LMFDB - Embedded newform 74.2.h.a.21.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(3,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("74.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.h (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			21.2
Root			$0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	74.21
Dual form			74.2.h.a.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 - 0.939693i) q^{2} +(0.326352 - 0.118782i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.839712 + 0.148064i) q^{5} -0.347296i q^{6} +(0.240460 - 1.36372i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})$	\(q+(0.342020 - 0.939693i) q^{2} +(0.326352 - 0.118782i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.839712 + 0.148064i) q^{5} -0.347296i q^{6} +(0.240460 - 1.36372i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.20574 + 1.85083i) q^{9} +(0.426333 - 0.738430i) q^{10} +(0.466006 + 0.807147i) q^{11} +(-0.326352 - 0.118782i) q^{12} +(-2.34092 + 2.78980i) q^{13} +(-1.19923 - 0.692377i) q^{14} +(0.291629 - 0.0514220i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.84539 + 3.39101i) q^{17} +(0.984808 + 2.70574i) q^{18} +(-1.30826 - 3.59443i) q^{19} +(-0.548083 - 0.653180i) q^{20} +(-0.0835109 - 0.473614i) q^{21} +(0.917853 - 0.161842i) q^{22} +(0.920780 + 0.531613i) q^{23} +(-0.223238 + 0.266044i) q^{24} +(-4.01527 - 1.46144i) q^{25} +(1.82091 + 3.15391i) q^{26} +(-1.02094 + 1.76833i) q^{27} +(-1.06078 + 0.890103i) q^{28} +(0.873775 - 0.504474i) q^{29} +(0.0514220 - 0.291629i) q^{30} -7.33920i q^{31} +(0.984808 + 0.173648i) q^{32} +(0.247957 + 0.208060i) q^{33} +(4.15968 - 1.51400i) q^{34} +(0.403834 - 1.10953i) q^{35} +2.87939 q^{36} +(1.15600 - 5.97191i) q^{37} -3.82511 q^{38} +(-0.432584 + 1.18851i) q^{39} +(-0.801244 + 0.291629i) q^{40} +(-0.186251 - 0.156283i) q^{41} +(-0.473614 - 0.0835109i) q^{42} -5.13740i q^{43} +(0.161842 - 0.917853i) q^{44} +(-2.12622 + 1.22758i) q^{45} +(0.814478 - 0.683428i) q^{46} +(3.89795 - 6.75145i) q^{47} +(0.173648 + 0.300767i) q^{48} +(4.77595 + 1.73830i) q^{49} +(-2.74661 + 3.27328i) q^{50} +(1.33139 + 0.768679i) q^{51} +(3.58649 - 0.632396i) q^{52} +(2.25380 + 12.7819i) q^{53} +(1.31250 + 1.56418i) q^{54} +(0.271802 + 0.746769i) q^{55} +(0.473614 + 1.30124i) q^{56} +(-0.853909 - 1.01765i) q^{57} +(-0.175202 - 0.993621i) q^{58} +(-9.61896 + 1.69608i) q^{59} +(-0.256454 - 0.148064i) q^{60} +(0.255191 - 0.304124i) q^{61} +(-6.89659 - 2.51015i) q^{62} +(1.99362 + 3.45305i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-2.37876 + 1.99602i) q^{65} +(0.280319 - 0.161842i) q^{66} +(-2.47277 + 14.0238i) q^{67} -4.42664i q^{68} +(0.363645 + 0.0641204i) q^{69} +(-0.904494 - 0.758960i) q^{70} +(12.8449 - 4.67517i) q^{71} +(0.984808 - 2.70574i) q^{72} -13.1543 q^{73} +(-5.21638 - 3.12879i) q^{74} -1.48398 q^{75} +(-1.30826 + 3.59443i) q^{76} +(1.21278 - 0.441414i) q^{77} +(0.968886 + 0.812992i) q^{78} +(3.43258 + 0.605257i) q^{79} +0.852666i q^{80} +(1.37686 - 7.80856i) q^{81} +(-0.210560 + 0.121567i) q^{82} +(-12.8078 + 10.7470i) q^{83} +(-0.240460 + 0.416489i) q^{84} +(1.88722 + 3.26877i) q^{85} +(-4.82758 - 1.75710i) q^{86} +(0.225236 - 0.268425i) q^{87} +(-0.807147 - 0.466006i) q^{88} +(6.19352 - 1.09209i) q^{89} +(0.426333 + 2.41785i) q^{90} +(3.24160 + 3.86318i) q^{91} +(-0.363645 - 0.999105i) q^{92} +(-0.871767 - 2.39516i) q^{93} +(-5.01111 - 5.97200i) q^{94} +(-0.566360 - 3.21199i) q^{95} +(0.342020 - 0.0603074i) q^{96} +(6.47160 + 3.73638i) q^{97} +(3.26694 - 3.89339i) q^{98} +(-2.52178 - 0.917853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$2$	0.342020	−	0.939693i	0.241845	−	0.664463i
$3$	0.326352	−	0.118782i	0.188419	−	0.0685790i	−0.246087	−	0.969248i	$-0.579145\pi$
$3$	0.326352	−	0.118782i	0.188419	−	0.0685790i	0.434507	+	0.900669i	$0.356923\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$	0.839712	+	0.148064i	0.375530	+	0.0662162i	0.358228	−	0.933634i	$-0.383381\pi$
$5$	0.839712	+	0.148064i	0.375530	+	0.0662162i	0.0173025	+	0.999850i	$0.494492\pi$
$6$		−	0.347296i		−	0.141783i
$7$	0.240460	−	1.36372i	0.0908854	−	0.515437i	−0.905045	−	0.425315i	$-0.860163\pi$
$7$	0.240460	−	1.36372i	0.0908854	−	0.515437i	0.995931	−	0.0901216i	$-0.0287256\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−2.20574	+	1.85083i	−0.735246	+	0.616944i
$10$	0.426333	−	0.738430i	0.134818	−	0.233512i
$11$	0.466006	+	0.807147i	0.140506	+	0.243364i	0.927687	−	0.373358i	$-0.121794\pi$
$11$	0.466006	+	0.807147i	0.140506	+	0.243364i	−0.787181	+	0.616722i	$0.788460\pi$
$12$	−0.326352	−	0.118782i	−0.0942097	−	0.0342895i
$13$	−2.34092	+	2.78980i	−0.649254	+	0.773750i	−0.985801	−	0.167916i	$-0.946296\pi$
$13$	−2.34092	+	2.78980i	−0.649254	+	0.773750i	0.336548	+	0.941666i	$0.390741\pi$
$14$	−1.19923	−	0.692377i	−0.320508	−	0.185046i
$15$	0.291629	−	0.0514220i	0.0752982	−	0.0132771i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	2.84539	+	3.39101i	0.690109	+	0.822440i	0.991369	−	0.131102i	$-0.0418517\pi$
$17$	2.84539	+	3.39101i	0.690109	+	0.822440i	−0.301260	+	0.953542i	$0.597407\pi$
$18$	0.984808	+	2.70574i	0.232121	+	0.637748i
$19$	−1.30826	−	3.59443i	−0.300136	−	0.824618i	−0.994475	−	0.104970i	$-0.966525\pi$
$19$	−1.30826	−	3.59443i	−0.300136	−	0.824618i	0.694339	−	0.719648i	$-0.255697\pi$
$20$	−0.548083	−	0.653180i	−0.122555	−	0.146055i
$21$	−0.0835109	−	0.473614i	−0.0182236	−	0.103351i
$22$	0.917853	−	0.161842i	0.195687	−	0.0345049i
$23$	0.920780	+	0.531613i	0.191996	+	0.110849i	0.592917	−	0.805264i	$-0.297976\pi$
$23$	0.920780	+	0.531613i	0.191996	+	0.110849i	−0.400921	+	0.916113i	$0.631310\pi$
$24$	−0.223238	+	0.266044i	−0.0455682	+	0.0543061i
$25$	−4.01527	−	1.46144i	−0.803054	−	0.292288i
$26$	1.82091	+	3.15391i	0.357110	+	0.618532i
$27$	−1.02094	+	1.76833i	−0.196481	+	0.340315i
$28$	−1.06078	+	0.890103i	−0.200469	+	0.168214i
$29$	0.873775	−	0.504474i	0.162256	−	0.0936786i	−0.416673	−	0.909056i	$-0.636804\pi$
$29$	0.873775	−	0.504474i	0.162256	−	0.0936786i	0.578929	+	0.815378i	$0.303471\pi$
$30$	0.0514220	−	0.291629i	0.00938833	−	0.0532439i
$31$		−	7.33920i		−	1.31816i	−0.752073	−	0.659080i	$-0.770946\pi$
$31$		−	7.33920i		−	1.31816i	0.752073	−	0.659080i	$-0.229054\pi$
$32$	0.984808	+	0.173648i	0.174091	+	0.0306970i
$33$	0.247957	+	0.208060i	0.0431637	+	0.0362187i
$34$	4.15968	−	1.51400i	0.713380	−	0.259649i
$35$	0.403834	−	1.10953i	0.0682605	−	0.187544i
$36$	2.87939			0.479898
$37$	1.15600	−	5.97191i	0.190045	−	0.981775i
$37$	1.15600	−	5.97191i	0.190045	−	0.981775i
$38$	−3.82511			−0.620515
$39$	−0.432584	+	1.18851i	−0.0692689	+	0.190315i
$40$	−0.801244	+	0.291629i	−0.126688	+	0.0461106i
$41$	−0.186251	−	0.156283i	−0.0290876	−	0.0244074i	0.628128	−	0.778110i	$-0.283821\pi$
$41$	−0.186251	−	0.156283i	−0.0290876	−	0.0244074i	−0.657216	+	0.753703i	$0.728266\pi$
$42$	−0.473614	−	0.0835109i	−0.0730802	−	0.0128860i
$43$		−	5.13740i		−	0.783447i	−0.920083	−	0.391723i	$-0.871879\pi$
$43$		−	5.13740i		−	0.783447i	0.920083	−	0.391723i	$-0.128121\pi$
$44$	0.161842	−	0.917853i	0.0243986	−	0.138372i
$45$	−2.12622	+	1.22758i	−0.316959	+	0.182996i
$46$	0.814478	−	0.683428i	0.120088	−	0.100766i
$47$	3.89795	−	6.75145i	0.568574	−	0.984800i	−0.428133	−	0.903716i	$-0.640829\pi$
$47$	3.89795	−	6.75145i	0.568574	−	0.984800i	0.996707	−	0.0810838i	$-0.0258381\pi$
$48$	0.173648	+	0.300767i	0.0250640	+	0.0434120i
$49$	4.77595	+	1.73830i	0.682278	+	0.248329i
$50$	−2.74661	+	3.27328i	−0.388429	+	0.462911i
$51$	1.33139	+	0.768679i	0.186432	+	0.107637i
$52$	3.58649	−	0.632396i	0.497357	−	0.0876975i
$53$	2.25380	+	12.7819i	0.309583	+	1.75573i	0.601106	+	0.799170i	$0.294727\pi$
$53$	2.25380	+	12.7819i	0.309583	+	1.75573i	−0.291522	+	0.956564i	$0.594162\pi$
$54$	1.31250	+	1.56418i	0.178609	+	0.212858i
$55$	0.271802	+	0.746769i	0.0366497	+	0.100694i
$56$	0.473614	+	1.30124i	0.0632893	+	0.173886i
$57$	−0.853909	−	1.01765i	−0.113103	−	0.134791i
$58$	−0.175202	−	0.993621i	−0.0230052	−	0.130469i
$59$	−9.61896	+	1.69608i	−1.25228	+	0.220811i	−0.760172	−	0.649722i	$-0.774885\pi$
$59$	−9.61896	+	1.69608i	−1.25228	+	0.220811i	−0.492110	+	0.870533i	$0.663774\pi$
$60$	−0.256454	−	0.148064i	−0.0331081	−	0.0191150i
$61$	0.255191	−	0.304124i	0.0326738	−	0.0389391i	−0.749460	−	0.662050i	$-0.769687\pi$
$61$	0.255191	−	0.304124i	0.0326738	−	0.0389391i	0.782134	+	0.623110i	$0.214131\pi$
$62$	−6.89659	−	2.51015i	−0.875868	−	0.318790i
$63$	1.99362	+	3.45305i	0.251173	+	0.435044i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−2.37876	+	1.99602i	−0.295049	+	0.247576i
$66$	0.280319	−	0.161842i	0.0345049	−	0.0199214i
$67$	−2.47277	+	14.0238i	−0.302097	+	1.71328i	0.334765	+	0.942302i	$0.391343\pi$
$67$	−2.47277	+	14.0238i	−0.302097	+	1.71328i	−0.636862	+	0.770978i	$0.719768\pi$
$68$		−	4.42664i		−	0.536809i
$69$	0.363645	+	0.0641204i	0.0437777	+	0.00771918i
$70$	−0.904494	−	0.758960i	−0.108108	−	0.0907131i
$71$	12.8449	−	4.67517i	1.52441	−	0.554840i	0.562166	−	0.827024i	$-0.309968\pi$
$71$	12.8449	−	4.67517i	1.52441	−	0.554840i	0.962245	+	0.272184i	$0.0877459\pi$
$72$	0.984808	−	2.70574i	0.116061	−	0.318874i
$73$	−13.1543			−1.53959			−0.769794	−	0.638292i	$-0.779641\pi$
$73$	−13.1543			−1.53959			−0.769794	+	0.638292i	$0.779641\pi$
$74$	−5.21638	−	3.12879i	−0.606392	−	0.363715i
$75$	−1.48398			−0.171356
$76$	−1.30826	+	3.59443i	−0.150068	+	0.412309i
$77$	1.21278	−	0.441414i	0.138209	−	0.0503038i
$78$	0.968886	+	0.812992i	0.109705	+	0.0920532i
$79$	3.43258	+	0.605257i	0.386196	+	0.0680968i	0.363375	−	0.931643i	$-0.381624\pi$
$79$	3.43258	+	0.605257i	0.386196	+	0.0680968i	0.0228205	+	0.999740i	$0.492735\pi$
$80$			0.852666i			0.0953309i
$81$	1.37686	−	7.80856i	0.152984	−	0.867617i
$82$	−0.210560	+	0.121567i	−0.0232525	+	0.0134248i
$83$	−12.8078	+	10.7470i	−1.40584	+	1.17964i	−0.447399	+	0.894335i	$0.647649\pi$
$83$	−12.8078	+	10.7470i	−1.40584	+	1.17964i	−0.958438	+	0.285302i	$0.907906\pi$
$84$	−0.240460	+	0.416489i	−0.0262363	+	0.0454427i
$85$	1.88722	+	3.26877i	0.204698	+	0.354548i
$86$	−4.82758	−	1.75710i	−0.520571	−	0.189472i
$87$	0.225236	−	0.268425i	0.0241478	−	0.0287782i
$88$	−0.807147	−	0.466006i	−0.0860421	−	0.0496764i
$89$	6.19352	−	1.09209i	0.656512	−	0.115761i	0.164538	−	0.986371i	$-0.447387\pi$
$89$	6.19352	−	1.09209i	0.656512	−	0.115761i	0.491974	+	0.870610i	$0.336275\pi$
$90$	0.426333	+	2.41785i	0.0449394	+	0.254864i
$91$	3.24160	+	3.86318i	0.339812	+	0.404972i
$92$	−0.363645	−	0.999105i	−0.0379126	−	0.104164i
$93$	−0.871767	−	2.39516i	−0.0903981	−	0.248367i
$94$	−5.01111	−	5.97200i	−0.516856	−	0.615965i
$95$	−0.566360	−	3.21199i	−0.0581073	−	0.329543i
$96$	0.342020	−	0.0603074i	0.0349073	−	0.00615510i
$97$	6.47160	+	3.73638i	0.657092	+	0.379372i	0.791168	−	0.611599i	$-0.209473\pi$
$97$	6.47160	+	3.73638i	0.657092	+	0.379372i	−0.134076	+	0.990971i	$0.542807\pi$
$98$	3.26694	−	3.89339i	0.330011	−	0.393291i
$99$	−2.52178	−	0.917853i	−0.253449	−	0.0922477i
$100$	2.13648	+	3.70049i	0.213648	+	0.370049i
$101$	2.01440	−	3.48904i	0.200440	−	0.347173i	−0.748230	−	0.663439i	$-0.769096\pi$
$101$	2.01440	−	3.48904i	0.200440	−	0.347173i	0.948670	+	0.316267i	$0.102429\pi$
$102$	1.17768	−	0.988194i	0.116608	−	0.0978458i
$103$	0.201874	−	0.116552i	0.0198912	−	0.0114842i	−0.490021	−	0.871710i	$-0.663011\pi$
$103$	0.201874	−	0.116552i	0.0198912	−	0.0114842i	0.509913	+	0.860226i	$0.329678\pi$
$104$	0.632396	−	3.58649i	0.0620115	−	0.351685i
$105$		−	0.410064i		−	0.0400182i
$106$	12.7819	+	2.25380i	1.24149	+	0.218908i
$107$	4.94031	+	4.14542i	0.477598	+	0.400753i	0.849557	−	0.527497i	$-0.176869\pi$
$107$	4.94031	+	4.14542i	0.477598	+	0.400753i	−0.371959	+	0.928249i	$0.621314\pi$
$108$	1.91875	−	0.698367i	0.184632	−	0.0672004i
$109$	4.71183	−	12.9456i	0.451311	−	1.23997i	−0.480491	−	0.877000i	$-0.659542\pi$
$109$	4.71183	−	12.9456i	0.451311	−	1.23997i	0.931802	−	0.362967i	$-0.118236\pi$
$110$	0.794695			0.0757712
$111$	−0.332095	−	2.08625i	−0.0315211	−	0.198019i
$112$	1.38475			0.130847
$113$	1.45712	−	4.00340i	0.137074	−	0.376608i	−0.852095	−	0.523387i	$-0.824668\pi$
$113$	1.45712	−	4.00340i	0.137074	−	0.376608i	0.989169	+	0.146779i	$0.0468905\pi$
$114$	−1.24833	+	0.454355i	−0.116917	+	0.0425543i
$115$	0.694477	+	0.582736i	0.0647604	+	0.0543404i
$116$	−0.993621	−	0.175202i	−0.0922554	−	0.0162671i
$117$		−	10.4862i		−	0.969450i
$118$	−1.69608	+	9.61896i	−0.156137	+	0.885497i
$119$	5.30857	−	3.06491i	0.486636	−	0.280960i
$120$	−0.226847	+	0.190347i	−0.0207082	+	0.0173762i
$121$	5.06568	−	8.77401i	0.460516	−	0.797637i
$122$	−0.198503	−	0.343818i	−0.0179716	−	0.0311278i
$123$	−0.0793472	−	0.0288800i	−0.00715449	−	0.00260402i
$124$	−4.71755	+	5.62215i	−0.423648	+	0.504884i
$125$	−6.84743	−	3.95337i	−0.612453	−	0.353600i
$126$	3.92667	−	0.692377i	0.349815	−	0.0616819i
$127$	2.00201	+	11.3540i	0.177649	+	1.00750i	0.935041	+	0.354539i	$0.115362\pi$
$127$	2.00201	+	11.3540i	0.177649	+	1.00750i	−0.757392	+	0.652961i	$0.773527\pi$
$128$	−0.642788	−	0.766044i	−0.0568149	−	0.0677094i
$129$	−0.610233	−	1.67660i	−0.0537280	−	0.147616i
$130$	1.06206	+	2.91799i	0.0931488	+	0.255924i
$131$	−6.71929	−	8.00774i	−0.587067	−	0.699640i	0.387972	−	0.921671i	$-0.373176\pi$
$131$	−6.71929	−	8.00774i	−0.587067	−	0.699640i	−0.975039	+	0.222032i	$0.928731\pi$
$132$	−0.0562072	−	0.318767i	−0.00489221	−	0.0277451i
$133$	−5.21637	+	0.919786i	−0.452316	+	0.0797556i
$134$	12.3323	+	7.12007i	1.06535	+	0.615080i
$135$	−1.11912	+	1.33372i	−0.0963189	+	0.114788i
$136$	−4.15968	−	1.51400i	−0.356690	−	0.129825i
$137$	3.38948	+	5.87074i	0.289582	+	0.501572i	0.973710	−	0.227791i	$-0.0731502\pi$
$137$	3.38948	+	5.87074i	0.289582	+	0.501572i	−0.684128	+	0.729362i	$0.739817\pi$
$138$	0.184627	−	0.319784i	0.0157165	−	0.0272218i
$139$	−14.6691	+	12.3088i	−1.24421	+	1.04402i	−0.247032	+	0.969007i	$0.579455\pi$
$139$	−14.6691	+	12.3088i	−1.24421	+	1.04402i	−0.997183	+	0.0750129i	$0.976100\pi$
$140$	−1.02254	+	0.590366i	−0.0864208	+	0.0498951i
$141$	0.470150	−	2.66635i	0.0395938	−	0.224548i
$142$		−	13.6693i		−	1.14710i
$143$	−3.34266	−	0.589401i	−0.279527	−	0.0492882i
$144$	−2.20574	−	1.85083i	−0.183811	−	0.154236i
$145$	0.808414	−	0.294239i	0.0671351	−	0.0244352i
$146$	−4.49902	+	12.3610i	−0.372341	+	1.02300i
$147$	1.76512			0.145584
$148$	−4.72421	+	3.83169i	−0.388328	+	0.314963i
$149$	4.47583			0.366674			0.183337	−	0.983050i	$-0.441310\pi$
$149$	4.47583			0.366674			0.183337	+	0.983050i	$0.441310\pi$
$150$	−0.507552	+	1.39449i	−0.0414415	+	0.113860i
$151$	−8.30906	+	3.02425i	−0.676181	+	0.246110i	−0.657207	−	0.753710i	$-0.728262\pi$
$151$	−8.30906	+	3.02425i	−0.676181	+	0.246110i	−0.0189744	+	0.999820i	$0.506040\pi$
$152$	2.93020	+	2.45873i	0.237671	+	0.199430i
$153$	−12.5524	−	2.21332i	−1.01480	−	0.178936i
$154$		−	1.29061i		−	0.104000i
$155$	1.08667	−	6.16281i	0.0872834	−	0.495009i
$156$	1.09534	−	0.632396i	0.0876975	−	0.0506322i
$157$	−14.1119	+	11.8413i	−1.12626	+	0.945041i	−0.998903	−	0.0468171i	$-0.985092\pi$
$157$	−14.1119	+	11.8413i	−1.12626	+	0.945041i	−0.127352	+	0.991858i	$0.540648\pi$
$158$	1.74277	−	3.01856i	0.138647	−	0.240144i
$159$	2.25380	+	3.90370i	0.178738	+	0.309583i
$160$	0.801244	+	0.291629i	0.0633439	+	0.0230553i
$161$	0.946380	−	1.12785i	0.0745852	−	0.0888872i
$162$	−6.86673	−	3.96451i	−0.539501	−	0.311481i
$163$	9.09259	−	1.60327i	0.712186	−	0.125578i	0.194194	−	0.980963i	$-0.437791\pi$
$163$	9.09259	−	1.60327i	0.712186	−	0.125578i	0.517992	+	0.855385i	$0.326680\pi$
$164$	0.0422197	+	0.239440i	0.00329681	+	0.0186971i
$165$	0.177406	+	0.211424i	0.0138110	+	0.0164594i
$166$	5.71836	+	15.7111i	0.443831	+	1.21942i
$167$	−5.57821	−	15.3260i	−0.431655	−	1.18596i	−0.944796	−	0.327658i	$-0.893741\pi$
$167$	−5.57821	−	15.3260i	−0.431655	−	1.18596i	0.513142	−	0.858304i	$-0.328482\pi$
$168$	0.309130	+	0.368406i	0.0238499	+	0.0284232i
$169$	−0.0456446	−	0.258863i	−0.00351112	−	0.0199126i
$170$	3.71710	−	0.655426i	0.285089	−	0.0502689i
$171$	9.53837	+	5.50698i	0.729417	+	0.421129i
$172$	−3.30226	+	3.93548i	−0.251795	+	0.300077i
$173$	−1.80631	−	0.657444i	−0.137331	−	0.0499846i	0.272440	−	0.962173i	$-0.412169\pi$
$173$	−1.80631	−	0.657444i	−0.137331	−	0.0499846i	−0.409772	+	0.912188i	$0.634392\pi$
$174$	−0.175202	−	0.303459i	−0.0132820	−	0.0230052i
$175$	−2.95850	+	5.12427i	−0.223642	+	0.387359i
$176$	−0.713963	+	0.599086i	−0.0538170	+	0.0451578i
$177$	−2.93770	+	1.69608i	−0.220811	+	0.127485i
$178$	1.09209	−	6.19352i	0.0818553	−	0.464224i
$179$			18.8954i			1.41231i	0.708059	+	0.706154i	$0.249571\pi$
$179$			18.8954i			1.41231i	−0.708059	+	0.706154i	$0.750429\pi$
$180$	2.41785	+	0.426333i	0.180216	+	0.0317770i
$181$	5.25019	+	4.40543i	0.390243	+	0.327453i	0.816708	−	0.577051i	$-0.195797\pi$
$181$	5.25019	+	4.40543i	0.390243	+	0.327453i	−0.426465	+	0.904504i	$0.640241\pi$
$182$	4.73890	−	1.72482i	0.351270	−	0.127852i
$183$	0.0471573	−	0.129564i	0.00348597	−	0.00957763i
$184$	−1.06323			−0.0783820
$185$	1.85493	−	4.84352i	0.136377	−	0.356103i
$186$	−2.54888			−0.186893
$187$	−1.41107	+	3.87688i	−0.103188	+	0.283505i
$188$	−7.32575	+	2.66635i	−0.534285	+	0.194464i
$189$	2.16600	+	1.81749i	0.157553	+	0.132203i
$190$	−3.21199	−	0.566360i	−0.233022	−	0.0410881i
$191$		−	21.1777i		−	1.53236i	−0.642625	−	0.766181i	$-0.722155\pi$
$191$		−	21.1777i		−	1.53236i	0.642625	−	0.766181i	$-0.277845\pi$
$192$	0.0603074	−	0.342020i	0.00435231	−	0.0246832i
$193$	6.64750	−	3.83793i	0.478497	−	0.276261i	−0.241293	−	0.970452i	$-0.577571\pi$
$193$	6.64750	−	3.83793i	0.478497	−	0.276261i	0.719790	+	0.694192i	$0.244238\pi$
$194$	5.72447	−	4.80340i	0.410993	−	0.344864i
$195$	−0.539222	+	0.933960i	−0.0386145	+	0.0668822i
$196$	−2.54123	−	4.40154i	−0.181516	−	0.314395i
$197$	10.6770	+	3.88610i	0.760703	+	0.276873i	0.693102	−	0.720839i	$-0.256243\pi$
$197$	10.6770	+	3.88610i	0.760703	+	0.276873i	0.0676007	+	0.997712i	$0.478466\pi$
$198$	−1.72500	+	2.05578i	−0.122590	+	0.146098i
$199$	21.5452	+	12.4391i	1.52730	+	0.881788i	0.999474	+	0.0324362i	$0.0103266\pi$
$199$	21.5452	+	12.4391i	1.52730	+	0.881788i	0.527828	+	0.849352i	$0.323007\pi$
$200$	4.20805	−	0.741992i	0.297554	−	0.0524668i
$201$	0.858785	+	4.87041i	0.0605740	+	0.343532i
$202$	−2.58966	−	3.08624i	−0.182208	−	0.217147i
$203$	−0.477852	−	1.31289i	−0.0335387	−	0.0921467i
$204$	−0.525807	−	1.44464i	−0.0368139	−	0.101145i
$205$	−0.133257	−	0.158810i	−0.00930711	−	0.0110918i
$206$	−0.0404781	−	0.229563i	−0.00282024	−	0.0159944i
$207$	−3.01493	+	0.531613i	−0.209552	+	0.0369496i
$208$	−3.15391	−	1.82091i	−0.218684	−	0.126257i
$209$	2.29157	−	2.73099i	0.158511	−	0.188906i
$210$	−0.385334	−	0.140250i	−0.0265906	−	0.00967818i
$211$	−6.56480	−	11.3706i	−0.451939	−	0.782782i	0.546567	−	0.837415i	$-0.315934\pi$
$211$	−6.56480	−	11.3706i	−0.451939	−	0.782782i	−0.998506	+	0.0546333i	$0.982601\pi$
$212$	6.48956	−	11.2402i	0.445705	−	0.771983i
$213$	3.63664	−	3.05150i	0.249178	−	0.209085i
$214$	5.58510	−	3.22456i	0.381790	−	0.220426i
$215$	0.760664	−	4.31394i	0.0518768	−	0.294208i
$216$		−	2.04189i		−	0.138933i
$217$	−10.0086	−	1.76478i	−0.679427	−	0.119801i
$218$	−10.5534	−	8.85533i	−0.714765	−	0.599759i
$219$	−4.29291	+	1.56249i	−0.290088	+	0.105583i
$220$	0.271802	−	0.746769i	0.0183249	−	0.0503472i
$221$	−16.1210			−1.08442
$222$	−2.07402	−	0.401474i	−0.139199	−	0.0269451i
$223$	1.40208			0.0938902			0.0469451	−	0.998897i	$-0.485051\pi$
$223$	1.40208			0.0938902			0.0469451	+	0.998897i	$0.485051\pi$
$224$	0.473614	−	1.30124i	0.0316447	−	0.0869430i
$225$	11.5615	−	4.20805i	0.770767	−	0.280536i
$226$	−3.26360	−	2.73849i	−0.217092	−	0.182161i
$227$	2.96048	+	0.522013i	0.196494	+	0.0346472i	0.271029	−	0.962571i	$-0.412636\pi$
$227$	2.96048	+	0.522013i	0.196494	+	0.0346472i	−0.0745348	+	0.997218i	$0.523747\pi$
$228$			1.32845i			0.0879785i
$229$	1.61197	−	9.14196i	0.106522	−	0.604118i	−0.884079	−	0.467337i	$-0.845213\pi$
$229$	1.61197	−	9.14196i	0.106522	−	0.604118i	0.990601	−	0.136780i	$-0.0436755\pi$
$230$	0.785118	−	0.453288i	0.0517691	−	0.0298889i
$231$	0.343359	−	0.288113i	0.0225914	−	0.0189564i
$232$	−0.504474	+	0.873775i	−0.0331204	+	0.0573662i
$233$	13.7108	+	23.7478i	0.898225	+	1.55577i	0.829762	+	0.558118i	$0.188476\pi$
$233$	13.7108	+	23.7478i	0.898225	+	1.55577i	0.0684634	+	0.997654i	$0.478190\pi$
$234$	−9.85381	−	3.58649i	−0.644164	−	0.234456i
$235$	4.27280	−	5.09212i	0.278727	−	0.332173i
$236$	8.45877	+	4.88367i	0.550619	+	0.317900i
$237$	1.19212	−	0.210204i	0.0774368	−	0.0136542i
$238$	−1.06443	−	6.03669i	−0.0689968	−	0.391300i
$239$	0.475493	+	0.566671i	0.0307571	+	0.0366549i	0.781204	−	0.624276i	$-0.214606\pi$
$239$	0.475493	+	0.566671i	0.0307571	+	0.0366549i	−0.750447	+	0.660931i	$0.770162\pi$
$240$	0.101282	+	0.278269i	0.00653770	+	0.0179622i
$241$	−0.315775	−	0.867585i	−0.0203409	−	0.0558861i	0.929107	−	0.369812i	$-0.120578\pi$
$241$	−0.315775	−	0.867585i	−0.0203409	−	0.0558861i	−0.949448	+	0.313926i	$0.898356\pi$
$242$	−6.51231	−	7.76107i	−0.418627	−	0.498900i
$243$	−1.54189	−	8.74449i	−0.0989122	−	0.560959i
$244$	−0.390975	+	0.0689394i	−0.0250296	+	0.00441339i
$245$	3.75304	+	2.16682i	0.239773	+	0.138433i
$246$	−0.0542767	+	0.0646844i	−0.00346055	+	0.00412413i
$247$	13.0903	+	4.76446i	0.832913	+	0.303156i
$248$	3.66960	+	6.35593i	0.233020	+	0.403602i
$249$	−2.90329	+	5.02864i	−0.183988	+	0.318677i
$250$	−6.05691	+	5.08235i	−0.383073	+	0.321436i
$251$	−8.51425	+	4.91571i	−0.537415	+	0.310277i	−0.744031	−	0.668146i	$-0.767088\pi$
$251$	−8.51425	+	4.91571i	−0.537415	+	0.310277i	0.206616	+	0.978422i	$0.433755\pi$
$252$	0.692377	−	3.92667i	0.0436157	−	0.247357i
$253$			0.990940i			0.0622999i
$254$	11.3540	+	2.00201i	0.712410	+	0.125617i
$255$	1.00417	+	0.842599i	0.0628836	+	0.0527656i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	1.76857	−	4.85911i	0.110320	−	0.303103i	−0.872231	−	0.489094i	$-0.837327\pi$
$257$	1.76857	−	4.85911i	0.110320	−	0.303103i	0.982551	+	0.185991i	$0.0595496\pi$
$258$	−1.78420			−0.111080
$259$	−7.86602	−	3.01246i	−0.488771	−	0.187185i
$260$	3.10525			0.192580
$261$	−0.993621	+	2.72995i	−0.0615036	+	0.168980i
$262$	−9.82295	+	3.57526i	−0.606864	+	0.220880i
$263$	−15.7224	−	13.1926i	−0.969483	−	0.813493i	0.0129864	−	0.999916i	$-0.495866\pi$
$263$	−15.7224	−	13.1926i	−0.969483	−	0.813493i	−0.982470	+	0.186423i	$0.940311\pi$
$264$	−0.318767	−	0.0562072i	−0.0196188	−	0.00345932i
$265$			11.0668i			0.679831i
$266$	−0.919786	+	5.21637i	−0.0563957	+	0.319836i
$267$	1.89155	−	1.09209i	0.115761	−	0.0668345i
$268$	10.9086	−	9.15338i	0.666347	−	0.559132i
$269$	−8.25822	+	14.3037i	−0.503512	+	0.872109i	0.496479	+	0.868049i	$0.334626\pi$
$269$	−8.25822	+	14.3037i	−0.503512	+	0.872109i	−0.999992	+	0.00406062i	$0.998707\pi$
$270$	0.870524	+	1.50779i	0.0529784	+	0.0917613i
$271$	9.99255	+	3.63699i	0.607004	+	0.220932i	0.627192	−	0.778865i	$-0.284204\pi$
$271$	9.99255	+	3.63699i	0.607004	+	0.220932i	−0.0201876	+	0.999796i	$0.506426\pi$
$272$	−2.84539	+	3.39101i	−0.172527	+	0.205610i
$273$	1.51678	+	0.875712i	0.0917996	+	0.0530005i
$274$	6.67596	−	1.17715i	0.403310	−	0.0711144i
$275$	−0.691546	−	3.92195i	−0.0417018	−	0.236503i
$276$	−0.237352	−	0.282865i	−0.0142869	−	0.0170265i
$277$	2.24164	+	6.15886i	0.134687	+	0.370050i	0.988641	−	0.150299i	$-0.0480238\pi$
$277$	2.24164	+	6.15886i	0.134687	+	0.370050i	−0.853953	+	0.520350i	$0.825802\pi$
$278$	6.54938	+	17.9943i	0.392806	+	1.07923i
$279$	13.5836	+	16.1883i	0.813231	+	0.969171i
$280$	0.205032	+	1.16279i	0.0122530	+	0.0694903i
$281$	−24.3511	+	4.29375i	−1.45266	+	0.256144i	−0.843598	−	0.536976i	$-0.819567\pi$
$281$	−24.3511	+	4.29375i	−1.45266	+	0.256144i	−0.609066	+	0.793119i	$0.708456\pi$
$282$	−2.34475	−	1.35374i	−0.139628	−	0.0806143i
$283$	12.6719	−	15.1018i	0.753267	−	0.897709i	−0.244135	−	0.969741i	$-0.578504\pi$
$283$	12.6719	−	15.1018i	0.753267	−	0.897709i	0.997402	+	0.0720321i	$0.0229484\pi$
$284$	−12.8449	−	4.67517i	−0.762206	−	0.277420i
$285$	−0.566360	−	0.980965i	−0.0335483	−	0.0581073i
$286$	−1.69711	+	2.93948i	−0.100352	+	0.173815i
$287$	−0.257912	+	0.216414i	−0.0152241	+	0.0127745i
$288$	−2.49362	+	1.43969i	−0.146938	+	0.0848347i
$289$	−0.450647	+	2.55575i	−0.0265086	+	0.150338i
$290$		−	0.860296i		−	0.0505183i
$291$	2.55584	+	0.450663i	0.149826	+	0.0264183i
$292$	10.0767	+	8.45539i	0.589697	+	0.494814i
$293$	−1.10192	+	0.401067i	−0.0643751	+	0.0234306i	−0.374007	−	0.927426i	$-0.622016\pi$
$293$	−1.10192	+	0.401067i	−0.0643751	+	0.0234306i	0.309632	+	0.950856i	$0.399794\pi$
$294$	0.603706	−	1.65867i	0.0352088	−	0.0967355i
$295$	−8.32828			−0.484891
$296$	1.98483	+	5.74982i	0.115366	+	0.334202i
$297$	−1.90307			−0.110427
$298$	1.53082	−	4.20590i	0.0886782	−	0.243641i
$299$	−3.63856	+	1.32433i	−0.210423	+	0.0765879i
$300$	1.13680	+	0.953886i	0.0656330	+	0.0550727i
$301$	−7.00596	−	1.23534i	−0.403817	−	0.0712038i
$302$			8.84231i			0.508818i
$303$	0.242966	−	1.37793i	0.0139581	−	0.0791601i
$304$	3.31264	−	1.91255i	0.189993	−	0.109693i
$305$	0.259316	−	0.217592i	0.0148484	−	0.0124593i
$306$	−6.37301	+	11.0384i	−0.364321	+	0.631022i
$307$	−9.36820	−	16.2262i	−0.534671	−	0.926078i	−0.999179	−	0.0405091i	$-0.987102\pi$
$307$	−9.36820	−	16.2262i	−0.534671	−	0.926078i	0.464508	−	0.885569i	$-0.346231\pi$
$308$	−1.21278	−	0.441414i	−0.0691043	−	0.0251519i
$309$	0.0520376	−	0.0620160i	0.00296032	−	0.00352797i
$310$	−5.41949	−	3.12894i	−0.307806	−	0.177712i
$311$	−32.3417	+	5.70271i	−1.83393	+	0.323371i	−0.980301	−	0.197511i	$-0.936714\pi$
$311$	−32.3417	+	5.70271i	−1.83393	+	0.323371i	−0.853628	+	0.520882i	$0.825603\pi$
$312$	−0.219629	−	1.24558i	−0.0124340	−	0.0705169i
$313$	−13.8536	−	16.5101i	−0.783052	−	0.933206i	0.216015	−	0.976390i	$-0.430694\pi$
$313$	−13.8536	−	16.5101i	−0.783052	−	0.933206i	−0.999067	+	0.0431845i	$0.986250\pi$
$314$	6.30064	+	17.3109i	0.355565	+	0.976908i
$315$	1.16279	+	3.19475i	0.0655160	+	0.180004i
$316$	−2.24046	−	2.67008i	−0.126036	−	0.150204i
$317$	3.06019	+	17.3552i	0.171877	+	0.974764i	0.941687	+	0.336490i	$0.109240\pi$
$317$	3.06019	+	17.3552i	0.171877	+	0.974764i	−0.769810	+	0.638273i	$0.779649\pi$
$318$	4.43912	−	0.782736i	0.248933	−	0.0438937i
$319$	0.814370	+	0.470177i	0.0455960	+	0.0263248i
$320$	0.548083	−	0.653180i	0.0306388	−	0.0365139i
$321$	2.10468	+	0.766042i	0.117472	+	0.0427563i
$322$	−0.736153	−	1.27505i	−0.0410242	−	0.0710560i
$323$	8.46620	−	14.6639i	0.471072	−	0.815920i
$324$	−6.07398	+	5.09667i	−0.337443	+	0.283148i
$325$	13.4765	−	7.78068i	0.747543	−	0.431594i
$326$	1.60327	−	9.09259i	0.0887968	−	0.503592i
$327$		−	4.78451i		−	0.264584i
$328$	0.239440	+	0.0422197i	0.0132209	+	0.00233120i
$329$	−8.26976	−	6.93915i	−0.455927	−	0.382568i
$330$	0.259350	−	0.0943958i	0.0142768	−	0.00519632i
$331$	2.42916	−	6.67405i	0.133518	−	0.366839i	−0.854859	−	0.518861i	$-0.826356\pi$
$331$	2.42916	−	6.67405i	0.133518	−	0.366839i	0.988377	+	0.152022i	$0.0485784\pi$
$332$	16.7194			0.917594
$333$	8.50318	+	15.3120i	0.465971	+	0.839093i
$334$	−16.3096			−0.892421
$335$	−4.15283	+	11.4098i	−0.226894	+	0.623385i
$336$	0.451917	−	0.164484i	0.0246541	−	0.00897336i
$337$	−0.781329	−	0.655612i	−0.0425617	−	0.0357135i	0.621259	−	0.783606i	$-0.286622\pi$
$337$	−0.781329	−	0.655612i	−0.0425617	−	0.0357135i	−0.663820	+	0.747892i	$0.731066\pi$
$338$	−0.258863	−	0.0456446i	−0.0140803	−	0.00248274i
$339$		−	1.47960i		−	0.0803607i
$340$	0.655426	−	3.71710i	0.0355455	−	0.201588i
$341$	5.92381	−	3.42011i	0.320792	−	0.185210i
$342$	8.43718	−	7.07964i	0.456231	−	0.382823i
$343$	8.36562	−	14.4897i	0.451701	−	0.782369i
$344$	2.56870	+	4.44912i	0.138495	+	0.239881i
$345$	0.295863	+	0.107685i	0.0159287	+	0.00579758i
$346$	−1.23559	+	1.47252i	−0.0664258	+	0.0791632i
$347$	−4.31707	−	2.49246i	−0.231752	−	0.133802i	0.379628	−	0.925139i	$-0.376052\pi$
$347$	−4.31707	−	2.49246i	−0.231752	−	0.133802i	−0.611380	+	0.791337i	$0.709385\pi$
$348$	−0.345081	+	0.0608471i	−0.0184983	+	0.00326175i
$349$	−4.46786	−	25.3385i	−0.239159	−	1.35634i	−0.833675	−	0.552255i	$-0.813767\pi$
$349$	−4.46786	−	25.3385i	−0.239159	−	1.35634i	0.594516	−	0.804084i	$-0.297344\pi$
$350$	3.80338	+	4.53269i	0.203299	+	0.242282i
$351$	−2.54333	−	6.98774i	−0.135753	−	0.372978i
$352$	0.318767	+	0.875805i	0.0169903	+	0.0466806i
$353$	17.2409	+	20.5469i	0.917642	+	1.09360i	0.995321	+	0.0966250i	$0.0308048\pi$
$353$	17.2409	+	20.5469i	0.917642	+	1.09360i	−0.0776786	+	0.996978i	$0.524751\pi$
$354$	0.589043	+	3.34063i	0.0313073	+	0.177552i
$355$	11.4783	−	2.02393i	0.609202	−	0.107419i
$356$	−5.44649	−	3.14453i	−0.288664	−	0.166660i
$357$	1.36841	−	1.63080i	0.0724237	−	0.0863112i
$358$	17.7559	+	6.46260i	0.938426	+	0.341559i
$359$	−9.96674	−	17.2629i	−0.526024	−	0.911101i	−0.999540	−	0.0303155i	$-0.990349\pi$
$359$	−9.96674	−	17.2629i	−0.526024	−	0.911101i	0.473516	−	0.880785i	$-0.342985\pi$
$360$	1.22758	−	2.12622i	0.0646990	−	0.112062i
$361$	3.34650	−	2.80805i	0.176132	−	0.147792i
$362$	5.93542	−	3.42682i	0.311959	−	0.180109i
$363$	0.610995	−	3.46513i	0.0320689	−	0.181872i
$364$		−	5.04303i		−	0.264326i
$365$	−11.0458	−	1.94767i	−0.578162	−	0.101946i
$366$	−0.105621	−	0.0886268i	−0.00552091	−	0.00463260i
$367$	−13.9399	+	5.07371i	−0.727657	+	0.264846i	−0.679173	−	0.733978i	$-0.737661\pi$
$367$	−13.9399	+	5.07371i	−0.727657	+	0.264846i	−0.0484843	+	0.998824i	$0.515439\pi$
$368$	−0.363645	+	0.999105i	−0.0189563	+	0.0520820i
$369$	0.700076			0.0364445
$370$	−3.91700	−	3.39964i	−0.203635	−	0.176739i
$371$	17.9729			0.933106
$372$	−0.871767	+	2.39516i	−0.0451990	+	0.124183i
$373$	2.54239	−	0.925355i	0.131640	−	0.0479131i	−0.275360	−	0.961341i	$-0.588797\pi$
$373$	2.54239	−	0.925355i	0.131640	−	0.0479131i	0.407000	+	0.913428i	$0.366575\pi$
$374$	3.16046	+	2.65194i	0.163424	+	0.137129i
$375$	−2.70426	−	0.476834i	−0.139648	−	0.0246236i
$376$			7.79590i			0.402043i
$377$	−0.638055	+	3.61859i	−0.0328615	+	0.186367i
$378$	2.44870	−	1.41376i	0.125948	−	0.0727158i
$379$	15.4191	−	12.9382i	0.792027	−	0.664589i	−0.154220	−	0.988037i	$-0.549286\pi$
$379$	15.4191	−	12.9382i	0.792027	−	0.664589i	0.946246	+	0.323447i	$0.104842\pi$
$380$	−1.63077	+	2.82458i	−0.0836567	+	0.144898i
$381$	2.00201	+	3.46758i	0.102566	+	0.177649i
$382$	−19.9005	−	7.24319i	−1.01820	−	0.370594i
$383$	17.2995	−	20.6168i	0.883965	−	1.05347i	−0.114233	−	0.993454i	$-0.536441\pi$
$383$	17.2995	−	20.6168i	0.883965	−	1.05347i	0.998198	−	0.0600143i	$-0.0191146\pi$
$384$	−0.300767	−	0.173648i	−0.0153485	−	0.00886145i
$385$	1.08374	−	0.191092i	0.0552325	−	0.00973897i
$386$	−1.33290	−	7.55925i	−0.0678428	−	0.384756i
$387$	9.50848	+	11.3318i	0.483343	+	0.576026i
$388$	−2.55584	−	7.02210i	−0.129753	−	0.356493i
$389$	−0.332286	−	0.912949i	−0.0168476	−	0.0462883i	0.930984	−	0.365061i	$-0.118952\pi$
$389$	−0.332286	−	0.912949i	−0.0168476	−	0.0462883i	−0.947831	+	0.318772i	$0.896729\pi$
$390$	0.693210	+	0.826136i	0.0351021	+	0.0418330i
$391$	0.817279	+	4.63502i	0.0413316	+	0.234403i
$392$	−5.00524	+	0.882559i	−0.252803	+	0.0445760i
$393$	−3.14403	−	1.81521i	−0.158595	−	0.0915651i
$394$	7.30348	−	8.70395i	0.367944	−	0.438499i
$395$	2.79276	+	1.01648i	0.140519	+	0.0511448i
$396$	1.34181	+	2.32409i	0.0674286	+	0.116790i
$397$	−11.0940	+	19.2154i	−0.556794	+	0.964395i	0.440968	+	0.897523i	$0.354635\pi$
$397$	−11.0940	+	19.2154i	−0.556794	+	0.964395i	−0.997762	+	0.0668724i	$0.978698\pi$
$398$	19.0579	−	15.9915i	0.955285	−	0.801579i
$399$	−1.59312	+	0.919786i	−0.0797556	+	0.0460469i
$400$	0.741992	−	4.20805i	0.0370996	−	0.210402i
$401$			23.0731i			1.15222i	0.817374	+	0.576108i	$0.195429\pi$
$401$			23.0731i			1.15222i	−0.817374	+	0.576108i	$0.804571\pi$
$402$	4.87041	+	0.858785i	0.242914	+	0.0428323i
$403$	20.4749	+	17.1805i	1.01993	+	0.855820i
$404$	−3.78583	+	1.37793i	−0.188352	+	0.0685546i
$405$	2.31233	−	6.35307i	0.114901	−	0.315687i
$406$	−1.39715			−0.0693392
$407$	5.35891	−	1.84989i	0.265631	−	0.0916955i
$408$	−1.53736			−0.0761105
$409$	4.96326	−	13.6365i	0.245418	−	0.674279i	−0.754422	−	0.656389i	$-0.772083\pi$
$409$	4.96326	−	13.6365i	0.245418	−	0.674279i	0.999840	−	0.0178901i	$-0.00569489\pi$
$410$	−0.194809	+	0.0709048i	−0.00962095	+	0.00350174i
$411$	1.80350	+	1.51332i	0.0889602	+	0.0746465i
$412$	−0.229563	−	0.0404781i	−0.0113097	−	0.00199421i
$413$			13.5254i			0.665540i
$414$	−0.531613	+	3.01493i	−0.0261273	+	0.148176i
$415$	−12.3461	+	7.12801i	−0.606045	+	0.349900i
$416$	−2.78980	+	2.34092i	−0.136781	+	0.114773i
$417$	−3.32521	+	5.75943i	−0.162836	+	0.282041i
$418$	−1.78252	−	3.08742i	−0.0871861	−	0.151011i
$419$	−15.9383	−	5.80108i	−0.778639	−	0.283401i	−0.0780339	−	0.996951i	$-0.524864\pi$
$419$	−15.9383	−	5.80108i	−0.778639	−	0.283401i	−0.700605	+	0.713549i	$0.747086\pi$
$420$	−0.263584	+	0.314127i	−0.0128616	+	0.0153278i
$421$	13.6763	+	7.89599i	0.666540	+	0.384827i	0.794764	−	0.606918i	$-0.207594\pi$
$421$	13.6763	+	7.89599i	0.666540	+	0.384827i	−0.128224	+	0.991745i	$0.540928\pi$
$422$	−12.9301	+	2.27993i	−0.629429	+	0.110985i
$423$	3.89795	+	22.1064i	0.189525	+	1.07485i
$424$	−8.34281	−	9.94258i	−0.405163	−	0.482854i
$425$	−6.46927	−	17.7742i	−0.313806	−	0.862174i
$426$	−1.62367	−	4.46099i	−0.0786670	−	0.216136i
$427$	−0.353376	−	0.421138i	−0.0171011	−	0.0203803i
$428$	−1.11988	−	6.35115i	−0.0541314	−	0.306994i
$429$	−1.16089	+	0.204697i	−0.0560484	+	0.00988285i
$430$	−3.79361	−	2.19024i	−0.182944	−	0.105623i
$431$	−24.0972	+	28.7180i	−1.16072	+	1.38330i	−0.251048	+	0.967975i	$0.580775\pi$
$431$	−24.0972	+	28.7180i	−1.16072	+	1.38330i	−0.909675	+	0.415321i	$0.863669\pi$
$432$	−1.91875	−	0.698367i	−0.0923158	−	0.0336002i
$433$	−8.01147	−	13.8763i	−0.385007	−	0.666852i	0.606763	−	0.794883i	$-0.292468\pi$
$433$	−8.01147	−	13.8763i	−0.385007	−	0.666852i	−0.991770	+	0.128031i	$0.959134\pi$
$434$	−5.08150	+	8.80141i	−0.243920	+	0.422481i
$435$	0.228877	−	0.192051i	0.0109738	−	0.00920812i
$436$	−11.9308	+	6.88823i	−0.571380	+	0.329886i
$437$	0.706219	−	4.00517i	0.0337830	−	0.191593i
$438$			4.56842i			0.218288i
$439$	−29.8670	−	5.26636i	−1.42548	−	0.251350i	−0.592907	−	0.805271i	$-0.702020\pi$
$439$	−29.8670	−	5.26636i	−1.42548	−	0.251350i	−0.832569	+	0.553921i	$0.813131\pi$
$440$	−0.608772	−	0.510820i	−0.0290221	−	0.0243524i
$441$	−13.7518	+	5.00524i	−0.654847	+	0.238345i
$442$	−5.51372	+	15.1488i	−0.262261	+	0.720556i
$443$	24.5626			1.16700			0.583502	−	0.812112i	$-0.301682\pi$
$443$	24.5626			1.16700			0.583502	+	0.812112i	$0.301682\pi$
$444$	−1.08662	+	1.81163i	−0.0515686	+	0.0859762i
$445$	5.36247			0.254206
$446$	0.479539	−	1.31752i	0.0227069	−	0.0623866i
$447$	1.46069	−	0.531649i	0.0690885	−	0.0251462i
$448$	−1.06078	−	0.890103i	−0.0501173	−	0.0420534i
$449$	26.1350	+	4.60830i	1.23339	+	0.217479i	0.752079	−	0.659073i	$-0.229051\pi$
$449$	26.1350	+	4.60830i	1.23339	+	0.217479i	0.481307	+	0.876552i	$0.340162\pi$
$450$		−	12.3035i		−	0.579993i
$451$	0.0393493	−	0.223161i	0.00185289	−	0.0105082i
$452$	−3.68955	+	2.13017i	−0.173542	+	0.100195i
$453$	−2.35245	+	1.97394i	−0.110528	+	0.0927437i
$454$	1.50308	−	2.60340i	0.0705429	−	0.122184i
$455$	2.15001	+	3.72392i	0.100794	+	0.174580i
$456$	1.24833	+	0.454355i	0.0584585	+	0.0212771i
$457$	−15.2270	+	18.1468i	−0.712288	+	0.848872i	−0.993857	−	0.110669i	$-0.964701\pi$
$457$	−15.2270	+	18.1468i	−0.712288	+	0.848872i	0.281569	+	0.959541i	$0.409145\pi$
$458$	−8.03930	−	4.64149i	−0.375652	−	0.216883i
$459$	−8.90140	+	1.56956i	−0.415482	+	0.0732606i
$460$	−0.157425	−	0.892803i	−0.00733999	−	0.0416272i
$461$	−11.4935	−	13.6974i	−0.535306	−	0.637953i	0.428823	−	0.903389i	$-0.358929\pi$
$461$	−11.4935	−	13.6974i	−0.535306	−	0.637953i	−0.964128	+	0.265436i	$0.914484\pi$
$462$	−0.153302	−	0.421193i	−0.00713223	−	0.0195956i
$463$	−3.97134	−	10.9112i	−0.184564	−	0.507085i	0.812560	−	0.582878i	$-0.198073\pi$
$463$	−3.97134	−	10.9112i	−0.184564	−	0.507085i	−0.997124	+	0.0757928i	$0.975851\pi$
$464$	0.648540	+	0.772900i	0.0301077	+	0.0358810i
$465$	−0.377397	−	2.14032i	−0.0175013	−	0.0992551i
$466$	27.0050	−	4.76171i	1.25098	−	0.220582i
$467$	−5.99577	−	3.46166i	−0.277451	−	0.160187i	0.354818	−	0.934935i	$-0.384543\pi$
$467$	−5.99577	−	3.46166i	−0.277451	−	0.160187i	−0.632269	+	0.774749i	$0.717876\pi$
$468$	−6.74040	+	8.03290i	−0.311575	+	0.371321i
$469$	18.5299	+	6.74433i	0.855631	+	0.311424i
$470$	−3.32365	−	5.75673i	−0.153308	−	0.265538i
$471$	−3.19892	+	5.54069i	−0.147398	+	0.255301i
$472$	7.48222	−	6.27833i	0.344397	−	0.288984i
$473$	4.14664	−	2.39406i	0.190663	−	0.110079i
$474$	0.210204	−	1.19212i	0.00965497	−	0.0547561i
$475$			16.3445i			0.749939i
$476$	−6.03669	−	1.06443i	−0.276691	−	0.0487881i
$477$	−28.6285	−	24.0222i	−1.31081	−	1.09990i
$478$	0.695124	−	0.253005i	0.0317942	−	0.0115722i
$479$	−10.5351	+	28.9450i	−0.481361	+	1.32253i	0.426966	+	0.904268i	$0.359583\pi$
$479$	−10.5351	+	28.9450i	−0.481361	+	1.32253i	−0.908327	+	0.418261i	$0.862640\pi$
$480$	0.296128			0.0135163
$481$	13.9543	+	17.2047i	0.636262	+	0.784468i
$482$	−0.923265			−0.0420536
$483$	0.174884	−	0.480490i	0.00795750	−	0.0218630i
$484$	−9.52036	+	3.46513i	−0.432743	+	0.157506i
$485$	4.88106	+	4.09569i	0.221637	+	0.185976i
$486$	−8.74449	−	1.54189i	−0.396658	−	0.0699415i
$487$			26.1340i			1.18425i	0.805848	+	0.592123i	$0.201710\pi$
$487$			26.1340i			1.18425i	−0.805848	+	0.592123i	$0.798290\pi$
$488$	−0.0689394	+	0.390975i	−0.00312074	+	0.0176986i
$489$	2.77694	−	1.60327i	0.125578	−	0.0725023i
$490$	3.31976	−	2.78561i	0.149971	−	0.125841i
$491$	−4.72126	+	8.17747i	−0.213068	+	0.369044i	−0.952673	−	0.303997i	$-0.901679\pi$
$491$	−4.72126	+	8.17747i	−0.213068	+	0.369044i	0.739605	+	0.673041i	$0.235012\pi$
$492$	0.0422197	+	0.0731267i	0.00190341	+	0.00329681i
$493$	4.19691	+	1.52755i	0.189019	+	0.0687974i
$494$	8.95426	−	10.6713i	0.402871	−	0.480123i
$495$	−1.98167	−	1.14412i	−0.0890694	−	0.0514242i
$496$	7.22770	−	1.27444i	0.324533	−	0.0572240i
$497$	−3.28692	−	18.6410i	−0.147438	−	0.836164i
$498$	3.73239	+	4.44809i	0.167253	+	0.199324i
$499$	−4.66741	−	12.8236i	−0.208942	−	0.574063i	0.790311	−	0.612706i	$-0.209919\pi$
$499$	−4.66741	−	12.8236i	−0.208942	−	0.574063i	−0.999253	+	0.0386425i	$0.987697\pi$
$500$	2.70426	+	7.42990i	0.120938	+	0.332275i
$501$	−3.64092	−	4.33908i	−0.162664	−	0.193856i
$502$	1.70721	+	9.68205i	0.0761964	+	0.432131i
$503$	19.6874	−	3.47142i	0.877817	−	0.154783i	0.283460	−	0.958984i	$-0.408518\pi$
$503$	19.6874	−	3.47142i	0.877817	−	0.154783i	0.594357	+	0.804201i	$0.297407\pi$
$504$	−3.45305	−	1.99362i	−0.153811	−	0.0888029i
$505$	2.20812	−	2.63153i	0.0982599	−	0.117102i
$506$	0.931179	+	0.338921i	0.0413959	+	0.0150669i
$507$	−0.0456446	−	0.0790588i	−0.00202715	−	0.00351112i
$508$	5.76455	−	9.98450i	0.255761	−	0.442990i
$509$	18.6781	−	15.6728i	0.827894	−	0.694685i	−0.126913	−	0.991914i	$-0.540507\pi$
$509$	18.6781	−	15.6728i	0.827894	−	0.694685i	0.954806	+	0.297229i	$0.0960624\pi$
$510$	1.13523	−	0.655426i	0.0502689	−	0.0290227i
$511$	−3.16307	+	17.9387i	−0.139926	+	0.793560i
$512$			1.00000i			0.0441942i
$513$	7.69179	+	1.35627i	0.339601	+	0.0598808i
$514$	−3.96118	−	3.32383i	−0.174720	−	0.146608i
$515$	0.186773	−	0.0679798i	0.00823020	−	0.00299555i
$516$	−0.610233	+	1.67660i	−0.0268640	+	0.0738082i
$517$	7.26588			0.319553
$518$	−5.52112	+	6.36132i	−0.242584	+	0.279500i
$519$	−0.667587			−0.0293038
$520$	1.06206	−	2.91799i	0.0465744	−	0.127962i
$521$	13.8664	−	5.04695i	0.607497	−	0.221111i	−0.0199104	−	0.999802i	$-0.506338\pi$
$521$	13.8664	−	5.04695i	0.607497	−	0.221111i	0.627408	+	0.778691i	$0.284116\pi$
$522$	2.22548	+	1.86740i	0.0974064	+	0.0817337i
$523$	9.25252	+	1.63147i	0.404585	+	0.0713392i	0.372237	−	0.928138i	$-0.378591\pi$
$523$	9.25252	+	1.63147i	0.404585	+	0.0713392i	0.0323471	+	0.999477i	$0.489702\pi$
$524$			10.4534i			0.456657i
$525$	−0.356839	+	2.02373i	−0.0155737	+	0.0883230i
$526$	−17.7744	+	10.2621i	−0.775000	+	0.447447i
$527$	24.8873	−	20.8829i	1.08411	−	0.909673i
$528$	−0.161842	+	0.280319i	−0.00704328	+	0.0121993i
$529$	−10.9348	−	18.9396i	−0.475425	−	0.823460i
$530$	10.3994	+	3.78508i	0.451722	+	0.164414i
$531$	18.0777	−	21.5442i	0.784507	−	0.934939i
$532$	4.58719	+	2.64842i	0.198880	+	0.114823i
$533$	0.871998	−	0.153757i	0.0377704	−	0.00665994i
$534$	−0.379277	−	2.15099i	−0.0164129	−	0.0930824i
$535$	3.53465	+	4.21244i	0.152816	+	0.182119i
$536$	−4.87041	−	13.3814i	−0.210370	−	0.577986i
$537$	2.24444	+	6.16654i	0.0968547	+	0.266106i
$538$	10.6166	+	12.6523i	0.457712	+	0.545480i
$539$	0.822556	+	4.66495i	0.0354300	+	0.200934i
$540$	1.71460	−	0.302330i	0.0737846	−	0.0130102i
$541$	−37.3740	−	21.5779i	−1.60684	−	0.927707i	−0.990072	−	0.140559i	$-0.955110\pi$
$541$	−37.3740	−	21.5779i	−1.60684	−	0.927707i	−0.616763	−	0.787149i	$-0.711556\pi$
$542$	6.83531	−	8.14600i	0.293602	−	0.349901i
$543$	2.23669	+	0.814090i	0.0959858	+	0.0349360i
$544$	2.21332	+	3.83359i	0.0948954	+	0.164364i
$545$	5.87335	−	10.1729i	0.251587	−	0.435761i
$546$	1.34167	−	1.12579i	0.0574181	−	0.0481795i
$547$	−21.1110	+	12.1884i	−0.902641	+	0.521140i	−0.878056	−	0.478558i	$-0.841160\pi$
$547$	−21.1110	+	12.1884i	−0.902641	+	0.521140i	−0.0245851	+	0.999698i	$0.507826\pi$
$548$	1.17715	−	6.67596i	0.0502855	−	0.285183i
$549$			1.14313i			0.0487878i
$550$	−3.92195	−	0.691546i	−0.167233	−	0.0294876i
$551$	−2.95643	−	2.48074i	−0.125948	−	0.105683i
$552$	−0.346986	+	0.126292i	−0.0147687	+	0.00537536i
$553$	1.65080	−	4.53553i	0.0701991	−	0.192870i
$554$	6.55413			0.278458
$555$	0.0300345	−	1.80102i	0.00127489	−	0.0764492i
$556$	19.1491			0.812104
$557$	10.4716	−	28.7704i	0.443695	−	1.21904i	−0.493350	−	0.869831i	$-0.664228\pi$
$557$	10.4716	−	28.7704i	0.443695	−	1.21904i	0.937045	−	0.349210i	$-0.113550\pi$
$558$	19.8579	−	7.22770i	0.840654	−	0.305973i
$559$	14.3323	+	12.0262i	0.606192	+	0.508656i
$560$	1.16279	+	0.205032i	0.0491370	+	0.00866418i
$561$			1.43284i			0.0604944i
$562$	−4.29375	+	24.3511i	−0.181121	+	1.02719i
$563$	3.05690	−	1.76490i	0.128833	−	0.0743819i	−0.434198	−	0.900817i	$-0.642968\pi$
$563$	3.05690	−	1.76490i	0.128833	−	0.0743819i	0.563032	+	0.826435i	$0.309635\pi$
$564$	−2.07406	+	1.74034i	−0.0873335	+	0.0732815i
$565$	1.81632	−	3.14596i	0.0764131	−	0.132351i
$566$	−9.85700	−	17.0728i	−0.414321	−	0.717625i
$567$	−10.3176	−	3.75529i	−0.433298	−	0.157707i
$568$	−8.78644	+	10.4713i	−0.368671	+	0.439365i
$569$	−31.5781	−	18.2316i	−1.32382	−	0.764310i	−0.339487	−	0.940611i	$-0.610254\pi$
$569$	−31.5781	−	18.2316i	−1.32382	−	0.764310i	−0.984336	+	0.176301i	$0.943587\pi$
$570$	−1.11551	+	0.196695i	−0.0467236	+	0.00823864i
$571$	−6.71527	−	38.0842i	−0.281025	−	1.59377i	−0.719147	−	0.694858i	$-0.755467\pi$
$571$	−6.71527	−	38.0842i	−0.281025	−	1.59377i	0.438122	−	0.898915i	$-0.355644\pi$
$572$	2.18176	+	2.60013i	0.0912242	+	0.108717i
$573$	−2.51553	−	6.91137i	−0.105088	−	0.288727i
$574$	0.115152	+	0.316376i	0.00480633	+	0.0132053i
$575$	−2.92026	−	3.48023i	−0.121783	−	0.145136i
$576$	0.500000	+	2.83564i	0.0208333	+	0.118152i
$577$	42.7190	−	7.53251i	1.77842	−	0.313583i	0.814574	−	0.580060i	$-0.196971\pi$
$577$	42.7190	−	7.53251i	1.77842	−	0.313583i	0.963841	+	0.266477i	$0.0858596\pi$
$578$	2.24749	+	1.29759i	0.0934831	+	0.0539725i
$579$	1.71354	−	2.04212i	0.0712124	−	0.0848677i
$580$	−0.808414	−	0.294239i	−0.0335676	−	0.0122176i
$581$	11.5761	+	20.0504i	0.480258	+	0.831831i
$582$	1.29763	−	2.24756i	0.0537886	−	0.0931646i
$583$	−9.26661	+	7.77561i	−0.383784	+	0.322033i
$584$	11.3919	−	6.57713i	0.471401	−	0.272163i
$585$	1.55263	−	8.80539i	0.0641932	−	0.364058i
$586$			1.17264i			0.0484414i
$587$	−0.0109487	−	0.00193056i	−0.000451903	−	7.96826e-5i	0.173422	−	0.984848i	$-0.444517\pi$
$587$	−0.0109487	−	0.00193056i	−0.000451903	−	7.96826e-5i	−0.173874	+	0.984768i	$0.555629\pi$
$588$	−1.35216	−	1.13460i	−0.0557621	−	0.0467900i
$589$	−26.3802	+	9.60161i	−1.08698	+	0.395628i
$590$	−2.84844	+	7.82602i	−0.117268	+	0.322192i
$591$	3.94605			0.162319
$592$	6.08192	+	0.101424i	0.249965	+	0.00416850i
$593$	−36.1152			−1.48307			−0.741537	−	0.670912i	$-0.765903\pi$
$593$	−36.1152			−1.48307			−0.741537	+	0.670912i	$0.765903\pi$
$594$	−0.650887	+	1.78830i	−0.0267062	+	0.0733747i
$595$	4.91147	−	1.78763i	0.201351	−	0.0732857i
$596$	−3.42868	−	2.87701i	−0.140444	−	0.117847i
$597$	8.50888	+	1.50034i	0.348245	+	0.0614050i
$598$			3.87208i			0.158341i
$599$	−2.78662	+	15.8037i	−0.113858	+	0.645721i	0.873451	+	0.486912i	$0.161877\pi$
$599$	−2.78662	+	15.8037i	−0.113858	+	0.645721i	−0.987309	+	0.158809i	$0.949234\pi$
$600$	1.28517	−	0.741992i	0.0524668	−	0.0302917i
$601$	−15.1796	+	12.7372i	−0.619189	+	0.519561i	−0.897549	−	0.440916i	$-0.854654\pi$
$601$	−15.1796	+	12.7372i	−0.619189	+	0.519561i	0.278359	+	0.960477i	$0.410209\pi$
$602$	−3.55702	+	6.16094i	−0.144973	+	0.251101i
$603$	−20.5014	−	35.5095i	−0.834882	−	1.44606i
$604$	8.30906	+	3.02425i	0.338091	+	0.123055i
$605$	5.55282	−	6.61759i	0.225754	−	0.269043i
$606$	−1.21173	−	0.699594i	−0.0492232	−	0.0284191i
$607$	−14.4410	+	2.54634i	−0.586143	+	0.103353i	−0.458852	−	0.888513i	$-0.651739\pi$
$607$	−14.4410	+	2.54634i	−0.586143	+	0.103353i	−0.127291	+	0.991865i	$0.540628\pi$
$608$	−0.664223	−	3.76700i	−0.0269378	−	0.152772i
$609$	−0.311896	−	0.371703i	−0.0126387	−	0.0150622i
$610$	−0.115778	−	0.318099i	−0.00468773	−	0.0128794i
$611$	9.71038	+	26.6791i	0.392840	+	1.07932i
$612$	8.19298	+	9.76401i	0.331182	+	0.394687i
$613$	−1.23791	−	7.02054i	−0.0499988	−	0.283557i	0.949549	−	0.313618i	$-0.101541\pi$
$613$	−1.23791	−	7.02054i	−0.0499988	−	0.283557i	−0.999548	+	0.0300607i	$0.990430\pi$
$614$	−18.4518	+	3.25354i	−0.744652	+	0.131302i
$615$	−0.0623527	−	0.0359993i	−0.00251430	−	0.00145163i
$616$	−0.829587	+	0.988664i	−0.0334250	+	0.0398344i
$617$	−1.54788	−	0.563382i	−0.0623153	−	0.0226809i	0.310674	−	0.950516i	$-0.399445\pi$
$617$	−1.54788	−	0.563382i	−0.0623153	−	0.0226809i	−0.372990	+	0.927835i	$0.621667\pi$
$618$	−0.0404781	−	0.0701101i	−0.00162827	−	0.00282024i
$619$	−6.28743	+	10.8902i	−0.252713	+	0.437712i	−0.964272	−	0.264914i	$-0.914656\pi$
$619$	−6.28743	+	10.8902i	−0.252713	+	0.437712i	0.711559	+	0.702627i	$0.247990\pi$
$620$	−4.79382	+	4.02249i	−0.192524	+	0.161547i
$621$	−1.88013	+	1.08549i	−0.0754471	+	0.0435594i
$622$	−5.70271	+	32.3417i	−0.228658	+	1.29678i
$623$		−	8.70882i		−	0.348911i
$624$	−1.24558	−	0.219629i	−0.0498629	−	0.00879218i
$625$	11.2019	+	9.39949i	0.448075	+	0.375979i
$626$	−20.2526	+	7.37135i	−0.809458	+	0.294619i
$627$	0.423465	−	1.16346i	0.0169116	−	0.0464641i
$628$	18.4218			0.735111
$629$	23.5400	−	13.0724i	0.938603	−	0.521232i
$630$	3.39978			0.135451
$631$	−7.72595	+	21.2269i	−0.307565	+	0.845028i	0.685565	+	0.728012i	$0.259555\pi$
$631$	−7.72595	+	21.2269i	−0.307565	+	0.845028i	−0.993130	+	0.117017i	$0.962667\pi$
$632$	−3.27533	+	1.19212i	−0.130286	+	0.0474201i
$633$	−3.49306	−	2.93102i	−0.138837	−	0.116498i
$634$	17.3552	+	3.06019i	0.689262	+	0.121535i
$635$			9.83047i			0.390110i
$636$	0.782736	−	4.43912i	0.0310375	−	0.176023i
$637$	−16.0296	+	9.25469i	−0.635116	+	0.366684i
$638$	0.720352	−	0.604447i	0.0285190	−	0.0239303i
$639$	−19.6796	+	34.0860i	−0.778511	+	1.34842i
$640$	−0.426333	−	0.738430i	−0.0168523	−	0.0291890i
$641$	29.1189	+	10.5984i	1.15013	+	0.418613i	0.845562	−	0.533878i	$-0.179266\pi$
$641$	29.1189	+	10.5984i	1.15013	+	0.418613i	0.304568	+	0.952491i	$0.401488\pi$
$642$	1.43969	−	1.71575i	0.0568199	−	0.0677154i
$643$	−0.920945	−	0.531708i	−0.0363185	−	0.0209685i	0.481731	−	0.876319i	$-0.340008\pi$
$643$	−0.920945	−	0.531708i	−0.0363185	−	0.0209685i	−0.518049	+	0.855351i	$0.673342\pi$
$644$	−1.44994	+	0.255663i	−0.0571356	+	0.0100745i
$645$	−0.264176	−	1.49821i	−0.0104019	−	0.0589922i
$646$	−10.8839	−	12.9710i	−0.428223	−	0.510336i
$647$	−4.56612	−	12.5453i	−0.179513	−	0.493207i	0.817001	−	0.576636i	$-0.195635\pi$
$647$	−4.56612	−	12.5453i	−0.179513	−	0.493207i	−0.996514	+	0.0834293i	$0.973413\pi$
$648$	2.71188	+	7.45084i	0.106533	+	0.292697i
$649$	−5.85148	−	6.97353i	−0.229691	−	0.273735i
$650$	−2.70220	−	15.3249i	−0.105989	−	0.601094i
$651$	−3.47595	+	0.612903i	−0.136233	+	0.0240216i
$652$	−7.99589	−	4.61643i	−0.313143	−	0.180793i
$653$	−5.99298	+	7.14215i	−0.234523	+	0.279494i	−0.870451	−	0.492254i	$-0.836173\pi$
$653$	−5.99298	+	7.14215i	−0.234523	+	0.279494i	0.635928	+	0.771748i	$0.280617\pi$
$654$	−4.49597	−	1.63640i	−0.175806	−	0.0639883i
$655$	−4.45661	−	7.71908i	−0.174134	−	0.301609i
$656$	0.121567	−	0.210560i	0.00474639	−	0.00822099i
$657$	29.0148	−	24.3463i	1.13198	−	0.949841i
$658$	−9.34909	+	5.39770i	−0.364466	+	0.210424i
$659$	−3.29553	+	18.6899i	−0.128376	+	0.728054i	0.850870	+	0.525376i	$0.176075\pi$
$659$	−3.29553	+	18.6899i	−0.128376	+	0.728054i	−0.979246	+	0.202677i	$0.935036\pi$
$660$		−	0.275995i		−	0.0107431i
$661$	21.2508	+	3.74709i	0.826560	+	0.145745i	0.570898	−	0.821021i	$-0.306595\pi$
$661$	21.2508	+	3.74709i	0.826560	+	0.145745i	0.255662	+	0.966766i	$0.417706\pi$
$662$	−5.44074	−	4.56532i	−0.211460	−	0.177436i
$663$	−5.26113	+	1.91490i	−0.204325	+	0.0743684i
$664$	5.71836	−	15.7111i	0.221915	−	0.609708i
$665$	−4.51643			−0.175140
$666$	17.2968	−	2.75336i	0.670239	−	0.106690i
$667$	1.07274			0.0415367
$668$	−5.57821	+	15.3260i	−0.215827	+	0.592981i
$669$	0.457571	−	0.166542i	0.0176907	−	0.00643890i
$670$	9.30137	+	7.80477i	0.359343	+	0.301525i
$671$	0.364394	+	0.0642524i	0.0140673	+	0.00248044i
$672$		−	0.480920i		−	0.0185519i
$673$	−7.18577	+	40.7525i	−0.276991	+	1.57089i	0.455574	+	0.890198i	$0.349434\pi$
$673$	−7.18577	+	40.7525i	−0.276991	+	1.57089i	−0.732565	+	0.680697i	$0.761677\pi$
$674$	−0.883304	+	0.509976i	−0.0340236	+	0.0196435i
$675$	6.68367	−	5.60827i	0.257255	−	0.215862i
$676$	−0.131428	+	0.227641i	−0.00505494	+	0.00875541i
$677$	2.29044	+	3.96715i	0.0880287	+	0.152470i	0.906678	−	0.421824i	$-0.138610\pi$
$677$	2.29044	+	3.96715i	0.0880287	+	0.152470i	−0.818649	+	0.574294i	$0.805277\pi$
$678$	−1.39037	−	0.506052i	−0.0533967	−	0.0194348i
$679$	6.65153	−	7.92699i	0.255262	−	0.304210i
$680$	−3.26877	−	1.88722i	−0.125351	−	0.0723717i
$681$	1.02816	−	0.181293i	0.0393994	−	0.00694717i
$682$	−1.18779	−	6.73631i	−0.0454830	−	0.257947i
$683$	23.1346	+	27.5707i	0.885220	+	1.05496i	0.998116	+	0.0613577i	$0.0195431\pi$
$683$	23.1346	+	27.5707i	0.885220	+	1.05496i	−0.112895	+	0.993607i	$0.536013\pi$
$684$	−3.76700	−	10.3497i	−0.144035	−	0.395732i
$685$	1.97694	+	5.43159i	0.0755349	+	0.207530i
$686$	−10.7546	−	12.8169i	−0.410614	−	0.489350i
$687$	−0.559833	−	3.17497i	−0.0213590	−	0.121133i
$688$	5.05935	−	0.892101i	0.192886	−	0.0340110i
$689$	−40.9350	−	23.6338i	−1.55950	−	0.900376i
$690$	0.202382	−	0.241189i	0.00770455	−	0.00918193i
$691$	33.8223	+	12.3103i	1.28666	+	0.468306i	0.892629	−	0.450791i	$-0.148858\pi$
$691$	33.8223	+	12.3103i	1.28666	+	0.468306i	0.394031	+	0.919097i	$0.371080\pi$
$692$	0.961119	+	1.66471i	0.0365363	+	0.0632827i
$693$	−1.85808	+	3.21829i	−0.0705826	+	0.122253i
$694$	−3.81867	+	3.20425i	−0.144955	+	0.121632i
$695$	−14.1403	+	8.16390i	−0.536372	+	0.309674i
$696$	−0.0608471	+	0.345081i	−0.00230640	+	0.0130803i
$697$		−	1.07627i		−	0.0407665i
$698$	−25.3385	−	4.46786i	−0.959077	−	0.169111i
$699$	7.29537	+	6.12154i	0.275936	+	0.231538i
$700$	5.56016	−	2.02373i	0.210154	−	0.0764900i
$701$	−2.16083	+	5.93682i	−0.0816132	+	0.224231i	−0.973787	−	0.227462i	$-0.926957\pi$
$701$	−2.16083	+	5.93682i	−0.0816132	+	0.224231i	0.892174	+	0.451692i	$0.149180\pi$
$702$	−7.43619			−0.280661
$703$	−22.9779	+	3.65769i	−0.866629	+	0.137952i
$704$	0.932013			0.0351266
$705$	0.789581	−	2.16936i	0.0297373	−	0.0817027i
$706$	25.2046	−	9.17371i	0.948586	−	0.345257i
$707$	−4.27368	−	3.58605i	−0.160728	−	0.134867i
$708$	3.34063	+	0.589043i	0.125549	+	0.0221376i
$709$			15.4046i			0.578533i	0.957249	+	0.289267i	$0.0934114\pi$
$709$			15.4046i			0.578533i	−0.957249	+	0.289267i	$0.906589\pi$
$710$	2.02393	−	11.4783i	0.0759566	−	0.430771i
$711$	−8.69161	+	5.01810i	−0.325961	+	0.188194i
$712$	−4.81771	+	4.04254i	−0.180551	+	0.151500i
$713$	3.90161	−	6.75779i	0.146117	−	0.253081i
$714$	−1.06443	−	1.84365i	−0.0398353	−	0.0689968i
$715$	−2.71960	−	0.989853i	−0.101707	−	0.0370184i
$716$	12.1457	−	14.4747i	0.453907	−	0.540945i
$717$	0.222489	+	0.128454i	0.00830899	+	0.00479719i
$718$	−19.6306	+	3.46141i	−0.732609	+	0.129179i
$719$	−0.517948	−	2.93743i	−0.0193162	−	0.109548i	0.973625	−	0.228153i	$-0.0732687\pi$
$719$	−0.517948	−	2.93743i	−0.0193162	−	0.109548i	−0.992941	+	0.118606i	$0.962158\pi$
$720$	−1.57814	−	1.88076i	−0.0588139	−	0.0700916i
$721$	−0.110401	−	0.303325i	−0.00411156	−	0.0112964i
$722$	−1.49413	−	4.10509i	−0.0556058	−	0.152776i
$723$	−0.206108	−	0.245630i	−0.00766523	−	0.00913506i
$724$	−1.19012	−	6.74951i	−0.0442305	−	0.250844i
$725$	−4.24570	+	0.748632i	−0.157681	+	0.0278035i
$726$	−3.04718	−	1.75929i	−0.113091	−	0.0652934i
$727$	−11.3263	+	13.4981i	−0.420068	+	0.500618i	−0.934030	−	0.357195i	$-0.883733\pi$
$727$	−11.3263	+	13.4981i	−0.420068	+	0.500618i	0.513961	+	0.857813i	$0.328177\pi$
$728$	−4.73890	−	1.72482i	−0.175635	−	0.0639260i
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$	−5.60809	+	9.71349i	−0.207565	+	0.359513i
$731$	17.4210	−	14.6179i	0.644338	−	0.540663i
$732$	−0.119407	+	0.0689394i	−0.00441339	+	0.00254807i
$733$	−3.34139	+	18.9500i	−0.123417	+	0.699933i	0.858818	+	0.512280i	$0.171199\pi$
$733$	−3.34139	+	18.9500i	−0.123417	+	0.699933i	−0.982235	+	0.187653i	$0.939912\pi$
$734$			14.8345i			0.547553i
$735$	1.48219	+	0.261350i	0.0546714	+	0.00964005i
$736$	0.814478	+	0.683428i	0.0300221	+	0.0251915i
$737$	−12.4716	+	4.53929i	−0.459397	+	0.167207i
$738$	0.239440	−	0.657856i	0.00881391	−	0.0242160i
$739$	33.3412			1.22648			0.613238	−	0.789898i	$-0.289867\pi$
$739$	33.3412			1.22648			0.613238	+	0.789898i	$0.289867\pi$
$740$	−4.53431	+	2.51803i	−0.166685	+	0.0925645i
$741$	4.83796			0.177727
$742$	6.14709	−	16.8890i	0.225667	−	0.620014i
$743$	34.4286	−	12.5310i	1.26306	−	0.459717i	0.378267	−	0.925697i	$-0.376520\pi$
$743$	34.4286	−	12.5310i	1.26306	−	0.459717i	0.884795	+	0.465980i	$0.154298\pi$
$744$	1.95255	+	1.63839i	0.0715841	+	0.0600662i
$745$	3.75840	+	0.662708i	0.137697	+	0.0242797i
$746$		−	2.70556i		−	0.0990575i
$747$	8.35968	−	47.4101i	0.305865	−	1.73465i
$748$	3.57295	−	2.06284i	0.130640	−	0.0754250i
$749$	6.84112	−	5.74038i	0.249969	−	0.209749i
$750$	−1.37299	+	2.37809i	−0.0501345	+	0.0868355i
$751$	−9.48212	−	16.4235i	−0.346008	−	0.599303i	0.639529	−	0.768767i	$-0.279130\pi$
$751$	−9.48212	−	16.4235i	−0.346008	−	0.599303i	−0.985536	+	0.169465i	$0.945796\pi$
$752$	7.32575	+	2.66635i	0.267143	+	0.0972319i
$753$	−2.19474	+	2.61559i	−0.0799809	+	0.0953175i
$754$	3.18213	+	1.83721i	0.115886	+	0.0669071i
$755$	−7.42499	+	1.30923i	−0.270223	+	0.0476476i
$756$	−0.490993	−	2.78456i	−0.0178572	−	0.101273i
$757$	−28.2928	−	33.7181i	−1.02832	−	1.22551i	−0.973898	−	0.226987i	$-0.927112\pi$
$757$	−28.2928	−	33.7181i	−1.02832	−	1.22551i	−0.0544232	−	0.998518i	$-0.517332\pi$
$758$	−6.88426	−	18.9143i	−0.250047	−	0.687000i
$759$	0.117706	+	0.323395i	0.00427246	+	0.0117385i
$760$	2.09648	+	2.49848i	0.0760472	+	0.0906295i
$761$	1.42559	+	8.08493i	0.0516776	+	0.293078i	0.999683	−	0.0251759i	$-0.00801457\pi$
$761$	1.42559	+	8.08493i	0.0516776	+	0.293078i	−0.948005	+	0.318254i	$0.896903\pi$
$762$	3.94319	−	0.695290i	0.142847	−	0.0251877i
$763$	−16.5212	−	9.53850i	−0.598107	−	0.345317i
$764$	−13.6127	+	16.2230i	−0.492492	+	0.586929i
$765$	−10.2127	−	3.71710i	−0.369239	−	0.134392i
$766$	−13.4566	−	23.3076i	−0.486208	−	0.842138i
$767$	17.7855	−	30.8053i	0.642196	−	1.11232i
$768$	−0.266044	+	0.223238i	−0.00960005	+	0.00805540i
$769$	46.6866	−	26.9545i	1.68356	−	0.972006i	0.724303	−	0.689482i	$-0.242162\pi$
$769$	46.6866	−	26.9545i	1.68356	−	0.972006i	0.959260	−	0.282524i	$-0.0911717\pi$
$770$	0.191092	−	1.08374i	0.00688649	−	0.0390553i
$771$		−	1.79585i		−	0.0646761i
$772$	−7.55925	−	1.33290i	−0.272063	−	0.0479721i
$773$	−2.07004	−	1.73697i	−0.0744543	−	0.0624746i	0.604801	−	0.796377i	$-0.293253\pi$
$773$	−2.07004	−	1.73697i	−0.0744543	−	0.0624746i	−0.679255	+	0.733902i	$0.737697\pi$
$774$	13.9005	−	5.05935i	0.499642	−	0.181855i
$775$	−10.7258	+	29.4689i	−0.385282	+	1.05855i
$776$	−7.47277			−0.268257
$777$	−2.92492	−	0.0487769i	−0.104931	−	0.00174986i
$778$	−0.971540			−0.0348314
$779$	−0.318083	+	0.873927i	−0.0113965	+	0.0313117i
$780$	1.01341	−	0.368849i	0.0362857	−	0.0132069i
$781$	9.75936	+	8.18908i	0.349217	+	0.293028i
$782$	4.63502	+	0.817279i	0.165748	+	0.0292258i
$783$			2.06016i			0.0736242i
$784$	−0.882559	+	5.00524i	−0.0315200	+	0.178759i
$785$	−13.6032	+	7.85383i	−0.485520	+	0.280315i
$786$	−2.78106	+	2.33359i	−0.0991971	+	0.0832362i
$787$	4.84358	−	8.38932i	0.172655	−	0.299047i	−0.766692	−	0.642015i	$-0.778099\pi$
$787$	4.84358	−	8.38932i	0.172655	−	0.299047i	0.939347	+	0.342968i	$0.111432\pi$
$788$	−5.68110	−	9.83995i	−0.202381	−	0.350534i
$789$	−6.69808	−	2.43790i	−0.238458	−	0.0867916i
$790$	1.91036	−	2.27668i	0.0679677	−	0.0810007i
$791$	−5.10913	−	2.94976i	−0.181660	−	0.104881i
$792$	2.64285	−	0.466006i	0.0939097	−	0.0165588i
$793$	0.251065	+	1.42386i	0.00891558	+	0.0505628i
$794$	14.2622	+	16.9971i	0.506147	+	0.603203i
$795$	1.31455	+	3.61169i	0.0466221	+	0.128093i
$796$	−8.50888	−	23.3780i	−0.301589	−	0.828610i
$797$	19.7365	+	23.5210i	0.699102	+	0.833157i	0.992424	−	0.122856i	$-0.0392055\pi$
$797$	19.7365	+	23.5210i	0.699102	+	0.833157i	−0.293323	+	0.956013i	$0.594761\pi$
$798$	0.319438	+	1.81162i	0.0113080	+	0.0641308i
$799$	33.9854	−	5.99254i	1.20232	−	0.212001i
$800$	−3.70049	−	2.13648i	−0.130832	−	0.0755360i
$801$	−11.6400	+	13.8720i	−0.411280	+	0.490144i
$802$	21.6816	+	7.89146i	0.765604	+	0.278657i
$803$	−6.12996	−	10.6174i	−0.216322	−	0.374680i
$804$	2.47277	−	4.28297i	0.0872080	−	0.151049i
$805$	0.961681	−	0.806946i	0.0338948	−	0.0284411i
$806$	23.1472	−	13.3640i	0.815324	−	0.470728i
$807$	−0.996063	+	5.64895i	−0.0350631	+	0.198853i
$808$			4.02880i			0.141733i
$809$	12.8727	+	2.26981i	0.452580	+	0.0798021i	0.395292	−	0.918556i	$-0.370643\pi$
$809$	12.8727	+	2.26981i	0.452580	+	0.0798021i	0.0572885	+	0.998358i	$0.481755\pi$
$810$	−5.17907	−	4.34576i	−0.181974	−	0.152694i
$811$	42.7071	−	15.5441i	1.49965	−	0.545828i	0.543680	−	0.839292i	$-0.317030\pi$
$811$	42.7071	−	15.5441i	1.49965	−	0.545828i	0.955970	+	0.293464i	$0.0948081\pi$
$812$	−0.477852	+	1.31289i	−0.0167693	+	0.0460733i
$813$	3.69310			0.129523
$814$	0.0945286	−	5.66842i	0.00331322	−	0.198678i
$815$	7.87254			0.275763
$816$	−0.525807	+	1.44464i	−0.0184069	+	0.0505726i
$817$	−18.4660	+	6.72108i	−0.646044	+	0.235141i
$818$	−11.1165	−	9.32789i	−0.388681	−	0.326142i
$819$	−14.3002	−	2.52151i	−0.499690	−	0.0881088i
$820$			0.207312i			0.00723964i
$821$	−4.91748	+	27.8884i	−0.171621	+	0.973312i	0.770351	+	0.637620i	$0.220081\pi$
$821$	−4.91748	+	27.8884i	−0.171621	+	0.973312i	−0.941972	+	0.335692i	$0.891030\pi$
$822$	2.03889	−	1.17715i	0.0711144	−	0.0410579i
$823$	18.9218	−	15.8772i	0.659571	−	0.553446i	−0.250387	−	0.968146i	$-0.580558\pi$
$823$	18.9218	−	15.8772i	0.659571	−	0.553446i	0.909958	+	0.414700i	$0.136113\pi$
$824$	−0.116552	+	0.201874i	−0.00406028	+	0.00703261i
$825$	−0.691546	−	1.19779i	−0.0240765	−	0.0417018i
$826$	12.7097	+	4.62595i	0.442227	+	0.160957i
$827$	−8.00202	+	9.53644i	−0.278258	+	0.331614i	−0.887014	−	0.461743i	$-0.847224\pi$
$827$	−8.00202	+	9.53644i	−0.278258	+	0.331614i	0.608756	+	0.793357i	$0.291669\pi$
$828$	2.65128	+	1.53072i	0.0921384	+	0.0531961i
$829$	10.6721	−	1.88178i	0.370658	−	0.0653570i	0.0147833	−	0.999891i	$-0.495294\pi$
$829$	10.6721	−	1.88178i	0.370658	−	0.0653570i	0.355874	+	0.934534i	$0.384183\pi$
$830$	2.47553	+	14.0394i	0.0859270	+	0.487316i
$831$	1.46313	+	1.74369i	0.0507554	+	0.0604879i
$832$	1.24558	+	3.42219i	0.0431826	+	0.118643i
$833$	7.69484	+	21.1414i	0.266611	+	0.732506i
$834$	4.27481	+	5.09452i	0.148024	+	0.176409i
$835$	−2.41486	−	13.6954i	−0.0835697	−	0.473947i
$836$	−3.51089	+	0.619064i	−0.121427	+	0.0214108i
$837$	12.9781	+	7.49292i	0.448589	+	0.258993i
$838$	−10.9025	+	12.9931i	−0.376620	+	0.448838i
$839$	−23.7039	−	8.62752i	−0.818350	−	0.297855i	−0.101282	−	0.994858i	$-0.532294\pi$
$839$	−23.7039	−	8.62752i	−0.818350	−	0.297855i	−0.717069	+	0.697003i	$0.754517\pi$
$840$	0.205032	+	0.355126i	0.00707428	+	0.0122530i
$841$	−13.9910	+	24.2331i	−0.482449	+	0.835626i
$842$	12.0974	−	10.1509i	0.416903	−	0.349823i
$843$	−7.43700	+	4.29375i	−0.256144	+	0.147885i
$844$	−2.27993	+	12.9301i	−0.0784785	+	0.445073i
$845$		−	0.224129i		−	0.00771027i
$846$	22.1064	+	3.89795i	0.760033	+	0.134014i
$847$	−10.7472	−	9.01795i	−0.369277	−	0.309860i
$848$	−12.1964	+	4.43912i	−0.418825	+	0.152440i
$849$	2.34168	−	6.43370i	0.0803661	−	0.220804i
$850$	−18.9149			−0.648775
$851$	4.23916	−	4.88427i	0.145317	−	0.167431i
$852$	−4.74729			−0.162639
$853$	3.72709	−	10.2401i	0.127613	−	0.350614i	−0.859389	−	0.511323i	$-0.829156\pi$
$853$	3.72709	−	10.2401i	0.127613	−	0.350614i	0.987002	+	0.160709i	$0.0513779\pi$
$854$	−0.516602	+	0.188028i	−0.0176778	+	0.00643418i
$855$	7.19410	+	6.03656i	0.246033	+	0.206446i
$856$	−6.35115	−	1.11988i	−0.217078	−	0.0382767i
$857$			18.7526i			0.640575i	0.947320	+	0.320288i	$0.103780\pi$
$857$			18.7526i			0.640575i	−0.947320	+	0.320288i	$0.896220\pi$
$858$	−0.204697	+	1.16089i	−0.00698823	+	0.0396322i
$859$	−33.6788	+	19.4444i	−1.14910	+	0.663436i	−0.948669	−	0.316271i	$-0.897569\pi$
$859$	−33.6788	+	19.4444i	−1.14910	+	0.663436i	−0.200436	+	0.979707i	$0.564236\pi$
$860$	−3.35565	+	2.81572i	−0.114427	+	0.0960154i
$861$	−0.0584640	+	0.101263i	−0.00199245	+	0.00345102i
$862$	18.7443	+	32.4661i	0.638434	+	1.10580i
$863$	−26.5719	−	9.67137i	−0.904517	−	0.329217i	−0.152455	−	0.988310i	$-0.548718\pi$
$863$	−26.5719	−	9.67137i	−0.904517	−	0.329217i	−0.752061	+	0.659093i	$0.770940\pi$
$864$	−1.31250	+	1.56418i	−0.0446522	+	0.0532144i
$865$	−1.41944	−	0.819513i	−0.0482624	−	0.0278643i
$866$	−15.7795	+	2.78236i	−0.536210	+	0.0945483i
$867$	0.156508	+	0.887601i	0.00531529	+	0.0301445i
$868$	6.53264	+	7.78530i	0.221732	+	0.264250i
$869$	1.11107	+	3.05265i	0.0376906	+	0.103554i
$870$	−0.102188	−	0.280759i	−0.00346450	−	0.00951863i
$871$	−33.3350	−	39.7271i	−1.12951	−	1.34610i
$872$	2.39226	+	13.5672i	0.0810120	+	0.459442i
$873$	−21.1901	+	3.73638i	−0.717176	+	0.126457i
$874$	−3.52209	−	2.03348i	−0.119136	−	0.0687834i
$875$	−7.03781	+	8.38733i	−0.237921	+	0.283544i
$876$	4.29291	+	1.56249i	0.145044	+	0.0527917i
$877$	−0.375638	−	0.650624i	−0.0126844	−	0.0219700i	0.859614	−	0.510945i	$-0.170704\pi$
$877$	−0.375638	−	0.650624i	−0.0126844	−	0.0219700i	−0.872298	+	0.488975i	$0.837371\pi$
$878$	−15.1639	+	26.2646i	−0.511756	+	0.886388i
$879$	−0.311975	+	0.261778i	−0.0105227	+	0.00882956i
$880$	−0.688226	+	0.397348i	−0.0232001	+	0.0133946i
$881$	9.26268	−	52.5313i	0.312068	−	1.76982i	−0.276143	−	0.961117i	$-0.589056\pi$
$881$	9.26268	−	52.5313i	0.312068	−	1.76982i	0.588211	−	0.808708i	$-0.299833\pi$
$882$			14.6343i			0.492764i
$883$	−23.7723	−	4.19169i	−0.800001	−	0.141062i	−0.241321	−	0.970445i	$-0.577581\pi$
$883$	−23.7723	−	4.19169i	−0.800001	−	0.141062i	−0.558680	+	0.829384i	$0.688692\pi$
$884$	12.3494	+	10.3624i	0.415356	+	0.348525i
$885$	−2.71795	+	0.989253i	−0.0913629	+	0.0332534i
$886$	8.40090	−	23.0813i	0.282234	−	0.775431i
$887$	47.2073			1.58506			0.792532	−	0.609830i	$-0.208762\pi$
$887$	47.2073			1.58506			0.792532	+	0.609830i	$0.208762\pi$
$888$	1.33073	+	1.64070i	0.0446564	+	0.0550584i
$889$	15.9650			0.535448
$890$	1.83407	−	5.03908i	0.0614783	−	0.168910i
$891$	6.94427	−	2.52751i	0.232642	−	0.0846747i
$892$	−1.07406	−	0.901239i	−0.0359620	−	0.0301757i
$893$	−29.3671	−	5.17822i	−0.982733	−	0.173282i
$894$		−	1.55444i		−	0.0519882i
$895$	−2.79772	+	15.8667i	−0.0935176	+	0.530364i
$896$	−1.19923	+	0.692377i	−0.0400635	+	0.0231307i
$897$	−1.03014	+	0.864394i	−0.0343955	+	0.0288613i
$898$	13.2691	−	22.9827i	0.442795	−	0.766943i
$899$	−3.70244	−	6.41281i	−0.123483	−	0.213879i
$900$	−11.5615	−	4.20805i	−0.385384	−	0.140268i
$901$	−36.9307	+	44.0123i	−1.23034	+	1.46626i
$902$	−0.196245	−	0.113302i	−0.00653423	−	0.00377254i
$903$	−2.43315	+	0.429029i	−0.0809700	+	0.0142772i
$904$	0.739799	+	4.19561i	0.0246053	+	0.139544i
$905$	3.75636	+	4.47665i	0.124866	+	0.148809i
$906$	1.05031	+	2.88571i	0.0348942	+	0.0958711i
$907$	−7.33846	−	20.1623i	−0.243670	−	0.669477i	−0.999885	−	0.0151542i	$-0.995176\pi$
$907$	−7.33846	−	20.1623i	−0.243670	−	0.669477i	0.756216	−	0.654323i	$-0.227046\pi$
$908$	−1.93232	−	2.30285i	−0.0641262	−	0.0764226i
$909$	2.01440	+	11.4242i	0.0668134	+	0.378918i
$910$	4.23469	−	0.746690i	0.140379	−	0.0247525i
$911$	18.1914	+	10.5028i	0.602707	+	0.347973i	0.770106	−	0.637916i	$-0.220203\pi$
$911$	18.1914	+	10.5028i	0.602707	+	0.347973i	−0.167399	+	0.985889i	$0.553537\pi$
$912$	0.853909	−	1.01765i	0.0282757	−	0.0336977i
$913$	−14.6429	−	5.32958i	−0.484610	−	0.176384i
$914$	11.8445	+	20.5153i	0.391781	+	0.678584i
$915$	0.0587823	−	0.101814i	0.00194328	−	0.00336586i
$916$	−7.11118	+	5.96699i	−0.234960	+	0.197155i
$917$	−12.5360	+	7.23767i	−0.413976	+	0.239009i
$918$	−1.56956	+	8.90140i	−0.0518031	+	0.293790i
$919$		−	44.9184i		−	1.48172i	−0.671659	−	0.740860i	$-0.734418\pi$
$919$		−	44.9184i		−	1.48172i	0.671659	−	0.740860i	$-0.265582\pi$
$920$	−0.892803	−	0.157425i	−0.0294348	−	0.00519016i
$921$	−4.98472	−	4.18267i	−0.164252	−	0.137824i
$922$	−16.8024	+	6.11557i	−0.553357	+	0.201405i
$923$	−17.0261	+	46.7789i	−0.560422	+	1.53975i
$924$	−0.448224			−0.0147455
$925$	−13.3692	+	22.2894i	−0.439577	+	0.732871i
$926$	−11.6114			−0.381575
$927$	−0.229563	+	0.630718i	−0.00753982	+	0.0207155i
$928$	0.948102	−	0.345081i	0.0311230	−	0.0113278i
$929$	26.7338	+	22.4324i	0.877109	+	0.735982i	0.965583	−	0.260097i	$-0.0837545\pi$
$929$	26.7338	+	22.4324i	0.877109	+	0.735982i	−0.0884738	+	0.996079i	$0.528199\pi$
$930$	−2.14032	−	0.377397i	−0.0701839	−	0.0123753i
$931$		−	19.4409i		−	0.637151i
$932$	4.76171	−	27.0050i	0.155975	−	0.884579i
$933$	−9.87739	+	5.70271i	−0.323371	+	0.186698i
$934$	−5.30357	+	4.45022i	−0.173538	+	0.145616i
$935$	−1.75892	+	3.04653i	−0.0575227	+	0.0996323i
$936$	5.24310	+	9.08132i	0.171376	+	0.296832i
$937$	−10.7395	−	3.90885i	−0.350844	−	0.127697i	0.160586	−	0.987022i	$-0.448662\pi$
$937$	−10.7395	−	3.90885i	−0.350844	−	0.127697i	−0.511430	+	0.859325i	$0.670884\pi$
$938$	12.6752	−	15.1057i	0.413860	−	0.493219i
$939$	−6.48226	−	3.74253i	−0.211541	−	0.122133i
$940$	−6.54631	+	1.15429i	−0.213517	+	0.0376488i
$941$	−6.15749	−	34.9209i	−0.200729	−	1.13839i	−0.904021	−	0.427488i	$-0.859399\pi$
$941$	−6.15749	−	34.9209i	−0.200729	−	1.13839i	0.703293	−	0.710901i	$-0.251712\pi$
$942$	4.11245	+	4.90103i	0.133991	+	0.159684i
$943$	−0.0884143	−	0.242916i	−0.00287917	−	0.00791044i
$944$	−3.34063	−	9.17831i	−0.108728	−	0.298728i
$945$	1.54971	+	1.84688i	0.0504122	+	0.0600789i
$946$	−0.831449	−	4.71538i	−0.0270327	−	0.153310i
$947$	−33.4708	+	5.90181i	−1.08765	+	0.191783i	−0.688598	−	0.725143i	$-0.741774\pi$
$947$	−33.4708	+	5.90181i	−1.08765	+	0.191783i	−0.399057	+	0.916926i	$0.630662\pi$
$948$	−1.04834	−	0.605257i	−0.0340484	−	0.0196578i
$949$	30.7930	−	36.6977i	0.999583	−	1.19126i
$950$	15.3588	+	5.59016i	0.498307	+	0.181369i
$951$	3.06019	+	5.30040i	0.0992333	+	0.171877i
$952$	−3.06491	+	5.30857i	−0.0993342	+	0.172052i
$953$	−15.3276	+	12.8614i	−0.496509	+	0.416621i	−0.856352	−	0.516392i	$-0.827275\pi$
$953$	−15.3276	+	12.8614i	−0.496509	+	0.416621i	0.359843	+	0.933013i	$0.382830\pi$
$954$	−32.3650	+	18.6859i	−1.04786	+	0.604980i
$955$	3.13565	−	17.7831i	0.101467	−	0.575449i
$956$		−	0.739736i		−	0.0239248i
$957$	0.321620	+	0.0567102i	0.0103965	+	0.00183318i
$958$	23.5961	+	19.7995i	0.762357	+	0.639693i
$959$	8.82107	−	3.21061i	0.284847	−	0.103676i
$960$	0.101282	−	0.278269i	0.00326885	−	0.00898109i
$961$	−22.8639			−0.737544
$962$	20.9398	−	7.22840i	0.675127	−	0.233053i
$963$	−18.5695			−0.598394
$964$	−0.315775	+	0.867585i	−0.0101704	+	0.0279430i
$965$	6.15024	−	2.23850i	0.197983	−	0.0720600i
$966$	−0.391699	−	0.328674i	−0.0126027	−	0.0105749i
$967$	21.1585	+	3.73082i	0.680413	+	0.119975i	0.503164	−	0.864191i	$-0.332169\pi$
$967$	21.1585	+	3.73082i	0.680413	+	0.119975i	0.177249	+	0.984166i	$0.443280\pi$
$968$			10.1314i			0.325634i
$969$	1.02115	−	5.79122i	0.0328040	−	0.186041i
$970$	5.51811	−	3.18588i	0.177176	−	0.102293i
$971$	0.671321	−	0.563305i	0.0215437	−	0.0180773i	−0.631952	−	0.775007i	$-0.717746\pi$
$971$	0.671321	−	0.563305i	0.0215437	−	0.0180773i	0.653496	+	0.756930i	$0.273302\pi$
$972$	−4.43969	+	7.68977i	−0.142403	+	0.246650i
$973$	13.2584	+	22.9642i	0.425045	+	0.736200i
$974$	24.5580	+	8.93836i	0.786887	+	0.286404i
$975$	3.47388	−	4.14001i	0.111253	−	0.132587i
$976$	0.343818	+	0.198503i	0.0110053	+	0.00635393i
$977$	14.3294	−	2.52665i	0.458437	−	0.0808348i	0.0603394	−	0.998178i	$-0.480782\pi$
$977$	14.3294	−	2.52665i	0.458437	−	0.0808348i	0.398097	+	0.917343i	$0.369671\pi$
$978$	−0.556809	−	3.15782i	−0.0178048	−	0.100976i
$979$	3.76770	+	4.49016i	0.120416	+	0.143506i
$980$	−1.48219	−	4.07228i	−0.0473468	−	0.130084i
$981$	13.5672	+	37.2755i	0.433166	+	1.19011i
$982$	6.06954	+	7.23339i	0.193687	+	0.230827i
$983$	−2.38729	−	13.5390i	−0.0761426	−	0.431826i	−0.998919	−	0.0464897i	$-0.985197\pi$
$983$	−2.38729	−	13.5390i	−0.0761426	−	0.431826i	0.922776	−	0.385336i	$-0.125915\pi$
$984$	0.0831567	−	0.0146628i	0.00265094	−	0.000467432i
$985$	8.39019	+	4.84408i	0.267334	+	0.154345i
$986$	2.87085	−	3.42135i	0.0914266	−	0.108958i
$987$	−3.52310	−	1.28230i	−0.112142	−	0.0408162i
$988$	−6.96518	−	12.0640i	−0.221592	−	0.383808i
$989$	2.73111	−	4.73042i	0.0868442	−	0.150419i
$990$	−1.75289	+	1.47085i	−0.0557105	+	0.0467466i
$991$	41.1867	−	23.7791i	1.30834	−	0.755370i	0.326520	−	0.945190i	$-0.394124\pi$
$991$	41.1867	−	23.7791i	1.30834	−	0.755370i	0.981819	+	0.189821i	$0.0607907\pi$
$992$	1.27444	−	7.22770i	0.0404635	−	0.229480i
$993$		−	2.46663i		−	0.0782761i
$994$	−18.6410	−	3.28692i	−0.591257	−	0.104255i
$995$	16.2500	+	13.6354i	0.515160	+	0.432270i
$996$	5.45640	−	1.98597i	0.172893	−	0.0629277i
$997$	18.4308	−	50.6383i	0.583711	−	1.60373i	−0.198077	−	0.980187i	$-0.563469\pi$
$997$	18.4308	−	50.6383i	0.583711	−	1.60373i	0.781787	−	0.623545i	$-0.214308\pi$
$998$	−13.6466			−0.431975
$999$	9.38008	+	8.14117i	0.296773	+	0.257575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.h.a.21.2	✓	12
3.2	odd	2		666.2.bj.c.613.1		12
4.3	odd	2		592.2.bq.b.465.1		12
37.17	odd	36		2738.2.a.s.1.3		6
37.20	odd	36		2738.2.a.r.1.4		6
37.30	even	18	inner	74.2.h.a.67.2	yes	12
111.104	odd	18		666.2.bj.c.289.1		12
148.67	odd	18		592.2.bq.b.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.21.2	✓	12	1.1	even	1	trivial
74.2.h.a.67.2	yes	12	37.30	even	18	inner
592.2.bq.b.289.1		12	148.67	odd	18
592.2.bq.b.465.1		12	4.3	odd	2
666.2.bj.c.289.1		12	111.104	odd	18
666.2.bj.c.613.1		12	3.2	odd	2
2738.2.a.r.1.4		6	37.20	odd	36
2738.2.a.s.1.3		6	37.17	odd	36

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 - 0.939693i) q^{2} +(0.326352 - 0.118782i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.839712 + 0.148064i) q^{5} -0.347296i q^{6} +(0.240460 - 1.36372i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})\)	\(q+(0.342020 - 0.939693i) q^{2} +(0.326352 - 0.118782i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.839712 + 0.148064i) q^{5} -0.347296i q^{6} +(0.240460 - 1.36372i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-2.20574 + 1.85083i) q^{9} +(0.426333 - 0.738430i) q^{10} +(0.466006 + 0.807147i) q^{11} +(-0.326352 - 0.118782i) q^{12} +(-2.34092 + 2.78980i) q^{13} +(-1.19923 - 0.692377i) q^{14} +(0.291629 - 0.0514220i) q^{15} +(0.173648 + 0.984808i) q^{16} +(2.84539 + 3.39101i) q^{17} +(0.984808 + 2.70574i) q^{18} +(-1.30826 - 3.59443i) q^{19} +(-0.548083 - 0.653180i) q^{20} +(-0.0835109 - 0.473614i) q^{21} +(0.917853 - 0.161842i) q^{22} +(0.920780 + 0.531613i) q^{23} +(-0.223238 + 0.266044i) q^{24} +(-4.01527 - 1.46144i) q^{25} +(1.82091 + 3.15391i) q^{26} +(-1.02094 + 1.76833i) q^{27} +(-1.06078 + 0.890103i) q^{28} +(0.873775 - 0.504474i) q^{29} +(0.0514220 - 0.291629i) q^{30} -7.33920i q^{31} +(0.984808 + 0.173648i) q^{32} +(0.247957 + 0.208060i) q^{33} +(4.15968 - 1.51400i) q^{34} +(0.403834 - 1.10953i) q^{35} +2.87939 q^{36} +(1.15600 - 5.97191i) q^{37} -3.82511 q^{38} +(-0.432584 + 1.18851i) q^{39} +(-0.801244 + 0.291629i) q^{40} +(-0.186251 - 0.156283i) q^{41} +(-0.473614 - 0.0835109i) q^{42} -5.13740i q^{43} +(0.161842 - 0.917853i) q^{44} +(-2.12622 + 1.22758i) q^{45} +(0.814478 - 0.683428i) q^{46} +(3.89795 - 6.75145i) q^{47} +(0.173648 + 0.300767i) q^{48} +(4.77595 + 1.73830i) q^{49} +(-2.74661 + 3.27328i) q^{50} +(1.33139 + 0.768679i) q^{51} +(3.58649 - 0.632396i) q^{52} +(2.25380 + 12.7819i) q^{53} +(1.31250 + 1.56418i) q^{54} +(0.271802 + 0.746769i) q^{55} +(0.473614 + 1.30124i) q^{56} +(-0.853909 - 1.01765i) q^{57} +(-0.175202 - 0.993621i) q^{58} +(-9.61896 + 1.69608i) q^{59} +(-0.256454 - 0.148064i) q^{60} +(0.255191 - 0.304124i) q^{61} +(-6.89659 - 2.51015i) q^{62} +(1.99362 + 3.45305i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-2.37876 + 1.99602i) q^{65} +(0.280319 - 0.161842i) q^{66} +(-2.47277 + 14.0238i) q^{67} -4.42664i q^{68} +(0.363645 + 0.0641204i) q^{69} +(-0.904494 - 0.758960i) q^{70} +(12.8449 - 4.67517i) q^{71} +(0.984808 - 2.70574i) q^{72} -13.1543 q^{73} +(-5.21638 - 3.12879i) q^{74} -1.48398 q^{75} +(-1.30826 + 3.59443i) q^{76} +(1.21278 - 0.441414i) q^{77} +(0.968886 + 0.812992i) q^{78} +(3.43258 + 0.605257i) q^{79} +0.852666i q^{80} +(1.37686 - 7.80856i) q^{81} +(-0.210560 + 0.121567i) q^{82} +(-12.8078 + 10.7470i) q^{83} +(-0.240460 + 0.416489i) q^{84} +(1.88722 + 3.26877i) q^{85} +(-4.82758 - 1.75710i) q^{86} +(0.225236 - 0.268425i) q^{87} +(-0.807147 - 0.466006i) q^{88} +(6.19352 - 1.09209i) q^{89} +(0.426333 + 2.41785i) q^{90} +(3.24160 + 3.86318i) q^{91} +(-0.363645 - 0.999105i) q^{92} +(-0.871767 - 2.39516i) q^{93} +(-5.01111 - 5.97200i) q^{94} +(-0.566360 - 3.21199i) q^{95} +(0.342020 - 0.0603074i) q^{96} +(6.47160 + 3.73638i) q^{97} +(3.26694 - 3.89339i) q^{98} +(-2.52178 - 0.917853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Introduction

L-functions

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