LMFDB - Embedded newform 351.2.bd.d.188.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [351,2,Mod(80,351)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(351, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("351.80");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 351 = 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	351.bd (of order $12$, degree $4$, 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:	$2.80274911095$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 88 x^{16} - 6 x^{15} + 48 x^{13} + 1980 x^{12} - 204 x^{11} + 18 x^{10} + 2076 x^{9} + \cdots + 81 $ x^20 + 88x^16 - 6x^15 + 48x^13 + 1980x^12 - 204x^11 + 18x^10 + 2076x^9 + 8020x^8 + 2220x^7 + 792x^6 + 4350x^5 + 10936x^4 + 6648x^3 + 1800x^2 - 540*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.4
Root			$-0.799987 - 0.799987i$ of defining polynomial
Character	$\chi$	$=$	351.188
Dual form			351.2.bd.d.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09280 - 0.292816i) q^{2} +(-0.623573 + 0.360020i) q^{4} +(1.12325 + 1.12325i) q^{5} +(-1.05984 + 3.95536i) q^{7} +(-2.17600 + 2.17600i) q^{8} +O(q^{10})$	\(q+(1.09280 - 0.292816i) q^{2} +(-0.623573 + 0.360020i) q^{4} +(1.12325 + 1.12325i) q^{5} +(-1.05984 + 3.95536i) q^{7} +(-2.17600 + 2.17600i) q^{8} +(1.55640 + 0.898588i) q^{10} +(0.0163954 + 0.0611884i) q^{11} +(1.34978 - 3.34336i) q^{13} +4.63277i q^{14} +(-1.02073 + 1.76796i) q^{16} +(4.09207 + 7.08767i) q^{17} +(-4.65740 - 1.24795i) q^{19} +(-1.10482 - 0.296037i) q^{20} +(0.0358339 + 0.0620661i) q^{22} +(2.27319 - 3.93728i) q^{23} -2.47661i q^{25} +(0.496060 - 4.04888i) q^{26} +(-0.763124 - 2.84802i) q^{28} +(6.43640 + 3.71606i) q^{29} +(5.87912 - 5.87912i) q^{31} +(0.995169 - 3.71402i) q^{32} +(6.54721 + 6.54721i) q^{34} +(-5.63333 + 3.25241i) q^{35} +(0.396302 - 0.106189i) q^{37} -5.45504 q^{38} -4.88839 q^{40} +(-2.14410 + 0.574509i) q^{41} +(-4.43719 + 2.56181i) q^{43} +(-0.0322528 - 0.0322528i) q^{44} +(1.33125 - 4.96830i) q^{46} +(1.10804 - 1.10804i) q^{47} +(-8.45944 - 4.88406i) q^{49} +(-0.725189 - 2.70644i) q^{50} +(0.361989 + 2.57078i) q^{52} +5.97216i q^{53} +(-0.0503139 + 0.0871462i) q^{55} +(-6.30065 - 10.9131i) q^{56} +(8.12183 + 2.17624i) q^{58} +(-2.39325 - 0.641268i) q^{59} +(2.76797 + 4.79426i) q^{61} +(4.70322 - 8.14621i) q^{62} -8.43302i q^{64} +(5.27159 - 2.23929i) q^{65} +(-2.32380 - 8.67254i) q^{67} +(-5.10341 - 2.94645i) q^{68} +(-5.20377 + 5.20377i) q^{70} +(2.10535 - 7.85727i) q^{71} +(4.18306 + 4.18306i) q^{73} +(0.401987 - 0.232087i) q^{74} +(3.35352 - 0.898573i) q^{76} -0.259399 q^{77} -8.14039 q^{79} +(-3.13240 + 0.839324i) q^{80} +(-2.17485 + 1.25565i) q^{82} +(2.89552 + 2.89552i) q^{83} +(-3.36482 + 12.5577i) q^{85} +(-4.09884 + 4.09884i) q^{86} +(-0.168822 - 0.0974695i) q^{88} +(-4.31594 - 16.1073i) q^{89} +(11.7937 + 8.88230i) q^{91} +3.27358i q^{92} +(0.886417 - 1.53532i) q^{94} +(-3.82968 - 6.63320i) q^{95} +(0.103775 + 0.0278066i) q^{97} +(-10.6746 - 2.86026i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{5}+O(q^{10}) $ 20 * q - 6 * q^5	$ 20 q - 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} + 12 q^{17} - 12 q^{19} - 36 q^{20} + 8 q^{22} + 42 q^{26} + 2 q^{28} + 6 q^{29} - 22 q^{31} + 36 q^{32} - 6 q^{34} + 36 q^{35} + 8 q^{37} - 72 q^{38} - 36 q^{40} - 30 q^{41} - 30 q^{43} - 36 q^{44} - 48 q^{46} - 6 q^{47} + 30 q^{49} - 54 q^{50} + 4 q^{52} - 28 q^{55} + 60 q^{56} + 44 q^{58} - 30 q^{59} - 16 q^{61} + 30 q^{62} + 78 q^{65} + 18 q^{67} - 6 q^{68} + 38 q^{70} + 60 q^{71} + 72 q^{74} - 8 q^{76} + 12 q^{77} - 16 q^{79} - 126 q^{80} + 78 q^{82} - 12 q^{83} + 12 q^{85} - 18 q^{86} - 84 q^{89} + 30 q^{91} - 22 q^{94} + 66 q^{95} + 26 q^{97} - 42 q^{98}+O(q^{100}) $ 20 * q - 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 + 12 * q^17 - 12 * q^19 - 36 * q^20 + 8 * q^22 + 42 * q^26 + 2 * q^28 + 6 * q^29 - 22 * q^31 + 36 * q^32 - 6 * q^34 + 36 * q^35 + 8 * q^37 - 72 * q^38 - 36 * q^40 - 30 * q^41 - 30 * q^43 - 36 * q^44 - 48 * q^46 - 6 * q^47 + 30 * q^49 - 54 * q^50 + 4 * q^52 - 28 * q^55 + 60 * q^56 + 44 * q^58 - 30 * q^59 - 16 * q^61 + 30 * q^62 + 78 * q^65 + 18 * q^67 - 6 * q^68 + 38 * q^70 + 60 * q^71 + 72 * q^74 - 8 * q^76 + 12 * q^77 - 16 * q^79 - 126 * q^80 + 78 * q^82 - 12 * q^83 + 12 * q^85 - 18 * q^86 - 84 * q^89 + 30 * q^91 - 22 * q^94 + 66 * q^95 + 26 * q^97 - 42 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/351\mathbb{Z}\right)^\times$.

$n$	$28$	$326$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.09280	−	0.292816i	0.772728	−	0.207052i	0.149152	−	0.988814i	$-0.452346\pi$
$2$	1.09280	−	0.292816i	0.772728	−	0.207052i	0.623577	+	0.781762i	$0.285679\pi$
$3$		0			0
$3$		0			0
$4$	−0.623573	+	0.360020i	−0.311787	+	0.180010i
$5$	1.12325	+	1.12325i	0.502334	+	0.502334i	0.912163	−	0.409829i	$-0.134411\pi$
$5$	1.12325	+	1.12325i	0.502334	+	0.502334i	−0.409829	+	0.912163i	$0.634411\pi$
$6$		0			0
$7$	−1.05984	+	3.95536i	−0.400580	+	1.49499i	0.411484	+	0.911417i	$0.365011\pi$
$7$	−1.05984	+	3.95536i	−0.400580	+	1.49499i	−0.812064	+	0.583568i	$0.801656\pi$
$8$	−2.17600	+	2.17600i	−0.769331	+	0.769331i
$9$		0			0
$10$	1.55640	+	0.898588i	0.492177	+	0.284158i
$11$	0.0163954	+	0.0611884i	0.00494339	+	0.0184490i	0.968353	−	0.249583i	$-0.0802935\pi$
$11$	0.0163954	+	0.0611884i	0.00494339	+	0.0184490i	−0.963410	+	0.268032i	$0.913627\pi$
$12$		0			0
$13$	1.34978	−	3.34336i	0.374363	−	0.927282i
$13$	1.34978	−	3.34336i	0.374363	−	0.927282i
$14$			4.63277i			1.23816i
$15$		0			0
$16$	−1.02073	+	1.76796i	−0.255183	+	0.441989i
$17$	4.09207	+	7.08767i	0.992472	+	1.71901i	0.602298	+	0.798272i	$0.294252\pi$
$17$	4.09207	+	7.08767i	0.992472	+	1.71901i	0.390175	+	0.920741i	$0.372415\pi$
$18$		0			0
$19$	−4.65740	−	1.24795i	−1.06848	−	0.286299i	−0.318613	−	0.947885i	$-0.603217\pi$
$19$	−4.65740	−	1.24795i	−1.06848	−	0.286299i	−0.749869	+	0.661586i	$0.769884\pi$
$20$	−1.10482	−	0.296037i	−0.247046	−	0.0661958i
$21$		0			0
$22$	0.0358339	+	0.0620661i	0.00763980	+	0.0132325i
$23$	2.27319	−	3.93728i	0.473993	−	0.820980i	−0.525564	−	0.850754i	$-0.676146\pi$
$23$	2.27319	−	3.93728i	0.473993	−	0.820980i	0.999557	+	0.0297743i	$0.00947885\pi$
$24$		0			0
$25$		−	2.47661i		−	0.495321i
$26$	0.496060	−	4.04888i	0.0972853	−	0.794050i
$27$		0			0
$28$	−0.763124	−	2.84802i	−0.144217	−	0.538225i
$29$	6.43640	+	3.71606i	1.19521	+	0.690054i	0.959483	−	0.281765i	$-0.0909200\pi$
$29$	6.43640	+	3.71606i	1.19521	+	0.690054i	0.235726	+	0.971820i	$0.424253\pi$
$30$		0			0
$31$	5.87912	−	5.87912i	1.05592	−	1.05592i	0.0575794	−	0.998341i	$-0.481662\pi$
$31$	5.87912	−	5.87912i	1.05592	−	1.05592i	0.998341	−	0.0575794i	$-0.0183382\pi$
$32$	0.995169	−	3.71402i	0.175923	−	0.656553i
$33$		0			0
$34$	6.54721	+	6.54721i	1.12284	+	1.12284i
$35$	−5.63333	+	3.25241i	−0.952207	+	0.549757i
$36$		0			0
$37$	0.396302	−	0.106189i	0.0651517	−	0.0174574i	−0.226096	−	0.974105i	$-0.572596\pi$
$37$	0.396302	−	0.106189i	0.0651517	−	0.0174574i	0.291248	+	0.956648i	$0.405930\pi$
$38$	−5.45504			−0.884925
$39$		0			0
$40$	−4.88839			−0.772923
$41$	−2.14410	+	0.574509i	−0.334852	+	0.0897233i	−0.422327	−	0.906443i	$-0.638787\pi$
$41$	−2.14410	+	0.574509i	−0.334852	+	0.0897233i	0.0874755	+	0.996167i	$0.472120\pi$
$42$		0			0
$43$	−4.43719	+	2.56181i	−0.676665	+	0.390673i	−0.798598	−	0.601865i	$-0.794424\pi$
$43$	−4.43719	+	2.56181i	−0.676665	+	0.390673i	0.121932	+	0.992538i	$0.461091\pi$
$44$	−0.0322528	−	0.0322528i	−0.00486229	−	0.00486229i
$45$		0			0
$46$	1.33125	−	4.96830i	0.196282	−	0.732536i
$47$	1.10804	−	1.10804i	0.161624	−	0.161624i	−0.621662	−	0.783286i	$-0.713542\pi$
$47$	1.10804	−	1.10804i	0.161624	−	0.161624i	0.783286	+	0.621662i	$0.213542\pi$
$48$		0			0
$49$	−8.45944	−	4.88406i	−1.20849	−	0.697723i
$50$	−0.725189	−	2.70644i	−0.102557	−	0.382749i
$51$		0			0
$52$	0.361989	+	2.57078i	0.0501988	+	0.356503i
$53$			5.97216i			0.820340i	0.912009	+	0.410170i	$0.134531\pi$
$53$			5.97216i			0.820340i	−0.912009	+	0.410170i	$0.865469\pi$
$54$		0			0
$55$	−0.0503139	+	0.0871462i	−0.00678432	+	0.0117508i
$56$	−6.30065	−	10.9131i	−0.841960	−	1.45832i
$57$		0			0
$58$	8.12183	+	2.17624i	1.06645	+	0.285754i
$59$	−2.39325	−	0.641268i	−0.311574	−	0.0834860i	0.0996436	−	0.995023i	$-0.468230\pi$
$59$	−2.39325	−	0.641268i	−0.311574	−	0.0834860i	−0.411218	+	0.911537i	$0.634896\pi$
$60$		0			0
$61$	2.76797	+	4.79426i	0.354402	+	0.613842i	0.987015	−	0.160626i	$-0.0513512\pi$
$61$	2.76797	+	4.79426i	0.354402	+	0.613842i	−0.632614	+	0.774468i	$0.718018\pi$
$62$	4.70322	−	8.14621i	0.597309	−	1.03457i
$63$		0			0
$64$		−	8.43302i		−	1.05413i
$65$	5.27159	−	2.23929i	0.653861	−	0.277750i
$66$		0			0
$67$	−2.32380	−	8.67254i	−0.283897	−	1.05952i	−0.949641	−	0.313339i	$-0.898552\pi$
$67$	−2.32380	−	8.67254i	−0.283897	−	1.05952i	0.665744	−	0.746180i	$-0.268114\pi$
$68$	−5.10341	−	2.94645i	−0.618879	−	0.357310i
$69$		0			0
$70$	−5.20377	+	5.20377i	−0.621969	+	0.621969i
$71$	2.10535	−	7.85727i	0.249859	−	0.932486i	−0.721020	−	0.692915i	$-0.756326\pi$
$71$	2.10535	−	7.85727i	0.249859	−	0.932486i	0.970879	−	0.239572i	$-0.0770071\pi$
$72$		0			0
$73$	4.18306	+	4.18306i	0.489591	+	0.489591i	0.908177	−	0.418586i	$-0.137474\pi$
$73$	4.18306	+	4.18306i	0.489591	+	0.489591i	−0.418586	+	0.908177i	$0.637474\pi$
$74$	0.401987	−	0.232087i	0.0467300	−	0.0269796i
$75$		0			0
$76$	3.35352	−	0.898573i	0.384675	−	0.103073i
$77$	−0.259399			−0.0295612
$78$		0			0
$79$	−8.14039			−0.915865			−0.457933	−	0.888987i	$-0.651410\pi$
$79$	−8.14039			−0.915865			−0.457933	+	0.888987i	$0.651410\pi$
$80$	−3.13240	+	0.839324i	−0.350213	+	0.0938393i
$81$		0			0
$82$	−2.17485	+	1.25565i	−0.240172	+	0.138663i
$83$	2.89552	+	2.89552i	0.317824	+	0.317824i	0.847931	−	0.530107i	$-0.177848\pi$
$83$	2.89552	+	2.89552i	0.317824	+	0.317824i	−0.530107	+	0.847931i	$0.677848\pi$
$84$		0			0
$85$	−3.36482	+	12.5577i	−0.364966	+	1.36207i
$86$	−4.09884	+	4.09884i	−0.441989	+	0.441989i
$87$		0			0
$88$	−0.168822	−	0.0974695i	−0.0179965	−	0.0103903i
$89$	−4.31594	−	16.1073i	−0.457489	−	1.70737i	−0.680666	−	0.732593i	$-0.738310\pi$
$89$	−4.31594	−	16.1073i	−0.457489	−	1.70737i	0.223178	−	0.974778i	$-0.428357\pi$
$90$		0			0
$91$	11.7937	+	8.88230i	1.23631	+	0.931118i
$92$			3.27358i			0.341294i
$93$		0			0
$94$	0.886417	−	1.53532i	0.0914269	−	0.158356i
$95$	−3.82968	−	6.63320i	−0.392917	−	0.680552i
$96$		0			0
$97$	0.103775	+	0.0278066i	0.0105368	+	0.00282333i	0.264084	−	0.964500i	$-0.414931\pi$
$97$	0.103775	+	0.0278066i	0.0105368	+	0.00282333i	−0.253547	+	0.967323i	$0.581597\pi$
$98$	−10.6746	−	2.86026i	−1.07830	−	0.288930i
$99$		0			0
$100$	0.891628	+	1.54435i	0.0891628	+	0.154435i
$101$	−0.0906555	+	0.157020i	−0.00902056	+	0.0156241i	−0.870500	−	0.492168i	$-0.836205\pi$
$101$	−0.0906555	+	0.157020i	−0.00902056	+	0.0156241i	0.861480	+	0.507792i	$0.169538\pi$
$102$		0			0
$103$			11.1210i			1.09579i	0.836548	+	0.547893i	$0.184570\pi$
$103$			11.1210i			1.09579i	−0.836548	+	0.547893i	$0.815430\pi$
$104$	4.33802	+	10.2123i	0.425378	+	1.00140i
$105$		0			0
$106$	1.74874	+	6.52640i	0.169853	+	0.633900i
$107$	12.9378	+	7.46962i	1.25074	+	0.722116i	0.971257	−	0.238034i	$-0.0765031\pi$
$107$	12.9378	+	7.46962i	1.25074	+	0.722116i	0.279484	+	0.960150i	$0.409836\pi$
$108$		0			0
$109$	2.04951	−	2.04951i	0.196307	−	0.196307i	−0.602108	−	0.798415i	$-0.705672\pi$
$109$	2.04951	−	2.04951i	0.196307	−	0.196307i	0.798415	+	0.602108i	$0.205672\pi$
$110$	−0.0294654	+	0.109966i	−0.00280942	+	0.0104849i
$111$		0			0
$112$	−5.91110	−	5.91110i	−0.558546	−	0.558546i
$113$	14.2118	−	8.20520i	1.33694	−	0.771880i	0.350584	−	0.936531i	$-0.385983\pi$
$113$	14.2118	−	8.20520i	1.33694	−	0.771880i	0.986352	+	0.164651i	$0.0526499\pi$
$114$		0			0
$115$	6.97593	−	1.86919i	0.650509	−	0.174303i
$116$	−5.35142			−0.496867
$117$		0			0
$118$	−2.80312			−0.258048
$119$	−32.3712	+	8.67384i	−2.96746	+	0.795129i
$120$		0			0
$121$	9.52280	−	5.49799i	0.865709	−	0.499818i
$122$	4.42868	+	4.42868i	0.400953	+	0.400953i
$123$		0			0
$124$	−1.54946	+	5.78266i	−0.139146	+	0.519298i
$125$	8.39812	−	8.39812i	0.751151	−	0.751151i
$126$		0			0
$127$	−5.68208	−	3.28055i	−0.504203	−	0.291102i	0.226244	−	0.974071i	$-0.427355\pi$
$127$	−5.68208	−	3.28055i	−0.504203	−	0.291102i	−0.730448	+	0.682969i	$0.760689\pi$
$128$	−0.478981	−	1.78758i	−0.0423363	−	0.158001i
$129$		0			0
$130$	5.10511	−	3.99071i	0.447748	−	0.350009i
$131$			10.6000i			0.926122i	0.886326	+	0.463061i	$0.153249\pi$
$131$			10.6000i			0.926122i	−0.886326	+	0.463061i	$0.846751\pi$
$132$		0			0
$133$	9.87216	−	17.0991i	0.856025	−	1.48268i
$134$	−5.07891	−	8.79694i	−0.438751	−	0.759939i
$135$		0			0
$136$	−24.3271	−	6.51842i	−2.08603	−	0.558950i
$137$	7.28002	+	1.95067i	0.621974	+	0.166657i	0.556025	−	0.831166i	$-0.312326\pi$
$137$	7.28002	+	1.95067i	0.621974	+	0.166657i	0.0659489	+	0.997823i	$0.478993\pi$
$138$		0			0
$139$	−1.15995	−	2.00910i	−0.0983861	−	0.170410i	0.812631	−	0.582779i	$-0.198035\pi$
$139$	−1.15995	−	2.00910i	−0.0983861	−	0.170410i	−0.911017	+	0.412369i	$0.864701\pi$
$140$	2.34186	−	4.05623i	0.197924	−	0.342814i
$141$		0			0
$142$		−	9.20293i		−	0.772293i
$143$	0.226705	+	0.0277755i	0.0189581	+	0.00232270i
$144$		0			0
$145$	3.05563	+	11.4038i	0.253756	+	0.947032i
$146$	5.79613	+	3.34640i	0.479691	+	0.276950i
$147$		0			0
$148$	−0.208894	+	0.208894i	−0.0171709	+	0.0171709i
$149$	−2.17822	+	8.12921i	−0.178446	+	0.665971i	0.817493	+	0.575939i	$0.195363\pi$
$149$	−2.17822	+	8.12921i	−0.178446	+	0.665971i	−0.995939	+	0.0900317i	$0.971303\pi$
$150$		0			0
$151$	1.10932	+	1.10932i	0.0902754	+	0.0902754i	0.750802	−	0.660527i	$-0.229667\pi$
$151$	1.10932	+	1.10932i	0.0902754	+	0.0902754i	−0.660527	+	0.750802i	$0.729667\pi$
$152$	12.8500	−	7.41897i	1.04228	−	0.601758i
$153$		0			0
$154$	−0.283472	+	0.0759560i	−0.0228428	+	0.00612071i
$155$	13.2075			1.06085
$156$		0			0
$157$	−13.7842			−1.10010			−0.550051	−	0.835131i	$-0.685392\pi$
$157$	−13.7842			−1.10010			−0.550051	+	0.835131i	$0.685392\pi$
$158$	−8.89584	+	2.38363i	−0.707715	+	0.189632i
$159$		0			0
$160$	5.28961	−	3.05396i	0.418181	−	0.241437i
$161$	13.1642	+	13.1642i	1.03748	+	1.03748i
$162$		0			0
$163$	−2.83139	+	10.5669i	−0.221771	+	0.827662i	0.761901	+	0.647693i	$0.224266\pi$
$163$	−2.83139	+	10.5669i	−0.221771	+	0.827662i	−0.983672	+	0.179968i	$0.942400\pi$
$164$	1.13017	−	1.13017i	0.0882512	−	0.0882512i
$165$		0			0
$166$	4.01208	+	2.31638i	0.311398	+	0.179786i
$167$	−1.96369	−	7.32859i	−0.151955	−	0.567104i	−0.999347	−	0.0361357i	$-0.988495\pi$
$167$	−1.96369	−	7.32859i	−0.151955	−	0.567104i	0.847392	−	0.530968i	$-0.178172\pi$
$168$		0			0
$169$	−9.35616	−	9.02564i	−0.719705	−	0.694280i
$170$			14.7083i			1.12808i
$171$		0			0
$172$	1.84461	−	3.19496i	0.140650	−	0.243613i
$173$	4.94362	+	8.56260i	0.375856	+	0.651002i	0.990455	−	0.137838i	$-0.0440152\pi$
$173$	4.94362	+	8.56260i	0.375856	+	0.651002i	−0.614598	+	0.788840i	$0.710682\pi$
$174$		0			0
$175$	9.79587	+	2.62480i	0.740498	+	0.198416i
$176$	−0.124914	−	0.0334705i	−0.00941573	−	0.00252294i
$177$		0			0
$178$	−9.43294	−	16.3383i	−0.707029	−	1.22461i
$179$	−6.84075	+	11.8485i	−0.511302	+	0.885601i	0.488612	+	0.872501i	$0.337503\pi$
$179$	−6.84075	+	11.8485i	−0.511302	+	0.885601i	−0.999914	+	0.0130996i	$0.995830\pi$
$180$		0			0
$181$		−	6.98163i		−	0.518940i	−0.965751	−	0.259470i	$-0.916452\pi$
$181$		−	6.98163i		−	0.518940i	0.965751	−	0.259470i	$-0.0835479\pi$
$182$	15.4890	+	6.25324i	1.14812	+	0.463521i
$183$		0			0
$184$	3.62106	+	13.5140i	0.266948	+	0.996264i
$185$	0.564425	+	0.325871i	0.0414973	+	0.0239585i
$186$		0			0
$187$	−0.366592	+	0.366592i	−0.0268079	+	0.0268079i
$188$	−0.292027	+	1.08986i	−0.0212983	+	0.0794862i
$189$		0			0
$190$	−6.12739	−	6.12739i	−0.444528	−	0.444528i
$191$	−15.1610	+	8.75323i	−1.09701	+	0.633362i	−0.935435	−	0.353498i	$-0.884992\pi$
$191$	−15.1610	+	8.75323i	−1.09701	+	0.633362i	−0.161579	+	0.986860i	$0.551659\pi$
$192$		0			0
$193$	−7.11926	+	1.90760i	−0.512456	+	0.137312i	−0.505775	−	0.862666i	$-0.668793\pi$
$193$	−7.11926	+	1.90760i	−0.512456	+	0.137312i	−0.00668087	+	0.999978i	$0.502127\pi$
$194$	0.121548			0.00872666
$195$		0			0
$196$	7.03344			0.502389
$197$	−17.0366	+	4.56493i	−1.21380	+	0.325238i	−0.808254	−	0.588834i	$-0.799587\pi$
$197$	−17.0366	+	4.56493i	−1.21380	+	0.325238i	−0.405551	+	0.914072i	$0.632920\pi$
$198$		0			0
$199$	10.0856	−	5.82294i	0.714951	−	0.412777i	−0.0979406	−	0.995192i	$-0.531226\pi$
$199$	10.0856	−	5.82294i	0.714951	−	0.412777i	0.812891	+	0.582415i	$0.197892\pi$
$200$	5.38909	+	5.38909i	0.381066	+	0.381066i
$201$		0			0
$202$	−0.0530907	+	0.198137i	−0.00373545	+	0.0139409i
$203$	−21.5199	+	21.5199i	−1.51040	+	1.51040i
$204$		0			0
$205$	−3.05368	−	1.76304i	−0.213278	−	0.123136i
$206$	3.25641	+	12.1531i	0.226885	+	0.846745i
$207$		0			0
$208$	4.53316	+	5.79903i	0.314318	+	0.402091i
$209$		−	0.305440i		−	0.0211277i
$210$		0			0
$211$	2.11825	−	3.66892i	0.145826	−	0.252579i	−0.783855	−	0.620944i	$-0.786749\pi$
$211$	2.11825	−	3.66892i	0.145826	−	0.252579i	0.929681	+	0.368366i	$0.120083\pi$
$212$	−2.15010	−	3.72408i	−0.147669	−	0.255771i
$213$		0			0
$214$	16.3257	+	4.37445i	1.11600	+	0.299031i
$215$	−7.86165	−	2.10652i	−0.536160	−	0.143664i
$216$		0			0
$217$	17.0231	+	29.4849i	1.15560	+	2.00157i
$218$	1.63958	−	2.83984i	0.111046	−	0.192338i
$219$		0			0
$220$		−	0.0724561i		−	0.00488499i
$221$	29.2201	−	4.11444i	1.96555	−	0.276767i
$222$		0			0
$223$	−6.35325	−	23.7106i	−0.425445	−	1.58778i	−0.762950	−	0.646458i	$-0.776250\pi$
$223$	−6.35325	−	23.7106i	−0.425445	−	1.58778i	0.337505	−	0.941324i	$-0.390417\pi$
$224$	13.6356	+	7.87251i	0.911065	+	0.526004i
$225$		0			0
$226$	13.1281	−	13.1281i	0.873269	−	0.873269i
$227$	6.38690	−	23.8362i	0.423913	−	1.58207i	−0.342371	−	0.939565i	$-0.611230\pi$
$227$	6.38690	−	23.8362i	0.423913	−	1.58207i	0.766284	−	0.642502i	$-0.222103\pi$
$228$		0			0
$229$	7.73587	+	7.73587i	0.511200	+	0.511200i	0.914894	−	0.403694i	$-0.132274\pi$
$229$	7.73587	+	7.73587i	0.511200	+	0.511200i	−0.403694	+	0.914894i	$0.632274\pi$
$230$	7.07599	−	4.08532i	0.466577	−	0.269378i
$231$		0			0
$232$	−22.0917	+	5.91946i	−1.45039	+	0.388631i
$233$	−2.57100			−0.168432			−0.0842159	−	0.996448i	$-0.526839\pi$
$233$	−2.57100			−0.168432			−0.0842159	+	0.996448i	$0.526839\pi$
$234$		0			0
$235$	2.48921			0.162378
$236$	1.72323	−	0.461739i	0.112173	−	0.0300567i
$237$		0			0
$238$	−32.8355	+	18.9576i	−2.12841	+	1.22884i
$239$	−9.87491	−	9.87491i	−0.638755	−	0.638755i	0.311494	−	0.950248i	$-0.399171\pi$
$239$	−9.87491	−	9.87491i	−0.638755	−	0.638755i	−0.950248	+	0.311494i	$0.899171\pi$
$240$		0			0
$241$	2.77804	−	10.3678i	0.178949	−	0.667848i	−0.816896	−	0.576785i	$-0.804307\pi$
$241$	2.77804	−	10.3678i	0.178949	−	0.667848i	0.995845	−	0.0910625i	$-0.0290263\pi$
$242$	8.79665	−	8.79665i	0.565470	−	0.565470i
$243$		0			0
$244$	−3.45206	−	1.99305i	−0.220995	−	0.127592i
$245$	−4.01606	−	14.9881i	−0.256576	−	0.957556i
$246$		0			0
$247$	−10.4588	+	13.8869i	−0.665480	+	0.883604i
$248$			25.5859i			1.62471i
$249$		0			0
$250$	6.71839	−	11.6366i	0.424908	−	0.735963i
$251$	1.25969	+	2.18185i	0.0795111	+	0.137717i	0.903039	−	0.429558i	$-0.141331\pi$
$251$	1.25969	+	2.18185i	0.0795111	+	0.137717i	−0.823528	+	0.567276i	$0.807997\pi$
$252$		0			0
$253$	0.278186	+	0.0745397i	0.0174894	+	0.00468627i
$254$	−7.16999	−	1.92119i	−0.449885	−	0.120546i
$255$		0			0
$256$	7.38615	+	12.7932i	0.461635	+	0.799575i
$257$	13.9407	−	24.1461i	0.869599	−	1.50619i	0.00719206	−	0.999974i	$-0.497711\pi$
$257$	13.9407	−	24.1461i	0.869599	−	1.50619i	0.862407	−	0.506216i	$-0.168956\pi$
$258$		0			0
$259$			1.68006i			0.104394i
$260$	−2.48103	+	3.29424i	−0.153867	+	0.204300i
$261$		0			0
$262$	3.10383	+	11.5837i	0.191755	+	0.715641i
$263$	5.29340	+	3.05615i	0.326405	+	0.188450i	0.654244	−	0.756284i	$-0.272987\pi$
$263$	5.29340	+	3.05615i	0.326405	+	0.188450i	−0.327839	+	0.944734i	$0.606320\pi$
$264$		0			0
$265$	−6.70825	+	6.70825i	−0.412085	+	0.412085i
$266$	5.78145	−	21.5767i	0.354483	−	1.32295i
$267$		0			0
$268$	4.57135	+	4.57135i	0.279240	+	0.279240i
$269$	−10.5240	+	6.07603i	−0.641659	+	0.370462i	−0.785253	−	0.619175i	$-0.787467\pi$
$269$	−10.5240	+	6.07603i	−0.641659	+	0.370462i	0.143594	+	0.989637i	$0.454134\pi$
$270$		0			0
$271$	−5.35044	+	1.43365i	−0.325016	+	0.0870878i	−0.417638	−	0.908614i	$-0.637142\pi$
$271$	−5.35044	+	1.43365i	−0.325016	+	0.0870878i	0.0926219	+	0.995701i	$0.470475\pi$
$272$	−16.7076			−1.01305
$273$		0			0
$274$	8.52681			0.515124
$275$	0.151540	−	0.0406049i	0.00913818	−	0.00244857i
$276$		0			0
$277$	3.09516	−	1.78699i	0.185970	−	0.107370i	−0.404125	−	0.914704i	$-0.632424\pi$
$277$	3.09516	−	1.78699i	0.185970	−	0.107370i	0.590095	+	0.807334i	$0.299090\pi$
$278$	−1.85590	−	1.85590i	−0.111309	−	0.111309i
$279$		0			0
$280$	5.18089	−	19.3353i	0.309617	−	1.15551i
$281$	1.72490	−	1.72490i	0.102899	−	0.102899i	−0.653783	−	0.756682i	$-0.726819\pi$
$281$	1.72490	−	1.72490i	0.102899	−	0.102899i	0.756682	+	0.653783i	$0.226819\pi$
$282$		0			0
$283$	16.4301	+	9.48595i	0.976671	+	0.563881i	0.901263	−	0.433272i	$-0.142641\pi$
$283$	16.4301	+	9.48595i	0.976671	+	0.563881i	0.0754076	+	0.997153i	$0.475974\pi$
$284$	1.51594	+	5.65755i	0.0899543	+	0.335714i
$285$		0			0
$286$	0.255877	−	0.0360298i	0.0151303	−	0.00213049i
$287$		−	9.08956i		−	0.536540i
$288$		0			0
$289$	−24.9900	+	43.2840i	−1.47000	+	2.54612i
$290$	6.67841	+	11.5673i	0.392170	+	0.679258i
$291$		0			0
$292$	−4.11444	−	1.10246i	−0.240779	−	0.0645166i
$293$	−24.6321	−	6.60016i	−1.43903	−	0.385586i	−0.546833	−	0.837242i	$-0.684167\pi$
$293$	−24.6321	−	6.60016i	−1.43903	−	0.385586i	−0.892192	+	0.451656i	$0.850833\pi$
$294$		0			0
$295$	−1.96791	−	3.40853i	−0.114576	−	0.198452i
$296$	−0.631286	+	1.09342i	−0.0366928	+	0.0635538i
$297$		0			0
$298$			9.52144i			0.551562i
$299$	−10.0954	−	12.9146i	−0.583835	−	0.746870i
$300$		0			0
$301$	−5.43020	−	20.2658i	−0.312992	−	1.16810i
$302$	1.53710	+	0.887444i	0.0884501	+	0.0510667i
$303$		0			0
$304$	6.96027	−	6.96027i	0.399199	−	0.399199i
$305$	−2.27604	+	8.49429i	−0.130326	+	0.486382i
$306$		0			0
$307$	−20.3952	−	20.3952i	−1.16402	−	1.16402i	−0.983588	−	0.180429i	$-0.942252\pi$
$307$	−20.3952	−	20.3952i	−1.16402	−	1.16402i	−0.180429	−	0.983588i	$-0.557748\pi$
$308$	0.161754	−	0.0933888i	0.00921679	−	0.00532132i
$309$		0			0
$310$	14.4332	−	3.86735i	0.819748	−	0.219651i
$311$	−11.9218			−0.676026			−0.338013	−	0.941142i	$-0.609755\pi$
$311$	−11.9218			−0.676026			−0.338013	+	0.941142i	$0.609755\pi$
$312$		0			0
$313$	−14.1120			−0.797656			−0.398828	−	0.917026i	$-0.630583\pi$
$313$	−14.1120			−0.797656			−0.398828	+	0.917026i	$0.630583\pi$
$314$	−15.0635	+	4.03624i	−0.850080	+	0.227778i
$315$		0			0
$316$	5.07613	−	2.93070i	0.285555	−	0.164865i
$317$	−8.02310	−	8.02310i	−0.450622	−	0.450622i	0.444939	−	0.895561i	$-0.353225\pi$
$317$	−8.02310	−	8.02310i	−0.450622	−	0.450622i	−0.895561	+	0.444939i	$0.853225\pi$
$318$		0			0
$319$	−0.121852	+	0.454759i	−0.00682242	+	0.0254616i
$320$	9.47241	−	9.47241i	0.529524	−	0.529524i
$321$		0			0
$322$	18.2405	+	10.5312i	1.01650	+	0.586879i
$323$	−10.2134	−	38.1168i	−0.568287	−	2.12088i
$324$		0			0
$325$	−8.28020	−	3.34289i	−0.459303	−	0.185430i
$326$			12.3766i			0.685476i
$327$		0			0
$328$	3.41542	−	5.91568i	0.188585	−	0.326639i
$329$	3.20835	+	5.55703i	0.176882	+	0.306369i
$330$		0			0
$331$	3.21443	+	0.861304i	0.176681	+	0.0473415i	0.346075	−	0.938207i	$-0.387514\pi$
$331$	3.21443	+	0.861304i	0.176681	+	0.0473415i	−0.169394	+	0.985548i	$0.554181\pi$
$332$	−2.84801	−	0.763122i	−0.156305	−	0.0418818i
$333$		0			0
$334$	−4.29185	−	7.43371i	−0.234840	−	0.406754i
$335$	7.13124	−	12.3517i	0.389621	−	0.674844i
$336$		0			0
$337$		−	5.46600i		−	0.297752i	−0.988856	−	0.148876i	$-0.952434\pi$
$337$		−	5.46600i		−	0.297752i	0.988856	−	0.148876i	$-0.0475655\pi$
$338$	−12.8673	−	7.12362i	−0.699888	−	0.387474i
$339$		0			0
$340$	−2.42281	−	9.04203i	−0.131395	−	0.490373i
$341$	0.456124	+	0.263343i	0.0247005	+	0.0142608i
$342$		0			0
$343$	8.01516	−	8.01516i	0.432778	−	0.432778i
$344$	4.08082	−	15.2298i	0.220023	−	0.821137i
$345$		0			0
$346$	7.90967	+	7.90967i	0.425226	+	0.425226i
$347$	1.94374	−	1.12222i	0.104346	−	0.0602439i	−0.446919	−	0.894574i	$-0.647479\pi$
$347$	1.94374	−	1.12222i	0.104346	−	0.0602439i	0.551265	+	0.834330i	$0.314145\pi$
$348$		0			0
$349$	23.8355	−	6.38670i	1.27588	−	0.341872i	0.443602	−	0.896224i	$-0.353700\pi$
$349$	23.8355	−	6.38670i	1.27588	−	0.341872i	0.832282	+	0.554352i	$0.187034\pi$
$350$	11.4735			0.613286
$351$		0			0
$352$	0.243571			0.0129824
$353$	17.3862	−	4.65862i	0.925375	−	0.247954i	0.235494	−	0.971876i	$-0.424329\pi$
$353$	17.3862	−	4.65862i	0.925375	−	0.247954i	0.689881	+	0.723922i	$0.257663\pi$
$354$		0			0
$355$	11.1905	−	6.46086i	0.593932	−	0.342907i
$356$	8.49026	+	8.49026i	0.449983	+	0.449983i
$357$		0			0
$358$	−4.00616	+	14.9512i	−0.211732	+	0.790195i
$359$	−13.8113	+	13.8113i	−0.728934	+	0.728934i	−0.970407	−	0.241473i	$-0.922369\pi$
$359$	−13.8113	+	13.8113i	−0.728934	+	0.728934i	0.241473	+	0.970407i	$0.422369\pi$
$360$		0			0
$361$	3.67955	+	2.12439i	0.193661	+	0.111810i
$362$	−2.04433	−	7.62954i	−0.107448	−	0.401000i
$363$		0			0
$364$	−10.5520	−	1.29281i	−0.553076	−	0.0677617i
$365$			9.39728i			0.491876i
$366$		0			0
$367$	0.601006	−	1.04097i	0.0313723	−	0.0543384i	−0.849913	−	0.526923i	$-0.823346\pi$
$367$	0.601006	−	1.04097i	0.0313723	−	0.0543384i	0.881285	+	0.472585i	$0.156679\pi$
$368$	4.64063	+	8.03781i	0.241910	+	0.419000i
$369$		0			0
$370$	0.712225	+	0.190840i	0.0370268	+	0.00992131i
$371$	−23.6221	−	6.32951i	−1.22640	−	0.328612i
$372$		0			0
$373$	−16.6071	−	28.7644i	−0.859886	−	1.48937i	−0.872037	−	0.489439i	$-0.837201\pi$
$373$	−16.6071	−	28.7644i	−0.859886	−	1.48937i	0.0121518	−	0.999926i	$-0.496132\pi$
$374$	−0.293269	+	0.507957i	−0.0151646	+	0.0262658i
$375$		0			0
$376$			4.82218i			0.248685i
$377$	21.1119	−	16.5033i	1.08732	−	0.849965i
$378$		0			0
$379$	1.14600	+	4.27694i	0.0588662	+	0.219692i	0.989093	−	0.147294i	$-0.0470564\pi$
$379$	1.14600	+	4.27694i	0.0588662	+	0.219692i	−0.930227	+	0.366986i	$0.880390\pi$
$380$	4.77617	+	2.75753i	0.245013	+	0.141458i
$381$		0			0
$382$	−14.0049	+	14.0049i	−0.716555	+	0.716555i
$383$	5.39767	−	20.1444i	0.275808	−	1.02933i	−0.679490	−	0.733685i	$-0.737799\pi$
$383$	5.39767	−	20.1444i	0.275808	−	1.02933i	0.955298	−	0.295645i	$-0.0955345\pi$
$384$		0			0
$385$	−0.291370	−	0.291370i	−0.0148496	−	0.0148496i
$386$	−7.22137	+	4.16926i	−0.367558	+	0.212210i
$387$		0			0
$388$	−0.0747226	+	0.0200218i	−0.00379346	+	0.00101646i
$389$	−20.0101			−1.01455			−0.507277	−	0.861783i	$-0.669348\pi$
$389$	−20.0101			−1.01455			−0.507277	+	0.861783i	$0.669348\pi$
$390$		0			0
$391$	37.2082			1.88170
$392$	29.0354	−	7.78002i	1.46651	−	0.392950i
$393$		0			0
$394$	−17.2809	+	9.97714i	−0.870600	+	0.502641i
$395$	−9.14371	−	9.14371i	−0.460070	−	0.460070i
$396$		0			0
$397$	6.03572	−	22.5256i	0.302924	−	1.13053i	−0.631794	−	0.775136i	$-0.717681\pi$
$397$	6.03572	−	22.5256i	0.302924	−	1.13053i	0.934718	−	0.355391i	$-0.115652\pi$
$398$	9.31655	−	9.31655i	0.466997	−	0.466997i
$399$		0			0
$400$	4.37853	+	2.52795i	0.218927	+	0.126397i
$401$	8.38291	+	31.2854i	0.418623	+	1.56232i	0.777467	+	0.628923i	$0.216504\pi$
$401$	8.38291	+	31.2854i	0.418623	+	1.56232i	−0.358845	+	0.933397i	$0.616829\pi$
$402$		0			0
$403$	−11.7205	−	27.5916i	−0.583839	−	1.37443i
$404$		−	0.130551i		−	0.00649517i
$405$		0			0
$406$	−17.2156	+	29.8183i	−0.854397	+	1.47986i
$407$	0.0129951	+	0.0225081i	0.000644141	+	0.00111569i
$408$		0			0
$409$	−26.3237	−	7.05341i	−1.30162	−	0.348769i	−0.459559	−	0.888147i	$-0.651993\pi$
$409$	−26.3237	−	7.05341i	−1.30162	−	0.348769i	−0.842064	+	0.539378i	$0.818659\pi$
$410$	−3.85332	−	1.03249i	−0.190302	−	0.0509912i
$411$		0			0
$412$	−4.00379	−	6.93477i	−0.197253	−	0.341651i
$413$	5.07289	−	8.78651i	0.249621	−	0.432356i
$414$		0			0
$415$			6.50479i			0.319308i
$416$	−11.0741	−	8.34034i	−0.542951	−	0.408919i
$417$		0			0
$418$	−0.0894375	−	0.333785i	−0.00437453	−	0.0163260i
$419$	−31.6814	−	18.2913i	−1.54774	−	0.893588i	−0.998314	−	0.0580445i	$-0.981513\pi$
$419$	−31.6814	−	18.2913i	−1.54774	−	0.893588i	−0.549425	−	0.835543i	$-0.685153\pi$
$420$		0			0
$421$	−22.0224	+	22.0224i	−1.07331	+	1.07331i	−0.0762148	+	0.997091i	$0.524283\pi$
$421$	−22.0224	+	22.0224i	−1.07331	+	1.07331i	−0.997091	+	0.0762148i	$0.975717\pi$
$422$	1.24051	−	4.62966i	0.0603872	−	0.225368i
$423$		0			0
$424$	−12.9954	−	12.9954i	−0.631113	−	0.631113i
$425$	17.5534	−	10.1344i	0.851463	−	0.491593i
$426$		0			0
$427$	−21.8966	+	5.86718i	−1.05965	+	0.283933i
$428$	−10.7569			−0.519953
$429$		0			0
$430$	−9.20806			−0.444052
$431$	−24.0427	+	6.44223i	−1.15810	+	0.310311i	−0.786206	−	0.617965i	$-0.787957\pi$
$431$	−24.0427	+	6.44223i	−1.15810	+	0.310311i	−0.371891	+	0.928276i	$0.621291\pi$
$432$		0			0
$433$	29.6280	−	17.1058i	1.42383	−	0.822050i	0.427209	−	0.904153i	$-0.359497\pi$
$433$	29.6280	−	17.1058i	1.42383	−	0.822050i	0.996624	+	0.0821030i	$0.0261637\pi$
$434$	27.2366	+	27.2366i	1.30740	+	1.30740i
$435$		0			0
$436$	−0.540155	+	2.01588i	−0.0258687	+	0.0965434i
$437$	−15.5007	+	15.5007i	−0.741498	+	0.741498i
$438$		0			0
$439$	−11.5992	−	6.69682i	−0.553602	−	0.319622i	0.196972	−	0.980409i	$-0.436889\pi$
$439$	−11.5992	−	6.69682i	−0.553602	−	0.319622i	−0.750573	+	0.660787i	$0.770223\pi$
$440$	−0.0801471	−	0.299113i	−0.00382086	−	0.0142596i
$441$		0			0
$442$	30.7270	−	13.0524i	1.46153	−	0.620838i
$443$			31.1539i			1.48017i	0.672516	+	0.740083i	$0.265214\pi$
$443$			31.1539i			1.48017i	−0.672516	+	0.740083i	$0.734786\pi$
$444$		0			0
$445$	13.2447	−	22.9405i	0.627858	−	1.08748i
$446$	−13.8857	−	24.0507i	−0.657507	−	1.13883i
$447$		0			0
$448$	33.3556	+	8.93761i	1.57590	+	0.422262i
$449$	20.2850	+	5.43534i	0.957307	+	0.256510i	0.703460	−	0.710735i	$-0.251637\pi$
$449$	20.2850	+	5.43534i	0.957307	+	0.256510i	0.253847	+	0.967244i	$0.418304\pi$
$450$		0			0
$451$	−0.0703066	−	0.121775i	−0.00331061	−	0.00573414i
$452$	−5.90808	+	10.2331i	−0.277892	+	0.481324i
$453$		0			0
$454$		−	27.9185i		−	1.31028i
$455$	3.27019	+	23.2243i	0.153309	+	1.08877i
$456$		0			0
$457$	5.03193	+	18.7794i	0.235384	+	0.878464i	0.977976	+	0.208720i	$0.0669296\pi$
$457$	5.03193	+	18.7794i	0.235384	+	0.878464i	−0.742592	+	0.669744i	$0.766404\pi$
$458$	10.7190	+	6.18859i	0.500864	+	0.289174i
$459$		0			0
$460$	−3.67706	+	3.67706i	−0.171444	+	0.171444i
$461$	−6.80846	+	25.4095i	−0.317102	+	1.18344i	0.604915	+	0.796290i	$0.293207\pi$
$461$	−6.80846	+	25.4095i	−0.317102	+	1.18344i	−0.922017	+	0.387150i	$0.873460\pi$
$462$		0			0
$463$	11.7377	+	11.7377i	0.545497	+	0.545497i	0.925135	−	0.379638i	$-0.123951\pi$
$463$	11.7377	+	11.7377i	0.545497	+	0.545497i	−0.379638	+	0.925135i	$0.623951\pi$
$464$	−13.1397	+	7.58618i	−0.609993	+	0.352180i
$465$		0			0
$466$	−2.80959	+	0.752829i	−0.130152	+	0.0348741i
$467$	21.4486			0.992522			0.496261	−	0.868173i	$-0.334706\pi$
$467$	21.4486			0.992522			0.496261	+	0.868173i	$0.334706\pi$
$468$		0			0
$469$	36.7659			1.69769
$470$	2.72022	−	0.728881i	0.125474	−	0.0336208i
$471$		0			0
$472$	6.60310	−	3.81230i	0.303932	−	0.175475i
$473$	−0.229503	−	0.229503i	−0.0105526	−	0.0105526i
$474$		0			0
$475$	−3.09068	+	11.5346i	−0.141810	+	0.529242i
$476$	17.0631	−	17.0631i	0.782084	−	0.782084i
$477$		0			0
$478$	−13.6829	−	7.89980i	−0.625839	−	0.361328i
$479$	4.42187	+	16.5026i	0.202040	+	0.754025i	0.990331	+	0.138722i	$0.0442996\pi$
$479$	4.42187	+	16.5026i	0.202040	+	0.754025i	−0.788291	+	0.615303i	$0.789034\pi$
$480$		0			0
$481$	0.179895	−	1.46832i	0.00820250	−	0.0669494i
$482$		−	12.1434i		−	0.553117i
$483$		0			0
$484$	−3.95878	+	6.85680i	−0.179944	+	0.311673i
$485$	0.0853323	+	0.147800i	0.00387474	+	0.00671125i
$486$		0			0
$487$	−28.9124	−	7.74707i	−1.31015	−	0.351053i	−0.464870	−	0.885379i	$-0.653899\pi$
$487$	−28.9124	−	7.74707i	−1.31015	−	0.351053i	−0.845278	+	0.534326i	$0.820565\pi$
$488$	−16.4554	−	4.40921i	−0.744900	−	0.199595i
$489$		0			0
$490$	−8.77752	−	15.2031i	−0.396528	−	0.686806i
$491$	2.62599	−	4.54835i	0.118509	−	0.205264i	−0.800668	−	0.599109i	$-0.795522\pi$
$491$	2.62599	−	4.54835i	0.118509	−	0.205264i	0.919177	+	0.393844i	$0.128855\pi$
$492$		0			0
$493$			60.8254i			2.73944i
$494$	−7.36314	+	18.2382i	−0.331283	+	0.820575i
$495$		0			0
$496$	4.39303	+	16.3950i	0.197253	+	0.736158i
$497$	28.8470	+	16.6548i	1.29397	+	0.747071i
$498$		0			0
$499$	−14.5193	+	14.5193i	−0.649971	+	0.649971i	−0.952986	−	0.303015i	$-0.902007\pi$
$499$	−14.5193	+	14.5193i	−0.649971	+	0.649971i	0.303015	+	0.952986i	$0.402007\pi$
$500$	−2.21335	+	8.26034i	−0.0989840	+	0.369413i
$501$		0			0
$502$	2.01548	+	2.01548i	0.0899551	+	0.0899551i
$503$	9.44832	−	5.45499i	0.421280	−	0.243226i	−0.274345	−	0.961631i	$-0.588461\pi$
$503$	9.44832	−	5.45499i	0.421280	−	0.243226i	0.695625	+	0.718405i	$0.255128\pi$
$504$		0			0
$505$	−0.278202	+	0.0745441i	−0.0123798	+	0.00331717i
$506$	0.325829			0.0144849
$507$		0			0
$508$	4.72426			0.209605
$509$	−5.82779	+	1.56155i	−0.258312	+	0.0692146i	−0.385651	−	0.922645i	$-0.626023\pi$
$509$	−5.82779	+	1.56155i	−0.258312	+	0.0692146i	0.127339	+	0.991859i	$0.459356\pi$
$510$		0			0
$511$	−20.9789	+	12.1122i	−0.928051	+	0.535811i
$512$	14.4349	+	14.4349i	0.637937	+	0.637937i
$513$		0			0
$514$	8.16413	−	30.4690i	0.360104	−	1.34393i
$515$	−12.4917	+	12.4917i	−0.550450	+	0.550450i
$516$		0			0
$517$	0.0859658	+	0.0496324i	0.00378077	+	0.00218283i
$518$	0.491948	+	1.83598i	0.0216150	+	0.0806682i
$519$		0			0
$520$	−6.59828	+	16.3437i	−0.289354	+	0.716717i
$521$		−	33.1174i		−	1.45090i	−0.688275	−	0.725450i	$-0.741632\pi$
$521$		−	33.1174i		−	1.45090i	0.688275	−	0.725450i	$-0.258368\pi$
$522$		0			0
$523$	−12.7952	+	22.1620i	−0.559496	+	0.969076i	0.438042	+	0.898955i	$0.355672\pi$
$523$	−12.7952	+	22.1620i	−0.559496	+	0.969076i	−0.997538	+	0.0701218i	$0.977661\pi$
$524$	−3.81620	−	6.60985i	−0.166711	−	0.288753i
$525$		0			0
$526$	6.67953	+	1.78978i	0.291242	+	0.0780379i
$527$	65.7270	+	17.6115i	2.86311	+	0.767169i
$528$		0			0
$529$	1.16521	+	2.01820i	0.0506612	+	0.0877478i
$530$	−5.36651	+	9.29508i	−0.233107	+	0.403752i
$531$		0			0
$532$			14.2167i			0.616373i
$533$	−0.973277	+	7.94396i	−0.0421573	+	0.344091i
$534$		0			0
$535$	6.14211	+	22.9227i	0.265546	+	0.991033i
$536$	23.9280	+	13.8148i	1.03353	+	0.596711i
$537$		0			0
$538$	−9.72149	+	9.72149i	−0.419123	+	0.419123i
$539$	0.160152	−	0.597696i	0.00689824	−	0.0257446i
$540$		0			0
$541$	−8.59261	−	8.59261i	−0.369425	−	0.369425i	0.497842	−	0.867268i	$-0.334126\pi$
$541$	−8.59261	−	8.59261i	−0.369425	−	0.369425i	−0.867268	+	0.497842i	$0.834126\pi$
$542$	−5.42718	+	3.13338i	−0.233117	+	0.134590i
$543$		0			0
$544$	30.3961	−	8.14460i	1.30322	−	0.349197i
$545$	4.60423			0.197224
$546$		0			0
$547$	44.7774			1.91454			0.957272	−	0.289189i	$-0.0933856\pi$
$547$	44.7774			1.91454			0.957272	+	0.289189i	$0.0933856\pi$
$548$	−5.24191	+	1.40456i	−0.223923	+	0.0600000i
$549$		0			0
$550$	0.153713	−	0.0887464i	0.00655435	−	0.00378416i
$551$	−25.3395	−	25.3395i	−1.07950	−	1.07950i
$552$		0			0
$553$	8.62747	−	32.1982i	0.366877	−	1.36921i
$554$	2.85914	−	2.85914i	0.121473	−	0.121473i
$555$		0			0
$556$	1.44663	+	0.835214i	0.0613509	+	0.0354210i
$557$	2.99375	+	11.1728i	0.126849	+	0.473408i	0.999899	−	0.0142235i	$-0.00452764\pi$
$557$	2.99375	+	11.1728i	0.126849	+	0.473408i	−0.873050	+	0.487632i	$0.837861\pi$
$558$		0			0
$559$	2.57582	+	18.2930i	0.108946	+	0.773713i
$560$		−	13.2793i		−	0.561154i
$561$		0			0
$562$	1.37990	−	2.39006i	0.0582076	−	0.100818i
$563$	12.0145	+	20.8097i	0.506350	+	0.877024i	0.999973	+	0.00734786i	$0.00233892\pi$
$563$	12.0145	+	20.8097i	0.506350	+	0.877024i	−0.493623	+	0.869676i	$0.664328\pi$
$564$		0			0
$565$	25.1800	+	6.74695i	1.05933	+	0.283847i
$566$	20.7326	+	5.55527i	0.871454	+	0.233505i
$567$		0			0
$568$	12.5162	+	21.6786i	0.525167	+	0.909616i
$569$	−6.79703	+	11.7728i	−0.284946	+	0.493541i	−0.972596	−	0.232501i	$-0.925309\pi$
$569$	−6.79703	+	11.7728i	−0.284946	+	0.493541i	0.687650	+	0.726042i	$0.258642\pi$
$570$		0			0
$571$			6.76951i			0.283295i	0.989917	+	0.141648i	$0.0452400\pi$
$571$			6.76951i			0.283295i	−0.989917	+	0.141648i	$0.954760\pi$
$572$	−0.151367	+	0.0642985i	−0.00632898	+	0.00268845i
$573$		0			0
$574$	−2.66157	−	9.93310i	−0.111092	−	0.414600i
$575$	−9.75110	−	5.62980i	−0.406649	−	0.234779i
$576$		0			0
$577$	25.0923	−	25.0923i	1.04461	−	1.04461i	0.0456482	−	0.998958i	$-0.485465\pi$
$577$	25.0923	−	25.0923i	1.04461	−	1.04461i	0.998958	−	0.0456482i	$-0.0145353\pi$
$578$	−14.6350	+	54.6184i	−0.608734	+	2.27183i
$579$		0			0
$580$	−6.01100	−	6.01100i	−0.249593	−	0.249593i
$581$	−14.5216	+	8.38404i	−0.602456	+	0.347828i
$582$		0			0
$583$	−0.365427	+	0.0979159i	−0.0151345	+	0.00405526i
$584$	−18.2047			−0.753315
$585$		0			0
$586$	−28.8507			−1.19181
$587$	−1.23212	+	0.330146i	−0.0508551	+	0.0136266i	−0.284157	−	0.958778i	$-0.591714\pi$
$587$	−1.23212	+	0.330146i	−0.0508551	+	0.0136266i	0.233302	+	0.972404i	$0.425047\pi$
$588$		0			0
$589$	−34.7182	+	20.0446i	−1.43054	+	0.825923i
$590$	−3.14861	−	3.14861i	−0.129626	−	0.129626i
$591$		0			0
$592$	−0.216781	+	0.809036i	−0.00890962	+	0.0332512i
$593$	−3.72897	+	3.72897i	−0.153130	+	0.153130i	−0.779514	−	0.626384i	$-0.784534\pi$
$593$	−3.72897	+	3.72897i	−0.153130	+	0.153130i	0.626384	+	0.779514i	$0.284534\pi$
$594$		0			0
$595$	−46.1040	−	26.6181i	−1.89008	−	1.09124i
$596$	−1.56840	−	5.85336i	−0.0642443	−	0.239763i
$597$		0			0
$598$	−14.8139	−	11.1570i	−0.605787	−	0.456243i
$599$		−	2.06185i		−	0.0842450i	−0.999112	−	0.0421225i	$-0.986588\pi$
$599$		−	2.06185i		−	0.0842450i	0.999112	−	0.0421225i	$-0.0134120\pi$
$600$		0			0
$601$	11.1507	−	19.3136i	0.454848	−	0.787819i	−0.543832	−	0.839194i	$-0.683027\pi$
$601$	11.1507	−	19.3136i	0.454848	−	0.787819i	0.998679	+	0.0513751i	$0.0163604\pi$
$602$	−11.8683	−	20.5565i	−0.483715	−	0.837819i
$603$		0			0
$604$	−1.09112	−	0.292366i	−0.0443972	−	0.0118962i
$605$	16.8722	+	4.52088i	0.685951	+	0.183800i
$606$		0			0
$607$	−7.03532	−	12.1855i	−0.285555	−	0.494596i	0.687189	−	0.726479i	$-0.258845\pi$
$607$	−7.03532	−	12.1855i	−0.285555	−	0.494596i	−0.972744	+	0.231883i	$0.925511\pi$
$608$	−9.26981	+	16.0558i	−0.375940	+	0.651148i
$609$		0			0
$610$			9.94904i			0.402825i
$611$	−2.20896	−	5.20019i	−0.0893650	−	0.210377i
$612$		0			0
$613$	−3.90166	−	14.5612i	−0.157586	−	0.588120i	−0.998870	−	0.0475264i	$-0.984866\pi$
$613$	−3.90166	−	14.5612i	−0.157586	−	0.588120i	0.841284	−	0.540594i	$-0.181800\pi$
$614$	−28.2600	−	16.3159i	−1.14048	−	0.658457i
$615$		0			0
$616$	0.564451	−	0.564451i	0.0227424	−	0.0227424i
$617$	−4.82463	+	18.0058i	−0.194232	+	0.724885i	0.798232	+	0.602350i	$0.205769\pi$
$617$	−4.82463	+	18.0058i	−0.194232	+	0.724885i	−0.992464	+	0.122535i	$0.960898\pi$
$618$		0			0
$619$	8.51385	+	8.51385i	0.342201	+	0.342201i	0.857194	−	0.514994i	$-0.172206\pi$
$619$	8.51385	+	8.51385i	0.342201	+	0.342201i	−0.514994	+	0.857194i	$0.672206\pi$
$620$	−8.23582	+	4.75496i	−0.330759	+	0.190964i
$621$		0			0
$622$	−13.0282	+	3.49090i	−0.522384	+	0.139972i
$623$	68.2844			2.73576
$624$		0			0
$625$	6.48339			0.259336
$626$	−15.4216	+	4.13221i	−0.616371	+	0.165156i
$627$		0			0
$628$	8.59548	−	4.96261i	0.342997	−	0.198029i
$629$	2.37433	+	2.37433i	0.0946707	+	0.0946707i
$630$		0			0
$631$	5.14892	−	19.2160i	0.204975	−	0.764977i	−0.784482	−	0.620152i	$-0.787071\pi$
$631$	5.14892	−	19.2160i	0.204975	−	0.764977i	0.989457	−	0.144826i	$-0.0462622\pi$
$632$	17.7135	−	17.7135i	0.704604	−	0.704604i
$633$		0			0
$634$	−11.1170	−	6.41838i	−0.441511	−	0.254906i
$635$	−2.69753	−	10.0673i	−0.107048	−	0.399509i
$636$		0			0
$637$	−27.7476	+	21.6906i	−1.09940	+	0.859411i
$638$			0.532642i			0.0210875i
$639$		0			0
$640$	1.46989	−	2.54592i	0.0581025	−	0.100636i
$641$	−0.938904	−	1.62623i	−0.0370845	−	0.0642322i	0.846887	−	0.531772i	$-0.178474\pi$
$641$	−0.938904	−	1.62623i	−0.0370845	−	0.0642322i	−0.883972	+	0.467540i	$0.845140\pi$
$642$		0			0
$643$	23.8512	+	6.39090i	0.940598	+	0.252032i	0.696368	−	0.717685i	$-0.254798\pi$
$643$	23.8512	+	6.39090i	0.940598	+	0.252032i	0.244230	+	0.969717i	$0.421465\pi$
$644$	−12.9482	−	3.46945i	−0.510230	−	0.136716i
$645$		0			0
$646$	−22.3224	−	38.6635i	−0.878263	−	1.52120i
$647$	−14.2911	+	24.7530i	−0.561843	+	0.973140i	0.435493	+	0.900192i	$0.356574\pi$
$647$	−14.2911	+	24.7530i	−0.561843	+	0.973140i	−0.997336	+	0.0729479i	$0.976759\pi$
$648$		0			0
$649$		−	0.156953i		−	0.00616093i
$650$	−10.0275	−	1.22854i	−0.393310	−	0.0481875i
$651$		0			0
$652$	−2.03871	−	7.60858i	−0.0798421	−	0.297975i
$653$	−28.0477	−	16.1933i	−1.09759	−	0.633694i	−0.162004	−	0.986790i	$-0.551796\pi$
$653$	−28.0477	−	16.1933i	−1.09759	−	0.633694i	−0.935587	+	0.353096i	$0.885129\pi$
$654$		0			0
$655$	−11.9064	+	11.9064i	−0.465223	+	0.465223i
$656$	1.17284	−	4.37709i	0.0457916	−	0.170897i
$657$		0			0
$658$	5.13328	+	5.13328i	0.200116	+	0.200116i
$659$	22.2039	−	12.8194i	0.864940	−	0.499373i	−0.000723538	−	1.00000i	$-0.500230\pi$
$659$	22.2039	−	12.8194i	0.864940	−	0.499373i	0.865663	+	0.500626i	$0.166897\pi$
$660$		0			0
$661$	10.3642	−	2.77708i	0.403121	−	0.108016i	−0.0515609	−	0.998670i	$-0.516420\pi$
$661$	10.3642	−	2.77708i	0.403121	−	0.108016i	0.454682	+	0.890654i	$0.349753\pi$
$662$	3.76494			0.146329
$663$		0			0
$664$	−12.6013			−0.489024
$665$	30.2955	−	8.11766i	1.17481	−	0.314789i
$666$		0			0
$667$	29.2623	−	16.8946i	1.13304	−	0.654162i
$668$	3.86295	+	3.86295i	0.149462	+	0.149462i
$669$		0			0
$670$	4.17628	−	15.5861i	0.161344	−	0.602143i
$671$	−0.247971	+	0.247971i	−0.00957282	+	0.00957282i
$672$		0			0
$673$	25.1982	+	14.5482i	0.971320	+	0.560792i	0.899638	−	0.436636i	$-0.143830\pi$
$673$	25.1982	+	14.5482i	0.971320	+	0.560792i	0.0716815	+	0.997428i	$0.477163\pi$
$674$	−1.60053	−	5.97326i	−0.0616501	−	0.230081i
$675$		0			0
$676$	9.08367	+	2.25974i	0.349372	+	0.0869132i
$677$		−	41.4226i		−	1.59200i	−0.605296	−	0.796000i	$-0.706945\pi$
$677$		−	41.4226i		−	1.59200i	0.605296	−	0.796000i	$-0.293055\pi$
$678$		0			0
$679$	−0.219970	+	0.380999i	−0.00844167	+	0.0146214i
$680$	−20.0036	−	34.6473i	−0.767104	−	1.32866i
$681$		0			0
$682$	0.575565	+	0.154222i	0.0220395	+	0.00590547i
$683$	−2.54542	−	0.682043i	−0.0973977	−	0.0260976i	0.209791	−	0.977746i	$-0.432722\pi$
$683$	−2.54542	−	0.682043i	−0.0973977	−	0.0260976i	−0.307189	+	0.951649i	$0.599388\pi$
$684$		0			0
$685$	5.98620	+	10.3684i	0.228721	+	0.396156i
$686$	6.41203	−	11.1060i	0.244812	−	0.424027i
$687$		0			0
$688$		−	10.4597i		−	0.398772i
$689$	19.9671	+	8.06114i	0.760687	+	0.307105i
$690$		0			0
$691$	−3.27990	−	12.2408i	−0.124773	−	0.465661i	0.875058	−	0.484018i	$-0.160823\pi$
$691$	−3.27990	−	12.2408i	−0.124773	−	0.465661i	−0.999831	+	0.0183572i	$0.994156\pi$
$692$	−6.16542	−	3.55961i	−0.234374	−	0.135316i
$693$		0			0
$694$	1.79552	−	1.79552i	0.0681571	−	0.0681571i
$695$	0.953805	−	3.55965i	0.0361799	−	0.135025i
$696$		0			0
$697$	−12.8457	−	12.8457i	−0.486566	−	0.486566i
$698$	24.1774	−	13.9588i	0.915127	−	0.528349i
$699$		0			0
$700$	−7.05342	+	1.88996i	−0.266594	+	0.0714337i
$701$	0.351700			0.0132835			0.00664176	−	0.999978i	$-0.497886\pi$
$701$	0.351700			0.0132835			0.00664176	+	0.999978i	$0.497886\pi$
$702$		0			0
$703$	−1.97826			−0.0746114
$704$	0.516003	−	0.138263i	0.0194476	−	0.00521097i
$705$		0			0
$706$	17.6356	−	10.1819i	0.663724	−	0.383201i
$707$	−0.524991	−	0.524991i	−0.0197443	−	0.0197443i
$708$		0			0
$709$	−8.54299	+	31.8829i	−0.320839	+	1.19739i	0.597591	+	0.801801i	$0.296125\pi$
$709$	−8.54299	+	31.8829i	−0.320839	+	1.19739i	−0.918429	+	0.395585i	$0.870542\pi$
$710$	10.3372	−	10.3372i	0.387949	−	0.387949i
$711$		0			0
$712$	44.4409	+	25.6580i	1.66549	+	0.961574i
$713$	−9.78338	−	36.5121i	−0.366391	−	1.36739i
$714$		0			0
$715$	0.223449	+	0.285846i	0.00835650	+	0.0106900i
$716$		−	9.85124i		−	0.368158i
$717$		0			0
$718$	−11.0489	+	19.1372i	−0.412341	+	0.714195i
$719$	2.02792	+	3.51246i	0.0756287	+	0.130993i	0.901359	−	0.433072i	$-0.142570\pi$
$719$	2.02792	+	3.51246i	0.0756287	+	0.130993i	−0.825731	+	0.564064i	$0.809237\pi$
$720$		0			0
$721$	−43.9876	−	11.7864i	−1.63818	−	0.438950i
$722$	4.64308	+	1.24411i	0.172798	+	0.0463010i
$723$		0			0
$724$	2.51353	+	4.35356i	0.0934145	+	0.161799i
$725$	9.20321	−	15.9404i	0.341799	−	0.592012i
$726$		0			0
$727$		−	37.5392i		−	1.39225i	−0.717919	−	0.696126i	$-0.754905\pi$
$727$		−	37.5392i		−	1.39225i	0.717919	−	0.696126i	$-0.245095\pi$
$728$	−44.9908	+	6.33511i	−1.66747	+	0.234795i
$729$		0			0
$730$	2.75167	+	10.2694i	0.101844	+	0.380087i
$731$	−36.3146	−	20.9662i	−1.34314	−	0.775464i
$732$		0			0
$733$	−11.7965	+	11.7965i	−0.435713	+	0.435713i	−0.890566	−	0.454853i	$-0.849692\pi$
$733$	−11.7965	+	11.7965i	−0.435713	+	0.435713i	0.454853	+	0.890566i	$0.349692\pi$
$734$	0.351968	−	1.31356i	0.0129914	−	0.0484845i
$735$		0			0
$736$	−12.3609	−	12.3609i	−0.455630	−	0.455630i
$737$	0.492560	−	0.284379i	0.0181437	−	0.0104752i
$738$		0			0
$739$	2.84402	−	0.762053i	0.104619	−	0.0280326i	−0.206130	−	0.978525i	$-0.566087\pi$
$739$	2.84402	−	0.762053i	0.104619	−	0.0280326i	0.310749	+	0.950492i	$0.399420\pi$
$740$	−0.469280			−0.0172511
$741$		0			0
$742$	−27.6676			−1.01571
$743$	5.40966	−	1.44951i	0.198461	−	0.0531775i	−0.158219	−	0.987404i	$-0.550575\pi$
$743$	5.40966	−	1.44951i	0.198461	−	0.0531775i	0.356680	+	0.934227i	$0.383909\pi$
$744$		0			0
$745$	−11.5778	+	6.68447i	−0.424179	+	0.244900i
$746$	−26.5710	−	26.5710i	−0.972834	−	0.972834i
$747$		0			0
$748$	0.0966165	−	0.360578i	0.00353265	−	0.0131840i
$749$	−43.2570	+	43.2570i	−1.58057	+	1.58057i
$750$		0			0
$751$	37.1363	+	21.4407i	1.35512	+	0.782381i	0.988962	−	0.148169i	$-0.0473381\pi$
$751$	37.1363	+	21.4407i	1.35512	+	0.782381i	0.366162	+	0.930551i	$0.380671\pi$
$752$	0.827955	+	3.08997i	0.0301924	+	0.112680i
$753$		0			0
$754$	18.2387	−	24.2168i	0.664214	−	0.881924i
$755$			2.49210i			0.0906968i
$756$		0			0
$757$	0.412628	−	0.714693i	0.0149972	−	0.0259759i	−0.858429	−	0.512932i	$-0.828559\pi$
$757$	0.412628	−	0.714693i	0.0149972	−	0.0259759i	0.873427	+	0.486956i	$0.161893\pi$
$758$	2.50471	+	4.33829i	0.0909752	+	0.157574i
$759$		0			0
$760$	22.7672	+	6.10046i	0.825854	+	0.221287i
$761$	2.46483	+	0.660450i	0.0893501	+	0.0239413i	0.303217	−	0.952921i	$-0.401939\pi$
$761$	2.46483	+	0.660450i	0.0893501	+	0.0239413i	−0.213867	+	0.976863i	$0.568606\pi$
$762$		0			0
$763$	5.93440	+	10.2787i	0.214840	+	0.372114i
$764$	6.30268	−	10.9166i	0.228023	−	0.394947i
$765$		0			0
$766$		−	23.5944i		−	0.852499i
$767$	−5.37436	+	7.13592i	−0.194057	+	0.257663i
$768$		0			0
$769$	−12.0950	−	45.1392i	−0.436158	−	1.62776i	−0.738281	−	0.674494i	$-0.764362\pi$
$769$	−12.0950	−	45.1392i	−0.436158	−	1.62776i	0.302123	−	0.953269i	$-0.402305\pi$
$770$	−0.403728	−	0.233092i	−0.0145493	−	0.00840007i
$771$		0			0
$772$	3.75261	−	3.75261i	0.135059	−	0.135059i
$773$	−11.7869	+	43.9893i	−0.423945	+	1.58218i	0.342271	+	0.939601i	$0.388804\pi$
$773$	−11.7869	+	43.9893i	−0.423945	+	1.58218i	−0.766216	+	0.642583i	$0.777863\pi$
$774$		0			0
$775$	−14.5603	−	14.5603i	−0.523020	−	0.523020i
$776$	−0.286322	+	0.165308i	−0.0102784	+	0.00593422i
$777$		0			0
$778$	−21.8671	+	5.85928i	−0.783975	+	0.210066i
$779$	10.7029			0.383471
$780$		0			0
$781$	0.515292			0.0184386
$782$	40.6612	−	10.8951i	1.45404	−	0.389610i
$783$		0			0
$784$	17.2696	−	9.97062i	0.616772	−	0.356093i
$785$	−15.4832	−	15.4832i	−0.552619	−	0.552619i
$786$		0			0
$787$	−7.82377	+	29.1987i	−0.278887	+	1.04082i	0.674304	+	0.738454i	$0.264444\pi$
$787$	−7.82377	+	29.1987i	−0.278887	+	1.04082i	−0.953191	+	0.302367i	$0.902223\pi$
$788$	8.98008	−	8.98008i	0.319902	−	0.319902i
$789$		0			0
$790$	−12.6697	−	7.31485i	−0.450768	−	0.260251i
$791$	17.3923	+	64.9090i	0.618400	+	2.30790i
$792$		0			0
$793$	19.7651	−	2.78310i	0.701880	−	0.0988308i
$794$		−	26.3834i		−	0.936312i
$795$		0			0
$796$	−4.19275	+	7.26206i	−0.148608	+	0.257397i
$797$	6.77500	+	11.7346i	0.239983	+	0.415663i	0.960709	−	0.277557i	$-0.0895248\pi$
$797$	6.77500	+	11.7346i	0.239983	+	0.415663i	−0.720726	+	0.693220i	$0.756191\pi$
$798$		0			0
$799$	12.3876	+	3.31924i	0.438241	+	0.117426i
$800$	−9.19817	−	2.46464i	−0.325205	−	0.0871383i
$801$		0			0
$802$	18.3217	+	31.7342i	0.646963	+	1.12057i
$803$	−0.187372	+	0.324538i	−0.00661222	+	0.0114527i
$804$		0			0
$805$			29.5734i			1.04232i
$806$	−20.8874	−	26.7202i	−0.735728	−	0.941179i
$807$		0			0
$808$	−0.144409	−	0.538941i	−0.00508029	−	0.0189599i
$809$	−12.3448	−	7.12727i	−0.434020	−	0.250582i	0.267038	−	0.963686i	$-0.413955\pi$
$809$	−12.3448	−	7.12727i	−0.434020	−	0.250582i	−0.701058	+	0.713105i	$0.747288\pi$
$810$		0			0
$811$	−10.0752	+	10.0752i	−0.353788	+	0.353788i	−0.861517	−	0.507729i	$-0.830485\pi$
$811$	−10.0752	+	10.0752i	−0.353788	+	0.353788i	0.507729	+	0.861517i	$0.330485\pi$
$812$	5.67163	−	21.1668i	0.199035	−	0.742809i
$813$		0			0
$814$	0.0207918	+	0.0207918i	0.000728751	+	0.000728751i
$815$	−15.0496	+	8.68891i	−0.527166	+	0.304359i
$816$		0			0
$817$	23.8628	−	6.39402i	0.834854	−	0.223698i
$818$	−30.8320			−1.07801
$819$		0			0
$820$	2.53893			0.0886632
$821$	−3.54536	+	0.949977i	−0.123734	+	0.0331544i	−0.320155	−	0.947365i	$-0.603735\pi$
$821$	−3.54536	+	0.949977i	−0.123734	+	0.0331544i	0.196421	+	0.980520i	$0.437068\pi$
$822$		0			0
$823$	27.2692	−	15.7439i	0.950546	−	0.548798i	0.0572954	−	0.998357i	$-0.481752\pi$
$823$	27.2692	−	15.7439i	0.950546	−	0.548798i	0.893250	+	0.449559i	$0.148419\pi$
$824$	−24.1993	−	24.1993i	−0.843023	−	0.843023i
$825$		0			0
$826$	2.97085	−	11.0873i	0.103369	−	0.385778i
$827$	0.725480	−	0.725480i	0.0252274	−	0.0252274i	−0.694381	−	0.719608i	$-0.744322\pi$
$827$	0.725480	−	0.725480i	0.0252274	−	0.0252274i	0.719608	+	0.694381i	$0.244322\pi$
$828$		0			0
$829$	31.2512	+	18.0429i	1.08540	+	0.626656i	0.932348	−	0.361562i	$-0.117757\pi$
$829$	31.2512	+	18.0429i	1.08540	+	0.626656i	0.153052	+	0.988218i	$0.451090\pi$
$830$	1.90471	+	7.10846i	0.0661133	+	0.246738i
$831$		0			0
$832$	−28.1946	−	11.3828i	−0.977473	−	0.394626i
$833$		−	79.9436i		−	2.76988i
$834$		0			0
$835$	6.02614	−	10.4376i	0.208543	−	0.361207i
$836$	0.109964	+	0.190464i	0.00380320	+	0.00658734i
$837$		0			0
$838$	−39.9775	−	10.7119i	−1.38100	−	0.370038i
$839$	49.1294	+	13.1642i	1.69614	+	0.454478i	0.971962	−	0.235139i	$-0.0755544\pi$
$839$	49.1294	+	13.1642i	1.69614	+	0.454478i	0.724174	+	0.689617i	$0.242221\pi$
$840$		0			0
$841$	13.1181	+	22.7213i	0.452350	+	0.783493i
$842$	−17.6176	+	30.5147i	−0.607144	+	1.05160i
$843$		0			0
$844$			3.05045i			0.105001i
$845$	−0.371256	−	20.6474i	−0.0127716	−	0.710293i
$846$		0			0
$847$	11.6539	+	43.4931i	0.400434	+	1.49444i
$848$	−10.5585	−	6.09597i	−0.362581	−	0.209336i
$849$		0			0
$850$	16.2149	−	16.2149i	0.556165	−	0.556165i
$851$	0.482775	−	1.80174i	0.0165493	−	0.0617629i
$852$		0			0
$853$	−9.19098	−	9.19098i	−0.314693	−	0.314693i	0.532032	−	0.846725i	$-0.321429\pi$
$853$	−9.19098	−	9.19098i	−0.314693	−	0.314693i	−0.846725	+	0.532032i	$0.821429\pi$
$854$	−22.2107	+	12.8233i	−0.760034	+	0.438806i
$855$		0			0
$856$	−44.4064	+	11.8987i	−1.51778	+	0.406688i
$857$	−11.0924			−0.378909			−0.189454	−	0.981890i	$-0.560672\pi$
$857$	−11.0924			−0.378909			−0.189454	+	0.981890i	$0.560672\pi$
$858$		0			0
$859$	−25.9605			−0.885760			−0.442880	−	0.896581i	$-0.646043\pi$
$859$	−25.9605			−0.885760			−0.442880	+	0.896581i	$0.646043\pi$
$860$	5.66071	−	1.51678i	0.193029	−	0.0517219i
$861$		0			0
$862$	−24.3876	+	14.0802i	−0.830644	+	0.479573i
$863$	9.54730	+	9.54730i	0.324994	+	0.324994i	0.850679	−	0.525685i	$-0.176191\pi$
$863$	9.54730	+	9.54730i	0.324994	+	0.324994i	−0.525685	+	0.850679i	$0.676191\pi$
$864$		0			0
$865$	−4.06503	+	15.1709i	−0.138215	+	0.515826i
$866$	27.3688	−	27.3688i	0.930029	−	0.930029i
$867$		0			0
$868$	−21.2303	−	12.2573i	−0.720604	−	0.416041i
$869$	−0.133465	−	0.498097i	−0.00452748	−	0.0168968i
$870$		0			0
$871$	−32.1321	−	3.93676i	−1.08875	−	0.133392i
$872$			8.91946i			0.302051i
$873$		0			0
$874$	−12.4004	+	21.4780i	−0.419448	+	0.726506i
$875$	24.3170	+	42.1182i	0.822063	+	1.42386i
$876$		0			0
$877$	16.4372	+	4.40435i	0.555046	+	0.148724i	0.525429	−	0.850837i	$-0.323905\pi$
$877$	16.4372	+	4.40435i	0.555046	+	0.148724i	0.0296167	+	0.999561i	$0.490571\pi$
$878$	−14.6366	−	3.92187i	−0.493962	−	0.132357i
$879$		0			0
$880$	−0.102714	−	0.177906i	−0.00346248	−	0.00599720i
$881$	7.17846	−	12.4335i	0.241849	−	0.418894i	−0.719392	−	0.694604i	$-0.755580\pi$
$881$	7.17846	−	12.4335i	0.241849	−	0.418894i	0.961241	+	0.275710i	$0.0889130\pi$
$882$		0			0
$883$		−	51.2506i		−	1.72472i	−0.506295	−	0.862360i	$-0.668985\pi$
$883$		−	51.2506i		−	1.72472i	0.506295	−	0.862360i	$-0.331015\pi$
$884$	−16.7396	+	13.0855i	−0.563013	+	0.440112i
$885$		0			0
$886$	9.12235	+	34.0451i	0.306471	+	1.14377i
$887$	17.2132	+	9.93807i	0.577964	+	0.333688i	0.760324	−	0.649544i	$-0.225040\pi$
$887$	17.2132	+	9.93807i	0.577964	+	0.333688i	−0.182360	+	0.983232i	$0.558374\pi$
$888$		0			0
$889$	18.9978	−	18.9978i	0.637167	−	0.637167i
$890$	7.75650	−	28.9477i	0.259999	−	0.970328i
$891$		0			0
$892$	12.4980	+	12.4980i	0.418465	+	0.418465i
$893$	−6.54336	+	3.77781i	−0.218965	+	0.126420i
$894$		0			0
$895$	−20.9928	+	5.62500i	−0.701711	+	0.188023i
$896$	7.57817			0.253169
$897$		0			0
$898$	23.7590			0.792849
$899$	59.6874	−	15.9932i	1.99069	−	0.533403i
$900$		0			0
$901$	−42.3287	+	24.4385i	−1.41017	+	0.814165i
$902$	−0.112489	−	0.112489i	−0.00374547	−	0.00374547i
$903$		0			0
$904$	−13.0704	+	48.7794i	−0.434715	+	1.62238i
$905$	7.84213	−	7.84213i	0.260681	−	0.260681i
$906$		0			0
$907$	25.3269	+	14.6225i	0.840967	+	0.485532i	0.857593	−	0.514329i	$-0.171959\pi$
$907$	25.3269	+	14.6225i	0.840967	+	0.485532i	−0.0166261	+	0.999862i	$0.505292\pi$
$908$	4.59883	+	17.1631i	0.152617	+	0.569576i
$909$		0			0
$910$	10.3741	+	24.4220i	0.343899	+	0.809583i
$911$		−	13.1894i		−	0.436984i	−0.975839	−	0.218492i	$-0.929886\pi$
$911$		−	13.1894i		−	0.436984i	0.975839	−	0.218492i	$-0.0701138\pi$
$912$		0			0
$913$	−0.129699	+	0.224645i	−0.00429241	+	0.00743467i
$914$	10.9978	+	19.0488i	0.363775	+	0.630077i
$915$		0			0
$916$	−7.60895	−	2.03881i	−0.251407	−	0.0673642i
$917$	−41.9266	−	11.2342i	−1.38454	−	0.370986i
$918$		0			0
$919$	−8.84004	−	15.3114i	−0.291606	−	0.505076i	0.682584	−	0.730807i	$-0.260856\pi$
$919$	−8.84004	−	15.3114i	−0.291606	−	0.505076i	−0.974190	+	0.225731i	$0.927523\pi$
$920$	−11.1122	+	19.2470i	−0.366360	+	0.634554i
$921$		0			0
$922$			29.7612i			0.980134i
$923$	−23.4279	−	17.6446i	−0.771140	−	0.580778i
$924$		0			0
$925$	−0.262988	−	0.981485i	−0.00864700	−	0.0322710i
$926$	16.2640	+	9.39002i	0.534468	+	0.308575i
$927$		0			0
$928$	20.2068	−	20.2068i	0.663321	−	0.663321i
$929$	5.15073	−	19.2228i	0.168990	−	0.630679i	−0.828508	−	0.559978i	$-0.810810\pi$
$929$	5.15073	−	19.2228i	0.168990	−	0.630679i	0.997498	−	0.0707011i	$-0.0225236\pi$
$930$		0			0
$931$	33.3040	+	33.3040i	1.09149	+	1.09149i
$932$	1.60321	−	0.925612i	0.0525148	−	0.0303194i
$933$		0			0
$934$	23.4391	−	6.28048i	0.766950	−	0.205504i
$935$	−0.823552			−0.0269330
$936$		0			0
$937$	−2.47893			−0.0809833			−0.0404916	−	0.999180i	$-0.512892\pi$
$937$	−2.47893			−0.0809833			−0.0404916	+	0.999180i	$0.512892\pi$
$938$	40.1779	−	10.7656i	1.31185	−	0.351510i
$939$		0			0
$940$	−1.55221	+	0.896167i	−0.0506274	+	0.0292298i
$941$	−0.367969	−	0.367969i	−0.0119954	−	0.0119954i	0.701084	−	0.713079i	$-0.252700\pi$
$941$	−0.367969	−	0.367969i	−0.0119954	−	0.0119954i	−0.713079	+	0.701084i	$0.752700\pi$
$942$		0			0
$943$	−2.61194	+	9.74788i	−0.0850564	+	0.317435i
$944$	3.57659	−	3.57659i	0.116408	−	0.116408i
$945$		0			0
$946$	−0.318003	−	0.183599i	−0.0103392	−	0.00596933i
$947$	3.01920	+	11.2678i	0.0981107	+	0.366154i	0.997473	−	0.0710505i	$-0.0226352\pi$
$947$	3.01920	+	11.2678i	0.0981107	+	0.366154i	−0.899362	+	0.437205i	$0.855968\pi$
$948$		0			0
$949$	19.6317	−	8.33927i	0.637273	−	0.270704i
$950$			13.5100i			0.438322i
$951$		0			0
$952$	51.5654	−	89.3139i	1.67124	−	2.89468i
$953$	15.1971	+	26.3222i	0.492283	+	0.852658i	0.999960	−	0.00888849i	$-0.00282933\pi$
$953$	15.1971	+	26.3222i	0.492283	+	0.852658i	−0.507678	+	0.861547i	$0.669496\pi$
$954$		0			0
$955$	−26.8618	−	7.19759i	−0.869227	−	0.232909i
$956$	9.71289	+	2.60256i	0.314137	+	0.0841729i
$957$		0			0
$958$	9.66447	+	16.7393i	0.312245	+	0.540824i
$959$	−15.4312	+	26.7277i	−0.498301	+	0.863082i
$960$		0			0
$961$		−	38.1280i		−	1.22994i
$962$	−0.233356	−	1.65726i	−0.00752370	−	0.0534321i
$963$		0			0
$964$	2.00030	+	7.46522i	0.0644253	+	0.240439i
$965$	−10.1394	−	5.85401i	−0.326400	−	0.188447i
$966$		0			0
$967$	29.7683	−	29.7683i	0.957284	−	0.957284i	−0.0418402	−	0.999124i	$-0.513322\pi$
$967$	29.7683	−	29.7683i	0.957284	−	0.957284i	0.999124	+	0.0418402i	$0.0133220\pi$
$968$	−8.75798	+	32.6852i	−0.281492	+	1.05054i
$969$		0			0
$970$	0.136530	+	0.136530i	0.00438370	+	0.00438370i
$971$	−35.7616	+	20.6470i	−1.14765	+	0.662593i	−0.948312	−	0.317339i	$-0.897211\pi$
$971$	−35.7616	+	20.6470i	−1.14765	+	0.662593i	−0.199333	+	0.979932i	$0.563877\pi$
$972$		0			0
$973$	9.17608	−	2.45872i	0.294172	−	0.0788230i
$974$	−33.8641			−1.08507
$975$		0			0
$976$	−11.3014			−0.361749
$977$	40.3059	−	10.7999i	1.28950	−	0.345521i	0.452030	−	0.892003i	$-0.350700\pi$
$977$	40.3059	−	10.7999i	1.28950	−	0.345521i	0.837471	+	0.546482i	$0.184033\pi$
$978$		0			0
$979$	0.914819	−	0.528171i	0.0292377	−	0.0168804i
$980$	7.90033	+	7.90033i	0.252367	+	0.252367i
$981$		0			0
$982$	1.53786	−	5.73939i	0.0490752	−	0.183151i
$983$	18.3428	−	18.3428i	0.585044	−	0.585044i	−0.351241	−	0.936285i	$-0.614240\pi$
$983$	18.3428	−	18.3428i	0.585044	−	0.585044i	0.936285	+	0.351241i	$0.114240\pi$
$984$		0			0
$985$	−24.2639	−	14.0088i	−0.773113	−	0.446357i
$986$	17.8106	+	66.4702i	0.567206	+	2.11684i
$987$		0			0
$988$	1.52227	−	12.4249i	0.0484300	−	0.395289i
$989$			23.2940i			0.740705i
$990$		0			0
$991$	1.08991	−	1.88779i	0.0346222	−	0.0599675i	−0.848195	−	0.529684i	$-0.822311\pi$
$991$	1.08991	−	1.88779i	0.0346222	−	0.0599675i	0.882817	+	0.469716i	$0.155644\pi$
$992$	−15.9845	−	27.6859i	−0.507507	−	0.879028i
$993$		0			0
$994$	36.4009	+	9.75359i	1.15457	+	0.309365i
$995$	17.8693	+	4.78807i	0.566496	+	0.151792i
$996$		0			0
$997$	−10.0497	−	17.4066i	−0.318278	−	0.551274i	0.661851	−	0.749636i	$-0.269771\pi$
$997$	−10.0497	−	17.4066i	−0.318278	−	0.551274i	−0.980129	+	0.198362i	$0.936438\pi$
$998$	−11.6152	+	20.1182i	−0.367673	+	0.636829i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	351.2.bd.d.188.4	✓	20
3.2	odd	2		351.2.bd.e.188.2	yes	20
13.11	odd	12		351.2.bd.e.323.2	yes	20
39.11	even	12	inner	351.2.bd.d.323.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.bd.d.188.4	✓	20	1.1	even	1	trivial
351.2.bd.d.323.4	yes	20	39.11	even	12	inner
351.2.bd.e.188.2	yes	20	3.2	odd	2
351.2.bd.e.323.2	yes	20	13.11	odd	12

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:	\( N \)	\(=\)	\( 351 = 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	351.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09280 - 0.292816i) q^{2} +(-0.623573 + 0.360020i) q^{4} +(1.12325 + 1.12325i) q^{5} +(-1.05984 + 3.95536i) q^{7} +(-2.17600 + 2.17600i) q^{8} +O(q^{10})\)	\(q+(1.09280 - 0.292816i) q^{2} +(-0.623573 + 0.360020i) q^{4} +(1.12325 + 1.12325i) q^{5} +(-1.05984 + 3.95536i) q^{7} +(-2.17600 + 2.17600i) q^{8} +(1.55640 + 0.898588i) q^{10} +(0.0163954 + 0.0611884i) q^{11} +(1.34978 - 3.34336i) q^{13} +4.63277i q^{14} +(-1.02073 + 1.76796i) q^{16} +(4.09207 + 7.08767i) q^{17} +(-4.65740 - 1.24795i) q^{19} +(-1.10482 - 0.296037i) q^{20} +(0.0358339 + 0.0620661i) q^{22} +(2.27319 - 3.93728i) q^{23} -2.47661i q^{25} +(0.496060 - 4.04888i) q^{26} +(-0.763124 - 2.84802i) q^{28} +(6.43640 + 3.71606i) q^{29} +(5.87912 - 5.87912i) q^{31} +(0.995169 - 3.71402i) q^{32} +(6.54721 + 6.54721i) q^{34} +(-5.63333 + 3.25241i) q^{35} +(0.396302 - 0.106189i) q^{37} -5.45504 q^{38} -4.88839 q^{40} +(-2.14410 + 0.574509i) q^{41} +(-4.43719 + 2.56181i) q^{43} +(-0.0322528 - 0.0322528i) q^{44} +(1.33125 - 4.96830i) q^{46} +(1.10804 - 1.10804i) q^{47} +(-8.45944 - 4.88406i) q^{49} +(-0.725189 - 2.70644i) q^{50} +(0.361989 + 2.57078i) q^{52} +5.97216i q^{53} +(-0.0503139 + 0.0871462i) q^{55} +(-6.30065 - 10.9131i) q^{56} +(8.12183 + 2.17624i) q^{58} +(-2.39325 - 0.641268i) q^{59} +(2.76797 + 4.79426i) q^{61} +(4.70322 - 8.14621i) q^{62} -8.43302i q^{64} +(5.27159 - 2.23929i) q^{65} +(-2.32380 - 8.67254i) q^{67} +(-5.10341 - 2.94645i) q^{68} +(-5.20377 + 5.20377i) q^{70} +(2.10535 - 7.85727i) q^{71} +(4.18306 + 4.18306i) q^{73} +(0.401987 - 0.232087i) q^{74} +(3.35352 - 0.898573i) q^{76} -0.259399 q^{77} -8.14039 q^{79} +(-3.13240 + 0.839324i) q^{80} +(-2.17485 + 1.25565i) q^{82} +(2.89552 + 2.89552i) q^{83} +(-3.36482 + 12.5577i) q^{85} +(-4.09884 + 4.09884i) q^{86} +(-0.168822 - 0.0974695i) q^{88} +(-4.31594 - 16.1073i) q^{89} +(11.7937 + 8.88230i) q^{91} +3.27358i q^{92} +(0.886417 - 1.53532i) q^{94} +(-3.82968 - 6.63320i) q^{95} +(0.103775 + 0.0278066i) q^{97} +(-10.6746 - 2.86026i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{5}+O(q^{10}) \) 20 * q - 6 * q^5	\( 20 q - 6 q^{5} - 12 q^{10} - 8 q^{13} + 24 q^{16} + 12 q^{17} - 12 q^{19} - 36 q^{20} + 8 q^{22} + 42 q^{26} + 2 q^{28} + 6 q^{29} - 22 q^{31} + 36 q^{32} - 6 q^{34} + 36 q^{35} + 8 q^{37} - 72 q^{38} - 36 q^{40} - 30 q^{41} - 30 q^{43} - 36 q^{44} - 48 q^{46} - 6 q^{47} + 30 q^{49} - 54 q^{50} + 4 q^{52} - 28 q^{55} + 60 q^{56} + 44 q^{58} - 30 q^{59} - 16 q^{61} + 30 q^{62} + 78 q^{65} + 18 q^{67} - 6 q^{68} + 38 q^{70} + 60 q^{71} + 72 q^{74} - 8 q^{76} + 12 q^{77} - 16 q^{79} - 126 q^{80} + 78 q^{82} - 12 q^{83} + 12 q^{85} - 18 q^{86} - 84 q^{89} + 30 q^{91} - 22 q^{94} + 66 q^{95} + 26 q^{97} - 42 q^{98}+O(q^{100}) \) 20 * q - 6 * q^5 - 12 * q^10 - 8 * q^13 + 24 * q^16 + 12 * q^17 - 12 * q^19 - 36 * q^20 + 8 * q^22 + 42 * q^26 + 2 * q^28 + 6 * q^29 - 22 * q^31 + 36 * q^32 - 6 * q^34 + 36 * q^35 + 8 * q^37 - 72 * q^38 - 36 * q^40 - 30 * q^41 - 30 * q^43 - 36 * q^44 - 48 * q^46 - 6 * q^47 + 30 * q^49 - 54 * q^50 + 4 * q^52 - 28 * q^55 + 60 * q^56 + 44 * q^58 - 30 * q^59 - 16 * q^61 + 30 * q^62 + 78 * q^65 + 18 * q^67 - 6 * q^68 + 38 * q^70 + 60 * q^71 + 72 * q^74 - 8 * q^76 + 12 * q^77 - 16 * q^79 - 126 * q^80 + 78 * q^82 - 12 * q^83 + 12 * q^85 - 18 * q^86 - 84 * q^89 + 30 * q^91 - 22 * q^94 + 66 * q^95 + 26 * q^97 - 42 * q^98

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