LMFDB - Embedded newform 1500.2.m.b.901.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	1500.901
Dual form			1500.2.m.b.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{3} -0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{3} -0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +(0.0646021 + 0.198825i) q^{11} +(0.773659 - 2.38108i) q^{13} +(-5.51712 - 4.00842i) q^{17} +(-1.00739 - 0.731913i) q^{19} +(-0.604528 + 0.439216i) q^{21} +(-1.00457 - 3.09174i) q^{23} +(-0.309017 - 0.951057i) q^{27} +(4.19332 - 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(0.169131 + 0.122881i) q^{33} +(-0.607352 + 1.86924i) q^{37} +(-0.773659 - 2.38108i) q^{39} +(0.993096 - 3.05644i) q^{41} +12.7127 q^{43} +(-5.24425 + 3.81017i) q^{47} -6.44163 q^{49} -6.81953 q^{51} +(3.35177 - 2.43520i) q^{53} -1.24520 q^{57} +(3.61882 - 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(-0.230909 + 0.710666i) q^{63} +(2.35995 + 1.71460i) q^{67} +(-2.62999 - 1.91080i) q^{69} +(-5.29912 + 3.85004i) q^{71} +(0.778516 + 2.39603i) q^{73} +(-0.0482732 - 0.148570i) q^{77} +(8.28621 - 6.02028i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-4.59240 - 3.33658i) q^{83} +(1.60171 - 4.92954i) q^{87} +(-0.284829 - 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} -3.73968 q^{93} +(-12.5757 + 9.13679i) q^{97} +0.209057 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 8 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 8 * q^7 - 2 * q^9	$ 8 q + 2 q^{3} + 8 q^{7} - 2 q^{9} - 2 q^{11} - 7 q^{17} + 5 q^{19} - 3 q^{21} - 7 q^{23} + 2 q^{27} + 27 q^{29} - 3 q^{31} - 3 q^{33} + 9 q^{37} + 20 q^{41} + 68 q^{43} + 7 q^{47} - 8 q^{49} - 8 q^{51} + 11 q^{53} + 10 q^{57} + 2 q^{59} - 14 q^{61} - 7 q^{63} - 28 q^{67} + 2 q^{69} - 15 q^{71} - 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{81} - 2 q^{83} + 23 q^{87} + 5 q^{91} + 18 q^{93} - 34 q^{97} - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 8 * q^7 - 2 * q^9 - 2 * q^11 - 7 * q^17 + 5 * q^19 - 3 * q^21 - 7 * q^23 + 2 * q^27 + 27 * q^29 - 3 * q^31 - 3 * q^33 + 9 * q^37 + 20 * q^41 + 68 * q^43 + 7 * q^47 - 8 * q^49 - 8 * q^51 + 11 * q^53 + 10 * q^57 + 2 * q^59 - 14 * q^61 - 7 * q^63 - 28 * q^67 + 2 * q^69 - 15 * q^71 - 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^81 - 2 * q^83 + 23 * q^87 + 5 * q^91 + 18 * q^93 - 34 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.747238			−0.282430			−0.141215	−	0.989979i	$-0.545101\pi$
$7$	−0.747238			−0.282430			−0.141215	+	0.989979i	$0.545101\pi$
$8$		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
$13$	0.773659	−	2.38108i	0.214574	−	0.660392i	−0.784609	−	0.619991i	$-0.787136\pi$
$13$	0.773659	−	2.38108i	0.214574	−	0.660392i	0.999184	−	0.0404014i	$-0.0128637\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.51712	−	4.00842i	−1.33810	−	0.972185i	−0.999512	−	0.0312497i	$-0.990051\pi$
$17$	−5.51712	−	4.00842i	−1.33810	−	0.972185i	−0.338586	−	0.940935i	$-0.609949\pi$
$18$		0			0
$19$	−1.00739	−	0.731913i	−0.231112	−	0.167912i	0.466203	−	0.884678i	$-0.345622\pi$
$19$	−1.00739	−	0.731913i	−0.231112	−	0.167912i	−0.697314	+	0.716766i	$0.745622\pi$
$20$		0			0
$21$	−0.604528	+	0.439216i	−0.131919	+	0.0958447i
$22$		0			0
$23$	−1.00457	−	3.09174i	−0.209467	−	0.644673i	−0.999500	−	0.0316092i	$-0.989937\pi$
$23$	−1.00457	−	3.09174i	−0.209467	−	0.644673i	0.790033	−	0.613064i	$-0.210063\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$		0			0
$29$	4.19332	−	3.04662i	0.778680	−	0.565744i	−0.125903	−	0.992043i	$-0.540183\pi$
$29$	4.19332	−	3.04662i	0.778680	−	0.565744i	0.904582	+	0.426299i	$0.140183\pi$
$30$		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
$33$	0.169131	+	0.122881i	0.0294419	+	0.0213908i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.607352	+	1.86924i	−0.0998480	+	0.307301i	−0.988487	−	0.151307i	$-0.951652\pi$
$37$	−0.607352	+	1.86924i	−0.0998480	+	0.307301i	0.888639	+	0.458608i	$0.151652\pi$
$38$		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
$43$	12.7127			1.93866			0.969332	−	0.245755i	$-0.0790358\pi$
$43$	12.7127			1.93866			0.969332	+	0.245755i	$0.0790358\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.24425	+	3.81017i	−0.764952	+	0.555770i	−0.900425	−	0.435011i	$-0.856745\pi$
$47$	−5.24425	+	3.81017i	−0.764952	+	0.555770i	0.135473	+	0.990781i	$0.456745\pi$
$48$		0			0
$49$	−6.44163			−0.920234
$50$		0			0
$51$	−6.81953			−0.954926
$52$		0			0
$53$	3.35177	−	2.43520i	0.460401	−	0.334501i	−0.333288	−	0.942825i	$-0.608158\pi$
$53$	3.35177	−	2.43520i	0.460401	−	0.334501i	0.793688	+	0.608325i	$0.208158\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.24520			−0.164931
$58$		0			0
$59$	3.61882	−	11.1376i	0.471131	−	1.44999i	−0.379975	−	0.924997i	$-0.624067\pi$
$59$	3.61882	−	11.1376i	0.471131	−	1.44999i	0.851106	−	0.524995i	$-0.175933\pi$
$60$		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
$63$	−0.230909	+	0.710666i	−0.0290918	+	0.0895355i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.35995	+	1.71460i	0.288314	+	0.209472i	0.722535	−	0.691334i	$-0.242977\pi$
$67$	2.35995	+	1.71460i	0.288314	+	0.209472i	−0.434222	+	0.900806i	$0.642977\pi$
$68$		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
$73$	0.778516	+	2.39603i	0.0911184	+	0.280434i	0.986223	−	0.165423i	$-0.0528990\pi$
$73$	0.778516	+	2.39603i	0.0911184	+	0.280434i	−0.895104	+	0.445857i	$0.852899\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.0482732	−	0.148570i	−0.00550124	−	0.0169311i
$78$		0			0
$79$	8.28621	−	6.02028i	0.932271	−	0.677335i	−0.0142765	−	0.999898i	$-0.504545\pi$
$79$	8.28621	−	6.02028i	0.932271	−	0.677335i	0.946548	+	0.322563i	$0.104545\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	−4.59240	−	3.33658i	−0.504082	−	0.366237i	0.306492	−	0.951873i	$-0.400845\pi$
$83$	−4.59240	−	3.33658i	−0.504082	−	0.366237i	−0.810574	+	0.585636i	$0.800845\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.60171	−	4.92954i	0.171721	−	0.528502i
$88$		0			0
$89$	−0.284829	−	0.876615i	−0.0301919	−	0.0929210i	0.934825	−	0.355109i	$-0.115556\pi$
$89$	−0.284829	−	0.876615i	−0.0301919	−	0.0929210i	−0.965017	+	0.262188i	$0.915556\pi$
$90$		0			0
$91$	−0.578108	+	1.77923i	−0.0606022	+	0.186514i
$92$		0			0
$93$	−3.73968			−0.387787
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−12.5757	+	9.13679i	−1.27687	+	0.927700i	−0.999454	−	0.0330496i	$-0.989478\pi$
$97$	−12.5757	+	9.13679i	−1.27687	+	0.927700i	−0.277416	+	0.960750i	$0.589478\pi$
$98$		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
$103$	11.2326	−	8.16097i	1.10678	−	0.804124i	0.124628	−	0.992203i	$-0.460226\pi$
$103$	11.2326	−	8.16097i	1.10678	−	0.804124i	0.982154	+	0.188079i	$0.0602262\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.02510			−0.0991002			−0.0495501	−	0.998772i	$-0.515779\pi$
$107$	−1.02510			−0.0991002			−0.0495501	+	0.998772i	$0.515779\pi$
$108$		0			0
$109$	−2.07199	+	6.37694i	−0.198461	+	0.610800i	0.801458	+	0.598051i	$0.204058\pi$
$109$	−2.07199	+	6.37694i	−0.198461	+	0.610800i	−0.999919	+	0.0127488i	$0.995942\pi$
$110$		0			0
$111$	0.607352	+	1.86924i	0.0576473	+	0.177420i
$112$		0			0
$113$	−2.57151	+	7.91428i	−0.241907	+	0.744513i	0.754223	+	0.656618i	$0.228014\pi$
$113$	−2.57151	+	7.91428i	−0.241907	+	0.744513i	−0.996130	+	0.0878944i	$0.971986\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.02547	−	1.47159i	−0.187254	−	0.136048i
$118$		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
$123$	−0.993096	−	3.05644i	−0.0895445	−	0.275590i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	4.49195	+	13.8248i	0.398597	+	1.22675i	0.926125	+	0.377217i	$0.123119\pi$
$127$	4.49195	+	13.8248i	0.398597	+	1.22675i	−0.527529	+	0.849537i	$0.676881\pi$
$128$		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
$133$	0.752762	+	0.546913i	0.0652727	+	0.0474234i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.26676	−	6.97636i	0.193662	−	0.596030i	−0.806328	−	0.591469i	$-0.798548\pi$
$137$	2.26676	−	6.97636i	0.193662	−	0.596030i	0.999990	−	0.00456114i	$-0.00145186\pi$
$138$		0			0
$139$	6.10219	+	18.7806i	0.517581	+	1.59295i	0.778536	+	0.627600i	$0.215963\pi$
$139$	6.10219	+	18.7806i	0.517581	+	1.59295i	−0.260954	+	0.965351i	$0.584037\pi$
$140$		0			0
$141$	−2.00313	+	6.16499i	−0.168694	+	0.519185i
$142$		0			0
$143$	0.523398			0.0437687
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.21139	+	3.78630i	−0.429828	+	0.312289i
$148$		0			0
$149$	−21.7551			−1.78224			−0.891122	−	0.453763i	$-0.850081\pi$
$149$	−21.7551			−1.78224			−0.891122	+	0.453763i	$0.850081\pi$
$150$		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
$153$	−5.51712	+	4.00842i	−0.446033	+	0.324062i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.99520			0.797704			0.398852	−	0.917015i	$-0.369409\pi$
$157$	9.99520			0.797704			0.398852	+	0.917015i	$0.369409\pi$
$158$		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
$163$	0.792035	−	2.43763i	0.0620369	−	0.190930i	−0.915235	−	0.402921i	$-0.867995\pi$
$163$	0.792035	−	2.43763i	0.0620369	−	0.190930i	0.977272	+	0.211991i	$0.0679948\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.8690	−	12.2560i	−1.30536	−	0.948401i	−0.305369	−	0.952234i	$-0.598780\pi$
$167$	−16.8690	−	12.2560i	−1.30536	−	0.948401i	−0.999993	+	0.00383355i	$0.998780\pi$
$168$		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
$173$	−0.635016	−	1.95438i	−0.0482794	−	0.148589i	0.924011	−	0.382367i	$-0.124891\pi$
$173$	−0.635016	−	1.95438i	−0.0482794	−	0.148589i	−0.972290	+	0.233778i	$0.924891\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.61882	−	11.1376i	−0.272007	−	0.837153i
$178$		0			0
$179$	15.8247	−	11.4973i	1.18279	−	0.859349i	0.190309	−	0.981724i	$-0.439051\pi$
$179$	15.8247	−	11.4973i	1.18279	−	0.859349i	0.992484	+	0.122375i	$0.0390510\pi$
$180$		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
$183$	−10.0960	−	7.33519i	−0.746319	−	0.542233i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.440557	−	1.35589i	0.0322167	−	0.0991528i
$188$		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
$193$	−1.10589			−0.0796035			−0.0398018	−	0.999208i	$-0.512673\pi$
$193$	−1.10589			−0.0796035			−0.0398018	+	0.999208i	$0.512673\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.6953	−	12.1299i	1.18949	−	0.864217i	0.196282	−	0.980547i	$-0.437113\pi$
$197$	16.6953	−	12.1299i	1.18949	−	0.864217i	0.993211	+	0.116331i	$0.0371132\pi$
$198$		0			0
$199$	−12.3822			−0.877749			−0.438874	−	0.898548i	$-0.644623\pi$
$199$	−12.3822			−0.877749			−0.438874	+	0.898548i	$0.644623\pi$
$200$		0			0
$201$	2.91706			0.205753
$202$		0			0
$203$	−3.13341	+	2.27655i	−0.219922	+	0.159783i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.25085			−0.225950
$208$		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
$213$	−2.02409	+	6.22949i	−0.138688	+	0.426838i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.26074	+	1.64253i	0.153469	+	0.111502i
$218$		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
$223$	1.28385	+	3.95129i	0.0859732	+	0.264598i	0.984796	−	0.173713i	$-0.0555766\pi$
$223$	1.28385	+	3.95129i	0.0859732	+	0.264598i	−0.898823	+	0.438312i	$0.855577\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.30175	+	22.4725i	0.484634	+	1.49155i	0.832510	+	0.554010i	$0.186903\pi$
$227$	7.30175	+	22.4725i	0.484634	+	1.49155i	−0.347876	+	0.937541i	$0.613097\pi$
$228$		0			0
$229$	−14.7565	+	10.7212i	−0.975139	+	0.708480i	−0.956617	−	0.291348i	$-0.905896\pi$
$229$	−14.7565	+	10.7212i	−0.975139	+	0.708480i	−0.0185221	+	0.999828i	$0.505896\pi$
$230$		0			0
$231$	−0.126381	−	0.0918211i	−0.00831525	−	0.00604138i
$232$		0			0
$233$	1.83438	+	1.33276i	0.120174	+	0.0873117i	0.646249	−	0.763127i	$-0.276337\pi$
$233$	1.83438	+	1.33276i	0.120174	+	0.0873117i	−0.526075	+	0.850438i	$0.676337\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.16505	−	9.74102i	0.205592	−	0.632747i
$238$		0			0
$239$	5.28631	+	16.2696i	0.341943	+	1.05239i	0.963200	+	0.268786i	$0.0866223\pi$
$239$	5.28631	+	16.2696i	0.341943	+	1.05239i	−0.621257	+	0.783607i	$0.713378\pi$
$240$		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
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.52212	+	1.83243i	−0.160479	+	0.116595i
$248$		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
$253$	0.549819	−	0.399467i	0.0345668	−	0.0251142i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	28.5421			1.78041			0.890204	−	0.455561i	$-0.150561\pi$
$257$	28.5421			1.78041			0.890204	+	0.455561i	$0.150561\pi$
$258$		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
$263$	1.09911	−	3.38270i	0.0677738	−	0.208586i	−0.911434	−	0.411447i	$-0.865024\pi$
$263$	1.09911	−	3.38270i	0.0677738	−	0.208586i	0.979208	+	0.202860i	$0.0650237\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.745693	−	0.541778i	−0.0456357	−	0.0331563i
$268$		0			0
$269$	−23.6733	−	17.1997i	−1.44339	−	1.04868i	−0.987321	−	0.158736i	$-0.949258\pi$
$269$	−23.6733	−	17.1997i	−1.44339	−	1.04868i	−0.456066	−	0.889946i	$-0.650742\pi$
$270$		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
$273$	0.578108	+	1.77923i	0.0349887	+	0.107684i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	5.38539	+	16.5745i	0.323577	+	0.995867i	0.972079	+	0.234654i	$0.0753958\pi$
$277$	5.38539	+	16.5745i	0.323577	+	0.995867i	−0.648502	+	0.761213i	$0.724604\pi$
$278$		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
$283$	13.2464	+	9.62409i	0.787418	+	0.572093i	0.907196	−	0.420708i	$-0.138218\pi$
$283$	13.2464	+	9.62409i	0.787418	+	0.572093i	−0.119778	+	0.992801i	$0.538218\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.742080	+	2.28389i	−0.0438036	+	0.134814i
$288$		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
$293$	−8.70991			−0.508838			−0.254419	−	0.967094i	$-0.581884\pi$
$293$	−8.70991			−0.508838			−0.254419	+	0.967094i	$0.581884\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.169131	−	0.122881i	0.00981395	−	0.00713025i
$298$		0			0
$299$	−8.13888			−0.470683
$300$		0			0
$301$	−9.49939			−0.547536
$302$		0			0
$303$	−8.93194	+	6.48944i	−0.513127	+	0.372808i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	17.7123			1.01090			0.505448	−	0.862857i	$-0.331327\pi$
$307$	17.7123			1.01090			0.505448	+	0.862857i	$0.331327\pi$
$308$		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
$313$	−6.41831	+	19.7535i	−0.362785	+	1.11654i	0.588572	+	0.808445i	$0.299690\pi$
$313$	−6.41831	+	19.7535i	−0.362785	+	1.11654i	−0.951357	+	0.308091i	$0.900310\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.5633	−	9.85429i	−0.761789	−	0.553472i	0.137670	−	0.990478i	$-0.456039\pi$
$317$	−13.5633	−	9.85429i	−0.761789	−	0.553472i	−0.899458	+	0.437006i	$0.856039\pi$
$318$		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
$323$	2.62408	+	8.07610i	0.146008	+	0.449366i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.07199	+	6.37694i	0.114582	+	0.352646i
$328$		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
$333$	1.59007	+	1.15525i	0.0871352	+	0.0633074i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.03519	−	24.7298i	0.437705	−	1.34712i	−0.452584	−	0.891722i	$-0.649498\pi$
$337$	8.03519	−	24.7298i	0.437705	−	1.34712i	0.890289	−	0.455395i	$-0.150502\pi$
$338$		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
$343$	10.0441			0.542331
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.72256	−	2.70460i	0.199838	−	0.145191i	−0.483366	−	0.875418i	$-0.660586\pi$
$347$	3.72256	−	2.70460i	0.199838	−	0.145191i	0.683204	+	0.730228i	$0.260586\pi$
$348$		0			0
$349$	−29.2108			−1.56362			−0.781810	−	0.623516i	$-0.785703\pi$
$349$	−29.2108			−1.56362			−0.781810	+	0.623516i	$0.785703\pi$
$350$		0			0
$351$	−2.50361			−0.133633
$352$		0			0
$353$	−22.7505	+	16.5292i	−1.21088	+	0.879759i	−0.995311	−	0.0967283i	$-0.969162\pi$
$353$	−22.7505	+	16.5292i	−1.21088	+	0.879759i	−0.215574	+	0.976488i	$0.569162\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.09582			0.269699
$358$		0			0
$359$	−2.90570	+	8.94282i	−0.153357	+	0.471984i	−0.997991	−	0.0633604i	$-0.979818\pi$
$359$	−2.90570	+	8.94282i	−0.153357	+	0.471984i	0.844634	+	0.535345i	$0.179818\pi$
$360$		0			0
$361$	−5.39218	−	16.5954i	−0.283799	−	0.873444i
$362$		0			0
$363$	3.38568	−	10.4201i	0.177702	−	0.546911i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	17.8033	+	12.9349i	0.929326	+	0.675195i	0.945828	−	0.324669i	$-0.105253\pi$
$367$	17.8033	+	12.9349i	0.929326	+	0.675195i	−0.0165016	+	0.999864i	$0.505253\pi$
$368$		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
$373$	−5.75384	−	17.7085i	−0.297923	−	0.916911i	−0.982224	−	0.187712i	$-0.939893\pi$
$373$	−5.75384	−	17.7085i	−0.297923	−	0.916911i	0.684302	−	0.729199i	$-0.260107\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.01005	−	12.3417i	−0.206528	−	0.635628i
$378$		0			0
$379$	13.6515	−	9.91838i	0.701230	−	0.509473i	−0.179103	−	0.983830i	$-0.557320\pi$
$379$	13.6515	−	9.91838i	0.701230	−	0.509473i	0.880332	+	0.474357i	$0.157320\pi$
$380$		0			0
$381$	11.7601	+	8.54421i	0.602488	+	0.437733i
$382$		0			0
$383$	−7.32847	−	5.32445i	−0.374467	−	0.272066i	0.384594	−	0.923086i	$-0.374342\pi$
$383$	−7.32847	−	5.32445i	−0.374467	−	0.272066i	−0.759061	+	0.651020i	$0.774342\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.92843	−	12.0905i	0.199693	−	0.614593i
$388$		0			0
$389$	10.2225	+	31.4616i	0.518301	+	1.59517i	0.777194	+	0.629261i	$0.216642\pi$
$389$	10.2225	+	31.4616i	0.518301	+	1.59517i	−0.258893	+	0.965906i	$0.583358\pi$
$390$		0			0
$391$	−6.85069	+	21.0843i	−0.346454	+	1.06628i
$392$		0			0
$393$	−7.42396			−0.374489
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−17.5773	+	12.7706i	−0.882177	+	0.640939i	−0.933827	−	0.357726i	$-0.883552\pi$
$397$	−17.5773	+	12.7706i	−0.882177	+	0.640939i	0.0516494	+	0.998665i	$0.483552\pi$
$398$		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
$403$	−7.57460	+	5.50327i	−0.377318	+	0.274137i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.410887			−0.0203669
$408$		0			0
$409$	−4.34139	+	13.3614i	−0.214668	+	0.660679i	0.784509	+	0.620117i	$0.212915\pi$
$409$	−4.34139	+	13.3614i	−0.214668	+	0.660679i	−0.999177	+	0.0405623i	$0.987085\pi$
$410$		0			0
$411$	−2.26676	−	6.97636i	−0.111811	−	0.344118i
$412$		0			0
$413$	−2.70412	+	8.32244i	−0.133061	+	0.409520i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	15.9757	+	11.6071i	0.782336	+	0.568400i
$418$		0			0
$419$	16.3919	+	11.9094i	0.800794	+	0.581811i	0.911147	−	0.412081i	$-0.135198\pi$
$419$	16.3919	+	11.9094i	0.800794	+	0.581811i	−0.110353	+	0.993892i	$0.535198\pi$
$420$		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
$423$	2.00313	+	6.16499i	0.0973953	+	0.299752i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.88160	+	8.86866i	0.139450	+	0.429184i
$428$		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
$433$	1.81940	+	1.32187i	0.0874347	+	0.0635250i	0.630644	−	0.776072i	$-0.282791\pi$
$433$	1.81940	+	1.32187i	0.0874347	+	0.0635250i	−0.543209	+	0.839597i	$0.682791\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.25089	+	3.84985i	−0.0598383	+	0.184163i
$438$		0			0
$439$	6.83477	+	21.0353i	0.326206	+	1.00396i	0.970893	+	0.239512i	$0.0769875\pi$
$439$	6.83477	+	21.0353i	0.326206	+	1.00396i	−0.644688	+	0.764446i	$0.723013\pi$
$440$		0			0
$441$	−1.99057	+	6.12636i	−0.0947893	+	0.291731i
$442$		0			0
$443$	−28.1534			−1.33761			−0.668804	−	0.743439i	$-0.733193\pi$
$443$	−28.1534			−1.33761			−0.668804	+	0.743439i	$0.733193\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−17.6002	+	12.7873i	−0.832462	+	0.604819i
$448$		0			0
$449$	16.5924			0.783044			0.391522	−	0.920169i	$-0.371949\pi$
$449$	16.5924			0.783044			0.391522	+	0.920169i	$0.371949\pi$
$450$		0			0
$451$	0.671852			0.0316363
$452$		0			0
$453$	8.19598	−	5.95473i	0.385081	−	0.279777i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	11.1599			0.522039			0.261019	−	0.965334i	$-0.415941\pi$
$457$	11.1599			0.522039			0.261019	+	0.965334i	$0.415941\pi$
$458$		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
$463$	5.26243	−	16.1961i	0.244566	−	0.752696i	−0.751142	−	0.660141i	$-0.770497\pi$
$463$	5.26243	−	16.1961i	0.244566	−	0.752696i	0.995708	−	0.0925550i	$-0.0295034\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.1159	−	10.9823i	−0.699481	−	0.508202i	0.180282	−	0.983615i	$-0.442299\pi$
$467$	−15.1159	−	10.9823i	−0.699481	−	0.508202i	−0.879763	+	0.475413i	$0.842299\pi$
$468$		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
$473$	0.821266	+	2.52760i	0.0377618	+	0.116219i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.28026	−	3.94024i	−0.0586191	−	0.180411i
$478$		0			0
$479$	−2.38111	+	1.72998i	−0.108796	+	0.0790448i	−0.640853	−	0.767664i	$-0.721419\pi$
$479$	−2.38111	+	1.72998i	−0.108796	+	0.0790448i	0.532057	+	0.846708i	$0.321419\pi$
$480$		0			0
$481$	3.98092	+	2.89230i	0.181514	+	0.131878i
$482$		0			0
$483$	1.96523	+	1.42782i	0.0894212	+	0.0649683i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	4.33109	−	13.3297i	0.196261	−	0.604028i	−0.803699	−	0.595036i	$-0.797138\pi$
$487$	4.33109	−	13.3297i	0.196261	−	0.604028i	0.999960	−	0.00899199i	$-0.00286228\pi$
$488$		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
$493$	−35.3472			−1.59196
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.95971	−	2.87690i	0.177617	−	0.129046i
$498$		0			0
$499$	−2.39366			−0.107155			−0.0535774	−	0.998564i	$-0.517062\pi$
$499$	−2.39366			−0.107155			−0.0535774	+	0.998564i	$0.517062\pi$
$500$		0			0
$501$	−20.8512			−0.931564
$502$		0			0
$503$	6.81519	−	4.95152i	0.303874	−	0.220777i	−0.425389	−	0.905010i	$-0.639863\pi$
$503$	6.81519	−	4.95152i	0.303874	−	0.220777i	0.729264	+	0.684233i	$0.239863\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.73192			0.298975
$508$		0			0
$509$	9.98528	−	30.7315i	0.442590	−	1.36215i	−0.442516	−	0.896761i	$-0.645914\pi$
$509$	9.98528	−	30.7315i	0.442590	−	1.36215i	0.885106	−	0.465390i	$-0.154086\pi$
$510$		0			0
$511$	−0.581737	−	1.79040i	−0.0257345	−	0.0792027i
$512$		0			0
$513$	−0.384789	+	1.18426i	−0.0169889	+	0.0522864i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−1.09635	−	0.796543i	−0.0482173	−	0.0350319i
$518$		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
$523$	10.0241	+	30.8511i	0.438325	+	1.34903i	0.889640	+	0.456662i	$0.150955\pi$
$523$	10.0241	+	30.8511i	0.438325	+	1.34903i	−0.451315	+	0.892365i	$0.649045\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.88082	+	24.2547i	0.343294	+	1.05655i
$528$		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
$533$	−6.50929	−	4.72928i	−0.281949	−	0.204848i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.04449	−	18.6030i	0.260839	−	0.802781i
$538$		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
$543$	7.37007			0.316280
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.31795	+	3.13718i	−0.184622	+	0.134136i	−0.676258	−	0.736665i	$-0.736399\pi$
$547$	−4.31795	+	3.13718i	−0.184622	+	0.134136i	0.491635	+	0.870801i	$0.336399\pi$
$548$		0			0
$549$	−12.4794			−0.532606
$550$		0			0
$551$	−6.45418			−0.274957
$552$		0			0
$553$	−6.19177	+	4.49859i	−0.263301	+	0.191299i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.0652731			0.00276571			0.00138286	−	0.999999i	$-0.499560\pi$
$557$	0.0652731			0.00276571			0.00138286	+	0.999999i	$0.499560\pi$
$558$		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
$563$	8.88197	−	27.3359i	0.374330	−	1.15207i	−0.569599	−	0.821923i	$-0.692902\pi$
$563$	8.88197	−	27.3359i	0.374330	−	1.15207i	0.943929	−	0.330147i	$-0.107098\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.604528	+	0.439216i	0.0253878	+	0.0184453i
$568$		0			0
$569$	6.68501	+	4.85694i	0.280250	+	0.203614i	0.719026	−	0.694983i	$-0.244588\pi$
$569$	6.68501	+	4.85694i	0.280250	+	0.203614i	−0.438776	+	0.898596i	$0.644588\pi$
$570$		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
$573$	0.693806	+	2.13532i	0.0289842	+	0.0892041i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−6.60944	−	20.3418i	−0.275154	−	0.846838i	−0.989178	−	0.146717i	$-0.953129\pi$
$577$	−6.60944	−	20.3418i	−0.275154	−	0.846838i	0.714024	−	0.700121i	$-0.246871\pi$
$578$		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
$583$	0.700710	+	0.509096i	0.0290204	+	0.0210846i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.7412	+	39.2133i	−0.525885	+	1.61851i	0.236674	+	0.971589i	$0.423943\pi$
$587$	−12.7412	+	39.2133i	−0.525885	+	1.61851i	−0.762559	+	0.646918i	$0.776057\pi$
$588$		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
$593$	23.2238			0.953685			0.476843	−	0.878989i	$-0.341781\pi$
$593$	23.2238			0.953685			0.476843	+	0.878989i	$0.341781\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.0174	+	7.27806i	−0.409984	+	0.297871i
$598$		0			0
$599$	−22.6226			−0.924335			−0.462168	−	0.886793i	$-0.652928\pi$
$599$	−22.6226			−0.924335			−0.462168	+	0.886793i	$0.652928\pi$
$600$		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
$603$	2.35995	−	1.71460i	0.0961045	−	0.0698240i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.54036			−0.184288			−0.0921439	−	0.995746i	$-0.529372\pi$
$607$	−4.54036			−0.184288			−0.0921439	+	0.995746i	$0.529372\pi$
$608$		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
$613$	7.83471	−	24.1128i	0.316441	−	0.973905i	−0.658716	−	0.752391i	$-0.728900\pi$
$613$	7.83471	−	24.1128i	0.316441	−	0.973905i	0.975157	−	0.221514i	$-0.0710997\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−36.5829	−	26.5790i	−1.47277	−	1.07003i	−0.979799	−	0.199986i	$-0.935910\pi$
$617$	−36.5829	−	26.5790i	−1.47277	−	1.07003i	−0.492972	−	0.870045i	$-0.664090\pi$
$618$		0			0
$619$	−25.3666	−	18.4299i	−1.01957	−	0.740762i	−0.0533766	−	0.998574i	$-0.516998\pi$
$619$	−25.3666	−	18.4299i	−1.01957	−	0.740762i	−0.966195	+	0.257812i	$0.916998\pi$
$620$		0			0
$621$	−2.62999	+	1.91080i	−0.105538	+	0.0766779i
$622$		0			0
$623$	0.212835	+	0.655040i	0.00852707	+	0.0262436i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.0804429	−	0.247578i	−0.00321258	−	0.00988730i
$628$		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
$633$	16.6879	+	12.1245i	0.663286	+	0.481905i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−4.98363	+	15.3380i	−0.197459	+	0.607715i
$638$		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
$643$	33.2313			1.31052			0.655258	−	0.755406i	$-0.272560\pi$
$643$	33.2313			1.31052			0.655258	+	0.755406i	$0.272560\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	27.2571	−	19.8034i	1.07159	−	0.778553i	0.0953892	−	0.995440i	$-0.469590\pi$
$647$	27.2571	−	19.8034i	1.07159	−	0.778553i	0.976197	+	0.216887i	$0.0695904\pi$
$648$		0			0
$649$	2.44822			0.0961009
$650$		0			0
$651$	2.79443			0.109522
$652$		0			0
$653$	17.6754	−	12.8419i	0.691692	−	0.502544i	−0.185524	−	0.982640i	$-0.559398\pi$
$653$	17.6754	−	12.8419i	0.691692	−	0.502544i	0.877216	+	0.480096i	$0.159398\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.51933			0.0982885
$658$		0			0
$659$	−3.48829	+	10.7359i	−0.135884	+	0.418209i	−0.995727	−	0.0923507i	$-0.970562\pi$
$659$	−3.48829	+	10.7359i	−0.135884	+	0.418209i	0.859842	+	0.510560i	$0.170562\pi$
$660$		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
$663$	−5.27599	+	16.2378i	−0.204903	+	0.630625i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−13.6319	−	9.90412i	−0.527828	−	0.383489i
$668$		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
$673$	−2.37563	−	7.31143i	−0.0915737	−	0.281835i	0.894772	−	0.446523i	$-0.147338\pi$
$673$	−2.37563	−	7.31143i	−0.0915737	−	0.281835i	−0.986346	+	0.164689i	$0.947338\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.5253	+	35.4711i	0.442952	+	1.36327i	0.884714	+	0.466133i	$0.154353\pi$
$677$	11.5253	+	35.4711i	0.442952	+	1.36327i	−0.441763	+	0.897132i	$0.645647\pi$
$678$		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
$683$	29.5125	+	21.4421i	1.12926	+	0.820458i	0.985587	−	0.169166i	$-0.0541075\pi$
$683$	29.5125	+	21.4421i	1.12926	+	0.820458i	0.143676	+	0.989625i	$0.454108\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.63649	+	17.3473i	−0.215046	+	0.661842i
$688$		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
$693$	−0.156215			−0.00593413
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−17.7305	+	12.8820i	−0.671591	+	0.487940i
$698$		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
$703$	1.97996	−	1.43853i	0.0746756	−	0.0542550i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.24988			0.310268
$708$		0			0
$709$	9.03055	−	27.7932i	0.339149	−	1.04379i	−0.625493	−	0.780230i	$-0.715102\pi$
$709$	9.03055	−	27.7932i	0.339149	−	1.04379i	0.964642	−	0.263564i	$-0.0848981\pi$
$710$		0			0
$711$	−3.16505	−	9.74102i	−0.118699	−	0.365317i
$712$		0			0
$713$	−3.75677	+	11.5621i	−0.140692	+	0.433005i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	13.8397	+	10.0552i	0.516855	+	0.375517i
$718$		0			0
$719$	−35.5675	−	25.8413i	−1.32644	−	0.963718i	−0.999828	−	0.0185605i	$-0.994092\pi$
$719$	−35.5675	−	25.8413i	−1.32644	−	0.963718i	−0.326616	−	0.945157i	$-0.605908\pi$
$720$		0			0
$721$	−8.39344	+	6.09819i	−0.312588	+	0.227108i
$722$		0			0
$723$	−8.71435	−	26.8200i	−0.324090	−	0.997447i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−9.24768	−	28.4614i	−0.342977	−	1.05558i	−0.962658	−	0.270721i	$-0.912738\pi$
$727$	−9.24768	−	28.4614i	−0.342977	−	1.05558i	0.619680	−	0.784854i	$-0.287262\pi$
$728$		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
$733$	−13.3702	−	9.71402i	−0.493840	−	0.358795i	0.312819	−	0.949813i	$-0.398727\pi$
$733$	−13.3702	−	9.71402i	−0.493840	−	0.358795i	−0.806659	+	0.591017i	$0.798727\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.188448	+	0.579984i	−0.00694158	+	0.0213640i
$738$		0			0
$739$	−15.7285	−	48.4073i	−0.578581	−	1.78069i	−0.623648	−	0.781706i	$-0.714350\pi$
$739$	−15.7285	−	48.4073i	−0.578581	−	1.78069i	0.0450666	−	0.998984i	$-0.485650\pi$
$740$		0			0
$741$	−0.963364	+	2.96493i	−0.0353901	+	0.108919i
$742$		0			0
$743$	28.6937			1.05267			0.526336	−	0.850277i	$-0.323566\pi$
$743$	28.6937			1.05267			0.526336	+	0.850277i	$0.323566\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.59240	+	3.33658i	−0.168027	+	0.122079i
$748$		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
$753$	19.3821	−	14.0819i	0.706322	−	0.513173i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−41.4243			−1.50559			−0.752796	−	0.658254i	$-0.771295\pi$
$757$	−41.4243			−1.50559			−0.752796	+	0.658254i	$0.771295\pi$
$758$		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
$763$	1.54827	−	4.76509i	0.0560513	−	0.172508i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−23.7197	−	17.2334i	−0.856470	−	0.622262i
$768$		0			0
$769$	1.06014	+	0.770234i	0.0382295	+	0.0277753i	0.606736	−	0.794903i	$-0.292479\pi$
$769$	1.06014	+	0.770234i	0.0382295	+	0.0277753i	−0.568506	+	0.822679i	$0.692479\pi$
$770$		0			0
$771$	23.0911	−	16.7766i	0.831604	−	0.604196i
$772$		0			0
$773$	−9.00241	−	27.7066i	−0.323794	−	0.996536i	−0.971982	−	0.235055i	$-0.924473\pi$
$773$	−9.00241	−	27.7066i	−0.323794	−	0.996536i	0.648188	−	0.761480i	$-0.275527\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.453837	−	1.39677i	−0.0162813	−	0.0501087i
$778$		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
$783$	−4.19332	−	3.04662i	−0.149857	−	0.108877i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	14.4050	−	44.3341i	0.513484	−	1.58034i	−0.272540	−	0.962145i	$-0.587864\pi$
$787$	14.4050	−	44.3341i	0.513484	−	1.58034i	0.786023	−	0.618197i	$-0.212136\pi$
$788$		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
$793$	−31.2435			−1.10949
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.1308	+	8.08703i	−0.394275	+	0.286457i	−0.767205	−	0.641402i	$-0.778353\pi$
$797$	−11.1308	+	8.08703i	−0.394275	+	0.286457i	0.372930	+	0.927859i	$0.378353\pi$
$798$		0			0
$799$	44.2059			1.56389
$800$		0			0
$801$	−0.921727			−0.0325676
$802$		0			0
$803$	−0.426096	+	0.309577i	−0.0150366	+	0.0109247i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−29.2618			−1.03006
$808$		0			0
$809$	3.08886	−	9.50654i	0.108599	−	0.334232i	−0.881960	−	0.471325i	$-0.843776\pi$
$809$	3.08886	−	9.50654i	0.108599	−	0.334232i	0.990558	+	0.137093i	$0.0437759\pi$
$810$		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
$813$	7.66927	−	23.6036i	0.268973	−	0.827814i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−12.8066	−	9.30457i	−0.448048	−	0.325526i
$818$		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
$823$	−3.70366	−	11.3987i	−0.129101	−	0.397333i	0.865525	−	0.500866i	$-0.166985\pi$
$823$	−3.70366	−	11.3987i	−0.129101	−	0.397333i	−0.994626	+	0.103533i	$0.966985\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.13191	−	12.7167i	−0.143681	−	0.442204i	0.853158	−	0.521652i	$-0.174684\pi$
$827$	−4.13191	−	12.7167i	−0.143681	−	0.442204i	−0.996839	+	0.0794485i	$0.974684\pi$
$828$		0			0
$829$	13.3909	−	9.72909i	0.465087	−	0.337905i	−0.330437	−	0.943828i	$-0.607196\pi$
$829$	13.3909	−	9.72909i	0.465087	−	0.337905i	0.795523	+	0.605923i	$0.207196\pi$
$830$		0			0
$831$	14.0991	+	10.2436i	0.489094	+	0.355347i
$832$		0			0
$833$	35.5393	+	25.8208i	1.23136	+	0.894637i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.15563	+	3.55665i	−0.0399442	+	0.122936i
$838$		0			0
$839$	7.56589	+	23.2854i	0.261204	+	0.803902i	0.992544	+	0.121889i	$0.0388953\pi$
$839$	7.56589	+	23.2854i	0.261204	+	0.803902i	−0.731340	+	0.682013i	$0.761105\pi$
$840$		0			0
$841$	−0.659493	+	2.02971i	−0.0227411	+	0.0699900i
$842$		0			0
$843$	−3.75349			−0.129277
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−6.62339	+	4.81218i	−0.227582	+	0.165348i
$848$		0			0
$849$	16.3735			0.561936
$850$		0			0
$851$	6.38933			0.219023
$852$		0			0
$853$	15.4809	−	11.2475i	0.530055	−	0.385108i	−0.290323	−	0.956929i	$-0.593763\pi$
$853$	15.4809	−	11.2475i	0.530055	−	0.385108i	0.820379	+	0.571821i	$0.193763\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.43367			0.253929			0.126965	−	0.991907i	$-0.459477\pi$
$857$	7.43367			0.253929			0.126965	+	0.991907i	$0.459477\pi$
$858$		0			0
$859$	12.7368	−	39.1999i	0.434575	−	1.33748i	−0.458947	−	0.888464i	$-0.651773\pi$
$859$	12.7368	−	39.1999i	0.434575	−	1.33748i	0.893522	−	0.449020i	$-0.148227\pi$
$860$		0			0
$861$	0.742080	+	2.28389i	0.0252900	+	0.0778346i
$862$		0			0
$863$	11.7794	−	36.2532i	0.400975	−	1.23407i	−0.523234	−	0.852189i	$-0.675275\pi$
$863$	11.7794	−	36.2532i	0.400975	−	1.23407i	0.924210	−	0.381886i	$-0.124725\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	23.8709	+	17.3432i	0.810698	+	0.589007i
$868$		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
$873$	4.80349	+	14.7836i	0.162574	+	0.500350i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−8.96931	−	27.6047i	−0.302872	−	0.932145i	−0.980463	−	0.196705i	$-0.936976\pi$
$877$	−8.96931	−	27.6047i	−0.302872	−	0.932145i	0.677591	−	0.735439i	$-0.263024\pi$
$878$		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
$883$	−31.3921	−	22.8077i	−1.05643	−	0.767539i	−0.0830028	−	0.996549i	$-0.526451\pi$
$883$	−31.3921	−	22.8077i	−1.05643	−	0.767539i	−0.973424	+	0.229010i	$0.926451\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1.78288	+	5.48715i	−0.0598634	+	0.184241i	−0.976516	−	0.215444i	$-0.930880\pi$
$887$	−1.78288	+	5.48715i	−0.0598634	+	0.184241i	0.916653	+	0.399684i	$0.130880\pi$
$888$		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
$893$	8.07173			0.270110
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−6.58449	+	4.78391i	−0.219850	+	0.159730i
$898$		0			0
$899$	−19.3836			−0.646480
$900$		0			0
$901$	−28.2534			−0.941257
$902$		0			0
$903$	−7.68517	+	5.58360i	−0.255746	+	0.185811i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−31.7260			−1.05345			−0.526723	−	0.850037i	$-0.676579\pi$
$907$	−31.7260			−1.05345			−0.526723	+	0.850037i	$0.676579\pi$
$908$		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
$913$	0.366716	−	1.12863i	0.0121365	−	0.0373523i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.48800	+	3.26072i	0.148207	+	0.107679i
$918$		0			0
$919$	8.82328	+	6.41049i	0.291053	+	0.211462i	0.723724	−	0.690089i	$-0.242429\pi$
$919$	8.82328	+	6.41049i	0.291053	+	0.211462i	−0.432671	+	0.901552i	$0.642429\pi$
$920$		0			0
$921$	14.3296	−	10.4111i	0.472176	−	0.343056i
$922$		0			0
$923$	5.06753	+	15.5962i	0.166800	+	0.513357i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.29048	−	13.2047i	−0.140918	−	0.433700i
$928$		0			0
$929$	−18.3021	+	13.2973i	−0.600473	+	0.436269i	−0.846047	−	0.533108i	$-0.821024\pi$
$929$	−18.3021	+	13.2973i	−0.600473	+	0.436269i	0.245573	+	0.969378i	$0.421024\pi$
$930$		0			0
$931$	6.48925	+	4.71472i	0.212677	+	0.154519i
$932$		0			0
$933$	16.4130	+	11.9247i	0.537337	+	0.390398i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	1.59323	−	4.90347i	0.0520487	−	0.160189i	−0.921654	−	0.388014i	$-0.873161\pi$
$937$	1.59323	−	4.90347i	0.0520487	−	0.160189i	0.973702	+	0.227824i	$0.0731612\pi$
$938$		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
$943$	−10.4474			−0.340213
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.4795	−	9.79345i	0.438026	−	0.318244i	−0.346824	−	0.937930i	$-0.612740\pi$
$947$	13.4795	−	9.79345i	0.438026	−	0.318244i	0.784850	+	0.619686i	$0.212740\pi$
$948$		0			0
$949$	6.30743			0.204748
$950$		0			0
$951$	−16.7651			−0.543646
$952$		0			0
$953$	41.9537	−	30.4812i	1.35901	−	0.987382i	0.360508	−	0.932756i	$-0.382604\pi$
$953$	41.9537	−	30.4812i	1.35901	−	0.987382i	0.998507	−	0.0546255i	$-0.0173965\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.08359			0.0350275
$958$		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
$963$	−0.316774	+	0.974929i	−0.0102079	+	0.0314166i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	10.3327	+	7.50713i	0.332277	+	0.241413i	0.741396	−	0.671068i	$-0.234164\pi$
$967$	10.3327	+	7.50713i	0.332277	+	0.241413i	−0.409119	+	0.912481i	$0.634164\pi$
$968$		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
$973$	−4.55979	−	14.0336i	−0.146180	−	0.449896i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.2613	+	31.5811i	0.328288	+	1.01037i	0.969934	+	0.243367i	$0.0782518\pi$
$977$	10.2613	+	31.5811i	0.328288	+	1.01037i	−0.641646	+	0.767001i	$0.721748\pi$
$978$		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
$983$	−39.7183	−	28.8570i	−1.26682	−	0.920395i	−0.267745	−	0.963490i	$-0.586278\pi$
$983$	−39.7183	−	28.8570i	−1.26682	−	0.920395i	−0.999071	+	0.0430944i	$0.986278\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.49681	−	4.60671i	0.0476440	−	0.146633i
$988$		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
$993$	26.2157			0.831932
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.76157	+	6.36565i	−0.277482	+	0.201602i	−0.717818	−	0.696231i	$-0.754859\pi$
$997$	−8.76157	+	6.36565i	−0.277482	+	0.201602i	0.440337	+	0.897833i	$0.354859\pi$
$998$		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.m.b.901.1		8
5.2	odd	4		1500.2.o.a.349.1		16
5.3	odd	4		1500.2.o.a.349.4		16
5.4	even	2		300.2.m.a.181.2	yes	8
15.14	odd	2		900.2.n.a.181.1		8
25.2	odd	20		7500.2.d.d.1249.5		8
25.3	odd	20		1500.2.o.a.649.2		16
25.4	even	10		300.2.m.a.121.2	✓	8
25.11	even	5		7500.2.a.d.1.1		4
25.14	even	10		7500.2.a.g.1.4		4
25.21	even	5	inner	1500.2.m.b.601.1		8
25.22	odd	20		1500.2.o.a.649.3		16
25.23	odd	20		7500.2.d.d.1249.4		8
75.29	odd	10		900.2.n.a.721.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.a.121.2	✓	8	25.4	even	10
300.2.m.a.181.2	yes	8	5.4	even	2
900.2.n.a.181.1		8	15.14	odd	2
900.2.n.a.721.1		8	75.29	odd	10
1500.2.m.b.601.1		8	25.21	even	5	inner
1500.2.m.b.901.1		8	1.1	even	1	trivial
1500.2.o.a.349.1		16	5.2	odd	4
1500.2.o.a.349.4		16	5.3	odd	4
1500.2.o.a.649.2		16	25.3	odd	20
1500.2.o.a.649.3		16	25.22	odd	20
7500.2.a.d.1.1		4	25.11	even	5
7500.2.a.g.1.4		4	25.14	even	10
7500.2.d.d.1249.4		8	25.23	odd	20
7500.2.d.d.1249.5		8	25.2	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{3} -0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{3} -0.747238 q^{7} +(0.309017 - 0.951057i) q^{9} +(0.0646021 + 0.198825i) q^{11} +(0.773659 - 2.38108i) q^{13} +(-5.51712 - 4.00842i) q^{17} +(-1.00739 - 0.731913i) q^{19} +(-0.604528 + 0.439216i) q^{21} +(-1.00457 - 3.09174i) q^{23} +(-0.309017 - 0.951057i) q^{27} +(4.19332 - 3.04662i) q^{29} +(-3.02547 - 2.19813i) q^{31} +(0.169131 + 0.122881i) q^{33} +(-0.607352 + 1.86924i) q^{37} +(-0.773659 - 2.38108i) q^{39} +(0.993096 - 3.05644i) q^{41} +12.7127 q^{43} +(-5.24425 + 3.81017i) q^{47} -6.44163 q^{49} -6.81953 q^{51} +(3.35177 - 2.43520i) q^{53} -1.24520 q^{57} +(3.61882 - 11.1376i) q^{59} +(-3.85634 - 11.8686i) q^{61} +(-0.230909 + 0.710666i) q^{63} +(2.35995 + 1.71460i) q^{67} +(-2.62999 - 1.91080i) q^{69} +(-5.29912 + 3.85004i) q^{71} +(0.778516 + 2.39603i) q^{73} +(-0.0482732 - 0.148570i) q^{77} +(8.28621 - 6.02028i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-4.59240 - 3.33658i) q^{83} +(1.60171 - 4.92954i) q^{87} +(-0.284829 - 0.876615i) q^{89} +(-0.578108 + 1.77923i) q^{91} -3.73968 q^{93} +(-12.5757 + 9.13679i) q^{97} +0.209057 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 8 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 8 * q^7 - 2 * q^9	\( 8 q + 2 q^{3} + 8 q^{7} - 2 q^{9} - 2 q^{11} - 7 q^{17} + 5 q^{19} - 3 q^{21} - 7 q^{23} + 2 q^{27} + 27 q^{29} - 3 q^{31} - 3 q^{33} + 9 q^{37} + 20 q^{41} + 68 q^{43} + 7 q^{47} - 8 q^{49} - 8 q^{51} + 11 q^{53} + 10 q^{57} + 2 q^{59} - 14 q^{61} - 7 q^{63} - 28 q^{67} + 2 q^{69} - 15 q^{71} - 6 q^{73} - 17 q^{77} + 24 q^{79} - 2 q^{81} - 2 q^{83} + 23 q^{87} + 5 q^{91} + 18 q^{93} - 34 q^{97} - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 8 * q^7 - 2 * q^9 - 2 * q^11 - 7 * q^17 + 5 * q^19 - 3 * q^21 - 7 * q^23 + 2 * q^27 + 27 * q^29 - 3 * q^31 - 3 * q^33 + 9 * q^37 + 20 * q^41 + 68 * q^43 + 7 * q^47 - 8 * q^49 - 8 * q^51 + 11 * q^53 + 10 * q^57 + 2 * q^59 - 14 * q^61 - 7 * q^63 - 28 * q^67 + 2 * q^69 - 15 * q^71 - 6 * q^73 - 17 * q^77 + 24 * q^79 - 2 * q^81 - 2 * q^83 + 23 * q^87 + 5 * q^91 + 18 * q^93 - 34 * q^97 - 2 * q^99

Introduction

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