LMFDB - Embedded newform 855.2.bs.c.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(226,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("855.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.bs (of order $9$, degree $6$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.1
Root			$0.653994 + 1.13275i$ of defining polynomial
Character	$\chi$	$=$	855.271
Dual form			855.2.bs.c.631.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.289414 + 0.105338i) q^{2} +(-1.45942 + 1.22460i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.0445979 - 0.0772459i) q^{7} +(0.601369 - 1.04160i) q^{8} +O(q^{10})$	\(q+(-0.289414 + 0.105338i) q^{2} +(-1.45942 + 1.22460i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.0445979 - 0.0772459i) q^{7} +(0.601369 - 1.04160i) q^{8} +(0.289414 + 0.105338i) q^{10} +(-1.68341 + 2.91575i) q^{11} +(0.0369645 + 0.209636i) q^{13} +(0.0210442 + 0.0176582i) q^{14} +(0.597325 - 3.38760i) q^{16} +(-2.36261 + 0.859918i) q^{17} +(0.949628 - 4.25420i) q^{19} +1.90514 q^{20} +(0.180063 - 1.02119i) q^{22} +(4.57098 - 3.83550i) q^{23} +(0.173648 + 0.984808i) q^{25} +(-0.0327807 - 0.0567779i) q^{26} +(0.159683 + 0.0581198i) q^{28} +(-4.51826 - 1.64451i) q^{29} +(-4.03407 - 6.98722i) q^{31} +(0.601676 + 3.41227i) q^{32} +(0.593190 - 0.497745i) q^{34} +(-0.0154887 + 0.0878408i) q^{35} +1.84372 q^{37} +(0.173294 + 1.33126i) q^{38} +(-1.13020 + 0.411361i) q^{40} +(0.523087 - 2.96657i) q^{41} +(-1.87518 - 1.57346i) q^{43} +(-1.11383 - 6.31683i) q^{44} +(-0.918881 + 1.59155i) q^{46} +(-7.15887 - 2.60562i) q^{47} +(3.49602 - 6.05529i) q^{49} +(-0.153994 - 0.266726i) q^{50} +(-0.310668 - 0.260681i) q^{52} +(6.43452 - 5.39920i) q^{53} +(3.16378 - 1.15152i) q^{55} -0.107279 q^{56} +1.48088 q^{58} +(9.80610 - 3.56913i) q^{59} +(-0.757296 + 0.635447i) q^{61} +(1.90354 + 1.59726i) q^{62} +(2.90628 + 5.03383i) q^{64} +(0.106435 - 0.184351i) q^{65} +(-9.37780 - 3.41324i) q^{67} +(2.39499 - 4.14824i) q^{68} +(-0.00477034 - 0.0270539i) q^{70} +(-4.73200 - 3.97062i) q^{71} +(2.73409 - 15.5058i) q^{73} +(-0.533599 + 0.194214i) q^{74} +(3.82379 + 7.37160i) q^{76} +0.300307 q^{77} +(-0.178596 + 1.01287i) q^{79} +(-2.63508 + 2.21110i) q^{80} +(0.161105 + 0.913670i) q^{82} +(8.96939 + 15.5354i) q^{83} +(2.36261 + 0.859918i) q^{85} +(0.708449 + 0.257854i) q^{86} +(2.02470 + 3.50689i) q^{88} +(-0.113975 - 0.646383i) q^{89} +(0.0145450 - 0.0122047i) q^{91} +(-1.97403 + 11.1953i) q^{92} +2.34635 q^{94} +(-3.46200 + 2.64850i) q^{95} +(-15.7991 + 5.75040i) q^{97} +(-0.373946 + 2.12075i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	$ 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) $ 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.289414	+	0.105338i	−0.204647	+	0.0744854i	−0.442310	−	0.896862i	$-0.645841\pi$
$2$	−0.289414	+	0.105338i	−0.204647	+	0.0744854i	0.237663	+	0.971348i	$0.423619\pi$
$3$		0			0
$3$		0			0
$4$	−1.45942	+	1.22460i	−0.729712	+	0.612301i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$5$	−0.766044	−	0.642788i	−0.342585	−	0.287463i
$6$		0			0
$7$	−0.0445979	−	0.0772459i	−0.0168564	−	0.0291962i	0.857474	−	0.514527i	$-0.172032\pi$
$7$	−0.0445979	−	0.0772459i	−0.0168564	−	0.0291962i	−0.874331	+	0.485331i	$0.838699\pi$
$8$	0.601369	−	1.04160i	0.212616	−	0.368262i
$9$		0			0
$10$	0.289414	+	0.105338i	0.0915208	+	0.0333109i
$11$	−1.68341	+	2.91575i	−0.507567	+	0.879133i	0.492394	+	0.870372i	$0.336122\pi$
$11$	−1.68341	+	2.91575i	−0.507567	+	0.879133i	−0.999962	+	0.00876033i	$0.997211\pi$
$12$		0			0
$13$	0.0369645	+	0.209636i	0.0102521	+	0.0581426i	0.989505	−	0.144501i	$-0.0461578\pi$
$13$	0.0369645	+	0.209636i	0.0102521	+	0.0581426i	−0.979253	+	0.202644i	$0.935047\pi$
$14$	0.0210442	+	0.0176582i	0.00562431	+	0.00471935i
$15$		0			0
$16$	0.597325	−	3.38760i	0.149331	−	0.846899i
$17$	−2.36261	+	0.859918i	−0.573016	+	0.208561i	−0.612243	−	0.790670i	$-0.709733\pi$
$17$	−2.36261	+	0.859918i	−0.573016	+	0.208561i	0.0392271	+	0.999230i	$0.487510\pi$
$18$		0			0
$19$	0.949628	−	4.25420i	0.217860	−	0.975980i
$19$	0.949628	−	4.25420i	0.217860	−	0.975980i
$20$	1.90514			0.426003
$21$		0			0
$22$	0.180063	−	1.02119i	0.0383896	−	0.217718i
$23$	4.57098	−	3.83550i	0.953114	−	0.799758i	−0.0267049	−	0.999643i	$-0.508501\pi$
$23$	4.57098	−	3.83550i	0.953114	−	0.799758i	0.979819	+	0.199885i	$0.0640570\pi$
$24$		0			0
$25$	0.173648	+	0.984808i	0.0347296	+	0.196962i
$26$	−0.0327807	−	0.0567779i	−0.00642883	−	0.0111351i
$27$		0			0
$28$	0.159683	+	0.0581198i	0.0301772	+	0.0109836i
$29$	−4.51826	−	1.64451i	−0.839019	−	0.305378i	−0.113464	−	0.993542i	$-0.536195\pi$
$29$	−4.51826	−	1.64451i	−0.839019	−	0.305378i	−0.725555	+	0.688164i	$0.758417\pi$
$30$		0			0
$31$	−4.03407	−	6.98722i	−0.724541	−	1.25494i	−0.959163	−	0.282855i	$-0.908718\pi$
$31$	−4.03407	−	6.98722i	−0.724541	−	1.25494i	0.234621	−	0.972087i	$-0.424615\pi$
$32$	0.601676	+	3.41227i	0.106362	+	0.603210i
$33$		0			0
$34$	0.593190	−	0.497745i	0.101731	−	0.0853626i
$35$	−0.0154887	+	0.0878408i	−0.00261807	+	0.0148478i
$36$		0			0
$37$	1.84372			0.303106			0.151553	−	0.988449i	$-0.451573\pi$
$37$	1.84372			0.303106			0.151553	+	0.988449i	$0.451573\pi$
$38$	0.173294	+	1.33126i	0.0281119	+	0.215959i
$39$		0			0
$40$	−1.13020	+	0.411361i	−0.178701	+	0.0650418i
$41$	0.523087	−	2.96657i	0.0816925	−	0.463301i	−0.916329	−	0.400426i	$-0.868862\pi$
$41$	0.523087	−	2.96657i	0.0816925	−	0.463301i	0.998021	−	0.0628748i	$-0.0200269\pi$
$42$		0			0
$43$	−1.87518	−	1.57346i	−0.285962	−	0.239951i	0.488511	−	0.872558i	$-0.337540\pi$
$43$	−1.87518	−	1.57346i	−0.285962	−	0.239951i	−0.774473	+	0.632607i	$0.781985\pi$
$44$	−1.11383	−	6.31683i	−0.167916	−	0.952298i
$45$		0			0
$46$	−0.918881	+	1.59155i	−0.135482	+	0.234661i
$47$	−7.15887	−	2.60562i	−1.04423	−	0.380068i	−0.237747	−	0.971327i	$-0.576409\pi$
$47$	−7.15887	−	2.60562i	−1.04423	−	0.380068i	−0.806482	+	0.591259i	$0.798631\pi$
$48$		0			0
$49$	3.49602	−	6.05529i	0.499432	−	0.865041i
$50$	−0.153994	−	0.266726i	−0.0217781	−	0.0377207i
$51$		0			0
$52$	−0.310668	−	0.260681i	−0.0430818	−	0.0361500i
$53$	6.43452	−	5.39920i	0.883849	−	0.741637i	−0.0831178	−	0.996540i	$-0.526488\pi$
$53$	6.43452	−	5.39920i	0.883849	−	0.741637i	0.966967	+	0.254902i	$0.0820433\pi$
$54$		0			0
$55$	3.16378	−	1.15152i	0.426604	−	0.155271i
$56$	−0.107279			−0.0143358
$57$		0			0
$58$	1.48088			0.194449
$59$	9.80610	−	3.56913i	1.27665	−	0.464661i	0.387324	−	0.921944i	$-0.373400\pi$
$59$	9.80610	−	3.56913i	1.27665	−	0.464661i	0.889321	+	0.457283i	$0.151177\pi$
$60$		0			0
$61$	−0.757296	+	0.635447i	−0.0969618	+	0.0813606i	−0.689980	−	0.723828i	$-0.742381\pi$
$61$	−0.757296	+	0.635447i	−0.0969618	+	0.0813606i	0.593018	+	0.805189i	$0.297936\pi$
$62$	1.90354	+	1.59726i	0.241750	+	0.202852i
$63$		0			0
$64$	2.90628	+	5.03383i	0.363285	+	0.629228i
$65$	0.106435	−	0.184351i	0.0132016	−	0.0228659i
$66$		0			0
$67$	−9.37780	−	3.41324i	−1.14568	−	0.416994i	−0.301719	−	0.953397i	$-0.597560\pi$
$67$	−9.37780	−	3.41324i	−1.14568	−	0.416994i	−0.843962	+	0.536403i	$0.819783\pi$
$68$	2.39499	−	4.14824i	0.290435	−	0.503048i
$69$		0			0
$70$	−0.00477034	−	0.0270539i	−0.000570165	−	0.00323356i
$71$	−4.73200	−	3.97062i	−0.561585	−	0.471226i	0.317256	−	0.948340i	$-0.397238\pi$
$71$	−4.73200	−	3.97062i	−0.561585	−	0.471226i	−0.878841	+	0.477114i	$0.841683\pi$
$72$		0			0
$73$	2.73409	−	15.5058i	0.320001	−	1.81482i	−0.222695	−	0.974888i	$-0.571485\pi$
$73$	2.73409	−	15.5058i	0.320001	−	1.81482i	0.542696	−	0.839929i	$-0.317403\pi$
$74$	−0.533599	+	0.194214i	−0.0620296	+	0.0225769i
$75$		0			0
$76$	3.82379	+	7.37160i	0.438619	+	0.845580i
$77$	0.300307			0.0342231
$78$		0			0
$79$	−0.178596	+	1.01287i	−0.0200936	+	0.113957i	−0.993205	−	0.116379i	$-0.962871\pi$
$79$	−0.178596	+	1.01287i	−0.0200936	+	0.113957i	0.973111	+	0.230336i	$0.0739824\pi$
$80$	−2.63508	+	2.21110i	−0.294611	+	0.247208i
$81$		0			0
$82$	0.161105	+	0.913670i	0.0177910	+	0.100898i
$83$	8.96939	+	15.5354i	0.984518	+	1.70524i	0.644059	+	0.764976i	$0.277249\pi$
$83$	8.96939	+	15.5354i	0.984518	+	1.70524i	0.340459	+	0.940259i	$0.389418\pi$
$84$		0			0
$85$	2.36261	+	0.859918i	0.256261	+	0.0932712i
$86$	0.708449	+	0.257854i	0.0763940	+	0.0278052i
$87$		0			0
$88$	2.02470	+	3.50689i	0.215834	+	0.373836i
$89$	−0.113975	−	0.646383i	−0.0120813	−	0.0685164i	0.978171	−	0.207801i	$-0.0666307\pi$
$89$	−0.113975	−	0.646383i	−0.0120813	−	0.0685164i	−0.990252	+	0.139285i	$0.955520\pi$
$90$		0			0
$91$	0.0145450	−	0.0122047i	0.00152473	−	0.00127940i
$92$	−1.97403	+	11.1953i	−0.205806	+	1.16719i
$93$		0			0
$94$	2.34635			0.242008
$95$	−3.46200	+	2.64850i	−0.355194	+	0.271730i
$96$		0			0
$97$	−15.7991	+	5.75040i	−1.60416	+	0.583865i	−0.980272	−	0.197653i	$-0.936668\pi$
$97$	−15.7991	+	5.75040i	−1.60416	+	0.583865i	−0.623883	+	0.781518i	$0.714446\pi$
$98$	−0.373946	+	2.12075i	−0.0377742	+	0.214228i
$99$		0			0
$100$	−1.45942	−	1.22460i	−0.145942	−	0.122460i
$101$	−0.638978	−	3.62382i	−0.0635806	−	0.360584i	−0.999954	−	0.00957849i	$-0.996951\pi$
$101$	−0.638978	−	3.62382i	−0.0635806	−	0.360584i	0.936373	−	0.351005i	$-0.114160\pi$
$102$		0			0
$103$	1.76710	−	3.06071i	0.174118	−	0.301580i	−0.765738	−	0.643153i	$-0.777626\pi$
$103$	1.76710	−	3.06071i	0.174118	−	0.301580i	0.939856	+	0.341572i	$0.110959\pi$
$104$	0.240587	+	0.0875664i	0.0235915	+	0.00858659i
$105$		0			0
$106$	−1.29350	+	2.24041i	−0.125636	+	0.217608i
$107$	−0.943300	−	1.63384i	−0.0911923	−	0.157950i	0.816821	−	0.576891i	$-0.195734\pi$
$107$	−0.943300	−	1.63384i	−0.0911923	−	0.157950i	−0.908013	+	0.418942i	$0.862401\pi$
$108$		0			0
$109$	−10.0810	−	8.45901i	−0.965589	−	0.810226i	0.0162639	−	0.999868i	$-0.494823\pi$
$109$	−10.0810	−	8.45901i	−0.965589	−	0.810226i	−0.981853	+	0.189642i	$0.939267\pi$
$110$	−0.794343	+	0.666533i	−0.0757377	+	0.0635515i
$111$		0			0
$112$	−0.288318	+	0.104939i	−0.0272434	+	0.00991580i
$113$	−12.3456			−1.16138			−0.580689	−	0.814125i	$-0.697217\pi$
$113$	−12.3456			−1.16138			−0.580689	+	0.814125i	$0.697217\pi$
$114$		0			0
$115$	−5.96699			−0.556424
$116$	8.60793	−	3.13303i	0.799226	−	0.290895i
$117$		0			0
$118$	−2.46206	+	2.06591i	−0.226651	+	0.190183i
$119$	0.171793	+	0.144151i	0.0157482	+	0.0132143i
$120$		0			0
$121$	−0.167744	−	0.290542i	−0.0152495	−	0.0264129i
$122$	0.152235	−	0.263680i	0.0137827	−	0.0238724i
$123$		0			0
$124$	14.4440	+	5.25718i	1.29711	+	0.472109i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$		0			0
$127$	3.68344	+	20.8898i	0.326852	+	1.85367i	0.496325	+	0.868137i	$0.334682\pi$
$127$	3.68344	+	20.8898i	0.326852	+	1.85367i	−0.169473	+	0.985535i	$0.554207\pi$
$128$	−6.67993	−	5.60512i	−0.590428	−	0.495428i
$129$		0			0
$130$	−0.0113846	+	0.0645654i	−0.000998498	+	0.00566276i
$131$	6.53156	−	2.37729i	0.570665	−	0.207705i	−0.0405392	−	0.999178i	$-0.512908\pi$
$131$	6.53156	−	2.37729i	0.570665	−	0.207705i	0.611204	+	0.791473i	$0.290685\pi$
$132$		0			0
$133$	−0.370971	+	0.116374i	−0.0321673	+	0.0100909i
$134$	3.07361			0.265520
$135$		0			0
$136$	−0.525106	+	2.97802i	−0.0450275	+	0.255363i
$137$	−16.0922	+	13.5029i	−1.37485	+	1.15363i	−0.403772	+	0.914860i	$0.632301\pi$
$137$	−16.0922	+	13.5029i	−1.37485	+	1.15363i	−0.971075	+	0.238774i	$0.923254\pi$
$138$		0			0
$139$	2.72999	+	15.4826i	0.231555	+	1.31321i	0.849749	+	0.527188i	$0.176754\pi$
$139$	2.72999	+	15.4826i	0.231555	+	1.31321i	−0.618194	+	0.786026i	$0.712135\pi$
$140$	−0.0849655	−	0.147165i	−0.00718089	−	0.0124377i
$141$		0			0
$142$	1.78777	+	0.650694i	0.150026	+	0.0546050i
$143$	−0.673473	−	0.245124i	−0.0563187	−	0.0204983i
$144$		0			0
$145$	2.40411	+	4.16405i	0.199651	+	0.345805i
$146$	0.842068	+	4.77561i	0.0696901	+	0.395232i
$147$		0			0
$148$	−2.69077	+	2.25782i	−0.221180	+	0.185592i
$149$	3.38951	−	19.2229i	0.277679	−	1.57480i	−0.452641	−	0.891693i	$-0.649518\pi$
$149$	3.38951	−	19.2229i	0.277679	−	1.57480i	0.730320	−	0.683105i	$-0.239371\pi$
$150$		0			0
$151$	11.2284			0.913758			0.456879	−	0.889529i	$-0.348967\pi$
$151$	11.2284			0.913758			0.456879	+	0.889529i	$0.348967\pi$
$152$	−3.86010	−	3.54748i	−0.313096	−	0.287739i
$153$		0			0
$154$	−0.0869131	+	0.0316338i	−0.00700365	+	0.00254912i
$155$	−1.40102	+	7.94558i	−0.112533	+	0.638204i
$156$		0			0
$157$	3.53362	+	2.96506i	0.282014	+	0.236637i	0.772811	−	0.634636i	$-0.218850\pi$
$157$	3.53362	+	2.96506i	0.282014	+	0.236637i	−0.490797	+	0.871274i	$0.663295\pi$
$158$	−0.0550055	−	0.311951i	−0.00437600	−	0.0248175i
$159$		0			0
$160$	1.73246	−	3.00070i	0.136963	−	0.237226i
$161$	−0.500133	−	0.182034i	−0.0394160	−	0.0143463i
$162$		0			0
$163$	0.287367	−	0.497735i	0.0225084	−	0.0389856i	−0.854552	−	0.519366i	$-0.826168\pi$
$163$	0.287367	−	0.497735i	0.0225084	−	0.0389856i	0.877060	+	0.480381i	$0.159501\pi$
$164$	2.86947	+	4.97007i	0.224068	+	0.388097i
$165$		0			0
$166$	−4.23234	−	3.55136i	−0.328494	−	0.275639i
$167$	−3.15765	+	2.64958i	−0.244346	+	0.205031i	−0.756733	−	0.653724i	$-0.773206\pi$
$167$	−3.15765	+	2.64958i	−0.244346	+	0.205031i	0.512387	+	0.858755i	$0.328761\pi$
$168$		0			0
$169$	12.1734	−	4.43076i	0.936417	−	0.340828i
$170$	−0.774354			−0.0593903
$171$		0			0
$172$	4.66355			0.355592
$173$	−6.04652	+	2.20075i	−0.459709	+	0.167320i	−0.561485	−	0.827487i	$-0.689770\pi$
$173$	−6.04652	+	2.20075i	−0.459709	+	0.167320i	0.101776	+	0.994807i	$0.467547\pi$
$174$		0			0
$175$	0.0683280	−	0.0573340i	0.00516511	−	0.00433404i
$176$	8.87186	+	7.44437i	0.668741	+	0.561141i
$177$		0			0
$178$	0.101075	+	0.175066i	0.00757587	+	0.0131218i
$179$	1.91516	−	3.31715i	0.143146	−	0.247936i	−0.785534	−	0.618819i	$-0.787612\pi$
$179$	1.91516	−	3.31715i	0.143146	−	0.247936i	0.928680	+	0.370883i	$0.120945\pi$
$180$		0			0
$181$	−15.6814	−	5.70755i	−1.16559	−	0.424239i	−0.314496	−	0.949259i	$-0.601836\pi$
$181$	−15.6814	−	5.70755i	−1.16559	−	0.424239i	−0.851090	+	0.525020i	$0.824058\pi$
$182$	−0.00292391	+	0.00506435i	−0.000216734	+	0.000375395i
$183$		0			0
$184$	−1.24622	−	7.06769i	−0.0918729	−	0.521037i
$185$	−1.41237	−	1.18512i	−0.103840	−	0.0871318i
$186$		0			0
$187$	1.46993	−	8.33637i	0.107492	−	0.609616i
$188$	13.6387	−	4.96407i	0.994703	−	0.362042i
$189$		0			0
$190$	0.722966	−	1.13119i	0.0524494	−	0.0820654i
$191$	−7.92694			−0.573573			−0.286787	−	0.957994i	$-0.592587\pi$
$191$	−7.92694			−0.573573			−0.286787	+	0.957994i	$0.592587\pi$
$192$		0			0
$193$	−3.69296	+	20.9438i	−0.265825	+	1.50757i	0.500851	+	0.865533i	$0.333020\pi$
$193$	−3.69296	+	20.9438i	−0.265825	+	1.50757i	−0.766676	+	0.642034i	$0.778091\pi$
$194$	3.96675	−	3.32850i	0.284796	−	0.238972i
$195$		0			0
$196$	2.31314	+	13.1185i	0.165224	+	0.937034i
$197$	1.44371	+	2.50058i	0.102860	+	0.178159i	0.912862	−	0.408268i	$-0.133867\pi$
$197$	1.44371	+	2.50058i	0.102860	+	0.178159i	−0.810002	+	0.586427i	$0.800534\pi$
$198$		0			0
$199$	−10.9144	−	3.97251i	−0.773701	−	0.281604i	−0.0751574	−	0.997172i	$-0.523946\pi$
$199$	−10.9144	−	3.97251i	−0.773701	−	0.281604i	−0.698544	+	0.715568i	$0.746168\pi$
$200$	1.13020	+	0.411361i	0.0799175	+	0.0290876i
$201$		0			0
$202$	0.566656	+	0.981477i	0.0398698	+	0.0690565i
$203$	0.0744732	+	0.422359i	0.00522700	+	0.0296438i
$204$		0			0
$205$	−2.30759	+	1.93629i	−0.161169	+	0.135237i
$206$	−0.189015	+	1.07196i	−0.0131693	+	0.0746867i
$207$		0			0
$208$	0.732242			0.0507719
$209$	10.8056	+	9.93045i	0.747437	+	0.686903i
$210$		0			0
$211$	22.2708	−	8.10590i	1.53318	−	0.558033i	0.568784	−	0.822487i	$-0.307414\pi$
$211$	22.2708	−	8.10590i	1.53318	−	0.558033i	0.964398	+	0.264454i	$0.0851916\pi$
$212$	−2.77882	+	15.7595i	−0.190850	+	1.08236i
$213$		0			0
$214$	0.445111	+	0.373492i	0.0304272	+	0.0255314i
$215$	0.425068	+	2.41068i	0.0289894	+	0.164407i
$216$		0			0
$217$	−0.359823	+	0.623232i	−0.0244264	+	0.0423077i
$218$	3.80866	+	1.38624i	0.257955	+	0.0938879i
$219$		0			0
$220$	−3.20714	+	5.55493i	−0.216225	+	0.374513i
$221$	−0.267602	−	0.463501i	−0.0180009	−	0.0311784i
$222$		0			0
$223$	−6.75335	−	5.66673i	−0.452237	−	0.379472i	0.388028	−	0.921648i	$-0.373156\pi$
$223$	−6.75335	−	5.66673i	−0.452237	−	0.379472i	−0.840265	+	0.542175i	$0.817601\pi$
$224$	0.236751	−	0.198657i	0.0158186	−	0.0132734i
$225$		0			0
$226$	3.57300	−	1.30047i	0.237672	−	0.0865057i
$227$	1.04512			0.0693671			0.0346835	−	0.999398i	$-0.488958\pi$
$227$	1.04512			0.0693671			0.0346835	+	0.999398i	$0.488958\pi$
$228$		0			0
$229$	−13.4837			−0.891031			−0.445515	−	0.895274i	$-0.646980\pi$
$229$	−13.4837			−0.891031			−0.445515	+	0.895274i	$0.646980\pi$
$230$	1.72693	−	0.628551i	0.113870	−	0.0414455i
$231$		0			0
$232$	−4.43007	+	3.71727i	−0.290848	+	0.244051i
$233$	−8.59336	−	7.21068i	−0.562970	−	0.472388i	0.316335	−	0.948648i	$-0.397548\pi$
$233$	−8.59336	−	7.21068i	−0.562970	−	0.472388i	−0.879305	+	0.476260i	$0.841992\pi$
$234$		0			0
$235$	3.80916	+	6.59765i	0.248482	+	0.430383i
$236$	−9.94050	+	17.2174i	−0.647071	+	1.12076i
$237$		0			0
$238$	−0.0649038	−	0.0236231i	−0.00420709	−	0.00153126i
$239$	−10.1645	+	17.6054i	−0.657487	+	1.13880i	0.323777	+	0.946133i	$0.395047\pi$
$239$	−10.1645	+	17.6054i	−0.657487	+	1.13880i	−0.981264	+	0.192667i	$0.938286\pi$
$240$		0			0
$241$	−0.667594	−	3.78611i	−0.0430035	−	0.243885i	0.955727	−	0.294254i	$-0.0950713\pi$
$241$	−0.667594	−	3.78611i	−0.0430035	−	0.243885i	−0.998731	+	0.0503694i	$0.983960\pi$
$242$	0.0791528	+	0.0664171i	0.00508814	+	0.00426945i
$243$		0			0
$244$	0.327046	−	1.85477i	0.0209370	−	0.118740i
$245$	−6.57037	+	2.39142i	−0.419766	+	0.152782i
$246$		0			0
$247$	0.926936	+	0.0418221i	0.0589795	+	0.00266107i
$248$	−9.70387			−0.616197
$249$		0			0
$250$	−0.0534816	+	0.303309i	−0.00338247	+	0.0191830i
$251$	6.08068	−	5.10229i	0.383809	−	0.322054i	−0.430387	−	0.902645i	$-0.641623\pi$
$251$	6.08068	−	5.10229i	0.383809	−	0.322054i	0.814196	+	0.580591i	$0.197178\pi$
$252$		0			0
$253$	3.48855	+	19.7846i	0.219323	+	1.24385i
$254$	−3.26654	−	5.65781i	−0.204961	−	0.355002i
$255$		0			0
$256$	−8.40034	−	3.05747i	−0.525021	−	0.191092i
$257$	22.7666	+	8.28638i	1.42014	+	0.516890i	0.934090	−	0.357038i	$-0.116213\pi$
$257$	22.7666	+	8.28638i	1.42014	+	0.516890i	0.486054	+	0.873929i	$0.338436\pi$
$258$		0			0
$259$	−0.0822262	−	0.142420i	−0.00510928	−	0.00884954i
$260$	0.0704226	+	0.399387i	0.00436743	+	0.0247689i
$261$		0			0
$262$	−1.63991	+	1.37605i	−0.101314	+	0.0850124i
$263$	2.14928	−	12.1892i	0.132530	−	0.751617i	−0.844017	−	0.536316i	$-0.819816\pi$
$263$	2.14928	−	12.1892i	0.132530	−	0.751617i	0.976548	−	0.215301i	$-0.0690733\pi$
$264$		0			0
$265$	−8.39967			−0.515987
$266$	0.0951057	−	0.0727576i	0.00583131	−	0.00446105i
$267$		0			0
$268$	17.8660	−	6.50271i	1.09134	−	0.397216i
$269$	4.23334	−	24.0085i	0.258111	−	1.46382i	−0.529846	−	0.848094i	$-0.677750\pi$
$269$	4.23334	−	24.0085i	0.258111	−	1.46382i	0.787958	−	0.615729i	$-0.211138\pi$
$270$		0			0
$271$	13.3432	+	11.1963i	0.810540	+	0.680124i	0.950737	−	0.310000i	$-0.100329\pi$
$271$	13.3432	+	11.1963i	0.810540	+	0.680124i	−0.140196	+	0.990124i	$0.544773\pi$
$272$	1.50181	+	8.51721i	0.0910608	+	0.516432i
$273$		0			0
$274$	3.23493	−	5.60306i	0.195429	−	0.338494i
$275$	−3.16378	−	1.15152i	−0.190783	−	0.0694393i
$276$		0			0
$277$	−10.3920	+	17.9994i	−0.624393	+	1.08148i	0.364265	+	0.931295i	$0.381320\pi$
$277$	−10.3920	+	17.9994i	−0.624393	+	1.08148i	−0.988658	+	0.150185i	$0.952013\pi$
$278$	−2.42100	−	4.19330i	−0.145202	−	0.251498i
$279$		0			0
$280$	0.0821807	+	0.0689578i	0.00491124	+	0.00412102i
$281$	4.60383	−	3.86307i	0.274641	−	0.230452i	−0.495055	−	0.868862i	$-0.664852\pi$
$281$	4.60383	−	3.86307i	0.274641	−	0.230452i	0.769696	+	0.638410i	$0.220408\pi$
$282$		0			0
$283$	−10.8759	+	3.95849i	−0.646502	+	0.235308i	−0.644398	−	0.764690i	$-0.722892\pi$
$283$	−10.8759	+	3.95849i	−0.646502	+	0.235308i	−0.00210419	+	0.999998i	$0.500670\pi$
$284$	11.7684			0.698327
$285$		0			0
$286$	0.220734			0.0130523
$287$	−0.252484	+	0.0918968i	−0.0149037	+	0.00542450i
$288$		0			0
$289$	−8.18031	+	6.86409i	−0.481195	+	0.403770i
$290$	−1.13442	−	0.951890i	−0.0666154	−	0.0558969i
$291$		0			0
$292$	14.9982	+	25.9777i	0.877706	+	1.52023i
$293$	8.73466	−	15.1289i	0.510284	−	0.883838i	−0.489645	−	0.871922i	$-0.662874\pi$
$293$	8.73466	−	15.1289i	0.510284	−	0.883838i	0.999929	−	0.0119163i	$-0.00379316\pi$
$294$		0			0
$295$	−9.80610	−	3.56913i	−0.570933	−	0.207803i
$296$	1.10876	−	1.92042i	0.0644452	−	0.111622i
$297$		0			0
$298$	1.04393	+	5.92042i	0.0604732	+	0.342961i
$299$	0.973024	+	0.816464i	0.0562714	+	0.0472173i
$300$		0			0
$301$	−0.0379144	+	0.215023i	−0.00218535	+	0.0123937i
$302$	−3.24967	+	1.18278i	−0.186998	+	0.0680616i
$303$		0			0
$304$	−13.8443	−	5.75810i	−0.794024	−	0.330250i
$305$	0.988579			0.0566059
$306$		0			0
$307$	5.14924	−	29.2028i	0.293883	−	1.66669i	−0.377827	−	0.925876i	$-0.623328\pi$
$307$	5.14924	−	29.2028i	0.293883	−	1.66669i	0.671709	−	0.740815i	$-0.265560\pi$
$308$	−0.438275	+	0.367756i	−0.0249730	+	0.0209549i
$309$		0			0
$310$	−0.431498	−	2.44714i	−0.0245074	−	0.138988i
$311$	−5.81119	−	10.0653i	−0.329522	−	0.570749i	0.652895	−	0.757449i	$-0.273554\pi$
$311$	−5.81119	−	10.0653i	−0.329522	−	0.570749i	−0.982417	+	0.186699i	$0.940221\pi$
$312$		0			0
$313$	0.446226	+	0.162413i	0.0252222	+	0.00918012i	0.354600	−	0.935018i	$-0.384617\pi$
$313$	0.446226	+	0.162413i	0.0252222	+	0.00918012i	−0.329378	+	0.944198i	$0.606839\pi$
$314$	−1.33501	−	0.485905i	−0.0753392	−	0.0274212i
$315$		0			0
$316$	−0.979713	−	1.69691i	−0.0551132	−	0.0954588i
$317$	3.51260	+	19.9209i	0.197287	+	1.11887i	0.909124	+	0.416526i	$0.136753\pi$
$317$	3.51260	+	19.9209i	0.197287	+	1.11887i	−0.711836	+	0.702345i	$0.752136\pi$
$318$		0			0
$319$	12.4011	−	10.4057i	0.694327	−	0.582609i
$320$	1.00934	−	5.72426i	0.0564239	−	0.319996i
$321$		0			0
$322$	0.163921			0.00913495
$323$	1.41467	+	10.8676i	0.0787141	+	0.604689i
$324$		0			0
$325$	−0.200032	+	0.0728058i	−0.0110958	+	0.00403854i
$326$	−0.0307377	+	0.174322i	−0.00170241	+	0.00965483i
$327$		0			0
$328$	−2.77542	−	2.32886i	−0.153247	−	0.128590i
$329$	0.117998	+	0.669199i	0.00650543	+	0.0368941i
$330$		0			0
$331$	3.00653	−	5.20746i	0.165254	−	0.286228i	−0.771492	−	0.636240i	$-0.780489\pi$
$331$	3.00653	−	5.20746i	0.165254	−	0.286228i	0.936745	+	0.350012i	$0.113822\pi$
$332$	−32.1149	−	11.6889i	−1.76253	−	0.641509i
$333$		0			0
$334$	0.634767	−	1.09945i	0.0347329	−	0.0601591i
$335$	4.98982	+	8.64263i	0.272623	+	0.472197i
$336$		0			0
$337$	−6.79277	−	5.69981i	−0.370026	−	0.310488i	0.438746	−	0.898611i	$-0.355423\pi$
$337$	−6.79277	−	5.69981i	−0.370026	−	0.310488i	−0.808772	+	0.588123i	$0.799867\pi$
$338$	−3.05643	+	2.56465i	−0.166248	+	0.139499i
$339$		0			0
$340$	−4.50110	+	1.63827i	−0.244107	+	0.0888475i
$341$	27.1640			1.47101
$342$		0			0
$343$	−1.24803			−0.0673874
$344$	−2.76660	+	1.00696i	−0.149165	+	0.0542916i
$345$		0			0
$346$	1.51813	−	1.27386i	0.0816150	−	0.0684831i
$347$	−15.2988	−	12.8372i	−0.821284	−	0.689139i	0.131989	−	0.991251i	$-0.457864\pi$
$347$	−15.2988	−	12.8372i	−0.821284	−	0.689139i	−0.953272	+	0.302112i	$0.902308\pi$
$348$		0			0
$349$	0.405107	+	0.701666i	0.0216849	+	0.0375593i	0.876664	−	0.481103i	$-0.159764\pi$
$349$	0.405107	+	0.701666i	0.0216849	+	0.0375593i	−0.854979	+	0.518662i	$0.826430\pi$
$350$	−0.0137356	+	0.0237908i	−0.000734201	+	0.00127167i
$351$		0			0
$352$	−10.9622	−	3.98992i	−0.584288	−	0.212663i
$353$	−10.4751	+	18.1435i	−0.557536	+	0.965681i	0.440165	+	0.897917i	$0.354920\pi$
$353$	−10.4751	+	18.1435i	−0.557536	+	0.965681i	−0.997701	+	0.0677639i	$0.978414\pi$
$354$		0			0
$355$	1.07266	+	6.08334i	0.0569307	+	0.322870i
$356$	0.957899	+	0.803773i	0.0507686	+	0.0425999i
$357$		0			0
$358$	−0.204851	+	1.16177i	−0.0108267	+	0.0614015i
$359$	24.1518	−	8.79055i	1.27469	−	0.463948i	0.386015	−	0.922493i	$-0.373851\pi$
$359$	24.1518	−	8.79055i	1.27469	−	0.463948i	0.888671	+	0.458545i	$0.151629\pi$
$360$		0			0
$361$	−17.1964	−	8.07982i	−0.905074	−	0.425253i
$362$	5.13963			0.270133
$363$		0			0
$364$	−0.00628141	+	0.0356236i	−0.000329235	+	0.00186719i
$365$	−12.0614	+	10.1207i	−0.631321	+	0.529741i
$366$		0			0
$367$	−4.21721	−	23.9170i	−0.220137	−	1.24846i	−0.871767	−	0.489921i	$-0.837026\pi$
$367$	−4.21721	−	23.9170i	−0.220137	−	1.24846i	0.651630	−	0.758537i	$-0.274085\pi$
$368$	−10.2628	−	17.7757i	−0.534985	−	0.926621i
$369$		0			0
$370$	0.533599	+	0.194214i	0.0277405	+	0.0100967i
$371$	−0.704033	−	0.256247i	−0.0365515	−	0.0133037i
$372$		0			0
$373$	−5.44043	−	9.42310i	−0.281695	−	0.487910i	0.690107	−	0.723707i	$-0.257563\pi$
$373$	−5.44043	−	9.42310i	−0.281695	−	0.487910i	−0.971802	+	0.235797i	$0.924230\pi$
$374$	0.452720	+	2.56750i	0.0234096	+	0.132763i
$375$		0			0
$376$	−7.01914	+	5.88976i	−0.361985	+	0.303741i
$377$	0.177734	−	1.00798i	0.00915375	−	0.0519135i
$378$		0			0
$379$	19.3318			0.993008			0.496504	−	0.868034i	$-0.334617\pi$
$379$	19.3318			0.993008			0.496504	+	0.868034i	$0.334617\pi$
$380$	1.80918	−	8.10486i	0.0928089	−	0.415770i
$381$		0			0
$382$	2.29417	−	0.835009i	0.117380	−	0.0427228i
$383$	0.181124	−	1.02720i	0.00925498	−	0.0524876i	−0.979831	−	0.199830i	$-0.935961\pi$
$383$	0.181124	−	1.02720i	0.00925498	−	0.0524876i	0.989086	+	0.147343i	$0.0470720\pi$
$384$		0			0
$385$	−0.230048	−	0.193033i	−0.0117243	−	0.00983789i
$386$	−1.13739	−	6.45045i	−0.0578915	−	0.328319i
$387$		0			0
$388$	16.0156	−	27.7399i	0.813070	−	1.40828i
$389$	24.9988	+	9.09880i	1.26749	+	0.461328i	0.886275	−	0.463160i	$-0.153284\pi$
$389$	24.9988	+	9.09880i	1.26749	+	0.461328i	0.381213	+	0.924487i	$0.375507\pi$
$390$		0			0
$391$	−7.50120	+	12.9925i	−0.379352	+	0.657056i
$392$	−4.20480	−	7.28293i	−0.212374	−	0.367843i
$393$		0			0
$394$	−0.681238	−	0.571627i	−0.0343203	−	0.0287981i
$395$	0.787871	−	0.661103i	0.0396421	−	0.0332637i
$396$		0			0
$397$	3.47457	−	1.26464i	0.174384	−	0.0634705i	−0.253353	−	0.967374i	$-0.581533\pi$
$397$	3.47457	−	1.26464i	0.174384	−	0.0634705i	0.427737	+	0.903903i	$0.359311\pi$
$398$	3.57724			0.179311
$399$		0			0
$400$	3.43986			0.171993
$401$	−19.0147	+	6.92080i	−0.949551	+	0.345608i	−0.769930	−	0.638128i	$-0.779709\pi$
$401$	−19.0147	+	6.92080i	−0.949551	+	0.345608i	−0.179620	+	0.983736i	$0.557487\pi$
$402$		0			0
$403$	1.31566	−	1.10397i	0.0655375	−	0.0549925i
$404$	5.37028	+	4.50620i	0.267181	+	0.224192i
$405$		0			0
$406$	−0.0660441	−	0.114392i	−0.00327772	−	0.00567717i
$407$	−3.10374	+	5.37583i	−0.153847	+	0.266470i
$408$		0			0
$409$	−11.7244	−	4.26733i	−0.579733	−	0.211006i	0.0354746	−	0.999371i	$-0.488706\pi$
$409$	−11.7244	−	4.26733i	−0.579733	−	0.211006i	−0.615208	+	0.788365i	$0.710928\pi$
$410$	0.463883	−	0.803468i	0.0229095	−	0.0396805i
$411$		0			0
$412$	1.16920	+	6.63087i	0.0576024	+	0.326679i
$413$	−0.713032	−	0.598305i	−0.0350860	−	0.0294407i
$414$		0			0
$415$	3.11504	−	17.6662i	0.152911	−	0.867202i
$416$	−0.693095	+	0.252266i	−0.0339818	+	0.0123683i
$417$		0			0
$418$	−4.17334	−	1.73577i	−0.204125	−	0.0848994i
$419$	−28.9962			−1.41656			−0.708279	−	0.705933i	$-0.750528\pi$
$419$	−28.9962			−1.41656			−0.708279	+	0.705933i	$0.750528\pi$
$420$		0			0
$421$	2.53458	−	14.3743i	0.123528	−	0.700561i	−0.858644	−	0.512573i	$-0.828692\pi$
$421$	2.53458	−	14.3743i	0.123528	−	0.700561i	0.982171	−	0.187988i	$-0.0601965\pi$
$422$	−5.59162	+	4.69193i	−0.272196	+	0.228399i
$423$		0			0
$424$	−1.75430	−	9.94912i	−0.0851963	−	0.483172i
$425$	−1.25712	−	2.17739i	−0.0609791	−	0.105619i
$426$		0			0
$427$	0.0828595	+	0.0301584i	0.00400985	+	0.00145947i
$428$	3.37749	+	1.22930i	0.163257	+	0.0594207i
$429$		0			0
$430$	−0.376958	−	0.652910i	−0.0181785	−	0.0314861i
$431$	−2.34566	−	13.3029i	−0.112986	−	0.640778i	−0.987727	−	0.156187i	$-0.950080\pi$
$431$	−2.34566	−	13.3029i	−0.112986	−	0.640778i	0.874741	−	0.484591i	$-0.161031\pi$
$432$		0			0
$433$	29.1254	−	24.4391i	1.39968	−	1.17447i	0.438438	−	0.898761i	$-0.355532\pi$
$433$	29.1254	−	24.4391i	1.39968	−	1.17447i	0.961241	−	0.275709i	$-0.0889127\pi$
$434$	0.0384878	−	0.218275i	0.00184747	−	0.0104775i
$435$		0			0
$436$	25.0714			1.20070
$437$	−11.9763	−	23.0881i	−0.572903	−	1.10446i
$438$		0			0
$439$	22.3525	−	8.13563i	1.06682	−	0.388292i	0.251836	−	0.967770i	$-0.418966\pi$
$439$	22.3525	−	8.13563i	1.06682	−	0.388292i	0.814988	+	0.579478i	$0.196743\pi$
$440$	0.703172	−	3.98789i	0.0335224	−	0.190115i
$441$		0			0
$442$	0.126272	+	0.105955i	0.00600616	+	0.00503977i
$443$	3.35126	+	19.0059i	0.159223	+	0.902999i	0.954823	+	0.297176i	$0.0960449\pi$
$443$	3.35126	+	19.0059i	0.159223	+	0.902999i	−0.795600	+	0.605823i	$0.792844\pi$
$444$		0			0
$445$	−0.328177	+	0.568419i	−0.0155571	+	0.0269457i
$446$	2.55144	+	0.928648i	0.120814	+	0.0439727i
$447$		0			0
$448$	0.259228	−	0.448997i	0.0122474	−	0.0212131i
$449$	−13.2068	−	22.8749i	−0.623268	−	1.07953i	−0.988873	−	0.148761i	$-0.952471\pi$
$449$	−13.2068	−	22.8749i	−0.623268	−	1.07953i	0.365605	−	0.930770i	$-0.380862\pi$
$450$		0			0
$451$	7.76923	+	6.51916i	0.365839	+	0.306975i
$452$	18.0175	−	15.1185i	0.847472	−	0.711113i
$453$		0			0
$454$	−0.302473	+	0.110091i	−0.0141958	+	0.00516683i
$455$	−0.0189871			−0.000890130
$456$		0			0
$457$	−38.4641			−1.79927			−0.899637	−	0.436638i	$-0.856169\pi$
$457$	−38.4641			−1.79927			−0.899637	+	0.436638i	$0.856169\pi$
$458$	3.90239	−	1.42035i	0.182347	−	0.0663687i
$459$		0			0
$460$	8.70836	−	7.30718i	0.406030	−	0.340699i
$461$	−26.0330	−	21.8442i	−1.21248	−	1.01739i	−0.999184	−	0.0403991i	$-0.987137\pi$
$461$	−26.0330	−	21.8442i	−1.21248	−	1.01739i	−0.213292	−	0.976989i	$-0.568418\pi$
$462$		0			0
$463$	2.69723	+	4.67174i	0.125351	+	0.217114i	0.921870	−	0.387499i	$-0.126661\pi$
$463$	2.69723	+	4.67174i	0.125351	+	0.217114i	−0.796519	+	0.604613i	$0.793328\pi$
$464$	−8.26981	+	14.3237i	−0.383916	+	0.664963i
$465$		0			0
$466$	3.24660	+	1.18167i	0.150396	+	0.0547396i
$467$	11.2144	−	19.4240i	0.518942	−	0.898834i	−0.480815	−	0.876822i	$-0.659659\pi$
$467$	11.2144	−	19.4240i	0.518942	−	0.898834i	0.999758	−	0.0220125i	$-0.00700736\pi$
$468$		0			0
$469$	0.154572	+	0.876620i	0.00713746	+	0.0404786i
$470$	−1.79741	−	1.50821i	−0.0829083	−	0.0695683i
$471$		0			0
$472$	2.17947	−	12.3604i	0.100318	−	0.568934i
$473$	7.74452	−	2.81878i	0.356093	−	0.129607i
$474$		0			0
$475$	4.35447	+	0.196468i	0.199797	+	0.00901455i
$476$	−0.427246			−0.0195828
$477$		0			0
$478$	1.08723	−	6.16597i	0.0497286	−	0.282025i
$479$	22.0166	−	18.4741i	1.00596	−	0.844104i	0.0181649	−	0.999835i	$-0.494218\pi$
$479$	22.0166	−	18.4741i	1.00596	−	0.844104i	0.987800	+	0.155731i	$0.0497732\pi$
$480$		0			0
$481$	0.0681522	+	0.386510i	0.00310747	+	0.0176233i
$482$	0.592033	+	1.02543i	0.0269664	+	0.0467071i
$483$		0			0
$484$	0.600609	+	0.218604i	0.0273004	+	0.00993653i
$485$	15.7991	+	5.75040i	0.717400	+	0.261112i
$486$		0			0
$487$	17.2221	+	29.8295i	0.780406	+	1.35170i	0.931705	+	0.363215i	$0.118321\pi$
$487$	17.2221	+	29.8295i	0.780406	+	1.35170i	−0.151299	+	0.988488i	$0.548346\pi$
$488$	0.206468	+	1.17094i	0.00934637	+	0.0530059i
$489$		0			0
$490$	1.64965	−	1.38422i	0.0745237	−	0.0625328i
$491$	3.36638	−	19.0917i	0.151923	−	0.861596i	−0.809623	−	0.586950i	$-0.800328\pi$
$491$	3.36638	−	19.0917i	0.151923	−	0.861596i	0.961546	−	0.274645i	$-0.0885605\pi$
$492$		0			0
$493$	12.0890			0.544462
$494$	−0.272674	+	0.0855378i	−0.0122682	+	0.00384853i
$495$		0			0
$496$	−26.0796	+	9.49218i	−1.17101	+	0.426212i
$497$	−0.0956766	+	0.542609i	−0.00429168	+	0.0243393i
$498$		0			0
$499$	8.63214	+	7.24323i	0.386428	+	0.324251i	0.815220	−	0.579152i	$-0.196616\pi$
$499$	8.63214	+	7.24323i	0.386428	+	0.324251i	−0.428792	+	0.903403i	$0.641061\pi$
$500$	0.330825	+	1.87620i	0.0147949	+	0.0839062i
$501$		0			0
$502$	−1.22237	+	2.11720i	−0.0545570	+	0.0944955i
$503$	9.95307	+	3.62262i	0.443785	+	0.161525i	0.554241	−	0.832356i	$-0.313009\pi$
$503$	9.95307	+	3.62262i	0.443785	+	0.161525i	−0.110455	+	0.993881i	$0.535231\pi$
$504$		0			0
$505$	−1.83986	+	3.18674i	−0.0818728	+	0.141808i
$506$	−3.09371	−	5.35846i	−0.137532	−	0.238213i
$507$		0			0
$508$	−30.9574	−	25.9764i	−1.37351	−	1.15251i
$509$	1.66949	−	1.40087i	0.0739990	−	0.0620925i	−0.605038	−	0.796197i	$-0.706842\pi$
$509$	1.66949	−	1.40087i	0.0739990	−	0.0620925i	0.679037	+	0.734104i	$0.262398\pi$
$510$		0			0
$511$	−1.31969	+	0.480330i	−0.0583799	+	0.0212485i
$512$	20.1933			0.892426
$513$		0			0
$514$	−7.46186			−0.329129
$515$	−3.32106	+	1.20877i	−0.146343	+	0.0532647i
$516$		0			0
$517$	19.6487	−	16.4872i	0.864147	−	0.725106i
$518$	0.0387997	+	0.0325568i	0.00170476	+	0.00143046i
$519$		0			0
$520$	−0.128013	−	0.221726i	−0.00561376	−	0.00972332i
$521$	−5.72367	+	9.91369i	−0.250759	+	0.434327i	−0.963735	−	0.266862i	$-0.914013\pi$
$521$	−5.72367	+	9.91369i	−0.250759	+	0.434327i	0.712976	+	0.701188i	$0.247347\pi$
$522$		0			0
$523$	9.16414	+	3.33548i	0.400720	+	0.145850i	0.534515	−	0.845159i	$-0.320494\pi$
$523$	9.16414	+	3.33548i	0.400720	+	0.145850i	−0.133795	+	0.991009i	$0.542716\pi$
$524$	−6.62108	+	11.4680i	−0.289243	+	0.500984i
$525$		0			0
$526$	0.661953	+	3.75412i	0.0288625	+	0.163688i
$527$	15.5394	+	13.0391i	0.676906	+	0.567991i
$528$		0			0
$529$	2.18882	−	12.4134i	0.0951661	−	0.539714i
$530$	2.43098	−	0.884806i	0.105595	−	0.0384335i
$531$		0			0
$532$	0.398893	−	0.624130i	0.0172942	−	0.0270595i
$533$	0.641237			0.0277750
$534$		0			0
$535$	−0.327605	+	1.85794i	−0.0141636	+	0.0803257i
$536$	−9.19476	+	7.71532i	−0.397153	+	0.333251i
$537$		0			0
$538$	1.30382	+	7.39433i	0.0562117	+	0.318792i
$539$	11.7705	+	20.3871i	0.506991	+	0.878133i
$540$		0			0
$541$	−21.4401	−	7.80354i	−0.921780	−	0.335501i	−0.162834	−	0.986654i	$-0.552063\pi$
$541$	−21.4401	−	7.80354i	−0.921780	−	0.335501i	−0.758947	+	0.651153i	$0.774286\pi$
$542$	−5.04110	−	1.83481i	−0.216534	−	0.0788118i
$543$		0			0
$544$	−4.35580	−	7.54446i	−0.186753	−	0.323466i
$545$	2.28519	+	12.9599i	0.0978867	+	0.555143i
$546$		0			0
$547$	23.6840	−	19.8732i	1.01265	−	0.849716i	0.0239661	−	0.999713i	$-0.492371\pi$
$547$	23.6840	−	19.8732i	1.01265	−	0.849716i	0.988687	+	0.149996i	$0.0479262\pi$
$548$	6.94958	−	39.4130i	0.296871	−	1.68364i
$549$		0			0
$550$	1.03694			0.0442153
$551$	−11.2867	+	17.6599i	−0.480831	+	0.752337i
$552$		0			0
$553$	0.0862049	−	0.0313760i	0.00366581	−	0.00133424i
$554$	1.11156	−	6.30396i	0.0472256	−	0.267830i
$555$		0			0
$556$	−22.9442	−	19.2525i	−0.973051	−	0.816486i
$557$	1.70677	+	9.67955i	0.0723180	+	0.410136i	0.999379	+	0.0352261i	$0.0112151\pi$
$557$	1.70677	+	9.67955i	0.0723180	+	0.410136i	−0.927061	+	0.374910i	$0.877674\pi$
$558$		0			0
$559$	0.260539	−	0.451267i	0.0110196	−	0.0190866i
$560$	0.288318	+	0.104939i	0.0121836	+	0.00443448i
$561$		0			0
$562$	−0.925485	+	1.60299i	−0.0390392	+	0.0676179i
$563$	16.7096	+	28.9420i	0.704228	+	1.21976i	0.966970	+	0.254892i	$0.0820398\pi$
$563$	16.7096	+	28.9420i	0.704228	+	1.21976i	−0.262742	+	0.964866i	$0.584627\pi$
$564$		0			0
$565$	9.45729	+	7.93561i	0.397871	+	0.333854i
$566$	2.73065	−	2.29129i	0.114778	−	0.0963099i
$567$		0			0
$568$	−6.98148	+	2.54105i	−0.292936	+	0.106620i
$569$	−37.6326			−1.57764			−0.788820	−	0.614624i	$-0.789308\pi$
$569$	−37.6326			−1.57764			−0.788820	+	0.614624i	$0.789308\pi$
$570$		0			0
$571$	−2.75232			−0.115181			−0.0575904	−	0.998340i	$-0.518342\pi$
$571$	−2.75232			−0.115181			−0.0575904	+	0.998340i	$0.518342\pi$
$572$	1.28306	−	0.466997i	0.0536476	−	0.0195261i
$573$		0			0
$574$	0.0633924	−	0.0531925i	0.00264595	−	0.00222021i
$575$	4.57098	+	3.83550i	0.190623	+	0.159952i
$576$		0			0
$577$	−0.0185500	−	0.0321295i	−0.000772245	−	0.00133757i	0.865639	−	0.500669i	$-0.166912\pi$
$577$	−0.0185500	−	0.0321295i	−0.000772245	−	0.00133757i	−0.866411	+	0.499331i	$0.833579\pi$
$578$	1.64445	−	2.84827i	0.0684000	−	0.118472i
$579$		0			0
$580$	−8.60793	−	3.13303i	−0.357425	−	0.130092i
$581$	0.800032	−	1.38570i	0.0331909	−	0.0574884i
$582$		0			0
$583$	4.91080	+	27.8505i	0.203385	+	1.15345i
$584$	−14.5067	−	12.1725i	−0.600291	−	0.503704i
$585$		0			0
$586$	−0.934287	+	5.29861i	−0.0385951	+	0.218883i
$587$	−3.38927	+	1.23359i	−0.139890	+	0.0509158i	−0.411016	−	0.911628i	$-0.634826\pi$
$587$	−3.38927	+	1.23359i	−0.139890	+	0.0509158i	0.271126	+	0.962544i	$0.412604\pi$
$588$		0			0
$589$	−33.5559	+	10.5265i	−1.38265	+	0.433736i
$590$	3.21399			0.132318
$591$		0			0
$592$	1.10130	−	6.24578i	0.0452632	−	0.256700i
$593$	−13.6689	+	11.4696i	−0.561314	+	0.470998i	−0.878751	−	0.477281i	$-0.841622\pi$
$593$	−13.6689	+	11.4696i	−0.561314	+	0.470998i	0.317437	+	0.948279i	$0.397178\pi$
$594$		0			0
$595$	−0.0389422	−	0.220852i	−0.00159647	−	0.00905406i
$596$	18.5936	+	32.2051i	0.761625	+	1.31917i
$597$		0			0
$598$	−0.367612	−	0.133800i	−0.0150328	−	0.00547148i
$599$	−20.6214	−	7.50558i	−0.842568	−	0.306670i	−0.115561	−	0.993300i	$-0.536867\pi$
$599$	−20.6214	−	7.50558i	−0.842568	−	0.306670i	−0.727006	+	0.686631i	$0.759089\pi$
$600$		0			0
$601$	−5.14039	−	8.90342i	−0.209681	−	0.363178i	0.741933	−	0.670474i	$-0.233909\pi$
$601$	−5.14039	−	8.90342i	−0.209681	−	0.363178i	−0.951614	+	0.307296i	$0.900576\pi$
$602$	−0.0116772	−	0.0662246i	−0.000475926	−	0.00269911i
$603$		0			0
$604$	−16.3871	+	13.7504i	−0.666780	+	0.559495i
$605$	−0.0582570	+	0.330392i	−0.00236849	+	0.0134323i
$606$		0			0
$607$	32.2616			1.30946			0.654729	−	0.755864i	$-0.272783\pi$
$607$	32.2616			1.30946			0.654729	+	0.755864i	$0.272783\pi$
$608$	15.0879	+	0.680743i	0.611893	+	0.0276078i
$609$		0			0
$610$	−0.286109	+	0.104135i	−0.0115842	+	0.00421631i
$611$	0.281607	−	1.59707i	0.0113926	−	0.0646107i
$612$		0			0
$613$	−12.5598	−	10.5389i	−0.507286	−	0.425664i	0.352887	−	0.935666i	$-0.385200\pi$
$613$	−12.5598	−	10.5389i	−0.507286	−	0.425664i	−0.860173	+	0.510002i	$0.829645\pi$
$614$	1.58591	+	8.99412i	0.0640019	+	0.362973i
$615$		0			0
$616$	0.180595	−	0.312800i	0.00727639	−	0.0126031i
$617$	−12.0063	−	4.36994i	−0.483356	−	0.175927i	0.0888371	−	0.996046i	$-0.471685\pi$
$617$	−12.0063	−	4.36994i	−0.483356	−	0.175927i	−0.572193	+	0.820119i	$0.693907\pi$
$618$		0			0
$619$	−2.14103	+	3.70838i	−0.0860555	+	0.149052i	−0.905840	−	0.423619i	$-0.860760\pi$
$619$	−2.14103	+	3.70838i	−0.0860555	+	0.149052i	0.819785	+	0.572671i	$0.194093\pi$
$620$	−7.68549	−	13.3117i	−0.308657	−	0.534609i
$621$		0			0
$622$	2.74210	+	2.30089i	0.109948	+	0.0922575i
$623$	−0.0448474	+	0.0376314i	−0.00179677	+	0.00150767i
$624$		0			0
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	−0.146252			−0.00584542
$627$		0			0
$628$	−8.78807			−0.350682
$629$	−4.35599	+	1.58545i	−0.173685	+	0.0632160i
$630$		0			0
$631$	−17.4565	+	14.6477i	−0.694933	+	0.583118i	−0.920327	−	0.391150i	$-0.872077\pi$
$631$	−17.4565	+	14.6477i	−0.694933	+	0.583118i	0.225394	+	0.974268i	$0.427633\pi$
$632$	0.947603	+	0.795133i	0.0376936	+	0.0316287i
$633$		0			0
$634$	−3.11503	−	5.39540i	−0.123714	−	0.214279i
$635$	10.6060	−	18.3702i	0.420888	−	0.728999i
$636$		0			0
$637$	1.39863	+	0.509061i	0.0554159	+	0.0201698i
$638$	−2.49293	+	4.31788i	−0.0986959	+	0.170946i
$639$		0			0
$640$	1.51422	+	8.58755i	0.0598547	+	0.339453i
$641$	24.0251	+	20.1595i	0.948935	+	0.796251i	0.979118	−	0.203293i	$-0.0651645\pi$
$641$	24.0251	+	20.1595i	0.948935	+	0.796251i	−0.0301829	+	0.999544i	$0.509609\pi$
$642$		0			0
$643$	−1.93601	+	10.9796i	−0.0763487	+	0.432995i	0.922542	+	0.385898i	$0.126108\pi$
$643$	−1.93601	+	10.9796i	−0.0763487	+	0.432995i	−0.998890	+	0.0470972i	$0.985003\pi$
$644$	0.952825	−	0.346800i	0.0375466	−	0.0136658i
$645$		0			0
$646$	−1.55420	−	2.99622i	−0.0611491	−	0.117885i
$647$	17.5536			0.690102			0.345051	−	0.938584i	$-0.387862\pi$
$647$	17.5536			0.690102			0.345051	+	0.938584i	$0.387862\pi$
$648$		0			0
$649$	−6.10100	+	34.6005i	−0.239485	+	1.35819i
$650$	0.0502230	−	0.0421421i	0.00196991	−	0.00165295i
$651$		0			0
$652$	0.190136	+	1.07832i	0.00744632	+	0.0422302i
$653$	−1.04766	−	1.81461i	−0.0409983	−	0.0710111i	0.844798	−	0.535085i	$-0.179720\pi$
$653$	−1.04766	−	1.81461i	−0.0409983	−	0.0710111i	−0.885796	+	0.464074i	$0.846387\pi$
$654$		0			0
$655$	−6.53156	−	2.37729i	−0.255209	−	0.0928885i
$656$	−9.73711	−	3.54402i	−0.380170	−	0.138371i
$657$		0			0
$658$	−0.104642	−	0.181246i	−0.00407939	−	0.00706571i
$659$	2.25744	+	12.8026i	0.0879373	+	0.498717i	0.996684	+	0.0813691i	$0.0259292\pi$
$659$	2.25744	+	12.8026i	0.0879373	+	0.498717i	−0.908747	+	0.417348i	$0.862960\pi$
$660$		0			0
$661$	29.1833	−	24.4877i	1.13510	−	0.952462i	0.135833	−	0.990732i	$-0.456629\pi$
$661$	29.1833	−	24.4877i	1.13510	−	0.952462i	0.999267	+	0.0382694i	$0.0121845\pi$
$662$	−0.321588	+	1.82382i	−0.0124989	+	0.0708846i
$663$		0			0
$664$	21.5756			0.837298
$665$	0.358984	+	0.149308i	0.0139208	+	0.00578992i
$666$		0			0
$667$	−26.9604	+	9.81278i	−1.04391	+	0.379952i
$668$	1.36367	−	7.73373i	0.0527618	−	0.299227i
$669$		0			0
$670$	−2.35452	−	1.97568i	−0.0909632	−	0.0763272i
$671$	−0.577966	−	3.27781i	−0.0223121	−	0.126538i
$672$		0			0
$673$	−16.9749	+	29.4013i	−0.654333	+	1.13334i	0.327728	+	0.944772i	$0.393717\pi$
$673$	−16.9749	+	29.4013i	−0.654333	+	1.13334i	−0.982061	+	0.188566i	$0.939616\pi$
$674$	2.56633	+	0.934069i	0.0988514	+	0.0359790i
$675$		0			0
$676$	−12.3403	+	21.3740i	−0.474626	+	0.822076i
$677$	−8.27810	−	14.3381i	−0.318153	−	0.551058i	0.661949	−	0.749549i	$-0.269729\pi$
$677$	−8.27810	−	14.3381i	−0.318153	−	0.551058i	−0.980103	+	0.198491i	$0.936396\pi$
$678$		0			0
$679$	1.14880	+	0.963959i	0.0440870	+	0.0369934i
$680$	2.31649	−	1.94377i	0.0888334	−	0.0745401i
$681$		0			0
$682$	−7.86166	+	2.86141i	−0.301038	+	0.109569i
$683$	−5.33328			−0.204072			−0.102036	−	0.994781i	$-0.532536\pi$
$683$	−5.33328			−0.204072			−0.102036	+	0.994781i	$0.532536\pi$
$684$		0			0
$685$	21.0068			0.802630
$686$	0.361199	−	0.131466i	0.0137906	−	0.00501938i
$687$		0			0
$688$	−6.45035	+	5.41248i	−0.245917	+	0.206349i
$689$	1.36972	+	1.14933i	0.0521820	+	0.0437859i
$690$		0			0
$691$	7.06510	+	12.2371i	0.268769	+	0.465522i	0.968544	−	0.248842i	$-0.0800498\pi$
$691$	7.06510	+	12.2371i	0.268769	+	0.465522i	−0.699775	+	0.714363i	$0.746717\pi$
$692$	6.12940	−	10.6164i	0.233005	−	0.403576i
$693$		0			0
$694$	5.77995	+	2.10373i	0.219404	+	0.0798565i
$695$	7.86070	−	13.6151i	0.298173	−	0.516451i
$696$		0			0
$697$	1.31516	+	7.45866i	0.0498153	+	0.282517i
$698$	−0.191156	−	0.160399i	−0.00723536	−	0.00607119i
$699$		0			0
$700$	−0.0295082	+	0.167349i	−0.00111531	+	0.00632521i
$701$	−35.8607	+	13.0522i	−1.35444	+	0.492976i	−0.914331	−	0.404967i	$-0.867283\pi$
$701$	−35.8607	+	13.0522i	−1.35444	+	0.492976i	−0.440110	+	0.897944i	$0.645061\pi$
$702$		0			0
$703$	1.75085	−	7.84355i	0.0660345	−	0.295825i
$704$	−19.5699			−0.737567
$705$		0			0
$706$	1.12046	−	6.35442i	0.0421689	−	0.239152i
$707$	−0.251428	+	0.210973i	−0.00945594	+	0.00793447i
$708$		0			0
$709$	5.75948	+	32.6636i	0.216302	+	1.22671i	0.878633	+	0.477497i	$0.158456\pi$
$709$	5.75948	+	32.6636i	0.216302	+	1.22671i	−0.662331	+	0.749211i	$0.730433\pi$
$710$	−0.951250	−	1.64761i	−0.0356998	−	0.0618339i
$711$		0			0
$712$	−0.741814	−	0.269998i	−0.0278007	−	0.0101186i
$713$	−45.2392	−	16.4657i	−1.69422	−	0.616646i
$714$		0			0
$715$	0.358348	+	0.620676i	0.0134014	+	0.0232120i
$716$	1.26716	+	7.18644i	0.0473561	+	0.268570i
$717$		0			0
$718$	−6.06391	+	5.08822i	−0.226303	+	0.189891i
$719$	−7.35244	+	41.6978i	−0.274200	+	1.55506i	0.467292	+	0.884103i	$0.345230\pi$
$719$	−7.35244	+	41.6978i	−0.274200	+	1.55506i	−0.741492	+	0.670962i	$0.765881\pi$
$720$		0			0
$721$	−0.315236			−0.0117400
$722$	5.82800	+	0.526975i	0.216896	+	0.0196120i
$723$		0			0
$724$	29.8752	−	10.8737i	1.11030	−	0.404118i
$725$	0.834940	−	4.73518i	0.0310089	−	0.175860i
$726$		0			0
$727$	−3.21863	−	2.70075i	−0.119372	−	0.100165i	0.581147	−	0.813798i	$-0.302604\pi$
$727$	−3.21863	−	2.70075i	−0.119372	−	0.100165i	−0.700520	+	0.713633i	$0.747048\pi$
$728$	−0.00396552	−	0.0224896i	−0.000146972	−	0.000833520i
$729$		0			0
$730$	2.42464	−	4.19960i	0.0897399	−	0.155434i
$731$	5.78336	+	2.10497i	0.213905	+	0.0778551i
$732$		0			0
$733$	−8.46787	+	14.6668i	−0.312768	+	0.541730i	−0.978960	−	0.204050i	$-0.934590\pi$
$733$	−8.46787	+	14.6668i	−0.312768	+	0.541730i	0.666193	+	0.745780i	$0.267923\pi$
$734$	3.73990	+	6.47769i	0.138042	+	0.239096i
$735$		0			0
$736$	15.8380	+	13.2897i	0.583798	+	0.489864i
$737$	25.7388	−	21.5975i	0.948103	−	0.795553i
$738$		0			0
$739$	−19.5893	+	7.12993i	−0.720605	+	0.262279i	−0.676183	−	0.736734i	$-0.736367\pi$
$739$	−19.5893	+	7.12993i	−0.720605	+	0.262279i	−0.0444223	+	0.999013i	$0.514145\pi$
$740$	3.51255			0.129124
$741$		0			0
$742$	0.230750			0.00847109
$743$	42.6150	−	15.5106i	1.56339	−	0.569028i	0.591881	−	0.806025i	$-0.298385\pi$
$743$	42.6150	−	15.5106i	1.56339	−	0.569028i	0.971510	+	0.236997i	$0.0761633\pi$
$744$		0			0
$745$	−14.9527	+	12.5468i	−0.547826	+	0.459680i
$746$	2.56715	+	2.15410i	0.0939901	+	0.0788671i
$747$		0			0
$748$	8.06349	+	13.9664i	0.294831	+	0.510661i
$749$	−0.0841385	+	0.145732i	−0.00307435	+	0.00532494i
$750$		0			0
$751$	8.15355	+	2.96765i	0.297527	+	0.108291i	0.486471	−	0.873697i	$-0.338284\pi$
$751$	8.15355	+	2.96765i	0.297527	+	0.108291i	−0.188943	+	0.981988i	$0.560506\pi$
$752$	−13.1030	+	22.6950i	−0.477816	+	0.827601i
$753$		0			0
$754$	0.0547399	+	0.310445i	0.00199351	+	0.0113058i
$755$	−8.60149	−	7.21751i	−0.313040	−	0.262672i
$756$		0			0
$757$	1.74973	−	9.92320i	0.0635950	−	0.360665i	−0.936359	−	0.351045i	$-0.885827\pi$
$757$	1.74973	−	9.92320i	0.0635950	−	0.360665i	0.999954	−	0.00962040i	$-0.00306232\pi$
$758$	−5.59490	+	2.03638i	−0.203216	+	0.0739645i
$759$		0			0
$760$	0.676736	+	5.19875i	0.0245478	+	0.188579i
$761$	−4.52014			−0.163855			−0.0819275	−	0.996638i	$-0.526108\pi$
$761$	−4.52014			−0.163855			−0.0819275	+	0.996638i	$0.526108\pi$
$762$		0			0
$763$	−0.203829	+	1.15597i	−0.00737912	+	0.0418491i
$764$	11.5688	−	9.70735i	0.418543	−	0.351200i
$765$		0			0
$766$	0.0557839	+	0.316366i	0.00201556	+	0.0114308i
$767$	1.11070	+	1.92378i	0.0401049	+	0.0694637i
$768$		0			0
$769$	37.1897	+	13.5360i	1.34110	+	0.488119i	0.910158	−	0.414262i	$-0.135960\pi$
$769$	37.1897	+	13.5360i	1.34110	+	0.488119i	0.430939	+	0.902381i	$0.358182\pi$
$770$	0.0869131	+	0.0316338i	0.00313213	+	0.00114000i
$771$		0			0
$772$	−20.2582	−	35.0883i	−0.729110	−	1.26286i
$773$	4.08049	+	23.1416i	0.146765	+	0.832347i	0.965933	+	0.258793i	$0.0833246\pi$
$773$	4.08049	+	23.1416i	0.146765	+	0.832347i	−0.819168	+	0.573554i	$0.805564\pi$
$774$		0			0
$775$	6.18056	−	5.18611i	0.222012	−	0.186290i
$776$	−3.51146	+	19.9145i	−0.126054	+	0.714888i
$777$		0			0
$778$	−8.19345			−0.293749
$779$	−12.1237	−	5.04246i	−0.434375	−	0.180665i
$780$		0			0
$781$	19.5432	−	7.11316i	0.699312	−	0.254529i
$782$	0.802352	−	4.55036i	0.0286920	−	0.162721i
$783$		0			0
$784$	−18.4246	−	15.4601i	−0.658022	−	0.552146i
$785$	−0.801006	−	4.54273i	−0.0285891	−	0.162137i
$786$		0			0
$787$	−3.76242	+	6.51669i	−0.134116	+	0.232295i	−0.925259	−	0.379335i	$-0.876153\pi$
$787$	−3.76242	+	6.51669i	−0.134116	+	0.232295i	0.791144	+	0.611630i	$0.209486\pi$
$788$	−5.16921	−	1.88144i	−0.184145	−	0.0670235i
$789$		0			0
$790$	−0.158382	+	0.274326i	−0.00563498	+	0.00976006i
$791$	0.550589	+	0.953649i	0.0195767	+	0.0339078i
$792$		0			0
$793$	−0.161206	−	0.135268i	−0.00572458	−	0.00480349i
$794$	−0.872376	+	0.732010i	−0.0309595	+	0.0259781i
$795$		0			0
$796$	20.7935	−	7.56821i	0.737006	−	0.268248i
$797$	18.7858			0.665426			0.332713	−	0.943028i	$-0.392036\pi$
$797$	18.7858			0.665426			0.332713	+	0.943028i	$0.392036\pi$
$798$		0			0
$799$	19.1542			0.677627
$800$	−3.25595	+	1.18507i	−0.115115	+	0.0418985i
$801$		0			0
$802$	4.77411	−	4.00596i	0.168580	−	0.141455i
$803$	40.6085	+	34.0746i	1.43304	+	1.20247i
$804$		0			0
$805$	0.266115	+	0.460925i	0.00937933	+	0.0162455i
$806$	−0.264480	+	0.458092i	−0.00931590	+	0.0161356i
$807$		0			0
$808$	−4.15884	−	1.51369i	−0.146308	−	0.0532516i
$809$	−9.74651	+	16.8815i	−0.342669	+	0.593520i	−0.984927	−	0.172968i	$-0.944664\pi$
$809$	−9.74651	+	16.8815i	−0.342669	+	0.593520i	0.642258	+	0.766488i	$0.277998\pi$
$810$		0			0
$811$	2.64049	+	14.9750i	0.0927201	+	0.525842i	0.995422	+	0.0955756i	$0.0304692\pi$
$811$	2.64049	+	14.9750i	0.0927201	+	0.525842i	−0.902702	+	0.430266i	$0.858420\pi$
$812$	−0.625910	−	0.525201i	−0.0219651	−	0.0184309i
$813$		0			0
$814$	0.331986	−	1.88279i	0.0116361	−	0.0659916i
$815$	−0.540074	+	0.196571i	−0.0189180	+	0.00688558i
$816$		0			0
$817$	−8.47454	+	6.48318i	−0.296487	+	0.226818i
$818$	3.84272			0.134357
$819$		0			0
$820$	0.996556	−	5.65175i	0.0348012	−	0.197368i
$821$	20.5043	−	17.2051i	0.715604	−	0.600463i	−0.210562	−	0.977581i	$-0.567529\pi$
$821$	20.5043	−	17.2051i	0.715604	−	0.600463i	0.926165	+	0.377118i	$0.123085\pi$
$822$		0			0
$823$	4.80109	+	27.2284i	0.167356	+	0.949121i	0.946602	+	0.322404i	$0.104491\pi$
$823$	4.80109	+	27.2284i	0.167356	+	0.949121i	−0.779247	+	0.626717i	$0.784398\pi$
$824$	−2.12536	−	3.68123i	−0.0740404	−	0.128242i
$825$		0			0
$826$	0.269386	+	0.0980486i	0.00937314	+	0.00341155i
$827$	12.0489	+	4.38543i	0.418980	+	0.152496i	0.542903	−	0.839796i	$-0.317325\pi$
$827$	12.0489	+	4.38543i	0.418980	+	0.152496i	−0.123923	+	0.992292i	$0.539547\pi$
$828$		0			0
$829$	−22.7266	−	39.3636i	−0.789326	−	1.36715i	−0.926380	−	0.376590i	$-0.877097\pi$
$829$	−22.7266	−	39.3636i	−0.789326	−	1.36715i	0.137054	−	0.990564i	$-0.456237\pi$
$830$	0.959394	+	5.44100i	0.0333011	+	0.188860i
$831$		0			0
$832$	−0.947842	+	0.795334i	−0.0328605	+	0.0275732i
$833$	−3.05267	+	17.3126i	−0.105769	+	0.599844i
$834$		0			0
$835$	4.12202			0.142648
$836$	−27.9308	−	1.26020i	−0.966006	−	0.0435849i
$837$		0			0
$838$	8.39192	−	3.05441i	0.289894	−	0.105513i
$839$	−4.04829	+	22.9590i	−0.139762	+	0.792632i	0.831662	+	0.555282i	$0.187390\pi$
$839$	−4.04829	+	22.9590i	−0.139762	+	0.792632i	−0.971424	+	0.237350i	$0.923721\pi$
$840$		0			0
$841$	−4.50505	−	3.78019i	−0.155347	−	0.130351i
$842$	0.780620	+	4.42712i	0.0269019	+	0.152569i
$843$		0			0
$844$	−22.5760	+	39.1028i	−0.777098	+	1.34597i
$845$	−12.1734	−	4.43076i	−0.418778	−	0.152423i
$846$		0			0
$847$	−0.0149621	+	0.0259151i	−0.000514104	+	0.000890455i
$848$	−14.4468	−	25.0226i	−0.496106	−	0.859281i
$849$		0			0
$850$	0.593190	+	0.497745i	0.0203462	+	0.0170725i
$851$	8.42760	−	7.07160i	0.288894	−	0.242411i
$852$		0			0
$853$	43.0221	−	15.6588i	1.47305	−	0.536146i	0.524122	−	0.851643i	$-0.324393\pi$
$853$	43.0221	−	15.6588i	1.47305	−	0.536146i	0.948927	+	0.315497i	$0.102171\pi$
$854$	−0.0271576			−0.000929312
$855$		0			0
$856$	−2.26909			−0.0775558
$857$	6.06004	−	2.20568i	0.207007	−	0.0753444i	−0.236436	−	0.971647i	$-0.575979\pi$
$857$	6.06004	−	2.20568i	0.207007	−	0.0753444i	0.443443	+	0.896303i	$0.353757\pi$
$858$		0			0
$859$	−11.1359	+	9.34415i	−0.379953	+	0.318818i	−0.812684	−	0.582705i	$-0.801994\pi$
$859$	−11.1359	+	9.34415i	−0.379953	+	0.318818i	0.432731	+	0.901523i	$0.357550\pi$
$860$	−3.57248	−	2.99767i	−0.121821	−	0.102220i
$861$		0			0
$862$	2.08017	+	3.60296i	0.0708509	+	0.122717i
$863$	−2.28568	+	3.95891i	−0.0778054	+	0.134763i	−0.902303	−	0.431103i	$-0.858125\pi$
$863$	−2.28568	+	3.95891i	−0.0778054	+	0.134763i	0.824497	+	0.565866i	$0.191458\pi$
$864$		0			0
$865$	6.04652	+	2.20075i	0.205588	+	0.0748279i
$866$	−5.85494	+	10.1411i	−0.198959	+	0.344607i
$867$		0			0
$868$	−0.238077	−	1.35020i	−0.00808085	−	0.0458288i
$869$	−2.65262	−	2.22581i	−0.0899841	−	0.0755056i
$870$		0			0
$871$	0.368892	−	2.09209i	0.0124994	−	0.0708879i
$872$	−14.8733	+	5.41346i	−0.503675	+	0.183323i
$873$		0			0
$874$	5.89817	+	5.42048i	0.199508	+	0.183351i
$875$	−0.0891959			−0.00301537
$876$		0			0
$877$	5.72291	−	32.4562i	0.193249	−	1.09597i	−0.721641	−	0.692267i	$-0.756612\pi$
$877$	5.72291	−	32.4562i	0.193249	−	1.09597i	0.914890	−	0.403702i	$-0.132277\pi$
$878$	−5.61213	+	4.70913i	−0.189400	+	0.158926i
$879$		0			0
$880$	−2.01109	−	11.4054i	−0.0677937	−	0.384477i
$881$	−8.12066	−	14.0654i	−0.273592	−	0.473875i	0.696187	−	0.717860i	$-0.254878\pi$
$881$	−8.12066	−	14.0654i	−0.273592	−	0.473875i	−0.969779	+	0.243985i	$0.921545\pi$
$882$		0			0
$883$	26.7945	+	9.75238i	0.901705	+	0.328194i	0.750936	−	0.660375i	$-0.229603\pi$
$883$	26.7945	+	9.75238i	0.901705	+	0.328194i	0.150769	+	0.988569i	$0.451825\pi$
$884$	0.958150	+	0.348738i	0.0322261	+	0.0117293i
$885$		0			0
$886$	−2.97195	−	5.14757i	−0.0998447	−	0.172936i
$887$	−6.70894	−	38.0483i	−0.225264	−	1.27754i	−0.862180	−	0.506602i	$-0.830901\pi$
$887$	−6.70894	−	38.0483i	−0.225264	−	1.27754i	0.636916	−	0.770933i	$-0.280210\pi$
$888$		0			0
$889$	1.44938	−	1.21617i	0.0486106	−	0.0407891i
$890$	0.0351029	−	0.199078i	0.00117665	−	0.00667312i
$891$		0			0
$892$	16.7955			0.562355
$893$	−17.8831	+	27.9809i	−0.598435	+	0.936345i
$894$		0			0
$895$	−3.59932	+	1.31005i	−0.120312	+	0.0437900i
$896$	−0.135062	+	0.765974i	−0.00451210	+	0.0255894i
$897$		0			0
$898$	6.23184	+	5.22913i	0.207959	+	0.174498i
$899$	6.73642	+	38.2042i	0.224672	+	1.27418i
$900$		0			0
$901$	−10.5594	+	18.2893i	−0.351783	+	0.609306i
$902$	−2.93524	−	1.06834i	−0.0977329	−	0.0355719i
$903$		0			0
$904$	−7.42428	+	12.8592i	−0.246928	+	0.427691i
$905$	8.34388	+	14.4520i	0.277360	+	0.480401i
$906$		0			0
$907$	21.9521	+	18.4200i	0.728908	+	0.611627i	0.929834	−	0.367980i	$-0.119951\pi$
$907$	21.9521	+	18.4200i	0.728908	+	0.611627i	−0.200926	+	0.979606i	$0.564395\pi$
$908$	−1.52527	+	1.27986i	−0.0506180	+	0.0424735i
$909$		0			0
$910$	0.00549515	−	0.00200007i	0.000182162	−	6.63017e-5i
$911$	47.5952			1.57690			0.788450	−	0.615099i	$-0.210884\pi$
$911$	47.5952			1.57690			0.788450	+	0.615099i	$0.210884\pi$
$912$		0			0
$913$	−60.3966			−1.99884
$914$	11.1321	−	4.05174i	0.368216	−	0.134020i
$915$		0			0
$916$	19.6785	−	16.5122i	0.650196	−	0.545579i
$917$	−0.474930	−	0.398514i	−0.0156836	−	0.0131601i
$918$		0			0
$919$	13.6098	+	23.5728i	0.448945	+	0.777596i	0.998318	−	0.0579814i	$-0.0184664\pi$
$919$	13.6098	+	23.5728i	0.448945	+	0.777596i	−0.549372	+	0.835578i	$0.685133\pi$
$920$	−3.58836	+	6.21522i	−0.118305	+	0.204910i
$921$		0			0
$922$	9.83534	+	3.57977i	0.323910	+	0.117894i
$923$	0.657469	−	1.13877i	0.0216408	−	0.0374830i
$924$		0			0
$925$	0.320159	+	1.81571i	0.0105268	+	0.0597002i
$926$	−1.27273	−	1.06795i	−0.0418245	−	0.0350949i
$927$		0			0
$928$	2.89300	−	16.4070i	0.0949672	−	0.538586i
$929$	−30.2956	+	11.0267i	−0.993967	+	0.361774i	−0.787255	−	0.616627i	$-0.788499\pi$
$929$	−30.2956	+	11.0267i	−0.993967	+	0.361774i	−0.206712	+	0.978402i	$0.566276\pi$
$930$		0			0
$931$	−22.4405	−	20.6230i	−0.735457	−	0.675893i
$932$	21.3716			0.700049
$933$		0			0
$934$	−1.19953	+	6.80288i	−0.0392499	+	0.222597i
$935$	−6.48455	+	5.44118i	−0.212067	+	0.177946i
$936$		0			0
$937$	3.15561	+	17.8964i	0.103089	+	0.584649i	0.991966	+	0.126503i	$0.0403753\pi$
$937$	3.15561	+	17.8964i	0.103089	+	0.584649i	−0.888877	+	0.458146i	$0.848514\pi$
$938$	−0.137077	−	0.237424i	−0.00447572	−	0.00775217i
$939$		0			0
$940$	−13.6387	−	4.96407i	−0.444845	−	0.161910i
$941$	22.1364	+	8.05700i	0.721627	+	0.262651i	0.676616	−	0.736336i	$-0.263446\pi$
$941$	22.1364	+	8.05700i	0.721627	+	0.262651i	0.0450107	+	0.998987i	$0.485668\pi$
$942$		0			0
$943$	−8.98729	−	15.5664i	−0.292666	−	0.506913i
$944$	−6.23334	−	35.3510i	−0.202878	−	1.15058i
$945$		0			0
$946$	−1.94445	+	1.63159i	−0.0632195	+	0.0530475i
$947$	1.46413	−	8.30348i	0.0475777	−	0.269827i	−0.951734	−	0.306924i	$-0.900700\pi$
$947$	1.46413	−	8.30348i	0.0475777	−	0.269827i	0.999312	+	0.0370976i	$0.0118113\pi$
$948$		0			0
$949$	3.35164			0.108799
$950$	−1.28094	+	0.401831i	−0.0415592	+	0.0130371i
$951$		0			0
$952$	0.253459	−	0.0922515i	0.00821465	−	0.00298989i
$953$	−8.69527	+	49.3134i	−0.281668	+	1.59742i	0.435284	+	0.900293i	$0.356648\pi$
$953$	−8.69527	+	49.3134i	−0.281668	+	1.59742i	−0.716952	+	0.697123i	$0.754463\pi$
$954$		0			0
$955$	6.07239	+	5.09534i	0.196498	+	0.164881i
$956$	−6.72533	−	38.1413i	−0.217513	−	1.23358i
$957$		0			0
$958$	−4.42589	+	7.66587i	−0.142994	+	0.247673i
$959$	1.76072	+	0.640851i	0.0568568	+	0.0206942i
$960$		0			0
$961$	−17.0475	+	29.5272i	−0.549920	+	0.952489i
$962$	−0.0604385	−	0.104683i	−0.00194862	−	0.00337510i
$963$		0			0
$964$	5.61078	+	4.70801i	0.180711	+	0.151635i
$965$	16.2914	−	13.6701i	0.524438	−	0.440056i
$966$		0			0
$967$	5.64610	−	2.05501i	0.181566	−	0.0660847i	−0.249637	−	0.968339i	$-0.580311\pi$
$967$	5.64610	−	2.05501i	0.181566	−	0.0660847i	0.431203	+	0.902255i	$0.358089\pi$
$968$	−0.403505			−0.0129692
$969$		0			0
$970$	−5.17822			−0.166263
$971$	33.8031	−	12.3033i	1.08479	−	0.394832i	0.263103	−	0.964768i	$-0.415254\pi$
$971$	33.8031	−	12.3033i	1.08479	−	0.394832i	0.821689	+	0.569936i	$0.193032\pi$
$972$		0			0
$973$	1.07421	−	0.901371i	0.0344377	−	0.0288966i
$974$	−8.12650	−	6.81894i	−0.260390	−	0.218493i
$975$		0			0
$976$	1.70029	+	2.94498i	0.0544248	+	0.0942666i
$977$	16.8174	−	29.1285i	0.538035	−	0.931905i	−0.460974	−	0.887413i	$-0.652500\pi$
$977$	16.8174	−	29.1285i	0.538035	−	0.931905i	0.999010	−	0.0444913i	$-0.0141667\pi$
$978$		0			0
$979$	2.07656	+	0.755805i	0.0663671	+	0.0241556i
$980$	6.66042	−	11.5362i	0.212759	−	0.368510i
$981$		0			0
$982$	1.03681	+	5.88002i	0.0330858	+	0.187639i
$983$	−34.5023	−	28.9508i	−1.10045	−	0.923388i	−0.102996	−	0.994682i	$-0.532843\pi$
$983$	−34.5023	−	28.9508i	−1.10045	−	0.923388i	−0.997455	+	0.0712938i	$0.977287\pi$
$984$		0			0
$985$	0.501396	−	2.84356i	0.0159758	−	0.0906033i
$986$	−3.49873	+	1.27343i	−0.111422	+	0.0405544i
$987$		0			0
$988$	−1.40401	+	1.07409i	−0.0446674	+	0.0341714i
$989$	−14.6064			−0.464457
$990$		0			0
$991$	−1.06445	+	6.03681i	−0.0338134	+	0.191765i	−0.997036	−	0.0769404i	$-0.975485\pi$
$991$	−1.06445	+	6.03681i	−0.0338134	+	0.191765i	0.963222	+	0.268706i	$0.0865960\pi$
$992$	21.4151	−	17.9694i	0.679930	−	0.570529i
$993$		0			0
$994$	−0.0294673	−	0.167117i	−0.000934645	−	0.00530064i
$995$	5.80743	+	10.0588i	0.184108	+	0.318884i
$996$		0			0
$997$	42.2085	+	15.3626i	1.33676	+	0.486539i	0.908789	−	0.417255i	$-0.137008\pi$
$997$	42.2085	+	15.3626i	1.33676	+	0.486539i	0.427967	+	0.903795i	$0.359230\pi$
$998$	−3.26125	−	1.18700i	−0.103233	−	0.0375738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.c.271.1		18
3.2	odd	2		95.2.k.a.81.3	yes	18
15.2	even	4		475.2.u.b.24.4		36
15.8	even	4		475.2.u.b.24.3		36
15.14	odd	2		475.2.l.c.176.1		18
19.4	even	9	inner	855.2.bs.c.631.1		18
57.2	even	18		1805.2.a.s.1.7		9
57.17	odd	18		1805.2.a.v.1.3		9
57.23	odd	18		95.2.k.a.61.3	✓	18
285.23	even	36		475.2.u.b.99.4		36
285.59	even	18		9025.2.a.cf.1.3		9
285.74	odd	18		9025.2.a.cc.1.7		9
285.137	even	36		475.2.u.b.99.3		36
285.194	odd	18		475.2.l.c.251.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.3	✓	18	57.23	odd	18
95.2.k.a.81.3	yes	18	3.2	odd	2
475.2.l.c.176.1		18	15.14	odd	2
475.2.l.c.251.1		18	285.194	odd	18
475.2.u.b.24.3		36	15.8	even	4
475.2.u.b.24.4		36	15.2	even	4
475.2.u.b.99.3		36	285.137	even	36
475.2.u.b.99.4		36	285.23	even	36
855.2.bs.c.271.1		18	1.1	even	1	trivial
855.2.bs.c.631.1		18	19.4	even	9	inner
1805.2.a.s.1.7		9	57.2	even	18
1805.2.a.v.1.3		9	57.17	odd	18
9025.2.a.cc.1.7		9	285.74	odd	18
9025.2.a.cf.1.3		9	285.59	even	18

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bs (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.289414 + 0.105338i) q^{2} +(-1.45942 + 1.22460i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.0445979 - 0.0772459i) q^{7} +(0.601369 - 1.04160i) q^{8} +O(q^{10})\)	\(q+(-0.289414 + 0.105338i) q^{2} +(-1.45942 + 1.22460i) q^{4} +(-0.766044 - 0.642788i) q^{5} +(-0.0445979 - 0.0772459i) q^{7} +(0.601369 - 1.04160i) q^{8} +(0.289414 + 0.105338i) q^{10} +(-1.68341 + 2.91575i) q^{11} +(0.0369645 + 0.209636i) q^{13} +(0.0210442 + 0.0176582i) q^{14} +(0.597325 - 3.38760i) q^{16} +(-2.36261 + 0.859918i) q^{17} +(0.949628 - 4.25420i) q^{19} +1.90514 q^{20} +(0.180063 - 1.02119i) q^{22} +(4.57098 - 3.83550i) q^{23} +(0.173648 + 0.984808i) q^{25} +(-0.0327807 - 0.0567779i) q^{26} +(0.159683 + 0.0581198i) q^{28} +(-4.51826 - 1.64451i) q^{29} +(-4.03407 - 6.98722i) q^{31} +(0.601676 + 3.41227i) q^{32} +(0.593190 - 0.497745i) q^{34} +(-0.0154887 + 0.0878408i) q^{35} +1.84372 q^{37} +(0.173294 + 1.33126i) q^{38} +(-1.13020 + 0.411361i) q^{40} +(0.523087 - 2.96657i) q^{41} +(-1.87518 - 1.57346i) q^{43} +(-1.11383 - 6.31683i) q^{44} +(-0.918881 + 1.59155i) q^{46} +(-7.15887 - 2.60562i) q^{47} +(3.49602 - 6.05529i) q^{49} +(-0.153994 - 0.266726i) q^{50} +(-0.310668 - 0.260681i) q^{52} +(6.43452 - 5.39920i) q^{53} +(3.16378 - 1.15152i) q^{55} -0.107279 q^{56} +1.48088 q^{58} +(9.80610 - 3.56913i) q^{59} +(-0.757296 + 0.635447i) q^{61} +(1.90354 + 1.59726i) q^{62} +(2.90628 + 5.03383i) q^{64} +(0.106435 - 0.184351i) q^{65} +(-9.37780 - 3.41324i) q^{67} +(2.39499 - 4.14824i) q^{68} +(-0.00477034 - 0.0270539i) q^{70} +(-4.73200 - 3.97062i) q^{71} +(2.73409 - 15.5058i) q^{73} +(-0.533599 + 0.194214i) q^{74} +(3.82379 + 7.37160i) q^{76} +0.300307 q^{77} +(-0.178596 + 1.01287i) q^{79} +(-2.63508 + 2.21110i) q^{80} +(0.161105 + 0.913670i) q^{82} +(8.96939 + 15.5354i) q^{83} +(2.36261 + 0.859918i) q^{85} +(0.708449 + 0.257854i) q^{86} +(2.02470 + 3.50689i) q^{88} +(-0.113975 - 0.646383i) q^{89} +(0.0145450 - 0.0122047i) q^{91} +(-1.97403 + 11.1953i) q^{92} +2.34635 q^{94} +(-3.46200 + 2.64850i) q^{95} +(-15.7991 + 5.75040i) q^{97} +(-0.373946 + 2.12075i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8}+O(q^{10}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8	\( 18 q + 3 q^{2} - 3 q^{4} + 6 q^{8} - 3 q^{10} - 3 q^{13} + 12 q^{14} - 3 q^{16} - 24 q^{17} - 12 q^{20} + 9 q^{22} + 9 q^{23} - 3 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} - 15 q^{32} - 12 q^{34} + 36 q^{37} + 33 q^{38} - 6 q^{40} + 30 q^{41} - 36 q^{43} - 42 q^{44} + 9 q^{46} - 21 q^{47} + 9 q^{49} + 6 q^{50} - 39 q^{52} + 12 q^{53} + 3 q^{55} + 12 q^{58} - 18 q^{59} - 30 q^{61} + 24 q^{62} + 36 q^{64} + 9 q^{65} - 51 q^{68} + 33 q^{70} + 12 q^{71} + 24 q^{73} + 15 q^{74} - 33 q^{76} + 60 q^{77} - 51 q^{79} - 15 q^{80} - 15 q^{82} + 24 q^{85} - 63 q^{86} - 27 q^{88} + 54 q^{89} + 30 q^{91} + 42 q^{92} + 30 q^{94} - 15 q^{95} + 27 q^{97} + 3 q^{98}+O(q^{100}) \) 18 * q + 3 * q^2 - 3 * q^4 + 6 * q^8 - 3 * q^10 - 3 * q^13 + 12 * q^14 - 3 * q^16 - 24 * q^17 - 12 * q^20 + 9 * q^22 + 9 * q^23 - 3 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 - 15 * q^32 - 12 * q^34 + 36 * q^37 + 33 * q^38 - 6 * q^40 + 30 * q^41 - 36 * q^43 - 42 * q^44 + 9 * q^46 - 21 * q^47 + 9 * q^49 + 6 * q^50 - 39 * q^52 + 12 * q^53 + 3 * q^55 + 12 * q^58 - 18 * q^59 - 30 * q^61 + 24 * q^62 + 36 * q^64 + 9 * q^65 - 51 * q^68 + 33 * q^70 + 12 * q^71 + 24 * q^73 + 15 * q^74 - 33 * q^76 + 60 * q^77 - 51 * q^79 - 15 * q^80 - 15 * q^82 + 24 * q^85 - 63 * q^86 - 27 * q^88 + 54 * q^89 + 30 * q^91 + 42 * q^92 + 30 * q^94 - 15 * q^95 + 27 * q^97 + 3 * q^98

Introduction

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