LMFDB - Embedded newform 1500.2.m.d.901.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1500.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.5
Character	$\chi$	$=$	1500.901
Dual form			1500.2.m.d.601.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{3} +1.57893 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{3} +1.57893 q^{7} +(0.309017 - 0.951057i) q^{9} +(1.19917 + 3.69066i) q^{11} +(-0.106078 + 0.326475i) q^{13} +(4.91117 + 3.56817i) q^{17} +(-2.98680 - 2.17004i) q^{19} +(1.27738 - 0.928073i) q^{21} +(0.429662 + 1.32236i) q^{23} +(-0.309017 - 0.951057i) q^{27} +(2.69395 - 1.95727i) q^{29} +(4.25135 + 3.08879i) q^{31} +(3.13946 + 2.28095i) q^{33} +(-2.64725 + 8.14739i) q^{37} +(0.106078 + 0.326475i) q^{39} +(-0.394970 + 1.21559i) q^{41} +1.42438 q^{43} +(0.303755 - 0.220691i) q^{47} -4.50698 q^{49} +6.07054 q^{51} +(9.14125 - 6.64151i) q^{53} -3.69189 q^{57} +(3.57899 - 11.0150i) q^{59} +(-3.38909 - 10.4305i) q^{61} +(0.487917 - 1.50165i) q^{63} +(8.46160 + 6.14771i) q^{67} +(1.12487 + 0.817265i) q^{69} +(8.19220 - 5.95198i) q^{71} +(4.07594 + 12.5444i) q^{73} +(1.89340 + 5.82730i) q^{77} +(-11.1640 + 8.11114i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(3.74136 + 2.71826i) q^{83} +(1.02900 - 3.16693i) q^{87} +(-2.24626 - 6.91326i) q^{89} +(-0.167490 + 0.515482i) q^{91} +5.25496 q^{93} +(4.89906 - 3.55938i) q^{97} +3.88059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	$ 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	1.57893			0.596780			0.298390	−	0.954444i	$-0.403550\pi$
$7$	1.57893			0.596780			0.298390	+	0.954444i	$0.403550\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	1.19917	+	3.69066i	0.361563	+	1.11278i	0.952106	+	0.305769i	$0.0989136\pi$
$11$	1.19917	+	3.69066i	0.361563	+	1.11278i	−0.590543	+	0.807006i	$0.701086\pi$
$12$		0			0
$13$	−0.106078	+	0.326475i	−0.0294208	+	0.0905480i	−0.964689	−	0.263393i	$-0.915159\pi$
$13$	−0.106078	+	0.326475i	−0.0294208	+	0.0905480i	0.935268	+	0.353941i	$0.115159\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.91117	+	3.56817i	1.19113	+	0.865409i	0.993384	−	0.114844i	$-0.0366367\pi$
$17$	4.91117	+	3.56817i	1.19113	+	0.865409i	0.197750	+	0.980253i	$0.436637\pi$
$18$		0			0
$19$	−2.98680	−	2.17004i	−0.685219	−	0.497841i	0.189866	−	0.981810i	$-0.439195\pi$
$19$	−2.98680	−	2.17004i	−0.685219	−	0.497841i	−0.875085	+	0.483969i	$0.839195\pi$
$20$		0			0
$21$	1.27738	−	0.928073i	0.278748	−	0.202522i
$22$		0			0
$23$	0.429662	+	1.32236i	0.0895906	+	0.275732i	0.985806	−	0.167887i	$-0.0536944\pi$
$23$	0.429662	+	1.32236i	0.0895906	+	0.275732i	−0.896216	+	0.443619i	$0.853694\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$		0			0
$29$	2.69395	−	1.95727i	0.500254	−	0.363455i	−0.308860	−	0.951107i	$-0.599948\pi$
$29$	2.69395	−	1.95727i	0.500254	−	0.363455i	0.809114	+	0.587652i	$0.199948\pi$
$30$		0			0
$31$	4.25135	+	3.08879i	0.763565	+	0.554763i	0.900002	−	0.435886i	$-0.143565\pi$
$31$	4.25135	+	3.08879i	0.763565	+	0.554763i	−0.136437	+	0.990649i	$0.543565\pi$
$32$		0			0
$33$	3.13946	+	2.28095i	0.546510	+	0.397063i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.64725	+	8.14739i	−0.435205	+	1.33942i	0.457672	+	0.889121i	$0.348683\pi$
$37$	−2.64725	+	8.14739i	−0.435205	+	1.33942i	−0.892877	+	0.450301i	$0.851317\pi$
$38$		0			0
$39$	0.106078	+	0.326475i	0.0169861	+	0.0522779i
$40$		0			0
$41$	−0.394970	+	1.21559i	−0.0616839	+	0.189844i	−0.977150	−	0.212552i	$-0.931822\pi$
$41$	−0.394970	+	1.21559i	−0.0616839	+	0.189844i	0.915466	+	0.402396i	$0.131822\pi$
$42$		0			0
$43$	1.42438			0.217216			0.108608	−	0.994085i	$-0.465361\pi$
$43$	1.42438			0.217216			0.108608	+	0.994085i	$0.465361\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.303755	−	0.220691i	0.0443072	−	0.0321911i	−0.565411	−	0.824809i	$-0.691283\pi$
$47$	0.303755	−	0.220691i	0.0443072	−	0.0321911i	0.609718	+	0.792618i	$0.291283\pi$
$48$		0			0
$49$	−4.50698			−0.643854
$50$		0			0
$51$	6.07054			0.850045
$52$		0			0
$53$	9.14125	−	6.64151i	1.25565	−	0.912282i	0.257112	−	0.966382i	$-0.417229\pi$
$53$	9.14125	−	6.64151i	1.25565	−	0.912282i	0.998536	+	0.0540999i	$0.0172289\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.69189			−0.489002
$58$		0			0
$59$	3.57899	−	11.0150i	0.465945	−	1.43403i	−0.391846	−	0.920031i	$-0.628163\pi$
$59$	3.57899	−	11.0150i	0.465945	−	1.43403i	0.857791	−	0.513999i	$-0.171837\pi$
$60$		0			0
$61$	−3.38909	−	10.4305i	−0.433928	−	1.33549i	−0.894181	−	0.447706i	$-0.852241\pi$
$61$	−3.38909	−	10.4305i	−0.433928	−	1.33549i	0.460252	−	0.887788i	$-0.347759\pi$
$62$		0			0
$63$	0.487917	−	1.50165i	0.0614717	−	0.189190i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	8.46160	+	6.14771i	1.03375	+	0.751063i	0.969056	−	0.246842i	$-0.0793930\pi$
$67$	8.46160	+	6.14771i	1.03375	+	0.751063i	0.0646937	+	0.997905i	$0.479393\pi$
$68$		0			0
$69$	1.12487	+	0.817265i	0.135418	+	0.0983871i
$70$		0			0
$71$	8.19220	−	5.95198i	0.972235	−	0.706370i	0.0162750	−	0.999868i	$-0.494819\pi$
$71$	8.19220	−	5.95198i	0.972235	−	0.706370i	0.955960	+	0.293498i	$0.0948193\pi$
$72$		0			0
$73$	4.07594	+	12.5444i	0.477052	+	1.46822i	0.843170	+	0.537648i	$0.180687\pi$
$73$	4.07594	+	12.5444i	0.477052	+	1.46822i	−0.366117	+	0.930569i	$0.619313\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.89340	+	5.82730i	0.215773	+	0.664082i
$78$		0			0
$79$	−11.1640	+	8.11114i	−1.25605	+	0.912574i	−0.998557	−	0.0537055i	$-0.982897\pi$
$79$	−11.1640	+	8.11114i	−1.25605	+	0.912574i	−0.257494	+	0.966280i	$0.582897\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	3.74136	+	2.71826i	0.410668	+	0.298367i	0.773872	−	0.633342i	$-0.218317\pi$
$83$	3.74136	+	2.71826i	0.410668	+	0.298367i	−0.363204	+	0.931709i	$0.618317\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.02900	−	3.16693i	0.110320	−	0.339530i
$88$		0			0
$89$	−2.24626	−	6.91326i	−0.238103	−	0.732805i	−0.996695	−	0.0812387i	$-0.974112\pi$
$89$	−2.24626	−	6.91326i	−0.238103	−	0.732805i	0.758592	−	0.651566i	$-0.225888\pi$
$90$		0			0
$91$	−0.167490	+	0.515482i	−0.0175578	+	0.0540372i
$92$		0			0
$93$	5.25496			0.544914
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.89906	−	3.55938i	0.497424	−	0.361400i	−0.310608	−	0.950538i	$-0.600533\pi$
$97$	4.89906	−	3.55938i	0.497424	−	0.361400i	0.808032	+	0.589138i	$0.200533\pi$
$98$		0			0
$99$	3.88059			0.390014
$100$		0			0
$101$	3.23036			0.321432			0.160716	−	0.987001i	$-0.448620\pi$
$101$	3.23036			0.321432			0.160716	+	0.987001i	$0.448620\pi$
$102$		0			0
$103$	−6.22721	+	4.52433i	−0.613585	+	0.445796i	−0.850675	−	0.525692i	$-0.823806\pi$
$103$	−6.22721	+	4.52433i	−0.613585	+	0.445796i	0.237090	+	0.971488i	$0.423806\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−18.0376			−1.74376			−0.871878	−	0.489722i	$-0.837098\pi$
$107$	−18.0376			−1.74376			−0.871878	+	0.489722i	$0.837098\pi$
$108$		0			0
$109$	5.16860	−	15.9073i	0.495062	−	1.52364i	−0.321799	−	0.946808i	$-0.604288\pi$
$109$	5.16860	−	15.9073i	0.495062	−	1.52364i	0.816861	−	0.576835i	$-0.195712\pi$
$110$		0			0
$111$	2.64725	+	8.14739i	0.251266	+	0.773316i
$112$		0			0
$113$	−0.701155	+	2.15793i	−0.0659591	+	0.203001i	−0.978604	−	0.205751i	$-0.934036\pi$
$113$	−0.701155	+	2.15793i	−0.0659591	+	0.203001i	0.912645	+	0.408753i	$0.134036\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.277717	+	0.201773i	0.0256749	+	0.0186539i
$118$		0			0
$119$	7.75440	+	5.63390i	0.710845	+	0.516459i
$120$		0			0
$121$	−3.28377	+	2.38580i	−0.298524	+	0.216891i
$122$		0			0
$123$	0.394970	+	1.21559i	0.0356132	+	0.109606i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.465767	+	1.43348i	0.0413301	+	0.127201i	0.969593	−	0.244725i	$-0.0786976\pi$
$127$	0.465767	+	1.43348i	0.0413301	+	0.127201i	−0.928262	+	0.371926i	$0.878698\pi$
$128$		0			0
$129$	1.15235	−	0.837231i	0.101459	−	0.0737141i
$130$		0			0
$131$	12.8948	+	9.36859i	1.12662	+	0.818537i	0.985199	−	0.171412i	$-0.0548330\pi$
$131$	12.8948	+	9.36859i	1.12662	+	0.818537i	0.141421	+	0.989950i	$0.454833\pi$
$132$		0			0
$133$	−4.71595	−	3.42634i	−0.408925	−	0.297101i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.68307	−	5.17996i	0.143795	−	0.442554i	−0.853059	−	0.521814i	$-0.825256\pi$
$137$	1.68307	−	5.17996i	0.143795	−	0.442554i	0.996854	+	0.0792596i	$0.0252556\pi$
$138$		0			0
$139$	−3.05409	−	9.39953i	−0.259045	−	0.797258i	−0.993006	−	0.118066i	$-0.962331\pi$
$139$	−3.05409	−	9.39953i	−0.259045	−	0.797258i	0.733961	−	0.679192i	$-0.237669\pi$
$140$		0			0
$141$	0.116024	−	0.357085i	0.00977099	−	0.0300720i
$142$		0			0
$143$	−1.33211			−0.111397
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.64622	+	2.64913i	−0.300735	+	0.218497i
$148$		0			0
$149$	0.0649364			0.00531979			0.00265990	−	0.999996i	$-0.499153\pi$
$149$	0.0649364			0.00531979			0.00265990	+	0.999996i	$0.499153\pi$
$150$		0			0
$151$	−12.1221			−0.986481			−0.493240	−	0.869893i	$-0.664188\pi$
$151$	−12.1221			−0.986481			−0.493240	+	0.869893i	$0.664188\pi$
$152$		0			0
$153$	4.91117	−	3.56817i	0.397044	−	0.288470i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	23.4721			1.87328			0.936638	−	0.350300i	$-0.113920\pi$
$157$	23.4721			1.87328			0.936638	+	0.350300i	$0.113920\pi$
$158$		0			0
$159$	3.49165	−	10.7462i	0.276906	−	0.852228i
$160$		0			0
$161$	0.678406	+	2.08792i	0.0534659	+	0.164551i
$162$		0			0
$163$	−1.85282	+	5.70240i	−0.145124	+	0.446646i	−0.997027	−	0.0770538i	$-0.975449\pi$
$163$	−1.85282	+	5.70240i	−0.145124	+	0.446646i	0.851903	+	0.523700i	$0.175449\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.17649	−	3.76094i	−0.400569	−	0.291030i	0.369204	−	0.929348i	$-0.379630\pi$
$167$	−5.17649	−	3.76094i	−0.400569	−	0.291030i	−0.769773	+	0.638318i	$0.779630\pi$
$168$		0			0
$169$	10.4219	+	7.57194i	0.801684	+	0.582457i
$170$		0			0
$171$	−2.98680	+	2.17004i	−0.228406	+	0.165947i
$172$		0			0
$173$	1.61350	+	4.96583i	0.122672	+	0.377545i	0.993470	−	0.114096i	$-0.0363972\pi$
$173$	1.61350	+	4.96583i	0.122672	+	0.377545i	−0.870798	+	0.491641i	$0.836397\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.57899	−	11.0150i	−0.269013	−	0.827937i
$178$		0			0
$179$	−18.8534	+	13.6978i	−1.40917	+	1.02382i	−0.415724	+	0.909491i	$0.636472\pi$
$179$	−18.8534	+	13.6978i	−1.40917	+	1.02382i	−0.993443	+	0.114329i	$0.963528\pi$
$180$		0			0
$181$	−20.3662	−	14.7969i	−1.51380	−	1.09984i	−0.964454	−	0.264251i	$-0.914875\pi$
$181$	−20.3662	−	14.7969i	−1.51380	−	1.09984i	−0.549350	−	0.835592i	$-0.685125\pi$
$182$		0			0
$183$	−8.87275	−	6.44643i	−0.655893	−	0.476534i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.27959	+	22.4043i	−0.532336	+	1.63836i
$188$		0			0
$189$	−0.487917	−	1.50165i	−0.0354907	−	0.109229i
$190$		0			0
$191$	2.48188	−	7.63843i	0.179582	−	0.552697i	−0.820231	−	0.572033i	$-0.806155\pi$
$191$	2.48188	−	7.63843i	0.179582	−	0.552697i	0.999813	+	0.0193354i	$0.00615503\pi$
$192$		0			0
$193$	−20.2575			−1.45817			−0.729084	−	0.684424i	$-0.760054\pi$
$193$	−20.2575			−1.45817			−0.729084	+	0.684424i	$0.760054\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.1931	−	11.7650i	1.15371	−	0.838221i	0.164742	−	0.986337i	$-0.447321\pi$
$197$	16.1931	−	11.7650i	1.15371	−	0.838221i	0.988970	+	0.148115i	$0.0473207\pi$
$198$		0			0
$199$	−22.4180			−1.58917			−0.794585	−	0.607153i	$-0.792311\pi$
$199$	−22.4180			−1.58917			−0.794585	+	0.607153i	$0.792311\pi$
$200$		0			0
$201$	10.4591			0.737729
$202$		0			0
$203$	4.25356	−	3.09039i	0.298541	−	0.216903i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.39041			0.0966404
$208$		0			0
$209$	4.42719	−	13.6255i	0.306235	−	0.942495i
$210$		0			0
$211$	2.67780	+	8.24142i	0.184347	+	0.567363i	0.999937	−	0.0112687i	$-0.00358702\pi$
$211$	2.67780	+	8.24142i	0.184347	+	0.567363i	−0.815589	+	0.578631i	$0.803587\pi$
$212$		0			0
$213$	3.12914	−	9.63050i	0.214405	−	0.659871i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	6.71259	+	4.87698i	0.455680	+	0.331071i
$218$		0			0
$219$	10.6709	+	7.75289i	0.721076	+	0.523892i
$220$		0			0
$221$	−1.68589	+	1.22487i	−0.113405	+	0.0823937i
$222$		0			0
$223$	−3.82686	−	11.7779i	−0.256266	−	0.788705i	−0.993578	−	0.113152i	$-0.963905\pi$
$223$	−3.82686	−	11.7779i	−0.256266	−	0.788705i	0.737312	−	0.675552i	$-0.236095\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.63116	−	17.3309i	−0.373753	−	1.15029i	−0.944316	−	0.329040i	$-0.893275\pi$
$227$	−5.63116	−	17.3309i	−0.373753	−	1.15029i	0.570563	−	0.821254i	$-0.306725\pi$
$228$		0			0
$229$	−13.2812	+	9.64932i	−0.877643	+	0.637645i	−0.932627	−	0.360842i	$-0.882489\pi$
$229$	−13.2812	+	9.64932i	−0.877643	+	0.637645i	0.0549837	+	0.998487i	$0.482489\pi$
$230$		0			0
$231$	4.95699	+	3.60147i	0.326146	+	0.236959i
$232$		0			0
$233$	4.15658	+	3.01993i	0.272307	+	0.197842i	0.715555	−	0.698557i	$-0.246174\pi$
$233$	4.15658	+	3.01993i	0.272307	+	0.197842i	−0.443248	+	0.896399i	$0.646174\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.26428	+	13.1241i	−0.276995	+	0.852502i
$238$		0			0
$239$	7.58924	+	23.3573i	0.490907	+	1.51086i	0.823239	+	0.567694i	$0.192165\pi$
$239$	7.58924	+	23.3573i	0.490907	+	1.51086i	−0.332332	+	0.943162i	$0.607835\pi$
$240$		0			0
$241$	1.49413	−	4.59846i	0.0962454	−	0.296213i	−0.891331	−	0.453353i	$-0.850228\pi$
$241$	1.49413	−	4.59846i	0.0962454	−	0.296213i	0.987576	+	0.157141i	$0.0502276\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.02530	−	0.744923i	0.0652382	−	0.0473983i
$248$		0			0
$249$	4.62458			0.293071
$250$		0			0
$251$	−15.1395			−0.955594			−0.477797	−	0.878470i	$-0.658565\pi$
$251$	−15.1395			−0.955594			−0.477797	+	0.878470i	$0.658565\pi$
$252$		0			0
$253$	−4.36515	+	3.17147i	−0.274435	+	0.199388i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−22.7976			−1.42207			−0.711036	−	0.703155i	$-0.751774\pi$
$257$	−22.7976			−1.42207			−0.711036	+	0.703155i	$0.751774\pi$
$258$		0			0
$259$	−4.17982	+	12.8642i	−0.259722	+	0.799341i
$260$		0			0
$261$	−1.02900	−	3.16693i	−0.0636933	−	0.196028i
$262$		0			0
$263$	2.91853	−	8.98231i	0.179964	−	0.553873i	−0.819861	−	0.572562i	$-0.805949\pi$
$263$	2.91853	−	8.98231i	0.179964	−	0.553873i	0.999825	+	0.0186895i	$0.00594941\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.88077	−	4.27263i	−0.359898	−	0.261481i
$268$		0			0
$269$	23.7720	+	17.2714i	1.44940	+	1.05305i	0.985970	+	0.166921i	$0.0533825\pi$
$269$	23.7720	+	17.2714i	1.44940	+	1.05305i	0.463433	+	0.886132i	$0.346618\pi$
$270$		0			0
$271$	−12.5303	+	9.10380i	−0.761162	+	0.553016i	−0.899266	−	0.437401i	$-0.855899\pi$
$271$	−12.5303	+	9.10380i	−0.761162	+	0.553016i	0.138105	+	0.990418i	$0.455899\pi$
$272$		0			0
$273$	0.167490	+	0.515482i	0.0101370	+	0.0311984i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.75225	−	14.6259i	−0.285535	−	0.878786i	−0.986238	−	0.165333i	$-0.947130\pi$
$277$	−4.75225	−	14.6259i	−0.285535	−	0.878786i	0.700703	−	0.713453i	$-0.252870\pi$
$278$		0			0
$279$	4.25135	−	3.08879i	0.254522	−	0.184921i
$280$		0			0
$281$	−3.13314	−	2.27636i	−0.186908	−	0.135796i	0.490397	−	0.871499i	$-0.336852\pi$
$281$	−3.13314	−	2.27636i	−0.186908	−	0.135796i	−0.677304	+	0.735703i	$0.736852\pi$
$282$		0			0
$283$	−9.61673	−	6.98697i	−0.571655	−	0.415332i	0.264051	−	0.964509i	$-0.414941\pi$
$283$	−9.61673	−	6.98697i	−0.571655	−	0.415332i	−0.835706	+	0.549177i	$0.814941\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.623630	+	1.91934i	−0.0368117	+	0.113295i
$288$		0			0
$289$	6.13443	+	18.8798i	0.360849	+	1.11058i
$290$		0			0
$291$	1.87127	−	5.75919i	0.109696	−	0.337610i
$292$		0			0
$293$	15.4596			0.903161			0.451581	−	0.892230i	$-0.350860\pi$
$293$	15.4596			0.903161			0.451581	+	0.892230i	$0.350860\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.13946	−	2.28095i	0.182170	−	0.132354i
$298$		0			0
$299$	−0.477297			−0.0276028
$300$		0			0
$301$	2.24900			0.129630
$302$		0			0
$303$	2.61341	−	1.89876i	0.150137	−	0.109081i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−26.6092			−1.51867			−0.759334	−	0.650702i	$-0.774475\pi$
$307$	−26.6092			−1.51867			−0.759334	+	0.650702i	$0.774475\pi$
$308$		0			0
$309$	−2.37858	+	7.32052i	−0.135313	+	0.416450i
$310$		0			0
$311$	−1.69361	−	5.21238i	−0.0960356	−	0.295567i	0.891487	−	0.453047i	$-0.149663\pi$
$311$	−1.69361	−	5.21238i	−0.0960356	−	0.295567i	−0.987522	+	0.157480i	$0.949663\pi$
$312$		0			0
$313$	−2.30248	+	7.08632i	−0.130144	+	0.400542i	−0.994803	−	0.101817i	$-0.967534\pi$
$313$	−2.30248	+	7.08632i	−0.130144	+	0.400542i	0.864659	+	0.502359i	$0.167534\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.40152	−	1.74481i	−0.134883	−	0.0979981i	0.518298	−	0.855200i	$-0.326566\pi$
$317$	−2.40152	−	1.74481i	−0.134883	−	0.0979981i	−0.653181	+	0.757202i	$0.726566\pi$
$318$		0			0
$319$	10.4541	+	7.59535i	0.585317	+	0.425258i
$320$		0			0
$321$	−14.5927	+	10.6022i	−0.814485	+	0.591758i
$322$		0			0
$323$	−6.92561	−	21.3148i	−0.385351	−	1.18599i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−5.16860	−	15.9073i	−0.285824	−	0.879676i
$328$		0			0
$329$	0.479608	−	0.348456i	0.0264416	−	0.0192110i
$330$		0			0
$331$	−22.1899	−	16.1219i	−1.21967	−	0.886140i	−0.223594	−	0.974682i	$-0.571779\pi$
$331$	−22.1899	−	16.1219i	−1.21967	−	0.886140i	−0.996072	+	0.0885426i	$0.971779\pi$
$332$		0			0
$333$	6.93058	+	5.03536i	0.379794	+	0.275936i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	2.32287	−	7.14905i	0.126535	−	0.389433i	−0.867643	−	0.497188i	$-0.834366\pi$
$337$	2.32287	−	7.14905i	0.126535	−	0.389433i	0.994178	+	0.107754i	$0.0343660\pi$
$338$		0			0
$339$	0.701155	+	2.15793i	0.0380815	+	0.117203i
$340$		0			0
$341$	−6.30157	+	19.3943i	−0.341249	+	1.05026i
$342$		0			0
$343$	−18.1687			−0.981019
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.70380	−	7.05022i	0.520927	−	0.378476i	−0.296026	−	0.955180i	$-0.595661\pi$
$347$	9.70380	−	7.05022i	0.520927	−	0.378476i	0.816953	+	0.576704i	$0.195661\pi$
$348$		0			0
$349$	−3.50169			−0.187441			−0.0937207	−	0.995599i	$-0.529876\pi$
$349$	−3.50169			−0.187441			−0.0937207	+	0.995599i	$0.529876\pi$
$350$		0			0
$351$	0.343277			0.0183227
$352$		0			0
$353$	−20.1867	+	14.6665i	−1.07443	+	0.780617i	−0.976703	−	0.214596i	$-0.931156\pi$
$353$	−20.1867	+	14.6665i	−1.07443	+	0.780617i	−0.0977244	+	0.995214i	$0.531156\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	9.58496			0.507290
$358$		0			0
$359$	0.247954	−	0.763123i	0.0130865	−	0.0402761i	−0.944300	−	0.329086i	$-0.893259\pi$
$359$	0.247954	−	0.763123i	0.0130865	−	0.0402761i	0.957387	+	0.288810i	$0.0932595\pi$
$360$		0			0
$361$	−1.65941	−	5.10714i	−0.0873374	−	0.268797i
$362$		0			0
$363$	−1.25429	+	3.86030i	−0.0658330	+	0.202613i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.7864	+	9.28986i	0.667445	+	0.484927i	0.869169	−	0.494515i	$-0.164654\pi$
$367$	12.7864	+	9.28986i	0.667445	+	0.484927i	−0.201724	+	0.979442i	$0.564654\pi$
$368$		0			0
$369$	1.03404	+	0.751277i	0.0538302	+	0.0391099i
$370$		0			0
$371$	14.4334	−	10.4865i	0.749346	−	0.544431i
$372$		0			0
$373$	−1.11542	−	3.43291i	−0.0577543	−	0.177750i	0.918018	−	0.396540i	$-0.129789\pi$
$373$	−1.11542	−	3.43291i	−0.0577543	−	0.177750i	−0.975772	+	0.218790i	$0.929789\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.353230	+	1.08713i	0.0181923	+	0.0559901i
$378$		0			0
$379$	−22.0967	+	16.0542i	−1.13503	+	0.824647i	−0.986419	−	0.164249i	$-0.947480\pi$
$379$	−22.0967	+	16.0542i	−1.13503	+	0.824647i	−0.148610	+	0.988896i	$0.547480\pi$
$380$		0			0
$381$	1.21939	+	0.885941i	0.0624714	+	0.0453881i
$382$		0			0
$383$	−15.5991	−	11.3334i	−0.797079	−	0.579112i	0.112977	−	0.993598i	$-0.463961\pi$
$383$	−15.5991	−	11.3334i	−0.797079	−	0.579112i	−0.910056	+	0.414486i	$0.863961\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.440159	−	1.35467i	0.0223745	−	0.0688617i
$388$		0			0
$389$	−5.27164	−	16.2244i	−0.267283	−	0.822612i	−0.991159	−	0.132682i	$-0.957641\pi$
$389$	−5.27164	−	16.2244i	−0.267283	−	0.822612i	0.723876	−	0.689930i	$-0.242359\pi$
$390$		0			0
$391$	−2.60828	+	8.02745i	−0.131906	+	0.405966i
$392$		0			0
$393$	15.9388			0.804006
$394$		0			0
$395$		0			0
$396$		0			0
$397$	22.1380	−	16.0842i	1.11108	−	0.807243i	0.128243	−	0.991743i	$-0.459066\pi$
$397$	22.1380	−	16.0842i	1.11108	−	0.807243i	0.982833	+	0.184499i	$0.0590664\pi$
$398$		0			0
$399$	−5.82924			−0.291827
$400$		0			0
$401$	−14.7793			−0.738042			−0.369021	−	0.929421i	$-0.620307\pi$
$401$	−14.7793			−0.738042			−0.369021	+	0.929421i	$0.620307\pi$
$402$		0			0
$403$	−1.45939	+	1.06031i	−0.0726974	+	0.0528177i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−33.2437			−1.64783
$408$		0			0
$409$	6.72523	−	20.6981i	0.332541	−	1.02346i	−0.635379	−	0.772200i	$-0.719156\pi$
$409$	6.72523	−	20.6981i	0.332541	−	1.02346i	0.967921	−	0.251256i	$-0.0808438\pi$
$410$		0			0
$411$	−1.68307	−	5.17996i	−0.0830198	−	0.255509i
$412$		0			0
$413$	5.65098	−	17.3919i	0.278066	−	0.855800i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−7.99572	−	5.80923i	−0.391552	−	0.284479i
$418$		0			0
$419$	3.67055	+	2.66681i	0.179318	+	0.130282i	0.673824	−	0.738892i	$-0.264651\pi$
$419$	3.67055	+	2.66681i	0.179318	+	0.130282i	−0.494505	+	0.869175i	$0.664651\pi$
$420$		0			0
$421$	−2.47193	+	1.79596i	−0.120475	+	0.0875300i	−0.646391	−	0.763006i	$-0.723722\pi$
$421$	−2.47193	+	1.79596i	−0.120475	+	0.0875300i	0.525916	+	0.850536i	$0.323722\pi$
$422$		0			0
$423$	−0.116024	−	0.357085i	−0.00564128	−	0.0173621i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.35114	−	16.4691i	−0.258960	−	0.796996i
$428$		0			0
$429$	−1.07770	+	0.782997i	−0.0520320	+	0.0378035i
$430$		0			0
$431$	15.2881	+	11.1074i	0.736400	+	0.535026i	0.891582	−	0.452860i	$-0.149596\pi$
$431$	15.2881	+	11.1074i	0.736400	+	0.535026i	−0.155181	+	0.987886i	$0.549596\pi$
$432$		0			0
$433$	−2.76602	−	2.00963i	−0.132927	−	0.0965768i	0.519335	−	0.854571i	$-0.326180\pi$
$433$	−2.76602	−	2.00963i	−0.132927	−	0.0965768i	−0.652262	+	0.757994i	$0.726180\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.58626	−	4.88201i	0.0758812	−	0.233538i
$438$		0			0
$439$	−1.84058	−	5.66473i	−0.0878462	−	0.270363i	0.897477	−	0.441061i	$-0.145398\pi$
$439$	−1.84058	−	5.66473i	−0.0878462	−	0.270363i	−0.985323	+	0.170698i	$0.945398\pi$
$440$		0			0
$441$	−1.39273	+	4.28639i	−0.0663206	+	0.204114i
$442$		0			0
$443$	−33.0705			−1.57122			−0.785612	−	0.618719i	$-0.787652\pi$
$443$	−33.0705			−1.57122			−0.785612	+	0.618719i	$0.787652\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.0525346	−	0.0381686i	0.00248480	−	0.00180531i
$448$		0			0
$449$	−8.68077			−0.409671			−0.204835	−	0.978796i	$-0.565666\pi$
$449$	−8.68077			−0.409671			−0.204835	+	0.978796i	$0.565666\pi$
$450$		0			0
$451$	−4.95997			−0.233556
$452$		0			0
$453$	−9.80697	+	7.12518i	−0.460771	+	0.334770i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.3667			−0.625269			−0.312635	−	0.949873i	$-0.601212\pi$
$457$	−13.3667			−0.625269			−0.312635	+	0.949873i	$0.601212\pi$
$458$		0			0
$459$	1.87590	−	5.77342i	0.0875595	−	0.269480i
$460$		0			0
$461$	−12.6568	−	38.9537i	−0.589487	−	1.81425i	−0.580453	−	0.814294i	$-0.697124\pi$
$461$	−12.6568	−	38.9537i	−0.589487	−	1.81425i	−0.00903372	−	0.999959i	$-0.502876\pi$
$462$		0			0
$463$	−7.14695	+	21.9961i	−0.332147	+	1.02224i	0.635963	+	0.771719i	$0.280603\pi$
$463$	−7.14695	+	21.9961i	−0.332147	+	1.02224i	−0.968110	+	0.250524i	$0.919397\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	24.5043	+	17.8034i	1.13392	+	0.823845i	0.986261	−	0.165193i	$-0.0528247\pi$
$467$	24.5043	+	17.8034i	1.13392	+	0.823845i	0.147664	+	0.989038i	$0.452825\pi$
$468$		0			0
$469$	13.3603	+	9.70682i	0.616921	+	0.448219i
$470$		0			0
$471$	18.9893	−	13.7965i	0.874981	−	0.635711i
$472$		0			0
$473$	1.70807	+	5.25691i	0.0785373	+	0.241713i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.49165	−	10.7462i	−0.159872	−	0.492034i
$478$		0			0
$479$	19.4809	−	14.1537i	0.890107	−	0.646700i	−0.0457990	−	0.998951i	$-0.514583\pi$
$479$	19.4809	−	14.1537i	0.890107	−	0.646700i	0.935906	+	0.352250i	$0.114583\pi$
$480$		0			0
$481$	−2.37911	−	1.72852i	−0.108478	−	0.0788138i
$482$		0			0
$483$	1.77609	+	1.29040i	0.0808149	+	0.0587155i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.696777	+	2.14446i	−0.0315740	+	0.0971747i	−0.965602	−	0.260026i	$-0.916269\pi$
$487$	−0.696777	+	2.14446i	−0.0315740	+	0.0971747i	0.934028	+	0.357201i	$0.116269\pi$
$488$		0			0
$489$	1.85282	+	5.70240i	0.0837875	+	0.257871i
$490$		0			0
$491$	−8.84093	+	27.2096i	−0.398986	+	1.22795i	0.526828	+	0.849972i	$0.323381\pi$
$491$	−8.84093	+	27.2096i	−0.398986	+	1.22795i	−0.925814	+	0.377980i	$0.876619\pi$
$492$		0			0
$493$	20.2143			0.910406
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.9349	−	9.39777i	0.580210	−	0.421547i
$498$		0			0
$499$	−26.9489			−1.20640			−0.603199	−	0.797590i	$-0.706108\pi$
$499$	−26.9489			−1.20640			−0.603199	+	0.797590i	$0.706108\pi$
$500$		0			0
$501$	−6.39850			−0.285864
$502$		0			0
$503$	0.337358	−	0.245105i	0.0150421	−	0.0109287i	−0.580239	−	0.814446i	$-0.697041\pi$
$503$	0.337358	−	0.245105i	0.0150421	−	0.0109287i	0.595281	+	0.803518i	$0.297041\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.8822			0.572117
$508$		0			0
$509$	4.14176	−	12.7470i	0.183580	−	0.565002i	−0.816341	−	0.577571i	$-0.804001\pi$
$509$	4.14176	−	12.7470i	0.183580	−	0.565002i	0.999921	+	0.0125684i	$0.00400074\pi$
$510$		0			0
$511$	6.43563	+	19.8068i	0.284695	+	0.876202i
$512$		0			0
$513$	−1.14086	+	3.51119i	−0.0503700	+	0.155023i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	1.17875	+	0.856410i	0.0518412	+	0.0376649i
$518$		0			0
$519$	4.22419	+	3.06905i	0.185421	+	0.134716i
$520$		0			0
$521$	−17.0496	+	12.3872i	−0.746956	+	0.542695i	−0.894882	−	0.446303i	$-0.852740\pi$
$521$	−17.0496	+	12.3872i	−0.746956	+	0.542695i	0.147926	+	0.988998i	$0.452740\pi$
$522$		0			0
$523$	−3.66974	−	11.2943i	−0.160467	−	0.493866i	0.838207	−	0.545352i	$-0.183604\pi$
$523$	−3.66974	−	11.2943i	−0.160467	−	0.493866i	−0.998674	+	0.0514866i	$0.983604\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.85777	+	30.3391i	0.429411	+	1.32159i
$528$		0			0
$529$	17.0434	−	12.3827i	0.741016	−	0.538379i
$530$		0			0
$531$	−9.36991	−	6.80764i	−0.406620	−	0.295426i
$532$		0			0
$533$	−0.354963	−	0.257896i	−0.0153752	−	0.0111707i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−7.20135	+	22.1635i	−0.310761	+	0.956424i
$538$		0			0
$539$	−5.40462	−	16.6337i	−0.232793	−	0.716464i
$540$		0			0
$541$	11.2993	−	34.7757i	0.485796	−	1.49513i	−0.345029	−	0.938592i	$-0.612131\pi$
$541$	11.2993	−	34.7757i	0.485796	−	1.49513i	0.830825	−	0.556534i	$-0.187869\pi$
$542$		0			0
$543$	−25.1739			−1.08032
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−32.0219	+	23.2652i	−1.36916	+	0.994750i	−0.371353	+	0.928492i	$0.621106\pi$
$547$	−32.0219	+	23.2652i	−1.36916	+	0.994750i	−0.997803	+	0.0662579i	$0.978894\pi$
$548$		0			0
$549$	−10.9673			−0.468074
$550$		0			0
$551$	−12.2936			−0.523726
$552$		0			0
$553$	−17.6272	+	12.8069i	−0.749586	+	0.544606i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.1804			−0.516102			−0.258051	−	0.966131i	$-0.583080\pi$
$557$	−12.1804			−0.516102			−0.258051	+	0.966131i	$0.583080\pi$
$558$		0			0
$559$	−0.151096	+	0.465026i	−0.00639068	+	0.0196685i
$560$		0			0
$561$	7.27959	+	22.4043i	0.307345	+	0.945909i
$562$		0			0
$563$	−11.3065	+	34.7979i	−0.476513	+	1.46656i	0.367394	+	0.930065i	$0.380250\pi$
$563$	−11.3065	+	34.7979i	−0.476513	+	1.46656i	−0.843907	+	0.536490i	$0.819750\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.27738	−	0.928073i	−0.0536450	−	0.0389754i
$568$		0			0
$569$	27.3735	+	19.8880i	1.14756	+	0.833749i	0.988154	−	0.153464i	$-0.0490430\pi$
$569$	27.3735	+	19.8880i	1.14756	+	0.833749i	0.159403	+	0.987214i	$0.449043\pi$
$570$		0			0
$571$	0.974239	−	0.707826i	0.0407706	−	0.0296216i	−0.567213	−	0.823571i	$-0.691978\pi$
$571$	0.974239	−	0.707826i	0.0407706	−	0.0296216i	0.607984	+	0.793949i	$0.291978\pi$
$572$		0			0
$573$	−2.48188	−	7.63843i	−0.103682	−	0.319100i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−5.06913	−	15.6012i	−0.211031	−	0.649485i	−0.999412	−	0.0342981i	$-0.989080\pi$
$577$	−5.06913	−	15.6012i	−0.211031	−	0.649485i	0.788381	−	0.615187i	$-0.210920\pi$
$578$		0			0
$579$	−16.3887	+	11.9071i	−0.681090	+	0.494841i
$580$		0			0
$581$	5.90735	+	4.29194i	0.245078	+	0.178060i
$582$		0			0
$583$	35.4734	+	25.7730i	1.46916	+	1.06741i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.4114	−	32.0429i	0.429724	−	1.32255i	−0.468674	−	0.883371i	$-0.655268\pi$
$587$	10.4114	−	32.0429i	0.429724	−	1.32255i	0.898398	−	0.439182i	$-0.144732\pi$
$588$		0			0
$589$	−5.99515	−	18.4512i	−0.247026	−	0.760267i
$590$		0			0
$591$	6.18522	−	19.0362i	0.254426	−	0.783043i
$592$		0			0
$593$	32.2208			1.32315			0.661576	−	0.749878i	$-0.269888\pi$
$593$	32.2208			1.32315			0.661576	+	0.749878i	$0.269888\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−18.1365	+	13.1770i	−0.742279	+	0.539297i
$598$		0			0
$599$	−14.7284			−0.601784			−0.300892	−	0.953658i	$-0.597284\pi$
$599$	−14.7284			−0.601784			−0.300892	+	0.953658i	$0.597284\pi$
$600$		0			0
$601$	35.5643			1.45070			0.725348	−	0.688382i	$-0.241679\pi$
$601$	35.5643			1.45070			0.725348	+	0.688382i	$0.241679\pi$
$602$		0			0
$603$	8.46160	−	6.14771i	0.344583	−	0.250354i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	16.0986			0.653421			0.326710	−	0.945124i	$-0.394060\pi$
$607$	16.0986			0.653421			0.326710	+	0.945124i	$0.394060\pi$
$608$		0			0
$609$	1.62471	−	5.00036i	0.0658368	−	0.202625i
$610$		0			0
$611$	0.0398283	+	0.122579i	0.00161128	+	0.00495902i
$612$		0			0
$613$	13.3700	−	41.1487i	0.540010	−	1.66198i	−0.192559	−	0.981285i	$-0.561679\pi$
$613$	13.3700	−	41.1487i	0.540010	−	1.66198i	0.732569	−	0.680693i	$-0.238321\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.28217	+	0.931550i	0.0516182	+	0.0375028i	0.613295	−	0.789854i	$-0.289844\pi$
$617$	1.28217	+	0.931550i	0.0516182	+	0.0375028i	−0.561677	+	0.827357i	$0.689844\pi$
$618$		0			0
$619$	10.9048	+	7.92281i	0.438301	+	0.318444i	0.784960	−	0.619547i	$-0.212684\pi$
$619$	10.9048	+	7.92281i	0.438301	+	0.318444i	−0.346658	+	0.937991i	$0.612684\pi$
$620$		0			0
$621$	1.12487	−	0.817265i	0.0451394	−	0.0327957i
$622$		0			0
$623$	−3.54668	−	10.9156i	−0.142095	−	0.437323i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−4.42719	−	13.6255i	−0.176805	−	0.544150i
$628$		0			0
$629$	−42.0724	+	30.5674i	−1.67754	+	1.21880i
$630$		0			0
$631$	23.6944	+	17.2150i	0.943261	+	0.685319i	0.949203	−	0.314663i	$-0.101892\pi$
$631$	23.6944	+	17.2150i	0.943261	+	0.685319i	−0.00594245	+	0.999982i	$0.501892\pi$
$632$		0			0
$633$	7.01057	+	5.09348i	0.278645	+	0.202448i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.478092	−	1.47142i	0.0189427	−	0.0582997i
$638$		0			0
$639$	−3.12914	−	9.63050i	−0.123787	−	0.380977i
$640$		0			0
$641$	−5.34325	+	16.4448i	−0.211046	+	0.649532i	0.788365	+	0.615208i	$0.210928\pi$
$641$	−5.34325	+	16.4448i	−0.211046	+	0.649532i	−0.999411	+	0.0343242i	$0.989072\pi$
$642$		0			0
$643$	46.8857			1.84899			0.924497	−	0.381190i	$-0.124486\pi$
$643$	46.8857			1.84899			0.924497	+	0.381190i	$0.124486\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.6474	−	8.46236i	0.457908	−	0.332690i	−0.334802	−	0.942288i	$-0.608669\pi$
$647$	11.6474	−	8.46236i	0.457908	−	0.332690i	0.792710	+	0.609599i	$0.208669\pi$
$648$		0			0
$649$	44.9444			1.76422
$650$		0			0
$651$	8.29722			0.325194
$652$		0			0
$653$	25.8746	−	18.7990i	1.01255	−	0.735661i	0.0478084	−	0.998857i	$-0.484776\pi$
$653$	25.8746	−	18.7990i	1.01255	−	0.735661i	0.964743	+	0.263195i	$0.0847763\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	13.1900			0.514591
$658$		0			0
$659$	5.77517	−	17.7742i	0.224969	−	0.692383i	−0.773326	−	0.634009i	$-0.781408\pi$
$659$	5.77517	−	17.7742i	0.224969	−	0.692383i	0.998295	−	0.0583742i	$-0.0185917\pi$
$660$		0			0
$661$	−0.209866	−	0.645901i	−0.00816284	−	0.0251226i	0.946892	−	0.321551i	$-0.104204\pi$
$661$	−0.209866	−	0.645901i	−0.00816284	−	0.0251226i	−0.955055	+	0.296429i	$0.904204\pi$
$662$		0			0
$663$	−0.643952	+	1.98188i	−0.0250090	+	0.0769699i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.74570	+	2.72141i	0.145034	+	0.105373i
$668$		0			0
$669$	−10.0189	−	7.27912i	−0.387351	−	0.281427i
$670$		0			0
$671$	34.4315	−	25.0159i	1.32921	−	0.965730i
$672$		0			0
$673$	2.24247	+	6.90162i	0.0864410	+	0.266038i	0.984929	−	0.172961i	$-0.0553333\pi$
$673$	2.24247	+	6.90162i	0.0864410	+	0.266038i	−0.898488	+	0.438999i	$0.855333\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.4922	+	32.2918i	0.403249	+	1.24107i	0.922348	+	0.386359i	$0.126267\pi$
$677$	10.4922	+	32.2918i	0.403249	+	1.24107i	−0.519099	+	0.854714i	$0.673733\pi$
$678$		0			0
$679$	7.73528	−	5.62001i	0.296853	−	0.215676i
$680$		0			0
$681$	−14.7426	−	10.7111i	−0.564936	−	0.410450i
$682$		0			0
$683$	22.7802	+	16.5508i	0.871660	+	0.633298i	0.931032	−	0.364938i	$-0.118910\pi$
$683$	22.7802	+	16.5508i	0.871660	+	0.633298i	−0.0593717	+	0.998236i	$0.518910\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−5.07295	+	15.6129i	−0.193545	+	0.595670i
$688$		0			0
$689$	1.19860	+	3.68892i	0.0456631	+	0.140536i
$690$		0			0
$691$	6.85416	−	21.0949i	0.260745	−	0.802489i	−0.731899	−	0.681413i	$-0.761366\pi$
$691$	6.85416	−	21.0949i	0.260745	−	0.802489i	0.992643	−	0.121076i	$-0.0386344\pi$
$692$		0			0
$693$	6.12718			0.232752
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−6.27721	+	4.56066i	−0.237766	+	0.172747i
$698$		0			0
$699$	5.13782			0.194330
$700$		0			0
$701$	16.9652			0.640768			0.320384	−	0.947288i	$-0.396188\pi$
$701$	16.9652			0.640768			0.320384	+	0.947288i	$0.396188\pi$
$702$		0			0
$703$	25.5869	−	18.5900i	0.965030	−	0.701135i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.10051			0.191824
$708$		0			0
$709$	4.42745	−	13.6263i	0.166276	−	0.511746i	−0.832852	−	0.553496i	$-0.813293\pi$
$709$	4.42745	−	13.6263i	0.166276	−	0.511746i	0.999128	+	0.0417503i	$0.0132934\pi$
$710$		0			0
$711$	4.26428	+	13.1241i	0.159923	+	0.492192i
$712$		0			0
$713$	−2.25785	+	6.94896i	−0.0845573	+	0.260241i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	19.8689	+	14.4356i	0.742017	+	0.539107i
$718$		0			0
$719$	−9.56382	−	6.94852i	−0.356670	−	0.259136i	0.394992	−	0.918685i	$-0.370747\pi$
$719$	−9.56382	−	6.94852i	−0.356670	−	0.259136i	−0.751662	+	0.659549i	$0.770747\pi$
$720$		0			0
$721$	−9.83234	+	7.14361i	−0.366175	+	0.266042i
$722$		0			0
$723$	−1.49413	−	4.59846i	−0.0555673	−	0.171019i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.382051	−	1.17583i	−0.0141695	−	0.0436092i	0.943722	−	0.330740i	$-0.107298\pi$
$727$	−0.382051	−	1.17583i	−0.0141695	−	0.0436092i	−0.957891	+	0.287131i	$0.907298\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	6.99538	+	5.08244i	0.258734	+	0.187981i
$732$		0			0
$733$	−13.3553	−	9.70319i	−0.493289	−	0.358395i	0.313159	−	0.949701i	$-0.398613\pi$
$733$	−13.3553	−	9.70319i	−0.493289	−	0.358395i	−0.806448	+	0.591305i	$0.798613\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.5422	+	38.6010i	−0.461999	+	1.42189i
$738$		0			0
$739$	−5.20573	−	16.0216i	−0.191496	−	0.589363i	−1.00000		0.000872485i	$-0.999722\pi$
$739$	−5.20573	−	16.0216i	−0.191496	−	0.589363i	0.808504	−	0.588491i	$-0.200278\pi$
$740$		0			0
$741$	0.391629	−	1.20531i	0.0143869	−	0.0442782i
$742$		0			0
$743$	11.8940			0.436347			0.218174	−	0.975910i	$-0.429990\pi$
$743$	11.8940			0.436347			0.218174	+	0.975910i	$0.429990\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.74136	−	2.71826i	0.136889	−	0.0994558i
$748$		0			0
$749$	−28.4801			−1.04064
$750$		0			0
$751$	0.821377			0.0299725			0.0149862	−	0.999888i	$-0.495230\pi$
$751$	0.821377			0.0299725			0.0149862	+	0.999888i	$0.495230\pi$
$752$		0			0
$753$	−12.2481	+	8.89875i	−0.446345	+	0.324288i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	32.5591			1.18338			0.591690	−	0.806166i	$-0.298461\pi$
$757$	32.5591			1.18338			0.591690	+	0.806166i	$0.298461\pi$
$758$		0			0
$759$	−1.66734	+	5.13154i	−0.0605206	+	0.186263i
$760$		0			0
$761$	−3.35824	−	10.3356i	−0.121736	−	0.374665i	0.871556	−	0.490295i	$-0.163111\pi$
$761$	−3.35824	−	10.3356i	−0.121736	−	0.374665i	−0.993292	+	0.115631i	$0.963111\pi$
$762$		0			0
$763$	8.16086	−	25.1165i	0.295443	−	0.909280i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.21647	+	2.33690i	0.116140	+	0.0843807i
$768$		0			0
$769$	1.92870	+	1.40128i	0.0695505	+	0.0505314i	0.622017	−	0.783004i	$-0.286313\pi$
$769$	1.92870	+	1.40128i	0.0695505	+	0.0505314i	−0.552467	+	0.833535i	$0.686313\pi$
$770$		0			0
$771$	−18.4436	+	13.4001i	−0.664230	+	0.482592i
$772$		0			0
$773$	11.5060	+	35.4118i	0.413841	+	1.27367i	0.913283	+	0.407325i	$0.133538\pi$
$773$	11.5060	+	35.4118i	0.413841	+	1.27367i	−0.499442	+	0.866347i	$0.666462\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	4.17982	+	12.8642i	0.149950	+	0.461500i
$778$		0			0
$779$	3.81757	−	2.77363i	0.136779	−	0.0993756i
$780$		0			0
$781$	31.7905	+	23.0972i	1.13755	+	0.826482i
$782$		0			0
$783$	−2.69395	−	1.95727i	−0.0962738	−	0.0699470i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.07570	+	21.7768i	−0.252221	+	0.776258i	0.742143	+	0.670242i	$0.233809\pi$
$787$	−7.07570	+	21.7768i	−0.252221	+	0.776258i	−0.994364	+	0.106016i	$0.966191\pi$
$788$		0			0
$789$	−2.91853	−	8.98231i	−0.103902	−	0.319779i
$790$		0			0
$791$	−1.10708	+	3.40723i	−0.0393631	+	0.121147i
$792$		0			0
$793$	3.76483			0.133693
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.17977	+	5.21641i	−0.254321	+	0.184775i	−0.707639	−	0.706574i	$-0.750240\pi$
$797$	−7.17977	+	5.21641i	−0.254321	+	0.184775i	0.453319	+	0.891348i	$0.350240\pi$
$798$		0			0
$799$	2.27925			0.0806342
$800$		0			0
$801$	−7.26904			−0.256839
$802$		0			0
$803$	−41.4095	+	30.0858i	−1.46131	+	1.06170i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	29.3838			1.03436
$808$		0			0
$809$	−12.5887	+	38.7442i	−0.442597	+	1.36217i	0.442502	+	0.896768i	$0.354091\pi$
$809$	−12.5887	+	38.7442i	−0.442597	+	1.36217i	−0.885098	+	0.465404i	$0.845909\pi$
$810$		0			0
$811$	13.8312	+	42.5680i	0.485679	+	1.49476i	0.830996	+	0.556279i	$0.187771\pi$
$811$	13.8312	+	42.5680i	0.485679	+	1.49476i	−0.345317	+	0.938486i	$0.612229\pi$
$812$		0			0
$813$	−4.78615	+	14.7303i	−0.167858	+	0.516613i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−4.25435	−	3.09096i	−0.148841	−	0.108139i
$818$		0			0
$819$	0.438495	+	0.318586i	0.0153223	+	0.0111323i
$820$		0			0
$821$	40.4077	−	29.3579i	1.41024	−	1.02460i	0.416949	−	0.908930i	$-0.363099\pi$
$821$	40.4077	−	29.3579i	1.41024	−	1.02460i	0.993288	−	0.115667i	$-0.0369005\pi$
$822$		0			0
$823$	4.93877	+	15.2000i	0.172155	+	0.529837i	0.999492	−	0.0318678i	$-0.0101456\pi$
$823$	4.93877	+	15.2000i	0.172155	+	0.529837i	−0.827338	+	0.561705i	$0.810146\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.9525	+	42.9415i	0.485177	+	1.49322i	0.831724	+	0.555190i	$0.187354\pi$
$827$	13.9525	+	42.9415i	0.485177	+	1.49322i	−0.346546	+	0.938033i	$0.612646\pi$
$828$		0			0
$829$	12.4972	−	9.07975i	0.434046	−	0.315353i	−0.349219	−	0.937041i	$-0.613553\pi$
$829$	12.4972	−	9.07975i	0.434046	−	0.315353i	0.783265	+	0.621688i	$0.213553\pi$
$830$		0			0
$831$	−12.4415	−	9.03931i	−0.431592	−	0.313570i
$832$		0			0
$833$	−22.1345	−	16.0817i	−0.766916	−	0.557197i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.62387	−	4.99776i	0.0561292	−	0.172748i
$838$		0			0
$839$	−7.15711	−	22.0273i	−0.247091	−	0.760468i	−0.995285	−	0.0969885i	$-0.969079\pi$
$839$	−7.15711	−	22.0273i	−0.247091	−	0.760468i	0.748194	−	0.663480i	$-0.230921\pi$
$840$		0			0
$841$	−5.53504	+	17.0351i	−0.190863	+	0.587417i
$842$		0			0
$843$	−3.87277			−0.133385
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−5.18484	+	3.76701i	−0.178153	+	0.129436i
$848$		0			0
$849$	−11.8869			−0.407959
$850$		0			0
$851$	−11.9112			−0.408311
$852$		0			0
$853$	−0.661719	+	0.480767i	−0.0226568	+	0.0164611i	−0.599056	−	0.800707i	$-0.704457\pi$
$853$	−0.661719	+	0.480767i	−0.0226568	+	0.0164611i	0.576399	+	0.817168i	$0.304457\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−38.5882			−1.31815			−0.659074	−	0.752078i	$-0.729052\pi$
$857$	−38.5882			−1.31815			−0.659074	+	0.752078i	$0.729052\pi$
$858$		0			0
$859$	12.4773	−	38.4012i	0.425720	−	1.31023i	−0.476583	−	0.879129i	$-0.658125\pi$
$859$	12.4773	−	38.4012i	0.425720	−	1.31023i	0.902303	−	0.431102i	$-0.141875\pi$
$860$		0			0
$861$	0.623630	+	1.91934i	0.0212533	+	0.0654108i
$862$		0			0
$863$	8.30758	−	25.5681i	0.282793	−	0.870349i	−0.704258	−	0.709944i	$-0.748720\pi$
$863$	8.30758	−	25.5681i	0.282793	−	0.870349i	0.987051	−	0.160404i	$-0.0512798\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	16.0601	+	11.6684i	0.545431	+	0.396279i
$868$		0			0
$869$	−43.3230	−	31.4760i	−1.46963	−	1.06775i
$870$		0			0
$871$	−2.90467	+	2.11037i	−0.0984210	+	0.0715070i
$872$		0			0
$873$	−1.87127	−	5.75919i	−0.0633331	−	0.194919i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.01303	−	21.5839i	−0.236813	−	0.728836i	−0.996876	−	0.0789861i	$-0.974832\pi$
$877$	−7.01303	−	21.5839i	−0.236813	−	0.728836i	0.760063	−	0.649850i	$-0.225168\pi$
$878$		0			0
$879$	12.5071	−	9.08694i	0.421854	−	0.306495i
$880$		0			0
$881$	24.3098	+	17.6621i	0.819017	+	0.595051i	0.916431	−	0.400193i	$-0.131057\pi$
$881$	24.3098	+	17.6621i	0.819017	+	0.595051i	−0.0974139	+	0.995244i	$0.531057\pi$
$882$		0			0
$883$	28.2268	+	20.5079i	0.949906	+	0.690147i	0.950785	−	0.309852i	$-0.100280\pi$
$883$	28.2268	+	20.5079i	0.949906	+	0.690147i	−0.000878603		1.00000i	$0.500280\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.9900	−	36.9015i	0.402586	−	1.23903i	−0.520308	−	0.853979i	$-0.674183\pi$
$887$	11.9900	−	36.9015i	0.402586	−	1.23903i	0.922894	−	0.385054i	$-0.125817\pi$
$888$		0			0
$889$	0.735413	+	2.26337i	0.0246650	+	0.0759110i
$890$		0			0
$891$	1.19917	−	3.69066i	0.0401736	−	0.123642i
$892$		0			0
$893$	−1.38616			−0.0463861
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.386141	+	0.280548i	−0.0128929	+	0.00936722i
$898$		0			0
$899$	17.4985			0.583608
$900$		0			0
$901$	68.5923			2.28514
$902$		0			0
$903$	1.81948	−	1.32193i	0.0605486	−	0.0439911i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	10.0886			0.334988			0.167494	−	0.985873i	$-0.446433\pi$
$907$	10.0886			0.334988			0.167494	+	0.985873i	$0.446433\pi$
$908$		0			0
$909$	0.998235	−	3.07225i	0.0331094	−	0.101900i
$910$		0			0
$911$	−8.87343	−	27.3096i	−0.293990	−	0.904808i	−0.983559	−	0.180588i	$-0.942200\pi$
$911$	−8.87343	−	27.3096i	−0.293990	−	0.904808i	0.689569	−	0.724220i	$-0.257800\pi$
$912$		0			0
$913$	−5.54564	+	17.0677i	−0.183534	+	0.564859i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	20.3599	+	14.7924i	0.672344	+	0.488487i
$918$		0			0
$919$	−1.19370	−	0.867272i	−0.0393764	−	0.0286086i	0.567923	−	0.823082i	$-0.307747\pi$
$919$	−1.19370	−	0.867272i	−0.0393764	−	0.0286086i	−0.607299	+	0.794473i	$0.707747\pi$
$920$		0			0
$921$	−21.5273	+	15.6405i	−0.709348	+	0.515372i
$922$		0			0
$923$	1.07416	+	3.30593i	0.0353564	+	0.108816i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.37858	+	7.32052i	0.0781229	+	0.240438i
$928$		0			0
$929$	33.0756	−	24.0308i	1.08517	−	0.788425i	0.106596	−	0.994302i	$-0.466005\pi$
$929$	33.0756	−	24.0308i	1.08517	−	0.788425i	0.978578	+	0.205878i	$0.0660049\pi$
$930$		0			0
$931$	13.4614	+	9.78030i	0.441181	+	0.320537i
$932$		0			0
$933$	−4.43392	−	3.22143i	−0.145160	−	0.105465i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−10.0378	+	30.8930i	−0.327919	+	1.00923i	0.642186	+	0.766549i	$0.278028\pi$
$937$	−10.0378	+	30.8930i	−0.327919	+	1.00923i	−0.970106	+	0.242683i	$0.921972\pi$
$938$		0			0
$939$	2.30248	+	7.08632i	0.0751387	+	0.231253i
$940$		0			0
$941$	−2.36379	+	7.27501i	−0.0770575	+	0.237159i	−0.982164	−	0.188026i	$-0.939791\pi$
$941$	−2.36379	+	7.27501i	−0.0770575	+	0.237159i	0.905106	+	0.425185i	$0.139791\pi$
$942$		0			0
$943$	−1.77716			−0.0578722
$944$		0			0
$945$		0			0
$946$		0			0
$947$	42.1558	−	30.6280i	1.36988	−	0.995276i	0.372134	−	0.928179i	$-0.378626\pi$
$947$	42.1558	−	30.6280i	1.36988	−	0.995276i	0.997746	−	0.0670970i	$-0.0213737\pi$
$948$		0			0
$949$	−4.52782			−0.146979
$950$		0			0
$951$	−2.96844			−0.0962584
$952$		0			0
$953$	3.40408	−	2.47321i	0.110269	−	0.0801151i	−0.531284	−	0.847194i	$-0.678290\pi$
$953$	3.40408	−	2.47321i	0.110269	−	0.0801151i	0.641553	+	0.767079i	$0.278290\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	12.9220			0.417708
$958$		0			0
$959$	2.65746	−	8.17881i	0.0858137	−	0.264107i
$960$		0			0
$961$	−1.04615	−	3.21972i	−0.0337468	−	0.103862i
$962$		0			0
$963$	−5.57391	+	17.1547i	−0.179617	+	0.552804i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−40.8816	−	29.7022i	−1.31466	−	0.955158i	−0.999982	−	0.00596071i	$-0.998103\pi$
$967$	−40.8816	−	29.7022i	−1.31466	−	0.955158i	−0.314680	−	0.949198i	$-0.601897\pi$
$968$		0			0
$969$	−18.1315	−	13.1733i	−0.582467	−	0.423187i
$970$		0			0
$971$	−12.8283	+	9.32029i	−0.411679	+	0.299102i	−0.774281	−	0.632842i	$-0.781888\pi$
$971$	−12.8283	+	9.32029i	−0.411679	+	0.299102i	0.362602	+	0.931944i	$0.381888\pi$
$972$		0			0
$973$	−4.82220	−	14.8412i	−0.154593	−	0.475787i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.3836	+	41.1903i	0.428178	+	1.31780i	0.899918	+	0.436058i	$0.143626\pi$
$977$	13.3836	+	41.1903i	0.428178	+	1.31780i	−0.471741	+	0.881737i	$0.656374\pi$
$978$		0			0
$979$	22.8209	−	16.5803i	0.729358	−	0.529909i
$980$		0			0
$981$	−13.5316	−	9.83125i	−0.432029	−	0.313888i
$982$		0			0
$983$	28.2920	+	20.5553i	0.902374	+	0.655613i	0.939075	−	0.343713i	$-0.111685\pi$
$983$	28.2920	+	20.5553i	0.902374	+	0.655613i	−0.0367008	+	0.999326i	$0.511685\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.183194	−	0.563813i	0.00583113	−	0.0179464i
$988$		0			0
$989$	0.612002	+	1.88355i	0.0194605	+	0.0598934i
$990$		0			0
$991$	−4.75904	+	14.6468i	−0.151176	+	0.465272i	−0.997753	−	0.0669939i	$-0.978659\pi$
$991$	−4.75904	+	14.6468i	−0.151176	+	0.465272i	0.846577	+	0.532266i	$0.178659\pi$
$992$		0			0
$993$	−27.4282			−0.870408
$994$		0			0
$995$		0			0
$996$		0			0
$997$	24.9124	−	18.1000i	0.788985	−	0.573231i	−0.118677	−	0.992933i	$-0.537865\pi$
$997$	24.9124	−	18.1000i	0.788985	−	0.573231i	0.907662	+	0.419702i	$0.137865\pi$
$998$		0			0
$999$	8.56667			0.271038

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1500.2.m.d.901.5		24
5.2	odd	4		300.2.o.a.169.1	✓	24
5.3	odd	4		1500.2.o.c.349.6		24
5.4	even	2		1500.2.m.c.901.2		24
15.2	even	4		900.2.w.c.469.6		24
25.2	odd	20		7500.2.d.g.1249.22		24
25.3	odd	20		300.2.o.a.229.1	yes	24
25.4	even	10		1500.2.m.c.601.2		24
25.11	even	5		7500.2.a.m.1.10		12
25.14	even	10		7500.2.a.n.1.3		12
25.21	even	5	inner	1500.2.m.d.601.5		24
25.22	odd	20		1500.2.o.c.649.6		24
25.23	odd	20		7500.2.d.g.1249.3		24
75.53	even	20		900.2.w.c.829.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.1	✓	24	5.2	odd	4
300.2.o.a.229.1	yes	24	25.3	odd	20
900.2.w.c.469.6		24	15.2	even	4
900.2.w.c.829.6		24	75.53	even	20
1500.2.m.c.601.2		24	25.4	even	10
1500.2.m.c.901.2		24	5.4	even	2
1500.2.m.d.601.5		24	25.21	even	5	inner
1500.2.m.d.901.5		24	1.1	even	1	trivial
1500.2.o.c.349.6		24	5.3	odd	4
1500.2.o.c.649.6		24	25.22	odd	20
7500.2.a.m.1.10		12	25.11	even	5
7500.2.a.n.1.3		12	25.14	even	10
7500.2.d.g.1249.3		24	25.23	odd	20
7500.2.d.g.1249.22		24	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{3} +1.57893 q^{7} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{3} +1.57893 q^{7} +(0.309017 - 0.951057i) q^{9} +(1.19917 + 3.69066i) q^{11} +(-0.106078 + 0.326475i) q^{13} +(4.91117 + 3.56817i) q^{17} +(-2.98680 - 2.17004i) q^{19} +(1.27738 - 0.928073i) q^{21} +(0.429662 + 1.32236i) q^{23} +(-0.309017 - 0.951057i) q^{27} +(2.69395 - 1.95727i) q^{29} +(4.25135 + 3.08879i) q^{31} +(3.13946 + 2.28095i) q^{33} +(-2.64725 + 8.14739i) q^{37} +(0.106078 + 0.326475i) q^{39} +(-0.394970 + 1.21559i) q^{41} +1.42438 q^{43} +(0.303755 - 0.220691i) q^{47} -4.50698 q^{49} +6.07054 q^{51} +(9.14125 - 6.64151i) q^{53} -3.69189 q^{57} +(3.57899 - 11.0150i) q^{59} +(-3.38909 - 10.4305i) q^{61} +(0.487917 - 1.50165i) q^{63} +(8.46160 + 6.14771i) q^{67} +(1.12487 + 0.817265i) q^{69} +(8.19220 - 5.95198i) q^{71} +(4.07594 + 12.5444i) q^{73} +(1.89340 + 5.82730i) q^{77} +(-11.1640 + 8.11114i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(3.74136 + 2.71826i) q^{83} +(1.02900 - 3.16693i) q^{87} +(-2.24626 - 6.91326i) q^{89} +(-0.167490 + 0.515482i) q^{91} +5.25496 q^{93} +(4.89906 - 3.55938i) q^{97} +3.88059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9	\( 24 q + 6 q^{3} - 16 q^{7} - 6 q^{9} - 6 q^{11} + 4 q^{17} - 10 q^{19} - 4 q^{21} + 14 q^{23} + 6 q^{27} - 4 q^{29} + 6 q^{31} - 4 q^{33} - 8 q^{37} - 10 q^{41} - 56 q^{43} + 26 q^{47} + 56 q^{49} + 16 q^{51} - 32 q^{53} - 20 q^{57} + 36 q^{59} - 12 q^{61} + 4 q^{63} + 36 q^{67} - 4 q^{69} + 40 q^{71} + 32 q^{73} - 46 q^{77} - 8 q^{79} - 6 q^{81} - 6 q^{83} + 4 q^{87} - 30 q^{91} + 4 q^{93} + 48 q^{97} + 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 16 * q^7 - 6 * q^9 - 6 * q^11 + 4 * q^17 - 10 * q^19 - 4 * q^21 + 14 * q^23 + 6 * q^27 - 4 * q^29 + 6 * q^31 - 4 * q^33 - 8 * q^37 - 10 * q^41 - 56 * q^43 + 26 * q^47 + 56 * q^49 + 16 * q^51 - 32 * q^53 - 20 * q^57 + 36 * q^59 - 12 * q^61 + 4 * q^63 + 36 * q^67 - 4 * q^69 + 40 * q^71 + 32 * q^73 - 46 * q^77 - 8 * q^79 - 6 * q^81 - 6 * q^83 + 4 * q^87 - 30 * q^91 + 4 * q^93 + 48 * q^97 + 4 * q^99

Introduction

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