LMFDB - Embedded newform 416.2.bd.a.83.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.7
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29289 - 0.573103i) q^{2} +(-0.377788 - 0.156485i) q^{3} +(1.34311 + 1.48191i) q^{4} +(-0.605904 + 1.46278i) q^{5} +(0.398755 + 0.418829i) q^{6} -0.514771i q^{7} +(-0.887196 - 2.68568i) q^{8} +(-2.00308 - 2.00308i) q^{9} +O(q^{10})$	\(q+(-1.29289 - 0.573103i) q^{2} +(-0.377788 - 0.156485i) q^{3} +(1.34311 + 1.48191i) q^{4} +(-0.605904 + 1.46278i) q^{5} +(0.398755 + 0.418829i) q^{6} -0.514771i q^{7} +(-0.887196 - 2.68568i) q^{8} +(-2.00308 - 2.00308i) q^{9} +(1.62169 - 1.54396i) q^{10} +(1.18377 + 0.490335i) q^{11} +(-0.275513 - 0.770025i) q^{12} +(3.33495 - 1.37044i) q^{13} +(-0.295017 + 0.665540i) q^{14} +(0.457807 - 0.457807i) q^{15} +(-0.392128 + 3.98073i) q^{16} +2.14260 q^{17} +(1.44179 + 3.73773i) q^{18} +(2.46054 + 5.94027i) q^{19} +(-2.98151 + 1.06678i) q^{20} +(-0.0805540 + 0.194475i) q^{21} +(-1.24947 - 1.31237i) q^{22} +(2.48571 + 2.48571i) q^{23} +(-0.0850968 + 1.15345i) q^{24} +(1.76292 + 1.76292i) q^{25} +(-5.09711 - 0.139444i) q^{26} +(0.912744 + 2.20356i) q^{27} +(0.762846 - 0.691393i) q^{28} +(2.05949 - 4.97205i) q^{29} +(-0.854263 + 0.329522i) q^{30} +(0.734578 + 0.734578i) q^{31} +(2.78835 - 4.92190i) q^{32} +(-0.370486 - 0.370486i) q^{33} +(-2.77014 - 1.22793i) q^{34} +(0.752998 + 0.311902i) q^{35} +(0.278039 - 5.65875i) q^{36} +(10.8217 + 4.48250i) q^{37} +(0.223187 - 9.09023i) q^{38} +(-1.47436 - 0.00413299i) q^{39} +(4.46612 + 0.329491i) q^{40} -3.72832 q^{41} +(0.215601 - 0.205268i) q^{42} +(-1.07795 - 2.60239i) q^{43} +(0.863300 + 2.41282i) q^{44} +(4.14375 - 1.71640i) q^{45} +(-1.78917 - 4.63830i) q^{46} +(-0.193010 - 0.193010i) q^{47} +(0.771067 - 1.44251i) q^{48} +6.73501 q^{49} +(-1.26892 - 3.28959i) q^{50} +(-0.809450 - 0.335285i) q^{51} +(6.51007 + 3.10145i) q^{52} +(-1.51275 - 3.65211i) q^{53} +(0.0827918 - 3.37205i) q^{54} +(-1.43451 + 1.43451i) q^{55} +(-1.38251 + 0.456703i) q^{56} -2.62920i q^{57} +(-5.51218 + 5.24799i) q^{58} +(-3.98767 + 9.62709i) q^{59} +(1.29331 + 0.0635461i) q^{60} +(5.11727 - 12.3542i) q^{61} +(-0.528737 - 1.37071i) q^{62} +(-1.03113 + 1.03113i) q^{63} +(-6.42577 + 4.76545i) q^{64} +(-0.0160028 + 5.70866i) q^{65} +(0.266669 + 0.691322i) q^{66} +(10.1248 - 4.19384i) q^{67} +(2.87774 + 3.17515i) q^{68} +(-0.550095 - 1.32805i) q^{69} +(-0.794789 - 0.834799i) q^{70} -13.8983 q^{71} +(-3.60252 + 7.15677i) q^{72} +1.32072i q^{73} +(-11.4223 - 11.9973i) q^{74} +(-0.390141 - 0.941883i) q^{75} +(-5.49819 + 11.6247i) q^{76} +(0.252410 - 0.609372i) q^{77} +(1.90381 + 0.850302i) q^{78} -9.86871 q^{79} +(-5.58535 - 2.98554i) q^{80} +7.52305i q^{81} +(4.82029 + 2.13671i) q^{82} +(2.34587 + 5.66344i) q^{83} +(-0.396387 + 0.141826i) q^{84} +(-1.29821 + 3.13416i) q^{85} +(-0.0977765 + 3.98237i) q^{86} +(-1.55610 + 1.55610i) q^{87} +(0.266645 - 3.61426i) q^{88} +4.73380 q^{89} +(-6.34107 - 0.155688i) q^{90} +(-0.705464 - 1.71674i) q^{91} +(-0.345030 + 7.02217i) q^{92} +(-0.162565 - 0.392466i) q^{93} +(0.138925 + 0.360154i) q^{94} -10.1802 q^{95} +(-1.82361 + 1.42310i) q^{96} +(-10.7268 + 10.7268i) q^{97} +(-8.70760 - 3.85985i) q^{98} +(-1.38901 - 3.35338i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.29289	−	0.573103i	−0.914208	−	0.405245i
$2$	−1.29289	−	0.573103i	−0.914208	−	0.405245i
$3$	−0.377788	−	0.156485i	−0.218116	−	0.0903467i	0.270950	−	0.962593i	$-0.412662\pi$
$3$	−0.377788	−	0.156485i	−0.218116	−	0.0903467i	−0.489066	+	0.872247i	$0.662662\pi$
$4$	1.34311	+	1.48191i	0.671553	+	0.740956i
$5$	−0.605904	+	1.46278i	−0.270969	+	0.654176i	−0.999525	−	0.0308095i	$-0.990191\pi$
$5$	−0.605904	+	1.46278i	−0.270969	+	0.654176i	0.728557	+	0.684985i	$0.240191\pi$
$6$	0.398755	+	0.418829i	0.162791	+	0.170986i
$7$		−	0.514771i		−	0.194565i	−0.995257	−	0.0972826i	$-0.968985\pi$
$7$		−	0.514771i		−	0.194565i	0.995257	−	0.0972826i	$-0.0310151\pi$
$8$	−0.887196	−	2.68568i	−0.313671	−	0.949532i
$9$	−2.00308	−	2.00308i	−0.667695	−	0.667695i
$10$	1.62169	−	1.54396i	0.512823	−	0.488244i
$11$	1.18377	+	0.490335i	0.356921	+	0.147842i	0.553937	−	0.832559i	$-0.313125\pi$
$11$	1.18377	+	0.490335i	0.356921	+	0.147842i	−0.197016	+	0.980400i	$0.563125\pi$
$12$	−0.275513	−	0.770025i	−0.0795338	−	0.222287i
$13$	3.33495	−	1.37044i	0.924949	−	0.380092i
$13$	3.33495	−	1.37044i	0.924949	−	0.380092i
$14$	−0.295017	+	0.665540i	−0.0788465	+	0.177873i
$15$	0.457807	−	0.457807i	0.118205	−	0.118205i
$16$	−0.392128	+	3.98073i	−0.0980321	+	0.995183i
$17$	2.14260			0.519657			0.259829	−	0.965655i	$-0.416334\pi$
$17$	2.14260			0.519657			0.259829	+	0.965655i	$0.416334\pi$
$18$	1.44179	+	3.73773i	0.339832	+	0.880992i
$19$	2.46054	+	5.94027i	0.564487	+	1.36279i	0.906145	+	0.422967i	$0.139012\pi$
$19$	2.46054	+	5.94027i	0.564487	+	1.36279i	−0.341658	+	0.939824i	$0.610988\pi$
$20$	−2.98151	+	1.06678i	−0.666686	+	0.238538i
$21$	−0.0805540	+	0.194475i	−0.0175783	+	0.0424378i
$22$	−1.24947	−	1.31237i	−0.266388	−	0.279798i
$23$	2.48571	+	2.48571i	0.518305	+	0.518305i	0.917058	−	0.398753i	$-0.130557\pi$
$23$	2.48571	+	2.48571i	0.518305	+	0.518305i	−0.398753	+	0.917058i	$0.630557\pi$
$24$	−0.0850968	+	1.15345i	−0.0173703	+	0.235447i
$25$	1.76292	+	1.76292i	0.352585	+	0.352585i
$26$	−5.09711	−	0.139444i	−0.999626	−	0.0273473i
$27$	0.912744	+	2.20356i	0.175658	+	0.424075i
$28$	0.762846	−	0.691393i	0.144164	−	0.130661i
$29$	2.05949	−	4.97205i	0.382438	−	0.923286i	−0.609055	−	0.793128i	$-0.708451\pi$
$29$	2.05949	−	4.97205i	0.382438	−	0.923286i	0.991493	−	0.130159i	$-0.0415487\pi$
$30$	−0.854263	+	0.329522i	−0.155966	+	0.0601622i
$31$	0.734578	+	0.734578i	0.131934	+	0.131934i	0.769990	−	0.638056i	$-0.220261\pi$
$31$	0.734578	+	0.734578i	0.131934	+	0.131934i	−0.638056	+	0.769990i	$0.720261\pi$
$32$	2.78835	−	4.92190i	0.492914	−	0.870078i
$33$	−0.370486	−	0.370486i	−0.0644933	−	0.0644933i
$34$	−2.77014	−	1.22793i	−0.475075	−	0.210588i
$35$	0.752998	+	0.311902i	0.127280	+	0.0527211i
$36$	0.278039	−	5.65875i	0.0463398	−	0.943125i
$37$	10.8217	+	4.48250i	1.77908	+	0.736919i	0.992904	+	0.118916i	$0.0379420\pi$
$37$	10.8217	+	4.48250i	1.77908	+	0.736919i	0.786176	+	0.618003i	$0.212058\pi$
$38$	0.223187	−	9.09023i	0.0362057	−	1.47463i
$39$	−1.47436	−	0.00413299i	−0.236086	−	0.000661809i
$40$	4.46612	+	0.329491i	0.706156	+	0.0520972i
$41$	−3.72832			−0.582266			−0.291133	−	0.956683i	$-0.594032\pi$
$41$	−3.72832			−0.582266			−0.291133	+	0.956683i	$0.594032\pi$
$42$	0.215601	−	0.205268i	0.0332680	−	0.0316735i
$43$	−1.07795	−	2.60239i	−0.164385	−	0.396861i	0.820126	−	0.572183i	$-0.193903\pi$
$43$	−1.07795	−	2.60239i	−0.164385	−	0.396861i	−0.984511	+	0.175322i	$0.943903\pi$
$44$	0.863300	+	2.41282i	0.130147	+	0.363746i
$45$	4.14375	−	1.71640i	0.617714	−	0.255866i
$46$	−1.78917	−	4.63830i	−0.263799	−	0.683880i
$47$	−0.193010	−	0.193010i	−0.0281533	−	0.0281533i	0.692890	−	0.721043i	$-0.256337\pi$
$47$	−0.193010	−	0.193010i	−0.0281533	−	0.0281533i	−0.721043	+	0.692890i	$0.756337\pi$
$48$	0.771067	−	1.44251i	0.111294	−	0.208209i
$49$	6.73501			0.962144
$50$	−1.26892	−	3.28959i	−0.179453	−	0.465219i
$51$	−0.809450	−	0.335285i	−0.113346	−	0.0469493i
$52$	6.51007	+	3.10145i	0.902784	+	0.430094i
$53$	−1.51275	−	3.65211i	−0.207793	−	0.501656i	0.785282	−	0.619138i	$-0.212518\pi$
$53$	−1.51275	−	3.65211i	−0.207793	−	0.501656i	−0.993075	+	0.117482i	$0.962518\pi$
$54$	0.0827918	−	3.37205i	0.0112665	−	0.458877i
$55$	−1.43451	+	1.43451i	−0.193429	+	0.193429i
$56$	−1.38251	+	0.456703i	−0.184746	+	0.0610295i
$57$		−	2.62920i		−	0.348247i
$58$	−5.51218	+	5.24799i	−0.723785	+	0.689095i
$59$	−3.98767	+	9.62709i	−0.519150	+	1.25334i	0.419275	+	0.907859i	$0.362284\pi$
$59$	−3.98767	+	9.62709i	−0.519150	+	1.25334i	−0.938426	+	0.345481i	$0.887716\pi$
$60$	1.29331	+	0.0635461i	0.166966	+	0.00820377i
$61$	5.11727	−	12.3542i	0.655199	−	1.58179i	−0.149935	−	0.988696i	$-0.547906\pi$
$61$	5.11727	−	12.3542i	0.655199	−	1.58179i	0.805133	−	0.593094i	$-0.202094\pi$
$62$	−0.528737	−	1.37071i	−0.0671497	−	0.174081i
$63$	−1.03113	+	1.03113i	−0.129910	+	0.129910i
$64$	−6.42577	+	4.76545i	−0.803221	+	0.595681i
$65$	−0.0160028	+	5.70866i	−0.00198490	+	0.708072i
$66$	0.266669	+	0.691322i	0.0328247	+	0.0850958i
$67$	10.1248	−	4.19384i	1.23694	−	0.512359i	0.334186	−	0.942507i	$-0.391539\pi$
$67$	10.1248	−	4.19384i	1.23694	−	0.512359i	0.902759	+	0.430148i	$0.141539\pi$
$68$	2.87774	+	3.17515i	0.348978	+	0.385043i
$69$	−0.550095	−	1.32805i	−0.0662237	−	0.159878i
$70$	−0.794789	−	0.834799i	−0.0949954	−	0.0997775i
$71$	−13.8983			−1.64943			−0.824714	−	0.565550i	$-0.808664\pi$
$71$	−13.8983			−1.64943			−0.824714	+	0.565550i	$0.808664\pi$
$72$	−3.60252	+	7.15677i	−0.424561	+	0.843434i
$73$			1.32072i			0.154578i	0.997009	+	0.0772890i	$0.0246264\pi$
$73$			1.32072i			0.154578i	−0.997009	+	0.0772890i	$0.975374\pi$
$74$	−11.4223	−	11.9973i	−1.32782	−	1.39466i
$75$	−0.390141	−	0.941883i	−0.0450496	−	0.108759i
$76$	−5.49819	+	11.6247i	−0.630686	+	1.33345i
$77$	0.252410	−	0.609372i	0.0287648	−	0.0694444i
$78$	1.90381	+	0.850302i	0.215564	+	0.0962778i
$79$	−9.86871			−1.11032			−0.555159	−	0.831745i	$-0.687342\pi$
$79$	−9.86871			−1.11032			−0.555159	+	0.831745i	$0.687342\pi$
$80$	−5.58535	−	2.98554i	−0.624461	−	0.333794i
$81$			7.52305i			0.835895i
$82$	4.82029	+	2.13671i	0.532312	+	0.235960i
$83$	2.34587	+	5.66344i	0.257493	+	0.621643i	0.998771	−	0.0495546i	$-0.0157802\pi$
$83$	2.34587	+	5.66344i	0.257493	+	0.621643i	−0.741278	+	0.671198i	$0.765780\pi$
$84$	−0.396387	+	0.141826i	−0.0432494	+	0.0154745i
$85$	−1.29821	+	3.13416i	−0.140811	+	0.339947i
$86$	−0.0977765	+	3.98237i	−0.0105435	+	0.429430i
$87$	−1.55610	+	1.55610i	−0.166832	+	0.166832i
$88$	0.266645	−	3.61426i	0.0284244	−	0.385281i
$89$	4.73380			0.501782			0.250891	−	0.968015i	$-0.419276\pi$
$89$	4.73380			0.501782			0.250891	+	0.968015i	$0.419276\pi$
$90$	−6.34107	−	0.155688i	−0.668407	−	0.0164110i
$91$	−0.705464	−	1.71674i	−0.0739527	−	0.179963i
$92$	−0.345030	+	7.02217i	−0.0359718	+	0.732111i
$93$	−0.162565	−	0.392466i	−0.0168572	−	0.0406968i
$94$	0.138925	+	0.360154i	0.0143290	+	0.0371470i
$95$	−10.1802			−1.04446
$96$	−1.82361	+	1.42310i	−0.186121	+	0.145245i
$97$	−10.7268	+	10.7268i	−1.08914	+	1.08914i	−0.0935226	+	0.995617i	$0.529813\pi$
$97$	−10.7268	+	10.7268i	−1.08914	+	1.08914i	−0.995617	+	0.0935226i	$0.970187\pi$
$98$	−8.70760	−	3.85985i	−0.879600	−	0.389904i
$99$	−1.38901	−	3.35338i	−0.139601	−	0.337027i
$100$	−0.244703	+	4.98029i	−0.0244703	+	0.498029i
$101$	−1.99734	−	4.82202i	−0.198743	−	0.479808i	0.792816	−	0.609461i	$-0.208614\pi$
$101$	−1.99734	−	4.82202i	−0.198743	−	0.479808i	−0.991560	+	0.129652i	$0.958614\pi$
$102$	0.854373	+	0.897383i	0.0845956	+	0.0888542i
$103$	2.48603	−	2.48603i	0.244956	−	0.244956i	−0.573941	−	0.818897i	$-0.694586\pi$
$103$	2.48603	−	2.48603i	0.244956	−	0.244956i	0.818897	+	0.573941i	$0.194586\pi$
$104$	−6.63932	−	7.74076i	−0.651039	−	0.759044i
$105$	−0.235666	−	0.235666i	−0.0229986	−	0.0229986i
$106$	−0.137217	+	5.58873i	−0.0133276	+	0.542825i
$107$	6.53452	−	2.70669i	0.631716	−	0.261665i	−0.0437660	−	0.999042i	$-0.513936\pi$
$107$	6.53452	−	2.70669i	0.631716	−	0.261665i	0.675482	+	0.737377i	$0.263936\pi$
$108$	−2.03957	+	4.31222i	−0.196258	+	0.414944i
$109$	7.24080	−	2.99924i	0.693542	−	0.287275i	−0.00793280	−	0.999969i	$-0.502525\pi$
$109$	7.24080	−	2.99924i	0.693542	−	0.287275i	0.701475	+	0.712694i	$0.252525\pi$
$110$	2.67677	−	1.03253i	0.255220	−	0.0984482i
$111$	−3.38688	−	3.38688i	−0.321468	−	0.321468i
$112$	2.04917	+	0.201856i	0.193628	+	0.0190736i
$113$		−	8.10966i		−	0.762893i	−0.924391	−	0.381447i	$-0.875426\pi$
$113$		−	8.10966i		−	0.762893i	0.924391	−	0.381447i	$-0.124574\pi$
$114$	−1.50680	+	3.39926i	−0.141125	+	0.318370i
$115$	−5.14214	+	2.12995i	−0.479507	+	0.198618i
$116$	10.1343	−	3.62601i	0.940942	−	0.336667i
$117$	−9.42529	−	3.93507i	−0.871369	−	0.363798i
$118$	10.6729	−	10.1614i	0.982521	−	0.935431i
$119$		−	1.10295i		−	0.101107i
$120$	−1.63569	−	0.823359i	−0.149317	−	0.0751621i
$121$	−6.61728	−	6.61728i	−0.601571	−	0.601571i
$122$	−13.6962	+	13.0398i	−1.24000	+	1.18057i
$123$	1.40852	+	0.583427i	0.127002	+	0.0526058i
$124$	−0.101964	+	2.07520i	−0.00915659	+	0.186358i
$125$	−10.9608	+	4.54013i	−0.980368	+	0.406082i
$126$	1.92408	−	0.742190i	0.171410	−	0.0661195i
$127$	4.05354			0.359693			0.179847	−	0.983695i	$-0.442440\pi$
$127$	4.05354			0.359693			0.179847	+	0.983695i	$0.442440\pi$
$128$	11.0389	−	2.47856i	0.975708	−	0.219076i
$129$			1.15184i			0.101413i
$130$	3.29234	−	7.37147i	0.288757	−	0.646521i
$131$	−2.66614	−	1.10435i	−0.232942	−	0.0964876i	0.263159	−	0.964752i	$-0.415235\pi$
$131$	−2.66614	−	1.10435i	−0.232942	−	0.0964876i	−0.496101	+	0.868265i	$0.665235\pi$
$132$	0.0514254	−	1.04663i	0.00447601	−	0.0910974i
$133$	3.05788	−	1.26662i	0.265152	−	0.109830i
$134$	−15.4937	−	0.380408i	−1.33846	−	0.0328623i
$135$	−3.77636			−0.325018
$136$	−1.90091	−	5.75434i	−0.163001	−	0.493431i
$137$			4.60029i			0.393029i	0.980501	+	0.196514i	$0.0629623\pi$
$137$			4.60029i			0.393029i	−0.980501	+	0.196514i	$0.937038\pi$
$138$	−0.0498971	+	2.03227i	−0.00424753	+	0.172999i
$139$	−16.8029	+	6.95999i	−1.42520	+	0.590339i	−0.956162	−	0.292837i	$-0.905401\pi$
$139$	−16.8029	+	6.95999i	−1.42520	+	0.590339i	−0.469042	+	0.883176i	$0.655401\pi$
$140$	0.549145	+	1.53479i	0.0464113	+	0.129714i
$141$	0.0427137	+	0.103120i	0.00359714	+	0.00868426i
$142$	17.9690	+	7.96517i	1.50792	+	0.668422i
$143$	4.61980	+	0.0129504i	0.386327	+	0.00108297i
$144$	8.75921	−	7.18828i	0.729934	−	0.599023i
$145$	6.02517	+	6.02517i	0.500363	+	0.500363i
$146$	0.756905	−	1.70753i	0.0626419	−	0.141317i
$147$	−2.54441	−	1.05393i	−0.209859	−	0.0869266i
$148$	7.89205	+	22.0573i	0.648723	+	1.81310i
$149$	−11.5774	−	4.79550i	−0.948455	−	0.392863i	−0.145805	−	0.989313i	$-0.546577\pi$
$149$	−11.5774	−	4.79550i	−0.948455	−	0.392863i	−0.802650	+	0.596450i	$0.796577\pi$
$150$	−0.0353883	+	1.44134i	−0.00288944	+	0.117685i
$151$	−4.77195			−0.388336			−0.194168	−	0.980968i	$-0.562201\pi$
$151$	−4.77195			−0.388336			−0.194168	+	0.980968i	$0.562201\pi$
$152$	13.7707	−	11.8784i	1.11695	−	0.963467i
$153$	−4.29181	−	4.29181i	−0.346972	−	0.346972i
$154$	−0.675570	+	0.643192i	−0.0544390	+	0.0518299i
$155$	−1.51961	+	0.629444i	−0.122058	+	0.0505581i
$156$	−1.97410	−	2.19042i	−0.158054	−	0.175374i
$157$	−1.10263	+	2.66198i	−0.0879994	+	0.212449i	−0.961752	−	0.273921i	$-0.911679\pi$
$157$	−1.10263	+	2.66198i	−0.0879994	+	0.212449i	0.873753	+	0.486370i	$0.161679\pi$
$158$	12.7591	+	5.65579i	1.01506	+	0.449950i
$159$			1.61645i			0.128193i
$160$	5.51020	+	7.06094i	0.435620	+	0.558216i
$161$	1.27957	−	1.27957i	0.100844	−	0.100844i
$162$	4.31148	−	9.72645i	0.338742	−	0.764182i
$163$	1.57513	+	3.80270i	0.123374	+	0.297850i	0.973484	−	0.228754i	$-0.0734650\pi$
$163$	1.57513	+	3.80270i	0.123374	+	0.297850i	−0.850111	+	0.526604i	$0.823465\pi$
$164$	−5.00754	−	5.52505i	−0.391023	−	0.431434i
$165$	0.766418	−	0.317461i	0.0596656	−	0.0247143i
$166$	0.212786	−	8.66660i	0.0165154	−	0.672659i
$167$			17.4490i			1.35025i	0.737705	+	0.675123i	$0.235910\pi$
$167$			17.4490i			1.35025i	−0.737705	+	0.675123i	$0.764090\pi$
$168$	0.593764	+	0.0438054i	0.0458099	+	0.00337966i
$169$	9.24378	−	9.14071i	0.711060	−	0.703131i
$170$	3.47463	−	3.30810i	0.266492	−	0.253720i
$171$	6.97019	−	16.8275i	0.533024	−	1.28683i
$172$	2.40872	−	5.09271i	0.183663	−	0.388315i
$173$	5.19257	−	12.5360i	0.394784	−	0.953092i	−0.594099	−	0.804392i	$-0.702491\pi$
$173$	5.19257	−	12.5360i	0.394784	−	0.953092i	0.988882	−	0.148700i	$-0.0475089\pi$
$174$	2.90367	−	1.12006i	0.220127	−	0.0849113i
$175$	0.907502	−	0.907502i	0.0686007	−	0.0686007i
$176$	−2.41608	+	4.52001i	−0.182119	+	0.340709i
$177$	3.01299	−	3.01299i	0.226470	−	0.226470i
$178$	−6.12026	−	2.71295i	−0.458733	−	0.203344i
$179$	23.6830	+	9.80981i	1.77015	+	0.733220i	0.994819	+	0.101665i	$0.0324169\pi$
$179$	23.6830	+	9.80981i	1.77015	+	0.733220i	0.775331	+	0.631555i	$0.217583\pi$
$180$	8.10905	+	3.83537i	0.604413	+	0.285872i
$181$	3.72761	−	1.54403i	0.277071	−	0.114767i	−0.239821	−	0.970817i	$-0.577089\pi$
$181$	3.72761	−	1.54403i	0.277071	−	0.114767i	0.516892	+	0.856051i	$0.327089\pi$
$182$	−0.0717819	+	2.62385i	−0.00532083	+	0.194492i
$183$	−3.86649	+	3.86649i	−0.285819	+	0.285819i
$184$	4.47051	−	8.88112i	0.329570	−	0.654725i
$185$	−13.1139	+	13.1139i	−0.964149	+	0.964149i
$186$	−0.0147457	+	0.600580i	−0.00108120	+	0.0440366i
$187$	2.53635	+	1.05059i	0.185477	+	0.0768269i
$188$	0.0267908	−	0.545256i	0.00195392	−	0.0397669i
$189$	1.13433	−	0.469855i	0.0825103	−	0.0341769i
$190$	13.1618	+	5.83428i	0.954857	+	0.423263i
$191$		−	8.82046i		−	0.638226i	−0.947717	−	0.319113i	$-0.896615\pi$
$191$		−	8.82046i		−	0.638226i	0.947717	−	0.319113i	$-0.103385\pi$
$192$	3.17330	−	0.794795i	0.229013	−	0.0573594i
$193$	0.196243	+	0.196243i	0.0141259	+	0.0141259i	0.714134	−	0.700009i	$-0.246821\pi$
$193$	0.196243	+	0.196243i	0.0141259	+	0.0141259i	−0.700009	+	0.714134i	$0.746821\pi$
$194$	20.0161	−	7.72096i	1.43707	−	0.554332i
$195$	0.899366	−	2.15416i	0.0644049	−	0.154263i
$196$	9.04584	+	9.98070i	0.646131	+	0.712907i
$197$	2.51138	−	6.06301i	0.178928	−	0.431971i	−0.808814	−	0.588065i	$-0.799890\pi$
$197$	2.51138	−	6.06301i	0.178928	−	0.431971i	0.987742	+	0.156093i	$0.0498901\pi$
$198$	−0.125993	+	5.13158i	−0.00895390	+	0.364686i
$199$	2.67816	−	2.67816i	0.189850	−	0.189850i	−0.605781	−	0.795631i	$-0.707139\pi$
$199$	2.67816	−	2.67816i	0.189850	−	0.189850i	0.795631	+	0.605781i	$0.207139\pi$
$200$	3.17059	−	6.29871i	0.224195	−	0.445386i
$201$	−4.48132			−0.316088
$202$	−0.181172	+	7.37900i	−0.0127472	+	0.519184i
$203$	−2.55947	−	1.06017i	−0.179639	−	0.0744091i
$204$	−0.590315	−	1.64986i	−0.0413303	−	0.115513i
$205$	2.25901	−	5.45372i	0.157776	−	0.380904i
$206$	−4.63891	+	1.78941i	−0.323208	+	0.124674i
$207$		−	9.95815i		−	0.692140i
$208$	4.14763	+	13.8129i	0.287587	+	0.957755i
$209$			8.23842i			0.569864i
$210$	0.169628	+	0.439750i	0.0117055	+	0.0303456i
$211$	−7.60161	+	18.3519i	−0.523316	+	1.26340i	0.412515	+	0.910951i	$0.364650\pi$
$211$	−7.60161	+	18.3519i	−0.523316	+	1.26340i	−0.935832	+	0.352447i	$0.885350\pi$
$212$	3.38032	−	7.14695i	0.232161	−	0.490854i
$213$	5.25063	+	2.17488i	0.359767	+	0.149020i
$214$	−9.99960	−	0.245514i	−0.683558	−	0.0167830i
$215$	4.45986			0.304160
$216$	5.10828	−	4.40633i	0.347574	−	0.299813i
$217$	0.378140	−	0.378140i	0.0256698	−	0.0256698i
$218$	−11.0804	−	0.272050i	−0.750459	−	0.0184255i
$219$	0.206672	−	0.498951i	0.0139656	−	0.0337160i
$220$	−4.05251	−	0.199117i	−0.273220	−	0.0134245i
$221$	7.14547	−	2.93631i	0.480656	−	0.197518i
$222$	2.43782	+	6.31987i	0.163615	+	0.424162i
$223$	−15.1483	−	15.1483i	−1.01440	−	1.01440i	−0.999895	−	0.0145096i	$-0.995381\pi$
$223$	−15.1483	−	15.1483i	−1.01440	−	1.01440i	−0.0145096	−	0.999895i	$-0.504619\pi$
$224$	−2.53365	−	1.43536i	−0.169287	−	0.0959040i
$225$		−	7.06256i		−	0.470838i
$226$	−4.64767	+	10.4849i	−0.309158	+	0.697443i
$227$	20.3484	−	8.42859i	1.35057	−	0.559425i	0.414120	−	0.910222i	$-0.364089\pi$
$227$	20.3484	−	8.42859i	1.35057	−	0.559425i	0.936451	+	0.350798i	$0.114089\pi$
$228$	3.89625	−	3.53130i	0.258035	−	0.233866i
$229$	−11.7050	−	4.84837i	−0.773489	−	0.320390i	−0.0392041	−	0.999231i	$-0.512482\pi$
$229$	−11.7050	−	4.84837i	−0.773489	−	0.320390i	−0.734285	+	0.678842i	$0.762482\pi$
$230$	7.86888	+	0.193200i	0.518859	+	0.0127392i
$231$	−0.190715	+	0.190715i	−0.0125481	+	0.0125481i
$232$	−15.1805	−	1.11995i	−0.996649	−	0.0735285i
$233$	−2.62188	+	2.62188i	−0.171765	+	0.171765i	−0.787754	−	0.615989i	$-0.788756\pi$
$233$	−2.62188	+	2.62188i	−0.171765	+	0.171765i	0.615989	+	0.787754i	$0.288756\pi$
$234$	9.93063	+	10.4893i	0.649185	+	0.685705i
$235$	0.399276	−	0.165386i	0.0260459	−	0.0107886i
$236$	−19.6224	+	7.02083i	−1.27731	+	0.457017i
$237$	3.72829	+	1.54431i	0.242178	+	0.100313i
$238$	−0.632103	+	1.42599i	−0.0409732	+	0.0924331i
$239$	15.5155	−	15.5155i	1.00362	−	1.00362i	0.00362367	−	0.999993i	$-0.498847\pi$
$239$	15.5155	−	15.5155i	1.00362	−	1.00362i	0.999993	−	0.00362367i	$-0.00115345\pi$
$240$	1.64289	+	2.00193i	0.106048	+	0.129224i
$241$	−1.93510	+	1.93510i	−0.124651	+	0.124651i	−0.766680	−	0.642029i	$-0.778093\pi$
$241$	−1.93510	+	1.93510i	−0.124651	+	0.124651i	0.642029	+	0.766680i	$0.278093\pi$
$242$	4.76301	+	12.3478i	0.306178	+	0.793745i
$243$	3.91548	−	9.45280i	0.251178	−	0.606398i
$244$	25.1808	−	9.00963i	1.61204	−	0.576783i
$245$	−4.08077	+	9.85185i	−0.260711	+	0.629412i
$246$	−1.48669	−	1.56153i	−0.0947878	−	0.0995594i
$247$	16.3466	+	16.4385i	1.04011	+	1.04596i
$248$	1.32113	−	2.62456i	0.0838917	−	0.166660i
$249$		−	2.50667i		−	0.158854i
$250$	16.7731	+	0.411819i	1.06082	+	0.0260457i
$251$	−14.7881	+	6.12543i	−0.933416	+	0.386633i	−0.796973	−	0.604015i	$-0.793567\pi$
$251$	−14.7881	+	6.12543i	−0.933416	+	0.386633i	−0.136442	+	0.990648i	$0.543567\pi$
$252$	−2.91296	−	0.143127i	−0.183499	−	0.00901612i
$253$	1.72368	+	4.16134i	0.108367	+	0.261621i
$254$	−5.24076	−	2.32309i	−0.328834	−	0.145764i
$255$	0.980898	−	0.980898i	0.0614262	−	0.0614262i
$256$	−15.6925	−	3.12192i	−0.980779	−	0.195120i
$257$			11.7533i			0.733148i	0.930389	+	0.366574i	$0.119469\pi$
$257$			11.7533i			0.733148i	−0.930389	+	0.366574i	$0.880531\pi$
$258$	0.660120	−	1.48919i	0.0410973	−	0.0927130i
$259$	2.30746	−	5.57071i	0.143379	−	0.346147i
$260$	−8.48123	+	7.64363i	−0.525983	+	0.474038i
$261$	−14.0848	+	5.83410i	−0.871825	+	0.361122i
$262$	2.81411	+	2.95577i	0.173856	+	0.182608i
$263$	−20.6729	−	20.6729i	−1.27475	−	1.27475i	−0.943568	−	0.331179i	$-0.892553\pi$
$263$	−20.6729	−	20.6729i	−1.27475	−	1.27475i	−0.331179	−	0.943568i	$-0.607447\pi$
$264$	−0.666313	+	1.32370i	−0.0410087	+	0.0814681i
$265$	6.25883			0.384477
$266$	−4.67939	−	0.114890i	−0.286912	−	0.00704437i
$267$	−1.78838	−	0.740769i	−0.109447	−	0.0453343i
$268$	19.8136	+	9.37133i	1.21031	+	0.572445i
$269$	8.79332	+	3.64231i	0.536138	+	0.222076i	0.634289	−	0.773096i	$-0.281293\pi$
$269$	8.79332	+	3.64231i	0.536138	+	0.222076i	−0.0981509	+	0.995172i	$0.531293\pi$
$270$	4.88241	+	2.16424i	0.297134	+	0.131712i
$271$	−11.9871	−	11.9871i	−0.728162	−	0.728162i	0.242092	−	0.970253i	$-0.422167\pi$
$271$	−11.9871	−	11.9871i	−0.728162	−	0.728162i	−0.970253	+	0.242092i	$0.922167\pi$
$272$	−0.840174	+	8.52912i	−0.0509431	+	0.517154i
$273$	−0.00212755	+	0.758958i	−0.000128765	+	0.0459342i
$274$	2.63644	−	5.94764i	0.159273	−	0.359310i
$275$	1.22248	+	2.95132i	0.0737182	+	0.177971i
$276$	1.22921	−	2.59890i	0.0739899	−	0.156435i
$277$	−14.8859	+	6.16594i	−0.894407	+	0.370475i	−0.782067	−	0.623194i	$-0.785835\pi$
$277$	−14.8859	+	6.16594i	−0.894407	+	0.370475i	−0.112340	+	0.993670i	$0.535835\pi$
$278$	25.7130	+	0.631316i	1.54217	+	0.0378638i
$279$		−	2.94284i		−	0.176183i
$280$	0.169613	−	2.29903i	0.0101363	−	0.137393i
$281$	−25.2289			−1.50503			−0.752516	−	0.658574i	$-0.771160\pi$
$281$	−25.2289			−1.50503			−0.752516	+	0.658574i	$0.771160\pi$
$282$	0.00387440	−	0.157802i	0.000230717	−	0.00939694i
$283$	−5.52228	+	2.28740i	−0.328265	+	0.135972i	−0.540729	−	0.841197i	$-0.681851\pi$
$283$	−5.52228	+	2.28740i	−0.328265	+	0.135972i	0.212463	+	0.977169i	$0.431851\pi$
$284$	−18.6669	−	20.5961i	−1.10768	−	1.22215i
$285$	3.84595	+	1.59305i	0.227815	+	0.0943639i
$286$	−5.96545	−	2.66436i	−0.352744	−	0.157547i
$287$			1.91923i			0.113289i
$288$	−15.4443	+	4.27369i	−0.910063	+	0.251830i
$289$	−12.4093			−0.729956
$290$	−4.33682	−	11.2429i	−0.254667	−	0.660206i
$291$	5.73104	−	2.37387i	0.335959	−	0.139159i
$292$	−1.95718	+	1.77386i	−0.114536	+	0.103807i
$293$	24.6065	+	10.1923i	1.43753	+	0.595442i	0.959197	−	0.282739i	$-0.0912429\pi$
$293$	24.6065	+	10.1923i	1.43753	+	0.595442i	0.478328	+	0.878181i	$0.341243\pi$
$294$	2.68562	+	2.82082i	0.156629	+	0.164513i
$295$	−11.6662	−	11.6662i	−0.679231	−	0.679231i
$296$	2.43759	−	33.0406i	0.141682	−	1.92044i
$297$			3.05606i			0.177331i
$298$	12.2199	+	12.8351i	0.707880	+	0.743515i
$299$	11.6962	+	4.88319i	0.676410	+	0.282402i
$300$	0.871787	−	1.84320i	0.0503327	−	0.106417i
$301$	−1.33964	+	0.554895i	−0.0772153	+	0.0319836i
$302$	6.16958	+	2.73482i	0.355020	+	0.157371i
$303$			2.13426i			0.122610i
$304$	−24.6115	+	7.46541i	−1.41157	+	0.428171i
$305$	14.9709	+	14.9709i	0.857230	+	0.857230i
$306$	3.08917	+	8.00847i	0.176596	+	0.457814i
$307$	20.7105	−	8.57855i	1.18201	−	0.489604i	0.296864	−	0.954920i	$-0.404059\pi$
$307$	20.7105	−	8.57855i	1.18201	−	0.489604i	0.885145	+	0.465316i	$0.154059\pi$
$308$	1.24205	−	0.444402i	0.0707724	−	0.0253222i
$309$	−1.32822	+	0.550168i	−0.0755599	+	0.0312979i
$310$	2.32542	+	0.0570946i	0.132075	+	0.00324275i
$311$	7.09781	+	7.09781i	0.402480	+	0.402480i	0.879106	−	0.476626i	$-0.158140\pi$
$311$	7.09781	+	7.09781i	0.402480	+	0.402480i	−0.476626	+	0.879106i	$0.658140\pi$
$312$	1.29695	+	3.96333i	0.0734251	+	0.224379i
$313$	8.11648	−	8.11648i	0.458771	−	0.458771i	−0.439481	−	0.898252i	$-0.644838\pi$
$313$	8.11648	−	8.11648i	0.458771	−	0.458771i	0.898252	+	0.439481i	$0.144838\pi$
$314$	2.95116	−	2.80972i	0.166544	−	0.158562i
$315$	−0.883552	−	2.13308i	−0.0497825	−	0.120186i
$316$	−13.2547	−	14.6246i	−0.745637	−	0.822696i
$317$	−2.70155	−	6.52212i	−0.151734	−	0.366319i	0.829675	−	0.558247i	$-0.188526\pi$
$317$	−2.70155	−	6.52212i	−0.151734	−	0.366319i	−0.981409	+	0.191928i	$0.938526\pi$
$318$	0.926391	−	2.08988i	0.0519494	−	0.117195i
$319$	4.87594	−	4.87594i	0.273000	−	0.273000i
$320$	−3.07741	−	12.2869i	−0.172033	−	0.686859i
$321$	−2.89222			−0.161428
$322$	−2.38766	+	0.921013i	−0.133059	+	0.0513260i
$323$	5.27196	+	12.7276i	0.293340	+	0.708185i
$324$	−11.1485	+	10.1043i	−0.619362	+	0.561348i
$325$	8.29524	+	3.46328i	0.460137	+	0.192108i
$326$	0.142874	−	5.81917i	0.00791308	−	0.322294i
$327$	−3.20482			−0.177227
$328$	3.30775	+	10.0131i	0.182640	+	0.552880i
$329$	−0.0993558	+	0.0993558i	−0.00547766	+	0.00547766i
$330$	−1.17283	−	0.0287957i	−0.0645621	−	0.00158515i
$331$	−4.85653	+	11.7247i	−0.266939	+	0.644448i	−0.999336	−	0.0364300i	$-0.988401\pi$
$331$	−4.85653	+	11.7247i	−0.266939	+	0.644448i	0.732397	+	0.680878i	$0.238401\pi$
$332$	−5.24196	+	11.0830i	−0.287690	+	0.608257i
$333$	−12.6980	−	30.6556i	−0.695845	−	1.67992i
$334$	10.0001	−	22.5596i	0.547180	−	1.23441i
$335$			17.3515i			0.948013i
$336$	−0.742564	−	0.396923i	−0.0405102	−	0.0216539i
$337$	13.2692			0.722818			0.361409	−	0.932407i	$-0.382296\pi$
$337$	13.2692			0.722818			0.361409	+	0.932407i	$0.382296\pi$
$338$	−17.1897	+	6.52025i	−0.934997	+	0.354655i
$339$	−1.26904	+	3.06374i	−0.0689249	+	0.166399i
$340$	−6.38818	+	2.28567i	−0.346448	+	0.123958i
$341$	0.509385	+	1.22976i	0.0275847	+	0.0665954i
$342$	−18.6556	+	17.7614i	−1.00878	+	0.960429i
$343$		−	7.07039i		−	0.381765i
$344$	−6.03284	+	5.20385i	−0.325269	+	0.280573i
$345$	2.27595			0.122533
$346$	−13.8978	+	13.2317i	−0.747150	+	0.711341i
$347$	1.30783	+	3.15737i	0.0702079	+	0.169497i	0.955088	−	0.296322i	$-0.0957600\pi$
$347$	1.30783	+	3.15737i	0.0702079	+	0.169497i	−0.884880	+	0.465818i	$0.845760\pi$
$348$	−4.39602	−	0.215996i	−0.235651	−	0.0115786i
$349$	−13.9534	+	5.77967i	−0.746906	+	0.309378i	−0.723478	−	0.690347i	$-0.757458\pi$
$349$	−13.9534	+	5.77967i	−0.746906	+	0.309378i	−0.0234274	+	0.999726i	$0.507458\pi$
$350$	−1.69339	+	0.653205i	−0.0905154	+	0.0349153i
$351$	6.06381	+	6.09790i	0.323662	+	0.325482i
$352$	5.71415	−	4.45919i	0.304565	−	0.237676i
$353$	−20.6253	+	20.6253i	−1.09777	+	1.09777i	−0.103102	+	0.994671i	$0.532877\pi$
$353$	−20.6253	+	20.6253i	−1.09777	+	1.09777i	−0.994671	+	0.103102i	$0.967123\pi$
$354$	−5.62221	+	2.16870i	−0.298817	+	0.115265i
$355$	8.42106	−	20.3302i	0.446943	−	1.07902i
$356$	6.35800	+	7.01508i	0.336973	+	0.371798i
$357$	−0.172595	+	0.416682i	−0.00913470	+	0.0220531i
$358$	−24.9974	−	26.2558i	−1.32115	−	1.38766i
$359$			25.9460i			1.36938i	0.728836	+	0.684688i	$0.240062\pi$
$359$			25.9460i			1.36938i	−0.728836	+	0.684688i	$0.759938\pi$
$360$	−8.28602	−	9.60601i	−0.436711	−	0.506281i
$361$	−15.7975	+	15.7975i	−0.831449	+	0.831449i
$362$	−5.70425	−	0.140053i	−0.299809	−	0.00736102i
$363$	1.46443	+	3.53544i	0.0768625	+	0.185562i
$364$	1.59654	−	3.35120i	0.0836814	−	0.175650i
$365$	−1.93192	−	0.800227i	−0.101121	−	0.0418858i
$366$	7.21482	−	2.78303i	0.377125	−	0.145471i
$367$	14.7623			0.770586			0.385293	−	0.922794i	$-0.374100\pi$
$367$	14.7623			0.770586			0.385293	+	0.922794i	$0.374100\pi$
$368$	−10.8696	+	8.92022i	−0.566620	+	0.464998i
$369$	7.46814	+	7.46814i	0.388776	+	0.388776i
$370$	24.4703	−	9.43913i	1.27215	−	0.490717i
$371$	−1.88000	+	0.778723i	−0.0976049	+	0.0404293i
$372$	0.363258	−	0.768030i	0.0188341	−	0.0398205i
$373$	−3.26507	−	7.88257i	−0.169059	−	0.408144i	0.816530	−	0.577303i	$-0.195895\pi$
$373$	−3.26507	−	7.88257i	−0.169059	−	0.408144i	−0.985589	+	0.169159i	$0.945895\pi$
$374$	−2.67712	−	2.81189i	−0.138430	−	0.145399i
$375$	4.85134			0.250522
$376$	−0.347125	+	0.689599i	−0.0179016	+	0.0355634i
$377$	0.0543941	−	19.4039i	0.00280144	−	0.999354i
$378$	−1.73583	−	0.0426188i	−0.0892816	−	0.00219208i
$379$	−29.8540	−	12.3659i	−1.53350	−	0.635194i	−0.553256	−	0.833011i	$-0.686615\pi$
$379$	−29.8540	−	12.3659i	−1.53350	−	0.635194i	−0.980239	+	0.197817i	$0.936615\pi$
$380$	−13.6731	−	15.0861i	−0.701413	−	0.773902i
$381$	−1.53138	−	0.634318i	−0.0784549	−	0.0324971i
$382$	−5.05503	+	11.4038i	−0.258638	+	0.583471i
$383$	−15.6442	−	15.6442i	−0.799381	−	0.799381i	0.183617	−	0.982998i	$-0.441219\pi$
$383$	−15.6442	−	15.6442i	−0.799381	−	0.799381i	−0.982998	+	0.183617i	$0.941219\pi$
$384$	−4.55822	−	0.791049i	−0.232610	−	0.0403680i
$385$	0.738442	+	0.738442i	0.0376345	+	0.0376345i
$386$	−0.141252	−	0.366187i	−0.00718955	−	0.0186384i
$387$	−3.05359	+	7.37202i	−0.155223	+	0.374741i
$388$	−30.3034	−	1.48894i	−1.53842	−	0.0755893i
$389$	7.23206	+	17.4597i	0.366680	+	0.885244i	0.994290	+	0.106716i	$0.0340335\pi$
$389$	7.23206	+	17.4597i	0.366680	+	0.885244i	−0.627609	+	0.778528i	$0.715967\pi$
$390$	−2.39733	+	2.26966i	−0.121394	+	0.114928i
$391$	5.32588	+	5.32588i	0.269341	+	0.269341i
$392$	−5.97527	−	18.0881i	−0.301797	−	0.913587i
$393$	0.834422	+	0.834422i	0.0420910	+	0.0420910i
$394$	−6.72165	+	6.39950i	−0.338632	+	0.322402i
$395$	5.97949	−	14.4358i	0.300861	−	0.726343i
$396$	3.10382	−	6.56234i	0.155973	−	0.329770i
$397$	8.33444	+	20.1211i	0.418294	+	1.00985i	0.982842	+	0.184450i	$0.0590504\pi$
$397$	8.33444	+	20.1211i	0.418294	+	1.00985i	−0.564548	+	0.825400i	$0.690950\pi$
$398$	−4.99742	+	1.92770i	−0.250498	+	0.0966268i
$399$	−1.35344			−0.0677567
$400$	−7.70902	+	6.32643i	−0.385451	+	0.316322i
$401$	7.41264	−	7.41264i	0.370170	−	0.370170i	−0.497369	−	0.867539i	$-0.665701\pi$
$401$	7.41264	−	7.41264i	0.370170	−	0.370170i	0.867539	+	0.497369i	$0.165701\pi$
$402$	5.79383	+	2.56825i	0.288970	+	0.128093i
$403$	3.45648	+	1.44309i	0.172179	+	0.0718852i
$404$	4.46316	−	9.43637i	0.222050	−	0.469477i
$405$	−11.0046	−	4.55825i	−0.546822	−	0.226501i
$406$	2.70152	+	2.83751i	0.134074	+	0.140823i
$407$	10.6125	+	10.6125i	0.526044	+	0.526044i
$408$	−0.182328	+	2.47139i	−0.00902660	+	0.122352i
$409$			9.92245i			0.490633i	0.969443	+	0.245317i	$0.0788919\pi$
$409$			9.92245i			0.490633i	−0.969443	+	0.245317i	$0.921108\pi$
$410$	−6.04618	+	5.75640i	−0.298599	+	0.284288i
$411$	0.719876	−	1.73793i	0.0355089	−	0.0857260i
$412$	7.02310	+	0.345075i	0.346003	+	0.0170006i
$413$	4.95575	+	2.05274i	0.243856	+	0.101009i
$414$	−5.70704	+	12.8748i	−0.280486	+	0.632760i
$415$	−9.70575			−0.476436
$416$	2.55381	−	20.2356i	0.125211	−	0.992130i
$417$	7.43708			0.364195
$418$	4.72146	−	10.6513i	0.230934	−	0.520974i
$419$	6.36707	+	2.63733i	0.311052	+	0.128842i	0.532748	−	0.846274i	$-0.321159\pi$
$419$	6.36707	+	2.63733i	0.311052	+	0.128842i	−0.221696	+	0.975116i	$0.571159\pi$
$420$	0.0327117	−	0.665761i	0.00159617	−	0.0324858i
$421$	−5.12207	+	12.3658i	−0.249634	+	0.602671i	−0.998173	−	0.0604205i	$-0.980756\pi$
$421$	−5.12207	+	12.3658i	−0.249634	+	0.602671i	0.748539	+	0.663091i	$0.230756\pi$
$422$	20.3455	−	19.3704i	0.990405	−	0.942937i
$423$			0.773229i			0.0375957i
$424$	−8.46630	+	7.30292i	−0.411160	+	0.354661i
$425$	3.77724	+	3.77724i	0.183223	+	0.183223i
$426$	−5.54203	−	5.82102i	−0.268512	−	0.282029i
$427$	−6.35957	−	2.63422i	−0.307761	−	0.127479i
$428$	12.7876	+	6.04822i	0.618114	+	0.292352i
$429$	−1.74328	−	0.727822i	−0.0841663	−	0.0351396i
$430$	−5.76609	−	2.55596i	−0.278066	−	0.123259i
$431$	25.7193	−	25.7193i	1.23885	−	1.23885i	0.278383	−	0.960470i	$-0.410202\pi$
$431$	25.7193	−	25.7193i	1.23885	−	1.23885i	0.960470	−	0.278383i	$-0.0897984\pi$
$432$	−9.12970	+	2.76931i	−0.439253	+	0.133239i
$433$	−11.4659			−0.551014			−0.275507	−	0.961299i	$-0.588846\pi$
$433$	−11.4659			−0.551014			−0.275507	+	0.961299i	$0.588846\pi$
$434$	−0.705604	+	0.272179i	−0.0338701	+	0.0130650i
$435$	−1.33339	−	3.21909i	−0.0639312	−	0.154343i
$436$	14.1698	+	6.70193i	0.678609	+	0.320964i
$437$	−8.64959	+	20.8820i	−0.413766	+	0.998919i
$438$	−0.553154	+	0.526642i	−0.0264307	+	0.0251639i
$439$	21.2946	+	21.2946i	1.01634	+	1.01634i	0.999864	+	0.0164713i	$0.00524322\pi$
$439$	21.2946	+	21.2946i	1.01634	+	1.01634i	0.0164713	+	0.999864i	$0.494757\pi$
$440$	5.12531	+	2.57994i	0.244340	+	0.122994i
$441$	−13.4908	−	13.4908i	−0.642419	−	0.642419i
$442$	−10.9211	−	0.298773i	−0.519463	−	0.0142112i
$443$	−9.67537	−	23.3584i	−0.459691	−	1.10979i	−0.968523	−	0.248926i	$-0.919922\pi$
$443$	−9.67537	−	23.3584i	−0.459691	−	1.10979i	0.508832	−	0.860866i	$-0.330078\pi$
$444$	0.470117	−	9.56799i	0.0223108	−	0.454077i
$445$	−2.86823	+	6.92452i	−0.135967	+	0.328254i
$446$	10.9035	+	28.2665i	0.516295	+	1.33846i
$447$	3.62337	+	3.62337i	0.171380	+	0.171380i
$448$	2.45312	+	3.30780i	0.115899	+	0.156279i
$449$	−18.3921	−	18.3921i	−0.867975	−	0.867975i	0.124273	−	0.992248i	$-0.460340\pi$
$449$	−18.3921	−	18.3921i	−0.867975	−	0.867975i	−0.992248	+	0.124273i	$0.960340\pi$
$450$	−4.04757	+	9.13109i	−0.190804	+	0.430444i
$451$	−4.41349	−	1.82813i	−0.207823	−	0.0860831i
$452$	12.0178	−	10.8921i	0.565270	−	0.512323i
$453$	1.80279	+	0.746739i	0.0847023	+	0.0350848i
$454$	−31.1386	−	0.764527i	−1.46141	−	0.0358810i
$455$	2.93865	+	0.00823778i	0.137766	+	0.000386193i
$456$	−7.06120	+	2.33262i	−0.330671	+	0.109235i
$457$	−1.61254			−0.0754316			−0.0377158	−	0.999289i	$-0.512008\pi$
$457$	−1.61254			−0.0754316			−0.0377158	+	0.999289i	$0.512008\pi$
$458$	12.3546	+	12.9766i	0.577294	+	0.606355i
$459$	1.95565	+	4.72135i	0.0912818	+	0.220374i
$460$	−10.0628	−	4.75946i	−0.469182	−	0.221911i
$461$	19.9388	−	8.25892i	0.928642	−	0.384656i	0.133479	−	0.991052i	$-0.457385\pi$
$461$	19.9388	−	8.25892i	0.928642	−	0.384656i	0.795163	+	0.606395i	$0.207385\pi$
$462$	0.355873	−	0.137274i	0.0165567	−	0.00638655i
$463$	−8.70776	−	8.70776i	−0.404684	−	0.404684i	0.475196	−	0.879880i	$-0.342377\pi$
$463$	−8.70776	−	8.70776i	−0.404684	−	0.404684i	−0.879880	+	0.475196i	$0.842377\pi$
$464$	18.9848	+	10.1480i	0.881348	+	0.471107i
$465$	0.672590			0.0311906
$466$	4.89240	−	1.88718i	0.226636	−	0.0874221i
$467$	8.92094	+	3.69517i	0.412812	+	0.170992i	0.579417	−	0.815032i	$-0.303280\pi$
$467$	8.92094	+	3.69517i	0.412812	+	0.170992i	−0.166605	+	0.986024i	$0.553280\pi$
$468$	−6.82774	−	19.2527i	−0.315612	−	0.889956i
$469$	−2.15887	−	5.21197i	−0.0996873	−	0.240666i
$470$	−0.611001	−	0.0150015i	−0.0281834	−	0.000691969i
$471$	0.833121	−	0.833121i	0.0383882	−	0.0383882i
$472$	29.3931	+	2.16850i	1.35293	+	0.0998133i
$473$		−	3.60919i		−	0.165951i
$474$	−3.93520	−	4.13330i	−0.180750	−	0.189849i
$475$	−6.13450	+	14.8100i	−0.281470	+	0.679529i
$476$	1.63447	−	1.48138i	0.0749160	−	0.0678989i
$477$	−4.28531	+	10.3457i	−0.196211	+	0.473695i
$478$	−28.9518	+	11.1678i	−1.32423	+	0.510804i
$479$	21.6977	−	21.6977i	0.991395	−	0.991395i	−0.00856810	−	0.999963i	$-0.502727\pi$
$479$	21.6977	−	21.6977i	0.991395	−	0.991395i	0.999963	+	0.00856810i	$0.00272735\pi$
$480$	−0.976758	−	3.52981i	−0.0445827	−	0.161113i
$481$	42.2329	+	0.118389i	1.92565	+	0.00539809i
$482$	3.61088	−	1.39286i	0.164471	−	0.0634428i
$483$	−0.683640	+	0.283173i	−0.0311067	+	0.0128848i
$484$	0.918516	−	18.6940i	0.0417507	−	0.849725i
$485$	−9.19154	−	22.1903i	−0.417366	−	1.00761i
$486$	−10.4797	+	9.97742i	−0.475368	+	0.452585i
$487$	7.52221			0.340864			0.170432	−	0.985369i	$-0.445484\pi$
$487$	7.52221			0.340864			0.170432	+	0.985369i	$0.445484\pi$
$488$	−37.7194	−	2.78278i	−1.70748	−	0.125970i
$489$		−	1.68310i		−	0.0761124i
$490$	10.9221	−	10.3986i	0.493410	−	0.469762i
$491$	14.9873	+	36.1827i	0.676369	+	1.63290i	0.770576	+	0.637348i	$0.219968\pi$
$491$	14.9873	+	36.1827i	0.676369	+	1.63290i	−0.0942069	+	0.995553i	$0.530032\pi$
$492$	1.02720	+	2.87090i	0.0463098	+	0.129430i
$493$	4.41267	−	10.6531i	0.198737	−	0.479792i
$494$	−11.7133	−	30.6213i	−0.527007	−	1.37772i
$495$	5.74687			0.258303
$496$	−3.21221	+	2.63611i	−0.144232	+	0.118365i
$497$			7.15446i			0.320921i
$498$	−1.43658	+	3.24084i	−0.0643748	+	0.145226i
$499$	−10.5392	−	25.4438i	−0.471798	−	1.13902i	−0.963368	−	0.268183i	$-0.913577\pi$
$499$	−10.5392	−	25.4438i	−0.471798	−	1.13902i	0.491570	−	0.870838i	$-0.336423\pi$
$500$	−21.4497	−	10.1451i	−0.959258	−	0.453704i
$501$	2.73051	−	6.59204i	0.121990	−	0.294511i
$502$	22.6298	+	0.555615i	1.01002	+	0.0247983i
$503$	9.31783	−	9.31783i	0.415461	−	0.415461i	−0.468175	−	0.883636i	$-0.655088\pi$
$503$	9.31783	−	9.31783i	0.415461	−	0.415461i	0.883636	+	0.468175i	$0.155088\pi$
$504$	3.68410	+	1.85447i	0.164103	+	0.0826048i
$505$	8.26376			0.367732
$506$	0.156349	−	6.36798i	0.00695057	−	0.283091i
$507$	−4.92258	+	2.00674i	−0.218619	+	0.0891224i
$508$	5.44433	+	6.00698i	0.241553	+	0.266517i
$509$	15.5852	+	37.6261i	0.690804	+	1.66775i	0.743155	+	0.669119i	$0.233328\pi$
$509$	15.5852	+	37.6261i	0.690804	+	1.66775i	−0.0523518	+	0.998629i	$0.516672\pi$
$510$	−1.83034	+	0.706034i	−0.0810490	+	0.0312637i
$511$	0.679866			0.0300755
$512$	18.4994	+	13.0297i	0.817565	+	0.575836i
$513$	−10.8439	+	10.8439i	−0.478770	+	0.478770i
$514$	6.73582	−	15.1956i	0.297104	−	0.670250i
$515$	2.13023	+	5.14282i	0.0938691	+	0.226620i
$516$	−1.70692	+	1.54704i	−0.0751429	+	0.0681045i
$517$	−0.133840	−	0.323119i	−0.00588628	−	0.0142107i
$518$	−6.17588	+	5.87988i	−0.271352	+	0.258347i
$519$	−3.92338	+	3.92338i	−0.172217	+	0.172217i
$520$	15.3458	−	5.02172i	0.672960	−	0.220217i
$521$	−6.15748	−	6.15748i	−0.269764	−	0.269764i	0.559241	−	0.829005i	$-0.311093\pi$
$521$	−6.15748	−	6.15748i	−0.269764	−	0.269764i	−0.829005	+	0.559241i	$0.811093\pi$
$522$	21.5535	+	0.529190i	0.943372	+	0.0231620i
$523$	27.5028	−	11.3920i	1.20261	−	0.498139i	0.310771	−	0.950485i	$-0.399413\pi$
$523$	27.5028	−	11.3920i	1.20261	−	0.498139i	0.891843	+	0.452346i	$0.149413\pi$
$524$	−1.94436	−	5.43425i	−0.0849397	−	0.237396i
$525$	−0.484854	+	0.200833i	−0.0211608	+	0.00876508i
$526$	14.8800	+	38.5754i	0.648800	+	1.68197i
$527$	1.57391	+	1.57391i	0.0685605	+	0.0685605i
$528$	1.62008	−	1.32953i	0.0705050	−	0.0578602i
$529$		−	10.6425i		−	0.462719i
$530$	−8.09195	−	3.58695i	−0.351492	−	0.155807i
$531$	27.2715	−	11.2962i	1.18348	−	0.490214i
$532$	5.98407	+	2.83031i	0.259443	+	0.122710i
$533$	−12.4338	+	5.10945i	−0.538566	+	0.221315i
$534$	1.88763	+	1.98265i	0.0816856	+	0.0857978i
$535$			11.1986i			0.484156i
$536$	−20.2460	−	23.4713i	−0.874495	−	1.01381i
$537$	−7.41207	−	7.41207i	−0.319854	−	0.319854i
$538$	−9.28134	−	9.74857i	−0.400147	−	0.420291i
$539$	7.97272	+	3.30241i	0.343409	+	0.142245i
$540$	−5.07206	−	5.59624i	−0.218267	−	0.240824i
$541$	−1.21138	+	0.501771i	−0.0520814	+	0.0215728i	−0.408572	−	0.912726i	$-0.633973\pi$
$541$	−1.21138	+	0.501771i	−0.0520814	+	0.0215728i	0.356491	+	0.934299i	$0.383973\pi$
$542$	8.62808	+	22.3677i	0.370608	+	0.960775i
$543$	−1.64986			−0.0708024
$544$	5.97431	−	10.5457i	0.256147	−	0.452142i
$545$			12.4090i			0.531541i
$546$	0.437711	−	0.980026i	0.0187323	−	0.0419412i
$547$	−36.8987	−	15.2839i	−1.57767	−	0.653493i	−0.589630	−	0.807674i	$-0.700726\pi$
$547$	−36.8987	−	15.2839i	−1.57767	−	0.653493i	−0.988043	+	0.154180i	$0.950726\pi$
$548$	−6.81722	+	6.17868i	−0.291217	+	0.263940i
$549$	−34.9968	+	14.4961i	−1.49363	+	0.618680i
$550$	0.110887	−	4.51633i	0.00472822	−	0.192577i
$551$	34.6028			1.47413
$552$	−3.07867	+	2.65562i	−0.131037	+	0.113031i
$553$			5.08013i			0.216029i
$554$	22.7795	+	0.559290i	0.967807	+	0.0237620i
$555$	7.00638	−	2.90214i	0.297404	−	0.123189i
$556$	−32.8822	−	15.5524i	−1.39452	−	0.659570i
$557$	−0.517552	−	1.24948i	−0.0219294	−	0.0529423i	0.912536	−	0.408997i	$-0.134122\pi$
$557$	−0.517552	−	1.24948i	−0.0219294	−	0.0529423i	−0.934465	+	0.356055i	$0.884122\pi$
$558$	−1.68655	+	3.80476i	−0.0713974	+	0.161068i
$559$	−7.16132	−	7.20158i	−0.302891	−	0.304594i
$560$	−1.53687	+	2.87518i	−0.0649446	+	0.121498i
$561$	−0.793803	−	0.793803i	−0.0335144	−	0.0335144i
$562$	32.6181	+	14.4588i	1.37591	+	0.609906i
$563$	−1.01743	−	0.421433i	−0.0428795	−	0.0177613i	0.361141	−	0.932511i	$-0.382387\pi$
$563$	−1.01743	−	0.421433i	−0.0428795	−	0.0177613i	−0.404020	+	0.914750i	$0.632387\pi$
$564$	−0.0954456	+	0.201799i	−0.00401899	+	0.00849727i
$565$	11.8627	+	4.91368i	0.499066	+	0.206720i
$566$	8.45059	+	0.207482i	0.355205	+	0.00872112i
$567$	3.87265			0.162636
$568$	12.3305	+	37.3265i	0.517378	+	1.56618i
$569$	2.35423	+	2.35423i	0.0986944	+	0.0986944i	0.754730	−	0.656036i	$-0.227768\pi$
$569$	2.35423	+	2.35423i	0.0986944	+	0.0986944i	−0.656036	+	0.754730i	$0.727768\pi$
$570$	−4.05940	−	4.26375i	−0.170029	−	0.178589i
$571$	24.4805	−	10.1402i	1.02448	−	0.424352i	0.193761	−	0.981049i	$-0.437931\pi$
$571$	24.4805	−	10.1402i	1.02448	−	0.424352i	0.830716	+	0.556696i	$0.187931\pi$
$572$	6.18569	+	6.86353i	0.258637	+	0.286979i
$573$	−1.38027	+	3.33227i	−0.0576616	+	0.139207i
$574$	1.09992	−	2.48135i	0.0459097	−	0.103570i
$575$			8.76422i			0.365493i
$576$	22.4169	+	3.32576i	0.934039	+	0.138573i
$577$	28.8832	−	28.8832i	1.20242	−	1.20242i	0.228994	−	0.973428i	$-0.426457\pi$
$577$	28.8832	−	28.8832i	1.20242	−	1.20242i	0.973428	−	0.228994i	$-0.0735435\pi$
$578$	16.0438	+	7.11178i	0.667332	+	0.295811i
$579$	−0.0434292	−	0.104847i	−0.00180486	−	0.00435731i
$580$	−0.836327	+	17.0212i	−0.0347266	+	0.706768i
$581$	2.91537	−	1.20759i	0.120950	−	0.0500992i
$582$	−8.77005	−	0.215325i	−0.363530	−	0.00892553i
$583$		−	5.06503i		−	0.209772i
$584$	3.54702	−	1.17173i	0.146777	−	0.0484867i
$585$	11.4670	−	11.4029i	0.474101	−	0.471451i
$586$	−25.9721	−	27.2796i	−1.07290	−	1.12691i
$587$	−2.35119	+	5.67627i	−0.0970439	+	0.234285i	−0.964945	−	0.262452i	$-0.915469\pi$
$587$	−2.35119	+	5.67627i	−0.0970439	+	0.234285i	0.867901	+	0.496737i	$0.165469\pi$
$588$	−1.85558	−	5.18613i	−0.0765230	−	0.213872i
$589$	−2.55613	+	6.17106i	−0.105324	+	0.254274i
$590$	8.39712	+	21.7690i	0.345704	+	0.896214i
$591$	−1.89754	+	1.89754i	−0.0780544	+	0.0780544i
$592$	−22.0872	+	41.3207i	−0.907776	+	1.69827i
$593$	2.47978	−	2.47978i	0.101832	−	0.101832i	−0.654355	−	0.756187i	$-0.727060\pi$
$593$	2.47978	−	2.47978i	0.101832	−	0.101832i	0.756187	+	0.654355i	$0.227060\pi$
$594$	1.75144	−	3.95114i	0.0718624	−	0.162117i
$595$	1.61337	+	0.668282i	0.0661419	+	0.0273969i
$596$	−8.44313	−	23.5975i	−0.345844	−	0.966592i
$597$	−1.43087	+	0.592687i	−0.0585617	+	0.0242571i
$598$	−12.3233	−	13.0165i	−0.503937	−	0.532286i
$599$	−14.2962	+	14.2962i	−0.584126	+	0.584126i	−0.936034	−	0.351909i	$-0.885533\pi$
$599$	−14.2962	+	14.2962i	−0.584126	+	0.584126i	0.351909	+	0.936034i	$0.385533\pi$
$600$	−2.18347	+	1.88343i	−0.0891396	+	0.0768906i
$601$	15.3855	−	15.3855i	0.627586	−	0.627586i	−0.319874	−	0.947460i	$-0.603641\pi$
$601$	15.3855	−	15.3855i	0.627586	−	0.627586i	0.947460	+	0.319874i	$0.103641\pi$
$602$	2.05001	+	0.0503325i	0.0835521	+	0.00205140i
$603$	−28.6815	−	11.8803i	−1.16800	−	0.483802i
$604$	−6.40923	−	7.07161i	−0.260788	−	0.287740i
$605$	13.6891	−	5.67020i	0.556540	−	0.230527i
$606$	1.22315	−	2.75935i	0.0496870	−	0.112091i
$607$			12.3215i			0.500114i	0.968231	+	0.250057i	$0.0804494\pi$
$607$			12.3215i			0.500114i	−0.968231	+	0.250057i	$0.919551\pi$
$608$	36.0983	+	4.45298i	1.46398	+	0.180592i
$609$	0.801037	+	0.801037i	0.0324597	+	0.0324597i
$610$	−10.7758	−	27.9355i	−0.436299	−	1.13108i
$611$	−0.908185	−	0.379169i	−0.0367412	−	0.0153395i
$612$	0.595727	−	12.1244i	0.0240808	−	0.490102i
$613$	−8.74372	+	21.1092i	−0.353156	+	0.852593i	0.643071	+	0.765806i	$0.277660\pi$
$613$	−8.74372	+	21.1092i	−0.353156	+	0.852593i	−0.996227	+	0.0867869i	$0.972340\pi$
$614$	−31.6926	−	0.778130i	−1.27901	−	0.0314028i
$615$	−1.70685	+	1.70685i	−0.0688269	+	0.0688269i
$616$	−1.86052	−	0.137261i	−0.0749624	−	0.00553040i
$617$	−4.15291			−0.167190			−0.0835950	−	0.996500i	$-0.526640\pi$
$617$	−4.15291			−0.167190			−0.0835950	+	0.996500i	$0.526640\pi$
$618$	2.03254	+	0.0499037i	0.0817608	+	0.00200742i
$619$	−38.5180	−	15.9547i	−1.54817	−	0.641272i	−0.565184	−	0.824965i	$-0.691195\pi$
$619$	−38.5180	−	15.9547i	−1.54817	−	0.641272i	−0.982984	+	0.183693i	$0.941195\pi$
$620$	−2.97378	−	1.40652i	−0.119430	−	0.0564873i
$621$	−3.20859	+	7.74622i	−0.128756	+	0.310845i
$622$	−5.10888	−	13.2444i	−0.204848	−	0.531053i
$623$		−	2.43682i		−	0.0976293i
$624$	0.594590	−	5.86741i	0.0238027	−	0.234884i
$625$		−	6.31846i		−	0.252738i
$626$	−15.1453	+	5.84211i	−0.605326	+	0.233497i
$627$	1.28919	−	3.11238i	0.0514853	−	0.124296i
$628$	−5.42577	+	1.94133i	−0.216512	+	0.0774674i
$629$	23.1866	+	9.60422i	0.924512	+	0.382945i
$630$	−0.0801439	+	3.26420i	−0.00319301	+	0.130049i
$631$	−32.7770			−1.30483			−0.652417	−	0.757861i	$-0.726245\pi$
$631$	−32.7770			−1.30483			−0.652417	+	0.757861i	$0.726245\pi$
$632$	8.75548	+	26.5042i	0.348274	+	1.05428i
$633$	5.74360	−	5.74360i	0.228288	−	0.228288i
$634$	−0.245048	+	9.98062i	−0.00973210	+	0.396381i
$635$	−2.45605	+	5.92944i	−0.0974655	+	0.235303i
$636$	−2.39544	+	2.17106i	−0.0949852	+	0.0860883i
$637$	22.4609	−	9.22994i	0.889934	−	0.365703i
$638$	−9.09844	+	3.50962i	−0.360211	+	0.138947i
$639$	27.8395	+	27.8395i	1.10131	+	1.10131i
$640$	−3.06291	+	17.6492i	−0.121072	+	0.697647i
$641$			29.9816i			1.18420i	0.805864	+	0.592101i	$0.201701\pi$
$641$			29.9816i			1.18420i	−0.805864	+	0.592101i	$0.798299\pi$
$642$	3.73931	+	1.65754i	0.147579	+	0.0654179i
$643$	−33.5781	+	13.9085i	−1.32419	+	0.548499i	−0.928993	−	0.370097i	$-0.879325\pi$
$643$	−33.5781	+	13.9085i	−1.32419	+	0.548499i	−0.395199	+	0.918595i	$0.629325\pi$
$644$	3.61481	+	0.177611i	0.142443	+	0.00699887i
$645$	−1.68488	−	0.697902i	−0.0663422	−	0.0274798i
$646$	0.478200	−	19.4768i	0.0188145	−	0.766302i
$647$	−15.3603	+	15.3603i	−0.603876	+	0.603876i	−0.941339	−	0.337463i	$-0.890431\pi$
$647$	−15.3603	+	15.3603i	−0.603876	+	0.603876i	0.337463	+	0.941339i	$0.390431\pi$
$648$	20.2045	−	6.67442i	0.793709	−	0.262196i
$649$	−9.44099	+	9.44099i	−0.370591	+	0.370591i
$650$	−8.73999	−	9.23165i	−0.342810	−	0.362095i
$651$	−0.202030	+	0.0836836i	−0.00791818	+	0.00327982i
$652$	−3.51970	+	7.44164i	−0.137842	+	0.291437i
$653$	−11.6021	−	4.80575i	−0.454025	−	0.188063i	0.143938	−	0.989587i	$-0.454023\pi$
$653$	−11.6021	−	4.80575i	−0.454025	−	0.188063i	−0.597964	+	0.801523i	$0.704023\pi$
$654$	4.14347	+	1.83669i	0.162023	+	0.0718204i
$655$	3.23085	−	3.23085i	0.126240	−	0.126240i
$656$	1.46198	−	14.8415i	0.0570807	−	0.579462i
$657$	2.64550	−	2.64550i	0.103211	−	0.103211i
$658$	0.185397	−	0.0715146i	0.00722752	−	0.00278793i
$659$	−17.2318	+	41.6013i	−0.671257	+	1.62056i	0.108221	+	0.994127i	$0.465485\pi$
$659$	−17.2318	+	41.6013i	−0.671257	+	1.62056i	−0.779478	+	0.626430i	$0.784515\pi$
$660$	1.49983	+	0.709381i	0.0583808	+	0.0276126i
$661$	6.22167	−	15.0204i	0.241995	−	0.584227i	−0.755486	−	0.655165i	$-0.772599\pi$
$661$	6.22167	−	15.0204i	0.241995	−	0.584227i	0.997481	+	0.0709376i	$0.0225991\pi$
$662$	12.9984	−	12.3754i	0.505197	−	0.480984i
$663$	−3.15896	−	0.00885536i	−0.122684	−	0.000343914i
$664$	13.1289	−	11.3248i	0.509502	−	0.439489i
$665$			5.24046i			0.203216i
$666$	−1.15179	+	46.9115i	−0.0446309	+	1.81778i
$667$	17.4783	−	7.23977i	0.676764	−	0.280325i
$668$	−25.8579	+	23.4359i	−1.00047	+	0.906763i
$669$	3.35237	+	8.09333i	0.129610	+	0.312906i
$670$	9.94418	−	22.4335i	0.384177	−	0.866681i
$671$	12.1154	−	12.1154i	0.467708	−	0.467708i
$672$	0.732573	+	0.938741i	0.0282596	+	0.0362127i
$673$		−	33.3926i		−	1.28719i	−0.765367	−	0.643594i	$-0.777442\pi$
$673$		−	33.3926i		−	1.28719i	0.765367	−	0.643594i	$-0.222558\pi$
$674$	−17.1555	−	7.60460i	−0.660806	−	0.292918i
$675$	−2.27561	+	5.49380i	−0.0875882	+	0.211457i
$676$	25.9611	+	1.42153i	0.998504	+	0.0546741i
$677$	−24.8361	+	10.2874i	−0.954528	+	0.395378i	−0.804931	−	0.593369i	$-0.797798\pi$
$677$	−24.8361	+	10.2874i	−0.954528	+	0.395378i	−0.149597	+	0.988747i	$0.547798\pi$
$678$	3.39656	−	3.23377i	0.130444	−	0.124192i
$679$	5.52184	+	5.52184i	0.211909	+	0.211909i
$680$	9.56912	+	0.705969i	0.366959	+	0.0270727i
$681$	−9.00634			−0.345124
$682$	0.0462044	−	1.88187i	0.00176926	−	0.0720606i
$683$	−26.6641	−	11.0446i	−1.02027	−	0.422612i	−0.191082	−	0.981574i	$-0.561200\pi$
$683$	−26.6641	−	11.0446i	−1.02027	−	0.422612i	−0.829193	+	0.558963i	$0.811200\pi$
$684$	34.2986	−	12.2720i	1.31144	−	0.469230i
$685$	−6.72922	−	2.78733i	−0.257110	−	0.106498i
$686$	−4.05206	+	9.14120i	−0.154708	+	0.349013i
$687$	3.66332	+	3.66332i	0.139764	+	0.139764i
$688$	10.7821	−	3.27054i	0.411064	−	0.124688i
$689$	−10.0500	−	10.1065i	−0.382873	−	0.385026i
$690$	−2.94254	−	1.30435i	−0.112021	−	0.0496558i
$691$	−14.2066	−	34.2977i	−0.540444	−	1.30475i	−0.924410	−	0.381400i	$-0.875442\pi$
$691$	−14.2066	−	34.2977i	−0.540444	−	1.30475i	0.383966	−	0.923347i	$-0.374558\pi$
$692$	25.5514	−	9.14222i	0.971318	−	0.347535i
$693$	−1.72622	+	0.715025i	−0.0655738	+	0.0271615i
$694$	0.118628	−	4.83164i	0.00450307	−	0.183407i
$695$		−	28.7961i		−	1.09230i
$696$	5.55977	+	2.79863i	0.210742	+	0.106082i
$697$	−7.98831			−0.302579
$698$	21.3524	+	0.524253i	0.808201	+	0.0198433i
$699$	1.40080	−	0.580231i	0.0529831	−	0.0219463i
$700$	2.56371	+	0.125966i	0.0968992	+	0.00476108i
$701$	−13.7143	−	5.68063i	−0.517980	−	0.214554i	0.108349	−	0.994113i	$-0.465444\pi$
$701$	−13.7143	−	5.68063i	−0.517980	−	0.214554i	−0.626330	+	0.779558i	$0.715444\pi$
$702$	−4.34509	−	11.3591i	−0.163995	−	0.428720i
$703$			75.3134i			2.84050i
$704$	−9.94332	+	2.49043i	−0.374753	+	0.0938617i
$705$	−0.176722			−0.00665575
$706$	38.4865	−	14.8457i	1.44846	−	0.558726i
$707$	−2.48223	+	1.02818i	−0.0933540	+	0.0386685i
$708$	8.51176	+	0.418220i	0.319891	+	0.0157177i
$709$	23.7139	+	9.82263i	0.890596	+	0.368897i	0.780597	−	0.625035i	$-0.214915\pi$
$709$	23.7139	+	9.82263i	0.890596	+	0.368897i	0.109999	+	0.993932i	$0.464915\pi$
$710$	−22.5388	+	21.4585i	−0.845865	+	0.805324i
$711$	19.7679	+	19.7679i	0.741353	+	0.741353i
$712$	−4.19981	−	12.7135i	−0.157394	−	0.476458i
$713$			3.65189i			0.136764i
$714$	0.461947	−	0.439807i	0.0172879	−	0.0164594i
$715$	−2.81810	+	6.74991i	−0.105391	+	0.252432i
$716$	17.2715	+	48.2717i	0.645466	+	1.80400i
$717$	−8.28954	+	3.43364i	−0.309579	+	0.128232i
$718$	14.8697	−	33.5452i	0.554933	−	1.25190i
$719$		−	9.13313i		−	0.340608i	−0.985392	−	0.170304i	$-0.945525\pi$
$719$		−	9.13313i		−	0.340608i	0.985392	−	0.170304i	$-0.0544750\pi$
$720$	5.20764	+	17.1682i	0.194077	+	0.639822i
$721$	−1.27974	−	1.27974i	−0.0476600	−	0.0476600i
$722$	29.4780	−	11.3708i	1.09706	−	0.423177i
$723$	1.03387	−	0.428245i	0.0384502	−	0.0159266i
$724$	7.29468	+	3.45020i	0.271105	+	0.128226i
$725$	12.3961	−	5.13462i	0.460378	−	0.190695i
$726$	0.132833	−	5.41019i	0.00492989	−	0.200791i
$727$	−20.8794	−	20.8794i	−0.774372	−	0.774372i	0.204495	−	0.978868i	$-0.434445\pi$
$727$	−20.8794	−	20.8794i	−0.774372	−	0.774372i	−0.978868	+	0.204495i	$0.934445\pi$
$728$	−3.98472	+	3.41773i	−0.147684	+	0.126670i
$729$	13.0004	−	13.0004i	0.481495	−	0.481495i
$730$	2.03914	+	2.14179i	0.0754719	+	0.0792712i
$731$	−2.30961	−	5.57588i	−0.0854239	−	0.206232i
$732$	−10.9229	−	0.536690i	−0.403722	−	0.0198366i
$733$	−6.55085	−	15.8151i	−0.241961	−	0.584146i	0.755516	−	0.655130i	$-0.227386\pi$
$733$	−6.55085	−	15.8151i	−0.241961	−	0.584146i	−0.997477	+	0.0709840i	$0.977386\pi$
$734$	−19.0860	−	8.46032i	−0.704476	−	0.312276i
$735$	3.08334	−	3.08334i	0.113731	−	0.113731i
$736$	19.1654	−	5.30340i	0.706446	−	0.195486i
$737$	14.0419			0.517240
$738$	−5.37544	−	13.9355i	−0.197873	−	0.512972i
$739$	−3.20079	−	7.72740i	−0.117743	−	0.284257i	0.854010	−	0.520256i	$-0.174164\pi$
$739$	−3.20079	−	7.72740i	−0.117743	−	0.284257i	−0.971753	+	0.235999i	$0.924164\pi$
$740$	−37.0469	−	1.82027i	−1.36187	−	0.0669146i
$741$	−3.60317	−	8.76826i	−0.132366	−	0.322110i
$742$	2.87692	+	0.0706351i	0.105615	+	0.00259310i
$743$	−18.3487			−0.673149			−0.336574	−	0.941657i	$-0.609268\pi$
$743$	−18.3487			−0.673149			−0.336574	+	0.941657i	$0.609268\pi$
$744$	−0.909811	+	0.784791i	−0.0333553	+	0.0287718i
$745$	14.0296	−	14.0296i	0.514003	−	0.514003i
$746$	−0.296163	+	12.0625i	−0.0108433	+	0.441639i
$747$	6.64536	−	16.0433i	0.243141	−	0.586994i
$748$	1.84971	+	5.16971i	0.0676320	+	0.189023i
$749$	−1.39332	−	3.36378i	−0.0509110	−	0.122910i
$750$	−6.27223	−	2.78032i	−0.229029	−	0.101523i
$751$			16.5406i			0.603574i	0.953375	+	0.301787i	$0.0975832\pi$
$751$			16.5406i			0.603574i	−0.953375	+	0.301787i	$0.902417\pi$
$752$	0.844004	−	0.692635i	0.0307777	−	0.0252578i
$753$	6.54531			0.238524
$754$	−11.1908	+	25.0559i	−0.407544	+	0.912482i
$755$	2.89134	−	6.98032i	0.105227	−	0.254040i
$756$	2.21981	+	1.04991i	0.0807337	+	0.0381849i
$757$	3.11853	+	7.52881i	0.113345	+	0.273639i	0.970365	−	0.241644i	$-0.0776867\pi$
$757$	3.11853	+	7.52881i	0.113345	+	0.273639i	−0.857020	+	0.515283i	$0.827687\pi$
$758$	31.5108	+	33.0971i	1.14452	+	1.20214i
$759$		−	1.84184i		−	0.0668544i
$760$	9.03181	+	27.3407i	0.327618	+	0.991751i
$761$	13.8306			0.501359			0.250679	−	0.968070i	$-0.419346\pi$
$761$	13.8306			0.501359			0.250679	+	0.968070i	$0.419346\pi$
$762$	1.61637	+	1.69774i	0.0585549	+	0.0615025i
$763$	−1.54392	−	3.72735i	−0.0558937	−	0.134939i
$764$	13.0711	−	11.8468i	0.472897	−	0.428603i
$765$	8.87841	−	3.67756i	0.320999	−	0.132962i
$766$	11.2604	+	29.1919i	0.406856	+	1.05475i
$767$	−0.105320	+	37.5707i	−0.00380289	+	1.35660i
$768$	5.43990	+	3.63506i	0.196295	+	0.131169i
$769$	16.2413	−

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29289 - 0.573103i) q^{2} +(-0.377788 - 0.156485i) q^{3} +(1.34311 + 1.48191i) q^{4} +(-0.605904 + 1.46278i) q^{5} +(0.398755 + 0.418829i) q^{6} -0.514771i q^{7} +(-0.887196 - 2.68568i) q^{8} +(-2.00308 - 2.00308i) q^{9} +O(q^{10})\)	\(q+(-1.29289 - 0.573103i) q^{2} +(-0.377788 - 0.156485i) q^{3} +(1.34311 + 1.48191i) q^{4} +(-0.605904 + 1.46278i) q^{5} +(0.398755 + 0.418829i) q^{6} -0.514771i q^{7} +(-0.887196 - 2.68568i) q^{8} +(-2.00308 - 2.00308i) q^{9} +(1.62169 - 1.54396i) q^{10} +(1.18377 + 0.490335i) q^{11} +(-0.275513 - 0.770025i) q^{12} +(3.33495 - 1.37044i) q^{13} +(-0.295017 + 0.665540i) q^{14} +(0.457807 - 0.457807i) q^{15} +(-0.392128 + 3.98073i) q^{16} +2.14260 q^{17} +(1.44179 + 3.73773i) q^{18} +(2.46054 + 5.94027i) q^{19} +(-2.98151 + 1.06678i) q^{20} +(-0.0805540 + 0.194475i) q^{21} +(-1.24947 - 1.31237i) q^{22} +(2.48571 + 2.48571i) q^{23} +(-0.0850968 + 1.15345i) q^{24} +(1.76292 + 1.76292i) q^{25} +(-5.09711 - 0.139444i) q^{26} +(0.912744 + 2.20356i) q^{27} +(0.762846 - 0.691393i) q^{28} +(2.05949 - 4.97205i) q^{29} +(-0.854263 + 0.329522i) q^{30} +(0.734578 + 0.734578i) q^{31} +(2.78835 - 4.92190i) q^{32} +(-0.370486 - 0.370486i) q^{33} +(-2.77014 - 1.22793i) q^{34} +(0.752998 + 0.311902i) q^{35} +(0.278039 - 5.65875i) q^{36} +(10.8217 + 4.48250i) q^{37} +(0.223187 - 9.09023i) q^{38} +(-1.47436 - 0.00413299i) q^{39} +(4.46612 + 0.329491i) q^{40} -3.72832 q^{41} +(0.215601 - 0.205268i) q^{42} +(-1.07795 - 2.60239i) q^{43} +(0.863300 + 2.41282i) q^{44} +(4.14375 - 1.71640i) q^{45} +(-1.78917 - 4.63830i) q^{46} +(-0.193010 - 0.193010i) q^{47} +(0.771067 - 1.44251i) q^{48} +6.73501 q^{49} +(-1.26892 - 3.28959i) q^{50} +(-0.809450 - 0.335285i) q^{51} +(6.51007 + 3.10145i) q^{52} +(-1.51275 - 3.65211i) q^{53} +(0.0827918 - 3.37205i) q^{54} +(-1.43451 + 1.43451i) q^{55} +(-1.38251 + 0.456703i) q^{56} -2.62920i q^{57} +(-5.51218 + 5.24799i) q^{58} +(-3.98767 + 9.62709i) q^{59} +(1.29331 + 0.0635461i) q^{60} +(5.11727 - 12.3542i) q^{61} +(-0.528737 - 1.37071i) q^{62} +(-1.03113 + 1.03113i) q^{63} +(-6.42577 + 4.76545i) q^{64} +(-0.0160028 + 5.70866i) q^{65} +(0.266669 + 0.691322i) q^{66} +(10.1248 - 4.19384i) q^{67} +(2.87774 + 3.17515i) q^{68} +(-0.550095 - 1.32805i) q^{69} +(-0.794789 - 0.834799i) q^{70} -13.8983 q^{71} +(-3.60252 + 7.15677i) q^{72} +1.32072i q^{73} +(-11.4223 - 11.9973i) q^{74} +(-0.390141 - 0.941883i) q^{75} +(-5.49819 + 11.6247i) q^{76} +(0.252410 - 0.609372i) q^{77} +(1.90381 + 0.850302i) q^{78} -9.86871 q^{79} +(-5.58535 - 2.98554i) q^{80} +7.52305i q^{81} +(4.82029 + 2.13671i) q^{82} +(2.34587 + 5.66344i) q^{83} +(-0.396387 + 0.141826i) q^{84} +(-1.29821 + 3.13416i) q^{85} +(-0.0977765 + 3.98237i) q^{86} +(-1.55610 + 1.55610i) q^{87} +(0.266645 - 3.61426i) q^{88} +4.73380 q^{89} +(-6.34107 - 0.155688i) q^{90} +(-0.705464 - 1.71674i) q^{91} +(-0.345030 + 7.02217i) q^{92} +(-0.162565 - 0.392466i) q^{93} +(0.138925 + 0.360154i) q^{94} -10.1802 q^{95} +(-1.82361 + 1.42310i) q^{96} +(-10.7268 + 10.7268i) q^{97} +(-8.70760 - 3.85985i) q^{98} +(-1.38901 - 3.35338i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more