LMFDB - Embedded newform 750.2.l.b.143.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			143.4
Character	$\chi$	$=$	750.143
Dual form			750.2.l.b.257.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(0.666690 + 1.59860i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.72703 - 0.131724i) q^{6} +(1.51403 - 1.51403i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.11105 + 2.13154i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(0.666690 + 1.59860i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.72703 - 0.131724i) q^{6} +(1.51403 - 1.51403i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.11105 + 2.13154i) q^{9} +(5.62798 - 1.82864i) q^{11} +(0.901424 - 1.47900i) q^{12} +(-0.941310 + 0.479621i) q^{13} +(0.661655 + 2.03636i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.899945 + 5.68203i) q^{17} +(-0.940823 - 2.84866i) q^{18} +(3.16950 - 4.36244i) q^{19} +(3.42972 + 1.41094i) q^{21} +(-0.925718 + 5.84476i) q^{22} +(1.37932 + 0.702799i) q^{23} +(0.908558 + 1.47463i) q^{24} -1.05646i q^{26} +(-4.81490 - 1.95364i) q^{27} +(-2.11480 - 0.334951i) q^{28} +(-3.67723 + 2.67167i) q^{29} +(8.62475 + 6.26624i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(6.67539 + 7.77776i) q^{33} +(-5.47129 - 1.77773i) q^{34} +(2.96530 + 0.454984i) q^{36} +(-0.100380 - 0.197006i) q^{37} +(2.44804 + 4.80455i) q^{38} +(-1.39429 - 1.18502i) q^{39} +(-1.54235 - 0.501139i) q^{41} +(-2.81421 + 2.41535i) q^{42} +(-1.33532 - 1.33532i) q^{43} +(-4.78745 - 3.47829i) q^{44} +(-1.25240 + 0.909919i) q^{46} +(-4.75083 - 0.752458i) q^{47} +(-1.72638 + 0.140065i) q^{48} +2.41543i q^{49} +(-8.48331 + 5.22681i) q^{51} +(0.941310 + 0.479621i) q^{52} +(0.949805 - 5.99683i) q^{53} +(3.92663 - 3.40317i) q^{54} +(1.25854 - 1.73224i) q^{56} +(9.08688 + 2.15837i) q^{57} +(-0.711043 - 4.48935i) q^{58} +(-2.24119 + 6.89769i) q^{59} +(-1.30934 - 4.02973i) q^{61} +(-9.49882 + 4.83989i) q^{62} +(0.0310298 + 6.42341i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-9.96060 + 2.41679i) q^{66} +(1.28043 - 0.202800i) q^{67} +(4.06788 - 4.06788i) q^{68} +(-0.203915 + 2.67353i) q^{69} +(-2.39892 - 3.30183i) q^{71} +(-1.75161 + 2.43554i) q^{72} +(-0.141918 + 0.278530i) q^{73} +0.221105 q^{74} -5.39228 q^{76} +(5.75231 - 11.2895i) q^{77} +(1.68885 - 0.704330i) q^{78} +(0.555462 + 0.764528i) q^{79} +(-0.0869513 - 8.99958i) q^{81} +(1.14673 - 1.14673i) q^{82} +(-7.47149 + 1.18337i) q^{83} +(-0.874463 - 3.60403i) q^{84} +(1.79600 - 0.583556i) q^{86} +(-6.72250 - 4.09725i) q^{87} +(5.27263 - 2.68654i) q^{88} +(-2.67429 - 8.23061i) q^{89} +(-0.699010 + 2.15133i) q^{91} +(-0.242168 - 1.52899i) q^{92} +(-4.26719 + 17.9652i) q^{93} +(2.82728 - 3.89142i) q^{94} +(0.658960 - 1.60180i) q^{96} +(-1.88725 + 11.9156i) q^{97} +(-2.15217 - 1.09658i) q^{98} +(-7.98311 + 15.8566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) $ 80 * q - 4 * q^3 - 4 * q^7	$ 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) $ 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	0.666690	+	1.59860i	0.384914	+	0.922953i
$3$	0.666690	+	1.59860i	0.384914	+	0.922953i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	−1.72703	−	0.131724i	−0.705059	−	0.0537762i
$7$	1.51403	−	1.51403i	0.572249	−	0.572249i	−0.360507	−	0.932756i	$-0.617396\pi$
$7$	1.51403	−	1.51403i	0.572249	−	0.572249i	0.932756	+	0.360507i	$0.117396\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−2.11105	+	2.13154i	−0.703683	+	0.710514i
$10$		0			0
$11$	5.62798	−	1.82864i	1.69690	−	0.551357i	0.708833	−	0.705376i	$-0.249222\pi$
$11$	5.62798	−	1.82864i	1.69690	−	0.551357i	0.988068	+	0.154020i	$0.0492219\pi$
$12$	0.901424	−	1.47900i	0.260219	−	0.426950i
$13$	−0.941310	+	0.479621i	−0.261072	+	0.133023i	−0.579628	−	0.814881i	$-0.696802\pi$
$13$	−0.941310	+	0.479621i	−0.261072	+	0.133023i	0.318556	+	0.947904i	$0.396802\pi$
$14$	0.661655	+	2.03636i	0.176835	+	0.544241i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.899945	+	5.68203i	0.218269	+	1.37809i	0.816766	+	0.576969i	$0.195765\pi$
$17$	0.899945	+	5.68203i	0.218269	+	1.37809i	−0.598497	+	0.801125i	$0.704235\pi$
$18$	−0.940823	−	2.84866i	−0.221754	−	0.671435i
$19$	3.16950	−	4.36244i	0.727133	−	1.00081i	−0.272123	−	0.962262i	$-0.587726\pi$
$19$	3.16950	−	4.36244i	0.727133	−	1.00081i	0.999257	−	0.0385508i	$-0.0122742\pi$
$20$		0			0
$21$	3.42972	+	1.41094i	0.748425	+	0.307892i
$22$	−0.925718	+	5.84476i	−0.197364	+	1.24611i
$23$	1.37932	+	0.702799i	0.287608	+	0.146544i	0.591843	−	0.806054i	$-0.298401\pi$
$23$	1.37932	+	0.702799i	0.287608	+	0.146544i	−0.304235	+	0.952597i	$0.598401\pi$
$24$	0.908558	+	1.47463i	0.185459	+	0.301007i
$25$		0			0
$26$		−	1.05646i		−	0.207188i
$27$	−4.81490	−	1.95364i	−0.926628	−	0.375979i
$28$	−2.11480	−	0.334951i	−0.399659	−	0.0632998i
$29$	−3.67723	+	2.67167i	−0.682845	+	0.496116i	−0.874300	−	0.485386i	$-0.838679\pi$
$29$	−3.67723	+	2.67167i	−0.682845	+	0.496116i	0.191455	+	0.981501i	$0.438679\pi$
$30$		0			0
$31$	8.62475	+	6.26624i	1.54905	+	1.12545i	0.944324	+	0.329017i	$0.106718\pi$
$31$	8.62475	+	6.26624i	1.54905	+	1.12545i	0.604726	+	0.796433i	$0.293282\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	6.67539	+	7.77776i	1.16204	+	1.35393i
$34$	−5.47129	−	1.77773i	−0.938319	−	0.304878i
$35$		0			0
$36$	2.96530	+	0.454984i	0.494216	+	0.0758307i
$37$	−0.100380	−	0.197006i	−0.0165023	−	0.0323876i	0.882608	−	0.470109i	$-0.155786\pi$
$37$	−0.100380	−	0.197006i	−0.0165023	−	0.0323876i	−0.899111	+	0.437722i	$0.855786\pi$
$38$	2.44804	+	4.80455i	0.397125	+	0.779402i
$39$	−1.39429	−	1.18502i	−0.223264	−	0.189755i
$40$		0			0
$41$	−1.54235	−	0.501139i	−0.240874	−	0.0782648i	0.186092	−	0.982532i	$-0.440418\pi$
$41$	−1.54235	−	0.501139i	−0.240874	−	0.0782648i	−0.426966	+	0.904268i	$0.640418\pi$
$42$	−2.81421	+	2.41535i	−0.434243	+	0.372696i
$43$	−1.33532	−	1.33532i	−0.203634	−	0.203634i	0.597921	−	0.801555i	$-0.295994\pi$
$43$	−1.33532	−	1.33532i	−0.203634	−	0.203634i	−0.801555	+	0.597921i	$0.795994\pi$
$44$	−4.78745	−	3.47829i	−0.721735	−	0.524371i
$45$		0			0
$46$	−1.25240	+	0.909919i	−0.184656	+	0.134160i
$47$	−4.75083	−	0.752458i	−0.692980	−	0.109757i	−0.199998	−	0.979796i	$-0.564093\pi$
$47$	−4.75083	−	0.752458i	−0.692980	−	0.109757i	−0.492983	+	0.870039i	$0.664093\pi$
$48$	−1.72638	+	0.140065i	−0.249181	+	0.0202167i
$49$			2.41543i			0.345062i
$50$		0			0
$51$	−8.48331	+	5.22681i	−1.18790	+	0.731899i
$52$	0.941310	+	0.479621i	0.130536	+	0.0665115i
$53$	0.949805	−	5.99683i	0.130466	−	0.823728i	−0.832484	−	0.554049i	$-0.813082\pi$
$53$	0.949805	−	5.99683i	0.130466	−	0.823728i	0.962950	−	0.269680i	$-0.0869178\pi$
$54$	3.92663	−	3.40317i	0.534347	−	0.463113i
$55$		0			0
$56$	1.25854	−	1.73224i	0.168180	−	0.231480i
$57$	9.08688	+	2.15837i	1.20359	+	0.285883i
$58$	−0.711043	−	4.48935i	−0.0933645	−	0.589480i
$59$	−2.24119	+	6.89769i	−0.291779	+	0.898002i	0.692506	+	0.721412i	$0.256507\pi$
$59$	−2.24119	+	6.89769i	−0.291779	+	0.898002i	−0.984285	+	0.176590i	$0.943493\pi$
$60$		0			0
$61$	−1.30934	−	4.02973i	−0.167644	−	0.515954i	0.831578	−	0.555408i	$-0.187438\pi$
$61$	−1.30934	−	4.02973i	−0.167644	−	0.515954i	−0.999221	+	0.0394543i	$0.987438\pi$
$62$	−9.49882	+	4.83989i	−1.20635	+	0.614667i
$63$	0.0310298	+	6.42341i	0.00390939	+	0.809273i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	−9.96060	+	2.41679i	−1.22607	+	0.297486i
$67$	1.28043	−	0.202800i	0.156429	−	0.0247759i	−0.0777287	−	0.996975i	$-0.524767\pi$
$67$	1.28043	−	0.202800i	0.156429	−	0.0247759i	0.234158	+	0.972199i	$0.424767\pi$
$68$	4.06788	−	4.06788i	0.493303	−	0.493303i
$69$	−0.203915	+	2.67353i	−0.0245485	+	0.321855i
$70$		0			0
$71$	−2.39892	−	3.30183i	−0.284700	−	0.391856i	0.642584	−	0.766215i	$-0.277862\pi$
$71$	−2.39892	−	3.30183i	−0.284700	−	0.391856i	−0.927283	+	0.374360i	$0.877862\pi$
$72$	−1.75161	+	2.43554i	−0.206429	+	0.287031i
$73$	−0.141918	+	0.278530i	−0.0166102	+	0.0325994i	−0.899163	−	0.437615i	$-0.855823\pi$
$73$	−0.141918	+	0.278530i	−0.0166102	+	0.0325994i	0.882552	+	0.470214i	$0.155823\pi$
$74$	0.221105			0.0257030
$75$		0			0
$76$	−5.39228			−0.618537
$77$	5.75231	−	11.2895i	0.655537	−	1.28656i
$78$	1.68885	−	0.704330i	0.191225	−	0.0797496i
$79$	0.555462	+	0.764528i	0.0624944	+	0.0860162i	0.839120	−	0.543946i	$-0.183070\pi$
$79$	0.555462	+	0.764528i	0.0624944	+	0.0860162i	−0.776626	+	0.629962i	$0.783070\pi$
$80$		0			0
$81$	−0.0869513	−	8.99958i	−0.00966125	−	0.999953i
$82$	1.14673	−	1.14673i	0.126635	−	0.126635i
$83$	−7.47149	+	1.18337i	−0.820102	+	0.129891i	−0.552367	−	0.833601i	$-0.686275\pi$
$83$	−7.47149	+	1.18337i	−0.820102	+	0.129891i	−0.267735	+	0.963493i	$0.586275\pi$
$84$	−0.874463	−	3.60403i	−0.0954117	−	0.393232i
$85$		0			0
$86$	1.79600	−	0.583556i	0.193668	−	0.0629264i
$87$	−6.72250	−	4.09725i	−0.720728	−	0.439272i
$88$	5.27263	−	2.68654i	0.562064	−	0.286386i
$89$	−2.67429	−	8.23061i	−0.283474	−	0.872443i	−0.986852	−	0.161627i	$-0.948326\pi$
$89$	−2.67429	−	8.23061i	−0.283474	−	0.872443i	0.703378	−	0.710816i	$-0.251674\pi$
$90$		0			0
$91$	−0.699010	+	2.15133i	−0.0732762	+	0.225521i
$92$	−0.242168	−	1.52899i	−0.0252477	−	0.159408i
$93$	−4.26719	+	17.9652i	−0.442487	+	1.86290i
$94$	2.82728	−	3.89142i	0.291612	−	0.401369i
$95$		0			0
$96$	0.658960	−	1.60180i	0.0672548	−	0.163483i
$97$	−1.88725	+	11.9156i	−0.191621	+	1.20985i	0.684956	+	0.728584i	$0.259821\pi$
$97$	−1.88725	+	11.9156i	−0.191621	+	1.20985i	−0.876577	+	0.481262i	$0.840179\pi$
$98$	−2.15217	−	1.09658i	−0.217402	−	0.110772i
$99$	−7.98311	+	15.8566i	−0.802333	+	1.59365i
$100$		0			0
$101$		−	0.310282i		−	0.0308742i	−0.999881	−	0.0154371i	$-0.995086\pi$
$101$		−	0.310282i		−	0.0308742i	0.999881	−	0.0154371i	$-0.00491398\pi$
$102$	−0.805776	−	9.93161i	−0.0797837	−	0.983375i
$103$	8.72553	+	1.38199i	0.859752	+	0.136171i	0.570717	−	0.821147i	$-0.306665\pi$
$103$	8.72553	+	1.38199i	0.859752	+	0.136171i	0.289035	+	0.957318i	$0.406665\pi$
$104$	−0.854692	+	0.620970i	−0.0838094	+	0.0608911i
$105$		0			0
$106$	4.91201	+	3.56879i	0.477097	+	0.346631i
$107$	4.19190	+	4.19190i	0.405246	+	0.405246i	0.880077	−	0.474831i	$-0.157491\pi$
$107$	4.19190	+	4.19190i	0.405246	+	0.405246i	−0.474831	+	0.880077i	$0.657491\pi$
$108$	1.24960	+	5.04366i	0.120243	+	0.485326i
$109$	1.79521	+	0.583300i	0.171950	+	0.0558700i	0.393727	−	0.919227i	$-0.371186\pi$
$109$	1.79521	+	0.583300i	0.171950	+	0.0558700i	−0.221777	+	0.975098i	$0.571186\pi$
$110$		0			0
$111$	0.248012	−	0.291809i	0.0235403	−	0.0276973i
$112$	0.972066	+	1.90779i	0.0918516	+	0.180269i
$113$	−3.85086	−	7.55774i	−0.362258	−	0.710972i	0.635891	−	0.771779i	$-0.280633\pi$
$113$	−3.85086	−	7.55774i	−0.362258	−	0.710972i	−0.998150	+	0.0608066i	$0.980633\pi$
$114$	−6.04848	+	7.11659i	−0.566492	+	0.666530i
$115$		0			0
$116$	4.32285	+	1.40458i	0.401366	+	0.130412i
$117$	0.964817	−	3.01895i	0.0891974	−	0.279102i
$118$	−5.12840	−	5.12840i	−0.472108	−	0.472108i
$119$	9.96530	+	7.24021i	0.913517	+	0.663709i
$120$		0			0
$121$	19.4311	−	14.1175i	1.76646	−	1.28341i
$122$	4.18494	+	0.662830i	0.378887	+	0.0600098i
$123$	−0.227147	−	2.79970i	−0.0204811	−	0.252441i
$124$		−	10.6608i		−	0.957366i
$125$		0			0
$126$	−5.73738	−	2.88852i	−0.511127	−	0.257330i
$127$	−9.31862	−	4.74807i	−0.826894	−	0.421323i	−0.0112913	−	0.999936i	$-0.503594\pi$
$127$	−9.31862	−	4.74807i	−0.826894	−	0.421323i	−0.815602	+	0.578613i	$0.803594\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	1.24440	−	3.02489i	0.109563	−	0.266326i
$130$		0			0
$131$	−11.4805	+	15.8015i	−1.00306	+	1.38059i	−0.0796236	+	0.996825i	$0.525372\pi$
$131$	−11.4805	+	15.8015i	−1.00306	+	1.38059i	−0.923432	+	0.383762i	$0.874628\pi$
$132$	2.36864	−	9.97216i	0.206164	−	0.867965i
$133$	−1.80615	−	11.4036i	−0.156613	−	0.988816i
$134$	−0.400605	+	1.23294i	−0.0346070	+	0.106510i
$135$		0			0
$136$	1.77773	+	5.47129i	0.152439	+	0.469159i
$137$	10.6831	−	5.44330i	0.912717	−	0.465053i	0.0664369	−	0.997791i	$-0.478837\pi$
$137$	10.6831	−	5.44330i	0.912717	−	0.465053i	0.846280	+	0.532738i	$0.178837\pi$
$138$	−2.28956	−	1.39545i	−0.194900	−	0.118788i
$139$	22.1318	−	7.19107i	1.87720	−	0.609939i	0.888747	−	0.458399i	$-0.151577\pi$
$139$	22.1318	−	7.19107i	1.87720	−	0.609939i	0.988451	−	0.151540i	$-0.0484232\pi$
$140$		0			0
$141$	−1.96445	−	8.09634i	−0.165437	−	0.681835i
$142$	4.03104	−	0.638455i	0.338278	−	0.0535779i
$143$	−4.42062	+	4.42062i	−0.369671	+	0.369671i
$144$	−1.37487	−	2.66641i	−0.114572	−	0.222201i
$145$		0			0
$146$	−0.183742	−	0.252900i	−0.0152066	−	0.0209301i
$147$	−3.86131	+	1.61035i	−0.318476	+	0.132819i
$148$	−0.100380	+	0.197006i	−0.00825116	+	0.0161938i
$149$	14.7140			1.20542			0.602711	−	0.797960i	$-0.294087\pi$
$149$	14.7140			1.20542			0.602711	+	0.797960i	$0.294087\pi$
$150$		0			0
$151$	−8.54879			−0.695691			−0.347845	−	0.937552i	$-0.613087\pi$
$151$	−8.54879			−0.695691			−0.347845	+	0.937552i	$0.613087\pi$
$152$	2.44804	−	4.80455i	0.198562	−	0.389701i
$153$	−14.0113	−	10.0768i	−1.13275	−	0.814658i
$154$	7.44757	+	10.2507i	0.600142	+	0.826025i
$155$		0			0
$156$	−0.139161	+	1.82454i	−0.0111418	+	0.146080i
$157$	17.5864	−	17.5864i	1.40355	−	1.40355i	0.615104	−	0.788446i	$-0.289114\pi$
$157$	17.5864	−	17.5864i	1.40355	−	1.40355i	0.788446	−	0.615104i	$-0.210886\pi$
$158$	−0.933375	+	0.147832i	−0.0742553	+	0.0117609i
$159$	10.2198	−	2.47967i	0.810480	−	0.196651i
$160$		0			0
$161$	3.15239	−	1.02427i	0.248443	−	0.0807240i
$162$	8.05816	+	4.00825i	0.633109	+	0.314918i
$163$	−1.79029	+	0.912200i	−0.140227	+	0.0714490i	−0.522696	−	0.852519i	$-0.675074\pi$
$163$	−1.79029	+	0.912200i	−0.140227	+	0.0714490i	0.382469	+	0.923968i	$0.375074\pi$
$164$	0.501139	+	1.54235i	0.0391324	+	0.120437i
$165$		0			0
$166$	2.33760	−	7.19438i	0.181433	−	0.558392i
$167$	−2.32146	−	14.6571i	−0.179640	−	1.13420i	−0.898477	−	0.439021i	$-0.855325\pi$
$167$	−2.32146	−	14.6571i	−0.179640	−	1.13420i	0.718837	−	0.695179i	$-0.244675\pi$
$168$	3.60821	+	0.857043i	0.278379	+	0.0661223i
$169$	−6.98518	+	9.61428i	−0.537322	+	0.739560i
$170$		0			0
$171$	2.60777	+	15.9653i	0.199421	+	1.22089i
$172$	−0.295415	+	1.86518i	−0.0225252	+	0.142218i
$173$	−4.46800	−	2.27656i	−0.339696	−	0.173084i	0.275818	−	0.961210i	$-0.411051\pi$
$173$	−4.46800	−	2.27656i	−0.339696	−	0.173084i	−0.615514	+	0.788126i	$0.711051\pi$
$174$	6.70263	−	4.12968i	0.508125	−	0.313070i
$175$		0			0
$176$			5.91761i			0.446057i
$177$	−12.5208	+	1.01585i	−0.941123	+	0.0763556i
$178$	8.54762	+	1.35381i	0.640672	+	0.101472i
$179$	2.56353	−	1.86252i	0.191607	−	0.139211i	−0.487846	−	0.872930i	$-0.662217\pi$
$179$	2.56353	−	1.86252i	0.191607	−	0.139211i	0.679453	+	0.733719i	$0.262217\pi$
$180$		0			0
$181$	−5.04884	−	3.66820i	−0.375278	−	0.272655i	0.384118	−	0.923284i	$-0.374505\pi$
$181$	−5.04884	−	3.66820i	−0.375278	−	0.272655i	−0.759396	+	0.650629i	$0.774505\pi$
$182$	−1.59951	−	1.59951i	−0.118563	−	0.118563i
$183$	5.56901	−	4.77969i	0.411673	−	0.353325i
$184$	1.47228	+	0.478373i	0.108538	+	0.0352661i
$185$		0			0
$186$	−14.0698	−	11.9581i	−1.03165	−	0.876811i
$187$	15.4553	+	30.3327i	1.13020	+	2.21815i
$188$	2.18372	+	4.28579i	0.159264	+	0.312573i
$189$	−10.2478	+	4.33203i	−0.745416	+	0.315109i
$190$		0			0
$191$	−19.9806	−	6.49209i	−1.44574	−	0.469751i	−0.522062	−	0.852908i	$-0.674837\pi$
$191$	−19.9806	−	6.49209i	−1.44574	−	0.469751i	−0.923683	+	0.383157i	$0.874837\pi$
$192$	1.12805	+	1.31434i	0.0814103	+	0.0948544i
$193$	−7.00922	−	7.00922i	−0.504535	−	0.504535i	0.408309	−	0.912844i	$-0.366119\pi$
$193$	−7.00922	−	7.00922i	−0.504535	−	0.504535i	−0.912844	+	0.408309i	$0.866119\pi$
$194$	−9.76009	−	7.09112i	−0.700734	−	0.509113i
$195$		0			0
$196$	1.95413	−	1.41976i	0.139580	−	0.101411i
$197$	−10.0821	−	1.59685i	−0.718320	−	0.113771i	−0.213435	−	0.976957i	$-0.568465\pi$
$197$	−10.0821	−	1.59685i	−0.718320	−	0.113771i	−0.504885	+	0.863186i	$0.668465\pi$
$198$	−10.5041	−	14.3118i	−0.746495	−	1.01709i
$199$		−	15.1147i		−	1.07146i	−0.844391	−	0.535728i	$-0.820037\pi$
$199$		−	15.1147i		−	1.07146i	0.844391	−	0.535728i	$-0.179963\pi$
$200$		0			0
$201$	1.17784	+	1.91169i	0.0830786	+	0.134840i
$202$	0.276463	+	0.140865i	0.0194519	+	0.00991123i
$203$	−1.52246	+	9.61241i	−0.106856	+	0.674659i
$204$	9.21494	+	3.79090i	0.645175	+	0.265416i
$205$		0			0
$206$	−5.19267	+	7.14709i	−0.361790	+	0.497962i
$207$	−4.40986	+	1.45644i	−0.306506	+	0.101229i
$208$	−0.165266	−	1.04345i	−0.0114592	−	0.0723503i
$209$	9.86055	−	30.3476i	0.682068	−	2.09919i
$210$		0			0
$211$	−1.22728	−	3.77719i	−0.0844897	−	0.260033i	0.899883	−	0.436132i	$-0.143652\pi$
$211$	−1.22728	−	3.77719i	−0.0844897	−	0.260033i	−0.984372	+	0.176099i	$0.943652\pi$
$212$	−5.40982	+	2.75644i	−0.371548	+	0.189313i
$213$	3.67898	−	6.03622i	0.252079	−	0.413595i
$214$	−5.63809	+	1.83193i	−0.385412	+	0.125228i
$215$		0			0
$216$	−5.06124	−	1.17637i	−0.344374	−	0.0800422i
$217$	22.5454	−	3.57084i	1.53048	−	0.242404i
$218$	−1.33473	+	1.33473i	−0.0903996	+	0.0903996i
$219$	−0.539873	−	0.0411771i	−0.0364812	−	0.00278249i
$220$		0			0
$221$	−3.57235	−	4.91692i	−0.240302	−	0.330748i
$222$	0.147409	+	0.353459i	0.00989342	+	0.0237226i
$223$	6.07755	−	11.9279i	0.406983	−	0.798748i	−0.592996	−	0.805205i	$-0.702055\pi$
$223$	6.07755	−	11.9279i	0.406983	−	0.798748i	0.999979	+	0.00645660i	$0.00205521\pi$
$224$	−2.14116			−0.143062
$225$		0			0
$226$	8.48225			0.564231
$227$	−0.388579	+	0.762629i	−0.0257909	+	0.0506175i	−0.903542	−	0.428499i	$-0.859043\pi$
$227$	−0.388579	+	0.762629i	−0.0257909	+	0.0506175i	0.877752	+	0.479116i	$0.159043\pi$
$228$	−3.59498	−	8.62010i	−0.238083	−	0.570880i
$229$	−9.72545	−	13.3859i	−0.642676	−	0.884567i	0.356079	−	0.934456i	$-0.384113\pi$
$229$	−9.72545	−	13.3859i	−0.642676	−	0.884567i	−0.998755	+	0.0498887i	$0.984113\pi$
$230$		0			0
$231$	21.8825	+	1.66902i	1.43976	+	0.109813i
$232$	−3.21402	+	3.21402i	−0.211011	+	0.211011i
$233$	5.38346	−	0.852656i	0.352682	−	0.0558593i	0.0224200	−	0.999749i	$-0.492863\pi$
$233$	5.38346	−	0.852656i	0.352682	−	0.0558593i	0.330262	+	0.943889i	$0.392863\pi$
$234$	2.25188	+	2.23023i	0.147210	+	0.145795i
$235$		0			0
$236$	6.89769	−	2.24119i	0.449001	−	0.145889i
$237$	−0.851854	+	1.39767i	−0.0553339	+	0.0907882i
$238$	−10.9752	+	5.59216i	−0.711418	+	0.362486i
$239$	−2.69306	−	8.28837i	−0.174199	−	0.536130i	0.825397	−	0.564553i	$-0.190951\pi$
$239$	−2.69306	−	8.28837i	−0.174199	−	0.536130i	−0.999596	+	0.0284230i	$0.990951\pi$
$240$		0			0
$241$	−7.85699	+	24.1813i	−0.506113	+	1.55766i	0.292779	+	0.956180i	$0.405420\pi$
$241$	−7.85699	+	24.1813i	−0.506113	+	1.55766i	−0.798892	+	0.601475i	$0.794580\pi$
$242$	3.75726	+	23.7224i	0.241526	+	1.52494i
$243$	14.3288	−	6.13893i	0.919191	−	0.393813i
$244$	−2.49051	+	3.42789i	−0.159439	+	0.219448i
$245$		0			0
$246$	2.59768	+	1.06865i	0.165622	+	0.0681346i
$247$	−0.891162	+	5.62657i	−0.0567033	+	0.358010i
$248$	9.49882	+	4.83989i	0.603176	+	0.307333i
$249$	−6.87290	−	11.1550i	−0.435552	−	0.706918i
$250$		0			0
$251$		−	21.0935i		−	1.33141i	−0.746215	−	0.665706i	$-0.768131\pi$
$251$		−	21.0935i		−	1.33141i	0.746215	−	0.665706i	$-0.231869\pi$
$252$	5.17841	−	3.80069i	0.326209	−	0.239421i
$253$	9.04796	+	1.43306i	0.568840	+	0.0900954i
$254$	8.46113	−	6.14737i	0.530898	−	0.385720i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	11.8588	+	11.8588i	0.739734	+	0.739734i	0.972526	−	0.232792i	$-0.0747863\pi$
$257$	11.8588	+	11.8588i	0.739734	+	0.739734i	−0.232792	+	0.972526i	$0.574786\pi$
$258$	2.13025	+	2.48204i	0.132623	+	0.154525i
$259$	−0.450251	−	0.146295i	−0.0279772	−	0.00909035i
$260$		0			0
$261$	2.06804	−	13.4782i	0.128009	−	0.834279i
$262$	−8.86724	−	17.4029i	−0.547820	−	1.07516i
$263$	−10.3291	−	20.2720i	−0.636919	−	1.25002i	−0.953481	−	0.301453i	$-0.902529\pi$
$263$	−10.3291	−	20.2720i	−0.636919	−	1.25002i	0.316562	−	0.948572i	$-0.397471\pi$
$264$	7.80992	+	6.63774i	0.480667	+	0.408525i
$265$		0			0
$266$	10.9806	+	3.56783i	0.673266	+	0.218757i
$267$	11.3745	−	9.76238i	0.696110	−	0.597448i
$268$	−0.916684	−	0.916684i	−0.0559954	−	0.0559954i
$269$	8.37684	+	6.08613i	0.510745	+	0.371078i	0.813106	−	0.582115i	$-0.197775\pi$
$269$	8.37684	+	6.08613i	0.510745	+	0.371078i	−0.302361	+	0.953193i	$0.597775\pi$
$270$		0			0
$271$	−0.517312	+	0.375849i	−0.0314245	+	0.0228312i	−0.603387	−	0.797449i	$-0.706182\pi$
$271$	−0.517312	+	0.375849i	−0.0314245	+	0.0228312i	0.571962	+	0.820280i	$0.306182\pi$
$272$	−5.68203	−	0.899945i	−0.344524	−	0.0545672i
$273$	−3.90514	+	0.316834i	−0.236350	+	0.0191757i
$274$			11.9899i			0.724336i
$275$		0			0
$276$	2.28279	−	1.40649i	0.137408	−	0.0846608i
$277$	−27.0524	−	13.7839i	−1.62542	−	0.828193i	−0.998805	−	0.0488650i	$-0.984440\pi$
$277$	−27.0524	−	13.7839i	−1.62542	−	0.828193i	−0.626616	−	0.779328i	$-0.715560\pi$
$278$	−3.64035	+	22.9843i	−0.218334	+	1.37851i
$279$	−31.5640	+	5.15567i	−1.88969	+	0.308662i
$280$		0			0
$281$	−12.7646	+	17.5690i	−0.761473	+	1.04808i	0.235617	+	0.971846i	$0.424289\pi$
$281$	−12.7646	+	17.5690i	−0.761473	+	1.04808i	−0.997090	+	0.0762322i	$0.975711\pi$
$282$	8.10574	+	1.92532i	0.482690	+	0.114651i
$283$	−0.541258	−	3.41737i	−0.0321745	−	0.203142i	0.966365	−	0.257176i	$-0.0827920\pi$
$283$	−0.541258	−	3.41737i	−0.0321745	−	0.203142i	−0.998539	+	0.0540343i	$0.982792\pi$
$284$	−1.26119	+	3.88154i	−0.0748378	+	0.230327i
$285$		0			0
$286$	−1.93188	−	5.94572i	−0.114235	−	0.351578i
$287$	−3.09390	+	1.57642i	−0.182627	+	0.0930531i
$288$	2.99996	−	0.0144920i	0.176775	−	0.000853952i
$289$	−15.3076	+	4.97374i	−0.900446	+	0.292573i
$290$		0			0
$291$	−20.3065	+	4.92706i	−1.19039	+	0.288830i
$292$	0.308752	−	0.0489016i	0.0180684	−	0.00286175i
$293$	12.2527	−	12.2527i	0.715808	−	0.715808i	−0.251936	−	0.967744i	$-0.581067\pi$
$293$	12.2527	−	12.2527i	0.715808	−	0.715808i	0.967744	+	0.251936i	$0.0810673\pi$
$294$	0.318171	−	4.17154i	0.0185561	−	0.243289i
$295$		0			0
$296$	−0.129962	−	0.178878i	−0.00755391	−	0.0103971i
$297$	−30.6707	−	2.19034i	−1.77969	−	0.127097i
$298$	−6.68004	+	13.1103i	−0.386964	+	0.759460i
$299$	−1.63544			−0.0945802
$300$		0			0
$301$	−4.04342			−0.233059
$302$	3.88107	−	7.61703i	0.223330	−	0.438311i
$303$	0.496017	−	0.206862i	0.0284954	−	0.0118839i
$304$	3.16950	+	4.36244i	0.181783	+	0.250203i
$305$		0			0
$306$	15.3395	−	7.90942i	0.876899	−	0.452151i
$307$	−16.8133	+	16.8133i	−0.959588	+	0.959588i	−0.999215	−	0.0396263i	$-0.987383\pi$
$307$	−16.8133	+	16.8133i	−0.959588	+	0.959588i	0.0396263	+	0.999215i	$0.487383\pi$
$308$	−12.5146	+	1.98211i	−0.713083	+	0.112941i
$309$	3.60798	+	14.8700i	0.205251	+	0.845924i
$310$		0			0
$311$	−7.39905	+	2.40410i	−0.419562	+	0.136324i	−0.511187	−	0.859470i	$-0.670794\pi$
$311$	−7.39905	+	2.40410i	−0.419562	+	0.136324i	0.0916250	+	0.995794i	$0.470794\pi$
$312$	−1.56250	−	0.952316i	−0.0884590	−	0.0539143i
$313$	−18.5326	+	9.44284i	−1.04753	+	0.533741i	−0.891033	−	0.453939i	$-0.850019\pi$
$313$	−18.5326	+	9.44284i	−1.04753	+	0.533741i	−0.156492	+	0.987679i	$0.550019\pi$
$314$	7.68555	+	23.6537i	0.433721	+	1.33486i
$315$		0			0
$316$	0.292024	−	0.898757i	0.0164276	−	0.0505590i
$317$	0.0339077	+	0.214085i	0.00190445	+	0.0120242i	0.988622	−	0.150419i	$-0.0480624\pi$
$317$	0.0339077	+	0.214085i	0.00190445	+	0.0120242i	−0.986718	+	0.162444i	$0.948062\pi$
$318$	−2.43027	+	10.2316i	−0.136283	+	0.573761i
$319$	−15.8099	+	21.7604i	−0.885183	+	1.21835i
$320$		0			0
$321$	−3.90647	+	9.49587i	−0.218038	+	0.530008i
$322$	−0.518520	+	3.27381i	−0.0288960	+	0.182442i
$323$	27.6399	+	14.0832i	1.53793	+	0.783612i
$324$	−7.22970	+	5.36017i	−0.401650	+	0.297787i
$325$		0			0
$326$		−	2.00929i		−	0.111284i
$327$	0.264387	+	3.25871i	0.0146207	+	0.180207i
$328$	−1.60175	−	0.253693i	−0.0884421	−	0.0140078i
$329$	−8.33214	+	6.05366i	−0.459366	+	0.333749i
$330$		0			0
$331$	5.81535	+	4.22510i	0.319640	+	0.232232i	0.736022	−	0.676958i	$-0.236702\pi$
$331$	5.81535	+	4.22510i	0.319640	+	0.232232i	−0.416382	+	0.909190i	$0.636702\pi$
$332$	5.34899	+	5.34899i	0.293564	+	0.293564i
$333$	0.631833	+	0.201926i	0.0346243	+	0.0110655i
$334$	14.1135	+	4.58575i	0.772255	+	0.250921i
$335$		0			0
$336$	−2.40172	+	2.82585i	−0.131025	+	0.154163i
$337$	−3.06621	−	6.01777i	−0.167027	−	0.327809i	0.792288	−	0.610147i	$-0.208890\pi$
$337$	−3.06621	−	6.01777i	−0.167027	−	0.327809i	−0.959315	+	0.282339i	$0.908890\pi$
$338$	−5.39518	−	10.5886i	−0.293459	−	0.575946i
$339$	9.51447	−	11.1947i	0.516755	−	0.608010i
$340$		0			0
$341$	59.9987	+	19.4947i	3.24911	+	1.05570i
$342$	−15.4090	−	4.92454i	−0.833226	−	0.266288i
$343$	14.2552	+	14.2552i	0.769710	+	0.769710i
$344$	−1.52777	−	1.10999i	−0.0823718	−	0.0598466i
$345$		0			0
$346$	4.05686	−	2.94748i	0.218098	−	0.158458i
$347$	4.52113	+	0.716076i	0.242707	+	0.0384410i	0.276603	−	0.960984i	$-0.410791\pi$
$347$	4.52113	+	0.716076i	0.242707	+	0.0384410i	−0.0338958	+	0.999425i	$0.510791\pi$
$348$	0.636640	+	7.84692i	0.0341275	+	0.420639i
$349$		−	9.78119i		−	0.523575i	−0.965126	−	0.261787i	$-0.915688\pi$
$349$		−	9.78119i		−	0.523575i	0.965126	−	0.261787i	$-0.0843120\pi$
$350$		0			0
$351$	5.46932	−	0.470345i	0.291931	−	0.0251052i
$352$	−5.27263	−	2.68654i	−0.281032	−	0.143193i
$353$	−1.69571	+	10.7063i	−0.0902538	+	0.569840i	0.900573	+	0.434704i	$0.143147\pi$
$353$	−1.69571	+	10.7063i	−0.0902538	+	0.569840i	−0.990827	+	0.135136i	$0.956853\pi$
$354$	4.77921	−	11.6173i	0.254012	−	0.617454i
$355$		0			0
$356$	−5.08679	+	7.00137i	−0.269600	+	0.371072i
$357$	−4.93044	+	20.7575i	−0.260947	+	1.09860i
$358$	0.495694	+	3.12969i	0.0261982	+	0.165409i
$359$	−6.51044	+	20.0371i	−0.343608	+	1.05752i	0.618717	+	0.785614i	$0.287653\pi$
$359$	−6.51044	+	20.0371i	−0.343608	+	1.05752i	−0.962325	+	0.271902i	$0.912347\pi$
$360$		0			0
$361$	−3.11386	−	9.58347i	−0.163887	−	0.504393i
$362$	5.56052	−	2.83323i	0.292254	−	0.148911i
$363$	35.5228	+	21.6505i	1.86446	+	1.13636i
$364$	2.15133	−	0.699010i	0.112760	−	0.0366381i
$365$		0			0
$366$	1.73046	+	7.13196i	0.0904526	+	0.372793i
$367$	−26.6770	+	4.22522i	−1.39253	+	0.220555i	−0.807218	−	0.590254i	$-0.799028\pi$
$367$	−26.6770	+	4.22522i	−1.39253	+	0.220555i	−0.585311	+	0.810809i	$0.699028\pi$
$368$	−1.09463	+	1.09463i	−0.0570618	+	0.0570618i
$369$	4.32417	−	2.22965i	0.225107	−	0.116071i
$370$		0			0
$371$	−7.64135	−	10.5174i	−0.396719	−	0.546037i
$372$	17.0423	−	7.10743i	0.883603	−	0.368503i
$373$	−12.1464	+	23.8387i	−0.628917	+	1.23432i	0.328197	+	0.944609i	$0.393559\pi$
$373$	−12.1464	+	23.8387i	−0.628917	+	1.23432i	−0.957114	+	0.289711i	$0.906441\pi$
$374$	−34.0432			−1.76033
$375$		0			0
$376$	−4.81005			−0.248060
$377$	2.18003	−	4.27854i	0.112277	−	0.220356i
$378$	0.792528	−	11.0975i	0.0407632	−	0.570795i
$379$	9.28018	+	12.7731i	0.476691	+	0.656109i	0.977865	−	0.209238i	$-0.0670983\pi$
$379$	9.28018	+	12.7731i	0.476691	+	0.656109i	−0.501174	+	0.865347i	$0.667098\pi$
$380$		0			0
$381$	1.37764	−	18.0622i	0.0705787	−	0.925357i
$382$	14.8555	−	14.8555i	0.760073	−	0.760073i
$383$	−15.7705	+	2.49780i	−0.805836	+	0.127632i	−0.545744	−	0.837952i	$-0.683753\pi$
$383$	−15.7705	+	2.49780i	−0.805836	+	0.127632i	−0.260092	+	0.965584i	$0.583753\pi$
$384$	−1.68321	+	0.408406i	−0.0858961	+	0.0208414i
$385$		0			0
$386$	9.42739	−	3.06314i	0.479841	−	0.155910i
$387$	5.66521	−	0.0273672i	0.287979	−	0.00139115i
$388$	10.7492	−	5.47700i	0.545709	−	0.278053i
$389$	−3.56490	−	10.9716i	−0.180748	−	0.556284i	0.819102	−	0.573648i	$-0.194472\pi$
$389$	−3.56490	−	10.9716i	−0.180748	−	0.556284i	−0.999849	+	0.0173647i	$0.994472\pi$
$390$		0			0
$391$	−2.75201	+	8.46982i	−0.139175	+	0.428337i
$392$	0.377857	+	2.38569i	0.0190847	+	0.120496i
$393$	−32.9143	−	7.81799i	−1.66031	−	0.394365i
$394$	5.99998	−	8.25827i	0.302275	−	0.416046i
$395$		0			0
$396$	17.5206	−	2.86183i	0.880446	−	0.143812i
$397$	3.27643	−	20.6866i	0.164439	−	1.03823i	−0.758047	−	0.652200i	$-0.773846\pi$
$397$	3.27643	−	20.6866i	0.164439	−	1.03823i	0.922486	−	0.386030i	$-0.126154\pi$
$398$	13.4673	+	6.86195i	0.675057	+	0.343958i
$399$	17.0256	−	10.4900i	0.852348	−	0.525155i
$400$		0			0
$401$		−	24.4394i		−	1.22045i	−0.792229	−	0.610223i	$-0.791080\pi$
$401$		−	24.4394i		−	1.22045i	0.792229	−	0.610223i	$-0.208920\pi$
$402$	−2.23805	+	0.181579i	−0.111624	+	0.00905633i
$403$	−11.1240	−	1.76187i	−0.554125	−	0.0877648i
$404$	−0.251023	+	0.182379i	−0.0124889	+	0.00907370i
$405$		0			0
$406$	−7.87354	−	5.72046i	−0.390757	−	0.283902i
$407$	−0.925189	−	0.925189i	−0.0458599	−	0.0458599i
$408$	−7.56121	+	6.48954i	−0.374336	+	0.321280i
$409$	−9.31361	−	3.02618i	−0.460528	−	0.149635i	0.0695588	−	0.997578i	$-0.477841\pi$
$409$	−9.31361	−	3.02618i	−0.460528	−	0.149635i	−0.530087	+	0.847943i	$0.677841\pi$
$410$		0			0
$411$	15.8240	+	13.4490i	0.780539	+	0.663389i
$412$	−4.01069	−	7.87141i	−0.197592	−	0.387797i
$413$	7.05006	+	13.8365i	0.346911	+	0.680851i
$414$	0.704337	−	4.59042i	0.0346163	−	0.225607i
$415$		0			0
$416$	1.00475	+	0.326463i	0.0492619	+	0.0160062i
$417$	26.2507	+	30.5858i	1.28550	+	1.49779i
$418$	22.5634	+	22.5634i	1.10361	+	1.10361i
$419$	20.8723	+	15.1646i	1.01968	+	0.740840i	0.966217	−	0.257730i	$-0.0829745\pi$
$419$	20.8723	+	15.1646i	1.01968	+	0.740840i	0.0534618	+	0.998570i	$0.482974\pi$
$420$		0			0
$421$	−31.8859	+	23.1664i	−1.55402	+	1.12906i	−0.613316	+	0.789837i	$0.710165\pi$
$421$	−31.8859	+	23.1664i	−1.55402	+	1.12906i	−0.940705	+	0.339225i	$0.889835\pi$
$422$	3.92268	+	0.621291i	0.190953	+	0.0302440i
$423$	11.6331	−	8.53813i	0.565623	−	0.415138i
$424$		−	6.07158i		−	0.294862i
$425$		0			0
$426$	3.70809	+	6.01838i	0.179658	+	0.291591i
$427$	−8.08350	−	4.11875i	−0.391188	−	0.199320i
$428$	0.927381	−	5.85525i	0.0448267	−	0.283024i
$429$	−10.0140	−	4.11962i	−0.483480	−	0.198897i
$430$		0			0
$431$	3.61295	−	4.97279i	0.174030	−	0.239531i	−0.713088	−	0.701074i	$-0.752704\pi$
$431$	3.61295	−	4.97279i	0.174030	−	0.239531i	0.887118	+	0.461543i	$0.152704\pi$
$432$	3.34591	−	3.97553i	0.160980	−	0.191273i
$433$	2.61783	+	16.5283i	0.125805	+	0.794299i	0.967225	+	0.253919i	$0.0817197\pi$
$433$	2.61783	+	16.5283i	0.125805	+	0.794299i	−0.841421	+	0.540380i	$0.818280\pi$
$434$	−7.05375	+	21.7092i	−0.338591	+	1.04208i
$435$		0			0
$436$	−0.583300	−	1.79521i	−0.0279350	−	0.0859752i
$437$	7.43768	−	3.78968i	0.355792	−	0.181285i
$438$	0.281786	−	0.462336i	0.0134643	−	0.0220913i
$439$	−19.1311	+	6.21606i	−0.913076	+	0.296676i	−0.727623	−	0.685977i	$-0.759375\pi$
$439$	−19.1311	+	6.21606i	−0.913076	+	0.296676i	−0.185453	+	0.982653i	$0.559375\pi$
$440$		0			0
$441$	−5.14860	−	5.09909i	−0.245171	−	0.242814i
$442$	6.00282	−	0.950753i	0.285525	−	0.0452227i
$443$	17.1571	−	17.1571i	0.815159	−	0.815159i	−0.170243	−	0.985402i	$-0.554455\pi$
$443$	17.1571	−	17.1571i	0.815159	−	0.815159i	0.985402	+	0.170243i	$0.0544552\pi$
$444$	−0.381856	−	0.0291249i	−0.0181221	−	0.00138221i
$445$		0			0
$446$	7.86865	+	10.8303i	0.372591	+	0.512828i
$447$	9.80971	+	23.5219i	0.463984	+	1.11255i
$448$	0.972066	−	1.90779i	0.0459258	−	0.0901345i
$449$	−15.9242			−0.751511			−0.375755	−	0.926719i	$-0.622617\pi$
$449$	−15.9242			−0.751511			−0.375755	+	0.926719i	$0.622617\pi$
$450$		0			0
$451$	−9.59671			−0.451891
$452$	−3.85086	+	7.55774i	−0.181129	+	0.355486i
$453$	−5.69940	−	13.6661i	−0.267781	−	0.642089i
$454$	−0.503096	−	0.692453i	−0.0236115	−	0.0324984i
$455$		0			0
$456$	9.31265	+	0.710293i	0.436105	+	0.0332625i
$457$	−2.30257	+	2.30257i	−0.107710	+	0.107710i	−0.758908	−	0.651198i	$-0.774267\pi$
$457$	−2.30257	+	2.30257i	−0.107710	+	0.107710i	0.651198	+	0.758908i	$0.274267\pi$
$458$	16.3422	−	2.58835i	0.763621	−	0.120946i
$459$	6.76752	−	29.1166i	0.315881	−	1.35905i
$460$		0			0
$461$	−9.43135	+	3.06443i	−0.439262	+	0.142725i	−0.520295	−	0.853987i	$-0.674178\pi$
$461$	−9.43135	+	3.06443i	−0.439262	+	0.142725i	0.0810333	+	0.996711i	$0.474178\pi$
$462$	−11.4215	+	18.7397i	−0.531379	+	0.871851i
$463$	20.5992	−	10.4958i	0.957328	−	0.487783i	0.0957485	−	0.995406i	$-0.469476\pi$
$463$	20.5992	−	10.4958i	0.957328	−	0.487783i	0.861580	+	0.507623i	$0.169476\pi$
$464$	−1.40458	−	4.32285i	−0.0652059	−	0.200683i
$465$		0			0
$466$	−1.68432	+	5.18379i	−0.0780245	+	0.240135i
$467$	−0.726976	−	4.58995i	−0.0336405	−	0.212397i	0.965142	−	0.261726i	$-0.0842918\pi$
$467$	−0.726976	−	4.58995i	−0.0336405	−	0.212397i	−0.998783	+	0.0493288i	$0.984292\pi$
$468$	−3.00948	+	0.993939i	−0.139113	+	0.0459448i
$469$	1.63156	−	2.24565i	0.0753383	−	0.103694i
$470$		0			0
$471$	39.8384	+	16.3890i	1.83566	+	0.755164i
$472$	−1.13457	+	7.16336i	−0.0522226	+	0.329721i
$473$	−9.95697	−	5.07333i	−0.457822	−	0.233272i
$474$	−0.858596	−	1.39353i	−0.0394366	−	0.0640072i
$475$		0			0
$476$		−	12.3178i		−	0.564585i
$477$	10.7774	+	14.6842i	0.493464	+	0.672341i
$478$	8.60761	+	1.36331i	0.393703	+	0.0623564i
$479$	−12.7801	+	9.28530i	−0.583939	+	0.424256i	−0.840142	−	0.542367i	$-0.817528\pi$
$479$	−12.7801	+	9.28530i	−0.583939	+	0.424256i	0.256203	+	0.966623i	$0.417528\pi$
$480$		0			0
$481$	0.188977	+	0.137300i	0.00861660	+	0.00626032i
$482$	−17.9787	−	17.9787i	−0.818908	−	0.818908i
$483$	3.73907	+	4.35654i	0.170134	+	0.198229i
$484$	−22.8426	−	7.42201i	−1.03830	−	0.337364i
$485$		0			0
$486$	−1.03529	+	15.5540i	−0.0469619	+	0.705546i
$487$	−0.0615473	−	0.120793i	−0.00278898	−	0.00547367i	0.889608	−	0.456725i	$-0.150978\pi$
$487$	−0.0615473	−	0.120793i	−0.00278898	−	0.00547367i	−0.892397	+	0.451252i	$0.850978\pi$
$488$	−1.92361	−	3.77529i	−0.0870776	−	0.170899i
$489$	−2.65182	−	2.25381i	−0.119919	−	0.101921i
$490$		0			0
$491$	−8.65368	−	2.81175i	−0.390535	−	0.126893i	0.107166	−	0.994241i	$-0.465822\pi$
$491$	−8.65368	−	2.81175i	−0.390535	−	0.126893i	−0.497701	+	0.867349i	$0.665822\pi$
$492$	−2.13149	+	1.82939i	−0.0960951	+	0.0824752i
$493$	−18.4898	−	18.4898i	−0.832738	−	0.832738i
$494$	−4.60873	−	3.34844i	−0.207357	−	0.150654i
$495$		0			0
$496$	−8.62475	+	6.26624i	−0.387263	+	0.281363i
$497$	−8.63111	−	1.36703i	−0.387158	−	0.0613198i
$498$	13.0594	−	1.05954i	0.585205	−	0.0474792i
$499$			27.5900i			1.23510i	0.786532	+	0.617549i	$0.211874\pi$
$499$			27.5900i			1.23510i	−0.786532	+	0.617549i	$0.788126\pi$
$500$		0			0
$501$	21.8831	−	13.4828i	0.977667	−	0.602368i
$502$	18.7945	+	9.57626i	0.838838	+	0.427409i
$503$	−1.71307	+	10.8159i	−0.0763820	+	0.482257i	0.919611	+	0.392829i	$0.128504\pi$
$503$	−1.71307	+	10.8159i	−0.0763820	+	0.482257i	−0.995993	+	0.0894274i	$0.971496\pi$
$504$	1.03549	+	6.33947i	0.0461244	+	0.282382i
$505$		0			0
$506$	−5.38455	+	7.41120i	−0.239372	+	0.329468i
$507$	−20.0263	−	4.75677i	−0.889401	−	0.211256i
$508$	1.63607	+	10.3298i	0.0725891	+	0.458309i
$509$	2.83257	−	8.71775i	0.125551	−	0.386407i	−0.868450	−	0.495777i	$-0.834883\pi$
$509$	2.83257	−	8.71775i	0.125551	−	0.386407i	0.994001	+	0.109370i	$0.0348833\pi$
$510$		0			0
$511$	0.206834	+	0.636570i	0.00914980	+	0.0281602i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−23.7835	+	14.8127i	−1.05007	+	0.653995i
$514$	−15.9501	+	5.18250i	−0.703529	+	0.228590i
$515$		0			0
$516$	−3.17862	+	0.771244i	−0.139931	+	0.0339521i
$517$	−28.1136	+	4.45276i	−1.23643	+	0.195832i
$518$	0.334760	−	0.334760i	0.0147085	−	0.0147085i
$519$	0.660538	−	8.66031i	0.0289944	−	0.380146i
$520$		0			0
$521$	−13.3932	−	18.4342i	−0.586767	−	0.807615i	0.407650	−	0.913138i	$-0.366348\pi$
$521$	−13.3932	−	18.4342i	−0.586767	−	0.807615i	−0.994417	+	0.105523i	$0.966348\pi$
$522$	11.0703	+	7.96161i	0.484533	+	0.348470i
$523$	−16.3751	+	32.1380i	−0.716035	+	1.40530i	0.189867	+	0.981810i	$0.439194\pi$
$523$	−16.3751	+	32.1380i	−0.716035	+	1.40530i	−0.905902	+	0.423488i	$0.860806\pi$
$524$	19.5318			0.853250
$525$		0			0
$526$	22.7518			0.992025
$527$	−27.8432	+	54.6453i	−1.21287	+	2.38039i
$528$	−9.45990	+	3.94521i	−0.411689	+	0.171693i
$529$	−12.1105	−	16.6686i	−0.526542	−	0.724723i
$530$		0			0
$531$	−9.97144	−	19.3385i	−0.432724	−	0.839221i
$532$	−8.16406	+	8.16406i	−0.353957	+	0.353957i
$533$	1.69218	−	0.268016i	0.0732966	−	0.0116090i
$534$	3.53442	+	14.5668i	0.152949	+	0.630368i
$535$		0			0
$536$	1.23294	−	0.400605i	0.0532548	−	0.0173035i
$537$	4.68650	+	2.85634i	0.202237	+	0.123260i
$538$	−9.22579	+	4.70077i	−0.397752	+	0.202665i
$539$	4.41696	+	13.5940i	0.190252	+	0.585536i
$540$		0			0
$541$	10.6711	−	32.8422i	0.458786	−	1.41200i	−0.407847	−	0.913050i	$-0.633720\pi$
$541$	10.6711	−	32.8422i	0.458786	−	1.41200i	0.866633	−	0.498947i	$-0.166280\pi$
$542$	−0.100029	−	0.631560i	−0.00429663	−	0.0271278i
$543$	2.49797	−	10.5166i	0.107198	−	0.451312i
$544$	3.38144	−	4.65416i	0.144978	−	0.199545i
$545$		0			0
$546$	1.49060	−	3.62335i	0.0637917	−	0.155065i
$547$	3.53445	−	22.3156i	0.151122	−	0.954148i	−0.789268	−	0.614049i	$-0.789540\pi$
$547$	3.53445	−	22.3156i	0.151122	−	0.954148i	0.940390	−	0.340098i	$-0.110460\pi$
$548$	−10.6831	−	5.44330i	−0.456359	−	0.232526i
$549$	11.3536	+	5.71604i	0.484561	+	0.243955i
$550$		0			0
$551$			24.5096i			1.04414i
$552$	0.216828	+	2.67251i	0.00922880	+	0.113750i
$553$	1.99850	+	0.316532i	0.0849851	+	0.0134603i
$554$	24.5631	−	17.8461i	1.04358	−	0.758209i
$555$		0			0
$556$	−18.8265	−	13.6782i	−0.798420	−	0.580086i
$557$	−3.76017	−	3.76017i	−0.159323	−	0.159323i	0.622943	−	0.782267i	$-0.285937\pi$
$557$	−3.76017	−	3.76017i	−0.159323	−	0.159323i	−0.782267	+	0.622943i	$0.785937\pi$
$558$	9.73603	−	30.4644i	0.412159	−	1.28966i
$559$	1.89740	+	0.616502i	0.0802513	+	0.0260752i
$560$		0			0
$561$	−38.1860	+	44.9293i	−1.61221	+	1.89692i
$562$	−9.85907	−	19.3495i	−0.415880	−	0.816210i
$563$	−11.0089	−	21.6061i	−0.463969	−	0.910590i	−0.997882	−	0.0650508i	$-0.979279\pi$
$563$	−11.0089	−	21.6061i	−0.463969	−	0.910590i	0.533913	−	0.845539i	$-0.320721\pi$
$564$	−5.39540	+	6.34819i	−0.227187	+	0.267307i
$565$		0			0
$566$	3.29063	+	1.06919i	0.138315	+	0.0449414i
$567$	−13.7573	−	13.4940i	−0.577751	−	0.566694i
$568$	−2.88591	−	2.88591i	−0.121090	−	0.121090i
$569$	−24.5934	−	17.8681i	−1.03101	−	0.749071i	−0.0624977	−	0.998045i	$-0.519907\pi$
$569$	−24.5934	−	17.8681i	−1.03101	−	0.749071i	−0.968510	+	0.248974i	$0.919907\pi$
$570$		0			0
$571$	4.57335	−	3.32274i	0.191389	−	0.139052i	−0.487964	−	0.872864i	$-0.662260\pi$
$571$	4.57335	−	3.32274i	0.191389	−	0.139052i	0.679353	+	0.733811i	$0.262260\pi$
$572$	6.17473	+	0.977982i	0.258179	+	0.0408915i
$573$	−2.94261	−	36.2692i	−0.122929	−	1.51517i
$574$		−	3.47236i		−	0.144934i
$575$		0			0
$576$	−1.34904	+	2.67957i	−0.0562101	+	0.111649i
$577$	22.8994	+	11.6678i	0.953316	+	0.485739i	0.860223	−	0.509919i	$-0.170324\pi$
$577$	22.8994	+	11.6678i	0.953316	+	0.485739i	0.0930933	+	0.995657i	$0.470324\pi$
$578$	2.51787	−	15.8972i	0.104729	−	0.661236i
$579$	6.53197	−	15.8779i	0.271459	−	0.659864i
$580$		0			0
$581$	−9.52039	+	13.1037i	−0.394972	+	0.543633i
$582$	4.82891	−	20.3301i	0.200165	−	0.842708i
$583$	−5.62058	−	35.4869i	−0.232781	−	1.46972i
$584$	−0.0965991	+	0.297301i	−0.00399730	+	0.0123024i
$585$		0			0
$586$	5.35461	+	16.4798i	0.221197	+	0.680773i
$587$	−12.8802	+	6.56280i	−0.531623	+	0.270876i	−0.699129	−	0.714995i	$-0.746429\pi$
$587$	−12.8802	+	6.56280i	−0.531623	+	0.270876i	0.167506	+	0.985871i	$0.446429\pi$
$588$	3.57242	+	2.17733i	0.147324	+	0.0897916i
$589$	54.6723	−	17.7641i	2.25273	−	0.731957i
$590$		0			0
$591$	−4.16892	−	17.1819i	−0.171486	−	0.706768i
$592$	0.218383	−	0.0345885i	0.00897549	−	0.00142158i
$593$	27.1124	−	27.1124i	1.11337	−	1.11337i	0.120680	−	0.992691i	$-0.461492\pi$
$593$	27.1124	−	27.1124i	1.11337	−	1.11337i	0.992691	−	0.120680i	$-0.0385075\pi$
$594$	15.8758	−	26.3334i	0.651393	−	1.08047i
$595$		0			0
$596$	−8.64870	−	11.9039i	−0.354265	−	0.487603i
$597$	24.1624	−	10.0769i	0.988903	−	0.412418i
$598$	0.742476	−	1.45719i	0.0303621	−	0.0595890i
$599$	22.2597			0.909506			0.454753	−	0.890618i	$-0.349728\pi$
$599$	22.2597			0.909506			0.454753	+	0.890618i	$0.349728\pi$
$600$		0			0
$601$	−0.661317			−0.0269757			−0.0134878	−	0.999909i	$-0.504293\pi$
$601$	−0.661317			−0.0269757			−0.0134878	+	0.999909i	$0.504293\pi$
$602$	1.83568	−	3.60272i	0.0748165	−	0.146836i
$603$	−2.27076	+	3.15740i	−0.0924727	+	0.128579i
$604$	5.02485	+	6.91612i	0.204458	+	0.281413i
$605$		0			0
$606$	−0.0408716	+	0.535868i	−0.00166030	+	0.0217681i
$607$	25.2285	−	25.2285i	1.02399	−	1.02399i	0.0242876	−	0.999705i	$-0.492268\pi$
$607$	25.2285	−	25.2285i	1.02399	−	1.02399i	0.999705	−	0.0242876i	$-0.00773174\pi$
$608$	−5.32589	+	0.843538i	−0.215993	+	0.0342100i
$609$	−16.3814	+	3.97470i	−0.663809	+	0.161063i
$610$		0			0
$611$	4.83290	−	1.57031i	0.195518	−	0.0635278i
$612$	0.0833706	+	17.2584i	0.00337006	+	0.697628i
$613$	22.2583	−	11.3412i	0.899003	−	0.458065i	0.0575173	−	0.998345i	$-0.481682\pi$
$613$	22.2583	−	11.3412i	0.899003	−	0.458065i	0.841485	+	0.540280i	$0.181682\pi$
$614$	−7.34770	−	22.6139i	−0.296529	−	0.912623i
$615$		0			0
$616$	3.91542	−	12.0504i	0.157757	−	0.485525i
$617$	−4.87738	−	30.7946i	−0.196356	−	1.23974i	−0.867131	−	0.498081i	$-0.834038\pi$
$617$	−4.87738	−	30.7946i	−0.196356	−	1.23974i	0.670775	−	0.741661i	$-0.265962\pi$
$618$	−14.8873	−	3.53610i	−0.598853	−	0.142243i
$619$	2.12975	−	2.93135i	0.0856019	−	0.117821i	−0.764068	−	0.645135i	$-0.776801\pi$
$619$	2.12975	−	2.93135i	0.0856019	−	0.117821i	0.849670	+	0.527314i	$0.176801\pi$
$620$		0			0
$621$	−5.26827	−	6.07861i	−0.211408	−	0.243926i
$622$	1.21703	−	7.68404i	0.0487985	−	0.308102i
$623$	−16.5103	−	8.41243i	−0.661472	−	0.337037i
$624$	1.55788	−	0.959853i	0.0623651	−	0.0384249i
$625$		0			0
$626$		−	20.7996i		−	0.831321i
$627$	55.0877	−	4.46940i	2.19999	−	0.178491i
$628$	−24.5648	−	3.89068i	−0.980241	−	0.155255i
$629$	1.02906	−	0.747655i	0.0410312	−	0.0298109i
$630$		0			0
$631$	4.12680	+	2.99829i	0.164285	+	0.119360i	0.666890	−	0.745156i	$-0.267625\pi$
$631$	4.12680	+	2.99829i	0.164285	+	0.119360i	−0.502605	+	0.864516i	$0.667625\pi$
$632$	0.668222	+	0.668222i	0.0265805	+	0.0265805i
$633$	5.22000	−	4.48015i	0.207477	−	0.178070i
$634$	−0.206145	−	0.0669805i	−0.00818706	−	0.00266014i
$635$		0			0
$636$	−8.01312	−	6.81045i	−0.317741	−	0.270052i
$637$	−1.15849	−	2.27367i	−0.0459012	−	0.0900861i
$638$	−12.2112	−	23.9657i	−0.483444	−	0.948813i
$639$	12.1022	+	1.85692i	0.478757	+	0.0734587i
$640$		0			0
$641$	45.1681	+	14.6760i	1.78403	+	0.579668i	0.999198	−	0.0400355i	$-0.0127471\pi$
$641$	45.1681	+	14.6760i	1.78403	+	0.579668i	0.784836	+	0.619703i	$0.212747\pi$
$642$	−6.68738	−	7.79173i	−0.263930	−	0.307515i
$643$	17.9186	+	17.9186i	0.706639	+	0.706639i	0.965827	−	0.259188i	$-0.0834550\pi$
$643$	17.9186	+	17.9186i	0.706639	+	0.706639i	−0.259188	+	0.965827i	$0.583455\pi$
$644$	−2.68158	−	1.94828i	−0.105669	−	0.0767731i
$645$		0			0
$646$	−25.0965	+	18.2337i	−0.987409	+	0.717395i
$647$	7.06356	+	1.11876i	0.277697	+	0.0439829i	0.293730	−	0.955889i	$-0.405103\pi$
$647$	7.06356	+	1.11876i	0.277697	+	0.0439829i	−0.0160323	+	0.999871i	$0.505103\pi$
$648$	−1.49373	−	8.87518i	−0.0586791	−	0.348650i
$649$			42.9184i			1.68469i
$650$		0			0
$651$	20.7391	+	33.6604i	0.812831	+	1.31926i
$652$	1.79029	+	0.912200i	0.0701133	+	0.0357245i
$653$	−3.64054	+	22.9855i	−0.142465	+	0.899490i	0.808118	+	0.589021i	$0.200486\pi$
$653$	−3.64054	+	22.9855i	−0.142465	+	0.899490i	−0.950583	+	0.310470i	$0.899514\pi$
$654$	−3.02356	−	1.24385i	−0.118231	−	0.0486385i
$655$		0			0
$656$	0.953223	−	1.31200i	0.0372171	−	0.0512250i
$657$	−0.294102	−	0.890494i	−0.0114740	−	0.0347415i
$658$	−1.61113	−	10.1723i	−0.0628085	−	0.396557i
$659$	1.14382	−	3.52031i	0.0445568	−	0.137132i	−0.926303	−	0.376779i	$-0.877032\pi$
$659$	1.14382	−	3.52031i	0.0445568	−	0.137132i	0.970860	+	0.239647i	$0.0770317\pi$
$660$		0			0
$661$	−11.4157	−	35.1339i	−0.444019	−	1.36655i	−0.883556	−	0.468326i	$-0.844857\pi$
$661$	−11.4157	−	35.1339i	−0.444019	−	1.36655i	0.439537	−	0.898224i	$-0.355143\pi$
$662$	−6.40470	+	3.26336i	−0.248926	+	0.126834i
$663$	5.47854	−	8.98882i	0.212769	−	0.349097i
$664$	−7.19438	+	2.33760i	−0.279196	+	0.0907163i
$665$		0			0
$666$	−0.466764	+	0.471295i	−0.0180867	+	0.0182623i
$667$	−6.94972	+	1.10073i	−0.269094	+	0.0426203i
$668$	−10.4933	+	10.4933i	−0.405999	+	0.405999i
$669$	23.1197	+	1.76338i	0.893860	+	0.0681764i
$670$		0			0
$671$	−14.7379	−	20.2849i	−0.568949	−	0.783092i
$672$	−1.42749	−	3.42286i	−0.0550667	−	0.132040i
$673$	0.542210	−	1.06415i	0.0209006	−	0.0410198i	−0.880320	−	0.474380i	$-0.842672\pi$
$673$	0.542210	−	1.06415i	0.0209006	−	0.0410198i	0.901221	+	0.433360i	$0.142672\pi$
$674$	6.75390			0.260151
$675$		0			0
$676$	11.8839			0.457073
$677$	15.6087	−	30.6338i	0.599892	−	1.17735i	−0.368898	−	0.929470i	$-0.620265\pi$
$677$	15.6087	−	30.6338i	0.599892	−	1.17735i	0.968790	−	0.247884i	$-0.0797351\pi$
$678$	5.65503	+	13.5597i	0.217180	+	0.520758i
$679$	15.1832	+	20.8979i	0.582679	+	0.801988i
$680$		0			0
$681$	−1.47820	−	0.112745i	−0.0566448	−	0.00432040i
$682$	−44.6088	+	44.6088i	−1.70816	+	1.70816i
$683$	−44.5125	+	7.05008i	−1.70322	+	0.269764i	−0.930849	−	0.365405i	$-0.880930\pi$
$683$	−44.5125	+	7.05008i	−1.70322	+	0.269764i	−0.772373	+	0.635169i	$0.780930\pi$
$684$	11.3834	−	11.4939i	0.435254	−	0.439479i
$685$		0			0
$686$	−19.1733	+	6.22977i	−0.732038	+	0.237854i
$687$	14.9149	−	24.4714i	0.569039	−	0.933641i
$688$	1.68260	−	0.857327i	0.0641485	−	0.0326853i
$689$	1.98215	+	6.10043i	0.0755138	+	0.232408i
$690$		0			0
$691$	1.10289	−	3.39434i	0.0419558	−	0.129127i	−0.927885	−	0.372867i	$-0.878375\pi$
$691$	1.10289	−	3.39434i	0.0419558	−	0.129127i	0.969840	+	0.243741i	$0.0783746\pi$
$692$	0.784450	+	4.95282i	0.0298203	+	0.188278i
$693$	11.9207	+	36.0941i	0.452832	+	1.37110i
$694$	−2.69058	+	3.70326i	−0.102133	+	0.140574i
$695$		0			0
$696$	−7.28069	−	2.99518i	−0.275974	−	0.113532i
$697$	1.45946	−	9.21466i	0.0552809	−	0.349030i
$698$	8.71510	+	4.44057i	0.329871	+	0.168078i
$699$	4.95215	+	8.03754i	0.187308	+	0.304008i
$700$		0			0
$701$			19.6139i			0.740807i	0.928871	+	0.370403i	$0.120781\pi$
$701$			19.6139i			0.740807i	−0.928871	+	0.370403i	$0.879219\pi$
$702$	−2.06394	+	5.08674i	−0.0778984	+	0.191986i
$703$	−1.17758	−	0.186511i	−0.0444133	−	0.00703438i
$704$	4.78745	−	3.47829i	0.180434	−	0.131093i
$705$		0			0
$706$	−8.76956	−	6.37146i	−0.330047	−	0.239793i
$707$	−0.469776	−	0.469776i	−0.0176677	−	0.0176677i
$708$	8.18139	+	9.53246i	0.307476	+	0.358252i
$709$	−22.4237	−	7.28590i	−0.842140	−	0.273628i	−0.143990	−	0.989579i	$-0.545993\pi$
$709$	−22.4237	−	7.28590i	−0.842140	−	0.273628i	−0.698150	+	0.715951i	$0.745993\pi$
$710$		0			0
$711$	−2.80223	−	0.429964i	−0.105092	−	0.0161249i
$712$	−3.92891	−	7.71092i	−0.147242	−	0.288979i
$713$	7.49238	+	14.7046i	0.280592	+	0.550692i
$714$	−16.2567	−	13.8168i	−0.608392	−	0.517080i
$715$		0			0
$716$	−3.01361	−	0.979183i	−0.112624	−	0.0365938i
$717$	11.4544	−	9.83090i	0.427771	−	0.367142i
$718$	−14.8975	−	14.8975i	−0.555969	−	0.555969i
$719$	−30.2210	−	21.9569i	−1.12705	−	0.818853i	−0.141791	−	0.989897i	$-0.545286\pi$
$719$	−30.2210	−	21.9569i	−1.12705	−	0.818853i	−0.985263	+	0.171044i	$0.945286\pi$
$720$		0			0
$721$	15.3031	−	11.1183i	0.569916	−	0.414068i
$722$	9.95259	+	1.57634i	0.370397	+	0.0586651i
$723$	−43.8944	+	3.56127i	−1.63245	+	0.132445i
$724$			6.24071i			0.231934i
$725$		0			0
$726$	−35.4178	+	21.8219i	−1.31448	+	0.809886i
$727$	37.8579	+	19.2896i	1.40407	+	0.715411i	0.981597	−	0.190964i	$-0.0611612\pi$
$727$	37.8579	+	19.2896i	1.40407	+	0.715411i	0.422476	+	0.906374i	$0.361161\pi$
$728$	−0.353862	+	2.23419i	−0.0131150	+	0.0828047i
$729$	19.3666	+	18.8132i	0.717280	+	0.696785i
$730$		0			0
$731$	6.38561	−	8.78903i	0.236180	−	0.325074i
$732$	−7.14023	−	1.69599i	−0.263911	−	0.0626855i
$733$	6.98056	+	44.0735i	0.257833	+	1.62789i	0.688398	+	0.725333i	$0.258314\pi$
$733$	6.98056	+	44.0735i	0.257833	+	1.62789i	−0.430565	+	0.902559i	$0.641686\pi$
$734$	8.34641	−	25.6876i	0.308072	−	0.948147i
$735$		0			0
$736$	−0.478373	−	1.47228i	−0.0176331	−	0.0542690i
$737$	6.83537	−	3.48279i	0.251784	−	0.128290i
$738$	0.0235020	+	4.86510i	0.000865122	+	0.179087i
$739$	−8.01855	+	2.60538i	−0.294967	+	0.0958406i	−0.452762	−	0.891631i	$-0.649561\pi$
$739$	−8.01855	+	2.60538i	−0.294967	+	0.0958406i	0.157795	+	0.987472i	$0.449561\pi$
$740$		0			0
$741$	−9.58877	+	2.32657i	−0.352252	+	0.0854687i
$742$	12.8402	−	2.03368i	0.471378	−	0.0746589i
$743$	−24.9192	+	24.9192i	−0.914196	+	0.914196i	−0.996599	−	0.0824029i	$-0.973741\pi$
$743$	−24.9192	+	24.9192i	−0.914196	+	0.914196i	0.0824029	+	0.996599i	$0.473741\pi$
$744$	−1.40428	+	18.4115i	−0.0514834	+	0.674999i
$745$		0			0
$746$	−15.7261	−	21.6451i	−0.575772	−	0.792482i
$747$	13.2503	−	18.4239i	0.484802	−	0.674097i
$748$	15.4553	−	30.3327i	0.565101	−	1.10907i
$749$	12.6933			0.463804
$750$		0			0
$751$	−8.40064			−0.306544			−0.153272	−	0.988184i	$-0.548981\pi$
$751$	−8.40064			−0.306544			−0.153272	+	0.988184i	$0.548981\pi$
$752$	2.18372	−	4.28579i	0.0796320	−	0.156287i
$753$	33.7201	−	14.0628i	1.22883	−	0.512478i
$754$	2.82250	+	3.88484i	0.102789	+	0.141477i
$755$		0			0
$756$	9.52817	+	5.74432i	0.346536	+	0.208919i
$757$	−5.57829	+	5.57829i	−0.202746	+	0.202746i	−0.801176	−	0.598429i	$-0.795792\pi$
$757$	−5.57829	+	5.57829i	−0.202746	+	0.202746i	0.598429	+	0.801176i	$0.295792\pi$
$758$	−15.5940	+	2.46985i	−0.566400	+	0.0897089i
$759$	3.74130	+	15.4195i	0.135801	+	0.559691i
$760$		0			0
$761$	5.92036	−	1.92364i	0.214613	−	0.0697320i	−0.199737	−	0.979849i	$-0.564009\pi$
$761$	5.92036	−	1.92364i	0.214613	−	0.0697320i	0.414350	+	0.910118i	$0.364009\pi$
$762$	15.4681	+	9.42757i	0.560352	+	0.341525i
$763$	3.60114	−	1.83487i	0.130370	−	0.0664268i
$764$	6.49209	+	19.9806i	0.234875	+	0.722872i
$765$		0			0
$766$	4.93411	−	15.1856i	0.178276	−	0.548679i
$767$	−1.19862	−	7.56779i	−0.0432796	−	0.273257i
$768$	0.400270	−	1.68517i	0.0144435	−	0.0608082i
$769$	−2.22958	+	3.06876i	−0.0804008	+	0.110662i	−0.847323	−	0.531078i	$-0.821787\pi$
$769$	−2.22958	+	3.06876i	−0.0804008	+	0.110662i	0.766922	+	0.641740i	$0.221787\pi$
$770$		0			0
$771$	−11.0514	+	26.8637i	−0.398006	+	0.967473i
$772$	−1.55066	+	9.79050i	−0.0558096	+	0.352368i
$773$	30.3587	+	15.4685i	1.09193	+	0.556364i	0.904742	−	0.425960i	$-0.140064\pi$
$773$	30.3587	+	15.4685i	1.09193	+	0.556364i	0.187185	+	0.982325i	$0.440064\pi$
$774$	−2.54757	+	5.06017i	−0.0915704	+	0.181884i
$775$		0			0
$776$			12.0641i			0.433077i
$777$	−0.0663100	−	0.817305i	−0.00237886	−	0.0293206i
$778$	11.3942	+	1.80467i	0.408503	+	0.0647005i
$779$	−7.07466	+	5.14004i	−0.253476	+	0.184161i
$780$		0			0
$781$	−19.5390	−	14.1959i	−0.699159	−	0.507969i
$782$	−6.29727	−	6.29727i	−0.225190	−	0.225190i
$783$	22.9250	−	5.67980i	0.819272	−	0.202980i
$784$	−2.29721	−	0.746410i	−0.0820433	−	0.0266575i
$785$		0			0
$786$	21.9087	−	25.7776i	0.781456	−	0.919455i
$787$	−14.2544	−	27.9758i	−0.508114	−	0.997230i	−0.992485	−	0.122367i	$-0.960951\pi$
$787$	−14.2544	−	27.9758i	−0.508114	−	0.997230i	0.484371	−	0.874863i	$-0.339049\pi$
$788$	4.63424	+	9.09520i	0.165088	+	0.324003i
$789$	25.5205	−	30.0272i	0.908554	−	1.06900i
$790$		0			0
$791$	−17.2729	−	5.61232i	−0.614155	−	0.199551i
$792$	−5.40430	+	16.9103i	−0.192034	+	0.600880i
$793$	3.16524	+	3.16524i	0.112401	+	0.112401i
$794$	16.9444	+	12.3108i	0.601334	+	0.436895i
$795$		0			0
$796$	−12.2281	+	8.88422i	−0.433413	+	0.314893i
$797$	10.4366	+	1.65300i	0.369685	+	0.0585523i	0.338513	−	0.940962i	$-0.390076\pi$
$797$	10.4366	+	1.65300i	0.369685	+	0.0585523i	0.0311718	+	0.999514i	$0.490076\pi$
$798$	1.61716	+	19.9323i	0.0572467	+	0.705596i
$799$		−	27.6716i		−	0.978949i
$800$		0			0
$801$	23.1894	+	11.6749i	0.819358	+	0.412511i
$802$	21.7757	+	11.0953i	0.768926	+	0.391787i
$803$	−0.289381	+	1.82708i	−0.0102120	+	0.0644762i
$804$	0.854267	−	2.07656i	0.0301277	−	0.0732345i
$805$		0			0
$806$	6.62002	−	9.11167i	0.233180	−	0.320945i
$807$	−4.14454	+	17.4488i	−0.145895	+	0.614227i
$808$	−0.0485388	−	0.306462i	−0.00170759	−	0.0107813i
$809$	−4.15772	+	12.7961i	−0.146178	+	0.449889i	−0.997161	−	0.0753048i	$-0.976007\pi$
$809$	−4.15772	+	12.7961i	−0.146178	+	0.449889i	0.850983	+	0.525193i	$0.176007\pi$
$810$		0			0
$811$	6.32531	+	19.4673i	0.222112	+	0.683590i	0.998572	+	0.0534235i	$0.0170133\pi$
$811$	6.32531	+	19.4673i	0.222112	+	0.683590i	−0.776460	+	0.630166i	$0.782987\pi$
$812$	8.67148	−	4.41834i	0.304309	−	0.155053i
$813$	−0.945720	−	0.576400i	−0.0331678	−	0.0202152i
$814$	1.24438	−	0.404322i	0.0436154	−	0.0141715i
$815$		0			0
$816$	−2.34950	−	9.68328i	−0.0822490	−	0.338983i
$817$	−10.0575	+	1.59296i	−0.351869	+	0.0557306i
$818$	6.92463	−	6.92463i	0.242114	−	0.242114i
$819$	−3.11001	−	6.03153i	−0.108673	−	0.210759i
$820$		0			0
$821$	−11.1279	−	15.3163i	−0.388368	−	0.534543i	0.569409	−	0.822054i	$-0.307172\pi$
$821$	−11.1279	−	15.3163i	−0.388368	−	0.534543i	−0.957777	+	0.287512i	$0.907172\pi$
$822$	−19.1671	+	7.99355i	−0.668528	+	0.278807i
$823$	7.17013	−	14.0722i	0.249935	−	0.490525i	−0.731618	−	0.681715i	$-0.761235\pi$
$823$	7.17013	−	14.0722i	0.249935	−	0.490525i	0.981553	+	0.191190i	$0.0612345\pi$
$824$	8.83429			0.307757
$825$		0			0
$826$	−15.5291			−0.540326
$827$	−3.08387	+	6.05244i	−0.107237	+	0.210464i	−0.938389	−	0.345581i	$-0.887682\pi$
$827$	−3.08387	+	6.05244i	−0.107237	+	0.210464i	0.831152	+	0.556045i	$0.187682\pi$
$828$	3.77033	+	2.71158i	0.131028	+	0.0942338i
$829$	11.0240	+	15.1733i	0.382880	+	0.526989i	0.956345	−	0.292241i	$-0.0944010\pi$
$829$	11.0240	+	15.1733i	0.382880	+	0.526989i	−0.573465	+	0.819230i	$0.694401\pi$
$830$		0			0
$831$	3.99936	−	52.4356i	0.138736	−	1.81897i
$832$	−0.747028	+	0.747028i	−0.0258985	+	0.0258985i
$833$	−13.7246	+	2.17376i	−0.475528	+	0.0753162i
$834$	−39.1697	+	9.50393i	−1.35634	+	0.329094i
$835$		0			0
$836$	−30.3476	+	9.86055i	−1.04960	+	0.341034i
$837$	−29.2853	−	47.0210i	−1.01225	−	1.62528i
$838$	−22.9876	+	11.7128i	−0.794093	+	0.404611i
$839$	5.00273	+	15.3968i	0.172713	+	0.531557i	0.999522	−	0.0309268i	$-0.00984587\pi$
$839$	5.00273	+	15.3968i	0.172713	+	0.531557i	−0.826808	+	0.562484i	$0.809846\pi$
$840$		0			0
$841$	−2.57725	+	7.93197i	−0.0888709	+	0.273516i
$842$	−6.16556	−	38.9278i	−0.212479	−	1.34154i
$843$	−36.5959	−	8.69245i	−1.26043	−	0.299384i
$844$	−2.33443	+	3.21307i	−0.0803545	+	0.110598i
$845$		0			0
$846$	2.32620	+	14.2414i	0.0799763	+	0.489631i
$847$	8.04490	−	50.7935i	0.276426	−	1.74529i
$848$	5.40982	+	2.75644i	0.185774	+	0.0946566i
$849$	5.10216	−	3.14358i	0.175106	−	0.107887i
$850$		0			0
$851$		−	0.342281i		−	0.0117332i
$852$	−7.04585	+	0.571647i	−0.241387	+	0.0195843i
$853$	32.4823	+	5.14470i	1.11217	+	0.176151i	0.685371	−	0.728194i	$-0.259640\pi$
$853$	32.4823	+	5.14470i	1.11217	+	0.176151i	0.426803	+	0.904345i	$0.359640\pi$
$854$	7.33967	−	5.33258i	0.251158	−	0.182477i
$855$		0			0
$856$	4.79605	+	3.48453i	0.163926	+	0.119099i
$857$	−14.2417	−	14.2417i	−0.486489	−	0.486489i	0.420708	−	0.907196i	$-0.361782\pi$
$857$	−14.2417	−	14.2417i	−0.486489	−	0.486489i	−0.907196	+	0.420708i	$0.861782\pi$
$858$	8.21687	−	7.05226i	0.280519	−	0.240760i
$859$	29.9968	+	9.74655i	1.02348	+	0.332548i	0.772208	−	0.635369i	$-0.219152\pi$
$859$	29.9968	+	9.74655i	1.02348	+	0.332548i	0.251269	+	0.967917i	$0.419152\pi$
$860$		0			0
$861$	−4.58274	−	3.89492i	−0.156179	−	0.132739i
$862$	2.79055	+	5.47676i	0.0950465	+	0.186539i
$863$	−9.85205	−	19.3357i	−0.335368	−	0.658196i	0.660318	−	0.750986i	$-0.270421\pi$
$863$	−9.85205	−	19.3357i	−0.335368	−	0.658196i	−0.995686	+	0.0927901i	$0.970421\pi$
$864$	2.02321	+	4.78608i	0.0688312	+	0.162826i
$865$		0			0
$866$	−15.9153	−	5.17119i	−0.540824	−	0.175724i
$867$	−18.1564	−	21.1548i	−0.616625	−	0.718454i
$868$	−16.1407	−	16.1407i	−0.547852	−	0.547852i
$869$	4.52418	+	3.28701i	0.153472	+	0.111504i
$870$		0			0
$871$	−1.10801	+	0.805017i	−0.0375435	+	0.0272770i
$872$	1.86436	+	0.295286i	0.0631352	+	0.00999963i
$873$	−21.4146	−	29.1772i	−0.724773	−	0.987497i
$874$			8.34750i			0.282358i
$875$		0			0
$876$	0.284016	+	0.460970i	0.00959602	+	0.0155747i
$877$	6.74142	+	3.43493i	0.227642	+	0.115989i	0.564092	−	0.825712i	$-0.309226\pi$
$877$	6.74142	+	3.43493i	0.227642	+	0.115989i	−0.336450	+	0.941701i	$0.609226\pi$
$878$	3.14677	−	19.8679i	0.106198	−	0.670510i
$879$	27.7558	+	11.4184i	0.936181	+	0.385132i
$880$		0			0
$881$	−18.8656	+	25.9662i	−0.635597	+	0.874825i	−0.998371	−	0.0570525i	$-0.981830\pi$
$881$	−18.8656	+	25.9662i	−0.635597	+	0.874825i	0.362774	+	0.931877i	$0.381830\pi$
$882$	6.88074	−	2.27249i	0.231687	−	0.0765189i
$883$	4.49099	+	28.3550i	0.151134	+	0.954222i	0.940375	+	0.340139i	$0.110474\pi$
$883$	4.49099	+	28.3550i	0.151134	+	0.954222i	−0.789241	+	0.614083i	$0.789526\pi$
$884$	−1.87810	+	5.78018i	−0.0631672	+	0.194409i
$885$		0			0
$886$	7.49794	+	23.0763i	0.251898	+	0.775263i
$887$	10.8136	−	5.50981i	0.363086	−	0.185001i	−0.262924	−	0.964816i	$-0.584687\pi$
$887$	10.8136	−	5.50981i	0.363086	−	0.185001i	0.626010	+	0.779815i	$0.284687\pi$
$888$	0.199310	−	0.327014i	0.00668839	−	0.0109739i
$889$	−21.2974	+	6.91994i	−0.714291	+	0.232087i
$890$		0			0
$891$	−16.9464	−	50.4905i	−0.567725	−	1.69149i
$892$	−13.2221	+	2.09418i	−0.442710	+	0.0701183i
$893$	−18.3403	+	18.3403i	−0.613736	+	0.613736i
$894$	−25.4117	−	1.93820i	−0.849893	−	0.0648230i
$895$		0			0
$896$	1.25854	+	1.73224i	0.0420450	+	0.0578699i
$897$	−1.09034	−	2.61442i	−0.0364052	−	0.0872931i
$898$	7.22945	−	14.1886i	0.241250	−	0.473479i
$899$	−48.4565			−1.61611
$900$		0			0
$901$	34.9289			1.16365
$902$	4.35682	−	8.55073i	0.145066	−	0.284708i
$903$	−2.69571	−	6.46382i	−0.0897076	−	0.215102i
$904$	−4.98574	−	6.86228i	−0.165823	−	0.228236i
$905$		0			0
$906$	14.7641	+	1.12608i	0.490503	+	0.0374116i
$907$	−18.7112	+	18.7112i	−0.621295	+	0.621295i	−0.945863	−	0.324567i	$-0.894781\pi$
$907$	−18.7112	+	18.7112i	−0.621295	+	0.621295i	0.324567	+	0.945863i	$0.394781\pi$
$908$	0.845381	−	0.133895i	0.0280549	−	0.00444347i
$909$	0.661379	+	0.655020i	0.0219366	+	0.0217257i
$910$		0			0
$911$	37.0222	−	12.0293i	1.22660	−	0.398547i	0.377119	−	0.926165i	$-0.376915\pi$
$911$	37.0222	−	12.0293i	1.22660	−	0.398547i	0.849482	+	0.527618i	$0.176915\pi$
$912$	−4.86073	+	7.97517i	−0.160955	+	0.264084i
$913$	−39.8854	+	20.3226i	−1.32002	+	0.672581i
$914$	−1.00626	−	3.09695i	−0.0332842	−	0.102438i
$915$		0			0
$916$	−5.11297	+	15.7361i	−0.168937	+	0.519935i
$917$	6.54220	+	41.3058i	0.216042	+	1.36404i
$918$	22.8707	+	19.2486i	0.754845	+	0.635297i
$919$	13.4831	−	18.5579i	0.444766	−	0.612168i	−0.526497	−	0.850177i	$-0.676495\pi$
$919$	13.4831	−	18.5579i	0.444766	−	0.612168i	0.971263	+	0.238009i	$0.0764948\pi$
$920$		0			0
$921$	−38.0871	−	15.6685i	−1.25501	−	0.516296i
$922$	1.55131	−	9.79461i	0.0510898	−	0.322568i
$923$	3.84176	+	1.95747i	0.126453	+	0.0644311i
$924$	−11.5119	−	18.6843i	−0.378715	−	0.614669i
$925$		0			0
$926$			23.1191i			0.759740i
$927$	−21.3658	+	15.6814i	−0.701744	+	0.515045i
$928$	4.48935	+	0.711043i	0.147370	+	0.0233411i
$929$	−0.473139	+	0.343755i	−0.0155232	+	0.0112782i	−0.595520	−	0.803341i	$-0.703054\pi$
$929$	−0.473139	+	0.343755i	−0.0155232	+	0.0112782i	0.579997	+	0.814619i	$0.303054\pi$
$930$		0			0
$931$	10.5372	+	7.65572i	0.345342	+	0.250906i
$932$	−3.85413	−	3.85413i	−0.126246	−	0.126246i
$933$	−8.77606	−	10.2253i	−0.287315	−	0.334763i
$934$	4.41971	+	1.43605i	0.144617	+	0.0469891i
$935$		0			0
$936$	0.480671	−	3.13271i	0.0157112	−	0.102396i
$937$	25.3343	+	49.7213i	0.827634	+	1.62432i	0.780268	+	0.625445i	$0.215083\pi$
$937$	25.3343	+	49.7213i	0.827634	+	1.62432i	0.0473659	+	0.998878i	$0.484917\pi$
$938$	1.26017	+	2.47323i	0.0411461	+	0.0807538i
$939$	−27.4508	−	23.3308i	−0.895824	−	0.761372i
$940$		0			0
$941$	12.5712	+	4.08462i	0.409808	+	0.133155i	0.506664	−	0.862144i	$-0.330879\pi$
$941$	12.5712	+	4.08462i	0.409808	+	0.133155i	−0.0968556	+	0.995298i	$0.530879\pi$
$942$	−32.6889	+	28.0558i	−1.06506	+	0.914108i
$943$	−1.77519	−	1.77519i	−0.0578082	−	0.0578082i
$944$	−5.86752	−	4.26300i	−0.190972	−	0.138749i
$945$		0			0
$946$	9.04074	−	6.56848i	0.293940	−	0.213560i
$947$	17.8550	+	2.82795i	0.580210	+	0.0918962i	0.439639	−	0.898174i	$-0.355106\pi$
$947$	17.8550	+	2.82795i	0.580210	+	0.0918962i	0.140571	+	0.990071i	$0.455106\pi$
$948$	1.63144	−	0.132363i	0.0529868	−	0.00429895i
$949$		−	0.330250i		−	0.0107204i
$950$		0			0
$951$	−0.319630	+	0.196933i	−0.0103647	+	0.00638600i
$952$	10.9752	+	5.59216i	0.355709	+	0.181243i
$953$	8.17990	−	51.6458i	0.264973	−	1.67297i	−0.392698	−	0.919667i	$-0.628458\pi$
$953$	8.17990	−	51.6458i	0.264973	−	1.67297i	0.657671	−	0.753305i	$-0.271542\pi$
$954$	−17.9765	+	2.93629i	−0.582011	+	0.0950658i
$955$		0			0
$956$	−5.12250	+	7.05051i	−0.165673	+	0.228030i
$957$	−45.3265	−	10.7662i	−1.46520	−	0.348022i
$958$	−2.47121	−	15.6026i	−0.0798412	−	0.504097i
$959$	7.93318	−	24.4158i	0.256176	−	0.788428i
$960$		0			0
$961$	25.5409	+	78.6068i	0.823900	+	2.53570i
$962$	−0.208129	+	0.106047i	−0.00671033	+	0.00341909i
$963$	−17.7845	+	0.0859123i	−0.573098	+	0.00276849i
$964$	24.1813	−	7.85699i	0.778828	−	0.253056i
$965$		0			0
$966$	−5.57920	+	1.35371i	−0.179508	+	0.0435549i
$967$	30.7047	−	4.86314i	0.987395	−	0.156388i	0.358208	−	0.933642i	$-0.383388\pi$
$967$	30.7047	−	4.86314i	0.987395	−	0.156388i	0.629187	+	0.777254i	$0.283388\pi$
$968$	16.9834	−	16.9834i	0.545867	−	0.545867i
$969$	−4.08621	+	53.5743i	−0.131268	+	1.72106i
$970$		0			0
$971$	25.2468	+	34.7493i	0.810210	+	1.11516i	0.991291	+	0.131690i	$0.0420404\pi$
$971$	25.2468	+	34.7493i	0.810210	+	1.11516i	−0.181081	+	0.983468i	$0.557960\pi$
$972$	−13.3887	−	7.98384i	−0.429444	−	0.256082i
$973$	22.6208	−	44.3957i	0.725188	−	1.42326i
$974$	0.135570			0.00434393
$975$		0			0
$976$	4.23711			0.135627
$977$	−26.9394	+	52.8715i	−0.861867	+	1.69151i	−0.150590	+	0.988596i	$0.548117\pi$
$977$	−26.9394	+	52.8715i	−0.861867	+	1.69151i	−0.711276	+	0.702912i	$0.751883\pi$
$978$	3.21206	−	1.33958i	0.102710	−	0.0428349i
$979$	−30.1017	−	41.4314i	−0.962054	−	1.32415i
$980$		0			0
$981$	−5.03311	+	2.59520i	−0.160695	+	0.0828584i
$982$	6.43398	−	6.43398i	0.205317	−	0.205317i
$983$	37.5537	−	5.94792i	1.19778	−	0.189709i	0.474492	−	0.880260i	$-0.342632\pi$
$983$	37.5537	−	5.94792i	1.19778	−	0.189709i	0.723284	+	0.690550i	$0.242632\pi$
$984$	−0.662320	−	2.72970i	−0.0211140	−	0.0870197i
$985$		0			0
$986$	24.8687	−	8.08033i	0.791981	−	0.257330i
$987$	−15.2323	−	9.28386i	−0.484851	−	0.295508i
$988$	5.07580	−	2.58625i	0.161483	−	0.0822796i
$989$	−0.903372	−	2.78029i	−0.0287255	−	0.0884081i
$990$		0			0
$991$	9.31171	−	28.6585i	0.295796	−	0.910367i	−0.687157	−	0.726509i	$-0.741141\pi$
$991$	9.31171	−	28.6585i	0.295796	−	0.910367i	0.982953	−	0.183858i	$-0.0588585\pi$
$992$	−1.66771	−	10.5295i	−0.0529499	−	0.334313i
$993$	−2.87721	+	12.1132i	−0.0913054	+	0.384402i
$994$	5.13648	−	7.06976i	0.162919	−	0.224239i
$995$		0			0
$996$	−4.98478	+	12.1170i	−0.157949	+	0.383943i
$997$	−5.29952	+	33.4599i	−0.167838	+	1.05968i	0.749625	+	0.661863i	$0.230234\pi$
$997$	−5.29952	+	33.4599i	−0.167838	+	1.05968i	−0.917463	+	0.397822i	$0.869766\pi$
$998$	−24.5829	−	12.5256i	−0.778157	−	0.396491i
$999$	0.0984382	+	1.14467i	0.00311445	+	0.0362158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.b.143.4		80
3.2	odd	2	inner	750.2.l.b.143.10		80
5.2	odd	4		750.2.l.a.107.5		80
5.3	odd	4		750.2.l.c.107.6		80
5.4	even	2		150.2.l.a.83.7	yes	80
15.2	even	4		750.2.l.a.107.6		80
15.8	even	4		750.2.l.c.107.5		80
15.14	odd	2		150.2.l.a.83.1	yes	80
25.3	odd	20		150.2.l.a.47.1	✓	80
25.4	even	10		750.2.l.c.743.5		80
25.21	even	5		750.2.l.a.743.6		80
25.22	odd	20	inner	750.2.l.b.257.10		80
75.29	odd	10		750.2.l.c.743.6		80
75.47	even	20	inner	750.2.l.b.257.4		80
75.53	even	20		150.2.l.a.47.7	yes	80
75.71	odd	10		750.2.l.a.743.5		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.1	✓	80	25.3	odd	20
150.2.l.a.47.7	yes	80	75.53	even	20
150.2.l.a.83.1	yes	80	15.14	odd	2
150.2.l.a.83.7	yes	80	5.4	even	2
750.2.l.a.107.5		80	5.2	odd	4
750.2.l.a.107.6		80	15.2	even	4
750.2.l.a.743.5		80	75.71	odd	10
750.2.l.a.743.6		80	25.21	even	5
750.2.l.b.143.4		80	1.1	even	1	trivial
750.2.l.b.143.10		80	3.2	odd	2	inner
750.2.l.b.257.4		80	75.47	even	20	inner
750.2.l.b.257.10		80	25.22	odd	20	inner
750.2.l.c.107.5		80	15.8	even	4
750.2.l.c.107.6		80	5.3	odd	4
750.2.l.c.743.5		80	25.4	even	10
750.2.l.c.743.6		80	75.29	odd	10

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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(0.666690 + 1.59860i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.72703 - 0.131724i) q^{6} +(1.51403 - 1.51403i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.11105 + 2.13154i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(0.666690 + 1.59860i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-1.72703 - 0.131724i) q^{6} +(1.51403 - 1.51403i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-2.11105 + 2.13154i) q^{9} +(5.62798 - 1.82864i) q^{11} +(0.901424 - 1.47900i) q^{12} +(-0.941310 + 0.479621i) q^{13} +(0.661655 + 2.03636i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.899945 + 5.68203i) q^{17} +(-0.940823 - 2.84866i) q^{18} +(3.16950 - 4.36244i) q^{19} +(3.42972 + 1.41094i) q^{21} +(-0.925718 + 5.84476i) q^{22} +(1.37932 + 0.702799i) q^{23} +(0.908558 + 1.47463i) q^{24} -1.05646i q^{26} +(-4.81490 - 1.95364i) q^{27} +(-2.11480 - 0.334951i) q^{28} +(-3.67723 + 2.67167i) q^{29} +(8.62475 + 6.26624i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(6.67539 + 7.77776i) q^{33} +(-5.47129 - 1.77773i) q^{34} +(2.96530 + 0.454984i) q^{36} +(-0.100380 - 0.197006i) q^{37} +(2.44804 + 4.80455i) q^{38} +(-1.39429 - 1.18502i) q^{39} +(-1.54235 - 0.501139i) q^{41} +(-2.81421 + 2.41535i) q^{42} +(-1.33532 - 1.33532i) q^{43} +(-4.78745 - 3.47829i) q^{44} +(-1.25240 + 0.909919i) q^{46} +(-4.75083 - 0.752458i) q^{47} +(-1.72638 + 0.140065i) q^{48} +2.41543i q^{49} +(-8.48331 + 5.22681i) q^{51} +(0.941310 + 0.479621i) q^{52} +(0.949805 - 5.99683i) q^{53} +(3.92663 - 3.40317i) q^{54} +(1.25854 - 1.73224i) q^{56} +(9.08688 + 2.15837i) q^{57} +(-0.711043 - 4.48935i) q^{58} +(-2.24119 + 6.89769i) q^{59} +(-1.30934 - 4.02973i) q^{61} +(-9.49882 + 4.83989i) q^{62} +(0.0310298 + 6.42341i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-9.96060 + 2.41679i) q^{66} +(1.28043 - 0.202800i) q^{67} +(4.06788 - 4.06788i) q^{68} +(-0.203915 + 2.67353i) q^{69} +(-2.39892 - 3.30183i) q^{71} +(-1.75161 + 2.43554i) q^{72} +(-0.141918 + 0.278530i) q^{73} +0.221105 q^{74} -5.39228 q^{76} +(5.75231 - 11.2895i) q^{77} +(1.68885 - 0.704330i) q^{78} +(0.555462 + 0.764528i) q^{79} +(-0.0869513 - 8.99958i) q^{81} +(1.14673 - 1.14673i) q^{82} +(-7.47149 + 1.18337i) q^{83} +(-0.874463 - 3.60403i) q^{84} +(1.79600 - 0.583556i) q^{86} +(-6.72250 - 4.09725i) q^{87} +(5.27263 - 2.68654i) q^{88} +(-2.67429 - 8.23061i) q^{89} +(-0.699010 + 2.15133i) q^{91} +(-0.242168 - 1.52899i) q^{92} +(-4.26719 + 17.9652i) q^{93} +(2.82728 - 3.89142i) q^{94} +(0.658960 - 1.60180i) q^{96} +(-1.88725 + 11.9156i) q^{97} +(-2.15217 - 1.09658i) q^{98} +(-7.98311 + 15.8566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{3} - 4 q^{7}+O(q^{10}) \) 80 * q - 4 * q^3 - 4 * q^7	\( 80 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 20 q^{16} + 8 q^{18} - 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} - 40 q^{34} + 24 q^{37} - 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} + 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} + 80 q^{79} - 40 q^{81} - 96 q^{82} + 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97}+O(q^{100}) \) 80 * q - 4 * q^3 - 4 * q^7 + 4 * q^12 + 20 * q^16 + 8 * q^18 - 40 * q^19 + 36 * q^22 - 4 * q^27 + 16 * q^28 - 4 * q^33 - 40 * q^34 + 24 * q^37 - 40 * q^39 + 4 * q^42 + 24 * q^43 + 4 * q^48 + 64 * q^57 - 20 * q^58 - 64 * q^63 - 96 * q^67 + 140 * q^69 - 8 * q^72 - 100 * q^73 - 100 * q^78 + 80 * q^79 - 40 * q^81 - 96 * q^82 + 60 * q^84 - 80 * q^87 - 4 * q^88 - 12 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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