LMFDB - Embedded newform 462.2.ba.a.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(19,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 25, 9]))

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

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

chi := DirichletCharacter("462.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.ba (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			61.7
Character	$\chi$	$=$	462.61
Dual form			462.2.ba.a.409.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207912 - 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.26898 + 1.14260i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.554537 - 2.58698i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(0.207912 - 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.26898 + 1.14260i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.554537 - 2.58698i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(0.853791 + 1.47881i) q^{10} +(0.800558 - 3.21856i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.93023 - 5.94064i) q^{13} +(-2.64575 + 0.00455429i) q^{14} +(-1.38146 + 1.00369i) q^{15} +(0.669131 + 0.743145i) q^{16} +(3.19637 - 0.679409i) q^{17} +(0.406737 - 0.913545i) q^{18} +(3.35975 - 1.49585i) q^{19} +(1.62401 - 0.527672i) q^{20} +(-0.281085 - 2.63078i) q^{21} +(-2.98178 - 1.45224i) q^{22} +(1.38888 - 2.40561i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-0.217854 + 2.07274i) q^{25} +(-6.21214 + 0.652922i) q^{26} +(0.951057 + 0.309017i) q^{27} +(-0.545627 + 2.58888i) q^{28} +(1.95231 + 2.68712i) q^{29} +(0.694537 + 1.55995i) q^{30} +(-7.47572 - 6.73116i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.13260 - 3.11724i) q^{33} -3.26778i q^{34} +(3.65957 + 2.64922i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.400705 + 3.81245i) q^{37} +(-0.764637 - 3.59733i) q^{38} +(-1.29869 - 6.10986i) q^{39} +(-0.178491 - 1.69823i) q^{40} +(4.85606 + 3.52813i) q^{41} +(-2.63173 - 0.272027i) q^{42} +7.25172i q^{43} +(-2.04045 + 2.61468i) q^{44} +(-1.47881 + 0.853791i) q^{45} +(-2.06428 - 1.85868i) q^{46} +(3.70069 + 8.31188i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-6.38498 + 2.86916i) q^{49} +(1.98215 + 0.644041i) q^{50} +(3.24987 - 0.341576i) q^{51} +(-0.652922 + 6.21214i) q^{52} +(-6.59303 + 7.32230i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.66162 + 4.99900i) q^{55} +(2.41886 + 1.07196i) q^{56} +(3.49770 - 1.13647i) q^{57} +(3.03431 - 1.35096i) q^{58} +(3.78468 - 8.50054i) q^{59} +(1.67027 - 0.355026i) q^{60} +(-3.45078 - 3.83248i) q^{61} +(-8.13836 + 5.91287i) q^{62} +(-0.00455429 - 2.64575i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(9.23717 + 5.33308i) q^{65} +(-2.81364 - 1.75596i) q^{66} +(0.0683384 + 0.118366i) q^{67} +(-3.19637 - 0.679409i) q^{68} +(1.63273 - 2.24725i) q^{69} +(3.35220 - 3.02880i) q^{70} +(-0.441852 + 1.35988i) q^{71} +(-0.743145 + 0.669131i) q^{72} +(-11.4831 - 5.11261i) q^{73} +(3.81245 + 0.400705i) q^{74} +(-0.433321 + 2.03862i) q^{75} -3.67770 q^{76} +(-8.77030 - 0.286224i) q^{77} -6.24635 q^{78} +(0.596378 - 2.80574i) q^{79} +(-1.69823 - 0.178491i) q^{80} +(0.913545 + 0.406737i) q^{81} +(4.46067 - 4.01640i) q^{82} +(0.642506 - 1.97743i) q^{83} +(-0.813250 + 2.51766i) q^{84} +(-3.27984 + 4.51431i) q^{85} +(7.09325 + 1.50772i) q^{86} +(1.66073 + 2.87647i) q^{87} +(2.13331 + 2.53949i) q^{88} +(8.14120 + 4.70032i) q^{89} +(0.527672 + 1.62401i) q^{90} +(-14.2980 + 8.28777i) q^{91} +(-2.24725 + 1.63273i) q^{92} +(-6.73116 - 7.47572i) q^{93} +(8.89966 - 1.89168i) q^{94} +(-2.55430 + 5.73704i) q^{95} +(0.913545 - 0.406737i) q^{96} +(12.7032 - 4.12751i) q^{97} +(1.47895 + 6.84198i) q^{98} +(1.45224 - 2.98178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	$ 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$2$	0.207912	−	0.978148i	0.147016	−	0.691655i
$3$	0.994522	+	0.104528i	0.574187	+	0.0603495i
$3$	0.994522	+	0.104528i	0.574187	+	0.0603495i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	−1.26898	+	1.14260i	−0.567506	+	0.510984i	−0.902186	−	0.431347i	$-0.858038\pi$
$5$	−1.26898	+	1.14260i	−0.567506	+	0.510984i	0.334680	+	0.942332i	$0.391372\pi$
$6$	0.309017	−	0.951057i	0.126156	−	0.388267i
$7$	−0.554537	−	2.58698i	−0.209595	−	0.977788i
$7$	−0.554537	−	2.58698i	−0.209595	−	0.977788i
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.978148	+	0.207912i	0.326049	+	0.0693039i
$10$	0.853791	+	1.47881i	0.269993	+	0.467641i
$11$	0.800558	−	3.21856i	0.241377	−	0.970431i
$11$	0.800558	−	3.21856i	0.241377	−	0.970431i
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	−1.93023	−	5.94064i	−0.535349	−	1.64764i	−0.742893	−	0.669410i	$-0.766547\pi$
$13$	−1.93023	−	5.94064i	−0.535349	−	1.64764i	0.207543	−	0.978226i	$-0.433453\pi$
$14$	−2.64575	+	0.00455429i	−0.707106	+	0.00121718i
$15$	−1.38146	+	1.00369i	−0.356692	+	0.259152i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	3.19637	−	0.679409i	0.775233	−	0.164781i	0.196726	−	0.980458i	$-0.436969\pi$
$17$	3.19637	−	0.679409i	0.775233	−	0.164781i	0.578507	+	0.815678i	$0.303636\pi$
$18$	0.406737	−	0.913545i	0.0958687	−	0.215325i
$19$	3.35975	−	1.49585i	0.770778	−	0.343173i	0.0166172	−	0.999862i	$-0.494710\pi$
$19$	3.35975	−	1.49585i	0.770778	−	0.343173i	0.754161	+	0.656689i	$0.228044\pi$
$20$	1.62401	−	0.527672i	0.363139	−	0.117991i
$21$	−0.281085	−	2.63078i	−0.0613378	−	0.574083i
$22$	−2.98178	−	1.45224i	−0.635717	−	0.309619i
$23$	1.38888	−	2.40561i	0.289601	−	0.501604i	−0.684113	−	0.729376i	$-0.739811\pi$
$23$	1.38888	−	2.40561i	0.289601	−	0.501604i	0.973715	+	0.227772i	$0.0731439\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	−0.217854	+	2.07274i	−0.0435708	+	0.414549i
$26$	−6.21214	+	0.652922i	−1.21830	+	0.128049i
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	−0.545627	+	2.58888i	−0.103114	+	0.489252i
$29$	1.95231	+	2.68712i	0.362535	+	0.498986i	0.950853	−	0.309644i	$-0.100210\pi$
$29$	1.95231	+	2.68712i	0.362535	+	0.498986i	−0.588318	+	0.808630i	$0.700210\pi$
$30$	0.694537	+	1.55995i	0.126804	+	0.284807i
$31$	−7.47572	−	6.73116i	−1.34268	−	1.20895i	−0.958296	−	0.285779i	$-0.907748\pi$
$31$	−7.47572	−	6.73116i	−1.34268	−	1.20895i	−0.384382	−	0.923174i	$-0.625586\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.13260	−	3.11724i	0.197161	−	0.542643i
$34$		−	3.26778i		−	0.560419i
$35$	3.65957	+	2.64922i	0.618581	+	0.447801i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	0.400705	+	3.81245i	0.0658754	+	0.626763i	0.976795	+	0.214178i	$0.0687073\pi$
$37$	0.400705	+	3.81245i	0.0658754	+	0.626763i	−0.910919	+	0.412585i	$0.864626\pi$
$38$	−0.764637	−	3.59733i	−0.124040	−	0.583564i
$39$	−1.29869	−	6.10986i	−0.207957	−	0.978360i
$40$	−0.178491	−	1.69823i	−0.0282219	−	0.268514i
$41$	4.85606	+	3.52813i	0.758389	+	0.551002i	0.898416	−	0.439146i	$-0.144719\pi$
$41$	4.85606	+	3.52813i	0.758389	+	0.551002i	−0.140027	+	0.990148i	$0.544719\pi$
$42$	−2.63173	−	0.272027i	−0.406085	−	0.0419746i
$43$			7.25172i			1.10588i	0.833222	+	0.552939i	$0.186494\pi$
$43$			7.25172i			1.10588i	−0.833222	+	0.552939i	$0.813506\pi$
$44$	−2.04045	+	2.61468i	−0.307610	+	0.394178i
$45$	−1.47881	+	0.853791i	−0.220448	+	0.127276i
$46$	−2.06428	−	1.85868i	−0.304361	−	0.274048i
$47$	3.70069	+	8.31188i	0.539800	+	1.21241i	0.953333	+	0.301922i	$0.0976283\pi$
$47$	3.70069	+	8.31188i	0.539800	+	1.21241i	−0.413532	+	0.910490i	$0.635705\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	−6.38498	+	2.86916i	−0.912140	+	0.409879i
$50$	1.98215	+	0.644041i	0.280319	+	0.0910812i
$51$	3.24987	−	0.341576i	0.455073	−	0.0478302i
$52$	−0.652922	+	6.21214i	−0.0905440	+	0.861468i
$53$	−6.59303	+	7.32230i	−0.905622	+	1.00580i	0.0943254	+	0.995541i	$0.469931\pi$
$53$	−6.59303	+	7.32230i	−0.905622	+	1.00580i	−0.999947	+	0.0102538i	$0.996736\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	2.66162	+	4.99900i	0.358892	+	0.674065i
$56$	2.41886	+	1.07196i	0.323234	+	0.143247i
$57$	3.49770	−	1.13647i	0.463282	−	0.150529i
$58$	3.03431	−	1.35096i	0.398424	−	0.177390i
$59$	3.78468	−	8.50054i	0.492724	−	1.10668i	−0.480537	−	0.876974i	$-0.659558\pi$
$59$	3.78468	−	8.50054i	0.492724	−	1.10668i	0.973261	−	0.229701i	$-0.0737750\pi$
$60$	1.67027	−	0.355026i	0.215631	−	0.0458337i
$61$	−3.45078	−	3.83248i	−0.441828	−	0.490699i	0.480562	−	0.876961i	$-0.340433\pi$
$61$	−3.45078	−	3.83248i	−0.441828	−	0.490699i	−0.922389	+	0.386262i	$0.873766\pi$
$62$	−8.13836	+	5.91287i	−1.03357	+	0.750935i
$63$	−0.00455429	−	2.64575i	−0.000573786	−	0.333333i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	9.23717	+	5.33308i	1.14573	+	0.661488i
$66$	−2.81364	−	1.75596i	−0.346336	−	0.216144i
$67$	0.0683384	+	0.118366i	0.00834887	+	0.0144607i	0.870170	−	0.492752i	$-0.164009\pi$
$67$	0.0683384	+	0.118366i	0.00834887	+	0.0144607i	−0.861821	+	0.507213i	$0.830676\pi$
$68$	−3.19637	−	0.679409i	−0.387616	−	0.0823904i
$69$	1.63273	−	2.24725i	0.196557	−	0.270538i
$70$	3.35220	−	3.02880i	0.400665	−	0.362011i
$71$	−0.441852	+	1.35988i	−0.0524382	+	0.161388i	−0.973846	−	0.227209i	$-0.927040\pi$
$71$	−0.441852	+	1.35988i	−0.0524382	+	0.161388i	0.921408	+	0.388597i	$0.127040\pi$
$72$	−0.743145	+	0.669131i	−0.0875805	+	0.0788578i
$73$	−11.4831	−	5.11261i	−1.34400	−	0.598386i	−0.396465	−	0.918050i	$-0.629763\pi$
$73$	−11.4831	−	5.11261i	−1.34400	−	0.598386i	−0.947531	+	0.319664i	$0.896430\pi$
$74$	3.81245	+	0.400705i	0.443188	+	0.0465810i
$75$	−0.433321	+	2.03862i	−0.0500356	+	0.235399i
$76$	−3.67770			−0.421861
$77$	−8.77030	−	0.286224i	−0.999468	−	0.0326183i
$78$	−6.24635			−0.707260
$79$	0.596378	−	2.80574i	0.0670978	−	0.315670i	−0.931780	−	0.363022i	$-0.881745\pi$
$79$	0.596378	−	2.80574i	0.0670978	−	0.315670i	0.998878	+	0.0473519i	$0.0150782\pi$
$80$	−1.69823	−	0.178491i	−0.189868	−	0.0199559i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	4.46067	−	4.01640i	0.492598	−	0.443537i
$83$	0.642506	−	1.97743i	0.0705242	−	0.217051i	−0.909582	−	0.415524i	$-0.863598\pi$
$83$	0.642506	−	1.97743i	0.0705242	−	0.217051i	0.980106	+	0.198473i	$0.0635982\pi$
$84$	−0.813250	+	2.51766i	−0.0887328	+	0.274700i
$85$	−3.27984	+	4.51431i	−0.355749	+	0.489646i
$86$	7.09325	+	1.50772i	0.764885	+	0.162581i
$87$	1.66073	+	2.87647i	0.178049	+	0.308390i
$88$	2.13331	+	2.53949i	0.227412	+	0.270710i
$89$	8.14120	+	4.70032i	0.862965	+	0.498233i	0.865004	−	0.501765i	$-0.167316\pi$
$89$	8.14120	+	4.70032i	0.862965	+	0.498233i	−0.00203901	+	0.999998i	$0.500649\pi$
$90$	0.527672	+	1.62401i	0.0556215	+	0.171185i
$91$	−14.2980	+	8.28777i	−1.49883	+	0.868795i
$92$	−2.24725	+	1.63273i	−0.234292	+	0.170223i
$93$	−6.73116	−	7.47572i	−0.697989	−	0.775196i
$94$	8.89966	−	1.89168i	0.917930	−	0.195112i
$95$	−2.55430	+	5.73704i	−0.262065	+	0.588608i
$96$	0.913545	−	0.406737i	0.0932383	−	0.0415124i
$97$	12.7032	−	4.12751i	1.28981	−	0.419085i	0.417785	−	0.908546i	$-0.362806\pi$
$97$	12.7032	−	4.12751i	1.28981	−	0.419085i	0.872025	+	0.489461i	$0.162806\pi$
$98$	1.47895	+	6.84198i	0.149396	+	0.691145i
$99$	1.45224	−	2.98178i	0.145956	−	0.299680i
$100$	1.04208	−	1.80494i	0.104208	−	0.180494i
$101$	1.65845	−	1.84190i	0.165022	−	0.183276i	−0.654962	−	0.755662i	$-0.727315\pi$
$101$	1.65845	−	1.84190i	0.165022	−	0.183276i	0.819984	+	0.572386i	$0.193982\pi$
$102$	0.341576	−	3.24987i	0.0338210	−	0.321786i
$103$	14.8054	−	1.55611i	1.45882	−	0.153328i	0.658355	−	0.752707i	$-0.271252\pi$
$103$	14.8054	−	1.55611i	1.45882	−	0.153328i	0.800465	+	0.599379i	$0.204586\pi$
$104$	5.94064	+	1.93023i	0.582527	+	0.189275i
$105$	3.36261	+	3.01724i	0.328157	+	0.294453i
$106$	5.79152	+	7.97135i	0.562522	+	0.774246i
$107$	4.98731	+	11.2017i	0.482142	+	1.08291i	0.976865	+	0.213858i	$0.0686028\pi$
$107$	4.98731	+	11.2017i	0.482142	+	1.08291i	−0.494723	+	0.869051i	$0.664730\pi$
$108$	−0.743145	−	0.669131i	−0.0715091	−	0.0643871i
$109$	12.2653	−	7.08136i	1.17480	−	0.678272i	0.219995	−	0.975501i	$-0.429396\pi$
$109$	12.2653	−	7.08136i	1.17480	−	0.678272i	0.954806	+	0.297229i	$0.0960626\pi$
$110$	5.44314	−	1.56410i	0.518983	−	0.149131i
$111$			3.83345i			0.363855i
$112$	1.55145	−	2.14313i	0.146598	−	0.202507i
$113$	3.78950	+	2.75323i	0.356486	+	0.259002i	0.751585	−	0.659636i	$-0.229290\pi$
$113$	3.78950	+	2.75323i	0.356486	+	0.259002i	−0.395099	+	0.918639i	$0.629290\pi$
$114$	−0.384424	−	3.65755i	−0.0360046	−	0.342561i
$115$	0.986178	+	4.63960i	0.0919615	+	0.432645i
$116$	−0.690571	−	3.24888i	−0.0641179	−	0.301651i
$117$	−0.652922	−	6.21214i	−0.0603626	−	0.574312i
$118$	−7.52790	−	5.46934i	−0.692999	−	0.503494i
$119$	−3.53012	−	7.89220i	−0.323606	−	0.723476i
$120$		−	1.70758i		−	0.155880i
$121$	−9.71821	−	5.15328i	−0.883474	−	0.468480i
$122$	−4.46619	+	2.57856i	−0.404350	+	0.233452i
$123$	4.46067	+	4.01640i	0.402205	+	0.362147i
$124$	4.09159	+	9.18987i	0.367436	+	0.825275i
$125$	−7.11032	−	9.78651i	−0.635966	−	0.875332i
$126$	−2.58888	−	0.545627i	−0.230636	−	0.0486083i
$127$	14.7535	+	4.79372i	1.30917	+	0.425374i	0.878761	−	0.477262i	$-0.158371\pi$
$127$	14.7535	+	4.79372i	1.30917	+	0.425374i	0.430405	+	0.902636i	$0.358371\pi$
$128$	−0.994522	+	0.104528i	−0.0879041	+	0.00923910i
$129$	−0.758011	+	7.21200i	−0.0667392	+	0.634981i
$130$	7.13706	−	7.92651i	0.625962	−	0.695201i
$131$	−9.26186	+	16.0420i	−0.809212	+	1.40160i	0.104198	+	0.994557i	$0.466772\pi$
$131$	−9.26186	+	16.0420i	−0.809212	+	1.40160i	−0.913410	+	0.407040i	$0.866561\pi$
$132$	−2.30258	+	2.38707i	−0.200414	+	0.207768i
$133$	−5.73286	−	7.86210i	−0.497102	−	0.681731i
$134$	0.129987	−	0.0422355i	0.0112292	−	0.00364859i
$135$	−1.55995	+	0.694537i	−0.134260	+	0.0597762i
$136$	−1.32912	+	2.98526i	−0.113971	+	0.255984i
$137$	−4.14848	+	0.881788i	−0.354429	+	0.0753362i	−0.381685	−	0.924292i	$-0.624656\pi$
$137$	−4.14848	+	0.881788i	−0.354429	+	0.0753362i	0.0272565	+	0.999628i	$0.491323\pi$
$138$	−1.85868	−	2.06428i	−0.158222	−	0.175723i
$139$	3.54679	−	2.57689i	0.300835	−	0.218569i	−0.427119	−	0.904195i	$-0.640472\pi$
$139$	3.54679	−	2.57689i	0.300835	−	0.218569i	0.727954	+	0.685626i	$0.240472\pi$
$140$	−2.26565	−	3.90867i	−0.191482	−	0.330343i
$141$	2.81159	+	8.65317i	0.236778	+	0.728728i
$142$	1.23830	+	0.714931i	0.103916	+	0.0599957i
$143$	−20.6655	+	1.45673i	−1.72814	+	0.121818i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−5.54774	−	1.17921i	−0.460715	−	0.0979279i
$146$	−7.38836	+	10.1692i	−0.611465	+	0.841609i
$147$	−6.64991	+	2.18603i	−0.548475	+	0.180300i
$148$	1.18460	−	3.64583i	0.0973736	−	0.299685i
$149$	6.98608	−	6.29030i	0.572322	−	0.515321i	−0.331372	−	0.943500i	$-0.607511\pi$
$149$	6.98608	−	6.29030i	0.572322	−	0.515321i	0.903694	+	0.428179i	$0.140845\pi$
$150$	1.90398	+	0.847705i	0.155459	+	0.0692148i
$151$	14.4324	+	1.51691i	1.17449	+	0.123444i	0.671606	−	0.740909i	$-0.265605\pi$
$151$	14.4324	+	1.51691i	1.17449	+	0.123444i	0.502886	+	0.864353i	$0.332272\pi$
$152$	−0.764637	+	3.59733i	−0.0620202	+	0.291782i
$153$	3.26778			0.264184
$154$	−2.10342	+	8.51913i	−0.169498	+	0.686491i
$155$	17.1775			1.37973
$156$	−1.29869	+	6.10986i	−0.103978	+	0.489180i
$157$	−10.6807	−	1.12259i	−0.852416	−	0.0895925i	−0.331765	−	0.943362i	$-0.607644\pi$
$157$	−10.6807	−	1.12259i	−0.852416	−	0.0895925i	−0.520651	+	0.853770i	$0.674311\pi$
$158$	−2.62043	−	1.16669i	−0.208470	−	0.0928170i
$159$	−7.32230	+	6.59303i	−0.580696	+	0.522861i
$160$	−0.527672	+	1.62401i	−0.0417161	+	0.128389i
$161$	−6.99346	−	2.25901i	−0.551162	−	0.178035i
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	16.9747	+	3.60808i	1.32956	+	0.282607i	0.817295	−	0.576220i	$-0.195473\pi$
$163$	16.9747	+	3.60808i	1.32956	+	0.282607i	0.512266	+	0.858827i	$0.328806\pi$
$164$	−3.00121	−	5.19825i	−0.234355	−	0.405915i
$165$	2.12450	+	5.24983i	0.165392	+	0.408699i
$166$	−1.80063	−	1.03960i	−0.139756	−	0.0806883i
$167$	3.79204	+	11.6707i	0.293437	+	0.903106i	0.983742	+	0.179587i	$0.0574762\pi$
$167$	3.79204	+	11.6707i	0.293437	+	0.903106i	−0.690305	+	0.723518i	$0.742524\pi$
$168$	2.29356	+	1.31893i	0.176952	+	0.101758i
$169$	−21.0482	+	15.2924i	−1.61909	+	1.17634i
$170$	3.73375	+	4.14675i	0.286365	+	0.318041i
$171$	3.59733	−	0.764637i	0.275095	−	0.0584732i
$172$	2.94954	−	6.62478i	0.224900	−	0.505134i
$173$	9.78100	−	4.35478i	0.743635	−	0.331088i	0.000293938	−	1.00000i	$-0.499906\pi$
$173$	9.78100	−	4.35478i	0.743635	−	0.331088i	0.743341	+	0.668912i	$0.233240\pi$
$174$	3.15890	−	1.02639i	0.239476	−	0.0778104i
$175$	5.48296	−	0.585827i	0.414473	−	0.0442843i
$176$	2.92753	−	1.55870i	0.220671	−	0.117492i
$177$	4.65250	−	8.05836i	0.349703	−	0.605704i
$178$	6.29026	−	6.98604i	0.471475	−	0.523626i
$179$	2.27005	−	21.5981i	0.169671	−	1.61432i	−0.496172	−	0.868224i	$-0.665261\pi$
$179$	2.27005	−	21.5981i	0.169671	−	1.61432i	0.665843	−	0.746092i	$-0.268072\pi$
$180$	1.69823	−	0.178491i	0.126578	−	0.0133039i
$181$	−21.3449	−	6.93537i	−1.58655	−	0.515502i	−0.622817	−	0.782367i	$-0.714012\pi$
$181$	−21.3449	−	6.93537i	−1.58655	−	0.515502i	−0.963734	+	0.266865i	$0.914012\pi$
$182$	5.13396	+	15.7086i	0.380554	+	1.16440i
$183$	−3.03128	−	4.17219i	−0.224078	−	0.308417i
$184$	1.12982	+	2.53761i	0.0832912	+	0.187075i
$185$	−4.86458	−	4.38008i	−0.357651	−	0.322030i
$186$	−8.71184	+	5.02978i	−0.638783	+	0.368802i
$187$	0.372162	−	10.8316i	0.0272152	−	0.792085i
$188$		−	9.09848i		−	0.663575i
$189$	0.272027	−	2.63173i	0.0197870	−	0.191430i
$190$	5.08061	+	3.69128i	0.368586	+	0.267793i
$191$	0.583863	+	5.55508i	0.0422468	+	0.401952i	0.995127	+	0.0986040i	$0.0314377\pi$
$191$	0.583863	+	5.55508i	0.0422468	+	0.401952i	−0.952880	+	0.303348i	$0.901896\pi$
$192$	−0.207912	−	0.978148i	−0.0150047	−	0.0705917i
$193$	0.943619	+	4.43938i	0.0679232	+	0.319553i	0.998972	−	0.0453425i	$-0.0144379\pi$
$193$	0.943619	+	4.43938i	0.0679232	+	0.319553i	−0.931048	+	0.364896i	$0.881105\pi$
$194$	−1.39618	−	13.2837i	−0.100240	−	0.953716i
$195$	8.62911	+	6.26942i	0.617944	+	0.448962i
$196$	6.99996	−	0.0240990i	0.499997	−	0.00172136i
$197$			5.69659i			0.405865i	0.979193	+	0.202933i	$0.0650472\pi$
$197$			5.69659i			0.405865i	−0.979193	+	0.202933i	$0.934953\pi$
$198$	−2.61468	−	2.04045i	−0.185817	−	0.145009i
$199$	−5.91633	+	3.41579i	−0.419398	+	0.242139i	−0.694820	−	0.719184i	$-0.744516\pi$
$199$	−5.91633	+	3.41579i	−0.419398	+	0.242139i	0.275422	+	0.961323i	$0.411182\pi$
$200$	−1.54883	−	1.39458i	−0.109519	−	0.0986114i
$201$	0.0555915	+	0.124861i	0.00392112	+	0.00880698i
$202$	−1.45684	−	2.00516i	−0.102503	−	0.141083i
$203$	5.86892	−	6.54070i	0.411917	−	0.459067i
$204$	−3.10784	−	1.00980i	−0.217592	−	0.0707000i
$205$	−10.1935	+	1.07138i	−0.711943	+	0.0748283i
$206$	1.55611	−	14.8054i	0.108419	−	1.03154i
$207$	1.85868	−	2.06428i	0.129187	−	0.143477i
$208$	3.12318	−	5.40950i	0.216553	−	0.375081i
$209$	−2.12482	−	12.0110i	−0.146977	−	0.830822i
$210$	3.65043	−	2.66181i	0.251904	−	0.183682i
$211$	11.5145	−	3.74128i	0.792690	−	0.257561i	0.115441	−	0.993314i	$-0.463172\pi$
$211$	11.5145	−	3.74128i	0.792690	−	0.257561i	0.677249	+	0.735754i	$0.263172\pi$
$212$	9.00128	−	4.00763i	0.618210	−	0.275245i
$213$	−0.581578	+	1.30624i	−0.0398490	+	0.0895024i
$214$	11.9938	−	2.54937i	0.819881	−	0.174271i
$215$	−8.28579	−	9.20230i	−0.565086	−	0.627592i
$216$	−0.809017	+	0.587785i	−0.0550466	+	0.0399937i
$217$	−13.2679	+	23.0722i	−0.900681	+	1.56625i
$218$	−4.37652	−	13.4696i	−0.296416	−	0.912273i
$219$	−10.8858	−	6.28491i	−0.735594	−	0.424695i
$220$	−0.398230	−	5.64939i	−0.0268486	−	0.380882i
$221$	−10.2058	−	17.6770i	−0.686519	−	1.18909i
$222$	3.74968	+	0.797019i	0.251662	+	0.0534924i
$223$	−6.15446	+	8.47089i	−0.412133	+	0.567253i	−0.963737	−	0.266853i	$-0.914016\pi$
$223$	−6.15446	+	8.47089i	−0.412133	+	0.567253i	0.551604	+	0.834106i	$0.314016\pi$
$224$	−1.77374	−	1.96313i	−0.118513	−	0.131167i
$225$	−0.644041	+	1.98215i	−0.0429361	+	0.132144i
$226$	3.48095	−	3.13426i	0.231549	−	0.208488i
$227$	−18.0098	−	8.01847i	−1.19535	−	0.532205i	−0.290065	−	0.957007i	$-0.593677\pi$
$227$	−18.0098	−	8.01847i	−1.19535	−	0.532205i	−0.905286	+	0.424802i	$0.860344\pi$
$228$	−3.65755	−	0.384424i	−0.242227	−	0.0254591i
$229$	0.813985	−	3.82950i	0.0537896	−	0.253060i	−0.943034	−	0.332695i	$-0.892042\pi$
$229$	0.813985	−	3.82950i	0.0537896	−	0.253060i	0.996824	+	0.0796346i	$0.0253754\pi$
$230$	4.74325			0.312761
$231$	−8.69233	−	1.20140i	−0.571913	−	0.0790464i
$232$	−3.32147			−0.218065
$233$	−4.25082	+	19.9985i	−0.278480	+	1.31015i	0.587156	+	0.809474i	$0.300248\pi$
$233$	−4.25082	+	19.9985i	−0.278480	+	1.31015i	−0.865636	+	0.500673i	$0.833086\pi$
$234$	−6.21214	−	0.652922i	−0.406100	−	0.0426828i
$235$	−14.1932	−	6.31923i	−0.925863	−	0.412221i
$236$	−6.91496	+	6.22626i	−0.450126	+	0.405295i
$237$	0.886391	−	2.72803i	0.0575773	−	0.177205i
$238$	−8.45369	+	1.81210i	−0.547971	+	0.117461i
$239$	−6.35735	+	8.75014i	−0.411223	+	0.566000i	−0.963516	−	0.267650i	$-0.913753\pi$
$239$	−6.35735	+	8.75014i	−0.411223	+	0.566000i	0.552293	+	0.833650i	$0.313753\pi$
$240$	−1.67027	−	0.355026i	−0.107815	−	0.0229169i
$241$	0.379855	+	0.657928i	0.0244686	+	0.0423809i	0.878000	−	0.478660i	$-0.158877\pi$
$241$	0.379855	+	0.657928i	0.0244686	+	0.0423809i	−0.853532	+	0.521041i	$0.825544\pi$
$242$	−7.06120	+	8.43442i	−0.453911	+	0.542185i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	1.59364	+	4.90471i	0.102022	+	0.313992i
$245$	4.82413	−	10.9364i	0.308203	−	0.698698i
$246$	4.85606	−	3.52813i	0.309611	−	0.224946i
$247$	−15.3714	−	17.0717i	−0.978059	−	1.08625i
$248$	9.83974	−	2.09150i	0.624824	−	0.132810i
$249$	0.845683	−	1.89944i	0.0535930	−	0.120372i
$250$	−11.0510	+	4.92021i	−0.698925	+	0.311181i
$251$	19.6686	−	6.39073i	1.24147	−	0.403379i	0.386615	−	0.922241i	$-0.373644\pi$
$251$	19.6686	−	6.39073i	1.24147	−	0.403379i	0.854858	+	0.518862i	$0.173644\pi$
$252$	−1.07196	+	2.41886i	−0.0675273	+	0.152374i
$253$	−6.63071	−	6.39602i	−0.416869	−	0.402114i
$254$	7.75640	−	13.4345i	0.486680	−	0.842954i
$255$	−3.73375	+	4.14675i	−0.233816	+	0.259679i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−13.8756	+	1.45838i	−0.865535	+	0.0909714i	−0.526880	−	0.849939i	$-0.676638\pi$
$257$	−13.8756	+	1.45838i	−0.865535	+	0.0909714i	−0.338655	+	0.940911i	$0.609972\pi$
$258$	6.89680	+	2.24090i	0.429376	+	0.139513i
$259$	9.64054	−	3.15076i	0.599034	−	0.195779i
$260$	−6.26942	−	8.62911i	−0.388813	−	0.535155i
$261$	1.35096	+	3.03431i	0.0836224	+	0.187819i
$262$	13.7658	+	12.3948i	0.850454	+	0.765752i
$263$	13.4844	−	7.78524i	0.831486	−	0.480058i	−0.0228755	−	0.999738i	$-0.507282\pi$
$263$	13.4844	−	7.78524i	0.831486	−	0.480058i	0.854361	+	0.519680i	$0.173949\pi$
$264$	1.85618	+	2.74857i	0.114240	+	0.169163i
$265$		−	16.8250i		−	1.03355i
$266$	−8.88222	+	3.97296i	−0.544604	+	0.243598i
$267$	7.60528	+	5.52556i	0.465436	+	0.338159i
$268$	−0.0142866	−	0.135928i	−0.000872694	−	0.00830313i
$269$	0.163821	+	0.770719i	0.00998836	+	0.0469915i	0.982860	−	0.184356i	$-0.0590199\pi$
$269$	0.163821	+	0.770719i	0.00998836	+	0.0469915i	−0.972871	+	0.231347i	$0.925687\pi$
$270$	0.355026	+	1.67027i	0.0216062	+	0.101649i
$271$	0.437818	+	4.16556i	0.0265955	+	0.253040i	0.999739	+	0.0228407i	$0.00727105\pi$
$271$	0.437818	+	4.16556i	0.0265955	+	0.253040i	−0.973144	+	0.230199i	$0.926062\pi$
$272$	2.64369	+	1.92075i	0.160297	+	0.116463i
$273$	−15.0859	+	6.74783i	−0.913042	+	0.408397i
$274$			4.24116i			0.256218i
$275$	6.49684	+	2.36053i	0.391774	+	0.142345i
$276$	−2.40561	+	1.38888i	−0.144801	+	0.0836007i
$277$	−12.7786	−	11.5059i	−0.767791	−	0.691322i	0.189040	−	0.981969i	$-0.439463\pi$
$277$	−12.7786	−	11.5059i	−0.767791	−	0.691322i	−0.956830	+	0.290648i	$0.906129\pi$
$278$	−1.78316	−	4.00505i	−0.106947	−	0.240207i
$279$	−5.91287	−	8.13836i	−0.353994	−	0.487231i
$280$	−4.29431	+	1.40348i	−0.256634	+	0.0838742i
$281$	−18.5133	−	6.01535i	−1.10441	−	0.358846i	−0.300614	−	0.953746i	$-0.597192\pi$
$281$	−18.5133	−	6.01535i	−1.10441	−	0.358846i	−0.803800	+	0.594900i	$0.797192\pi$
$282$	9.04864	−	0.951050i	0.538839	−	0.0566342i
$283$	0.543437	−	5.17045i	0.0323040	−	0.307352i	−0.966425	−	0.256949i	$-0.917283\pi$
$283$	0.543437	−	5.17045i	0.0323040	−	0.307352i	0.998729	−	0.0504028i	$-0.0160505\pi$
$284$	0.956765	−	1.06260i	0.0567736	−	0.0630534i
$285$	−3.13999	+	5.43862i	−0.185997	+	0.322156i
$286$	−2.87171	+	20.5168i	−0.169808	+	1.21318i
$287$	6.43436	−	14.5190i	0.379808	−	0.857031i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	−5.77511	+	2.57124i	−0.339712	+	0.151250i
$290$	−2.30688	+	5.18133i	−0.135465	+	0.304258i
$291$	13.0650	−	2.77705i	0.765885	−	0.162794i
$292$	8.41086	+	9.34120i	0.492208	+	0.546653i
$293$	−14.9063	+	10.8300i	−0.870834	+	0.632698i	−0.930811	−	0.365502i	$-0.880897\pi$
$293$	−14.9063	+	10.8300i	−0.870834	+	0.632698i	0.0599768	+	0.998200i	$0.480897\pi$
$294$	0.755662	+	6.95909i	0.0440711	+	0.405863i
$295$	4.90999	+	15.1114i	0.285871	+	0.879819i
$296$	−3.31987	−	1.91673i	−0.192963	−	0.111407i
$297$	1.75596	−	2.81364i	0.101891	−	0.163264i
$298$	−4.70035	−	8.14124i	−0.272284	−	0.471610i
$299$	−16.9717	−	3.60745i	−0.981499	−	0.208624i
$300$	1.22504	−	1.68612i	0.0707277	−	0.0973483i
$301$	18.7601	−	4.02134i	1.08131	−	0.231786i
$302$	4.48442	−	13.8016i	0.258049	−	0.794194i
$303$	1.84190	−	1.65845i	0.105814	−	0.0952756i
$304$	3.35975	+	1.49585i	0.192695	+	0.0857932i
$305$	8.75796	+	0.920499i	0.501479	+	0.0527076i
$306$	0.679409	−	3.19637i	0.0388392	−	0.182724i
$307$	16.2660			0.928348			0.464174	−	0.885744i	$-0.346351\pi$
$307$	16.2660			0.928348			0.464174	+	0.885744i	$0.346351\pi$
$308$	7.89565	+	3.82868i	0.449896	+	0.218159i
$309$	14.8870			0.846890
$310$	3.57141	−	16.8022i	0.202843	−	0.954299i
$311$	−21.8550	−	2.29705i	−1.23928	−	0.130254i	−0.537882	−	0.843020i	$-0.680775\pi$
$311$	−21.8550	−	2.29705i	−1.23928	−	0.130254i	−0.701401	+	0.712767i	$0.747442\pi$
$312$	5.70633	+	2.54062i	0.323057	+	0.143834i
$313$	−8.00739	+	7.20989i	−0.452604	+	0.407527i	−0.863653	−	0.504087i	$-0.831829\pi$
$313$	−8.00739	+	7.20989i	−0.452604	+	0.407527i	0.411049	+	0.911613i	$0.365163\pi$
$314$	−3.31871	+	10.2139i	−0.187286	+	0.576406i
$315$	3.02880	+	3.35220i	0.170654	+	0.188875i
$316$	−1.68602	+	2.32060i	−0.0948458	+	0.130544i
$317$	−23.0169	−	4.89238i	−1.29276	−	0.274784i	−0.490330	−	0.871537i	$-0.663124\pi$
$317$	−23.0169	−	4.89238i	−1.29276	−	0.274784i	−0.802425	+	0.596753i	$0.796457\pi$
$318$	4.92656	+	8.53306i	0.276268	+	0.478510i
$319$	10.2116	−	4.13242i	0.571739	−	0.231371i
$320$	1.47881	+	0.853791i	0.0826680	+	0.0477284i
$321$	3.78910	+	11.6616i	0.211487	+	0.650889i
$322$	−3.66367	+	6.37096i	−0.204168	+	0.355040i
$323$	9.72268	−	7.06394i	0.540985	−	0.393048i
$324$	−0.669131	−	0.743145i	−0.0371739	−	0.0412858i
$325$	12.7339	−	2.70668i	0.706351	−	0.150140i
$326$	7.05848	−	15.8536i	0.390933	−	0.878049i
$327$	12.9383	−	5.76050i	0.715489	−	0.318556i
$328$	−5.70864	+	1.85485i	−0.315207	+	0.102417i
$329$	19.4505	−	14.1829i	1.07234	−	0.781926i
$330$	5.57682	−	0.986571i	0.306994	−	0.0543089i
$331$	−16.6861	+	28.9012i	−0.917151	+	1.58855i	−0.113431	+	0.993546i	$0.536184\pi$
$331$	−16.6861	+	28.9012i	−0.917151	+	1.58855i	−0.803721	+	0.595007i	$0.797149\pi$
$332$	−1.39125	+	1.54514i	−0.0763548	+	0.0848006i
$333$	−0.400705	+	3.81245i	−0.0219585	+	0.208921i
$334$	12.2041	−	1.28270i	0.667777	−	0.0701862i
$335$	−0.221964	−	0.0721206i	−0.0121272	−	0.00394037i
$336$	1.76697	−	1.96922i	0.0963959	−	0.107430i
$337$	13.2363	+	18.2182i	0.721027	+	0.992409i	0.999489	+	0.0319613i	$0.0101753\pi$
$337$	13.2363	+	18.2182i	0.721027	+	0.992409i	−0.278462	+	0.960447i	$0.589825\pi$
$338$	10.5820	+	23.7677i	0.575587	+	1.29279i
$339$	3.48095	+	3.13426i	0.189059	+	0.170230i
$340$	4.83242	−	2.79000i	0.262075	−	0.151309i
$341$	−27.6494	+	18.6723i	−1.49730	+	1.01116i
$342$		−	3.67770i		−	0.198867i
$343$	10.9632	+	14.9268i	0.591955	+	0.805971i
$344$	−5.86677	−	4.26245i	−0.316315	−	0.229816i
$345$	0.495805	+	4.71727i	0.0266932	+	0.253969i
$346$	−2.22603	−	10.4727i	−0.119672	−	0.563014i
$347$	−2.37533	−	11.1751i	−0.127514	−	0.599908i	−0.994778	−	0.102059i	$-0.967457\pi$
$347$	−2.37533	−	11.1751i	−0.127514	−	0.599908i	0.867264	−	0.497849i	$-0.165877\pi$
$348$	−0.347188	−	3.30327i	−0.0186112	−	0.177074i
$349$	1.89879	+	1.37955i	0.101640	+	0.0738457i	0.637444	−	0.770496i	$-0.279992\pi$
$349$	1.89879	+	1.37955i	0.101640	+	0.0738457i	−0.535804	+	0.844342i	$0.679992\pi$
$350$	0.566947	−	5.48495i	0.0303046	−	0.293183i
$351$		−	6.24635i		−	0.333406i
$352$	−0.915975	−	3.18763i	−0.0488216	−	0.169901i
$353$	29.4010	−	16.9747i	1.56486	−	0.903470i	0.568102	−	0.822958i	$-0.307678\pi$
$353$	29.4010	−	16.9747i	1.56486	−	0.903470i	0.996754	−	0.0805114i	$-0.0256554\pi$
$354$	−6.91496	−	6.22626i	−0.367526	−	0.330922i
$355$	−0.993092	−	2.23052i	−0.0527079	−	0.118384i
$356$	−5.52556	−	7.60528i	−0.292854	−	0.403079i
$357$	−2.68583	−	8.21796i	−0.142149	−	0.434941i
$358$	−20.6541	−	6.71094i	−1.09160	−	0.354684i
$359$	30.3144	−	3.18617i	1.59993	−	0.168160i	0.737863	−	0.674951i	$-0.235835\pi$
$359$	30.3144	−	3.18617i	1.59993	−	0.168160i	0.862069	+	0.506791i	$0.169169\pi$
$360$	0.178491	−	1.69823i	0.00940730	−	0.0895045i
$361$	−3.66318	+	4.06837i	−0.192799	+	0.214125i
$362$	−11.2217	+	19.4365i	−0.589797	+	1.02156i
$363$	−9.12631	−	6.14088i	−0.479007	−	0.322313i
$364$	16.4328	−	1.75576i	0.861311	−	0.0920267i
$365$	20.4135	−	6.63275i	1.06849	−	0.347174i
$366$	−4.71126	+	2.09759i	−0.246261	+	0.109643i
$367$	−2.31366	+	5.19656i	−0.120772	+	0.271258i	−0.963807	−	0.266600i	$-0.914100\pi$
$367$	−2.31366	+	5.19656i	−0.120772	+	0.271258i	0.843035	+	0.537858i	$0.180766\pi$
$368$	2.71706	−	0.577528i	0.141636	−	0.0301058i
$369$	4.01640	+	4.46067i	0.209085	+	0.232213i
$370$	−5.29577	+	3.84760i	−0.275314	+	0.200027i
$371$	22.5988	+	12.9956i	1.17327	+	0.674697i
$372$	3.10858	+	9.56722i	0.161172	+	0.496037i
$373$	−21.8641	−	12.6232i	−1.13208	−	0.653605i	−0.187621	−	0.982241i	$-0.560078\pi$
$373$	−21.8641	−	12.6232i	−1.13208	−	0.653605i	−0.944457	+	0.328636i	$0.893411\pi$
$374$	−10.5175	−	2.61604i	−0.543848	−	0.135272i
$375$	−6.04840	−	10.4761i	−0.312338	−	0.540985i
$376$	−8.89966	−	1.89168i	−0.458965	−	0.0975560i
$377$	12.1948	−	16.7847i	0.628065	−	0.864457i
$378$	−2.51766	−	0.813250i	−0.129495	−	0.0418290i
$379$	0.636487	−	1.95890i	0.0326941	−	0.100622i	−0.933378	−	0.358895i	$-0.883153\pi$
$379$	0.636487	−	1.95890i	0.0326941	−	0.100622i	0.966072	+	0.258273i	$0.0831535\pi$
$380$	4.66693	−	4.20212i	0.239409	−	0.215564i
$381$	14.1716	+	6.30962i	0.726035	+	0.323252i
$382$	5.55508	+	0.583863i	0.284223	+	0.0298730i
$383$	−4.80091	+	22.5865i	−0.245315	+	1.15412i	0.667138	+	0.744934i	$0.267519\pi$
$383$	−4.80091	+	22.5865i	−0.245315	+	1.15412i	−0.912453	+	0.409182i	$0.865814\pi$
$384$	−1.00000			−0.0510310
$385$	11.4564	−	9.65769i	0.583871	−	0.492201i
$386$	4.53856			0.231006
$387$	−1.50772	+	7.09325i	−0.0766416	+	0.360570i
$388$	−13.2837	−	1.39618i	−0.674379	−	0.0708801i
$389$	32.7032	+	14.5604i	1.65812	+	0.738242i	0.999894	−	0.0145801i	$-0.00464115\pi$
$389$	32.7032	+	14.5604i	1.65812	+	0.738242i	0.658224	+	0.752822i	$0.271308\pi$
$390$	7.92651	−	7.13706i	0.401374	−	0.361399i
$391$	2.80498	−	8.63283i	0.141854	−	0.436581i
$392$	1.43180	−	6.85200i	0.0723169	−	0.346078i
$393$	−10.8880	+	14.9860i	−0.549225	+	0.755944i
$394$	5.57210	+	1.18439i	0.280719	+	0.0596686i
$395$	2.44903	+	4.24185i	0.123224	+	0.213431i
$396$	−2.53949	+	2.13331i	−0.127614	+	0.107203i
$397$	25.0717	+	14.4751i	1.25831	+	0.726486i	0.972746	−	0.231874i	$-0.0744857\pi$
$397$	25.0717	+	14.4751i	1.25831	+	0.726486i	0.285564	+	0.958360i	$0.407819\pi$
$398$	2.11108	+	6.49723i	0.105819	+	0.325677i
$399$	−4.87964	−	8.41828i	−0.244287	−	0.421441i
$400$	−1.68612	+	1.22504i	−0.0843061	+	0.0612519i
$401$	2.27202	+	2.52333i	0.113459	+	0.126009i	0.797199	−	0.603717i	$-0.206314\pi$
$401$	2.27202	+	2.52333i	0.113459	+	0.126009i	−0.683740	+	0.729726i	$0.739648\pi$
$402$	0.133690	−	0.0284167i	0.00666786	−	0.00141730i
$403$	−25.5576	+	57.4032i	−1.27311	+	2.85946i
$404$	−2.26424	+	1.00810i	−0.112650	+	0.0501550i
$405$	−1.62401	+	0.527672i	−0.0806976	+	0.0262202i
$406$	−5.17755	−	7.10055i	−0.256958	−	0.352395i
$407$	12.5914	+	1.76240i	0.624131	+	0.0873588i
$408$	−1.63389	+	2.82998i	−0.0808895	+	0.140105i
$409$	5.56808	−	6.18398i	0.275324	−	0.305778i	−0.589586	−	0.807706i	$-0.700709\pi$
$409$	5.56808	−	6.18398i	0.275324	−	0.305778i	0.864910	+	0.501928i	$0.167376\pi$
$410$	−1.07138	+	10.1935i	−0.0529116	+	0.503420i
$411$	−4.21793	+	0.443322i	−0.208055	+	0.0218675i
$412$	−14.1583	−	4.60033i	−0.697532	−	0.226642i
$413$	−24.0895	−	5.07706i	−1.18537	−	0.249826i
$414$	−1.63273	−	2.24725i	−0.0802441	−	0.110446i
$415$	1.44407	+	3.24344i	0.0708868	+	0.159214i
$416$	−4.64195	−	4.17963i	−0.227590	−	0.204923i
$417$	3.79672	−	2.19204i	0.185926	−	0.107344i
$418$	−12.1904	−	0.418848i	−0.596250	−	0.0204865i
$419$		−	8.04446i		−	0.392997i	−0.980504	−	0.196499i	$-0.937043\pi$
$419$		−	8.04446i		−	0.392997i	0.980504	−	0.196499i	$-0.0629571\pi$
$420$	−1.84467	−	4.12408i	−0.0900108	−	0.201235i
$421$	−18.8724	−	13.7116i	−0.919783	−	0.668261i	0.0236873	−	0.999719i	$-0.492459\pi$
$421$	−18.8724	−	13.7116i	−0.919783	−	0.668261i	−0.943470	+	0.331458i	$0.892459\pi$
$422$	−1.26553	−	12.0407i	−0.0616051	−	0.586133i
$423$	1.89168	+	8.89966i	0.0919767	+	0.432716i
$424$	−2.04858	−	9.63781i	−0.0994878	−	0.468054i
$425$	0.711898	+	6.77326i	0.0345321	+	0.328551i
$426$	1.15678	+	0.840452i	0.0560463	+	0.0407201i
$427$	−8.00099	+	11.0524i	−0.387195	+	0.534862i
$428$		−	12.2618i		−	0.592695i
$429$	−20.7046	−	0.711388i	−0.999627	−	0.0343461i
$430$	−10.7239	+	6.19146i	−0.517153	+	0.298579i
$431$	6.14118	+	5.52954i	0.295810	+	0.266349i	0.803649	−	0.595103i	$-0.202889\pi$
$431$	6.14118	+	5.52954i	0.295810	+	0.266349i	−0.507839	+	0.861452i	$0.669556\pi$
$432$	0.406737	+	0.913545i	0.0195691	+	0.0439530i
$433$	17.3403	+	23.8669i	0.833322	+	1.14697i	0.987296	+	0.158894i	$0.0507929\pi$
$433$	17.3403	+	23.8669i	0.833322	+	1.14697i	−0.153974	+	0.988075i	$0.549207\pi$
$434$	19.8095	+	17.7749i	0.950887	+	0.853223i
$435$	−5.39409	−	1.75264i	−0.258627	−	0.0840329i
$436$	−14.0851	+	1.48041i	−0.674556	+	0.0708987i
$437$	1.06784	−	10.1598i	0.0510816	−	0.486009i
$438$	−8.41086	+	9.34120i	−0.401886	+	0.446340i
$439$	9.27315	−	16.0616i	0.442584	−	0.766577i	−0.555297	−	0.831652i	$-0.687395\pi$
$439$	9.27315	−	16.0616i	0.442584	−	0.766577i	0.997880	+	0.0650750i	$0.0207287\pi$
$440$	−5.60874	−	0.785047i	−0.267386	−	0.0374257i
$441$	−6.84198	+	1.47895i	−0.325809	+	0.0704260i
$442$	−19.4127	+	6.30756i	−0.923366	+	0.300020i
$443$	−32.7630	+	14.5870i	−1.55662	+	0.693051i	−0.991276	−	0.131806i	$-0.957922\pi$
$443$	−32.7630	+	14.5870i	−1.55662	+	0.693051i	−0.565342	+	0.824857i	$0.691256\pi$
$444$	1.55920	−	3.50203i	0.0739966	−	0.166199i
$445$	−15.7016	+	3.33748i	−0.744327	+	0.158212i
$446$	7.00620	+	7.78117i	0.331753	+	0.368449i
$447$	7.60532	−	5.52559i	0.359720	−	0.261352i
$448$	−2.28901	+	1.32682i	−0.108145	+	0.0626862i
$449$	4.18601	+	12.8832i	0.197550	+	0.607997i	0.999937	+	0.0111929i	$0.00356287\pi$
$449$	4.18601	+	12.8832i	0.197550	+	0.607997i	−0.802387	+	0.596804i	$0.796437\pi$
$450$	1.80494	+	1.04208i	0.0850855	+	0.0491241i
$451$	15.2431	−	12.8050i	0.717767	−	0.602965i
$452$	−2.34204	−	4.05653i	−0.110160	−	0.190803i
$453$	14.1948	+	3.01719i	0.666929	+	0.141760i
$454$	−11.5877	+	15.9491i	−0.543837	+	0.748528i
$455$	8.67426	−	26.8538i	0.406655	−	1.25893i
$456$	−1.13647	+	3.49770i	−0.0532202	+	0.163795i
$457$	15.8268	−	14.2506i	0.740349	−	0.666613i	−0.210035	−	0.977694i	$-0.567358\pi$
$457$	15.8268	−	14.2506i	0.740349	−	0.666613i	0.950383	+	0.311081i	$0.100691\pi$
$458$	−3.57658	−	1.59239i	−0.167122	−	0.0744077i
$459$	3.24987	+	0.341576i	0.151691	+	0.0159434i
$460$	0.986178	−	4.63960i	0.0459808	−	0.216323i
$461$	−4.94605			−0.230360			−0.115180	−	0.993345i	$-0.536745\pi$
$461$	−4.94605			−0.230360			−0.115180	+	0.993345i	$0.536745\pi$
$462$	−2.98239	+	8.25260i	−0.138753	+	0.383946i
$463$	15.2357			0.708064			0.354032	−	0.935233i	$-0.384810\pi$
$463$	15.2357			0.708064			0.354032	+	0.935233i	$0.384810\pi$
$464$	−0.690571	+	3.24888i	−0.0320590	+	0.150826i
$465$	17.0834	+	1.79554i	0.792226	+	0.0832663i
$466$	18.6777	+	8.31586i	0.865229	+	0.385225i
$467$	−5.99296	+	5.39609i	−0.277321	+	0.249701i	−0.796040	−	0.605244i	$-0.793076\pi$
$467$	−5.99296	+	5.39609i	−0.277321	+	0.249701i	0.518719	+	0.854945i	$0.326409\pi$
$468$	−1.93023	+	5.94064i	−0.0892249	+	0.274606i
$469$	0.268314	−	0.242429i	0.0123896	−	0.0111943i
$470$	−9.13207	+	12.5692i	−0.421231	+	0.579775i
$471$	−10.5049	−	2.23288i	−0.484040	−	0.102886i
$472$	4.65250	+	8.05836i	0.214149	+	0.370916i
$473$	23.3401	+	5.80542i	1.07318	+	0.266934i
$474$	−2.48413	−	1.43421i	−0.114100	−	0.0658755i
$475$	2.36859	+	7.28977i	0.108678	+	0.334478i
$476$	0.0148824	+	8.64571i	0.000682133	+	0.396275i
$477$	−7.97135	+	5.79152i	−0.364983	+	0.265176i
$478$	7.23716	+	8.03768i	0.331020	+	0.367635i
$479$	0.649600	−	0.138077i	0.0296810	−	0.00630889i	−0.193047	−	0.981189i	$-0.561837\pi$
$479$	0.649600	−	0.138077i	0.0296810	−	0.00630889i	0.222728	+	0.974881i	$0.428504\pi$
$480$	−0.694537	+	1.55995i	−0.0317011	+	0.0712019i
$481$	21.8749	−	9.73935i	0.997411	−	0.444076i
$482$	0.722527	−	0.234763i	0.0329102	−	0.0106932i
$483$	−6.71902	−	2.97765i	−0.305726	−	0.135488i
$484$	6.78200	+	8.66051i	0.308273	+	0.393660i
$485$	−11.4040	+	19.7523i	−0.517829	+	0.896906i
$486$	0.669131	−	0.743145i	0.0303524	−	0.0337097i
$487$	−1.26710	+	12.0557i	−0.0574179	+	0.546295i	0.927567	+	0.373656i	$0.121896\pi$
$487$	−1.26710	+	12.0557i	−0.0574179	+	0.546295i	−0.984985	+	0.172639i	$0.944771\pi$
$488$	5.12886	−	0.539065i	0.232173	−	0.0244023i
$489$	16.5046	+	5.36266i	0.746362	+	0.242508i
$490$	−9.69438	−	6.99251i	−0.437947	−	0.315889i
$491$	−16.1399	−	22.2147i	−0.728384	−	1.00253i	−0.999204	−	0.0399042i	$-0.987295\pi$
$491$	−16.1399	−	22.2147i	−0.728384	−	1.00253i	0.270820	−	0.962630i	$-0.412705\pi$
$492$	−2.44140	−	5.48348i	−0.110067	−	0.247214i
$493$	8.06595	+	7.26261i	0.363272	+	0.327092i
$494$	−19.8945	+	11.4861i	−0.895097	+	0.516784i
$495$	1.56410	+	5.44314i	0.0703012	+	0.244651i
$496$		−	10.0596i		−	0.451688i
$497$	3.76301	+	0.388961i	0.168794	+	0.0174473i
$498$	−1.68210	−	1.22212i	−0.0753768	−	0.0547644i
$499$	−3.74405	−	35.6223i	−0.167607	−	1.59467i	−0.678219	−	0.734860i	$-0.737248\pi$
$499$	−3.74405	−	35.6223i	−0.167607	−	1.59467i	0.510612	−	0.859811i	$-0.329419\pi$
$500$	2.51506	+	11.8324i	0.112477	+	0.529163i
$501$	2.55135	+	12.0031i	0.113986	+	0.536261i
$502$	−2.16174	−	20.5675i	−0.0964830	−	0.917974i
$503$	−24.3021	−	17.6565i	−1.08358	−	0.787266i	−0.105275	−	0.994443i	$-0.533572\pi$
$503$	−24.3021	−	17.6565i	−1.08358	−	0.787266i	−0.978303	+	0.207177i	$0.933572\pi$
$504$	2.14313	+	1.55145i	0.0954627	+	0.0691069i
$505$			4.23227i			0.188334i
$506$	−7.63485	+	5.15601i	−0.339411	+	0.229213i
$507$	−22.5313	+	13.0085i	−1.00065	+	0.577727i
$508$	−11.5283	−	10.3801i	−0.511484	−	0.460542i
$509$	2.91719	+	6.55211i	0.129302	+	0.290417i	0.966582	−	0.256357i	$-0.0825223\pi$
$509$	2.91719	+	6.55211i	0.129302	+	0.290417i	−0.837280	+	0.546774i	$0.815856\pi$
$510$	3.27984	+	4.51431i	0.145234	+	0.199897i
$511$	−6.85844	+	32.5418i	−0.303399	+	1.43956i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	3.65755	−	0.384424i	0.161485	−	0.0169727i
$514$	−1.45838	+	13.8756i	−0.0643265	+	0.612026i
$515$	−17.0098	+	18.8913i	−0.749541	+	0.832449i
$516$	3.62586	−	6.28017i	0.159620	−	0.276469i
$517$	29.7149	−	5.25673i	1.30686	−	0.231191i
$518$	−1.07753	−	10.0850i	−0.0473438	−	0.443108i
$519$	10.1826	−	3.30853i	0.446967	−	0.145228i
$520$	−9.74403	+	4.33832i	−0.427304	+	0.190248i
$521$	1.21766	−	2.73492i	0.0533468	−	0.119819i	−0.884906	−	0.465770i	$-0.845777\pi$
$521$	1.21766	−	2.73492i	0.0533468	−	0.119819i	0.938252	+	0.345952i	$0.112444\pi$
$522$	3.24888	−	0.690571i	0.142200	−	0.0302255i
$523$	6.33820	+	7.03928i	0.277150	+	0.307806i	0.865609	−	0.500721i	$-0.166932\pi$
$523$	6.33820	+	7.03928i	0.277150	+	0.307806i	−0.588459	+	0.808527i	$0.700265\pi$
$524$	14.9860	−	10.8880i	0.654667	−	0.475643i
$525$	5.51416	−	0.00949187i	0.240658	−	0.000414259i
$526$	−4.81154	−	14.8084i	−0.209793	−	0.645677i
$527$	−28.4683	−	16.4362i	−1.24010	−	0.715972i
$528$	3.07442	−	1.24415i	0.133797	−	0.0541449i
$529$	7.64203	+	13.2364i	0.332262	+	0.575495i
$530$	−16.4574	−	3.49812i	−0.714862	−	0.151949i
$531$	5.46934	−	7.52790i	0.237349	−	0.326683i
$532$	2.03942	+	9.51415i	0.0884200	+	0.412491i
$533$	11.5860	−	35.6582i	0.501847	−	1.54453i
$534$	6.98604	−	6.29026i	0.302316	−	0.272206i
$535$	−19.1278	−	8.51625i	−0.826967	−	0.368190i
$536$	−0.135928	−	0.0142866i	−0.00587120	−	0.000617088i
$537$	4.51523	−	21.2425i	0.194846	−	0.916680i
$538$	0.787937			0.0339704
$539$	4.12299	+	22.8473i	0.177590	+	0.984105i
$540$	1.70758			0.0734827
$541$	8.52153	−	40.0906i	0.366369	−	1.72363i	−0.279467	−	0.960155i	$-0.590158\pi$
$541$	8.52153	−	40.0906i	0.366369	−	1.72363i	0.645836	−	0.763476i	$-0.276509\pi$
$542$	4.16556	+	0.437818i	0.178926	+	0.0188059i
$543$	−20.5030	−	9.12852i	−0.879868	−	0.391742i
$544$	2.42843	−	2.18657i	0.104118	−	0.0937484i
$545$	−7.47328	+	23.0004i	−0.320120	+	0.985228i
$546$	3.46383	+	16.1592i	0.148238	+	0.691551i
$547$	11.1955	−	15.4093i	0.478684	−	0.658852i	−0.499567	−	0.866275i	$-0.666508\pi$
$547$	11.1955	−	15.4093i	0.478684	−	0.658852i	0.978251	+	0.207423i	$0.0665076\pi$
$548$	4.14848	+	0.881788i	0.177214	+	0.0376681i
$549$	−2.57856	−	4.46619i	−0.110050	−	0.190612i
$550$	3.65971	−	5.86408i	0.156051	−	0.250045i
$551$	10.5788	+	6.10767i	0.450672	+	0.260196i
$552$	0.858375	+	2.64181i	0.0365348	+	0.112443i
$553$	−7.58912	+	0.0130636i	−0.322722	+	0.000555522i
$554$	−13.9113	+	10.1071i	−0.591033	+	0.429411i
$555$	−4.38008	−	4.86458i	−0.185924	−	0.206490i
$556$	−4.28827	+	0.911499i	−0.181863	+	0.0386562i
$557$	−16.2308	+	36.4550i	−0.687721	+	1.54465i	0.144076	+	0.989567i	$0.453979\pi$
$557$	−16.2308	+	36.4550i	−0.687721	+	1.54465i	−0.831797	+	0.555080i	$0.812688\pi$
$558$	−9.18987	+	4.09159i	−0.389038	+	0.173211i
$559$	43.0798	−	13.9975i	1.82208	−	0.592031i
$560$	0.479976	+	4.49227i	0.0202827	+	0.189833i
$561$	1.50233	−	10.7334i	0.0634286	−	0.453163i
$562$	−9.73304	+	16.8581i	−0.410564	+	0.711117i
$563$	−12.6237	+	14.0200i	−0.532026	+	0.590875i	−0.947908	−	0.318544i	$-0.896806\pi$
$563$	−12.6237	+	14.0200i	−0.532026	+	0.590875i	0.415882	+	0.909418i	$0.363473\pi$
$564$	0.951050	−	9.04864i	0.0400464	−	0.381016i
$565$	−7.95463	+	0.836066i	−0.334654	+	0.0351736i
$566$	−4.94448	−	1.60656i	−0.207832	−	0.0675287i
$567$	0.545627	−	2.58888i	0.0229142	−	0.108723i
$568$	−0.840452	−	1.15678i	−0.0352646	−	0.0485376i
$569$	13.1361	+	29.5041i	0.550692	+	1.23687i	0.947730	+	0.319073i	$0.103371\pi$
$569$	13.1361	+	29.5041i	0.550692	+	1.23687i	−0.397038	+	0.917802i	$0.629962\pi$
$570$	4.66693	+	4.20212i	0.195476	+	0.176008i
$571$	13.4577	−	7.76979i	0.563186	−	0.325155i	−0.191237	−	0.981544i	$-0.561250\pi$
$571$	13.4577	−	7.76979i	0.563186	−	0.325155i	0.754423	+	0.656388i	$0.227917\pi$
$572$	19.4714	+	7.07464i	0.814141	+	0.295806i
$573$			5.58568i			0.233345i
$574$	−12.8640	−	9.31243i	−0.536932	−	0.388693i
$575$	4.68364	+	3.40286i	0.195321	+	0.141909i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−0.846148	−	3.98081i	−0.0352256	−	0.165723i	0.957019	−	0.290026i	$-0.0936640\pi$
$577$	−0.846148	−	3.98081i	−0.0352256	−	0.165723i	−0.992244	+	0.124303i	$0.960331\pi$
$578$	1.31434	+	6.18350i	0.0546695	+	0.257200i
$579$	0.474408	+	4.51369i	0.0197157	+	0.187583i
$580$	4.58848	+	3.33373i	0.190526	+	0.138426i
$581$	−5.47187	−	0.565595i	−0.227011	−	0.0234649i
$582$		−	13.3569i		−	0.553661i
$583$	18.2891	+	27.0820i	0.757458	+	1.12162i
$584$	10.8858	−	6.28491i	0.450457	−	0.260072i
$585$	7.92651	+	7.13706i	0.327721	+	0.295081i
$586$	7.49419	+	16.8322i	0.309582	+	0.695333i
$587$	−12.2998	−	16.9292i	−0.507666	−	0.698743i	0.475857	−	0.879523i	$-0.342138\pi$
$587$	−12.2998	−	16.9292i	−0.507666	−	0.698743i	−0.983524	+	0.180780i	$0.942138\pi$
$588$	6.96413	+	0.707728i	0.287196	+	0.0291862i
$589$	−35.1853	−	11.4324i	−1.44979	−	0.471064i
$590$	15.8020	−	1.66086i	0.650558	−	0.0683765i
$591$	−0.595456	+	5.66538i	−0.0244938	+	0.233043i
$592$	−2.56508	+	2.84881i	−0.105424	+	0.117085i
$593$	11.9429	−	20.6856i	0.490434	−	0.849457i	−0.509505	−	0.860468i	$-0.670172\pi$
$593$	11.9429	−	20.6856i	0.490434	−	0.849457i	0.999939	+	0.0110107i	$0.00350489\pi$
$594$	−2.38707	−	2.30258i	−0.0979428	−	0.0944761i
$595$	13.4973	+	5.98155i	0.553333	+	0.245219i
$596$	−8.94060	+	2.90498i	−0.366221	+	0.118992i
$597$	−6.24097	+	2.77866i	−0.255426	+	0.113723i
$598$	−7.05723	+	15.8508i	−0.288592	+	0.648188i
$599$	−38.5668	+	8.19762i	−1.57580	+	0.334946i	−0.911105	−	0.412174i	$-0.864770\pi$
$599$	−38.5668	+	8.19762i	−1.57580	+	0.334946i	−0.664690	+	0.747119i	$0.731436\pi$
$600$	−1.39458	−	1.54883i	−0.0569333	−	0.0632309i
$601$	12.8714	−	9.35163i	0.525036	−	0.381461i	−0.293462	−	0.955971i	$-0.594807\pi$
$601$	12.8714	−	9.35163i	0.525036	−	0.381461i	0.818498	+	0.574510i	$0.194807\pi$
$602$	−0.0330264	−	19.1862i	−0.00134606	−	0.781972i
$603$	0.0422355	+	0.129987i	0.00171996	+	0.00529350i
$604$	−12.5677	−	7.25595i	−0.511371	−	0.295240i
$605$	18.2204	−	4.56457i	0.740763	−	0.185576i
$606$	−1.23926	−	2.14646i	−0.0503414	−	0.0871939i
$607$	−5.32415	−	1.13168i	−0.216101	−	0.0459336i	0.0985890	−	0.995128i	$-0.468567\pi$
$607$	−5.32415	−	1.13168i	−0.216101	−	0.0459336i	−0.314690	+	0.949195i	$0.601900\pi$
$608$	2.16170	−	2.97532i	0.0876684	−	0.120665i
$609$	6.52045	−	5.89140i	0.264222	−	0.238732i
$610$	2.72127	−	8.37519i	0.110181	−	0.339102i
$611$	42.2347	−	38.0283i	1.70863	−	1.53846i
$612$	−2.98526	−	1.32912i	−0.120672	−	0.0537267i
$613$	−30.9363	−	3.25154i	−1.24951	−	0.131328i	−0.543424	−	0.839458i	$-0.682872\pi$
$613$	−30.9363	−	3.25154i	−1.24951	−	0.131328i	−0.706082	+	0.708130i	$0.749539\pi$
$614$	3.38189	−	15.9105i	0.136482	−	0.642096i
$615$	−10.2496			−0.413305
$616$	5.38661	−	6.92708i	0.217033	−	0.279100i
$617$	−33.4940			−1.34842			−0.674209	−	0.738541i	$-0.735515\pi$
$617$	−33.4940			−1.34842			−0.674209	+	0.738541i	$0.735515\pi$
$618$	3.09517	−	14.5616i	0.124506	−	0.585755i
$619$	37.1791	+	3.90768i	1.49435	+	0.157063i	0.816163	−	0.577822i	$-0.196097\pi$
$619$	37.1791	+	3.90768i	1.49435	+	0.157063i	0.678192	+	0.734885i	$0.262764\pi$
$620$	−15.6925	−	6.98674i	−0.630225	−	0.280594i
$621$	2.06428	−	1.85868i	0.0828366	−	0.0745864i
$622$	−6.79076	+	20.8998i	−0.272285	+	0.838007i
$623$	7.64507	−	23.6676i	0.306293	−	0.948224i
$624$	3.67152	−	5.05341i	0.146978	−	0.202298i
$625$	10.0118	+	2.12807i	0.400472	+	0.0851230i
$626$	5.38750	+	9.33143i	0.215328	+	0.372959i
$627$	−0.857686	−	12.1674i	−0.0342527	−	0.485917i
$628$	9.30074	+	5.36979i	0.371140	+	0.214278i
$629$	3.87101	+	11.9137i	0.154347	+	0.475032i
$630$	3.90867	−	2.26565i	0.155725	−	0.0902657i
$631$	−2.41984	+	1.75812i	−0.0963324	+	0.0699896i	−0.634909	−	0.772587i	$-0.718962\pi$
$631$	−2.41984	+	1.75812i	−0.0963324	+	0.0699896i	0.538576	+	0.842577i	$0.318962\pi$
$632$	1.91935	+	2.13165i	0.0763476	+	0.0847926i
$633$	11.8425	−	2.51720i	0.470696	−	0.100050i
$634$	−9.57094	+	21.4967i	−0.380111	+	0.853743i
$635$	−24.1993	+	10.7742i	−0.960318	+	0.427561i
$636$	9.37088	−	3.04478i	0.371580	−	0.120734i
$637$	29.3691	+	32.3927i	1.16365	+	1.28345i
$638$	−1.91901	−	10.8476i	−0.0759741	−	0.429461i
$639$	−0.714931	+	1.23830i	−0.0282823	+	0.0489863i
$640$	1.14260	−	1.26898i	0.0451651	−	0.0501609i
$641$	1.03851	−	9.88074i	0.0410186	−	0.390266i	−0.954681	−	0.297630i	$-0.903804\pi$
$641$	1.03851	−	9.88074i	0.0410186	−	0.390266i	0.995700	−	0.0926362i	$-0.0295294\pi$
$642$	12.1946	−	1.28170i	0.481283	−	0.0505848i
$643$	−34.1972	−	11.1114i	−1.34861	−	0.438189i	−0.456384	−	0.889783i	$-0.650856\pi$
$643$	−34.1972	−	11.1114i	−1.34861	−	0.438189i	−0.892224	+	0.451594i	$0.850856\pi$
$644$	5.47002	+	4.90820i	0.215549	+	0.193410i
$645$	−7.27849	−	10.0180i	−0.286590	−	0.394458i
$646$	−4.88812	−	10.9789i	−0.192320	−	0.431959i
$647$	13.1079	+	11.8024i	0.515324	+	0.464000i	0.885286	−	0.465047i	$-0.153963\pi$
$647$	13.1079	+	11.8024i	0.515324	+	0.464000i	−0.369962	+	0.929047i	$0.620629\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−24.3296	−	18.9864i	−0.955020	−	0.745281i
$650$		−	13.0184i		−	0.510624i
$651$	−15.6069	+	21.5590i	−0.611682	+	0.844963i
$652$	−14.0396	−	10.2004i	−0.549834	−	0.399478i
$653$	0.997885	+	9.49424i	0.0390503	+	0.371538i	0.996543	+	0.0830806i	$0.0264759\pi$
$653$	0.997885	+	9.49424i	0.0390503	+	0.371538i	−0.957493	+	0.288458i	$0.906857\pi$
$654$	−2.94460	−	13.8532i	−0.115143	−	0.541705i
$655$	−6.57641	−	30.9396i	−0.256962	−	1.20891i
$656$	0.627423	+	5.96954i	0.0244968	+	0.233071i
$657$	−10.1692	−	7.38836i	−0.396738	−	0.288247i
$658$	−9.82893	−	21.9743i	−0.383172	−	0.856646i
$659$			21.6584i			0.843691i	0.906668	+	0.421846i	$0.138618\pi$
$659$			21.6584i			0.843691i	−0.906668	+	0.421846i	$0.861382\pi$
$660$	0.194474	−	5.66007i	0.00756989	−	0.220318i
$661$	−5.12498	+	2.95891i	−0.199339	+	0.115088i	−0.596347	−	0.802727i	$-0.703382\pi$
$661$	−5.12498	+	2.95891i	−0.199339	+	0.115088i	0.397008	+	0.917815i	$0.370048\pi$
$662$	24.8004	+	22.3304i	0.963894	+	0.867894i
$663$	−8.30218	−	18.6470i	−0.322430	−	0.724190i
$664$	1.22212	+	1.68210i	0.0474274	+	0.0652782i
$665$	16.2581	+	3.42652i	0.630462	+	0.132875i
$666$	3.64583	+	1.18460i	0.141273	+	0.0459024i
$667$	9.17569	−	0.964403i	0.355284	−	0.0373419i
$668$	1.28270	−	12.2041i	0.0496291	−	0.472190i
$669$	−7.00620	+	7.78117i	−0.270875	+	0.300837i
$670$	−0.116694	+	0.202119i	−0.00450827	+	0.00780854i
$671$	−15.0976	+	8.03842i	−0.582837	+	0.310320i
$672$	−1.55882	−	2.13778i	−0.0601326	−	0.0824666i
$673$	−12.1519	+	3.94840i	−0.468422	+	0.152200i	−0.533711	−	0.845667i	$-0.679203\pi$
$673$	−12.1519	+	3.94840i	−0.468422	+	0.152200i	0.0652891	+	0.997866i	$0.479203\pi$
$674$	20.5721	−	9.15927i	0.792406	−	0.352802i
$675$	−0.847705	+	1.90398i	−0.0326282	+	0.0732841i
$676$	25.4484	−	5.40923i	0.978785	−	0.208047i
$677$	−8.58861	−	9.53862i	−0.330087	−	0.366599i	0.555141	−	0.831756i	$-0.312664\pi$
$677$	−8.58861	−	9.53862i	−0.330087	−	0.366599i	−0.885228	+	0.465157i	$0.845998\pi$
$678$	3.78950	−	2.75323i	0.145535	−	0.105737i
$679$	−17.7222	−	30.5740i	−0.680114	−	1.17332i
$680$	−1.72431	−	5.30689i	−0.0661244	−	0.203510i
$681$	−17.0730	−	9.85708i	−0.654237	−	0.377724i
$682$	12.5157	+	30.9274i	0.479249	+	1.18427i
$683$	4.62249	+	8.00639i	0.176875	+	0.306356i	0.940808	−	0.338939i	$-0.110068\pi$
$683$	4.62249	+	8.00639i	0.176875	+	0.306356i	−0.763934	+	0.645295i	$0.776735\pi$
$684$	−3.59733	−	0.764637i	−0.137547	−	0.0292366i
$685$	4.25682	−	5.85901i	0.162645	−	0.223861i
$686$	16.8800	−	7.62014i	0.644480	−	0.290938i
$687$	1.20982	−	3.72344i	0.0461574	−	0.142058i
$688$	−5.38908	+	4.85235i	−0.205457	+	0.184994i
$689$	56.2252	+	25.0331i	2.14201	+	0.953684i
$690$	4.71727	+	0.495805i	0.179583	+	0.0188750i
$691$	4.53535	−	21.3371i	0.172533	−	0.811703i	−0.803710	−	0.595022i	$-0.797144\pi$
$691$	4.53535	−	21.3371i	0.172533	−	0.811703i	0.976242	−	0.216681i	$-0.0695231\pi$
$692$	−10.7066			−0.407005
$693$	−8.51913	−	2.10342i	−0.323615	−	0.0799022i
$694$	−11.4247			−0.433676
$695$	−1.55646	+	7.32257i	−0.0590399	+	0.277761i
$696$	−3.30327	−	0.347188i	−0.125210	−	0.0131601i
$697$	17.9188	+	7.97796i	0.678723	+	0.302187i
$698$	1.74418	−	1.57047i	0.0660184	−	0.0594432i
$699$	−6.31795	+	19.4446i	−0.238967	+	0.735464i
$700$	−5.24721	−	1.69494i	−0.198326	−	0.0640628i
$701$	2.44854	−	3.37012i	0.0924800	−	0.127288i	−0.760270	−	0.649608i	$-0.774933\pi$
$701$	2.44854	−	3.37012i	0.0924800	−	0.127288i	0.852750	+	0.522320i	$0.174933\pi$
$702$	−6.10986	−	1.29869i	−0.230602	−	0.0490159i
$703$	7.04914	+	12.2095i	0.265863	+	0.460489i
$704$	−3.30842	+	0.233213i	−0.124691	+	0.00878953i
$705$	−13.4549	−	7.76820i	−0.506742	−	0.292568i
$706$	−10.4909	−	32.2877i	−0.394831	−	1.21516i
$707$	−5.68463	−	3.26899i	−0.213793	−	0.122943i
$708$	−7.52790	+	5.46934i	−0.282916	+	0.205550i
$709$	2.10725	+	2.34033i	0.0791393	+	0.0878931i	0.781414	−	0.624013i	$-0.214499\pi$
$709$	2.10725	+	2.34033i	0.0791393	+	0.0878931i	−0.702275	+	0.711906i	$0.747832\pi$
$710$	−2.38825	+	0.507639i	−0.0896296	+	0.0190514i
$711$	1.16669	−	2.62043i	0.0437544	−	0.0982739i
$712$	−8.58792	+	3.82359i	−0.321846	+	0.143295i
$713$	−26.5754	+	8.63488i	−0.995257	+	0.323379i
$714$	−8.59679	+	0.918524i	−0.321727	+	0.0343749i
$715$	24.5597	−	25.4609i	0.918482	−	0.952184i
$716$	−10.8585	+	18.8075i	−0.405802	+	0.702870i
$717$	−7.23716	+	8.03768i	−0.270277	+	0.300173i
$718$	3.18617	−	30.3144i	0.118907	−	1.13132i
$719$	25.5812	−	2.68870i	0.954019	−	0.100271i	0.385289	−	0.922796i	$-0.374102\pi$
$719$	25.5812	−	2.68870i	0.954019	−	0.100271i	0.568730	+	0.822524i	$0.307435\pi$
$720$	−1.62401	−	0.527672i	−0.0605232	−	0.0196652i
$721$	−12.2358	−	37.4385i	−0.455684	−	1.39428i
$722$	3.21785	+	4.42899i	0.119756	+	0.164830i
$723$	0.309002	+	0.694029i	0.0114919	+	0.0258112i
$724$	16.6786	+	15.0175i	0.619857	+	0.558121i
$725$	−5.99503	+	3.46123i	−0.222650	+	0.128547i
$726$	−7.90416	+	7.65012i	−0.293351	+	0.283922i
$727$			9.26646i			0.343674i	0.985125	+	0.171837i	$0.0549702\pi$
$727$			9.26646i			0.343674i	−0.985125	+	0.171837i	$0.945030\pi$
$728$	1.69917	−	16.4387i	0.0629756	−	0.609259i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−2.24360	−	21.3464i	−0.0830394	−	0.790067i
$731$	4.92688	+	23.1792i	0.182227	+	0.857312i
$732$	1.07222	+	5.04442i	0.0396306	+	0.186447i
$733$	−4.88550	−	46.4824i	−0.180450	−	1.71687i	−0.592386	−	0.805654i	$-0.701814\pi$
$733$	−4.88550	−	46.4824i	−0.180450	−	1.71687i	0.411937	−	0.911213i	$-0.364853\pi$
$734$	4.60197	+	3.34353i	0.169862	+	0.123412i
$735$	5.94087	−	10.3722i	0.219132	−	0.382584i
$736$		−	2.77776i		−	0.102390i
$737$	0.435675	−	0.125193i	0.0160483	−	0.00461153i
$738$	5.19825	−	3.00121i	0.191350	−	0.110476i
$739$	−29.8313	−	26.8602i	−1.09736	−	0.988070i	−0.0973883	−	0.995246i	$-0.531049\pi$
$739$	−29.8313	−	26.8602i	−1.09736	−	0.988070i	−0.999974	+	0.00717678i	$0.997716\pi$
$740$	2.66247	+	5.98001i	0.0978744	+	0.219829i
$741$	−13.5027	−	18.5849i	−0.496035	−	0.682734i
$742$	17.4101	−	19.4030i	0.639146	−	0.712306i
$743$	−10.7452	−	3.49133i	−0.394204	−	0.128085i	0.105206	−	0.994450i	$-0.466450\pi$
$743$	−10.7452	−	3.49133i	−0.394204	−	0.128085i	−0.499410	+	0.866366i	$0.666450\pi$
$744$	10.0045	−	1.05151i	0.366781	−	0.0385503i
$745$	−1.67794	+	15.9645i	−0.0614750	+	0.584895i
$746$	−16.8932	+	18.7618i	−0.618503	+	0.686917i
$747$	1.03960	−	1.80063i	0.0380368	−	0.0658817i
$748$	−4.74559	+	9.74378i	−0.173516	+	0.356268i
$749$	26.2130	−	19.1139i	0.957800	−	0.698405i
$750$	−11.5047	+	3.73811i	−0.420093	+	0.136497i
$751$	3.07128	−	1.36742i	0.112072	−	0.0498979i	−0.349935	−	0.936774i	$-0.613796\pi$
$751$	3.07128	−	1.36742i	0.112072	−	0.0498979i	0.462007	+	0.886876i	$0.347129\pi$
$752$	−3.70069	+	8.31188i	−0.134950	+	0.303103i
$753$	20.2289	−	4.29979i	0.737182	−	0.156693i
$754$	−13.8825	−	15.4181i	−0.505570	−	0.561493i
$755$	−20.0476	+	14.5655i	−0.729609	+	0.530092i
$756$	−1.31893	+	2.29356i	−0.0479690	+	0.0834160i
$757$	−1.70805	−	5.25683i	−0.0620800	−	0.191063i	0.915206	−	0.402985i	$-0.132027\pi$
$757$	−1.70805	−	5.25683i	−0.0620800	−	0.191063i	−0.977286	+	0.211923i	$0.932027\pi$
$758$	−1.78376	−	1.02986i	−0.0647892	−	0.0374061i
$759$	−5.92582	−	7.05408i	−0.215094	−	0.256047i
$760$	−3.13999	−	5.43862i	−0.113899	−	0.197279i
$761$	18.0294	+	3.83226i	0.653564	+	0.138919i	0.522748	−	0.852487i	$-0.324907\pi$
$761$	18.0294	+	3.83226i	0.653564	+	0.138919i	0.130816	+	0.991407i	$0.458240\pi$
$762$	9.11819	−	12.5501i	0.330317	−	0.454643i
$763$	−25.1209	−	27.8032i	−0.909439	−	1.00654i
$764$	1.72607	−	5.31230i	0.0624471	−	0.192192i
$765$	−4.14675	+	3.73375i	−0.149926	+	0.134994i
$766$	21.0948	+	9.39200i	0.762185	+	0.339347i
$767$	−57.8039	−	6.07544i	−2.08718	−	0.219371i
$768$	−0.207912	+	0.978148i	−0.00750237	+	0.0352959i
$769$	24.7632			0.892985			0.446493	−	0.894787i	$-0.352673\pi$
$769$	24.7632			0.892985			0.446493	+	0.894787i	$0.352673\pi$
$770$	−7.06473	−	13.2140i	−0.254595	−	0.476199i
$771$	−13.9520			−0.502469
$772$	0.943619	−	4.43938i	0.0339616	−	0.159777i
$773$	2.81789	+	0.296172i	0.101352	+	0.0106526i	0.155069	−	0.987904i	$-0.450440\pi$
$773$	2.81789	+	0.296172i	0.101352	+	0.0106526i	−0.0537165	+	0.998556i	$0.517107\pi$
$774$	6.62478	+	2.94954i	0.238123	+	0.106019i
$775$	15.5806	−	14.0288i	0.559671	−	0.503930i
$776$	−4.12751	+	12.7032i	−0.148169	+	0.456017i
$777$	9.91708	−	2.12579i	0.355773	−	0.0762622i
$778$	21.0416	−	28.9613i	0.754378	−	1.03831i
$779$	21.5927	+	4.58967i	0.773638	+	0.164442i
$780$	−5.33308	−	9.23717i	−0.190955	−	0.330744i
$781$	4.02312	+	2.51079i	0.143959	+	0.0898431i
$782$	−7.86099	−	4.53855i	−0.281109	−	0.162298i
$783$	1.02639	+	3.15890i	0.0366802	+	0.112890i
$784$	−6.40458	−	2.82512i	−0.228735	−	0.100897i
$785$	14.8363	−	10.7792i	0.529531	−	0.384727i
$786$	12.3948	+	13.7658i	0.442107	+	0.491010i
$787$	−2.82293	+	0.600031i	−0.100626	+	0.0213888i	−0.257950	−	0.966158i	$-0.583047\pi$
$787$	−2.82293	+	0.600031i	−0.100626	+	0.0213888i	0.157323	+	0.987547i	$0.449714\pi$
$788$	2.31701	−	5.20409i	0.0825401	−	0.185388i
$789$	14.2243	−	6.33308i	0.506400	−	0.225464i
$790$	4.65834	−	1.51359i	0.165736	−	0.0538510i
$791$	5.02115	−	11.3301i	0.178532	−	0.402853i
$792$	1.55870	+	2.92753i	0.0553861	+	0.104025i
$793$	−16.1066	+	27.8974i	−0.571962	+	0.990666i
$794$	19.3715	−	21.5142i	0.687469	−	0.763511i
$795$	1.75869	−	16.7329i	0.0623745	−	0.593453i
$796$	6.79417	−	0.714096i	0.240813	−	0.0253104i
$797$	−22.9528	−	7.45780i	−0.813028	−	0.264169i	−0.127148	−	0.991884i	$-0.540582\pi$
$797$	−22.9528	−	7.45780i	−0.813028	−	0.264169i	−0.685880	+	0.727715i	$0.740582\pi$
$798$	−9.24885	+	3.02275i	−0.327406	+	0.107004i
$799$	17.4759	+	24.0535i	0.618253	+	0.850953i
$800$	0.847705	+	1.90398i	0.0299709	+	0.0673157i
$801$	6.98604	+	6.29026i	0.246840	+	0.222255i
$802$	2.94057	−	1.69774i	0.103835	−	0.0599493i
$803$	−25.6481	+	32.8661i	−0.905103	+	1.15982i
$804$		−	0.136677i		−	0.00482022i
$805$	11.4557	−	5.12406i	0.403761	−	0.180599i
$806$	50.8351	+	36.9339i	1.79059	+	1.30094i
$807$	0.0823618	+	0.783621i	0.00289927	+	0.0275848i
$808$	0.515313	+	2.42436i	0.0181286	+	0.0852885i
$809$	−1.55958	−	7.33726i	−0.0548320	−	0.257964i	0.942190	−	0.335078i	$-0.108763\pi$
$809$	−1.55958	−	7.33726i	−0.0548320	−	0.257964i	−0.997022	+	0.0771139i	$0.975429\pi$
$810$	0.178491	+	1.69823i	0.00627153	+	0.0596697i
$811$	−18.2587	−	13.2657i	−0.641150	−	0.465823i	0.219095	−	0.975703i	$-0.429689\pi$
$811$	−18.2587	−	13.2657i	−0.641150	−	0.465823i	−0.860245	+	0.509881i	$0.829689\pi$
$812$	−8.02186	+	3.58812i	−0.281512	+	0.125918i
$813$			4.18850i			0.146897i
$814$	4.34178	−	11.9498i	0.152179	−	0.418840i
$815$	−25.6632	+	14.8166i	−0.898941	+	0.519004i
$816$	2.42843	+	2.18657i	0.0850121	+	0.0765452i
$817$	10.8475	+	24.3639i	0.379507	+	0.852386i
$818$	−4.89118	−	6.73213i	−0.171016	−	0.235383i
$819$	−15.7086	+	5.13396i	−0.548904	+	0.179395i
$820$	9.74797	+	3.16731i	0.340414	+	0.110607i
$821$	−12.7893	+	1.34421i	−0.446348	+	0.0469131i	−0.325037	−	0.945701i	$-0.605377\pi$
$821$	−12.7893	+	1.34421i	−0.446348	+	0.0469131i	−0.121311	+	0.992614i	$0.538710\pi$
$822$	−0.443322	+	4.21793i	−0.0154626	+	0.147117i
$823$	−6.46960	+	7.18522i	−0.225516	+	0.250461i	−0.845275	−	0.534331i	$-0.820564\pi$
$823$	−6.46960	+	7.18522i	−0.225516	+	0.250461i	0.619759	+	0.784792i	$0.287230\pi$
$824$	−7.44348	+	12.8925i	−0.259306	+	0.449131i
$825$	6.21450	+	3.02670i	0.216361	+	0.105376i
$826$	−9.97460	+	22.5075i	−0.347061	+	0.783136i
$827$	−22.6274	+	7.35209i	−0.786832	+	0.255657i	−0.674755	−	0.738042i	$-0.735751\pi$
$827$	−22.6274	+	7.35209i	−0.786832	+	0.255657i	−0.112078	+	0.993699i	$0.535751\pi$
$828$	−2.53761	+	1.12982i	−0.0881880	+	0.0392638i
$829$	4.63544	−	10.4114i	0.160996	−	0.361602i	−0.814978	−	0.579492i	$-0.803251\pi$
$829$	4.63544	−	10.4114i	0.160996	−	0.361602i	0.975973	+	0.217890i	$0.0699175\pi$
$830$	3.47281	−	0.738168i	0.120543	−	0.0256222i
$831$	−11.5059	−	12.7786i	−0.399135	−	0.443284i
$832$	−5.05341	+	3.67152i	−0.175195	+	0.127287i
$833$	−18.4594	+	13.5089i	−0.639581	+	0.468055i
$834$	−1.35475	−	4.16950i	−0.0469112	−	0.144378i
$835$	−18.1469	−	10.4771i	−0.628000	−	0.362576i
$836$	−2.94421	+	11.8369i	−0.101828	+	0.409387i
$837$	−5.02978	−	8.71184i	−0.173855	−	0.301125i
$838$	−7.86866	−	1.67254i	−0.271819	−	0.0577768i
$839$	24.0831	−	33.1475i	0.831440	−	1.14438i	−0.156213	−	0.987723i	$-0.549929\pi$
$839$	24.0831	−	33.1475i	0.831440	−	1.14438i	0.987653	−	0.156656i	$-0.0500714\pi$
$840$	−4.41749	+	0.946917i	−0.152418	+	0.0326717i
$841$	5.55238	−	17.0885i	0.191461	−	0.589257i
$842$	−17.3357	+	15.6092i	−0.597429	+	0.537927i
$843$	−17.7832	−	7.91757i	−0.612484	−	0.272696i
$844$	−12.0407	−	1.26553i	−0.414459	−	0.0435614i
$845$	9.23670	−	43.4553i	0.317752	−	1.49491i
$846$	9.09848			0.312812
$847$	−7.94236	+	27.9986i	−0.272903	+	0.962042i
$848$	−9.85313			−0.338358
$849$	1.08092	−	5.08533i	0.0370971	−	0.174528i
$850$	6.77326	+	0.711898i	0.232321	+	0.0244179i
$851$	9.72780	+	4.33109i	0.333465	+	0.148468i
$852$	1.06260	−	0.956765i	0.0364039	−	0.0327782i
$853$	−14.3544	+	44.1783i	−0.491485	+	1.51264i	0.330879	+	0.943673i	$0.392655\pi$
$853$	−14.3544	+	44.1783i	−0.491485	+	1.51264i	−0.822364	+	0.568962i	$0.807345\pi$
$854$	9.14736	+	10.1241i	0.313016	+	0.346438i
$855$	−3.69128	+	5.08061i	−0.126239	+	0.173753i
$856$	−11.9938	−	2.54937i	−0.409941	−	0.0871356i
$857$	−13.5316	−	23.4374i	−0.462229	−	0.800605i	0.536842	−	0.843683i	$-0.319617\pi$
$857$	−13.5316	−	23.4374i	−0.462229	−	0.800605i	−0.999072	+	0.0430779i	$0.986284\pi$
$858$	−5.00057	+	20.1042i	−0.170717	+	0.686348i
$859$	14.7896	+	8.53878i	0.504615	+	0.291339i	0.730617	−	0.682787i	$-0.239232\pi$
$859$	14.7896	+	8.53878i	0.504615	+	0.291339i	−0.226003	+	0.974127i	$0.572566\pi$
$860$	3.82653	+	11.7769i	0.130484	+	0.401587i
$861$	7.91677	−	13.7669i	0.269803	−	0.469175i
$862$	6.68553	−	4.85732i	0.227710	−	0.165441i
$863$	15.6502	+	17.3813i	0.532740	+	0.591668i	0.948093	−	0.317993i	$-0.103009\pi$
$863$	15.6502	+	17.3813i	0.532740	+	0.591668i	−0.415353	+	0.909660i	$0.636342\pi$
$864$	0.978148	−	0.207912i	0.0332773	−	0.00707330i
$865$	−7.43615	+	16.7019i	−0.252837	+	0.567880i
$866$	26.9506	−	11.9992i	0.915818	−	0.407748i
$867$	−6.01224	+	1.95349i	−0.204186	+	0.0663441i
$868$	21.5051	−	15.6810i	0.729931	−	0.532248i
$869$	−8.55300	−	4.16564i	−0.290141	−	0.141309i
$870$	−2.83584	+	4.91182i	−0.0961439	+	0.166526i
$871$	0.571258	−	0.634447i	0.0193564	−	0.0214974i
$872$	−1.48041	+	14.0851i	−0.0501330	+	0.476983i
$873$	13.2837	−	1.39618i	0.449586	−	0.0472534i
$874$	−9.71576	−	3.15684i	−0.328641	−	0.106782i
$875$	−21.3746	+	23.8213i	−0.722594	+	0.805305i
$876$	7.38836	+	10.1692i	0.249630	+	0.343586i
$877$	5.51141	+	12.3788i	0.186107	+	0.418003i	0.982370	−	0.186947i	$-0.0598594\pi$
$877$	5.51141	+	12.3788i	0.186107	+	0.418003i	−0.796263	+	0.604951i	$0.793193\pi$
$878$	−13.7826	−	12.4099i	−0.465140	−	0.418814i
$879$	−15.9567	+	9.21258i	−0.538205	+	0.310733i
$880$	−1.93401	+	5.32295i	−0.0651956	+	0.179437i
$881$			27.0223i			0.910406i	0.890388	+	0.455203i	$0.150433\pi$
$881$			27.0223i			0.910406i	−0.890388	+	0.455203i	$0.849567\pi$
$882$	0.0240990	+	6.99996i	0.000811455	+	0.235701i
$883$	−20.2924	−	14.7433i	−0.682894	−	0.496152i	0.191422	−	0.981508i	$-0.438690\pi$
$883$	−20.2924	−	14.7433i	−0.682894	−	0.496152i	−0.874317	+	0.485356i	$0.838690\pi$
$884$	2.13360	+	20.2999i	0.0717608	+	0.682759i
$885$	3.30352	+	15.5418i	0.111047	+	0.522433i
$886$	7.45646	+	35.0799i	0.250505	+	1.17853i
$887$	−0.855086	−	8.13560i	−0.0287110	−	0.273167i	−0.999454	−	0.0330453i	$-0.989479\pi$
$887$	−0.855086	−	8.13560i	−0.0287110	−	0.273167i	0.970743	−	0.240121i	$-0.0771872\pi$
$888$	−3.10133	−	2.25325i	−0.104074	−	0.0756140i
$889$	4.21989	−	40.8255i	0.141531	−	1.36924i
$890$			16.0524i			0.538077i
$891$	2.04045	−	2.61468i	0.0683577	−	0.0875951i
$892$	9.06781	−	5.23530i	0.303613	−	0.175291i
$893$	24.8667	+	22.3901i	0.832133	+	0.749256i
$894$	−3.82361	−	8.58797i	−0.127881	−	0.287225i
$895$	21.7972	+	30.0013i	0.728601	+	1.00283i
$896$	0.821912	+	2.51485i	0.0274582	+	0.0840152i
$897$	−16.5017	−	5.36171i	−0.550974	−	0.179022i
$898$	13.4720	−	1.41596i	0.449567	−	0.0472514i
$899$	3.49256	−	33.2295i	0.116483	−	1.10826i
$900$	1.39458	−	1.54883i	0.0464859	−	0.0516278i
$901$	−16.0989	+	27.8841i	−0.536332	+	0.928955i
$902$	−9.35599	−	17.5723i	−0.311520	−	0.585093i
$903$	19.0777	−	2.03835i	0.634865	−	0.0678321i
$904$	−4.45482	+	1.44746i	−0.148165	+	0.0481418i
$905$	35.0106	−	15.5877i	1.16379	−	0.518153i
$906$	5.90252	−	13.2573i	0.196098	−	0.440443i
$907$	16.4421	−	3.49488i	0.545951	−	0.116046i	0.0733244	−	0.997308i	$-0.476639\pi$
$907$	16.4421	−	3.49488i	0.545951	−	0.116046i	0.472627	+	0.881263i	$0.343306\pi$
$908$	13.1913	+	14.6505i	0.437770	+	0.486193i
$909$	2.00516	−	1.45684i	0.0665070	−	0.0483202i
$910$	−24.4635	−	14.0679i	−0.810958	−	0.466347i
$911$	6.62347	+	20.3849i	0.219445	+	0.675383i	0.998808	+	0.0488101i	$0.0155429\pi$
$911$	6.62347	+	20.3849i	0.219445	+	0.675383i	−0.779363	+	0.626573i	$0.784457\pi$
$912$	3.18498	+	1.83885i	0.105465	+	0.0608904i
$913$	−5.85010	−	3.65099i	−0.193610	−	0.120830i
$914$	−10.6486	−	18.4439i	−0.352223	−	0.610068i
$915$	8.61376	+	1.83091i	0.284762	+	0.0605281i
$916$	−2.30121	+	3.16734i	−0.0760341	+	0.104652i
$917$	46.6365	+	15.0644i	1.54007	+	0.497470i
$918$	1.00980	−	3.10784i	0.0333283	−	0.102574i
$919$	−37.7017	+	33.9468i	−1.24367	+	1.11980i	−0.255436	+	0.966826i	$0.582219\pi$
$919$	−37.7017	+	33.9468i	−1.24367	+	1.11980i	−0.988230	+	0.152976i	$0.951114\pi$
$920$	−4.33318	−	1.92925i	−0.142861	−	0.0636056i
$921$	16.1769	+	1.70026i	0.533046	+	0.0560254i
$922$	−1.02834	+	4.83796i	−0.0338666	+	0.159330i
$923$	8.93143			0.293982
$924$	7.45219	+	4.63303i	0.245159	+	0.152415i
$925$	−7.98953			−0.262694
$926$	3.16768	−	14.9028i	0.104097	−	0.489736i
$927$	14.8054	+	1.55611i	0.486274	+	0.0511094i
$928$	3.03431	+	1.35096i	0.0996061	+	0.0443475i
$929$	−33.1270	+	29.8277i	−1.08686	+	0.978616i	−0.999845	−	0.0175910i	$-0.994400\pi$
$929$	−33.1270	+	29.8277i	−1.08686	+	0.978616i	−0.0870176	+	0.996207i	$0.527734\pi$
$930$	5.30815	−	16.3368i	0.174061	−	0.535705i
$931$	−17.1601	+	19.1906i	−0.562398	+	0.628948i
$932$	12.0175	−	16.5406i	0.393645	−	0.541806i
$933$	−21.4952	−	4.56894i	−0.703720	−	0.149580i
$934$	4.03216	+	6.98391i	0.131936	+	0.228521i
$935$	11.9039	+	14.1703i	0.389298	+	0.463419i
$936$	5.40950	+	3.12318i	0.176815	+	0.102084i
$937$	−8.44327	−	25.9857i	−0.275829	−	0.848916i	−0.988999	−	0.147924i	$-0.952741\pi$
$937$	−8.44327	−	25.9857i	−0.275829	−	0.848916i	0.713169	−	0.700992i	$-0.247259\pi$
$938$	−0.181345	−	0.312854i	−0.00592113	−	0.0102151i
$939$	−8.71716	+	6.33339i	−0.284474	+	0.206682i
$940$	10.3959	+	11.5458i	0.339076	+	0.376583i
$941$	−2.39925	+	0.509976i	−0.0782133	+	0.0166248i	−0.246852	−	0.969053i	$-0.579396\pi$
$941$	−2.39925	+	0.509976i	−0.0782133	+	0.0166248i	0.168639	+	0.985678i	$0.446063\pi$
$942$	−4.36818	+	9.81109i	−0.142323	+	0.319663i
$943$	15.2318	−	6.78163i	0.496015	−	0.220840i
$944$	8.84958	−	2.87540i	0.288029	−	0.0935864i
$945$	2.66181	+	3.65043i	0.0865886	+	0.118749i
$946$	10.5312	−	21.6230i	0.342400	−	0.703025i
$947$	−19.1979	+	33.2518i	−0.623849	+	1.08054i	0.364913	+	0.931042i	$0.381099\pi$
$947$	−19.1979	+	33.2518i	−0.623849	+	1.08054i	−0.988762	+	0.149497i	$0.952235\pi$
$948$	−1.91935	+	2.13165i	−0.0623375	+	0.0692329i
$949$	−8.20712	+	78.0855i	−0.266414	+	2.53476i
$950$	7.62293	−	0.801202i	0.247320	−	0.0259944i
$951$	−22.3794	−	7.27150i	−0.725701	−	0.235794i
$952$	8.45987	+	1.78299i	0.274186	+	0.0577869i
$953$	8.59392	+	11.8285i	0.278384	+	0.383163i	0.925198	−	0.379485i	$-0.123899\pi$
$953$	8.59392	+	11.8285i	0.278384	+	0.383163i	−0.646813	+	0.762648i	$0.723899\pi$
$954$	4.00763	+	9.00128i	0.129752	+	0.291427i
$955$	−7.08813	−	6.38218i	−0.229366	−	0.206522i
$956$	9.36673	−	5.40789i	0.302942	−	0.174904i
$957$	10.5876	−	3.04238i	0.342249	−	0.0983461i
$958$		−	0.664113i		−	0.0214565i
$959$	4.58166	+	10.2431i	0.147949	+	0.330766i
$960$	1.38146	+	1.00369i	0.0445865	+	0.0323940i
$961$	7.33736	+	69.8104i	0.236689	+	2.25195i
$962$	−4.97846	−	23.4218i	−0.160512	−	0.755150i
$963$	2.54937	+	11.9938i	0.0821522	+	0.386496i
$964$	−0.0794113	−	0.755548i	−0.00255767	−	0.0243346i
$965$	−6.26985	−	4.55531i	−0.201834	−	0.146641i
$966$	−4.30954	+	5.95310i	−0.138657	+	0.191538i
$967$		−	29.6863i		−	0.954646i	−0.878728	−	0.477323i	$-0.841607\pi$
$967$		−	29.6863i		−	0.954646i	0.878728	−	0.477323i	$-0.158393\pi$
$968$	9.88132	−	4.83318i	0.317598	−	0.155344i
$969$	10.4078	−	6.00895i	0.334347	−	0.193035i
$970$	16.9497	+	15.2615i	0.544220	+	0.490018i
$971$	−14.8113	−	33.2668i	−0.475318	−	1.06758i	−0.979031	−	0.203711i	$-0.934700\pi$
$971$	−14.8113	−	33.2668i	−0.475318	−	1.06758i	0.503713	−	0.863871i	$-0.331967\pi$
$972$	−0.587785	−	0.809017i	−0.0188532	−	0.0259492i
$973$	−8.63320	−	7.74650i	−0.276768	−	0.248342i
$974$	11.5288	+	3.74593i	0.369406	+	0.120027i
$975$	12.9471	−	1.36079i	0.414639	−	0.0435803i
$976$	0.539065	−	5.12886i	0.0172551	−	0.164171i
$977$	−24.3859	+	27.0833i	−0.780175	+	0.866472i	−0.993884	−	0.110425i	$-0.964779\pi$
$977$	−24.3859	+	27.0833i	−0.780175	+	0.866472i	0.213709	+	0.976897i	$0.431446\pi$
$978$	8.67696	−	15.0289i	0.277459	−	0.480572i
$979$	21.6458	−	22.4400i	0.691801	−	0.717186i
$980$	−8.85528	+	8.02871i	−0.282872	+	0.256468i
$981$	13.4696	−	4.37652i	0.430050	−	0.139732i
$982$	−25.0849	+	11.1685i	−0.800492	+	0.356402i
$983$	−11.1921	+	25.1379i	−0.356973	+	0.801774i	0.642400	+	0.766369i	$0.277939\pi$
$983$	−11.1921	+	25.1379i	−0.356973	+	0.801774i	−0.999373	+	0.0354049i	$0.988728\pi$
$984$	−5.87125	+	1.24797i	−0.187169	+	0.0397839i
$985$	−6.50890	−	7.22886i	−0.207391	−	0.230331i
$986$	8.78091	−	6.37971i	0.279641	−	0.203171i
$987$	20.8265	−	12.0720i	0.662914	−	0.384257i
$988$	7.09880	+	21.8479i	0.225843	+	0.695073i
$989$	17.4448	+	10.0718i	0.554713	+	0.320263i
$990$	5.64939	−	0.398230i	0.179550	−	0.0126566i
$991$	−17.5277	−	30.3588i	−0.556785	−	0.964380i	−0.997762	−	0.0668617i	$-0.978701\pi$
$991$	−17.5277	−	30.3588i	−0.556785	−	0.964380i	0.440977	−	0.897518i	$-0.354632\pi$
$992$	−9.83974	−	2.09150i	−0.312412	−	0.0664052i
$993$	−19.6157	+	26.9987i	−0.622485	+	0.856777i
$994$	1.16284	−	3.59991i	0.0368829	−	0.114182i
$995$	3.60484	−	11.0946i	0.114281	−	0.351721i
$996$	−1.54514	+	1.39125i	−0.0489597	+	0.0440835i
$997$	0.604687	+	0.269224i	0.0191506	+	0.00852641i	0.416290	−	0.909232i	$-0.363330\pi$
$997$	0.604687	+	0.269224i	0.0191506	+	0.00852641i	−0.397139	+	0.917758i	$0.629997\pi$
$998$	−35.6223	−	3.74405i	−1.12760	−	0.118516i
$999$	−0.797019	+	3.74968i	−0.0252166	+	0.118635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.ba.a.61.7	✓	64
7.3	odd	6		462.2.ba.b.325.6	yes	64
11.2	odd	10		462.2.ba.b.145.6	yes	64
77.24	even	30	inner	462.2.ba.a.409.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.ba.a.61.7	✓	64	1.1	even	1	trivial
462.2.ba.a.409.7	yes	64	77.24	even	30	inner
462.2.ba.b.145.6	yes	64	11.2	odd	10
462.2.ba.b.325.6	yes	64	7.3	odd	6

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.ba (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207912 - 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.26898 + 1.14260i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.554537 - 2.58698i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.207912 - 0.978148i) q^{2} +(0.994522 + 0.104528i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(-1.26898 + 1.14260i) q^{5} +(0.309017 - 0.951057i) q^{6} +(-0.554537 - 2.58698i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.978148 + 0.207912i) q^{9} +(0.853791 + 1.47881i) q^{10} +(0.800558 - 3.21856i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-1.93023 - 5.94064i) q^{13} +(-2.64575 + 0.00455429i) q^{14} +(-1.38146 + 1.00369i) q^{15} +(0.669131 + 0.743145i) q^{16} +(3.19637 - 0.679409i) q^{17} +(0.406737 - 0.913545i) q^{18} +(3.35975 - 1.49585i) q^{19} +(1.62401 - 0.527672i) q^{20} +(-0.281085 - 2.63078i) q^{21} +(-2.98178 - 1.45224i) q^{22} +(1.38888 - 2.40561i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-0.217854 + 2.07274i) q^{25} +(-6.21214 + 0.652922i) q^{26} +(0.951057 + 0.309017i) q^{27} +(-0.545627 + 2.58888i) q^{28} +(1.95231 + 2.68712i) q^{29} +(0.694537 + 1.55995i) q^{30} +(-7.47572 - 6.73116i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.13260 - 3.11724i) q^{33} -3.26778i q^{34} +(3.65957 + 2.64922i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(0.400705 + 3.81245i) q^{37} +(-0.764637 - 3.59733i) q^{38} +(-1.29869 - 6.10986i) q^{39} +(-0.178491 - 1.69823i) q^{40} +(4.85606 + 3.52813i) q^{41} +(-2.63173 - 0.272027i) q^{42} +7.25172i q^{43} +(-2.04045 + 2.61468i) q^{44} +(-1.47881 + 0.853791i) q^{45} +(-2.06428 - 1.85868i) q^{46} +(3.70069 + 8.31188i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-6.38498 + 2.86916i) q^{49} +(1.98215 + 0.644041i) q^{50} +(3.24987 - 0.341576i) q^{51} +(-0.652922 + 6.21214i) q^{52} +(-6.59303 + 7.32230i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.66162 + 4.99900i) q^{55} +(2.41886 + 1.07196i) q^{56} +(3.49770 - 1.13647i) q^{57} +(3.03431 - 1.35096i) q^{58} +(3.78468 - 8.50054i) q^{59} +(1.67027 - 0.355026i) q^{60} +(-3.45078 - 3.83248i) q^{61} +(-8.13836 + 5.91287i) q^{62} +(-0.00455429 - 2.64575i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(9.23717 + 5.33308i) q^{65} +(-2.81364 - 1.75596i) q^{66} +(0.0683384 + 0.118366i) q^{67} +(-3.19637 - 0.679409i) q^{68} +(1.63273 - 2.24725i) q^{69} +(3.35220 - 3.02880i) q^{70} +(-0.441852 + 1.35988i) q^{71} +(-0.743145 + 0.669131i) q^{72} +(-11.4831 - 5.11261i) q^{73} +(3.81245 + 0.400705i) q^{74} +(-0.433321 + 2.03862i) q^{75} -3.67770 q^{76} +(-8.77030 - 0.286224i) q^{77} -6.24635 q^{78} +(0.596378 - 2.80574i) q^{79} +(-1.69823 - 0.178491i) q^{80} +(0.913545 + 0.406737i) q^{81} +(4.46067 - 4.01640i) q^{82} +(0.642506 - 1.97743i) q^{83} +(-0.813250 + 2.51766i) q^{84} +(-3.27984 + 4.51431i) q^{85} +(7.09325 + 1.50772i) q^{86} +(1.66073 + 2.87647i) q^{87} +(2.13331 + 2.53949i) q^{88} +(8.14120 + 4.70032i) q^{89} +(0.527672 + 1.62401i) q^{90} +(-14.2980 + 8.28777i) q^{91} +(-2.24725 + 1.63273i) q^{92} +(-6.73116 - 7.47572i) q^{93} +(8.89966 - 1.89168i) q^{94} +(-2.55430 + 5.73704i) q^{95} +(0.913545 - 0.406737i) q^{96} +(12.7032 - 4.12751i) q^{97} +(1.47895 + 6.84198i) q^{98} +(1.45224 - 2.98178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9	\( 64 q - 8 q^{4} - 22 q^{5} - 16 q^{6} + 4 q^{7} - 8 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{14} - 6 q^{15} + 8 q^{16} + 30 q^{17} + 10 q^{19} + 20 q^{20} - 4 q^{21} - 2 q^{22} + 4 q^{23} - 8 q^{24} - 12 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{30} - 16 q^{31} - 14 q^{33} + 42 q^{35} - 16 q^{36} - 14 q^{37} + 12 q^{38} + 18 q^{39} + 18 q^{40} - 28 q^{41} - 6 q^{42} + 6 q^{44} - 12 q^{45} - 42 q^{46} + 24 q^{47} + 116 q^{49} + 26 q^{51} + 32 q^{54} - 14 q^{55} - 4 q^{56} + 20 q^{58} + 30 q^{59} + 2 q^{60} - 32 q^{61} - 8 q^{62} + 4 q^{63} + 16 q^{64} + 12 q^{65} + 4 q^{66} + 16 q^{67} - 30 q^{68} - 20 q^{70} - 24 q^{71} - 64 q^{73} + 4 q^{74} + 12 q^{75} - 48 q^{77} - 60 q^{79} - 18 q^{80} + 8 q^{81} - 68 q^{82} + 8 q^{83} + 2 q^{84} - 80 q^{85} - 18 q^{86} + 10 q^{87} - 8 q^{88} - 24 q^{89} + 4 q^{90} - 172 q^{91} + 8 q^{92} - 104 q^{93} - 6 q^{94} - 118 q^{95} + 8 q^{96} + 120 q^{97} + 40 q^{98} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^4 - 22 * q^5 - 16 * q^6 + 4 * q^7 - 8 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^14 - 6 * q^15 + 8 * q^16 + 30 * q^17 + 10 * q^19 + 20 * q^20 - 4 * q^21 - 2 * q^22 + 4 * q^23 - 8 * q^24 - 12 * q^26 - 10 * q^28 - 20 * q^29 + 18 * q^30 - 16 * q^31 - 14 * q^33 + 42 * q^35 - 16 * q^36 - 14 * q^37 + 12 * q^38 + 18 * q^39 + 18 * q^40 - 28 * q^41 - 6 * q^42 + 6 * q^44 - 12 * q^45 - 42 * q^46 + 24 * q^47 + 116 * q^49 + 26 * q^51 + 32 * q^54 - 14 * q^55 - 4 * q^56 + 20 * q^58 + 30 * q^59 + 2 * q^60 - 32 * q^61 - 8 * q^62 + 4 * q^63 + 16 * q^64 + 12 * q^65 + 4 * q^66 + 16 * q^67 - 30 * q^68 - 20 * q^70 - 24 * q^71 - 64 * q^73 + 4 * q^74 + 12 * q^75 - 48 * q^77 - 60 * q^79 - 18 * q^80 + 8 * q^81 - 68 * q^82 + 8 * q^83 + 2 * q^84 - 80 * q^85 - 18 * q^86 + 10 * q^87 - 8 * q^88 - 24 * q^89 + 4 * q^90 - 172 * q^91 + 8 * q^92 - 104 * q^93 - 6 * q^94 - 118 * q^95 + 8 * q^96 + 120 * q^97 + 40 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more