LMFDB - Embedded newform 1078.2.i.d.1011.12

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			1011.12
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.d.901.12

$q$-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	0.678985	−	0.734152i	$-0.262420\pi$
$3$	0.662827	+	0.382683i	0.382683	+	0.220942i	−0.296302	+	0.955094i	$0.595753\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.37695	−	1.94969i	1.51022	−	0.871926i	0.510291	−	0.860002i	$-0.329538\pi$
$5$	3.37695	−	1.94969i	1.51022	−	0.871926i	0.999929	−	0.0119244i	$-0.00379573\pi$
$6$	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	$-0.418828\pi$
$13$	1.81903			0.504507			0.252254	+	0.967661i	$0.418828\pi$
$14$		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	$0.430345\pi$
$17$	−3.03803	+	5.26202i	−0.736830	+	1.27623i	−0.953916	+	0.300075i	$0.902988\pi$
$18$	−2.09077	−	1.20711i	−0.492799	−	0.284518i
$19$	−3.41476	−	5.91454i	−0.783400	−	1.35689i	−0.929950	−	0.367685i	$-0.880150\pi$
$19$	−3.41476	−	5.91454i	−0.783400	−	1.35689i	0.146550	−	0.989203i	$-0.453183\pi$
$20$		−	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	−0.259945	−	0.965623i	$-0.583704\pi$
$31$	−6.82704	−	3.94159i	−1.22617	−	0.707931i	−0.966227	+	0.257693i	$0.917038\pi$
$32$	−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	$-0.590246\pi$
$41$	−3.58235			−0.559469			−0.279734	+	0.960077i	$0.590246\pi$
$42$		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	−0.487069	−	0.873363i	$-0.661934\pi$
$47$	0.176542	−	0.101927i	0.0257513	−	0.0148675i	0.512820	+	0.858496i	$0.328601\pi$
$48$		−	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	0.177512	−	0.984119i	$-0.443195\pi$
$59$	−4.50118	−	2.59876i	−0.586004	−	0.338330i	−0.763516	+	0.645789i	$0.776529\pi$
$60$	1.49222	−	2.58461i	0.192645	−	0.333672i
$61$	4.49186	+	7.78013i	0.575124	+	0.996143i	0.996028	+	0.0890385i	$0.0283794\pi$
$61$	4.49186	+	7.78013i	0.575124	+	0.996143i	−0.420905	+	0.907105i	$0.638287\pi$
$62$	−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	−0.864391	−	0.502821i	$-0.832296\pi$
$73$	0.0278530	−	0.0482428i	0.00325995	−	0.00564639i	0.867651	+	0.497174i	$0.165629\pi$
$74$	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	$-0.305203\pi$
$83$	10.4676			1.14897			0.574483	+	0.818517i	$0.305203\pi$
$84$		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	−0.575460	−	0.817830i	$-0.695177\pi$
$89$	−1.46160	+	0.843855i	−0.154929	+	0.0894484i	0.420531	+	0.907278i	$0.361844\pi$
$90$	−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	$0.155396\pi$
$97$			9.23880i			0.938058i	−0.883183	+	0.469029i	$0.844604\pi$
$98$		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	−0.701857	−	0.712318i	$-0.747645\pi$
$101$	2.67283	−	4.62948i	0.265957	−	0.460651i	0.967814	+	0.251667i	$0.0809788\pi$
$102$	−2.32521	+	4.02738i	−0.230230	+	0.398770i
$103$	3.67639	−	2.12256i	0.362246	−	0.209143i	−0.307820	−	0.951445i	$-0.599599\pi$
$103$	3.67639	−	2.12256i	0.362246	−	0.209143i	0.670065	+	0.742302i	$0.266266\pi$
$104$		−	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	0.693156	−	0.720788i	$-0.256220\pi$
$131$	−3.17776	−	5.50404i	−0.277642	−	0.480890i	−0.970798	+	0.239897i	$0.922886\pi$
$132$	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	$-0.668320\pi$
$139$	−11.8957			−1.00898			−0.504491	+	0.863417i	$0.668320\pi$
$140$		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	0.412941	−	0.910758i	$-0.364502\pi$
$157$	−2.12168	−	1.22495i	−0.169329	−	0.0977619i	−0.582269	+	0.812996i	$0.697835\pi$
$158$	−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	$-0.606853\pi$
$167$	−8.51406			−0.658838			−0.329419	+	0.944184i	$0.606853\pi$
$168$		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	$-0.801170\pi$
$173$	−11.9961	−	20.7778i	−0.912044	−	1.57971i	−0.100872	−	0.994899i	$-0.532163\pi$
$174$			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	$0.135530\pi$
$181$			11.1135i			0.826062i	−0.910717	+	0.413031i	$0.864470\pi$
$182$		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	0.190894	−	0.981611i	$-0.438861\pi$
$199$	−7.95279	−	4.59154i	−0.563758	−	0.325486i	−0.754653	+	0.656125i	$0.772195\pi$
$200$	−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	$-0.938052\pi$
$223$		−	5.77586i		−	0.386780i	0.981122	−	0.193390i	$-0.0619483\pi$
$224$		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	−0.845240	−	0.534387i	$-0.820542\pi$
$227$	0.605269	−	1.04836i	0.0401731	−	0.0695819i	0.885413	+	0.464805i	$0.153876\pi$
$228$	−4.52679	−	2.61355i	−0.299794	−	0.173086i
$229$	−16.8020	+	9.70062i	−1.11031	+	0.641035i	−0.938909	−	0.344167i	$-0.888161\pi$
$229$	−16.8020	+	9.70062i	−1.11031	+	0.641035i	−0.171397	+	0.985202i	$0.554828\pi$
$230$	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	$-0.489766\pi$
$241$	13.6869	−	23.7064i	0.881651	−	1.52706i	0.849505	−	0.527581i	$-0.176901\pi$
$242$	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	$0.140120\pi$
$251$			13.5021i			0.852243i	−0.904666	+	0.426122i	$0.859880\pi$
$252$		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	−0.573883	−	0.818937i	$-0.694564\pi$
$257$	−2.43041	+	1.40320i	−0.151605	+	0.0875289i	0.422279	+	0.906466i	$0.361230\pi$
$258$		−	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	0.937951	−	0.346768i	$-0.112721\pi$
$269$	18.1498	+	10.4788i	1.10662	+	0.638905i	0.168665	+	0.985673i	$0.446054\pi$
$270$	−13.9936	−	8.07922i	−0.851625	−	0.491686i
$271$	7.30660	+	12.6554i	0.443844	+	0.768761i	0.997971	−	0.0636717i	$-0.0202810\pi$
$271$	7.30660	+	12.6554i	0.443844	+	0.768761i	−0.554127	+	0.832432i	$0.686948\pi$
$272$	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	−0.999621	−	0.0275349i	$-0.991234\pi$
$283$	−8.00696	+	13.8685i	−0.475965	+	0.824395i	0.523656	+	0.851930i	$0.324568\pi$
$284$	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	$-0.636705\pi$
$293$	−14.2550			−0.832783			−0.416392	+	0.909185i	$0.636705\pi$
$294$		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	$-0.438294\pi$
$307$	6.75074			0.385285			0.192643	+	0.981269i	$0.438294\pi$
$308$		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	0.869860	−	0.493298i	$-0.164209\pi$
$311$	15.4763	+	8.93526i	0.877581	+	0.506672i	0.00772127	+	0.999970i	$0.497542\pi$
$312$	0.696111	−	1.20570i	0.0394095	−	0.0682593i
$313$	13.0188	−	7.51640i	0.735865	−	0.424852i	−0.0846986	−	0.996407i	$-0.526993\pi$
$313$	13.0188	−	7.51640i	0.735865	−	0.424852i	0.820564	+	0.571554i	$0.193659\pi$
$314$	−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	$-0.278049\pi$
$349$	23.9921			1.28427			0.642135	+	0.766592i	$0.278049\pi$
$350$		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	0.0793204	−	0.996849i	$-0.474725\pi$
$353$	−13.9844	−	8.07391i	−0.744316	−	0.429731i	−0.823636	+	0.567118i	$0.808058\pi$
$354$	−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	0.384763	−	0.923015i	$-0.374283\pi$
$367$	−4.25692	−	2.45773i	−0.222209	−	0.128293i	−0.606973	+	0.794723i	$0.707616\pi$
$368$	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	−0.652161	−	0.758081i	$-0.726137\pi$
$383$	−6.29627	+	3.63515i	−0.321724	+	0.185748i	0.330437	+	0.943828i	$0.392804\pi$
$384$	−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	−0.849893	−	0.526956i	$-0.823333\pi$
$397$	−16.3081	+	9.41550i	−0.818481	+	0.472550i	0.0314111	+	0.999507i	$0.490000\pi$
$398$	−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	−0.720595	−	0.693356i	$-0.756131\pi$
$409$	4.85705	−	8.41267i	0.240166	−	0.415980i	0.960761	+	0.277376i	$0.0894648\pi$
$410$	−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	$-0.809659\pi$
$419$		−	23.0474i		−	1.12594i	0.826478	−	0.562970i	$-0.190341\pi$
$420$		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	$-0.722612\pi$
$433$		−	31.8479i		−	1.53051i	0.643726	−	0.765256i	$-0.277388\pi$
$434$		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	0.685837	−	0.727755i	$-0.259436\pi$
$439$	−6.02035	−	10.4276i	−0.287336	−	0.497680i	−0.973173	+	0.230075i	$0.926103\pi$
$440$	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	$-0.502313\pi$
$461$	−0.312096			−0.0145357			−0.00726787	+	0.999974i	$0.502313\pi$
$462$		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	−0.827676	−	0.561206i	$-0.810337\pi$
$467$	−16.3264	+	9.42604i	−0.755495	+	0.436185i	0.0721810	+	0.997392i	$0.477004\pi$
$468$	−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	$-0.602295\pi$
$479$	14.5270	−	25.1615i	0.663755	−	1.14966i	0.979621	−	0.200854i	$-0.0643717\pi$
$480$	−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	$-0.155907\pi$
$503$	39.5816			1.76486			0.882429	+	0.470446i	$0.155907\pi$
$504$		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	−0.597884	−	0.801583i	$-0.703992\pi$
$509$	−4.57165	+	2.63944i	−0.202635	+	0.116991i	0.395249	+	0.918574i	$0.370658\pi$
$510$			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	−0.117392	−	0.993086i	$-0.537453\pi$
$521$	−23.6500	−	13.6543i	−1.03613	−	0.598207i	−0.918733	+	0.394878i	$0.870787\pi$
$522$	11.2999	−	19.5720i	0.494582	−	0.856641i
$523$	4.32645	+	7.49363i	0.189182	+	0.327673i	0.944978	−	0.327134i	$-0.106083\pi$
$523$	4.32645	+	7.49363i	0.189182	+	0.327673i	−0.755796	+	0.654808i	$0.772750\pi$
$524$	−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	−0.928345	−	0.371719i	$-0.878769\pi$
$563$	−3.37537	+	5.84631i	−0.142255	+	0.246393i	0.786090	+	0.618111i	$0.212102\pi$
$564$	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	0.703755	−	0.710443i	$-0.251505\pi$
$577$	10.5781	+	6.10726i	0.440371	+	0.254248i	−0.263384	+	0.964691i	$0.584839\pi$
$578$	−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	$-0.845781\pi$
$587$		−	22.5689i		−	0.931519i	0.884911	−	0.465759i	$-0.154219\pi$
$588$		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	$0.104689\pi$
$593$	18.3348	+	31.7568i	0.752920	+	1.30410i	−0.193481	+	0.981104i	$0.561978\pi$
$594$	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	$-0.489602\pi$
$601$	1.60141			0.0653230			0.0326615	+	0.999466i	$0.489602\pi$
$602$		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	0.984398	−	0.175957i	$-0.0563021\pi$
$607$	8.37216	+	14.5010i	0.339815	+	0.588578i	−0.644582	+	0.764535i	$0.722969\pi$
$608$			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	−0.413576	−	0.910470i	$-0.635720\pi$
$619$	−35.0519	−	20.2372i	−1.40885	−	0.813402i	−0.995278	+	0.0970680i	$0.969054\pi$
$620$	−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	$0.280967\pi$
$643$			39.1745i			1.54489i	−0.635081	+	0.772446i	$0.719033\pi$
$644$		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	0.754410	−	0.656404i	$-0.227923\pi$
$647$	14.3245	+	8.27023i	0.563153	+	0.325136i	−0.191257	+	0.981540i	$0.561256\pi$
$648$	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	0.872373	−	0.488840i	$-0.162580\pi$
$661$	22.7587	+	13.1398i	0.885212	+	0.511077i	0.0128383	+	0.999918i	$0.495913\pi$
$662$	−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	$-0.960281\pi$
$677$	−15.7129	−	27.2155i	−0.603896	−	1.04598i	0.388329	−	0.921521i	$-0.373052\pi$
$678$	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	0.0515887	−	0.998668i	$-0.483572\pi$
$691$	24.7690	−	14.3004i	0.942255	−	0.544011i	0.890667	+	0.454657i	$0.150238\pi$
$692$	−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	−0.953081	−	0.302714i	$-0.902107\pi$
$719$	−31.3046	+	18.0737i	−1.16746	+	0.674036i	−0.214383	+	0.976750i	$0.568774\pi$
$720$			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	$-0.948171\pi$
$727$		−	8.74172i		−	0.324212i	0.986773	−	0.162106i	$-0.0518287\pi$
$728$		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	0.963155	−	0.268948i	$-0.0866760\pi$
$733$	6.73225	+	11.6606i	0.248661	+	0.430694i	−0.714493	+	0.699642i	$0.753343\pi$
$734$	−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	0.926527	−	0.376227i	$-0.122779\pi$
$761$	3.79149	+	6.56706i	0.137442	+	0.238056i	−0.789086	+	0.614283i	$0.789445\pi$
$762$		−	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	$-0.488761\pi$
$769$	1.95786			0.0706022			0.0353011	+	0.999377i	$0.488761\pi$
$770$		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	0.345622	−	0.938374i	$-0.387668\pi$
$773$	−8.18023	−	4.72286i	−0.294223	−	0.169869i	−0.639845	+	0.768504i	$0.721001\pi$
$774$	−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	−0.987629	−	0.156807i	$-0.949880\pi$
$787$	−10.0436	+	17.3960i	−0.358016	+	0.620101i	0.629614	+	0.776908i	$0.283213\pi$
$788$	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	$-0.778303\pi$
$797$		−	36.2219i		−	1.28304i	0.767105	−	0.641522i	$-0.221697\pi$
$798$		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	$-0.574169\pi$
$811$	−13.1515			−0.461811			−0.230905	+	0.972976i	$0.574169\pi$
$812$		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	0.355917	−	0.934517i	$-0.384168\pi$
$829$	−7.93057	−	4.57871i	−0.275440	−	0.159025i	−0.631357	+	0.775492i	$0.717502\pi$
$830$	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	$-0.739021\pi$
$839$		−	42.3516i		−	1.46214i	0.682302	−	0.731070i	$-0.260979\pi$
$840$		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	$-0.0826307\pi$
$853$	56.4552			1.93299			0.966495	+	0.256686i	$0.0826307\pi$
$854$		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	$0.377771\pi$
$857$	−18.0227	+	31.2163i	−0.615644	+	1.06633i	−0.990271	+	0.139151i	$0.955563\pi$
$858$	3.84087	+	2.56297i	0.131125	+	0.0874984i
$859$	0.0732103	−	0.0422680i	0.00249790	−	0.00144217i	−0.498751	−	0.866746i	$-0.666208\pi$
$859$	0.0732103	−	0.0422680i	0.00249790	−	0.00144217i	0.501248	+	0.865303i	$0.332874\pi$
$860$	−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	$0.216188\pi$
$881$			37.2892i			1.25630i	−0.778091	+	0.628152i	$0.783812\pi$
$882$		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	0.946198	−	0.323588i	$-0.104889\pi$
$887$	5.74396	+	9.94883i	0.192863	+	0.334049i	−0.753335	+	0.657637i	$0.771556\pi$
$888$	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	−0.379832	−	0.925055i	$-0.624018\pi$
$929$	7.05212	−	4.07155i	0.231373	−	0.133583i	0.611205	+	0.791472i	$0.290685\pi$
$930$	−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	$-0.659444\pi$
$937$	−29.3997			−0.960445			−0.480222	+	0.877147i	$0.659444\pi$
$938$		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	−0.585617	−	0.810588i	$-0.699148\pi$
$941$	12.5519	−	21.7406i	0.409181	−	0.708722i	0.994798	+	0.101866i	$0.0324811\pi$
$942$	−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	0.260409	−	0.965499i	$-0.416143\pi$
$971$	38.2269	−	22.0703i	1.22676	−	0.708270i	0.966351	+	0.257229i	$0.0828094\pi$
$972$			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	0.821159	−	0.570700i	$-0.193328\pi$
$983$	23.1226	+	13.3498i	0.737497	+	0.425794i	−0.0836616	+	0.996494i	$0.526661\pi$
$984$	−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	−0.998941	−	0.0460077i	$-0.985350\pi$
$997$	−14.5129	+	25.1370i	−0.459627	+	0.796097i	0.539314	+	0.842104i	$0.318683\pi$
$998$	−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.1011.12		32
7.2	even	3	inner	1078.2.i.d.901.1		32
7.3	odd	6		1078.2.c.c.1077.13	yes	16
7.4	even	3		1078.2.c.c.1077.12	yes	16
7.5	odd	6	inner	1078.2.i.d.901.2		32
7.6	odd	2	inner	1078.2.i.d.1011.11		32
11.10	odd	2	inner	1078.2.i.d.1011.2		32
77.10	even	6		1078.2.c.c.1077.5	yes	16
77.32	odd	6		1078.2.c.c.1077.4	✓	16
77.54	even	6	inner	1078.2.i.d.901.12		32
77.65	odd	6	inner	1078.2.i.d.901.11		32
77.76	even	2	inner	1078.2.i.d.1011.1		32

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

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

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Database

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