LMFDB - Embedded newform 833.2.g.h.540.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(344,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("833.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.g (of order $4$, degree $2$, 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
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} + 32 x^{18} + 432 x^{16} + 3200 x^{14} + 14160 x^{12} + 38162 x^{10} + 61088 x^{8} + 53872 x^{6} + \cdots + 49 $ x^20 + 32x^18 + 432x^16 + 3200x^14 + 14160x^12 + 38162x^10 + 61088x^8 + 53872x^6 + 22464x^4 + 3504*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			540.8
Root			$1.57229i$ of defining polynomial
Character	$\chi$	$=$	833.540
Dual form			833.2.g.h.344.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.57229i q^{2} +(1.43847 + 1.43847i) q^{3} -0.472100 q^{4} +(-2.40051 - 2.40051i) q^{5} +(-2.26170 + 2.26170i) q^{6} +2.40230i q^{8} +1.13841i q^{9} +O(q^{10})$	\(q+1.57229i q^{2} +(1.43847 + 1.43847i) q^{3} -0.472100 q^{4} +(-2.40051 - 2.40051i) q^{5} +(-2.26170 + 2.26170i) q^{6} +2.40230i q^{8} +1.13841i q^{9} +(3.77429 - 3.77429i) q^{10} +(-3.30263 + 3.30263i) q^{11} +(-0.679103 - 0.679103i) q^{12} -3.63777 q^{13} -6.90613i q^{15} -4.72132 q^{16} +(-1.70860 + 3.75243i) q^{17} -1.78992 q^{18} +6.19754i q^{19} +(1.13328 + 1.13328i) q^{20} +(-5.19270 - 5.19270i) q^{22} +(0.475240 - 0.475240i) q^{23} +(-3.45565 + 3.45565i) q^{24} +6.52485i q^{25} -5.71963i q^{26} +(2.67784 - 2.67784i) q^{27} +(-3.95461 - 3.95461i) q^{29} +10.8584 q^{30} +(5.41543 + 5.41543i) q^{31} -2.61868i q^{32} -9.50150 q^{33} +(-5.89991 - 2.68641i) q^{34} -0.537445i q^{36} +(-0.967703 - 0.967703i) q^{37} -9.74433 q^{38} +(-5.23284 - 5.23284i) q^{39} +(5.76674 - 5.76674i) q^{40} +(-0.492170 + 0.492170i) q^{41} +6.64216i q^{43} +(1.55917 - 1.55917i) q^{44} +(2.73277 - 2.73277i) q^{45} +(0.747216 + 0.747216i) q^{46} -4.32592 q^{47} +(-6.79150 - 6.79150i) q^{48} -10.2590 q^{50} +(-7.85554 + 2.94000i) q^{51} +1.71739 q^{52} -4.07940i q^{53} +(4.21035 + 4.21035i) q^{54} +15.8560 q^{55} +(-8.91500 + 8.91500i) q^{57} +(6.21780 - 6.21780i) q^{58} +2.73239i q^{59} +3.26038i q^{60} +(8.55455 - 8.55455i) q^{61} +(-8.51463 + 8.51463i) q^{62} -5.32531 q^{64} +(8.73248 + 8.73248i) q^{65} -14.9391i q^{66} +12.5590 q^{67} +(0.806627 - 1.77152i) q^{68} +1.36724 q^{69} +(3.04461 + 3.04461i) q^{71} -2.73482 q^{72} +(1.16753 + 1.16753i) q^{73} +(1.52151 - 1.52151i) q^{74} +(-9.38583 + 9.38583i) q^{75} -2.92586i q^{76} +(8.22754 - 8.22754i) q^{78} +(7.07442 - 7.07442i) q^{79} +(11.3336 + 11.3336i) q^{80} +11.1193 q^{81} +(-0.773834 - 0.773834i) q^{82} -4.69160i q^{83} +(13.1092 - 4.90623i) q^{85} -10.4434 q^{86} -11.3772i q^{87} +(-7.93393 - 7.93393i) q^{88} +2.04706 q^{89} +(4.29671 + 4.29671i) q^{90} +(-0.224361 + 0.224361i) q^{92} +15.5799i q^{93} -6.80161i q^{94} +(14.8772 - 14.8772i) q^{95} +(3.76691 - 3.76691i) q^{96} +(2.99116 + 2.99116i) q^{97} +(-3.75976 - 3.75976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) $ 20 * q + 4 * q^3 - 24 * q^4 + 8 * q^5 - 4 * q^6	$ 20 q + 4 q^{3} - 24 q^{4} + 8 q^{5} - 4 q^{6} - 4 q^{10} - 4 q^{11} - 12 q^{12} + 16 q^{16} + 12 q^{17} - 8 q^{18} - 20 q^{20} - 20 q^{22} - 4 q^{24} - 8 q^{27} + 16 q^{29} - 36 q^{30} - 4 q^{31} + 16 q^{33} - 36 q^{34} - 28 q^{37} - 48 q^{38} + 20 q^{39} + 24 q^{40} + 24 q^{41} - 28 q^{44} - 36 q^{45} + 8 q^{46} - 40 q^{47} + 8 q^{48} - 28 q^{50} - 40 q^{51} + 28 q^{54} + 40 q^{55} + 36 q^{57} + 56 q^{58} + 16 q^{61} + 40 q^{62} + 32 q^{64} + 8 q^{65} + 32 q^{68} + 88 q^{69} - 8 q^{71} + 108 q^{72} - 8 q^{73} + 36 q^{74} - 8 q^{75} - 44 q^{78} - 4 q^{79} + 116 q^{80} + 4 q^{81} + 16 q^{82} + 16 q^{85} + 44 q^{86} + 72 q^{88} - 48 q^{89} - 56 q^{90} - 32 q^{92} + 44 q^{95} - 68 q^{96} - 24 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 24 * q^4 + 8 * q^5 - 4 * q^6 - 4 * q^10 - 4 * q^11 - 12 * q^12 + 16 * q^16 + 12 * q^17 - 8 * q^18 - 20 * q^20 - 20 * q^22 - 4 * q^24 - 8 * q^27 + 16 * q^29 - 36 * q^30 - 4 * q^31 + 16 * q^33 - 36 * q^34 - 28 * q^37 - 48 * q^38 + 20 * q^39 + 24 * q^40 + 24 * q^41 - 28 * q^44 - 36 * q^45 + 8 * q^46 - 40 * q^47 + 8 * q^48 - 28 * q^50 - 40 * q^51 + 28 * q^54 + 40 * q^55 + 36 * q^57 + 56 * q^58 + 16 * q^61 + 40 * q^62 + 32 * q^64 + 8 * q^65 + 32 * q^68 + 88 * q^69 - 8 * q^71 + 108 * q^72 - 8 * q^73 + 36 * q^74 - 8 * q^75 - 44 * q^78 - 4 * q^79 + 116 * q^80 + 4 * q^81 + 16 * q^82 + 16 * q^85 + 44 * q^86 + 72 * q^88 - 48 * q^89 - 56 * q^90 - 32 * q^92 + 44 * q^95 - 68 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.57229i			1.11178i	0.831257	+	0.555889i	$0.187622\pi$
$2$			1.57229i			1.11178i	−0.831257	+	0.555889i	$0.812378\pi$
$3$	1.43847	+	1.43847i	0.830503	+	0.830503i	0.987586	−	0.157082i	$-0.0502088\pi$
$3$	1.43847	+	1.43847i	0.830503	+	0.830503i	−0.157082	+	0.987586i	$0.550209\pi$
$4$	−0.472100			−0.236050
$5$	−2.40051	−	2.40051i	−1.07354	−	1.07354i	−0.997072	−	0.0764665i	$-0.975636\pi$
$5$	−2.40051	−	2.40051i	−1.07354	−	1.07354i	−0.0764665	−	0.997072i	$-0.524364\pi$
$6$	−2.26170	+	2.26170i	−0.923335	+	0.923335i
$7$		0			0
$7$		0			0
$8$			2.40230i			0.849343i
$9$			1.13841i			0.379471i
$10$	3.77429	−	3.77429i	1.19354	−	1.19354i
$11$	−3.30263	+	3.30263i	−0.995781	+	0.995781i	−0.999991	−	0.00421022i	$-0.998660\pi$
$11$	−3.30263	+	3.30263i	−0.995781	+	0.995781i	0.00421022	+	0.999991i	$0.498660\pi$
$12$	−0.679103	−	0.679103i	−0.196040	−	0.196040i
$13$	−3.63777			−1.00894			−0.504468	−	0.863430i	$-0.668311\pi$
$13$	−3.63777			−1.00894			−0.504468	+	0.863430i	$0.668311\pi$
$14$		0			0
$15$		−	6.90613i		−	1.78315i
$16$	−4.72132			−1.18033
$17$	−1.70860	+	3.75243i	−0.414395	+	0.910097i
$17$	−1.70860	+	3.75243i	−0.414395	+	0.910097i
$18$	−1.78992			−0.421888
$19$			6.19754i			1.42181i	0.703287	+	0.710906i	$0.251715\pi$
$19$			6.19754i			1.42181i	−0.703287	+	0.710906i	$0.748285\pi$
$20$	1.13328	+	1.13328i	0.253409	+	0.253409i
$21$		0			0
$22$	−5.19270	−	5.19270i	−1.10709	−	1.10709i
$23$	0.475240	−	0.475240i	0.0990945	−	0.0990945i	−0.655822	−	0.754916i	$-0.727678\pi$
$23$	0.475240	−	0.475240i	0.0990945	−	0.0990945i	0.754916	+	0.655822i	$0.227678\pi$
$24$	−3.45565	+	3.45565i	−0.705382	+	0.705382i
$25$			6.52485i			1.30497i
$26$		−	5.71963i		−	1.12171i
$27$	2.67784	−	2.67784i	0.515351	−	0.515351i
$28$		0			0
$29$	−3.95461	−	3.95461i	−0.734353	−	0.734353i	0.237126	−	0.971479i	$-0.423795\pi$
$29$	−3.95461	−	3.95461i	−0.734353	−	0.734353i	−0.971479	+	0.237126i	$0.923795\pi$
$30$	10.8584			1.98247
$31$	5.41543	+	5.41543i	0.972640	+	0.972640i	0.999636	−	0.0269959i	$-0.00859411\pi$
$31$	5.41543	+	5.41543i	0.972640	+	0.972640i	−0.0269959	+	0.999636i	$0.508594\pi$
$32$		−	2.61868i		−	0.462922i
$33$	−9.50150			−1.65400
$34$	−5.89991	−	2.68641i	−1.01183	−	0.460715i
$35$		0			0
$36$		−	0.537445i		−	0.0895742i
$37$	−0.967703	−	0.967703i	−0.159089	−	0.159089i	0.623074	−	0.782163i	$-0.285884\pi$
$37$	−0.967703	−	0.967703i	−0.159089	−	0.159089i	−0.782163	+	0.623074i	$0.785884\pi$
$38$	−9.74433			−1.58074
$39$	−5.23284	−	5.23284i	−0.837924	−	0.837924i
$40$	5.76674	−	5.76674i	0.911802	−	0.911802i
$41$	−0.492170	+	0.492170i	−0.0768640	+	0.0768640i	−0.744494	−	0.667630i	$-0.767309\pi$
$41$	−0.492170	+	0.492170i	−0.0768640	+	0.0768640i	0.667630	+	0.744494i	$0.267309\pi$
$42$		0			0
$43$			6.64216i			1.01292i	0.862264	+	0.506460i	$0.169046\pi$
$43$			6.64216i			1.01292i	−0.862264	+	0.506460i	$0.830954\pi$
$44$	1.55917	−	1.55917i	0.235054	−	0.235054i
$45$	2.73277	−	2.73277i	0.407377	−	0.407377i
$46$	0.747216	+	0.747216i	0.110171	+	0.110171i
$47$	−4.32592			−0.631000			−0.315500	−	0.948926i	$-0.602172\pi$
$47$	−4.32592			−0.631000			−0.315500	+	0.948926i	$0.602172\pi$
$48$	−6.79150	−	6.79150i	−0.980268	−	0.980268i
$49$		0			0
$50$	−10.2590			−1.45084
$51$	−7.85554	+	2.94000i	−1.10000	+	0.411682i
$52$	1.71739			0.238159
$53$		−	4.07940i		−	0.560349i	−0.959949	−	0.280175i	$-0.909608\pi$
$53$		−	4.07940i		−	0.560349i	0.959949	−	0.280175i	$-0.0903924\pi$
$54$	4.21035	+	4.21035i	0.572956	+	0.572956i
$55$	15.8560			2.13802
$56$		0			0
$57$	−8.91500	+	8.91500i	−1.18082	+	1.18082i
$58$	6.21780	−	6.21780i	0.816437	−	0.816437i
$59$			2.73239i			0.355727i	0.984055	+	0.177864i	$0.0569186\pi$
$59$			2.73239i			0.355727i	−0.984055	+	0.177864i	$0.943081\pi$
$60$			3.26038i			0.420914i
$61$	8.55455	−	8.55455i	1.09530	−	1.09530i	0.100345	−	0.994953i	$-0.468005\pi$
$61$	8.55455	−	8.55455i	1.09530	−	1.09530i	0.994953	−	0.100345i	$-0.0319946\pi$
$62$	−8.51463	+	8.51463i	−1.08136	+	1.08136i
$63$		0			0
$64$	−5.32531			−0.665664
$65$	8.73248	+	8.73248i	1.08313	+	1.08313i
$66$		−	14.9391i		−	1.83888i
$67$	12.5590			1.53433			0.767165	−	0.641450i	$-0.221667\pi$
$67$	12.5590			1.53433			0.767165	+	0.641450i	$0.221667\pi$
$68$	0.806627	−	1.77152i	0.0978179	−	0.214828i
$69$	1.36724			0.164597
$70$		0			0
$71$	3.04461	+	3.04461i	0.361328	+	0.361328i	0.864302	−	0.502973i	$-0.167761\pi$
$71$	3.04461	+	3.04461i	0.361328	+	0.361328i	−0.502973	+	0.864302i	$0.667761\pi$
$72$	−2.73482			−0.322301
$73$	1.16753	+	1.16753i	0.136649	+	0.136649i	0.772123	−	0.635474i	$-0.219195\pi$
$73$	1.16753	+	1.16753i	0.136649	+	0.136649i	−0.635474	+	0.772123i	$0.719195\pi$
$74$	1.52151	−	1.52151i	0.176872	−	0.176872i
$75$	−9.38583	+	9.38583i	−1.08378	+	1.08378i
$76$		−	2.92586i		−	0.335619i
$77$		0			0
$78$	8.22754	−	8.22754i	0.931586	−	0.931586i
$79$	7.07442	−	7.07442i	0.795935	−	0.795935i	−0.186517	−	0.982452i	$-0.559720\pi$
$79$	7.07442	−	7.07442i	0.795935	−	0.795935i	0.982452	+	0.186517i	$0.0597199\pi$
$80$	11.3336	+	11.3336i	1.26713	+	1.26713i
$81$	11.1193			1.23547
$82$	−0.773834	−	0.773834i	−0.0854557	−	0.0854557i
$83$		−	4.69160i		−	0.514970i	−0.966282	−	0.257485i	$-0.917106\pi$
$83$		−	4.69160i		−	0.514970i	0.966282	−	0.257485i	$-0.0828938\pi$
$84$		0			0
$85$	13.1092	−	4.90623i	1.42189	−	0.532155i
$86$	−10.4434			−1.12614
$87$		−	11.3772i		−	1.21977i
$88$	−7.93393	−	7.93393i	−0.845759	−	0.845759i
$89$	2.04706			0.216988			0.108494	−	0.994097i	$-0.465397\pi$
$89$	2.04706			0.216988			0.108494	+	0.994097i	$0.465397\pi$
$90$	4.29671	+	4.29671i	0.452913	+	0.452913i
$91$		0			0
$92$	−0.224361	+	0.224361i	−0.0233912	+	0.0233912i
$93$			15.5799i			1.61556i
$94$		−	6.80161i		−	0.701532i
$95$	14.8772	−	14.8772i	1.52637	−	1.52637i
$96$	3.76691	−	3.76691i	0.384459	−	0.384459i
$97$	2.99116	+	2.99116i	0.303706	+	0.303706i	0.842462	−	0.538756i	$-0.181105\pi$
$97$	2.99116	+	2.99116i	0.303706	+	0.303706i	−0.538756	+	0.842462i	$0.681105\pi$
$98$		0			0
$99$	−3.75976	−	3.75976i	−0.377870	−	0.377870i
$100$		−	3.08038i		−	0.308038i
$101$	5.38529			0.535856			0.267928	−	0.963439i	$-0.413661\pi$
$101$	5.38529			0.535856			0.267928	+	0.963439i	$0.413661\pi$
$102$	−4.62253	−	12.3512i	−0.457699	−	1.22295i
$103$	3.96255			0.390442			0.195221	−	0.980759i	$-0.437458\pi$
$103$	3.96255			0.390442			0.195221	+	0.980759i	$0.437458\pi$
$104$		−	8.73903i		−	0.856932i
$105$		0			0
$106$	6.41401			0.622984
$107$	8.04673	+	8.04673i	0.777907	+	0.777907i	0.979475	−	0.201568i	$-0.0646035\pi$
$107$	8.04673	+	8.04673i	0.777907	+	0.777907i	−0.201568	+	0.979475i	$0.564604\pi$
$108$	−1.26421	+	1.26421i	−0.121649	+	0.121649i
$109$	−3.11536	+	3.11536i	−0.298398	+	0.298398i	−0.840386	−	0.541988i	$-0.817672\pi$
$109$	−3.11536	+	3.11536i	−0.298398	+	0.298398i	0.541988	+	0.840386i	$0.317672\pi$
$110$			24.9302i			2.37700i
$111$		−	2.78403i		−	0.264248i
$112$		0			0
$113$	−8.20042	+	8.20042i	−0.771430	+	0.771430i	−0.978357	−	0.206926i	$-0.933654\pi$
$113$	−8.20042	+	8.20042i	−0.771430	+	0.771430i	0.206926	+	0.978357i	$0.433654\pi$
$114$	−14.0170	−	14.0170i	−1.31281	−	1.31281i
$115$	−2.28163			−0.212764
$116$	1.86697	+	1.86697i	0.173344	+	0.173344i
$117$		−	4.14129i		−	0.382862i
$118$	−4.29612			−0.395490
$119$		0			0
$120$	16.5906			1.51451
$121$		−	10.8148i		−	0.983159i
$122$	13.4502	+	13.4502i	1.21773	+	1.21773i
$123$	−1.41595			−0.127672
$124$	−2.55662	−	2.55662i	−0.229591	−	0.229591i
$125$	3.66041	−	3.66041i	0.327397	−	0.327397i
$126$		0			0
$127$			5.12889i			0.455115i	0.973765	+	0.227558i	$0.0730740\pi$
$127$			5.12889i			0.455115i	−0.973765	+	0.227558i	$0.926926\pi$
$128$		−	13.6103i		−	1.20299i
$129$	−9.55457	+	9.55457i	−0.841233	+	0.841233i
$130$	−13.7300	+	13.7300i	−1.20420	+	1.20420i
$131$	−5.90678	−	5.90678i	−0.516078	−	0.516078i	0.400304	−	0.916382i	$-0.368904\pi$
$131$	−5.90678	−	5.90678i	−0.516078	−	0.516078i	−0.916382	+	0.400304i	$0.868904\pi$
$132$	4.48566			0.390426
$133$		0			0
$134$			19.7465i			1.70583i
$135$	−12.8564			−1.10650
$136$	−9.01447	−	4.10456i	−0.772984	−	0.351964i
$137$	−20.1939			−1.72528			−0.862639	−	0.505821i	$-0.831190\pi$
$137$	−20.1939			−1.72528			−0.862639	+	0.505821i	$0.831190\pi$
$138$			2.14970i			0.182995i
$139$	−5.51905	−	5.51905i	−0.468120	−	0.468120i	0.433185	−	0.901305i	$-0.357390\pi$
$139$	−5.51905	−	5.51905i	−0.468120	−	0.468120i	−0.901305	+	0.433185i	$0.857390\pi$
$140$		0			0
$141$	−6.22272	−	6.22272i	−0.524048	−	0.524048i
$142$	−4.78701	+	4.78701i	−0.401717	+	0.401717i
$143$	12.0142	−	12.0142i	1.00468	−	1.00468i
$144$		−	5.37482i		−	0.447902i
$145$			18.9861i			1.57671i
$146$	−1.83570	+	1.83570i	−0.151923	+	0.151923i
$147$		0			0
$148$	0.456852	+	0.456852i	0.0375530	+	0.0375530i
$149$	0.670580			0.0549361			0.0274680	−	0.999623i	$-0.491256\pi$
$149$	0.670580			0.0549361			0.0274680	+	0.999623i	$0.491256\pi$
$150$	−14.7573	−	14.7573i	−1.20492	−	1.20492i
$151$			11.4237i			0.929644i	0.885404	+	0.464822i	$0.153882\pi$
$151$			11.4237i			0.929644i	−0.885404	+	0.464822i	$0.846118\pi$
$152$	−14.8884			−1.20761
$153$	−4.27182	−	1.94509i	−0.345356	−	0.157251i
$154$		0			0
$155$		−	25.9995i		−	2.08833i
$156$	2.47042	+	2.47042i	0.197792	+	0.197792i
$157$	−23.3832			−1.86618			−0.933090	−	0.359642i	$-0.882899\pi$
$157$	−23.3832			−1.86618			−0.933090	+	0.359642i	$0.882899\pi$
$158$	11.1231	+	11.1231i	0.884903	+	0.884903i
$159$	5.86812	−	5.86812i	0.465372	−	0.465372i
$160$	−6.28617	+	6.28617i	−0.496965	+	0.496965i
$161$		0			0
$162$			17.4827i			1.37357i
$163$	8.53975	−	8.53975i	0.668885	−	0.668885i	−0.288573	−	0.957458i	$-0.593181\pi$
$163$	8.53975	−	8.53975i	0.668885	−	0.668885i	0.957458	+	0.288573i	$0.0931808\pi$
$164$	0.232353	−	0.232353i	0.0181437	−	0.0181437i
$165$	22.8084	+	22.8084i	1.77563	+	1.77563i
$166$	7.37656			0.572532
$167$	17.3482	+	17.3482i	1.34244	+	1.34244i	0.893620	+	0.448823i	$0.148157\pi$
$167$	17.3482	+	17.3482i	1.34244	+	1.34244i	0.448823	+	0.893620i	$0.351843\pi$
$168$		0			0
$169$	0.233365			0.0179511
$170$	7.71402	+	20.6115i	0.591638	+	1.58083i
$171$	−7.05537			−0.539537
$172$		−	3.13576i		−	0.239100i
$173$	−2.52101	−	2.52101i	−0.191669	−	0.191669i	0.604748	−	0.796417i	$-0.293274\pi$
$173$	−2.52101	−	2.52101i	−0.191669	−	0.191669i	−0.796417	+	0.604748i	$0.793274\pi$
$174$	17.8883			1.35611
$175$		0			0
$176$	15.5928	−	15.5928i	1.17535	−	1.17535i
$177$	−3.93047	+	3.93047i	−0.295433	+	0.295433i
$178$			3.21857i			0.241242i
$179$			3.96115i			0.296071i	0.988982	+	0.148035i	$0.0472949\pi$
$179$			3.96115i			0.296071i	−0.988982	+	0.148035i	$0.952705\pi$
$180$	−1.29014	+	1.29014i	−0.0961614	+	0.0961614i
$181$	1.36267	−	1.36267i	0.101287	−	0.101287i	−0.654648	−	0.755934i	$-0.727183\pi$
$181$	1.36267	−	1.36267i	0.101287	−	0.101287i	0.755934	+	0.654648i	$0.227183\pi$
$182$		0			0
$183$	24.6110			1.81930
$184$	1.14167	+	1.14167i	0.0841652	+	0.0841652i
$185$			4.64595i			0.341577i
$186$	−24.4961			−1.79614
$187$	−6.75002	−	18.0357i	−0.493610	−	1.31890i
$188$	2.04227			0.148948
$189$		0			0
$190$	23.3913	+	23.3913i	1.69699	+	1.69699i
$191$	−25.1726			−1.82143			−0.910714	−	0.413038i	$-0.864468\pi$
$191$	−25.1726			−1.82143			−0.910714	+	0.413038i	$0.864468\pi$
$192$	−7.66032	−	7.66032i	−0.552836	−	0.552836i
$193$	7.95263	−	7.95263i	0.572443	−	0.572443i	−0.360367	−	0.932810i	$-0.617349\pi$
$193$	7.95263	−	7.95263i	0.572443	−	0.572443i	0.932810	+	0.360367i	$0.117349\pi$
$194$	−4.70297	+	4.70297i	−0.337654	+	0.337654i
$195$			25.1229i			1.79909i
$196$		0			0
$197$	−16.0035	+	16.0035i	−1.14020	+	1.14020i	−0.151789	+	0.988413i	$0.548503\pi$
$197$	−16.0035	+	16.0035i	−1.14020	+	1.14020i	−0.988413	+	0.151789i	$0.951497\pi$
$198$	5.91144	−	5.91144i	0.420108	−	0.420108i
$199$	3.71192	+	3.71192i	0.263131	+	0.263131i	0.826325	−	0.563194i	$-0.190428\pi$
$199$	3.71192	+	3.71192i	0.263131	+	0.263131i	−0.563194	+	0.826325i	$0.690428\pi$
$200$	−15.6747			−1.10837
$201$	18.0658	+	18.0658i	1.27427	+	1.27427i
$202$			8.46724i			0.595753i
$203$		0			0
$204$	3.70860	−	1.38797i	0.259654	−	0.0971775i
$205$	2.36291			0.165033
$206$			6.23029i			0.434085i
$207$	0.541021	+	0.541021i	0.0376035	+	0.0376035i
$208$	17.1751			1.19088
$209$	−20.4682	−	20.4682i	−1.41581	−	1.41581i
$210$		0			0
$211$	−6.87817	+	6.87817i	−0.473513	+	0.473513i	−0.903050	−	0.429536i	$-0.858677\pi$
$211$	−6.87817	+	6.87817i	−0.473513	+	0.473513i	0.429536	+	0.903050i	$0.358677\pi$
$212$			1.92589i			0.132270i
$213$			8.75918i			0.600169i
$214$	−12.6518	+	12.6518i	−0.864860	+	0.864860i
$215$	15.9445	−	15.9445i	1.08741	−	1.08741i
$216$	6.43299	+	6.43299i	0.437710	+	0.437710i
$217$		0			0
$218$	−4.89826	−	4.89826i	−0.331752	−	0.331752i
$219$			3.35892i			0.226975i
$220$	−7.48560			−0.504679
$221$	6.21547	−	13.6505i	0.418098	−	0.918229i
$222$	4.37731			0.293786
$223$			17.5438i			1.17482i	0.809289	+	0.587411i	$0.199853\pi$
$223$			17.5438i			1.17482i	−0.809289	+	0.587411i	$0.800147\pi$
$224$		0			0
$225$	−7.42798			−0.495199
$226$	−12.8934	−	12.8934i	−0.857659	−	0.857659i
$227$	5.89982	−	5.89982i	0.391585	−	0.391585i	−0.483667	−	0.875252i	$-0.660695\pi$
$227$	5.89982	−	5.89982i	0.391585	−	0.391585i	0.875252	+	0.483667i	$0.160695\pi$
$228$	4.20877	−	4.20877i	0.278732	−	0.278732i
$229$		−	15.3443i		−	1.01398i	−0.861952	−	0.506990i	$-0.830758\pi$
$229$		−	15.3443i		−	1.01398i	0.861952	−	0.506990i	$-0.169242\pi$
$230$		−	3.58739i		−	0.236546i
$231$		0			0
$232$	9.50018	−	9.50018i	0.623717	−	0.623717i
$233$	17.3081	+	17.3081i	1.13389	+	1.13389i	0.989524	+	0.144371i	$0.0461158\pi$
$233$	17.3081	+	17.3081i	1.13389	+	1.13389i	0.144371	+	0.989524i	$0.453884\pi$
$234$	6.51131			0.425658
$235$	10.3844	+	10.3844i	0.677403	+	0.677403i
$236$		−	1.28996i		−	0.0839694i
$237$	20.3527			1.32205
$238$		0			0
$239$	14.5771			0.942916			0.471458	−	0.881889i	$-0.343728\pi$
$239$	14.5771			0.942916			0.471458	+	0.881889i	$0.343728\pi$
$240$			32.6061i			2.10471i
$241$	10.7589	+	10.7589i	0.693041	+	0.693041i	0.962900	−	0.269859i	$-0.0869770\pi$
$241$	10.7589	+	10.7589i	0.693041	+	0.693041i	−0.269859	+	0.962900i	$0.586977\pi$
$242$	17.0039			1.09305
$243$	7.96123	+	7.96123i	0.510713	+	0.510713i
$244$	−4.03860	+	4.03860i	−0.258545	+	0.258545i
$245$		0			0
$246$		−	2.22628i		−	0.141942i
$247$		−	22.5452i		−	1.43452i
$248$	−13.0095	+	13.0095i	−0.826104	+	0.826104i
$249$	6.74874	−	6.74874i	0.427684	−	0.427684i
$250$	5.75524	+	5.75524i	0.363993	+	0.363993i
$251$	−1.54033			−0.0972246			−0.0486123	−	0.998818i	$-0.515480\pi$
$251$	−1.54033			−0.0972246			−0.0486123	+	0.998818i	$0.515480\pi$
$252$		0			0
$253$			3.13909i			0.197353i
$254$	−8.06411			−0.505987
$255$	25.9147	+	11.7998i	1.62284	+	0.738931i
$256$	10.7487			0.671797
$257$			4.02923i			0.251337i	0.992072	+	0.125668i	$0.0401075\pi$
$257$			4.02923i			0.251337i	−0.992072	+	0.125668i	$0.959893\pi$
$258$	−15.0226	−	15.0226i	−0.935264	−	0.935264i
$259$		0			0
$260$	−4.12260	−	4.12260i	−0.255673	−	0.255673i
$261$	4.50199	−	4.50199i	0.278666	−	0.278666i
$262$	9.28718	−	9.28718i	0.573764	−	0.573764i
$263$			17.9741i			1.10833i	0.832407	+	0.554164i	$0.186962\pi$
$263$			17.9741i			1.10833i	−0.832407	+	0.554164i	$0.813038\pi$
$264$		−	22.8255i		−	1.40481i
$265$	−9.79263	+	9.79263i	−0.601557	+	0.601557i
$266$		0			0
$267$	2.94464	+	2.94464i	0.180209	+	0.180209i
$268$	−5.92912			−0.362178
$269$	−12.7503	−	12.7503i	−0.777400	−	0.777400i	0.201988	−	0.979388i	$-0.435260\pi$
$269$	−12.7503	−	12.7503i	−0.777400	−	0.777400i	−0.979388	+	0.201988i	$0.935260\pi$
$270$		−	20.2139i		−	1.23018i
$271$	−16.7080			−1.01494			−0.507469	−	0.861670i	$-0.669419\pi$
$271$	−16.7080			−1.01494			−0.507469	+	0.861670i	$0.669419\pi$
$272$	8.06683	−	17.7164i	0.489123	−	1.07422i
$273$		0			0
$274$		−	31.7506i		−	1.91812i
$275$	−21.5492	−	21.5492i	−1.29946	−	1.29946i
$276$	−0.645475			−0.0388530
$277$	−0.737934	−	0.737934i	−0.0443381	−	0.0443381i	0.684590	−	0.728928i	$-0.259981\pi$
$277$	−0.737934	−	0.737934i	−0.0443381	−	0.0443381i	−0.728928	+	0.684590i	$0.759981\pi$
$278$	8.67755	−	8.67755i	0.520445	−	0.520445i
$279$	−6.16500	+	6.16500i	−0.369089	+	0.369089i
$280$		0			0
$281$		−	3.53036i		−	0.210604i	−0.994440	−	0.105302i	$-0.966419\pi$
$281$		−	3.53036i		−	0.210604i	0.994440	−	0.105302i	$-0.0335809\pi$
$282$	9.78393	−	9.78393i	0.582625	−	0.582625i
$283$	1.28939	−	1.28939i	0.0766462	−	0.0766462i	−0.667744	−	0.744391i	$-0.732740\pi$
$283$	1.28939	−	1.28939i	0.0766462	−	0.0766462i	0.744391	+	0.667744i	$0.232740\pi$
$284$	−1.43736	−	1.43736i	−0.0852915	−	0.0852915i
$285$	42.8010			2.53531
$286$	18.8898	+	18.8898i	1.11698	+	1.11698i
$287$		0			0
$288$	2.98115			0.175666
$289$	−11.1614	−	12.8228i	−0.656553	−	0.754280i
$290$	−29.8517			−1.75295
$291$			8.60540i			0.504458i
$292$	−0.551191	−	0.551191i	−0.0322560	−	0.0322560i
$293$	−14.9585			−0.873883			−0.436942	−	0.899490i	$-0.643938\pi$
$293$	−14.9585			−0.873883			−0.436942	+	0.899490i	$0.643938\pi$
$294$		0			0
$295$	6.55912	−	6.55912i	0.381887	−	0.381887i
$296$	2.32472	−	2.32472i	0.135121	−	0.135121i
$297$			17.6879i			1.02635i
$298$			1.05435i			0.0610767i
$299$	−1.72882	+	1.72882i	−0.0999800	+	0.0999800i
$300$	4.43105	−	4.43105i	0.255827	−	0.255827i
$301$		0			0
$302$	−17.9613			−1.03356
$303$	7.74659	+	7.74659i	0.445030	+	0.445030i
$304$		−	29.2606i		−	1.67821i
$305$	−41.0705			−2.35169
$306$	3.05825	−	6.71654i	0.174828	−	0.383959i
$307$	7.16409			0.408876			0.204438	−	0.978879i	$-0.434463\pi$
$307$	7.16409			0.408876			0.204438	+	0.978879i	$0.434463\pi$
$308$		0			0
$309$	5.70003	+	5.70003i	0.324263	+	0.324263i
$310$	40.8788			2.32176
$311$	4.45087	+	4.45087i	0.252386	+	0.252386i	0.821948	−	0.569562i	$-0.192887\pi$
$311$	4.45087	+	4.45087i	0.252386	+	0.252386i	−0.569562	+	0.821948i	$0.692887\pi$
$312$	12.5709	−	12.5709i	0.711685	−	0.711685i
$313$	−22.1833	+	22.1833i	−1.25387	+	1.25387i	−0.299905	+	0.953969i	$0.596955\pi$
$313$	−22.1833	+	22.1833i	−1.25387	+	1.25387i	−0.953969	+	0.299905i	$0.903045\pi$
$314$		−	36.7652i		−	2.07478i
$315$		0			0
$316$	−3.33983	+	3.33983i	−0.187880	+	0.187880i
$317$	11.7136	−	11.7136i	0.657900	−	0.657900i	−0.296983	−	0.954883i	$-0.595980\pi$
$317$	11.7136	−	11.7136i	0.657900	−	0.657900i	0.954883	+	0.296983i	$0.0959805\pi$
$318$	9.22639	+	9.22639i	0.517390	+	0.517390i
$319$	26.1213			1.46251
$320$	12.7834	+	12.7834i	0.714616	+	0.714616i
$321$			23.1500i			1.29211i
$322$		0			0
$323$	−23.2558	−	10.5891i	−1.29399	−	0.589192i
$324$	−5.24940			−0.291633
$325$		−	23.7359i		−	1.31663i
$326$	13.4270	+	13.4270i	0.743651	+	0.743651i
$327$	−8.96274			−0.495640
$328$	−1.18234	−	1.18234i	−0.0652839	−	0.0652839i
$329$		0			0
$330$	−35.8614	+	35.8614i	−1.97411	+	1.97411i
$331$			4.73294i			0.260146i	0.991504	+	0.130073i	$0.0415212\pi$
$331$			4.73294i			0.260146i	−0.991504	+	0.130073i	$0.958479\pi$
$332$			2.21490i			0.121559i
$333$	1.10165	−	1.10165i	0.0603698	−	0.0603698i
$334$	−27.2764	+	27.2764i	−1.49250	+	1.49250i
$335$	−30.1480	−	30.1480i	−1.64716	−	1.64716i
$336$		0			0
$337$	17.0523	+	17.0523i	0.928898	+	0.928898i	0.997635	−	0.0687369i	$-0.0218969\pi$
$337$	17.0523	+	17.0523i	0.928898	+	0.928898i	−0.0687369	+	0.997635i	$0.521897\pi$
$338$			0.366917i			0.0199577i
$339$	−23.5922			−1.28135
$340$	−6.18886	+	2.31623i	−0.335638	+	0.125615i
$341$	−35.7703			−1.93707
$342$		−	11.0931i		−	0.599846i
$343$		0			0
$344$	−15.9565			−0.860316
$345$	−3.28207	−	3.28207i	−0.176701	−	0.176701i
$346$	3.96376	−	3.96376i	0.213093	−	0.213093i
$347$	−16.1971	+	16.1971i	−0.869505	+	0.869505i	−0.992418	−	0.122912i	$-0.960777\pi$
$347$	−16.1971	+	16.1971i	−0.869505	+	0.869505i	0.122912	+	0.992418i	$0.460777\pi$
$348$			5.37118i			0.287925i
$349$			10.1897i			0.545442i	0.962093	+	0.272721i	$0.0879235\pi$
$349$			10.1897i			0.545442i	−0.962093	+	0.272721i	$0.912076\pi$
$350$		0			0
$351$	−9.74137	+	9.74137i	−0.519956	+	0.519956i
$352$	8.64855	+	8.64855i	0.460969	+	0.460969i
$353$	16.7999			0.894167			0.447084	−	0.894492i	$-0.352463\pi$
$353$	16.7999			0.894167			0.447084	+	0.894492i	$0.352463\pi$
$354$	−6.17985	−	6.17985i	−0.328455	−	0.328455i
$355$		−	14.6172i		−	0.775800i
$356$	−0.966416			−0.0512199
$357$		0			0
$358$	−6.22809			−0.329165
$359$			28.2418i			1.49055i	0.666759	+	0.745273i	$0.267681\pi$
$359$			28.2418i			1.49055i	−0.666759	+	0.745273i	$0.732319\pi$
$360$	6.56494	+	6.56494i	0.346003	+	0.346003i
$361$	−19.4095			−1.02155
$362$	2.14252	+	2.14252i	0.112608	+	0.112608i
$363$	15.5567	−	15.5567i	0.816517	−	0.816517i
$364$		0			0
$365$		−	5.60532i		−	0.293396i
$366$			38.6956i			2.02265i
$367$	13.3024	−	13.3024i	0.694382	−	0.694382i	−0.268811	−	0.963193i	$-0.586631\pi$
$367$	13.3024	−	13.3024i	0.694382	−	0.694382i	0.963193	+	0.268811i	$0.0866307\pi$
$368$	−2.24376	+	2.24376i	−0.116964	+	0.116964i
$369$	−0.560293	−	0.560293i	−0.0291677	−	0.0291677i
$370$	−7.30479			−0.379758
$371$		0			0
$372$		−	7.35527i		−	0.381353i
$373$	30.9655			1.60333			0.801666	−	0.597772i	$-0.203947\pi$
$373$	30.9655			1.60333			0.801666	+	0.597772i	$0.203947\pi$
$374$	28.3574	−	10.6130i	1.46633	−	0.548785i
$375$	10.5308			0.543809
$376$		−	10.3922i		−	0.535936i
$377$	14.3860	+	14.3860i	0.740915	+	0.740915i
$378$		0			0
$379$	−8.80375	−	8.80375i	−0.452218	−	0.452218i	0.443872	−	0.896090i	$-0.353604\pi$
$379$	−8.80375	−	8.80375i	−0.452218	−	0.452218i	−0.896090	+	0.443872i	$0.853604\pi$
$380$	−7.02353	+	7.02353i	−0.360300	+	0.360300i
$381$	−7.37778	+	7.37778i	−0.377975	+	0.377975i
$382$		−	39.5787i		−	2.02502i
$383$			29.8457i			1.52505i	0.646961	+	0.762523i	$0.276040\pi$
$383$			29.8457i			1.52505i	−0.646961	+	0.762523i	$0.723960\pi$
$384$	19.5781	−	19.5781i	0.999089	−	0.999089i
$385$		0			0
$386$	12.5039	+	12.5039i	0.636429	+	0.636429i
$387$	−7.56153			−0.384374
$388$	−1.41212	−	1.41212i	−0.0716898	−	0.0716898i
$389$		−	20.9404i		−	1.06172i	−0.847459	−	0.530861i	$-0.821869\pi$
$389$		−	20.9404i		−	1.06172i	0.847459	−	0.530861i	$-0.178131\pi$
$390$	−39.5005			−2.00019
$391$	0.971311	+	2.59530i	0.0491213	+	0.131250i
$392$		0			0
$393$		−	16.9935i		−	0.857208i
$394$	−25.1622	−	25.1622i	−1.26765	−	1.26765i
$395$	−33.9644			−1.70893
$396$	1.77498	+	1.77498i	0.0891963	+	0.0891963i
$397$	20.0540	−	20.0540i	1.00648	−	1.00648i	0.00650493	−	0.999979i	$-0.497929\pi$
$397$	20.0540	−	20.0540i	1.00648	−	1.00648i	0.999979	−	0.00650493i	$-0.00207060\pi$
$398$	−5.83622	+	5.83622i	−0.292543	+	0.292543i
$399$		0			0
$400$		−	30.8059i		−	1.54030i
$401$	2.31141	−	2.31141i	0.115426	−	0.115426i	−0.647034	−	0.762461i	$-0.723991\pi$
$401$	2.31141	−	2.31141i	0.115426	−	0.115426i	0.762461	+	0.647034i	$0.223991\pi$
$402$	−28.4048	+	28.4048i	−1.41670	+	1.41670i
$403$	−19.7001	−	19.7001i	−0.981331	−	0.981331i
$404$	−2.54239			−0.126489
$405$	−26.6918	−	26.6918i	−1.32633	−	1.32633i
$406$		0			0
$407$	6.39193			0.316836
$408$	−7.06277	−	18.8714i	−0.349659	−	0.934273i
$409$	34.3864			1.70030			0.850149	−	0.526542i	$-0.176512\pi$
$409$	34.3864			1.70030			0.850149	+	0.526542i	$0.176512\pi$
$410$			3.71518i			0.183480i
$411$	−29.0483	−	29.0483i	−1.43285	−	1.43285i
$412$	−1.87072			−0.0921638
$413$		0			0
$414$	−0.850642	+	0.850642i	−0.0418068	+	0.0418068i
$415$	−11.2622	+	11.2622i	−0.552840	+	0.552840i
$416$			9.52617i			0.467059i
$417$		−	15.8780i		−	0.777550i
$418$	32.1819	−	32.1819i	1.57407	−	1.57407i
$419$	12.3869	−	12.3869i	0.605140	−	0.605140i	−0.336532	−	0.941672i	$-0.609254\pi$
$419$	12.3869	−	12.3869i	0.605140	−	0.605140i	0.941672	+	0.336532i	$0.109254\pi$
$420$		0			0
$421$	−13.1028			−0.638593			−0.319296	−	0.947655i	$-0.603447\pi$
$421$	−13.1028			−0.638593			−0.319296	+	0.947655i	$0.603447\pi$
$422$	−10.8145	−	10.8145i	−0.526441	−	0.526441i
$423$		−	4.92469i		−	0.239447i
$424$	9.79997			0.475929
$425$	−24.4840	−	11.1483i	−1.18765	−	0.540773i
$426$	−13.7720			−0.667254
$427$		0			0
$428$	−3.79886	−	3.79886i	−0.183625	−	0.183625i
$429$	34.5643			1.66878
$430$	25.0695	+	25.0695i	1.20896	+	1.20896i
$431$	18.5848	−	18.5848i	0.895197	−	0.895197i	−0.0998095	−	0.995007i	$-0.531823\pi$
$431$	18.5848	−	18.5848i	0.895197	−	0.895197i	0.995007	+	0.0998095i	$0.0318233\pi$
$432$	−12.6430	+	12.6430i	−0.608284	+	0.608284i
$433$		−	0.783681i		−	0.0376613i	−0.999823	−	0.0188307i	$-0.994006\pi$
$433$		−	0.783681i		−	0.0376613i	0.999823	−	0.0188307i	$-0.00599434\pi$
$434$		0			0
$435$	−27.3111	+	27.3111i	−1.30947	+	1.30947i
$436$	1.47076	−	1.47076i	0.0704367	−	0.0704367i
$437$	2.94532	+	2.94532i	0.140894	+	0.140894i
$438$	−5.28120			−0.252346
$439$	−17.7866	−	17.7866i	−0.848908	−	0.848908i	0.141089	−	0.989997i	$-0.454940\pi$
$439$	−17.7866	−	17.7866i	−0.848908	−	0.848908i	−0.989997	+	0.141089i	$0.954940\pi$
$440$			38.0909i			1.81591i
$441$		0			0
$442$	21.4625	+	9.77254i	1.02087	+	0.464832i
$443$	−12.1317			−0.576395			−0.288197	−	0.957571i	$-0.593056\pi$
$443$	−12.1317			−0.576395			−0.288197	+	0.957571i	$0.593056\pi$
$444$			1.31434i			0.0623758i
$445$	−4.91397	−	4.91397i	−0.232945	−	0.232945i
$446$	−27.5840			−1.30614
$447$	0.964612	+	0.964612i	0.0456246	+	0.0456246i
$448$		0			0
$449$	26.1661	−	26.1661i	1.23485	−	1.23485i	0.272777	−	0.962077i	$-0.412058\pi$
$449$	26.1661	−	26.1661i	1.23485	−	1.23485i	0.962077	−	0.272777i	$-0.0879421\pi$
$450$		−	11.6790i		−	0.550551i
$451$		−	3.25091i		−	0.153079i
$452$	3.87142	−	3.87142i	0.182096	−	0.182096i
$453$	−16.4326	+	16.4326i	−0.772073	+	0.772073i
$454$	9.27624	+	9.27624i	0.435355	+	0.435355i
$455$		0			0
$456$	−21.4165	−	21.4165i	−1.00292	−	1.00292i
$457$			12.7879i			0.598192i	0.954223	+	0.299096i	$0.0966851\pi$
$457$			12.7879i			0.598192i	−0.954223	+	0.299096i	$0.903315\pi$
$458$	24.1257			1.12732
$459$	5.47306	+	14.6238i	0.255460	+	0.682578i
$460$	1.07716			0.0502228
$461$			4.58089i			0.213353i	0.994294	+	0.106677i	$0.0340210\pi$
$461$			4.58089i			0.213353i	−0.994294	+	0.106677i	$0.965979\pi$
$462$		0			0
$463$	−1.53844			−0.0714973			−0.0357486	−	0.999361i	$-0.511382\pi$
$463$	−1.53844			−0.0714973			−0.0357486	+	0.999361i	$0.511382\pi$
$464$	18.6710	+	18.6710i	0.866779	+	0.866779i
$465$	37.3996	−	37.3996i	1.73437	−	1.73437i
$466$	−27.2134	+	27.2134i	−1.26064	+	1.26064i
$467$			11.0027i			0.509143i	0.967054	+	0.254572i	$0.0819345\pi$
$467$			11.0027i			0.509143i	−0.967054	+	0.254572i	$0.918066\pi$
$468$			1.95510i			0.0903746i
$469$		0			0
$470$	−16.3273	+	16.3273i	−0.753122	+	0.753122i
$471$	−33.6361	−	33.6361i	−1.54987	−	1.54987i
$472$	−6.56404			−0.302134
$473$	−21.9366	−	21.9366i	−1.00865	−	1.00865i
$474$			32.0004i			1.46983i
$475$	−40.4380			−1.85542
$476$		0			0
$477$	4.64405			0.212637
$478$			22.9195i			1.04831i
$479$	−16.4487	−	16.4487i	−0.751558	−	0.751558i	0.223212	−	0.974770i	$-0.428346\pi$
$479$	−16.4487	−	16.4487i	−0.751558	−	0.751558i	−0.974770	+	0.223212i	$0.928346\pi$
$480$	−18.0850			−0.825462
$481$	3.52028	+	3.52028i	0.160511	+	0.160511i
$482$	−16.9161	+	16.9161i	−0.770508	+	0.770508i
$483$		0			0
$484$			5.10564i			0.232075i
$485$		−	14.3606i		−	0.652080i
$486$	−12.5174	+	12.5174i	−0.567800	+	0.567800i
$487$	15.5818	−	15.5818i	0.706079	−	0.706079i	−0.259629	−	0.965708i	$-0.583600\pi$
$487$	15.5818	−	15.5818i	0.706079	−	0.706079i	0.965708	+	0.259629i	$0.0836003\pi$
$488$	20.5506	+	20.5506i	0.930283	+	0.930283i
$489$	24.5684			1.11102
$490$		0			0
$491$		−	19.2671i		−	0.869512i	−0.900548	−	0.434756i	$-0.856835\pi$
$491$		−	19.2671i		−	0.869512i	0.900548	−	0.434756i	$-0.143165\pi$
$492$	0.668468			0.0301369
$493$	21.5962	−	8.08256i	0.972645	−	0.364020i
$494$	35.4476			1.59486
$495$			18.0507i			0.811317i
$496$	−25.5680	−	25.5680i	−1.14804	−	1.14804i
$497$		0			0
$498$	10.6110	+	10.6110i	0.475490	+	0.475490i
$499$	29.9541	−	29.9541i	1.34093	−	1.34093i	0.445793	−	0.895136i	$-0.352922\pi$
$499$	29.9541	−	29.9541i	1.34093	−	1.34093i	0.895136	−	0.445793i	$-0.147078\pi$
$500$	−1.72808	+	1.72808i	−0.0772821	+	0.0772821i
$501$			49.9099i			2.22981i
$502$		−	2.42184i		−	0.108092i
$503$	7.89613	−	7.89613i	0.352071	−	0.352071i	−0.508809	−	0.860880i	$-0.669914\pi$
$503$	7.89613	−	7.89613i	0.352071	−	0.352071i	0.860880	+	0.508809i	$0.169914\pi$
$504$		0			0
$505$	−12.9274	−	12.9274i	−0.575262	−	0.575262i
$506$	−4.93556			−0.219412
$507$	0.335689	+	0.335689i	0.0149085	+	0.0149085i
$508$		−	2.42135i		−	0.107430i
$509$	33.7960			1.49798			0.748991	−	0.662580i	$-0.230538\pi$
$509$	33.7960			1.49798			0.748991	+	0.662580i	$0.230538\pi$
$510$	−18.5527	+	40.7455i	−0.821527	+	1.80424i
$511$		0			0
$512$		−	10.3205i		−	0.456104i
$513$	16.5960	+	16.5960i	0.732733	+	0.732733i
$514$	−6.33513			−0.279430
$515$	−9.51213	−	9.51213i	−0.419154	−	0.419154i
$516$	4.51071	−	4.51071i	0.198573	−	0.198573i
$517$	14.2869	−	14.2869i	0.628338	−	0.628338i
$518$		0			0
$519$		−	7.25281i		−	0.318363i
$520$	−20.9781	+	20.9781i	−0.919950	+	0.919950i
$521$	−10.4802	+	10.4802i	−0.459145	+	0.459145i	−0.898375	−	0.439230i	$-0.855251\pi$
$521$	−10.4802	+	10.4802i	−0.459145	+	0.459145i	0.439230	+	0.898375i	$0.355251\pi$
$522$	7.07843	+	7.07843i	0.309815	+	0.309815i
$523$	2.75940			0.120660			0.0603300	−	0.998178i	$-0.480785\pi$
$523$	2.75940			0.120660			0.0603300	+	0.998178i	$0.480785\pi$
$524$	2.78859	+	2.78859i	0.121820	+	0.121820i
$525$		0			0
$526$	−28.2605			−1.23221
$527$	−29.5738	+	11.0682i	−1.28825	+	0.482139i
$528$	44.8596			1.95226
$529$			22.5483i			0.980361i
$530$	−15.3969	−	15.3969i	−0.668797	−	0.668797i
$531$	−3.11059			−0.134988
$532$		0			0
$533$	1.79040	−	1.79040i	0.0775508	−	0.0775508i
$534$	−4.62983	+	4.62983i	−0.200352	+	0.200352i
$535$		−	38.6325i		−	1.67023i
$536$			30.1706i			1.30317i
$537$	−5.69802	+	5.69802i	−0.245888	+	0.245888i
$538$	20.0472	−	20.0472i	0.864296	−	0.864296i
$539$		0			0
$540$	6.06948			0.261189
$541$	7.88750	+	7.88750i	0.339110	+	0.339110i	0.856032	−	0.516922i	$-0.172922\pi$
$541$	7.88750	+	7.88750i	0.339110	+	0.339110i	−0.516922	+	0.856032i	$0.672922\pi$
$542$		−	26.2698i		−	1.12839i
$543$	3.92034			0.168238
$544$	9.82642	+	4.47427i	0.421304	+	0.191833i
$545$	14.9569			0.640683
$546$		0			0
$547$	5.17129	+	5.17129i	0.221108	+	0.221108i	0.808965	−	0.587857i	$-0.200028\pi$
$547$	5.17129	+	5.17129i	0.221108	+	0.221108i	−0.587857	+	0.808965i	$0.700028\pi$
$548$	9.53351			0.407252
$549$	9.73862	+	9.73862i	0.415634	+	0.415634i
$550$	33.8816	−	33.8816i	1.44472	−	1.44472i
$551$	24.5089	−	24.5089i	1.04411	−	1.04411i
$552$			3.28453i			0.139799i
$553$		0			0
$554$	1.16025	−	1.16025i	0.0492942	−	0.0492942i
$555$	−6.68308	+	6.68308i	−0.283681	+	0.283681i
$556$	2.60554	+	2.60554i	0.110500	+	0.110500i
$557$	15.3543			0.650583			0.325291	−	0.945614i	$-0.394538\pi$
$557$	15.3543			0.650583			0.325291	+	0.945614i	$0.394538\pi$
$558$	−9.69318	−	9.69318i	−0.410345	−	0.410345i
$559$		−	24.1626i		−	1.02197i
$560$		0			0
$561$	16.2342	−	35.6537i	0.685409	−	1.50530i
$562$	5.55076			0.234145
$563$			6.62599i			0.279252i	0.990204	+	0.139626i	$0.0445901\pi$
$563$			6.62599i			0.279252i	−0.990204	+	0.139626i	$0.955410\pi$
$564$	2.93775	+	2.93775i	0.123701	+	0.123701i
$565$	39.3703			1.65632
$566$	2.02730	+	2.02730i	0.0852136	+	0.0852136i
$567$		0			0
$568$	−7.31407	+	7.31407i	−0.306892	+	0.306892i
$569$		−	36.9677i		−	1.54977i	−0.632105	−	0.774883i	$-0.717809\pi$
$569$		−	36.9677i		−	1.54977i	0.632105	−	0.774883i	$-0.282191\pi$
$570$			67.2956i			2.81870i
$571$	−25.8702	+	25.8702i	−1.08264	+	1.08264i	−0.0863725	+	0.996263i	$0.527528\pi$
$571$	−25.8702	+	25.8702i	−1.08264	+	1.08264i	−0.996263	+	0.0863725i	$0.972472\pi$
$572$	−5.67191	+	5.67191i	−0.237154	+	0.237154i
$573$	−36.2102	−	36.2102i	−1.51270	−	1.51270i
$574$		0			0
$575$	3.10087	+	3.10087i	0.129315	+	0.129315i
$576$		−	6.06241i		−	0.252600i
$577$	−6.70916			−0.279306			−0.139653	−	0.990200i	$-0.544599\pi$
$577$	−6.70916			−0.279306			−0.139653	+	0.990200i	$0.544599\pi$
$578$	20.1611	−	17.5490i	0.838591	−	0.729941i
$579$	22.8793			0.950832
$580$		−	8.96335i		−	0.372183i
$581$		0			0
$582$	−13.5302			−0.560845
$583$	13.4728	+	13.4728i	0.557985	+	0.557985i
$584$	−2.80476	+	2.80476i	−0.116062	+	0.116062i
$585$	−9.94118	+	9.94118i	−0.411017	+	0.411017i
$586$		−	23.5191i		−	0.971564i
$587$			0.653601i			0.0269770i	0.999909	+	0.0134885i	$0.00429365\pi$
$587$			0.653601i			0.0269770i	−0.999909	+	0.0134885i	$0.995706\pi$
$588$		0			0
$589$	−33.5623	+	33.5623i	−1.38291	+	1.38291i
$590$	10.3129	+	10.3129i	0.424573	+	0.424573i
$591$	−46.0412			−1.89388
$592$	4.56883	+	4.56883i	0.187778	+	0.187778i
$593$		−	27.7090i		−	1.13787i	−0.822381	−	0.568937i	$-0.807355\pi$
$593$		−	27.7090i		−	1.13787i	0.822381	−	0.568937i	$-0.192645\pi$
$594$	−27.8105			−1.14108
$595$		0			0
$596$	−0.316581			−0.0129677
$597$			10.6790i			0.437063i
$598$	−2.71820	−	2.71820i	−0.111155	−	0.111155i
$599$	−7.54536			−0.308295			−0.154148	−	0.988048i	$-0.549263\pi$
$599$	−7.54536			−0.308295			−0.154148	+	0.988048i	$0.549263\pi$
$600$	−22.5476	−	22.5476i	−0.920503	−	0.920503i
$601$	−12.8735	+	12.8735i	−0.525119	+	0.525119i	−0.919113	−	0.393994i	$-0.871093\pi$
$601$	−12.8735	+	12.8735i	−0.525119	+	0.525119i	0.393994	+	0.919113i	$0.371093\pi$
$602$		0			0
$603$			14.2974i			0.582234i
$604$		−	5.39311i		−	0.219442i
$605$	−25.9609	+	25.9609i	−1.05546	+	1.05546i
$606$	−12.1799	+	12.1799i	−0.494775	+	0.494775i
$607$	8.64742	+	8.64742i	0.350988	+	0.350988i	0.860477	−	0.509489i	$-0.170166\pi$
$607$	8.64742	+	8.64742i	0.350988	+	0.350988i	−0.509489	+	0.860477i	$0.670166\pi$
$608$	16.2294			0.658189
$609$		0			0
$610$		−	64.5748i		−	2.61456i
$611$	15.7367			0.636639
$612$	2.01672	+	0.918276i	0.0815212	+	0.0371191i
$613$	−39.4099			−1.59175			−0.795876	−	0.605460i	$-0.792989\pi$
$613$	−39.4099			−1.59175			−0.795876	+	0.605460i	$0.792989\pi$
$614$			11.2640i			0.454580i
$615$	3.39899	+	3.39899i	0.137060	+	0.137060i
$616$		0			0
$617$	10.4142	+	10.4142i	0.419260	+	0.419260i	0.884948	−	0.465689i	$-0.154193\pi$
$617$	10.4142	+	10.4142i	0.419260	+	0.419260i	−0.465689	+	0.884948i	$0.654193\pi$
$618$	−8.96211	+	8.96211i	−0.360509	+	0.360509i
$619$	−26.1584	+	26.1584i	−1.05140	+	1.05140i	−0.0527903	+	0.998606i	$0.516812\pi$
$619$	−26.1584	+	26.1584i	−1.05140	+	1.05140i	−0.998606	+	0.0527903i	$0.983188\pi$
$620$			12.2744i			0.492951i
$621$		−	2.54524i		−	0.102137i
$622$	−6.99806	+	6.99806i	−0.280597	+	0.280597i
$623$		0			0
$624$	24.7059	+	24.7059i	0.989028	+	0.989028i
$625$	15.0506			0.602023
$626$	−34.8786	−	34.8786i	−1.39403	−	1.39403i
$627$		−	58.8859i		−	2.35168i
$628$	11.0392			0.440512
$629$	5.28464	−	1.97782i	0.210713	−	0.0788609i
$630$		0			0
$631$			31.7794i			1.26512i	0.774512	+	0.632559i	$0.217996\pi$
$631$			31.7794i			1.26512i	−0.774512	+	0.632559i	$0.782004\pi$
$632$	16.9949	+	16.9949i	0.676021	+	0.676021i
$633$	−19.7881			−0.786508
$634$	18.4171	+	18.4171i	0.731438	+	0.731438i
$635$	12.3119	−	12.3119i	0.488584	−	0.488584i
$636$	−2.77034	+	2.77034i	−0.109851	+	0.109851i
$637$		0			0
$638$			41.0702i			1.62599i
$639$	−3.46602	+	3.46602i	−0.137114	+	0.137114i
$640$	−32.6716	+	32.6716i	−1.29146	+	1.29146i
$641$	−13.4016	−	13.4016i	−0.529331	−	0.529331i	0.391042	−	0.920373i	$-0.372115\pi$
$641$	−13.4016	−	13.4016i	−0.529331	−	0.529331i	−0.920373	+	0.391042i	$0.872115\pi$
$642$	−36.3986			−1.43654
$643$	19.0600	+	19.0600i	0.751652	+	0.751652i	0.974787	−	0.223135i	$-0.0716292\pi$
$643$	19.0600	+	19.0600i	0.751652	+	0.751652i	−0.223135	+	0.974787i	$0.571629\pi$
$644$		0			0
$645$	45.8716			1.80619
$646$	16.6491	−	36.5649i	0.655051	−	1.43863i
$647$	−0.816139			−0.0320858			−0.0160429	−	0.999871i	$-0.505107\pi$
$647$	−0.816139			−0.0320858			−0.0160429	+	0.999871i	$0.505107\pi$
$648$			26.7118i			1.04934i
$649$	−9.02408	−	9.02408i	−0.354226	−	0.354226i
$650$	37.3198			1.46380
$651$		0			0
$652$	−4.03161	+	4.03161i	−0.157890	+	0.157890i
$653$	18.7492	−	18.7492i	0.733712	−	0.733712i	−0.237641	−	0.971353i	$-0.576374\pi$
$653$	18.7492	−	18.7492i	0.733712	−	0.733712i	0.971353	+	0.237641i	$0.0763743\pi$
$654$		−	14.0920i		−	0.551042i
$655$			28.3585i			1.10806i
$656$	2.32369	−	2.32369i	0.0907249	−	0.0907249i
$657$	−1.32913	+	1.32913i	−0.0518544	+	0.0518544i
$658$		0			0
$659$	−15.6995			−0.611566			−0.305783	−	0.952101i	$-0.598918\pi$
$659$	−15.6995			−0.611566			−0.305783	+	0.952101i	$0.598918\pi$
$660$	−10.7678	−	10.7678i	−0.419138	−	0.419138i
$661$			15.5120i			0.603348i	0.953411	+	0.301674i	$0.0975454\pi$
$661$			15.5120i			0.603348i	−0.953411	+	0.301674i	$0.902455\pi$
$662$	−7.44156			−0.289224
$663$	28.5766	−	10.6950i	1.10982	−	0.415361i
$664$	11.2707			0.437386
$665$		0			0
$666$	1.73211	+	1.73211i	0.0671179	+	0.0671179i
$667$	−3.75878			−0.145541
$668$	−8.19008	−	8.19008i	−0.316884	−	0.316884i
$669$	−25.2364	+	25.2364i	−0.975694	+	0.975694i
$670$	47.4015	−	47.4015i	1.83128	−	1.83128i
$671$			56.5050i			2.18135i
$672$		0			0
$673$	25.7151	−	25.7151i	0.991243	−	0.991243i	−0.00871919	−	0.999962i	$-0.502775\pi$
$673$	25.7151	−	25.7151i	0.991243	−	0.991243i	0.999962	+	0.00871919i	$0.00277544\pi$
$674$	−26.8112	+	26.8112i	−1.03273	+	1.03273i
$675$	17.4725	+	17.4725i	0.672518	+	0.672518i
$676$	−0.110171			−0.00423736
$677$	20.2679	+	20.2679i	0.778959	+	0.778959i	0.979654	−	0.200695i	$-0.0643199\pi$
$677$	20.2679	+	20.2679i	0.778959	+	0.778959i	−0.200695	+	0.979654i	$0.564320\pi$
$678$		−	37.0938i		−	1.42458i
$679$		0			0
$680$	11.7863	+	31.4923i	0.451982	+	1.20768i
$681$	16.9735			0.650425
$682$		−	56.2414i		−	2.15359i
$683$	13.9866	+	13.9866i	0.535181	+	0.535181i	0.922110	−	0.386929i	$-0.126464\pi$
$683$	13.9866	+	13.9866i	0.535181	+	0.535181i	−0.386929	+	0.922110i	$0.626464\pi$
$684$	3.33084			0.127358
$685$	48.4754	+	48.4754i	1.85215	+	1.85215i
$686$		0			0
$687$	22.0724	−	22.0724i	0.842114	−	0.842114i
$688$		−	31.3598i		−	1.19558i
$689$			14.8399i			0.565356i
$690$	5.16037	−	5.16037i	0.196452	−	0.196452i
$691$	−26.6547	+	26.6547i	−1.01399	+	1.01399i	−0.0140930	+	0.999901i	$0.504486\pi$
$691$	−26.6547	+	26.6547i	−1.01399	+	1.01399i	−0.999901	+	0.0140930i	$0.995514\pi$
$692$	1.19017	+	1.19017i	0.0452434	+	0.0452434i
$693$		0			0
$694$	−25.4665	−	25.4665i	−0.966697	−	0.966697i
$695$			26.4970i			1.00509i
$696$	27.3315			1.03600
$697$	−1.00591	−	2.68775i	−0.0381016	−	0.101806i
$698$	−16.0212			−0.606410
$699$			49.7946i			1.88341i
$700$		0			0
$701$	12.4612			0.470652			0.235326	−	0.971916i	$-0.424384\pi$
$701$	12.4612			0.470652			0.235326	+	0.971916i	$0.424384\pi$
$702$	−15.3163	−	15.3163i	−0.578076	−	0.578076i
$703$	5.99737	−	5.99737i	0.226195	−	0.226195i
$704$	17.5875	−	17.5875i	0.662855	−	0.662855i
$705$			29.8754i			1.12517i
$706$			26.4143i			0.994116i
$707$		0			0
$708$	1.85558	−	1.85558i	0.0697368	−	0.0697368i
$709$	−10.2099	−	10.2099i	−0.383439	−	0.383439i	0.488900	−	0.872340i	$-0.337398\pi$
$709$	−10.2099	−	10.2099i	−0.383439	−	0.383439i	−0.872340	+	0.488900i	$0.837398\pi$
$710$	22.9825			0.862517
$711$	8.05362	+	8.05362i	0.302034	+	0.302034i
$712$			4.91766i			0.184297i
$713$	5.14726			0.192766
$714$		0			0
$715$	−57.6804			−2.15712
$716$		−	1.87006i		−	0.0698874i
$717$	20.9688	+	20.9688i	0.783095	+	0.783095i
$718$	−44.4044			−1.65716
$719$	6.54115	+	6.54115i	0.243944	+	0.243944i	0.818479	−	0.574536i	$-0.194817\pi$
$719$	6.54115	+	6.54115i	0.243944	+	0.243944i	−0.574536	+	0.818479i	$0.694817\pi$
$720$	−12.9023	+	12.9023i	−0.480840	+	0.480840i
$721$		0			0
$722$		−	30.5173i		−	1.13574i
$723$			30.9528i			1.15115i
$724$	−0.643317	+	0.643317i	−0.0239087	+	0.0239087i
$725$	25.8033	−	25.8033i	0.958309	−	0.958309i
$726$	24.4597	+	24.4597i	0.907785	+	0.907785i
$727$	−33.0618			−1.22619			−0.613096	−	0.790008i	$-0.710076\pi$
$727$	−33.0618			−1.22619			−0.613096	+	0.790008i	$0.710076\pi$
$728$		0			0
$729$		−	10.4537i		−	0.387175i
$730$	8.81320			0.326191
$731$	−24.9242	−	11.3488i	−0.921855	−	0.419749i
$732$	−11.6188			−0.429445
$733$		−	1.81758i		−	0.0671338i	−0.999436	−	0.0335669i	$-0.989313\pi$
$733$		−	1.81758i		−	0.0671338i	0.999436	−	0.0335669i	$-0.0106867\pi$
$734$	20.9153	+	20.9153i	0.771998	+	0.771998i
$735$		0			0
$736$	−1.24450	−	1.24450i	−0.0458730	−	0.0458730i
$737$	−41.4779	+	41.4779i	−1.52786	+	1.52786i
$738$	0.880943	−	0.880943i	0.0324280	−	0.0324280i
$739$		−	30.1602i		−	1.10946i	−0.832031	−	0.554730i	$-0.812822\pi$
$739$		−	30.1602i		−	1.10946i	0.832031	−	0.554730i	$-0.187178\pi$
$740$		−	2.19335i		−	0.0806292i
$741$	32.4307	−	32.4307i	1.19137	−	1.19137i
$742$		0			0
$743$	28.0426	+	28.0426i	1.02878	+	1.02878i	0.999573	+	0.0292082i	$0.00929860\pi$
$743$	28.0426	+	28.0426i	1.02878	+	1.02878i	0.0292082	+	0.999573i	$0.490701\pi$
$744$	−37.4277			−1.37216
$745$	−1.60973	−	1.60973i	−0.0589760	−	0.0589760i
$746$			48.6867i			1.78255i
$747$	5.34098			0.195416
$748$	3.18668	+	8.51467i	0.116517	+	0.311327i
$749$		0			0
$750$			16.5575i			0.604595i
$751$	−29.5789	−	29.5789i	−1.07935	−	1.07935i	−0.996568	−	0.0827803i	$-0.973620\pi$
$751$	−29.5789	−	29.5789i	−1.07935	−	1.07935i	−0.0827803	−	0.996568i	$-0.526380\pi$
$752$	20.4241			0.744789
$753$	−2.21572	−	2.21572i	−0.0807454	−	0.0807454i
$754$	−22.6189	+	22.6189i	−0.823733	+	0.823733i
$755$	27.4226	−	27.4226i	0.998009	−	0.998009i
$756$		0			0
$757$			29.9024i			1.08682i	0.839467	+	0.543411i	$0.182867\pi$
$757$			29.9024i			1.08682i	−0.839467	+	0.543411i	$0.817133\pi$
$758$	13.8421	−	13.8421i	0.502766	−	0.502766i
$759$	−4.51550	+	4.51550i	−0.163902	+	0.163902i
$760$	35.7396	+	35.7396i	1.29641	+	1.29641i
$761$	29.8807			1.08318			0.541588	−	0.840644i	$-0.317823\pi$
$761$	29.8807			1.08318			0.541588	+	0.840644i	$0.317823\pi$
$762$	−11.6000	−	11.6000i	−0.420224	−	0.420224i
$763$		0			0
$764$	11.8840			0.429948
$765$	5.58532	+	14.9237i	0.201938	+	0.539568i
$766$	−46.9262			−1.69551
$767$		−	9.93981i		−	0.358906i
$768$	15.4618	+	15.4618i	0.557929	+	0.557929i
$769$	−35.8821			−1.29394			−0.646971	−	0.762514i	$-0.723965\pi$
$769$	−35.8821			−1.29394			−0.646971	+	0.762514i	$0.723965\pi$
$770$		0			0
$771$	−5.79594	+	5.79594i	−0.208736	+	0.208736i
$772$	−3.75444	+	3.75444i	−0.135125	+	0.135125i
$773$		−	13.1964i		−	0.474642i	−0.971431	−	0.237321i	$-0.923731\pi$
$773$		−	13.1964i		−	0.474642i	0.971431	−	0.237321i	$-0.0762692\pi$
$774$		−	11.8889i		−	0.427338i
$775$	−35.3349	+	35.3349i	−1.26927	+	1.26927i
$776$	−7.18567	+	7.18567i	−0.257950	+	0.257950i
$777$		0			0
$778$	32.9245			1.18040
$779$	−3.05024	−	3.05024i	−0.109286	−	0.109286i
$780$		−	11.8605i		−	0.424675i
$781$	−20.1104			−0.719608
$782$	−4.08056	+	1.52718i	−0.145921	+	0.0546120i
$783$	−21.1797			−0.756899
$784$		0			0
$785$	56.1314	+	56.1314i	2.00342	+	2.00342i
$786$	26.7187			0.953025
$787$	−20.2916	−	20.2916i	−0.723318	−	0.723318i	0.245962	−	0.969280i	$-0.420896\pi$
$787$	−20.2916	−	20.2916i	−0.723318	−	0.723318i	−0.969280	+	0.245962i	$0.920896\pi$
$788$	7.55525	−	7.55525i	0.269144	−	0.269144i
$789$	−25.8552	+	25.8552i	−0.920470	+	0.920470i
$790$		−	53.4019i		−	1.89995i
$791$		0			0
$792$	9.03209	−	9.03209i	0.320941	−	0.320941i
$793$	−31.1195	+	31.1195i	−1.10508	+	1.10508i
$794$	31.5308	+	31.5308i	1.11899	+	1.11899i
$795$	−28.1729			−0.999189
$796$	−1.75240	−	1.75240i	−0.0621121	−	0.0621121i
$797$		−	10.8120i		−	0.382980i	−0.981495	−	0.191490i	$-0.938668\pi$
$797$		−	10.8120i		−	0.382980i	0.981495	−	0.191490i	$-0.0613320\pi$
$798$		0			0
$799$	7.39125	−	16.2327i	0.261484	−	0.574272i
$800$	17.0865			0.604100
$801$			2.33040i			0.0823406i
$802$	3.63421	+	3.63421i	0.128328	+	0.128328i
$803$	−7.71184			−0.272145
$804$	−8.52888	−	8.52888i	−0.300790	−	0.300790i
$805$		0			0
$806$	30.9743	−	30.9743i	1.09102	−	1.09102i
$807$		−	36.6820i		−	1.29127i
$808$			12.9371i			0.455125i
$809$	36.0543	−	36.0543i	1.26760	−	1.26760i	0.320276	−	0.947324i	$-0.396224\pi$
$809$	36.0543	−	36.0543i	1.26760	−	1.26760i	0.947324	−	0.320276i	$-0.103776\pi$
$810$	41.9673	−	41.9673i	1.47458	−	1.47458i
$811$	−10.8591	−	10.8591i	−0.381315	−	0.381315i	0.490261	−	0.871576i	$-0.336902\pi$
$811$	−10.8591	−	10.8591i	−0.381315	−	0.381315i	−0.871576	+	0.490261i	$0.836902\pi$
$812$		0			0
$813$	−24.0340	−	24.0340i	−0.842910	−	0.842910i
$814$			10.0500i			0.352251i
$815$	−40.9994			−1.43615
$816$	37.0885	−	13.8807i	1.29836	−	0.485921i
$817$	−41.1650			−1.44018
$818$			54.0654i			1.89035i
$819$		0			0
$820$	−1.11553			−0.0389560
$821$	9.85365	+	9.85365i	0.343895	+	0.343895i	0.857829	−	0.513935i	$-0.171813\pi$
$821$	9.85365	+	9.85365i	0.343895	+	0.343895i	−0.513935	+	0.857829i	$0.671813\pi$
$822$	45.6724	−	45.6724i	1.59301	−	1.59301i
$823$	8.67935	−	8.67935i	0.302543	−	0.302543i	−0.539465	−	0.842008i	$-0.681373\pi$
$823$	8.67935	−	8.67935i	0.302543	−	0.302543i	0.842008	+	0.539465i	$0.181373\pi$
$824$			9.51926i			0.331619i
$825$		−	61.9959i		−	2.15842i
$826$		0			0
$827$	11.8528	−	11.8528i	0.412162	−	0.412162i	−0.470329	−	0.882491i	$-0.655865\pi$
$827$	11.8528	−	11.8528i	0.412162	−	0.412162i	0.882491	+	0.470329i	$0.155865\pi$
$828$	−0.255416	−	0.255416i	−0.00887631	−	0.00887631i
$829$	43.4266			1.50827			0.754134	−	0.656721i	$-0.228057\pi$
$829$	43.4266			1.50827			0.754134	+	0.656721i	$0.228057\pi$
$830$	−17.7075	−	17.7075i	−0.614635	−	0.614635i
$831$		−	2.12300i		−	0.0736459i
$832$	19.3722			0.671612
$833$		0			0
$834$	24.9649			0.864463
$835$		−	83.2889i		−	2.88233i
$836$	9.66303	+	9.66303i	0.334203	+	0.334203i
$837$	29.0033			1.00250
$838$	19.4758	+	19.4758i	0.672781	+	0.672781i
$839$	−4.20215	+	4.20215i	−0.145074	+	0.145074i	−0.775914	−	0.630839i	$-0.782711\pi$
$839$	−4.20215	+	4.20215i	−0.145074	+	0.145074i	0.630839	+	0.775914i	$0.282711\pi$
$840$		0			0
$841$			2.27792i			0.0785488i
$842$		−	20.6015i		−	0.709973i
$843$	5.07834	−	5.07834i	0.174907	−	0.174907i
$844$	3.24718	−	3.24718i	0.111773	−	0.111773i
$845$	−0.560193	−	0.560193i	−0.0192712	−	0.0192712i
$846$	7.74305			0.266211
$847$		0			0
$848$			19.2602i			0.661397i
$849$	3.70950			0.127310
$850$	17.5284	−	38.4960i	0.601220	−	1.32040i
$851$	−0.919783			−0.0315297
$852$		−	4.13521i		−	0.141670i
$853$	9.18348	+	9.18348i	0.314436	+	0.314436i	0.846625	−	0.532189i	$-0.178630\pi$
$853$	9.18348	+	9.18348i	0.314436	+	0.314436i	−0.532189	+	0.846625i	$0.678630\pi$
$854$		0			0
$855$	16.9364	+	16.9364i	0.579214	+	0.579214i
$856$	−19.3307	+	19.3307i	−0.660710	+	0.660710i
$857$	20.3600	−	20.3600i	0.695483	−	0.695483i	−0.267950	−	0.963433i	$-0.586346\pi$
$857$	20.3600	−	20.3600i	0.695483	−	0.695483i	0.963433	+	0.267950i	$0.0863461\pi$
$858$			54.3451i			1.85531i
$859$		−	8.24733i		−	0.281395i	−0.990053	−	0.140698i	$-0.955065\pi$
$859$		−	8.24733i		−	0.281395i	0.990053	−	0.140698i	$-0.0449345\pi$
$860$	−7.52741	+	7.52741i	−0.256683	+	0.256683i
$861$		0			0
$862$	29.2207	+	29.2207i	0.995260	+	0.995260i
$863$	−35.6828			−1.21466			−0.607329	−	0.794450i	$-0.707759\pi$
$863$	−35.6828			−1.21466			−0.607329	+	0.794450i	$0.707759\pi$
$864$	−7.01242	−	7.01242i	−0.238567	−	0.238567i
$865$			12.1034i			0.411527i
$866$	1.23218			0.0418710
$867$	2.38981	−	34.5006i	0.0811621	−	1.17170i
$868$		0			0
$869$			46.7284i			1.58515i
$870$	−42.9409	−	42.9409i	−1.45583	−	1.45583i
$871$	−45.6869			−1.54804
$872$	−7.48405	−	7.48405i	−0.253442	−	0.253442i
$873$	−3.40518	+	3.40518i	−0.115248	+	0.115248i
$874$	−4.63090	+	4.63090i	−0.156643	+	0.156643i
$875$		0			0
$876$		−	1.58575i		−	0.0535774i
$877$	−9.95149	+	9.95149i	−0.336038	+	0.336038i	−0.854874	−	0.518836i	$-0.826366\pi$
$877$	−9.95149	+	9.95149i	−0.336038	+	0.336038i	0.518836	+	0.854874i	$0.326366\pi$
$878$	27.9657	−	27.9657i	0.943797	−	0.943797i
$879$	−21.5174	−	21.5174i	−0.725763	−	0.725763i
$880$	−74.8611			−2.52357
$881$	−10.4454	−	10.4454i	−0.351914	−	0.351914i	0.508907	−	0.860821i	$-0.330050\pi$
$881$	−10.4454	−	10.4454i	−0.351914	−	0.351914i	−0.860821	+	0.508907i	$0.830050\pi$
$882$		0			0
$883$	4.72305			0.158943			0.0794717	−	0.996837i	$-0.474677\pi$
$883$	4.72305			0.158943			0.0794717	+	0.996837i	$0.474677\pi$
$884$	−2.93432	+	6.44438i	−0.0986920	+	0.216748i
$885$	18.8703			0.634317
$886$		−	19.0746i		−	0.640823i
$887$	31.9047	+	31.9047i	1.07126	+	1.07126i	0.997258	+	0.0739977i	$0.0235758\pi$
$887$	31.9047	+	31.9047i	1.07126	+	1.07126i	0.0739977	+	0.997258i	$0.476424\pi$
$888$	6.68809			0.224437
$889$		0			0
$890$	7.72620	−	7.72620i	0.258983	−	0.258983i
$891$	−36.7228	+	36.7228i	−1.23026	+	1.23026i
$892$		−	8.28245i		−	0.277317i
$893$		−	26.8101i		−	0.897164i
$894$	−1.51665	+	1.51665i	−0.0507244	+	0.0507244i
$895$	9.50877	−	9.50877i	0.317843	−	0.317843i
$896$		0			0
$897$	−4.97371			−0.166067
$898$	41.1407	+	41.1407i	1.37288	+	1.37288i
$899$		−	42.8318i		−	1.42852i
$900$	3.50675			0.116892
$901$	15.3077	+	6.97005i	0.509972	+	0.232206i
$902$	5.11138			0.170190
$903$		0			0
$904$	−19.6999	−	19.6999i	−0.655209	−	0.655209i
$905$	−6.54220			−0.217470
$906$	−25.8369	−	25.8369i	−0.858373	−	0.858373i
$907$	23.9495	−	23.9495i	0.795231	−	0.795231i	−0.187108	−	0.982339i	$-0.559911\pi$
$907$	23.9495	−	23.9495i	0.795231	−	0.795231i	0.982339	+	0.187108i	$0.0599114\pi$
$908$	−2.78530	+	2.78530i	−0.0924336	+	0.0924336i
$909$			6.13069i			0.203342i
$910$		0			0
$911$	7.16704	−	7.16704i	0.237455	−	0.237455i	−0.578341	−	0.815795i	$-0.696300\pi$
$911$	7.16704	−	7.16704i	0.237455	−	0.237455i	0.815795	+	0.578341i	$0.196300\pi$
$912$	42.0906	−	42.0906i	1.39376	−	1.39376i
$913$	15.4946	+	15.4946i	0.512797	+	0.512797i
$914$	−20.1063			−0.665057
$915$	−59.0788	−	59.0788i	−1.95309	−	1.95309i
$916$			7.24404i			0.239350i
$917$		0			0
$918$	−22.9928	+	8.60524i	−0.758876	+	0.284015i
$919$	−7.90071			−0.260620			−0.130310	−	0.991473i	$-0.541597\pi$
$919$	−7.90071			−0.260620			−0.130310	+	0.991473i	$0.541597\pi$
$920$		−	5.48118i		−	0.180709i
$921$	10.3054	+	10.3054i	0.339573	+	0.339573i
$922$	−7.20249			−0.237201
$923$	−11.0756	−	11.0756i	−0.364557	−	0.364557i
$924$		0			0
$925$	6.31412	−	6.31412i	0.207607	−	0.207607i
$926$		−	2.41887i		−	0.0794891i
$927$			4.51103i			0.148162i
$928$	−10.3559	+	10.3559i	−0.339948	+	0.339948i
$929$	6.47675	−	6.47675i	0.212495	−	0.212495i	−0.592831	−	0.805327i	$-0.701990\pi$
$929$	6.47675	−	6.47675i	0.212495	−	0.212495i	0.805327	+	0.592831i	$0.201990\pi$
$930$	58.8031	+	58.8031i	1.92823	+	1.92823i
$931$		0			0
$932$	−8.17117	−	8.17117i	−0.267656	−	0.267656i
$933$			12.8049i			0.419214i
$934$	−17.2994			−0.566054
$935$	−27.0914	+	59.4984i	−0.885985	+	1.94580i
$936$	9.94863			0.325181
$937$		−	53.4400i		−	1.74581i	−0.487891	−	0.872905i	$-0.662234\pi$
$937$		−	53.4400i		−	1.74581i	0.487891	−	0.872905i	$-0.337766\pi$
$938$		0			0
$939$	−63.8202			−2.08269
$940$	−4.90247	−	4.90247i	−0.159901	−	0.159901i
$941$	−35.4583	+	35.4583i	−1.15591	+	1.15591i	−0.170562	+	0.985347i	$0.554558\pi$
$941$	−35.4583	+	35.4583i	−1.15591	+	1.15591i	−0.985347	+	0.170562i	$0.945442\pi$
$942$	52.8857	−	52.8857i	1.72311	−	1.72311i
$943$			0.467798i			0.0152336i
$944$		−	12.9005i		−	0.419876i
$945$		0			0
$946$	34.4907	−	34.4907i	1.12139	−	1.12139i
$947$	−10.3757	−	10.3757i	−0.337165	−	0.337165i	0.518135	−	0.855299i	$-0.326627\pi$
$947$	−10.3757	−	10.3757i	−0.337165	−	0.337165i	−0.855299	+	0.518135i	$0.826627\pi$
$948$	−9.60853			−0.312070
$949$	−4.24720	−	4.24720i	−0.137870	−	0.137870i
$950$		−	63.5803i		−	2.06282i
$951$	33.6993			1.09278
$952$		0			0
$953$	−4.66197			−0.151016			−0.0755080	−	0.997145i	$-0.524058\pi$
$953$	−4.66197			−0.151016			−0.0755080	+	0.997145i	$0.524058\pi$
$954$			7.30180i			0.236405i
$955$	60.4270	+	60.4270i	1.95537	+	1.95537i
$956$	−6.88186			−0.222575
$957$	37.5747	+	37.5747i	1.21462	+	1.21462i
$958$	25.8621	−	25.8621i	0.835566	−	0.835566i
$959$		0			0
$960$			36.7773i			1.18698i
$961$			27.6537i			0.892056i
$962$	−5.53490	+	5.53490i	−0.178452	+	0.178452i
$963$	−9.16052	+	9.16052i	−0.295194	+	0.295194i
$964$	−5.07927	−	5.07927i	−0.163592	−	0.163592i
$965$	−38.1807			−1.22908
$966$		0			0
$967$			15.2606i			0.490748i	0.969428	+	0.245374i	$0.0789108\pi$
$967$			15.2606i			0.490748i	−0.969428	+	0.245374i	$0.921089\pi$
$968$	25.9803			0.835039
$969$	−18.2207	−	48.6850i	−0.585335	−	1.56399i
$970$	22.5790			0.724968
$971$			18.5971i			0.596810i	0.954439	+	0.298405i	$0.0964546\pi$
$971$			18.5971i			0.596810i	−0.954439	+	0.298405i	$0.903545\pi$
$972$	−3.75850	−	3.75850i	−0.120554	−	0.120554i
$973$		0			0
$974$	24.4991	+	24.4991i	0.785003	+	0.785003i
$975$	34.1435	−	34.1435i	1.09347	−	1.09347i
$976$	−40.3888	+	40.3888i	−1.29281	+	1.29281i
$977$			21.7450i			0.695683i	0.937553	+	0.347842i	$0.113085\pi$
$977$			21.7450i			0.695683i	−0.937553	+	0.347842i	$0.886915\pi$
$978$			38.6287i			1.23521i
$979$	−6.76068	+	6.76068i	−0.216072	+	0.216072i
$980$		0			0
$981$	−3.54657	−	3.54657i	−0.113233	−	0.113233i
$982$	30.2935			0.966704
$983$	2.52556	+	2.52556i	0.0805529	+	0.0805529i	0.746235	−	0.665682i	$-0.231859\pi$
$983$	2.52556	+	2.52556i	0.0805529	+	0.0805529i	−0.665682	+	0.746235i	$0.731859\pi$
$984$		−	3.40153i		−	0.108437i
$985$	76.8329			2.44810
$986$	12.7081	+	33.9556i	0.404710	+	1.08137i
$987$		0			0
$988$			10.6436i			0.338618i
$989$	3.15662	+	3.15662i	0.100375	+	0.100375i
$990$	−28.3809			−0.902004
$991$	−0.300053	−	0.300053i	−0.00953151	−	0.00953151i	0.702325	−	0.711856i	$-0.252145\pi$
$991$	−0.300053	−	0.300053i	−0.00953151	−	0.00953151i	−0.711856	+	0.702325i	$0.752145\pi$
$992$	14.1813	−	14.1813i	0.450257	−	0.450257i
$993$	−6.80821	+	6.80821i	−0.216052	+	0.216052i
$994$		0			0
$995$		−	17.8210i		−	0.564963i
$996$	−3.18608	+	3.18608i	−0.100955	+	0.100955i
$997$	26.4732	−	26.4732i	0.838416	−	0.838416i	−0.150234	−	0.988650i	$-0.548003\pi$
$997$	26.4732	−	26.4732i	0.838416	−	0.838416i	0.988650	+	0.150234i	$0.0480028\pi$
$998$	47.0966	+	47.0966i	1.49082	+	1.49082i
$999$	−5.18271			−0.163974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.g.h.540.8		20
7.2	even	3		833.2.o.f.557.8		40
7.3	odd	6		833.2.o.g.30.3		40
7.4	even	3		833.2.o.f.30.3		40
7.5	odd	6		833.2.o.g.557.8		40
7.6	odd	2		119.2.g.a.64.8	✓	20
17.4	even	4	inner	833.2.g.h.344.3		20
21.20	even	2		1071.2.n.c.64.3		20
119.4	even	12		833.2.o.f.667.8		40
119.38	odd	12		833.2.o.g.667.8		40
119.55	odd	4		119.2.g.a.106.3	yes	20
119.72	even	12		833.2.o.f.361.3		40
119.83	odd	8		2023.2.a.n.1.3		10
119.89	odd	12		833.2.o.g.361.3		40
119.104	odd	8		2023.2.a.m.1.3		10
357.293	even	4		1071.2.n.c.820.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.g.a.64.8	✓	20	7.6	odd	2
119.2.g.a.106.3	yes	20	119.55	odd	4
833.2.g.h.344.3		20	17.4	even	4	inner
833.2.g.h.540.8		20	1.1	even	1	trivial
833.2.o.f.30.3		40	7.4	even	3
833.2.o.f.361.3		40	119.72	even	12
833.2.o.f.557.8		40	7.2	even	3
833.2.o.f.667.8		40	119.4	even	12
833.2.o.g.30.3		40	7.3	odd	6
833.2.o.g.361.3		40	119.89	odd	12
833.2.o.g.557.8		40	7.5	odd	6
833.2.o.g.667.8		40	119.38	odd	12
1071.2.n.c.64.3		20	21.20	even	2
1071.2.n.c.820.8		20	357.293	even	4
2023.2.a.m.1.3		10	119.104	odd	8
2023.2.a.n.1.3		10	119.83	odd	8

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.57229i q^{2} +(1.43847 + 1.43847i) q^{3} -0.472100 q^{4} +(-2.40051 - 2.40051i) q^{5} +(-2.26170 + 2.26170i) q^{6} +2.40230i q^{8} +1.13841i q^{9} +O(q^{10})\)	\(q+1.57229i q^{2} +(1.43847 + 1.43847i) q^{3} -0.472100 q^{4} +(-2.40051 - 2.40051i) q^{5} +(-2.26170 + 2.26170i) q^{6} +2.40230i q^{8} +1.13841i q^{9} +(3.77429 - 3.77429i) q^{10} +(-3.30263 + 3.30263i) q^{11} +(-0.679103 - 0.679103i) q^{12} -3.63777 q^{13} -6.90613i q^{15} -4.72132 q^{16} +(-1.70860 + 3.75243i) q^{17} -1.78992 q^{18} +6.19754i q^{19} +(1.13328 + 1.13328i) q^{20} +(-5.19270 - 5.19270i) q^{22} +(0.475240 - 0.475240i) q^{23} +(-3.45565 + 3.45565i) q^{24} +6.52485i q^{25} -5.71963i q^{26} +(2.67784 - 2.67784i) q^{27} +(-3.95461 - 3.95461i) q^{29} +10.8584 q^{30} +(5.41543 + 5.41543i) q^{31} -2.61868i q^{32} -9.50150 q^{33} +(-5.89991 - 2.68641i) q^{34} -0.537445i q^{36} +(-0.967703 - 0.967703i) q^{37} -9.74433 q^{38} +(-5.23284 - 5.23284i) q^{39} +(5.76674 - 5.76674i) q^{40} +(-0.492170 + 0.492170i) q^{41} +6.64216i q^{43} +(1.55917 - 1.55917i) q^{44} +(2.73277 - 2.73277i) q^{45} +(0.747216 + 0.747216i) q^{46} -4.32592 q^{47} +(-6.79150 - 6.79150i) q^{48} -10.2590 q^{50} +(-7.85554 + 2.94000i) q^{51} +1.71739 q^{52} -4.07940i q^{53} +(4.21035 + 4.21035i) q^{54} +15.8560 q^{55} +(-8.91500 + 8.91500i) q^{57} +(6.21780 - 6.21780i) q^{58} +2.73239i q^{59} +3.26038i q^{60} +(8.55455 - 8.55455i) q^{61} +(-8.51463 + 8.51463i) q^{62} -5.32531 q^{64} +(8.73248 + 8.73248i) q^{65} -14.9391i q^{66} +12.5590 q^{67} +(0.806627 - 1.77152i) q^{68} +1.36724 q^{69} +(3.04461 + 3.04461i) q^{71} -2.73482 q^{72} +(1.16753 + 1.16753i) q^{73} +(1.52151 - 1.52151i) q^{74} +(-9.38583 + 9.38583i) q^{75} -2.92586i q^{76} +(8.22754 - 8.22754i) q^{78} +(7.07442 - 7.07442i) q^{79} +(11.3336 + 11.3336i) q^{80} +11.1193 q^{81} +(-0.773834 - 0.773834i) q^{82} -4.69160i q^{83} +(13.1092 - 4.90623i) q^{85} -10.4434 q^{86} -11.3772i q^{87} +(-7.93393 - 7.93393i) q^{88} +2.04706 q^{89} +(4.29671 + 4.29671i) q^{90} +(-0.224361 + 0.224361i) q^{92} +15.5799i q^{93} -6.80161i q^{94} +(14.8772 - 14.8772i) q^{95} +(3.76691 - 3.76691i) q^{96} +(2.99116 + 2.99116i) q^{97} +(-3.75976 - 3.75976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) \) 20 * q + 4 * q^3 - 24 * q^4 + 8 * q^5 - 4 * q^6	\( 20 q + 4 q^{3} - 24 q^{4} + 8 q^{5} - 4 q^{6} - 4 q^{10} - 4 q^{11} - 12 q^{12} + 16 q^{16} + 12 q^{17} - 8 q^{18} - 20 q^{20} - 20 q^{22} - 4 q^{24} - 8 q^{27} + 16 q^{29} - 36 q^{30} - 4 q^{31} + 16 q^{33} - 36 q^{34} - 28 q^{37} - 48 q^{38} + 20 q^{39} + 24 q^{40} + 24 q^{41} - 28 q^{44} - 36 q^{45} + 8 q^{46} - 40 q^{47} + 8 q^{48} - 28 q^{50} - 40 q^{51} + 28 q^{54} + 40 q^{55} + 36 q^{57} + 56 q^{58} + 16 q^{61} + 40 q^{62} + 32 q^{64} + 8 q^{65} + 32 q^{68} + 88 q^{69} - 8 q^{71} + 108 q^{72} - 8 q^{73} + 36 q^{74} - 8 q^{75} - 44 q^{78} - 4 q^{79} + 116 q^{80} + 4 q^{81} + 16 q^{82} + 16 q^{85} + 44 q^{86} + 72 q^{88} - 48 q^{89} - 56 q^{90} - 32 q^{92} + 44 q^{95} - 68 q^{96} - 24 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 24 * q^4 + 8 * q^5 - 4 * q^6 - 4 * q^10 - 4 * q^11 - 12 * q^12 + 16 * q^16 + 12 * q^17 - 8 * q^18 - 20 * q^20 - 20 * q^22 - 4 * q^24 - 8 * q^27 + 16 * q^29 - 36 * q^30 - 4 * q^31 + 16 * q^33 - 36 * q^34 - 28 * q^37 - 48 * q^38 + 20 * q^39 + 24 * q^40 + 24 * q^41 - 28 * q^44 - 36 * q^45 + 8 * q^46 - 40 * q^47 + 8 * q^48 - 28 * q^50 - 40 * q^51 + 28 * q^54 + 40 * q^55 + 36 * q^57 + 56 * q^58 + 16 * q^61 + 40 * q^62 + 32 * q^64 + 8 * q^65 + 32 * q^68 + 88 * q^69 - 8 * q^71 + 108 * q^72 - 8 * q^73 + 36 * q^74 - 8 * q^75 - 44 * q^78 - 4 * q^79 + 116 * q^80 + 4 * q^81 + 16 * q^82 + 16 * q^85 + 44 * q^86 + 72 * q^88 - 48 * q^89 - 56 * q^90 - 32 * q^92 + 44 * q^95 - 68 * q^96 - 24 * q^99

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