LMFDB - Embedded newform 950.2.l.c.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (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:	$7.58578819202$
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:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	950.101
Dual form			950.2.l.c.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-1.43969 - 0.524005i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.43969 - 0.524005i) q^{6} +(-0.347296 + 0.601535i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.500000 - 0.419550i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-1.43969 - 0.524005i) q^{3} +(0.173648 - 0.984808i) q^{4} +(1.43969 - 0.524005i) q^{6} +(-0.347296 + 0.601535i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.500000 - 0.419550i) q^{9} +(1.06031 + 1.83651i) q^{11} +(-0.766044 + 1.32683i) q^{12} +(1.00000 - 0.363970i) q^{13} +(-0.120615 - 0.684040i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(0.233956 - 0.196312i) q^{17} +0.652704 q^{18} +(-4.11721 - 1.43128i) q^{19} +(0.815207 - 0.684040i) q^{21} +(-1.99273 - 0.725293i) q^{22} +(0.162504 - 0.921605i) q^{23} +(-0.266044 - 1.50881i) q^{24} +(-0.532089 + 0.921605i) q^{26} +(2.79813 + 4.84651i) q^{27} +(0.532089 + 0.446476i) q^{28} +(-0.467911 - 0.392624i) q^{29} +(-1.41147 + 2.44474i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.564178 - 3.19961i) q^{33} +(-0.0530334 + 0.300767i) q^{34} +(-0.500000 + 0.419550i) q^{36} +4.00000 q^{37} +(4.07398 - 1.55007i) q^{38} -1.63041 q^{39} +(7.39053 + 2.68993i) q^{41} +(-0.184793 + 1.04801i) q^{42} +(0.117211 + 0.664738i) q^{43} +(1.99273 - 0.725293i) q^{44} +(0.467911 + 0.810446i) q^{46} +(4.34730 + 3.64781i) q^{47} +(1.17365 + 0.984808i) q^{48} +(3.25877 + 5.64436i) q^{49} +(-0.439693 + 0.160035i) q^{51} +(-0.184793 - 1.04801i) q^{52} +(0.467911 - 2.65366i) q^{53} +(-5.25877 - 1.91404i) q^{54} -0.694593 q^{56} +(5.17752 + 4.21805i) q^{57} +0.610815 q^{58} +(7.56805 - 6.35035i) q^{59} +(-1.16250 + 6.59289i) q^{61} +(-0.490200 - 2.78006i) q^{62} +(0.426022 - 0.155059i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.48886 + 2.08840i) q^{66} +(9.71941 + 8.15555i) q^{67} +(-0.152704 - 0.264490i) q^{68} +(-0.716881 + 1.24168i) q^{69} +(2.12061 + 12.0266i) q^{71} +(0.113341 - 0.642788i) q^{72} +(-6.52481 - 2.37484i) q^{73} +(-3.06418 + 2.57115i) q^{74} +(-2.12449 + 3.80612i) q^{76} -1.47296 q^{77} +(1.24897 - 1.04801i) q^{78} +(2.30541 + 0.839100i) q^{79} +(-1.14883 - 6.51536i) q^{81} +(-7.39053 + 2.68993i) q^{82} +(-8.69119 + 15.0536i) q^{83} +(-0.532089 - 0.921605i) q^{84} +(-0.517074 - 0.433877i) q^{86} +(0.467911 + 0.810446i) q^{87} +(-1.06031 + 1.83651i) q^{88} +(15.0680 - 5.48432i) q^{89} +(-0.128356 + 0.727940i) q^{91} +(-0.879385 - 0.320070i) q^{92} +(3.31315 - 2.78006i) q^{93} -5.67499 q^{94} -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} + 6 q^{17} + 6 q^{18} + 6 q^{19} + 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} - 3 q^{36} + 24 q^{37} + 9 q^{38} - 24 q^{39} + 27 q^{41} + 6 q^{42} - 30 q^{43} - 6 q^{44} + 12 q^{46} + 24 q^{47} + 6 q^{48} - 3 q^{49} + 3 q^{51} + 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{57} + 12 q^{58} + 3 q^{59} - 12 q^{61} + 18 q^{63} - 3 q^{64} + 21 q^{66} + 27 q^{67} - 3 q^{68} + 12 q^{69} + 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} - 24 q^{86} + 12 q^{87} - 12 q^{88} + 48 q^{89} + 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 + 6 * q^17 + 6 * q^18 + 6 * q^19 + 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 - 3 * q^36 + 24 * q^37 + 9 * q^38 - 24 * q^39 + 27 * q^41 + 6 * q^42 - 30 * q^43 - 6 * q^44 + 12 * q^46 + 24 * q^47 + 6 * q^48 - 3 * q^49 + 3 * q^51 + 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^57 + 12 * q^58 + 3 * q^59 - 12 * q^61 + 18 * q^63 - 3 * q^64 + 21 * q^66 + 27 * q^67 - 3 * q^68 + 12 * q^69 + 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 - 24 * q^86 + 12 * q^87 - 12 * q^88 + 48 * q^89 + 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	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	$-0.534718\pi$
$3$	−1.43969	−	0.524005i	−0.831207	−	0.302535i	−0.722354	+	0.691523i	$0.756940\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	1.43969	−	0.524005i	0.587752	−	0.213924i
$7$	−0.347296	+	0.601535i	−0.131266	+	0.227359i	−0.924165	−	0.381994i	$-0.875237\pi$
$7$	−0.347296	+	0.601535i	−0.131266	+	0.227359i	0.792899	+	0.609353i	$0.208571\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.500000	−	0.419550i	−0.166667	−	0.139850i
$10$		0			0
$11$	1.06031	+	1.83651i	0.319695	+	0.553727i	0.980424	−	0.196897i	$-0.0630863\pi$
$11$	1.06031	+	1.83651i	0.319695	+	0.553727i	−0.660730	+	0.750624i	$0.729753\pi$
$12$	−0.766044	+	1.32683i	−0.221138	+	0.383022i
$13$	1.00000	−	0.363970i	0.277350	−	0.100947i	−0.199600	−	0.979877i	$-0.563964\pi$
$13$	1.00000	−	0.363970i	0.277350	−	0.100947i	0.476950	+	0.878930i	$0.341742\pi$
$14$	−0.120615	−	0.684040i	−0.0322357	−	0.182817i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.233956	−	0.196312i	0.0567426	−	0.0476127i	−0.613975	−	0.789325i	$-0.710431\pi$
$17$	0.233956	−	0.196312i	0.0567426	−	0.0476127i	0.670718	+	0.741713i	$0.265986\pi$
$18$	0.652704			0.153844
$19$	−4.11721	−	1.43128i	−0.944553	−	0.328359i
$19$	−4.11721	−	1.43128i	−0.944553	−	0.328359i
$20$		0			0
$21$	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	$-0.913339\pi$
$23$	0.162504	−	0.921605i	0.0338844	−	0.192168i	0.997051	+	0.0767357i	$0.0244498\pi$
$24$	−0.266044	−	1.50881i	−0.0543061	−	0.307985i
$25$		0			0
$26$	−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	0.598309	−	0.801266i	$-0.295840\pi$
$29$	−0.467911	−	0.392624i	−0.0868889	−	0.0729085i	−0.685198	+	0.728357i	$0.740284\pi$
$30$		0			0
$31$	−1.41147	+	2.44474i	−0.253508	+	0.439089i	−0.964489	−	0.264122i	$-0.914918\pi$
$31$	−1.41147	+	2.44474i	−0.253508	+	0.439089i	0.710981	+	0.703211i	$0.248251\pi$
$32$	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			0
$36$	−0.500000	+	0.419550i	−0.0833333	+	0.0699250i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	4.07398	−	1.55007i	0.660886	−	0.251454i
$39$	−1.63041			−0.261075
$40$		0			0
$41$	7.39053	+	2.68993i	1.15421	+	0.420097i	0.847025	−	0.531554i	$-0.178392\pi$
$41$	7.39053	+	2.68993i	1.15421	+	0.420097i	0.307182	+	0.951651i	$0.400614\pi$
$42$	−0.184793	+	1.04801i	−0.0285141	+	0.161712i
$43$	0.117211	+	0.664738i	0.0178745	+	0.101372i	0.992440	−	0.122732i	$-0.0391656\pi$
$43$	0.117211	+	0.664738i	0.0178745	+	0.101372i	−0.974565	+	0.224104i	$0.928055\pi$
$44$	1.99273	−	0.725293i	0.300415	−	0.109342i
$45$		0			0
$46$	0.467911	+	0.810446i	0.0689897	+	0.119494i
$47$	4.34730	+	3.64781i	0.634118	+	0.532088i	0.902206	−	0.431306i	$-0.141947\pi$
$47$	4.34730	+	3.64781i	0.634118	+	0.532088i	−0.268087	+	0.963395i	$0.586392\pi$
$48$	1.17365	+	0.984808i	0.169402	+	0.142145i
$49$	3.25877	+	5.64436i	0.465539	+	0.806337i
$50$		0			0
$51$	−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	−0.935660	−	0.352902i	$-0.885195\pi$
$53$	0.467911	−	2.65366i	0.0642725	−	0.364508i	0.999933	−	0.0116052i	$-0.00369414\pi$
$54$	−5.25877	−	1.91404i	−0.715628	−	0.260467i
$55$		0			0
$56$	−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	0.000398990	−	1.00000i	$-0.499873\pi$
$59$	7.56805	−	6.35035i	0.985276	−	0.826745i	0.984877	+	0.173255i	$0.0554286\pi$
$60$		0			0
$61$	−1.16250	+	6.59289i	−0.148843	+	0.844133i	0.815357	+	0.578958i	$0.196541\pi$
$61$	−1.16250	+	6.59289i	−0.148843	+	0.844133i	−0.964200	+	0.265174i	$0.914570\pi$
$62$	−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			0
$66$	2.48886	+	2.08840i	0.306357	+	0.257064i
$67$	9.71941	+	8.15555i	1.18741	+	0.996359i	0.999901	+	0.0140972i	$0.00448744\pi$
$67$	9.71941	+	8.15555i	1.18741	+	0.996359i	0.187514	+	0.982262i	$0.439957\pi$
$68$	−0.152704	−	0.264490i	−0.0185180	−	0.0320742i
$69$	−0.716881	+	1.24168i	−0.0863024	+	0.149480i
$70$		0			0
$71$	2.12061	+	12.0266i	0.251671	+	1.42730i	0.804476	+	0.593985i	$0.202446\pi$
$71$	2.12061	+	12.0266i	0.251671	+	1.42730i	−0.552805	+	0.833310i	$0.686443\pi$
$72$	0.113341	−	0.642788i	0.0133573	−	0.0757532i
$73$	−6.52481	−	2.37484i	−0.763672	−	0.277954i	−0.0693248	−	0.997594i	$-0.522084\pi$
$73$	−6.52481	−	2.37484i	−0.763672	−	0.277954i	−0.694347	+	0.719640i	$0.744307\pi$
$74$	−3.06418	+	2.57115i	−0.356203	+	0.298890i
$75$		0			0
$76$	−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	0.468436	−	0.883497i	$-0.344817\pi$
$79$	2.30541	+	0.839100i	0.259379	+	0.0944061i	−0.209058	+	0.977903i	$0.567040\pi$
$80$		0			0
$81$	−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	−0.217301	+	0.976105i	$0.569725\pi$
$83$	−8.69119	+	15.0536i	−0.953982	+	1.65235i	−0.736681	+	0.676241i	$0.763608\pi$
$84$	−0.532089	−	0.921605i	−0.0580557	−	0.100555i
$85$		0			0
$86$	−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	0.618356	−	0.785898i	$-0.287799\pi$
$89$	15.0680	−	5.48432i	1.59721	−	0.581337i	0.978854	+	0.204561i	$0.0655767\pi$
$90$		0			0
$91$	−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			0
$96$	−1.53209			−0.156368
$97$	−4.77584	+	4.00741i	−0.484914	+	0.406891i	−0.852199	−	0.523217i	$-0.824732\pi$
$97$	−4.77584	+	4.00741i	−0.484914	+	0.406891i	0.367286	+	0.930108i	$0.380287\pi$
$98$	−6.12449	−	2.22913i	−0.618666	−	0.225176i
$99$	0.240352	−	1.36310i	0.0241563	−	0.136997i
$100$		0			0
$101$	13.5030	−	4.91469i	1.34360	−	0.489030i	0.432654	−	0.901560i	$-0.357577\pi$
$101$	13.5030	−	4.91469i	1.34360	−	0.489030i	0.910944	+	0.412530i	$0.135355\pi$
$102$	0.233956	−	0.405223i	0.0231651	−	0.0401230i
$103$	9.80066	+	16.9752i	0.965688	+	1.67262i	0.707756	+	0.706457i	$0.249708\pi$
$103$	9.80066	+	16.9752i	0.965688	+	1.67262i	0.257932	+	0.966163i	$0.416959\pi$
$104$	0.815207	+	0.684040i	0.0799377	+	0.0670757i
$105$		0			0
$106$	1.34730	+	2.33359i	0.130861	+	0.226658i
$107$	1.03209	−	1.78763i	0.0997758	−	0.172817i	−0.811816	−	0.583913i	$-0.801521\pi$
$107$	1.03209	−	1.78763i	0.0997758	−	0.172817i	0.911592	+	0.411097i	$0.134854\pi$
$108$	5.25877	−	1.91404i	0.506025	−	0.184178i
$109$	1.58172	+	8.97037i	0.151501	+	0.859206i	0.961915	+	0.273348i	$0.0881311\pi$
$109$	1.58172	+	8.97037i	0.151501	+	0.859206i	−0.810414	+	0.585858i	$0.800758\pi$
$110$		0			0
$111$	−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	$-0.609732\pi$
$113$	−7.18479			−0.675888			−0.337944	+	0.941166i	$0.609732\pi$
$114$	−6.67752	+	0.0968323i	−0.625407	+	0.00906917i
$115$		0			0
$116$	−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
$120$		0			0
$121$	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			0
$126$	−0.226682	+	0.392624i	−0.0201944	+	0.0349777i
$127$	−1.53209	+	0.557635i	−0.135951	+	0.0494821i	−0.409100	−	0.912490i	$-0.634157\pi$
$127$	−1.53209	+	0.557635i	−0.135951	+	0.0494821i	0.273149	+	0.961972i	$0.411935\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	0.179578	−	1.01844i	0.0158110	−	0.0896684i
$130$		0			0
$131$	−7.40033	+	6.20961i	−0.646570	+	0.542536i	−0.906028	−	0.423218i	$-0.860900\pi$
$131$	−7.40033	+	6.20961i	−0.646570	+	0.542536i	0.259458	+	0.965754i	$0.416456\pi$
$132$	−3.24897			−0.282787
$133$	2.29086	−	1.97957i	0.198643	−	0.171650i
$134$	−12.6878			−1.09606
$135$		0			0
$136$	0.286989	+	0.104455i	0.0246091	+	0.00895698i
$137$	2.00253	−	11.3569i	0.171087	−	0.970285i	−0.771476	−	0.636258i	$-0.780481\pi$
$137$	2.00253	−	11.3569i	0.171087	−	0.970285i	0.942564	−	0.334027i	$-0.108408\pi$
$138$	−0.248970	−	1.41198i	−0.0211938	−	0.120196i
$139$	−6.43242	+	2.34121i	−0.545591	+	0.198579i	−0.600086	−	0.799935i	$-0.704867\pi$
$139$	−6.43242	+	2.34121i	−0.545591	+	0.198579i	0.0544957	+	0.998514i	$0.482645\pi$
$140$		0			0
$141$	−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			0
$146$	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	0.661277	−	0.750142i	$-0.270015\pi$
$149$	8.36959	+	3.04628i	0.685663	+	0.249561i	0.0243859	+	0.999703i	$0.492237\pi$
$150$		0			0
$151$	−10.8229			−0.880759			−0.440380	−	0.897812i	$-0.645156\pi$
$151$	−10.8229			−0.880759			−0.440380	+	0.897812i	$0.645156\pi$
$152$	−0.819078	−	4.28125i	−0.0664360	−	0.347255i
$153$	−0.199340			−0.0161157
$154$	1.12836	−	0.946803i	0.0909255	−	0.0762955i
$155$		0			0
$156$	−0.283119	+	1.60565i	−0.0226676	+	0.128555i
$157$	−1.85710	−	10.5321i	−0.148212	−	0.840555i	−0.964731	−	0.263236i	$-0.915210\pi$
$157$	−1.85710	−	10.5321i	−0.148212	−	0.840555i	0.816519	−	0.577319i	$-0.195901\pi$
$158$	−2.30541	+	0.839100i	−0.183408	+	0.0667552i
$159$	−2.06418	+	3.57526i	−0.163700	+	0.283537i
$160$		0			0
$161$	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	$-0.135854\pi$
$163$	1.23396	+	2.13727i	0.0966509	+	0.167404i	−0.813646	+	0.581361i	$0.802520\pi$
$164$	3.93242	−	6.81115i	0.307070	−	0.531861i
$165$		0			0
$166$	−3.01842	−	17.1183i	−0.234275	−	1.32864i
$167$	2.11381	−	11.9880i	0.163571	−	0.927659i	−0.786954	−	0.617012i	$-0.788343\pi$
$167$	2.11381	−	11.9880i	0.163571	−	0.927659i	0.950525	−	0.310647i	$-0.100546\pi$
$168$	1.00000	+	0.363970i	0.0771517	+	0.0280809i
$169$	−9.09105	+	7.62830i	−0.699312	+	0.586792i
$170$		0			0
$171$	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	$-0.542389\pi$
$173$	10.7888	−	9.05288i	0.820257	−	0.688278i	0.953032	+	0.302869i	$0.0979443\pi$
$174$	−0.879385	−	0.320070i	−0.0666660	−	0.0242644i
$175$		0			0
$176$	−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	0.634828	−	0.772653i	$-0.281071\pi$
$179$	−4.70574	−	8.15058i	−0.351723	−	0.609203i	−0.986552	+	0.163451i	$0.947738\pi$
$180$		0			0
$181$	−18.7442	−	15.7283i	−1.39325	−	1.16907i	−0.964005	−	0.265884i	$-0.914336\pi$
$181$	−18.7442	−	15.7283i	−1.39325	−	1.16907i	−0.429242	−	0.903190i	$-0.641219\pi$
$182$	−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			0
$186$	−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
$190$		0			0
$191$	−2.04458			−0.147940			−0.0739702	−	0.997260i	$-0.523567\pi$
$191$	−2.04458			−0.147940			−0.0739702	+	0.997260i	$0.523567\pi$
$192$	1.17365	−	0.984808i	0.0847008	−	0.0710724i
$193$	13.4427	+	4.89274i	0.967626	+	0.352187i	0.777017	−	0.629479i	$-0.216732\pi$
$193$	13.4427	+	4.89274i	0.967626	+	0.352187i	0.190608	+	0.981666i	$0.438954\pi$
$194$	1.08260	−	6.13971i	0.0777259	−	0.440805i
$195$		0			0
$196$	6.12449	−	2.22913i	0.437463	−	0.159224i
$197$	6.98545	−	12.0992i	0.497693	−	0.862029i	−0.502304	−	0.864691i	$-0.667514\pi$
$197$	6.98545	−	12.0992i	0.497693	−	0.862029i	0.999996	+	0.00266202i	$0.000847348\pi$
$198$	0.692066	+	1.19869i	0.0491830	+	0.0851875i
$199$	14.4311	+	12.1091i	1.02299	+	0.858392i	0.990001	−	0.141064i	$-0.0450522\pi$
$199$	14.4311	+	12.1091i	1.02299	+	0.858392i	0.0329912	+	0.999456i	$0.489497\pi$
$200$		0			0
$201$	−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
$205$		0			0
$206$	−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
$210$		0			0
$211$	−0.211667	+	0.177610i	−0.0145717	+	0.0122271i	−0.650044	−	0.759896i	$-0.725250\pi$
$211$	−0.211667	+	0.177610i	−0.0145717	+	0.0122271i	0.635473	+	0.772123i	$0.280805\pi$
$212$	−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			0
$216$	−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
$220$		0			0
$221$	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	0.998270	+	0.0587999i	$0.0187274\pi$
$223$	1.19934	+	6.80180i	0.0803138	+	0.455482i	−0.917956	+	0.396682i	$0.870162\pi$
$224$	−0.120615	+	0.684040i	−0.00805891	+	0.0457044i
$225$		0			0
$226$	5.50387	−	4.61830i	0.366112	−	0.307204i
$227$	−2.30272			−0.152837			−0.0764184	−	0.997076i	$-0.524348\pi$
$227$	−2.30272			−0.152837			−0.0764184	+	0.997076i	$0.524348\pi$
$228$	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			0
$231$	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	−0.899275	−	0.437383i	$-0.855905\pi$
$233$	−3.11128	−	17.6450i	−0.203827	−	1.15596i	0.695448	−	0.718576i	$-0.255206\pi$
$234$	0.652704	−	0.237565i	0.0426686	−	0.0155301i
$235$		0			0
$236$	−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	0.956115	−	0.292990i	$-0.0946504\pi$
$239$	3.46791	+	6.00660i	0.224321	+	0.388535i	−0.731795	+	0.681525i	$0.761317\pi$
$240$		0			0
$241$	16.7160	−	6.08413i	1.07677	−	0.391913i	0.258067	−	0.966127i	$-0.416914\pi$
$241$	16.7160	−	6.08413i	1.07677	−	0.391913i	0.818705	+	0.574214i	$0.194692\pi$
$242$	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
$245$		0			0
$246$	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			0
$251$	−2.89915	+	16.4419i	−0.182993	+	1.03780i	0.745515	+	0.666489i	$0.232204\pi$
$251$	−2.89915	+	16.4419i	−0.182993	+	1.03780i	−0.928508	+	0.371314i	$0.878907\pi$
$252$	−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			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	20.0043	+	16.7856i	1.24784	+	1.04706i	0.996870	+	0.0790632i	$0.0251929\pi$
$257$	20.0043	+	16.7856i	1.24784	+	1.04706i	0.250967	+	0.967996i	$0.419252\pi$
$258$	0.517074	+	0.895599i	0.0321916	+	0.0557575i
$259$	−1.38919	+	2.40614i	−0.0863198	+	0.149510i
$260$		0			0
$261$	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	$-0.514801\pi$
$263$	−11.7442	−	4.27455i	−0.724180	−	0.263580i	−0.677699	+	0.735339i	$0.737023\pi$
$264$	2.48886	−	2.08840i	0.153178	−	0.128532i
$265$		0			0
$266$	−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	0.318337	−	0.947977i	$-0.396875\pi$
$269$	−0.773318	−	0.281465i	−0.0471501	−	0.0171612i	−0.365488	+	0.930816i	$0.619098\pi$
$270$		0			0
$271$	−2.09833	−	11.9002i	−0.127464	−	0.722886i	−0.979814	−	0.199913i	$-0.935934\pi$
$271$	−2.09833	−	11.9002i	−0.127464	−	0.722886i	0.852349	−	0.522973i	$-0.175177\pi$
$272$	−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
$275$		0			0
$276$	1.09833	+	0.921605i	0.0661115	+	0.0554741i
$277$	−5.63041	−	9.75216i	−0.338299	−	0.585951i	0.645814	−	0.763495i	$-0.276518\pi$
$277$	−5.63041	−	9.75216i	−0.338299	−	0.585951i	−0.984113	+	0.177544i	$0.943185\pi$
$278$	3.42262	−	5.92815i	0.205275	−	0.355547i
$279$	1.73143	−	0.630189i	0.103658	−	0.0377284i
$280$		0			0
$281$	4.55185	−	25.8148i	0.271541	−	1.53998i	−0.478199	−	0.878251i	$-0.658710\pi$
$281$	4.55185	−	25.8148i	0.271541	−	1.53998i	0.749740	−	0.661732i	$-0.230179\pi$
$282$	8.17024	+	2.97373i	0.486531	+	0.177083i
$283$	−19.7160	+	16.5437i	−1.17199	+	0.983420i	−0.999999	−	0.00167722i	$-0.999466\pi$
$283$	−19.7160	+	16.5437i	−1.17199	+	0.983420i	−0.171996	+	0.985098i	$0.555022\pi$
$284$	12.2121			0.724657
$285$		0			0
$286$	−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			0
$291$	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	0.935182	+	0.354166i	$0.115235\pi$
$293$	13.2540	+	22.9566i	0.774308	+	1.34114i	−0.160874	+	0.986975i	$0.551431\pi$
$294$	7.64930	+	6.41852i	0.446116	+	0.374336i
$295$		0			0
$296$	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			0
$301$	−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
$305$		0			0
$306$	0.152704	−	0.128134i	0.00872949	−	0.00732491i
$307$	2.99273	+	1.08926i	0.170804	+	0.0621675i	0.426007	−	0.904720i	$-0.359920\pi$
$307$	2.99273	+	1.08926i	0.170804	+	0.0621675i	−0.255203	+	0.966888i	$0.582142\pi$
$308$	−0.255777	+	1.45059i	−0.0145743	+	0.0826548i
$309$	−5.21482	−	29.5747i	−0.296661	−	1.68245i
$310$		0			0
$311$	−0.411474	+	0.712694i	−0.0233326	+	0.0404132i	−0.877456	−	0.479657i	$-0.840761\pi$
$311$	−0.411474	+	0.712694i	−0.0233326	+	0.0404132i	0.854123	+	0.520070i	$0.174094\pi$
$312$	−0.815207	−	1.41198i	−0.0461520	−	0.0799377i
$313$	−16.7672	−	14.0694i	−0.947740	−	0.795248i	0.0311758	−	0.999514i	$-0.490075\pi$
$313$	−16.7672	−	14.0694i	−0.947740	−	0.795248i	−0.978915	+	0.204266i	$0.934519\pi$
$314$	8.19253	+	6.87435i	0.462331	+	0.387942i
$315$		0			0
$316$	1.22668	−	2.12467i	0.0690062	−	0.119522i
$317$	−12.4243	+	4.52206i	−0.697816	+	0.253984i	−0.666478	−	0.745524i	$-0.732199\pi$
$317$	−12.4243	+	4.52206i	−0.697816	+	0.253984i	−0.0313381	+	0.999509i	$0.509977\pi$
$318$	−0.716881	−	4.06564i	−0.0402007	−	0.227990i
$319$	0.224927	−	1.27562i	0.0125935	−	0.0714212i
$320$		0			0
$321$	−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			0
$326$	−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
$330$		0			0
$331$	−0.819078	−	1.41868i	−0.0450206	−	0.0779780i	0.842637	−	0.538482i	$-0.181002\pi$
$331$	−0.819078	−	1.41868i	−0.0450206	−	0.0779780i	−0.887658	+	0.460504i	$0.847669\pi$
$332$	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
$335$		0			0
$336$	−1.00000	+	0.363970i	−0.0545545	+	0.0198562i
$337$	5.44134	+	30.8594i	0.296409	+	1.68102i	0.661421	+	0.750015i	$0.269954\pi$
$337$	5.44134	+	30.8594i	0.296409	+	1.68102i	−0.365012	+	0.931003i	$0.618935\pi$
$338$	2.06077	−	11.6872i	0.112091	−	0.635702i
$339$	10.3439	+	3.76487i	0.561803	+	0.204480i
$340$		0			0
$341$	−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
$345$		0			0
$346$	−2.44562	+	13.8698i	−0.131477	+	0.745646i
$347$	−4.41534	−	25.0407i	−0.237028	−	1.34425i	−0.838300	−	0.545209i	$-0.816450\pi$
$347$	−4.41534	−	25.0407i	−0.237028	−	1.34425i	0.601272	−	0.799044i	$-0.294661\pi$
$348$	0.879385	−	0.320070i	0.0471400	−	0.0171576i
$349$	−16.0993	+	27.8847i	−0.861774	+	1.49264i	0.00844186	+	0.999964i	$0.497313\pi$
$349$	−16.0993	+	27.8847i	−0.861774	+	1.49264i	−0.870215	+	0.492671i	$0.836020\pi$
$350$		0			0
$351$	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	0.999101	+	0.0423828i	$0.0134949\pi$
$353$	10.0753	+	17.4510i	0.536255	+	0.928821i	−0.462846	+	0.886439i	$0.653172\pi$
$354$	7.56805	−	13.1082i	0.402237	−	0.696695i
$355$		0			0
$356$	−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	−0.571362	−	0.820698i	$-0.693585\pi$
$359$	2.60813	−	2.18848i	0.137652	−	0.115503i	0.709014	+	0.705195i	$0.249140\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	1.78106	+	10.1009i	0.0930975	+	0.527982i
$367$	7.41147	−	2.69756i	0.386876	−	0.140811i	−0.141257	−	0.989973i	$-0.545114\pi$
$367$	7.41147	−	2.69756i	0.386876	−	0.140811i	0.528133	+	0.849162i	$0.322892\pi$
$368$	−0.467911	+	0.810446i	−0.0243916	+	0.0422474i
$369$	−2.56670	−	4.44566i	−0.133617	−	0.231432i
$370$		0			0
$371$	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	−0.353846	−	0.935304i	$-0.615126\pi$
$373$	12.2267	−	21.1772i	0.633074	−	1.09652i	0.986920	−	0.161212i	$-0.0515403\pi$
$374$	−0.608593	+	0.221510i	−0.0314696	+	0.0114540i
$375$		0			0
$376$	−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	$0.834877\pi$
$380$		0			0
$381$	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	$-0.0979769\pi$
$383$	29.1266	+	10.6012i	1.48830	+	0.541697i	0.535298	+	0.844663i	$0.320199\pi$
$384$	−0.266044	+	1.50881i	−0.0135765	+	0.0769963i
$385$		0			0
$386$	−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	−0.993503	−	0.113803i	$-0.963697\pi$
$389$	−25.2080	−	21.1520i	−1.27810	−	1.07245i	−0.284594	−	0.958648i	$-0.591859\pi$
$390$		0			0
$391$	−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			0
$396$	−1.30066	−	0.473401i	−0.0653606	−	0.0237893i
$397$	−8.90941	+	7.47589i	−0.447151	+	0.375204i	−0.838377	−	0.545090i	$-0.816495\pi$
$397$	−8.90941	+	7.47589i	−0.447151	+	0.375204i	0.391227	+	0.920294i	$0.372051\pi$
$398$	−18.8384			−0.944285
$399$	−4.33544	+	1.64955i	−0.217043	+	0.0825806i
$400$		0			0
$401$	−10.3191	+	8.65873i	−0.515310	+	0.432397i	−0.862993	−	0.505216i	$-0.831413\pi$
$401$	−10.3191	+	8.65873i	−0.515310	+	0.432397i	0.347683	+	0.937612i	$0.386969\pi$
$402$	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
$405$		0			0
$406$	−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	0.872905	−	0.487891i	$-0.162234\pi$
$409$	11.0018	+	9.23162i	0.544005	+	0.456474i	−0.328900	+	0.944365i	$0.606678\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	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			0
$421$	12.3969	+	4.51211i	0.604189	+	0.219907i	0.625959	−	0.779856i	$-0.284708\pi$
$421$	12.3969	+	4.51211i	0.604189	+	0.219907i	−0.0217696	+	0.999763i	$0.506930\pi$
$422$	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			0
$426$	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			0
$431$	−4.49020	+	1.63430i	−0.216285	+	0.0787214i	−0.447890	−	0.894088i	$-0.647825\pi$
$431$	−4.49020	+	1.63430i	−0.216285	+	0.0787214i	0.231605	+	0.972810i	$0.425602\pi$
$432$	−0.971782	−	5.51125i	−0.0467549	−	0.265160i
$433$	−4.87433	+	27.6437i	−0.234245	+	1.32847i	0.609951	+	0.792439i	$0.291189\pi$
$433$	−4.87433	+	27.6437i	−0.234245	+	1.32847i	−0.844197	+	0.536033i	$0.819922\pi$
$434$	1.84255	+	0.670633i	0.0884452	+	0.0321914i
$435$		0			0
$436$	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	−0.107439	−	0.994212i	$-0.534265\pi$
$439$	17.8726	−	14.9969i	0.853012	−	0.715762i	0.960451	+	0.278450i	$0.0898206\pi$
$440$		0			0
$441$	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	$-0.495539\pi$
$443$	14.0488	−	5.11333i	0.667476	−	0.242942i	0.653461	+	0.756960i	$0.273316\pi$
$444$	−3.06418	+	5.30731i	−0.145419	+	0.251874i
$445$		0			0
$446$	−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	−0.742939	−	0.669359i	$-0.766569\pi$
$449$	4.41194	−	7.64171i	0.208212	−	0.360634i	0.951151	+	0.308725i	$0.0999022\pi$
$450$		0			0
$451$	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			0
$456$	−1.06418	+	6.59289i	−0.0498347	+	0.308740i
$457$	−19.4561			−0.910116			−0.455058	−	0.890462i	$-0.650381\pi$
$457$	−19.4561			−0.910116			−0.455058	+	0.890462i	$0.650381\pi$
$458$	17.0155	−	14.2777i	0.795081	−	0.667152i
$459$	1.60607	+	0.584561i	0.0749648	+	0.0272849i
$460$		0			0
$461$	4.56624	+	25.8964i	0.212671	+	1.20612i	0.884903	+	0.465776i	$0.154225\pi$
$461$	4.56624	+	25.8964i	0.212671	+	1.20612i	−0.672232	+	0.740341i	$0.734664\pi$
$462$	−2.12061	+	0.771841i	−0.0986599	+	0.0359093i
$463$	−17.0993	+	29.6168i	−0.794670	+	1.37641i	0.128379	+	0.991725i	$0.459023\pi$
$463$	−17.0993	+	29.6168i	−0.794670	+	1.37641i	−0.923049	+	0.384684i	$0.874311\pi$
$464$	0.305407	+	0.528981i	0.0141782	+	0.0245573i
$465$		0			0
$466$	13.7253	+	11.5169i	0.635814	+	0.533511i
$467$	−0.00340357	−	0.00589515i	−0.000157498	−	0.000272795i	0.865947	−	0.500136i	$-0.166717\pi$
$467$	−0.00340357	−	0.00589515i	−0.000157498	−	0.000272795i	−0.866104	+	0.499864i	$0.833383\pi$
$468$	−0.347296	+	0.601535i	−0.0160538	+	0.0278060i
$469$	−8.28136	+	3.01417i	−0.382398	+	0.139181i
$470$		0			0
$471$	−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
$475$		0			0
$476$	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	−0.824875	−	0.565315i	$-0.808755\pi$
$479$	3.14290	−	17.8243i	0.143603	−	0.814413i	0.968478	−	0.249098i	$-0.0801341\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	3.32635	+	5.76141i	0.150886	+	0.261343i
$487$	0.369585	−	0.640140i	0.0167475	−	0.0290075i	−0.857530	−	0.514434i	$-0.828002\pi$
$487$	0.369585	−	0.640140i	0.0167475	−	0.0290075i	0.874278	+	0.485426i	$0.161336\pi$
$488$	−6.29086	+	2.28969i	−0.284774	+	0.103649i
$489$	−0.656574	−	3.72362i	−0.0296913	−	0.168388i
$490$		0			0
$491$	11.6566	+	4.24265i	0.526054	+	0.191468i	0.591375	−	0.806396i	$-0.298585\pi$
$491$	11.6566	+	4.24265i	0.526054	+	0.191468i	−0.0653217	+	0.997864i	$0.520807\pi$
$492$	−9.23055	+	7.74535i	−0.416145	+	0.349187i
$493$	−0.186547			−0.00840166
$494$	3.50980	−	3.03287i	0.157913	−	0.136455i
$495$		0			0
$496$	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	−0.985835	−	0.167718i	$-0.946360\pi$
$499$	−2.60947	−	14.7990i	−0.116816	−	0.662496i	0.869019	−	0.494778i	$-0.164751\pi$
$500$		0			0
$501$	−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	$-0.272739\pi$
$503$	0.543948	+	0.456427i	0.0242535	+	0.0203511i	−0.630580	+	0.776124i	$0.717183\pi$
$504$	0.347296	+	0.291416i	0.0154698	+	0.0129807i
$505$		0			0
$506$	−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	−0.615201	−	0.788370i	$-0.710925\pi$
$509$	5.24628	−	29.7531i	0.232537	−	1.31878i	0.847738	−	0.530415i	$-0.177964\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	−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			0
$521$	10.2390	+	17.7345i	0.448579	+	0.776962i	0.998294	−	0.0583907i	$-0.0185969\pi$
$521$	10.2390	+	17.7345i	0.448579	+	0.776962i	−0.549715	+	0.835352i	$0.685264\pi$
$522$	−0.305407	−	0.256267i	−0.0133673	−	0.0112165i
$523$	−11.9554	−	10.0318i	−0.522774	−	0.438660i	0.342823	−	0.939400i	$-0.388617\pi$
$523$	−11.9554	−	10.0318i	−0.522774	−	0.438660i	−0.865598	+	0.500740i	$0.833061\pi$
$524$	4.83022	+	8.36619i	0.211009	+	0.365479i
$525$		0			0
$526$	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
$530$		0			0
$531$	−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
$535$		0			0
$536$	−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
$540$		0			0
$541$	1.91353	+	1.60565i	0.0822692	+	0.0690321i	0.682995	−	0.730423i	$-0.260677\pi$
$541$	1.91353	+	1.60565i	0.0822692	+	0.0690321i	−0.600726	+	0.799455i	$0.705122\pi$
$542$	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
$545$		0			0
$546$	0.196652	+	1.11527i	0.00841593	+	0.0477291i
$547$	0.628766	−	3.56591i	0.0268841	−	0.152467i	−0.968411	−	0.249361i	$-0.919780\pi$
$547$	0.628766	−	3.56591i	0.0268841	−	0.152467i	0.995295	+	0.0968935i	$0.0308906\pi$
$548$	−10.8366	−	3.94421i	−0.462917	−	0.168488i
$549$	3.34730	−	2.80872i	0.142859	−	0.119873i
$550$		0			0
$551$	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
$555$		0			0
$556$	1.18866	+	6.74124i	0.0504105	+	0.285892i
$557$	−10.4338	+	3.79758i	−0.442093	+	0.160909i	−0.553469	−	0.832870i	$-0.686696\pi$
$557$	−10.4338	+	3.79758i	−0.442093	+	0.160909i	0.111376	+	0.993778i	$0.464474\pi$
$558$	−0.921274	+	1.59569i	−0.0390007	+	0.0675511i
$559$	0.359156	+	0.622076i	0.0151907	+	0.0263110i
$560$		0			0
$561$	−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	$-0.747460\pi$
$563$	6.32383	−	10.9532i	0.266517	−	0.461622i	0.967960	+	0.251104i	$0.0807937\pi$
$564$	−8.17024	+	2.97373i	−0.344029	+	0.125216i
$565$		0			0
$566$	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	$0.504698\pi$
$570$		0			0
$571$	10.3396			0.432697			0.216348	−	0.976316i	$-0.430585\pi$
$571$	10.3396			0.432697			0.216348	+	0.976316i	$0.430585\pi$
$572$	1.72874	−	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			0
$576$	0.613341	−	0.223238i	0.0255559	−	0.00930157i
$577$	0.769448	−	1.33272i	0.0320325	−	0.0554820i	−0.849565	−	0.527484i	$-0.823135\pi$
$577$	0.769448	−	1.33272i	0.0320325	−	0.0554820i	0.881597	+	0.472002i	$0.156469\pi$
$578$	−8.45336	−	14.6417i	−0.351614	−	0.609013i
$579$	−16.7895	−	14.0881i	−0.697748	−	0.585480i
$580$		0			0
$581$	−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			0
$586$	−24.9094	−	9.06629i	−1.02900	−	0.374525i
$587$	5.27173	−	4.42350i	0.217587	−	0.182578i	−0.527478	−	0.849568i	$-0.676862\pi$
$587$	5.27173	−	4.42350i	0.217587	−	0.182578i	0.745066	+	0.666991i	$0.232418\pi$
$588$	−9.98545			−0.411793
$589$	9.31046	−	8.04531i	0.383631	−	0.331501i
$590$		0			0
$591$	−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	$-0.917189\pi$
$593$	0.723278	−	4.10191i	0.0297015	−	0.168445i	0.996050	+	0.0887893i	$0.0282998\pi$
$594$	−2.06077	−	11.6872i	−0.0845546	−	0.479533i
$595$		0			0
$596$	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	0.943033	+	0.332698i	$0.107959\pi$
$599$	35.1070	+	29.4583i	1.43443	+	1.20363i	0.491400	+	0.870934i	$0.336485\pi$
$600$		0			0
$601$	1.05257	−	1.82310i	0.0429351	−	0.0743658i	−0.843759	−	0.536722i	$-0.819662\pi$
$601$	1.05257	−	1.82310i	0.0429351	−	0.0743658i	0.886694	+	0.462356i	$0.152996\pi$
$602$	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
$605$		0			0
$606$	16.8648	−	14.1513i	0.685087	−	0.574856i
$607$	26.7648			1.08635			0.543174	−	0.839620i	$-0.317222\pi$
$607$	26.7648			1.08635			0.543174	+	0.839620i	$0.317222\pi$
$608$	−4.35844	+	0.0632028i	−0.176758	+	0.00256321i
$609$	−0.650015			−0.0263399
$610$		0			0
$611$	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	−0.722401	−	0.691475i	$-0.756961\pi$
$613$	−6.93407	−	39.3251i	−0.280064	−	1.58832i	0.442336	−	0.896849i	$-0.354150\pi$
$614$	−2.99273	+	1.08926i	−0.120777	+	0.0439591i
$615$		0			0
$616$	−0.736482	−	1.27562i	−0.0296737	−	0.0513963i
$617$	30.1575	+	25.3052i	1.21410	+	1.01875i	0.999112	+	0.0421294i	$0.0134142\pi$
$617$	30.1575	+	25.3052i	1.21410	+	1.01875i	0.214983	+	0.976618i	$0.431030\pi$
$618$	23.0051	+	19.3035i	0.925399	+	0.776502i
$619$	14.5273	+	25.1621i	0.583903	+	1.01135i	0.995011	+	0.0997633i	$0.0318086\pi$
$619$	14.5273	+	25.1621i	0.583903	+	1.01135i	−0.411108	+	0.911587i	$0.634858\pi$
$620$		0			0
$621$	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			0
$626$	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			0
$631$	5.72369	−	32.4607i	0.227856	−	1.29224i	−0.629292	−	0.777169i	$-0.716655\pi$
$631$	5.72369	−	32.4607i	0.227856	−	1.29224i	0.857149	−	0.515069i	$-0.172234\pi$
$632$	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			0
$636$	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			0
$641$	3.77214	+	21.3928i	0.148990	+	0.844967i	0.964076	+	0.265626i	$0.0855787\pi$
$641$	3.77214	+	21.3928i	0.148990	+	0.844967i	−0.815086	+	0.579340i	$0.803310\pi$
$642$	0.549163	−	3.11446i	0.0216737	−	0.122918i
$643$	39.6400	+	14.4278i	1.56325	+	0.568976i	0.971478	−	0.237131i	$-0.0762071\pi$
$643$	39.6400	+	14.4278i	1.56325	+	0.568976i	0.591770	+	0.806107i	$0.298429\pi$
$644$	0.497941	−	0.417822i	0.0196216	−	0.0164645i
$645$		0			0
$646$	0.648833	−	1.16242i	0.0255280	−	0.0457347i
$647$	−45.2526			−1.77906			−0.889531	−	0.456874i	$-0.848969\pi$
$647$	−45.2526			−1.77906			−0.889531	+	0.456874i	$0.848969\pi$
$648$	5.06805	−	4.25260i	0.199092	−	0.167058i
$649$	19.6869	+	7.16545i	0.772779	+	0.281268i
$650$		0			0
$651$	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	$-0.771016\pi$
$653$	4.97090	−	8.60986i	0.194527	−	0.336930i	0.946745	+	0.321984i	$0.104350\pi$
$654$	6.97771	+	12.0858i	0.272850	+	0.472590i
$655$		0			0
$656$	−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	−0.707496	−	0.706717i	$-0.750175\pi$
$659$	−20.4136	+	7.42994i	−0.795201	+	0.289429i	−0.0877044	+	0.996147i	$0.527953\pi$
$660$		0			0
$661$	4.99319	−	28.3178i	0.194213	−	1.10143i	−0.719323	−	0.694676i	$-0.755548\pi$
$661$	4.99319	−	28.3178i	0.194213	−	1.10143i	0.913536	−	0.406759i	$-0.133341\pi$
$662$	1.53936	+	0.560282i	0.0598290	+	0.0217760i
$663$	−0.381445	+	0.320070i	−0.0148141	+	0.0124305i
$664$	−17.3824			−0.674567
$665$		0			0
$666$	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
$670$		0			0
$671$	−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	−0.972060	−	0.234733i	$-0.924578\pi$
$673$	−17.8824	−	30.9732i	−0.689315	−	1.19393i	0.282745	−	0.959195i	$-0.408755\pi$
$674$	−24.0043	−	20.1420i	−0.924613	−	0.775842i
$675$		0			0
$676$	5.93376	+	10.2776i	0.228222	+	0.395291i
$677$	7.72193	−	13.3748i	0.296778	−	0.514035i	−0.678619	−	0.734491i	$-0.737421\pi$
$677$	7.72193	−	13.3748i	0.296778	−	0.514035i	0.975397	+	0.220456i	$0.0707545\pi$
$678$	−10.3439	+	3.76487i	−0.397255	+	0.144589i
$679$	−0.751963	−	4.26460i	−0.0288577	−	0.163660i
$680$		0			0
$681$	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	$-0.680637\pi$
$683$	−28.0951			−1.07503			−0.537515	+	0.843254i	$0.680637\pi$
$684$	2.65910	−	1.01173i	0.101673	−	0.0386846i
$685$		0			0
$686$	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
$690$		0			0
$691$	19.7841	−	34.2670i	0.752621	−	1.30358i	−0.193928	−	0.981016i	$-0.562123\pi$
$691$	19.7841	−	34.2670i	0.752621	−	1.30358i	0.946548	−	0.322562i	$-0.104544\pi$
$692$	−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
$695$		0			0
$696$	−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			0
$701$	−14.1898	+	11.9067i	−0.535943	+	0.449710i	−0.870148	−	0.492791i	$-0.835977\pi$
$701$	−14.1898	+	11.9067i	−0.535943	+	0.449710i	0.334205	+	0.942501i	$0.391532\pi$
$702$	−5.95542			−0.224773
$703$	−16.4688	−	5.72513i	−0.621134	−	0.215927i
$704$	−2.12061			−0.0799237
$705$		0			0
$706$	−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	−0.642996	−	0.765869i	$-0.722309\pi$
$709$	−17.1284	+	6.23421i	−0.643269	+	0.234131i	−0.000272535		1.00000i	$0.500087\pi$
$710$		0			0
$711$	−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
$715$		0			0
$716$	−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	0.717610	−	0.696445i	$-0.245236\pi$
$719$	21.9786	+	7.99957i	0.819665	+	0.298334i	0.102055	+	0.994779i	$0.467458\pi$
$720$		0			0
$721$	−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			0
$726$	1.73009	−	9.81180i	0.0642095	−	0.364150i
$727$	−0.928081	−	5.26341i	−0.0344206	−	0.195209i	0.962749	−	0.270398i	$-0.0871552\pi$
$727$	−0.928081	−	5.26341i	−0.0344206	−	0.195209i	−0.997169	+	0.0751887i	$0.976044\pi$
$728$	−0.694593	+	0.252811i	−0.0257433	+	0.00936980i
$729$	−15.0201	+	26.0155i	−0.556299	+	0.963538i
$730$		0			0
$731$	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	0.995329	+	0.0965450i	$0.0307792\pi$
$733$	15.7374	+	27.2580i	0.581275	+	1.00680i	−0.414054	+	0.910252i	$0.635888\pi$
$734$	−3.94356	+	6.83045i	−0.145560	+	0.252117i
$735$		0			0
$736$	−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	−0.199039	−	0.979992i	$-0.563782\pi$
$739$	19.8855	−	16.6859i	0.731501	−	0.613802i	0.930540	+	0.366189i	$0.119338\pi$
$740$		0			0
$741$	6.71276	+	2.33359i	0.246599	+	0.0857264i
$742$	−1.87164			−0.0687102
$743$	33.6432	−	28.2300i	1.23425	−	1.03566i	0.236298	−	0.971681i	$-0.424066\pi$
$743$	33.6432	−	28.2300i	1.23425	−	1.03566i	0.997951	−	0.0639778i	$-0.0203787\pi$
$744$	4.06418	+	1.47924i	0.149000	+	0.0542316i
$745$		0			0
$746$	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
$750$		0			0
$751$	−25.3746	−	21.2918i	−0.925934	−	0.776951i	0.0491492	−	0.998791i	$-0.484349\pi$
$751$	−25.3746	−	21.2918i	−0.925934	−	0.776951i	−0.975083	+	0.221841i	$0.928793\pi$
$752$	−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
$755$		0			0
$756$	−0.674992	+	3.82807i	−0.0245492	+	0.139226i
$757$	18.8179	+	6.84915i	0.683948	+	0.248937i	0.660542	−	0.750789i	$-0.270327\pi$
$757$	18.8179	+	6.84915i	0.683948	+	0.248937i	0.0234063	+	0.999726i	$0.492549\pi$
$758$	25.9026	−	21.7349i	0.940825	−	0.789446i
$759$	−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	$0.366862\pi$
$762$	−1.91353	+	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			0
$766$	−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	0.496241	−	0.868185i	$-0.334713\pi$
$769$	−7.55896	−	6.34272i	−0.272583	−	0.228724i	−0.768824	+	0.639460i	$0.779158\pi$
$770$		0			0
$771$	−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	$-0.723828\pi$
$773$	−18.1189	+	6.59473i	−0.651690	+	0.237196i	−0.00504555	+	0.999987i	$0.501606\pi$
$774$	0.0765042	+	0.433877i	0.00274989	+	0.0155954i
$775$		0			0
$776$	−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
$780$		0			0
$781$	−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
$785$		0			0
$786$	−7.40033	+	12.8177i	−0.263961	+	0.457194i
$787$	7.38026	+	12.7830i	0.263078	+	0.455664i	0.967058	−	0.254555i	$-0.0819290\pi$
$787$	7.38026	+	12.7830i	0.263078	+	0.455664i	−0.703980	+	0.710219i	$0.748596\pi$
$788$	−10.7023	−	8.98032i	−0.381255	−	0.319911i
$789$	14.6682	+	12.3081i	0.522201	+	0.438179i
$790$		0			0
$791$	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
$795$		0			0
$796$	14.4311	−	12.1091i	0.511496	−	0.429196i
$797$	−29.2627			−1.03654			−0.518269	−	0.855218i	$-0.673423\pi$
$797$	−29.2627			−1.03654			−0.518269	+	0.855218i	$0.673423\pi$
$798$	2.26083	−	4.05039i	0.0800325	−	0.143382i
$799$	1.73318			0.0613156
$800$		0			0
$801$	−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			0
$806$	−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	0.897890	+	0.440220i	$0.145099\pi$
$809$	23.6129	+	40.8988i	0.830186	+	1.43793i	−0.0677037	+	0.997705i	$0.521567\pi$
$810$		0			0
$811$	−17.4338	+	6.34537i	−0.612182	+	0.222816i	−0.629458	−	0.777035i	$-0.716723\pi$
$811$	−17.4338	+	6.34537i	−0.612182	+	0.222816i	0.0172756	+	0.999851i	$0.494501\pi$
$812$	−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
$815$		0			0
$816$	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
$820$		0			0
$821$	8.55850	−	48.5376i	0.298694	−	1.69398i	−0.353105	−	0.935584i	$-0.614874\pi$
$821$	8.55850	−	48.5376i	0.298694	−	1.69398i	0.651799	−	0.758392i	$-0.274015\pi$
$822$	−3.06805	−	17.3998i	−0.107010	−	0.606887i
$823$	22.7425	−	8.27758i	0.792753	−	0.288538i	0.0862728	−	0.996272i	$-0.472504\pi$
$823$	22.7425	−	8.27758i	0.792753	−	0.288538i	0.706480	+	0.707733i	$0.250282\pi$
$824$	−9.80066	+	16.9752i	−0.341422	+	0.591361i
$825$		0			0
$826$	−5.25671	−	4.41090i	−0.182904	−	0.153475i
$827$	−11.8289	−	9.92561i	−0.411330	−	0.345147i	0.413523	−	0.910494i	$-0.364298\pi$
$827$	−11.8289	−	9.92561i	−0.411330	−	0.345147i	−0.824854	+	0.565346i	$0.808743\pi$
$828$	0.305407	+	0.528981i	0.0106136	+	0.0183834i
$829$	1.47565	−	2.55590i	0.0512515	−	0.0887702i	−0.839261	−	0.543728i	$-0.817012\pi$
$829$	1.47565	−	2.55590i	0.0512515	−	0.0887702i	0.890513	+	0.454958i	$0.150346\pi$
$830$		0			0
$831$	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
$835$		0			0
$836$	−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	0.402025	−	0.915629i	$-0.368307\pi$
$839$	3.51754	+	1.28028i	0.121439	+	0.0442002i	−0.280586	+	0.959829i	$0.590529\pi$
$840$		0			0
$841$	−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
$845$		0			0
$846$	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			0
$851$	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	$-0.951557\pi$
$853$	−29.5212	+	24.7712i	−1.01079	+	0.848150i	−0.0223436	+	0.999750i	$0.507113\pi$
$854$	4.65002			0.159120
$855$		0			0
$856$	2.06418			0.0705521
$857$	36.7367	−	30.8258i	1.25490	−	1.05299i	0.258696	−	0.965959i	$-0.416707\pi$
$857$	36.7367	−	30.8258i	1.25490	−	1.05299i	0.996206	−	0.0870288i	$-0.0277372\pi$
$858$	3.24897	+	1.18253i	0.110918	+	0.0403709i
$859$	8.46750	−	48.0216i	0.288907	−	1.63848i	−0.402077	−	0.915606i	$-0.631712\pi$
$859$	8.46750	−	48.0216i	0.288907	−	1.63848i	0.690985	−	0.722869i	$-0.257177\pi$
$860$		0			0
$861$	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	$-0.237879\pi$
$863$	−6.51754	−	11.2887i	−0.221860	−	0.384272i	−0.955373	+	0.295403i	$0.904546\pi$
$864$	4.28699	+	3.59721i	0.145846	+	0.122380i
$865$		0			0
$866$	−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			0
$871$	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			0
$876$	8.14930	−	6.83807i	0.275339	−	0.231037i
$877$	−44.7921	−	16.3030i	−1.51252	−	0.550513i	−0.553254	−	0.833012i	$-0.686614\pi$
$877$	−44.7921	−	16.3030i	−1.51252	−	0.550513i	−0.959267	+	0.282500i	$0.908836\pi$
$878$	−4.05138	+	22.9765i	−0.136728	+	0.775421i
$879$	−7.05232	−	39.9957i	−0.237869	−	1.34902i
$880$		0			0
$881$	2.92973	−	5.07444i	0.0987051	−	0.170962i	−0.812444	−	0.583040i	$-0.801863\pi$
$881$	2.92973	−	5.07444i	0.0987051	−	0.170962i	0.911149	+	0.412077i	$0.135197\pi$
$882$	2.12701	+	3.68409i	0.0716202	+	0.124050i
$883$	1.96064	+	1.64517i	0.0659807	+	0.0553644i	0.675182	−	0.737652i	$-0.264065\pi$
$883$	1.96064	+	1.64517i	0.0659807	+	0.0553644i	−0.609201	+	0.793016i	$0.708510\pi$
$884$	−0.248970	−	0.208911i	−0.00837378	−	0.00702643i
$885$		0			0
$886$	−7.47519	+	12.9474i	−0.251134	+	0.434976i
$887$	−14.3696	+	5.23010i	−0.482483	+	0.175610i	−0.571799	−	0.820394i	$-0.693754\pi$
$887$	−14.3696	+	5.23010i	−0.482483	+	0.175610i	0.0893155	+	0.996003i	$0.471532\pi$
$888$	−1.06418	−	6.03525i	−0.0357115	−	0.202530i
$889$	0.196652	−	1.11527i	0.00659550	−	0.0374049i
$890$		0			0
$891$	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
$895$		0			0
$896$	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			0
$901$	−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
$905$		0			0
$906$	−15.5817	+	5.67128i	−0.517668	+	0.188416i
$907$	2.45295	+	13.9114i	0.0814490	+	0.461920i	0.998067	+	0.0621548i	$0.0197972\pi$
$907$	2.45295	+	13.9114i	0.0814490	+	0.461920i	−0.916618	+	0.399765i	$0.869092\pi$
$908$	−0.399863	+	2.26774i	−0.0132699	+	0.0752574i
$909$	−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	$0.325988\pi$
$912$	−3.42262	−	5.73448i	−0.113334	−	0.189888i
$913$	−36.8613			−1.21993
$914$	14.9042	−	12.5061i	0.492987	−	0.413665i
$915$		0			0
$916$	−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	−0.996097	−	0.0882656i	$-0.971868\pi$
$919$	−12.7811	+	22.1374i	−0.421608	+	0.730247i	0.574489	+	0.818512i	$0.305201\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	−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	−0.745884	−	0.666076i	$-0.767973\pi$
$929$	−6.68866	+	5.61245i	−0.219448	+	0.184139i	0.526436	+	0.850215i	$0.323528\pi$
$930$		0			0
$931$	−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			0
$936$	−0.120615	−	0.684040i	−0.00394242	−	0.0223586i
$937$	25.1771	−	9.16372i	0.822500	−	0.299366i	0.103723	−	0.994606i	$-0.466924\pi$
$937$	25.1771	−	9.16372i	0.822500	−	0.299366i	0.718777	+	0.695241i	$0.244702\pi$
$938$	4.40642	−	7.63215i	0.143875	−	0.249198i
$939$	16.7672	+	29.0417i	0.547178	+	0.947740i
$940$		0			0
$941$	−9.51754	−	7.98617i	−0.310263	−	0.260342i	0.474338	−	0.880343i	$-0.342688\pi$
$941$	−9.51754	−	7.98617i	−0.310263	−	0.260342i	−0.784601	+	0.620001i	$0.787132\pi$
$942$	−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			0
$946$	0.248560	−	1.40965i	0.00808138	−	0.0458318i
$947$	−39.2181	−	14.2742i	−1.27442	−	0.463850i	−0.385835	−	0.922568i	$-0.626087\pi$
$947$	−39.2181	−	14.2742i	−1.27442	−	0.463850i	−0.888582	+	0.458718i	$0.848309\pi$
$948$	−2.87939	+	2.41609i	−0.0935181	+	0.0784710i
$949$	−7.38919			−0.239863
$950$		0			0
$951$	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	$-0.349943\pi$
$953$	7.08095	+	2.57725i	0.229374	+	0.0834854i	−0.224776	+	0.974410i	$0.572165\pi$
$954$	0.305407	−	1.73205i	0.00988793	−	0.0560772i
$955$		0			0
$956$	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
$960$		0			0
$961$	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
$965$		0			0
$966$	0.935822	+	0.340611i	0.0301096	+	0.0109590i
$967$	11.5963	−	9.73042i	0.372911	−	0.312909i	−0.437001	−	0.899461i	$-0.643959\pi$
$967$	11.5963	−	9.73042i	0.372911	−	0.312909i	0.809912	+	0.586552i	$0.199515\pi$
$968$	6.50299			0.209014
$969$	2.03936	−	0.0295733i	0.0655138	−	0.000950031i
$970$		0			0
$971$	−40.6921	+	34.1447i	−1.30587	+	1.09576i	−0.316774	+	0.948501i	$0.602600\pi$
$971$	−40.6921	+	34.1447i	−1.30587	+	1.09576i	−0.989098	+	0.147256i	$0.952956\pi$
$972$	−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
$975$		0			0
$976$	3.34730	−	5.79769i	0.107144	−	0.185579i
$977$	−10.7173	−	18.5630i	−0.342878	−	0.593883i	0.642088	−	0.766631i	$-0.278069\pi$
$977$	−10.7173	−	18.5630i	−0.342878	−	0.593883i	−0.984966	+	0.172749i	$0.944735\pi$
$978$	2.89646	+	2.43042i	0.0926186	+	0.0777162i
$979$	26.0488	+	21.8575i	0.832522	+	0.698569i
$980$		0			0
$981$	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	0.973994	+	0.226574i	$0.0727526\pi$
$983$	4.27126	+	24.2235i	0.136232	+	0.772610i	−0.837762	+	0.546036i	$0.816136\pi$
$984$	2.09240	−	11.8666i	0.0667032	−	0.378292i
$985$		0			0
$986$	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
$990$		0			0
$991$	−38.8256	−	14.1314i	−1.23334	−	0.448898i	−0.358598	−	0.933492i	$-0.616745\pi$
$991$	−38.8256	−	14.1314i	−1.23334	−	0.448898i	−0.874739	+	0.484594i	$0.838967\pi$
$992$	−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
$995$		0			0
$996$	−13.3157	−	23.0634i	−0.421923	−	0.730793i
$997$	−33.3405	−	27.9760i	−1.05590	−	0.886009i	−0.0622019	−	0.998064i	$-0.519812\pi$
$997$	−33.3405	−	27.9760i	−1.05590	−	0.886009i	−0.993702	+	0.112055i	$0.964257\pi$
$998$	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	950.2.l.c.101.1		6
5.2	odd	4		950.2.u.c.899.1		12
5.3	odd	4		950.2.u.c.899.2		12
5.4	even	2		190.2.k.a.101.1	✓	6
19.16	even	9	inner	950.2.l.c.301.1		6
95.4	even	18		3610.2.a.x.1.1		3
95.34	odd	18		3610.2.a.w.1.3		3
95.54	even	18		190.2.k.a.111.1	yes	6
95.73	odd	36		950.2.u.c.149.1		12
95.92	odd	36		950.2.u.c.149.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.a.101.1	✓	6	5.4	even	2
190.2.k.a.111.1	yes	6	95.54	even	18
950.2.l.c.101.1		6	1.1	even	1	trivial
950.2.l.c.301.1		6	19.16	even	9	inner
950.2.u.c.149.1		12	95.73	odd	36
950.2.u.c.149.2		12	95.92	odd	36
950.2.u.c.899.1		12	5.2	odd	4
950.2.u.c.899.2		12	5.3	odd	4
3610.2.a.w.1.3		3	95.34	odd	18
3610.2.a.x.1.1		3	95.4	even	18

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.l (of order \(9\), degree \(6\), minimal)

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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more