LMFDB - Embedded newform 891.2.n.e.136.1

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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} - 15x^{12} + 116x^{10} + 69x^{8} - 814x^{6} + 2420x^{4} - 7986x^{2} + 14641 $ x^16 - x^14 - 15x^12 + 116x^10 + 69x^8 - 814x^6 + 2420x^4 - 7986x^2 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			136.1
Root			$-1.96317 + 0.874061i$ of defining polynomial
Character	$\chi$	$=$	891.136
Dual form			891.2.n.e.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96317 + 0.874061i) q^{2} +(1.75181 - 1.94558i) q^{4} +(1.96317 + 0.874061i) q^{5} +(4.14350 + 0.880728i) q^{7} +(-0.410415 + 1.26313i) q^{8} -4.61803 q^{10} +(-2.28779 + 2.40125i) q^{11} +(-0.0246758 + 0.234775i) q^{13} +(-8.90422 + 1.89265i) q^{14} +(0.248983 + 2.36892i) q^{16} +(-4.96199 + 3.60510i) q^{17} +(-0.736068 + 2.26538i) q^{19} +(5.13966 - 2.28832i) q^{20} +(2.39248 - 6.71375i) q^{22} +(1.99220 + 3.45059i) q^{23} +(-0.255585 - 0.283856i) q^{25} +(-0.156765 - 0.482472i) q^{26} +(8.97214 - 6.51864i) q^{28} +(6.80222 + 1.44586i) q^{29} +(0.482716 - 4.59274i) q^{31} +(-3.88751 - 6.73336i) q^{32} +(6.59017 - 11.4145i) q^{34} +(7.36460 + 5.35069i) q^{35} +(0.545085 + 1.67760i) q^{37} +(-0.535055 - 5.09071i) q^{38} +(-1.90977 + 2.12101i) q^{40} +(-2.90489 + 0.617454i) q^{41} +(-1.35410 + 2.34537i) q^{43} +(0.664066 + 8.65761i) q^{44} +(-6.92705 - 5.03280i) q^{46} +(-2.32663 - 2.58398i) q^{47} +(9.99809 + 4.45144i) q^{49} +(0.749866 + 0.333862i) q^{50} +(0.413545 + 0.459289i) q^{52} +(-1.48490 - 1.07884i) q^{53} +(-6.59017 + 2.71441i) q^{55} +(-2.81303 + 4.87231i) q^{56} +(-14.6177 + 3.10709i) q^{58} +(4.99271 - 5.54496i) q^{59} +(1.18391 + 11.2642i) q^{61} +(3.06668 + 9.43826i) q^{62} +(9.66312 + 7.02067i) q^{64} +(-0.253650 + 0.439335i) q^{65} +(1.42705 + 2.47172i) q^{67} +(-1.67845 + 15.9694i) q^{68} +(-19.1348 - 4.06723i) q^{70} +(8.69273 - 6.31564i) q^{71} +(0.763932 + 2.35114i) q^{73} +(-2.53642 - 2.81698i) q^{74} +(3.11803 + 5.40059i) q^{76} +(-11.5943 + 7.93468i) q^{77} +(-8.65323 + 3.85266i) q^{79} +(-1.58178 + 4.86822i) q^{80} +(5.16312 - 3.75123i) q^{82} +(0.865738 + 8.23694i) q^{83} +(-12.8923 + 2.74035i) q^{85} +(0.608337 - 5.78794i) q^{86} +(-2.09415 - 3.87528i) q^{88} -8.90937 q^{89} +(-0.309017 + 0.951057i) q^{91} +(10.2033 + 2.16878i) q^{92} +(6.82614 + 3.03919i) q^{94} +(-3.42511 + 3.80397i) q^{95} +(10.7784 - 4.79883i) q^{97} -23.5188 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) $ 16 * q - 2 * q^4 + 6 * q^7 - 56 * q^10 + 6 * q^13 - 2 * q^16 + 24 * q^19 - 28 * q^22 - 8 * q^25 + 72 * q^28 - 12 * q^31 + 16 * q^34 - 36 * q^37 + 16 * q^40 + 32 * q^43 - 84 * q^46 + 44 * q^49 - 6 * q^52 - 16 * q^55 - 28 * q^58 - 42 * q^61 + 92 * q^64 - 4 * q^67 - 26 * q^70 + 48 * q^73 + 32 * q^76 - 30 * q^79 + 20 * q^82 - 46 * q^85 + 14 * q^88 + 4 * q^91 + 26 * q^94 + 54 * q^97

Character values

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

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.96317	+	0.874061i	−1.38817	+	0.618055i	−0.958542	−	0.284950i	$-0.908023\pi$
$2$	−1.96317	+	0.874061i	−1.38817	+	0.618055i	−0.429631	+	0.903005i	$0.641356\pi$
$3$		0			0
$3$		0			0
$4$	1.75181	−	1.94558i	0.875903	−	0.972789i
$5$	1.96317	+	0.874061i	0.877958	+	0.390892i	0.795680	−	0.605717i	$-0.207114\pi$
$5$	1.96317	+	0.874061i	0.877958	+	0.390892i	0.0822781	+	0.996609i	$0.473780\pi$
$6$		0			0
$7$	4.14350	+	0.880728i	1.56610	+	0.332884i	0.907645	−	0.419740i	$-0.137879\pi$
$7$	4.14350	+	0.880728i	1.56610	+	0.332884i	0.658451	+	0.752623i	$0.271212\pi$
$8$	−0.410415	+	1.26313i	−0.145104	+	0.446583i
$9$		0			0
$10$	−4.61803			−1.46035
$11$	−2.28779	+	2.40125i	−0.689794	+	0.724005i
$11$	−2.28779	+	2.40125i	−0.689794	+	0.724005i
$12$		0			0
$13$	−0.0246758	+	0.234775i	−0.00684384	+	0.0651148i	−0.997411	−	0.0719150i	$-0.977089\pi$
$13$	−0.0246758	+	0.234775i	−0.00684384	+	0.0651148i	0.990567	+	0.137030i	$0.0437556\pi$
$14$	−8.90422	+	1.89265i	−2.37975	+	0.505832i
$15$		0			0
$16$	0.248983	+	2.36892i	0.0622458	+	0.592229i
$17$	−4.96199	+	3.60510i	−1.20346	+	0.874364i	−0.994620	−	0.103586i	$-0.966968\pi$
$17$	−4.96199	+	3.60510i	−1.20346	+	0.874364i	−0.208838	+	0.977950i	$0.566968\pi$
$18$		0			0
$19$	−0.736068	+	2.26538i	−0.168866	+	0.519715i	−0.999300	−	0.0374011i	$-0.988092\pi$
$19$	−0.736068	+	2.26538i	−0.168866	+	0.519715i	0.830435	+	0.557116i	$0.188092\pi$
$20$	5.13966	−	2.28832i	1.14926	−	0.511684i
$21$		0			0
$22$	2.39248	−	6.71375i	0.510079	−	1.43138i
$23$	1.99220	+	3.45059i	0.415402	+	0.719497i	0.995471	−	0.0950706i	$-0.0303077\pi$
$23$	1.99220	+	3.45059i	0.415402	+	0.719497i	−0.580069	+	0.814567i	$0.696974\pi$
$24$		0			0
$25$	−0.255585	−	0.283856i	−0.0511170	−	0.0567712i
$26$	−0.156765	−	0.482472i	−0.0307441	−	0.0946205i
$27$		0			0
$28$	8.97214	−	6.51864i	1.69557	−	1.23191i
$29$	6.80222	+	1.44586i	1.26314	+	0.268489i	0.790333	−	0.612677i	$-0.209907\pi$
$29$	6.80222	+	1.44586i	1.26314	+	0.268489i	0.472807	+	0.881166i	$0.343241\pi$
$30$		0			0
$31$	0.482716	−	4.59274i	0.0866984	−	0.824880i	−0.861619	−	0.507556i	$-0.830549\pi$
$31$	0.482716	−	4.59274i	0.0866984	−	0.824880i	0.948317	−	0.317324i	$-0.102784\pi$
$32$	−3.88751	−	6.73336i	−0.687221	−	1.19030i
$33$		0			0
$34$	6.59017	−	11.4145i	1.13020	−	1.95757i
$35$	7.36460	+	5.35069i	1.24484	+	0.904432i
$36$		0			0
$37$	0.545085	+	1.67760i	0.0896114	+	0.275796i	0.985812	−	0.167854i	$-0.0536836\pi$
$37$	0.545085	+	1.67760i	0.0896114	+	0.275796i	−0.896201	+	0.443649i	$0.853684\pi$
$38$	−0.535055	−	5.09071i	−0.0867974	−	0.825822i
$39$		0			0
$40$	−1.90977	+	2.12101i	−0.301961	+	0.335361i
$41$	−2.90489	+	0.617454i	−0.453668	+	0.0964302i	−0.429078	−	0.903267i	$-0.641161\pi$
$41$	−2.90489	+	0.617454i	−0.453668	+	0.0964302i	−0.0245903	+	0.999698i	$0.507828\pi$
$42$		0			0
$43$	−1.35410	+	2.34537i	−0.206499	+	0.357666i	−0.950609	−	0.310390i	$-0.899540\pi$
$43$	−1.35410	+	2.34537i	−0.206499	+	0.357666i	0.744111	+	0.668056i	$0.232874\pi$
$44$	0.664066	+	8.65761i	0.100112	+	1.30518i
$45$		0			0
$46$	−6.92705	−	5.03280i	−1.02134	−	0.742045i
$47$	−2.32663	−	2.58398i	−0.339374	−	0.376913i	0.549165	−	0.835714i	$-0.314946\pi$
$47$	−2.32663	−	2.58398i	−0.339374	−	0.376913i	−0.888539	+	0.458801i	$0.848279\pi$
$48$		0			0
$49$	9.99809	+	4.45144i	1.42830	+	0.635919i
$50$	0.749866	+	0.333862i	0.106047	+	0.0472152i
$51$		0			0
$52$	0.413545	+	0.459289i	0.0573484	+	0.0636919i
$53$	−1.48490	−	1.07884i	−0.203966	−	0.148190i	0.481113	−	0.876658i	$-0.340233\pi$
$53$	−1.48490	−	1.07884i	−0.203966	−	0.148190i	−0.685079	+	0.728468i	$0.740233\pi$
$54$		0			0
$55$	−6.59017	+	2.71441i	−0.888618	+	0.366011i
$56$	−2.81303	+	4.87231i	−0.375906	+	0.651089i
$57$		0			0
$58$	−14.6177	+	3.10709i	−1.91940	+	0.407981i
$59$	4.99271	−	5.54496i	0.649995	−	0.721893i	−0.324604	−	0.945850i	$-0.605231\pi$
$59$	4.99271	−	5.54496i	0.649995	−	0.721893i	0.974599	+	0.223957i	$0.0718976\pi$
$60$		0			0
$61$	1.18391	+	11.2642i	0.151585	+	1.44223i	0.760676	+	0.649132i	$0.224868\pi$
$61$	1.18391	+	11.2642i	0.151585	+	1.44223i	−0.609091	+	0.793100i	$0.708466\pi$
$62$	3.06668	+	9.43826i	0.389468	+	1.19866i
$63$		0			0
$64$	9.66312	+	7.02067i	1.20789	+	0.877583i
$65$	−0.253650	+	0.439335i	−0.0314615	+	0.0544929i
$66$		0			0
$67$	1.42705	+	2.47172i	0.174342	+	0.301969i	0.939933	−	0.341358i	$-0.110887\pi$
$67$	1.42705	+	2.47172i	0.174342	+	0.301969i	−0.765591	+	0.643327i	$0.777553\pi$
$68$	−1.67845	+	15.9694i	−0.203542	+	1.93657i
$69$		0			0
$70$	−19.1348	−	4.06723i	−2.28705	−	0.486127i
$71$	8.69273	−	6.31564i	1.03164	−	0.749528i	0.0630016	−	0.998013i	$-0.479933\pi$
$71$	8.69273	−	6.31564i	1.03164	−	0.749528i	0.968636	+	0.248485i	$0.0799327\pi$
$72$		0			0
$73$	0.763932	+	2.35114i	0.0894115	+	0.275180i	0.985757	−	0.168176i	$-0.0537877\pi$
$73$	0.763932	+	2.35114i	0.0894115	+	0.275180i	−0.896346	+	0.443356i	$0.853788\pi$
$74$	−2.53642	−	2.81698i	−0.294853	−	0.327467i
$75$		0			0
$76$	3.11803	+	5.40059i	0.357663	+	0.619491i
$77$	−11.5943	+	7.93468i	−1.32129	+	0.904240i
$78$		0			0
$79$	−8.65323	+	3.85266i	−0.973564	+	0.433459i	−0.830967	−	0.556322i	$-0.812212\pi$
$79$	−8.65323	+	3.85266i	−0.973564	+	0.433459i	−0.142597	+	0.989781i	$0.545545\pi$
$80$	−1.58178	+	4.86822i	−0.176849	+	0.544284i
$81$		0			0
$82$	5.16312	−	3.75123i	0.570171	−	0.414254i
$83$	0.865738	+	8.23694i	0.0950271	+	0.904122i	0.933355	+	0.358955i	$0.116867\pi$
$83$	0.865738	+	8.23694i	0.0950271	+	0.904122i	−0.838328	+	0.545167i	$0.816466\pi$
$84$		0			0
$85$	−12.8923	+	2.74035i	−1.39837	+	0.297232i
$86$	0.608337	−	5.78794i	0.0655987	−	0.624130i
$87$		0			0
$88$	−2.09415	−	3.87528i	−0.223237	−	0.413106i
$89$	−8.90937			−0.944392			−0.472196	−	0.881494i	$-0.656538\pi$
$89$	−8.90937			−0.944392			−0.472196	+	0.881494i	$0.656538\pi$
$90$		0			0
$91$	−0.309017	+	0.951057i	−0.0323938	+	0.0996978i
$92$	10.2033	+	2.16878i	1.06377	+	0.226111i
$93$		0			0
$94$	6.82614	+	3.03919i	0.704062	+	0.313469i
$95$	−3.42511	+	3.80397i	−0.351409	+	0.390280i
$96$		0			0
$97$	10.7784	−	4.79883i	1.09438	−	0.487247i	0.221485	−	0.975164i	$-0.428910\pi$
$97$	10.7784	−	4.79883i	1.09438	−	0.487247i	0.872890	+	0.487916i	$0.162243\pi$
$98$	−23.5188			−2.37576
$99$		0			0
$100$	−1.00000			−0.100000
$101$	0.286423	−	0.127524i	0.0285002	−	0.0126891i	−0.392437	−	0.919779i	$-0.628368\pi$
$101$	0.286423	−	0.127524i	0.0285002	−	0.0126891i	0.420937	+	0.907090i	$0.361701\pi$
$102$		0			0
$103$	−7.32315	+	8.13318i	−0.721571	+	0.801386i	−0.986652	−	0.162840i	$-0.947935\pi$
$103$	−7.32315	+	8.13318i	−0.721571	+	0.801386i	0.265081	+	0.964226i	$0.414601\pi$
$104$	−0.286423	−	0.127524i	−0.0280861	−	0.0125047i
$105$		0			0
$106$	3.85808	+	0.820060i	0.374730	+	0.0796513i
$107$	3.38021	−	10.4032i	0.326777	−	1.00572i	−0.643855	−	0.765147i	$-0.722666\pi$
$107$	3.38021	−	10.4032i	0.326777	−	1.00572i	0.970632	−	0.240569i	$-0.0773339\pi$
$108$		0			0
$109$	−13.7082			−1.31301			−0.656504	−	0.754323i	$-0.727965\pi$
$109$	−13.7082			−1.31301			−0.656504	+	0.754323i	$0.727965\pi$
$110$	10.5651	−	11.0891i	1.00734	−	1.05730i
$111$		0			0
$112$	−1.05471	+	10.0349i	−0.0996607	+	0.948208i
$113$	17.5018	−	3.72011i	1.64643	−	0.349959i	0.710922	−	0.703271i	$-0.248278\pi$
$113$	17.5018	−	3.72011i	1.64643	−	0.349959i	0.935505	+	0.353312i	$0.114945\pi$
$114$		0			0
$115$	0.895005	+	8.51540i	0.0834596	+	0.794065i
$116$	14.7292	−	10.7014i	1.36757	−	0.993599i
$117$		0			0
$118$	−4.95492	+	15.2497i	−0.456137	+	1.40385i
$119$	−23.7351	+	10.5675i	−2.17579	+	0.968726i
$120$		0			0
$121$	−0.532046	−	10.9871i	−0.0483678	−	0.998830i
$122$	−12.1698	−	21.0788i	−1.10180	−	1.90838i
$123$		0			0
$124$	−8.08990	−	8.98475i	−0.726495	−	0.806854i
$125$	−3.57398	−	10.9996i	−0.319666	−	0.983832i
$126$		0			0
$127$	2.23607	−	1.62460i	0.198419	−	0.144160i	−0.484139	−	0.874991i	$-0.660867\pi$
$127$	2.23607	−	1.62460i	0.198419	−	0.144160i	0.682558	+	0.730831i	$0.260867\pi$
$128$	−9.89665	−	2.10360i	−0.874749	−	0.185934i
$129$		0			0
$130$	0.113954	−	1.08420i	0.00999441	−	0.0950904i
$131$	1.23125	+	2.13258i	0.107574	+	0.186324i	0.914787	−	0.403936i	$-0.132358\pi$
$131$	1.23125	+	2.13258i	0.107574	+	0.186324i	−0.807213	+	0.590261i	$0.799025\pi$
$132$		0			0
$133$	−5.04508	+	8.73834i	−0.437464	+	0.757710i
$134$	−4.96199	−	3.60510i	−0.428650	−	0.311433i
$135$		0			0
$136$	−2.51722	−	7.74721i	−0.215850	−	0.664318i
$137$	0.0327727	+	0.311812i	0.00279996	+	0.0266399i	0.995833	−	0.0911992i	$-0.0290700\pi$
$137$	0.0327727	+	0.311812i	0.00279996	+	0.0266399i	−0.993033	+	0.117839i	$0.962403\pi$
$138$		0			0
$139$	−7.61602	+	8.45845i	−0.645983	+	0.717436i	−0.973826	−	0.227296i	$-0.927012\pi$
$139$	−7.61602	+	8.45845i	−0.645983	+	0.717436i	0.327843	+	0.944732i	$0.393678\pi$
$140$	23.3116	−	4.95502i	1.97019	−	0.418776i
$141$		0			0
$142$	−11.5451	+	19.9967i	−0.968842	+	1.67808i
$143$	−0.507301	−	0.596368i	−0.0424226	−	0.0498708i
$144$		0			0
$145$	12.0902	+	8.78402i	1.00403	+	0.729473i
$146$	−3.55477	−	3.94797i	−0.294195	−	0.326737i
$147$		0			0
$148$	4.21878	+	1.87832i	0.346782	+	0.154397i
$149$	4.21277	+	1.87565i	0.345124	+	0.153659i	0.571976	−	0.820270i	$-0.306177\pi$
$149$	4.21277	+	1.87565i	0.345124	+	0.153659i	−0.226853	+	0.973929i	$0.572844\pi$
$150$		0			0
$151$	−8.85666	−	9.83632i	−0.720745	−	0.800468i	0.265788	−	0.964031i	$-0.414368\pi$
$151$	−8.85666	−	9.83632i	−0.720745	−	0.800468i	−0.986533	+	0.163563i	$0.947701\pi$
$152$	−2.55938	−	1.85950i	−0.207593	−	0.150825i
$153$		0			0
$154$	15.8262	−	25.7113i	1.27531	−	2.07187i
$155$	4.96199	−	8.59441i	0.398556	−	0.690320i
$156$		0			0
$157$	20.2012	−	4.29389i	1.61223	−	0.342690i	0.688351	−	0.725378i	$-0.258335\pi$
$157$	20.2012	−	4.29389i	1.61223	−	0.342690i	0.923878	+	0.382688i	$0.125002\pi$
$158$	13.6203	−	15.1269i	1.08357	−	1.20343i
$159$		0			0
$160$	−1.74648	−	16.6167i	−0.138072	−	1.31366i
$161$	5.21564	+	16.0521i	0.411050	+	1.26508i
$162$		0			0
$163$	−1.11803	−	0.812299i	−0.0875712	−	0.0636242i	0.543138	−	0.839643i	$-0.317236\pi$
$163$	−1.11803	−	0.812299i	−0.0875712	−	0.0636242i	−0.630709	+	0.776019i	$0.717236\pi$
$164$	−3.88751	+	6.73336i	−0.303563	+	0.525787i
$165$		0			0
$166$	−8.89919	−	15.4138i	−0.690711	−	1.19635i
$167$	−1.12314	+	10.6859i	−0.0869110	+	0.826903i	0.861051	+	0.508519i	$0.169807\pi$
$167$	−1.12314	+	10.6859i	−0.0869110	+	0.826903i	−0.947962	+	0.318384i	$0.896860\pi$
$168$		0			0
$169$	12.6614	+	2.69127i	0.973955	+	0.207020i
$170$	22.9146	−	16.6485i	1.75747	−	1.27688i
$171$		0			0
$172$	2.19098	+	6.74315i	0.167061	+	0.514161i
$173$	8.96706	+	9.95893i	0.681753	+	0.757164i	0.980361	−	0.197212i	$-0.0631888\pi$
$173$	8.96706	+	9.95893i	0.681753	+	0.757164i	−0.298608	+	0.954376i	$0.596522\pi$
$174$		0			0
$175$	−0.809017	−	1.40126i	−0.0611559	−	0.105925i
$176$	−6.25799	−	4.82171i	−0.471714	−	0.363450i
$177$		0			0
$178$	17.4906	−	7.78734i	1.31098	−	0.583686i
$179$	−0.604187	+	1.85950i	−0.0451590	+	0.138985i	−0.971094	−	0.238698i	$-0.923279\pi$
$179$	−0.604187	+	1.85950i	−0.0451590	+	0.138985i	0.925935	+	0.377684i	$0.123279\pi$
$180$		0			0
$181$	−9.89919	+	7.19218i	−0.735801	+	0.534591i	−0.891393	−	0.453231i	$-0.850271\pi$
$181$	−9.89919	+	7.19218i	−0.735801	+	0.534591i	0.155592	+	0.987821i	$0.450271\pi$
$182$	−0.224628	−	2.13719i	−0.0166505	−	0.158419i
$183$		0			0
$184$	−5.17616	+	1.10023i	−0.381591	+	0.0811098i
$185$	−0.396228	+	3.76986i	−0.0291312	+	0.277165i
$186$		0			0
$187$	2.69523	−	20.1627i	0.197095	−	1.47444i
$188$	−9.10315			−0.663915
$189$		0			0
$190$	3.39919	−	10.4616i	0.246603	−	0.758966i
$191$	−9.70711	−	2.06331i	−0.702382	−	0.149296i	−0.157142	−	0.987576i	$-0.550228\pi$
$191$	−9.70711	−	2.06331i	−0.702382	−	0.149296i	−0.545240	+	0.838280i	$0.683561\pi$
$192$		0			0
$193$	6.74376	+	3.00252i	0.485427	+	0.216126i	0.634832	−	0.772650i	$-0.281069\pi$
$193$	6.74376	+	3.00252i	0.485427	+	0.216126i	−0.149405	+	0.988776i	$0.547736\pi$
$194$	−16.9653	+	18.8419i	−1.21804	+	1.35277i
$195$		0			0
$196$	26.1753	−	11.6540i	1.86967	−	0.832429i
$197$	2.46249			0.175445			0.0877226	−	0.996145i	$-0.472041\pi$
$197$	2.46249			0.175445			0.0877226	+	0.996145i	$0.472041\pi$
$198$		0			0
$199$	0.416408			0.0295184			0.0147592	−	0.999891i	$-0.495302\pi$
$199$	0.416408			0.0295184			0.0147592	+	0.999891i	$0.495302\pi$
$200$	0.463442	−	0.206338i	0.0327703	−	0.0145903i
$201$		0			0
$202$	−0.450835	+	0.500703i	−0.0317206	+	0.0352293i
$203$	26.9116	+	11.9818i	1.88882	+	0.840958i
$204$		0			0
$205$	−6.24250	−	1.32689i	−0.435995	−	0.0926737i
$206$	7.26771	−	22.3677i	0.506366	−	1.55843i
$207$		0			0
$208$	−0.562306			−0.0389889
$209$	−3.75580	−	6.95021i	−0.259794	−	0.480756i
$210$		0			0
$211$	1.88511	−	17.9356i	0.129776	−	1.23474i	−0.714809	−	0.699320i	$-0.753486\pi$
$211$	1.88511	−	17.9356i	0.129776	−	1.23474i	0.844585	−	0.535421i	$-0.179847\pi$
$212$	−4.70022	+	0.999062i	−0.322812	+	0.0686159i
$213$		0			0
$214$	2.45711	+	23.3778i	0.167964	+	1.59807i
$215$	−4.70834	+	3.42081i	−0.321106	+	0.233297i
$216$		0			0
$217$	6.04508	−	18.6049i	0.410367	−	1.26298i
$218$	26.9116	−	11.9818i	1.82268	−	0.811511i
$219$		0			0
$220$	−6.26360	+	17.5768i	−0.422292	+	1.18503i
$221$	−0.723944	−	1.25391i	−0.0486978	−	0.0843470i
$222$		0			0
$223$	2.12806	+	2.36345i	0.142506	+	0.158269i	0.810172	−	0.586192i	$-0.199374\pi$
$223$	2.12806	+	2.36345i	0.142506	+	0.158269i	−0.667667	+	0.744460i	$0.732707\pi$
$224$	−10.1776	−	31.3235i	−0.680021	−	2.09289i
$225$		0			0
$226$	−31.1074	+	22.6008i	−2.06923	+	1.50339i
$227$	10.6995	+	2.27426i	0.710154	+	0.150948i	0.548806	−	0.835950i	$-0.315083\pi$
$227$	10.6995	+	2.27426i	0.710154	+	0.150948i	0.161348	+	0.986898i	$0.448416\pi$
$228$		0			0
$229$	1.93086	−	18.3709i	0.127595	−	1.21399i	−0.724005	−	0.689794i	$-0.757701\pi$
$229$	1.93086	−	18.3709i	0.127595	−	1.21399i	0.851600	−	0.524192i	$-0.175632\pi$
$230$	−9.20003	−	15.9349i	−0.606632	−	1.05072i
$231$		0			0
$232$	−4.61803	+	7.99867i	−0.303189	+	0.525138i
$233$	18.6167	+	13.5258i	1.21962	+	0.886106i	0.996069	−	0.0885854i	$-0.0282346\pi$
$233$	18.6167	+	13.5258i	1.21962	+	0.886106i	0.223552	+	0.974692i	$0.428235\pi$
$234$		0			0
$235$	−2.30902	−	7.10642i	−0.150624	−	0.463572i
$236$	−2.04190	−	19.4274i	−0.132917	−	1.26462i
$237$		0			0
$238$	37.3594	−	41.4919i	2.42165	−	2.68952i
$239$	11.1958	−	2.37973i	0.724193	−	0.153932i	0.168956	−	0.985624i	$-0.445961\pi$
$239$	11.1958	−	2.37973i	0.724193	−	0.153932i	0.555238	+	0.831692i	$0.312627\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	10.6479	+	21.1046i	0.684474	+	1.35665i
$243$		0			0
$244$	23.9894	+	17.4293i	1.53576	+	1.11580i
$245$	15.7372	+	17.4779i	1.00541	+	1.11662i
$246$		0			0
$247$	−0.513692	−	0.228710i	−0.0326854	−	0.0145525i
$248$	5.60310	+	2.49466i	0.355797	+	0.158411i
$249$		0			0
$250$	16.6306	+	18.4702i	1.05181	+	1.16816i
$251$	−18.3631	−	13.3415i	−1.15907	−	0.842111i	−0.169406	−	0.985546i	$-0.554185\pi$
$251$	−18.3631	−	13.3415i	−1.15907	−	0.842111i	−0.989660	+	0.143436i	$0.954185\pi$
$252$		0			0
$253$	−12.8435	−	3.11044i	−0.807461	−	0.195552i
$254$	−2.96979	+	5.14383i	−0.186341	+	0.322753i
$255$		0			0
$256$	−2.09901	+	0.446157i	−0.131188	+	0.0278848i
$257$	8.28816	−	9.20494i	0.517001	−	0.574188i	−0.426949	−	0.904276i	$-0.640412\pi$
$257$	8.28816	−	9.20494i	0.517001	−	0.574188i	0.943950	+	0.330087i	$0.107078\pi$
$258$		0			0
$259$	0.781051	+	7.43120i	0.0485321	+	0.461752i
$260$	0.410415	+	1.26313i	0.0254529	+	0.0783359i
$261$		0			0
$262$	−4.28115	−	3.11044i	−0.264491	−	0.192164i
$263$	−3.22344	+	5.58316i	−0.198766	+	0.344273i	−0.948129	−	0.317887i	$-0.897027\pi$
$263$	−3.22344	+	5.58316i	−0.198766	+	0.344273i	0.749363	+	0.662160i	$0.230360\pi$
$264$		0			0
$265$	−1.97214	−	3.41584i	−0.121147	−	0.209833i
$266$	2.26653	−	21.5646i	0.138970	−	1.32221i
$267$		0			0
$268$	7.30885	+	1.55354i	0.446459	+	0.0948978i
$269$	16.3709	−	11.8941i	0.998149	−	0.725198i	0.0364584	−	0.999335i	$-0.488392\pi$
$269$	16.3709	−	11.8941i	0.998149	−	0.725198i	0.961690	+	0.274138i	$0.0883924\pi$
$270$		0			0
$271$	−0.298374	−	0.918300i	−0.0181249	−	0.0557828i	0.941585	−	0.336775i	$-0.109336\pi$
$271$	−0.298374	−	0.918300i	−0.0181249	−	0.0557828i	−0.959710	+	0.280993i	$0.909336\pi$
$272$	−9.77562	−	10.8569i	−0.592734	−	0.658298i
$273$		0			0
$274$	−0.336881	−	0.583495i	−0.0203517	−	0.0352502i
$275$	1.26634	+	0.0356777i	0.0763629	+	0.00215145i
$276$		0			0
$277$	17.7063	−	7.88336i	1.06387	−	0.473665i	0.201261	−	0.979538i	$-0.435496\pi$
$277$	17.7063	−	7.88336i	1.06387	−	0.473665i	0.862608	+	0.505873i	$0.168829\pi$
$278$	7.55837	−	23.2623i	0.453321	−	1.39518i
$279$		0			0
$280$	−9.78115	+	7.10642i	−0.584536	+	0.424690i
$281$	−1.73148	−	16.4739i	−0.103291	−	0.982750i	−0.916298	−	0.400496i	$-0.868838\pi$
$281$	−1.73148	−	16.4739i	−0.103291	−	0.982750i	0.813007	−	0.582254i	$-0.197829\pi$
$282$		0			0
$283$	10.7051	−	2.27544i	0.636353	−	0.135261i	0.121572	−	0.992583i	$-0.461207\pi$
$283$	10.7051	−	2.27544i	0.636353	−	0.135261i	0.514781	+	0.857322i	$0.327873\pi$
$284$	2.94041	−	27.9762i	0.174481	−	1.66008i
$285$		0			0
$286$	1.51718	+	0.727362i	0.0897128	+	0.0430098i
$287$	−12.5802			−0.742588
$288$		0			0
$289$	6.37132	−	19.6089i	0.374784	−	1.15347i
$290$	−31.4129	−	6.67701i	−1.84463	−	0.392088i
$291$		0			0
$292$	5.91259	+	2.63245i	0.346008	+	0.154053i
$293$	3.34498	−	3.71498i	0.195416	−	0.217031i	−0.637471	−	0.770474i	$-0.720020\pi$
$293$	3.34498	−	3.71498i	0.195416	−	0.217031i	0.832887	+	0.553443i	$0.186686\pi$
$294$		0			0
$295$	14.6482	−	6.52180i	0.852851	−	0.379714i
$296$	−2.34273			−0.136169
$297$		0			0
$298$	−9.90983			−0.574061
$299$	−0.859270	+	0.382571i	−0.0496928	+	0.0221247i
$300$		0			0
$301$	−7.67636	+	8.52546i	−0.442458	+	0.491399i
$302$	25.9847	+	11.5691i	1.49525	+	0.665729i
$303$		0			0
$304$	−5.54978	−	1.17964i	−0.318302	−	0.0676571i
$305$	−7.52136	+	23.1484i	−0.430672	+	1.32547i
$306$		0			0
$307$	17.2705			0.985680			0.492840	−	0.870120i	$-0.335959\pi$
$307$	17.2705			0.985680			0.492840	+	0.870120i	$0.335959\pi$
$308$	−4.87344	+	36.4576i	−0.277690	+	2.07737i
$309$		0			0
$310$	−2.22920	+	21.2094i	−0.126610	+	1.20461i
$311$	−28.1289	+	5.97898i	−1.59504	+	0.339037i	−0.917900	−	0.396813i	$-0.870116\pi$
$311$	−28.1289	+	5.97898i	−1.59504	+	0.339037i	−0.677145	+	0.735850i	$0.736783\pi$
$312$		0			0
$313$	−3.30858	−	31.4791i	−0.187012	−	1.77930i	−0.538022	−	0.842931i	$-0.680828\pi$
$313$	−3.30858	−	31.4791i	−0.187012	−	1.77930i	0.351010	−	0.936372i	$-0.385838\pi$
$314$	−35.9053	+	26.0867i	−2.02625	+	1.47216i
$315$		0			0
$316$	−7.66312	+	23.5847i	−0.431084	+	1.32674i
$317$	0.286423	−	0.127524i	0.0160871	−	0.00716245i	−0.398677	−	0.917091i	$-0.630531\pi$
$317$	0.286423	−	0.127524i	0.0160871	−	0.00716245i	0.414764	+	0.909929i	$0.363864\pi$
$318$		0			0
$319$	−19.0339	+	13.0260i	−1.06569	+	0.729318i
$320$	12.8339	+	22.2289i	0.717436	+	1.24264i
$321$		0			0
$322$	−24.2697	−	26.9542i	−1.35250	−	1.50210i
$323$	−4.51457	−	13.8944i	−0.251197	−	0.773105i
$324$		0			0
$325$	0.0729490	−	0.0530006i	0.00404648	−	0.00293994i
$326$	2.90489	+	0.617454i	0.160887	+	0.0341976i
$327$		0			0
$328$	0.412289	−	3.92266i	0.0227648	−	0.216593i
$329$	−7.36460	−	12.7559i	−0.406024	−	0.703253i
$330$		0			0
$331$	−3.64590	+	6.31488i	−0.200397	+	0.347097i	−0.948656	−	0.316309i	$-0.897556\pi$
$331$	−3.64590	+	6.31488i	−0.200397	+	0.347097i	0.748260	+	0.663406i	$0.230890\pi$
$332$	17.5422	+	12.7452i	0.962755	+	0.699482i
$333$		0			0
$334$	−7.13525	−	21.9601i	−0.390424	−	1.20160i
$335$	0.641110	+	6.09976i	0.0350276	+	0.333265i
$336$		0			0
$337$	−17.8340	+	19.8066i	−0.971479	+	1.07894i	0.0253749	+	0.999678i	$0.491922\pi$
$337$	−17.8340	+	19.8066i	−0.971479	+	1.07894i	−0.996854	+	0.0792589i	$0.974745\pi$
$338$	−27.2089	+	5.78342i	−1.47997	+	0.314577i
$339$		0			0
$340$	−17.2533	+	29.8836i	−0.935691	+	1.62066i
$341$	9.92398	+	11.6663i	0.537413	+	0.631767i
$342$		0			0
$343$	13.5172	+	9.82084i	0.729861	+	0.530275i
$344$	−2.40676	−	2.67298i	−0.129764	−	0.144117i
$345$		0			0
$346$	−26.3086	−	11.7134i	−1.41436	−	0.629714i
$347$	−22.9852	−	10.2337i	−1.23391	−	0.549373i	−0.316986	−	0.948430i	$-0.602671\pi$
$347$	−22.9852	−	10.2337i	−1.23391	−	0.549373i	−0.916926	+	0.399057i	$0.869338\pi$
$348$		0			0
$349$	6.14285	+	6.82232i	0.328819	+	0.365191i	0.884773	−	0.466023i	$-0.154314\pi$
$349$	6.14285	+	6.82232i	0.328819	+	0.365191i	−0.555954	+	0.831213i	$0.687647\pi$
$350$	2.81303	+	2.04378i	0.150363	+	0.109245i
$351$		0			0
$352$	25.0623	+	6.06961i	1.33583	+	0.323511i
$353$	−16.8782	+	29.2338i	−0.898334	+	1.55596i	−0.0687102	+	0.997637i	$0.521888\pi$
$353$	−16.8782	+	29.2338i	−0.898334	+	1.55596i	−0.829624	+	0.558323i	$0.811445\pi$
$354$		0			0
$355$	22.5856	−	4.80072i	1.19872	−	0.254796i
$356$	−15.6075	+	17.3339i	−0.827196	+	0.918694i
$357$		0			0
$358$	−0.439190	−	4.17861i	−0.0232119	−	0.220846i
$359$	−0.627058	−	1.92989i	−0.0330949	−	0.101856i	0.933145	−	0.359501i	$-0.117053\pi$
$359$	−0.627058	−	1.92989i	−0.0330949	−	0.101856i	−0.966239	+	0.257646i	$0.917053\pi$
$360$		0			0
$361$	10.7812	+	7.83297i	0.567429	+	0.412261i
$362$	13.1474	−	22.7720i	0.691013	−	1.19687i
$363$		0			0
$364$	1.30902	+	2.26728i	0.0686111	+	0.118838i
$365$	−0.555310	+	5.28342i	−0.0290663	+	0.276547i
$366$		0			0
$367$	−22.5311	−	4.78913i	−1.17611	−	0.249991i	−0.421914	−	0.906636i	$-0.638641\pi$
$367$	−22.5311	−	4.78913i	−1.17611	−	0.249991i	−0.754199	+	0.656645i	$0.771975\pi$
$368$	−7.67813	+	5.57849i	−0.400250	+	0.290799i
$369$		0			0
$370$	−2.51722	−	7.74721i	−0.130864	−	0.402758i
$371$	−5.20250	−	5.77796i	−0.270100	−	0.299977i
$372$		0			0
$373$	7.20820	+	12.4850i	0.373227	+	0.646448i	0.990060	−	0.140646i	$-0.0449180\pi$
$373$	7.20820	+	12.4850i	0.373227	+	0.646448i	−0.616833	+	0.787094i	$0.711585\pi$
$374$	12.3322	+	41.9387i	0.637684	+	2.16860i
$375$		0			0
$376$	4.21878	−	1.87832i	0.217567	−	0.0968671i
$377$	−0.507301	+	1.56131i	−0.0261273	+	0.0804116i
$378$		0			0
$379$	−5.04508	+	3.66547i	−0.259149	+	0.188282i	−0.709772	−	0.704432i	$-0.751202\pi$
$379$	−5.04508	+	3.66547i	−0.259149	+	0.188282i	0.450623	+	0.892714i	$0.351202\pi$
$380$	1.40079	+	13.3277i	0.0718592	+	0.683694i
$381$		0			0
$382$	20.8602	−	4.43397i	1.06730	−	0.226862i
$383$	−3.56127	+	33.8832i	−0.181972	+	1.73135i	0.398585	+	0.917132i	$0.369502\pi$
$383$	−3.56127	+	33.8832i	−0.181972	+	1.73135i	−0.580557	+	0.814220i	$0.697165\pi$
$384$		0			0
$385$	−29.6970	+	5.44302i	−1.51350	+	0.277402i
$386$	−15.8636			−0.807434
$387$		0			0
$388$	9.54508	−	29.3768i	0.484578	−	1.49138i
$389$	21.8229	+	4.63860i	1.10647	+	0.235186i	0.724694	−	0.689071i	$-0.241981\pi$
$389$	21.8229	+	4.63860i	1.10647	+	0.235186i	0.381771	+	0.924257i	$0.375314\pi$
$390$		0			0
$391$	−22.3249	−	9.93971i	−1.12902	−	0.502673i
$392$	−9.72610	+	10.8019i	−0.491242	+	0.545580i
$393$		0			0
$394$	−4.83430	+	2.15237i	−0.243548	+	0.108435i
$395$	−20.3553			−1.02418
$396$		0			0
$397$	24.4164			1.22542			0.612712	−	0.790306i	$-0.290078\pi$
$397$	24.4164			1.22542			0.612712	+	0.790306i	$0.290078\pi$
$398$	−0.817481	+	0.363966i	−0.0409766	+	0.0182440i
$399$		0			0
$400$	0.608795	−	0.676135i	0.0304398	−	0.0338068i
$401$	17.3821	+	7.73903i	0.868023	+	0.386469i	0.791915	−	0.610631i	$-0.209084\pi$
$401$	17.3821	+	7.73903i	0.868023	+	0.386469i	0.0761074	+	0.997100i	$0.475751\pi$
$402$		0			0
$403$	1.06635	+	0.226659i	0.0531185	+	0.0112907i
$404$	0.253650	−	0.780656i	0.0126196	−	0.0388391i
$405$		0			0
$406$	−63.3050			−3.14177
$407$	−5.27538	−	2.52910i	−0.261491	−	0.125363i
$408$		0			0
$409$	0.528467	−	5.02803i	0.0261310	−	0.248620i	−0.973657	−	0.228019i	$-0.926775\pi$
$409$	0.528467	−	5.02803i	0.0261310	−	0.248620i	0.999788	−	0.0206014i	$-0.00655810\pi$
$410$	13.4149	−	2.85143i	0.662515	−	0.140822i
$411$		0			0
$412$	2.99500	+	28.4955i	0.147553	+	1.40387i
$413$	25.5709	−	18.5783i	1.25826	−	0.914180i
$414$		0			0
$415$	−5.50000	+	16.9273i	−0.269984	+	0.830926i
$416$	1.67675	−	0.746537i	0.0822095	−	0.0366020i
$417$		0			0
$418$	13.4482	+	10.3617i	0.657772	+	0.506806i
$419$	−17.6391	−	30.5518i	−0.861727	−	1.49255i	−0.870261	−	0.492591i	$-0.836050\pi$
$419$	−17.6391	−	30.5518i	−0.861727	−	1.49255i	0.00853378	−	0.999964i	$-0.497284\pi$
$420$		0			0
$421$	−19.5485	−	21.7108i	−0.952736	−	1.05812i	−0.998249	−	0.0591566i	$-0.981159\pi$
$421$	−19.5485	−	21.7108i	−0.952736	−	1.05812i	0.0455129	−	0.998964i	$-0.485508\pi$
$422$	11.9761	+	36.8585i	0.582985	+	1.79424i
$423$		0			0
$424$	1.97214	−	1.43284i	0.0957754	−	0.0695849i
$425$	2.29154	+	0.487082i	0.111156	+	0.0236269i
$426$		0			0
$427$	−5.01514	+	47.7159i	−0.242700	+	2.30913i
$428$	−14.3188	−	24.8009i	−0.692125	−	1.19879i
$429$		0			0
$430$	6.25329	−	10.8310i	0.301560	−	0.522318i
$431$	−28.7943	−	20.9203i	−1.38697	−	1.00770i	−0.996190	−	0.0872135i	$-0.972204\pi$
$431$	−28.7943	−	20.9203i	−1.38697	−	1.00770i	−0.390785	−	0.920482i	$-0.627796\pi$
$432$		0			0
$433$	−0.819660	−	2.52265i	−0.0393904	−	0.121231i	0.929428	−	0.369004i	$-0.120301\pi$
$433$	−0.819660	−	2.52265i	−0.0393904	−	0.121231i	−0.968818	+	0.247773i	$0.920301\pi$
$434$	4.39423	+	41.8083i	0.210930	+	2.00686i
$435$		0			0
$436$	−24.0141	+	26.6704i	−1.15007	+	1.27728i
$437$	−9.28329	+	1.97323i	−0.444080	+	0.0943922i
$438$		0			0
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	−0.396728	−	0.917936i	$-0.629854\pi$
$439$	12.5000	−	21.6506i	0.596592	−	1.03333i	0.993320	−	0.115392i	$-0.0368124\pi$
$440$	−0.723944	−	9.43826i	−0.0345127	−	0.449951i
$441$		0			0
$442$	2.51722	+	1.82887i	0.119732	+	0.0869904i
$443$	−14.6387	−	16.2579i	−0.695504	−	0.772436i	0.287149	−	0.957886i	$-0.407292\pi$
$443$	−14.6387	−	16.2579i	−0.695504	−	0.772436i	−0.982654	+	0.185450i	$0.940626\pi$
$444$		0			0
$445$	−17.4906	−	7.78734i	−0.829136	−	0.369155i
$446$	−6.24356	−	2.77981i	−0.295641	−	0.131628i
$447$		0			0
$448$	33.8558	+	37.6007i	1.59954	+	1.77647i
$449$	23.8323	+	17.3152i	1.12472	+	0.817155i	0.984918	−	0.173024i	$-0.0553539\pi$
$449$	23.8323	+	17.3152i	1.12472	+	0.817155i	0.139800	+	0.990180i	$0.455354\pi$
$450$		0			0
$451$	5.16312	−	8.38800i	0.243122	−	0.394975i
$452$	23.4219	−	40.5680i	1.10167	−	1.90816i
$453$		0			0
$454$	−22.9929	+	4.88729i	−1.07911	+	0.229372i
$455$	−1.43794	+	1.59699i	−0.0674115	+	0.0748680i
$456$		0			0
$457$	−3.66792	−	34.8979i	−0.171578	−	1.63246i	−0.653984	−	0.756509i	$-0.726903\pi$
$457$	−3.66792	−	34.8979i	−0.171578	−	1.63246i	0.482405	−	0.875948i	$-0.339763\pi$
$458$	12.2667	+	37.7530i	0.573186	+	1.76408i
$459$		0			0
$460$	18.1353	+	13.1760i	0.845561	+	0.614336i
$461$	0.760951	−	1.31801i	0.0354410	−	0.0613857i	−0.847761	−	0.530379i	$-0.822050\pi$
$461$	0.760951	−	1.31801i	0.0354410	−	0.0613857i	0.883202	+	0.468993i	$0.155383\pi$
$462$		0			0
$463$	10.7812	+	18.6735i	0.501043	+	0.867831i	0.999999	+	0.00120439i	$0.000383369\pi$
$463$	10.7812	+	18.6735i	0.501043	+	0.867831i	−0.498957	+	0.866627i	$0.666283\pi$
$464$	−1.73148	+	16.4739i	−0.0803817	+	0.764781i
$465$		0			0
$466$	−48.3702	−	10.2814i	−2.24071	−	0.476277i
$467$	17.1318	−	12.4470i	0.792766	−	0.575978i	−0.116017	−	0.993247i	$-0.537013\pi$
$467$	17.1318	−	12.4470i	0.792766	−	0.575978i	0.908783	+	0.417269i	$0.137013\pi$
$468$		0			0
$469$	3.73607	+	11.4984i	0.172516	+	0.530948i
$470$	10.7445	+	11.9329i	0.495605	+	0.550425i
$471$		0			0
$472$	4.95492	+	8.58216i	0.228068	+	0.395026i
$473$	−2.53394	−	8.61726i	−0.116511	−	0.396222i
$474$		0			0
$475$	0.831171	−	0.370061i	0.0381367	−	0.0169796i
$476$	−21.0193	+	64.6908i	−0.963419	+	2.96510i
$477$		0			0
$478$	−19.8992	+	14.4576i	−0.910168	+	0.661275i
$479$	−3.85144	−	36.6440i	−0.175977	−	1.67431i	−0.624875	−	0.780725i	$-0.714850\pi$
$479$	−3.85144	−	36.6440i	−0.175977	−	1.67431i	0.448898	−	0.893583i	$-0.351817\pi$
$480$		0			0
$481$	−0.407308	+	0.0865761i	−0.0185717	+	0.00394753i
$482$	3.14479	−	29.9206i	0.143241	−	1.36285i
$483$		0			0
$484$	−22.3084	−	18.2122i	−1.01402	−	0.827826i
$485$	25.3542			1.15128
$486$		0			0
$487$	5.83688	−	17.9641i	0.264494	−	0.814030i	−0.727315	−	0.686304i	$-0.759232\pi$
$487$	5.83688	−	17.9641i	0.264494	−	0.814030i	0.991809	−	0.127726i	$-0.0407679\pi$
$488$	−14.7140	−	3.12756i	−0.666072	−	0.141578i
$489$		0			0
$490$	−46.1715	−	20.5569i	−2.08582	−	0.928665i
$491$	12.9909	−	14.4279i	0.586273	−	0.651122i	−0.374901	−	0.927065i	$-0.622323\pi$
$491$	12.9909	−	14.4279i	0.586273	−	0.651122i	0.961174	+	0.275943i	$0.0889899\pi$
$492$		0			0
$493$	−38.9650	+	17.3483i	−1.75489	+	0.781329i
$494$	1.20837			0.0543673
$495$		0			0
$496$	11.0000			0.493915
$497$	41.5807	−	18.5129i	1.86515	−	0.830418i
$498$		0			0
$499$	21.9091	−	24.3325i	0.980786	−	1.08927i	−0.0152105	−	0.999884i	$-0.504842\pi$
$499$	21.9091	−	24.3325i	0.980786	−	1.08927i	0.995997	−	0.0893892i	$-0.0284915\pi$
$500$	−27.6615	−	12.3157i	−1.23706	−	0.550774i
$501$		0			0
$502$	47.7112	+	10.1413i	2.12945	+	0.452630i
$503$	−1.83543	+	5.64888i	−0.0818379	+	0.251871i	−0.983601	−	0.180360i	$-0.942274\pi$
$503$	−1.83543	+	5.64888i	−0.0818379	+	0.251871i	0.901763	+	0.432231i	$0.142274\pi$
$504$		0			0
$505$	0.673762			0.0299820
$506$	27.9327	−	5.11964i	1.24176	−	0.227596i
$507$		0			0
$508$	0.756375	−	7.19643i	0.0335587	−	0.319290i
$509$	16.0131	−	3.40369i	0.709769	−	0.150866i	0.161139	−	0.986932i	$-0.448483\pi$
$509$	16.0131	−	3.40369i	0.709769	−	0.150866i	0.548629	+	0.836066i	$0.315150\pi$
$510$		0			0
$511$	1.09464	+	10.4148i	0.0484239	+	0.460722i
$512$	20.1016	−	14.6047i	0.888374	−	0.645441i
$513$		0			0
$514$	−8.22542	+	25.3153i	−0.362808	+	1.11661i
$515$	−21.4855	+	9.56596i	−0.946765	+	0.421527i
$516$		0			0
$517$	11.5276	+	0.324779i	0.506985	+	0.0142838i
$518$	−8.02866	−	13.9061i	−0.352759	−	0.610997i
$519$		0			0
$520$	−0.450835	−	0.500703i	−0.0197704	−	0.0219573i
$521$	8.28232	+	25.4903i	0.362855	+	1.11675i	0.951313	+	0.308225i	$0.0997350\pi$
$521$	8.28232	+	25.4903i	0.362855	+	1.11675i	−0.588459	+	0.808527i	$0.700265\pi$
$522$		0			0
$523$	30.2984	−	22.0131i	1.32486	−	0.962564i	0.324997	−	0.945715i	$-0.394637\pi$
$523$	30.2984	−	22.0131i	1.32486	−	0.962564i	0.999858	−	0.0168489i	$-0.00536341\pi$
$524$	6.30600	+	1.34038i	0.275479	+	0.0585549i
$525$		0			0
$526$	1.44815	−	13.7782i	0.0631423	−	0.600758i
$527$	14.1620	+	24.5293i	0.616907	+	1.06851i
$528$		0			0
$529$	3.56231	−	6.17009i	0.154883	−	0.268265i
$530$	6.85730	+	4.98212i	0.297862	+	0.216409i
$531$		0			0
$532$	8.16312	+	25.1235i	0.353916	+	1.08924i
$533$	−0.0732820	−	0.697232i	−0.00317420	−	0.0302005i
$534$		0			0
$535$	15.7290	−	17.4688i	0.680023	−	0.755242i
$536$	−3.70779	+	0.788114i	−0.160152	+	0.0340414i
$537$		0			0
$538$	−21.7426	+	37.6594i	−0.937392	+	1.62361i
$539$	−33.5625	+	13.8240i	−1.44564	+	0.595442i
$540$		0			0
$541$	−31.2533	−	22.7068i	−1.34368	−	0.976243i	−0.999300	−	0.0374146i	$-0.988088\pi$
$541$	−31.2533	−	22.7068i	−1.34368	−	0.976243i	−0.344384	−	0.938829i	$-0.611912\pi$
$542$	1.38841	+	1.54199i	0.0596373	+	0.0662340i
$543$		0			0
$544$	43.5642	+	19.3960i	1.86780	+	0.831597i
$545$	−26.9116	−	11.9818i	−1.15277	−	0.513244i
$546$		0			0
$547$	13.4057	+	14.8885i	0.573185	+	0.636586i	0.958123	−	0.286356i	$-0.0924441\pi$
$547$	13.4057	+	14.8885i	0.573185	+	0.636586i	−0.384939	+	0.922942i	$0.625777\pi$
$548$	0.664066	+	0.482472i	0.0283675	+	0.0206102i
$549$		0			0
$550$	−2.51722	+	1.03681i	−0.107335	+	0.0442099i
$551$	−8.28232	+	14.3454i	−0.352838	+	0.611134i
$552$		0			0
$553$	−39.2478	+	8.34238i	−1.66899	+	0.354754i
$554$	−27.8700	+	30.9528i	−1.18408	+	1.31506i
$555$		0			0
$556$	3.11478	+	29.6351i	0.132096	+	1.25681i
$557$	−1.67867	−	5.16641i	−0.0711274	−	0.218908i	0.909173	−	0.416418i	$-0.136715\pi$
$557$	−1.67867	−	5.16641i	−0.0711274	−	0.218908i	−0.980301	+	0.197510i	$0.936715\pi$
$558$		0			0
$559$	−0.517221	−	0.375783i	−0.0218761	−	0.0158939i
$560$	−10.8417	+	18.7784i	−0.458145	+	0.793531i
$561$		0			0
$562$	17.7984	+	30.8277i	0.750779	+	1.30039i
$563$	1.63316	−	15.5385i	0.0688294	−	0.654868i	−0.904660	−	0.426135i	$-0.859875\pi$
$563$	1.63316	−	15.5385i	0.0688294	−	0.654868i	0.973489	−	0.228733i	$-0.0734583\pi$
$564$		0			0
$565$	37.6106	+	7.99438i	1.58229	+	0.336326i
$566$	−19.0271	+	13.8240i	−0.799770	+	0.581067i
$567$		0			0
$568$	4.40983	+	13.5721i	0.185032	+	0.569471i
$569$	−21.2296	−	23.5778i	−0.889990	−	0.988435i	0.109994	−	0.993932i	$-0.464917\pi$
$569$	−21.2296	−	23.5778i	−0.889990	−	0.988435i	−0.999985	+	0.00549764i	$0.998250\pi$
$570$		0			0
$571$	−5.98936	−	10.3739i	−0.250647	−	0.434133i	0.713057	−	0.701106i	$-0.247310\pi$
$571$	−5.98936	−	10.3739i	−0.250647	−	0.434133i	−0.963704	+	0.266973i	$0.913977\pi$
$572$	−2.04897	−	0.0577277i	−0.0856719	−	0.00241372i
$573$		0			0
$574$	24.6972	−	10.9959i	1.03084	−	0.458960i
$575$	0.470294	−	1.44742i	0.0196126	−	0.0603614i
$576$		0			0
$577$	1.09017	−	0.792055i	0.0453844	−	0.0329737i	−0.564862	−	0.825186i	$-0.691071\pi$
$577$	1.09017	−	0.792055i	0.0453844	−	0.0329737i	0.610246	+	0.792212i	$0.291071\pi$
$578$	4.63138	+	44.0646i	0.192640	+	1.83285i
$579$		0			0
$580$	38.2696	−	8.13446i	1.58906	−	0.337765i
$581$	−3.66732	+	34.8923i	−0.152146	+	1.44757i
$582$		0			0
$583$	5.98770	−	1.09745i	0.247985	−	0.0454519i
$584$	−3.28332			−0.135865
$585$		0			0
$586$	−3.31966	+	10.2169i	−0.137134	+	0.422055i
$587$	35.9236	+	7.63579i	1.48272	+	0.315163i	0.876992	−	0.480506i	$-0.159547\pi$
$587$	35.9236	+	7.63579i	1.48272	+	0.315163i	0.605732	+	0.795668i	$0.292880\pi$
$588$		0			0
$589$	10.0490	+	4.47410i	0.414062	+	0.184352i
$590$	−23.0565	+	25.6068i	−0.949221	+	1.05422i
$591$		0			0
$592$	−3.83838	+	1.70896i	−0.157756	+	0.0702376i
$593$	−27.3094			−1.12146			−0.560732	−	0.827997i	$-0.689480\pi$
$593$	−27.3094			−1.12146			−0.560732	+	0.827997i	$0.689480\pi$
$594$		0			0
$595$	−55.8328			−2.28892
$596$	11.0292	−	4.91051i	0.451773	−	0.201142i
$597$		0			0
$598$	1.35250	−	1.50211i	0.0553080	−	0.0614258i
$599$	−15.7054	−	6.99249i	−0.641705	−	0.285705i	0.0599728	−	0.998200i	$-0.480899\pi$
$599$	−15.7054	−	6.99249i	−0.641705	−	0.285705i	−0.701678	+	0.712495i	$0.747565\pi$
$600$		0			0
$601$	9.15613	+	1.94619i	0.373486	+	0.0793869i	0.390831	−	0.920463i	$-0.372188\pi$
$601$	9.15613	+	1.94619i	0.373486	+	0.0793869i	−0.0173444	+	0.999850i	$0.505521\pi$
$602$	7.61825	−	23.4466i	0.310497	−	0.955611i
$603$		0			0
$604$	−34.6525			−1.40999
$605$	8.55892	−	22.0347i	0.347970	−	0.895837i
$606$		0			0
$607$	2.99140	−	28.4613i	0.121417	−	1.15521i	−0.748889	−	0.662696i	$-0.769412\pi$
$607$	2.99140	−	28.4613i	0.121417	−	1.15521i	0.870306	−	0.492511i	$-0.163921\pi$
$608$	18.1151	−	3.85049i	0.734665	−	0.156158i
$609$		0			0
$610$	−5.46736	−	52.0184i	−0.221367	−	2.10616i
$611$	0.664066	−	0.482472i	0.0268652	−	0.0195187i
$612$		0			0
$613$	7.74265	−	23.8294i	0.312723	−	0.962461i	−0.663959	−	0.747769i	$-0.731125\pi$
$613$	7.74265	−	23.8294i	0.312723	−	0.962461i	0.976682	−	0.214692i	$-0.0688748\pi$
$614$	−33.9050	+	15.0955i	−1.36829	+	0.609204i
$615$		0			0
$616$	−5.26403	−	17.9016i	−0.212094	−	0.721276i
$617$	8.43908	+	14.6169i	0.339745	+	0.588455i	0.984385	−	0.176031i	$-0.0563260\pi$
$617$	8.43908	+	14.6169i	0.339745	+	0.588455i	−0.644640	+	0.764486i	$0.722993\pi$
$618$		0			0
$619$	4.60934	+	5.11919i	0.185265	+	0.205757i	0.828622	−	0.559809i	$-0.189125\pi$
$619$	4.60934	+	5.11919i	0.185265	+	0.205757i	−0.643357	+	0.765566i	$0.722459\pi$
$620$	−8.02866	−	24.7097i	−0.322439	−	0.992365i
$621$		0			0
$622$	49.9959	−	36.3242i	2.00465	−	1.45647i
$623$	−36.9160	−	7.84674i	−1.47901	−	0.314373i
$624$		0			0
$625$	2.39833	−	22.8186i	0.0959332	−	0.912743i
$626$	34.0100	+	58.9070i	1.35931	+	2.35440i
$627$		0			0
$628$	27.0344	−	46.8250i	1.07879	−	1.86852i
$629$	−8.75261	−	6.35914i	−0.348989	−	0.253556i
$630$		0			0
$631$	−5.37132	−	16.5312i	−0.213829	−	0.658098i	−0.999235	−	0.0391166i	$-0.987546\pi$
$631$	−5.37132	−	16.5312i	−0.213829	−	0.658098i	0.785406	−	0.618981i	$-0.212454\pi$
$632$	−1.31499	−	12.5113i	−0.0523076	−	0.497674i
$633$		0			0
$634$	−0.450835	+	0.500703i	−0.0179049	+	0.0198854i
$635$	5.80979	−	1.23491i	0.230554	−	0.0490059i
$636$		0			0
$637$	−1.29180	+	2.23746i	−0.0511828	+	0.0886513i
$638$	25.9813	−	42.2092i	1.02861	−	1.67108i
$639$		0			0
$640$	−17.5902	−	12.7800i	−0.695313	−	0.505174i
$641$	14.2992	+	15.8809i	0.564785	+	0.627258i	0.956115	−	0.292993i	$-0.0946513\pi$
$641$	14.2992	+	15.8809i	0.564785	+	0.627258i	−0.391329	+	0.920251i	$0.627985\pi$
$642$		0			0
$643$	−37.6007	−	16.7409i	−1.48283	−	0.660196i	−0.503779	−	0.863833i	$-0.668057\pi$
$643$	−37.6007	−	16.7409i	−1.48283	−	0.660196i	−0.979047	+	0.203636i	$0.934724\pi$
$644$	40.3674	+	17.9727i	1.59070	+	0.708224i
$645$		0			0
$646$	21.0074	+	23.3311i	0.826527	+	0.917951i
$647$	−9.45368	−	6.86850i	−0.371663	−	0.270029i	0.386237	−	0.922399i	$-0.373775\pi$
$647$	−9.45368	−	6.86850i	−0.371663	−	0.270029i	−0.757900	+	0.652371i	$0.773775\pi$
$648$		0			0
$649$	1.89261	+	24.6745i	0.0742914	+	0.968558i
$650$	−0.0968859	+	0.167811i	−0.00380018	+	0.00658210i
$651$		0			0
$652$	−3.53897	+	0.752232i	−0.138597	+	0.0294597i
$653$	22.8773	−	25.4078i	0.895258	−	0.994285i	−0.104742	−	0.994499i	$-0.533402\pi$
$653$	22.8773	−	25.4078i	0.895258	−	0.994285i	1.00000		0.000214284i	$6.82086e-5\pi$
$654$		0			0
$655$	0.553143	+	5.26281i	0.0216131	+	0.205635i
$656$	−2.18597	−	6.72772i	−0.0853477	−	0.262673i
$657$		0			0
$658$	25.6074	+	18.6049i	0.998280	+	0.725293i
$659$	−16.8782	+	29.2338i	−0.657480	+	1.13879i	0.323786	+	0.946130i	$0.395044\pi$
$659$	−16.8782	+	29.2338i	−0.657480	+	1.13879i	−0.981266	+	0.192658i	$0.938289\pi$
$660$		0			0
$661$	−1.21885	−	2.11111i	−0.0474077	−	0.0821125i	0.841348	−	0.540494i	$-0.181763\pi$
$661$	−1.21885	−	2.11111i	−0.0474077	−	0.0821125i	−0.888755	+	0.458382i	$0.848429\pi$
$662$	1.63794	−	15.5839i	0.0636603	−	0.605687i
$663$		0			0
$664$	−10.7596	−	2.28703i	−0.417554	−	0.0887539i
$665$	−17.5422	+	12.7452i	−0.680258	+	0.494237i
$666$		0			0
$667$	8.56231	+	26.3521i	0.331534	+	1.02036i
$668$	18.8228	+	20.9049i	0.728277	+	0.808833i
$669$		0			0
$670$	−6.59017	−	11.4145i	−0.254600	−	0.440981i
$671$	−29.7567	−	22.9272i	−1.14875	−	0.885095i
$672$		0			0
$673$	16.6595	−	7.41728i	0.642176	−	0.285915i	−0.0596980	−	0.998216i	$-0.519014\pi$
$673$	16.6595	−	7.41728i	0.642176	−	0.285915i	0.701874	+	0.712301i	$0.252347\pi$
$674$	17.6990	−	54.4719i	0.681740	−	2.09818i
$675$		0			0
$676$	27.4164	−	19.9192i	1.05448	−	0.766123i
$677$	−0.898510	−	8.54876i	−0.0345326	−	0.328555i	−0.998126	−	0.0611851i	$-0.980512\pi$
$677$	−0.898510	−	8.54876i	−0.0345326	−	0.328555i	0.963594	−	0.267370i	$-0.0861547\pi$
$678$		0			0
$679$	48.8866	−	10.3912i	1.87609	−	0.398776i
$680$	1.82979	−	17.4093i	0.0701694	−	0.667617i
$681$		0			0
$682$	−29.6796	−	14.2289i	−1.13649	−	0.544852i
$683$	0.940588			0.0359906			0.0179953	−	0.999838i	$-0.494272\pi$
$683$	0.940588			0.0359906			0.0179953	+	0.999838i	$0.494272\pi$
$684$		0			0
$685$	−0.208204	+	0.640786i	−0.00795506	+	0.0244832i
$686$	−35.1207	−	7.46513i	−1.34091	−	0.285020i
$687$		0			0
$688$	−5.89314	−	2.62380i	−0.224674	−	0.100031i
$689$	0.289925	−	0.321995i	0.0110453	−	0.0122670i
$690$		0			0
$691$	29.5630	−	13.1623i	1.12463	−	0.500717i	0.241759	−	0.970336i	$-0.422276\pi$
$691$	29.5630	−	13.1623i	1.12463	−	0.500717i	0.882869	+	0.469620i	$0.155609\pi$
$692$	35.0845			1.33371
$693$		0			0
$694$	54.0689			2.05243
$695$	−22.3448	+	9.94854i	−0.847586	+	0.377369i
$696$		0			0
$697$	12.1881	−	13.5362i	0.461656	−	0.512721i
$698$	−18.0226	−	8.02418i	−0.682166	−	0.303720i
$699$		0			0
$700$	−4.14350	−	0.880728i	−0.156610	−	0.0332884i
$701$	−7.23071	+	22.2538i	−0.273100	+	0.840515i	0.716616	+	0.697468i	$0.245690\pi$
$701$	−7.23071	+	22.2538i	−0.273100	+	0.840515i	−0.989716	+	0.143047i	$0.954310\pi$
$702$		0			0
$703$	−4.20163			−0.158467
$704$	−38.9656	+	7.14181i	−1.46857	+	0.269167i
$705$		0			0
$706$	7.58260	−	72.1436i	0.285375	−	2.71516i
$707$	1.29911	−	0.276134i	0.0488580	−	0.0103851i
$708$		0			0
$709$	1.58900	+	15.1184i	0.0596762	+	0.567782i	0.982980	+	0.183712i	$0.0588112\pi$
$709$	1.58900	+	15.1184i	0.0596762	+	0.567782i	−0.923304	+	0.384070i	$0.874522\pi$
$710$	−40.1433	+	29.1658i	−1.50655	+	1.09457i
$711$		0			0
$712$	3.65654	−	11.2537i	0.137035	−	0.421749i
$713$	16.8093	−	7.48398i	0.629513	−	0.280277i
$714$		0			0
$715$	−0.474658	−	1.61419i	−0.0177512	−	0.0603671i
$716$	2.55938	+	4.43297i	0.0956484	+	0.165668i
$717$		0			0
$718$	2.91786	+	3.24062i	0.108894	+	0.120939i
$719$	4.00726	+	12.3331i	0.149446	+	0.459947i	0.997556	−	0.0698732i	$-0.0222595\pi$
$719$	4.00726	+	12.3331i	0.149446	+	0.459947i	−0.848110	+	0.529820i	$0.822259\pi$
$720$		0			0
$721$	−37.5066	+	27.2501i	−1.39682	+	1.01485i
$722$	−28.0118	−	5.95409i	−1.04249	−	0.221588i
$723$		0			0
$724$	−3.34851	+	31.8590i	−0.124446	+	1.18403i
$725$	−1.32813	−	2.30039i	−0.0493255	−	0.0854344i
$726$		0			0
$727$	−9.78115	+	16.9415i	−0.362763	+	0.628324i	−0.988414	−	0.151779i	$-0.951500\pi$
$727$	−9.78115	+	16.9415i	−0.362763	+	0.628324i	0.625652	+	0.780103i	$0.284833\pi$
$728$	−1.07448	−	0.780656i	−0.0398229	−	0.0289330i
$729$		0			0
$730$	−3.52786	−	10.8576i	−0.130572	−	0.401860i
$731$	−1.73626	−	16.5194i	−0.0642178	−	0.610991i
$732$		0			0
$733$	−9.80442	+	10.8889i	−0.362135	+	0.402191i	−0.896487	−	0.443071i	$-0.853889\pi$
$733$	−9.80442	+	10.8889i	−0.362135	+	0.402191i	0.534352	+	0.845262i	$0.320556\pi$
$734$	48.4184	−	10.2917i	1.78716	−	0.379872i
$735$		0			0
$736$	15.4894	−	26.8284i	0.570945	−	0.988906i
$737$	−9.20003	−	2.22807i	−0.338888	−	0.0820721i
$738$		0			0
$739$	−14.7533	−	10.7189i	−0.542709	−	0.394301i	0.282381	−	0.959302i	$-0.408876\pi$
$739$	−14.7533	−	10.7189i	−0.542709	−	0.394301i	−0.825090	+	0.565001i	$0.808876\pi$
$740$	6.64044	+	7.37495i	0.244107	+	0.271109i
$741$		0			0
$742$	15.2637	+	6.79584i	0.560348	+	0.249483i
$743$	−16.5647	−	7.37506i	−0.607698	−	0.270565i	0.0797305	−	0.996816i	$-0.474594\pi$
$743$	−16.5647	−	7.37506i	−0.607698	−	0.270565i	−0.687429	+	0.726252i	$0.741261\pi$
$744$		0			0
$745$	6.63097	+	7.36444i	0.242940	+	0.269812i
$746$	−25.0636	−	18.2098i	−0.917643	−	0.666707i
$747$		0			0
$748$	−34.5066	−	40.5649i	−1.26169	−	1.48320i
$749$	23.1683	−	40.1286i	0.846550	−	1.46627i
$750$		0			0
$751$	1.47366	−	0.313235i	0.0537745	−	0.0114301i	−0.180946	−	0.983493i	$-0.557916\pi$
$751$	1.47366	−	0.313235i	0.0537745	−	0.0114301i	0.234720	+	0.972063i	$0.424583\pi$
$752$	5.54195	−	6.15496i	0.202094	−	0.224448i
$753$		0			0
$754$	−0.368762	−	3.50854i	−0.0134295	−	0.127773i
$755$	−8.78962	−	27.0517i	−0.319887	−	0.984511i
$756$		0			0
$757$	33.0795	+	24.0337i	1.20230	+	0.873519i	0.994509	−	0.104655i	$-0.0333738\pi$
$757$	33.0795	+	24.0337i	1.20230	+	0.873519i	0.207787	+	0.978174i	$0.433374\pi$
$758$	6.70053	−	11.6057i	0.243374	−	0.421537i
$759$		0			0
$760$	−3.39919	−	5.88756i	−0.123301	−	0.213564i
$761$	3.49572	−	33.2596i	0.126720	−	1.20566i	−0.727633	−	0.685966i	$-0.759380\pi$
$761$	3.49572	−	33.2596i	0.126720	−	1.20566i	0.854353	−	0.519693i	$-0.173954\pi$
$762$		0			0
$763$	−56.7999	−	12.0732i	−2.05630	−	0.437079i
$764$	−21.0193	+	15.2714i	−0.760452	+	0.552501i
$765$		0			0
$766$	−22.6246	−	69.6314i	−0.817460	−	2.51588i
$767$	1.17862	+	1.30899i	0.0425574	+	0.0472648i
$768$		0			0
$769$	11.1353	+	19.2868i	0.401548	+	0.695501i	0.993913	−	0.110169i	$-0.0351391\pi$
$769$	11.1353	+	19.2868i	0.401548	+	0.695501i	−0.592365	+	0.805669i	$0.701806\pi$
$770$	53.5429	−	36.6426i	1.92955	−	1.32051i
$771$		0			0
$772$	17.6554	−	7.86069i	0.635432	−	0.282912i
$773$	10.4084	−	32.0338i	0.374364	−	1.15217i	−0.569542	−	0.821962i	$-0.692879\pi$
$773$	10.4084	−	32.0338i	0.374364	−	1.15217i	0.943907	−	0.330213i	$-0.107121\pi$
$774$		0			0
$775$	−1.42705	+	1.03681i	−0.0512612	+	0.0372434i
$776$	1.63794	+	15.5839i	0.0587986	+	0.559431i
$777$		0			0
$778$	−46.8966	+	9.96817i	−1.68132	+	0.357376i
$779$	0.739428	−	7.03519i	0.0264928	−	0.252062i
$780$		0			0
$781$	−4.72167	+	35.3223i	−0.168955	+	1.26393i
$782$	52.5157			1.87796
$783$		0			0
$784$	−8.05573	+	24.7930i	−0.287705	+	0.885464i
$785$	43.4115	+	9.22741i	1.54942	+	0.329340i
$786$		0			0
$787$	25.3756	+	11.2980i	0.904544	+	0.402729i	0.805665	−	0.592371i	$-0.201808\pi$
$787$	25.3756	+	11.2980i	0.904544	+	0.402729i	0.0988781	+	0.995100i	$0.468475\pi$
$788$	4.31381	−	4.79097i	0.153673	−	0.170671i
$789$		0			0
$790$	39.9609	−	17.7917i	1.42174	−	0.633002i
$791$	75.7950			2.69496
$792$		0			0
$793$	−2.67376			−0.0949481
$794$	−47.9336	+	21.3414i	−1.70110	+	0.757379i
$795$		0			0
$796$	0.729466	−	0.810154i	0.0258552	−	0.0287152i
$797$	−3.92635	−	1.74812i	−0.139078	−	0.0619217i	0.336017	−	0.941856i	$-0.390920\pi$
$797$	−3.92635	−	1.74812i	−0.139078	−	0.0619217i	−0.475096	+	0.879934i	$0.657587\pi$
$798$		0			0
$799$	20.8602	+	4.43397i	0.737981	+	0.156863i
$800$	−0.917716	+	2.82444i	−0.0324462	+	0.0998590i
$801$		0			0
$802$	−40.8885			−1.44382
$803$	−7.39340	−	3.54452i	−0.260908	−	0.125083i
$804$		0			0
$805$	−3.79130	+	36.0718i	−0.133626	+	1.27136i
$806$	−2.29154	+	0.487082i	−0.0807160	+	0.0171567i
$807$		0			0
$808$	0.0435265	+	0.414127i	0.00153126	+	0.0145689i
$809$	−5.72294	+	4.15796i	−0.201208	+	0.146186i	−0.683827	−	0.729644i	$-0.739686\pi$
$809$	−5.72294	+	4.15796i	−0.201208	+	0.146186i	0.482619	+	0.875830i	$0.339686\pi$
$810$		0			0
$811$	−13.6631	+	42.0508i	−0.479777	+	1.47660i	0.359628	+	0.933096i	$0.382904\pi$
$811$	−13.6631	+	42.0508i	−0.479777	+	1.47660i	−0.839405	+	0.543506i	$0.817096\pi$
$812$	70.4554	−	31.3688i	2.47250	−	1.10083i
$813$		0			0
$814$	12.5671	+	0.354065i	0.440476	+	0.0124100i
$815$	−1.48490	−	2.57191i	−0.0520136	−	0.0900902i
$816$		0			0
$817$	−4.31646	−	4.79392i	−0.151014	−	0.167718i
$818$	3.35733	+	10.3328i	0.117386	+	0.361278i
$819$		0			0
$820$	−13.5172	+	9.82084i	−0.472042	+	0.342958i
$821$	38.9008	+	8.26863i	1.35765	+	0.288577i	0.828518	−	0.559963i	$-0.189185\pi$
$821$	38.9008	+	8.26863i	1.35765	+	0.288577i	0.529131	+	0.848540i	$0.322518\pi$
$822$		0			0
$823$	−1.99769	+	19.0068i	−0.0696351	+	0.662534i	0.902912	+	0.429826i	$0.141425\pi$
$823$	−1.99769	+	19.0068i	−0.0696351	+	0.662534i	−0.972547	+	0.232708i	$0.925241\pi$
$824$	−7.26771	−	12.5880i	−0.253183	−	0.438525i
$825$		0			0
$826$	−33.9615	+	58.8230i	−1.18167	+	2.04672i
$827$	9.41667	+	6.84161i	0.327450	+	0.237906i	0.739348	−	0.673324i	$-0.235134\pi$
$827$	9.41667	+	6.84161i	0.327450	+	0.237906i	−0.411898	+	0.911230i	$0.635134\pi$
$828$		0			0
$829$	6.19098	+	19.0539i	0.215022	+	0.661769i	0.999152	+	0.0411726i	$0.0131094\pi$
$829$	6.19098	+	19.0539i	0.215022	+	0.661769i	−0.784130	+	0.620596i	$0.786891\pi$
$830$	−3.99801	−	38.0385i	−0.138773	−	1.32034i
$831$		0			0
$832$	−1.88672	+	2.09542i	−0.0654103	+	0.0726455i
$833$	−65.6583	+	13.9561i	−2.27492	+	0.483550i
$834$		0			0
$835$	−11.5451	+	19.9967i	−0.399534	+	0.692013i
$836$	−20.1016	−	4.86822i	−0.695228	−	0.168371i
$837$		0			0
$838$	61.3328	+	44.5609i	2.11871	+	1.53933i
$839$	9.35604	+	10.3909i	0.323006	+	0.358735i	0.882677	−	0.469980i	$-0.155739\pi$
$839$	9.35604	+	10.3909i	0.323006	+	0.358735i	−0.559671	+	0.828715i	$0.689072\pi$
$840$		0			0
$841$	17.6869	+	7.87470i	0.609892	+	0.271541i
$842$	57.3537	+	25.5355i	1.97654	+	0.880012i
$843$		0			0
$844$	−31.5929	−	35.0874i	−1.08747	−	1.20776i
$845$	22.5042	+	16.3503i	0.774168	+	0.562466i
$846$		0			0
$847$	7.47214	−	45.9937i	0.256746	−	1.58036i
$848$	2.18597	−	3.78621i	0.0750665	−	0.130019i
$849$		0			0
$850$	−4.92443	+	1.04672i	−0.168906	+	0.0359022i
$851$	−4.70278	+	5.22297i	−0.161209	+	0.179041i
$852$		0			0
$853$	0.123379	+	1.17387i	0.00422442	+	0.0401927i	0.996431	−	0.0844108i	$-0.0269008\pi$
$853$	0.123379	+	1.17387i	0.00422442	+	0.0401927i	−0.992207	+	0.124603i	$0.960234\pi$
$854$	−31.8610	−	98.0581i	−1.09026	−	3.35548i
$855$		0			0
$856$	11.7533	+	8.53926i	0.401719	+	0.291866i
$857$	6.91718	−	11.9809i	0.236286	−	0.409260i	−0.723359	−	0.690472i	$-0.757403\pi$
$857$	6.91718	−	11.9809i	0.236286	−	0.409260i	0.959646	+	0.281212i	$0.0907364\pi$
$858$		0			0
$859$	−21.2082	−	36.7337i	−0.723615	−	1.25334i	−0.959542	−	0.281566i	$-0.909146\pi$
$859$	−21.2082	−	36.7337i	−0.723615	−	1.25334i	0.235927	−	0.971771i	$-0.424187\pi$
$860$	−1.59265	+	15.1530i	−0.0543088	+	0.516714i
$861$		0			0
$862$	74.8139	+	15.9022i	2.54817	+	0.541631i
$863$	−27.8167	+	20.2100i	−0.946893	+	0.687958i	−0.950070	−	0.312037i	$-0.898989\pi$
$863$	−27.8167	+	20.2100i	−0.946893	+	0.687958i	0.00317717	+	0.999995i	$0.498989\pi$
$864$		0			0
$865$	8.89919	+	27.3889i	0.302581	+	0.931250i
$866$	3.81409	+	4.23598i	0.129608	+	0.143944i
$867$		0			0
$868$	−25.6074	−	44.3533i	−0.869171	−	1.50545i
$869$	10.5455	−	29.5927i	0.357732	−	1.00386i
$870$		0			0
$871$	−0.615512	+	0.274044i	−0.0208558	+	0.00928562i
$872$	5.62605	−	17.3152i	0.190522	−	0.586367i
$873$		0			0
$874$	16.5000	−	11.9880i	0.558121	−	0.405499i
$875$	−5.12114	−	48.7244i	−0.173126	−	1.64719i
$876$		0			0
$877$	−11.2214	+	2.38519i	−0.378921	+	0.0805422i	−0.393435	−	0.919352i	$-0.628713\pi$
$877$	−11.2214	+	2.38519i	−0.378921	+	0.0805422i	0.0145137	+	0.999895i	$0.495380\pi$
$878$	−5.61569	+	53.4297i	−0.189520	+	1.80317i
$879$		0			0
$880$	−8.07106	−	14.9357i	−0.272075	−	0.503483i
$881$	−34.3376			−1.15686			−0.578432	−	0.815730i	$-0.696335\pi$
$881$	−34.3376			−1.15686			−0.578432	+	0.815730i	$0.696335\pi$
$882$		0			0
$883$	−4.36068	+	13.4208i	−0.146749	+	0.451646i	−0.997232	−	0.0743567i	$-0.976310\pi$
$883$	−4.36068	+	13.4208i	−0.146749	+	0.451646i	0.850483	+	0.526002i	$0.176310\pi$
$884$	−3.70779	−	0.788114i	−0.124706	−	0.0265072i
$885$		0			0
$886$	42.9487	+	19.1220i	1.44289	+	0.642415i
$887$	37.8554	−	42.0427i	1.27106	−	1.41166i	0.402999	−	0.915200i	$-0.367968\pi$
$887$	37.8554	−	42.0427i	1.27106	−	1.41166i	0.868062	−	0.496456i	$-0.165366\pi$
$888$		0			0
$889$	10.6960	−	4.76216i	0.358732	−	0.159718i
$890$	41.1438			1.37914
$891$		0			0
$892$	8.32624			0.278783
$893$	7.56627	−	3.36872i	0.253196	−	0.112730i
$894$		0			0
$895$	−2.81144	+	3.12242i	−0.0939760	+	0.104371i
$896$	−39.1541	−	17.4325i	−1.30805	−	0.582379i
$897$		0			0
$898$	−61.9216	−	13.1618i	−2.06635	−	0.439216i
$899$	9.92398	−	30.5429i	0.330983	−	1.01866i
$900$		0			0
$901$	11.2574			0.375037
$902$	−2.80448	+	20.9800i	−0.0933789	+	0.698557i
$903$		0			0
$904$	−2.48401	+	23.6338i	−0.0826169	+	0.786047i
$905$	−25.7202	+	5.46700i	−0.854969	+	0.181729i
$906$		0			0
$907$	3.74915	+	35.6708i	0.124488	+	1.18443i	0.861216	+	0.508239i	$0.169703\pi$
$907$	3.74915	+	35.6708i	0.124488	+	1.18443i	−0.736728	+	0.676190i	$0.763630\pi$
$908$	23.1683	−	16.8327i	0.768866	−	0.558614i
$909$		0			0
$910$	1.42705	−	4.39201i	0.0473063	−	0.145594i
$911$	−8.71196	+	3.87882i	−0.288640	+	0.128511i	−0.545949	−	0.837818i	$-0.683831\pi$
$911$	−8.71196	+	3.87882i	−0.288640	+	0.128511i	0.257309	+	0.966329i	$0.417164\pi$
$912$		0			0
$913$	−21.7596	−	16.7655i	−0.720138	−	0.554858i
$914$	37.7037	+	65.3047i	1.24713	+	2.16009i
$915$		0			0
$916$	−32.3596	−	35.9390i	−1.06919	−	1.18746i
$917$	3.22344	+	9.92073i	0.106447	+	0.327611i
$918$		0			0
$919$	20.3713	−	14.8006i	0.671988	−	0.488228i	−0.198702	−	0.980060i	$-0.563673\pi$
$919$	20.3713	−	14.8006i	0.671988	−	0.488228i	0.870690	+	0.491832i	$0.163673\pi$
$920$	−11.1234	−	2.36434i	−0.366726	−	0.0779501i
$921$		0			0
$922$	−0.341861	+	3.25259i	−0.0112586	+	0.107118i
$923$	1.26825	+	2.19668i	0.0417450	+	0.0723045i
$924$		0			0
$925$	0.336881	−	0.583495i	0.0110766	−	0.0191852i
$926$	−37.4871	−	27.2359i	−1.23190	−	0.895029i
$927$		0			0
$928$	−16.7082	−	51.4226i	−0.548474	−	1.68803i
$929$	4.39423	+	41.8083i	0.144170	+	1.37169i	0.792288	+	0.610147i	$0.208890\pi$
$929$	4.39423	+	41.8083i	0.144170	+	1.37169i	−0.648118	+	0.761540i	$0.724444\pi$
$930$		0			0
$931$	−17.4435	+	19.3730i	−0.571687	+	0.634923i
$932$	58.9284	−	12.5256i	1.93026	−	0.410290i
$933$		0			0
$934$	−22.7533	+	39.4099i	−0.744510	+	1.28953i
$935$	22.9146	−	37.2271i	0.749388	−	1.21746i
$936$		0			0
$937$	−8.75329	−	6.35964i	−0.285957	−	0.207760i	0.435554	−	0.900162i	$-0.356552\pi$
$937$	−8.75329	−	6.35964i	−0.285957	−	0.207760i	−0.721512	+	0.692402i	$0.756552\pi$
$938$	−17.3849	−	19.3079i	−0.567637	−	0.630424i
$939$		0			0
$940$	−17.8711	−	7.95671i	−0.582890	−	0.259519i
$941$	8.38375	+	3.73269i	0.273303	+	0.121682i	0.538812	−	0.842426i	$-0.318873\pi$
$941$	8.38375	+	3.73269i	0.273303	+	0.121682i	−0.265509	+	0.964108i	$0.585540\pi$
$942$		0			0
$943$	−7.91770	−	8.79350i	−0.257836	−	0.286356i
$944$	14.3787	+	10.4467i	0.467986	+	0.340011i
$945$		0			0
$946$	12.5066	+	14.7024i	0.406624	+	0.478015i
$947$	−11.1922	+	19.3855i	−0.363699	+	0.629944i	−0.988566	−	0.150786i	$-0.951820\pi$
$947$	−11.1922	+	19.3855i	−0.363699	+	0.629944i	0.624868	+	0.780731i	$0.285153\pi$
$948$		0			0
$949$	−0.570839	+	0.121336i	−0.0185302	+	0.00393872i
$950$	−1.30828	+	1.45299i	−0.0424461	+	0.0471412i
$951$		0			0
$952$	−3.60692	−	34.3175i	−0.116901	−	1.11224i
$953$	−5.19277	−	15.9817i	−0.168210	−	0.517698i	0.831048	−	0.556200i	$-0.187741\pi$
$953$	−5.19277	−	15.9817i	−0.168210	−	0.517698i	−0.999259	+	0.0385025i	$0.987741\pi$
$954$		0			0
$955$	−17.2533	−	12.5352i	−0.558303	−	0.405631i
$956$	14.9828	−	25.9511i	0.484580	−	0.839317i
$957$		0			0
$958$	39.5902	+	68.5722i	1.27910	+	2.21547i
$959$	−0.138827	+	1.32086i	−0.00448297	+	0.0426526i
$960$		0			0
$961$	9.46237	+	2.01129i	0.305238	+	0.0648803i
$962$	0.723944	−	0.525976i	0.0233409	−	0.0169582i
$963$		0			0
$964$	11.3262	+	34.8586i	0.364794	+	1.12272i
$965$	10.6148	+	11.7889i	0.341702	+	0.379499i
$966$		0			0
$967$	8.84346	+	15.3173i	0.284386	+	0.492572i	0.972460	−	0.233069i	$-0.0748768\pi$
$967$	8.84346	+	15.3173i	0.284386	+	0.492572i	−0.688074	+	0.725641i	$0.741543\pi$
$968$	14.0965	+	3.83724i	0.453079	+	0.123334i
$969$		0			0
$970$	−49.7748	+	22.1612i	−1.59817	+	0.711552i
$971$	−0.313529	+	0.964944i	−0.0100616	+	0.0309665i	−0.955961	−	0.293493i	$-0.905182\pi$
$971$	−0.313529	+	0.964944i	−0.0100616	+	0.0309665i	0.945900	+	0.324459i	$0.105182\pi$
$972$		0			0
$973$	−39.0066	+	28.3399i	−1.25049	+	0.908537i
$974$	4.24289	+	40.3684i	0.135951	+	1.29349i
$975$		0			0
$976$	−26.3892	+	5.60919i	−0.844697	+	0.179546i
$977$	−0.350937	+	3.33894i	−0.0112275	+	0.106822i	−0.998700	−	0.0509665i	$-0.983770\pi$
$977$	−0.350937	+	3.33894i	−0.0112275	+	0.106822i	0.987473	+	0.157789i	$0.0504365\pi$
$978$		0			0
$979$	20.3828	−	21.3937i	0.651436	−	0.683745i
$980$	61.5731			1.96688
$981$		0			0
$982$	−12.8926	+	39.6794i	−0.411420	+	1.26622i
$983$	−49.6004	−	10.5429i	−1.58201	−	0.336266i	−0.668698	−	0.743534i	$-0.733148\pi$
$983$	−49.6004	−	10.5429i	−1.58201	−	0.336266i	−0.913309	+	0.407268i	$0.866481\pi$
$984$		0			0
$985$	4.83430	+	2.15237i	0.154033	+	0.0685801i
$986$	61.3315	−	68.1155i	1.95319	−	2.16924i
$987$		0			0
$988$	−1.34486	+	0.598772i	−0.0427858	+	0.0190495i
$989$	−10.7905			−0.343119
$990$		0			0
$991$	−58.2705			−1.85102			−0.925512	−	0.378719i	$-0.876365\pi$
$991$	−58.2705			−1.85102			−0.925512	+	0.378719i	$0.876365\pi$
$992$	−32.8011	+	14.6040i	−1.04144	+	0.463677i
$993$		0			0
$994$	−65.4487	+	72.6881i	−2.07591	+	2.30553i
$995$	0.817481	+	0.363966i	0.0259159	+	0.0115385i
$996$		0			0
$997$	−37.8960	−	8.05505i	−1.20018	−	0.255106i	−0.435902	−	0.899994i	$-0.643571\pi$
$997$	−37.8960	−	8.05505i	−1.20018	−	0.255106i	−0.764277	+	0.644888i	$0.776904\pi$
$998$	−21.7433	+	66.9189i	−0.688271	+	2.11828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.e.136.1		16
3.2	odd	2	inner	891.2.n.e.136.2		16
9.2	odd	6		99.2.f.c.37.1	✓	8
9.4	even	3	inner	891.2.n.e.433.2		16
9.5	odd	6	inner	891.2.n.e.433.1		16
9.7	even	3		99.2.f.c.37.2	yes	8
11.3	even	5	inner	891.2.n.e.784.2		16
33.14	odd	10	inner	891.2.n.e.784.1		16
99.14	odd	30	inner	891.2.n.e.190.2		16
99.16	even	15		1089.2.a.v.1.1		4
99.25	even	15		99.2.f.c.91.2	yes	8
99.38	odd	30		1089.2.a.v.1.4		4
99.47	odd	30		99.2.f.c.91.1	yes	8
99.58	even	15	inner	891.2.n.e.190.1		16
99.61	odd	30		1089.2.a.w.1.4		4
99.83	even	30		1089.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.f.c.37.1	✓	8	9.2	odd	6
99.2.f.c.37.2	yes	8	9.7	even	3
99.2.f.c.91.1	yes	8	99.47	odd	30
99.2.f.c.91.2	yes	8	99.25	even	15
891.2.n.e.136.1		16	1.1	even	1	trivial
891.2.n.e.136.2		16	3.2	odd	2	inner
891.2.n.e.190.1		16	99.58	even	15	inner
891.2.n.e.190.2		16	99.14	odd	30	inner
891.2.n.e.433.1		16	9.5	odd	6	inner
891.2.n.e.433.2		16	9.4	even	3	inner
891.2.n.e.784.1		16	33.14	odd	10	inner
891.2.n.e.784.2		16	11.3	even	5	inner
1089.2.a.v.1.1		4	99.16	even	15
1089.2.a.v.1.4		4	99.38	odd	30
1089.2.a.w.1.1		4	99.83	even	30
1089.2.a.w.1.4		4	99.61	odd	30

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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.96317 + 0.874061i) q^{2} +(1.75181 - 1.94558i) q^{4} +(1.96317 + 0.874061i) q^{5} +(4.14350 + 0.880728i) q^{7} +(-0.410415 + 1.26313i) q^{8} -4.61803 q^{10} +(-2.28779 + 2.40125i) q^{11} +(-0.0246758 + 0.234775i) q^{13} +(-8.90422 + 1.89265i) q^{14} +(0.248983 + 2.36892i) q^{16} +(-4.96199 + 3.60510i) q^{17} +(-0.736068 + 2.26538i) q^{19} +(5.13966 - 2.28832i) q^{20} +(2.39248 - 6.71375i) q^{22} +(1.99220 + 3.45059i) q^{23} +(-0.255585 - 0.283856i) q^{25} +(-0.156765 - 0.482472i) q^{26} +(8.97214 - 6.51864i) q^{28} +(6.80222 + 1.44586i) q^{29} +(0.482716 - 4.59274i) q^{31} +(-3.88751 - 6.73336i) q^{32} +(6.59017 - 11.4145i) q^{34} +(7.36460 + 5.35069i) q^{35} +(0.545085 + 1.67760i) q^{37} +(-0.535055 - 5.09071i) q^{38} +(-1.90977 + 2.12101i) q^{40} +(-2.90489 + 0.617454i) q^{41} +(-1.35410 + 2.34537i) q^{43} +(0.664066 + 8.65761i) q^{44} +(-6.92705 - 5.03280i) q^{46} +(-2.32663 - 2.58398i) q^{47} +(9.99809 + 4.45144i) q^{49} +(0.749866 + 0.333862i) q^{50} +(0.413545 + 0.459289i) q^{52} +(-1.48490 - 1.07884i) q^{53} +(-6.59017 + 2.71441i) q^{55} +(-2.81303 + 4.87231i) q^{56} +(-14.6177 + 3.10709i) q^{58} +(4.99271 - 5.54496i) q^{59} +(1.18391 + 11.2642i) q^{61} +(3.06668 + 9.43826i) q^{62} +(9.66312 + 7.02067i) q^{64} +(-0.253650 + 0.439335i) q^{65} +(1.42705 + 2.47172i) q^{67} +(-1.67845 + 15.9694i) q^{68} +(-19.1348 - 4.06723i) q^{70} +(8.69273 - 6.31564i) q^{71} +(0.763932 + 2.35114i) q^{73} +(-2.53642 - 2.81698i) q^{74} +(3.11803 + 5.40059i) q^{76} +(-11.5943 + 7.93468i) q^{77} +(-8.65323 + 3.85266i) q^{79} +(-1.58178 + 4.86822i) q^{80} +(5.16312 - 3.75123i) q^{82} +(0.865738 + 8.23694i) q^{83} +(-12.8923 + 2.74035i) q^{85} +(0.608337 - 5.78794i) q^{86} +(-2.09415 - 3.87528i) q^{88} -8.90937 q^{89} +(-0.309017 + 0.951057i) q^{91} +(10.2033 + 2.16878i) q^{92} +(6.82614 + 3.03919i) q^{94} +(-3.42511 + 3.80397i) q^{95} +(10.7784 - 4.79883i) q^{97} -23.5188 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) \) 16 * q - 2 * q^4 + 6 * q^7 - 56 * q^10 + 6 * q^13 - 2 * q^16 + 24 * q^19 - 28 * q^22 - 8 * q^25 + 72 * q^28 - 12 * q^31 + 16 * q^34 - 36 * q^37 + 16 * q^40 + 32 * q^43 - 84 * q^46 + 44 * q^49 - 6 * q^52 - 16 * q^55 - 28 * q^58 - 42 * q^61 + 92 * q^64 - 4 * q^67 - 26 * q^70 + 48 * q^73 + 32 * q^76 - 30 * q^79 + 20 * q^82 - 46 * q^85 + 14 * q^88 + 4 * q^91 + 26 * q^94 + 54 * q^97

Introduction

L-functions

Modular forms

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