LMFDB - Embedded newform 252.2.n.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(31,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 1]))

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

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

chi := DirichletCharacter("252.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.n (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	252.31
Dual form			252.2.n.b.187.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41219 + 0.0755732i) q^{2} +(-1.69164 + 0.371957i) q^{3} +(1.98858 - 0.213448i) q^{4} +1.05993i q^{5} +(2.36081 - 0.653118i) q^{6} +(0.349222 - 2.62260i) q^{7} +(-2.79212 + 0.451713i) q^{8} +(2.72330 - 1.25843i) q^{9} +O(q^{10})$	\(q+(-1.41219 + 0.0755732i) q^{2} +(-1.69164 + 0.371957i) q^{3} +(1.98858 - 0.213448i) q^{4} +1.05993i q^{5} +(2.36081 - 0.653118i) q^{6} +(0.349222 - 2.62260i) q^{7} +(-2.79212 + 0.451713i) q^{8} +(2.72330 - 1.25843i) q^{9} +(-0.0801021 - 1.49682i) q^{10} +2.69962i q^{11} +(-3.28456 + 1.10074i) q^{12} +(-2.33504 - 1.34814i) q^{13} +(-0.294971 + 3.73001i) q^{14} +(-0.394248 - 1.79302i) q^{15} +(3.90888 - 0.848915i) q^{16} +(7.01250 + 4.04867i) q^{17} +(-3.75072 + 1.98296i) q^{18} +(3.48409 + 6.03463i) q^{19} +(0.226239 + 2.10775i) q^{20} +(0.384736 + 4.56640i) q^{21} +(-0.204019 - 3.81238i) q^{22} -3.26452i q^{23} +(4.55525 - 1.80269i) q^{24} +3.87655 q^{25} +(3.39941 + 1.72736i) q^{26} +(-4.13875 + 3.14177i) q^{27} +(0.134667 - 5.28979i) q^{28} +(0.511543 + 0.886019i) q^{29} +(0.692258 + 2.50229i) q^{30} +(4.25476 + 7.36946i) q^{31} +(-5.45594 + 1.49424i) q^{32} +(-1.00414 - 4.56678i) q^{33} +(-10.2090 - 5.18755i) q^{34} +(2.77977 + 0.370150i) q^{35} +(5.14687 - 3.08378i) q^{36} +(0.487561 + 0.844481i) q^{37} +(-5.37627 - 8.25875i) q^{38} +(4.45150 + 1.41203i) q^{39} +(-0.478783 - 2.95945i) q^{40} +(-3.77646 - 2.18034i) q^{41} +(-0.888419 - 6.41956i) q^{42} +(5.77718 - 3.33546i) q^{43} +(0.576227 + 5.36840i) q^{44} +(1.33385 + 2.88650i) q^{45} +(0.246710 + 4.61014i) q^{46} +(-2.37636 + 4.11598i) q^{47} +(-6.29666 + 2.88999i) q^{48} +(-6.75609 - 1.83174i) q^{49} +(-5.47444 + 0.292963i) q^{50} +(-13.3686 - 4.24055i) q^{51} +(-4.93117 - 2.18247i) q^{52} +(1.93958 - 3.35945i) q^{53} +(5.60729 - 4.74956i) q^{54} -2.86140 q^{55} +(0.209590 + 7.48038i) q^{56} +(-8.13846 - 8.91249i) q^{57} +(-0.789357 - 1.21257i) q^{58} +(-1.19560 - 2.07084i) q^{59} +(-1.16671 - 3.48140i) q^{60} +(-3.20716 - 1.85166i) q^{61} +(-6.56548 - 10.0856i) q^{62} +(-2.34934 - 7.58160i) q^{63} +(7.59191 - 2.52247i) q^{64} +(1.42893 - 2.47498i) q^{65} +(1.76317 + 6.37329i) q^{66} +(1.69381 - 0.977924i) q^{67} +(14.8091 + 6.55429i) q^{68} +(1.21426 + 5.52240i) q^{69} +(-3.95354 - 0.312648i) q^{70} -12.7952i q^{71} +(-7.03533 + 4.74385i) q^{72} +(2.43771 + 1.40741i) q^{73} +(-0.752350 - 1.15572i) q^{74} +(-6.55773 + 1.44191i) q^{75} +(8.21647 + 11.2567i) q^{76} +(7.08003 + 0.942767i) q^{77} +(-6.39309 - 1.65764i) q^{78} +(6.57420 + 3.79562i) q^{79} +(0.899789 + 4.14313i) q^{80} +(5.83268 - 6.85418i) q^{81} +(5.49786 + 2.79366i) q^{82} +(1.06909 + 1.85171i) q^{83} +(1.73977 + 8.99851i) q^{84} +(-4.29130 + 7.43275i) q^{85} +(-7.90642 + 5.14691i) q^{86} +(-1.19491 - 1.30855i) q^{87} +(-1.21945 - 7.53767i) q^{88} +(3.80947 - 2.19940i) q^{89} +(-2.10180 - 3.97549i) q^{90} +(-4.35108 + 5.65309i) q^{91} +(-0.696805 - 6.49176i) q^{92} +(-9.93865 - 10.8839i) q^{93} +(3.04482 - 5.99214i) q^{94} +(-6.39627 + 3.69289i) q^{95} +(8.67369 - 4.55709i) q^{96} +(-4.91146 + 2.83563i) q^{97} +(9.67933 + 2.07620i) q^{98} +(3.39729 + 7.35186i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9}+O(q^{10}) $ 84 * q - q^2 + q^4 - 16 * q^8 - 14 * q^9	$ 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9} - 18 q^{10} + 9 q^{12} - 18 q^{13} - 25 q^{14} - 7 q^{16} + 6 q^{17} - 13 q^{18} + 24 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{24} - 32 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 14 q^{30} + 9 q^{32} - 6 q^{33} + 24 q^{34} - 38 q^{36} + 2 q^{37} - 6 q^{41} + 7 q^{42} - 13 q^{44} - 18 q^{45} + 10 q^{46} - 9 q^{48} + 2 q^{49} - 17 q^{50} - 2 q^{53} - 42 q^{54} - 32 q^{56} + 6 q^{57} + 26 q^{58} + 8 q^{60} - 24 q^{61} - 8 q^{64} + 50 q^{65} + 27 q^{66} + 18 q^{69} - 4 q^{70} - 7 q^{72} + 30 q^{73} + 46 q^{74} + 46 q^{77} + 15 q^{78} + 3 q^{80} - 26 q^{81} - 18 q^{82} + 29 q^{84} - 50 q^{85} + 18 q^{86} - 2 q^{88} - 102 q^{89} + 39 q^{90} + 28 q^{92} - 24 q^{93} + 3 q^{94} - 30 q^{96} - 6 q^{97} + 21 q^{98}+O(q^{100}) $ 84 * q - q^2 + q^4 - 16 * q^8 - 14 * q^9 - 18 * q^10 + 9 * q^12 - 18 * q^13 - 25 * q^14 - 7 * q^16 + 6 * q^17 - 13 * q^18 + 24 * q^20 + 4 * q^21 + 6 * q^22 + 6 * q^24 - 32 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 14 * q^30 + 9 * q^32 - 6 * q^33 + 24 * q^34 - 38 * q^36 + 2 * q^37 - 6 * q^41 + 7 * q^42 - 13 * q^44 - 18 * q^45 + 10 * q^46 - 9 * q^48 + 2 * q^49 - 17 * q^50 - 2 * q^53 - 42 * q^54 - 32 * q^56 + 6 * q^57 + 26 * q^58 + 8 * q^60 - 24 * q^61 - 8 * q^64 + 50 * q^65 + 27 * q^66 + 18 * q^69 - 4 * q^70 - 7 * q^72 + 30 * q^73 + 46 * q^74 + 46 * q^77 + 15 * q^78 + 3 * q^80 - 26 * q^81 - 18 * q^82 + 29 * q^84 - 50 * q^85 + 18 * q^86 - 2 * q^88 - 102 * q^89 + 39 * q^90 + 28 * q^92 - 24 * q^93 + 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41219	+	0.0755732i	−0.998571	+	0.0534383i
$2$	−1.41219	+	0.0755732i	−0.998571	+	0.0534383i
$3$	−1.69164	+	0.371957i	−0.976669	+	0.214749i
$3$	−1.69164	+	0.371957i	−0.976669	+	0.214749i
$4$	1.98858	−	0.213448i	0.994289	−	0.106724i
$5$			1.05993i			0.474014i	0.971508	+	0.237007i	$0.0761665\pi$
$5$			1.05993i			0.474014i	−0.971508	+	0.237007i	$0.923834\pi$
$6$	2.36081	−	0.653118i	0.963798	−	0.266634i
$7$	0.349222	−	2.62260i	0.131994	−	0.991251i
$7$	0.349222	−	2.62260i	0.131994	−	0.991251i
$8$	−2.79212	+	0.451713i	−0.987165	+	0.159704i
$9$	2.72330	−	1.25843i	0.907765	−	0.419478i
$10$	−0.0801021	−	1.49682i	−0.0253305	−	0.473337i
$11$			2.69962i			0.813966i	0.913436	+	0.406983i	$0.133419\pi$
$11$			2.69962i			0.813966i	−0.913436	+	0.406983i	$0.866581\pi$
$12$	−3.28456	+	1.10074i	−0.948172	+	0.317757i
$13$	−2.33504	−	1.34814i	−0.647624	−	0.373906i	0.139921	−	0.990163i	$-0.455315\pi$
$13$	−2.33504	−	1.34814i	−0.647624	−	0.373906i	−0.787545	+	0.616257i	$0.788648\pi$
$14$	−0.294971	+	3.73001i	−0.0788343	+	0.996888i
$15$	−0.394248	−	1.79302i	−0.101794	−	0.462955i
$16$	3.90888	−	0.848915i	0.977220	−	0.212229i
$17$	7.01250	+	4.04867i	1.70078	+	0.981947i	0.944970	+	0.327158i	$0.106091\pi$
$17$	7.01250	+	4.04867i	1.70078	+	0.981947i	0.755812	+	0.654789i	$0.227243\pi$
$18$	−3.75072	+	1.98296i	−0.884052	+	0.467388i
$19$	3.48409	+	6.03463i	0.799306	+	1.38444i	0.920069	+	0.391757i	$0.128133\pi$
$19$	3.48409	+	6.03463i	0.799306	+	1.38444i	−0.120763	+	0.992681i	$0.538534\pi$
$20$	0.226239	+	2.10775i	0.0505886	+	0.471307i
$21$	0.384736	+	4.56640i	0.0839564	+	0.996469i
$22$	−0.204019	−	3.81238i	−0.0434969	−	0.812802i
$23$		−	3.26452i		−	0.680700i	−0.940299	−	0.340350i	$-0.889454\pi$
$23$		−	3.26452i		−	0.680700i	0.940299	−	0.340350i	$-0.110546\pi$
$24$	4.55525	−	1.80269i	0.929837	−	0.367972i
$25$	3.87655			0.775311
$26$	3.39941	+	1.72736i	0.666680	+	0.338764i
$27$	−4.13875	+	3.14177i	−0.796504	+	0.604634i
$28$	0.134667	−	5.28979i	0.0254497	−	0.999676i
$29$	0.511543	+	0.886019i	0.0949912	+	0.164530i	0.909605	−	0.415474i	$-0.136384\pi$
$29$	0.511543	+	0.886019i	0.0949912	+	0.164530i	−0.814614	+	0.580004i	$0.803051\pi$
$30$	0.692258	+	2.50229i	0.126388	+	0.456854i
$31$	4.25476	+	7.36946i	0.764178	+	1.32359i	0.940680	+	0.339295i	$0.110188\pi$
$31$	4.25476	+	7.36946i	0.764178	+	1.32359i	−0.176502	+	0.984300i	$0.556478\pi$
$32$	−5.45594	+	1.49424i	−0.964483	+	0.264146i
$33$	−1.00414	−	4.56678i	−0.174799	−	0.794975i
$34$	−10.2090	−	5.18755i	−1.75082	−	0.889657i
$35$	2.77977	+	0.370150i	0.469867	+	0.0625669i
$36$	5.14687	−	3.08378i	0.857812	−	0.513963i
$37$	0.487561	+	0.844481i	0.0801546	+	0.138832i	0.903316	−	0.428975i	$-0.141125\pi$
$37$	0.487561	+	0.844481i	0.0801546	+	0.138832i	−0.823162	+	0.567807i	$0.807792\pi$
$38$	−5.37627	−	8.25875i	−0.872146	−	1.33975i
$39$	4.45150	+	1.41203i	0.712811	+	0.226106i
$40$	−0.478783	−	2.95945i	−0.0757022	−	0.467930i
$41$	−3.77646	−	2.18034i	−0.589784	−	0.340512i	0.175228	−	0.984528i	$-0.443934\pi$
$41$	−3.77646	−	2.18034i	−0.589784	−	0.340512i	−0.765012	+	0.644016i	$0.777267\pi$
$42$	−0.888419	−	6.41956i	−0.137086	−	0.990559i
$43$	5.77718	−	3.33546i	0.881012	−	0.508652i	0.0100199	−	0.999950i	$-0.496811\pi$
$43$	5.77718	−	3.33546i	0.881012	−	0.508652i	0.870992	+	0.491297i	$0.163477\pi$
$44$	0.576227	+	5.36840i	0.0868696	+	0.809317i
$45$	1.33385	+	2.88650i	0.198839	+	0.430294i
$46$	0.246710	+	4.61014i	0.0363754	+	0.679727i
$47$	−2.37636	+	4.11598i	−0.346628	+	0.600377i	−0.985648	−	0.168813i	$-0.946007\pi$
$47$	−2.37636	+	4.11598i	−0.346628	+	0.600377i	0.639020	+	0.769190i	$0.279340\pi$
$48$	−6.29666	+	2.88999i	−0.908845	+	0.417135i
$49$	−6.75609	−	1.83174i	−0.965155	−	0.261678i
$50$	−5.47444	+	0.292963i	−0.774203	+	0.0414313i
$51$	−13.3686	−	4.24055i	−1.87197	−	0.593795i
$52$	−4.93117	−	2.18247i	−0.683830	−	0.302654i
$53$	1.93958	−	3.35945i	0.266422	−	0.461456i	−0.701513	−	0.712656i	$-0.747492\pi$
$53$	1.93958	−	3.35945i	0.266422	−	0.461456i	0.967935	+	0.251200i	$0.0808252\pi$
$54$	5.60729	−	4.74956i	0.763055	−	0.646334i
$55$	−2.86140			−0.385831
$56$	0.209590	+	7.48038i	0.0280077	+	0.999608i
$57$	−8.13846	−	8.91249i	−1.07796	−	1.18049i
$58$	−0.789357	−	1.21257i	−0.103648	−	0.159218i
$59$	−1.19560	−	2.07084i	−0.155654	−	0.269601i	0.777643	−	0.628706i	$-0.216415\pi$
$59$	−1.19560	−	2.07084i	−0.155654	−	0.269601i	−0.933297	+	0.359105i	$0.883082\pi$
$60$	−1.16671	−	3.48140i	−0.150621	−	0.449447i
$61$	−3.20716	−	1.85166i	−0.410635	−	0.237080i	0.280428	−	0.959875i	$-0.409524\pi$
$61$	−3.20716	−	1.85166i	−0.410635	−	0.237080i	−0.691063	+	0.722795i	$0.742857\pi$
$62$	−6.56548	−	10.0856i	−0.833817	−	1.28087i
$63$	−2.34934	−	7.58160i	−0.295989	−	0.955191i
$64$	7.59191	−	2.52247i	0.948989	−	0.315309i
$65$	1.42893	−	2.47498i	0.177237	−	0.306983i
$66$	1.76317	+	6.37329i	0.217031	+	0.784498i
$67$	1.69381	−	0.977924i	0.206932	−	0.119472i	−0.392953	−	0.919559i	$-0.628546\pi$
$67$	1.69381	−	0.977924i	0.206932	−	0.119472i	0.599885	+	0.800086i	$0.295213\pi$
$68$	14.8091	+	6.55429i	1.79586	+	0.794824i
$69$	1.21426	+	5.52240i	0.146180	+	0.664819i
$70$	−3.95354	−	0.312648i	−0.472539	−	0.0373686i
$71$		−	12.7952i		−	1.51851i	−0.650793	−	0.759255i	$-0.725564\pi$
$71$		−	12.7952i		−	1.51851i	0.650793	−	0.759255i	$-0.274436\pi$
$72$	−7.03533	+	4.74385i	−0.829122	+	0.559068i
$73$	2.43771	+	1.40741i	0.285312	+	0.164725i	0.635826	−	0.771833i	$-0.280660\pi$
$73$	2.43771	+	1.40741i	0.285312	+	0.164725i	−0.350514	+	0.936558i	$0.613993\pi$
$74$	−0.752350	−	1.15572i	−0.0874590	−	0.134350i
$75$	−6.55773	+	1.44191i	−0.757222	+	0.166498i
$76$	8.21647	+	11.2567i	0.942493	+	1.29123i
$77$	7.08003	+	0.942767i	0.806844	+	0.107438i
$78$	−6.39309	−	1.65764i	−0.723875	−	0.187691i
$79$	6.57420	+	3.79562i	0.739655	+	0.427040i	0.821944	−	0.569568i	$-0.192890\pi$
$79$	6.57420	+	3.79562i	0.739655	+	0.427040i	−0.0822886	+	0.996609i	$0.526223\pi$
$80$	0.899789	+	4.14313i	0.100599	+	0.463216i
$81$	5.83268	−	6.85418i	0.648076	−	0.761576i
$82$	5.49786	+	2.79366i	0.607137	+	0.308508i
$83$	1.06909	+	1.85171i	0.117348	+	0.203252i	0.918716	−	0.394919i	$-0.129228\pi$
$83$	1.06909	+	1.85171i	0.117348	+	0.203252i	−0.801368	+	0.598171i	$0.795894\pi$
$84$	1.73977	+	8.99851i	0.189824	+	0.981818i
$85$	−4.29130	+	7.43275i	−0.465457	+	0.806195i
$86$	−7.90642	+	5.14691i	−0.852571	+	0.555005i
$87$	−1.19491	−	1.30855i	−0.128108	−	0.140292i
$88$	−1.21945	−	7.53767i	−0.129994	−	0.803518i
$89$	3.80947	−	2.19940i	0.403803	−	0.233136i	−0.284321	−	0.958729i	$-0.591768\pi$
$89$	3.80947	−	2.19940i	0.403803	−	0.233136i	0.688124	+	0.725593i	$0.258435\pi$
$90$	−2.10180	−	3.97549i	−0.221549	−	0.419053i
$91$	−4.35108	+	5.65309i	−0.456117	+	0.592605i
$92$	−0.696805	−	6.49176i	−0.0726469	−	0.676812i
$93$	−9.93865	−	10.8839i	−1.03059	−	1.12861i
$94$	3.04482	−	5.99214i	0.314049	−	0.618042i
$95$	−6.39627	+	3.69289i	−0.656243	+	0.378882i
$96$	8.67369	−	4.55709i	0.885255	−	0.465106i
$97$	−4.91146	+	2.83563i	−0.498683	+	0.287915i	−0.728170	−	0.685397i	$-0.759629\pi$
$97$	−4.91146	+	2.83563i	−0.498683	+	0.287915i	0.229486	+	0.973312i	$0.426295\pi$
$98$	9.67933	+	2.07620i	0.977760	+	0.209727i
$99$	3.39729	+	7.35186i	0.341441	+	0.738890i
$100$	7.70883	−	0.827442i	0.770883	−	0.0827442i
$101$		−	8.43606i		−	0.839420i	−0.907658	−	0.419710i	$-0.862132\pi$
$101$		−	8.43606i		−	0.839420i	0.907658	−	0.419710i	$-0.137868\pi$
$102$	19.1995	+	4.97816i	1.90103	+	0.492912i
$103$	−7.86520			−0.774981			−0.387490	−	0.921874i	$-0.626658\pi$
$103$	−7.86520			−0.774981			−0.387490	+	0.921874i	$0.626658\pi$
$104$	7.12870	+	2.70940i	0.699026	+	0.265678i
$105$	−4.84005	+	0.407793i	−0.472341	+	0.0397965i
$106$	−2.48518	+	4.89078i	−0.241382	+	0.475034i
$107$	4.00395	−	2.31168i	0.387076	−	0.223479i	−0.293816	−	0.955862i	$-0.594925\pi$
$107$	4.00395	−	2.31168i	0.387076	−	0.223479i	0.680893	+	0.732383i	$0.261592\pi$
$108$	−7.55963	+	7.13106i	−0.727426	+	0.686186i
$109$	−8.80372	+	15.2485i	−0.843244	+	1.46054i	0.0438939	+	0.999036i	$0.486024\pi$
$109$	−8.80372	+	15.2485i	−0.843244	+	1.46054i	−0.887138	+	0.461505i	$0.847310\pi$
$110$	4.04085	−	0.216245i	0.385280	−	0.0206182i
$111$	−1.13889	−	1.24721i	−0.108099	−	0.118380i
$112$	−0.861298	−	10.5479i	−0.0813850	−	0.996683i
$113$	−8.00328	+	13.8621i	−0.752886	+	1.30404i	0.193533	+	0.981094i	$0.438005\pi$
$113$	−8.00328	+	13.8621i	−0.752886	+	1.30404i	−0.946419	+	0.322942i	$0.895328\pi$
$114$	12.1666	+	11.9711i	1.13951	+	1.12120i
$115$	3.46016			0.322661
$116$	1.20636	+	1.65273i	0.112008	+	0.153452i
$117$	−8.05555	−	0.732878i	−0.744736	−	0.0677546i
$118$	1.84492	+	2.83408i	0.169839	+	0.260898i
$119$	13.0670	−	16.9771i	1.19785	−	1.55629i
$120$	1.91072	+	4.82824i	0.174424	+	0.440756i
$121$	3.71206			0.337460
$122$	4.66907	+	2.37252i	0.422717	+	0.214798i
$123$	7.19940	+	2.28367i	0.649148	+	0.205912i
$124$	10.0339	+	13.7466i	0.901073	+	1.23448i
$125$			9.40851i			0.841522i
$126$	3.89068	+	10.5291i	0.346610	+	0.938009i
$127$		−	14.4863i		−	1.28545i	−0.766098	−	0.642724i	$-0.777804\pi$
$127$		−	14.4863i		−	1.28545i	0.766098	−	0.642724i	$-0.222196\pi$
$128$	−10.5306	+	4.13597i	−0.930783	+	0.365571i
$129$	−8.53227	+	7.79126i	−0.751224	+	0.685982i
$130$	−1.83088	+	3.60313i	−0.160579	+	0.316016i
$131$	10.8598			0.948824			0.474412	−	0.880303i	$-0.342661\pi$
$131$	10.8598			0.948824			0.474412	+	0.880303i	$0.342661\pi$
$132$	−2.97158	−	8.86707i	−0.258643	−	0.771779i
$133$	17.0432	−	7.02997i	1.47783	−	0.609575i
$134$	−2.31809	+	1.50902i	−0.200252	+	0.130360i
$135$	−3.33005	−	4.38678i	−0.286605	−	0.377554i
$136$	−21.4086	−	8.13675i	−1.83577	−	0.697721i
$137$	−9.73636			−0.831833			−0.415917	−	0.909403i	$-0.636539\pi$
$137$	−9.73636			−0.831833			−0.415917	+	0.909403i	$0.636539\pi$
$138$	−2.13212	−	7.70693i	−0.181498	−	0.656057i
$139$	2.46836	−	4.27533i	0.209364	−	0.362628i	−0.742151	−	0.670233i	$-0.766194\pi$
$139$	2.46836	−	4.27533i	0.209364	−	0.362628i	0.951514	+	0.307605i	$0.0995274\pi$
$140$	5.60679	+	0.142737i	0.473861	+	0.0120635i
$141$	2.48898	−	7.84665i	0.209610	−	0.660807i
$142$	0.966973	+	18.0693i	0.0811466	+	1.51634i
$143$	3.63946	−	6.30372i	0.304347	−	0.527144i
$144$	9.57673	−	7.23092i	0.798061	−	0.602576i
$145$	−0.939116	+	0.542199i	−0.0779894	+	0.0450272i
$146$	−3.54888	−	1.80331i	−0.293707	−	0.149243i
$147$	12.1102	+	0.585677i	0.998833	+	0.0483058i
$148$	1.14981	+	1.57525i	0.0945134	+	0.129484i
$149$	9.06574			0.742694			0.371347	−	0.928494i	$-0.378896\pi$
$149$	9.06574			0.742694			0.371347	+	0.928494i	$0.378896\pi$
$150$	9.15182	−	2.53184i	0.747243	−	0.206724i
$151$			2.10052i			0.170938i	0.996341	+	0.0854689i	$0.0272388\pi$
$151$			2.10052i			0.170938i	−0.996341	+	0.0854689i	$0.972761\pi$
$152$	−12.4539	−	15.2756i	−1.01015	−	1.23902i
$153$	24.1921	+	2.20095i	1.95582	+	0.177936i
$154$	−10.0696	−	0.796309i	−0.811432	−	0.0641684i
$155$	−7.81110	+	4.50974i	−0.627403	+	0.362231i
$156$	9.15355	+	1.85777i	0.732871	+	0.148740i
$157$	−15.9400	+	9.20296i	−1.27215	+	0.734476i	−0.975392	−	0.220477i	$-0.929239\pi$
$157$	−15.9400	+	9.20296i	−1.27215	+	0.734476i	−0.296758	+	0.954953i	$0.595905\pi$
$158$	−9.57089	−	4.86331i	−0.761419	−	0.386904i
$159$	−2.03150	+	6.40443i	−0.161109	+	0.507904i
$160$	−1.58378	−	5.78290i	−0.125209	−	0.457178i
$161$	−8.56154	−	1.14004i	−0.674744	−	0.0898481i
$162$	−7.71888	+	10.1202i	−0.606453	+	0.795120i
$163$	−13.8740	+	8.01017i	−1.08670	+	0.627405i	−0.932695	−	0.360665i	$-0.882550\pi$
$163$	−13.8740	+	8.01017i	−1.08670	+	0.627405i	−0.154002	+	0.988070i	$0.549216\pi$
$164$	−7.97517	−	3.52970i	−0.622756	−	0.275623i
$165$	4.84046	−	1.06432i	0.376829	−	0.0828570i
$166$	−1.64970	−	2.53418i	−0.128041	−	0.196691i
$167$	0.0138224	−	0.0239411i	0.00106961	−	0.00185262i	−0.865490	−	0.500926i	$-0.832993\pi$
$167$	0.0138224	−	0.0239411i	0.00106961	−	0.00185262i	0.866560	+	0.499073i	$0.166326\pi$
$168$	−3.13693	−	12.5762i	−0.242019	−	0.970271i
$169$	−2.86505	−	4.96241i	−0.220389	−	0.381724i
$170$	5.49842	−	10.8208i	0.421710	−	0.829916i
$171$	17.0824	+	12.0496i	1.30632	+	0.921454i
$172$	10.7764	−	7.86594i	0.821695	−	0.599772i
$173$	−4.11732	−	2.37714i	−0.313034	−	0.180730i	0.335249	−	0.942129i	$-0.391179\pi$
$173$	−4.11732	−	2.37714i	−0.313034	−	0.180730i	−0.648283	+	0.761399i	$0.724513\pi$
$174$	1.78633	+	1.75763i	0.135422	+	0.133245i
$175$	1.35378	−	10.1667i	0.102336	−	0.768527i
$176$	2.29175	+	10.5525i	0.172747	+	0.795423i
$177$	2.79279	+	3.05841i	0.209919	+	0.229884i
$178$	−5.21349	+	3.39387i	−0.390768	+	0.254381i
$179$	−3.17006	−	1.83024i	−0.236941	−	0.136798i	0.376829	−	0.926283i	$-0.377015\pi$
$179$	−3.17006	−	1.83024i	−0.236941	−	0.136798i	−0.613770	+	0.789485i	$0.710348\pi$
$180$	3.26858	+	5.45532i	0.243626	+	0.406615i
$181$		−	12.2768i		−	0.912526i	−0.889845	−	0.456263i	$-0.849188\pi$
$181$		−	12.2768i		−	0.912526i	0.889845	−	0.456263i	$-0.150812\pi$
$182$	5.71734	−	8.31208i	0.423797	−	0.616132i
$183$	6.11410	+	1.93941i	0.451967	+	0.143365i
$184$	1.47463	+	9.11495i	0.108711	+	0.671963i
$185$	−0.895089	+	0.516780i	−0.0658082	+	0.0379944i
$186$	14.8578	+	14.6191i	1.08943	+	1.07192i
$187$	−10.9299	+	18.9311i	−0.799271	+	1.38438i
$188$	−3.84703	+	8.69216i	−0.280573	+	0.633941i
$189$	6.79426	+	11.9515i	0.494210	+	0.869343i
$190$	8.75368	−	5.69846i	0.635059	−	0.413409i
$191$	−15.0060	−	8.66370i	−1.08579	−	0.626883i	−0.153340	−	0.988173i	$-0.549003\pi$
$191$	−15.0060	−	8.66370i	−1.08579	−	0.626883i	−0.932453	+	0.361290i	$0.882336\pi$
$192$	−11.9045	+	7.09098i	−0.859136	+	0.511748i
$193$	1.07157	+	1.85602i	0.0771334	+	0.133599i	0.902012	−	0.431711i	$-0.142090\pi$
$193$	1.07157	+	1.85602i	0.0771334	+	0.133599i	−0.824879	+	0.565310i	$0.808757\pi$
$194$	6.72163	−	4.37564i	0.482585	−	0.314152i
$195$	−1.49665	+	4.71827i	−0.107177	+	0.337882i
$196$	−13.8260	−	2.20049i	−0.987570	−	0.157178i
$197$	15.3799			1.09577			0.547886	−	0.836553i	$-0.315433\pi$
$197$	15.3799			1.09577			0.547886	+	0.836553i	$0.315433\pi$
$198$	−5.35324	−	10.1255i	−0.380438	−	0.719588i
$199$	−2.79870	+	4.84750i	−0.198395	+	0.343630i	−0.948008	−	0.318246i	$-0.896906\pi$
$199$	−2.79870	+	4.84750i	−0.198395	+	0.343630i	0.749613	+	0.661876i	$0.230239\pi$
$200$	−10.8238	+	1.75109i	−0.765359	+	0.123821i
$201$	−2.50158	+	2.28432i	−0.176448	+	0.161124i
$202$	0.637540	+	11.9133i	0.0448572	+	0.838220i
$203$	2.50232	−	1.03216i	0.175628	−	0.0724432i
$204$	−27.4896	−	5.57916i	−1.92465	−	0.390620i
$205$	2.31100	−	4.00277i	0.161407	−	0.279566i
$206$	11.1072	−	0.594398i	0.773874	−	0.0414137i
$207$	−4.10819	−	8.89026i	−0.285539	−	0.617916i
$208$	−10.2719	−	3.28746i	−0.712225	−	0.227944i
$209$	−16.2912	+	9.40572i	−1.12689	+	0.650607i
$210$	6.80427	−	0.941660i	0.469539	−	0.0649807i
$211$	−5.47775	−	3.16258i	−0.377104	−	0.217721i	0.299454	−	0.954111i	$-0.403196\pi$
$211$	−5.47775	−	3.16258i	−0.377104	−	0.217721i	−0.676557	+	0.736390i	$0.736529\pi$
$212$	3.13994	−	7.09453i	0.215652	−	0.487255i
$213$	4.75926	+	21.6449i	0.326099	+	1.48308i
$214$	−5.47965	+	3.56713i	−0.374581	+	0.243844i
$215$	3.53534	+	6.12339i	0.241108	+	0.417612i
$216$	10.1367	−	10.6417i	0.689718	−	0.724078i
$217$	20.8130	−	8.58497i	1.41288	−	0.582786i
$218$	11.2802	−	22.1991i	0.763990	−	1.50352i
$219$	−4.64722	−	1.47411i	−0.314030	−	0.0996113i
$220$	−5.69012	+	0.610760i	−0.383628	+	0.0411774i
$221$	−10.9163	−	18.9076i	−0.734312	−	1.27186i
$222$	1.70259	+	1.67523i	0.114270	+	0.112434i
$223$	6.11784	+	10.5964i	0.409681	+	0.709588i	0.994854	−	0.101320i	$-0.0323067\pi$
$223$	6.11784	+	10.5964i	0.409681	+	0.709588i	−0.585173	+	0.810909i	$0.698973\pi$
$224$	2.01346	+	14.8306i	0.134530	+	0.990910i
$225$	10.5570	−	4.87839i	0.703800	−	0.325226i
$226$	10.2546	−	20.1808i	0.682124	−	1.34241i
$227$	9.05993			0.601328			0.300664	−	0.953730i	$-0.402792\pi$
$227$	9.05993			0.601328			0.300664	+	0.953730i	$0.402792\pi$
$228$	−18.0863	−	15.9860i	−1.19779	−	1.05870i
$229$		−	13.8428i		−	0.914756i	−0.889272	−	0.457378i	$-0.848789\pi$
$229$		−	13.8428i		−	0.914756i	0.889272	−	0.457378i	$-0.151211\pi$
$230$	−4.88641	+	0.261495i	−0.322200	+	0.0172425i
$231$	−12.3275	+	1.03864i	−0.811092	+	0.0683376i
$232$	−1.82852	−	2.24280i	−0.120048	−	0.147247i
$233$	−9.76646	−	16.9160i	−0.639822	−	1.10820i	−0.985472	−	0.169841i	$-0.945675\pi$
$233$	−9.76646	−	16.9160i	−0.639822	−	1.10820i	0.345649	−	0.938364i	$-0.387659\pi$
$234$	11.4314	+	0.426182i	0.747293	+	0.0278604i
$235$	−4.36264	−	2.51877i	−0.284587	−	0.164306i
$236$	−2.81957	−	3.86284i	−0.183538	−	0.251449i
$237$	−12.5330	−	3.97550i	−0.814105	−	0.258236i
$238$	−17.1701	+	24.9625i	−1.11297	+	1.61808i
$239$	7.53604	+	4.35094i	0.487466	+	0.281439i	0.723523	−	0.690301i	$-0.242522\pi$
$239$	7.53604	+	4.35094i	0.487466	+	0.281439i	−0.236057	+	0.971739i	$0.575855\pi$
$240$	−3.06319	−	6.67401i	−0.197728	−	0.430805i
$241$		−	14.6933i		−	0.946479i	−0.880934	−	0.473240i	$-0.843084\pi$
$241$		−	14.6933i		−	0.946479i	0.880934	−	0.473240i	$-0.156916\pi$
$242$	−5.24215	+	0.280532i	−0.336978	+	0.0180333i
$243$	−7.31734	+	13.7643i	−0.469408	+	0.882981i
$244$	−6.77292	−	2.99760i	−0.433592	−	0.191902i
$245$	1.94152	−	7.16097i	0.124039	−	0.457497i
$246$	−10.3395	−	2.68090i	−0.659224	−	0.170928i
$247$		−	18.7881i		−	1.19546i
$248$	−15.2087	−	18.6545i	−0.965754	−	1.18456i
$249$	−2.49727	−	2.73478i	−0.158258	−	0.173310i
$250$	−0.711031	−	13.2866i	−0.0449695	−	0.840320i
$251$	−24.9521			−1.57496			−0.787481	−	0.616339i	$-0.788615\pi$
$251$	−24.9521			−1.57496			−0.787481	+	0.616339i	$0.788615\pi$
$252$	−6.29012	−	14.5751i	−0.396240	−	0.918147i
$253$	8.81296			0.554066
$254$	1.09477	+	20.4574i	0.0686922	+	1.28361i
$255$	4.49467	−	14.1697i	0.281467	−	0.887342i
$256$	14.5587	−	6.63661i	0.909918	−	0.414788i
$257$			8.35180i			0.520971i	0.965478	+	0.260485i	$0.0838826\pi$
$257$			8.35180i			0.520971i	−0.965478	+	0.260485i	$0.916117\pi$
$258$	11.4604	−	11.6476i	0.713493	−	0.725146i
$259$	2.38500	−	0.983768i	0.148197	−	0.0611283i
$260$	2.31326	−	5.22668i	0.143462	−	0.324145i
$261$	2.50808	+	1.76915i	0.155246	+	0.109508i
$262$	−15.3361	+	0.820709i	−0.947468	+	0.0507035i
$263$			13.6382i			0.840970i	0.907299	+	0.420485i	$0.138140\pi$
$263$			13.6382i			0.840970i	−0.907299	+	0.420485i	$0.861860\pi$
$264$	4.86656	+	12.2974i	0.299516	+	0.756855i
$265$	3.56078	+	2.05582i	0.218737	+	0.126288i
$266$	−23.5369	+	11.2157i	−1.44314	+	0.687677i
$267$	−5.62617	+	5.13755i	−0.344316	+	0.314413i
$268$	3.15954	−	2.30622i	0.193000	−	0.140875i
$269$	1.96107	+	1.13222i	0.119568	+	0.0690329i	0.558591	−	0.829443i	$-0.311342\pi$
$269$	1.96107	+	1.13222i	0.119568	+	0.0690329i	−0.439023	+	0.898476i	$0.644675\pi$
$270$	5.03419	+	5.94332i	0.306371	+	0.361699i
$271$	−9.35385	−	16.2013i	−0.568206	−	0.984162i	−0.996743	−	0.0806376i	$-0.974304\pi$
$271$	−9.35385	−	16.2013i	−0.568206	−	0.984162i	0.428538	−	0.903524i	$-0.359029\pi$
$272$	30.8480	+	9.87275i	1.87043	+	0.598623i
$273$	5.25775	−	11.1814i	0.318214	−	0.676730i
$274$	13.7496	−	0.735808i	0.830645	−	0.0444518i
$275$			10.4652i			0.631076i
$276$	3.59340	+	10.7225i	0.216297	+	0.645421i
$277$	−10.1500			−0.609854			−0.304927	−	0.952376i	$-0.598632\pi$
$277$	−10.1500			−0.609854			−0.304927	+	0.952376i	$0.598632\pi$
$278$	−3.16270	+	6.22413i	−0.189686	+	0.373298i
$279$	20.8610	+	14.7149i	1.24891	+	0.880957i
$280$	−7.92866	+	0.222151i	−0.473828	+	0.0132760i
$281$	16.5394	+	28.6470i	0.986656	+	1.70894i	0.634335	+	0.773059i	$0.281274\pi$
$281$	16.5394	+	28.6470i	0.986656	+	1.70894i	0.352321	+	0.935879i	$0.385393\pi$
$282$	−2.92192	+	11.2691i	−0.173998	+	0.671065i
$283$	−1.66921	−	2.89115i	−0.0992240	−	0.171861i	0.812140	−	0.583463i	$-0.198303\pi$
$283$	−1.66921	−	2.89115i	−0.0992240	−	0.171861i	−0.911364	+	0.411602i	$0.864969\pi$
$284$	−2.73111	−	25.4442i	−0.162061	−	1.50984i
$285$	9.44659	−	8.62618i	0.559568	−	0.510971i
$286$	−4.66322	+	9.17712i	−0.275742	+	0.542654i
$287$	−7.03699	+	9.14273i	−0.415380	+	0.539678i
$288$	−12.9777	+	10.9352i	−0.764720	+	0.644363i
$289$	24.2835	+	42.0602i	1.42844	+	2.47413i
$290$	1.28524	−	0.836662i	0.0754717	−	0.0491305i
$291$	7.25370	−	6.62373i	0.425219	−	0.388290i
$292$	5.14798	+	2.27842i	0.301263	+	0.133335i
$293$	−2.78361	−	1.60712i	−0.162620	−	0.0938888i	0.416481	−	0.909144i	$-0.363263\pi$
$293$	−2.78361	−	1.60712i	−0.162620	−	0.0938888i	−0.579101	+	0.815256i	$0.696596\pi$
$294$	−17.1462	+	0.0881177i	−0.999987	+	0.00513913i
$295$	2.19495	−	1.26725i	0.127795	−	0.0737823i
$296$	−1.74279	−	2.13766i	−0.101298	−	0.124249i
$297$	−8.48158	−	11.1731i	−0.492151	−	0.648327i
$298$	−12.8026	+	0.685126i	−0.741633	+	0.0396883i
$299$	−4.40102	+	7.62280i	−0.254518	+	0.440838i
$300$	−12.7328	+	4.26708i	−0.735128	+	0.246360i
$301$	−6.73006	−	16.3161i	−0.387914	−	0.940442i
$302$	−0.158743	−	2.96634i	−0.00913462	−	0.170694i
$303$	3.13785	+	14.2708i	0.180265	+	0.819835i
$304$	18.7418	+	20.6309i	1.07492	+	1.18327i
$305$	1.96262	−	3.39936i	0.112379	−	0.194647i
$306$	−34.3303	−	1.27989i	−1.96253	−	0.0731665i
$307$	24.8754			1.41971			0.709857	−	0.704345i	$-0.248759\pi$
$307$	24.8754			1.41971			0.709857	+	0.704345i	$0.248759\pi$
$308$	14.2804	+	0.363549i	0.813702	+	0.0207151i
$309$	13.3051	−	2.92551i	0.756900	−	0.166427i
$310$	10.6900	−	6.95893i	0.607149	−	0.395241i
$311$	1.22570	+	2.12297i	0.0695028	+	0.120382i	0.898683	−	0.438600i	$-0.144525\pi$
$311$	1.22570	+	2.12297i	0.0695028	+	0.120382i	−0.829180	+	0.558982i	$0.811192\pi$
$312$	−13.0670	−	1.93176i	−0.739772	−	0.109364i
$313$	12.7905	+	7.38459i	0.722961	+	0.417402i	0.815841	−	0.578276i	$-0.196274\pi$
$313$	12.7905	+	7.38459i	0.722961	+	0.417402i	−0.0928807	+	0.995677i	$0.529608\pi$
$314$	21.8148	−	14.2010i	1.23108	−	0.801408i
$315$	8.03595	−	2.49013i	0.452774	−	0.140303i
$316$	13.8835	+	6.14463i	0.781006	+	0.345662i
$317$	13.0215	−	22.5540i	0.731362	−	1.26676i	−0.224939	−	0.974373i	$-0.572218\pi$
$317$	13.0215	−	22.5540i	0.731362	−	1.26676i	0.956301	−	0.292384i	$-0.0944484\pi$
$318$	2.38487	−	9.19782i	0.133737	−	0.515788i
$319$	−2.39191	+	1.38097i	−0.133921	+	0.0773196i
$320$	2.67364	+	8.04688i	0.149461	+	0.449834i
$321$	−5.91340	+	5.39983i	−0.330054	+	0.301389i
$322$	12.1767	+	0.962939i	0.678581	+	0.0536625i
$323$			56.4238i			3.13950i
$324$	10.1357	−	14.8750i	0.563096	−	0.826391i
$325$	−9.05192	−	5.22613i	−0.502110	−	0.289893i
$326$	18.9875	−	12.3604i	1.05162	−	0.684580i
$327$	9.22095	−	29.0696i	0.509920	−	1.60755i
$328$	11.5292	+	4.38190i	0.636595	+	0.241950i
$329$	9.96469	+	7.66964i	0.549371	+	0.422841i
$330$	−6.75523	+	1.86883i	−0.371863	+	0.102876i
$331$	−16.5799	−	9.57238i	−0.911311	−	0.526146i	−0.0304583	−	0.999536i	$-0.509697\pi$
$331$	−16.5799	−	9.57238i	−0.911311	−	0.526146i	−0.880853	+	0.473390i	$0.843030\pi$
$332$	2.52121	+	3.45408i	0.138369	+	0.189567i
$333$	2.39050	+	1.68621i	0.130998	+	0.0924036i
$334$	−0.0177106	+	0.0348541i	−0.000969081	+	0.00190713i
$335$	1.03653	+	1.79532i	0.0566316	+	0.0980888i
$336$	5.38037	+	17.5229i	0.293523	+	0.955952i
$337$	−0.842812	+	1.45979i	−0.0459109	+	0.0795200i	−0.888068	−	0.459713i	$-0.847952\pi$
$337$	−0.842812	+	1.45979i	−0.0459109	+	0.0795200i	0.842157	+	0.539233i	$0.181286\pi$
$338$	4.42103	+	6.79137i	0.240472	+	0.369402i
$339$	8.38258	−	26.4266i	0.455279	−	1.43529i
$340$	−6.94708	+	15.6966i	−0.376758	+	0.851265i
$341$	−19.8947	+	11.4862i	−1.07736	+	0.622014i
$342$	−25.0343	−	15.7253i	−1.35370	−	0.850329i
$343$	−7.16331	+	17.0788i	−0.386782	+	0.922171i
$344$	−14.6239	+	11.9226i	−0.788470	+	0.642825i
$345$	−5.85334	+	1.28703i	−0.315133	+	0.0692914i
$346$	5.99410	+	3.04582i	0.322245	+	0.163744i
$347$	−8.69149	+	5.01803i	−0.466584	+	0.269382i	−0.714808	−	0.699320i	$-0.753486\pi$
$347$	−8.69149	+	5.01803i	−0.466584	+	0.269382i	0.248225	+	0.968702i	$0.420153\pi$
$348$	−2.65548	−	2.34711i	−0.142348	−	0.125818i
$349$	14.3598	−	8.29062i	0.768661	−	0.443787i	−0.0637355	−	0.997967i	$-0.520301\pi$
$349$	14.3598	−	8.29062i	0.768661	−	0.443787i	0.832397	+	0.554180i	$0.186968\pi$
$350$	−1.14347	+	14.4596i	−0.0611211	+	0.772898i
$351$	13.8997	−	1.75655i	0.741911	−	0.0937578i
$352$	−4.03387	−	14.7289i	−0.215006	−	0.785056i
$353$		−	21.8233i		−	1.16154i	−0.814068	−	0.580770i	$-0.802752\pi$
$353$		−	21.8233i		−	1.16154i	0.814068	−	0.580770i	$-0.197248\pi$
$354$	−4.17510	−	4.10801i	−0.221904	−	0.218338i
$355$	13.5620			0.719795
$356$	7.10597	−	5.18680i	0.376616	−	0.274900i
$357$	−15.7899	+	33.5795i	−0.835688	+	1.77722i
$358$	4.61505	+	2.34507i	0.243913	+	0.123941i
$359$	16.2283	−	9.36941i	0.856497	−	0.494499i	−0.00634068	−	0.999980i	$-0.502018\pi$
$359$	16.2283	−	9.36941i	0.856497	−	0.494499i	0.862838	+	0.505481i	$0.168685\pi$
$360$	−5.02814	−	7.45694i	−0.265006	−	0.393015i
$361$	−14.7778	+	25.5959i	−0.777780	+	1.34715i
$362$	0.927795	+	17.3372i	0.0487638	+	0.911222i
$363$	−6.27947	+	1.38073i	−0.329587	+	0.0724694i
$364$	−7.44581	+	12.1703i	−0.390267	+	0.637899i
$365$	−1.49176	+	2.58380i	−0.0780820	+	0.135242i
$366$	−8.78086	−	2.27676i	−0.458983	−	0.119008i
$367$	−7.84465			−0.409488			−0.204744	−	0.978816i	$-0.565636\pi$
$367$	−7.84465			−0.409488			−0.204744	+	0.978816i	$0.565636\pi$
$368$	−2.77130	−	12.7606i	−0.144464	−	0.665194i
$369$	−13.0282	−	1.18528i	−0.678222	−	0.0617033i
$370$	1.22498	−	0.797437i	0.0636838	−	0.0414568i
$371$	−8.13317	−	6.25995i	−0.422253	−	0.325000i
$372$	−22.0869	−	19.5221i	−1.14515	−	1.01217i
$373$	11.2419			0.582084			0.291042	−	0.956710i	$-0.405998\pi$
$373$	11.2419			0.582084			0.291042	+	0.956710i	$0.405998\pi$
$374$	14.0044	−	27.5603i	0.724150	−	1.42511i
$375$	−3.49956	−	15.9158i	−0.180716	−	0.821889i
$376$	4.77585	−	12.5657i	0.246296	−	0.648029i
$377$		−	2.75852i		−	0.142071i
$378$	−10.4980	−	16.3643i	−0.539960	−	0.841691i
$379$			3.63286i			0.186608i	0.995638	+	0.0933039i	$0.0297428\pi$
$379$			3.63286i			0.186608i	−0.995638	+	0.0933039i	$0.970257\pi$
$380$	−11.9312	+	8.70886i	−0.612060	+	0.446755i
$381$	5.38827	+	24.5056i	0.276049	+	1.25546i
$382$	21.8461	+	11.1008i	1.11774	+	0.567965i
$383$	−15.3699			−0.785366			−0.392683	−	0.919674i	$-0.628453\pi$
$383$	−15.3699			−0.785366			−0.392683	+	0.919674i	$0.628453\pi$
$384$	16.2756	−	10.9135i	0.830561	−	0.556927i
$385$	−0.999265	+	7.50432i	−0.0509273	+	0.382455i
$386$	−1.65353	−	2.54007i	−0.0841624	−	0.129286i
$387$	11.5355	−	16.3536i	0.586383	−	0.831302i
$388$	−9.16156	+	6.68722i	−0.465108	+	0.339492i
$389$	27.1114			1.37460			0.687300	−	0.726373i	$-0.258796\pi$
$389$	27.1114			1.37460			0.687300	+	0.726373i	$0.258796\pi$
$390$	1.75698	−	6.77621i	0.0889682	−	0.343127i
$391$	13.2170	−	22.8925i	0.668411	−	1.15772i
$392$	19.6913	+	2.06264i	0.994559	+	0.104179i
$393$	−18.3709	+	4.03937i	−0.926687	+	0.203759i
$394$	−21.7194	+	1.16231i	−1.09421	+	0.0585562i
$395$	−4.02308	+	6.96818i	−0.202423	+	0.350607i
$396$	8.32502	+	13.8946i	0.418348	+	0.698230i
$397$	−16.9366	+	9.77834i	−0.850023	+	0.490761i	−0.860658	−	0.509183i	$-0.829948\pi$
$397$	−16.9366	+	9.77834i	−0.850023	+	0.490761i	0.0106358	+	0.999943i	$0.496614\pi$
$398$	3.58597	−	7.05711i	0.179748	−	0.353741i
$399$	−26.2160	+	18.2315i	−1.31244	+	0.912716i
$400$	15.1530	−	3.29086i	0.757649	−	0.164543i
$401$	−24.9871			−1.24779			−0.623897	−	0.781506i	$-0.714452\pi$
$401$	−24.9871			−1.24779			−0.623897	+	0.781506i	$0.714452\pi$
$402$	3.36008	−	3.41495i	0.167585	−	0.170322i
$403$		−	22.9440i		−	1.14292i
$404$	−1.80066	−	16.7758i	−0.0895861	−	0.834625i
$405$	7.26494	+	6.18222i	0.360998	+	0.307197i
$406$	−3.45575	+	1.64671i	−0.171506	+	0.0817250i
$407$	−2.27978	+	1.31623i	−0.113004	+	0.0652430i
$408$	39.2422	+	5.80138i	1.94278	+	0.287211i
$409$	10.7510	−	6.20707i	0.531601	−	0.306920i	−0.210067	−	0.977687i	$-0.567368\pi$
$409$	10.7510	−	6.20707i	0.531601	−	0.306920i	0.741668	+	0.670767i	$0.234035\pi$
$410$	−2.96108	+	5.82734i	−0.146237	+	0.287792i
$411$	16.4704	−	3.62151i	0.812426	−	0.178636i
$412$	−15.6406	+	1.67881i	−0.770555	+	0.0827090i
$413$	−5.84853	+	2.41241i	−0.287787	+	0.118707i
$414$	6.47342	+	12.2443i	0.318151	+	0.601774i
$415$	−1.96268	+	1.13316i	−0.0963443	+	0.0556244i
$416$	14.7543	+	3.86624i	0.723388	+	0.189558i
$417$	−2.58534	+	8.15044i	−0.126605	+	0.399129i
$418$	22.2955	−	14.5139i	1.09051	−	0.709897i
$419$	15.0148	−	26.0064i	0.733521	−	1.27050i	−0.221848	−	0.975081i	$-0.571209\pi$
$419$	15.0148	−	26.0064i	0.733521	−	1.27050i	0.955369	−	0.295415i	$-0.0954578\pi$
$420$	−9.53777	+	1.84403i	−0.465396	+	0.0899793i
$421$	−17.0435	−	29.5202i	−0.830649	−	1.43873i	−0.897524	−	0.440965i	$-0.854636\pi$
$421$	−17.0435	−	29.5202i	−0.830649	−	1.43873i	0.0668755	−	0.997761i	$-0.478697\pi$
$422$	7.97465	+	4.05220i	0.388200	+	0.197258i
$423$	−1.29184	+	14.1995i	−0.0628116	+	0.690404i
$424$	−3.89804	+	10.2561i	−0.189306	+	0.498082i
$425$	27.1843	+	15.6949i	1.31863	+	0.761314i
$426$	−8.35676	−	30.2071i	−0.404887	−	1.46354i
$427$	−5.97617	+	7.76447i	−0.289207	+	0.375749i
$428$	7.46874	−	5.45159i	0.361015	−	0.263513i
$429$	−3.81194	+	12.0174i	−0.184042	+	0.580203i
$430$	−5.45535	−	8.38024i	−0.263080	−	0.404131i
$431$	8.99967	+	5.19596i	0.433499	+	0.250281i	0.700836	−	0.713322i	$-0.252810\pi$
$431$	8.99967	+	5.19596i	0.433499	+	0.250281i	−0.267337	+	0.963603i	$0.586144\pi$
$432$	−13.5108	+	15.7942i	−0.650039	+	0.759901i
$433$		−	37.3442i		−	1.79465i	−0.441371	−	0.897325i	$-0.645508\pi$
$433$		−	37.3442i		−	1.79465i	0.441371	−	0.897325i	$-0.354492\pi$
$434$	−28.7432	+	13.6965i	−1.37972	+	0.657455i
$435$	1.38697	−	1.26652i	0.0665002	−	0.0607248i
$436$	−14.2521	+	32.2020i	−0.682553	+	1.54219i
$437$	19.7002	−	11.3739i	0.942387	−	0.544087i
$438$	6.67418	+	1.73053i	0.318905	+	0.0826877i
$439$	9.49100	−	16.4389i	0.452981	−	0.784585i	−0.545589	−	0.838053i	$-0.683694\pi$
$439$	9.49100	−	16.4389i	0.452981	−	0.784585i	0.998570	+	0.0534676i	$0.0170274\pi$
$440$	7.98939	−	1.29253i	0.380879	−	0.0616190i
$441$	−20.7040	+	3.51372i	−0.985903	+	0.167320i
$442$	16.8449	+	25.8762i	0.801229	+	1.23081i
$443$	14.1654	+	8.17837i	0.673017	+	0.388566i	0.797219	−	0.603691i	$-0.206304\pi$
$443$	14.1654	+	8.17837i	0.673017	+	0.388566i	−0.124202	+	0.992257i	$0.539637\pi$
$444$	−2.53098	−	2.23707i	−0.120115	−	0.106167i
$445$	2.33120	+	4.03776i	0.110510	+	0.191408i
$446$	−9.44038	−	14.5018i	−0.447015	−	0.686682i
$447$	−15.3360	+	3.37206i	−0.725366	+	0.159493i
$448$	−3.96418	−	20.7915i	−0.187290	−	0.982305i
$449$	−16.7544			−0.790690			−0.395345	−	0.918533i	$-0.629375\pi$
$449$	−16.7544			−0.790690			−0.395345	+	0.918533i	$0.629375\pi$
$450$	−14.5398	+	7.68705i	−0.685415	+	0.362371i
$451$	5.88608	−	10.1950i	0.277165	−	0.480064i
$452$	−12.9563	+	29.2741i	−0.609414	+	1.37694i
$453$	−0.781302	−	3.55332i	−0.0367088	−	0.166950i
$454$	−12.7944	+	0.684687i	−0.600469	+	0.0321340i
$455$	−5.99187	−	4.61183i	−0.280903	−	0.216206i
$456$	26.7495	+	21.2085i	1.25266	+	0.993180i
$457$	−2.18675	+	3.78755i	−0.102292	+	0.177174i	−0.912628	−	0.408790i	$-0.865951\pi$
$457$	−2.18675	+	3.78755i	−0.102292	+	0.177174i	0.810337	+	0.585964i	$0.199284\pi$
$458$	1.04614	+	19.5487i	0.0488830	+	0.913449i
$459$	−41.7430	+	5.27521i	−1.94840	+	0.246226i
$460$	6.88079	−	0.738563i	0.320819	−	0.0344357i
$461$	−26.4257	+	15.2569i	−1.23077	+	0.710584i	−0.967190	−	0.254054i	$-0.918236\pi$
$461$	−26.4257	+	15.2569i	−1.23077	+	0.710584i	−0.263578	+	0.964638i	$0.584902\pi$
$462$	17.3304	−	2.39839i	0.806281	−	0.111583i
$463$	−20.1336	−	11.6242i	−0.935689	−	0.540221i	−0.0470829	−	0.998891i	$-0.514993\pi$
$463$	−20.1336	−	11.6242i	−0.935689	−	0.540221i	−0.888606	+	0.458670i	$0.848326\pi$
$464$	2.75172	+	3.02909i	0.127745	+	0.140622i
$465$	11.5361	−	10.5343i	0.534976	−	0.488514i
$466$	15.0705	+	23.1506i	0.698128	+	1.07243i
$467$	−9.93664	−	17.2108i	−0.459813	−	0.796419i	0.539138	−	0.842218i	$-0.318750\pi$
$467$	−9.93664	−	17.2108i	−0.459813	−	0.796419i	−0.998951	+	0.0457981i	$0.985417\pi$
$468$	−16.1755	+	0.262055i	−0.747714	+	0.0121135i
$469$	−1.97319	−	4.78371i	−0.0911133	−	0.220891i
$470$	6.35124	+	3.22729i	0.292961	+	0.148864i
$471$	23.5416	−	21.4971i	1.08474	−	0.990534i
$472$	4.27370	+	5.24199i	0.196713	+	0.241282i
$473$	9.00446	+	15.5962i	0.414025	+	0.717113i
$474$	17.9994	+	4.66701i	0.826742	+	0.214363i
$475$	13.5063	+	23.3936i	0.619710	+	1.07337i
$476$	22.3610	−	36.5494i	1.02491	−	1.67524i
$477$	1.05440	−	11.5896i	0.0482777	−	0.530652i
$478$	−10.9712	−	5.57484i	−0.501809	−	0.254987i
$479$	−4.67514			−0.213613			−0.106806	−	0.994280i	$-0.534062\pi$
$479$	−4.67514			−0.213613			−0.106806	+	0.994280i	$0.534062\pi$
$480$	4.83018	+	9.19349i	0.220467	+	0.419623i
$481$		−	2.62920i		−	0.119881i
$482$	1.11042	+	20.7498i	0.0505782	+	0.945127i
$483$	14.9071	−	1.25598i	0.678297	−	0.0571491i
$484$	7.38172	−	0.792331i	0.335533	−	0.0360151i
$485$	−3.00557	−	5.20580i	−0.136476	−	0.236383i
$486$	9.29329	−	19.9909i	0.421552	−	0.906804i
$487$	26.7465	+	15.4421i	1.21200	+	0.699750i	0.963195	−	0.268804i	$-0.0866282\pi$
$487$	26.7465	+	15.4421i	1.21200	+	0.699750i	0.248807	+	0.968553i	$0.419962\pi$
$488$	9.79121	+	3.72134i	0.443227	+	0.168457i
$489$	20.4904	−	18.7109i	0.926609	−	0.846135i
$490$	−2.20062	+	10.2594i	−0.0994137	+	0.463472i
$491$	−17.7038	−	10.2213i	−0.798962	−	0.461281i	0.0441461	−	0.999025i	$-0.485943\pi$
$491$	−17.7038	−	10.2213i	−0.798962	−	0.461281i	−0.843108	+	0.537744i	$0.819277\pi$
$492$	14.8040	+	3.00456i	0.667416	+	0.135456i
$493$			8.28428i			0.373105i
$494$	1.41988	+	26.5325i	0.0638834	+	1.19375i
$495$	−7.79244	+	3.60089i	−0.350244	+	0.161848i
$496$	22.8874	+	25.1944i	1.02767	+	1.13126i
$497$	−33.5567	−	4.46837i	−1.50522	−	0.200434i
$498$	3.73330	+	3.67331i	0.167293	+	0.164605i
$499$			15.4758i			0.692790i	0.938089	+	0.346395i	$0.112594\pi$
$499$			15.4758i			0.692790i	−0.938089	+	0.346395i	$0.887406\pi$
$500$	2.00822	+	18.7095i	0.0898105	+	0.836716i
$501$	−0.0144775	+	0.0456411i	−0.000646806	+	0.00203909i
$502$	35.2372	−	1.88571i	1.57271	−	0.0841633i
$503$	2.70437			0.120582			0.0602909	−	0.998181i	$-0.480797\pi$
$503$	2.70437			0.120582			0.0602909	+	0.998181i	$0.480797\pi$
$504$	9.98435	+	20.1075i	0.444738	+	0.895661i
$505$	8.94162			0.397897
$506$	−12.4456	+	0.666024i	−0.553275	+	0.0296084i
$507$	6.69244	+	7.32895i	0.297222	+	0.325490i
$508$	−3.09206	−	28.8071i	−0.137188	−	1.27811i
$509$		−	35.2806i		−	1.56379i	−0.623413	−	0.781893i	$-0.714254\pi$
$509$		−	35.2806i		−	1.56379i	0.623413	−	0.781893i	$-0.285746\pi$
$510$	−5.27649	+	20.3500i	−0.233647	+	0.901115i
$511$	4.54238	−	5.90164i	0.200943	−	0.261073i
$512$	−20.0581	+	10.4724i	−0.886452	+	0.462820i
$513$	−33.3792	−	14.0296i	−1.47373	−	0.619423i
$514$	−0.631172	−	11.7943i	−0.0278398	−	0.520226i
$515$		−	8.33654i		−	0.367352i
$516$	−15.3040	+	17.3147i	−0.673723	+	0.762238i
$517$	−11.1116	−	6.41526i	−0.488686	−	0.282143i
$518$	−3.29374	+	1.56951i	−0.144719	+	0.0689604i
$519$	7.84922	+	2.48980i	0.344543	+	0.109290i
$520$	−2.87177	+	7.55591i	−0.125935	+	0.331348i
$521$	−23.4381	−	13.5320i	−1.02684	−	0.592847i	−0.110763	−	0.993847i	$-0.535329\pi$
$521$	−23.4381	−	13.5320i	−1.02684	−	0.592847i	−0.916078	+	0.401000i	$0.868663\pi$
$522$	−3.67559	−	2.30883i	−0.160876	−	0.101055i
$523$	−16.0435	−	27.7882i	−0.701534	−	1.21509i	−0.967928	−	0.251228i	$-0.919166\pi$
$523$	−16.0435	−	27.7882i	−0.701534	−	1.21509i	0.266394	−	0.963864i	$-0.414168\pi$
$524$	21.5955	−	2.31800i	0.943405	−	0.101262i
$525$	1.49145	+	17.7019i	0.0650923	+	0.772573i
$526$	−1.03069	−	19.2598i	−0.0449400	−	0.839768i
$527$			68.9045i			3.00153i
$528$	−7.80188	−	16.9986i	−0.339533	−	0.739768i
$529$	12.3429			0.536648
$530$	−5.18387	−	2.63411i	−0.225173	−	0.114418i
$531$	−5.86200	−	4.13493i	−0.254389	−	0.179441i
$532$	32.3911	−	17.6175i	1.40433	−	0.763814i
$533$	5.87879	+	10.1824i	0.254639	+	0.441047i
$534$	7.55698	−	7.68040i	0.327023	−	0.332363i
$535$	2.45022	+	4.24390i	0.105932	+	0.183480i
$536$	−4.28760	+	3.49560i	−0.185196	+	0.150987i
$537$	6.04337	+	1.91697i	0.260791	+	0.0827236i
$538$	−2.85497	−	1.45071i	−0.123087	−	0.0625447i
$539$	4.94501	−	18.2389i	0.212996	−	0.785603i
$540$	−7.55841	−	8.01266i	−0.325262	−	0.344810i
$541$	−20.6581	−	35.7809i	−0.888161	−	1.53834i	−0.842047	−	0.539404i	$-0.818650\pi$
$541$	−20.6581	−	35.7809i	−0.888161	−	1.53834i	−0.0461139	−	0.998936i	$-0.514684\pi$
$542$	14.4338	+	22.1725i	0.619986	+	0.952391i
$543$	4.56643	+	20.7679i	0.195964	+	0.891236i
$544$	−44.3094	−	11.6109i	−1.89975	−	0.497815i
$545$	−16.1623	−	9.33131i	−0.692317	−	0.399710i
$546$	−6.57995	+	16.1876i	−0.281596	+	0.692767i
$547$	2.51810	−	1.45383i	0.107666	−	0.0621612i	−0.445200	−	0.895431i	$-0.646867\pi$
$547$	2.51810	−	1.45383i	0.107666	−	0.0621612i	0.552866	+	0.833270i	$0.313534\pi$
$548$	−19.3615	+	2.07820i	−0.827083	+	0.0887765i
$549$	−11.0642	−	1.00660i	−0.472210	−	0.0429607i
$550$	−0.790889	−	14.7789i	−0.0337236	−	0.630174i
$551$	−3.56453	+	6.17395i	−0.151854	+	0.263019i
$552$	−5.88491	−	14.8707i	−0.250478	−	0.632940i
$553$	12.2503	−	15.9160i	0.520934	−	0.676817i
$554$	14.3337	−	0.767067i	0.608982	−	0.0325896i
$555$	1.32195	−	1.20714i	0.0561136	−	0.0512402i
$556$	3.99597	−	9.02868i	0.169467	−	0.382901i
$557$	−3.49428	+	6.05228i	−0.148058	+	0.256443i	−0.930510	−	0.366268i	$-0.880635\pi$
$557$	−3.49428	+	6.05228i	−0.148058	+	0.256443i	0.782452	+	0.622711i	$0.213969\pi$
$558$	−30.5718	−	19.2037i	−1.29421	−	0.812959i
$559$	−17.9866			−0.760753
$560$	11.1800	−	0.912914i	0.472442	−	0.0385776i
$561$	11.4479	−	36.0900i	0.483329	−	1.52372i
$562$	−25.5217	−	39.2052i	−1.07657	−	1.65377i
$563$	−11.6828	−	20.2352i	−0.492372	−	0.852813i	0.507589	−	0.861599i	$-0.330537\pi$
$563$	−11.6828	−	20.2352i	−0.492372	−	0.852813i	−0.999961	+	0.00878586i	$0.997203\pi$
$564$	3.27468	−	16.1349i	0.137889	−	0.679404i
$565$	−14.6928	−	8.48290i	−0.618132	−	0.356878i
$566$	2.57573	+	3.95671i	0.108266	+	0.166313i
$567$	−15.9389	−	17.6904i	−0.669370	−	0.742929i
$568$	5.77975	+	35.7258i	0.242513	+	1.49902i
$569$	−17.4511	+	30.2262i	−0.731589	+	1.26715i	0.224615	+	0.974448i	$0.427888\pi$
$569$	−17.4511	+	30.2262i	−0.731589	+	1.26715i	−0.956204	+	0.292702i	$0.905446\pi$
$570$	−12.6885	+	12.8957i	−0.531463	+	0.540143i
$571$	−27.1650	+	15.6837i	−1.13682	+	0.656343i	−0.945641	−	0.325213i	$-0.894564\pi$
$571$	−27.1650	+	15.6837i	−1.13682	+	0.656343i	−0.191178	+	0.981555i	$0.561231\pi$
$572$	5.89182	−	13.3123i	0.246350	−	0.556614i
$573$	28.6072	+	9.07429i	1.19508	+	0.379084i
$574$	9.24664	−	13.4431i	0.385947	−	0.561104i
$575$		−	12.6551i		−	0.527754i
$576$	17.5007	−	16.4234i	0.729194	−	0.684307i
$577$	22.7304	+	13.1234i	0.946278	+	0.546334i	0.891923	−	0.452188i	$-0.149356\pi$
$577$	22.7304	+	13.1234i	0.946278	+	0.546334i	0.0543554	+	0.998522i	$0.482690\pi$
$578$	−37.4715	−	57.5619i	−1.55861	−	2.39426i
$579$	−2.50307	−	2.74113i	−0.104024	−	0.113918i
$580$	−1.75177	+	1.27866i	−0.0727385	+	0.0530933i
$581$	5.22966	−	2.15713i	0.216963	−	0.0894929i
$582$	−9.74304	+	9.90216i	−0.403862	+	0.410458i
$583$	9.06924	+	5.23613i	0.375610	+	0.216858i
$584$	−7.44213	−	2.82852i	−0.307958	−	0.117045i
$585$	0.776798	−	8.53831i	0.0321167	−	0.353016i
$586$	4.05245	+	2.05919i	0.167405	+	0.0850645i
$587$	−5.56925	−	9.64623i	−0.229868	−	0.398143i	0.727901	−	0.685682i	$-0.240496\pi$
$587$	−5.56925	−	9.64623i	−0.229868	−	0.398143i	−0.957769	+	0.287540i	$0.907163\pi$
$588$	24.2071	−	1.42023i	0.998283	−	0.0585694i
$589$	−29.6480	+	51.3518i	−1.22162	+	2.11591i
$590$	−3.00392	+	1.95548i	−0.123669	+	0.0805060i
$591$	−26.0172	+	5.72065i	−1.07021	+	0.235316i
$592$	2.62271	+	2.88708i	0.107793	+	0.118658i
$593$	2.12516	−	1.22696i	0.0872700	−	0.0503854i	−0.455730	−	0.890118i	$-0.650622\pi$
$593$	2.12516	−	1.22696i	0.0872700	−	0.0503854i	0.543000	+	0.839733i	$0.317288\pi$
$594$	12.8220	+	15.1375i	0.526093	+	0.621100i
$595$	17.9945	+	13.8500i	0.737703	+	0.567797i
$596$	18.0279	−	1.93506i	0.738452	−	0.0792632i
$597$	2.93134	−	9.24122i	0.119972	−	0.378218i
$598$	5.63902	−	11.0975i	0.230597	−	0.453809i
$599$	31.8737	−	18.4023i	1.30232	−	0.751896i	0.321521	−	0.946903i	$-0.395806\pi$
$599$	31.8737	−	18.4023i	1.30232	−	0.751896i	0.980802	+	0.195006i	$0.0624727\pi$
$600$	17.6587	−	6.98820i	0.720912	−	0.285292i
$601$	−21.1705	+	12.2228i	−0.863561	+	0.498577i	−0.865203	−	0.501421i	$-0.832811\pi$
$601$	−21.1705	+	12.2228i	−0.863561	+	0.498577i	0.00164203	+	0.999999i	$0.499477\pi$
$602$	10.7372	+	22.5328i	0.437615	+	0.918369i
$603$	3.38210	−	4.79473i	0.137730	−	0.195257i
$604$	0.448351	+	4.17704i	0.0182431	+	0.169961i
$605$			3.93452i			0.159961i
$606$	−5.50974	−	19.9160i	−0.223818	−	0.809031i
$607$	12.3053			0.499459			0.249729	−	0.968316i	$-0.419658\pi$
$607$	12.3053			0.499459			0.249729	+	0.968316i	$0.419658\pi$
$608$	−28.0262	−	27.7185i	−1.13661	−	1.12413i
$609$	−3.84910	+	2.67679i	−0.155974	+	0.108469i
$610$	−2.51470	+	4.94887i	−0.101817	+	0.200374i
$611$	11.0978	−	6.40732i	0.448969	−	0.259212i
$612$	48.5777	−	0.786993i	1.96364	−	0.0318123i
$613$	2.07499	−	3.59399i	0.0838080	−	0.145160i	−0.821075	−	0.570821i	$-0.806625\pi$
$613$	2.07499	−	3.59399i	0.0838080	−	0.145160i	0.904883	+	0.425661i	$0.139958\pi$
$614$	−35.1289	+	1.87991i	−1.41769	+	0.0758671i
$615$	−2.42053	+	7.63085i	−0.0976050	+	0.307705i
$616$	−20.1942	+	0.565814i	−0.813646	+	0.0227973i
$617$	2.21526	−	3.83693i	0.0891828	−	0.154469i	−0.817983	−	0.575242i	$-0.804908\pi$
$617$	2.21526	−	3.83693i	0.0891828	−	0.154469i	0.907166	+	0.420773i	$0.138241\pi$
$618$	−18.5683	+	5.13690i	−0.746925	+	0.206636i
$619$	−39.4764			−1.58669			−0.793345	−	0.608772i	$-0.791662\pi$
$619$	−39.4764			−1.58669			−0.793345	+	0.608772i	$0.791662\pi$
$620$	−14.5704	+	10.6352i	−0.585161	+	0.427121i
$621$	10.2564	+	13.5111i	0.411574	+	0.542180i
$622$	−1.89136	−	2.90541i	−0.0758366	−	0.116496i
$623$	−4.43780	−	10.7588i	−0.177797	−	0.431042i
$624$	18.5991	+	1.74051i	0.744559	+	0.0696760i
$625$	9.41043			0.376417
$626$	−18.6207	−	9.46185i	−0.744233	−	0.378171i
$627$	24.0603	−	21.9707i	0.960876	−	0.877426i
$628$	−29.7336	+	21.7032i	−1.18650	+	0.866050i
$629$			7.89590i			0.314830i
$630$	−11.1601	+	4.12385i	−0.444630	+	0.164298i
$631$		−	6.09451i		−	0.242618i	−0.992615	−	0.121309i	$-0.961291\pi$
$631$		−	6.09451i		−	0.242618i	0.992615	−	0.121309i	$-0.0387093\pi$
$632$	−20.0705	−	7.62818i	−0.798362	−	0.303433i
$633$	10.4427	+	3.31246i	0.415061	+	0.131659i
$634$	−16.6844	+	32.8346i	−0.662624	+	1.30403i
$635$	15.3544			0.609321
$636$	−2.67279	+	13.1693i	−0.105983	+	0.522198i
$637$	13.3063	+	13.3853i	0.527215	+	0.530346i
$638$	3.27348	−	2.13096i	0.129598	−	0.0843656i
$639$	−16.1019	−	34.8451i	−0.636982	−	1.37845i
$640$	−4.38383	−	11.1617i	−0.173286	−	0.441205i
$641$	14.3839			0.568129			0.284064	−	0.958805i	$-0.408317\pi$
$641$	14.3839			0.568129			0.284064	+	0.958805i	$0.408317\pi$
$642$	7.94278	−	8.07250i	0.313476	−	0.318596i
$643$	2.34451	−	4.06080i	0.0924583	−	0.160142i	−0.816087	−	0.577930i	$-0.803861\pi$
$643$	2.34451	−	4.06080i	0.0924583	−	0.160142i	0.908545	+	0.417787i	$0.137194\pi$
$644$	−17.2686	−	0.439623i	−0.680479	−	0.0173236i
$645$	−8.25817	−	9.04359i	−0.325165	−	0.356091i
$646$	−4.26412	−	79.6813i	−0.167770	−	3.13502i
$647$	−12.5308	+	21.7040i	−0.492638	+	0.853274i	−0.999964	−	0.00848030i	$-0.997301\pi$
$647$	−12.5308	+	21.7040i	−0.492638	+	0.853274i	0.507326	+	0.861754i	$0.330634\pi$
$648$	−13.1895	+	21.7724i	−0.518131	+	0.855301i
$649$	5.59049	−	3.22767i	0.219446	−	0.126697i
$650$	13.1780	+	6.69622i	0.516884	+	0.262647i
$651$	−32.0149	+	22.2642i	−1.25476	+	0.872604i
$652$	−25.8798	+	18.8902i	−1.01353	+	0.739799i
$653$	48.2429			1.88789			0.943946	−	0.330100i	$-0.107082\pi$
$653$	48.2429			1.88789			0.943946	+	0.330100i	$0.107082\pi$
$654$	−10.8249	+	41.7487i	−0.423286	+	1.63250i
$655$			11.5106i			0.449756i
$656$	−16.6126	−	5.31679i	−0.648615	−	0.207586i
$657$	8.40974	+	0.765101i	0.328095	+	0.0298494i
$658$	−14.6517	−	10.0779i	−0.571182	−	0.392879i
$659$	20.2388	−	11.6849i	0.788392	−	0.455179i	−0.0510039	−	0.998698i	$-0.516242\pi$
$659$	20.2388	−	11.6849i	0.788392	−	0.455179i	0.839396	+	0.543520i	$0.182909\pi$
$660$	9.39846	−	3.14966i	0.365834	−	0.122601i
$661$	2.44769	−	1.41317i	0.0952039	−	0.0549660i	−0.451642	−	0.892199i	$-0.649162\pi$
$661$	2.44769	−	1.41317i	0.0952039	−	0.0549660i	0.546846	+	0.837233i	$0.315828\pi$
$662$	24.1374	+	12.2651i	0.938125	+	0.476695i
$663$	25.4993	+	27.9245i	0.990312	+	1.08450i
$664$	−3.82147	−	4.68729i	−0.148302	−	0.181902i
$665$	7.45126	+	18.0645i	0.288947	+	0.700512i
$666$	−3.50328	−	2.20059i	−0.135749	−	0.0852712i
$667$	2.89243	−	1.66994i	0.111995	−	0.0646605i
$668$	0.0223767	−	0.0505591i	0.000865782	−	0.00195619i
$669$	−14.2906	−	15.6497i	−0.552506	−	0.605054i
$670$	−1.59946	−	2.45700i	−0.0617924	−	0.0949224i
$671$	4.99876	−	8.65811i	0.192975	−	0.334243i
$672$	−8.92238	−	24.3391i	−0.344188	−	0.938901i
$673$	3.06361	+	5.30633i	0.118094	+	0.204544i	0.919012	−	0.394229i	$-0.128988\pi$
$673$	3.06361	+	5.30633i	0.118094	+	0.204544i	−0.800919	+	0.598773i	$0.795655\pi$
$674$	1.07989	−	2.12520i	0.0415959	−	0.0818598i
$675$	−16.0441	+	12.1792i	−0.617538	+	0.468779i
$676$	−6.75659	−	9.25661i	−0.259869	−	0.356023i
$677$	3.19573	+	1.84506i	0.122822	+	0.0709112i	0.560152	−	0.828390i	$-0.310743\pi$
$677$	3.19573	+	1.84506i	0.122822	+	0.0709112i	−0.437330	+	0.899301i	$0.644076\pi$
$678$	−9.84068	+	37.9529i	−0.377929	+	1.45757i
$679$	5.72155	+	13.8711i	0.219573	+	0.532323i
$680$	8.62437	−	22.6916i	0.330730	−	0.870182i
$681$	−15.3261	+	3.36990i	−0.587299	+	0.129135i
$682$	27.2272	−	17.7243i	1.04258	−	0.678698i
$683$	−2.48721	−	1.43599i	−0.0951704	−	0.0549466i	0.451659	−	0.892190i	$-0.350832\pi$
$683$	−2.48721	−	1.43599i	−0.0951704	−	0.0549466i	−0.546830	+	0.837244i	$0.684166\pi$
$684$	36.5416	+	20.3153i	1.39720	+	0.776775i
$685$		−	10.3198i		−	0.394301i
$686$	8.82527	−	24.6600i	0.336950	−	0.941522i
$687$	5.14891	+	23.4170i	0.196443	+	0.893414i
$688$	19.7508	−	17.9422i	0.752992	−	0.684041i
$689$	−9.05801	+	5.22964i	−0.345083	+	0.199234i
$690$	8.16879	−	2.25989i	0.310980	−	0.0860325i
$691$	12.6905	−	21.9807i	0.482771	−	0.836184i	−0.517033	−	0.855965i	$-0.672964\pi$
$691$	12.6905	−	21.9807i	0.482771	−	0.836184i	0.999804	+	0.0197814i	$0.00629702\pi$
$692$	−8.69501	−	3.84829i	−0.330535	−	0.146290i
$693$	20.4674	−	6.34232i	0.777493	−	0.240925i
$694$	11.8948	−	7.74327i	0.451522	−	0.293931i
$695$	4.53154	+	2.61628i	0.171891	+	0.0992413i
$696$	3.92742	+	3.11389i	0.148869	+	0.118032i
$697$	−17.6549	−	30.5793i	−0.668729	−	1.15827i
$698$	−19.6522	+	12.7932i	−0.743848	+	0.484229i
$699$	22.8134	+	24.9831i	0.862881	+	0.944948i
$700$	0.522044	−	20.5061i	0.0197314	−	0.775059i
$701$	23.9938			0.906233			0.453117	−	0.891451i	$-0.350312\pi$
$701$	23.9938			0.906233			0.453117	+	0.891451i	$0.350312\pi$
$702$	−19.4963	+	3.53104i	−0.735841	+	0.133270i
$703$	−3.39742	+	5.88450i	−0.128136	+	0.221938i
$704$	6.80972	+	20.4953i	0.256651	+	0.772444i
$705$	8.31689	+	2.63814i	0.313232	+	0.0993581i
$706$	1.64926	+	30.8188i	0.0620707	+	1.15988i
$707$	−22.1244	−	2.94606i	−0.832075	−	0.110798i
$708$	6.20650	+	5.48577i	0.233255	+	0.206168i
$709$	−17.5122	+	30.3320i	−0.657684	+	1.13914i	0.323530	+	0.946218i	$0.395130\pi$
$709$	−17.5122	+	30.3320i	−0.657684	+	1.13914i	−0.981214	+	0.192924i	$0.938203\pi$
$710$	−19.1521	+	1.02492i	−0.718767	+	0.0384646i
$711$	22.6800	+	2.06338i	0.850568	+	0.0773829i
$712$	−9.64302	+	7.86178i	−0.361387	+	0.294633i
$713$	24.0578	−	13.8898i	0.900971	−	0.520176i
$714$	19.7606	−	48.6141i	0.739523	−	1.81934i
$715$	6.68149	+	3.85756i	0.249874	+	0.144265i
$716$	−6.69457	−	2.96292i	−0.250188	−	0.110730i
$717$	−14.3666	−	4.55714i	−0.536532	−	0.170189i
$718$	−22.2094	+	14.4578i	−0.828848	+	0.539562i
$719$	−19.7380	−	34.1872i	−0.736102	−	1.27497i	−0.954238	−	0.299048i	$-0.903331\pi$
$719$	−19.7380	−	34.1872i	−0.736102	−	1.27497i	0.218136	−	0.975918i	$-0.430002\pi$
$720$	7.66425	+	10.1506i	0.285630	+	0.378292i
$721$	−2.74670	+	20.6273i	−0.102293	+	0.768200i
$722$	18.9348	−	37.2632i	0.704679	−	1.38679i
$723$	5.46528	+	24.8558i	0.203256	+	0.924397i
$724$	−2.62045	−	24.4133i	−0.0973883	−	0.907314i
$725$	1.98302	+	3.43470i	0.0736477	+	0.127562i
$726$	8.76348	−	2.42441i	0.325243	−	0.0899784i
$727$	−9.31052	−	16.1263i	−0.345308	−	0.598091i	0.640102	−	0.768290i	$-0.278892\pi$
$727$	−9.31052	−	16.1263i	−0.345308	−	0.598091i	−0.985410	+	0.170199i	$0.945559\pi$
$728$	9.59518	−	17.7496i	0.355621	−	0.657842i
$729$	7.25858	−	26.0060i	0.268836	−	0.963186i
$730$	1.91138	−	3.76155i	0.0707434	−	0.139221i
$731$	54.0166			1.99788
$732$	12.5723	+	2.55163i	0.464687	+	0.0943108i
$733$			44.3030i			1.63637i	0.574956	+	0.818184i	$0.305019\pi$
$733$			44.3030i			1.63637i	−0.574956	+	0.818184i	$0.694981\pi$
$734$	11.0782	−	0.592845i	0.408902	−	0.0218823i
$735$	−0.620775	+	12.8359i	−0.0228976	+	0.473461i
$736$	4.87797	+	17.8110i	0.179804	+	0.656523i
$737$	2.64002	+	4.57265i	0.0972464	+	0.168436i
$738$	18.4879	+	0.689263i	0.680551	+	0.0253721i
$739$	7.61365	+	4.39574i	0.280072	+	0.161700i	0.633456	−	0.773779i	$-0.281636\pi$
$739$	7.61365	+	4.39574i	0.280072	+	0.161700i	−0.353384	+	0.935478i	$0.614969\pi$
$740$	−1.66965	+	1.21871i	−0.0613775	+	0.0448007i
$741$	6.98838	+	31.7828i	0.256725	+	1.16757i
$742$	11.9587	+	8.22560i	0.439017	+	0.301971i
$743$	−18.7141	−	10.8046i	−0.686553	−	0.396382i	0.115766	−	0.993276i	$-0.463068\pi$
$743$	−18.7141	−	10.8046i	−0.686553	−	0.396382i	−0.802319	+	0.596895i	$0.796401\pi$
$744$	32.6663	+	25.8998i	1.19761	+	0.949532i
$745$			9.60903i			0.352047i
$746$	−15.8758	+	0.849587i	−0.581253	+	0.0311056i
$747$	5.24170	+	3.69739i	0.191784	+	0.135280i
$748$	−17.6941	+	39.9789i	−0.646960	+	1.46177i
$749$	−4.66435	−	11.3081i	−0.170432	−	0.413187i
$750$	6.14486	+	22.2117i	0.224379	+	0.811057i
$751$			49.4586i			1.80477i	0.430930	+	0.902385i	$0.358186\pi$
$751$			49.4586i			1.80477i	−0.430930	+	0.902385i	$0.641814\pi$
$752$	−5.79479	+	18.1062i	−0.211314	+	0.660264i
$753$	42.2100	−	9.28110i	1.53822	−	0.338222i
$754$	0.208470	+	3.89557i	0.00759204	+	0.141868i
$755$	−2.22640			−0.0810269
$756$	16.0619	+	22.3162i	0.584167	+	0.811633i
$757$	−48.1032			−1.74834			−0.874170	−	0.485620i	$-0.838594\pi$
$757$	−48.1032			−1.74834			−0.874170	+	0.485620i	$0.838594\pi$
$758$	−0.274547	−	5.13031i	−0.00997200	−	0.186341i
$759$	−14.9084	+	3.27804i	−0.541139	+	0.118985i
$760$	16.1911	−	13.2003i	0.587311	−	0.478824i
$761$			3.23146i			0.117140i	0.998283	+	0.0585702i	$0.0186541\pi$
$761$			3.23146i			0.117140i	−0.998283	+	0.0585702i	$0.981346\pi$
$762$	−9.46124	−	34.1994i	−0.342744	−	1.23891i
$763$	36.9163	+	28.4138i	1.33646	+	1.02865i
$764$	−31.6898	−	14.0254i	−1.14650	−	0.507423i
$765$	−2.33285	+	25.6419i	−0.0843443	+	0.927084i
$766$	21.7053	−	1.16155i	0.784243	−	0.0419686i
$767$			6.44735i			0.232800i
$768$	−22.1595	+	16.6420i	−0.799613	+	0.600515i
$769$	34.6628	+	20.0126i	1.24997	+	0.721672i	0.971104	−	0.238657i	$-0.0767071\pi$
$769$	34.6628	+	20.0126i	1.24997	+	0.721672i	0.278869	+	0.960329i	$0.410040\pi$
$770$	0.844030	−	10.6731i	0.0304167	−	0.384630i
$771$	−3.10651	−	14.1282i	−0.111878	−	0.508816i
$772$	2.52706	+	3.46211i	0.0909510	+	0.124604i
$773$	27.1598	+	15.6807i	0.976869	+	0.563995i	0.901323	−	0.433147i	$-0.142597\pi$
$773$	27.1598	+	15.6807i	0.976869	+	0.563995i	0.0755453	+	0.997142i	$0.475930\pi$
$774$	−15.0545	+	23.9663i	−0.541122	+	0.861450i
$775$	16.4938	+	28.5681i	0.592475	+	1.02620i
$776$	12.4325	−	10.1360i	0.446301	−	0.363862i
$777$	−3.66865	+	2.55130i	−0.131612	+	0.0915274i
$778$	−38.2865	+	2.04889i	−1.37264	+	0.0734563i
$779$		−	30.3860i		−	1.08869i
$780$	−1.96910	+	9.70210i	−0.0705050	+	0.347391i
$781$	34.5421			1.23601
$782$	−16.9349	+	33.3274i	−0.605589	+	1.19179i
$783$	−4.90082	−	2.05986i	−0.175141	−	0.0736136i
$784$	−27.9637	−	1.42472i	−0.998705	−	0.0508828i
$785$	−9.75447	−	16.8952i	−0.348152	−	0.603017i
$786$	25.6379	−	7.09272i	0.914475	−	0.252989i
$787$	16.0992	+	27.8846i	0.573875	+	0.993980i	0.996163	+	0.0875186i	$0.0278937\pi$
$787$	16.0992	+	27.8846i	0.573875	+	0.993980i	−0.422288	+	0.906462i	$0.638773\pi$
$788$	30.5841	−	3.28280i	1.08951	−	0.116945i
$789$	−5.07284	−	23.0710i	−0.180598	−	0.821349i
$790$	5.15476	−	10.1444i	0.183398	−	0.360923i
$791$	33.5598	+	25.8304i	1.19325	+	0.918423i
$792$	−12.8066	−	18.9927i	−0.455062	−	0.674876i
$793$	4.99257	+	8.64739i	0.177291	+	0.307078i
$794$	23.1787	−	15.0889i	0.822583	−	0.535483i
$795$	−6.78823	−	2.15325i	−0.240754	−	0.0763678i
$796$	−4.53075	+	10.2370i	−0.160588	+	0.362841i
$797$	16.7898	+	9.69358i	0.594724	+	0.343364i	0.766963	−	0.641691i	$-0.221767\pi$
$797$	16.7898	+	9.69358i	0.594724	+	0.343364i	−0.172239	+	0.985055i	$0.555100\pi$
$798$	35.6443	−	27.7276i	1.26179	−	0.981547i
$799$	−33.3284	+	19.2422i	−1.17908	+	0.680740i
$800$	−21.1502	+	5.79249i	−0.747774	+	0.204796i
$801$	7.60652	−	10.7836i	0.268763	−	0.381019i
$802$	35.2866	−	1.88835i	1.24601	−	0.0666800i
$803$	−3.79947	+	6.58088i	−0.134081	+	0.232234i
$804$	−4.48700	+	5.07651i	−0.158244	+	0.179035i
$805$	1.20836	−	9.07462i	0.0425893	−	0.319838i
$806$	1.73395	+	32.4014i	0.0610758	+	1.14129i
$807$	−3.73856	−	1.18588i	−0.131604	−	0.0417450i
$808$	3.81068	+	23.5545i	0.134059	+	0.828646i
$809$	16.7748	−	29.0549i	0.589772	−	1.02152i	−0.404490	−	0.914543i	$-0.632551\pi$
$809$	16.7748	−	29.0549i	0.589772	−	1.02152i	0.994262	−	0.106973i	$-0.0341158\pi$
$810$	−10.7267	−	8.18146i	−0.376898	−	0.287467i
$811$	−12.0196			−0.422064			−0.211032	−	0.977479i	$-0.567682\pi$
$811$	−12.0196			−0.422064			−0.211032	+	0.977479i	$0.567682\pi$
$812$	4.75574	−	2.58664i	0.166894	−	0.0907732i
$813$	21.8496	+	23.9276i	0.766297	+	0.839178i
$814$	3.12001	−	2.03106i	0.109356	−	0.0711886i
$815$	−8.49021	−	14.7055i	−0.297399	−	0.515110i
$816$	−55.8560	−	5.22701i	−1.95535	−	0.182982i
$817$	40.2565	+	23.2421i	1.40840	+	0.813138i
$818$	−14.7133	+	9.57806i	−0.514440	+	0.334889i
$819$	−4.73523	+	20.8706i	−0.165462	+	0.729277i
$820$	3.74122	−	8.45310i	0.130649	−	0.295195i
$821$	5.79127	−	10.0308i	0.202117	−	0.350076i	−0.747094	−	0.664719i	$-0.768551\pi$
$821$	5.79127	−	10.0308i	0.202117	−	0.350076i	0.949210	+	0.314642i	$0.101885\pi$
$822$	−22.9857	+	6.35899i	−0.801719	+	0.221795i
$823$	−36.5262	+	21.0884i	−1.27322	+	0.735096i	−0.975593	−	0.219586i	$-0.929529\pi$
$823$	−36.5262	+	21.0884i	−1.27322	+	0.735096i	−0.297630	+	0.954681i	$0.596196\pi$
$824$	21.9606	−	3.55281i	0.765034	−	0.123768i
$825$	−3.89261	−	17.7034i	−0.135523	−	0.616353i
$826$	8.07694	−	3.84877i	0.281033	−	0.133916i
$827$		−	27.0948i		−	0.942178i	−0.882086	−	0.471089i	$-0.843861\pi$
$827$		−	27.0948i		−	0.942178i	0.882086	−	0.471089i	$-0.156139\pi$
$828$	−10.0671	−	16.8021i	−0.349854	−	0.583913i
$829$	−3.83015	−	2.21134i	−0.133027	−	0.0768029i	0.432010	−	0.901869i	$-0.357805\pi$
$829$	−3.83015	−	2.21134i	−0.133027	−	0.0768029i	−0.565036	+	0.825066i	$0.691138\pi$
$830$	2.68605	−	1.74856i	0.0932342	−	0.0606934i
$831$	17.1701	−	3.77536i	0.595625	−	0.130966i
$832$	−21.1281	−	4.34485i	−0.732484	−	0.150631i
$833$	−39.9610	−	40.1983i	−1.38456	−	1.39279i
$834$	3.03505	−	11.7054i	0.105095	−	0.405324i
$835$	0.0253758	+	0.0146508i	0.000878167	+	0.000507010i
$836$	−30.3887	+	22.1813i	−1.05101	+	0.767157i
$837$	−40.7626	−	17.1329i	−1.40896	−	0.592201i
$838$	−19.2384	+	37.8608i	−0.664580	+	1.30788i
$839$	−25.3280	−	43.8694i	−0.874420	−	1.51454i	−0.857379	−	0.514685i	$-0.827909\pi$
$839$	−25.3280	−	43.8694i	−0.874420	−	1.51454i	−0.0170407	−	0.999855i	$-0.505424\pi$
$840$	13.3298	−	3.32492i	0.459922	−	0.114721i
$841$	13.9766	−	24.2083i	0.481953	−	0.834768i
$842$	26.2996	+	40.4002i	0.906345	+	1.39228i
$843$	−38.6341	−	42.3085i	−1.33063	−	1.45718i
$844$	−11.5680	−	5.11982i	−0.398186	−	0.176232i
$845$	5.25980	−	3.03675i	0.180943	−	0.104467i
$846$	0.751230	−	20.1501i	0.0258278	−	0.692774i
$847$	1.29633	−	9.73526i	0.0445426	−	0.334508i
$848$	4.72970	−	14.7782i	0.162419	−	0.507487i
$849$	3.89908	+	4.26991i	0.133816	+	0.146543i
$850$	−39.5756	−	20.1098i	−1.35743	−	0.689760i
$851$	2.75683	−	1.59165i	0.0945028	−	0.0545612i
$852$	14.0842	+	42.0266i	0.482517	+	1.43981i
$853$	−23.5900	+	13.6197i	−0.807705	+	0.466329i	−0.846158	−	0.532931i	$-0.821090\pi$
$853$	−23.5900	+	13.6197i	−0.807705	+	0.466329i	0.0384530	+	0.999260i	$0.487757\pi$
$854$	7.85272	−	11.4166i	0.268715	−	0.390667i
$855$	−12.7717	+	18.1061i	−0.436782	+	0.619216i
$856$	−10.1353	+	8.26314i	−0.346418	+	0.282428i
$857$			17.3398i			0.592317i	0.955139	+	0.296159i	$0.0957057\pi$
$857$			17.3398i			0.592317i	−0.955139	+	0.296159i	$0.904294\pi$
$858$	4.47500	−	17.2589i	0.152774	−	0.589209i
$859$	4.32980			0.147731			0.0738654	−	0.997268i	$-0.476466\pi$
$859$	4.32980			0.147731			0.0738654	+	0.997268i	$0.476466\pi$
$860$	8.33733	+	11.4222i	0.284301	+	0.389495i
$861$	8.50335	−	18.0837i	0.289793	−	0.616290i
$862$	−13.1019	−	6.65756i	−0.446254	−	0.226758i
$863$	33.6005	−	19.3992i	1.14377	−	0.660358i	0.196411	−	0.980522i	$-0.437071\pi$
$863$	33.6005	−	19.3992i	1.14377	−	0.660358i	0.947362	+	0.320164i	$0.103738\pi$
$864$	17.8862	−	23.3256i	0.608502	−	0.793552i
$865$	2.51959	−	4.36407i	0.0856688	−	0.148383i
$866$	2.82222	+	52.7373i	0.0959030	+	1.79209i
$867$	−56.7234	−	62.1183i	−1.92643	−	2.10965i
$868$	39.5559	−	21.5144i	1.34261	−	0.730245i
$869$	−10.2467	+	17.7478i	−0.347596	+	0.602054i
$870$	−1.86296	+	1.89338i	−0.0631602	+	0.0641917i
$871$	−5.27350			−0.178686
$872$	17.6932	−	46.5524i	0.599166	−	1.57646i
$873$	−9.80691	+	13.9030i	−0.331913	+	0.470546i
$874$	−26.9609	+	17.5509i	−0.911966	+	0.593670i
$875$	24.6748	+	3.28566i	0.834160	+	0.111076i
$876$	−9.55601	−	1.93945i	−0.322868	−	0.0655278i
$877$	28.3411			0.957012			0.478506	−	0.878084i	$-0.341178\pi$
$877$	28.3411			0.957012			0.478506	+	0.878084i	$0.341178\pi$
$878$	−12.1608	+	23.9321i	−0.410406	+	0.807671i
$879$	5.30664	+	1.68328i	0.178989	+	0.0567757i
$880$	−11.1849	+	2.42909i	−0.377042	+	0.0818845i
$881$			47.2247i			1.59104i	0.605927	+	0.795520i	$0.292802\pi$
$881$			47.2247i			1.59104i	−0.605927	+	0.795520i	$0.707198\pi$
$882$	28.9724	−	6.52671i	0.975553	−	0.219766i
$883$		−	31.8848i		−	1.07301i	−0.843897	−	0.536505i	$-0.819744\pi$
$883$		−	31.8848i		−	1.07301i	0.843897	−	0.536505i	$-0.180256\pi$
$884$	−25.7437	−	35.2692i	−0.865856	−	1.18623i
$885$	−3.24170	+	2.96016i	−0.108968	+	0.0995047i
$886$	−20.6223	−	10.4789i	−0.692819	−	0.352046i
$887$	31.6593			1.06302			0.531508	−	0.847053i	$-0.321625\pi$
$887$	31.6593			1.06302			0.531508	+	0.847053i	$0.321625\pi$
$888$	3.74330	+	2.96790i	0.125617	+	0.0995963i
$889$	−37.9917	−	5.05893i	−1.27420	−	0.169671i
$890$	−3.59726	−	5.52592i	−0.120580	−	0.185229i
$891$	18.5037	+	15.7460i	0.619896	+	0.527511i
$892$	14.4276	+	19.7659i	0.483071	+	0.661813i
$893$	−33.1178			−1.10825
$894$	21.4025	−	5.92099i	0.715807	−	0.198028i
$895$	1.93992	−	3.36004i	0.0648443	−	0.112314i
$896$	7.16947	+	29.0620i	0.239515	+	0.970893i
$897$	4.60960	−	14.5320i	0.153910	−	0.485210i
$898$	23.6605	−	1.26618i	0.789560	−	0.0422531i
$899$	−4.35299	+	7.53960i	−0.145180	+	0.251460i
$900$	19.9521	−	11.9544i	0.665071	−	0.398481i
$901$	27.2026	−	15.7054i	0.906251	−	0.523224i
$902$	−7.54182	+	14.8421i	−0.251115	+	0.494189i
$903$	17.4537	+	25.0976i	0.580823	+	0.835197i
$904$	16.0845	−	42.3199i	0.534962	−	1.40754i
$905$	13.0125			0.432550
$906$	1.37189	+	4.95893i	0.0455778	+	0.164749i
$907$		−	50.0286i		−	1.66117i	−0.556891	−	0.830586i	$-0.688006\pi$
$907$		−	50.0286i		−	1.66117i	0.556891	−	0.830586i	$-0.311994\pi$
$908$	18.0164	−	1.93382i	0.597894	−	0.0641761i
$909$	−10.6162	−	22.9739i	−0.352118	−	0.761996i
$910$	8.81020	+	6.05997i	0.292055	+	0.200886i
$911$	−25.2297	+	14.5664i	−0.835897	+	0.482605i	−0.855867	−	0.517195i	$-0.826976\pi$
$911$	−25.2297	+	14.5664i	−0.835897	+	0.482605i	0.0199707	+	0.999801i	$0.493643\pi$
$912$	−39.3782	−	27.9290i	−1.30394	−	0.924821i
$913$	−4.99892	+	2.88613i	−0.165440	+	0.0955169i
$914$	2.80187	−	5.51402i	0.0926776	−	0.182387i
$915$	−2.05564	+	6.48051i	−0.0679572	+	0.214239i
$916$	−2.95471	−	27.5274i	−0.0976263	−	0.909531i
$917$	3.79248	−	28.4809i	0.125239	−	0.940522i
$918$	58.5505	−	10.6043i	1.93245	−	0.349993i
$919$	−19.2593	+	11.1193i	−0.635304	+	0.366793i	−0.782803	−	0.622269i	$-0.786211\pi$
$919$	−19.2593	+	11.1193i	−0.635304	+	0.366793i	0.147499	+	0.989062i	$0.452878\pi$
$920$	−9.66119	+	1.56300i	−0.318520	+	0.0515305i
$921$	−42.0803	+	9.25258i	−1.38659	+	0.304883i
$922$	36.1652	−	23.5427i	1.19104	−	0.775339i
$923$	−17.2497	+	29.8773i	−0.567780	+	0.983424i
$924$	−24.2925	+	4.69670i	−0.799166	+	0.154510i
$925$	1.89006	+	3.27367i	0.0621447	+	0.107638i
$926$	29.3111	+	14.8940i	0.963221	+	0.489447i
$927$	−21.4193	+	9.89784i	−0.703501	+	0.325088i
$928$	−4.11487	−	4.06970i	−0.135077	−	0.133594i
$929$	36.0808	+	20.8312i	1.18377	+	0.683451i	0.956884	−	0.290470i	$-0.0938116\pi$
$929$	36.0808	+	20.8312i	1.18377	+	0.683451i	0.226888	+	0.973921i	$0.427145\pi$
$930$	−15.4952	+	15.7482i	−0.508106	+	0.516405i
$931$	−12.4850	−	47.1524i	−0.409178	−	1.54536i
$932$	−23.0320	−	31.5542i	−0.754440	−	1.03359i
$933$	−2.86309	−	3.13539i	−0.0937333	−	0.102648i
$934$	15.3331	+	23.5540i	0.501715	+	0.770710i
$935$	−20.0656	−	11.5849i	−0.656215	−	0.378866i
$936$	22.8232	−	1.59251i	0.745998	−	0.0520527i
$937$		−	38.4609i		−	1.25646i	−0.778026	−	0.628232i	$-0.783779\pi$
$937$		−	38.4609i		−	1.25646i	0.778026	−	0.628232i	$-0.216221\pi$
$938$	3.14804	+	6.60641i	0.102787	+	0.215707i
$939$	−24.3836	−	7.73456i	−0.795730	−	0.252408i
$940$	−9.21307	−	4.07757i	−0.300497	−	0.132996i
$941$	−2.73114	+	1.57682i	−0.0890326	+	0.0514030i	−0.543855	−	0.839179i	$-0.683036\pi$
$941$	−2.73114	+	1.57682i	−0.0890326	+	0.0514030i	0.454823	+	0.890582i	$0.349703\pi$
$942$	−31.6207	+	32.1372i	−1.03026	+	1.04709i
$943$	−7.11777	+	12.3283i	−0.231786	+	0.401466i
$944$	−6.43144	−	7.07972i	−0.209325	−	0.230425i
$945$	−12.6677	+	7.20143i	−0.412081	+	0.234263i
$946$	−13.8947	−	21.3443i	−0.451755	−	0.693964i
$947$	17.3803	+	10.0345i	0.564782	+	0.326077i	0.755063	−	0.655653i	$-0.227606\pi$
$947$	17.3803	+	10.0345i	0.564782	+	0.326077i	−0.190280	+	0.981730i	$0.560940\pi$
$948$	−25.7714	−	5.23045i	−0.837016	−	0.169877i
$949$	−3.79477	−	6.57273i	−0.123183	−	0.213360i
$950$	−20.8414	−	32.0155i	−0.676184	−	1.03872i
$951$	−13.6387	+	42.9966i	−0.442264	+	1.39426i
$952$	−28.8158	+	53.3047i	−0.933926	+	1.72762i
$953$	29.2121			0.946273			0.473136	−	0.880989i	$-0.343122\pi$
$953$	29.2121			0.946273			0.473136	+	0.880989i	$0.343122\pi$
$954$	−0.613153	+	16.4465i	−0.0198516	+	0.532474i
$955$	9.18290	−	15.9052i	0.297152	−	0.514682i
$956$	15.9147	+	7.04362i	0.514718	+	0.227807i
$957$	3.53260	−	3.22580i	0.114193	−	0.104275i
$958$	6.60220	−	0.353315i	0.213307	−	0.0114151i
$959$	−3.40015	+	25.5346i	−0.109797	+	0.824555i
$960$	−7.51593	−	12.6179i	−0.242576	−	0.407243i
$961$	−20.7060	+	35.8638i	−0.667935	+	1.15690i
$962$	0.198697	+	3.71293i	0.00640624	+	0.119710i
$963$	7.99484	−	11.3341i	0.257630	−	0.365236i
$964$	−3.13625	−	29.2188i	−0.101012	−	0.941074i
$965$	−1.96724	+	1.13579i	−0.0633278	+	0.0365623i
$966$	−20.9568	+	2.90026i	−0.674274	+	0.0933145i
$967$	40.7844	+	23.5469i	1.31154	+	0.757217i	0.982351	−	0.187047i	$-0.0598918\pi$
$967$	40.7844	+	23.5469i	1.31154	+	0.757217i	0.329188	+	0.944265i	$0.393225\pi$
$968$	−10.3645	+	1.67678i	−0.333129	+	0.0538939i
$969$	−20.9872	−	95.4488i	−0.674206	−	3.06626i
$970$	4.63786	+	7.12445i	0.148913	+	0.228752i
$971$	1.53241	+	2.65421i	0.0491774	+	0.0851777i	0.889566	−	0.456806i	$-0.151007\pi$
$971$	1.53241	+	2.65421i	0.0491774	+	0.0851777i	−0.840389	+	0.541984i	$0.817673\pi$
$972$	−11.6131	+	28.9333i	−0.372492	+	0.928036i
$973$	−10.3505	−	7.96657i	−0.331821	−	0.255396i
$974$	−38.9383	−	19.7859i	−1.24766	−	0.633982i
$975$	17.2565	+	5.47380i	0.552650	+	0.175302i
$976$	−14.1083	−	4.51529i	−0.451596	−	0.144531i
$977$	12.4473	+	21.5594i	0.398226	+	0.689747i	0.993507	−	0.113770i	$-0.0362928\pi$
$977$	12.4473	+	21.5594i	0.398226	+	0.689747i	−0.595281	+	0.803517i	$0.702959\pi$
$978$	−27.5224	+	27.9719i	−0.880069	+	0.894443i
$979$	5.93754	+	10.2841i	0.189764	+	0.328682i
$980$	2.33236	−	14.6545i	0.0745045	−	0.468122i
$981$	−4.78591	+	52.6051i	−0.152802	+	1.67955i
$982$	25.7737	+	13.0965i	0.822470	+	0.417927i
$983$	−38.2016			−1.21844			−0.609222	−	0.793000i	$-0.708518\pi$
$983$	−38.2016			−1.21844			−0.609222	+	0.793000i	$0.708518\pi$
$984$	−21.1332	−	3.12423i	−0.673701	−	0.0995968i
$985$			16.3016i			0.519411i
$986$	−0.626069	−	11.6990i	−0.0199381	−	0.372572i
$987$	−19.7094	−	9.26783i	−0.627359	−	0.294998i
$988$	−4.01029	−	37.3617i	−0.127584	−	1.18863i
$989$	−10.8887	−	18.8597i	−0.346240	−	0.599705i
$990$	10.7323	−	5.67405i	0.341095	−	0.180333i
$991$	16.6116	+	9.59071i	0.527685	+	0.304659i	0.740073	−	0.672526i	$-0.234791\pi$
$991$	16.6116	+	9.59071i	0.527685	+	0.304659i	−0.212388	+	0.977185i	$0.568124\pi$
$992$	−34.2254	−	33.8497i	−1.08666	−	1.07473i
$993$	31.6077	+	10.0260i	1.00304	+	0.318167i
$994$	47.7262	+	3.77421i	1.51378	+	0.119711i
$995$	−5.13800	−	2.96642i	−0.162885	−	0.0940420i
$996$	−5.54975	−	4.90528i	−0.175850	−	0.155430i
$997$		−	16.7831i		−	0.531525i	−0.964039	−	0.265762i	$-0.914376\pi$
$997$		−	16.7831i		−	0.531525i	0.964039	−	0.265762i	$-0.0856237\pi$
$998$	−1.16955	−	21.8548i	−0.0370215	−	0.691800i
$999$	−4.67106	−	1.96329i	−0.147786	−	0.0621159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.n.b.31.2	✓	84
3.2	odd	2		756.2.n.b.199.41		84
4.3	odd	2	inner	252.2.n.b.31.27	yes	84
7.5	odd	6		252.2.bj.b.103.30	yes	84
9.2	odd	6		756.2.bj.b.451.13		84
9.7	even	3		252.2.bj.b.115.30	yes	84
12.11	even	2		756.2.n.b.199.16		84
21.5	even	6		756.2.bj.b.523.13		84
28.19	even	6		252.2.bj.b.103.29	yes	84
36.7	odd	6		252.2.bj.b.115.29	yes	84
36.11	even	6		756.2.bj.b.451.14		84
63.47	even	6		756.2.n.b.19.16		84
63.61	odd	6	inner	252.2.n.b.187.27	yes	84
84.47	odd	6		756.2.bj.b.523.14		84
252.47	odd	6		756.2.n.b.19.41		84
252.187	even	6	inner	252.2.n.b.187.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.2	✓	84	1.1	even	1	trivial
252.2.n.b.31.27	yes	84	4.3	odd	2	inner
252.2.n.b.187.2	yes	84	252.187	even	6	inner
252.2.n.b.187.27	yes	84	63.61	odd	6	inner
252.2.bj.b.103.29	yes	84	28.19	even	6
252.2.bj.b.103.30	yes	84	7.5	odd	6
252.2.bj.b.115.29	yes	84	36.7	odd	6
252.2.bj.b.115.30	yes	84	9.7	even	3
756.2.n.b.19.16		84	63.47	even	6
756.2.n.b.19.41		84	252.47	odd	6
756.2.n.b.199.16		84	12.11	even	2
756.2.n.b.199.41		84	3.2	odd	2
756.2.bj.b.451.13		84	9.2	odd	6
756.2.bj.b.451.14		84	36.11	even	6
756.2.bj.b.523.13		84	21.5	even	6
756.2.bj.b.523.14		84	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41219 + 0.0755732i) q^{2} +(-1.69164 + 0.371957i) q^{3} +(1.98858 - 0.213448i) q^{4} +1.05993i q^{5} +(2.36081 - 0.653118i) q^{6} +(0.349222 - 2.62260i) q^{7} +(-2.79212 + 0.451713i) q^{8} +(2.72330 - 1.25843i) q^{9} +O(q^{10})\)	\(q+(-1.41219 + 0.0755732i) q^{2} +(-1.69164 + 0.371957i) q^{3} +(1.98858 - 0.213448i) q^{4} +1.05993i q^{5} +(2.36081 - 0.653118i) q^{6} +(0.349222 - 2.62260i) q^{7} +(-2.79212 + 0.451713i) q^{8} +(2.72330 - 1.25843i) q^{9} +(-0.0801021 - 1.49682i) q^{10} +2.69962i q^{11} +(-3.28456 + 1.10074i) q^{12} +(-2.33504 - 1.34814i) q^{13} +(-0.294971 + 3.73001i) q^{14} +(-0.394248 - 1.79302i) q^{15} +(3.90888 - 0.848915i) q^{16} +(7.01250 + 4.04867i) q^{17} +(-3.75072 + 1.98296i) q^{18} +(3.48409 + 6.03463i) q^{19} +(0.226239 + 2.10775i) q^{20} +(0.384736 + 4.56640i) q^{21} +(-0.204019 - 3.81238i) q^{22} -3.26452i q^{23} +(4.55525 - 1.80269i) q^{24} +3.87655 q^{25} +(3.39941 + 1.72736i) q^{26} +(-4.13875 + 3.14177i) q^{27} +(0.134667 - 5.28979i) q^{28} +(0.511543 + 0.886019i) q^{29} +(0.692258 + 2.50229i) q^{30} +(4.25476 + 7.36946i) q^{31} +(-5.45594 + 1.49424i) q^{32} +(-1.00414 - 4.56678i) q^{33} +(-10.2090 - 5.18755i) q^{34} +(2.77977 + 0.370150i) q^{35} +(5.14687 - 3.08378i) q^{36} +(0.487561 + 0.844481i) q^{37} +(-5.37627 - 8.25875i) q^{38} +(4.45150 + 1.41203i) q^{39} +(-0.478783 - 2.95945i) q^{40} +(-3.77646 - 2.18034i) q^{41} +(-0.888419 - 6.41956i) q^{42} +(5.77718 - 3.33546i) q^{43} +(0.576227 + 5.36840i) q^{44} +(1.33385 + 2.88650i) q^{45} +(0.246710 + 4.61014i) q^{46} +(-2.37636 + 4.11598i) q^{47} +(-6.29666 + 2.88999i) q^{48} +(-6.75609 - 1.83174i) q^{49} +(-5.47444 + 0.292963i) q^{50} +(-13.3686 - 4.24055i) q^{51} +(-4.93117 - 2.18247i) q^{52} +(1.93958 - 3.35945i) q^{53} +(5.60729 - 4.74956i) q^{54} -2.86140 q^{55} +(0.209590 + 7.48038i) q^{56} +(-8.13846 - 8.91249i) q^{57} +(-0.789357 - 1.21257i) q^{58} +(-1.19560 - 2.07084i) q^{59} +(-1.16671 - 3.48140i) q^{60} +(-3.20716 - 1.85166i) q^{61} +(-6.56548 - 10.0856i) q^{62} +(-2.34934 - 7.58160i) q^{63} +(7.59191 - 2.52247i) q^{64} +(1.42893 - 2.47498i) q^{65} +(1.76317 + 6.37329i) q^{66} +(1.69381 - 0.977924i) q^{67} +(14.8091 + 6.55429i) q^{68} +(1.21426 + 5.52240i) q^{69} +(-3.95354 - 0.312648i) q^{70} -12.7952i q^{71} +(-7.03533 + 4.74385i) q^{72} +(2.43771 + 1.40741i) q^{73} +(-0.752350 - 1.15572i) q^{74} +(-6.55773 + 1.44191i) q^{75} +(8.21647 + 11.2567i) q^{76} +(7.08003 + 0.942767i) q^{77} +(-6.39309 - 1.65764i) q^{78} +(6.57420 + 3.79562i) q^{79} +(0.899789 + 4.14313i) q^{80} +(5.83268 - 6.85418i) q^{81} +(5.49786 + 2.79366i) q^{82} +(1.06909 + 1.85171i) q^{83} +(1.73977 + 8.99851i) q^{84} +(-4.29130 + 7.43275i) q^{85} +(-7.90642 + 5.14691i) q^{86} +(-1.19491 - 1.30855i) q^{87} +(-1.21945 - 7.53767i) q^{88} +(3.80947 - 2.19940i) q^{89} +(-2.10180 - 3.97549i) q^{90} +(-4.35108 + 5.65309i) q^{91} +(-0.696805 - 6.49176i) q^{92} +(-9.93865 - 10.8839i) q^{93} +(3.04482 - 5.99214i) q^{94} +(-6.39627 + 3.69289i) q^{95} +(8.67369 - 4.55709i) q^{96} +(-4.91146 + 2.83563i) q^{97} +(9.67933 + 2.07620i) q^{98} +(3.39729 + 7.35186i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9}+O(q^{10}) \) 84 * q - q^2 + q^4 - 16 * q^8 - 14 * q^9	\( 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9} - 18 q^{10} + 9 q^{12} - 18 q^{13} - 25 q^{14} - 7 q^{16} + 6 q^{17} - 13 q^{18} + 24 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{24} - 32 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 14 q^{30} + 9 q^{32} - 6 q^{33} + 24 q^{34} - 38 q^{36} + 2 q^{37} - 6 q^{41} + 7 q^{42} - 13 q^{44} - 18 q^{45} + 10 q^{46} - 9 q^{48} + 2 q^{49} - 17 q^{50} - 2 q^{53} - 42 q^{54} - 32 q^{56} + 6 q^{57} + 26 q^{58} + 8 q^{60} - 24 q^{61} - 8 q^{64} + 50 q^{65} + 27 q^{66} + 18 q^{69} - 4 q^{70} - 7 q^{72} + 30 q^{73} + 46 q^{74} + 46 q^{77} + 15 q^{78} + 3 q^{80} - 26 q^{81} - 18 q^{82} + 29 q^{84} - 50 q^{85} + 18 q^{86} - 2 q^{88} - 102 q^{89} + 39 q^{90} + 28 q^{92} - 24 q^{93} + 3 q^{94} - 30 q^{96} - 6 q^{97} + 21 q^{98}+O(q^{100}) \) 84 * q - q^2 + q^4 - 16 * q^8 - 14 * q^9 - 18 * q^10 + 9 * q^12 - 18 * q^13 - 25 * q^14 - 7 * q^16 + 6 * q^17 - 13 * q^18 + 24 * q^20 + 4 * q^21 + 6 * q^22 + 6 * q^24 - 32 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 14 * q^30 + 9 * q^32 - 6 * q^33 + 24 * q^34 - 38 * q^36 + 2 * q^37 - 6 * q^41 + 7 * q^42 - 13 * q^44 - 18 * q^45 + 10 * q^46 - 9 * q^48 + 2 * q^49 - 17 * q^50 - 2 * q^53 - 42 * q^54 - 32 * q^56 + 6 * q^57 + 26 * q^58 + 8 * q^60 - 24 * q^61 - 8 * q^64 + 50 * q^65 + 27 * q^66 + 18 * q^69 - 4 * q^70 - 7 * q^72 + 30 * q^73 + 46 * q^74 + 46 * q^77 + 15 * q^78 + 3 * q^80 - 26 * q^81 - 18 * q^82 + 29 * q^84 - 50 * q^85 + 18 * q^86 - 2 * q^88 - 102 * q^89 + 39 * q^90 + 28 * q^92 - 24 * q^93 + 3 * q^94 - 30 * q^96 - 6 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more