LMFDB - Embedded newform 600.2.m.e.299.20

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			299.20
Character	$\chi$	$=$	600.299
Dual form			600.2.m.e.299.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.639662 + 1.26128i) q^{2} +(-0.730070 + 1.57067i) q^{3} +(-1.18166 + 1.61359i) q^{4} +(-2.44805 + 0.0838735i) q^{6} -1.25539 q^{7} +(-2.79106 - 0.458259i) q^{8} +(-1.93400 - 2.29339i) q^{9} +O(q^{10})$	\(q+(0.639662 + 1.26128i) q^{2} +(-0.730070 + 1.57067i) q^{3} +(-1.18166 + 1.61359i) q^{4} +(-2.44805 + 0.0838735i) q^{6} -1.25539 q^{7} +(-2.79106 - 0.458259i) q^{8} +(-1.93400 - 2.29339i) q^{9} -3.02346i q^{11} +(-1.67172 - 3.03403i) q^{12} -5.65509 q^{13} +(-0.803023 - 1.58339i) q^{14} +(-1.20734 - 3.81344i) q^{16} +2.45546 q^{17} +(1.65551 - 3.90631i) q^{18} -1.77801 q^{19} +(0.916519 - 1.97179i) q^{21} +(3.81344 - 1.93400i) q^{22} +8.84074i q^{23} +(2.75744 - 4.04926i) 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} +(5.98593 - 0.410653i) q^{36} -6.45436 q^{37} +(-1.13732 - 2.24257i) q^{38} +(4.12861 - 8.88227i) q^{39} -7.57276i q^{41} +(3.07325 - 0.105293i) q^{42} +4.37266i q^{43} +(4.87863 + 3.57272i) q^{44} +(-11.1507 + 5.65509i) q^{46} +1.83304i q^{47} +(6.87109 + 0.887748i) q^{48} -5.42401 q^{49} +(-1.79266 + 3.85672i) q^{51} +(6.68241 - 9.12499i) q^{52} -12.0528i q^{53} +(4.92688 + 5.45214i) 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} +(0.253588 + 7.40160i) q^{66} +8.50466i q^{67} +(-2.90153 + 3.96211i) q^{68} +(-13.8859 - 6.45436i) q^{69} +7.00770 q^{71} +(4.34692 + 7.28727i) q^{72} -4.59465i q^{73} +(-4.12861 - 8.14076i) q^{74} +(2.10101 - 2.86897i) q^{76} +3.79561i q^{77} +(13.8440 - 0.474312i) q^{78} -7.36659i q^{79} +(-1.51932 + 8.87083i) q^{81} +(9.55139 - 4.84401i) q^{82} -15.7510 q^{83} +(2.09865 + 3.80888i) 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} +(3.27548 + 9.23424i) 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
$6$	−2.44805	+	0.0838735i	−0.999414	+	0.0342412i
$7$	−1.25539			−0.474491			−0.237245	−	0.971450i	$-0.576245\pi$
$7$	−1.25539			−0.474491			−0.237245	+	0.971450i	$0.576245\pi$
$8$	−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	$-0.150648\pi$
$12$	−1.67172	−	3.03403i	−0.482583	−	0.875850i
$13$	−5.65509			−1.56844			−0.784220	−	0.620483i	$-0.786936\pi$
$13$	−5.65509			−1.56844			−0.784220	+	0.620483i	$0.786936\pi$
$14$	−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	$0.403758\pi$
$18$	1.65551	−	3.90631i	0.390208	−	0.920727i
$19$	−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	$0.373208\pi$
$23$			8.84074i			1.84342i	−0.387878	+	0.921711i	$0.626792\pi$
$24$	2.75744	−	4.04926i	0.562860	−	0.826552i
$25$		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	$-0.614639\pi$
$29$	−3.79561			−0.704827			−0.352414	+	0.935844i	$0.614639\pi$
$30$		0			0
$31$			5.19897i			0.933763i	0.884320	+	0.466881i	$0.154623\pi$
$31$			5.19897i			0.933763i	−0.884320	+	0.466881i	$0.845377\pi$
$32$	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
$36$	5.98593	−	0.410653i	0.997655	−	0.0684422i
$37$	−6.45436			−1.06109			−0.530545	−	0.847657i	$-0.678013\pi$
$37$	−6.45436			−1.06109			−0.530545	+	0.847657i	$0.678013\pi$
$38$	−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	$-0.201398\pi$
$42$	3.07325	−	0.105293i	0.474213	−	0.0162471i
$43$			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	$0.0426820\pi$
$47$			1.83304i			0.267376i	−0.991023	+	0.133688i	$0.957318\pi$
$48$	6.87109	+	0.887748i	0.991757	+	0.128135i
$49$	−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	$-0.689597\pi$
$53$		−	12.0528i		−	1.65558i	0.561035	−	0.827792i	$-0.310403\pi$
$54$	4.92688	+	5.45214i	0.670464	+	0.741942i
$55$		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	$0.175100\pi$
$61$			8.16586i			1.04553i	−0.852477	+	0.522766i	$0.824900\pi$
$62$	−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
$66$	0.253588	+	7.40160i	0.0312146	+	0.911074i
$67$			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	$-0.363491\pi$
$71$	7.00770			0.831661			0.415831	+	0.909442i	$0.363491\pi$
$72$	4.34692	+	7.28727i	0.512290	+	0.858813i
$73$		−	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
$78$	13.8440	−	0.474312i	1.56752	−	0.0537052i
$79$		−	7.36659i		−	0.828806i	−0.910093	−	0.414403i	$-0.863990\pi$
$79$		−	7.36659i		−	0.828806i	0.910093	−	0.414403i	$-0.136010\pi$
$80$		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	$0.832333\pi$
$84$	2.09865	+	3.80888i	0.228981	+	0.415583i
$85$		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
$96$	3.27548	+	9.23424i	0.334302	+	0.942466i
$97$			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	$-0.742763\pi$
$101$	−13.8859			−1.38170			−0.690848	+	0.723000i	$0.742763\pi$
$102$	−6.01111	+	0.205948i	−0.595188	+	0.0203919i
$103$	7.36659			0.725852			0.362926	−	0.931818i	$-0.381778\pi$
$103$	7.36659			0.725852			0.362926	+	0.931818i	$0.381778\pi$
$104$	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	$0.628735\pi$
$108$	−3.72515	+	9.70172i	−0.358452	+	0.933548i
$109$			5.65509i			0.541659i	0.962627	+	0.270830i	$0.0872980\pi$
$109$			5.65509i			0.541659i	−0.962627	+	0.270830i	$0.912702\pi$
$110$		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	$0.318285\pi$
$114$	4.35266	−	0.149128i	0.407664	−	0.0139671i
$115$		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
$126$	−2.07831	+	4.90393i	−0.185150	+	0.436877i
$127$	−21.7081			−1.92628			−0.963142	−	0.268993i	$-0.913309\pi$
$127$	−21.7081			−1.92628			−0.963142	+	0.268993i	$0.913309\pi$
$128$	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	$0.815773\pi$
$132$	−9.17330	+	5.05437i	−0.798433	+	0.439927i
$133$	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	$0.789288\pi$
$138$	−0.741503	−	21.6426i	−0.0631210	−	1.84234i
$139$	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
$144$	−6.41073	+	10.1441i	−0.534228	+	0.845341i
$145$		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	$-0.337582\pi$
$149$	11.9233			0.976794			0.488397	+	0.872621i	$0.337582\pi$
$150$		0			0
$151$		−	10.0548i		−	0.818247i	−0.912479	−	0.409124i	$-0.865834\pi$
$151$		−	10.0548i		−	0.818247i	0.912479	−	0.409124i	$-0.134166\pi$
$152$	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
$156$	9.45370	+	17.1577i	0.756902	+	1.37372i
$157$	1.71150			0.136593			0.0682964	−	0.997665i	$-0.478244\pi$
$157$	1.71150			0.136593			0.0682964	+	0.997665i	$0.478244\pi$
$158$	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
$162$	−12.1605	+	3.75805i	−0.955417	+	0.295260i
$163$		−	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	$-0.992813\pi$
$167$		−	0.583522i		−	0.0451543i	0.999745	−	0.0225771i	$-0.00718713\pi$
$168$	−3.46165	+	5.08338i	−0.267072	+	0.392192i
$169$	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	$-0.848502\pi$
$173$		−	12.0528i		−	0.916360i	0.888860	−	0.458180i	$-0.151498\pi$
$174$	9.29186	−	0.318351i	0.704414	−	0.0241341i
$175$		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	$0.0848505\pi$
$181$			7.08790i			0.526840i	−0.964681	+	0.263420i	$0.915150\pi$
$182$	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
$186$	−0.436056	−	12.7274i	−0.0319732	−	0.933215i
$187$		−	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	$-0.259846\pi$
$191$	18.9310			1.36980			0.684899	+	0.728638i	$0.259846\pi$
$192$	−9.55178	+	10.0381i	−0.689341	+	0.724437i
$193$			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	$-0.882964\pi$
$197$		−	10.0903i		−	0.718901i	0.933164	−	0.359450i	$-0.117036\pi$
$198$	−11.8106	−	5.00538i	−0.839343	−	0.355717i
$199$			19.0199i			1.34829i	0.738601	+	0.674143i	$0.235487\pi$
$199$			19.0199i			1.34829i	−0.738601	+	0.674143i	$0.764513\pi$
$200$		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
$204$	−4.10484	−	7.44996i	−0.287396	−	0.521602i
$205$		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
$216$	−14.6194	+	1.50736i	−0.994727	+	0.102563i
$217$		−	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
$222$	15.8006	−	0.541349i	1.06047	−	0.0363330i
$223$	7.70974			0.516282			0.258141	−	0.966107i	$-0.416890\pi$
$223$	7.70974			0.516282			0.258141	+	0.966107i	$0.416890\pi$
$224$	−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	$0.420980\pi$
$228$	2.97232	+	5.39454i	0.196847	+	0.357262i
$229$			17.1310i			1.13205i	0.824389	+	0.566024i	$0.191519\pi$
$229$			17.1310i			1.13205i	−0.824389	+	0.566024i	$0.808481\pi$
$230$		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	$0.485313\pi$
$234$	−9.36207	+	22.0905i	−0.612018	+	1.44410i
$235$		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	$-0.599482\pi$
$239$	−9.50673			−0.614939			−0.307470	+	0.951558i	$0.599482\pi$
$240$		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
$246$	0.635154	+	18.5385i	0.0404959	+	1.18197i
$247$	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	$-0.0969017\pi$
$252$	−7.51465	+	0.515528i	−0.473378	+	0.0324752i
$253$	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	$0.175443\pi$
$258$	−0.366750	−	10.7045i	−0.0228329	−	0.666433i
$259$	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	$0.0122657\pi$
$263$			1.24952i			0.0770484i	−0.999258	+	0.0385242i	$0.987734\pi$
$264$	−12.2428	−	8.33702i	−0.753492	−	0.513108i
$265$		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	$-0.340927\pi$
$269$	15.7189			0.958399			0.479199	+	0.877706i	$0.340927\pi$
$270$		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
$276$	26.8231	−	14.7792i	1.61456	−	0.889603i
$277$	0.633548			0.0380662			0.0190331	−	0.999819i	$-0.493941\pi$
$277$	0.633548			0.0380662			0.0190331	+	0.999819i	$0.493941\pi$
$278$	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	$0.785505\pi$
$282$	−0.153743	−	4.48737i	−0.00915527	−	0.267219i
$283$			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
$288$	−16.8953	−	1.59695i	−0.995563	−	0.0941013i
$289$	−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	$-0.948647\pi$
$293$		−	5.49911i		−	0.321262i	0.987015	−	0.160631i	$-0.0513528\pi$
$294$	13.2783	−	0.454930i	0.774404	−	0.0265321i
$295$		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
$306$	4.06505	−	9.59181i	0.232384	−	0.548327i
$307$			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	$-0.552200\pi$
$311$	−5.75819			−0.326517			−0.163258	+	0.986583i	$0.552200\pi$
$312$	−15.5936	+	22.8989i	−0.882812	+	1.29640i
$313$		−	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	$-0.834602\pi$
$317$		−	17.6815i		−	0.993091i	0.868011	−	0.496545i	$-0.165398\pi$
$318$	1.01091	+	29.5060i	0.0566892	+	1.65461i
$319$			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
$324$	−12.5186	−	12.9339i	−0.695475	−	0.718550i
$325$		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
$336$	−8.62587	−	1.11447i	−0.470580	−	0.0607991i
$337$		−	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
$342$	−2.94351	+	6.94545i	−0.159167	+	0.375567i
$343$	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	$0.495467\pi$
$348$	6.34518	+	11.5160i	0.340138	+	0.617323i
$349$		−	7.36659i		−	0.394325i	−0.980371	−	0.197162i	$-0.936827\pi$
$349$		−	7.36659i		−	0.394325i	0.980371	−	0.197162i	$-0.0631726\pi$
$350$		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	$0.596604\pi$
$354$	−0.411897	−	12.0222i	−0.0218921	−	0.638974i
$355$		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	$-0.649003\pi$
$359$	−17.0980			−0.902396			−0.451198	+	0.892424i	$0.649003\pi$
$360$		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
$366$	−0.684899	−	19.9905i	−0.0358002	−	1.04492i
$367$	13.9984			0.730709			0.365355	−	0.930868i	$-0.380948\pi$
$367$	13.9984			0.730709			0.365355	+	0.930868i	$0.380948\pi$
$368$	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
$372$	15.7739	−	8.69120i	0.817837	−	0.450618i
$373$	−21.5952			−1.11815			−0.559077	−	0.829116i	$-0.688845\pi$
$373$	−21.5952			−1.11815			−0.559077	+	0.829116i	$0.688845\pi$
$374$	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
$378$	−6.18513	−	6.84454i	−0.318129	−	0.352045i
$379$	−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	$-0.867303\pi$
$383$		−	15.8484i		−	0.809818i	0.914357	−	0.404909i	$-0.132697\pi$
$384$	−18.7708	−	5.62650i	−0.957893	−	0.287126i
$385$		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	$-0.344827\pi$
$389$	18.4770			0.936822			0.468411	+	0.883511i	$0.344827\pi$
$390$		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
$396$	−1.24160	−	18.0982i	−0.0623925	−	0.909471i
$397$	−18.3981			−0.923373			−0.461687	−	0.887043i	$-0.652756\pi$
$397$	−18.3981			−0.923373			−0.461687	+	0.887043i	$0.652756\pi$
$398$	−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	$-0.00145814\pi$
$402$	−0.713316	−	20.8199i	−0.0355770	−	1.03840i
$403$		−	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
$408$	6.77079	−	9.94282i	0.335204	−	0.492243i
$409$	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
$414$	34.5347	+	14.6360i	1.69729	+	0.719318i
$415$		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	$-0.774198\pi$
$421$		−	26.7297i		−	1.30272i	0.758767	−	0.651362i	$-0.225802\pi$
$422$	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
$426$	−17.1552	+	0.587760i	−0.831174	+	0.0284771i
$427$		−	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	$-0.816061\pi$
$431$	−34.7794			−1.67527			−0.837633	+	0.546233i	$0.816061\pi$
$432$	−11.2527	−	17.4750i	−0.541396	−	0.840768i
$433$			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
$438$	0.385369	+	11.2479i	0.0184136	+	0.537448i
$439$		−	2.85392i		−	0.136210i	−0.997678	−	0.0681051i	$-0.978305\pi$
$439$		−	2.85392i		−	0.136210i	0.997678	−	0.0681051i	$-0.0216953\pi$
$440$		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	$0.394600\pi$
$444$	10.7898	+	19.5827i	0.512064	+	0.929356i
$445$		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
$456$	−4.90275	+	7.19962i	−0.229592	+	0.337153i
$457$		−	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	$-0.400389\pi$
$461$	13.2199			0.615711			0.307855	+	0.951433i	$0.400389\pi$
$462$	−0.318351	−	9.29186i	−0.0148110	−	0.432296i
$463$	−40.5506			−1.88455			−0.942273	−	0.334845i	$-0.891316\pi$
$463$	−40.5506			−1.88455			−0.942273	+	0.334845i	$0.891316\pi$
$464$	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	$0.576209\pi$
$468$	−33.8510	+	2.32228i	−1.56476	+	0.107347i
$469$		−	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
$474$	0.617861	+	18.0338i	0.0283793	+	0.828320i
$475$		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	$-0.755041\pi$
$479$	−31.4378			−1.43643			−0.718215	+	0.695821i	$0.755041\pi$
$480$		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
$486$	2.97534	−	21.8437i	0.134964	−	0.990850i
$487$	−0.177431			−0.00804018			−0.00402009	−	0.999992i	$-0.501280\pi$
$487$	−0.177431			−0.00804018			−0.00402009	+	0.999992i	$0.501280\pi$
$488$	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	$0.944002\pi$
$492$	−22.9760	+	12.6595i	−1.03584	+	0.570735i
$493$	−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
$498$	38.5593	−	1.32109i	1.72788	−	0.0591996i
$499$	−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	$-0.954846\pi$
$503$		−	6.34171i		−	0.282763i	0.989955	−	0.141381i	$-0.0451544\pi$
$504$	−5.45706	−	9.14833i	−0.243077	−	0.407499i
$505$		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	$-0.226248\pi$
$509$	34.1959			1.51571			0.757854	+	0.652425i	$0.226248\pi$
$510$		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
$516$	13.2668	−	7.30984i	0.584038	−	0.321798i
$517$	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	$0.746678\pi$
$522$	−6.28368	+	14.8268i	−0.275029	+	0.648953i
$523$			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
$528$	2.68407	−	20.7745i	0.116809	−	0.904094i
$529$	−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
$534$	−0.306739	−	8.95292i	−0.0132739	−	0.387431i
$535$		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	$0.0903089\pi$
$541$			13.0217i			0.559846i	−0.960023	+	0.279923i	$0.909691\pi$
$542$		0			0
$543$	−11.1327	−	5.17466i	−0.477752	−	0.222066i
$544$	9.91402	−	9.72882i	0.425060	−	0.417120i
$545$		0			0
$546$	−17.3795	+	0.595444i	−0.743774	+	0.0254827i
$547$			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
$552$	35.7985	+	24.3778i	1.52368	+	1.03759i
$553$			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	$-0.845561\pi$
$557$		−	22.0135i		−	0.932744i	0.884589	−	0.466372i	$-0.154439\pi$
$558$	20.3088	+	8.60696i	0.859740	+	0.364362i
$559$		−	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	$0.433739\pi$
$564$	5.56150	−	3.06432i	0.234181	−	0.129031i
$565$		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
$576$	−8.79305	−	22.3312i	−0.366377	−	0.930466i
$577$			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
$582$	−1.16394	−	33.9724i	−0.0482468	−	1.40820i
$583$	−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	$0.706969\pi$
$588$	9.06740	+	16.4566i	0.373933	+	0.678660i
$589$		−	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	$0.331058\pi$
$594$	16.4844	−	14.8962i	0.676361	−	0.611200i
$595$		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	$-0.708871\pi$
$599$	−29.8638			−1.22020			−0.610102	+	0.792323i	$0.708871\pi$
$600$		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
$606$	33.9933	−	1.16466i	1.38089	−	0.0473109i
$607$	25.8174			1.04790			0.523949	−	0.851750i	$-0.324458\pi$
$607$	25.8174			1.04790			0.523949	+	0.851750i	$0.324458\pi$
$608$	−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
$612$	14.6982	−	1.00834i	0.594141	−	0.0407599i
$613$	16.6866			0.673965			0.336982	−	0.941511i	$-0.390594\pi$
$613$	16.6866			0.673965			0.336982	+	0.941511i	$0.390594\pi$
$614$	−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	$0.556001\pi$
$618$	−18.0338	+	0.617861i	−0.725426	+	0.0248540i
$619$	−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
$624$	−38.8566	−	5.02029i	−1.55551	−	0.200973i
$625$		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	$0.0286302\pi$
$631$			4.51267i			0.179647i	−0.995958	+	0.0898233i	$0.971370\pi$
$632$	−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
$636$	−36.5687	+	20.1489i	−1.45004	+	0.798956i
$637$	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	$-0.164670\pi$
$642$	19.9290	−	0.682794i	0.786536	−	0.0269477i
$643$			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	$0.137840\pi$
$647$			21.3476i			0.839259i	−0.907695	+	0.419629i	$0.862160\pi$
$648$	8.30564	−	24.0628i	0.326276	−	0.945274i
$649$	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	$0.169441\pi$
$653$			25.9387i			1.01506i	−0.861634	+	0.507530i	$0.830559\pi$
$654$	−0.474312	−	13.8440i	−0.0185471	−	0.541342i
$655$		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	$0.0580152\pi$
$661$			9.31999i			0.362506i	−0.983437	+	0.181253i	$0.941985\pi$
$662$	−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
$666$	−10.6853	+	25.2127i	−0.414046	+	0.976974i
$667$		−	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
$672$	−4.11199	−	11.5925i	−0.158623	−	0.447192i
$673$			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	$0.252342\pi$
$677$			37.0665i			1.42458i	−0.701885	+	0.712290i	$0.747658\pi$
$678$	−28.1241	+	0.963569i	−1.08010	+	0.0370056i
$679$		−	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	$0.333646\pi$
$684$	−10.6430	+	0.730145i	−0.406946	+	0.0279178i
$685$		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
$696$	−10.4662	+	15.3694i	−0.396719	+	0.582577i
$697$		−	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	$-0.422790\pi$
$701$	12.7188			0.480383			0.240192	+	0.970725i	$0.422790\pi$
$702$	−27.8619	−	30.8323i	−1.05158	−	1.16369i
$703$	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
$708$	14.8999	−	8.20968i	0.559974	−	0.308539i
$709$		−	46.7263i		−	1.75484i	−0.479721	−	0.877421i	$-0.659262\pi$
$709$		−	46.7263i		−	1.75484i	0.479721	−	0.877421i	$-0.340738\pi$
$710$		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
$714$	7.54625	−	0.258544i	0.282411	−	0.00967578i
$715$		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	$-0.443273\pi$
$719$	9.50673			0.354541			0.177271	+	0.984162i	$0.443273\pi$
$720$		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
$726$	−4.55011	+	0.155893i	−0.168870	+	0.00578572i
$727$	−31.7629			−1.17802			−0.589011	−	0.808125i	$-0.700482\pi$
$727$	−31.7629			−1.17802			−0.589011	+	0.808125i	$0.700482\pi$
$728$	−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
$732$	24.7755	−	13.6510i	0.915729	−	0.504555i
$733$	−15.5852			−0.575653			−0.287826	−	0.957683i	$-0.592933\pi$
$733$	−15.5852			−0.575653			−0.287826	+	0.957683i	$0.592933\pi$
$734$	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
$738$	−29.5816	−	12.5368i	−1.08891	−	0.461486i
$739$	−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	$-0.879298\pi$
$743$		−	20.1805i		−	0.740351i	0.928962	−	0.370176i	$-0.120702\pi$
$744$	21.0520	+	14.3358i	0.771804	+	0.525578i
$745$		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	$-0.887120\pi$
$751$		−	19.0316i		−	0.694474i	0.937777	−	0.347237i	$-0.112880\pi$
$752$	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
$756$	4.67649	−	12.1794i	0.170082	−	0.442960i
$757$	−4.22227			−0.153461			−0.0767305	−	0.997052i	$-0.524448\pi$
$757$	−4.22227			−0.153461			−0.0767305	+	0.997052i	$0.524448\pi$
$758$	−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	$-0.242473\pi$
$762$	53.1426	−	1.82074i	1.92515	−	0.0659583i
$763$		−	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
$768$	−4.91037	−	27.2743i	−0.177188	−	0.984177i
$769$	−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	$-0.904793\pi$
$773$		−	16.3849i		−	0.589324i	0.955602	−	0.294662i	$-0.0952070\pi$
$774$	17.0810	+	7.23899i	0.613963	+	0.260200i
$775$		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
$786$	−1.05019	−	30.6525i	−0.0374592	−	1.09334i
$787$		−	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
$792$	22.0328	−	13.1428i	0.782901	−	0.467008i
$793$		−	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	$0.0783406\pi$
$797$			13.7563i			0.487274i	−0.969866	+	0.243637i	$0.921659\pi$
$798$	−5.46426	+	0.187213i	−0.193433	+	0.00662726i
$799$			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
$804$	25.8034	−	14.2174i	0.910017	−	0.501408i
$805$		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
$816$	16.8717	+	2.17983i	0.590628	+	0.0763094i
$817$		−	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	$-0.860329\pi$
$821$	−51.8774			−1.81053			−0.905267	+	0.424844i	$0.860329\pi$
$822$	45.2031	−	1.54872i	1.57664	−	0.0540177i
$823$	−36.0379			−1.25620			−0.628102	−	0.778131i	$-0.716168\pi$
$823$	−36.0379			−1.25620			−0.628102	+	0.778131i	$0.716168\pi$
$824$	−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	$0.326306\pi$
$828$	3.63048	+	52.9201i	0.126168	+	1.83910i
$829$		−	22.2287i		−	0.772035i	−0.922492	−	0.386017i	$-0.873850\pi$
$829$		−	22.2287i		−	0.772035i	0.922492	−	0.386017i	$-0.126150\pi$
$830$		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
$834$	−28.4072	+	0.973266i	−0.983659	+	0.0337014i
$835$		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	$-0.471529\pi$
$839$	5.17466			0.178649			0.0893246	+	0.996003i	$0.471529\pi$
$840$		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
$846$	7.16042	+	3.03462i	0.246180	+	0.104332i
$847$	−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
$852$	−11.7149	−	21.2616i	−0.401345	−	0.728411i
$853$	36.3283			1.24386			0.621929	−	0.783073i	$-0.286349\pi$
$853$	36.3283			1.24386			0.621929	+	0.783073i	$0.286349\pi$
$854$	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	$0.551452\pi$
$858$	−1.43406	−	41.8567i	−0.0489582	−	1.42896i
$859$	−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	$0.101092\pi$
$863$			18.3475i			0.624555i	−0.949991	+	0.312278i	$0.898908\pi$
$864$	14.8430	−	25.3710i	0.504969	−	0.863137i
$865$		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
$876$	−13.9403	+	7.68095i	−0.471000	+	0.259515i
$877$	16.5736			0.559651			0.279826	−	0.960051i	$-0.409723\pi$
$877$	16.5736			0.559651			0.279826	+	0.960051i	$0.409723\pi$
$878$	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	$0.858155\pi$
$882$	−8.97951	+	21.1879i	−0.302356	+	0.713433i
$883$		−	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	$-0.860525\pi$
$887$		−	25.2727i		−	0.848574i	0.905528	−	0.424287i	$-0.139475\pi$
$888$	−17.7975	+	26.1354i	−0.597245	+	0.877046i
$889$	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
$894$	−29.1889	+	1.00005i	−0.976221	+	0.0334466i
$895$		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
$906$	0.843330	+	24.6147i	0.0280178	+	0.817768i
$907$		−	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	$-0.452774\pi$
$911$	8.92321			0.295639			0.147820	+	0.989014i	$0.452774\pi$
$912$	−12.2169	−	1.57842i	−0.404541	−	0.0522668i
$913$			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
$918$	12.0978	+	13.3875i	0.399286	+	0.441855i
$919$		−	33.7531i		−	1.11341i	−0.830710	−	0.556706i	$-0.812065\pi$
$919$		−	33.7531i		−	1.11341i	0.830710	−	0.556706i	$-0.187935\pi$
$920$		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
$924$	11.5160	−	6.34518i	0.378849	−	0.208741i
$925$		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
$936$	−24.5822	−	41.2101i	−0.803496	−	1.34700i
$937$		−	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	$-0.707338\pi$
$941$	−37.1960			−1.21255			−0.606277	+	0.795253i	$0.707338\pi$
$942$	−4.18985	+	0.143550i	−0.136513	+	0.00467710i
$943$	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	$0.702573\pi$
$948$	−22.3505	+	12.3148i	−0.725910	+	0.399968i
$949$			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	$0.663590\pi$
$954$	−47.0821	−	19.9536i	−1.52434	−	0.646022i
$955$		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
$966$	0.930872	+	27.1698i	0.0299503	+	0.874174i
$967$	25.8174			0.830232			0.415116	−	0.909768i	$-0.363741\pi$
$967$	25.8174			0.830232			0.415116	+	0.909768i	$0.363741\pi$
$968$	−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	$-0.120265\pi$
$972$	29.4543	−	10.2199i	0.944746	−	0.327802i
$973$	−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	$0.697179\pi$
$978$	1.00296	+	29.2738i	0.0320710	+	0.936072i
$979$	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	$0.0352261\pi$
$983$			6.92523i			0.220881i	−0.993883	+	0.110440i	$0.964774\pi$
$984$	−30.6641	−	20.8814i	−0.977536	−	0.665676i
$985$		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	$-0.762633\pi$
$991$		−	42.7182i		−	1.35699i	0.734605	−	0.678495i	$-0.237367\pi$
$992$	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
$996$	26.3312	+	47.7891i	0.834337	+	1.51426i
$997$	−15.7743			−0.499579			−0.249789	−	0.968300i	$-0.580361\pi$
$997$	−15.7743			−0.499579			−0.249789	+	0.968300i	$0.580361\pi$
$998$	−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.299.20		24
3.2	odd	2	inner	600.2.m.e.299.6		24
4.3	odd	2		2400.2.m.e.1199.14		24
5.2	odd	4		600.2.b.h.251.4	yes	12
5.3	odd	4		600.2.b.g.251.9	yes	12
5.4	even	2	inner	600.2.m.e.299.5		24
8.3	odd	2	inner	600.2.m.e.299.18		24
8.5	even	2		2400.2.m.e.1199.13		24
12.11	even	2		2400.2.m.e.1199.10		24
15.2	even	4		600.2.b.h.251.9	yes	12
15.8	even	4		600.2.b.g.251.4	yes	12
15.14	odd	2	inner	600.2.m.e.299.19		24
20.3	even	4		2400.2.b.h.2351.11		12
20.7	even	4		2400.2.b.g.2351.2		12
20.19	odd	2		2400.2.m.e.1199.11		24
24.5	odd	2		2400.2.m.e.1199.9		24
24.11	even	2	inner	600.2.m.e.299.8		24
40.3	even	4		600.2.b.g.251.3	✓	12
40.13	odd	4		2400.2.b.h.2351.12		12
40.19	odd	2	inner	600.2.m.e.299.7		24
40.27	even	4		600.2.b.h.251.10	yes	12
40.29	even	2		2400.2.m.e.1199.12		24
40.37	odd	4		2400.2.b.g.2351.1		12
60.23	odd	4		2400.2.b.h.2351.9		12
60.47	odd	4		2400.2.b.g.2351.4		12
60.59	even	2		2400.2.m.e.1199.15		24
120.29	odd	2		2400.2.m.e.1199.16		24
120.53	even	4		2400.2.b.h.2351.10		12
120.59	even	2	inner	600.2.m.e.299.17		24
120.77	even	4		2400.2.b.g.2351.3		12
120.83	odd	4		600.2.b.g.251.10	yes	12
120.107	odd	4		600.2.b.h.251.3	yes	12

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

\(f(q)\)	\(=\)	\(q+(0.639662 + 1.26128i) q^{2} +(-0.730070 + 1.57067i) q^{3} +(-1.18166 + 1.61359i) q^{4} +(-2.44805 + 0.0838735i) q^{6} -1.25539 q^{7} +(-2.79106 - 0.458259i) q^{8} +(-1.93400 - 2.29339i) q^{9} +O(q^{10})\)	\(q+(0.639662 + 1.26128i) q^{2} +(-0.730070 + 1.57067i) q^{3} +(-1.18166 + 1.61359i) q^{4} +(-2.44805 + 0.0838735i) q^{6} -1.25539 q^{7} +(-2.79106 - 0.458259i) q^{8} +(-1.93400 - 2.29339i) q^{9} -3.02346i q^{11} +(-1.67172 - 3.03403i) q^{12} -5.65509 q^{13} +(-0.803023 - 1.58339i) q^{14} +(-1.20734 - 3.81344i) q^{16} +2.45546 q^{17} +(1.65551 - 3.90631i) q^{18} -1.77801 q^{19} +(0.916519 - 1.97179i) q^{21} +(3.81344 - 1.93400i) q^{22} +8.84074i q^{23} +(2.75744 - 4.04926i) 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} +(5.98593 - 0.410653i) q^{36} -6.45436 q^{37} +(-1.13732 - 2.24257i) q^{38} +(4.12861 - 8.88227i) q^{39} -7.57276i q^{41} +(3.07325 - 0.105293i) q^{42} +4.37266i q^{43} +(4.87863 + 3.57272i) q^{44} +(-11.1507 + 5.65509i) q^{46} +1.83304i q^{47} +(6.87109 + 0.887748i) q^{48} -5.42401 q^{49} +(-1.79266 + 3.85672i) q^{51} +(6.68241 - 9.12499i) q^{52} -12.0528i q^{53} +(4.92688 + 5.45214i) 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} +(0.253588 + 7.40160i) q^{66} +8.50466i q^{67} +(-2.90153 + 3.96211i) q^{68} +(-13.8859 - 6.45436i) q^{69} +7.00770 q^{71} +(4.34692 + 7.28727i) q^{72} -4.59465i q^{73} +(-4.12861 - 8.14076i) q^{74} +(2.10101 - 2.86897i) q^{76} +3.79561i q^{77} +(13.8440 - 0.474312i) q^{78} -7.36659i q^{79} +(-1.51932 + 8.87083i) q^{81} +(9.55139 - 4.84401i) q^{82} -15.7510 q^{83} +(2.09865 + 3.80888i) 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} +(3.27548 + 9.23424i) 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