LMFDB - Embedded newform 1500.2.m.d.301.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(301,1500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.m (of order $5$, degree $4$, 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:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.4
Character	$\chi$	$=$	1500.301
Dual form			1500.2.m.d.1201.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{3} +0.595901 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{3} +0.595901 q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.71474 + 1.97238i) q^{11} +(3.85825 + 2.80319i) q^{13} +(-2.31143 - 7.11384i) q^{17} +(1.91242 + 5.88583i) q^{19} +(-0.184143 + 0.566735i) q^{21} +(-3.56694 + 2.59154i) q^{23} +(0.809017 - 0.587785i) q^{27} +(-0.853035 + 2.62537i) q^{29} +(1.38708 + 4.26899i) q^{31} +(-1.03694 - 3.19137i) q^{33} +(-1.05226 - 0.764512i) q^{37} +(-3.85825 + 2.80319i) q^{39} +(7.61184 + 5.53032i) q^{41} -7.59854 q^{43} +(1.36026 - 4.18645i) q^{47} -6.64490 q^{49} +7.47993 q^{51} +(-2.53620 + 7.80561i) q^{53} -6.18873 q^{57} +(1.80309 + 1.31002i) q^{59} +(-10.2014 + 7.41175i) q^{61} +(-0.482094 - 0.350262i) q^{63} +(2.58288 + 7.94930i) q^{67} +(-1.36245 - 4.19319i) q^{69} +(2.09986 - 6.46271i) q^{71} +(5.91570 - 4.29801i) q^{73} +(-1.61772 + 1.17534i) q^{77} +(-3.26546 + 10.0500i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.29219 + 3.97694i) q^{83} +(-2.23328 - 1.62257i) q^{87} +(-3.43862 + 2.49830i) q^{89} +(2.29914 + 1.67042i) q^{91} -4.48868 q^{93} +(3.79326 - 11.6744i) q^{97} +3.35561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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			0
$2$		0			0
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.595901			0.225229			0.112615	−	0.993639i	$-0.464077\pi$
$7$	0.595901			0.225229			0.112615	+	0.993639i	$0.464077\pi$
$8$		0			0
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	−2.71474	+	1.97238i	−0.818526	+	0.594694i	−0.916290	−	0.400515i	$-0.868831\pi$
$11$	−2.71474	+	1.97238i	−0.818526	+	0.594694i	0.0977636	+	0.995210i	$0.468831\pi$
$12$		0			0
$13$	3.85825	+	2.80319i	1.07009	+	0.777464i	0.975928	−	0.218094i	$-0.0699838\pi$
$13$	3.85825	+	2.80319i	1.07009	+	0.777464i	0.0941591	+	0.995557i	$0.469984\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.31143	−	7.11384i	−0.560603	−	1.72536i	−0.680667	−	0.732593i	$-0.738310\pi$
$17$	−2.31143	−	7.11384i	−0.560603	−	1.72536i	0.120064	−	0.992766i	$-0.461690\pi$
$18$		0			0
$19$	1.91242	+	5.88583i	0.438740	+	1.35030i	0.889205	+	0.457508i	$0.151258\pi$
$19$	1.91242	+	5.88583i	0.438740	+	1.35030i	−0.450466	+	0.892794i	$0.648742\pi$
$20$		0			0
$21$	−0.184143	+	0.566735i	−0.0401834	+	0.123672i
$22$		0			0
$23$	−3.56694	+	2.59154i	−0.743759	+	0.540373i	−0.893886	−	0.448294i	$-0.852032\pi$
$23$	−3.56694	+	2.59154i	−0.743759	+	0.540373i	0.150127	+	0.988667i	$0.452032\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$		0			0
$29$	−0.853035	+	2.62537i	−0.158405	+	0.487519i	−0.998490	−	0.0549349i	$-0.982505\pi$
$29$	−0.853035	+	2.62537i	−0.158405	+	0.487519i	0.840085	+	0.542454i	$0.182505\pi$
$30$		0			0
$31$	1.38708	+	4.26899i	0.249127	+	0.766734i	0.994930	+	0.100567i	$0.0320658\pi$
$31$	1.38708	+	4.26899i	0.249127	+	0.766734i	−0.745803	+	0.666166i	$0.767934\pi$
$32$		0			0
$33$	−1.03694	−	3.19137i	−0.180508	−	0.555547i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.05226	−	0.764512i	−0.172991	−	0.125685i	0.497921	−	0.867222i	$-0.334097\pi$
$37$	−1.05226	−	0.764512i	−0.172991	−	0.125685i	−0.670912	+	0.741537i	$0.734097\pi$
$38$		0			0
$39$	−3.85825	+	2.80319i	−0.617815	+	0.448869i
$40$		0			0
$41$	7.61184	+	5.53032i	1.18877	+	0.863691i	0.993134	−	0.116985i	$-0.0373230\pi$
$41$	7.61184	+	5.53032i	1.18877	+	0.863691i	0.195636	+	0.980677i	$0.437323\pi$
$42$		0			0
$43$	−7.59854			−1.15877			−0.579383	−	0.815055i	$-0.696706\pi$
$43$	−7.59854			−1.15877			−0.579383	+	0.815055i	$0.696706\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.36026	−	4.18645i	0.198414	−	0.610656i	−0.801506	−	0.597987i	$-0.795967\pi$
$47$	1.36026	−	4.18645i	0.198414	−	0.610656i	0.999920	−	0.0126688i	$-0.00403271\pi$
$48$		0			0
$49$	−6.64490			−0.949272
$50$		0			0
$51$	7.47993			1.04740
$52$		0			0
$53$	−2.53620	+	7.80561i	−0.348373	+	1.07218i	0.611379	+	0.791338i	$0.290615\pi$
$53$	−2.53620	+	7.80561i	−0.348373	+	1.07218i	−0.959753	+	0.280846i	$0.909385\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−6.18873			−0.819717
$58$		0			0
$59$	1.80309	+	1.31002i	0.234743	+	0.170550i	0.698938	−	0.715182i	$-0.253656\pi$
$59$	1.80309	+	1.31002i	0.234743	+	0.170550i	−0.464195	+	0.885733i	$0.653656\pi$
$60$		0			0
$61$	−10.2014	+	7.41175i	−1.30615	+	0.948977i	−0.999995	−	0.00300353i	$-0.999044\pi$
$61$	−10.2014	+	7.41175i	−1.30615	+	0.948977i	−0.306159	+	0.951980i	$0.599044\pi$
$62$		0			0
$63$	−0.482094	−	0.350262i	−0.0607381	−	0.0441288i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.58288	+	7.94930i	0.315549	+	0.971161i	0.975528	+	0.219877i	$0.0705655\pi$
$67$	2.58288	+	7.94930i	0.315549	+	0.971161i	−0.659978	+	0.751285i	$0.729435\pi$
$68$		0			0
$69$	−1.36245	−	4.19319i	−0.164020	−	0.504801i
$70$		0			0
$71$	2.09986	−	6.46271i	0.249208	−	0.766983i	−0.745708	−	0.666273i	$-0.767889\pi$
$71$	2.09986	−	6.46271i	0.249208	−	0.766983i	0.994916	−	0.100710i	$-0.0321114\pi$
$72$		0			0
$73$	5.91570	−	4.29801i	0.692381	−	0.503044i	−0.185061	−	0.982727i	$-0.559248\pi$
$73$	5.91570	−	4.29801i	0.692381	−	0.503044i	0.877442	+	0.479683i	$0.159248\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.61772	+	1.17534i	−0.184356	+	0.133943i
$78$		0			0
$79$	−3.26546	+	10.0500i	−0.367393	+	1.13072i	0.581076	+	0.813849i	$0.302632\pi$
$79$	−3.26546	+	10.0500i	−0.367393	+	1.13072i	−0.948469	+	0.316870i	$0.897368\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		0			0
$83$	1.29219	+	3.97694i	0.141836	+	0.436526i	0.996591	−	0.0825062i	$-0.0262924\pi$
$83$	1.29219	+	3.97694i	0.141836	+	0.436526i	−0.854755	+	0.519032i	$0.826292\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−2.23328	−	1.62257i	−0.239432	−	0.173958i
$88$		0			0
$89$	−3.43862	+	2.49830i	−0.364493	+	0.264819i	−0.754924	−	0.655813i	$-0.772326\pi$
$89$	−3.43862	+	2.49830i	−0.364493	+	0.264819i	0.390431	+	0.920632i	$0.372326\pi$
$90$		0			0
$91$	2.29914	+	1.67042i	0.241015	+	0.175108i
$92$		0			0
$93$	−4.48868			−0.465455
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.79326	−	11.6744i	0.385147	−	1.18536i	−0.551227	−	0.834355i	$-0.685840\pi$
$97$	3.79326	−	11.6744i	0.385147	−	1.18536i	0.936374	−	0.351004i	$-0.114160\pi$
$98$		0			0
$99$	3.35561			0.337251
$100$		0			0
$101$	−8.00835			−0.796860			−0.398430	−	0.917199i	$-0.630445\pi$
$101$	−8.00835			−0.796860			−0.398430	+	0.917199i	$0.630445\pi$
$102$		0			0
$103$	−1.73829	+	5.34989i	−0.171278	+	0.527141i	−0.999444	−	0.0333428i	$-0.989385\pi$
$103$	−1.73829	+	5.34989i	−0.171278	+	0.527141i	0.828166	+	0.560484i	$0.189385\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.7701			−1.33120			−0.665601	−	0.746308i	$-0.731825\pi$
$107$	−13.7701			−1.33120			−0.665601	+	0.746308i	$0.731825\pi$
$108$		0			0
$109$	10.3566	+	7.52450i	0.991981	+	0.720716i	0.960354	−	0.278784i	$-0.0899313\pi$
$109$	10.3566	+	7.52450i	0.991981	+	0.720716i	0.0316266	+	0.999500i	$0.489931\pi$
$110$		0			0
$111$	1.05226	−	0.764512i	0.0998761	−	0.0725643i
$112$		0			0
$113$	−9.41647	−	6.84147i	−0.885827	−	0.643591i	0.0489597	−	0.998801i	$-0.484409\pi$
$113$	−9.41647	−	6.84147i	−0.885827	−	0.643591i	−0.934787	+	0.355210i	$0.884409\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.47372	−	4.53565i	−0.136246	−	0.419321i
$118$		0			0
$119$	−1.37738	−	4.23914i	−0.126264	−	0.388601i
$120$		0			0
$121$	0.0803793	−	0.247382i	0.00730721	−	0.0224893i
$122$		0			0
$123$	−7.61184	+	5.53032i	−0.686336	+	0.498652i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.15338	+	1.56452i	−0.191081	+	0.138829i	−0.679213	−	0.733941i	$-0.737679\pi$
$127$	−2.15338	+	1.56452i	−0.191081	+	0.138829i	0.488132	+	0.872770i	$0.337679\pi$
$128$		0			0
$129$	2.34808	−	7.22664i	0.206737	−	0.636270i
$130$		0			0
$131$	3.00070	+	9.23520i	0.262172	+	0.806883i	0.992331	+	0.123606i	$0.0394458\pi$
$131$	3.00070	+	9.23520i	0.262172	+	0.806883i	−0.730159	+	0.683277i	$0.760554\pi$
$132$		0			0
$133$	1.13961	+	3.50737i	0.0988170	+	0.304128i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.10819	−	2.25823i	−0.265551	−	0.192934i	0.447040	−	0.894514i	$-0.352478\pi$
$137$	−3.10819	−	2.25823i	−0.265551	−	0.192934i	−0.712591	+	0.701580i	$0.752478\pi$
$138$		0			0
$139$	3.98655	−	2.89640i	0.338135	−	0.245670i	−0.405740	−	0.913989i	$-0.632986\pi$
$139$	3.98655	−	2.89640i	0.338135	−	0.245670i	0.743875	+	0.668319i	$0.232986\pi$
$140$		0			0
$141$	3.56121	+	2.58737i	0.299908	+	0.217896i
$142$		0			0
$143$	−16.0031			−1.33825
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.05339	−	6.31968i	0.169361	−	0.521238i
$148$		0			0
$149$	−6.59040			−0.539907			−0.269953	−	0.962873i	$-0.587008\pi$
$149$	−6.59040			−0.539907			−0.269953	+	0.962873i	$0.587008\pi$
$150$		0			0
$151$	−19.5433			−1.59041			−0.795207	−	0.606338i	$-0.792638\pi$
$151$	−19.5433			−1.59041			−0.795207	+	0.606338i	$0.792638\pi$
$152$		0			0
$153$	−2.31143	+	7.11384i	−0.186868	+	0.575120i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.341995			−0.0272942			−0.0136471	−	0.999907i	$-0.504344\pi$
$157$	−0.341995			−0.0272942			−0.0136471	+	0.999907i	$0.504344\pi$
$158$		0			0
$159$	−6.63985	−	4.82413i	−0.526574	−	0.382579i
$160$		0			0
$161$	−2.12554	+	1.54430i	−0.167516	+	0.121708i
$162$		0			0
$163$	18.2161	+	13.2347i	1.42679	+	1.03663i	0.990603	+	0.136770i	$0.0436723\pi$
$163$	18.2161	+	13.2347i	1.42679	+	1.03663i	0.436190	+	0.899855i	$0.356328\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.33339	+	4.10375i	0.103181	+	0.317557i	0.989299	−	0.145901i	$-0.0466082\pi$
$167$	1.33339	+	4.10375i	0.103181	+	0.317557i	−0.886118	+	0.463459i	$0.846608\pi$
$168$		0			0
$169$	3.01105	+	9.26706i	0.231619	+	0.712851i
$170$		0			0
$171$	1.91242	−	5.88583i	0.146247	−	0.450101i
$172$		0			0
$173$	13.8898	−	10.0916i	1.05602	−	0.767247i	0.0826755	−	0.996577i	$-0.473653\pi$
$173$	13.8898	−	10.0916i	1.05602	−	0.767247i	0.973349	+	0.229330i	$0.0736535\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.80309	+	1.31002i	−0.135529	+	0.0984674i
$178$		0			0
$179$	0.328670	−	1.01154i	0.0245659	−	0.0756062i	−0.938022	−	0.346576i	$-0.887344\pi$
$179$	0.328670	−	1.01154i	0.0245659	−	0.0756062i	0.962588	+	0.270970i	$0.0873443\pi$
$180$		0			0
$181$	−3.71645	−	11.4380i	−0.276241	−	0.850183i	−0.988888	−	0.148660i	$-0.952504\pi$
$181$	−3.71645	−	11.4380i	−0.276241	−	0.850183i	0.712647	−	0.701523i	$-0.247496\pi$
$182$		0			0
$183$	−3.89659	−	11.9925i	−0.288044	−	0.886508i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	20.3061	+	14.7533i	1.48493	+	1.07886i
$188$		0			0
$189$	0.482094	−	0.350262i	0.0350672	−	0.0254778i
$190$		0			0
$191$	17.7737	+	12.9134i	1.28606	+	0.934379i	0.999718	−	0.0237480i	$-0.00755992\pi$
$191$	17.7737	+	12.9134i	1.28606	+	0.934379i	0.286344	+	0.958127i	$0.407560\pi$
$192$		0			0
$193$	20.4002			1.46844			0.734220	−	0.678912i	$-0.237548\pi$
$193$	20.4002			1.46844			0.734220	+	0.678912i	$0.237548\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.26852	−	3.90410i	0.0903781	−	0.278155i	−0.895644	−	0.444773i	$-0.853284\pi$
$197$	1.26852	−	3.90410i	0.0903781	−	0.278155i	0.986022	+	0.166617i	$0.0532845\pi$
$198$		0			0
$199$	25.5940			1.81431			0.907156	−	0.420795i	$-0.138249\pi$
$199$	25.5940			1.81431			0.907156	+	0.420795i	$0.138249\pi$
$200$		0			0
$201$	−8.35839			−0.589555
$202$		0			0
$203$	−0.508324	+	1.56446i	−0.0356774	+	0.109804i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.40898			0.306446
$208$		0			0
$209$	−16.8008	−	12.2065i	−1.16214	−	0.844342i
$210$		0			0
$211$	−15.7826	+	11.4667i	−1.08652	+	0.789402i	−0.978808	−	0.204781i	$-0.934352\pi$
$211$	−15.7826	+	11.4667i	−1.08652	+	0.789402i	−0.107710	+	0.994182i	$0.534352\pi$
$212$		0			0
$213$	5.49751	+	3.99418i	0.376683	+	0.273676i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.826561	+	2.54389i	0.0561106	+	0.172691i
$218$		0			0
$219$	2.25960	+	6.95433i	0.152689	+	0.469930i
$220$		0			0
$221$	11.0233	−	33.9263i	0.741510	−	2.28213i
$222$		0			0
$223$	1.80271	−	1.30975i	0.120718	−	0.0877071i	−0.525788	−	0.850616i	$-0.676229\pi$
$223$	1.80271	−	1.30975i	0.120718	−	0.0877071i	0.646506	+	0.762909i	$0.276229\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.67938	−	2.67322i	0.244209	−	0.177428i	−0.458947	−	0.888463i	$-0.651773\pi$
$227$	3.67938	−	2.67322i	0.244209	−	0.177428i	0.703156	+	0.711035i	$0.251773\pi$
$228$		0			0
$229$	1.05533	−	3.24796i	0.0697380	−	0.214631i	−0.910113	−	0.414359i	$-0.864006\pi$
$229$	1.05533	−	3.24796i	0.0697380	−	0.214631i	0.979851	+	0.199728i	$0.0640058\pi$
$230$		0			0
$231$	−0.617913	−	1.90174i	−0.0406557	−	0.125125i
$232$		0			0
$233$	−5.17279	−	15.9202i	−0.338881	−	1.04297i	−0.964779	−	0.263063i	$-0.915267\pi$
$233$	−5.17279	−	15.9202i	−0.338881	−	1.04297i	0.625898	−	0.779905i	$-0.284733\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−8.54908	−	6.21127i	−0.555323	−	0.403465i
$238$		0			0
$239$	18.0931	−	13.1454i	1.17035	−	0.850306i	0.179295	−	0.983795i	$-0.442618\pi$
$239$	18.0931	−	13.1454i	1.17035	−	0.850306i	0.991050	+	0.133490i	$0.0426184\pi$
$240$		0			0
$241$	−0.214678	−	0.155973i	−0.0138286	−	0.0100471i	0.580849	−	0.814011i	$-0.302720\pi$
$241$	−0.214678	−	0.155973i	−0.0138286	−	0.0100471i	−0.594678	+	0.803964i	$0.702720\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.12046	+	28.0699i	−0.580321	+	1.78604i
$248$		0			0
$249$	−4.18160			−0.264998
$250$		0			0
$251$	29.0694			1.83484			0.917422	−	0.397915i	$-0.130266\pi$
$251$	29.0694			1.83484			0.917422	+	0.397915i	$0.130266\pi$
$252$		0			0
$253$	4.57185	−	14.0707i	0.287430	−	0.884619i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.05952			0.440361			0.220180	−	0.975459i	$-0.429335\pi$
$257$	7.05952			0.440361			0.220180	+	0.975459i	$0.429335\pi$
$258$		0			0
$259$	−0.627043	−	0.455573i	−0.0389625	−	0.0283079i
$260$		0			0
$261$	2.23328	−	1.62257i	0.138236	−	0.100435i
$262$		0			0
$263$	1.12170	+	0.814961i	0.0691669	+	0.0502527i	0.621831	−	0.783151i	$-0.286389\pi$
$263$	1.12170	+	0.814961i	0.0691669	+	0.0502527i	−0.552665	+	0.833404i	$0.686389\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.31343	−	4.04234i	−0.0803809	−	0.247387i
$268$		0			0
$269$	−4.38039	−	13.4815i	−0.267077	−	0.821979i	−0.991208	−	0.132316i	$-0.957759\pi$
$269$	−4.38039	−	13.4815i	−0.267077	−	0.821979i	0.724130	−	0.689663i	$-0.242241\pi$
$270$		0			0
$271$	4.64795	−	14.3049i	0.282343	−	0.868963i	−0.704839	−	0.709367i	$-0.748981\pi$
$271$	4.64795	−	14.3049i	0.282343	−	0.868963i	0.987182	−	0.159596i	$-0.0510191\pi$
$272$		0			0
$273$	−2.29914	+	1.67042i	−0.139150	+	0.101098i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	10.3500	−	7.51973i	0.621873	−	0.451817i	−0.231703	−	0.972787i	$-0.574430\pi$
$277$	10.3500	−	7.51973i	0.621873	−	0.451817i	0.853575	+	0.520970i	$0.174430\pi$
$278$		0			0
$279$	1.38708	−	4.26899i	0.0830423	−	0.255578i
$280$		0			0
$281$	−4.72976	−	14.5567i	−0.282154	−	0.868380i	−0.987237	−	0.159256i	$-0.949091\pi$
$281$	−4.72976	−	14.5567i	−0.282154	−	0.868380i	0.705084	−	0.709124i	$-0.250909\pi$
$282$		0			0
$283$	−7.21559	−	22.2073i	−0.428923	−	1.32009i	−0.899188	−	0.437563i	$-0.855842\pi$
$283$	−7.21559	−	22.2073i	−0.428923	−	1.32009i	0.470265	−	0.882525i	$-0.344158\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.53590	+	3.29552i	0.267746	+	0.194529i
$288$		0			0
$289$	−31.5107	+	22.8939i	−1.85357	+	1.34670i
$290$		0			0
$291$	9.93087	+	7.21520i	0.582158	+	0.422963i
$292$		0			0
$293$	−6.36651			−0.371936			−0.185968	−	0.982556i	$-0.559542\pi$
$293$	−6.36651			−0.371936			−0.185968	+	0.982556i	$0.559542\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.03694	+	3.19137i	−0.0601694	+	0.185182i
$298$		0			0
$299$	−21.0267			−1.21601
$300$		0			0
$301$	−4.52797			−0.260988
$302$		0			0
$303$	2.47472	−	7.61639i	0.142169	−	0.437550i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	27.2317			1.55419			0.777096	−	0.629382i	$-0.216692\pi$
$307$	27.2317			1.55419			0.777096	+	0.629382i	$0.216692\pi$
$308$		0			0
$309$	−4.55089	−	3.30642i	−0.258891	−	0.188095i
$310$		0			0
$311$	−13.8814	+	10.0854i	−0.787142	+	0.571892i	−0.907114	−	0.420885i	$-0.861719\pi$
$311$	−13.8814	+	10.0854i	−0.787142	+	0.571892i	0.119972	+	0.992777i	$0.461719\pi$
$312$		0			0
$313$	16.3955	+	11.9120i	0.926728	+	0.673307i	0.945189	−	0.326523i	$-0.105877\pi$
$313$	16.3955	+	11.9120i	0.926728	+	0.673307i	−0.0184618	+	0.999830i	$0.505877\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.49409	+	19.9868i	0.364745	+	1.12257i	0.950141	+	0.311821i	$0.100939\pi$
$317$	6.49409	+	19.9868i	0.364745	+	1.12257i	−0.585396	+	0.810747i	$0.699061\pi$
$318$		0			0
$319$	−2.86245	−	8.80972i	−0.160267	−	0.493250i
$320$		0			0
$321$	4.25518	−	13.0961i	0.237501	−	0.730953i
$322$		0			0
$323$	37.4504	−	27.2093i	2.08380	−	1.51397i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−10.3566	+	7.52450i	−0.572720	+	0.416106i
$328$		0			0
$329$	0.810579	−	2.49471i	0.0446887	−	0.137538i
$330$		0			0
$331$	−3.93765	−	12.1188i	−0.216433	−	0.666111i	−0.999049	−	0.0436066i	$-0.986115\pi$
$331$	−3.93765	−	12.1188i	−0.216433	−	0.666111i	0.782616	−	0.622505i	$-0.213885\pi$
$332$		0			0
$333$	0.401928	+	1.23701i	0.0220255	+	0.0677875i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.98868	+	7.25720i	0.544118	+	0.395325i	0.825612	−	0.564238i	$-0.190830\pi$
$337$	9.98868	+	7.25720i	0.544118	+	0.395325i	−0.281494	+	0.959563i	$0.590830\pi$
$338$		0			0
$339$	9.41647	−	6.84147i	0.511432	−	0.371577i
$340$		0			0
$341$	−12.1856	−	8.85338i	−0.659889	−	0.479437i
$342$		0			0
$343$	−8.13100			−0.439033
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.06718	+	12.5175i	−0.218337	+	0.671974i	0.780562	+	0.625078i	$0.214933\pi$
$347$	−4.06718	+	12.5175i	−0.218337	+	0.671974i	−0.998900	+	0.0468956i	$0.985067\pi$
$348$		0			0
$349$	20.8060			1.11372			0.556861	−	0.830606i	$-0.312006\pi$
$349$	20.8060			1.11372			0.556861	+	0.830606i	$0.312006\pi$
$350$		0			0
$351$	4.76906			0.254554
$352$		0			0
$353$	−8.89800	+	27.3852i	−0.473593	+	1.45757i	0.374254	+	0.927326i	$0.377899\pi$
$353$	−8.89800	+	27.3852i	−0.473593	+	1.45757i	−0.847846	+	0.530242i	$0.822101\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.45730			0.235905
$358$		0			0
$359$	26.9627	+	19.5896i	1.42304	+	1.03390i	0.991260	+	0.131919i	$0.0421139\pi$
$359$	26.9627	+	19.5896i	1.42304	+	1.03390i	0.431779	+	0.901979i	$0.357886\pi$
$360$		0			0
$361$	−15.6143	+	11.3445i	−0.821806	+	0.597077i
$362$		0			0
$363$	0.210436	+	0.152891i	0.0110450	+	0.00802468i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	0.586288	+	1.80441i	0.0306040	+	0.0941894i	0.965192	−	0.261543i	$-0.0842314\pi$
$367$	0.586288	+	1.80441i	0.0306040	+	0.0941894i	−0.934588	+	0.355733i	$0.884231\pi$
$368$		0			0
$369$	−2.90746	−	8.94825i	−0.151356	−	0.465827i
$370$		0			0
$371$	−1.51132	+	4.65137i	−0.0784639	+	0.241487i
$372$		0			0
$373$	24.9912	−	18.1572i	1.29400	−	0.940143i	0.294118	−	0.955769i	$-0.404974\pi$
$373$	24.9912	−	18.1572i	1.29400	−	0.940143i	0.999878	+	0.0156262i	$0.00497417\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.6506	+	7.73814i	−0.548535	+	0.398534i
$378$		0			0
$379$	6.96979	−	21.4508i	0.358014	−	1.10185i	−0.596227	−	0.802816i	$-0.703334\pi$
$379$	6.96979	−	21.4508i	0.358014	−	1.10185i	0.954241	−	0.299038i	$-0.0966658\pi$
$380$		0			0
$381$	−0.822516	−	2.53145i	−0.0421388	−	0.129690i
$382$		0			0
$383$	1.34229	+	4.13113i	0.0685877	+	0.211091i	0.979476	−	0.201563i	$-0.0646020\pi$
$383$	1.34229	+	4.13113i	0.0685877	+	0.211091i	−0.910888	+	0.412654i	$0.864602\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.14735	+	4.46631i	0.312487	+	0.227035i
$388$		0			0
$389$	15.0039	−	10.9010i	0.760729	−	0.552702i	−0.138405	−	0.990376i	$-0.544198\pi$
$389$	15.0039	−	10.9010i	0.760729	−	0.552702i	0.899134	+	0.437674i	$0.144198\pi$
$390$		0			0
$391$	26.6805	+	19.3845i	1.34929	+	0.980317i
$392$		0			0
$393$	−9.71046			−0.489828
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−0.218473	+	0.672391i	−0.0109648	+	0.0337463i	−0.956389	−	0.292095i	$-0.905648\pi$
$397$	−0.218473	+	0.672391i	−0.0109648	+	0.0337463i	0.945424	+	0.325842i	$0.105648\pi$
$398$		0			0
$399$	−3.68787			−0.184624
$400$		0			0
$401$	−24.8304			−1.23997			−0.619986	−	0.784613i	$-0.712862\pi$
$401$	−24.8304			−1.23997			−0.619986	+	0.784613i	$0.712862\pi$
$402$		0			0
$403$	−6.61507	+	20.3591i	−0.329520	+	1.01416i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.36453			0.216341
$408$		0			0
$409$	0.590588	+	0.429087i	0.0292027	+	0.0212170i	0.602291	−	0.798277i	$-0.294255\pi$
$409$	0.590588	+	0.429087i	0.0292027	+	0.0212170i	−0.573088	+	0.819494i	$0.694255\pi$
$410$		0			0
$411$	3.10819	−	2.25823i	0.153316	−	0.111390i
$412$		0			0
$413$	1.07446	+	0.780643i	0.0528709	+	0.0384130i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.52273	+	4.68647i	0.0745683	+	0.229498i
$418$		0			0
$419$	−3.98923	−	12.2776i	−0.194887	−	0.599799i	−0.999978	−	0.00664830i	$-0.997884\pi$
$419$	−3.98923	−	12.2776i	−0.194887	−	0.599799i	0.805091	−	0.593151i	$-0.202116\pi$
$420$		0			0
$421$	11.7828	−	36.2639i	0.574261	−	1.76739i	−0.0644219	−	0.997923i	$-0.520520\pi$
$421$	11.7828	−	36.2639i	0.574261	−	1.76739i	0.638683	−	0.769470i	$-0.279480\pi$
$422$		0			0
$423$	−3.56121	+	2.58737i	−0.173152	+	0.125802i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−6.07902	+	4.41666i	−0.294184	+	0.213737i
$428$		0			0
$429$	4.94523	−	15.2199i	0.238758	−	0.734822i
$430$		0			0
$431$	−11.1829	−	34.4175i	−0.538663	−	1.65783i	−0.735599	−	0.677418i	$-0.763099\pi$
$431$	−11.1829	−	34.4175i	−0.538663	−	1.65783i	0.196936	−	0.980416i	$-0.436901\pi$
$432$		0			0
$433$	−6.72071	−	20.6842i	−0.322977	−	0.994021i	−0.972346	−	0.233547i	$-0.924967\pi$
$433$	−6.72071	−	20.6842i	−0.322977	−	0.994021i	0.649369	−	0.760474i	$-0.275033\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−22.0748	−	16.0383i	−1.05598	−	0.767217i
$438$		0			0
$439$	31.8418	−	23.1344i	1.51973	−	1.10415i	0.558103	−	0.829772i	$-0.311529\pi$
$439$	31.8418	−	23.1344i	1.51973	−	1.10415i	0.961623	−	0.274374i	$-0.0884705\pi$
$440$		0			0
$441$	5.37584	+	3.90578i	0.255992	+	0.185989i
$442$		0			0
$443$	−27.4919			−1.30618			−0.653089	−	0.757281i	$-0.726527\pi$
$443$	−27.4919			−1.30618			−0.653089	+	0.757281i	$0.726527\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.03655	−	6.26784i	0.0963253	−	0.296459i
$448$		0			0
$449$	3.51087			0.165688			0.0828441	−	0.996563i	$-0.473600\pi$
$449$	3.51087			0.165688			0.0828441	+	0.996563i	$0.473600\pi$
$450$		0			0
$451$	−31.5721			−1.48667
$452$		0			0
$453$	6.03923	−	18.5868i	0.283748	−	0.873285i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.1677			−0.475624			−0.237812	−	0.971311i	$-0.576430\pi$
$457$	−10.1677			−0.475624			−0.237812	+	0.971311i	$0.576430\pi$
$458$		0			0
$459$	−6.05139	−	4.39659i	−0.282455	−	0.205215i
$460$		0			0
$461$	−0.755758	+	0.549090i	−0.0351992	+	0.0255737i	−0.605246	−	0.796039i	$-0.706925\pi$
$461$	−0.755758	+	0.549090i	−0.0351992	+	0.0255737i	0.570047	+	0.821612i	$0.306925\pi$
$462$		0			0
$463$	−3.95274	−	2.87183i	−0.183699	−	0.133465i	0.492135	−	0.870519i	$-0.336217\pi$
$463$	−3.95274	−	2.87183i	−0.183699	−	0.133465i	−0.675835	+	0.737053i	$0.736217\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.97406	−	24.5416i	−0.368996	−	1.13565i	−0.947441	−	0.319931i	$-0.896340\pi$
$467$	−7.97406	−	24.5416i	−0.368996	−	1.13565i	0.578445	−	0.815721i	$-0.303660\pi$
$468$		0			0
$469$	1.53914	+	4.73699i	0.0710710	+	0.218734i
$470$		0			0
$471$	0.105682	−	0.325257i	0.00486958	−	0.0149870i
$472$		0			0
$473$	20.6281	−	14.9872i	0.948480	−	0.689111i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	6.63985	−	4.82413i	0.304018	−	0.220882i
$478$		0			0
$479$	−5.22721	+	16.0877i	−0.238837	+	0.735065i	0.757752	+	0.652543i	$0.226298\pi$
$479$	−5.22721	+	16.0877i	−0.238837	+	0.735065i	−0.996589	+	0.0825225i	$0.973702\pi$
$480$		0			0
$481$	−1.91682	−	5.89936i	−0.0873994	−	0.268988i
$482$		0			0
$483$	−0.811885	−	2.49873i	−0.0369421	−	0.113696i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−13.2578	−	9.63237i	−0.600769	−	0.436484i	0.245383	−	0.969426i	$-0.421086\pi$
$487$	−13.2578	−	9.63237i	−0.600769	−	0.436484i	−0.846152	+	0.532942i	$0.821086\pi$
$488$		0			0
$489$	−18.2161	+	13.2347i	−0.823759	+	0.598496i
$490$		0			0
$491$	8.30972	+	6.03737i	0.375013	+	0.272463i	0.759286	−	0.650757i	$-0.225548\pi$
$491$	8.30972	+	6.03737i	0.375013	+	0.272463i	−0.384274	+	0.923219i	$0.625548\pi$
$492$		0			0
$493$	20.6482			0.929948
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.25131	−	3.85113i	0.0561289	−	0.172747i
$498$		0			0
$499$	−16.5015			−0.738707			−0.369354	−	0.929289i	$-0.620421\pi$
$499$	−16.5015			−0.738707			−0.369354	+	0.929289i	$0.620421\pi$
$500$		0			0
$501$	−4.31493			−0.192777
$502$		0			0
$503$	−2.34863	+	7.22834i	−0.104720	+	0.322296i	−0.989665	−	0.143401i	$-0.954196\pi$
$503$	−2.34863	+	7.22834i	−0.104720	+	0.322296i	0.884944	+	0.465697i	$0.154196\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.74397			−0.432745
$508$		0			0
$509$	17.7590	+	12.9027i	0.787154	+	0.571901i	0.907118	−	0.420877i	$-0.138278\pi$
$509$	17.7590	+	12.9027i	0.787154	+	0.571901i	−0.119963	+	0.992778i	$0.538278\pi$
$510$		0			0
$511$	3.52517	−	2.56119i	0.155944	−	0.113300i
$512$		0			0
$513$	5.00679	+	3.63764i	0.221055	+	0.160606i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.56450	+	14.0481i	0.200746	+	0.617834i
$518$		0			0
$519$	5.30544	+	16.3285i	0.232883	+	0.716741i
$520$		0			0
$521$	−11.3835	+	35.0349i	−0.498722	+	1.53491i	0.312353	+	0.949966i	$0.398883\pi$
$521$	−11.3835	+	35.0349i	−0.498722	+	1.53491i	−0.811075	+	0.584942i	$0.801117\pi$
$522$		0			0
$523$	−33.6548	+	24.4517i	−1.47162	+	1.06920i	−0.491484	+	0.870887i	$0.663545\pi$
$523$	−33.6548	+	24.4517i	−1.47162	+	1.06920i	−0.980139	+	0.198310i	$0.936455\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	27.1628	−	19.7349i	1.18323	−	0.859667i
$528$		0			0
$529$	−1.10036	+	3.38657i	−0.0478419	+	0.147242i
$530$		0			0
$531$	−0.688720	−	2.11966i	−0.0298879	−	0.0919855i
$532$		0			0
$533$	13.8659	+	42.6748i	0.600598	+	1.84845i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	0.860469	+	0.625167i	0.0371320	+	0.0269779i
$538$		0			0
$539$	18.0392	−	13.1063i	0.777004	−	0.564526i
$540$		0			0
$541$	12.5570	+	9.12319i	0.539867	+	0.392237i	0.824036	−	0.566538i	$-0.191717\pi$
$541$	12.5570	+	9.12319i	0.539867	+	0.392237i	−0.284168	+	0.958774i	$0.591717\pi$
$542$		0			0
$543$	12.0267			0.516114
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−7.20130	+	22.1633i	−0.307906	+	0.947636i	0.670671	+	0.741755i	$0.266006\pi$
$547$	−7.20130	+	22.1633i	−0.307906	+	0.947636i	−0.978577	+	0.205881i	$0.933994\pi$
$548$		0			0
$549$	12.6096			0.538165
$550$		0			0
$551$	−17.0839			−0.727797
$552$		0			0
$553$	−1.94589	+	5.98883i	−0.0827476	+	0.254671i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.0914			0.469959			0.234979	−	0.972000i	$-0.424498\pi$
$557$	11.0914			0.469959			0.234979	+	0.972000i	$0.424498\pi$
$558$		0			0
$559$	−29.3171	−	21.3001i	−1.23998	−	0.900898i
$560$		0			0
$561$	−20.3061	+	14.7533i	−0.857325	+	0.622883i
$562$		0			0
$563$	−11.5731	−	8.40836i	−0.487749	−	0.354370i	0.316569	−	0.948569i	$-0.397469\pi$
$563$	−11.5731	−	8.40836i	−0.487749	−	0.354370i	−0.804318	+	0.594199i	$0.797469\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.184143	+	0.566735i	0.00773330	+	0.0238006i
$568$		0			0
$569$	−8.89176	−	27.3660i	−0.372762	−	1.14724i	−0.944976	−	0.327139i	$-0.893915\pi$
$569$	−8.89176	−	27.3660i	−0.372762	−	1.14724i	0.572214	−	0.820104i	$-0.306085\pi$
$570$		0			0
$571$	−4.02941	+	12.4012i	−0.168625	+	0.518976i	−0.999285	−	0.0378048i	$-0.987963\pi$
$571$	−4.02941	+	12.4012i	−0.168625	+	0.518976i	0.830660	+	0.556780i	$0.187963\pi$
$572$		0			0
$573$	−17.7737	+	12.9134i	−0.742508	+	0.539464i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.45601	+	1.05786i	−0.0606147	+	0.0440391i	−0.617680	−	0.786430i	$-0.711927\pi$
$577$	−1.45601	+	1.05786i	−0.0606147	+	0.0440391i	0.557065	+	0.830469i	$0.311927\pi$
$578$		0			0
$579$	−6.30401	+	19.4018i	−0.261986	+	0.806309i
$580$		0			0
$581$	0.770015	+	2.36986i	0.0319456	+	0.0983184i
$582$		0			0
$583$	−8.51049	−	26.1926i	−0.352468	−	1.08479i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	32.8432	+	23.8620i	1.35558	+	0.984889i	0.998712	+	0.0507360i	$0.0161567\pi$
$587$	32.8432	+	23.8620i	1.35558	+	0.984889i	0.356872	+	0.934153i	$0.383843\pi$
$588$		0			0
$589$	−22.4739	+	16.3282i	−0.926020	+	0.672793i
$590$		0			0
$591$	3.32102	+	2.41286i	0.136609	+	0.0992519i
$592$		0			0
$593$	−29.4991			−1.21138			−0.605690	−	0.795700i	$-0.707103\pi$
$593$	−29.4991			−1.21138			−0.605690	+	0.795700i	$0.707103\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.90898	+	24.3413i	−0.323693	+	0.996225i
$598$		0			0
$599$	−8.91418			−0.364224			−0.182112	−	0.983278i	$-0.558293\pi$
$599$	−8.91418			−0.364224			−0.182112	+	0.983278i	$0.558293\pi$
$600$		0			0
$601$	16.6757			0.680217			0.340109	−	0.940386i	$-0.389536\pi$
$601$	16.6757			0.680217			0.340109	+	0.940386i	$0.389536\pi$
$602$		0			0
$603$	2.58288	−	7.94930i	0.105183	−	0.323720i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−26.9626			−1.09438			−0.547190	−	0.837008i	$-0.684302\pi$
$607$	−26.9626			−1.09438			−0.547190	+	0.837008i	$0.684302\pi$
$608$		0			0
$609$	−1.33081	−	0.966890i	−0.0539271	−	0.0391804i
$610$		0			0
$611$	16.9836	−	12.3393i	0.687083	−	0.499195i
$612$		0			0
$613$	13.3673	+	9.71195i	0.539902	+	0.392262i	0.824049	−	0.566519i	$-0.191710\pi$
$613$	13.3673	+	9.71195i	0.539902	+	0.392262i	−0.284147	+	0.958781i	$0.591710\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.10364	−	21.8628i	−0.285982	−	0.880161i	−0.986103	−	0.166137i	$-0.946871\pi$
$617$	−7.10364	−	21.8628i	−0.285982	−	0.880161i	0.700121	−	0.714024i	$-0.253129\pi$
$618$		0			0
$619$	15.2396	+	46.9028i	0.612533	+	1.88518i	0.432875	+	0.901454i	$0.357499\pi$
$619$	15.2396	+	46.9028i	0.612533	+	1.88518i	0.179658	+	0.983729i	$0.442501\pi$
$620$		0			0
$621$	−1.36245	+	4.19319i	−0.0546733	+	0.168267i
$622$		0			0
$623$	−2.04907	+	1.48874i	−0.0820944	+	0.0596451i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	16.8008	−	12.2065i	0.670960	−	0.487481i
$628$		0			0
$629$	−3.00639	+	9.25273i	−0.119873	+	0.368930i
$630$		0			0
$631$	7.47148	+	22.9948i	0.297435	+	0.915410i	0.982393	+	0.186828i	$0.0598206\pi$
$631$	7.47148	+	22.9948i	0.297435	+	0.915410i	−0.684958	+	0.728583i	$0.740179\pi$
$632$		0			0
$633$	−6.02841	−	18.5535i	−0.239608	−	0.737437i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−25.6377	−	18.6269i	−1.01580	−	0.738024i
$638$		0			0
$639$	−5.49751	+	3.99418i	−0.217478	+	0.158007i
$640$		0			0
$641$	39.9382	+	29.0168i	1.57746	+	1.14610i	0.919530	+	0.393020i	$0.128570\pi$
$641$	39.9382	+	29.0168i	1.57746	+	1.14610i	0.657935	+	0.753075i	$0.271430\pi$
$642$		0			0
$643$	−3.97743			−0.156854			−0.0784272	−	0.996920i	$-0.524990\pi$
$643$	−3.97743			−0.156854			−0.0784272	+	0.996920i	$0.524990\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.313471	+	0.964765i	−0.0123238	+	0.0379288i	−0.957029	−	0.289991i	$-0.906348\pi$
$647$	−0.313471	+	0.964765i	−0.0123238	+	0.0379288i	0.944706	+	0.327920i	$0.106348\pi$
$648$		0			0
$649$	−7.47879			−0.293568
$650$		0			0
$651$	−2.67481			−0.104834
$652$		0			0
$653$	2.52515	−	7.77161i	0.0988167	−	0.304127i	−0.889413	−	0.457105i	$-0.848886\pi$
$653$	2.52515	−	7.77161i	0.0988167	−	0.304127i	0.988230	+	0.152978i	$0.0488864\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−7.31221			−0.285277
$658$		0			0
$659$	−6.22020	−	4.51924i	−0.242305	−	0.176045i	0.460005	−	0.887916i	$-0.347848\pi$
$659$	−6.22020	−	4.51924i	−0.242305	−	0.176045i	−0.702309	+	0.711872i	$0.747848\pi$
$660$		0			0
$661$	29.2864	−	21.2778i	1.13911	−	0.827611i	0.152114	−	0.988363i	$-0.451392\pi$
$661$	29.2864	−	21.2778i	1.13911	−	0.827611i	0.986995	+	0.160752i	$0.0513919\pi$
$662$		0			0
$663$	28.8595	+	20.9676i	1.12081	+	0.814316i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.76102	−	11.5752i	−0.145627	−	0.448195i
$668$		0			0
$669$	0.688574	+	2.11921i	0.0266218	+	0.0819335i
$670$		0			0
$671$	13.0754	−	40.2420i	0.504771	−	1.55353i
$672$		0			0
$673$	−24.4177	+	17.7405i	−0.941233	+	0.683845i	−0.948717	−	0.316127i	$-0.897618\pi$
$673$	−24.4177	+	17.7405i	−0.941233	+	0.683845i	0.00748451	+	0.999972i	$0.497618\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−38.0362	+	27.6349i	−1.46185	+	1.06210i	−0.478975	+	0.877829i	$0.658991\pi$
$677$	−38.0362	+	27.6349i	−1.46185	+	1.06210i	−0.982876	+	0.184268i	$0.941009\pi$
$678$		0			0
$679$	2.26040	−	6.95680i	0.0867463	−	0.266978i
$680$		0			0
$681$	1.40540	+	4.32537i	0.0538549	+	0.165748i
$682$		0			0
$683$	−0.677379	−	2.08476i	−0.0259192	−	0.0797710i	0.937260	−	0.348631i	$-0.113353\pi$
$683$	−0.677379	−	2.08476i	−0.0259192	−	0.0797710i	−0.963179	+	0.268860i	$0.913353\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	2.76288	+	2.00735i	0.105411	+	0.0765852i
$688$		0			0
$689$	−31.6659	+	23.0066i	−1.20637	+	0.876482i
$690$		0			0
$691$	−1.44427	−	1.04932i	−0.0549425	−	0.0399181i	0.559975	−	0.828509i	$-0.310811\pi$
$691$	−1.44427	−	1.04932i	−0.0549425	−	0.0399181i	−0.614918	+	0.788591i	$0.710811\pi$
$692$		0			0
$693$	1.99961			0.0759589
$694$		0			0
$695$		0			0
$696$		0			0
$697$	21.7476	−	66.9323i	0.823750	−	2.53524i
$698$		0			0
$699$	16.7395			0.633146
$700$		0			0
$701$	−11.0728			−0.418215			−0.209107	−	0.977893i	$-0.567056\pi$
$701$	−11.0728			−0.418215			−0.209107	+	0.977893i	$0.567056\pi$
$702$		0			0
$703$	2.48742	−	7.65550i	0.0938149	−	0.288733i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.77218			−0.179476
$708$		0			0
$709$	−16.1099	−	11.7045i	−0.605020	−	0.439573i	0.242637	−	0.970117i	$-0.421988\pi$
$709$	−16.1099	−	11.7045i	−0.605020	−	0.439573i	−0.847657	+	0.530544i	$0.821988\pi$
$710$		0			0
$711$	8.54908	−	6.21127i	0.320616	−	0.232941i
$712$		0			0
$713$	−16.0109	−	11.6326i	−0.599612	−	0.435644i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	6.91095	+	21.2697i	0.258094	+	0.794332i
$718$		0			0
$719$	10.7477	+	33.0782i	0.400823	+	1.23361i	0.924333	+	0.381587i	$0.124623\pi$
$719$	10.7477	+	33.0782i	0.400823	+	1.23361i	−0.523509	+	0.852020i	$0.675377\pi$
$720$		0			0
$721$	−1.03585	+	3.18801i	−0.0385769	+	0.118728i
$722$		0			0
$723$	0.214678	−	0.155973i	0.00798395	−	0.00580068i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	12.9181	−	9.38558i	0.479107	−	0.348092i	−0.321873	−	0.946783i	$-0.604312\pi$
$727$	12.9181	−	9.38558i	0.479107	−	0.348092i	0.800980	+	0.598691i	$0.204312\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	17.5635	+	54.0548i	0.649608	+	1.99929i
$732$		0			0
$733$	−3.13420	−	9.64606i	−0.115764	−	0.356286i	0.876341	−	0.481690i	$-0.159977\pi$
$733$	−3.13420	−	9.64606i	−0.115764	−	0.356286i	−0.992106	+	0.125405i	$0.959977\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−22.6909	−	16.4859i	−0.835830	−	0.607266i
$738$		0			0
$739$	−2.65234	+	1.92704i	−0.0975681	+	0.0708873i	−0.635500	−	0.772101i	$-0.719206\pi$
$739$	−2.65234	+	1.92704i	−0.0975681	+	0.0708873i	0.537932	+	0.842988i	$0.319206\pi$
$740$		0			0
$741$	−23.8777	−	17.3482i	−0.877169	−	0.637300i
$742$		0			0
$743$	38.7278			1.42078			0.710392	−	0.703806i	$-0.248518\pi$
$743$	38.7278			1.42078			0.710392	+	0.703806i	$0.248518\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.29219	−	3.97694i	0.0472786	−	0.145509i
$748$		0			0
$749$	−8.20559			−0.299826
$750$		0			0
$751$	13.0211			0.475146			0.237573	−	0.971370i	$-0.423648\pi$
$751$	13.0211			0.475146			0.237573	+	0.971370i	$0.423648\pi$
$752$		0			0
$753$	−8.98294	+	27.6466i	−0.327357	+	1.00750i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	33.4057			1.21415			0.607075	−	0.794645i	$-0.292343\pi$
$757$	33.4057			1.21415			0.607075	+	0.794645i	$0.292343\pi$
$758$		0			0
$759$	11.9693	+	8.69618i	0.434457	+	0.315651i
$760$		0			0
$761$	−24.0536	+	17.4760i	−0.871943	+	0.633504i	−0.931108	−	0.364745i	$-0.881156\pi$
$761$	−24.0536	+	17.4760i	−0.871943	+	0.633504i	0.0591647	+	0.998248i	$0.481156\pi$
$762$		0			0
$763$	6.17149	+	4.48385i	0.223423	+	0.162326i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.28455	+	10.1088i	0.118598	+	0.365008i
$768$		0			0
$769$	−1.68546	−	5.18732i	−0.0607794	−	0.187060i	0.916057	−	0.401049i	$-0.131354\pi$
$769$	−1.68546	−	5.18732i	−0.0607794	−	0.187060i	−0.976836	+	0.213989i	$0.931354\pi$
$770$		0			0
$771$	−2.18151	+	6.71400i	−0.0785652	+	0.241799i
$772$		0			0
$773$	23.5297	−	17.0953i	0.846303	−	0.614875i	−0.0778211	−	0.996967i	$-0.524796\pi$
$773$	23.5297	−	17.0953i	0.846303	−	0.614875i	0.924124	+	0.382092i	$0.124796\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.627043	−	0.455573i	0.0224950	−	0.0163436i
$778$		0			0
$779$	−17.9935	+	55.3783i	−0.644684	+	1.98413i
$780$		0			0
$781$	7.04632	+	21.6863i	0.252137	+	0.775998i
$782$		0			0
$783$	0.853035	+	2.62537i	0.0304850	+	0.0938232i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−27.5989	−	20.0518i	−0.983794	−	0.714768i	−0.0252406	−	0.999681i	$-0.508035\pi$
$787$	−27.5989	−	20.0518i	−0.983794	−	0.714768i	−0.958553	+	0.284913i	$0.908035\pi$
$788$		0			0
$789$	−1.12170	+	0.814961i	−0.0399335	+	0.0290134i
$790$		0			0
$791$	−5.61128	−	4.07683i	−0.199514	−	0.144955i
$792$		0			0
$793$	−60.1361			−2.13549
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.55732	+	23.2590i	−0.267694	+	0.823877i	0.723367	+	0.690464i	$0.242594\pi$
$797$	−7.55732	+	23.2590i	−0.267694	+	0.823877i	−0.991061	+	0.133413i	$0.957406\pi$
$798$		0			0
$799$	−32.9259			−1.16483
$800$		0			0
$801$	4.25036			0.150179
$802$		0			0
$803$	−7.58233	+	23.3360i	−0.267574	+	0.823510i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14.1752			0.498992
$808$		0			0
$809$	42.2701	+	30.7110i	1.48614	+	1.07974i	0.975514	+	0.219937i	$0.0705851\pi$
$809$	42.2701	+	30.7110i	1.48614	+	1.07974i	0.510623	+	0.859805i	$0.329415\pi$
$810$		0			0
$811$	−14.2781	+	10.3736i	−0.501371	+	0.364267i	−0.809540	−	0.587064i	$-0.800284\pi$
$811$	−14.2781	+	10.3736i	−0.501371	+	0.364267i	0.308170	+	0.951331i	$0.400284\pi$
$812$		0			0
$813$	12.1685	+	8.84093i	0.426768	+	0.310065i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−14.5316	−	44.7237i	−0.508397	−	1.56468i
$818$		0			0
$819$	−0.878192	−	2.70280i	−0.0306865	−	0.0944433i
$820$		0			0
$821$	−10.5469	+	32.4602i	−0.368091	+	1.13287i	0.579932	+	0.814665i	$0.303079\pi$
$821$	−10.5469	+	32.4602i	−0.368091	+	1.13287i	−0.948023	+	0.318202i	$0.896921\pi$
$822$		0			0
$823$	−36.8331	+	26.7608i	−1.28392	+	0.932823i	−0.999664	−	0.0259255i	$-0.991747\pi$
$823$	−36.8331	+	26.7608i	−1.28392	+	0.932823i	−0.284257	+	0.958748i	$0.591747\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	15.4496	−	11.2248i	0.537234	−	0.390323i	−0.285823	−	0.958282i	$-0.592267\pi$
$827$	15.4496	−	11.2248i	0.537234	−	0.390323i	0.823057	+	0.567959i	$0.192267\pi$
$828$		0			0
$829$	3.51719	−	10.8248i	0.122157	−	0.375961i	−0.871215	−	0.490901i	$-0.836668\pi$
$829$	3.51719	−	10.8248i	0.122157	−	0.375961i	0.993372	+	0.114940i	$0.0366676\pi$
$830$		0			0
$831$	3.95336	+	12.1672i	0.137140	+	0.422075i
$832$		0			0
$833$	15.3592	+	47.2708i	0.532165	+	1.63783i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.63142	+	2.63838i	0.125520	+	0.0911958i
$838$		0			0
$839$	−20.8665	+	15.1604i	−0.720391	+	0.523395i	−0.886509	−	0.462711i	$-0.846877\pi$
$839$	−20.8665	+	15.1604i	−0.720391	+	0.523395i	0.166118	+	0.986106i	$0.446877\pi$
$840$		0			0
$841$	17.2966	+	12.5667i	0.596434	+	0.433335i
$842$		0			0
$843$	15.3058			0.527160
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.0478981	−	0.147415i	0.00164580	−	0.00506525i
$848$		0			0
$849$	23.3502			0.801375
$850$		0			0
$851$	5.73461			0.196580
$852$		0			0
$853$	−4.86423	+	14.9706i	−0.166548	+	0.512582i	−0.999147	−	0.0412941i	$-0.986852\pi$
$853$	−4.86423	+	14.9706i	−0.166548	+	0.512582i	0.832599	+	0.553876i	$0.186852\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	46.4948			1.58823			0.794116	−	0.607767i	$-0.207934\pi$
$857$	46.4948			1.58823			0.794116	+	0.607767i	$0.207934\pi$
$858$		0			0
$859$	−9.86663	−	7.16852i	−0.336645	−	0.244587i	0.406600	−	0.913606i	$-0.366714\pi$
$859$	−9.86663	−	7.16852i	−0.336645	−	0.244587i	−0.743245	+	0.669019i	$0.766714\pi$
$860$		0			0
$861$	−4.53590	+	3.29552i	−0.154583	+	0.112311i
$862$		0			0
$863$	−36.7234	−	26.6811i	−1.25008	−	0.908235i	−0.251852	−	0.967766i	$-0.581040\pi$
$863$	−36.7234	−	26.6811i	−1.25008	−	0.908235i	−0.998226	+	0.0595307i	$0.981040\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−12.0360	−	37.0431i	−0.408765	−	1.25805i
$868$		0			0
$869$	−10.9576	−	33.7240i	−0.371711	−	1.14401i
$870$		0			0
$871$	−12.3179	+	37.9107i	−0.417377	+	1.28456i
$872$		0			0
$873$	−9.93087	+	7.21520i	−0.336109	+	0.244198i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.3960	+	11.1859i	−0.519887	+	0.377720i	−0.816561	−	0.577259i	$-0.804122\pi$
$877$	−15.3960	+	11.1859i	−0.519887	+	0.377720i	0.296675	+	0.954979i	$0.404122\pi$
$878$		0			0
$879$	1.96736	−	6.05491i	0.0663574	−	0.204227i
$880$		0			0
$881$	−4.70004	−	14.4652i	−0.158348	−	0.487346i	0.840136	−	0.542375i	$-0.182475\pi$
$881$	−4.70004	−	14.4652i	−0.158348	−	0.487346i	−0.998485	+	0.0550289i	$0.982475\pi$
$882$		0			0
$883$	14.9311	+	45.9532i	0.502472	+	1.54645i	0.804979	+	0.593303i	$0.202176\pi$
$883$	14.9311	+	45.9532i	0.502472	+	1.54645i	−0.302507	+	0.953147i	$0.597824\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−26.2130	−	19.0449i	−0.880146	−	0.639464i	0.0531439	−	0.998587i	$-0.483076\pi$
$887$	−26.2130	−	19.0449i	−0.880146	−	0.639464i	−0.933290	+	0.359123i	$0.883076\pi$
$888$		0			0
$889$	−1.28320	+	0.932298i	−0.0430371	+	0.0312683i
$890$		0			0
$891$	−2.71474	−	1.97238i	−0.0909474	−	0.0660771i
$892$		0			0
$893$	27.2421			0.911622
$894$		0			0
$895$		0			0
$896$		0			0
$897$	6.49762	−	19.9976i	0.216949	−	0.667701i
$898$		0			0
$899$	−12.3909			−0.413260
$900$		0			0
$901$	61.3901			2.04520
$902$		0			0
$903$	1.39922	−	4.30636i	0.0465631	−	0.143307i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−30.8525			−1.02444			−0.512220	−	0.858854i	$-0.671177\pi$
$907$	−30.8525			−1.02444			−0.512220	+	0.858854i	$0.671177\pi$
$908$		0			0
$909$	6.47889	+	4.70719i	0.214891	+	0.156128i
$910$		0			0
$911$	−29.3011	+	21.2885i	−0.970787	+	0.705318i	−0.955631	−	0.294567i	$-0.904825\pi$
$911$	−29.3011	+	21.2885i	−0.970787	+	0.705318i	−0.0151564	+	0.999885i	$0.504825\pi$
$912$		0			0
$913$	−11.3520	−	8.24770i	−0.375696	−	0.272959i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.78812	+	5.50326i	0.0590488	+	0.181734i
$918$		0			0
$919$	−11.7420	−	36.1380i	−0.387331	−	1.19208i	−0.934775	−	0.355240i	$-0.884399\pi$
$919$	−11.7420	−	36.1380i	−0.387331	−	1.19208i	0.547444	−	0.836842i	$-0.315601\pi$
$920$		0			0
$921$	−8.41505	+	25.8988i	−0.277285	+	0.853396i
$922$		0			0
$923$	26.2180	−	19.0485i	0.862975	−	0.626988i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	4.55089	−	3.30642i	0.149471	−	0.108597i
$928$		0			0
$929$	−3.23230	+	9.94801i	−0.106048	+	0.326384i	−0.989975	−	0.141242i	$-0.954890\pi$
$929$	−3.23230	+	9.94801i	−0.106048	+	0.326384i	0.883927	+	0.467626i	$0.154890\pi$
$930$		0			0
$931$	−12.7079	−	39.1108i	−0.416483	−	1.28180i
$932$		0			0
$933$	−5.30222	−	16.3186i	−0.173587	−	0.534246i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−27.3155	−	19.8458i	−0.892357	−	0.648335i	0.0441344	−	0.999026i	$-0.485947\pi$
$937$	−27.3155	−	19.8458i	−0.892357	−	0.648335i	−0.936492	+	0.350690i	$0.885947\pi$
$938$		0			0
$939$	−16.3955	+	11.9120i	−0.535046	+	0.388734i
$940$		0			0
$941$	−1.80449	−	1.31104i	−0.0588247	−	0.0427386i	0.557984	−	0.829851i	$-0.311575\pi$
$941$	−1.80449	−	1.31104i	−0.0588247	−	0.0427386i	−0.616809	+	0.787113i	$0.711575\pi$
$942$		0			0
$943$	−41.4830			−1.35087
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.36444	−	7.27701i	0.0768341	−	0.236471i	−0.905261	−	0.424855i	$-0.860325\pi$
$947$	2.36444	−	7.27701i	0.0768341	−	0.236471i	0.982095	+	0.188384i	$0.0603250\pi$
$948$		0			0
$949$	34.8724			1.13201
$950$		0			0
$951$	−21.0153			−0.681469
$952$		0			0
$953$	−3.60086	+	11.0823i	−0.116643	+	0.358991i	−0.992286	−	0.123968i	$-0.960438\pi$
$953$	−3.60086	+	11.0823i	−0.116643	+	0.358991i	0.875643	+	0.482959i	$0.160438\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	9.26309			0.299433
$958$		0			0
$959$	−1.85217	−	1.34568i	−0.0598098	−	0.0434544i
$960$		0			0
$961$	8.77922	−	6.37848i	0.283201	−	0.205757i
$962$		0			0
$963$	11.1402	+	8.09384i	0.358988	+	0.260820i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−10.4380	−	32.1250i	−0.335665	−	1.03307i	−0.966394	−	0.257067i	$-0.917244\pi$
$967$	−10.4380	−	32.1250i	−0.335665	−	1.03307i	0.630729	−	0.776004i	$-0.282756\pi$
$968$		0			0
$969$	14.3048	+	44.0256i	0.459536	+	1.41431i
$970$		0			0
$971$	10.4403	−	32.1319i	0.335045	−	1.03116i	−0.631655	−	0.775250i	$-0.717624\pi$
$971$	10.4403	−	32.1319i	0.335045	−	1.03116i	0.966700	−	0.255913i	$-0.0823760\pi$
$972$		0			0
$973$	2.37559	−	1.72597i	0.0761579	−	0.0553320i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.05079	−	2.21653i	0.0976035	−	0.0709131i	−0.537913	−	0.843000i	$-0.680787\pi$
$977$	3.05079	−	2.21653i	0.0976035	−	0.0709131i	0.635517	+	0.772087i	$0.280787\pi$
$978$		0			0
$979$	4.40737	−	13.5645i	0.140860	−	0.433523i
$980$		0			0
$981$	−3.95586	−	12.1749i	−0.126301	−	0.388714i
$982$		0			0
$983$	13.0727	+	40.2335i	0.416953	+	1.28325i	0.910492	+	0.413526i	$0.135703\pi$
$983$	13.0727	+	40.2335i	0.416953	+	1.28325i	−0.493539	+	0.869723i	$0.664297\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.12212	+	1.54181i	0.0675480	+	0.0490765i
$988$		0			0
$989$	27.1036	−	19.6919i	0.861843	−	0.626165i
$990$		0			0
$991$	−25.8789	−	18.8021i	−0.822071	−	0.597269i	0.0952341	−	0.995455i	$-0.469640\pi$
$991$	−25.8789	−	18.8021i	−0.822071	−	0.597269i	−0.917305	+	0.398186i	$0.869640\pi$
$992$		0			0
$993$	12.7425			0.404371
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.16296	+	15.8900i	−0.163513	+	0.503240i	−0.998924	−	0.0463858i	$-0.985230\pi$
$997$	−5.16296	+	15.8900i	−0.163513	+	0.503240i	0.835411	+	0.549626i	$0.185230\pi$
$998$		0			0
$999$	−1.30067			−0.0411512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.d.301.4		24
5.2	odd	4		1500.2.o.c.949.5		24
5.3	odd	4		300.2.o.a.289.1	yes	24
5.4	even	2		1500.2.m.c.301.3		24
15.8	even	4		900.2.w.c.289.6		24
25.3	odd	20		7500.2.d.g.1249.6		24
25.4	even	10		7500.2.a.n.1.6		12
25.9	even	10		1500.2.m.c.1201.3		24
25.12	odd	20		300.2.o.a.109.1	✓	24
25.13	odd	20		1500.2.o.c.49.5		24
25.16	even	5	inner	1500.2.m.d.1201.4		24
25.21	even	5		7500.2.a.m.1.7		12
25.22	odd	20		7500.2.d.g.1249.19		24
75.62	even	20		900.2.w.c.109.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.1	✓	24	25.12	odd	20
300.2.o.a.289.1	yes	24	5.3	odd	4
900.2.w.c.109.6		24	75.62	even	20
900.2.w.c.289.6		24	15.8	even	4
1500.2.m.c.301.3		24	5.4	even	2
1500.2.m.c.1201.3		24	25.9	even	10
1500.2.m.d.301.4		24	1.1	even	1	trivial
1500.2.m.d.1201.4		24	25.16	even	5	inner
1500.2.o.c.49.5		24	25.13	odd	20
1500.2.o.c.949.5		24	5.2	odd	4
7500.2.a.m.1.7		12	25.21	even	5
7500.2.a.n.1.6		12	25.4	even	10
7500.2.d.g.1249.6		24	25.3	odd	20
7500.2.d.g.1249.19		24	25.22	odd	20

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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.m (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{3} +0.595901 q^{7} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{3} +0.595901 q^{7} +(-0.809017 - 0.587785i) q^{9} +(-2.71474 + 1.97238i) q^{11} +(3.85825 + 2.80319i) q^{13} +(-2.31143 - 7.11384i) q^{17} +(1.91242 + 5.88583i) q^{19} +(-0.184143 + 0.566735i) q^{21} +(-3.56694 + 2.59154i) q^{23} +(0.809017 - 0.587785i) q^{27} +(-0.853035 + 2.62537i) q^{29} +(1.38708 + 4.26899i) q^{31} +(-1.03694 - 3.19137i) q^{33} +(-1.05226 - 0.764512i) q^{37} +(-3.85825 + 2.80319i) q^{39} +(7.61184 + 5.53032i) q^{41} -7.59854 q^{43} +(1.36026 - 4.18645i) q^{47} -6.64490 q^{49} +7.47993 q^{51} +(-2.53620 + 7.80561i) q^{53} -6.18873 q^{57} +(1.80309 + 1.31002i) q^{59} +(-10.2014 + 7.41175i) q^{61} +(-0.482094 - 0.350262i) q^{63} +(2.58288 + 7.94930i) q^{67} +(-1.36245 - 4.19319i) q^{69} +(2.09986 - 6.46271i) q^{71} +(5.91570 - 4.29801i) q^{73} +(-1.61772 + 1.17534i) q^{77} +(-3.26546 + 10.0500i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.29219 + 3.97694i) q^{83} +(-2.23328 - 1.62257i) q^{87} +(-3.43862 + 2.49830i) q^{89} +(2.29914 + 1.67042i) q^{91} -4.48868 q^{93} +(3.79326 - 11.6744i) q^{97} +3.35561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Introduction

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