LMFDB - Embedded newform 190.2.k.a.111.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(61,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("190.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.k (of order $9$, 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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			111.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	190.111
Dual form			190.2.k.a.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(1.43969 - 0.524005i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{5} +(1.43969 + 0.524005i) q^{6} +(0.347296 + 0.601535i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.419550i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(1.43969 - 0.524005i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{5} +(1.43969 + 0.524005i) q^{6} +(0.347296 + 0.601535i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.419550i) q^{9} +(0.766044 - 0.642788i) q^{10} +(1.06031 - 1.83651i) q^{11} +(0.766044 + 1.32683i) q^{12} +(-1.00000 - 0.363970i) q^{13} +(-0.120615 + 0.684040i) q^{14} +(-0.266044 - 1.50881i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.233956 - 0.196312i) q^{17} -0.652704 q^{18} +(-4.11721 + 1.43128i) q^{19} +1.00000 q^{20} +(0.815207 + 0.684040i) q^{21} +(1.99273 - 0.725293i) q^{22} +(-0.162504 - 0.921605i) q^{23} +(-0.266044 + 1.50881i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-0.532089 - 0.921605i) q^{26} +(-2.79813 + 4.84651i) q^{27} +(-0.532089 + 0.446476i) q^{28} +(-0.467911 + 0.392624i) q^{29} +(0.766044 - 1.32683i) q^{30} +(-1.41147 - 2.44474i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.564178 - 3.19961i) q^{33} +(-0.0530334 - 0.300767i) q^{34} +(0.652704 - 0.237565i) q^{35} +(-0.500000 - 0.419550i) q^{36} -4.00000 q^{37} +(-4.07398 - 1.55007i) q^{38} -1.63041 q^{39} +(0.766044 + 0.642788i) q^{40} +(7.39053 - 2.68993i) q^{41} +(0.184793 + 1.04801i) q^{42} +(-0.117211 + 0.664738i) q^{43} +(1.99273 + 0.725293i) q^{44} +(0.326352 + 0.565258i) q^{45} +(0.467911 - 0.810446i) q^{46} +(-4.34730 + 3.64781i) q^{47} +(-1.17365 + 0.984808i) q^{48} +(3.25877 - 5.64436i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.439693 - 0.160035i) q^{51} +(0.184793 - 1.04801i) q^{52} +(-0.467911 - 2.65366i) q^{53} +(-5.25877 + 1.91404i) q^{54} +(-1.62449 - 1.36310i) q^{55} -0.694593 q^{56} +(-5.17752 + 4.21805i) q^{57} -0.610815 q^{58} +(7.56805 + 6.35035i) q^{59} +(1.43969 - 0.524005i) q^{60} +(-1.16250 - 6.59289i) q^{61} +(0.490200 - 2.78006i) q^{62} +(-0.426022 - 0.155059i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.532089 + 0.921605i) q^{65} +(2.48886 - 2.08840i) q^{66} +(-9.71941 + 8.15555i) q^{67} +(0.152704 - 0.264490i) q^{68} +(-0.716881 - 1.24168i) q^{69} +(0.652704 + 0.237565i) q^{70} +(2.12061 - 12.0266i) q^{71} +(-0.113341 - 0.642788i) q^{72} +(6.52481 - 2.37484i) q^{73} +(-3.06418 - 2.57115i) q^{74} -1.53209 q^{75} +(-2.12449 - 3.80612i) q^{76} +1.47296 q^{77} +(-1.24897 - 1.04801i) q^{78} +(2.30541 - 0.839100i) q^{79} +(0.173648 + 0.984808i) q^{80} +(-1.14883 + 6.51536i) q^{81} +(7.39053 + 2.68993i) q^{82} +(8.69119 + 15.0536i) q^{83} +(-0.532089 + 0.921605i) q^{84} +(-0.233956 + 0.196312i) q^{85} +(-0.517074 + 0.433877i) q^{86} +(-0.467911 + 0.810446i) q^{87} +(1.06031 + 1.83651i) q^{88} +(15.0680 + 5.48432i) q^{89} +(-0.113341 + 0.642788i) q^{90} +(-0.128356 - 0.727940i) q^{91} +(0.879385 - 0.320070i) q^{92} +(-3.31315 - 2.78006i) q^{93} -5.67499 q^{94} +(0.694593 + 4.30320i) q^{95} -1.53209 q^{96} +(4.77584 + 4.00741i) q^{97} +(6.12449 - 2.22913i) q^{98} +(0.240352 + 1.36310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} + 3 q^{6} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 + 3 * q^6 - 3 * q^8 - 3 * q^9	$ 6 q + 3 q^{3} + 3 q^{6} - 3 q^{8} - 3 q^{9} + 12 q^{11} - 6 q^{13} - 12 q^{14} + 3 q^{15} - 6 q^{17} - 6 q^{18} + 6 q^{19} + 6 q^{20} + 12 q^{21} - 6 q^{22} - 6 q^{23} + 3 q^{24} + 6 q^{26} - 3 q^{27} + 6 q^{28} - 12 q^{29} + 12 q^{31} - 15 q^{33} + 12 q^{34} + 6 q^{35} - 3 q^{36} - 24 q^{37} - 9 q^{38} - 24 q^{39} + 27 q^{41} - 6 q^{42} + 30 q^{43} - 6 q^{44} + 3 q^{45} + 12 q^{46} - 24 q^{47} - 6 q^{48} - 3 q^{49} - 3 q^{50} + 3 q^{51} - 6 q^{52} - 12 q^{53} - 9 q^{54} + 3 q^{55} - 6 q^{57} - 12 q^{58} + 3 q^{59} + 3 q^{60} - 12 q^{61} - 18 q^{63} - 3 q^{64} + 6 q^{65} + 21 q^{66} - 27 q^{67} + 3 q^{68} + 12 q^{69} + 6 q^{70} + 24 q^{71} + 6 q^{72} + 12 q^{73} - 12 q^{77} + 18 q^{78} + 18 q^{79} - 33 q^{81} + 27 q^{82} + 6 q^{83} + 6 q^{84} - 6 q^{85} - 24 q^{86} - 12 q^{87} + 12 q^{88} + 48 q^{89} + 6 q^{90} + 36 q^{91} - 6 q^{92} + 24 q^{93} - 24 q^{94} + 27 q^{97} + 24 q^{98} - 33 q^{99}+O(q^{100}) $ 6 * q + 3 * q^3 + 3 * q^6 - 3 * q^8 - 3 * q^9 + 12 * q^11 - 6 * q^13 - 12 * q^14 + 3 * q^15 - 6 * q^17 - 6 * q^18 + 6 * q^19 + 6 * q^20 + 12 * q^21 - 6 * q^22 - 6 * q^23 + 3 * q^24 + 6 * q^26 - 3 * q^27 + 6 * q^28 - 12 * q^29 + 12 * q^31 - 15 * q^33 + 12 * q^34 + 6 * q^35 - 3 * q^36 - 24 * q^37 - 9 * q^38 - 24 * q^39 + 27 * q^41 - 6 * q^42 + 30 * q^43 - 6 * q^44 + 3 * q^45 + 12 * q^46 - 24 * q^47 - 6 * q^48 - 3 * q^49 - 3 * q^50 + 3 * q^51 - 6 * q^52 - 12 * q^53 - 9 * q^54 + 3 * q^55 - 6 * q^57 - 12 * q^58 + 3 * q^59 + 3 * q^60 - 12 * q^61 - 18 * q^63 - 3 * q^64 + 6 * q^65 + 21 * q^66 - 27 * q^67 + 3 * q^68 + 12 * q^69 + 6 * q^70 + 24 * q^71 + 6 * q^72 + 12 * q^73 - 12 * q^77 + 18 * q^78 + 18 * q^79 - 33 * q^81 + 27 * q^82 + 6 * q^83 + 6 * q^84 - 6 * q^85 - 24 * q^86 - 12 * q^87 + 12 * q^88 + 48 * q^89 + 6 * q^90 + 36 * q^91 - 6 * q^92 + 24 * q^93 - 24 * q^94 + 27 * q^97 + 24 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	1.43969	−	0.524005i	0.831207	−	0.302535i	0.108853	−	0.994058i	$-0.465282\pi$
$3$	1.43969	−	0.524005i	0.831207	−	0.302535i	0.722354	+	0.691523i	$0.243060\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$6$	1.43969	+	0.524005i	0.587752	+	0.213924i
$7$	0.347296	+	0.601535i	0.131266	+	0.227359i	0.924165	−	0.381994i	$-0.124763\pi$
$7$	0.347296	+	0.601535i	0.131266	+	0.227359i	−0.792899	+	0.609353i	$0.791429\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.500000	+	0.419550i	−0.166667	+	0.139850i
$10$	0.766044	−	0.642788i	0.242245	−	0.203267i
$11$	1.06031	−	1.83651i	0.319695	−	0.553727i	−0.660730	−	0.750624i	$-0.729753\pi$
$11$	1.06031	−	1.83651i	0.319695	−	0.553727i	0.980424	+	0.196897i	$0.0630863\pi$
$12$	0.766044	+	1.32683i	0.221138	+	0.383022i
$13$	−1.00000	−	0.363970i	−0.277350	−	0.100947i	0.199600	−	0.979877i	$-0.436036\pi$
$13$	−1.00000	−	0.363970i	−0.277350	−	0.100947i	−0.476950	+	0.878930i	$0.658258\pi$
$14$	−0.120615	+	0.684040i	−0.0322357	+	0.182817i
$15$	−0.266044	−	1.50881i	−0.0686924	−	0.389574i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.233956	−	0.196312i	−0.0567426	−	0.0476127i	0.613975	−	0.789325i	$-0.289569\pi$
$17$	−0.233956	−	0.196312i	−0.0567426	−	0.0476127i	−0.670718	+	0.741713i	$0.734014\pi$
$18$	−0.652704			−0.153844
$19$	−4.11721	+	1.43128i	−0.944553	+	0.328359i
$19$	−4.11721	+	1.43128i	−0.944553	+	0.328359i
$20$	1.00000			0.223607
$21$	0.815207	+	0.684040i	0.177893	+	0.149270i
$22$	1.99273	−	0.725293i	0.424851	−	0.154633i
$23$	−0.162504	−	0.921605i	−0.0338844	−	0.192168i	0.963167	−	0.268904i	$-0.0866613\pi$
$23$	−0.162504	−	0.921605i	−0.0338844	−	0.192168i	−0.997051	+	0.0767357i	$0.975550\pi$
$24$	−0.266044	+	1.50881i	−0.0543061	+	0.307985i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	−0.532089	−	0.921605i	−0.104351	−	0.180742i
$27$	−2.79813	+	4.84651i	−0.538501	+	0.932711i
$28$	−0.532089	+	0.446476i	−0.100555	+	0.0843760i
$29$	−0.467911	+	0.392624i	−0.0868889	+	0.0729085i	−0.685198	−	0.728357i	$-0.740284\pi$
$29$	−0.467911	+	0.392624i	−0.0868889	+	0.0729085i	0.598309	+	0.801266i	$0.295840\pi$
$30$	0.766044	−	1.32683i	0.139860	−	0.242245i
$31$	−1.41147	−	2.44474i	−0.253508	−	0.439089i	0.710981	−	0.703211i	$-0.248251\pi$
$31$	−1.41147	−	2.44474i	−0.253508	−	0.439089i	−0.964489	+	0.264122i	$0.914918\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.564178	−	3.19961i	0.0982107	−	0.556981i
$34$	−0.0530334	−	0.300767i	−0.00909516	−	0.0515812i
$35$	0.652704	−	0.237565i	0.110327	−	0.0401558i
$36$	−0.500000	−	0.419550i	−0.0833333	−	0.0699250i
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	−4.07398	−	1.55007i	−0.660886	−	0.251454i
$39$	−1.63041			−0.261075
$40$	0.766044	+	0.642788i	0.121122	+	0.101634i
$41$	7.39053	−	2.68993i	1.15421	−	0.420097i	0.307182	−	0.951651i	$-0.400614\pi$
$41$	7.39053	−	2.68993i	1.15421	−	0.420097i	0.847025	+	0.531554i	$0.178392\pi$
$42$	0.184793	+	1.04801i	0.0285141	+	0.161712i
$43$	−0.117211	+	0.664738i	−0.0178745	+	0.101372i	−0.992440	−	0.122732i	$-0.960834\pi$
$43$	−0.117211	+	0.664738i	−0.0178745	+	0.101372i	0.974565	+	0.224104i	$0.0719455\pi$
$44$	1.99273	+	0.725293i	0.300415	+	0.109342i
$45$	0.326352	+	0.565258i	0.0486497	+	0.0842637i
$46$	0.467911	−	0.810446i	0.0689897	−	0.119494i
$47$	−4.34730	+	3.64781i	−0.634118	+	0.532088i	−0.902206	−	0.431306i	$-0.858053\pi$
$47$	−4.34730	+	3.64781i	−0.634118	+	0.532088i	0.268087	+	0.963395i	$0.413608\pi$
$48$	−1.17365	+	0.984808i	−0.169402	+	0.142145i
$49$	3.25877	−	5.64436i	0.465539	−	0.806337i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.439693	−	0.160035i	−0.0615693	−	0.0224094i
$52$	0.184793	−	1.04801i	0.0256261	−	0.145333i
$53$	−0.467911	−	2.65366i	−0.0642725	−	0.364508i	−0.999933	−	0.0116052i	$-0.996306\pi$
$53$	−0.467911	−	2.65366i	−0.0642725	−	0.364508i	0.935660	−	0.352902i	$-0.114805\pi$
$54$	−5.25877	+	1.91404i	−0.715628	+	0.260467i
$55$	−1.62449	−	1.36310i	−0.219046	−	0.183801i
$56$	−0.694593			−0.0928189
$57$	−5.17752	+	4.21805i	−0.685779	+	0.558694i
$58$	−0.610815			−0.0802039
$59$	7.56805	+	6.35035i	0.985276	+	0.826745i	0.984877	−	0.173255i	$-0.0554286\pi$
$59$	7.56805	+	6.35035i	0.985276	+	0.826745i	0.000398990		1.00000i	$0.499873\pi$
$60$	1.43969	−	0.524005i	0.185864	−	0.0676488i
$61$	−1.16250	−	6.59289i	−0.148843	−	0.844133i	−0.964200	−	0.265174i	$-0.914570\pi$
$61$	−1.16250	−	6.59289i	−0.148843	−	0.844133i	0.815357	−	0.578958i	$-0.196541\pi$
$62$	0.490200	−	2.78006i	0.0622554	−	0.353068i
$63$	−0.426022	−	0.155059i	−0.0536737	−	0.0195356i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.532089	+	0.921605i	−0.0659975	+	0.114311i
$66$	2.48886	−	2.08840i	0.306357	−	0.257064i
$67$	−9.71941	+	8.15555i	−1.18741	+	0.996359i	−0.187514	+	0.982262i	$0.560043\pi$
$67$	−9.71941	+	8.15555i	−1.18741	+	0.996359i	−0.999901	+	0.0140972i	$0.995513\pi$
$68$	0.152704	−	0.264490i	0.0185180	−	0.0320742i
$69$	−0.716881	−	1.24168i	−0.0863024	−	0.149480i
$70$	0.652704	+	0.237565i	0.0780130	+	0.0283944i
$71$	2.12061	−	12.0266i	0.251671	−	1.42730i	−0.552805	−	0.833310i	$-0.686443\pi$
$71$	2.12061	−	12.0266i	0.251671	−	1.42730i	0.804476	−	0.593985i	$-0.202446\pi$
$72$	−0.113341	−	0.642788i	−0.0133573	−	0.0757532i
$73$	6.52481	−	2.37484i	0.763672	−	0.277954i	0.0693248	−	0.997594i	$-0.477916\pi$
$73$	6.52481	−	2.37484i	0.763672	−	0.277954i	0.694347	+	0.719640i	$0.255693\pi$
$74$	−3.06418	−	2.57115i	−0.356203	−	0.298890i
$75$	−1.53209			−0.176910
$76$	−2.12449	−	3.80612i	−0.243695	−	0.436592i
$77$	1.47296			0.167860
$78$	−1.24897	−	1.04801i	−0.141418	−	0.118664i
$79$	2.30541	−	0.839100i	0.259379	−	0.0944061i	−0.209058	−	0.977903i	$-0.567040\pi$
$79$	2.30541	−	0.839100i	0.259379	−	0.0944061i	0.468436	+	0.883497i	$0.344817\pi$
$80$	0.173648	+	0.984808i	0.0194145	+	0.110105i
$81$	−1.14883	+	6.51536i	−0.127648	+	0.723929i
$82$	7.39053	+	2.68993i	0.816147	+	0.297053i
$83$	8.69119	+	15.0536i	0.953982	+	1.65235i	0.736681	+	0.676241i	$0.236392\pi$
$83$	8.69119	+	15.0536i	0.953982	+	1.65235i	0.217301	+	0.976105i	$0.430275\pi$
$84$	−0.532089	+	0.921605i	−0.0580557	+	0.100555i
$85$	−0.233956	+	0.196312i	−0.0253760	+	0.0212930i
$86$	−0.517074	+	0.433877i	−0.0557575	+	0.0467861i
$87$	−0.467911	+	0.810446i	−0.0501653	+	0.0868889i
$88$	1.06031	+	1.83651i	0.113029	+	0.195772i
$89$	15.0680	+	5.48432i	1.59721	+	0.581337i	0.978854	−	0.204561i	$-0.0655767\pi$
$89$	15.0680	+	5.48432i	1.59721	+	0.581337i	0.618356	+	0.785898i	$0.287799\pi$
$90$	−0.113341	+	0.642788i	−0.0119472	+	0.0677558i
$91$	−0.128356	−	0.727940i	−0.0134553	−	0.0763089i
$92$	0.879385	−	0.320070i	0.0916822	−	0.0333696i
$93$	−3.31315	−	2.78006i	−0.343557	−	0.288279i
$94$	−5.67499			−0.585331
$95$	0.694593	+	4.30320i	0.0712637	+	0.441499i
$96$	−1.53209			−0.156368
$97$	4.77584	+	4.00741i	0.484914	+	0.406891i	0.852199	−	0.523217i	$-0.175268\pi$
$97$	4.77584	+	4.00741i	0.484914	+	0.406891i	−0.367286	+	0.930108i	$0.619713\pi$
$98$	6.12449	−	2.22913i	0.618666	−	0.225176i
$99$	0.240352	+	1.36310i	0.0241563	+	0.136997i
$100$	0.173648	−	0.984808i	0.0173648	−	0.0984808i
$101$	13.5030	+	4.91469i	1.34360	+	0.489030i	0.910944	−	0.412530i	$-0.135355\pi$
$101$	13.5030	+	4.91469i	1.34360	+	0.489030i	0.432654	+	0.901560i	$0.357577\pi$
$102$	−0.233956	−	0.405223i	−0.0231651	−	0.0401230i
$103$	−9.80066	+	16.9752i	−0.965688	+	1.67262i	−0.257932	+	0.966163i	$0.583041\pi$
$103$	−9.80066	+	16.9752i	−0.965688	+	1.67262i	−0.707756	+	0.706457i	$0.750292\pi$
$104$	0.815207	−	0.684040i	0.0799377	−	0.0670757i
$105$	0.815207	−	0.684040i	0.0795561	−	0.0667555i
$106$	1.34730	−	2.33359i	0.130861	−	0.226658i
$107$	−1.03209	−	1.78763i	−0.0997758	−	0.172817i	0.811816	−	0.583913i	$-0.198479\pi$
$107$	−1.03209	−	1.78763i	−0.0997758	−	0.172817i	−0.911592	+	0.411097i	$0.865146\pi$
$108$	−5.25877	−	1.91404i	−0.506025	−	0.184178i
$109$	1.58172	−	8.97037i	0.151501	−	0.859206i	−0.810414	−	0.585858i	$-0.800758\pi$
$109$	1.58172	−	8.97037i	0.151501	−	0.859206i	0.961915	−	0.273348i	$-0.0881311\pi$
$110$	−0.368241	−	2.08840i	−0.0351104	−	0.199121i
$111$	−5.75877	+	2.09602i	−0.546598	+	0.198946i
$112$	−0.532089	−	0.446476i	−0.0502777	−	0.0421880i
$113$	7.18479			0.675888			0.337944	−	0.941166i	$-0.390268\pi$
$113$	7.18479			0.675888			0.337944	+	0.941166i	$0.390268\pi$
$114$	−6.67752	−	0.0968323i	−0.625407	−	0.00906917i
$115$	−0.935822			−0.0872659
$116$	−0.467911	−	0.392624i	−0.0434445	−	0.0364542i
$117$	0.652704	−	0.237565i	0.0603425	−	0.0219629i
$118$	1.71554	+	9.72930i	0.157928	+	0.895654i
$119$	0.0368366	−	0.208911i	0.00337681	−	0.0191508i
$120$	1.43969	+	0.524005i	0.131425	+	0.0478349i
$121$	3.25150	+	5.63176i	0.295591	+	0.511978i
$122$	3.34730	−	5.79769i	0.303050	−	0.524898i
$123$	9.23055	−	7.74535i	0.832291	−	0.698375i
$124$	2.16250	−	1.81456i	0.194199	−	0.162952i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	−0.226682	−	0.392624i	−0.0201944	−	0.0349777i
$127$	1.53209	+	0.557635i	0.135951	+	0.0494821i	0.409100	−	0.912490i	$-0.365843\pi$
$127$	1.53209	+	0.557635i	0.135951	+	0.0494821i	−0.273149	+	0.961972i	$0.588065\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	0.179578	+	1.01844i	0.0158110	+	0.0896684i
$130$	−1.00000	+	0.363970i	−0.0877058	+	0.0319223i
$131$	−7.40033	−	6.20961i	−0.646570	−	0.542536i	0.259458	−	0.965754i	$-0.416456\pi$
$131$	−7.40033	−	6.20961i	−0.646570	−	0.542536i	−0.906028	+	0.423218i	$0.860900\pi$
$132$	3.24897			0.282787
$133$	−2.29086	−	1.97957i	−0.198643	−	0.171650i
$134$	−12.6878			−1.09606
$135$	4.28699	+	3.59721i	0.368965	+	0.309599i
$136$	0.286989	−	0.104455i	0.0246091	−	0.00895698i
$137$	−2.00253	−	11.3569i	−0.171087	−	0.970285i	−0.942564	−	0.334027i	$-0.891592\pi$
$137$	−2.00253	−	11.3569i	−0.171087	−	0.970285i	0.771476	−	0.636258i	$-0.219519\pi$
$138$	0.248970	−	1.41198i	0.0211938	−	0.120196i
$139$	−6.43242	−	2.34121i	−0.545591	−	0.198579i	0.0544957	−	0.998514i	$-0.482645\pi$
$139$	−6.43242	−	2.34121i	−0.545591	−	0.198579i	−0.600086	+	0.799935i	$0.704867\pi$
$140$	0.347296	+	0.601535i	0.0293519	+	0.0508390i
$141$	−4.34730	+	7.52974i	−0.366108	+	0.634118i
$142$	9.35504	−	7.84981i	0.785057	−	0.658741i
$143$	−1.72874	+	1.45059i	−0.144565	+	0.121304i
$144$	0.326352	−	0.565258i	0.0271960	−	0.0471048i
$145$	0.305407	+	0.528981i	0.0253627	+	0.0439295i
$146$	6.52481	+	2.37484i	0.539998	+	0.196543i
$147$	1.73396	−	9.83375i	0.143014	−	0.811074i
$148$	−0.694593	−	3.93923i	−0.0570952	−	0.323803i
$149$	8.36959	−	3.04628i	0.685663	−	0.249561i	0.0243859	−	0.999703i	$-0.492237\pi$
$149$	8.36959	−	3.04628i	0.685663	−	0.249561i	0.661277	+	0.750142i	$0.270015\pi$
$150$	−1.17365	−	0.984808i	−0.0958280	−	0.0804092i
$151$	−10.8229			−0.880759			−0.440380	−	0.897812i	$-0.645156\pi$
$151$	−10.8229			−0.880759			−0.440380	+	0.897812i	$0.645156\pi$
$152$	0.819078	−	4.28125i	0.0664360	−	0.347255i
$153$	0.199340			0.0161157
$154$	1.12836	+	0.946803i	0.0909255	+	0.0762955i
$155$	−2.65270	+	0.965505i	−0.213070	+	0.0775512i
$156$	−0.283119	−	1.60565i	−0.0226676	−	0.128555i
$157$	1.85710	−	10.5321i	0.148212	−	0.840555i	−0.816519	−	0.577319i	$-0.804099\pi$
$157$	1.85710	−	10.5321i	0.148212	−	0.840555i	0.964731	−	0.263236i	$-0.0847898\pi$
$158$	2.30541	+	0.839100i	0.183408	+	0.0667552i
$159$	−2.06418	−	3.57526i	−0.163700	−	0.283537i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	0.497941	−	0.417822i	0.0392432	−	0.0329290i
$162$	−5.06805	+	4.25260i	−0.398183	+	0.334116i
$163$	−1.23396	+	2.13727i	−0.0966509	+	0.167404i	−0.910296	−	0.413957i	$-0.864146\pi$
$163$	−1.23396	+	2.13727i	−0.0966509	+	0.167404i	0.813646	+	0.581361i	$0.197480\pi$
$164$	3.93242	+	6.81115i	0.307070	+	0.531861i
$165$	−3.05303	−	1.11121i	−0.237678	−	0.0865078i
$166$	−3.01842	+	17.1183i	−0.234275	+	1.32864i
$167$	−2.11381	−	11.9880i	−0.163571	−	0.927659i	−0.950525	−	0.310647i	$-0.899454\pi$
$167$	−2.11381	−	11.9880i	−0.163571	−	0.927659i	0.786954	−	0.617012i	$-0.211657\pi$
$168$	−1.00000	+	0.363970i	−0.0771517	+	0.0280809i
$169$	−9.09105	−	7.62830i	−0.699312	−	0.586792i
$170$	−0.305407			−0.0234237
$171$	1.45811	−	2.44302i	0.111505	−	0.186822i
$172$	−0.674992			−0.0514677
$173$	−10.7888	−	9.05288i	−0.820257	−	0.688278i	0.132775	−	0.991146i	$-0.457611\pi$
$173$	−10.7888	−	9.05288i	−0.820257	−	0.688278i	−0.953032	+	0.302869i	$0.902056\pi$
$174$	−0.879385	+	0.320070i	−0.0666660	+	0.0242644i
$175$	−0.120615	−	0.684040i	−0.00911762	−	0.0517086i
$176$	−0.368241	+	2.08840i	−0.0277572	+	0.157419i
$177$	14.2233	+	5.17685i	1.06909	+	0.389116i
$178$	8.01754	+	13.8868i	0.600940	+	1.04086i
$179$	−4.70574	+	8.15058i	−0.351723	+	0.609203i	−0.986552	−	0.163451i	$-0.947738\pi$
$179$	−4.70574	+	8.15058i	−0.351723	+	0.609203i	0.634828	+	0.772653i	$0.281071\pi$
$180$	−0.500000	+	0.419550i	−0.0372678	+	0.0312714i
$181$	−18.7442	+	15.7283i	−1.39325	+	1.16907i	−0.429242	+	0.903190i	$0.641219\pi$
$181$	−18.7442	+	15.7283i	−1.39325	+	1.16907i	−0.964005	+	0.265884i	$0.914336\pi$
$182$	0.369585	−	0.640140i	0.0273955	−	0.0474503i
$183$	−5.12836	−	8.88257i	−0.379099	−	0.656619i
$184$	0.879385	+	0.320070i	0.0648291	+	0.0235959i
$185$	−0.694593	+	3.93923i	−0.0510675	+	0.289618i
$186$	−0.751030	−	4.25930i	−0.0550682	−	0.312307i
$187$	−0.608593	+	0.221510i	−0.0445047	+	0.0161984i
$188$	−4.34730	−	3.64781i	−0.317059	−	0.266044i
$189$	−3.88713			−0.282747
$190$	−2.23396	+	3.74292i	−0.162068	+	0.271540i
$191$	−2.04458			−0.147940			−0.0739702	−	0.997260i	$-0.523567\pi$
$191$	−2.04458			−0.147940			−0.0739702	+	0.997260i	$0.523567\pi$
$192$	−1.17365	−	0.984808i	−0.0847008	−	0.0710724i
$193$	−13.4427	+	4.89274i	−0.967626	+	0.352187i	−0.777017	−	0.629479i	$-0.783268\pi$
$193$	−13.4427	+	4.89274i	−0.967626	+	0.352187i	−0.190608	+	0.981666i	$0.561046\pi$
$194$	1.08260	+	6.13971i	0.0777259	+	0.440805i
$195$	−0.283119	+	1.60565i	−0.0202745	+	0.114983i
$196$	6.12449	+	2.22913i	0.437463	+	0.159224i
$197$	−6.98545	−	12.0992i	−0.497693	−	0.862029i	0.502304	−	0.864691i	$-0.332486\pi$
$197$	−6.98545	−	12.0992i	−0.497693	−	0.862029i	−0.999996	+	0.00266202i	$0.999153\pi$
$198$	−0.692066	+	1.19869i	−0.0491830	+	0.0851875i
$199$	14.4311	−	12.1091i	1.02299	−	0.858392i	0.0329912	−	0.999456i	$-0.489497\pi$
$199$	14.4311	−	12.1091i	1.02299	−	0.858392i	0.990001	+	0.141064i	$0.0450522\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	−9.71941	+	16.8345i	−0.685554	+	1.18741i
$202$	7.18479	+	12.4444i	0.505520	+	0.875587i
$203$	−0.398681	−	0.145108i	−0.0279819	−	0.0101846i
$204$	0.0812519	−	0.460802i	0.00568877	−	0.0322626i
$205$	−1.36571	−	7.74535i	−0.0953856	−	0.540959i
$206$	−18.4192	+	6.70405i	−1.28333	+	0.467093i
$207$	0.467911	+	0.392624i	0.0325221	+	0.0272893i
$208$	1.06418			0.0737875
$209$	−1.73695	+	9.07888i	−0.120147	+	0.628000i
$210$	1.06418			0.0734352
$211$	−0.211667	−	0.177610i	−0.0145717	−	0.0122271i	0.635473	−	0.772123i	$-0.280805\pi$
$211$	−0.211667	−	0.177610i	−0.0145717	−	0.0122271i	−0.650044	+	0.759896i	$0.725250\pi$
$212$	2.53209	−	0.921605i	0.173905	−	0.0632961i
$213$	−3.24897	−	18.4258i	−0.222616	−	1.26252i
$214$	0.358441	−	2.03282i	0.0245025	−	0.138961i
$215$	0.634285	+	0.230861i	0.0432579	+	0.0157446i
$216$	−2.79813	−	4.84651i	−0.190389	−	0.329763i
$217$	0.980400	−	1.69810i	0.0665539	−	0.115275i
$218$	6.97771	−	5.85499i	0.472590	−	0.396550i
$219$	8.14930	−	6.83807i	0.550679	−	0.462074i
$220$	1.06031	−	1.83651i	0.0714859	−	0.123817i
$221$	0.162504	+	0.281465i	0.0109312	+	0.0189334i
$222$	−5.75877	−	2.09602i	−0.386503	−	0.140676i
$223$	−1.19934	+	6.80180i	−0.0803138	+	0.455482i	0.917956	+	0.396682i	$0.129838\pi$
$223$	−1.19934	+	6.80180i	−0.0803138	+	0.455482i	−0.998270	+	0.0587999i	$0.981273\pi$
$224$	−0.120615	−	0.684040i	−0.00805891	−	0.0457044i
$225$	0.613341	−	0.223238i	0.0408894	−	0.0148825i
$226$	5.50387	+	4.61830i	0.366112	+	0.307204i
$227$	2.30272			0.152837			0.0764184	−	0.997076i	$-0.475652\pi$
$227$	2.30272			0.152837			0.0764184	+	0.997076i	$0.475652\pi$
$228$	−5.05303	−	4.36640i	−0.334645	−	0.289172i
$229$	−22.2121			−1.46782			−0.733910	−	0.679247i	$-0.762306\pi$
$229$	−22.2121			−1.46782			−0.733910	+	0.679247i	$0.762306\pi$
$230$	−0.716881	−	0.601535i	−0.0472698	−	0.0396640i
$231$	2.12061	−	0.771841i	0.139526	−	0.0507834i
$232$	−0.106067	−	0.601535i	−0.00696363	−	0.0394927i
$233$	3.11128	−	17.6450i	0.203827	−	1.15596i	−0.695448	−	0.718576i	$-0.744794\pi$
$233$	3.11128	−	17.6450i	0.203827	−	1.15596i	0.899275	−	0.437383i	$-0.144095\pi$
$234$	0.652704	+	0.237565i	0.0426686	+	0.0155301i
$235$	2.83750	+	4.91469i	0.185098	+	0.320599i
$236$	−4.93969	+	8.55580i	−0.321547	+	0.556935i
$237$	2.87939	−	2.41609i	0.187036	−	0.156942i
$238$	0.162504	−	0.136357i	0.0105336	−	0.00883870i
$239$	3.46791	−	6.00660i	0.224321	−	0.388535i	−0.731795	−	0.681525i	$-0.761317\pi$
$239$	3.46791	−	6.00660i	0.224321	−	0.388535i	0.956115	+	0.292990i	$0.0946504\pi$
$240$	0.766044	+	1.32683i	0.0494480	+	0.0856464i
$241$	16.7160	+	6.08413i	1.07677	+	0.391913i	0.818705	−	0.574214i	$-0.194692\pi$
$241$	16.7160	+	6.08413i	1.07677	+	0.391913i	0.258067	+	0.966127i	$0.416914\pi$
$242$	−1.12923	+	6.40420i	−0.0725898	+	0.411677i
$243$	−1.15523	−	6.55163i	−0.0741080	−	0.420288i
$244$	6.29086	−	2.28969i	0.402731	−	0.146582i
$245$	−4.99273	−	4.18939i	−0.318974	−	0.267651i
$246$	12.0496			0.768256
$247$	4.63816	+	0.0672590i	0.295119	+	0.00427959i
$248$	2.82295			0.179257
$249$	20.4008	+	17.1183i	1.29285	+	1.08483i
$250$	−0.939693	+	0.342020i	−0.0594314	+	0.0216313i
$251$	−2.89915	−	16.4419i	−0.182993	−	1.03780i	−0.928508	−	0.371314i	$-0.878907\pi$
$251$	−2.89915	−	16.4419i	−0.182993	−	1.03780i	0.745515	−	0.666489i	$-0.232204\pi$
$252$	0.0787257	−	0.446476i	0.00495925	−	0.0281253i
$253$	−1.86484	−	0.678745i	−0.117241	−	0.0426723i
$254$	0.815207	+	1.41198i	0.0511507	+	0.0885956i
$255$	−0.233956	+	0.405223i	−0.0146509	+	0.0253760i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−20.0043	+	16.7856i	−1.24784	+	1.04706i	−0.250967	+	0.967996i	$0.580748\pi$
$257$	−20.0043	+	16.7856i	−1.24784	+	1.04706i	−0.996870	+	0.0790632i	$0.974807\pi$
$258$	−0.517074	+	0.895599i	−0.0321916	+	0.0557575i
$259$	−1.38919	−	2.40614i	−0.0863198	−	0.149510i
$260$	−1.00000	−	0.363970i	−0.0620174	−	0.0225725i
$261$	0.0692302	−	0.392624i	0.00428524	−	0.0243028i
$262$	−1.67752	−	9.51368i	−0.103637	−	0.587757i
$263$	11.7442	−	4.27455i	0.724180	−	0.263580i	0.0464807	−	0.998919i	$-0.485199\pi$
$263$	11.7442	−	4.27455i	0.724180	−	0.263580i	0.677699	+	0.735339i	$0.262977\pi$
$264$	2.48886	+	2.08840i	0.153178	+	0.128532i
$265$	−2.69459			−0.165528
$266$	−0.482459	−	2.98897i	−0.0295815	−	0.183266i
$267$	24.5672			1.50349
$268$	−9.71941	−	8.15555i	−0.593707	−	0.498180i
$269$	−0.773318	+	0.281465i	−0.0471501	+	0.0171612i	−0.365488	−	0.930816i	$-0.619098\pi$
$269$	−0.773318	+	0.281465i	−0.0471501	+	0.0171612i	0.318337	+	0.947977i	$0.396875\pi$
$270$	0.971782	+	5.51125i	0.0591407	+	0.335404i
$271$	−2.09833	+	11.9002i	−0.127464	+	0.722886i	0.852349	+	0.522973i	$0.175177\pi$
$271$	−2.09833	+	11.9002i	−0.127464	+	0.722886i	−0.979814	+	0.199913i	$0.935934\pi$
$272$	0.286989	+	0.104455i	0.0174013	+	0.00633354i
$273$	−0.566237	−	0.980752i	−0.0342702	−	0.0593578i
$274$	5.76604	−	9.98708i	0.348339	−	0.603342i
$275$	−1.62449	+	1.36310i	−0.0979601	+	0.0821983i
$276$	1.09833	−	0.921605i	0.0661115	−	0.0554741i
$277$	5.63041	−	9.75216i	0.338299	−	0.585951i	−0.645814	−	0.763495i	$-0.723482\pi$
$277$	5.63041	−	9.75216i	0.338299	−	0.585951i	0.984113	+	0.177544i	$0.0568152\pi$
$278$	−3.42262	−	5.92815i	−0.205275	−	0.355547i
$279$	1.73143	+	0.630189i	0.103658	+	0.0377284i
$280$	−0.120615	+	0.684040i	−0.00720811	+	0.0408792i
$281$	4.55185	+	25.8148i	0.271541	+	1.53998i	0.749740	+	0.661732i	$0.230179\pi$
$281$	4.55185	+	25.8148i	0.271541	+	1.53998i	−0.478199	+	0.878251i	$0.658710\pi$
$282$	−8.17024	+	2.97373i	−0.486531	+	0.177083i
$283$	19.7160	+	16.5437i	1.17199	+	0.983420i	0.999999	−	0.00167722i	$-0.000533875\pi$
$283$	19.7160	+	16.5437i	1.17199	+	0.983420i	0.171996	+	0.985098i	$0.444978\pi$
$284$	12.2121			0.724657
$285$	3.25490	+	5.83132i	0.192804	+	0.345417i
$286$	−2.25671			−0.133442
$287$	4.18479	+	3.51146i	0.247020	+	0.207275i
$288$	0.613341	−	0.223238i	0.0361415	−	0.0131544i
$289$	−2.93582	−	16.6499i	−0.172695	−	0.979404i
$290$	−0.106067	+	0.601535i	−0.00622846	+	0.0353233i
$291$	8.97565	+	3.26687i	0.526162	+	0.191507i
$292$	3.47178	+	6.01330i	0.203171	+	0.351902i
$293$	−13.2540	+	22.9566i	−0.774308	+	1.34114i	0.160874	+	0.986975i	$0.448569\pi$
$293$	−13.2540	+	22.9566i	−0.774308	+	1.34114i	−0.935182	+	0.354166i	$0.884765\pi$
$294$	7.64930	−	6.41852i	0.446116	−	0.374336i
$295$	7.56805	−	6.35035i	0.440629	−	0.369731i
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	5.93376	+	10.2776i	0.344312	+	0.596366i
$298$	8.36959	+	3.04628i	0.484837	+	0.176466i
$299$	−0.172933	+	0.980752i	−0.0100010	+	0.0567183i
$300$	−0.266044	−	1.50881i	−0.0153601	−	0.0871114i
$301$	−0.440570	+	0.160354i	−0.0253940	+	0.00924267i
$302$	−8.29086	−	6.95686i	−0.477085	−	0.400322i
$303$	22.0155			1.26476
$304$	3.37939	−	2.75314i	0.193821	−	0.157903i
$305$	−6.69459			−0.383331
$306$	0.152704	+	0.128134i	0.00872949	+	0.00732491i
$307$	−2.99273	+	1.08926i	−0.170804	+	0.0621675i	−0.426007	−	0.904720i	$-0.640080\pi$
$307$	−2.99273	+	1.08926i	−0.170804	+	0.0621675i	0.255203	+	0.966888i	$0.417858\pi$
$308$	0.255777	+	1.45059i	0.0145743	+	0.0826548i
$309$	−5.21482	+	29.5747i	−0.296661	+	1.68245i
$310$	−2.65270	−	0.965505i	−0.150663	−	0.0548370i
$311$	−0.411474	−	0.712694i	−0.0233326	−	0.0404132i	0.854123	−	0.520070i	$-0.174094\pi$
$311$	−0.411474	−	0.712694i	−0.0233326	−	0.0404132i	−0.877456	+	0.479657i	$0.840761\pi$
$312$	0.815207	−	1.41198i	0.0461520	−	0.0799377i
$313$	16.7672	−	14.0694i	0.947740	−	0.795248i	−0.0311758	−	0.999514i	$-0.509925\pi$
$313$	16.7672	−	14.0694i	0.947740	−	0.795248i	0.978915	+	0.204266i	$0.0654807\pi$
$314$	8.19253	−	6.87435i	0.462331	−	0.387942i
$315$	−0.226682	+	0.392624i	−0.0127721	+	0.0221219i
$316$	1.22668	+	2.12467i	0.0690062	+	0.119522i
$317$	12.4243	+	4.52206i	0.697816	+	0.253984i	0.666478	−	0.745524i	$-0.267801\pi$
$317$	12.4243	+	4.52206i	0.697816	+	0.253984i	0.0313381	+	0.999509i	$0.490023\pi$
$318$	0.716881	−	4.06564i	0.0402007	−	0.227990i
$319$	0.224927	+	1.27562i	0.0125935	+	0.0714212i
$320$	−0.939693	+	0.342020i	−0.0525304	+	0.0191195i
$321$	−2.42262	−	2.03282i	−0.135217	−	0.113461i
$322$	0.650015			0.0362239
$323$	1.24422	+	0.473401i	0.0692304	+	0.0263408i
$324$	−6.61587			−0.367548
$325$	0.815207	+	0.684040i	0.0452196	+	0.0379437i
$326$	−2.31908	+	0.844075i	−0.128442	+	0.0467490i
$327$	−2.42333	−	13.7434i	−0.134011	−	0.760012i
$328$	−1.36571	+	7.74535i	−0.0754090	+	0.427666i
$329$	−3.70409	−	1.34818i	−0.204213	−	0.0743275i
$330$	−1.62449	−	2.81369i	−0.0894250	−	0.154889i
$331$	−0.819078	+	1.41868i	−0.0450206	+	0.0779780i	−0.887658	−	0.460504i	$-0.847669\pi$
$331$	−0.819078	+	1.41868i	−0.0450206	+	0.0779780i	0.842637	+	0.538482i	$0.181002\pi$
$332$	−13.3157	+	11.1732i	−0.730793	+	0.613208i
$333$	2.00000	−	1.67820i	0.109599	−	0.0919648i
$334$	6.08647	−	10.5421i	0.333037	−	0.576836i
$335$	6.34389	+	10.9879i	0.346604	+	0.600336i
$336$	−1.00000	−	0.363970i	−0.0545545	−	0.0198562i
$337$	−5.44134	+	30.8594i	−0.296409	+	1.68102i	0.365012	+	0.931003i	$0.381065\pi$
$337$	−5.44134	+	30.8594i	−0.296409	+	1.68102i	−0.661421	+	0.750015i	$0.730046\pi$
$338$	−2.06077	−	11.6872i	−0.112091	−	0.635702i
$339$	10.3439	−	3.76487i	0.561803	−	0.204480i
$340$	−0.233956	−	0.196312i	−0.0126880	−	0.0106465i
$341$	−5.98639			−0.324181
$342$	2.68732	−	0.934204i	0.145314	−	0.0505160i
$343$	9.38919			0.506968
$344$	−0.517074	−	0.433877i	−0.0278788	−	0.0233931i
$345$	−1.34730	+	0.490376i	−0.0725360	+	0.0264009i
$346$	−2.44562	−	13.8698i	−0.131477	−	0.745646i
$347$	4.41534	−	25.0407i	0.237028	−	1.34425i	−0.601272	−	0.799044i	$-0.705339\pi$
$347$	4.41534	−	25.0407i	0.237028	−	1.34425i	0.838300	−	0.545209i	$-0.183550\pi$
$348$	−0.879385	−	0.320070i	−0.0471400	−	0.0171576i
$349$	−16.0993	−	27.8847i	−0.861774	−	1.49264i	−0.870215	−	0.492671i	$-0.836020\pi$
$349$	−16.0993	−	27.8847i	−0.861774	−	1.49264i	0.00844186	−	0.999964i	$-0.497313\pi$
$350$	0.347296	−	0.601535i	0.0185638	−	0.0321534i
$351$	4.56212	−	3.82807i	0.243508	−	0.204327i
$352$	−1.62449	+	1.36310i	−0.0865853	+	0.0726537i
$353$	−10.0753	+	17.4510i	−0.536255	+	0.928821i	0.462846	+	0.886439i	$0.346828\pi$
$353$	−10.0753	+	17.4510i	−0.536255	+	0.928821i	−0.999101	+	0.0423828i	$0.986505\pi$
$354$	7.56805	+	13.1082i	0.402237	+	0.696695i
$355$	−11.4757	−	4.17680i	−0.609064	−	0.221681i
$356$	−2.78446	+	15.7915i	−0.147576	+	0.836946i
$357$	−0.0564370	−	0.320070i	−0.00298696	−	0.0169399i
$358$	−8.84389	+	3.21891i	−0.467414	+	0.170125i
$359$	2.60813	+	2.18848i	0.137652	+	0.115503i	0.709014	−	0.705195i	$-0.249140\pi$
$359$	2.60813	+	2.18848i	0.137652	+	0.115503i	−0.571362	+	0.820698i	$0.693585\pi$
$360$	−0.652704			−0.0344005
$361$	14.9029	−	11.7858i	0.784361	−	0.620305i
$362$	−24.4688			−1.28605
$363$	7.63223	+	6.40420i	0.400588	+	0.336133i
$364$	0.694593	−	0.252811i	0.0364066	−	0.0132509i
$365$	−1.20574	−	6.83807i	−0.0631112	−	0.357921i
$366$	1.78106	−	10.1009i	0.0930975	−	0.527982i
$367$	−7.41147	−	2.69756i	−0.386876	−	0.140811i	0.141257	−	0.989973i	$-0.454886\pi$
$367$	−7.41147	−	2.69756i	−0.386876	−	0.140811i	−0.528133	+	0.849162i	$0.677108\pi$
$368$	0.467911	+	0.810446i	0.0243916	+	0.0422474i
$369$	−2.56670	+	4.44566i	−0.133617	+	0.231432i
$370$	−3.06418	+	2.57115i	−0.159299	+	0.133668i
$371$	1.43376	−	1.20307i	0.0744373	−	0.0624603i
$372$	2.16250	−	3.74557i	0.112121	−	0.194199i
$373$	−12.2267	−	21.1772i	−0.633074	−	1.09652i	−0.986920	−	0.161212i	$-0.948460\pi$
$373$	−12.2267	−	21.1772i	−0.633074	−	1.09652i	0.353846	−	0.935304i	$-0.384874\pi$
$374$	−0.608593	−	0.221510i	−0.0314696	−	0.0114540i
$375$	−0.266044	+	1.50881i	−0.0137385	+	0.0779148i
$376$	−0.985452	−	5.58878i	−0.0508208	−	0.288219i
$377$	0.610815	−	0.222318i	0.0314586	−	0.0114500i
$378$	−2.97771	−	2.49860i	−0.153157	−	0.128514i
$379$	−33.8135			−1.73688			−0.868440	−	0.495794i	$-0.834877\pi$
$379$	−33.8135			−1.73688			−0.868440	+	0.495794i	$0.834877\pi$
$380$	−4.11721	+	1.43128i	−0.211208	+	0.0734233i
$381$	2.49794			0.127973
$382$	−1.56624	−	1.31423i	−0.0801357	−	0.0672418i
$383$	−29.1266	+	10.6012i	−1.48830	+	0.541697i	−0.953001	−	0.302966i	$-0.902023\pi$
$383$	−29.1266	+	10.6012i	−1.48830	+	0.541697i	−0.535298	+	0.844663i	$0.679801\pi$
$384$	−0.266044	−	1.50881i	−0.0135765	−	0.0769963i
$385$	0.255777	−	1.45059i	0.0130356	−	0.0739287i
$386$	−13.4427	−	4.89274i	−0.684215	−	0.249034i
$387$	−0.220285	−	0.381545i	−0.0111977	−	0.0193950i
$388$	−3.11721	+	5.39917i	−0.158252	+	0.274101i
$389$	−25.2080	+	21.1520i	−1.27810	+	1.07245i	−0.284594	+	0.958648i	$0.591859\pi$
$389$	−25.2080	+	21.1520i	−1.27810	+	1.07245i	−0.993503	+	0.113803i	$0.963697\pi$
$390$	−1.24897	+	1.04801i	−0.0632441	+	0.0530681i
$391$	−0.142903	+	0.247516i	−0.00722694	+	0.0125174i
$392$	3.25877	+	5.64436i	0.164593	+	0.285083i
$393$	−13.9081	−	5.06212i	−0.701569	−	0.255350i
$394$	2.42602	−	13.7587i	0.122221	−	0.693151i
$395$	−0.426022	−	2.41609i	−0.0214355	−	0.121567i
$396$	−1.30066	+	0.473401i	−0.0653606	+	0.0237893i
$397$	8.90941	+	7.47589i	0.447151	+	0.375204i	0.838377	−	0.545090i	$-0.183505\pi$
$397$	8.90941	+	7.47589i	0.447151	+	0.375204i	−0.391227	+	0.920294i	$0.627949\pi$
$398$	18.8384			0.944285
$399$	−4.33544	−	1.64955i	−0.217043	−	0.0825806i
$400$	1.00000			0.0500000
$401$	−10.3191	−	8.65873i	−0.515310	−	0.432397i	0.347683	−	0.937612i	$-0.386969\pi$
$401$	−10.3191	−	8.65873i	−0.515310	−	0.432397i	−0.862993	+	0.505216i	$0.831413\pi$
$402$	−18.2665	+	6.64847i	−0.911051	+	0.331595i
$403$	0.521660	+	2.95848i	0.0259857	+	0.147372i
$404$	−2.49525	+	14.1513i	−0.124143	+	0.704052i
$405$	6.21688	+	2.26276i	0.308919	+	0.112437i
$406$	−0.212134	−	0.367426i	−0.0105280	−	0.0182351i
$407$	−4.24123	+	7.34603i	−0.210230	+	0.364129i
$408$	0.358441	−	0.300767i	0.0177455	−	0.0148902i
$409$	11.0018	−	9.23162i	0.544005	−	0.456474i	−0.328900	−	0.944365i	$-0.606678\pi$
$409$	11.0018	−	9.23162i	0.544005	−	0.456474i	0.872905	+	0.487891i	$0.162234\pi$
$410$	3.93242	−	6.81115i	0.194208	−	0.336379i
$411$	−8.83409	−	15.3011i	−0.435754	−	0.754747i
$412$	−18.4192	−	6.70405i	−0.907450	−	0.330285i
$413$	−1.19160	+	6.75790i	−0.0586348	+	0.332534i
$414$	0.106067	+	0.601535i	0.00521290	+	0.0295638i
$415$	16.3341	−	5.94512i	0.801809	−	0.291835i
$416$	0.815207	+	0.684040i	0.0399688	+	0.0335378i
$417$	−10.4875			−0.513576
$418$	−7.16637	+	5.83834i	−0.350519	+	0.285563i
$419$	−32.2763			−1.57680			−0.788400	−	0.615162i	$-0.789090\pi$
$419$	−32.2763			−1.57680			−0.788400	+	0.615162i	$0.789090\pi$
$420$	0.815207	+	0.684040i	0.0397781	+	0.0333777i
$421$	12.3969	−	4.51211i	0.604189	−	0.219907i	−0.0217696	−	0.999763i	$-0.506930\pi$
$421$	12.3969	−	4.51211i	0.604189	−	0.219907i	0.625959	+	0.779856i	$0.284708\pi$
$422$	−0.0479810	−	0.272114i	−0.00233568	−	0.0132463i
$423$	0.643208	−	3.64781i	0.0312739	−	0.177363i
$424$	2.53209	+	0.921605i	0.122969	+	0.0447571i
$425$	0.152704	+	0.264490i	0.00740721	+	0.0128297i
$426$	9.35504	−	16.2034i	0.453253	−	0.785057i
$427$	3.56212	−	2.98897i	0.172383	−	0.144647i
$428$	1.58125	−	1.32683i	0.0764327	−	0.0641346i
$429$	−1.72874	+	2.99427i	−0.0834644	+	0.144565i
$430$	0.337496	+	0.584561i	0.0162755	+	0.0281900i
$431$	−4.49020	−	1.63430i	−0.216285	−	0.0787214i	0.231605	−	0.972810i	$-0.425602\pi$
$431$	−4.49020	−	1.63430i	−0.216285	−	0.0787214i	−0.447890	+	0.894088i	$0.647825\pi$
$432$	0.971782	−	5.51125i	0.0467549	−	0.265160i
$433$	4.87433	+	27.6437i	0.234245	+	1.32847i	0.844197	+	0.536033i	$0.180078\pi$
$433$	4.87433	+	27.6437i	0.234245	+	1.32847i	−0.609951	+	0.792439i	$0.708811\pi$
$434$	1.84255	−	0.670633i	0.0884452	−	0.0321914i
$435$	0.716881	+	0.601535i	0.0343718	+	0.0288414i
$436$	9.10876			0.436230
$437$	1.98814	+	3.56185i	0.0951057	+	0.170387i
$438$	10.6382			0.508311
$439$	17.8726	+	14.9969i	0.853012	+	0.715762i	0.960451	−	0.278450i	$-0.0898206\pi$
$439$	17.8726	+	14.9969i	0.853012	+	0.715762i	−0.107439	+	0.994212i	$0.534265\pi$
$440$	1.99273	−	0.725293i	0.0949995	−	0.0345770i
$441$	0.738703	+	4.18939i	0.0351763	+	0.199495i
$442$	−0.0564370	+	0.320070i	−0.00268443	+	0.0152242i
$443$	−14.0488	−	5.11333i	−0.667476	−	0.242942i	−0.0140154	−	0.999902i	$-0.504461\pi$
$443$	−14.0488	−	5.11333i	−0.667476	−	0.242942i	−0.653461	+	0.756960i	$0.726684\pi$
$444$	−3.06418	−	5.30731i	−0.145419	−	0.251874i
$445$	8.01754	−	13.8868i	0.380068	−	0.658297i
$446$	−5.29086	+	4.43956i	−0.250529	+	0.210219i
$447$	10.4534	−	8.77141i	0.494427	−	0.414874i
$448$	0.347296	−	0.601535i	0.0164082	−	0.0284199i
$449$	4.41194	+	7.64171i	0.208212	+	0.360634i	0.951151	−	0.308725i	$-0.0999022\pi$
$449$	4.41194	+	7.64171i	0.208212	+	0.360634i	−0.742939	+	0.669359i	$0.766569\pi$
$450$	0.613341	+	0.223238i	0.0289132	+	0.0105235i
$451$	2.89615	−	16.4249i	0.136375	−	0.773419i
$452$	1.24763	+	7.07564i	0.0586834	+	0.332810i
$453$	−15.5817	+	5.67128i	−0.732093	+	0.266460i
$454$	1.76399	+	1.48016i	0.0827879	+	0.0694673i
$455$	−0.739170			−0.0346528
$456$	−1.06418	−	6.59289i	−0.0498347	−	0.308740i
$457$	19.4561			0.910116			0.455058	−	0.890462i	$-0.349619\pi$
$457$	19.4561			0.910116			0.455058	+	0.890462i	$0.349619\pi$
$458$	−17.0155	−	14.2777i	−0.795081	−	0.667152i
$459$	1.60607	−	0.584561i	0.0749648	−	0.0272849i
$460$	−0.162504	−	0.921605i	−0.00757678	−	0.0429701i
$461$	4.56624	−	25.8964i	0.212671	−	1.20612i	−0.672232	−	0.740341i	$-0.734664\pi$
$461$	4.56624	−	25.8964i	0.212671	−	1.20612i	0.884903	−	0.465776i	$-0.154225\pi$
$462$	2.12061	+	0.771841i	0.0986599	+	0.0359093i
$463$	17.0993	+	29.6168i	0.794670	+	1.37641i	0.923049	+	0.384684i	$0.125689\pi$
$463$	17.0993	+	29.6168i	0.794670	+	1.37641i	−0.128379	+	0.991725i	$0.540977\pi$
$464$	0.305407	−	0.528981i	0.0141782	−	0.0245573i
$465$	−3.31315	+	2.78006i	−0.153644	+	0.128922i
$466$	13.7253	−	11.5169i	0.635814	−	0.533511i
$467$	0.00340357	−	0.00589515i	0.000157498	−	0.000272795i	−0.865947	−	0.500136i	$-0.833283\pi$
$467$	0.00340357	−	0.00589515i	0.000157498	−	0.000272795i	0.866104	+	0.499864i	$0.166617\pi$
$468$	0.347296	+	0.601535i	0.0160538	+	0.0278060i
$469$	−8.28136	−	3.01417i	−0.382398	−	0.139181i
$470$	−0.985452	+	5.58878i	−0.0454555	+	0.257791i
$471$	−2.84524	−	16.1361i	−0.131102	−	0.743514i
$472$	−9.28359	+	3.37895i	−0.427312	+	0.155529i
$473$	1.09652	+	0.920085i	0.0504178	+	0.0423056i
$474$	3.75877			0.172646
$475$	4.35844	+	0.0632028i	0.199979	+	0.00289994i
$476$	0.212134			0.00972313
$477$	1.34730	+	1.13052i	0.0616885	+	0.0517628i
$478$	6.51754	−	2.37219i	0.298105	−	0.108501i
$479$	3.14290	+	17.8243i	0.143603	+	0.814413i	0.968478	+	0.249098i	$0.0801341\pi$
$479$	3.14290	+	17.8243i	0.143603	+	0.814413i	−0.824875	+	0.565315i	$0.808755\pi$
$480$	−0.266044	+	1.50881i	−0.0121432	+	0.0688676i
$481$	4.00000	+	1.45588i	0.182384	+	0.0663825i
$482$	8.89440	+	15.4056i	0.405129	+	0.701704i
$483$	0.497941	−	0.862458i	0.0226571	−	0.0392432i
$484$	−4.98158	+	4.18004i	−0.226436	+	0.190002i
$485$	4.77584	−	4.00741i	0.216860	−	0.181967i
$486$	3.32635	−	5.76141i	0.150886	−	0.261343i
$487$	−0.369585	−	0.640140i	−0.0167475	−	0.0290075i	0.857530	−	0.514434i	$-0.171998\pi$
$487$	−0.369585	−	0.640140i	−0.0167475	−	0.0290075i	−0.874278	+	0.485426i	$0.838664\pi$
$488$	6.29086	+	2.28969i	0.284774	+	0.103649i
$489$	−0.656574	+	3.72362i	−0.0296913	+	0.168388i
$490$	−1.13176	−	6.41852i	−0.0511277	−	0.289959i
$491$	11.6566	−	4.24265i	0.526054	−	0.191468i	−0.0653217	−	0.997864i	$-0.520807\pi$
$491$	11.6566	−	4.24265i	0.526054	−	0.191468i	0.591375	+	0.806396i	$0.298585\pi$
$492$	9.23055	+	7.74535i	0.416145	+	0.349187i
$493$	0.186547			0.00840166
$494$	3.50980	+	3.03287i	0.157913	+	0.136455i
$495$	1.38413			0.0622122
$496$	2.16250	+	1.81456i	0.0970993	+	0.0814760i
$497$	7.97090	−	2.90117i	0.357544	−	0.130135i
$498$	4.62449	+	26.2268i	0.207228	+	1.17525i
$499$	−2.60947	+	14.7990i	−0.116816	+	0.662496i	0.869019	+	0.494778i	$0.164751\pi$
$499$	−2.60947	+	14.7990i	−0.116816	+	0.662496i	−0.985835	+	0.167718i	$0.946360\pi$
$500$	−0.939693	−	0.342020i	−0.0420243	−	0.0152956i
$501$	−9.32501	−	16.1514i	−0.416611	−	0.721591i
$502$	8.34776	−	14.4587i	0.372579	−	0.645326i
$503$	−0.543948	+	0.456427i	−0.0242535	+	0.0203511i	−0.654834	−	0.755773i	$-0.727261\pi$
$503$	−0.543948	+	0.456427i	−0.0242535	+	0.0203511i	0.630580	+	0.776124i	$0.282817\pi$
$504$	0.347296	−	0.291416i	0.0154698	−	0.0129807i
$505$	7.18479	−	12.4444i	0.319719	−	0.553770i
$506$	−0.992259	−	1.71864i	−0.0441113	−	0.0764030i
$507$	−17.0856	−	6.21865i	−0.758798	−	0.276180i
$508$	−0.283119	+	1.60565i	−0.0125614	+	0.0712390i
$509$	5.24628	+	29.7531i	0.232537	+	1.31878i	0.847738	+	0.530415i	$0.177964\pi$
$509$	5.24628	+	29.7531i	0.232537	+	1.31878i	−0.615201	+	0.788370i	$0.710925\pi$
$510$	−0.439693	+	0.160035i	−0.0194699	+	0.00708647i
$511$	3.69459	+	3.10013i	0.163439	+	0.137142i
$512$	1.00000			0.0441942
$513$	4.58378	−	23.9590i	0.202379	−	1.05782i
$514$	−26.1138			−1.15183
$515$	15.0155	+	12.5995i	0.661661	+	0.555200i
$516$	−0.971782	+	0.353700i	−0.0427803	+	0.0155708i
$517$	2.08976	+	11.8516i	0.0919077	+	0.521235i
$518$	0.482459	−	2.73616i	0.0211980	−	0.120220i
$519$	−20.2763	−	7.37997i	−0.890031	−	0.323945i
$520$	−0.532089	−	0.921605i	−0.0233336	−	0.0404151i
$521$	10.2390	−	17.7345i	0.448579	−	0.776962i	−0.549715	−	0.835352i	$-0.685264\pi$
$521$	10.2390	−	17.7345i	0.448579	−	0.776962i	0.998294	+	0.0583907i	$0.0185969\pi$
$522$	0.305407	−	0.256267i	0.0133673	−	0.0112165i
$523$	11.9554	−	10.0318i	0.522774	−	0.438660i	−0.342823	−	0.939400i	$-0.611383\pi$
$523$	11.9554	−	10.0318i	0.522774	−	0.438660i	0.865598	+	0.500740i	$0.166939\pi$
$524$	4.83022	−	8.36619i	0.211009	−	0.365479i
$525$	−0.532089	−	0.921605i	−0.0232223	−	0.0402221i
$526$	11.7442	+	4.27455i	0.512072	+	0.186379i
$527$	−0.149711	+	0.849051i	−0.00652150	+	0.0369852i
$528$	0.564178	+	3.19961i	0.0245527	+	0.139245i
$529$	20.7900	−	7.56693i	0.903912	−	0.328997i
$530$	−2.06418	−	1.73205i	−0.0896622	−	0.0752355i
$531$	−6.44831			−0.279833
$532$	1.55169	−	2.59980i	0.0672743	−	0.112716i
$533$	−8.36959			−0.362527
$534$	18.8195	+	15.7915i	0.814401	+	0.683364i
$535$	−1.93969	+	0.705990i	−0.0838602	+	0.0305226i
$536$	−2.20321	−	12.4950i	−0.0951642	−	0.539703i
$537$	−2.50387	+	14.2002i	−0.108050	+	0.612782i
$538$	−0.773318	−	0.281465i	−0.0333401	−	0.0121348i
$539$	−6.91060	−	11.9695i	−0.297660	−	0.515563i
$540$	−2.79813	+	4.84651i	−0.120412	+	0.208561i
$541$	1.91353	−	1.60565i	0.0822692	−	0.0690321i	−0.600726	−	0.799455i	$-0.705122\pi$
$541$	1.91353	−	1.60565i	0.0822692	−	0.0690321i	0.682995	+	0.730423i	$0.260677\pi$
$542$	−9.25671	+	7.76730i	−0.397610	+	0.333634i
$543$	−18.7442	+	32.4659i	−0.804392	+	1.39325i
$544$	0.152704	+	0.264490i	0.00654711	+	0.0113399i
$545$	−8.55943	−	3.11538i	−0.366646	−	0.133448i
$546$	0.196652	−	1.11527i	0.00841593	−	0.0477291i
$547$	−0.628766	−	3.56591i	−0.0268841	−	0.152467i	0.968411	−	0.249361i	$-0.0802205\pi$
$547$	−0.628766	−	3.56591i	−0.0268841	−	0.152467i	−0.995295	+	0.0968935i	$0.969109\pi$
$548$	10.8366	−	3.94421i	0.462917	−	0.168488i
$549$	3.34730	+	2.80872i	0.142859	+	0.119873i
$550$	−2.12061			−0.0904233
$551$	1.36453	−	2.28623i	0.0581310	−	0.0973967i
$552$	1.43376			0.0610250
$553$	1.30541	+	1.09537i	0.0555116	+	0.0465797i
$554$	10.5817	−	3.85143i	0.449574	−	0.163632i
$555$	1.06418	+	6.03525i	0.0451718	+	0.256182i
$556$	1.18866	−	6.74124i	0.0504105	−	0.285892i
$557$	10.4338	+	3.79758i	0.442093	+	0.160909i	0.553469	−	0.832870i	$-0.313304\pi$
$557$	10.4338	+	3.79758i	0.442093	+	0.160909i	−0.111376	+	0.993778i	$0.535526\pi$
$558$	0.921274	+	1.59569i	0.0390007	+	0.0675511i
$559$	0.359156	−	0.622076i	0.0151907	−	0.0263110i
$560$	−0.532089	+	0.446476i	−0.0224849	+	0.0188670i
$561$	−0.760115	+	0.637812i	−0.0320921	+	0.0269284i
$562$	−13.1065	+	22.7012i	−0.552866	+	0.957592i
$563$	−6.32383	−	10.9532i	−0.266517	−	0.461622i	0.701443	−	0.712726i	$-0.252540\pi$
$563$	−6.32383	−	10.9532i	−0.266517	−	0.461622i	−0.967960	+	0.251104i	$0.919206\pi$
$564$	−8.17024	−	2.97373i	−0.344029	−	0.125216i
$565$	1.24763	−	7.07564i	0.0524880	−	0.297674i
$566$	4.46926	+	25.3464i	0.187857	+	1.06539i
$567$	−4.31820	+	1.57170i	−0.181347	+	0.0660050i
$568$	9.35504	+	7.84981i	0.392529	+	0.329371i
$569$	−0.704088			−0.0295169			−0.0147585	−	0.999891i	$-0.504698\pi$
$569$	−0.704088			−0.0295169			−0.0147585	+	0.999891i	$0.504698\pi$
$570$	−1.25490	+	6.55926i	−0.0525620	+	0.274737i
$571$	10.3396			0.432697			0.216348	−	0.976316i	$-0.430585\pi$
$571$	10.3396			0.432697			0.216348	+	0.976316i	$0.430585\pi$
$572$	−1.72874	−	1.45059i	−0.0722823	−	0.0606520i
$573$	−2.94356	+	1.07137i	−0.122969	+	0.0447571i
$574$	0.948615	+	5.37987i	0.0395944	+	0.224551i
$575$	−0.162504	+	0.921605i	−0.00677688	+	0.0384336i
$576$	0.613341	+	0.223238i	0.0255559	+	0.00930157i
$577$	−0.769448	−	1.33272i	−0.0320325	−	0.0554820i	0.849565	−	0.527484i	$-0.176865\pi$
$577$	−0.769448	−	1.33272i	−0.0320325	−	0.0554820i	−0.881597	+	0.472002i	$0.843531\pi$
$578$	8.45336	−	14.6417i	0.351614	−	0.609013i
$579$	−16.7895	+	14.0881i	−0.697748	+	0.585480i
$580$	−0.467911	+	0.392624i	−0.0194290	+	0.0163028i
$581$	−6.03684	+	10.4561i	−0.250450	+	0.433792i
$582$	4.77584	+	8.27201i	0.197965	+	0.342886i
$583$	−5.36959	−	1.95437i	−0.222385	−	0.0809417i
$584$	−1.20574	+	6.83807i	−0.0498938	+	0.282962i
$585$	−0.120615	−	0.684040i	−0.00498681	−	0.0282816i
$586$	−24.9094	+	9.06629i	−1.02900	+	0.374525i
$587$	−5.27173	−	4.42350i	−0.217587	−	0.182578i	0.527478	−	0.849568i	$-0.323138\pi$
$587$	−5.27173	−	4.42350i	−0.217587	−	0.182578i	−0.745066	+	0.666991i	$0.767582\pi$
$588$	9.98545			0.411793
$589$	9.31046	+	8.04531i	0.383631	+	0.331501i
$590$	9.87939			0.406728
$591$	−16.3969	−	13.7587i	−0.674479	−	0.565955i
$592$	3.75877	−	1.36808i	0.154485	−	0.0562278i
$593$	−0.723278	−	4.10191i	−0.0297015	−	0.168445i	0.966349	−	0.257235i	$-0.0828113\pi$
$593$	−0.723278	−	4.10191i	−0.0297015	−	0.168445i	−0.996050	+	0.0887893i	$0.971700\pi$
$594$	−2.06077	+	11.6872i	−0.0845546	+	0.479533i
$595$	−0.199340	−	0.0725540i	−0.00817216	−	0.00297442i
$596$	4.45336	+	7.71345i	0.182417	+	0.315955i
$597$	14.4311	−	24.9954i	0.590625	−	1.02299i
$598$	−0.762889	+	0.640140i	−0.0311969	+	0.0261773i
$599$	35.1070	−	29.4583i	1.43443	−	1.20363i	0.491400	−	0.870934i	$-0.336485\pi$
$599$	35.1070	−	29.4583i	1.43443	−	1.20363i	0.943033	−	0.332698i	$-0.107959\pi$
$600$	0.766044	−	1.32683i	0.0312736	−	0.0541675i
$601$	1.05257	+	1.82310i	0.0429351	+	0.0743658i	0.886694	−	0.462356i	$-0.152996\pi$
$601$	1.05257	+	1.82310i	0.0429351	+	0.0743658i	−0.843759	+	0.536722i	$0.819662\pi$
$602$	−0.440570	−	0.160354i	−0.0179563	−	0.00653556i
$603$	1.43804	−	8.15555i	0.0585617	−	0.332120i
$604$	−1.87939	−	10.6585i	−0.0764711	−	0.433689i
$605$	6.11081	−	2.22415i	0.248440	−	0.0904247i
$606$	16.8648	+	14.1513i	0.685087	+	0.574856i
$607$	−26.7648			−1.08635			−0.543174	−	0.839620i	$-0.682778\pi$
$607$	−26.7648			−1.08635			−0.543174	+	0.839620i	$0.682778\pi$
$608$	4.35844	+	0.0632028i	0.176758	+	0.00256321i
$609$	−0.650015			−0.0263399
$610$	−5.12836	−	4.30320i	−0.207641	−	0.174232i
$611$	5.67499	−	2.06553i	0.229586	−	0.0835623i
$612$	0.0346151	+	0.196312i	0.00139923	+	0.00793544i
$613$	6.93407	−	39.3251i	0.280064	−	1.58832i	−0.442336	−	0.896849i	$-0.645850\pi$
$613$	6.93407	−	39.3251i	0.280064	−	1.58832i	0.722401	−	0.691475i	$-0.243039\pi$
$614$	−2.99273	−	1.08926i	−0.120777	−	0.0439591i
$615$	−6.02481	−	10.4353i	−0.242944	−	0.420791i
$616$	−0.736482	+	1.27562i	−0.0296737	+	0.0513963i
$617$	−30.1575	+	25.3052i	−1.21410	+	1.01875i	−0.214983	+	0.976618i	$0.568970\pi$
$617$	−30.1575	+	25.3052i	−1.21410	+	1.01875i	−0.999112	+	0.0421294i	$0.986586\pi$
$618$	−23.0051	+	19.3035i	−0.925399	+	0.776502i
$619$	14.5273	−	25.1621i	0.583903	−	1.01135i	−0.411108	−	0.911587i	$-0.634858\pi$
$619$	14.5273	−	25.1621i	0.583903	−	1.01135i	0.995011	−	0.0997633i	$-0.0318086\pi$
$620$	−1.41147	−	2.44474i	−0.0566862	−	0.0981833i
$621$	4.92127	+	1.79120i	0.197484	+	0.0718783i
$622$	0.142903	−	0.810446i	0.00572991	−	0.0324959i
$623$	1.93407	+	10.9686i	0.0774868	+	0.439449i
$624$	1.53209	−	0.557635i	0.0613326	−	0.0223233i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	21.8881			0.874823
$627$	2.25671	+	13.9810i	0.0901244	+	0.558346i
$628$	10.6946			0.426761
$629$	0.935822	+	0.785248i	0.0373137	+	0.0313099i
$630$	−0.426022	+	0.155059i	−0.0169731	+	0.00617771i
$631$	5.72369	+	32.4607i	0.227856	+	1.29224i	0.857149	+	0.515069i	$0.172234\pi$
$631$	5.72369	+	32.4607i	0.227856	+	1.29224i	−0.629292	+	0.777169i	$0.716655\pi$
$632$	−0.426022	+	2.41609i	−0.0169462	+	0.0961069i
$633$	−0.397804	−	0.144789i	−0.0158113	−	0.00575483i
$634$	6.61081	+	11.4503i	0.262549	+	0.454748i
$635$	0.815207	−	1.41198i	0.0323505	−	0.0560327i
$636$	3.16250	−	2.65366i	0.125401	−	0.105224i
$637$	−5.31315	+	4.45826i	−0.210515	+	0.176643i
$638$	−0.647651	+	1.12176i	−0.0256408	+	0.0444111i
$639$	3.98545	+	6.90301i	0.157662	+	0.273079i
$640$	−0.939693	−	0.342020i	−0.0371446	−	0.0135195i
$641$	3.77214	−	21.3928i	0.148990	−	0.844967i	−0.815086	−	0.579340i	$-0.803310\pi$
$641$	3.77214	−	21.3928i	0.148990	−	0.844967i	0.964076	−	0.265626i	$-0.0855787\pi$
$642$	−0.549163	−	3.11446i	−0.0216737	−	0.122918i
$643$	−39.6400	+	14.4278i	−1.56325	+	0.568976i	−0.971478	−	0.237131i	$-0.923793\pi$
$643$	−39.6400	+	14.4278i	−1.56325	+	0.568976i	−0.591770	+	0.806107i	$0.701571\pi$
$644$	0.497941	+	0.417822i	0.0196216	+	0.0164645i
$645$	1.03415			0.0407195
$646$	0.648833	+	1.16242i	0.0255280	+	0.0457347i
$647$	45.2526			1.77906			0.889531	−	0.456874i	$-0.151031\pi$
$647$	45.2526			1.77906			0.889531	+	0.456874i	$0.151031\pi$
$648$	−5.06805	−	4.25260i	−0.199092	−	0.167058i
$649$	19.6869	−	7.16545i	0.772779	−	0.281268i
$650$	0.184793	+	1.04801i	0.00724816	+	0.0411064i
$651$	0.521660	−	2.95848i	0.0204455	−	0.115952i
$652$	−2.31908	−	0.844075i	−0.0908221	−	0.0330565i
$653$	−4.97090	−	8.60986i	−0.194527	−	0.336930i	0.752219	−	0.658914i	$-0.228984\pi$
$653$	−4.97090	−	8.60986i	−0.194527	−	0.336930i	−0.946745	+	0.321984i	$0.895650\pi$
$654$	6.97771	−	12.0858i	0.272850	−	0.472590i
$655$	−7.40033	+	6.20961i	−0.289155	+	0.242630i
$656$	−6.02481	+	5.05542i	−0.235230	+	0.197381i
$657$	−2.26604	+	3.92490i	−0.0884068	+	0.153125i
$658$	−1.97090	−	3.41371i	−0.0768338	−	0.133080i
$659$	−20.4136	−	7.42994i	−0.795201	−	0.289429i	−0.0877044	−	0.996147i	$-0.527953\pi$
$659$	−20.4136	−	7.42994i	−0.795201	−	0.289429i	−0.707496	+	0.706717i	$0.750175\pi$
$660$	0.564178	−	3.19961i	0.0219606	−	0.124545i
$661$	4.99319	+	28.3178i	0.194213	+	1.10143i	0.913536	+	0.406759i	$0.133341\pi$
$661$	4.99319	+	28.3178i	0.194213	+	1.10143i	−0.719323	+	0.694676i	$0.755548\pi$
$662$	−1.53936	+	0.560282i	−0.0598290	+	0.0217760i
$663$	0.381445	+	0.320070i	0.0148141	+	0.0124305i
$664$	−17.3824			−0.674567
$665$	−2.34730	+	1.91231i	−0.0910242	+	0.0741561i
$666$	2.61081			0.101167
$667$	0.437882	+	0.367426i	0.0169548	+	0.0142268i
$668$	11.4388	−	4.16339i	0.442581	−	0.161086i
$669$	1.83750	+	10.4210i	0.0710417	+	0.402898i
$670$	−2.20321	+	12.4950i	−0.0851175	+	0.482725i
$671$	−13.3405	−	4.85554i	−0.515004	−	0.187446i
$672$	−0.532089	−	0.921605i	−0.0205258	−	0.0355517i
$673$	17.8824	−	30.9732i	0.689315	−	1.19393i	−0.282745	−	0.959195i	$-0.591245\pi$
$673$	17.8824	−	30.9732i	0.689315	−	1.19393i	0.972060	−	0.234733i	$-0.0754217\pi$
$674$	−24.0043	+	20.1420i	−0.924613	+	0.775842i
$675$	4.28699	−	3.59721i	0.165006	−	0.138457i
$676$	5.93376	−	10.2776i	0.228222	−	0.395291i
$677$	−7.72193	−	13.3748i	−0.296778	−	0.514035i	0.678619	−	0.734491i	$-0.262579\pi$
$677$	−7.72193	−	13.3748i	−0.296778	−	0.514035i	−0.975397	+	0.220456i	$0.929245\pi$
$678$	10.3439	+	3.76487i	0.397255	+	0.144589i
$679$	−0.751963	+	4.26460i	−0.0288577	+	0.163660i
$680$	−0.0530334	−	0.300767i	−0.00203374	−	0.0115339i
$681$	3.31521	−	1.20664i	0.127039	−	0.0462384i
$682$	−4.58584	−	3.84797i	−0.175601	−	0.147347i
$683$	28.0951			1.07503			0.537515	−	0.843254i	$-0.319363\pi$
$683$	28.0951			1.07503			0.537515	+	0.843254i	$0.319363\pi$
$684$	2.65910	+	1.01173i	0.101673	+	0.0386846i
$685$	−11.5321			−0.440618
$686$	7.19253	+	6.03525i	0.274612	+	0.230427i
$687$	−31.9786	+	11.6393i	−1.22006	+	0.444066i
$688$	−0.117211	−	0.664738i	−0.00446863	−	0.0253429i
$689$	−0.497941	+	2.82396i	−0.0189700	+	0.107584i
$690$	−1.34730	−	0.490376i	−0.0512907	−	0.0186683i
$691$	19.7841	+	34.2670i	0.752621	+	1.30358i	0.946548	+	0.322562i	$0.104544\pi$
$691$	19.7841	+	34.2670i	0.752621	+	1.30358i	−0.193928	+	0.981016i	$0.562123\pi$
$692$	7.04189	−	12.1969i	0.267692	−	0.463657i
$693$	−0.736482	+	0.617982i	−0.0279766	+	0.0234752i
$694$	19.4782	−	16.3441i	0.739382	−	0.620415i
$695$	−3.42262	+	5.92815i	−0.129827	+	0.224868i
$696$	−0.467911	−	0.810446i	−0.0177361	−	0.0307199i
$697$	−2.25712	−	0.821525i	−0.0854946	−	0.0311175i
$698$	5.59121	−	31.7094i	0.211631	−	1.20022i
$699$	−4.76676	−	27.0336i	−0.180295	−	1.02251i
$700$	0.652704	−	0.237565i	0.0246699	−	0.00897910i
$701$	−14.1898	−	11.9067i	−0.535943	−	0.449710i	0.334205	−	0.942501i	$-0.391532\pi$
$701$	−14.1898	−	11.9067i	−0.535943	−	0.449710i	−0.870148	+	0.492791i	$0.835977\pi$
$702$	5.95542			0.224773
$703$	16.4688	−	5.72513i	0.621134	−	0.215927i
$704$	−2.12061			−0.0799237
$705$	6.66044	+	5.58878i	0.250847	+	0.210485i
$706$	−18.9354	+	6.89193i	−0.712644	+	0.259381i
$707$	1.73318	+	9.82938i	0.0651831	+	0.369672i
$708$	−2.62836	+	14.9061i	−0.0987797	+	0.560207i
$709$	−17.1284	−	6.23421i	−0.643269	−	0.234131i	−0.000272535	−	1.00000i	$-0.500087\pi$
$709$	−17.1284	−	6.23421i	−0.643269	−	0.234131i	−0.642996	+	0.765869i	$0.722309\pi$
$710$	−6.10607	−	10.5760i	−0.229157	−	0.396911i
$711$	−0.800660	+	1.38678i	−0.0300271	+	0.0520084i
$712$	−12.2836	+	10.3072i	−0.460347	+	0.386277i
$713$	−2.02372	+	1.69810i	−0.0757889	+	0.0635944i
$714$	0.162504	−	0.281465i	0.00608155	−	0.0105336i
$715$	1.12836	+	1.95437i	0.0421981	+	0.0730893i
$716$	−8.84389	−	3.21891i	−0.330512	−	0.120296i
$717$	1.84524	−	10.4649i	0.0689116	−	0.390817i
$718$	0.591214	+	3.35294i	0.0220639	+	0.125131i
$719$	21.9786	−	7.99957i	0.819665	−	0.298334i	0.102055	−	0.994779i	$-0.467458\pi$
$719$	21.9786	−	7.99957i	0.819665	−	0.298334i	0.717610	+	0.696445i	$0.245236\pi$
$720$	−0.500000	−	0.419550i	−0.0186339	−	0.0156357i
$721$	−13.6149			−0.507047
$722$	18.9920	+	0.550931i	0.706809	+	0.0205035i
$723$	27.2540			1.01359
$724$	−18.7442	−	15.7283i	−0.696624	−	0.584537i
$725$	0.573978	−	0.208911i	0.0213170	−	0.00775876i
$726$	1.73009	+	9.81180i	0.0642095	+	0.364150i
$727$	0.928081	−	5.26341i	0.0344206	−	0.195209i	−0.962749	−	0.270398i	$-0.912845\pi$
$727$	0.928081	−	5.26341i	0.0344206	−	0.195209i	0.997169	+	0.0751887i	$0.0239559\pi$
$728$	0.694593	+	0.252811i	0.0257433	+	0.00936980i
$729$	−15.0201	−	26.0155i	−0.556299	−	0.963538i
$730$	3.47178	−	6.01330i	0.128496	−	0.222562i
$731$	0.157918	−	0.132509i	0.00584082	−	0.00490103i
$732$	7.85710	−	6.59289i	0.290407	−	0.243680i
$733$	−15.7374	+	27.2580i	−0.581275	+	1.00680i	0.414054	+	0.910252i	$0.364112\pi$
$733$	−15.7374	+	27.2580i	−0.581275	+	1.00680i	−0.995329	+	0.0965450i	$0.969221\pi$
$734$	−3.94356	−	6.83045i	−0.145560	−	0.252117i
$735$	−9.38326	−	3.41523i	−0.346107	−	0.125972i
$736$	−0.162504	+	0.921605i	−0.00598997	+	0.0339708i
$737$	4.67216	+	26.4971i	0.172101	+	0.976035i
$738$	−4.82383	+	1.75573i	−0.177567	+	0.0646293i
$739$	19.8855	+	16.6859i	0.731501	+	0.613802i	0.930540	−	0.366189i	$-0.119338\pi$
$739$	19.8855	+	16.6859i	0.731501	+	0.613802i	−0.199039	+	0.979992i	$0.563782\pi$
$740$	−4.00000			−0.147043
$741$	6.71276	−	2.33359i	0.246599	−	0.0857264i
$742$	1.87164			0.0687102
$743$	−33.6432	−	28.2300i	−1.23425	−	1.03566i	−0.997951	−	0.0639778i	$-0.979621\pi$
$743$	−33.6432	−	28.2300i	−1.23425	−	1.03566i	−0.236298	−	0.971681i	$-0.575934\pi$
$744$	4.06418	−	1.47924i	0.149000	−	0.0542316i
$745$	−1.54664	−	8.77141i	−0.0566644	−	0.321360i
$746$	4.24628	−	24.0819i	0.155467	−	0.881700i
$747$	−10.6613	−	3.88040i	−0.390077	−	0.141977i
$748$	−0.323826	−	0.560882i	−0.0118402	−	0.0205079i
$749$	0.716881	−	1.24168i	0.0261943	−	0.0453698i
$750$	−1.17365	+	0.984808i	−0.0428556	+	0.0359601i
$751$	−25.3746	+	21.2918i	−0.925934	+	0.776951i	−0.975083	−	0.221841i	$-0.928793\pi$
$751$	−25.3746	+	21.2918i	−0.925934	+	0.776951i	0.0491492	+	0.998791i	$0.484349\pi$
$752$	2.83750	−	4.91469i	0.103473	−	0.179220i
$753$	−12.7895	−	22.1521i	−0.466076	−	0.807267i
$754$	0.610815	+	0.222318i	0.0222446	+	0.00809636i
$755$	−1.87939	+	10.6585i	−0.0683978	+	0.387903i
$756$	−0.674992	−	3.82807i	−0.0245492	−	0.139226i
$757$	−18.8179	+	6.84915i	−0.683948	+	0.248937i	−0.660542	−	0.750789i	$-0.729673\pi$
$757$	−18.8179	+	6.84915i	−0.683948	+	0.248937i	−0.0234063	+	0.999726i	$0.507451\pi$
$758$	−25.9026	−	21.7349i	−0.940825	−	0.789446i
$759$	−3.04046			−0.110362
$760$	−4.07398	−	1.55007i	−0.147779	−	0.0562268i
$761$	22.4097			0.812352			0.406176	−	0.913795i	$-0.366862\pi$
$761$	22.4097			0.812352			0.406176	+	0.913795i	$0.366862\pi$
$762$	1.91353	+	1.60565i	0.0693200	+	0.0581664i
$763$	5.94532	−	2.16392i	0.215235	−	0.0783391i
$764$	−0.355037	−	2.01352i	−0.0128448	−	0.0728464i
$765$	0.0346151	−	0.196312i	0.00125151	−	0.00709768i
$766$	−29.1266	−	10.6012i	−1.05239	−	0.383037i
$767$	−5.25671	−	9.10489i	−0.189809	−	0.328759i
$768$	0.766044	−	1.32683i	0.0276422	−	0.0478778i
$769$	−7.55896	+	6.34272i	−0.272583	+	0.228724i	−0.768824	−	0.639460i	$-0.779158\pi$
$769$	−7.55896	+	6.34272i	−0.272583	+	0.228724i	0.496241	+	0.868185i	$0.334713\pi$
$770$	1.12836	−	0.946803i	0.0406631	−	0.0341204i
$771$	−20.0043	+	34.6485i	−0.720439	+	1.24784i
$772$	−7.15270	−	12.3888i	−0.257431	−	0.445884i
$773$	18.1189	+	6.59473i	0.651690	+	0.237196i	0.646645	−	0.762791i	$-0.276172\pi$
$773$	18.1189	+	6.59473i	0.651690	+	0.237196i	0.00504555	+	0.999987i	$0.498394\pi$
$774$	0.0765042	−	0.433877i	0.00274989	−	0.0155954i
$775$	0.490200	+	2.78006i	0.0176085	+	0.0998628i
$776$	−5.85844	+	2.13230i	−0.210306	+	0.0765450i
$777$	−3.26083	−	2.73616i	−0.116982	−	0.0981592i
$778$	−32.9067			−1.17976
$779$	−26.5783	+	21.6530i	−0.952267	+	0.775798i
$780$	−1.63041			−0.0583782
$781$	−19.8384	−	16.6464i	−0.709875	−	0.595656i
$782$	−0.268571	+	0.0977517i	−0.00960407	+	0.00349559i
$783$	−0.593578	−	3.36635i	−0.0212128	−	0.120304i
$784$	−1.13176	+	6.41852i	−0.0404200	+	0.229233i
$785$	−10.0496	−	3.65777i	−0.358687	−	0.130551i
$786$	−7.40033	−	12.8177i	−0.263961	−	0.457194i
$787$	−7.38026	+	12.7830i	−0.263078	+	0.455664i	−0.967058	−	0.254555i	$-0.918071\pi$
$787$	−7.38026	+	12.7830i	−0.263078	+	0.455664i	0.703980	+	0.710219i	$0.251404\pi$
$788$	10.7023	−	8.98032i	0.381255	−	0.319911i
$789$	14.6682	−	12.3081i	0.522201	−	0.438179i
$790$	1.22668	−	2.12467i	0.0436434	−	0.0755925i
$791$	2.49525	+	4.32190i	0.0887210	+	0.153669i
$792$	−1.30066	−	0.473401i	−0.0462169	−	0.0168216i
$793$	−1.23711	+	7.01600i	−0.0439311	+	0.249146i
$794$	2.01960	+	11.4537i	0.0716729	+	0.406477i
$795$	−3.87939	+	1.41198i	−0.137588	+	0.0500778i
$796$	14.4311	+	12.1091i	0.511496	+	0.429196i
$797$	29.2627			1.03654			0.518269	−	0.855218i	$-0.326577\pi$
$797$	29.2627			1.03654			0.518269	+	0.855218i	$0.326577\pi$
$798$	−2.26083	−	4.05039i	−0.0800325	−	0.143382i
$799$	1.73318			0.0613156
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	−9.83497	+	3.57964i	−0.347502	+	0.126480i
$802$	−2.33915	−	13.2660i	−0.0825981	−	0.468437i
$803$	2.55690	−	14.5009i	0.0902312	−	0.511726i
$804$	−18.2665	−	6.64847i	−0.644210	−	0.234473i
$805$	−0.325008	−	0.562930i	−0.0114550	−	0.0198407i
$806$	−1.50206	+	2.60164i	−0.0529078	+	0.0916390i
$807$	−0.965852	+	0.810446i	−0.0339996	+	0.0285290i
$808$	−11.0077	+	9.23659i	−0.387251	+	0.324942i
$809$	23.6129	−	40.8988i	0.830186	−	1.43793i	−0.0677037	−	0.997705i	$-0.521567\pi$
$809$	23.6129	−	40.8988i	0.830186	−	1.43793i	0.897890	−	0.440220i	$-0.145099\pi$
$810$	3.30793	+	5.72951i	0.116229	+	0.201314i
$811$	−17.4338	−	6.34537i	−0.612182	−	0.222816i	0.0172756	−	0.999851i	$-0.494501\pi$
$811$	−17.4338	−	6.34537i	−0.612182	−	0.222816i	−0.629458	+	0.777035i	$0.716723\pi$
$812$	0.0736733	−	0.417822i	0.00258542	−	0.0146627i
$813$	3.21482	+	18.2322i	0.112749	+	0.639430i
$814$	−7.97090	+	2.90117i	−0.279380	+	0.101686i
$815$	1.89053	+	1.58634i	0.0662224	+	0.0555672i
$816$	0.467911			0.0163802
$817$	−0.468845	−	2.90463i	−0.0164028	−	0.101620i
$818$	14.3618			0.502150
$819$	0.369585	+	0.310119i	0.0129143	+	0.0108364i
$820$	7.39053	−	2.68993i	0.258088	−	0.0939365i
$821$	8.55850	+	48.5376i	0.298694	+	1.69398i	0.651799	+	0.758392i	$0.274015\pi$
$821$	8.55850	+	48.5376i	0.298694	+	1.69398i	−0.353105	+	0.935584i	$0.614874\pi$
$822$	3.06805	−	17.3998i	0.107010	−	0.606887i
$823$	−22.7425	−	8.27758i	−0.792753	−	0.288538i	−0.0862728	−	0.996272i	$-0.527496\pi$
$823$	−22.7425	−	8.27758i	−0.792753	−	0.288538i	−0.706480	+	0.707733i	$0.749718\pi$
$824$	−9.80066	−	16.9752i	−0.341422	−	0.591361i
$825$	−1.62449	+	2.81369i	−0.0565573	+	0.0979601i
$826$	−5.25671	+	4.41090i	−0.182904	+	0.153475i
$827$	11.8289	−	9.92561i	0.411330	−	0.345147i	−0.413523	−	0.910494i	$-0.635702\pi$
$827$	11.8289	−	9.92561i	0.411330	−	0.345147i	0.824854	+	0.565346i	$0.191257\pi$
$828$	−0.305407	+	0.528981i	−0.0106136	+	0.0183834i
$829$	1.47565	+	2.55590i	0.0512515	+	0.0887702i	0.890513	−	0.454958i	$-0.150346\pi$
$829$	1.47565	+	2.55590i	0.0512515	+	0.0887702i	−0.839261	+	0.543728i	$0.817012\pi$
$830$	16.3341	+	5.94512i	0.566965	+	0.206358i
$831$	2.99588	−	16.9905i	0.103926	−	0.589393i
$832$	0.184793	+	1.04801i	0.00640653	+	0.0363332i
$833$	−1.87046	+	0.680793i	−0.0648077	+	0.0235881i
$834$	−8.03390	−	6.74124i	−0.278191	−	0.233430i
$835$	−12.1729			−0.421262
$836$	−9.24257	−	0.134029i	−0.319661	−	0.00463548i
$837$	15.7980			0.546058
$838$	−24.7251	−	20.7468i	−0.854114	−	0.716687i
$839$	3.51754	−	1.28028i	0.121439	−	0.0442002i	−0.280586	−	0.959829i	$-0.590529\pi$
$839$	3.51754	−	1.28028i	0.121439	−	0.0442002i	0.402025	+	0.915629i	$0.368307\pi$
$840$	0.184793	+	1.04801i	0.00637595	+	0.0361598i
$841$	−4.97101	+	28.1920i	−0.171414	+	0.972138i
$842$	12.3969	+	4.51211i	0.427226	+	0.155498i
$843$	20.0804	+	34.7802i	0.691605	+	1.19789i
$844$	0.138156	−	0.239293i	0.00475552	−	0.00823680i
$845$	−9.09105	+	7.62830i	−0.312742	+	0.262421i
$846$	2.83750	−	2.38094i	0.0975551	−	0.0818585i
$847$	−2.25847	+	3.91178i	−0.0776018	+	0.134410i
$848$	1.34730	+	2.33359i	0.0462663	+	0.0801357i
$849$	37.0540	+	13.4865i	1.27169	+	0.462857i
$850$	−0.0530334	+	0.300767i	−0.00181903	+	0.0103162i
$851$	0.650015	+	3.68642i	0.0222822	+	0.126369i
$852$	17.5817	−	6.39922i	0.602340	−	0.219234i
$853$	29.5212	+	24.7712i	1.01079	+	0.848150i	0.988442	−	0.151601i	$-0.0484428\pi$
$853$	29.5212	+	24.7712i	1.01079	+	0.848150i	0.0223436	+	0.999750i	$0.492887\pi$
$854$	4.65002			0.159120
$855$	−2.15270	−	1.86018i	−0.0736209	−	0.0636170i
$856$	2.06418			0.0705521
$857$	−36.7367	−	30.8258i	−1.25490	−	1.05299i	−0.996206	−	0.0870288i	$-0.972263\pi$
$857$	−36.7367	−	30.8258i	−1.25490	−	1.05299i	−0.258696	−	0.965959i	$-0.583293\pi$
$858$	−3.24897	+	1.18253i	−0.110918	+	0.0403709i
$859$	8.46750	+	48.0216i	0.288907	+	1.63848i	0.690985	+	0.722869i	$0.257177\pi$
$859$	8.46750	+	48.0216i	0.288907	+	1.63848i	−0.402077	+	0.915606i	$0.631712\pi$
$860$	−0.117211	+	0.664738i	−0.00399687	+	0.0226674i
$861$	7.86484	+	2.86257i	0.268033	+	0.0975560i
$862$	−2.38919	−	4.13819i	−0.0813760	−	0.140947i
$863$	6.51754	−	11.2887i	0.221860	−	0.384272i	−0.733513	−	0.679675i	$-0.762121\pi$
$863$	6.51754	−	11.2887i	0.221860	−	0.384272i	0.955373	+	0.295403i	$0.0954540\pi$
$864$	4.28699	−	3.59721i	0.145846	−	0.122380i
$865$	−10.7888	+	9.05288i	−0.366830	+	0.307807i
$866$	−14.0351	+	24.3095i	−0.476931	+	0.826070i
$867$	−12.9513	−	22.4323i	−0.439849	−	0.761841i
$868$	1.84255	+	0.670633i	0.0625402	+	0.0227628i
$869$	0.903429	−	5.12360i	0.0306467	−	0.173806i
$870$	0.162504	+	0.921605i	0.00550940	+	0.0312453i
$871$	12.6878	−	4.61798i	0.429909	−	0.156474i
$872$	6.97771	+	5.85499i	0.236295	+	0.198275i
$873$	−4.06923			−0.137723
$874$	−0.766511	+	4.00649i	−0.0259276	+	0.135522i
$875$	−0.694593			−0.0234815
$876$	8.14930	+	6.83807i	0.275339	+	0.231037i
$877$	44.7921	−	16.3030i	1.51252	−	0.550513i	0.553254	−	0.833012i	$-0.313386\pi$
$877$	44.7921	−	16.3030i	1.51252	−	0.550513i	0.959267	+	0.282500i	$0.0911636\pi$
$878$	4.05138	+	22.9765i	0.136728	+	0.775421i
$879$	−7.05232	+	39.9957i	−0.237869	+	1.34902i
$880$	1.99273	+	0.725293i	0.0671748	+	0.0244496i
$881$	2.92973	+	5.07444i	0.0987051	+	0.170962i	0.911149	−	0.412077i	$-0.135197\pi$
$881$	2.92973	+	5.07444i	0.0987051	+	0.170962i	−0.812444	+	0.583040i	$0.801863\pi$
$882$	−2.12701	+	3.68409i	−0.0716202	+	0.124050i
$883$	−1.96064	+	1.64517i	−0.0659807	+	0.0553644i	−0.675182	−	0.737652i	$-0.735935\pi$
$883$	−1.96064	+	1.64517i	−0.0659807	+	0.0553644i	0.609201	+	0.793016i	$0.291490\pi$
$884$	−0.248970	+	0.208911i	−0.00837378	+	0.00702643i
$885$	7.56805	−	13.1082i	0.254397	−	0.440629i
$886$	−7.47519	−	12.9474i	−0.251134	−	0.434976i
$887$	14.3696	+	5.23010i	0.482483	+	0.175610i	0.571799	−	0.820394i	$-0.306246\pi$
$887$	14.3696	+	5.23010i	0.482483	+	0.175610i	−0.0893155	+	0.996003i	$0.528468\pi$
$888$	1.06418	−	6.03525i	0.0357115	−	0.202530i
$889$	0.196652	+	1.11527i	0.00659550	+	0.0374049i
$890$	15.0680	−	5.48432i	0.505082	−	0.183835i
$891$	10.7474	+	9.01812i	0.360051	+	0.302118i
$892$	−6.90673			−0.231254
$893$	12.6777	−	21.2410i	0.424242	−	0.710804i
$894$	13.6459			0.456387
$895$	7.20961	+	6.04958i	0.240991	+	0.202215i
$896$	0.652704	−	0.237565i	0.0218053	−	0.00793648i
$897$	0.264949	+	1.50260i	0.00884638	+	0.0501703i
$898$	−1.53225	+	8.68983i	−0.0511319	+	0.289983i
$899$	1.62031	+	0.589745i	0.0540404	+	0.0196691i
$900$	0.326352	+	0.565258i	0.0108784	+	0.0188419i
$901$	−0.411474	+	0.712694i	−0.0137082	+	0.0237433i
$902$	12.7763	−	10.7206i	0.425405	−	0.356957i
$903$	−0.550259	+	0.461722i	−0.0183115	+	0.0153651i
$904$	−3.59240	+	6.22221i	−0.119481	+	0.206948i
$905$	12.2344	+	21.1906i	0.406686	+	0.704401i
$906$	−15.5817	−	5.67128i	−0.517668	−	0.188416i
$907$	−2.45295	+	13.9114i	−0.0814490	+	0.461920i	0.916618	+	0.399765i	$0.130908\pi$
$907$	−2.45295	+	13.9114i	−0.0814490	+	0.461920i	−0.998067	+	0.0621548i	$0.980203\pi$
$908$	0.399863	+	2.26774i	0.0132699	+	0.0752574i
$909$	−8.81345	+	3.20783i	−0.292324	+	0.106397i
$910$	−0.566237	−	0.475129i	−0.0187706	−	0.0157504i
$911$	31.3809			1.03970			0.519849	−	0.854258i	$-0.325988\pi$
$911$	31.3809			1.03970			0.519849	+	0.854258i	$0.325988\pi$
$912$	3.42262	−	5.73448i	0.113334	−	0.189888i
$913$	36.8613			1.21993
$914$	14.9042	+	12.5061i	0.492987	+	0.413665i
$915$	−9.63816	+	3.50800i	−0.318628	+	0.115971i
$916$	−3.85710	−	21.8747i	−0.127442	−	0.722760i
$917$	1.16519	−	6.60813i	0.0384780	−	0.218220i
$918$	1.60607	+	0.584561i	0.0530081	+	0.0192934i
$919$	−12.7811	−	22.1374i	−0.421608	−	0.730247i	0.574489	−	0.818512i	$-0.305201\pi$
$919$	−12.7811	−	22.1374i	−0.421608	−	0.730247i	−0.996097	+	0.0882656i	$0.971868\pi$
$920$	0.467911	−	0.810446i	0.0154266	−	0.0267196i
$921$	−3.73783	+	3.13641i	−0.123166	+	0.103348i
$922$	20.1438	−	16.9027i	0.663402	−	0.556660i
$923$	−6.49794	+	11.2548i	−0.213882	+	0.370455i
$924$	1.12836	+	1.95437i	0.0371202	+	0.0642940i
$925$	3.75877	+	1.36808i	0.123588	+	0.0449822i
$926$	−5.93851	+	33.6790i	−0.195152	+	1.10676i
$927$	−2.22163	−	12.5995i	−0.0729679	−	0.413821i
$928$	0.573978	−	0.208911i	0.0188417	−	0.00685784i
$929$	−6.68866	−	5.61245i	−0.219448	−	0.184139i	0.526436	−	0.850215i	$-0.323528\pi$
$929$	−6.68866	−	5.61245i	−0.219448	−	0.184139i	−0.745884	+	0.666076i	$0.767973\pi$
$930$	−4.32501			−0.141823
$931$	−5.33837	+	27.9032i	−0.174958	+	0.914491i
$932$	17.9172			0.586896
$933$	−0.965852	−	0.810446i	−0.0316206	−	0.0265328i
$934$	0.00639661	−	0.00232818i	0.000209304	−	7.61803e-5i
$935$	0.112463	+	0.637812i	0.00367795	+	0.0208587i
$936$	−0.120615	+	0.684040i	−0.00394242	+	0.0223586i
$937$	−25.1771	−	9.16372i	−0.822500	−	0.299366i	−0.103723	−	0.994606i	$-0.533076\pi$
$937$	−25.1771	−	9.16372i	−0.822500	−	0.299366i	−0.718777	+	0.695241i	$0.755298\pi$
$938$	−4.40642	−	7.63215i	−0.143875	−	0.249198i
$939$	16.7672	−	29.0417i	0.547178	−	0.947740i
$940$	−4.34730	+	3.64781i	−0.141793	+	0.118979i
$941$	−9.51754	+	7.98617i	−0.310263	+	0.260342i	−0.784601	−	0.620001i	$-0.787132\pi$
$941$	−9.51754	+	7.98617i	−0.310263	+	0.260342i	0.474338	+	0.880343i	$0.342688\pi$
$942$	8.19253	−	14.1899i	0.266927	−	0.462331i
$943$	−3.68004	−	6.37402i	−0.119839	−	0.207567i
$944$	−9.28359	−	3.37895i	−0.302155	−	0.109975i
$945$	−0.674992	+	3.82807i	−0.0219575	+	0.124527i
$946$	0.248560	+	1.40965i	0.00808138	+	0.0458318i
$947$	39.2181	−	14.2742i	1.27442	−	0.463850i	0.385835	−	0.922568i	$-0.373913\pi$
$947$	39.2181	−	14.2742i	1.27442	−	0.463850i	0.888582	+	0.458718i	$0.151691\pi$
$948$	2.87939	+	2.41609i	0.0935181	+	0.0784710i
$949$	−7.38919			−0.239863
$950$	3.29813	+	2.84997i	0.107006	+	0.0924652i
$951$	20.2567			0.656869
$952$	0.162504	+	0.136357i	0.00526678	+	0.00441935i
$953$	−7.08095	+	2.57725i	−0.229374	+	0.0834854i	−0.454150	−	0.890925i	$-0.650057\pi$
$953$	−7.08095	+	2.57725i	−0.229374	+	0.0834854i	0.224776	+	0.974410i	$0.427835\pi$
$954$	0.305407	+	1.73205i	0.00988793	+	0.0560772i
$955$	−0.355037	+	2.01352i	−0.0114887	+	0.0651558i
$956$	6.51754	+	2.37219i	0.210792	+	0.0767221i
$957$	0.992259	+	1.71864i	0.0320752	+	0.0555559i
$958$	−9.04963	+	15.6744i	−0.292380	+	0.506417i
$959$	6.13610	−	5.14880i	0.198145	−	0.166263i
$960$	−1.17365	+	0.984808i	−0.0378793	+	0.0317845i
$961$	11.5155	−	19.9454i	0.371467	−	0.643400i
$962$	2.12836	+	3.68642i	0.0686209	+	0.118855i
$963$	1.26604	+	0.460802i	0.0407977	+	0.0148492i
$964$	−3.08899	+	17.5185i	−0.0994898	+	0.564234i
$965$	2.48411	+	14.0881i	0.0799663	+	0.453511i
$966$	0.935822	−	0.340611i	0.0301096	−	0.0109590i
$967$	−11.5963	−	9.73042i	−0.372911	−	0.312909i	0.437001	−	0.899461i	$-0.356041\pi$
$967$	−11.5963	−	9.73042i	−0.372911	−	0.312909i	−0.809912	+	0.586552i	$0.800485\pi$
$968$	−6.50299			−0.209014
$969$	2.03936	+	0.0295733i	0.0655138	+	0.000950031i
$970$	6.23442			0.200175
$971$	−40.6921	−	34.1447i	−1.30587	−	1.09576i	−0.989098	−	0.147256i	$-0.952956\pi$
$971$	−40.6921	−	34.1447i	−1.30587	−	1.09576i	−0.316774	−	0.948501i	$-0.602600\pi$
$972$	6.25150	−	2.27536i	0.200517	−	0.0729822i
$973$	−0.825637	−	4.68242i	−0.0264687	−	0.150111i
$974$	0.128356	−	0.727940i	0.00411278	−	0.0233247i
$975$	1.53209	+	0.557635i	0.0490661	+	0.0178586i
$976$	3.34730	+	5.79769i	0.107144	+	0.185579i
$977$	10.7173	−	18.5630i	0.342878	−	0.593883i	−0.642088	−	0.766631i	$-0.721931\pi$
$977$	10.7173	−	18.5630i	0.342878	−	0.593883i	0.984966	+	0.172749i	$0.0552648\pi$
$978$	−2.89646	+	2.43042i	−0.0926186	+	0.0777162i
$979$	26.0488	−	21.8575i	0.832522	−	0.698569i
$980$	3.25877	−	5.64436i	0.104098	−	0.180302i
$981$	2.97266	+	5.14880i	0.0949097	+	0.164388i
$982$	11.6566	+	4.24265i	0.371976	+	0.135388i
$983$	−4.27126	+	24.2235i	−0.136232	+	0.772610i	0.837762	+	0.546036i	$0.183864\pi$
$983$	−4.27126	+	24.2235i	−0.136232	+	0.772610i	−0.973994	+	0.226574i	$0.927247\pi$
$984$	2.09240	+	11.8666i	0.0667032	+	0.378292i
$985$	−13.1284	+	4.77833i	−0.418304	+	0.152250i
$986$	0.142903	+	0.119910i	0.00455097	+	0.00381872i
$987$	−6.03920			−0.192230
$988$	0.739170	+	4.57937i	0.0235161	+	0.145689i
$989$	0.631673			0.0200860
$990$	1.06031	+	0.889704i	0.0336988	+	0.0282766i
$991$	−38.8256	+	14.1314i	−1.23334	+	0.448898i	−0.874739	−	0.484594i	$-0.838967\pi$
$991$	−38.8256	+	14.1314i	−1.23334	+	0.448898i	−0.358598	+	0.933492i	$0.616745\pi$
$992$	0.490200	+	2.78006i	0.0155639	+	0.0882670i
$993$	−0.435822	+	2.47167i	−0.0138304	+	0.0784361i
$994$	7.97090	+	2.90117i	0.252822	+	0.0920196i
$995$	−9.41921	−	16.3146i	−0.298609	−	0.517206i
$996$	−13.3157	+	23.0634i	−0.421923	+	0.730793i
$997$	33.3405	−	27.9760i	1.05590	−	0.886009i	0.0622019	−	0.998064i	$-0.480188\pi$
$997$	33.3405	−	27.9760i	1.05590	−	0.886009i	0.993702	+	0.112055i	$0.0357433\pi$
$998$	−11.5116	+	9.65939i	−0.364394	+	0.305763i
$999$	11.1925	−	19.3860i	0.354116	−	0.613347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.k.a.111.1	yes	6
5.2	odd	4		950.2.u.c.149.1		12
5.3	odd	4		950.2.u.c.149.2		12
5.4	even	2		950.2.l.c.301.1		6
19.5	even	9		3610.2.a.x.1.1		3
19.6	even	9	inner	190.2.k.a.101.1	✓	6
19.14	odd	18		3610.2.a.w.1.3		3
95.44	even	18		950.2.l.c.101.1		6
95.63	odd	36		950.2.u.c.899.1		12
95.82	odd	36		950.2.u.c.899.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.a.101.1	✓	6	19.6	even	9	inner
190.2.k.a.111.1	yes	6	1.1	even	1	trivial
950.2.l.c.101.1		6	95.44	even	18
950.2.l.c.301.1		6	5.4	even	2
950.2.u.c.149.1		12	5.2	odd	4
950.2.u.c.149.2		12	5.3	odd	4
950.2.u.c.899.1		12	95.63	odd	36
950.2.u.c.899.2		12	95.82	odd	36
3610.2.a.w.1.3		3	19.14	odd	18
3610.2.a.x.1.1		3	19.5	even	9

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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.k (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.43969 - 0.524005i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{5} +(1.43969 + 0.524005i) q^{6} +(0.347296 + 0.601535i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.419550i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(1.43969 - 0.524005i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.173648 - 0.984808i) q^{5} +(1.43969 + 0.524005i) q^{6} +(0.347296 + 0.601535i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.500000 + 0.419550i) q^{9} +(0.766044 - 0.642788i) q^{10} +(1.06031 - 1.83651i) q^{11} +(0.766044 + 1.32683i) q^{12} +(-1.00000 - 0.363970i) q^{13} +(-0.120615 + 0.684040i) q^{14} +(-0.266044 - 1.50881i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.233956 - 0.196312i) q^{17} -0.652704 q^{18} +(-4.11721 + 1.43128i) q^{19} +1.00000 q^{20} +(0.815207 + 0.684040i) q^{21} +(1.99273 - 0.725293i) q^{22} +(-0.162504 - 0.921605i) q^{23} +(-0.266044 + 1.50881i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-0.532089 - 0.921605i) q^{26} +(-2.79813 + 4.84651i) q^{27} +(-0.532089 + 0.446476i) q^{28} +(-0.467911 + 0.392624i) q^{29} +(0.766044 - 1.32683i) q^{30} +(-1.41147 - 2.44474i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.564178 - 3.19961i) q^{33} +(-0.0530334 - 0.300767i) q^{34} +(0.652704 - 0.237565i) q^{35} +(-0.500000 - 0.419550i) q^{36} -4.00000 q^{37} +(-4.07398 - 1.55007i) q^{38} -1.63041 q^{39} +(0.766044 + 0.642788i) q^{40} +(7.39053 - 2.68993i) q^{41} +(0.184793 + 1.04801i) q^{42} +(-0.117211 + 0.664738i) q^{43} +(1.99273 + 0.725293i) q^{44} +(0.326352 + 0.565258i) q^{45} +(0.467911 - 0.810446i) q^{46} +(-4.34730 + 3.64781i) q^{47} +(-1.17365 + 0.984808i) q^{48} +(3.25877 - 5.64436i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.439693 - 0.160035i) q^{51} +(0.184793 - 1.04801i) q^{52} +(-0.467911 - 2.65366i) q^{53} +(-5.25877 + 1.91404i) q^{54} +(-1.62449 - 1.36310i) q^{55} -0.694593 q^{56} +(-5.17752 + 4.21805i) q^{57} -0.610815 q^{58} +(7.56805 + 6.35035i) q^{59} +(1.43969 - 0.524005i) q^{60} +(-1.16250 - 6.59289i) q^{61} +(0.490200 - 2.78006i) q^{62} +(-0.426022 - 0.155059i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.532089 + 0.921605i) q^{65} +(2.48886 - 2.08840i) q^{66} +(-9.71941 + 8.15555i) q^{67} +(0.152704 - 0.264490i) q^{68} +(-0.716881 - 1.24168i) q^{69} +(0.652704 + 0.237565i) q^{70} +(2.12061 - 12.0266i) q^{71} +(-0.113341 - 0.642788i) q^{72} +(6.52481 - 2.37484i) q^{73} +(-3.06418 - 2.57115i) q^{74} -1.53209 q^{75} +(-2.12449 - 3.80612i) q^{76} +1.47296 q^{77} +(-1.24897 - 1.04801i) q^{78} +(2.30541 - 0.839100i) q^{79} +(0.173648 + 0.984808i) q^{80} +(-1.14883 + 6.51536i) q^{81} +(7.39053 + 2.68993i) q^{82} +(8.69119 + 15.0536i) q^{83} +(-0.532089 + 0.921605i) q^{84} +(-0.233956 + 0.196312i) q^{85} +(-0.517074 + 0.433877i) q^{86} +(-0.467911 + 0.810446i) q^{87} +(1.06031 + 1.83651i) q^{88} +(15.0680 + 5.48432i) q^{89} +(-0.113341 + 0.642788i) q^{90} +(-0.128356 - 0.727940i) q^{91} +(0.879385 - 0.320070i) q^{92} +(-3.31315 - 2.78006i) q^{93} -5.67499 q^{94} +(0.694593 + 4.30320i) q^{95} -1.53209 q^{96} +(4.77584 + 4.00741i) q^{97} +(6.12449 - 2.22913i) q^{98} +(0.240352 + 1.36310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} + 3 q^{6} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 + 3 * q^6 - 3 * q^8 - 3 * q^9	\( 6 q + 3 q^{3} + 3 q^{6} - 3 q^{8} - 3 q^{9} + 12 q^{11} - 6 q^{13} - 12 q^{14} + 3 q^{15} - 6 q^{17} - 6 q^{18} + 6 q^{19} + 6 q^{20} + 12 q^{21} - 6 q^{22} - 6 q^{23} + 3 q^{24} + 6 q^{26} - 3 q^{27} + 6 q^{28} - 12 q^{29} + 12 q^{31} - 15 q^{33} + 12 q^{34} + 6 q^{35} - 3 q^{36} - 24 q^{37} - 9 q^{38} - 24 q^{39} + 27 q^{41} - 6 q^{42} + 30 q^{43} - 6 q^{44} + 3 q^{45} + 12 q^{46} - 24 q^{47} - 6 q^{48} - 3 q^{49} - 3 q^{50} + 3 q^{51} - 6 q^{52} - 12 q^{53} - 9 q^{54} + 3 q^{55} - 6 q^{57} - 12 q^{58} + 3 q^{59} + 3 q^{60} - 12 q^{61} - 18 q^{63} - 3 q^{64} + 6 q^{65} + 21 q^{66} - 27 q^{67} + 3 q^{68} + 12 q^{69} + 6 q^{70} + 24 q^{71} + 6 q^{72} + 12 q^{73} - 12 q^{77} + 18 q^{78} + 18 q^{79} - 33 q^{81} + 27 q^{82} + 6 q^{83} + 6 q^{84} - 6 q^{85} - 24 q^{86} - 12 q^{87} + 12 q^{88} + 48 q^{89} + 6 q^{90} + 36 q^{91} - 6 q^{92} + 24 q^{93} - 24 q^{94} + 27 q^{97} + 24 q^{98} - 33 q^{99}+O(q^{100}) \) 6 * q + 3 * q^3 + 3 * q^6 - 3 * q^8 - 3 * q^9 + 12 * q^11 - 6 * q^13 - 12 * q^14 + 3 * q^15 - 6 * q^17 - 6 * q^18 + 6 * q^19 + 6 * q^20 + 12 * q^21 - 6 * q^22 - 6 * q^23 + 3 * q^24 + 6 * q^26 - 3 * q^27 + 6 * q^28 - 12 * q^29 + 12 * q^31 - 15 * q^33 + 12 * q^34 + 6 * q^35 - 3 * q^36 - 24 * q^37 - 9 * q^38 - 24 * q^39 + 27 * q^41 - 6 * q^42 + 30 * q^43 - 6 * q^44 + 3 * q^45 + 12 * q^46 - 24 * q^47 - 6 * q^48 - 3 * q^49 - 3 * q^50 + 3 * q^51 - 6 * q^52 - 12 * q^53 - 9 * q^54 + 3 * q^55 - 6 * q^57 - 12 * q^58 + 3 * q^59 + 3 * q^60 - 12 * q^61 - 18 * q^63 - 3 * q^64 + 6 * q^65 + 21 * q^66 - 27 * q^67 + 3 * q^68 + 12 * q^69 + 6 * q^70 + 24 * q^71 + 6 * q^72 + 12 * q^73 - 12 * q^77 + 18 * q^78 + 18 * q^79 - 33 * q^81 + 27 * q^82 + 6 * q^83 + 6 * q^84 - 6 * q^85 - 24 * q^86 - 12 * q^87 + 12 * q^88 + 48 * q^89 + 6 * q^90 + 36 * q^91 - 6 * q^92 + 24 * q^93 - 24 * q^94 + 27 * q^97 + 24 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

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