LMFDB - Embedded newform 750.2.l.b.143.10

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			143.10
Character	$\chi$	$=$	750.143
Dual form			750.2.l.b.257.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 - 0.891007i) q^{2} +(1.12805 - 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(1.51403 - 1.51403i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +O(q^{10})$	\(q+(0.453990 - 0.891007i) q^{2} +(1.12805 - 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(1.51403 - 1.51403i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +(-5.62798 + 1.82864i) q^{11} +(-1.72638 - 0.140065i) 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} +(-2.84866 - 0.940823i) q^{18} +(3.16950 - 4.36244i) q^{19} +(-0.282042 - 3.69786i) q^{21} +(-0.925718 + 5.84476i) q^{22} +(-1.37932 - 0.702799i) q^{23} +(-0.908558 + 1.47463i) q^{24} +1.05646i q^{26} +(-4.41066 - 2.74701i) 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} +(-3.94521 + 9.45990i) q^{33} +(-5.47129 - 1.77773i) q^{34} +(-2.13154 + 2.11105i) q^{36} +(-0.100380 - 0.197006i) q^{37} +(-2.44804 - 4.80455i) q^{38} +(-0.431463 + 1.77824i) q^{39} +(1.54235 + 0.501139i) q^{41} +(-3.42286 - 1.42749i) 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} +(0.901424 + 1.47900i) q^{48} +2.41543i q^{49} +(-8.48331 - 5.22681i) q^{51} +(0.941310 + 0.479621i) q^{52} +(-0.949805 + 5.99683i) q^{53} +(-4.45000 + 2.68281i) q^{54} +(-1.25854 + 1.73224i) q^{56} +(-2.15837 - 9.08688i) 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} +(-5.17841 - 3.80069i) q^{63} +(0.951057 - 0.309017i) q^{64} +(6.63774 + 7.80992i) q^{66} +(1.28043 - 0.202800i) q^{67} +(-4.06788 + 4.06788i) q^{68} +(-2.47967 + 1.02010i) q^{69} +(2.39892 + 3.30183i) q^{71} +(0.913257 + 2.85761i) q^{72} +(-0.141918 + 0.278530i) q^{73} -0.221105 q^{74} -5.39228 q^{76} +(-5.75231 + 11.2895i) q^{77} +(1.38854 + 1.19174i) q^{78} +(0.555462 + 0.764528i) q^{79} +(-8.58598 + 2.69833i) q^{81} +(1.14673 - 1.14673i) q^{82} +(7.47149 - 1.18337i) q^{83} +(-2.82585 + 2.40172i) q^{84} +(-1.79600 + 0.583556i) q^{86} +(0.636640 - 7.84692i) 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} +(17.9652 - 4.26719i) q^{93} +(2.82728 - 3.89142i) q^{94} +(1.72703 - 0.131724i) 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
$3$	1.12805	−	1.31434i	0.651283	−	0.758835i
$3$	1.12805	−	1.31434i	0.651283	−	0.758835i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	−0.658960	−	1.60180i	−0.269019	−	0.653933i
$7$	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
$9$	−0.454984	−	2.96530i	−0.151661	−	0.988433i
$10$		0			0
$11$	−5.62798	+	1.82864i	−1.69690	+	0.551357i	−0.988068	−	0.154020i	$-0.950778\pi$
$11$	−5.62798	+	1.82864i	−1.69690	+	0.551357i	−0.708833	+	0.705376i	$0.750778\pi$
$12$	−1.72638	−	0.140065i	−0.498362	−	0.0404334i
$13$	−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	$-0.804235\pi$
$17$	−0.899945	−	5.68203i	−0.218269	−	1.37809i	0.598497	−	0.801125i	$-0.295765\pi$
$18$	−2.84866	−	0.940823i	−0.671435	−	0.221754i
$19$	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
$21$	−0.282042	−	3.69786i	−0.0615467	−	0.806939i
$22$	−0.925718	+	5.84476i	−0.197364	+	1.24611i
$23$	−1.37932	−	0.702799i	−0.287608	−	0.146544i	0.304235	−	0.952597i	$-0.401599\pi$
$23$	−1.37932	−	0.702799i	−0.287608	−	0.146544i	−0.591843	+	0.806054i	$0.701599\pi$
$24$	−0.908558	+	1.47463i	−0.185459	+	0.301007i
$25$		0			0
$26$			1.05646i			0.207188i
$27$	−4.41066	−	2.74701i	−0.848832	−	0.528663i
$28$	−2.11480	−	0.334951i	−0.399659	−	0.0632998i
$29$	3.67723	−	2.67167i	0.682845	−	0.496116i	−0.191455	−	0.981501i	$-0.561321\pi$
$29$	3.67723	−	2.67167i	0.682845	−	0.496116i	0.874300	+	0.485386i	$0.161321\pi$
$30$		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
$33$	−3.94521	+	9.45990i	−0.686774	+	1.64676i
$34$	−5.47129	−	1.77773i	−0.938319	−	0.304878i
$35$		0			0
$36$	−2.13154	+	2.11105i	−0.355257	+	0.351841i
$37$	−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
$39$	−0.431463	+	1.77824i	−0.0690894	+	0.284747i
$40$		0			0
$41$	1.54235	+	0.501139i	0.240874	+	0.0782648i	0.426966	−	0.904268i	$-0.359582\pi$
$41$	1.54235	+	0.501139i	0.240874	+	0.0782648i	−0.186092	+	0.982532i	$0.559582\pi$
$42$	−3.42286	−	1.42749i	−0.528159	−	0.220267i
$43$	−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	0.492983	−	0.870039i	$-0.335907\pi$
$47$	4.75083	+	0.752458i	0.692980	+	0.109757i	0.199998	+	0.979796i	$0.435907\pi$
$48$	0.901424	+	1.47900i	0.130109	+	0.213475i
$49$			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	$0.186918\pi$
$53$	−0.949805	+	5.99683i	−0.130466	+	0.823728i	−0.962950	+	0.269680i	$0.913082\pi$
$54$	−4.45000	+	2.68281i	−0.605569	+	0.365084i
$55$		0			0
$56$	−1.25854	+	1.73224i	−0.168180	+	0.231480i
$57$	−2.15837	−	9.08688i	−0.285883	−	1.20359i
$58$	−0.711043	−	4.48935i	−0.0933645	−	0.589480i
$59$	2.24119	−	6.89769i	0.291779	−	0.898002i	−0.692506	−	0.721412i	$-0.743493\pi$
$59$	2.24119	−	6.89769i	0.291779	−	0.898002i	0.984285	−	0.176590i	$-0.0565066\pi$
$60$		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
$63$	−5.17841	−	3.80069i	−0.652418	−	0.478842i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	6.63774	+	7.80992i	0.817050	+	0.961334i
$67$	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
$69$	−2.47967	+	1.02010i	−0.298517	+	0.122806i
$70$		0			0
$71$	2.39892	+	3.30183i	0.284700	+	0.391856i	0.927283	−	0.374360i	$-0.122138\pi$
$71$	2.39892	+	3.30183i	0.284700	+	0.391856i	−0.642584	+	0.766215i	$0.722138\pi$
$72$	0.913257	+	2.85761i	0.107628	+	0.336773i
$73$	−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
$78$	1.38854	+	1.19174i	0.157222	+	0.134938i
$79$	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
$81$	−8.58598	+	2.69833i	−0.953998	+	0.299814i
$82$	1.14673	−	1.14673i	0.126635	−	0.126635i
$83$	7.47149	−	1.18337i	0.820102	−	0.129891i	0.267735	−	0.963493i	$-0.413725\pi$
$83$	7.47149	−	1.18337i	0.820102	−	0.129891i	0.552367	+	0.833601i	$0.313725\pi$
$84$	−2.82585	+	2.40172i	−0.308325	+	0.262050i
$85$		0			0
$86$	−1.79600	+	0.583556i	−0.193668	+	0.0629264i
$87$	0.636640	−	7.84692i	0.0682550	−	0.841278i
$88$	5.27263	−	2.68654i	0.562064	−	0.286386i
$89$	2.67429	+	8.23061i	0.283474	+	0.872443i	0.986852	+	0.161627i	$0.0516741\pi$
$89$	2.67429	+	8.23061i	0.283474	+	0.872443i	−0.703378	+	0.710816i	$0.748326\pi$
$90$		0			0
$91$	−0.699010	+	2.15133i	−0.0732762	+	0.225521i
$92$	0.242168	+	1.52899i	0.0252477	+	0.159408i
$93$	17.9652	−	4.26719i	1.86290	−	0.442487i
$94$	2.82728	−	3.89142i	0.291612	−	0.401369i
$95$		0			0
$96$	1.72703	−	0.131724i	0.176265	−	0.0134440i
$97$	−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	$0.00491398\pi$
$101$			0.310282i			0.0308742i	−0.999881	+	0.0154371i	$0.995086\pi$
$102$	−8.50846	+	5.18576i	−0.842463	+	0.513467i
$103$	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	0.474831	−	0.880077i	$-0.342509\pi$
$107$	−4.19190	−	4.19190i	−0.405246	−	0.405246i	−0.880077	+	0.474831i	$0.842509\pi$
$108$	0.370140	+	5.18295i	0.0356167	+	0.498730i
$109$	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
$111$	−0.372167	−	0.0903007i	−0.0353245	−	0.00857096i
$112$	0.972066	+	1.90779i	0.0918516	+	0.180269i
$113$	3.85086	+	7.55774i	0.362258	+	0.710972i	0.998150	−	0.0608066i	$-0.0193673\pi$
$113$	3.85086	+	7.55774i	0.362258	+	0.710972i	−0.635891	+	0.771779i	$0.719367\pi$
$114$	−9.07635	−	2.20224i	−0.850078	−	0.206258i
$115$		0			0
$116$	−4.32285	−	1.40458i	−0.401366	−	0.130412i
$117$	1.85050	+	2.57304i	0.171079	+	0.237878i
$118$	−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
$123$	2.39852	−	1.46186i	0.216267	−	0.131811i
$124$		−	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
$129$	−3.26138	+	0.248751i	−0.287148	+	0.0219013i
$130$		0			0
$131$	11.4805	−	15.8015i	1.00306	−	1.38059i	0.0796236	−	0.996825i	$-0.474628\pi$
$131$	11.4805	−	15.8015i	1.00306	−	1.38059i	0.923432	−	0.383762i	$-0.125372\pi$
$132$	9.97216	−	2.36864i	0.867965	−	0.206164i
$133$	−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	−0.846280	−	0.532738i	$-0.821163\pi$
$137$	−10.6831	+	5.44330i	−0.912717	+	0.465053i	−0.0664369	+	0.997791i	$0.521163\pi$
$138$	−0.216828	+	2.67251i	−0.0184576	+	0.227500i
$139$	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
$141$	6.34819	−	5.39540i	0.534614	−	0.454375i
$142$	4.03104	−	0.638455i	0.338278	−	0.0535779i
$143$	4.42062	−	4.42062i	0.369671	−	0.369671i
$144$	2.96076	+	0.483612i	0.246730	+	0.0403010i
$145$		0			0
$146$	0.183742	+	0.252900i	0.0152066	+	0.0209301i
$147$	3.17470	+	2.72474i	0.261845	+	0.224733i
$148$	−0.100380	+	0.197006i	−0.00825116	+	0.0161938i
$149$	−14.7140			−1.20542			−0.602711	−	0.797960i	$-0.705913\pi$
$149$	−14.7140			−1.20542			−0.602711	+	0.797960i	$0.705913\pi$
$150$		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
$153$	−16.4394	+	5.25384i	−1.32905	+	0.424748i
$154$	7.44757	+	10.2507i	0.600142	+	0.826025i
$155$		0			0
$156$	1.69224	−	0.696163i	0.135487	−	0.0557377i
$157$	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
$159$	6.81045	+	8.01312i	0.540104	+	0.635482i
$160$		0			0
$161$	−3.15239	+	1.02427i	−0.248443	+	0.0807240i
$162$	−1.49373	+	8.87518i	−0.117358	+	0.697300i
$163$	−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	$0.144675\pi$
$167$	2.32146	+	14.6571i	0.179640	+	1.13420i	−0.718837	+	0.695179i	$0.755325\pi$
$168$	0.857043	+	3.60821i	0.0661223	+	0.278379i
$169$	−6.98518	+	9.61428i	−0.537322	+	0.739560i
$170$		0			0
$171$	−14.3780	−	7.41367i	−1.09951	−	0.566937i
$172$	−0.295415	+	1.86518i	−0.0225252	+	0.142218i
$173$	4.46800	+	2.27656i	0.339696	+	0.173084i	0.615514	−	0.788126i	$-0.288949\pi$
$173$	4.46800	+	2.27656i	0.339696	+	0.173084i	−0.275818	+	0.961210i	$0.588949\pi$
$174$	−6.70263	−	4.12968i	−0.508125	−	0.313070i
$175$		0			0
$176$		−	5.91761i		−	0.446057i
$177$	−6.53772	−	10.7267i	−0.491405	−	0.806265i
$178$	8.54762	+	1.35381i	0.640672	+	0.101472i
$179$	−2.56353	+	1.86252i	−0.191607	+	0.139211i	−0.679453	−	0.733719i	$-0.737783\pi$
$179$	−2.56353	+	1.86252i	−0.191607	+	0.139211i	0.487846	+	0.872930i	$0.337783\pi$
$180$		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
$183$	−6.77345	−	2.82484i	−0.500707	−	0.208818i
$184$	1.47228	+	0.478373i	0.108538	+	0.0352661i
$185$		0			0
$186$	4.35392	−	17.9443i	0.319245	−	1.31574i
$187$	15.4553	+	30.3327i	1.13020	+	2.21815i
$188$	−2.18372	−	4.28579i	−0.159264	−	0.312573i
$189$	−10.8369	+	2.51881i	−0.788270	+	0.183216i
$190$		0			0
$191$	19.9806	+	6.49209i	1.44574	+	0.469751i	0.923683	−	0.383157i	$-0.125163\pi$
$191$	19.9806	+	6.49209i	1.44574	+	0.469751i	0.522062	+	0.852908i	$0.325163\pi$
$192$	0.666690	−	1.59860i	0.0481142	−	0.115369i
$193$	−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	0.504885	−	0.863186i	$-0.331535\pi$
$197$	10.0821	+	1.59685i	0.718320	+	0.113771i	0.213435	+	0.976957i	$0.431535\pi$
$198$	17.7526	+	0.0857583i	1.26162	+	0.00609458i
$199$		−	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
$204$	0.757790	+	9.93538i	0.0530559	+	0.695616i
$205$		0			0
$206$	5.19267	−	7.14709i	0.361790	−	0.497962i
$207$	−1.45644	+	4.40986i	−0.101229	+	0.306506i
$208$	−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
$213$	7.04585	+	0.571647i	0.482774	+	0.0391686i
$214$	−5.63809	+	1.83193i	−0.385412	+	0.125228i
$215$		0			0
$216$	4.78608	+	2.02321i	0.325652	+	0.137662i
$217$	22.5454	−	3.57084i	1.53048	−	0.242404i
$218$	1.33473	−	1.33473i	0.0903996	−	0.0903996i
$219$	0.205992	+	0.500725i	0.0139196	+	0.0338359i
$220$		0			0
$221$	3.57235	+	4.91692i	0.240302	+	0.330748i
$222$	−0.249419	+	0.290608i	−0.0167399	+	0.0195043i
$223$	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	−0.877752	−	0.479116i	$-0.840957\pi$
$227$	0.388579	−	0.762629i	0.0257909	−	0.0506175i	0.903542	+	0.428499i	$0.140957\pi$
$228$	−6.08278	+	7.08729i	−0.402842	+	0.469367i
$229$	−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
$231$	8.34939	+	20.2957i	0.549350	+	1.33536i
$232$	−3.21402	+	3.21402i	−0.211011	+	0.211011i
$233$	−5.38346	+	0.852656i	−0.352682	+	0.0558593i	−0.330262	−	0.943889i	$-0.607137\pi$
$233$	−5.38346	+	0.852656i	−0.352682	+	0.0558593i	−0.0224200	+	0.999749i	$0.507137\pi$
$234$	3.13271	−	0.480671i	0.204792	−	0.0314225i
$235$		0			0
$236$	−6.89769	+	2.24119i	−0.449001	+	0.145889i
$237$	1.63144	+	0.132363i	0.105974	+	0.00859790i
$238$	−10.9752	+	5.59216i	−0.711418	+	0.362486i
$239$	2.69306	+	8.28837i	0.174199	+	0.536130i	0.999596	−	0.0284230i	$-0.00904853\pi$
$239$	2.69306	+	8.28837i	0.174199	+	0.536130i	−0.825397	+	0.564553i	$0.809049\pi$
$240$		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
$243$	−6.13893	+	14.3288i	−0.393813	+	0.919191i
$244$	−2.49051	+	3.42789i	−0.159439	+	0.219448i
$245$		0			0
$246$	−0.213620	−	2.80077i	−0.0136199	−	0.178570i
$247$	−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	$0.231869\pi$
$251$			21.0935i			1.33141i	−0.746215	+	0.665706i	$0.768131\pi$
$252$	−0.0310298	+	6.42341i	−0.00195469	+	0.404637i
$253$	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	0.232792	−	0.972526i	$-0.425214\pi$
$257$	−11.8588	−	11.8588i	−0.739734	−	0.739734i	−0.972526	+	0.232792i	$0.925214\pi$
$258$	−1.25900	+	3.01884i	−0.0783816	+	0.187945i
$259$	−0.450251	−	0.146295i	−0.0279772	−	0.00909035i
$260$		0			0
$261$	−9.59537	−	9.68852i	−0.593938	−	0.599704i
$262$	−8.86724	−	17.4029i	−0.547820	−	1.07516i
$263$	10.3291	+	20.2720i	0.636919	+	1.25002i	0.953481	+	0.301453i	$0.0974715\pi$
$263$	10.3291	+	20.2720i	0.636919	+	1.25002i	−0.316562	+	0.948572i	$0.602529\pi$
$264$	2.41679	−	9.96060i	0.148743	−	0.613033i
$265$		0			0
$266$	−10.9806	−	3.56783i	−0.673266	−	0.218757i
$267$	13.8346	+	5.76965i	0.846662	+	0.353097i
$268$	−0.916684	−	0.916684i	−0.0559954	−	0.0559954i
$269$	−8.37684	−	6.08613i	−0.510745	−	0.371078i	0.302361	−	0.953193i	$-0.402225\pi$
$269$	−8.37684	−	6.08613i	−0.510745	−	0.371078i	−0.813106	+	0.582115i	$0.802225\pi$
$270$		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
$273$	2.03906	+	3.34556i	0.123410	+	0.202482i
$274$			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
$279$	14.6572	−	28.4260i	0.877501	−	1.70182i
$280$		0			0
$281$	12.7646	−	17.5690i	0.761473	−	1.04808i	−0.235617	−	0.971846i	$-0.575711\pi$
$281$	12.7646	−	17.5690i	0.761473	−	1.04808i	0.997090	−	0.0762322i	$-0.0242890\pi$
$282$	−1.92532	−	8.10574i	−0.114651	−	0.482690i
$283$	−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
$288$	1.77506	−	2.41850i	0.104596	−	0.142512i
$289$	−15.3076	+	4.97374i	−0.900446	+	0.292573i
$290$		0			0
$291$	13.5323	+	15.9219i	0.793275	+	0.933361i
$292$	0.308752	−	0.0489016i	0.0180684	−	0.00286175i
$293$	−12.2527	+	12.2527i	−0.715808	+	0.715808i	−0.967744	−	0.251936i	$-0.918933\pi$
$293$	−12.2527	+	12.2527i	−0.715808	+	0.715808i	0.251936	+	0.967744i	$0.418933\pi$
$294$	3.86905	−	1.59167i	0.225647	−	0.0928283i
$295$		0			0
$296$	0.129962	+	0.178878i	0.00755391	+	0.0103971i
$297$	29.8464	+	7.39463i	1.73187	+	0.429080i
$298$	−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
$303$	0.407816	+	0.350015i	0.0234284	+	0.0201078i
$304$	3.16950	+	4.36244i	0.181783	+	0.250203i
$305$		0			0
$306$	−2.78215	+	17.0328i	−0.159045	+	0.973703i
$307$	−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
$309$	11.6593	−	9.90936i	0.663273	−	0.563724i
$310$		0			0
$311$	7.39905	−	2.40410i	0.419562	−	0.136324i	−0.0916250	−	0.995794i	$-0.529206\pi$
$311$	7.39905	−	2.40410i	0.419562	−	0.136324i	0.511187	+	0.859470i	$0.329206\pi$
$312$	0.147973	−	1.82384i	0.00837732	−	0.103255i
$313$	−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	0.986718	−	0.162444i	$-0.0519376\pi$
$317$	−0.0339077	−	0.214085i	−0.00190445	−	0.0120242i	−0.988622	+	0.150419i	$0.951938\pi$
$318$	10.2316	−	2.43027i	0.573761	−	0.136283i
$319$	−15.8099	+	21.7604i	−0.885183	+	1.21835i
$320$		0			0
$321$	−10.2383	+	0.780892i	−0.571445	+	0.0435852i
$322$	−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
$327$	2.79176	−	1.70153i	0.154384	−	0.0940947i
$328$	−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
$333$	−0.538511	+	0.387290i	−0.0295102	+	0.0212234i
$334$	14.1135	+	4.58575i	0.772255	+	0.250921i
$335$		0			0
$336$	3.60403	+	0.874463i	0.196616	+	0.0477058i
$337$	−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
$339$	14.2774	+	3.46420i	0.775443	+	0.188150i
$340$		0			0
$341$	−59.9987	−	19.4947i	−3.24911	−	1.05570i
$342$	−13.1331	+	9.44517i	−0.710157	+	0.510736i
$343$	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	0.0338958	−	0.999425i	$-0.489209\pi$
$347$	−4.52113	−	0.716076i	−0.242707	−	0.0384410i	−0.276603	+	0.960984i	$0.589209\pi$
$348$	−6.72250	+	4.09725i	−0.360364	+	0.219636i
$349$		−	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	$-0.856853\pi$
$353$	1.69571	−	10.7063i	0.0902538	−	0.569840i	0.990827	−	0.135136i	$-0.0431471\pi$
$354$	−12.5256	+	0.955350i	−0.665727	+	0.0507763i
$355$		0			0
$356$	5.08679	−	7.00137i	0.269600	−	0.371072i
$357$	−20.7575	+	4.93044i	−1.09860	+	0.260947i
$358$	0.495694	+	3.12969i	0.0261982	+	0.165409i
$359$	6.51044	−	20.0371i	0.343608	−	1.05752i	−0.618717	−	0.785614i	$-0.712347\pi$
$359$	6.51044	−	20.0371i	0.343608	−	1.05752i	0.962325	−	0.271902i	$-0.0876527\pi$
$360$		0			0
$361$	−3.11386	−	9.58347i	−0.163887	−	0.504393i
$362$	−5.56052	+	2.83323i	−0.292254	+	0.148911i
$363$	3.36411	−	41.4644i	0.176570	−	2.17632i
$364$	2.15133	−	0.699010i	0.112760	−	0.0366381i
$365$		0			0
$366$	−5.59203	+	4.75273i	−0.292300	+	0.248429i
$367$	−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
$369$	0.784283	−	4.80153i	0.0408281	−	0.249958i
$370$		0			0
$371$	7.64135	+	10.5174i	0.396719	+	0.546037i
$372$	−14.0119	−	12.0259i	−0.726483	−	0.623516i
$373$	−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
$378$	−2.67559	+	10.7993i	−0.137617	+	0.555455i
$379$	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
$381$	−16.7525	+	6.89175i	−0.858257	+	0.353075i
$382$	14.8555	−	14.8555i	0.760073	−	0.760073i
$383$	15.7705	−	2.49780i	0.805836	−	0.127632i	0.260092	−	0.965584i	$-0.416247\pi$
$383$	15.7705	−	2.49780i	0.805836	−	0.127632i	0.545744	+	0.837952i	$0.316247\pi$
$384$	−1.12169	−	1.31977i	−0.0572411	−	0.0673495i
$385$		0			0
$386$	−9.42739	+	3.06314i	−0.479841	+	0.155910i
$387$	−3.35207	+	4.56717i	−0.170395	+	0.232162i
$388$	10.7492	−	5.47700i	0.545709	−	0.278053i
$389$	3.56490	+	10.9716i	0.180748	+	0.556284i	0.999849	−	0.0173647i	$-0.00552762\pi$
$389$	3.56490	+	10.9716i	0.180748	+	0.556284i	−0.819102	+	0.573648i	$0.805528\pi$
$390$		0			0
$391$	−2.75201	+	8.46982i	−0.139175	+	0.428337i
$392$	−0.377857	−	2.38569i	−0.0190847	−	0.120496i
$393$	−7.81799	−	32.9143i	−0.394365	−	1.66031i
$394$	5.99998	−	8.25827i	0.302275	−	0.416046i
$395$		0			0
$396$	8.13594	−	15.7788i	0.408846	−	0.792913i
$397$	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	$0.208920\pi$
$401$			24.4394i			1.22045i	−0.792229	+	0.610223i	$0.791080\pi$
$402$	−1.16859	−	1.91735i	−0.0582842	−	0.0956289i
$403$	−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
$408$	9.19652	+	3.83537i	0.455296	+	0.189879i
$409$	−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
$411$	−4.89675	+	20.1816i	−0.241539	+	0.995483i
$412$	−4.01069	−	7.87141i	−0.197592	−	0.387797i
$413$	−7.05006	−	13.8365i	−0.346911	−	0.680851i
$414$	3.26800	+	3.29973i	0.160614	+	0.162173i
$415$		0			0
$416$	−1.00475	−	0.326463i	−0.0492619	−	0.0160062i
$417$	15.5144	−	37.2007i	0.759744	−	1.82173i
$418$	22.5634	+	22.5634i	1.10361	+	1.10361i
$419$	−20.8723	−	15.1646i	−1.01968	−	0.740840i	−0.0534618	−	0.998570i	$-0.517026\pi$
$419$	−20.8723	−	15.1646i	−1.01968	−	0.740840i	−0.966217	+	0.257730i	$0.917026\pi$
$420$		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
$423$	0.0697075	−	14.4300i	0.00338930	−	0.701610i
$424$		−	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
$429$	−0.823500	−	10.7969i	−0.0397590	−	0.521280i
$430$		0			0
$431$	−3.61295	+	4.97279i	−0.174030	+	0.239531i	−0.887118	−	0.461543i	$-0.847296\pi$
$431$	−3.61295	+	4.97279i	−0.174030	+	0.239531i	0.713088	+	0.701074i	$0.247296\pi$
$432$	3.97553	−	3.34591i	0.191273	−	0.160980i
$433$	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
$438$	0.539668	+	0.0437846i	0.0257863	+	0.00209211i
$439$	−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
$441$	7.16248	−	1.09898i	0.341070	−	0.0523326i
$442$	6.00282	−	0.950753i	0.285525	−	0.0452227i
$443$	−17.1571	+	17.1571i	−0.815159	+	0.815159i	−0.985402	−	0.170243i	$-0.945545\pi$
$443$	−17.1571	+	17.1571i	−0.815159	+	0.815159i	0.170243	+	0.985402i	$0.445545\pi$
$444$	0.145699	+	0.354167i	0.00691459	+	0.0168080i
$445$		0			0
$446$	−7.86865	−	10.8303i	−0.372591	−	0.512828i
$447$	−16.5983	+	19.3393i	−0.785071	+	0.914716i
$448$	0.972066	−	1.90779i	0.0459258	−	0.0901345i
$449$	15.9242			0.751511			0.375755	−	0.926719i	$-0.377383\pi$
$449$	15.9242			0.751511			0.375755	+	0.926719i	$0.377383\pi$
$450$		0			0
$451$	−9.59671			−0.451891
$452$	3.85086	−	7.55774i	0.181129	−	0.355486i
$453$	−9.64350	+	11.2360i	−0.453091	+	0.527914i
$454$	−0.503096	−	0.692453i	−0.0236115	−	0.0324984i
$455$		0			0
$456$	3.55330	+	8.63736i	0.166398	+	0.404482i
$457$	−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
$459$	−11.6393	+	27.5337i	−0.543274	+	1.28516i
$460$		0			0
$461$	9.43135	−	3.06443i	0.439262	−	0.142725i	−0.0810333	−	0.996711i	$-0.525822\pi$
$461$	9.43135	−	3.06443i	0.439262	−	0.142725i	0.520295	+	0.853987i	$0.325822\pi$
$462$	21.8742	+	1.77471i	1.01768	+	0.0825668i
$463$	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	0.998783	−	0.0493288i	$-0.0157082\pi$
$467$	0.726976	+	4.58995i	0.0336405	+	0.212397i	−0.965142	+	0.261726i	$0.915708\pi$
$468$	0.993939	−	3.00948i	0.0459448	−	0.139113i
$469$	1.63156	−	2.24565i	0.0753383	−	0.103694i
$470$		0			0
$471$	−3.27611	−	42.9530i	−0.150955	−	1.97917i
$472$	−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
$477$	18.2145	+	0.0879897i	0.833986	+	0.00402877i
$478$	8.60761	+	1.36331i	0.393703	+	0.0623564i
$479$	12.7801	−	9.28530i	0.583939	−	0.424256i	−0.256203	−	0.966623i	$-0.582472\pi$
$479$	12.7801	−	9.28530i	0.583939	−	0.424256i	0.840142	+	0.542367i	$0.182472\pi$
$480$		0			0
$481$	0.188977	+	0.137300i	0.00861660	+	0.00626032i
$482$	17.9787	+	17.9787i	0.818908	+	0.818908i
$483$	−2.20982	+	5.29875i	−0.100550	+	0.241101i
$484$	−22.8426	−	7.42201i	−1.03830	−	0.337364i
$485$		0			0
$486$	9.98001	+	11.9750i	0.452702	+	0.543195i
$487$	−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
$489$	−0.820608	+	3.38207i	−0.0371092	+	0.152942i
$490$		0			0
$491$	8.65368	+	2.81175i	0.390535	+	0.126893i	0.497701	−	0.867349i	$-0.334178\pi$
$491$	8.65368	+	2.81175i	0.390535	+	0.126893i	−0.107166	+	0.994241i	$0.534178\pi$
$492$	−2.59248	−	1.08119i	−0.116878	−	0.0487436i
$493$	−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
$498$	−6.81893	−	11.1881i	−0.305564	−	0.501349i
$499$			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	$-0.871496\pi$
$503$	1.71307	−	10.8159i	0.0763820	−	0.482257i	0.995993	−	0.0894274i	$-0.0285037\pi$
$504$	5.70921	+	2.94381i	0.254308	+	0.131128i
$505$		0			0
$506$	5.38455	−	7.41120i	0.239372	−	0.329468i
$507$	4.75677	+	20.0263i	0.211256	+	0.889401i
$508$	1.63607	+	10.3298i	0.0725891	+	0.458309i
$509$	−2.83257	+	8.71775i	−0.125551	+	0.386407i	−0.994001	−	0.109370i	$-0.965117\pi$
$509$	−2.83257	+	8.71775i	−0.125551	+	0.386407i	0.868450	+	0.495777i	$0.165117\pi$
$510$		0			0
$511$	0.206834	+	0.636570i	0.00914980	+	0.0281602i
$512$	−0.891007	+	0.453990i	−0.0393773	+	0.0200637i
$513$	−25.9633	+	10.5346i	−1.14631	+	0.465114i
$514$	−15.9501	+	5.18250i	−0.703529	+	0.228590i
$515$		0			0
$516$	2.11823	+	2.49230i	0.0932500	+	0.109717i
$517$	−28.1136	+	4.45276i	−1.23643	+	0.195832i
$518$	−0.334760	+	0.334760i	−0.0147085	+	0.0147085i
$519$	8.03233	−	3.30439i	0.352580	−	0.145047i
$520$		0			0
$521$	13.3932	+	18.4342i	0.586767	+	0.807615i	0.994417	−	0.105523i	$-0.0336517\pi$
$521$	13.3932	+	18.4342i	0.586767	+	0.807615i	−0.407650	+	0.913138i	$0.633652\pi$
$522$	−12.9887	+	4.15104i	−0.568502	+	0.181686i
$523$	−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
$528$	−7.77776	−	6.67539i	−0.338484	−	0.290509i
$529$	−12.1105	−	16.6686i	−0.526542	−	0.724723i
$530$		0			0
$531$	−21.4734	−	3.50747i	−0.931866	−	0.152211i
$532$	−8.16406	+	8.16406i	−0.353957	+	0.353957i
$533$	−1.69218	+	0.268016i	−0.0732966	+	0.0116090i
$534$	11.4216	−	9.70732i	0.494259	−	0.420077i
$535$		0			0
$536$	−1.23294	+	0.400605i	−0.0532548	+	0.0173035i
$537$	−0.443825	+	5.47038i	−0.0191525	+	0.236064i
$538$	−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
$543$	−10.5166	+	2.49797i	−0.451312	+	0.107198i
$544$	3.38144	−	4.65416i	0.144978	−	0.199545i
$545$		0			0
$546$	3.90663	−	0.297966i	0.167188	−	0.0127518i
$547$	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
$552$	2.28956	−	1.39545i	0.0974500	−	0.0593942i
$553$	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	0.782267	−	0.622943i	$-0.214063\pi$
$557$	3.76017	+	3.76017i	0.159323	+	0.159323i	−0.622943	+	0.782267i	$0.714063\pi$
$558$	−18.6735	−	25.9647i	−0.790513	−	1.09918i
$559$	1.89740	+	0.616502i	0.0802513	+	0.0260752i
$560$		0			0
$561$	57.3019	+	13.9034i	2.41929	+	0.587003i
$562$	−9.85907	−	19.3495i	−0.415880	−	0.816210i
$563$	11.0089	+	21.6061i	0.463969	+	0.910590i	0.997882	+	0.0650508i	$0.0207209\pi$
$563$	11.0089	+	21.6061i	0.463969	+	0.910590i	−0.533913	+	0.845539i	$0.679279\pi$
$564$	−8.09634	−	1.96445i	−0.340918	−	0.0827185i
$565$		0			0
$566$	−3.29063	−	1.06919i	−0.138315	−	0.0449414i
$567$	−8.91407	+	17.0848i	−0.374356	+	0.717493i
$568$	−2.88591	−	2.88591i	−0.121090	−	0.121090i
$569$	24.5934	+	17.8681i	1.03101	+	0.749071i	0.968510	−	0.248974i	$-0.0800934\pi$
$569$	24.5934	+	17.8681i	1.03101	+	0.749071i	0.0624977	+	0.998045i	$0.480093\pi$
$570$		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
$573$	31.0720	−	18.9379i	1.29805	−	0.791141i
$574$		−	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
$579$	−17.1193	+	1.30572i	−0.711454	+	0.0542639i
$580$		0			0
$581$	9.52039	−	13.1037i	0.394972	−	0.543633i
$582$	20.3301	−	4.82891i	0.842708	−	0.200165i
$583$	−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	−0.167506	−	0.985871i	$-0.553571\pi$
$587$	12.8802	−	6.56280i	0.531623	−	0.270876i	0.699129	+	0.714995i	$0.253571\pi$
$588$	0.338318	−	4.16995i	0.0139520	−	0.171966i
$589$	54.6723	−	17.7641i	2.25273	−	0.731957i
$590$		0			0
$591$	13.4720	−	11.4500i	0.554163	−	0.470990i
$592$	0.218383	−	0.0345885i	0.00897549	−	0.00142158i
$593$	−27.1124	+	27.1124i	−1.11337	+	1.11337i	−0.120680	+	0.992691i	$0.538508\pi$
$593$	−27.1124	+	27.1124i	−1.11337	+	1.11337i	−0.992691	+	0.120680i	$0.961492\pi$
$594$	20.1387	−	23.2363i	0.826299	−	0.953396i
$595$		0			0
$596$	8.64870	+	11.9039i	0.354265	+	0.487603i
$597$	−19.8659	−	17.0503i	−0.813058	−	0.697821i
$598$	0.742476	−	1.45719i	0.0303621	−	0.0595890i
$599$	−22.2597			−0.909506			−0.454753	−	0.890618i	$-0.650272\pi$
$599$	−22.2597			−0.909506			−0.454753	+	0.890618i	$0.650272\pi$
$600$		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
$603$	−1.18393	−	3.70457i	−0.0482135	−	0.150862i
$604$	5.02485	+	6.91612i	0.204458	+	0.281413i
$605$		0			0
$606$	0.497011	−	0.204463i	0.0201897	−	0.00830576i
$607$	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
$609$	−10.9166	−	12.8444i	−0.442362	−	0.520480i
$610$		0			0
$611$	−4.83290	+	1.57031i	−0.195518	+	0.0635278i
$612$	13.9133	+	10.2117i	0.562412	+	0.412782i
$613$	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	$0.165962\pi$
$617$	4.87738	+	30.7946i	0.196356	+	1.23974i	−0.670775	+	0.741661i	$0.734038\pi$
$618$	−3.53610	−	14.8873i	−0.142243	−	0.598853i
$619$	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
$621$	4.15311	+	6.88882i	0.166659	+	0.276439i
$622$	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
$627$	28.7639	+	47.1939i	1.14872	+	1.88474i
$628$	−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
$633$	−6.34896	−	2.64781i	−0.252349	−	0.105241i
$634$	−0.206145	−	0.0669805i	−0.00818706	−	0.00266014i
$635$		0			0
$636$	2.47967	−	10.2198i	0.0983253	−	0.405240i
$637$	−1.15849	−	2.27367i	−0.0459012	−	0.0900861i
$638$	12.2112	+	23.9657i	0.483444	+	0.948813i
$639$	8.69945	−	8.61580i	0.344145	−	0.340836i
$640$		0			0
$641$	−45.1681	−	14.6760i	−1.78403	−	0.579668i	−0.784836	−	0.619703i	$-0.787253\pi$
$641$	−45.1681	−	14.6760i	−1.78403	−	0.579668i	−0.999198	+	0.0400355i	$0.987253\pi$
$642$	−3.95230	+	9.47689i	−0.155985	+	0.374023i
$643$	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	0.0160323	−	0.999871i	$-0.494897\pi$
$647$	−7.06356	−	1.11876i	−0.277697	−	0.0439829i	−0.293730	+	0.955889i	$0.594897\pi$
$648$	8.05816	−	4.00825i	0.316554	−	0.157459i
$649$			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	$-0.799514\pi$
$653$	3.64054	−	22.9855i	0.142465	−	0.899490i	0.950583	−	0.310470i	$-0.100486\pi$
$654$	−0.248642	−	3.25995i	−0.00972269	−	0.127474i
$655$		0			0
$656$	−0.953223	+	1.31200i	−0.0372171	+	0.0512250i
$657$	0.890494	+	0.294102i	0.0347415	+	0.0114740i
$658$	−1.61113	−	10.1723i	−0.0628085	−	0.396557i
$659$	−1.14382	+	3.52031i	−0.0445568	+	0.137132i	−0.970860	−	0.239647i	$-0.922968\pi$
$659$	−1.14382	+	3.52031i	−0.0445568	+	0.137132i	0.926303	+	0.376779i	$0.122968\pi$
$660$		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
$663$	10.4923	+	0.851267i	0.407488	+	0.0330605i
$664$	−7.19438	+	2.33760i	−0.279196	+	0.0907163i
$665$		0			0
$666$	0.100599	+	0.655643i	0.00389815	+	0.0254056i
$667$	−6.94972	+	1.10073i	−0.269094	+	0.0426203i
$668$	10.4933	−	10.4933i	0.405999	−	0.405999i
$669$	−8.82147	−	21.4432i	−0.341058	−	0.829044i
$670$		0			0
$671$	14.7379	+	20.2849i	0.568949	+	0.783092i
$672$	2.41535	−	2.81421i	0.0931740	−	0.108561i
$673$	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	$0.379735\pi$
$677$	−15.6087	+	30.6338i	−0.599892	+	1.17735i	−0.968790	+	0.247884i	$0.920265\pi$
$678$	9.56844	−	11.1486i	0.367474	−	0.428158i
$679$	15.1832	+	20.8979i	0.582679	+	0.801988i
$680$		0			0
$681$	−0.564016	−	1.37101i	−0.0216132	−	0.0525373i
$682$	−44.6088	+	44.6088i	−1.70816	+	1.70816i
$683$	44.5125	−	7.05008i	1.70322	−	0.269764i	0.772373	−	0.635169i	$-0.219070\pi$
$683$	44.5125	−	7.05008i	1.70322	−	0.269764i	0.930849	+	0.365405i	$0.119070\pi$
$684$	2.45340	+	15.9897i	0.0938081	+	0.611382i
$685$		0			0
$686$	19.1733	−	6.22977i	0.732038	−	0.237854i
$687$	−28.5645	−	2.31751i	−1.08980	−	0.0884185i
$688$	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
$693$	36.0941	+	11.9207i	1.37110	+	0.452832i
$694$	−2.69058	+	3.70326i	−0.102133	+	0.140574i
$695$		0			0
$696$	0.598727	+	7.84991i	0.0226947	+	0.297550i
$697$	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	$-0.879219\pi$
$701$		−	19.6139i		−	0.740807i	0.928871	−	0.370403i	$-0.120781\pi$
$702$	2.90210	−	4.65967i	0.109533	−	0.175868i
$703$	−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
$708$	−4.83527	+	11.5941i	−0.181721	+	0.435733i
$709$	−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
$711$	2.01433	−	1.99496i	0.0755432	−	0.0748168i
$712$	−3.92891	−	7.71092i	−0.147242	−	0.288979i
$713$	−7.49238	−	14.7046i	−0.280592	−	0.550692i
$714$	−5.03066	+	20.7335i	−0.188268	+	0.775930i
$715$		0			0
$716$	3.01361	+	0.979183i	0.112624	+	0.0365938i
$717$	13.9317	+	5.81015i	0.520287	+	0.216984i
$718$	−14.8975	−	14.8975i	−0.555969	−	0.555969i
$719$	30.2210	+	21.9569i	1.12705	+	0.818853i	0.985263	−	0.171044i	$-0.0547140\pi$
$719$	30.2210	+	21.9569i	1.12705	+	0.818853i	0.141791	+	0.989897i	$0.454714\pi$
$720$		0			0
$721$	15.3031	−	11.1183i	0.569916	−	0.414068i
$722$	−9.95259	−	1.57634i	−0.370397	−	0.0586651i
$723$	22.9194	+	37.6046i	0.852381	+	1.39853i
$724$			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
$729$	11.9078	+	24.2323i	0.441031	+	0.897492i
$730$		0			0
$731$	−6.38561	+	8.78903i	−0.236180	+	0.325074i
$732$	1.69599	+	7.14023i	0.0626855	+	0.263911i
$733$	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
$738$	−3.92214	−	2.87865i	−0.144376	−	0.105965i
$739$	−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
$741$	6.38996	+	7.51837i	0.234741	+	0.276194i
$742$	12.8402	−	2.03368i	0.471378	−	0.0746589i
$743$	24.9192	−	24.9192i	0.914196	−	0.914196i	−0.0824029	−	0.996599i	$-0.526259\pi$
$743$	24.9192	−	24.9192i	0.914196	−	0.914196i	0.996599	+	0.0824029i	$0.0262594\pi$
$744$	−17.0765	+	7.02502i	−0.626053	+	0.257550i
$745$		0			0
$746$	15.7261	+	21.6451i	0.575772	+	0.792482i
$747$	−6.90844	−	21.6168i	−0.252767	−	0.790916i
$748$	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
$753$	27.7241	+	23.7946i	1.01032	+	0.867125i
$754$	2.82250	+	3.88484i	0.102789	+	0.141477i
$755$		0			0
$756$	8.40754	+	7.28674i	0.305779	+	0.265016i
$757$	−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
$759$	12.0901	−	10.2755i	0.438843	−	0.372978i
$760$		0			0
$761$	−5.92036	+	1.92364i	−0.214613	+	0.0697320i	−0.414350	−	0.910118i	$-0.635991\pi$
$761$	−5.92036	+	1.92364i	−0.214613	+	0.0697320i	0.199737	+	0.979849i	$0.435991\pi$
$762$	−1.46488	+	18.0554i	−0.0530669	+	0.654077i
$763$	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
$768$	−1.68517	+	0.400270i	−0.0608082	+	0.0144435i
$769$	−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
$771$	−28.9640	+	2.20914i	−1.04311	+	0.0795601i
$772$	−1.55066	+	9.79050i	−0.0558096	+	0.352368i
$773$	−30.3587	−	15.4685i	−1.09193	−	0.556364i	−0.187185	−	0.982325i	$-0.559936\pi$
$773$	−30.3587	−	15.4685i	−1.09193	−	0.556364i	−0.904742	+	0.425960i	$0.859936\pi$
$774$	2.54757	+	5.06017i	0.0915704	+	0.181884i
$775$		0			0
$776$		−	12.0641i		−	0.433077i
$777$	−0.700189	+	0.426754i	−0.0251192	+	0.0153097i
$778$	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
$783$	−23.5581	+	1.68240i	−0.841898	+	0.0601240i
$784$	−2.29721	−	0.746410i	−0.0820433	−	0.0266575i
$785$		0			0
$786$	−32.8761	−	7.97690i	−1.17265	−	0.284527i
$787$	−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
$789$	38.2961	+	9.29197i	1.36338	+	0.330803i
$790$		0			0
$791$	17.2729	+	5.61232i	0.614155	+	0.199551i
$792$	−10.3654	−	14.4126i	−0.368317	−	0.512129i
$793$	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	−0.0311718	−	0.999514i	$-0.509924\pi$
$797$	−10.4366	−	1.65300i	−0.369685	−	0.0585523i	−0.338513	+	0.940962i	$0.609924\pi$
$798$	−17.0761	+	10.4076i	−0.604488	+	0.368425i
$799$		−	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
$804$	−2.23890	+	0.170765i	−0.0789601	+	0.00602243i
$805$		0			0
$806$	−6.62002	+	9.11167i	−0.233180	+	0.320945i
$807$	−17.4488	+	4.14454i	−0.614227	+	0.145895i
$808$	−0.0485388	−	0.306462i	−0.00170759	−	0.0107813i
$809$	4.15772	−	12.7961i	0.146178	−	0.449889i	−0.850983	−	0.525193i	$-0.823993\pi$
$809$	4.15772	−	12.7961i	0.146178	−	0.449889i	0.997161	+	0.0753048i	$0.0239930\pi$
$810$		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
$813$	−0.0895624	+	1.10390i	−0.00314109	+	0.0387156i
$814$	1.24438	−	0.404322i	0.0436154	−	0.0141715i
$815$		0			0
$816$	7.59247	−	6.45294i	0.265790	−	0.225898i
$817$	−10.0575	+	1.59296i	−0.351869	+	0.0557306i
$818$	−6.92463	+	6.92463i	−0.242114	+	0.242114i
$819$	6.69738	+	1.09395i	0.234025	+	0.0382257i
$820$		0			0
$821$	11.1279	+	15.3163i	0.388368	+	0.534543i	0.957777	−	0.287512i	$-0.0928280\pi$
$821$	11.1279	+	15.3163i	0.388368	+	0.534543i	−0.569409	+	0.822054i	$0.692828\pi$
$822$	15.7588	+	13.5253i	0.549652	+	0.471748i
$823$	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	−0.831152	−	0.556045i	$-0.812318\pi$
$827$	3.08387	−	6.05244i	0.107237	−	0.210464i	0.938389	+	0.345581i	$0.112318\pi$
$828$	4.42372	−	1.41377i	0.153735	−	0.0491317i
$829$	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
$831$	−48.6333	+	20.0071i	−1.68707	+	0.694038i
$832$	−0.747028	+	0.747028i	−0.0258985	+	0.0258985i
$833$	13.7246	−	2.17376i	0.475528	−	0.0753162i
$834$	−26.1027	−	30.7122i	−0.903862	−	1.06348i
$835$		0			0
$836$	30.3476	−	9.86055i	1.04960	−	0.341034i
$837$	−20.8274	−	51.3306i	−0.719899	−	1.77424i
$838$	−22.9876	+	11.7128i	−0.794093	+	0.404611i
$839$	−5.00273	−	15.3968i	−0.172713	−	0.531557i	0.826808	−	0.562484i	$-0.190154\pi$
$839$	−5.00273	−	15.3968i	−0.172713	−	0.531557i	−0.999522	+	0.0309268i	$0.990154\pi$
$840$		0			0
$841$	−2.57725	+	7.93197i	−0.0888709	+	0.273516i
$842$	6.16556	+	38.9278i	0.212479	+	1.34154i
$843$	−8.69245	−	36.5959i	−0.299384	−	1.26043i
$844$	−2.33443	+	3.21307i	−0.0803545	+	0.110598i
$845$		0			0
$846$	−12.8256	−	6.61319i	−0.440952	−	0.227366i
$847$	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
$852$	−3.67898	−	6.03622i	−0.126040	−	0.206797i
$853$	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	0.907196	−	0.420708i	$-0.138218\pi$
$857$	14.2417	+	14.2417i	0.486489	+	0.486489i	−0.420708	+	0.907196i	$0.638218\pi$
$858$	−9.99398	−	4.16795i	−0.341189	−	0.142291i
$859$	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
$861$	1.41813	−	5.84472i	0.0483299	−	0.199188i
$862$	2.79055	+	5.47676i	0.0950465	+	0.186539i
$863$	9.85205	+	19.3357i	0.335368	+	0.658196i	0.995686	−	0.0927901i	$-0.0295785\pi$
$863$	9.85205	+	19.3357i	0.335368	+	0.658196i	−0.660318	+	0.750986i	$0.729579\pi$
$864$	−1.17637	−	5.06124i	−0.0400211	−	0.172187i
$865$		0			0
$866$	15.9153	+	5.17119i	0.540824	+	0.175724i
$867$	−10.7306	+	25.7300i	−0.364431	+	0.873838i
$868$	−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
$873$	36.1920	+	0.174834i	1.22491	+	0.00591723i
$874$			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
$879$	2.28250	+	29.9258i	0.0769868	+	1.00937i
$880$		0			0
$881$	18.8656	−	25.9662i	0.635597	−	0.874825i	−0.362774	−	0.931877i	$-0.618170\pi$
$881$	18.8656	−	25.9662i	0.635597	−	0.874825i	0.998371	+	0.0570525i	$0.0181702\pi$
$882$	2.27249	−	6.88074i	0.0765189	−	0.231687i
$883$	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	−0.626010	−	0.779815i	$-0.715313\pi$
$887$	−10.8136	+	5.50981i	−0.363086	+	0.185001i	0.262924	+	0.964816i	$0.415313\pi$
$888$	0.381711	+	0.0309692i	0.0128094	+	0.00103926i
$889$	−21.2974	+	6.91994i	−0.714291	+	0.232087i
$890$		0			0
$891$	43.3875	−	30.8868i	1.45353	−	1.03475i
$892$	−13.2221	+	2.09418i	−0.442710	+	0.0701183i
$893$	18.3403	−	18.3403i	0.613736	−	0.613736i
$894$	9.69597	+	23.5690i	0.324282	+	0.788265i
$895$		0			0
$896$	−1.25854	−	1.73224i	−0.0420450	−	0.0578699i
$897$	1.84487	−	2.14953i	0.0615985	−	0.0717708i
$898$	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
$903$	−4.56120	+	5.31444i	−0.151787	+	0.176853i
$904$	−4.98574	−	6.86228i	−0.165823	−	0.228236i
$905$		0			0
$906$	5.63331	+	13.6935i	0.187154	+	0.454935i
$907$	−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
$909$	0.920078	−	0.141173i	0.0305171	−	0.00468243i
$910$		0			0
$911$	−37.0222	+	12.0293i	−1.22660	+	0.398547i	−0.849482	−	0.527618i	$-0.823085\pi$
$911$	−37.0222	+	12.0293i	−1.22660	+	0.398547i	−0.377119	+	0.926165i	$0.623085\pi$
$912$	9.30911	+	0.755271i	0.308255	+	0.0250095i
$913$	−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
$918$	19.2486	+	22.8707i	0.635297	+	0.754845i
$919$	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
$921$	3.13209	+	41.0648i	0.103206	+	1.35313i
$922$	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
$927$	0.128027	−	26.5026i	0.00420496	−	0.870459i
$928$	4.48935	+	0.711043i	0.147370	+	0.0233411i
$929$	0.473139	−	0.343755i	0.0155232	−	0.0112782i	−0.579997	−	0.814619i	$-0.696946\pi$
$929$	0.473139	−	0.343755i	0.0155232	−	0.0112782i	0.595520	+	0.803341i	$0.296946\pi$
$930$		0			0
$931$	10.5372	+	7.65572i	0.345342	+	0.250906i
$932$	3.85413	+	3.85413i	0.126246	+	0.126246i
$933$	5.18673	−	12.4368i	0.169806	−	0.407163i
$934$	4.41971	+	1.43605i	0.144617	+	0.0469891i
$935$		0			0
$936$	−2.23023	−	2.25188i	−0.0728974	−	0.0736051i
$937$	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
$939$	−8.49469	+	35.0102i	−0.277214	+	1.14251i
$940$		0			0
$941$	−12.5712	−	4.08462i	−0.409808	−	0.133155i	0.0968556	−	0.995298i	$-0.469121\pi$
$941$	−12.5712	−	4.08462i	−0.409808	−	0.133155i	−0.506664	+	0.862144i	$0.669121\pi$
$942$	−39.7588	−	16.5812i	−1.29541	−	0.540246i
$943$	−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	−0.140571	−	0.990071i	$-0.544894\pi$
$947$	−17.8550	−	2.82795i	−0.580210	−	0.0918962i	−0.439639	+	0.898174i	$0.644894\pi$
$948$	−0.851854	−	1.39767i	−0.0276669	−	0.0453941i
$949$		−	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	$0.371542\pi$
$953$	−8.17990	+	51.6458i	−0.264973	+	1.67297i	−0.657671	+	0.753305i	$0.728458\pi$
$954$	8.34763	−	16.1893i	0.270264	−	0.524149i
$955$		0			0
$956$	5.12250	−	7.05051i	0.165673	−	0.228030i
$957$	10.7662	+	45.3265i	0.348022	+	1.46520i
$958$	−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
$963$	−10.5230	+	14.3375i	−0.339098	+	0.462019i
$964$	24.1813	−	7.85699i	0.778828	−	0.253056i
$965$		0			0
$966$	3.71798	+	4.37455i	0.119624	+	0.140749i
$967$	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
$969$	−49.6895	+	20.4416i	−1.59626	+	0.656679i
$970$		0			0
$971$	−25.2468	−	34.7493i	−0.810210	−	1.11516i	−0.991291	−	0.131690i	$-0.957960\pi$
$971$	−25.2468	−	34.7493i	−0.810210	−	1.11516i	0.181081	−	0.983468i	$-0.442040\pi$
$972$	15.2006	−	3.45574i	0.487559	−	0.110843i
$973$	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	$-0.451883\pi$
$977$	26.9394	−	52.8715i	0.861867	−	1.69151i	0.711276	−	0.702912i	$-0.248117\pi$
$978$	2.64090	+	2.26659i	0.0844466	+	0.0724777i
$979$	−30.1017	−	41.4314i	−0.962054	−	1.32415i
$980$		0			0
$981$	0.912865	−	5.58874i	0.0291455	−	0.178435i
$982$	6.43398	−	6.43398i	0.205317	−	0.205317i
$983$	−37.5537	+	5.94792i	−1.19778	+	0.189709i	−0.723284	−	0.690550i	$-0.757368\pi$
$983$	−37.5537	+	5.94792i	−1.19778	+	0.189709i	−0.474492	+	0.880260i	$0.657368\pi$
$984$	−2.14031	+	1.81907i	−0.0682305	+	0.0579899i
$985$		0			0
$986$	−24.8687	+	8.08033i	−0.791981	+	0.257330i
$987$	1.44255	−	17.7801i	0.0459168	−	0.565948i
$988$	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
$993$	12.1132	−	2.87721i	0.384402	−	0.0913054i
$994$	5.13648	−	7.06976i	0.162919	−	0.224239i
$995$		0			0
$996$	−13.0644	+	0.996443i	−0.413960	+	0.0315735i
$997$	−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.143.10		80
3.2	odd	2	inner	750.2.l.b.143.4		80
5.2	odd	4		750.2.l.a.107.6		80
5.3	odd	4		750.2.l.c.107.5		80
5.4	even	2		150.2.l.a.83.1	yes	80
15.2	even	4		750.2.l.a.107.5		80
15.8	even	4		750.2.l.c.107.6		80
15.14	odd	2		150.2.l.a.83.7	yes	80
25.3	odd	20		150.2.l.a.47.7	yes	80
25.4	even	10		750.2.l.c.743.6		80
25.21	even	5		750.2.l.a.743.5		80
25.22	odd	20	inner	750.2.l.b.257.4		80
75.29	odd	10		750.2.l.c.743.5		80
75.47	even	20	inner	750.2.l.b.257.10		80
75.53	even	20		150.2.l.a.47.1	✓	80
75.71	odd	10		750.2.l.a.743.6		80

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

\(f(q)\)	\(=\)	\(q+(0.453990 - 0.891007i) q^{2} +(1.12805 - 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(1.51403 - 1.51403i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +O(q^{10})\)	\(q+(0.453990 - 0.891007i) q^{2} +(1.12805 - 1.31434i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.658960 - 1.60180i) q^{6} +(1.51403 - 1.51403i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.454984 - 2.96530i) q^{9} +(-5.62798 + 1.82864i) q^{11} +(-1.72638 - 0.140065i) 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} +(-2.84866 - 0.940823i) q^{18} +(3.16950 - 4.36244i) q^{19} +(-0.282042 - 3.69786i) q^{21} +(-0.925718 + 5.84476i) q^{22} +(-1.37932 - 0.702799i) q^{23} +(-0.908558 + 1.47463i) q^{24} +1.05646i q^{26} +(-4.41066 - 2.74701i) 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} +(-3.94521 + 9.45990i) q^{33} +(-5.47129 - 1.77773i) q^{34} +(-2.13154 + 2.11105i) q^{36} +(-0.100380 - 0.197006i) q^{37} +(-2.44804 - 4.80455i) q^{38} +(-0.431463 + 1.77824i) q^{39} +(1.54235 + 0.501139i) q^{41} +(-3.42286 - 1.42749i) 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} +(0.901424 + 1.47900i) q^{48} +2.41543i q^{49} +(-8.48331 - 5.22681i) q^{51} +(0.941310 + 0.479621i) q^{52} +(-0.949805 + 5.99683i) q^{53} +(-4.45000 + 2.68281i) q^{54} +(-1.25854 + 1.73224i) q^{56} +(-2.15837 - 9.08688i) 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} +(-5.17841 - 3.80069i) q^{63} +(0.951057 - 0.309017i) q^{64} +(6.63774 + 7.80992i) q^{66} +(1.28043 - 0.202800i) q^{67} +(-4.06788 + 4.06788i) q^{68} +(-2.47967 + 1.02010i) q^{69} +(2.39892 + 3.30183i) q^{71} +(0.913257 + 2.85761i) q^{72} +(-0.141918 + 0.278530i) q^{73} -0.221105 q^{74} -5.39228 q^{76} +(-5.75231 + 11.2895i) q^{77} +(1.38854 + 1.19174i) q^{78} +(0.555462 + 0.764528i) q^{79} +(-8.58598 + 2.69833i) q^{81} +(1.14673 - 1.14673i) q^{82} +(7.47149 - 1.18337i) q^{83} +(-2.82585 + 2.40172i) q^{84} +(-1.79600 + 0.583556i) q^{86} +(0.636640 - 7.84692i) 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} +(17.9652 - 4.26719i) q^{93} +(2.82728 - 3.89142i) q^{94} +(1.72703 - 0.131724i) 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

Fields

Representations

Groups

Database

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