LMFDB - Embedded newform 110.2.j.b.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(9,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("110.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.j (of order $10$, 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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 8 x^{14} + 10 x^{13} - 109 x^{12} + 280 x^{11} - 198 x^{10} - 1168 x^{9} + \cdots + 390625 $ x^16 - 4x^15 + 8x^14 + 10x^13 - 109x^12 + 280x^11 - 198x^10 - 1168x^9 + 4281x^8 - 5840x^7 - 4950x^6 + 35000x^5 - 68125x^4 + 31250x^3 + 125000x^2 - 312500*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			59.2
Root			$-2.23122 + 0.147217i$ of defining polynomial
Character	$\chi$	$=$	110.59
Dual form			110.2.j.b.69.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-1.53884 - 0.500000i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.829496 - 2.07652i) q^{5} +(1.30902 - 0.951057i) q^{6} +(4.76878 - 1.54947i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.224514i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.53884 - 0.500000i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.829496 - 2.07652i) q^{5} +(1.30902 - 0.951057i) q^{6} +(4.76878 - 1.54947i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.224514i) q^{9} +(2.16751 + 0.549472i) q^{10} +(-0.969425 - 3.17178i) q^{11} +1.61803i q^{12} +(-1.37249 + 1.88906i) q^{13} +(-1.54947 + 4.76878i) q^{14} +(0.238203 + 3.61018i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.0359433 - 0.0494717i) q^{17} +(0.363271 - 0.118034i) q^{18} +(0.636930 - 1.96027i) q^{19} +(-1.71856 + 1.43058i) q^{20} -8.11314 q^{21} +(3.13584 + 1.08005i) q^{22} -3.91525i q^{23} +(-1.30902 - 0.951057i) q^{24} +(-3.62387 + 3.44493i) q^{25} +(-0.721558 - 2.22073i) q^{26} +(3.21644 + 4.42705i) q^{27} +(-2.94727 - 4.05657i) q^{28} +(1.27844 + 3.93464i) q^{29} +(-3.06071 - 1.92930i) q^{30} +(7.18170 + 5.21781i) q^{31} -1.00000i q^{32} +(-0.0941007 + 5.36559i) q^{33} +0.0611504 q^{34} +(-7.17320 - 8.61720i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(-4.33385 + 1.40815i) q^{37} +(1.21151 + 1.66751i) q^{38} +(3.05657 - 2.22073i) q^{39} +(-0.147217 - 2.23122i) q^{40} +(-1.41525 + 4.35570i) q^{41} +(4.76878 - 6.56367i) q^{42} -3.61803i q^{43} +(-2.71698 + 1.90211i) q^{44} +(-0.209880 + 0.827913i) q^{45} +(3.16751 + 2.30133i) q^{46} +(8.44260 + 2.74317i) q^{47} +(1.53884 - 0.500000i) q^{48} +(14.6773 - 10.6637i) q^{49} +(-0.656948 - 4.95665i) q^{50} +(0.0305752 + 0.0941007i) q^{51} +(2.22073 + 0.721558i) q^{52} +(-1.30598 + 1.79753i) q^{53} -5.47214 q^{54} +(-5.78214 + 4.64401i) q^{55} +5.01420 q^{56} +(-1.96027 + 2.69808i) q^{57} +(-3.93464 - 1.27844i) q^{58} +(-0.599137 - 1.84396i) q^{59} +(3.35988 - 1.34215i) q^{60} +(7.84211 - 5.69763i) q^{61} +(-8.44260 + 2.74317i) q^{62} +(-1.82151 - 0.591846i) q^{63} +(0.809017 + 0.587785i) q^{64} +(5.06115 + 1.28302i) q^{65} +(-4.28554 - 3.22994i) q^{66} +2.49573i q^{67} +(-0.0359433 + 0.0494717i) q^{68} +(-1.95763 + 6.02495i) q^{69} +(11.1878 - 0.738177i) q^{70} +(-7.13254 + 5.18210i) q^{71} +(-0.224514 - 0.309017i) q^{72} +(5.13205 - 1.66751i) q^{73} +(1.40815 - 4.33385i) q^{74} +(7.29903 - 3.48927i) q^{75} -2.06115 q^{76} +(-9.53757 - 13.6235i) q^{77} +3.77813i q^{78} +(-5.38417 - 3.91183i) q^{79} +(1.89162 + 1.19237i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(-2.69197 - 3.70518i) q^{82} +(6.49620 + 8.94125i) q^{83} +(2.50710 + 7.71605i) q^{84} +(-0.0729142 + 0.115674i) q^{85} +(2.92705 + 2.12663i) q^{86} -6.69401i q^{87} +(0.0581575 - 3.31611i) q^{88} -6.09017 q^{89} +(-0.546432 - 0.656431i) q^{90} +(-3.61803 + 11.1352i) q^{91} +(-3.72363 + 1.20988i) q^{92} +(-8.44260 - 11.6202i) q^{93} +(-7.18170 + 5.21781i) q^{94} +(-4.59887 + 0.303437i) q^{95} +(-0.500000 + 1.53884i) q^{96} +(-4.29216 + 5.90765i) q^{97} +18.1422i q^{98} +(-0.412541 + 1.19778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 - 6 * q^5 + 12 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 20 q^{11} - 12 q^{14} + 2 q^{15} - 4 q^{16} - 16 q^{19} + 6 q^{20} - 16 q^{21} - 12 q^{24} - 16 q^{26} + 16 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{34} - 48 q^{35} + 16 q^{36} - 8 q^{39} - 4 q^{40} + 40 q^{41} - 4 q^{45} + 20 q^{46} + 84 q^{49} + 4 q^{50} - 4 q^{51} - 16 q^{54} + 32 q^{55} - 8 q^{56} + 8 q^{60} + 20 q^{61} + 4 q^{64} + 72 q^{65} - 20 q^{66} + 36 q^{70} - 56 q^{71} + 4 q^{74} + 32 q^{75} - 24 q^{76} + 36 q^{79} + 4 q^{80} - 56 q^{81} - 4 q^{84} - 54 q^{85} + 20 q^{86} - 8 q^{89} - 4 q^{90} - 40 q^{91} + 4 q^{94} - 50 q^{95} - 8 q^{96} - 20 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 - 6 * q^5 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 20 * q^11 - 12 * q^14 + 2 * q^15 - 4 * q^16 - 16 * q^19 + 6 * q^20 - 16 * q^21 - 12 * q^24 - 16 * q^26 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^34 - 48 * q^35 + 16 * q^36 - 8 * q^39 - 4 * q^40 + 40 * q^41 - 4 * q^45 + 20 * q^46 + 84 * q^49 + 4 * q^50 - 4 * q^51 - 16 * q^54 + 32 * q^55 - 8 * q^56 + 8 * q^60 + 20 * q^61 + 4 * q^64 + 72 * q^65 - 20 * q^66 + 36 * q^70 - 56 * q^71 + 4 * q^74 + 32 * q^75 - 24 * q^76 + 36 * q^79 + 4 * q^80 - 56 * q^81 - 4 * q^84 - 54 * q^85 + 20 * q^86 - 8 * q^89 - 4 * q^90 - 40 * q^91 + 4 * q^94 - 50 * q^95 - 8 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−1.53884	−	0.500000i	−0.888451	−	0.288675i	−0.170989	−	0.985273i	$-0.554696\pi$
$3$	−1.53884	−	0.500000i	−0.888451	−	0.288675i	−0.717462	+	0.696598i	$0.754696\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−0.829496	−	2.07652i	−0.370962	−	0.928648i
$5$	−0.829496	−	2.07652i	−0.370962	−	0.928648i
$6$	1.30902	−	0.951057i	0.534404	−	0.388267i
$7$	4.76878	−	1.54947i	1.80243	−	0.585645i	0.802491	−	0.596664i	$-0.203507\pi$
$7$	4.76878	−	1.54947i	1.80243	−	0.585645i	0.999939	+	0.0110184i	$0.00350733\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−0.309017	−	0.224514i	−0.103006	−	0.0748380i
$10$	2.16751	+	0.549472i	0.685425	+	0.173758i
$11$	−0.969425	−	3.17178i	−0.292293	−	0.956329i
$11$	−0.969425	−	3.17178i	−0.292293	−	0.956329i
$12$			1.61803i			0.467086i
$13$	−1.37249	+	1.88906i	−0.380659	+	0.523932i	−0.955759	−	0.294151i	$-0.904963\pi$
$13$	−1.37249	+	1.88906i	−0.380659	+	0.523932i	0.575100	+	0.818083i	$0.304963\pi$
$14$	−1.54947	+	4.76878i	−0.414114	+	1.27451i
$15$	0.238203	+	3.61018i	0.0615037	+	0.932146i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.0359433	−	0.0494717i	−0.00871753	−	0.0119986i	0.804636	−	0.593768i	$-0.202360\pi$
$17$	−0.0359433	−	0.0494717i	−0.00871753	−	0.0119986i	−0.813354	+	0.581770i	$0.802360\pi$
$18$	0.363271	−	0.118034i	0.0856239	−	0.0278209i
$19$	0.636930	−	1.96027i	0.146122	−	0.449717i	−0.851032	−	0.525114i	$-0.824023\pi$
$19$	0.636930	−	1.96027i	0.146122	−	0.449717i	0.997154	+	0.0753974i	$0.0240226\pi$
$20$	−1.71856	+	1.43058i	−0.384282	+	0.319887i
$21$	−8.11314			−1.77043
$22$	3.13584	+	1.08005i	0.668564	+	0.230267i
$23$		−	3.91525i		−	0.816387i	−0.912896	−	0.408193i	$-0.866159\pi$
$23$		−	3.91525i		−	0.816387i	0.912896	−	0.408193i	$-0.133841\pi$
$24$	−1.30902	−	0.951057i	−0.267202	−	0.194134i
$25$	−3.62387	+	3.44493i	−0.724775	+	0.688986i
$26$	−0.721558	−	2.22073i	−0.141509	−	0.435521i
$27$	3.21644	+	4.42705i	0.619004	+	0.851986i
$28$	−2.94727	−	4.05657i	−0.556982	−	0.766620i
$29$	1.27844	+	3.93464i	0.237401	+	0.730644i	0.996794	+	0.0800122i	$0.0254959\pi$
$29$	1.27844	+	3.93464i	0.237401	+	0.730644i	−0.759393	+	0.650632i	$0.774504\pi$
$30$	−3.06071	−	1.92930i	−0.558807	−	0.352241i
$31$	7.18170	+	5.21781i	1.28987	+	0.937147i	0.999803	−	0.0198592i	$-0.00632179\pi$
$31$	7.18170	+	5.21781i	1.28987	+	0.937147i	0.290069	+	0.957006i	$0.406322\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.0941007	+	5.36559i	−0.0163808	+	0.934029i
$34$	0.0611504			0.0104872
$35$	−7.17320	−	8.61720i	−1.21249	−	1.45657i
$36$	−0.118034	+	0.363271i	−0.0196723	+	0.0605452i
$37$	−4.33385	+	1.40815i	−0.712481	+	0.231499i	−0.642760	−	0.766067i	$-0.722211\pi$
$37$	−4.33385	+	1.40815i	−0.712481	+	0.231499i	−0.0697209	+	0.997567i	$0.522211\pi$
$38$	1.21151	+	1.66751i	0.196533	+	0.270505i
$39$	3.05657	−	2.22073i	0.489443	−	0.355601i
$40$	−0.147217	−	2.23122i	−0.0232771	−	0.352786i
$41$	−1.41525	+	4.35570i	−0.221025	+	0.680246i	0.777646	+	0.628703i	$0.216414\pi$
$41$	−1.41525	+	4.35570i	−0.221025	+	0.680246i	−0.998671	+	0.0515429i	$0.983586\pi$
$42$	4.76878	−	6.56367i	0.735839	−	1.01280i
$43$		−	3.61803i		−	0.551745i	−0.961194	−	0.275873i	$-0.911033\pi$
$43$		−	3.61803i		−	0.551745i	0.961194	−	0.275873i	$-0.0889668\pi$
$44$	−2.71698	+	1.90211i	−0.409600	+	0.286754i
$45$	−0.209880	+	0.827913i	−0.0312870	+	0.123418i
$46$	3.16751	+	2.30133i	0.467023	+	0.339312i
$47$	8.44260	+	2.74317i	1.23148	+	0.400132i	0.851250	−	0.524760i	$-0.175845\pi$
$47$	8.44260	+	2.74317i	1.23148	+	0.400132i	0.380229	+	0.924892i	$0.375845\pi$
$48$	1.53884	−	0.500000i	0.222113	−	0.0721688i
$49$	14.6773	−	10.6637i	2.09676	−	1.52338i
$50$	−0.656948	−	4.95665i	−0.0929065	−	0.700977i
$51$	0.0305752	+	0.0941007i	0.00428138	+	0.0131767i
$52$	2.22073	+	0.721558i	0.307960	+	0.100062i
$53$	−1.30598	+	1.79753i	−0.179391	+	0.246910i	−0.889237	−	0.457446i	$-0.848764\pi$
$53$	−1.30598	+	1.79753i	−0.179391	+	0.246910i	0.709847	+	0.704356i	$0.248764\pi$
$54$	−5.47214			−0.744663
$55$	−5.78214	+	4.64401i	−0.779664	+	0.626199i
$56$	5.01420			0.670050
$57$	−1.96027	+	2.69808i	−0.259644	+	0.357370i
$58$	−3.93464	−	1.27844i	−0.516643	−	0.167868i
$59$	−0.599137	−	1.84396i	−0.0780011	−	0.240063i	0.904451	−	0.426577i	$-0.140281\pi$
$59$	−0.599137	−	1.84396i	−0.0780011	−	0.240063i	−0.982452	+	0.186515i	$0.940281\pi$
$60$	3.35988	−	1.34215i	0.433759	−	0.173271i
$61$	7.84211	−	5.69763i	1.00408	−	0.729506i	0.0411202	−	0.999154i	$-0.486907\pi$
$61$	7.84211	−	5.69763i	1.00408	−	0.729506i	0.962959	+	0.269648i	$0.0869073\pi$
$62$	−8.44260	+	2.74317i	−1.07221	+	0.348382i
$63$	−1.82151	−	0.591846i	−0.229489	−	0.0745655i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	5.06115	+	1.28302i	0.627758	+	0.159139i
$66$	−4.28554	−	3.22994i	−0.527513	−	0.397578i
$67$			2.49573i			0.304902i	0.988311	+	0.152451i	$0.0487167\pi$
$67$			2.49573i			0.304902i	−0.988311	+	0.152451i	$0.951283\pi$
$68$	−0.0359433	+	0.0494717i	−0.00435876	+	0.00599932i
$69$	−1.95763	+	6.02495i	−0.235670	+	0.725319i
$70$	11.1878	−	0.738177i	1.33719	−	0.0882290i
$71$	−7.13254	+	5.18210i	−0.846477	+	0.615002i	−0.924172	−	0.381975i	$-0.875244\pi$
$71$	−7.13254	+	5.18210i	−0.846477	+	0.615002i	0.0776953	+	0.996977i	$0.475244\pi$
$72$	−0.224514	−	0.309017i	−0.0264592	−	0.0364180i
$73$	5.13205	−	1.66751i	0.600662	−	0.195167i	0.00712611	−	0.999975i	$-0.497732\pi$
$73$	5.13205	−	1.66751i	0.600662	−	0.195167i	0.593535	+	0.804808i	$0.297732\pi$
$74$	1.40815	−	4.33385i	0.163695	−	0.503800i
$75$	7.29903	−	3.48927i	0.842820	−	0.402906i
$76$	−2.06115			−0.236430
$77$	−9.53757	−	13.6235i	−1.08691	−	1.55254i
$78$			3.77813i			0.427789i
$79$	−5.38417	−	3.91183i	−0.605766	−	0.440115i	0.242155	−	0.970238i	$-0.422146\pi$
$79$	−5.38417	−	3.91183i	−0.605766	−	0.440115i	−0.847921	+	0.530123i	$0.822146\pi$
$80$	1.89162	+	1.19237i	0.211490	+	0.133312i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	−2.69197	−	3.70518i	−0.297278	−	0.409169i
$83$	6.49620	+	8.94125i	0.713050	+	0.981429i	0.999726	+	0.0234017i	$0.00744968\pi$
$83$	6.49620	+	8.94125i	0.713050	+	0.981429i	−0.286676	+	0.958028i	$0.592550\pi$
$84$	2.50710	+	7.71605i	0.273547	+	0.841890i
$85$	−0.0729142	+	0.115674i	−0.00790865	+	0.0125466i
$86$	2.92705	+	2.12663i	0.315632	+	0.229320i
$87$		−	6.69401i		−	0.717673i
$88$	0.0581575	−	3.31611i	0.00619961	−	0.353499i
$89$	−6.09017			−0.645557			−0.322778	−	0.946475i	$-0.604617\pi$
$89$	−6.09017			−0.645557			−0.322778	+	0.946475i	$0.604617\pi$
$90$	−0.546432	−	0.656431i	−0.0575990	−	0.0691939i
$91$	−3.61803	+	11.1352i	−0.379273	+	1.16728i
$92$	−3.72363	+	1.20988i	−0.388215	+	0.126139i
$93$	−8.44260	−	11.6202i	−0.875456	−	1.20496i
$94$	−7.18170	+	5.21781i	−0.740736	+	0.538176i
$95$	−4.59887	+	0.303437i	−0.471834	+	0.0311320i
$96$	−0.500000	+	1.53884i	−0.0510310	+	0.157057i
$97$	−4.29216	+	5.90765i	−0.435802	+	0.599831i	−0.969273	−	0.245988i	$-0.920888\pi$
$97$	−4.29216	+	5.90765i	−0.435802	+	0.599831i	0.533470	+	0.845819i	$0.320888\pi$
$98$			18.1422i			1.83263i
$99$	−0.412541	+	1.19778i	−0.0414620	+	0.120382i
$100$	4.39616	+	2.38197i	0.439616	+	0.238197i
$101$	0.179498	+	0.130413i	0.0178608	+	0.0129766i	0.596680	−	0.802479i	$-0.296486\pi$
$101$	0.179498	+	0.130413i	0.0178608	+	0.0129766i	−0.578819	+	0.815456i	$0.696486\pi$
$102$	−0.0941007	−	0.0305752i	−0.00931736	−	0.00302739i
$103$	0.538341	−	0.174918i	0.0530443	−	0.0172351i	−0.282375	−	0.959304i	$-0.591122\pi$
$103$	0.538341	−	0.174918i	0.0530443	−	0.0172351i	0.335419	+	0.942069i	$0.391122\pi$
$104$	−1.88906	+	1.37249i	−0.185238	+	0.134583i
$105$	6.72982	+	16.8471i	0.656763	+	1.64411i
$106$	−0.686596	−	2.11313i	−0.0666881	−	0.205245i
$107$	−2.12087	−	0.689113i	−0.205033	−	0.0666191i	0.204700	−	0.978825i	$-0.434378\pi$
$107$	−2.12087	−	0.689113i	−0.205033	−	0.0666191i	−0.409733	+	0.912206i	$0.634378\pi$
$108$	3.21644	−	4.42705i	0.309502	−	0.425993i
$109$	−7.86288			−0.753127			−0.376563	−	0.926391i	$-0.622894\pi$
$109$	−7.86288			−0.753127			−0.376563	+	0.926391i	$0.622894\pi$
$110$	−0.358428	−	7.40753i	−0.0341748	−	0.706280i
$111$	7.37319			0.699832
$112$	−2.94727	+	4.05657i	−0.278491	+	0.383310i
$113$	11.9469	+	3.88177i	1.12387	+	0.365166i	0.811242	−	0.584710i	$-0.198792\pi$
$113$	11.9469	+	3.88177i	1.12387	+	0.365166i	0.312624	+	0.949877i	$0.398792\pi$
$114$	−1.03058	−	3.17178i	−0.0965222	−	0.297065i
$115$	−8.13010	+	3.24769i	−0.758136	+	0.302848i
$116$	3.34700	−	2.43174i	0.310762	−	0.225781i
$117$	0.848243	−	0.275611i	0.0784200	−	0.0254802i
$118$	1.84396	+	0.599137i	0.169750	+	0.0551551i
$119$	−0.248061	−	0.180227i	−0.0227397	−	0.0165214i
$120$	−0.889064	+	3.50710i	−0.0811601	+	0.320153i
$121$	−9.12043	+	6.14961i	−0.829130	+	0.559056i
$122$			9.69338i			0.877597i
$123$	4.35570	−	5.99511i	0.392740	−	0.540560i
$124$	2.74317	−	8.44260i	0.246344	−	0.758168i
$125$	10.1595	+	4.66749i	0.908689	+	0.417473i
$126$	1.54947	−	1.12576i	0.138038	−	0.100290i
$127$	−8.50112	−	11.7008i	−0.754353	−	1.03828i	−0.997663	−	0.0683289i	$-0.978233\pi$
$127$	−8.50112	−	11.7008i	−0.754353	−	1.03828i	0.243310	−	0.969949i	$-0.421767\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−1.80902	+	5.56758i	−0.159275	+	0.490198i
$130$	−4.01286	+	3.34041i	−0.351951	+	0.292974i
$131$	15.3256			1.33900			0.669502	−	0.742810i	$-0.266507\pi$
$131$	15.3256			1.33900			0.669502	+	0.742810i	$0.266507\pi$
$132$	5.13205	−	1.56856i	0.446688	−	0.136526i
$133$		−	10.3350i		−	0.896159i
$134$	−2.01909	−	1.46696i	−0.174423	−	0.126726i
$135$	6.52484	−	10.3512i	0.561569	−	0.890892i
$136$	−0.0188965	−	0.0581575i	−0.00162036	−	0.00498696i
$137$	0.649130	+	0.893451i	0.0554589	+	0.0763326i	0.835846	−	0.548964i	$-0.184978\pi$
$137$	0.649130	+	0.893451i	0.0554589	+	0.0763326i	−0.780387	+	0.625297i	$0.784978\pi$
$138$	−3.72363	−	5.12513i	−0.316976	−	0.436280i
$139$	3.06115	+	9.42125i	0.259643	+	0.799100i	0.992879	+	0.119126i	$0.0380092\pi$
$139$	3.06115	+	9.42125i	0.259643	+	0.799100i	−0.733236	+	0.679974i	$0.761991\pi$
$140$	−5.97880	+	9.48497i	−0.505301	+	0.801627i
$141$	−11.6202	−	8.44260i	−0.978600	−	0.710995i
$142$		−	8.81631i		−	0.739848i
$143$	7.32222	+	2.52192i	0.612315	+	0.210894i
$144$	0.381966			0.0318305
$145$	7.10990	−	5.91848i	0.590445	−	0.491503i
$146$	−1.66751	+	5.13205i	−0.138004	+	0.424732i
$147$	−27.9179	+	9.07108i	−2.30263	+	0.748170i
$148$	2.67847	+	3.68660i	0.220169	+	0.303036i
$149$	7.11314	−	5.16800i	0.582731	−	0.423379i	−0.256977	−	0.966418i	$-0.582726\pi$
$149$	7.11314	−	5.16800i	0.582731	−	0.423379i	0.839708	+	0.543039i	$0.182726\pi$
$150$	−1.46739	+	7.95598i	−0.119812	+	0.649603i
$151$	6.67177	−	20.5336i	0.542941	−	1.67100i	−0.182894	−	0.983133i	$-0.558547\pi$
$151$	6.67177	−	20.5336i	0.542941	−	1.67100i	0.725835	−	0.687868i	$-0.241453\pi$
$152$	1.21151	−	1.66751i	0.0982667	−	0.135253i
$153$			0.0233574i			0.00188833i
$154$	16.6276	+	0.291613i	1.33989	+	0.0234988i
$155$	4.87770	−	19.2411i	0.391786	−	1.54548i
$156$	−3.05657	−	2.22073i	−0.244721	−	0.177801i
$157$	3.24760	+	1.05521i	0.259186	+	0.0842148i	0.435728	−	0.900078i	$-0.356491\pi$
$157$	3.24760	+	1.05521i	0.259186	+	0.0842148i	−0.176542	+	0.984293i	$0.556491\pi$
$158$	6.32947	−	2.05657i	0.503546	−	0.163612i
$159$	2.90847	−	2.11313i	0.230657	−	0.167582i
$160$	−2.07652	+	0.829496i	−0.164163	+	0.0655774i
$161$	−6.06657	−	18.6710i	−0.478113	−	1.47148i
$162$	7.33094	+	2.38197i	0.575973	+	0.187145i
$163$	−10.2336	+	14.0853i	−0.801554	+	1.10324i	0.191019	+	0.981586i	$0.438821\pi$
$163$	−10.2336	+	14.0853i	−0.801554	+	1.10324i	−0.992572	+	0.121657i	$0.961179\pi$
$164$	4.57985			0.357626
$165$	11.2198	−	4.25533i	0.873461	−	0.331277i
$166$	−11.0520			−0.857801
$167$	1.94321	−	2.67460i	0.150370	−	0.206967i	−0.727186	−	0.686440i	$-0.759172\pi$
$167$	1.94321	−	2.67460i	0.150370	−	0.206967i	0.877556	+	0.479473i	$0.159172\pi$
$168$	−7.71605	−	2.50710i	−0.595306	−	0.193427i
$169$	2.33237	+	7.17831i	0.179413	+	0.552178i
$170$	−0.0507240	−	0.126980i	−0.00389035	−	0.00973892i
$171$	−0.636930	+	0.462757i	−0.0487073	+	0.0353879i
$172$	−3.44095	+	1.11803i	−0.262370	+	0.0852493i
$173$	−4.87758	−	1.58482i	−0.370836	−	0.120492i	0.117670	−	0.993053i	$-0.462458\pi$
$173$	−4.87758	−	1.58482i	−0.370836	−	0.120492i	−0.488505	+	0.872561i	$0.662458\pi$
$174$	5.41557	+	3.93464i	0.410553	+	0.298284i
$175$	−11.9436	+	22.0432i	−0.902855	+	1.66631i
$176$	2.64861	+	1.99621i	0.199646	+	0.150470i
$177$			3.13712i			0.235801i
$178$	3.57971	−	4.92705i	0.268311	−	0.369298i
$179$	4.46201	−	13.7327i	0.333507	−	1.02643i	−0.633947	−	0.773377i	$-0.718566\pi$
$179$	4.46201	−	13.7327i	0.333507	−	1.02643i	0.967453	−	0.253051i	$-0.0814339\pi$
$180$	0.852249	−	0.0562321i	0.0635229	−	0.00419129i
$181$	−9.63223	+	6.99822i	−0.715958	+	0.520174i	−0.885090	−	0.465419i	$-0.845903\pi$
$181$	−9.63223	+	6.99822i	−0.715958	+	0.520174i	0.169132	+	0.985593i	$0.445903\pi$
$182$	−6.88191	−	9.47214i	−0.510121	−	0.702121i
$183$	−14.9166	+	4.84669i	−1.10267	+	0.358278i
$184$	1.20988	−	3.72363i	0.0891935	−	0.274509i
$185$	6.51898	+	7.83128i	0.479285	+	0.575767i
$186$	14.3634			1.05318
$187$	−0.122069	+	0.161963i	−0.00892658	+	0.0118439i
$188$		−	8.87707i		−	0.647427i
$189$	22.1981	+	16.1279i	1.61467	+	1.17313i
$190$	2.45766	−	3.89892i	0.178298	−	0.282858i
$191$	3.25026	+	10.0033i	0.235181	+	0.723812i	0.997097	+	0.0761369i	$0.0242586\pi$
$191$	3.25026	+	10.0033i	0.235181	+	0.723812i	−0.761917	+	0.647675i	$0.775741\pi$
$192$	−0.951057	−	1.30902i	−0.0686366	−	0.0944702i
$193$	2.86174	+	3.93885i	0.205993	+	0.283525i	0.899496	−	0.436929i	$-0.143934\pi$
$193$	2.86174	+	3.93885i	0.205993	+	0.283525i	−0.693503	+	0.720453i	$0.743934\pi$
$194$	−2.25652	−	6.94485i	−0.162009	−	0.498612i
$195$	−7.14680	−	4.50494i	−0.511793	−	0.322606i
$196$	−14.6773	−	10.6637i	−1.04838	−	0.761692i
$197$		−	15.9760i		−	1.13824i	−0.822253	−	0.569122i	$-0.807283\pi$
$197$		−	15.9760i		−	1.13824i	0.822253	−	0.569122i	$-0.192717\pi$
$198$	−0.726543	−	1.03779i	−0.0516331	−	0.0737527i
$199$	−16.7076			−1.18437			−0.592184	−	0.805803i	$-0.701734\pi$
$199$	−16.7076			−1.18437			−0.592184	+	0.805803i	$0.701734\pi$
$200$	−4.51105	+	2.15649i	−0.318979	+	0.152487i
$201$	1.24787	−	3.84054i	0.0880177	−	0.270891i
$202$	−0.211013	+	0.0685623i	−0.0148468	+	0.00482403i
$203$	12.1932	+	16.7825i	0.855797	+	1.17790i
$204$	0.0800469	−	0.0581575i	0.00560440	−	0.00407184i
$205$	10.2186	−	0.674234i	0.713701	−	0.0470906i
$206$	−0.174918	+	0.538341i	−0.0121871	+	0.0375080i
$207$	−0.879029	+	1.20988i	−0.0610967	+	0.0840924i
$208$		−	2.33501i		−	0.161904i
$209$	−6.83501	−	0.119871i	−0.472788	−	0.00829167i
$210$	−17.5853	−	4.45794i	−1.21350	−	0.307627i
$211$	12.7388	+	9.25526i	0.876974	+	0.637159i	0.932449	−	0.361301i	$-0.117667\pi$
$211$	12.7388	+	9.25526i	0.876974	+	0.637159i	−0.0554754	+	0.998460i	$0.517667\pi$
$212$	2.11313	+	0.686596i	0.145130	+	0.0471556i
$213$	13.5669	−	4.40815i	0.929589	−	0.302042i
$214$	1.80412	−	1.31077i	0.123327	−	0.0896025i
$215$	−7.51292	+	3.00114i	−0.512377	+	0.204676i
$216$	1.69098	+	5.20431i	0.115057	+	0.354108i
$217$	42.3328	+	13.7548i	2.87374	+	0.933735i
$218$	4.62168	−	6.36120i	0.313020	−	0.430835i
$219$	−8.73117			−0.589998
$220$	6.20350	+	4.06406i	0.418240	+	0.273999i
$221$	0.142787			0.00960488
$222$	−4.33385	+	5.96504i	−0.290869	+	0.400347i
$223$	−13.8432	−	4.49794i	−0.927011	−	0.301204i	−0.193671	−	0.981067i	$-0.562039\pi$
$223$	−13.8432	−	4.49794i	−0.927011	−	0.301204i	−0.733340	+	0.679862i	$0.762039\pi$
$224$	−1.54947	−	4.76878i	−0.103528	−	0.318628i
$225$	1.89327	−	0.250932i	0.126218	−	0.0167288i
$226$	−10.1626	+	7.38357i	−0.676007	+	0.491148i
$227$	9.35512	−	3.03966i	0.620921	−	0.201749i	0.0183719	−	0.999831i	$-0.494152\pi$
$227$	9.35512	−	3.03966i	0.620921	−	0.201749i	0.602549	+	0.798082i	$0.294152\pi$
$228$	3.17178	+	1.03058i	0.210057	+	0.0682515i
$229$	−12.5785	−	9.13881i	−0.831210	−	0.603909i	0.0886913	−	0.996059i	$-0.471732\pi$
$229$	−12.5785	−	9.13881i	−0.831210	−	0.603909i	−0.919901	+	0.392150i	$0.871732\pi$
$230$	2.15132	−	8.48633i	0.141854	−	0.559572i
$231$	7.86508	+	25.7331i	0.517484	+	1.69312i
$232$			4.13712i			0.271616i
$233$	−15.2217	+	20.9509i	−0.997206	+	1.37254i	−0.0701824	+	0.997534i	$0.522358\pi$
$233$	−15.2217	+	20.9509i	−0.997206	+	1.37254i	−0.927024	+	0.375002i	$0.877642\pi$
$234$	−0.275611	+	0.848243i	−0.0180172	+	0.0554513i
$235$	−1.30686	−	19.8067i	−0.0852501	−	1.29204i
$236$	−1.56856	+	1.13963i	−0.102105	+	0.0741834i
$237$	6.32947	+	8.71177i	0.411143	+	0.565890i
$238$	0.291613	−	0.0947508i	0.0189025	−	0.00614178i
$239$	−6.17911	+	19.0173i	−0.399693	+	1.23013i	0.525552	+	0.850761i	$0.323859\pi$
$239$	−6.17911	+	19.0173i	−0.399693	+	1.23013i	−0.925246	+	0.379369i	$0.876141\pi$
$240$	−2.31472	−	2.78069i	−0.149415	−	0.179493i
$241$	9.01381			0.580630			0.290315	−	0.956931i	$-0.406240\pi$
$241$	9.01381			0.580630			0.290315	+	0.956931i	$0.406240\pi$
$242$	0.385714	−	10.9932i	0.0247946	−	0.706672i
$243$		−	3.94427i		−	0.253025i
$244$	−7.84211	−	5.69763i	−0.502040	−	0.364753i
$245$	−34.3181	−	21.6323i	−2.19251	−	1.38203i
$246$	2.28993	+	7.04767i	0.146000	+	0.449343i
$247$	2.82890	+	3.89364i	0.179998	+	0.247747i
$248$	5.21781	+	7.18170i	0.331331	+	0.456038i
$249$	−5.52599	−	17.0073i	−0.350196	−	1.07779i
$250$	−9.74766	+	5.47569i	−0.616496	+	0.346313i
$251$	−1.06115	−	0.770971i	−0.0669792	−	0.0486632i	0.553792	−	0.832655i	$-0.313180\pi$
$251$	−1.06115	−	0.770971i	−0.0669792	−	0.0486632i	−0.620771	+	0.783992i	$0.713180\pi$
$252$			1.91525i			0.120650i
$253$	−12.4183	+	3.79554i	−0.780734	+	0.238624i
$254$	14.4630			0.907488
$255$	0.170040	−	0.141546i	0.0106483	−	0.00886397i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.24551	+	1.37945i	−0.264827	+	0.0860477i	−0.438421	−	0.898770i	$-0.644462\pi$
$257$	−4.24551	+	1.37945i	−0.264827	+	0.0860477i	0.173594	+	0.984817i	$0.444462\pi$
$258$	−3.44095	−	4.73607i	−0.214224	−	0.294855i
$259$	−18.4853	+	13.4304i	−1.14862	+	0.834522i
$260$	−0.343754	−	5.20992i	−0.0213187	−	0.323105i
$261$	0.488321	−	1.50290i	0.0302263	−	0.0930271i
$262$	−9.00817	+	12.3987i	−0.556526	+	0.765993i
$263$		−	14.1791i		−	0.874320i	−0.899384	−	0.437160i	$-0.855984\pi$
$263$		−	14.1791i		−	0.874320i	0.899384	−	0.437160i	$-0.144016\pi$
$264$	−1.74755	+	5.07390i	−0.107554	+	0.312277i
$265$	4.81592	+	1.22086i	0.295840	+	0.0749966i
$266$	8.36120	+	6.07477i	0.512658	+	0.372468i
$267$	9.37181	+	3.04508i	0.573545	+	0.186356i
$268$	2.37358	−	0.771224i	0.144990	−	0.0471100i
$269$	−25.8847	+	18.8063i	−1.57822	+	1.14664i	−0.659516	+	0.751691i	$0.729239\pi$
$269$	−25.8847	+	18.8063i	−1.57822	+	1.14664i	−0.918702	+	0.394952i	$0.870761\pi$
$270$	4.53911	+	11.3630i	0.276242	+	0.691530i
$271$	0.327988	+	1.00944i	0.0199238	+	0.0613192i	0.960524	−	0.278197i	$-0.0897367\pi$
$271$	0.327988	+	1.00944i	0.0199238	+	0.0613192i	−0.940600	+	0.339516i	$0.889737\pi$
$272$	0.0581575	+	0.0188965i	0.00352631	+	0.00114577i
$273$	11.1352	−	15.3262i	0.673931	−	0.927586i
$274$	−1.10437			−0.0667172
$275$	14.4396	+	8.15454i	0.870744	+	0.491737i
$276$	6.33501			0.381323
$277$	−3.89892	+	5.36641i	−0.234264	+	0.322436i	−0.909923	−	0.414778i	$-0.863859\pi$
$277$	−3.89892	+	5.36641i	−0.234264	+	0.322436i	0.675659	+	0.737214i	$0.263859\pi$
$278$	−9.42125	−	3.06115i	−0.565049	−	0.183596i
$279$	−1.04780	−	3.22478i	−0.0627299	−	0.193063i
$280$	−4.15925	−	10.4121i	−0.248563	−	0.622241i
$281$	−12.6582	+	9.19674i	−0.755126	+	0.548631i	−0.897412	−	0.441194i	$-0.854555\pi$
$281$	−12.6582	+	9.19674i	−0.755126	+	0.548631i	0.142285	+	0.989826i	$0.454555\pi$
$282$	13.6604	−	4.43854i	0.813465	−	0.264311i
$283$	−21.3993	−	6.95305i	−1.27205	−	0.413316i	−0.406280	−	0.913749i	$-0.633174\pi$
$283$	−21.3993	−	6.95305i	−1.27205	−	0.413316i	−0.865775	+	0.500433i	$0.833174\pi$
$284$	7.13254	+	5.18210i	0.423239	+	0.307501i
$285$	7.22866	+	1.83249i	0.428189	+	0.108548i
$286$	−6.34417	+	4.44146i	−0.375139	+	0.262629i
$287$			22.9643i			1.35554i
$288$	−0.224514	+	0.309017i	−0.0132296	+	0.0182090i
$289$	5.25213	−	16.1644i	0.308949	−	0.950847i
$290$	0.609057	+	9.23082i	0.0357651	+	0.542052i
$291$	9.55877	−	6.94485i	0.560345	−	0.407115i
$292$	−3.17178	−	4.36559i	−0.185615	−	0.255477i
$293$	17.2985	−	5.62063i	1.01059	−	0.328360i	0.243500	−	0.969901i	$-0.421704\pi$
$293$	17.2985	−	5.62063i	1.01059	−	0.328360i	0.767089	+	0.641540i	$0.221704\pi$
$294$	9.07108	−	27.9179i	0.529036	−	1.62821i
$295$	−3.33203	+	2.77367i	−0.193998	+	0.161490i
$296$	−4.55688			−0.264863
$297$	10.9236	−	14.4935i	0.633849	−	0.841001i
$298$			8.79232i			0.509326i
$299$	7.39616	+	5.37363i	0.427731	+	0.310765i
$300$	−5.57401	−	5.86355i	−0.321816	−	0.338532i
$301$	−5.60604	−	17.2536i	−0.323127	−	0.994482i
$302$	12.6905	+	17.4669i	0.730254	+	1.00511i
$303$	−0.211013	−	0.290435i	−0.0121224	−	0.0166850i
$304$	0.636930	+	1.96027i	0.0365305	+	0.112429i
$305$	−18.3362	−	11.5581i	−1.04993	−	0.661817i
$306$	−0.0188965	−	0.0137291i	−0.00108024	−	0.000784841i
$307$		−	12.3820i		−	0.706676i	−0.935496	−	0.353338i	$-0.885047\pi$
$307$		−	12.3820i		−	0.706676i	0.935496	−	0.353338i	$-0.114953\pi$
$308$	−10.0094	+	13.2806i	−0.570339	+	0.756735i
$309$	−0.915880			−0.0521026
$310$	12.6993	+	15.2558i	0.721274	+	0.866470i
$311$	2.90784	−	8.94941i	0.164889	−	0.507475i	−0.834140	−	0.551553i	$-0.814035\pi$
$311$	2.90784	−	8.94941i	0.164889	−	0.507475i	0.999028	+	0.0440788i	$0.0140353\pi$
$312$	3.59321	−	1.16751i	0.203426	−	0.0660970i
$313$	−8.95297	−	12.3227i	−0.506052	−	0.696520i	0.477196	−	0.878797i	$-0.341653\pi$
$313$	−8.95297	−	12.3227i	−0.506052	−	0.696520i	−0.983247	+	0.182277i	$0.941653\pi$
$314$	−2.76257	+	2.00712i	−0.155901	+	0.113269i
$315$	0.281959	+	4.27334i	0.0158866	+	0.240776i
$316$	−2.05657	+	6.32947i	−0.115691	+	0.356061i
$317$	7.90964	−	10.8867i	0.444250	−	0.611457i	−0.526900	−	0.849927i	$-0.676646\pi$
$317$	7.90964	−	10.8867i	0.444250	−	0.611457i	0.971150	+	0.238470i	$0.0766459\pi$
$318$			3.59506i			0.201601i
$319$	11.2405	−	7.86928i	0.629346	−	0.440595i
$320$	0.549472	−	2.16751i	0.0307164	−	0.121167i
$321$	2.91913	+	2.12087i	0.162930	+	0.118376i
$322$	18.6710	+	6.06657i	1.04049	+	0.338077i
$323$	−0.119871	+	0.0389485i	−0.00666982	+	0.00216715i
$324$	−6.23607	+	4.53077i	−0.346448	+	0.251709i
$325$	−1.53398	−	11.5738i	−0.0850900	−	0.642001i
$326$	−5.38010	−	16.5582i	−0.297976	−	0.917076i
$327$	12.0997	+	3.93144i	0.669116	+	0.217409i
$328$	−2.69197	+	3.70518i	−0.148639	+	0.204584i
$329$	44.5114			2.45399
$330$	−3.15220	+	11.5782i	−0.173523	+	0.637361i
$331$	−3.82236			−0.210096			−0.105048	−	0.994467i	$-0.533500\pi$
$331$	−3.82236			−0.210096			−0.105048	+	0.994467i	$0.533500\pi$
$332$	6.49620	−	8.94125i	0.356525	−	0.490715i
$333$	1.65538	+	0.537867i	0.0907145	+	0.0294749i
$334$	1.02161	+	3.14419i	0.0558999	+	0.172042i
$335$	5.18244	−	2.07020i	0.283147	−	0.113107i
$336$	6.56367	−	4.76878i	0.358077	−	0.260158i
$337$	−9.00338	+	2.92538i	−0.490445	+	0.159355i	−0.543791	−	0.839221i	$-0.683012\pi$
$337$	−9.00338	+	2.92538i	−0.490445	+	0.159355i	0.0533455	+	0.998576i	$0.483012\pi$
$338$	−7.17831	−	2.33237i	−0.390449	−	0.126864i
$339$	−16.4434	−	11.9469i	−0.893086	−	0.648865i
$340$	0.132544	+	0.0336004i	0.00718820	+	0.00182224i
$341$	9.58765	−	27.8371i	0.519201	−	1.50746i
$342$		−	0.787289i		−	0.0425717i
$343$	32.8390	−	45.1989i	1.77314	−	2.44051i
$344$	1.11803	−	3.44095i	0.0602804	−	0.185524i
$345$	14.1348	−	0.932624i	0.760991	−	0.0502108i
$346$	4.14912	−	3.01451i	0.223058	−	0.162061i
$347$	−9.72341	−	13.3831i	−0.521980	−	0.718444i	0.463902	−	0.885887i	$-0.346449\pi$
$347$	−9.72341	−	13.3831i	−0.521980	−	0.718444i	−0.985882	+	0.167443i	$0.946449\pi$
$348$	−6.36638	+	2.06856i	−0.341274	+	0.110887i
$349$	−9.03161	+	27.7964i	−0.483451	+	1.48791i	0.350761	+	0.936465i	$0.385923\pi$
$349$	−9.03161	+	27.7964i	−0.483451	+	1.48791i	−0.834212	+	0.551444i	$0.814077\pi$
$350$	−10.8130	−	22.6193i	−0.577981	−	1.20905i
$351$	−12.7775			−0.682012
$352$	−3.17178	+	0.969425i	−0.169057	+	0.0516705i
$353$			27.9200i			1.48603i	0.669272	+	0.743017i	$0.266606\pi$
$353$			27.9200i			1.48603i	−0.669272	+	0.743017i	$0.733394\pi$
$354$	−2.53799	−	1.84396i	−0.134892	−	0.0980051i
$355$	16.6771	+	10.5123i	0.885131	+	0.557937i
$356$	1.88197	+	5.79210i	0.0997440	+	0.306980i
$357$	0.291613	+	0.401371i	0.0154338	+	0.0212428i
$358$	8.48725	+	11.6817i	0.448565	+	0.617397i
$359$	−5.25768	−	16.1815i	−0.277490	−	0.854025i	−0.988550	−	0.150894i	$-0.951785\pi$
$359$	−5.25768	−	16.1815i	−0.277490	−	0.854025i	0.711060	−	0.703131i	$-0.248215\pi$
$360$	−0.455447	+	0.722536i	−0.0240041	+	0.0380810i
$361$	11.9343	+	8.67081i	0.628123	+	0.456358i
$362$		−	11.9061i		−	0.625770i
$363$	17.1097	−	4.90307i	0.898027	−	0.257344i
$364$	11.7082			0.613677
$365$	−7.71963	−	9.27363i	−0.404064	−	0.485404i
$366$	4.84669	−	14.9166i	0.253341	−	0.779702i
$367$	−27.9983	+	9.09719i	−1.46150	+	0.474870i	−0.928527	−	0.371264i	$-0.878925\pi$
$367$	−27.9983	+	9.09719i	−1.46150	+	0.474870i	−0.532971	+	0.846133i	$0.678925\pi$
$368$	2.30133	+	3.16751i	0.119965	+	0.165118i
$369$	1.41525	−	1.02824i	0.0736751	−	0.0535281i
$370$	−10.1674	+	0.670853i	−0.528578	+	0.0348760i
$371$	−3.44273	+	10.5956i	−0.178738	+	0.550098i
$372$	−8.44260	+	11.6202i	−0.437728	+	0.602481i
$373$			16.0743i			0.832297i	0.909297	+	0.416149i	$0.136620\pi$
$373$			16.0743i			0.832297i	−0.909297	+	0.416149i	$0.863380\pi$
$374$	−0.0592807	−	0.193956i	−0.00306533	−	0.0100292i
$375$	−13.3000	−	12.2623i	−0.686812	−	0.633220i
$376$	7.18170	+	5.21781i	0.370368	+	0.269088i
$377$	−9.18743	−	2.98518i	−0.473177	−	0.153744i
$378$	−26.0954	+	8.47892i	−1.34220	+	0.436109i
$379$	14.6618	−	10.6524i	0.753125	−	0.547178i	−0.143669	−	0.989626i	$-0.545890\pi$
$379$	14.6618	−	10.6524i	0.753125	−	0.547178i	0.896794	+	0.442448i	$0.145890\pi$
$380$	1.70972	+	4.28002i	0.0877066	+	0.219560i
$381$	7.23149	+	22.2562i	0.370480	+	1.14022i
$382$	−10.0033	−	3.25026i	−0.511812	−	0.166298i
$383$	−7.76587	+	10.6888i	−0.396817	+	0.546172i	−0.959942	−	0.280200i	$-0.909599\pi$
$383$	−7.76587	+	10.6888i	−0.396817	+	0.546172i	0.563124	+	0.826372i	$0.309599\pi$
$384$	1.61803			0.0825700
$385$	−20.3780	+	31.1056i	−1.03856	+	1.58529i
$386$	−4.86869			−0.247810
$387$	−0.812299	+	1.11803i	−0.0412915	+	0.0568329i
$388$	6.94485	+	2.25652i	0.352572	+	0.114557i
$389$	8.19653	+	25.2263i	0.415580	+	1.27902i	0.911731	+	0.410788i	$0.134746\pi$
$389$	8.19653	+	25.2263i	0.415580	+	1.27902i	−0.496150	+	0.868237i	$0.665254\pi$
$390$	7.84536	−	3.13394i	0.397265	−	0.158693i
$391$	−0.193694	+	0.140727i	−0.00979553	+	0.00711687i
$392$	17.2542	−	5.60624i	0.871470	−	0.283158i
$393$	−23.5837	−	7.66280i	−1.18964	−	0.386537i
$394$	12.9249	+	9.39047i	0.651145	+	0.473085i
$395$	−3.65684	+	14.4252i	−0.183996	+	0.725810i
$396$	1.26664	+	0.0222142i	0.0636512	+	0.00111630i
$397$			30.3246i			1.52195i	0.648783	+	0.760974i	$0.275278\pi$
$397$			30.3246i			1.52195i	−0.648783	+	0.760974i	$0.724722\pi$
$398$	9.82047	−	13.5167i	0.492256	−	0.677532i
$399$	−5.16751	+	15.9039i	−0.258699	+	0.796193i
$400$	0.906896	−	4.91707i	0.0453448	−	0.245853i
$401$	−15.7565	+	11.4478i	−0.786844	+	0.571676i	−0.907025	−	0.421076i	$-0.861652\pi$
$401$	−15.7565	+	11.4478i	−0.786844	+	0.571676i	0.120181	+	0.992752i	$0.461652\pi$
$402$	2.37358	+	3.26696i	0.118384	+	0.162941i
$403$	−19.7136	+	6.40532i	−0.982002	+	0.319072i
$404$	0.0685623	−	0.211013i	0.00341110	−	0.0104983i
$405$	−13.2470	+	11.0272i	−0.658249	+	0.547945i
$406$	−20.7444			−1.02952
$407$	8.66771	+	12.3809i	0.429642	+	0.613701i
$408$			0.0989434i			0.00489843i
$409$	−22.9197	−	16.6521i	−1.13330	−	0.823394i	−0.147132	−	0.989117i	$-0.547004\pi$
$409$	−22.9197	−	16.6521i	−1.13330	−	0.823394i	−0.986172	+	0.165723i	$0.947004\pi$
$410$	−5.46090	+	8.66336i	−0.269695	+	0.427853i
$411$	−0.552183	−	1.69944i	−0.0272372	−	0.0838274i
$412$	−0.332713	−	0.457940i	−0.0163916	−	0.0225611i
$413$	−5.71431	−	7.86508i	−0.281183	−	0.387015i
$414$	−0.462133	−	1.42230i	−0.0227126	−	0.0699022i
$415$	13.1781	−	20.9062i	0.646888	−	1.02625i
$416$	1.88906	+	1.37249i	0.0926190	+	0.0672916i
$417$		−	16.0284i		−	0.784914i
$418$	4.11450	−	5.45918i	0.201247	−	0.267017i
$419$	15.4826			0.756374			0.378187	−	0.925729i	$-0.376548\pi$
$419$	15.4826			0.756374			0.378187	+	0.925729i	$0.376548\pi$
$420$	13.9429	−	11.6065i	0.680345	−	0.566338i
$421$	6.63964	−	20.4347i	0.323596	−	0.995927i	−0.648474	−	0.761237i	$-0.724592\pi$
$421$	6.63964	−	20.4347i	0.323596	−	0.995927i	0.972070	−	0.234690i	$-0.0754076\pi$
$422$	−14.9753	+	4.86578i	−0.728988	+	0.236862i
$423$	−1.99303	−	2.74317i	−0.0969043	−	0.133377i
$424$	−1.79753	+	1.30598i	−0.0872959	+	0.0634242i
$425$	0.300680	+	0.0554570i	0.0145851	+	0.00269006i
$426$	−4.40815	+	13.5669i	−0.213576	+	0.657319i
$427$	28.5690	−	39.3219i	1.38255	−	1.90292i
$428$			2.23002i			0.107792i
$429$	−10.0068	−	7.54195i	−0.483132	−	0.364129i
$430$	1.98801	−	7.84211i	0.0958702	−	0.378180i
$431$	−21.3896	−	15.5404i	−1.03030	−	0.748557i	−0.0619316	−	0.998080i	$-0.519726\pi$
$431$	−21.3896	−	15.5404i	−1.03030	−	0.748557i	−0.968369	+	0.249523i	$0.919726\pi$
$432$	−5.20431	−	1.69098i	−0.250393	−	0.0813575i
$433$	31.2725	−	10.1611i	1.50286	−	0.488309i	0.562010	−	0.827130i	$-0.310028\pi$
$433$	31.2725	−	10.1611i	1.50286	−	0.488309i	0.940851	+	0.338821i	$0.110028\pi$
$434$	−36.0105	+	26.1631i	−1.72856	+	1.25587i
$435$	−13.9002	+	5.55265i	−0.666466	+	0.266229i
$436$	2.42976	+	7.47804i	0.116365	+	0.358133i
$437$	−7.67495	−	2.49374i	−0.367143	−	0.119292i
$438$	5.13205	−	7.06367i	0.245219	−	0.337515i
$439$	12.1796			0.581299			0.290649	−	0.956830i	$-0.406129\pi$
$439$	12.1796			0.581299			0.290649	+	0.956830i	$0.406129\pi$
$440$	−6.93422	+	2.62994i	−0.330576	+	0.125377i
$441$	−6.92969			−0.329985
$442$	−0.0839280	+	0.115517i	−0.00399205	+	0.00549458i
$443$	15.7961	+	5.13247i	0.750496	+	0.243851i	0.659195	−	0.751972i	$-0.270897\pi$
$443$	15.7961	+	5.13247i	0.750496	+	0.243851i	0.0913015	+	0.995823i	$0.470897\pi$
$444$	−2.27844	−	7.01232i	−0.108130	−	0.332790i
$445$	5.05177	+	12.6464i	0.239477	+	0.599495i
$446$	11.7757	−	8.55558i	0.557598	−	0.405119i
$447$	−13.5300	+	4.39616i	−0.639947	+	0.207931i
$448$	4.76878	+	1.54947i	0.225304	+	0.0732057i
$449$	−4.33928	−	3.15267i	−0.204783	−	0.148784i	0.480667	−	0.876903i	$-0.340395\pi$
$449$	−4.33928	−	3.15267i	−0.204783	−	0.148784i	−0.685450	+	0.728119i	$0.740395\pi$
$450$	−0.909830	+	1.67918i	−0.0428898	+	0.0791575i
$451$	15.1873	+	0.266353i	0.715143	+	0.0125421i
$452$		−	12.5617i		−	0.590852i
$453$	−20.5336	+	28.2621i	−0.964753	+	1.32787i
$454$	−3.03966	+	9.35512i	−0.142658	+	0.439058i
$455$	26.1235	−	1.72365i	1.22469	−	0.0808061i
$456$	−2.69808	+	1.96027i	−0.126349	+	0.0917981i
$457$	2.12330	+	2.92247i	0.0993237	+	0.136707i	0.855786	−	0.517330i	$-0.173074\pi$
$457$	2.12330	+	2.92247i	0.0993237	+	0.136707i	−0.756462	+	0.654037i	$0.773074\pi$
$458$	14.7869	−	4.80456i	0.690947	−	0.224502i
$459$	0.103404	−	0.318246i	0.00482650	−	0.0148544i
$460$	5.60107	+	6.72860i	0.261151	+	0.313722i
$461$	−40.6625			−1.89384			−0.946922	−	0.321464i	$-0.895825\pi$
$461$	−40.6625			−1.89384			−0.946922	+	0.321464i	$0.895825\pi$
$462$	−25.4415	−	8.76257i	−1.18365	−	0.407672i
$463$			2.11880i			0.0984690i	0.998787	+	0.0492345i	$0.0156782\pi$
$463$			2.11880i			0.0984690i	−0.998787	+	0.0492345i	$0.984322\pi$
$464$	−3.34700	−	2.43174i	−0.155381	−	0.112891i
$465$	−17.1266	+	27.1702i	−0.794225	+	1.25999i
$466$	−8.00252	−	24.6292i	−0.370709	−	1.14093i
$467$	8.08494	+	11.1280i	0.374126	+	0.514941i	0.954017	−	0.299754i	$-0.0969046\pi$
$467$	8.08494	+	11.1280i	0.374126	+	0.514941i	−0.579890	+	0.814695i	$0.696905\pi$
$468$	−0.524243	−	0.721558i	−0.0242331	−	0.0333540i
$469$	3.86707	+	11.9016i	0.178565	+	0.549565i
$470$	16.7921	+	10.5848i	0.774561	+	0.488240i
$471$	−4.46993	−	3.24760i	−0.205964	−	0.149641i
$472$		−	1.93885i		−	0.0892428i
$473$	−11.4756	+	3.50741i	−0.527650	+	0.161271i
$474$	−10.7683			−0.494606
$475$	4.44484	+	9.29795i	0.203943	+	0.426619i
$476$	−0.0947508	+	0.291613i	−0.00434289	+	0.0133661i
$477$	0.807142	−	0.262256i	0.0369565	−	0.0120079i
$478$	−11.7534	−	16.1771i	−0.537586	−	0.739924i
$479$	25.4118	−	18.4628i	1.16110	−	0.843586i	0.171180	−	0.985240i	$-0.445242\pi$
$479$	25.4118	−	18.4628i	1.16110	−	0.843586i	0.989916	+	0.141654i	$0.0452421\pi$
$480$	3.61018	−	0.238203i	0.164782	−	0.0108724i
$481$	3.28806	−	10.1196i	0.149922	−	0.461414i
$482$	−5.29818	+	7.29232i	−0.241326	+	0.332156i
$483$			31.7650i			1.44536i
$484$	8.66700	+	6.77371i	0.393954	+	0.307896i
$485$	15.8277	+	4.01238i	0.718698	+	0.182193i
$486$	3.19098	+	2.31838i	0.144746	+	0.105164i
$487$	−7.14274	−	2.32082i	−0.323668	−	0.105166i	0.142676	−	0.989769i	$-0.454429\pi$
$487$	−7.14274	−	2.32082i	−0.323668	−	0.105166i	−0.466344	+	0.884603i	$0.654429\pi$
$488$	9.21895	−	2.99542i	0.417322	−	0.135596i
$489$	22.7905	−	16.5582i	1.03062	−	0.748789i
$490$	37.6726	−	15.0488i	1.70187	−	0.679838i
$491$	3.48008	+	10.7106i	0.157054	+	0.483361i	0.998363	−	0.0571923i	$-0.0182148\pi$
$491$	3.48008	+	10.7106i	0.157054	+	0.483361i	−0.841310	+	0.540554i	$0.818215\pi$
$492$	−7.04767	−	2.28993i	−0.317733	−	0.103238i
$493$	0.148702	−	0.204671i	0.00669719	−	0.00921790i
$494$	−4.81281			−0.216539
$495$	2.82943	−	0.136907i	0.127173	−	0.00615353i
$496$	−8.87707			−0.398592
$497$	−25.9840	+	35.7640i	−1.16554	+	1.60423i
$498$	17.0073	+	5.52599i	0.762114	+	0.247626i
$499$	8.33753	+	25.6603i	0.373239	+	1.14871i	0.944659	+	0.328054i	$0.106393\pi$
$499$	8.33753	+	25.6603i	0.373239	+	1.14871i	−0.571420	+	0.820658i	$0.693607\pi$
$500$	1.29960	−	11.1046i	0.0581200	−	0.496611i
$501$	−4.32760	+	3.14419i	−0.193343	+	0.140472i
$502$	1.24746	−	0.405323i	0.0556767	−	0.0180905i
$503$	30.5818	+	9.93662i	1.36357	+	0.443052i	0.897235	−	0.441554i	$-0.145573\pi$
$503$	30.5818	+	9.93662i	1.36357	+	0.443052i	0.466339	+	0.884606i	$0.345573\pi$
$504$	−1.54947	−	1.12576i	−0.0690190	−	0.0501452i
$505$	0.121913	−	0.480909i	0.00542504	−	0.0214002i
$506$	4.22866	−	12.2776i	0.187987	−	0.545806i
$507$		−	12.2125i		−	0.542375i
$508$	−8.50112	+	11.7008i	−0.377176	+	0.519139i
$509$	−3.64048	+	11.2043i	−0.161362	+	0.496620i	−0.998750	−	0.0499888i	$-0.984081\pi$
$509$	−3.64048	+	11.2043i	−0.161362	+	0.496620i	0.837388	+	0.546609i	$0.184081\pi$
$510$	0.0145662	+	0.220764i	0.000645002	+	0.00977560i
$511$	21.8899	−	15.9039i	0.968352	−	0.703549i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	10.7269	−	3.48537i	0.473603	−	0.153883i
$514$	1.37945	−	4.24551i	0.0608449	−	0.187261i
$515$	−0.809772	−	0.972783i	−0.0356828	−	0.0428659i
$516$	5.85410			0.257712
$517$	0.516268	−	29.4374i	0.0227054	−	1.29465i
$518$		−	22.8491i		−	1.00393i
$519$	6.71341	+	4.87758i	0.294686	+	0.214102i
$520$	4.41696	+	2.78421i	0.193697	+	0.122096i
$521$	0.718847	+	2.21238i	0.0314933	+	0.0969263i	0.965568	−	0.260152i	$-0.0837728\pi$
$521$	0.718847	+	2.21238i	0.0314933	+	0.0969263i	−0.934074	+	0.357079i	$0.883773\pi$
$522$	0.928842	+	1.27844i	0.0406543	+	0.0559559i
$523$	0.901612	+	1.24096i	0.0394248	+	0.0542635i	0.828274	−	0.560323i	$-0.189323\pi$
$523$	0.901612	+	1.24096i	0.0394248	+	0.0542635i	−0.788850	+	0.614586i	$0.789323\pi$
$524$	−4.73587	−	14.5755i	−0.206888	−	0.636735i
$525$	29.4010	−	27.9492i	1.28316	−	1.21980i
$526$	11.4711	+	8.33426i	0.500165	+	0.363391i
$527$		−	0.542836i		−	0.0236463i
$528$	−3.07768	−	4.39616i	−0.133939	−	0.191318i
$529$	7.67080			0.333513
$530$	−3.81842	+	3.17856i	−0.165862	+	0.138068i
$531$	−0.228850	+	0.704328i	−0.00993125	+	0.0305652i
$532$	−9.82918	+	3.19369i	−0.426149	+	0.138464i
$533$	−6.28578	−	8.65163i	−0.272267	−	0.374744i
$534$	−7.97214	+	5.79210i	−0.344988	+	0.250648i
$535$	0.328298	+	4.97565i	0.0141935	+	0.215116i
$536$	−0.771224	+	2.37358i	−0.0333118	+	0.102523i
$537$	−13.7327	+	18.9014i	−0.592608	+	0.815655i
$538$		−	31.9952i		−	1.37941i
$539$	−48.0515	−	36.2156i	−2.06972	−	1.55992i
$540$	−11.8609	−	3.00678i	−0.510411	−	0.129391i
$541$	12.4927	+	9.07650i	0.537104	+	0.390229i	0.823008	−	0.568029i	$-0.192294\pi$
$541$	12.4927	+	9.07650i	0.537104	+	0.390229i	−0.285904	+	0.958258i	$0.592294\pi$
$542$	−1.00944	−	0.327988i	−0.0433593	−	0.0140883i
$543$	18.3216	−	5.95305i	0.786255	−	0.255470i
$544$	−0.0494717	+	0.0359433i	−0.00212108	+	0.00154106i
$545$	6.52222	+	16.3274i	0.279381	+	0.699390i
$546$	5.85410	+	18.0171i	0.250532	+	0.771060i
$547$	−10.1261	−	3.29017i	−0.432960	−	0.140677i	0.0844251	−	0.996430i	$-0.473095\pi$
$547$	−10.1261	−	3.29017i	−0.432960	−	0.140677i	−0.517385	+	0.855752i	$0.673095\pi$
$548$	0.649130	−	0.893451i	0.0277295	−	0.0381663i
$549$	−3.70254			−0.158021
$550$	−15.0846	+	6.88880i	−0.643208	+	0.293739i
$551$	8.52724			0.363272
$552$	−3.72363	+	5.12513i	−0.158488	+	0.218140i
$553$	−31.7372	−	10.3120i	−1.34960	−	0.438513i
$554$	−2.04979	−	6.30859i	−0.0870871	−	0.268026i
$555$	−6.11603	−	15.3106i	−0.259611	−	0.649898i
$556$	8.01420	−	5.82265i	0.339878	−	0.246936i
$557$	−32.2595	+	10.4818i	−1.36688	+	0.444126i	−0.898334	−	0.439313i	$-0.855222\pi$
$557$	−32.2595	+	10.4818i	−1.36688	+	0.444126i	−0.468545	+	0.883439i	$0.655222\pi$
$558$	3.22478	+	1.04780i	0.136516	+	0.0443567i
$559$	6.83470	+	4.96570i	0.289077	+	0.210027i
$560$	10.8683	+	2.75516i	0.459269	+	0.116427i
$561$	0.268827	−	0.188201i	0.0113499	−	0.00794587i
$562$		−	15.6464i		−	0.660005i
$563$	−0.789857	+	1.08714i	−0.0332885	+	0.0458177i	−0.825337	−	0.564641i	$-0.809015\pi$
$563$	−0.789857	+	1.08714i	−0.0332885	+	0.0458177i	0.792048	+	0.610458i	$0.209015\pi$
$564$	−4.43854	+	13.6604i	−0.186896	+	0.575207i
$565$	−1.84930	−	28.0278i	−0.0778006	−	1.17914i
$566$	18.2033	−	13.2255i	0.765142	−	0.555908i
$567$	−22.7182	−	31.2689i	−0.954073	−	1.31317i
$568$	−8.38481	+	2.72439i	−0.351819	+	0.114313i
$569$	9.70595	−	29.8718i	0.406894	−	1.25229i	−0.512409	−	0.858742i	$-0.671247\pi$
$569$	9.70595	−	29.8718i	0.406894	−	1.25229i	0.919303	−	0.393550i	$-0.128753\pi$
$570$	−5.73142	+	4.77099i	−0.240063	+	0.199835i
$571$	9.25361			0.387252			0.193626	−	0.981075i	$-0.437975\pi$
$571$	9.25361			0.387252			0.193626	+	0.981075i	$0.437975\pi$
$572$	0.135798	−	7.74317i	0.00567801	−	0.323758i
$573$		−	17.0186i		−	0.710962i
$574$	−18.5785	−	13.4981i	−0.775451	−	0.563398i
$575$	13.4878	+	14.1884i	0.562479	+	0.591696i
$576$	−0.118034	−	0.363271i	−0.00491808	−	0.0151363i
$577$	−25.4998	−	35.0975i	−1.06157	−	1.46113i	−0.878327	−	0.478060i	$-0.841340\pi$
$577$	−25.4998	−	35.0975i	−1.06157	−	1.46113i	−0.183244	−	0.983068i	$-0.558660\pi$
$578$	9.99015	+	13.7503i	0.415536	+	0.571936i
$579$	−2.43434	−	7.49214i	−0.101168	−	0.311363i
$580$	−7.82589	−	4.93300i	−0.324952	−	0.204832i
$581$	44.8332	+	32.5732i	1.85999	+	1.35136i
$582$			11.8153i			0.489760i
$583$	6.96744	+	2.39973i	0.288562	+	0.0993865i
$584$	5.39616			0.223295
$585$	−1.27592	−	1.53277i	−0.0527530	−	0.0633724i
$586$	−5.62063	+	17.2985i	−0.232186	+	0.714595i
$587$	3.05524	−	0.992708i	0.126103	−	0.0409734i	−0.245285	−	0.969451i	$-0.578882\pi$
$587$	3.05524	−	0.992708i	0.126103	−	0.0409734i	0.371389	+	0.928477i	$0.378882\pi$
$588$	17.2542	+	23.7484i	0.711552	+	0.979367i
$589$	14.8026	−	10.7547i	0.609929	−	0.443139i
$590$	−0.285433	−	4.32599i	−0.0117511	−	0.178098i
$591$	−7.98801	+	24.5846i	−0.328583	+	1.01127i
$592$	2.67847	−	3.68660i	0.110084	−	0.151518i
$593$		−	0.0315027i		−	0.00129366i	−1.00000		0.000646829i	$-0.999794\pi$
$593$		−	0.0315027i		−	0.00129366i	1.00000		0.000646829i	$-0.000205892\pi$
$594$	5.30482	+	17.3564i	0.217660	+	0.712143i
$595$	−0.168479	+	0.664600i	−0.00690696	+	0.0272460i
$596$	−7.11314	−	5.16800i	−0.291366	−	0.211689i
$597$	25.7103	+	8.35379i	1.05225	+	0.341898i
$598$	−8.69471	+	2.82508i	−0.355553	+	0.115526i
$599$	−8.50993	+	6.18283i	−0.347706	+	0.252623i	−0.747906	−	0.663804i	$-0.768941\pi$
$599$	−8.50993	+	6.18283i	−0.347706	+	0.252623i	0.400200	+	0.916428i	$0.368941\pi$
$600$	8.02003	−	1.06296i	0.327417	−	0.0433953i
$601$	7.45305	+	22.9381i	0.304016	+	0.935665i	0.980043	+	0.198788i	$0.0637005\pi$
$601$	7.45305	+	22.9381i	0.304016	+	0.935665i	−0.676026	+	0.736877i	$0.736300\pi$
$602$	17.2536	+	5.60604i	0.703205	+	0.228485i
$603$	0.560327	−	0.771224i	0.0228183	−	0.0314067i
$604$	−21.5903			−0.878497
$605$	20.3352	+	13.8377i	0.826742	+	0.562582i
$606$	0.358997			0.0145833
$607$	1.46340	−	2.01420i	0.0593975	−	0.0817537i	−0.778285	−	0.627911i	$-0.783910\pi$
$607$	1.46340	−	2.01420i	0.0593975	−	0.0817537i	0.837682	+	0.546158i	$0.183910\pi$
$608$	−1.96027	−	0.636930i	−0.0794995	−	0.0258309i
$609$	−10.3722	−	31.9223i	−0.420302	−	1.29356i
$610$	20.1285	−	8.04062i	0.814979	−	0.325555i
$611$	−16.7694	+	12.1836i	−0.678415	+	0.492898i
$612$	0.0222142	−	0.00721782i	0.000897955	−	0.000291763i
$613$	35.7338	+	11.6106i	1.44328	+	0.468949i	0.922917	−	0.384999i	$-0.125798\pi$
$613$	35.7338	+	11.6106i	1.44328	+	0.468949i	0.520359	+	0.853948i	$0.325798\pi$
$614$	10.0172	+	7.27794i	0.404262	+	0.293714i
$615$	−16.0620	−	4.07178i	−0.647682	−	0.164190i
$616$	−4.86089	−	15.9039i	−0.195851	−	0.640788i
$617$		−	45.5803i		−	1.83499i	−0.397744	−	0.917496i	$-0.630207\pi$
$617$		−	45.5803i		−	1.83499i	0.397744	−	0.917496i	$-0.369793\pi$
$618$	0.538341	−	0.740963i	0.0216553	−	0.0298059i
$619$	−1.77382	+	5.45924i	−0.0712957	+	0.219425i	−0.980355	−	0.197241i	$-0.936802\pi$
$619$	−1.77382	+	5.45924i	−0.0712957	+	0.219425i	0.909059	+	0.416667i	$0.136802\pi$
$620$	−19.8067	+	1.30686i	−0.795455	+	0.0524848i
$621$	17.3330	−	12.5932i	0.695550	−	0.505347i
$622$	5.53104	+	7.61283i	0.221775	+	0.305246i
$623$	−29.0427	+	9.43655i	−1.16357	+	0.378067i
$624$	−1.16751	+	3.59321i	−0.0467376	+	0.143844i
$625$	1.26491	−	24.9680i	0.0505964	−	0.998719i
$626$	15.2317			0.608781
$627$	10.4581	+	3.60197i	0.417655	+	0.143849i
$628$		−	3.41472i		−	0.136262i
$629$	0.225437	+	0.163789i	0.00898875	+	0.00653071i
$630$	−3.62294	−	2.28370i	−0.144341	−	0.0909847i
$631$	3.70103	+	11.3906i	0.147336	+	0.453453i	0.997304	−	0.0733811i	$-0.0233790\pi$
$631$	3.70103	+	11.3906i	0.147336	+	0.453453i	−0.849968	+	0.526834i	$0.823379\pi$
$632$	−3.91183	−	5.38417i	−0.155604	−	0.214171i
$633$	−14.9753	−	20.6118i	−0.595216	−	0.819245i
$634$	4.15834	+	12.7981i	0.165149	+	0.508276i
$635$	−17.2453	+	27.3585i	−0.684358	+	1.08569i
$636$	−2.90847	−	2.11313i	−0.115328	−	0.0837909i
$637$			42.3621i			1.67845i
$638$	−0.240605	+	13.7192i	−0.00952563	+	0.543148i
$639$	3.36753			0.133217
$640$	1.43058	+	1.71856i	0.0565485	+	0.0679320i
$641$	−10.8526	+	33.4007i	−0.428650	+	1.31925i	0.470805	+	0.882237i	$0.343964\pi$
$641$	−10.8526	+	33.4007i	−0.428650	+	1.31925i	−0.899455	+	0.437013i	$0.856036\pi$
$642$	−3.43164	+	1.11501i	−0.135436	+	0.0440059i
$643$	20.9529	+	28.8392i	0.826302	+	1.13731i	0.988600	+	0.150565i	$0.0481093\pi$
$643$	20.9529	+	28.8392i	0.826302	+	1.13731i	−0.162298	+	0.986742i	$0.551891\pi$
$644$	−15.8825	+	11.5393i	−0.625858	+	0.454712i
$645$	13.0618	−	0.861826i	0.514307	−	0.0339344i
$646$	0.0389485	−	0.119871i	0.00153241	−	0.00471627i
$647$	−11.8476	+	16.3068i	−0.465778	+	0.641088i	−0.975694	−	0.219136i	$-0.929676\pi$
$647$	−11.8476	+	16.3068i	−0.465778	+	0.641088i	0.509917	+	0.860224i	$0.329676\pi$
$648$		−	7.70820i		−	0.302807i
$649$	−5.26781	+	3.68791i	−0.206780	+	0.144763i
$650$	10.2651	+	5.56192i	0.402630	+	0.218156i
$651$	−58.2661	−	42.3328i	−2.28363	−	1.65915i
$652$	16.5582	+	5.38010i	0.648470	+	0.210701i
$653$	−23.1905	+	7.53504i	−0.907513	+	0.294869i	−0.725334	−	0.688397i	$-0.758315\pi$
$653$	−23.1905	+	7.53504i	−0.907513	+	0.294869i	−0.182178	+	0.983266i	$0.558315\pi$
$654$	−10.2926	+	7.47804i	−0.402474	+	0.292414i
$655$	−12.7125	−	31.8239i	−0.496720	−	1.24346i
$656$	−1.41525	−	4.35570i	−0.0552563	−	0.170061i
$657$	−1.96027	−	0.636930i	−0.0764774	−	0.0248490i
$658$	−26.1631	+	36.0105i	−1.01994	+	1.40383i
$659$	6.98788			0.272209			0.136104	−	0.990694i	$-0.456542\pi$
$659$	6.98788			0.272209			0.136104	+	0.990694i	$0.456542\pi$
$660$	−7.51417	−	9.35570i	−0.292489	−	0.364170i
$661$	−3.61827			−0.140735			−0.0703673	−	0.997521i	$-0.522417\pi$
$661$	−3.61827			−0.140735			−0.0703673	+	0.997521i	$0.522417\pi$
$662$	2.24673	−	3.09235i	0.0873215	−	0.120188i
$663$	−0.219726	−	0.0713934i	−0.00853346	−	0.00277269i
$664$	3.41525	+	10.5111i	0.132537	+	0.407908i
$665$	−21.4609	+	8.57285i	−0.832216	+	0.332441i
$666$	−1.40815	+	1.02308i	−0.0545649	+	0.0396437i
$667$	15.4051	−	5.00542i	0.596488	−	0.193811i
$668$	−3.14419	−	1.02161i	−0.121652	−	0.0395272i
$669$	19.0536	+	13.8432i	0.736653	+	0.535210i
$670$	−1.37133	+	5.40952i	−0.0529793	+	0.208988i
$671$	−25.6740	−	19.3501i	−0.991133	−	0.747001i
$672$			8.11314i			0.312971i
$673$	4.68377	−	6.44665i	0.180546	−	0.248500i	−0.709146	−	0.705062i	$-0.750919\pi$
$673$	4.68377	−	6.44665i	0.180546	−	0.248500i	0.889692	+	0.456562i	$0.150919\pi$
$674$	2.92538	−	9.00338i	0.112681	−	0.346797i
$675$	−26.9069	−	4.96266i	−1.03565	−	0.191013i
$676$	6.10624	−	4.43644i	0.234855	−	0.170632i
$677$	8.48443	+	11.6778i	0.326083	+	0.448815i	0.940312	−	0.340313i	$-0.110533\pi$
$677$	8.48443	+	11.6778i	0.326083	+	0.448815i	−0.614229	+	0.789128i	$0.710533\pi$
$678$	19.3304	−	6.28084i	0.742381	−	0.241214i
$679$	−11.3146	+	34.8229i	−0.434216	+	1.33638i
$680$	−0.105091	+	0.0874803i	−0.00403004	+	0.00335472i
$681$	−15.9159			−0.609898
$682$	16.8852	+	24.1188i	0.646567	+	0.923557i
$683$		−	29.6723i		−	1.13538i	−0.823242	−	0.567690i	$-0.807837\pi$
$683$		−	29.6723i		−	1.13538i	0.823242	−	0.567690i	$-0.192163\pi$
$684$	0.636930	+	0.462757i	0.0243536	+	0.0176940i
$685$	1.31682	−	2.08904i	0.0503130	−	0.0798183i
$686$	17.2645	+	53.1345i	0.659160	+	2.02869i
$687$	14.7869	+	20.3524i	0.564156	+	0.776493i
$688$	2.12663	+	2.92705i	0.0810769	+	0.111593i
$689$	−1.60321	−	4.93417i	−0.0610774	−	0.187977i
$690$	−7.55371	+	11.9835i	−0.287565	+	0.456203i
$691$	−26.1812	−	19.0218i	−0.995980	−	0.723622i	−0.0347577	−	0.999396i	$-0.511066\pi$
$691$	−26.1812	−	19.0218i	−0.995980	−	0.723622i	−0.961223	+	0.275774i	$0.911066\pi$
$692$			5.12859i			0.194960i
$693$	−0.111386	+	6.35120i	−0.00423121	+	0.241262i
$694$	16.5424			0.627943
$695$	17.0242	−	14.1714i	0.645765	−	0.537553i
$696$	2.06856	−	6.36638i	0.0784087	−	0.241317i
$697$	0.266353	−	0.0865432i	0.0100888	−	0.00327806i
$698$	−17.1791	−	23.6451i	−0.650240	−	0.894979i
$699$	33.8992	−	24.6292i	1.28219	−	0.931562i
$700$	24.6551	+	4.54735i	0.931876	+	0.171874i
$701$	5.86089	−	18.0380i	0.221363	−	0.681284i	−0.777278	−	0.629157i	$-0.783400\pi$
$701$	5.86089	−	18.0380i	0.221363	−	0.681284i	0.998640	−	0.0521266i	$-0.0165999\pi$
$702$	7.51043	−	10.3372i	0.283463	−	0.390153i
$703$			9.39242i			0.354242i
$704$	1.08005	−	3.13584i	0.0407058	−	0.118186i
$705$	−7.89228	+	31.1328i	−0.297241	+	1.17253i
$706$	−22.5878	−	16.4110i	−0.850103	−	0.617636i
$707$	1.05806	+	0.343785i	0.0397925	+	0.0129294i
$708$	2.98358	−	0.969425i	0.112130	−	0.0364332i
$709$	6.78617	−	4.93044i	0.254860	−	0.185167i	−0.453018	−	0.891501i	$-0.649653\pi$
$709$	6.78617	−	4.93044i	0.254860	−	0.185167i	0.707878	+	0.706335i	$0.249653\pi$
$710$	−18.3072	+	7.31309i	−0.687059	+	0.274455i
$711$	0.785540	+	2.41764i	0.0294600	+	0.0906687i
$712$	−5.79210	−	1.88197i	−0.217068	−	0.0705297i
$713$	20.4290	−	28.1182i	0.765074	−	1.05303i
$714$	−0.496121			−0.0185669
$715$	−0.836934	−	17.2967i	−0.0312995	−	0.646859i
$716$	−14.4394			−0.539625
$717$	19.0173	−	26.1751i	0.710216	−	0.977528i
$718$	16.1815	+	5.25768i	0.603887	+	0.196215i
$719$	−2.33218	−	7.17771i	−0.0869756	−	0.267684i	0.898104	−	0.439783i	$-0.144945\pi$
$719$	−2.33218	−	7.17771i	−0.0869756	−	0.267684i	−0.985079	+	0.172100i	$0.944945\pi$
$720$	−0.316839	−	0.793160i	−0.0118079	−	0.0295593i
$721$	2.29620	−	1.66829i	0.0855150	−	0.0621303i
$722$	−14.0297	+	4.55851i	−0.522130	+	0.169650i
$723$	−13.8708	−	4.50690i	−0.515861	−	0.167614i
$724$	9.63223	+	6.99822i	0.357979	+	0.260087i
$725$	−18.1875	−	9.85449i	−0.675466	−	0.365987i
$726$	−6.09017	+	16.7240i	−0.226027	+	0.620686i
$727$			24.2826i			0.900593i	0.892879	+	0.450297i	$0.148682\pi$
$727$			24.2826i			0.900593i	−0.892879	+	0.450297i	$0.851318\pi$
$728$	−6.88191	+	9.47214i	−0.255061	+	0.351061i
$729$	−9.11803	+	28.0624i	−0.337705	+	1.03935i
$730$	12.0400	−	0.794409i	0.445621	−	0.0294024i
$731$	−0.178990	+	0.130044i	−0.00662019	+	0.00480985i
$732$	9.21895	+	12.6888i	0.340742	+	0.468992i
$733$	20.3541	−	6.61345i	0.751796	−	0.244273i	0.0920424	−	0.995755i	$-0.470660\pi$
$733$	20.3541	−	6.61345i	0.751796	−	0.244273i	0.659754	+	0.751482i	$0.270660\pi$
$734$	9.09719	−	27.9983i	0.335784	−	1.03344i
$735$	41.9941	+	50.4477i	1.54897	+	1.86079i
$736$	−3.91525			−0.144318
$737$	7.91593	−	2.41943i	0.291587	−	0.0891207i
$738$			1.74935i			0.0643944i
$739$	28.4419	+	20.6642i	1.04625	+	0.760147i	0.971496	−	0.237055i	$-0.0761823\pi$
$739$	28.4419	+	20.6642i	1.04625	+	0.760147i	0.0747558	+	0.997202i	$0.476182\pi$
$740$	5.43351	−	8.61991i	0.199740	−	0.316874i
$741$	−2.40640	−	7.40615i	−0.0884015	−	0.272072i
$742$	−6.54846	−	9.01318i	−0.240401	−	0.330884i
$743$	−20.0435	−	27.5875i	−0.735324	−	1.01209i	−0.998874	−	0.0474407i	$-0.984893\pi$
$743$	−20.0435	−	27.5875i	−0.735324	−	1.01209i	0.263550	−	0.964646i	$-0.415107\pi$
$744$	−4.43854	−	13.6604i	−0.162725	−	0.500815i
$745$	−16.6318	−	10.4837i	−0.609341	−	0.384095i
$746$	−13.0044	−	9.44825i	−0.476125	−	0.345925i
$747$		−	4.22148i		−	0.154456i
$748$	0.191758	+	0.0660453i	0.00701136	+	0.00241485i
$749$	−11.1817			−0.408572
$750$	17.7379	−	3.55239i	0.647698	−	0.129715i
$751$	−11.0690	+	34.0669i	−0.403914	+	1.24312i	0.517884	+	0.855451i	$0.326720\pi$
$751$	−11.0690	+	34.0669i	−0.403914	+	1.24312i	−0.921799	+	0.387669i	$0.873280\pi$
$752$	−8.44260	+	2.74317i	−0.307870	+	0.100033i
$753$	1.24746	+	1.71698i	0.0454599	+	0.0625701i
$754$	7.81529	−	5.67814i	0.284616	−	0.206786i
$755$	−48.1727	+	3.17847i	−1.75318	+	0.115676i
$756$	8.47892	−	26.0954i	0.308375	−	0.949082i
$757$	14.2408	−	19.6008i	0.517592	−	0.712404i	−0.467584	−	0.883948i	$-0.654876\pi$
$757$	14.2408	−	19.6008i	0.517592	−	0.712404i	0.985176	+	0.171544i	$0.0548756\pi$
$758$			18.1230i			0.658256i
$759$	21.0076	+	0.368428i	0.762528	+	0.0133731i
$760$	−4.46756	−	1.13254i	−0.162055	−	0.0410817i
$761$	−8.62191	−	6.26419i	−0.312544	−	0.227077i	0.420443	−	0.907319i	$-0.361875\pi$
$761$	−8.62191	−	6.26419i	−0.312544	−	0.227077i	−0.732987	+	0.680242i	$0.761875\pi$
$762$	−22.2562	−	7.23149i	−0.806258	−	0.261969i
$763$	−37.4964	+	12.1833i	−1.35746	+	0.441065i
$764$	8.50930	−	6.18237i	0.307856	−	0.223670i
$765$	0.0485020	−	0.0193748i	0.00175359	−	0.000700499i
$766$	−4.08276	−	12.5654i	−0.147516	−	0.454008i
$767$	4.30566	+	1.39899i	0.155468	+	0.0505147i
$768$	−0.951057	+	1.30902i	−0.0343183	+	0.0472351i
$769$	−25.8297			−0.931444			−0.465722	−	0.884931i	$-0.654205\pi$
$769$	−25.8297			−0.931444			−0.465722	+	0.884931i	$0.654205\pi$
$770$	−13.1870	−	34.7695i	−0.475227	−	1.25301i
$771$	7.22289			0.260126
$772$	2.86174	−	3.93885i	0.102996	−	0.141762i
$773$	11.4679	+	3.72614i	0.412471	+	0.134020i	0.507899	−	0.861416i	$-0.330422\pi$
$773$	11.4679	+	3.72614i	0.412471	+	0.134020i	−0.0954286	+	0.995436i	$0.530422\pi$
$774$	−0.427051	−	1.31433i	−0.0153500	−	0.0472425i
$775$	−44.0006	+	5.83177i	−1.58055	+	0.209484i
$776$	−5.90765	+	4.29216i	−0.212072	+	0.154079i
$777$	35.1612	−	11.4246i	1.26140	−	0.409854i
$778$	−25.2263	−	8.19653i	−0.904407	−	0.293860i
$779$	7.63693	+	5.54855i	0.273621	+	0.198798i
$780$	−2.07597	+	8.18911i	−0.0743318	+	0.293217i
$781$	23.3510	+	17.5992i	0.835563	+	0.629750i
$782$		−	0.239419i		−	0.00856161i
$783$	−13.3068	+	18.3153i	−0.475547	+	0.654534i
$784$	−5.60624	+	17.2542i	−0.200223	+	0.616222i
$785$	−0.502707	−	7.61899i	−0.0179424	−	0.271933i
$786$	20.0615	−	14.5755i	0.715569	−	0.519892i
$787$	10.6725	+	14.6895i	0.380435	+	0.523624i	0.955700	−	0.294343i	$-0.0951009\pi$
$787$	10.6725	+	14.6895i	0.380435	+	0.523624i	−0.575265	+	0.817967i	$0.695101\pi$
$788$	−15.1941	+	4.93686i	−0.541267	+	0.175868i
$789$	−7.08954	+	21.8194i	−0.252394	+	0.776790i
$790$	−9.52078	−	11.4374i	−0.338734	−	0.406923i
$791$	62.9867			2.23955
$792$	−0.762486	+	1.01168i	−0.0270938	+	0.0359484i
$793$			22.6342i			0.803762i
$794$	−24.5331	−	17.8243i	−0.870648	−	0.632562i
$795$	−6.80051	−	4.28666i	−0.241189	−	0.152032i
$796$	5.16292	+	15.8898i	0.182995	+	0.563201i
$797$	−0.946725	−	1.30306i	−0.0335347	−	0.0461566i	0.791920	−	0.610624i	$-0.209081\pi$
$797$	−0.946725	−	1.30306i	−0.0335347	−	0.0461566i	−0.825455	+	0.564468i	$0.809081\pi$
$798$	−9.82918	−	13.5287i	−0.347949	−	0.478911i
$799$	−0.167746	−	0.516268i	−0.00593441	−	0.0182642i
$800$	3.44493	+	3.62387i	0.121797	+	0.128123i
$801$	1.88197	+	1.36733i	0.0664960	+	0.0483122i
$802$		−	19.4762i		−	0.687727i
$803$	−10.2641	−	14.6612i	−0.362213	−	0.517384i
$804$	−4.03818			−0.142416
$805$	−33.7385	+	28.0849i	−1.18913	+	0.989862i
$806$	6.40532	−	19.7136i	0.225618	−	0.694380i
$807$	49.2356	−	15.9976i	1.73318	−	0.563143i
$808$	0.130413	+	0.179498i	0.00458792	+	0.00631473i
$809$	20.7273	−	15.0593i	0.728733	−	0.529455i	−0.160429	−	0.987047i	$-0.551288\pi$
$809$	20.7273	−	15.0593i	0.728733	−	0.529455i	0.889162	+	0.457592i	$0.151288\pi$
$810$	−1.13478	−	17.1987i	−0.0398722	−	0.604300i
$811$	13.5506	−	41.7045i	0.475827	−	1.46444i	−0.369012	−	0.929424i	$-0.620304\pi$
$811$	13.5506	−	41.7045i	0.475827	−	1.46444i	0.844839	−	0.535020i	$-0.179696\pi$
$812$	12.1932	−	16.7825i	0.427898	−	0.588951i
$813$		−	1.71737i		−	0.0602306i
$814$	−15.1111	−	0.265017i	−0.529646	−	0.00928883i
$815$	37.7370	+	9.56650i	1.32187	+	0.335100i
$816$	−0.0800469	−	0.0581575i	−0.00280220	−	0.00203592i
$817$	−7.09233	−	2.30444i	−0.248129	−	0.0806220i
$818$	26.9437	−	8.75453i	0.942063	−	0.306095i
$819$	3.61803	−	2.62866i	0.126424	−	0.0918527i
$820$	−3.79897	−	9.51016i	−0.132666	−	0.332109i
$821$	−5.43938	−	16.7407i	−0.189836	−	0.584254i	0.810163	−	0.586205i	$-0.199379\pi$
$821$	−5.43938	−	16.7407i	−0.189836	−	0.584254i	−0.999998	+	0.00195152i	$0.999379\pi$
$822$	1.69944	+	0.552183i	0.0592749	+	0.0192596i
$823$	7.43854	−	10.2383i	0.259291	−	0.356884i	−0.659447	−	0.751751i	$-0.729209\pi$
$823$	7.43854	−	10.2383i	0.259291	−	0.356884i	0.918738	+	0.394867i	$0.129209\pi$
$824$	0.566045			0.0197191
$825$	−18.1431	−	19.7684i	−0.631660	−	0.688246i
$826$	9.72177			0.338264
$827$	5.19856	−	7.15520i	0.180772	−	0.248811i	−0.709009	−	0.705200i	$-0.750857\pi$
$827$	5.19856	−	7.15520i	0.180772	−	0.248811i	0.889780	+	0.456389i	$0.150857\pi$
$828$	1.42230	+	0.462133i	0.0494283	+	0.0160602i
$829$	−11.6571	−	35.8767i	−0.404866	−	1.24605i	−0.921007	−	0.389546i	$-0.872632\pi$
$829$	−11.6571	−	35.8767i	−0.404866	−	1.24605i	0.516141	−	0.856504i	$-0.327368\pi$
$830$	9.16758	+	22.9497i	0.318211	+	0.796595i
$831$	8.68303	−	6.30859i	0.301211	−	0.218843i
$832$	−2.22073	+	0.721558i	−0.0769899	+	0.0250155i
$833$	−1.05510	−	0.342823i	−0.0365571	−	0.0118781i
$834$	12.9672	+	9.42125i	0.449019	+	0.326231i
$835$	−7.16576	−	1.81655i	−0.247981	−	0.0628643i
$836$	1.99813	+	6.53752i	0.0691068	+	0.226105i
$837$			48.5765i			1.67905i
$838$	−9.10044	+	12.5257i	−0.314369	+	0.432692i
$839$	11.8934	−	36.6041i	0.410606	−	1.26372i	−0.505517	−	0.862817i	$-0.668698\pi$
$839$	11.8934	−	36.6041i	0.410606	−	1.26372i	0.916123	−	0.400898i	$-0.131302\pi$
$840$	1.19440	+	18.1022i	0.0412106	+	0.624584i
$841$	9.61452	−	6.98536i	0.331535	−	0.240874i
$842$	12.6293	+	17.3828i	0.435236	+	0.599051i
$843$	24.0774	−	7.82321i	0.829269	−	0.269446i
$844$	4.86578	−	14.9753i	0.167487	−	0.515472i
$845$	12.9712	−	10.7976i	0.446223	−	0.371449i
$846$	3.39074			0.116576
$847$	−33.9647	+	43.4580i	−1.16704	+	1.49324i
$848$		−	2.22187i		−	0.0762994i
$849$	29.4536	+	21.3993i	1.01084	+	0.734421i
$850$	−0.221601	+	0.210659i	−0.00760086	+	0.00722554i
$851$	5.51328	+	16.9681i	0.188993	+	0.581660i
$852$	−8.38481	−	11.5407i	−0.287259	−	0.395378i
$853$	29.9122	+	41.1706i	1.02417	+	1.40965i	0.909237	+	0.416280i	$0.136666\pi$
$853$	29.9122	+	41.1706i	1.02417	+	1.40965i	0.114936	+	0.993373i	$0.463334\pi$
$854$	15.0196	+	46.2256i	0.513961	+	1.58181i
$855$	1.48926	+	0.938744i	0.0509315	+	0.0321044i
$856$	−1.80412	−	1.31077i	−0.0616636	−	0.0448012i
$857$			11.5197i			0.393506i	0.980453	+	0.196753i	$0.0630397\pi$
$857$			11.5197i			0.393506i	−0.980453	+	0.196753i	$0.936960\pi$
$858$	11.9834	−	3.66261i	0.409107	−	0.125039i
$859$	−23.9497			−0.817153			−0.408577	−	0.912724i	$-0.633975\pi$
$859$	−23.9497			−0.817153			−0.408577	+	0.912724i	$0.633975\pi$
$860$	5.17588	+	6.21781i	0.176496	+	0.212025i
$861$	11.4821	−	35.3384i	0.391310	−	1.20433i
$862$	25.1450	−	8.17010i	0.856441	−	0.278275i
$863$	−23.5170	−	32.3684i	−0.800530	−	1.10183i	−0.992716	−	0.120476i	$-0.961558\pi$
$863$	−23.5170	−	32.3684i	−0.800530	−	1.10183i	0.192187	−	0.981358i	$-0.438442\pi$
$864$	4.42705	−	3.21644i	0.150611	−	0.109426i
$865$	0.755018	+	11.4430i	0.0256714	+	0.389074i
$866$	−10.1611	+	31.2725i	−0.345287	+	1.06268i
$867$	−16.1644	+	22.2484i	−0.548972	+	0.755595i
$868$		−	44.5114i		−	1.51081i
$869$	−7.18793	+	20.8696i	−0.243834	+	0.707954i
$870$	3.67817	−	14.5093i	0.124702	−	0.491911i
$871$	−4.71460	−	3.42536i	−0.159748	−	0.116064i
$872$	−7.47804	−	2.42976i	−0.253238	−	0.0822821i
$873$	2.65270	−	0.861914i	0.0897802	−	0.0291714i
$874$	6.52871	−	4.74338i	0.220837	−	0.160447i
$875$	55.6804	+	6.51646i	1.88234	+	0.220297i
$876$	2.69808	+	8.30384i	0.0911597	+	0.280561i
$877$	−24.7104	−	8.02891i	−0.834413	−	0.271117i	−0.139510	−	0.990221i	$-0.544553\pi$
$877$	−24.7104	−	8.02891i	−0.834413	−	0.271117i	−0.694903	+	0.719104i	$0.744553\pi$
$878$	−7.15897	+	9.85347i	−0.241603	+	0.332539i
$879$	−29.4300			−0.992648
$880$	1.94817	−	7.15574i	0.0656727	−	0.241220i
$881$	25.1372			0.846893			0.423446	−	0.905921i	$-0.360820\pi$
$881$	25.1372			0.846893			0.423446	+	0.905921i	$0.360820\pi$
$882$	4.07317	−	5.60624i	0.137151	−	0.188772i
$883$	−41.3431	−	13.4332i	−1.39131	−	0.452063i	−0.484937	−	0.874549i	$-0.661157\pi$
$883$	−41.3431	−	13.4332i	−1.39131	−	0.452063i	−0.906369	+	0.422486i	$0.861157\pi$
$884$	−0.0441236	−	0.135798i	−0.00148404	−	0.00456739i
$885$	6.51430	−	2.60223i	0.218976	−	0.0874731i
$886$	−13.4370	+	9.76254i	−0.451424	+	0.327979i
$887$	27.2078	−	8.84036i	0.913549	−	0.296830i	0.185731	−	0.982601i	$-0.440535\pi$
$887$	27.2078	−	8.84036i	0.913549	−	0.296830i	0.727818	+	0.685770i	$0.240535\pi$
$888$	7.01232	+	2.27844i	0.235318	+	0.0764595i
$889$	−58.6701	−	42.6263i	−1.96773	−	1.42964i
$890$	−13.2005	−	3.34638i	−0.442481	−	0.112171i
$891$	−20.9430	+	14.6619i	−0.701617	+	0.491191i
$892$			14.5556i			0.487358i
$893$	10.7547	−	14.8026i	0.359892	−	0.495349i
$894$	4.39616	−	13.5300i	0.147030	−	0.452511i
$895$	−32.2174	+	2.12573i	−1.07691	+	0.0710553i
$896$	−4.05657	+	2.94727i	−0.135520	+	0.0984614i
$897$	−8.69471	−	11.9672i	−0.290308	−	0.399575i
$898$	5.10113	−	1.65746i	0.170227	−	0.0553100i
$899$	−11.3488	+	34.9281i	−0.378504	+	1.16492i
$900$	−0.823704	−	1.72307i	−0.0274568	−	0.0574356i
$901$	0.135868			0.00452643
$902$	−9.14237	+	12.1302i	−0.304407	+	0.403893i
$903$			29.3536i			0.976827i
$904$	10.1626	+	7.38357i	0.338003	+	0.245574i
$905$	22.5219	+	14.1965i	0.748652	+	0.471908i
$906$	−10.7952	−	33.2241i	−0.358645	−	1.10380i
$907$	28.0438	+	38.5990i	0.931179	+	1.28166i	0.959398	+	0.282056i	$0.0910165\pi$
$907$	28.0438	+	38.5990i	0.931179	+	1.28166i	−0.0282187	+	0.999602i	$0.508983\pi$
$908$	−5.78178	−	7.95794i	−0.191875	−	0.264094i
$909$	−0.0261885	−	0.0805998i	−0.000868617	−	0.00267333i
$910$	−13.9606	+	22.1475i	−0.462788	+	0.734183i
$911$	−40.3003	−	29.2799i	−1.33521	−	0.970085i	−0.999606	−	0.0280809i	$-0.991060\pi$
$911$	−40.3003	−	29.2799i	−1.33521	−	0.970085i	−0.335602	−	0.942004i	$-0.608940\pi$
$912$		−	3.33501i		−	0.110433i
$913$	22.0621	−	29.2724i	0.730150	−	0.968775i
$914$	−3.61237			−0.119487
$915$	22.4375	+	26.9543i	0.741761	+	0.891081i
$916$	−4.80456	+	14.7869i	−0.158747	+	0.488573i
$917$	73.0845	−	23.7466i	2.41346	−	0.784182i
$918$	0.196687	+	0.270716i	0.00649162	+	0.00893495i
$919$	−34.7058	+	25.2153i	−1.14484	+	0.831775i	−0.987786	−	0.155815i	$-0.950199\pi$
$919$	−34.7058	+	25.2153i	−1.14484	+	0.831775i	−0.157053	+	0.987590i	$0.550199\pi$
$920$	−8.73578	+	0.576394i	−0.288010	+	0.0190031i
$921$	−6.19098	+	19.0539i	−0.204000	+	0.627847i
$922$	23.9008	−	32.8967i	0.787132	−	1.08339i
$923$		−	20.5862i		−	0.677602i
$924$	22.0432	−	15.4321i	0.725169	−	0.507679i
$925$	10.8543	−	20.0328i	0.356889	−	0.658674i
$926$	−1.71415	−	1.24540i	−0.0563303	−	0.0409264i
$927$	−0.205628	−	0.0668126i	−0.00675371	−	0.00219441i
$928$	3.93464	−	1.27844i	0.129161	−	0.0419669i
$929$	−3.20719	+	2.33016i	−0.105224	+	0.0764500i	−0.639153	−	0.769079i	$-0.720715\pi$
$929$	−3.20719	+	2.33016i	−0.105224	+	0.0764500i	0.533929	+	0.845529i	$0.320715\pi$
$930$	−11.9144	−	29.8259i	−0.390688	−	0.978030i
$931$	−11.5553	−	35.5635i	−0.378709	−	1.16555i
$932$	24.6292	+	8.00252i	0.806757	+	0.262131i
$933$	−8.94941	+	12.3178i	−0.292991	+	0.403267i
$934$	−13.7549			−0.450075
$935$	0.437576	+	0.119131i	0.0143103	+	0.00389601i
$936$	0.891895			0.0291525
$937$	1.24563	−	1.71446i	0.0406929	−	0.0560090i	−0.788186	−	0.615437i	$-0.788979\pi$
$937$	1.24563	−	1.71446i	0.0406929	−	0.0560090i	0.828879	+	0.559429i	$0.188979\pi$
$938$	−11.9016	−	3.86707i	−0.388601	−	0.126264i
$939$	7.61585	+	23.4392i	0.248534	+	0.764909i
$940$	−18.4334	+	7.36349i	−0.601232	+	0.240171i
$941$	−4.08118	+	2.96515i	−0.133043	+	0.0966612i	−0.652316	−	0.757947i	$-0.726203\pi$
$941$	−4.08118	+	2.96515i	−0.133043	+	0.0966612i	0.519274	+	0.854608i	$0.326203\pi$
$942$	5.25472	−	1.70736i	0.171208	−	0.0556289i
$943$	17.0537	+	5.54107i	0.555344	+	0.180442i
$944$	1.56856	+	1.13963i	0.0510524	+	0.0370917i
$945$	15.0766	−	59.4728i	0.490442	−	1.93465i
$946$	3.90765	−	11.3456i	0.127049	−	0.368877i
$947$			0.986192i			0.0320470i	0.999872	+	0.0160235i	$0.00510065\pi$
$947$			0.986192i			0.0320470i	−0.999872	+	0.0160235i	$0.994899\pi$
$948$	6.32947	−	8.71177i	0.205572	−	0.282945i
$949$	−3.89364	+	11.9834i	−0.126393	+	0.388998i
$950$	−10.1348	−	1.86925i	−0.328817	−	0.0606464i
$951$	−17.6150	+	12.7981i	−0.571206	+	0.415006i
$952$	−0.180227	−	0.248061i	−0.00584118	−	0.00803969i
$953$	−21.8386	+	7.09580i	−0.707422	+	0.229855i	−0.640562	−	0.767907i	$-0.721298\pi$
$953$	−21.8386	+	7.09580i	−0.707422	+	0.229855i	−0.0668608	+	0.997762i	$0.521298\pi$
$954$	−0.262256	+	0.807142i	−0.00849087	+	0.0261322i
$955$	18.0759	−	15.0469i	0.584924	−	0.486907i
$956$	19.9960			0.646718
$957$	−21.2320	+	6.48934i	−0.686331	+	0.209770i
$958$			31.4107i			1.01484i
$959$	4.47994	+	3.25486i	0.144665	+	0.105105i
$960$	−1.92930	+	3.06071i	−0.0622680	+	0.0987841i
$961$	14.7718	+	45.4628i	0.476508	+	1.46654i
$962$	6.25426	+	8.60824i	0.201645	+	0.277541i
$963$	0.500670	+	0.689113i	0.0161339	+	0.0222064i
$964$	−2.78542	−	8.57264i	−0.0897123	−	0.276106i
$965$	5.80530	−	9.20972i	0.186879	−	0.296472i
$966$	−25.6984	−	18.6710i	−0.826833	−	0.600729i
$967$		−	20.1267i		−	0.647231i	−0.946189	−	0.323616i	$-0.895102\pi$
$967$		−	20.1267i		−	0.647231i	0.946189	−	0.323616i	$-0.104898\pi$
$968$	−10.5744	+	3.03026i	−0.339873	+	0.0973963i
$969$	0.203937			0.00655141
$970$	−12.5494	+	10.4464i	−0.402936	+	0.335415i
$971$	−6.77852	+	20.8621i	−0.217533	+	0.669498i	0.781431	+	0.623991i	$0.214490\pi$
$971$	−6.77852	+	20.8621i	−0.217533	+	0.669498i	−0.998964	+	0.0455060i	$0.985510\pi$
$972$	−3.75123	+	1.21885i	−0.120321	+	0.0390945i
$973$	29.1959	+	40.1847i	0.935978	+	1.28826i
$974$	6.07597	−	4.41445i	0.194687	−	0.141448i
$975$	−3.42637	+	18.5773i	−0.109732	+	0.594950i
$976$	−2.99542	+	9.21895i	−0.0958810	+	0.295091i
$977$	−34.7133	+	47.7788i	−1.11058	+	1.52858i	−0.290015	+	0.957022i	$0.593660\pi$
$977$	−34.7133	+	47.7788i	−1.11058	+	1.52858i	−0.820562	+	0.571557i	$0.806340\pi$
$978$			28.1706i			0.900795i
$979$	5.90396	+	19.3167i	0.188691	+	0.617365i
$980$	−9.96860	+	39.3232i	−0.318435	+	1.25613i
$981$	2.42976	+	1.76533i	0.0775763	+	0.0563625i
$982$	−10.7106	−	3.48008i	−0.341788	−	0.111054i
$983$	−45.9751	+	14.9382i	−1.46638	+	0.476455i	−0.930012	−	0.367530i	$-0.880204\pi$
$983$	−45.9751	+	14.9382i	−1.46638	+	0.476455i	−0.536367	+	0.843985i	$0.680204\pi$
$984$	5.99511	−	4.35570i	0.191117	−	0.138855i
$985$	−33.1745	+	13.2520i	−1.05703	+	0.422245i
$986$	0.0781772	+	0.240605i	0.00248967	+	0.00766241i
$987$	−68.4960	−	22.2557i	−2.18025	−	0.708406i
$988$	2.82890	−	3.89364i	0.0899992	−	0.123873i
$989$	−14.1655			−0.450437
$990$	−1.55233	+	2.36953i	−0.0493364	+	0.0753085i
$991$	−55.0154			−1.74762			−0.873811	−	0.486266i	$-0.838359\pi$
$991$	−55.0154			−1.74762			−0.873811	+	0.486266i	$0.838359\pi$
$992$	5.21781	−	7.18170i	0.165666	−	0.228019i
$993$	5.88201	+	1.91118i	0.186660	+	0.0606495i
$994$	−13.6606	−	42.0431i	−0.433289	−	1.33353i
$995$	13.8589	+	34.6936i	0.439356	+	1.09986i
$996$	−14.4672	+	10.5111i	−0.458412	+	0.333056i
$997$	−21.8457	+	7.09810i	−0.691861	+	0.224799i	−0.633781	−	0.773513i	$-0.718498\pi$
$997$	−21.8457	+	7.09810i	−0.691861	+	0.224799i	−0.0580799	+	0.998312i	$0.518498\pi$
$998$	−25.6603	−	8.33753i	−0.812262	−	0.263920i
$999$	−20.1736	−	14.6569i	−0.638263	−	0.463725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.j.b.59.2	✓	16
3.2	odd	2		990.2.ba.h.829.3		16
4.3	odd	2		880.2.cd.b.609.4		16
5.2	odd	4		550.2.h.j.301.2		8
5.3	odd	4		550.2.h.n.301.1		8
5.4	even	2	inner	110.2.j.b.59.4	yes	16
11.3	even	5	inner	110.2.j.b.69.4	yes	16
11.5	even	5		1210.2.b.k.969.1		8
11.6	odd	10		1210.2.b.l.969.5		8
15.14	odd	2		990.2.ba.h.829.1		16
20.19	odd	2		880.2.cd.b.609.2		16
33.14	odd	10		990.2.ba.h.289.1		16
44.3	odd	10		880.2.cd.b.289.2		16
55.3	odd	20		550.2.h.n.201.1		8
55.14	even	10	inner	110.2.j.b.69.2	yes	16
55.17	even	20		6050.2.a.da.1.1		4
55.27	odd	20		6050.2.a.di.1.2		4
55.28	even	20		6050.2.a.dl.1.4		4
55.38	odd	20		6050.2.a.dd.1.3		4
55.39	odd	10		1210.2.b.l.969.3		8
55.47	odd	20		550.2.h.j.201.2		8
55.49	even	10		1210.2.b.k.969.7		8
165.14	odd	10		990.2.ba.h.289.3		16
220.179	odd	10		880.2.cd.b.289.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	1.1	even	1	trivial
110.2.j.b.59.4	yes	16	5.4	even	2	inner
110.2.j.b.69.2	yes	16	55.14	even	10	inner
110.2.j.b.69.4	yes	16	11.3	even	5	inner
550.2.h.j.201.2		8	55.47	odd	20
550.2.h.j.301.2		8	5.2	odd	4
550.2.h.n.201.1		8	55.3	odd	20
550.2.h.n.301.1		8	5.3	odd	4
880.2.cd.b.289.2		16	44.3	odd	10
880.2.cd.b.289.4		16	220.179	odd	10
880.2.cd.b.609.2		16	20.19	odd	2
880.2.cd.b.609.4		16	4.3	odd	2
990.2.ba.h.289.1		16	33.14	odd	10
990.2.ba.h.289.3		16	165.14	odd	10
990.2.ba.h.829.1		16	15.14	odd	2
990.2.ba.h.829.3		16	3.2	odd	2
1210.2.b.k.969.1		8	11.5	even	5
1210.2.b.k.969.7		8	55.49	even	10
1210.2.b.l.969.3		8	55.39	odd	10
1210.2.b.l.969.5		8	11.6	odd	10
6050.2.a.da.1.1		4	55.17	even	20
6050.2.a.dd.1.3		4	55.38	odd	20
6050.2.a.di.1.2		4	55.27	odd	20
6050.2.a.dl.1.4		4	55.28	even	20

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.53884 - 0.500000i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.829496 - 2.07652i) q^{5} +(1.30902 - 0.951057i) q^{6} +(4.76878 - 1.54947i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.224514i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.53884 - 0.500000i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.829496 - 2.07652i) q^{5} +(1.30902 - 0.951057i) q^{6} +(4.76878 - 1.54947i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.224514i) q^{9} +(2.16751 + 0.549472i) q^{10} +(-0.969425 - 3.17178i) q^{11} +1.61803i q^{12} +(-1.37249 + 1.88906i) q^{13} +(-1.54947 + 4.76878i) q^{14} +(0.238203 + 3.61018i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.0359433 - 0.0494717i) q^{17} +(0.363271 - 0.118034i) q^{18} +(0.636930 - 1.96027i) q^{19} +(-1.71856 + 1.43058i) q^{20} -8.11314 q^{21} +(3.13584 + 1.08005i) q^{22} -3.91525i q^{23} +(-1.30902 - 0.951057i) q^{24} +(-3.62387 + 3.44493i) q^{25} +(-0.721558 - 2.22073i) q^{26} +(3.21644 + 4.42705i) q^{27} +(-2.94727 - 4.05657i) q^{28} +(1.27844 + 3.93464i) q^{29} +(-3.06071 - 1.92930i) q^{30} +(7.18170 + 5.21781i) q^{31} -1.00000i q^{32} +(-0.0941007 + 5.36559i) q^{33} +0.0611504 q^{34} +(-7.17320 - 8.61720i) q^{35} +(-0.118034 + 0.363271i) q^{36} +(-4.33385 + 1.40815i) q^{37} +(1.21151 + 1.66751i) q^{38} +(3.05657 - 2.22073i) q^{39} +(-0.147217 - 2.23122i) q^{40} +(-1.41525 + 4.35570i) q^{41} +(4.76878 - 6.56367i) q^{42} -3.61803i q^{43} +(-2.71698 + 1.90211i) q^{44} +(-0.209880 + 0.827913i) q^{45} +(3.16751 + 2.30133i) q^{46} +(8.44260 + 2.74317i) q^{47} +(1.53884 - 0.500000i) q^{48} +(14.6773 - 10.6637i) q^{49} +(-0.656948 - 4.95665i) q^{50} +(0.0305752 + 0.0941007i) q^{51} +(2.22073 + 0.721558i) q^{52} +(-1.30598 + 1.79753i) q^{53} -5.47214 q^{54} +(-5.78214 + 4.64401i) q^{55} +5.01420 q^{56} +(-1.96027 + 2.69808i) q^{57} +(-3.93464 - 1.27844i) q^{58} +(-0.599137 - 1.84396i) q^{59} +(3.35988 - 1.34215i) q^{60} +(7.84211 - 5.69763i) q^{61} +(-8.44260 + 2.74317i) q^{62} +(-1.82151 - 0.591846i) q^{63} +(0.809017 + 0.587785i) q^{64} +(5.06115 + 1.28302i) q^{65} +(-4.28554 - 3.22994i) q^{66} +2.49573i q^{67} +(-0.0359433 + 0.0494717i) q^{68} +(-1.95763 + 6.02495i) q^{69} +(11.1878 - 0.738177i) q^{70} +(-7.13254 + 5.18210i) q^{71} +(-0.224514 - 0.309017i) q^{72} +(5.13205 - 1.66751i) q^{73} +(1.40815 - 4.33385i) q^{74} +(7.29903 - 3.48927i) q^{75} -2.06115 q^{76} +(-9.53757 - 13.6235i) q^{77} +3.77813i q^{78} +(-5.38417 - 3.91183i) q^{79} +(1.89162 + 1.19237i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(-2.69197 - 3.70518i) q^{82} +(6.49620 + 8.94125i) q^{83} +(2.50710 + 7.71605i) q^{84} +(-0.0729142 + 0.115674i) q^{85} +(2.92705 + 2.12663i) q^{86} -6.69401i q^{87} +(0.0581575 - 3.31611i) q^{88} -6.09017 q^{89} +(-0.546432 - 0.656431i) q^{90} +(-3.61803 + 11.1352i) q^{91} +(-3.72363 + 1.20988i) q^{92} +(-8.44260 - 11.6202i) q^{93} +(-7.18170 + 5.21781i) q^{94} +(-4.59887 + 0.303437i) q^{95} +(-0.500000 + 1.53884i) q^{96} +(-4.29216 + 5.90765i) q^{97} +18.1422i q^{98} +(-0.412541 + 1.19778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 - 6 * q^5 + 12 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} - 6 q^{5} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 20 q^{11} - 12 q^{14} + 2 q^{15} - 4 q^{16} - 16 q^{19} + 6 q^{20} - 16 q^{21} - 12 q^{24} - 16 q^{26} + 16 q^{29} - 2 q^{30} - 4 q^{31} - 8 q^{34} - 48 q^{35} + 16 q^{36} - 8 q^{39} - 4 q^{40} + 40 q^{41} - 4 q^{45} + 20 q^{46} + 84 q^{49} + 4 q^{50} - 4 q^{51} - 16 q^{54} + 32 q^{55} - 8 q^{56} + 8 q^{60} + 20 q^{61} + 4 q^{64} + 72 q^{65} - 20 q^{66} + 36 q^{70} - 56 q^{71} + 4 q^{74} + 32 q^{75} - 24 q^{76} + 36 q^{79} + 4 q^{80} - 56 q^{81} - 4 q^{84} - 54 q^{85} + 20 q^{86} - 8 q^{89} - 4 q^{90} - 40 q^{91} + 4 q^{94} - 50 q^{95} - 8 q^{96} - 20 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 - 6 * q^5 + 12 * q^6 + 4 * q^9 + 4 * q^10 - 20 * q^11 - 12 * q^14 + 2 * q^15 - 4 * q^16 - 16 * q^19 + 6 * q^20 - 16 * q^21 - 12 * q^24 - 16 * q^26 + 16 * q^29 - 2 * q^30 - 4 * q^31 - 8 * q^34 - 48 * q^35 + 16 * q^36 - 8 * q^39 - 4 * q^40 + 40 * q^41 - 4 * q^45 + 20 * q^46 + 84 * q^49 + 4 * q^50 - 4 * q^51 - 16 * q^54 + 32 * q^55 - 8 * q^56 + 8 * q^60 + 20 * q^61 + 4 * q^64 + 72 * q^65 - 20 * q^66 + 36 * q^70 - 56 * q^71 + 4 * q^74 + 32 * q^75 - 24 * q^76 + 36 * q^79 + 4 * q^80 - 56 * q^81 - 4 * q^84 - 54 * q^85 + 20 * q^86 - 8 * q^89 - 4 * q^90 - 40 * q^91 + 4 * q^94 - 50 * q^95 - 8 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more