LMFDB - Embedded newform 1078.2.i.a.1011.1

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1011.1
Root			$0.608761 - 0.793353i$ of defining polynomial
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.a.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-2.26303 - 1.30656i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.26303 + 1.30656i) q^{5} +2.61313 q^{6} +1.00000i q^{8} +(1.91421 + 3.31552i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.26303 - 1.30656i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.26303 + 1.30656i) q^{5} +2.61313 q^{6} +1.00000i q^{8} +(1.91421 + 3.31552i) q^{9} +(1.30656 - 2.26303i) q^{10} +(-3.30518 - 0.275255i) q^{11} +(-2.26303 + 1.30656i) q^{12} -5.54328 q^{13} +6.82843 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.31552 - 1.91421i) q^{18} +(1.14805 + 1.98848i) q^{19} +2.61313i q^{20} +(3.00000 - 1.41421i) q^{22} +(1.12132 + 1.94218i) q^{23} +(1.30656 - 2.26303i) q^{24} +(0.914214 - 1.58346i) q^{25} +(4.80062 - 2.77164i) q^{26} -2.16478i q^{27} +10.2426i q^{29} +(-5.91359 + 3.41421i) q^{30} +(-6.12627 - 3.53701i) q^{31} +(0.866025 + 0.500000i) q^{32} +(7.12010 + 4.94134i) q^{33} +3.82843 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-1.98848 - 1.14805i) q^{38} +(12.5446 + 7.24264i) q^{39} +(-1.30656 - 2.26303i) q^{40} -11.0866 q^{41} -4.24264i q^{43} +(-1.89097 + 2.72474i) q^{44} +(-8.66386 - 5.00208i) q^{45} +(-1.94218 - 1.12132i) q^{46} +(5.73800 - 3.31283i) q^{47} +2.61313i q^{48} +1.82843i q^{50} +(-2.77164 + 4.80062i) q^{52} +(6.24264 - 10.8126i) q^{53} +(1.08239 + 1.87476i) q^{54} +(7.83938 - 3.69552i) q^{55} -6.00000i q^{57} +(-5.12132 - 8.87039i) q^{58} +(10.5386 + 6.08447i) q^{59} +(3.41421 - 5.91359i) q^{60} +(1.14805 + 1.98848i) q^{61} +7.07401 q^{62} -1.00000 q^{64} +(12.5446 - 7.24264i) q^{65} +(-8.63686 - 0.719276i) q^{66} +(-0.171573 + 0.297173i) q^{67} -5.86030i q^{69} +2.00000 q^{71} +(-3.31552 + 1.91421i) q^{72} +(3.24718 - 5.62427i) q^{73} +(5.19615 + 3.00000i) q^{74} +(-4.13779 + 2.38896i) q^{75} +2.29610 q^{76} -14.4853 q^{78} +(7.34847 - 4.24264i) q^{79} +(2.26303 + 1.30656i) q^{80} +(2.91421 - 5.04757i) q^{81} +(9.60124 - 5.54328i) q^{82} +0.951076 q^{83} +(2.12132 + 3.67423i) q^{86} +(13.3827 - 23.1794i) q^{87} +(0.275255 - 3.30518i) q^{88} +(10.6523 - 6.15013i) q^{89} +10.0042 q^{90} +2.24264 q^{92} +(9.24264 + 16.0087i) q^{93} +(-3.31283 + 5.73800i) q^{94} +(-5.19615 - 3.00000i) q^{95} +(-1.30656 - 2.26303i) q^{96} -5.09494i q^{97} +(-5.41421 - 11.4853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 8 * q^9	$ 16 q + 8 q^{4} + 8 q^{9} + 64 q^{15} - 8 q^{16} + 48 q^{22} - 16 q^{23} - 8 q^{25} + 16 q^{36} - 48 q^{37} + 32 q^{53} - 48 q^{58} + 32 q^{60} - 16 q^{64} - 48 q^{67} + 32 q^{71} - 96 q^{78} + 24 q^{81} + 24 q^{88} - 32 q^{92} + 80 q^{93} - 64 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 8 * q^9 + 64 * q^15 - 8 * q^16 + 48 * q^22 - 16 * q^23 - 8 * q^25 + 16 * q^36 - 48 * q^37 + 32 * q^53 - 48 * q^58 + 32 * q^60 - 16 * q^64 - 48 * q^67 + 32 * q^71 - 96 * q^78 + 24 * q^81 + 24 * q^88 - 32 * q^92 + 80 * q^93 - 64 * 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
$3$	−2.26303	−	1.30656i	−1.30656	−	0.754344i	−0.325042	−	0.945700i	$-0.605378\pi$
$3$	−2.26303	−	1.30656i	−1.30656	−	0.754344i	−0.981521	+	0.191355i	$0.938712\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.26303	+	1.30656i	−1.01206	+	0.584313i	−0.911794	−	0.410648i	$-0.865303\pi$
$5$	−2.26303	+	1.30656i	−1.01206	+	0.584313i	−0.100265	+	0.994961i	$0.531969\pi$
$6$	2.61313			1.06680
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.91421	+	3.31552i	0.638071	+	1.10517i
$10$	1.30656	−	2.26303i	0.413171	−	0.715634i
$11$	−3.30518	−	0.275255i	−0.996550	−	0.0829925i
$11$	−3.30518	−	0.275255i	−0.996550	−	0.0829925i
$12$	−2.26303	+	1.30656i	−0.653281	+	0.377172i
$13$	−5.54328			−1.53743			−0.768714	−	0.639592i	$-0.779103\pi$
$13$	−5.54328			−1.53743			−0.768714	+	0.639592i	$0.779103\pi$
$14$		0			0
$15$	6.82843			1.76309
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−3.31552	−	1.91421i	−0.781474	−	0.451184i
$19$	1.14805	+	1.98848i	0.263381	+	0.456189i	0.967138	−	0.254252i	$-0.0818291\pi$
$19$	1.14805	+	1.98848i	0.263381	+	0.456189i	−0.703757	+	0.710440i	$0.748496\pi$
$20$			2.61313i			0.584313i
$21$		0			0
$22$	3.00000	−	1.41421i	0.639602	−	0.301511i
$23$	1.12132	+	1.94218i	0.233811	+	0.404973i	0.958927	−	0.283654i	$-0.0915468\pi$
$23$	1.12132	+	1.94218i	0.233811	+	0.404973i	−0.725115	+	0.688628i	$0.758213\pi$
$24$	1.30656	−	2.26303i	0.266701	−	0.461940i
$25$	0.914214	−	1.58346i	0.182843	−	0.316693i
$26$	4.80062	−	2.77164i	0.941479	−	0.543563i
$27$		−	2.16478i		−	0.416613i
$28$		0			0
$29$			10.2426i			1.90201i	0.309175	+	0.951005i	$0.399947\pi$
$29$			10.2426i			1.90201i	−0.309175	+	0.951005i	$0.600053\pi$
$30$	−5.91359	+	3.41421i	−1.07967	+	0.623347i
$31$	−6.12627	−	3.53701i	−1.10031	−	0.635265i	−0.164008	−	0.986459i	$-0.552442\pi$
$31$	−6.12627	−	3.53701i	−1.10031	−	0.635265i	−0.936303	+	0.351194i	$0.885776\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	7.12010	+	4.94134i	1.23945	+	0.860177i
$34$		0			0
$35$		0			0
$36$	3.82843			0.638071
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$	−1.98848	−	1.14805i	−0.322574	−	0.186238i
$39$	12.5446	+	7.24264i	2.00875	+	1.15975i
$40$	−1.30656	−	2.26303i	−0.206586	−	0.357817i
$41$	−11.0866			−1.73143			−0.865714	−	0.500538i	$-0.833135\pi$
$41$	−11.0866			−1.73143			−0.865714	+	0.500538i	$0.833135\pi$
$42$		0			0
$43$		−	4.24264i		−	0.646997i	−0.946229	−	0.323498i	$-0.895141\pi$
$43$		−	4.24264i		−	0.646997i	0.946229	−	0.323498i	$-0.104859\pi$
$44$	−1.89097	+	2.72474i	−0.285074	+	0.410771i
$45$	−8.66386	−	5.00208i	−1.29153	−	0.745666i
$46$	−1.94218	−	1.12132i	−0.286359	−	0.165330i
$47$	5.73800	−	3.31283i	0.836973	−	0.483227i	−0.0192611	−	0.999814i	$-0.506131\pi$
$47$	5.73800	−	3.31283i	0.836973	−	0.483227i	0.856234	+	0.516588i	$0.172798\pi$
$48$			2.61313i			0.377172i
$49$		0			0
$50$			1.82843i			0.258579i
$51$		0			0
$52$	−2.77164	+	4.80062i	−0.384357	+	0.665726i
$53$	6.24264	−	10.8126i	0.857493	−	1.48522i	−0.0168205	−	0.999859i	$-0.505354\pi$
$53$	6.24264	−	10.8126i	0.857493	−	1.48522i	0.874313	−	0.485362i	$-0.161312\pi$
$54$	1.08239	+	1.87476i	0.147295	+	0.255122i
$55$	7.83938	−	3.69552i	1.05706	−	0.498304i
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$	−5.12132	−	8.87039i	−0.672462	−	1.16474i
$59$	10.5386	+	6.08447i	1.37201	+	0.792131i	0.991181	−	0.132514i	$-0.0423050\pi$
$59$	10.5386	+	6.08447i	1.37201	+	0.792131i	0.380830	+	0.924645i	$0.375638\pi$
$60$	3.41421	−	5.91359i	0.440773	−	0.763441i
$61$	1.14805	+	1.98848i	0.146993	+	0.254599i	0.930115	−	0.367269i	$-0.119707\pi$
$61$	1.14805	+	1.98848i	0.146993	+	0.254599i	−0.783122	+	0.621868i	$0.786374\pi$
$62$	7.07401			0.898400
$63$		0			0
$64$	−1.00000			−0.125000
$65$	12.5446	−	7.24264i	1.55597	−	0.898339i
$66$	−8.63686	−	0.719276i	−1.06312	−	0.0885368i
$67$	−0.171573	+	0.297173i	−0.0209610	+	0.0363055i	−0.876316	−	0.481737i	$-0.840006\pi$
$67$	−0.171573	+	0.297173i	−0.0209610	+	0.0363055i	0.855355	+	0.518043i	$0.173339\pi$
$68$		0			0
$69$		−	5.86030i		−	0.705498i
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−3.31552	+	1.91421i	−0.390737	+	0.225592i
$73$	3.24718	−	5.62427i	0.380053	−	0.658272i	−0.611016	−	0.791618i	$-0.709239\pi$
$73$	3.24718	−	5.62427i	0.380053	−	0.658272i	0.991069	+	0.133347i	$0.0425723\pi$
$74$	5.19615	+	3.00000i	0.604040	+	0.348743i
$75$	−4.13779	+	2.38896i	−0.477791	+	0.275853i
$76$	2.29610			0.263381
$77$		0			0
$78$	−14.4853			−1.64014
$79$	7.34847	−	4.24264i	0.826767	−	0.477334i	−0.0259772	−	0.999663i	$-0.508270\pi$
$79$	7.34847	−	4.24264i	0.826767	−	0.477334i	0.852745	+	0.522328i	$0.174936\pi$
$80$	2.26303	+	1.30656i	0.253015	+	0.146078i
$81$	2.91421	−	5.04757i	0.323802	−	0.560841i
$82$	9.60124	−	5.54328i	1.06028	−	0.612153i
$83$	0.951076			0.104394			0.0521971	−	0.998637i	$-0.483378\pi$
$83$	0.951076			0.104394			0.0521971	+	0.998637i	$0.483378\pi$
$84$		0			0
$85$		0			0
$86$	2.12132	+	3.67423i	0.228748	+	0.396203i
$87$	13.3827	−	23.1794i	1.43477	−	2.48510i
$88$	0.275255	−	3.30518i	0.0293423	−	0.352334i
$89$	10.6523	−	6.15013i	1.12915	−	0.651913i	0.185426	−	0.982658i	$-0.440634\pi$
$89$	10.6523	−	6.15013i	1.12915	−	0.651913i	0.943720	+	0.330746i	$0.107300\pi$
$90$	10.0042			1.05453
$91$		0			0
$92$	2.24264			0.233811
$93$	9.24264	+	16.0087i	0.958417	+	1.66003i
$94$	−3.31283	+	5.73800i	−0.341693	+	0.591829i
$95$	−5.19615	−	3.00000i	−0.533114	−	0.307794i
$96$	−1.30656	−	2.26303i	−0.133351	−	0.230970i
$97$		−	5.09494i		−	0.517312i	−0.965969	−	0.258656i	$-0.916720\pi$
$97$		−	5.09494i		−	0.517312i	0.965969	−	0.258656i	$-0.0832797\pi$
$98$		0			0
$99$	−5.41421	−	11.4853i	−0.544149	−	1.15431i
$100$	−0.914214	−	1.58346i	−0.0914214	−	0.158346i
$101$	−3.44415	+	5.96544i	−0.342706	+	0.593584i	−0.984934	−	0.172929i	$-0.944677\pi$
$101$	−3.44415	+	5.96544i	−0.342706	+	0.593584i	0.642228	+	0.766513i	$0.278010\pi$
$102$		0			0
$103$	8.93841	−	5.16059i	0.880728	−	0.508488i	0.00982947	−	0.999952i	$-0.496871\pi$
$103$	8.93841	−	5.16059i	0.880728	−	0.508488i	0.870898	+	0.491463i	$0.163538\pi$
$104$		−	5.54328i		−	0.543563i
$105$		0			0
$106$			12.4853i			1.21268i
$107$	−11.0227	+	6.36396i	−1.06561	+	0.615227i	−0.926977	−	0.375117i	$-0.877602\pi$
$107$	−11.0227	+	6.36396i	−1.06561	+	0.615227i	−0.138628	+	0.990345i	$0.544269\pi$
$108$	−1.87476	−	1.08239i	−0.180399	−	0.104153i
$109$	−17.7408	−	10.2426i	−1.69926	−	0.981067i	−0.946463	−	0.322812i	$-0.895372\pi$
$109$	−17.7408	−	10.2426i	−1.69926	−	0.981067i	−0.752795	−	0.658255i	$-0.771295\pi$
$110$	−4.94134	+	7.12010i	−0.471138	+	0.678875i
$111$			15.6788i			1.48816i
$112$		0			0
$113$	1.41421			0.133038			0.0665190	−	0.997785i	$-0.478811\pi$
$113$	1.41421			0.133038			0.0665190	+	0.997785i	$0.478811\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	−5.07517	−	2.93015i	−0.473262	−	0.273238i
$116$	8.87039	+	5.12132i	0.823595	+	0.475503i
$117$	−10.6110	−	18.3788i	−0.980989	−	1.69912i
$118$	−12.1689			−1.12024
$119$		0			0
$120$			6.82843i			0.623347i
$121$	10.8485	+	1.81954i	0.986224	+	0.165412i
$122$	−1.98848	−	1.14805i	−0.180029	−	0.103940i
$123$	25.0892	+	14.4853i	2.26222	+	1.30609i
$124$	−6.12627	+	3.53701i	−0.550156	+	0.317632i
$125$		−	8.28772i		−	0.741276i
$126$		0			0
$127$		−	6.00000i		−	0.532414i	−0.963916	−	0.266207i	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−5.54328	+	9.60124i	−0.488058	+	0.845342i
$130$	−7.24264	+	12.5446i	−0.635222	+	1.10024i
$131$	8.31492	+	14.4019i	0.726478	+	1.25830i	0.958363	+	0.285553i	$0.0921772\pi$
$131$	8.31492	+	14.4019i	0.726478	+	1.25830i	−0.231885	+	0.972743i	$0.574489\pi$
$132$	7.83938	−	3.69552i	0.682330	−	0.321654i
$133$		0			0
$134$		−	0.343146i		−	0.0296433i
$135$	2.82843	+	4.89898i	0.243432	+	0.421637i
$136$		0			0
$137$	−8.48528	+	14.6969i	−0.724947	+	1.25564i	0.234050	+	0.972225i	$0.424802\pi$
$137$	−8.48528	+	14.6969i	−0.724947	+	1.25564i	−0.958996	+	0.283420i	$0.908531\pi$
$138$	2.93015	+	5.07517i	0.249431	+	0.432027i
$139$	0.951076			0.0806692			0.0403346	−	0.999186i	$-0.487158\pi$
$139$	0.951076			0.0806692			0.0403346	+	0.999186i	$0.487158\pi$
$140$		0			0
$141$	−17.3137			−1.45808
$142$	−1.73205	+	1.00000i	−0.145350	+	0.0839181i
$143$	18.3215	+	1.52582i	1.53212	+	0.127595i
$144$	1.91421	−	3.31552i	0.159518	−	0.276293i
$145$	−13.3827	−	23.1794i	−1.11137	−	1.92495i
$146$			6.49435i			0.537476i
$147$		0			0
$148$	−6.00000			−0.493197
$149$	−16.2189	+	9.36396i	−1.32870	+	0.767126i	−0.985099	−	0.171990i	$-0.944980\pi$
$149$	−16.2189	+	9.36396i	−1.32870	+	0.767126i	−0.343602	+	0.939115i	$0.611647\pi$
$150$	2.38896	−	4.13779i	0.195057	−	0.337849i
$151$	5.19615	+	3.00000i	0.422857	+	0.244137i	0.696299	−	0.717752i	$-0.254829\pi$
$151$	5.19615	+	3.00000i	0.422857	+	0.244137i	−0.273442	+	0.961888i	$0.588162\pi$
$152$	−1.98848	+	1.14805i	−0.161287	+	0.0931192i
$153$		0			0
$154$		0			0
$155$	18.4853			1.48477
$156$	12.5446	−	7.24264i	1.00437	−	0.579875i
$157$	−1.48648	−	0.858221i	−0.118634	−	0.0684935i	0.439509	−	0.898238i	$-0.355153\pi$
$157$	−1.48648	−	0.858221i	−0.118634	−	0.0684935i	−0.558143	+	0.829745i	$0.688486\pi$
$158$	−4.24264	+	7.34847i	−0.337526	+	0.584613i
$159$	−28.2546	+	16.3128i	−2.24074	+	1.29369i
$160$	−2.61313			−0.206586
$161$		0			0
$162$			5.82843i			0.457924i
$163$	−10.0711	−	17.4436i	−0.788827	−	1.36629i	−0.926686	−	0.375836i	$-0.877355\pi$
$163$	−10.0711	−	17.4436i	−0.788827	−	1.36629i	0.137859	−	0.990452i	$-0.455978\pi$
$164$	−5.54328	+	9.60124i	−0.432857	+	0.749731i
$165$	−22.5692	−	1.87956i	−1.75701	−	0.146324i
$166$	−0.823656	+	0.475538i	−0.0639281	+	0.0369089i
$167$	17.5809			1.36045			0.680226	−	0.733003i	$-0.261882\pi$
$167$	17.5809			1.36045			0.680226	+	0.733003i	$0.261882\pi$
$168$		0			0
$169$	17.7279			1.36369
$170$		0			0
$171$	−4.39523	+	7.61276i	−0.336111	+	0.582162i
$172$	−3.67423	−	2.12132i	−0.280158	−	0.161749i
$173$	−7.64240	−	13.2370i	−0.581041	−	1.00639i	−0.995356	−	0.0962593i	$-0.969312\pi$
$173$	−7.64240	−	13.2370i	−0.581041	−	1.00639i	0.414315	−	0.910134i	$-0.364021\pi$
$174$			26.7653i			2.02907i
$175$		0			0
$176$	1.41421	+	3.00000i	0.106600	+	0.226134i
$177$	−15.8995	−	27.5387i	−1.19508	−	2.06994i
$178$	−6.15013	+	10.6523i	−0.460972	+	0.798427i
$179$	−2.82843	+	4.89898i	−0.211407	+	0.366167i	−0.952155	−	0.305616i	$-0.901138\pi$
$179$	−2.82843	+	4.89898i	−0.211407	+	0.366167i	0.740748	+	0.671783i	$0.234471\pi$
$180$	−8.66386	+	5.00208i	−0.645766	+	0.372833i
$181$			2.35049i			0.174711i	0.996177	+	0.0873554i	$0.0278416\pi$
$181$			2.35049i			0.174711i	−0.996177	+	0.0873554i	$0.972158\pi$
$182$		0			0
$183$		−	6.00000i		−	0.443533i
$184$	−1.94218	+	1.12132i	−0.143180	+	0.0826648i
$185$	13.5782	+	7.83938i	0.998289	+	0.576363i
$186$	−16.0087	−	9.24264i	−1.17382	−	0.677703i
$187$		0			0
$188$		−	6.62567i		−	0.483227i
$189$		0			0
$190$	6.00000			0.435286
$191$	5.12132	+	8.87039i	0.370566	+	0.641839i	0.989653	−	0.143484i	$-0.0458305\pi$
$191$	5.12132	+	8.87039i	0.370566	+	0.641839i	−0.619087	+	0.785322i	$0.712497\pi$
$192$	2.26303	+	1.30656i	0.163320	+	0.0942931i
$193$	12.5446	+	7.24264i	0.902982	+	0.521337i	0.878166	−	0.478355i	$-0.158767\pi$
$193$	12.5446	+	7.24264i	0.902982	+	0.521337i	0.0248153	+	0.999692i	$0.492100\pi$
$194$	2.54747	+	4.41234i	0.182898	+	0.316788i
$195$	−37.8519			−2.71063
$196$		0			0
$197$			3.51472i			0.250413i	0.992131	+	0.125207i	$0.0399594\pi$
$197$			3.51472i			0.250413i	−0.992131	+	0.125207i	$0.960041\pi$
$198$	10.4315	+	7.23944i	0.741334	+	0.514485i
$199$	16.3432	+	9.43577i	1.15854	+	0.668884i	0.950954	−	0.309333i	$-0.100106\pi$
$199$	16.3432	+	9.43577i	1.15854	+	0.668884i	0.207587	+	0.978217i	$0.433439\pi$
$200$	1.58346	+	0.914214i	0.111968	+	0.0646447i
$201$	0.776550	−	0.448342i	0.0547736	−	0.0316236i
$202$		−	6.88830i		−	0.484659i
$203$		0			0
$204$		0			0
$205$	25.0892	−	14.4853i	1.75231	−	1.01170i
$206$	−5.16059	+	8.93841i	−0.359556	+	0.622769i
$207$	−4.29289	+	7.43551i	−0.298377	+	0.516804i
$208$	2.77164	+	4.80062i	0.192179	+	0.332863i
$209$	−3.24718	−	6.88830i	−0.224612	−	0.476474i
$210$		0			0
$211$			0.727922i			0.0501122i	0.999686	+	0.0250561i	$0.00797644\pi$
$211$			0.727922i			0.0501122i	−0.999686	+	0.0250561i	$0.992024\pi$
$212$	−6.24264	−	10.8126i	−0.428746	−	0.742610i
$213$	−4.52607	−	2.61313i	−0.310121	−	0.179048i
$214$	6.36396	−	11.0227i	0.435031	−	0.753497i
$215$	5.54328	+	9.60124i	0.378048	+	0.654799i
$216$	2.16478			0.147295
$217$		0			0
$218$	20.4853			1.38744
$219$	−14.6969	+	8.48528i	−0.993127	+	0.573382i
$220$	0.719276	−	8.63686i	0.0484936	−	0.582297i
$221$		0			0
$222$	−7.83938	−	13.5782i	−0.526145	−	0.911309i
$223$			22.7528i			1.52364i	0.647790	+	0.761819i	$0.275693\pi$
$223$			22.7528i			1.52364i	−0.647790	+	0.761819i	$0.724307\pi$
$224$		0			0
$225$	7.00000			0.466667
$226$	−1.22474	+	0.707107i	−0.0814688	+	0.0470360i
$227$	6.69133	−	11.5897i	0.444119	−	0.769237i	−0.553871	−	0.832602i	$-0.686850\pi$
$227$	6.69133	−	11.5897i	0.444119	−	0.769237i	0.997990	+	0.0633656i	$0.0201834\pi$
$228$	−5.19615	−	3.00000i	−0.344124	−	0.198680i
$229$	8.34220	−	4.81637i	0.551268	−	0.318275i	−0.198365	−	0.980128i	$-0.563563\pi$
$229$	8.34220	−	4.81637i	0.551268	−	0.318275i	0.749633	+	0.661853i	$0.230230\pi$
$230$	5.86030			0.386417
$231$		0			0
$232$	−10.2426			−0.672462
$233$	7.34847	−	4.24264i	0.481414	−	0.277945i	−0.239591	−	0.970874i	$-0.577013\pi$
$233$	7.34847	−	4.24264i	0.481414	−	0.277945i	0.721006	+	0.692929i	$0.243680\pi$
$234$	18.3788	+	10.6110i	1.20146	+	0.693664i
$235$	−8.65685	+	14.9941i	−0.564711	+	0.978108i
$236$	10.5386	−	6.08447i	0.686006	−	0.396065i
$237$	−22.1731			−1.44030
$238$		0			0
$239$			9.51472i			0.615456i	0.951474	+	0.307728i	$0.0995687\pi$
$239$			9.51472i			0.615456i	−0.951474	+	0.307728i	$0.900431\pi$
$240$	−3.41421	−	5.91359i	−0.220387	−	0.381721i
$241$	−5.54328	+	9.60124i	−0.357074	+	0.618470i	−0.987471	−	0.157803i	$-0.949559\pi$
$241$	−5.54328	+	9.60124i	−0.357074	+	0.618470i	0.630397	+	0.776273i	$0.282892\pi$
$242$	−10.3048	+	3.84847i	−0.662419	+	0.247389i
$243$	−18.8142	+	10.8624i	−1.20693	+	0.696822i
$244$	2.29610			0.146993
$245$		0			0
$246$	−28.9706			−1.84710
$247$	−6.36396	−	11.0227i	−0.404929	−	0.701358i
$248$	3.53701	−	6.12627i	0.224600	−	0.389019i
$249$	−2.15232	−	1.24264i	−0.136398	−	0.0787492i
$250$	4.14386	+	7.17738i	0.262081	+	0.453937i
$251$		−	7.20533i		−	0.454796i	−0.973802	−	0.227398i	$-0.926978\pi$
$251$		−	7.20533i		−	0.454796i	0.973802	−	0.227398i	$-0.0730219\pi$
$252$		0			0
$253$	−3.17157	−	6.72792i	−0.199395	−	0.422981i
$254$	3.00000	+	5.19615i	0.188237	+	0.326036i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−17.2806	+	9.97697i	−1.07793	+	0.622346i	−0.930339	−	0.366702i	$-0.880487\pi$
$257$	−17.2806	+	9.97697i	−1.07793	+	0.622346i	−0.147596	+	0.989048i	$0.547154\pi$
$258$		−	11.0866i		−	0.690219i
$259$		0			0
$260$		−	14.4853i		−	0.898339i
$261$	−33.9596	+	19.6066i	−2.10205	+	1.21362i
$262$	−14.4019	−	8.31492i	−0.889750	−	0.513697i
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.304487	−	0.952517i	$-0.598485\pi$
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.977147	+	0.212565i	$0.931818\pi$
$264$	−4.94134	+	7.12010i	−0.304119	+	0.438212i
$265$			32.6256i			2.00418i
$266$		0			0
$267$	−32.1421			−1.96707
$268$	0.171573	+	0.297173i	0.0104805	+	0.0181527i
$269$	11.8643	+	6.84984i	0.723377	+	0.417642i	0.815994	−	0.578060i	$-0.196190\pi$
$269$	11.8643	+	6.84984i	0.723377	+	0.417642i	−0.0926171	+	0.995702i	$0.529523\pi$
$270$	−4.89898	−	2.82843i	−0.298142	−	0.172133i
$271$	0.951076	+	1.64731i	0.0577738	+	0.100067i	0.893466	−	0.449131i	$-0.148266\pi$
$271$	0.951076	+	1.64731i	0.0577738	+	0.100067i	−0.835692	+	0.549198i	$0.814933\pi$
$272$		0			0
$273$		0			0
$274$		−	16.9706i		−	1.02523i
$275$	−3.45750	+	4.98200i	−0.208495	+	0.300426i
$276$	−5.07517	−	2.93015i	−0.305489	−	0.176374i
$277$	−5.82655	−	3.36396i	−0.350084	−	0.202121i	0.314639	−	0.949212i	$-0.398117\pi$
$277$	−5.82655	−	3.36396i	−0.350084	−	0.202121i	−0.664722	+	0.747091i	$0.731450\pi$
$278$	−0.823656	+	0.475538i	−0.0493996	+	0.0285209i
$279$		−	27.0823i		−	1.62138i
$280$		0			0
$281$		−	12.0000i		−	0.715860i	−0.933748	−	0.357930i	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$	14.9941	−	8.65685i	0.892886	−	0.515508i
$283$	−11.5621	+	20.0261i	−0.687295	+	1.19043i	0.285415	+	0.958404i	$0.407869\pi$
$283$	−11.5621	+	20.0261i	−0.687295	+	1.19043i	−0.972710	+	0.232026i	$0.925465\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$	7.83938	+	13.5782i	0.464365	+	0.804303i
$286$	−16.6298	+	7.83938i	−0.983343	+	0.463552i
$287$		0			0
$288$			3.82843i			0.225592i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	23.1794	+	13.3827i	1.36114	+	0.785857i
$291$	−6.65685	+	11.5300i	−0.390232	+	0.675901i
$292$	−3.24718	−	5.62427i	−0.190027	−	0.329136i
$293$	13.3827			0.781823			0.390912	−	0.920428i	$-0.372160\pi$
$293$	13.3827			0.781823			0.390912	+	0.920428i	$0.372160\pi$
$294$		0			0
$295$	−31.7990			−1.85141
$296$	5.19615	−	3.00000i	0.302020	−	0.174371i
$297$	−0.595868	+	7.15501i	−0.0345758	+	0.415176i
$298$	9.36396	−	16.2189i	0.542440	−	0.939533i
$299$	−6.21579	−	10.7661i	−0.359468	−	0.622618i
$300$			4.77791i			0.275853i
$301$		0			0
$302$	−6.00000			−0.345261
$303$	15.5885	−	9.00000i	0.895533	−	0.517036i
$304$	1.14805	−	1.98848i	0.0658452	−	0.114047i
$305$	−5.19615	−	3.00000i	−0.297531	−	0.171780i
$306$		0			0
$307$	29.0614			1.65862			0.829311	−	0.558787i	$-0.188733\pi$
$307$	29.0614			1.65862			0.829311	+	0.558787i	$0.188733\pi$
$308$		0			0
$309$	−26.9706			−1.53430
$310$	−16.0087	+	9.24264i	−0.909234	+	0.524947i
$311$	−2.60420	−	1.50354i	−0.147671	−	0.0852578i	0.424344	−	0.905501i	$-0.360505\pi$
$311$	−2.60420	−	1.50354i	−0.147671	−	0.0852578i	−0.572015	+	0.820243i	$0.693838\pi$
$312$	−7.24264	+	12.5446i	−0.410034	+	0.710199i
$313$	5.57717	−	3.21998i	0.315240	−	0.182004i	−0.334029	−	0.942563i	$-0.608408\pi$
$313$	5.57717	−	3.21998i	0.315240	−	0.182004i	0.649269	+	0.760559i	$0.275075\pi$
$314$	1.71644			0.0968645
$315$		0			0
$316$		−	8.48528i		−	0.477334i
$317$	−5.48528	−	9.50079i	−0.308084	−	0.533617i	0.669859	−	0.742488i	$-0.266354\pi$
$317$	−5.48528	−	9.50079i	−0.308084	−	0.533617i	−0.977943	+	0.208871i	$0.933021\pi$
$318$	16.3128	−	28.2546i	0.914777	−	1.58444i
$319$	2.81934	−	33.8538i	0.157853	−	1.89545i
$320$	2.26303	−	1.30656i	0.126507	−	0.0730391i
$321$	33.2597			1.85637
$322$		0			0
$323$		0			0
$324$	−2.91421	−	5.04757i	−0.161901	−	0.280420i
$325$	−5.06774	+	8.77758i	−0.281108	+	0.486893i
$326$	17.4436	+	10.0711i	0.966112	+	0.557785i
$327$	26.7653	+	46.3589i	1.48013	+	2.56365i
$328$		−	11.0866i		−	0.612153i
$329$		0			0
$330$	20.4853	−	9.65685i	1.12768	−	0.531592i
$331$	−1.75736	−	3.04384i	−0.0965932	−	0.167304i	0.813679	−	0.581314i	$-0.197461\pi$
$331$	−1.75736	−	3.04384i	−0.0965932	−	0.167304i	−0.910272	+	0.414010i	$0.864128\pi$
$332$	0.475538	−	0.823656i	0.0260985	−	0.0452040i
$333$	11.4853	−	19.8931i	0.629390	−	1.09013i
$334$	−15.2255	+	8.79045i	−0.833103	+	0.480992i
$335$		−	0.896683i		−	0.0489910i
$336$		0			0
$337$		−	9.51472i		−	0.518300i	−0.965837	−	0.259150i	$-0.916558\pi$
$337$		−	9.51472i		−	0.518300i	0.965837	−	0.259150i	$-0.0834424\pi$
$338$	−15.3528	+	8.86396i	−0.835084	+	0.482136i
$339$	−3.20041	−	1.84776i	−0.173823	−	0.100356i
$340$		0			0
$341$	19.2749	+	13.3767i	1.04379	+	0.724391i
$342$		−	8.79045i		−	0.475333i
$343$		0			0
$344$	4.24264			0.228748
$345$	7.65685	+	13.2621i	0.412231	+	0.714005i
$346$	13.2370	+	7.64240i	0.711627	+	0.410858i
$347$	14.0665	+	8.12132i	0.755131	+	0.435975i	0.827545	−	0.561399i	$-0.189737\pi$
$347$	14.0665	+	8.12132i	0.755131	+	0.435975i	−0.0724136	+	0.997375i	$0.523070\pi$
$348$	−13.3827	−	23.1794i	−0.717386	−	1.24255i
$349$	−7.44543			−0.398545			−0.199272	−	0.979944i	$-0.563858\pi$
$349$	−7.44543			−0.398545			−0.199272	+	0.979944i	$0.563858\pi$
$350$		0			0
$351$			12.0000i			0.640513i
$352$	−2.72474	−	1.89097i	−0.145229	−	0.100789i
$353$	−7.06365	−	4.07820i	−0.375960	−	0.217061i	0.300099	−	0.953908i	$-0.402980\pi$
$353$	−7.06365	−	4.07820i	−0.375960	−	0.217061i	−0.676059	+	0.736847i	$0.736314\pi$
$354$	27.5387	+	15.8995i	1.46367	+	0.845049i
$355$	−4.52607	+	2.61313i	−0.240219	+	0.138690i
$356$		−	12.3003i		−	0.651913i
$357$		0			0
$358$		−	5.65685i		−	0.298974i
$359$	12.5446	−	7.24264i	0.662080	−	0.382252i	−0.130989	−	0.991384i	$-0.541815\pi$
$359$	12.5446	−	7.24264i	0.662080	−	0.382252i	0.793069	+	0.609132i	$0.208482\pi$
$360$	5.00208	−	8.66386i	0.263633	−	0.456625i
$361$	6.86396	−	11.8887i	0.361261	−	0.625723i
$362$	−1.17525	−	2.03559i	−0.0617696	−	0.106988i
$363$	−22.1731	−	18.2919i	−1.16379	−	0.960075i
$364$		0			0
$365$			16.9706i			0.888280i
$366$	3.00000	+	5.19615i	0.156813	+	0.271607i
$367$	−26.4936	−	15.2961i	−1.38295	−	0.798448i	−0.390445	−	0.920626i	$-0.627679\pi$
$367$	−26.4936	−	15.2961i	−1.38295	−	0.798448i	−0.992508	+	0.122178i	$0.961012\pi$
$368$	1.12132	−	1.94218i	0.0584529	−	0.101243i
$369$	−21.2220	−	36.7576i	−1.10477	−	1.91353i
$370$	−15.6788			−0.815100
$371$		0			0
$372$	18.4853			0.958417
$373$	−3.04384	+	1.75736i	−0.157604	+	0.0909926i	−0.576728	−	0.816936i	$-0.695671\pi$
$373$	−3.04384	+	1.75736i	−0.157604	+	0.0909926i	0.419124	+	0.907929i	$0.362337\pi$
$374$		0			0
$375$	−10.8284	+	18.7554i	−0.559178	+	0.968524i
$376$	3.31283	+	5.73800i	0.170846	+	0.295915i
$377$		−	56.7778i		−	2.92421i
$378$		0			0
$379$	−0.343146			−0.0176262			−0.00881311	−	0.999961i	$-0.502805\pi$
$379$	−0.343146			−0.0176262			−0.00881311	+	0.999961i	$0.502805\pi$
$380$	−5.19615	+	3.00000i	−0.266557	+	0.153897i
$381$	−7.83938	+	13.5782i	−0.401623	+	0.695632i
$382$	−8.87039	−	5.12132i	−0.453848	−	0.262030i
$383$	−1.43938	+	0.831025i	−0.0735488	+	0.0424634i	−0.536323	−	0.844013i	$-0.680187\pi$
$383$	−1.43938	+	0.831025i	−0.0735488	+	0.0424634i	0.462775	+	0.886476i	$0.346854\pi$
$384$	−2.61313			−0.133351
$385$		0			0
$386$	−14.4853			−0.737281
$387$	14.0665	−	8.12132i	0.715042	−	0.412830i
$388$	−4.41234	−	2.54747i	−0.224003	−	0.129328i
$389$	16.0000	−	27.7128i	0.811232	−	1.40510i	−0.100770	−	0.994910i	$-0.532131\pi$
$389$	16.0000	−	27.7128i	0.811232	−	1.40510i	0.912002	−	0.410186i	$-0.134536\pi$
$390$	32.7807	−	18.9259i	1.65991	−	0.958352i
$391$		0			0
$392$		0			0
$393$		−	43.4558i		−	2.19206i
$394$	−1.75736	−	3.04384i	−0.0885345	−	0.153346i
$395$	−11.0866	+	19.2025i	−0.557825	+	0.966181i
$396$	−12.6537	−	1.05379i	−0.635870	−	0.0529552i
$397$	−9.98951	+	5.76745i	−0.501359	+	0.289460i	−0.729275	−	0.684221i	$-0.760142\pi$
$397$	−9.98951	+	5.76745i	−0.501359	+	0.289460i	0.227915	+	0.973681i	$0.426809\pi$
$398$	−18.8715			−0.945945
$399$		0			0
$400$	−1.82843			−0.0914214
$401$	8.24264	+	14.2767i	0.411618	+	0.712943i	0.995067	−	0.0992068i	$-0.0316305\pi$
$401$	8.24264	+	14.2767i	0.411618	+	0.712943i	−0.583449	+	0.812150i	$0.698297\pi$
$402$	−0.448342	+	0.776550i	−0.0223612	+	0.0387308i
$403$	33.9596	+	19.6066i	1.69165	+	0.976674i
$404$	3.44415	+	5.96544i	0.171353	+	0.296792i
$405$			15.2304i			0.756805i
$406$		0			0
$407$	8.48528	+	18.0000i	0.420600	+	0.892227i
$408$		0			0
$409$	−1.34502	+	2.32965i	−0.0665072	+	0.115194i	−0.897362	−	0.441296i	$-0.854519\pi$
$409$	−1.34502	+	2.32965i	−0.0665072	+	0.115194i	0.830854	+	0.556490i	$0.187852\pi$
$410$	−14.4853	+	25.0892i	−0.715377	+	1.23907i
$411$	38.4050	−	22.1731i	1.89438	−	1.09372i
$412$		−	10.3212i		−	0.508488i
$413$		0			0
$414$		−	8.58579i		−	0.421968i
$415$	−2.15232	+	1.24264i	−0.105653	+	0.0609988i
$416$	−4.80062	−	2.77164i	−0.235370	−	0.135891i
$417$	−2.15232	−	1.24264i	−0.105399	−	0.0608524i
$418$	6.25629	+	4.34186i	0.306005	+	0.212367i
$419$			5.67459i			0.277222i	0.990347	+	0.138611i	$0.0442638\pi$
$419$			5.67459i			0.277222i	−0.990347	+	0.138611i	$0.955736\pi$
$420$		0			0
$421$	6.34315			0.309146			0.154573	−	0.987981i	$-0.450600\pi$
$421$	6.34315			0.309146			0.154573	+	0.987981i	$0.450600\pi$
$422$	−0.363961	−	0.630399i	−0.0177173	−	0.0306873i
$423$	21.9675	+	12.6829i	1.06810	+	0.616666i
$424$	10.8126	+	6.24264i	0.525105	+	0.303169i
$425$		0			0
$426$	5.22625			0.253213
$427$		0			0
$428$			12.7279i			0.615227i
$429$	−39.4687	−	27.3912i	−1.90557	−	1.32246i
$430$	−9.60124	−	5.54328i	−0.463013	−	0.267321i
$431$	−12.5446	−	7.24264i	−0.604253	−	0.348866i	0.166460	−	0.986048i	$-0.446766\pi$
$431$	−12.5446	−	7.24264i	−0.604253	−	0.348866i	−0.770713	+	0.637183i	$0.780100\pi$
$432$	−1.87476	+	1.08239i	−0.0901994	+	0.0520766i
$433$			28.8757i			1.38768i	0.720130	+	0.693839i	$0.244082\pi$
$433$			28.8757i			1.38768i	−0.720130	+	0.693839i	$0.755918\pi$
$434$		0			0
$435$			69.9411i			3.35342i
$436$	−17.7408	+	10.2426i	−0.849629	+	0.490534i
$437$	−2.57466	+	4.45945i	−0.123163	+	0.213324i
$438$	8.48528	−	14.6969i	0.405442	−	0.702247i
$439$	−7.83938	−	13.5782i	−0.374153	−	0.648052i	0.616047	−	0.787710i	$-0.288733\pi$
$439$	−7.83938	−	13.5782i	−0.374153	−	0.648052i	−0.990200	+	0.139657i	$0.955400\pi$
$440$	3.69552	+	7.83938i	0.176177	+	0.373728i
$441$		0			0
$442$		0			0
$443$	11.3137	+	19.5959i	0.537531	+	0.931030i	0.999036	+	0.0438929i	$0.0139760\pi$
$443$	11.3137	+	19.5959i	0.537531	+	0.931030i	−0.461506	+	0.887137i	$0.652691\pi$
$444$	13.5782	+	7.83938i	0.644393	+	0.372040i
$445$	−16.0711	+	27.8359i	−0.761842	+	1.31955i
$446$	−11.3764	−	19.7045i	−0.538687	−	0.933034i
$447$	48.9384			2.31471
$448$		0			0
$449$	−15.2721			−0.720734			−0.360367	−	0.932811i	$-0.617349\pi$
$449$	−15.2721			−0.720734			−0.360367	+	0.932811i	$0.617349\pi$
$450$	−6.06218	+	3.50000i	−0.285774	+	0.164992i
$451$	36.6431	+	3.05163i	1.72546	+	0.143696i
$452$	0.707107	−	1.22474i	0.0332595	−	0.0576072i
$453$	−7.83938	−	13.5782i	−0.368326	−	0.637960i
$454$			13.3827i			0.628079i
$455$		0			0
$456$	6.00000			0.280976
$457$	16.8493	−	9.72792i	0.788175	−	0.455053i	−0.0511447	−	0.998691i	$-0.516287\pi$
$457$	16.8493	−	9.72792i	0.788175	−	0.455053i	0.839320	+	0.543638i	$0.182954\pi$
$458$	−4.81637	+	8.34220i	−0.225054	+	0.389805i
$459$		0			0
$460$	−5.07517	+	2.93015i	−0.236631	+	0.136619i
$461$	−7.44543			−0.346768			−0.173384	−	0.984854i	$-0.555470\pi$
$461$	−7.44543			−0.346768			−0.173384	+	0.984854i	$0.555470\pi$
$462$		0			0
$463$	17.3137			0.804636			0.402318	−	0.915500i	$-0.368205\pi$
$463$	17.3137			0.804636			0.402318	+	0.915500i	$0.368205\pi$
$464$	8.87039	−	5.12132i	0.411797	−	0.237751i
$465$	−41.8328	−	24.1522i	−1.93995	−	1.12003i
$466$	−4.24264	+	7.34847i	−0.196537	+	0.340411i
$467$	−9.66786	+	5.58174i	−0.447375	+	0.258292i	−0.706721	−	0.707492i	$-0.749826\pi$
$467$	−9.66786	+	5.58174i	−0.447375	+	0.258292i	0.259346	+	0.965784i	$0.416493\pi$
$468$	−21.2220			−0.980989
$469$		0			0
$470$		−	17.3137i		−	0.798622i
$471$	2.24264	+	3.88437i	0.103335	+	0.178982i
$472$	−6.08447	+	10.5386i	−0.280061	+	0.485079i
$473$	−1.16781	+	14.0227i	−0.0536959	+	0.644765i
$474$	19.2025	−	11.0866i	0.881999	−	0.509222i
$475$	4.19825			0.192629
$476$		0			0
$477$	47.7990			2.18857
$478$	−4.75736	−	8.23999i	−0.217597	−	0.376888i
$479$	11.0866	−	19.2025i	0.506558	−	0.877383i	−0.493414	−	0.869795i	$-0.664251\pi$
$479$	11.0866	−	19.2025i	0.506558	−	0.877383i	0.999971	−	0.00758869i	$-0.00241558\pi$
$480$	5.91359	+	3.41421i	0.269917	+	0.155837i
$481$	16.6298	+	28.8037i	0.758255	+	1.31334i
$482$		−	11.0866i		−	0.504979i
$483$		0			0
$484$	7.00000	−	8.48528i	0.318182	−	0.385695i
$485$	6.65685	+	11.5300i	0.302272	+	0.523551i
$486$	10.8624	−	18.8142i	0.492728	−	0.853429i
$487$	16.7782	−	29.0607i	0.760292	−	1.31686i	−0.182409	−	0.983223i	$-0.558389\pi$
$487$	16.7782	−	29.0607i	0.760292	−	1.31686i	0.942700	−	0.333641i	$-0.108277\pi$
$488$	−1.98848	+	1.14805i	−0.0900143	+	0.0519698i
$489$			52.6339i			2.38019i
$490$		0			0
$491$			27.9411i			1.26097i	0.776203	+	0.630483i	$0.217143\pi$
$491$			27.9411i			1.26097i	−0.776203	+	0.630483i	$0.782857\pi$
$492$	25.0892	−	14.4853i	1.13111	−	0.653047i
$493$		0			0
$494$	11.0227	+	6.36396i	0.495935	+	0.286328i
$495$	27.2588	+	18.9176i	1.22519	+	0.850281i
$496$			7.07401i			0.317632i
$497$		0			0
$498$	2.48528			0.111368
$499$	8.31371	+	14.3998i	0.372173	+	0.644622i	0.989900	−	0.141771i	$-0.0452796\pi$
$499$	8.31371	+	14.3998i	0.372173	+	0.644622i	−0.617727	+	0.786393i	$0.711946\pi$
$500$	−7.17738	−	4.14386i	−0.320982	−	0.185319i
$501$	−39.7862	−	22.9706i	−1.77752	−	1.02625i
$502$	3.60266	+	6.24000i	0.160795	+	0.278505i
$503$	15.6788			0.699081			0.349541	−	0.936921i	$-0.386338\pi$
$503$	15.6788			0.699081			0.349541	+	0.936921i	$0.386338\pi$
$504$		0			0
$505$		−	18.0000i		−	0.800989i
$506$	6.11062	+	4.24076i	0.271650	+	0.188525i
$507$	−40.1189	−	23.1626i	−1.78174	−	1.02869i
$508$	−5.19615	−	3.00000i	−0.230542	−	0.133103i
$509$	8.98552	−	5.18779i	0.398276	−	0.229945i	−0.287464	−	0.957791i	$-0.592812\pi$
$509$	8.98552	−	5.18779i	0.398276	−	0.229945i	0.685740	+	0.727847i	$0.259479\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	4.30463	−	2.48528i	0.190054	−	0.109728i
$514$	9.97697	−	17.2806i	0.440065	−	0.762215i
$515$	−13.4853	+	23.3572i	−0.594232	+	1.02924i
$516$	5.54328	+	9.60124i	0.244029	+	0.422671i
$517$	−19.8770	+	9.37011i	−0.874190	+	0.412097i
$518$		0			0
$519$			39.9411i			1.75322i
$520$	7.24264	+	12.5446i	0.317611	+	0.550118i
$521$	−17.6689	−	10.2011i	−0.774088	−	0.446920i	0.0602430	−	0.998184i	$-0.480812\pi$
$521$	−17.6689	−	10.2011i	−0.774088	−	0.446920i	−0.834331	+	0.551264i	$0.814146\pi$
$522$	19.6066	−	33.9596i	0.858158	−	1.48637i
$523$	−6.69133	−	11.5897i	−0.292591	−	0.506783i	0.681830	−	0.731510i	$-0.261184\pi$
$523$	−6.69133	−	11.5897i	−0.292591	−	0.506783i	−0.974422	+	0.224727i	$0.927851\pi$
$524$	16.6298			0.726478
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$	0.719276	−	8.63686i	0.0313025	−	0.375871i
$529$	8.98528	−	15.5630i	0.390664	−	0.676651i
$530$	−16.3128	−	28.2546i	−0.708583	−	1.22730i
$531$			46.5879i			2.02174i
$532$		0			0
$533$	61.4558			2.66195
$534$	27.8359	−	16.0711i	1.20458	−	0.695463i
$535$	16.6298	−	28.8037i	0.718970	−	1.24529i
$536$	−0.297173	−	0.171573i	−0.0128359	−	0.00741082i
$537$	12.8017	−	7.39104i	0.552432	−	0.318947i
$538$	−13.6997			−0.590635
$539$		0			0
$540$	5.65685			0.243432
$541$	19.8931	−	11.4853i	0.855271	−	0.493791i	−0.00715497	−	0.999974i	$-0.502278\pi$
$541$	19.8931	−	11.4853i	0.855271	−	0.493791i	0.862426	+	0.506184i	$0.168944\pi$
$542$	−1.64731	−	0.951076i	−0.0707581	−	0.0408522i
$543$	3.07107	−	5.31925i	0.131792	−	0.228271i
$544$		0			0
$545$	53.5306			2.29300
$546$		0			0
$547$			24.0000i			1.02617i	0.858339	+	0.513083i	$0.171497\pi$
$547$			24.0000i			1.02617i	−0.858339	+	0.513083i	$0.828503\pi$
$548$	8.48528	+	14.6969i	0.362473	+	0.627822i
$549$	−4.39523	+	7.61276i	−0.187584	+	0.324905i
$550$	0.503284	−	6.04329i	0.0214601	−	0.257687i
$551$	−20.3673	+	11.7591i	−0.867676	+	0.500953i
$552$	5.86030			0.249431
$553$		0			0
$554$	6.72792			0.285842
$555$	−20.4853	−	35.4815i	−0.869552	−	1.50611i
$556$	0.475538	−	0.823656i	0.0201673	−	0.0349308i
$557$	5.19615	+	3.00000i	0.220168	+	0.127114i	0.606028	−	0.795443i	$-0.292762\pi$
$557$	5.19615	+	3.00000i	0.220168	+	0.127114i	−0.385860	+	0.922557i	$0.626095\pi$
$558$	13.5412	+	23.4540i	0.573243	+	0.992887i
$559$			23.5181i			0.994711i
$560$		0			0
$561$		0			0
$562$	6.00000	+	10.3923i	0.253095	+	0.438373i
$563$	17.1054	−	29.6274i	0.720905	−	1.24864i	−0.239732	−	0.970839i	$-0.577060\pi$
$563$	17.1054	−	29.6274i	0.720905	−	1.24864i	0.960637	−	0.277806i	$-0.0896071\pi$
$564$	−8.65685	+	14.9941i	−0.364519	+	0.631366i
$565$	−3.20041	+	1.84776i	−0.134642	+	0.0777358i
$566$		−	23.1242i		−	0.971982i
$567$		0			0
$568$			2.00000i			0.0839181i
$569$	−25.9808	+	15.0000i	−1.08917	+	0.628833i	−0.933355	−	0.358954i	$-0.883134\pi$
$569$	−25.9808	+	15.0000i	−1.08917	+	0.628833i	−0.155815	+	0.987786i	$0.549800\pi$
$570$	−13.5782	−	7.83938i	−0.568728	−	0.328355i
$571$	31.1769	+	18.0000i	1.30471	+	0.753277i	0.981209	−	0.192950i	$-0.0618055\pi$
$571$	31.1769	+	18.0000i	1.30471	+	0.753277i	0.323505	+	0.946227i	$0.395139\pi$
$572$	10.4822	−	15.1040i	0.438281	−	0.631531i
$573$		−	26.7653i		−	1.11814i
$574$		0			0
$575$	4.10051			0.171003
$576$	−1.91421	−	3.31552i	−0.0797589	−	0.138146i
$577$	−10.5857	−	6.11167i	−0.440689	−	0.254432i	0.263201	−	0.964741i	$-0.415222\pi$
$577$	−10.5857	−	6.11167i	−0.440689	−	0.254432i	−0.703890	+	0.710309i	$0.748555\pi$
$578$	−14.7224	−	8.50000i	−0.612372	−	0.353553i
$579$	−18.9259	−	32.7807i	−0.786535	−	1.36232i
$580$	−26.7653			−1.11137
$581$		0			0
$582$		−	13.3137i		−	0.551871i
$583$	−23.6093	+	34.0192i	−0.977797	+	1.40893i
$584$	5.62427	+	3.24718i	0.232734	+	0.134369i
$585$	48.0262	+	27.7279i	1.98564	+	1.14641i
$586$	−11.5897	+	6.69133i	−0.478767	+	0.276416i
$587$		−	21.4621i		−	0.885837i	−0.896562	−	0.442919i	$-0.853943\pi$
$587$		−	21.4621i		−	0.885837i	0.896562	−	0.442919i	$-0.146057\pi$
$588$		0			0
$589$		−	16.2426i		−	0.669266i
$590$	27.5387	−	15.8995i	1.13375	−	0.654572i
$591$	4.59220	−	7.95393i	0.188898	−	0.327181i
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	12.4316	+	21.5321i	0.510504	+	0.884218i	0.999926	+	0.0121715i	$0.00387439\pi$
$593$	12.4316	+	21.5321i	0.510504	+	0.884218i	−0.489422	+	0.872047i	$0.662792\pi$
$594$	−3.06147	−	6.49435i	−0.125614	−	0.266467i
$595$		0			0
$596$			18.7279i			0.767126i
$597$	−24.6569	−	42.7069i	−1.00914	−	1.74788i
$598$	10.7661	+	6.21579i	0.440257	+	0.254183i
$599$	13.0000	−	22.5167i	0.531166	−	0.920006i	−0.468173	−	0.883637i	$-0.655088\pi$
$599$	13.0000	−	22.5167i	0.531166	−	0.920006i	0.999338	−	0.0363689i	$-0.0115791\pi$
$600$	−2.38896	−	4.13779i	−0.0975287	−	0.168925i
$601$	24.0753			0.982050			0.491025	−	0.871145i	$-0.336622\pi$
$601$	24.0753			0.982050			0.491025	+	0.871145i	$0.336622\pi$
$602$		0			0
$603$	−1.31371			−0.0534983
$604$	5.19615	−	3.00000i	0.211428	−	0.122068i
$605$	−26.9278	+	10.0565i	−1.09477	+	0.408856i
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	−22.5671	−	39.0873i	−0.915969	−	1.58650i	−0.805477	−	0.592627i	$-0.798091\pi$
$607$	−22.5671	−	39.0873i	−0.915969	−	1.58650i	−0.110492	−	0.993877i	$-0.535243\pi$
$608$			2.29610i			0.0931192i
$609$		0			0
$610$	6.00000			0.242933
$611$	−31.8073	+	18.3640i	−1.28679	+	0.742926i
$612$		0			0
$613$	−19.2627	−	11.1213i	−0.778013	−	0.449186i	0.0577128	−	0.998333i	$-0.481619\pi$
$613$	−19.2627	−	11.1213i	−0.778013	−	0.449186i	−0.835726	+	0.549147i	$0.814953\pi$
$614$	−25.1679	+	14.5307i	−1.01569	+	0.586412i
$615$	−75.7037			−3.05267
$616$		0			0
$617$	−1.41421			−0.0569341			−0.0284670	−	0.999595i	$-0.509063\pi$
$617$	−1.41421			−0.0569341			−0.0284670	+	0.999595i	$0.509063\pi$
$618$	23.3572	−	13.4853i	0.939564	−	0.542458i
$619$	−9.98951	−	5.76745i	−0.401512	−	0.231813i	0.285624	−	0.958342i	$-0.407799\pi$
$619$	−9.98951	−	5.76745i	−0.401512	−	0.231813i	−0.687136	+	0.726528i	$0.741133\pi$
$620$	9.24264	−	16.0087i	0.371193	−	0.642926i
$621$	4.20441	−	2.42742i	0.168717	−	0.0974089i
$622$	3.00707			0.120573
$623$		0			0
$624$		−	14.4853i		−	0.579875i
$625$	15.3995	+	26.6727i	0.615980	+	1.06691i
$626$	−3.21998	+	5.57717i	−0.128696	+	0.222909i
$627$	−1.65153	+	19.8311i	−0.0659558	+	0.791978i
$628$	−1.48648	+	0.858221i	−0.0593171	+	0.0342468i
$629$		0			0
$630$		0			0
$631$	−27.2132			−1.08334			−0.541670	−	0.840591i	$-0.682208\pi$
$631$	−27.2132			−1.08334			−0.541670	+	0.840591i	$0.682208\pi$
$632$	4.24264	+	7.34847i	0.168763	+	0.292306i
$633$	0.951076	−	1.64731i	0.0378019	−	0.0654748i
$634$	9.50079	+	5.48528i	0.377324	+	0.217848i
$635$	7.83938	+	13.5782i	0.311096	+	0.538834i
$636$			32.6256i			1.29369i
$637$		0			0
$638$	14.4853	+	30.7279i	0.573478	+	1.21653i
$639$	3.82843	+	6.63103i	0.151450	+	0.262320i
$640$	−1.30656	+	2.26303i	−0.0516464	+	0.0894543i
$641$	−22.6066	+	39.1558i	−0.892907	+	1.54656i	−0.0565334	+	0.998401i	$0.518005\pi$
$641$	−22.6066	+	39.1558i	−0.892907	+	1.54656i	−0.836374	+	0.548160i	$0.815329\pi$
$642$	−28.8037	+	16.6298i	−1.13679	+	0.656327i
$643$		−	17.3952i		−	0.686000i	−0.939335	−	0.343000i	$-0.888557\pi$
$643$		−	17.3952i		−	0.686000i	0.939335	−	0.343000i	$-0.111443\pi$
$644$		0			0
$645$		−	28.9706i		−	1.14071i
$646$		0			0
$647$	10.6523	+	6.15013i	0.418787	+	0.241787i	0.694558	−	0.719437i	$-0.255600\pi$
$647$	10.6523	+	6.15013i	0.418787	+	0.241787i	−0.275771	+	0.961223i	$0.588933\pi$
$648$	5.04757	+	2.91421i	0.198287	+	0.114481i
$649$	−33.1573	−	23.0111i	−1.30154	−	0.903265i
$650$		−	10.1355i		−	0.397546i
$651$		0			0
$652$	−20.1421			−0.788827
$653$	14.7279	+	25.5095i	0.576348	+	0.998264i	0.995894	+	0.0905300i	$0.0288561\pi$
$653$	14.7279	+	25.5095i	0.576348	+	0.998264i	−0.419546	+	0.907734i	$0.637811\pi$
$654$	−46.3589	−	26.7653i	−1.81278	−	1.04661i
$655$	−37.6339	−	21.7279i	−1.47048	−	0.848980i
$656$	5.54328	+	9.60124i	0.216429	+	0.374865i
$657$	24.8632			0.970004
$658$		0			0
$659$		−	33.2132i		−	1.29380i	−0.762574	−	0.646901i	$-0.776065\pi$
$659$		−	33.2132i		−	1.29380i	0.762574	−	0.646901i	$-0.223935\pi$
$660$	−12.9123	+	18.6057i	−0.502612	+	0.724227i
$661$	−25.1208	−	14.5035i	−0.977086	−	0.564121i	−0.0756972	−	0.997131i	$-0.524118\pi$
$661$	−25.1208	−	14.5035i	−0.977086	−	0.564121i	−0.901389	+	0.433010i	$0.857452\pi$
$662$	3.04384	+	1.75736i	0.118302	+	0.0683017i
$663$		0			0
$664$			0.951076i			0.0369089i
$665$		0			0
$666$			22.9706i			0.890091i
$667$	−19.8931	+	11.4853i	−0.770264	+	0.444712i
$668$	8.79045	−	15.2255i	0.340113	−	0.589093i
$669$	29.7279	−	51.4903i	1.14935	−	1.99073i
$670$	0.448342	+	0.776550i	0.0173209	+	0.0300008i
$671$	−3.24718	−	6.88830i	−0.125356	−	0.265920i
$672$		0			0
$673$			21.9411i			0.845768i	0.906184	+	0.422884i	$0.138982\pi$
$673$			21.9411i			0.845768i	−0.906184	+	0.422884i	$0.861018\pi$
$674$	4.75736	+	8.23999i	0.183247	+	0.317392i
$675$	−3.42786	−	1.97908i	−0.131938	−	0.0761746i
$676$	8.86396	−	15.3528i	0.340922	−	0.590493i
$677$	7.36384	+	12.7545i	0.283015	+	0.490197i	0.972126	−	0.234459i	$-0.0753319\pi$
$677$	7.36384	+	12.7545i	0.283015	+	0.490197i	−0.689111	+	0.724656i	$0.741999\pi$
$678$	3.69552			0.141926
$679$		0			0
$680$		0			0
$681$	−30.2854	+	17.4853i	−1.16054	+	0.670037i
$682$	−23.3809	−	1.94716i	−0.895301	−	0.0745605i
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$	4.39523	+	7.61276i	0.168056	+	0.291081i
$685$		−	44.3462i		−	1.69438i
$686$		0			0
$687$	−25.1716			−0.960355
$688$	−3.67423	+	2.12132i	−0.140079	+	0.0808746i
$689$	−34.6047	+	59.9371i	−1.31833	+	2.28342i
$690$	−13.2621	−	7.65685i	−0.504878	−	0.291491i
$691$	40.8954	−	23.6110i	1.55574	−	0.898204i	0.558079	−	0.829788i	$-0.311539\pi$
$691$	40.8954	−	23.6110i	1.55574	−	0.898204i	0.997657	−	0.0684162i	$-0.0217946\pi$
$692$	−15.2848			−0.581041
$693$		0			0
$694$	−16.2426			−0.616562
$695$	−2.15232	+	1.24264i	−0.0816420	+	0.0471360i
$696$	23.1794	+	13.3827i	0.878614	+	0.507268i
$697$		0			0
$698$	6.44793	−	3.72271i	0.244058	−	0.140907i
$699$	−22.1731			−0.838664
$700$		0			0
$701$		−	27.9411i		−	1.05532i	−0.849455	−	0.527661i	$-0.823069\pi$
$701$		−	27.9411i		−	1.05532i	0.849455	−	0.527661i	$-0.176931\pi$
$702$	−6.00000	−	10.3923i	−0.226455	−	0.392232i
$703$	6.88830	−	11.9309i	0.259797	−	0.449982i
$704$	3.30518	+	0.275255i	0.124569	+	0.0103741i
$705$	39.1815	−	22.6215i	1.47566	−	0.851973i
$706$	8.15640			0.306970
$707$		0			0
$708$	−31.7990			−1.19508
$709$	0.343146	+	0.594346i	0.0128871	+	0.0223211i	0.872397	−	0.488798i	$-0.162564\pi$
$709$	0.343146	+	0.594346i	0.0128871	+	0.0223211i	−0.859510	+	0.511119i	$0.829231\pi$
$710$	2.61313	−	4.52607i	0.0980689	−	0.169860i
$711$	28.1331	+	16.2426i	1.05507	+	0.609147i
$712$	6.15013	+	10.6523i	0.230486	+	0.399213i
$713$		−	15.8645i		−	0.594129i
$714$		0			0
$715$	−43.4558	+	20.4853i	−1.62516	+	0.766106i
$716$	2.82843	+	4.89898i	0.105703	+	0.183083i
$717$	12.4316	−	21.5321i	0.464266	−	0.804132i
$718$	−7.24264	+	12.5446i	−0.270293	+	0.468161i
$719$	12.2997	−	7.10121i	0.458700	−	0.264830i	−0.252798	−	0.967519i	$-0.581351\pi$
$719$	12.2997	−	7.10121i	0.458700	−	0.264830i	0.711497	+	0.702689i	$0.248017\pi$
$720$			10.0042i			0.372833i
$721$		0			0
$722$			13.7279i			0.510900i
$723$	25.0892	−	14.4853i	0.933079	−	0.538713i
$724$	2.03559	+	1.17525i	0.0756520	+	0.0436777i
$725$	16.2189	+	9.36396i	0.602353	+	0.347769i
$726$	28.3484	+	4.75468i	1.05211	+	0.176463i
$727$		−	0.0543929i		−	0.00201732i	−0.999999	−	0.00100866i	$-0.999679\pi$
$727$		−	0.0543929i		−	0.00201732i	0.999999	−	0.00100866i	$-0.000321067\pi$
$728$		0			0
$729$	39.2843			1.45497
$730$	−8.48528	−	14.6969i	−0.314054	−	0.543958i
$731$		0			0
$732$	−5.19615	−	3.00000i	−0.192055	−	0.110883i
$733$	6.69133	+	11.5897i	0.247150	+	0.428076i	0.962734	−	0.270451i	$-0.0871727\pi$
$733$	6.69133	+	11.5897i	0.247150	+	0.428076i	−0.715584	+	0.698527i	$0.753839\pi$
$734$	30.5921			1.12918
$735$		0			0
$736$			2.24264i			0.0826648i
$737$	0.648878	−	0.934985i	0.0239017	−	0.0344406i
$738$	36.7576	+	21.2220i	1.35307	+	0.781194i
$739$	20.7846	+	12.0000i	0.764574	+	0.441427i	0.830936	−	0.556369i	$-0.187806\pi$
$739$	20.7846	+	12.0000i	0.764574	+	0.441427i	−0.0663614	+	0.997796i	$0.521139\pi$
$740$	13.5782	−	7.83938i	0.499145	−	0.288181i
$741$			33.2597i			1.22182i
$742$		0			0
$743$		−	48.4264i		−	1.77659i	−0.459271	−	0.888296i	$-0.651889\pi$
$743$		−	48.4264i		−	1.77659i	0.459271	−	0.888296i	$-0.348111\pi$
$744$	−16.0087	+	9.24264i	−0.586908	+	0.338852i
$745$	24.4692	−	42.3819i	0.896482	−	1.55275i
$746$	1.75736	−	3.04384i	0.0643415	−	0.111443i
$747$	1.82056	+	3.15331i	0.0666109	+	0.115373i
$748$		0			0
$749$		0			0
$750$		−	21.6569i		−	0.790797i
$751$	−8.29289	−	14.3637i	−0.302612	−	0.524139i	0.674115	−	0.738627i	$-0.264525\pi$
$751$	−8.29289	−	14.3637i	−0.302612	−	0.524139i	−0.976727	+	0.214487i	$0.931192\pi$
$752$	−5.73800	−	3.31283i	−0.209243	−	0.120807i
$753$	−9.41421	+	16.3059i	−0.343073	+	0.594220i
$754$	28.3889	+	49.1710i	1.03386	+	1.79070i
$755$	−15.6788			−0.570608
$756$		0			0
$757$	−9.85786			−0.358290			−0.179145	−	0.983823i	$-0.557333\pi$
$757$	−9.85786			−0.358290			−0.179145	+	0.983823i	$0.557333\pi$
$758$	0.297173	−	0.171573i	0.0107938	−	0.00623181i
$759$	−1.61308	+	19.3694i	−0.0585510	+	0.703064i
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	−12.4316	−	21.5321i	−0.450644	−	0.780539i	0.547782	−	0.836621i	$-0.315472\pi$
$761$	−12.4316	−	21.5321i	−0.450644	−	0.780539i	−0.998426	+	0.0560823i	$0.982139\pi$
$762$		−	15.6788i		−	0.567981i
$763$		0			0
$764$	10.2426			0.370566
$765$		0			0
$766$	0.831025	−	1.43938i	0.0300262	−	0.0520068i
$767$	−58.4185	−	33.7279i	−2.10937	−	1.21784i
$768$	2.26303	−	1.30656i	0.0816602	−	0.0471465i
$769$	−15.6788			−0.565390			−0.282695	−	0.959210i	$-0.591228\pi$
$769$	−15.6788			−0.565390			−0.282695	+	0.959210i	$0.591228\pi$
$770$		0			0
$771$	52.1421			1.87785
$772$	12.5446	−	7.24264i	0.451491	−	0.260668i
$773$	3.91035	+	2.25764i	0.140645	+	0.0812016i	0.568672	−	0.822565i	$-0.307458\pi$
$773$	3.91035	+	2.25764i	0.140645	+	0.0812016i	−0.428026	+	0.903766i	$0.640791\pi$
$774$	−8.12132	+	14.0665i	−0.291915	+	0.505611i
$775$	−11.2014	+	6.46716i	−0.402368	+	0.232307i
$776$	5.09494			0.182898
$777$		0			0
$778$			32.0000i			1.14726i
$779$	−12.7279	−	22.0454i	−0.456025	−	0.789859i
$780$	−18.9259	+	32.7807i	−0.677657	+	1.17374i
$781$	−6.61037	−	0.550510i	−0.236537	−	0.0196988i
$782$		0			0
$783$	22.1731			0.792402
$784$		0			0
$785$	4.48528			0.160087
$786$	21.7279	+	37.6339i	0.775009	+	1.34236i
$787$	−5.06774	+	8.77758i	−0.180645	+	0.312887i	−0.942101	−	0.335331i	$-0.891152\pi$
$787$	−5.06774	+	8.77758i	−0.180645	+	0.312887i	0.761455	+	0.648218i	$0.224485\pi$
$788$	3.04384	+	1.75736i	0.108432	+	0.0626033i
$789$	31.3575	+	54.3128i	1.11636	+	1.93359i
$790$		−	22.1731i		−	0.788884i
$791$		0			0
$792$	11.4853	−	5.41421i	0.408112	−	0.192386i
$793$	−6.36396	−	11.0227i	−0.225991	−	0.391428i
$794$	5.76745	−	9.98951i	0.204679	−	0.354515i
$795$	42.6274	−	73.8329i	1.51184	−	2.61858i
$796$	16.3432	−	9.43577i	0.579271	−	0.334442i
$797$		−	25.9456i		−	0.919039i	−0.888168	−	0.459519i	$-0.848022\pi$
$797$		−	25.9456i		−	0.919039i	0.888168	−	0.459519i	$-0.151978\pi$
$798$		0			0
$799$		0			0
$800$	1.58346	−	0.914214i	0.0559839	−	0.0323223i
$801$	40.7817	+	23.5453i	1.44095	+	0.831933i
$802$	−14.2767	−	8.24264i	−0.504127	−	0.291058i
$803$	−12.2806	+	17.6955i	−0.433374	+	0.624459i
$804$		−	0.896683i		−	0.0316236i
$805$		0			0
$806$	−39.2132			−1.38123
$807$	−17.8995	−	31.0028i	−0.630092	−	1.09135i
$808$	−5.96544	−	3.44415i	−0.209864	−	0.121165i
$809$	2.15232	+	1.24264i	0.0756714	+	0.0436889i	0.537358	−	0.843354i	$-0.319422\pi$
$809$	2.15232	+	1.24264i	0.0756714	+	0.0436889i	−0.461687	+	0.887043i	$0.652756\pi$
$810$	−7.61521	−	13.1899i	−0.267571	−	0.463447i
$811$	16.6298			0.583952			0.291976	−	0.956426i	$-0.405687\pi$
$811$	16.6298			0.583952			0.291976	+	0.956426i	$0.405687\pi$
$812$		0			0
$813$		−	4.97056i		−	0.174325i
$814$	−16.3485	−	11.3458i	−0.573014	−	0.397671i
$815$	45.5823	+	26.3170i	1.59668	+	0.921843i
$816$		0			0
$817$	8.43641	−	4.87076i	0.295153	−	0.170406i
$818$		−	2.69005i		−	0.0940554i
$819$		0			0
$820$		−	28.9706i		−	1.01170i
$821$	−19.2627	+	11.1213i	−0.672273	+	0.388137i	−0.796937	−	0.604062i	$-0.793548\pi$
$821$	−19.2627	+	11.1213i	−0.672273	+	0.388137i	0.124665	+	0.992199i	$0.460215\pi$
$822$	−22.1731	+	38.4050i	−0.773376	+	1.33953i
$823$	−25.6066	+	44.3519i	−0.892590	+	1.54601i	−0.0558308	+	0.998440i	$0.517781\pi$
$823$	−25.6066	+	44.3519i	−0.892590	+	1.54601i	−0.836759	+	0.547571i	$0.815553\pi$
$824$	5.16059	+	8.93841i	0.179778	+	0.311384i
$825$	14.3337	−	6.75699i	0.499036	−	0.235248i
$826$		0			0
$827$		−	16.9706i		−	0.590124i	−0.955478	−	0.295062i	$-0.904660\pi$
$827$		−	16.9706i		−	0.590124i	0.955478	−	0.295062i	$-0.0953404\pi$
$828$	4.29289	+	7.43551i	0.149188	+	0.258402i
$829$	−5.23600	−	3.02301i	−0.181854	−	0.104993i	0.406310	−	0.913735i	$-0.366815\pi$
$829$	−5.23600	−	3.02301i	−0.181854	−	0.104993i	−0.588163	+	0.808742i	$0.700149\pi$
$830$	1.24264	−	2.15232i	0.0431327	−	0.0747080i
$831$	8.79045	+	15.2255i	0.304937	+	0.528167i
$832$	5.54328			0.192179
$833$		0			0
$834$	2.48528			0.0860583
$835$	−39.7862	+	22.9706i	−1.37686	+	0.794929i
$836$	−7.58903	−	0.632013i	−0.262472	−	0.0218586i
$837$	−7.65685	+	13.2621i	−0.264660	+	0.458404i
$838$	−2.83730	−	4.91434i	−0.0980128	−	0.169763i
$839$		−	2.55873i		−	0.0883373i	−0.999024	−	0.0441686i	$-0.985936\pi$
$839$		−	2.55873i		−	0.0883373i	0.999024	−	0.0441686i	$-0.0140639\pi$
$840$		0			0
$841$	−75.9117			−2.61764
$842$	−5.49333	+	3.17157i	−0.189312	+	0.109300i
$843$	−15.6788	+	27.1564i	−0.540005	+	0.935316i
$844$	0.630399	+	0.363961i	0.0216992	+	0.0125281i
$845$	−40.1189	+	23.1626i	−1.38013	+	0.796819i
$846$	−25.3659			−0.872097
$847$		0			0
$848$	−12.4853			−0.428746
$849$	52.3308	−	30.2132i	1.79599	−	1.03691i
$850$		0			0
$851$	6.72792	−	11.6531i	0.230630	−	0.399463i
$852$	−4.52607	+	2.61313i	−0.155060	+	0.0895242i
$853$	2.29610			0.0786170			0.0393085	−	0.999227i	$-0.487484\pi$
$853$	2.29610			0.0786170			0.0393085	+	0.999227i	$0.487484\pi$
$854$		0			0
$855$		−	22.9706i		−	0.785577i
$856$	−6.36396	−	11.0227i	−0.217516	−	0.376748i
$857$	−13.3827	+	23.1794i	−0.457143	+	0.791795i	−0.998809	−	0.0487994i	$-0.984460\pi$
$857$	−13.3827	+	23.1794i	−0.457143	+	0.791795i	0.541666	+	0.840594i	$0.317794\pi$
$858$	47.8765	+	3.98715i	1.63448	+	0.136119i
$859$	1.48648	−	0.858221i	0.0507181	−	0.0292821i	−0.474427	−	0.880295i	$-0.657345\pi$
$859$	1.48648	−	0.858221i	0.0507181	−	0.0292821i	0.525145	+	0.851013i	$0.324011\pi$
$860$	11.0866			0.378048
$861$		0			0
$862$	14.4853			0.493371
$863$	2.63604	+	4.56575i	0.0897318	+	0.155420i	0.907398	−	0.420273i	$-0.138066\pi$
$863$	2.63604	+	4.56575i	0.0897318	+	0.155420i	−0.817666	+	0.575693i	$0.804732\pi$
$864$	1.08239	−	1.87476i	0.0368237	−	0.0637806i
$865$	34.5900	+	19.9706i	1.17610	+	0.679020i
$866$	−14.4379	−	25.0071i	−0.490618	−	0.849776i
$867$		−	44.4231i		−	1.50869i
$868$		0			0
$869$	−25.4558	+	12.0000i	−0.863530	+	0.407072i
$870$	−34.9706	−	60.5708i	−1.18561	−	2.05354i
$871$	0.951076	−	1.64731i	0.0322260	−	0.0558170i
$872$	10.2426	−	17.7408i	0.346860	−	0.600778i
$873$	16.8923	−	9.75279i	0.571719	−	0.330082i
$874$		−	5.14933i		−	0.174179i
$875$		0			0
$876$			16.9706i			0.573382i
$877$	46.7654	−	27.0000i	1.57915	−	0.911725i	0.584177	−	0.811626i	$-0.301417\pi$
$877$	46.7654	−	27.0000i	1.57915	−	0.911725i	0.994977	−	0.100099i	$-0.0319159\pi$
$878$	13.5782	+	7.83938i	0.458242	+	0.264566i
$879$	−30.2854	−	17.4853i	−1.02150	−	0.589764i
$880$	−7.12010	−	4.94134i	−0.240019	−	0.166573i
$881$			23.7582i			0.800435i	0.916420	+	0.400218i	$0.131065\pi$
$881$			23.7582i			0.800435i	−0.916420	+	0.400218i	$0.868935\pi$
$882$		0			0
$883$	42.4264			1.42776			0.713881	−	0.700267i	$-0.246936\pi$
$883$	42.4264			1.42776			0.713881	+	0.700267i	$0.246936\pi$
$884$		0			0
$885$	71.9622	+	41.5474i	2.41898	+	1.39660i
$886$	−19.5959	−	11.3137i	−0.658338	−	0.380091i
$887$	−11.0866	−	19.2025i	−0.372250	−	0.644756i	0.617661	−	0.786444i	$-0.288080\pi$
$887$	−11.0866	−	19.2025i	−0.372250	−	0.644756i	−0.989911	+	0.141688i	$0.954747\pi$
$888$	−15.6788			−0.526145
$889$		0			0
$890$		−	32.1421i		−	1.07741i
$891$	−11.0214	+	15.8810i	−0.369230	+	0.532033i
$892$	19.7045	+	11.3764i	0.659755	+	0.380909i
$893$	13.1750	+	7.60660i	0.440885	+	0.254545i
$894$	−42.3819	+	24.4692i	−1.41746	+	0.818373i
$895$		−	14.7821i		−	0.494110i
$896$		0			0
$897$			32.4853i			1.08465i
$898$	13.2260	−	7.63604i	0.441358	−	0.254818i
$899$	36.2283	−	62.7492i	1.20828	−	2.09280i
$900$	3.50000	−	6.06218i	0.116667	−	0.202073i
$901$		0			0
$902$	−33.2597	+	15.6788i	−1.10743	+	0.522045i
$903$		0			0
$904$			1.41421i			0.0470360i
$905$	−3.07107	−	5.31925i	−0.102086	−	0.176818i
$906$	13.5782	+	7.83938i	0.451106	+	0.260446i
$907$	−18.8995	+	32.7349i	−0.627547	+	1.08694i	0.360495	+	0.932761i	$0.382608\pi$
$907$	−18.8995	+	32.7349i	−0.627547	+	1.08694i	−0.988042	+	0.154183i	$0.950726\pi$
$908$	−6.69133	−	11.5897i	−0.222060	−	0.384618i
$909$	−26.3714			−0.874683
$910$		0			0
$911$	29.7574			0.985905			0.492953	−	0.870056i	$-0.335918\pi$
$911$	29.7574			0.985905			0.492953	+	0.870056i	$0.335918\pi$
$912$	−5.19615	+	3.00000i	−0.172062	+	0.0993399i
$913$	−3.14348	−	0.261789i	−0.104034	−	0.00866394i
$914$	−9.72792	+	16.8493i	−0.321771	+	0.557324i
$915$	7.83938	+	13.5782i	0.259162	+	0.448881i
$916$		−	9.63274i		−	0.318275i
$917$		0			0
$918$		0			0
$919$	47.1347	−	27.2132i	1.55483	−	0.897681i	0.557091	−	0.830451i	$-0.311917\pi$
$919$	47.1347	−	27.2132i	1.55483	−	0.897681i	0.997738	−	0.0672294i	$-0.0214159\pi$
$920$	2.93015	−	5.07517i	0.0966042	−	0.167323i
$921$	−65.7669	−	37.9706i	−2.16709	−	1.25117i
$922$	6.44793	−	3.72271i	0.212351	−	0.122601i
$923$	−11.0866			−0.364918
$924$		0			0
$925$	−10.9706			−0.360710
$926$	−14.9941	+	8.65685i	−0.492737	+	0.284482i
$927$	34.2201	+	19.7570i	1.12393	+	0.648904i
$928$	−5.12132	+	8.87039i	−0.168116	+	0.291185i
$929$	−42.9781	+	24.8134i	−1.41007	+	0.814102i	−0.995394	−	0.0958685i	$-0.969437\pi$
$929$	−42.9781	+	24.8134i	−1.41007	+	0.814102i	−0.414672	+	0.909971i	$0.636104\pi$
$930$	48.3044			1.58396
$931$		0			0
$932$		−	8.48528i		−	0.277945i
$933$	3.92893	+	6.80511i	0.128627	+	0.222789i
$934$	5.58174	−	9.66786i	0.182640	−	0.316342i
$935$		0			0
$936$	18.3788	−	10.6110i	0.600731	−	0.346832i
$937$	24.0753			0.786504			0.393252	−	0.919431i	$-0.371350\pi$
$937$	24.0753			0.786504			0.393252	+	0.919431i	$0.371350\pi$
$938$		0			0
$939$	−16.8284			−0.549175
$940$	8.65685	+	14.9941i	0.282355	+	0.489054i
$941$	−1.42661	+	2.47097i	−0.0465063	+	0.0805513i	−0.888342	−	0.459183i	$-0.848142\pi$
$941$	−1.42661	+	2.47097i	−0.0465063	+	0.0805513i	0.841835	+	0.539735i	$0.181475\pi$
$942$	−3.88437	−	2.24264i	−0.126560	−	0.0730692i
$943$	−12.4316	−	21.5321i	−0.404828	−	0.701183i
$944$		−	12.1689i		−	0.396065i
$945$		0			0
$946$	−6.00000	−	12.7279i	−0.195077	−	0.413820i
$947$	10.2426	+	17.7408i	0.332841	+	0.576498i	0.983068	−	0.183243i	$-0.0586594\pi$
$947$	10.2426	+	17.7408i	0.332841	+	0.576498i	−0.650227	+	0.759740i	$0.725326\pi$
$948$	−11.0866	+	19.2025i	−0.360075	+	0.623667i
$949$	−18.0000	+	31.1769i	−0.584305	+	1.01205i
$950$	−3.63579	+	2.09913i	−0.117961	+	0.0681047i
$951$			28.6675i			0.929606i
$952$		0			0
$953$			21.9411i			0.710743i	0.934725	+	0.355371i	$0.115646\pi$
$953$			21.9411i			0.710743i	−0.934725	+	0.355371i	$0.884354\pi$
$954$	−41.3951	+	23.8995i	−1.34022	+	0.773775i
$955$	−23.1794	−	13.3827i	−0.750069	−	0.433053i
$956$	8.23999	+	4.75736i	0.266500	+	0.153864i
$957$	−50.6124	+	72.9286i	−1.63607	+	2.35745i
$958$			22.1731i			0.716381i
$959$		0			0
$960$	−6.82843			−0.220387
$961$	9.52082	+	16.4905i	0.307123	+	0.531953i
$962$	−28.8037	−	16.6298i	−0.928669	−	0.536167i
$963$	−42.1996	−	24.3640i	−1.35986	−	0.785118i
$964$	5.54328	+	9.60124i	0.178537	+	0.309235i
$965$	−37.8519			−1.21849
$966$		0			0
$967$			31.4558i			1.01155i	0.862665	+	0.505776i	$0.168794\pi$
$967$			31.4558i			1.01155i	−0.862665	+	0.505776i	$0.831206\pi$
$968$	−1.81954	+	10.8485i	−0.0584821	+	0.348683i
$969$		0			0
$970$	−11.5300	−	6.65685i	−0.370206	−	0.213739i
$971$	37.3734	−	21.5775i	1.19937	−	0.692456i	0.238954	−	0.971031i	$-0.423196\pi$
$971$	37.3734	−	21.5775i	1.19937	−	0.692456i	0.960414	+	0.278575i	$0.0898622\pi$
$972$			21.7248i			0.696822i
$973$		0			0
$974$			33.5563i			1.07521i
$975$	22.9369	−	13.2426i	0.734570	−	0.424104i
$976$	1.14805	−	1.98848i	0.0367482	−	0.0636497i
$977$	17.8787	−	30.9668i	0.571990	−	0.990715i	−0.424372	−	0.905488i	$-0.639505\pi$
$977$	17.8787	−	30.9668i	0.571990	−	0.990715i	0.996362	−	0.0852271i	$-0.0271616\pi$
$978$	−26.3170	−	45.5823i	−0.841524	−	1.45756i
$979$	−36.9008	+	17.3952i	−1.17935	+	0.555953i
$980$		0			0
$981$		−	78.4264i		−	2.50396i
$982$	−13.9706	−	24.1977i	−0.445819	−	0.772180i
$983$	−30.7256	−	17.7394i	−0.979994	−	0.565800i	−0.0777255	−	0.996975i	$-0.524766\pi$
$983$	−30.7256	−	17.7394i	−0.979994	−	0.565800i	−0.902268	+	0.431175i	$0.858099\pi$
$984$	−14.4853	+	25.0892i	−0.461774	+	0.799816i
$985$	−4.59220	−	7.95393i	−0.146320	−	0.253433i
$986$		0			0
$987$		0			0
$988$	−12.7279			−0.404929
$989$	8.23999	−	4.75736i	0.262016	−	0.151275i
$990$	−33.0656	−	2.75370i	−1.05089	−	0.0875182i
$991$	−10.7990	+	18.7044i	−0.343041	+	0.594165i	−0.984996	−	0.172578i	$-0.944790\pi$
$991$	−10.7990	+	18.7044i	−0.343041	+	0.594165i	0.641955	+	0.766743i	$0.278124\pi$
$992$	−3.53701	−	6.12627i	−0.112300	−	0.194509i
$993$			9.18440i			0.291458i
$994$		0			0
$995$	−49.3137			−1.56335
$996$	−2.15232	+	1.24264i	−0.0681988	+	0.0393746i
$997$	23.9937	−	41.5583i	0.759887	−	1.31616i	−0.183021	−	0.983109i	$-0.558587\pi$
$997$	23.9937	−	41.5583i	0.759887	−	1.31616i	0.942908	−	0.333054i	$-0.108079\pi$
$998$	−14.3998	−	8.31371i	−0.455817	−	0.263166i
$999$	−11.2485	+	6.49435i	−0.355888	+	0.205472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.a.1011.1		16
7.2	even	3	inner	1078.2.i.a.901.8		16
7.3	odd	6		1078.2.c.a.1077.1	✓	8
7.4	even	3		1078.2.c.a.1077.4	yes	8
7.5	odd	6	inner	1078.2.i.a.901.5		16
7.6	odd	2	inner	1078.2.i.a.1011.4		16
11.10	odd	2	inner	1078.2.i.a.1011.5		16
77.10	even	6		1078.2.c.a.1077.5	yes	8
77.32	odd	6		1078.2.c.a.1077.8	yes	8
77.54	even	6	inner	1078.2.i.a.901.1		16
77.65	odd	6	inner	1078.2.i.a.901.4		16
77.76	even	2	inner	1078.2.i.a.1011.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1078.2.c.a.1077.1	✓	8	7.3	odd	6
1078.2.c.a.1077.4	yes	8	7.4	even	3
1078.2.c.a.1077.5	yes	8	77.10	even	6
1078.2.c.a.1077.8	yes	8	77.32	odd	6
1078.2.i.a.901.1		16	77.54	even	6	inner
1078.2.i.a.901.4		16	77.65	odd	6	inner
1078.2.i.a.901.5		16	7.5	odd	6	inner
1078.2.i.a.901.8		16	7.2	even	3	inner
1078.2.i.a.1011.1		16	1.1	even	1	trivial
1078.2.i.a.1011.4		16	7.6	odd	2	inner
1078.2.i.a.1011.5		16	11.10	odd	2	inner
1078.2.i.a.1011.8		16	77.76	even	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.26303 - 1.30656i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.26303 + 1.30656i) q^{5} +2.61313 q^{6} +1.00000i q^{8} +(1.91421 + 3.31552i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.26303 - 1.30656i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.26303 + 1.30656i) q^{5} +2.61313 q^{6} +1.00000i q^{8} +(1.91421 + 3.31552i) q^{9} +(1.30656 - 2.26303i) q^{10} +(-3.30518 - 0.275255i) q^{11} +(-2.26303 + 1.30656i) q^{12} -5.54328 q^{13} +6.82843 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.31552 - 1.91421i) q^{18} +(1.14805 + 1.98848i) q^{19} +2.61313i q^{20} +(3.00000 - 1.41421i) q^{22} +(1.12132 + 1.94218i) q^{23} +(1.30656 - 2.26303i) q^{24} +(0.914214 - 1.58346i) q^{25} +(4.80062 - 2.77164i) q^{26} -2.16478i q^{27} +10.2426i q^{29} +(-5.91359 + 3.41421i) q^{30} +(-6.12627 - 3.53701i) q^{31} +(0.866025 + 0.500000i) q^{32} +(7.12010 + 4.94134i) q^{33} +3.82843 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-1.98848 - 1.14805i) q^{38} +(12.5446 + 7.24264i) q^{39} +(-1.30656 - 2.26303i) q^{40} -11.0866 q^{41} -4.24264i q^{43} +(-1.89097 + 2.72474i) q^{44} +(-8.66386 - 5.00208i) q^{45} +(-1.94218 - 1.12132i) q^{46} +(5.73800 - 3.31283i) q^{47} +2.61313i q^{48} +1.82843i q^{50} +(-2.77164 + 4.80062i) q^{52} +(6.24264 - 10.8126i) q^{53} +(1.08239 + 1.87476i) q^{54} +(7.83938 - 3.69552i) q^{55} -6.00000i q^{57} +(-5.12132 - 8.87039i) q^{58} +(10.5386 + 6.08447i) q^{59} +(3.41421 - 5.91359i) q^{60} +(1.14805 + 1.98848i) q^{61} +7.07401 q^{62} -1.00000 q^{64} +(12.5446 - 7.24264i) q^{65} +(-8.63686 - 0.719276i) q^{66} +(-0.171573 + 0.297173i) q^{67} -5.86030i q^{69} +2.00000 q^{71} +(-3.31552 + 1.91421i) q^{72} +(3.24718 - 5.62427i) q^{73} +(5.19615 + 3.00000i) q^{74} +(-4.13779 + 2.38896i) q^{75} +2.29610 q^{76} -14.4853 q^{78} +(7.34847 - 4.24264i) q^{79} +(2.26303 + 1.30656i) q^{80} +(2.91421 - 5.04757i) q^{81} +(9.60124 - 5.54328i) q^{82} +0.951076 q^{83} +(2.12132 + 3.67423i) q^{86} +(13.3827 - 23.1794i) q^{87} +(0.275255 - 3.30518i) q^{88} +(10.6523 - 6.15013i) q^{89} +10.0042 q^{90} +2.24264 q^{92} +(9.24264 + 16.0087i) q^{93} +(-3.31283 + 5.73800i) q^{94} +(-5.19615 - 3.00000i) q^{95} +(-1.30656 - 2.26303i) q^{96} -5.09494i q^{97} +(-5.41421 - 11.4853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 8 * q^9	\( 16 q + 8 q^{4} + 8 q^{9} + 64 q^{15} - 8 q^{16} + 48 q^{22} - 16 q^{23} - 8 q^{25} + 16 q^{36} - 48 q^{37} + 32 q^{53} - 48 q^{58} + 32 q^{60} - 16 q^{64} - 48 q^{67} + 32 q^{71} - 96 q^{78} + 24 q^{81} + 24 q^{88} - 32 q^{92} + 80 q^{93} - 64 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 8 * q^9 + 64 * q^15 - 8 * q^16 + 48 * q^22 - 16 * q^23 - 8 * q^25 + 16 * q^36 - 48 * q^37 + 32 * q^53 - 48 * q^58 + 32 * q^60 - 16 * q^64 - 48 * q^67 + 32 * q^71 - 96 * q^78 + 24 * q^81 + 24 * q^88 - 32 * q^92 + 80 * q^93 - 64 * q^99

Introduction

L-functions

Modular forms

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Database

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