LMFDB - Embedded newform 1500.2.o.a.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1500,2,Mod(49,1500)]

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, 7]))

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

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.4
Root			$0.994522 + 0.104528i$ of defining polynomial
Character	$\chi$	$=$	1500.349
Dual form			1500.2.o.a.649.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{3} +0.747238i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{3} +0.747238i q^{7} +(-0.309017 + 0.951057i) q^{9} +(0.0646021 + 0.198825i) q^{11} +(2.38108 + 0.773659i) q^{13} +(-4.00842 + 5.51712i) q^{17} +(1.00739 + 0.731913i) q^{19} +(-0.604528 + 0.439216i) q^{21} +(3.09174 - 1.00457i) q^{23} +(-0.951057 + 0.309017i) q^{27} +(-4.19332 + 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(-0.122881 + 0.169131i) q^{33} +(1.86924 + 0.607352i) q^{37} +(0.773659 + 2.38108i) q^{39} +(0.993096 - 3.05644i) q^{41} +12.7127i q^{43} +(3.81017 + 5.24425i) q^{47} +6.44163 q^{49} -6.81953 q^{51} +(2.43520 + 3.35177i) q^{53} +1.24520i q^{57} +(-3.61882 + 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(-0.710666 - 0.230909i) q^{63} +(1.71460 - 2.35995i) q^{67} +(2.62999 + 1.91080i) q^{69} +(-5.29912 + 3.85004i) q^{71} +(-2.39603 + 0.778516i) q^{73} +(-0.148570 + 0.0482732i) q^{77} +(-8.28621 + 6.02028i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(3.33658 - 4.59240i) q^{83} +(-4.92954 - 1.60171i) q^{87} +(0.284829 + 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} -3.73968i q^{93} +(9.13679 + 12.5757i) q^{97} -0.209057 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^9	$ 16 q + 4 q^{9} - 4 q^{11} - 10 q^{19} - 6 q^{21} - 54 q^{29} - 6 q^{31} + 40 q^{41} + 16 q^{49} - 16 q^{51} - 4 q^{59} - 28 q^{61} - 4 q^{69} - 30 q^{71} - 48 q^{79} - 4 q^{81} + 10 q^{91} + 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^9 - 4 * q^11 - 10 * q^19 - 6 * q^21 - 54 * q^29 - 6 * q^31 + 40 * q^41 + 16 * q^49 - 16 * q^51 - 4 * q^59 - 28 * q^61 - 4 * q^69 - 30 * q^71 - 48 * q^79 - 4 * q^81 + 10 * q^91 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$1$

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
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$3$	0.587785	+	0.809017i	0.339358	+	0.467086i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			0.747238i			0.282430i	0.989979	+	0.141215i	$0.0451008\pi$
$7$			0.747238i			0.282430i	−0.989979	+	0.141215i	$0.954899\pi$
$8$		0			0
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$		0			0
$11$	0.0646021	+	0.198825i	0.0194783	+	0.0599480i	0.960323	−	0.278889i	$-0.0899663\pi$
$11$	0.0646021	+	0.198825i	0.0194783	+	0.0599480i	−0.940845	+	0.338837i	$0.889966\pi$
$12$		0			0
$13$	2.38108	+	0.773659i	0.660392	+	0.214574i	0.619991	−	0.784609i	$-0.287136\pi$
$13$	2.38108	+	0.773659i	0.660392	+	0.214574i	0.0404014	+	0.999184i	$0.487136\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.00842	+	5.51712i	−0.972185	+	1.33810i	−0.0312497	+	0.999512i	$0.509949\pi$
$17$	−4.00842	+	5.51712i	−0.972185	+	1.33810i	−0.940935	+	0.338586i	$0.890051\pi$
$18$		0			0
$19$	1.00739	+	0.731913i	0.231112	+	0.167912i	0.697314	−	0.716766i	$-0.254378\pi$
$19$	1.00739	+	0.731913i	0.231112	+	0.167912i	−0.466203	+	0.884678i	$0.654378\pi$
$20$		0			0
$21$	−0.604528	+	0.439216i	−0.131919	+	0.0958447i
$22$		0			0
$23$	3.09174	−	1.00457i	0.644673	−	0.209467i	0.0316092	−	0.999500i	$-0.489937\pi$
$23$	3.09174	−	1.00457i	0.644673	−	0.209467i	0.613064	+	0.790033i	$0.289937\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$		0			0
$29$	−4.19332	+	3.04662i	−0.778680	+	0.565744i	−0.904582	−	0.426299i	$-0.859817\pi$
$29$	−4.19332	+	3.04662i	−0.778680	+	0.565744i	0.125903	+	0.992043i	$0.459817\pi$
$30$		0			0
$31$	−3.02547	−	2.19813i	−0.543390	−	0.394796i	0.281953	−	0.959428i	$-0.409018\pi$
$31$	−3.02547	−	2.19813i	−0.543390	−	0.394796i	−0.825342	+	0.564633i	$0.809018\pi$
$32$		0			0
$33$	−0.122881	+	0.169131i	−0.0213908	+	0.0294419i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.86924	+	0.607352i	0.307301	+	0.0998480i	0.458608	−	0.888639i	$-0.348348\pi$
$37$	1.86924	+	0.607352i	0.307301	+	0.0998480i	−0.151307	+	0.988487i	$0.548348\pi$
$38$		0			0
$39$	0.773659	+	2.38108i	0.123885	+	0.381278i
$40$		0			0
$41$	0.993096	−	3.05644i	0.155096	−	0.477335i	−0.843075	−	0.537796i	$-0.819257\pi$
$41$	0.993096	−	3.05644i	0.155096	−	0.477335i	0.998171	+	0.0604609i	$0.0192570\pi$
$42$		0			0
$43$			12.7127i			1.93866i	0.245755	+	0.969332i	$0.420964\pi$
$43$			12.7127i			1.93866i	−0.245755	+	0.969332i	$0.579036\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.81017	+	5.24425i	0.555770	+	0.764952i	0.990781	−	0.135473i	$-0.0432554\pi$
$47$	3.81017	+	5.24425i	0.555770	+	0.764952i	−0.435011	+	0.900425i	$0.643255\pi$
$48$		0			0
$49$	6.44163			0.920234
$50$		0			0
$51$	−6.81953			−0.954926
$52$		0			0
$53$	2.43520	+	3.35177i	0.334501	+	0.460401i	0.942825	−	0.333288i	$-0.108158\pi$
$53$	2.43520	+	3.35177i	0.334501	+	0.460401i	−0.608325	+	0.793688i	$0.708158\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			1.24520i			0.164931i
$58$		0			0
$59$	−3.61882	+	11.1376i	−0.471131	+	1.44999i	0.379975	+	0.924997i	$0.375933\pi$
$59$	−3.61882	+	11.1376i	−0.471131	+	1.44999i	−0.851106	+	0.524995i	$0.824067\pi$
$60$		0			0
$61$	−3.85634	−	11.8686i	−0.493753	−	1.51962i	−0.818891	−	0.573949i	$-0.805411\pi$
$61$	−3.85634	−	11.8686i	−0.493753	−	1.51962i	0.325138	−	0.945667i	$-0.394589\pi$
$62$		0			0
$63$	−0.710666	−	0.230909i	−0.0895355	−	0.0290918i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.71460	−	2.35995i	0.209472	−	0.288314i	−0.691334	−	0.722535i	$-0.742977\pi$
$67$	1.71460	−	2.35995i	0.209472	−	0.288314i	0.900806	+	0.434222i	$0.142977\pi$
$68$		0			0
$69$	2.62999	+	1.91080i	0.316614	+	0.230034i
$70$		0			0
$71$	−5.29912	+	3.85004i	−0.628890	+	0.456916i	−0.856016	−	0.516950i	$-0.827067\pi$
$71$	−5.29912	+	3.85004i	−0.628890	+	0.456916i	0.227125	+	0.973866i	$0.427067\pi$
$72$		0			0
$73$	−2.39603	+	0.778516i	−0.280434	+	0.0911184i	−0.445857	−	0.895104i	$-0.647101\pi$
$73$	−2.39603	+	0.778516i	−0.280434	+	0.0911184i	0.165423	+	0.986223i	$0.447101\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.148570	+	0.0482732i	−0.0169311	+	0.00550124i
$78$		0			0
$79$	−8.28621	+	6.02028i	−0.932271	+	0.677335i	−0.946548	−	0.322563i	$-0.895455\pi$
$79$	−8.28621	+	6.02028i	−0.932271	+	0.677335i	0.0142765	+	0.999898i	$0.495455\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	3.33658	−	4.59240i	0.366237	−	0.504082i	−0.585636	−	0.810574i	$-0.699155\pi$
$83$	3.33658	−	4.59240i	0.366237	−	0.504082i	0.951873	+	0.306492i	$0.0991553\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.92954	−	1.60171i	−0.528502	−	0.171721i
$88$		0			0
$89$	0.284829	+	0.876615i	0.0301919	+	0.0929210i	0.965017	−	0.262188i	$-0.0844439\pi$
$89$	0.284829	+	0.876615i	0.0301919	+	0.0929210i	−0.934825	+	0.355109i	$0.884444\pi$
$90$		0			0
$91$	−0.578108	+	1.77923i	−0.0606022	+	0.186514i
$92$		0			0
$93$		−	3.73968i		−	0.387787i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.13679	+	12.5757i	0.927700	+	1.27687i	0.960750	+	0.277416i	$0.0894781\pi$
$97$	9.13679	+	12.5757i	0.927700	+	1.27687i	−0.0330496	+	0.999454i	$0.510522\pi$
$98$		0			0
$99$	−0.209057			−0.0210110
$100$		0			0
$101$	−11.0405			−1.09857			−0.549285	−	0.835635i	$-0.685100\pi$
$101$	−11.0405			−1.09857			−0.549285	+	0.835635i	$0.685100\pi$
$102$		0			0
$103$	8.16097	+	11.2326i	0.804124	+	1.10678i	0.992203	+	0.124628i	$0.0397738\pi$
$103$	8.16097	+	11.2326i	0.804124	+	1.10678i	−0.188079	+	0.982154i	$0.560226\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			1.02510i			0.0991002i	0.998772	+	0.0495501i	$0.0157788\pi$
$107$			1.02510i			0.0991002i	−0.998772	+	0.0495501i	$0.984221\pi$
$108$		0			0
$109$	2.07199	−	6.37694i	0.198461	−	0.610800i	−0.801458	−	0.598051i	$-0.795942\pi$
$109$	2.07199	−	6.37694i	0.198461	−	0.610800i	0.999919	−	0.0127488i	$-0.00405817\pi$
$110$		0			0
$111$	0.607352	+	1.86924i	0.0576473	+	0.177420i
$112$		0			0
$113$	−7.91428	−	2.57151i	−0.744513	−	0.241907i	−0.0878944	−	0.996130i	$-0.528014\pi$
$113$	−7.91428	−	2.57151i	−0.744513	−	0.241907i	−0.656618	+	0.754223i	$0.728014\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.47159	+	2.02547i	−0.136048	+	0.187254i
$118$		0			0
$119$	−4.12260	−	2.99525i	−0.377918	−	0.274574i
$120$		0			0
$121$	8.86383	−	6.43995i	0.805803	−	0.585450i
$122$		0			0
$123$	3.05644	−	0.993096i	0.275590	−	0.0895445i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	13.8248	−	4.49195i	1.22675	−	0.398597i	0.377217	−	0.926125i	$-0.376881\pi$
$127$	13.8248	−	4.49195i	1.22675	−	0.398597i	0.849537	+	0.527529i	$0.176881\pi$
$128$		0			0
$129$	−10.2848	+	7.47232i	−0.905523	+	0.657901i
$130$		0			0
$131$	−6.00611	−	4.36370i	−0.524757	−	0.381258i	0.293636	−	0.955917i	$-0.405135\pi$
$131$	−6.00611	−	4.36370i	−0.524757	−	0.381258i	−0.818393	+	0.574659i	$0.805135\pi$
$132$		0			0
$133$	−0.546913	+	0.752762i	−0.0474234	+	0.0652727i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.97636	−	2.26676i	−0.596030	−	0.193662i	−0.00456114	−	0.999990i	$-0.501452\pi$
$137$	−6.97636	−	2.26676i	−0.596030	−	0.193662i	−0.591469	+	0.806328i	$0.701452\pi$
$138$		0			0
$139$	−6.10219	−	18.7806i	−0.517581	−	1.59295i	−0.778536	−	0.627600i	$-0.784037\pi$
$139$	−6.10219	−	18.7806i	−0.517581	−	1.59295i	0.260954	−	0.965351i	$-0.415963\pi$
$140$		0			0
$141$	−2.00313	+	6.16499i	−0.168694	+	0.519185i
$142$		0			0
$143$			0.523398i			0.0437687i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.78630	+	5.21139i	0.312289	+	0.429828i
$148$		0			0
$149$	21.7551			1.78224			0.891122	−	0.453763i	$-0.149919\pi$
$149$	21.7551			1.78224			0.891122	+	0.453763i	$0.149919\pi$
$150$		0			0
$151$	10.1308			0.824432			0.412216	−	0.911086i	$-0.364755\pi$
$151$	10.1308			0.824432			0.412216	+	0.911086i	$0.364755\pi$
$152$		0			0
$153$	−4.00842	−	5.51712i	−0.324062	−	0.446033i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	9.99520i		−	0.797704i	−0.917015	−	0.398852i	$-0.869409\pi$
$157$		−	9.99520i		−	0.797704i	0.917015	−	0.398852i	$-0.130591\pi$
$158$		0			0
$159$	−1.28026	+	3.94024i	−0.101531	+	0.312481i
$160$		0			0
$161$	0.750652	+	2.31027i	0.0591597	+	0.182075i
$162$		0			0
$163$	2.43763	+	0.792035i	0.190930	+	0.0620369i	0.402921	−	0.915235i	$-0.367995\pi$
$163$	2.43763	+	0.792035i	0.190930	+	0.0620369i	−0.211991	+	0.977272i	$0.567995\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.2560	+	16.8690i	−0.948401	+	1.30536i	0.00383355	+	0.999993i	$0.498780\pi$
$167$	−12.2560	+	16.8690i	−0.948401	+	1.30536i	−0.952234	+	0.305369i	$0.901220\pi$
$168$		0			0
$169$	−5.44624	−	3.95692i	−0.418941	−	0.304379i
$170$		0			0
$171$	−1.00739	+	0.731913i	−0.0770372	+	0.0559708i
$172$		0			0
$173$	1.95438	−	0.635016i	0.148589	−	0.0482794i	−0.233778	−	0.972290i	$-0.575109\pi$
$173$	1.95438	−	0.635016i	0.148589	−	0.0482794i	0.382367	+	0.924011i	$0.375109\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−11.1376	+	3.61882i	−0.837153	+	0.272007i
$178$		0			0
$179$	−15.8247	+	11.4973i	−1.18279	+	0.859349i	−0.992484	−	0.122375i	$-0.960949\pi$
$179$	−15.8247	+	11.4973i	−1.18279	+	0.859349i	−0.190309	+	0.981724i	$0.560949\pi$
$180$		0			0
$181$	5.96251	+	4.33202i	0.443190	+	0.321996i	0.786901	−	0.617079i	$-0.211684\pi$
$181$	5.96251	+	4.33202i	0.443190	+	0.321996i	−0.343711	+	0.939075i	$0.611684\pi$
$182$		0			0
$183$	7.33519	−	10.0960i	0.542233	−	0.746319i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.35589	−	0.440557i	−0.0991528	−	0.0322167i
$188$		0			0
$189$	−0.230909	−	0.710666i	−0.0167962	−	0.0516933i
$190$		0			0
$191$	−0.693806	+	2.13532i	−0.0502021	+	0.154506i	−0.973015	−	0.230743i	$-0.925884\pi$
$191$	−0.693806	+	2.13532i	−0.0502021	+	0.154506i	0.922813	+	0.385249i	$0.125884\pi$
$192$		0			0
$193$		−	1.10589i		−	0.0796035i	−0.999208	−	0.0398018i	$-0.987327\pi$
$193$		−	1.10589i		−	0.0796035i	0.999208	−	0.0398018i	$-0.0126726\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.1299	−	16.6953i	−0.864217	−	1.18949i	−0.980547	−	0.196282i	$-0.937113\pi$
$197$	−12.1299	−	16.6953i	−0.864217	−	1.18949i	0.116331	−	0.993211i	$-0.462887\pi$
$198$		0			0
$199$	12.3822			0.877749			0.438874	−	0.898548i	$-0.355377\pi$
$199$	12.3822			0.877749			0.438874	+	0.898548i	$0.355377\pi$
$200$		0			0
$201$	2.91706			0.205753
$202$		0			0
$203$	−2.27655	−	3.13341i	−0.159783	−	0.219922i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			3.25085i			0.225950i
$208$		0			0
$209$	−0.0804429	+	0.247578i	−0.00556435	+	0.0171253i
$210$		0			0
$211$	6.37422	+	19.6178i	0.438820	+	1.35055i	0.889121	+	0.457671i	$0.151316\pi$
$211$	6.37422	+	19.6178i	0.438820	+	1.35055i	−0.450302	+	0.892876i	$0.648684\pi$
$212$		0			0
$213$	−6.22949	−	2.02409i	−0.426838	−	0.138688i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.64253	−	2.26074i	0.111502	−	0.153469i
$218$		0			0
$219$	−2.03818	−	1.48083i	−0.137728	−	0.100065i
$220$		0			0
$221$	−13.8127	+	10.0355i	−0.929145	+	0.675063i
$222$		0			0
$223$	−3.95129	+	1.28385i	−0.264598	+	0.0859732i	−0.438312	−	0.898823i	$-0.644423\pi$
$223$	−3.95129	+	1.28385i	−0.264598	+	0.0859732i	0.173713	+	0.984796i	$0.444423\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	22.4725	−	7.30175i	1.49155	−	0.484634i	0.554010	−	0.832510i	$-0.313097\pi$
$227$	22.4725	−	7.30175i	1.49155	−	0.484634i	0.937541	+	0.347876i	$0.113097\pi$
$228$		0			0
$229$	14.7565	−	10.7212i	0.975139	−	0.708480i	0.0185221	−	0.999828i	$-0.494104\pi$
$229$	14.7565	−	10.7212i	0.975139	−	0.708480i	0.956617	+	0.291348i	$0.0941039\pi$
$230$		0			0
$231$	−0.126381	−	0.0918211i	−0.00831525	−	0.00604138i
$232$		0			0
$233$	−1.33276	+	1.83438i	−0.0873117	+	0.120174i	−0.850438	−	0.526075i	$-0.823663\pi$
$233$	−1.33276	+	1.83438i	−0.0873117	+	0.120174i	0.763127	+	0.646249i	$0.223663\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.74102	−	3.16505i	−0.632747	−	0.205592i
$238$		0			0
$239$	−5.28631	−	16.2696i	−0.341943	−	1.05239i	−0.963200	−	0.268786i	$-0.913378\pi$
$239$	−5.28631	−	16.2696i	−0.341943	−	1.05239i	0.621257	−	0.783607i	$-0.286622\pi$
$240$		0			0
$241$	8.71435	−	26.8200i	0.561341	−	1.72763i	−0.117240	−	0.993104i	$-0.537405\pi$
$241$	8.71435	−	26.8200i	0.561341	−	1.72763i	0.678581	−	0.734526i	$-0.262595\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.83243	+	2.52212i	0.116595	+	0.160479i
$248$		0			0
$249$	5.67652			0.359735
$250$		0			0
$251$	23.9575			1.51219			0.756093	−	0.654464i	$-0.227106\pi$
$251$	23.9575			1.51219			0.756093	+	0.654464i	$0.227106\pi$
$252$		0			0
$253$	0.399467	+	0.549819i	0.0251142	+	0.0345668i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	28.5421i		−	1.78041i	−0.455561	−	0.890204i	$-0.650561\pi$
$257$		−	28.5421i		−	1.78041i	0.455561	−	0.890204i	$-0.349439\pi$
$258$		0			0
$259$	−0.453837	+	1.39677i	−0.0282000	+	0.0867908i
$260$		0			0
$261$	−1.60171	−	4.92954i	−0.0991431	−	0.305131i
$262$		0			0
$263$	3.38270	+	1.09911i	0.208586	+	0.0677738i	0.411447	−	0.911434i	$-0.365024\pi$
$263$	3.38270	+	1.09911i	0.208586	+	0.0677738i	−0.202860	+	0.979208i	$0.565024\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.541778	+	0.745693i	−0.0331563	+	0.0456357i
$268$		0			0
$269$	23.6733	+	17.1997i	1.44339	+	1.04868i	0.987321	+	0.158736i	$0.0507419\pi$
$269$	23.6733	+	17.1997i	1.44339	+	1.04868i	0.456066	+	0.889946i	$0.349258\pi$
$270$		0			0
$271$	20.0784	−	14.5878i	1.21968	−	0.886147i	0.223603	−	0.974680i	$-0.428218\pi$
$271$	20.0784	−	14.5878i	1.21968	−	0.886147i	0.996073	+	0.0885338i	$0.0282181\pi$
$272$		0			0
$273$	−1.77923	+	0.578108i	−0.107684	+	0.0349887i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	16.5745	−	5.38539i	0.995867	−	0.323577i	0.234654	−	0.972079i	$-0.424604\pi$
$277$	16.5745	−	5.38539i	0.995867	−	0.323577i	0.761213	+	0.648502i	$0.224604\pi$
$278$		0			0
$279$	3.02547	−	2.19813i	0.181130	−	0.131599i
$280$		0			0
$281$	−3.03664	−	2.20625i	−0.181151	−	0.131614i	0.493515	−	0.869738i	$-0.335712\pi$
$281$	−3.03664	−	2.20625i	−0.181151	−	0.131614i	−0.674665	+	0.738124i	$0.735712\pi$
$282$		0			0
$283$	−9.62409	+	13.2464i	−0.572093	+	0.787418i	−0.992801	−	0.119778i	$-0.961782\pi$
$283$	−9.62409	+	13.2464i	−0.572093	+	0.787418i	0.420708	+	0.907196i	$0.361782\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.28389	+	0.742080i	0.134814	+	0.0438036i
$288$		0			0
$289$	−9.11787	−	28.0619i	−0.536345	−	1.65070i
$290$		0			0
$291$	−4.80349	+	14.7836i	−0.281586	+	0.866632i
$292$		0			0
$293$		−	8.70991i		−	0.508838i	−0.967094	−	0.254419i	$-0.918116\pi$
$293$		−	8.70991i		−	0.508838i	0.967094	−	0.254419i	$-0.0818843\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.122881	−	0.169131i	−0.00713025	−	0.00981395i
$298$		0			0
$299$	8.13888			0.470683
$300$		0			0
$301$	−9.49939			−0.547536
$302$		0			0
$303$	−6.48944	−	8.93194i	−0.372808	−	0.513127i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	17.7123i		−	1.01090i	−0.862857	−	0.505448i	$-0.831327\pi$
$307$		−	17.7123i		−	1.01090i	0.862857	−	0.505448i	$-0.168673\pi$
$308$		0			0
$309$	−4.29048	+	13.2047i	−0.244077	+	0.751191i
$310$		0			0
$311$	6.26921	+	19.2946i	0.355494	+	1.09410i	0.955722	+	0.294270i	$0.0950763\pi$
$311$	6.26921	+	19.2946i	0.355494	+	1.09410i	−0.600228	+	0.799829i	$0.704924\pi$
$312$		0			0
$313$	−19.7535	−	6.41831i	−1.11654	−	0.362785i	−0.308091	−	0.951357i	$-0.599690\pi$
$313$	−19.7535	−	6.41831i	−1.11654	−	0.362785i	−0.808445	+	0.588572i	$0.799690\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.85429	+	13.5633i	−0.553472	+	0.761789i	−0.990478	−	0.137670i	$-0.956039\pi$
$317$	−9.85429	+	13.5633i	−0.553472	+	0.761789i	0.437006	+	0.899458i	$0.356039\pi$
$318$		0			0
$319$	−0.876642	−	0.636918i	−0.0490825	−	0.0356606i
$320$		0			0
$321$	−0.829324	+	0.602539i	−0.0462884	+	0.0336305i
$322$		0			0
$323$	−8.07610	+	2.62408i	−0.449366	+	0.146008i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.37694	−	2.07199i	0.352646	−	0.114582i
$328$		0			0
$329$	−3.91870	+	2.84711i	−0.216045	+	0.156966i
$330$		0			0
$331$	21.2090	+	15.4092i	1.16575	+	0.846968i	0.990494	−	0.137555i	$-0.0439243\pi$
$331$	21.2090	+	15.4092i	1.16575	+	0.846968i	0.175257	+	0.984523i	$0.443924\pi$
$332$		0			0
$333$	−1.15525	+	1.59007i	−0.0633074	+	0.0871352i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−24.7298	−	8.03519i	−1.34712	−	0.437705i	−0.455395	−	0.890289i	$-0.650502\pi$
$337$	−24.7298	−	8.03519i	−1.34712	−	0.437705i	−0.891722	+	0.452584i	$0.850502\pi$
$338$		0			0
$339$	−2.57151	−	7.91428i	−0.139665	−	0.429845i
$340$		0			0
$341$	0.241591	−	0.743542i	0.0130829	−	0.0402651i
$342$		0			0
$343$			10.0441i			0.542331i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.70460	−	3.72256i	−0.145191	−	0.199838i	0.730228	−	0.683204i	$-0.239414\pi$
$347$	−2.70460	−	3.72256i	−0.145191	−	0.199838i	−0.875418	+	0.483366i	$0.839414\pi$
$348$		0			0
$349$	29.2108			1.56362			0.781810	−	0.623516i	$-0.214297\pi$
$349$	29.2108			1.56362			0.781810	+	0.623516i	$0.214297\pi$
$350$		0			0
$351$	−2.50361			−0.133633
$352$		0			0
$353$	−16.5292	−	22.7505i	−0.879759	−	1.21088i	−0.976488	−	0.215574i	$-0.930838\pi$
$353$	−16.5292	−	22.7505i	−0.879759	−	1.21088i	0.0967283	−	0.995311i	$-0.469162\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	5.09582i		−	0.269699i
$358$		0			0
$359$	2.90570	−	8.94282i	0.153357	−	0.471984i	−0.844634	−	0.535345i	$-0.820182\pi$
$359$	2.90570	−	8.94282i	0.153357	−	0.471984i	0.997991	+	0.0633604i	$0.0201817\pi$
$360$		0			0
$361$	−5.39218	−	16.5954i	−0.283799	−	0.873444i
$362$		0			0
$363$	10.4201	+	3.38568i	0.546911	+	0.177702i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.9349	−	17.8033i	0.675195	−	0.929326i	−0.324669	−	0.945828i	$-0.605253\pi$
$367$	12.9349	−	17.8033i	0.675195	−	0.929326i	0.999864	+	0.0165016i	$0.00525285\pi$
$368$		0			0
$369$	2.59996	+	1.88898i	0.135349	+	0.0983365i
$370$		0			0
$371$	−2.50457	+	1.81968i	−0.130031	+	0.0944728i
$372$		0			0
$373$	17.7085	−	5.75384i	0.916911	−	0.297923i	0.187712	−	0.982224i	$-0.439893\pi$
$373$	17.7085	−	5.75384i	0.916911	−	0.297923i	0.729199	+	0.684302i	$0.239893\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.3417	+	4.01005i	−0.635628	+	0.206528i
$378$		0			0
$379$	−13.6515	+	9.91838i	−0.701230	+	0.509473i	−0.880332	−	0.474357i	$-0.842680\pi$
$379$	−13.6515	+	9.91838i	−0.701230	+	0.509473i	0.179103	+	0.983830i	$0.442680\pi$
$380$		0			0
$381$	11.7601	+	8.54421i	0.602488	+	0.437733i
$382$		0			0
$383$	5.32445	−	7.32847i	0.272066	−	0.374467i	−0.651020	−	0.759061i	$-0.725658\pi$
$383$	5.32445	−	7.32847i	0.272066	−	0.374467i	0.923086	+	0.384594i	$0.125658\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.0905	−	3.92843i	−0.614593	−	0.199693i
$388$		0			0
$389$	−10.2225	−	31.4616i	−0.518301	−	1.59517i	−0.777194	−	0.629261i	$-0.783358\pi$
$389$	−10.2225	−	31.4616i	−0.518301	−	1.59517i	0.258893	−	0.965906i	$-0.416642\pi$
$390$		0			0
$391$	−6.85069	+	21.0843i	−0.346454	+	1.06628i
$392$		0			0
$393$		−	7.42396i		−	0.374489i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	12.7706	+	17.5773i	0.640939	+	0.882177i	0.998665	−	0.0516494i	$-0.0164478\pi$
$397$	12.7706	+	17.5773i	0.640939	+	0.882177i	−0.357726	+	0.933827i	$0.616448\pi$
$398$		0			0
$399$	−0.930465			−0.0465815
$400$		0			0
$401$	20.1663			1.00706			0.503529	−	0.863978i	$-0.332035\pi$
$401$	20.1663			1.00706			0.503529	+	0.863978i	$0.332035\pi$
$402$		0			0
$403$	−5.50327	−	7.57460i	−0.274137	−	0.377318i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			0.410887i			0.0203669i
$408$		0			0
$409$	4.34139	−	13.3614i	0.214668	−	0.660679i	−0.784509	−	0.620117i	$-0.787085\pi$
$409$	4.34139	−	13.3614i	0.214668	−	0.660679i	0.999177	−	0.0405623i	$-0.0129149\pi$
$410$		0			0
$411$	−2.26676	−	6.97636i	−0.111811	−	0.344118i
$412$		0			0
$413$	−8.32244	−	2.70412i	−0.409520	−	0.133061i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	11.6071	−	15.9757i	0.568400	−	0.782336i
$418$		0			0
$419$	−16.3919	−	11.9094i	−0.800794	−	0.581811i	0.110353	−	0.993892i	$-0.464802\pi$
$419$	−16.3919	−	11.9094i	−0.800794	−	0.581811i	−0.911147	+	0.412081i	$0.864802\pi$
$420$		0			0
$421$	−3.54258	+	2.57384i	−0.172655	+	0.125441i	−0.670757	−	0.741677i	$-0.734031\pi$
$421$	−3.54258	+	2.57384i	−0.172655	+	0.125441i	0.498102	+	0.867119i	$0.334031\pi$
$422$		0			0
$423$	−6.16499	+	2.00313i	−0.299752	+	0.0973953i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	8.86866	−	2.88160i	0.429184	−	0.139450i
$428$		0			0
$429$	−0.423438	+	0.307645i	−0.0204438	+	0.0148533i
$430$		0			0
$431$	−0.944967	−	0.686559i	−0.0455175	−	0.0330704i	0.564794	−	0.825232i	$-0.308956\pi$
$431$	−0.944967	−	0.686559i	−0.0455175	−	0.0330704i	−0.610311	+	0.792162i	$0.708956\pi$
$432$		0			0
$433$	−1.32187	+	1.81940i	−0.0635250	+	0.0874347i	−0.839597	−	0.543209i	$-0.817209\pi$
$433$	−1.32187	+	1.81940i	−0.0635250	+	0.0874347i	0.776072	+	0.630644i	$0.217209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.84985	+	1.25089i	0.184163	+	0.0598383i
$438$		0			0
$439$	−6.83477	−	21.0353i	−0.326206	−	1.00396i	−0.970893	−	0.239512i	$-0.923013\pi$
$439$	−6.83477	−	21.0353i	−0.326206	−	1.00396i	0.644688	−	0.764446i	$-0.276987\pi$
$440$		0			0
$441$	−1.99057	+	6.12636i	−0.0947893	+	0.291731i
$442$		0			0
$443$		−	28.1534i		−	1.33761i	−0.743439	−	0.668804i	$-0.766807\pi$
$443$		−	28.1534i		−	1.33761i	0.743439	−	0.668804i	$-0.233193\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.7873	+	17.6002i	0.604819	+	0.832462i
$448$		0			0
$449$	−16.5924			−0.783044			−0.391522	−	0.920169i	$-0.628051\pi$
$449$	−16.5924			−0.783044			−0.391522	+	0.920169i	$0.628051\pi$
$450$		0			0
$451$	0.671852			0.0316363
$452$		0			0
$453$	5.95473	+	8.19598i	0.279777	+	0.385081i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	11.1599i		−	0.522039i	−0.965334	−	0.261019i	$-0.915941\pi$
$457$		−	11.1599i		−	0.522039i	0.965334	−	0.261019i	$-0.0840586\pi$
$458$		0			0
$459$	2.10735	−	6.48576i	0.0983628	−	0.302729i
$460$		0			0
$461$	1.93631	+	5.95935i	0.0901830	+	0.277555i	0.985968	−	0.166932i	$-0.0533861\pi$
$461$	1.93631	+	5.95935i	0.0901830	+	0.277555i	−0.895785	+	0.444487i	$0.853386\pi$
$462$		0			0
$463$	16.1961	+	5.26243i	0.752696	+	0.244566i	0.660141	−	0.751142i	$-0.270497\pi$
$463$	16.1961	+	5.26243i	0.752696	+	0.244566i	0.0925550	+	0.995708i	$0.470497\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.9823	+	15.1159i	−0.508202	+	0.699481i	−0.983615	−	0.180282i	$-0.942299\pi$
$467$	−10.9823	+	15.1159i	−0.508202	+	0.699481i	0.475413	+	0.879763i	$0.342299\pi$
$468$		0			0
$469$	1.76344	+	1.28122i	0.0814283	+	0.0591611i
$470$		0			0
$471$	8.08629	−	5.87503i	0.372597	−	0.270707i
$472$		0			0
$473$	−2.52760	+	0.821266i	−0.116219	+	0.0377618i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.94024	+	1.28026i	−0.180411	+	0.0586191i
$478$		0			0
$479$	2.38111	−	1.72998i	0.108796	−	0.0790448i	−0.532057	−	0.846708i	$-0.678581\pi$
$479$	2.38111	−	1.72998i	0.108796	−	0.0790448i	0.640853	+	0.767664i	$0.278581\pi$
$480$		0			0
$481$	3.98092	+	2.89230i	0.181514	+	0.131878i
$482$		0			0
$483$	−1.42782	+	1.96523i	−0.0649683	+	0.0894212i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−13.3297	−	4.33109i	−0.604028	−	0.196261i	−0.00899199	−	0.999960i	$-0.502862\pi$
$487$	−13.3297	−	4.33109i	−0.604028	−	0.196261i	−0.595036	+	0.803699i	$0.702862\pi$
$488$		0			0
$489$	0.792035	+	2.43763i	0.0358170	+	0.110234i
$490$		0			0
$491$	2.76416	−	8.50720i	0.124745	−	0.383925i	−0.869110	−	0.494619i	$-0.835308\pi$
$491$	2.76416	−	8.50720i	0.124745	−	0.383925i	0.993854	+	0.110695i	$0.0353075\pi$
$492$		0			0
$493$		−	35.3472i		−	1.59196i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.87690	−	3.95971i	−0.129046	−	0.177617i
$498$		0			0
$499$	2.39366			0.107155			0.0535774	−	0.998564i	$-0.482938\pi$
$499$	2.39366			0.107155			0.0535774	+	0.998564i	$0.482938\pi$
$500$		0			0
$501$	−20.8512			−0.931564
$502$		0			0
$503$	4.95152	+	6.81519i	0.220777	+	0.303874i	0.905010	−	0.425389i	$-0.139863\pi$
$503$	4.95152	+	6.81519i	0.220777	+	0.303874i	−0.684233	+	0.729264i	$0.739863\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	6.73192i		−	0.298975i
$508$		0			0
$509$	−9.98528	+	30.7315i	−0.442590	+	1.36215i	0.442516	+	0.896761i	$0.354086\pi$
$509$	−9.98528	+	30.7315i	−0.442590	+	1.36215i	−0.885106	+	0.465390i	$0.845914\pi$
$510$		0			0
$511$	−0.581737	−	1.79040i	−0.0257345	−	0.0792027i
$512$		0			0
$513$	−1.18426	−	0.384789i	−0.0522864	−	0.0169889i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.796543	+	1.09635i	−0.0350319	+	0.0482173i
$518$		0			0
$519$	1.66249	+	1.20787i	0.0729754	+	0.0530197i
$520$		0			0
$521$	−2.88427	+	2.09554i	−0.126362	+	0.0918074i	−0.649171	−	0.760642i	$-0.724884\pi$
$521$	−2.88427	+	2.09554i	−0.126362	+	0.0918074i	0.522809	+	0.852450i	$0.324884\pi$
$522$		0			0
$523$	−30.8511	+	10.0241i	−1.34903	+	0.438325i	−0.892365	−	0.451315i	$-0.850955\pi$
$523$	−30.8511	+	10.0241i	−1.34903	+	0.438325i	−0.456662	+	0.889640i	$0.650955\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	24.2547	−	7.88082i	1.05655	−	0.343294i
$528$		0			0
$529$	−10.0577	+	7.30732i	−0.437290	+	0.317710i
$530$		0			0
$531$	−9.47420	−	6.88341i	−0.411145	−	0.298715i
$532$		0			0
$533$	4.72928	−	6.50929i	0.204848	−	0.281949i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−18.6030	−	6.04449i	−0.802781	−	0.260839i
$538$		0			0
$539$	0.416143	+	1.28076i	0.0179246	+	0.0551661i
$540$		0			0
$541$	−3.40378	+	10.4757i	−0.146340	+	0.450388i	−0.997181	−	0.0750356i	$-0.976093\pi$
$541$	−3.40378	+	10.4757i	−0.146340	+	0.450388i	0.850841	+	0.525423i	$0.176093\pi$
$542$		0			0
$543$			7.37007i			0.316280i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.13718	+	4.31795i	0.134136	+	0.184622i	0.870801	−	0.491635i	$-0.163601\pi$
$547$	3.13718	+	4.31795i	0.134136	+	0.184622i	−0.736665	+	0.676258i	$0.763601\pi$
$548$		0			0
$549$	12.4794			0.532606
$550$		0			0
$551$	−6.45418			−0.274957
$552$		0			0
$553$	−4.49859	−	6.19177i	−0.191299	−	0.263301i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	0.0652731i		−	0.00276571i	−0.999999	−	0.00138286i	$-0.999560\pi$
$557$		−	0.0652731i		−	0.00276571i	0.999999	−	0.00138286i	$-0.000440177\pi$
$558$		0			0
$559$	−9.83527	+	30.2699i	−0.415988	+	1.28028i
$560$		0			0
$561$	−0.440557	−	1.35589i	−0.0186003	−	0.0572459i
$562$		0			0
$563$	27.3359	+	8.88197i	1.15207	+	0.374330i	0.821923	−	0.569599i	$-0.192902\pi$
$563$	27.3359	+	8.88197i	1.15207	+	0.374330i	0.330147	+	0.943929i	$0.392902\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.439216	−	0.604528i	0.0184453	−	0.0253878i
$568$		0			0
$569$	−6.68501	−	4.85694i	−0.280250	−	0.203614i	0.438776	−	0.898596i	$-0.355412\pi$
$569$	−6.68501	−	4.85694i	−0.280250	−	0.203614i	−0.719026	+	0.694983i	$0.755412\pi$
$570$		0			0
$571$	−9.49451	+	6.89817i	−0.397333	+	0.288679i	−0.768454	−	0.639905i	$-0.778974\pi$
$571$	−9.49451	+	6.89817i	−0.397333	+	0.288679i	0.371121	+	0.928585i	$0.378974\pi$
$572$		0			0
$573$	−2.13532	+	0.693806i	−0.0892041	+	0.0289842i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−20.3418	+	6.60944i	−0.846838	+	0.275154i	−0.700121	−	0.714024i	$-0.746871\pi$
$577$	−20.3418	+	6.60944i	−0.846838	+	0.275154i	−0.146717	+	0.989178i	$0.546871\pi$
$578$		0			0
$579$	0.894682	−	0.650024i	0.0371817	−	0.0270141i
$580$		0			0
$581$	3.43162	+	2.49322i	0.142368	+	0.103436i
$582$		0			0
$583$	−0.509096	+	0.700710i	−0.0210846	+	0.0290204i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	39.2133	+	12.7412i	1.61851	+	0.525885i	0.971589	−	0.236674i	$-0.0760574\pi$
$587$	39.2133	+	12.7412i	1.61851	+	0.525885i	0.646918	+	0.762559i	$0.276057\pi$
$588$		0			0
$589$	−1.43899	−	4.42876i	−0.0592925	−	0.182484i
$590$		0			0
$591$	6.37705	−	19.6265i	0.262317	−	0.807328i
$592$		0			0
$593$			23.2238i			0.953685i	0.878989	+	0.476843i	$0.158219\pi$
$593$			23.2238i			0.953685i	−0.878989	+	0.476843i	$0.841781\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.27806	+	10.0174i	0.297871	+	0.409984i
$598$		0			0
$599$	22.6226			0.924335			0.462168	−	0.886793i	$-0.347072\pi$
$599$	22.6226			0.924335			0.462168	+	0.886793i	$0.347072\pi$
$600$		0			0
$601$	−12.9540			−0.528405			−0.264203	−	0.964467i	$-0.585109\pi$
$601$	−12.9540			−0.528405			−0.264203	+	0.964467i	$0.585109\pi$
$602$		0			0
$603$	1.71460	+	2.35995i	0.0698240	+	0.0961045i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			4.54036i			0.184288i	0.995746	+	0.0921439i	$0.0293720\pi$
$607$			4.54036i			0.184288i	−0.995746	+	0.0921439i	$0.970628\pi$
$608$		0			0
$609$	1.19686	−	3.68354i	0.0484990	−	0.149265i
$610$		0			0
$611$	5.01505	+	15.4347i	0.202887	+	0.624423i
$612$		0			0
$613$	24.1128	+	7.83471i	0.973905	+	0.316441i	0.752391	−	0.658716i	$-0.228900\pi$
$613$	24.1128	+	7.83471i	0.973905	+	0.316441i	0.221514	+	0.975157i	$0.428900\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−26.5790	+	36.5829i	−1.07003	+	1.47277i	−0.199986	+	0.979799i	$0.564090\pi$
$617$	−26.5790	+	36.5829i	−1.07003	+	1.47277i	−0.870045	+	0.492972i	$0.835910\pi$
$618$		0			0
$619$	25.3666	+	18.4299i	1.01957	+	0.740762i	0.966195	−	0.257812i	$-0.0830016\pi$
$619$	25.3666	+	18.4299i	1.01957	+	0.740762i	0.0533766	+	0.998574i	$0.483002\pi$
$620$		0			0
$621$	−2.62999	+	1.91080i	−0.105538	+	0.0766779i
$622$		0			0
$623$	−0.655040	+	0.212835i	−0.0262436	+	0.00852707i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.247578	+	0.0804429i	−0.00988730	+	0.00321258i
$628$		0			0
$629$	−10.8435	+	7.87828i	−0.432360	+	0.314128i
$630$		0			0
$631$	−25.8455	−	18.7779i	−1.02889	−	0.747535i	−0.0608071	−	0.998150i	$-0.519367\pi$
$631$	−25.8455	−	18.7779i	−1.02889	−	0.747535i	−0.968087	+	0.250614i	$0.919367\pi$
$632$		0			0
$633$	−12.1245	+	16.6879i	−0.481905	+	0.663286i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	15.3380	+	4.98363i	0.607715	+	0.197459i
$638$		0			0
$639$	−2.02409	−	6.22949i	−0.0800716	−	0.246435i
$640$		0			0
$641$	12.7727	−	39.3103i	0.504491	−	1.55267i	−0.297132	−	0.954836i	$-0.596030\pi$
$641$	12.7727	−	39.3103i	0.504491	−	1.55267i	0.801624	−	0.597829i	$-0.203970\pi$
$642$		0			0
$643$			33.2313i			1.31052i	0.755406	+	0.655258i	$0.227440\pi$
$643$			33.2313i			1.31052i	−0.755406	+	0.655258i	$0.772560\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.8034	−	27.2571i	−0.778553	−	1.07159i	−0.995440	−	0.0953892i	$-0.969590\pi$
$647$	−19.8034	−	27.2571i	−0.778553	−	1.07159i	0.216887	−	0.976197i	$-0.430410\pi$
$648$		0			0
$649$	−2.44822			−0.0961009
$650$		0			0
$651$	2.79443			0.109522
$652$		0			0
$653$	12.8419	+	17.6754i	0.502544	+	0.691692i	0.982640	−	0.185524i	$-0.0593982\pi$
$653$	12.8419	+	17.6754i	0.502544	+	0.691692i	−0.480096	+	0.877216i	$0.659398\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	2.51933i		−	0.0982885i
$658$		0			0
$659$	3.48829	−	10.7359i	0.135884	−	0.418209i	−0.859842	−	0.510560i	$-0.829438\pi$
$659$	3.48829	−	10.7359i	0.135884	−	0.418209i	0.995727	+	0.0923507i	$0.0294381\pi$
$660$		0			0
$661$	−11.3014	−	34.7821i	−0.439573	−	1.35287i	−0.888327	−	0.459211i	$-0.848132\pi$
$661$	−11.3014	−	34.7821i	−0.439573	−	1.35287i	0.448754	−	0.893655i	$-0.351868\pi$
$662$		0			0
$663$	−16.2378	−	5.27599i	−0.630625	−	0.204903i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−9.90412	+	13.6319i	−0.383489	+	0.527828i
$668$		0			0
$669$	−3.36117	−	2.44203i	−0.129950	−	0.0944145i
$670$		0			0
$671$	2.11064	−	1.53347i	0.0814804	−	0.0591990i
$672$		0			0
$673$	7.31143	−	2.37563i	0.281835	−	0.0915737i	−0.164689	−	0.986346i	$-0.552662\pi$
$673$	7.31143	−	2.37563i	0.281835	−	0.0915737i	0.446523	+	0.894772i	$0.352662\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	35.4711	−	11.5253i	1.36327	−	0.442952i	0.466133	−	0.884714i	$-0.345647\pi$
$677$	35.4711	−	11.5253i	1.36327	−	0.442952i	0.897132	+	0.441763i	$0.145647\pi$
$678$		0			0
$679$	−9.39705	+	6.82736i	−0.360626	+	0.262010i
$680$		0			0
$681$	19.1162	+	13.8888i	0.732535	+	0.532218i
$682$		0			0
$683$	−21.4421	+	29.5125i	−0.820458	+	1.12926i	0.169166	+	0.985587i	$0.445892\pi$
$683$	−21.4421	+	29.5125i	−0.820458	+	1.12926i	−0.989625	+	0.143676i	$0.954108\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	17.3473	+	5.63649i	0.661842	+	0.215046i
$688$		0			0
$689$	3.20528	+	9.86483i	0.122111	+	0.375820i
$690$		0			0
$691$	−9.99734	+	30.7686i	−0.380317	+	1.17049i	0.559504	+	0.828827i	$0.310992\pi$
$691$	−9.99734	+	30.7686i	−0.380317	+	1.17049i	−0.939821	+	0.341667i	$0.889008\pi$
$692$		0			0
$693$		−	0.156215i		−	0.00593413i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	12.8820	+	17.7305i	0.487940	+	0.671591i
$698$		0			0
$699$	−2.26742			−0.0857617
$700$		0			0
$701$	5.27498			0.199233			0.0996166	−	0.995026i	$-0.468238\pi$
$701$	5.27498			0.199233			0.0996166	+	0.995026i	$0.468238\pi$
$702$		0			0
$703$	1.43853	+	1.97996i	0.0542550	+	0.0746756i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	8.24988i		−	0.310268i
$708$		0			0
$709$	−9.03055	+	27.7932i	−0.339149	+	1.04379i	0.625493	+	0.780230i	$0.284898\pi$
$709$	−9.03055	+	27.7932i	−0.339149	+	1.04379i	−0.964642	+	0.263564i	$0.915102\pi$
$710$		0			0
$711$	−3.16505	−	9.74102i	−0.118699	−	0.365317i
$712$		0			0
$713$	−11.5621	−	3.75677i	−0.433005	−	0.140692i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.0552	−	13.8397i	0.375517	−	0.516855i
$718$		0			0
$719$	35.5675	+	25.8413i	1.32644	+	0.963718i	0.999828	+	0.0185605i	$0.00590834\pi$
$719$	35.5675	+	25.8413i	1.32644	+	0.963718i	0.326616	+	0.945157i	$0.394092\pi$
$720$		0			0
$721$	−8.39344	+	6.09819i	−0.312588	+	0.227108i
$722$		0			0
$723$	26.8200	−	8.71435i	0.997447	−	0.324090i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−28.4614	+	9.24768i	−1.05558	+	0.342977i	−0.784854	−	0.619680i	$-0.787262\pi$
$727$	−28.4614	+	9.24768i	−1.05558	+	0.342977i	−0.270721	+	0.962658i	$0.587262\pi$
$728$		0			0
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$		0			0
$731$	−70.1373	−	50.9577i	−2.59412	−	1.88474i
$732$		0			0
$733$	9.71402	−	13.3702i	0.358795	−	0.493840i	−0.591017	−	0.806659i	$-0.701273\pi$
$733$	9.71402	−	13.3702i	0.358795	−	0.493840i	0.949813	+	0.312819i	$0.101273\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.579984	+	0.188448i	0.0213640	+	0.00694158i
$738$		0			0
$739$	15.7285	+	48.4073i	0.578581	+	1.78069i	0.623648	+	0.781706i	$0.285650\pi$
$739$	15.7285	+	48.4073i	0.578581	+	1.78069i	−0.0450666	+	0.998984i	$0.514350\pi$
$740$		0			0
$741$	−0.963364	+	2.96493i	−0.0353901	+	0.108919i
$742$		0			0
$743$			28.6937i			1.05267i	0.850277	+	0.526336i	$0.176434\pi$
$743$			28.6937i			1.05267i	−0.850277	+	0.526336i	$0.823566\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.33658	+	4.59240i	0.122079	+	0.168027i
$748$		0			0
$749$	−0.765995			−0.0279888
$750$		0			0
$751$	−0.927935			−0.0338608			−0.0169304	−	0.999857i	$-0.505389\pi$
$751$	−0.927935			−0.0338608			−0.0169304	+	0.999857i	$0.505389\pi$
$752$		0			0
$753$	14.0819	+	19.3821i	0.513173	+	0.706322i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			41.4243i			1.50559i	0.658254	+	0.752796i	$0.271295\pi$
$757$			41.4243i			1.50559i	−0.658254	+	0.752796i	$0.728705\pi$
$758$		0			0
$759$	−0.210012	+	0.646350i	−0.00762295	+	0.0234610i
$760$		0			0
$761$	1.17031	+	3.60185i	0.0424237	+	0.130567i	0.970025	−	0.243005i	$-0.0781330\pi$
$761$	1.17031	+	3.60185i	0.0424237	+	0.130567i	−0.927601	+	0.373572i	$0.878133\pi$
$762$		0			0
$763$	4.76509	+	1.54827i	0.172508	+	0.0560513i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−17.2334	+	23.7197i	−0.622262	+	0.856470i
$768$		0			0
$769$	−1.06014	−	0.770234i	−0.0382295	−	0.0277753i	0.568506	−	0.822679i	$-0.307521\pi$
$769$	−1.06014	−	0.770234i	−0.0382295	−	0.0277753i	−0.606736	+	0.794903i	$0.707521\pi$
$770$		0			0
$771$	23.0911	−	16.7766i	0.831604	−	0.604196i
$772$		0			0
$773$	27.7066	−	9.00241i	0.996536	−	0.323794i	0.235055	−	0.971982i	$-0.424473\pi$
$773$	27.7066	−	9.00241i	0.996536	−	0.323794i	0.761480	+	0.648188i	$0.224473\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.39677	+	0.453837i	−0.0501087	+	0.0162813i
$778$		0			0
$779$	3.23748	−	2.35217i	0.115995	−	0.0842752i
$780$		0			0
$781$	−1.10782	−	0.804877i	−0.0396409	−	0.0288008i
$782$		0			0
$783$	3.04662	−	4.19332i	0.108877	−	0.149857i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−44.3341	−	14.4050i	−1.58034	−	0.513484i	−0.618197	−	0.786023i	$-0.712136\pi$
$787$	−44.3341	−	14.4050i	−1.58034	−	0.513484i	−0.962145	+	0.272540i	$0.912136\pi$
$788$		0			0
$789$	1.09911	+	3.38270i	0.0391292	+	0.120427i
$790$		0			0
$791$	1.92153	−	5.91385i	0.0683217	−	0.210272i
$792$		0			0
$793$		−	31.2435i		−	1.10949i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	8.08703	+	11.1308i	0.286457	+	0.394275i	0.927859	−	0.372930i	$-0.121647\pi$
$797$	8.08703	+	11.1308i	0.286457	+	0.394275i	−0.641402	+	0.767205i	$0.721647\pi$
$798$		0			0
$799$	−44.2059			−1.56389
$800$		0			0
$801$	−0.921727			−0.0325676
$802$		0			0
$803$	−0.309577	−	0.426096i	−0.0109247	−	0.0150366i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			29.2618i			1.03006i
$808$		0			0
$809$	−3.08886	+	9.50654i	−0.108599	+	0.334232i	−0.990558	−	0.137093i	$-0.956224\pi$
$809$	−3.08886	+	9.50654i	−0.108599	+	0.334232i	0.881960	+	0.471325i	$0.156224\pi$
$810$		0			0
$811$	5.72277	+	17.6129i	0.200954	+	0.618472i	0.999855	+	0.0170101i	$0.00541474\pi$
$811$	5.72277	+	17.6129i	0.200954	+	0.618472i	−0.798902	+	0.601462i	$0.794585\pi$
$812$		0			0
$813$	23.6036	+	7.66927i	0.827814	+	0.268973i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−9.30457	+	12.8066i	−0.325526	+	0.448048i
$818$		0			0
$819$	−1.51351	−	1.09963i	−0.0528862	−	0.0384240i
$820$		0			0
$821$	−22.9081	+	16.6437i	−0.799498	+	0.580869i	−0.910767	−	0.412921i	$-0.864509\pi$
$821$	−22.9081	+	16.6437i	−0.799498	+	0.580869i	0.111269	+	0.993790i	$0.464509\pi$
$822$		0			0
$823$	11.3987	−	3.70366i	0.397333	−	0.129101i	−0.103533	−	0.994626i	$-0.533015\pi$
$823$	11.3987	−	3.70366i	0.397333	−	0.129101i	0.500866	+	0.865525i	$0.333015\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.7167	+	4.13191i	−0.442204	+	0.143681i	−0.521652	−	0.853158i	$-0.674684\pi$
$827$	−12.7167	+	4.13191i	−0.442204	+	0.143681i	0.0794485	+	0.996839i	$0.474684\pi$
$828$		0			0
$829$	−13.3909	+	9.72909i	−0.465087	+	0.337905i	−0.795523	−	0.605923i	$-0.792804\pi$
$829$	−13.3909	+	9.72909i	−0.465087	+	0.337905i	0.330437	+	0.943828i	$0.392804\pi$
$830$		0			0
$831$	14.0991	+	10.2436i	0.489094	+	0.355347i
$832$		0			0
$833$	−25.8208	+	35.5393i	−0.894637	+	1.23136i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	3.55665	+	1.15563i	0.122936	+	0.0399442i
$838$		0			0
$839$	−7.56589	−	23.2854i	−0.261204	−	0.803902i	−0.992544	−	0.121889i	$-0.961105\pi$
$839$	−7.56589	−	23.2854i	−0.261204	−	0.803902i	0.731340	−	0.682013i	$-0.238895\pi$
$840$		0			0
$841$	−0.659493	+	2.02971i	−0.0227411	+	0.0699900i
$842$		0			0
$843$		−	3.75349i		−	0.129277i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	4.81218	+	6.62339i	0.165348	+	0.227582i
$848$		0			0
$849$	−16.3735			−0.561936
$850$		0			0
$851$	6.38933			0.219023
$852$		0			0
$853$	11.2475	+	15.4809i	0.385108	+	0.530055i	0.956929	−	0.290323i	$-0.0937628\pi$
$853$	11.2475	+	15.4809i	0.385108	+	0.530055i	−0.571821	+	0.820379i	$0.693763\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	7.43367i		−	0.253929i	−0.991907	−	0.126965i	$-0.959477\pi$
$857$		−	7.43367i		−	0.253929i	0.991907	−	0.126965i	$-0.0405235\pi$
$858$		0			0
$859$	−12.7368	+	39.1999i	−0.434575	+	1.33748i	0.458947	+	0.888464i	$0.348227\pi$
$859$	−12.7368	+	39.1999i	−0.434575	+	1.33748i	−0.893522	+	0.449020i	$0.851773\pi$
$860$		0			0
$861$	0.742080	+	2.28389i	0.0252900	+	0.0778346i
$862$		0			0
$863$	36.2532	+	11.7794i	1.23407	+	0.400975i	0.852189	−	0.523234i	$-0.175275\pi$
$863$	36.2532	+	11.7794i	1.23407	+	0.400975i	0.381886	+	0.924210i	$0.375275\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	17.3432	−	23.8709i	0.589007	−	0.810698i
$868$		0			0
$869$	−1.73229	−	1.25858i	−0.0587639	−	0.0426945i
$870$		0			0
$871$	5.90840	−	4.29270i	0.200198	−	0.145453i
$872$		0			0
$873$	−14.7836	+	4.80349i	−0.500350	+	0.162574i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−27.6047	+	8.96931i	−0.932145	+	0.302872i	−0.735439	−	0.677591i	$-0.763024\pi$
$877$	−27.6047	+	8.96931i	−0.932145	+	0.302872i	−0.196705	+	0.980463i	$0.563024\pi$
$878$		0			0
$879$	7.04647	−	5.11956i	0.237671	−	0.172678i
$880$		0			0
$881$	27.8503	+	20.2344i	0.938300	+	0.681715i	0.948011	−	0.318238i	$-0.103091\pi$
$881$	27.8503	+	20.2344i	0.938300	+	0.681715i	−0.00971098	+	0.999953i	$0.503091\pi$
$882$		0			0
$883$	22.8077	−	31.3921i	0.767539	−	1.05643i	−0.229010	−	0.973424i	$-0.573549\pi$
$883$	22.8077	−	31.3921i	0.767539	−	1.05643i	0.996549	−	0.0830028i	$-0.0264510\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.48715	+	1.78288i	0.184241	+	0.0598634i	0.399684	−	0.916653i	$-0.369120\pi$
$887$	5.48715	+	1.78288i	0.184241	+	0.0598634i	−0.215444	+	0.976516i	$0.569120\pi$
$888$		0			0
$889$	3.35656	+	10.3304i	0.112575	+	0.346472i
$890$		0			0
$891$	0.0646021	−	0.198825i	0.00216425	−	0.00666089i
$892$		0			0
$893$			8.07173i			0.270110i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	4.78391	+	6.58449i	0.159730	+	0.219850i
$898$		0			0
$899$	19.3836			0.646480
$900$		0			0
$901$	−28.2534			−0.941257
$902$		0			0
$903$	−5.58360	−	7.68517i	−0.185811	−	0.255746i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			31.7260i			1.05345i	0.850037	+	0.526723i	$0.176579\pi$
$907$			31.7260i			1.05345i	−0.850037	+	0.526723i	$0.823421\pi$
$908$		0			0
$909$	3.41170	−	10.5001i	0.113159	−	0.348267i
$910$		0			0
$911$	−4.95450	−	15.2484i	−0.164150	−	0.505202i	0.834823	−	0.550519i	$-0.185570\pi$
$911$	−4.95450	−	15.2484i	−0.164150	−	0.505202i	−0.998973	+	0.0453174i	$0.985570\pi$
$912$		0			0
$913$	1.12863	+	0.366716i	0.0373523	+	0.0121365i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.26072	−	4.48800i	0.107679	−	0.148207i
$918$		0			0
$919$	−8.82328	−	6.41049i	−0.291053	−	0.211462i	0.432671	−	0.901552i	$-0.357571\pi$
$919$	−8.82328	−	6.41049i	−0.291053	−	0.211462i	−0.723724	+	0.690089i	$0.757571\pi$
$920$		0			0
$921$	14.3296	−	10.4111i	0.472176	−	0.343056i
$922$		0			0
$923$	−15.5962	+	5.06753i	−0.513357	+	0.166800i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−13.2047	+	4.29048i	−0.433700	+	0.140918i
$928$		0			0
$929$	18.3021	−	13.2973i	0.600473	−	0.436269i	−0.245573	−	0.969378i	$-0.578976\pi$
$929$	18.3021	−	13.2973i	0.600473	−	0.436269i	0.846047	+	0.533108i	$0.178976\pi$
$930$		0			0
$931$	6.48925	+	4.71472i	0.212677	+	0.154519i
$932$		0			0
$933$	−11.9247	+	16.4130i	−0.390398	+	0.537337i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−4.90347	−	1.59323i	−0.160189	−	0.0520487i	0.227824	−	0.973702i	$-0.426839\pi$
$937$	−4.90347	−	1.59323i	−0.160189	−	0.0520487i	−0.388014	+	0.921654i	$0.626839\pi$
$938$		0			0
$939$	−6.41831	−	19.7535i	−0.209454	−	0.644632i
$940$		0			0
$941$	3.84942	−	11.8473i	0.125488	−	0.386211i	−0.868502	−	0.495686i	$-0.834917\pi$
$941$	3.84942	−	11.8473i	0.125488	−	0.386211i	0.993990	+	0.109475i	$0.0349168\pi$
$942$		0			0
$943$		−	10.4474i		−	0.340213i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.79345	−	13.4795i	−0.318244	−	0.438026i	0.619686	−	0.784850i	$-0.287260\pi$
$947$	−9.79345	−	13.4795i	−0.318244	−	0.438026i	−0.937930	+	0.346824i	$0.887260\pi$
$948$		0			0
$949$	−6.30743			−0.204748
$950$		0			0
$951$	−16.7651			−0.543646
$952$		0			0
$953$	30.4812	+	41.9537i	0.987382	+	1.35901i	0.932756	+	0.360508i	$0.117396\pi$
$953$	30.4812	+	41.9537i	0.987382	+	1.35901i	0.0546255	+	0.998507i	$0.482604\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	1.08359i		−	0.0350275i
$958$		0			0
$959$	1.69381	−	5.21300i	0.0546959	−	0.168337i
$960$		0			0
$961$	−5.25786	−	16.1820i	−0.169608	−	0.522001i
$962$		0			0
$963$	−0.974929	−	0.316774i	−0.0314166	−	0.0102079i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	7.50713	−	10.3327i	0.241413	−	0.332277i	−0.671068	−	0.741396i	$-0.734164\pi$
$967$	7.50713	−	10.3327i	0.241413	−	0.332277i	0.912481	+	0.409119i	$0.134164\pi$
$968$		0			0
$969$	−6.86994	−	4.99131i	−0.220694	−	0.160344i
$970$		0			0
$971$	12.5679	−	9.13110i	0.403323	−	0.293031i	−0.367570	−	0.929996i	$-0.619810\pi$
$971$	12.5679	−	9.13110i	0.403323	−	0.293031i	0.770893	+	0.636965i	$0.219810\pi$
$972$		0			0
$973$	14.0336	−	4.55979i	0.449896	−	0.146180i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	31.5811	−	10.2613i	1.01037	−	0.328288i	0.243367	−	0.969934i	$-0.421748\pi$
$977$	31.5811	−	10.2613i	1.01037	−	0.328288i	0.767001	+	0.641646i	$0.221748\pi$
$978$		0			0
$979$	−0.155892	+	0.113262i	−0.00498234	+	0.00361988i
$980$		0			0
$981$	5.42455	+	3.94117i	0.173193	+	0.125832i
$982$		0			0
$983$	28.8570	−	39.7183i	0.920395	−	1.26682i	−0.0430944	−	0.999071i	$-0.513722\pi$
$983$	28.8570	−	39.7183i	0.920395	−	1.26682i	0.963490	−	0.267745i	$-0.0862784\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.60671	−	1.49681i	−0.146633	−	0.0476440i
$988$		0			0
$989$	12.7707	+	39.3043i	0.406086	+	1.24980i
$990$		0			0
$991$	−7.91583	+	24.3624i	−0.251455	+	0.773898i	0.743053	+	0.669233i	$0.233377\pi$
$991$	−7.91583	+	24.3624i	−0.251455	+	0.773898i	−0.994508	+	0.104665i	$0.966623\pi$
$992$		0			0
$993$			26.2157i			0.831932i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.36565	+	8.76157i	0.201602	+	0.277482i	0.897833	−	0.440337i	$-0.145141\pi$
$997$	6.36565	+	8.76157i	0.201602	+	0.277482i	−0.696231	+	0.717818i	$0.745141\pi$
$998$		0			0
$999$	−1.96543			−0.0621835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.o.a.349.4		16
5.2	odd	4		1500.2.m.b.901.1		8
5.3	odd	4		300.2.m.a.181.2	yes	8
5.4	even	2	inner	1500.2.o.a.349.1		16
15.8	even	4		900.2.n.a.181.1		8
25.2	odd	20		7500.2.a.d.1.1		4
25.3	odd	20		300.2.m.a.121.2	✓	8
25.4	even	10	inner	1500.2.o.a.649.3		16
25.11	even	5		7500.2.d.d.1249.4		8
25.14	even	10		7500.2.d.d.1249.5		8
25.21	even	5	inner	1500.2.o.a.649.2		16
25.22	odd	20		1500.2.m.b.601.1		8
25.23	odd	20		7500.2.a.g.1.4		4
75.53	even	20		900.2.n.a.721.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.121.2	✓	8	25.3	odd	20
300.2.m.a.181.2	yes	8	5.3	odd	4
900.2.n.a.181.1		8	15.8	even	4
900.2.n.a.721.1		8	75.53	even	20
1500.2.m.b.601.1		8	25.22	odd	20
1500.2.m.b.901.1		8	5.2	odd	4
1500.2.o.a.349.1		16	5.4	even	2	inner
1500.2.o.a.349.4		16	1.1	even	1	trivial
1500.2.o.a.649.2		16	25.21	even	5	inner
1500.2.o.a.649.3		16	25.4	even	10	inner
7500.2.a.d.1.1		4	25.2	odd	20
7500.2.a.g.1.4		4	25.23	odd	20
7500.2.d.d.1249.4		8	25.11	even	5
7500.2.d.d.1249.5		8	25.14	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:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{3} +0.747238i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{3} +0.747238i q^{7} +(-0.309017 + 0.951057i) q^{9} +(0.0646021 + 0.198825i) q^{11} +(2.38108 + 0.773659i) q^{13} +(-4.00842 + 5.51712i) q^{17} +(1.00739 + 0.731913i) q^{19} +(-0.604528 + 0.439216i) q^{21} +(3.09174 - 1.00457i) q^{23} +(-0.951057 + 0.309017i) q^{27} +(-4.19332 + 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(-0.122881 + 0.169131i) q^{33} +(1.86924 + 0.607352i) q^{37} +(0.773659 + 2.38108i) q^{39} +(0.993096 - 3.05644i) q^{41} +12.7127i q^{43} +(3.81017 + 5.24425i) q^{47} +6.44163 q^{49} -6.81953 q^{51} +(2.43520 + 3.35177i) q^{53} +1.24520i q^{57} +(-3.61882 + 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(-0.710666 - 0.230909i) q^{63} +(1.71460 - 2.35995i) q^{67} +(2.62999 + 1.91080i) q^{69} +(-5.29912 + 3.85004i) q^{71} +(-2.39603 + 0.778516i) q^{73} +(-0.148570 + 0.0482732i) q^{77} +(-8.28621 + 6.02028i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(3.33658 - 4.59240i) q^{83} +(-4.92954 - 1.60171i) q^{87} +(0.284829 + 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} -3.73968i q^{93} +(9.13679 + 12.5757i) q^{97} -0.209057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^9	\( 16 q + 4 q^{9} - 4 q^{11} - 10 q^{19} - 6 q^{21} - 54 q^{29} - 6 q^{31} + 40 q^{41} + 16 q^{49} - 16 q^{51} - 4 q^{59} - 28 q^{61} - 4 q^{69} - 30 q^{71} - 48 q^{79} - 4 q^{81} + 10 q^{91} + 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^9 - 4 * q^11 - 10 * q^19 - 6 * q^21 - 54 * q^29 - 6 * q^31 + 40 * q^41 + 16 * q^49 - 16 * q^51 - 4 * q^59 - 28 * q^61 - 4 * q^69 - 30 * q^71 - 48 * q^79 - 4 * q^81 + 10 * q^91 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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