LMFDB - Embedded newform 1500.2.m.d.601.5

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			601.5
Character	$\chi$	$=$	1500.601
Dual form			1500.2.m.d.901.5

$q$-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 $\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times$.

$n$	$751$	$877$	$1001$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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	−0.590543	−	0.807006i	$-0.701086\pi$
$11$	1.19917	−	3.69066i	0.361563	−	1.11278i	0.952106	−	0.305769i	$-0.0989136\pi$
$12$		0			0
$13$	−0.106078	−	0.326475i	−0.0294208	−	0.0905480i	0.935268	−	0.353941i	$-0.115159\pi$
$13$	−0.106078	−	0.326475i	−0.0294208	−	0.0905480i	−0.964689	+	0.263393i	$0.915159\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.91117	−	3.56817i	1.19113	−	0.865409i	0.197750	−	0.980253i	$-0.436637\pi$
$17$	4.91117	−	3.56817i	1.19113	−	0.865409i	0.993384	+	0.114844i	$0.0366367\pi$
$18$		0			0
$19$	−2.98680	+	2.17004i	−0.685219	+	0.497841i	−0.875085	−	0.483969i	$-0.839195\pi$
$19$	−2.98680	+	2.17004i	−0.685219	+	0.497841i	0.189866	+	0.981810i	$0.439195\pi$
$20$		0			0
$21$	1.27738	+	0.928073i	0.278748	+	0.202522i
$22$		0			0
$23$	0.429662	−	1.32236i	0.0895906	−	0.275732i	−0.896216	−	0.443619i	$-0.853694\pi$
$23$	0.429662	−	1.32236i	0.0895906	−	0.275732i	0.985806	+	0.167887i	$0.0536944\pi$
$24$		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	0.809114	−	0.587652i	$-0.199948\pi$
$29$	2.69395	+	1.95727i	0.500254	+	0.363455i	−0.308860	+	0.951107i	$0.599948\pi$
$30$		0			0
$31$	4.25135	−	3.08879i	0.763565	−	0.554763i	−0.136437	−	0.990649i	$-0.543565\pi$
$31$	4.25135	−	3.08879i	0.763565	−	0.554763i	0.900002	+	0.435886i	$0.143565\pi$
$32$		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	−0.892877	−	0.450301i	$-0.851317\pi$
$37$	−2.64725	−	8.14739i	−0.435205	−	1.33942i	0.457672	−	0.889121i	$-0.348683\pi$
$38$		0			0
$39$	0.106078	−	0.326475i	0.0169861	−	0.0522779i
$40$		0			0
$41$	−0.394970	−	1.21559i	−0.0616839	−	0.189844i	0.915466	−	0.402396i	$-0.131822\pi$
$41$	−0.394970	−	1.21559i	−0.0616839	−	0.189844i	−0.977150	+	0.212552i	$0.931822\pi$
$42$		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	0.609718	−	0.792618i	$-0.291283\pi$
$47$	0.303755	+	0.220691i	0.0443072	+	0.0321911i	−0.565411	+	0.824809i	$0.691283\pi$
$48$		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	0.998536	−	0.0540999i	$-0.0172289\pi$
$53$	9.14125	+	6.64151i	1.25565	+	0.912282i	0.257112	+	0.966382i	$0.417229\pi$
$54$		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	0.857791	+	0.513999i	$0.171837\pi$
$59$	3.57899	+	11.0150i	0.465945	+	1.43403i	−0.391846	+	0.920031i	$0.628163\pi$
$60$		0			0
$61$	−3.38909	+	10.4305i	−0.433928	+	1.33549i	0.460252	+	0.887788i	$0.347759\pi$
$61$	−3.38909	+	10.4305i	−0.433928	+	1.33549i	−0.894181	+	0.447706i	$0.852241\pi$
$62$		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	0.0646937	−	0.997905i	$-0.479393\pi$
$67$	8.46160	−	6.14771i	1.03375	−	0.751063i	0.969056	+	0.246842i	$0.0793930\pi$
$68$		0			0
$69$	1.12487	−	0.817265i	0.135418	−	0.0983871i
$70$		0			0
$71$	8.19220	+	5.95198i	0.972235	+	0.706370i	0.955960	−	0.293498i	$-0.0948193\pi$
$71$	8.19220	+	5.95198i	0.972235	+	0.706370i	0.0162750	+	0.999868i	$0.494819\pi$
$72$		0			0
$73$	4.07594	−	12.5444i	0.477052	−	1.46822i	−0.366117	−	0.930569i	$-0.619313\pi$
$73$	4.07594	−	12.5444i	0.477052	−	1.46822i	0.843170	−	0.537648i	$-0.180687\pi$
$74$		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	−0.257494	−	0.966280i	$-0.582897\pi$
$79$	−11.1640	−	8.11114i	−1.25605	−	0.912574i	−0.998557	+	0.0537055i	$0.982897\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	3.74136	−	2.71826i	0.410668	−	0.298367i	−0.363204	−	0.931709i	$-0.618317\pi$
$83$	3.74136	−	2.71826i	0.410668	−	0.298367i	0.773872	+	0.633342i	$0.218317\pi$
$84$		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	0.758592	+	0.651566i	$0.225888\pi$
$89$	−2.24626	+	6.91326i	−0.238103	+	0.732805i	−0.996695	+	0.0812387i	$0.974112\pi$
$90$		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	0.808032	−	0.589138i	$-0.200533\pi$
$97$	4.89906	+	3.55938i	0.497424	+	0.361400i	−0.310608	+	0.950538i	$0.600533\pi$
$98$		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	0.237090	−	0.971488i	$-0.423806\pi$
$103$	−6.22721	−	4.52433i	−0.613585	−	0.445796i	−0.850675	+	0.525692i	$0.823806\pi$
$104$		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	0.816861	+	0.576835i	$0.195712\pi$
$109$	5.16860	+	15.9073i	0.495062	+	1.52364i	−0.321799	+	0.946808i	$0.604288\pi$
$110$		0			0
$111$	2.64725	−	8.14739i	0.251266	−	0.773316i
$112$		0			0
$113$	−0.701155	−	2.15793i	−0.0659591	−	0.203001i	0.912645	−	0.408753i	$-0.134036\pi$
$113$	−0.701155	−	2.15793i	−0.0659591	−	0.203001i	−0.978604	+	0.205751i	$0.934036\pi$
$114$		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	−0.928262	−	0.371926i	$-0.878698\pi$
$127$	0.465767	−	1.43348i	0.0413301	−	0.127201i	0.969593	+	0.244725i	$0.0786976\pi$
$128$		0			0
$129$	1.15235	+	0.837231i	0.101459	+	0.0737141i
$130$		0			0
$131$	12.8948	−	9.36859i	1.12662	−	0.818537i	0.141421	−	0.989950i	$-0.454833\pi$
$131$	12.8948	−	9.36859i	1.12662	−	0.818537i	0.985199	+	0.171412i	$0.0548330\pi$
$132$		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	0.996854	−	0.0792596i	$-0.0252556\pi$
$137$	1.68307	+	5.17996i	0.143795	+	0.442554i	−0.853059	+	0.521814i	$0.825256\pi$
$138$		0			0
$139$	−3.05409	+	9.39953i	−0.259045	+	0.797258i	0.733961	+	0.679192i	$0.237669\pi$
$139$	−3.05409	+	9.39953i	−0.259045	+	0.797258i	−0.993006	+	0.118066i	$0.962331\pi$
$140$		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	0.851903	−	0.523700i	$-0.175449\pi$
$163$	−1.85282	−	5.70240i	−0.145124	−	0.446646i	−0.997027	+	0.0770538i	$0.975449\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.17649	+	3.76094i	−0.400569	+	0.291030i	−0.769773	−	0.638318i	$-0.779630\pi$
$167$	−5.17649	+	3.76094i	−0.400569	+	0.291030i	0.369204	+	0.929348i	$0.379630\pi$
$168$		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	−0.870798	−	0.491641i	$-0.836397\pi$
$173$	1.61350	−	4.96583i	0.122672	−	0.377545i	0.993470	+	0.114096i	$0.0363972\pi$
$174$		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	−0.993443	−	0.114329i	$-0.963528\pi$
$179$	−18.8534	−	13.6978i	−1.40917	−	1.02382i	−0.415724	−	0.909491i	$-0.636472\pi$
$180$		0			0
$181$	−20.3662	+	14.7969i	−1.51380	+	1.09984i	−0.549350	+	0.835592i	$0.685125\pi$
$181$	−20.3662	+	14.7969i	−1.51380	+	1.09984i	−0.964454	+	0.264251i	$0.914875\pi$
$182$		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	0.999813	−	0.0193354i	$-0.00615503\pi$
$191$	2.48188	+	7.63843i	0.179582	+	0.552697i	−0.820231	+	0.572033i	$0.806155\pi$
$192$		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	0.988970	−	0.148115i	$-0.0473207\pi$
$197$	16.1931	+	11.7650i	1.15371	+	0.838221i	0.164742	+	0.986337i	$0.447321\pi$
$198$		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	−0.815589	−	0.578631i	$-0.803587\pi$
$211$	2.67780	−	8.24142i	0.184347	−	0.567363i	0.999937	+	0.0112687i	$0.00358702\pi$
$212$		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	0.737312	+	0.675552i	$0.236095\pi$
$223$	−3.82686	+	11.7779i	−0.256266	+	0.788705i	−0.993578	+	0.113152i	$0.963905\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.63116	+	17.3309i	−0.373753	+	1.15029i	0.570563	+	0.821254i	$0.306725\pi$
$227$	−5.63116	+	17.3309i	−0.373753	+	1.15029i	−0.944316	+	0.329040i	$0.893275\pi$
$228$		0			0
$229$	−13.2812	−	9.64932i	−0.877643	−	0.637645i	0.0549837	−	0.998487i	$-0.482489\pi$
$229$	−13.2812	−	9.64932i	−0.877643	−	0.637645i	−0.932627	+	0.360842i	$0.882489\pi$
$230$		0			0
$231$	4.95699	−	3.60147i	0.326146	−	0.236959i
$232$		0			0
$233$	4.15658	−	3.01993i	0.272307	−	0.197842i	−0.443248	−	0.896399i	$-0.646174\pi$
$233$	4.15658	−	3.01993i	0.272307	−	0.197842i	0.715555	+	0.698557i	$0.246174\pi$
$234$		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	−0.332332	−	0.943162i	$-0.607835\pi$
$239$	7.58924	−	23.3573i	0.490907	−	1.51086i	0.823239	−	0.567694i	$-0.192165\pi$
$240$		0			0
$241$	1.49413	+	4.59846i	0.0962454	+	0.296213i	0.987576	−	0.157141i	$-0.0502276\pi$
$241$	1.49413	+	4.59846i	0.0962454	+	0.296213i	−0.891331	+	0.453353i	$0.850228\pi$
$242$		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	0.999825	−	0.0186895i	$-0.00594941\pi$
$263$	2.91853	+	8.98231i	0.179964	+	0.553873i	−0.819861	+	0.572562i	$0.805949\pi$
$264$		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	0.463433	−	0.886132i	$-0.346618\pi$
$269$	23.7720	−	17.2714i	1.44940	−	1.05305i	0.985970	−	0.166921i	$-0.0533825\pi$
$270$		0			0
$271$	−12.5303	−	9.10380i	−0.761162	−	0.553016i	0.138105	−	0.990418i	$-0.455899\pi$
$271$	−12.5303	−	9.10380i	−0.761162	−	0.553016i	−0.899266	+	0.437401i	$0.855899\pi$
$272$		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	0.700703	+	0.713453i	$0.252870\pi$
$277$	−4.75225	+	14.6259i	−0.285535	+	0.878786i	−0.986238	+	0.165333i	$0.947130\pi$
$278$		0			0
$279$	4.25135	+	3.08879i	0.254522	+	0.184921i
$280$		0			0
$281$	−3.13314	+	2.27636i	−0.186908	+	0.135796i	−0.677304	−	0.735703i	$-0.736852\pi$
$281$	−3.13314	+	2.27636i	−0.186908	+	0.135796i	0.490397	+	0.871499i	$0.336852\pi$
$282$		0			0
$283$	−9.61673	+	6.98697i	−0.571655	+	0.415332i	−0.835706	−	0.549177i	$-0.814941\pi$
$283$	−9.61673	+	6.98697i	−0.571655	+	0.415332i	0.264051	+	0.964509i	$0.414941\pi$
$284$		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	−0.987522	−	0.157480i	$-0.949663\pi$
$311$	−1.69361	+	5.21238i	−0.0960356	+	0.295567i	0.891487	+	0.453047i	$0.149663\pi$
$312$		0			0
$313$	−2.30248	−	7.08632i	−0.130144	−	0.400542i	0.864659	−	0.502359i	$-0.167534\pi$
$313$	−2.30248	−	7.08632i	−0.130144	−	0.400542i	−0.994803	+	0.101817i	$0.967534\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.40152	+	1.74481i	−0.134883	+	0.0979981i	−0.653181	−	0.757202i	$-0.726566\pi$
$317$	−2.40152	+	1.74481i	−0.134883	+	0.0979981i	0.518298	+	0.855200i	$0.326566\pi$
$318$		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	−0.996072	−	0.0885426i	$-0.971779\pi$
$331$	−22.1899	+	16.1219i	−1.21967	+	0.886140i	−0.223594	+	0.974682i	$0.571779\pi$
$332$		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	0.994178	−	0.107754i	$-0.0343660\pi$
$337$	2.32287	+	7.14905i	0.126535	+	0.389433i	−0.867643	+	0.497188i	$0.834366\pi$
$338$		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	0.816953	−	0.576704i	$-0.195661\pi$
$347$	9.70380	+	7.05022i	0.520927	+	0.378476i	−0.296026	+	0.955180i	$0.595661\pi$
$348$		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	−0.0977244	−	0.995214i	$-0.531156\pi$
$353$	−20.1867	−	14.6665i	−1.07443	−	0.780617i	−0.976703	+	0.214596i	$0.931156\pi$
$354$		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	0.957387	−	0.288810i	$-0.0932595\pi$
$359$	0.247954	+	0.763123i	0.0130865	+	0.0402761i	−0.944300	+	0.329086i	$0.893259\pi$
$360$		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	−0.201724	−	0.979442i	$-0.564654\pi$
$367$	12.7864	−	9.28986i	0.667445	−	0.484927i	0.869169	+	0.494515i	$0.164654\pi$
$368$		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	−0.975772	−	0.218790i	$-0.929789\pi$
$373$	−1.11542	+	3.43291i	−0.0577543	+	0.177750i	0.918018	+	0.396540i	$0.129789\pi$
$374$		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	−0.148610	−	0.988896i	$-0.547480\pi$
$379$	−22.0967	−	16.0542i	−1.13503	−	0.824647i	−0.986419	+	0.164249i	$0.947480\pi$
$380$		0			0
$381$	1.21939	−	0.885941i	0.0624714	−	0.0453881i
$382$		0			0
$383$	−15.5991	+	11.3334i	−0.797079	+	0.579112i	−0.910056	−	0.414486i	$-0.863961\pi$
$383$	−15.5991	+	11.3334i	−0.797079	+	0.579112i	0.112977	+	0.993598i	$0.463961\pi$
$384$		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	0.723876	+	0.689930i	$0.242359\pi$
$389$	−5.27164	+	16.2244i	−0.267283	+	0.822612i	−0.991159	+	0.132682i	$0.957641\pi$
$390$		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	0.982833	−	0.184499i	$-0.0590664\pi$
$397$	22.1380	+	16.0842i	1.11108	+	0.807243i	0.128243	+	0.991743i	$0.459066\pi$
$398$		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	0.967921	+	0.251256i	$0.0808438\pi$
$409$	6.72523	+	20.6981i	0.332541	+	1.02346i	−0.635379	+	0.772200i	$0.719156\pi$
$410$		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	−0.494505	−	0.869175i	$-0.664651\pi$
$419$	3.67055	−	2.66681i	0.179318	−	0.130282i	0.673824	+	0.738892i	$0.264651\pi$
$420$		0			0
$421$	−2.47193	−	1.79596i	−0.120475	−	0.0875300i	0.525916	−	0.850536i	$-0.323722\pi$
$421$	−2.47193	−	1.79596i	−0.120475	−	0.0875300i	−0.646391	+	0.763006i	$0.723722\pi$
$422$		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	−0.155181	−	0.987886i	$-0.549596\pi$
$431$	15.2881	−	11.1074i	0.736400	−	0.535026i	0.891582	+	0.452860i	$0.149596\pi$
$432$		0			0
$433$	−2.76602	+	2.00963i	−0.132927	+	0.0965768i	−0.652262	−	0.757994i	$-0.726180\pi$
$433$	−2.76602	+	2.00963i	−0.132927	+	0.0965768i	0.519335	+	0.854571i	$0.326180\pi$
$434$		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	−0.985323	−	0.170698i	$-0.945398\pi$
$439$	−1.84058	+	5.66473i	−0.0878462	+	0.270363i	0.897477	+	0.441061i	$0.145398\pi$
$440$		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	−0.00903372	+	0.999959i	$0.502876\pi$
$461$	−12.6568	+	38.9537i	−0.589487	+	1.81425i	−0.580453	+	0.814294i	$0.697124\pi$
$462$		0			0
$463$	−7.14695	−	21.9961i	−0.332147	−	1.02224i	−0.968110	−	0.250524i	$-0.919397\pi$
$463$	−7.14695	−	21.9961i	−0.332147	−	1.02224i	0.635963	−	0.771719i	$-0.280603\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	24.5043	−	17.8034i	1.13392	−	0.823845i	0.147664	−	0.989038i	$-0.452825\pi$
$467$	24.5043	−	17.8034i	1.13392	−	0.823845i	0.986261	+	0.165193i	$0.0528247\pi$
$468$		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	0.935906	−	0.352250i	$-0.114583\pi$
$479$	19.4809	+	14.1537i	0.890107	+	0.646700i	−0.0457990	+	0.998951i	$0.514583\pi$
$480$		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	0.934028	−	0.357201i	$-0.116269\pi$
$487$	−0.696777	−	2.14446i	−0.0315740	−	0.0971747i	−0.965602	+	0.260026i	$0.916269\pi$
$488$		0			0
$489$	1.85282	−	5.70240i	0.0837875	−	0.257871i
$490$		0			0
$491$	−8.84093	−	27.2096i	−0.398986	−	1.22795i	−0.925814	−	0.377980i	$-0.876619\pi$
$491$	−8.84093	−	27.2096i	−0.398986	−	1.22795i	0.526828	−	0.849972i	$-0.323381\pi$
$492$		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	0.595281	−	0.803518i	$-0.297041\pi$
$503$	0.337358	+	0.245105i	0.0150421	+	0.0109287i	−0.580239	+	0.814446i	$0.697041\pi$
$504$		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	0.999921	−	0.0125684i	$-0.00400074\pi$
$509$	4.14176	+	12.7470i	0.183580	+	0.565002i	−0.816341	+	0.577571i	$0.804001\pi$
$510$		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	0.147926	−	0.988998i	$-0.452740\pi$
$521$	−17.0496	−	12.3872i	−0.746956	−	0.542695i	−0.894882	+	0.446303i	$0.852740\pi$
$522$		0			0
$523$	−3.66974	+	11.2943i	−0.160467	+	0.493866i	−0.998674	−	0.0514866i	$-0.983604\pi$
$523$	−3.66974	+	11.2943i	−0.160467	+	0.493866i	0.838207	+	0.545352i	$0.183604\pi$
$524$		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	0.830825	+	0.556534i	$0.187869\pi$
$541$	11.2993	+	34.7757i	0.485796	+	1.49513i	−0.345029	+	0.938592i	$0.612131\pi$
$542$		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	−0.997803	−	0.0662579i	$-0.978894\pi$
$547$	−32.0219	−	23.2652i	−1.36916	−	0.994750i	−0.371353	−	0.928492i	$-0.621106\pi$
$548$		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	−0.843907	−	0.536490i	$-0.819750\pi$
$563$	−11.3065	−	34.7979i	−0.476513	−	1.46656i	0.367394	−	0.930065i	$-0.380250\pi$
$564$		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	0.159403	−	0.987214i	$-0.449043\pi$
$569$	27.3735	−	19.8880i	1.14756	−	0.833749i	0.988154	+	0.153464i	$0.0490430\pi$
$570$		0			0
$571$	0.974239	+	0.707826i	0.0407706	+	0.0296216i	0.607984	−	0.793949i	$-0.291978\pi$
$571$	0.974239	+	0.707826i	0.0407706	+	0.0296216i	−0.567213	+	0.823571i	$0.691978\pi$
$572$		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	0.788381	+	0.615187i	$0.210920\pi$
$577$	−5.06913	+	15.6012i	−0.211031	+	0.649485i	−0.999412	+	0.0342981i	$0.989080\pi$
$578$		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	0.898398	+	0.439182i	$0.144732\pi$
$587$	10.4114	+	32.0429i	0.429724	+	1.32255i	−0.468674	+	0.883371i	$0.655268\pi$
$588$		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	0.732569	+	0.680693i	$0.238321\pi$
$613$	13.3700	+	41.1487i	0.540010	+	1.66198i	−0.192559	+	0.981285i	$0.561679\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.28217	−	0.931550i	0.0516182	−	0.0375028i	−0.561677	−	0.827357i	$-0.689844\pi$
$617$	1.28217	−	0.931550i	0.0516182	−	0.0375028i	0.613295	+	0.789854i	$0.289844\pi$
$618$		0			0
$619$	10.9048	−	7.92281i	0.438301	−	0.318444i	−0.346658	−	0.937991i	$-0.612684\pi$
$619$	10.9048	−	7.92281i	0.438301	−	0.318444i	0.784960	+	0.619547i	$0.212684\pi$
$620$		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	−0.00594245	−	0.999982i	$-0.501892\pi$
$631$	23.6944	−	17.2150i	0.943261	−	0.685319i	0.949203	+	0.314663i	$0.101892\pi$
$632$		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	−0.999411	−	0.0343242i	$-0.989072\pi$
$641$	−5.34325	−	16.4448i	−0.211046	−	0.649532i	0.788365	−	0.615208i	$-0.210928\pi$
$642$		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	0.792710	−	0.609599i	$-0.208669\pi$
$647$	11.6474	+	8.46236i	0.457908	+	0.332690i	−0.334802	+	0.942288i	$0.608669\pi$
$648$		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	0.964743	−	0.263195i	$-0.0847763\pi$
$653$	25.8746	+	18.7990i	1.01255	+	0.735661i	0.0478084	+	0.998857i	$0.484776\pi$
$654$		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	0.998295	+	0.0583742i	$0.0185917\pi$
$659$	5.77517	+	17.7742i	0.224969	+	0.692383i	−0.773326	+	0.634009i	$0.781408\pi$
$660$		0			0
$661$	−0.209866	+	0.645901i	−0.00816284	+	0.0251226i	−0.955055	−	0.296429i	$-0.904204\pi$
$661$	−0.209866	+	0.645901i	−0.00816284	+	0.0251226i	0.946892	+	0.321551i	$0.104204\pi$
$662$		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	−0.898488	−	0.438999i	$-0.855333\pi$
$673$	2.24247	−	6.90162i	0.0864410	−	0.266038i	0.984929	+	0.172961i	$0.0553333\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	10.4922	−	32.2918i	0.403249	−	1.24107i	−0.519099	−	0.854714i	$-0.673733\pi$
$677$	10.4922	−	32.2918i	0.403249	−	1.24107i	0.922348	−	0.386359i	$-0.126267\pi$
$678$		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	−0.0593717	−	0.998236i	$-0.518910\pi$
$683$	22.7802	−	16.5508i	0.871660	−	0.633298i	0.931032	+	0.364938i	$0.118910\pi$
$684$		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	0.992643	+	0.121076i	$0.0386344\pi$
$691$	6.85416	+	21.0949i	0.260745	+	0.802489i	−0.731899	+	0.681413i	$0.761366\pi$
$692$		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	0.999128	−	0.0417503i	$-0.0132934\pi$
$709$	4.42745	+	13.6263i	0.166276	+	0.511746i	−0.832852	+	0.553496i	$0.813293\pi$
$710$		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	−0.751662	−	0.659549i	$-0.770747\pi$
$719$	−9.56382	+	6.94852i	−0.356670	+	0.259136i	0.394992	+	0.918685i	$0.370747\pi$
$720$		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	−0.957891	−	0.287131i	$-0.907298\pi$
$727$	−0.382051	+	1.17583i	−0.0141695	+	0.0436092i	0.943722	+	0.330740i	$0.107298\pi$
$728$		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	−0.806448	−	0.591305i	$-0.798613\pi$
$733$	−13.3553	+	9.70319i	−0.493289	+	0.358395i	0.313159	+	0.949701i	$0.398613\pi$
$734$		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	0.808504	+	0.588491i	$0.200278\pi$
$739$	−5.20573	+	16.0216i	−0.191496	+	0.589363i	−1.00000		0.000872485i	$0.999722\pi$
$740$		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	−0.993292	−	0.115631i	$-0.963111\pi$
$761$	−3.35824	+	10.3356i	−0.121736	+	0.374665i	0.871556	+	0.490295i	$0.163111\pi$
$762$		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	−0.552467	−	0.833535i	$-0.686313\pi$
$769$	1.92870	−	1.40128i	0.0695505	−	0.0505314i	0.622017	+	0.783004i	$0.286313\pi$
$770$		0			0
$771$	−18.4436	−	13.4001i	−0.664230	−	0.482592i
$772$		0			0
$773$	11.5060	−	35.4118i	0.413841	−	1.27367i	−0.499442	−	0.866347i	$-0.666462\pi$
$773$	11.5060	−	35.4118i	0.413841	−	1.27367i	0.913283	−	0.407325i	$-0.133538\pi$
$774$		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	−0.994364	−	0.106016i	$-0.966191\pi$
$787$	−7.07570	−	21.7768i	−0.252221	−	0.776258i	0.742143	−	0.670242i	$-0.233809\pi$
$788$		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	0.453319	−	0.891348i	$-0.350240\pi$
$797$	−7.17977	−	5.21641i	−0.254321	−	0.184775i	−0.707639	+	0.706574i	$0.750240\pi$
$798$		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	−0.885098	−	0.465404i	$-0.845909\pi$
$809$	−12.5887	−	38.7442i	−0.442597	−	1.36217i	0.442502	−	0.896768i	$-0.354091\pi$
$810$		0			0
$811$	13.8312	−	42.5680i	0.485679	−	1.49476i	−0.345317	−	0.938486i	$-0.612229\pi$
$811$	13.8312	−	42.5680i	0.485679	−	1.49476i	0.830996	−	0.556279i	$-0.187771\pi$
$812$		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	0.993288	+	0.115667i	$0.0369005\pi$
$821$	40.4077	+	29.3579i	1.41024	+	1.02460i	0.416949	+	0.908930i	$0.363099\pi$
$822$		0			0
$823$	4.93877	−	15.2000i	0.172155	−	0.529837i	−0.827338	−	0.561705i	$-0.810146\pi$
$823$	4.93877	−	15.2000i	0.172155	−	0.529837i	0.999492	+	0.0318678i	$0.0101456\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.9525	−	42.9415i	0.485177	−	1.49322i	−0.346546	−	0.938033i	$-0.612646\pi$
$827$	13.9525	−	42.9415i	0.485177	−	1.49322i	0.831724	−	0.555190i	$-0.187354\pi$
$828$		0			0
$829$	12.4972	+	9.07975i	0.434046	+	0.315353i	0.783265	−	0.621688i	$-0.213553\pi$
$829$	12.4972	+	9.07975i	0.434046	+	0.315353i	−0.349219	+	0.937041i	$0.613553\pi$
$830$		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	0.748194	+	0.663480i	$0.230921\pi$
$839$	−7.15711	+	22.0273i	−0.247091	+	0.760468i	−0.995285	+	0.0969885i	$0.969079\pi$
$840$		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	0.576399	−	0.817168i	$-0.304457\pi$
$853$	−0.661719	−	0.480767i	−0.0226568	−	0.0164611i	−0.599056	+	0.800707i	$0.704457\pi$
$854$		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	0.902303	+	0.431102i	$0.141875\pi$
$859$	12.4773	+	38.4012i	0.425720	+	1.31023i	−0.476583	+	0.879129i	$0.658125\pi$
$860$		0			0
$861$	0.623630	−	1.91934i	0.0212533	−	0.0654108i
$862$		0			0
$863$	8.30758	+	25.5681i	0.282793	+	0.870349i	0.987051	+	0.160404i	$0.0512798\pi$
$863$	8.30758	+	25.5681i	0.282793	+	0.870349i	−0.704258	+	0.709944i	$0.748720\pi$
$864$		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	0.760063	+	0.649850i	$0.225168\pi$
$877$	−7.01303	+	21.5839i	−0.236813	+	0.728836i	−0.996876	+	0.0789861i	$0.974832\pi$
$878$		0			0
$879$	12.5071	+	9.08694i	0.421854	+	0.306495i
$880$		0			0
$881$	24.3098	−	17.6621i	0.819017	−	0.595051i	−0.0974139	−	0.995244i	$-0.531057\pi$
$881$	24.3098	−	17.6621i	0.819017	−	0.595051i	0.916431	+	0.400193i	$0.131057\pi$
$882$		0			0
$883$	28.2268	−	20.5079i	0.949906	−	0.690147i	−0.000878603	−	1.00000i	$-0.500280\pi$
$883$	28.2268	−	20.5079i	0.949906	−	0.690147i	0.950785	+	0.309852i	$0.100280\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.9900	+	36.9015i	0.402586	+	1.23903i	0.922894	+	0.385054i	$0.125817\pi$
$887$	11.9900	+	36.9015i	0.402586	+	1.23903i	−0.520308	+	0.853979i	$0.674183\pi$
$888$		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	0.689569	+	0.724220i	$0.257800\pi$
$911$	−8.87343	+	27.3096i	−0.293990	+	0.904808i	−0.983559	+	0.180588i	$0.942200\pi$
$912$		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	−0.607299	−	0.794473i	$-0.707747\pi$
$919$	−1.19370	+	0.867272i	−0.0393764	+	0.0286086i	0.567923	+	0.823082i	$0.307747\pi$
$920$		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	0.978578	−	0.205878i	$-0.0660049\pi$
$929$	33.0756	+	24.0308i	1.08517	+	0.788425i	0.106596	+	0.994302i	$0.466005\pi$
$930$		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	−0.970106	−	0.242683i	$-0.921972\pi$
$937$	−10.0378	−	30.8930i	−0.327919	−	1.00923i	0.642186	−	0.766549i	$-0.278028\pi$
$938$		0			0
$939$	2.30248	−	7.08632i	0.0751387	−	0.231253i
$940$		0			0
$941$	−2.36379	−	7.27501i	−0.0770575	−	0.237159i	0.905106	−	0.425185i	$-0.139791\pi$
$941$	−2.36379	−	7.27501i	−0.0770575	−	0.237159i	−0.982164	+	0.188026i	$0.939791\pi$
$942$		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	0.997746	+	0.0670970i	$0.0213737\pi$
$947$	42.1558	+	30.6280i	1.36988	+	0.995276i	0.372134	+	0.928179i	$0.378626\pi$
$948$		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	0.641553	−	0.767079i	$-0.278290\pi$
$953$	3.40408	+	2.47321i	0.110269	+	0.0801151i	−0.531284	+	0.847194i	$0.678290\pi$
$954$		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	−0.314680	+	0.949198i	$0.601897\pi$
$967$	−40.8816	+	29.7022i	−1.31466	+	0.955158i	−0.999982	+	0.00596071i	$0.998103\pi$
$968$		0			0
$969$	−18.1315	+	13.1733i	−0.582467	+	0.423187i
$970$		0			0
$971$	−12.8283	−	9.32029i	−0.411679	−	0.299102i	0.362602	−	0.931944i	$-0.381888\pi$
$971$	−12.8283	−	9.32029i	−0.411679	−	0.299102i	−0.774281	+	0.632842i	$0.781888\pi$
$972$		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	−0.471741	−	0.881737i	$-0.656374\pi$
$977$	13.3836	−	41.1903i	0.428178	−	1.31780i	0.899918	−	0.436058i	$-0.143626\pi$
$978$		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	−0.0367008	−	0.999326i	$-0.511685\pi$
$983$	28.2920	−	20.5553i	0.902374	−	0.655613i	0.939075	+	0.343713i	$0.111685\pi$
$984$		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	0.846577	−	0.532266i	$-0.178659\pi$
$991$	−4.75904	−	14.6468i	−0.151176	−	0.465272i	−0.997753	+	0.0669939i	$0.978659\pi$
$992$		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	0.907662	−	0.419702i	$-0.137865\pi$
$997$	24.9124	+	18.1000i	0.788985	+	0.573231i	−0.118677	+	0.992933i	$0.537865\pi$
$998$		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.601.5		24
5.2	odd	4		1500.2.o.c.649.6		24
5.3	odd	4		300.2.o.a.229.1	yes	24
5.4	even	2		1500.2.m.c.601.2		24
15.8	even	4		900.2.w.c.829.6		24
25.6	even	5	inner	1500.2.m.d.901.5		24
25.8	odd	20		1500.2.o.c.349.6		24
25.9	even	10		7500.2.a.n.1.3		12
25.12	odd	20		7500.2.d.g.1249.22		24
25.13	odd	20		7500.2.d.g.1249.3		24
25.16	even	5		7500.2.a.m.1.10		12
25.17	odd	20		300.2.o.a.169.1	✓	24
25.19	even	10		1500.2.m.c.901.2		24
75.17	even	20		900.2.w.c.469.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.1	✓	24	25.17	odd	20
300.2.o.a.229.1	yes	24	5.3	odd	4
900.2.w.c.469.6		24	75.17	even	20
900.2.w.c.829.6		24	15.8	even	4
1500.2.m.c.601.2		24	5.4	even	2
1500.2.m.c.901.2		24	25.19	even	10
1500.2.m.d.601.5		24	1.1	even	1	trivial
1500.2.m.d.901.5		24	25.6	even	5	inner
1500.2.o.c.349.6		24	25.8	odd	20
1500.2.o.c.649.6		24	5.2	odd	4
7500.2.a.m.1.10		12	25.16	even	5
7500.2.a.n.1.3		12	25.9	even	10
7500.2.d.g.1249.3		24	25.13	odd	20
7500.2.d.g.1249.22		24	25.12	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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