LMFDB - Embedded newform 600.2.m.e.299.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(299,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.m (of order $2$, degree $1$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.18
Character	$\chi$	$=$	600.299
Dual form			600.2.m.e.299.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.639662 - 1.26128i) q^{2} +(-0.730070 + 1.57067i) q^{3} +(-1.18166 - 1.61359i) q^{4} +(1.51406 + 1.92552i) q^{6} +1.25539 q^{7} +(-2.79106 + 0.458259i) q^{8} +(-1.93400 - 2.29339i) q^{9} +O(q^{10})$	\(q+(0.639662 - 1.26128i) q^{2} +(-0.730070 + 1.57067i) q^{3} +(-1.18166 - 1.61359i) q^{4} +(1.51406 + 1.92552i) q^{6} +1.25539 q^{7} +(-2.79106 + 0.458259i) q^{8} +(-1.93400 - 2.29339i) q^{9} -3.02346i q^{11} +(3.39711 - 0.677969i) q^{12} +5.65509 q^{13} +(0.803023 - 1.58339i) q^{14} +(-1.20734 + 3.81344i) q^{16} +2.45546 q^{17} +(-4.12972 + 0.972316i) q^{18} -1.77801 q^{19} +(-0.916519 + 1.97179i) q^{21} +(-3.81344 - 1.93400i) q^{22} -8.84074i q^{23} +(1.31789 - 4.71839i) q^{24} +(3.61735 - 7.13266i) q^{26} +(5.01411 - 1.36333i) q^{27} +(-1.48344 - 2.02568i) q^{28} +3.79561 q^{29} -5.19897i q^{31} +(4.03753 + 3.96211i) q^{32} +(4.74886 + 2.20734i) q^{33} +(1.57067 - 3.09703i) q^{34} +(-1.41526 + 5.83070i) q^{36} +6.45436 q^{37} +(-1.13732 + 2.24257i) q^{38} +(-4.12861 + 8.88227i) q^{39} -7.57276i q^{41} +(1.90072 + 2.41727i) q^{42} +4.37266i q^{43} +(-4.87863 + 3.57272i) q^{44} +(-11.1507 - 5.65509i) q^{46} -1.83304i q^{47} +(-5.10821 - 4.68041i) q^{48} -5.42401 q^{49} +(-1.79266 + 3.85672i) q^{51} +(-6.68241 - 9.12499i) q^{52} +12.0528i q^{53} +(1.48780 - 7.19628i) q^{54} +(-3.50385 + 0.575292i) q^{56} +(1.29807 - 2.79266i) q^{57} +(2.42791 - 4.78734i) q^{58} +4.91093i q^{59} -8.16586i q^{61} +(-6.55737 - 3.32559i) q^{62} +(-2.42791 - 2.87909i) q^{63} +(7.58000 - 2.55806i) q^{64} +(5.82174 - 4.57770i) q^{66} +8.50466i q^{67} +(-2.90153 - 3.96211i) q^{68} +(13.8859 + 6.45436i) q^{69} -7.00770 q^{71} +(6.44886 + 5.51472i) q^{72} -4.59465i q^{73} +(4.12861 - 8.14076i) q^{74} +(2.10101 + 2.86897i) q^{76} -3.79561i q^{77} +(8.56213 + 10.8890i) q^{78} +7.36659i q^{79} +(-1.51932 + 8.87083i) q^{81} +(-9.55139 - 4.84401i) q^{82} -15.7510 q^{83} +(4.26468 - 0.851113i) q^{84} +(5.51515 + 2.79702i) q^{86} +(-2.77106 + 5.96165i) q^{87} +(1.38553 + 8.43866i) q^{88} +3.65716i q^{89} +7.09931 q^{91} +(-14.2653 + 10.4468i) q^{92} +(8.16586 + 3.79561i) q^{93} +(-2.31198 - 1.17252i) q^{94} +(-9.17084 + 3.44901i) q^{96} +13.8773i q^{97} +(-3.46953 + 6.84120i) q^{98} +(-6.93400 + 5.84737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) $ 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9	$ 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9} - 12 q^{16} + 8 q^{19} - 10 q^{24} + 4 q^{34} + 38 q^{36} - 32 q^{46} + 72 q^{49} - 60 q^{51} + 60 q^{54} - 20 q^{64} + 14 q^{66} - 76 q^{76} - 20 q^{81} + 68 q^{84} - 48 q^{91} - 56 q^{94} - 62 q^{96} - 116 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9 - 12 * q^16 + 8 * q^19 - 10 * q^24 + 4 * q^34 + 38 * q^36 - 32 * q^46 + 72 * q^49 - 60 * q^51 + 60 * q^54 - 20 * q^64 + 14 * q^66 - 76 * q^76 - 20 * q^81 + 68 * q^84 - 48 * q^91 - 56 * q^94 - 62 * q^96 - 116 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.639662	−	1.26128i	0.452310	−	0.891861i
$2$	0.639662	−	1.26128i	0.452310	−	0.891861i
$3$	−0.730070	+	1.57067i	−0.421506	+	0.906826i
$3$	−0.730070	+	1.57067i	−0.421506	+	0.906826i
$4$	−1.18166	−	1.61359i	−0.590832	−	0.806795i
$5$		0			0
$5$		0			0
$6$	1.51406	+	1.92552i	0.618111	+	0.786091i
$7$	1.25539			0.474491			0.237245	−	0.971450i	$-0.423755\pi$
$7$	1.25539			0.474491			0.237245	+	0.971450i	$0.423755\pi$
$8$	−2.79106	+	0.458259i	−0.986788	+	0.162019i
$9$	−1.93400	−	2.29339i	−0.644665	−	0.764465i
$10$		0			0
$11$		−	3.02346i		−	0.911609i	−0.890080	−	0.455804i	$-0.849352\pi$
$11$		−	3.02346i		−	0.911609i	0.890080	−	0.455804i	$-0.150648\pi$
$12$	3.39711	−	0.677969i	0.980661	−	0.195713i
$13$	5.65509			1.56844			0.784220	−	0.620483i	$-0.213064\pi$
$13$	5.65509			1.56844			0.784220	+	0.620483i	$0.213064\pi$
$14$	0.803023	−	1.58339i	0.214617	−	0.423180i
$15$		0			0
$16$	−1.20734	+	3.81344i	−0.301835	+	0.953360i
$17$	2.45546			0.595538			0.297769	−	0.954638i	$-0.403758\pi$
$17$	2.45546			0.595538			0.297769	+	0.954638i	$0.403758\pi$
$18$	−4.12972	+	0.972316i	−0.973385	+	0.229177i
$19$	−1.77801			−0.407903			−0.203951	−	0.978981i	$-0.565378\pi$
$19$	−1.77801			−0.407903			−0.203951	+	0.978981i	$0.565378\pi$
$20$		0			0
$21$	−0.916519	+	1.97179i	−0.200001	+	0.430281i
$22$	−3.81344	−	1.93400i	−0.813028	−	0.412329i
$23$		−	8.84074i		−	1.84342i	−0.387878	−	0.921711i	$-0.626792\pi$
$23$		−	8.84074i		−	1.84342i	0.387878	−	0.921711i	$-0.373208\pi$
$24$	1.31789	−	4.71839i	0.269014	−	0.963136i
$25$		0			0
$26$	3.61735	−	7.13266i	0.709420	−	1.39883i
$27$	5.01411	−	1.36333i	0.964967	−	0.262373i
$28$	−1.48344	−	2.02568i	−0.280344	−	0.382817i
$29$	3.79561			0.704827			0.352414	−	0.935844i	$-0.385361\pi$
$29$	3.79561			0.704827			0.352414	+	0.935844i	$0.385361\pi$
$30$		0			0
$31$		−	5.19897i		−	0.933763i	−0.884320	−	0.466881i	$-0.845377\pi$
$31$		−	5.19897i		−	0.933763i	0.884320	−	0.466881i	$-0.154623\pi$
$32$	4.03753	+	3.96211i	0.713742	+	0.700409i
$33$	4.74886	+	2.20734i	0.826670	+	0.384249i
$34$	1.57067	−	3.09703i	0.269367	−	0.531137i
$35$		0			0
$36$	−1.41526	+	5.83070i	−0.235877	+	0.971783i
$37$	6.45436			1.06109			0.530545	−	0.847657i	$-0.321987\pi$
$37$	6.45436			1.06109			0.530545	+	0.847657i	$0.321987\pi$
$38$	−1.13732	+	2.24257i	−0.184498	+	0.363793i
$39$	−4.12861	+	8.88227i	−0.661107	+	1.42230i
$40$		0			0
$41$		−	7.57276i		−	1.18267i	−0.806427	−	0.591333i	$-0.798602\pi$
$41$		−	7.57276i		−	1.18267i	0.806427	−	0.591333i	$-0.201398\pi$
$42$	1.90072	+	2.41727i	0.293288	+	0.372993i
$43$			4.37266i			0.666824i	0.942781	+	0.333412i	$0.108200\pi$
$43$			4.37266i			0.666824i	−0.942781	+	0.333412i	$0.891800\pi$
$44$	−4.87863	+	3.57272i	−0.735481	+	0.538608i
$45$		0			0
$46$	−11.1507	−	5.65509i	−1.64408	−	0.833797i
$47$		−	1.83304i		−	0.267376i	−0.991023	−	0.133688i	$-0.957318\pi$
$47$		−	1.83304i		−	0.267376i	0.991023	−	0.133688i	$-0.0426820\pi$
$48$	−5.10821	−	4.68041i	−0.737306	−	0.675559i
$49$	−5.42401			−0.774858
$50$		0			0
$51$	−1.79266	+	3.85672i	−0.251023	+	0.540049i
$52$	−6.68241	−	9.12499i	−0.926684	−	1.26541i
$53$			12.0528i			1.65558i	0.561035	+	0.827792i	$0.310403\pi$
$53$			12.0528i			1.65558i	−0.561035	+	0.827792i	$0.689597\pi$
$54$	1.48780	−	7.19628i	0.202464	−	0.979290i
$55$		0			0
$56$	−3.50385	+	0.575292i	−0.468222	+	0.0768766i
$57$	1.29807	−	2.79266i	0.171934	−	0.369897i
$58$	2.42791	−	4.78734i	0.318800	−	0.628608i
$59$			4.91093i			0.639348i	0.947528	+	0.319674i	$0.103573\pi$
$59$			4.91093i			0.639348i	−0.947528	+	0.319674i	$0.896427\pi$
$60$		0			0
$61$		−	8.16586i		−	1.04553i	−0.852477	−	0.522766i	$-0.824900\pi$
$61$		−	8.16586i		−	1.04553i	0.852477	−	0.522766i	$-0.175100\pi$
$62$	−6.55737	−	3.32559i	−0.832787	−	0.422350i
$63$	−2.42791	−	2.87909i	−0.305888	−	0.362732i
$64$	7.58000	−	2.55806i	0.947500	−	0.319757i
$65$		0			0
$66$	5.82174	−	4.57770i	0.716607	−	0.563476i
$67$			8.50466i			1.03901i	0.854467	+	0.519505i	$0.173884\pi$
$67$			8.50466i			1.03901i	−0.854467	+	0.519505i	$0.826116\pi$
$68$	−2.90153	−	3.96211i	−0.351863	−	0.480476i
$69$	13.8859	+	6.45436i	1.67166	+	0.777013i
$70$		0			0
$71$	−7.00770			−0.831661			−0.415831	−	0.909442i	$-0.636509\pi$
$71$	−7.00770			−0.831661			−0.415831	+	0.909442i	$0.636509\pi$
$72$	6.44886	+	5.51472i	0.760006	+	0.649916i
$73$		−	4.59465i		−	0.537763i	−0.963173	−	0.268881i	$-0.913346\pi$
$73$		−	4.59465i		−	0.537763i	0.963173	−	0.268881i	$-0.0866540\pi$
$74$	4.12861	−	8.14076i	0.479941	−	0.946344i
$75$		0			0
$76$	2.10101	+	2.86897i	0.241002	+	0.329094i
$77$		−	3.79561i		−	0.432550i
$78$	8.56213	+	10.8890i	0.969470	+	1.23294i
$79$			7.36659i			0.828806i	0.910093	+	0.414403i	$0.136010\pi$
$79$			7.36659i			0.828806i	−0.910093	+	0.414403i	$0.863990\pi$
$80$		0			0
$81$	−1.51932	+	8.87083i	−0.168813	+	0.985648i
$82$	−9.55139	−	4.84401i	−1.05477	−	0.534932i
$83$	−15.7510			−1.72890			−0.864449	−	0.502720i	$-0.832333\pi$
$83$	−15.7510			−1.72890			−0.864449	+	0.502720i	$0.832333\pi$
$84$	4.26468	−	0.851113i	0.465315	−	0.0928640i
$85$		0			0
$86$	5.51515	+	2.79702i	0.594714	+	0.301611i
$87$	−2.77106	+	5.96165i	−0.297089	+	0.639156i
$88$	1.38553	+	8.43866i	0.147698	+	0.899564i
$89$			3.65716i			0.387658i	0.981035	+	0.193829i	$0.0620907\pi$
$89$			3.65716i			0.387658i	−0.981035	+	0.193829i	$0.937909\pi$
$90$		0			0
$91$	7.09931			0.744210
$92$	−14.2653	+	10.4468i	−1.48726	+	1.08915i
$93$	8.16586	+	3.79561i	0.846760	+	0.393587i
$94$	−2.31198	−	1.17252i	−0.238462	−	0.120937i
$95$		0			0
$96$	−9.17084	+	3.44901i	−0.935995	+	0.352013i
$97$			13.8773i			1.40903i	0.709690	+	0.704514i	$0.248835\pi$
$97$			13.8773i			1.40903i	−0.709690	+	0.704514i	$0.751165\pi$
$98$	−3.46953	+	6.84120i	−0.350476	+	0.691066i
$99$	−6.93400	+	5.84737i	−0.696893	+	0.587683i
$100$		0			0
$101$	13.8859			1.38170			0.690848	−	0.723000i	$-0.257237\pi$
$101$	13.8859			1.38170			0.690848	+	0.723000i	$0.257237\pi$
$102$	3.71771	+	4.72805i	0.368108	+	0.468147i
$103$	−7.36659			−0.725852			−0.362926	−	0.931818i	$-0.618222\pi$
$103$	−7.36659			−0.725852			−0.362926	+	0.931818i	$0.618222\pi$
$104$	−15.7837	+	2.59150i	−1.54772	+	0.254117i
$105$		0			0
$106$	15.2020	+	7.70974i	1.47655	+	0.748836i
$107$	−8.14076			−0.786997			−0.393499	−	0.919325i	$-0.628735\pi$
$107$	−8.14076			−0.786997			−0.393499	+	0.919325i	$0.628735\pi$
$108$	−8.12485	−	6.47972i	−0.781814	−	0.623512i
$109$		−	5.65509i		−	0.541659i	−0.962627	−	0.270830i	$-0.912702\pi$
$109$		−	5.65509i		−	0.541659i	0.962627	−	0.270830i	$-0.0872980\pi$
$110$		0			0
$111$	−4.71213	+	10.1377i	−0.447256	+	0.962223i
$112$	−1.51568	+	4.78734i	−0.143218	+	0.452361i
$113$	11.4884			1.08073			0.540367	−	0.841429i	$-0.318285\pi$
$113$	11.4884			1.08073			0.540367	+	0.841429i	$0.318285\pi$
$114$	−2.69201	−	3.42359i	−0.252129	−	0.320649i
$115$		0			0
$116$	−4.48514	−	6.12456i	−0.416435	−	0.568651i
$117$	−10.9369	−	12.9693i	−1.01112	−	1.19902i
$118$	6.19407	+	3.14134i	0.570210	+	0.289183i
$119$	3.08255			0.282577
$120$		0			0
$121$	1.85866			0.168969
$122$	−10.2994	−	5.22339i	−0.932468	−	0.472904i
$123$	11.8943	+	5.52865i	1.07247	+	0.498501i
$124$	−8.38900	+	6.14344i	−0.753355	+	0.551697i
$125$		0			0
$126$	−5.18439	+	1.22063i	−0.461862	+	0.108742i
$127$	21.7081			1.92628			0.963142	−	0.268993i	$-0.0866909\pi$
$127$	21.7081			1.92628			0.963142	+	0.268993i	$0.0866909\pi$
$128$	1.62221	−	11.1968i	0.143384	−	0.989667i
$129$	−6.86799	−	3.19234i	−0.604693	−	0.281070i
$130$		0			0
$131$			12.5212i			1.09398i	0.837139	+	0.546990i	$0.184227\pi$
$131$			12.5212i			1.09398i	−0.837139	+	0.546990i	$0.815773\pi$
$132$	−2.04982	−	10.2710i	−0.178414	−	0.893979i
$133$	−2.23208			−0.193546
$134$	10.7268	+	5.44011i	0.926653	+	0.469954i
$135$		0			0
$136$	−6.85334	+	1.12524i	−0.587669	+	0.0964885i
$137$	−18.4649			−1.57757			−0.788783	−	0.614672i	$-0.789288\pi$
$137$	−18.4649			−1.57757			−0.788783	+	0.614672i	$0.789288\pi$
$138$	17.0230	−	13.3854i	1.44910	−	1.13944i
$139$	11.6040			0.984237			0.492118	−	0.870528i	$-0.336223\pi$
$139$	11.6040			0.984237			0.492118	+	0.870528i	$0.336223\pi$
$140$		0			0
$141$	2.87909	+	1.33825i	0.242463	+	0.112701i
$142$	−4.48256	+	8.83869i	−0.376168	+	0.741726i
$143$		−	17.0980i		−	1.42980i
$144$	11.0807	−	4.60627i	0.923393	−	0.383856i
$145$		0			0
$146$	−5.79515	−	2.93902i	−0.479610	−	0.243235i
$147$	3.95990	−	8.51932i	0.326607	−	0.702661i
$148$	−7.62688	−	10.4147i	−0.626926	−	0.856081i
$149$	−11.9233			−0.976794			−0.488397	−	0.872621i	$-0.662418\pi$
$149$	−11.9233			−0.976794			−0.488397	+	0.872621i	$0.662418\pi$
$150$		0			0
$151$			10.0548i			0.818247i	0.912479	+	0.409124i	$0.134166\pi$
$151$			10.0548i			0.818247i	−0.912479	+	0.409124i	$0.865834\pi$
$152$	4.96252	−	0.814789i	0.402514	−	0.0660881i
$153$	−4.74886	−	5.63135i	−0.383922	−	0.455268i
$154$	−4.78734	−	2.42791i	−0.385775	−	0.195647i
$155$		0			0
$156$	19.2110	−	3.83398i	1.53811	−	0.306964i
$157$	−1.71150			−0.136593			−0.0682964	−	0.997665i	$-0.521756\pi$
$157$	−1.71150			−0.136593			−0.0682964	+	0.997665i	$0.521756\pi$
$158$	9.29135	+	4.71213i	0.739180	+	0.374877i
$159$	−18.9310	−	8.79941i	−1.50133	−	0.697838i
$160$		0			0
$161$		−	11.0985i		−	0.874687i
$162$	10.2168	+	7.59062i	0.802705	+	0.596376i
$163$		−	11.9580i		−	0.936621i	−0.883564	−	0.468311i	$-0.844863\pi$
$163$		−	11.9580i		−	0.936621i	0.883564	−	0.468311i	$-0.155137\pi$
$164$	−12.2193	+	8.94846i	−0.954169	+	0.698758i
$165$		0			0
$166$	−10.0753	+	19.8665i	−0.781997	+	1.54194i
$167$			0.583522i			0.0451543i	0.999745	+	0.0225771i	$0.00718713\pi$
$167$			0.583522i			0.0451543i	−0.999745	+	0.0225771i	$0.992813\pi$
$168$	1.65446	−	5.92339i	0.127645	−	0.456999i
$169$	18.9800			1.46000
$170$		0			0
$171$	3.43866	+	4.07767i	0.262961	+	0.311827i
$172$	7.05567	−	5.16701i	0.537990	−	0.393981i
$173$			12.0528i			0.916360i	0.888860	+	0.458180i	$0.151498\pi$
$173$			12.0528i			0.916360i	−0.888860	+	0.458180i	$0.848502\pi$
$174$	5.74677	+	7.30853i	0.435662	+	0.554058i
$175$		0			0
$176$	11.5298	+	3.65035i	0.869092	+	0.275155i
$177$	−7.71344	−	3.58532i	−0.579778	−	0.269489i
$178$	4.61271	+	2.33935i	0.345737	+	0.175341i
$179$			0.605490i			0.0452565i	0.999744	+	0.0226282i	$0.00720340\pi$
$179$			0.605490i			0.0452565i	−0.999744	+	0.0226282i	$0.992797\pi$
$180$		0			0
$181$		−	7.08790i		−	0.526840i	−0.964681	−	0.263420i	$-0.915150\pi$
$181$		−	7.08790i		−	0.526840i	0.964681	−	0.263420i	$-0.0848505\pi$
$182$	4.54116	−	8.95424i	0.336613	−	0.663732i
$183$	12.8259	+	5.96165i	0.948114	+	0.440698i
$184$	4.05135	+	24.6750i	0.298670	+	1.81907i
$185$		0			0
$186$	10.0107	−	7.87154i	0.734022	−	0.577169i
$187$		−	7.42401i		−	0.542897i
$188$	−2.95777	+	2.16603i	−0.215717	+	0.157974i
$189$	6.29464	−	1.71150i	0.457868	−	0.124493i
$190$		0			0
$191$	−18.9310			−1.36980			−0.684899	−	0.728638i	$-0.740154\pi$
$191$	−18.9310			−1.36980			−0.684899	+	0.728638i	$0.740154\pi$
$192$	−1.51607	+	13.7732i	−0.109413	+	0.993996i
$193$			4.27334i			0.307602i	0.988102	+	0.153801i	$0.0491515\pi$
$193$			4.27334i			0.307602i	−0.988102	+	0.153801i	$0.950849\pi$
$194$	17.5032	+	8.87680i	1.25666	+	0.637317i
$195$		0			0
$196$	6.40936	+	8.75212i	0.457811	+	0.625151i
$197$			10.0903i			0.718901i	0.933164	+	0.359450i	$0.117036\pi$
$197$			10.0903i			0.718901i	−0.933164	+	0.359450i	$0.882964\pi$
$198$	2.93976	+	12.4861i	0.208920	+	0.887346i
$199$		−	19.0199i		−	1.34829i	−0.738601	−	0.674143i	$-0.764513\pi$
$199$		−	19.0199i		−	1.34829i	0.738601	−	0.674143i	$-0.235487\pi$
$200$		0			0
$201$	−13.3580	−	6.20900i	−0.942201	−	0.437949i
$202$	8.88227	−	17.5140i	0.624954	−	1.23228i
$203$	4.76495			0.334434
$204$	8.34148	−	1.66473i	0.584021	−	0.116554i
$205$		0			0
$206$	−4.71213	+	9.29135i	−0.328310	+	0.647359i
$207$	−20.2753	+	17.0980i	−1.40923	+	1.18839i
$208$	−6.82761	+	21.5653i	−0.473410	+	1.49529i
$209$			5.37574i			0.371848i
$210$		0			0
$211$	5.49534			0.378315			0.189157	−	0.981947i	$-0.439424\pi$
$211$	5.49534			0.378315			0.189157	+	0.981947i	$0.439424\pi$
$212$	19.4483	−	14.2424i	1.33572	−	0.978172i
$213$	5.11611	−	11.0068i	0.350550	−	0.754172i
$214$	−5.20734	+	10.2678i	−0.355966	+	0.701892i
$215$		0			0
$216$	−13.3699	+	6.10289i	−0.909708	+	0.415249i
$217$		−	6.52671i		−	0.443062i
$218$	−7.13266	−	3.61735i	−0.483085	−	0.244998i
$219$	7.21667	+	3.35441i	0.487657	+	0.226670i
$220$		0			0
$221$	13.8859			0.934065
$222$	9.77226	+	12.4280i	0.655871	+	0.834113i
$223$	−7.70974			−0.516282			−0.258141	−	0.966107i	$-0.583110\pi$
$223$	−7.70974			−0.516282			−0.258141	+	0.966107i	$0.583110\pi$
$224$	5.06866	+	4.97397i	0.338664	+	0.332338i
$225$		0			0
$226$	7.34868	−	14.4901i	0.488827	−	0.963865i
$227$	7.40388			0.491413			0.245706	−	0.969344i	$-0.420980\pi$
$227$	7.40388			0.491413			0.245706	+	0.969344i	$0.420980\pi$
$228$	−6.04009	+	1.20544i	−0.400015	+	0.0798319i
$229$		−	17.1310i		−	1.13205i	−0.824389	−	0.566024i	$-0.808481\pi$
$229$		−	17.1310i		−	1.13205i	0.824389	−	0.566024i	$-0.191519\pi$
$230$		0			0
$231$	5.96165	+	2.77106i	0.392248	+	0.182322i
$232$	−10.5938	+	1.73937i	−0.695515	+	0.114196i
$233$	1.40807			0.0922454			0.0461227	−	0.998936i	$-0.485313\pi$
$233$	1.40807			0.0922454			0.0461227	+	0.998936i	$0.485313\pi$
$234$	−23.3539	+	5.49854i	−1.52669	+	0.359450i
$235$		0			0
$236$	7.92422	−	5.80307i	0.515823	−	0.377748i
$237$	−11.5705	−	5.37812i	−0.751583	−	0.349347i
$238$	1.97179	−	3.88797i	0.127812	−	0.252020i
$239$	9.50673			0.614939			0.307470	−	0.951558i	$-0.400518\pi$
$239$	9.50673			0.614939			0.307470	+	0.951558i	$0.400518\pi$
$240$		0			0
$241$	2.27334			0.146439			0.0732195	−	0.997316i	$-0.476673\pi$
$241$	2.27334			0.146439			0.0732195	+	0.997316i	$0.476673\pi$
$242$	1.18892	−	2.34430i	0.0764265	−	0.150697i
$243$	−12.8239	−	8.86267i	−0.822655	−	0.568540i
$244$	−13.1763	+	9.64930i	−0.843529	+	0.617733i
$245$		0			0
$246$	14.5815	−	11.4656i	0.929683	−	0.731020i
$247$	−10.0548			−0.639771
$248$	2.38248	+	14.5106i	0.151287	+	0.921426i
$249$	11.4993	−	24.7396i	0.728741	−	1.56781i
$250$		0			0
$251$		−	9.49772i		−	0.599491i	−0.954019	−	0.299745i	$-0.903098\pi$
$251$		−	9.49772i		−	0.599491i	0.954019	−	0.299745i	$-0.0969017\pi$
$252$	−1.77670	+	7.31977i	−0.111922	+	0.461102i
$253$	−26.7297			−1.68048
$254$	13.8859	−	27.3801i	0.871277	−	1.71798i
$255$		0			0
$256$	−13.0847	−	9.20824i	−0.817791	−	0.575515i
$257$	27.3144			1.70382			0.851912	−	0.523686i	$-0.175443\pi$
$257$	27.3144			1.70382			0.851912	+	0.523686i	$0.175443\pi$
$258$	−8.41964	+	6.62045i	−0.524184	+	0.412171i
$259$	8.10270			0.503477
$260$		0			0
$261$	−7.34070	−	8.70484i	−0.454378	−	0.538816i
$262$	15.7927	+	8.00933i	0.975679	+	0.494818i
$263$		−	1.24952i		−	0.0770484i	−0.999258	−	0.0385242i	$-0.987734\pi$
$263$		−	1.24952i		−	0.0770484i	0.999258	−	0.0385242i	$-0.0122657\pi$
$264$	−14.2659	−	3.98460i	−0.878004	−	0.245235i
$265$		0			0
$266$	−1.42778	+	2.81529i	−0.0875428	+	0.172616i
$267$	−5.74418	−	2.66998i	−0.351538	−	0.163400i
$268$	13.7230	−	10.0497i	0.838268	−	0.613880i
$269$	−15.7189			−0.958399			−0.479199	−	0.877706i	$-0.659073\pi$
$269$	−15.7189			−0.958399			−0.479199	+	0.877706i	$0.659073\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−2.96458	+	9.36377i	−0.179754	+	0.567762i
$273$	−5.18299	+	11.1507i	−0.313689	+	0.674869i
$274$	−11.8113	+	23.2895i	−0.713548	+	1.40697i
$275$		0			0
$276$	−5.99375	−	30.0330i	−0.360781	−	1.80777i
$277$	−0.633548			−0.0380662			−0.0190331	−	0.999819i	$-0.506059\pi$
$277$	−0.633548			−0.0380662			−0.0190331	+	0.999819i	$0.506059\pi$
$278$	7.42263	−	14.6359i	0.445180	−	0.877802i
$279$	−11.9233	+	10.0548i	−0.713829	+	0.601965i
$280$		0			0
$281$			20.9204i			1.24801i	0.781422	+	0.624003i	$0.214495\pi$
$281$			20.9204i			1.24801i	−0.781422	+	0.624003i	$0.785505\pi$
$282$	3.52955	−	2.77532i	0.210182	−	0.165268i
$283$			14.6846i			0.872911i	0.899726	+	0.436455i	$0.143766\pi$
$283$			14.6846i			0.872911i	−0.899726	+	0.436455i	$0.856234\pi$
$284$	8.28075	+	11.3076i	0.491372	+	0.670980i
$285$		0			0
$286$	−21.5653	−	10.9369i	−1.27519	−	0.646714i
$287$		−	9.50673i		−	0.561165i
$288$	1.27811	−	16.9224i	0.0753131	−	0.997160i
$289$	−10.9707			−0.645335
$290$		0			0
$291$	−21.7967	−	10.1314i	−1.27774	−	0.593914i
$292$	−7.41388	+	5.42933i	−0.433864	+	0.317728i
$293$			5.49911i			0.321262i	0.987015	+	0.160631i	$0.0513528\pi$
$293$			5.49911i			0.321262i	−0.987015	+	0.160631i	$0.948647\pi$
$294$	−8.21226	−	10.4440i	−0.478949	−	0.609109i
$295$		0			0
$296$	−18.0145	+	2.95777i	−1.04707	+	0.171917i
$297$	−4.12197	−	15.1600i	−0.239181	−	0.879672i
$298$	−7.62688	+	15.0386i	−0.441813	+	0.871165i
$299$		−	49.9952i		−	2.89129i
$300$		0			0
$301$			5.48937i			0.316402i
$302$	12.6819	+	6.43167i	0.729763	+	0.370101i
$303$	−10.1377	+	21.8101i	−0.582393	+	1.25296i
$304$	2.14666	−	6.78033i	0.123119	−	0.388878i
$305$		0			0
$306$	−10.1404	+	2.38749i	−0.579687	+	0.136484i
$307$			6.11929i			0.349246i	0.984635	+	0.174623i	$0.0558707\pi$
$307$			6.11929i			0.349246i	−0.984635	+	0.174623i	$0.944129\pi$
$308$	−6.12456	+	4.48514i	−0.348979	+	0.255564i
$309$	5.37812	−	11.5705i	0.305951	−	0.658221i
$310$		0			0
$311$	5.75819			0.326517			0.163258	−	0.986583i	$-0.447800\pi$
$311$	5.75819			0.326517			0.163258	+	0.986583i	$0.447800\pi$
$312$	7.45280	−	26.6829i	0.421932	−	1.51062i
$313$		−	21.9800i		−	1.24238i	−0.783658	−	0.621192i	$-0.786649\pi$
$313$		−	21.9800i		−	1.24238i	0.783658	−	0.621192i	$-0.213351\pi$
$314$	−1.09478	+	2.15869i	−0.0617822	+	0.121822i
$315$		0			0
$316$	11.8867	−	8.70484i	0.668676	−	0.489685i
$317$			17.6815i			0.993091i	0.868011	+	0.496545i	$0.165398\pi$
$317$			17.6815i			0.993091i	−0.868011	+	0.496545i	$0.834602\pi$
$318$	−23.2080	+	18.2487i	−1.30144	+	1.02333i
$319$		−	11.4759i		−	0.642527i
$320$		0			0
$321$	5.94333	−	12.7864i	0.331724	−	0.713669i
$322$	−13.9984	−	7.09931i	−0.780099	−	0.395629i
$323$	−4.36583			−0.242922
$324$	16.1092	−	8.03079i	0.894956	−	0.446155i
$325$		0			0
$326$	−15.0824	−	7.64907i	−0.835336	−	0.423643i
$327$	8.88227	+	4.12861i	0.491190	+	0.228313i
$328$	3.47029	+	21.1360i	0.191615	+	1.16704i
$329$		−	2.30117i		−	0.126867i
$330$		0			0
$331$	−7.14134			−0.392523			−0.196262	−	0.980552i	$-0.562880\pi$
$331$	−7.14134			−0.392523			−0.196262	+	0.980552i	$0.562880\pi$
$332$	18.6124	+	25.4157i	1.02149	+	1.39487i
$333$	−12.4827	−	14.8024i	−0.684048	−	0.811166i
$334$	0.735985	+	0.373257i	0.0402713	+	0.0204237i
$335$		0			0
$336$	−6.41277	−	5.87571i	−0.349845	−	0.320546i
$337$		−	1.90663i		−	0.103861i	−0.998651	−	0.0519303i	$-0.983463\pi$
$337$		−	1.90663i		−	0.103861i	0.998651	−	0.0519303i	$-0.0165374\pi$
$338$	12.1408	−	23.9392i	0.660373	−	1.30212i
$339$	−8.38731	+	18.0444i	−0.455536	+	0.980038i
$340$		0			0
$341$	−15.7189			−0.851226
$342$	7.34268	−	1.72879i	0.397047	−	0.0934821i
$343$	−15.5969			−0.842154
$344$	−2.00381	−	12.2043i	−0.108038	−	0.658014i
$345$		0			0
$346$	15.2020	+	7.70974i	0.817265	+	0.414478i
$347$	0.530510			0.0284793			0.0142396	−	0.999899i	$-0.495467\pi$
$347$	0.530510			0.0284793			0.0142396	+	0.999899i	$0.495467\pi$
$348$	12.8941	−	2.57331i	0.691197	−	0.137944i
$349$			7.36659i			0.394325i	0.980371	+	0.197162i	$0.0631726\pi$
$349$			7.36659i			0.394325i	−0.980371	+	0.197162i	$0.936827\pi$
$350$		0			0
$351$	28.3553	−	7.70974i	1.51349	−	0.411516i
$352$	11.9793	−	12.2073i	0.638499	−	0.650653i
$353$	−11.2299			−0.597708			−0.298854	−	0.954299i	$-0.596604\pi$
$353$	−11.2299			−0.597708			−0.298854	+	0.954299i	$0.596604\pi$
$354$	−9.45610	+	7.43543i	−0.502586	+	0.395188i
$355$		0			0
$356$	5.90115	−	4.32153i	0.312760	−	0.229041i
$357$	−2.25048	+	4.84167i	−0.119108	+	0.256248i
$358$	0.763694	+	0.387309i	0.0403625	+	0.0204699i
$359$	17.0980			0.902396			0.451198	−	0.892424i	$-0.350997\pi$
$359$	17.0980			0.902396			0.451198	+	0.892424i	$0.350997\pi$
$360$		0			0
$361$	−15.8387			−0.833615
$362$	−8.93985	−	4.53387i	−0.469868	−	0.238295i
$363$	−1.35695	+	2.91934i	−0.0712216	+	0.153226i
$364$	−8.38900	−	11.4554i	−0.439703	−	0.600425i
$365$		0			0
$366$	15.7235	−	12.3636i	0.821882	−	0.646254i
$367$	−13.9984			−0.730709			−0.365355	−	0.930868i	$-0.619052\pi$
$367$	−13.9984			−0.730709			−0.365355	+	0.930868i	$0.619052\pi$
$368$	33.7136	+	10.6738i	1.75744	+	0.556409i
$369$	−17.3673	+	14.6457i	−0.904107	+	0.762424i
$370$		0			0
$371$			15.1309i			0.785559i
$372$	−3.52474	−	17.6615i	−0.182749	−	0.915705i
$373$	21.5952			1.11815			0.559077	−	0.829116i	$-0.311155\pi$
$373$	21.5952			1.11815			0.559077	+	0.829116i	$0.311155\pi$
$374$	−9.36377	−	4.74886i	−0.484189	−	0.245558i
$375$		0			0
$376$	0.840006	+	5.11611i	0.0433200	+	0.263843i
$377$	21.4645			1.10548
$378$	1.86776	−	9.03410i	0.0960672	−	0.464664i
$379$	−11.7780			−0.604996			−0.302498	−	0.953150i	$-0.597820\pi$
$379$	−11.7780			−0.604996			−0.302498	+	0.953150i	$0.597820\pi$
$380$		0			0
$381$	−15.8484	+	34.0963i	−0.811940	+	1.74680i
$382$	−12.1094	+	23.8773i	−0.619573	+	1.22167i
$383$			15.8484i			0.809818i	0.914357	+	0.404909i	$0.132697\pi$
$383$			15.8484i			0.809818i	−0.914357	+	0.404909i	$0.867303\pi$
$384$	16.4021	+	10.7224i	0.837018	+	0.547175i
$385$		0			0
$386$	5.38989	+	2.73350i	0.274338	+	0.139131i
$387$	10.0282	−	8.45670i	0.509763	−	0.429878i
$388$	22.3923	−	16.3983i	1.13680	−	0.832499i
$389$	−18.4770			−0.936822			−0.468411	−	0.883511i	$-0.655173\pi$
$389$	−18.4770			−0.936822			−0.468411	+	0.883511i	$0.655173\pi$
$390$		0			0
$391$		−	21.7081i		−	1.09783i
$392$	15.1387	−	2.48560i	0.764621	−	0.125542i
$393$	−19.6666	−	9.14134i	−0.992050	−	0.461119i
$394$	12.7267	+	6.45436i	0.641160	+	0.325166i
$395$		0			0
$396$	17.6289	+	4.27900i	0.885886	+	0.215028i
$397$	18.3981			0.923373			0.461687	−	0.887043i	$-0.347244\pi$
$397$	18.3981			0.923373			0.461687	+	0.887043i	$0.347244\pi$
$398$	−23.9895	−	12.1663i	−1.20248	−	0.609843i
$399$	1.62958	−	3.50586i	0.0815809	−	0.175513i
$400$		0			0
$401$		−	0.183464i		−	0.00916176i	−0.999990	−	0.00458088i	$-0.998542\pi$
$401$		−	0.183464i		−	0.00916176i	0.999990	−	0.00458088i	$-0.00145814\pi$
$402$	−16.3759	+	12.8765i	−0.816756	+	0.642224i
$403$		−	29.4006i		−	1.46455i
$404$	−16.4084	−	22.4061i	−0.816350	−	1.11474i
$405$		0			0
$406$	3.04796	−	6.00995i	0.151268	−	0.298269i
$407$		−	19.5145i		−	0.967299i
$408$	3.23604	−	11.5858i	0.160208	−	0.573584i
$409$	30.5933			1.51274			0.756371	−	0.654142i	$-0.226970\pi$
$409$	30.5933			1.51274			0.756371	+	0.654142i	$0.226970\pi$
$410$		0			0
$411$	13.4807	−	29.0023i	0.664953	−	1.43058i
$412$	8.70484	+	11.8867i	0.428856	+	0.585613i
$413$			6.16511i			0.303365i
$414$	8.59600	+	36.5098i	0.422470	+	1.79436i
$415$		0			0
$416$	22.8326	+	22.4061i	1.11946	+	1.09855i
$417$	−8.47171	+	18.2260i	−0.414862	+	0.892531i
$418$	6.78033	+	3.43866i	0.331637	+	0.168190i
$419$			13.9813i			0.683032i	0.939876	+	0.341516i	$0.110940\pi$
$419$			13.9813i			0.683032i	−0.939876	+	0.341516i	$0.889060\pi$
$420$		0			0
$421$			26.7297i			1.30272i	0.758767	+	0.651362i	$0.225802\pi$
$421$			26.7297i			1.30272i	−0.758767	+	0.651362i	$0.774198\pi$
$422$	3.51516	−	6.93117i	0.171115	−	0.337404i
$423$	−4.20388	+	3.54509i	−0.204400	+	0.172368i
$424$	−5.52332	−	33.6401i	−0.268236	−	1.63371i
$425$		0			0
$426$	−10.6101	−	13.4935i	−0.514059	−	0.653761i
$427$		−	10.2513i		−	0.496095i
$428$	9.61965	+	13.1358i	0.464983	+	0.634945i
$429$	26.8552	+	12.4827i	1.29658	+	0.602671i
$430$		0			0
$431$	34.7794			1.67527			0.837633	−	0.546233i	$-0.183939\pi$
$431$	34.7794			1.67527			0.837633	+	0.546233i	$0.183939\pi$
$432$	−0.854768	+	20.7670i	−0.0411250	+	0.999154i
$433$			19.8667i			0.954731i	0.878705	+	0.477366i	$0.158408\pi$
$433$			19.8667i			0.954731i	−0.878705	+	0.477366i	$0.841592\pi$
$434$	−8.23202	−	4.17489i	−0.395150	−	0.200401i
$435$		0			0
$436$	−9.12499	+	6.68241i	−0.437008	+	0.320030i
$437$			15.7189i			0.751937i
$438$	8.84709	−	6.95656i	0.422730	−	0.332397i
$439$			2.85392i			0.136210i	0.997678	+	0.0681051i	$0.0216953\pi$
$439$			2.85392i			0.136210i	−0.997678	+	0.0681051i	$0.978305\pi$
$440$		0			0
$441$	10.4900	+	12.4394i	0.499524	+	0.592352i
$442$	8.88227	−	17.5140i	0.422486	−	0.833056i
$443$	13.6854			0.650212			0.325106	−	0.945678i	$-0.394600\pi$
$443$	13.6854			0.650212			0.325106	+	0.945678i	$0.394600\pi$
$444$	21.9262	−	4.37586i	1.04057	−	0.207669i
$445$		0			0
$446$	−4.93163	+	9.72416i	−0.233520	+	0.460452i
$447$	8.70484	−	18.7275i	0.411725	−	0.885782i
$448$	9.51581	−	3.21134i	0.449580	−	0.151722i
$449$			19.1132i			0.902008i	0.892522	+	0.451004i	$0.148934\pi$
$449$			19.1132i			0.902008i	−0.892522	+	0.451004i	$0.851066\pi$
$450$		0			0
$451$	−22.8960			−1.07813
$452$	−13.5754	−	18.5375i	−0.638533	−	0.871931i
$453$	−15.7927	−	7.34070i	−0.742008	−	0.344896i
$454$	4.73599	−	9.33838i	0.222271	−	0.438272i
$455$		0			0
$456$	−2.34322	+	8.38933i	−0.109732	+	0.392866i
$457$		−	22.6133i		−	1.05781i	−0.848682	−	0.528903i	$-0.822604\pi$
$457$		−	22.6133i		−	1.05781i	0.848682	−	0.528903i	$-0.177396\pi$
$458$	−21.6070	−	10.9580i	−1.00963	−	0.512036i
$459$	12.3120	−	3.34760i	0.574674	−	0.156253i
$460$		0			0
$461$	−13.2199			−0.615711			−0.307855	−	0.951433i	$-0.599611\pi$
$461$	−13.2199			−0.615711			−0.307855	+	0.951433i	$0.599611\pi$
$462$	7.30853	−	5.74677i	0.340024	−	0.267364i
$463$	40.5506			1.88455			0.942273	−	0.334845i	$-0.108684\pi$
$463$	40.5506			1.88455			0.942273	+	0.334845i	$0.108684\pi$
$464$	−4.58259	+	14.4743i	−0.212742	+	0.671954i
$465$		0			0
$466$	0.900687	−	1.77597i	0.0417235	−	0.0822701i
$467$	−10.2492			−0.474276			−0.237138	−	0.971476i	$-0.576209\pi$
$467$	−10.2492			−0.474276			−0.237138	+	0.971476i	$0.576209\pi$
$468$	−8.00343	+	32.9731i	−0.369959	+	1.52418i
$469$			10.6766i			0.493001i
$470$		0			0
$471$	1.24952	−	2.68820i	0.0575746	−	0.123866i
$472$	−2.25048	−	13.7067i	−0.103587	−	0.630901i
$473$	13.2206			0.607883
$474$	−14.1845	+	11.1534i	−0.651517	+	0.512294i
$475$		0			0
$476$	−3.64254	−	4.97397i	−0.166956	−	0.227982i
$477$	27.6419	−	23.3101i	1.26564	−	1.06730i
$478$	6.08110	−	11.9907i	0.278143	−	0.548441i
$479$	31.4378			1.43643			0.718215	−	0.695821i	$-0.244959\pi$
$479$	31.4378			1.43643			0.718215	+	0.695821i	$0.244959\pi$
$480$		0			0
$481$	36.5000			1.66425
$482$	1.45417	−	2.86733i	0.0662357	−	0.130603i
$483$	17.4321	+	8.10270i	0.793188	+	0.368686i
$484$	−2.19632	−	2.99912i	−0.0998326	−	0.136324i
$485$		0			0
$486$	−19.3813	+	10.5055i	−0.879154	+	0.476538i
$487$	0.177431			0.00804018			0.00402009	−	0.999992i	$-0.498720\pi$
$487$	0.177431			0.00804018			0.00402009	+	0.999992i	$0.498720\pi$
$488$	3.74208	+	22.7914i	0.169396	+	1.03172i
$489$	18.7820	+	8.73016i	0.849352	+	0.394791i
$490$		0			0
$491$			7.75623i			0.350034i	0.984565	+	0.175017i	$0.0559980\pi$
$491$			7.75623i			0.350034i	−0.984565	+	0.175017i	$0.944002\pi$
$492$	−5.13410	−	25.7255i	−0.231463	−	1.15980i
$493$	9.31999			0.419751
$494$	−6.43167	+	12.6819i	−0.289375	+	0.570587i
$495$		0			0
$496$	19.8260	+	6.27693i	0.890212	+	0.281842i
$497$	−8.79736			−0.394616
$498$	−23.8479	−	30.3289i	−1.06865	−	1.35907i
$499$	−5.22067			−0.233709			−0.116855	−	0.993149i	$-0.537281\pi$
$499$	−5.22067			−0.233709			−0.116855	+	0.993149i	$0.537281\pi$
$500$		0			0
$501$	−0.916519	−	0.426011i	−0.0409470	−	0.0190328i
$502$	−11.9793	−	6.07533i	−0.534662	−	0.271155i
$503$			6.34171i			0.282763i	0.989955	+	0.141381i	$0.0451544\pi$
$503$			6.34171i			0.282763i	−0.989955	+	0.141381i	$0.954846\pi$
$504$	8.09581	+	6.92310i	0.360616	+	0.308379i
$505$		0			0
$506$	−17.0980	+	33.7136i	−0.760097	+	1.49875i
$507$	−13.8567	+	29.8113i	−0.615399	+	1.32397i
$508$	−25.6517	−	35.0280i	−1.13811	−	1.55412i
$509$	−34.1959			−1.51571			−0.757854	−	0.652425i	$-0.773752\pi$
$509$	−34.1959			−1.51571			−0.757854	+	0.652425i	$0.773752\pi$
$510$		0			0
$511$		−	5.76805i		−	0.255164i
$512$	−19.9839	+	10.6133i	−0.883174	+	0.469045i
$513$	−8.91513	+	2.42401i	−0.393613	+	0.107023i
$514$	17.4720	−	34.4511i	0.770656	−	1.51957i
$515$		0			0
$516$	2.96453	+	14.8544i	0.130506	+	0.653928i
$517$	−5.54212			−0.243742
$518$	5.18299	−	10.2198i	0.227728	−	0.449032i
$519$	−18.9310	−	8.79941i	−0.830978	−	0.386251i
$520$		0			0
$521$			32.6151i			1.42889i	0.699689	+	0.714447i	$0.253322\pi$
$521$			32.6151i			1.42889i	−0.699689	+	0.714447i	$0.746678\pi$
$522$	−15.6748	+	3.69054i	−0.686068	+	0.161530i
$523$			14.6074i			0.638736i	0.947631	+	0.319368i	$0.103471\pi$
$523$			14.6074i			0.638736i	−0.947631	+	0.319368i	$0.896529\pi$
$524$	20.2040	−	14.7958i	0.882618	−	0.646359i
$525$		0			0
$526$	−1.57599	−	0.799268i	−0.0687165	−	0.0348498i
$527$		−	12.7659i		−	0.556091i
$528$	−14.1510	+	15.4445i	−0.615845	+	0.672135i
$529$	−55.1587			−2.39820
$530$		0			0
$531$	11.2627	−	9.49772i	0.488759	−	0.412166i
$532$	2.63757	+	3.60167i	0.114353	+	0.156152i
$533$		−	42.8246i		−	1.85494i
$534$	−7.04194	+	5.53715i	−0.304734	+	0.239616i
$535$		0			0
$536$	−3.89734	−	23.7370i	−0.168340	−	1.02528i
$537$	−0.951024	−	0.442050i	−0.0410397	−	0.0190759i
$538$	−10.0548	+	19.8260i	−0.433493	+	0.854758i
$539$			16.3993i			0.706368i
$540$		0			0
$541$		−	13.0217i		−	0.559846i	−0.960023	−	0.279923i	$-0.909691\pi$
$541$		−	13.0217i		−	0.559846i	0.960023	−	0.279923i	$-0.0903089\pi$
$542$		0			0
$543$	11.1327	+	5.17466i	0.477752	+	0.222066i
$544$	9.91402	+	9.72882i	0.425060	+	0.417120i
$545$		0			0
$546$	10.7488	+	13.6699i	0.460005	+	0.585017i
$547$			37.8280i			1.61741i	0.588214	+	0.808705i	$0.299831\pi$
$547$			37.8280i			1.61741i	−0.588214	+	0.808705i	$0.700169\pi$
$548$	21.8193	+	29.7948i	0.932076	+	1.27277i
$549$	−18.7275	+	15.7927i	−0.799272	+	0.674018i
$550$		0			0
$551$	−6.74863			−0.287501
$552$	−41.7140	−	11.6511i	−1.77547	−	0.495906i
$553$			9.24791i			0.393261i
$554$	−0.405257	+	0.799083i	−0.0172177	+	0.0339498i
$555$		0			0
$556$	−13.7120	−	18.7241i	−0.581519	−	0.794077i
$557$			22.0135i			0.932744i	0.884589	+	0.466372i	$0.154439\pi$
$557$			22.0135i			0.932744i	−0.884589	+	0.466372i	$0.845561\pi$
$558$	5.05505	+	21.4703i	0.213997	+	0.908910i
$559$			24.7278i			1.04587i
$560$		0			0
$561$	11.6607	+	5.42004i	0.492313	+	0.228834i
$562$	26.3865	+	13.3820i	1.11305	+	0.564485i
$563$	9.80727			0.413327			0.206664	−	0.978412i	$-0.433739\pi$
$563$	9.80727			0.413327			0.206664	+	0.978412i	$0.433739\pi$
$564$	−1.24274	−	6.22703i	−0.0523289	−	0.262205i
$565$		0			0
$566$	18.5215	+	9.39321i	0.778515	+	0.394826i
$567$	−1.90733	+	11.1363i	−0.0801002	+	0.467681i
$568$	19.5589	−	3.21134i	0.820673	−	0.134745i
$569$		−	22.4555i		−	0.941384i	−0.882298	−	0.470692i	$-0.844004\pi$
$569$		−	22.4555i		−	0.941384i	0.882298	−	0.470692i	$-0.155996\pi$
$570$		0			0
$571$	5.92867			0.248107			0.124054	−	0.992276i	$-0.460411\pi$
$571$	5.92867			0.248107			0.124054	+	0.992276i	$0.460411\pi$
$572$	−27.5891	+	20.2040i	−1.15356	+	0.844773i
$573$	13.8209	−	29.7343i	0.577378	−	1.24217i
$574$	−11.9907	−	6.08110i	−0.500481	−	0.253820i
$575$		0			0
$576$	−20.5263	−	12.4367i	−0.855263	−	0.518194i
$577$			39.1587i			1.63020i	0.579322	+	0.815098i	$0.303317\pi$
$577$			39.1587i			1.63020i	−0.579322	+	0.815098i	$0.696683\pi$
$578$	−7.01754	+	13.8371i	−0.291891	+	0.575549i
$579$	−6.71200	−	3.11984i	−0.278941	−	0.129656i
$580$		0			0
$581$	−19.7736			−0.820347
$582$	−26.7211	+	21.0111i	−1.10762	+	0.870936i
$583$	36.4413			1.50924
$584$	2.10554	+	12.8239i	0.0871279	+	0.530658i
$585$		0			0
$586$	6.93593	+	3.51757i	0.286521	+	0.145310i
$587$	−29.3332			−1.21071			−0.605356	−	0.795955i	$-0.706969\pi$
$587$	−29.3332			−1.21071			−0.605356	+	0.795955i	$0.706969\pi$
$588$	−18.4260	+	3.67731i	−0.759874	+	0.151650i
$589$			9.24381i			0.380885i
$590$		0			0
$591$	−15.8484	−	7.36659i	−0.651918	−	0.303021i
$592$	−7.79260	+	24.6133i	−0.320274	+	1.01160i
$593$	24.6525			1.01236			0.506179	−	0.862428i	$-0.331058\pi$
$593$	24.6525			1.01236			0.506179	+	0.862428i	$0.331058\pi$
$594$	−21.7577	−	4.49831i	−0.892729	−	0.184568i
$595$		0			0
$596$	14.0893	+	19.2393i	0.577121	+	0.788072i
$597$	29.8740	+	13.8859i	1.22266	+	0.568311i
$598$	−63.0580	−	31.9800i	−2.57863	−	1.30776i
$599$	29.8638			1.22020			0.610102	−	0.792323i	$-0.291129\pi$
$599$	29.8638			1.22020			0.610102	+	0.792323i	$0.291129\pi$
$600$		0			0
$601$	−17.7267			−0.723085			−0.361543	−	0.932356i	$-0.617750\pi$
$601$	−17.7267			−0.723085			−0.361543	+	0.932356i	$0.617750\pi$
$602$	6.92364	+	3.51134i	0.282187	+	0.143112i
$603$	19.5046	−	16.4480i	0.794287	−	0.669814i
$604$	16.2243	−	11.8814i	0.660158	−	0.483447i
$605$		0			0
$606$	21.0240	+	26.7375i	0.854041	+	1.08614i
$607$	−25.8174			−1.04790			−0.523949	−	0.851750i	$-0.675542\pi$
$607$	−25.8174			−1.04790			−0.523949	+	0.851750i	$0.675542\pi$
$608$	−7.17877	−	7.04466i	−0.291137	−	0.285699i
$609$	−3.47875	+	7.48416i	−0.140966	+	0.303274i
$610$		0			0
$611$		−	10.3660i		−	0.419363i
$612$	−3.47513	+	14.3171i	−0.140474	+	0.578733i
$613$	−16.6866			−0.673965			−0.336982	−	0.941511i	$-0.609406\pi$
$613$	−16.6866			−0.673965			−0.336982	+	0.941511i	$0.609406\pi$
$614$	7.71815	+	3.91428i	0.311479	+	0.157967i
$615$		0			0
$616$	1.73937	+	10.5938i	0.0700814	+	0.426835i
$617$	−8.69514			−0.350053			−0.175027	−	0.984564i	$-0.556001\pi$
$617$	−8.69514			−0.350053			−0.175027	+	0.984564i	$0.556001\pi$
$618$	−11.1534	−	14.1845i	−0.448657	−	0.570585i
$619$	−20.3727			−0.818846			−0.409423	−	0.912345i	$-0.634270\pi$
$619$	−20.3727			−0.818846			−0.409423	+	0.912345i	$0.634270\pi$
$620$		0			0
$621$	−12.0528	−	44.3285i	−0.483663	−	1.77884i
$622$	3.68330	−	7.26270i	0.147687	−	0.291208i
$623$			4.59114i			0.183940i
$624$	−28.8874	−	26.4681i	−1.15642	−	1.05957i
$625$		0			0
$626$	−27.7230	−	14.0598i	−1.10803	−	0.561942i
$627$	−8.44351	−	3.92467i	−0.337201	−	0.156736i
$628$	2.02242	+	2.76166i	0.0807034	+	0.110202i
$629$	15.8484			0.631919
$630$		0			0
$631$		−	4.51267i		−	0.179647i	−0.995958	−	0.0898233i	$-0.971370\pi$
$631$		−	4.51267i		−	0.179647i	0.995958	−	0.0898233i	$-0.0286302\pi$
$632$	−3.37581	−	20.5606i	−0.134282	−	0.817856i
$633$	−4.01198	+	8.63135i	−0.159462	+	0.343065i
$634$	22.3013	+	11.3102i	0.885699	+	0.449184i
$635$		0			0
$636$	8.17145	+	40.9448i	0.324019	+	1.62357i
$637$	−30.6732			−1.21532
$638$	−14.4743	−	7.34070i	−0.573045	−	0.290621i
$639$	13.5529	+	16.0714i	0.536143	+	0.635776i
$640$		0			0
$641$		−	25.0424i		−	0.989114i	−0.869145	−	0.494557i	$-0.835330\pi$
$641$		−	25.0424i		−	0.989114i	0.869145	−	0.494557i	$-0.164670\pi$
$642$	−12.3256	−	15.6752i	−0.486452	−	0.618651i
$643$			21.7360i			0.857184i	0.903498	+	0.428592i	$0.140990\pi$
$643$			21.7360i			0.857184i	−0.903498	+	0.428592i	$0.859010\pi$
$644$	−17.9085	+	13.1147i	−0.705693	+	0.516793i
$645$		0			0
$646$	−2.79266	+	5.50655i	−0.109876	+	0.216652i
$647$		−	21.3476i		−	0.839259i	−0.907695	−	0.419629i	$-0.862160\pi$
$647$		−	21.3476i		−	0.839259i	0.907695	−	0.419629i	$-0.137840\pi$
$648$	0.175357	−	25.4552i	0.00688868	−	0.999976i
$649$	14.8480			0.582836
$650$		0			0
$651$	10.2513	+	4.76495i	0.401780	+	0.186753i
$652$	−19.2953	+	14.1303i	−0.755661	+	0.553386i
$653$		−	25.9387i		−	1.01506i	−0.861634	−	0.507530i	$-0.830559\pi$
$653$		−	25.9387i		−	1.01506i	0.861634	−	0.507530i	$-0.169441\pi$
$654$	10.8890	−	8.56213i	0.425793	−	0.334806i
$655$		0			0
$656$	28.8783	+	9.14290i	1.12751	+	0.356970i
$657$	−10.5373	+	8.88603i	−0.411101	+	0.346677i
$658$	−2.90242	−	1.47197i	−0.113148	−	0.0573834i
$659$		−	20.6474i		−	0.804307i	−0.915572	−	0.402153i	$-0.868262\pi$
$659$		−	20.6474i		−	0.804307i	0.915572	−	0.402153i	$-0.131738\pi$
$660$		0			0
$661$		−	9.31999i		−	0.362506i	−0.983437	−	0.181253i	$-0.941985\pi$
$661$		−	9.31999i		−	0.362506i	0.983437	−	0.181253i	$-0.0580152\pi$
$662$	−4.56804	+	9.00724i	−0.177542	+	0.350076i
$663$	−10.1377	+	21.8101i	−0.393714	+	0.847034i
$664$	43.9620	−	7.21805i	1.70606	−	0.280115i
$665$		0			0
$666$	−26.6547	+	6.27568i	−1.03285	+	0.243178i
$667$		−	33.5560i		−	1.29929i
$668$	0.941564	−	0.689526i	0.0364302	−	0.0266786i
$669$	5.62865	−	12.1094i	0.217616	−	0.468178i
$670$		0			0
$671$	−24.6892			−0.953115
$672$	−11.5129	+	4.32983i	−0.444121	+	0.167027i
$673$			37.2520i			1.43596i	0.696063	+	0.717980i	$0.254933\pi$
$673$			37.2520i			1.43596i	−0.696063	+	0.717980i	$0.745067\pi$
$674$	−2.40479	−	1.21960i	−0.0926292	−	0.0469771i
$675$		0			0
$676$	−22.4280	−	30.6260i	−0.862616	−	1.17792i
$677$		−	37.0665i		−	1.42458i	−0.701885	−	0.712290i	$-0.747658\pi$
$677$		−	37.0665i		−	1.42458i	0.701885	−	0.712290i	$-0.252342\pi$
$678$	17.3940	+	22.1211i	0.668014	+	0.849555i
$679$			17.4214i			0.668571i
$680$		0			0
$681$	−5.40535	+	11.6290i	−0.207133	+	0.445626i
$682$	−10.0548	+	19.8260i	−0.385018	+	0.759176i
$683$	26.0898			0.998297			0.499149	−	0.866516i	$-0.333646\pi$
$683$	26.0898			0.998297			0.499149	+	0.866516i	$0.333646\pi$
$684$	2.51635	−	10.3670i	0.0962150	−	0.396393i
$685$		0			0
$686$	−9.97676	+	19.6721i	−0.380914	+	0.751085i
$687$	26.9071	+	12.5068i	1.02657	+	0.477165i
$688$	−16.6749	−	5.27928i	−0.635723	−	0.201271i
$689$			68.1598i			2.59668i
$690$		0			0
$691$	34.8187			1.32457			0.662283	−	0.749254i	$-0.269588\pi$
$691$	34.8187			1.32457			0.662283	+	0.749254i	$0.269588\pi$
$692$	19.4483	−	14.2424i	0.739314	−	0.541415i
$693$	−8.70484	+	7.34070i	−0.330669	+	0.278850i
$694$	0.339347	−	0.669123i	0.0128814	−	0.0253995i
$695$		0			0
$696$	5.00221	−	17.9092i	0.189608	−	0.678845i
$697$		−	18.5946i		−	0.704323i
$698$	9.29135	+	4.71213i	0.351683	+	0.178357i
$699$	−1.02799	+	2.21160i	−0.0388820	+	0.0836505i
$700$		0			0
$701$	−12.7188			−0.480383			−0.240192	−	0.970725i	$-0.577210\pi$
$701$	−12.7188			−0.480383			−0.240192	+	0.970725i	$0.577210\pi$
$702$	8.41363	−	40.6956i	0.317552	−	1.53596i
$703$	−11.4759			−0.432822
$704$	−7.73419	−	22.9178i	−0.291493	−	0.863749i
$705$		0			0
$706$	−7.18336	+	14.1641i	−0.270349	+	0.533073i
$707$	17.4321			0.655602
$708$	3.32946	+	16.6830i	0.125129	+	0.626984i
$709$			46.7263i			1.75484i	0.479721	+	0.877421i	$0.340738\pi$
$709$			46.7263i			1.75484i	−0.479721	+	0.877421i	$0.659262\pi$
$710$		0			0
$711$	16.8945	−	14.2470i	0.633593	−	0.534303i
$712$	−1.67593	−	10.2073i	−0.0628080	−	0.382536i
$713$	−45.9628			−1.72132
$714$	4.66716	+	5.93552i	0.174664	+	0.222131i
$715$		0			0
$716$	0.977012	−	0.715486i	0.0365127	−	0.0267390i
$717$	−6.94058	+	14.9319i	−0.259201	+	0.557643i
$718$	10.9369	−	21.5653i	0.408162	−	0.804812i
$719$	−9.50673			−0.354541			−0.177271	−	0.984162i	$-0.556727\pi$
$719$	−9.50673			−0.354541			−0.177271	+	0.984162i	$0.556727\pi$
$720$		0			0
$721$	−9.24791			−0.344410
$722$	−10.1314	+	19.9771i	−0.377052	+	0.743469i
$723$	−1.65970	+	3.57067i	−0.0617249	+	0.132795i
$724$	−11.4370	+	8.37552i	−0.425051	+	0.311274i
$725$		0			0
$726$	2.81412	+	3.57890i	0.104442	+	0.132825i
$727$	31.7629			1.17802			0.589011	−	0.808125i	$-0.299518\pi$
$727$	31.7629			1.17802			0.589011	+	0.808125i	$0.299518\pi$
$728$	−19.8146	+	3.25333i	−0.734377	+	0.120576i
$729$	23.2827	−	13.6718i	0.862321	−	0.506362i
$730$		0			0
$731$			10.7369i			0.397119i
$732$	−5.53620	−	27.7403i	−0.204624	−	1.02531i
$733$	15.5852			0.575653			0.287826	−	0.957683i	$-0.407067\pi$
$733$	15.5852			0.575653			0.287826	+	0.957683i	$0.407067\pi$
$734$	−8.95424	+	17.6559i	−0.330507	+	0.651691i
$735$		0			0
$736$	35.0280	−	35.6948i	1.29115	−	1.31573i
$737$	25.7135			0.947171
$738$	7.36312	+	31.2734i	0.271040	+	1.15119i
$739$	−4.17997			−0.153763			−0.0768813	−	0.997040i	$-0.524496\pi$
$739$	−4.17997			−0.153763			−0.0768813	+	0.997040i	$0.524496\pi$
$740$		0			0
$741$	7.34070	−	15.7927i	0.269667	−	0.580161i
$742$	19.0844	+	9.67869i	0.700610	+	0.355316i
$743$			20.1805i			0.740351i	0.928962	+	0.370176i	$0.120702\pi$
$743$			20.1805i			0.740351i	−0.928962	+	0.370176i	$0.879298\pi$
$744$	−24.5307	−	6.85169i	−0.899341	−	0.251195i
$745$		0			0
$746$	13.8136	−	27.2376i	0.505752	−	0.997239i
$747$	30.4624	+	36.1233i	1.11456	+	1.32168i
$748$	−11.9793	+	8.77268i	−0.438007	+	0.320761i
$749$	−10.2198			−0.373423
$750$		0			0
$751$			19.0316i			0.694474i	0.937777	+	0.347237i	$0.112880\pi$
$751$			19.0316i			0.694474i	−0.937777	+	0.347237i	$0.887120\pi$
$752$	6.99018	+	2.21310i	0.254906	+	0.0807034i
$753$	14.9178	+	6.93400i	0.543633	+	0.252689i
$754$	13.7300	−	27.0728i	0.500019	−	0.985934i
$755$		0			0
$756$	−10.1998	−	8.13455i	−0.370964	−	0.295851i
$757$	4.22227			0.153461			0.0767305	−	0.997052i	$-0.475552\pi$
$757$	4.22227			0.153461			0.0767305	+	0.997052i	$0.475552\pi$
$758$	−7.53395	+	14.8554i	−0.273645	+	0.539572i
$759$	19.5145	−	41.9834i	0.708332	−	1.52390i
$760$		0			0
$761$		−	38.0795i		−	1.38038i	−0.723628	−	0.690190i	$-0.757527\pi$
$761$		−	38.0795i		−	1.38038i	0.723628	−	0.690190i	$-0.242473\pi$
$762$	32.8673	+	41.7994i	1.19066	+	1.51423i
$763$		−	7.09931i		−	0.257012i
$764$	22.3701	+	30.5468i	0.809321	+	1.10515i
$765$		0			0
$766$	19.9894	+	10.1377i	0.722245	+	0.366288i
$767$			27.7717i			1.00278i
$768$	24.0158	−	13.8290i	0.866596	−	0.499011i
$769$	−16.9600			−0.611595			−0.305797	−	0.952097i	$-0.598923\pi$
$769$	−16.9600			−0.611595			−0.305797	+	0.952097i	$0.598923\pi$
$770$		0			0
$771$	−19.9414	+	42.9018i	−0.718172	+	1.54507i
$772$	6.89542	−	5.04966i	0.248172	−	0.181741i
$773$			16.3849i			0.589324i	0.955602	+	0.294662i	$0.0952070\pi$
$773$			16.3849i			0.589324i	−0.955602	+	0.294662i	$0.904793\pi$
$774$	−4.25161	−	18.0579i	−0.152821	−	0.649076i
$775$		0			0
$776$	−6.35941	−	38.7324i	−0.228290	−	1.39041i
$777$	−5.91554	+	12.7267i	−0.212219	+	0.456566i
$778$	−11.8190	+	23.3047i	−0.423733	+	0.835515i
$779$			13.4644i			0.482413i
$780$		0			0
$781$			21.1875i			0.758150i
$782$	−27.3801	−	13.8859i	−0.979109	−	0.496558i
$783$	19.0316	−	5.17466i	0.680135	−	0.184927i
$784$	6.54862	−	20.6841i	0.233879	−	0.738719i
$785$		0			0
$786$	−24.1098	+	18.9578i	−0.859968	+	0.676202i
$787$		−	25.6833i		−	0.915511i	−0.889078	−	0.457756i	$-0.848653\pi$
$787$		−	25.6833i		−	0.915511i	0.889078	−	0.457756i	$-0.151347\pi$
$788$	16.2815	−	11.9233i	0.580005	−	0.424750i
$789$	1.96257	+	0.912234i	0.0698695	+	0.0324764i
$790$		0			0
$791$	14.4223			0.512799
$792$	16.6736	−	19.4979i	0.592469	−	0.692828i
$793$		−	46.1787i		−	1.63985i
$794$	11.7686	−	23.2052i	0.417651	−	0.823521i
$795$		0			0
$796$	−30.6903	+	22.4752i	−1.08779	+	0.796611i
$797$		−	13.7563i		−	0.487274i	−0.969866	−	0.243637i	$-0.921659\pi$
$797$		−	13.7563i		−	0.487274i	0.969866	−	0.243637i	$-0.0783406\pi$
$798$	−3.37950	−	4.29793i	−0.119633	−	0.152145i
$799$		−	4.50096i		−	0.159232i
$800$		0			0
$801$	8.38731	−	7.07293i	0.296351	−	0.249910i
$802$	−0.231400	−	0.117355i	−0.00817102	−	0.00414395i
$803$	−13.8918			−0.490229
$804$	5.76590	+	28.8913i	0.203348	+	1.01892i
$805$		0			0
$806$	−37.0825	−	18.8065i	−1.30618	−	0.662430i
$807$	11.4759	−	24.6892i	0.403971	−	0.869100i
$808$	−38.7562	+	6.36333i	−1.36344	+	0.223861i
$809$		−	6.42314i		−	0.225826i	−0.993605	−	0.112913i	$-0.963982\pi$
$809$		−	6.42314i		−	0.225826i	0.993605	−	0.112913i	$-0.0360181\pi$
$810$		0			0
$811$	−40.8353			−1.43392			−0.716961	−	0.697114i	$-0.754467\pi$
$811$	−40.8353			−1.43392			−0.716961	+	0.697114i	$0.754467\pi$
$812$	−5.63058	−	7.68868i	−0.197594	−	0.269820i
$813$		0			0
$814$	−24.6133	−	12.4827i	−0.862696	−	0.437518i
$815$		0			0
$816$	−12.5430	−	11.4926i	−0.439094	−	0.402321i
$817$		−	7.77462i		−	0.271999i
$818$	19.5694	−	38.5868i	0.684228	−	1.34916i
$819$	−13.7300	−	16.2815i	−0.479767	−	0.568923i
$820$		0			0
$821$	51.8774			1.81053			0.905267	−	0.424844i	$-0.139671\pi$
$821$	51.8774			1.81053			0.905267	+	0.424844i	$0.139671\pi$
$822$	−27.9570	−	35.5546i	−0.975111	−	1.24011i
$823$	36.0379			1.25620			0.628102	−	0.778131i	$-0.283832\pi$
$823$	36.0379			1.25620			0.628102	+	0.778131i	$0.283832\pi$
$824$	20.5606	−	3.37581i	0.716261	−	0.117602i
$825$		0			0
$826$	7.77594	+	3.94359i	0.270559	+	0.137215i
$827$	29.8501			1.03799			0.518995	−	0.854777i	$-0.326306\pi$
$827$	29.8501			1.03799			0.518995	+	0.854777i	$0.326306\pi$
$828$	51.5477	+	12.5120i	1.79141	+	0.434821i
$829$			22.2287i			0.772035i	0.922492	+	0.386017i	$0.126150\pi$
$829$			22.2287i			0.772035i	−0.922492	+	0.386017i	$0.873850\pi$
$830$		0			0
$831$	0.462534	−	0.995094i	0.0160451	−	0.0345194i
$832$	42.8656	−	14.4660i	1.48610	−	0.501519i
$833$	−13.3185			−0.461457
$834$	17.5691	+	22.3437i	0.608368	+	0.773699i
$835$		0			0
$836$	8.67424	−	6.35232i	0.300005	−	0.219700i
$837$	−7.08790	−	26.0682i	−0.244994	−	0.901050i
$838$	17.6344	+	8.94333i	0.609170	+	0.308942i
$839$	−5.17466			−0.178649			−0.0893246	−	0.996003i	$-0.528471\pi$
$839$	−5.17466			−0.178649			−0.0893246	+	0.996003i	$0.528471\pi$
$840$		0			0
$841$	−14.5933			−0.503218
$842$	33.7136	+	17.0980i	1.16185	+	0.589235i
$843$	−32.8590	−	15.2733i	−1.13172	−	0.526042i
$844$	−6.49364	−	8.86721i	−0.223520	−	0.305222i
$845$		0			0
$846$	1.78229	+	7.56993i	0.0612765	+	0.260260i
$847$	2.33334			0.0801745
$848$	−45.9628	−	14.5519i	−1.57837	−	0.499713i
$849$	−23.0647	−	10.7208i	−0.791578	−	0.367937i
$850$		0			0
$851$		−	57.0613i		−	1.95604i
$852$	−23.8059	+	4.75101i	−0.815578	+	0.162767i
$853$	−36.3283			−1.24386			−0.621929	−	0.783073i	$-0.713651\pi$
$853$	−36.3283			−1.24386			−0.621929	+	0.783073i	$0.713651\pi$
$854$	−12.9298	−	6.55737i	−0.442448	−	0.224389i
$855$		0			0
$856$	22.7213	−	3.73058i	0.776599	−	0.127509i
$857$	−9.42274			−0.321875			−0.160937	−	0.986965i	$-0.551452\pi$
$857$	−9.42274			−0.321875			−0.160937	+	0.986965i	$0.551452\pi$
$858$	32.9225	−	25.8873i	1.12395	−	0.883777i
$859$	−18.0480			−0.615789			−0.307894	−	0.951421i	$-0.599624\pi$
$859$	−18.0480			−0.615789			−0.307894	+	0.951421i	$0.599624\pi$
$860$		0			0
$861$	14.9319	+	6.94058i	0.508879	+	0.236534i
$862$	22.2471	−	43.8667i	0.757739	−	1.49410i
$863$		−	18.3475i		−	0.624555i	−0.949991	−	0.312278i	$-0.898908\pi$
$863$		−	18.3475i		−	0.624555i	0.949991	−	0.312278i	$-0.101092\pi$
$864$	25.6463	+	14.3620i	0.872505	+	0.488605i
$865$		0			0
$866$	25.0575	+	12.7080i	0.851488	+	0.431834i
$867$	8.00937	−	17.2313i	0.272013	−	0.585206i
$868$	−10.5314	+	7.71238i	−0.357460	+	0.261775i
$869$	22.2726			0.755547
$870$		0			0
$871$			48.0946i			1.62962i
$872$	2.59150	+	15.7837i	0.0877592	+	0.534503i
$873$	31.8262	−	26.8387i	1.07715	−	0.908352i
$874$	19.8260	+	10.0548i	0.670623	+	0.340108i
$875$		0			0
$876$	−3.11503	−	15.6085i	−0.105247	−	0.527363i
$877$	−16.5736			−0.559651			−0.279826	−	0.960051i	$-0.590277\pi$
$877$	−16.5736			−0.559651			−0.279826	+	0.960051i	$0.590277\pi$
$878$	3.59960	+	1.82555i	0.121481	+	0.0616092i
$879$	−8.63728	−	4.01474i	−0.291328	−	0.135414i
$880$		0			0
$881$			25.5865i			0.862031i	0.902345	+	0.431015i	$0.141845\pi$
$881$			25.5865i			0.862031i	−0.902345	+	0.431015i	$0.858155\pi$
$882$	22.3996	−	5.27385i	0.754235	−	0.177580i
$883$		−	21.2127i		−	0.713863i	−0.934131	−	0.356931i	$-0.883823\pi$
$883$		−	21.2127i		−	0.713863i	0.934131	−	0.356931i	$-0.116177\pi$
$884$	−16.4084	−	22.4061i	−0.551875	−	0.753598i
$885$		0			0
$886$	8.75403	−	17.2611i	0.294097	−	0.579899i
$887$			25.2727i			0.848574i	0.905528	+	0.424287i	$0.139475\pi$
$887$			25.2727i			0.848574i	−0.905528	+	0.424287i	$0.860525\pi$
$888$	8.50615	−	30.4541i	0.285448	−	1.02197i
$889$	27.2520			0.914004
$890$		0			0
$891$	26.8206	+	4.59360i	0.898525	+	0.153891i
$892$	9.11033	+	12.4404i	0.305036	+	0.416534i
$893$			3.25915i			0.109063i
$894$	−18.0525	−	22.9586i	−0.603767	−	0.767849i
$895$		0			0
$896$	2.03650	−	14.0563i	0.0680346	−	0.469588i
$897$	78.5258	+	36.5000i	2.62190	+	1.21870i
$898$	24.1071	+	12.2260i	0.804466	+	0.407987i
$899$		−	19.7333i		−	0.658142i
$900$		0			0
$901$			29.5953i			0.985962i
$902$	−14.6457	+	28.8783i	−0.487648	+	0.961542i
$903$	−8.62198	−	4.00762i	−0.286921	−	0.133365i
$904$	−32.0647	+	5.26465i	−1.06646	+	0.175100i
$905$		0			0
$906$	−19.3607	+	15.2235i	−0.643217	+	0.505768i
$907$		−	22.7267i		−	0.754626i	−0.926086	−	0.377313i	$-0.876848\pi$
$907$		−	22.7267i		−	0.754626i	0.926086	−	0.377313i	$-0.123152\pi$
$908$	−8.74890	−	11.9468i	−0.290343	−	0.396469i
$909$	−26.8552	−	31.8458i	−0.890731	−	1.05626i
$910$		0			0
$911$	−8.92321			−0.295639			−0.147820	−	0.989014i	$-0.547226\pi$
$911$	−8.92321			−0.295639			−0.147820	+	0.989014i	$0.547226\pi$
$912$	9.08243	+	8.32180i	0.300749	+	0.275562i
$913$			47.6226i			1.57608i
$914$	−28.5218	−	14.4649i	−0.943416	−	0.478456i
$915$		0			0
$916$	−27.6424	+	20.2431i	−0.913330	+	0.668850i
$917$			15.7189i			0.519084i
$918$	3.65324	−	17.6702i	0.120575	−	0.583204i
$919$			33.7531i			1.11341i	0.830710	+	0.556706i	$0.187935\pi$
$919$			33.7531i			1.11341i	−0.830710	+	0.556706i	$0.812065\pi$
$920$		0			0
$921$	−9.61137	−	4.46751i	−0.316705	−	0.147209i
$922$	−8.45626	+	16.6740i	−0.278492	+	0.549129i
$923$	−39.6292			−1.30441
$924$	−2.57331	−	12.8941i	−0.0846556	−	0.424185i
$925$		0			0
$926$	25.9387	−	51.1457i	0.852398	−	1.68075i
$927$	14.2470	+	16.8945i	0.467932	+	0.554888i
$928$	15.3249	+	15.0386i	0.503065	+	0.493667i
$929$		−	51.1823i		−	1.67924i	−0.543177	−	0.839618i	$-0.682779\pi$
$929$		−	51.1823i		−	1.67924i	0.543177	−	0.839618i	$-0.317221\pi$
$930$		0			0
$931$	9.64393			0.316067
$932$	−1.66386	−	2.27204i	−0.0545016	−	0.0744231i
$933$	−4.20388	+	9.04420i	−0.137629	+	0.296094i
$934$	−6.55602	+	12.9271i	−0.214519	+	0.422988i
$935$		0			0
$936$	36.4689	+	31.1862i	1.19202	+	1.01935i
$937$		−	56.9974i		−	1.86202i	−0.364990	−	0.931011i	$-0.618928\pi$
$937$		−	56.9974i		−	1.86202i	0.364990	−	0.931011i	$-0.381072\pi$
$938$	13.4662	+	6.82944i	0.439688	+	0.222989i
$939$	34.5233	+	16.0470i	1.12663	+	0.523672i
$940$		0			0
$941$	37.1960			1.21255			0.606277	−	0.795253i	$-0.292662\pi$
$941$	37.1960			1.21255			0.606277	+	0.795253i	$0.292662\pi$
$942$	−2.59131	−	3.29553i	−0.0844295	−	0.107374i
$943$	−66.9488			−2.18015
$944$	−18.7275	−	5.92916i	−0.609529	−	0.192978i
$945$		0			0
$946$	8.45670	−	16.6749i	0.274951	−	0.542147i
$947$	−36.5775			−1.18861			−0.594305	−	0.804240i	$-0.702573\pi$
$947$	−36.5775			−1.18861			−0.594305	+	0.804240i	$0.702573\pi$
$948$	4.99432	+	25.0251i	0.162208	+	0.812778i
$949$		−	25.9831i		−	0.843449i
$950$		0			0
$951$	−27.7717	−	12.9087i	−0.900560	−	0.418594i
$952$	−8.60358	+	1.41261i	−0.278844	+	0.0457829i
$953$	−30.3524			−0.983211			−0.491606	−	0.870818i	$-0.663590\pi$
$953$	−30.3524			−0.983211			−0.491606	+	0.870818i	$0.663590\pi$
$954$	−11.7192	−	49.7748i	−0.379422	−	1.61152i
$955$		0			0
$956$	−11.2338	−	15.3400i	−0.363326	−	0.496130i
$957$	18.0248	+	8.37821i	0.582660	+	0.270829i
$958$	20.1096	−	39.6519i	0.649711	−	1.28110i
$959$	−23.1806			−0.748540
$960$		0			0
$961$	3.97070			0.128087
$962$	23.3476	−	46.0367i	0.752758	−	1.48428i
$963$	15.7442	+	18.6700i	0.507350	+	0.601632i
$964$	−2.68633	−	3.66824i	−0.0865208	−	0.118146i
$965$		0			0
$966$	21.3705	−	16.8038i	0.687583	−	0.540654i
$967$	−25.8174			−0.830232			−0.415116	−	0.909768i	$-0.636259\pi$
$967$	−25.8174			−0.830232			−0.415116	+	0.909768i	$0.636259\pi$
$968$	−5.18764	+	0.851750i	−0.166737	+	0.0273763i
$969$	3.18736	−	6.85728i	0.102393	−	0.220287i
$970$		0			0
$971$		−	22.9904i		−	0.737796i	−0.929470	−	0.368898i	$-0.879735\pi$
$971$		−	22.9904i		−	0.737796i	0.929470	−	0.368898i	$-0.120265\pi$
$972$	0.852868	+	31.1652i	0.0273557	+	0.999626i
$973$	14.5675			0.467011
$974$	0.113496	−	0.223791i	0.00363665	−	0.00717072i
$975$		0			0
$976$	31.1400	+	9.85897i	0.996768	+	0.315578i
$977$	−36.2952			−1.16119			−0.580593	−	0.814194i	$-0.697179\pi$
$977$	−36.2952			−1.16119			−0.580593	+	0.814194i	$0.697179\pi$
$978$	23.0253	−	18.1051i	0.736269	−	0.578936i
$979$	11.0573			0.353393
$980$		0			0
$981$	−12.9693	+	10.9369i	−0.414079	+	0.349189i
$982$	9.78279	+	4.96137i	0.312181	+	0.158324i
$983$		−	6.92523i		−	0.220881i	−0.993883	−	0.110440i	$-0.964774\pi$
$983$		−	6.92523i		−	0.220881i	0.993883	−	0.110440i	$-0.0352261\pi$
$984$	−35.7312	−	9.98009i	−1.13907	−	0.318154i
$985$		0			0
$986$	5.96165	−	11.7551i	0.189857	−	0.374360i
$987$	3.61437	+	1.68001i	0.115047	+	0.0534754i
$988$	11.8814	+	16.2243i	0.377997	+	0.516164i
$989$	38.6575			1.22924
$990$		0			0
$991$			42.7182i			1.35699i	0.734605	+	0.678495i	$0.237367\pi$
$991$			42.7182i			1.35699i	−0.734605	+	0.678495i	$0.762633\pi$
$992$	20.5989	−	20.9910i	0.654016	−	0.666466i
$993$	5.21367	−	11.2167i	0.165451	−	0.355950i
$994$	−5.62734	+	11.0960i	−0.178488	+	0.351942i
$995$		0			0
$996$	−53.5079	+	10.6787i	−1.69546	+	0.338368i
$997$	15.7743			0.499579			0.249789	−	0.968300i	$-0.419639\pi$
$997$	15.7743			0.499579			0.249789	+	0.968300i	$0.419639\pi$
$998$	−3.33947	+	6.58474i	−0.105709	+	0.208436i
$999$	32.3629	−	8.79941i	1.02392	−	0.278401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.m.e.299.18		24
3.2	odd	2	inner	600.2.m.e.299.8		24
4.3	odd	2		2400.2.m.e.1199.13		24
5.2	odd	4		600.2.b.h.251.10	yes	12
5.3	odd	4		600.2.b.g.251.3	✓	12
5.4	even	2	inner	600.2.m.e.299.7		24
8.3	odd	2	inner	600.2.m.e.299.20		24
8.5	even	2		2400.2.m.e.1199.14		24
12.11	even	2		2400.2.m.e.1199.9		24
15.2	even	4		600.2.b.h.251.3	yes	12
15.8	even	4		600.2.b.g.251.10	yes	12
15.14	odd	2	inner	600.2.m.e.299.17		24
20.3	even	4		2400.2.b.h.2351.12		12
20.7	even	4		2400.2.b.g.2351.1		12
20.19	odd	2		2400.2.m.e.1199.12		24
24.5	odd	2		2400.2.m.e.1199.10		24
24.11	even	2	inner	600.2.m.e.299.6		24
40.3	even	4		600.2.b.g.251.9	yes	12
40.13	odd	4		2400.2.b.h.2351.11		12
40.19	odd	2	inner	600.2.m.e.299.5		24
40.27	even	4		600.2.b.h.251.4	yes	12
40.29	even	2		2400.2.m.e.1199.11		24
40.37	odd	4		2400.2.b.g.2351.2		12
60.23	odd	4		2400.2.b.h.2351.10		12
60.47	odd	4		2400.2.b.g.2351.3		12
60.59	even	2		2400.2.m.e.1199.16		24
120.29	odd	2		2400.2.m.e.1199.15		24
120.53	even	4		2400.2.b.h.2351.9		12
120.59	even	2	inner	600.2.m.e.299.19		24
120.77	even	4		2400.2.b.g.2351.4		12
120.83	odd	4		600.2.b.g.251.4	yes	12
120.107	odd	4		600.2.b.h.251.9	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.b.g.251.3	✓	12	5.3	odd	4
600.2.b.g.251.4	yes	12	120.83	odd	4
600.2.b.g.251.9	yes	12	40.3	even	4
600.2.b.g.251.10	yes	12	15.8	even	4
600.2.b.h.251.3	yes	12	15.2	even	4
600.2.b.h.251.4	yes	12	40.27	even	4
600.2.b.h.251.9	yes	12	120.107	odd	4
600.2.b.h.251.10	yes	12	5.2	odd	4
600.2.m.e.299.5		24	40.19	odd	2	inner
600.2.m.e.299.6		24	24.11	even	2	inner
600.2.m.e.299.7		24	5.4	even	2	inner
600.2.m.e.299.8		24	3.2	odd	2	inner
600.2.m.e.299.17		24	15.14	odd	2	inner
600.2.m.e.299.18		24	1.1	even	1	trivial
600.2.m.e.299.19		24	120.59	even	2	inner
600.2.m.e.299.20		24	8.3	odd	2	inner
2400.2.b.g.2351.1		12	20.7	even	4
2400.2.b.g.2351.2		12	40.37	odd	4
2400.2.b.g.2351.3		12	60.47	odd	4
2400.2.b.g.2351.4		12	120.77	even	4
2400.2.b.h.2351.9		12	120.53	even	4
2400.2.b.h.2351.10		12	60.23	odd	4
2400.2.b.h.2351.11		12	40.13	odd	4
2400.2.b.h.2351.12		12	20.3	even	4
2400.2.m.e.1199.9		24	12.11	even	2
2400.2.m.e.1199.10		24	24.5	odd	2
2400.2.m.e.1199.11		24	40.29	even	2
2400.2.m.e.1199.12		24	20.19	odd	2
2400.2.m.e.1199.13		24	4.3	odd	2
2400.2.m.e.1199.14		24	8.5	even	2
2400.2.m.e.1199.15		24	120.29	odd	2
2400.2.m.e.1199.16		24	60.59	even	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.639662 - 1.26128i) q^{2} +(-0.730070 + 1.57067i) q^{3} +(-1.18166 - 1.61359i) q^{4} +(1.51406 + 1.92552i) q^{6} +1.25539 q^{7} +(-2.79106 + 0.458259i) q^{8} +(-1.93400 - 2.29339i) q^{9} +O(q^{10})\)	\(q+(0.639662 - 1.26128i) q^{2} +(-0.730070 + 1.57067i) q^{3} +(-1.18166 - 1.61359i) q^{4} +(1.51406 + 1.92552i) q^{6} +1.25539 q^{7} +(-2.79106 + 0.458259i) q^{8} +(-1.93400 - 2.29339i) q^{9} -3.02346i q^{11} +(3.39711 - 0.677969i) q^{12} +5.65509 q^{13} +(0.803023 - 1.58339i) q^{14} +(-1.20734 + 3.81344i) q^{16} +2.45546 q^{17} +(-4.12972 + 0.972316i) q^{18} -1.77801 q^{19} +(-0.916519 + 1.97179i) q^{21} +(-3.81344 - 1.93400i) q^{22} -8.84074i q^{23} +(1.31789 - 4.71839i) q^{24} +(3.61735 - 7.13266i) q^{26} +(5.01411 - 1.36333i) q^{27} +(-1.48344 - 2.02568i) q^{28} +3.79561 q^{29} -5.19897i q^{31} +(4.03753 + 3.96211i) q^{32} +(4.74886 + 2.20734i) q^{33} +(1.57067 - 3.09703i) q^{34} +(-1.41526 + 5.83070i) q^{36} +6.45436 q^{37} +(-1.13732 + 2.24257i) q^{38} +(-4.12861 + 8.88227i) q^{39} -7.57276i q^{41} +(1.90072 + 2.41727i) q^{42} +4.37266i q^{43} +(-4.87863 + 3.57272i) q^{44} +(-11.1507 - 5.65509i) q^{46} -1.83304i q^{47} +(-5.10821 - 4.68041i) q^{48} -5.42401 q^{49} +(-1.79266 + 3.85672i) q^{51} +(-6.68241 - 9.12499i) q^{52} +12.0528i q^{53} +(1.48780 - 7.19628i) q^{54} +(-3.50385 + 0.575292i) q^{56} +(1.29807 - 2.79266i) q^{57} +(2.42791 - 4.78734i) q^{58} +4.91093i q^{59} -8.16586i q^{61} +(-6.55737 - 3.32559i) q^{62} +(-2.42791 - 2.87909i) q^{63} +(7.58000 - 2.55806i) q^{64} +(5.82174 - 4.57770i) q^{66} +8.50466i q^{67} +(-2.90153 - 3.96211i) q^{68} +(13.8859 + 6.45436i) q^{69} -7.00770 q^{71} +(6.44886 + 5.51472i) q^{72} -4.59465i q^{73} +(4.12861 - 8.14076i) q^{74} +(2.10101 + 2.86897i) q^{76} -3.79561i q^{77} +(8.56213 + 10.8890i) q^{78} +7.36659i q^{79} +(-1.51932 + 8.87083i) q^{81} +(-9.55139 - 4.84401i) q^{82} -15.7510 q^{83} +(4.26468 - 0.851113i) q^{84} +(5.51515 + 2.79702i) q^{86} +(-2.77106 + 5.96165i) q^{87} +(1.38553 + 8.43866i) q^{88} +3.65716i q^{89} +7.09931 q^{91} +(-14.2653 + 10.4468i) q^{92} +(8.16586 + 3.79561i) q^{93} +(-2.31198 - 1.17252i) q^{94} +(-9.17084 + 3.44901i) q^{96} +13.8773i q^{97} +(-3.46953 + 6.84120i) q^{98} +(-6.93400 + 5.84737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9	\( 24 q - 20 q^{4} + 14 q^{6} + 4 q^{9} - 12 q^{16} + 8 q^{19} - 10 q^{24} + 4 q^{34} + 38 q^{36} - 32 q^{46} + 72 q^{49} - 60 q^{51} + 60 q^{54} - 20 q^{64} + 14 q^{66} - 76 q^{76} - 20 q^{81} + 68 q^{84} - 48 q^{91} - 56 q^{94} - 62 q^{96} - 116 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 14 * q^6 + 4 * q^9 - 12 * q^16 + 8 * q^19 - 10 * q^24 + 4 * q^34 + 38 * q^36 - 32 * q^46 + 72 * q^49 - 60 * q^51 + 60 * q^54 - 20 * q^64 + 14 * q^66 - 76 * q^76 - 20 * q^81 + 68 * q^84 - 48 * q^91 - 56 * q^94 - 62 * q^96 - 116 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more