LMFDB - Embedded newform 950.2.u.c.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not 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:	$7.58578819202$
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:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.1
Root			$0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	950.149
Dual form			950.2.u.c.899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	−0.524005	−	1.43969i	−0.302535	−	0.831207i	−0.994058	−	0.108853i	$-0.965282\pi$
$3$	−0.524005	−	1.43969i	−0.302535	−	0.831207i	0.691523	−	0.722354i	$-0.256940\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	1.43969	+	0.524005i	0.587752	+	0.213924i
$7$	−0.601535	+	0.347296i	−0.227359	+	0.131266i	−0.609353	−	0.792899i	$-0.708571\pi$
$7$	−0.601535	+	0.347296i	−0.227359	+	0.131266i	0.381994	+	0.924165i	$0.375237\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	0.500000	−	0.419550i	0.166667	−	0.139850i
$10$		0			0
$11$	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	$0.0630863\pi$
$12$	−1.32683	+	0.766044i	−0.383022	+	0.221138i
$13$	−0.363970	+	1.00000i	−0.100947	+	0.277350i	−0.979877	−	0.199600i	$-0.936036\pi$
$13$	−0.363970	+	1.00000i	−0.100947	+	0.277350i	0.878930	+	0.476950i	$0.158258\pi$
$14$	0.120615	−	0.684040i	0.0322357	−	0.182817i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.196312	−	0.233956i	0.0476127	−	0.0567426i	−0.741713	−	0.670718i	$-0.765986\pi$
$17$	0.196312	−	0.233956i	0.0476127	−	0.0567426i	0.789325	+	0.613975i	$0.210431\pi$
$18$			0.652704i			0.153844i
$19$	4.11721	−	1.43128i	0.944553	−	0.328359i
$19$	4.11721	−	1.43128i	0.944553	−	0.328359i
$20$		0			0
$21$	0.815207	+	0.684040i	0.177893	+	0.149270i
$22$	0.725293	+	1.99273i	0.154633	+	0.424851i
$23$	−0.921605	+	0.162504i	−0.192168	+	0.0338844i	−0.268904	−	0.963167i	$-0.586661\pi$
$23$	−0.921605	+	0.162504i	−0.192168	+	0.0338844i	0.0767357	+	0.997051i	$0.475550\pi$
$24$	0.266044	−	1.50881i	0.0543061	−	0.307985i
$25$		0			0
$26$	−0.532089	−	0.921605i	−0.104351	−	0.180742i
$27$	−4.84651	−	2.79813i	−0.932711	−	0.538501i
$28$	0.446476	+	0.532089i	0.0843760	+	0.100555i
$29$	0.467911	−	0.392624i	0.0868889	−	0.0729085i	−0.598309	−	0.801266i	$-0.704160\pi$
$29$	0.467911	−	0.392624i	0.0868889	−	0.0729085i	0.685198	+	0.728357i	$0.259716\pi$
$30$		0			0
$31$	−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	$0.914918\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	−3.19961	−	0.564178i	−0.556981	−	0.0982107i
$34$	0.0530334	+	0.300767i	0.00909516	+	0.0515812i
$35$		0			0
$36$	−0.500000	−	0.419550i	−0.0833333	−	0.0699250i
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	−1.55007	+	4.07398i	−0.251454	+	0.660886i
$39$	1.63041			0.261075
$40$		0			0
$41$	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	$0.178392\pi$
$42$	−1.04801	+	0.184793i	−0.161712	+	0.0285141i
$43$	0.664738	+	0.117211i	0.101372	+	0.0178745i	0.224104	−	0.974565i	$-0.428055\pi$
$43$	0.664738	+	0.117211i	0.101372	+	0.0178745i	−0.122732	+	0.992440i	$0.539166\pi$
$44$	−1.99273	−	0.725293i	−0.300415	−	0.109342i
$45$		0			0
$46$	0.467911	−	0.810446i	0.0689897	−	0.119494i
$47$	−3.64781	−	4.34730i	−0.532088	−	0.634118i	0.431306	−	0.902206i	$-0.358053\pi$
$47$	−3.64781	−	4.34730i	−0.532088	−	0.634118i	−0.963395	+	0.268087i	$0.913608\pi$
$48$	0.984808	+	1.17365i	0.142145	+	0.169402i
$49$	−3.25877	+	5.64436i	−0.465539	+	0.806337i
$50$		0			0
$51$	−0.439693	−	0.160035i	−0.0615693	−	0.0224094i
$52$	1.04801	+	0.184793i	0.145333	+	0.0256261i
$53$	−2.65366	+	0.467911i	−0.364508	+	0.0642725i	−0.352902	−	0.935660i	$-0.614805\pi$
$53$	−2.65366	+	0.467911i	−0.364508	+	0.0642725i	−0.0116052	+	0.999933i	$0.503694\pi$
$54$	5.25877	−	1.91404i	0.715628	−	0.260467i
$55$		0			0
$56$	−0.694593			−0.0928189
$57$	−4.21805	−	5.17752i	−0.558694	−	0.685779i
$58$			0.610815i			0.0802039i
$59$	−7.56805	−	6.35035i	−0.985276	−	0.826745i	−0.000398990	−	1.00000i	$-0.500127\pi$
$59$	−7.56805	−	6.35035i	−0.985276	−	0.826745i	−0.984877	+	0.173255i	$0.944571\pi$
$60$		0			0
$61$	−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	$-0.196541\pi$
$62$	2.78006	+	0.490200i	0.353068	+	0.0622554i
$63$	−0.155059	+	0.426022i	−0.0195356	+	0.0536737i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	2.48886	−	2.08840i	0.306357	−	0.257064i
$67$	−8.15555	−	9.71941i	−0.996359	−	1.18741i	−0.982262	−	0.187514i	$-0.939957\pi$
$67$	−8.15555	−	9.71941i	−0.996359	−	1.18741i	−0.0140972	−	0.999901i	$-0.504487\pi$
$68$	−0.264490	−	0.152704i	−0.0320742	−	0.0185180i
$69$	0.716881	+	1.24168i	0.0863024	+	0.149480i
$70$		0			0
$71$	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	$-0.202446\pi$
$72$	0.642788	−	0.113341i	0.0757532	−	0.0133573i
$73$	−2.37484	−	6.52481i	−0.277954	−	0.763672i	−0.997594	−	0.0693248i	$-0.977916\pi$
$73$	−2.37484	−	6.52481i	−0.277954	−	0.763672i	0.719640	−	0.694347i	$-0.244307\pi$
$74$	3.06418	+	2.57115i	0.356203	+	0.298890i
$75$		0			0
$76$	−2.12449	−	3.80612i	−0.243695	−	0.436592i
$77$			1.47296i			0.167860i
$78$	−1.04801	+	1.24897i	−0.118664	+	0.141418i
$79$	−2.30541	+	0.839100i	−0.259379	+	0.0944061i	−0.468436	−	0.883497i	$-0.655183\pi$
$79$	−2.30541	+	0.839100i	−0.259379	+	0.0944061i	0.209058	+	0.977903i	$0.432960\pi$
$80$		0			0
$81$	−1.14883	+	6.51536i	−0.127648	+	0.723929i
$82$	−2.68993	+	7.39053i	−0.297053	+	0.816147i
$83$	15.0536	−	8.69119i	1.65235	−	0.953982i	0.676241	−	0.736681i	$-0.263608\pi$
$83$	15.0536	−	8.69119i	1.65235	−	0.953982i	0.976105	−	0.217301i	$-0.0697253\pi$
$84$	0.532089	−	0.921605i	0.0580557	−	0.100555i
$85$		0			0
$86$	−0.517074	+	0.433877i	−0.0557575	+	0.0467861i
$87$	−0.810446	−	0.467911i	−0.0868889	−	0.0501653i
$88$	1.83651	−	1.06031i	0.195772	−	0.113029i
$89$	−15.0680	−	5.48432i	−1.59721	−	0.581337i	−0.618356	−	0.785898i	$-0.712201\pi$
$89$	−15.0680	−	5.48432i	−1.59721	−	0.581337i	−0.978854	+	0.204561i	$0.934423\pi$
$90$		0			0
$91$	−0.128356	−	0.727940i	−0.0134553	−	0.0763089i
$92$	0.320070	+	0.879385i	0.0333696	+	0.0916822i
$93$	−2.78006	+	3.31315i	−0.288279	+	0.343557i
$94$	5.67499			0.585331
$95$		0			0
$96$	−1.53209			−0.156368
$97$	−4.00741	+	4.77584i	−0.406891	+	0.484914i	−0.930108	−	0.367286i	$-0.880287\pi$
$97$	−4.00741	+	4.77584i	−0.406891	+	0.484914i	0.523217	+	0.852199i	$0.324732\pi$
$98$	−2.22913	−	6.12449i	−0.225176	−	0.618666i
$99$	−0.240352	−	1.36310i	−0.0241563	−	0.136997i
$100$		0			0
$101$	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	$0.357577\pi$
$102$	0.405223	−	0.233956i	0.0401230	−	0.0231651i
$103$	16.9752	+	9.80066i	1.67262	+	0.965688i	0.966163	+	0.257932i	$0.0830409\pi$
$103$	16.9752	+	9.80066i	1.67262	+	0.965688i	0.706457	+	0.707756i	$0.250292\pi$
$104$	−0.815207	+	0.684040i	−0.0799377	+	0.0670757i
$105$		0			0
$106$	1.34730	−	2.33359i	0.130861	−	0.226658i
$107$	1.78763	−	1.03209i	0.172817	−	0.0997758i	−0.411097	−	0.911592i	$-0.634854\pi$
$107$	1.78763	−	1.03209i	0.172817	−	0.0997758i	0.583913	+	0.811816i	$0.301521\pi$
$108$	−1.91404	+	5.25877i	−0.184178	+	0.506025i
$109$	−1.58172	+	8.97037i	−0.151501	+	0.859206i	0.810414	+	0.585858i	$0.199242\pi$
$109$	−1.58172	+	8.97037i	−0.151501	+	0.859206i	−0.961915	+	0.273348i	$0.911869\pi$
$110$		0			0
$111$	−5.75877	+	2.09602i	−0.546598	+	0.198946i
$112$	0.446476	−	0.532089i	0.0421880	−	0.0502777i
$113$		−	7.18479i		−	0.675888i	−0.941166	−	0.337944i	$-0.890268\pi$
$113$		−	7.18479i		−	0.675888i	0.941166	−	0.337944i	$-0.109732\pi$
$114$	6.67752	+	0.0968323i	0.625407	+	0.00906917i
$115$		0			0
$116$	−0.467911	−	0.392624i	−0.0434445	−	0.0364542i
$117$	0.237565	+	0.652704i	0.0219629	+	0.0603425i
$118$	9.72930	−	1.71554i	0.895654	−	0.157928i
$119$	−0.0368366	+	0.208911i	−0.00337681	+	0.0191508i
$120$		0			0
$121$	3.25150	+	5.63176i	0.295591	+	0.511978i
$122$	5.79769	+	3.34730i	0.524898	+	0.303050i
$123$	−7.74535	−	9.23055i	−0.698375	−	0.832291i
$124$	−2.16250	+	1.81456i	−0.194199	+	0.162952i
$125$		0			0
$126$	−0.226682	−	0.392624i	−0.0201944	−	0.0349777i
$127$	−0.557635	+	1.53209i	−0.0494821	+	0.135951i	−0.961972	−	0.273149i	$-0.911935\pi$
$127$	−0.557635	+	1.53209i	−0.0494821	+	0.135951i	0.912490	+	0.409100i	$0.134157\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	−0.179578	−	1.01844i	−0.0158110	−	0.0896684i
$130$		0			0
$131$	−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	$0.860900\pi$
$132$			3.24897i			0.282787i
$133$	−1.97957	+	2.29086i	−0.171650	+	0.198643i
$134$	12.6878			1.09606
$135$		0			0
$136$	0.286989	−	0.104455i	0.0246091	−	0.00895698i
$137$	11.3569	−	2.00253i	0.970285	−	0.171087i	0.334027	−	0.942564i	$-0.391592\pi$
$137$	11.3569	−	2.00253i	0.970285	−	0.171087i	0.636258	+	0.771476i	$0.280481\pi$
$138$	−1.41198	−	0.248970i	−0.120196	−	0.0211938i
$139$	6.43242	+	2.34121i	0.545591	+	0.198579i	0.600086	−	0.799935i	$-0.295133\pi$
$139$	6.43242	+	2.34121i	0.545591	+	0.198579i	−0.0544957	+	0.998514i	$0.517355\pi$
$140$		0			0
$141$	−4.34730	+	7.52974i	−0.366108	+	0.634118i
$142$	7.84981	+	9.35504i	0.658741	+	0.785057i
$143$	1.45059	+	1.72874i	0.121304	+	0.144565i
$144$	−0.326352	+	0.565258i	−0.0271960	+	0.0471048i
$145$		0			0
$146$	6.52481	+	2.37484i	0.539998	+	0.196543i
$147$	9.83375	+	1.73396i	0.811074	+	0.143014i
$148$	−3.93923	+	0.694593i	−0.323803	+	0.0570952i
$149$	−8.36959	+	3.04628i	−0.685663	+	0.249561i	−0.661277	−	0.750142i	$-0.729985\pi$
$149$	−8.36959	+	3.04628i	−0.685663	+	0.249561i	−0.0243859	+	0.999703i	$0.507763\pi$
$150$		0			0
$151$	−10.8229			−0.880759			−0.440380	−	0.897812i	$-0.645156\pi$
$151$	−10.8229			−0.880759			−0.440380	+	0.897812i	$0.645156\pi$
$152$	4.28125	+	0.819078i	0.347255	+	0.0664360i
$153$		−	0.199340i		−	0.0161157i
$154$	−1.12836	−	0.946803i	−0.0909255	−	0.0762955i
$155$		0			0
$156$	−0.283119	−	1.60565i	−0.0226676	−	0.128555i
$157$	10.5321	+	1.85710i	0.840555	+	0.148212i	0.577319	−	0.816519i	$-0.304099\pi$
$157$	10.5321	+	1.85710i	0.840555	+	0.148212i	0.263236	+	0.964731i	$0.415210\pi$
$158$	0.839100	−	2.30541i	0.0667552	−	0.183408i
$159$	2.06418	+	3.57526i	0.163700	+	0.283537i
$160$		0			0
$161$	0.497941	−	0.417822i	0.0392432	−	0.0329290i
$162$	−4.25260	−	5.06805i	−0.334116	−	0.398183i
$163$	2.13727	+	1.23396i	0.167404	+	0.0966509i	0.581361	−	0.813646i	$-0.302520\pi$
$163$	2.13727	+	1.23396i	0.167404	+	0.0966509i	−0.413957	+	0.910296i	$0.635854\pi$
$164$	−3.93242	−	6.81115i	−0.307070	−	0.531861i
$165$		0			0
$166$	−3.01842	+	17.1183i	−0.234275	+	1.32864i
$167$	11.9880	−	2.11381i	0.927659	−	0.163571i	0.310647	−	0.950525i	$-0.399454\pi$
$167$	11.9880	−	2.11381i	0.927659	−	0.163571i	0.617012	+	0.786954i	$0.288343\pi$
$168$	0.363970	+	1.00000i	0.0280809	+	0.0771517i
$169$	9.09105	+	7.62830i	0.699312	+	0.586792i
$170$		0			0
$171$	1.45811	−	2.44302i	0.111505	−	0.186822i
$172$		−	0.674992i		−	0.0514677i
$173$	−9.05288	+	10.7888i	−0.688278	+	0.820257i	−0.991146	−	0.132775i	$-0.957611\pi$
$173$	−9.05288	+	10.7888i	−0.688278	+	0.820257i	0.302869	+	0.953032i	$0.402056\pi$
$174$	0.879385	−	0.320070i	0.0666660	−	0.0242644i
$175$		0			0
$176$	−0.368241	+	2.08840i	−0.0277572	+	0.157419i
$177$	−5.17685	+	14.2233i	−0.389116	+	1.06909i
$178$	13.8868	−	8.01754i	1.04086	−	0.600940i
$179$	4.70574	−	8.15058i	0.351723	−	0.609203i	−0.634828	−	0.772653i	$-0.718929\pi$
$179$	4.70574	−	8.15058i	0.351723	−	0.609203i	0.986552	+	0.163451i	$0.0522625\pi$
$180$		0			0
$181$	−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	$0.914336\pi$
$182$	0.640140	+	0.369585i	0.0474503	+	0.0273955i
$183$	−8.88257	+	5.12836i	−0.656619	+	0.379099i
$184$	−0.879385	−	0.320070i	−0.0648291	−	0.0235959i
$185$		0			0
$186$	−0.751030	−	4.25930i	−0.0550682	−	0.312307i
$187$	−0.221510	−	0.608593i	−0.0161984	−	0.0445047i
$188$	−3.64781	+	4.34730i	−0.266044	+	0.317059i
$189$	3.88713			0.282747
$190$		0			0
$191$	−2.04458			−0.147940			−0.0739702	−	0.997260i	$-0.523567\pi$
$191$	−2.04458			−0.147940			−0.0739702	+	0.997260i	$0.523567\pi$
$192$	0.984808	−	1.17365i	0.0710724	−	0.0847008i
$193$	4.89274	+	13.4427i	0.352187	+	0.967626i	0.981666	+	0.190608i	$0.0610461\pi$
$193$	4.89274	+	13.4427i	0.352187	+	0.967626i	−0.629479	+	0.777017i	$0.716732\pi$
$194$	−1.08260	−	6.13971i	−0.0777259	−	0.440805i
$195$		0			0
$196$	6.12449	+	2.22913i	0.437463	+	0.159224i
$197$	12.0992	−	6.98545i	0.862029	−	0.497693i	−0.00266202	−	0.999996i	$-0.500847\pi$
$197$	12.0992	−	6.98545i	0.862029	−	0.497693i	0.864691	+	0.502304i	$0.167514\pi$
$198$	1.19869	+	0.692066i	0.0851875	+	0.0491830i
$199$	−14.4311	+	12.1091i	−1.02299	+	0.858392i	−0.990001	−	0.141064i	$-0.954948\pi$
$199$	−14.4311	+	12.1091i	−1.02299	+	0.858392i	−0.0329912	+	0.999456i	$0.510503\pi$
$200$		0			0
$201$	−9.71941	+	16.8345i	−0.685554	+	1.18741i
$202$	−12.4444	+	7.18479i	−0.875587	+	0.505520i
$203$	−0.145108	+	0.398681i	−0.0101846	+	0.0279819i
$204$	−0.0812519	+	0.460802i	−0.00568877	+	0.0322626i
$205$		0			0
$206$	−18.4192	+	6.70405i	−1.28333	+	0.467093i
$207$	−0.392624	+	0.467911i	−0.0272893	+	0.0325221i
$208$		−	1.06418i		−	0.0737875i
$209$	1.73695	−	9.07888i	0.120147	−	0.628000i
$210$		0			0
$211$	−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	$0.725250\pi$
$212$	0.921605	+	2.53209i	0.0632961	+	0.173905i
$213$	−18.4258	+	3.24897i	−1.26252	+	0.222616i
$214$	−0.358441	+	2.03282i	−0.0245025	+	0.138961i
$215$		0			0
$216$	−2.79813	−	4.84651i	−0.190389	−	0.329763i
$217$	1.69810	+	0.980400i	0.115275	+	0.0665539i
$218$	−5.85499	−	6.97771i	−0.396550	−	0.472590i
$219$	−8.14930	+	6.83807i	−0.550679	+	0.462074i
$220$		0			0
$221$	0.162504	+	0.281465i	0.0109312	+	0.0189334i
$222$	2.09602	−	5.75877i	0.140676	−	0.386503i
$223$	6.80180	+	1.19934i	0.455482	+	0.0803138i	0.396682	−	0.917956i	$-0.370162\pi$
$223$	6.80180	+	1.19934i	0.455482	+	0.0803138i	0.0587999	+	0.998270i	$0.481273\pi$
$224$	0.120615	+	0.684040i	0.00805891	+	0.0457044i
$225$		0			0
$226$	5.50387	+	4.61830i	0.366112	+	0.307204i
$227$			2.30272i			0.152837i	0.997076	+	0.0764184i	$0.0243485\pi$
$227$			2.30272i			0.152837i	−0.997076	+	0.0764184i	$0.975652\pi$
$228$	−4.36640	+	5.05303i	−0.289172	+	0.334645i
$229$	22.2121			1.46782			0.733910	−	0.679247i	$-0.237694\pi$
$229$	22.2121			1.46782			0.733910	+	0.679247i	$0.237694\pi$
$230$		0			0
$231$	2.12061	−	0.771841i	0.139526	−	0.0507834i
$232$	0.601535	−	0.106067i	0.0394927	−	0.00696363i
$233$	−17.6450	−	3.11128i	−1.15596	−	0.203827i	−0.437383	−	0.899275i	$-0.644095\pi$
$233$	−17.6450	−	3.11128i	−1.15596	−	0.203827i	−0.718576	+	0.695448i	$0.755206\pi$
$234$	−0.652704	−	0.237565i	−0.0426686	−	0.0155301i
$235$		0			0
$236$	−4.93969	+	8.55580i	−0.321547	+	0.556935i
$237$	2.41609	+	2.87939i	0.156942	+	0.187036i
$238$	−0.136357	−	0.162504i	−0.00883870	−	0.0105336i
$239$	−3.46791	+	6.00660i	−0.224321	+	0.388535i	−0.956115	−	0.292990i	$-0.905350\pi$
$239$	−3.46791	+	6.00660i	−0.224321	+	0.388535i	0.731795	+	0.681525i	$0.238683\pi$
$240$		0			0
$241$	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	$0.416914\pi$
$242$	−6.40420	−	1.12923i	−0.411677	−	0.0725898i
$243$	−6.55163	+	1.15523i	−0.420288	+	0.0741080i
$244$	−6.29086	+	2.28969i	−0.402731	+	0.146582i
$245$		0			0
$246$	12.0496			0.768256
$247$	−0.0672590	+	4.63816i	−0.00427959	+	0.295119i
$248$		−	2.82295i		−	0.179257i
$249$	−20.4008	−	17.1183i	−1.29285	−	1.08483i
$250$		0			0
$251$	−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	$-0.232204\pi$
$252$	0.446476	+	0.0787257i	0.0281253	+	0.00495925i
$253$	−0.678745	+	1.86484i	−0.0426723	+	0.117241i
$254$	−0.815207	−	1.41198i	−0.0511507	−	0.0885956i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−16.7856	−	20.0043i	−1.04706	−	1.24784i	−0.967996	−	0.250967i	$-0.919252\pi$
$257$	−16.7856	−	20.0043i	−1.04706	−	1.24784i	−0.0790632	−	0.996870i	$-0.525193\pi$
$258$	0.895599	+	0.517074i	0.0557575	+	0.0321916i
$259$	1.38919	+	2.40614i	0.0863198	+	0.149510i
$260$		0			0
$261$	0.0692302	−	0.392624i	0.00428524	−	0.0243028i
$262$	9.51368	−	1.67752i	0.587757	−	0.103637i
$263$	−4.27455	−	11.7442i	−0.263580	−	0.724180i	−0.998919	−	0.0464807i	$-0.985199\pi$
$263$	−4.27455	−	11.7442i	−0.263580	−	0.724180i	0.735339	−	0.677699i	$-0.237023\pi$
$264$	−2.48886	−	2.08840i	−0.153178	−	0.128532i
$265$		0			0
$266$	−0.482459	−	2.98897i	−0.0295815	−	0.183266i
$267$			24.5672i			1.50349i
$268$	−8.15555	+	9.71941i	−0.498180	+	0.593707i
$269$	0.773318	−	0.281465i	0.0471501	−	0.0171612i	−0.318337	−	0.947977i	$-0.603125\pi$
$269$	0.773318	−	0.281465i	0.0471501	−	0.0171612i	0.365488	+	0.930816i	$0.380902\pi$
$270$		0			0
$271$	−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	$0.935934\pi$
$272$	−0.104455	+	0.286989i	−0.00633354	+	0.0174013i
$273$	−0.980752	+	0.566237i	−0.0593578	+	0.0342702i
$274$	−5.76604	+	9.98708i	−0.348339	+	0.603342i
$275$		0			0
$276$	1.09833	−	0.921605i	0.0661115	−	0.0554741i
$277$	9.75216	+	5.63041i	0.585951	+	0.338299i	0.763495	−	0.645814i	$-0.223482\pi$
$277$	9.75216	+	5.63041i	0.585951	+	0.338299i	−0.177544	+	0.984113i	$0.556815\pi$
$278$	−5.92815	+	3.42262i	−0.355547	+	0.205275i
$279$	−1.73143	−	0.630189i	−0.103658	−	0.0377284i
$280$		0			0
$281$	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	$0.658710\pi$
$282$	−2.97373	−	8.17024i	−0.177083	−	0.486531i
$283$	16.5437	−	19.7160i	0.983420	−	1.17199i	−0.00167722	−	0.999999i	$-0.500534\pi$
$283$	16.5437	−	19.7160i	0.983420	−	1.17199i	0.985098	−	0.171996i	$-0.0550217\pi$
$284$	−12.2121			−0.724657
$285$		0			0
$286$	−2.25671			−0.133442
$287$	−3.51146	+	4.18479i	−0.207275	+	0.247020i
$288$	−0.223238	−	0.613341i	−0.0131544	−	0.0361415i
$289$	2.93582	+	16.6499i	0.172695	+	0.979404i
$290$		0			0
$291$	8.97565	+	3.26687i	0.526162	+	0.191507i
$292$	−6.01330	+	3.47178i	−0.351902	+	0.203171i
$293$	22.9566	+	13.2540i	1.34114	+	0.774308i	0.986975	−	0.160874i	$-0.0514313\pi$
$293$	22.9566	+	13.2540i	1.34114	+	0.774308i	0.354166	+	0.935182i	$0.384765\pi$
$294$	−7.64930	+	6.41852i	−0.446116	+	0.374336i
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−10.2776	+	5.93376i	−0.596366	+	0.344312i
$298$	3.04628	−	8.36959i	0.176466	−	0.484837i
$299$	0.172933	−	0.980752i	0.0100010	−	0.0567183i
$300$		0			0
$301$	−0.440570	+	0.160354i	−0.0253940	+	0.00924267i
$302$	6.95686	−	8.29086i	0.400322	−	0.477085i
$303$		−	22.0155i		−	1.26476i
$304$	−3.37939	+	2.75314i	−0.193821	+	0.157903i
$305$		0			0
$306$	0.152704	+	0.128134i	0.00872949	+	0.00732491i
$307$	−1.08926	−	2.99273i	−0.0621675	−	0.170804i	0.904720	−	0.426007i	$-0.140080\pi$
$307$	−1.08926	−	2.99273i	−0.0621675	−	0.170804i	−0.966888	+	0.255203i	$0.917858\pi$
$308$	1.45059	−	0.255777i	0.0826548	−	0.0145743i
$309$	5.21482	−	29.5747i	0.296661	−	1.68245i
$310$		0			0
$311$	−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	$0.840761\pi$
$312$	1.41198	+	0.815207i	0.0799377	+	0.0461520i
$313$	−14.0694	−	16.7672i	−0.795248	−	0.947740i	0.204266	−	0.978915i	$-0.434519\pi$
$313$	−14.0694	−	16.7672i	−0.795248	−	0.947740i	−0.999514	+	0.0311758i	$0.990075\pi$
$314$	−8.19253	+	6.87435i	−0.462331	+	0.387942i
$315$		0			0
$316$	1.22668	+	2.12467i	0.0690062	+	0.119522i
$317$	−4.52206	+	12.4243i	−0.253984	+	0.697816i	0.745524	+	0.666478i	$0.232199\pi$
$317$	−4.52206	+	12.4243i	−0.253984	+	0.697816i	−0.999509	+	0.0313381i	$0.990023\pi$
$318$	−4.06564	−	0.716881i	−0.227990	−	0.0402007i
$319$	−0.224927	−	1.27562i	−0.0125935	−	0.0714212i
$320$		0			0
$321$	−2.42262	−	2.03282i	−0.135217	−	0.113461i
$322$			0.650015i			0.0362239i
$323$	0.473401	−	1.24422i	0.0263408	−	0.0692304i
$324$	6.61587			0.367548
$325$		0			0
$326$	−2.31908	+	0.844075i	−0.128442	+	0.0467490i
$327$	13.7434	−	2.42333i	0.760012	−	0.134011i
$328$	7.74535	+	1.36571i	0.427666	+	0.0754090i
$329$	3.70409	+	1.34818i	0.204213	+	0.0743275i
$330$		0			0
$331$	−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	$0.181002\pi$
$332$	−11.1732	−	13.3157i	−0.613208	−	0.730793i
$333$	−1.67820	−	2.00000i	−0.0919648	−	0.109599i
$334$	−6.08647	+	10.5421i	−0.333037	+	0.576836i
$335$		0			0
$336$	−1.00000	−	0.363970i	−0.0545545	−	0.0198562i
$337$	−30.8594	−	5.44134i	−1.68102	−	0.296409i	−0.750015	−	0.661421i	$-0.769954\pi$
$337$	−30.8594	−	5.44134i	−1.68102	−	0.296409i	−0.931003	+	0.365012i	$0.881065\pi$
$338$	−11.6872	+	2.06077i	−0.635702	+	0.112091i
$339$	−10.3439	+	3.76487i	−0.561803	+	0.204480i
$340$		0			0
$341$	−5.98639			−0.324181
$342$	0.934204	+	2.68732i	0.0505160	+	0.145314i
$343$		−	9.38919i		−	0.506968i
$344$	0.517074	+	0.433877i	0.0278788	+	0.0233931i
$345$		0			0
$346$	−2.44562	−	13.8698i	−0.131477	−	0.745646i
$347$	25.0407	+	4.41534i	1.34425	+	0.237028i	0.799044	−	0.601272i	$-0.205339\pi$
$347$	25.0407	+	4.41534i	1.34425	+	0.237028i	0.545209	+	0.838300i	$0.316450\pi$
$348$	−0.320070	+	0.879385i	−0.0171576	+	0.0471400i
$349$	16.0993	+	27.8847i	0.861774	+	1.49264i	0.870215	+	0.492671i	$0.163980\pi$
$349$	16.0993	+	27.8847i	0.861774	+	1.49264i	−0.00844186	+	0.999964i	$0.502687\pi$
$350$		0			0
$351$	4.56212	−	3.82807i	0.243508	−	0.204327i
$352$	−1.36310	−	1.62449i	−0.0726537	−	0.0865853i
$353$	17.4510	+	10.0753i	0.928821	+	0.536255i	0.886439	−	0.462846i	$-0.153172\pi$
$353$	17.4510	+	10.0753i	0.928821	+	0.536255i	0.0423828	+	0.999101i	$0.486505\pi$
$354$	−7.56805	−	13.1082i	−0.402237	−	0.696695i
$355$		0			0
$356$	−2.78446	+	15.7915i	−0.147576	+	0.836946i
$357$	0.320070	−	0.0564370i	0.0169399	−	0.00298696i
$358$	3.21891	+	8.84389i	0.170125	+	0.467414i
$359$	−2.60813	−	2.18848i	−0.137652	−	0.115503i	0.571362	−	0.820698i	$-0.306415\pi$
$359$	−2.60813	−	2.18848i	−0.137652	−	0.115503i	−0.709014	+	0.705195i	$0.750860\pi$
$360$		0			0
$361$	14.9029	−	11.7858i	0.784361	−	0.620305i
$362$		−	24.4688i		−	1.28605i
$363$	6.40420	−	7.63223i	0.336133	−	0.400588i
$364$	−0.694593	+	0.252811i	−0.0364066	+	0.0132509i
$365$		0			0
$366$	1.78106	−	10.1009i	0.0930975	−	0.527982i
$367$	2.69756	−	7.41147i	0.140811	−	0.386876i	−0.849162	−	0.528133i	$-0.822892\pi$
$367$	2.69756	−	7.41147i	0.140811	−	0.386876i	0.989973	+	0.141257i	$0.0451145\pi$
$368$	0.810446	−	0.467911i	0.0422474	−	0.0243916i
$369$	2.56670	−	4.44566i	0.133617	−	0.231432i
$370$		0			0
$371$	1.43376	−	1.20307i	0.0744373	−	0.0624603i
$372$	3.74557	+	2.16250i	0.194199	+	0.112121i
$373$	−21.1772	+	12.2267i	−1.09652	+	0.633074i	−0.935304	−	0.353846i	$-0.884874\pi$
$373$	−21.1772	+	12.2267i	−1.09652	+	0.633074i	−0.161212	+	0.986920i	$0.551540\pi$
$374$	0.608593	+	0.221510i	0.0314696	+	0.0114540i
$375$		0			0
$376$	−0.985452	−	5.58878i	−0.0508208	−	0.288219i
$377$	0.222318	+	0.610815i	0.0114500	+	0.0314586i
$378$	−2.49860	+	2.97771i	−0.128514	+	0.153157i
$379$	33.8135			1.73688			0.868440	−	0.495794i	$-0.165123\pi$
$379$	33.8135			1.73688			0.868440	+	0.495794i	$0.165123\pi$
$380$		0			0
$381$	2.49794			0.127973
$382$	1.31423	−	1.56624i	0.0672418	−	0.0801357i
$383$	10.6012	+	29.1266i	0.541697	+	1.48830i	0.844663	+	0.535298i	$0.179801\pi$
$383$	10.6012	+	29.1266i	0.541697	+	1.48830i	−0.302966	+	0.953001i	$0.597977\pi$
$384$	0.266044	+	1.50881i	0.0135765	+	0.0769963i
$385$		0			0
$386$	−13.4427	−	4.89274i	−0.684215	−	0.249034i
$387$	0.381545	−	0.220285i	0.0193950	−	0.0111977i
$388$	5.39917	+	3.11721i	0.274101	+	0.158252i
$389$	25.2080	−	21.1520i	1.27810	−	1.07245i	0.284594	−	0.958648i	$-0.408141\pi$
$389$	25.2080	−	21.1520i	1.27810	−	1.07245i	0.993503	−	0.113803i	$-0.0363031\pi$
$390$		0			0
$391$	−0.142903	+	0.247516i	−0.00722694	+	0.0125174i
$392$	−5.64436	+	3.25877i	−0.285083	+	0.164593i
$393$	−5.06212	+	13.9081i	−0.255350	+	0.701569i
$394$	−2.42602	+	13.7587i	−0.122221	+	0.693151i
$395$		0			0
$396$	−1.30066	+	0.473401i	−0.0653606	+	0.0237893i
$397$	−7.47589	+	8.90941i	−0.375204	+	0.447151i	−0.920294	−	0.391227i	$-0.872051\pi$
$397$	−7.47589	+	8.90941i	−0.375204	+	0.447151i	0.545090	+	0.838377i	$0.316495\pi$
$398$		−	18.8384i		−	0.944285i
$399$	4.33544	+	1.64955i	0.217043	+	0.0825806i
$400$		0			0
$401$	−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	$0.831413\pi$
$402$	−6.64847	−	18.2665i	−0.331595	−	0.911051i
$403$	2.95848	−	0.521660i	0.147372	−	0.0259857i
$404$	2.49525	−	14.1513i	0.124143	−	0.704052i
$405$		0			0
$406$	−0.212134	−	0.367426i	−0.0105280	−	0.0182351i
$407$	−7.34603	−	4.24123i	−0.364129	−	0.210230i
$408$	−0.300767	−	0.358441i	−0.0148902	−	0.0177455i
$409$	−11.0018	+	9.23162i	−0.544005	+	0.456474i	−0.872905	−	0.487891i	$-0.837766\pi$
$409$	−11.0018	+	9.23162i	−0.544005	+	0.456474i	0.328900	+	0.944365i	$0.393322\pi$
$410$		0			0
$411$	−8.83409	−	15.3011i	−0.435754	−	0.754747i
$412$	6.70405	−	18.4192i	0.330285	−	0.907450i
$413$	6.75790	+	1.19160i	0.332534	+	0.0586348i
$414$	−0.106067	−	0.601535i	−0.00521290	−	0.0295638i
$415$		0			0
$416$	0.815207	+	0.684040i	0.0399688	+	0.0335378i
$417$		−	10.4875i		−	0.513576i
$418$	5.83834	+	7.16637i	0.285563	+	0.350519i
$419$	32.2763			1.57680			0.788400	−	0.615162i	$-0.210910\pi$
$419$	32.2763			1.57680			0.788400	+	0.615162i	$0.210910\pi$
$420$		0			0
$421$	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	$0.284708\pi$
$422$	0.272114	−	0.0479810i	0.0132463	−	0.00233568i
$423$	−3.64781	−	0.643208i	−0.177363	−	0.0312739i
$424$	−2.53209	−	0.921605i	−0.122969	−	0.0447571i
$425$		0			0
$426$	9.35504	−	16.2034i	0.453253	−	0.785057i
$427$	2.98897	+	3.56212i	0.144647	+	0.172383i
$428$	−1.32683	−	1.58125i	−0.0641346	−	0.0764327i
$429$	1.72874	−	2.99427i	0.0834644	−	0.144565i
$430$		0			0
$431$	−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	$0.647825\pi$
$432$	5.51125	+	0.971782i	0.265160	+	0.0467549i
$433$	27.6437	−	4.87433i	1.32847	−	0.234245i	0.536033	−	0.844197i	$-0.319922\pi$
$433$	27.6437	−	4.87433i	1.32847	−	0.234245i	0.792439	+	0.609951i	$0.208811\pi$
$434$	−1.84255	+	0.670633i	−0.0884452	+	0.0321914i
$435$		0			0
$436$	9.10876			0.436230
$437$	−3.56185	+	1.98814i	−0.170387	+	0.0951057i
$438$		−	10.6382i		−	0.508311i
$439$	−17.8726	−	14.9969i	−0.853012	−	0.715762i	0.107439	−	0.994212i	$-0.465735\pi$
$439$	−17.8726	−	14.9969i	−0.853012	−	0.715762i	−0.960451	+	0.278450i	$0.910179\pi$
$440$		0			0
$441$	0.738703	+	4.18939i	0.0351763	+	0.199495i
$442$	−0.320070	−	0.0564370i	−0.0152242	−	0.00268443i
$443$	−5.11333	+	14.0488i	−0.242942	+	0.667476i	0.756960	+	0.653461i	$0.226684\pi$
$443$	−5.11333	+	14.0488i	−0.242942	+	0.667476i	−0.999902	+	0.0140154i	$0.995539\pi$
$444$	3.06418	+	5.30731i	0.145419	+	0.251874i
$445$		0			0
$446$	−5.29086	+	4.43956i	−0.250529	+	0.210219i
$447$	8.77141	+	10.4534i	0.414874	+	0.494427i
$448$	−0.601535	−	0.347296i	−0.0284199	−	0.0164082i
$449$	−4.41194	−	7.64171i	−0.208212	−	0.360634i	0.742939	−	0.669359i	$-0.233431\pi$
$449$	−4.41194	−	7.64171i	−0.208212	−	0.360634i	−0.951151	+	0.308725i	$0.900098\pi$
$450$		0			0
$451$	2.89615	−	16.4249i	0.136375	−	0.773419i
$452$	−7.07564	+	1.24763i	−0.332810	+	0.0586834i
$453$	5.67128	+	15.5817i	0.266460	+	0.732093i
$454$	−1.76399	−	1.48016i	−0.0827879	−	0.0694673i
$455$		0			0
$456$	−1.06418	−	6.59289i	−0.0498347	−	0.308740i
$457$			19.4561i			0.910116i	0.890462	+	0.455058i	$0.150381\pi$
$457$			19.4561i			0.910116i	−0.890462	+	0.455058i	$0.849619\pi$
$458$	−14.2777	+	17.0155i	−0.667152	+	0.795081i
$459$	−1.60607	+	0.584561i	−0.0749648	+	0.0272849i
$460$		0			0
$461$	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	$-0.154225\pi$
$462$	−0.771841	+	2.12061i	−0.0359093	+	0.0986599i
$463$	29.6168	−	17.0993i	1.37641	−	0.794670i	0.384684	−	0.923049i	$-0.374311\pi$
$463$	29.6168	−	17.0993i	1.37641	−	0.794670i	0.991725	+	0.128379i	$0.0409772\pi$
$464$	−0.305407	+	0.528981i	−0.0141782	+	0.0245573i
$465$		0			0
$466$	13.7253	−	11.5169i	0.635814	−	0.533511i
$467$	0.00589515	+	0.00340357i	0.000272795	+	0.000157498i	0.500136	−	0.865947i	$-0.333283\pi$
$467$	0.00589515	+	0.00340357i	0.000272795	+	0.000157498i	−0.499864	+	0.866104i	$0.666617\pi$
$468$	0.601535	−	0.347296i	0.0278060	−	0.0160538i
$469$	8.28136	+	3.01417i	0.382398	+	0.139181i
$470$		0			0
$471$	−2.84524	−	16.1361i	−0.131102	−	0.743514i
$472$	−3.37895	−	9.28359i	−0.155529	−	0.427312i
$473$	0.920085	−	1.09652i	0.0423056	−	0.0504178i
$474$	−3.75877			−0.172646
$475$		0			0
$476$	0.212134			0.00972313
$477$	−1.13052	+	1.34730i	−0.0517628	+	0.0616885i
$478$	−2.37219	−	6.51754i	−0.108501	−	0.298105i
$479$	−3.14290	−	17.8243i	−0.143603	−	0.814413i	−0.968478	−	0.249098i	$-0.919866\pi$
$479$	−3.14290	−	17.8243i	−0.143603	−	0.814413i	0.824875	−	0.565315i	$-0.191245\pi$
$480$		0			0
$481$	4.00000	+	1.45588i	0.182384	+	0.0663825i
$482$	−15.4056	+	8.89440i	−0.701704	+	0.405129i
$483$	−0.862458	−	0.497941i	−0.0392432	−	0.0226571i
$484$	4.98158	−	4.18004i	0.226436	−	0.190002i
$485$		0			0
$486$	3.32635	−	5.76141i	0.150886	−	0.261343i
$487$	0.640140	−	0.369585i	0.0290075	−	0.0167475i	−0.485426	−	0.874278i	$-0.661336\pi$
$487$	0.640140	−	0.369585i	0.0290075	−	0.0167475i	0.514434	+	0.857530i	$0.328002\pi$
$488$	2.28969	−	6.29086i	0.103649	−	0.284774i
$489$	0.656574	−	3.72362i	0.0296913	−	0.168388i
$490$		0			0
$491$	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	$0.298585\pi$
$492$	−7.74535	+	9.23055i	−0.349187	+	0.416145i
$493$		−	0.186547i		−	0.00840166i
$494$	−3.50980	−	3.03287i	−0.157913	−	0.136455i
$495$		0			0
$496$	2.16250	+	1.81456i	0.0970993	+	0.0814760i
$497$	2.90117	+	7.97090i	0.130135	+	0.357544i
$498$	26.2268	−	4.62449i	1.17525	−	0.207228i
$499$	2.60947	−	14.7990i	0.116816	−	0.662496i	−0.869019	−	0.494778i	$-0.835249\pi$
$499$	2.60947	−	14.7990i	0.116816	−	0.662496i	0.985835	−	0.167718i	$-0.0536397\pi$
$500$		0			0
$501$	−9.32501	−	16.1514i	−0.416611	−	0.721591i
$502$	14.4587	+	8.34776i	0.645326	+	0.372579i
$503$	0.456427	+	0.543948i	0.0203511	+	0.0242535i	0.776124	−	0.630580i	$-0.217183\pi$
$503$	0.456427	+	0.543948i	0.0203511	+	0.0242535i	−0.755773	+	0.654834i	$0.772739\pi$
$504$	−0.347296	+	0.291416i	−0.0154698	+	0.0129807i
$505$		0			0
$506$	−0.992259	−	1.71864i	−0.0441113	−	0.0764030i
$507$	6.21865	−	17.0856i	0.276180	−	0.758798i
$508$	1.60565	+	0.283119i	0.0712390	+	0.0125614i
$509$	−5.24628	−	29.7531i	−0.232537	−	1.31878i	−0.847738	−	0.530415i	$-0.822036\pi$
$509$	−5.24628	−	29.7531i	−0.232537	−	1.31878i	0.615201	−	0.788370i	$-0.289075\pi$
$510$		0			0
$511$	3.69459	+	3.10013i	0.163439	+	0.137142i
$512$			1.00000i			0.0441942i
$513$	−23.9590	−	4.58378i	−1.05782	−	0.202379i
$514$	26.1138			1.15183
$515$		0			0
$516$	−0.971782	+	0.353700i	−0.0427803	+	0.0155708i
$517$	−11.8516	+	2.08976i	−0.521235	+	0.0919077i
$518$	−2.73616	−	0.482459i	−0.120220	−	0.0211980i
$519$	20.2763	+	7.37997i	0.890031	+	0.323945i
$520$		0			0
$521$	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	$0.0185969\pi$
$522$	0.256267	+	0.305407i	0.0112165	+	0.0133673i
$523$	−10.0318	−	11.9554i	−0.438660	−	0.522774i	0.500740	−	0.865598i	$-0.333061\pi$
$523$	−10.0318	−	11.9554i	−0.438660	−	0.522774i	−0.939400	+	0.342823i	$0.888617\pi$
$524$	−4.83022	+	8.36619i	−0.211009	+	0.365479i
$525$		0			0
$526$	11.7442	+	4.27455i	0.512072	+	0.186379i
$527$	−0.849051	−	0.149711i	−0.0369852	−	0.00652150i
$528$	3.19961	−	0.564178i	0.139245	−	0.0245527i
$529$	−20.7900	+	7.56693i	−0.903912	+	0.328997i
$530$		0			0
$531$	−6.44831			−0.279833
$532$	2.59980	+	1.55169i	0.112716	+	0.0672743i
$533$			8.36959i			0.362527i
$534$	−18.8195	−	15.7915i	−0.814401	−	0.683364i
$535$		0			0
$536$	−2.20321	−	12.4950i	−0.0951642	−	0.539703i
$537$	−14.2002	−	2.50387i	−0.612782	−	0.108050i
$538$	−0.281465	+	0.773318i	−0.0121348	+	0.0333401i
$539$	6.91060	+	11.9695i	0.297660	+	0.515563i
$540$		0			0
$541$	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	$0.260677\pi$
$542$	−7.76730	−	9.25671i	−0.333634	−	0.397610i
$543$	32.4659	+	18.7442i	1.39325	+	0.804392i
$544$	−0.152704	−	0.264490i	−0.00654711	−	0.0113399i
$545$		0			0
$546$	0.196652	−	1.11527i	0.00841593	−	0.0477291i
$547$	3.56591	−	0.628766i	0.152467	−	0.0268841i	−0.0968935	−	0.995295i	$-0.530891\pi$
$547$	3.56591	−	0.628766i	0.152467	−	0.0268841i	0.249361	+	0.968411i	$0.419780\pi$
$548$	−3.94421	−	10.8366i	−0.168488	−	0.462917i
$549$	−3.34730	−	2.80872i	−0.142859	−	0.119873i
$550$		0			0
$551$	1.36453	−	2.28623i	0.0581310	−	0.0973967i
$552$			1.43376i			0.0610250i
$553$	1.09537	−	1.30541i	0.0465797	−	0.0555116i
$554$	−10.5817	+	3.85143i	−0.449574	+	0.163632i
$555$		0			0
$556$	1.18866	−	6.74124i	0.0504105	−	0.285892i
$557$	−3.79758	+	10.4338i	−0.160909	+	0.442093i	−0.993778	−	0.111376i	$-0.964474\pi$
$557$	−3.79758	+	10.4338i	−0.160909	+	0.442093i	0.832870	+	0.553469i	$0.186696\pi$
$558$	1.59569	−	0.921274i	0.0675511	−	0.0390007i
$559$	−0.359156	+	0.622076i	−0.0151907	+	0.0263110i
$560$		0			0
$561$	−0.760115	+	0.637812i	−0.0320921	+	0.0269284i
$562$	−22.7012	−	13.1065i	−0.957592	−	0.552866i
$563$	−10.9532	+	6.32383i	−0.461622	+	0.266517i	−0.712726	−	0.701443i	$-0.752540\pi$
$563$	−10.9532	+	6.32383i	−0.461622	+	0.266517i	0.251104	+	0.967960i	$0.419206\pi$
$564$	8.17024	+	2.97373i	0.344029	+	0.125216i
$565$		0			0
$566$	4.46926	+	25.3464i	0.187857	+	1.06539i
$567$	−1.57170	−	4.31820i	−0.0660050	−	0.181347i
$568$	7.84981	−	9.35504i	0.329371	−	0.392529i
$569$	0.704088			0.0295169			0.0147585	−	0.999891i	$-0.495302\pi$
$569$	0.704088			0.0295169			0.0147585	+	0.999891i	$0.495302\pi$
$570$		0			0
$571$	10.3396			0.432697			0.216348	−	0.976316i	$-0.430585\pi$
$571$	10.3396			0.432697			0.216348	+	0.976316i	$0.430585\pi$
$572$	1.45059	−	1.72874i	0.0606520	−	0.0722823i
$573$	1.07137	+	2.94356i	0.0447571	+	0.122969i
$574$	−0.948615	−	5.37987i	−0.0395944	−	0.224551i
$575$		0			0
$576$	0.613341	+	0.223238i	0.0255559	+	0.00930157i
$577$	1.33272	−	0.769448i	0.0554820	−	0.0320325i	−0.472002	−	0.881597i	$-0.656469\pi$
$577$	1.33272	−	0.769448i	0.0554820	−	0.0320325i	0.527484	+	0.849565i	$0.323135\pi$
$578$	−14.6417	−	8.45336i	−0.609013	−	0.351614i
$579$	16.7895	−	14.0881i	0.697748	−	0.585480i
$580$		0			0
$581$	−6.03684	+	10.4561i	−0.250450	+	0.433792i
$582$	−8.27201	+	4.77584i	−0.342886	+	0.197965i
$583$	−1.95437	+	5.36959i	−0.0809417	+	0.222385i
$584$	1.20574	−	6.83807i	0.0498938	−	0.282962i
$585$		0			0
$586$	−24.9094	+	9.06629i	−1.02900	+	0.374525i
$587$	4.42350	−	5.27173i	0.182578	−	0.217587i	−0.666991	−	0.745066i	$-0.732418\pi$
$587$	4.42350	−	5.27173i	0.182578	−	0.217587i	0.849568	+	0.527478i	$0.176862\pi$
$588$		−	9.98545i		−	0.411793i
$589$	−9.31046	−	8.04531i	−0.383631	−	0.331501i
$590$		0			0
$591$	−16.3969	−	13.7587i	−0.674479	−	0.565955i
$592$	1.36808	+	3.75877i	0.0562278	+	0.154485i
$593$	−4.10191	+	0.723278i	−0.168445	+	0.0297015i	−0.257235	−	0.966349i	$-0.582811\pi$
$593$	−4.10191	+	0.723278i	−0.168445	+	0.0297015i	0.0887893	+	0.996050i	$0.471700\pi$
$594$	2.06077	−	11.6872i	0.0845546	−	0.479533i
$595$		0			0
$596$	4.45336	+	7.71345i	0.182417	+	0.315955i
$597$	24.9954	+	14.4311i	1.02299	+	0.590625i
$598$	0.640140	+	0.762889i	0.0261773	+	0.0311969i
$599$	−35.1070	+	29.4583i	−1.43443	+	1.20363i	−0.491400	+	0.870934i	$0.663515\pi$
$599$	−35.1070	+	29.4583i	−1.43443	+	1.20363i	−0.943033	+	0.332698i	$0.892041\pi$
$600$		0			0
$601$	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	$0.819662\pi$
$602$	0.160354	−	0.440570i	0.00653556	−	0.0179563i
$603$	−8.15555	−	1.43804i	−0.332120	−	0.0585617i
$604$	1.87939	+	10.6585i	0.0764711	+	0.433689i
$605$		0			0
$606$	16.8648	+	14.1513i	0.685087	+	0.574856i
$607$		−	26.7648i		−	1.08635i	−0.839620	−	0.543174i	$-0.817222\pi$
$607$		−	26.7648i		−	1.08635i	0.839620	−	0.543174i	$-0.182778\pi$
$608$	0.0632028	−	4.35844i	0.00256321	−	0.176758i
$609$	0.650015			0.0263399
$610$		0			0
$611$	5.67499	−	2.06553i	0.229586	−	0.0835623i
$612$	−0.196312	+	0.0346151i	−0.00793544	+	0.00139923i
$613$	−39.3251	−	6.93407i	−1.58832	−	0.280064i	−0.691475	−	0.722401i	$-0.743039\pi$
$613$	−39.3251	−	6.93407i	−1.58832	−	0.280064i	−0.896849	+	0.442336i	$0.854150\pi$
$614$	2.99273	+	1.08926i	0.120777	+	0.0439591i
$615$		0			0
$616$	−0.736482	+	1.27562i	−0.0296737	+	0.0513963i
$617$	−25.3052	−	30.1575i	−1.01875	−	1.21410i	−0.976618	−	0.214983i	$-0.931030\pi$
$617$	−25.3052	−	30.1575i	−1.01875	−	1.21410i	−0.0421294	−	0.999112i	$-0.513414\pi$
$618$	19.3035	+	23.0051i	0.776502	+	0.925399i
$619$	−14.5273	+	25.1621i	−0.583903	+	1.01135i	0.411108	+	0.911587i	$0.365142\pi$
$619$	−14.5273	+	25.1621i	−0.583903	+	1.01135i	−0.995011	+	0.0997633i	$0.968191\pi$
$620$		0			0
$621$	4.92127	+	1.79120i	0.197484	+	0.0718783i
$622$	0.810446	+	0.142903i	0.0324959	+	0.00572991i
$623$	10.9686	−	1.93407i	0.439449	−	0.0774868i
$624$	−1.53209	+	0.557635i	−0.0613326	+	0.0223233i
$625$		0			0
$626$	21.8881			0.874823
$627$	−13.9810	+	2.25671i	−0.558346	+	0.0901244i
$628$		−	10.6946i		−	0.426761i
$629$	−0.935822	−	0.785248i	−0.0373137	−	0.0313099i
$630$		0			0
$631$	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	$0.716655\pi$
$632$	−2.41609	−	0.426022i	−0.0961069	−	0.0169462i
$633$	−0.144789	+	0.397804i	−0.00575483	+	0.0158113i
$634$	−6.61081	−	11.4503i	−0.262549	−	0.454748i
$635$		0			0
$636$	3.16250	−	2.65366i	0.125401	−	0.105224i
$637$	−4.45826	−	5.31315i	−0.176643	−	0.210515i
$638$	1.12176	+	0.647651i	0.0444111	+	0.0256408i
$639$	−3.98545	−	6.90301i	−0.157662	−	0.273079i
$640$		0			0
$641$	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	$-0.0855787\pi$
$642$	3.11446	−	0.549163i	0.122918	−	0.0216737i
$643$	14.4278	+	39.6400i	0.568976	+	1.56325i	0.806107	+	0.591770i	$0.201571\pi$
$643$	14.4278	+	39.6400i	0.568976	+	1.56325i	−0.237131	+	0.971478i	$0.576207\pi$
$644$	−0.497941	−	0.417822i	−0.0196216	−	0.0164645i
$645$		0			0
$646$	0.648833	+	1.16242i	0.0255280	+	0.0457347i
$647$			45.2526i			1.77906i	0.456874	+	0.889531i	$0.348969\pi$
$647$			45.2526i			1.77906i	−0.456874	+	0.889531i	$0.651031\pi$
$648$	−4.25260	+	5.06805i	−0.167058	+	0.199092i
$649$	−19.6869	+	7.16545i	−0.772779	+	0.281268i
$650$		0			0
$651$	0.521660	−	2.95848i	0.0204455	−	0.115952i
$652$	0.844075	−	2.31908i	0.0330565	−	0.0908221i
$653$	−8.60986	+	4.97090i	−0.336930	+	0.194527i	−0.658914	−	0.752219i	$-0.728984\pi$
$653$	−8.60986	+	4.97090i	−0.336930	+	0.194527i	0.321984	+	0.946745i	$0.395650\pi$
$654$	−6.97771	+	12.0858i	−0.272850	+	0.472590i
$655$		0			0
$656$	−6.02481	+	5.05542i	−0.235230	+	0.197381i
$657$	−3.92490	−	2.26604i	−0.153125	−	0.0884068i
$658$	−3.41371	+	1.97090i	−0.133080	+	0.0768338i
$659$	20.4136	+	7.42994i	0.795201	+	0.289429i	0.707496	−	0.706717i	$-0.249825\pi$
$659$	20.4136	+	7.42994i	0.795201	+	0.289429i	0.0877044	+	0.996147i	$0.472047\pi$
$660$		0			0
$661$	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	$0.755548\pi$
$662$	−0.560282	−	1.53936i	−0.0217760	−	0.0598290i
$663$	0.320070	−	0.381445i	0.0124305	−	0.0148141i
$664$	17.3824			0.674567
$665$		0			0
$666$	2.61081			0.101167
$667$	−0.367426	+	0.437882i	−0.0142268	+	0.0169548i
$668$	−4.16339	−	11.4388i	−0.161086	−	0.442581i
$669$	−1.83750	−	10.4210i	−0.0710417	−	0.402898i
$670$		0			0
$671$	−13.3405	−	4.85554i	−0.515004	−	0.187446i
$672$	0.921605	−	0.532089i	0.0355517	−	0.0205258i
$673$	−30.9732	−	17.8824i	−1.19393	−	0.689315i	−0.234733	−	0.972060i	$-0.575422\pi$
$673$	−30.9732	−	17.8824i	−1.19393	−	0.689315i	−0.959195	+	0.282745i	$0.908755\pi$
$674$	24.0043	−	20.1420i	0.924613	−	0.775842i
$675$		0			0
$676$	5.93376	−	10.2776i	0.228222	−	0.395291i
$677$	13.3748	−	7.72193i	0.514035	−	0.296778i	−0.220456	−	0.975397i	$-0.570755\pi$
$677$	13.3748	−	7.72193i	0.514035	−	0.296778i	0.734491	+	0.678619i	$0.237421\pi$
$678$	3.76487	−	10.3439i	0.144589	−	0.397255i
$679$	0.751963	−	4.26460i	0.0288577	−	0.163660i
$680$		0			0
$681$	3.31521	−	1.20664i	0.127039	−	0.0462384i
$682$	3.84797	−	4.58584i	0.147347	−	0.175601i
$683$		−	28.0951i		−	1.07503i	−0.843254	−	0.537515i	$-0.819363\pi$
$683$		−	28.0951i		−	1.07503i	0.843254	−	0.537515i	$-0.180637\pi$
$684$	−2.65910	−	1.01173i	−0.101673	−	0.0386846i
$685$		0			0
$686$	7.19253	+	6.03525i	0.274612	+	0.230427i
$687$	−11.6393	−	31.9786i	−0.444066	−	1.22006i
$688$	−0.664738	+	0.117211i	−0.0253429	+	0.00446863i
$689$	0.497941	−	2.82396i	0.0189700	−	0.107584i
$690$		0			0
$691$	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	$0.562123\pi$
$692$	12.1969	+	7.04189i	0.463657	+	0.267692i
$693$	0.617982	+	0.736482i	0.0234752	+	0.0279766i
$694$	−19.4782	+	16.3441i	−0.739382	+	0.620415i
$695$		0			0
$696$	−0.467911	−	0.810446i	−0.0177361	−	0.0307199i
$697$	0.821525	−	2.25712i	0.0311175	−	0.0854946i
$698$	−31.7094	−	5.59121i	−1.20022	−	0.211631i
$699$	4.76676	+	27.0336i	0.180295	+	1.02251i
$700$		0			0
$701$	−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	$0.835977\pi$
$702$			5.95542i			0.224773i
$703$	−5.72513	−	16.4688i	−0.215927	−	0.621134i
$704$	2.12061			0.0799237
$705$		0			0
$706$	−18.9354	+	6.89193i	−0.712644	+	0.259381i
$707$	−9.82938	+	1.73318i	−0.369672	+	0.0651831i
$708$	14.9061	+	2.62836i	0.560207	+	0.0987797i
$709$	17.1284	+	6.23421i	0.643269	+	0.234131i	0.642996	−	0.765869i	$-0.277691\pi$
$709$	17.1284	+	6.23421i	0.643269	+	0.234131i	0.000272535		1.00000i	$0.499913\pi$
$710$		0			0
$711$	−0.800660	+	1.38678i	−0.0300271	+	0.0520084i
$712$	−10.3072	−	12.2836i	−0.386277	−	0.460347i
$713$	1.69810	+	2.02372i	0.0635944	+	0.0757889i
$714$	−0.162504	+	0.281465i	−0.00608155	+	0.0105336i
$715$		0			0
$716$	−8.84389	−	3.21891i	−0.330512	−	0.120296i
$717$	10.4649	+	1.84524i	0.390817	+	0.0689116i
$718$	3.35294	−	0.591214i	0.125131	−	0.0220639i
$719$	−21.9786	+	7.99957i	−0.819665	+	0.298334i	−0.717610	−	0.696445i	$-0.754764\pi$
$719$	−21.9786	+	7.99957i	−0.819665	+	0.298334i	−0.102055	+	0.994779i	$0.532542\pi$
$720$		0			0
$721$	−13.6149			−0.507047
$722$	−0.550931	+	18.9920i	−0.0205035	+	0.706809i
$723$		−	27.2540i		−	1.01359i
$724$	18.7442	+	15.7283i	0.696624	+	0.584537i
$725$		0			0
$726$	1.73009	+	9.81180i	0.0642095	+	0.364150i
$727$	5.26341	+	0.928081i	0.195209	+	0.0344206i	0.270398	−	0.962749i	$-0.412845\pi$
$727$	5.26341	+	0.928081i	0.195209	+	0.0344206i	−0.0751887	+	0.997169i	$0.523956\pi$
$728$	0.252811	−	0.694593i	0.00936980	−	0.0257433i
$729$	15.0201	+	26.0155i	0.556299	+	0.963538i
$730$		0			0
$731$	0.157918	−	0.132509i	0.00584082	−	0.00490103i
$732$	6.59289	+	7.85710i	0.243680	+	0.290407i
$733$	27.2580	+	15.7374i	1.00680	+	0.581275i	0.910252	−	0.414054i	$-0.135888\pi$
$733$	27.2580	+	15.7374i	1.00680	+	0.581275i	0.0965450	+	0.995329i	$0.469221\pi$
$734$	3.94356	+	6.83045i	0.145560	+	0.252117i
$735$		0			0
$736$	−0.162504	+	0.921605i	−0.00598997	+	0.0339708i
$737$	−26.4971	+	4.67216i	−0.976035	+	0.172101i
$738$	1.75573	+	4.82383i	0.0646293	+	0.177567i
$739$	−19.8855	−	16.6859i	−0.731501	−	0.613802i	0.199039	−	0.979992i	$-0.436218\pi$
$739$	−19.8855	−	16.6859i	−0.731501	−	0.613802i	−0.930540	+	0.366189i	$0.880662\pi$
$740$		0			0
$741$	6.71276	−	2.33359i	0.246599	−	0.0857264i
$742$			1.87164i			0.0687102i
$743$	−28.2300	+	33.6432i	−1.03566	+	1.23425i	−0.0639778	+	0.997951i	$0.520379\pi$
$743$	−28.2300	+	33.6432i	−1.03566	+	1.23425i	−0.971681	+	0.236298i	$0.924066\pi$
$744$	−4.06418	+	1.47924i	−0.149000	+	0.0542316i
$745$		0			0
$746$	4.24628	−	24.0819i	0.155467	−	0.881700i
$747$	3.88040	−	10.6613i	0.141977	−	0.390077i
$748$	−0.560882	+	0.323826i	−0.0205079	+	0.0118402i
$749$	−0.716881	+	1.24168i	−0.0261943	+	0.0453698i
$750$		0			0
$751$	−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	$0.484349\pi$
$752$	4.91469	+	2.83750i	0.179220	+	0.103473i
$753$	−22.1521	+	12.7895i	−0.807267	+	0.466076i
$754$	−0.610815	−	0.222318i	−0.0222446	−	0.00809636i
$755$		0			0
$756$	−0.674992	−	3.82807i	−0.0245492	−	0.139226i
$757$	−6.84915	−	18.8179i	−0.248937	−	0.683948i	−0.999726	−	0.0234063i	$-0.992549\pi$
$757$	−6.84915	−	18.8179i	−0.248937	−	0.683948i	0.750789	−	0.660542i	$-0.229673\pi$
$758$	−21.7349	+	25.9026i	−0.789446	+	0.940825i
$759$	3.04046			0.110362
$760$		0			0
$761$	22.4097			0.812352			0.406176	−	0.913795i	$-0.366862\pi$
$761$	22.4097			0.812352			0.406176	+	0.913795i	$0.366862\pi$
$762$	−1.60565	+	1.91353i	−0.0581664	+	0.0693200i
$763$	−2.16392	−	5.94532i	−0.0783391	−	0.215235i
$764$	0.355037	+	2.01352i	0.0128448	+	0.0728464i
$765$		0			0
$766$	−29.1266	−	10.6012i	−1.05239	−	0.383037i
$767$	9.10489	−	5.25671i	0.328759	−	0.189809i
$768$	−1.32683	−	0.766044i	−0.0478778	−	0.0276422i
$769$	7.55896	−	6.34272i	0.272583	−	0.228724i	−0.496241	−	0.868185i	$-0.665287\pi$
$769$	7.55896	−	6.34272i	0.272583	−	0.228724i	0.768824	+	0.639460i	$0.220842\pi$
$770$		0			0
$771$	−20.0043	+	34.6485i	−0.720439	+	1.24784i
$772$	12.3888	−	7.15270i	0.445884	−	0.257431i
$773$	6.59473	−	18.1189i	0.237196	−	0.651690i	−0.762791	−	0.646645i	$-0.776172\pi$
$773$	6.59473	−	18.1189i	0.237196	−	0.651690i	0.999987	−	0.00504555i	$-0.00160606\pi$
$774$	−0.0765042	+	0.433877i	−0.00274989	+	0.0155954i
$775$		0			0
$776$	−5.85844	+	2.13230i	−0.210306	+	0.0765450i
$777$	2.73616	−	3.26083i	0.0981592	−	0.116982i
$778$			32.9067i			1.17976i
$779$	26.5783	−	21.6530i	0.952267	−	0.775798i
$780$		0			0
$781$	−19.8384	−	16.6464i	−0.709875	−	0.595656i
$782$	−0.0977517	−	0.268571i	−0.00349559	−	0.00960407i
$783$	−3.36635	+	0.593578i	−0.120304	+	0.0212128i
$784$	1.13176	−	6.41852i	0.0404200	−	0.229233i
$785$		0			0
$786$	−7.40033	−	12.8177i	−0.263961	−	0.457194i
$787$	−12.7830	−	7.38026i	−0.455664	−	0.263078i	0.254555	−	0.967058i	$-0.418071\pi$
$787$	−12.7830	−	7.38026i	−0.455664	−	0.263078i	−0.710219	+	0.703980i	$0.751404\pi$
$788$	−8.98032	−	10.7023i	−0.319911	−	0.381255i
$789$	−14.6682	+	12.3081i	−0.522201	+	0.438179i
$790$		0			0
$791$	2.49525	+	4.32190i	0.0887210	+	0.153669i
$792$	0.473401	−	1.30066i	0.0168216	−	0.0462169i
$793$	7.01600	+	1.23711i	0.249146	+	0.0439311i
$794$	−2.01960	−	11.4537i	−0.0716729	−	0.406477i
$795$		0			0
$796$	14.4311	+	12.1091i	0.511496	+	0.429196i
$797$			29.2627i			1.03654i	0.855218	+	0.518269i	$0.173423\pi$
$797$			29.2627i			1.03654i	−0.855218	+	0.518269i	$0.826577\pi$
$798$	−4.05039	+	2.26083i	−0.143382	+	0.0800325i
$799$	−1.73318			−0.0613156
$800$		0			0
$801$	−9.83497	+	3.57964i	−0.347502	+	0.126480i
$802$	13.2660	−	2.33915i	0.468437	−	0.0825981i
$803$	−14.5009	−	2.55690i	−0.511726	−	0.0902312i
$804$	18.2665	+	6.64847i	0.644210	+	0.234473i
$805$		0			0
$806$	−1.50206	+	2.60164i	−0.0529078	+	0.0916390i
$807$	−0.810446	−	0.965852i	−0.0285290	−	0.0339996i
$808$	9.23659	+	11.0077i	0.324942	+	0.387251i
$809$	−23.6129	+	40.8988i	−0.830186	+	1.43793i	0.0677037	+	0.997705i	$0.478433\pi$
$809$	−23.6129	+	40.8988i	−0.830186	+	1.43793i	−0.897890	+	0.440220i	$0.854901\pi$
$810$		0			0
$811$	−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	$0.716723\pi$
$812$	0.417822	+	0.0736733i	0.0146627	+	0.00258542i
$813$	18.2322	−	3.21482i	0.639430	−	0.112749i
$814$	7.97090	−	2.90117i	0.279380	−	0.101686i
$815$		0			0
$816$	0.467911			0.0163802
$817$	2.90463	−	0.468845i	0.101620	−	0.0164028i
$818$		−	14.3618i		−	0.502150i
$819$	−0.369585	−	0.310119i	−0.0129143	−	0.0108364i
$820$		0			0
$821$	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	$0.614874\pi$
$822$	17.3998	+	3.06805i	0.606887	+	0.107010i
$823$	−8.27758	+	22.7425i	−0.288538	+	0.792753i	0.707733	+	0.706480i	$0.249718\pi$
$823$	−8.27758	+	22.7425i	−0.288538	+	0.792753i	−0.996272	+	0.0862728i	$0.972504\pi$
$824$	9.80066	+	16.9752i	0.341422	+	0.591361i
$825$		0			0
$826$	−5.25671	+	4.41090i	−0.182904	+	0.153475i
$827$	9.92561	+	11.8289i	0.345147	+	0.411330i	0.910494	−	0.413523i	$-0.135702\pi$
$827$	9.92561	+	11.8289i	0.345147	+	0.411330i	−0.565346	+	0.824854i	$0.691257\pi$
$828$	0.528981	+	0.305407i	0.0183834	+	0.0106136i
$829$	−1.47565	−	2.55590i	−0.0512515	−	0.0887702i	0.839261	−	0.543728i	$-0.182988\pi$
$829$	−1.47565	−	2.55590i	−0.0512515	−	0.0887702i	−0.890513	+	0.454958i	$0.849654\pi$
$830$		0			0
$831$	2.99588	−	16.9905i	0.103926	−	0.589393i
$832$	−1.04801	+	0.184793i	−0.0363332	+	0.00640653i
$833$	0.680793	+	1.87046i	0.0235881	+	0.0648077i
$834$	8.03390	+	6.74124i	0.278191	+	0.233430i
$835$		0			0
$836$	−9.24257	−	0.134029i	−0.319661	−	0.00463548i
$837$			15.7980i			0.546058i
$838$	−20.7468	+	24.7251i	−0.716687	+	0.854114i
$839$	−3.51754	+	1.28028i	−0.121439	+	0.0442002i	−0.402025	−	0.915629i	$-0.631693\pi$
$839$	−3.51754	+	1.28028i	−0.121439	+	0.0442002i	0.280586	+	0.959829i	$0.409471\pi$
$840$		0			0
$841$	−4.97101	+	28.1920i	−0.171414	+	0.972138i
$842$	−4.51211	+	12.3969i	−0.155498	+	0.427226i
$843$	34.7802	−	20.0804i	1.19789	−	0.691605i
$844$	−0.138156	+	0.239293i	−0.00475552	+	0.00823680i
$845$		0			0
$846$	2.83750	−	2.38094i	0.0975551	−	0.0818585i
$847$	−3.91178	−	2.25847i	−0.134410	−	0.0776018i
$848$	2.33359	−	1.34730i	0.0801357	−	0.0462663i
$849$	−37.0540	−	13.4865i	−1.27169	−	0.462857i
$850$		0			0
$851$	0.650015	+	3.68642i	0.0222822	+	0.126369i
$852$	6.39922	+	17.5817i	0.219234	+	0.602340i
$853$	24.7712	−	29.5212i	0.848150	−	1.01079i	−0.151601	−	0.988442i	$-0.548443\pi$
$853$	24.7712	−	29.5212i	0.848150	−	1.01079i	0.999750	−	0.0223436i	$-0.00711277\pi$
$854$	−4.65002			−0.159120
$855$		0			0
$856$	2.06418			0.0705521
$857$	30.8258	−	36.7367i	1.05299	−	1.25490i	0.0870288	−	0.996206i	$-0.472263\pi$
$857$	30.8258	−	36.7367i	1.05299	−	1.25490i	0.965959	−	0.258696i	$-0.0832928\pi$
$858$	1.18253	+	3.24897i	0.0403709	+	0.110918i
$859$	−8.46750	−	48.0216i	−0.288907	−	1.63848i	−0.690985	−	0.722869i	$-0.742823\pi$
$859$	−8.46750	−	48.0216i	−0.288907	−	1.63848i	0.402077	−	0.915606i	$-0.368288\pi$
$860$		0			0
$861$	7.86484	+	2.86257i	0.268033	+	0.0975560i
$862$	4.13819	−	2.38919i	0.140947	−	0.0813760i
$863$	−11.2887	−	6.51754i	−0.384272	−	0.221860i	0.295403	−	0.955373i	$-0.404546\pi$
$863$	−11.2887	−	6.51754i	−0.384272	−	0.221860i	−0.679675	+	0.733513i	$0.737879\pi$
$864$	−4.28699	+	3.59721i	−0.145846	+	0.122380i
$865$		0			0
$866$	−14.0351	+	24.3095i	−0.476931	+	0.826070i
$867$	22.4323	−	12.9513i	0.761841	−	0.439849i
$868$	0.670633	−	1.84255i	0.0227628	−	0.0625402i
$869$	−0.903429	+	5.12360i	−0.0306467	+	0.173806i
$870$		0			0
$871$	12.6878	−	4.61798i	0.429909	−	0.156474i
$872$	−5.85499	+	6.97771i	−0.198275	+	0.236295i
$873$			4.06923i			0.137723i
$874$	0.766511	−	4.00649i	0.0259276	−	0.135522i
$875$		0			0
$876$	8.14930	+	6.83807i	0.275339	+	0.231037i
$877$	16.3030	+	44.7921i	0.550513	+	1.51252i	0.833012	+	0.553254i	$0.186614\pi$
$877$	16.3030	+	44.7921i	0.550513	+	1.51252i	−0.282500	+	0.959267i	$0.591164\pi$
$878$	22.9765	−	4.05138i	0.775421	−	0.136728i
$879$	7.05232	−	39.9957i	0.237869	−	1.34902i
$880$		0			0
$881$	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	$0.801863\pi$
$882$	−3.68409	−	2.12701i	−0.124050	−	0.0716202i
$883$	1.64517	+	1.96064i	0.0553644	+	0.0659807i	0.793016	−	0.609201i	$-0.208510\pi$
$883$	1.64517	+	1.96064i	0.0553644	+	0.0659807i	−0.737652	+	0.675182i	$0.764065\pi$
$884$	0.248970	−	0.208911i	0.00837378	−	0.00702643i
$885$		0			0
$886$	−7.47519	−	12.9474i	−0.251134	−	0.434976i
$887$	−5.23010	+	14.3696i	−0.175610	+	0.482483i	−0.996003	−	0.0893155i	$-0.971532\pi$
$887$	−5.23010	+	14.3696i	−0.175610	+	0.482483i	0.820394	+	0.571799i	$0.193754\pi$
$888$	−6.03525	−	1.06418i	−0.202530	−	0.0357115i
$889$	−0.196652	−	1.11527i	−0.00659550	−	0.0374049i
$890$		0			0
$891$	10.7474	+	9.01812i	0.360051	+	0.302118i
$892$		−	6.90673i		−	0.231254i
$893$	−21.2410	−	12.6777i	−0.710804	−	0.424242i
$894$	−13.6459			−0.456387
$895$		0			0
$896$	0.652704	−	0.237565i	0.0218053	−	0.00793648i
$897$	−1.50260	+	0.264949i	−0.0501703	+	0.00884638i
$898$	8.68983	+	1.53225i	0.289983	+	0.0511319i
$899$	−1.62031	−	0.589745i	−0.0540404	−	0.0196691i
$900$		0			0
$901$	−0.411474	+	0.712694i	−0.0137082	+	0.0237433i
$902$	10.7206	+	12.7763i	0.356957	+	0.425405i
$903$	0.461722	+	0.550259i	0.0153651	+	0.0183115i
$904$	3.59240	−	6.22221i	0.119481	−	0.206948i
$905$		0			0
$906$	−15.5817	−	5.67128i	−0.517668	−	0.188416i
$907$	−13.9114	−	2.45295i	−0.461920	−	0.0814490i	−0.0621548	−	0.998067i	$-0.519797\pi$
$907$	−13.9114	−	2.45295i	−0.461920	−	0.0814490i	−0.399765	+	0.916618i	$0.630908\pi$
$908$	2.26774	−	0.399863i	0.0752574	−	0.0132699i
$909$	8.81345	−	3.20783i	0.292324	−	0.106397i
$910$		0			0
$911$	31.3809			1.03970			0.519849	−	0.854258i	$-0.325988\pi$
$911$	31.3809			1.03970			0.519849	+	0.854258i	$0.325988\pi$
$912$	5.73448	+	3.42262i	0.189888	+	0.113334i
$913$		−	36.8613i		−	1.21993i
$914$	−14.9042	−	12.5061i	−0.492987	−	0.413665i
$915$		0			0
$916$	−3.85710	−	21.8747i	−0.127442	−	0.722760i
$917$	6.60813	+	1.16519i	0.218220	+	0.0384780i
$918$	0.584561	−	1.60607i	0.0192934	−	0.0530081i
$919$	12.7811	+	22.1374i	0.421608	+	0.730247i	0.996097	−	0.0882656i	$-0.0281324\pi$
$919$	12.7811	+	22.1374i	0.421608	+	0.730247i	−0.574489	+	0.818512i	$0.694799\pi$
$920$		0			0
$921$	−3.73783	+	3.13641i	−0.123166	+	0.103348i
$922$	16.9027	+	20.1438i	0.556660	+	0.663402i
$923$	11.2548	+	6.49794i	0.370455	+	0.213882i
$924$	−1.12836	−	1.95437i	−0.0371202	−	0.0642940i
$925$		0			0
$926$	−5.93851	+	33.6790i	−0.195152	+	1.10676i
$927$	12.5995	−	2.22163i	0.413821	−	0.0729679i
$928$	−0.208911	−	0.573978i	−0.00685784	−	0.0188417i
$929$	6.68866	+	5.61245i	0.219448	+	0.184139i	0.745884	−	0.666076i	$-0.232027\pi$
$929$	6.68866	+	5.61245i	0.219448	+	0.184139i	−0.526436	+	0.850215i	$0.676472\pi$
$930$		0			0
$931$	−5.33837	+	27.9032i	−0.174958	+	0.914491i
$932$			17.9172i			0.586896i
$933$	−0.810446	+	0.965852i	−0.0265328	+	0.0316206i
$934$	−0.00639661	+	0.00232818i	−0.000209304	+	7.61803e-5i
$935$		0			0
$936$	−0.120615	+	0.684040i	−0.00394242	+	0.0223586i
$937$	9.16372	−	25.1771i	0.299366	−	0.822500i	−0.695241	−	0.718777i	$-0.744702\pi$
$937$	9.16372	−	25.1771i	0.299366	−	0.822500i	0.994606	−	0.103723i	$-0.0330756\pi$
$938$	−7.63215	+	4.40642i	−0.249198	+	0.143875i
$939$	−16.7672	+	29.0417i	−0.547178	+	0.947740i
$940$		0			0
$941$	−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	$0.342688\pi$
$942$	14.1899	+	8.19253i	0.462331	+	0.266927i
$943$	−6.37402	+	3.68004i	−0.207567	+	0.119839i
$944$	9.28359	+	3.37895i	0.302155	+	0.109975i
$945$		0			0
$946$	0.248560	+	1.40965i	0.00808138	+	0.0458318i
$947$	14.2742	+	39.2181i	0.463850	+	1.27442i	0.922568	+	0.385835i	$0.126087\pi$
$947$	14.2742	+	39.2181i	0.463850	+	1.27442i	−0.458718	+	0.888582i	$0.651691\pi$
$948$	2.41609	−	2.87939i	0.0784710	−	0.0935181i
$949$	7.38919			0.239863
$950$		0			0
$951$	20.2567			0.656869
$952$	−0.136357	+	0.162504i	−0.00441935	+	0.00526678i
$953$	2.57725	+	7.08095i	0.0834854	+	0.229374i	0.974410	−	0.224776i	$-0.0721651\pi$
$953$	2.57725	+	7.08095i	0.0834854	+	0.229374i	−0.890925	+	0.454150i	$0.849943\pi$
$954$	−0.305407	−	1.73205i	−0.00988793	−	0.0560772i
$955$		0			0
$956$	6.51754	+	2.37219i	0.210792	+	0.0767221i
$957$	−1.71864	+	0.992259i	−0.0555559	+	0.0320752i
$958$	15.6744	+	9.04963i	0.506417	+	0.292380i
$959$	−6.13610	+	5.14880i	−0.198145	+	0.166263i
$960$		0			0
$961$	11.5155	−	19.9454i	0.371467	−	0.643400i
$962$	−3.68642	+	2.12836i	−0.118855	+	0.0686209i
$963$	0.460802	−	1.26604i	0.0148492	−	0.0407977i
$964$	3.08899	−	17.5185i	0.0994898	−	0.564234i
$965$		0			0
$966$	0.935822	−	0.340611i	0.0301096	−	0.0109590i
$967$	9.73042	−	11.5963i	0.312909	−	0.372911i	−0.586552	−	0.809912i	$-0.699515\pi$
$967$	9.73042	−	11.5963i	0.312909	−	0.372911i	0.899461	+	0.437001i	$0.143959\pi$
$968$			6.50299i			0.209014i
$969$	−2.03936	−	0.0295733i	−0.0655138	−	0.000950031i
$970$		0			0
$971$	−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	$-0.602600\pi$
$972$	2.27536	+	6.25150i	0.0729822	+	0.200517i
$973$	−4.68242	+	0.825637i	−0.150111	+	0.0264687i
$974$	−0.128356	+	0.727940i	−0.00411278	+	0.0233247i
$975$		0			0
$976$	3.34730	+	5.79769i	0.107144	+	0.185579i
$977$	18.5630	+	10.7173i	0.593883	+	0.342878i	0.766631	−	0.642088i	$-0.221931\pi$
$977$	18.5630	+	10.7173i	0.593883	+	0.342878i	−0.172749	+	0.984966i	$0.555265\pi$
$978$	2.43042	+	2.89646i	0.0777162	+	0.0926186i
$979$	−26.0488	+	21.8575i	−0.832522	+	0.698569i
$980$		0			0
$981$	2.97266	+	5.14880i	0.0949097	+	0.164388i
$982$	−4.24265	+	11.6566i	−0.135388	+	0.371976i
$983$	24.2235	+	4.27126i	0.772610	+	0.136232i	0.546036	−	0.837762i	$-0.316136\pi$
$983$	24.2235	+	4.27126i	0.772610	+	0.136232i	0.226574	+	0.973994i	$0.427247\pi$
$984$	−2.09240	−	11.8666i	−0.0667032	−	0.378292i
$985$		0			0
$986$	0.142903	+	0.119910i	0.00455097	+	0.00381872i
$987$		−	6.03920i		−	0.192230i
$988$	4.57937	−	0.739170i	0.145689	−	0.0235161i
$989$	−0.631673			−0.0200860
$990$		0			0
$991$	−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	$0.616745\pi$
$992$	−2.78006	+	0.490200i	−0.0882670	+	0.0155639i
$993$	2.47167	+	0.435822i	0.0784361	+	0.0138304i
$994$	−7.97090	−	2.90117i	−0.252822	−	0.0920196i
$995$		0			0
$996$	−13.3157	+	23.0634i	−0.421923	+	0.730793i
$997$	27.9760	+	33.3405i	0.886009	+	1.05590i	0.998064	+	0.0622019i	$0.0198123\pi$
$997$	27.9760	+	33.3405i	0.886009	+	1.05590i	−0.112055	+	0.993702i	$0.535743\pi$
$998$	9.65939	+	11.5116i	0.305763	+	0.364394i
$999$	−11.1925	+	19.3860i	−0.354116	+	0.613347i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.a.101.1	✓	6	95.63	odd	36
190.2.k.a.111.1	yes	6	5.3	odd	4
950.2.l.c.101.1		6	95.82	odd	36
950.2.l.c.301.1		6	5.2	odd	4
950.2.u.c.149.1		12	1.1	even	1	trivial
950.2.u.c.149.2		12	5.4	even	2	inner
950.2.u.c.899.1		12	95.44	even	18	inner
950.2.u.c.899.2		12	19.6	even	9	inner
3610.2.a.w.1.3		3	95.33	even	36
3610.2.a.x.1.1		3	95.43	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

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

Introduction

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