LMFDB - Embedded newform 1500.2.o.c.649.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1500.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1500 = 2^{2} \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1500.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.9775603032$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			649.6
Character	$\chi$	$=$	1500.649
Dual form			1500.2.o.c.349.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{3} +1.57893i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{3} +1.57893i q^{7} +(-0.309017 - 0.951057i) q^{9} +(1.19917 - 3.69066i) q^{11} +(-0.326475 + 0.106078i) q^{13} +(3.56817 + 4.91117i) q^{17} +(2.98680 - 2.17004i) q^{19} +(1.27738 + 0.928073i) q^{21} +(-1.32236 - 0.429662i) q^{23} +(-0.951057 - 0.309017i) q^{27} +(-2.69395 - 1.95727i) q^{29} +(4.25135 - 3.08879i) q^{31} +(-2.28095 - 3.13946i) q^{33} +(8.14739 - 2.64725i) q^{37} +(-0.106078 + 0.326475i) q^{39} +(-0.394970 - 1.21559i) q^{41} -1.42438i q^{43} +(-0.220691 + 0.303755i) q^{47} +4.50698 q^{49} +6.07054 q^{51} +(6.64151 - 9.14125i) q^{53} -3.69189i q^{57} +(-3.57899 - 11.0150i) q^{59} +(-3.38909 + 10.4305i) q^{61} +(1.50165 - 0.487917i) q^{63} +(6.14771 + 8.46160i) q^{67} +(-1.12487 + 0.817265i) q^{69} +(8.19220 + 5.95198i) q^{71} +(-12.5444 - 4.07594i) q^{73} +(5.82730 + 1.89340i) q^{77} +(11.1640 + 8.11114i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.71826 - 3.74136i) q^{83} +(-3.16693 + 1.02900i) q^{87} +(2.24626 - 6.91326i) q^{89} +(-0.167490 - 0.515482i) q^{91} -5.25496i q^{93} +(-3.55938 + 4.89906i) q^{97} -3.88059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^9	$ 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			1.57893i			0.596780i	0.954444	+	0.298390i	$0.0964496\pi$
$7$			1.57893i			0.596780i	−0.954444	+	0.298390i	$0.903550\pi$
$8$		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
$13$	−0.326475	+	0.106078i	−0.0905480	+	0.0294208i	−0.353941	−	0.935268i	$-0.615159\pi$
$13$	−0.326475	+	0.106078i	−0.0905480	+	0.0294208i	0.263393	+	0.964689i	$0.415159\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.56817	+	4.91117i	0.865409	+	1.19113i	0.980253	+	0.197750i	$0.0633633\pi$
$17$	3.56817	+	4.91117i	0.865409	+	1.19113i	−0.114844	+	0.993384i	$0.536637\pi$
$18$		0			0
$19$	2.98680	−	2.17004i	0.685219	−	0.497841i	−0.189866	−	0.981810i	$-0.560805\pi$
$19$	2.98680	−	2.17004i	0.685219	−	0.497841i	0.875085	+	0.483969i	$0.160805\pi$
$20$		0			0
$21$	1.27738	+	0.928073i	0.278748	+	0.202522i
$22$		0			0
$23$	−1.32236	−	0.429662i	−0.275732	−	0.0895906i	0.167887	−	0.985806i	$-0.446306\pi$
$23$	−1.32236	−	0.429662i	−0.275732	−	0.0895906i	−0.443619	+	0.896216i	$0.646306\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$		0			0
$29$	−2.69395	−	1.95727i	−0.500254	−	0.363455i	0.308860	−	0.951107i	$-0.400052\pi$
$29$	−2.69395	−	1.95727i	−0.500254	−	0.363455i	−0.809114	+	0.587652i	$0.800052\pi$
$30$		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
$33$	−2.28095	−	3.13946i	−0.397063	−	0.546510i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.14739	−	2.64725i	1.33942	−	0.435205i	0.450301	−	0.892877i	$-0.351317\pi$
$37$	8.14739	−	2.64725i	1.33942	−	0.435205i	0.889121	+	0.457672i	$0.151317\pi$
$38$		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
$43$		−	1.42438i		−	0.217216i	−0.994085	−	0.108608i	$-0.965361\pi$
$43$		−	1.42438i		−	0.217216i	0.994085	−	0.108608i	$-0.0346394\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.220691	+	0.303755i	−0.0321911	+	0.0443072i	−0.824809	−	0.565411i	$-0.808717\pi$
$47$	−0.220691	+	0.303755i	−0.0321911	+	0.0443072i	0.792618	+	0.609718i	$0.208717\pi$
$48$		0			0
$49$	4.50698			0.643854
$50$		0			0
$51$	6.07054			0.850045
$52$		0			0
$53$	6.64151	−	9.14125i	0.912282	−	1.25565i	−0.0540999	−	0.998536i	$-0.517229\pi$
$53$	6.64151	−	9.14125i	0.912282	−	1.25565i	0.966382	−	0.257112i	$-0.0827711\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	3.69189i		−	0.489002i
$58$		0			0
$59$	−3.57899	−	11.0150i	−0.465945	−	1.43403i	−0.857791	−	0.513999i	$-0.828163\pi$
$59$	−3.57899	−	11.0150i	−0.465945	−	1.43403i	0.391846	−	0.920031i	$-0.371837\pi$
$60$		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
$63$	1.50165	−	0.487917i	0.189190	−	0.0614717i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.14771	+	8.46160i	0.751063	+	1.03375i	0.997905	+	0.0646937i	$0.0206070\pi$
$67$	6.14771	+	8.46160i	0.751063	+	1.03375i	−0.246842	+	0.969056i	$0.579393\pi$
$68$		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
$73$	−12.5444	−	4.07594i	−1.46822	−	0.477052i	−0.537648	−	0.843170i	$-0.680687\pi$
$73$	−12.5444	−	4.07594i	−1.46822	−	0.477052i	−0.930569	+	0.366117i	$0.880687\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.82730	+	1.89340i	0.664082	+	0.215773i
$78$		0			0
$79$	11.1640	+	8.11114i	1.25605	+	0.912574i	0.998557	−	0.0537055i	$-0.0171032\pi$
$79$	11.1640	+	8.11114i	1.25605	+	0.912574i	0.257494	+	0.966280i	$0.417103\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−2.71826	−	3.74136i	−0.298367	−	0.410668i	0.633342	−	0.773872i	$-0.281683\pi$
$83$	−2.71826	−	3.74136i	−0.298367	−	0.410668i	−0.931709	+	0.363204i	$0.881683\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.16693	+	1.02900i	−0.339530	+	0.110320i
$88$		0			0
$89$	2.24626	−	6.91326i	0.238103	−	0.732805i	−0.758592	−	0.651566i	$-0.774112\pi$
$89$	2.24626	−	6.91326i	0.238103	−	0.732805i	0.996695	−	0.0812387i	$-0.0258876\pi$
$90$		0			0
$91$	−0.167490	−	0.515482i	−0.0175578	−	0.0540372i
$92$		0			0
$93$		−	5.25496i		−	0.544914i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.55938	+	4.89906i	−0.361400	+	0.497424i	−0.950538	−	0.310608i	$-0.899467\pi$
$97$	−3.55938	+	4.89906i	−0.361400	+	0.497424i	0.589138	+	0.808032i	$0.299467\pi$
$98$		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
$103$	−4.52433	+	6.22721i	−0.445796	+	0.613585i	−0.971488	−	0.237090i	$-0.923806\pi$
$103$	−4.52433	+	6.22721i	−0.445796	+	0.613585i	0.525692	+	0.850675i	$0.323806\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	18.0376i		−	1.74376i	−0.489722	−	0.871878i	$-0.662902\pi$
$107$		−	18.0376i		−	1.74376i	0.489722	−	0.871878i	$-0.337098\pi$
$108$		0			0
$109$	−5.16860	−	15.9073i	−0.495062	−	1.52364i	−0.816861	−	0.576835i	$-0.804288\pi$
$109$	−5.16860	−	15.9073i	−0.495062	−	1.52364i	0.321799	−	0.946808i	$-0.395712\pi$
$110$		0			0
$111$	2.64725	−	8.14739i	0.251266	−	0.773316i
$112$		0			0
$113$	−2.15793	+	0.701155i	−0.203001	+	0.0659591i	−0.408753	−	0.912645i	$-0.634036\pi$
$113$	−2.15793	+	0.701155i	−0.203001	+	0.0659591i	0.205751	+	0.978604i	$0.434036\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.201773	+	0.277717i	0.0186539	+	0.0256749i
$118$		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
$123$	−1.21559	−	0.394970i	−0.109606	−	0.0356132i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.43348	+	0.465767i	0.127201	+	0.0413301i	0.371926	−	0.928262i	$-0.378698\pi$
$127$	1.43348	+	0.465767i	0.127201	+	0.0413301i	−0.244725	+	0.969593i	$0.578698\pi$
$128$		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
$133$	3.42634	+	4.71595i	0.297101	+	0.408925i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.17996	+	1.68307i	−0.442554	+	0.143795i	−0.521814	−	0.853059i	$-0.674744\pi$
$137$	−5.17996	+	1.68307i	−0.442554	+	0.143795i	0.0792596	+	0.996854i	$0.474744\pi$
$138$		0			0
$139$	3.05409	−	9.39953i	0.259045	−	0.797258i	−0.733961	−	0.679192i	$-0.762331\pi$
$139$	3.05409	−	9.39953i	0.259045	−	0.797258i	0.993006	−	0.118066i	$-0.0376694\pi$
$140$		0			0
$141$	0.116024	+	0.357085i	0.00977099	+	0.0300720i
$142$		0			0
$143$			1.33211i			0.111397i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.64913	−	3.64622i	0.218497	−	0.300735i
$148$		0			0
$149$	−0.0649364			−0.00531979			−0.00265990	−	0.999996i	$-0.500847\pi$
$149$	−0.0649364			−0.00531979			−0.00265990	+	0.999996i	$0.500847\pi$
$150$		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
$153$	3.56817	−	4.91117i	0.288470	−	0.397044i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			23.4721i			1.87328i	0.350300	+	0.936638i	$0.386080\pi$
$157$			23.4721i			1.87328i	−0.350300	+	0.936638i	$0.613920\pi$
$158$		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
$163$	−5.70240	+	1.85282i	−0.446646	+	0.145124i	−0.523700	−	0.851903i	$-0.675449\pi$
$163$	−5.70240	+	1.85282i	−0.446646	+	0.145124i	0.0770538	+	0.997027i	$0.475449\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.76094	−	5.17649i	−0.291030	−	0.400569i	0.638318	−	0.769773i	$-0.279630\pi$
$167$	−3.76094	−	5.17649i	−0.291030	−	0.400569i	−0.929348	+	0.369204i	$0.879630\pi$
$168$		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
$173$	−4.96583	−	1.61350i	−0.377545	−	0.122672i	0.114096	−	0.993470i	$-0.463603\pi$
$173$	−4.96583	−	1.61350i	−0.377545	−	0.122672i	−0.491641	+	0.870798i	$0.663603\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−11.0150	−	3.57899i	−0.827937	−	0.269013i
$178$		0			0
$179$	18.8534	+	13.6978i	1.40917	+	1.02382i	0.993443	+	0.114329i	$0.0364718\pi$
$179$	18.8534	+	13.6978i	1.40917	+	1.02382i	0.415724	+	0.909491i	$0.363528\pi$
$180$		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
$183$	6.44643	+	8.87275i	0.476534	+	0.655893i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	22.4043	−	7.27959i	1.63836	−	0.532336i
$188$		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
$193$			20.2575i			1.45817i	0.684424	+	0.729084i	$0.260054\pi$
$193$			20.2575i			1.45817i	−0.684424	+	0.729084i	$0.739946\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−11.7650	+	16.1931i	−0.838221	+	1.15371i	0.148115	+	0.988970i	$0.452679\pi$
$197$	−11.7650	+	16.1931i	−0.838221	+	1.15371i	−0.986337	+	0.164742i	$0.947321\pi$
$198$		0			0
$199$	22.4180			1.58917			0.794585	−	0.607153i	$-0.207689\pi$
$199$	22.4180			1.58917			0.794585	+	0.607153i	$0.207689\pi$
$200$		0			0
$201$	10.4591			0.737729
$202$		0			0
$203$	3.09039	−	4.25356i	0.216903	−	0.298541i
$204$		0			0
$205$		0			0
$206$		0			0
$207$			1.39041i			0.0966404i
$208$		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
$213$	9.63050	−	3.12914i	0.659871	−	0.214405i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.87698	+	6.71259i	0.331071	+	0.455680i
$218$		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
$223$	11.7779	+	3.82686i	0.788705	+	0.256266i	0.675552	−	0.737312i	$-0.263905\pi$
$223$	11.7779	+	3.82686i	0.788705	+	0.256266i	0.113152	+	0.993578i	$0.463905\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−17.3309	−	5.63116i	−1.15029	−	0.373753i	−0.329040	−	0.944316i	$-0.606725\pi$
$227$	−17.3309	−	5.63116i	−1.15029	−	0.373753i	−0.821254	+	0.570563i	$0.806725\pi$
$228$		0			0
$229$	13.2812	+	9.64932i	0.877643	+	0.637645i	0.932627	−	0.360842i	$-0.117511\pi$
$229$	13.2812	+	9.64932i	0.877643	+	0.637645i	−0.0549837	+	0.998487i	$0.517511\pi$
$230$		0			0
$231$	4.95699	−	3.60147i	0.326146	−	0.236959i
$232$		0			0
$233$	−3.01993	−	4.15658i	−0.197842	−	0.272307i	0.698557	−	0.715555i	$-0.253826\pi$
$233$	−3.01993	−	4.15658i	−0.197842	−	0.272307i	−0.896399	+	0.443248i	$0.853826\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	13.1241	−	4.26428i	0.852502	−	0.276995i
$238$		0			0
$239$	−7.58924	+	23.3573i	−0.490907	+	1.51086i	0.332332	+	0.943162i	$0.392165\pi$
$239$	−7.58924	+	23.3573i	−0.490907	+	1.51086i	−0.823239	+	0.567694i	$0.807835\pi$
$240$		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
$243$			1.00000i			0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.744923	+	1.02530i	−0.0473983	+	0.0652382i
$248$		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
$253$	−3.17147	+	4.36515i	−0.199388	+	0.274435i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	22.7976i		−	1.42207i	−0.703155	−	0.711036i	$-0.748226\pi$
$257$		−	22.7976i		−	1.42207i	0.703155	−	0.711036i	$-0.251774\pi$
$258$		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
$263$	8.98231	−	2.91853i	0.553873	−	0.179964i	−0.0186895	−	0.999825i	$-0.505949\pi$
$263$	8.98231	−	2.91853i	0.553873	−	0.179964i	0.572562	+	0.819861i	$0.305949\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.27263	−	5.88077i	−0.261481	−	0.359898i
$268$		0			0
$269$	−23.7720	+	17.2714i	−1.44940	+	1.05305i	−0.463433	+	0.886132i	$0.653382\pi$
$269$	−23.7720	+	17.2714i	−1.44940	+	1.05305i	−0.985970	+	0.166921i	$0.946618\pi$
$270$		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
$273$	−0.515482	−	0.167490i	−0.0311984	−	0.0101370i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−14.6259	−	4.75225i	−0.878786	−	0.285535i	−0.165333	−	0.986238i	$-0.552870\pi$
$277$	−14.6259	−	4.75225i	−0.878786	−	0.285535i	−0.713453	+	0.700703i	$0.752870\pi$
$278$		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
$283$	6.98697	+	9.61673i	0.415332	+	0.571655i	0.964509	−	0.264051i	$-0.0850586\pi$
$283$	6.98697	+	9.61673i	0.415332	+	0.571655i	−0.549177	+	0.835706i	$0.685059\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.91934	−	0.623630i	0.113295	−	0.0368117i
$288$		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
$293$		−	15.4596i		−	0.903161i	−0.892230	−	0.451581i	$-0.850860\pi$
$293$		−	15.4596i		−	0.903161i	0.892230	−	0.451581i	$-0.149140\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.28095	+	3.13946i	−0.132354	+	0.182170i
$298$		0			0
$299$	0.477297			0.0276028
$300$		0			0
$301$	2.24900			0.129630
$302$		0			0
$303$	1.89876	−	2.61341i	0.109081	−	0.150137i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	26.6092i		−	1.51867i	−0.650702	−	0.759334i	$-0.725525\pi$
$307$		−	26.6092i		−	1.51867i	0.650702	−	0.759334i	$-0.274475\pi$
$308$		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
$313$	−7.08632	+	2.30248i	−0.400542	+	0.130144i	−0.502359	−	0.864659i	$-0.667534\pi$
$313$	−7.08632	+	2.30248i	−0.400542	+	0.130144i	0.101817	+	0.994803i	$0.467534\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.74481	−	2.40152i	−0.0979981	−	0.134883i	0.757202	−	0.653181i	$-0.226566\pi$
$317$	−1.74481	−	2.40152i	−0.0979981	−	0.134883i	−0.855200	+	0.518298i	$0.826566\pi$
$318$		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
$323$	21.3148	+	6.92561i	1.18599	+	0.385351i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−15.9073	−	5.16860i	−0.879676	−	0.285824i
$328$		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
$333$	−5.03536	−	6.93058i	−0.275936	−	0.379794i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−7.14905	+	2.32287i	−0.389433	+	0.126535i	−0.497188	−	0.867643i	$-0.665634\pi$
$337$	−7.14905	+	2.32287i	−0.389433	+	0.126535i	0.107754	+	0.994178i	$0.465634\pi$
$338$		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
$343$			18.1687i			0.981019i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.05022	+	9.70380i	−0.378476	+	0.520927i	−0.955180	−	0.296026i	$-0.904339\pi$
$347$	−7.05022	+	9.70380i	−0.378476	+	0.520927i	0.576704	+	0.816953i	$0.304339\pi$
$348$		0			0
$349$	3.50169			0.187441			0.0937207	−	0.995599i	$-0.470124\pi$
$349$	3.50169			0.187441			0.0937207	+	0.995599i	$0.470124\pi$
$350$		0			0
$351$	0.343277			0.0183227
$352$		0			0
$353$	−14.6665	+	20.1867i	−0.780617	+	1.07443i	0.214596	+	0.976703i	$0.431156\pi$
$353$	−14.6665	+	20.1867i	−0.780617	+	1.07443i	−0.995214	+	0.0977244i	$0.968844\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			9.58496i			0.507290i
$358$		0			0
$359$	−0.247954	−	0.763123i	−0.0130865	−	0.0402761i	0.944300	−	0.329086i	$-0.106741\pi$
$359$	−0.247954	−	0.763123i	−0.0130865	−	0.0402761i	−0.957387	+	0.288810i	$0.906741\pi$
$360$		0			0
$361$	−1.65941	+	5.10714i	−0.0873374	+	0.268797i
$362$		0			0
$363$	−3.86030	+	1.25429i	−0.202613	+	0.0658330i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.28986	+	12.7864i	0.484927	+	0.667445i	0.979442	−	0.201724i	$-0.0646544\pi$
$367$	9.28986	+	12.7864i	0.484927	+	0.667445i	−0.494515	+	0.869169i	$0.664654\pi$
$368$		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
$373$	3.43291	+	1.11542i	0.177750	+	0.0577543i	0.396540	−	0.918018i	$-0.370211\pi$
$373$	3.43291	+	1.11542i	0.177750	+	0.0577543i	−0.218790	+	0.975772i	$0.570211\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.08713	+	0.353230i	0.0559901	+	0.0181923i
$378$		0			0
$379$	22.0967	+	16.0542i	1.13503	+	0.824647i	0.986419	−	0.164249i	$-0.0525201\pi$
$379$	22.0967	+	16.0542i	1.13503	+	0.824647i	0.148610	+	0.988896i	$0.452520\pi$
$380$		0			0
$381$	1.21939	−	0.885941i	0.0624714	−	0.0453881i
$382$		0			0
$383$	11.3334	+	15.5991i	0.579112	+	0.797079i	0.993598	−	0.112977i	$-0.0360386\pi$
$383$	11.3334	+	15.5991i	0.579112	+	0.797079i	−0.414486	+	0.910056i	$0.636039\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.35467	+	0.440159i	−0.0688617	+	0.0223745i
$388$		0			0
$389$	5.27164	−	16.2244i	0.267283	−	0.822612i	−0.723876	−	0.689930i	$-0.757641\pi$
$389$	5.27164	−	16.2244i	0.267283	−	0.822612i	0.991159	−	0.132682i	$-0.0423589\pi$
$390$		0			0
$391$	−2.60828	−	8.02745i	−0.131906	−	0.405966i
$392$		0			0
$393$		−	15.9388i		−	0.804006i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−16.0842	+	22.1380i	−0.807243	+	1.11108i	0.184499	+	0.982833i	$0.440934\pi$
$397$	−16.0842	+	22.1380i	−0.807243	+	1.11108i	−0.991743	+	0.128243i	$0.959066\pi$
$398$		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
$403$	−1.06031	+	1.45939i	−0.0528177	+	0.0726974i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	33.2437i		−	1.64783i
$408$		0			0
$409$	−6.72523	−	20.6981i	−0.332541	−	1.02346i	−0.967921	−	0.251256i	$-0.919156\pi$
$409$	−6.72523	−	20.6981i	−0.332541	−	1.02346i	0.635379	−	0.772200i	$-0.280844\pi$
$410$		0			0
$411$	−1.68307	+	5.17996i	−0.0830198	+	0.255509i
$412$		0			0
$413$	17.3919	−	5.65098i	0.855800	−	0.278066i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.80923	−	7.99572i	−0.284479	−	0.391552i
$418$		0			0
$419$	−3.67055	+	2.66681i	−0.179318	+	0.130282i	−0.673824	−	0.738892i	$-0.735349\pi$
$419$	−3.67055	+	2.66681i	−0.179318	+	0.130282i	0.494505	+	0.869175i	$0.335349\pi$
$420$		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
$423$	0.357085	+	0.116024i	0.0173621	+	0.00564128i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−16.4691	−	5.35114i	−0.796996	−	0.258960i
$428$		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
$433$	2.00963	+	2.76602i	0.0965768	+	0.132927i	0.854571	−	0.519335i	$-0.173820\pi$
$433$	2.00963	+	2.76602i	0.0965768	+	0.132927i	−0.757994	+	0.652262i	$0.773820\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.88201	+	1.58626i	−0.233538	+	0.0758812i
$438$		0			0
$439$	1.84058	−	5.66473i	0.0878462	−	0.270363i	−0.897477	−	0.441061i	$-0.854602\pi$
$439$	1.84058	−	5.66473i	0.0878462	−	0.270363i	0.985323	+	0.170698i	$0.0546023\pi$
$440$		0			0
$441$	−1.39273	−	4.28639i	−0.0663206	−	0.204114i
$442$		0			0
$443$			33.0705i			1.57122i	0.618719	+	0.785612i	$0.287652\pi$
$443$			33.0705i			1.57122i	−0.618719	+	0.785612i	$0.712348\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.0381686	+	0.0525346i	−0.00180531	+	0.00248480i
$448$		0			0
$449$	8.68077			0.409671			0.204835	−	0.978796i	$-0.434334\pi$
$449$	8.68077			0.409671			0.204835	+	0.978796i	$0.434334\pi$
$450$		0			0
$451$	−4.95997			−0.233556
$452$		0			0
$453$	−7.12518	+	9.80697i	−0.334770	+	0.460771i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	13.3667i		−	0.625269i	−0.949873	−	0.312635i	$-0.898788\pi$
$457$		−	13.3667i		−	0.625269i	0.949873	−	0.312635i	$-0.101212\pi$
$458$		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
$463$	−21.9961	+	7.14695i	−1.02224	+	0.332147i	−0.771719	−	0.635963i	$-0.780603\pi$
$463$	−21.9961	+	7.14695i	−1.02224	+	0.332147i	−0.250524	+	0.968110i	$0.580603\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	17.8034	+	24.5043i	0.823845	+	1.13392i	0.989038	+	0.147664i	$0.0471753\pi$
$467$	17.8034	+	24.5043i	0.823845	+	1.13392i	−0.165193	+	0.986261i	$0.552825\pi$
$468$		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
$473$	−5.25691	−	1.70807i	−0.241713	−	0.0785373i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−10.7462	−	3.49165i	−0.492034	−	0.159872i
$478$		0			0
$479$	−19.4809	−	14.1537i	−0.890107	−	0.646700i	0.0457990	−	0.998951i	$-0.485417\pi$
$479$	−19.4809	−	14.1537i	−0.890107	−	0.646700i	−0.935906	+	0.352250i	$0.885417\pi$
$480$		0			0
$481$	−2.37911	+	1.72852i	−0.108478	+	0.0788138i
$482$		0			0
$483$	−1.29040	−	1.77609i	−0.0587155	−	0.0808149i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	2.14446	−	0.696777i	0.0971747	−	0.0315740i	−0.260026	−	0.965602i	$-0.583731\pi$
$487$	2.14446	−	0.696777i	0.0971747	−	0.0315740i	0.357201	+	0.934028i	$0.383731\pi$
$488$		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
$493$		−	20.2143i		−	0.910406i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.39777	+	12.9349i	−0.421547	+	0.580210i
$498$		0			0
$499$	26.9489			1.20640			0.603199	−	0.797590i	$-0.293892\pi$
$499$	26.9489			1.20640			0.603199	+	0.797590i	$0.293892\pi$
$500$		0			0
$501$	−6.39850			−0.285864
$502$		0			0
$503$	0.245105	−	0.337358i	0.0109287	−	0.0150421i	−0.803518	−	0.595281i	$-0.797041\pi$
$503$	0.245105	−	0.337358i	0.0109287	−	0.0150421i	0.814446	+	0.580239i	$0.197041\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			12.8822i			0.572117i
$508$		0			0
$509$	−4.14176	−	12.7470i	−0.183580	−	0.565002i	0.816341	−	0.577571i	$-0.195999\pi$
$509$	−4.14176	−	12.7470i	−0.183580	−	0.565002i	−0.999921	+	0.0125684i	$0.995999\pi$
$510$		0			0
$511$	6.43563	−	19.8068i	0.284695	−	0.876202i
$512$		0			0
$513$	−3.51119	+	1.14086i	−0.155023	+	0.0503700i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.856410	+	1.17875i	0.0376649	+	0.0518412i
$518$		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
$523$	11.2943	+	3.66974i	0.493866	+	0.160467i	0.545352	−	0.838207i	$-0.316396\pi$
$523$	11.2943	+	3.66974i	0.493866	+	0.160467i	−0.0514866	+	0.998674i	$0.516396\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	30.3391	+	9.85777i	1.32159	+	0.429411i
$528$		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
$533$	0.257896	+	0.354963i	0.0111707	+	0.0153752i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	22.1635	−	7.20135i	0.956424	−	0.310761i
$538$		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
$543$			25.1739i			1.08032i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	23.2652	−	32.0219i	0.994750	−	1.36916i	0.0662579	−	0.997803i	$-0.478894\pi$
$547$	23.2652	−	32.0219i	0.994750	−	1.36916i	0.928492	−	0.371353i	$-0.121106\pi$
$548$		0			0
$549$	10.9673			0.468074
$550$		0			0
$551$	−12.2936			−0.523726
$552$		0			0
$553$	−12.8069	+	17.6272i	−0.544606	+	0.749586i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	12.1804i		−	0.516102i	−0.966131	−	0.258051i	$-0.916920\pi$
$557$		−	12.1804i		−	0.516102i	0.966131	−	0.258051i	$-0.0830802\pi$
$558$		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
$563$	−34.7979	+	11.3065i	−1.46656	+	0.476513i	−0.930065	−	0.367394i	$-0.880250\pi$
$563$	−34.7979	+	11.3065i	−1.46656	+	0.476513i	−0.536490	+	0.843907i	$0.680250\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.928073	−	1.27738i	−0.0389754	−	0.0536450i
$568$		0			0
$569$	−27.3735	+	19.8880i	−1.14756	+	0.833749i	−0.988154	−	0.153464i	$-0.950957\pi$
$569$	−27.3735	+	19.8880i	−1.14756	+	0.833749i	−0.159403	+	0.987214i	$0.550957\pi$
$570$		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
$573$	7.63843	+	2.48188i	0.319100	+	0.103682i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−15.6012	−	5.06913i	−0.649485	−	0.211031i	−0.0342981	−	0.999412i	$-0.510920\pi$
$577$	−15.6012	−	5.06913i	−0.649485	−	0.211031i	−0.615187	+	0.788381i	$0.710920\pi$
$578$		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
$583$	−25.7730	−	35.4734i	−1.06741	−	1.46916i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−32.0429	+	10.4114i	−1.32255	+	0.429724i	−0.883371	−	0.468674i	$-0.844732\pi$
$587$	−32.0429	+	10.4114i	−1.32255	+	0.429724i	−0.439182	+	0.898398i	$0.644732\pi$
$588$		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
$593$		−	32.2208i		−	1.32315i	−0.749878	−	0.661576i	$-0.769888\pi$
$593$		−	32.2208i		−	1.32315i	0.749878	−	0.661576i	$-0.230112\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	13.1770	−	18.1365i	0.539297	−	0.742279i
$598$		0			0
$599$	14.7284			0.601784			0.300892	−	0.953658i	$-0.402716\pi$
$599$	14.7284			0.601784			0.300892	+	0.953658i	$0.402716\pi$
$600$		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
$603$	6.14771	−	8.46160i	0.250354	−	0.344583i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			16.0986i			0.653421i	0.945124	+	0.326710i	$0.105940\pi$
$607$			16.0986i			0.653421i	−0.945124	+	0.326710i	$0.894060\pi$
$608$		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
$613$	41.1487	−	13.3700i	1.66198	−	0.540010i	0.680693	−	0.732569i	$-0.261679\pi$
$613$	41.1487	−	13.3700i	1.66198	−	0.540010i	0.981285	+	0.192559i	$0.0616787\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.931550	+	1.28217i	0.0375028	+	0.0516182i	0.827357	−	0.561677i	$-0.189844\pi$
$617$	0.931550	+	1.28217i	0.0375028	+	0.0516182i	−0.789854	+	0.613295i	$0.789844\pi$
$618$		0			0
$619$	−10.9048	+	7.92281i	−0.438301	+	0.318444i	−0.784960	−	0.619547i	$-0.787316\pi$
$619$	−10.9048	+	7.92281i	−0.438301	+	0.318444i	0.346658	+	0.937991i	$0.387316\pi$
$620$		0			0
$621$	1.12487	+	0.817265i	0.0451394	+	0.0327957i
$622$		0			0
$623$	10.9156	+	3.54668i	0.437323	+	0.142095i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−13.6255	−	4.42719i	−0.544150	−	0.176805i
$628$		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
$633$	−5.09348	−	7.01057i	−0.202448	−	0.278645i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.47142	+	0.478092i	−0.0582997	+	0.0189427i
$638$		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
$643$		−	46.8857i		−	1.84899i	−0.381190	−	0.924497i	$-0.624486\pi$
$643$		−	46.8857i		−	1.84899i	0.381190	−	0.924497i	$-0.375514\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.46236	+	11.6474i	−0.332690	+	0.457908i	−0.942288	−	0.334802i	$-0.891331\pi$
$647$	−8.46236	+	11.6474i	−0.332690	+	0.457908i	0.609599	+	0.792710i	$0.291331\pi$
$648$		0			0
$649$	−44.9444			−1.76422
$650$		0			0
$651$	8.29722			0.325194
$652$		0			0
$653$	18.7990	−	25.8746i	0.735661	−	1.01255i	−0.263195	−	0.964743i	$-0.584776\pi$
$653$	18.7990	−	25.8746i	0.735661	−	1.01255i	0.998857	−	0.0478084i	$-0.0152237\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			13.1900i			0.514591i
$658$		0			0
$659$	−5.77517	−	17.7742i	−0.224969	−	0.692383i	−0.998295	−	0.0583742i	$-0.981408\pi$
$659$	−5.77517	−	17.7742i	−0.224969	−	0.692383i	0.773326	−	0.634009i	$-0.218592\pi$
$660$		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
$663$	−1.98188	+	0.643952i	−0.0769699	+	0.0250090i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.72141	+	3.74570i	0.105373	+	0.145034i
$668$		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
$673$	−6.90162	−	2.24247i	−0.266038	−	0.0864410i	0.172961	−	0.984929i	$-0.444667\pi$
$673$	−6.90162	−	2.24247i	−0.266038	−	0.0864410i	−0.438999	+	0.898488i	$0.644667\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	32.2918	+	10.4922i	1.24107	+	0.403249i	0.854714	−	0.519099i	$-0.173733\pi$
$677$	32.2918	+	10.4922i	1.24107	+	0.403249i	0.386359	+	0.922348i	$0.373733\pi$
$678$		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
$683$	−16.5508	−	22.7802i	−0.633298	−	0.871660i	0.364938	−	0.931032i	$-0.381090\pi$
$683$	−16.5508	−	22.7802i	−0.633298	−	0.871660i	−0.998236	+	0.0593717i	$0.981090\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	15.6129	−	5.07295i	0.595670	−	0.193545i
$688$		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
$693$		−	6.12718i		−	0.232752i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.56066	−	6.27721i	0.172747	−	0.237766i
$698$		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
$703$	18.5900	−	25.5869i	0.701135	−	0.965030i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			5.10051i			0.191824i
$708$		0			0
$709$	−4.42745	−	13.6263i	−0.166276	−	0.511746i	0.832852	−	0.553496i	$-0.186707\pi$
$709$	−4.42745	−	13.6263i	−0.166276	−	0.511746i	−0.999128	+	0.0417503i	$0.986707\pi$
$710$		0			0
$711$	4.26428	−	13.1241i	0.159923	−	0.492192i
$712$		0			0
$713$	−6.94896	+	2.25785i	−0.260241	+	0.0845573i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	14.4356	+	19.8689i	0.539107	+	0.742017i
$718$		0			0
$719$	9.56382	−	6.94852i	0.356670	−	0.259136i	−0.394992	−	0.918685i	$-0.629253\pi$
$719$	9.56382	−	6.94852i	0.356670	−	0.259136i	0.751662	+	0.659549i	$0.229253\pi$
$720$		0			0
$721$	−9.83234	−	7.14361i	−0.366175	−	0.266042i
$722$		0			0
$723$	4.59846	+	1.49413i	0.171019	+	0.0555673i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−1.17583	−	0.382051i	−0.0436092	−	0.0141695i	0.287131	−	0.957891i	$-0.407298\pi$
$727$	−1.17583	−	0.382051i	−0.0436092	−	0.0141695i	−0.330740	+	0.943722i	$0.607298\pi$
$728$		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
$733$	9.70319	+	13.3553i	0.358395	+	0.493289i	0.949701	−	0.313159i	$-0.101387\pi$
$733$	9.70319	+	13.3553i	0.358395	+	0.493289i	−0.591305	+	0.806448i	$0.701387\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	38.6010	−	12.5422i	1.42189	−	0.461999i
$738$		0			0
$739$	5.20573	−	16.0216i	0.191496	−	0.589363i	−0.808504	−	0.588491i	$-0.799722\pi$
$739$	5.20573	−	16.0216i	0.191496	−	0.589363i	1.00000		0.000872485i	$-0.000277721\pi$
$740$		0			0
$741$	0.391629	+	1.20531i	0.0143869	+	0.0442782i
$742$		0			0
$743$		−	11.8940i		−	0.436347i	−0.975910	−	0.218174i	$-0.929990\pi$
$743$		−	11.8940i		−	0.436347i	0.975910	−	0.218174i	$-0.0700099\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−2.71826	+	3.74136i	−0.0994558	+	0.136889i
$748$		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
$753$	−8.89875	+	12.2481i	−0.324288	+	0.446345i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			32.5591i			1.18338i	0.806166	+	0.591690i	$0.201539\pi$
$757$			32.5591i			1.18338i	−0.806166	+	0.591690i	$0.798461\pi$
$758$		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
$763$	25.1165	−	8.16086i	0.909280	−	0.295443i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.33690	+	3.21647i	0.0843807	+	0.116140i
$768$		0			0
$769$	−1.92870	+	1.40128i	−0.0695505	+	0.0505314i	−0.622017	−	0.783004i	$-0.713687\pi$
$769$	−1.92870	+	1.40128i	−0.0695505	+	0.0505314i	0.552467	+	0.833535i	$0.313687\pi$
$770$		0			0
$771$	−18.4436	−	13.4001i	−0.664230	−	0.482592i
$772$		0			0
$773$	−35.4118	−	11.5060i	−1.27367	−	0.413841i	−0.407325	−	0.913283i	$-0.633538\pi$
$773$	−35.4118	−	11.5060i	−1.27367	−	0.413841i	−0.866347	+	0.499442i	$0.833538\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	12.8642	+	4.17982i	0.461500	+	0.149950i
$778$		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
$783$	1.95727	+	2.69395i	0.0699470	+	0.0962738i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	21.7768	−	7.07570i	0.776258	−	0.252221i	0.106016	−	0.994364i	$-0.466191\pi$
$787$	21.7768	−	7.07570i	0.776258	−	0.252221i	0.670242	+	0.742143i	$0.266191\pi$
$788$		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
$793$		−	3.76483i		−	0.133693i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.21641	−	7.17977i	0.184775	−	0.254321i	−0.706574	−	0.707639i	$-0.749760\pi$
$797$	5.21641	−	7.17977i	0.184775	−	0.254321i	0.891348	+	0.453319i	$0.149760\pi$
$798$		0			0
$799$	−2.27925			−0.0806342
$800$		0			0
$801$	−7.26904			−0.256839
$802$		0			0
$803$	−30.0858	+	41.4095i	−1.06170	+	1.46131i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			29.3838i			1.03436i
$808$		0			0
$809$	12.5887	+	38.7442i	0.442597	+	1.36217i	0.885098	+	0.465404i	$0.154091\pi$
$809$	12.5887	+	38.7442i	0.442597	+	1.36217i	−0.442502	+	0.896768i	$0.645909\pi$
$810$		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
$813$	−14.7303	+	4.78615i	−0.516613	+	0.167858i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−3.09096	−	4.25435i	−0.108139	−	0.148841i
$818$		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
$823$	−15.2000	−	4.93877i	−0.529837	−	0.172155i	0.0318678	−	0.999492i	$-0.489854\pi$
$823$	−15.2000	−	4.93877i	−0.529837	−	0.172155i	−0.561705	+	0.827338i	$0.689854\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	42.9415	+	13.9525i	1.49322	+	0.485177i	0.938033	−	0.346546i	$-0.112646\pi$
$827$	42.9415	+	13.9525i	1.49322	+	0.485177i	0.555190	+	0.831724i	$0.312646\pi$
$828$		0			0
$829$	−12.4972	−	9.07975i	−0.434046	−	0.315353i	0.349219	−	0.937041i	$-0.386447\pi$
$829$	−12.4972	−	9.07975i	−0.434046	−	0.315353i	−0.783265	+	0.621688i	$0.786447\pi$
$830$		0			0
$831$	−12.4415	+	9.03931i	−0.431592	+	0.313570i
$832$		0			0
$833$	16.0817	+	22.1345i	0.557197	+	0.766916i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.99776	+	1.62387i	−0.172748	+	0.0561292i
$838$		0			0
$839$	7.15711	−	22.0273i	0.247091	−	0.760468i	−0.748194	−	0.663480i	$-0.769079\pi$
$839$	7.15711	−	22.0273i	0.247091	−	0.760468i	0.995285	−	0.0969885i	$-0.0309210\pi$
$840$		0			0
$841$	−5.53504	−	17.0351i	−0.190863	−	0.587417i
$842$		0			0
$843$			3.87277i			0.133385i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.76701	−	5.18484i	0.129436	−	0.178153i
$848$		0			0
$849$	11.8869			0.407959
$850$		0			0
$851$	−11.9112			−0.408311
$852$		0			0
$853$	−0.480767	+	0.661719i	−0.0164611	+	0.0226568i	−0.817168	−	0.576399i	$-0.804457\pi$
$853$	−0.480767	+	0.661719i	−0.0164611	+	0.0226568i	0.800707	+	0.599056i	$0.204457\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	38.5882i		−	1.31815i	−0.752078	−	0.659074i	$-0.770948\pi$
$857$		−	38.5882i		−	1.31815i	0.752078	−	0.659074i	$-0.229052\pi$
$858$		0			0
$859$	−12.4773	−	38.4012i	−0.425720	−	1.31023i	−0.902303	−	0.431102i	$-0.858125\pi$
$859$	−12.4773	−	38.4012i	−0.425720	−	1.31023i	0.476583	−	0.879129i	$-0.341875\pi$
$860$		0			0
$861$	0.623630	−	1.91934i	0.0212533	−	0.0654108i
$862$		0			0
$863$	25.5681	−	8.30758i	0.870349	−	0.282793i	0.160404	−	0.987051i	$-0.448720\pi$
$863$	25.5681	−	8.30758i	0.870349	−	0.282793i	0.709944	+	0.704258i	$0.248720\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	11.6684	+	16.0601i	0.396279	+	0.545431i
$868$		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
$873$	5.75919	+	1.87127i	0.194919	+	0.0633331i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−21.5839	−	7.01303i	−0.728836	−	0.236813i	−0.0789861	−	0.996876i	$-0.525168\pi$
$877$	−21.5839	−	7.01303i	−0.728836	−	0.236813i	−0.649850	+	0.760063i	$0.725168\pi$
$878$		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
$883$	−20.5079	−	28.2268i	−0.690147	−	0.949906i	0.309852	−	0.950785i	$-0.399720\pi$
$883$	−20.5079	−	28.2268i	−0.690147	−	0.949906i	−1.00000		0.000878603i	$0.999720\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−36.9015	+	11.9900i	−1.23903	+	0.402586i	−0.853979	−	0.520308i	$-0.825817\pi$
$887$	−36.9015	+	11.9900i	−1.23903	+	0.402586i	−0.385054	+	0.922894i	$0.625817\pi$
$888$		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
$893$			1.38616i			0.0463861i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.280548	−	0.386141i	0.00936722	−	0.0128929i
$898$		0			0
$899$	−17.4985			−0.583608
$900$		0			0
$901$	68.5923			2.28514
$902$		0			0
$903$	1.32193	−	1.81948i	0.0439911	−	0.0605486i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			10.0886i			0.334988i	0.985873	+	0.167494i	$0.0535675\pi$
$907$			10.0886i			0.334988i	−0.985873	+	0.167494i	$0.946433\pi$
$908$		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
$913$	−17.0677	+	5.54564i	−0.564859	+	0.183534i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.7924	+	20.3599i	0.488487	+	0.672344i
$918$		0			0
$919$	1.19370	−	0.867272i	0.0393764	−	0.0286086i	−0.567923	−	0.823082i	$-0.692253\pi$
$919$	1.19370	−	0.867272i	0.0393764	−	0.0286086i	0.607299	+	0.794473i	$0.292253\pi$
$920$		0			0
$921$	−21.5273	−	15.6405i	−0.709348	−	0.515372i
$922$		0			0
$923$	−3.30593	−	1.07416i	−0.108816	−	0.0353564i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	7.32052	+	2.37858i	0.240438	+	0.0781229i
$928$		0			0
$929$	−33.0756	−	24.0308i	−1.08517	−	0.788425i	−0.106596	−	0.994302i	$-0.533995\pi$
$929$	−33.0756	−	24.0308i	−1.08517	−	0.788425i	−0.978578	+	0.205878i	$0.933995\pi$
$930$		0			0
$931$	13.4614	−	9.78030i	0.441181	−	0.320537i
$932$		0			0
$933$	3.22143	+	4.43392i	0.105465	+	0.145160i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.8930	−	10.0378i	1.00923	−	0.327919i	0.242683	−	0.970106i	$-0.421972\pi$
$937$	30.8930	−	10.0378i	1.00923	−	0.327919i	0.766549	+	0.642186i	$0.221972\pi$
$938$		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
$943$			1.77716i			0.0578722i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−30.6280	+	42.1558i	−0.995276	+	1.36988i	−0.0670970	+	0.997746i	$0.521374\pi$
$947$	−30.6280	+	42.1558i	−0.995276	+	1.36988i	−0.928179	+	0.372134i	$0.878626\pi$
$948$		0			0
$949$	4.52782			0.146979
$950$		0			0
$951$	−2.96844			−0.0962584
$952$		0			0
$953$	2.47321	−	3.40408i	0.0801151	−	0.110269i	−0.767079	−	0.641553i	$-0.778290\pi$
$953$	2.47321	−	3.40408i	0.0801151	−	0.110269i	0.847194	+	0.531284i	$0.178290\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			12.9220i			0.417708i
$958$		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
$963$	−17.1547	+	5.57391i	−0.552804	+	0.179617i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−29.7022	−	40.8816i	−0.955158	−	1.31466i	−0.949198	−	0.314680i	$-0.898103\pi$
$967$	−29.7022	−	40.8816i	−0.955158	−	1.31466i	−0.00596071	−	0.999982i	$-0.501897\pi$
$968$		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
$973$	14.8412	+	4.82220i	0.475787	+	0.154593i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	41.1903	+	13.3836i	1.31780	+	0.428178i	0.881737	−	0.471741i	$-0.156374\pi$
$977$	41.1903	+	13.3836i	1.31780	+	0.428178i	0.436058	+	0.899918i	$0.356374\pi$
$978$		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
$983$	−20.5553	−	28.2920i	−0.655613	−	0.902374i	0.343713	−	0.939075i	$-0.388315\pi$
$983$	−20.5553	−	28.2920i	−0.655613	−	0.902374i	−0.999326	+	0.0367008i	$0.988315\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.563813	+	0.183194i	−0.0179464	+	0.00583113i
$988$		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
$993$			27.4282i			0.870408i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−18.1000	+	24.9124i	−0.573231	+	0.788985i	−0.992933	−	0.118677i	$-0.962135\pi$
$997$	−18.1000	+	24.9124i	−0.573231	+	0.788985i	0.419702	+	0.907662i	$0.362135\pi$
$998$		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.o.c.649.6		24
5.2	odd	4		1500.2.m.c.601.2		24
5.3	odd	4		1500.2.m.d.601.5		24
5.4	even	2		300.2.o.a.229.1	yes	24
15.14	odd	2		900.2.w.c.829.6		24
25.6	even	5		300.2.o.a.169.1	✓	24
25.8	odd	20		1500.2.m.d.901.5		24
25.9	even	10		7500.2.d.g.1249.3		24
25.12	odd	20		7500.2.a.n.1.3		12
25.13	odd	20		7500.2.a.m.1.10		12
25.16	even	5		7500.2.d.g.1249.22		24
25.17	odd	20		1500.2.m.c.901.2		24
25.19	even	10	inner	1500.2.o.c.349.6		24
75.56	odd	10		900.2.w.c.469.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.1	✓	24	25.6	even	5
300.2.o.a.229.1	yes	24	5.4	even	2
900.2.w.c.469.6		24	75.56	odd	10
900.2.w.c.829.6		24	15.14	odd	2
1500.2.m.c.601.2		24	5.2	odd	4
1500.2.m.c.901.2		24	25.17	odd	20
1500.2.m.d.601.5		24	5.3	odd	4
1500.2.m.d.901.5		24	25.8	odd	20
1500.2.o.c.349.6		24	25.19	even	10	inner
1500.2.o.c.649.6		24	1.1	even	1	trivial
7500.2.a.m.1.10		12	25.13	odd	20
7500.2.a.n.1.3		12	25.12	odd	20
7500.2.d.g.1249.3		24	25.9	even	10
7500.2.d.g.1249.22		24	25.16	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1500.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{3} +1.57893i q^{7} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{3} +1.57893i q^{7} +(-0.309017 - 0.951057i) q^{9} +(1.19917 - 3.69066i) q^{11} +(-0.326475 + 0.106078i) q^{13} +(3.56817 + 4.91117i) q^{17} +(2.98680 - 2.17004i) q^{19} +(1.27738 + 0.928073i) q^{21} +(-1.32236 - 0.429662i) q^{23} +(-0.951057 - 0.309017i) q^{27} +(-2.69395 - 1.95727i) q^{29} +(4.25135 - 3.08879i) q^{31} +(-2.28095 - 3.13946i) q^{33} +(8.14739 - 2.64725i) q^{37} +(-0.106078 + 0.326475i) q^{39} +(-0.394970 - 1.21559i) q^{41} -1.42438i q^{43} +(-0.220691 + 0.303755i) q^{47} +4.50698 q^{49} +6.07054 q^{51} +(6.64151 - 9.14125i) q^{53} -3.69189i q^{57} +(-3.57899 - 11.0150i) q^{59} +(-3.38909 + 10.4305i) q^{61} +(1.50165 - 0.487917i) q^{63} +(6.14771 + 8.46160i) q^{67} +(-1.12487 + 0.817265i) q^{69} +(8.19220 + 5.95198i) q^{71} +(-12.5444 - 4.07594i) q^{73} +(5.82730 + 1.89340i) q^{77} +(11.1640 + 8.11114i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-2.71826 - 3.74136i) q^{83} +(-3.16693 + 1.02900i) q^{87} +(2.24626 - 6.91326i) q^{89} +(-0.167490 - 0.515482i) q^{91} -5.25496i q^{93} +(-3.55938 + 4.89906i) q^{97} -3.88059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^9	\( 24 q + 6 q^{9} - 6 q^{11} - 10 q^{17} + 10 q^{19} - 4 q^{21} - 40 q^{23} + 4 q^{29} + 6 q^{31} - 10 q^{33} - 10 q^{41} + 40 q^{47} - 56 q^{49} + 16 q^{51} + 60 q^{53} - 36 q^{59} - 12 q^{61} + 10 q^{63} - 20 q^{67} + 4 q^{69} + 40 q^{71} - 60 q^{73} + 40 q^{77} + 8 q^{79} - 6 q^{81} + 50 q^{83} + 20 q^{87} - 30 q^{91} + 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q + 6 * q^9 - 6 * q^11 - 10 * q^17 + 10 * q^19 - 4 * q^21 - 40 * q^23 + 4 * q^29 + 6 * q^31 - 10 * q^33 - 10 * q^41 + 40 * q^47 - 56 * q^49 + 16 * q^51 + 60 * q^53 - 36 * q^59 - 12 * q^61 + 10 * q^63 - 20 * q^67 + 4 * q^69 + 40 * q^71 - 60 * q^73 + 40 * q^77 + 8 * q^79 - 6 * q^81 + 50 * q^83 + 20 * q^87 - 30 * q^91 + 40 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

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Database

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