LMFDB - Embedded newform 441.2.bg.a.395.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.14
Character	$\chi$	$=$	441.395
Dual form			441.2.bg.a.278.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50023 + 0.588795i) q^{2} +(0.437895 + 0.406307i) q^{4} +(-3.18030 - 2.16829i) q^{5} +(2.37141 - 1.17321i) q^{7} +(-0.980812 - 2.03668i) q^{8} +O(q^{10})$	\(q+(1.50023 + 0.588795i) q^{2} +(0.437895 + 0.406307i) q^{4} +(-3.18030 - 2.16829i) q^{5} +(2.37141 - 1.17321i) q^{7} +(-0.980812 - 2.03668i) q^{8} +(-3.49449 - 5.12548i) q^{10} +(-0.655355 - 4.34800i) q^{11} +(-3.43618 + 2.74026i) q^{13} +(4.24843 - 0.363804i) q^{14} +(-0.361535 - 4.82435i) q^{16} +(3.21706 + 0.992330i) q^{17} +(-0.776988 + 0.448594i) q^{19} +(-0.511645 - 2.24166i) q^{20} +(1.57690 - 6.90885i) q^{22} +(-0.732111 - 2.37344i) q^{23} +(3.58612 + 9.13730i) q^{25} +(-6.76850 + 2.08781i) q^{26} +(1.51511 + 0.449778i) q^{28} +(8.30122 - 1.89470i) q^{29} +(4.67386 + 2.69846i) q^{31} +(0.965559 - 3.13027i) q^{32} +(4.24203 + 3.38291i) q^{34} +(-10.0857 - 1.41075i) q^{35} +(5.45716 - 5.06350i) q^{37} +(-1.42979 + 0.215506i) q^{38} +(-1.29684 + 8.60394i) q^{40} +(-5.36277 + 2.58258i) q^{41} +(-2.54826 - 1.22718i) q^{43} +(1.47965 - 2.17024i) q^{44} +(0.299142 - 3.99177i) q^{46} +(1.55456 - 3.96096i) q^{47} +(4.24716 - 5.56432i) q^{49} +15.8195i q^{50} +(-2.61807 - 0.196198i) q^{52} +(-8.87284 + 9.56264i) q^{53} +(-7.34351 + 15.2490i) q^{55} +(-4.71536 - 3.67910i) q^{56} +(13.5693 + 2.04524i) q^{58} +(-6.88259 + 4.69247i) q^{59} +(2.93497 + 3.16315i) q^{61} +(5.42301 + 6.80024i) q^{62} +(-2.74110 + 3.43722i) q^{64} +(16.8698 - 1.26422i) q^{65} +(-1.42922 + 2.47548i) q^{67} +(1.00554 + 1.74165i) q^{68} +(-14.3001 - 8.05484i) q^{70} +(7.30694 + 1.66776i) q^{71} +(3.88677 - 1.52545i) q^{73} +(11.1683 - 4.38325i) q^{74} +(-0.522506 - 0.119259i) q^{76} +(-6.65522 - 9.54201i) q^{77} +(-1.80778 - 3.13117i) q^{79} +(-9.31082 + 16.1268i) q^{80} +(-9.56598 + 0.716871i) q^{82} +(8.34856 - 10.4688i) q^{83} +(-8.07955 - 10.1314i) q^{85} +(-3.10041 - 3.34145i) q^{86} +(-8.21269 + 5.59932i) q^{88} +(-3.95521 - 0.596152i) q^{89} +(-4.93369 + 10.5296i) q^{91} +(0.643760 - 1.33678i) q^{92} +(4.66439 - 5.02702i) q^{94} +(3.44374 + 0.258073i) q^{95} -18.1405i q^{97} +(9.64795 - 5.84702i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	1.50023	+	0.588795i	1.06082	+	0.416341i	0.830642	−	0.556807i	$-0.187974\pi$
$2$	1.50023	+	0.588795i	1.06082	+	0.416341i	0.230178	+	0.973148i	$0.426069\pi$
$3$		0			0
$3$		0			0
$4$	0.437895	+	0.406307i	0.218947	+	0.203154i
$5$	−3.18030	−	2.16829i	−1.42227	−	0.969691i	−0.997938	−	0.0641862i	$-0.979555\pi$
$5$	−3.18030	−	2.16829i	−1.42227	−	0.969691i	−0.424337	−	0.905504i	$-0.639493\pi$
$6$		0			0
$7$	2.37141	−	1.17321i	0.896308	−	0.443431i
$7$	2.37141	−	1.17321i	0.896308	−	0.443431i
$8$	−0.980812	−	2.03668i	−0.346770	−	0.720074i
$9$		0			0
$10$	−3.49449	−	5.12548i	−1.10506	−	1.62082i
$11$	−0.655355	−	4.34800i	−0.197597	−	1.31097i	−0.839153	−	0.543895i	$-0.816949\pi$
$11$	−0.655355	−	4.34800i	−0.197597	−	1.31097i	0.641556	−	0.767076i	$-0.278289\pi$
$12$		0			0
$13$	−3.43618	+	2.74026i	−0.953025	+	0.760012i	−0.970815	−	0.239830i	$-0.922908\pi$
$13$	−3.43618	+	2.74026i	−0.953025	+	0.760012i	0.0177899	+	0.999842i	$0.494337\pi$
$14$	4.24843	−	0.363804i	1.13544	−	0.0972306i
$15$		0			0
$16$	−0.361535	−	4.82435i	−0.0903838	−	1.20609i
$17$	3.21706	+	0.992330i	0.780250	+	0.240675i	0.659197	−	0.751971i	$-0.270896\pi$
$17$	3.21706	+	0.992330i	0.780250	+	0.240675i	0.121054	+	0.992646i	$0.461373\pi$
$18$		0			0
$19$	−0.776988	+	0.448594i	−0.178253	+	0.102915i	−0.586472	−	0.809970i	$-0.699483\pi$
$19$	−0.776988	+	0.448594i	−0.178253	+	0.102915i	0.408218	+	0.912884i	$0.366150\pi$
$20$	−0.511645	−	2.24166i	−0.114407	−	0.501251i
$21$		0			0
$22$	1.57690	−	6.90885i	0.336196	−	1.47297i
$23$	−0.732111	−	2.37344i	−0.152656	−	0.494897i	0.846650	−	0.532150i	$-0.178616\pi$
$23$	−0.732111	−	2.37344i	−0.152656	−	0.494897i	−0.999306	+	0.0372524i	$0.988139\pi$
$24$		0			0
$25$	3.58612	+	9.13730i	0.717225	+	1.82746i
$26$	−6.76850	+	2.08781i	−1.32741	+	0.409453i
$27$		0			0
$28$	1.51511	+	0.449778i	0.286329	+	0.0850001i
$29$	8.30122	−	1.89470i	1.54150	−	0.351837i	0.634484	−	0.772936i	$-0.281213\pi$
$29$	8.30122	−	1.89470i	1.54150	−	0.351837i	0.907015	+	0.421099i	$0.138356\pi$
$30$		0			0
$31$	4.67386	+	2.69846i	0.839451	+	0.484657i	0.857077	−	0.515188i	$-0.172278\pi$
$31$	4.67386	+	2.69846i	0.839451	+	0.484657i	−0.0176268	+	0.999845i	$0.505611\pi$
$32$	0.965559	−	3.13027i	0.170688	−	0.553358i
$33$		0			0
$34$	4.24203	+	3.38291i	0.727502	+	0.580164i
$35$	−10.0857	−	1.41075i	−1.70479	−	0.238461i
$36$		0			0
$37$	5.45716	−	5.06350i	0.897151	−	0.832435i	−0.0893816	−	0.995997i	$-0.528489\pi$
$37$	5.45716	−	5.06350i	0.897151	−	0.832435i	0.986533	+	0.163563i	$0.0522986\pi$
$38$	−1.42979	+	0.215506i	−0.231942	+	0.0349597i
$39$		0			0
$40$	−1.29684	+	8.60394i	−0.205048	+	1.36040i
$41$	−5.36277	+	2.58258i	−0.837524	+	0.403331i	−0.802932	−	0.596071i	$-0.796728\pi$
$41$	−5.36277	+	2.58258i	−0.837524	+	0.403331i	−0.0345927	+	0.999401i	$0.511013\pi$
$42$		0			0
$43$	−2.54826	−	1.22718i	−0.388606	−	0.187143i	0.229371	−	0.973339i	$-0.426333\pi$
$43$	−2.54826	−	1.22718i	−0.388606	−	0.187143i	−0.617977	+	0.786196i	$0.712047\pi$
$44$	1.47965	−	2.17024i	0.223065	−	0.327176i
$45$		0			0
$46$	0.299142	−	3.99177i	0.0441060	−	0.588554i
$47$	1.55456	−	3.96096i	0.226756	−	0.577765i	−0.771536	−	0.636186i	$-0.780511\pi$
$47$	1.55456	−	3.96096i	0.226756	−	0.577765i	0.998292	+	0.0584204i	$0.0186064\pi$
$48$		0			0
$49$	4.24716	−	5.56432i	0.606738	−	0.794902i
$50$			15.8195i			2.23722i
$51$		0			0
$52$	−2.61807	−	0.196198i	−0.363062	−	0.0272077i
$53$	−8.87284	+	9.56264i	−1.21878	+	1.31353i	−0.283775	+	0.958891i	$0.591587\pi$
$53$	−8.87284	+	9.56264i	−1.21878	+	1.31353i	−0.935003	+	0.354639i	$0.884604\pi$
$54$		0			0
$55$	−7.34351	+	15.2490i	−0.990199	+	2.05617i
$56$	−4.71536	−	3.67910i	−0.630116	−	0.491640i
$57$		0			0
$58$	13.5693	+	2.04524i	1.78174	+	0.268554i
$59$	−6.88259	+	4.69247i	−0.896037	+	0.610908i	−0.921334	−	0.388772i	$-0.872899\pi$
$59$	−6.88259	+	4.69247i	−0.896037	+	0.610908i	0.0252968	+	0.999680i	$0.491947\pi$
$60$		0			0
$61$	2.93497	+	3.16315i	0.375784	+	0.404999i	0.892420	−	0.451206i	$-0.149006\pi$
$61$	2.93497	+	3.16315i	0.375784	+	0.404999i	−0.516635	+	0.856206i	$0.672816\pi$
$62$	5.42301	+	6.80024i	0.688723	+	0.863632i
$63$		0			0
$64$	−2.74110	+	3.43722i	−0.342637	+	0.429653i
$65$	16.8698	−	1.26422i	2.09244	−	0.156807i
$66$		0			0
$67$	−1.42922	+	2.47548i	−0.174607	+	0.302428i	−0.940025	−	0.341105i	$-0.889199\pi$
$67$	−1.42922	+	2.47548i	−0.174607	+	0.302428i	0.765418	+	0.643533i	$0.222532\pi$
$68$	1.00554	+	1.74165i	0.121940	+	0.211206i
$69$		0			0
$70$	−14.3001	−	8.05484i	−1.70919	−	0.962737i
$71$	7.30694	+	1.66776i	0.867175	+	0.197927i	0.632891	−	0.774241i	$-0.281868\pi$
$71$	7.30694	+	1.66776i	0.867175	+	0.197927i	0.234284	+	0.972168i	$0.424725\pi$
$72$		0			0
$73$	3.88677	−	1.52545i	0.454912	−	0.178540i	−0.126811	−	0.991927i	$-0.540474\pi$
$73$	3.88677	−	1.52545i	0.454912	−	0.178540i	0.581723	+	0.813387i	$0.302379\pi$
$74$	11.1683	−	4.38325i	1.29829	−	0.509543i
$75$		0			0
$76$	−0.522506	−	0.119259i	−0.0599356	−	0.0136799i
$77$	−6.65522	−	9.54201i	−0.758433	−	1.08741i
$78$		0			0
$79$	−1.80778	−	3.13117i	−0.203391	−	0.352284i	0.746228	−	0.665691i	$-0.231863\pi$
$79$	−1.80778	−	3.13117i	−0.203391	−	0.352284i	−0.949619	+	0.313407i	$0.898530\pi$
$80$	−9.31082	+	16.1268i	−1.04098	+	1.80303i
$81$		0			0
$82$	−9.56598	+	0.716871i	−1.05639	+	0.0791652i
$83$	8.34856	−	10.4688i	0.916373	−	1.14910i	−0.0720540	−	0.997401i	$-0.522955\pi$
$83$	8.34856	−	10.4688i	0.916373	−	1.14910i	0.988427	−	0.151695i	$-0.0484732\pi$
$84$		0			0
$85$	−8.07955	−	10.1314i	−0.876350	−	1.09891i
$86$	−3.10041	−	3.34145i	−0.334326	−	0.360318i
$87$		0			0
$88$	−8.21269	+	5.59932i	−0.875476	+	0.596889i
$89$	−3.95521	−	0.596152i	−0.419251	−	0.0631919i	−0.0639709	−	0.997952i	$-0.520376\pi$
$89$	−3.95521	−	0.596152i	−0.419251	−	0.0631919i	−0.355280	+	0.934760i	$0.615615\pi$
$90$		0			0
$91$	−4.93369	+	10.5296i	−0.517191	+	1.10381i
$92$	0.643760	−	1.33678i	0.0671166	−	0.139369i
$93$		0			0
$94$	4.66439	−	5.02702i	0.481095	−	0.518497i
$95$	3.44374	+	0.258073i	0.353320	+	0.0264777i
$96$		0			0
$97$		−	18.1405i		−	1.84189i	−0.389690	−	0.920946i	$-0.627418\pi$
$97$		−	18.1405i		−	1.84189i	0.389690	−	0.920946i	$-0.372582\pi$
$98$	9.64795	−	5.84702i	0.974590	−	0.590638i
$99$		0			0
$100$	−2.14220	+	5.45824i	−0.214220	+	0.545824i
$101$	−0.182498	+	2.43527i	−0.0181593	+	0.242319i	0.980736	+	0.195336i	$0.0625797\pi$
$101$	−0.182498	+	2.43527i	−0.0181593	+	0.242319i	−0.998896	+	0.0469828i	$0.985039\pi$
$102$		0			0
$103$	10.6815	−	15.6669i	1.05248	−	1.54370i	0.231424	−	0.972853i	$-0.425662\pi$
$103$	10.6815	−	15.6669i	1.05248	−	1.54370i	0.821055	−	0.570849i	$-0.193386\pi$
$104$	8.95128	+	4.31071i	0.877745	+	0.422700i
$105$		0			0
$106$	−18.9417	+	9.12184i	−1.83978	+	0.885992i
$107$	0.405749	−	2.69197i	0.0392252	−	0.260242i	−0.960619	−	0.277867i	$-0.910372\pi$
$107$	0.405749	−	2.69197i	0.0392252	−	0.260242i	0.999845	+	0.0176251i	$0.00561054\pi$
$108$		0			0
$109$	11.5445	−	1.74005i	1.10576	−	0.166667i	0.429313	−	0.903156i	$-0.358756\pi$
$109$	11.5445	−	1.74005i	1.10576	−	0.166667i	0.676449	+	0.736489i	$0.263518\pi$
$110$	−19.9954	+	18.5531i	−1.90649	+	1.76896i
$111$		0			0
$112$	−6.51732	−	11.0164i	−0.615829	−	1.04095i
$113$	9.04782	+	7.21539i	0.851147	+	0.678767i	0.948602	−	0.316473i	$-0.102499\pi$
$113$	9.04782	+	7.21539i	0.851147	+	0.678767i	−0.0974544	+	0.995240i	$0.531070\pi$
$114$		0			0
$115$	−2.81799	+	9.13570i	−0.262779	+	0.851909i
$116$	4.40489	+	2.54317i	0.408984	+	0.236127i
$117$		0			0
$118$	−13.0883	+	2.98733i	−1.20488	+	0.275006i
$119$	8.79316	−	1.42106i	0.806068	−	0.130268i
$120$		0			0
$121$	−7.96429	+	2.45666i	−0.724026	+	0.223333i
$122$	2.54067	+	6.47353i	0.230022	+	0.586086i
$123$		0			0
$124$	0.950259	+	3.08066i	0.0853358	+	0.276652i
$125$	4.12482	−	18.0720i	0.368935	−	1.61641i
$126$		0			0
$127$	2.54710	+	11.1596i	0.226018	+	0.990251i	0.952852	+	0.303437i	$0.0981342\pi$
$127$	2.54710	+	11.1596i	0.226018	+	0.990251i	−0.726833	+	0.686814i	$0.759009\pi$
$128$	−11.8099	+	6.81847i	−1.04386	+	0.602673i
$129$		0			0
$130$	26.0529	+	8.03625i	2.28499	+	0.704825i
$131$	−0.421231	−	5.62093i	−0.0368031	−	0.491103i	−0.984900	−	0.173123i	$-0.944614\pi$
$131$	−0.421231	−	5.62093i	−0.0368031	−	0.491103i	0.948097	−	0.317981i	$-0.103005\pi$
$132$		0			0
$133$	−1.31626	+	1.97537i	−0.114134	+	0.171286i
$134$	−3.60170	+	2.87226i	−0.311139	+	0.248125i
$135$		0			0
$136$	−1.13427	−	7.52539i	−0.0972629	−	0.645297i
$137$	10.1322	+	14.8611i	0.865648	+	1.26967i	0.961647	+	0.274291i	$0.0884433\pi$
$137$	10.1322	+	14.8611i	0.865648	+	1.26967i	−0.0959983	+	0.995381i	$0.530604\pi$
$138$		0			0
$139$	2.66447	+	5.53282i	0.225997	+	0.469288i	0.982876	−	0.184267i	$-0.0589911\pi$
$139$	2.66447	+	5.53282i	0.225997	+	0.469288i	−0.756879	+	0.653555i	$0.773277\pi$
$140$	−3.84326	−	4.71564i	−0.324815	−	0.398544i
$141$		0			0
$142$	9.98010	+	6.80431i	0.837511	+	0.571005i
$143$	14.1666	+	13.1447i	1.18467	+	1.09921i
$144$		0			0
$145$	−30.5087	−	11.9738i	−2.53361	−	0.994368i
$146$	6.72921			0.556913
$147$		0			0
$148$	4.44700			0.365541
$149$	−6.21653	−	2.43981i	−0.509278	−	0.199877i	0.0967671	−	0.995307i	$-0.469150\pi$
$149$	−6.21653	−	2.43981i	−0.509278	−	0.199877i	−0.606045	+	0.795430i	$0.707245\pi$
$150$		0			0
$151$	8.46747	+	7.85666i	0.689073	+	0.639366i	0.944901	−	0.327356i	$-0.106158\pi$
$151$	8.46747	+	7.85666i	0.689073	+	0.639366i	−0.255828	+	0.966722i	$0.582348\pi$
$152$	1.67572	+	1.14249i	0.135919	+	0.0926680i
$153$		0			0
$154$	−4.36605	−	18.2337i	−0.351826	−	1.46932i
$155$	−9.01326	−	18.7162i	−0.723962	−	1.50332i
$156$		0			0
$157$	2.61302	+	3.83259i	0.208541	+	0.305874i	0.916232	−	0.400649i	$-0.131215\pi$
$157$	2.61302	+	3.83259i	0.208541	+	0.305874i	−0.707690	+	0.706523i	$0.750263\pi$
$158$	−0.868463	−	5.76187i	−0.0690912	−	0.458390i
$159$		0			0
$160$	−9.85811	+	7.86158i	−0.779352	+	0.621512i
$161$	−4.52068	−	4.76949i	−0.356279	−	0.375888i
$162$		0			0
$163$	−0.887218	−	11.8391i	−0.0694923	−	0.927310i	−0.917605	−	0.397494i	$-0.869880\pi$
$163$	−0.887218	−	11.8391i	−0.0694923	−	0.927310i	0.848112	−	0.529816i	$-0.177739\pi$
$164$	−3.39765	−	1.04804i	−0.265312	−	0.0818379i
$165$		0			0
$166$	18.6887	−	10.7899i	1.45052	−	0.837460i
$167$	5.11430	+	22.4072i	0.395756	+	1.73392i	0.643819	+	0.765177i	$0.277349\pi$
$167$	5.11430	+	22.4072i	0.395756	+	1.73392i	−0.248063	+	0.968744i	$0.579794\pi$
$168$		0			0
$169$	1.40553	−	6.15801i	0.108117	−	0.473693i
$170$	−6.15581	−	19.9566i	−0.472129	−	1.53060i
$171$		0			0
$172$	−0.617260	−	1.57275i	−0.0470656	−	0.119921i
$173$	−12.5556	+	3.87288i	−0.954583	+	0.294450i	−0.732645	−	0.680611i	$-0.761715\pi$
$173$	−12.5556	+	3.87288i	−0.954583	+	0.294450i	−0.221938	+	0.975061i	$0.571238\pi$
$174$		0			0
$175$	19.2241	+	17.4610i	1.45321	+	1.31993i
$176$	−20.7393	+	4.73362i	−1.56329	+	0.356810i
$177$		0			0
$178$	−5.58269	−	3.22317i	−0.418441	−	0.241587i
$179$	5.16876	−	16.7567i	0.386331	−	1.25246i	−0.528609	−	0.848866i	$-0.677286\pi$
$179$	5.16876	−	16.7567i	0.386331	−	1.25246i	0.914940	−	0.403590i	$-0.132238\pi$
$180$		0			0
$181$	−4.95113	−	3.94840i	−0.368015	−	0.293482i	0.421968	−	0.906611i	$-0.361339\pi$
$181$	−4.95113	−	3.94840i	−0.368015	−	0.293482i	−0.789983	+	0.613129i	$0.789911\pi$
$182$	−13.6015	+	12.8919i	−1.00821	+	0.955612i
$183$		0			0
$184$	−4.11588	+	3.81898i	−0.303427	+	0.281539i
$185$	−28.3346	+	4.27075i	−2.08320	+	0.313992i
$186$		0			0
$187$	2.20633	−	14.6381i	0.161343	−	1.07044i
$188$	2.29010	−	1.10285i	0.167023	−	0.0804339i
$189$		0			0
$190$	5.01444	+	2.41483i	0.363786	+	0.175190i
$191$	2.58021	−	3.78448i	0.186698	−	0.273835i	−0.721467	−	0.692449i	$-0.756532\pi$
$191$	2.58021	−	3.78448i	0.186698	−	0.273835i	0.908164	+	0.418614i	$0.137484\pi$
$192$		0			0
$193$	0.0550106	−	0.734065i	0.00395975	−	0.0528392i	−0.994874	−	0.101123i	$-0.967756\pi$
$193$	0.0550106	−	0.734065i	0.00395975	−	0.0528392i	0.998834	+	0.0482843i	$0.0153753\pi$
$194$	10.6811	−	27.2149i	0.766856	−	1.95392i
$195$		0			0
$196$	4.12063	−	0.710933i	0.294331	−	0.0507809i
$197$			5.02513i			0.358025i	0.983847	+	0.179013i	$0.0572903\pi$
$197$			5.02513i			0.358025i	−0.983847	+	0.179013i	$0.942710\pi$
$198$		0			0
$199$	1.83712	+	0.137673i	0.130230	+	0.00975937i	0.139685	−	0.990196i	$-0.455391\pi$
$199$	1.83712	+	0.137673i	0.130230	+	0.00975937i	−0.00945574	+	0.999955i	$0.503010\pi$
$200$	15.0924	−	16.2658i	1.06719	−	1.15016i
$201$		0			0
$202$	−1.70767	+	3.54600i	−0.120151	+	0.249496i
$203$	17.4627	−	14.2322i	1.22564	−	0.998903i
$204$		0			0
$205$	22.6550	+	3.41470i	1.58230	+	0.238493i
$206$	25.2492	−	17.2146i	1.75920	−	1.19940i
$207$		0			0
$208$	14.4623	+	15.5866i	1.00278	+	1.08074i
$209$	2.45969	+	3.08435i	0.170140	+	0.213349i
$210$		0			0
$211$	−7.68161	+	9.63244i	−0.528824	+	0.663124i	−0.972456	−	0.233084i	$-0.925118\pi$
$211$	−7.68161	+	9.63244i	−0.528824	+	0.663124i	0.443632	+	0.896209i	$0.353690\pi$
$212$	−7.77074	+	0.582336i	−0.533697	+	0.0399950i
$213$		0			0
$214$	2.19373	−	3.79966i	0.149960	−	0.259739i
$215$	5.44336	+	9.42818i	0.371234	+	0.642997i
$216$		0			0
$217$	14.2495	+	0.915727i	0.967319	+	0.0621636i
$218$	18.3439	+	4.18687i	1.24240	+	0.283571i
$219$		0			0
$220$	−9.41144	+	3.69372i	−0.634519	+	0.249031i
$221$	−13.7736	+	5.40575i	−0.926514	+	0.363630i
$222$		0			0
$223$	−0.0216823	−	0.00494884i	−0.00145195	−	0.000331399i	0.221795	−	0.975093i	$-0.428808\pi$
$223$	−0.0216823	−	0.00494884i	−0.00145195	−	0.000331399i	−0.223247	+	0.974762i	$0.571666\pi$
$224$	−1.38272	−	8.55594i	−0.0923868	−	0.571668i
$225$		0			0
$226$	9.32538	+	16.1520i	0.620315	+	1.07442i
$227$	−4.56676	+	7.90986i	−0.303106	+	0.524996i	−0.976838	−	0.213980i	$-0.931357\pi$
$227$	−4.56676	+	7.90986i	−0.303106	+	0.524996i	0.673732	+	0.738976i	$0.264690\pi$
$228$		0			0
$229$	−3.95603	+	0.296463i	−0.261422	+	0.0195908i	−0.204796	−	0.978805i	$-0.565653\pi$
$229$	−3.95603	+	0.296463i	−0.261422	+	0.0195908i	−0.0566254	+	0.998395i	$0.518034\pi$
$230$	−9.60668	+	12.0464i	−0.633446	+	0.794316i
$231$		0			0
$232$	−12.0008	−	15.0486i	−0.787893	−	0.987987i
$233$	−10.0603	−	10.8424i	−0.659069	−	0.710307i	0.311738	−	0.950168i	$-0.399089\pi$
$233$	−10.0603	−	10.8424i	−0.659069	−	0.710307i	−0.970807	+	0.239861i	$0.922898\pi$
$234$		0			0
$235$	−13.5325	+	9.22631i	−0.882763	+	0.601858i
$236$	−4.92044	−	0.741636i	−0.320293	−	0.0482764i
$237$		0			0
$238$	14.0284	+	3.04547i	0.909329	+	0.197408i
$239$	−5.51570	+	11.4535i	−0.356781	+	0.740863i	−0.999685	−	0.0250833i	$-0.992015\pi$
$239$	−5.51570	+	11.4535i	−0.356781	+	0.740863i	0.642905	+	0.765946i	$0.277729\pi$
$240$		0			0
$241$	−8.72384	+	9.40207i	−0.561952	+	0.605640i	−0.948558	−	0.316605i	$-0.897457\pi$
$241$	−8.72384	+	9.40207i	−0.561952	+	0.605640i	0.386605	+	0.922245i	$0.373648\pi$
$242$	−13.3947	−	1.00379i	−0.861044	−	0.0645264i
$243$		0			0
$244$			2.57762i			0.165015i
$245$	−25.5723	+	8.48711i	−1.63376	+	0.542222i
$246$		0			0
$247$	1.44061	−	3.67060i	0.0916635	−	0.233555i
$248$	0.911703	−	12.1658i	0.0578932	−	0.772531i
$249$		0			0
$250$	16.8289	−	24.6834i	1.06435	−	1.56112i
$251$	−14.8498	−	7.15128i	−0.937310	−	0.451385i	−0.0980903	−	0.995178i	$-0.531273\pi$
$251$	−14.8498	−	7.15128i	−0.937310	−	0.451385i	−0.839219	+	0.543793i	$0.816988\pi$
$252$		0			0
$253$	−9.83994	+	4.73866i	−0.618632	+	0.297917i
$254$	−2.74948	+	18.2416i	−0.172517	+	1.14458i
$255$		0			0
$256$	−13.0377	+	1.96512i	−0.814857	+	0.122820i
$257$	−8.36052	+	7.75743i	−0.521515	+	0.483895i	−0.896443	−	0.443159i	$-0.853858\pi$
$257$	−8.36052	+	7.75743i	−0.521515	+	0.483895i	0.374928	+	0.927054i	$0.377667\pi$
$258$		0			0
$259$	7.00061	−	18.4100i	0.434997	−	1.14394i
$260$	7.90086	+	6.30072i	0.489990	+	0.390754i
$261$		0			0
$262$	2.67764	−	8.68069i	0.165425	−	0.536295i
$263$	6.94717	+	4.01095i	0.428381	+	0.247326i	0.698657	−	0.715457i	$-0.253782\pi$
$263$	6.94717	+	4.01095i	0.428381	+	0.247326i	−0.270276	+	0.962783i	$0.587115\pi$
$264$		0			0
$265$	48.9529	−	11.1732i	3.00715	−	0.686363i
$266$	−3.13778	+	2.18849i	−0.192390	+	0.134185i
$267$		0			0
$268$	−1.63165	+	0.503298i	−0.0996689	+	0.0307438i
$269$	0.0713278	+	0.181740i	0.00434893	+	0.0110809i	0.933032	−	0.359794i	$-0.117153\pi$
$269$	0.0713278	+	0.181740i	0.00434893	+	0.0110809i	−0.928683	+	0.370875i	$0.879058\pi$
$270$		0			0
$271$	−0.693161	−	2.24717i	−0.0421065	−	0.136506i	0.932079	−	0.362255i	$-0.117993\pi$
$271$	−0.693161	−	2.24717i	−0.0421065	−	0.136506i	−0.974185	+	0.225749i	$0.927517\pi$
$272$	3.62427	−	15.8790i	0.219754	−	0.962804i
$273$		0			0
$274$	6.45035	+	28.2608i	0.389680	+	1.70730i
$275$	37.3788	−	21.5806i	2.25402	−	1.30136i
$276$		0			0
$277$	−22.3119	−	6.88231i	−1.34059	−	0.413518i	−0.460221	−	0.887804i	$-0.652230\pi$
$277$	−22.3119	−	6.88231i	−1.34059	−	0.413518i	−0.880371	+	0.474286i	$0.842706\pi$
$278$	0.739603	+	9.86931i	0.0443584	+	0.591922i
$279$		0			0
$280$	7.01889	+	21.9249i	0.419459	+	1.31027i
$281$	7.57759	−	6.04292i	0.452041	−	0.360491i	−0.370847	−	0.928694i	$-0.620933\pi$
$281$	7.57759	−	6.04292i	0.452041	−	0.360491i	0.822888	+	0.568203i	$0.192361\pi$
$282$		0			0
$283$	−1.79996	−	11.9419i	−0.106996	−	0.709874i	−0.976432	−	0.215827i	$-0.930755\pi$
$283$	−1.79996	−	11.9419i	−0.106996	−	0.709874i	0.869435	−	0.494047i	$-0.164483\pi$
$284$	2.52205	+	3.69917i	0.149656	+	0.219505i
$285$		0			0
$286$	13.5136	+	28.0612i	0.799073	+	1.65929i
$287$	−9.68743	+	12.4160i	−0.571831	+	0.732893i
$288$		0			0
$289$	−4.68133	−	3.19168i	−0.275373	−	0.187746i
$290$	−38.7198	−	35.9267i	−2.27371	−	2.10969i
$291$		0			0
$292$	2.32180	+	0.911238i	0.135873	+	0.0533262i
$293$	11.9276			0.696817			0.348409	−	0.937343i	$-0.386722\pi$
$293$	11.9276			0.696817			0.348409	+	0.937343i	$0.386722\pi$
$294$		0			0
$295$	32.0634			1.86680
$296$	−15.6652	−	6.14813i	−0.910520	−	0.357353i
$297$		0			0
$298$	−7.88966	−	7.32053i	−0.457036	−	0.424067i
$299$	9.01952	+	6.14941i	0.521613	+	0.355629i
$300$		0			0
$301$	−7.48271	+	0.0795013i	−0.431296	+	0.00458238i
$302$	8.07715	+	16.7724i	0.464788	+	0.965142i
$303$		0			0
$304$	2.44509	+	3.58628i	0.140235	+	0.205687i
$305$	−2.47547	−	16.4236i	−0.141745	−	0.940415i
$306$		0			0
$307$	22.0802	−	17.6084i	1.26018	−	1.00496i	0.260968	−	0.965347i	$-0.415958\pi$
$307$	22.0802	−	17.6084i	1.26018	−	1.00496i	0.999215	−	0.0396152i	$-0.0126132\pi$
$308$	0.962699	−	6.88246i	0.0548549	−	0.392165i
$309$		0			0
$310$	−2.50190	−	33.3855i	−0.142098	−	1.89617i
$311$	18.2667	+	5.63452i	1.03581	+	0.319504i	0.765613	−	0.643301i	$-0.222436\pi$
$311$	18.2667	+	5.63452i	1.03581	+	0.319504i	0.270195	+	0.962806i	$0.412912\pi$
$312$		0			0
$313$	−29.5626	+	17.0680i	−1.67098	+	0.964739i	−0.703885	+	0.710314i	$0.748553\pi$
$313$	−29.5626	+	17.0680i	−1.67098	+	0.964739i	−0.967093	+	0.254425i	$0.918114\pi$
$314$	1.66350	+	7.28829i	0.0938770	+	0.411302i
$315$		0			0
$316$	0.480598	−	2.10564i	0.0270357	−	0.118451i
$317$	2.40572	+	7.79916i	0.135119	+	0.438044i	0.997693	−	0.0678861i	$-0.0216255\pi$
$317$	2.40572	+	7.79916i	0.135119	+	0.438044i	−0.862574	+	0.505930i	$0.831149\pi$
$318$		0			0
$319$	−13.6784	−	34.8520i	−0.765843	−	1.95134i
$320$	16.1704	−	4.98792i	0.903954	−	0.278833i
$321$		0			0
$322$	−3.97379	−	9.81707i	−0.221451	−	0.547084i
$323$	−2.94477	+	0.672124i	−0.163851	+	0.0373980i
$324$		0			0
$325$	−37.3612	−	21.5705i	−2.07242	−	1.19651i
$326$	5.63978	−	18.2837i	0.312359	−	1.01264i
$327$		0			0
$328$	10.5197	+	8.38922i	0.580856	+	0.463217i
$329$	−0.960530	−	11.2169i	−0.0529557	−	0.618407i
$330$		0			0
$331$	−22.0820	+	20.4891i	−1.21374	+	1.12618i	−0.225341	+	0.974280i	$0.572350\pi$
$331$	−22.0820	+	20.4891i	−1.21374	+	1.12618i	−0.988395	+	0.151903i	$0.951460\pi$
$332$	7.90932	−	1.19214i	0.434081	−	0.0654271i
$333$		0			0
$334$	−5.52065	+	36.6271i	−0.302077	+	2.00415i
$335$	9.91290	−	4.77380i	0.541600	−	0.260821i
$336$		0			0
$337$	−26.1851	−	12.6101i	−1.42640	−	0.686916i	−0.448072	−	0.893998i	$-0.647889\pi$
$337$	−26.1851	−	12.6101i	−1.42640	−	0.686916i	−0.978324	+	0.207082i	$0.933603\pi$
$338$	5.73442	−	8.41085i	0.311911	−	0.457490i
$339$		0			0
$340$	0.578480	−	7.71928i	0.0313725	−	0.418637i
$341$	8.66984	−	22.0904i	0.469498	−	1.19626i
$342$		0			0
$343$	3.54366	−	18.1781i	0.191339	−	0.981524i
$344$			6.39362i			0.344721i
$345$		0			0
$346$	−21.1166	−	1.58247i	−1.13523	−	0.0850739i
$347$	8.34219	−	8.99074i	0.447832	−	0.482648i	−0.468275	−	0.883583i	$-0.655124\pi$
$347$	8.34219	−	8.99074i	0.447832	−	0.482648i	0.916107	+	0.400935i	$0.131315\pi$
$348$		0			0
$349$	−1.40591	+	2.91940i	−0.0752565	+	0.156272i	−0.935203	−	0.354113i	$-0.884783\pi$
$349$	−1.40591	+	2.91940i	−0.0752565	+	0.156272i	0.859946	+	0.510385i	$0.170497\pi$
$350$	18.5596	+	37.5145i	0.992051	+	2.00524i
$351$		0			0
$352$	−14.2432	−	2.14681i	−0.759163	−	0.114425i
$353$	−4.43190	+	3.02162i	−0.235886	+	0.160824i	−0.675494	−	0.737365i	$-0.736070\pi$
$353$	−4.43190	+	3.02162i	−0.235886	+	0.160824i	0.439608	+	0.898190i	$0.355117\pi$
$354$		0			0
$355$	−19.6221	−	21.1476i	−1.04143	−	1.12240i
$356$	−1.48974	−	1.86808i	−0.0789563	−	0.0990081i
$357$		0			0
$358$	17.6206	−	22.0955i	0.931277	−	1.16778i
$359$	31.7494	−	2.37929i	1.67567	−	0.125574i	0.797307	−	0.603574i	$-0.206257\pi$
$359$	31.7494	−	2.37929i	1.67567	−	0.125574i	0.878360	+	0.478000i	$0.158638\pi$
$360$		0			0
$361$	−9.09753	+	15.7574i	−0.478817	+	0.829336i
$362$	−5.10302	−	8.83869i	−0.268209	−	0.464551i
$363$		0			0
$364$	−6.43871	+	2.60628i	−0.337480	+	0.136606i
$365$	−15.6687	−	3.57628i	−0.820139	−	0.187191i
$366$		0			0
$367$	−9.53927	+	3.74389i	−0.497946	+	0.195429i	−0.601004	−	0.799246i	$-0.705232\pi$
$367$	−9.53927	+	3.74389i	−0.497946	+	0.195429i	0.103058	+	0.994675i	$0.467137\pi$
$368$	−11.1856	+	4.39004i	−0.583092	+	0.228847i
$369$		0			0
$370$	−45.0229	−	10.2762i	−2.34063	−	0.534233i
$371$	−9.82215	+	33.0866i	−0.509941	+	1.71777i
$372$		0			0
$373$	6.35426	+	11.0059i	0.329011	+	0.569864i	0.982316	−	0.187231i	$-0.0599512\pi$
$373$	6.35426	+	11.0059i	0.329011	+	0.569864i	−0.653305	+	0.757095i	$0.726618\pi$
$374$	11.9288	−	20.6613i	0.616825	−	1.06837i
$375$		0			0
$376$	−9.59193	+	0.718816i	−0.494666	+	0.0370701i
$377$	−23.3325	+	29.2581i	−1.20169	+	1.50687i
$378$		0			0
$379$	23.0179	+	28.8635i	1.18235	+	1.48262i	0.839610	+	0.543190i	$0.182784\pi$
$379$	23.0179	+	28.8635i	1.18235	+	1.48262i	0.342740	+	0.939430i	$0.388645\pi$
$380$	1.40314	+	1.51223i	0.0719796	+	0.0775755i
$381$		0			0
$382$	6.09919	−	4.15836i	0.312062	−	0.212760i
$383$	−2.39721	−	0.361321i	−0.122492	−	0.0184627i	0.0875103	−	0.996164i	$-0.472109\pi$
$383$	−2.39721	−	0.361321i	−0.122492	−	0.0184627i	−0.210002	+	0.977701i	$0.567347\pi$
$384$		0			0
$385$	0.475741	+	44.7770i	0.0242460	+	2.28205i
$386$	0.514742	−	1.06887i	0.0261997	−	0.0544042i
$387$		0			0
$388$	7.37063	−	7.94365i	0.374187	−	0.403278i
$389$	3.19974	+	0.239787i	0.162233	+	0.0121577i	0.155599	−	0.987820i	$-0.450269\pi$
$389$	3.19974	+	0.239787i	0.162233	+	0.0121577i	0.00663415	+	0.999978i	$0.497888\pi$
$390$		0			0
$391$		−	8.36200i		−	0.422884i
$392$	−15.4984	−	3.19255i	−0.782787	−	0.161248i
$393$		0			0
$394$	−2.95877	+	7.53883i	−0.149061	+	0.379801i
$395$	−1.04000	+	13.8779i	−0.0523282	+	0.698271i
$396$		0			0
$397$	17.6855	−	25.9398i	0.887608	−	1.30188i	−0.0650632	−	0.997881i	$-0.520725\pi$
$397$	17.6855	−	25.9398i	0.887608	−	1.30188i	0.952672	−	0.304001i	$-0.0983227\pi$
$398$	2.67503	+	1.28823i	0.134087	+	0.0645729i
$399$		0			0
$400$	42.7850	−	20.6042i	2.13925	−	1.03021i
$401$	−3.40985	+	22.6229i	−0.170280	+	1.12973i	0.726471	+	0.687197i	$0.241159\pi$
$401$	−3.40985	+	22.6229i	−0.170280	+	1.12973i	−0.896751	+	0.442535i	$0.854079\pi$
$402$		0			0
$403$	−23.4547	+	3.53523i	−1.16836	+	0.176102i
$404$	−1.06938	+	0.992243i	−0.0532038	+	0.0493659i
$405$		0			0
$406$	34.5779	−	11.0695i	1.71607	−	0.549371i
$407$	−25.5925	−	20.4093i	−1.26857	−	1.01165i
$408$		0			0
$409$	−0.786141	+	2.54861i	−0.0388721	+	0.126020i	−0.972929	−	0.231103i	$-0.925766\pi$
$409$	−0.786141	+	2.54861i	−0.0388721	+	0.126020i	0.934057	+	0.357124i	$0.116243\pi$
$410$	31.9771	+	18.4620i	1.57924	+	0.911773i
$411$		0			0
$412$	11.0429	−	2.52048i	0.544046	−	0.124175i
$413$	−10.8162	+	19.2025i	−0.532230	+	0.944893i
$414$		0			0
$415$	−49.2503	+	15.1917i	−2.41760	+	0.745732i
$416$	5.25991	+	13.4020i	0.257889	+	0.657089i
$417$		0			0
$418$	1.87404	+	6.07548i	0.0916622	+	0.297162i
$419$	−7.01996	+	30.7565i	−0.342947	+	1.50255i	0.449871	+	0.893093i	$0.351470\pi$
$419$	−7.01996	+	30.7565i	−0.342947	+	1.50255i	−0.792819	+	0.609458i	$0.791387\pi$
$420$		0			0
$421$	2.52739	+	11.0732i	0.123178	+	0.539676i	0.998430	+	0.0560100i	$0.0178379\pi$
$421$	2.52739	+	11.0732i	0.123178	+	0.539676i	−0.875253	+	0.483666i	$0.839305\pi$
$422$	−17.1957	+	9.92794i	−0.837073	+	0.483284i
$423$		0			0
$424$	28.1786	+	8.69195i	1.36847	+	0.422118i
$425$	2.46955	+	32.9538i	0.119791	+	1.59849i
$426$		0			0
$427$	10.6710	+	4.05778i	0.516408	+	0.196370i
$428$	1.27144	−	1.01394i	0.0614574	−	0.0490106i
$429$		0			0
$430$	2.61501	+	17.3494i	0.126107	+	0.836664i
$431$	−4.08471	−	5.99117i	−0.196754	−	0.288585i	0.715165	−	0.698956i	$-0.246352\pi$
$431$	−4.08471	−	5.99117i	−0.196754	−	0.288585i	−0.911919	+	0.410371i	$0.865399\pi$
$432$		0			0
$433$	−5.40026	−	11.2138i	−0.259520	−	0.538899i	0.729974	−	0.683475i	$-0.239532\pi$
$433$	−5.40026	−	11.2138i	−0.259520	−	0.538899i	−0.989494	+	0.144577i	$0.953818\pi$
$434$	20.8383	+	9.76383i	1.00027	+	0.468679i
$435$		0			0
$436$	5.76227	+	3.92865i	0.275963	+	0.188148i
$437$	1.63355	+	1.51572i	0.0781435	+	0.0725066i
$438$		0			0
$439$	34.4035	+	13.5024i	1.64199	+	0.644433i	0.993188	−	0.116525i	$-0.0371754\pi$
$439$	34.4035	+	13.5024i	1.64199	+	0.644433i	0.648801	+	0.760958i	$0.275271\pi$
$440$	38.2598			1.82396
$441$		0			0
$442$	−23.8464			−1.13426
$443$	−9.19111	−	3.60724i	−0.436683	−	0.171385i	0.136808	−	0.990598i	$-0.456316\pi$
$443$	−9.19111	−	3.60724i	−0.436683	−	0.171385i	−0.573490	+	0.819212i	$0.694411\pi$
$444$		0			0
$445$	11.2861	+	10.4720i	0.535014	+	0.496420i
$446$	−0.0296145	−	0.0201908i	−0.00140229	−	0.000956063i
$447$		0			0
$448$	−2.46768	+	11.3669i	−0.116587	+	0.537038i
$449$	2.05379	+	4.26475i	0.0969245	+	0.201266i	0.943793	−	0.330536i	$-0.107229\pi$
$449$	2.05379	+	4.26475i	0.0969245	+	0.201266i	−0.846869	+	0.531802i	$0.821515\pi$
$450$		0			0
$451$	14.7436	+	21.6248i	0.694247	+	1.01827i
$452$	1.03033	+	6.83578i	0.0484625	+	0.321528i
$453$		0			0
$454$	−11.5085	+	9.17769i	−0.540119	+	0.430730i
$455$	38.5220	−	22.7898i	1.80594	−	1.06840i
$456$		0			0
$457$	−1.23467	−	16.4756i	−0.0577556	−	0.770695i	−0.948618	−	0.316423i	$-0.897518\pi$
$457$	−1.23467	−	16.4756i	−0.0577556	−	0.770695i	0.890863	−	0.454273i	$-0.150101\pi$
$458$	−6.10949	−	1.88453i	−0.285478	−	0.0880582i
$459$		0			0
$460$	−4.94589	+	2.85551i	−0.230603	+	0.133139i
$461$	2.95601	+	12.9511i	0.137675	+	0.603194i	0.995943	+	0.0899916i	$0.0286840\pi$
$461$	2.95601	+	12.9511i	0.137675	+	0.603194i	−0.858267	+	0.513203i	$0.828459\pi$
$462$		0			0
$463$	−8.14915	+	35.7038i	−0.378723	+	1.65929i	0.322664	+	0.946514i	$0.395422\pi$
$463$	−8.14915	+	35.7038i	−0.378723	+	1.65929i	−0.701387	+	0.712781i	$0.747435\pi$
$464$	−12.1419	−	39.3630i	−0.563673	−	1.82738i
$465$		0			0
$466$	−8.70871	−	22.1894i	−0.403423	−	1.02791i
$467$	−6.35492	+	1.96023i	−0.294071	+	0.0907088i	−0.438280	−	0.898838i	$-0.644412\pi$
$467$	−6.35492	+	1.96023i	−0.294071	+	0.0907088i	0.144210	+	0.989547i	$0.453936\pi$
$468$		0			0
$469$	−0.485008	+	7.54714i	−0.0223956	+	0.348494i
$470$	−25.7342	+	5.87367i	−1.18703	+	0.270932i
$471$		0			0
$472$	16.3076	+	9.41519i	0.750617	+	0.433369i
$473$	−3.66575	+	11.8841i	−0.168551	+	0.546430i
$474$		0			0
$475$	−6.88531	−	5.49085i	−0.315920	−	0.251938i
$476$	4.42787	+	2.95045i	0.202951	+	0.135234i
$477$		0			0
$478$	−15.0185	+	13.9352i	−0.686932	+	0.637380i
$479$	19.8784	−	2.99619i	0.908268	−	0.136899i	0.321740	−	0.946828i	$-0.395732\pi$
$479$	19.8784	−	2.99619i	0.908268	−	0.136899i	0.586528	+	0.809929i	$0.300494\pi$
$480$		0			0
$481$	−4.87645	+	32.3532i	−0.222347	+	1.47518i
$482$	−18.6236	+	8.96867i	−0.848283	+	0.408512i
$483$		0			0
$484$	−4.48568	−	2.16019i	−0.203895	−	0.0981905i
$485$	−39.3340	+	57.6924i	−1.78607	+	2.61968i
$486$		0			0
$487$	−0.296814	+	3.96071i	−0.0134499	+	0.179477i	0.986433	+	0.164165i	$0.0524931\pi$
$487$	−0.296814	+	3.96071i	−0.0134499	+	0.179477i	−0.999883	+	0.0153116i	$0.995126\pi$
$488$	3.56365	−	9.08004i	0.161319	−	0.411034i
$489$		0			0
$490$	−43.3615	−	2.32428i	−1.95887	−	0.105000i
$491$		−	11.1315i		−	0.502357i	−0.967941	−	0.251179i	$-0.919182\pi$
$491$		−	11.1315i		−	0.502357i	0.967941	−	0.251179i	$-0.0808182\pi$
$492$		0			0
$493$	28.5857	+	2.14220i	1.28743	+	0.0964798i
$494$	4.32247	−	4.65851i	0.194477	−	0.209596i
$495$		0			0
$496$	11.3285	−	23.5240i	0.508666	−	1.05626i
$497$	19.2844	−	4.61762i	0.865023	−	0.207129i
$498$		0			0
$499$	29.2283	+	4.40545i	1.30844	+	0.197215i	0.765978	−	0.642867i	$-0.222255\pi$
$499$	29.2283	+	4.40545i	1.30844	+	0.197215i	0.542459	+	0.840082i	$0.317493\pi$
$500$	9.14902	−	6.23770i	0.409157	−	0.278958i
$501$		0			0
$502$	−18.0674	−	19.4720i	−0.806387	−	0.869079i
$503$	−19.4052	−	24.3333i	−0.865235	−	1.08497i	−0.995619	−	0.0935062i	$-0.970192\pi$
$503$	−19.4052	−	24.3333i	−0.865235	−	1.08497i	0.130384	−	0.991464i	$-0.458379\pi$
$504$		0			0
$505$	5.86079	−	7.34919i	0.260802	−	0.327035i
$506$	−17.5522	+	1.31536i	−0.780292	+	0.0584748i
$507$		0			0
$508$	−3.41885	+	5.92162i	−0.151687	+	0.262729i
$509$	−7.33336	−	12.7017i	−0.325045	−	0.562995i	0.656476	−	0.754347i	$-0.272046\pi$
$509$	−7.33336	−	12.7017i	−0.325045	−	0.562995i	−0.981522	+	0.191352i	$0.938713\pi$
$510$		0			0
$511$	7.42746	−	8.17745i	0.328571	−	0.361749i
$512$	5.87349	+	1.34059i	0.259574	+	0.0592461i
$513$		0			0
$514$	−17.1102	+	6.71527i	−0.754699	+	0.296198i
$515$	−67.9408	+	26.6648i	−2.99383	+	1.17499i
$516$		0			0
$517$	−18.2410	−	4.16340i	−0.802240	−	0.183106i
$518$	21.3422	−	23.4973i	0.937724	−	1.03241i
$519$		0			0
$520$	−19.1209	−	33.1184i	−0.838507	−	1.45234i
$521$	10.3784	−	17.9759i	0.454686	−	0.787540i	−0.543984	−	0.839096i	$-0.683085\pi$
$521$	10.3784	−	17.9759i	0.454686	−	0.787540i	0.998670	+	0.0515557i	$0.0164180\pi$
$522$		0			0
$523$	27.5060	−	2.06129i	1.20275	−	0.0901340i	0.541765	−	0.840530i	$-0.317756\pi$
$523$	27.5060	−	2.06129i	1.20275	−	0.0901340i	0.660989	+	0.750396i	$0.270137\pi$
$524$	2.09937	−	2.63253i	0.0917114	−	0.115002i
$525$		0			0
$526$	8.06069	+	10.1078i	0.351463	+	0.440721i
$527$	12.3583	+	13.3191i	0.538337	+	0.580189i
$528$		0			0
$529$	13.9062	−	9.48111i	0.604619	−	0.412222i
$530$	80.0192	+	12.0610i	3.47581	+	0.523894i
$531$		0			0
$532$	−1.37899	+	0.330198i	−0.0597868	+	0.0143159i
$533$	11.3505	−	23.5696i	0.491646	−	1.02091i
$534$		0			0
$535$	−7.12738	+	7.68149i	−0.308143	+	0.332100i
$536$	6.44354	+	0.482877i	0.278319	+	0.0208571i
$537$		0			0
$538$			0.314649i			0.0135655i
$539$	−26.9770	−	14.8200i	−1.16198	−	0.638345i
$540$		0			0
$541$	−3.00765	+	7.66336i	−0.129309	+	0.329474i	−0.980835	−	0.194838i	$-0.937582\pi$
$541$	−3.00765	+	7.66336i	−0.129309	+	0.329474i	0.851527	+	0.524311i	$0.175677\pi$
$542$	0.283227	−	3.77940i	0.0121656	−	0.162339i
$543$		0			0
$544$	6.21251	−	9.11208i	0.266359	−	0.390677i
$545$	−40.4879	−	19.4980i	−1.73431	−	0.835201i
$546$		0			0
$547$	−30.9935	+	14.9257i	−1.32519	+	0.638177i	−0.956597	−	0.291415i	$-0.905874\pi$
$547$	−30.9935	+	14.9257i	−1.32519	+	0.638177i	−0.368591	+	0.929592i	$0.620160\pi$
$548$	−1.60137	+	10.6244i	−0.0684071	+	0.453851i
$549$		0			0
$550$	68.7832	−	10.3674i	2.93292	−	0.442067i
$551$	−5.60000	+	5.19604i	−0.238568	+	0.221359i
$552$		0			0
$553$	−7.96050	−	5.30438i	−0.338515	−	0.225565i
$554$	−29.4206	−	23.4622i	−1.24996	−	0.996812i
$555$		0			0
$556$	−1.08127	+	3.50539i	−0.0458560	+	0.148662i
$557$	−13.2494	−	7.64952i	−0.561394	−	0.324121i	0.192311	−	0.981334i	$-0.438402\pi$
$557$	−13.2494	−	7.64952i	−0.561394	−	0.324121i	−0.753705	+	0.657213i	$0.771735\pi$
$558$		0			0
$559$	12.1191	−	2.76610i	0.512582	−	0.116994i
$560$	−3.15965	+	49.1668i	−0.133519	+	2.07768i
$561$		0			0
$562$	14.9261	−	4.60410i	0.629621	−	0.194212i
$563$	6.01917	+	15.3366i	0.253678	+	0.646360i	0.999811	−	0.0194364i	$-0.00618720\pi$
$563$	6.01917	+	15.3366i	0.253678	+	0.646360i	−0.746134	+	0.665796i	$0.768092\pi$
$564$		0			0
$565$	−13.1297	−	42.5655i	−0.552371	−	1.79074i
$566$	4.33101	−	18.9754i	0.182046	−	0.797596i
$567$		0			0
$568$	−3.77005	−	16.5177i	−0.158188	−	0.693065i
$569$	−13.2052	+	7.62404i	−0.553592	+	0.319616i	−0.750569	−	0.660792i	$-0.770221\pi$
$569$	−13.2052	+	7.62404i	−0.553592	+	0.319616i	0.196978	+	0.980408i	$0.436887\pi$
$570$		0			0
$571$	−38.7414	−	11.9502i	−1.62128	−	0.500098i	−0.654575	−	0.755997i	$-0.727153\pi$
$571$	−38.7414	−	11.9502i	−1.62128	−	0.500098i	−0.966704	+	0.255899i	$0.917629\pi$
$572$	0.862702	+	11.5120i	0.0360714	+	0.481339i
$573$		0			0
$574$	−21.8438	+	12.9229i	−0.911743	+	0.539391i
$575$	19.0614	−	15.2010i	0.794916	−	0.633925i
$576$		0			0
$577$	−3.75825	−	24.9343i	−0.156458	−	1.03803i	−0.919900	−	0.392154i	$-0.871730\pi$
$577$	−3.75825	−	24.9343i	−0.156458	−	1.03803i	0.763442	−	0.645877i	$-0.223508\pi$
$578$	−5.14381	−	7.54459i	−0.213954	−	0.313814i
$579$		0			0
$580$	−8.49456	−	17.6391i	−0.352718	−	0.732426i
$581$	7.51581	−	34.6203i	0.311808	−	1.43629i
$582$		0			0
$583$	47.3932	+	32.3121i	1.96283	+	1.33823i
$584$	−6.91903	−	6.41993i	−0.286312	−	0.265658i
$585$		0			0
$586$	17.8941	+	7.02291i	0.739198	+	0.290114i
$587$	2.24197			0.0925360			0.0462680	−	0.998929i	$-0.485267\pi$
$587$	2.24197			0.0925360			0.0462680	+	0.998929i	$0.485267\pi$
$588$		0			0
$589$	−4.84205			−0.199513
$590$	48.1023	+	18.8788i	1.98034	+	0.777227i
$591$		0			0
$592$	−26.4011	−	24.4966i	−1.08508	−	1.00680i
$593$	−32.4557	−	22.1279i	−1.33279	−	0.908684i	−0.333376	−	0.942794i	$-0.608188\pi$
$593$	−32.4557	−	22.1279i	−1.33279	−	0.908684i	−0.999418	+	0.0341103i	$0.989140\pi$
$594$		0			0
$595$	−31.0462	−	14.5468i	−1.27277	−	0.596360i
$596$	−1.73088	−	3.59420i	−0.0708995	−	0.147224i
$597$		0			0
$598$	9.91058	+	14.5362i	0.405274	+	0.594428i
$599$	4.17473	+	27.6976i	0.170575	+	1.13169i	0.896216	+	0.443618i	$0.146305\pi$
$599$	4.17473	+	27.6976i	0.170575	+	1.13169i	−0.725641	+	0.688074i	$0.758457\pi$
$600$		0			0
$601$	19.9039	−	15.8728i	0.811896	−	0.647466i	−0.126909	−	0.991914i	$-0.540506\pi$
$601$	19.9039	−	15.8728i	0.811896	−	0.647466i	0.938805	+	0.344449i	$0.111934\pi$
$602$	−11.2726	−	4.28651i	−0.459435	−	0.174705i
$603$		0			0
$604$	0.515643	+	6.88078i	0.0209812	+	0.279975i
$605$	30.6556	+	9.45601i	1.24633	+	0.384441i
$606$		0			0
$607$	−11.0459	+	6.37734i	−0.448338	+	0.258848i	−0.707128	−	0.707086i	$-0.750010\pi$
$607$	−11.0459	+	6.37734i	−0.448338	+	0.258848i	0.258790	+	0.965934i	$0.416676\pi$
$608$	0.653991	+	2.86532i	0.0265228	+	0.116204i
$609$		0			0
$610$	5.95641	−	26.0967i	0.241168	−	1.05663i
$611$	5.51231	+	17.8705i	0.223004	+	0.722962i
$612$		0			0
$613$	−5.50861	−	14.0357i	−0.222491	−	0.566897i	0.775424	−	0.631441i	$-0.217536\pi$
$613$	−5.50861	−	14.0357i	−0.222491	−	0.566897i	−0.997915	+	0.0645435i	$0.979441\pi$
$614$	43.4930	−	13.4158i	1.75524	−	0.541418i
$615$		0			0
$616$	−12.9065	+	22.9135i	−0.520017	+	0.923210i
$617$	28.8631	−	6.58782i	1.16199	−	0.265216i	0.402301	−	0.915507i	$-0.368210\pi$
$617$	28.8631	−	6.58782i	1.16199	−	0.265216i	0.759685	+	0.650292i	$0.225353\pi$
$618$		0			0
$619$	19.2524	+	11.1154i	0.773819	+	0.446765i	0.834235	−	0.551409i	$-0.185910\pi$
$619$	19.2524	+	11.1154i	0.773819	+	0.446765i	−0.0604163	+	0.998173i	$0.519243\pi$
$620$	3.65767	−	11.8579i	0.146896	−	0.476224i
$621$		0			0
$622$	24.0865	+	19.2084i	0.965783	+	0.770186i
$623$	−10.0788	+	3.22656i	−0.403800	+	0.129270i
$624$		0			0
$625$	−16.3260	+	15.1484i	−0.653042	+	0.605934i
$626$	−54.4001	+	8.19950i	−2.17427	+	0.327718i
$627$		0			0
$628$	−0.412982	+	2.73996i	−0.0164798	+	0.109336i
$629$	22.5806	−	10.8743i	0.900349	−	0.433585i
$630$		0			0
$631$	6.82205	+	3.28533i	0.271582	+	0.130787i	0.564718	−	0.825284i	$-0.308985\pi$
$631$	6.82205	+	3.28533i	0.271582	+	0.130787i	−0.293137	+	0.956071i	$0.594699\pi$
$632$	−4.60409	+	6.75296i	−0.183141	+	0.268618i
$633$		0			0
$634$	−0.982981	+	13.1170i	−0.0390392	+	0.520942i
$635$	16.0967	−	41.0136i	0.638777	−	1.62758i
$636$		0			0
$637$	0.653668	+	30.7583i	0.0258993	+	1.21869i
$638$		−	60.3396i		−	2.38887i
$639$		0			0
$640$	52.3436	+	3.92261i	2.06906	+	0.155055i
$641$	−5.33852	+	5.75356i	−0.210859	+	0.227252i	−0.829622	−	0.558326i	$-0.811444\pi$
$641$	−5.33852	+	5.75356i	−0.210859	+	0.227252i	0.618763	+	0.785578i	$0.287634\pi$
$642$		0			0
$643$	−13.2286	+	27.4694i	−0.521684	+	1.08329i	0.459135	+	0.888367i	$0.348160\pi$
$643$	−13.2286	+	27.4694i	−0.521684	+	1.08329i	−0.980819	+	0.194922i	$0.937555\pi$
$644$	−0.0417052	−	3.92532i	−0.00164342	−	0.154679i
$645$		0			0
$646$	−4.81356	−	0.725527i	−0.189387	−	0.0285455i
$647$	−7.77763	+	5.30270i	−0.305770	+	0.208471i	−0.706478	−	0.707736i	$-0.749717\pi$
$647$	−7.77763	+	5.30270i	−0.305770	+	0.208471i	0.400707	+	0.916206i	$0.368764\pi$
$648$		0			0
$649$	24.9134	+	26.8503i	0.977936	+	1.05396i
$650$	−43.3496	−	54.3587i	−1.70031	−	2.13212i
$651$		0			0
$652$	4.42181	−	5.54477i	0.173171	−	0.217150i
$653$	12.8389	−	0.962144i	0.502426	−	0.0376516i	0.178893	−	0.983869i	$-0.442748\pi$
$653$	12.8389	−	0.962144i	0.502426	−	0.0376516i	0.323533	+	0.946217i	$0.395129\pi$
$654$		0			0
$655$	−10.8482	+	18.7896i	−0.423874	+	0.734171i
$656$	14.3981	+	24.9382i	0.562151	+	0.973674i
$657$		0			0
$658$	5.16344	−	17.3934i	0.201292	−	0.678066i
$659$	−1.07593	−	0.245573i	−0.0419121	−	0.00956617i	0.201513	−	0.979486i	$-0.435414\pi$
$659$	−1.07593	−	0.245573i	−0.0419121	−	0.00956617i	−0.243426	+	0.969920i	$0.578271\pi$
$660$		0			0
$661$	23.8238	−	9.35014i	0.926637	−	0.363678i	0.146445	−	0.989219i	$-0.453217\pi$
$661$	23.8238	−	9.35014i	0.926637	−	0.363678i	0.780192	+	0.625541i	$0.215122\pi$
$662$	−45.1919	+	17.7365i	−1.75643	+	0.689349i
$663$		0			0
$664$	−29.5099	−	6.73543i	−1.14520	−	0.261386i
$665$	8.46929	−	3.42823i	0.328425	−	0.132941i
$666$		0			0
$667$	−10.5744	−	18.3154i	−0.409441	−	0.709173i
$668$	−6.86468	+	11.8900i	−0.265602	+	0.460037i
$669$		0			0
$670$	17.6824	−	1.32511i	0.683130	−	0.0511935i
$671$	11.8299	−	14.8342i	0.456688	−	0.572669i
$672$		0			0
$673$	−10.2056	−	12.7974i	−0.393395	−	0.493302i	0.545208	−	0.838301i	$-0.316451\pi$
$673$	−10.2056	−	12.7974i	−0.393395	−	0.493302i	−0.938603	+	0.344999i	$0.887879\pi$
$674$	−31.8589	−	34.3357i	−1.22716	−	1.32256i
$675$		0			0
$676$	3.11752	−	2.12549i	0.119905	−	0.0817495i
$677$	15.7345	+	2.37159i	0.604725	+	0.0911477i	0.444266	−	0.895895i	$-0.353464\pi$
$677$	15.7345	+	2.37159i	0.604725	+	0.0911477i	0.160459	+	0.987042i	$0.448703\pi$
$678$		0			0
$679$	−21.2826	−	43.0186i	−0.816752	−	1.65090i
$680$	−12.7099	+	26.3925i	−0.487404	+	1.01211i
$681$		0			0
$682$	26.0134	−	28.0358i	0.996106	−	1.07355i
$683$	−29.2178	−	2.18957i	−1.11799	−	0.0837818i	−0.497110	−	0.867688i	$-0.665605\pi$
$683$	−29.2178	−	2.18957i	−1.11799	−	0.0837818i	−0.620880	+	0.783906i	$0.713225\pi$
$684$		0			0
$685$		−	69.2324i		−	2.64523i
$686$	16.0195	−	25.1847i	0.611626	−	0.961558i
$687$		0			0
$688$	−4.99905	+	12.7374i	−0.190587	+	0.485608i
$689$	4.28451	−	57.1729i	0.163227	−	2.17811i
$690$		0			0
$691$	−0.376066	+	0.551588i	−0.0143062	+	0.0209834i	−0.833325	−	0.552783i	$-0.813566\pi$
$691$	−0.376066	+	0.551588i	−0.0143062	+	0.0209834i	0.819019	+	0.573766i	$0.194518\pi$
$692$	−7.07161	−	3.40551i	−0.268822	−	0.129458i
$693$		0			0
$694$	17.8089	−	8.57630i	0.676016	−	0.325552i
$695$	3.52297	−	23.3734i	0.133634	−	0.886604i
$696$		0			0
$697$	−19.8151	+	2.98665i	−0.750551	+	0.113127i
$698$	−3.82811	+	3.55196i	−0.144896	+	0.134444i
$699$		0			0
$700$	1.32362	+	15.4570i	0.0500281	+	0.584219i
$701$	14.6783	+	11.7056i	0.554394	+	0.442114i	0.860183	−	0.509985i	$-0.170349\pi$
$701$	14.6783	+	11.7056i	0.554394	+	0.442114i	−0.305790	+	0.952099i	$0.598920\pi$
$702$		0			0
$703$	−1.96869	+	6.38233i	−0.0742505	+	0.240714i
$704$	16.7414	+	9.66567i	0.630967	+	0.364289i
$705$		0			0
$706$	−8.42796	+	1.92363i	−0.317191	+	0.0723967i
$707$	2.42430	+	5.98913i	0.0911753	+	0.225245i
$708$		0			0
$709$	32.8575	−	10.1352i	1.23399	−	0.380635i	0.391917	−	0.920001i	$-0.371812\pi$
$709$	32.8575	−	10.1352i	1.23399	−	0.380635i	0.842072	+	0.539366i	$0.181336\pi$
$710$	−16.9860	−	43.2796i	−0.637472	−	1.62425i
$711$		0			0
$712$	2.66515	+	8.64020i	0.0998806	+	0.323805i
$713$	2.98285	−	13.0687i	0.111709	−	0.489427i
$714$		0			0
$715$	−16.5525	−	72.5213i	−0.619029	−	2.71214i
$716$	9.07174	−	5.23757i	0.339027	−	0.195737i
$717$		0			0
$718$	49.0321	+	15.1244i	1.82986	+	0.564438i
$719$	3.06099	+	40.8461i	0.114156	+	1.52330i	0.700741	+	0.713415i	$0.252853\pi$
$719$	3.06099	+	40.8461i	0.114156	+	1.52330i	−0.586586	+	0.809887i	$0.699528\pi$
$720$		0			0
$721$	6.94968	−	49.6842i	0.258819	−	1.85034i
$722$	−22.9262	+	18.2830i	−0.853226	+	0.680425i
$723$		0			0
$724$	−0.563814	−	3.74066i	−0.0209540	−	0.139021i
$725$	47.0816	+	69.0561i	1.74857	+	2.56468i
$726$		0			0
$727$	16.9262	+	35.1477i	0.627759	+	1.30356i	0.935917	+	0.352220i	$0.114573\pi$
$727$	16.9262	+	35.1477i	0.627759	+	1.30356i	−0.308158	+	0.951335i	$0.599713\pi$
$728$	26.2845	−	0.279264i	0.974169	−	0.0103502i
$729$		0			0
$730$	−21.4009	−	14.5909i	−0.792084	−	0.540034i
$731$	−6.98013	−	6.47662i	−0.258170	−	0.239546i
$732$		0			0
$733$	−15.3173	−	6.01161i	−0.565759	−	0.222044i	0.0651842	−	0.997873i	$-0.479237\pi$
$733$	−15.3173	−	6.01161i	−0.565759	−	0.222044i	−0.630943	+	0.775829i	$0.717332\pi$
$734$	−16.5154			−0.609596
$735$		0			0
$736$	−8.13641			−0.299912
$737$	11.7000	+	4.59192i	0.430975	+	0.169145i
$738$		0			0
$739$	16.0870	+	14.9265i	0.591769	+	0.549081i	0.918189	−	0.396144i	$-0.129652\pi$
$739$	16.0870	+	14.9265i	0.591769	+	0.549081i	−0.326420	+	0.945225i	$0.605842\pi$
$740$	−14.1428	−	9.64240i	−0.519900	−	0.354462i
$741$		0			0
$742$	−34.2167	+	43.8542i	−1.25613	+	1.60994i
$743$	−6.05682	−	12.5771i	−0.222203	−	0.461409i	0.759829	−	0.650123i	$-0.225283\pi$
$743$	−6.05682	−	12.5771i	−0.222203	−	0.461409i	−0.982032	+	0.188713i	$0.939568\pi$
$744$		0			0
$745$	14.4802	+	21.2386i	0.530515	+	0.778122i
$746$	3.05261	+	20.2527i	0.111764	+	0.741504i
$747$		0			0
$748$	6.91370	−	5.51349i	0.252790	−	0.201593i
$749$	−2.19604	−	6.85978i	−0.0802416	−	0.250651i
$750$		0			0
$751$	0.0540646	+	0.721442i	0.00197285	+	0.0263258i	0.998103	−	0.0615607i	$-0.0196078\pi$
$751$	0.0540646	+	0.721442i	0.00197285	+	0.0263258i	−0.996130	+	0.0878865i	$0.971989\pi$
$752$	−19.6711	−	6.06773i	−0.717331	−	0.221267i
$753$		0			0
$754$	−52.2311	+	30.1556i	−1.90214	+	1.09820i
$755$	−9.89356	−	43.3465i	−0.360063	−	1.57754i
$756$		0			0
$757$	−9.26950	+	40.6123i	−0.336906	+	1.47608i	0.468556	+	0.883434i	$0.344774\pi$
$757$	−9.26950	+	40.6123i	−0.336906	+	1.47608i	−0.805462	+	0.592647i	$0.798083\pi$
$758$	17.5373	+	56.8547i	0.636985	+	2.06505i
$759$		0			0
$760$	−2.85205	−	7.26691i	−0.103455	−	0.263599i
$761$	−13.4562	+	4.15068i	−0.487786	+	0.150462i	−0.528886	−	0.848693i	$-0.677390\pi$
$761$	−13.4562	+	4.15068i	−0.487786	+	0.150462i	0.0410997	+	0.999155i	$0.486914\pi$
$762$		0			0
$763$	25.3353	−	17.6705i	0.917198	−	0.639714i
$764$	2.66752	−	0.608845i	0.0965076	−	0.0220272i
$765$		0			0
$766$	−3.38361	−	1.95353i	−0.122255	−	0.0705839i
$767$	10.7912	−	34.9843i	0.389649	−	1.26321i
$768$		0			0
$769$	−7.77227	−	6.19818i	−0.280275	−	0.223512i	0.473255	−	0.880926i	$-0.343079\pi$
$769$	−7.77227	−	6.19818i	−0.280275	−	0.223512i	−0.753530	+	0.657414i	$0.771650\pi$
$770$	−25.6508	+	67.4557i	−0.924389	+	2.43093i
$771$		0			0
$772$	0.322345	−	0.299092i	0.0116014	−	0.0107646i
$773$	40.8349	−	6.15487i	1.46873	−	0.221375i	0.634555	−	0.772878i	$-0.281183\pi$
$773$	40.8349	−	6.15487i	1.46873	−	0.221375i	0.834173	+	0.551503i	$0.185945\pi$
$774$		0			0
$775$	−7.89554	+	52.3835i	−0.283616	+	1.88167i
$776$	−36.9464	+	17.7925i	−1.32630	+	0.638712i
$777$		0			0
$778$	4.65915	+	2.24373i	0.167038	+	0.0804415i
$779$	3.00828	−	4.41234i	0.107783	−	0.158088i
$780$		0			0
$781$	2.46278	−	32.8635i	0.0881253	−	1.17595i
$782$	4.92350	−	12.5449i	0.176064	−	0.448604i
$783$		0			0
$784$	−28.3797	−	18.4781i	−1.01356	−	0.659933i
$785$		−	17.8546i		−	0.637258i
$786$		0			0
$787$	27.0998	+	2.03085i	0.966004	+	0.0723920i	0.548381	−	0.836229i	$-0.315244\pi$
$787$	27.0998	+	2.03085i	0.966004	+	0.0723920i	0.417623	+	0.908621i	$0.362863\pi$
$788$	−2.04174	+	2.20048i	−0.0727341	+	0.0783888i
$789$		0			0
$790$	−9.73146	+	20.2076i	−0.346230	+	0.718954i
$791$	29.9212	+	6.49567i	1.06388	+	0.230960i
$792$		0			0
$793$	−18.7529	−	2.82655i	−0.665936	−	0.100374i
$794$	41.8055	−	28.5025i	1.48362	−	1.01152i
$795$		0			0
$796$	0.748527	+	0.806720i	0.0265308	+	0.0285934i
$797$	15.2817	+	19.1626i	0.541304	+	0.678774i	0.974979	−	0.222295i	$-0.0713549\pi$
$797$	15.2817	+	19.1626i	0.541304	+	0.678774i	−0.433675	+	0.901069i	$0.642783\pi$
$798$		0			0
$799$	8.93169	−	11.2000i	0.315981	−	0.396227i
$800$	32.0648	−	2.40292i	1.13366	−	0.0849561i
$801$		0			0
$802$	−18.4358	+	31.9317i	−0.650990	+	1.12755i
$803$	−9.17985	−	15.9000i	−0.323950	−	0.561098i
$804$		0			0
$805$	4.03548	+	24.9706i	0.142232	+	0.880097i
$806$	−37.2689	−	8.50639i	−1.31274	−	0.299625i
$807$		0			0
$808$	5.13886	−	2.01685i	0.180785	−	0.0709527i
$809$	25.3246	−	9.93918i	0.890366	−	0.349443i	0.124330	−	0.992241i	$-0.460322\pi$
$809$	25.3246	−	9.93918i	0.890366	−	0.349443i	0.766036	+	0.642798i	$0.222226\pi$
$810$		0			0
$811$	1.16493	+	0.265887i	0.0409062	+	0.00933656i	0.242925	−	0.970045i	$-0.421893\pi$
$811$	1.16493	+	0.265887i	0.0409062	+	0.00933656i	−0.202019	+	0.979382i	$0.564750\pi$
$812$	13.4295	+	0.863029i	0.471282	+	0.0302864i
$813$		0			0
$814$	−26.3776	−	45.6873i	−0.924534	−	1.60134i
$815$	−22.8490	+	39.5757i	−0.800367	+	1.38628i
$816$		0			0
$817$	2.53047	−	0.189633i	0.0885301	−	0.00663441i
$818$	−2.68000	+	3.36061i	−0.0937038	+	0.117501i
$819$		0			0
$820$	8.53311	+	10.7002i	0.297989	+	0.373666i
$821$	−14.9254	−	16.0858i	−0.520900	−	0.561397i	0.416730	−	0.909030i	$-0.363176\pi$
$821$	−14.9254	−	16.0858i	−0.520900	−	0.561397i	−0.937631	+	0.347633i	$0.886985\pi$
$822$		0			0
$823$	−4.96524	+	3.38524i	−0.173077	+	0.118002i	−0.646760	−	0.762693i	$-0.723877\pi$
$823$	−4.96524	+	3.38524i	−0.173077	+	0.118002i	0.473683	+	0.880695i	$0.342924\pi$
$824$	−42.3849	−	6.38850i	−1.47655	−	0.222554i
$825$		0			0
$826$	−27.5331	+	22.4395i	−0.957998	+	0.780772i
$827$	12.6790	−	26.3282i	0.440892	−	0.915522i	−0.555569	−	0.831470i	$-0.687500\pi$
$827$	12.6790	−	26.3282i	0.440892	−	0.915522i	0.996461	−	0.0840519i	$-0.0267862\pi$
$828$		0			0
$829$	13.9609	−	15.0463i	0.484883	−	0.522580i	−0.442462	−	0.896787i	$-0.645895\pi$
$829$	13.9609	−	15.0463i	0.484883	−	0.522580i	0.927345	+	0.374208i	$0.122085\pi$
$830$	−82.8314	−	6.20736i	−2.87512	−	0.215460i
$831$		0			0
$832$		−	19.3222i		−	0.669878i
$833$	19.1850	−	13.6861i	0.664721	−	0.474196i
$834$		0			0
$835$	32.3204	−	82.3510i	1.11849	−	2.84987i
$836$	−0.176109	+	2.35001i	−0.00609086	+	0.0812769i
$837$		0			0
$838$	−28.6408	+	42.0083i	−0.989379	+	1.45115i
$839$	−3.86101	−	1.85937i	−0.133297	−	0.0641924i	0.366047	−	0.930597i	$-0.380711\pi$
$839$	−3.86101	−	1.85937i	−0.133297	−	0.0641924i	−0.499343	+	0.866404i	$0.666425\pi$
$840$		0			0
$841$	39.1923	−	18.8740i	1.35146	−	0.650828i
$842$	−2.72821	+	18.1005i	−0.0940202	+	0.623783i
$843$		0			0
$844$	−7.27747	+	1.09690i	−0.250501	+	0.0377569i
$845$	−17.8224	+	16.5368i	−0.613109	+	0.568882i
$846$		0			0
$847$	−16.0044	+	15.1695i	−0.549918	+	0.521231i
$848$	49.3414	+	39.3485i	1.69439	+	1.35123i
$849$		0			0
$850$	−15.6982	+	50.8922i	−0.538443	+	1.74559i
$851$	−16.0132	−	9.24522i	−0.548925	−	0.316922i
$852$		0			0
$853$	17.0442	−	3.89023i	0.583583	−	0.133199i	0.0794710	−	0.996837i	$-0.474677\pi$
$853$	17.0442	−	3.89023i	0.583583	−	0.133199i	0.504112	+	0.863638i	$0.331820\pi$
$854$	13.6198	+	12.3706i	0.466059	+	0.423315i
$855$		0			0
$856$	−5.88063	+	1.81393i	−0.200996	+	0.0619990i
$857$	15.1470	+	38.5938i	0.517410	+	1.31834i	0.915988	+	0.401205i	$0.131409\pi$
$857$	15.1470	+	38.5938i	0.517410	+	1.31834i	−0.398578	+	0.917135i	$0.630496\pi$
$858$		0			0
$859$	3.69007	+	11.9629i	0.125904	+	0.408170i	0.996477	−	0.0838695i	$-0.0267279\pi$
$859$	3.69007	+	11.9629i	0.125904	+	0.408170i	−0.870573	+	0.492039i	$0.836252\pi$
$860$	−1.44712	+	6.34023i	−0.0493462	+	0.216200i
$861$		0			0
$862$	−2.60042	−	11.3932i	−0.0885706	−	0.388053i
$863$	−1.23502	+	0.713038i	−0.0420405	+	0.0242721i	−0.520873	−	0.853634i	$-0.674393\pi$
$863$	−1.23502	+	0.713038i	−0.0420405	+	0.0242721i	0.478832	+	0.877906i	$0.341060\pi$
$864$		0			0
$865$	48.3281	+	14.9072i	1.64321	+	0.506862i
$866$	−1.49900	−	20.0028i	−0.0509382	−	0.679723i
$867$		0			0
$868$	5.86772	+	6.19066i	0.199163	+	0.210125i
$869$	−12.4296	+	9.91225i	−0.421644	+	0.336250i
$870$		0			0
$871$	−1.87241	−	12.4226i	−0.0634441	−	0.420924i
$872$	−14.8669	−	21.8057i	−0.503457	−	0.738436i
$873$		0			0
$874$	1.55825	+	3.23575i	0.0527087	+	0.109451i
$875$	−11.4206	−	47.6954i	−0.386087	−	1.61240i
$876$		0			0
$877$	−7.07045	−	4.82055i	−0.238752	−	0.162778i	0.438033	−	0.898959i	$-0.355675\pi$
$877$	−7.07045	−	4.82055i	−0.238752	−	0.162778i	−0.676785	+	0.736180i	$0.736628\pi$
$878$	43.6629	+	40.5132i	1.47355	+	1.36726i
$879$		0			0
$880$	76.2213	+	29.9146i	2.56942	+	1.00842i
$881$	−46.2571			−1.55844			−0.779221	−	0.626749i	$-0.784385\pi$
$881$	−46.2571			−1.55844			−0.779221	+	0.626749i	$0.784385\pi$
$882$		0			0
$883$	47.2579			1.59035			0.795177	−	0.606378i	$-0.207378\pi$
$883$	47.2579			1.59035			0.795177	+	0.606378i	$0.207378\pi$
$884$	−8.22780	−	3.22917i	−0.276731	−	0.108609i
$885$		0			0
$886$	−11.6648	−	10.8234i	−0.391887	−	0.363618i
$887$	−34.3701	−	23.4331i	−1.15403	−	0.786807i	−0.173826	−	0.984776i	$-0.555613\pi$
$887$	−34.3701	−	23.4331i	−1.15403	−	0.786807i	−0.980208	+	0.197969i	$0.936565\pi$
$888$		0			0
$889$	19.1327	+	23.4756i	0.641690	+	0.787347i
$890$	10.7659	+	22.3556i	0.360873	+	0.749361i
$891$		0			0
$892$	−0.00748381	−	0.0109767i	−0.000250577	−	0.000367528i
$893$	0.568988	+	3.77499i	0.0190404	+	0.126325i
$894$		0			0
$895$	−52.7717	+	42.0840i	−1.76396	+	1.40671i
$896$	−20.0067	+	30.0249i	−0.668377	+	1.00306i
$897$		0			0
$898$	0.570092	+	7.60735i	0.0190242	+	0.253861i
$899$	43.9115	+	13.5449i	1.46453	+	0.451748i
$900$		0			0
$901$	−38.0337	+	21.9588i	−1.26709	+	0.731553i
$902$	9.38607	+	41.1231i	0.312522	+	1.36925i
$903$		0			0
$904$	5.82122	−	25.5044i	0.193611	−	0.848265i
$905$	7.18482	+	23.2926i	0.238832	+	0.774273i
$906$		0			0
$907$	−3.60632	−	9.18876i	−0.119746	−	0.305108i	0.858415	−	0.512955i	$-0.171449\pi$
$907$	−3.60632	−	9.18876i	−0.119746	−	0.305108i	−0.978161	+	0.207848i	$0.933354\pi$
$908$	−5.21359	+	1.60818i	−0.173019	+	0.0533693i
$909$		0			0
$910$	71.2102	−	11.5082i	2.36060	−	0.381494i
$911$	44.0955	−	10.0645i	1.46095	−	0.333452i	0.583105	−	0.812397i	$-0.301838\pi$
$911$	44.0955	−	10.0645i	1.46095	−	0.333452i	0.877845	+	0.478944i	$0.158980\pi$
$912$		0			0
$913$	−50.9894	−	29.4388i	−1.68750	−	0.974281i
$914$	7.84845	−	25.4441i	0.259604	−	0.841615i
$915$		0			0
$916$	−1.85278	−	1.47754i	−0.0612175	−	0.0488194i
$917$	−7.59344	−	12.8353i	−0.250757	−	0.423860i
$918$		0			0
$919$	−18.5948	+	17.2534i	−0.613385	+	0.569138i	−0.924475	−	0.381243i	$-0.875496\pi$
$919$	−18.5948	+	17.2534i	−0.613385	+	0.569138i	0.311090	+	0.950380i	$0.399306\pi$
$920$	21.3704	−	3.22107i	0.704561	−	0.106196i
$921$		0			0
$922$	−3.19088	+	21.1701i	−0.105086	+	0.697201i
$923$	−29.6781	+	14.2922i	−0.976866	+	0.470434i
$924$		0			0
$925$	65.8368	+	31.7053i	2.16470	+	1.04246i
$926$	−33.2478	+	48.7655i	−1.09259	+	1.60253i
$927$		0			0
$928$	2.08441	−	27.8145i	0.0684240	−	0.913055i
$929$	−13.6488	+	34.7767i	−0.447804	+	1.14099i	0.511669	+	0.859183i	$0.329028\pi$
$929$	−13.6488	+	34.7767i	−0.447804	+	1.14099i	−0.959472	+	0.281803i	$0.909068\pi$
$930$		0			0
$931$	−0.803875	+	6.22866i	−0.0263459	+	0.204136i
$932$		−	8.83537i		−	0.289412i
$933$		0			0
$934$	−10.6880	−	0.800955i	−0.349722	−	0.0262080i
$935$	−38.7565	+	41.7695i	−1.26747	+	1.36601i
$936$		0			0
$937$	−11.1684	+	23.1914i	−0.364856	+	0.757631i	−0.999890	−	0.0148533i	$-0.995272\pi$
$937$	−11.1684	+	23.1914i	−0.364856	+	0.757631i	0.635034	+	0.772484i	$0.280986\pi$
$938$	−5.17134	+	11.0368i	−0.168850	+	0.360366i
$939$		0			0
$940$	−9.67453	−	1.45820i	−0.315548	−	0.0475613i
$941$	15.0278	−	10.2458i	0.489894	−	0.334004i	−0.293049	−	0.956097i	$-0.594670\pi$
$941$	15.0278	−	10.2458i	0.489894	−	0.334004i	0.782943	+	0.622093i	$0.213718\pi$
$942$		0			0
$943$	10.0557	+	10.8375i	0.327460	+	0.352918i
$944$	25.1264	+	31.5076i	0.817796	+	1.02548i
$945$		0			0
$946$	−12.4967	+	15.6704i	−0.406304	+	0.509489i
$947$	1.95112	−	0.146216i	0.0634028	−	0.00475138i	−0.0429909	−	0.999075i	$-0.513689\pi$
$947$	1.95112	−	0.146216i	0.0634028	−	0.00475138i	0.106394	+	0.994324i	$0.466070\pi$
$948$		0			0
$949$	−9.17553	+	15.8925i	−0.297850	+	0.515892i
$950$	−7.09654	−	12.2916i	−0.230242	−	0.398791i
$951$		0			0
$952$	−11.5187	−	16.5151i	−0.373323	−	0.535256i
$953$	−25.7801	−	5.88414i	−0.835099	−	0.190606i	−0.216470	−	0.976289i	$-0.569454\pi$
$953$	−25.7801	−	5.88414i	−0.835099	−	0.190606i	−0.618629	+	0.785683i	$0.712312\pi$
$954$		0			0
$955$	−16.4117	+	6.44113i	−0.531071	+	0.208430i
$956$	−7.06892	+	2.77435i	−0.228625	+	0.0897288i
$957$		0			0
$958$	31.5863	+	7.20936i	1.02051	+	0.232924i
$959$	41.4627	+	23.3547i	1.33890	+	0.754163i
$960$		0			0
$961$	−0.936667	−	1.62236i	−0.0302151	−	0.0523340i
$962$	−26.3652	+	45.6658i	−0.850047	+	1.47233i
$963$		0			0
$964$	−7.64025	+	0.572558i	−0.246076	+	0.0184408i
$965$	−1.76662	+	2.21527i	−0.0568695	+	0.0713121i
$966$		0			0
$967$	−9.01074	−	11.2991i	−0.289766	−	0.363355i	0.615547	−	0.788100i	$-0.288935\pi$
$967$	−9.01074	−	11.2991i	−0.289766	−	0.363355i	−0.905313	+	0.424745i	$0.860364\pi$
$968$	12.8149	+	13.8112i	0.411886	+	0.443908i
$969$		0			0
$970$	−92.9789	+	63.3920i	−2.98537	+	2.03539i
$971$	22.0429	+	3.32244i	0.707391	+	0.106622i	0.492877	−	0.870099i	$-0.335945\pi$
$971$	22.0429	+	3.32244i	0.707391	+	0.106622i	0.214514	+	0.976721i	$0.431183\pi$
$972$		0			0
$973$	12.8097	+	9.99461i	0.410660	+	0.320413i
$974$	−2.77734	+	5.76720i	−0.0889917	+	0.184793i
$975$		0			0
$976$	14.1990	−	15.3029i	0.454500	−	0.489834i
$977$	−5.43664	−	0.407420i	−0.173933	−	0.0130345i	−0.0125213	−	0.999922i	$-0.503986\pi$
$977$	−5.43664	−	0.407420i	−0.173933	−	0.0130345i	−0.161412	+	0.986887i	$0.551605\pi$
$978$		0			0
$979$			17.5879i			0.562112i
$980$	−14.6464	−	6.67376i	−0.467861	−	0.213185i
$981$		0			0
$982$	6.55417	−	16.6998i	0.209152	−	0.532911i
$983$	2.26325	−	30.2010i	0.0721865	−	0.963261i	−0.837089	−	0.547067i	$-0.815744\pi$
$983$	2.26325	−	30.2010i	0.0721865	−	0.963261i	0.909275	−	0.416195i	$-0.136637\pi$
$984$		0			0
$985$	10.8960	−	15.9814i	0.347174	−	0.509211i
$986$	41.6236	+	20.0449i	1.32557	+	0.638359i
$987$		0			0
$988$	2.12223	−	1.02201i	0.0675170	−	0.0325145i
$989$	−1.04703	+	6.94659i	−0.0332936	+	0.220889i
$990$		0			0
$991$	26.4333	−	3.98418i	0.839681	−	0.126562i	0.284899	−	0.958557i	$-0.408040\pi$
$991$	26.4333	−	3.98418i	0.839681	−	0.126562i	0.554782	+	0.831996i	$0.312802\pi$
$992$	12.9598	−	12.0249i	0.411473	−	0.381791i
$993$		0			0
$994$	31.6498	+	4.42708i	1.00387	+	0.140418i
$995$	−5.54407	−	4.42125i	−0.175759	−	0.140163i
$996$		0			0
$997$	−11.6386	+	37.7315i	−0.368599	+	1.19497i	0.561444	+	0.827515i	$0.310246\pi$
$997$	−11.6386	+	37.7315i	−0.368599	+	1.19497i	−0.930042	+	0.367452i	$0.880230\pi$
$998$	41.2551	+	23.8187i	1.30591	+	0.753966i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.395.14	yes	216
3.2	odd	2	inner	441.2.bg.a.395.5	yes	216
49.33	odd	42	inner	441.2.bg.a.278.5	✓	216
147.131	even	42	inner	441.2.bg.a.278.14	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.5	✓	216	49.33	odd	42	inner
441.2.bg.a.278.14	yes	216	147.131	even	42	inner
441.2.bg.a.395.5	yes	216	3.2	odd	2	inner
441.2.bg.a.395.14	yes	216	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50023 + 0.588795i) q^{2} +(0.437895 + 0.406307i) q^{4} +(-3.18030 - 2.16829i) q^{5} +(2.37141 - 1.17321i) q^{7} +(-0.980812 - 2.03668i) q^{8} +O(q^{10})\)	\(q+(1.50023 + 0.588795i) q^{2} +(0.437895 + 0.406307i) q^{4} +(-3.18030 - 2.16829i) q^{5} +(2.37141 - 1.17321i) q^{7} +(-0.980812 - 2.03668i) q^{8} +(-3.49449 - 5.12548i) q^{10} +(-0.655355 - 4.34800i) q^{11} +(-3.43618 + 2.74026i) q^{13} +(4.24843 - 0.363804i) q^{14} +(-0.361535 - 4.82435i) q^{16} +(3.21706 + 0.992330i) q^{17} +(-0.776988 + 0.448594i) q^{19} +(-0.511645 - 2.24166i) q^{20} +(1.57690 - 6.90885i) q^{22} +(-0.732111 - 2.37344i) q^{23} +(3.58612 + 9.13730i) q^{25} +(-6.76850 + 2.08781i) q^{26} +(1.51511 + 0.449778i) q^{28} +(8.30122 - 1.89470i) q^{29} +(4.67386 + 2.69846i) q^{31} +(0.965559 - 3.13027i) q^{32} +(4.24203 + 3.38291i) q^{34} +(-10.0857 - 1.41075i) q^{35} +(5.45716 - 5.06350i) q^{37} +(-1.42979 + 0.215506i) q^{38} +(-1.29684 + 8.60394i) q^{40} +(-5.36277 + 2.58258i) q^{41} +(-2.54826 - 1.22718i) q^{43} +(1.47965 - 2.17024i) q^{44} +(0.299142 - 3.99177i) q^{46} +(1.55456 - 3.96096i) q^{47} +(4.24716 - 5.56432i) q^{49} +15.8195i q^{50} +(-2.61807 - 0.196198i) q^{52} +(-8.87284 + 9.56264i) q^{53} +(-7.34351 + 15.2490i) q^{55} +(-4.71536 - 3.67910i) q^{56} +(13.5693 + 2.04524i) q^{58} +(-6.88259 + 4.69247i) q^{59} +(2.93497 + 3.16315i) q^{61} +(5.42301 + 6.80024i) q^{62} +(-2.74110 + 3.43722i) q^{64} +(16.8698 - 1.26422i) q^{65} +(-1.42922 + 2.47548i) q^{67} +(1.00554 + 1.74165i) q^{68} +(-14.3001 - 8.05484i) q^{70} +(7.30694 + 1.66776i) q^{71} +(3.88677 - 1.52545i) q^{73} +(11.1683 - 4.38325i) q^{74} +(-0.522506 - 0.119259i) q^{76} +(-6.65522 - 9.54201i) q^{77} +(-1.80778 - 3.13117i) q^{79} +(-9.31082 + 16.1268i) q^{80} +(-9.56598 + 0.716871i) q^{82} +(8.34856 - 10.4688i) q^{83} +(-8.07955 - 10.1314i) q^{85} +(-3.10041 - 3.34145i) q^{86} +(-8.21269 + 5.59932i) q^{88} +(-3.95521 - 0.596152i) q^{89} +(-4.93369 + 10.5296i) q^{91} +(0.643760 - 1.33678i) q^{92} +(4.66439 - 5.02702i) q^{94} +(3.44374 + 0.258073i) q^{95} -18.1405i q^{97} +(9.64795 - 5.84702i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more