LMFDB - Embedded newform 1078.2.i.d.1011.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1011.11
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.d.901.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.37695 + 1.94969i) q^{5} -0.765367 q^{6} -1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.37695 + 1.94969i) q^{5} -0.765367 q^{6} -1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +(-1.94969 + 3.37695i) q^{10} +(2.75881 + 1.84092i) q^{11} +(-0.662827 + 0.382683i) q^{12} -1.81903 q^{13} +2.98445 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.03803 - 5.26202i) q^{17} +(-2.09077 - 1.20711i) q^{18} +(3.41476 + 5.91454i) q^{19} +3.89937i q^{20} +(3.30966 + 0.214882i) q^{22} +(2.18834 + 3.79031i) q^{23} +(-0.382683 + 0.662827i) q^{24} +(5.10255 - 8.83788i) q^{25} +(-1.57532 + 0.909513i) q^{26} +4.14386i q^{27} +9.36112i q^{29} +(2.58461 - 1.49222i) q^{30} +(6.82704 + 3.94159i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.12412 - 2.27596i) q^{33} -6.07606i q^{34} -2.41421 q^{36} +(2.30389 + 3.99045i) q^{37} +(5.91454 + 3.41476i) q^{38} +(1.20570 + 0.696111i) q^{39} +(1.94969 + 3.37695i) q^{40} +3.58235 q^{41} -3.25819i q^{43} +(2.97369 - 1.46874i) q^{44} +(8.15269 + 4.70696i) q^{45} +(3.79031 + 2.18834i) q^{46} +(-0.176542 + 0.101927i) q^{47} +0.765367i q^{48} -10.2051i q^{50} +(-4.02738 + 2.32521i) q^{51} +(-0.909513 + 1.57532i) q^{52} +(-2.49222 + 4.31666i) q^{53} +(2.07193 + 3.58869i) q^{54} +(-12.9056 - 0.837904i) q^{55} -5.22709i q^{57} +(4.68056 + 8.10697i) q^{58} +(4.50118 + 2.59876i) q^{59} +(1.49222 - 2.58461i) q^{60} +(-4.49186 - 7.78013i) q^{61} +7.88318 q^{62} -1.00000 q^{64} +(6.14277 - 3.54653i) q^{65} +(-2.11150 - 1.40898i) q^{66} +(4.01676 - 6.95724i) q^{67} +(-3.03803 - 5.26202i) q^{68} -3.34976i q^{69} +8.86195 q^{71} +(-2.09077 + 1.20711i) q^{72} +(-0.0278530 + 0.0482428i) q^{73} +(3.99045 + 2.30389i) q^{74} +(-6.76422 + 3.90532i) q^{75} +6.82952 q^{76} +1.39222 q^{78} +(-7.34847 + 4.24264i) q^{79} +(3.37695 + 1.94969i) q^{80} +(-2.03553 + 3.52565i) q^{81} +(3.10240 - 1.79117i) q^{82} -10.4676 q^{83} +23.6928i q^{85} +(-1.62910 - 2.82168i) q^{86} +(3.58235 - 6.20481i) q^{87} +(1.84092 - 2.75881i) q^{88} +(1.46160 - 0.843855i) q^{89} +9.41392 q^{90} +4.37667 q^{92} +(-3.01676 - 5.22519i) q^{93} +(-0.101927 + 0.176542i) q^{94} +(-23.0630 - 13.3154i) q^{95} +(0.382683 + 0.662827i) q^{96} -9.23880i q^{97} +(0.518771 - 7.99022i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^9	$ 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^22 + 16 * q^23 + 64 * q^25 - 32 * q^36 + 80 * q^37 + 16 * q^44 - 32 * q^53 + 48 * q^58 - 32 * q^64 - 16 * q^67 - 96 * q^71 + 32 * q^78 + 48 * q^81 - 32 * q^86 - 8 * q^88 + 32 * q^92 + 48 * q^93 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.662827	−	0.382683i	−0.382683	−	0.220942i	0.296302	−	0.955094i	$-0.404247\pi$
$3$	−0.662827	−	0.382683i	−0.382683	−	0.220942i	−0.678985	+	0.734152i	$0.737580\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−3.37695	+	1.94969i	−1.51022	+	0.871926i	−0.510291	+	0.860002i	$0.670462\pi$
$5$	−3.37695	+	1.94969i	−1.51022	+	0.871926i	−0.999929	+	0.0119244i	$0.996204\pi$
$6$	−0.765367			−0.312460
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.20711	−	2.09077i	−0.402369	−	0.696923i
$10$	−1.94969	+	3.37695i	−0.616545	+	1.06789i
$11$	2.75881	+	1.84092i	0.831811	+	0.555059i
$11$	2.75881	+	1.84092i	0.831811	+	0.555059i
$12$	−0.662827	+	0.382683i	−0.191342	+	0.110471i
$13$	−1.81903			−0.504507			−0.252254	−	0.967661i	$-0.581172\pi$
$13$	−1.81903			−0.504507			−0.252254	+	0.967661i	$0.581172\pi$
$14$		0			0
$15$	2.98445			0.770582
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.03803	−	5.26202i	0.736830	−	1.27623i	−0.217085	−	0.976153i	$-0.569655\pi$
$17$	3.03803	−	5.26202i	0.736830	−	1.27623i	0.953916	−	0.300075i	$-0.0970116\pi$
$18$	−2.09077	−	1.20711i	−0.492799	−	0.284518i
$19$	3.41476	+	5.91454i	0.783400	+	1.35689i	0.929950	+	0.367685i	$0.119850\pi$
$19$	3.41476	+	5.91454i	0.783400	+	1.35689i	−0.146550	+	0.989203i	$0.546817\pi$
$20$			3.89937i			0.871926i
$21$		0			0
$22$	3.30966	+	0.214882i	0.705621	+	0.0458130i
$23$	2.18834	+	3.79031i	0.456300	+	0.790334i	0.998762	−	0.0497460i	$-0.0158412\pi$
$23$	2.18834	+	3.79031i	0.456300	+	0.790334i	−0.542462	+	0.840080i	$0.682508\pi$
$24$	−0.382683	+	0.662827i	−0.0781149	+	0.135299i
$25$	5.10255	−	8.83788i	1.02051	−	1.76758i
$26$	−1.57532	+	0.909513i	−0.308946	+	0.178370i
$27$			4.14386i			0.797486i
$28$		0			0
$29$			9.36112i			1.73832i	0.494534	+	0.869158i	$0.335339\pi$
$29$			9.36112i			1.73832i	−0.494534	+	0.869158i	$0.664661\pi$
$30$	2.58461	−	1.49222i	0.471883	−	0.272442i
$31$	6.82704	+	3.94159i	1.22617	+	0.707931i	0.966227	−	0.257693i	$-0.0829622\pi$
$31$	6.82704	+	3.94159i	1.22617	+	0.707931i	0.259945	+	0.965623i	$0.416296\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.12412	−	2.27596i	−0.195684	−	0.396194i
$34$		−	6.07606i		−	1.04204i
$35$		0			0
$36$	−2.41421			−0.402369
$37$	2.30389	+	3.99045i	0.378757	+	0.656026i	0.990882	−	0.134735i	$-0.0430183\pi$
$37$	2.30389	+	3.99045i	0.378757	+	0.656026i	−0.612125	+	0.790761i	$0.709685\pi$
$38$	5.91454	+	3.41476i	0.959465	+	0.553947i
$39$	1.20570	+	0.696111i	0.193067	+	0.111467i
$40$	1.94969	+	3.37695i	0.308272	+	0.533943i
$41$	3.58235			0.559469			0.279734	−	0.960077i	$-0.409754\pi$
$41$	3.58235			0.559469			0.279734	+	0.960077i	$0.409754\pi$
$42$		0			0
$43$		−	3.25819i		−	0.496869i	−0.968649	−	0.248435i	$-0.920084\pi$
$43$		−	3.25819i		−	0.496869i	0.968649	−	0.248435i	$-0.0799161\pi$
$44$	2.97369	−	1.46874i	0.448300	−	0.221420i
$45$	8.15269	+	4.70696i	1.21533	+	0.701672i
$46$	3.79031	+	2.18834i	0.558851	+	0.322653i
$47$	−0.176542	+	0.101927i	−0.0257513	+	0.0148675i	−0.512820	−	0.858496i	$-0.671399\pi$
$47$	−0.176542	+	0.101927i	−0.0257513	+	0.0148675i	0.487069	+	0.873363i	$0.338066\pi$
$48$			0.765367i			0.110471i
$49$		0			0
$50$		−	10.2051i		−	1.44322i
$51$	−4.02738	+	2.32521i	−0.563945	+	0.325594i
$52$	−0.909513	+	1.57532i	−0.126127	+	0.218458i
$53$	−2.49222	+	4.31666i	−0.342333	+	0.592939i	−0.984866	−	0.173320i	$-0.944551\pi$
$53$	−2.49222	+	4.31666i	−0.342333	+	0.592939i	0.642532	+	0.766259i	$0.277884\pi$
$54$	2.07193	+	3.58869i	0.281954	+	0.488359i
$55$	−12.9056	−	0.837904i	−1.74019	−	0.112983i
$56$		0			0
$57$		−	5.22709i		−	0.692345i
$58$	4.68056	+	8.10697i	0.614588	+	1.06450i
$59$	4.50118	+	2.59876i	0.586004	+	0.338330i	0.763516	−	0.645789i	$-0.223471\pi$
$59$	4.50118	+	2.59876i	0.586004	+	0.338330i	−0.177512	+	0.984119i	$0.556805\pi$
$60$	1.49222	−	2.58461i	0.192645	−	0.333672i
$61$	−4.49186	−	7.78013i	−0.575124	−	0.996143i	−0.996028	−	0.0890385i	$-0.971621\pi$
$61$	−4.49186	−	7.78013i	−0.575124	−	0.996143i	0.420905	−	0.907105i	$-0.361713\pi$
$62$	7.88318			1.00117
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.14277	−	3.54653i	0.761917	−	0.439893i
$66$	−2.11150	−	1.40898i	−0.259907	−	0.173433i
$67$	4.01676	−	6.95724i	0.490726	−	0.849962i	−0.509217	−	0.860638i	$-0.670065\pi$
$67$	4.01676	−	6.95724i	0.490726	−	0.849962i	0.999943	+	0.0106761i	$0.00339837\pi$
$68$	−3.03803	−	5.26202i	−0.368415	−	0.638114i
$69$		−	3.34976i		−	0.403264i
$70$		0			0
$71$	8.86195			1.05172			0.525860	−	0.850571i	$-0.323744\pi$
$71$	8.86195			1.05172			0.525860	+	0.850571i	$0.323744\pi$
$72$	−2.09077	+	1.20711i	−0.246400	+	0.142259i
$73$	−0.0278530	+	0.0482428i	−0.00325995	+	0.00564639i	−0.867651	−	0.497174i	$-0.834371\pi$
$73$	−0.0278530	+	0.0482428i	−0.00325995	+	0.00564639i	0.864391	+	0.502821i	$0.167704\pi$
$74$	3.99045	+	2.30389i	0.463881	+	0.267822i
$75$	−6.76422	+	3.90532i	−0.781064	+	0.450948i
$76$	6.82952			0.783400
$77$		0			0
$78$	1.39222			0.157638
$79$	−7.34847	+	4.24264i	−0.826767	+	0.477334i	−0.852745	−	0.522328i	$-0.825064\pi$
$79$	−7.34847	+	4.24264i	−0.826767	+	0.477334i	0.0259772	+	0.999663i	$0.491730\pi$
$80$	3.37695	+	1.94969i	0.377555	+	0.217982i
$81$	−2.03553	+	3.52565i	−0.226170	+	0.391739i
$82$	3.10240	−	1.79117i	0.342603	−	0.197802i
$83$	−10.4676			−1.14897			−0.574483	−	0.818517i	$-0.694797\pi$
$83$	−10.4676			−1.14897			−0.574483	+	0.818517i	$0.694797\pi$
$84$		0			0
$85$			23.6928i			2.56985i
$86$	−1.62910	−	2.82168i	−0.175670	−	0.304269i
$87$	3.58235	−	6.20481i	0.384068	−	0.665225i
$88$	1.84092	−	2.75881i	0.196243	−	0.294090i
$89$	1.46160	−	0.843855i	0.154929	−	0.0894484i	−0.420531	−	0.907278i	$-0.638156\pi$
$89$	1.46160	−	0.843855i	0.154929	−	0.0894484i	0.575460	+	0.817830i	$0.304823\pi$
$90$	9.41392			0.992314
$91$		0			0
$92$	4.37667			0.456300
$93$	−3.01676	−	5.22519i	−0.312824	−	0.541827i
$94$	−0.101927	+	0.176542i	−0.0105129	+	0.0182090i
$95$	−23.0630	−	13.3154i	−2.36621	−	1.36613i
$96$	0.382683	+	0.662827i	0.0390575	+	0.0676495i
$97$		−	9.23880i		−	0.938058i	−0.883183	−	0.469029i	$-0.844604\pi$
$97$		−	9.23880i		−	0.938058i	0.883183	−	0.469029i	$-0.155396\pi$
$98$		0			0
$99$	0.518771	−	7.99022i	0.0521384	−	0.803047i
$100$	−5.10255	−	8.83788i	−0.510255	−	0.883788i
$101$	−2.67283	+	4.62948i	−0.265957	+	0.460651i	−0.967814	−	0.251667i	$-0.919021\pi$
$101$	−2.67283	+	4.62948i	−0.265957	+	0.460651i	0.701857	+	0.712318i	$0.252355\pi$
$102$	−2.32521	+	4.02738i	−0.230230	+	0.398770i
$103$	−3.67639	+	2.12256i	−0.362246	+	0.209143i	−0.670065	−	0.742302i	$-0.733734\pi$
$103$	−3.67639	+	2.12256i	−0.362246	+	0.209143i	0.307820	+	0.951445i	$0.400401\pi$
$104$			1.81903i			0.178370i
$105$		0			0
$106$			4.98445i			0.484133i
$107$	−6.26883	+	3.61931i	−0.606031	+	0.349892i	−0.771411	−	0.636338i	$-0.780448\pi$
$107$	−6.26883	+	3.61931i	−0.606031	+	0.349892i	0.165379	+	0.986230i	$0.447115\pi$
$108$	3.58869	+	2.07193i	0.345322	+	0.199372i
$109$	−5.19615	−	3.00000i	−0.497701	−	0.287348i	0.230063	−	0.973176i	$-0.426107\pi$
$109$	−5.19615	−	3.00000i	−0.497701	−	0.287348i	−0.727764	+	0.685828i	$0.759440\pi$
$110$	−11.5955	+	5.72714i	−1.10559	+	0.546062i
$111$		−	3.52664i		−	0.334734i
$112$		0			0
$113$	16.8400			1.58417			0.792085	−	0.610411i	$-0.208996\pi$
$113$	16.8400			1.58417			0.792085	+	0.610411i	$0.208996\pi$
$114$	−2.61355	−	4.52679i	−0.244781	−	0.423973i
$115$	−14.7798	−	8.53314i	−1.37823	−	0.795719i
$116$	8.10697	+	4.68056i	0.752713	+	0.434579i
$117$	2.19576	+	3.80317i	0.202998	+	0.351603i
$118$	5.19752			0.478470
$119$		0			0
$120$		−	2.98445i		−	0.272442i
$121$	4.22202	+	10.1575i	0.383820	+	0.923408i
$122$	−7.78013	−	4.49186i	−0.704380	−	0.406674i
$123$	−2.37448	−	1.37090i	−0.214099	−	0.123610i
$124$	6.82704	−	3.94159i	0.613086	−	0.353965i
$125$			20.2966i			1.81538i
$126$		0			0
$127$		−	17.3300i		−	1.53779i	−0.639375	−	0.768895i	$-0.720807\pi$
$127$		−	17.3300i		−	1.53779i	0.639375	−	0.768895i	$-0.279193\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−1.24686	+	2.15962i	−0.109780	+	0.190144i
$130$	3.54653	−	6.14277i	0.311051	−	0.538757i
$131$	3.17776	+	5.50404i	0.277642	+	0.480890i	0.970798	−	0.239897i	$-0.0771137\pi$
$131$	3.17776	+	5.50404i	0.277642	+	0.480890i	−0.693156	+	0.720788i	$0.743780\pi$
$132$	−2.53310	−	0.164463i	−0.220478	−	0.0143147i
$133$		0			0
$134$		−	8.03353i		−	0.693991i
$135$	−8.07922	−	13.9936i	−0.695349	−	1.20438i
$136$	−5.26202	−	3.03803i	−0.451215	−	0.260509i
$137$	−0.674793	+	1.16878i	−0.0576515	+	0.0998553i	−0.893411	−	0.449241i	$-0.851695\pi$
$137$	−0.674793	+	1.16878i	−0.0576515	+	0.0998553i	0.835759	+	0.549096i	$0.185028\pi$
$138$	−1.67488	−	2.90098i	−0.142575	−	0.246948i
$139$	11.8957			1.00898			0.504491	−	0.863417i	$-0.331680\pi$
$139$	11.8957			1.00898			0.504491	+	0.863417i	$0.331680\pi$
$140$		0			0
$141$	0.156023			0.0131395
$142$	7.67468	−	4.43098i	0.644045	−	0.371839i
$143$	−5.01834	−	3.34868i	−0.419655	−	0.280031i
$144$	−1.20711	+	2.09077i	−0.100592	+	0.174231i
$145$	−18.2512	−	31.6121i	−1.51568	−	2.62524i
$146$			0.0557060i			0.00461026i
$147$		0			0
$148$	4.60778			0.378757
$149$	−5.69557	+	3.28834i	−0.466599	+	0.269391i	−0.714815	−	0.699314i	$-0.753489\pi$
$149$	−5.69557	+	3.28834i	−0.466599	+	0.269391i	0.248216	+	0.968705i	$0.420156\pi$
$150$	−3.90532	+	6.76422i	−0.318868	+	0.552296i
$151$	7.48149	+	4.31944i	0.608835	+	0.351511i	0.772509	−	0.635003i	$-0.219001\pi$
$151$	7.48149	+	4.31944i	0.608835	+	0.351511i	−0.163674	+	0.986514i	$0.552335\pi$
$152$	5.91454	−	3.41476i	0.479733	−	0.276974i
$153$	−14.6689			−1.18591
$154$		0			0
$155$	−30.7395			−2.46905
$156$	1.20570	−	0.696111i	0.0965333	−	0.0557335i
$157$	2.12168	+	1.22495i	0.169329	+	0.0977619i	0.582269	−	0.812996i	$-0.302165\pi$
$157$	2.12168	+	1.22495i	0.169329	+	0.0977619i	−0.412941	+	0.910758i	$0.635498\pi$
$158$	−4.24264	+	7.34847i	−0.337526	+	0.584613i
$159$	3.30383	−	1.90747i	0.262011	−	0.151272i
$160$	3.89937			0.308272
$161$		0			0
$162$			4.07107i			0.319853i
$163$	−1.14503	−	1.98325i	−0.0896854	−	0.155340i	0.817693	−	0.575655i	$-0.195253\pi$
$163$	−1.14503	−	1.98325i	−0.0896854	−	0.155340i	−0.907378	+	0.420315i	$0.861920\pi$
$164$	1.79117	−	3.10240i	0.139867	−	0.242257i
$165$	8.23352	+	5.49414i	0.640978	+	0.427718i
$166$	−9.06519	+	5.23379i	−0.703595	+	0.406221i
$167$	8.51406			0.658838			0.329419	−	0.944184i	$-0.393147\pi$
$167$	8.51406			0.658838			0.329419	+	0.944184i	$0.393147\pi$
$168$		0			0
$169$	−9.69114			−0.745473
$170$	11.8464	+	20.5186i	0.908578	+	1.57370i
$171$	8.24396	−	14.2790i	0.630432	−	1.09194i
$172$	−2.82168	−	1.62910i	−0.215151	−	0.124217i
$173$	11.9961	+	20.7778i	0.912044	+	1.57971i	0.811172	+	0.584807i	$0.198830\pi$
$173$	11.9961	+	20.7778i	0.912044	+	1.57971i	0.100872	+	0.994899i	$0.467837\pi$
$174$		−	7.16469i		−	0.543154i
$175$		0			0
$176$	0.214882	−	3.30966i	0.0161973	−	0.249475i
$177$	−1.98900	−	3.44506i	−0.149503	−	0.258946i
$178$	0.843855	−	1.46160i	0.0632496	−	0.109552i
$179$	−10.0792	+	17.4577i	−0.753357	+	1.30485i	0.192831	+	0.981232i	$0.438233\pi$
$179$	−10.0792	+	17.4577i	−0.753357	+	1.30485i	−0.946187	+	0.323620i	$0.895100\pi$
$180$	8.15269	−	4.70696i	0.607666	−	0.350836i
$181$		−	11.1135i		−	0.826062i	−0.910717	−	0.413031i	$-0.864470\pi$
$181$		−	11.1135i		−	0.826062i	0.910717	−	0.413031i	$-0.135530\pi$
$182$		0			0
$183$			6.87584i			0.508277i
$184$	3.79031	−	2.18834i	0.279425	−	0.161326i
$185$	−15.5603	−	8.98372i	−1.14401	−	0.660496i
$186$	−5.22519	−	3.01676i	−0.383129	−	0.221200i
$187$	18.0683	−	8.92412i	1.32128	−	0.652596i
$188$			0.203854i			0.0148675i
$189$		0			0
$190$	−26.6308			−1.93200
$191$	12.2542	+	21.2249i	0.886681	+	1.53578i	0.843775	+	0.536698i	$0.180328\pi$
$191$	12.2542	+	21.2249i	0.886681	+	1.53578i	0.0429063	+	0.999079i	$0.486338\pi$
$192$	0.662827	+	0.382683i	0.0478354	+	0.0276178i
$193$	10.9286	+	6.30966i	0.786661	+	0.454179i	0.838786	−	0.544462i	$-0.183266\pi$
$193$	10.9286	+	6.30966i	0.786661	+	0.454179i	−0.0521247	+	0.998641i	$0.516599\pi$
$194$	−4.61940	−	8.00103i	−0.331653	−	0.574441i
$195$	−5.42879			−0.388764
$196$		0			0
$197$			17.2697i			1.23042i	0.788364	+	0.615209i	$0.210928\pi$
$197$			17.2697i			1.23042i	−0.788364	+	0.615209i	$0.789072\pi$
$198$	−3.54584	−	7.17912i	−0.251992	−	0.510198i
$199$	7.95279	+	4.59154i	0.563758	+	0.325486i	0.754653	−	0.656125i	$-0.227805\pi$
$199$	7.95279	+	4.59154i	0.563758	+	0.325486i	−0.190894	+	0.981611i	$0.561139\pi$
$200$	−8.83788	−	5.10255i	−0.624932	−	0.360805i
$201$	−5.32484	+	3.07430i	−0.375585	+	0.216844i
$202$			5.34567i			0.376120i
$203$		0			0
$204$			4.65041i			0.325594i
$205$	−12.0974	+	6.98445i	−0.844921	+	0.487815i
$206$	−2.12256	+	3.67639i	−0.147886	+	0.256146i
$207$	5.28311	−	9.15062i	0.367202	−	0.636012i
$208$	0.909513	+	1.57532i	0.0630634	+	0.109229i
$209$	−1.46754	+	22.6034i	−0.101512	+	1.56351i
$210$		0			0
$211$			2.12250i			0.146119i	0.997328	+	0.0730593i	$0.0232762\pi$
$211$			2.12250i			0.146119i	−0.997328	+	0.0730593i	$0.976724\pi$
$212$	2.49222	+	4.31666i	0.171167	+	0.296469i
$213$	−5.87394	−	3.39132i	−0.402476	−	0.232370i
$214$	−3.61931	+	6.26883i	−0.247411	+	0.428529i
$215$	6.35245	+	11.0028i	0.433233	+	0.750382i
$216$	4.14386			0.281954
$217$		0			0
$218$	−6.00000			−0.406371
$219$	0.0369234	−	0.0213178i	0.00249505	−	0.00144052i
$220$	−7.17844	+	10.7576i	−0.483970	+	0.725278i
$221$	−5.52625	+	9.57175i	−0.371736	+	0.643866i
$222$	−1.76332	−	3.05416i	−0.118346	−	0.204982i
$223$			5.77586i			0.386780i	0.981122	+	0.193390i	$0.0619483\pi$
$223$			5.77586i			0.386780i	−0.981122	+	0.193390i	$0.938052\pi$
$224$		0			0
$225$	−24.6373			−1.64249
$226$	14.5838	−	8.41998i	0.970102	−	0.560089i
$227$	−0.605269	+	1.04836i	−0.0401731	+	0.0695819i	−0.885413	−	0.464805i	$-0.846124\pi$
$227$	−0.605269	+	1.04836i	−0.0401731	+	0.0695819i	0.845240	+	0.534387i	$0.179458\pi$
$228$	−4.52679	−	2.61355i	−0.299794	−	0.173086i
$229$	16.8020	−	9.70062i	1.11031	−	0.641035i	0.171397	−	0.985202i	$-0.445172\pi$
$229$	16.8020	−	9.70062i	1.11031	−	0.641035i	0.938909	+	0.344167i	$0.111839\pi$
$230$	−17.0663			−1.12532
$231$		0			0
$232$	9.36112			0.614588
$233$	−17.0714	+	9.85619i	−1.11839	+	0.645700i	−0.940988	−	0.338439i	$-0.890101\pi$
$233$	−17.0714	+	9.85619i	−1.11839	+	0.645700i	−0.177397	+	0.984139i	$0.556768\pi$
$234$	3.80317	+	2.19576i	0.248621	+	0.143541i
$235$	0.397450	−	0.688404i	0.0259268	−	0.0449065i
$236$	4.50118	−	2.59876i	0.293002	−	0.169165i
$237$	6.49435			0.421854
$238$		0			0
$239$		−	11.6292i		−	0.752229i	−0.926573	−	0.376115i	$-0.877260\pi$
$239$		−	11.6292i		−	0.752229i	0.926573	−	0.376115i	$-0.122740\pi$
$240$	−1.49222	−	2.58461i	−0.0963227	−	0.166836i
$241$	−13.6869	+	23.7064i	−0.881651	+	1.52706i	−0.0321456	+	0.999483i	$0.510234\pi$
$241$	−13.6869	+	23.7064i	−0.881651	+	1.52706i	−0.849505	+	0.527581i	$0.823099\pi$
$242$	8.73512	+	6.68563i	0.561515	+	0.429769i
$243$	13.4645	−	7.77372i	0.863747	−	0.498684i
$244$	−8.98372			−0.575124
$245$		0			0
$246$	−2.74181			−0.174811
$247$	−6.21154	−	10.7587i	−0.395231	−	0.684560i
$248$	3.94159	−	6.82704i	0.250291	−	0.433517i
$249$	6.93819	+	4.00577i	0.439690	+	0.253855i
$250$	10.1483	+	17.5774i	0.641835	+	1.11169i
$251$		−	13.5021i		−	0.852243i	−0.904666	−	0.426122i	$-0.859880\pi$
$251$		−	13.5021i		−	0.852243i	0.904666	−	0.426122i	$-0.140120\pi$
$252$		0			0
$253$	−0.940467	+	14.4853i	−0.0591267	+	0.910682i
$254$	−8.66501	−	15.0082i	−0.543691	−	0.941701i
$255$	9.06684	−	15.7042i	0.567788	−	0.983437i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.43041	−	1.40320i	0.151605	−	0.0875289i	−0.422279	−	0.906466i	$-0.638770\pi$
$257$	2.43041	−	1.40320i	0.151605	−	0.0875289i	0.573883	+	0.818937i	$0.305436\pi$
$258$			2.49371i			0.155252i
$259$		0			0
$260$		−	7.09306i		−	0.439893i
$261$	19.5720	−	11.2999i	1.21147	−	0.699445i
$262$	5.50404	+	3.17776i	0.340041	+	0.196323i
$263$	7.34847	+	4.24264i	0.453126	+	0.261612i	0.709150	−	0.705058i	$-0.249079\pi$
$263$	7.34847	+	4.24264i	0.453126	+	0.261612i	−0.256023	+	0.966671i	$0.582412\pi$
$264$	−2.27596	+	1.12412i	−0.140076	+	0.0691849i
$265$		−	19.4362i		−	1.19396i
$266$		0			0
$267$	−1.29172			−0.0790518
$268$	−4.01676	−	6.95724i	−0.245363	−	0.424981i
$269$	−18.1498	−	10.4788i	−1.10662	−	0.638905i	−0.168665	−	0.985673i	$-0.553946\pi$
$269$	−18.1498	−	10.4788i	−1.10662	−	0.638905i	−0.937951	+	0.346768i	$0.887279\pi$
$270$	−13.9936	−	8.07922i	−0.851625	−	0.491686i
$271$	−7.30660	−	12.6554i	−0.443844	−	0.768761i	0.554127	−	0.832432i	$-0.313052\pi$
$271$	−7.30660	−	12.6554i	−0.443844	−	0.768761i	−0.997971	+	0.0636717i	$0.979719\pi$
$272$	−6.07606			−0.368415
$273$		0			0
$274$			1.34959i			0.0815315i
$275$	30.3468	−	14.9886i	1.82998	−	0.903846i
$276$	−2.90098	−	1.67488i	−0.174618	−	0.100816i
$277$	−9.63380	−	5.56208i	−0.578839	−	0.334193i	0.181833	−	0.983329i	$-0.441797\pi$
$277$	−9.63380	−	5.56208i	−0.578839	−	0.334193i	−0.760672	+	0.649136i	$0.775130\pi$
$278$	10.3020	−	5.94786i	0.617873	−	0.356729i
$279$		−	19.0317i		−	1.13940i
$280$		0			0
$281$		−	7.28929i		−	0.434843i	−0.976078	−	0.217421i	$-0.930235\pi$
$281$		−	7.28929i		−	0.434843i	0.976078	−	0.217421i	$-0.0697646\pi$
$282$	0.135120	−	0.0780114i	0.00804626	−	0.00464551i
$283$	8.00696	−	13.8685i	0.475965	−	0.824395i	−0.523656	−	0.851930i	$-0.675432\pi$
$283$	8.00696	−	13.8685i	0.475965	−	0.824395i	0.999621	+	0.0275349i	$0.00876573\pi$
$284$	4.43098	−	7.67468i	0.262930	−	0.455408i
$285$	10.1912	+	17.6516i	0.603674	+	1.04559i
$286$	−6.02035	−	0.390876i	−0.355991	−	0.0231130i
$287$		0			0
$288$			2.41421i			0.142259i
$289$	−9.95924	−	17.2499i	−0.585838	−	1.01470i
$290$	−31.6121	−	18.2512i	−1.85633	−	1.07175i
$291$	−3.53553	+	6.12372i	−0.207257	+	0.358979i
$292$	0.0278530	+	0.0482428i	0.00162997	+	0.00282320i
$293$	14.2550			0.832783			0.416392	−	0.909185i	$-0.363295\pi$
$293$	14.2550			0.832783			0.416392	+	0.909185i	$0.363295\pi$
$294$		0			0
$295$	−20.2671			−1.17999
$296$	3.99045	−	2.30389i	0.231940	−	0.133911i
$297$	−7.62852	+	11.4321i	−0.442652	+	0.663358i
$298$	−3.28834	+	5.69557i	−0.190488	+	0.329935i
$299$	−3.98064	−	6.89467i	−0.230206	−	0.398729i
$300$			7.81064i			0.450948i
$301$		0			0
$302$	8.63888			0.497112
$303$	3.54325	−	2.04570i	0.203555	−	0.117522i
$304$	3.41476	−	5.91454i	0.195850	−	0.339222i
$305$	30.3376	+	17.5154i	1.73713	+	1.00293i
$306$	−12.7036	+	7.33445i	−0.726219	+	0.419283i
$307$	−6.75074			−0.385285			−0.192643	−	0.981269i	$-0.561706\pi$
$307$	−6.75074			−0.385285			−0.192643	+	0.981269i	$0.561706\pi$
$308$		0			0
$309$	3.24908			0.184834
$310$	−26.6212	+	15.3697i	−1.51198	+	0.872942i
$311$	−15.4763	−	8.93526i	−0.877581	−	0.506672i	−0.00772127	−	0.999970i	$-0.502458\pi$
$311$	−15.4763	−	8.93526i	−0.877581	−	0.506672i	−0.869860	+	0.493298i	$0.835791\pi$
$312$	0.696111	−	1.20570i	0.0394095	−	0.0682593i
$313$	−13.0188	+	7.51640i	−0.735865	+	0.424852i	−0.820564	−	0.571554i	$-0.806341\pi$
$313$	−13.0188	+	7.51640i	−0.735865	+	0.424852i	0.0846986	+	0.996407i	$0.473007\pi$
$314$	2.44991			0.138256
$315$		0			0
$316$			8.48528i			0.477334i
$317$	−4.86597	−	8.42810i	−0.273300	−	0.473370i	0.696405	−	0.717649i	$-0.254782\pi$
$317$	−4.86597	−	8.42810i	−0.273300	−	0.473370i	−0.969705	+	0.244280i	$0.921449\pi$
$318$	1.90747	−	3.30383i	0.106965	−	0.185270i
$319$	−17.2331	+	25.8255i	−0.964868	+	1.44595i
$320$	3.37695	−	1.94969i	0.188778	−	0.108991i
$321$	5.54020			0.309224
$322$		0			0
$323$	41.4966			2.30893
$324$	2.03553	+	3.52565i	0.113085	+	0.195869i
$325$	−9.28167	+	16.0763i	−0.514854	+	0.891754i
$326$	−1.98325	−	1.14503i	−0.109842	−	0.0634172i
$327$	2.29610	+	3.97696i	0.126975	+	0.219927i
$328$		−	3.58235i		−	0.197802i
$329$		0			0
$330$	9.87750	+	0.641304i	0.543739	+	0.0353026i
$331$	−9.12993	−	15.8135i	−0.501826	−	0.869188i	−0.999998	−	0.00210996i	$-0.999328\pi$
$331$	−9.12993	−	15.8135i	−0.501826	−	0.869188i	0.498172	−	0.867078i	$-0.334005\pi$
$332$	−5.23379	+	9.06519i	−0.287241	+	0.497517i
$333$	5.56208	−	9.63380i	0.304800	−	0.527929i
$334$	7.37339	−	4.25703i	0.403454	−	0.232934i
$335$			31.3257i			1.71151i
$336$		0			0
$337$		−	29.6928i		−	1.61747i	−0.588173	−	0.808735i	$-0.700153\pi$
$337$		−	29.6928i		−	1.61747i	0.588173	−	0.808735i	$-0.299847\pi$
$338$	−8.39278	+	4.84557i	−0.456507	+	0.263564i
$339$	−11.1620	−	6.44437i	−0.606236	−	0.350010i
$340$	20.5186	+	11.8464i	1.11278	+	0.642461i
$341$	11.5783	+	23.4421i	0.627000	+	1.26946i
$342$		−	16.4879i		−	0.891565i
$343$		0			0
$344$	−3.25819			−0.175670
$345$	6.53098	+	11.3120i	0.351616	+	0.609017i
$346$	20.7778	+	11.9961i	1.11702	+	0.644913i
$347$	−16.6981	−	9.64063i	−0.896399	−	0.517536i	−0.0203688	−	0.999793i	$-0.506484\pi$
$347$	−16.6981	−	9.64063i	−0.896399	−	0.517536i	−0.876030	+	0.482256i	$0.839817\pi$
$348$	−3.58235	−	6.20481i	−0.192034	−	0.332613i
$349$	−23.9921			−1.28427			−0.642135	−	0.766592i	$-0.721951\pi$
$349$	−23.9921			−1.28427			−0.642135	+	0.766592i	$0.721951\pi$
$350$		0			0
$351$		−	7.53779i		−	0.402337i
$352$	−1.46874	−	2.97369i	−0.0782838	−	0.158498i
$353$	13.9844	+	8.07391i	0.744316	+	0.429731i	0.823636	−	0.567118i	$-0.191942\pi$
$353$	13.9844	+	8.07391i	0.744316	+	0.429731i	−0.0793204	+	0.996849i	$0.525275\pi$
$354$	−3.44506	−	1.98900i	−0.183103	−	0.105714i
$355$	−29.9264	+	17.2780i	−1.58833	+	0.917022i
$356$		−	1.68771i		−	0.0894484i
$357$		0			0
$358$			20.1584i			1.06541i
$359$	15.7145	−	9.07278i	0.829381	−	0.478843i	−0.0242599	−	0.999706i	$-0.507723\pi$
$359$	15.7145	−	9.07278i	0.829381	−	0.478843i	0.853641	+	0.520862i	$0.174390\pi$
$360$	4.70696	−	8.15269i	0.248078	−	0.429685i
$361$	−13.8212	+	23.9390i	−0.727431	+	1.25995i
$362$	−5.55676	−	9.62460i	−0.292057	−	0.505858i
$363$	1.08864	−	8.34836i	0.0571385	−	0.438175i
$364$		0			0
$365$		−	0.217218i		−	0.0113697i
$366$	3.43792	+	5.95465i	0.179703	+	0.311255i
$367$	4.25692	+	2.45773i	0.222209	+	0.128293i	0.606973	−	0.794723i	$-0.292384\pi$
$367$	4.25692	+	2.45773i	0.222209	+	0.128293i	−0.384763	+	0.923015i	$0.625717\pi$
$368$	2.18834	−	3.79031i	0.114075	−	0.197584i
$369$	−4.32427	−	7.48986i	−0.225113	−	0.389907i
$370$	−17.9674			−0.934083
$371$		0			0
$372$	−6.03353			−0.312824
$373$	−1.96420	+	1.13403i	−0.101702	+	0.0587179i	−0.549989	−	0.835172i	$-0.685368\pi$
$373$	−1.96420	+	1.13403i	−0.101702	+	0.0587179i	0.448286	+	0.893890i	$0.352035\pi$
$374$	11.1855	−	16.7627i	0.578391	−	0.866777i
$375$	7.76718	−	13.4531i	0.401095	−	0.694718i
$376$	0.101927	+	0.176542i	0.00525647	+	0.00910448i
$377$		−	17.0281i		−	0.876993i
$378$		0			0
$379$	14.7984			0.760143			0.380072	−	0.924957i	$-0.375899\pi$
$379$	14.7984			0.760143			0.380072	+	0.924957i	$0.375899\pi$
$380$	−23.0630	+	13.3154i	−1.18311	+	0.683067i
$381$	−6.63191	+	11.4868i	−0.339763	+	0.588487i
$382$	21.2249	+	12.2542i	1.08596	+	0.626978i
$383$	6.29627	−	3.63515i	0.321724	−	0.185748i	−0.330437	−	0.943828i	$-0.607196\pi$
$383$	6.29627	−	3.63515i	0.321724	−	0.185748i	0.652161	+	0.758081i	$0.273863\pi$
$384$	0.765367			0.0390575
$385$		0			0
$386$	12.6193			0.642306
$387$	−6.81213	+	3.93298i	−0.346280	+	0.199925i
$388$	−8.00103	−	4.61940i	−0.406191	−	0.234514i
$389$	17.5968	−	30.4786i	0.892194	−	1.54533i	0.0549549	−	0.998489i	$-0.482498\pi$
$389$	17.5968	−	30.4786i	0.892194	−	1.54533i	0.837239	−	0.546837i	$-0.184168\pi$
$390$	−4.70147	+	2.71440i	−0.238068	+	0.137449i
$391$	26.5929			1.34486
$392$		0			0
$393$		−	4.86431i		−	0.245372i
$394$	8.63486	+	14.9560i	0.435018	+	0.753473i
$395$	16.5436	−	28.6544i	0.832401	−	1.44176i
$396$	−6.66035	−	4.44438i	−0.334695	−	0.223338i
$397$	16.3081	−	9.41550i	0.818481	−	0.472550i	−0.0314111	−	0.999507i	$-0.510000\pi$
$397$	16.3081	−	9.41550i	0.818481	−	0.472550i	0.849893	+	0.526956i	$0.176667\pi$
$398$	9.18309			0.460307
$399$		0			0
$400$	−10.2051			−0.510255
$401$	3.55347	+	6.15480i	0.177452	+	0.307356i	0.941007	−	0.338387i	$-0.109881\pi$
$401$	3.55347	+	6.15480i	0.177452	+	0.307356i	−0.763555	+	0.645743i	$0.776548\pi$
$402$	−3.07430	+	5.32484i	−0.153332	+	0.265579i
$403$	−12.4186	−	7.16986i	−0.618612	−	0.357156i
$404$	2.67283	+	4.62948i	0.132978	+	0.230325i
$405$		−	15.8746i		−	0.788816i
$406$		0			0
$407$	−0.990128	+	15.2502i	−0.0490788	+	0.755922i
$408$	2.32521	+	4.02738i	0.115115	+	0.199385i
$409$	−4.85705	+	8.41267i	−0.240166	+	0.415980i	−0.960761	−	0.277376i	$-0.910535\pi$
$409$	−4.85705	+	8.41267i	−0.240166	+	0.415980i	0.720595	+	0.693356i	$0.243869\pi$
$410$	−6.98445	+	12.0974i	−0.344937	+	0.597449i
$411$	0.894543	−	0.516465i	0.0441245	−	0.0254753i
$412$			4.24513i			0.209143i
$413$		0			0
$414$		−	10.5662i		−	0.519301i
$415$	35.3485	−	20.4085i	1.73519	−	1.00181i
$416$	1.57532	+	0.909513i	0.0772366	+	0.0445925i
$417$	−7.88481	−	4.55230i	−0.386121	−	0.222927i
$418$	10.0308	+	20.3089i	0.490621	+	0.993339i
$419$			23.0474i			1.12594i	0.826478	+	0.562970i	$0.190341\pi$
$419$			23.0474i			1.12594i	−0.826478	+	0.562970i	$0.809659\pi$
$420$		0			0
$421$	−1.67074			−0.0814270			−0.0407135	−	0.999171i	$-0.512963\pi$
$421$	−1.67074			−0.0814270			−0.0407135	+	0.999171i	$0.512963\pi$
$422$	1.06125	+	1.83814i	0.0516608	+	0.0894790i
$423$	0.426211	+	0.246073i	0.0207231	+	0.0119645i
$424$	4.31666	+	2.49222i	0.209636	+	0.121033i
$425$	−31.0034	−	53.6994i	−1.50389	−	2.60481i
$426$	−6.78265			−0.328620
$427$		0			0
$428$			7.23863i			0.349892i
$429$	2.04481	+	4.14003i	0.0987242	+	0.199883i
$430$	11.0028	+	6.35245i	0.530600	+	0.306342i
$431$	−33.6434	−	19.4240i	−1.62055	−	0.935623i	−0.986774	−	0.162103i	$-0.948172\pi$
$431$	−33.6434	−	19.4240i	−1.62055	−	0.935623i	−0.633772	−	0.773520i	$-0.718494\pi$
$432$	3.58869	−	2.07193i	0.172661	−	0.0996858i
$433$			31.8479i			1.53051i	0.643726	+	0.765256i	$0.277388\pi$
$433$			31.8479i			1.53051i	−0.643726	+	0.765256i	$0.722612\pi$
$434$		0			0
$435$			27.9378i			1.33951i
$436$	−5.19615	+	3.00000i	−0.248851	+	0.143674i
$437$	−14.9453	+	25.8860i	−0.714930	+	1.23830i
$438$	0.0213178	−	0.0369234i	0.00101860	−	0.00176427i
$439$	6.02035	+	10.4276i	0.287336	+	0.497680i	0.973173	−	0.230075i	$-0.0738971\pi$
$439$	6.02035	+	10.4276i	0.287336	+	0.497680i	−0.685837	+	0.727755i	$0.740564\pi$
$440$	−0.837904	+	12.9056i	−0.0399455	+	0.615249i
$441$		0			0
$442$			11.0525i			0.525714i
$443$	15.2762	+	26.4591i	0.725793	+	1.25711i	0.958647	+	0.284598i	$0.0918601\pi$
$443$	15.2762	+	26.4591i	0.725793	+	1.25711i	−0.232854	+	0.972512i	$0.574807\pi$
$444$	−3.05416	−	1.76332i	−0.144944	−	0.0836835i
$445$	−3.29050	+	5.69932i	−0.155985	+	0.270174i
$446$	2.88793	+	5.00204i	0.136748	+	0.236854i
$447$	5.03357			0.238080
$448$		0			0
$449$	15.7378			0.742712			0.371356	−	0.928490i	$-0.378893\pi$
$449$	15.7378			0.742712			0.371356	+	0.928490i	$0.378893\pi$
$450$	−21.3365	+	12.3186i	−1.00581	+	0.580706i
$451$	9.88300	+	6.59482i	0.465372	+	0.310538i
$452$	8.41998	−	14.5838i	0.396043	−	0.685966i
$453$	−3.30596	−	5.72608i	−0.155327	−	0.269035i
$454$			1.21054i			0.0568134i
$455$		0			0
$456$	−5.22709			−0.244781
$457$	−14.8669	+	8.58340i	−0.695443	+	0.401514i	−0.805648	−	0.592395i	$-0.798183\pi$
$457$	−14.8669	+	8.58340i	−0.695443	+	0.401514i	0.110205	+	0.993909i	$0.464849\pi$
$458$	9.70062	−	16.8020i	0.453280	−	0.785105i
$459$	21.8051	+	12.5892i	1.01777	+	0.587612i
$460$	−14.7798	+	8.53314i	−0.689113	+	0.397860i
$461$	0.312096			0.0145357			0.00726787	−	0.999974i	$-0.497687\pi$
$461$	0.312096			0.0145357			0.00726787	+	0.999974i	$0.497687\pi$
$462$		0			0
$463$	−31.9402			−1.48439			−0.742194	−	0.670185i	$-0.766215\pi$
$463$	−31.9402			−1.48439			−0.742194	+	0.670185i	$0.766215\pi$
$464$	8.10697	−	4.68056i	0.376357	−	0.217290i
$465$	20.3749	+	11.7635i	0.944866	+	0.545518i
$466$	−9.85619	+	17.0714i	−0.456579	+	0.790818i
$467$	16.3264	−	9.42604i	0.755495	−	0.436185i	−0.0721810	−	0.997392i	$-0.522996\pi$
$467$	16.3264	−	9.42604i	0.755495	−	0.436185i	0.827676	+	0.561206i	$0.189663\pi$
$468$	4.39152			0.202998
$469$		0			0
$470$		−	0.794901i		−	0.0366660i
$471$	−0.937539	−	1.62386i	−0.0431995	−	0.0748237i
$472$	2.59876	−	4.50118i	0.119618	−	0.207184i
$473$	5.99807	−	8.98872i	0.275792	−	0.413302i
$474$	5.62427	−	3.24718i	0.258331	−	0.149148i
$475$	69.6960			3.19787
$476$		0			0
$477$	12.0335			0.550977
$478$	−5.81459	−	10.0712i	−0.265953	−	0.460645i
$479$	−14.5270	+	25.1615i	−0.663755	+	1.14966i	0.315866	+	0.948804i	$0.397705\pi$
$479$	−14.5270	+	25.1615i	−0.663755	+	1.14966i	−0.979621	+	0.200854i	$0.935628\pi$
$480$	−2.58461	−	1.49222i	−0.117971	−	0.0681104i
$481$	−4.19083	−	7.25874i	−0.191086	−	0.330970i
$482$			27.3738i			1.24684i
$483$		0			0
$484$	10.9077	+	1.42237i	0.495802	+	0.0646532i
$485$	18.0127	+	31.1990i	0.817917	+	1.41667i
$486$	7.77372	−	13.4645i	0.352623	−	0.610761i
$487$	16.5674	−	28.6956i	0.750742	−	1.30032i	−0.196721	−	0.980459i	$-0.563029\pi$
$487$	16.5674	−	28.6956i	0.750742	−	1.30032i	0.947463	−	0.319864i	$-0.103637\pi$
$488$	−7.78013	+	4.49186i	−0.352190	+	0.203337i
$489$			1.75273i			0.0792613i
$490$		0			0
$491$		−	42.4151i		−	1.91416i	−0.289817	−	0.957082i	$-0.593594\pi$
$491$		−	42.4151i		−	1.91416i	0.289817	−	0.957082i	$-0.406406\pi$
$492$	−2.37448	+	1.37090i	−0.107050	+	0.0618052i
$493$	49.2584	+	28.4394i	2.21849	+	1.28084i
$494$	−10.7587	−	6.21154i	−0.484057	−	0.279470i
$495$	13.8265	+	27.9940i	0.621457	+	1.25824i
$496$		−	7.88318i		−	0.353965i
$497$		0			0
$498$	8.01154			0.359005
$499$	−7.72103	−	13.3732i	−0.345641	−	0.598667i	0.639829	−	0.768517i	$-0.279005\pi$
$499$	−7.72103	−	13.3732i	−0.345641	−	0.598667i	−0.985470	+	0.169850i	$0.945672\pi$
$500$	17.5774	+	10.1483i	0.786085	+	0.453846i
$501$	−5.64335	−	3.25819i	−0.252126	−	0.145565i
$502$	−6.75103	−	11.6931i	−0.301313	−	0.521890i
$503$	−39.5816			−1.76486			−0.882429	−	0.470446i	$-0.844093\pi$
$503$	−39.5816			−1.76486			−0.882429	+	0.470446i	$0.844093\pi$
$504$		0			0
$505$		−	20.8447i		−	0.927579i
$506$	6.42817	+	13.0149i	0.285767	+	0.578581i
$507$	6.42355	+	3.70864i	0.285280	+	0.164706i
$508$	−15.0082	−	8.66501i	−0.665883	−	0.384448i
$509$	4.57165	−	2.63944i	0.202635	−	0.116991i	−0.395249	−	0.918574i	$-0.629342\pi$
$509$	4.57165	−	2.63944i	0.202635	−	0.116991i	0.597884	+	0.801583i	$0.296008\pi$
$510$		−	18.1337i		−	0.802973i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−24.5090	+	14.1503i	−1.08210	+	0.624751i
$514$	1.40320	−	2.43041i	0.0618923	−	0.107201i
$515$	8.27667	−	14.3356i	0.364714	−	0.631703i
$516$	1.24686	+	2.15962i	0.0548898	+	0.0950719i
$517$	−0.674685	−	0.0438044i	−0.0296726	−	0.00192652i
$518$		0			0
$519$		−	18.3628i		−	0.806037i
$520$	−3.54653	−	6.14277i	−0.155526	−	0.269378i
$521$	23.6500	+	13.6543i	1.03613	+	0.598207i	0.918733	−	0.394878i	$-0.129213\pi$
$521$	23.6500	+	13.6543i	1.03613	+	0.598207i	0.117392	+	0.993086i	$0.462547\pi$
$522$	11.2999	−	19.5720i	0.494582	−	0.856641i
$523$	−4.32645	−	7.49363i	−0.189182	−	0.327673i	0.755796	−	0.654808i	$-0.227250\pi$
$523$	−4.32645	−	7.49363i	−0.189182	−	0.327673i	−0.944978	+	0.327134i	$0.893917\pi$
$524$	6.35552			0.277642
$525$		0			0
$526$	8.48528			0.369976
$527$	41.4815	−	23.9493i	1.80696	−	1.04325i
$528$	−1.40898	+	2.11150i	−0.0613180	+	0.0918912i
$529$	1.92237	−	3.32964i	0.0835813	−	0.144767i
$530$	−9.71811	−	16.8323i	−0.422128	−	0.731147i
$531$		−	12.5479i		−	0.544533i
$532$		0			0
$533$	−6.51638			−0.282256
$534$	−1.11866	+	0.645859i	−0.0484092	+	0.0279490i
$535$	14.1130	−	24.4445i	0.610160	−	1.05683i
$536$	−6.95724	−	4.01676i	−0.300507	−	0.173498i
$537$	13.3616	−	7.71430i	0.576594	−	0.332897i
$538$	−20.9576			−0.903548
$539$		0			0
$540$	−16.1584			−0.695349
$541$	−0.447200	+	0.258191i	−0.0192266	+	0.0111005i	−0.509583	−	0.860422i	$-0.670200\pi$
$541$	−0.447200	+	0.258191i	−0.0192266	+	0.0111005i	0.490356	+	0.871522i	$0.336867\pi$
$542$	−12.6554	−	7.30660i	−0.543596	−	0.313845i
$543$	−4.25296	+	7.36635i	−0.182512	+	0.316120i
$544$	−5.26202	+	3.03803i	−0.225607	+	0.130254i
$545$	23.3962			1.00218
$546$		0			0
$547$		−	28.0407i		−	1.19894i	−0.800399	−	0.599468i	$-0.795379\pi$
$547$		−	28.0407i		−	1.19894i	0.800399	−	0.599468i	$-0.204621\pi$
$548$	0.674793	+	1.16878i	0.0288257	+	0.0499277i
$549$	−10.8443	+	18.7829i	−0.462824	+	0.801634i
$550$	18.7868	−	28.1539i	0.801071	−	1.20049i
$551$	−55.3667	+	31.9660i	−2.35870	+	1.36180i
$552$	−3.34976			−0.142575
$553$		0			0
$554$	−11.1242			−0.472620
$555$	6.87584	+	11.9093i	0.291863	+	0.505522i
$556$	5.94786	−	10.3020i	0.252246	−	0.436902i
$557$	24.8942	+	14.3727i	1.05480	+	0.608989i	0.923989	−	0.382418i	$-0.124909\pi$
$557$	24.8942	+	14.3727i	1.05480	+	0.608989i	0.130811	+	0.991407i	$0.458242\pi$
$558$	−9.51584	−	16.4819i	−0.402838	−	0.697735i
$559$			5.92673i			0.250674i
$560$		0			0
$561$	−15.3913	−	0.999289i	−0.649820	−	0.0421900i
$562$	−3.64465	−	6.31271i	−0.153740	−	0.266286i
$563$	3.37537	−	5.84631i	0.142255	−	0.246393i	−0.786090	−	0.618111i	$-0.787898\pi$
$563$	3.37537	−	5.84631i	0.142255	−	0.246393i	0.928345	+	0.371719i	$0.121231\pi$
$564$	0.0780114	−	0.135120i	0.00328487	−	0.00568956i
$565$	−56.8678	+	32.8326i	−2.39245	+	1.38128i
$566$		−	16.0139i		−	0.673115i
$567$		0			0
$568$		−	8.86195i		−	0.371839i
$569$	−8.41827	+	4.86029i	−0.352912	+	0.203754i	−0.665967	−	0.745981i	$-0.731981\pi$
$569$	−8.41827	+	4.86029i	−0.352912	+	0.203754i	0.313055	+	0.949735i	$0.398648\pi$
$570$	17.6516	+	10.1912i	0.739346	+	0.426862i
$571$	17.6516	+	10.1912i	0.738698	+	0.426487i	0.821596	−	0.570071i	$-0.193084\pi$
$571$	17.6516	+	10.1912i	0.738698	+	0.426487i	−0.0828978	+	0.996558i	$0.526418\pi$
$572$	−5.40922	+	2.67167i	−0.226171	+	0.111708i
$573$		−	18.7579i		−	0.783622i
$574$		0			0
$575$	44.6644			1.86263
$576$	1.20711	+	2.09077i	0.0502961	+	0.0871154i
$577$	−10.5781	−	6.10726i	−0.440371	−	0.254248i	0.263384	−	0.964691i	$-0.415161\pi$
$577$	−10.5781	−	6.10726i	−0.440371	−	0.254248i	−0.703755	+	0.710443i	$0.748495\pi$
$578$	−17.2499	−	9.95924i	−0.717502	−	0.414250i
$579$	−4.82920	−	8.36442i	−0.200695	−	0.347614i
$580$	−36.5025			−1.51568
$581$		0			0
$582$			7.07107i			0.293105i
$583$	−14.8222	+	7.32084i	−0.613873	+	0.303198i
$584$	0.0482428	+	0.0278530i	0.00199630	+	0.00115257i
$585$	−14.8300	−	8.56208i	−0.613143	−	0.353998i
$586$	12.3451	−	7.12748i	0.509973	−	0.294433i
$587$			22.5689i			0.931519i	0.884911	+	0.465759i	$0.154219\pi$
$587$			22.5689i			0.931519i	−0.884911	+	0.465759i	$0.845781\pi$
$588$		0			0
$589$			53.8384i			2.21837i
$590$	−17.5518	+	10.1335i	−0.722596	+	0.417191i
$591$	6.60884	−	11.4468i	0.271851	−	0.470860i
$592$	2.30389	−	3.99045i	0.0946892	−	0.164007i
$593$	−18.3348	−	31.7568i	−0.752920	−	1.30410i	−0.946402	−	0.322992i	$-0.895311\pi$
$593$	−18.3348	−	31.7568i	−0.752920	−	1.30410i	0.193481	−	0.981104i	$-0.438022\pi$
$594$	−0.890440	+	13.7148i	−0.0365352	+	0.562723i
$595$		0			0
$596$			6.57668i			0.269391i
$597$	−3.51422	−	6.08680i	−0.143827	−	0.249116i
$598$	−6.89467	−	3.98064i	−0.281944	−	0.162780i
$599$	−3.17279	+	5.49543i	−0.129637	+	0.224537i	−0.923536	−	0.383512i	$-0.874714\pi$
$599$	−3.17279	+	5.49543i	−0.129637	+	0.224537i	0.793899	+	0.608049i	$0.208048\pi$
$600$	3.90532	+	6.76422i	0.159434	+	0.276148i
$601$	−1.60141			−0.0653230			−0.0326615	−	0.999466i	$-0.510398\pi$
$601$	−1.60141			−0.0653230			−0.0326615	+	0.999466i	$0.510398\pi$
$602$		0			0
$603$	−19.3946			−0.789811
$604$	7.48149	−	4.31944i	0.304417	−	0.175755i
$605$	−34.0615	−	26.0698i	−1.38480	−	1.05989i
$606$	2.04570	−	3.54325i	0.0831008	−	0.143935i
$607$	−8.37216	−	14.5010i	−0.339815	−	0.588578i	0.644582	−	0.764535i	$-0.277031\pi$
$607$	−8.37216	−	14.5010i	−0.339815	−	0.588578i	−0.984398	+	0.175957i	$0.943698\pi$
$608$		−	6.82952i		−	0.276974i
$609$		0			0
$610$	35.0309			1.41836
$611$	0.321135	−	0.185407i	0.0129917	−	0.00750078i
$612$	−7.33445	+	12.7036i	−0.296478	+	0.513514i
$613$	−1.57905	−	0.911666i	−0.0637773	−	0.0368219i	0.467772	−	0.883849i	$-0.345057\pi$
$613$	−1.57905	−	0.911666i	−0.0637773	−	0.0368219i	−0.531550	+	0.847027i	$0.678390\pi$
$614$	−5.84631	+	3.37537i	−0.235938	+	0.136219i
$615$	10.6913			0.431116
$616$		0			0
$617$	46.7616			1.88255			0.941276	−	0.337638i	$-0.109628\pi$
$617$	46.7616			1.88255			0.941276	+	0.337638i	$0.109628\pi$
$618$	2.81379	−	1.62454i	0.113187	−	0.0653486i
$619$	35.0519	+	20.2372i	1.40885	+	0.813402i	0.995278	−	0.0970680i	$-0.0309464\pi$
$619$	35.0519	+	20.2372i	1.40885	+	0.813402i	0.413576	+	0.910470i	$0.364280\pi$
$620$	−15.3697	+	26.6212i	−0.617263	+	1.06913i
$621$	−15.7065	+	9.06816i	−0.630281	+	0.363893i
$622$	−17.8705			−0.716542
$623$		0			0
$624$		−	1.39222i		−	0.0557335i
$625$	−14.0593	−	24.3514i	−0.562371	−	0.974055i
$626$	−7.51640	+	13.0188i	−0.300416	+	0.520335i
$627$	9.62266	−	14.4205i	0.384292	−	0.575900i
$628$	2.12168	−	1.22495i	0.0846643	−	0.0488810i
$629$	27.9971			1.11632
$630$		0			0
$631$	12.6619			0.504064			0.252032	−	0.967719i	$-0.418901\pi$
$631$	12.6619			0.504064			0.252032	+	0.967719i	$0.418901\pi$
$632$	4.24264	+	7.34847i	0.168763	+	0.292306i
$633$	0.812244	−	1.40685i	0.0322838	−	0.0559172i
$634$	−8.42810	−	4.86597i	−0.334723	−	0.193252i
$635$	33.7881	+	58.5227i	1.34084	+	2.32240i
$636$		−	3.81493i		−	0.151272i
$637$		0			0
$638$	−2.01154	+	30.9821i	−0.0796374	+	1.22659i
$639$	−10.6973	−	18.5283i	−0.423180	−	0.732969i
$640$	1.94969	−	3.37695i	0.0770681	−	0.133486i
$641$	0.653476	−	1.13185i	0.0258107	−	0.0447055i	−0.852832	−	0.522186i	$-0.825117\pi$
$641$	0.653476	−	1.13185i	0.0258107	−	0.0447055i	0.878642	+	0.477481i	$0.158450\pi$
$642$	4.79796	−	2.77010i	0.189360	−	0.109327i
$643$		−	39.1745i		−	1.54489i	−0.635081	−	0.772446i	$-0.719033\pi$
$643$		−	39.1745i		−	1.54489i	0.635081	−	0.772446i	$-0.280967\pi$
$644$		0			0
$645$		−	9.72391i		−	0.382878i
$646$	35.9371	−	20.7483i	1.41393	−	0.816330i
$647$	−14.3245	−	8.27023i	−0.563153	−	0.325136i	0.191257	−	0.981540i	$-0.438744\pi$
$647$	−14.3245	−	8.27023i	−0.563153	−	0.325136i	−0.754410	+	0.656404i	$0.772077\pi$
$648$	3.52565	+	2.03553i	0.138501	+	0.0799633i
$649$	7.63378	+	15.4558i	0.299652	+	0.606693i
$650$			18.5633i			0.728114i
$651$		0			0
$652$	−2.29005			−0.0896854
$653$	−17.3853	−	30.1122i	−0.680339	−	1.17838i	−0.974878	−	0.222741i	$-0.928499\pi$
$653$	−17.3853	−	30.1122i	−0.680339	−	1.17838i	0.294539	−	0.955639i	$-0.404834\pi$
$654$	3.97696	+	2.29610i	0.155512	+	0.0897846i
$655$	−21.4623	−	12.3913i	−0.838602	−	0.484167i
$656$	−1.79117	−	3.10240i	−0.0699336	−	0.121128i
$657$	0.134486			0.00524680
$658$		0			0
$659$			22.4888i			0.876039i	0.898966	+	0.438019i	$0.144320\pi$
$659$			22.4888i			0.876039i	−0.898966	+	0.438019i	$0.855680\pi$
$660$	8.87482	−	4.38337i	0.345452	−	0.170622i
$661$	−22.7587	−	13.1398i	−0.885212	−	0.511077i	−0.0128383	−	0.999918i	$-0.504087\pi$
$661$	−22.7587	−	13.1398i	−0.885212	−	0.511077i	−0.872373	+	0.488840i	$0.837420\pi$
$662$	−15.8135	−	9.12993i	−0.614609	−	0.354845i
$663$	7.32590	−	4.22961i	0.284514	−	0.164265i
$664$			10.4676i			0.406221i
$665$		0			0
$666$		−	11.1242i		−	0.431052i
$667$	−35.4815	+	20.4853i	−1.37385	+	0.793193i
$668$	4.25703	−	7.37339i	0.164709	−	0.285285i
$669$	2.21033	−	3.82840i	0.0854562	−	0.148014i
$670$	15.6629	+	27.1289i	0.605109	+	1.04808i
$671$	1.93044	−	29.7330i	0.0745237	−	1.14783i
$672$		0			0
$673$		−	3.77457i		−	0.145499i	−0.997350	−	0.0727495i	$-0.976823\pi$
$673$		−	3.77457i		−	0.145499i	0.997350	−	0.0727495i	$-0.0231774\pi$
$674$	−14.8464	−	25.7147i	−0.571862	−	0.990494i
$675$	36.6229	+	21.1442i	1.40962	+	0.813843i
$676$	−4.84557	+	8.39278i	−0.186368	+	0.322799i
$677$	15.7129	+	27.2155i	0.603896	+	1.04598i	0.992225	+	0.124457i	$0.0397190\pi$
$677$	15.7129	+	27.2155i	0.603896	+	1.04598i	−0.388329	+	0.921521i	$0.626948\pi$
$678$	−12.8887			−0.494989
$679$		0			0
$680$	23.6928			0.908578
$681$	0.802378	−	0.463253i	0.0307472	−	0.0177519i
$682$	21.7482	+	14.5123i	0.832780	+	0.555705i
$683$	9.95029	−	17.2344i	0.380737	−	0.659456i	−0.610431	−	0.792070i	$-0.709004\pi$
$683$	9.95029	−	17.2344i	0.380737	−	0.659456i	0.991168	+	0.132614i	$0.0423369\pi$
$684$	−8.24396	−	14.2790i	−0.315216	−	0.545970i
$685$		−	5.26254i		−	0.201071i
$686$		0			0
$687$	−14.8491			−0.566527
$688$	−2.82168	+	1.62910i	−0.107575	+	0.0621087i
$689$	4.53342	−	7.85212i	0.172710	−	0.299142i
$690$	11.3120	+	6.53098i	0.430640	+	0.248630i
$691$	−24.7690	+	14.3004i	−0.942255	+	0.544011i	−0.890667	−	0.454657i	$-0.849762\pi$
$691$	−24.7690	+	14.3004i	−0.942255	+	0.544011i	−0.0515887	+	0.998668i	$0.516428\pi$
$692$	23.9921			0.912044
$693$		0			0
$694$	−19.2813			−0.731907
$695$	−40.1713	+	23.1929i	−1.52379	+	0.879758i
$696$	−6.20481	−	3.58235i	−0.235193	−	0.135788i
$697$	10.8833	−	18.8504i	0.412233	−	0.714009i
$698$	−20.7778	+	11.9961i	−0.786451	+	0.454058i
$699$	15.0872			0.570650
$700$		0			0
$701$		−	21.2928i		−	0.804218i	−0.915592	−	0.402109i	$-0.868277\pi$
$701$		−	21.2928i		−	0.804218i	0.915592	−	0.402109i	$-0.131723\pi$
$702$	−3.76889	−	6.52792i	−0.142248	−	0.246380i
$703$	−15.7345	+	27.2529i	−0.593436	+	1.02786i
$704$	−2.75881	−	1.84092i	−0.103976	−	0.0693823i
$705$	−0.526882	+	0.304195i	−0.0198435	+	0.0114567i
$706$	16.1478			0.607731
$707$		0			0
$708$	−3.97801			−0.149503
$709$	8.43913	+	14.6170i	0.316938	+	0.548953i	0.979848	−	0.199746i	$-0.0640118\pi$
$709$	8.43913	+	14.6170i	0.316938	+	0.548953i	−0.662909	+	0.748700i	$0.730679\pi$
$710$	−17.2780	+	29.9264i	−0.648433	+	1.12312i
$711$	17.7408	+	10.2426i	0.665331	+	0.384129i
$712$	−0.843855	−	1.46160i	−0.0316248	−	0.0547758i
$713$			34.5021i			1.29211i
$714$		0			0
$715$	23.4756	+	1.52417i	0.877937	+	0.0570007i
$716$	10.0792	+	17.4577i	0.376678	+	0.652426i
$717$	−4.45030	+	7.70814i	−0.166199	+	0.287866i
$718$	9.07278	−	15.7145i	0.338593	−	0.586461i
$719$	31.3046	−	18.0737i	1.16746	−	0.674036i	0.214383	−	0.976750i	$-0.431226\pi$
$719$	31.3046	−	18.0737i	1.16746	−	0.674036i	0.953081	+	0.302714i	$0.0978927\pi$
$720$		−	9.41392i		−	0.350836i
$721$		0			0
$722$			27.6424i			1.02874i
$723$	18.1441	−	10.4755i	0.674786	−	0.389588i
$724$	−9.62460	−	5.55676i	−0.357695	−	0.206515i
$725$	82.7324	+	47.7656i	3.07261	+	1.77397i
$726$	−3.23139	−	7.77421i	−0.119928	−	0.288528i
$727$			8.74172i			0.324212i	0.986773	+	0.162106i	$0.0518287\pi$
$727$			8.74172i			0.324212i	−0.986773	+	0.162106i	$0.948171\pi$
$728$		0			0
$729$	0.313708			0.0116188
$730$	−0.108609	−	0.188117i	−0.00401981	−	0.00696251i
$731$	−17.1447	−	9.89848i	−0.634118	−	0.366108i
$732$	5.95465	+	3.43792i	0.220090	+	0.127069i
$733$	−6.73225	−	11.6606i	−0.248661	−	0.430694i	0.714493	−	0.699642i	$-0.246657\pi$
$733$	−6.73225	−	11.6606i	−0.248661	−	0.430694i	−0.963155	+	0.268948i	$0.913324\pi$
$734$	4.91547			0.181433
$735$		0			0
$736$		−	4.37667i		−	0.161326i
$737$	23.8892	−	11.7991i	0.879970	−	0.434626i
$738$	−7.48986	−	4.32427i	−0.275706	−	0.159179i
$739$	−32.3387	−	18.6708i	−1.18960	−	0.686816i	−0.231384	−	0.972862i	$-0.574325\pi$
$739$	−32.3387	−	18.6708i	−1.18960	−	0.686816i	−0.958216	+	0.286047i	$0.907659\pi$
$740$	−15.5603	+	8.98372i	−0.572006	+	0.330248i
$741$			9.50821i			0.349293i
$742$		0			0
$743$		−	17.5472i		−	0.643746i	−0.946783	−	0.321873i	$-0.895688\pi$
$743$		−	17.5472i		−	0.643746i	0.946783	−	0.321873i	$-0.104312\pi$
$744$	−5.22519	+	3.01676i	−0.191565	+	0.110600i
$745$	12.8225	−	22.2091i	0.469778	−	0.813680i
$746$	−1.13403	+	1.96420i	−0.0415198	+	0.0719145i
$747$	12.6355	+	21.8853i	0.462308	+	0.800741i
$748$	1.30563	−	20.1097i	0.0477387	−	0.735282i
$749$		0			0
$750$		−	15.5344i		−	0.567235i
$751$	17.3623	+	30.0724i	0.633561	+	1.09736i	0.986818	+	0.161833i	$0.0517406\pi$
$751$	17.3623	+	30.0724i	0.633561	+	1.09736i	−0.353258	+	0.935526i	$0.614926\pi$
$752$	0.176542	+	0.101927i	0.00643784	+	0.00371689i
$753$	−5.16702	+	8.94954i	−0.188297	+	0.326139i
$754$	−8.51406	−	14.7468i	−0.310064	−	0.537046i
$755$	−33.6862			−1.22597
$756$		0			0
$757$	28.0627			1.01996			0.509978	−	0.860187i	$-0.329653\pi$
$757$	28.0627			1.01996			0.509978	+	0.860187i	$0.329653\pi$
$758$	12.8158	−	7.39920i	0.465491	−	0.268751i
$759$	6.16664	−	9.24134i	0.223835	−	0.335439i
$760$	−13.3154	+	23.0630i	−0.483001	+	0.836583i
$761$	−3.79149	−	6.56706i	−0.137442	−	0.238056i	0.789086	−	0.614283i	$-0.210555\pi$
$761$	−3.79149	−	6.56706i	−0.137442	−	0.238056i	−0.926527	+	0.376227i	$0.877221\pi$
$762$			13.2638i			0.480498i
$763$		0			0
$764$	24.5084			0.886681
$765$	49.5362	−	28.5997i	1.79099	−	1.03403i
$766$	3.63515	−	6.29627i	0.131343	−	0.227494i
$767$	−8.18777	−	4.72721i	−0.295643	−	0.170690i
$768$	0.662827	−	0.382683i	0.0239177	−	0.0138089i
$769$	−1.95786			−0.0706022			−0.0353011	−	0.999377i	$-0.511239\pi$
$769$	−1.95786			−0.0706022			−0.0353011	+	0.999377i	$0.511239\pi$
$770$		0			0
$771$	−2.14792			−0.0773554
$772$	10.9286	−	6.30966i	0.393331	−	0.227090i
$773$	8.18023	+	4.72286i	0.294223	+	0.169869i	0.639845	−	0.768504i	$-0.278999\pi$
$773$	8.18023	+	4.72286i	0.294223	+	0.169869i	−0.345622	+	0.938374i	$0.612332\pi$
$774$	−3.93298	+	6.81213i	−0.141368	+	0.244857i
$775$	69.6706	−	40.2243i	2.50264	−	1.44490i
$776$	−9.23880			−0.331653
$777$		0			0
$778$		−	35.1936i		−	1.26175i
$779$	12.2329	+	21.1879i	0.438288	+	0.759136i
$780$	−2.71440	+	4.70147i	−0.0971910	+	0.168340i
$781$	24.4484	+	16.3142i	0.874833	+	0.583767i
$782$	23.0301	−	13.2965i	0.823556	−	0.475480i
$783$	−38.7912			−1.38628
$784$		0			0
$785$	−9.55310			−0.340965
$786$	−2.43215	−	4.21261i	−0.0867520	−	0.150259i
$787$	10.0436	−	17.3960i	0.358016	−	0.620101i	−0.629614	−	0.776908i	$-0.716787\pi$
$787$	10.0436	−	17.3960i	0.358016	−	0.620101i	0.987629	+	0.156807i	$0.0501201\pi$
$788$	14.9560	+	8.63486i	0.532786	+	0.307604i
$789$	−3.24718	−	5.62427i	−0.115603	−	0.200229i
$790$		−	33.0873i		−	1.17719i
$791$		0			0
$792$	−7.99022	−	0.518771i	−0.283920	−	0.0184337i
$793$	8.17081	+	14.1523i	0.290154	+	0.502561i
$794$	9.41550	−	16.3081i	0.334144	−	0.578754i
$795$	−7.43792	+	12.8829i	−0.263796	+	0.456908i
$796$	7.95279	−	4.59154i	0.281879	−	0.162743i
$797$			36.2219i			1.28304i	0.767105	+	0.641522i	$0.221697\pi$
$797$			36.2219i			1.28304i	−0.767105	+	0.641522i	$0.778303\pi$
$798$		0			0
$799$			1.23863i			0.0438194i
$800$	−8.83788	+	5.10255i	−0.312466	+	0.180402i
$801$	−3.52861	−	2.03725i	−0.124677	−	0.0719826i
$802$	6.15480	+	3.55347i	0.217333	+	0.125477i
$803$	−0.165652	+	0.0818173i	−0.00584574	+	0.00288727i
$804$			6.14859i			0.216844i
$805$		0			0
$806$	−14.3397			−0.505095
$807$	8.02014	+	13.8913i	0.282322	+	0.488997i
$808$	4.62948	+	2.67283i	0.162865	+	0.0940299i
$809$	−0.169942	−	0.0981160i	−0.00597484	−	0.00344958i	0.497010	−	0.867745i	$-0.334431\pi$
$809$	−0.169942	−	0.0981160i	−0.00597484	−	0.00344958i	−0.502984	+	0.864295i	$0.667765\pi$
$810$	−7.93730	−	13.7478i	−0.278888	−	0.483049i
$811$	13.1515			0.461811			0.230905	−	0.972976i	$-0.425831\pi$
$811$	13.1515			0.461811			0.230905	+	0.972976i	$0.425831\pi$
$812$		0			0
$813$			11.1845i			0.392256i
$814$	6.76760	+	13.7021i	0.237204	+	0.480258i
$815$	7.73341	+	4.46489i	0.270890	+	0.156398i
$816$	4.02738	+	2.32521i	0.140986	+	0.0813985i
$817$	19.2707	−	11.1259i	0.674196	−	0.389248i
$818$			9.71411i			0.339646i
$819$		0			0
$820$			13.9689i			0.487815i
$821$	16.2662	−	9.39127i	0.567693	−	0.327758i	−0.188535	−	0.982067i	$-0.560374\pi$
$821$	16.2662	−	9.39127i	0.567693	−	0.327758i	0.756227	+	0.654309i	$0.227040\pi$
$822$	0.516465	−	0.894543i	0.0180138	−	0.0312008i
$823$	−18.1347	+	31.4103i	−0.632137	+	1.09489i	0.354977	+	0.934875i	$0.384489\pi$
$823$	−18.1347	+	31.4103i	−0.632137	+	1.09489i	−0.987114	+	0.160019i	$0.948844\pi$
$824$	2.12256	+	3.67639i	0.0739431	+	0.128073i
$825$	−25.8506	−	1.67837i	−0.900001	−	0.0584332i
$826$		0			0
$827$		−	26.5489i		−	0.923196i	−0.887089	−	0.461598i	$-0.847276\pi$
$827$		−	26.5489i		−	0.923196i	0.887089	−	0.461598i	$-0.152724\pi$
$828$	−5.28311	−	9.15062i	−0.183601	−	0.318006i
$829$	7.93057	+	4.57871i	0.275440	+	0.159025i	0.631357	−	0.775492i	$-0.282498\pi$
$829$	7.93057	+	4.57871i	0.275440	+	0.159025i	−0.355917	+	0.934517i	$0.615832\pi$
$830$	20.4085	−	35.3485i	0.708389	−	1.22697i
$831$	4.25703	+	7.37339i	0.147675	+	0.255780i
$832$	1.81903			0.0630634
$833$		0			0
$834$	−9.10459			−0.315266
$835$	−28.7516	+	16.5997i	−0.994990	+	0.574458i
$836$	18.8413	+	12.5726i	0.651641	+	0.434833i
$837$	−16.3334	+	28.2903i	−0.564565	+	0.977855i
$838$	11.5237	+	19.9596i	0.398080	+	0.689494i
$839$			42.3516i			1.46214i	0.682302	+	0.731070i	$0.260979\pi$
$839$			42.3516i			1.46214i	−0.682302	+	0.731070i	$0.739021\pi$
$840$		0			0
$841$	−58.6306			−2.02175
$842$	−1.44690	+	0.835371i	−0.0498636	+	0.0287888i
$843$	−2.78949	+	4.83154i	−0.0960752	+	0.166407i
$844$	1.83814	+	1.06125i	0.0632712	+	0.0365297i
$845$	32.7266	−	18.8947i	1.12583	−	0.649997i
$846$	0.492146			0.0169203
$847$		0			0
$848$	4.98445			0.171167
$849$	−10.6145	+	6.12826i	−0.364287	+	0.210321i
$850$	−53.6994	−	31.0034i	−1.84188	−	1.06341i
$851$	−10.0834	+	17.4649i	−0.345653	+	0.598689i
$852$	−5.87394	+	3.39132i	−0.201238	+	0.116185i
$853$	−56.4552			−1.93299			−0.966495	−	0.256686i	$-0.917369\pi$
$853$	−56.4552			−1.93299			−0.966495	+	0.256686i	$0.917369\pi$
$854$		0			0
$855$			64.2926i			2.19876i
$856$	3.61931	+	6.26883i	0.123706	+	0.214264i
$857$	18.0227	−	31.2163i	0.615644	−	1.06633i	−0.374627	−	0.927176i	$-0.622229\pi$
$857$	18.0227	−	31.2163i	0.615644	−	1.06633i	0.990271	−	0.139151i	$-0.0444374\pi$
$858$	3.84087	+	2.56297i	0.131125	+	0.0874984i
$859$	−0.0732103	+	0.0422680i	−0.00249790	+	0.00144217i	−0.501248	−	0.865303i	$-0.667126\pi$
$859$	−0.0732103	+	0.0422680i	−0.00249790	+	0.00144217i	0.498751	+	0.866746i	$0.333792\pi$
$860$	12.7049			0.433233
$861$		0			0
$862$	−38.8481			−1.32317
$863$	−22.8620	−	39.5981i	−0.778230	−	1.34793i	−0.932961	−	0.359977i	$-0.882784\pi$
$863$	−22.8620	−	39.5981i	−0.778230	−	1.34793i	0.154731	−	0.987957i	$-0.450549\pi$
$864$	2.07193	−	3.58869i	0.0704885	−	0.122090i
$865$	−81.0204	−	46.7771i	−2.75477	−	1.59047i
$866$	15.9239	+	27.5811i	0.541118	+	0.937244i
$867$			15.2449i			0.517745i
$868$		0			0
$869$	−28.0834	−	1.82333i	−0.952663	−	0.0618523i
$870$	13.9689	+	24.1948i	0.473590	+	0.820282i
$871$	−7.30660	+	12.6554i	−0.247575	+	0.428812i
$872$	−3.00000	+	5.19615i	−0.101593	+	0.175964i
$873$	−19.3162	+	11.1522i	−0.653754	+	0.377445i
$874$			29.8906i			1.01106i
$875$		0			0
$876$		−	0.0426355i		−	0.00144052i
$877$	40.0453	−	23.1201i	1.35223	−	0.780712i	0.363671	−	0.931528i	$-0.381523\pi$
$877$	40.0453	−	23.1201i	1.35223	−	0.780712i	0.988562	+	0.150816i	$0.0481900\pi$
$878$	10.4276	+	6.02035i	0.351913	+	0.203177i
$879$	−9.44857	−	5.45513i	−0.318692	−	0.183997i
$880$	5.72714	+	11.5955i	0.193062	+	0.390885i
$881$		−	37.2892i		−	1.25630i	−0.778091	−	0.628152i	$-0.783812\pi$
$881$		−	37.2892i		−	1.25630i	0.778091	−	0.628152i	$-0.216188\pi$
$882$		0			0
$883$	−24.3548			−0.819603			−0.409801	−	0.912175i	$-0.634402\pi$
$883$	−24.3548			−0.819603			−0.409801	+	0.912175i	$0.634402\pi$
$884$	5.52625	+	9.57175i	0.185868	+	0.321933i
$885$	13.4336	+	7.75587i	0.451564	+	0.260711i
$886$	26.4591	+	15.2762i	0.888911	+	0.513213i
$887$	−5.74396	−	9.94883i	−0.192863	−	0.334049i	0.753335	−	0.657637i	$-0.228444\pi$
$887$	−5.74396	−	9.94883i	−0.192863	−	0.334049i	−0.946198	+	0.323588i	$0.895111\pi$
$888$	−3.52664			−0.118346
$889$		0			0
$890$			6.58101i			0.220596i
$891$	−12.1061	+	5.97932i	−0.405569	+	0.200315i
$892$	5.00204	+	2.88793i	0.167481	+	0.0966951i
$893$	−1.20570	−	0.696111i	−0.0403472	−	0.0232945i
$894$	4.35920	−	2.51679i	0.145793	−	0.0841739i
$895$		−	78.6053i		−	2.62748i
$896$		0			0
$897$			6.09330i			0.203449i
$898$	13.6293	−	7.86890i	0.454817	−	0.262588i
$899$	−36.8977	+	63.9087i	−1.23061	+	2.13148i
$900$	−12.3186	+	21.3365i	−0.410621	+	0.711217i
$901$	15.1429	+	26.2283i	0.504483	+	0.873791i
$902$	11.8563	+	0.769781i	0.394773	+	0.0256309i
$903$		0			0
$904$		−	16.8400i		−	0.560089i
$905$	21.6679	+	37.5299i	0.720265	+	1.24754i
$906$	−5.72608	−	3.30596i	−0.190236	−	0.109833i
$907$	11.6507	−	20.1796i	0.386854	−	0.670051i	−0.605170	−	0.796096i	$-0.706895\pi$
$907$	11.6507	−	20.1796i	0.386854	−	0.670051i	0.992025	+	0.126045i	$0.0402283\pi$
$908$	0.605269	+	1.04836i	0.0200866	+	0.0347910i
$909$	12.9056			0.428051
$910$		0			0
$911$	−32.6447			−1.08157			−0.540784	−	0.841161i	$-0.681872\pi$
$911$	−32.6447			−1.08157			−0.540784	+	0.841161i	$0.681872\pi$
$912$	−4.52679	+	2.61355i	−0.149897	+	0.0865431i
$913$	−28.8780	−	19.2700i	−0.955722	−	0.637743i
$914$	−8.58340	+	14.8669i	−0.283914	+	0.491753i
$915$	−13.4057	−	23.2194i	−0.443180	−	0.767610i
$916$		−	19.4012i		−	0.641035i
$917$		0			0
$918$	25.1783			0.831009
$919$	−33.0701	+	19.0931i	−1.09088	+	0.629822i	−0.933812	−	0.357765i	$-0.883539\pi$
$919$	−33.0701	+	19.0931i	−1.09088	+	0.629822i	−0.157072	+	0.987587i	$0.550205\pi$
$920$	−8.53314	+	14.7798i	−0.281329	+	0.487276i
$921$	4.47458	+	2.58340i	0.147442	+	0.0851258i
$922$	0.270283	−	0.156048i	0.00890129	−	0.00513916i
$923$	−16.1201			−0.530600
$924$		0			0
$925$	47.0228			1.54610
$926$	−27.6610	+	15.9701i	−0.908998	+	0.524810i
$927$	8.87559	+	5.12433i	0.291513	+	0.168305i
$928$	4.68056	−	8.10697i	0.153647	−	0.266124i
$929$	−7.05212	+	4.07155i	−0.231373	+	0.133583i	−0.611205	−	0.791472i	$-0.709315\pi$
$929$	−7.05212	+	4.07155i	−0.231373	+	0.133583i	0.379832	+	0.925055i	$0.375982\pi$
$930$	23.5270			0.771479
$931$		0			0
$932$			19.7124i			0.645700i
$933$	6.83875	+	11.8451i	0.223891	+	0.387790i
$934$	9.42604	−	16.3264i	0.308429	−	0.534216i
$935$	−43.6166	+	65.3638i	−1.42642	+	2.13763i
$936$	3.80317	−	2.19576i	0.124310	−	0.0717706i
$937$	29.3997			0.960445			0.480222	−	0.877147i	$-0.340556\pi$
$937$	29.3997			0.960445			0.480222	+	0.877147i	$0.340556\pi$
$938$		0			0
$939$	11.5056			0.375471
$940$	−0.397450	−	0.688404i	−0.0129634	−	0.0224533i
$941$	−12.5519	+	21.7406i	−0.409181	+	0.708722i	−0.994798	−	0.101866i	$-0.967519\pi$
$941$	−12.5519	+	21.7406i	−0.409181	+	0.708722i	0.585617	+	0.810588i	$0.300852\pi$
$942$	−1.62386	−	0.937539i	−0.0529084	−	0.0305467i
$943$	7.83938	+	13.5782i	0.255285	+	0.442167i
$944$		−	5.19752i		−	0.169165i
$945$		0			0
$946$	0.700126	−	10.7835i	0.0227631	−	0.350602i
$947$	−29.0590	−	50.3316i	−0.944290	−	1.63556i	−0.757166	−	0.653222i	$-0.773417\pi$
$947$	−29.0590	−	50.3316i	−0.944290	−	1.63556i	−0.187124	−	0.982336i	$-0.559917\pi$
$948$	3.24718	−	5.62427i	0.105463	−	0.182668i
$949$	0.0506653	−	0.0877549i	0.00164467	−	0.00284864i
$950$	60.3585	−	34.8480i	1.95829	−	1.13062i
$951$			7.44850i			0.241534i
$952$		0			0
$953$			56.3237i			1.82450i	0.409632	+	0.912251i	$0.365657\pi$
$953$			56.3237i			1.82450i	−0.409632	+	0.912251i	$0.634343\pi$
$954$	10.4213	−	6.01676i	0.337403	−	0.194800i
$955$	−82.7636	−	47.7836i	−2.67817	−	1.54624i
$956$	−10.0712	−	5.81459i	−0.325725	−	0.188057i
$957$	21.3056	−	10.5230i	0.688711	−	0.340161i
$958$			29.0540i			0.938692i
$959$		0			0
$960$	−2.98445			−0.0963227
$961$	15.5723	+	26.9720i	0.502332	+	0.870064i
$962$	−7.25874	−	4.19083i	−0.234031	−	0.135118i
$963$	15.1343	+	8.73779i	0.487696	+	0.281571i
$964$	13.6869	+	23.7064i	0.440825	+	0.763532i
$965$	−49.2074			−1.58404
$966$		0			0
$967$		−	28.3825i		−	0.912721i	−0.889795	−	0.456360i	$-0.849153\pi$
$967$		−	28.3825i		−	0.912721i	0.889795	−	0.456360i	$-0.150847\pi$
$968$	10.1575	−	4.22202i	0.326474	−	0.135701i
$969$	−27.5051	−	15.8801i	−0.883590	−	0.510141i
$970$	31.1990	+	18.0127i	1.00174	+	0.578354i
$971$	−38.2269	+	22.0703i	−1.22676	+	0.708270i	−0.966351	−	0.257229i	$-0.917191\pi$
$971$	−38.2269	+	22.0703i	−1.22676	+	0.708270i	−0.260409	+	0.965499i	$0.583857\pi$
$972$		−	15.5474i		−	0.498684i
$973$		0			0
$974$		−	33.1349i		−	1.06171i
$975$	12.3043	−	7.10388i	0.394053	−	0.227506i
$976$	−4.49186	+	7.78013i	−0.143781	+	0.249036i
$977$	4.83203	−	8.36932i	0.154590	−	0.267758i	−0.778319	−	0.627868i	$-0.783928\pi$
$977$	4.83203	−	8.36932i	0.154590	−	0.267758i	0.932910	+	0.360110i	$0.117261\pi$
$978$	0.876366	+	1.51791i	0.0280231	+	0.0485374i
$979$	5.58574	+	0.362658i	0.178521	+	0.0115906i
$980$		0			0
$981$			14.4853i			0.462479i
$982$	−21.2075	−	36.7325i	−0.676759	−	1.17218i
$983$	−23.1226	−	13.3498i	−0.737497	−	0.425794i	0.0836616	−	0.996494i	$-0.473339\pi$
$983$	−23.1226	−	13.3498i	−0.737497	−	0.425794i	−0.821159	+	0.570700i	$0.806672\pi$
$984$	−1.37090	+	2.37448i	−0.0437028	+	0.0756955i
$985$	−33.6705	−	58.3191i	−1.07283	−	1.85820i
$986$	56.8787			1.81139
$987$		0			0
$988$	−12.4231			−0.395231
$989$	12.3496	−	7.13002i	0.392693	−	0.226721i
$990$	25.9712	+	17.3303i	0.825418	+	0.550792i
$991$	18.2219	−	31.5612i	0.578837	−	1.00257i	−0.416777	−	0.909009i	$-0.636840\pi$
$991$	18.2219	−	31.5612i	0.578837	−	1.00257i	0.995613	−	0.0935654i	$-0.0298264\pi$
$992$	−3.94159	−	6.82704i	−0.125146	−	0.216759i
$993$			13.9755i			0.443499i
$994$		0			0
$995$	−35.8083			−1.13520
$996$	6.93819	−	4.00577i	0.219845	−	0.126928i
$997$	14.5129	−	25.1370i	0.459627	−	0.796097i	−0.539314	−	0.842104i	$-0.681317\pi$
$997$	14.5129	−	25.1370i	0.459627	−	0.796097i	0.998941	+	0.0460077i	$0.0146499\pi$
$998$	−13.3732	−	7.72103i	−0.423322	−	0.244405i
$999$	−16.5359	+	9.54699i	−0.523172	+	0.302053i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.d.1011.11		32
7.2	even	3	inner	1078.2.i.d.901.2		32
7.3	odd	6		1078.2.c.c.1077.12	yes	16
7.4	even	3		1078.2.c.c.1077.13	yes	16
7.5	odd	6	inner	1078.2.i.d.901.1		32
7.6	odd	2	inner	1078.2.i.d.1011.12		32
11.10	odd	2	inner	1078.2.i.d.1011.1		32
77.10	even	6		1078.2.c.c.1077.4	✓	16
77.32	odd	6		1078.2.c.c.1077.5	yes	16
77.54	even	6	inner	1078.2.i.d.901.11		32
77.65	odd	6	inner	1078.2.i.d.901.12		32
77.76	even	2	inner	1078.2.i.d.1011.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.c.1077.4	✓	16	77.10	even	6
1078.2.c.c.1077.5	yes	16	77.32	odd	6
1078.2.c.c.1077.12	yes	16	7.3	odd	6
1078.2.c.c.1077.13	yes	16	7.4	even	3
1078.2.i.d.901.1		32	7.5	odd	6	inner
1078.2.i.d.901.2		32	7.2	even	3	inner
1078.2.i.d.901.11		32	77.54	even	6	inner
1078.2.i.d.901.12		32	77.65	odd	6	inner
1078.2.i.d.1011.1		32	11.10	odd	2	inner
1078.2.i.d.1011.2		32	77.76	even	2	inner
1078.2.i.d.1011.11		32	1.1	even	1	trivial
1078.2.i.d.1011.12		32	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.37695 + 1.94969i) q^{5} -0.765367 q^{6} -1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.662827 - 0.382683i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-3.37695 + 1.94969i) q^{5} -0.765367 q^{6} -1.00000i q^{8} +(-1.20711 - 2.09077i) q^{9} +(-1.94969 + 3.37695i) q^{10} +(2.75881 + 1.84092i) q^{11} +(-0.662827 + 0.382683i) q^{12} -1.81903 q^{13} +2.98445 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.03803 - 5.26202i) q^{17} +(-2.09077 - 1.20711i) q^{18} +(3.41476 + 5.91454i) q^{19} +3.89937i q^{20} +(3.30966 + 0.214882i) q^{22} +(2.18834 + 3.79031i) q^{23} +(-0.382683 + 0.662827i) q^{24} +(5.10255 - 8.83788i) q^{25} +(-1.57532 + 0.909513i) q^{26} +4.14386i q^{27} +9.36112i q^{29} +(2.58461 - 1.49222i) q^{30} +(6.82704 + 3.94159i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.12412 - 2.27596i) q^{33} -6.07606i q^{34} -2.41421 q^{36} +(2.30389 + 3.99045i) q^{37} +(5.91454 + 3.41476i) q^{38} +(1.20570 + 0.696111i) q^{39} +(1.94969 + 3.37695i) q^{40} +3.58235 q^{41} -3.25819i q^{43} +(2.97369 - 1.46874i) q^{44} +(8.15269 + 4.70696i) q^{45} +(3.79031 + 2.18834i) q^{46} +(-0.176542 + 0.101927i) q^{47} +0.765367i q^{48} -10.2051i q^{50} +(-4.02738 + 2.32521i) q^{51} +(-0.909513 + 1.57532i) q^{52} +(-2.49222 + 4.31666i) q^{53} +(2.07193 + 3.58869i) q^{54} +(-12.9056 - 0.837904i) q^{55} -5.22709i q^{57} +(4.68056 + 8.10697i) q^{58} +(4.50118 + 2.59876i) q^{59} +(1.49222 - 2.58461i) q^{60} +(-4.49186 - 7.78013i) q^{61} +7.88318 q^{62} -1.00000 q^{64} +(6.14277 - 3.54653i) q^{65} +(-2.11150 - 1.40898i) q^{66} +(4.01676 - 6.95724i) q^{67} +(-3.03803 - 5.26202i) q^{68} -3.34976i q^{69} +8.86195 q^{71} +(-2.09077 + 1.20711i) q^{72} +(-0.0278530 + 0.0482428i) q^{73} +(3.99045 + 2.30389i) q^{74} +(-6.76422 + 3.90532i) q^{75} +6.82952 q^{76} +1.39222 q^{78} +(-7.34847 + 4.24264i) q^{79} +(3.37695 + 1.94969i) q^{80} +(-2.03553 + 3.52565i) q^{81} +(3.10240 - 1.79117i) q^{82} -10.4676 q^{83} +23.6928i q^{85} +(-1.62910 - 2.82168i) q^{86} +(3.58235 - 6.20481i) q^{87} +(1.84092 - 2.75881i) q^{88} +(1.46160 - 0.843855i) q^{89} +9.41392 q^{90} +4.37667 q^{92} +(-3.01676 - 5.22519i) q^{93} +(-0.101927 + 0.176542i) q^{94} +(-23.0630 - 13.3154i) q^{95} +(0.382683 + 0.662827i) q^{96} -9.23880i q^{97} +(0.518771 - 7.99022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^9	\( 32 q + 16 q^{4} - 16 q^{9} - 16 q^{11} - 16 q^{16} - 16 q^{22} + 16 q^{23} + 64 q^{25} - 32 q^{36} + 80 q^{37} + 16 q^{44} - 32 q^{53} + 48 q^{58} - 32 q^{64} - 16 q^{67} - 96 q^{71} + 32 q^{78} + 48 q^{81} - 32 q^{86} - 8 q^{88} + 32 q^{92} + 48 q^{93} + 48 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^9 - 16 * q^11 - 16 * q^16 - 16 * q^22 + 16 * q^23 + 64 * q^25 - 32 * q^36 + 80 * q^37 + 16 * q^44 - 32 * q^53 + 48 * q^58 - 32 * q^64 - 16 * q^67 - 96 * q^71 + 32 * q^78 + 48 * q^81 - 32 * q^86 - 8 * q^88 + 32 * q^92 + 48 * q^93 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more