55835i	0.645894	+	1.11872i	−0.338201	+	0.941074i	$0.609818\pi$
$74$	0.792101	−	0.457320i	0.0920799	−	0.0531623i
$75$		0			0
$76$			3.54282i			0.406390i
$77$	0.501930	+	4.20460i	0.0572002	+	0.479158i
$78$		0			0
$79$	1.45086	−	2.51296i	0.163234	−	0.282730i	−0.772792	−	0.634659i	$-0.781141\pi$
$79$	1.45086	−	2.51296i	0.163234	−	0.282730i	0.936027	+	0.351928i	$0.114474\pi$
$80$		0			0
$81$		0			0
$82$	2.44083	−	4.22765i	0.269545	−	0.466865i
$83$			11.9777i			1.31472i	0.753576	+	0.657361i	$0.228327\pi$
$83$			11.9777i			1.31472i	−0.753576	+	0.657361i	$0.771673\pi$
$84$		0			0
$85$		0			0
$86$	−8.02773	−	4.63481i	−0.865653	−	0.499785i
$87$		0			0
$88$	−1.38605	+	0.800236i	−0.147753	+	0.0853055i
$89$	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
$92$	3.22770			0.336511
$93$		0			0
$94$	2.31462	−	1.33635i	0.238735	−	0.137834i
$95$		0			0
$96$		0			0
$97$	5.31224			0.539376			0.269688	−	0.962948i	$-0.413079\pi$
$97$	5.31224			0.539376			0.269688	+	0.962948i	$0.413079\pi$
$98$	6.80329	−	1.64779i	0.687236	−	0.166452i
$99$		0			0
$100$		0			0
$101$	4.62663	+	8.01356i	0.460367	+	0.797379i	0.998979	−	0.0451749i	$-0.0143845\pi$
$101$	4.62663	+	8.01356i	0.460367	+	0.797379i	−0.538612	+	0.842554i	$0.681051\pi$
$102$		0			0
$103$	−7.91290	+	13.7055i	−0.779681	+	1.35045i	0.152444	+	0.988312i	$0.451286\pi$
$103$	−7.91290	+	13.7055i	−0.779681	+	1.35045i	−0.932125	+	0.362136i	$0.882048\pi$
$104$	0.770726			0.0755759
$105$		0			0
$106$	−9.29040			−0.902363
$107$	−6.20735	+	10.7514i	−0.600087	+	1.03938i	0.392720	+	0.919658i	$0.371534\pi$
$107$	−6.20735	+	10.7514i	−0.600087	+	1.03938i	−0.992807	+	0.119724i	$0.961799\pi$
$108$		0			0
$109$	−5.51750	−	9.55659i	−0.528480	−	0.915355i	−0.999449	−	0.0332048i	$-0.989429\pi$
$109$	−5.51750	−	9.55659i	−0.528480	−	0.915355i	0.470968	−	0.882150i	$-0.343905\pi$
$110$		0			0
$111$		0			0
$112$	1.58515	+	2.11833i	0.149782	+	0.200163i
$113$	15.0301			1.41391			0.706957	−	0.707256i	$-0.250067\pi$
$113$	15.0301			1.41391			0.706957	+	0.707256i	$0.250067\pi$
$114$		0			0
$115$		0			0
$116$	0.606888	−	0.350387i	0.0563482	−	0.0325326i
$117$		0			0
$118$	−3.12395			−0.287583
$119$	1.10459	+	9.25303i	0.101258	+	0.848223i
$120$		0			0
$121$	−4.21924	+	7.30795i	−0.383568	+	0.664359i
$122$	9.43214	−	5.44565i	0.853946	−	0.493026i
$123$		0			0
$124$	−1.13725	−	0.656589i	−0.102128	−	0.0589634i
$125$		0			0
$126$		0			0
$127$			2.66506i			0.236486i	0.992985	+	0.118243i	$0.0377262\pi$
$127$			2.66506i			0.236486i	−0.992985	+	0.118243i	$0.962274\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	−7.10987	+	12.3147i	−0.621192	+	1.07594i	0.368071	+	0.929797i	$0.380018\pi$
$131$	−7.10987	+	12.3147i	−0.621192	+	1.07594i	−0.989264	+	0.146139i	$0.953315\pi$
$132$		0			0
$133$	−7.50486	+	5.61590i	−0.650754	+	0.486960i
$134$			6.81636i			0.588844i
$135$		0			0
$136$	−3.05027	+	1.76107i	−0.261558	+	0.151011i
$137$	−0.0650662	−	0.112698i	−0.00555898	−	0.00962843i	0.863233	−	0.504806i	$-0.168436\pi$
$137$	−0.0650662	−	0.112698i	−0.00555898	−	0.00962843i	−0.868792	+	0.495178i	$0.835103\pi$
$138$		0			0
$139$			3.63572i			0.308378i	0.988041	+	0.154189i	$0.0492765\pi$
$139$			3.63572i			0.308378i	−0.988041	+	0.154189i	$0.950724\pi$
$140$		0			0
$141$		0			0
$142$	−5.61123	−	3.23965i	−0.470884	−	0.271865i
$143$	−1.06826	+	0.616762i	−0.0893327	+	0.0515763i
$144$		0			0
$145$		0			0
$146$	−11.0370			−0.913432
$147$		0			0
$148$			0.914639i			0.0751829i
$149$	−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	$0.927140\pi$
$152$	−3.06818	−	1.77141i	−0.248862	−	0.143681i
$153$		0			0
$154$	−3.89225	−	1.66762i	−0.313647	−	0.134380i
$155$		0			0
$156$		0			0
$157$	7.15702	+	12.3963i	0.571192	+	0.989334i	0.996444	+	0.0842589i	$0.0268523\pi$
$157$	7.15702	+	12.3963i	0.571192	+	0.989334i	−0.425252	+	0.905075i	$0.639814\pi$
$158$	1.45086	+	2.51296i	0.115424	+	0.199921i
$159$		0			0
$160$		0			0
$161$	5.11638	+	6.83732i	0.403227	+	0.538857i
$162$		0			0
$163$	−6.24313	−	3.60448i	−0.489000	−	0.282324i	0.235159	−	0.971957i	$-0.424439\pi$
$163$	−6.24313	−	3.60448i	−0.489000	−	0.282324i	−0.724160	+	0.689632i	$0.757772\pi$
$164$	2.44083	+	4.22765i	0.190597	+	0.330124i
$165$		0			0
$166$	−10.3730	−	5.98884i	−0.805099	−	0.464824i
$167$		−	13.8952i		−	1.07524i	−0.843187	−	0.537620i	$-0.819323\pi$
$167$		−	13.8952i		−	1.07524i	0.843187	−	0.537620i	$-0.180677\pi$
$168$		0			0
$169$	−12.4060			−0.954306
$170$		0			0
$171$		0			0
$172$	8.02773	−	4.63481i	0.612109	−	0.353401i
$173$	−2.05023	−	1.18370i	−0.155876	−	0.0899951i	0.420033	−	0.907509i	$-0.362018\pi$
$173$	−2.05023	−	1.18370i	−0.155876	−	0.0899951i	−0.575909	+	0.817514i	$0.695352\pi$
$174$		0			0
$175$		0			0
$176$		−	1.60047i		−	0.120640i
$177$		0			0
$178$	4.40369	+	7.62742i	0.330071	+	0.571700i
$179$	−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	$-0.212638\pi$
$182$	1.22171	+	1.63265i	0.0905594	+	0.121020i
$183$		0			0
$184$	−1.61385	+	2.79527i	−0.118975	+	0.206070i
$185$		0			0
$186$		0			0
$187$	2.81855	−	4.88187i	0.206113	−	0.356998i
$188$			2.67270i			0.194926i
$189$		0			0
$190$		0			0
$191$	21.4359	+	12.3760i	1.55104	+	0.895496i	0.998057	+	0.0623063i	$0.0198456\pi$
$191$	21.4359	+	12.3760i	1.55104	+	0.895496i	0.552987	+	0.833190i	$0.313488\pi$
$192$		0			0
$193$	−10.8917	+	6.28835i	−0.784005	+	0.452645i	−0.837848	−	0.545904i	$-0.816186\pi$
$193$	−10.8917	+	6.28835i	−0.784005	+	0.452645i	0.0538428	+	0.998549i	$0.482853\pi$
$194$	−2.65612	+	4.60054i	−0.190698	+	0.330299i
$195$		0			0
$196$	−1.97462	+	6.71572i	−0.141044	+	0.479694i
$197$	−19.7360			−1.40613			−0.703066	−	0.711125i	$-0.748186\pi$
$197$	−19.7360			−1.40613			−0.703066	+	0.711125i	$0.748186\pi$
$198$		0			0
$199$	−9.82275	+	5.67117i	−0.696316	+	0.402018i	−0.805974	−	0.591951i	$-0.798358\pi$
$199$	−9.82275	+	5.67117i	−0.696316	+	0.402018i	0.109658	+	0.993969i	$0.465025\pi$
$200$		0			0
$201$		0			0
$202$	−9.25326			−0.651057
$203$	1.70424	+	0.730173i	0.119614	+	0.0512481i
$204$		0			0
$205$		0			0
$206$	−7.91290	−	13.7055i	−0.551318	−	0.954911i
$207$		0			0
$208$	−0.385363	+	0.667468i	−0.0267201	+	0.0462806i
$209$	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	$0.313494\pi$
$212$	4.64520	−	8.04572i	0.319034	−	0.552582i
$213$		0			0
$214$	−6.20735	−	10.7514i	−0.424326	−	0.734954i
$215$		0			0
$216$		0			0
$217$	−0.411830	−	3.44985i	−0.0279569	−	0.234191i
$218$	11.0350			0.747384
$219$		0			0
$220$		0			0
$221$	−2.35092	+	1.35730i	−0.158140	+	0.0913022i
$222$		0			0
$223$	2.00917			0.134544			0.0672720	−	0.997735i	$-0.478570\pi$
$223$	2.00917			0.134544			0.0672720	+	0.997735i	$0.478570\pi$
$224$	−2.62710	+	0.313613i	−0.175530	+	0.0209542i
$225$		0			0
$226$	−7.51506	+	13.0165i	−0.499894	+	0.865842i
$227$	3.38249	−	1.95288i	0.224504	−	0.129617i	−0.383530	−	0.923528i	$-0.625292\pi$
$227$	3.38249	−	1.95288i	0.224504	−	0.129617i	0.608034	+	0.793911i	$0.291958\pi$
$228$		0			0
$229$	−11.5904	−	6.69174i	−0.765918	−	0.442203i	0.0654987	−	0.997853i	$-0.479136\pi$
$229$	−11.5904	−	6.69174i	−0.765918	−	0.442203i	−0.831416	+	0.555650i	$0.812470\pi$
$230$		0			0
$231$		0			0
$232$			0.700774i			0.0460081i
$233$	−5.14808	+	8.91673i	−0.337262	+	0.584154i	−0.983917	−	0.178628i	$-0.942834\pi$
$233$	−5.14808	+	8.91673i	−0.337262	+	0.584154i	0.646655	+	0.762783i	$0.276167\pi$
$234$		0			0
$235$		0			0
$236$	1.56198	−	2.70542i	0.101676	−	0.176108i
$237$		0			0
$238$	−8.56565	−	3.66991i	−0.555229	−	0.237885i
$239$			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	$0.228947\pi$
$242$	−4.21924	−	7.30795i	−0.271223	−	0.469773i
$243$		0			0
$244$			10.8913i			0.697244i
$245$		0			0
$246$		0			0
$247$	−2.36472	−	1.36527i	−0.150464	−	0.0868702i
$248$	1.13725	−	0.656589i	0.0722152	−	0.0416935i
$249$		0			0
$250$		0			0
$251$	−3.55412			−0.224334			−0.112167	−	0.993689i	$-0.535779\pi$
$251$	−3.55412			−0.224334			−0.112167	+	0.993689i	$0.535779\pi$
$252$		0			0
$253$		−	5.16584i		−	0.324774i
$254$	−2.30801	−	1.33253i	−0.144818	−	0.0836105i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.15756	−	3.55507i	−0.384098	−	0.221759i	0.295502	−	0.955342i	$-0.404513\pi$
$257$	−6.15756	−	3.55507i	−0.384098	−	0.221759i	−0.679600	+	0.733583i	$0.737847\pi$
$258$		0			0
$259$	−1.93751	+	1.44984i	−0.120391	+	0.0900885i
$260$		0			0
$261$		0			0
$262$	−7.10987	−	12.3147i	−0.439249	−	0.760802i
$263$	−14.2752	−	24.7253i	−0.880245	−	1.52463i	−0.851069	−	0.525054i	$-0.824045\pi$
$263$	−14.2752	−	24.7253i	−0.880245	−	1.52463i	−0.0291760	−	0.999574i	$-0.509288\pi$
$264$		0			0
$265$		0			0
$266$	−1.11108	−	9.30735i	−0.0681245	−	0.570670i
$267$		0			0
$268$	−5.90314	−	3.40818i	−0.360592	−	0.208188i
$269$	−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	$0.988547\pi$
$272$		−	3.52215i		−	0.213561i
$273$		0			0
$274$	0.130132			0.00786158
$275$		0			0
$276$		0			0
$277$	8.98042	−	5.18485i	0.539581	−	0.311527i	−0.205328	−	0.978693i	$-0.565826\pi$
$277$	8.98042	−	5.18485i	0.539581	−	0.311527i	0.744909	+	0.667166i	$0.232493\pi$
$278$	−3.14863	−	1.81786i	−0.188842	−	0.109028i
$279$		0			0
$280$		0			0
$281$			21.0412i			1.25521i	0.778530	+	0.627607i	$0.215965\pi$
$281$			21.0412i			1.25521i	−0.778530	+	0.627607i	$0.784035\pi$
$282$		0			0
$283$	13.6859	+	23.7046i	0.813541	+	1.40909i	0.910371	+	0.413794i	$0.135797\pi$
$283$	13.6859	+	23.7046i	0.813541	+	1.40909i	−0.0968293	+	0.995301i	$0.530870\pi$
$284$	5.61123	−	3.23965i	0.332965	−	0.192238i
$285$		0			0
$286$		−	1.23352i		−	0.0729399i
$287$	−5.08646	+	11.8719i	−0.300244	+	0.700777i
$288$		0			0
$289$	−2.29724	+	3.97894i	−0.135132	+	0.234055i
$290$		0			0
$291$		0			0
$292$	5.51852	−	9.55835i	0.322947	−	0.559360i
$293$			16.9059i			0.987654i	0.869560	+	0.493827i	$0.164402\pi$
$293$			16.9059i			0.987654i	−0.869560	+	0.493827i	$0.835598\pi$
$294$		0			0
$295$		0			0
$296$	−0.792101	−	0.457320i	−0.0460399	−	0.0265812i
$297$		0			0
$298$	2.53957	−	1.46622i	0.147113	−	0.0849358i
$299$	−1.24384	+	2.15439i	−0.0719328	+	0.124591i
$300$		0			0
$301$	22.5432	+	9.65851i	1.29937	+	0.556707i
$302$	7.13837			0.410767
$303$		0			0
$304$	3.06818	−	1.77141i	0.175972	−	0.101597i
$305$		0			0
$306$		0			0
$307$	−14.0139			−0.799813			−0.399906	−	0.916556i	$-0.630957\pi$
$307$	−14.0139			−0.799813			−0.399906	+	0.916556i	$0.630957\pi$
$308$	3.39032	−	2.53698i	0.193182	−	0.144558i
$309$		0			0
$310$		0			0
$311$	−6.72211	−	11.6430i	−0.381176	−	0.660216i	0.610055	−	0.792359i	$-0.291147\pi$
$311$	−6.72211	−	11.6430i	−0.381176	−	0.660216i	−0.991231	+	0.132143i	$0.957814\pi$
$312$		0			0
$313$	2.12904	−	3.68760i	0.120340	−	0.208436i	−0.799562	−	0.600584i	$-0.794935\pi$
$313$	2.12904	−	3.68760i	0.120340	−	0.208436i	0.919902	+	0.392149i	$0.128268\pi$
$314$	−14.3140			−0.807788
$315$		0			0
$316$	−2.90172			−0.163234
$317$	−0.0987910	+	0.171111i	−0.00554866	+	0.00961055i	−0.868786	−	0.495187i	$-0.835100\pi$
$317$	−0.0987910	+	0.171111i	−0.00554866	+	0.00961055i	0.863238	+	0.504798i	$0.168433\pi$
$318$		0			0
$319$	−0.560785	−	0.971308i	−0.0313979	−	0.0543828i
$320$		0			0
$321$		0			0
$322$	−8.47948	+	1.01225i	−0.472543	+	0.0564105i
$323$	12.4783			0.694314
$324$		0			0
$325$		0			0
$326$	6.24313	−	3.60448i	0.345775	−	0.199633i
$327$		0			0
$328$	−4.88167			−0.269545
$329$	−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	$0.206969\pi$
$332$	10.3730	−	5.98884i	0.569291	−	0.328680i
$333$		0			0
$334$	12.0336	+	6.94758i	0.658447	+	0.380155i
$335$		0			0
$336$		0			0
$337$			6.05076i			0.329606i	0.986327	+	0.164803i	$0.0526988\pi$
$337$			6.05076i			0.329606i	−0.986327	+	0.164803i	$0.947301\pi$
$338$	6.20299	−	10.7439i	0.337398	−	0.584391i
$339$		0			0
$340$		0			0
$341$	−1.05085	+	1.82013i	−0.0569069	+	0.0985656i
$342$		0			0
$343$	−17.3562	+	6.46250i	−0.937144	+	0.348942i
$344$			9.26963i			0.499785i
$345$		0			0
$346$	2.05023	−	1.18370i	0.110221	−	0.0636362i
$347$	−1.59102	−	2.75573i	−0.0854104	−	0.147935i	0.820156	−	0.572140i	$-0.193887\pi$
$347$	−1.59102	−	2.75573i	−0.0854104	−	0.147935i	−0.905566	+	0.424205i	$0.860553\pi$
$348$		0			0
$349$			29.0573i			1.55540i	0.628636	+	0.777700i	$0.283614\pi$
$349$			29.0573i			1.55540i	−0.628636	+	0.777700i	$0.716386\pi$
$350$		0			0
$351$		0			0
$352$	1.38605	+	0.800236i	0.0738767	+	0.0426527i
$353$	6.63942	−	3.83327i	0.353381	−	0.204025i	−0.312792	−	0.949822i	$-0.601264\pi$
$353$	6.63942	−	3.83327i	0.353381	−	0.204025i	0.666173	+	0.745797i	$0.267931\pi$
$354$		0			0
$355$		0			0
$356$	−8.80739			−0.466791
$357$		0			0
$358$		−	17.8791i		−	0.944938i
$359$	−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
$362$	14.4343	+	8.33363i	0.758649	+	0.438006i
$363$		0			0
$364$	−2.02477	+	0.241710i	−0.106127	+	0.0126690i
$365$		0			0
$366$		0			0
$367$	9.37433	+	16.2368i	0.489336	+	0.847555i	0.999925	−	0.0122703i	$-0.00390585\pi$
$367$	9.37433	+	16.2368i	0.489336	+	0.847555i	−0.510589	+	0.859825i	$0.670573\pi$
$368$	−1.61385	−	2.79527i	−0.0841277	−	0.145713i
$369$		0			0
$370$		0			0
$371$	24.4068	−	2.91359i	1.26714	−	0.151266i
$372$		0			0
$373$	−2.46050	−	1.42057i	−0.127400	−	0.0735545i	0.434946	−	0.900457i	$-0.356768\pi$
$373$	−2.46050	−	1.42057i	−0.127400	−	0.0735545i	−0.562346	+	0.826902i	$0.690101\pi$
$374$	2.81855	+	4.88187i	0.145744	+	0.252435i
$375$		0			0
$376$	−2.31462	−	1.33635i	−0.119368	−	0.0689169i
$377$			0.540105i			0.0278168i
$378$		0			0
$379$	27.2750			1.40102			0.700510	−	0.713642i	$-0.252956\pi$
$379$	27.2750			1.40102			0.700510	+	0.713642i	$0.252956\pi$
$380$		0			0
$381$		0			0
$382$	−21.4359	+	12.3760i	−1.09675	+	0.633211i
$383$	−26.1843	−	15.1175i	−1.33796	−	0.772469i	−0.351451	−	0.936206i	$-0.614312\pi$
$383$	−26.1843	−	15.1175i	−1.33796	−	0.772469i	−0.986504	+	0.163737i	$0.947645\pi$
$384$		0			0
$385$		0			0
$386$		−	12.5767i		−	0.640137i
$387$		0			0
$388$	−2.65612	−	4.60054i	−0.134844	−	0.233557i
$389$	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
$392$	−4.82867	−	5.06793i	−0.243885	−	0.255969i
$393$		0			0
$394$	9.86800	−	17.0919i	0.497143	−	0.861077i
$395$		0			0
$396$		0			0
$397$	7.30213	−	12.6477i	0.366483	−	0.634768i	−0.622530	−	0.782596i	$-0.713895\pi$
$397$	7.30213	−	12.6477i	0.366483	−	0.634768i	0.989013	+	0.147828i	$0.0472283\pi$
$398$		−	11.3423i		−	0.568540i
$399$		0			0
$400$		0			0
$401$	17.5622	+	10.1395i	0.877014	+	0.506345i	0.869673	−	0.493629i	$-0.164330\pi$
$401$	17.5622	+	10.1395i	0.877014	+	0.506345i	0.00734158	+	0.999973i	$0.497663\pi$
$402$		0			0
$403$	0.876505	−	0.506050i	0.0436618	−	0.0252082i
$404$	4.62663	−	8.01356i	0.230183	−	0.398689i
$405$		0			0
$406$	−1.48447	+	1.11083i	−0.0736730	+	0.0551296i
$407$	1.46385			0.0725606
$408$		0			0
$409$	−4.26877	+	2.46458i	−0.211077	+	0.121865i	−0.601812	−	0.798638i	$-0.705554\pi$
$409$	−4.26877	+	2.46458i	−0.211077	+	0.121865i	0.390735	+	0.920503i	$0.372221\pi$
$410$		0			0
$411$		0			0
$412$	15.8258			0.779681
$413$	8.20693	−	0.979714i	0.403837	−	0.0482086i
$414$		0			0
$415$		0			0
$416$	−0.385363	−	0.667468i	−0.0188940	−	0.0327253i
$417$		0			0
$418$	−2.83510	+	4.91053i	−0.138669	+	0.240182i
$419$	−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	$0.371957\pi$
$422$	−8.03236	+	13.9125i	−0.391009	+	0.677248i
$423$		0			0
$424$	4.64520	+	8.04572i	0.225591	+	0.390735i
$425$		0			0
$426$		0			0
$427$	−23.0713	+	17.2643i	−1.11650	+	0.835478i
$428$	12.4147			0.600087
$429$		0			0
$430$		0			0
$431$	0.373691	−	0.215751i	0.0180001	−	0.0103923i	−0.490973	−	0.871175i	$-0.663359\pi$
$431$	0.373691	−	0.215751i	0.0180001	−	0.0103923i	0.508973	+	0.860782i	$0.330025\pi$
$432$		0			0
$433$	30.5287			1.46711			0.733557	−	0.679628i	$-0.237859\pi$
$433$	30.5287			1.46711			0.733557	+	0.679628i	$0.237859\pi$
$434$	3.19357	+	1.36827i	0.153296	+	0.0656790i
$435$		0			0
$436$	−5.51750	+	9.55659i	−0.264240	+	0.457677i
$437$	9.90315	−	5.71759i	0.473732	−	0.273509i
$438$		0			0
$439$	32.9059	+	18.9982i	1.57051	+	0.906735i	0.996106	+	0.0881648i	$0.0281002\pi$
$439$	32.9059	+	18.9982i	1.57051	+	0.906735i	0.574406	+	0.818571i	$0.305233\pi$
$440$		0			0
$441$		0			0
$442$		−	2.71461i		−	0.129121i
$443$	−11.6503	+	20.1789i	−0.553522	+	0.958728i	0.444495	+	0.895781i	$0.353383\pi$
$443$	−11.6503	+	20.1789i	−0.553522	+	0.958728i	−0.998017	+	0.0629464i	$0.979950\pi$
$444$		0			0
$445$		0			0
$446$	−1.00459	+	1.73999i	−0.0475685	+	0.0823911i
$447$		0			0
$448$	1.04195	−	2.43194i	0.0492276	−	0.114898i
$449$		−	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
$452$	−7.51506	−	13.0165i	−0.353479	−	0.612243i
$453$		0			0
$454$			3.90576i			0.183306i
$455$		0			0
$456$		0			0
$457$	−34.0904	−	19.6821i	−1.59468	−	0.920691i	−0.992488	−	0.122341i	$-0.960960\pi$
$457$	−34.0904	−	19.6821i	−1.59468	−	0.920691i	−0.602195	−	0.798349i	$-0.705707\pi$
$458$	11.5904	−	6.69174i	0.541586	−	0.312685i
$459$		0			0
$460$		0			0
$461$	−2.35282			−0.109582			−0.0547909	−	0.998498i	$-0.517449\pi$
$461$	−2.35282			−0.109582			−0.0547909	+	0.998498i	$0.517449\pi$
$462$		0			0
$463$			2.24550i			0.104357i	0.998638	+	0.0521787i	$0.0166165\pi$
$463$			2.24550i			0.104357i	−0.998638	+	0.0521787i	$0.983383\pi$
$464$	−0.606888	−	0.350387i	−0.0281741	−	0.0162663i
$465$		0			0
$466$	−5.14808	−	8.91673i	−0.238480	−	0.413059i
$467$	−27.8740	−	16.0931i	−1.28986	−	0.744699i	−0.311228	−	0.950335i	$-0.600740\pi$
$467$	−27.8740	−	16.0931i	−1.28986	−	0.744699i	−0.978628	+	0.205636i	$0.934074\pi$
$468$		0			0
$469$	−2.13770	−	17.9072i	−0.0987099	−	0.826880i
$470$		0			0
$471$		0			0
$472$	1.56198	+	2.70542i	0.0718958	+	0.124527i
$473$	−7.41789	−	12.8482i	−0.341075	−	0.590759i
$474$		0			0
$475$		0			0
$476$	7.46106	−	5.58312i	0.341977	−	0.255902i
$477$		0			0
$478$	−15.1952	−	8.77298i	−0.695014	−	0.401267i
$479$	−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
$482$			10.0005i			0.455510i
$483$		0			0
$484$	8.43849			0.383568
$485$		0			0
$486$		0			0
$487$	4.99120	−	2.88167i	0.226173	−	0.130581i	−0.382632	−	0.923901i	$-0.624982\pi$
$487$	4.99120	−	2.88167i	0.226173	−	0.130581i	0.608805	+	0.793320i	$0.291649\pi$
$488$	−9.43214	−	5.44565i	−0.426973	−	0.246513i
$489$		0			0
$490$		0			0
$491$		−	2.90529i		−	0.131114i	−0.997849	−	0.0655570i	$-0.979118\pi$
$491$		−	2.90529i		−	0.131114i	0.997849	−	0.0655570i	$-0.0208824\pi$
$492$		0			0
$493$	−1.23411	−	2.13755i	−0.0555817	−	0.0962704i
$494$	2.36472	−	1.36527i	0.106394	−	0.0614265i
$495$		0			0
$496$			1.31318i			0.0589634i
$497$	15.7573	+	6.75111i	0.706810	+	0.302829i
$498$		0			0
$499$	1.14104	−	1.97634i	0.0510800	−	0.0884732i	−0.839355	−	0.543584i	$-0.817067\pi$
$499$	1.14104	−	1.97634i	0.0510800	−	0.0884732i	0.890435	+	0.455111i	$0.150400\pi$
$500$		0			0
$501$		0			0
$502$	1.77706	−	3.07796i	0.0793141	−	0.137376i
$503$			1.32664i			0.0591520i	0.999563	+	0.0295760i	$0.00941571\pi$
$503$			1.32664i			0.0591520i	−0.999563	+	0.0295760i	$0.990584\pi$
$504$		0			0
$505$		0			0
$506$	4.47375	+	2.58292i	0.198882	+	0.114825i
$507$		0			0
$508$	2.30801	−	1.33253i	0.102402	−	0.0591215i
$509$	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
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.15756	−	3.55507i	0.271598	−	0.156807i
$515$		0			0
$516$		0			0
$517$	4.27758			0.188128
$518$	−0.286843	−	2.40285i	−0.0126032	−	0.105575i
$519$		0			0
$520$		0			0
$521$	−19.8838	−	34.4397i	−0.871124	−	1.50883i	−0.860835	−	0.508884i	$-0.830058\pi$
$521$	−19.8838	−	34.4397i	−0.871124	−	1.50883i	−0.0102890	−	0.999947i	$-0.503275\pi$
$522$		0			0
$523$	19.8804	−	34.4338i	0.869307	−	1.50568i	0.00660128	−	0.999978i	$-0.497899\pi$
$523$	19.8804	−	34.4338i	0.869307	−	1.50568i	0.862706	−	0.505706i	$-0.168768\pi$
$524$	14.2197			0.621192
$525$		0			0
$526$	28.5503			1.24485
$527$	−2.31260	+	4.00555i	−0.100739	+	0.174484i
$528$		0			0
$529$	6.29098	+	10.8963i	0.273521	+	0.473752i
$530$		0			0
$531$		0			0
$532$	8.61594	+	3.69145i	0.373548	+	0.160045i
$533$	−3.76242			−0.162969
$534$		0			0
$535$		0			0
$536$	5.90314	−	3.40818i	0.254977	−	0.147211i
$537$		0			0
$538$	25.9257			1.11774
$539$	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	$0.309656\pi$
$542$	24.1643	−	13.9513i	1.03795	−	0.599258i
$543$		0			0
$544$	3.05027	+	1.76107i	0.130779	+	0.0755054i
$545$		0			0
$546$		0			0
$547$			34.5631i			1.47781i	0.673810	+	0.738905i	$0.264657\pi$
$547$			34.5631i			1.47781i	−0.673810	+	0.738905i	$0.735343\pi$
$548$	−0.0650662	+	0.112698i	−0.00277949	+	0.00481422i
$549$		0			0
$550$		0			0
$551$	1.24136	−	2.15010i	0.0528837	−	0.0915973i
$552$		0			0
$553$	−4.59965	−	6.14679i	−0.195597	−	0.261388i
$554$			10.3697i			0.440566i
$555$		0			0
$556$	3.14863	−	1.81786i	0.133532	−	0.0770945i
$557$	16.2396	+	28.1278i	0.688094	+	1.19181i	0.972454	+	0.233096i	$0.0748856\pi$
$557$	16.2396	+	28.1278i	0.688094	+	1.19181i	−0.284360	+	0.958718i	$0.591781\pi$
$558$		0			0
$559$			7.14434i			0.302173i
$560$		0			0
$561$		0			0
$562$	−18.2222	−	10.5206i	−0.768658	−	0.443785i
$563$	−12.4603	+	7.19395i	−0.525139	+	0.303189i	−0.739035	−	0.673668i	$-0.764718\pi$
$563$	−12.4603	+	7.19395i	−0.525139	+	0.303189i	0.213896	+	0.976856i	$0.431385\pi$
$564$		0			0
$565$		0			0
$566$	−27.3718			−1.15052
$567$		0			0
$568$			6.47930i			0.271865i
$569$	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	$0.555250\pi$
$572$	1.06826	+	0.616762i	0.0446664	+	0.0257881i
$573$		0			0
$574$	−7.73815	−	10.3410i	−0.322984	−	0.431624i
$575$		0			0
$576$		0			0
$577$	11.6961	+	20.2583i	0.486916	+	0.843363i	0.999887	−	0.0150431i	$-0.00478854\pi$
$577$	11.6961	+	20.2583i	0.486916	+	0.843363i	−0.512971	+	0.858406i	$0.671455\pi$
$578$	−2.29724	−	3.97894i	−0.0955527	−	0.165502i
$579$		0			0
$580$		0			0
$581$	29.1290	+	12.4802i	1.20848	+	0.517765i
$582$		0			0
$583$	−12.8770	−	7.43451i	−0.533309	−	0.307906i
$584$	5.51852	+	9.55835i	0.228358	+	0.395527i
$585$		0			0
$586$	−14.6409	−	8.45295i	−0.604812	−	0.349188i
$587$		−	23.7776i		−	0.981407i	−0.871327	−	0.490704i	$-0.836740\pi$
$587$		−	23.7776i		−	0.981407i	0.871327	−	0.490704i	$-0.163260\pi$
$588$		0			0
$589$	−4.65236			−0.191697
$590$		0			0
$591$		0			0
$592$	0.792101	−	0.457320i	0.0325551	−	0.0187957i
$593$	−33.6979	−	19.4555i	−1.38381	−	0.798942i	−0.391200	−	0.920306i	$-0.627940\pi$
$593$	−33.6979	−	19.4555i	−1.38381	−	0.798942i	−0.992608	+	0.121364i	$0.961273\pi$
$594$		0			0
$595$		0			0
$596$			2.93244i			0.120117i
$597$		0			0
$598$	−1.24384	−	2.15439i	−0.0508642	−	0.0880994i
$599$	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	$0.856821\pi$
$602$	−19.6361	+	14.6937i	−0.800308	+	0.598871i
$603$		0			0
$604$	−3.56919	+	6.18201i	−0.145228	+	0.251543i
$605$		0			0
$606$		0			0
$607$	0.285402	−	0.494331i	0.0115841	−	0.0200643i	−0.860175	−	0.509999i	$-0.829646\pi$
$607$	0.285402	−	0.494331i	0.0115841	−	0.0200643i	0.871759	+	0.489934i	$0.162979\pi$
$608$			3.54282i			0.143681i
$609$		0			0
$610$		0			0
$611$	−1.78394	−	1.02996i	−0.0721705	−	0.0416676i
$612$		0			0
$613$	29.5954	−	17.0869i	1.19535	−	0.690134i	0.235833	−	0.971794i	$-0.424218\pi$
$613$	29.5954	−	17.0869i	1.19535	−	0.690134i	0.959514	+	0.281659i	$0.0908848\pi$
$614$	7.00693	−	12.1364i	0.282777	−	0.489783i
$615$		0			0
$616$	0.501930	+	4.20460i	0.0202233	+	0.169408i
$617$	20.1713			0.812066			0.406033	−	0.913858i	$-0.366912\pi$
$617$	20.1713			0.812066			0.406033	+	0.913858i	$0.366912\pi$
$618$		0			0
$619$	−13.9621	+	8.06104i	−0.561186	+	0.324001i	−0.753621	−	0.657309i	$-0.771695\pi$
$619$	−13.9621	+	8.06104i	−0.561186	+	0.324001i	0.192436	+	0.981310i	$0.438361\pi$
$620$		0			0
$621$		0			0
$622$	13.4442			0.539064
$623$	−13.9610	−	18.6569i	−0.559336	−	0.747474i
$624$		0			0
$625$		0			0
$626$	2.12904	+	3.68760i	0.0850935	+	0.147386i
$627$		0			0
$628$	7.15702	−	12.3963i	0.285596	−	0.494667i
$629$	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	$0.480305\pi$
$632$	1.45086	−	2.51296i	0.0577121	−	0.0999603i
$633$		0			0
$634$	−0.0987910	−	0.171111i	−0.00392349	−	0.00679569i
$635$		0			0
$636$		0			0
$637$	−3.72158	−	3.90598i	−0.147454	−	0.154761i
$638$	1.12157			0.0444034
$639$		0			0
$640$		0			0
$641$	−18.9248	+	10.9262i	−0.747483	+	0.431559i	−0.824784	−	0.565448i	$-0.808703\pi$
$641$	−18.9248	+	10.9262i	−0.747483	+	0.431559i	0.0773008	+	0.997008i	$0.475370\pi$
$642$		0			0
$643$	25.4873			1.00512			0.502560	−	0.864542i	$-0.332391\pi$
$643$	25.4873			1.00512			0.502560	+	0.864542i	$0.332391\pi$
$644$	3.36311	−	7.84957i	0.132525	−	0.309317i
$645$		0			0
$646$	−6.23917	+	10.8066i	−0.245477	+	0.425179i
$647$	−41.5745	+	24.0030i	−1.63446	+	0.943657i	−0.651768	+	0.758418i	$0.725973\pi$
$647$	−41.5745	+	24.0030i	−1.63446	+	0.943657i	−0.982694	+	0.185239i	$0.940694\pi$
$648$		0			0
$649$	−4.32995	−	2.49990i	−0.169966	−	0.0981296i
$650$		0			0
$651$		0			0
$652$			7.20895i			0.282324i
$653$	−23.0213	+	39.8741i	−0.900894	+	1.56039i	−0.0745575	+	0.997217i	$0.523754\pi$
$653$	−23.0213	+	39.8741i	−0.900894	+	1.56039i	−0.826336	+	0.563177i	$0.809579\pi$
$654$		0			0
$655$		0			0
$656$	2.44083	−	4.22765i	0.0952985	−	0.165062i
$657$		0			0
$658$	−0.838194	−	7.02144i	−0.0326762	−	0.273724i
$659$			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	$0.0237775\pi$
$662$	−2.29740	−	3.97922i	−0.0892911	−	0.154657i
$663$		0			0
$664$			11.9777i			0.464824i
$665$		0			0
$666$		0			0
$667$	−1.95885	−	1.13094i	−0.0758471	−	0.0437903i
$668$	−12.0336	+	6.94758i	−0.465593	+	0.268810i
$669$		0			0
$670$		0			0
$671$	17.4312			0.672925
$672$		0			0
$673$		−	50.6101i		−	1.95088i	−0.220270	−	0.975439i	$-0.570694\pi$
$673$		−	50.6101i		−	1.95088i	0.220270	−	0.975439i	$-0.429306\pi$
$674$	−5.24011	−	3.02538i	−0.201841	−	0.116533i
$675$		0			0
$676$	6.20299	+	10.7439i	0.238577	+	0.413227i
$677$	29.9259	+	17.2777i	1.15015	+	0.664037i	0.948923	−	0.315508i	$-0.102175\pi$
$677$	29.9259	+	17.2777i	1.15015	+	0.664037i	0.201223	+	0.979545i	$0.435508\pi$
$678$		0			0
$679$	5.53510	−	12.9191i	0.212418	−	0.495788i
$680$		0			0
$681$		0			0
$682$	−1.05085	−	1.82013i	−0.0402392	−	0.0696964i
$683$	−8.57731	−	14.8563i	−0.328202	−	0.568462i	0.653953	−	0.756535i	$-0.273109\pi$
$683$	−8.57731	−	14.8563i	−0.328202	−	0.568462i	−0.982155	+	0.188073i	$0.939776\pi$
$684$		0			0
$685$		0			0
$686$	3.08138	−	18.2621i	0.117648	−	0.697251i
$687$		0			0
$688$	−8.02773	−	4.63481i	−0.306055	−	0.176701i
$689$	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	$0.903763\pi$
$692$			2.36740i			0.0899951i
$693$		0			0
$694$	3.18204			0.120788
$695$		0			0
$696$		0			0
$697$	14.8904	−	8.59697i	0.564014	−	0.325633i
$698$	−25.1643	−	14.5286i	−0.952484	−	0.549917i
$699$		0			0
$700$		0			0
$701$		−	23.0808i		−	0.871751i	−0.900007	−	0.435876i	$-0.856439\pi$
$701$		−	23.0808i		−	0.871751i	0.900007	−	0.435876i	$-0.143561\pi$
$702$		0			0
$703$	1.62020	+	2.80627i	0.0611071	+	0.105841i
$704$	−1.38605	+	0.800236i	−0.0522387	+	0.0301600i
$705$		0			0
$706$			7.66655i			0.288534i
$707$	24.3092	−	2.90195i	0.914243	−	0.109139i
$708$		0			0
$709$	4.08362	−	7.07303i	0.153363	−	0.265633i	−0.779098	−	0.626902i	$-0.784323\pi$
$709$	4.08362	−	7.07303i	0.153363	−	0.265633i	0.932462	+	0.361268i	$0.117656\pi$
$710$		0			0
$711$		0			0
$712$	4.40369	−	7.62742i	0.165035	−	0.285850i
$713$			4.23854i			0.158735i
$714$		0			0
$715$		0			0
$716$	15.4837	+	8.93953i	0.578654	+	0.334086i
$717$		0			0
$718$	19.6694	−	11.3561i	0.734054	−	0.423806i
$719$	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
$722$	6.44839			0.239984
$723$		0			0
$724$	−14.4343	+	8.33363i	−0.536446	+	0.309717i
$725$		0			0
$726$		0			0
$727$	−4.27807			−0.158665			−0.0793325	−	0.996848i	$-0.525279\pi$
$727$	−4.27807			−0.158665			−0.0793325	+	0.996848i	$0.525279\pi$
$728$	0.803059	−	1.87436i	0.0297634	−	0.0694684i
$729$		0			0
$730$		0			0
$731$	−16.3245	−	28.2749i	−0.603783	−	1.04578i
$732$		0			0
$733$	16.7810	−	29.0656i	0.619822	−	1.07356i	−0.369696	−	0.929153i	$-0.620538\pi$
$733$	16.7810	−	29.0656i	0.619822	−	1.07356i	0.989518	−	0.144410i	$-0.0461286\pi$
$734$	−18.7487			−0.692026
$735$		0			0
$736$	3.22770			0.118975
$737$	−5.45470	+	9.44781i	−0.200926	+	0.348015i
$738$		0			0
$739$	17.3726	+	30.0902i	0.639060	+	1.10688i	0.985639	+	0.168864i	$0.0540099\pi$
$739$	17.3726	+	30.0902i	0.639060	+	1.10688i	−0.346579	+	0.938021i	$0.612657\pi$
$740$		0			0
$741$		0			0
$742$	−9.68015	+	22.5937i	−0.355369	+	0.829441i
$743$	−14.3040			−0.524762			−0.262381	−	0.964964i	$-0.584508\pi$
$743$	−14.3040			−0.524762			−0.262381	+	0.964964i	$0.584508\pi$
$744$		0			0
$745$		0			0
$746$	2.46050	−	1.42057i	0.0900854	−	0.0520109i
$747$		0			0
$748$	−5.63710			−0.206113
$749$	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	$0.882965\pi$
$752$	2.31462	−	1.33635i	0.0844056	−	0.0487316i
$753$		0			0
$754$	−0.467744	−	0.270052i	−0.0170342	−	0.00983473i
$755$		0			0
$756$		0			0
$757$			2.92253i			0.106221i	0.998589	+	0.0531107i	$0.0169136\pi$
$757$			2.92253i			0.106221i	−0.998589	+	0.0531107i	$0.983086\pi$
$758$	−13.6375	+	23.6208i	−0.495336	+	0.857946i
$759$		0			0
$760$		0			0
$761$	−15.2447	+	26.4046i	−0.552621	+	0.957167i	0.445464	+	0.895300i	$0.353039\pi$
$761$	−15.2447	+	26.4046i	−0.552621	+	0.957167i	−0.998084	+	0.0618669i	$0.980295\pi$
$762$		0			0
$763$	−28.9900	+	3.46072i	−1.04951	+	0.125287i
$764$		−	24.7520i		−	0.895496i
$765$		0			0
$766$	26.1843	−	15.1175i	0.946077	−	0.546218i
$767$	1.20386	+	2.08514i	0.0434687	+	0.0752900i
$768$		0			0
$769$		−	42.7989i		−	1.54337i	−0.636005	−	0.771685i	$-0.719414\pi$
$769$		−	42.7989i		−	1.54337i	0.636005	−	0.771685i	$-0.280586\pi$
$770$		0			0
$771$		0			0
$772$	10.8917	+	6.28835i	0.392002	+	0.226323i
$773$	34.9867	−	20.1996i	1.25838	−	0.726529i	0.285624	−	0.958342i	$-0.407799\pi$
$773$	34.9867	−	20.1996i	1.25838	−	0.726529i	0.972760	+	0.231813i	$0.0744657\pi$
$774$		0			0
$775$		0			0
$776$	5.31224			0.190698
$777$		0			0
$778$			4.96045i			0.177841i
$779$	14.9778	+	8.64744i	0.536636	+	0.309827i
$780$		0			0
$781$	−5.18497	−	8.98062i	−0.185533	−	0.321352i
$782$	9.84535	+	5.68421i	0.352069	+	0.203267i
$783$		0			0
$784$	6.80329	−	1.64779i	0.242975	−	0.0588495i
$785$		0			0
$786$		0			0
$787$	15.8780	+	27.5015i	0.565990	+	0.980323i	0.996957	+	0.0779556i	$0.0248392\pi$
$787$	15.8780	+	27.5015i	0.565990	+	0.980323i	−0.430967	+	0.902368i	$0.641827\pi$
$788$	9.86800	+	17.0919i	0.351533	+	0.608873i
$789$		0			0
$790$		0			0
$791$	15.6607	−	36.5524i	0.556829	−	1.29965i
$792$		0			0
$793$	−7.26959	−	4.19710i	−0.258151	−	0.149043i
$794$	7.30213	+	12.6477i	0.259143	+	0.448849i
$795$		0			0
$796$	9.82275	+	5.67117i	0.348158	+	0.201009i
$797$			2.25420i			0.0798477i	0.999203	+	0.0399239i	$0.0127115\pi$
$797$			2.25420i			0.0798477i	−0.999203	+	0.0399239i	$0.987288\pi$
$798$		0			0
$799$	9.41363			0.333030
$800$		0			0
$801$		0			0
$802$	−17.5622	+	10.1395i	−0.620143	+	0.358040i
$803$	−15.2979	−	8.83223i	−0.539850	−	0.311683i
$804$		0			0
$805$		0			0
$806$			1.01210i			0.0356497i
$807$		0			0
$808$	4.62663	+	8.01356i	0.162764	+	0.281916i
$809$	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	$-0.0691883\pi$
$812$	−0.219772	−	1.84100i	−0.00771250	−	0.0646065i
$813$		0			0
$814$	−0.731927	+	1.26774i	−0.0256540	+	0.0444341i
$815$		0			0
$816$		0			0
$817$	16.4203	−	28.4409i	0.574475	−	0.995020i
$818$		−	4.92915i		−	0.172344i
$819$		0			0
$820$		0			0
$821$	31.8702	+	18.4003i	1.11228	+	0.642174i	0.939418	−	0.342773i	$-0.111366\pi$
$821$	31.8702	+	18.4003i	1.11228	+	0.642174i	0.172859	+	0.984947i	$0.444699\pi$
$822$		0			0
$823$	13.9608	−	8.06030i	0.486644	−	0.280964i	−0.236537	−	0.971622i	$-0.576012\pi$
$823$	13.9608	−	8.06030i	0.486644	−	0.280964i	0.723181	+	0.690658i	$0.242679\pi$
$824$	−7.91290	+	13.7055i	−0.275659	+	0.477455i
$825$		0			0
$826$	−3.25501	+	7.59727i	−0.113256	+	0.264343i
$827$	−35.1713			−1.22302			−0.611512	−	0.791235i	$-0.709438\pi$
$827$	−35.1713			−1.22302			−0.611512	+	0.791235i	$0.709438\pi$
$828$		0			0
$829$	−3.89744	+	2.25019i	−0.135364	+	0.0781522i	−0.566152	−	0.824301i	$-0.691569\pi$
$829$	−3.89744	+	2.25019i	−0.135364	+	0.0781522i	0.430789	+	0.902453i	$0.358235\pi$
$830$		0			0
$831$		0			0
$832$	0.770726			0.0267201
$833$	23.6537	+	6.95490i	0.819554	+	0.240973i
$834$		0			0
$835$		0			0
$836$	−2.83510	−	4.91053i	−0.0980539	−	0.169834i
$837$		0			0
$838$	12.0343	−	20.8440i	0.415718	−	0.720044i
$839$	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
$842$	−8.03286	+	13.9133i	−0.276831	+	0.479485i
$843$		0			0
$844$	−8.03236	−	13.9125i	−0.276485	−	0.478886i
$845$		0			0
$846$		0			0
$847$	13.3762	+	17.8755i	0.459613	+	0.614209i
$848$	−9.29040			−0.319034
$849$		0			0
$850$		0			0
$851$	2.55666	−	1.47609i	0.0876413	−	0.0505997i
$852$		0			0
$853$	33.4928			1.14677			0.573386	−	0.819285i	$-0.305629\pi$
$853$	33.4928			1.14677			0.573386	+	0.819285i	$0.305629\pi$
$854$	−3.41566	−	28.6125i	−0.116881	−	0.979100i
$855$		0			0
$856$	−6.20735	+	10.7514i	−0.212163	+	0.367477i
$857$	38.7373	−	22.3650i	1.32324	−	0.763973i	0.338996	−	0.940788i	$-0.389913\pi$
$857$	38.7373	−	22.3650i	1.32324	−	0.763973i	0.984244	+	0.176815i	$0.0565793\pi$
$858$		0			0
$859$	26.4154	+	15.2509i	0.901281	+	0.520355i	0.877616	−	0.479365i	$-0.159133\pi$
$859$	26.4154	+	15.2509i	0.901281	+	0.520355i	0.0236654	+	0.999720i	$0.492466\pi$
$860$		0			0
$861$		0			0
$862$			0.431501i			0.0146970i
$863$	11.8770	−	20.5715i	0.404297	−	0.700262i	−0.589943	−	0.807445i	$-0.700850\pi$
$863$	11.8770	−	20.5715i	0.404297	−	0.700262i	0.994239	+	0.107183i	$0.0341830\pi$
$864$		0			0
$865$		0			0
$866$	−15.2643	+	26.4386i	−0.518703	+	0.898420i
$867$		0			0
$868$	−2.78174	+	2.08158i	−0.0944185	+	0.0706534i
$869$			4.64412i			0.157541i
$870$		0			0
$871$	4.54970	−	2.62677i	0.154161	−	0.0890047i
$872$	−5.51750	−	9.55659i	−0.186846	−	0.323627i
$873$		0			0
$874$			11.4352i			0.386800i
$875$		0			0
$876$		0			0
$877$	−11.8940	−	6.86700i	−0.401632	−	0.231882i	0.285556	−	0.958362i	$-0.407822\pi$
$877$	−11.8940	−	6.86700i	−0.401632	−	0.231882i	−0.687188	+	0.726480i	$0.741155\pi$
$878$	−32.9059	+	18.9982i	−1.11052	+	0.641159i
$879$		0			0
$880$		0			0
$881$	−45.0753			−1.51863			−0.759313	−	0.650726i	$-0.774465\pi$
$881$	−45.0753			−1.51863			−0.759313	+	0.650726i	$0.774465\pi$
$882$		0			0
$883$		−	5.61116i		−	0.188831i	−0.995533	−	0.0944153i	$-0.969902\pi$
$883$		−	5.61116i		−	0.188831i	0.995533	−	0.0944153i	$-0.0300981\pi$
$884$	2.35092	+	1.35730i	0.0790700	+	0.0456511i
$885$		0			0
$886$	−11.6503	−	20.1789i	−0.391399	−	0.677923i
$887$	−11.9041	−	6.87285i	−0.399701	−	0.230768i	0.286654	−	0.958034i	$-0.407457\pi$
$887$	−11.9041	−	6.87285i	−0.399701	−	0.230768i	−0.686355	+	0.727267i	$0.740790\pi$
$888$		0			0
$889$	6.48128	+	2.77687i	0.217375	+	0.0931332i
$890$		0			0
$891$		0			0
$892$	−1.00459	−	1.73999i	−0.0336360	−	0.0582593i
$893$	4.73445	+	8.20031i	0.158432	+	0.274413i
$894$		0			0
$895$		0			0
$896$	1.58515	+	2.11833i	0.0529560	+	0.0707683i
$897$		0			0
$898$	18.9762	+	10.9559i	0.633245	+	0.365604i
$899$	0.460121	+	0.796953i	0.0153459	+	0.0265799i
$900$		0			0
$901$	−28.3382	−	16.3611i	−0.944083	−	0.545066i
$902$			7.81297i			0.260143i
$903$		0			0
$904$	15.0301			0.499894
$905$		0			0
$906$		0			0
$907$	−5.01644	+	2.89624i	−0.166568	+	0.0961681i	−0.580967	−	0.813927i	$-0.697325\pi$
$907$	−5.01644	+	2.89624i	−0.166568	+	0.0961681i	0.414399	+	0.910096i	$0.363992\pi$
$908$	−3.38249	−	1.95288i	−0.112252	−	0.0648086i
$909$		0			0
$910$		0			0
$911$		−	14.9139i		−	0.494120i	−0.969000	−	0.247060i	$-0.920535\pi$
$911$		−	14.9139i		−	0.494120i	0.969000	−	0.247060i	$-0.0794645\pi$
$912$		0			0
$913$	−9.58497	−	16.6017i	−0.317216	−	0.549435i
$914$	34.0904	−	19.6821i	1.12761	−	0.651027i
$915$		0			0
$916$			13.3835i			0.442203i
$917$	22.5404	+	30.1221i	0.744349	+	0.994719i
$918$		0			0
$919$	27.3387	−	47.3520i	0.901821	−	1.56200i	0.0766921	−	0.997055i	$-0.475564\pi$
$919$	27.3387	−	47.3520i	0.901821	−	1.56200i	0.825129	−	0.564945i	$-0.191103\pi$
$920$		0			0
$921$		0			0
$922$	1.17641	−	2.03760i	0.0387430	−	0.0671049i
$923$			4.99376i			0.164372i
$924$		0			0
$925$		0			0
$926$	−1.94466	−	1.12275i	−0.0639056	−	0.0368959i
$927$		0			0
$928$	0.606888	−	0.350387i	0.0199221	−	0.0115020i
$929$	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
$932$	10.2962			0.337262
$933$		0			0
$934$	27.8740	−	16.0931i	0.912066	−	0.526582i
$935$		0			0
$936$		0			0
$937$	−12.4762			−0.407578			−0.203789	−	0.979015i	$-0.565326\pi$
$937$	−12.4762			−0.407578			−0.203789	+	0.979015i	$0.565326\pi$
$938$	16.5770	+	7.10232i	0.541258	+	0.231899i
$939$		0			0
$940$		0			0
$941$	−6.11387	−	10.5895i	−0.199307	−	0.345209i	0.748997	−	0.662573i	$-0.230536\pi$
$941$	−6.11387	−	10.5895i	−0.199307	−	0.345209i	−0.948304	+	0.317364i	$0.897202\pi$
$942$		0			0
$943$	7.87827	−	13.6456i	0.256552	−	0.444361i
$944$	−3.12395			−0.101676
$945$		0			0
$946$	14.8358			0.482353
$947$	0.915974	−	1.58651i	0.0297652	−	0.0515548i	−0.850759	−	0.525556i	$-0.823857\pi$
$947$	0.915974	−	1.58651i	0.0297652	−	0.0515548i	0.880524	+	0.474001i	$0.157191\pi$
$948$		0			0
$949$	4.25326	+	7.36687i	0.138067	+	0.239139i
$950$		0			0
$951$		0			0
$952$	1.10459	+	9.25303i	0.0358001	+	0.299892i
$953$	42.7813			1.38582			0.692911	−	0.721023i	$-0.256328\pi$
$953$	42.7813			1.38582			0.692911	+	0.721023i	$0.256328\pi$
$954$		0			0
$955$		0			0
$956$	15.1952	−	8.77298i	0.491449	−	0.283738i
$957$		0			0
$958$	6.61111			0.213595
$959$	−0.341870	+	0.0408113i	−0.0110396	+	0.00131786i
$960$		0			0
$961$	−14.6378	+	25.3534i	−0.472186	+	0.817851i
$962$	0.610493	−	0.352468i	0.0196831	−	0.0113640i
$963$		0			0
$964$	−8.66068	−	5.00024i	−0.278942	−	0.161047i
$965$		0			0
$966$		0			0
$967$			24.5160i			0.788380i	0.919029	+	0.394190i	$0.128975\pi$
$967$			24.5160i			0.788380i	−0.919029	+	0.394190i	$0.871025\pi$
$968$	−4.21924	+	7.30795i	−0.135612	+	0.234886i
$969$		0			0
$970$		0			0
$971$	11.5704	−	20.0405i	0.371312	−	0.643131i	−0.618456	−	0.785820i	$-0.712241\pi$
$971$	11.5704	−	20.0405i	0.371312	−	0.643131i	0.989768	+	0.142688i	$0.0455747\pi$
$972$		0			0
$973$	8.84186	+	3.78825i	0.283457	+	0.121446i
$974$			5.76335i			0.184669i
$975$		0			0
$976$	9.43214	−	5.44565i	0.301915	−	0.174311i
$977$	23.3254	+	40.4007i	0.746244	+	1.29253i	0.949611	+	0.313430i	$0.101478\pi$
$977$	23.3254	+	40.4007i	0.746244	+	1.29253i	−0.203367	+	0.979103i	$0.565188\pi$
$978$		0			0
$979$			14.0960i			0.450510i
$980$		0			0
$981$		0			0
$982$	2.51606	+	1.45265i	0.0802906	+	0.0463558i
$983$	−4.26934	+	2.46490i	−0.136171	+	0.0786182i	−0.566538	−	0.824036i	$-0.691717\pi$
$983$	−4.26934	+	2.46490i	−0.136171	+	0.0786182i	0.430367	+	0.902654i	$0.358384\pi$
$984$		0			0
$985$		0			0
$986$	2.46823			0.0786044
$987$		0			0
$988$			2.73055i			0.0868702i
$989$	−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	$0.947722\pi$
$992$	−1.13725	−	0.656589i	−0.0361076	−	0.0208467i
$993$		0			0
$994$	−13.7253	+	10.2706i	−0.435339	+	0.325765i
$995$		0			0
$996$		0			0
$997$	6.94487	+	12.0289i	0.219946	+	0.380958i	0.954791	−	0.297277i	$-0.0960785\pi$
$997$	6.94487	+	12.0289i	0.219946	+	0.380958i	−0.734845	+	0.678235i	$0.762745\pi$
$998$	1.14104	+	1.97634i	0.0361190	+	0.0625600i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.bf.d.1151.5	✓	24	35.3	even	12
3150.2.bf.d.1151.8	yes	24	105.38	odd	12
3150.2.bf.d.1601.5	yes	24	15.8	even	4
3150.2.bf.d.1601.8	yes	24	5.3	odd	4
3150.2.bf.e.1151.5	yes	24	105.17	odd	12
3150.2.bf.e.1151.8	yes	24	35.17	even	12
3150.2.bf.e.1601.5	yes	24	5.2	odd	4
3150.2.bf.e.1601.8	yes	24	15.2	even	4
3150.2.bp.g.899.6		24	7.3	odd	6	inner
3150.2.bp.g.899.7		24	105.59	even	6	inner
3150.2.bp.g.1349.6		24	15.14	odd	2	inner
3150.2.bp.g.1349.7		24	1.1	even	1	trivial
3150.2.bp.h.899.6		24	21.17	even	6
3150.2.bp.h.899.7		24	35.24	odd	6
3150.2.bp.h.1349.6		24	5.4	even	2
3150.2.bp.h.1349.7		24	3.2	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.bp (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.04195 - 2.43194i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.04195 - 2.43194i) q^{7} +1.00000 q^{8} +(-1.38605 + 0.800236i) q^{11} +0.770726 q^{13} +(1.58515 + 2.11833i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.05027 + 1.76107i) q^{17} +(-3.06818 - 1.77141i) q^{19} -1.60047i q^{22} +(-1.61385 + 2.79527i) q^{23} +(-0.385363 + 0.667468i) q^{26} +(-2.62710 + 0.313613i) q^{28} +0.700774i q^{29} +(1.13725 - 0.656589i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.52215i q^{34} +(-0.792101 - 0.457320i) q^{37} +(3.06818 - 1.77141i) q^{38} -4.88167 q^{41} +9.26963i q^{43} +(1.38605 + 0.800236i) q^{44} +(-1.61385 - 2.79527i) q^{46} +(-2.31462 - 1.33635i) q^{47} +(-4.82867 - 5.06793i) q^{49} +(-0.385363 - 0.667468i) q^{52} +(4.64520 + 8.04572i) q^{53} +(1.04195 - 2.43194i) q^{56} +(-0.606888 - 0.350387i) q^{58} +(1.56198 + 2.70542i) q^{59} +(-9.43214 - 5.44565i) q^{61} +1.31318i q^{62} +1.00000 q^{64} +(5.90314 - 3.40818i) q^{67} +(3.05027 + 1.76107i) q^{68} +6.47930i q^{71} +(5.51852 + 9.55835i) q^{73} +(0.792101 - 0.457320i) q^{74} +3.54282i q^{76} +(0.501930 + 4.20460i) q^{77} +(1.45086 - 2.51296i) q^{79} +(2.44083 - 4.22765i) q^{82} +11.9777i q^{83} +(-8.02773 - 4.63481i) q^{86} +(-1.38605 + 0.800236i) q^{88} +(4.40369 - 7.62742i) q^{89} +(0.803059 - 1.87436i) q^{91} +3.22770 q^{92} +(2.31462 - 1.33635i) q^{94} +5.31224 q^{97} +(6.80329 - 1.64779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 12 q^{16} + 24 q^{17} - 12 q^{19} - 8 q^{23} - 12 q^{32} + 12 q^{38} - 8 q^{46} - 24 q^{47} + 52 q^{49} - 32 q^{53} - 12 q^{61} + 24 q^{64} - 24 q^{68} - 16 q^{77} - 4 q^{79} + 68 q^{91} + 16 q^{92} + 24 q^{94} - 20 q^{98}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 12 * q^16 + 24 * q^17 - 12 * q^19 - 8 * q^23 - 12 * q^32 + 12 * q^38 - 8 * q^46 - 24 * q^47 + 52 * q^49 - 32 * q^53 - 12 * q^61 + 24 * q^64 - 24 * q^68 - 16 * q^77 - 4 * q^79 + 68 * q^91 + 16 * q^92 + 24 * q^94 - 20 * q^98

Introduction

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