LMFDB - Embedded newform 833.2.g.f.344.8

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 230x^{12} + 1126x^{10} + 2987x^{8} + 4170x^{6} + 2679x^{4} + 502x^{2} + 1 $ x^16 + 24x^14 + 230x^12 + 1126x^10 + 2987x^8 + 4170x^6 + 2679x^4 + 502*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			344.8
Root			$2.46018i$ of defining polynomial
Character	$\chi$	$=$	833.344
Dual form			833.2.g.f.540.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46018i q^{2} +(-1.82950 + 1.82950i) q^{3} -4.05250 q^{4} +(-2.12385 + 2.12385i) q^{5} +(-4.50090 - 4.50090i) q^{6} -5.04951i q^{8} -3.69415i q^{9} +O(q^{10})$	\(q+2.46018i q^{2} +(-1.82950 + 1.82950i) q^{3} -4.05250 q^{4} +(-2.12385 + 2.12385i) q^{5} +(-4.50090 - 4.50090i) q^{6} -5.04951i q^{8} -3.69415i q^{9} +(-5.22506 - 5.22506i) q^{10} +(0.0608963 + 0.0608963i) q^{11} +(7.41404 - 7.41404i) q^{12} -4.28579 q^{13} -7.77117i q^{15} +4.31773 q^{16} +(4.01303 + 0.946345i) q^{17} +9.08827 q^{18} +6.85431i q^{19} +(8.60689 - 8.60689i) q^{20} +(-0.149816 + 0.149816i) q^{22} +(-0.498840 - 0.498840i) q^{23} +(9.23809 + 9.23809i) q^{24} -4.02148i q^{25} -10.5438i q^{26} +(1.26994 + 1.26994i) q^{27} +(1.07782 - 1.07782i) q^{29} +19.1185 q^{30} +(0.571355 - 0.571355i) q^{31} +0.523372i q^{32} -0.222820 q^{33} +(-2.32818 + 9.87279i) q^{34} +14.9705i q^{36} +(-2.72027 + 2.72027i) q^{37} -16.8628 q^{38} +(7.84086 - 7.84086i) q^{39} +(10.7244 + 10.7244i) q^{40} +(-0.0255918 - 0.0255918i) q^{41} +8.49396i q^{43} +(-0.246782 - 0.246782i) q^{44} +(7.84581 + 7.84581i) q^{45} +(1.22724 - 1.22724i) q^{46} -9.76592 q^{47} +(-7.89929 + 7.89929i) q^{48} +9.89358 q^{50} +(-9.07318 + 5.61051i) q^{51} +17.3682 q^{52} +11.8406i q^{53} +(-3.12428 + 3.12428i) q^{54} -0.258669 q^{55} +(-12.5400 - 12.5400i) q^{57} +(2.65163 + 2.65163i) q^{58} -4.25843i q^{59} +31.4926i q^{60} +(-1.78521 - 1.78521i) q^{61} +(1.40564 + 1.40564i) q^{62} +7.34787 q^{64} +(9.10239 - 9.10239i) q^{65} -0.548177i q^{66} +4.92443 q^{67} +(-16.2628 - 3.83506i) q^{68} +1.82526 q^{69} +(4.95688 - 4.95688i) q^{71} -18.6536 q^{72} +(2.69644 - 2.69644i) q^{73} +(-6.69236 - 6.69236i) q^{74} +(7.35730 + 7.35730i) q^{75} -27.7770i q^{76} +(19.2900 + 19.2900i) q^{78} +(4.64414 + 4.64414i) q^{79} +(-9.17021 + 9.17021i) q^{80} +6.43573 q^{81} +(0.0629605 - 0.0629605i) q^{82} +3.86659i q^{83} +(-10.5330 + 6.51319i) q^{85} -20.8967 q^{86} +3.94373i q^{87} +(0.307497 - 0.307497i) q^{88} +5.04050 q^{89} +(-19.3021 + 19.3021i) q^{90} +(2.02155 + 2.02155i) q^{92} +2.09059i q^{93} -24.0259i q^{94} +(-14.5575 - 14.5575i) q^{95} +(-0.957509 - 0.957509i) q^{96} +(6.55546 - 6.55546i) q^{97} +(0.224960 - 0.224960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 8 q^{5} + 6 q^{6}+O(q^{10}) $ 16 * q - 16 * q^4 - 8 * q^5 + 6 * q^6	$ 16 q - 16 q^{4} - 8 q^{5} + 6 q^{6} - 6 q^{10} + 18 q^{11} + 26 q^{12} + 8 q^{16} + 10 q^{17} + 40 q^{18} + 12 q^{20} + 26 q^{22} + 12 q^{23} + 14 q^{24} - 30 q^{27} - 16 q^{29} + 44 q^{30} - 6 q^{31} - 8 q^{33} + 20 q^{34} + 2 q^{37} - 32 q^{38} - 14 q^{39} + 72 q^{40} - 2 q^{41} - 24 q^{44} - 4 q^{46} - 36 q^{47} - 36 q^{48} - 40 q^{50} + 20 q^{51} + 12 q^{52} - 18 q^{54} - 36 q^{55} - 24 q^{57} - 8 q^{58} - 52 q^{61} - 18 q^{62} + 12 q^{64} + 2 q^{65} + 28 q^{67} + 24 q^{68} + 4 q^{69} + 40 q^{71} - 36 q^{72} - 16 q^{73} - 60 q^{74} - 2 q^{75} + 32 q^{78} + 6 q^{79} + 30 q^{80} - 40 q^{82} + 34 q^{85} + 4 q^{86} - 30 q^{88} + 8 q^{89} + 10 q^{90} - 20 q^{92} + 12 q^{95} - 30 q^{96} + 38 q^{97} - 46 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 - 8 * q^5 + 6 * q^6 - 6 * q^10 + 18 * q^11 + 26 * q^12 + 8 * q^16 + 10 * q^17 + 40 * q^18 + 12 * q^20 + 26 * q^22 + 12 * q^23 + 14 * q^24 - 30 * q^27 - 16 * q^29 + 44 * q^30 - 6 * q^31 - 8 * q^33 + 20 * q^34 + 2 * q^37 - 32 * q^38 - 14 * q^39 + 72 * q^40 - 2 * q^41 - 24 * q^44 - 4 * q^46 - 36 * q^47 - 36 * q^48 - 40 * q^50 + 20 * q^51 + 12 * q^52 - 18 * q^54 - 36 * q^55 - 24 * q^57 - 8 * q^58 - 52 * q^61 - 18 * q^62 + 12 * q^64 + 2 * q^65 + 28 * q^67 + 24 * q^68 + 4 * q^69 + 40 * q^71 - 36 * q^72 - 16 * q^73 - 60 * q^74 - 2 * q^75 + 32 * q^78 + 6 * q^79 + 30 * q^80 - 40 * q^82 + 34 * q^85 + 4 * q^86 - 30 * q^88 + 8 * q^89 + 10 * q^90 - 20 * q^92 + 12 * q^95 - 30 * q^96 + 38 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			2.46018i			1.73961i	0.493394	+	0.869806i	$0.335756\pi$
$2$			2.46018i			1.73961i	−0.493394	+	0.869806i	$0.664244\pi$
$3$	−1.82950	+	1.82950i	−1.05626	+	1.05626i	−0.0579428	+	0.998320i	$0.518454\pi$
$3$	−1.82950	+	1.82950i	−1.05626	+	1.05626i	−0.998320	+	0.0579428i	$0.981546\pi$
$4$	−4.05250			−2.02625
$5$	−2.12385	+	2.12385i	−0.949815	+	0.949815i	−0.998800	−	0.0489847i	$-0.984401\pi$
$5$	−2.12385	+	2.12385i	−0.949815	+	0.949815i	0.0489847	+	0.998800i	$0.484401\pi$
$6$	−4.50090	−	4.50090i	−1.83749	−	1.83749i
$7$		0			0
$7$		0			0
$8$		−	5.04951i		−	1.78527i
$9$		−	3.69415i		−	1.23138i
$10$	−5.22506	−	5.22506i	−1.65231	−	1.65231i
$11$	0.0608963	+	0.0608963i	0.0183609	+	0.0183609i	0.716228	−	0.697867i	$-0.245867\pi$
$11$	0.0608963	+	0.0608963i	0.0183609	+	0.0183609i	−0.697867	+	0.716228i	$0.745867\pi$
$12$	7.41404	−	7.41404i	2.14025	−	2.14025i
$13$	−4.28579			−1.18867			−0.594333	−	0.804219i	$-0.702584\pi$
$13$	−4.28579			−1.18867			−0.594333	+	0.804219i	$0.702584\pi$
$14$		0			0
$15$		−	7.77117i		−	2.00651i
$16$	4.31773			1.07943
$17$	4.01303	+	0.946345i	0.973303	+	0.229522i
$17$	4.01303	+	0.946345i	0.973303	+	0.229522i
$18$	9.08827			2.14213
$19$			6.85431i			1.57249i	0.617918	+	0.786243i	$0.287977\pi$
$19$			6.85431i			1.57249i	−0.617918	+	0.786243i	$0.712023\pi$
$20$	8.60689	−	8.60689i	1.92456	−	1.92456i
$21$		0			0
$22$	−0.149816	+	0.149816i	−0.0319409	+	0.0319409i
$23$	−0.498840	−	0.498840i	−0.104015	−	0.104015i	0.653184	−	0.757199i	$-0.273433\pi$
$23$	−0.498840	−	0.498840i	−0.104015	−	0.104015i	−0.757199	+	0.653184i	$0.773433\pi$
$24$	9.23809	+	9.23809i	1.88572	+	1.88572i
$25$		−	4.02148i		−	0.804296i
$26$		−	10.5438i		−	2.06782i
$27$	1.26994	+	1.26994i	0.244400	+	0.244400i
$28$		0			0
$29$	1.07782	−	1.07782i	0.200146	−	0.200146i	−0.599917	−	0.800062i	$-0.704800\pi$
$29$	1.07782	−	1.07782i	0.200146	−	0.200146i	0.800062	+	0.599917i	$0.204800\pi$
$30$	19.1185			3.49054
$31$	0.571355	−	0.571355i	0.102618	−	0.102618i	−0.653934	−	0.756552i	$-0.726882\pi$
$31$	0.571355	−	0.571355i	0.102618	−	0.102618i	0.756552	+	0.653934i	$0.226882\pi$
$32$			0.523372i			0.0925199i
$33$	−0.222820			−0.0387879
$34$	−2.32818	+	9.87279i	−0.399280	+	1.69317i
$35$		0			0
$36$			14.9705i			2.49508i
$37$	−2.72027	+	2.72027i	−0.447210	+	0.447210i	−0.894426	−	0.447216i	$-0.852415\pi$
$37$	−2.72027	+	2.72027i	−0.447210	+	0.447210i	0.447216	+	0.894426i	$0.352415\pi$
$38$	−16.8628			−2.73551
$39$	7.84086	−	7.84086i	1.25554	−	1.25554i
$40$	10.7244	+	10.7244i	1.69568	+	1.69568i
$41$	−0.0255918	−	0.0255918i	−0.00399677	−	0.00399677i	0.705106	−	0.709102i	$-0.250900\pi$
$41$	−0.0255918	−	0.0255918i	−0.00399677	−	0.00399677i	−0.709102	+	0.705106i	$0.750900\pi$
$42$		0			0
$43$			8.49396i			1.29532i	0.761931	+	0.647658i	$0.224252\pi$
$43$			8.49396i			1.29532i	−0.761931	+	0.647658i	$0.775748\pi$
$44$	−0.246782	−	0.246782i	−0.0372038	−	0.0372038i
$45$	7.84581	+	7.84581i	1.16958	+	1.16958i
$46$	1.22724	−	1.22724i	0.180946	−	0.180946i
$47$	−9.76592			−1.42451			−0.712253	−	0.701923i	$-0.752325\pi$
$47$	−9.76592			−1.42451			−0.712253	+	0.701923i	$0.752325\pi$
$48$	−7.89929	+	7.89929i	−1.14016	+	1.14016i
$49$		0			0
$50$	9.89358			1.39916
$51$	−9.07318	+	5.61051i	−1.27050	+	0.785628i
$52$	17.3682			2.40853
$53$			11.8406i			1.62644i	0.581960	+	0.813218i	$0.302286\pi$
$53$			11.8406i			1.62644i	−0.581960	+	0.813218i	$0.697714\pi$
$54$	−3.12428	+	3.12428i	−0.425161	+	0.425161i
$55$	−0.258669			−0.0348790
$56$		0			0
$57$	−12.5400	−	12.5400i	−1.66096	−	1.66096i
$58$	2.65163	+	2.65163i	0.348176	+	0.348176i
$59$		−	4.25843i		−	0.554400i	−0.960812	−	0.277200i	$-0.910594\pi$
$59$		−	4.25843i		−	0.554400i	0.960812	−	0.277200i	$-0.0894065\pi$
$60$			31.4926i			4.06568i
$61$	−1.78521	−	1.78521i	−0.228572	−	0.228572i	0.583524	−	0.812096i	$-0.301673\pi$
$61$	−1.78521	−	1.78521i	−0.228572	−	0.228572i	−0.812096	+	0.583524i	$0.801673\pi$
$62$	1.40564	+	1.40564i	0.178516	+	0.178516i
$63$		0			0
$64$	7.34787			0.918483
$65$	9.10239	−	9.10239i	1.12901	−	1.12901i
$66$		−	0.548177i		−	0.0674759i
$67$	4.92443			0.601615			0.300808	−	0.953685i	$-0.402744\pi$
$67$	4.92443			0.601615			0.300808	+	0.953685i	$0.402744\pi$
$68$	−16.2628	−	3.83506i	−1.97215	−	0.465069i
$69$	1.82526			0.219735
$70$		0			0
$71$	4.95688	−	4.95688i	0.588274	−	0.588274i	−0.348890	−	0.937164i	$-0.613441\pi$
$71$	4.95688	−	4.95688i	0.588274	−	0.588274i	0.937164	+	0.348890i	$0.113441\pi$
$72$	−18.6536			−2.19835
$73$	2.69644	−	2.69644i	0.315595	−	0.315595i	−0.531477	−	0.847072i	$-0.678363\pi$
$73$	2.69644	−	2.69644i	0.315595	−	0.315595i	0.847072	+	0.531477i	$0.178363\pi$
$74$	−6.69236	−	6.69236i	−0.777971	−	0.777971i
$75$	7.35730	+	7.35730i	0.849548	+	0.849548i
$76$		−	27.7770i		−	3.18625i
$77$		0			0
$78$	19.2900	+	19.2900i	2.18416	+	2.18416i
$79$	4.64414	+	4.64414i	0.522506	+	0.522506i	0.918328	−	0.395821i	$-0.129540\pi$
$79$	4.64414	+	4.64414i	0.522506	+	0.522506i	−0.395821	+	0.918328i	$0.629540\pi$
$80$	−9.17021	+	9.17021i	−1.02526	+	1.02526i
$81$	6.43573			0.715081
$82$	0.0629605	−	0.0629605i	0.00695282	−	0.00695282i
$83$			3.86659i			0.424413i	0.977225	+	0.212207i	$0.0680650\pi$
$83$			3.86659i			0.424413i	−0.977225	+	0.212207i	$0.931935\pi$
$84$		0			0
$85$	−10.5330	+	6.51319i	−1.14246	+	0.706454i
$86$	−20.8967			−2.25335
$87$			3.94373i			0.422813i
$88$	0.307497	−	0.307497i	0.0327792	−	0.0327792i
$89$	5.04050			0.534292			0.267146	−	0.963656i	$-0.413919\pi$
$89$	5.04050			0.534292			0.267146	+	0.963656i	$0.413919\pi$
$90$	−19.3021	+	19.3021i	−2.03462	+	2.03462i
$91$		0			0
$92$	2.02155	+	2.02155i	0.210761	+	0.210761i
$93$			2.09059i			0.216784i
$94$		−	24.0259i		−	2.47809i
$95$	−14.5575	−	14.5575i	−1.49357	−	1.49357i
$96$	−0.957509	−	0.957509i	−0.0977253	−	0.0977253i
$97$	6.55546	−	6.55546i	0.665606	−	0.665606i	−0.291090	−	0.956696i	$-0.594018\pi$
$97$	6.55546	−	6.55546i	0.665606	−	0.665606i	0.956696	+	0.291090i	$0.0940178\pi$
$98$		0			0
$99$	0.224960	−	0.224960i	0.0226093	−	0.0226093i
$100$			16.2970i			1.62970i
$101$	2.51898			0.250648			0.125324	−	0.992116i	$-0.460003\pi$
$101$	2.51898			0.250648			0.125324	+	0.992116i	$0.460003\pi$
$102$	−13.8029	−	22.3217i	−1.36669	−	2.21018i
$103$	5.86303			0.577701			0.288851	−	0.957374i	$-0.406727\pi$
$103$	5.86303			0.577701			0.288851	+	0.957374i	$0.406727\pi$
$104$			21.6412i			2.12209i
$105$		0			0
$106$	−29.1301			−2.82937
$107$	−0.579374	+	0.579374i	−0.0560102	+	0.0560102i	−0.734557	−	0.678547i	$-0.762610\pi$
$107$	−0.579374	+	0.579374i	−0.0560102	+	0.0560102i	0.678547	+	0.734557i	$0.262610\pi$
$108$	−5.14642	−	5.14642i	−0.495215	−	0.495215i
$109$	−5.51366	−	5.51366i	−0.528112	−	0.528112i	0.391897	−	0.920009i	$-0.371819\pi$
$109$	−5.51366	−	5.51366i	−0.528112	−	0.528112i	−0.920009	+	0.391897i	$0.871819\pi$
$110$		−	0.636373i		−	0.0606758i
$111$		−	9.95348i		−	0.944742i
$112$		0			0
$113$	−10.7494	−	10.7494i	−1.01122	−	1.01122i	−0.999936	−	0.0112860i	$-0.996407\pi$
$113$	−10.7494	−	10.7494i	−1.01122	−	1.01122i	−0.0112860	−	0.999936i	$-0.503593\pi$
$114$	30.8506	−	30.8506i	2.88942	−	2.88942i
$115$	2.11892			0.197591
$116$	−4.36785	+	4.36785i	−0.405545	+	0.405545i
$117$			15.8323i			1.46370i
$118$	10.4765			0.964441
$119$		0			0
$120$	−39.2406			−3.58216
$121$		−	10.9926i		−	0.999326i
$122$	4.39193	−	4.39193i	0.397627	−	0.397627i
$123$	0.0936404			0.00844327
$124$	−2.31541	+	2.31541i	−0.207930	+	0.207930i
$125$	−2.07823	−	2.07823i	−0.185882	−	0.185882i
$126$		0			0
$127$			11.6441i			1.03324i	0.856214	+	0.516622i	$0.172811\pi$
$127$			11.6441i			1.03324i	−0.856214	+	0.516622i	$0.827189\pi$
$128$			19.1238i			1.69032i
$129$	−15.5397	−	15.5397i	−1.36819	−	1.36819i
$130$	22.3935	+	22.3935i	1.96404	+	1.96404i
$131$	14.0644	−	14.0644i	1.22881	−	1.22881i	0.264401	−	0.964413i	$-0.414826\pi$
$131$	14.0644	−	14.0644i	1.22881	−	1.22881i	0.964413	−	0.264401i	$-0.0851741\pi$
$132$	0.902976			0.0785939
$133$		0			0
$134$			12.1150i			1.04658i
$135$	−5.39432			−0.464269
$136$	4.77858	−	20.2639i	0.409760	−	1.73761i
$137$	−6.42627			−0.549033			−0.274517	−	0.961582i	$-0.588518\pi$
$137$	−6.42627			−0.549033			−0.274517	+	0.961582i	$0.588518\pi$
$138$			4.49047i			0.382254i
$139$	1.97504	−	1.97504i	0.167521	−	0.167521i	−0.618368	−	0.785889i	$-0.712206\pi$
$139$	1.97504	−	1.97504i	0.167521	−	0.167521i	0.785889	+	0.618368i	$0.212206\pi$
$140$		0			0
$141$	17.8667	−	17.8667i	1.50465	−	1.50465i
$142$	12.1948	+	12.1948i	1.02337	+	1.02337i
$143$	−0.260989	−	0.260989i	−0.0218250	−	0.0218250i
$144$		−	15.9503i		−	1.32919i
$145$			4.57824i			0.380203i
$146$	6.63374	+	6.63374i	0.549013	+	0.549013i
$147$		0			0
$148$	11.0239	−	11.0239i	0.906158	−	0.906158i
$149$	−12.5727			−1.02999			−0.514997	−	0.857192i	$-0.672207\pi$
$149$	−12.5727			−1.02999			−0.514997	+	0.857192i	$0.672207\pi$
$150$	−18.1003	+	18.1003i	−1.47788	+	1.47788i
$151$			12.9559i			1.05433i	0.849762	+	0.527166i	$0.176746\pi$
$151$			12.9559i			1.05433i	−0.849762	+	0.527166i	$0.823254\pi$
$152$	34.6109			2.80731
$153$	3.49593	−	14.8247i	0.282630	−	1.19851i
$154$		0			0
$155$			2.42695i			0.194937i
$156$	−31.7751	+	31.7751i	−2.54404	+	2.54404i
$157$	2.89454			0.231010			0.115505	−	0.993307i	$-0.463151\pi$
$157$	2.89454			0.231010			0.115505	+	0.993307i	$0.463151\pi$
$158$	−11.4254	+	11.4254i	−0.908958	+	0.908958i
$159$	−21.6624	−	21.6624i	−1.71794	−	1.71794i
$160$	−1.11156	−	1.11156i	−0.0878768	−	0.0878768i
$161$		0			0
$162$			15.8331i			1.24396i
$163$	−3.67687	−	3.67687i	−0.287995	−	0.287995i	0.548292	−	0.836287i	$-0.315278\pi$
$163$	−3.67687	−	3.67687i	−0.287995	−	0.287995i	−0.836287	+	0.548292i	$0.815278\pi$
$164$	0.103711	+	0.103711i	0.00809844	+	0.00809844i
$165$	0.473236	−	0.473236i	0.0368413	−	0.0368413i
$166$	−9.51252			−0.738314
$167$	11.0613	−	11.0613i	0.855946	−	0.855946i	−0.134911	−	0.990858i	$-0.543075\pi$
$167$	11.0613	−	11.0613i	0.855946	−	0.855946i	0.990858	+	0.134911i	$0.0430750\pi$
$168$		0			0
$169$	5.36803			0.412926
$170$	−16.0236	−	25.9130i	−1.22896	−	1.98744i
$171$	25.3208			1.93633
$172$		−	34.4217i		−	2.62463i
$173$	−11.5251	+	11.5251i	−0.876239	+	0.876239i	−0.993143	−	0.116904i	$-0.962703\pi$
$173$	−11.5251	+	11.5251i	−0.876239	+	0.876239i	0.116904	+	0.993143i	$0.462703\pi$
$174$	−9.70230			−0.735530
$175$		0			0
$176$	0.262934	+	0.262934i	0.0198194	+	0.0198194i
$177$	7.79080	+	7.79080i	0.585592	+	0.585592i
$178$			12.4006i			0.929461i
$179$		−	16.9954i		−	1.27030i	−0.772391	−	0.635148i	$-0.780939\pi$
$179$		−	16.9954i		−	1.27030i	0.772391	−	0.635148i	$-0.219061\pi$
$180$	−31.7951	−	31.7951i	−2.36987	−	2.36987i
$181$	−7.97604	−	7.97604i	−0.592854	−	0.592854i	0.345547	−	0.938401i	$-0.387693\pi$
$181$	−7.97604	−	7.97604i	−0.592854	−	0.592854i	−0.938401	+	0.345547i	$0.887693\pi$
$182$		0			0
$183$	6.53207			0.482864
$184$	−2.51890	+	2.51890i	−0.185696	+	0.185696i
$185$		−	11.5549i		−	0.849533i
$186$	−5.14323			−0.377120
$187$	0.186750	+	0.302008i	0.0136565	+	0.0220850i
$188$	39.5763			2.88640
$189$		0			0
$190$	35.8142	−	35.8142i	2.59823	−	2.59823i
$191$	5.29535			0.383158			0.191579	−	0.981477i	$-0.438639\pi$
$191$	5.29535			0.383158			0.191579	+	0.981477i	$0.438639\pi$
$192$	−13.4429	+	13.4429i	−0.970160	+	0.970160i
$193$	8.26580	+	8.26580i	0.594985	+	0.594985i	0.938974	−	0.343989i	$-0.111778\pi$
$193$	8.26580	+	8.26580i	0.594985	+	0.594985i	−0.343989	+	0.938974i	$0.611778\pi$
$194$	16.1276	+	16.1276i	1.15790	+	1.15790i
$195$			33.3056i			2.38507i
$196$		0			0
$197$	−8.06724	−	8.06724i	−0.574767	−	0.574767i	0.358690	−	0.933457i	$-0.383224\pi$
$197$	−8.06724	−	8.06724i	−0.574767	−	0.574767i	−0.933457	+	0.358690i	$0.883224\pi$
$198$	0.553442	+	0.553442i	0.0393314	+	0.0393314i
$199$	−13.8198	+	13.8198i	−0.979660	+	0.979660i	−0.999797	−	0.0201375i	$-0.993590\pi$
$199$	−13.8198	+	13.8198i	−0.979660	+	0.979660i	0.0201375	+	0.999797i	$0.493590\pi$
$200$	−20.3065			−1.43589
$201$	−9.00925	+	9.00925i	−0.635464	+	0.635464i
$202$			6.19716i			0.436030i
$203$		0			0
$204$	36.7690	−	22.7366i	2.57435	−	1.59188i
$205$	0.108706			0.00759238
$206$			14.4241i			1.00498i
$207$	−1.84279	+	1.84279i	−0.128083	+	0.128083i
$208$	−18.5049			−1.28308
$209$	−0.417402	+	0.417402i	−0.0288723	+	0.0288723i
$210$		0			0
$211$	9.68185	+	9.68185i	0.666526	+	0.666526i	0.956910	−	0.290384i	$-0.0937831\pi$
$211$	9.68185	+	9.68185i	0.666526	+	0.666526i	−0.290384	+	0.956910i	$0.593783\pi$
$212$		−	47.9841i		−	3.29556i
$213$			18.1372i			1.24274i
$214$	−1.42537	−	1.42537i	−0.0974360	−	0.0974360i
$215$	−18.0399	−	18.0399i	−1.23031	−	1.23031i
$216$	6.41257	−	6.41257i	0.436320	−	0.436320i
$217$		0			0
$218$	13.5646	−	13.5646i	0.918710	−	0.918710i
$219$			9.86630i			0.666702i
$220$	1.04826			0.0706734
$221$	−17.1990	−	4.05584i	−1.15693	−	0.272825i
$222$	24.4874			1.64348
$223$			26.7496i			1.79129i	0.444772	+	0.895644i	$0.353285\pi$
$223$			26.7496i			1.79129i	−0.444772	+	0.895644i	$0.646715\pi$
$224$		0			0
$225$	−14.8559			−0.990396
$226$	26.4456	−	26.4456i	1.75913	−	1.75913i
$227$	−1.14866	−	1.14866i	−0.0762392	−	0.0762392i	0.667959	−	0.744198i	$-0.267168\pi$
$227$	−1.14866	−	1.14866i	−0.0762392	−	0.0762392i	−0.744198	+	0.667959i	$0.767168\pi$
$228$	50.8181	+	50.8181i	3.36551	+	3.36551i
$229$		−	25.0433i		−	1.65491i	−0.561533	−	0.827454i	$-0.689788\pi$
$229$		−	25.0433i		−	1.65491i	0.561533	−	0.827454i	$-0.310212\pi$
$230$			5.21294i			0.343731i
$231$		0			0
$232$	−5.44245	−	5.44245i	−0.357314	−	0.357314i
$233$	−5.88342	+	5.88342i	−0.385436	+	0.385436i	−0.873056	−	0.487620i	$-0.837865\pi$
$233$	−5.88342	+	5.88342i	−0.385436	+	0.385436i	0.487620	+	0.873056i	$0.337865\pi$
$234$	−38.9505			−2.54627
$235$	20.7413	−	20.7413i	1.35302	−	1.35302i
$236$			17.2573i			1.12335i
$237$	−16.9929			−1.10381
$238$		0			0
$239$	−11.3488			−0.734093			−0.367046	−	0.930203i	$-0.619631\pi$
$239$	−11.3488			−0.734093			−0.367046	+	0.930203i	$0.619631\pi$
$240$		−	33.5538i		−	2.16589i
$241$	−4.67491	+	4.67491i	−0.301137	+	0.301137i	−0.841459	−	0.540322i	$-0.818303\pi$
$241$	−4.67491	+	4.67491i	−0.301137	+	0.301137i	0.540322	+	0.841459i	$0.318303\pi$
$242$	27.0438			1.73844
$243$	−15.5840	+	15.5840i	−0.999713	+	0.999713i
$244$	7.23454	+	7.23454i	0.463144	+	0.463144i
$245$		0			0
$246$			0.230372i			0.0146880i
$247$		−	29.3761i		−	1.86916i
$248$	−2.88506	−	2.88506i	−0.183202	−	0.183202i
$249$	−7.07393	−	7.07393i	−0.448292	−	0.448292i
$250$	5.11281	−	5.11281i	0.323363	−	0.323363i
$251$	−12.3828			−0.781595			−0.390798	−	0.920477i	$-0.627801\pi$
$251$	−12.3828			−0.781595			−0.390798	+	0.920477i	$0.627801\pi$
$252$		0			0
$253$		−	0.0607551i		−	0.00381964i
$254$	−28.6465			−1.79744
$255$	7.35421	−	31.1860i	0.460538	−	1.95294i
$256$	−32.3524			−2.02202
$257$		−	27.3692i		−	1.70725i	−0.520892	−	0.853623i	$-0.674401\pi$
$257$		−	27.3692i		−	1.70725i	0.520892	−	0.853623i	$-0.325599\pi$
$258$	38.2305	−	38.2305i	2.38013	−	2.38013i
$259$		0			0
$260$	−36.8874	+	36.8874i	−2.28766	+	2.28766i
$261$	−3.98161	−	3.98161i	−0.246456	−	0.246456i
$262$	34.6010	+	34.6010i	2.13766	+	2.13766i
$263$			18.6728i			1.15141i	0.817657	+	0.575706i	$0.195273\pi$
$263$			18.6728i			1.15141i	−0.817657	+	0.575706i	$0.804727\pi$
$264$			1.12513i			0.0692470i
$265$	−25.1477	−	25.1477i	−1.54481	−	1.54481i
$266$		0			0
$267$	−9.22160	+	9.22160i	−0.564353	+	0.564353i
$268$	−19.9562			−1.21902
$269$	0.131401	−	0.131401i	0.00801168	−	0.00801168i	−0.703090	−	0.711101i	$-0.748197\pi$
$269$	0.131401	−	0.131401i	0.00801168	−	0.00801168i	0.711101	+	0.703090i	$0.248197\pi$
$270$		−	13.2710i		−	0.807648i
$271$	−5.26632			−0.319906			−0.159953	−	0.987125i	$-0.551134\pi$
$271$	−5.26632			−0.319906			−0.159953	+	0.987125i	$0.551134\pi$
$272$	17.3272	+	4.08606i	1.05061	+	0.247754i
$273$		0			0
$274$		−	15.8098i		−	0.955104i
$275$	0.244893	−	0.244893i	0.0147676	−	0.0147676i
$276$	−7.39685			−0.445238
$277$	−8.98863	+	8.98863i	−0.540074	+	0.540074i	−0.923551	−	0.383476i	$-0.874727\pi$
$277$	−8.98863	+	8.98863i	−0.540074	+	0.540074i	0.383476	+	0.923551i	$0.374727\pi$
$278$	4.85896	+	4.85896i	0.291421	+	0.291421i
$279$	−2.11067	−	2.11067i	−0.126362	−	0.126362i
$280$		0			0
$281$		−	5.52979i		−	0.329879i	−0.986304	−	0.164940i	$-0.947257\pi$
$281$		−	5.52979i		−	0.329879i	0.986304	−	0.164940i	$-0.0527429\pi$
$282$	43.9555	+	43.9555i	2.61751	+	2.61751i
$283$	6.69776	+	6.69776i	0.398140	+	0.398140i	0.877577	−	0.479436i	$-0.159159\pi$
$283$	6.69776	+	6.69776i	0.398140	+	0.398140i	−0.479436	+	0.877577i	$0.659159\pi$
$284$	−20.0877	+	20.0877i	−1.19199	+	1.19199i
$285$	53.2660			3.15521
$286$	0.642080	−	0.642080i	0.0379670	−	0.0379670i
$287$		0			0
$288$	1.93341			0.113927
$289$	15.2089	+	7.59543i	0.894639	+	0.446790i
$290$	−11.2633			−0.661405
$291$			23.9864i			1.40611i
$292$	−10.9273	+	10.9273i	−0.639474	+	0.639474i
$293$	4.68516			0.273710			0.136855	−	0.990591i	$-0.456301\pi$
$293$	4.68516			0.273710			0.136855	+	0.990591i	$0.456301\pi$
$294$		0			0
$295$	9.04427	+	9.04427i	0.526578	+	0.526578i
$296$	13.7360	+	13.7360i	0.798391	+	0.798391i
$297$			0.154669i			0.00897482i
$298$		−	30.9311i		−	1.79179i
$299$	2.13793	+	2.13793i	0.123640	+	0.123640i
$300$	−29.8154	−	29.8154i	−1.72140	−	1.72140i
$301$		0			0
$302$	−31.8738			−1.83413
$303$	−4.60848	+	4.60848i	−0.264750	+	0.264750i
$304$			29.5950i			1.69739i
$305$	7.58302			0.434202
$306$	36.4715	+	8.60064i	2.08494	+	0.491666i
$307$	1.84567			0.105338			0.0526689	−	0.998612i	$-0.483227\pi$
$307$	1.84567			0.105338			0.0526689	+	0.998612i	$0.483227\pi$
$308$		0			0
$309$	−10.7264	+	10.7264i	−0.610204	+	0.610204i
$310$	−5.97073			−0.339115
$311$	−20.0679	+	20.0679i	−1.13795	+	1.13795i	−0.149128	+	0.988818i	$0.547647\pi$
$311$	−20.0679	+	20.0679i	−1.13795	+	1.13795i	−0.988818	+	0.149128i	$0.952353\pi$
$312$	−39.5925	−	39.5925i	−2.24149	−	2.24149i
$313$	−15.4443	−	15.4443i	−0.872962	−	0.872962i	0.119832	−	0.992794i	$-0.461764\pi$
$313$	−15.4443	−	15.4443i	−0.872962	−	0.872962i	−0.992794	+	0.119832i	$0.961764\pi$
$314$			7.12110i			0.401867i
$315$		0			0
$316$	−18.8203	−	18.8203i	−1.05873	−	1.05873i
$317$	−21.2922	−	21.2922i	−1.19589	−	1.19589i	−0.975387	−	0.220502i	$-0.929231\pi$
$317$	−21.2922	−	21.2922i	−1.19589	−	1.19589i	−0.220502	−	0.975387i	$-0.570769\pi$
$318$	53.2935	−	53.2935i	2.98855	−	2.98855i
$319$	0.131270			0.00734972
$320$	−15.6058	+	15.6058i	−0.872389	+	0.872389i
$321$		−	2.11993i		−	0.118323i
$322$		0			0
$323$	−6.48654	+	27.5066i	−0.360921	+	1.53051i
$324$	−26.0808			−1.44893
$325$			17.2352i			0.956039i
$326$	9.04577	−	9.04577i	0.500999	−	0.500999i
$327$	20.1745			1.11565
$328$	−0.129226	+	0.129226i	−0.00713532	+	0.00713532i
$329$		0			0
$330$	1.16425	+	1.16425i	0.0640896	+	0.0640896i
$331$			25.3606i			1.39394i	0.717099	+	0.696971i	$0.245469\pi$
$331$			25.3606i			1.39394i	−0.717099	+	0.696971i	$0.754531\pi$
$332$		−	15.6693i		−	0.859967i
$333$	10.0491	+	10.0491i	0.550686	+	0.550686i
$334$	27.2127	+	27.2127i	1.48901	+	1.48901i
$335$	−10.4588	+	10.4588i	−0.571423	+	0.571423i
$336$		0			0
$337$	−4.86208	+	4.86208i	−0.264854	+	0.264854i	−0.827023	−	0.562168i	$-0.809967\pi$
$337$	−4.86208	+	4.86208i	−0.264854	+	0.264854i	0.562168	+	0.827023i	$0.309967\pi$
$338$			13.2063i			0.718330i
$339$	39.3322			2.13623
$340$	42.6848	−	26.3947i	2.31491	−	1.43145i
$341$	0.0695868			0.00376834
$342$			62.2938i			3.36846i
$343$		0			0
$344$	42.8903			2.31249
$345$	−3.87657	+	3.87657i	−0.208708	+	0.208708i
$346$	−28.3539	−	28.3539i	−1.52432	−	1.52432i
$347$	3.80824	+	3.80824i	0.204437	+	0.204437i	0.801898	−	0.597461i	$-0.203824\pi$
$347$	3.80824	+	3.80824i	0.204437	+	0.204437i	−0.597461	+	0.801898i	$0.703824\pi$
$348$		−	15.9820i		−	0.856723i
$349$			9.88628i			0.529201i	0.964358	+	0.264600i	$0.0852400\pi$
$349$			9.88628i			0.529201i	−0.964358	+	0.264600i	$0.914760\pi$
$350$		0			0
$351$	−5.44270	−	5.44270i	−0.290510	−	0.290510i
$352$	−0.0318714	+	0.0318714i	−0.00169875	+	0.00169875i
$353$	21.5085			1.14478			0.572392	−	0.819980i	$-0.306016\pi$
$353$	21.5085			1.14478			0.572392	+	0.819980i	$0.306016\pi$
$354$	−19.1668	+	19.1668i	−1.01870	+	1.01870i
$355$			21.0554i			1.11750i
$356$	−20.4266			−1.08261
$357$		0			0
$358$	41.8118			2.20982
$359$		−	18.6160i		−	0.982515i	−0.871014	−	0.491257i	$-0.836537\pi$
$359$		−	18.6160i		−	0.982515i	0.871014	−	0.491257i	$-0.163463\pi$
$360$	39.6175	−	39.6175i	2.08803	−	2.08803i
$361$	−27.9815			−1.47271
$362$	19.6225	−	19.6225i	1.03134	−	1.03134i
$363$	20.1109	+	20.1109i	1.05555	+	1.05555i
$364$		0			0
$365$			11.4537i			0.599514i
$366$			16.0701i			0.839996i
$367$	−5.86254	−	5.86254i	−0.306022	−	0.306022i	0.537342	−	0.843364i	$-0.319428\pi$
$367$	−5.86254	−	5.86254i	−0.306022	−	0.306022i	−0.843364	+	0.537342i	$0.819428\pi$
$368$	−2.15386	−	2.15386i	−0.112278	−	0.112278i
$369$	−0.0945398	+	0.0945398i	−0.00492155	+	0.00492155i
$370$	28.4272			1.47786
$371$		0			0
$372$		−	8.47210i		−	0.439258i
$373$	−22.9495			−1.18828			−0.594140	−	0.804362i	$-0.702507\pi$
$373$	−22.9495			−1.18828			−0.594140	+	0.804362i	$0.702507\pi$
$374$	−0.742994	+	0.459439i	−0.0384193	+	0.0237570i
$375$	7.60423			0.392681
$376$			49.3131i			2.54313i
$377$	−4.61930	+	4.61930i	−0.237906	+	0.237906i
$378$		0			0
$379$	18.4121	−	18.4121i	0.945764	−	0.945764i	−0.0528386	−	0.998603i	$-0.516827\pi$
$379$	18.4121	−	18.4121i	0.945764	−	0.945764i	0.998603	+	0.0528386i	$0.0168269\pi$
$380$	58.9943	+	58.9943i	3.02634	+	3.02634i
$381$	−21.3028	−	21.3028i	−1.09138	−	1.09138i
$382$			13.0275i			0.666547i
$383$		−	4.86744i		−	0.248715i	−0.992237	−	0.124357i	$-0.960313\pi$
$383$		−	4.86744i		−	0.248715i	0.992237	−	0.124357i	$-0.0396869\pi$
$384$	−34.9871	−	34.9871i	−1.78543	−	1.78543i
$385$		0			0
$386$	−20.3354	+	20.3354i	−1.03504	+	1.03504i
$387$	31.3779			1.59503
$388$	−26.5660	+	26.5660i	−1.34868	+	1.34868i
$389$		−	2.95606i		−	0.149878i	−0.997188	−	0.0749392i	$-0.976124\pi$
$389$		−	2.95606i		−	0.149878i	0.997188	−	0.0749392i	$-0.0238763\pi$
$390$	−81.9379			−4.14909
$391$	−1.52979	−	2.47394i	−0.0773647	−	0.125112i
$392$		0			0
$393$			51.4617i			2.59590i
$394$	19.8469	−	19.8469i	0.999871	−	0.999871i
$395$	−19.7269			−0.992569
$396$	−0.911648	+	0.911648i	−0.0458121	+	0.0458121i
$397$	9.40656	+	9.40656i	0.472102	+	0.472102i	0.902594	−	0.430492i	$-0.141660\pi$
$397$	9.40656	+	9.40656i	0.472102	+	0.472102i	−0.430492	+	0.902594i	$0.641660\pi$
$398$	−33.9992	−	33.9992i	−1.70423	−	1.70423i
$399$		0			0
$400$		−	17.3637i		−	0.868183i
$401$	−17.2807	−	17.2807i	−0.862959	−	0.862959i	0.128722	−	0.991681i	$-0.458912\pi$
$401$	−17.2807	−	17.2807i	−0.862959	−	0.862959i	−0.991681	+	0.128722i	$0.958912\pi$
$402$	−22.1644	−	22.1644i	−1.10546	−	1.10546i
$403$	−2.44871	+	2.44871i	−0.121979	+	0.121979i
$404$	−10.2082			−0.507875
$405$	−13.6685	+	13.6685i	−0.679194	+	0.679194i
$406$		0			0
$407$	−0.331309			−0.0164224
$408$	28.3303	+	45.8152i	1.40256	+	2.26819i
$409$	−34.1540			−1.68880			−0.844402	−	0.535710i	$-0.820044\pi$
$409$	−34.1540			−1.68880			−0.844402	+	0.535710i	$0.820044\pi$
$410$			0.267437i			0.0132078i
$411$	11.7569	−	11.7569i	0.579923	−	0.579923i
$412$	−23.7599			−1.17057
$413$		0			0
$414$	−4.53360	−	4.53360i	−0.222814	−	0.222814i
$415$	−8.21206	−	8.21206i	−0.403114	−	0.403114i
$416$		−	2.24306i		−	0.109975i
$417$			7.22667i			0.353892i
$418$	−1.02688	−	1.02688i	−0.0502266	−	0.0502266i
$419$	14.4175	+	14.4175i	0.704341	+	0.704341i	0.965339	−	0.260999i	$-0.0840518\pi$
$419$	14.4175	+	14.4175i	0.704341	+	0.704341i	−0.260999	+	0.965339i	$0.584052\pi$
$420$		0			0
$421$	−13.3004			−0.648223			−0.324111	−	0.946019i	$-0.605065\pi$
$421$	−13.3004			−0.648223			−0.324111	+	0.946019i	$0.605065\pi$
$422$	−23.8191	+	23.8191i	−1.15950	+	1.15950i
$423$			36.0767i			1.75411i
$424$	59.7894			2.90363
$425$	3.80571	−	16.1383i	0.184604	−	0.782824i
$426$	−44.6209			−2.16189
$427$		0			0
$428$	2.34791	−	2.34791i	0.113491	−	0.113491i
$429$	0.954959			0.0461059
$430$	44.3814	−	44.3814i	2.14026	−	2.14026i
$431$	−6.09127	−	6.09127i	−0.293406	−	0.293406i	0.545018	−	0.838424i	$-0.316523\pi$
$431$	−6.09127	−	6.09127i	−0.293406	−	0.293406i	−0.838424	+	0.545018i	$0.816523\pi$
$432$	5.48325	+	5.48325i	0.263813	+	0.263813i
$433$			0.475114i			0.0228325i	0.999935	+	0.0114163i	$0.00363399\pi$
$433$			0.475114i			0.0228325i	−0.999935	+	0.0114163i	$0.996366\pi$
$434$		0			0
$435$	−8.37590	−	8.37590i	−0.401594	−	0.401594i
$436$	22.3441	+	22.3441i	1.07009	+	1.07009i
$437$	3.41920	−	3.41920i	0.163563	−	0.163563i
$438$	−24.2729			−1.15980
$439$	−13.8013	+	13.8013i	−0.658699	+	0.658699i	−0.955072	−	0.296373i	$-0.904223\pi$
$439$	−13.8013	+	13.8013i	−0.658699	+	0.658699i	0.296373	+	0.955072i	$0.404223\pi$
$440$			1.30615i			0.0622684i
$441$		0			0
$442$	9.97810	−	42.3128i	0.474610	−	2.01261i
$443$	17.7805			0.844775			0.422388	−	0.906415i	$-0.361192\pi$
$443$	17.7805			0.844775			0.422388	+	0.906415i	$0.361192\pi$
$444$			40.3364i			1.91428i
$445$	−10.7053	+	10.7053i	−0.507479	+	0.507479i
$446$	−65.8090			−3.11615
$447$	23.0017	−	23.0017i	1.08795	−	1.08795i
$448$		0			0
$449$	−22.2726	−	22.2726i	−1.05111	−	1.05111i	−0.998622	−	0.0524889i	$-0.983285\pi$
$449$	−22.2726	−	22.2726i	−1.05111	−	1.05111i	−0.0524889	−	0.998622i	$-0.516715\pi$
$450$		−	36.5483i		−	1.72290i
$451$		−	0.00311689i		−	0.000146769i
$452$	43.5621	+	43.5621i	2.04899	+	2.04899i
$453$	−23.7028	−	23.7028i	−1.11365	−	1.11365i
$454$	2.82591	−	2.82591i	0.132627	−	0.132627i
$455$		0			0
$456$	−63.3207	+	63.3207i	−2.96526	+	2.96526i
$457$			35.5384i			1.66242i	0.555960	+	0.831209i	$0.312351\pi$
$457$			35.5384i			1.66242i	−0.555960	+	0.831209i	$0.687649\pi$
$458$	61.6111			2.87890
$459$	3.89451	+	6.29811i	0.181780	+	0.293970i
$460$	−8.58693			−0.400368
$461$		−	0.834154i		−	0.0388504i	−0.999811	−	0.0194252i	$-0.993816\pi$
$461$		−	0.834154i		−	0.0388504i	0.999811	−	0.0194252i	$-0.00618362\pi$
$462$		0			0
$463$	24.3516			1.13172			0.565858	−	0.824503i	$-0.308545\pi$
$463$	24.3516			1.13172			0.565858	+	0.824503i	$0.308545\pi$
$464$	4.65372	−	4.65372i	0.216044	−	0.216044i
$465$	−4.44010	−	4.44010i	−0.205905	−	0.205905i
$466$	−14.4743	−	14.4743i	−0.670508	−	0.670508i
$467$			23.7847i			1.10062i	0.834959	+	0.550312i	$0.185491\pi$
$467$			23.7847i			1.10062i	−0.834959	+	0.550312i	$0.814509\pi$
$468$		−	64.1605i		−	2.96582i
$469$		0			0
$470$	51.0275	+	51.0275i	2.35372	+	2.35372i
$471$	−5.29557	+	5.29557i	−0.244007	+	0.244007i
$472$	−21.5030			−0.989755
$473$	−0.517251	+	0.517251i	−0.0237832	+	0.0237832i
$474$		−	41.8056i		−	1.92020i
$475$	27.5645			1.26474
$476$		0			0
$477$	43.7410			2.00276
$478$		−	27.9201i		−	1.27704i
$479$	20.6072	−	20.6072i	0.941568	−	0.941568i	−0.0568168	−	0.998385i	$-0.518095\pi$
$479$	20.6072	−	20.6072i	0.941568	−	0.941568i	0.998385	+	0.0568168i	$0.0180951\pi$
$480$	4.06721			0.185642
$481$	11.6585	−	11.6585i	0.531583	−	0.531583i
$482$	−11.5011	−	11.5011i	−0.523862	−	0.523862i
$483$		0			0
$484$			44.5474i			2.02488i
$485$			27.8456i			1.26441i
$486$	−38.3394	−	38.3394i	−1.73911	−	1.73911i
$487$	17.5672	+	17.5672i	0.796045	+	0.796045i	0.982469	−	0.186424i	$-0.0596899\pi$
$487$	17.5672	+	17.5672i	0.796045	+	0.796045i	−0.186424	+	0.982469i	$0.559690\pi$
$488$	−9.01441	+	9.01441i	−0.408063	+	0.408063i
$489$	13.4537			0.608396
$490$		0			0
$491$			16.3483i			0.737790i	0.929471	+	0.368895i	$0.120264\pi$
$491$			16.3483i			0.737790i	−0.929471	+	0.368895i	$0.879736\pi$
$492$	−0.379477			−0.0171082
$493$	5.34530	−	3.30533i	0.240740	−	0.148865i
$494$	72.2707			3.25161
$495$			0.955562i			0.0429493i
$496$	2.46696	−	2.46696i	0.110770	−	0.110770i
$497$		0			0
$498$	17.4032	−	17.4032i	0.779854	−	0.779854i
$499$	16.7642	+	16.7642i	0.750470	+	0.750470i	0.974567	−	0.224097i	$-0.0719433\pi$
$499$	16.7642	+	16.7642i	0.750470	+	0.750470i	−0.224097	+	0.974567i	$0.571943\pi$
$500$	8.42200	+	8.42200i	0.376643	+	0.376643i
$501$			40.4732i			1.80821i
$502$		−	30.4639i		−	1.35967i
$503$	9.37050	+	9.37050i	0.417810	+	0.417810i	0.884448	−	0.466638i	$-0.154535\pi$
$503$	9.37050	+	9.37050i	0.417810	+	0.417810i	−0.466638	+	0.884448i	$0.654535\pi$
$504$		0			0
$505$	−5.34994	+	5.34994i	−0.238069	+	0.238069i
$506$	0.149468			0.00664469
$507$	−9.82082	+	9.82082i	−0.436158	+	0.436158i
$508$		−	47.1875i		−	2.09361i
$509$	23.2510			1.03058			0.515290	−	0.857016i	$-0.327684\pi$
$509$	23.2510			1.03058			0.515290	+	0.857016i	$0.327684\pi$
$510$	76.7232	+	18.0927i	3.39736	+	0.801158i
$511$		0			0
$512$		−	41.3451i		−	1.82721i
$513$	−8.70455	+	8.70455i	−0.384315	+	0.384315i
$514$	67.3333			2.96994
$515$	−12.4522	+	12.4522i	−0.548709	+	0.548709i
$516$	62.9746	+	62.9746i	2.77230	+	2.77230i
$517$	−0.594708	−	0.594708i	−0.0261552	−	0.0261552i
$518$		0			0
$519$		−	42.1705i		−	1.85108i
$520$	−45.9626	−	45.9626i	−2.01559	−	2.01559i
$521$	8.04403	+	8.04403i	0.352416	+	0.352416i	0.861008	−	0.508592i	$-0.169834\pi$
$521$	8.04403	+	8.04403i	0.352416	+	0.352416i	−0.508592	+	0.861008i	$0.669834\pi$
$522$	9.79549	−	9.79549i	0.428737	−	0.428737i
$523$	−44.1104			−1.92881			−0.964407	−	0.264421i	$-0.914819\pi$
$523$	−44.1104			−1.92881			−0.964407	+	0.264421i	$0.914819\pi$
$524$	−56.9960	+	56.9960i	−2.48988	+	2.48988i
$525$		0			0
$526$	−45.9384			−2.00301
$527$	2.83357	−	1.75217i	0.123432	−	0.0763256i
$528$	−0.962074			−0.0418689
$529$		−	22.5023i		−	0.978362i
$530$	61.8680	−	61.8680i	2.68737	−	2.68737i
$531$	−15.7313			−0.682678
$532$		0			0
$533$	0.109681	+	0.109681i	0.00475082	+	0.00475082i
$534$	−22.6868	−	22.6868i	−0.981754	−	0.981754i
$535$		−	2.46101i		−	0.106399i
$536$		−	24.8660i		−	1.07405i
$537$	31.0931	+	31.0931i	1.34177	+	1.34177i
$538$	0.323271	+	0.323271i	0.0139372	+	0.0139372i
$539$		0			0
$540$	21.8605			0.940725
$541$	18.0196	−	18.0196i	0.774725	−	0.774725i	−0.204203	−	0.978928i	$-0.565460\pi$
$541$	18.0196	−	18.0196i	0.774725	−	0.774725i	0.978928	+	0.204203i	$0.0654604\pi$
$542$		−	12.9561i		−	0.556512i
$543$	29.1843			1.25242
$544$	−0.495290	+	2.10031i	−0.0212354	+	0.0900500i
$545$	23.4204			1.00322
$546$		0			0
$547$	1.86454	−	1.86454i	0.0797218	−	0.0797218i	−0.666121	−	0.745843i	$-0.732047\pi$
$547$	1.86454	−	1.86454i	0.0797218	−	0.0797218i	0.745843	+	0.666121i	$0.232047\pi$
$548$	26.0424			1.11248
$549$	−6.59481	+	6.59481i	−0.281459	+	0.281459i
$550$	0.602482	+	0.602482i	0.0256899	+	0.0256899i
$551$	7.38769	+	7.38769i	0.314726	+	0.314726i
$552$		−	9.21666i		−	0.392287i
$553$		0			0
$554$	−22.1137	−	22.1137i	−0.939520	−	0.939520i
$555$	21.1397	+	21.1397i	0.897330	+	0.897330i
$556$	−8.00384	+	8.00384i	−0.339438	+	0.339438i
$557$	19.9156			0.843850			0.421925	−	0.906631i	$-0.361354\pi$
$557$	19.9156			0.843850			0.421925	+	0.906631i	$0.361354\pi$
$558$	5.19263	−	5.19263i	0.219821	−	0.219821i
$559$		−	36.4034i		−	1.53970i
$560$		0			0
$561$	−0.894182	−	0.210864i	−0.0377524	−	0.00890269i
$562$	13.6043			0.573862
$563$			13.8507i			0.583738i	0.956458	+	0.291869i	$0.0942772\pi$
$563$			13.8507i			0.583738i	−0.956458	+	0.291869i	$0.905723\pi$
$564$	−72.4049	+	72.4049i	−3.04880	+	3.04880i
$565$	45.6604			1.92095
$566$	−16.4777	+	16.4777i	−0.692610	+	0.692610i
$567$		0			0
$568$	−25.0298	−	25.0298i	−1.05023	−	1.05023i
$569$			32.2138i			1.35047i	0.737602	+	0.675236i	$0.235958\pi$
$569$			32.2138i			1.35047i	−0.737602	+	0.675236i	$0.764042\pi$
$570$			131.044i			5.48883i
$571$	−33.5251	−	33.5251i	−1.40298	−	1.40298i	−0.790435	−	0.612546i	$-0.790145\pi$
$571$	−33.5251	−	33.5251i	−1.40298	−	1.40298i	−0.612546	−	0.790435i	$-0.709855\pi$
$572$	1.05766	+	1.05766i	0.0442229	+	0.0442229i
$573$	−9.68785	+	9.68785i	−0.404716	+	0.404716i
$574$		0			0
$575$	−2.00608	+	2.00608i	−0.0836592	+	0.0836592i
$576$		−	27.1441i		−	1.13100i
$577$	−42.9790			−1.78924			−0.894619	−	0.446829i	$-0.852553\pi$
$577$	−42.9790			−1.78924			−0.894619	+	0.446829i	$0.852553\pi$
$578$	−18.6861	+	37.4166i	−0.777240	+	1.55632i
$579$	−30.2446			−1.25692
$580$		−	18.5533i		−	0.770385i
$581$		0			0
$582$	−59.0110			−2.44608
$583$	−0.721050	+	0.721050i	−0.0298629	+	0.0298629i
$584$	−13.6157	−	13.6157i	−0.563423	−	0.563423i
$585$	−33.6255	−	33.6255i	−1.39024	−	1.39024i
$586$			11.5264i			0.476149i
$587$		−	22.7031i		−	0.937056i	−0.883449	−	0.468528i	$-0.844785\pi$
$587$		−	22.7031i		−	0.937056i	0.883449	−	0.468528i	$-0.155215\pi$
$588$		0			0
$589$	3.91624	+	3.91624i	0.161366	+	0.161366i
$590$	−22.2505	+	22.2505i	−0.916040	+	0.916040i
$591$	29.5180			1.21421
$592$	−11.7454	+	11.7454i	−0.482733	+	0.482733i
$593$			17.4887i			0.718173i	0.933304	+	0.359087i	$0.116912\pi$
$593$			17.4887i			0.718173i	−0.933304	+	0.359087i	$0.883088\pi$
$594$	−0.380514			−0.0156127
$595$		0			0
$596$	50.9508			2.08702
$597$		−	50.5667i		−	2.06956i
$598$	−5.25969	+	5.25969i	−0.215085	+	0.215085i
$599$	8.42222			0.344122			0.172061	−	0.985086i	$-0.444957\pi$
$599$	8.42222			0.344122			0.172061	+	0.985086i	$0.444957\pi$
$600$	37.1508	−	37.1508i	1.51667	−	1.51667i
$601$	−12.1106	−	12.1106i	−0.494002	−	0.494002i	0.415563	−	0.909565i	$-0.363585\pi$
$601$	−12.1106	−	12.1106i	−0.494002	−	0.494002i	−0.909565	+	0.415563i	$0.863585\pi$
$602$		0			0
$603$		−	18.1916i		−	0.740818i
$604$		−	52.5036i		−	2.13634i
$605$	23.3466	+	23.3466i	0.949174	+	0.949174i
$606$	−11.3377	−	11.3377i	−0.460563	−	0.460563i
$607$	5.83904	−	5.83904i	0.236999	−	0.236999i	−0.578607	−	0.815606i	$-0.696404\pi$
$607$	5.83904	−	5.83904i	0.236999	−	0.236999i	0.815606	+	0.578607i	$0.196404\pi$
$608$	−3.58735			−0.145486
$609$		0			0
$610$			18.6556i			0.755343i
$611$	41.8547			1.69326
$612$	−14.1673	+	60.0771i	−0.572678	+	2.42847i
$613$	3.01545			0.121793			0.0608965	−	0.998144i	$-0.480604\pi$
$613$	3.01545			0.121793			0.0608965	+	0.998144i	$0.480604\pi$
$614$			4.54068i			0.183247i
$615$	−0.198878	+	0.198878i	−0.00801954	+	0.00801954i
$616$		0			0
$617$	17.1700	−	17.1700i	0.691237	−	0.691237i	−0.271267	−	0.962504i	$-0.587443\pi$
$617$	17.1700	−	17.1700i	0.691237	−	0.691237i	0.962504	+	0.271267i	$0.0874426\pi$
$618$	−26.3889	−	26.3889i	−1.06152	−	1.06152i
$619$	−19.3714	−	19.3714i	−0.778602	−	0.778602i	0.200991	−	0.979593i	$-0.435584\pi$
$619$	−19.3714	−	19.3714i	−0.778602	−	0.778602i	−0.979593	+	0.200991i	$0.935584\pi$
$620$		−	9.83518i		−	0.394991i
$621$		−	1.26699i		−	0.0508427i
$622$	−49.3707	−	49.3707i	−1.97958	−	1.97958i
$623$		0			0
$624$	33.8547	−	33.8547i	1.35527	−	1.35527i
$625$	28.9351			1.15740
$626$	37.9957	−	37.9957i	1.51861	−	1.51861i
$627$		−	1.52727i		−	0.0609934i
$628$	−11.7301			−0.468083
$629$	−13.4909	+	8.34222i	−0.537915	+	0.332626i
$630$		0			0
$631$		−	47.9472i		−	1.90875i	−0.298615	−	0.954374i	$-0.596525\pi$
$631$		−	47.9472i		−	1.90875i	0.298615	−	0.954374i	$-0.403475\pi$
$632$	23.4506	−	23.4506i	0.932816	−	0.932816i
$633$	−35.4259			−1.40805
$634$	52.3826	−	52.3826i	2.08038	−	2.08038i
$635$	−24.7303	−	24.7303i	−0.981390	−	0.981390i
$636$	87.7869	+	87.7869i	3.48098	+	3.48098i
$637$		0			0
$638$			0.322948i			0.0127857i
$639$	−18.3114	−	18.3114i	−0.724390	−	0.724390i
$640$	−40.6162	−	40.6162i	−1.60549	−	1.60549i
$641$	11.2207	−	11.2207i	0.443189	−	0.443189i	−0.449893	−	0.893082i	$-0.648538\pi$
$641$	11.2207	−	11.2207i	0.443189	−	0.443189i	0.893082	+	0.449893i	$0.148538\pi$
$642$	5.21541			0.205836
$643$	−24.0648	+	24.0648i	−0.949024	+	0.949024i	−0.998762	−	0.0497384i	$-0.984161\pi$
$643$	−24.0648	+	24.0648i	−0.949024	+	0.949024i	0.0497384	+	0.998762i	$0.484161\pi$
$644$		0			0
$645$	66.0080			2.59906
$646$	−67.6711	−	15.9581i	−2.66249	−	0.627862i
$647$	−2.32115			−0.0912539			−0.0456270	−	0.998959i	$-0.514529\pi$
$647$	−2.32115			−0.0912539			−0.0456270	+	0.998959i	$0.514529\pi$
$648$		−	32.4973i		−	1.27661i
$649$	0.259323	−	0.259323i	0.0101793	−	0.0101793i
$650$	−42.4018			−1.66314
$651$		0			0
$652$	14.9005	+	14.9005i	0.583549	+	0.583549i
$653$	−32.9317	−	32.9317i	−1.28872	−	1.28872i	−0.935567	−	0.353149i	$-0.885111\pi$
$653$	−32.9317	−	32.9317i	−1.28872	−	1.28872i	−0.353149	−	0.935567i	$-0.614889\pi$
$654$			49.6329i			1.94080i
$655$			59.7414i			2.33429i
$656$	−0.110498	−	0.110498i	−0.00431424	−	0.00431424i
$657$	−9.96106	−	9.96106i	−0.388618	−	0.388618i
$658$		0			0
$659$	−24.5226			−0.955264			−0.477632	−	0.878560i	$-0.658505\pi$
$659$	−24.5226			−0.955264			−0.477632	+	0.878560i	$0.658505\pi$
$660$	−1.91779	+	1.91779i	−0.0746497	+	0.0746497i
$661$		−	7.37340i		−	0.286792i	−0.989665	−	0.143396i	$-0.954198\pi$
$661$		−	7.37340i		−	0.286792i	0.989665	−	0.143396i	$-0.0458022\pi$
$662$	−62.3916			−2.42492
$663$	38.8858	−	24.0455i	1.51020	−	0.933849i
$664$	19.5244			0.757693
$665$		0			0
$666$	−24.7226	+	24.7226i	−0.957980	+	0.957980i
$667$	−1.07532			−0.0416364
$668$	−44.8257	+	44.8257i	−1.73436	+	1.73436i
$669$	−48.9385	−	48.9385i	−1.89207	−	1.89207i
$670$	−25.7304	−	25.7304i	−0.994054	−	0.994054i
$671$		−	0.217425i		−	0.00839359i
$672$		0			0
$673$	−25.5728	−	25.5728i	−0.985757	−	0.985757i	0.0141427	−	0.999900i	$-0.495498\pi$
$673$	−25.5728	−	25.5728i	−0.985757	−	0.985757i	−0.999900	+	0.0141427i	$0.995498\pi$
$674$	−11.9616	−	11.9616i	−0.460743	−	0.460743i
$675$	5.10704	−	5.10704i	0.196570	−	0.196570i
$676$	−21.7539			−0.836690
$677$	4.95004	−	4.95004i	0.190246	−	0.190246i	−0.605557	−	0.795802i	$-0.707049\pi$
$677$	4.95004	−	4.95004i	0.190246	−	0.190246i	0.795802	+	0.605557i	$0.207049\pi$
$678$			96.7644i			3.71621i
$679$		0			0
$680$	32.8884	+	53.1864i	1.26121	+	2.03961i
$681$	4.20295			0.161057
$682$			0.171196i			0.00655544i
$683$	6.23201	−	6.23201i	0.238461	−	0.238461i	−0.577751	−	0.816213i	$-0.696070\pi$
$683$	6.23201	−	6.23201i	0.238461	−	0.238461i	0.816213	+	0.577751i	$0.196070\pi$
$684$	−102.612			−3.92348
$685$	13.6484	−	13.6484i	0.521480	−	0.521480i
$686$		0			0
$687$	45.8168	+	45.8168i	1.74802	+	1.74802i
$688$			36.6746i			1.39821i
$689$		−	50.7465i		−	1.93329i
$690$	−9.53708	−	9.53708i	−0.363070	−	0.363070i
$691$	34.6705	+	34.6705i	1.31893	+	1.31893i	0.914624	+	0.404304i	$0.132486\pi$
$691$	34.6705	+	34.6705i	1.31893	+	1.31893i	0.404304	+	0.914624i	$0.367514\pi$
$692$	46.7055	−	46.7055i	1.77548	−	1.77548i
$693$		0			0
$694$	−9.36897	+	9.36897i	−0.355641	+	0.355641i
$695$			8.38938i			0.318227i
$696$	19.9139			0.754836
$697$	−0.0784820	−	0.126919i	−0.00297272	−	0.00480741i
$698$	−24.3221			−0.920603
$699$		−	21.5274i		−	0.814242i
$700$		0			0
$701$	−44.4219			−1.67779			−0.838897	−	0.544290i	$-0.816799\pi$
$701$	−44.4219			−1.67779			−0.838897	+	0.544290i	$0.816799\pi$
$702$	13.3900	−	13.3900i	0.505374	−	0.505374i
$703$	−18.6456	−	18.6456i	−0.703231	−	0.703231i
$704$	0.447458	+	0.447458i	0.0168642	+	0.0168642i
$705$			75.8926i			2.85828i
$706$			52.9149i			1.99148i
$707$		0			0
$708$	−31.5722	−	31.5722i	−1.18655	−	1.18655i
$709$	6.32284	−	6.32284i	0.237459	−	0.237459i	−0.578338	−	0.815797i	$-0.696299\pi$
$709$	6.32284	−	6.32284i	0.237459	−	0.237459i	0.815797	+	0.578338i	$0.196299\pi$
$710$	−51.8000			−1.94402
$711$	17.1561	−	17.1561i	0.643405	−	0.643405i
$712$		−	25.4521i		−	0.953857i
$713$	−0.570030			−0.0213478
$714$		0			0
$715$	1.10860			0.0414594
$716$			68.8737i			2.57393i
$717$	20.7626	−	20.7626i	0.775395	−	0.775395i
$718$	45.7987			1.70919
$719$	−24.1100	+	24.1100i	−0.899152	+	0.899152i	−0.995361	−	0.0962090i	$-0.969328\pi$
$719$	−24.1100	+	24.1100i	−0.899152	+	0.899152i	0.0962090	+	0.995361i	$0.469328\pi$
$720$	33.8761	+	33.8761i	1.26249	+	1.26249i
$721$		0			0
$722$		−	68.8396i		−	2.56195i
$723$		−	17.1055i		−	0.636160i
$724$	32.3229	+	32.3229i	1.20127	+	1.20127i
$725$	−4.33442	−	4.33442i	−0.160976	−	0.160976i
$726$	−49.4766	+	49.4766i	−1.83625	+	1.83625i
$727$	10.9742			0.407009			0.203504	−	0.979074i	$-0.434767\pi$
$727$	10.9742			0.407009			0.203504	+	0.979074i	$0.434767\pi$
$728$		0			0
$729$		−	37.7146i		−	1.39684i
$730$	−28.1782			−1.04292
$731$	−8.03821	+	34.0865i	−0.297304	+	1.26074i
$732$	−26.4712			−0.978403
$733$			18.4764i			0.682443i	0.939983	+	0.341221i	$0.110841\pi$
$733$			18.4764i			0.682443i	−0.939983	+	0.341221i	$0.889159\pi$
$734$	14.4229	−	14.4229i	0.532360	−	0.532360i
$735$		0			0
$736$	0.261079	−	0.261079i	0.00962350	−	0.00962350i
$737$	0.299880	+	0.299880i	0.0110462	+	0.0110462i
$738$	−0.232585	−	0.232585i	−0.00856158	−	0.00856158i
$739$			32.2803i			1.18745i	0.804668	+	0.593725i	$0.202343\pi$
$739$			32.2803i			1.18745i	−0.804668	+	0.593725i	$0.797657\pi$
$740$			46.8262i			1.72136i
$741$	53.7437	+	53.7437i	1.97432	+	1.97432i
$742$		0			0
$743$	11.9889	−	11.9889i	0.439832	−	0.439832i	−0.452124	−	0.891955i	$-0.649333\pi$
$743$	11.9889	−	11.9889i	0.439832	−	0.439832i	0.891955	+	0.452124i	$0.149333\pi$
$744$	10.5565			0.387018
$745$	26.7025	−	26.7025i	0.978304	−	0.978304i
$746$		−	56.4599i		−	2.06714i
$747$	14.2837			0.522615
$748$	−0.756803	−	1.22388i	−0.0276715	−	0.0447497i
$749$		0			0
$750$			18.7078i			0.683112i
$751$	−31.5072	+	31.5072i	−1.14971	+	1.14971i	−0.163104	+	0.986609i	$0.552151\pi$
$751$	−31.5072	+	31.5072i	−1.14971	+	1.14971i	−0.986609	+	0.163104i	$0.947849\pi$
$752$	−42.1666			−1.53766
$753$	22.6543	−	22.6543i	0.825570	−	0.825570i
$754$	−11.3643	−	11.3643i	−0.413864	−	0.413864i
$755$	−27.5163	−	27.5163i	−1.00142	−	1.00142i
$756$		0			0
$757$			19.1445i			0.695817i	0.937528	+	0.347909i	$0.113108\pi$
$757$			19.1445i			0.695817i	−0.937528	+	0.347909i	$0.886892\pi$
$758$	45.2970	+	45.2970i	1.64526	+	1.64526i
$759$	0.111151	+	0.111151i	0.00403454	+	0.00403454i
$760$	−73.5084	+	73.5084i	−2.66643	+	2.66643i
$761$	21.2182			0.769160			0.384580	−	0.923092i	$-0.374346\pi$
$761$	21.2182			0.769160			0.384580	+	0.923092i	$0.374346\pi$
$762$	52.4088	−	52.4088i	1.89857	−	1.89857i
$763$		0			0
$764$	−21.4594			−0.776374
$765$	24.0607	+	38.9103i	0.869915	+	1.40681i
$766$	11.9748			0.432667
$767$			18.2508i			0.658996i
$768$	59.1887	−	59.1887i	2.13579	−	2.13579i
$769$	30.7011			1.10711			0.553556	−	0.832812i	$-0.313271\pi$
$769$	30.7011			1.10711			0.553556	+	0.832812i	$0.313271\pi$
$770$		0			0
$771$	50.0720	+	50.0720i	1.80330	+	1.80330i
$772$	−33.4971	−	33.4971i	−1.20559	−	1.20559i
$773$			40.2083i			1.44619i	0.690748	+	0.723096i	$0.257281\pi$
$773$			40.2083i			1.44619i	−0.690748	+	0.723096i	$0.742719\pi$
$774$			77.1954i			2.77473i
$775$	−2.29769	−	2.29769i	−0.0825356	−	0.0825356i
$776$	−33.1019	−	33.1019i	−1.18829	−	1.18829i
$777$		0			0
$778$	7.27246			0.260730
$779$	0.175414	−	0.175414i	0.00628486	−	0.00628486i
$780$		−	134.971i		−	4.83274i
$781$	0.603712			0.0216025
$782$	6.08634	−	3.76356i	0.217647	−	0.134584i
$783$	2.73752			0.0978311
$784$		0			0
$785$	−6.14757	+	6.14757i	−0.219416	+	0.219416i
$786$	−126.605			−4.51586
$787$	11.6266	−	11.6266i	0.414442	−	0.414442i	−0.468841	−	0.883283i	$-0.655328\pi$
$787$	11.6266	−	11.6266i	0.414442	−	0.414442i	0.883283	+	0.468841i	$0.155328\pi$
$788$	32.6924	+	32.6924i	1.16462	+	1.16462i
$789$	−34.1619	−	34.1619i	−1.21619	−	1.21619i
$790$		−	48.5318i		−	1.72668i
$791$		0			0
$792$	−1.13594	−	1.13594i	−0.0403638	−	0.0403638i
$793$	7.65102	+	7.65102i	0.271696	+	0.271696i
$794$	−23.1419	+	23.1419i	−0.821274	+	0.821274i
$795$	92.0156			3.26346
$796$	56.0047	−	56.0047i	1.98503	−	1.98503i
$797$		−	5.05018i		−	0.178887i	−0.995992	−	0.0894433i	$-0.971491\pi$
$797$		−	5.05018i		−	0.178887i	0.995992	−	0.0894433i	$-0.0285088\pi$
$798$		0			0
$799$	−39.1909	−	9.24192i	−1.38648	−	0.326956i
$800$	2.10473			0.0744134
$801$		−	18.6203i		−	0.657917i
$802$	42.5137	−	42.5137i	1.50121	−	1.50121i
$803$	0.328407			0.0115892
$804$	36.5100	−	36.5100i	1.28761	−	1.28761i
$805$		0			0
$806$	−6.02427	−	6.02427i	−0.212196	−	0.212196i
$807$			0.480798i			0.0169249i
$808$		−	12.7196i		−	0.447475i
$809$	3.86211	+	3.86211i	0.135785	+	0.135785i	0.771732	−	0.635948i	$-0.219391\pi$
$809$	3.86211	+	3.86211i	0.135785	+	0.135785i	−0.635948	+	0.771732i	$0.719391\pi$
$810$	−33.6271	−	33.6271i	−1.18153	−	1.18153i
$811$	15.7978	−	15.7978i	0.554737	−	0.554737i	−0.373067	−	0.927804i	$-0.621694\pi$
$811$	15.7978	−	15.7978i	0.554737	−	0.554737i	0.927804	+	0.373067i	$0.121694\pi$
$812$		0			0
$813$	9.63473	−	9.63473i	0.337905	−	0.337905i
$814$		−	0.815080i		−	0.0285685i
$815$	15.6183			0.547084
$816$	−39.1755	+	24.2246i	−1.37142	+	0.848032i
$817$	−58.2202			−2.03687
$818$		−	84.0249i		−	2.93786i
$819$		0			0
$820$	−0.440532			−0.0153840
$821$	34.2442	−	34.2442i	1.19513	−	1.19513i	0.219521	−	0.975608i	$-0.429550\pi$
$821$	34.2442	−	34.2442i	1.19513	−	1.19513i	0.975608	−	0.219521i	$-0.0704496\pi$
$822$	28.9240	+	28.9240i	1.00884	+	1.00884i
$823$	10.6670	+	10.6670i	0.371829	+	0.371829i	0.868143	−	0.496314i	$-0.165314\pi$
$823$	10.6670	+	10.6670i	0.371829	+	0.371829i	−0.496314	+	0.868143i	$0.665314\pi$
$824$		−	29.6054i		−	1.03135i
$825$			0.896065i			0.0311970i
$826$		0			0
$827$	−10.6145	−	10.6145i	−0.369104	−	0.369104i	0.498047	−	0.867150i	$-0.334051\pi$
$827$	−10.6145	−	10.6145i	−0.369104	−	0.369104i	−0.867150	+	0.498047i	$0.834051\pi$
$828$	7.46789	−	7.46789i	0.259527	−	0.259527i
$829$	13.0861			0.454498			0.227249	−	0.973837i	$-0.427027\pi$
$829$	13.0861			0.454498			0.227249	+	0.973837i	$0.427027\pi$
$830$	20.2032	−	20.2032i	0.701262	−	0.701262i
$831$		−	32.8894i		−	1.14092i
$832$	−31.4914			−1.09177
$833$		0			0
$834$	−17.7789			−0.615634
$835$			46.9849i			1.62598i
$836$	1.69152	−	1.69152i	0.0585024	−	0.0585024i
$837$	1.45117			0.0501598
$838$	−35.4697	+	35.4697i	−1.22528	+	1.22528i
$839$	−18.6567	−	18.6567i	−0.644099	−	0.644099i	0.307461	−	0.951561i	$-0.400521\pi$
$839$	−18.6567	−	18.6567i	−0.644099	−	0.644099i	−0.951561	+	0.307461i	$0.900521\pi$
$840$		0			0
$841$			26.6766i			0.919883i
$842$		−	32.7214i		−	1.12766i
$843$	10.1167	+	10.1167i	0.348439	+	0.348439i
$844$	−39.2356	−	39.2356i	−1.35055	−	1.35055i
$845$	−11.4009	+	11.4009i	−0.392203	+	0.392203i
$846$	−88.7553			−3.05147
$847$		0			0
$848$			51.1246i			1.75563i
$849$	−24.5071			−0.841082
$850$	39.7033	+	9.36274i	1.36181	+	0.321139i
$851$	2.71396			0.0930334
$852$		−	73.5011i		−	2.51811i
$853$	−33.7388	+	33.7388i	−1.15519	+	1.15519i	−0.169697	+	0.985496i	$0.554279\pi$
$853$	−33.7388	+	33.7388i	−1.15519	+	1.15519i	−0.985496	+	0.169697i	$0.945721\pi$
$854$		0			0
$855$	−53.7776	+	53.7776i	−1.83916	+	1.83916i
$856$	2.92556	+	2.92556i	0.0999935	+	0.0999935i
$857$	−8.93016	−	8.93016i	−0.305048	−	0.305048i	0.537937	−	0.842985i	$-0.319204\pi$
$857$	−8.93016	−	8.93016i	−0.305048	−	0.305048i	−0.842985	+	0.537937i	$0.819204\pi$
$858$			2.34937i			0.0802063i
$859$		−	31.2215i		−	1.06526i	−0.846347	−	0.532632i	$-0.821203\pi$
$859$		−	31.2215i		−	1.06526i	0.846347	−	0.532632i	$-0.178797\pi$
$860$	73.1066	+	73.1066i	2.49291	+	2.49291i
$861$		0			0
$862$	14.9856	−	14.9856i	0.510413	−	0.510413i
$863$	−20.3484			−0.692668			−0.346334	−	0.938111i	$-0.612574\pi$
$863$	−20.3484			−0.692668			−0.346334	+	0.938111i	$0.612574\pi$
$864$	−0.664650	+	0.664650i	−0.0226119	+	0.0226119i
$865$		−	48.9553i		−	1.66453i
$866$	−1.16887			−0.0397197
$867$	−41.7205	+	13.9288i	−1.41690	+	0.473047i
$868$		0			0
$869$			0.565622i			0.0191874i
$870$	20.6062	−	20.6062i	0.698617	−	0.698617i
$871$	−21.1051			−0.715119
$872$	−27.8413	+	27.8413i	−0.942824	+	0.942824i
$873$	−24.2168	−	24.2168i	−0.819615	−	0.819615i
$874$	8.41186	+	8.41186i	0.284536	+	0.284536i
$875$		0			0
$876$		−	39.9831i		−	1.35090i
$877$	30.2587	+	30.2587i	1.02177	+	1.02177i	0.999758	+	0.0220075i	$0.00700578\pi$
$877$	30.2587	+	30.2587i	1.02177	+	1.02177i	0.0220075	+	0.999758i	$0.492994\pi$
$878$	−33.9536	−	33.9536i	−1.14588	−	1.14588i
$879$	−8.57151	+	8.57151i	−0.289110	+	0.289110i
$880$	−1.11686			−0.0376495
$881$	−33.0350	+	33.0350i	−1.11298	+	1.11298i	−0.120231	+	0.992746i	$0.538363\pi$
$881$	−33.0350	+	33.0350i	−1.11298	+	1.11298i	−0.992746	+	0.120231i	$0.961637\pi$
$882$		0			0
$883$	20.4430			0.687962			0.343981	−	0.938977i	$-0.388224\pi$
$883$	20.4430			0.687962			0.343981	+	0.938977i	$0.388224\pi$
$884$	69.6990	+	16.4363i	2.34423	+	0.552812i
$885$	−33.0930			−1.11241
$886$			43.7432i			1.46958i
$887$	−12.6493	+	12.6493i	−0.424723	+	0.424723i	−0.886826	−	0.462103i	$-0.847095\pi$
$887$	−12.6493	+	12.6493i	−0.424723	+	0.424723i	0.462103	+	0.886826i	$0.347095\pi$
$888$	−50.2602			−1.68662
$889$		0			0
$890$	−26.3369	−	26.3369i	−0.882815	−	0.882815i
$891$	0.391912	+	0.391912i	0.0131295	+	0.0131295i
$892$		−	108.403i		−	3.62959i
$893$		−	66.9386i		−	2.24001i
$894$	56.5885	+	56.5885i	1.89260	+	1.89260i
$895$	36.0957	+	36.0957i	1.20655	+	1.20655i
$896$		0			0
$897$	−7.82268			−0.261192
$898$	54.7947	−	54.7947i	1.82852	−	1.82852i
$899$		−	1.23163i		−	0.0410772i
$900$	60.2036			2.00679
$901$	−11.2053	+	47.5168i	−0.373303	+	1.58302i
$902$	0.00766812			0.000255320
$903$		0			0
$904$	−54.2794	+	54.2794i	−1.80531	+	1.80531i
$905$	33.8798			1.12620
$906$	58.3131	−	58.3131i	1.93732	−	1.93732i
$907$	16.6354	+	16.6354i	0.552368	+	0.552368i	0.927124	−	0.374755i	$-0.122273\pi$
$907$	16.6354	+	16.6354i	0.552368	+	0.552368i	−0.374755	+	0.927124i	$0.622273\pi$
$908$	4.65494	+	4.65494i	0.154480	+	0.154480i
$909$		−	9.30549i		−	0.308644i
$910$		0			0
$911$	22.2004	+	22.2004i	0.735532	+	0.735532i	0.971710	−	0.236178i	$-0.0758948\pi$
$911$	22.2004	+	22.2004i	0.735532	+	0.735532i	−0.236178	+	0.971710i	$0.575895\pi$
$912$	−54.1441	−	54.1441i	−1.79289	−	1.79289i
$913$	−0.235461	+	0.235461i	−0.00779262	+	0.00779262i
$914$	−87.4310			−2.89196
$915$	−13.8731	+	13.8731i	−0.458632	+	0.458632i
$916$			101.488i			3.35326i
$917$		0			0
$918$	−15.4945	+	9.58120i	−0.511394	+	0.316227i
$919$	−44.0188			−1.45205			−0.726024	−	0.687670i	$-0.758634\pi$
$919$	−44.0188			−1.45205			−0.726024	+	0.687670i	$0.758634\pi$
$920$		−	10.6995i		−	0.352753i
$921$	−3.37665	+	3.37665i	−0.111264	+	0.111264i
$922$	2.05217			0.0675846
$923$	−21.2442	+	21.2442i	−0.699261	+	0.699261i
$924$		0			0
$925$	10.9395	+	10.9395i	0.359689	+	0.359689i
$926$			59.9094i			1.96875i
$927$		−	21.6589i		−	0.711371i
$928$	0.564099	+	0.564099i	0.0185175	+	0.0185175i
$929$	31.0797	+	31.0797i	1.01969	+	1.01969i	0.999802	+	0.0198887i	$0.00633118\pi$
$929$	31.0797	+	31.0797i	1.01969	+	1.01969i	0.0198887	+	0.999802i	$0.493669\pi$
$930$	10.9234	−	10.9234i	0.358194	−	0.358194i
$931$		0			0
$932$	23.8425	−	23.8425i	0.780988	−	0.780988i
$933$		−	73.4284i		−	2.40394i
$934$	−58.5146			−1.91466
$935$	−1.03805	−	0.244790i	−0.0339478	−	0.00800550i
$936$	79.9456			2.61310
$937$			0.0537818i			0.00175697i	1.00000		0.000878487i	$0.000279631\pi$
$937$			0.0537818i			0.00175697i	−1.00000		0.000878487i	$0.999720\pi$
$938$		0			0
$939$	56.5106			1.84415
$940$	−84.0542	+	84.0542i	−2.74155	+	2.74155i
$941$	22.6452	+	22.6452i	0.738213	+	0.738213i	0.972232	−	0.234019i	$-0.0751879\pi$
$941$	22.6452	+	22.6452i	0.738213	+	0.738213i	−0.234019	+	0.972232i	$0.575188\pi$
$942$	−13.0281	−	13.0281i	−0.424477	−	0.424477i
$943$			0.0255324i			0.000831450i
$944$		−	18.3867i		−	0.598437i
$945$		0			0
$946$	−1.27253	−	1.27253i	−0.0413735	−	0.0413735i
$947$	17.9053	−	17.9053i	0.581844	−	0.581844i	−0.353566	−	0.935410i	$-0.615031\pi$
$947$	17.9053	−	17.9053i	0.581844	−	0.581844i	0.935410	+	0.353566i	$0.115031\pi$
$948$	68.8637			2.23659
$949$	−11.5564	+	11.5564i	−0.375137	+	0.375137i
$950$			67.8136i			2.20016i
$951$	77.9081			2.52634
$952$		0			0
$953$	18.3016			0.592847			0.296424	−	0.955057i	$-0.404206\pi$
$953$	18.3016			0.592847			0.296424	+	0.955057i	$0.404206\pi$
$954$			107.611i			3.48403i
$955$	−11.2465	+	11.2465i	−0.363929	+	0.363929i
$956$	45.9909			1.48745
$957$	−0.240159	+	0.240159i	−0.00776323	+	0.00776323i
$958$	50.6975	+	50.6975i	1.63796	+	1.63796i
$959$		0			0
$960$		−	57.1015i		−	1.84294i
$961$			30.3471i			0.978939i
$962$	28.6821	+	28.6821i	0.924748	+	0.924748i
$963$	2.14029	+	2.14029i	0.0689699	+	0.0689699i
$964$	18.9450	−	18.9450i	0.610178	−	0.610178i
$965$	−35.1106			−1.13025
$966$		0			0
$967$		−	12.0520i		−	0.387567i	−0.981044	−	0.193784i	$-0.937924\pi$
$967$		−	12.0520i		−	0.387567i	0.981044	−	0.193784i	$-0.0620760\pi$
$968$	−55.5072			−1.78407
$969$	−38.4561	−	62.1904i	−1.23539	−	1.99784i
$970$	−68.5053			−2.19957
$971$			2.70923i			0.0869432i	0.999055	+	0.0434716i	$0.0138418\pi$
$971$			2.70923i			0.0869432i	−0.999055	+	0.0434716i	$0.986158\pi$
$972$	63.1540	−	63.1540i	2.02567	−	2.02567i
$973$		0			0
$974$	−43.2185	+	43.2185i	−1.38481	+	1.38481i
$975$	−31.5319	−	31.5319i	−1.00983	−	1.00983i
$976$	−7.70803	−	7.70803i	−0.246728	−	0.246728i
$977$		−	6.46601i		−	0.206866i	−0.994636	−	0.103433i	$-0.967017\pi$
$977$		−	6.46601i		−	0.206866i	0.994636	−	0.103433i	$-0.0329828\pi$
$978$			33.0985i			1.05837i
$979$	0.306948	+	0.306948i	0.00981010	+	0.00981010i
$980$		0			0
$981$	−20.3682	+	20.3682i	−0.650308	+	0.650308i
$982$	−40.2199			−1.28347
$983$	−27.9105	+	27.9105i	−0.890207	+	0.890207i	−0.994542	−	0.104335i	$-0.966728\pi$
$983$	−27.9105	+	27.9105i	−0.890207	+	0.890207i	0.104335	+	0.994542i	$0.466728\pi$
$984$		−	0.472838i		−	0.0150735i
$985$	34.2672			1.09184
$986$	8.13171	+	13.1504i	0.258966	+	0.418795i
$987$		0			0
$988$			119.047i			3.78738i
$989$	4.23713	−	4.23713i	0.134733	−	0.134733i
$990$	−2.35086			−0.0747151
$991$	2.67882	−	2.67882i	0.0850954	−	0.0850954i	−0.663278	−	0.748373i	$-0.730835\pi$
$991$	2.67882	−	2.67882i	0.0850954	−	0.0850954i	0.748373	+	0.663278i	$0.230835\pi$
$992$	0.299031	+	0.299031i	0.00949425	+	0.00949425i
$993$	−46.3971	−	46.3971i	−1.47237	−	1.47237i
$994$		0			0
$995$		−	58.7024i		−	1.86099i
$996$	28.6671	+	28.6671i	0.908351	+	0.908351i
$997$	24.5675	+	24.5675i	0.778060	+	0.778060i	0.979501	−	0.201441i	$-0.0645623\pi$
$997$	24.5675	+	24.5675i	0.778060	+	0.778060i	−0.201441	+	0.979501i	$0.564562\pi$
$998$	−41.2430	+	41.2430i	−1.30553	+	1.30553i
$999$	−6.90916			−0.218596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.g.f.344.8		16
7.2	even	3		833.2.o.d.361.8		32
7.3	odd	6		119.2.n.b.72.1	yes	32
7.4	even	3		833.2.o.d.667.1		32
7.5	odd	6		119.2.n.b.4.8	✓	32
7.6	odd	2		833.2.g.g.344.8		16
17.13	even	4	inner	833.2.g.f.540.1		16
119.13	odd	4		833.2.g.g.540.1		16
119.30	even	12		833.2.o.d.557.1		32
119.47	odd	12		119.2.n.b.81.1	yes	32
119.81	even	12		833.2.o.d.30.8		32
119.115	odd	12		119.2.n.b.30.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.n.b.4.8	✓	32	7.5	odd	6
119.2.n.b.30.8	yes	32	119.115	odd	12
119.2.n.b.72.1	yes	32	7.3	odd	6
119.2.n.b.81.1	yes	32	119.47	odd	12
833.2.g.f.344.8		16	1.1	even	1	trivial
833.2.g.f.540.1		16	17.13	even	4	inner
833.2.g.g.344.8		16	7.6	odd	2
833.2.g.g.540.1		16	119.13	odd	4
833.2.o.d.30.8		32	119.81	even	12
833.2.o.d.361.8		32	7.2	even	3
833.2.o.d.557.1		32	119.30	even	12
833.2.o.d.667.1		32	7.4	even	3

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)

\(f(q)\)	\(=\)	\(q+2.46018i q^{2} +(-1.82950 + 1.82950i) q^{3} -4.05250 q^{4} +(-2.12385 + 2.12385i) q^{5} +(-4.50090 - 4.50090i) q^{6} -5.04951i q^{8} -3.69415i q^{9} +O(q^{10})\)	\(q+2.46018i q^{2} +(-1.82950 + 1.82950i) q^{3} -4.05250 q^{4} +(-2.12385 + 2.12385i) q^{5} +(-4.50090 - 4.50090i) q^{6} -5.04951i q^{8} -3.69415i q^{9} +(-5.22506 - 5.22506i) q^{10} +(0.0608963 + 0.0608963i) q^{11} +(7.41404 - 7.41404i) q^{12} -4.28579 q^{13} -7.77117i q^{15} +4.31773 q^{16} +(4.01303 + 0.946345i) q^{17} +9.08827 q^{18} +6.85431i q^{19} +(8.60689 - 8.60689i) q^{20} +(-0.149816 + 0.149816i) q^{22} +(-0.498840 - 0.498840i) q^{23} +(9.23809 + 9.23809i) q^{24} -4.02148i q^{25} -10.5438i q^{26} +(1.26994 + 1.26994i) q^{27} +(1.07782 - 1.07782i) q^{29} +19.1185 q^{30} +(0.571355 - 0.571355i) q^{31} +0.523372i q^{32} -0.222820 q^{33} +(-2.32818 + 9.87279i) q^{34} +14.9705i q^{36} +(-2.72027 + 2.72027i) q^{37} -16.8628 q^{38} +(7.84086 - 7.84086i) q^{39} +(10.7244 + 10.7244i) q^{40} +(-0.0255918 - 0.0255918i) q^{41} +8.49396i q^{43} +(-0.246782 - 0.246782i) q^{44} +(7.84581 + 7.84581i) q^{45} +(1.22724 - 1.22724i) q^{46} -9.76592 q^{47} +(-7.89929 + 7.89929i) q^{48} +9.89358 q^{50} +(-9.07318 + 5.61051i) q^{51} +17.3682 q^{52} +11.8406i q^{53} +(-3.12428 + 3.12428i) q^{54} -0.258669 q^{55} +(-12.5400 - 12.5400i) q^{57} +(2.65163 + 2.65163i) q^{58} -4.25843i q^{59} +31.4926i q^{60} +(-1.78521 - 1.78521i) q^{61} +(1.40564 + 1.40564i) q^{62} +7.34787 q^{64} +(9.10239 - 9.10239i) q^{65} -0.548177i q^{66} +4.92443 q^{67} +(-16.2628 - 3.83506i) q^{68} +1.82526 q^{69} +(4.95688 - 4.95688i) q^{71} -18.6536 q^{72} +(2.69644 - 2.69644i) q^{73} +(-6.69236 - 6.69236i) q^{74} +(7.35730 + 7.35730i) q^{75} -27.7770i q^{76} +(19.2900 + 19.2900i) q^{78} +(4.64414 + 4.64414i) q^{79} +(-9.17021 + 9.17021i) q^{80} +6.43573 q^{81} +(0.0629605 - 0.0629605i) q^{82} +3.86659i q^{83} +(-10.5330 + 6.51319i) q^{85} -20.8967 q^{86} +3.94373i q^{87} +(0.307497 - 0.307497i) q^{88} +5.04050 q^{89} +(-19.3021 + 19.3021i) q^{90} +(2.02155 + 2.02155i) q^{92} +2.09059i q^{93} -24.0259i q^{94} +(-14.5575 - 14.5575i) q^{95} +(-0.957509 - 0.957509i) q^{96} +(6.55546 - 6.55546i) q^{97} +(0.224960 - 0.224960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 8 q^{5} + 6 q^{6}+O(q^{10}) \) 16 * q - 16 * q^4 - 8 * q^5 + 6 * q^6	\( 16 q - 16 q^{4} - 8 q^{5} + 6 q^{6} - 6 q^{10} + 18 q^{11} + 26 q^{12} + 8 q^{16} + 10 q^{17} + 40 q^{18} + 12 q^{20} + 26 q^{22} + 12 q^{23} + 14 q^{24} - 30 q^{27} - 16 q^{29} + 44 q^{30} - 6 q^{31} - 8 q^{33} + 20 q^{34} + 2 q^{37} - 32 q^{38} - 14 q^{39} + 72 q^{40} - 2 q^{41} - 24 q^{44} - 4 q^{46} - 36 q^{47} - 36 q^{48} - 40 q^{50} + 20 q^{51} + 12 q^{52} - 18 q^{54} - 36 q^{55} - 24 q^{57} - 8 q^{58} - 52 q^{61} - 18 q^{62} + 12 q^{64} + 2 q^{65} + 28 q^{67} + 24 q^{68} + 4 q^{69} + 40 q^{71} - 36 q^{72} - 16 q^{73} - 60 q^{74} - 2 q^{75} + 32 q^{78} + 6 q^{79} + 30 q^{80} - 40 q^{82} + 34 q^{85} + 4 q^{86} - 30 q^{88} + 8 q^{89} + 10 q^{90} - 20 q^{92} + 12 q^{95} - 30 q^{96} + 38 q^{97} - 46 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 - 8 * q^5 + 6 * q^6 - 6 * q^10 + 18 * q^11 + 26 * q^12 + 8 * q^16 + 10 * q^17 + 40 * q^18 + 12 * q^20 + 26 * q^22 + 12 * q^23 + 14 * q^24 - 30 * q^27 - 16 * q^29 + 44 * q^30 - 6 * q^31 - 8 * q^33 + 20 * q^34 + 2 * q^37 - 32 * q^38 - 14 * q^39 + 72 * q^40 - 2 * q^41 - 24 * q^44 - 4 * q^46 - 36 * q^47 - 36 * q^48 - 40 * q^50 + 20 * q^51 + 12 * q^52 - 18 * q^54 - 36 * q^55 - 24 * q^57 - 8 * q^58 - 52 * q^61 - 18 * q^62 + 12 * q^64 + 2 * q^65 + 28 * q^67 + 24 * q^68 + 4 * q^69 + 40 * q^71 - 36 * q^72 - 16 * q^73 - 60 * q^74 - 2 * q^75 + 32 * q^78 + 6 * q^79 + 30 * q^80 - 40 * q^82 + 34 * q^85 + 4 * q^86 - 30 * q^88 + 8 * q^89 + 10 * q^90 - 20 * q^92 + 12 * q^95 - 30 * q^96 + 38 * q^97 - 46 * q^99

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