LMFDB - Embedded newform 300.2.o.a.229.1

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			229.1
Character	$\chi$	$=$	300.229
Dual form			300.2.o.a.169.1

$q$-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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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	$-0.903550\pi$
$7$		−	1.57893i		−	0.596780i	0.954444	−	0.298390i	$-0.0964496\pi$
$8$		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	−0.263393	−	0.964689i	$-0.584841\pi$
$13$	0.326475	−	0.106078i	0.0905480	−	0.0294208i	0.353941	+	0.935268i	$0.384841\pi$
$14$		0			0
$15$	2.15854	−	0.583692i	0.557333	−	0.150709i
$16$		0			0
$17$	−3.56817	−	4.91117i	−0.865409	−	1.19113i	−0.980253	−	0.197750i	$-0.936637\pi$
$17$	−3.56817	−	4.91117i	−0.865409	−	1.19113i	0.114844	−	0.993384i	$-0.463363\pi$
$18$		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	0.443619	−	0.896216i	$-0.353694\pi$
$23$	1.32236	+	0.429662i	0.275732	+	0.0895906i	−0.167887	+	0.985806i	$0.553694\pi$
$24$		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	0.308860	−	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
$35$	−2.21557	+	2.74888i	−0.374500	+	0.464646i
$36$		0			0
$37$	−8.14739	+	2.64725i	−1.33942	+	0.435205i	−0.889121	−	0.457672i	$-0.848683\pi$
$37$	−8.14739	+	2.64725i	−1.33942	+	0.435205i	−0.450301	+	0.892877i	$0.648683\pi$
$38$		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	$0.0346394\pi$
$43$			1.42438i			0.217216i	−0.994085	+	0.108608i	$0.965361\pi$
$44$		0			0
$45$	−0.796542	+	2.08938i	−0.118742	+	0.311467i
$46$		0			0
$47$	0.220691	−	0.303755i	0.0321911	−	0.0443072i	−0.792618	−	0.609718i	$-0.791283\pi$
$47$	0.220691	−	0.303755i	0.0321911	−	0.0443072i	0.824809	+	0.565411i	$0.191283\pi$
$48$		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	$0.482771\pi$
$53$	−6.64151	+	9.14125i	−0.912282	+	1.25565i	−0.966382	+	0.257112i	$0.917229\pi$
$54$		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	−0.857791	−	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
$65$	−0.717236	−	0.273434i	−0.0889622	−	0.0339154i
$66$		0			0
$67$	−6.14771	−	8.46160i	−0.751063	−	1.03375i	−0.997905	−	0.0646937i	$-0.979393\pi$
$67$	−6.14771	−	8.46160i	−0.751063	−	1.03375i	0.246842	−	0.969056i	$-0.420607\pi$
$68$		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	0.930569	−	0.366117i	$-0.119313\pi$
$73$	12.5444	+	4.07594i	1.46822	+	0.477052i	0.537648	+	0.843170i	$0.319313\pi$
$74$		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	0.998557	−	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	0.931709	−	0.363204i	$-0.118317\pi$
$83$	2.71826	+	3.74136i	0.298367	+	0.410668i	−0.633342	+	0.773872i	$0.718317\pi$
$84$		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	−0.758592	−	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
$95$	−8.24497	−	0.413129i	−0.845916	−	0.0423862i
$96$		0			0
$97$	3.55938	−	4.89906i	0.361400	−	0.497424i	−0.589138	−	0.808032i	$-0.700533\pi$
$97$	3.55938	−	4.89906i	0.361400	−	0.497424i	0.950538	+	0.310608i	$0.100533\pi$
$98$		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	−0.525692	−	0.850675i	$-0.676194\pi$
$103$	4.52433	−	6.22721i	0.445796	−	0.613585i	0.971488	+	0.237090i	$0.0761936\pi$
$104$		0			0
$105$	−0.921610	−	3.40819i	−0.0899399	−	0.332605i
$106$		0			0
$107$			18.0376i			1.74376i	0.489722	+	0.871878i	$0.337098\pi$
$107$			18.0376i			1.74376i	−0.489722	+	0.871878i	$0.662902\pi$
$108$		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	−0.205751	−	0.978604i	$-0.565964\pi$
$113$	2.15793	−	0.701155i	0.203001	−	0.0659591i	0.408753	+	0.912645i	$0.365964\pi$
$114$		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	0.244725	−	0.969593i	$-0.421302\pi$
$127$	−1.43348	−	0.465767i	−0.127201	−	0.0413301i	−0.371926	+	0.928262i	$0.621302\pi$
$128$		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
$135$	−1.22215	−	1.87252i	−0.105186	−	0.161161i
$136$		0			0
$137$	5.17996	−	1.68307i	0.442554	−	0.143795i	−0.0792596	−	0.996854i	$-0.525256\pi$
$137$	5.17996	−	1.68307i	0.442554	−	0.143795i	0.521814	+	0.853059i	$0.325256\pi$
$138$		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
$145$	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	$-0.613920\pi$
$157$		−	23.4721i		−	1.87328i	0.350300	−	0.936638i	$-0.386080\pi$
$158$		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	−0.0770538	−	0.997027i	$-0.524551\pi$
$163$	5.70240	−	1.85282i	0.446646	−	0.145124i	0.523700	+	0.851903i	$0.324551\pi$
$164$		0			0
$165$	0.434245	−	8.66638i	0.0338059	−	0.674677i
$166$		0			0
$167$	3.76094	+	5.17649i	0.291030	+	0.400569i	0.929348	−	0.369204i	$-0.120370\pi$
$167$	3.76094	+	5.17649i	0.291030	+	0.400569i	−0.638318	+	0.769773i	$0.720370\pi$
$168$		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	0.491641	−	0.870798i	$-0.336397\pi$
$173$	4.96583	+	1.61350i	0.377545	+	0.122672i	−0.114096	+	0.993470i	$0.536397\pi$
$174$		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	0.993443	+	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
$185$	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	0.999813	−	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	$-0.739946\pi$
$193$		−	20.2575i		−	1.45817i	0.684424	−	0.729084i	$-0.260054\pi$
$194$		0			0
$195$	0.642794	−	0.419536i	0.0460314	−	0.0300436i
$196$		0			0
$197$	11.7650	−	16.1931i	0.838221	−	1.15371i	−0.148115	−	0.988970i	$-0.547321\pi$
$197$	11.7650	−	16.1931i	0.838221	−	1.15371i	0.986337	−	0.164742i	$-0.0526793\pi$
$198$		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	−0.815589	−	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
$215$	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	−0.113152	−	0.993578i	$-0.536095\pi$
$223$	−11.7779	−	3.82686i	−0.788705	−	0.256266i	−0.675552	+	0.737312i	$0.736095\pi$
$224$		0			0
$225$	4.31861	−	2.51985i	0.287907	−	0.167990i
$226$		0			0
$227$	17.3309	+	5.63116i	1.15029	+	0.373753i	0.821254	−	0.570563i	$-0.193275\pi$
$227$	17.3309	+	5.63116i	1.15029	+	0.373753i	0.329040	+	0.944316i	$0.393275\pi$
$228$		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	0.896399	−	0.443248i	$-0.146174\pi$
$233$	3.01993	+	4.15658i	0.197842	+	0.272307i	−0.698557	+	0.715555i	$0.746174\pi$
$234$		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	0.332332	+	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
$245$	−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	$0.251774\pi$
$257$			22.7976i			1.42207i	−0.703155	+	0.711036i	$0.748226\pi$
$258$		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	−0.572562	−	0.819861i	$-0.694051\pi$
$263$	−8.98231	+	2.91853i	−0.553873	+	0.179964i	0.0186895	+	0.999825i	$0.494051\pi$
$264$		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	−0.463433	+	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
$275$	19.3058	+	1.93957i	1.16418	+	0.116960i
$276$		0			0
$277$	14.6259	+	4.75225i	0.878786	+	0.285535i	0.713453	−	0.700703i	$-0.247130\pi$
$277$	14.6259	+	4.75225i	0.878786	+	0.285535i	0.165333	+	0.986238i	$0.447130\pi$
$278$		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	0.549177	−	0.835706i	$-0.314941\pi$
$283$	−6.98697	−	9.61673i	−0.415332	−	0.571655i	−0.964509	+	0.264051i	$0.914941\pi$
$284$		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	$0.149140\pi$
$293$			15.4596i			0.903161i	−0.892230	+	0.451581i	$0.850860\pi$
$294$		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	$0.274475\pi$
$307$			26.6092i			1.51867i	−0.650702	+	0.759334i	$0.725525\pi$
$308$		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	−0.101817	−	0.994803i	$-0.532466\pi$
$313$	7.08632	−	2.30248i	0.400542	−	0.130144i	0.502359	+	0.864659i	$0.332466\pi$
$314$		0			0
$315$	3.29899	+	1.25769i	0.185877	+	0.0708626i
$316$		0			0
$317$	1.74481	+	2.40152i	0.0979981	+	0.134883i	0.855200	−	0.518298i	$-0.173434\pi$
$317$	1.74481	+	2.40152i	0.0979981	+	0.134883i	−0.757202	+	0.653181i	$0.773434\pi$
$318$		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	−0.996072	−	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
$335$	−1.17039	+	23.3580i	−0.0639455	+	1.27618i
$336$		0			0
$337$	7.14905	−	2.32287i	0.389433	−	0.126535i	−0.107754	−	0.994178i	$-0.534366\pi$
$337$	7.14905	−	2.32287i	0.389433	−	0.126535i	0.497188	+	0.867643i	$0.334366\pi$
$338$		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	−0.576704	−	0.816953i	$-0.695661\pi$
$347$	7.05022	−	9.70380i	0.378476	−	0.520927i	0.955180	+	0.296026i	$0.0956614\pi$
$348$		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	$-0.568844\pi$
$353$	14.6665	−	20.1867i	0.780617	−	1.07443i	0.995214	−	0.0977244i	$-0.0311564\pi$
$354$		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	0.944300	−	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
$365$	−16.1202	−	24.6986i	−0.843769	−	1.29278i
$366$		0			0
$367$	−9.28986	−	12.7864i	−0.484927	−	0.667445i	0.494515	−	0.869169i	$-0.335346\pi$
$367$	−9.28986	−	12.7864i	−0.484927	−	0.667445i	−0.979442	+	0.201724i	$0.935346\pi$
$368$		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	0.218790	−	0.975772i	$-0.429789\pi$
$373$	−3.43291	−	1.11542i	−0.177750	−	0.0577543i	−0.396540	+	0.918018i	$0.629789\pi$
$374$		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	0.986419	−	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	0.414486	−	0.910056i	$-0.363961\pi$
$383$	−11.3334	−	15.5991i	−0.579112	−	0.797079i	−0.993598	+	0.112977i	$0.963961\pi$
$384$		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	−0.723876	−	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
$395$	−8.05466	−	29.7868i	−0.405274	−	1.49874i
$396$		0			0
$397$	16.0842	−	22.1380i	0.807243	−	1.11108i	−0.184499	−	0.982833i	$-0.559066\pi$
$397$	16.0842	−	22.1380i	0.807243	−	1.11108i	0.991743	−	0.128243i	$-0.0409336\pi$
$398$		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	−0.967921	−	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
$415$	0.517499	−	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	−0.673824	−	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
$425$	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	−0.155181	−	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	0.757994	−	0.652262i	$-0.226180\pi$
$433$	−2.00963	−	2.76602i	−0.0965768	−	0.132927i	−0.854571	+	0.519335i	$0.826180\pi$
$434$		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	−0.897477	−	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	$-0.712348\pi$
$443$		−	33.0705i		−	1.57122i	0.618719	−	0.785612i	$-0.287652\pi$
$444$		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	$0.101212\pi$
$457$			13.3667i			0.625269i	−0.949873	+	0.312635i	$0.898788\pi$
$458$		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	0.250524	−	0.968110i	$-0.419397\pi$
$463$	21.9961	−	7.14695i	1.02224	−	0.332147i	0.771719	+	0.635963i	$0.219397\pi$
$464$		0			0
$465$	7.37382	−	9.14876i	0.341953	−	0.424263i
$466$		0			0
$467$	−17.8034	−	24.5043i	−0.823845	−	1.13392i	−0.989038	−	0.147664i	$-0.952825\pi$
$467$	−17.8034	−	24.5043i	−0.823845	−	1.13392i	0.165193	−	0.986261i	$-0.447175\pi$
$468$		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	0.0457990	−	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
$485$	−13.0712	+	3.53459i	−0.593533	+	0.160497i
$486$		0			0
$487$	−2.14446	+	0.696777i	−0.0971747	+	0.0315740i	−0.357201	−	0.934028i	$-0.616269\pi$
$487$	−2.14446	+	0.696777i	−0.0971747	+	0.0315740i	0.260026	+	0.965602i	$0.416269\pi$
$488$		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
$495$	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	−0.814446	−	0.580239i	$-0.802959\pi$
$503$	−0.245105	+	0.337358i	−0.0109287	+	0.0150421i	0.803518	+	0.595281i	$0.202959\pi$
$504$		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	0.816341	−	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
$515$	−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	0.147926	−	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	0.0514866	−	0.998674i	$-0.483604\pi$
$523$	−11.2943	−	3.66974i	−0.493866	−	0.160467i	−0.545352	+	0.838207i	$0.683604\pi$
$524$		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	0.830825	+	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
$545$	−13.3229	+	34.9469i	−0.570691	+	1.49696i
$546$		0			0
$547$	−23.2652	+	32.0219i	−0.994750	+	1.36916i	−0.0662579	+	0.997803i	$0.521106\pi$
$547$	−23.2652	+	32.0219i	−0.994750	+	1.36916i	−0.928492	+	0.371353i	$0.878894\pi$
$548$		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	$0.0830802\pi$
$557$			12.1804i			0.516102i	−0.966131	+	0.258051i	$0.916920\pi$
$558$		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	0.536490	−	0.843907i	$-0.319750\pi$
$563$	34.7979	−	11.3065i	1.46656	−	0.476513i	0.930065	+	0.367394i	$0.119750\pi$
$564$		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	−0.988154	−	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
$575$	−0.694947	+	6.91725i	−0.0289813	+	0.288469i
$576$		0			0
$577$	15.6012	+	5.06913i	0.649485	+	0.211031i	0.615187	−	0.788381i	$-0.289080\pi$
$577$	15.6012	+	5.06913i	0.649485	+	0.211031i	0.0342981	+	0.999412i	$0.489080\pi$
$578$		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	0.439182	−	0.898398i	$-0.355268\pi$
$587$	32.0429	−	10.4114i	1.32255	−	0.429724i	0.883371	+	0.468674i	$0.155268\pi$
$588$		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	$0.230112\pi$
$593$			32.2208i			1.32315i	−0.749878	+	0.661576i	$0.769888\pi$
$594$		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	$-0.894060\pi$
$607$		−	16.0986i		−	0.653421i	0.945124	−	0.326710i	$-0.105940\pi$
$608$		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	−0.981285	−	0.192559i	$-0.938321\pi$
$613$	−41.1487	+	13.3700i	−1.66198	+	0.540010i	−0.680693	+	0.732569i	$0.738321\pi$
$614$		0			0
$615$	−1.56209	−	2.39337i	−0.0629896	−	0.0965098i
$616$		0			0
$617$	−0.931550	−	1.28217i	−0.0375028	−	0.0516182i	0.789854	−	0.613295i	$-0.210156\pi$
$617$	−0.931550	−	1.28217i	−0.0375028	−	0.0516182i	−0.827357	+	0.561677i	$0.810156\pi$
$618$		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
$625$	−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	−0.00594245	−	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
$635$	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	−0.999411	−	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	$0.375514\pi$
$643$			46.8857i			1.84899i	−0.381190	+	0.924497i	$0.624486\pi$
$644$		0			0
$645$	0.831401	+	3.07459i	0.0327364	+	0.121062i
$646$		0			0
$647$	8.46236	−	11.6474i	0.332690	−	0.457908i	−0.609599	−	0.792710i	$-0.708669\pi$
$647$	8.46236	−	11.6474i	0.332690	−	0.457908i	0.942288	+	0.334802i	$0.108669\pi$
$648$		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	$0.415224\pi$
$653$	−18.7990	+	25.8746i	−0.735661	+	1.01255i	−0.998857	+	0.0478084i	$0.984776\pi$
$654$		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	−0.998295	−	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
$665$	−0.652303	+	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	0.438999	−	0.898488i	$-0.355333\pi$
$673$	6.90162	+	2.24247i	0.266038	+	0.0864410i	−0.172961	+	0.984929i	$0.555333\pi$
$674$		0			0
$675$	−0.499813	+	4.97496i	−0.0192378	+	0.191486i
$676$		0			0
$677$	−32.2918	−	10.4922i	−1.24107	−	0.403249i	−0.386359	−	0.922348i	$-0.626267\pi$
$677$	−32.2918	−	10.4922i	−1.24107	−	0.403249i	−0.854714	+	0.519099i	$0.826267\pi$
$678$		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	0.998236	−	0.0593717i	$-0.0189097\pi$
$683$	16.5508	+	22.7802i	0.633298	+	0.871660i	−0.364938	+	0.931032i	$0.618910\pi$
$684$		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	0.992643	+	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
$695$	−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	0.832852	−	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
$715$	−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	−0.394992	−	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
$725$	6.70208	−	15.2410i	0.248909	−	0.566037i
$726$		0			0
$727$	1.17583	+	0.382051i	0.0436092	+	0.0141695i	0.330740	−	0.943722i	$-0.392702\pi$
$727$	1.17583	+	0.382051i	0.0436092	+	0.0141695i	−0.287131	+	0.957891i	$0.592702\pi$
$728$		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	0.591305	−	0.806448i	$-0.298613\pi$
$733$	−9.70319	−	13.3553i	−0.358395	−	0.493289i	−0.949701	+	0.313159i	$0.898613\pi$
$734$		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	−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	$0.0700099\pi$
$743$			11.8940i			0.436347i	−0.975910	+	0.218174i	$0.929990\pi$
$744$		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	$-0.798461\pi$
$757$		−	32.5591i		−	1.18338i	0.806166	−	0.591690i	$-0.201539\pi$
$758$		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
$765$	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	−0.622017	−	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	0.866347	−	0.499442i	$-0.166462\pi$
$773$	35.4118	+	11.5060i	1.27367	+	0.413841i	0.407325	+	0.913283i	$0.366462\pi$
$774$		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	−0.670242	−	0.742143i	$-0.733809\pi$
$787$	−21.7768	+	7.07570i	−0.776258	+	0.252221i	−0.106016	+	0.994364i	$0.533809\pi$
$788$		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	−0.891348	−	0.453319i	$-0.850240\pi$
$797$	−5.21641	+	7.17977i	−0.184775	+	0.254321i	0.706574	+	0.707639i	$0.250240\pi$
$798$		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	0.885098	+	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
$815$	−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	0.993288	+	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	0.561705	−	0.827338i	$-0.310146\pi$
$823$	15.2000	+	4.93877i	0.529837	+	0.172155i	−0.0318678	+	0.999492i	$0.510146\pi$
$824$		0			0
$825$	−12.9168	+	14.4786i	−0.449705	+	0.504081i
$826$		0			0
$827$	−42.9415	−	13.9525i	−1.49322	−	0.485177i	−0.555190	−	0.831724i	$-0.687354\pi$
$827$	−42.9415	−	13.9525i	−1.49322	−	0.485177i	−0.938033	+	0.346546i	$0.887354\pi$
$828$		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
$835$	0.716004	−	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	−0.748194	−	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
$845$	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	−0.800707	−	0.599056i	$-0.795543\pi$
$853$	0.480767	−	0.661719i	0.0164611	−	0.0226568i	0.817168	+	0.576399i	$0.195543\pi$
$854$		0			0
$855$	2.15493	+	7.96909i	0.0736969	+	0.272537i
$856$		0			0
$857$			38.5882i			1.31815i	0.752078	+	0.659074i	$0.229052\pi$
$857$			38.5882i			1.31815i	−0.752078	+	0.659074i	$0.770948\pi$
$858$		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	−0.709944	−	0.704258i	$-0.751280\pi$
$863$	−25.5681	+	8.30758i	−0.870349	+	0.282793i	−0.160404	+	0.987051i	$0.551280\pi$
$864$		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	0.649850	−	0.760063i	$-0.274832\pi$
$877$	21.5839	+	7.01303i	0.728836	+	0.236813i	0.0789861	+	0.996876i	$0.474832\pi$
$878$		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	1.00000		0.000878603i	$-0.000279668\pi$
$883$	20.5079	+	28.2268i	0.690147	+	0.949906i	−0.309852	+	0.950785i	$0.600280\pi$
$884$		0			0
$885$	−14.1548	−	21.6873i	−0.475807	−	0.729010i
$886$		0			0
$887$	36.9015	−	11.9900i	1.23903	−	0.402586i	0.385054	−	0.922894i	$-0.374183\pi$
$887$	36.9015	−	11.9900i	1.23903	−	0.402586i	0.853979	+	0.520308i	$0.174183\pi$
$888$		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	$-0.946433\pi$
$907$		−	10.0886i		−	0.334988i	0.985873	−	0.167494i	$-0.0535675\pi$
$908$		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
$915$	−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	−0.567923	−	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
$925$	−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	−0.106596	−	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
$935$	49.2201	+	18.7643i	1.60967	+	0.613660i
$936$		0			0
$937$	−30.8930	+	10.0378i	−1.00923	+	0.327919i	−0.766549	−	0.642186i	$-0.778028\pi$
$937$	−30.8930	+	10.0378i	−1.00923	+	0.327919i	−0.242683	+	0.970106i	$0.578028\pi$
$938$		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
$945$	−2.95659	+	1.92969i	−0.0961778	+	0.0627729i
$946$		0			0
$947$	30.6280	−	42.1558i	0.995276	−	1.36988i	0.0670970	−	0.997746i	$-0.478626\pi$
$947$	30.6280	−	42.1558i	0.995276	−	1.36988i	0.928179	−	0.372134i	$-0.121374\pi$
$948$		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	−0.847194	−	0.531284i	$-0.821710\pi$
$953$	−2.47321	+	3.40408i	−0.0801151	+	0.110269i	0.767079	+	0.641553i	$0.221710\pi$
$954$		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	0.949198	+	0.314680i	$0.101897\pi$
$967$	29.7022	+	40.8816i	0.955158	+	1.31466i	0.00596071	+	0.999982i	$0.498103\pi$
$968$		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
$975$	−1.70779	−	0.171574i	−0.0546929	−	0.00549477i
$976$		0			0
$977$	−41.1903	−	13.3836i	−1.31780	−	0.428178i	−0.436058	−	0.899918i	$-0.643626\pi$
$977$	−41.1903	−	13.3836i	−1.31780	−	0.428178i	−0.881737	+	0.471741i	$0.843626\pi$
$978$		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	0.999326	−	0.0367008i	$-0.0116848\pi$
$983$	20.5553	+	28.2920i	0.655613	+	0.902374i	−0.343713	+	0.939075i	$0.611685\pi$
$984$		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	0.846577	−	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
$995$	−39.0292	−	31.4572i	−1.23731	−	0.997260i
$996$		0			0
$997$	18.1000	−	24.9124i	0.573231	−	0.788985i	−0.419702	−	0.907662i	$-0.637865\pi$
$997$	18.1000	−	24.9124i	0.573231	−	0.788985i	0.992933	+	0.118677i	$0.0378653\pi$
$998$		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.229.1	yes	24
3.2	odd	2		900.2.w.c.829.6		24
5.2	odd	4		1500.2.m.d.601.5		24
5.3	odd	4		1500.2.m.c.601.2		24
5.4	even	2		1500.2.o.c.649.6		24
25.6	even	5		1500.2.o.c.349.6		24
25.8	odd	20		1500.2.m.c.901.2		24
25.9	even	10		7500.2.d.g.1249.22		24
25.12	odd	20		7500.2.a.m.1.10		12
25.13	odd	20		7500.2.a.n.1.3		12
25.16	even	5		7500.2.d.g.1249.3		24
25.17	odd	20		1500.2.m.d.901.5		24
25.19	even	10	inner	300.2.o.a.169.1	✓	24
75.44	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	25.19	even	10	inner
300.2.o.a.229.1	yes	24	1.1	even	1	trivial
900.2.w.c.469.6		24	75.44	odd	10
900.2.w.c.829.6		24	3.2	odd	2
1500.2.m.c.601.2		24	5.3	odd	4
1500.2.m.c.901.2		24	25.8	odd	20
1500.2.m.d.601.5		24	5.2	odd	4
1500.2.m.d.901.5		24	25.17	odd	20
1500.2.o.c.349.6		24	25.6	even	5
1500.2.o.c.649.6		24	5.4	even	2
7500.2.a.m.1.10		12	25.12	odd	20
7500.2.a.n.1.3		12	25.13	odd	20
7500.2.d.g.1249.3		24	25.16	even	5
7500.2.d.g.1249.22		24	25.9	even	10

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

L-functions

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