LMFDB - Embedded newform 720.2.cq.a.173.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(173,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2, 9]))

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

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

chi := DirichletCharacter("720.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cq (of order $12$, degree $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$560$
Relative dimension:	$140$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			173.15
Character	$\chi$	$=$	720.173
Dual form			720.2.cq.a.437.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32706 + 0.488794i) q^{2} +(-0.132011 + 1.72701i) q^{3} +(1.52216 - 1.29732i) q^{4} +(-1.20259 - 1.88514i) q^{5} +(-0.668967 - 2.35637i) q^{6} +(1.44560 - 0.387347i) q^{7} +(-1.38587 + 2.46563i) q^{8} +(-2.96515 - 0.455971i) q^{9} +O(q^{10})$	\(q+(-1.32706 + 0.488794i) q^{2} +(-0.132011 + 1.72701i) q^{3} +(1.52216 - 1.29732i) q^{4} +(-1.20259 - 1.88514i) q^{5} +(-0.668967 - 2.35637i) q^{6} +(1.44560 - 0.387347i) q^{7} +(-1.38587 + 2.46563i) q^{8} +(-2.96515 - 0.455971i) q^{9} +(2.51736 + 1.91387i) q^{10} +(-2.75664 + 0.738640i) q^{11} +(2.03954 + 2.80005i) q^{12} +(3.97353 - 2.29412i) q^{13} +(-1.72906 + 1.22063i) q^{14} +(3.41442 - 1.82803i) q^{15} +(0.633945 - 3.94944i) q^{16} +(0.666811 + 0.666811i) q^{17} +(4.15779 - 0.844247i) q^{18} +(-5.84993 + 5.84993i) q^{19} +(-4.27617 - 1.30935i) q^{20} +(0.478117 + 2.54770i) q^{21} +(3.29718 - 2.32765i) q^{22} +(-2.10861 + 7.86944i) q^{23} +(-4.07523 - 2.71891i) q^{24} +(-2.10754 + 4.53412i) q^{25} +(-4.15174 + 4.98666i) q^{26} +(1.17890 - 5.06065i) q^{27} +(1.69792 - 2.46500i) q^{28} +(3.00203 - 0.804391i) q^{29} +(-3.63760 + 4.09486i) q^{30} +(3.80555 + 6.59140i) q^{31} +(1.08918 + 5.55101i) q^{32} +(-0.911733 - 4.85827i) q^{33} +(-1.21083 - 0.558963i) q^{34} +(-2.46867 - 2.25934i) q^{35} +(-5.10497 + 3.15267i) q^{36} +1.80855i q^{37} +(4.90378 - 10.6226i) q^{38} +(3.43742 + 7.16518i) q^{39} +(6.31472 - 0.352584i) q^{40} +(4.00440 + 6.93583i) q^{41} +(-1.87979 - 3.14724i) q^{42} +(0.642478 - 1.11280i) q^{43} +(-3.23780 + 4.70057i) q^{44} +(2.70629 + 6.13808i) q^{45} +(-1.04829 - 11.4739i) q^{46} +(-6.00187 + 1.60820i) q^{47} +(6.73705 + 1.61620i) q^{48} +(-4.12246 + 2.38011i) q^{49} +(0.580570 - 7.04719i) q^{50} +(-1.23962 + 1.06357i) q^{51} +(3.07215 - 8.64693i) q^{52} -5.08929i q^{53} +(0.909150 + 7.29201i) q^{54} +(4.70756 + 4.30839i) q^{55} +(-1.04836 + 4.10113i) q^{56} +(-9.33065 - 10.8752i) q^{57} +(-3.59068 + 2.53485i) q^{58} +(2.99453 + 0.802382i) q^{59} +(2.82577 - 7.21215i) q^{60} +(-9.93474 + 2.66201i) q^{61} +(-8.27201 - 6.88703i) q^{62} +(-4.46303 + 0.489390i) q^{63} +(-4.15871 - 6.83412i) q^{64} +(-9.10328 - 4.73178i) q^{65} +(3.58461 + 6.00155i) q^{66} +(0.304816 + 0.527956i) q^{67} +(1.88006 + 0.149929i) q^{68} +(-13.3123 - 4.68045i) q^{69} +(4.38042 + 1.79160i) q^{70} -10.4321 q^{71} +(5.23357 - 6.67905i) q^{72} +(1.82463 - 1.82463i) q^{73} +(-0.884009 - 2.40005i) q^{74} +(-7.55227 - 4.23830i) q^{75} +(-1.31533 + 16.4937i) q^{76} +(-3.69889 + 2.13555i) q^{77} +(-8.06395 - 7.82841i) q^{78} +(0.0288873 + 0.0166781i) q^{79} +(-8.20765 + 3.55450i) q^{80} +(8.58418 + 2.70404i) q^{81} +(-8.70427 - 7.24691i) q^{82} +(-0.935801 + 1.62086i) q^{83} +(4.03294 + 3.25774i) q^{84} +(0.455133 - 2.05894i) q^{85} +(-0.308673 + 1.79080i) q^{86} +(0.992892 + 5.29073i) q^{87} +(1.99914 - 7.82054i) q^{88} -4.07641i q^{89} +(-6.59166 - 6.82275i) q^{90} +(4.85550 - 4.85550i) q^{91} +(6.99950 + 14.7141i) q^{92} +(-11.8858 + 5.70209i) q^{93} +(7.17875 - 5.06785i) q^{94} +(18.0631 + 3.99288i) q^{95} +(-9.73044 + 1.14824i) q^{96} +(1.20521 + 4.49792i) q^{97} +(4.30736 - 5.17357i) q^{98} +(8.51065 - 0.933228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6}+O(q^{10}) $ 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6	$ 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6} - 12 q^{11} - 10 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{18} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 24 q^{24} + 8 q^{28} + 28 q^{30} - 8 q^{31} + 54 q^{32} - 8 q^{33} - 12 q^{34} + 8 q^{36} - 18 q^{38} - 24 q^{39} + 8 q^{40} - 46 q^{42} - 4 q^{43} - 14 q^{45} - 40 q^{46} - 12 q^{47} - 22 q^{48} - 6 q^{50} - 8 q^{51} - 18 q^{52} + 24 q^{54} - 12 q^{56} + 24 q^{57} - 10 q^{58} - 88 q^{60} - 4 q^{61} + 20 q^{63} - 24 q^{64} - 12 q^{65} + 24 q^{66} - 4 q^{67} - 30 q^{68} + 12 q^{69} + 2 q^{70} - 22 q^{72} + 24 q^{74} - 66 q^{75} + 8 q^{76} - 12 q^{77} - 122 q^{78} - 16 q^{81} - 12 q^{84} - 12 q^{85} - 12 q^{86} + 12 q^{87} - 10 q^{88} - 94 q^{90} - 16 q^{91} - 120 q^{92} - 12 q^{95} + 48 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) $ 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6 - 12 * q^11 - 10 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^18 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 24 * q^24 + 8 * q^28 + 28 * q^30 - 8 * q^31 + 54 * q^32 - 8 * q^33 - 12 * q^34 + 8 * q^36 - 18 * q^38 - 24 * q^39 + 8 * q^40 - 46 * q^42 - 4 * q^43 - 14 * q^45 - 40 * q^46 - 12 * q^47 - 22 * q^48 - 6 * q^50 - 8 * q^51 - 18 * q^52 + 24 * q^54 - 12 * q^56 + 24 * q^57 - 10 * q^58 - 88 * q^60 - 4 * q^61 + 20 * q^63 - 24 * q^64 - 12 * q^65 + 24 * q^66 - 4 * q^67 - 30 * q^68 + 12 * q^69 + 2 * q^70 - 22 * q^72 + 24 * q^74 - 66 * q^75 + 8 * q^76 - 12 * q^77 - 122 * q^78 - 16 * q^81 - 12 * q^84 - 12 * q^85 - 12 * q^86 + 12 * q^87 - 10 * q^88 - 94 * q^90 - 16 * q^91 - 120 * q^92 - 12 * q^95 + 48 * q^96 - 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.32706	+	0.488794i	−0.938371	+	0.345630i
$2$	−1.32706	+	0.488794i	−0.938371	+	0.345630i
$3$	−0.132011	+	1.72701i	−0.0762168	+	0.997091i
$3$	−0.132011	+	1.72701i	−0.0762168	+	0.997091i
$4$	1.52216	−	1.29732i	0.761080	−	0.648658i
$5$	−1.20259	−	1.88514i	−0.537816	−	0.843062i
$5$	−1.20259	−	1.88514i	−0.537816	−	0.843062i
$6$	−0.668967	−	2.35637i	−0.273105	−	0.961984i
$7$	1.44560	−	0.387347i	0.546384	−	0.146403i	0.0249407	−	0.999689i	$-0.492060\pi$
$7$	1.44560	−	0.387347i	0.546384	−	0.146403i	0.521444	+	0.853286i	$0.325394\pi$
$8$	−1.38587	+	2.46563i	−0.489980	+	0.871733i
$9$	−2.96515	−	0.455971i	−0.988382	−	0.151990i
$10$	2.51736	+	1.91387i	0.796058	+	0.605220i
$11$	−2.75664	+	0.738640i	−0.831159	+	0.222708i	−0.649219	−	0.760601i	$-0.724904\pi$
$11$	−2.75664	+	0.738640i	−0.831159	+	0.222708i	−0.181940	+	0.983310i	$0.558238\pi$
$12$	2.03954	+	2.80005i	0.588764	+	0.808305i
$13$	3.97353	−	2.29412i	1.10206	−	0.636273i	0.165297	−	0.986244i	$-0.447142\pi$
$13$	3.97353	−	2.29412i	1.10206	−	0.636273i	0.936761	+	0.349970i	$0.113808\pi$
$14$	−1.72906	+	1.22063i	−0.462110	+	0.326227i
$15$	3.41442	−	1.82803i	0.881601	−	0.471996i
$16$	0.633945	−	3.94944i	0.158486	−	0.987361i
$17$	0.666811	+	0.666811i	0.161726	+	0.161726i	0.783331	−	0.621605i	$-0.213519\pi$
$17$	0.666811	+	0.666811i	0.161726	+	0.161726i	−0.621605	+	0.783331i	$0.713519\pi$
$18$	4.15779	−	0.844247i	0.980001	−	0.198991i
$19$	−5.84993	+	5.84993i	−1.34207	+	1.34207i	−0.448066	+	0.894001i	$0.647887\pi$
$19$	−5.84993	+	5.84993i	−1.34207	+	1.34207i	−0.894001	+	0.448066i	$0.852113\pi$
$20$	−4.27617	−	1.30935i	−0.956180	−	0.292779i
$21$	0.478117	+	2.54770i	0.104334	+	0.555954i
$22$	3.29718	−	2.32765i	0.702961	−	0.496256i
$23$	−2.10861	+	7.86944i	−0.439676	+	1.64089i	0.289948	+	0.957042i	$0.406362\pi$
$23$	−2.10861	+	7.86944i	−0.439676	+	1.64089i	−0.729623	+	0.683849i	$0.760305\pi$
$24$	−4.07523	−	2.71891i	−0.831853	−	0.554996i
$25$	−2.10754	+	4.53412i	−0.421508	+	0.906825i
$26$	−4.15174	+	4.98666i	−0.814224	+	0.977964i
$27$	1.17890	−	5.06065i	0.226879	−	0.973923i
$28$	1.69792	−	2.46500i	0.320877	−	0.465841i
$29$	3.00203	−	0.804391i	0.557463	−	0.149372i	0.0309224	−	0.999522i	$-0.490156\pi$
$29$	3.00203	−	0.804391i	0.557463	−	0.149372i	0.526540	+	0.850150i	$0.323489\pi$
$30$	−3.63760	+	4.09486i	−0.664132	+	0.747615i
$31$	3.80555	+	6.59140i	0.683496	+	1.18385i	0.973907	+	0.226948i	$0.0728747\pi$
$31$	3.80555	+	6.59140i	0.683496	+	1.18385i	−0.290411	+	0.956902i	$0.593792\pi$
$32$	1.08918	+	5.55101i	0.192542	+	0.981289i
$33$	−0.911733	−	4.85827i	−0.158712	−	0.845716i
$34$	−1.21083	−	0.558963i	−0.207656	−	0.0958614i
$35$	−2.46867	−	2.25934i	−0.417281	−	0.381898i
$36$	−5.10497	+	3.15267i	−0.850828	+	0.525445i
$37$			1.80855i			0.297324i	0.988888	+	0.148662i	$0.0474966\pi$
$37$			1.80855i			0.297324i	−0.988888	+	0.148662i	$0.952503\pi$
$38$	4.90378	−	10.6226i	0.795498	−	1.72321i
$39$	3.43742	+	7.16518i	0.550427	+	1.14735i
$40$	6.31472	−	0.352584i	0.998445	−	0.0557484i
$41$	4.00440	+	6.93583i	0.625383	+	1.08319i	0.988467	+	0.151438i	$0.0483905\pi$
$41$	4.00440	+	6.93583i	0.625383	+	1.08319i	−0.363084	+	0.931756i	$0.618276\pi$
$42$	−1.87979	−	3.14724i	−0.290058	−	0.485630i
$43$	0.642478	−	1.11280i	0.0979770	−	0.169701i	−0.812870	−	0.582445i	$-0.802096\pi$
$43$	0.642478	−	1.11280i	0.0979770	−	0.169701i	0.910847	+	0.412744i	$0.135430\pi$
$44$	−3.23780	+	4.70057i	−0.488117	+	0.708637i
$45$	2.70629	+	6.13808i	0.403431	+	0.915010i
$46$	−1.04829	−	11.4739i	−0.154562	−	1.69173i
$47$	−6.00187	+	1.60820i	−0.875463	+	0.234580i	−0.668449	−	0.743758i	$-0.733041\pi$
$47$	−6.00187	+	1.60820i	−0.875463	+	0.234580i	−0.207014	+	0.978338i	$0.566375\pi$
$48$	6.73705	+	1.61620i	0.972410	+	0.233279i
$49$	−4.12246	+	2.38011i	−0.588923	+	0.340015i
$50$	0.580570	−	7.04719i	0.0821050	−	0.996624i
$51$	−1.23962	+	1.06357i	−0.173581	+	0.148929i
$52$	3.07215	−	8.64693i	0.426031	−	1.19911i
$53$		−	5.08929i		−	0.699067i	−0.936924	−	0.349534i	$-0.886340\pi$
$53$		−	5.08929i		−	0.699067i	0.936924	−	0.349534i	$-0.113660\pi$
$54$	0.909150	+	7.29201i	0.123720	+	0.992317i
$55$	4.70756	+	4.30839i	0.634768	+	0.580943i
$56$	−1.04836	+	4.10113i	−0.140093	+	0.548036i
$57$	−9.33065	−	10.8752i	−1.23587	−	1.44045i
$58$	−3.59068	+	2.53485i	−0.471480	+	0.332842i
$59$	2.99453	+	0.802382i	0.389855	+	0.104461i	0.448421	−	0.893822i	$-0.351986\pi$
$59$	2.99453	+	0.802382i	0.389855	+	0.104461i	−0.0585668	+	0.998283i	$0.518653\pi$
$60$	2.82577	−	7.21215i	0.364805	−	0.931084i
$61$	−9.93474	+	2.66201i	−1.27201	+	0.340835i	−0.830802	−	0.556568i	$-0.812118\pi$
$61$	−9.93474	+	2.66201i	−1.27201	+	0.340835i	−0.441211	+	0.897403i	$0.645451\pi$
$62$	−8.27201	−	6.88703i	−1.05055	−	0.874654i
$63$	−4.46303	+	0.489390i	−0.562288	+	0.0616573i
$64$	−4.15871	−	6.83412i	−0.519839	−	0.854265i
$65$	−9.10328	−	4.73178i	−1.12912	−	0.586905i
$66$	3.58461	+	6.00155i	0.441236	+	0.738739i
$67$	0.304816	+	0.527956i	0.0372392	+	0.0645001i	0.884044	−	0.467403i	$-0.154810\pi$
$67$	0.304816	+	0.527956i	0.0372392	+	0.0645001i	−0.846805	+	0.531903i	$0.821477\pi$
$68$	1.88006	+	0.149929i	0.227991	+	0.0181816i
$69$	−13.3123	−	4.68045i	−1.60261	−	0.563460i
$70$	4.38042	+	1.79160i	0.523560	+	0.214137i
$71$	−10.4321			−1.23806			−0.619032	−	0.785366i	$-0.712475\pi$
$71$	−10.4321			−1.23806			−0.619032	+	0.785366i	$0.712475\pi$
$72$	5.23357	−	6.67905i	0.616783	−	0.787134i
$73$	1.82463	−	1.82463i	0.213557	−	0.213557i	−0.592220	−	0.805777i	$-0.701748\pi$
$73$	1.82463	−	1.82463i	0.213557	−	0.213557i	0.805777	+	0.592220i	$0.201748\pi$
$74$	−0.884009	−	2.40005i	−0.102764	−	0.279000i
$75$	−7.55227	−	4.23830i	−0.872061	−	0.489397i
$76$	−1.31533	+	16.4937i	−0.150879	+	1.89196i
$77$	−3.69889	+	2.13555i	−0.421527	+	0.243369i
$78$	−8.06395	−	7.82841i	−0.913062	−	0.886393i
$79$	0.0288873	+	0.0166781i	0.00325008	+	0.00187643i	0.501624	−	0.865086i	$-0.332736\pi$
$79$	0.0288873	+	0.0166781i	0.00325008	+	0.00187643i	−0.498374	+	0.866962i	$0.666069\pi$
$80$	−8.20765	+	3.55450i	−0.917643	+	0.397405i
$81$	8.58418	+	2.70404i	0.953798	+	0.300449i
$82$	−8.70427	−	7.24691i	−0.961225	−	0.800288i
$83$	−0.935801	+	1.62086i	−0.102718	+	0.177912i	−0.912803	−	0.408399i	$-0.866087\pi$
$83$	−0.935801	+	1.62086i	−0.102718	+	0.177912i	0.810086	+	0.586311i	$0.199420\pi$
$84$	4.03294	+	3.25774i	0.440030	+	0.355448i
$85$	0.455133	−	2.05894i	0.0493661	−	0.223323i
$86$	−0.308673	+	1.79080i	−0.0332850	+	0.193106i
$87$	0.992892	+	5.29073i	0.106449	+	0.567226i
$88$	1.99914	−	7.82054i	0.213109	−	0.833672i
$89$		−	4.07641i		−	0.432099i	−0.976382	−	0.216049i	$-0.930683\pi$
$89$		−	4.07641i		−	0.432099i	0.976382	−	0.216049i	$-0.0693172\pi$
$90$	−6.59166	−	6.82275i	−0.694822	−	0.719182i
$91$	4.85550	−	4.85550i	0.508995	−	0.508995i
$92$	6.99950	+	14.7141i	0.729749	+	1.53405i
$93$	−11.8858	+	5.70209i	−1.23250	+	0.591279i
$94$	7.17875	−	5.06785i	0.740432	−	0.522709i
$95$	18.0631	+	3.99288i	1.85323	+	0.409660i
$96$	−9.73044	+	1.14824i	−0.993109	+	0.117192i
$97$	1.20521	+	4.49792i	0.122371	+	0.456694i	0.999732	−	0.0231357i	$-0.00736499\pi$
$97$	1.20521	+	4.49792i	0.122371	+	0.456694i	−0.877361	+	0.479830i	$0.840698\pi$
$98$	4.30736	−	5.17357i	0.435109	−	0.522610i
$99$	8.51065	−	0.933228i	0.855352	−	0.0937930i
$100$	2.67418	+	9.63581i	0.267418	+	0.963581i
$101$	−17.5615	+	4.70559i	−1.74743	+	0.468224i	−0.984076	−	0.177751i	$-0.943118\pi$
$101$	−17.5615	+	4.70559i	−1.74743	+	0.468224i	−0.763359	+	0.645974i	$0.776451\pi$
$102$	1.12518	−	2.01733i	0.111409	−	0.199745i
$103$	12.1149	+	3.24618i	1.19372	+	0.319855i	0.800354	−	0.599528i	$-0.204645\pi$
$103$	12.1149	+	3.24618i	1.19372	+	0.319855i	0.393362	+	0.919383i	$0.371312\pi$
$104$	0.149648	+	12.9766i	0.0146742	+	1.27246i
$105$	4.22780	−	3.96517i	0.412591	−	0.386961i
$106$	2.48761	+	6.75377i	0.241618	+	0.655985i
$107$	15.7121			1.51895			0.759474	−	0.650538i	$-0.225456\pi$
$107$	15.7121			1.51895			0.759474	+	0.650538i	$0.225456\pi$
$108$	−4.77079	−	9.23253i	−0.459069	−	0.888401i
$109$	3.20326	−	3.20326i	0.306817	−	0.306817i	−0.536857	−	0.843674i	$-0.680388\pi$
$109$	3.20326	−	3.20326i	0.306817	−	0.306817i	0.843674	+	0.536857i	$0.180388\pi$
$110$	−8.35312	−	3.41644i	−0.796439	−	0.325745i
$111$	−3.12339	−	0.238749i	−0.296459	−	0.0226611i
$112$	−0.613374	−	5.95486i	−0.0579584	−	0.562682i
$113$	−1.63921	−	0.439226i	−0.154204	−	0.0413189i	0.180891	−	0.983503i	$-0.442102\pi$
$113$	−1.63921	−	0.439226i	−0.154204	−	0.0413189i	−0.335095	+	0.942184i	$0.608769\pi$
$114$	17.6980	+	9.87120i	1.65757	+	0.924522i
$115$	17.3708	−	5.48870i	1.61984	−	0.511824i
$116$	3.52602	−	5.11899i	0.327383	−	0.475286i
$117$	−12.8281	+	4.99058i	−1.18596	+	0.461379i
$118$	−4.36611	+	0.398902i	−0.401933	+	0.0367219i
$119$	1.22223	+	0.705654i	0.112041	+	0.0646872i
$120$	−0.224697	+	10.9521i	−0.0205120	+	0.999790i
$121$	−2.47279	+	1.42766i	−0.224799	+	0.129788i
$122$	11.8828	−	8.38868i	1.07582	−	0.759475i
$123$	−12.5069	+	6.00005i	−1.12771	+	0.541006i
$124$	14.3438	+	5.09617i	1.28811	+	0.457650i
$125$	11.0820	−	1.47969i	0.991203	−	0.132348i
$126$	5.68348	−	2.83095i	0.506325	−	0.252201i
$127$	−2.08767	+	2.08767i	−0.185250	+	0.185250i	−0.793639	−	0.608389i	$-0.791816\pi$
$127$	−2.08767	+	2.08767i	−0.185250	+	0.185250i	0.608389	+	0.793639i	$0.291816\pi$
$128$	8.85932	+	7.03651i	0.783061	+	0.621945i
$129$	1.83701	+	1.25647i	0.161740	+	0.110626i
$130$	14.3934	+	1.82971i	1.26239	+	0.160477i
$131$	−15.4243	−	4.13293i	−1.34763	−	0.361096i	−0.488369	−	0.872637i	$-0.662408\pi$
$131$	−15.4243	−	4.13293i	−1.34763	−	0.361096i	−0.859259	+	0.511541i	$0.829075\pi$
$132$	−7.69051	−	6.21226i	−0.669373	−	0.540708i
$133$	−6.19069	+	10.7226i	−0.536801	+	0.929767i
$134$	−0.662570	−	0.551636i	−0.0572373	−	0.0476541i
$135$	−10.9578	+	3.86351i	−0.943097	+	0.332518i
$136$	−2.56823	+	0.719997i	−0.220224	+	0.0617392i
$137$	0.158210	+	0.590447i	0.0135168	+	0.0504453i	0.972355	−	0.233508i	$-0.0750206\pi$
$137$	0.158210	+	0.590447i	0.0135168	+	0.0504453i	−0.958838	+	0.283953i	$0.908354\pi$
$138$	19.9539	−	0.295730i	1.69859	−	0.0251742i
$139$	2.90092	−	10.8264i	0.246053	−	0.918281i	−0.726799	−	0.686850i	$-0.758993\pi$
$139$	2.90092	−	10.8264i	0.246053	−	0.918281i	0.972851	−	0.231431i	$-0.0743406\pi$
$140$	−6.68879	−	0.236433i	−0.565306	−	0.0199822i
$141$	−1.98506	−	10.5776i	−0.167172	−	0.890796i
$142$	13.8440	−	5.09916i	1.16176	−	0.427912i
$143$	−9.25907	+	9.25907i	−0.774282	+	0.774282i
$144$	−3.68057	+	11.4216i	−0.306714	+	0.951802i
$145$	−5.12661	−	4.69190i	−0.425742	−	0.389641i
$146$	−1.52952	+	3.31326i	−0.126584	+	0.274207i
$147$	−3.56626	−	7.43375i	−0.294140	−	0.613125i
$148$	2.34626	+	2.75291i	0.192862	+	0.226287i
$149$	19.7620	+	5.29521i	1.61897	+	0.433801i	0.950698	−	0.310119i	$-0.100369\pi$
$149$	19.7620	+	5.29521i	1.61897	+	0.433801i	0.668269	+	0.743920i	$0.267036\pi$
$150$	12.0940	+	1.93296i	0.987467	+	0.157826i
$151$	−8.57187	−	4.94897i	−0.697569	−	0.402742i	0.108872	−	0.994056i	$-0.465276\pi$
$151$	−8.57187	−	4.94897i	−0.697569	−	0.402742i	−0.806441	+	0.591314i	$0.798609\pi$
$152$	−6.31653	−	22.5311i	−0.512338	−	1.82751i
$153$	−1.67315	−	2.28124i	−0.135266	−	0.184427i
$154$	3.86479	−	4.64199i	0.311433	−	0.374063i
$155$	7.84921	−	15.1008i	0.630464	−	1.21292i
$156$	14.5278	+	6.44714i	1.16315	+	0.516184i
$157$	−4.03224	−	6.98404i	−0.321808	−	0.557387i	0.659053	−	0.752096i	$-0.270957\pi$
$157$	−4.03224	−	6.98404i	−0.321808	−	0.557387i	−0.980861	+	0.194709i	$0.937624\pi$
$158$	−0.0464873	−	0.00801284i	−0.00369833	−	0.000637468i
$159$	8.78926	+	0.671844i	0.697034	+	0.0532807i
$160$	9.15460	−	8.72887i	0.723735	−	0.690078i
$161$			12.1928i			0.960928i
$162$	−12.7134	+	0.607485i	−0.998860	+	0.0477285i
$163$			16.3965i			1.28427i	0.766591	+	0.642136i	$0.221952\pi$
$163$			16.3965i			1.28427i	−0.766591	+	0.642136i	$0.778048\pi$
$164$	15.0933	+	5.36247i	1.17859	+	0.418739i
$165$	−8.06209	+	7.56127i	−0.627633	+	0.588644i
$166$	0.449597	−	2.60838i	0.0348955	−	0.202450i
$167$	22.9180	+	6.14086i	1.77345	+	0.475194i	0.989364	−	0.145460i	$-0.0464661\pi$
$167$	22.9180	+	6.14086i	1.77345	+	0.475194i	0.784085	+	0.620654i	$0.213133\pi$
$168$	−6.94431	−	2.35193i	−0.535765	−	0.181455i
$169$	4.02594	−	6.97313i	0.309688	−	0.536395i
$170$	0.402410	+	2.95480i	0.0308634	+	0.226622i
$171$	20.0133	−	14.6785i	1.53046	−	1.12249i
$172$	−0.465704	−	2.52736i	−0.0355096	−	0.192710i
$173$	5.78964	−	10.0279i	0.440178	−	0.762411i	−0.557524	−	0.830161i	$-0.688249\pi$
$173$	5.78964	−	10.0279i	0.440178	−	0.762411i	0.997702	+	0.0677500i	$0.0215820\pi$
$174$	−3.90370	−	6.53578i	−0.295939	−	0.495476i
$175$	−1.29037	+	7.37087i	−0.0975431	+	0.557185i
$176$	1.16966	+	11.3555i	0.0881663	+	0.855951i
$177$	−1.78104	+	5.06567i	−0.133871	+	0.380759i
$178$	1.99253	+	5.40963i	0.149346	+	0.405469i
$179$	−8.51553	−	8.51553i	−0.636480	−	0.636480i	0.313205	−	0.949686i	$-0.398597\pi$
$179$	−8.51553	−	8.51553i	−0.636480	−	0.636480i	−0.949686	+	0.313205i	$0.898597\pi$
$180$	12.0824	+	5.83222i	0.900572	+	0.434708i
$181$	−15.2114	+	15.2114i	−1.13065	+	1.13065i	−0.140583	+	0.990069i	$0.544898\pi$
$181$	−15.2114	+	15.2114i	−1.13065	+	1.13065i	−0.990069	+	0.140583i	$0.955102\pi$
$182$	−4.07019	+	8.81687i	−0.301702	+	0.653550i
$183$	−3.28582	−	17.5088i	−0.242895	−	1.29429i
$184$	−16.4809	−	16.1051i	−1.21499	−	1.18728i
$185$	3.40938	−	2.17495i	0.250663	−	0.159906i
$186$	12.9860	−	13.3767i	0.952179	−	0.980828i
$187$	−2.33070	−	1.34563i	−0.170437	−	0.0984020i
$188$	−7.04948	+	10.2343i	−0.514136	+	0.746410i
$189$	−0.256012	−	7.77231i	−0.0186221	−	0.565352i
$190$	−25.9224	+	3.53034i	−1.88061	+	0.256118i
$191$	21.0718	+	12.1658i	1.52470	+	0.880287i	0.999572	+	0.0292660i	$0.00931700\pi$
$191$	21.0718	+	12.1658i	1.52470	+	0.880287i	0.525131	+	0.851021i	$0.324016\pi$
$192$	12.3516	−	6.27996i	0.891400	−	0.453217i
$193$	−3.97254	+	14.8257i	−0.285950	+	1.06718i	0.662193	+	0.749333i	$0.269626\pi$
$193$	−3.97254	+	14.8257i	−0.285950	+	1.06718i	−0.948143	+	0.317845i	$0.897041\pi$
$194$	−3.79794	−	5.37989i	−0.272676	−	0.386254i
$195$	9.37358	−	15.0968i	0.671256	−	1.08111i
$196$	−3.18730	+	8.97104i	−0.227665	+	0.640788i
$197$	20.4682			1.45830			0.729149	−	0.684355i	$-0.239916\pi$
$197$	20.4682			1.45830			0.729149	+	0.684355i	$0.239916\pi$
$198$	−10.8380	+	5.39840i	−0.770220	+	0.383648i
$199$	3.91396			0.277453			0.138727	−	0.990331i	$-0.455699\pi$
$199$	3.91396			0.277453			0.138727	+	0.990331i	$0.455699\pi$
$200$	−8.25871	−	11.4801i	−0.583979	−	0.811769i
$201$	−0.952026	+	0.456724i	−0.0671508	+	0.0322149i
$202$	21.0050	−	14.8285i	1.47791	−	1.04333i
$203$	4.02815	−	2.32565i	0.282721	−	0.163229i
$204$	−0.507119	+	3.22709i	−0.0355054	+	0.225942i
$205$	8.25937	−	15.8899i	0.576860	−	1.10980i
$206$	−17.6639	+	1.61383i	−1.23070	+	0.112441i
$207$	9.84057	−	22.3726i	0.683967	−	1.55500i
$208$	−6.54149	−	17.1476i	−0.453570	−	1.18897i
$209$	11.8052	−	20.4472i	0.816581	−	1.41436i
$210$	−3.67238	+	7.32853i	−0.253418	+	0.505716i
$211$	4.97567	−	18.5695i	0.342539	−	1.27837i	−0.552921	−	0.833233i	$-0.686487\pi$
$211$	4.97567	−	18.5695i	0.342539	−	1.27837i	0.895461	−	0.445141i	$-0.146846\pi$
$212$	−6.60241	−	7.74671i	−0.453455	−	0.532046i
$213$	1.37716	−	18.0164i	0.0943613	−	1.23446i
$214$	−20.8509	+	7.67999i	−1.42534	+	0.524993i
$215$	−2.87044	+	0.127088i	−0.195762	+	0.00866731i
$216$	10.8439	+	9.92016i	0.737835	+	0.674981i
$217$	8.05444	+	8.05444i	0.546771	+	0.546771i
$218$	−2.68518	+	5.81665i	−0.181863	+	0.393953i
$219$	2.91029	+	3.39203i	0.196659	+	0.229212i
$220$	12.7550	+	0.450860i	0.859942	+	0.0303970i
$221$	4.17934	+	1.11985i	0.281133	+	0.0753292i
$222$	4.26162	−	1.20986i	0.286021	−	0.0812006i
$223$	11.0169	−	2.95197i	0.737747	−	0.197679i	0.129670	−	0.991557i	$-0.458608\pi$
$223$	11.0169	−	2.95197i	0.737747	−	0.197679i	0.608076	+	0.793879i	$0.291941\pi$
$224$	3.72469	+	7.60263i	0.248866	+	0.507972i
$225$	8.31659	−	12.4834i	0.554439	−	0.832224i
$226$	2.39002	−	0.218360i	0.158982	−	0.0145251i
$227$	−17.2410	−	9.95412i	−1.14433	−	0.660678i	−0.196829	−	0.980438i	$-0.563065\pi$
$227$	−17.2410	−	9.95412i	−1.14433	−	0.660678i	−0.947499	+	0.319760i	$0.896398\pi$
$228$	−28.3113	−	4.44895i	−1.87496	−	0.294639i
$229$	−3.22731	+	12.0445i	−0.213267	+	0.795922i	0.773503	+	0.633793i	$0.218503\pi$
$229$	−3.22731	+	12.0445i	−0.213267	+	0.795922i	−0.986770	+	0.162129i	$0.948164\pi$
$230$	−20.3692	+	15.7746i	−1.34311	+	1.04015i
$231$	−3.19983	−	6.66994i	−0.210534	−	0.438850i
$232$	−2.17710	+	8.51669i	−0.142933	+	0.559148i
$233$	14.4154	+	14.4154i	0.944386	+	0.944386i	0.998533	−	0.0541472i	$-0.0172440\pi$
$233$	14.4154	+	14.4154i	0.944386	+	0.944386i	−0.0541472	+	0.998533i	$0.517244\pi$
$234$	14.5843	−	12.8931i	0.953406	−	0.842848i
$235$	10.2495	+	9.38039i	0.668603	+	0.611909i
$236$	5.59910	−	2.66350i	0.364470	−	0.173379i
$237$	−0.0326168	+	0.0476871i	−0.00211869	+	0.00309761i
$238$	−1.96689	−	0.339025i	−0.127494	−	0.0219757i
$239$	−5.40984	−	9.37012i	−0.349934	−	0.606103i	0.636304	−	0.771439i	$-0.280463\pi$
$239$	−5.40984	−	9.37012i	−0.349934	−	0.606103i	−0.986237	+	0.165336i	$0.947129\pi$
$240$	−5.05516	−	14.6440i	−0.326309	−	0.945263i
$241$	3.63407	−	6.29439i	0.234091	−	0.405457i	−0.724917	−	0.688836i	$-0.758122\pi$
$241$	3.63407	−	6.29439i	0.234091	−	0.405457i	0.959008	+	0.283379i	$0.0914554\pi$
$242$	2.58369	−	3.10328i	0.166086	−	0.199486i
$243$	−5.80312	+	14.4680i	−0.372270	+	0.928124i
$244$	−11.6688	+	16.9405i	−0.747019	+	1.08450i
$245$	9.44449	+	4.90914i	0.603386	+	0.313633i
$246$	13.6646	−	14.0757i	0.871221	−	0.897434i
$247$	−9.82443	+	36.6653i	−0.625114	+	2.33296i
$248$	−21.5260	+	0.248240i	−1.36690	+	0.0157633i
$249$	−2.67570	−	1.83011i	−0.169566	−	0.115979i
$250$	−13.9832	+	7.38045i	−0.884373	+	0.466781i
$251$	−2.42116	−	2.42116i	−0.152822	−	0.152822i	0.626555	−	0.779377i	$-0.284464\pi$
$251$	−2.42116	−	2.42116i	−0.152822	−	0.152822i	−0.779377	+	0.626555i	$0.784464\pi$
$252$	−6.15855	+	6.53488i	−0.387952	+	0.411659i
$253$		−	23.2507i		−	1.46176i
$254$	1.75001	−	3.79089i	0.109806	−	0.237862i
$255$	3.49573	+	1.05782i	0.218911	+	0.0662435i
$256$	−15.1962	−	5.00747i	−0.949764	−	0.312967i
$257$	−0.0333703	+	0.124540i	−0.00208159	+	0.00776858i	−0.966959	−	0.254933i	$-0.917947\pi$
$257$	−0.0333703	+	0.124540i	−0.00208159	+	0.00776858i	0.964877	+	0.262701i	$0.0846134\pi$
$258$	−3.05198	−	0.769487i	−0.190008	−	0.0479062i
$259$	0.700536	+	2.61444i	0.0435292	+	0.162453i
$260$	−19.9953	+	4.60729i	−1.24005	+	0.285732i
$261$	−9.26823	+	1.01630i	−0.573689	+	0.0629074i
$262$	22.4891	−	2.05468i	1.38938	−	0.126938i
$263$	−15.3775	+	4.12040i	−0.948219	+	0.254074i	−0.699606	−	0.714529i	$-0.746641\pi$
$263$	−15.3775	+	4.12040i	−0.948219	+	0.254074i	−0.248612	+	0.968603i	$0.579975\pi$
$264$	13.2423	+	4.48494i	0.815005	+	0.276029i
$265$	−9.59404	+	6.12034i	−0.589357	+	0.375970i
$266$	2.97426	−	17.2555i	0.182364	−	1.05800i
$267$	7.04002	+	0.538133i	0.430842	+	0.0329332i
$268$	1.14890	+	0.408192i	0.0701805	+	0.0249343i
$269$	2.16148	+	2.16148i	0.131787	+	0.131787i	0.769924	−	0.638136i	$-0.220294\pi$
$269$	2.16148	+	2.16148i	0.131787	+	0.131787i	−0.638136	+	0.769924i	$0.720294\pi$
$270$	12.6532	−	10.4832i	0.770047	−	0.637987i
$271$	−2.23939			−0.136033			−0.0680167	−	0.997684i	$-0.521667\pi$
$271$	−2.23939			−0.136033			−0.0680167	+	0.997684i	$0.521667\pi$
$272$	3.05626	−	2.21081i	0.185313	−	0.134050i
$273$	7.74453	+	9.02649i	0.468720	+	0.546308i
$274$	−0.498561	−	0.706225i	−0.0301191	−	0.0426646i
$275$	2.46064	−	14.0557i	0.148382	−	0.847589i
$276$	−26.3354	+	10.1458i	−1.58521	+	0.610706i
$277$	−18.5730	−	10.7231i	−1.11594	−	0.644290i	−0.175581	−	0.984465i	$-0.556180\pi$
$277$	−18.5730	−	10.7231i	−1.11594	−	0.644290i	−0.940362	+	0.340175i	$0.889514\pi$
$278$	1.44218	+	15.7852i	0.0864965	+	0.946731i
$279$	−8.27851	−	21.2797i	−0.495622	−	1.27398i
$280$	8.99197	−	2.95568i	0.537373	−	0.176636i
$281$	−4.69487	+	8.13175i	−0.280072	+	0.485100i	−0.971402	−	0.237440i	$-0.923692\pi$
$281$	−4.69487	+	8.13175i	−0.280072	+	0.485100i	0.691330	+	0.722539i	$0.257025\pi$
$282$	7.80456	+	13.0668i	0.464755	+	0.778117i
$283$	12.6805	+	21.9633i	0.753779	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$283$	12.6805	+	21.9633i	0.753779	+	1.30558i	−0.192201	+	0.981356i	$0.561562\pi$
$284$	−15.8794	+	13.5337i	−0.942266	+	0.803080i
$285$	−9.28028	+	30.6680i	−0.549716	+	1.81662i
$286$	7.76153	−	16.8131i	0.458949	−	0.994179i
$287$	8.47533	+	8.47533i	0.500283	+	0.500283i
$288$	−0.698493	−	16.9562i	−0.0411591	−	0.999153i
$289$		−	16.1107i		−	0.947690i
$290$	9.09668	+	3.72056i	0.534176	+	0.218479i
$291$	−7.92706	+	1.48764i	−0.464693	+	0.0872072i
$292$	0.410259	−	5.14450i	0.0240086	−	0.301059i
$293$	12.7036	−	7.33443i	0.742152	−	0.428482i	−0.0806991	−	0.996739i	$-0.525715\pi$
$293$	12.7036	−	7.33443i	0.742152	−	0.428482i	0.822851	+	0.568257i	$0.192382\pi$
$294$	8.36620	+	8.12184i	0.487927	+	0.473675i
$295$	−2.08860	−	6.61006i	−0.121603	−	0.384853i
$296$	−4.45923	−	2.50642i	−0.259187	−	0.145683i
$297$	0.488195	+	14.8212i	0.0283279	+	0.860013i
$298$	−28.8136	+	2.63250i	−1.66913	+	0.152497i
$299$	9.67479	+	36.1068i	0.559508	+	2.08811i
$300$	−16.9942	+	3.34630i	−0.981160	+	0.193199i
$301$	0.497724	−	1.85753i	0.0286883	−	0.107066i
$302$	13.7944	+	2.37769i	0.793778	+	0.136821i
$303$	−5.80830	−	30.9501i	−0.333678	−	1.77804i
$304$	19.3954	+	26.8125i	1.11240	+	1.53780i
$305$	16.9657	+	15.5271i	0.971454	+	0.889080i
$306$	3.33542	+	2.20951i	0.190673	+	0.126309i
$307$	−18.7460			−1.06989			−0.534945	−	0.844887i	$-0.679668\pi$
$307$	−18.7460			−1.06989			−0.534945	+	0.844887i	$0.679668\pi$
$308$	−2.85981	+	8.04928i	−0.162953	+	0.458650i
$309$	−7.20549	+	20.4940i	−0.409906	+	1.16587i
$310$	−3.03518	+	23.8762i	−0.172387	+	1.35608i
$311$	−1.33984	−	2.32067i	−0.0759753	−	0.131593i	0.825535	−	0.564351i	$-0.190874\pi$
$311$	−1.33984	−	2.32067i	−0.0759753	−	0.131593i	−0.901510	+	0.432758i	$0.857540\pi$
$312$	−22.4305	−	1.45462i	−1.26988	−	0.0823515i
$313$	−7.66941	−	28.6226i	−0.433500	−	1.61785i	−0.744629	−	0.667478i	$-0.767374\pi$
$313$	−7.66941	−	28.6226i	−0.433500	−	1.61785i	0.311129	−	0.950368i	$-0.399293\pi$
$314$	8.76477	+	7.29729i	0.494625	+	0.411810i
$315$	6.28978	+	7.82491i	0.354389	+	0.440884i
$316$	0.0656079	−	0.0120892i	0.00369073	−	0.000680072i
$317$	−17.7077	−	10.2235i	−0.994563	−	0.574211i	−0.0879278	−	0.996127i	$-0.528024\pi$
$317$	−17.7077	−	10.2235i	−0.994563	−	0.574211i	−0.906635	+	0.421916i	$0.861358\pi$
$318$	−11.9922	+	3.40457i	−0.672492	+	0.190919i
$319$	−7.68137	+	4.43484i	−0.430074	+	0.248303i
$320$	−7.88206	+	16.0584i	−0.440621	+	0.897693i
$321$	−2.07418	+	27.1350i	−0.115769	+	1.51453i
$322$	−5.95977	−	16.1805i	−0.332125	−	0.901707i
$323$	−7.80160			−0.434093
$324$	16.5745	−	7.02041i	0.920805	−	0.390023i
$325$	2.02745	+	22.8514i	0.112463	+	1.26757i
$326$	−8.01451	−	21.7591i	−0.443883	−	1.20512i
$327$	5.10921	+	5.95494i	0.282540	+	0.329309i
$328$	−22.6508	+	0.261212i	−1.25068	+	0.0144230i
$329$	−8.05336	+	4.64961i	−0.443996	+	0.256341i
$330$	7.00295	−	13.9749i	0.385500	−	0.769295i
$331$	2.19394	+	8.18790i	0.120590	+	0.450048i	0.999644	−	0.0266741i	$-0.00849163\pi$
$331$	2.19394	+	8.18790i	0.120590	+	0.450048i	−0.879054	+	0.476722i	$0.841825\pi$
$332$	0.678321	+	3.68123i	0.0372277	+	0.202034i
$333$	0.824646	−	5.36262i	0.0451903	−	0.293870i
$334$	−33.4151	+	3.05292i	−1.82839	+	0.167048i
$335$	0.628705	−	1.20954i	0.0343498	−	0.0660841i
$336$	10.3651	−	0.273196i	0.565462	−	0.0149040i
$337$	1.39260	+	0.373146i	0.0758598	+	0.0203266i	0.296549	−	0.955018i	$-0.404164\pi$
$337$	1.39260	+	0.373146i	0.0758598	+	0.0203266i	−0.220690	+	0.975344i	$0.570831\pi$
$338$	−1.93423	+	11.2216i	−0.105208	+	0.610375i
$339$	0.974943	−	2.77296i	0.0529516	−	0.150606i
$340$	−1.97831	−	3.72449i	−0.107289	−	0.201989i
$341$	−15.3592	−	15.3592i	−0.831747	−	0.831747i
$342$	−19.3840	+	29.2616i	−1.04817	+	1.58229i
$343$	−12.4453	+	12.4453i	−0.671980	+	0.671980i
$344$	1.85338	+	3.12632i	0.0999274	+	0.168560i
$345$	7.18591	+	30.7242i	0.386876	+	1.65414i
$346$	−2.78158	+	16.1376i	−0.149539	+	0.867563i
$347$	−10.7612	−	18.6390i	−0.577693	−	1.00059i	−0.995743	−	0.0921702i	$-0.970620\pi$
$347$	−10.7612	−	18.6390i	−0.577693	−	1.00059i	0.418050	−	0.908424i	$-0.362714\pi$
$348$	8.37509	+	6.76525i	0.448952	+	0.362655i
$349$	1.51005	+	5.63560i	0.0808313	+	0.301667i	0.994492	−	0.104811i	$-0.0334237\pi$
$349$	1.51005	+	5.63560i	0.0808313	+	0.301667i	−0.913661	+	0.406477i	$0.866757\pi$
$350$	−1.89044	−	10.4123i	−0.101048	−	0.556560i
$351$	−6.92533	−	22.8132i	−0.369647	−	1.21768i
$352$	−7.10269	−	14.4976i	−0.378575	−	0.772726i
$353$	−0.687905	−	2.56730i	−0.0366135	−	0.136643i	0.945200	−	0.326493i	$-0.105867\pi$
$353$	−0.687905	−	2.56730i	−0.0366135	−	0.136643i	−0.981813	+	0.189849i	$0.939200\pi$
$354$	−0.112533	−	7.59299i	−0.00598106	−	0.403563i
$355$	12.5456	+	19.6660i	0.665851	+	1.04377i
$356$	−5.28839	−	6.20495i	−0.280284	−	0.328862i
$357$	−1.38002	+	2.01765i	−0.0730385	+	0.106785i
$358$	15.4629	+	7.13825i	0.817241	+	0.377268i
$359$		−	9.59034i		−	0.506159i	−0.967446	−	0.253079i	$-0.918557\pi$
$359$		−	9.59034i		−	0.506159i	0.967446	−	0.253079i	$-0.0814434\pi$
$360$	−18.8848	−	1.83386i	−0.995318	−	0.0966531i
$361$		−	49.4434i		−	2.60228i
$362$	12.7511	−	27.6216i	0.670184	−	1.45176i
$363$	−2.13916	−	4.45900i	−0.112277	−	0.234037i
$364$	1.09174	−	13.6900i	0.0572225	−	0.717549i
$365$	−5.63398	−	1.24540i	−0.294896	−	0.0651874i
$366$	12.9187	+	21.6291i	0.675271	+	1.13057i
$367$	5.03077	+	18.7751i	0.262604	+	0.980051i	0.963701	+	0.266985i	$0.0860274\pi$
$367$	5.03077	+	18.7751i	0.262604	+	0.980051i	−0.701097	+	0.713066i	$0.747306\pi$
$368$	29.7432	+	13.3166i	1.55047	+	0.694178i
$369$	−8.71111	−	22.3916i	−0.453482	−	1.16566i
$370$	−3.46134	+	4.55277i	−0.179946	+	0.236687i
$371$	−1.97132	−	7.35706i	−0.102346	−	0.381960i
$372$	−10.6947	+	24.0991i	−0.554494	+	1.24948i
$373$	−1.90283	−	3.29580i	−0.0985248	−	0.170650i	0.812549	−	0.582892i	$-0.198079\pi$
$373$	−1.90283	−	3.29580i	−0.0985248	−	0.170650i	−0.911074	+	0.412242i	$0.864746\pi$
$374$	3.75070	+	0.646494i	0.193944	+	0.0334294i
$375$	1.09250	+	19.3341i	0.0564165	+	0.998407i
$376$	4.35261	−	17.0272i	0.224469	−	0.878110i
$377$	10.0833	−	10.0833i	0.519315	−	0.519315i
$378$	4.13880	+	10.1892i	0.212877	+	0.524074i
$379$	−0.420668	−	0.420668i	−0.0216083	−	0.0216083i	0.696220	−	0.717828i	$-0.254864\pi$
$379$	−0.420668	−	0.420668i	−0.0216083	−	0.0216083i	−0.717828	+	0.696220i	$0.754864\pi$
$380$	32.6749	−	17.3557i	1.67619	−	0.890328i
$381$	−3.32983	−	3.88102i	−0.170592	−	0.198831i
$382$	−33.9101	−	5.84495i	−1.73499	−	0.299054i
$383$	14.6498	+	3.92541i	0.748571	+	0.200579i	0.612884	−	0.790173i	$-0.290009\pi$
$383$	14.6498	+	3.92541i	0.748571	+	0.200579i	0.135687	+	0.990752i	$0.456676\pi$
$384$	−13.3217	+	14.3713i	−0.679819	+	0.733380i
$385$	8.47408	+	4.40473i	0.431879	+	0.224486i
$386$	−1.97494	−	21.6163i	−0.100522	−	1.10024i
$387$	−2.41245	+	3.00668i	−0.122632	+	0.152838i
$388$	7.66975	+	5.28301i	0.389372	+	0.268204i
$389$	1.46965	+	5.48482i	0.0745144	+	0.278091i	0.993123	−	0.117078i	$-0.0373527\pi$
$389$	1.46965	+	5.48482i	0.0745144	+	0.278091i	−0.918608	+	0.395169i	$0.870686\pi$
$390$	−5.06004	+	24.6161i	−0.256225	+	1.24648i
$391$	−6.65348	+	3.84139i	−0.336481	+	0.194267i
$392$	−0.155257	−	13.4630i	−0.00784166	−	0.679985i
$393$	9.17381	−	26.0924i	0.462757	−	1.31619i
$394$	−27.1624	+	10.0047i	−1.36842	+	0.504031i
$395$	−0.00329907	−	0.0745138i	−0.000165994	−	0.00374920i
$396$	11.7439	−	12.4615i	0.590152	−	0.626215i
$397$	6.10219			0.306260			0.153130	−	0.988206i	$-0.451065\pi$
$397$	6.10219			0.306260			0.153130	+	0.988206i	$0.451065\pi$
$398$	−5.19404	+	1.91312i	−0.260354	+	0.0958960i
$399$	−17.7008	−	12.1069i	−0.886149	−	0.606104i
$400$	16.5712	+	11.1980i	0.828560	+	0.559900i
$401$	19.2400	−	11.1082i	0.960801	−	0.554719i	0.0643814	−	0.997925i	$-0.479493\pi$
$401$	19.2400	−	11.1082i	0.960801	−	0.554719i	0.896419	+	0.443207i	$0.146159\pi$
$402$	1.04015	−	1.07144i	0.0518779	−	0.0534388i
$403$	30.2429	+	17.4607i	1.50650	+	0.869781i
$404$	−20.6268	+	29.9455i	−1.02622	+	1.48984i
$405$	−5.22578	−	19.4343i	−0.259671	−	0.965697i
$406$	−4.20882	+	5.05521i	−0.208880	+	0.250886i
$407$	−1.33587	−	4.98553i	−0.0662166	−	0.247124i
$408$	−0.904409	−	4.53041i	−0.0447749	−	0.224289i
$409$	−4.91834	−	8.51882i	−0.243196	−	0.421229i	0.718427	−	0.695603i	$-0.244863\pi$
$409$	−4.91834	−	8.51882i	−0.243196	−	0.421229i	−0.961623	+	0.274374i	$0.911529\pi$
$410$	−3.19379	+	25.1239i	−0.157730	+	1.24078i
$411$	−1.04060	+	0.195285i	−0.0513288	+	0.00963268i
$412$	22.6521	−	10.7756i	1.11599	−	0.530878i
$413$	4.63969			0.228304
$414$	−2.12341	+	34.4997i	−0.104360	+	1.69557i
$415$	4.18094	−	0.185109i	0.205234	−	0.00908667i
$416$	17.0626	+	19.5584i	0.836561	+	0.958927i
$417$	18.3143	+	6.43913i	0.896857	+	0.315325i
$418$	−5.67169	+	32.9049i	−0.277411	+	1.60943i
$419$	7.81519	−	29.1667i	0.381797	−	1.42489i	−0.461357	−	0.887215i	$-0.652637\pi$
$419$	7.81519	−	29.1667i	0.381797	−	1.42489i	0.843154	−	0.537672i	$-0.180696\pi$
$420$	1.29132	−	11.5204i	0.0630099	−	0.562138i
$421$	7.01824	+	26.1924i	0.342048	+	1.27654i	0.896023	+	0.444008i	$0.146444\pi$
$421$	7.01824	+	26.1924i	0.342048	+	1.27654i	−0.553975	+	0.832534i	$0.686890\pi$
$422$	2.47364	+	27.0748i	0.120415	+	1.31798i
$423$	18.5297	−	2.03186i	0.900946	−	0.0987925i
$424$	12.5483	+	7.05311i	0.609400	+	0.342529i
$425$	−4.42874	+	1.61808i	−0.214825	+	0.0784882i
$426$	6.97874	+	24.5819i	0.338121	+	1.19100i
$427$	−13.3305	+	7.69638i	−0.645109	+	0.372454i
$428$	23.9164	−	20.3836i	1.15604	−	0.985277i
$429$	−14.7682	−	17.2128i	−0.713017	−	0.831043i
$430$	3.74712	−	1.57171i	0.180702	−	0.0757944i
$431$			12.2525i			0.590184i	0.955469	+	0.295092i	$0.0953503\pi$
$431$			12.2525i			0.590184i	−0.955469	+	0.295092i	$0.904650\pi$
$432$	−19.2394	−	7.86418i	−0.925656	−	0.378365i
$433$	−2.53651	−	2.53651i	−0.121897	−	0.121897i	0.643527	−	0.765424i	$-0.277470\pi$
$433$	−2.53651	−	2.53651i	−0.121897	−	0.121897i	−0.765424	+	0.643527i	$0.777470\pi$
$434$	−14.6257	−	6.75174i	−0.702055	−	0.324094i
$435$	8.77975	−	8.23434i	0.420957	−	0.394807i
$436$	0.720238	−	9.03152i	0.0344932	−	0.432532i
$437$	−33.7005	−	58.3709i	−1.61211	−	2.79226i
$438$	−5.52012	−	3.07889i	−0.263762	−	0.147115i
$439$	−3.69787	+	6.40491i	−0.176490	+	0.305690i	−0.940676	−	0.339306i	$-0.889808\pi$
$439$	−3.69787	+	6.40491i	−0.176490	+	0.305690i	0.764186	+	0.644996i	$0.223141\pi$
$440$	−17.1470	+	5.63626i	−0.817451	+	0.268698i
$441$	13.3090	−	5.17764i	0.633760	−	0.246554i
$442$	−6.09359	+	0.556731i	−0.289843	+	0.0264810i
$443$	−19.4939	−	11.2548i	−0.926183	−	0.534732i	−0.0405805	−	0.999176i	$-0.512921\pi$
$443$	−19.4939	−	11.2548i	−0.926183	−	0.534732i	−0.885602	+	0.464444i	$0.846254\pi$
$444$	−5.06404	+	3.68861i	−0.240329	+	0.175054i
$445$	−7.68462	+	4.90227i	−0.364286	+	0.232390i
$446$	−13.1772	+	9.30244i	−0.623957	+	0.440483i
$447$	−11.7537	+	33.4302i	−0.555931	+	1.58119i
$448$	−8.65899	−	8.26852i	−0.409099	−	0.390651i
$449$	21.3226			1.00628			0.503138	−	0.864206i	$-0.332179\pi$
$449$	21.3226			1.00628			0.503138	+	0.864206i	$0.332179\pi$
$450$	−4.93479	+	20.6312i	−0.232628	+	0.972566i
$451$	−16.1618	−	16.1618i	−0.761029	−	0.761029i
$452$	−3.06496	+	1.45800i	−0.144164	+	0.0685787i
$453$	9.67852	−	14.1504i	0.454737	−	0.664844i
$454$	27.7454	+	4.78236i	1.30215	+	0.224447i
$455$	−14.9925	−	3.31413i	−0.702860	−	0.155369i
$456$	39.7453	−	7.93437i	1.86124	−	0.371561i
$457$	−20.6465	+	5.53222i	−0.965804	+	0.258786i	−0.707055	−	0.707158i	$-0.749977\pi$
$457$	−20.6465	+	5.53222i	−0.965804	+	0.258786i	−0.258749	+	0.965945i	$0.583310\pi$
$458$	−1.60445	−	17.5612i	−0.0749710	−	0.820581i
$459$	4.16060	−	2.58840i	0.194200	−	0.120816i
$460$	19.3206	−	30.8901i	0.900828	−	1.44026i
$461$	−3.67694	−	13.7225i	−0.171252	−	0.639122i	−0.997160	−	0.0753164i	$-0.976003\pi$
$461$	−3.67694	−	13.7225i	−0.171252	−	0.639122i	0.825907	−	0.563806i	$-0.190663\pi$
$462$	7.50659	+	7.28733i	0.349238	+	0.339037i
$463$	−1.44512	+	5.39326i	−0.0671604	+	0.250646i	−0.991342	−	0.131308i	$-0.958082\pi$
$463$	−1.44512	+	5.39326i	−0.0671604	+	0.250646i	0.924181	+	0.381954i	$0.124749\pi$
$464$	−1.27378	−	12.3663i	−0.0591336	−	0.574091i
$465$	25.0430	+	15.5492i	1.16134	+	0.721075i
$466$	−26.1763	−	12.0839i	−1.21259	−	0.559776i
$467$			8.20104i			0.379499i	0.981833	+	0.189749i	$0.0607676\pi$
$467$			8.20104i			0.379499i	−0.981833	+	0.189749i	$0.939232\pi$
$468$	−13.0521	+	24.2386i	−0.603335	+	1.12043i
$469$	0.645143	+	0.645143i	0.0297899	+	0.0297899i
$470$	−18.1867	−	7.43842i	−0.838892	−	0.343109i
$471$	12.5938	−	6.04176i	0.580293	−	0.278389i
$472$	−6.12842	+	6.27142i	−0.282083	+	0.288665i
$473$	−0.949121	+	3.54217i	−0.0436406	+	0.162869i
$474$	0.0199751	−	0.0792264i	0.000917488	−	0.00363899i
$475$	−14.1954	−	38.8533i	−0.651328	−	1.78271i
$476$	2.77588	−	0.511497i	0.127232	−	0.0234444i
$477$	−2.32057	+	15.0905i	−0.106251	+	0.690946i
$478$	11.7592	+	9.79039i	0.537855	+	0.447802i
$479$	2.19377	−	3.79972i	0.100236	−	0.173614i	−0.811546	−	0.584289i	$-0.801374\pi$
$479$	2.19377	−	3.79972i	0.100236	−	0.173614i	0.911782	+	0.410675i	$0.134707\pi$
$480$	13.8664	+	16.9624i	0.632910	+	0.774225i
$481$	4.14903	+	7.18633i	0.189179	+	0.327668i
$482$	−1.74595	+	10.1293i	−0.0795260	+	0.461378i
$483$	−21.0571	−	1.60959i	−0.958133	−	0.0732388i
$484$	−1.91185	+	5.38112i	−0.0869022	+	0.244596i
$485$	7.02984	−	7.68117i	0.319209	−	0.348784i
$486$	0.629182	−	22.0364i	0.0285403	−	0.999593i
$487$	−4.37697	−	4.37697i	−0.198340	−	0.198340i	0.600948	−	0.799288i	$-0.294790\pi$
$487$	−4.37697	−	4.37697i	−0.198340	−	0.198340i	−0.799288	+	0.600948i	$0.794790\pi$
$488$	7.20476	−	28.1846i	0.326144	−	1.27586i
$489$	−28.3170	−	2.16452i	−1.28054	−	0.0978831i
$490$	−14.9329	−	1.89830i	−0.674601	−	0.0857563i
$491$	−8.97360	+	33.4899i	−0.404973	+	1.51138i	0.399133	+	0.916893i	$0.369311\pi$
$491$	−8.97360	+	33.4899i	−0.404973	+	1.51138i	−0.804106	+	0.594486i	$0.797356\pi$
$492$	−11.2535	+	25.3584i	−0.507349	+	1.14325i
$493$	2.53816	+	1.46541i	0.114313	+	0.0659988i
$494$	−4.88419	−	53.4590i	−0.219750	−	2.40524i
$495$	−11.9941	−	14.9215i	−0.539096	−	0.670672i
$496$	28.4449	−	10.8512i	1.27721	−	0.487233i
$497$	−15.0806	+	4.04084i	−0.676459	+	0.181257i
$498$	4.44536	+	1.12080i	0.199201	+	0.0502241i
$499$	4.01145	+	1.07486i	0.179577	+	0.0481175i	0.347487	−	0.937685i	$-0.387035\pi$
$499$	4.01145	+	1.07486i	0.179577	+	0.0481175i	−0.167910	+	0.985802i	$0.553702\pi$
$500$	14.9489	−	16.6292i	0.668537	−	0.743679i
$501$	−13.6308	+	38.7690i	−0.608979	+	1.73207i
$502$	4.39646	+	2.02956i	0.196224	+	0.0905839i
$503$	11.1170	+	11.1170i	0.495682	+	0.495682i	0.910091	−	0.414409i	$-0.136012\pi$
$503$	11.1170	+	11.1170i	0.495682	+	0.495682i	−0.414409	+	0.910091i	$0.636012\pi$
$504$	4.97853	−	11.6824i	0.221762	−	0.520377i
$505$	29.9901	+	27.4471i	1.33454	+	1.22138i
$506$	11.3648	+	30.8551i	0.505228	+	1.37167i
$507$	11.5112	+	7.87338i	0.511231	+	0.349669i
$508$	−0.469402	+	5.88613i	−0.0208263	+	0.261155i
$509$	2.68132	−	10.0068i	0.118847	−	0.443544i	−0.880699	−	0.473677i	$-0.842926\pi$
$509$	2.68132	−	10.0068i	0.118847	−	0.443544i	0.999546	+	0.0301331i	$0.00959310\pi$
$510$	−5.15609	+	0.304901i	−0.228316	+	0.0135012i
$511$	1.93092	−	3.34445i	0.0854187	−	0.147950i
$512$	22.6139	−	0.782635i	0.999402	−	0.0345879i
$513$	22.7080	+	36.5009i	1.00258	+	1.61156i
$514$	−0.0165900	−	0.181583i	−0.000731753	−	0.00800927i
$515$	−8.44978	−	26.7422i	−0.372342	−	1.17840i
$516$	4.42627	−	0.470636i	0.194856	−	0.0207186i
$517$	15.3571	−	8.86645i	0.675406	−	0.389946i
$518$	−2.20757	−	3.12709i	−0.0969952	−	0.137396i
$519$	16.5541	+	11.3226i	0.726644	+	0.497006i
$520$	24.2828	−	15.8877i	1.06487	−	0.696722i
$521$	5.07005			0.222123			0.111062	−	0.993814i	$-0.464575\pi$
$521$	5.07005			0.222123			0.111062	+	0.993814i	$0.464575\pi$
$522$	11.8027	−	5.87895i	0.516591	−	0.257315i
$523$	−40.8383			−1.78573			−0.892867	−	0.450321i	$-0.851310\pi$
$523$	−40.8383			−1.78573			−0.892867	+	0.450321i	$0.851310\pi$
$524$	−28.8400	+	13.7192i	−1.25988	+	0.599326i
$525$	−12.5592	−	3.20153i	−0.548130	−	0.139726i
$526$	18.3928	−	12.9844i	0.801965	−	0.566149i
$527$	−1.85764	+	6.93280i	−0.0809200	+	0.301998i
$528$	−19.7654	+	0.520963i	−0.860181	+	0.0226720i
$529$	−37.5633	−	21.6872i	−1.63319	−	0.942920i
$530$	9.74025	−	12.8116i	0.423089	−	0.556498i
$531$	−8.51336	−	3.74460i	−0.369448	−	0.162502i
$532$	4.48736	+	24.3528i	0.194552	+	1.05583i
$533$	31.8232	+	18.3731i	1.37842	+	0.795829i
$534$	−9.60554	+	2.72699i	−0.415672	+	0.118008i
$535$	−18.8953	−	29.6196i	−0.816915	−	1.28057i
$536$	−1.72418	+	0.0198835i	−0.0744734	+	0.000858835i
$537$	15.8306	−	13.5823i	0.683140	−	0.586119i
$538$	−3.92492	−	1.81188i	−0.169215	−	0.0781159i
$539$	9.60612	−	9.60612i	0.413765	−	0.413765i
$540$	−11.6673	+	20.0966i	−0.502082	+	0.864820i
$541$	6.46105	+	6.46105i	0.277782	+	0.277782i	0.832223	−	0.554441i	$-0.187068\pi$
$541$	6.46105	+	6.46105i	0.277782	+	0.277782i	−0.554441	+	0.832223i	$0.687068\pi$
$542$	2.97180	−	1.09460i	0.127650	−	0.0470172i
$543$	−24.2621	−	28.2783i	−1.04119	−	1.21354i
$544$	−2.97519	+	4.42775i	−0.127560	+	0.189838i
$545$	−9.89084	−	2.18639i	−0.423677	−	0.0936547i
$546$	−14.6895	−	8.19319i	−0.628654	−	0.350636i
$547$	9.33984	−	16.1771i	0.399343	−	0.691682i	−0.594302	−	0.804242i	$-0.702572\pi$
$547$	9.33984	−	16.1771i	0.399343	−	0.691682i	0.993645	+	0.112560i	$0.0359050\pi$
$548$	1.00682	+	0.693507i	0.0430091	+	0.0296252i
$549$	30.6718	−	3.36329i	1.30904	−	0.143542i
$550$	3.60492	+	19.8554i	0.153714	+	0.846638i
$551$	−12.8560	+	22.2673i	−0.547685	+	0.948619i
$552$	29.9894	−	26.3367i	1.27643	−	1.12096i
$553$	0.0482197	+	0.0129204i	0.00205051	+	0.000549432i
$554$	29.8888	+	5.15183i	1.26985	+	0.218880i
$555$	3.30609	+	6.17516i	0.140336	+	0.262121i
$556$	−9.62956	−	20.2429i	−0.408384	−	0.858490i
$557$			11.6193i			0.492328i	0.969228	+	0.246164i	$0.0791701\pi$
$557$			11.6193i			0.492328i	−0.969228	+	0.246164i	$0.920830\pi$
$558$	21.3874	+	24.1928i	0.905403	+	1.02416i
$559$		−	5.89568i		−	0.249361i
$560$	−10.4881	+	8.31758i	−0.443205	+	0.351482i
$561$	2.63159	−	3.84750i	0.111106	−	0.162442i
$562$	2.25561	−	13.0861i	0.0951470	−	0.552005i
$563$	0.913854	+	1.58284i	0.0385144	+	0.0667088i	0.884640	−	0.466275i	$-0.154404\pi$
$563$	0.913854	+	1.58284i	0.0385144	+	0.0667088i	−0.846126	+	0.532983i	$0.821071\pi$
$564$	−16.7441	−	13.5256i	−0.705053	−	0.569529i
$565$	1.14330	+	3.61836i	0.0480991	+	0.152226i
$566$	−27.5633	−	22.9484i	−1.15857	−	0.964593i
$567$	13.4567	+	0.583897i	0.565127	+	0.0245214i
$568$	14.4576	−	25.7218i	0.606627	−	1.07926i
$569$	12.6800	+	7.32080i	0.531573	+	0.306904i	0.741657	−	0.670779i	$-0.234040\pi$
$569$	12.6800	+	7.32080i	0.531573	+	0.306904i	−0.210084	+	0.977683i	$0.567374\pi$
$570$	−2.67489	−	45.2344i	−0.112039	−	1.89466i
$571$	−40.8004	−	10.9324i	−1.70744	−	0.457508i	−0.732648	−	0.680608i	$-0.761716\pi$
$571$	−40.8004	−	10.9324i	−1.70744	−	0.457508i	−0.974796	+	0.223100i	$0.928382\pi$
$572$	−2.08186	+	26.1057i	−0.0870468	+	1.09153i
$573$	−23.7922	+	34.7853i	−0.993935	+	1.45317i
$574$	−15.3899	−	7.10455i	−0.642363	−	0.296538i
$575$	−31.2370	−	26.1458i	−1.30267	−	1.09036i
$576$	9.21502	+	22.1604i	0.383959	+	0.923350i
$577$	16.5723	−	16.5723i	0.689916	−	0.689916i	−0.272297	−	0.962213i	$-0.587783\pi$
$577$	16.5723	−	16.5723i	0.689916	−	0.689916i	0.962213	+	0.272297i	$0.0877834\pi$
$578$	7.87483	+	21.3799i	0.327550	+	0.889285i
$579$	−25.0798	−	8.81779i	−1.04228	−	0.366455i
$580$	−13.8904	−	0.490994i	−0.576768	−	0.0203874i
$581$	−0.724959	+	2.70558i	−0.0300764	+	0.112247i
$582$	9.79251	−	5.84889i	0.405913	−	0.242444i
$583$	3.75915	+	14.0293i	0.155688	+	0.581036i
$584$	1.97017	+	7.02758i	0.0815260	+	0.290803i
$585$	24.8350	+	18.1812i	1.02680	+	0.751702i
$586$	−13.2734	+	15.9426i	−0.548318	+	0.658585i
$587$	−8.55171	+	14.8120i	−0.352967	+	0.611357i	−0.986768	−	0.162140i	$-0.948161\pi$
$587$	−8.55171	+	14.8120i	−0.352967	+	0.611357i	0.633801	+	0.773496i	$0.281494\pi$
$588$	−15.0723	−	6.68879i	−0.621573	−	0.275841i
$589$	−60.8214	−	16.2970i	−2.50610	−	0.671508i
$590$	6.00265	+	7.75103i	0.247125	+	0.319105i
$591$	−2.70203	+	35.3488i	−0.111147	+	1.45406i
$592$	7.14277	+	1.14652i	0.293566	+	0.0471218i
$593$	19.5601	−	19.5601i	0.803237	−	0.803237i	−0.180363	−	0.983600i	$-0.557727\pi$
$593$	19.5601	−	19.5601i	0.803237	−	0.803237i	0.983600	+	0.180363i	$0.0577274\pi$
$594$	−7.89238	−	19.4299i	−0.323828	−	0.797220i
$595$	−0.139584	−	3.15269i	−0.00572240	−	0.129248i
$596$	36.9505	−	17.5774i	1.51355	−	0.719998i
$597$	−0.516687	+	6.75945i	−0.0211466	+	0.276646i
$598$	−30.4878	−	43.1868i	−1.24674	−	1.76604i
$599$	20.3938	−	11.7744i	0.833270	−	0.481089i	−0.0217011	−	0.999765i	$-0.506908\pi$
$599$	20.3938	−	11.7744i	0.833270	−	0.481089i	0.854971	+	0.518676i	$0.173575\pi$
$600$	20.9166	−	12.7474i	0.853916	−	0.520410i
$601$	−8.27115	−	4.77535i	−0.337387	−	0.194791i	0.321729	−	0.946832i	$-0.395736\pi$
$601$	−8.27115	−	4.77535i	−0.337387	−	0.194791i	−0.659116	+	0.752041i	$0.729069\pi$
$602$	0.247442	+	2.70833i	0.0100850	+	0.110383i
$603$	−0.663091	−	1.70445i	−0.0270031	−	0.0694108i
$604$	−19.4681	+	3.58729i	−0.792147	+	0.145965i
$605$	5.66511	+	2.94466i	0.230319	+	0.119717i
$606$	22.8362	+	38.2335i	0.927656	+	1.55313i
$607$	−2.07653	−	0.556404i	−0.0842836	−	0.0225837i	0.216431	−	0.976298i	$-0.430558\pi$
$607$	−2.07653	−	0.556404i	−0.0842836	−	0.0225837i	−0.300714	+	0.953714i	$0.597225\pi$
$608$	−38.8447	−	26.1014i	−1.57536	−	1.05855i
$609$	3.48467	+	7.26367i	0.141206	+	0.294339i
$610$	−30.1040	−	12.3126i	−1.21888	−	0.498523i
$611$	−20.1592	+	20.1592i	−0.815554	+	0.815554i
$612$	−5.50629	−	1.30181i	−0.222578	−	0.0526227i
$613$	33.7691			1.36392			0.681960	−	0.731389i	$-0.261128\pi$
$613$	33.7691			1.36392			0.681960	+	0.731389i	$0.261128\pi$
$614$	24.8770	−	9.16293i	1.00395	−	0.369786i
$615$	26.3517	+	16.3617i	1.06260	+	0.659767i
$616$	−0.139305	−	12.0797i	−0.00561274	−	0.486705i
$617$	−26.9502	−	7.22130i	−1.08498	−	0.290718i	−0.328343	−	0.944558i	$-0.606490\pi$
$617$	−26.9502	−	7.22130i	−1.08498	−	0.290718i	−0.756633	+	0.653840i	$0.773157\pi$
$618$	−0.455272	−	30.7188i	−0.0183137	−	1.23569i
$619$	24.0407	−	6.44168i	0.966276	−	0.258913i	0.259021	−	0.965872i	$-0.416600\pi$
$619$	24.0407	−	6.44168i	0.966276	−	0.258913i	0.707255	+	0.706959i	$0.249933\pi$
$620$	−7.64270	−	33.1687i	−0.306938	−	1.33209i
$621$	37.3387	+	19.9482i	1.49835	+	0.800495i
$622$	2.91237	+	2.42476i	0.116776	+	0.0972239i
$623$	−1.57898	−	5.89285i	−0.0632607	−	0.236092i
$624$	30.4776	−	9.03356i	1.22008	−	0.361632i
$625$	−16.1166	−	19.1117i	−0.644663	−	0.764467i
$626$	24.1683	+	34.2351i	0.965960	+	1.36831i
$627$	33.7541	+	23.0870i	1.34801	+	0.922004i
$628$	−15.1982	−	5.39975i	−0.606475	−	0.215473i
$629$	−1.20596	+	1.20596i	−0.0480849	+	0.0480849i
$630$	−12.1717	−	7.30970i	−0.484931	−	0.291225i
$631$		−	19.2146i		−	0.764921i	−0.923972	−	0.382461i	$-0.875077\pi$
$631$		−	19.2146i		−	0.764921i	0.923972	−	0.382461i	$-0.124923\pi$
$632$	−0.0811563	+	0.0481119i	−0.00322823	+	0.00191379i
$633$	31.4128	+	11.0444i	1.24855	+	0.438976i
$634$	28.4963	+	4.91180i	1.13173	+	0.195073i
$635$	6.44617	+	1.42494i	0.255808	+	0.0565470i
$636$	14.2503	−	10.3798i	0.565060	−	0.411586i
$637$	−10.9205	+	18.9148i	−0.432685	+	0.749433i
$638$	8.02589	−	9.63989i	0.317748	−	0.381647i
$639$	30.9327	+	4.75674i	1.22368	+	0.188174i
$640$	2.61068	−	25.1632i	0.103196	−	0.994661i
$641$	3.98048	+	2.29813i	0.157220	+	0.0907708i	0.576546	−	0.817065i	$-0.304400\pi$
$641$	3.98048	+	2.29813i	0.157220	+	0.0907708i	−0.419326	+	0.907836i	$0.637734\pi$
$642$	−10.5109	−	37.0236i	−0.414832	−	1.46120i
$643$	34.3107	−	19.8093i	1.35308	−	0.781201i	0.364401	−	0.931242i	$-0.381274\pi$
$643$	34.3107	−	19.8093i	1.35308	−	0.781201i	0.988680	+	0.150041i	$0.0479405\pi$
$644$	15.8179	+	18.5594i	0.623313	+	0.731343i
$645$	0.159448	−	4.97406i	0.00627828	−	0.195853i
$646$	10.3532	−	3.81338i	0.407340	−	0.150035i
$647$	11.0731	−	11.0731i	0.435330	−	0.435330i	−0.455107	−	0.890437i	$-0.650399\pi$
$647$	11.0731	−	11.0731i	0.435330	−	0.435330i	0.890437	+	0.455107i	$0.150399\pi$
$648$	−18.5638	+	17.4180i	−0.729253	+	0.684244i
$649$	−8.84752			−0.347296
$650$	−13.8602	−	29.3341i	−0.543641	−	1.15058i
$651$	−14.9734	+	12.8468i	−0.586854	+	0.503508i
$652$	21.2714	+	24.9581i	0.833053	+	0.977434i
$653$	16.5232	+	28.6190i	0.646602	+	1.11995i	0.983929	+	0.178560i	$0.0571438\pi$
$653$	16.5232	+	28.6190i	0.646602	+	1.11995i	−0.337327	+	0.941387i	$0.609523\pi$
$654$	−9.69095	−	5.40520i	−0.378946	−	0.211360i
$655$	10.7580	+	34.0473i	0.420350	+	1.33034i
$656$	29.9313	−	11.4182i	1.16862	−	0.445807i
$657$	−6.24227	+	4.57832i	−0.243534	+	0.178617i
$658$	8.41457	−	10.1067i	0.328034	−	0.394002i
$659$	−28.6748	+	7.68339i	−1.11701	+	0.299302i	−0.769673	−	0.638438i	$-0.779581\pi$
$659$	−28.6748	+	7.68339i	−1.11701	+	0.299302i	−0.347338	+	0.937740i	$0.612914\pi$
$660$	−2.46245	+	21.9685i	−0.0958506	+	0.855124i
$661$	37.1525	+	9.95499i	1.44507	+	0.387204i	0.894305	−	0.447458i	$-0.147671\pi$
$661$	37.1525	+	9.95499i	1.44507	+	0.387204i	0.550762	+	0.834663i	$0.314337\pi$
$662$	−6.91368	−	9.79342i	−0.268708	−	0.380632i
$663$	−2.48571	+	7.06993i	−0.0965371	+	0.274573i
$664$	−2.69954	−	4.55365i	−0.104762	−	0.176716i
$665$	27.6585	−	1.22457i	1.07255	−	0.0474869i
$666$	1.52686	+	7.51958i	0.0591648	+	0.291378i
$667$			25.3204i			0.980411i
$668$	42.8515	−	20.3845i	1.65798	−	0.788700i
$669$	3.64374	+	19.4160i	0.140875	+	0.750667i
$670$	−0.243111	+	1.91243i	−0.00939221	+	0.0738838i
$671$	25.4203	−	14.6764i	0.981339	−	0.566576i
$672$	−13.6215	+	5.42895i	−0.525462	+	0.209426i
$673$	47.7823	−	12.8032i	1.84187	−	0.493528i	0.842867	−	0.538123i	$-0.180866\pi$
$673$	47.7823	−	12.8032i	1.84187	−	0.493528i	0.999005	+	0.0445946i	$0.0141996\pi$
$674$	−2.03045	+	0.185509i	−0.0782101	+	0.00714553i
$675$	20.4610	+	16.0108i	0.787546	+	0.616256i
$676$	−2.91823	−	15.8371i	−0.112239	−	0.609121i
$677$	8.22549	−	14.2470i	0.316131	−	0.547555i	−0.663546	−	0.748135i	$-0.730949\pi$
$677$	8.22549	−	14.2470i	0.316131	−	0.547555i	0.979677	+	0.200580i	$0.0642827\pi$
$678$	0.0616008	+	4.15642i	0.00236576	+	0.159626i
$679$	3.48451	+	6.03534i	0.133723	+	0.231615i
$680$	4.44583	+	3.97562i	0.170490	+	0.152458i
$681$	19.4669	−	28.4614i	0.745973	−	1.09064i
$682$	27.8900	+	12.8750i	1.06796	+	0.493011i
$683$			5.92490i			0.226710i	0.993555	+	0.113355i	$0.0361597\pi$
$683$			5.92490i			0.226710i	−0.993555	+	0.113355i	$0.963840\pi$
$684$	11.4208	−	48.3066i	0.436685	−	1.84705i
$685$	0.922816	−	1.00832i	0.0352590	−	0.0385258i
$686$	10.4324	−	22.5987i	0.398311	−	0.862823i
$687$	−20.3749	−	7.16361i	−0.777352	−	0.273309i
$688$	−3.98767	−	3.24289i	−0.152028	−	0.123634i
$689$	−11.6754	−	20.2224i	−0.444798	−	0.770413i
$690$	−24.5539	−	37.2604i	−0.934752	−	1.41848i
$691$	45.5588	−	12.2074i	1.73314	−	0.464393i	0.752235	−	0.658895i	$-0.228976\pi$
$691$	45.5588	−	12.2074i	1.73314	−	0.464393i	0.980902	+	0.194502i	$0.0623091\pi$
$692$	−4.19665	−	22.7751i	−0.159533	−	0.865780i
$693$	11.9415	−	4.64564i	0.453620	−	0.176473i
$694$	23.3914	+	19.4750i	0.887926	+	0.739261i
$695$	−23.8979	+	7.55108i	−0.906499	+	0.286429i
$696$	−14.4210	−	4.88418i	−0.546628	−	0.185134i
$697$	−1.95471	+	7.29507i	−0.0740399	+	0.276321i
$698$	−4.75858	−	6.74065i	−0.180115	−	0.255138i
$699$	−26.7986	+	22.9926i	−1.01362	+	0.869661i
$700$	7.59818	+	12.8937i	0.287184	+	0.487335i
$701$	−23.1203	+	23.1203i	−0.873242	+	0.873242i	−0.992824	−	0.119583i	$-0.961844\pi$
$701$	−23.1203	+	23.1203i	−0.873242	+	0.873242i	0.119583	+	0.992824i	$0.461844\pi$
$702$	20.3413	+	26.8893i	0.767731	+	1.01487i
$703$	−10.5799	−	10.5799i	−0.399029	−	0.399029i
$704$	16.5120	+	15.7674i	0.622321	+	0.594257i
$705$	−17.5531	+	16.4627i	−0.661088	+	0.620021i
$706$	2.16777	+	3.07071i	0.0815851	+	0.115568i
$707$	−23.5642	+	13.6048i	−0.886222	+	0.511660i
$708$	3.86075	+	10.0213i	0.145096	+	0.376625i
$709$	−48.2779	+	12.9360i	−1.81312	+	0.485823i	−0.995896	−	0.0905039i	$-0.971152\pi$
$709$	−48.2779	+	12.9360i	−1.81312	+	0.485823i	−0.817219	+	0.576327i	$0.804486\pi$
$710$	−26.2614	−	19.9657i	−0.985571	−	0.749301i
$711$	−0.0780504	−	0.0626248i	−0.00292712	−	0.00234861i
$712$	10.0509	+	5.64939i	0.376675	+	0.211720i
$713$	−59.8950	+	16.0488i	−2.24309	+	0.601033i
$714$	0.845151	−	3.35208i	0.0316290	−	0.125448i
$715$	28.5896	+	6.31979i	1.06919	+	0.236347i
$716$	−24.0093	−	1.91468i	−0.897271	−	0.0715548i
$717$	16.8965	−	8.10591i	0.631011	−	0.302721i
$718$	4.68770	+	12.7269i	0.174943	+	0.474965i
$719$	−24.8428			−0.926482			−0.463241	−	0.886232i	$-0.653314\pi$
$719$	−24.8428			−0.926482			−0.463241	+	0.886232i	$0.653314\pi$
$720$	25.9576	−	6.79716i	0.967384	−	0.253315i
$721$	18.7707			0.699056
$722$	24.1676	+	65.6142i	0.899427	+	2.44191i
$723$	10.3907	+	7.10701i	0.386436	+	0.264312i
$724$	−3.42020	+	42.8881i	−0.127111	+	1.59392i
$725$	−2.67968	+	15.3069i	−0.0995209	+	0.568483i
$726$	5.01832	+	4.87174i	0.186247	+	0.180807i
$727$	9.92931	−	2.66055i	0.368258	−	0.0986744i	−0.0699442	−	0.997551i	$-0.522282\pi$
$727$	9.92931	−	2.66055i	0.368258	−	0.0986744i	0.438202	+	0.898877i	$0.355615\pi$
$728$	5.24278	+	18.7010i	0.194310	+	0.693105i
$729$	−24.2204	−	11.9320i	−0.897051	−	0.441926i
$730$	8.08536	−	1.10114i	0.299253	−	0.0407549i
$731$	1.17044	−	0.313619i	0.0432904	−	0.0115996i
$732$	−27.7160	−	22.3885i	−1.02441	−	0.827504i
$733$	15.1643	−	8.75511i	0.560106	−	0.323377i	−0.193082	−	0.981183i	$-0.561848\pi$
$733$	15.1643	−	8.75511i	0.560106	−	0.323377i	0.753188	+	0.657805i	$0.228515\pi$
$734$	−15.8533	−	22.4566i	−0.585155	−	0.828888i
$735$	−9.72493	+	15.6627i	−0.358709	+	0.577727i
$736$	−45.9800	−	3.13364i	−1.69484	−	0.115508i
$737$	−1.23024	−	1.23024i	−0.0453164	−	0.0453164i
$738$	22.5050	+	25.4570i	0.828422	+	0.937087i
$739$	−5.82170	+	5.82170i	−0.214155	+	0.214155i	−0.806030	−	0.591875i	$-0.798388\pi$
$739$	−5.82170	+	5.82170i	−0.214155	+	0.214155i	0.591875	+	0.806030i	$0.298388\pi$
$740$	2.36803	−	7.73367i	0.0870504	−	0.284295i
$741$	−62.0245	−	21.8072i	−2.27853	−	0.801106i
$742$	6.21214	+	8.79967i	0.228055	+	0.323046i
$743$	−0.389207	+	1.45254i	−0.0142786	+	0.0532886i	−0.972698	−	0.232076i	$-0.925448\pi$
$743$	−0.389207	+	1.45254i	−0.0142786	+	0.0532886i	0.958419	+	0.285365i	$0.0921148\pi$
$744$	2.41296	−	37.2084i	0.0884634	−	1.36413i
$745$	−13.7834	−	43.6222i	−0.504985	−	1.59819i
$746$	4.13613	+	3.44362i	0.151435	+	0.126080i
$747$	3.51385	−	4.37938i	0.128565	−	0.160233i
$748$	−5.29340	+	0.975386i	−0.193546	+	0.0356636i
$749$	22.7134	−	6.08604i	0.829930	−	0.222379i
$750$	−10.9002	−	25.1234i	−0.398019	−	0.917377i
$751$	6.46666	+	11.2006i	0.235972	+	0.408715i	0.959555	−	0.281522i	$-0.0908393\pi$
$751$	6.46666	+	11.2006i	0.235972	+	0.408715i	−0.723583	+	0.690238i	$0.757506\pi$
$752$	2.54662	+	24.7236i	0.0928659	+	0.901576i
$753$	4.50099	−	3.86175i	0.164025	−	0.140730i
$754$	−8.45243	+	18.3097i	−0.307820	+	0.666801i
$755$	0.978948	+	22.1108i	0.0356276	+	0.804695i
$756$	−10.4728	−	11.4986i	−0.380893	−	0.418199i
$757$		−	13.9938i		−	0.508612i	−0.967124	−	0.254306i	$-0.918153\pi$
$757$		−	13.9938i		−	0.508612i	0.967124	−	0.254306i	$-0.0818470\pi$
$758$	0.763871	+	0.352630i	0.0277450	+	0.0128081i
$759$	40.1543	+	3.06936i	1.45751	+	0.111411i
$760$	−34.8781	+	39.0033i	−1.26516	+	1.41480i
$761$	12.1093	+	20.9740i	0.438962	+	0.760305i	0.997610	−	0.0691001i	$-0.0220128\pi$
$761$	12.1093	+	20.9740i	0.438962	+	0.760305i	−0.558647	+	0.829405i	$0.688679\pi$
$762$	6.31590	+	3.52274i	0.228801	+	0.127615i
$763$	3.38986	−	5.87140i	0.122721	−	0.212559i
$764$	47.8576	−	8.81846i	1.73143	−	0.319041i
$765$	−2.28835	+	5.89753i	−0.0827355	+	0.213226i
$766$	−21.3599	+	1.95151i	−0.771764	+	0.0705109i
$767$	13.7396	−	3.68152i	0.496108	−	0.132932i
$768$	10.6540	−	25.5830i	0.384444	−	0.923148i
$769$	27.1778	−	15.6911i	0.980056	−	0.565836i	0.0777691	−	0.996971i	$-0.475220\pi$
$769$	27.1778	−	15.6911i	0.980056	−	0.565836i	0.902287	+	0.431136i	$0.141887\pi$
$770$	−13.3986	−	1.70325i	−0.482852	−	0.0613809i
$771$	−0.210677	−	0.0740717i	−0.00758733	−	0.00266763i
$772$	13.1868	+	27.7208i	0.474603	+	0.997692i
$773$			33.4712i			1.20387i	0.798544	+	0.601937i	$0.205604\pi$
$773$			33.4712i			1.20387i	−0.798544	+	0.601937i	$0.794396\pi$
$774$	1.73181	−	5.16922i	0.0622486	−	0.185804i
$775$	−37.9065	+	3.36319i	−1.36164	+	0.120809i
$776$	−12.7605	−	3.26193i	−0.458075	−	0.117096i
$777$	−4.60765	+	0.864700i	−0.165298	+	0.0310209i
$778$	−4.63126	−	6.56031i	−0.166039	−	0.235199i
$779$	−63.9996	−	17.1486i	−2.29302	−	0.614414i
$780$	−5.31725	−	35.1403i	−0.190388	−	1.25822i
$781$	28.7576	−	7.70558i	1.02903	−	0.275727i
$782$	6.95190	−	8.34992i	0.248599	−	0.298593i
$783$	−0.531652	−	16.1405i	−0.0189997	−	0.576815i
$784$	6.78668	+	17.7903i	0.242381	+	0.635368i
$785$	−8.31679	+	16.0003i	−0.296839	+	0.571076i
$786$	0.579638	+	39.1102i	0.0206750	+	1.39501i
$787$	11.4530	+	19.8372i	0.408257	+	0.707122i	0.994695	−	0.102873i	$-0.0328035\pi$
$787$	11.4530	+	19.8372i	0.408257	+	0.707122i	−0.586438	+	0.809994i	$0.699470\pi$
$788$	31.1559	−	26.5537i	1.10988	−	0.945936i
$789$	−5.08597	−	27.1011i	−0.181065	−	0.964825i
$790$	0.0408000	+	0.0972715i	0.00145160	+	0.00346076i
$791$	−2.53977			−0.0903040
$792$	−9.49368	+	22.2775i	−0.337343	+	0.791596i
$793$	−33.3690	+	33.3690i	−1.18497	+	1.18497i
$794$	−8.09796	+	2.98272i	−0.287386	+	0.105853i
$795$	−9.30339	−	17.3770i	−0.329957	−	0.616298i
$796$	5.95767	−	5.07764i	0.211164	−	0.179972i
$797$	−2.16215	+	1.24832i	−0.0765873	+	0.0442177i	−0.537805	−	0.843070i	$-0.680746\pi$
$797$	−2.16215	+	1.24832i	−0.0765873	+	0.0442177i	0.461217	+	0.887287i	$0.347413\pi$
$798$	29.4078	+	7.41451i	1.04102	+	0.262471i
$799$	−5.07448	−	2.92975i	−0.179522	−	0.103647i
$800$	−27.4645	−	6.76047i	−0.971015	−	0.239019i
$801$	−1.85872	+	12.0872i	−0.0656748	+	0.427079i
$802$	−20.1030	+	24.1457i	−0.709860	+	0.852613i
$803$	−3.68211	+	6.37760i	−0.129939	+	0.225061i
$804$	−0.856621	+	1.93029i	−0.0302107	+	0.0680760i
$805$	22.9852	−	14.6630i	0.810122	−	0.516802i
$806$	−48.6687	−	8.38884i	−1.71428	−	0.295484i
$807$	−4.01823	+	3.44756i	−0.141449	+	0.121360i
$808$	12.7358	−	49.8216i	0.448042	−	1.75272i
$809$			52.9515i			1.86168i	0.365433	+	0.930838i	$0.380921\pi$
$809$			52.9515i			1.86168i	−0.365433	+	0.930838i	$0.619079\pi$
$810$	16.4343	+	23.2361i	0.577441	+	0.816432i
$811$	26.7587	−	26.7587i	0.939626	−	0.939626i	−0.0586521	−	0.998278i	$-0.518680\pi$
$811$	26.7587	−	26.7587i	0.939626	−	0.939626i	0.998278	+	0.0586521i	$0.0186803\pi$
$812$	3.11438	−	8.76579i	0.109293	−	0.307619i
$813$	0.295625	−	3.86746i	0.0103680	−	0.135638i
$814$	4.20967	+	5.96312i	0.147549	+	0.209007i
$815$	30.9098	−	19.7183i	1.08272	−	0.690702i
$816$	3.41464	+	5.57005i	0.119536	+	0.194991i
$817$	2.75138	+	10.2683i	0.0962586	+	0.359242i
$818$	10.6909	+	8.90091i	0.373798	+	0.311213i
$819$	−16.6112	+	12.1833i	−0.580443	+	0.425719i
$820$	−8.04207	−	34.9019i	−0.280841	−	1.21883i
$821$	6.14337	−	1.64611i	0.214405	−	0.0574497i	−0.150017	−	0.988683i	$-0.547933\pi$
$821$	6.14337	−	1.64611i	0.214405	−	0.0574497i	0.364423	+	0.931234i	$0.381266\pi$
$822$	1.28548	−	0.767791i	0.0448361	−	0.0267798i
$823$	−25.4843	−	6.82850i	−0.888327	−	0.238026i	−0.214331	−	0.976761i	$-0.568757\pi$
$823$	−25.4843	−	6.82850i	−0.888327	−	0.238026i	−0.673996	+	0.738735i	$0.735424\pi$
$824$	−24.7936	+	25.3721i	−0.863726	+	0.883880i
$825$	23.9495	+	6.10507i	0.833815	+	0.212551i
$826$	−6.15713	+	2.26785i	−0.214234	+	0.0789086i
$827$	13.1979			0.458938			0.229469	−	0.973316i	$-0.426301\pi$
$827$	13.1979			0.458938			0.229469	+	0.973316i	$0.426301\pi$
$828$	−14.0454	−	46.8210i	−0.488110	−	1.62714i
$829$	0.849642	−	0.849642i	0.0295093	−	0.0295093i	−0.692198	−	0.721707i	$-0.743358\pi$
$829$	0.849642	−	0.849642i	0.0295093	−	0.0295093i	0.721707	+	0.692198i	$0.243358\pi$
$830$	−5.45786	+	2.28927i	−0.189445	+	0.0794616i
$831$	20.9708	−	30.6602i	0.727470	−	1.06359i
$832$	−32.2030	−	17.6150i	−1.11644	−	0.610689i
$833$	−4.33599	−	1.16182i	−0.150233	−	0.0402548i
$834$	−27.4516	+	0.406850i	−0.950570	+	0.0140881i
$835$	−15.9846	−	50.5887i	−0.553171	−	1.75069i
$836$	−8.55705	−	46.4389i	−0.295952	−	1.60612i
$837$	37.8431	−	11.4879i	1.30805	−	0.397081i
$838$	3.88531	+	42.5259i	0.134216	+	1.46903i
$839$	16.3113	+	9.41735i	0.563129	+	0.325123i	0.754401	−	0.656414i	$-0.227928\pi$
$839$	16.3113	+	9.41735i	0.563129	+	0.325123i	−0.191271	+	0.981537i	$0.561261\pi$
$840$	3.91746	+	15.9194i	0.135165	+	0.549273i
$841$	−16.7496	+	9.67039i	−0.577572	+	0.333462i
$842$	−22.1163	−	31.3284i	−0.762179	−	1.07965i
$843$	−13.4239	−	9.18158i	−0.462343	−	0.316231i
$844$	−16.5167	−	34.7207i	−0.568527	−	1.19514i
$845$	−17.9869	+	0.796365i	−0.618769	+	0.0273958i
$846$	−23.5968	+	11.7536i	−0.811276	+	0.404098i
$847$	−3.02165	+	3.02165i	−0.103825	+	0.103825i
$848$	−20.0999	−	3.22633i	−0.690232	−	0.110793i
$849$	−39.6049	+	19.0000i	−1.35924	+	0.652079i
$850$	5.08628	−	4.31202i	0.174458	−	0.147901i
$851$	−14.2323	−	3.81353i	−0.487877	−	0.130726i
$852$	−21.2767	−	29.2105i	−0.728927	−	1.00073i
$853$	−0.503117	+	0.871424i	−0.0172264	+	0.0298370i	−0.874510	−	0.485007i	$-0.838817\pi$
$853$	−0.503117	+	0.871424i	−0.0172264	+	0.0298370i	0.857284	+	0.514844i	$0.172150\pi$
$854$	13.9284	−	16.7294i	0.476620	−	0.572469i
$855$	−51.7390	−	20.0757i	−1.76944	−	0.686574i
$856$	−21.7750	+	38.7403i	−0.744255	+	1.32412i
$857$	4.22393	+	15.7639i	0.144287	+	0.538485i	0.999786	+	0.0206816i	$0.00658362\pi$
$857$	4.22393	+	15.7639i	0.144287	+	0.538485i	−0.855499	+	0.517804i	$0.826750\pi$
$858$	28.0118	+	15.6238i	0.956307	+	0.533387i
$859$	8.72663	−	32.5682i	0.297749	−	1.11121i	−0.641261	−	0.767323i	$-0.721588\pi$
$859$	8.72663	−	32.5682i	0.297749	−	1.11121i	0.939010	−	0.343891i	$-0.111745\pi$
$860$	−4.20439	+	3.91731i	−0.143369	+	0.133579i
$861$	−15.7558	+	13.5182i	−0.536958	+	0.460698i
$862$	−5.98897	−	16.2598i	−0.203985	−	0.553812i
$863$	−5.62919	+	5.62919i	−0.191620	+	0.191620i	−0.796396	−	0.604776i	$-0.793263\pi$
$863$	−5.62919	+	5.62919i	−0.191620	+	0.191620i	0.604776	+	0.796396i	$0.293263\pi$
$864$	29.3758	+	1.03210i	0.999383	+	0.0351128i
$865$	−25.8667	+	1.14524i	−0.879494	+	0.0389393i
$866$	4.60592	+	2.12626i	0.156516	+	0.0722533i
$867$	27.8234	+	2.12680i	0.944933	+	0.0722299i
$868$	22.7093	+	1.81100i	0.770804	+	0.0614694i
$869$	−0.0919512	−	0.0246383i	−0.00311923	−	0.000835795i
$870$	−7.62633	+	15.2189i	−0.258557	+	0.515970i
$871$	2.42239	+	1.39857i	0.0820794	+	0.0473886i
$872$	3.45876	+	12.3374i	0.117128	+	0.417797i
$873$	−1.52272	−	13.8865i	−0.0515361	−	0.469988i
$874$	73.2538	+	60.9889i	2.47785	+	2.06298i
$875$	15.4469	−	6.43161i	0.522202	−	0.217428i
$876$	8.83046	+	1.38766i	0.298354	+	0.0468845i
$877$	23.6326	+	40.9328i	0.798015	+	1.38220i	0.920907	+	0.389783i	$0.127450\pi$
$877$	23.6326	+	40.9328i	0.798015	+	1.38220i	−0.122892	+	0.992420i	$0.539217\pi$
$878$	1.77661	−	10.3072i	0.0599577	−	0.347850i
$879$	10.9896	+	22.9075i	0.370671	+	0.772651i
$880$	20.0001	−	15.8610i	0.674202	−	0.534674i
$881$		−	28.6298i		−	0.964564i	−0.876016	−	0.482282i	$-0.839808\pi$
$881$		−	28.6298i		−	0.964564i	0.876016	−	0.482282i	$-0.160192\pi$
$882$	−15.1310	+	13.3764i	−0.509486	+	0.450406i
$883$			46.4560i			1.56337i	0.623674	+	0.781685i	$0.285639\pi$
$883$			46.4560i			1.56337i	−0.623674	+	0.781685i	$0.714361\pi$
$884$	7.81442	−	3.71733i	0.262827	−	0.125027i
$885$	11.6914	−	2.73443i	0.393001	−	0.0919168i
$886$	31.3708	+	5.40727i	1.05392	+	0.181661i
$887$	−43.4193	−	11.6342i	−1.45788	−	0.390637i	−0.559121	−	0.829086i	$-0.688861\pi$
$887$	−43.4193	−	11.6342i	−1.45788	−	0.390637i	−0.898756	+	0.438450i	$0.855528\pi$
$888$	4.91729	−	7.37027i	0.165014	−	0.247330i
$889$	−2.20928	+	3.82658i	−0.0740967	+	0.128339i
$890$	7.80174	−	10.2618i	0.261515	−	0.343976i
$891$	−25.6608	−	1.11345i	−0.859670	−	0.0373019i
$892$	12.9399	−	18.7858i	0.433259	−	0.628994i
$893$	25.7027	−	44.5184i	0.860108	−	1.48975i
$894$	−0.742647	−	50.1089i	−0.0248378	−	1.67589i
$895$	−5.81228	+	26.2937i	−0.194283	+	0.878902i
$896$	15.5326	+	6.74033i	0.518907	+	0.225179i
$897$	−63.6341	+	11.9420i	−2.12468	+	0.398731i
$898$	−28.2963	+	10.4224i	−0.944261	+	0.347799i
$899$	16.7264	+	16.7264i	0.557857	+	0.557857i
$900$	−3.53568	−	29.7909i	−0.117856	−	0.993031i
$901$	3.39359	−	3.39359i	0.113057	−	0.113057i
$902$	29.3474	+	13.5478i	0.977162	+	0.451094i
$903$	3.14227	+	1.10479i	0.104568	+	0.0367651i
$904$	3.35471	−	3.43299i	0.111576	−	0.114179i
$905$	46.9687	+	10.3825i	1.56129	+	0.345127i
$906$	−5.92731	+	23.5092i	−0.196922	+	0.781041i
$907$	17.7477	+	10.2466i	0.589302	+	0.340234i	0.764822	−	0.644242i	$-0.222827\pi$
$907$	17.7477	+	10.2466i	0.589302	+	0.340234i	−0.175519	+	0.984476i	$0.556160\pi$
$908$	−39.1573	+	7.21530i	−1.29948	+	0.239448i
$909$	54.2180	−	5.94523i	1.79830	−	0.197191i
$910$	21.5158	−	2.93022i	0.713243	−	0.0971358i
$911$	−24.9662	−	14.4142i	−0.827166	−	0.477564i	0.0257155	−	0.999669i	$-0.491814\pi$
$911$	−24.9662	−	14.4142i	−0.827166	−	0.477564i	−0.852881	+	0.522105i	$0.825147\pi$
$912$	−48.8660	+	29.9566i	−1.61811	+	0.991963i
$913$	1.38244	−	5.15934i	0.0457521	−	0.170749i
$914$	24.6950	−	17.4335i	0.816838	−	0.576648i
$915$	−29.0552	+	27.2503i	−0.960535	+	0.900866i
$916$	10.7130	+	22.5205i	0.353968	+	0.744097i
$917$	−23.8982			−0.789188
$918$	−4.25617	+	5.46863i	−0.140474	+	0.180492i
$919$	−29.0046			−0.956772			−0.478386	−	0.878150i	$-0.658778\pi$
$919$	−29.0046			−0.956772			−0.478386	+	0.878150i	$0.658778\pi$
$920$	−10.5406	+	50.4368i	−0.347515	+	1.66285i
$921$	2.47468	−	32.3746i	0.0815436	−	1.06678i
$922$	11.5870	+	16.4133i	0.381598	+	0.540544i
$923$	−41.4523	+	23.9325i	−1.36442	+	0.787747i
$924$	−13.5237	−	6.00153i	−0.444896	−	0.197436i
$925$	−8.20020	−	3.81159i	−0.269621	−	0.125324i
$926$	−0.718438	−	7.86353i	−0.0236093	−	0.258412i
$927$	−34.4423	−	15.1494i	−1.13123	−	0.497572i
$928$	7.73494	+	15.7882i	0.253912	+	0.518272i
$929$	−15.5583	+	26.9477i	−0.510450	+	0.884126i	0.489476	+	0.872017i	$0.337188\pi$
$929$	−15.5583	+	26.9477i	−0.510450	+	0.884126i	−0.999927	+	0.0121094i	$0.996145\pi$
$930$	−40.8339	−	8.39373i	−1.33900	−	0.275241i
$931$	10.1927	−	38.0396i	0.334051	−	1.24670i
$932$	40.6439	+	3.24124i	1.33134	+	0.106170i
$933$	4.18470	−	2.00757i	0.137001	−	0.0657247i
$934$	−4.00862	−	10.8832i	−0.131166	−	0.356111i
$935$	0.266177	+	6.01194i	0.00870490	+	0.196611i
$936$	5.47323	−	38.5458i	0.178898	−	1.25991i
$937$	9.62546	+	9.62546i	0.314450	+	0.314450i	0.846631	−	0.532181i	$-0.178627\pi$
$937$	9.62546	+	9.62546i	0.314450	+	0.314450i	−0.532181	+	0.846631i	$0.678627\pi$
$938$	−1.17148	−	0.540799i	−0.0382503	−	0.0176577i
$939$	50.4441	−	9.46665i	1.64618	−	0.308933i
$940$	27.7707	+	0.981630i	0.905780	+	0.0320172i
$941$	26.0289	+	6.97442i	0.848517	+	0.227360i	0.656776	−	0.754086i	$-0.271920\pi$
$941$	26.0289	+	6.97442i	0.848517	+	0.227360i	0.191742	+	0.981445i	$0.438586\pi$
$942$	−13.7596	+	14.1735i	−0.448311	+	0.461799i
$943$	−63.0248	+	16.8875i	−2.05237	+	0.549931i
$944$	5.06733	−	11.3181i	0.164928	−	0.368372i
$945$	−14.3440	+	9.82955i	−0.466612	+	0.319755i
$946$	−0.471853	−	5.16458i	−0.0153413	−	0.167915i
$947$	−27.2240	−	15.7178i	−0.884660	−	0.510759i	−0.0124678	−	0.999922i	$-0.503969\pi$
$947$	−27.2240	−	15.7178i	−0.884660	−	0.510759i	−0.872192	+	0.489164i	$0.837302\pi$
$948$	0.0122173	+	0.114902i	0.000396798	+	0.00373183i
$949$	3.06430	−	11.4361i	0.0994715	−	0.371233i
$950$	37.8293	+	44.6219i	1.22734	+	1.44773i
$951$	19.9938	−	29.2318i	0.648343	−	0.947905i
$952$	−3.43374	+	2.03562i	−0.111288	+	0.0659749i
$953$	−15.1771	−	15.1771i	−0.491634	−	0.491634i	0.417187	−	0.908821i	$-0.363016\pi$
$953$	−15.1771	−	15.1771i	−0.491634	−	0.491634i	−0.908821	+	0.417187i	$0.863016\pi$
$954$	−4.29662	−	21.1602i	−0.139108	−	0.685087i
$955$	−2.40650	−	54.3539i	−0.0778726	−	1.75885i
$956$	−20.3907	−	7.24456i	−0.659481	−	0.234306i
$957$	−6.64500	−	13.8513i	−0.214802	−	0.447748i
$958$	−1.05398	+	6.11475i	−0.0340524	+	0.197559i
$959$	0.457415	+	0.792267i	0.0147707	+	0.0255836i
$960$	−26.6926	−	15.7323i	−0.861500	−	0.507758i
$961$	−13.4643	+	23.3209i	−0.434334	+	0.752288i
$962$	−9.01863	−	7.50864i	−0.290772	−	0.242088i
$963$	−46.5887	−	7.16426i	−1.50130	−	0.230865i
$964$	−2.63417	−	14.2956i	−0.0848410	−	0.460430i
$965$	32.7260	−	10.3405i	1.05349	−	0.332873i
$966$	28.7308	−	8.15659i	0.924397	−	0.262434i
$967$	−2.60279	+	9.71376i	−0.0837002	+	0.312374i	−0.995065	−	0.0992264i	$-0.968363\pi$
$967$	−2.60279	+	9.71376i	−0.0837002	+	0.312374i	0.911365	+	0.411600i	$0.135030\pi$
$968$	−0.0931282	−	8.07555i	−0.00299325	−	0.259558i
$969$	1.02990	−	13.4735i	0.0330852	−	0.432830i
$970$	−5.57449	+	13.6295i	−0.178986	+	0.437617i
$971$	1.05533	+	1.05533i	0.0338670	+	0.0338670i	0.723838	−	0.689970i	$-0.242377\pi$
$971$	1.05533	+	1.05533i	0.0338670	+	0.0338670i	−0.689970	+	0.723838i	$0.742377\pi$
$972$	9.93632	+	29.5511i	0.318708	+	0.947853i
$973$		−	16.7742i		−	0.537757i
$974$	7.94793	+	3.66905i	0.254668	+	0.117564i
$975$	−39.7323	+	0.484788i	−1.27245	+	0.0155256i
$976$	4.21536	+	40.9243i	0.134930	+	1.30995i
$977$	−2.08663	+	7.78742i	−0.0667573	+	0.249142i	−0.991238	−	0.132087i	$-0.957832\pi$
$977$	−2.08663	+	7.78742i	−0.0667573	+	0.249142i	0.924481	+	0.381229i	$0.124499\pi$
$978$	38.6362	−	10.9687i	1.23545	−	0.350741i
$979$	3.01100	+	11.2372i	0.0962321	+	0.359143i
$980$	20.7447	−	4.77998i	0.662666	−	0.152691i
$981$	−10.9587	+	8.03755i	−0.349886	+	0.256619i
$982$	−4.46120	−	48.8293i	−0.142363	−	1.55820i
$983$	18.5105	−	4.95986i	0.590392	−	0.158195i	0.0487595	−	0.998811i	$-0.484473\pi$
$983$	18.5105	−	4.95986i	0.590392	−	0.158195i	0.541632	+	0.840616i	$0.317807\pi$
$984$	2.53905	−	39.1527i	0.0809419	−	1.24814i
$985$	−24.6149	−	38.5855i	−0.784296	−	1.22944i
$986$	−4.08457	−	0.704043i	−0.130079	−	0.0224213i
$987$	−6.96680	−	14.5221i	−0.221756	−	0.462242i
$988$	32.6121	+	68.5558i	1.03753	+	2.18105i
$989$	7.40242	+	7.40242i	0.235383	+	0.235383i
$990$	23.2104	+	13.9390i	0.737676	+	0.443012i
$991$	0.235643			0.00748544			0.00374272	−	0.999993i	$-0.498809\pi$
$991$	0.235643			0.00748544			0.00374272	+	0.999993i	$0.498809\pi$
$992$	−32.4440	+	28.3039i	−1.03010	+	0.898648i
$993$	−14.4302	+	2.70807i	−0.457929	+	0.0859379i
$994$	18.0377	−	12.7338i	0.572122	−	0.403890i
$995$	−4.70690	−	7.37837i	−0.149219	−	0.233910i
$996$	−6.44708	+	0.685505i	−0.204284	+	0.0217210i
$997$	23.5265	+	13.5830i	0.745091	+	0.430178i	0.823917	−	0.566710i	$-0.191784\pi$
$997$	23.5265	+	13.5830i	0.745091	+	0.430178i	−0.0788266	+	0.996888i	$0.525117\pi$
$998$	−5.84881	+	0.534366i	−0.185141	+	0.0169151i
$999$	9.15245	+	2.13210i	0.289571	+	0.0674567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cq.a.173.15	yes	560
5.2	odd	4		720.2.cm.a.317.55	yes	560
9.5	odd	6	inner	720.2.cq.a.653.62	yes	560
16.5	even	4		720.2.cm.a.533.8	yes	560
45.32	even	12		720.2.cm.a.77.8	✓	560
80.37	odd	4	inner	720.2.cq.a.677.62	yes	560
144.5	odd	12		720.2.cm.a.293.55	yes	560
720.437	even	12	inner	720.2.cq.a.437.15	yes	560

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cm.a.77.8	✓	560	45.32	even	12
720.2.cm.a.293.55	yes	560	144.5	odd	12
720.2.cm.a.317.55	yes	560	5.2	odd	4
720.2.cm.a.533.8	yes	560	16.5	even	4
720.2.cq.a.173.15	yes	560	1.1	even	1	trivial
720.2.cq.a.437.15	yes	560	720.437	even	12	inner
720.2.cq.a.653.62	yes	560	9.5	odd	6	inner
720.2.cq.a.677.62	yes	560	80.37	odd	4	inner

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32706 + 0.488794i) q^{2} +(-0.132011 + 1.72701i) q^{3} +(1.52216 - 1.29732i) q^{4} +(-1.20259 - 1.88514i) q^{5} +(-0.668967 - 2.35637i) q^{6} +(1.44560 - 0.387347i) q^{7} +(-1.38587 + 2.46563i) q^{8} +(-2.96515 - 0.455971i) q^{9} +O(q^{10})\)	\(q+(-1.32706 + 0.488794i) q^{2} +(-0.132011 + 1.72701i) q^{3} +(1.52216 - 1.29732i) q^{4} +(-1.20259 - 1.88514i) q^{5} +(-0.668967 - 2.35637i) q^{6} +(1.44560 - 0.387347i) q^{7} +(-1.38587 + 2.46563i) q^{8} +(-2.96515 - 0.455971i) q^{9} +(2.51736 + 1.91387i) q^{10} +(-2.75664 + 0.738640i) q^{11} +(2.03954 + 2.80005i) q^{12} +(3.97353 - 2.29412i) q^{13} +(-1.72906 + 1.22063i) q^{14} +(3.41442 - 1.82803i) q^{15} +(0.633945 - 3.94944i) q^{16} +(0.666811 + 0.666811i) q^{17} +(4.15779 - 0.844247i) q^{18} +(-5.84993 + 5.84993i) q^{19} +(-4.27617 - 1.30935i) q^{20} +(0.478117 + 2.54770i) q^{21} +(3.29718 - 2.32765i) q^{22} +(-2.10861 + 7.86944i) q^{23} +(-4.07523 - 2.71891i) q^{24} +(-2.10754 + 4.53412i) q^{25} +(-4.15174 + 4.98666i) q^{26} +(1.17890 - 5.06065i) q^{27} +(1.69792 - 2.46500i) q^{28} +(3.00203 - 0.804391i) q^{29} +(-3.63760 + 4.09486i) q^{30} +(3.80555 + 6.59140i) q^{31} +(1.08918 + 5.55101i) q^{32} +(-0.911733 - 4.85827i) q^{33} +(-1.21083 - 0.558963i) q^{34} +(-2.46867 - 2.25934i) q^{35} +(-5.10497 + 3.15267i) q^{36} +1.80855i q^{37} +(4.90378 - 10.6226i) q^{38} +(3.43742 + 7.16518i) q^{39} +(6.31472 - 0.352584i) q^{40} +(4.00440 + 6.93583i) q^{41} +(-1.87979 - 3.14724i) q^{42} +(0.642478 - 1.11280i) q^{43} +(-3.23780 + 4.70057i) q^{44} +(2.70629 + 6.13808i) q^{45} +(-1.04829 - 11.4739i) q^{46} +(-6.00187 + 1.60820i) q^{47} +(6.73705 + 1.61620i) q^{48} +(-4.12246 + 2.38011i) q^{49} +(0.580570 - 7.04719i) q^{50} +(-1.23962 + 1.06357i) q^{51} +(3.07215 - 8.64693i) q^{52} -5.08929i q^{53} +(0.909150 + 7.29201i) q^{54} +(4.70756 + 4.30839i) q^{55} +(-1.04836 + 4.10113i) q^{56} +(-9.33065 - 10.8752i) q^{57} +(-3.59068 + 2.53485i) q^{58} +(2.99453 + 0.802382i) q^{59} +(2.82577 - 7.21215i) q^{60} +(-9.93474 + 2.66201i) q^{61} +(-8.27201 - 6.88703i) q^{62} +(-4.46303 + 0.489390i) q^{63} +(-4.15871 - 6.83412i) q^{64} +(-9.10328 - 4.73178i) q^{65} +(3.58461 + 6.00155i) q^{66} +(0.304816 + 0.527956i) q^{67} +(1.88006 + 0.149929i) q^{68} +(-13.3123 - 4.68045i) q^{69} +(4.38042 + 1.79160i) q^{70} -10.4321 q^{71} +(5.23357 - 6.67905i) q^{72} +(1.82463 - 1.82463i) q^{73} +(-0.884009 - 2.40005i) q^{74} +(-7.55227 - 4.23830i) q^{75} +(-1.31533 + 16.4937i) q^{76} +(-3.69889 + 2.13555i) q^{77} +(-8.06395 - 7.82841i) q^{78} +(0.0288873 + 0.0166781i) q^{79} +(-8.20765 + 3.55450i) q^{80} +(8.58418 + 2.70404i) q^{81} +(-8.70427 - 7.24691i) q^{82} +(-0.935801 + 1.62086i) q^{83} +(4.03294 + 3.25774i) q^{84} +(0.455133 - 2.05894i) q^{85} +(-0.308673 + 1.79080i) q^{86} +(0.992892 + 5.29073i) q^{87} +(1.99914 - 7.82054i) q^{88} -4.07641i q^{89} +(-6.59166 - 6.82275i) q^{90} +(4.85550 - 4.85550i) q^{91} +(6.99950 + 14.7141i) q^{92} +(-11.8858 + 5.70209i) q^{93} +(7.17875 - 5.06785i) q^{94} +(18.0631 + 3.99288i) q^{95} +(-9.73044 + 1.14824i) q^{96} +(1.20521 + 4.49792i) q^{97} +(4.30736 - 5.17357i) q^{98} +(8.51065 - 0.933228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6}+O(q^{10}) \) 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6	\( 560 q - 6 q^{2} - 6 q^{5} - 8 q^{6} - 12 q^{11} - 10 q^{12} - 8 q^{15} - 4 q^{16} + 20 q^{18} - 6 q^{20} - 8 q^{21} + 6 q^{22} - 24 q^{24} + 8 q^{28} + 28 q^{30} - 8 q^{31} + 54 q^{32} - 8 q^{33} - 12 q^{34} + 8 q^{36} - 18 q^{38} - 24 q^{39} + 8 q^{40} - 46 q^{42} - 4 q^{43} - 14 q^{45} - 40 q^{46} - 12 q^{47} - 22 q^{48} - 6 q^{50} - 8 q^{51} - 18 q^{52} + 24 q^{54} - 12 q^{56} + 24 q^{57} - 10 q^{58} - 88 q^{60} - 4 q^{61} + 20 q^{63} - 24 q^{64} - 12 q^{65} + 24 q^{66} - 4 q^{67} - 30 q^{68} + 12 q^{69} + 2 q^{70} - 22 q^{72} + 24 q^{74} - 66 q^{75} + 8 q^{76} - 12 q^{77} - 122 q^{78} - 16 q^{81} - 12 q^{84} - 12 q^{85} - 12 q^{86} + 12 q^{87} - 10 q^{88} - 94 q^{90} - 16 q^{91} - 120 q^{92} - 12 q^{95} + 48 q^{96} - 4 q^{97} + 32 q^{99}+O(q^{100}) \) 560 * q - 6 * q^2 - 6 * q^5 - 8 * q^6 - 12 * q^11 - 10 * q^12 - 8 * q^15 - 4 * q^16 + 20 * q^18 - 6 * q^20 - 8 * q^21 + 6 * q^22 - 24 * q^24 + 8 * q^28 + 28 * q^30 - 8 * q^31 + 54 * q^32 - 8 * q^33 - 12 * q^34 + 8 * q^36 - 18 * q^38 - 24 * q^39 + 8 * q^40 - 46 * q^42 - 4 * q^43 - 14 * q^45 - 40 * q^46 - 12 * q^47 - 22 * q^48 - 6 * q^50 - 8 * q^51 - 18 * q^52 + 24 * q^54 - 12 * q^56 + 24 * q^57 - 10 * q^58 - 88 * q^60 - 4 * q^61 + 20 * q^63 - 24 * q^64 - 12 * q^65 + 24 * q^66 - 4 * q^67 - 30 * q^68 + 12 * q^69 + 2 * q^70 - 22 * q^72 + 24 * q^74 - 66 * q^75 + 8 * q^76 - 12 * q^77 - 122 * q^78 - 16 * q^81 - 12 * q^84 - 12 * q^85 - 12 * q^86 + 12 * q^87 - 10 * q^88 - 94 * q^90 - 16 * q^91 - 120 * q^92 - 12 * q^95 + 48 * q^96 - 4 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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