LMFDB - Embedded newform 637.2.bl.b.625.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			625.11
Character	$\chi$	$=$	637.625
Dual form			637.2.bl.b.53.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.610286 + 0.416086i) q^{2} +(-2.18416 + 2.02661i) q^{3} +(-0.531361 + 1.35388i) q^{4} +(-2.47946 - 0.764813i) q^{5} +(0.489722 - 2.14561i) q^{6} +(1.83554 + 1.90546i) q^{7} +(-0.567772 - 2.48757i) q^{8} +(0.439242 - 5.86128i) q^{9} +O(q^{10})$	\(q+(-0.610286 + 0.416086i) q^{2} +(-2.18416 + 2.02661i) q^{3} +(-0.531361 + 1.35388i) q^{4} +(-2.47946 - 0.764813i) q^{5} +(0.489722 - 2.14561i) q^{6} +(1.83554 + 1.90546i) q^{7} +(-0.567772 - 2.48757i) q^{8} +(0.439242 - 5.86128i) q^{9} +(1.83141 - 0.564915i) q^{10} +(-0.116712 - 1.55742i) q^{11} +(-1.58322 - 4.03397i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(-1.91304 - 0.399136i) q^{14} +(6.96553 - 3.35442i) q^{15} +(-0.750789 - 0.696630i) q^{16} +(-5.91891 - 0.892132i) q^{17} +(2.17073 + 3.75982i) q^{18} +(-0.151312 + 0.262080i) q^{19} +(2.35296 - 2.95051i) q^{20} +(-7.87075 - 0.441929i) q^{21} +(0.719246 + 0.901906i) q^{22} +(3.12319 - 0.470745i) q^{23} +(6.28145 + 4.28262i) q^{24} +(1.43160 + 0.976047i) q^{25} +(0.730381 - 0.110087i) q^{26} +(5.34599 + 6.70366i) q^{27} +(-3.55511 + 1.47262i) q^{28} +(2.28797 - 2.86903i) q^{29} +(-2.85524 + 4.94541i) q^{30} +(3.43290 + 5.94596i) q^{31} +(5.79415 + 0.873327i) q^{32} +(3.41119 + 3.16512i) q^{33} +(3.98343 - 1.91832i) q^{34} +(-3.09383 - 6.12837i) q^{35} +(7.70211 + 3.70914i) q^{36} +(1.53383 + 3.90813i) q^{37} +(-0.0167042 - 0.222902i) q^{38} +(2.84718 - 0.878238i) q^{39} +(-0.494758 + 6.60208i) q^{40} +(-0.928580 - 4.06838i) q^{41} +(4.98729 - 3.00521i) q^{42} +(0.421199 - 1.84540i) q^{43} +(2.17058 + 0.669534i) q^{44} +(-5.57187 + 14.1969i) q^{45} +(-1.71017 + 1.58680i) q^{46} +(-0.766145 + 0.522349i) q^{47} +3.05164 q^{48} +(-0.261591 + 6.99511i) q^{49} -1.27980 q^{50} +(14.7359 - 10.0467i) q^{51} +(1.06617 - 0.989259i) q^{52} +(-3.77304 + 9.61355i) q^{53} +(-6.05188 - 1.86676i) q^{54} +(-0.901748 + 3.95082i) q^{55} +(3.69781 - 5.64791i) q^{56} +(-0.200643 - 0.879076i) q^{57} +(-0.202556 + 2.70292i) q^{58} +(2.99966 - 0.925274i) q^{59} +(0.840293 + 11.2129i) q^{60} +(-3.37912 - 8.60985i) q^{61} +(-4.56908 - 2.20035i) q^{62} +(11.9747 - 9.92166i) q^{63} +(-2.05393 + 0.989120i) q^{64} +(1.90208 + 1.76487i) q^{65} +(-3.39876 - 0.512281i) q^{66} +(-6.59946 - 11.4306i) q^{67} +(4.35292 - 7.53948i) q^{68} +(-5.86754 + 7.35767i) q^{69} +(4.43805 + 2.45276i) q^{70} +(-2.25638 - 2.82941i) q^{71} +(-14.8298 + 2.23523i) q^{72} +(8.48581 + 5.78553i) q^{73} +(-2.56219 - 1.74687i) q^{74} +(-5.10491 + 0.769442i) q^{75} +(-0.274425 - 0.344118i) q^{76} +(2.75337 - 3.08109i) q^{77} +(-1.37217 + 1.72065i) q^{78} +(1.75973 - 3.04795i) q^{79} +(1.32876 + 2.30148i) q^{80} +(-7.82603 - 1.17958i) q^{81} +(2.25949 + 2.09650i) q^{82} +(-13.4047 + 6.45535i) q^{83} +(4.78053 - 10.4213i) q^{84} +(13.9934 + 6.73886i) q^{85} +(0.510791 + 1.30147i) q^{86} +(0.817086 + 10.9033i) q^{87} +(-3.80792 + 1.17459i) q^{88} +(1.22833 - 16.3909i) q^{89} +(-2.50669 - 10.9825i) q^{90} +(-0.827014 - 2.51318i) q^{91} +(-1.02221 + 4.47857i) q^{92} +(-19.5482 - 6.02981i) q^{93} +(0.250226 - 0.637565i) q^{94} +(0.575614 - 0.534092i) q^{95} +(-14.4253 + 9.83498i) q^{96} -5.41958 q^{97} +(-2.75092 - 4.37786i) q^{98} -9.17972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{16}{21}\right)$

Coefficient data

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

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

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

$2$	−0.610286	+	0.416086i	−0.431537	+	0.294217i	−0.759541	−	0.650459i	$-0.774576\pi$
$2$	−0.610286	+	0.416086i	−0.431537	+	0.294217i	0.328004	+	0.944676i	$0.393624\pi$
$3$	−2.18416	+	2.02661i	−1.26103	+	1.17006i	−0.283566	+	0.958953i	$0.591517\pi$
$3$	−2.18416	+	2.02661i	−1.26103	+	1.17006i	−0.977462	+	0.211110i	$0.932292\pi$
$4$	−0.531361	+	1.35388i	−0.265680	+	0.676942i
$5$	−2.47946	−	0.764813i	−1.10885	−	0.342035i	−0.314354	−	0.949306i	$-0.601788\pi$
$5$	−2.47946	−	0.764813i	−1.10885	−	0.342035i	−0.794495	+	0.607271i	$0.792264\pi$
$6$	0.489722	−	2.14561i	0.199928	−	0.875942i
$7$	1.83554	+	1.90546i	0.693769	+	0.720198i
$7$	1.83554	+	1.90546i	0.693769	+	0.720198i
$8$	−0.567772	−	2.48757i	−0.200738	−	0.879490i
$9$	0.439242	−	5.86128i	0.146414	−	1.95376i
$10$	1.83141	−	0.564915i	0.579142	−	0.178642i
$11$	−0.116712	−	1.55742i	−0.0351900	−	0.469578i	−0.986764	−	0.162160i	$-0.948154\pi$
$11$	−0.116712	−	1.55742i	−0.0351900	−	0.469578i	0.951574	−	0.307418i	$-0.0994651\pi$
$12$	−1.58322	−	4.03397i	−0.457035	−	1.16451i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$13$	−0.900969	−	0.433884i	−0.249884	−	0.120338i
$14$	−1.91304	−	0.399136i	−0.511282	−	0.106674i
$15$	6.96553	−	3.35442i	1.79849	−	0.866108i
$16$	−0.750789	−	0.696630i	−0.187697	−	0.174158i
$17$	−5.91891	−	0.892132i	−1.43555	−	0.216374i	−0.615259	−	0.788325i	$-0.710948\pi$
$17$	−5.91891	−	0.892132i	−1.43555	−	0.216374i	−0.820287	+	0.571952i	$0.806186\pi$
$18$	2.17073	+	3.75982i	0.511647	+	0.886198i
$19$	−0.151312	+	0.262080i	−0.0347133	+	0.0601253i	−0.882860	−	0.469636i	$-0.844385\pi$
$19$	−0.151312	+	0.262080i	−0.0347133	+	0.0601253i	0.848147	+	0.529761i	$0.177718\pi$
$20$	2.35296	−	2.95051i	0.526137	−	0.659755i
$21$	−7.87075	−	0.441929i	−1.71754	−	0.0964368i
$22$	0.719246	+	0.901906i	0.153344	+	0.192287i
$23$	3.12319	−	0.470745i	0.651230	−	0.0981571i	0.184885	−	0.982760i	$-0.440809\pi$
$23$	3.12319	−	0.470745i	0.651230	−	0.0981571i	0.466345	+	0.884603i	$0.345571\pi$
$24$	6.28145	+	4.28262i	1.28219	+	0.874186i
$25$	1.43160	+	0.976047i	0.286320	+	0.195209i
$26$	0.730381	−	0.110087i	0.143240	−	0.0215899i
$27$	5.34599	+	6.70366i	1.02884	+	1.29012i
$28$	−3.55511	+	1.47262i	−0.671853	+	0.278299i
$29$	2.28797	−	2.86903i	0.424866	−	0.532765i	−0.522618	−	0.852567i	$-0.675045\pi$
$29$	2.28797	−	2.86903i	0.424866	−	0.532765i	0.947485	+	0.319801i	$0.103616\pi$
$30$	−2.85524	+	4.94541i	−0.521292	+	0.902905i
$31$	3.43290	+	5.94596i	0.616568	+	1.06793i	0.990107	+	0.140312i	$0.0448107\pi$
$31$	3.43290	+	5.94596i	0.616568	+	1.06793i	−0.373540	+	0.927614i	$0.621856\pi$
$32$	5.79415	+	0.873327i	1.02427	+	0.154384i
$33$	3.41119	+	3.16512i	0.593812	+	0.550977i
$34$	3.98343	−	1.91832i	0.683152	−	0.328989i
$35$	−3.09383	−	6.12837i	−0.522952	−	1.03588i
$36$	7.70211	+	3.70914i	1.28368	+	0.618190i
$37$	1.53383	+	3.90813i	0.252159	+	0.642492i	0.999766	−	0.0216505i	$-0.00689212\pi$
$37$	1.53383	+	3.90813i	0.252159	+	0.642492i	−0.747606	+	0.664142i	$0.768797\pi$
$38$	−0.0167042	−	0.222902i	−0.00270978	−	0.0361596i
$39$	2.84718	−	0.878238i	0.455913	−	0.140631i
$40$	−0.494758	+	6.60208i	−0.0782281	+	1.04388i
$41$	−0.928580	−	4.06838i	−0.145020	−	0.635373i	−0.994225	−	0.107311i	$-0.965776\pi$
$41$	−0.928580	−	4.06838i	−0.145020	−	0.635373i	0.849206	−	0.528062i	$-0.177081\pi$
$42$	4.98729	−	3.00521i	0.769555	−	0.463713i
$43$	0.421199	−	1.84540i	0.0642323	−	0.281420i	−0.932604	−	0.360901i	$-0.882469\pi$
$43$	0.421199	−	1.84540i	0.0642323	−	0.281420i	0.996836	+	0.0794810i	$0.0253263\pi$
$44$	2.17058	+	0.669534i	0.327227	+	0.100936i
$45$	−5.57187	+	14.1969i	−0.830605	+	2.11635i
$46$	−1.71017	+	1.58680i	−0.252150	+	0.233961i
$47$	−0.766145	+	0.522349i	−0.111754	+	0.0761924i	−0.617907	−	0.786251i	$-0.712019\pi$
$47$	−0.766145	+	0.522349i	−0.111754	+	0.0761924i	0.506154	+	0.862443i	$0.331067\pi$
$48$	3.05164			0.440467
$49$	−0.261591	+	6.99511i	−0.0373702	+	0.999301i
$50$	−1.27980			−0.180992
$51$	14.7359	−	10.0467i	2.06343	−	1.40683i
$52$	1.06617	−	0.989259i	0.147851	−	0.137186i
$53$	−3.77304	+	9.61355i	−0.518267	+	1.32052i	0.397053	+	0.917796i	$0.370033\pi$
$53$	−3.77304	+	9.61355i	−0.518267	+	1.32052i	−0.915320	+	0.402727i	$0.868062\pi$
$54$	−6.05188	−	1.86676i	−0.823557	−	0.254034i
$55$	−0.901748	+	3.95082i	−0.121592	+	0.532728i
$56$	3.69781	−	5.64791i	0.494141	−	0.754733i
$57$	−0.200643	−	0.879076i	−0.0265759	−	0.116436i
$58$	−0.202556	+	2.70292i	−0.0265969	+	0.354911i
$59$	2.99966	−	0.925274i	0.390523	−	0.120460i	−0.0932743	−	0.995640i	$-0.529733\pi$
$59$	2.99966	−	0.925274i	0.390523	−	0.120460i	0.483797	+	0.875180i	$0.339257\pi$
$60$	0.840293	+	11.2129i	0.108481	+	1.44758i
$61$	−3.37912	−	8.60985i	−0.432652	−	1.10238i	−0.966470	−	0.256780i	$-0.917339\pi$
$61$	−3.37912	−	8.60985i	−0.432652	−	1.10238i	0.533818	−	0.845599i	$-0.320757\pi$
$62$	−4.56908	−	2.20035i	−0.580274	−	0.279445i
$63$	11.9747	−	9.92166i	1.50867	−	1.25001i
$64$	−2.05393	+	0.989120i	−0.256741	+	0.123640i
$65$	1.90208	+	1.76487i	0.235924	+	0.218905i
$66$	−3.39876	−	0.512281i	−0.418359	−	0.0630575i
$67$	−6.59946	−	11.4306i	−0.806252	−	1.39647i	−0.915442	−	0.402449i	$-0.868159\pi$
$67$	−6.59946	−	11.4306i	−0.806252	−	1.39647i	0.109190	−	0.994021i	$-0.465174\pi$
$68$	4.35292	−	7.53948i	0.527869	−	0.914296i
$69$	−5.86754	+	7.35767i	−0.706369	+	0.885759i
$70$	4.43805	+	2.45276i	0.530448	+	0.293161i
$71$	−2.25638	−	2.82941i	−0.267783	−	0.335789i	0.629700	−	0.776838i	$-0.283178\pi$
$71$	−2.25638	−	2.82941i	−0.267783	−	0.335789i	−0.897483	+	0.441050i	$0.854606\pi$
$72$	−14.8298	+	2.23523i	−1.74770	+	0.263424i
$73$	8.48581	+	5.78553i	0.993189	+	0.677145i	0.946815	−	0.321779i	$-0.104281\pi$
$73$	8.48581	+	5.78553i	0.993189	+	0.677145i	0.0463743	+	0.998924i	$0.485233\pi$
$74$	−2.56219	−	1.74687i	−0.297848	−	0.203070i
$75$	−5.10491	+	0.769442i	−0.589464	+	0.0888475i
$76$	−0.274425	−	0.344118i	−0.0314787	−	0.0394730i
$77$	2.75337	−	3.08109i	0.313776	−	0.351123i
$78$	−1.37217	+	1.72065i	−0.155368	+	0.194825i
$79$	1.75973	−	3.04795i	0.197986	−	0.342921i	−0.749890	−	0.661563i	$-0.769893\pi$
$79$	1.75973	−	3.04795i	0.197986	−	0.342921i	0.947875	+	0.318642i	$0.103227\pi$
$80$	1.32876	+	2.30148i	0.148560	+	0.257313i
$81$	−7.82603	−	1.17958i	−0.869559	−	0.131065i
$82$	2.25949	+	2.09650i	0.249519	+	0.231520i
$83$	−13.4047	+	6.45535i	−1.47135	+	0.708567i	−0.986153	−	0.165836i	$-0.946968\pi$
$83$	−13.4047	+	6.45535i	−1.47135	+	0.708567i	−0.485201	+	0.874403i	$0.661254\pi$
$84$	4.78053	−	10.4213i	0.521598	−	1.13705i
$85$	13.9934	+	6.73886i	1.51780	+	0.730932i
$86$	0.510791	+	1.30147i	0.0550800	+	0.140342i
$87$	0.817086	+	10.9033i	0.0876009	+	1.16895i
$88$	−3.80792	+	1.17459i	−0.405926	+	0.125211i
$89$	1.22833	−	16.3909i	0.130203	−	1.73744i	−0.424535	−	0.905412i	$-0.639562\pi$
$89$	1.22833	−	16.3909i	0.130203	−	1.73744i	0.554738	−	0.832025i	$-0.312819\pi$
$90$	−2.50669	−	10.9825i	−0.264229	−	1.15766i
$91$	−0.827014	−	2.51318i	−0.0866946	−	0.263452i
$92$	−1.02221	+	4.47857i	−0.106572	+	0.466924i
$93$	−19.5482	−	6.02981i	−2.02705	−	0.625262i
$94$	0.250226	−	0.637565i	0.0258088	−	0.0657598i
$95$	0.575614	−	0.534092i	0.0590568	−	0.0547967i
$96$	−14.4253	+	9.83498i	−1.47227	+	1.00378i
$97$	−5.41958			−0.550274			−0.275137	−	0.961405i	$-0.588723\pi$
$97$	−5.41958			−0.550274			−0.275137	+	0.961405i	$0.588723\pi$
$98$	−2.75092	−	4.37786i	−0.277885	−	0.442231i
$99$	−9.17972			−0.922596
$100$	−2.08215	+	1.41959i	−0.208215	+	0.141959i
$101$	8.64501	−	8.02140i	0.860210	−	0.798159i	−0.120686	−	0.992691i	$-0.538509\pi$
$101$	8.64501	−	8.02140i	0.860210	−	0.798159i	0.980896	+	0.194532i	$0.0623188\pi$
$102$	−4.81278	+	12.2628i	−0.476537	+	1.21420i
$103$	11.9567	+	3.68817i	1.17813	+	0.363406i	0.821154	−	0.570706i	$-0.193331\pi$
$103$	11.9567	+	3.68817i	1.17813	+	0.363406i	0.356979	+	0.934112i	$0.383807\pi$
$104$	−0.567772	+	2.48757i	−0.0556747	+	0.243927i
$105$	19.1772	+	7.11540i	1.87151	+	0.694392i
$106$	−1.69743	−	7.43692i	−0.164869	−	0.722338i
$107$	1.18558	−	15.8205i	0.114615	−	1.52943i	−0.582716	−	0.812676i	$-0.698010\pi$
$107$	1.18558	−	15.8205i	0.114615	−	1.52943i	0.697331	−	0.716749i	$-0.254371\pi$
$108$	−11.9166	+	3.67580i	−1.14668	+	0.353704i
$109$	−0.965705	−	12.8864i	−0.0924978	−	1.23430i	−0.829539	−	0.558449i	$-0.811397\pi$
$109$	−0.965705	−	12.8864i	−0.0924978	−	1.23430i	0.737041	−	0.675848i	$-0.236222\pi$
$110$	−1.09355	−	2.78633i	−0.104266	−	0.265666i
$111$	−11.2704	−	5.42752i	−1.06974	−	0.515158i
$112$	−0.0506980	−	2.70929i	−0.00479051	−	0.256004i
$113$	7.17696	−	3.45624i	0.675152	−	0.325136i	−0.0647011	−	0.997905i	$-0.520609\pi$
$113$	7.17696	−	3.45624i	0.675152	−	0.325136i	0.739853	+	0.672769i	$0.234895\pi$
$114$	0.488221	+	0.453003i	0.0457261	+	0.0424276i
$115$	−8.10386	−	1.22146i	−0.755689	−	0.113902i
$116$	2.66860	+	4.62214i	0.247773	+	0.429155i
$117$	−2.93886	+	5.09025i	−0.271698	+	0.470594i
$118$	−1.44566	+	1.81280i	−0.133084	+	0.166882i
$119$	−9.16446	−	12.9158i	−0.840105	−	1.18399i
$120$	−12.2992	−	15.4227i	−1.12276	−	1.40789i
$121$	8.46522	−	1.27593i	0.769565	−	0.115993i
$122$	5.64467	+	3.84847i	0.511044	+	0.348424i
$123$	10.2732	+	7.00413i	0.926301	+	0.631541i
$124$	−9.87426	+	1.48831i	−0.886735	+	0.133654i
$125$	5.28587	+	6.62827i	0.472782	+	0.592850i
$126$	−3.17974	+	11.0376i	−0.283274	+	0.983304i
$127$	10.8084	−	13.5533i	0.959092	−	1.20266i	−0.0201149	−	0.999798i	$-0.506403\pi$
$127$	10.8084	−	13.5533i	0.959092	−	1.20266i	0.979207	−	0.202865i	$-0.0650254\pi$
$128$	−5.01767	+	8.69086i	−0.443504	+	0.768171i
$129$	2.81993	+	4.88425i	0.248281	+	0.430035i
$130$	−1.89515	−	0.285648i	−0.166216	−	0.0250530i
$131$	9.66662	+	8.96932i	0.844577	+	0.783653i	0.978262	−	0.207371i	$-0.0664907\pi$
$131$	9.66662	+	8.96932i	0.844577	+	0.783653i	−0.133685	+	0.991024i	$0.542681\pi$
$132$	−6.09778	+	2.93654i	−0.530744	+	0.255593i
$133$	−0.777123	+	0.192739i	−0.0673851	+	0.0167125i
$134$	8.78367	+	4.22999i	0.758793	+	0.365416i
$135$	−8.12814	−	20.7102i	−0.699559	−	1.78245i
$136$	1.14135	+	15.2302i	0.0978699	+	1.30598i
$137$	13.6472	−	4.20961i	1.16596	−	0.359652i	0.349436	−	0.936960i	$-0.386373\pi$
$137$	13.6472	−	4.20961i	1.16596	−	0.359652i	0.816526	+	0.577309i	$0.195897\pi$
$138$	0.519458	−	6.93168i	0.0442192	−	0.590064i
$139$	−4.35517	−	19.0813i	−0.369401	−	1.61845i	−0.728426	−	0.685124i	$-0.759748\pi$
$139$	−4.35517	−	19.0813i	−0.369401	−	1.61845i	0.359025	−	0.933328i	$-0.383109\pi$
$140$	9.94105	−	0.932309i	0.840172	−	0.0787945i
$141$	0.614791	−	2.69357i	0.0517747	−	0.226840i
$142$	2.55431	+	0.787900i	0.214353	+	0.0661191i
$143$	−0.570583	+	1.45382i	−0.0477146	+	0.121575i
$144$	−4.41292	+	4.09460i	−0.367744	+	0.341216i
$145$	−7.86721	+	5.36378i	−0.653337	+	0.445437i
$146$	−7.58605			−0.627826
$147$	−13.6050	−	15.8086i	−1.12212	−	1.30387i
$148$	−6.10617			−0.501924
$149$	−8.26236	+	5.63318i	−0.676879	+	0.461488i	−0.852333	−	0.522999i	$-0.824813\pi$
$149$	−8.26236	+	5.63318i	−0.676879	+	0.461488i	0.175454	+	0.984488i	$0.443861\pi$
$150$	2.79530	−	2.59366i	0.228235	−	0.211772i
$151$	−1.35944	+	3.46380i	−0.110630	+	0.281880i	−0.975457	−	0.220189i	$-0.929332\pi$
$151$	−1.35944	+	3.46380i	−0.110630	+	0.281880i	0.864827	+	0.502069i	$0.167428\pi$
$152$	0.737854	+	0.227598i	0.0598479	+	0.0184606i
$153$	−7.82887	+	34.3005i	−0.632927	+	2.77303i
$154$	−0.398346	+	3.02598i	−0.0320996	+	0.243841i
$155$	−3.96421	−	17.3683i	−0.318413	−	1.39506i
$156$	−0.323845	+	4.32141i	−0.0259283	+	0.345990i
$157$	−10.8507	+	3.34699i	−0.865977	+	0.267119i	−0.695748	−	0.718286i	$-0.744927\pi$
$157$	−10.8507	+	3.34699i	−0.865977	+	0.267119i	−0.170229	+	0.985405i	$0.554451\pi$
$158$	0.194268	+	2.59232i	0.0154551	+	0.206234i
$159$	−11.2420	−	28.6441i	−0.891546	−	2.27162i
$160$	−13.6984	−	6.59682i	−1.08296	−	0.521524i
$161$	6.62972	+	5.08706i	0.522495	+	0.400916i
$162$	5.26692	−	2.53642i	0.413808	−	0.199280i
$163$	6.24828	+	5.79755i	0.489403	+	0.454100i	0.885859	−	0.463954i	$-0.153570\pi$
$163$	6.24828	+	5.79755i	0.489403	+	0.454100i	−0.396456	+	0.918054i	$0.629760\pi$
$164$	6.00152	+	0.904584i	0.468640	+	0.0706361i
$165$	−6.03719	−	10.4567i	−0.469995	−	0.814055i
$166$	5.49470	−	9.51711i	0.426472	−	0.738671i
$167$	−7.38676	+	9.26271i	−0.571605	+	0.716770i	−0.980655	−	0.195742i	$-0.937289\pi$
$167$	−7.38676	+	9.26271i	−0.571605	+	0.716770i	0.409051	+	0.912512i	$0.365860\pi$
$168$	3.36946	+	19.8300i	0.259960	+	1.52992i
$169$	0.623490	+	0.781831i	0.0479608	+	0.0601409i
$170$	−11.3439	+	1.70982i	−0.870038	+	0.131137i
$171$	1.46966	+	1.00200i	0.112388	+	0.0766248i
$172$	2.27464	+	1.55083i	0.173440	+	0.118249i
$173$	10.6518	−	1.60551i	0.809845	−	0.122065i	0.268950	−	0.963154i	$-0.413324\pi$
$173$	10.6518	−	1.60551i	0.809845	−	0.122065i	0.540896	+	0.841090i	$0.318085\pi$
$174$	−5.03535	−	6.31413i	−0.381729	−	0.478673i
$175$	0.767931	+	4.51943i	0.0580502	+	0.341637i
$176$	−0.997316	+	1.25060i	−0.0751755	+	0.0942671i
$177$	−4.67659	+	8.10010i	−0.351514	+	0.608841i
$178$	6.07041	+	10.5143i	0.454996	+	0.788077i
$179$	6.74295	+	1.01634i	0.503992	+	0.0759645i	0.396117	−	0.918200i	$-0.370357\pi$
$179$	6.74295	+	1.01634i	0.503992	+	0.0759645i	0.107874	+	0.994165i	$0.465596\pi$
$180$	−16.2603	−	15.0873i	−1.21197	−	1.12454i
$181$	−22.3042	+	10.7411i	−1.65786	+	0.798382i	−0.658925	+	0.752209i	$0.728988\pi$
$181$	−22.3042	+	10.7411i	−1.65786	+	0.798382i	−0.998933	+	0.0461737i	$0.985297\pi$
$182$	1.55041	+	1.18965i	0.114924	+	0.0881825i
$183$	24.8294	+	11.9572i	1.83544	+	0.883901i
$184$	−2.94427	−	7.50189i	−0.217055	−	0.553046i
$185$	−0.814080	−	10.8631i	−0.0598523	−	0.798674i
$186$	14.4389	−	4.45381i	1.05871	−	0.326569i
$187$	−0.698611	+	9.32232i	−0.0510875	+	0.681716i
$188$	−0.300101	−	1.31483i	−0.0218871	−	0.0958937i
$189$	−2.96081	+	22.4914i	−0.215368	+	1.63601i
$190$	−0.129061	+	0.565454i	−0.00936308	+	0.0410223i
$191$	−6.24480	−	1.92627i	−0.451858	−	0.139380i	0.0604693	−	0.998170i	$-0.480740\pi$
$191$	−6.24480	−	1.92627i	−0.451858	−	0.139380i	−0.512327	+	0.858790i	$0.671216\pi$
$192$	2.48156	−	6.32291i	0.179091	−	0.456317i
$193$	−2.53435	+	2.35153i	−0.182426	+	0.169267i	−0.766100	−	0.642721i	$-0.777805\pi$
$193$	−2.53435	+	2.35153i	−0.182426	+	0.169267i	0.583674	+	0.811988i	$0.301615\pi$
$194$	3.30749	−	2.25501i	0.237464	−	0.161900i
$195$	−7.73115			−0.553639
$196$	−9.33157	−	4.07109i	−0.666541	−	0.290792i
$197$	0.775559			0.0552563			0.0276282	−	0.999618i	$-0.491205\pi$
$197$	0.775559			0.0552563			0.0276282	+	0.999618i	$0.491205\pi$
$198$	5.60225	−	3.81955i	0.398135	−	0.271444i
$199$	13.2492	−	12.2935i	0.939214	−	0.871464i	−0.0526693	−	0.998612i	$-0.516773\pi$
$199$	13.2492	−	12.2935i	0.939214	−	0.871464i	0.991884	+	0.127148i	$0.0405825\pi$
$200$	1.61517	−	4.11538i	0.114210	−	0.291001i
$201$	37.5797	+	11.5918i	2.65066	+	0.817622i
$202$	−1.93834	+	8.49241i	−0.136381	+	0.597524i
$203$	9.66650	−	0.906561i	0.678455	−	0.0636281i
$204$	5.77208	+	25.2891i	0.404126	+	1.77059i
$205$	−0.809166	+	10.7976i	−0.0565146	+	0.754135i
$206$	−8.83163	+	2.72420i	−0.615329	+	0.189804i
$207$	−1.38733	−	18.5127i	−0.0964263	−	1.28672i
$208$	0.374181	+	0.953397i	0.0259448	+	0.0661062i
$209$	0.425827	+	0.205068i	0.0294551	+	0.0141848i
$210$	−14.6642	+	3.63695i	−1.01193	+	0.250973i
$211$	−17.2538	+	8.30899i	−1.18780	+	0.572014i	−0.920174	−	0.391509i	$-0.871953\pi$
$211$	−17.2538	+	8.30899i	−1.18780	+	0.572014i	−0.267626	+	0.963523i	$0.586239\pi$
$212$	−11.0108	−	10.2165i	−0.756225	−	0.701674i
$213$	10.6624	+	1.60710i	0.730575	+	0.110117i
$214$	5.85914	+	10.1483i	0.400523	+	0.693726i
$215$	−2.45573	+	4.25345i	−0.167479	+	0.290083i
$216$	13.6405	−	17.1047i	0.928122	−	1.16383i
$217$	−5.02859	+	17.4553i	−0.341363	+	1.18494i
$218$	5.95122	+	7.46260i	0.403068	+	0.505431i
$219$	−30.2594	+	4.56087i	−2.04474	+	0.308195i
$220$	−4.86980	−	3.32017i	−0.328322	−	0.223846i
$221$	4.94567	+	3.37190i	0.332682	+	0.226819i
$222$	9.13646	−	1.37710i	0.613199	−	0.0924249i
$223$	11.3291	+	14.2062i	0.758651	+	0.951318i	0.999816	−	0.0191656i	$-0.00610098\pi$
$223$	11.3291	+	14.2062i	0.758651	+	0.951318i	−0.241165	+	0.970484i	$0.577530\pi$
$224$	8.97129	+	12.6436i	0.599420	+	0.844784i
$225$	6.34971	−	7.96228i	0.423314	−	0.530819i
$226$	−2.94190	+	5.09553i	−0.195693	+	0.338950i
$227$	−13.3759	−	23.1677i	−0.887789	−	1.53770i	−0.842483	−	0.538722i	$-0.818907\pi$
$227$	−13.3759	−	23.1677i	−0.887789	−	1.53770i	−0.0453054	−	0.998973i	$-0.514426\pi$
$228$	1.29678	+	0.195458i	0.0858815	+	0.0129445i
$229$	−16.5348	−	15.3420i	−1.09265	−	1.01383i	−0.999835	−	0.0181469i	$-0.994223\pi$
$229$	−16.5348	−	15.3420i	−1.09265	−	1.01383i	−0.0928140	−	0.995683i	$-0.529586\pi$
$230$	5.45390	−	2.62646i	0.359620	−	0.173184i
$231$	0.230345	+	12.3096i	0.0151556	+	0.809913i
$232$	−8.43597	−	4.06255i	−0.553848	−	0.266719i
$233$	8.64020	+	22.0149i	0.566038	+	1.44224i	0.871670	+	0.490093i	$0.163037\pi$
$233$	8.64020	+	22.0149i	0.566038	+	1.44224i	−0.305632	+	0.952150i	$0.598868\pi$
$234$	−0.324438	−	4.32933i	−0.0212092	−	0.283017i
$235$	2.29913	−	0.709187i	0.149979	−	0.0462623i
$236$	−0.341189	+	4.55285i	−0.0222095	+	0.296366i
$237$	2.33345	+	10.2235i	0.151574	+	0.664089i
$238$	10.9670	+	4.06913i	0.710887	+	0.263763i
$239$	2.92405	−	12.8111i	0.189141	−	0.828680i	−0.787930	−	0.615765i	$-0.788847\pi$
$239$	2.92405	−	12.8111i	0.189141	−	0.828680i	0.977071	−	0.212915i	$-0.0682958\pi$
$240$	−7.56643	−	2.33393i	−0.488411	−	0.150655i
$241$	4.65298	−	11.8556i	0.299725	−	0.763686i	−0.699091	−	0.715032i	$-0.746412\pi$
$241$	4.65298	−	11.8556i	0.299725	−	0.763686i	0.998816	−	0.0486531i	$-0.0154929\pi$
$242$	−4.63531	+	4.30094i	−0.297969	+	0.276475i
$243$	−1.76939	+	1.20635i	−0.113506	+	0.0773874i
$244$	13.4523			0.861194
$245$	5.99856	−	17.1440i	0.383234	−	1.09529i
$246$	−9.18390			−0.585544
$247$	0.250040	−	0.170474i	0.0159096	−	0.0108470i
$248$	12.8419	−	11.9156i	0.815462	−	0.756638i
$249$	16.1955	−	41.2656i	1.02635	−	2.61510i
$250$	−5.98382	−	1.84576i	−0.378450	−	0.116736i
$251$	5.18320	−	22.7091i	0.327161	−	1.43338i	−0.497356	−	0.867547i	$-0.665696\pi$
$251$	5.18320	−	22.7091i	0.327161	−	1.43338i	0.824517	−	0.565838i	$-0.191447\pi$
$252$	7.06989	+	21.4844i	0.445361	+	1.35339i
$253$	−1.09766	−	4.80916i	−0.0690093	−	0.302349i
$254$	−0.956877	+	12.7686i	−0.0600398	+	0.801175i
$255$	−44.2209	+	13.6403i	−2.76922	+	0.854191i
$256$	−0.894653	−	11.9383i	−0.0559158	−	0.746145i
$257$	−7.34253	−	18.7085i	−0.458014	−	1.16700i	−0.954302	−	0.298843i	$-0.903399\pi$
$257$	−7.34253	−	18.7085i	−0.458014	−	1.16700i	0.496288	−	0.868158i	$-0.334696\pi$
$258$	−3.75323	−	1.80746i	−0.233666	−	0.112528i
$259$	−4.63140	+	10.0962i	−0.287781	+	0.627345i
$260$	−3.40012	+	1.63741i	−0.210867	+	0.101548i
$261$	−15.8112	−	14.6707i	−0.978690	−	0.908091i
$262$	−9.63141	−	1.45170i	−0.595031	−	0.0896864i
$263$	6.20861	+	10.7536i	0.382840	+	0.663097i	0.991467	−	0.130359i	$-0.0416129\pi$
$263$	6.20861	+	10.7536i	0.382840	+	0.663097i	−0.608627	+	0.793456i	$0.708280\pi$
$264$	5.93669	−	10.2827i	0.365378	−	0.632854i
$265$	16.7077	−	20.9508i	1.02634	−	1.28700i
$266$	0.394072	−	0.440976i	0.0241621	−	0.0270379i
$267$	30.5352	+	38.2899i	1.86872	+	2.34330i
$268$	18.9824	−	2.86114i	1.15953	−	0.174772i
$269$	11.3787	+	7.75789i	0.693774	+	0.473007i	0.858155	−	0.513390i	$-0.171611\pi$
$269$	11.3787	+	7.75789i	0.693774	+	0.473007i	−0.164382	+	0.986397i	$0.552563\pi$
$270$	13.5777	+	9.25712i	0.826312	+	0.563370i
$271$	18.0051	−	2.71384i	1.09373	−	0.164854i	0.422692	−	0.906273i	$-0.361085\pi$
$271$	18.0051	−	2.71384i	1.09373	−	0.164854i	0.671042	+	0.741420i	$0.265847\pi$
$272$	3.82236	+	4.79309i	0.231765	+	0.290624i
$273$	6.89956	+	3.81316i	0.417580	+	0.230783i
$274$	−6.57715	+	8.24749i	−0.397340	+	0.498249i
$275$	1.35303	−	2.34351i	0.0815905	−	0.141319i
$276$	−6.84365	−	11.8536i	−0.411939	−	0.713500i
$277$	−1.73372	−	0.261316i	−0.104169	−	0.0157009i	0.0967509	−	0.995309i	$-0.469155\pi$
$277$	−1.73372	−	0.261316i	−0.104169	−	0.0157009i	−0.200920	+	0.979608i	$0.564393\pi$
$278$	10.5973	+	9.83290i	0.635587	+	0.589738i
$279$	36.3589	−	17.5095i	2.17675	−	1.04827i
$280$	−13.4882	+	11.1756i	−0.806073	+	0.667872i
$281$	−17.9536	−	8.64598i	−1.07102	−	0.515776i	−0.186585	−	0.982439i	$-0.559742\pi$
$281$	−17.9536	−	8.64598i	−1.07102	−	0.515776i	−0.884435	+	0.466663i	$0.845456\pi$
$282$	0.745560	+	1.89966i	0.0443974	+	0.113123i
$283$	−1.67910	−	22.4061i	−0.0998124	−	1.33190i	−0.792148	−	0.610328i	$-0.791037\pi$
$283$	−1.67910	−	22.4061i	−0.0998124	−	1.33190i	0.692336	−	0.721575i	$-0.256582\pi$
$284$	5.02964	−	1.55144i	0.298454	−	0.0920609i
$285$	−0.174841	+	2.33309i	−0.0103567	+	0.138200i
$286$	−0.256696	−	1.12466i	−0.0151788	−	0.0665025i
$287$	6.04770	−	9.23704i	0.356984	−	0.545245i
$288$	7.66385	−	33.5775i	0.451597	−	1.97858i
$289$	17.9928	+	5.55005i	1.05840	+	0.326474i
$290$	2.56946	−	6.54687i	0.150884	−	0.384446i
$291$	11.8372	−	10.9834i	0.693912	−	0.643856i
$292$	−12.3420	+	8.41461i	−0.722259	+	0.492428i
$293$	−28.9766			−1.69283			−0.846415	−	0.532524i	$-0.821244\pi$
$293$	−28.9766			−1.69283			−0.846415	+	0.532524i	$0.821244\pi$
$294$	14.8807	+	3.98693i	0.867859	+	0.232523i
$295$	−8.14521			−0.474233
$296$	8.85088	−	6.03443i	0.514447	−	0.350744i
$297$	9.81645	−	9.10833i	0.569608	−	0.528519i
$298$	2.69851	−	6.87570i	0.156321	−	0.398299i
$299$	−3.01814	−	0.930974i	−0.174544	−	0.0538396i
$300$	1.67081	−	7.32031i	0.0964645	−	0.422639i
$301$	4.28946	−	2.58471i	0.247241	−	0.148980i
$302$	−0.611590	−	2.67955i	−0.0351931	−	0.154191i
$303$	−2.62589	+	35.0401i	−0.150854	+	2.01300i
$304$	0.296176	−	0.0913582i	0.0169869	−	0.00523975i
$305$	1.79347	+	23.9322i	0.102694	+	1.37035i
$306$	−9.49412	−	24.1906i	−0.542743	−	1.38289i
$307$	−3.07170	−	1.47925i	−0.175311	−	0.0844254i	0.344170	−	0.938907i	$-0.388160\pi$
$307$	−3.07170	−	1.47925i	−0.175311	−	0.0844254i	−0.519481	+	0.854482i	$0.673875\pi$
$308$	2.70841	+	5.36492i	0.154326	+	0.305694i
$309$	−33.5900	+	16.1761i	−1.91087	+	0.920225i
$310$	9.64601	+	8.95019i	0.547857	+	0.508337i
$311$	−8.33329	−	1.25604i	−0.472537	−	0.0712235i	−0.0915434	−	0.995801i	$-0.529180\pi$
$311$	−8.33329	−	1.25604i	−0.472537	−	0.0712235i	−0.380994	+	0.924578i	$0.624418\pi$
$312$	−3.80123	−	6.58392i	−0.215202	−	0.372741i
$313$	9.55796	−	16.5549i	0.540248	−	0.935737i	−0.458641	−	0.888621i	$-0.651664\pi$
$313$	9.55796	−	16.5549i	0.540248	−	0.935737i	0.998889	−	0.0471157i	$-0.0150029\pi$
$314$	5.22937	−	6.55742i	0.295110	−	0.370057i
$315$	−37.2791	+	15.4419i	−2.10044	+	0.870055i
$316$	3.19152	+	4.00204i	0.179537	+	0.225132i
$317$	8.44992	−	1.27362i	0.474595	−	0.0715336i	0.0926103	−	0.995702i	$-0.470479\pi$
$317$	8.44992	−	1.27362i	0.474595	−	0.0715336i	0.381984	+	0.924169i	$0.375241\pi$
$318$	18.7792	+	12.8034i	1.05309	+	0.717981i
$319$	−4.73530	−	3.22848i	−0.265126	−	0.180760i
$320$	5.84913	−	0.881614i	0.326976	−	0.0492837i
$321$	29.4725	+	36.9573i	1.64499	+	2.06275i
$322$	−6.16268	−	0.346024i	−0.343433	−	0.0192831i
$323$	1.12941	−	1.41624i	0.0628421	−	0.0788015i
$324$	5.75546	−	9.96875i	0.319748	−	0.553820i
$325$	−0.866334	−	1.50054i	−0.0480556	−	0.0832347i
$326$	−6.22552	−	0.938346i	−0.344799	−	0.0519702i
$327$	28.2250	+	26.1890i	1.56085	+	1.44826i
$328$	−9.59316	+	4.61982i	−0.529694	+	0.255087i
$329$	−2.40161	−	0.501071i	−0.132405	−	0.0276249i
$330$	8.03531	+	3.86960i	0.442329	+	0.213014i
$331$	−3.64648	−	9.29107i	−0.200428	−	0.510683i	0.794954	−	0.606669i	$-0.207495\pi$
$331$	−3.64648	−	9.29107i	−0.200428	−	0.510683i	−0.995383	+	0.0959861i	$0.969400\pi$
$332$	−1.61709	−	21.5785i	−0.0887491	−	1.18427i
$333$	23.5804	−	7.27358i	1.29220	−	0.398589i
$334$	0.653955	−	8.72643i	0.0357828	−	0.477489i
$335$	7.62084	+	33.3891i	0.416371	+	1.82424i
$336$	5.60141	+	5.81480i	0.305582	+	0.317223i
$337$	1.30350	−	5.71099i	0.0710059	−	0.311097i	−0.926936	−	0.375219i	$-0.877567\pi$
$337$	1.30350	−	5.71099i	0.0710059	−	0.311097i	0.997942	+	0.0641218i	$0.0204246\pi$
$338$	−0.705816	−	0.217715i	−0.0383913	−	0.0118422i
$339$	−8.67122	+	22.0939i	−0.470956	+	1.19998i
$340$	−16.5592	+	15.3647i	−0.898048	+	0.833266i
$341$	8.85967	−	6.04042i	0.479778	−	0.327107i
$342$	−1.31383			−0.0710439
$343$	−13.8091	+	12.3413i	−0.745621	+	0.666370i
$344$	−4.82970			−0.260400
$345$	20.1756	−	13.7555i	1.08622	−	0.740570i
$346$	−5.83264	+	5.41190i	−0.313565	+	0.290946i
$347$	1.83481	−	4.67502i	0.0984979	−	0.250968i	−0.873128	−	0.487491i	$-0.837912\pi$
$347$	1.83481	−	4.67502i	0.0984979	−	0.250968i	0.971626	+	0.236522i	$0.0760076\pi$
$348$	−15.1959	−	4.68732i	−0.814587	−	0.251267i
$349$	−4.38643	+	19.2182i	−0.234800	+	1.02873i	0.710799	+	0.703395i	$0.248333\pi$
$349$	−4.38643	+	19.2182i	−0.234800	+	1.02873i	−0.945600	+	0.325333i	$0.894524\pi$
$350$	−2.34913	−	2.43862i	−0.125566	−	0.130350i
$351$	−1.90796	−	8.35933i	−0.101840	−	0.446188i
$352$	0.683886	−	9.12582i	0.0364512	−	0.486408i
$353$	−18.3351	+	5.65563i	−0.975880	+	0.301019i	−0.741371	−	0.671095i	$-0.765824\pi$
$353$	−18.3351	+	5.65563i	−0.975880	+	0.301019i	−0.234508	+	0.972114i	$0.575348\pi$
$354$	−0.516277	−	6.88924i	−0.0274398	−	0.366159i
$355$	3.43063	+	8.74111i	0.182079	+	0.463930i
$356$	21.5388	+	10.3725i	1.14155	+	0.549743i
$357$	46.1920	+	9.63748i	2.44474	+	0.510070i
$358$	−4.53801	+	2.18539i	−0.239841	+	0.115501i
$359$	−24.0363	−	22.3024i	−1.26859	−	1.17708i	−0.975259	−	0.221064i	$-0.929047\pi$
$359$	−24.0363	−	22.3024i	−1.26859	−	1.17708i	−0.293327	−	0.956012i	$-0.594763\pi$
$360$	38.4794	+	5.79983i	2.02804	+	0.305678i
$361$	9.45421	+	16.3752i	0.497590	+	0.861851i
$362$	9.14270	−	15.8356i	0.480530	−	0.832302i
$363$	−15.9036	+	19.9425i	−0.834724	+	1.04671i
$364$	3.84199	+	0.215721i	0.201375	+	0.0113069i
$365$	−16.6154	−	20.8350i	−0.869690	−	1.09056i
$366$	−20.1282	+	3.03384i	−1.05212	+	0.158581i
$367$	−9.16481	−	6.24846i	−0.478399	−	0.326167i	0.299997	−	0.953940i	$-0.403014\pi$
$367$	−9.16481	−	6.24846i	−0.478399	−	0.326167i	−0.778396	+	0.627773i	$0.783967\pi$
$368$	−2.67279	−	1.82228i	−0.139329	−	0.0949928i
$369$	−24.2538	+	3.65567i	−1.26260	+	0.190306i
$370$	5.01682	+	6.29089i	0.260812	+	0.327048i
$371$	−25.2438	+	10.4567i	−1.31060	+	0.542882i
$372$	18.5508	−	23.2620i	0.961814	−	1.20608i
$373$	10.5169	−	18.2158i	0.544543	−	0.943177i	−0.454092	−	0.890955i	$-0.650036\pi$
$373$	10.5169	−	18.2158i	0.544543	−	0.943177i	0.998636	−	0.0522220i	$-0.0166303\pi$
$374$	−3.45253	−	5.97996i	−0.178526	−	0.309217i
$375$	−24.9781	−	3.76484i	−1.28986	−	0.194416i
$376$	1.73438	+	1.60927i	0.0894437	+	0.0829916i
$377$	−3.30622	+	1.59219i	−0.170279	+	0.0820020i
$378$	−7.55143	−	14.9582i	−0.388404	−	0.769365i
$379$	4.62209	+	2.22588i	0.237421	+	0.114336i	0.548811	−	0.835946i	$-0.315080\pi$
$379$	4.62209	+	2.22588i	0.237421	+	0.114336i	−0.311391	+	0.950282i	$0.600795\pi$
$380$	0.417240	+	1.06311i	0.0214040	+	0.0545364i
$381$	3.85993	+	51.5071i	0.197750	+	2.63879i
$382$	4.61260	−	1.42280i	0.236001	−	0.0727968i
$383$	−0.425991	+	5.68446i	−0.0217671	+	0.290462i	0.975688	+	0.219164i	$0.0703331\pi$
$383$	−0.425991	+	5.68446i	−0.0217671	+	0.290462i	−0.997455	+	0.0712978i	$0.977286\pi$
$384$	−6.65355	−	29.1511i	−0.339538	−	1.48761i
$385$	−9.18333	+	5.53363i	−0.468026	+	0.282020i
$386$	0.568238	−	2.48961i	0.0289225	−	0.126718i
$387$	−10.6314	−	3.27935i	−0.540423	−	0.166698i
$388$	2.87975	−	7.33748i	0.146197	−	0.372504i
$389$	−2.59399	+	2.40687i	−0.131521	+	0.122033i	−0.743191	−	0.669080i	$-0.766689\pi$
$389$	−2.59399	+	2.40687i	−0.131521	+	0.122033i	0.611670	+	0.791113i	$0.290498\pi$
$390$	4.71821	−	3.21682i	0.238916	−	0.162890i
$391$	−18.9058			−0.956109
$392$	17.5494	−	3.32090i	0.886377	−	0.167731i
$393$	−39.2908			−1.98196
$394$	−0.473313	+	0.322699i	−0.0238452	+	0.0162574i
$395$	−6.69431	+	6.21141i	−0.336827	+	0.312530i
$396$	4.87774	−	12.4283i	0.245116	−	0.624545i
$397$	21.0638	+	6.49732i	1.05716	+	0.326091i	0.774134	−	0.633021i	$-0.218185\pi$
$397$	21.0638	+	6.49732i	1.05716	+	0.326091i	0.283026	+	0.959112i	$0.408662\pi$
$398$	−2.97068	+	13.0154i	−0.148906	+	0.652402i
$399$	1.30676	−	1.99590i	0.0654198	−	0.0999198i
$400$	−0.394884	−	1.73010i	−0.0197442	−	0.0865050i
$401$	0.749784	−	10.0052i	0.0374424	−	0.499634i	−0.946684	−	0.322164i	$-0.895590\pi$
$401$	0.749784	−	10.0052i	0.0374424	−	0.499634i	0.984126	−	0.177470i	$-0.0567913\pi$
$402$	−27.7575	+	8.56206i	−1.38442	+	0.427037i
$403$	−0.513082	−	6.84661i	−0.0255585	−	0.341054i
$404$	6.26643	+	15.9666i	0.311766	+	0.794368i
$405$	18.5022	+	8.91018i	0.919380	+	0.442750i
$406$	−5.52212	+	4.57536i	−0.274058	+	0.227071i
$407$	5.90756	−	2.84493i	0.292827	−	0.141018i
$408$	−33.3586	−	30.9523i	−1.65150	−	1.53237i
$409$	−15.4573	−	2.32981i	−0.764313	−	0.115202i	−0.244695	−	0.969600i	$-0.578688\pi$
$409$	−15.4573	−	2.32981i	−0.764313	−	0.115202i	−0.519618	+	0.854398i	$0.673926\pi$
$410$	−3.99889	−	6.92629i	−0.197491	−	0.342065i
$411$	−21.2766	+	36.8521i	−1.04950	+	1.81778i
$412$	−11.3467	+	14.2283i	−0.559012	+	0.700979i
$413$	7.26908	+	4.01738i	0.357688	+	0.197682i
$414$	8.54953	+	10.7208i	0.420186	+	0.526897i
$415$	38.1735	−	5.75373i	1.87386	−	0.282440i
$416$	−4.84142	−	3.30083i	−0.237370	−	0.161836i
$417$	48.1827	+	32.8504i	2.35952	+	1.60869i
$418$	−0.345202	+	0.0520309i	−0.0168844	+	0.00254491i
$419$	−13.3791	−	16.7768i	−0.653611	−	0.819602i	0.339020	−	0.940779i	$-0.389905\pi$
$419$	−13.3791	−	16.7768i	−0.653611	−	0.819602i	−0.992631	+	0.121177i	$0.961333\pi$
$420$	−19.8235	+	22.1829i	−0.967286	+	1.08242i
$421$	−7.09132	+	8.89223i	−0.345610	+	0.433381i	−0.924008	−	0.382374i	$-0.875107\pi$
$421$	−7.09132	+	8.89223i	−0.345610	+	0.433381i	0.578398	+	0.815755i	$0.303678\pi$
$422$	7.07249	−	12.2499i	0.344284	−	0.596317i
$423$	2.72511	+	4.72003i	0.132500	+	0.229496i
$424$	26.0566	+	3.92741i	1.26542	+	0.190732i
$425$	−7.60273	−	7.05431i	−0.368787	−	0.342184i
$426$	−7.17580	+	3.45568i	−0.347669	+	0.167428i
$427$	10.2033	−	22.2425i	0.493771	−	1.07639i
$428$	20.7892	+	10.0115i	1.00488	+	0.483926i
$429$	−1.70008	−	4.33174i	−0.0820807	−	0.209138i
$430$	−0.271103	−	3.61761i	−0.0130737	−	0.174457i
$431$	−7.86562	+	2.42622i	−0.378874	+	0.116867i	−0.478342	−	0.878174i	$-0.658762\pi$
$431$	−7.86562	+	2.42622i	−0.378874	+	0.116867i	0.0994683	+	0.995041i	$0.468286\pi$
$432$	0.656263	−	8.75721i	0.0315744	−	0.421332i
$433$	3.36449	+	14.7408i	0.161687	+	0.708398i	0.989154	+	0.146883i	$0.0469241\pi$
$433$	3.36449	+	14.7408i	0.161687	+	0.708398i	−0.827467	+	0.561515i	$0.810219\pi$
$434$	−4.19403	−	12.7451i	−0.201320	−	0.611783i
$435$	6.31302	−	27.6591i	0.302686	−	1.32615i
$436$	17.9599	+	5.53989i	0.860123	+	0.265313i
$437$	−0.349203	+	0.889755i	−0.0167046	+	0.0425627i
$438$	16.5692	−	15.3739i	0.791706	−	0.734596i
$439$	29.7387	−	20.2755i	1.41935	−	0.967696i	0.421195	−	0.906970i	$-0.361611\pi$
$439$	29.7387	−	20.2755i	1.41935	−	0.967696i	0.998154	−	0.0607265i	$-0.0193417\pi$
$440$	10.3399			0.492937
$441$	40.8854	+	4.60581i	1.94693	+	0.219324i
$442$	−4.42127			−0.210298
$443$	−23.2480	+	15.8502i	−1.10455	+	0.753068i	−0.971263	−	0.238010i	$-0.923505\pi$
$443$	−23.2480	+	15.8502i	−1.10455	+	0.753068i	−0.133285	+	0.991078i	$0.542553\pi$
$444$	13.3369	−	12.3748i	0.632940	−	0.587282i
$445$	−15.5816	+	39.7013i	−0.738639	+	1.88202i
$446$	−12.8250	−	3.95598i	−0.607280	−	0.187321i
$447$	6.63010	−	29.0484i	0.313593	−	1.37394i
$448$	−5.65480	−	2.09812i	−0.267164	−	0.0991269i
$449$	−3.38583	−	14.8343i	−0.159787	−	0.700074i	−0.989816	−	0.142353i	$-0.954533\pi$
$449$	−3.38583	−	14.8343i	−0.159787	−	0.700074i	0.830028	−	0.557721i	$-0.188324\pi$
$450$	−0.562144	+	7.50129i	−0.0264997	+	0.353614i
$451$	−6.22777	+	1.92101i	−0.293254	+	0.0904570i
$452$	0.865799	+	11.5533i	0.0407238	+	0.543421i
$453$	−4.05052	−	10.3206i	−0.190310	−	0.484902i
$454$	17.8029	+	8.57341i	0.835530	+	0.402370i
$455$	0.128440	+	6.86383i	0.00602138	+	0.321781i
$456$	−2.07285	+	0.998230i	−0.0970699	+	0.0467464i
$457$	−17.5660	−	16.2988i	−0.821701	−	0.762427i	0.152453	−	0.988311i	$-0.451283\pi$
$457$	−17.5660	−	16.2988i	−0.821701	−	0.762427i	−0.974154	+	0.225883i	$0.927473\pi$
$458$	16.4746	+	2.48314i	0.769805	+	0.116029i
$459$	−25.6619	−	44.4477i	−1.19779	−	2.07464i
$460$	5.95979	−	10.3227i	0.277877	−	0.481296i
$461$	24.6819	−	30.9501i	1.14955	−	1.44149i	0.271814	−	0.962350i	$-0.412376\pi$
$461$	24.6819	−	30.9501i	1.14955	−	1.44149i	0.877737	−	0.479142i	$-0.159052\pi$
$462$	−5.26243	−	7.41654i	−0.244830	−	0.345049i
$463$	6.34628	+	7.95799i	0.294937	+	0.369839i	0.907116	−	0.420880i	$-0.138279\pi$
$463$	6.34628	+	7.95799i	0.294937	+	0.369839i	−0.612180	+	0.790719i	$0.709707\pi$
$464$	−3.71644	+	0.560163i	−0.172531	+	0.0260049i
$465$	43.8573	+	29.9014i	2.03383	+	1.38664i
$466$	−14.4331	−	9.84030i	−0.668599	−	0.455843i
$467$	5.60401	−	0.844668i	0.259322	−	0.0390866i	−0.0180942	−	0.999836i	$-0.505760\pi$
$467$	5.60401	−	0.844668i	0.259322	−	0.0390866i	0.277417	+	0.960750i	$0.410522\pi$
$468$	−5.33002	−	6.68364i	−0.246380	−	0.308951i
$469$	9.66703	−	33.5563i	0.446382	−	1.54949i
$470$	−1.10804	+	1.38944i	−0.0511102	+	0.0640901i
$471$	16.9166	−	29.3004i	0.779476	−	1.35009i
$472$	−4.00481	−	6.93654i	−0.184336	−	0.319280i
$473$	−2.92321	−	0.440602i	−0.134409	−	0.0202589i
$474$	−5.67793	−	5.26835i	−0.260796	−	0.241983i
$475$	−0.472420	+	0.227506i	−0.0216761	+	0.0104387i
$476$	22.3562	−	5.54467i	1.02469	−	0.254140i
$477$	54.6905	+	26.3375i	2.50410	+	1.20591i
$478$	3.54601	+	9.03508i	0.162191	+	0.413255i
$479$	−0.290630	−	3.87819i	−0.0132792	−	0.177199i	−0.999900	−	0.0141650i	$-0.995491\pi$
$479$	−0.290630	−	3.87819i	−0.0132792	−	0.177199i	0.986620	−	0.163034i	$-0.0521280\pi$
$480$	43.2888	−	13.3528i	1.97585	−	0.609471i
$481$	0.313742	−	4.18660i	0.0143054	−	0.190893i
$482$	2.09330	+	9.17134i	0.0953471	+	0.417743i
$483$	−24.7899	+	2.32489i	−1.12798	+	0.105786i
$484$	−2.77063	+	12.1389i	−0.125938	+	0.551769i
$485$	13.4376	+	4.14496i	0.610171	+	0.188213i
$486$	0.577889	−	1.47244i	0.0262136	−	0.0667911i
$487$	−16.3882	+	15.2060i	−0.742620	+	0.689050i	−0.957772	−	0.287530i	$-0.907166\pi$
$487$	−16.3882	+	15.2060i	−0.742620	+	0.689050i	0.215152	+	0.976581i	$0.430975\pi$
$488$	−19.4991	+	13.2942i	−0.882681	+	0.601802i
$489$	−25.3966			−1.14848
$490$	3.47256	+	12.9587i	0.156874	+	0.585413i
$491$	7.48648			0.337860			0.168930	−	0.985628i	$-0.445969\pi$
$491$	7.48648			0.337860			0.168930	+	0.985628i	$0.445969\pi$
$492$	−14.9416	+	10.1870i	−0.673617	+	0.459264i
$493$	−16.1019	+	14.9403i	−0.725191	+	0.672879i
$494$	−0.0816638	+	0.208076i	−0.00367423	+	0.00936178i
$495$	22.7608	+	7.02077i	1.02302	+	0.315560i
$496$	1.56475	−	6.85563i	0.0702594	−	0.307827i
$497$	1.24967	−	9.49293i	0.0560552	−	0.425816i
$498$	7.28611	+	31.9225i	0.326499	+	1.43048i
$499$	−0.958334	+	12.7881i	−0.0429009	+	0.572473i	0.933790	+	0.357822i	$0.116481\pi$
$499$	−0.958334	+	12.7881i	−0.0429009	+	0.572473i	−0.976691	+	0.214651i	$0.931139\pi$
$500$	−11.7826	+	3.63445i	−0.526934	+	0.162538i
$501$	−2.63798	−	35.2014i	−0.117856	−	1.57268i
$502$	6.28569	+	16.0157i	0.280544	+	0.714815i
$503$	−21.6192	−	10.4112i	−0.963951	−	0.464214i	−0.115395	−	0.993320i	$-0.536813\pi$
$503$	−21.6192	−	10.4112i	−0.963951	−	0.464214i	−0.848556	+	0.529105i	$0.822528\pi$
$504$	−31.4798	−	24.1547i	−1.40222	−	1.07594i
$505$	−27.5698	+	13.2769i	−1.22684	+	0.590816i
$506$	2.67091	+	2.47824i	0.118736	+	0.110171i
$507$	−2.94627	−	0.444079i	−0.130848	−	0.0197222i
$508$	12.6065	+	21.8351i	0.559322	+	0.968774i
$509$	−0.406402	+	0.703910i	−0.0180135	+	0.0312002i	−0.874892	−	0.484319i	$-0.839068\pi$
$509$	−0.406402	+	0.703910i	−0.0180135	+	0.0312002i	0.856878	+	0.515519i	$0.172401\pi$
$510$	21.3118	−	26.7242i	0.943704	−	1.18337i
$511$	4.55192	+	26.7890i	0.201365	+	1.18507i
$512$	−7.00050	−	8.77835i	−0.309381	−	0.387952i
$513$	−2.56581	+	0.386733i	−0.113283	+	0.0170747i
$514$	12.2654	+	8.36238i	0.541002	+	0.368849i
$515$	−26.8255	−	18.2893i	−1.18207	−	0.805925i
$516$	−8.11111	+	1.22255i	−0.357072	+	0.0538199i
$517$	0.902933	+	1.13224i	0.0397109	+	0.0497960i
$518$	−1.37440	−	8.08861i	−0.0603875	−	0.355393i
$519$	−20.0117	+	25.0938i	−0.878414	+	1.10150i
$520$	3.31030	−	5.73360i	0.145166	−	0.251435i
$521$	−0.819090	−	1.41871i	−0.0358850	−	0.0621546i	0.847525	−	0.530755i	$-0.178092\pi$
$521$	−0.819090	−	1.41871i	−0.0358850	−	0.0621546i	−0.883410	+	0.468601i	$0.844758\pi$
$522$	15.7536	+	2.37448i	0.689517	+	0.103928i
$523$	13.7925	+	12.7976i	0.603105	+	0.559600i	0.921510	−	0.388355i	$-0.126957\pi$
$523$	13.7925	+	12.7976i	0.603105	+	0.559600i	−0.318405	+	0.947955i	$0.603147\pi$
$524$	−17.2799	+	8.32155i	−0.754875	+	0.363529i
$525$	−10.8364	−	8.31489i	−0.472940	−	0.362892i
$526$	−8.26346	−	3.97947i	−0.360304	−	0.173513i
$527$	−15.0145	−	38.2562i	−0.654040	−	1.66647i
$528$	−0.356164	−	4.75268i	−0.0155000	−	0.206834i
$529$	−12.4455	+	3.83892i	−0.541107	+	0.166909i
$530$	−1.47914	+	19.7378i	−0.0642498	+	0.857355i
$531$	−4.10571	−	17.9883i	−0.178173	−	0.780626i
$532$	0.151987	−	1.15455i	0.00658947	−	0.0500560i
$533$	−0.928580	+	4.06838i	−0.0402213	+	0.176221i
$534$	−34.5670	−	10.6625i	−1.49586	−	0.461412i
$535$	−15.0393	+	38.3196i	−0.650207	+	1.65670i
$536$	−24.6875	+	22.9066i	−1.06634	+	0.989415i
$537$	−16.7874	+	11.4455i	−0.724431	+	0.493909i
$538$	−10.1722			−0.438556
$539$	10.9248	−	0.409008i	0.470565	−	0.0176172i
$540$	32.3581			1.39247
$541$	−23.5251	+	16.0391i	−1.01142	+	0.689576i	−0.951189	−	0.308609i	$-0.900137\pi$
$541$	−23.5251	+	16.0391i	−1.01142	+	0.689576i	−0.0602328	+	0.998184i	$0.519184\pi$
$542$	−9.85909	+	9.14790i	−0.423484	+	0.392936i
$543$	26.9480	−	68.6623i	1.15645	−	2.94658i
$544$	−33.5159	−	10.3383i	−1.43698	−	0.443250i
$545$	−7.46129	+	32.6900i	−0.319606	+	1.40029i
$546$	−5.79730	+	0.543693i	−0.248102	+	0.0232679i
$547$	−8.70135	−	38.1231i	−0.372043	−	1.63003i	−0.721034	−	0.692900i	$-0.756333\pi$
$547$	−8.70135	−	38.1231i	−0.372043	−	1.63003i	0.348991	−	0.937126i	$-0.386524\pi$
$548$	−1.55227	+	20.7136i	−0.0663097	+	0.884842i
$549$	−51.9490	+	16.0242i	−2.21713	+	0.683894i
$550$	0.149369	+	1.99319i	0.00636910	+	0.0849897i
$551$	0.405717	+	1.03375i	0.0172841	+	0.0440393i
$552$	21.6342	+	10.4185i	0.920811	+	0.443439i
$553$	9.03782	−	2.24152i	0.384327	−	0.0953191i
$554$	1.16679	−	0.561898i	0.0495723	−	0.0238727i
$555$	23.7934	+	22.0771i	1.00997	+	0.937119i
$556$	28.1480	+	4.24263i	1.19374	+	0.179928i
$557$	−5.60819	−	9.71367i	−0.237627	−	0.411582i	0.722406	−	0.691469i	$-0.243036\pi$
$557$	−5.60819	−	9.71367i	−0.237627	−	0.411582i	−0.960033	+	0.279887i	$0.909703\pi$
$558$	−14.9038	+	25.8142i	−0.630930	+	1.09280i
$559$	−1.18017	+	1.47989i	−0.0499161	+	0.0625928i
$560$	−1.94640	+	6.75636i	−0.0822503	+	0.285508i
$561$	−17.3668	−	21.7773i	−0.733227	−	0.919438i
$562$	14.5543	−	2.19370i	0.613935	−	0.0925358i
$563$	14.1125	+	9.62174i	0.594771	+	0.405508i	0.822952	−	0.568111i	$-0.192326\pi$
$563$	14.1125	+	9.62174i	0.594771	+	0.405508i	−0.228181	+	0.973619i	$0.573278\pi$
$564$	3.32011	+	2.26361i	0.139802	+	0.0953154i
$565$	−20.4384	+	3.08059i	−0.859849	+	0.129601i
$566$	10.3476	+	12.9755i	0.434942	+	0.545400i
$567$	−12.1173	−	17.0774i	−0.508880	−	0.717183i
$568$	−5.75725	+	7.21936i	−0.241569	+	0.302918i
$569$	−16.9082	+	29.2858i	−0.708827	+	1.22772i	0.256465	+	0.966553i	$0.417442\pi$
$569$	−16.9082	+	29.2858i	−0.708827	+	1.22772i	−0.965293	+	0.261171i	$0.915891\pi$
$570$	−0.864063	−	1.49660i	−0.0361916	−	0.0626857i
$571$	−20.6638	−	3.11457i	−0.864755	−	0.130341i	−0.298339	−	0.954460i	$-0.596432\pi$
$571$	−20.6638	−	3.11457i	−0.864755	−	0.130341i	−0.566416	+	0.824119i	$0.691671\pi$
$572$	−1.66512	−	1.54501i	−0.0696223	−	0.0646000i
$573$	17.5435	−	8.44848i	0.732888	−	0.352940i
$574$	0.152575	+	8.15360i	0.00636837	+	0.340325i
$575$	4.93062	+	2.37446i	0.205621	+	0.0990219i
$576$	4.89534	+	12.4731i	0.203972	+	0.519713i
$577$	1.06661	+	14.2329i	0.0444035	+	0.592524i	0.974380	+	0.224906i	$0.0722075\pi$
$577$	1.06661	+	14.2329i	0.0444035	+	0.592524i	−0.929977	+	0.367618i	$0.880173\pi$
$578$	−13.2901	+	4.09944i	−0.552794	+	0.170514i
$579$	0.769800	−	10.2723i	0.0319918	−	0.426901i
$580$	−3.08161	−	13.5014i	−0.127957	−	0.560615i
$581$	−36.9053	−	13.6931i	−1.53109	−	0.568085i
$582$	−2.65408	+	11.6283i	−0.110015	+	0.482008i
$583$	15.4127	+	4.75417i	0.638327	+	0.196898i
$584$	9.57391	−	24.3939i	0.396171	−	1.00943i
$585$	11.1799	−	10.3734i	0.462231	−	0.428888i
$586$	17.6840	−	12.0567i	0.730519	−	0.498060i
$587$	40.0126			1.65150			0.825748	−	0.564040i	$-0.190753\pi$
$587$	40.0126			1.65150			0.825748	+	0.564040i	$0.190753\pi$
$588$	28.6322	−	10.0195i	1.18077	−	0.413198i
$589$	−2.07776			−0.0856125
$590$	4.97091	−	3.38911i	0.204649	−	0.139527i
$591$	−1.69395	+	1.57176i	−0.0696798	+	0.0646534i
$592$	1.57094	−	4.00269i	0.0645652	−	0.164509i
$593$	−1.39796	−	0.431213i	−0.0574072	−	0.0177078i	0.265919	−	0.963995i	$-0.414325\pi$
$593$	−1.39796	−	0.431213i	−0.0574072	−	0.0177078i	−0.323326	+	0.946288i	$0.604801\pi$
$594$	−2.20099	+	9.64317i	−0.0903078	+	0.395664i
$595$	12.8448	+	39.0334i	0.526584	+	1.60021i
$596$	−3.23639	−	14.1795i	−0.132568	−	0.580816i
$597$	−4.02442	+	53.7021i	−0.164708	+	2.19788i
$598$	2.22930	−	0.687647i	0.0911627	−	0.0281200i
$599$	0.941893	+	12.5687i	0.0384847	+	0.513543i	0.982821	+	0.184561i	$0.0590864\pi$
$599$	0.941893	+	12.5687i	0.0384847	+	0.513543i	−0.944336	+	0.328982i	$0.893295\pi$
$600$	4.81247	+	12.2620i	0.196468	+	0.500593i
$601$	−8.99953	−	4.33395i	−0.367099	−	0.176785i	0.241235	−	0.970467i	$-0.422447\pi$
$601$	−8.99953	−	4.33395i	−0.367099	−	0.176785i	−0.608334	+	0.793681i	$0.708162\pi$
$602$	−1.54234	+	3.36220i	−0.0628609	+	0.137033i
$603$	−69.8967	+	33.6605i	−2.84642	+	1.37076i
$604$	−3.96723	−	3.68105i	−0.161424	−	0.149780i
$605$	−21.9650	−	3.31070i	−0.893005	−	0.134599i
$606$	−12.9771	−	22.4771i	−0.527160	−	0.913069i
$607$	−3.35562	+	5.81211i	−0.136200	+	0.235906i	−0.926055	−	0.377388i	$-0.876822\pi$
$607$	−3.35562	+	5.81211i	−0.136200	+	0.235906i	0.789855	+	0.613294i	$0.210156\pi$
$608$	−1.10561	+	1.38639i	−0.0448382	+	0.0562253i
$609$	−19.2760	+	21.5703i	−0.781102	+	0.874072i
$610$	−11.0524	−	13.8592i	−0.447498	−	0.561144i
$611$	0.916912	−	0.138202i	0.0370943	−	0.00559106i
$612$	−42.2790	−	28.8253i	−1.70903	−	1.16520i
$613$	−0.278644	−	0.189976i	−0.0112543	−	0.00767308i	0.557680	−	0.830056i	$-0.311692\pi$
$613$	−0.278644	−	0.189976i	−0.0112543	−	0.00767308i	−0.568934	+	0.822383i	$0.692644\pi$
$614$	2.49011	−	0.375324i	0.100493	−	0.0151468i
$615$	−20.1151	−	25.2235i	−0.811119	−	1.01711i
$616$	−9.22772	−	5.09985i	−0.371795	−	0.205479i
$617$	−0.340556	+	0.427044i	−0.0137103	+	0.0171922i	−0.788639	−	0.614856i	$-0.789214\pi$
$617$	−0.340556	+	0.427044i	−0.0137103	+	0.0171922i	0.774929	+	0.632048i	$0.217786\pi$
$618$	13.7689	−	23.8484i	0.553864	−	0.959321i
$619$	−17.5661	−	30.4254i	−0.706042	−	1.22290i	−0.966314	−	0.257365i	$-0.917146\pi$
$619$	−17.5661	−	30.4254i	−0.706042	−	1.22290i	0.260273	−	0.965535i	$-0.416188\pi$
$620$	25.6211	+	3.86176i	1.02897	+	0.155092i
$621$	19.8523	+	18.4202i	0.796644	+	0.739178i
$622$	5.60831	−	2.70082i	0.224873	−	0.108293i
$623$	33.4870	−	27.7457i	1.34163	−	1.11161i
$624$	−2.74944	−	1.32406i	−0.110065	−	0.0530047i
$625$	−11.2018	−	28.5417i	−0.448072	−	1.14167i
$626$	1.05516	+	14.0801i	0.0421727	+	0.562756i
$627$	−1.34567	+	0.415084i	−0.0537408	+	0.0165769i
$628$	1.23418	−	16.4690i	0.0492492	−	0.657185i
$629$	−5.59201	−	24.5002i	−0.222968	−	0.976887i
$630$	16.3257	−	24.9353i	0.650432	−	0.993446i
$631$	5.06092	−	22.1733i	0.201472	−	0.882707i	−0.768569	−	0.639767i	$-0.779031\pi$
$631$	5.06092	−	22.1733i	0.201472	−	0.882707i	0.970041	−	0.242940i	$-0.0781119\pi$
$632$	−8.58113	−	2.64693i	−0.341339	−	0.105289i
$633$	20.8461	−	53.1149i	0.828556	−	2.11113i
$634$	−4.62693	+	4.29316i	−0.183759	+	0.170503i
$635$	−37.1648	+	25.3385i	−1.47484	+	1.00553i
$636$	44.7543			1.77462
$637$	3.27075	−	6.18888i	0.129592	−	0.245212i
$638$	4.23321			0.167594
$639$	−17.5750	+	11.9825i	−0.695258	+	0.474019i
$640$	19.0880	−	17.7111i	0.754519	−	0.700092i
$641$	−4.02339	+	10.2514i	−0.158914	+	0.404907i	−0.988049	−	0.154142i	$-0.950739\pi$
$641$	−4.02339	+	10.2514i	−0.158914	+	0.404907i	0.829134	+	0.559049i	$0.188834\pi$
$642$	−33.3640	−	10.2914i	−1.31677	−	0.406171i
$643$	0.616747	−	2.70214i	0.0243221	−	0.106562i	−0.961310	−	0.275469i	$-0.911167\pi$
$643$	0.616747	−	2.70214i	0.0243221	−	0.106562i	0.985632	+	0.168907i	$0.0540238\pi$
$644$	−10.4101	+	6.27282i	−0.410214	+	0.247184i
$645$	−3.25636	−	14.2670i	−0.128219	−	0.561764i
$646$	−0.0999876	+	1.33424i	−0.00393396	+	0.0524950i
$647$	2.98194	−	0.919808i	0.117232	−	0.0361614i	−0.235584	−	0.971854i	$-0.575700\pi$
$647$	2.98194	−	0.919808i	0.117232	−	0.0361614i	0.352816	+	0.935693i	$0.385224\pi$
$648$	1.50910	+	20.1375i	0.0592831	+	0.791078i
$649$	−1.79113	−	4.56373i	−0.0703081	−	0.179142i
$650$	1.15306	+	0.555286i	0.0452269	+	0.0217801i
$651$	−24.3918	−	48.3163i	−0.955992	−	1.89367i
$652$	−11.1693	+	5.37886i	−0.437424	+	0.210652i
$653$	−22.0571	−	20.4660i	−0.863162	−	0.800897i	0.118215	−	0.992988i	$-0.462283\pi$
$653$	−22.0571	−	20.4660i	−0.863162	−	0.800897i	−0.981377	+	0.192091i	$0.938473\pi$
$654$	−28.1222	−	4.23874i	−1.09967	−	0.165748i
$655$	−17.1082	−	29.6322i	−0.668472	−	1.15783i
$656$	−2.13698	+	3.70137i	−0.0834352	+	0.144514i
$657$	37.6379	−	47.1965i	1.46840	−	1.84131i
$658$	1.67416	−	0.693479i	0.0652654	−	0.0270346i
$659$	12.5007	+	15.6754i	0.486957	+	0.610625i	0.963232	−	0.268671i	$-0.0865846\pi$
$659$	12.5007	+	15.6754i	0.486957	+	0.610625i	−0.476275	+	0.879297i	$0.658013\pi$
$660$	17.3651	−	2.61737i	0.675936	−	0.101881i
$661$	24.5881	+	16.7639i	0.956368	+	0.652040i	0.937575	−	0.347783i	$-0.113065\pi$
$661$	24.5881	+	16.7639i	0.956368	+	0.652040i	0.0187927	+	0.999823i	$0.494018\pi$
$662$	6.09127	+	4.15296i	0.236744	+	0.161409i
$663$	−17.6357	+	2.65815i	−0.684913	+	0.103234i
$664$	23.6690	+	29.6799i	0.918534	+	1.15181i
$665$	2.07426	+	0.116466i	0.0804362	+	0.00451635i
$666$	−11.3643	+	14.2504i	−0.440359	+	0.552192i
$667$	5.79520	−	10.0376i	0.224391	−	0.388656i
$668$	−8.61561	−	14.9227i	−0.333348	−	0.577375i
$669$	−53.5350	−	8.06910i	−2.06978	−	0.311970i
$670$	−18.5436	−	17.2060i	−0.716402	−	0.664724i
$671$	−13.0147	+	6.26757i	−0.502428	+	0.241957i
$672$	−45.2183	−	9.43434i	−1.74434	−	0.363938i
$673$	−23.6346	−	11.3818i	−0.911048	−	0.438737i	−0.0811811	−	0.996699i	$-0.525869\pi$
$673$	−23.6346	−	11.3818i	−0.911048	−	0.438737i	−0.829867	+	0.557962i	$0.811583\pi$
$674$	1.58076	+	4.02770i	0.0608885	+	0.155141i
$675$	1.11022	+	14.8149i	0.0427325	+	0.570226i
$676$	−1.38981	+	0.428699i	−0.0534541	+	0.0164884i
$677$	−2.68075	+	35.7721i	−0.103030	+	1.37483i	0.670894	+	0.741554i	$0.265911\pi$
$677$	−2.68075	+	35.7721i	−0.103030	+	1.37483i	−0.773923	+	0.633280i	$0.781708\pi$
$678$	−3.90104	−	17.0916i	−0.149818	−	0.656398i
$679$	−9.94784	−	10.3268i	−0.381763	−	0.396307i
$680$	8.81835	−	38.6357i	0.338168	−	1.48161i
$681$	76.1670	+	23.4944i	2.91873	+	0.900308i
$682$	−2.89360	+	7.37277i	−0.110802	+	0.282318i
$683$	−26.6374	+	24.7159i	−1.01925	+	0.945726i	−0.998538	−	0.0540590i	$-0.982784\pi$
$683$	−26.6374	+	24.7159i	−1.01925	+	0.945726i	−0.0207130	+	0.999785i	$0.506594\pi$
$684$	−2.13751	+	1.45733i	−0.0817298	+	0.0557224i
$685$	−37.0574			−1.41589
$686$	3.29244	−	13.2775i	0.125706	−	0.506938i
$687$	67.2070			2.56411
$688$	−1.60179	+	1.09208i	−0.0610677	+	0.0416352i
$689$	7.57056	−	7.02445i	0.288415	−	0.267610i
$690$	−6.58941	+	16.7896i	−0.250855	+	0.639167i
$691$	17.4265	+	5.37537i	0.662936	+	0.204489i	0.607922	−	0.793997i	$-0.292003\pi$
$691$	17.4265	+	5.37537i	0.662936	+	0.204489i	0.0550141	+	0.998486i	$0.482480\pi$
$692$	−3.48630	+	15.2745i	−0.132529	+	0.580649i
$693$	−16.8497	−	17.4916i	−0.640068	−	0.664452i
$694$	0.825452	+	3.61654i	0.0313337	+	0.137282i
$695$	−3.79511	+	50.6422i	−0.143957	+	1.92097i
$696$	26.6587	−	8.22313i	1.01050	−	0.311697i
$697$	1.86665	+	24.9088i	0.0707045	+	0.943486i
$698$	−5.31945	−	13.5537i	−0.201344	−	0.513016i
$699$	−63.4872	−	30.5738i	−2.40130	−	1.15641i
$700$	−6.52684	−	1.36176i	−0.246691	−	0.0514696i
$701$	−1.74192	+	0.838865i	−0.0657915	+	0.0316835i	−0.466490	−	0.884526i	$-0.654482\pi$
$701$	−1.74192	+	0.838865i	−0.0657915	+	0.0316835i	0.400699	+	0.916210i	$0.368767\pi$
$702$	4.64260	+	4.30771i	0.175224	+	0.162584i
$703$	−1.25633	−	0.189361i	−0.0473833	−	0.00714188i
$704$	1.78019	+	3.08338i	0.0670934	+	0.116209i
$705$	−3.58443	+	6.20841i	−0.134997	+	0.233822i
$706$	8.83643	−	11.0805i	0.332563	−	0.417021i
$707$	31.1527	+	1.74917i	1.17162	+	0.0657844i
$708$	−8.48164	−	10.6356i	−0.318760	−	0.399712i
$709$	33.0808	−	4.98612i	1.24237	−	0.187258i	0.505225	−	0.862988i	$-0.331410\pi$
$709$	33.0808	−	4.98612i	1.24237	−	0.187258i	0.737149	+	0.675730i	$0.236171\pi$
$710$	−5.73072	−	3.90714i	−0.215070	−	0.146632i
$711$	−17.0920	−	11.6531i	−0.640998	−	0.437025i
$712$	−41.4711	+	6.25076i	−1.55419	+	0.234257i
$713$	13.5206	+	16.9543i	0.506352	+	0.634945i
$714$	−32.2003	+	13.3382i	−1.20507	+	0.499170i
$715$	2.52664	−	3.16831i	0.0944910	−	0.118488i
$716$	−4.95894	+	8.58913i	−0.185324	+	0.320991i
$717$	19.5765	+	33.9074i	0.731096	+	1.26630i
$718$	23.9487	+	3.60969i	0.893758	+	0.134712i
$719$	−5.21368	−	4.83759i	−0.194438	−	0.180412i	0.576946	−	0.816782i	$-0.304244\pi$
$719$	−5.21368	−	4.83759i	−0.194438	−	0.180412i	−0.771383	+	0.636371i	$0.780435\pi$
$720$	14.0733	−	6.77733i	0.524480	−	0.252576i
$721$	14.9194	+	29.5529i	0.555628	+	1.10061i
$722$	−12.5832	−	6.05977i	−0.468300	−	0.225521i
$723$	13.8638	+	35.3243i	0.515599	+	1.31373i
$724$	−2.69069	−	35.9047i	−0.0999986	−	1.33439i
$725$	6.07577	−	1.87413i	0.225648	−	0.0696033i
$726$	1.40796	−	18.7879i	0.0522543	−	0.697285i
$727$	−6.45588	−	28.2851i	−0.239435	−	1.04903i	−0.941524	−	0.336945i	$-0.890606\pi$
$727$	−6.45588	−	28.2851i	−0.239435	−	1.04903i	0.702089	−	0.712089i	$-0.252251\pi$
$728$	−5.78215	+	3.48417i	−0.214301	+	0.129132i
$729$	6.70322	−	29.3687i	0.248267	−	1.08773i
$730$	18.8093	+	5.80190i	0.696164	+	0.214738i
$731$	−4.13938	+	10.5470i	−0.153100	+	0.390093i
$732$	−29.3820	+	27.2625i	−1.08599	+	1.00765i
$733$	14.9921	−	10.2214i	0.553745	−	0.377537i	−0.253878	−	0.967236i	$-0.581706\pi$
$733$	14.9921	−	10.2214i	0.553745	−	0.377537i	0.807623	+	0.589699i	$0.200754\pi$
$734$	8.19305			0.302411
$735$	21.6424	+	49.6021i	0.798293	+	1.82960i
$736$	18.5073			0.682189
$737$	−17.0320	+	11.6122i	−0.627380	+	0.427740i
$738$	13.2807	−	12.3227i	0.488868	−	0.453603i
$739$	−17.7600	+	45.2517i	−0.653312	+	1.66461i	0.0902290	+	0.995921i	$0.471240\pi$
$739$	−17.7600	+	45.2517i	−0.653312	+	1.66461i	−0.743541	+	0.668690i	$0.766855\pi$
$740$	15.1400	+	4.67007i	0.556558	+	0.171675i
$741$	−0.200643	+	0.879076i	−0.00737082	+	0.0322937i
$742$	11.0551	−	16.8852i	0.405845	−	0.619874i
$743$	−4.26371	−	18.6805i	−0.156420	−	0.685323i	−0.990936	−	0.134338i	$-0.957109\pi$
$743$	−4.26371	−	18.6805i	−0.156420	−	0.685323i	0.834515	−	0.550985i	$-0.185748\pi$
$744$	−3.90069	+	52.0511i	−0.143006	+	1.90828i
$745$	24.7945	−	7.64810i	0.908402	−	0.280205i
$746$	1.16102	+	15.4928i	0.0425080	+	0.567230i
$747$	31.9487	+	81.4041i	1.16894	+	2.97842i
$748$	−12.2501	−	5.89935i	−0.447909	−	0.215702i
$749$	32.3216	−	26.7801i	1.18100	−	0.978522i
$750$	16.8103	−	8.09541i	0.613825	−	0.295602i
$751$	21.1158	+	19.5926i	0.770528	+	0.714946i	0.963925	−	0.266175i	$-0.0857599\pi$
$751$	21.1158	+	19.5926i	0.770528	+	0.714946i	−0.193396	+	0.981121i	$0.561950\pi$
$752$	0.939097	+	0.141546i	0.0342454	+	0.00516166i
$753$	34.7015	+	60.1047i	1.26459	+	2.19034i
$754$	1.35525	−	2.34736i	0.0493553	−	0.0854859i
$755$	6.01984	−	7.54864i	0.219084	−	0.274723i
$756$	−28.8776	−	15.9597i	−1.05027	−	0.580448i
$757$	5.51287	+	6.91292i	0.200369	+	0.251254i	0.871857	−	0.489761i	$-0.162916\pi$
$757$	5.51287	+	6.91292i	0.200369	+	0.251254i	−0.671488	+	0.741015i	$0.734345\pi$
$758$	−3.74695	+	0.564762i	−0.136095	+	0.0205131i
$759$	12.1438	+	8.27947i	0.440791	+	0.300526i
$760$	−1.65541	−	1.12864i	−0.0600481	−	0.0409401i
$761$	−6.07060	+	0.914996i	−0.220059	+	0.0331686i	−0.258146	−	0.966106i	$-0.583112\pi$
$761$	−6.07060	+	0.914996i	−0.220059	+	0.0331686i	0.0380872	+	0.999274i	$0.487874\pi$
$762$	−23.7870	−	29.8280i	−0.861714	−	1.08055i
$763$	22.7821	−	25.4937i	0.824766	−	0.922934i
$764$	5.92618	−	7.43120i	0.214402	−	0.268851i
$765$	45.6449	−	79.0592i	1.65029	−	2.85839i
$766$	−2.10525	−	3.64639i	−0.0760656	−	0.131750i
$767$	−3.10407	−	0.467863i	−0.112081	−	0.0168935i
$768$	26.1484	+	24.2621i	0.943548	+	0.875485i
$769$	−26.5590	+	12.7901i	−0.957741	+	0.461224i	−0.846394	−	0.532558i	$-0.821231\pi$
$769$	−26.5590	+	12.7901i	−0.957741	+	0.461224i	−0.111347	+	0.993782i	$0.535517\pi$
$770$	3.30199	−	7.19815i	0.118996	−	0.259403i
$771$	53.9520	+	25.9819i	1.94303	+	0.935716i
$772$	−1.83705	−	4.68073i	−0.0661169	−	0.168463i
$773$	2.51187	+	33.5185i	0.0903456	+	1.20558i	0.839566	+	0.543257i	$0.182809\pi$
$773$	2.51187	+	33.5185i	0.0903456	+	1.20558i	−0.749221	+	0.662320i	$0.769572\pi$
$774$	7.85267	−	2.42223i	0.282258	−	0.0870652i
$775$	−0.889002	+	11.8629i	−0.0319339	+	0.426128i
$776$	3.07708	+	13.4816i	0.110461	+	0.483961i
$777$	−10.3453	−	31.4377i	−0.371134	−	1.12782i
$778$	0.581611	−	2.54821i	0.0208518	−	0.0913576i
$779$	1.20674	+	0.372232i	0.0432361	+	0.0133366i
$780$	4.10803	−	10.4671i	0.147091	−	0.374782i
$781$	−4.14321	+	3.84434i	−0.148256	+	0.137561i
$782$	11.5380	−	7.86645i	0.412597	−	0.281304i
$783$	31.4645			1.12445
$784$	5.06940	−	5.06962i	0.181050	−	0.181058i
$785$	29.4636			1.05160
$786$	23.9786	−	16.3483i	0.855289	−	0.583126i
$787$	38.2034	−	35.4476i	1.36180	−	1.26357i	0.428944	−	0.903331i	$-0.358886\pi$
$787$	38.2034	−	35.4476i	1.36180	−	1.26357i	0.932860	−	0.360238i	$-0.117305\pi$
$788$	−0.412102	+	1.05002i	−0.0146805	+	0.0374054i
$789$	−35.3540	−	10.9053i	−1.25864	−	0.388238i
$790$	1.50096	−	6.57614i	0.0534018	−	0.233969i
$791$	19.7593	+	7.33138i	0.702561	+	0.260674i
$792$	5.21199	+	22.8352i	0.185200	+	0.811414i
$793$	−0.691195	+	9.22335i	−0.0245450	+	0.327531i
$794$	−15.5584	+	4.79912i	−0.552146	+	0.170314i
$795$	5.96668	+	79.6198i	0.211616	+	2.82383i
$796$	9.60386	+	24.4702i	0.340400	+	0.867325i
$797$	3.41706	+	1.64557i	0.121038	+	0.0582890i	0.493423	−	0.869789i	$-0.335745\pi$
$797$	3.41706	+	1.64557i	0.121038	+	0.0582890i	−0.372385	+	0.928079i	$0.621460\pi$
$798$	0.0329678	+	1.76179i	0.00116705	+	0.0623668i
$799$	5.00075	−	2.40823i	0.176914	−	0.0851972i
$800$	7.44248	+	6.90561i	0.263132	+	0.244150i
$801$	−95.5324	−	14.3992i	−3.37547	−	0.508771i
$802$	3.70543	+	6.41799i	0.130843	+	0.226627i
$803$	8.02007	−	13.8912i	0.283022	−	0.490209i
$804$	−35.6623	+	44.7191i	−1.25771	+	1.57712i
$805$	−12.5475	−	17.6837i	−0.442241	−	0.623267i
$806$	3.16190	+	3.96490i	0.111373	+	0.139658i
$807$	−40.5752	+	6.11573i	−1.42832	+	0.215284i
$808$	−24.8622	−	16.9508i	−0.874649	−	0.596326i
$809$	18.6171	+	12.6929i	0.654542	+	0.446259i	0.844516	−	0.535530i	$-0.179888\pi$
$809$	18.6171	+	12.6929i	0.654542	+	0.446259i	−0.189975	+	0.981789i	$0.560841\pi$
$810$	−14.9990	+	2.26074i	−0.527012	+	0.0794342i
$811$	−0.372307	−	0.466858i	−0.0130735	−	0.0163936i	0.775252	−	0.631652i	$-0.217623\pi$
$811$	−0.372307	−	0.466858i	−0.0130735	−	0.0163936i	−0.788325	+	0.615259i	$0.789052\pi$
$812$	−3.90902	+	13.5690i	−0.137180	+	0.476180i
$813$	−33.8263	+	42.4168i	−1.18634	+	1.48762i
$814$	−2.42156	+	4.19427i	−0.0848758	+	0.147009i
$815$	−11.0583	−	19.1536i	−0.387356	−	0.670921i
$816$	−18.0624	−	2.72247i	−0.632310	−	0.0953054i
$817$	0.419909	+	0.389618i	0.0146907	+	0.0136310i
$818$	10.4028	−	5.00971i	0.363724	−	0.175160i
$819$	−15.0937	+	3.74347i	−0.527416	+	0.130807i
$820$	−14.1887	−	6.83292i	−0.495491	−	0.238616i
$821$	−19.2341	−	49.0078i	−0.671276	−	1.71038i	−0.703297	−	0.710896i	$-0.748290\pi$
$821$	−19.2341	−	49.0078i	−0.671276	−	1.71038i	0.0320208	−	0.999487i	$-0.489806\pi$
$822$	−2.34885	−	31.3432i	−0.0819255	−	1.09322i
$823$	17.4694	−	5.38860i	0.608945	−	0.187835i	0.0250800	−	0.999685i	$-0.492016\pi$
$823$	17.4694	−	5.38860i	0.608945	−	0.187835i	0.583865	+	0.811851i	$0.301540\pi$
$824$	2.38588	−	31.8373i	0.0831160	−	1.10911i
$825$	1.79415	+	7.86067i	0.0624641	+	0.273673i
$826$	−6.10779	+	0.572812i	−0.212517	+	0.0199307i
$827$	−8.67716	+	38.0171i	−0.301734	+	1.32199i	0.565773	+	0.824561i	$0.308578\pi$
$827$	−8.67716	+	38.0171i	−0.301734	+	1.32199i	−0.867508	+	0.497424i	$0.834279\pi$
$828$	25.8012	+	7.95861i	0.896654	+	0.276581i
$829$	11.7131	−	29.8446i	0.406814	−	1.03655i	−0.569845	−	0.821752i	$-0.692997\pi$
$829$	11.7131	−	29.8446i	0.406814	−	1.03655i	0.976659	−	0.214794i	$-0.0689080\pi$
$830$	−20.9027	+	19.3949i	−0.725544	+	0.673206i
$831$	4.31631	−	2.94281i	0.149731	−	0.102085i
$832$	2.27969			0.0790340
$833$	7.78890	−	41.1700i	0.269869	−	1.42646i
$834$	−43.0738			−1.49152
$835$	25.3994	−	17.3170i	0.878984	−	0.599281i
$836$	−0.503906	+	0.467556i	−0.0174280	+	0.0161708i
$837$	−21.5075	+	54.8001i	−0.743407	+	1.89417i
$838$	15.1457	+	4.67182i	0.523199	+	0.161385i
$839$	2.17617	−	9.53441i	0.0751296	−	0.329164i	−0.923371	−	0.383909i	$-0.874577\pi$
$839$	2.17617	−	9.53441i	0.0751296	−	0.329164i	0.998500	+	0.0547451i	$0.0174346\pi$
$840$	6.81177	−	51.7447i	0.235028	−	1.78536i
$841$	3.45661	+	15.1444i	0.119193	+	0.522220i
$842$	0.627800	−	8.37740i	0.0216354	−	0.288704i
$843$	56.7356	−	17.5006i	1.95408	−	0.602753i
$844$	−2.08143	−	27.7747i	−0.0716457	−	0.956045i
$845$	−0.947964	−	2.41537i	−0.0326110	−	0.0830914i
$846$	−3.62704	−	1.74669i	−0.124700	−	0.0600524i
$847$	17.9695	+	13.7882i	0.617438	+	0.473767i
$848$	9.52985	−	4.58933i	0.327256	−	0.157598i
$849$	49.0758	+	45.5357i	1.68428	+	1.56278i
$850$	7.57504	+	1.14175i	0.259822	+	0.0391618i
$851$	6.63016	+	11.4838i	0.227279	+	0.393659i
$852$	−7.84140	+	13.5817i	−0.268642	+	0.465302i
$853$	31.3294	−	39.2858i	1.07270	−	1.34512i	0.137697	−	0.990474i	$-0.456030\pi$
$853$	31.3294	−	39.2858i	1.07270	−	1.34512i	0.935001	−	0.354646i	$-0.115399\pi$
$854$	3.02789	+	17.8197i	0.103612	+	0.609779i
$855$	−2.87763	−	3.60843i	−0.0984129	−	0.123406i
$856$	−40.0278	+	6.03322i	−1.36812	+	0.206211i
$857$	−13.5180	−	9.21643i	−0.461767	−	0.314827i	0.309996	−	0.950738i	$-0.399672\pi$
$857$	−13.5180	−	9.21643i	−0.461767	−	0.314827i	−0.771763	+	0.635911i	$0.780625\pi$
$858$	2.83991	+	1.93622i	0.0969529	+	0.0661014i
$859$	22.4354	−	3.38160i	0.765488	−	0.115379i	0.245319	−	0.969442i	$-0.421107\pi$
$859$	22.4354	−	3.38160i	0.765488	−	0.115379i	0.520168	+	0.854064i	$0.325869\pi$
$860$	−4.45380	−	5.58489i	−0.151873	−	0.190443i
$861$	5.51069	+	32.4315i	0.187804	+	1.10526i
$862$	3.79076	−	4.75346i	0.129114	−	0.161904i
$863$	−2.30643	+	3.99486i	−0.0785119	+	0.135987i	−0.902608	−	0.430463i	$-0.858350\pi$
$863$	−2.30643	+	3.99486i	−0.0785119	+	0.135987i	0.824096	+	0.566450i	$0.191684\pi$
$864$	25.1210	+	43.5108i	0.854633	+	1.48027i
$865$	−27.6388	−	4.16587i	−0.939746	−	0.141644i
$866$	−8.18674	−	7.59619i	−0.278197	−	0.258129i
$867$	−50.5471	+	24.3422i	−1.71667	+	0.826704i
$868$	−20.9605	−	16.0832i	−0.711446	−	0.545900i
$869$	−4.95231	−	2.38491i	−0.167996	−	0.0809024i
$870$	7.65583	+	19.5067i	0.259557	+	0.661340i
$871$	0.986356	+	13.1620i	0.0334214	+	0.445978i
$872$	−31.5077	+	9.71883i	−1.06698	+	0.329121i
$873$	−2.38051	+	31.7657i	−0.0805680	+	1.07510i
$874$	−0.157101	−	0.688303i	−0.00531401	−	0.0232822i
$875$	−2.92751	+	22.2385i	−0.0989680	+	0.751798i
$876$	9.90376	−	43.3912i	0.334617	−	1.46605i
$877$	−13.1461	−	4.05504i	−0.443913	−	0.136929i	0.0647370	−	0.997902i	$-0.479379\pi$
$877$	−13.1461	−	4.05504i	−0.443913	−	0.136929i	−0.508650	+	0.860973i	$0.669855\pi$
$878$	−9.71275	+	24.7477i	−0.327790	+	0.835194i
$879$	63.2896	−	58.7242i	2.13471	−	1.98072i
$880$	3.42928	−	2.33804i	0.115601	−	0.0788154i
$881$	23.8356			0.803042			0.401521	−	0.915850i	$-0.368482\pi$
$881$	23.8356			0.803042			0.401521	+	0.915850i	$0.368482\pi$
$882$	−26.8682	+	14.2010i	−0.904700	+	0.478172i
$883$	58.7692			1.97774			0.988871	−	0.148775i	$-0.0475330\pi$
$883$	58.7692			1.97774			0.988871	+	0.148775i	$0.0475330\pi$
$884$	−7.19310	+	4.90417i	−0.241930	+	0.164945i
$885$	17.7905	−	16.5072i	0.598021	−	0.554882i
$886$	7.59289	−	19.3464i	0.255088	−	0.649954i
$887$	−20.6529	−	6.37058i	−0.693457	−	0.213903i	−0.0720613	−	0.997400i	$-0.522958\pi$
$887$	−20.6529	−	6.37058i	−0.693457	−	0.213903i	−0.621395	+	0.783497i	$0.713434\pi$
$888$	−7.10236	+	31.1175i	−0.238340	+	1.04423i
$889$	45.6646	−	4.28260i	1.53154	−	0.143634i
$890$	−7.00991	−	30.7124i	−0.234973	−	1.02948i
$891$	−0.923710	+	12.3260i	−0.0309454	+	0.412938i
$892$	−25.2534	+	7.78964i	−0.845547	+	0.260817i
$893$	−0.0209703	−	0.279829i	−0.000701744	−	0.00936412i
$894$	8.04036	+	20.4865i	0.268910	+	0.685171i
$895$	−15.9416	−	7.67706i	−0.532868	−	0.256616i
$896$	−25.7703	+	6.39142i	−0.860924	+	0.213522i
$897$	8.47885	−	4.08320i	0.283100	−	0.136334i
$898$	8.23867	+	7.64437i	0.274928	+	0.255096i
$899$	24.9135	+	3.75511i	0.830913	+	0.125240i
$900$	7.40603	+	12.8276i	0.246868	+	0.427587i
$901$	30.9088	−	53.5357i	1.02972	−	1.78353i
$902$	3.00142	−	3.76366i	0.0999362	−	0.125316i
$903$	−4.13069	+	14.3385i	−0.137461	+	0.477156i
$904$	−12.6725	−	15.8909i	−0.421482	−	0.528522i
$905$	63.5174	−	9.57370i	2.11139	−	0.318241i
$906$	6.76622	+	4.61313i	0.224792	+	0.153261i
$907$	4.68391	+	3.19344i	0.155527	+	0.106036i	0.638583	−	0.769553i	$-0.279521\pi$
$907$	4.68391	+	3.19344i	0.155527	+	0.106036i	−0.483056	+	0.875589i	$0.660473\pi$
$908$	38.4738	−	5.79900i	1.27680	−	0.192447i
$909$	−43.2184	−	54.1942i	−1.43346	−	1.79751i
$910$	−2.93433	−	4.13546i	−0.0972720	−	0.137089i
$911$	32.5229	−	40.7824i	1.07753	−	1.35118i	0.145273	−	0.989392i	$-0.453594\pi$
$911$	32.5229	−	40.7824i	1.07753	−	1.35118i	0.932259	−	0.361791i	$-0.117835\pi$
$912$	−0.461750	+	0.799774i	−0.0152901	+	0.0264832i
$913$	11.6182	+	20.1232i	0.384505	+	0.665982i
$914$	17.5020	+	2.63800i	0.578914	+	0.0872572i
$915$	−52.4184	−	48.6372i	−1.73290	−	1.60790i
$916$	29.5573	−	14.2340i	0.976600	−	0.470306i
$917$	0.652752	+	34.8829i	0.0215558	+	1.15194i
$918$	34.1551	+	16.4483i	1.12729	+	0.542873i
$919$	9.55366	+	24.3423i	0.315146	+	0.802979i	0.997414	+	0.0718766i	$0.0228988\pi$
$919$	9.55366	+	24.3423i	0.315146	+	0.802979i	−0.682267	+	0.731103i	$0.739006\pi$
$920$	1.56268	+	20.8525i	0.0515199	+	0.687485i
$921$	9.70696	−	2.99420i	0.319855	−	0.0986623i
$922$	−2.18511	+	29.1582i	−0.0719627	+	0.960275i
$923$	0.805291	+	3.52821i	0.0265065	+	0.116133i
$924$	−16.7882	−	6.22898i	−0.552291	−	0.204918i
$925$	−1.61869	+	7.09195i	−0.0532223	+	0.233182i
$926$	−7.18425	−	2.21605i	−0.236089	−	0.0728239i
$927$	26.8693	−	68.4619i	0.882504	−	2.24858i
$928$	15.7625	−	14.6254i	0.517428	−	0.480103i
$929$	−5.16032	+	3.51825i	−0.169305	+	0.115430i	−0.645008	−	0.764176i	$-0.723146\pi$
$929$	−5.16032	+	3.51825i	−0.169305	+	0.115430i	0.475703	+	0.879606i	$0.342194\pi$
$930$	−39.2070			−1.28565
$931$	−1.79370	−	1.12700i	−0.0587860	−	0.0369360i
$932$	−34.3967			−1.12670
$933$	20.7468	−	14.1449i	0.679219	−	0.463084i
$934$	−3.06859	+	2.84724i	−0.100407	+	0.0931644i
$935$	8.86201	−	22.5800i	0.289819	−	0.738446i
$936$	14.3310	+	4.42052i	0.468423	+	0.144489i
$937$	10.1466	−	44.4551i	0.331475	−	1.45229i	−0.484801	−	0.874624i	$-0.661108\pi$
$937$	10.1466	−	44.4551i	0.331475	−	1.45229i	0.816276	−	0.577662i	$-0.196035\pi$
$938$	8.06267	+	24.5013i	0.263255	+	0.799995i
$939$	12.6741	+	55.5288i	0.413603	+	1.81212i
$940$	−0.261508	+	3.48959i	−0.00852947	+	0.113818i
$941$	26.9145	−	8.30204i	0.877389	−	0.270639i	0.176837	−	0.984240i	$-0.443413\pi$
$941$	26.9145	−	8.30204i	0.877389	−	0.270639i	0.700552	+	0.713601i	$0.252937\pi$
$942$	1.86752	+	24.9204i	0.0608472	+	0.811950i
$943$	−4.81530	−	12.2692i	−0.156808	−	0.399539i
$944$	−2.89669	−	1.39497i	−0.0942791	−	0.0454024i
$945$	24.5430	−	53.5022i	0.798383	−	1.74043i
$946$	1.96732	−	0.947411i	0.0639631	−	0.0308030i
$947$	29.0718	+	26.9747i	0.944707	+	0.876560i	0.992493	−	0.122298i	$-0.0390263\pi$
$947$	29.0718	+	26.9747i	0.944707	+	0.876560i	−0.0477867	+	0.998858i	$0.515217\pi$
$948$	−15.0814	−	2.27315i	−0.489820	−	0.0738285i
$949$	−5.13520	−	8.89444i	−0.166696	−	0.288726i
$950$	0.193650	−	0.335411i	0.00628282	−	0.0108822i
$951$	−15.8749	+	19.9065i	−0.514778	+	0.645512i
$952$	−26.9257	+	30.1305i	−0.872667	+	0.976535i
$953$	−0.684678	−	0.858559i	−0.0221789	−	0.0278114i	0.770618	−	0.637297i	$-0.219947\pi$
$953$	−0.684678	−	0.858559i	−0.0221789	−	0.0278114i	−0.792797	+	0.609485i	$0.791376\pi$
$954$	−44.3355	+	6.68250i	−1.43541	+	0.216354i
$955$	14.0105	+	9.55220i	0.453369	+	0.309102i
$956$	15.7910	+	10.7661i	0.510718	+	0.348201i
$957$	16.8855	−	2.54509i	0.545832	−	0.0822710i
$958$	1.79103	+	2.24588i	0.0578655	+	0.0725610i
$959$	33.0713	+	18.2774i	1.06793	+	0.590208i
$960$	−10.9888	+	13.7795i	−0.354661	+	0.444731i
$961$	−8.06966	+	13.9771i	−0.260312	+	0.450873i
$962$	1.55051	+	2.68557i	0.0499905	+	0.0865862i
$963$	−92.2077	−	13.8981i	−2.97135	−	0.447859i
$964$	13.5787	+	12.5992i	0.437340	+	0.405792i
$965$	8.08230	−	3.89223i	0.260178	−	0.125295i
$966$	14.1616	−	11.7336i	0.455641	−	0.377521i
$967$	−4.98426	−	2.40029i	−0.160283	−	0.0771882i	0.352022	−	0.935992i	$-0.385494\pi$
$967$	−4.98426	−	2.40029i	−0.160283	−	0.0771882i	−0.512305	+	0.858803i	$0.671208\pi$
$968$	−7.98028	−	20.3334i	−0.256496	−	0.653541i
$969$	0.403338	+	5.38217i	0.0129571	+	0.172900i
$970$	−9.92545	+	3.06160i	−0.318687	+	0.0983020i
$971$	−1.80746	+	24.1189i	−0.0580041	+	0.774011i	0.890042	+	0.455878i	$0.150675\pi$
$971$	−1.80746	+	24.1189i	−0.0580041	+	0.774011i	−0.948046	+	0.318133i	$0.896944\pi$
$972$	−0.693075	−	3.03656i	−0.0222304	−	0.0973977i
$973$	28.3646	−	43.3230i	0.909327	−	1.38887i
$974$	3.67447	−	16.0989i	0.117738	−	0.515842i
$975$	4.93322	+	1.52170i	0.157989	+	0.0487333i
$976$	−3.46088	+	8.81818i	−0.110780	+	0.282263i
$977$	−20.3211	+	18.8553i	−0.650131	+	0.603233i	−0.934707	−	0.355420i	$-0.884338\pi$
$977$	−20.3211	+	18.8553i	−0.650131	+	0.603233i	0.284576	+	0.958654i	$0.408147\pi$
$978$	15.4992	−	10.5672i	0.495610	−	0.337901i
$979$	−25.6709			−0.820445
$980$	20.0237	+	17.2310i	0.639632	+	0.550425i
$981$	−75.9553			−2.42507
$982$	−4.56889	+	3.11502i	−0.145799	+	0.0994043i
$983$	−26.9611	+	25.0162i	−0.859925	+	0.797894i	−0.980849	−	0.194768i	$-0.937605\pi$
$983$	−26.9611	+	25.0162i	−0.859925	+	0.797894i	0.120924	+	0.992662i	$0.461414\pi$
$984$	11.5905	−	29.5320i	0.369491	−	0.941447i
$985$	−1.92297	−	0.593158i	−0.0612709	−	0.0188996i
$986$	3.61027	−	15.8176i	0.114974	−	0.503736i
$987$	6.26098	−	3.77270i	0.199289	−	0.120086i
$988$	0.0979411	+	0.429108i	0.00311592	+	0.0136517i
$989$	0.446775	−	5.96180i	0.0142066	−	0.189574i
$990$	−16.8118	+	5.18576i	−0.534314	+	0.164814i
$991$	−2.80176	−	37.3869i	−0.0890009	−	1.18763i	−0.845622	−	0.533782i	$-0.820770\pi$
$991$	−2.80176	−	37.3869i	−0.0890009	−	1.18763i	0.756621	−	0.653853i	$-0.226849\pi$
$992$	14.6980	+	37.4498i	0.466661	+	1.18903i
$993$	26.7939	+	12.9032i	0.850277	+	0.409472i
$994$	3.18722	+	6.31337i	0.101092	+	0.200248i
$995$	−42.2532	+	20.3481i	−1.33952	+	0.645078i
$996$	47.2632	+	43.8538i	1.49759	+	1.38956i
$997$	−56.7659	−	8.55609i	−1.79780	−	0.270974i	−0.836794	−	0.547518i	$-0.815573\pi$
$997$	−56.7659	−	8.55609i	−1.79780	−	0.270974i	−0.961001	+	0.276544i	$0.910811\pi$
$998$	−4.73608	−	8.20314i	−0.149918	−	0.259666i
$999$	−17.9989	+	31.1751i	−0.569461	+	0.986335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.625.11	yes	348
49.4	even	21	inner	637.2.bl.b.53.11	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.11	✓	348	49.4	even	21	inner
637.2.bl.b.625.11	yes	348	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.610286 + 0.416086i) q^{2} +(-2.18416 + 2.02661i) q^{3} +(-0.531361 + 1.35388i) q^{4} +(-2.47946 - 0.764813i) q^{5} +(0.489722 - 2.14561i) q^{6} +(1.83554 + 1.90546i) q^{7} +(-0.567772 - 2.48757i) q^{8} +(0.439242 - 5.86128i) q^{9} +O(q^{10})\)	\(q+(-0.610286 + 0.416086i) q^{2} +(-2.18416 + 2.02661i) q^{3} +(-0.531361 + 1.35388i) q^{4} +(-2.47946 - 0.764813i) q^{5} +(0.489722 - 2.14561i) q^{6} +(1.83554 + 1.90546i) q^{7} +(-0.567772 - 2.48757i) q^{8} +(0.439242 - 5.86128i) q^{9} +(1.83141 - 0.564915i) q^{10} +(-0.116712 - 1.55742i) q^{11} +(-1.58322 - 4.03397i) q^{12} +(-0.900969 - 0.433884i) q^{13} +(-1.91304 - 0.399136i) q^{14} +(6.96553 - 3.35442i) q^{15} +(-0.750789 - 0.696630i) q^{16} +(-5.91891 - 0.892132i) q^{17} +(2.17073 + 3.75982i) q^{18} +(-0.151312 + 0.262080i) q^{19} +(2.35296 - 2.95051i) q^{20} +(-7.87075 - 0.441929i) q^{21} +(0.719246 + 0.901906i) q^{22} +(3.12319 - 0.470745i) q^{23} +(6.28145 + 4.28262i) q^{24} +(1.43160 + 0.976047i) q^{25} +(0.730381 - 0.110087i) q^{26} +(5.34599 + 6.70366i) q^{27} +(-3.55511 + 1.47262i) q^{28} +(2.28797 - 2.86903i) q^{29} +(-2.85524 + 4.94541i) q^{30} +(3.43290 + 5.94596i) q^{31} +(5.79415 + 0.873327i) q^{32} +(3.41119 + 3.16512i) q^{33} +(3.98343 - 1.91832i) q^{34} +(-3.09383 - 6.12837i) q^{35} +(7.70211 + 3.70914i) q^{36} +(1.53383 + 3.90813i) q^{37} +(-0.0167042 - 0.222902i) q^{38} +(2.84718 - 0.878238i) q^{39} +(-0.494758 + 6.60208i) q^{40} +(-0.928580 - 4.06838i) q^{41} +(4.98729 - 3.00521i) q^{42} +(0.421199 - 1.84540i) q^{43} +(2.17058 + 0.669534i) q^{44} +(-5.57187 + 14.1969i) q^{45} +(-1.71017 + 1.58680i) q^{46} +(-0.766145 + 0.522349i) q^{47} +3.05164 q^{48} +(-0.261591 + 6.99511i) q^{49} -1.27980 q^{50} +(14.7359 - 10.0467i) q^{51} +(1.06617 - 0.989259i) q^{52} +(-3.77304 + 9.61355i) q^{53} +(-6.05188 - 1.86676i) q^{54} +(-0.901748 + 3.95082i) q^{55} +(3.69781 - 5.64791i) q^{56} +(-0.200643 - 0.879076i) q^{57} +(-0.202556 + 2.70292i) q^{58} +(2.99966 - 0.925274i) q^{59} +(0.840293 + 11.2129i) q^{60} +(-3.37912 - 8.60985i) q^{61} +(-4.56908 - 2.20035i) q^{62} +(11.9747 - 9.92166i) q^{63} +(-2.05393 + 0.989120i) q^{64} +(1.90208 + 1.76487i) q^{65} +(-3.39876 - 0.512281i) q^{66} +(-6.59946 - 11.4306i) q^{67} +(4.35292 - 7.53948i) q^{68} +(-5.86754 + 7.35767i) q^{69} +(4.43805 + 2.45276i) q^{70} +(-2.25638 - 2.82941i) q^{71} +(-14.8298 + 2.23523i) q^{72} +(8.48581 + 5.78553i) q^{73} +(-2.56219 - 1.74687i) q^{74} +(-5.10491 + 0.769442i) q^{75} +(-0.274425 - 0.344118i) q^{76} +(2.75337 - 3.08109i) q^{77} +(-1.37217 + 1.72065i) q^{78} +(1.75973 - 3.04795i) q^{79} +(1.32876 + 2.30148i) q^{80} +(-7.82603 - 1.17958i) q^{81} +(2.25949 + 2.09650i) q^{82} +(-13.4047 + 6.45535i) q^{83} +(4.78053 - 10.4213i) q^{84} +(13.9934 + 6.73886i) q^{85} +(0.510791 + 1.30147i) q^{86} +(0.817086 + 10.9033i) q^{87} +(-3.80792 + 1.17459i) q^{88} +(1.22833 - 16.3909i) q^{89} +(-2.50669 - 10.9825i) q^{90} +(-0.827014 - 2.51318i) q^{91} +(-1.02221 + 4.47857i) q^{92} +(-19.5482 - 6.02981i) q^{93} +(0.250226 - 0.637565i) q^{94} +(0.575614 - 0.534092i) q^{95} +(-14.4253 + 9.83498i) q^{96} -5.41958 q^{97} +(-2.75092 - 4.37786i) q^{98} -9.17972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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