LMFDB - Embedded newform 891.2.n.h.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			379.1
Character	$\chi$	$=$	891.379
Dual form			891.2.n.h.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.40657 - 0.511531i) q^{2} +(3.70281 + 1.64860i) q^{4} +(-0.968153 + 0.205787i) q^{5} +(-0.451792 - 4.29851i) q^{7} +(-4.08684 - 2.96926i) q^{8} +2.43519 q^{10} +(-0.155819 - 3.31296i) q^{11} +(2.42094 - 2.68872i) q^{13} +(-1.11156 + 10.5758i) q^{14} +(2.89211 + 3.21201i) q^{16} +(0.816208 - 2.51203i) q^{17} +(3.09629 + 2.24958i) q^{19} +(-3.92414 - 0.834103i) q^{20} +(-1.31970 + 8.05257i) q^{22} +(-1.72506 - 2.98789i) q^{23} +(-3.67275 + 1.63522i) q^{25} +(-7.20151 + 5.23221i) q^{26} +(5.41361 - 16.6614i) q^{28} +(1.08941 + 10.3650i) q^{29} +(-1.12941 + 1.25433i) q^{31} +(-0.265393 - 0.459674i) q^{32} +(-3.24924 + 5.62785i) q^{34} +(1.32198 + 4.06865i) q^{35} +(-2.61803 + 1.90211i) q^{37} +(-6.30069 - 6.99762i) q^{38} +(4.56773 + 2.03368i) q^{40} +(1.24467 - 11.8422i) q^{41} +(1.06153 - 1.83863i) q^{43} +(4.88477 - 12.5241i) q^{44} +(2.62307 + 8.07297i) q^{46} +(3.92806 - 1.74888i) q^{47} +(-11.4261 + 2.42868i) q^{49} +(9.67519 - 2.05653i) q^{50} +(13.3969 - 5.96467i) q^{52} +(-2.93021 - 9.01826i) q^{53} +(0.832623 + 3.17539i) q^{55} +(-10.9170 + 18.9088i) q^{56} +(2.68031 - 25.5014i) q^{58} +(5.91260 + 2.63246i) q^{59} +(-3.21892 - 3.57498i) q^{61} +(3.35963 - 2.44091i) q^{62} +(-2.26771 - 6.97930i) q^{64} +(-1.79053 + 3.10129i) q^{65} +(-0.427051 - 0.739674i) q^{67} +(7.16358 - 7.95596i) q^{68} +(-1.10020 - 10.4677i) q^{70} +(-1.16751 + 3.59324i) q^{71} +(-9.22952 + 6.70564i) q^{73} +(7.27346 - 3.23835i) q^{74} +(7.75630 + 13.4343i) q^{76} +(-14.1704 + 2.16656i) q^{77} +(-6.00915 - 1.27728i) q^{79} +(-3.46100 - 2.51456i) q^{80} +(-9.05306 + 27.8625i) q^{82} +(2.24830 + 2.49699i) q^{83} +(-0.273271 + 2.60000i) q^{85} +(-3.49517 + 3.88177i) q^{86} +(-9.20025 + 14.0022i) q^{88} -13.2605 q^{89} +(-12.6513 - 9.19169i) q^{91} +(-1.46174 - 13.9075i) q^{92} +(-10.3477 + 2.19948i) q^{94} +(-3.46062 - 1.54077i) q^{95} +(0.363252 + 0.0772116i) q^{97} +28.7399 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{4} + 24 q^{10} + 10 q^{16} - 4 q^{19} + 36 q^{22} - 32 q^{25} + 84 q^{28} + 26 q^{31} + 48 q^{34} - 48 q^{37} + 20 q^{40} - 24 q^{43} - 32 q^{46} - 24 q^{49} + 40 q^{52} - 32 q^{55} - 106 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) $ 32 * q + 10 * q^4 + 24 * q^10 + 10 * q^16 - 4 * q^19 + 36 * q^22 - 32 * q^25 + 84 * q^28 + 26 * q^31 + 48 * q^34 - 48 * q^37 + 20 * q^40 - 24 * q^43 - 32 * q^46 - 24 * q^49 + 40 * q^52 - 32 * q^55 - 106 * q^58 + 6 * q^61 + 124 * q^64 + 40 * q^67 + 58 * q^70 - 60 * q^76 - 64 * q^79 - 168 * q^82 + 18 * q^85 - 80 * q^88 - 20 * q^91 - 90 * q^94 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.40657	−	0.511531i	−1.70170	−	0.361707i	−0.748286	−	0.663376i	$-0.769123\pi$
$2$	−2.40657	−	0.511531i	−1.70170	−	0.361707i	−0.953413	+	0.301668i	$0.902456\pi$
$3$		0			0
$3$		0			0
$4$	3.70281	+	1.64860i	1.85140	+	0.824298i
$5$	−0.968153	+	0.205787i	−0.432971	+	0.0920309i	−0.419241	−	0.907875i	$-0.637704\pi$
$5$	−0.968153	+	0.205787i	−0.432971	+	0.0920309i	−0.0137300	+	0.999906i	$0.504371\pi$
$6$		0			0
$7$	−0.451792	−	4.29851i	−0.170761	−	1.62468i	−0.659117	−	0.752040i	$-0.729070\pi$
$7$	−0.451792	−	4.29851i	−0.170761	−	1.62468i	0.488356	−	0.872645i	$-0.337597\pi$
$8$	−4.08684	−	2.96926i	−1.44492	−	1.04979i
$9$		0			0
$10$	2.43519			0.770075
$11$	−0.155819	−	3.31296i	−0.0469813	−	0.998896i
$11$	−0.155819	−	3.31296i	−0.0469813	−	0.998896i
$12$		0			0
$13$	2.42094	−	2.68872i	0.671447	−	0.745718i	−0.307114	−	0.951673i	$-0.599363\pi$
$13$	2.42094	−	2.68872i	0.671447	−	0.745718i	0.978561	+	0.205955i	$0.0660301\pi$
$14$	−1.11156	+	10.5758i	−0.297076	+	2.82649i
$15$		0			0
$16$	2.89211	+	3.21201i	0.723027	+	0.803003i
$17$	0.816208	−	2.51203i	0.197959	−	0.609257i	−0.801970	−	0.597365i	$-0.796215\pi$
$17$	0.816208	−	2.51203i	0.197959	−	0.609257i	0.999929	−	0.0118921i	$-0.00378545\pi$
$18$		0			0
$19$	3.09629	+	2.24958i	0.710337	+	0.516090i	0.883282	−	0.468841i	$-0.155328\pi$
$19$	3.09629	+	2.24958i	0.710337	+	0.516090i	−0.172945	+	0.984931i	$0.555328\pi$
$20$	−3.92414	−	0.834103i	−0.877465	−	0.186511i
$21$		0			0
$22$	−1.31970	+	8.05257i	−0.281360	+	1.71681i
$23$	−1.72506	−	2.98789i	−0.359699	−	0.623017i	0.628211	−	0.778043i	$-0.283787\pi$
$23$	−1.72506	−	2.98789i	−0.359699	−	0.623017i	−0.987910	+	0.155026i	$0.950454\pi$
$24$		0			0
$25$	−3.67275	+	1.63522i	−0.734551	+	0.327043i
$26$	−7.20151	+	5.23221i	−1.41233	+	1.02612i
$27$		0			0
$28$	5.41361	−	16.6614i	1.02308	−	3.14870i
$29$	1.08941	+	10.3650i	0.202298	+	1.92474i	0.351986	+	0.936005i	$0.385506\pi$
$29$	1.08941	+	10.3650i	0.202298	+	1.92474i	−0.149688	+	0.988733i	$0.547827\pi$
$30$		0			0
$31$	−1.12941	+	1.25433i	−0.202848	+	0.225285i	−0.835982	−	0.548757i	$-0.815101\pi$
$31$	−1.12941	+	1.25433i	−0.202848	+	0.225285i	0.633134	+	0.774042i	$0.281768\pi$
$32$	−0.265393	−	0.459674i	−0.0469152	−	0.0812596i
$33$		0			0
$34$	−3.24924	+	5.62785i	−0.557240	+	0.965168i
$35$	1.32198	+	4.06865i	0.223456	+	0.687727i
$36$		0			0
$37$	−2.61803	+	1.90211i	−0.430402	+	0.312705i	−0.781810	−	0.623517i	$-0.785703\pi$
$37$	−2.61803	+	1.90211i	−0.430402	+	0.312705i	0.351408	+	0.936223i	$0.385703\pi$
$38$	−6.30069	−	6.99762i	−1.02211	−	1.13516i
$39$		0			0
$40$	4.56773	+	2.03368i	0.722221	+	0.321554i
$41$	1.24467	−	11.8422i	0.194385	−	1.84945i	−0.268813	−	0.963192i	$-0.586631\pi$
$41$	1.24467	−	11.8422i	0.194385	−	1.84945i	0.463197	−	0.886255i	$-0.346702\pi$
$42$		0			0
$43$	1.06153	−	1.83863i	0.161882	−	0.280388i	−0.773661	−	0.633599i	$-0.781577\pi$
$43$	1.06153	−	1.83863i	0.161882	−	0.280388i	0.935544	+	0.353211i	$0.114910\pi$
$44$	4.88477	−	12.5241i	0.736406	−	1.88809i
$45$		0			0
$46$	2.62307	+	8.07297i	0.386750	+	1.19029i
$47$	3.92806	−	1.74888i	0.572966	−	0.255101i	−0.0997364	−	0.995014i	$-0.531800\pi$
$47$	3.92806	−	1.74888i	0.572966	−	0.255101i	0.672703	+	0.739913i	$0.265133\pi$
$48$		0			0
$49$	−11.4261	+	2.42868i	−1.63229	+	0.346955i
$50$	9.67519	−	2.05653i	1.36828	−	0.290837i
$51$		0			0
$52$	13.3969	−	5.96467i	1.85781	−	0.827152i
$53$	−2.93021	−	9.01826i	−0.402496	−	1.23875i	−0.922968	−	0.384876i	$-0.874244\pi$
$53$	−2.93021	−	9.01826i	−0.402496	−	1.23875i	0.520473	−	0.853878i	$-0.325756\pi$
$54$		0			0
$55$	0.832623	+	3.17539i	0.112271	+	0.428170i
$56$	−10.9170	+	18.9088i	−1.45885	+	2.52680i
$57$		0			0
$58$	2.68031	−	25.5014i	0.351941	−	3.34850i
$59$	5.91260	+	2.63246i	0.769755	+	0.342717i	0.753755	−	0.657155i	$-0.228240\pi$
$59$	5.91260	+	2.63246i	0.769755	+	0.342717i	0.0159992	+	0.999872i	$0.494907\pi$
$60$		0			0
$61$	−3.21892	−	3.57498i	−0.412141	−	0.457729i	0.500955	−	0.865473i	$-0.332982\pi$
$61$	−3.21892	−	3.57498i	−0.412141	−	0.457729i	−0.913096	+	0.407744i	$0.866316\pi$
$62$	3.35963	−	2.44091i	0.426673	−	0.309996i
$63$		0			0
$64$	−2.26771	−	6.97930i	−0.283464	−	0.872413i
$65$	−1.79053	+	3.10129i	−0.222088	+	0.384668i
$66$		0			0
$67$	−0.427051	−	0.739674i	−0.0521726	−	0.0903656i	0.838760	−	0.544502i	$-0.183281\pi$
$67$	−0.427051	−	0.739674i	−0.0521726	−	0.0903656i	−0.890932	+	0.454136i	$0.849948\pi$
$68$	7.16358	−	7.95596i	0.868712	−	0.964802i
$69$		0			0
$70$	−1.10020	−	10.4677i	−0.131499	−	1.25113i
$71$	−1.16751	+	3.59324i	−0.138558	+	0.426439i	−0.996127	−	0.0879314i	$-0.971974\pi$
$71$	−1.16751	+	3.59324i	−0.138558	+	0.426439i	0.857568	+	0.514371i	$0.171974\pi$
$72$		0			0
$73$	−9.22952	+	6.70564i	−1.08023	+	0.784835i	−0.977724	−	0.209897i	$-0.932687\pi$
$73$	−9.22952	+	6.70564i	−1.08023	+	0.784835i	−0.102510	+	0.994732i	$0.532687\pi$
$74$	7.27346	−	3.23835i	0.845523	−	0.376451i
$75$		0			0
$76$	7.75630	+	13.4343i	0.889708	+	1.54102i
$77$	−14.1704	+	2.16656i	−1.61487	+	0.246902i
$78$		0			0
$79$	−6.00915	−	1.27728i	−0.676082	−	0.143706i	−0.142940	−	0.989731i	$-0.545656\pi$
$79$	−6.00915	−	1.27728i	−0.676082	−	0.143706i	−0.533142	+	0.846026i	$0.678989\pi$
$80$	−3.46100	−	2.51456i	−0.386951	−	0.281137i
$81$		0			0
$82$	−9.05306	+	27.8625i	−0.999743	+	3.07689i
$83$	2.24830	+	2.49699i	0.246783	+	0.274080i	0.853792	−	0.520615i	$-0.174297\pi$
$83$	2.24830	+	2.49699i	0.246783	+	0.274080i	−0.607008	+	0.794695i	$0.707631\pi$
$84$		0			0
$85$	−0.273271	+	2.60000i	−0.0296403	+	0.282009i
$86$	−3.49517	+	3.88177i	−0.376893	+	0.418583i
$87$		0			0
$88$	−9.20025	+	14.0022i	−0.980750	+	1.49264i
$89$	−13.2605			−1.40561			−0.702806	−	0.711381i	$-0.748070\pi$
$89$	−13.2605			−1.40561			−0.702806	+	0.711381i	$0.748070\pi$
$90$		0			0
$91$	−12.6513	−	9.19169i	−1.32621	−	0.963550i
$92$	−1.46174	−	13.9075i	−0.152396	−	1.44996i
$93$		0			0
$94$	−10.3477	+	2.19948i	−1.06729	+	0.226859i
$95$	−3.46062	−	1.54077i	−0.355052	−	0.158079i
$96$		0			0
$97$	0.363252	+	0.0772116i	0.0368827	+	0.00783965i	0.226316	−	0.974054i	$-0.427332\pi$
$97$	0.363252	+	0.0772116i	0.0368827	+	0.00783965i	−0.189433	+	0.981894i	$0.560665\pi$
$98$	28.7399			2.90317
$99$		0			0
$100$	−16.2953			−1.62953
$101$	−12.7103	−	2.70167i	−1.26473	−	0.268826i	−0.473743	−	0.880663i	$-0.657097\pi$
$101$	−12.7103	−	2.70167i	−1.26473	−	0.268826i	−0.790984	+	0.611837i	$0.790431\pi$
$102$		0			0
$103$	−10.7835	−	4.80114i	−1.06253	−	0.473071i	−0.200381	−	0.979718i	$-0.564218\pi$
$103$	−10.7835	−	4.80114i	−1.06253	−	0.473071i	−0.862153	+	0.506647i	$0.830885\pi$
$104$	−17.8775	+	3.79998i	−1.75304	+	0.372619i
$105$		0			0
$106$	2.43862	+	23.2019i	0.236860	+	2.25357i
$107$	3.82493	+	2.77898i	0.369770	+	0.268654i	0.757116	−	0.653281i	$-0.226608\pi$
$107$	3.82493	+	2.77898i	0.369770	+	0.268654i	−0.387345	+	0.921935i	$0.626608\pi$
$108$		0			0
$109$	16.1864			1.55037			0.775186	−	0.631733i	$-0.217656\pi$
$109$	16.1864			1.55037			0.775186	+	0.631733i	$0.217656\pi$
$110$	−0.379450	−	8.06770i	−0.0361791	−	0.769225i
$111$		0			0
$112$	12.5002	−	13.8829i	1.18116	−	1.31181i
$113$	−0.0888161	+	0.845028i	−0.00835511	+	0.0794936i	−0.997905	−	0.0646982i	$-0.979392\pi$
$113$	−0.0888161	+	0.845028i	−0.00835511	+	0.0794936i	0.989550	+	0.144192i	$0.0460582\pi$
$114$		0			0
$115$	2.28499	+	2.53774i	0.213076	+	0.236645i
$116$	−13.0539	+	40.1757i	−1.21202	+	3.73022i
$117$		0			0
$118$	−12.8825	−	9.35966i	−1.18593	−	0.861627i
$119$	−11.1667	−	2.37357i	−1.02365	−	0.217584i
$120$		0			0
$121$	−10.9514	+	1.03245i	−0.995586	+	0.0938588i
$122$	5.91784	+	10.2500i	0.535776	+	0.927992i
$123$		0			0
$124$	−6.24987	+	2.78262i	−0.561255	+	0.249887i
$125$	7.22304	−	5.24784i	0.646048	−	0.469381i
$126$		0			0
$127$	3.60148	−	11.0842i	0.319580	−	0.983566i	−0.654248	−	0.756280i	$-0.727015\pi$
$127$	3.60148	−	11.0842i	0.319580	−	0.983566i	0.973828	−	0.227286i	$-0.0729853\pi$
$128$	1.99823	+	19.0119i	0.176620	+	1.68043i
$129$		0			0
$130$	5.89545	−	6.54756i	0.517065	−	0.574259i
$131$	0.121401	+	0.210272i	0.0106068	+	0.0183716i	0.871280	−	0.490786i	$-0.163290\pi$
$131$	0.121401	+	0.210272i	0.0106068	+	0.0183716i	−0.860673	+	0.509158i	$0.829957\pi$
$132$		0			0
$133$	8.27099	−	14.3258i	0.717186	−	1.24220i
$134$	0.649360	+	1.99852i	0.0560962	+	0.172646i
$135$		0			0
$136$	−10.7946	+	7.84273i	−0.925629	+	0.672509i
$137$	0.304247	+	0.337900i	0.0259935	+	0.0288688i	0.756001	−	0.654570i	$-0.227150\pi$
$137$	0.304247	+	0.337900i	0.0259935	+	0.0288688i	−0.730008	+	0.683439i	$0.760484\pi$
$138$		0			0
$139$	−16.2986	−	7.25659i	−1.38243	−	0.615496i	−0.425270	−	0.905067i	$-0.639821\pi$
$139$	−16.2986	−	7.25659i	−1.38243	−	0.615496i	−0.957157	+	0.289571i	$0.906487\pi$
$140$	−1.81250	+	17.2448i	−0.153185	+	1.45745i
$141$		0			0
$142$	4.64776	−	8.05015i	0.390031	−	0.675554i
$143$	−9.28487	−	7.60152i	−0.776440	−	0.635671i
$144$		0			0
$145$	−3.18771	−	9.81076i	−0.264725	−	0.814739i
$146$	25.6416	−	11.4164i	2.12211	−	0.944826i
$147$		0			0
$148$	−12.8299	+	2.72708i	−1.05461	+	0.224164i
$149$	−15.5901	+	3.31378i	−1.27719	+	0.271475i	−0.796084	−	0.605187i	$-0.793099\pi$
$149$	−15.5901	+	3.31378i	−1.27719	+	0.271475i	−0.481107	+	0.876662i	$0.659765\pi$
$150$		0			0
$151$	5.53020	−	2.46220i	0.450041	−	0.200371i	−0.169184	−	0.985584i	$-0.554113\pi$
$151$	5.53020	−	2.46220i	0.450041	−	0.200371i	0.619226	+	0.785213i	$0.287447\pi$
$152$	−5.97443	−	18.3874i	−0.484590	−	1.49141i
$153$		0			0
$154$	35.2103	+	2.03464i	2.83733	+	0.163956i
$155$	0.835314	−	1.44681i	0.0670940	−	0.116210i
$156$		0			0
$157$	−0.782068	+	7.44088i	−0.0624158	+	0.593847i	0.917955	+	0.396685i	$0.129839\pi$
$157$	−0.782068	+	7.44088i	−0.0624158	+	0.593847i	−0.980371	+	0.197162i	$0.936827\pi$
$158$	13.8080	+	6.14774i	1.09851	+	0.489088i
$159$		0			0
$160$	0.351536	+	0.390420i	0.0277913	+	0.0308654i
$161$	−12.0641	+	8.76508i	−0.950784	+	0.690785i
$162$		0			0
$163$	4.31902	+	13.2926i	0.338292	+	1.04115i	0.965078	+	0.261963i	$0.0843699\pi$
$163$	4.31902	+	13.2926i	0.338292	+	1.04115i	−0.626786	+	0.779191i	$0.715630\pi$
$164$	24.1318	−	41.7976i	1.88438	−	3.26384i
$165$		0			0
$166$	−4.13340	−	7.15925i	−0.320814	−	0.555666i
$167$	4.27655	−	4.74959i	0.330930	−	0.367535i	−0.554600	−	0.832117i	$-0.687129\pi$
$167$	4.27655	−	4.74959i	0.330930	−	0.367535i	0.885530	+	0.464582i	$0.153796\pi$
$168$		0			0
$169$	−0.00942533	−	0.0896760i	−0.000725025	−	0.00689815i
$170$	1.98762	−	6.11727i	0.152444	−	0.469174i
$171$		0			0
$172$	6.96181	−	5.05805i	0.530833	−	0.385673i
$173$	7.16735	−	3.19111i	0.544924	−	0.242616i	−0.115764	−	0.993277i	$-0.536932\pi$
$173$	7.16735	−	3.19111i	0.544924	−	0.242616i	0.660687	+	0.750661i	$0.270265\pi$
$174$		0			0
$175$	8.68832	+	15.0486i	0.656775	+	1.13757i
$176$	10.1906	−	10.0819i	0.768148	−	0.759955i
$177$		0			0
$178$	31.9123	+	6.78317i	2.39193	+	0.508420i
$179$	3.94392	+	2.86542i	0.294782	+	0.214172i	0.725339	−	0.688392i	$-0.241683\pi$
$179$	3.94392	+	2.86542i	0.294782	+	0.214172i	−0.430557	+	0.902563i	$0.641683\pi$
$180$		0			0
$181$	2.79558	−	8.60390i	0.207794	−	0.639523i	−0.791794	−	0.610789i	$-0.790852\pi$
$181$	2.79558	−	8.60390i	0.207794	−	0.639523i	0.999587	−	0.0287340i	$-0.00914758\pi$
$182$	25.7443	+	28.5919i	1.90829	+	2.11937i
$183$		0			0
$184$	−1.82179	+	17.3332i	−0.134304	+	1.27782i
$185$	2.14323	−	2.38030i	0.157573	−	0.175003i
$186$		0			0
$187$	−8.44944	−	2.31264i	−0.617884	−	0.169117i
$188$	17.4280			1.27107
$189$		0			0
$190$	7.54005	+	5.47817i	0.547013	+	0.397428i
$191$	1.96175	+	18.6648i	0.141947	+	1.35054i	0.801100	+	0.598530i	$0.204248\pi$
$191$	1.96175	+	18.6648i	0.141947	+	1.35054i	−0.659153	+	0.752009i	$0.729085\pi$
$192$		0			0
$193$	16.9244	−	3.59740i	1.21825	−	0.258947i	0.446446	−	0.894810i	$-0.352689\pi$
$193$	16.9244	−	3.59740i	1.21825	−	0.258947i	0.771801	+	0.635864i	$0.219356\pi$
$194$	−0.834694	−	0.371630i	−0.0599276	−	0.0266815i
$195$		0			0
$196$	−46.3124	−	9.84400i	−3.30803	−	0.703143i
$197$	−6.06800			−0.432327			−0.216164	−	0.976357i	$-0.569354\pi$
$197$	−6.06800			−0.432327			−0.216164	+	0.976357i	$0.569354\pi$
$198$		0			0
$199$	−10.1108			−0.716738			−0.358369	−	0.933580i	$-0.616667\pi$
$199$	−10.1108			−0.716738			−0.358369	+	0.933580i	$0.616667\pi$
$200$	19.8654	+	4.22251i	1.40469	+	0.298577i
$201$		0			0
$202$	29.2063	+	13.0035i	2.05495	+	0.914922i
$203$	44.0620	−	9.36568i	3.09255	−	0.657342i
$204$		0			0
$205$	1.23195	+	11.7212i	0.0860433	+	0.818647i
$206$	23.4954	+	17.0704i	1.63700	+	1.18935i
$207$		0			0
$208$	15.6378			1.08429
$209$	6.97033	−	10.6084i	0.482148	−	0.733799i
$210$		0			0
$211$	9.86394	−	10.9550i	0.679062	−	0.754175i	−0.300836	−	0.953676i	$-0.597266\pi$
$211$	9.86394	−	10.9550i	0.679062	−	0.754175i	0.979898	+	0.199501i	$0.0639323\pi$
$212$	4.01746	−	38.2236i	0.275921	−	2.62521i
$213$		0			0
$214$	−7.78342	−	8.64437i	−0.532064	−	0.590917i
$215$	−0.649360	+	1.99852i	−0.0442860	+	0.136298i
$216$		0			0
$217$	5.90203	+	4.28807i	0.400656	+	0.291093i
$218$	−38.9535	−	8.27983i	−2.63827	−	0.560781i
$219$		0			0
$220$	−2.15189	+	13.1305i	−0.145081	+	0.885259i
$221$	−4.77816	−	8.27602i	−0.321414	−	0.556706i
$222$		0			0
$223$	0.560904	−	0.249730i	0.0375609	−	0.0167232i	−0.387870	−	0.921714i	$-0.626789\pi$
$223$	0.560904	−	0.249730i	0.0375609	−	0.0167232i	0.425431	+	0.904991i	$0.360122\pi$
$224$	−1.85601	+	1.34847i	−0.124010	+	0.0900985i
$225$		0			0
$226$	0.646000	−	1.98818i	0.0429713	−	0.132252i
$227$	−1.21361	−	11.5467i	−0.0805502	−	0.766384i	−0.958010	−	0.286734i	$-0.907430\pi$
$227$	−1.21361	−	11.5467i	−0.0805502	−	0.766384i	0.877460	−	0.479650i	$-0.159236\pi$
$228$		0			0
$229$	0.544298	−	0.604504i	0.0359682	−	0.0399468i	−0.724892	−	0.688862i	$-0.758110\pi$
$229$	0.544298	−	0.604504i	0.0359682	−	0.0399468i	0.760860	+	0.648915i	$0.224777\pi$
$230$	−4.20084	−	7.27608i	−0.276995	−	0.479770i
$231$		0			0
$232$	26.3243	−	45.5950i	1.72827	−	2.99346i
$233$	−5.33097	−	16.4070i	−0.349243	−	1.07486i	−0.959273	−	0.282482i	$-0.908842\pi$
$233$	−5.33097	−	16.4070i	−0.349243	−	1.07486i	0.610029	−	0.792379i	$-0.291158\pi$
$234$		0			0
$235$	−3.44307	+	2.50153i	−0.224601	+	0.163182i
$236$	17.5533	+	19.4950i	1.14263	+	1.26901i
$237$		0			0
$238$	25.6594	+	11.4243i	1.66325	+	0.740526i
$239$	0.0208798	−	0.198658i	0.00135060	−	0.0128501i	−0.993826	−	0.110951i	$-0.964610\pi$
$239$	0.0208798	−	0.198658i	0.00135060	−	0.0128501i	0.995176	+	0.0981012i	$0.0312769\pi$
$240$		0			0
$241$	−7.41547	+	12.8440i	−0.477672	+	0.827353i	−0.999672	−	0.0255926i	$-0.991853\pi$
$241$	−7.41547	+	12.8440i	−0.477672	+	0.827353i	0.522000	+	0.852945i	$0.325186\pi$
$242$	26.8835	+	3.11736i	1.72814	+	0.200391i
$243$		0			0
$244$	−6.02536	−	18.5442i	−0.385734	−	1.18717i
$245$	10.5624	−	4.70268i	0.674806	−	0.300443i
$246$		0			0
$247$	13.5444	−	2.87896i	0.861811	−	0.183184i
$248$	8.34016	−	1.77276i	0.529601	−	0.112570i
$249$		0			0
$250$	−20.0672	+	8.93447i	−1.26916	+	0.565066i
$251$	2.63483	+	8.10917i	0.166309	+	0.511846i	0.999130	−	0.0416955i	$-0.0132759\pi$
$251$	2.63483	+	8.10917i	0.166309	+	0.511846i	−0.832821	+	0.553542i	$0.813276\pi$
$252$		0			0
$253$	−9.62996	+	6.18062i	−0.605430	+	0.388572i
$254$	−14.3371	+	24.8327i	−0.899592	+	1.55814i
$255$		0			0
$256$	3.38215	−	32.1790i	0.211385	−	2.01119i
$257$	−11.8748	−	5.28701i	−0.740731	−	0.329795i	0.00144558	−	0.999999i	$-0.499540\pi$
$257$	−11.8748	−	5.28701i	−0.740731	−	0.329795i	−0.742177	+	0.670204i	$0.766207\pi$
$258$		0			0
$259$	9.35906	+	10.3943i	0.581544	+	0.645870i
$260$	−11.7428	+	8.53163i	−0.728256	+	0.529109i
$261$		0			0
$262$	−0.184598	−	0.568135i	−0.0114045	−	0.0350995i
$263$	7.42644	−	12.8630i	0.457934	−	0.793165i	−0.540918	−	0.841075i	$-0.681923\pi$
$263$	7.42644	−	12.8630i	0.457934	−	0.793165i	0.998852	+	0.0479108i	$0.0152563\pi$
$264$		0			0
$265$	4.69274	+	8.12806i	0.288273	+	0.499303i
$266$	−27.2328	+	30.2450i	−1.66975	+	1.85444i
$267$		0			0
$268$	−0.361864	−	3.44290i	−0.0221043	−	0.210309i
$269$	−1.17789	+	3.62517i	−0.0718172	+	0.221031i	−0.980522	−	0.196408i	$-0.937072\pi$
$269$	−1.17789	+	3.62517i	−0.0718172	+	0.221031i	0.908705	+	0.417439i	$0.137072\pi$
$270$		0			0
$271$	11.1948	−	8.13347i	0.680033	−	0.494073i	−0.193335	−	0.981133i	$-0.561931\pi$
$271$	11.1948	−	8.13347i	0.680033	−	0.494073i	0.873369	+	0.487060i	$0.161931\pi$
$272$	10.4292	−	4.64339i	0.632365	−	0.281547i
$273$		0			0
$274$	−0.559343	−	0.968811i	−0.0337912	−	0.0585280i
$275$	5.98969	+	11.9129i	0.361192	+	0.718375i
$276$		0			0
$277$	−2.40431	−	0.511052i	−0.144461	−	0.0307061i	0.135114	−	0.990830i	$-0.456860\pi$
$277$	−2.40431	−	0.511052i	−0.144461	−	0.0307061i	−0.279575	+	0.960124i	$0.590193\pi$
$278$	35.5116	+	25.8007i	2.12984	+	1.54742i
$279$		0			0
$280$	6.67815	−	20.5532i	0.399096	−	1.22829i
$281$	13.3295	+	14.8039i	0.795171	+	0.883126i	0.995319	−	0.0966391i	$-0.0308093\pi$
$281$	13.3295	+	14.8039i	0.795171	+	0.883126i	−0.200149	+	0.979765i	$0.564143\pi$
$282$		0			0
$283$	−0.751406	+	7.14915i	−0.0446664	+	0.424973i	0.949224	+	0.314601i	$0.101871\pi$
$283$	−0.751406	+	7.14915i	−0.0446664	+	0.424973i	−0.993890	+	0.110372i	$0.964796\pi$
$284$	−10.2469	+	11.3803i	−0.608040	+	0.675297i
$285$		0			0
$286$	18.4562	+	23.0431i	1.09134	+	1.36256i
$287$	−51.4664			−3.03796
$288$		0			0
$289$	8.10919	+	5.89167i	0.477011	+	0.346569i
$290$	2.65292	+	25.2408i	0.155785	+	1.48219i
$291$		0			0
$292$	−45.2300	+	9.61393i	−2.64689	+	0.562613i
$293$	−15.5867	−	6.93966i	−0.910586	−	0.405419i	−0.102669	−	0.994716i	$-0.532738\pi$
$293$	−15.5867	−	6.93966i	−0.910586	−	0.405419i	−0.807917	+	0.589297i	$0.799405\pi$
$294$		0			0
$295$	−6.26603	−	1.33189i	−0.364822	−	0.0775454i
$296$	16.3474			0.950172
$297$		0			0
$298$	39.2137			2.27159
$299$	−12.2099	−	2.59528i	−0.706114	−	0.150089i
$300$		0			0
$301$	−8.38296	−	3.73233i	−0.483186	−	0.215128i
$302$	−14.5683	+	3.09658i	−0.838311	+	0.178188i
$303$		0			0
$304$	1.72911	+	16.4514i	0.0991711	+	0.943550i
$305$	3.85210	+	2.79871i	0.220571	+	0.160254i
$306$		0			0
$307$	7.48842			0.427387			0.213693	−	0.976901i	$-0.431451\pi$
$307$	7.48842			0.427387			0.213693	+	0.976901i	$0.431451\pi$
$308$	−56.0421	−	15.3389i	−3.19329	−	0.874016i
$309$		0			0
$310$	−2.75032	+	3.05455i	−0.156208	+	0.173487i
$311$	−1.09973	+	10.4632i	−0.0623599	+	0.593314i	0.918066	+	0.396427i	$0.129750\pi$
$311$	−1.09973	+	10.4632i	−0.0623599	+	0.593314i	−0.980426	+	0.196887i	$0.936917\pi$
$312$		0			0
$313$	−6.98215	−	7.75446i	−0.394654	−	0.438308i	0.512768	−	0.858527i	$-0.328620\pi$
$313$	−6.98215	−	7.75446i	−0.394654	−	0.438308i	−0.907423	+	0.420219i	$0.861953\pi$
$314$	5.68834	−	17.5069i	0.321012	−	0.987973i
$315$		0			0
$316$	−20.1450	−	14.6362i	−1.13324	−	0.823350i
$317$	−12.5086	−	2.65879i	−0.702554	−	0.149332i	−0.157235	−	0.987561i	$-0.550258\pi$
$317$	−12.5086	−	2.65879i	−0.702554	−	0.149332i	−0.545319	+	0.838229i	$0.683591\pi$
$318$		0			0
$319$	34.1692	−	5.22424i	1.91311	−	0.292501i
$320$	3.63175	+	6.29037i	0.203021	+	0.351642i
$321$		0			0
$322$	33.5167	−	14.9226i	1.86781	−	0.831603i
$323$	8.17824	−	5.94184i	0.455049	−	0.330613i
$324$		0			0
$325$	−4.49487	+	13.8338i	−0.249330	+	0.767360i
$326$	−3.59443	−	34.1988i	−0.199077	−	1.89409i
$327$		0			0
$328$	−40.2495	+	44.7016i	−2.22241	+	2.46823i
$329$	−9.29227	−	16.0947i	−0.512299	−	0.887328i
$330$		0			0
$331$	−8.19247	+	14.1898i	−0.450299	+	0.779941i	−0.998404	−	0.0564686i	$-0.982016\pi$
$331$	−8.19247	+	14.1898i	−0.450299	+	0.779941i	0.548105	+	0.836409i	$0.315349\pi$
$332$	4.20849	+	12.9524i	0.230971	+	0.710856i
$333$		0			0
$334$	−12.7214	+	9.24262i	−0.696083	+	0.505734i
$335$	0.565666	+	0.628236i	0.0309057	+	0.0343242i
$336$		0			0
$337$	26.5543	+	11.8228i	1.44651	+	0.644026i	0.971733	−	0.236082i	$-0.0758633\pi$
$337$	26.5543	+	11.8228i	1.44651	+	0.644026i	0.474774	+	0.880108i	$0.342530\pi$
$338$	−0.0231894	+	0.220633i	−0.00126134	+	0.0120008i
$339$		0			0
$340$	−5.29821	+	9.17677i	−0.287336	+	0.497680i
$341$	4.33155	+	3.54624i	0.234566	+	0.192039i
$342$		0			0
$343$	6.25252	+	19.2433i	0.337604	+	1.03904i
$344$	−9.79769	+	4.36221i	−0.528256	+	0.235195i
$345$		0			0
$346$	−18.8811	+	4.01329i	−1.01505	+	0.215756i
$347$	21.1110	−	4.48728i	1.13330	−	0.240890i	0.397178	−	0.917742i	$-0.369990\pi$
$347$	21.1110	−	4.48728i	1.13330	−	0.240890i	0.736119	+	0.676852i	$0.236656\pi$
$348$		0			0
$349$	22.1081	−	9.84316i	1.18342	−	0.526893i	0.281822	−	0.959467i	$-0.409061\pi$
$349$	22.1081	−	9.84316i	1.18342	−	0.526893i	0.901598	+	0.432574i	$0.142395\pi$
$350$	−13.2112	−	40.6598i	−0.706167	−	2.17336i
$351$		0			0
$352$	−1.48153	+	0.950862i	−0.0789657	+	0.0506811i
$353$	10.4900	−	18.1693i	0.558328	−	0.967052i	−0.439309	−	0.898336i	$-0.644777\pi$
$353$	10.4900	−	18.1693i	0.558328	−	0.967052i	0.997636	−	0.0687156i	$-0.0218901\pi$
$354$		0			0
$355$	0.390890	−	3.71907i	0.0207463	−	0.197388i
$356$	−49.1011	−	21.8612i	−2.60236	−	1.15864i
$357$		0			0
$358$	−8.02554	−	8.91327i	−0.424163	−	0.471081i
$359$	−12.6882	+	9.21850i	−0.669657	+	0.486534i	−0.869910	−	0.493210i	$-0.835823\pi$
$359$	−12.6882	+	9.21850i	−0.669657	+	0.486534i	0.200254	+	0.979744i	$0.435823\pi$
$360$		0			0
$361$	−1.34496	−	4.13936i	−0.0707873	−	0.217861i
$362$	−11.1289	+	19.2758i	−0.584922	+	1.01312i
$363$		0			0
$364$	−31.6918	−	54.8919i	−1.66110	−	2.87712i
$365$	7.55565	−	8.39140i	0.395481	−	0.439226i
$366$		0			0
$367$	0.856563	+	8.14965i	0.0447122	+	0.425408i	0.993866	+	0.110594i	$0.0352754\pi$
$367$	0.856563	+	8.14965i	0.0447122	+	0.425408i	−0.949153	+	0.314814i	$0.898058\pi$
$368$	4.60807	−	14.1822i	0.240212	−	0.739298i
$369$		0			0
$370$	−6.37542	+	4.63201i	−0.331442	+	0.240807i
$371$	−37.4413	+	16.6699i	−1.94385	+	0.865460i
$372$		0			0
$373$	−15.4086	−	26.6884i	−0.797826	−	1.38188i	−0.921029	−	0.389494i	$-0.872650\pi$
$373$	−15.4086	−	26.6884i	−0.797826	−	1.38188i	0.123203	−	0.992381i	$-0.460683\pi$
$374$	19.1511	+	9.88769i	0.990282	+	0.511280i
$375$		0			0
$376$	−21.2463	−	4.51603i	−1.09569	−	0.232897i
$377$	30.5061	+	22.1640i	1.57114	+	1.14150i
$378$		0			0
$379$	6.12378	−	18.8470i	0.314557	−	0.968108i	−0.661379	−	0.750052i	$-0.730029\pi$
$379$	6.12378	−	18.8470i	0.314557	−	0.968108i	0.975936	−	0.218056i	$-0.0699715\pi$
$380$	−10.2739	−	11.4103i	−0.527040	−	0.585337i
$381$		0			0
$382$	4.82656	−	45.9216i	0.246948	−	2.34956i
$383$	−15.8421	+	17.5945i	−0.809495	+	0.899035i	−0.996523	−	0.0833197i	$-0.973448\pi$
$383$	−15.8421	+	17.5945i	−0.809495	+	0.899035i	0.187028	+	0.982355i	$0.440114\pi$
$384$		0			0
$385$	13.2733	−	5.01365i	0.676469	−	0.255519i
$386$	−42.5700			−2.16675
$387$		0			0
$388$	1.21776	+	0.884756i	0.0618225	+	0.0449167i
$389$	−0.890219	−	8.46987i	−0.0451359	−	0.429440i	−0.993634	−	0.112657i	$-0.964064\pi$
$389$	−0.890219	−	8.46987i	−0.0451359	−	0.429440i	0.948498	−	0.316783i	$-0.102603\pi$
$390$		0			0
$391$	−8.91366	+	1.89466i	−0.450783	+	0.0958169i
$392$	53.9079	+	24.0013i	2.72276	+	1.21225i
$393$		0			0
$394$	14.6031	+	3.10397i	0.735691	+	0.156376i
$395$	6.08063			0.305949
$396$		0			0
$397$	−3.78373			−0.189900			−0.0949499	−	0.995482i	$-0.530269\pi$
$397$	−3.78373			−0.189900			−0.0949499	+	0.995482i	$0.530269\pi$
$398$	24.3324	+	5.17201i	1.21967	+	0.259249i
$399$		0			0
$400$	−15.8743	−	7.06771i	−0.793717	−	0.353386i
$401$	−17.1698	+	3.64955i	−0.857417	+	0.182250i	−0.615587	−	0.788069i	$-0.711081\pi$
$401$	−17.1698	+	3.64955i	−0.857417	+	0.182250i	−0.241830	+	0.970319i	$0.577748\pi$
$402$		0			0
$403$	0.638333	+	6.07333i	0.0317976	+	0.302534i
$404$	−42.6100	−	30.9580i	−2.11993	−	1.54022i
$405$		0			0
$406$	−110.829			−5.50035
$407$	6.70957	+	8.37706i	0.332581	+	0.415236i
$408$		0			0
$409$	18.9300	−	21.0239i	0.936031	−	1.03957i	−0.0631055	−	0.998007i	$-0.520100\pi$
$409$	18.9300	−	21.0239i	0.936031	−	1.03957i	0.999136	−	0.0415603i	$-0.0132329\pi$
$410$	3.03101	−	28.8381i	0.149691	−	1.42421i
$411$		0			0
$412$	−32.0142	−	35.5554i	−1.57723	−	1.75169i
$413$	8.64439	−	26.6047i	0.425363	−	1.30913i
$414$		0			0
$415$	−2.69055	−	1.95480i	−0.132074	−	0.0959573i
$416$	−1.87843	−	0.399273i	−0.0920978	−	0.0195760i
$417$		0			0
$418$	−22.2011	+	21.9643i	−1.08589	+	1.07431i
$419$	16.1179	+	27.9170i	0.787409	+	1.36383i	0.927549	+	0.373701i	$0.121912\pi$
$419$	16.1179	+	27.9170i	0.787409	+	1.36383i	−0.140140	+	0.990132i	$0.544755\pi$
$420$		0			0
$421$	−25.9830	+	11.5684i	−1.26633	+	0.563807i	−0.926364	−	0.376630i	$-0.877083\pi$
$421$	−25.9830	+	11.5684i	−1.26633	+	0.563807i	−0.339968	+	0.940437i	$0.610416\pi$
$422$	−29.3421	+	21.3183i	−1.42835	+	1.03776i
$423$		0			0
$424$	−14.8023	+	45.5568i	−0.718863	+	2.21243i
$425$	1.10998	+	10.5607i	0.0538419	+	0.512271i
$426$		0			0
$427$	−13.9128	+	15.4517i	−0.673288	+	0.747762i
$428$	9.58158	+	16.5958i	0.463143	+	0.802188i
$429$		0			0
$430$	2.58504	−	4.47741i	0.124662	−	0.215920i
$431$	−8.27921	−	25.4808i	−0.398796	−	1.22737i	−0.925966	−	0.377607i	$-0.876747\pi$
$431$	−8.27921	−	25.4808i	−0.398796	−	1.22737i	0.527170	−	0.849760i	$-0.323253\pi$
$432$		0			0
$433$	7.60672	−	5.52661i	0.365556	−	0.265592i	−0.389810	−	0.920895i	$-0.627459\pi$
$433$	7.60672	−	5.52661i	0.365556	−	0.265592i	0.755366	+	0.655304i	$0.227459\pi$
$434$	−12.0101	−	13.3386i	−0.576505	−	0.640274i
$435$		0			0
$436$	59.9349	+	26.6848i	2.87036	+	1.27797i
$437$	1.38023	−	13.1320i	0.0660254	−	0.628189i
$438$		0			0
$439$	8.94810	−	15.4986i	0.427069	−	0.739706i	−0.569542	−	0.821962i	$-0.692879\pi$
$439$	8.94810	−	15.4986i	0.427069	−	0.739706i	0.996611	+	0.0822565i	$0.0262127\pi$
$440$	6.02578	−	15.4496i	0.287268	−	0.736531i
$441$		0			0
$442$	7.26552	+	22.3610i	0.345586	+	1.06360i
$443$	−16.7921	+	7.47633i	−0.797818	+	0.355211i	−0.764820	−	0.644244i	$-0.777172\pi$
$443$	−16.7921	+	7.47633i	−0.797818	+	0.355211i	−0.0329977	+	0.999455i	$0.510505\pi$
$444$		0			0
$445$	12.8382	−	2.72885i	0.608590	−	0.129360i
$446$	−1.47760	+	0.314073i	−0.0699663	+	0.0148718i
$447$		0			0
$448$	−28.9761	+	12.9010i	−1.36899	+	0.609514i
$449$	1.85302	+	5.70301i	0.0874494	+	0.269142i	0.985212	−	0.171337i	$-0.0548087\pi$
$449$	1.85302	+	5.70301i	0.0874494	+	0.269142i	−0.897763	+	0.440479i	$0.854809\pi$
$450$		0			0
$451$	−39.4268	−	2.27830i	−1.85654	−	0.107281i
$452$	−1.72198	+	2.98255i	−0.0809951	+	0.140288i
$453$		0			0
$454$	−2.98589	+	28.4088i	−0.140135	+	1.33329i
$455$	14.1399	+	6.29549i	0.662889	+	0.295137i
$456$		0			0
$457$	17.0861	+	18.9760i	0.799254	+	0.887661i	0.995679	−	0.0928576i	$-0.0296001\pi$
$457$	17.0861	+	18.9760i	0.799254	+	0.887661i	−0.196426	+	0.980519i	$0.562933\pi$
$458$	−1.61911	+	1.17635i	−0.0756562	+	0.0549674i
$459$		0			0
$460$	4.27717	+	13.1638i	0.199424	+	0.613764i
$461$	15.7842	−	27.3390i	0.735142	−	1.27330i	−0.219519	−	0.975608i	$-0.570449\pi$
$461$	15.7842	−	27.3390i	0.735142	−	1.27330i	0.954661	−	0.297695i	$-0.0962180\pi$
$462$		0			0
$463$	−1.88207	−	3.25984i	−0.0874671	−	0.151498i	0.818973	−	0.573832i	$-0.194544\pi$
$463$	−1.88207	−	3.25984i	−0.0874671	−	0.151498i	−0.906440	+	0.422335i	$0.861211\pi$
$464$	−30.1419	+	33.4760i	−1.39930	+	1.55408i
$465$		0			0
$466$	4.43662	+	42.2116i	0.205522	+	1.95541i
$467$	1.80825	−	5.56521i	0.0836756	−	0.257527i	−0.900462	−	0.434935i	$-0.856771\pi$
$467$	1.80825	−	5.56521i	0.0836756	−	0.257527i	0.984137	+	0.177408i	$0.0567713\pi$
$468$		0			0
$469$	−2.98656	+	2.16986i	−0.137907	+	0.100195i
$470$	9.56558	−	4.25887i	0.441227	−	0.196447i
$471$		0			0
$472$	−16.3474	−	28.3145i	−0.752449	−	1.30328i
$473$	−6.25671	−	3.23032i	−0.287684	−	0.148530i
$474$		0			0
$475$	−15.0505	−	3.19907i	−0.690562	−	0.146784i
$476$	−37.4352	−	27.1983i	−1.71584	−	1.24663i
$477$		0			0
$478$	−0.151868	+	0.467402i	−0.00694629	+	0.0213785i
$479$	17.1897	+	19.0911i	0.785418	+	0.872295i	0.994406	−	0.105623i	$-0.0336836\pi$
$479$	17.1897	+	19.0911i	0.785418	+	0.872295i	−0.208988	+	0.977918i	$0.567017\pi$
$480$		0			0
$481$	−1.22384	+	11.6441i	−0.0558023	+	0.530924i
$482$	24.4159	−	27.1166i	1.11211	−	1.23513i
$483$		0			0
$484$	−42.2532	−	14.2315i	−1.92060	−	0.646889i
$485$	−0.367573			−0.0166906
$486$		0			0
$487$	4.29919	+	3.12355i	0.194815	+	0.141541i	0.680917	−	0.732361i	$-0.261582\pi$
$487$	4.29919	+	3.12355i	0.194815	+	0.141541i	−0.486102	+	0.873902i	$0.661582\pi$
$488$	2.54018	+	24.1682i	0.114989	+	1.09404i
$489$		0			0
$490$	−27.8246	+	5.91431i	−1.25699	+	0.267181i
$491$	−2.25156	−	1.00246i	−0.101611	−	0.0452403i	0.355301	−	0.934752i	$-0.384378\pi$
$491$	−2.25156	−	1.00246i	−0.101611	−	0.0452403i	−0.456913	+	0.889511i	$0.651045\pi$
$492$		0			0
$493$	26.9265	+	5.72339i	1.21271	+	0.257769i
$494$	−34.0682			−1.53280
$495$		0			0
$496$	−7.29531			−0.327569
$497$	15.9731	+	3.39518i	0.716490	+	0.152295i
$498$		0			0
$499$	20.3744	+	9.07126i	0.912083	+	0.406085i	0.808473	−	0.588533i	$-0.200294\pi$
$499$	20.3744	+	9.07126i	0.912083	+	0.406085i	0.103609	+	0.994618i	$0.466961\pi$
$500$	35.3971	−	7.52388i	1.58301	−	0.336478i
$501$		0			0
$502$	−2.19280	−	20.8631i	−0.0978692	−	0.931164i
$503$	21.0129	+	15.2667i	0.936917	+	0.680710i	0.947677	−	0.319232i	$-0.103425\pi$
$503$	21.0129	+	15.2667i	0.936917	+	0.680710i	−0.0107594	+	0.999942i	$0.503425\pi$
$504$		0			0
$505$	12.8615			0.572331
$506$	26.3367	−	9.94804i	1.17081	−	0.442244i
$507$		0			0
$508$	31.6090	−	35.1054i	1.40242	−	1.55755i
$509$	−2.91364	+	27.7214i	−0.129145	+	1.22873i	0.717495	+	0.696563i	$0.245288\pi$
$509$	−2.91364	+	27.7214i	−0.129145	+	1.22873i	−0.846640	+	0.532166i	$0.821378\pi$
$510$		0			0
$511$	32.9941	+	36.6436i	1.45957	+	1.62102i
$512$	−12.7852	+	39.3489i	−0.565033	+	1.73899i
$513$		0			0
$514$	25.8731	+	18.7979i	1.14121	+	0.829139i
$515$	11.4281	+	2.42913i	0.503584	+	0.107040i
$516$		0			0
$517$	−6.40606	−	12.7410i	−0.281738	−	0.560349i
$518$	−17.2062	−	29.8020i	−0.755997	−	1.30943i
$519$		0			0
$520$	16.5262	−	7.35793i	0.724721	−	0.322667i
$521$	20.9287	−	15.2056i	0.916902	−	0.666168i	−0.0258491	−	0.999666i	$-0.508229\pi$
$521$	20.9287	−	15.2056i	0.916902	−	0.666168i	0.942751	+	0.333498i	$0.108229\pi$
$522$		0			0
$523$	−8.42503	+	25.9296i	−0.368401	+	1.13382i	0.579423	+	0.815027i	$0.303278\pi$
$523$	−8.42503	+	25.9296i	−0.368401	+	1.13382i	−0.947824	+	0.318794i	$0.896722\pi$
$524$	0.102870	+	0.978739i	0.00449388	+	0.0427564i
$525$		0			0
$526$	−24.4520	+	27.1567i	−1.06616	+	1.18409i
$527$	2.22909	+	3.86090i	0.0971008	+	0.168184i
$528$		0			0
$529$	5.54836	−	9.61004i	0.241233	−	0.417828i
$530$	−7.13563	−	21.9612i	−0.309952	−	0.953934i
$531$		0			0
$532$	54.2433	−	39.4100i	2.35174	−	1.70864i
$533$	−28.8272	−	32.0159i	−1.24865	−	1.38676i
$534$		0			0
$535$	−4.27500	−	1.90335i	−0.184824	−	0.0822891i
$536$	−0.450998	+	4.29096i	−0.0194801	+	0.185341i
$537$		0			0
$538$	4.68906	−	8.12169i	0.202160	−	0.350151i
$539$	9.82654	+	37.4757i	0.423259	+	1.61419i
$540$		0			0
$541$	−7.22580	−	22.2387i	−0.310661	−	0.956118i	−0.977504	−	0.210919i	$-0.932354\pi$
$541$	−7.22580	−	22.2387i	−0.310661	−	0.956118i	0.666842	−	0.745199i	$-0.267646\pi$
$542$	−31.1015	+	13.8473i	−1.33592	+	0.594791i
$543$		0			0
$544$	−1.37133	+	0.291485i	−0.0587953	+	0.0124973i
$545$	−15.6709	+	3.33095i	−0.671266	+	0.142682i
$546$		0			0
$547$	13.9617	−	6.21614i	0.596958	−	0.265783i	−0.0859357	−	0.996301i	$-0.527388\pi$
$547$	13.9617	−	6.21614i	0.596958	−	0.265783i	0.682894	+	0.730518i	$0.260721\pi$
$548$	0.569506	+	1.75276i	0.0243281	+	0.0748741i
$549$		0			0
$550$	−8.32077	−	31.7331i	−0.354799	−	1.35310i
$551$	−19.9439	+	34.5438i	−0.849638	+	1.47162i
$552$		0			0
$553$	−2.77554	+	26.4075i	−0.118028	+	1.12296i
$554$	5.52471	+	2.45976i	0.234723	+	0.104505i
$555$		0			0
$556$	−48.3873	−	53.7395i	−2.05208	−	2.27906i
$557$	5.85761	−	4.25580i	0.248195	−	0.180324i	−0.456732	−	0.889605i	$-0.650980\pi$
$557$	5.85761	−	4.25580i	0.248195	−	0.180324i	0.704926	+	0.709280i	$0.250980\pi$
$558$		0			0
$559$	−2.37366	−	7.30537i	−0.100395	−	0.308984i
$560$	−9.24522	+	16.0132i	−0.390682	+	0.676681i
$561$		0			0
$562$	−24.5056	−	42.4450i	−1.03371	−	1.79043i
$563$	21.1044	−	23.4389i	0.889446	−	0.987830i	−0.110535	−	0.993872i	$-0.535257\pi$
$563$	21.1044	−	23.4389i	0.889446	−	0.987830i	0.999982	+	0.00604200i	$0.00192324\pi$
$564$		0			0
$565$	−0.0879086	−	0.836394i	−0.00369834	−	0.0351874i
$566$	5.46532	−	16.8205i	0.229725	−	0.707019i
$567$		0			0
$568$	15.4407	−	11.2183i	0.647879	−	0.470711i
$569$	10.2155	−	4.54824i	0.428256	−	0.190672i	−0.181278	−	0.983432i	$-0.558023\pi$
$569$	10.2155	−	4.54824i	0.428256	−	0.190672i	0.609534	+	0.792760i	$0.291357\pi$
$570$		0			0
$571$	−5.79531	−	10.0378i	−0.242526	−	0.420068i	0.718907	−	0.695106i	$-0.244643\pi$
$571$	−5.79531	−	10.0378i	−0.242526	−	0.420068i	−0.961433	+	0.275039i	$0.911309\pi$
$572$	−21.8482	−	43.4539i	−0.913521	−	1.81690i
$573$		0			0
$574$	123.857	+	26.3267i	5.16970	+	1.09885i
$575$	11.2215	+	8.15293i	0.467971	+	0.340001i
$576$		0			0
$577$	5.23344	−	16.1069i	0.217871	−	0.670537i	−0.781067	−	0.624448i	$-0.785324\pi$
$577$	5.23344	−	16.1069i	0.217871	−	0.670537i	0.998937	−	0.0460895i	$-0.0146760\pi$
$578$	−16.5015	−	18.3268i	−0.686373	−	0.762295i
$579$		0			0
$580$	4.37050	−	41.5826i	0.181475	−	1.72662i
$581$	9.71758	−	10.7925i	0.403153	−	0.447747i
$582$		0			0
$583$	−29.4206	+	11.1129i	−1.21848	+	0.460249i
$584$	57.6304			2.38476
$585$		0			0
$586$	33.9606	+	24.6738i	1.40290	+	1.01927i
$587$	−0.945646	−	8.99722i	−0.0390310	−	0.371355i	−0.996551	−	0.0829870i	$-0.973554\pi$
$587$	−0.945646	−	8.99722i	−0.0390310	−	0.371355i	0.957520	−	0.288368i	$-0.0931127\pi$
$588$		0			0
$589$	−6.31870	+	1.34308i	−0.260358	+	0.0553407i
$590$	14.3983	+	6.41054i	0.592769	+	0.263918i
$591$		0			0
$592$	−13.6813	−	2.90804i	−0.562296	−	0.119520i
$593$	−20.4127			−0.838248			−0.419124	−	0.907929i	$-0.637663\pi$
$593$	−20.4127			−0.838248			−0.419124	+	0.907929i	$0.637663\pi$
$594$		0			0
$595$	11.2996			0.463237
$596$	−63.1902	−	13.4315i	−2.58837	−	0.550175i
$597$		0			0
$598$	28.0562	+	12.4914i	1.14731	+	0.510813i
$599$	−41.1036	+	8.73685i	−1.67945	+	0.356978i	−0.946350	−	0.323144i	$-0.895260\pi$
$599$	−41.1036	+	8.73685i	−1.67945	+	0.356978i	−0.733099	+	0.680122i	$0.761927\pi$
$600$		0			0
$601$	1.11794	+	10.6365i	0.0456018	+	0.433872i	0.993374	+	0.114925i	$0.0366627\pi$
$601$	1.11794	+	10.6365i	0.0456018	+	0.433872i	−0.947772	+	0.318948i	$0.896671\pi$
$602$	18.2649	+	13.2703i	0.744423	+	0.540855i
$603$		0			0
$604$	24.5364			0.998373
$605$	10.3902	−	3.25323i	0.422422	−	0.132263i
$606$		0			0
$607$	−30.5120	+	33.8870i	−1.23844	+	1.37543i	−0.337595	+	0.941291i	$0.609614\pi$
$607$	−30.5120	+	33.8870i	−1.23844	+	1.37543i	−0.900847	+	0.434138i	$0.857053\pi$
$608$	0.212343	−	2.02030i	0.00861163	−	0.0819342i
$609$		0			0
$610$	−7.83870	−	8.70576i	−0.317380	−	0.352486i
$611$	4.80732	−	14.7954i	0.194483	−	0.598558i
$612$		0			0
$613$	−21.9790	−	15.9687i	−0.887725	−	0.644970i	0.0475592	−	0.998868i	$-0.484856\pi$
$613$	−21.9790	−	15.9687i	−0.887725	−	0.644970i	−0.935284	+	0.353899i	$0.884856\pi$
$614$	−18.0214	−	3.83056i	−0.727284	−	0.154589i
$615$		0			0
$616$	64.3453	+	33.2213i	2.59255	+	1.33852i
$617$	3.91559	+	6.78199i	0.157636	+	0.273033i	0.934016	−	0.357232i	$-0.116280\pi$
$617$	3.91559	+	6.78199i	0.157636	+	0.273033i	−0.776380	+	0.630265i	$0.782946\pi$
$618$		0			0
$619$	34.6480	−	15.4263i	1.39262	−	0.620034i	0.433015	−	0.901387i	$-0.357450\pi$
$619$	34.6480	−	15.4263i	1.39262	−	0.620034i	0.959604	+	0.281353i	$0.0907831\pi$
$620$	5.47820	−	3.98015i	0.220010	−	0.159847i
$621$		0			0
$622$	7.99883	−	24.6179i	0.320724	−	0.987087i
$623$	5.99100	+	57.0005i	0.240024	+	2.28368i
$624$		0			0
$625$	7.53756	−	8.37131i	0.301503	−	0.334852i
$626$	12.8364	+	22.2332i	0.513044	+	0.888618i
$627$		0			0
$628$	−15.1629	+	26.2628i	−0.605064	+	1.04800i
$629$	2.64130	+	8.12910i	0.105316	+	0.324128i
$630$		0			0
$631$	22.3432	−	16.2333i	0.889468	−	0.646237i	−0.0462710	−	0.998929i	$-0.514734\pi$
$631$	22.3432	−	16.2333i	0.889468	−	0.646237i	0.935739	+	0.352692i	$0.114734\pi$
$632$	20.7658	+	23.0628i	0.826021	+	0.917389i
$633$		0			0
$634$	28.7428	+	12.7971i	1.14152	+	0.508238i
$635$	−1.20579	+	11.4724i	−0.0478505	+	0.455267i
$636$		0			0
$637$	−21.1317	+	36.6012i	−0.837269	+	1.45019i
$638$	−84.9029	−	4.90614i	−3.36134	−	0.194236i
$639$		0			0
$640$	−5.84701	−	17.9952i	−0.231123	−	0.711324i
$641$	−4.08552	+	1.81899i	−0.161368	+	0.0718457i	−0.485831	−	0.874053i	$-0.661483\pi$
$641$	−4.08552	+	1.81899i	−0.161368	+	0.0718457i	0.324463	+	0.945898i	$0.394816\pi$
$642$		0			0
$643$	7.30833	−	1.55343i	0.288212	−	0.0612614i	−0.0615368	−	0.998105i	$-0.519600\pi$
$643$	7.30833	−	1.55343i	0.288212	−	0.0612614i	0.349749	+	0.936843i	$0.386267\pi$
$644$	−59.1211	+	12.5666i	−2.32970	+	0.495192i
$645$		0			0
$646$	−22.7209	+	10.1160i	−0.893942	+	0.398009i
$647$	−3.55862	−	10.9523i	−0.139904	−	0.430579i	0.856417	−	0.516285i	$-0.172686\pi$
$647$	−3.55862	−	10.9523i	−0.139904	−	0.430579i	−0.996320	+	0.0857057i	$0.972686\pi$
$648$		0			0
$649$	7.79994	−	19.9984i	0.306174	−	0.785006i
$650$	17.8936	−	30.9926i	0.701845	−	1.21563i
$651$		0			0
$652$	−5.92158	+	56.3401i	−0.231907	+	2.20645i
$653$	19.3109	+	8.59776i	0.755693	+	0.336456i	0.748163	−	0.663515i	$-0.230936\pi$
$653$	19.3109	+	8.59776i	0.755693	+	0.336456i	0.00753058	+	0.999972i	$0.497603\pi$
$654$		0			0
$655$	−0.160806	−	0.178593i	−0.00628321	−	0.00697821i
$656$	41.6372	−	30.2512i	1.62566	−	1.18111i
$657$		0			0
$658$	14.1295	+	43.4862i	0.550826	+	1.69527i
$659$	−13.5177	+	23.4133i	−0.526575	+	0.912054i	0.472946	+	0.881091i	$0.343191\pi$
$659$	−13.5177	+	23.4133i	−0.526575	+	0.912054i	−0.999521	+	0.0309624i	$0.990143\pi$
$660$		0			0
$661$	13.3809	+	23.1764i	0.520456	+	0.901457i	0.999717	+	0.0237842i	$0.00757146\pi$
$661$	13.3809	+	23.1764i	0.520456	+	0.901457i	−0.479261	+	0.877673i	$0.659095\pi$
$662$	26.9742	−	29.9579i	1.04838	−	1.16435i
$663$		0			0
$664$	−1.77422	−	16.8806i	−0.0688532	−	0.655095i
$665$	−5.05952	+	15.5716i	−0.196200	+	0.603841i
$666$		0			0
$667$	29.0902	−	21.1353i	1.12638	−	0.818362i
$668$	23.6654	−	10.5365i	0.915642	−	0.407670i
$669$		0			0
$670$	−1.03995	−	1.80125i	−0.0401768	−	0.0695883i
$671$	−11.3422	+	11.2212i	−0.437861	+	0.433191i
$672$		0			0
$673$	−48.0644	−	10.2164i	−1.85275	−	0.393813i	−0.859627	−	0.510922i	$-0.829304\pi$
$673$	−48.0644	−	10.2164i	−1.85275	−	0.393813i	−0.993119	+	0.117108i	$0.962638\pi$
$674$	−57.8571	−	42.0356i	−2.22857	−	1.61915i
$675$		0			0
$676$	0.112939	−	0.347591i	0.00434382	−	0.0133689i
$677$	−30.5707	−	33.9522i	−1.17493	−	1.30489i	−0.943245	−	0.332097i	$-0.892244\pi$
$677$	−30.5707	−	33.9522i	−1.17493	−	1.30489i	−0.231681	−	0.972792i	$-0.574423\pi$
$678$		0			0
$679$	0.167781	−	1.59633i	0.00643883	−	0.0612614i
$680$	8.83689	−	9.81436i	0.338879	−	0.376363i
$681$		0			0
$682$	−8.61014	−	10.7500i	−0.329699	−	0.411638i
$683$	47.1991			1.80602			0.903012	−	0.429615i	$-0.141351\pi$
$683$	47.1991			1.80602			0.903012	+	0.429615i	$0.141351\pi$
$684$		0			0
$685$	−0.364093	−	0.264529i	−0.0139113	−	0.0101071i
$686$	−5.20356	−	49.5086i	−0.198673	−	1.89025i
$687$		0			0
$688$	8.97577	−	1.90786i	0.342198	−	0.0727364i
$689$	−31.3415	−	13.9541i	−1.19402	−	0.531610i
$690$		0			0
$691$	−29.1327	−	6.19234i	−1.10826	−	0.235568i	−0.382799	−	0.923832i	$-0.625040\pi$
$691$	−29.1327	−	6.19234i	−1.10826	−	0.235568i	−0.725460	+	0.688264i	$0.758373\pi$
$692$	31.8002			1.20886
$693$		0			0
$694$	−53.1004			−2.01566
$695$	17.2728	+	3.67145i	0.655196	+	0.139266i
$696$		0			0
$697$	−28.7322	−	12.7924i	−1.08831	−	0.484546i
$698$	−58.2397	+	12.3792i	−2.20441	+	0.468561i
$699$		0			0
$700$	7.36209	+	70.0456i	0.278261	+	2.64747i
$701$	0.479434	+	0.348329i	0.0181080	+	0.0131562i	0.596802	−	0.802388i	$-0.296438\pi$
$701$	0.479434	+	0.348329i	0.0181080	+	0.0131562i	−0.578694	+	0.815544i	$0.696438\pi$
$702$		0			0
$703$	−12.3851			−0.467115
$704$	−22.7688	+	8.60036i	−0.858132	+	0.324138i
$705$		0			0
$706$	−34.5391	+	38.3595i	−1.29990	+	1.44368i
$707$	−5.87072	+	55.8562i	−0.220791	+	2.10069i
$708$		0			0
$709$	−22.6402	−	25.1445i	−0.850272	−	0.944323i	0.148735	−	0.988877i	$-0.452480\pi$
$709$	−22.6402	−	25.1445i	−0.850272	−	0.944323i	−0.999007	+	0.0445541i	$0.985813\pi$
$710$	−2.84312	+	8.75023i	−0.106700	+	0.328390i
$711$		0			0
$712$	54.1937	+	39.3740i	2.03099	+	1.47560i
$713$	5.69610	+	1.21074i	0.213321	+	0.0453427i
$714$		0			0
$715$	10.5535	+	5.44873i	0.394678	+	0.203771i
$716$	9.87963	+	17.1120i	0.369219	+	0.639507i
$717$		0			0
$718$	35.2505	−	15.6945i	1.31554	−	0.585715i
$719$	39.3929	−	28.6206i	1.46911	−	1.06737i	0.488236	−	0.872712i	$-0.337641\pi$
$719$	39.3929	−	28.6206i	1.46911	−	1.06737i	0.980871	−	0.194657i	$-0.0623593\pi$
$720$		0			0
$721$	−15.7659	+	48.5223i	−0.587151	+	1.80707i
$722$	1.11932	+	10.6496i	0.0416568	+	0.396338i
$723$		0			0
$724$	24.5358	−	27.2498i	0.911867	−	1.01273i
$725$	−20.9502	−	36.2868i	−0.778071	−	1.34766i
$726$		0			0
$727$	19.2353	−	33.3166i	0.713399	−	1.23564i	−0.250175	−	0.968201i	$-0.580488\pi$
$727$	19.2353	−	33.3166i	0.713399	−	1.23564i	0.963574	−	0.267442i	$-0.0861784\pi$
$728$	24.4112	+	75.1299i	0.904739	+	2.78450i
$729$		0			0
$730$	−22.4756	+	16.3295i	−0.831861	+	0.604382i
$731$	−3.75226	−	4.16730i	−0.138782	−	0.154133i
$732$		0			0
$733$	8.72641	+	3.88525i	0.322317	+	0.143505i	0.561516	−	0.827466i	$-0.310218\pi$
$733$	8.72641	+	3.88525i	0.322317	+	0.143505i	−0.239199	+	0.970971i	$0.576885\pi$
$734$	2.10743	−	20.0508i	0.0777866	−	0.740090i
$735$		0			0
$736$	−0.915635	+	1.58593i	−0.0337507	+	0.0584580i
$737$	−2.38397	+	1.53006i	−0.0878146	+	0.0563605i
$738$		0			0
$739$	5.87978	+	18.0961i	0.216291	+	0.665675i	0.999059	+	0.0433623i	$0.0138070\pi$
$739$	5.87978	+	18.0961i	0.216291	+	0.665675i	−0.782768	+	0.622313i	$0.786193\pi$
$740$	11.8601	−	5.28046i	0.435986	−	0.194113i
$741$		0			0
$742$	98.6321	−	20.9649i	3.62090	−	0.769646i
$743$	12.4371	−	2.64358i	0.456272	−	0.0969837i	0.0259585	−	0.999663i	$-0.491736\pi$
$743$	12.4371	−	2.64358i	0.456272	−	0.0969837i	0.430314	+	0.902679i	$0.358403\pi$
$744$		0			0
$745$	14.4117	−	6.41649i	0.528003	−	0.235082i
$746$	23.4298	+	72.1095i	0.857826	+	2.64012i
$747$		0			0
$748$	−27.4740	−	22.4930i	−1.00455	−	0.822425i
$749$	10.2174	−	17.6970i	0.373335	−	0.646636i
$750$		0			0
$751$	3.98798	−	37.9431i	0.145523	−	1.38456i	−0.641256	−	0.767327i	$-0.721586\pi$
$751$	3.98798	−	37.9431i	0.145523	−	1.38456i	0.786779	−	0.617235i	$-0.211747\pi$
$752$	16.9778	+	7.55901i	0.619117	+	0.275649i
$753$		0			0
$754$	−62.0774	−	68.9439i	−2.26072	−	2.51079i
$755$	−4.84739	+	3.52184i	−0.176415	+	0.128173i
$756$		0			0
$757$	2.01311	+	6.19571i	0.0731677	+	0.225187i	0.980952	−	0.194250i	$-0.0622274\pi$
$757$	2.01311	+	6.19571i	0.0731677	+	0.225187i	−0.907784	+	0.419437i	$0.862227\pi$
$758$	−24.3781	+	42.2242i	−0.885453	+	1.53365i
$759$		0			0
$760$	9.56805	+	16.5724i	0.347070	+	0.601142i
$761$	30.0628	−	33.3881i	1.08977	−	1.21032i	0.113555	−	0.993532i	$-0.463776\pi$
$761$	30.0628	−	33.3881i	1.08977	−	1.21032i	0.976219	−	0.216785i	$-0.0695570\pi$
$762$		0			0
$763$	−7.31286	−	69.5772i	−0.264743	−	2.51887i
$764$	−23.5068	+	72.3464i	−0.850445	+	2.61740i
$765$		0			0
$766$	47.1252	−	34.2385i	1.70270	−	1.23709i
$767$	21.3920	−	9.52432i	0.772419	−	0.343903i
$768$		0			0
$769$	0.0411390	+	0.0712548i	0.00148351	+	0.00256951i	0.866766	−	0.498715i	$-0.166194\pi$
$769$	0.0411390	+	0.0712548i	0.00148351	+	0.00256951i	−0.865283	+	0.501284i	$0.832861\pi$
$770$	−34.5077	+	5.27599i	−1.24357	+	0.190133i
$771$		0			0
$772$	68.5986	+	14.5811i	2.46892	+	0.524784i
$773$	15.3850	+	11.1779i	0.553361	+	0.402040i	0.829023	−	0.559215i	$-0.188897\pi$
$773$	15.3850	+	11.1779i	0.553361	+	0.402040i	−0.275662	+	0.961255i	$0.588897\pi$
$774$		0			0
$775$	2.09693	−	6.45369i	0.0753240	−	0.231823i
$776$	−1.25529	−	1.39414i	−0.0450624	−	0.0500468i
$777$		0			0
$778$	−2.19023	+	20.8387i	−0.0785237	+	0.747103i
$779$	30.4940	−	33.8670i	1.09256	−	1.21341i
$780$		0			0
$781$	12.0862	+	3.30804i	0.432478	+	0.118371i
$782$	22.4205			0.801755
$783$		0			0
$784$	−40.8464	−	29.6766i	−1.45880	−	1.05988i
$785$	−0.774077	−	7.36485i	−0.0276280	−	0.262863i
$786$		0			0
$787$	−8.44126	+	1.79425i	−0.300899	+	0.0639580i	−0.355887	−	0.934529i	$-0.615821\pi$
$787$	−8.44126	+	1.79425i	−0.300899	+	0.0639580i	0.0549883	+	0.998487i	$0.482488\pi$
$788$	−22.4686	−	10.0037i	−0.800412	−	0.356366i
$789$		0			0
$790$	−14.6334	−	3.11043i	−0.520634	−	0.110664i
$791$	3.67249			0.130579
$792$		0			0
$793$	−17.4049			−0.618068
$794$	9.10579	+	1.93550i	0.323152	+	0.0686882i
$795$		0			0
$796$	−37.4385	−	16.6687i	−1.32697	−	0.590805i
$797$	16.2116	−	3.44587i	0.574243	−	0.122059i	0.0883685	−	0.996088i	$-0.471835\pi$
$797$	16.2116	−	3.44587i	0.574243	−	0.122059i	0.485874	+	0.874029i	$0.338501\pi$
$798$		0			0
$799$	−1.18714	−	11.2949i	−0.0419979	−	0.399583i
$800$	1.72639	+	1.25429i	0.0610370	+	0.0443460i
$801$		0			0
$802$	43.1870			1.52499
$803$	23.6537	+	29.5322i	0.834720	+	1.04217i
$804$		0			0
$805$	9.87615	−	10.9686i	0.348089	−	0.386592i
$806$	1.57051	−	14.9424i	0.0553188	−	0.526324i
$807$		0			0
$808$	43.9232	+	48.7817i	1.54521	+	1.71613i
$809$	−6.99703	+	21.5347i	−0.246003	+	0.757118i	0.749467	+	0.662041i	$0.230310\pi$
$809$	−6.99703	+	21.5347i	−0.246003	+	0.757118i	−0.995470	+	0.0950768i	$0.969690\pi$
$810$		0			0
$811$	45.7773	+	33.2592i	1.60746	+	1.16789i	0.870823	+	0.491597i	$0.163587\pi$
$811$	45.7773	+	33.2592i	1.60746	+	1.16789i	0.736635	+	0.676290i	$0.236413\pi$
$812$	178.593	+	37.9612i	6.26740	+	1.33218i
$813$		0			0
$814$	−11.8619	−	23.5921i	−0.415759	−	0.826903i
$815$	−6.91691	−	11.9804i	−0.242289	−	0.419657i
$816$		0			0
$817$	7.42296	−	3.30491i	0.259696	−	0.115624i
$818$	−56.3108	+	40.9122i	−1.96886	+	1.43046i
$819$		0			0
$820$	−14.7619	+	45.4325i	−0.515508	+	1.58657i
$821$	−4.94936	−	47.0900i	−0.172734	−	1.64345i	−0.646581	−	0.762845i	$-0.723802\pi$
$821$	−4.94936	−	47.0900i	−0.172734	−	1.64345i	0.473847	−	0.880607i	$-0.342865\pi$
$822$		0			0
$823$	−4.67112	+	5.18781i	−0.162825	+	0.180836i	−0.819036	−	0.573742i	$-0.805491\pi$
$823$	−4.67112	+	5.18781i	−0.162825	+	0.180836i	0.656211	+	0.754577i	$0.272158\pi$
$824$	29.8148	+	51.6407i	1.03865	+	1.79899i
$825$		0			0
$826$	−34.4124	+	59.6041i	−1.19736	+	2.07389i
$827$	−12.3062	−	37.8747i	−0.427929	−	1.31703i	−0.900161	−	0.435557i	$-0.856551\pi$
$827$	−12.3062	−	37.8747i	−0.427929	−	1.31703i	0.472232	−	0.881474i	$-0.343449\pi$
$828$		0			0
$829$	26.7634	−	19.4447i	0.929530	−	0.675343i	−0.0163480	−	0.999866i	$-0.505204\pi$
$829$	26.7634	−	19.4447i	0.929530	−	0.675343i	0.945878	+	0.324524i	$0.105204\pi$
$830$	5.47505	+	6.08065i	0.190042	+	0.211063i
$831$		0			0
$832$	−24.2554	−	10.7992i	−0.840905	−	0.374395i
$833$	−3.22511	+	30.6849i	−0.111744	+	1.06317i
$834$		0			0
$835$	−3.16295	+	5.47840i	−0.109459	+	0.189588i
$836$	43.2987	−	27.7896i	1.49752	−	0.961125i
$837$		0			0
$838$	−24.5083	−	75.4288i	−0.846626	−	2.60565i
$839$	31.2378	−	13.9080i	1.07845	−	0.480156i	0.210899	−	0.977508i	$-0.432361\pi$
$839$	31.2378	−	13.9080i	1.07845	−	0.480156i	0.867549	+	0.497352i	$0.165694\pi$
$840$		0			0
$841$	−77.8808	+	16.5541i	−2.68555	+	0.570830i
$842$	68.4473	−	14.5489i	2.35885	−	0.501389i
$843$		0			0
$844$	54.5847	−	24.3027i	1.87888	−	0.836532i
$845$	0.0275793	+	0.0848805i	0.000948758	+	0.00291998i
$846$		0			0
$847$	9.38576	+	46.6085i	0.322498	+	1.60149i
$848$	20.4923	−	35.4937i	0.703708	−	1.21886i
$849$		0			0
$850$	2.73092	−	25.9829i	0.0936696	−	0.891207i
$851$	10.1996	+	4.54113i	0.349636	+	0.155668i
$852$		0			0
$853$	−5.11297	−	5.67853i	−0.175065	−	0.194429i	0.649226	−	0.760595i	$-0.275093\pi$
$853$	−5.11297	−	5.67853i	−0.175065	−	0.194429i	−0.824291	+	0.566166i	$0.808426\pi$
$854$	41.3861	−	30.0688i	1.41620	−	1.02893i
$855$		0			0
$856$	−7.38038	−	22.7145i	−0.252256	−	0.776365i
$857$	−13.8026	+	23.9068i	−0.471488	+	0.816641i	−0.999468	−	0.0326159i	$-0.989616\pi$
$857$	−13.8026	+	23.9068i	−0.471488	+	0.816641i	0.527980	+	0.849257i	$0.322950\pi$
$858$		0			0
$859$	8.51219	+	14.7435i	0.290432	+	0.503043i	0.973912	−	0.226926i	$-0.0728676\pi$
$859$	8.51219	+	14.7435i	0.290432	+	0.503043i	−0.683480	+	0.729969i	$0.739534\pi$
$860$	−5.69921	+	6.32962i	−0.194342	+	0.215838i
$861$		0			0
$862$	6.89025	+	65.5563i	0.234683	+	2.23286i
$863$	3.17117	−	9.75984i	0.107948	−	0.332229i	−0.882463	−	0.470381i	$-0.844116\pi$
$863$	3.17117	−	9.75984i	0.107948	−	0.332229i	0.990411	+	0.138152i	$0.0441164\pi$
$864$		0			0
$865$	−6.28240	+	4.56443i	−0.213608	+	0.155195i
$866$	−21.1331	+	9.40907i	−0.718132	+	0.319733i
$867$		0			0
$868$	14.7848	+	25.6080i	0.501828	+	0.869191i
$869$	−3.29525	+	20.1071i	−0.111784	+	0.682087i
$870$		0			0
$871$	−3.02264	−	0.642482i	−0.102418	−	0.0217697i
$872$	−66.1511	−	48.0616i	−2.24016	−	1.62757i
$873$		0			0
$874$	−10.0391	+	30.8970i	−0.339576	+	1.04511i
$875$	−25.8212	−	28.6774i	−0.872917	−	0.969472i
$876$		0			0
$877$	2.32707	−	22.1406i	0.0785796	−	0.747635i	−0.882304	−	0.470681i	$-0.844008\pi$
$877$	2.32707	−	22.1406i	0.0785796	−	0.747635i	0.960883	−	0.276954i	$-0.0893250\pi$
$878$	−29.4622	+	32.7211i	−0.994301	+	1.10428i
$879$		0			0
$880$	−7.79136	+	11.8580i	−0.262647	+	0.399732i
$881$	−3.58540			−0.120795			−0.0603976	−	0.998174i	$-0.519237\pi$
$881$	−3.58540			−0.120795			−0.0603976	+	0.998174i	$0.519237\pi$
$882$		0			0
$883$	−36.3972	−	26.4441i	−1.22486	−	0.889916i	−0.228370	−	0.973574i	$-0.573340\pi$
$883$	−36.3972	−	26.4441i	−1.22486	−	0.889916i	−0.996495	+	0.0836583i	$0.973340\pi$
$884$	−4.04880	−	38.5218i	−0.136176	−	1.29563i
$885$		0			0
$886$	44.2357	−	9.40259i	1.48613	−	0.315886i
$887$	13.5238	+	6.02120i	0.454086	+	0.202172i	0.621018	−	0.783796i	$-0.286719\pi$
$887$	13.5238	+	6.02120i	0.454086	+	0.202172i	−0.166932	+	0.985968i	$0.553386\pi$
$888$		0			0
$889$	−49.2728	−	10.4733i	−1.65256	−	0.351262i
$890$	−32.2919			−1.08243
$891$		0			0
$892$	2.48862			0.0833253
$893$	16.0967	+	3.42145i	0.538654	+	0.114494i
$894$		0			0
$895$	−4.40798	−	1.96256i	−0.147343	−	0.0656012i
$896$	80.8202	−	17.1789i	2.70001	−	0.573905i
$897$		0			0
$898$	−1.54215	−	14.6726i	−0.0514621	−	0.489629i
$899$	−14.2316	−	10.3399i	−0.474651	−	0.344854i
$900$		0			0
$901$	−25.0458			−0.834397
$902$	93.7179	+	25.6509i	3.12047	+	0.854083i
$903$		0			0
$904$	2.87209	−	3.18978i	0.0955243	−	0.106090i
$905$	−0.935973	+	8.90519i	−0.0311128	+	0.296019i
$906$		0			0
$907$	16.0417	+	17.8162i	0.532657	+	0.591576i	0.948072	−	0.318056i	$-0.103030\pi$
$907$	16.0417	+	17.8162i	0.532657	+	0.591576i	−0.415415	+	0.909632i	$0.636363\pi$
$908$	14.5421	−	44.7561i	0.482598	−	1.48528i
$909$		0			0
$910$	−30.8083	−	22.3835i	−1.02128	−	0.742006i
$911$	21.9582	+	4.66736i	0.727507	+	0.154636i	0.556754	−	0.830677i	$-0.312047\pi$
$911$	21.9582	+	4.66736i	0.727507	+	0.154636i	0.170753	+	0.985314i	$0.445380\pi$
$912$		0			0
$913$	7.92211	−	7.83762i	0.262184	−	0.259387i
$914$	−31.4120	−	54.4071i	−1.03902	−	1.79963i
$915$		0			0
$916$	3.01201	−	1.34103i	0.0995197	−	0.0443090i
$917$	0.849011	−	0.616842i	0.0280368	−	0.0203699i
$918$		0			0
$919$	5.84951	−	18.0029i	0.192958	−	0.593862i	−0.807037	−	0.590501i	$-0.798930\pi$
$919$	5.84951	−	18.0029i	0.192958	−	0.593862i	0.999994	−	0.00336124i	$-0.00106992\pi$
$920$	−1.80318	−	17.1561i	−0.0594489	−	0.565619i
$921$		0			0
$922$	−51.9704	+	57.7190i	−1.71155	+	1.90087i
$923$	6.83475	+	11.8381i	0.224969	+	0.389657i
$924$		0			0
$925$	6.50503	−	11.2670i	0.213884	−	0.370458i
$926$	2.86181	+	8.80775i	0.0940450	+	0.289441i
$927$		0			0
$928$	4.47541	−	3.25158i	0.146913	−	0.106738i
$929$	14.7766	+	16.4111i	0.484805	+	0.538431i	0.935069	−	0.354464i	$-0.115337\pi$
$929$	14.7766	+	16.4111i	0.484805	+	0.538431i	−0.450264	+	0.892895i	$0.648670\pi$
$930$		0			0
$931$	−40.8419	−	18.1840i	−1.33854	−	0.595956i
$932$	7.30902	−	69.5407i	0.239415	−	2.27788i
$933$		0			0
$934$	−7.19844	+	12.4681i	−0.235540	+	0.407968i
$935$	8.65627	+	0.500206i	0.283090	+	0.0163585i
$936$		0			0
$937$	3.73772	+	11.5035i	0.122106	+	0.375804i	0.993363	−	0.115024i	$-0.0366945\pi$
$937$	3.73772	+	11.5035i	0.122106	+	0.375804i	−0.871257	+	0.490828i	$0.836694\pi$
$938$	8.29731	−	3.69420i	0.270917	−	0.120620i
$939$		0			0
$940$	−16.8730	+	3.58647i	−0.550337	+	0.116978i
$941$	20.1849	−	4.29044i	0.658009	−	0.139864i	0.133207	−	0.991088i	$-0.457472\pi$
$941$	20.1849	−	4.29044i	0.658009	−	0.139864i	0.524803	+	0.851224i	$0.324139\pi$
$942$		0			0
$943$	−37.5304	+	16.7096i	−1.22216	+	0.544140i
$944$	8.64439	+	26.6047i	0.281351	+	0.865909i
$945$		0			0
$946$	13.4048	+	10.9745i	0.435827	+	0.356812i
$947$	2.63723	−	4.56781i	0.0856983	−	0.148434i	−0.819990	−	0.572378i	$-0.806021\pi$
$947$	2.63723	−	4.56781i	0.0856983	−	0.148434i	0.905689	+	0.423944i	$0.139355\pi$
$948$		0			0
$949$	−4.31448	+	41.0495i	−0.140054	+	1.33252i
$950$	34.5835	+	15.3976i	1.12204	+	0.499563i
$951$		0			0
$952$	38.5890	+	42.8574i	1.25068	+	1.38902i
$953$	−43.2076	+	31.3922i	−1.39963	+	1.01689i	−0.404902	+	0.914360i	$0.632694\pi$
$953$	−43.2076	+	31.3922i	−1.39963	+	1.01689i	−0.994730	+	0.102532i	$0.967306\pi$
$954$		0			0
$955$	−5.74026	−	17.6667i	−0.185751	−	0.571681i
$956$	0.404820	−	0.701169i	0.0130928	−	0.0226774i
$957$		0			0
$958$	−31.6025	−	54.7371i	−1.02103	−	1.76848i
$959$	1.31501	−	1.46047i	0.0424639	−	0.0471610i
$960$		0			0
$961$	2.94259	+	27.9969i	0.0949222	+	0.903125i
$962$	8.90156	−	27.3962i	0.286998	−	0.883288i
$963$		0			0
$964$	−48.6326	+	35.3336i	−1.56635	+	1.13802i
$965$	−15.6452	+	6.96567i	−0.503635	+	0.224233i
$966$		0			0
$967$	−22.2765	−	38.5840i	−0.716363	−	1.24078i	−0.962432	−	0.271524i	$-0.912472\pi$
$967$	−22.2765	−	38.5840i	−0.716363	−	1.24078i	0.246069	−	0.969252i	$-0.420861\pi$
$968$	47.8224	+	28.2983i	1.53707	+	0.909541i
$969$		0			0
$970$	0.884589	+	0.188025i	0.0284024	+	0.00603712i
$971$	32.0517	+	23.2869i	1.02859	+	0.747313i	0.968026	−	0.250852i	$-0.0807106\pi$
$971$	32.0517	+	23.2869i	1.02859	+	0.747313i	0.0605623	+	0.998164i	$0.480711\pi$
$972$		0			0
$973$	−23.8290	+	73.3381i	−0.763922	+	2.35111i
$974$	−8.74850	−	9.71619i	−0.280320	−	0.311327i
$975$		0			0
$976$	2.17339	−	20.6785i	0.0695686	−	0.661901i
$977$	−38.0403	+	42.2480i	−1.21702	+	1.35163i	−0.299421	+	0.954121i	$0.596794\pi$
$977$	−38.0403	+	42.2480i	−1.21702	+	1.35163i	−0.917596	+	0.397514i	$0.869873\pi$
$978$		0			0
$979$	2.06624	+	43.9316i	0.0660374	+	1.40406i
$980$	46.8633			1.49699
$981$		0			0
$982$	4.90574	+	3.56423i	0.156548	+	0.113739i
$983$	−1.16822	−	11.1149i	−0.0372604	−	0.354509i	−0.997229	−	0.0743996i	$-0.976296\pi$
$983$	−1.16822	−	11.1149i	−0.0372604	−	0.354509i	0.959968	−	0.280109i	$-0.0903707\pi$
$984$		0			0
$985$	5.87476	−	1.24872i	0.187185	−	0.0397875i
$986$	−61.8726	−	27.5475i	−1.97043	−	0.877290i
$987$		0			0
$988$	54.8986	+	11.6691i	1.74656	+	0.371242i
$989$	−7.32482			−0.232916
$990$		0			0
$991$	−37.0475			−1.17685			−0.588426	−	0.808551i	$-0.700252\pi$
$991$	−37.0475			−1.17685			−0.588426	+	0.808551i	$0.700252\pi$
$992$	0.876321	+	0.186268i	0.0278232	+	0.00591401i
$993$		0			0
$994$	−36.7035	−	16.3414i	−1.16416	−	0.518319i
$995$	9.78884	−	2.08068i	0.310327	−	0.0659620i
$996$		0			0
$997$	−4.50445	−	42.8570i	−0.142657	−	1.35729i	−0.798317	−	0.602237i	$-0.794276\pi$
$997$	−4.50445	−	42.8570i	−0.142657	−	1.35729i	0.655660	−	0.755056i	$-0.272390\pi$
$998$	−44.3921	−	32.2527i	−1.40521	−	1.02094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.h.379.1		32
3.2	odd	2	inner	891.2.n.h.379.4		32
9.2	odd	6		297.2.f.b.82.1	✓	16
9.4	even	3	inner	891.2.n.h.676.4		32
9.5	odd	6	inner	891.2.n.h.676.1		32
9.7	even	3		297.2.f.b.82.4	yes	16
11.9	even	5	inner	891.2.n.h.460.4		32
33.20	odd	10	inner	891.2.n.h.460.1		32
99.20	odd	30		297.2.f.b.163.1	yes	16
99.25	even	15		3267.2.a.bj.1.8		8
99.31	even	15	inner	891.2.n.h.757.1		32
99.47	odd	30		3267.2.a.bj.1.1		8
99.52	odd	30		3267.2.a.bi.1.1		8
99.74	even	30		3267.2.a.bi.1.8		8
99.86	odd	30	inner	891.2.n.h.757.4		32
99.97	even	15		297.2.f.b.163.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.b.82.1	✓	16	9.2	odd	6
297.2.f.b.82.4	yes	16	9.7	even	3
297.2.f.b.163.1	yes	16	99.20	odd	30
297.2.f.b.163.4	yes	16	99.97	even	15
891.2.n.h.379.1		32	1.1	even	1	trivial
891.2.n.h.379.4		32	3.2	odd	2	inner
891.2.n.h.460.1		32	33.20	odd	10	inner
891.2.n.h.460.4		32	11.9	even	5	inner
891.2.n.h.676.1		32	9.5	odd	6	inner
891.2.n.h.676.4		32	9.4	even	3	inner
891.2.n.h.757.1		32	99.31	even	15	inner
891.2.n.h.757.4		32	99.86	odd	30	inner
3267.2.a.bi.1.1		8	99.52	odd	30
3267.2.a.bi.1.8		8	99.74	even	30
3267.2.a.bj.1.1		8	99.47	odd	30
3267.2.a.bj.1.8		8	99.25	even	15

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.40657 - 0.511531i) q^{2} +(3.70281 + 1.64860i) q^{4} +(-0.968153 + 0.205787i) q^{5} +(-0.451792 - 4.29851i) q^{7} +(-4.08684 - 2.96926i) q^{8} +2.43519 q^{10} +(-0.155819 - 3.31296i) q^{11} +(2.42094 - 2.68872i) q^{13} +(-1.11156 + 10.5758i) q^{14} +(2.89211 + 3.21201i) q^{16} +(0.816208 - 2.51203i) q^{17} +(3.09629 + 2.24958i) q^{19} +(-3.92414 - 0.834103i) q^{20} +(-1.31970 + 8.05257i) q^{22} +(-1.72506 - 2.98789i) q^{23} +(-3.67275 + 1.63522i) q^{25} +(-7.20151 + 5.23221i) q^{26} +(5.41361 - 16.6614i) q^{28} +(1.08941 + 10.3650i) q^{29} +(-1.12941 + 1.25433i) q^{31} +(-0.265393 - 0.459674i) q^{32} +(-3.24924 + 5.62785i) q^{34} +(1.32198 + 4.06865i) q^{35} +(-2.61803 + 1.90211i) q^{37} +(-6.30069 - 6.99762i) q^{38} +(4.56773 + 2.03368i) q^{40} +(1.24467 - 11.8422i) q^{41} +(1.06153 - 1.83863i) q^{43} +(4.88477 - 12.5241i) q^{44} +(2.62307 + 8.07297i) q^{46} +(3.92806 - 1.74888i) q^{47} +(-11.4261 + 2.42868i) q^{49} +(9.67519 - 2.05653i) q^{50} +(13.3969 - 5.96467i) q^{52} +(-2.93021 - 9.01826i) q^{53} +(0.832623 + 3.17539i) q^{55} +(-10.9170 + 18.9088i) q^{56} +(2.68031 - 25.5014i) q^{58} +(5.91260 + 2.63246i) q^{59} +(-3.21892 - 3.57498i) q^{61} +(3.35963 - 2.44091i) q^{62} +(-2.26771 - 6.97930i) q^{64} +(-1.79053 + 3.10129i) q^{65} +(-0.427051 - 0.739674i) q^{67} +(7.16358 - 7.95596i) q^{68} +(-1.10020 - 10.4677i) q^{70} +(-1.16751 + 3.59324i) q^{71} +(-9.22952 + 6.70564i) q^{73} +(7.27346 - 3.23835i) q^{74} +(7.75630 + 13.4343i) q^{76} +(-14.1704 + 2.16656i) q^{77} +(-6.00915 - 1.27728i) q^{79} +(-3.46100 - 2.51456i) q^{80} +(-9.05306 + 27.8625i) q^{82} +(2.24830 + 2.49699i) q^{83} +(-0.273271 + 2.60000i) q^{85} +(-3.49517 + 3.88177i) q^{86} +(-9.20025 + 14.0022i) q^{88} -13.2605 q^{89} +(-12.6513 - 9.19169i) q^{91} +(-1.46174 - 13.9075i) q^{92} +(-10.3477 + 2.19948i) q^{94} +(-3.46062 - 1.54077i) q^{95} +(0.363252 + 0.0772116i) q^{97} +28.7399 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{4} + 24 q^{10} + 10 q^{16} - 4 q^{19} + 36 q^{22} - 32 q^{25} + 84 q^{28} + 26 q^{31} + 48 q^{34} - 48 q^{37} + 20 q^{40} - 24 q^{43} - 32 q^{46} - 24 q^{49} + 40 q^{52} - 32 q^{55} - 106 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) \) 32 * q + 10 * q^4 + 24 * q^10 + 10 * q^16 - 4 * q^19 + 36 * q^22 - 32 * q^25 + 84 * q^28 + 26 * q^31 + 48 * q^34 - 48 * q^37 + 20 * q^40 - 24 * q^43 - 32 * q^46 - 24 * q^49 + 40 * q^52 - 32 * q^55 - 106 * q^58 + 6 * q^61 + 124 * q^64 + 40 * q^67 + 58 * q^70 - 60 * q^76 - 64 * q^79 - 168 * q^82 + 18 * q^85 - 80 * q^88 - 20 * q^91 - 90 * q^94 - 72 * q^97

Introduction

L-functions

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