LMFDB - Embedded newform 300.2.o.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(109,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, 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("300.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.o (of order $10$, degree $4$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	300.169
Dual form			300.2.o.a.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{3} +(-1.74098 + 1.40321i) q^{5} +1.57893i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{3} +(-1.74098 + 1.40321i) q^{5} +1.57893i q^{7} +(-0.309017 + 0.951057i) q^{9} +(1.19917 + 3.69066i) q^{11} +(0.326475 + 0.106078i) q^{13} +(2.15854 + 0.583692i) q^{15} +(-3.56817 + 4.91117i) q^{17} +(2.98680 + 2.17004i) q^{19} +(1.27738 - 0.928073i) q^{21} +(1.32236 - 0.429662i) q^{23} +(1.06200 - 4.88592i) q^{25} +(0.951057 - 0.309017i) q^{27} +(-2.69395 + 1.95727i) q^{29} +(4.25135 + 3.08879i) q^{31} +(2.28095 - 3.13946i) q^{33} +(-2.21557 - 2.74888i) q^{35} +(-8.14739 - 2.64725i) q^{37} +(-0.106078 - 0.326475i) q^{39} +(-0.394970 + 1.21559i) q^{41} -1.42438i q^{43} +(-0.796542 - 2.08938i) q^{45} +(0.220691 + 0.303755i) q^{47} +4.50698 q^{49} +6.07054 q^{51} +(-6.64151 - 9.14125i) q^{53} +(-7.26650 - 4.74266i) q^{55} -3.69189i q^{57} +(-3.57899 + 11.0150i) q^{59} +(-3.38909 - 10.4305i) q^{61} +(-1.50165 - 0.487917i) q^{63} +(-0.717236 + 0.273434i) q^{65} +(-6.14771 + 8.46160i) q^{67} +(-1.12487 - 0.817265i) q^{69} +(8.19220 - 5.95198i) q^{71} +(12.5444 - 4.07594i) q^{73} +(-4.57701 + 2.01270i) q^{75} +(-5.82730 + 1.89340i) q^{77} +(11.1640 - 8.11114i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(2.71826 - 3.74136i) q^{83} +(-0.679305 - 13.5571i) q^{85} +(3.16693 + 1.02900i) q^{87} +(2.24626 + 6.91326i) q^{89} +(-0.167490 + 0.515482i) q^{91} -5.25496i q^{93} +(-8.24497 + 0.413129i) q^{95} +(3.55938 + 4.89906i) q^{97} -3.88059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^5 + 6 * q^9	$ 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) $ 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{10}\right)$

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
$5$	−1.74098	+	1.40321i	−0.778588	+	0.627535i
$5$	−1.74098	+	1.40321i	−0.778588	+	0.627535i
$6$		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	0.952106	+	0.305769i	$0.0989136\pi$
$11$	1.19917	+	3.69066i	0.361563	+	1.11278i	−0.590543	+	0.807006i	$0.701086\pi$
$12$		0			0
$13$	0.326475	+	0.106078i	0.0905480	+	0.0294208i	0.353941	−	0.935268i	$-0.384841\pi$
$13$	0.326475	+	0.106078i	0.0905480	+	0.0294208i	−0.263393	+	0.964689i	$0.584841\pi$
$14$		0			0
$15$	2.15854	+	0.583692i	0.557333	+	0.150709i
$16$		0			0
$17$	−3.56817	+	4.91117i	−0.865409	+	1.19113i	0.114844	+	0.993384i	$0.463363\pi$
$17$	−3.56817	+	4.91117i	−0.865409	+	1.19113i	−0.980253	+	0.197750i	$0.936637\pi$
$18$		0			0
$19$	2.98680	+	2.17004i	0.685219	+	0.497841i	0.875085	−	0.483969i	$-0.160805\pi$
$19$	2.98680	+	2.17004i	0.685219	+	0.497841i	−0.189866	+	0.981810i	$0.560805\pi$
$20$		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	$-0.553694\pi$
$23$	1.32236	−	0.429662i	0.275732	−	0.0895906i	0.443619	+	0.896216i	$0.353694\pi$
$24$		0			0
$25$	1.06200	−	4.88592i	0.212399	−	0.977183i
$26$		0			0
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$		0			0
$29$	−2.69395	+	1.95727i	−0.500254	+	0.363455i	−0.809114	−	0.587652i	$-0.800052\pi$
$29$	−2.69395	+	1.95727i	−0.500254	+	0.363455i	0.308860	+	0.951107i	$0.400052\pi$
$30$		0			0
$31$	4.25135	+	3.08879i	0.763565	+	0.554763i	0.900002	−	0.435886i	$-0.143565\pi$
$31$	4.25135	+	3.08879i	0.763565	+	0.554763i	−0.136437	+	0.990649i	$0.543565\pi$
$32$		0			0
$33$	2.28095	−	3.13946i	0.397063	−	0.546510i
$34$		0			0
$35$	−2.21557	−	2.74888i	−0.374500	−	0.464646i
$36$		0			0
$37$	−8.14739	−	2.64725i	−1.33942	−	0.435205i	−0.450301	−	0.892877i	$-0.648683\pi$
$37$	−8.14739	−	2.64725i	−1.33942	−	0.435205i	−0.889121	+	0.457672i	$0.848683\pi$
$38$		0			0
$39$	−0.106078	−	0.326475i	−0.0169861	−	0.0522779i
$40$		0			0
$41$	−0.394970	+	1.21559i	−0.0616839	+	0.189844i	−0.977150	−	0.212552i	$-0.931822\pi$
$41$	−0.394970	+	1.21559i	−0.0616839	+	0.189844i	0.915466	+	0.402396i	$0.131822\pi$
$42$		0			0
$43$		−	1.42438i		−	0.217216i	−0.994085	−	0.108608i	$-0.965361\pi$
$43$		−	1.42438i		−	0.217216i	0.994085	−	0.108608i	$-0.0346394\pi$
$44$		0			0
$45$	−0.796542	−	2.08938i	−0.118742	−	0.311467i
$46$		0			0
$47$	0.220691	+	0.303755i	0.0321911	+	0.0443072i	0.824809	−	0.565411i	$-0.191283\pi$
$47$	0.220691	+	0.303755i	0.0321911	+	0.0443072i	−0.792618	+	0.609718i	$0.791283\pi$
$48$		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	−0.966382	−	0.257112i	$-0.917229\pi$
$53$	−6.64151	−	9.14125i	−0.912282	−	1.25565i	0.0540999	−	0.998536i	$-0.482771\pi$
$54$		0			0
$55$	−7.26650	−	4.74266i	−0.979814	−	0.639500i
$56$		0			0
$57$		−	3.69189i		−	0.489002i
$58$		0			0
$59$	−3.57899	+	11.0150i	−0.465945	+	1.43403i	0.391846	+	0.920031i	$0.371837\pi$
$59$	−3.57899	+	11.0150i	−0.465945	+	1.43403i	−0.857791	+	0.513999i	$0.828163\pi$
$60$		0			0
$61$	−3.38909	−	10.4305i	−0.433928	−	1.33549i	−0.894181	−	0.447706i	$-0.852241\pi$
$61$	−3.38909	−	10.4305i	−0.433928	−	1.33549i	0.460252	−	0.887788i	$-0.347759\pi$
$62$		0			0
$63$	−1.50165	−	0.487917i	−0.189190	−	0.0614717i
$64$		0			0
$65$	−0.717236	+	0.273434i	−0.0889622	+	0.0339154i
$66$		0			0
$67$	−6.14771	+	8.46160i	−0.751063	+	1.03375i	0.246842	+	0.969056i	$0.420607\pi$
$67$	−6.14771	+	8.46160i	−0.751063	+	1.03375i	−0.997905	+	0.0646937i	$0.979393\pi$
$68$		0			0
$69$	−1.12487	−	0.817265i	−0.135418	−	0.0983871i
$70$		0			0
$71$	8.19220	−	5.95198i	0.972235	−	0.706370i	0.0162750	−	0.999868i	$-0.494819\pi$
$71$	8.19220	−	5.95198i	0.972235	−	0.706370i	0.955960	+	0.293498i	$0.0948193\pi$
$72$		0			0
$73$	12.5444	−	4.07594i	1.46822	−	0.477052i	0.537648	−	0.843170i	$-0.319313\pi$
$73$	12.5444	−	4.07594i	1.46822	−	0.477052i	0.930569	+	0.366117i	$0.119313\pi$
$74$		0			0
$75$	−4.57701	+	2.01270i	−0.528508	+	0.232406i
$76$		0			0
$77$	−5.82730	+	1.89340i	−0.664082	+	0.215773i
$78$		0			0
$79$	11.1640	−	8.11114i	1.25605	−	0.912574i	0.257494	−	0.966280i	$-0.417103\pi$
$79$	11.1640	−	8.11114i	1.25605	−	0.912574i	0.998557	+	0.0537055i	$0.0171032\pi$
$80$		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	$-0.718317\pi$
$83$	2.71826	−	3.74136i	0.298367	−	0.410668i	0.931709	+	0.363204i	$0.118317\pi$
$84$		0			0
$85$	−0.679305	−	13.5571i	−0.0736809	−	1.47048i
$86$		0			0
$87$	3.16693	+	1.02900i	0.339530	+	0.110320i
$88$		0			0
$89$	2.24626	+	6.91326i	0.238103	+	0.732805i	0.996695	+	0.0812387i	$0.0258876\pi$
$89$	2.24626	+	6.91326i	0.238103	+	0.732805i	−0.758592	+	0.651566i	$0.774112\pi$
$90$		0			0
$91$	−0.167490	+	0.515482i	−0.0175578	+	0.0540372i
$92$		0			0
$93$		−	5.25496i		−	0.544914i
$94$		0			0
$95$	−8.24497	+	0.413129i	−0.845916	+	0.0423862i
$96$		0			0
$97$	3.55938	+	4.89906i	0.361400	+	0.497424i	0.950538	−	0.310608i	$-0.100533\pi$
$97$	3.55938	+	4.89906i	0.361400	+	0.497424i	−0.589138	+	0.808032i	$0.700533\pi$
$98$		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	$-0.0761936\pi$
$103$	4.52433	+	6.22721i	0.445796	+	0.613585i	−0.525692	+	0.850675i	$0.676194\pi$
$104$		0			0
$105$	−0.921610	+	3.40819i	−0.0899399	+	0.332605i
$106$		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	0.321799	+	0.946808i	$0.395712\pi$
$109$	−5.16860	+	15.9073i	−0.495062	+	1.52364i	−0.816861	+	0.576835i	$0.804288\pi$
$110$		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	$-0.365964\pi$
$113$	2.15793	+	0.701155i	0.203001	+	0.0659591i	−0.205751	+	0.978604i	$0.565964\pi$
$114$		0			0
$115$	−1.69929	+	2.60358i	−0.158460	+	0.242785i
$116$		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
$125$	5.00706	+	9.99646i	0.447845	+	0.894111i
$126$		0			0
$127$	−1.43348	+	0.465767i	−0.127201	+	0.0413301i	−0.371926	−	0.928262i	$-0.621302\pi$
$127$	−1.43348	+	0.465767i	−0.127201	+	0.0413301i	0.244725	+	0.969593i	$0.421302\pi$
$128$		0			0
$129$	−1.15235	+	0.837231i	−0.101459	+	0.0737141i
$130$		0			0
$131$	12.8948	+	9.36859i	1.12662	+	0.818537i	0.985199	−	0.171412i	$-0.0548330\pi$
$131$	12.8948	+	9.36859i	1.12662	+	0.818537i	0.141421	+	0.989950i	$0.454833\pi$
$132$		0			0
$133$	−3.42634	+	4.71595i	−0.297101	+	0.408925i
$134$		0			0
$135$	−1.22215	+	1.87252i	−0.105186	+	0.161161i
$136$		0			0
$137$	5.17996	+	1.68307i	0.442554	+	0.143795i	0.521814	−	0.853059i	$-0.325256\pi$
$137$	5.17996	+	1.68307i	0.442554	+	0.143795i	−0.0792596	+	0.996854i	$0.525256\pi$
$138$		0			0
$139$	3.05409	+	9.39953i	0.259045	+	0.797258i	0.993006	+	0.118066i	$0.0376694\pi$
$139$	3.05409	+	9.39953i	0.259045	+	0.797258i	−0.733961	+	0.679192i	$0.762331\pi$
$140$		0			0
$141$	0.116024	−	0.357085i	0.00977099	−	0.0300720i
$142$		0			0
$143$			1.33211i			0.111397i
$144$		0			0
$145$	1.94364	−	7.18773i	0.161410	−	0.596909i
$146$		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
$155$	−11.7357	+	0.588040i	−0.942636	+	0.0472325i
$156$		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	$-0.324551\pi$
$163$	5.70240	+	1.85282i	0.446646	+	0.145124i	−0.0770538	+	0.997027i	$0.524551\pi$
$164$		0			0
$165$	0.434245	+	8.66638i	0.0338059	+	0.674677i
$166$		0			0
$167$	3.76094	−	5.17649i	0.291030	−	0.400569i	−0.638318	−	0.769773i	$-0.720370\pi$
$167$	3.76094	−	5.17649i	0.291030	−	0.400569i	0.929348	+	0.369204i	$0.120370\pi$
$168$		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	$-0.536397\pi$
$173$	4.96583	−	1.61350i	0.377545	−	0.122672i	0.491641	+	0.870798i	$0.336397\pi$
$174$		0			0
$175$	7.71452	+	1.67682i	0.583163	+	0.126755i
$176$		0			0
$177$	11.0150	−	3.57899i	0.827937	−	0.269013i
$178$		0			0
$179$	18.8534	−	13.6978i	1.40917	−	1.02382i	0.415724	−	0.909491i	$-0.363528\pi$
$179$	18.8534	−	13.6978i	1.40917	−	1.02382i	0.993443	−	0.114329i	$-0.0364718\pi$
$180$		0			0
$181$	−20.3662	−	14.7969i	−1.51380	−	1.09984i	−0.964454	−	0.264251i	$-0.914875\pi$
$181$	−20.3662	−	14.7969i	−1.51380	−	1.09984i	−0.549350	−	0.835592i	$-0.685125\pi$
$182$		0			0
$183$	−6.44643	+	8.87275i	−0.476534	+	0.655893i
$184$		0			0
$185$	17.8991	−	6.82372i	1.31596	−	0.501690i
$186$		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	−0.820231	−	0.572033i	$-0.806155\pi$
$191$	2.48188	−	7.63843i	0.179582	−	0.552697i	0.999813	+	0.0193354i	$0.00615503\pi$
$192$		0			0
$193$			20.2575i			1.45817i	0.684424	+	0.729084i	$0.260054\pi$
$193$			20.2575i			1.45817i	−0.684424	+	0.729084i	$0.739946\pi$
$194$		0			0
$195$	0.642794	+	0.419536i	0.0460314	+	0.0300436i
$196$		0			0
$197$	11.7650	+	16.1931i	0.838221	+	1.15371i	0.986337	+	0.164742i	$0.0526793\pi$
$197$	11.7650	+	16.1931i	0.838221	+	1.15371i	−0.148115	+	0.988970i	$0.547321\pi$
$198$		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
$205$	−1.01810	−	2.67054i	−0.0711072	−	0.186519i
$206$		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	0.999937	−	0.0112687i	$-0.00358702\pi$
$211$	2.67780	+	8.24142i	0.184347	+	0.567363i	−0.815589	+	0.578631i	$0.803587\pi$
$212$		0			0
$213$	−9.63050	−	3.12914i	−0.659871	−	0.214405i
$214$		0			0
$215$	1.99871	+	2.47982i	0.136311	+	0.169122i
$216$		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	$-0.736095\pi$
$223$	−11.7779	+	3.82686i	−0.788705	+	0.256266i	−0.113152	+	0.993578i	$0.536095\pi$
$224$		0			0
$225$	4.31861	+	2.51985i	0.287907	+	0.167990i
$226$		0			0
$227$	17.3309	−	5.63116i	1.15029	−	0.373753i	0.329040	−	0.944316i	$-0.393275\pi$
$227$	17.3309	−	5.63116i	1.15029	−	0.373753i	0.821254	+	0.570563i	$0.193275\pi$
$228$		0			0
$229$	13.2812	−	9.64932i	0.877643	−	0.637645i	−0.0549837	−	0.998487i	$-0.517511\pi$
$229$	13.2812	−	9.64932i	0.877643	−	0.637645i	0.932627	+	0.360842i	$0.117511\pi$
$230$		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	$-0.746174\pi$
$233$	3.01993	−	4.15658i	0.197842	−	0.272307i	0.896399	+	0.443248i	$0.146174\pi$
$234$		0			0
$235$	−0.810450	−	0.219154i	−0.0528679	−	0.0142960i
$236$		0			0
$237$	−13.1241	−	4.26428i	−0.852502	−	0.276995i
$238$		0			0
$239$	−7.58924	−	23.3573i	−0.490907	−	1.51086i	−0.823239	−	0.567694i	$-0.807835\pi$
$239$	−7.58924	−	23.3573i	−0.490907	−	1.51086i	0.332332	−	0.943162i	$-0.392165\pi$
$240$		0			0
$241$	1.49413	−	4.59846i	0.0962454	−	0.296213i	−0.891331	−	0.453353i	$-0.850228\pi$
$241$	1.49413	−	4.59846i	0.0962454	−	0.296213i	0.987576	+	0.157141i	$0.0502276\pi$
$242$		0			0
$243$			1.00000i			0.0641500i
$244$		0			0
$245$	−7.84654	+	6.32424i	−0.501297	+	0.404041i
$246$		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
$255$	−10.5687	+	8.51825i	−0.661835	+	0.533433i
$256$		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	$-0.494051\pi$
$263$	−8.98231	−	2.91853i	−0.553873	−	0.179964i	−0.572562	+	0.819861i	$0.694051\pi$
$264$		0			0
$265$	24.3898	+	6.59526i	1.49825	+	0.405144i
$266$		0			0
$267$	4.27263	−	5.88077i	0.261481	−	0.359898i
$268$		0			0
$269$	−23.7720	−	17.2714i	−1.44940	−	1.05305i	−0.985970	−	0.166921i	$-0.946618\pi$
$269$	−23.7720	−	17.2714i	−1.44940	−	1.05305i	−0.463433	−	0.886132i	$-0.653382\pi$
$270$		0			0
$271$	−12.5303	+	9.10380i	−0.761162	+	0.553016i	−0.899266	−	0.437401i	$-0.855899\pi$
$271$	−12.5303	+	9.10380i	−0.761162	+	0.553016i	0.138105	+	0.990418i	$0.455899\pi$
$272$		0			0
$273$	0.515482	−	0.167490i	0.0311984	−	0.0101370i
$274$		0			0
$275$	19.3058	−	1.93957i	1.16418	−	0.116960i
$276$		0			0
$277$	14.6259	−	4.75225i	0.878786	−	0.285535i	0.165333	−	0.986238i	$-0.447130\pi$
$277$	14.6259	−	4.75225i	0.878786	−	0.285535i	0.713453	+	0.700703i	$0.247130\pi$
$278$		0			0
$279$	−4.25135	+	3.08879i	−0.254522	+	0.184921i
$280$		0			0
$281$	−3.13314	−	2.27636i	−0.186908	−	0.135796i	0.490397	−	0.871499i	$-0.336852\pi$
$281$	−3.13314	−	2.27636i	−0.186908	−	0.135796i	−0.677304	+	0.735703i	$0.736852\pi$
$282$		0			0
$283$	−6.98697	+	9.61673i	−0.415332	+	0.571655i	−0.964509	−	0.264051i	$-0.914941\pi$
$283$	−6.98697	+	9.61673i	−0.415332	+	0.571655i	0.549177	+	0.835706i	$0.314941\pi$
$284$		0			0
$285$	5.18050	+	6.42749i	0.306866	+	0.380731i
$286$		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
$295$	−9.22543	−	24.1989i	−0.537125	−	1.40892i
$296$		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
$305$	20.5366	+	13.4037i	1.17592	+	0.767495i
$306$		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	0.891487	−	0.453047i	$-0.149663\pi$
$311$	−1.69361	−	5.21238i	−0.0960356	−	0.295567i	−0.987522	+	0.157480i	$0.949663\pi$
$312$		0			0
$313$	7.08632	+	2.30248i	0.400542	+	0.130144i	0.502359	−	0.864659i	$-0.332466\pi$
$313$	7.08632	+	2.30248i	0.400542	+	0.130144i	−0.101817	+	0.994803i	$0.532466\pi$
$314$		0			0
$315$	3.29899	−	1.25769i	0.185877	−	0.0708626i
$316$		0			0
$317$	1.74481	−	2.40152i	0.0979981	−	0.134883i	−0.757202	−	0.653181i	$-0.773434\pi$
$317$	1.74481	−	2.40152i	0.0979981	−	0.134883i	0.855200	+	0.518298i	$0.173434\pi$
$318$		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
$325$	0.865005	−	1.48248i	0.0479818	−	0.0822330i
$326$		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	−0.223594	−	0.974682i	$-0.571779\pi$
$331$	−22.1899	−	16.1219i	−1.21967	−	0.886140i	−0.996072	+	0.0885426i	$0.971779\pi$
$332$		0			0
$333$	5.03536	−	6.93058i	0.275936	−	0.379794i
$334$		0			0
$335$	−1.17039	−	23.3580i	−0.0639455	−	1.27618i
$336$		0			0
$337$	7.14905	+	2.32287i	0.389433	+	0.126535i	0.497188	−	0.867643i	$-0.334366\pi$
$337$	7.14905	+	2.32287i	0.389433	+	0.126535i	−0.107754	+	0.994178i	$0.534366\pi$
$338$		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
$345$	3.10516	−	0.155590i	0.167176	−	0.00837668i
$346$		0			0
$347$	7.05022	+	9.70380i	0.378476	+	0.520927i	0.955180	−	0.296026i	$-0.0956614\pi$
$347$	7.05022	+	9.70380i	0.378476	+	0.520927i	−0.576704	+	0.816953i	$0.695661\pi$
$348$		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	0.995214	+	0.0977244i	$0.0311564\pi$
$353$	14.6665	+	20.1867i	0.780617	+	1.07443i	−0.214596	+	0.976703i	$0.568844\pi$
$354$		0			0
$355$	−5.91053	+	21.8576i	−0.313698	+	1.16008i
$356$		0			0
$357$			9.58496i			0.507290i
$358$		0			0
$359$	−0.247954	+	0.763123i	−0.0130865	+	0.0402761i	−0.957387	−	0.288810i	$-0.906741\pi$
$359$	−0.247954	+	0.763123i	−0.0130865	+	0.0402761i	0.944300	+	0.329086i	$0.106741\pi$
$360$		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
$365$	−16.1202	+	24.6986i	−0.843769	+	1.29278i
$366$		0			0
$367$	−9.28986	+	12.7864i	−0.484927	+	0.667445i	−0.979442	−	0.201724i	$-0.935346\pi$
$367$	−9.28986	+	12.7864i	−0.484927	+	0.667445i	0.494515	+	0.869169i	$0.335346\pi$
$368$		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	$-0.629789\pi$
$373$	−3.43291	+	1.11542i	−0.177750	+	0.0577543i	0.218790	+	0.975772i	$0.429789\pi$
$374$		0			0
$375$	5.14423	−	9.92657i	0.265647	−	0.512606i
$376$		0			0
$377$	−1.08713	+	0.353230i	−0.0559901	+	0.0181923i
$378$		0			0
$379$	22.0967	−	16.0542i	1.13503	−	0.824647i	0.148610	−	0.988896i	$-0.452520\pi$
$379$	22.0967	−	16.0542i	1.13503	−	0.824647i	0.986419	+	0.164249i	$0.0525201\pi$
$380$		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	$-0.963961\pi$
$383$	−11.3334	+	15.5991i	−0.579112	+	0.797079i	0.414486	+	0.910056i	$0.363961\pi$
$384$		0			0
$385$	7.48834	−	11.4733i	0.381641	−	0.584733i
$386$		0			0
$387$	1.35467	+	0.440159i	0.0688617	+	0.0223745i
$388$		0			0
$389$	5.27164	+	16.2244i	0.267283	+	0.822612i	0.991159	+	0.132682i	$0.0423589\pi$
$389$	5.27164	+	16.2244i	0.267283	+	0.822612i	−0.723876	+	0.689930i	$0.757641\pi$
$390$		0			0
$391$	−2.60828	+	8.02745i	−0.131906	+	0.405966i
$392$		0			0
$393$		−	15.9388i		−	0.804006i
$394$		0			0
$395$	−8.05466	+	29.7868i	−0.405274	+	1.49874i
$396$		0			0
$397$	16.0842	+	22.1380i	0.807243	+	1.11108i	0.991743	+	0.128243i	$0.0409336\pi$
$397$	16.0842	+	22.1380i	0.807243	+	1.11108i	−0.184499	+	0.982833i	$0.559066\pi$
$398$		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
$405$	2.23327	−	0.111902i	0.110972	−	0.00556045i
$406$		0			0
$407$		−	33.2437i		−	1.64783i
$408$		0			0
$409$	−6.72523	+	20.6981i	−0.332541	+	1.02346i	0.635379	+	0.772200i	$0.280844\pi$
$409$	−6.72523	+	20.6981i	−0.332541	+	1.02346i	−0.967921	+	0.251256i	$0.919156\pi$
$410$		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
$415$	0.517499	+	10.3279i	0.0254030	+	0.506977i
$416$		0			0
$417$	5.80923	−	7.99572i	0.284479	−	0.391552i
$418$		0			0
$419$	−3.67055	−	2.66681i	−0.179318	−	0.130282i	0.494505	−	0.869175i	$-0.335349\pi$
$419$	−3.67055	−	2.66681i	−0.179318	−	0.130282i	−0.673824	+	0.738892i	$0.735349\pi$
$420$		0			0
$421$	−2.47193	+	1.79596i	−0.120475	+	0.0875300i	−0.646391	−	0.763006i	$-0.723722\pi$
$421$	−2.47193	+	1.79596i	−0.120475	+	0.0875300i	0.525916	+	0.850536i	$0.323722\pi$
$422$		0			0
$423$	−0.357085	+	0.116024i	−0.0173621	+	0.00564128i
$424$		0			0
$425$	20.2062	+	22.6494i	0.980143	+	1.09866i
$426$		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	0.891582	−	0.452860i	$-0.149596\pi$
$431$	15.2881	+	11.1074i	0.736400	+	0.535026i	−0.155181	+	0.987886i	$0.549596\pi$
$432$		0			0
$433$	−2.00963	+	2.76602i	−0.0965768	+	0.132927i	−0.854571	−	0.519335i	$-0.826180\pi$
$433$	−2.00963	+	2.76602i	−0.0965768	+	0.132927i	0.757994	+	0.652262i	$0.226180\pi$
$434$		0			0
$435$	−6.95744	+	2.65241i	−0.333584	+	0.127173i
$436$		0			0
$437$	4.88201	+	1.58626i	0.233538	+	0.0758812i
$438$		0			0
$439$	1.84058	+	5.66473i	0.0878462	+	0.270363i	0.985323	−	0.170698i	$-0.0546023\pi$
$439$	1.84058	+	5.66473i	0.0878462	+	0.270363i	−0.897477	+	0.441061i	$0.854602\pi$
$440$		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
$445$	−13.6115	−	8.88386i	−0.645245	−	0.421135i
$446$		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
$455$	−0.431734	−	1.13247i	−0.0202400	−	0.0530909i
$456$		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	−0.580453	−	0.814294i	$-0.697124\pi$
$461$	−12.6568	−	38.9537i	−0.589487	−	1.81425i	−0.00903372	−	0.999959i	$-0.502876\pi$
$462$		0			0
$463$	21.9961	+	7.14695i	1.02224	+	0.332147i	0.771719	−	0.635963i	$-0.219397\pi$
$463$	21.9961	+	7.14695i	1.02224	+	0.332147i	0.250524	+	0.968110i	$0.419397\pi$
$464$		0			0
$465$	7.37382	+	9.14876i	0.341953	+	0.424263i
$466$		0			0
$467$	−17.8034	+	24.5043i	−0.823845	+	1.13392i	0.165193	+	0.986261i	$0.447175\pi$
$467$	−17.8034	+	24.5043i	−0.823845	+	1.13392i	−0.989038	+	0.147664i	$0.952825\pi$
$468$		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
$475$	13.7746	−	12.2887i	0.632021	−	0.563843i
$476$		0			0
$477$	10.7462	−	3.49165i	0.492034	−	0.159872i
$478$		0			0
$479$	−19.4809	+	14.1537i	−0.890107	+	0.646700i	−0.935906	−	0.352250i	$-0.885417\pi$
$479$	−19.4809	+	14.1537i	−0.890107	+	0.646700i	0.0457990	+	0.998951i	$0.485417\pi$
$480$		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
$485$	−13.0712	−	3.53459i	−0.593533	−	0.160497i
$486$		0			0
$487$	−2.14446	−	0.696777i	−0.0971747	−	0.0315740i	0.260026	−	0.965602i	$-0.416269\pi$
$487$	−2.14446	−	0.696777i	−0.0971747	−	0.0315740i	−0.357201	+	0.934028i	$0.616269\pi$
$488$		0			0
$489$	−1.85282	−	5.70240i	−0.0837875	−	0.257871i
$490$		0			0
$491$	−8.84093	+	27.2096i	−0.398986	+	1.22795i	0.526828	+	0.849972i	$0.323381\pi$
$491$	−8.84093	+	27.2096i	−0.398986	+	1.22795i	−0.925814	+	0.377980i	$0.876619\pi$
$492$		0			0
$493$		−	20.2143i		−	0.910406i
$494$		0			0
$495$	6.75601	−	5.44528i	0.303660	−	0.244747i
$496$		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	$-0.202959\pi$
$503$	−0.245105	−	0.337358i	−0.0109287	−	0.0150421i	−0.814446	+	0.580239i	$0.802959\pi$
$504$		0			0
$505$	−5.62397	+	4.53287i	−0.250263	+	0.201710i
$506$		0			0
$507$			12.8822i			0.572117i
$508$		0			0
$509$	−4.14176	+	12.7470i	−0.183580	+	0.565002i	−0.999921	−	0.0125684i	$-0.995999\pi$
$509$	−4.14176	+	12.7470i	−0.183580	+	0.565002i	0.816341	+	0.577571i	$0.195999\pi$
$510$		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
$515$	−16.6148	−	4.49283i	−0.732138	−	0.197978i
$516$		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	−0.894882	−	0.446303i	$-0.852740\pi$
$521$	−17.0496	+	12.3872i	−0.746956	+	0.542695i	0.147926	+	0.988998i	$0.452740\pi$
$522$		0			0
$523$	−11.2943	+	3.66974i	−0.493866	+	0.160467i	−0.545352	−	0.838207i	$-0.683604\pi$
$523$	−11.2943	+	3.66974i	−0.493866	+	0.160467i	0.0514866	+	0.998674i	$0.483604\pi$
$524$		0			0
$525$	−3.17791	−	7.22679i	−0.138695	−	0.315403i
$526$		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
$535$	25.3105	+	31.4030i	1.09427	+	1.35767i
$536$		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	−0.345029	−	0.938592i	$-0.612131\pi$
$541$	11.2993	−	34.7757i	0.485796	−	1.49513i	0.830825	−	0.556534i	$-0.187869\pi$
$542$		0			0
$543$			25.1739i			1.08032i
$544$		0			0
$545$	−13.3229	−	34.9469i	−0.570691	−	1.49696i
$546$		0			0
$547$	−23.2652	−	32.0219i	−0.994750	−	1.36916i	−0.928492	−	0.371353i	$-0.878894\pi$
$547$	−23.2652	−	32.0219i	−0.994750	−	1.36916i	−0.0662579	−	0.997803i	$-0.521106\pi$
$548$		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
$555$	−16.0413	−	10.4698i	−0.680915	−	0.444417i
$556$		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	$-0.119750\pi$
$563$	34.7979	+	11.3065i	1.46656	+	0.476513i	0.536490	+	0.843907i	$0.319750\pi$
$564$		0			0
$565$	−4.74078	+	1.80734i	−0.199446	+	0.0760355i
$566$		0			0
$567$	0.928073	−	1.27738i	0.0389754	−	0.0536450i
$568$		0			0
$569$	−27.3735	−	19.8880i	−1.14756	−	0.833749i	−0.159403	−	0.987214i	$-0.550957\pi$
$569$	−27.3735	−	19.8880i	−1.14756	−	0.833749i	−0.988154	+	0.153464i	$0.950957\pi$
$570$		0			0
$571$	0.974239	−	0.707826i	0.0407706	−	0.0296216i	−0.567213	−	0.823571i	$-0.691978\pi$
$571$	0.974239	−	0.707826i	0.0407706	−	0.0296216i	0.607984	+	0.793949i	$0.291978\pi$
$572$		0			0
$573$	−7.63843	+	2.48188i	−0.319100	+	0.103682i
$574$		0			0
$575$	−0.694947	−	6.91725i	−0.0289813	−	0.288469i
$576$		0			0
$577$	15.6012	−	5.06913i	0.649485	−	0.211031i	0.0342981	−	0.999412i	$-0.489080\pi$
$577$	15.6012	−	5.06913i	0.649485	−	0.211031i	0.615187	+	0.788381i	$0.289080\pi$
$578$		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
$585$	−0.0384133	−	0.766628i	−0.00158819	−	0.0316962i
$586$		0			0
$587$	32.0429	+	10.4114i	1.32255	+	0.429724i	0.883371	−	0.468674i	$-0.155268\pi$
$587$	32.0429	+	10.4114i	1.32255	+	0.429724i	0.439182	+	0.898398i	$0.355268\pi$
$588$		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
$595$	21.4058	−	1.07258i	0.877551	−	0.0439713i
$596$		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
$605$	2.36918	−	8.76143i	0.0963210	−	0.356203i
$606$		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	$-0.738321\pi$
$613$	−41.1487	−	13.3700i	−1.66198	−	0.540010i	−0.981285	+	0.192559i	$0.938321\pi$
$614$		0			0
$615$	−1.56209	+	2.39337i	−0.0629896	+	0.0965098i
$616$		0			0
$617$	−0.931550	+	1.28217i	−0.0375028	+	0.0516182i	−0.827357	−	0.561677i	$-0.810156\pi$
$617$	−0.931550	+	1.28217i	−0.0375028	+	0.0516182i	0.789854	+	0.613295i	$0.210156\pi$
$618$		0			0
$619$	−10.9048	−	7.92281i	−0.438301	−	0.318444i	0.346658	−	0.937991i	$-0.387316\pi$
$619$	−10.9048	−	7.92281i	−0.438301	−	0.318444i	−0.784960	+	0.619547i	$0.787316\pi$
$620$		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
$625$	−22.7443	−	10.3776i	−0.909773	−	0.415105i
$626$		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	0.949203	−	0.314663i	$-0.101892\pi$
$631$	23.6944	+	17.2150i	0.943261	+	0.685319i	−0.00594245	+	0.999982i	$0.501892\pi$
$632$		0			0
$633$	5.09348	−	7.01057i	0.202448	−	0.278645i
$634$		0			0
$635$	1.84209	−	2.82237i	0.0731011	−	0.112002i
$636$		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	0.788365	+	0.615208i	$0.210928\pi$
$641$	−5.34325	+	16.4448i	−0.211046	+	0.649532i	−0.999411	+	0.0343242i	$0.989072\pi$
$642$		0			0
$643$		−	46.8857i		−	1.84899i	−0.381190	−	0.924497i	$-0.624486\pi$
$643$		−	46.8857i		−	1.84899i	0.381190	−	0.924497i	$-0.375514\pi$
$644$		0			0
$645$	0.831401	−	3.07459i	0.0327364	−	0.121062i
$646$		0			0
$647$	8.46236	+	11.6474i	0.332690	+	0.457908i	0.942288	−	0.334802i	$-0.108669\pi$
$647$	8.46236	+	11.6474i	0.332690	+	0.457908i	−0.609599	+	0.792710i	$0.708669\pi$
$648$		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	−0.998857	−	0.0478084i	$-0.984776\pi$
$653$	−18.7990	−	25.8746i	−0.735661	−	1.01255i	0.263195	−	0.964743i	$-0.415224\pi$
$654$		0			0
$655$	−35.5956	+	1.78358i	−1.39083	+	0.0696903i
$656$		0			0
$657$			13.1900i			0.514591i
$658$		0			0
$659$	−5.77517	+	17.7742i	−0.224969	+	0.692383i	0.773326	+	0.634009i	$0.218592\pi$
$659$	−5.77517	+	17.7742i	−0.224969	+	0.692383i	−0.998295	+	0.0583742i	$0.981408\pi$
$660$		0			0
$661$	−0.209866	−	0.645901i	−0.00816284	−	0.0251226i	0.946892	−	0.321551i	$-0.104204\pi$
$661$	−0.209866	−	0.645901i	−0.00816284	−	0.0251226i	−0.955055	+	0.296429i	$0.904204\pi$
$662$		0			0
$663$	1.98188	+	0.643952i	0.0769699	+	0.0250090i
$664$		0			0
$665$	−0.652303	−	13.0182i	−0.0252952	−	0.504826i
$666$		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	$-0.555333\pi$
$673$	6.90162	−	2.24247i	0.266038	−	0.0864410i	0.438999	+	0.898488i	$0.355333\pi$
$674$		0			0
$675$	−0.499813	−	4.97496i	−0.0192378	−	0.191486i
$676$		0			0
$677$	−32.2918	+	10.4922i	−1.24107	+	0.403249i	−0.854714	−	0.519099i	$-0.826267\pi$
$677$	−32.2918	+	10.4922i	−1.24107	+	0.403249i	−0.386359	+	0.922348i	$0.626267\pi$
$678$		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	$-0.618910\pi$
$683$	16.5508	−	22.7802i	0.633298	−	0.871660i	0.998236	+	0.0593717i	$0.0189097\pi$
$684$		0			0
$685$	−11.3799	+	4.33840i	−0.434804	+	0.165762i
$686$		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	−0.731899	−	0.681413i	$-0.761366\pi$
$691$	6.85416	−	21.0949i	0.260745	−	0.802489i	0.992643	−	0.121076i	$-0.0386344\pi$
$692$		0			0
$693$		−	6.12718i		−	0.232752i
$694$		0			0
$695$	−18.5066	−	12.0788i	−0.701996	−	0.458176i
$696$		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
$705$	0.299071	+	0.784483i	0.0112637	+	0.0295453i
$706$		0			0
$707$			5.10051i			0.191824i
$708$		0			0
$709$	−4.42745	+	13.6263i	−0.166276	+	0.511746i	−0.999128	−	0.0417503i	$-0.986707\pi$
$709$	−4.42745	+	13.6263i	−0.166276	+	0.511746i	0.832852	+	0.553496i	$0.186707\pi$
$710$		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
$715$	−1.86924	−	2.31918i	−0.0699056	−	0.0867324i
$716$		0			0
$717$	−14.4356	+	19.8689i	−0.539107	+	0.742017i
$718$		0			0
$719$	9.56382	+	6.94852i	0.356670	+	0.259136i	0.751662	−	0.659549i	$-0.229253\pi$
$719$	9.56382	+	6.94852i	0.356670	+	0.259136i	−0.394992	+	0.918685i	$0.629253\pi$
$720$		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
$725$	6.70208	+	15.2410i	0.248909	+	0.566037i
$726$		0			0
$727$	1.17583	−	0.382051i	0.0436092	−	0.0141695i	−0.287131	−	0.957891i	$-0.592702\pi$
$727$	1.17583	−	0.382051i	0.0436092	−	0.0141695i	0.330740	+	0.943722i	$0.392702\pi$
$728$		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	$-0.898613\pi$
$733$	−9.70319	+	13.3553i	−0.358395	+	0.493289i	0.591305	+	0.806448i	$0.298613\pi$
$734$		0			0
$735$	9.72850	+	2.63069i	0.358841	+	0.0970343i
$736$		0			0
$737$	−38.6010	−	12.5422i	−1.42189	−	0.461999i
$738$		0			0
$739$	5.20573	+	16.0216i	0.191496	+	0.589363i	1.00000		0.000872485i	$0.000277721\pi$
$739$	5.20573	+	16.0216i	0.191496	+	0.589363i	−0.808504	+	0.588491i	$0.799722\pi$
$740$		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
$745$	0.113053	−	0.0911194i	0.00414193	−	0.00333836i
$746$		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
$755$	21.1042	−	17.0098i	0.768062	−	0.619051i
$756$		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	0.871556	−	0.490295i	$-0.163111\pi$
$761$	−3.35824	−	10.3356i	−0.121736	−	0.374665i	−0.993292	+	0.115631i	$0.963111\pi$
$762$		0			0
$763$	−25.1165	−	8.16086i	−0.909280	−	0.295443i
$764$		0			0
$765$	13.1035	+	3.54333i	0.473758	+	0.128109i
$766$		0			0
$767$	−2.33690	+	3.21647i	−0.0843807	+	0.116140i
$768$		0			0
$769$	−1.92870	−	1.40128i	−0.0695505	−	0.0505314i	0.552467	−	0.833535i	$-0.313687\pi$
$769$	−1.92870	−	1.40128i	−0.0695505	−	0.0505314i	−0.622017	+	0.783004i	$0.713687\pi$
$770$		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	$-0.366462\pi$
$773$	35.4118	−	11.5060i	1.27367	−	0.413841i	0.866347	+	0.499442i	$0.166462\pi$
$774$		0			0
$775$	19.6065	−	17.4915i	0.704285	−	0.628312i
$776$		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
$785$	−32.9363	−	40.8643i	−1.17555	−	1.45851i
$786$		0			0
$787$	−21.7768	−	7.07570i	−0.776258	−	0.252221i	−0.106016	−	0.994364i	$-0.533809\pi$
$787$	−21.7768	−	7.07570i	−0.776258	−	0.252221i	−0.670242	+	0.742143i	$0.733809\pi$
$788$		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
$795$	−9.00030	−	23.6084i	−0.319208	−	0.837303i
$796$		0			0
$797$	−5.21641	−	7.17977i	−0.184775	−	0.254321i	0.706574	−	0.707639i	$-0.250240\pi$
$797$	−5.21641	−	7.17977i	−0.184775	−	0.254321i	−0.891348	+	0.453319i	$0.850240\pi$
$798$		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
$805$	−4.11088	−	2.68307i	−0.144890	−	0.0945658i
$806$		0			0
$807$			29.3838i			1.03436i
$808$		0			0
$809$	12.5887	−	38.7442i	0.442597	−	1.36217i	−0.442502	−	0.896768i	$-0.645909\pi$
$809$	12.5887	−	38.7442i	0.442597	−	1.36217i	0.885098	−	0.465404i	$-0.154091\pi$
$810$		0			0
$811$	13.8312	+	42.5680i	0.485679	+	1.49476i	0.830996	+	0.556279i	$0.187771\pi$
$811$	13.8312	+	42.5680i	0.485679	+	1.49476i	−0.345317	+	0.938486i	$0.612229\pi$
$812$		0			0
$813$	14.7303	+	4.78615i	0.516613	+	0.167858i
$814$		0			0
$815$	−12.5276	+	4.77595i	−0.438824	+	0.167294i
$816$		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	0.416949	−	0.908930i	$-0.363099\pi$
$821$	40.4077	−	29.3579i	1.41024	−	1.02460i	0.993288	−	0.115667i	$-0.0369005\pi$
$822$		0			0
$823$	15.2000	−	4.93877i	0.529837	−	0.172155i	−0.0318678	−	0.999492i	$-0.510146\pi$
$823$	15.2000	−	4.93877i	0.529837	−	0.172155i	0.561705	+	0.827338i	$0.310146\pi$
$824$		0			0
$825$	−12.9168	−	14.4786i	−0.449705	−	0.504081i
$826$		0			0
$827$	−42.9415	+	13.9525i	−1.49322	+	0.485177i	−0.938033	−	0.346546i	$-0.887354\pi$
$827$	−42.9415	+	13.9525i	−1.49322	+	0.485177i	−0.555190	+	0.831724i	$0.687354\pi$
$828$		0			0
$829$	−12.4972	+	9.07975i	−0.434046	+	0.315353i	−0.783265	−	0.621688i	$-0.786447\pi$
$829$	−12.4972	+	9.07975i	−0.434046	+	0.315353i	0.349219	+	0.937041i	$0.386447\pi$
$830$		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
$835$	0.716004	+	14.2895i	0.0247783	+	0.494510i
$836$		0			0
$837$	4.99776	+	1.62387i	0.172748	+	0.0561292i
$838$		0			0
$839$	7.15711	+	22.0273i	0.247091	+	0.760468i	0.995285	+	0.0969885i	$0.0309210\pi$
$839$	7.15711	+	22.0273i	0.247091	+	0.760468i	−0.748194	+	0.663480i	$0.769079\pi$
$840$		0			0
$841$	−5.53504	+	17.0351i	−0.190863	+	0.587417i
$842$		0			0
$843$			3.87277i			0.133385i
$844$		0			0
$845$	28.7693	−	1.44154i	0.989694	−	0.0495904i
$846$		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	$-0.195543\pi$
$853$	0.480767	+	0.661719i	0.0164611	+	0.0226568i	−0.800707	+	0.599056i	$0.795543\pi$
$854$		0			0
$855$	2.15493	−	7.96909i	0.0736969	−	0.272537i
$856$		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	0.476583	+	0.879129i	$0.341875\pi$
$859$	−12.4773	+	38.4012i	−0.425720	+	1.31023i	−0.902303	+	0.431102i	$0.858125\pi$
$860$		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	$-0.551280\pi$
$863$	−25.5681	−	8.30758i	−0.870349	−	0.282793i	−0.709944	+	0.704258i	$0.751280\pi$
$864$		0			0
$865$	−6.38131	+	9.77716i	−0.216971	+	0.332433i
$866$		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
$875$	−15.7837	+	7.90581i	−0.533588	+	0.267265i
$876$		0			0
$877$	21.5839	−	7.01303i	0.728836	−	0.236813i	0.0789861	−	0.996876i	$-0.474832\pi$
$877$	21.5839	−	7.01303i	0.728836	−	0.236813i	0.649850	+	0.760063i	$0.274832\pi$
$878$		0			0
$879$	−12.5071	+	9.08694i	−0.421854	+	0.306495i
$880$		0			0
$881$	24.3098	+	17.6621i	0.819017	+	0.595051i	0.916431	−	0.400193i	$-0.131057\pi$
$881$	24.3098	+	17.6621i	0.819017	+	0.595051i	−0.0974139	+	0.995244i	$0.531057\pi$
$882$		0			0
$883$	20.5079	−	28.2268i	0.690147	−	0.949906i	−0.309852	−	0.950785i	$-0.600280\pi$
$883$	20.5079	−	28.2268i	0.690147	−	0.949906i	1.00000		0.000878603i	$0.000279668\pi$
$884$		0			0
$885$	−14.1548	+	21.6873i	−0.475807	+	0.729010i
$886$		0			0
$887$	36.9015	+	11.9900i	1.23903	+	0.402586i	0.853979	−	0.520308i	$-0.174183\pi$
$887$	36.9015	+	11.9900i	1.23903	+	0.402586i	0.385054	+	0.922894i	$0.374183\pi$
$888$		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
$895$	−13.6024	+	50.3028i	−0.454678	+	1.68144i
$896$		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
$905$	56.2201	−	2.81701i	1.86882	−	0.0936406i
$906$		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	−0.983559	−	0.180588i	$-0.942200\pi$
$911$	−8.87343	−	27.3096i	−0.293990	−	0.904808i	0.689569	−	0.724220i	$-0.257800\pi$
$912$		0			0
$913$	17.0677	+	5.54564i	0.564859	+	0.183534i
$914$		0			0
$915$	−1.22726	−	24.4930i	−0.0405721	−	0.809712i
$916$		0			0
$917$	−14.7924	+	20.3599i	−0.488487	+	0.672344i
$918$		0			0
$919$	1.19370	+	0.867272i	0.0393764	+	0.0286086i	0.607299	−	0.794473i	$-0.292253\pi$
$919$	1.19370	+	0.867272i	0.0393764	+	0.0286086i	−0.567923	+	0.823082i	$0.692253\pi$
$920$		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
$925$	−21.5867	+	36.9961i	−0.709767	+	1.21642i
$926$		0			0
$927$	−7.32052	+	2.37858i	−0.240438	+	0.0781229i
$928$		0			0
$929$	−33.0756	+	24.0308i	−1.08517	+	0.788425i	−0.978578	−	0.205878i	$-0.933995\pi$
$929$	−33.0756	+	24.0308i	−1.08517	+	0.788425i	−0.106596	+	0.994302i	$0.533995\pi$
$930$		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
$935$	49.2201	−	18.7643i	1.60967	−	0.613660i
$936$		0			0
$937$	−30.8930	−	10.0378i	−1.00923	−	0.327919i	−0.242683	−	0.970106i	$-0.578028\pi$
$937$	−30.8930	−	10.0378i	−1.00923	−	0.327919i	−0.766549	+	0.642186i	$0.778028\pi$
$938$		0			0
$939$	−2.30248	−	7.08632i	−0.0751387	−	0.231253i
$940$		0			0
$941$	−2.36379	+	7.27501i	−0.0770575	+	0.237159i	−0.982164	−	0.188026i	$-0.939791\pi$
$941$	−2.36379	+	7.27501i	−0.0770575	+	0.237159i	0.905106	+	0.425185i	$0.139791\pi$
$942$		0			0
$943$			1.77716i			0.0578722i
$944$		0			0
$945$	−2.95659	−	1.92969i	−0.0961778	−	0.0627729i
$946$		0			0
$947$	30.6280	+	42.1558i	0.995276	+	1.36988i	0.928179	+	0.372134i	$0.121374\pi$
$947$	30.6280	+	42.1558i	0.995276	+	1.36988i	0.0670970	+	0.997746i	$0.478626\pi$
$948$		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	$-0.221710\pi$
$953$	−2.47321	−	3.40408i	−0.0801151	−	0.110269i	−0.847194	+	0.531284i	$0.821710\pi$
$954$		0			0
$955$	6.39744	+	16.7809i	0.207016	+	0.543018i
$956$		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
$965$	−28.4256	−	35.2679i	−0.915052	−	1.13531i
$966$		0			0
$967$	29.7022	−	40.8816i	0.955158	−	1.31466i	0.00596071	−	0.999982i	$-0.498103\pi$
$967$	29.7022	−	40.8816i	0.955158	−	1.31466i	0.949198	−	0.314680i	$-0.101897\pi$
$968$		0			0
$969$	18.1315	+	13.1733i	0.582467	+	0.423187i
$970$		0			0
$971$	−12.8283	+	9.32029i	−0.411679	+	0.299102i	−0.774281	−	0.632842i	$-0.781888\pi$
$971$	−12.8283	+	9.32029i	−0.411679	+	0.299102i	0.362602	+	0.931944i	$0.381888\pi$
$972$		0			0
$973$	−14.8412	+	4.82220i	−0.475787	+	0.154593i
$974$		0			0
$975$	−1.70779	+	0.171574i	−0.0546929	+	0.00549477i
$976$		0			0
$977$	−41.1903	+	13.3836i	−1.31780	+	0.428178i	−0.881737	−	0.471741i	$-0.843626\pi$
$977$	−41.1903	+	13.3836i	−1.31780	+	0.428178i	−0.436058	+	0.899918i	$0.643626\pi$
$978$		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	$-0.611685\pi$
$983$	20.5553	−	28.2920i	0.655613	−	0.902374i	0.999326	+	0.0367008i	$0.0116848\pi$
$984$		0			0
$985$	−43.2050	−	11.6831i	−1.37662	−	0.372254i
$986$		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	−0.997753	−	0.0669939i	$-0.978659\pi$
$991$	−4.75904	+	14.6468i	−0.151176	+	0.465272i	0.846577	+	0.532266i	$0.178659\pi$
$992$		0			0
$993$			27.4282i			0.870408i
$994$		0			0
$995$	−39.0292	+	31.4572i	−1.23731	+	0.997260i
$996$		0			0
$997$	18.1000	+	24.9124i	0.573231	+	0.788985i	0.992933	−	0.118677i	$-0.0378653\pi$
$997$	18.1000	+	24.9124i	0.573231	+	0.788985i	−0.419702	+	0.907662i	$0.637865\pi$
$998$		0			0
$999$	−8.56667			−0.271038

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.1	✓	24	1.1	even	1	trivial
300.2.o.a.229.1	yes	24	25.4	even	10	inner
900.2.w.c.469.6		24	3.2	odd	2
900.2.w.c.829.6		24	75.29	odd	10
1500.2.m.c.601.2		24	25.22	odd	20
1500.2.m.c.901.2		24	5.2	odd	4
1500.2.m.d.601.5		24	25.3	odd	20
1500.2.m.d.901.5		24	5.3	odd	4
1500.2.o.c.349.6		24	5.4	even	2
1500.2.o.c.649.6		24	25.21	even	5
7500.2.a.m.1.10		12	25.23	odd	20
7500.2.a.n.1.3		12	25.2	odd	20
7500.2.d.g.1249.3		24	25.14	even	10
7500.2.d.g.1249.22		24	25.11	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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{3} +(-1.74098 + 1.40321i) q^{5} +1.57893i q^{7} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{3} +(-1.74098 + 1.40321i) q^{5} +1.57893i q^{7} +(-0.309017 + 0.951057i) q^{9} +(1.19917 + 3.69066i) q^{11} +(0.326475 + 0.106078i) q^{13} +(2.15854 + 0.583692i) q^{15} +(-3.56817 + 4.91117i) q^{17} +(2.98680 + 2.17004i) q^{19} +(1.27738 - 0.928073i) q^{21} +(1.32236 - 0.429662i) q^{23} +(1.06200 - 4.88592i) q^{25} +(0.951057 - 0.309017i) q^{27} +(-2.69395 + 1.95727i) q^{29} +(4.25135 + 3.08879i) q^{31} +(2.28095 - 3.13946i) q^{33} +(-2.21557 - 2.74888i) q^{35} +(-8.14739 - 2.64725i) q^{37} +(-0.106078 - 0.326475i) q^{39} +(-0.394970 + 1.21559i) q^{41} -1.42438i q^{43} +(-0.796542 - 2.08938i) q^{45} +(0.220691 + 0.303755i) q^{47} +4.50698 q^{49} +6.07054 q^{51} +(-6.64151 - 9.14125i) q^{53} +(-7.26650 - 4.74266i) q^{55} -3.69189i q^{57} +(-3.57899 + 11.0150i) q^{59} +(-3.38909 - 10.4305i) q^{61} +(-1.50165 - 0.487917i) q^{63} +(-0.717236 + 0.273434i) q^{65} +(-6.14771 + 8.46160i) q^{67} +(-1.12487 - 0.817265i) q^{69} +(8.19220 - 5.95198i) q^{71} +(12.5444 - 4.07594i) q^{73} +(-4.57701 + 2.01270i) q^{75} +(-5.82730 + 1.89340i) q^{77} +(11.1640 - 8.11114i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(2.71826 - 3.74136i) q^{83} +(-0.679305 - 13.5571i) q^{85} +(3.16693 + 1.02900i) q^{87} +(2.24626 + 6.91326i) q^{89} +(-0.167490 + 0.515482i) q^{91} -5.25496i q^{93} +(-8.24497 + 0.413129i) q^{95} +(3.55938 + 4.89906i) q^{97} -3.88059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{5} + 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^5 + 6 * q^9	\( 24 q - 2 q^{5} + 6 q^{9} - 6 q^{11} + 4 q^{15} + 10 q^{17} + 10 q^{19} - 4 q^{21} + 40 q^{23} - 4 q^{25} + 4 q^{29} + 6 q^{31} + 10 q^{33} - 6 q^{35} - 10 q^{41} + 2 q^{45} - 40 q^{47} - 56 q^{49} + 16 q^{51} - 60 q^{53} - 62 q^{55} - 36 q^{59} - 12 q^{61} - 10 q^{63} + 20 q^{67} + 4 q^{69} + 40 q^{71} + 60 q^{73} + 8 q^{75} - 40 q^{77} + 8 q^{79} - 6 q^{81} - 50 q^{83} + 34 q^{85} - 20 q^{87} - 30 q^{91} - 60 q^{95} - 40 q^{97} - 4 q^{99}+O(q^{100}) \) 24 * q - 2 * q^5 + 6 * q^9 - 6 * q^11 + 4 * q^15 + 10 * q^17 + 10 * q^19 - 4 * q^21 + 40 * q^23 - 4 * q^25 + 4 * q^29 + 6 * q^31 + 10 * q^33 - 6 * q^35 - 10 * q^41 + 2 * q^45 - 40 * q^47 - 56 * q^49 + 16 * q^51 - 60 * q^53 - 62 * q^55 - 36 * q^59 - 12 * q^61 - 10 * q^63 + 20 * q^67 + 4 * q^69 + 40 * q^71 + 60 * q^73 + 8 * q^75 - 40 * q^77 + 8 * q^79 - 6 * q^81 - 50 * q^83 + 34 * q^85 - 20 * q^87 - 30 * q^91 - 60 * q^95 - 40 * q^97 - 4 * q^99

Introduction

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