LMFDB - Embedded newform 855.2.bs.b.766.3

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} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} + \cdots + 361 $ x^18 + 12x^16 - 8x^15 + 96x^14 - 75x^13 + 448x^12 - 405x^11 + 1521x^10 - 1294x^9 + 3333x^8 - 2616x^7 + 5113x^6 - 3126x^5 + 4032x^4 - 1359x^3 + 1698x^2 - 513x + 361
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			766.3
Root			$0.785237 + 1.36007i$ of defining polynomial
Character	$\chi$	$=$	855.766
Dual form			855.2.bs.b.586.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20305 - 1.00948i) q^{2} +(0.0809872 - 0.459301i) q^{4} +(0.173648 + 0.984808i) q^{5} +(2.00668 - 3.47568i) q^{7} +(1.20425 + 2.08582i) q^{8} +O(q^{10})$	\(q+(1.20305 - 1.00948i) q^{2} +(0.0809872 - 0.459301i) q^{4} +(0.173648 + 0.984808i) q^{5} +(2.00668 - 3.47568i) q^{7} +(1.20425 + 2.08582i) q^{8} +(1.20305 + 1.00948i) q^{10} +(1.38310 + 2.39560i) q^{11} +(-2.61923 + 0.953321i) q^{13} +(-1.09448 - 6.20713i) q^{14} +(4.43089 + 1.61271i) q^{16} +(2.76292 - 2.31836i) q^{17} +(1.79089 - 3.97401i) q^{19} +0.466387 q^{20} +(4.08226 + 1.48582i) q^{22} +(-0.237457 + 1.34669i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-2.18871 + 3.79096i) q^{26} +(-1.43387 - 1.20316i) q^{28} +(7.28463 + 6.11253i) q^{29} +(-0.776853 + 1.34555i) q^{31} +(2.43210 - 0.885212i) q^{32} +(0.983591 - 5.57822i) q^{34} +(3.77133 + 1.37265i) q^{35} +8.51183 q^{37} +(-1.85715 - 6.58880i) q^{38} +(-1.84502 + 1.54815i) q^{40} +(-6.21041 - 2.26041i) q^{41} +(-1.08613 - 6.15974i) q^{43} +(1.21232 - 0.441247i) q^{44} +(1.07378 + 1.85984i) q^{46} +(-6.97857 - 5.85572i) q^{47} +(-4.55356 - 7.88699i) q^{49} +(-0.785237 + 1.36007i) q^{50} +(0.225738 + 1.28022i) q^{52} +(0.684965 - 3.88463i) q^{53} +(-2.11903 + 1.77808i) q^{55} +9.66619 q^{56} +14.9343 q^{58} +(-2.76682 + 2.32164i) q^{59} +(-1.30047 + 7.37531i) q^{61} +(0.423711 + 2.40298i) q^{62} +(-2.68292 + 4.64695i) q^{64} +(-1.39366 - 2.41389i) q^{65} +(-11.1628 - 9.36668i) q^{67} +(-0.841066 - 1.45677i) q^{68} +(5.92277 - 2.15571i) q^{70} +(0.576318 + 3.26846i) q^{71} +(9.40420 + 3.42285i) q^{73} +(10.2402 - 8.59253i) q^{74} +(-1.68023 - 1.14440i) q^{76} +11.1018 q^{77} +(1.82991 + 0.666034i) q^{79} +(-0.818796 + 4.64362i) q^{80} +(-9.75329 + 3.54991i) q^{82} +(0.809339 - 1.40182i) q^{83} +(2.76292 + 2.31836i) q^{85} +(-7.52481 - 6.31406i) q^{86} +(-3.33120 + 5.76980i) q^{88} +(-11.5122 + 4.19008i) q^{89} +(-1.94252 + 11.0166i) q^{91} +(0.599304 + 0.218129i) q^{92} -14.3068 q^{94} +(4.22462 + 1.07360i) q^{95} +(-8.87934 + 7.45065i) q^{97} +(-13.4399 - 4.89173i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	$ 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) $ 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	1.20305	−	1.00948i	0.850687	−	0.713811i	−0.109254	−	0.994014i	$-0.534846\pi$
$2$	1.20305	−	1.00948i	0.850687	−	0.713811i	0.959941	+	0.280203i	$0.0904018\pi$
$3$		0			0
$3$		0			0
$4$	0.0809872	−	0.459301i	0.0404936	−	0.229651i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$5$	0.173648	+	0.984808i	0.0776578	+	0.440419i
$6$		0			0
$7$	2.00668	−	3.47568i	0.758455	−	1.31368i	−0.185183	−	0.982704i	$-0.559288\pi$
$7$	2.00668	−	3.47568i	0.758455	−	1.31368i	0.943638	−	0.330979i	$-0.107379\pi$
$8$	1.20425	+	2.08582i	0.425766	+	0.737449i
$9$		0			0
$10$	1.20305	+	1.00948i	0.380439	+	0.319226i
$11$	1.38310	+	2.39560i	0.417021	+	0.722301i	0.995638	−	0.0932980i	$-0.0297409\pi$
$11$	1.38310	+	2.39560i	0.417021	+	0.722301i	−0.578618	+	0.815599i	$0.696408\pi$
$12$		0			0
$13$	−2.61923	+	0.953321i	−0.726443	+	0.264404i	−0.678659	−	0.734454i	$-0.737438\pi$
$13$	−2.61923	+	0.953321i	−0.726443	+	0.264404i	−0.0477847	+	0.998858i	$0.515216\pi$
$14$	−1.09448	−	6.20713i	−0.292513	−	1.65893i
$15$		0			0
$16$	4.43089	+	1.61271i	1.10772	+	0.403178i
$17$	2.76292	−	2.31836i	0.670106	−	0.562286i	−0.242991	−	0.970029i	$-0.578129\pi$
$17$	2.76292	−	2.31836i	0.670106	−	0.562286i	0.913097	+	0.407743i	$0.133684\pi$
$18$		0			0
$19$	1.79089	−	3.97401i	0.410858	−	0.911699i
$19$	1.79089	−	3.97401i	0.410858	−	0.911699i
$20$	0.466387			0.104287
$21$		0			0
$22$	4.08226	+	1.48582i	0.870340	+	0.316778i
$23$	−0.237457	+	1.34669i	−0.0495133	+	0.280804i	−0.999505	−	0.0314725i	$-0.989980\pi$
$23$	−0.237457	+	1.34669i	−0.0495133	+	0.280804i	0.949991	+	0.312276i	$0.101091\pi$
$24$		0			0
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−2.18871	+	3.79096i	−0.429241	+	0.743468i
$27$		0			0
$28$	−1.43387	−	1.20316i	−0.270975	−	0.227375i
$29$	7.28463	+	6.11253i	1.35272	+	1.13507i	0.978157	+	0.207866i	$0.0666520\pi$
$29$	7.28463	+	6.11253i	1.35272	+	1.13507i	0.374564	+	0.927201i	$0.377792\pi$
$30$		0			0
$31$	−0.776853	+	1.34555i	−0.139527	+	0.241668i	−0.927318	−	0.374275i	$-0.877891\pi$
$31$	−0.776853	+	1.34555i	−0.139527	+	0.241668i	0.787791	+	0.615943i	$0.211225\pi$
$32$	2.43210	−	0.885212i	0.429939	−	0.156485i
$33$		0			0
$34$	0.983591	−	5.57822i	0.168685	−	0.956658i
$35$	3.77133	+	1.37265i	0.637471	+	0.232021i
$36$		0			0
$37$	8.51183			1.39934			0.699668	−	0.714468i	$-0.253331\pi$
$37$	8.51183			1.39934			0.699668	+	0.714468i	$0.253331\pi$
$38$	−1.85715	−	6.58880i	−0.301269	−	1.06885i
$39$		0			0
$40$	−1.84502	+	1.54815i	−0.291723	+	0.244785i
$41$	−6.21041	−	2.26041i	−0.969904	−	0.353016i	−0.191997	−	0.981396i	$-0.561496\pi$
$41$	−6.21041	−	2.26041i	−0.969904	−	0.353016i	−0.777907	+	0.628379i	$0.783719\pi$
$42$		0			0
$43$	−1.08613	−	6.15974i	−0.165633	−	0.939351i	−0.948409	−	0.317048i	$-0.897308\pi$
$43$	−1.08613	−	6.15974i	−0.165633	−	0.939351i	0.782776	−	0.622303i	$-0.213803\pi$
$44$	1.21232	−	0.441247i	0.182764	−	0.0665205i
$45$		0			0
$46$	1.07378	+	1.85984i	0.158320	+	0.274219i
$47$	−6.97857	−	5.85572i	−1.01793	−	0.854144i	−0.0285637	−	0.999592i	$-0.509093\pi$
$47$	−6.97857	−	5.85572i	−1.01793	−	0.854144i	−0.989366	+	0.145448i	$0.953538\pi$
$48$		0			0
$49$	−4.55356	−	7.88699i	−0.650508	−	1.12671i
$50$	−0.785237	+	1.36007i	−0.111049	+	0.192343i
$51$		0			0
$52$	0.225738	+	1.28022i	0.0313042	+	0.177535i
$53$	0.684965	−	3.88463i	0.0940872	−	0.533595i	−0.900936	−	0.433952i	$-0.857119\pi$
$53$	0.684965	−	3.88463i	0.0940872	−	0.533595i	0.995023	−	0.0996432i	$-0.0317701\pi$
$54$		0			0
$55$	−2.11903	+	1.77808i	−0.285730	+	0.239756i
$56$	9.66619			1.29170
$57$		0			0
$58$	14.9343			1.96096
$59$	−2.76682	+	2.32164i	−0.360209	+	0.302251i	−0.804874	−	0.593446i	$-0.797767\pi$
$59$	−2.76682	+	2.32164i	−0.360209	+	0.302251i	0.444665	+	0.895697i	$0.353323\pi$
$60$		0			0
$61$	−1.30047	+	7.37531i	−0.166508	+	0.944311i	0.780989	+	0.624545i	$0.214716\pi$
$61$	−1.30047	+	7.37531i	−0.166508	+	0.944311i	−0.947496	+	0.319766i	$0.896396\pi$
$62$	0.423711	+	2.40298i	0.0538113	+	0.305179i
$63$		0			0
$64$	−2.68292	+	4.64695i	−0.335365	+	0.580869i
$65$	−1.39366	−	2.41389i	−0.172863	−	0.299407i
$66$		0			0
$67$	−11.1628	−	9.36668i	−1.36375	−	1.14432i	−0.974804	−	0.223061i	$-0.928395\pi$
$67$	−11.1628	−	9.36668i	−1.36375	−	1.14432i	−0.388946	−	0.921261i	$-0.627161\pi$
$68$	−0.841066	−	1.45677i	−0.101994	−	0.176659i
$69$		0			0
$70$	5.92277	−	2.15571i	0.707907	−	0.257657i
$71$	0.576318	+	3.26846i	0.0683964	+	0.387895i	0.999719	+	0.0237002i	$0.00754470\pi$
$71$	0.576318	+	3.26846i	0.0683964	+	0.387895i	−0.931323	+	0.364195i	$0.881344\pi$
$72$		0			0
$73$	9.40420	+	3.42285i	1.10068	+	0.400614i	0.827566	−	0.561368i	$-0.189725\pi$
$73$	9.40420	+	3.42285i	1.10068	+	0.400614i	0.273112	+	0.961982i	$0.411947\pi$
$74$	10.2402	−	8.59253i	1.19040	−	0.998862i
$75$		0			0
$76$	−1.68023	−	1.14440i	−0.192735	−	0.131272i
$77$	11.1018			1.26517
$78$		0			0
$79$	1.82991	+	0.666034i	0.205881	+	0.0749347i	0.442902	−	0.896570i	$-0.353949\pi$
$79$	1.82991	+	0.666034i	0.205881	+	0.0749347i	−0.237021	+	0.971505i	$0.576171\pi$
$80$	−0.818796	+	4.64362i	−0.0915441	+	0.519173i
$81$		0			0
$82$	−9.75329	+	3.54991i	−1.07707	+	0.392022i
$83$	0.809339	−	1.40182i	0.0888365	−	0.153869i	−0.818183	−	0.574958i	$-0.805018\pi$
$83$	0.809339	−	1.40182i	0.0888365	−	0.153869i	0.907020	+	0.421088i	$0.138352\pi$
$84$		0			0
$85$	2.76292	+	2.31836i	0.299680	+	0.251462i
$86$	−7.52481	−	6.31406i	−0.811421	−	0.680863i
$87$		0			0
$88$	−3.33120	+	5.76980i	−0.355107	+	0.615063i
$89$	−11.5122	+	4.19008i	−1.22029	+	0.444148i	−0.870260	−	0.492593i	$-0.836049\pi$
$89$	−11.5122	+	4.19008i	−1.22029	+	0.444148i	−0.350025	+	0.936740i	$0.613827\pi$
$90$		0			0
$91$	−1.94252	+	11.0166i	−0.203632	+	1.15485i
$92$	0.599304	+	0.218129i	0.0624818	+	0.0227415i
$93$		0			0
$94$	−14.3068			−1.47564
$95$	4.22462	+	1.07360i	0.433436	+	0.110149i
$96$		0			0
$97$	−8.87934	+	7.45065i	−0.901560	+	0.756499i	−0.970495	−	0.241122i	$-0.922485\pi$
$97$	−8.87934	+	7.45065i	−0.901560	+	0.756499i	0.0689344	+	0.997621i	$0.478040\pi$
$98$	−13.4399	−	4.89173i	−1.35764	−	0.494140i
$99$		0			0
$100$	0.0809872	+	0.459301i	0.00809872	+	0.0459301i
$101$	−6.56131	+	2.38812i	−0.652874	+	0.237627i	−0.647157	−	0.762357i	$-0.724042\pi$
$101$	−6.56131	+	2.38812i	−0.652874	+	0.237627i	−0.00571740	+	0.999984i	$0.501820\pi$
$102$		0			0
$103$	−5.06688	−	8.77610i	−0.499255	−	0.864735i	0.500745	−	0.865595i	$-0.333060\pi$
$103$	−5.06688	−	8.77610i	−0.499255	−	0.864735i	−1.00000		0.000860217i	$0.999726\pi$
$104$	−5.14266	−	4.31521i	−0.504279	−	0.423141i
$105$		0			0
$106$	−3.09741	−	5.36487i	−0.300847	−	0.521083i
$107$	−5.89176	+	10.2048i	−0.569578	+	0.986538i	0.427030	+	0.904238i	$0.359560\pi$
$107$	−5.89176	+	10.2048i	−0.569578	+	0.986538i	−0.996608	+	0.0823003i	$0.973773\pi$
$108$		0			0
$109$	−0.278545	−	1.57971i	−0.0266797	−	0.151308i	0.968558	−	0.248789i	$-0.0800326\pi$
$109$	−0.278545	−	1.57971i	−0.0266797	−	0.151308i	−0.995237	+	0.0974809i	$0.968922\pi$
$110$	−0.754371	+	4.27825i	−0.0719264	+	0.407915i
$111$		0			0
$112$	14.4967	−	12.1641i	1.36981	−	1.14940i
$113$	−12.9449			−1.21775			−0.608876	−	0.793266i	$-0.708379\pi$
$113$	−12.9449			−1.21775			−0.608876	+	0.793266i	$0.708379\pi$
$114$		0			0
$115$	−1.36746			−0.127517
$116$	3.39745	−	2.85080i	0.315445	−	0.264690i
$117$		0			0
$118$	−0.984981	+	5.58610i	−0.0906748	+	0.514242i
$119$	−2.51358	−	14.2552i	−0.230420	−	1.30677i
$120$		0			0
$121$	1.67406	−	2.89956i	0.152187	−	0.263596i
$122$	5.88070	+	10.1857i	0.532414	+	0.922168i
$123$		0			0
$124$	0.555097	+	0.465781i	0.0498492	+	0.0418284i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	7.79759	−	2.83809i	0.691924	−	0.251840i	0.0279654	−	0.999609i	$-0.491097\pi$
$127$	7.79759	−	2.83809i	0.691924	−	0.251840i	0.663959	+	0.747769i	$0.268875\pi$
$128$	2.36218	+	13.3966i	0.208790	+	1.18410i
$129$		0			0
$130$	−4.11343	−	1.49717i	−0.360772	−	0.131310i
$131$	4.98836	−	4.18573i	0.435835	−	0.365709i	−0.398313	−	0.917250i	$-0.630404\pi$
$131$	4.98836	−	4.18573i	0.435835	−	0.365709i	0.834148	+	0.551540i	$0.185960\pi$
$132$		0			0
$133$	−10.2186	−	14.1991i	−0.886066	−	1.23122i
$134$	−22.8849			−1.97695
$135$		0			0
$136$	8.16293	+	2.97106i	0.699966	+	0.254767i
$137$	−2.58191	+	14.6427i	−0.220587	+	1.25101i	0.650356	+	0.759630i	$0.274620\pi$
$137$	−2.58191	+	14.6427i	−0.220587	+	1.25101i	−0.870943	+	0.491384i	$0.836491\pi$
$138$		0			0
$139$	−9.35768	+	3.40592i	−0.793708	+	0.288886i	−0.706876	−	0.707337i	$-0.749896\pi$
$139$	−9.35768	+	3.40592i	−0.793708	+	0.288886i	−0.0868313	+	0.996223i	$0.527674\pi$
$140$	0.935890	−	1.62101i	0.0790972	−	0.137000i
$141$		0			0
$142$	3.99279	+	3.35035i	0.335068	+	0.281155i
$143$	−5.90644	−	4.95609i	−0.493921	−	0.414449i
$144$		0			0
$145$	−4.75470	+	8.23538i	−0.394856	+	0.683911i
$146$	14.7690	−	5.37549i	1.22229	−	0.444879i
$147$		0			0
$148$	0.689349	−	3.90949i	0.0566642	−	0.321358i
$149$	−1.34529	−	0.489644i	−0.110210	−	0.0401132i	0.286326	−	0.958132i	$-0.407566\pi$
$149$	−1.34529	−	0.489644i	−0.110210	−	0.0401132i	−0.396537	+	0.918019i	$0.629788\pi$
$150$		0			0
$151$	−8.18383			−0.665990			−0.332995	−	0.942929i	$-0.608059\pi$
$151$	−8.18383			−0.665990			−0.332995	+	0.942929i	$0.608059\pi$
$152$	10.4457	−	1.05022i	0.847262	−	0.0851841i
$153$		0			0
$154$	13.3560	−	11.2070i	1.07626	−	0.903089i
$155$	−1.46001	−	0.531399i	−0.117270	−	0.0426830i
$156$		0			0
$157$	−1.36055	−	7.71609i	−0.108584	−	0.615811i	−0.989728	−	0.142963i	$-0.954337\pi$
$157$	−1.36055	−	7.71609i	−0.108584	−	0.615811i	0.881144	−	0.472848i	$-0.156774\pi$
$158$	2.87383	−	1.04599i	0.228630	−	0.0832144i
$159$		0			0
$160$	1.29409	+	2.24144i	0.102307	+	0.177201i
$161$	4.20415	+	3.52770i	0.331333	+	0.278022i
$162$		0			0
$163$	9.64968	+	16.7137i	0.755821	+	1.30912i	0.944965	+	0.327171i	$0.106095\pi$
$163$	9.64968	+	16.7137i	0.755821	+	1.30912i	−0.189144	+	0.981949i	$0.560571\pi$
$164$	−1.54117	+	2.66939i	−0.120345	+	0.208444i
$165$		0			0
$166$	−0.441429	−	2.50347i	−0.0342616	−	0.194307i
$167$	−1.63050	+	9.24703i	−0.126172	+	0.715556i	0.854433	+	0.519562i	$0.173905\pi$
$167$	−1.63050	+	9.24703i	−0.126172	+	0.715556i	−0.980605	+	0.195995i	$0.937206\pi$
$168$		0			0
$169$	−4.00704	+	3.36231i	−0.308234	+	0.258639i
$170$	5.66428			0.434430
$171$		0			0
$172$	−2.91714			−0.222430
$173$	−6.36647	+	5.34210i	−0.484034	+	0.406153i	−0.851882	−	0.523733i	$-0.824539\pi$
$173$	−6.36647	+	5.34210i	−0.484034	+	0.406153i	0.367849	+	0.929886i	$0.380094\pi$
$174$		0			0
$175$	−0.696914	+	3.95239i	−0.0526817	+	0.298773i
$176$	2.26495	+	12.8452i	0.170727	+	0.968243i
$177$		0			0
$178$	−9.61991	+	16.6622i	−0.721043	+	1.24888i
$179$	−9.26593	−	16.0491i	−0.692568	−	1.19956i	−0.970994	−	0.239105i	$-0.923146\pi$
$179$	−9.26593	−	16.0491i	−0.692568	−	1.19956i	0.278425	−	0.960458i	$-0.410187\pi$
$180$		0			0
$181$	8.67868	+	7.28228i	0.645081	+	0.541288i	0.905574	−	0.424188i	$-0.139441\pi$
$181$	8.67868	+	7.28228i	0.645081	+	0.541288i	−0.260493	+	0.965476i	$0.583885\pi$
$182$	8.78409	+	15.2145i	0.651120	+	1.12777i
$183$		0			0
$184$	−3.09491	+	1.12645i	−0.228160	+	0.0830433i
$185$	1.47806	+	8.38252i	0.108669	+	0.616295i
$186$		0			0
$187$	9.37527	+	3.41232i	0.685587	+	0.249533i
$188$	−3.25471	+	2.73103i	−0.237374	+	0.199181i
$189$		0			0
$190$	6.16622	−	2.97307i	0.447344	−	0.215689i
$191$	−11.8879			−0.860175			−0.430088	−	0.902787i	$-0.641517\pi$
$191$	−11.8879			−0.860175			−0.430088	+	0.902787i	$0.641517\pi$
$192$		0			0
$193$	0.900069	+	0.327598i	0.0647884	+	0.0235810i	0.374211	−	0.927344i	$-0.377914\pi$
$193$	0.900069	+	0.327598i	0.0647884	+	0.0235810i	−0.309423	+	0.950925i	$0.600136\pi$
$194$	−3.16102	+	17.9270i	−0.226948	+	1.28709i
$195$		0			0
$196$	−3.99128	+	1.45271i	−0.285092	+	0.103765i
$197$	7.13881	−	12.3648i	0.508619	−	0.880955i	−0.491331	−	0.870973i	$-0.663489\pi$
$197$	7.13881	−	12.3648i	0.508619	−	0.880955i	0.999950	−	0.00998159i	$-0.00317729\pi$
$198$		0			0
$199$	−5.94888	−	4.99170i	−0.421705	−	0.353852i	0.407106	−	0.913381i	$-0.366538\pi$
$199$	−5.94888	−	4.99170i	−0.421705	−	0.353852i	−0.828811	+	0.559528i	$0.810982\pi$
$200$	−1.84502	−	1.54815i	−0.130462	−	0.109471i
$201$		0			0
$202$	−5.48283	+	9.49655i	−0.385771	+	0.668175i
$203$	35.8631	−	13.0531i	2.51710	−	0.916148i
$204$		0			0
$205$	1.14764	−	6.50858i	0.0801545	−	0.454579i
$206$	−14.9550	−	5.44319i	−1.04197	−	0.379245i
$207$		0			0
$208$	−13.1430			−0.911300
$209$	11.9971	−	1.20620i	0.829858	−	0.0834343i
$210$		0			0
$211$	5.83936	−	4.89980i	0.401998	−	0.337316i	−0.419267	−	0.907863i	$-0.637713\pi$
$211$	5.83936	−	4.89980i	0.401998	−	0.337316i	0.821265	+	0.570546i	$0.193269\pi$
$212$	−1.72874	−	0.629211i	−0.118731	−	0.0432144i
$213$		0			0
$214$	3.21348	+	18.2246i	0.219669	+	1.24581i
$215$	5.87755	−	2.13925i	0.400846	−	0.145896i
$216$		0			0
$217$	3.11779	+	5.40018i	0.211650	+	0.366588i
$218$	−1.92979	−	1.61928i	−0.130702	−	0.109672i
$219$		0			0
$220$	0.645060	+	1.11728i	0.0434899	+	0.0753268i
$221$	−5.02657	+	8.70627i	−0.338123	+	0.585647i
$222$		0			0
$223$	−1.38976	−	7.88173i	−0.0930653	−	0.527799i	−0.995323	−	0.0966024i	$-0.969202\pi$
$223$	−1.38976	−	7.88173i	−0.0930653	−	0.527799i	0.902258	−	0.431197i	$-0.141909\pi$
$224$	1.80374	−	10.2295i	0.120518	−	0.683490i
$225$		0			0
$226$	−15.5734	+	13.0676i	−1.03592	+	0.869244i
$227$	17.7409			1.17750			0.588752	−	0.808314i	$-0.299619\pi$
$227$	17.7409			1.17750			0.588752	+	0.808314i	$0.299619\pi$
$228$		0			0
$229$	−24.2231			−1.60071			−0.800354	−	0.599528i	$-0.795355\pi$
$229$	−24.2231			−1.60071			−0.800354	+	0.599528i	$0.795355\pi$
$230$	−1.64513	+	1.38043i	−0.108477	+	0.0910227i
$231$		0			0
$232$	−3.97713	+	22.5554i	−0.261111	+	1.48084i
$233$	−2.37014	−	13.4418i	−0.155273	−	0.880598i	−0.958536	−	0.284973i	$-0.908015\pi$
$233$	−2.37014	−	13.4418i	−0.155273	−	0.880598i	0.803262	−	0.595625i	$-0.203096\pi$
$234$		0			0
$235$	4.55494	−	7.88939i	0.297132	−	0.514647i
$236$	0.842254	+	1.45883i	0.0548260	+	0.0949615i
$237$		0			0
$238$	−17.4144	−	14.6124i	−1.12880	−	0.947180i
$239$	1.86882	+	3.23689i	0.120884	+	0.209377i	0.920117	−	0.391645i	$-0.128094\pi$
$239$	1.86882	+	3.23689i	0.120884	+	0.209377i	−0.799233	+	0.601022i	$0.794760\pi$
$240$		0			0
$241$	4.96295	−	1.80636i	0.319691	−	0.116358i	−0.177190	−	0.984177i	$-0.556701\pi$
$241$	4.96295	−	1.80636i	0.319691	−	0.116358i	0.496881	+	0.867819i	$0.334478\pi$
$242$	−0.913066	−	5.17826i	−0.0586941	−	0.332871i
$243$		0			0
$244$	3.28217	+	1.19461i	0.210119	+	0.0764771i
$245$	6.97645	−	5.85394i	0.445709	−	0.373994i
$246$		0			0
$247$	−0.902244	+	12.1161i	−0.0574084	+	0.770930i
$248$	−3.74210			−0.237623
$249$		0			0
$250$	−1.47576	−	0.537134i	−0.0933354	−	0.0339713i
$251$	2.17833	−	12.3539i	0.137495	−	0.779772i	−0.835595	−	0.549346i	$-0.814877\pi$
$251$	2.17833	−	12.3539i	0.137495	−	0.779772i	0.973090	−	0.230426i	$-0.0740119\pi$
$252$		0			0
$253$	−3.55455	+	1.29375i	−0.223473	+	0.0813375i
$254$	6.51591	−	11.2859i	0.408845	−	0.708140i
$255$		0			0
$256$	8.14452	+	6.83406i	0.509032	+	0.427129i
$257$	−6.58784	−	5.52786i	−0.410938	−	0.344818i	0.413765	−	0.910384i	$-0.364214\pi$
$257$	−6.58784	−	5.52786i	−0.410938	−	0.344818i	−0.824703	+	0.565565i	$0.808658\pi$
$258$		0			0
$259$	17.0806	−	29.5844i	1.06133	−	1.83828i
$260$	−1.22157	+	0.444616i	−0.0757587	+	0.0275739i
$261$		0			0
$262$	1.77584	−	10.0713i	0.109712	−	0.622208i
$263$	25.0807	+	9.12863i	1.54654	+	0.562895i	0.967603	−	0.252475i	$-0.0812447\pi$
$263$	25.0807	+	9.12863i	1.54654	+	0.562895i	0.578939	+	0.815371i	$0.303467\pi$
$264$		0			0
$265$	3.94456			0.242312
$266$	−26.6273	−	6.76679i	−1.63262	−	0.414899i
$267$		0			0
$268$	−5.20617	+	4.36849i	−0.318017	+	0.266848i
$269$	−3.10399	−	1.12976i	−0.189254	−	0.0688828i	0.245655	−	0.969357i	$-0.420997\pi$
$269$	−3.10399	−	1.12976i	−0.189254	−	0.0688828i	−0.434909	+	0.900475i	$0.643219\pi$
$270$		0			0
$271$	−3.19296	−	18.1082i	−0.193959	−	1.09999i	−0.913894	−	0.405953i	$-0.866940\pi$
$271$	−3.19296	−	18.1082i	−0.193959	−	1.09999i	0.719935	−	0.694041i	$-0.244172\pi$
$272$	15.9810	−	5.81662i	0.968993	−	0.352685i
$273$		0			0
$274$	11.6754	+	20.2224i	0.705336	+	1.22168i
$275$	−2.11903	−	1.77808i	−0.127783	−	0.107222i
$276$		0			0
$277$	−13.3893	−	23.1910i	−0.804488	−	1.39341i	−0.916636	−	0.399722i	$-0.869107\pi$
$277$	−13.3893	−	23.1910i	−0.804488	−	1.39341i	0.112148	−	0.993691i	$-0.464227\pi$
$278$	−7.81957	+	13.5439i	−0.468987	+	0.812308i
$279$		0			0
$280$	1.67852	+	9.51934i	0.100311	+	0.568889i
$281$	−3.74145	+	21.2188i	−0.223196	+	1.26581i	0.642907	+	0.765945i	$0.277728\pi$
$281$	−3.74145	+	21.2188i	−0.223196	+	1.26581i	−0.866103	+	0.499865i	$0.833383\pi$
$282$		0			0
$283$	14.0547	−	11.7933i	0.835465	−	0.701038i	−0.121074	−	0.992643i	$-0.538634\pi$
$283$	14.0547	−	11.7933i	0.835465	−	0.701038i	0.956539	+	0.291605i	$0.0941894\pi$
$284$	1.54788			0.0918499
$285$		0			0
$286$	−12.1088			−0.716010
$287$	−20.3188	+	17.0495i	−1.19938	+	1.00640i
$288$		0			0
$289$	−0.693114	+	3.93084i	−0.0407714	+	0.231226i
$290$	2.59331	+	14.7074i	0.152284	+	0.863647i
$291$		0			0
$292$	2.33374	−	4.04215i	0.136572	−	0.236549i
$293$	−4.64436	−	8.04426i	−0.271326	−	0.469951i	0.697875	−	0.716219i	$-0.254129\pi$
$293$	−4.64436	−	8.04426i	−0.271326	−	0.469951i	−0.969202	+	0.246268i	$0.920796\pi$
$294$		0			0
$295$	−2.76682	−	2.32164i	−0.161090	−	0.135171i
$296$	10.2504	+	17.7542i	0.595791	+	1.03194i
$297$		0			0
$298$	−2.11274	+	0.768973i	−0.122388	+	0.0445454i
$299$	−0.661871	−	3.75366i	−0.0382770	−	0.217079i
$300$		0			0
$301$	−23.5888	−	8.58561i	−1.35963	−	0.494867i
$302$	−9.84557	+	8.26142i	−0.566549	+	0.475391i
$303$		0			0
$304$	14.3442	−	14.7202i	0.822694	−	0.844261i
$305$	−7.48908			−0.428824
$306$		0			0
$307$	10.3508	+	3.76739i	0.590753	+	0.215017i	0.620061	−	0.784554i	$-0.287108\pi$
$307$	10.3508	+	3.76739i	0.590753	+	0.215017i	−0.0293076	+	0.999570i	$0.509330\pi$
$308$	0.899102	−	5.09906i	0.0512311	−	0.290546i
$309$		0			0
$310$	−2.29290	+	0.834547i	−0.130228	+	0.0473991i
$311$	12.6911	−	21.9816i	0.719644	−	1.24646i	−0.241497	−	0.970402i	$-0.577638\pi$
$311$	12.6911	−	21.9816i	0.719644	−	1.24646i	0.961141	−	0.276058i	$-0.0890283\pi$
$312$		0			0
$313$	16.1297	+	13.5345i	0.911707	+	0.765013i	0.972443	−	0.233141i	$-0.0749004\pi$
$313$	16.1297	+	13.5345i	0.911707	+	0.765013i	−0.0607363	+	0.998154i	$0.519345\pi$
$314$	−9.42606	−	7.90940i	−0.531943	−	0.446353i
$315$		0			0
$316$	0.454110	−	0.786541i	0.0255457	−	0.0442464i
$317$	3.76804	−	1.37145i	0.211634	−	0.0770285i	−0.234028	−	0.972230i	$-0.575191\pi$
$317$	3.76804	−	1.37145i	0.211634	−	0.0770285i	0.445662	+	0.895201i	$0.352968\pi$
$318$		0			0
$319$	−4.56780	+	25.9053i	−0.255748	+	1.45042i
$320$	−5.04224	−	1.83522i	−0.281870	−	0.102592i
$321$		0			0
$322$	8.61896			0.480316
$323$	−4.26511	−	15.1318i	−0.237317	−	0.841955i
$324$		0			0
$325$	2.13521	−	1.79166i	0.118440	−	0.0993833i
$326$	28.4813	+	10.3663i	1.57743	+	0.574138i
$327$		0			0
$328$	−2.76409	−	15.6759i	−0.152621	−	0.865557i
$329$	−34.3564	+	12.5047i	−1.89413	+	0.689406i
$330$		0			0
$331$	16.0680	+	27.8306i	0.883176	+	1.52971i	0.847790	+	0.530332i	$0.177933\pi$
$331$	16.0680	+	27.8306i	0.883176	+	1.52971i	0.0353860	+	0.999374i	$0.488734\pi$
$332$	−0.578309	−	0.485259i	−0.0317389	−	0.0266321i
$333$		0			0
$334$	7.37312	+	12.7706i	0.403439	+	0.698777i
$335$	7.28598	−	12.6197i	0.398076	−	0.689488i
$336$		0			0
$337$	4.07164	+	23.0914i	0.221796	+	1.25787i	0.868716	+	0.495310i	$0.164946\pi$
$337$	4.07164	+	23.0914i	0.221796	+	1.25787i	−0.646920	+	0.762558i	$0.723943\pi$
$338$	−1.42650	+	8.09007i	−0.0775912	+	0.440042i
$339$		0			0
$340$	1.28859	−	1.08125i	0.0698835	−	0.0586392i
$341$	−4.29786			−0.232742
$342$		0			0
$343$	−8.45661			−0.456614
$344$	11.5401	−	9.68333i	0.622203	−	0.522090i
$345$		0			0
$346$	−2.26645	+	12.8537i	−0.121845	+	0.691017i
$347$	−1.12759	−	6.39487i	−0.0605321	−	0.343295i	−1.00000		0.000657202i	$-0.999791\pi$
$347$	−1.12759	−	6.39487i	−0.0605321	−	0.343295i	0.939468	−	0.342638i	$-0.111320\pi$
$348$		0			0
$349$	13.6004	−	23.5566i	0.728013	−	1.26096i	−0.229709	−	0.973259i	$-0.573777\pi$
$349$	13.6004	−	23.5566i	0.728013	−	1.26096i	0.957722	−	0.287696i	$-0.0928893\pi$
$350$	3.15144	+	5.45846i	0.168452	+	0.291767i
$351$		0			0
$352$	5.48446	+	4.60201i	0.292323	+	0.245288i
$353$	−3.28062	−	5.68221i	−0.174610	−	0.302433i	0.765416	−	0.643536i	$-0.222533\pi$
$353$	−3.28062	−	5.68221i	−0.174610	−	0.302433i	−0.940026	+	0.341102i	$0.889200\pi$
$354$		0			0
$355$	−3.11873	+	1.13513i	−0.165525	+	0.0602462i
$356$	0.992172	+	5.62689i	0.0525850	+	0.298224i
$357$		0			0
$358$	−27.3486	−	9.95408i	−1.44542	−	0.526090i
$359$	2.09279	−	1.75606i	0.110453	−	0.0926813i	−0.585888	−	0.810392i	$-0.699254\pi$
$359$	2.09279	−	1.75606i	0.110453	−	0.0926813i	0.696342	+	0.717710i	$0.254810\pi$
$360$		0			0
$361$	−12.5854	−	14.2340i	−0.662391	−	0.749158i
$362$	17.7922			0.935139
$363$		0			0
$364$	4.90262	+	1.78441i	0.256967	+	0.0935284i
$365$	−1.73783	+	9.85570i	−0.0909619	+	0.515871i
$366$		0			0
$367$	−6.18227	+	2.25016i	−0.322712	+	0.117457i	−0.498296	−	0.867007i	$-0.666041\pi$
$367$	−6.18227	+	2.25016i	−0.322712	+	0.117457i	0.175584	+	0.984464i	$0.443819\pi$
$368$	−3.22397	+	5.58408i	−0.168061	+	0.291090i
$369$		0			0
$370$	10.2402	+	8.59253i	0.532362	+	0.446704i
$371$	−12.1272	−	10.1759i	−0.629614	−	0.528309i
$372$		0			0
$373$	4.27996	−	7.41311i	0.221608	−	0.383836i	−0.733688	−	0.679486i	$-0.762203\pi$
$373$	4.27996	−	7.41311i	0.221608	−	0.383836i	0.955296	+	0.295650i	$0.0955361\pi$
$374$	14.7236	−	5.35896i	0.761340	−	0.277105i
$375$		0			0
$376$	3.81004	−	21.6078i	0.196488	−	1.11434i
$377$	−24.9073	−	9.06551i	−1.28279	−	0.466898i
$378$		0			0
$379$	14.2477			0.731856			0.365928	−	0.930643i	$-0.380752\pi$
$379$	14.2477			0.731856			0.365928	+	0.930643i	$0.380752\pi$
$380$	0.835247	−	1.85342i	0.0428472	−	0.0950786i
$381$		0			0
$382$	−14.3017	+	12.0006i	−0.731739	+	0.614002i
$383$	20.0778	+	7.30773i	1.02593	+	0.373408i	0.799529	−	0.600627i	$-0.205082\pi$
$383$	20.0778	+	7.30773i	1.02593	+	0.373408i	0.226399	+	0.974035i	$0.427305\pi$
$384$		0			0
$385$	1.92780	+	10.9331i	0.0982500	+	0.557204i
$386$	1.41353	−	0.514485i	0.0719470	−	0.0261866i
$387$		0			0
$388$	2.70298	+	4.68170i	0.137223	+	0.237677i
$389$	−11.7148	−	9.82991i	−0.593965	−	0.498396i	0.295534	−	0.955332i	$-0.404502\pi$
$389$	−11.7148	−	9.82991i	−0.593965	−	0.498396i	−0.889500	+	0.456936i	$0.848947\pi$
$390$		0			0
$391$	2.46604	+	4.27130i	0.124713	+	0.216009i
$392$	10.9672	−	18.9958i	0.553929	−	0.959433i
$393$		0			0
$394$	−3.89365	−	22.0820i	−0.196159	−	1.11247i
$395$	−0.338154	+	1.91777i	−0.0170144	+	0.0964934i
$396$		0			0
$397$	24.9746	−	20.9562i	1.25344	−	1.05176i	0.257090	−	0.966387i	$-0.417236\pi$
$397$	24.9746	−	20.9562i	1.25344	−	1.05176i	0.996349	−	0.0853727i	$-0.0272081\pi$
$398$	−12.1958			−0.611322
$399$		0			0
$400$	−4.71526			−0.235763
$401$	13.2617	−	11.1279i	0.662258	−	0.555701i	−0.248505	−	0.968631i	$-0.579939\pi$
$401$	13.2617	−	11.1279i	0.662258	−	0.555701i	0.910763	+	0.412930i	$0.135495\pi$
$402$		0			0
$403$	0.752015	−	4.26489i	0.0374605	−	0.212449i
$404$	0.565485	+	3.20702i	0.0281339	+	0.159555i
$405$		0			0
$406$	29.9683	−	51.9067i	1.48730	−	2.57609i
$407$	11.7727	+	20.3910i	0.583552	+	1.01074i
$408$		0			0
$409$	−8.29411	−	6.95959i	−0.410117	−	0.344129i	0.414271	−	0.910153i	$-0.364036\pi$
$409$	−8.29411	−	6.95959i	−0.410117	−	0.344129i	−0.824389	+	0.566024i	$0.808481\pi$
$410$	−5.18962	−	8.98868i	−0.256297	−	0.443919i
$411$		0			0
$412$	−4.44123	+	1.61647i	−0.218803	+	0.0796379i
$413$	2.51713	+	14.2754i	0.123860	+	0.702445i
$414$		0			0
$415$	1.52106	+	0.553620i	0.0746659	+	0.0271761i
$416$	−5.52633	+	4.63715i	−0.270951	+	0.227355i
$417$		0			0
$418$	13.2155	−	13.5620i	0.646392	−	0.663338i
$419$	−33.9763			−1.65985			−0.829925	−	0.557876i	$-0.811617\pi$
$419$	−33.9763			−1.65985			−0.829925	+	0.557876i	$0.811617\pi$
$420$		0			0
$421$	−7.80720	−	2.84159i	−0.380500	−	0.138491i	0.144687	−	0.989477i	$-0.453782\pi$
$421$	−7.80720	−	2.84159i	−0.380500	−	0.138491i	−0.525187	+	0.850987i	$0.676005\pi$
$422$	2.07880	−	11.7894i	0.101194	−	0.573901i
$423$		0			0
$424$	8.92752	−	3.24935i	0.433559	−	0.157802i
$425$	−1.80337	+	3.12352i	−0.0874761	+	0.151513i
$426$		0			0
$427$	23.0246	+	19.3199i	1.11424	+	0.934956i
$428$	4.20993	+	3.53255i	0.203495	+	0.170752i
$429$		0			0
$430$	4.91147	−	8.50691i	0.236852	−	0.410240i
$431$	−11.3983	+	4.14863i	−0.549035	+	0.199832i	−0.601618	−	0.798784i	$-0.705477\pi$
$431$	−11.3983	+	4.14863i	−0.549035	+	0.199832i	0.0525827	+	0.998617i	$0.483255\pi$
$432$		0			0
$433$	−0.943849	+	5.35283i	−0.0453585	+	0.257241i	−0.999052	−	0.0435404i	$-0.986136\pi$
$433$	−0.943849	+	5.35283i	−0.0453585	+	0.257241i	0.953693	+	0.300781i	$0.0972474\pi$
$434$	9.20225	+	3.34934i	0.441722	+	0.160774i
$435$		0			0
$436$	−0.748119			−0.0358284
$437$	4.92648	+	3.35542i	0.235666	+	0.160512i
$438$		0			0
$439$	−19.4428	+	16.3144i	−0.927952	+	0.778644i	−0.975449	−	0.220227i	$-0.929320\pi$
$439$	−19.4428	+	16.3144i	−0.927952	+	0.778644i	0.0474965	+	0.998871i	$0.484876\pi$
$440$	−6.26060	−	2.27867i	−0.298463	−	0.108632i
$441$		0			0
$442$	2.74159	+	15.5483i	0.130404	+	0.739558i
$443$	−4.62446	+	1.68317i	−0.219715	+	0.0799697i	−0.449532	−	0.893264i	$-0.648409\pi$
$443$	−4.62446	+	1.68317i	−0.219715	+	0.0799697i	0.229817	+	0.973234i	$0.426187\pi$
$444$		0			0
$445$	−6.12549	−	10.6097i	−0.290376	−	0.502946i
$446$	−9.62841	−	8.07919i	−0.455918	−	0.382561i
$447$		0			0
$448$	10.7675	+	18.6499i	0.508718	+	0.881125i
$449$	2.03325	−	3.52169i	0.0959548	−	0.166199i	−0.814052	−	0.580792i	$-0.802743\pi$
$449$	2.03325	−	3.52169i	0.0959548	−	0.166199i	0.910007	+	0.414594i	$0.136076\pi$
$450$		0			0
$451$	−3.17460	−	18.0041i	−0.149486	−	0.847778i
$452$	−1.04837	+	5.94560i	−0.0493111	+	0.279657i
$453$		0			0
$454$	21.3432	−	17.9091i	1.00169	−	0.840515i
$455$	−11.1866			−0.524434
$456$		0			0
$457$	−13.5517			−0.633922			−0.316961	−	0.948439i	$-0.602662\pi$
$457$	−13.5517			−0.633922			−0.316961	+	0.948439i	$0.602662\pi$
$458$	−29.1417	+	24.4528i	−1.36170	+	1.14260i
$459$		0			0
$460$	−0.110747	+	0.628077i	−0.00516360	+	0.0292842i
$461$	−3.10504	−	17.6096i	−0.144616	−	0.820160i	−0.967674	−	0.252203i	$-0.918845\pi$
$461$	−3.10504	−	17.6096i	−0.144616	−	0.820160i	0.823058	−	0.567957i	$-0.192266\pi$
$462$		0			0
$463$	−0.653477	+	1.13185i	−0.0303696	+	0.0526017i	−0.880811	−	0.473468i	$-0.843002\pi$
$463$	−0.653477	+	1.13185i	−0.0303696	+	0.0526017i	0.850441	+	0.526070i	$0.176335\pi$
$464$	22.4196	+	38.8320i	1.04081	+	1.80273i
$465$		0			0
$466$	−16.4206	−	13.7785i	−0.760669	−	0.638277i
$467$	13.5133	+	23.4057i	0.625321	+	1.08309i	0.988479	+	0.151360i	$0.0483653\pi$
$467$	13.5133	+	23.4057i	0.625321	+	1.08309i	−0.363158	+	0.931728i	$0.618301\pi$
$468$		0			0
$469$	−54.9557	+	20.0022i	−2.53762	+	0.923618i
$470$	−2.48435	−	14.0895i	−0.114595	−	0.649899i
$471$		0			0
$472$	−8.17446	−	2.97526i	−0.376260	−	0.136947i
$473$	13.2541	−	11.1215i	0.609422	−	0.511366i
$474$		0			0
$475$	−0.323695	+	4.34686i	−0.0148522	+	0.199448i
$476$	−6.75101			−0.309432
$477$		0			0
$478$	5.51587	+	2.00761i	0.252290	+	0.0918261i
$479$	−0.0502667	+	0.285076i	−0.00229674	+	0.0130255i	−0.985935	−	0.167132i	$-0.946550\pi$
$479$	−0.0502667	+	0.285076i	−0.00229674	+	0.0130255i	0.983638	+	0.180157i	$0.0576606\pi$
$480$		0			0
$481$	−22.2944	+	8.11451i	−1.01654	+	0.369990i
$482$	4.14719	−	7.18315i	0.188899	−	0.327184i
$483$		0			0
$484$	−1.19619	−	1.00373i	−0.0543724	−	0.0456239i
$485$	−8.87934	−	7.45065i	−0.403190	−	0.338317i
$486$		0			0
$487$	−7.68554	+	13.3117i	−0.348265	+	0.603212i	−0.985941	−	0.167092i	$-0.946562\pi$
$487$	−7.68554	+	13.3117i	−0.348265	+	0.603212i	0.637676	+	0.770304i	$0.279896\pi$
$488$	−16.9497	+	6.16917i	−0.767275	+	0.279265i
$489$		0			0
$490$	2.48360	−	14.0852i	0.112198	−	0.636304i
$491$	13.6351	+	4.96276i	0.615342	+	0.223966i	0.630839	−	0.775914i	$-0.282711\pi$
$491$	13.6351	+	4.96276i	0.615342	+	0.223966i	−0.0154969	+	0.999880i	$0.504933\pi$
$492$		0			0
$493$	34.2979			1.54470
$494$	11.1455	+	15.4871i	0.501462	+	0.696799i
$495$		0			0
$496$	−5.61213	+	4.70914i	−0.251992	+	0.211447i
$497$	12.5166	+	4.55567i	0.561447	+	0.204350i
$498$		0			0
$499$	−2.55922	−	14.5140i	−0.114566	−	0.649737i	−0.986964	−	0.160941i	$-0.948547\pi$
$499$	−2.55922	−	14.5140i	−0.114566	−	0.649737i	0.872398	−	0.488797i	$-0.162564\pi$
$500$	−0.438260	+	0.159514i	−0.0195996	+	0.00713367i
$501$		0			0
$502$	−9.85039	−	17.0614i	−0.439644	−	0.761486i
$503$	−3.33423	−	2.79775i	−0.148666	−	0.124746i	0.565421	−	0.824802i	$-0.308714\pi$
$503$	−3.33423	−	2.79775i	−0.148666	−	0.124746i	−0.714087	+	0.700057i	$0.753158\pi$
$504$		0			0
$505$	−3.49120	−	6.04693i	−0.155356	−	0.269085i
$506$	−2.97030	+	5.14471i	−0.132046	+	0.228710i
$507$		0			0
$508$	−0.672034	−	3.81129i	−0.0298167	−	0.169099i
$509$	−1.49227	+	8.46308i	−0.0661437	+	0.375119i	0.933710	+	0.358029i	$0.116551\pi$
$509$	−1.49227	+	8.46308i	−0.0661437	+	0.375119i	−0.999854	+	0.0170899i	$0.994560\pi$
$510$		0			0
$511$	30.7680	−	25.8174i	1.36109	−	1.14209i
$512$	−10.5094			−0.464455
$513$		0			0
$514$	−13.5058			−0.595715
$515$	7.76292	−	6.51386i	0.342075	−	0.287035i
$516$		0			0
$517$	4.37590	−	24.8169i	0.192452	−	1.09145i
$518$	−9.31607	−	52.8341i	−0.409325	−	2.32140i
$519$		0			0
$520$	3.35663	−	5.81386i	0.147198	−	0.254955i
$521$	1.03475	+	1.79225i	0.0453334	+	0.0785197i	0.887802	−	0.460226i	$-0.152232\pi$
$521$	1.03475	+	1.79225i	0.0453334	+	0.0785197i	−0.842468	+	0.538746i	$0.818898\pi$
$522$		0			0
$523$	10.7338	+	9.00674i	0.469357	+	0.393837i	0.846560	−	0.532293i	$-0.178670\pi$
$523$	10.7338	+	9.00674i	0.469357	+	0.393837i	−0.377203	+	0.926131i	$0.623114\pi$
$524$	−1.51852	−	2.63015i	−0.0663368	−	0.114899i
$525$		0			0
$526$	39.3886	−	14.3363i	1.71742	−	0.625091i
$527$	0.973090	+	5.51866i	0.0423884	+	0.240397i
$528$		0			0
$529$	19.8557	+	7.22690i	0.863293	+	0.314213i
$530$	4.74551	−	3.98196i	0.206132	−	0.172965i
$531$		0			0
$532$	−7.34925	+	3.54347i	−0.318630	+	0.153629i
$533$	18.4214			0.797919
$534$		0			0
$535$	−11.0729	−	4.03020i	−0.478723	−	0.174241i
$536$	6.09446	−	34.5634i	0.263240	−	1.49291i
$537$		0			0
$538$	−4.87474	+	1.77426i	−0.210165	+	0.0764938i
$539$	12.5961	−	21.8170i	0.542551	−	0.939725i
$540$		0			0
$541$	−12.7311	−	10.6827i	−0.547354	−	0.459285i	0.326690	−	0.945132i	$-0.394067\pi$
$541$	−12.7311	−	10.6827i	−0.547354	−	0.459285i	−0.874044	+	0.485847i	$0.838511\pi$
$542$	−22.1212	−	18.5619i	−0.950186	−	0.797301i
$543$		0			0
$544$	4.66745	−	8.08426i	0.200115	−	0.346610i
$545$	1.50734	−	0.548626i	0.0645672	−	0.0235005i
$546$		0			0
$547$	−1.04789	+	5.94288i	−0.0448045	+	0.254099i	−0.998980	−	0.0451475i	$-0.985624\pi$
$547$	−1.04789	+	5.94288i	−0.0448045	+	0.254099i	0.954176	+	0.299247i	$0.0967353\pi$
$548$	6.51632	+	2.37175i	0.278364	+	0.101316i
$549$		0			0
$550$	−4.34425			−0.185239
$551$	37.3372	−	18.0023i	1.59062	−	0.766923i
$552$		0			0
$553$	5.98698	−	5.02367i	0.254592	−	0.213628i
$554$	−39.5190	−	14.3837i	−1.67900	−	0.611106i
$555$		0			0
$556$	0.806489	+	4.57383i	0.0342028	+	0.193973i
$557$	−26.4311	+	9.62013i	−1.11992	+	0.407618i	−0.834623	−	0.550821i	$-0.814315\pi$
$557$	−26.4311	+	9.62013i	−1.11992	+	0.407618i	−0.285298	+	0.958439i	$0.592093\pi$
$558$		0			0
$559$	8.71703	+	15.0983i	0.368691	+	0.638591i
$560$	14.4967	+	12.1641i	0.612596	+	0.514029i
$561$		0			0
$562$	16.9188	+	29.3043i	0.713679	+	1.23613i
$563$	−0.605777	+	1.04924i	−0.0255305	+	0.0442201i	−0.878508	−	0.477727i	$-0.841461\pi$
$563$	−0.605777	+	1.04924i	−0.0255305	+	0.0442201i	0.852978	+	0.521947i	$0.174794\pi$
$564$		0			0
$565$	−2.24785	−	12.7482i	−0.0945679	−	0.536321i
$566$	5.00343	−	28.3759i	0.210310	−	1.19273i
$567$		0			0
$568$	−6.12340	+	5.13814i	−0.256932	+	0.215592i
$569$	17.5814			0.737049			0.368524	−	0.929618i	$-0.379863\pi$
$569$	17.5814			0.737049			0.368524	+	0.929618i	$0.379863\pi$
$570$		0			0
$571$	42.6982			1.78686			0.893432	−	0.449198i	$-0.148290\pi$
$571$	42.6982			1.78686			0.893432	+	0.449198i	$0.148290\pi$
$572$	−2.75468	+	2.31145i	−0.115179	+	0.0966467i
$573$		0			0
$574$	−7.23343	+	41.0228i	−0.301918	+	1.71226i
$575$	−0.237457	−	1.34669i	−0.00990266	−	0.0561608i
$576$		0			0
$577$	−2.74678	+	4.75757i	−0.114350	+	0.198060i	−0.917520	−	0.397690i	$-0.869812\pi$
$577$	−2.74678	+	4.75757i	−0.114350	+	0.198060i	0.803170	+	0.595750i	$0.203145\pi$
$578$	3.13426	+	5.42869i	0.130368	+	0.225804i
$579$		0			0
$580$	3.39745	+	2.85080i	0.141071	+	0.118373i
$581$	−3.24817	−	5.62600i	−0.134757	−	0.233406i
$582$		0			0
$583$	10.2534	−	3.73193i	0.424653	−	0.154561i
$584$	4.18555	+	23.7374i	0.173199	+	0.982262i
$585$		0			0
$586$	−13.7079	−	4.98928i	−0.566270	−	0.206105i
$587$	9.51705	−	7.98576i	0.392811	−	0.329607i	−0.424896	−	0.905242i	$-0.639689\pi$
$587$	9.51705	−	7.98576i	0.392811	−	0.329607i	0.817707	+	0.575635i	$0.195245\pi$
$588$		0			0
$589$	3.95596	+	5.49694i	0.163002	+	0.226498i
$590$	−5.67228			−0.233524
$591$		0			0
$592$	37.7150	+	13.7271i	1.55008	+	0.564182i
$593$	0.194097	−	1.10078i	0.00797061	−	0.0452036i	−0.980563	−	0.196204i	$-0.937138\pi$
$593$	0.194097	−	1.10078i	0.00797061	−	0.0452036i	0.988534	+	0.151001i	$0.0482496\pi$
$594$		0			0
$595$	13.6022	−	4.95079i	0.557635	−	0.202963i
$596$	−0.333845	+	0.578237i	−0.0136748	+	0.0236855i
$597$		0			0
$598$	−4.58551	−	3.84770i	−0.187515	−	0.157344i
$599$	21.0736	+	17.6829i	0.861044	+	0.722502i	0.962193	−	0.272370i	$-0.0878073\pi$
$599$	21.0736	+	17.6829i	0.861044	+	0.722502i	−0.101149	+	0.994871i	$0.532252\pi$
$600$		0			0
$601$	−7.02686	+	12.1709i	−0.286631	+	0.496460i	−0.973004	−	0.230790i	$-0.925869\pi$
$601$	−7.02686	+	12.1709i	−0.286631	+	0.496460i	0.686372	+	0.727251i	$0.259202\pi$
$602$	−37.0455	+	13.4835i	−1.50986	+	0.549545i
$603$		0			0
$604$	−0.662785	+	3.75884i	−0.0269683	+	0.152945i
$605$	3.14621	+	1.14513i	0.127912	+	0.0465560i
$606$		0			0
$607$	−16.1942			−0.657304			−0.328652	−	0.944451i	$-0.606594\pi$
$607$	−16.1942			−0.657304			−0.328652	+	0.944451i	$0.606594\pi$
$608$	0.837784	−	11.2505i	0.0339766	−	0.456268i
$609$		0			0
$610$	−9.00976	+	7.56008i	−0.364794	+	0.306099i
$611$	23.8609	+	8.68464i	0.965307	+	0.351343i
$612$		0			0
$613$	4.80621	+	27.2574i	0.194121	+	1.10091i	0.913665	+	0.406468i	$0.133240\pi$
$613$	4.80621	+	27.2574i	0.194121	+	1.10091i	−0.719544	+	0.694447i	$0.755649\pi$
$614$	16.2557	−	5.91659i	0.656027	−	0.238774i
$615$		0			0
$616$	13.3693	+	23.1563i	0.538665	+	0.932995i
$617$	−4.66949	−	3.91817i	−0.187987	−	0.157739i	0.543937	−	0.839126i	$-0.316933\pi$
$617$	−4.66949	−	3.91817i	−0.187987	−	0.157739i	−0.731924	+	0.681386i	$0.761377\pi$
$618$		0			0
$619$	5.85935	+	10.1487i	0.235507	+	0.407910i	0.959420	−	0.281981i	$-0.0909916\pi$
$619$	5.85935	+	10.1487i	0.235507	+	0.407910i	−0.723913	+	0.689891i	$0.757658\pi$
$620$	−0.362314	+	0.627546i	−0.0145509	+	0.0252028i
$621$		0			0
$622$	−6.92195	−	39.2564i	−0.277545	−	1.57404i
$623$	−8.53787	+	48.4207i	−0.342063	+	1.93993i
$624$		0			0
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	33.0677			1.32165
$627$		0			0
$628$	−3.65419			−0.145818
$629$	23.5175	−	19.7335i	0.937704	−	0.786827i
$630$		0			0
$631$	3.63291	−	20.6033i	0.144624	−	0.820203i	−0.823045	−	0.567977i	$-0.807726\pi$
$631$	3.63291	−	20.6033i	0.144624	−	0.820203i	0.967668	−	0.252226i	$-0.0811626\pi$
$632$	0.814445	+	4.61895i	0.0323969	+	0.183732i
$633$		0			0
$634$	3.14869	−	5.45369i	0.125050	−	0.216594i
$635$	4.14901	+	7.18630i	0.164649	+	0.285180i
$636$		0			0
$637$	19.4456	+	16.3168i	0.770464	+	0.646496i
$638$	20.6556	+	35.7765i	0.817763	+	1.41641i
$639$		0			0
$640$	−12.7829	+	4.65259i	−0.505288	+	0.183910i
$641$	1.64737	+	9.34270i	0.0650672	+	0.369015i	0.999903	+	0.0139340i	$0.00443547\pi$
$641$	1.64737	+	9.34270i	0.0650672	+	0.369015i	−0.934836	+	0.355081i	$0.884453\pi$
$642$		0			0
$643$	−11.7831	−	4.28868i	−0.464678	−	0.169129i	0.0990618	−	0.995081i	$-0.468416\pi$
$643$	−11.7831	−	4.28868i	−0.464678	−	0.169129i	−0.563740	+	0.825952i	$0.690638\pi$
$644$	1.96076	−	1.64527i	0.0772647	−	0.0648328i
$645$		0			0
$646$	−20.4064	−	13.8988i	−0.802879	−	0.546840i
$647$	15.6504			0.615281			0.307640	−	0.951503i	$-0.400461\pi$
$647$	15.6504			0.615281			0.307640	+	0.951503i	$0.400461\pi$
$648$		0			0
$649$	−9.38851	−	3.41714i	−0.368531	−	0.134134i
$650$	0.760131	−	4.31092i	0.0298148	−	0.169088i
$651$		0			0
$652$	8.45814	−	3.07851i	0.331246	−	0.120564i
$653$	9.54528	−	16.5329i	0.373536	−	0.646983i	−0.616571	−	0.787299i	$-0.711479\pi$
$653$	9.54528	−	16.5329i	0.373536	−	0.646983i	0.990107	+	0.140317i	$0.0448120\pi$
$654$		0			0
$655$	4.98836	+	4.18573i	0.194911	+	0.163550i
$656$	−23.8723	−	20.0312i	−0.932056	−	0.782088i
$657$		0			0
$658$	−28.7093	+	49.7259i	−1.11920	+	1.93852i
$659$	−9.83688	+	3.58033i	−0.383190	+	0.139470i	−0.526431	−	0.850218i	$-0.676470\pi$
$659$	−9.83688	+	3.58033i	−0.383190	+	0.139470i	0.143240	+	0.989688i	$0.454248\pi$
$660$		0			0
$661$	−5.06045	+	28.6992i	−0.196829	+	1.11627i	0.712962	+	0.701203i	$0.247353\pi$
$661$	−5.06045	+	28.6992i	−0.196829	+	1.11627i	−0.909791	+	0.415068i	$0.863758\pi$
$662$	47.4250	+	17.2613i	1.84323	+	0.670880i
$663$		0			0
$664$	3.89858			0.151294
$665$	12.2090	−	12.5290i	0.473443	−	0.485855i
$666$		0			0
$667$	−9.96145	+	8.35865i	−0.385709	+	0.323648i
$668$	4.11512	+	1.49778i	0.159219	+	0.0579509i
$669$		0			0
$670$	−3.97392	−	22.5372i	−0.153526	−	0.870689i
$671$	−19.4670	+	7.08540i	−0.751514	+	0.273529i
$672$		0			0
$673$	7.27748	+	12.6050i	0.280526	+	0.485886i	0.971514	−	0.236980i	$-0.0761577\pi$
$673$	7.27748	+	12.6050i	0.280526	+	0.485886i	−0.690988	+	0.722866i	$0.742824\pi$
$674$	28.2087	+	23.6699i	1.08656	+	0.911731i
$675$		0			0
$676$	1.21979	+	2.11274i	0.0469151	+	0.0812594i
$677$	−5.48999	+	9.50895i	−0.210998	+	0.365459i	−0.952027	−	0.306014i	$-0.901005\pi$
$677$	−5.48999	+	9.50895i	−0.210998	+	0.365459i	0.741029	+	0.671473i	$0.234338\pi$
$678$		0			0
$679$	8.07804	+	45.8128i	0.310007	+	1.75813i
$680$	−1.50845	+	8.55484i	−0.0578464	+	0.328063i
$681$		0			0
$682$	−5.17055	+	4.33861i	−0.197991	+	0.166134i
$683$	43.3449			1.65854			0.829272	−	0.558844i	$-0.188755\pi$
$683$	43.3449			1.65854			0.829272	+	0.558844i	$0.188755\pi$
$684$		0			0
$685$	−14.8686			−0.568101
$686$	−10.1737	+	8.53678i	−0.388435	+	0.325936i
$687$		0			0
$688$	5.12137	−	29.0447i	0.195251	−	1.10732i
$689$	1.90922	+	10.8277i	0.0727355	+	0.412504i
$690$		0			0
$691$	−15.2029	+	26.3321i	−0.578344	+	1.00172i	0.417325	+	0.908757i	$0.362968\pi$
$691$	−15.2029	+	26.3321i	−0.578344	+	1.00172i	−0.995669	+	0.0929641i	$0.970366\pi$
$692$	1.93803	+	3.35677i	0.0736729	+	0.127605i
$693$		0			0
$694$	−7.81205	−	6.55509i	−0.296541	−	0.248828i
$695$	−4.97912	−	8.62408i	−0.188869	−	0.327130i
$696$		0			0
$697$	−22.3993	+	8.15268i	−0.848434	+	0.308805i
$698$	−7.41793	−	42.0692i	−0.280773	−	1.59234i
$699$		0			0
$700$	1.75890	+	0.640187i	0.0664801	+	0.0241968i
$701$	−16.3694	+	13.7356i	−0.618266	+	0.518786i	−0.897258	−	0.441507i	$-0.854444\pi$
$701$	−16.3694	+	13.7356i	−0.618266	+	0.518786i	0.278992	+	0.960293i	$0.410000\pi$
$702$		0			0
$703$	15.2437	−	33.8261i	0.574929	−	1.27577i
$704$	−14.8430			−0.559416
$705$		0			0
$706$	−9.68284	−	3.52427i	−0.364419	−	0.132638i
$707$	−4.86613	+	27.5972i	−0.183010	+	1.03790i
$708$		0			0
$709$	18.8045	−	6.84427i	0.706217	−	0.257042i	0.0361542	−	0.999346i	$-0.488489\pi$
$709$	18.8045	−	6.84427i	0.706217	−	0.257042i	0.670063	+	0.742304i	$0.266267\pi$
$710$	−2.60611	+	4.51391i	−0.0978055	+	0.169404i
$711$		0			0
$712$	−22.6033	−	18.9664i	−0.847093	−	0.710795i
$713$	−1.62756	−	1.36569i	−0.0609527	−	0.0511454i
$714$		0			0
$715$	3.85515	−	6.67732i	0.144175	−	0.249718i
$716$	−8.12177	+	2.95608i	−0.303525	+	0.110474i
$717$		0			0
$718$	0.745028	−	4.22526i	0.0278042	−	0.157685i
$719$	−3.85410	−	1.40278i	−0.143734	−	0.0523147i	0.269152	−	0.963098i	$-0.413257\pi$
$719$	−3.85410	−	1.40278i	−0.143734	−	0.0523147i	−0.412885	+	0.910783i	$0.635479\pi$
$720$		0			0
$721$	−40.6705			−1.51465
$722$	−29.5099	−	4.41950i	−1.09824	−	0.164477i
$723$		0			0
$724$	4.04762	−	3.39636i	0.150429	−	0.126225i
$725$	−8.93592	−	3.25241i	−0.331872	−	0.120791i
$726$		0			0
$727$	−6.20784	−	35.2064i	−0.230236	−	1.30573i	−0.852418	−	0.522861i	$-0.824865\pi$
$727$	−6.20784	−	35.2064i	−0.230236	−	1.30573i	0.622182	−	0.782872i	$-0.286246\pi$
$728$	−25.3180	+	9.21498i	−0.938346	+	0.341530i
$729$		0			0
$730$	7.85844	+	13.6112i	0.290854	+	0.503774i
$731$	−17.2814	−	14.5008i	−0.639175	−	0.536332i
$732$		0			0
$733$	15.6472	+	27.1018i	0.577943	+	1.00103i	0.995715	+	0.0924752i	$0.0294779\pi$
$733$	15.6472	+	27.1018i	0.577943	+	1.00103i	−0.417772	+	0.908552i	$0.637189\pi$
$734$	−5.16610	+	8.94794i	−0.190684	+	0.330274i
$735$		0			0
$736$	0.614584	+	3.48548i	0.0226539	+	0.128476i
$737$	6.99959	−	39.6966i	0.257833	−	1.46224i
$738$		0			0
$739$	24.9062	−	20.8988i	0.916188	−	0.768773i	−0.0570981	−	0.998369i	$-0.518185\pi$
$739$	24.9062	−	20.8988i	0.916188	−	0.768773i	0.973286	+	0.229596i	$0.0737403\pi$
$740$	3.96980			0.145933
$741$		0			0
$742$	−24.8621			−0.912716
$743$	−29.7586	+	24.9704i	−1.09174	+	0.916076i	−0.996842	−	0.0794116i	$-0.974696\pi$
$743$	−29.7586	+	24.9704i	−1.09174	+	0.916076i	−0.0948946	+	0.995487i	$0.530251\pi$
$744$		0			0
$745$	0.248599	−	1.40987i	0.00910796	−	0.0516538i
$746$	−2.33438	−	13.2389i	−0.0854676	−	0.484711i
$747$		0			0
$748$	2.32656	−	4.02972i	0.0850674	−	0.147341i
$749$	23.6458	+	40.9557i	0.863998	+	1.49649i
$750$		0			0
$751$	−1.38487	−	1.16204i	−0.0505345	−	0.0424035i	0.617171	−	0.786829i	$-0.288279\pi$
$751$	−1.38487	−	1.16204i	−0.0505345	−	0.0424035i	−0.667705	+	0.744426i	$0.732723\pi$
$752$	−21.4777	−	37.2005i	−0.783212	−	1.35656i
$753$		0			0
$754$	−39.1162	+	14.2371i	−1.42453	+	0.518486i
$755$	−1.42111	−	8.05950i	−0.0517194	−	0.293315i
$756$		0			0
$757$	−21.2025	−	7.71707i	−0.770617	−	0.280482i	−0.0733625	−	0.997305i	$-0.523373\pi$
$757$	−21.2025	−	7.71707i	−0.770617	−	0.280482i	−0.697254	+	0.716824i	$0.745595\pi$
$758$	17.1408	−	14.3828i	0.622580	−	0.522407i
$759$		0			0
$760$	2.84815	+	10.1047i	0.103313	+	0.366535i
$761$	−2.85080			−0.103341			−0.0516707	−	0.998664i	$-0.516455\pi$
$761$	−2.85080			−0.103341			−0.0516707	+	0.998664i	$0.516455\pi$
$762$		0			0
$763$	−6.04950	−	2.20184i	−0.219006	−	0.0797118i
$764$	−0.962764	+	5.46011i	−0.0348316	+	0.197540i
$765$		0			0
$766$	31.5317	−	11.4766i	1.13929	−	0.414666i
$767$	5.03367	−	8.71856i	0.181755	−	0.314809i
$768$		0			0
$769$	4.68799	+	3.93369i	0.169053	+	0.141852i	0.723389	−	0.690441i	$-0.242583\pi$
$769$	4.68799	+	3.93369i	0.169053	+	0.141852i	−0.554336	+	0.832293i	$0.687028\pi$
$770$	13.3560	+	11.2070i	0.481318	+	0.403874i
$771$		0			0
$772$	0.223360	−	0.386872i	0.00803892	−	0.0139238i
$773$	47.1328	−	17.1549i	1.69525	−	0.617020i	0.699978	−	0.714164i	$-0.253193\pi$
$773$	47.1328	−	17.1549i	1.69525	−	0.617020i	0.995270	+	0.0971441i	$0.0309708\pi$
$774$		0			0
$775$	0.269798	−	1.53010i	0.00969143	−	0.0549629i
$776$	−26.2337	−	9.54827i	−0.941734	−	0.342763i
$777$		0			0
$778$	−24.0167			−0.861039
$779$	−20.1050	+	20.6321i	−0.720337	+	0.739221i
$780$		0			0
$781$	−7.03283	+	5.90124i	−0.251654	+	0.211163i
$782$	7.27856	+	2.64918i	0.260281	+	0.0947345i
$783$		0			0
$784$	−7.45686	−	42.2900i	−0.266317	−	1.51036i
$785$	7.36260	−	2.67977i	0.262783	−	0.0956450i
$786$		0			0
$787$	16.5102	+	28.5964i	0.588524	+	1.01935i	0.994426	+	0.105437i	$0.0336240\pi$
$787$	16.5102	+	28.5964i	0.588524	+	1.01935i	−0.405902	+	0.913917i	$0.633043\pi$
$788$	−5.10101	−	4.28025i	−0.181716	−	0.152478i
$789$		0			0
$790$	1.52913	+	2.64854i	0.0544041	+	0.0942307i
$791$	−25.9763	+	44.9922i	−0.923610	+	1.59974i
$792$		0			0
$793$	−3.62482	−	20.5574i	−0.128721	−	0.730014i
$794$	8.89089	−	50.4227i	0.315526	−	1.78944i
$795$		0			0
$796$	−2.77448	+	2.32806i	−0.0983388	+	0.0825160i
$797$	−47.2358			−1.67318			−0.836590	−	0.547830i	$-0.815454\pi$
$797$	−47.2358			−1.67318			−0.836590	+	0.547830i	$0.815454\pi$
$798$		0			0
$799$	−32.8569			−1.16239
$800$	−1.98267	+	1.66365i	−0.0700978	+	0.0588191i
$801$		0			0
$802$	4.72113	−	26.7749i	0.166709	−	0.945454i
$803$	4.80718	+	27.2629i	0.169642	+	0.962085i
$804$		0			0
$805$	−2.74406	+	4.75286i	−0.0967156	+	0.167516i
$806$	−3.40061	−	5.89003i	−0.119781	−	0.207467i
$807$		0			0
$808$	−12.8826	−	10.8098i	−0.453210	−	0.380288i
$809$	2.19118	+	3.79524i	0.0770378	+	0.133433i	0.901971	−	0.431797i	$-0.142120\pi$
$809$	2.19118	+	3.79524i	0.0770378	+	0.133433i	−0.824933	+	0.565231i	$0.808787\pi$
$810$		0			0
$811$	31.9131	−	11.6154i	1.12062	−	0.407873i	0.285743	−	0.958306i	$-0.407760\pi$
$811$	31.9131	−	11.6154i	1.12062	−	0.407873i	0.834879	+	0.550433i	$0.185537\pi$
$812$	−3.09085	−	17.5291i	−0.108468	−	0.615151i
$813$		0			0
$814$	34.7475	+	12.6471i	1.21790	+	0.443279i
$815$	−14.7842	+	12.4054i	−0.517867	+	0.434542i
$816$		0			0
$817$	−26.4240	−	6.71513i	−0.924458	−	0.234933i
$818$	−17.0038			−0.594525
$819$		0			0
$820$	−2.89645	−	1.05422i	−0.101149	−	0.0368151i
$821$	−6.96961	+	39.5266i	−0.243241	+	1.37949i	0.581301	+	0.813688i	$0.302544\pi$
$821$	−6.96961	+	39.5266i	−0.243241	+	1.37949i	−0.824542	+	0.565800i	$0.808567\pi$
$822$		0			0
$823$	−5.93493	+	2.16014i	−0.206879	+	0.0752976i	−0.443381	−	0.896333i	$-0.646221\pi$
$823$	−5.93493	+	2.16014i	−0.206879	+	0.0752976i	0.236502	+	0.971631i	$0.423999\pi$
$824$	12.2036	−	21.1372i	0.425132	−	0.736350i
$825$		0			0
$826$	17.4389	+	14.6330i	0.606779	+	0.509148i
$827$	−16.3638	−	13.7308i	−0.569024	−	0.477468i	0.312298	−	0.949984i	$-0.398901\pi$
$827$	−16.3638	−	13.7308i	−0.569024	−	0.477468i	−0.881322	+	0.472516i	$0.843346\pi$
$828$		0			0
$829$	−24.5301	+	42.4874i	−0.851966	+	1.47565i	0.0274658	+	0.999623i	$0.491256\pi$
$829$	−24.5301	+	42.4874i	−0.851966	+	1.47565i	−0.879432	+	0.476025i	$0.842077\pi$
$830$	2.38878	−	0.869446i	0.0829159	−	0.0301789i
$831$		0			0
$832$	2.59714	−	14.7291i	0.0900396	−	0.510640i
$833$	−30.8660	−	11.2343i	−1.06944	−	0.389246i
$834$		0			0
$835$	−9.38968			−0.324943
$836$	0.417606	−	5.60797i	0.0144432	−	0.193956i
$837$		0			0
$838$	−40.8752	+	34.2984i	−1.41201	+	1.18482i
$839$	−6.94430	−	2.52752i	−0.239744	−	0.0872597i	0.219354	−	0.975645i	$-0.429605\pi$
$839$	−6.94430	−	2.52752i	−0.239744	−	0.0872597i	−0.459098	+	0.888386i	$0.651827\pi$
$840$		0			0
$841$	10.6670	+	60.4955i	0.367827	+	2.08605i
$842$	−12.2610	+	4.46264i	−0.422542	+	0.153793i
$843$		0			0
$844$	−1.77757	−	3.07884i	−0.0611865	−	0.105978i
$845$	−4.00704	−	3.36231i	−0.137846	−	0.115667i
$846$		0			0
$847$	−6.71862	−	11.6370i	−0.230855	−	0.399852i
$848$	9.29980	−	16.1077i	0.319357	−	0.553142i
$849$		0			0
$850$	0.983591	+	5.57822i	0.0337369	+	0.191332i
$851$	−2.02120	+	11.4628i	−0.0692858	+	0.392939i
$852$		0			0
$853$	2.10899	−	1.76966i	0.0722106	−	0.0605919i	−0.605968	−	0.795489i	$-0.707214\pi$
$853$	2.10899	−	1.76966i	0.0722106	−	0.0605919i	0.678179	+	0.734897i	$0.262770\pi$
$854$	47.2028			1.61525
$855$		0			0
$856$	−28.3806			−0.970029
$857$	33.8025	−	28.3637i	1.15467	−	0.968885i	0.154854	−	0.987937i	$-0.450509\pi$
$857$	33.8025	−	28.3637i	1.15467	−	0.968885i	0.999818	+	0.0190524i	$0.00606493\pi$
$858$		0			0
$859$	−2.04090	+	11.5745i	−0.0696347	+	0.394918i	0.929992	+	0.367581i	$0.119814\pi$
$859$	−2.04090	+	11.5745i	−0.0696347	+	0.394918i	−0.999626	+	0.0273372i	$0.991297\pi$
$860$	−0.506556	−	2.87282i	−0.0172734	−	0.0979623i
$861$		0			0
$862$	−9.52474	+	16.4973i	−0.324414	+	0.561902i
$863$	−17.1415	−	29.6900i	−0.583504	−	1.01066i	−0.995060	−	0.0992746i	$-0.968348\pi$
$863$	−17.1415	−	29.6900i	−0.583504	−	1.01066i	0.411556	−	0.911385i	$-0.364986\pi$
$864$		0			0
$865$	−6.36647	−	5.34210i	−0.216466	−	0.181637i
$866$	4.26808	+	7.39254i	0.145035	+	0.251209i
$867$		0			0
$868$	2.73281	−	0.994661i	0.0927576	−	0.0337610i
$869$	0.935404	+	5.30494i	0.0317314	+	0.179958i
$870$		0			0
$871$	38.1673	+	13.8918i	1.29325	+	0.470704i
$872$	2.95955	−	2.48335i	0.100223	−	0.0840970i
$873$		0			0
$874$	9.31406	−	0.936439i	0.315053	−	0.0316755i
$875$	−4.01337			−0.135677
$876$		0			0
$877$	22.7444	+	8.27828i	0.768023	+	0.279537i	0.696169	−	0.717878i	$-0.254886\pi$
$877$	22.7444	+	8.27828i	0.768023	+	0.279537i	0.0718537	+	0.997415i	$0.477109\pi$
$878$	−6.92157	+	39.2542i	−0.233592	+	1.32476i
$879$		0			0
$880$	−12.2567	+	4.46109i	−0.413175	+	0.150383i
$881$	−19.5867	+	33.9251i	−0.659892	+	1.14297i	0.320752	+	0.947163i	$0.396064\pi$
$881$	−19.5867	+	33.9251i	−0.659892	+	1.14297i	−0.980643	+	0.195802i	$0.937269\pi$
$882$		0			0
$883$	24.7964	+	20.8067i	0.834467	+	0.700201i	0.956312	−	0.292348i	$-0.0944366\pi$
$883$	24.7964	+	20.8067i	0.834467	+	0.700201i	−0.121845	+	0.992549i	$0.538881\pi$
$884$	3.59171	+	3.01380i	0.120802	+	0.101365i
$885$		0			0
$886$	−3.86435	+	6.69325i	−0.129825	+	0.224864i
$887$	0.357853	−	0.130248i	0.0120155	−	0.00437329i	−0.336005	−	0.941860i	$-0.609076\pi$
$887$	0.357853	−	0.130248i	0.0120155	−	0.00437329i	0.348021	+	0.937487i	$0.386854\pi$
$888$		0			0
$889$	5.78301	−	32.7971i	0.193956	−	1.09998i
$890$	−18.0795	−	6.58041i	−0.606027	−	0.220576i
$891$		0			0
$892$	−3.73264			−0.124978
$893$	−35.7685	+	17.2459i	−1.19695	+	0.577114i
$894$		0			0
$895$	14.1962	−	11.9121i	0.474528	−	0.398176i
$896$	51.3024	+	18.6726i	1.71389	+	0.623807i
$897$		0			0
$898$	−1.10897	−	6.28930i	−0.0370069	−	0.209877i
$899$	−13.8838	+	5.05328i	−0.463050	+	0.168536i
$900$		0			0
$901$	−7.11348	−	12.3209i	−0.236984	−	0.410469i
$902$	−21.9940	−	18.4551i	−0.732319	−	0.614488i
$903$		0			0
$904$	−15.5889	−	27.0007i	−0.518478	−	0.898030i
$905$	−5.66461	+	9.81139i	−0.188298	+	0.326142i
$906$		0			0
$907$	−0.855419	−	4.85132i	−0.0284037	−	0.161086i	0.967307	−	0.253609i	$-0.0816177\pi$
$907$	−0.855419	−	4.85132i	−0.0284037	−	0.161086i	−0.995710	+	0.0925237i	$0.970507\pi$
$908$	1.43678	−	8.14841i	0.0476814	−	0.270415i
$909$		0			0
$910$	−13.4580	+	11.2926i	−0.446129	+	0.374346i
$911$	−20.6775			−0.685075			−0.342537	−	0.939504i	$-0.611286\pi$
$911$	−20.6775			−0.685075			−0.342537	+	0.939504i	$0.611286\pi$
$912$		0			0
$913$	4.47759			0.148187
$914$	−16.3034	+	13.6802i	−0.539269	+	0.452500i
$915$		0			0
$916$	−1.96176	+	11.1257i	−0.0648184	+	0.367604i
$917$	−4.53819	−	25.7374i	−0.149864	−	0.849923i
$918$		0			0
$919$	30.2934	−	52.4697i	0.999287	−	1.73082i	0.466943	−	0.884287i	$-0.345355\pi$
$919$	30.2934	−	52.4697i	0.999287	−	1.73082i	0.532344	−	0.846528i	$-0.321311\pi$
$920$	−1.64677	−	2.85228i	−0.0542923	−	0.0940370i
$921$		0			0
$922$	−21.5121	−	18.0508i	−0.708462	−	0.594470i
$923$	−4.62540	−	8.01143i	−0.152247	−	0.263699i
$924$		0			0
$925$	−7.99851	+	2.91122i	−0.262989	+	0.0957203i
$926$	0.356419	+	2.02135i	0.0117127	+	0.0664258i
$927$		0			0
$928$	23.1278	+	8.41784i	0.759208	+	0.276329i
$929$	0.222628	−	0.186807i	0.00730419	−	0.00612894i	−0.639128	−	0.769100i	$-0.720705\pi$
$929$	0.222628	−	0.186807i	0.00730419	−	0.00612894i	0.646432	+	0.762971i	$0.276260\pi$
$930$		0			0
$931$	−39.4978	+	3.97113i	−1.29449	+	0.130149i
$932$	−6.36576			−0.208517
$933$		0			0
$934$	39.8848	+	14.5169i	1.30507	+	0.475007i
$935$	−1.73248	+	9.82538i	−0.0566581	+	0.321324i
$936$		0			0
$937$	−4.98587	+	1.81471i	−0.162881	+	0.0592839i	−0.422174	−	0.906515i	$-0.638733\pi$
$937$	−4.98587	+	1.81471i	−0.162881	+	0.0592839i	0.259293	+	0.965799i	$0.416511\pi$
$938$	−45.9227	+	79.5405i	−1.49943	+	2.59709i
$939$		0			0
$940$	−3.25471	−	2.73103i	−0.106157	−	0.0890763i
$941$	21.7752	+	18.2716i	0.709852	+	0.595637i	0.924558	−	0.381042i	$-0.124435\pi$
$941$	21.7752	+	18.2716i	0.709852	+	0.595637i	−0.214706	+	0.976679i	$0.568879\pi$
$942$		0			0
$943$	4.51877	−	7.82674i	0.147151	−	0.254874i
$944$	−16.0036	+	5.82484i	−0.520873	+	0.189582i
$945$		0			0
$946$	4.71841	−	26.7594i	0.153409	−	0.870024i
$947$	−46.9649	−	17.0938i	−1.52615	−	0.555474i	−0.563478	−	0.826131i	$-0.690537\pi$
$947$	−46.9649	−	17.0938i	−1.52615	−	0.555474i	−0.962676	+	0.270657i	$0.912759\pi$
$948$		0			0
$949$	−27.8948			−0.905504
$950$	3.99865	+	5.55627i	0.129733	+	0.180269i
$951$		0			0
$952$	26.7069	−	22.4097i	0.865575	−	0.726304i
$953$	−11.3705	−	4.13854i	−0.368328	−	0.134060i	0.151224	−	0.988500i	$-0.451679\pi$
$953$	−11.3705	−	4.13854i	−0.368328	−	0.134060i	−0.519551	+	0.854439i	$0.673901\pi$
$954$		0			0
$955$	−2.06430	−	11.7073i	−0.0667993	−	0.378838i
$956$	1.63806	−	0.596205i	0.0529786	−	0.0192826i
$957$		0			0
$958$	0.227306	+	0.393705i	0.00734391	+	0.0127200i
$959$	45.7124	+	38.3572i	1.47613	+	1.23862i
$960$		0			0
$961$	14.2930	+	24.7562i	0.461065	+	0.798587i
$962$	−18.6299	+	32.2680i	−0.600653	+	1.04036i
$963$		0			0
$964$	−0.427730	−	2.42578i	−0.0137763	−	0.0781291i
$965$	−0.166326	+	0.943282i	−0.00535423	+	0.0303653i
$966$		0			0
$967$	10.0879	−	8.46474i	0.324404	−	0.272208i	−0.466011	−	0.884779i	$-0.654309\pi$
$967$	10.0879	−	8.46474i	0.324404	−	0.272208i	0.790415	+	0.612571i	$0.209865\pi$
$968$	8.06395			0.259185
$969$		0			0
$970$	−18.2036			−0.584482
$971$	13.4161	−	11.2575i	0.430544	−	0.361269i	−0.401613	−	0.915809i	$-0.631550\pi$
$971$	13.4161	−	11.2575i	0.430544	−	0.361269i	0.832157	+	0.554540i	$0.187106\pi$
$972$		0			0
$973$	−6.94003	+	39.3589i	−0.222487	+	1.26179i
$974$	4.19184	+	23.7731i	0.134315	+	0.761740i
$975$		0			0
$976$	−17.6565	+	30.5819i	−0.565170	+	0.978903i
$977$	−5.26807	−	9.12457i	−0.168541	−	0.291921i	0.769366	−	0.638808i	$-0.220572\pi$
$977$	−5.26807	−	9.12457i	−0.168541	−	0.291921i	−0.937907	+	0.346887i	$0.887239\pi$
$978$		0			0
$979$	−25.9602	−	21.7832i	−0.829693	−	0.696195i
$980$	−2.12372	−	3.67839i	−0.0678397	−	0.117502i
$981$		0			0
$982$	21.4135	−	7.79388i	0.683333	−	0.248713i
$983$	−9.02591	−	51.1885i	−0.287882	−	1.63266i	−0.694807	−	0.719197i	$-0.744510\pi$
$983$	−9.02591	−	51.1885i	−0.287882	−	1.63266i	0.406925	−	0.913462i	$-0.366601\pi$
$984$		0			0
$985$	13.4166	+	4.88324i	0.427488	+	0.155593i
$986$	41.2621	−	34.6230i	1.31405	−	1.10262i
$987$		0			0
$988$	5.49188	+	1.39565i	0.174720	+	0.0444016i
$989$	8.55315			0.271974
$990$		0			0
$991$	−6.36762	−	2.31763i	−0.202274	−	0.0736218i	0.238896	−	0.971045i	$-0.423214\pi$
$991$	−6.36762	−	2.31763i	−0.202274	−	0.0736218i	−0.441171	+	0.897423i	$0.645437\pi$
$992$	−0.698288	+	3.96019i	−0.0221707	+	0.125736i
$993$		0			0
$994$	19.6570	−	7.15456i	0.623482	−	0.226929i
$995$	3.88286	−	6.72530i	0.123095	−	0.213206i
$996$		0			0
$997$	−30.8481	−	25.8846i	−0.976968	−	0.819774i	0.00666090	−	0.999978i	$-0.497880\pi$
$997$	−30.8481	−	25.8846i	−0.976968	−	0.819774i	−0.983629	+	0.180204i	$0.942324\pi$
$998$	−17.7305	−	14.8777i	−0.561250	−	0.470944i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.bs.b.766.3		18
3.2	odd	2		95.2.k.b.6.1	✓	18
15.2	even	4		475.2.u.c.424.2		36
15.8	even	4		475.2.u.c.424.5		36
15.14	odd	2		475.2.l.b.101.3		18
19.16	even	9	inner	855.2.bs.b.586.3		18
57.23	odd	18		1805.2.a.t.1.2		9
57.35	odd	18		95.2.k.b.16.1	yes	18
57.53	even	18		1805.2.a.u.1.8		9
285.92	even	36		475.2.u.c.149.5		36
285.149	odd	18		475.2.l.b.301.3		18
285.194	odd	18		9025.2.a.ce.1.8		9
285.224	even	18		9025.2.a.cd.1.2		9
285.263	even	36		475.2.u.c.149.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.6.1	✓	18	3.2	odd	2
95.2.k.b.16.1	yes	18	57.35	odd	18
475.2.l.b.101.3		18	15.14	odd	2
475.2.l.b.301.3		18	285.149	odd	18
475.2.u.c.149.2		36	285.263	even	36
475.2.u.c.149.5		36	285.92	even	36
475.2.u.c.424.2		36	15.2	even	4
475.2.u.c.424.5		36	15.8	even	4
855.2.bs.b.586.3		18	19.16	even	9	inner
855.2.bs.b.766.3		18	1.1	even	1	trivial
1805.2.a.t.1.2		9	57.23	odd	18
1805.2.a.u.1.8		9	57.53	even	18
9025.2.a.cd.1.2		9	285.224	even	18
9025.2.a.ce.1.8		9	285.194	odd	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)

\(f(q)\)	\(=\)	\(q+(1.20305 - 1.00948i) q^{2} +(0.0809872 - 0.459301i) q^{4} +(0.173648 + 0.984808i) q^{5} +(2.00668 - 3.47568i) q^{7} +(1.20425 + 2.08582i) q^{8} +O(q^{10})\)	\(q+(1.20305 - 1.00948i) q^{2} +(0.0809872 - 0.459301i) q^{4} +(0.173648 + 0.984808i) q^{5} +(2.00668 - 3.47568i) q^{7} +(1.20425 + 2.08582i) q^{8} +(1.20305 + 1.00948i) q^{10} +(1.38310 + 2.39560i) q^{11} +(-2.61923 + 0.953321i) q^{13} +(-1.09448 - 6.20713i) q^{14} +(4.43089 + 1.61271i) q^{16} +(2.76292 - 2.31836i) q^{17} +(1.79089 - 3.97401i) q^{19} +0.466387 q^{20} +(4.08226 + 1.48582i) q^{22} +(-0.237457 + 1.34669i) q^{23} +(-0.939693 + 0.342020i) q^{25} +(-2.18871 + 3.79096i) q^{26} +(-1.43387 - 1.20316i) q^{28} +(7.28463 + 6.11253i) q^{29} +(-0.776853 + 1.34555i) q^{31} +(2.43210 - 0.885212i) q^{32} +(0.983591 - 5.57822i) q^{34} +(3.77133 + 1.37265i) q^{35} +8.51183 q^{37} +(-1.85715 - 6.58880i) q^{38} +(-1.84502 + 1.54815i) q^{40} +(-6.21041 - 2.26041i) q^{41} +(-1.08613 - 6.15974i) q^{43} +(1.21232 - 0.441247i) q^{44} +(1.07378 + 1.85984i) q^{46} +(-6.97857 - 5.85572i) q^{47} +(-4.55356 - 7.88699i) q^{49} +(-0.785237 + 1.36007i) q^{50} +(0.225738 + 1.28022i) q^{52} +(0.684965 - 3.88463i) q^{53} +(-2.11903 + 1.77808i) q^{55} +9.66619 q^{56} +14.9343 q^{58} +(-2.76682 + 2.32164i) q^{59} +(-1.30047 + 7.37531i) q^{61} +(0.423711 + 2.40298i) q^{62} +(-2.68292 + 4.64695i) q^{64} +(-1.39366 - 2.41389i) q^{65} +(-11.1628 - 9.36668i) q^{67} +(-0.841066 - 1.45677i) q^{68} +(5.92277 - 2.15571i) q^{70} +(0.576318 + 3.26846i) q^{71} +(9.40420 + 3.42285i) q^{73} +(10.2402 - 8.59253i) q^{74} +(-1.68023 - 1.14440i) q^{76} +11.1018 q^{77} +(1.82991 + 0.666034i) q^{79} +(-0.818796 + 4.64362i) q^{80} +(-9.75329 + 3.54991i) q^{82} +(0.809339 - 1.40182i) q^{83} +(2.76292 + 2.31836i) q^{85} +(-7.52481 - 6.31406i) q^{86} +(-3.33120 + 5.76980i) q^{88} +(-11.5122 + 4.19008i) q^{89} +(-1.94252 + 11.0166i) q^{91} +(0.599304 + 0.218129i) q^{92} -14.3068 q^{94} +(4.22462 + 1.07360i) q^{95} +(-8.87934 + 7.45065i) q^{97} +(-13.4399 - 4.89173i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8}+O(q^{10}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8	\( 18 q - 3 q^{2} - 3 q^{4} + 12 q^{8} - 3 q^{10} - 3 q^{13} - 24 q^{14} + 21 q^{16} + 24 q^{17} - 12 q^{19} + 12 q^{20} + 15 q^{22} - 21 q^{23} + 21 q^{26} - 24 q^{28} + 9 q^{29} + 30 q^{31} - 45 q^{32} + 24 q^{34} + 6 q^{35} - 60 q^{37} + 15 q^{38} - 6 q^{40} + 6 q^{41} - 6 q^{43} + 30 q^{44} + 21 q^{46} - 33 q^{47} - 3 q^{49} + 9 q^{52} - 24 q^{53} - 3 q^{55} + 72 q^{56} + 36 q^{58} - 18 q^{59} + 6 q^{61} - 12 q^{62} - 24 q^{64} - 3 q^{65} - 24 q^{67} + 3 q^{68} + 39 q^{70} - 24 q^{71} + 6 q^{73} + 39 q^{74} + 27 q^{76} - 24 q^{77} + 9 q^{79} - 33 q^{80} - 57 q^{82} + 24 q^{85} + 33 q^{86} + 39 q^{88} + 6 q^{89} - 6 q^{91} + 66 q^{92} - 66 q^{94} + 15 q^{95} - 87 q^{97} - 39 q^{98}+O(q^{100}) \) 18 * q - 3 * q^2 - 3 * q^4 + 12 * q^8 - 3 * q^10 - 3 * q^13 - 24 * q^14 + 21 * q^16 + 24 * q^17 - 12 * q^19 + 12 * q^20 + 15 * q^22 - 21 * q^23 + 21 * q^26 - 24 * q^28 + 9 * q^29 + 30 * q^31 - 45 * q^32 + 24 * q^34 + 6 * q^35 - 60 * q^37 + 15 * q^38 - 6 * q^40 + 6 * q^41 - 6 * q^43 + 30 * q^44 + 21 * q^46 - 33 * q^47 - 3 * q^49 + 9 * q^52 - 24 * q^53 - 3 * q^55 + 72 * q^56 + 36 * q^58 - 18 * q^59 + 6 * q^61 - 12 * q^62 - 24 * q^64 - 3 * q^65 - 24 * q^67 + 3 * q^68 + 39 * q^70 - 24 * q^71 + 6 * q^73 + 39 * q^74 + 27 * q^76 - 24 * q^77 + 9 * q^79 - 33 * q^80 - 57 * q^82 + 24 * q^85 + 33 * q^86 + 39 * q^88 + 6 * q^89 - 6 * q^91 + 66 * q^92 - 66 * q^94 + 15 * q^95 - 87 * q^97 - 39 * q^98

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