LMFDB - Embedded newform 819.2.do.e.361.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(361,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.do (of order $6$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.5
Root			$-1.38488 + 0.286553i$ of defining polynomial
Character	$\chi$	$=$	819.361
Dual form			819.2.do.e.667.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19430 + 0.689527i) q^{2} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(-2.25549 + 1.38302i) q^{7} -2.89354i q^{8} +O(q^{10})$	\(q+(1.19430 + 0.689527i) q^{2} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(-2.25549 + 1.38302i) q^{7} -2.89354i q^{8} -1.11145 q^{10} +5.27158i q^{11} +(-2.36581 + 2.72084i) q^{13} +(-3.64736 + 0.0965159i) q^{14} +(1.89697 - 3.28565i) q^{16} +(0.280051 + 0.485062i) q^{17} +5.84469i q^{19} +(0.0685460 + 0.0395750i) q^{20} +(-3.63490 + 6.29583i) q^{22} +(0.802438 - 1.38986i) q^{23} +(-2.17522 + 3.76760i) q^{25} +(-4.70157 + 1.61820i) q^{26} +(0.228379 + 0.123918i) q^{28} +(1.14008 + 1.97467i) q^{29} +(-3.01022 - 1.73795i) q^{31} +(-0.480674 + 0.277517i) q^{32} +0.772411i q^{34} +(1.01695 - 1.87422i) q^{35} +(1.07557 + 0.620979i) q^{37} +(-4.03007 + 6.98029i) q^{38} +(1.16602 + 2.01961i) q^{40} +(-0.803413 + 0.463851i) q^{41} +(2.22356 - 3.85131i) q^{43} +(0.448348 - 0.258854i) q^{44} +(1.91670 - 1.10661i) q^{46} +(-3.32915 + 1.92209i) q^{47} +(3.17449 - 6.23880i) q^{49} +(-5.19572 + 2.99975i) q^{50} +(0.347577 + 0.0676087i) q^{52} +(2.72727 - 4.72377i) q^{53} +(-2.12431 - 3.67941i) q^{55} +(4.00184 + 6.52637i) q^{56} +3.14446i q^{58} +(-9.52106 + 5.49698i) q^{59} +7.30215 q^{61} +(-2.39673 - 4.15126i) q^{62} -8.35330 q^{64} +(0.554837 - 2.85243i) q^{65} -7.34556i q^{67} +(0.0275031 - 0.0476367i) q^{68} +(2.50686 - 1.53716i) q^{70} +(8.06668 + 4.65730i) q^{71} +(-4.33139 - 2.50073i) q^{73} +(0.856364 + 1.48327i) q^{74} +(0.497091 - 0.286996i) q^{76} +(-7.29072 - 11.8900i) q^{77} +(-5.68437 - 9.84562i) q^{79} +3.05772i q^{80} -1.27935 q^{82} +5.81962i q^{83} +(-0.390935 - 0.225707i) q^{85} +(5.31117 - 3.06641i) q^{86} +15.2535 q^{88} +(-4.33832 - 2.50473i) q^{89} +(1.57307 - 9.40880i) q^{91} -0.157611 q^{92} -5.30133 q^{94} +(-2.35526 - 4.07942i) q^{95} +(9.22171 + 5.32416i) q^{97} +(8.09311 - 5.26207i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	$ 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.19430	+	0.689527i	0.844495	+	0.487570i	0.858790	−	0.512328i	$-0.171217\pi$
$2$	1.19430	+	0.689527i	0.844495	+	0.487570i	−0.0142944	+	0.999898i	$0.504550\pi$
$3$		0			0
$3$		0			0
$4$	−0.0491037	−	0.0850501i	−0.0245518	−	0.0425250i
$5$	−0.697972	+	0.402974i	−0.312142	+	0.180216i	−0.647885	−	0.761738i	$-0.724346\pi$
$5$	−0.697972	+	0.402974i	−0.312142	+	0.180216i	0.335742	+	0.941954i	$0.391013\pi$
$6$		0			0
$7$	−2.25549	+	1.38302i	−0.852496	+	0.522734i
$7$	−2.25549	+	1.38302i	−0.852496	+	0.522734i
$8$		−	2.89354i		−	1.02302i
$9$		0			0
$10$	−1.11145			−0.351470
$11$			5.27158i			1.58944i	0.606976	+	0.794720i	$0.292382\pi$
$11$			5.27158i			1.58944i	−0.606976	+	0.794720i	$0.707618\pi$
$12$		0			0
$13$	−2.36581	+	2.72084i	−0.656156	+	0.754625i
$13$	−2.36581	+	2.72084i	−0.656156	+	0.754625i
$14$	−3.64736	+	0.0965159i	−0.974798	+	0.0257950i
$15$		0			0
$16$	1.89697	−	3.28565i	0.474243	−	0.821412i
$17$	0.280051	+	0.485062i	0.0679223	+	0.117645i	0.897987	−	0.440023i	$-0.145030\pi$
$17$	0.280051	+	0.485062i	0.0679223	+	0.117645i	−0.830064	+	0.557668i	$0.811696\pi$
$18$		0			0
$19$			5.84469i			1.34086i	0.741972	+	0.670431i	$0.233891\pi$
$19$			5.84469i			1.34086i	−0.741972	+	0.670431i	$0.766109\pi$
$20$	0.0685460	+	0.0395750i	0.0153273	+	0.00884925i
$21$		0			0
$22$	−3.63490	+	6.29583i	−0.774963	+	1.34228i
$23$	0.802438	−	1.38986i	0.167320	−	0.289807i	−0.770157	−	0.637855i	$-0.779822\pi$
$23$	0.802438	−	1.38986i	0.167320	−	0.289807i	0.937477	+	0.348048i	$0.113155\pi$
$24$		0			0
$25$	−2.17522	+	3.76760i	−0.435045	+	0.753520i
$26$	−4.70157	+	1.61820i	−0.922053	+	0.317355i
$27$		0			0
$28$	0.228379	+	0.123918i	0.0431596	+	0.0234184i
$29$	1.14008	+	1.97467i	0.211707	+	0.366687i	0.952249	−	0.305323i	$-0.0987644\pi$
$29$	1.14008	+	1.97467i	0.211707	+	0.366687i	−0.740542	+	0.672010i	$0.765431\pi$
$30$		0			0
$31$	−3.01022	−	1.73795i	−0.540651	−	0.312145i	0.204692	−	0.978827i	$-0.434381\pi$
$31$	−3.01022	−	1.73795i	−0.540651	−	0.312145i	−0.745343	+	0.666681i	$0.767714\pi$
$32$	−0.480674	+	0.277517i	−0.0849719	+	0.0490585i
$33$		0			0
$34$			0.772411i			0.132467i
$35$	1.01695	−	1.87422i	0.171895	−	0.316800i
$36$		0			0
$37$	1.07557	+	0.620979i	0.176822	+	0.102088i	0.585799	−	0.810457i	$-0.300781\pi$
$37$	1.07557	+	0.620979i	0.176822	+	0.102088i	−0.408977	+	0.912545i	$0.634114\pi$
$38$	−4.03007	+	6.98029i	−0.653764	+	1.13235i
$39$		0			0
$40$	1.16602	+	2.01961i	0.184364	+	0.319329i
$41$	−0.803413	+	0.463851i	−0.125472	+	0.0724413i	−0.561422	−	0.827529i	$-0.689746\pi$
$41$	−0.803413	+	0.463851i	−0.125472	+	0.0724413i	0.435950	+	0.899971i	$0.356412\pi$
$42$		0			0
$43$	2.22356	−	3.85131i	0.339089	−	0.587320i	−0.645172	−	0.764037i	$-0.723214\pi$
$43$	2.22356	−	3.85131i	0.339089	−	0.587320i	0.984262	+	0.176717i	$0.0565478\pi$
$44$	0.448348	−	0.258854i	0.0675910	−	0.0390237i
$45$		0			0
$46$	1.91670	−	1.10661i	0.282602	−	0.163160i
$47$	−3.32915	+	1.92209i	−0.485607	+	0.280365i	−0.722750	−	0.691109i	$-0.757122\pi$
$47$	−3.32915	+	1.92209i	−0.485607	+	0.280365i	0.237143	+	0.971475i	$0.423789\pi$
$48$		0			0
$49$	3.17449	−	6.23880i	0.453499	−	0.891257i
$50$	−5.19572	+	2.99975i	−0.734786	+	0.424229i
$51$		0			0
$52$	0.347577	+	0.0676087i	0.0482003	+	0.00937564i
$53$	2.72727	−	4.72377i	0.374620	−	0.648860i	−0.615650	−	0.788019i	$-0.711107\pi$
$53$	2.72727	−	4.72377i	0.374620	−	0.648860i	0.990270	+	0.139159i	$0.0444400\pi$
$54$		0			0
$55$	−2.12431	−	3.67941i	−0.286442	−	0.496132i
$56$	4.00184	+	6.52637i	0.534768	+	0.872122i
$57$		0			0
$58$			3.14446i			0.412887i
$59$	−9.52106	+	5.49698i	−1.23954	+	0.715646i	−0.968999	−	0.247063i	$-0.920534\pi$
$59$	−9.52106	+	5.49698i	−1.23954	+	0.715646i	−0.270537	+	0.962710i	$0.587201\pi$
$60$		0			0
$61$	7.30215			0.934944			0.467472	−	0.884008i	$-0.345165\pi$
$61$	7.30215			0.934944			0.467472	+	0.884008i	$0.345165\pi$
$62$	−2.39673	−	4.15126i	−0.304385	−	0.527210i
$63$		0			0
$64$	−8.35330			−1.04416
$65$	0.554837	−	2.85243i	0.0688191	−	0.353800i
$66$		0			0
$67$		−	7.34556i		−	0.897403i	−0.893682	−	0.448701i	$-0.851887\pi$
$67$		−	7.34556i		−	0.897403i	0.893682	−	0.448701i	$-0.148113\pi$
$68$	0.0275031	−	0.0476367i	0.00333524	−	0.00577680i
$69$		0			0
$70$	2.50686	−	1.53716i	0.299627	−	0.183725i
$71$	8.06668	+	4.65730i	0.957339	+	0.552720i	0.895353	−	0.445357i	$-0.146923\pi$
$71$	8.06668	+	4.65730i	0.957339	+	0.552720i	0.0619857	+	0.998077i	$0.480257\pi$
$72$		0			0
$73$	−4.33139	−	2.50073i	−0.506951	−	0.292688i	0.224629	−	0.974444i	$-0.427883\pi$
$73$	−4.33139	−	2.50073i	−0.506951	−	0.292688i	−0.731579	+	0.681756i	$0.761216\pi$
$74$	0.856364	+	1.48327i	0.0995503	+	0.172426i
$75$		0			0
$76$	0.497091	−	0.286996i	0.0570202	−	0.0329207i
$77$	−7.29072	−	11.8900i	−0.830854	−	1.35499i
$78$		0			0
$79$	−5.68437	−	9.84562i	−0.639542	−	1.10772i	−0.985533	−	0.169481i	$-0.945791\pi$
$79$	−5.68437	−	9.84562i	−0.639542	−	1.10772i	0.345992	−	0.938238i	$-0.387543\pi$
$80$			3.05772i			0.341863i
$81$		0			0
$82$	−1.27935			−0.141281
$83$			5.81962i			0.638786i	0.947622	+	0.319393i	$0.103479\pi$
$83$			5.81962i			0.638786i	−0.947622	+	0.319393i	$0.896521\pi$
$84$		0			0
$85$	−0.390935	−	0.225707i	−0.0424029	−	0.0244813i
$86$	5.31117	−	3.06641i	0.572719	−	0.330659i
$87$		0			0
$88$	15.2535			1.62603
$89$	−4.33832	−	2.50473i	−0.459861	−	0.265501i	0.252125	−	0.967695i	$-0.418871\pi$
$89$	−4.33832	−	2.50473i	−0.459861	−	0.265501i	−0.711986	+	0.702194i	$0.752204\pi$
$90$		0			0
$91$	1.57307	−	9.40880i	0.164903	−	0.986310i
$92$	−0.157611			−0.0164320
$93$		0			0
$94$	−5.30133			−0.546791
$95$	−2.35526	−	4.07942i	−0.241644	−	0.418540i
$96$		0			0
$97$	9.22171	+	5.32416i	0.936323	+	0.540586i	0.888806	−	0.458284i	$-0.151536\pi$
$97$	9.22171	+	5.32416i	0.936323	+	0.540586i	0.0475172	+	0.998870i	$0.484869\pi$
$98$	8.09311	−	5.26207i	0.817527	−	0.531550i
$99$		0			0
$100$	0.427246			0.0427246
$101$	3.91554			0.389611			0.194805	−	0.980842i	$-0.437592\pi$
$101$	3.91554			0.389611			0.194805	+	0.980842i	$0.437592\pi$
$102$		0			0
$103$	4.22690	+	7.32120i	0.416488	+	0.721379i	0.995583	−	0.0938810i	$-0.0299273\pi$
$103$	4.22690	+	7.32120i	0.416488	+	0.721379i	−0.579095	+	0.815260i	$0.696594\pi$
$104$	7.87287	+	6.84556i	0.771998	+	0.671262i
$105$		0			0
$106$	6.51434	−	3.76106i	0.632729	−	0.365306i
$107$	−4.83761	+	8.37899i	−0.467670	+	0.810028i	−0.999318	−	0.0369379i	$-0.988240\pi$
$107$	−4.83761	+	8.37899i	−0.467670	+	0.810028i	0.531648	+	0.846965i	$0.321573\pi$
$108$		0			0
$109$	12.6126	+	7.28189i	1.20807	+	0.697478i	0.962337	−	0.271860i	$-0.0876388\pi$
$109$	12.6126	+	7.28189i	1.20807	+	0.697478i	0.245731	+	0.969338i	$0.420972\pi$
$110$		−	5.85908i		−	0.558641i
$111$		0			0
$112$	0.265526	+	10.0343i	0.0250899	+	0.948153i
$113$	9.75572	−	16.8974i	0.917741	−	1.58957i	0.114903	−	0.993377i	$-0.463344\pi$
$113$	9.75572	−	16.8974i	0.917741	−	1.58957i	0.802838	−	0.596197i	$-0.203322\pi$
$114$		0			0
$115$			1.29345i			0.120615i
$116$	0.111964	−	0.193927i	0.0103956	−	0.0180057i
$117$		0			0
$118$	−15.1613			−1.39571
$119$	−1.30251	−	0.706738i	−0.119400	−	0.0647865i
$120$		0			0
$121$	−16.7895			−1.52632
$122$	8.72093	+	5.03503i	0.789556	+	0.455850i
$123$		0			0
$124$			0.341359i			0.0306550i
$125$		−	7.53598i		−	0.674038i
$126$		0			0
$127$	−0.958656	−	1.66044i	−0.0850670	−	0.147340i	0.820353	−	0.571858i	$-0.193777\pi$
$127$	−0.958656	−	1.66044i	−0.0850670	−	0.147340i	−0.905420	+	0.424517i	$0.860444\pi$
$128$	−9.01498	−	5.20480i	−0.796819	−	0.460044i
$129$		0			0
$130$	2.62947	−	3.02407i	0.230619	−	0.265228i
$131$	7.79078	+	13.4940i	0.680684	+	1.17898i	0.974772	+	0.223201i	$0.0716506\pi$
$131$	7.79078	+	13.4940i	0.680684	+	1.17898i	−0.294089	+	0.955778i	$0.595016\pi$
$132$		0			0
$133$	−8.08334	−	13.1826i	−0.700914	−	1.14308i
$134$	5.06496	−	8.77278i	0.437546	−	0.757852i
$135$		0			0
$136$	1.40355	−	0.810339i	0.120353	−	0.0694860i
$137$	−6.79921	+	3.92553i	−0.580896	+	0.335380i	−0.761489	−	0.648178i	$-0.775531\pi$
$137$	−6.79921	+	3.92553i	−0.580896	+	0.335380i	0.180594	+	0.983558i	$0.442198\pi$
$138$		0			0
$139$	−4.96241	+	8.59514i	−0.420906	+	0.729030i	−0.996028	−	0.0890370i	$-0.971621\pi$
$139$	−4.96241	+	8.59514i	−0.420906	+	0.729030i	0.575122	+	0.818067i	$0.304954\pi$
$140$	−0.209338	+	0.00553947i	−0.0176923	+	0.000468171i
$141$		0			0
$142$	6.42267	+	11.1244i	0.538979	+	0.933538i
$143$	−14.3431	−	12.4715i	−1.19943	−	1.04292i
$144$		0			0
$145$	−1.59148	−	0.918843i	−0.132165	−	0.0763058i
$146$	−3.44864	−	5.97322i	−0.285412	−	0.494347i
$147$		0			0
$148$		−	0.121969i		−	0.0100258i
$149$		−	7.91925i		−	0.648770i	−0.945925	−	0.324385i	$-0.894843\pi$
$149$		−	7.91925i		−	0.648770i	0.945925	−	0.324385i	$-0.105157\pi$
$150$		0			0
$151$	−1.30005	−	0.750582i	−0.105796	−	0.0610815i	0.446168	−	0.894949i	$-0.352788\pi$
$151$	−1.30005	−	0.750582i	−0.105796	−	0.0610815i	−0.551965	+	0.833868i	$0.686122\pi$
$152$	16.9118			1.37173
$153$		0			0
$154$	−0.508791	−	19.2273i	−0.0409996	−	1.54938i
$155$	2.80140			0.225014
$156$		0			0
$157$	−1.92846	+	3.34019i	−0.153908	+	0.266576i	−0.932661	−	0.360754i	$-0.882519\pi$
$157$	−1.92846	+	3.34019i	−0.153908	+	0.266576i	0.778753	+	0.627331i	$0.215853\pi$
$158$		−	15.6781i		−	1.24728i
$159$		0			0
$160$	0.223664	−	0.387398i	0.0176822	−	0.0306265i
$161$	0.112320	+	4.24462i	0.00885209	+	0.334523i
$162$		0			0
$163$			14.3608i			1.12483i	0.826856	+	0.562414i	$0.190127\pi$
$163$			14.3608i			1.12483i	−0.826856	+	0.562414i	$0.809873\pi$
$164$	0.0789011	+	0.0455536i	0.00616114	+	0.00355714i
$165$		0			0
$166$	−4.01279	+	6.95035i	−0.311453	+	0.539452i
$167$	3.91563	−	2.26069i	0.303000	−	0.174937i	−0.340790	−	0.940140i	$-0.610694\pi$
$167$	3.91563	−	2.26069i	0.303000	−	0.174937i	0.643790	+	0.765202i	$0.277361\pi$
$168$		0			0
$169$	−1.80593	−	12.8740i	−0.138918	−	0.990304i
$170$	−0.311262	−	0.539121i	−0.0238727	−	0.0413487i
$171$		0			0
$172$	−0.436739			−0.0333011
$173$	−19.5179			−1.48392			−0.741960	−	0.670444i	$-0.766104\pi$
$173$	−19.5179			−1.48392			−0.741960	+	0.670444i	$0.766104\pi$
$174$		0			0
$175$	−0.304475	−	11.5062i	−0.0230161	−	0.869785i
$176$	17.3206	+	10.0000i	1.30559	+	0.753780i
$177$		0			0
$178$	−3.45416	−	5.98278i	−0.258900	−	0.448428i
$179$	20.8196			1.55613			0.778065	−	0.628183i	$-0.216201\pi$
$179$	20.8196			1.55613			0.778065	+	0.628183i	$0.216201\pi$
$180$		0			0
$181$	16.5522			1.23031			0.615157	−	0.788405i	$-0.289093\pi$
$181$	16.5522			1.23031			0.615157	+	0.788405i	$0.289093\pi$
$182$	8.36634	−	10.1522i	0.620154	−	0.752532i
$183$		0			0
$184$	−4.02163	−	2.32189i	−0.296478	−	0.171172i
$185$	−1.00095			−0.0735916
$186$		0			0
$187$	−2.55704	+	1.47631i	−0.186990	+	0.107958i
$188$	0.326948	+	0.188763i	0.0238451	+	0.0137670i
$189$		0			0
$190$		−	6.49606i		−	0.471274i
$191$	4.25008			0.307525			0.153762	−	0.988108i	$-0.450861\pi$
$191$	4.25008			0.307525			0.153762	+	0.988108i	$0.450861\pi$
$192$		0			0
$193$			11.5972i			0.834787i	0.908726	+	0.417393i	$0.137056\pi$
$193$			11.5972i			0.834787i	−0.908726	+	0.417393i	$0.862944\pi$
$194$	7.34231	+	12.7172i	0.527147	+	0.913045i
$195$		0			0
$196$	−0.686490	+	0.0363570i	−0.0490350	+	0.00259693i
$197$	12.4892	−	7.21066i	0.889821	−	0.513738i	0.0159371	−	0.999873i	$-0.494927\pi$
$197$	12.4892	−	7.21066i	0.889821	−	0.513738i	0.873884	+	0.486135i	$0.161594\pi$
$198$		0			0
$199$	3.52962	+	6.11348i	0.250208	+	0.433373i	0.963583	−	0.267409i	$-0.0861676\pi$
$199$	3.52962	+	6.11348i	0.250208	+	0.433373i	−0.713375	+	0.700783i	$0.752834\pi$
$200$	10.9017	+	6.29410i	0.770867	+	0.445060i
$201$		0			0
$202$	4.67632	+	2.69987i	0.329024	+	0.189962i
$203$	−5.30245	−	2.87710i	−0.372159	−	0.201933i
$204$		0			0
$205$	0.373840	−	0.647509i	0.0261101	−	0.0452240i
$206$			11.6582i			0.812268i
$207$		0			0
$208$	4.45186	+	12.9346i	0.308681	+	0.896850i
$209$	−30.8107			−2.13122
$210$		0			0
$211$	13.2113	+	22.8827i	0.909505	+	1.57531i	0.814754	+	0.579807i	$0.196872\pi$
$211$	13.2113	+	22.8827i	0.909505	+	1.57531i	0.0947513	+	0.995501i	$0.469794\pi$
$212$	−0.535677			−0.0367904
$213$		0			0
$214$	−11.5551	+	6.67133i	−0.789890	+	0.456043i
$215$			3.58414i			0.244437i
$216$		0			0
$217$	9.19315	−	0.243268i	0.624072	−	0.0165141i
$218$	10.0421	+	17.3935i	0.680138	+	1.17803i
$219$		0			0
$220$	−0.208623	+	0.361345i	−0.0140654	+	0.0243619i
$221$	−1.98232	−	0.385590i	−0.133345	−	0.0259376i
$222$		0			0
$223$	19.9191	−	11.5003i	1.33388	−	0.770115i	0.347987	−	0.937499i	$-0.386865\pi$
$223$	19.9191	−	11.5003i	1.33388	−	0.770115i	0.985892	+	0.167384i	$0.0535321\pi$
$224$	0.700343	−	1.29072i	0.0467937	−	0.0862399i
$225$		0			0
$226$	23.3024	−	13.4537i	1.55006	−	0.894925i
$227$	0.392628	−	0.226684i	0.0260596	−	0.0150455i	−0.486914	−	0.873450i	$-0.661877\pi$
$227$	0.392628	−	0.226684i	0.0260596	−	0.0150455i	0.512973	+	0.858405i	$0.328544\pi$
$228$		0			0
$229$	−15.0112	+	8.66674i	−0.991970	+	0.572714i	−0.905863	−	0.423571i	$-0.860776\pi$
$229$	−15.0112	+	8.66674i	−0.991970	+	0.572714i	−0.0861077	+	0.996286i	$0.527443\pi$
$230$	−0.891867	+	1.54476i	−0.0588080	+	0.101858i
$231$		0			0
$232$	5.71380	−	3.29886i	0.375129	−	0.216581i
$233$	−3.90756	−	6.76809i	−0.255992	−	0.443392i	0.709172	−	0.705035i	$-0.249069\pi$
$233$	−3.90756	−	6.76809i	−0.255992	−	0.443392i	−0.965165	+	0.261643i	$0.915736\pi$
$234$		0			0
$235$	1.54910	−	2.68313i	0.101052	−	0.175028i
$236$	0.935038	+	0.539844i	0.0608658	+	0.0351409i
$237$		0			0
$238$	−1.06826	−	1.74217i	−0.0692452	−	0.112928i
$239$			13.5314i			0.875276i	0.899151	+	0.437638i	$0.144185\pi$
$239$			13.5314i			0.875276i	−0.899151	+	0.437638i	$0.855815\pi$
$240$		0			0
$241$	−19.5369	+	11.2796i	−1.25848	+	0.726583i	−0.972779	−	0.231736i	$-0.925560\pi$
$241$	−19.5369	+	11.2796i	−1.25848	+	0.726583i	−0.285701	+	0.958319i	$0.592226\pi$
$242$	−20.0517	−	11.5768i	−1.28897	−	0.744188i
$243$		0			0
$244$	−0.358563	−	0.621049i	−0.0229546	−	0.0397586i
$245$	0.298367	+	5.63374i	0.0190620	+	0.359927i
$246$		0			0
$247$	−15.9024	−	13.8274i	−1.01185	−	0.879815i
$248$	−5.02884	+	8.71020i	−0.319331	+	0.553098i
$249$		0			0
$250$	5.19626	−	9.00019i	0.328641	−	0.569222i
$251$	3.36618	−	5.83039i	0.212471	−	0.368011i	−0.740016	−	0.672589i	$-0.765182\pi$
$251$	3.36618	−	5.83039i	0.212471	−	0.368011i	0.952487	+	0.304578i	$0.0985154\pi$
$252$		0			0
$253$	7.32677	+	4.23011i	0.460630	+	0.265945i
$254$		−	2.64408i		−	0.165904i
$255$		0			0
$256$	1.17560	+	2.03620i	0.0734750	+	0.127262i
$257$	−8.26907	+	14.3225i	−0.515811	+	0.893410i	0.484021	+	0.875056i	$0.339176\pi$
$257$	−8.26907	+	14.3225i	−0.515811	+	0.893410i	−0.999832	+	0.0183536i	$0.994158\pi$
$258$		0			0
$259$	−3.28476	+	0.0869209i	−0.204105	+	0.00540100i
$260$	−0.269844	+	0.0928757i	−0.0167350	+	0.00575991i
$261$		0			0
$262$			21.4878i			1.32752i
$263$	10.0227			0.618028			0.309014	−	0.951057i	$-0.400001\pi$
$263$	10.0227			0.618028			0.309014	+	0.951057i	$0.400001\pi$
$264$		0			0
$265$			4.39608i			0.270049i
$266$	−0.564105	−	21.3177i	−0.0345875	−	1.30707i
$267$		0			0
$268$	−0.624740	+	0.360694i	−0.0381621	+	0.0220329i
$269$	−7.86149	−	13.6165i	−0.479323	−	0.830212i	0.520395	−	0.853925i	$-0.325785\pi$
$269$	−7.86149	−	13.6165i	−0.479323	−	0.830212i	−0.999719	+	0.0237130i	$0.992451\pi$
$270$		0			0
$271$	−4.51734	−	2.60809i	−0.274409	−	0.158430i	0.356481	−	0.934303i	$-0.383977\pi$
$271$	−4.51734	−	2.60809i	−0.274409	−	0.158430i	−0.630890	+	0.775873i	$0.717310\pi$
$272$	2.12499			0.128847
$273$		0			0
$274$	−10.8270			−0.654085
$275$	−19.8612	−	11.4669i	−1.19767	−	0.691478i
$276$		0			0
$277$	−9.63619	−	16.6904i	−0.578983	−	1.00283i	−0.995596	−	0.0937439i	$-0.970117\pi$
$277$	−9.63619	−	16.6904i	−0.578983	−	1.00283i	0.416614	−	0.909084i	$-0.363217\pi$
$278$	−11.8532	+	6.84343i	−0.710906	+	0.410442i
$279$		0			0
$280$	−5.42313	−	2.94258i	−0.324094	−	0.175853i
$281$			2.14283i			0.127831i	0.997955	+	0.0639153i	$0.0203588\pi$
$281$			2.14283i			0.127831i	−0.997955	+	0.0639153i	$0.979641\pi$
$282$		0			0
$283$	15.7502			0.936255			0.468127	−	0.883661i	$-0.344929\pi$
$283$	15.7502			0.936255			0.468127	+	0.883661i	$0.344929\pi$
$284$		−	0.914762i		−	0.0542812i
$285$		0			0
$286$	−8.53048	−	24.7847i	−0.504418	−	1.46555i
$287$	1.17058	−	2.15735i	0.0690969	−	0.127344i
$288$		0			0
$289$	8.34314	−	14.4507i	0.490773	−	0.850044i
$290$	−1.26714	−	2.19474i	−0.0744087	−	0.128880i
$291$		0			0
$292$			0.491180i			0.0287441i
$293$	20.0474	+	11.5744i	1.17118	+	0.676182i	0.953958	−	0.299940i	$-0.0969668\pi$
$293$	20.0474	+	11.5744i	1.17118	+	0.676182i	0.217223	+	0.976122i	$0.430300\pi$
$294$		0			0
$295$	4.43029	−	7.67348i	0.257941	−	0.446767i
$296$	1.79683	−	3.11220i	0.104439	−	0.180893i
$297$		0			0
$298$	5.46054	−	9.45793i	0.316320	−	0.547883i
$299$	1.88318	+	5.47145i	0.108907	+	0.316422i
$300$		0			0
$301$	0.311240	+	11.7618i	0.0179396	+	0.677941i
$302$	−1.03509	−	1.79283i	−0.0595629	−	0.103166i
$303$		0			0
$304$	19.2036	+	11.0872i	1.10140	+	0.635894i
$305$	−5.09669	+	2.94258i	−0.291836	+	0.168491i
$306$		0			0
$307$			4.23590i			0.241756i	0.992667	+	0.120878i	$0.0385709\pi$
$307$			4.23590i			0.241756i	−0.992667	+	0.120878i	$0.961429\pi$
$308$	−0.653245	+	1.20392i	−0.0372221	+	0.0685997i
$309$		0			0
$310$	3.34570	+	1.93164i	0.190023	+	0.109710i
$311$	−13.6251	+	23.5993i	−0.772606	+	1.33819i	0.163524	+	0.986539i	$0.447714\pi$
$311$	−13.6251	+	23.5993i	−0.772606	+	1.33819i	−0.936130	+	0.351654i	$0.885619\pi$
$312$		0			0
$313$	−1.34849	−	2.33565i	−0.0762209	−	0.132018i	0.825396	−	0.564555i	$-0.190952\pi$
$313$	−1.34849	−	2.33565i	−0.0762209	−	0.132018i	−0.901617	+	0.432536i	$0.857619\pi$
$314$	−4.60631	+	2.65945i	−0.259949	+	0.150082i
$315$		0			0
$316$	−0.558247	+	0.966913i	−0.0314039	+	0.0543931i
$317$	20.8456	−	12.0352i	1.17081	−	0.675966i	0.216937	−	0.976186i	$-0.430393\pi$
$317$	20.8456	−	12.0352i	1.17081	−	0.675966i	0.953870	+	0.300220i	$0.0970600\pi$
$318$		0			0
$319$	−10.4096	+	6.01000i	−0.582828	+	0.336496i
$320$	5.83037	−	3.36617i	0.325928	−	0.188174i
$321$		0			0
$322$	−2.79264	+	5.14678i	−0.155628	+	0.286819i
$323$	−2.83504	+	1.63681i	−0.157746	+	0.0910745i
$324$		0			0
$325$	−5.10487	−	14.8318i	−0.283167	−	0.822722i
$326$	−9.90220	+	17.1511i	−0.548432	+	0.949912i
$327$		0			0
$328$	1.34217	+	2.32471i	0.0741091	+	0.128361i
$329$	4.85059	−	8.93955i	0.267422	−	0.492854i
$330$		0			0
$331$			0.619723i			0.0340631i	0.999855	+	0.0170315i	$0.00542157\pi$
$331$			0.619723i			0.0340631i	−0.999855	+	0.0170315i	$0.994578\pi$
$332$	0.494959	−	0.285765i	0.0271644	−	0.0156834i
$333$		0			0
$334$	6.23523			0.341177
$335$	2.96007	+	5.12699i	0.161726	+	0.280117i
$336$		0			0
$337$	−5.72118			−0.311652			−0.155826	−	0.987784i	$-0.549804\pi$
$337$	−5.72118			−0.311652			−0.155826	+	0.987784i	$0.549804\pi$
$338$	6.72012	−	16.6206i	0.365527	−	0.904039i
$339$		0			0
$340$			0.0443321i			0.00240425i
$341$	9.16174	−	15.8686i	0.496136	−	0.859333i
$342$		0			0
$343$	1.46836	+	18.4620i	0.0792837	+	0.996852i
$344$	−11.1439	−	6.43396i	−0.600841	−	0.346896i
$345$		0			0
$346$	−23.3102	−	13.4581i	−1.25316	−	0.723514i
$347$	−0.932429	−	1.61501i	−0.0500554	−	0.0866985i	0.839912	−	0.542722i	$-0.182606\pi$
$347$	−0.932429	−	1.61501i	−0.0500554	−	0.0866985i	−0.889968	+	0.456024i	$0.849273\pi$
$348$		0			0
$349$	−19.3273	+	11.1586i	−1.03457	+	0.597307i	−0.918290	−	0.395909i	$-0.870429\pi$
$349$	−19.3273	+	11.1586i	−1.03457	+	0.597307i	−0.116277	+	0.993217i	$0.537096\pi$
$350$	7.57019	−	13.9517i	0.404644	−	0.745751i
$351$		0			0
$352$	−1.46295	−	2.53391i	−0.0779756	−	0.135058i
$353$			2.33199i			0.124119i	0.998072	+	0.0620597i	$0.0197669\pi$
$353$			2.33199i			0.124119i	−0.998072	+	0.0620597i	$0.980233\pi$
$354$		0			0
$355$	−7.50708			−0.398435
$356$			0.491966i			0.0260741i
$357$		0			0
$358$	24.8648	+	14.3557i	1.31415	+	0.758722i
$359$	−2.83281	+	1.63553i	−0.149510	+	0.0863197i	−0.572889	−	0.819633i	$-0.694177\pi$
$359$	−2.83281	+	1.63553i	−0.149510	+	0.0863197i	0.423379	+	0.905953i	$0.360844\pi$
$360$		0			0
$361$	−15.1603			−0.797913
$362$	19.7682	+	11.4132i	1.03899	+	0.599863i
$363$		0			0
$364$	−0.877463	+	0.328217i	−0.0459915	+	0.0172032i
$365$	4.03092			0.210988
$366$		0			0
$367$	4.15290			0.216780			0.108390	−	0.994108i	$-0.465431\pi$
$367$	4.15290			0.216780			0.108390	+	0.994108i	$0.465431\pi$
$368$	−3.04440	−	5.27306i	−0.158700	−	0.274877i
$369$		0			0
$370$	−1.19544	−	0.690185i	−0.0621477	−	0.0358810i
$371$	0.381747	+	14.4263i	0.0198193	+	0.748977i
$372$		0			0
$373$	−11.1089			−0.575198			−0.287599	−	0.957751i	$-0.592857\pi$
$373$	−11.1089			−0.575198			−0.287599	+	0.957751i	$0.592857\pi$
$374$	−4.07183			−0.210549
$375$		0			0
$376$	5.56165	+	9.63305i	0.286820	+	0.496787i
$377$	−8.06996	−	1.56972i	−0.415624	−	0.0808447i
$378$		0			0
$379$	−4.01862	+	2.32015i	−0.206422	+	0.119178i	−0.599648	−	0.800264i	$-0.704693\pi$
$379$	−4.01862	+	2.32015i	−0.206422	+	0.119178i	0.393225	+	0.919442i	$0.371359\pi$
$380$	−0.231304	+	0.400630i	−0.0118656	+	0.0205519i
$381$		0			0
$382$	5.07586	+	2.93055i	0.259703	+	0.149940i
$383$			3.66933i			0.187494i	0.995596	+	0.0937469i	$0.0298845\pi$
$383$			3.66933i			0.187494i	−0.995596	+	0.0937469i	$0.970116\pi$
$384$		0			0
$385$	9.88008	+	5.36092i	0.503535	+	0.273218i
$386$	−7.99661	+	13.8505i	−0.407017	+	0.704973i
$387$		0			0
$388$		−	1.04574i		−	0.0530896i
$389$	−8.44156	+	14.6212i	−0.428004	+	0.741324i	−0.996696	−	0.0812262i	$-0.974116\pi$
$389$	−8.44156	+	14.6212i	−0.428004	+	0.741324i	0.568692	+	0.822551i	$0.307450\pi$
$390$		0			0
$391$	0.898894			0.0454590
$392$	−18.0522	−	9.18553i	−0.911775	−	0.463940i
$393$		0			0
$394$	19.8878			1.00193
$395$	7.93506	+	4.58131i	0.399256	+	0.230511i
$396$		0			0
$397$		−	16.7086i		−	0.838578i	−0.907853	−	0.419289i	$-0.862279\pi$
$397$		−	16.7086i		−	0.838578i	0.907853	−	0.419289i	$-0.137721\pi$
$398$			9.73508i			0.487976i
$399$		0			0
$400$	8.25267	+	14.2940i	0.412633	+	0.714702i
$401$	−21.9221	−	12.6567i	−1.09474	−	0.632046i	−0.159902	−	0.987133i	$-0.551118\pi$
$401$	−21.9221	−	12.6567i	−1.09474	−	0.632046i	−0.934833	+	0.355087i	$0.884451\pi$
$402$		0			0
$403$	11.8503	−	4.07867i	0.590304	−	0.203173i
$404$	−0.192267	−	0.333017i	−0.00956566	−	0.0165682i
$405$		0			0
$406$	−4.34886	−	7.09230i	−0.215830	−	0.351985i
$407$	−3.27354	+	5.66994i	−0.162263	+	0.281048i
$408$		0			0
$409$	4.96529	−	2.86671i	0.245518	−	0.141750i	−0.372192	−	0.928156i	$-0.621394\pi$
$409$	4.96529	−	2.86671i	0.245518	−	0.141750i	0.617710	+	0.786406i	$0.288060\pi$
$410$	0.892951	−	0.515546i	0.0440997	−	0.0254610i
$411$		0			0
$412$	0.415112	−	0.718996i	0.0204511	−	0.0354224i
$413$	13.8722	−	25.5663i	0.682607	−	1.25803i
$414$		0			0
$415$	−2.34516	−	4.06193i	−0.115119	−	0.199392i
$416$	0.382101	−	1.96439i	0.0187340	−	0.0963120i
$417$		0			0
$418$	−36.7971	−	21.2448i	−1.79981	−	1.03912i
$419$	−17.1729	−	29.7443i	−0.838950	−	1.45310i	−0.890773	−	0.454448i	$-0.849836\pi$
$419$	−17.1729	−	29.7443i	−0.838950	−	1.45310i	0.0518229	−	0.998656i	$-0.483497\pi$
$420$		0			0
$421$		−	2.94167i		−	0.143368i	−0.997427	−	0.0716842i	$-0.977163\pi$
$421$		−	2.94167i		−	0.143368i	0.997427	−	0.0716842i	$-0.0228374\pi$
$422$			36.4383i			1.77379i
$423$		0			0
$424$	−13.6684	−	7.89148i	−0.663798	−	0.383244i
$425$	−2.43669			−0.118197
$426$		0			0
$427$	−16.4699	+	10.0990i	−0.797036	+	0.488727i
$428$	0.950178			0.0459286
$429$		0			0
$430$	−2.47137	+	4.28053i	−0.119180	+	0.206426i
$431$			39.6955i			1.91207i	0.293258	+	0.956033i	$0.405261\pi$
$431$			39.6955i			1.91207i	−0.293258	+	0.956033i	$0.594739\pi$
$432$		0			0
$433$	−4.91827	+	8.51869i	−0.236357	+	0.409382i	−0.959666	−	0.281142i	$-0.909287\pi$
$433$	−4.91827	+	8.51869i	−0.236357	+	0.409382i	0.723309	+	0.690524i	$0.242620\pi$
$434$	11.1471	+	6.04840i	0.535078	+	0.290332i
$435$		0			0
$436$		−	1.43027i		−	0.0684975i
$437$	8.12331	+	4.69000i	0.388591	+	0.224353i
$438$		0			0
$439$	14.2733	−	24.7220i	0.681226	−	1.17992i	−0.293381	−	0.955996i	$-0.594780\pi$
$439$	14.2733	−	24.7220i	0.681226	−	1.17992i	0.974607	−	0.223922i	$-0.0718863\pi$
$440$	−10.6465	+	6.14678i	−0.507554	+	0.293036i
$441$		0			0
$442$	−2.10161	−	1.82737i	−0.0999632	−	0.0869193i
$443$	1.66951	+	2.89167i	0.0793207	+	0.137387i	0.902957	−	0.429731i	$-0.141392\pi$
$443$	1.66951	+	2.89167i	0.0793207	+	0.137387i	−0.823636	+	0.567118i	$0.808058\pi$
$444$		0			0
$445$	4.03736			0.191389
$446$	31.7190			1.50194
$447$		0			0
$448$	18.8408	−	11.5528i	0.890145	−	0.545819i
$449$	−15.7487	−	9.09253i	−0.743228	−	0.429103i	0.0800136	−	0.996794i	$-0.474504\pi$
$449$	−15.7487	−	9.09253i	−0.743228	−	0.429103i	−0.823242	+	0.567691i	$0.807837\pi$
$450$		0			0
$451$	−2.44523	−	4.23526i	−0.115141	−	0.199430i
$452$	−1.91617			−0.0901289
$453$		0			0
$454$	0.625219			0.0293430
$455$	2.69354	+	7.20098i	0.126275	+	0.337587i
$456$		0			0
$457$	7.55982	+	4.36466i	0.353633	+	0.204170i	0.666284	−	0.745698i	$-0.267884\pi$
$457$	7.55982	+	4.36466i	0.353633	+	0.204170i	−0.312651	+	0.949868i	$0.601217\pi$
$458$	−23.9038			−1.11695
$459$		0			0
$460$	0.110008	−	0.0635130i	0.00512914	−	0.00296131i
$461$	1.96695	+	1.13562i	0.0916099	+	0.0528910i	0.545105	−	0.838368i	$-0.316490\pi$
$461$	1.96695	+	1.13562i	0.0916099	+	0.0528910i	−0.453495	+	0.891259i	$0.649823\pi$
$462$		0			0
$463$		−	5.48326i		−	0.254829i	−0.991850	−	0.127414i	$-0.959332\pi$
$463$		−	5.48326i		−	0.254829i	0.991850	−	0.127414i	$-0.0406678\pi$
$464$	8.65077			0.401602
$465$		0			0
$466$		−	10.7775i		−	0.499257i
$467$	−9.44095	−	16.3522i	−0.436875	−	0.756690i	0.560572	−	0.828106i	$-0.310581\pi$
$467$	−9.44095	−	16.3522i	−0.436875	−	0.756690i	−0.997447	+	0.0714164i	$0.977248\pi$
$468$		0			0
$469$	10.1591	+	16.5679i	0.469103	+	0.765032i
$470$	3.70018	−	2.13630i	0.170677	−	0.0985401i
$471$		0			0
$472$	15.9058	+	27.5496i	0.732122	+	1.26807i
$473$	20.3025	+	11.7217i	0.933510	+	0.538962i
$474$		0			0
$475$	−22.0204	−	12.7135i	−1.01037	−	0.583335i
$476$	0.00384971	+	0.145482i	0.000176451	+	0.00666814i
$477$		0			0
$478$	−9.33030	+	16.1606i	−0.426758	+	0.739166i
$479$		−	33.1354i		−	1.51399i	−0.653418	−	0.756997i	$-0.726666\pi$
$479$		−	33.1354i		−	1.51399i	0.653418	−	0.756997i	$-0.273334\pi$
$480$		0			0
$481$	−4.23417	+	1.45733i	−0.193061	+	0.0664485i
$482$	−31.1104			−1.41704
$483$		0			0
$484$	0.824428	+	1.42795i	0.0374740	+	0.0649069i
$485$	−8.58199			−0.389688
$486$		0			0
$487$	−13.8185	+	7.97814i	−0.626178	+	0.361524i	−0.779270	−	0.626688i	$-0.784410\pi$
$487$	−13.8185	+	7.97814i	−0.626178	+	0.361524i	0.153093	+	0.988212i	$0.451077\pi$
$488$		−	21.1291i		−	0.956469i
$489$		0			0
$490$	−3.52828	+	6.93409i	−0.159391	+	0.313250i
$491$	15.8464	+	27.4468i	0.715138	+	1.23866i	0.962906	+	0.269836i	$0.0869694\pi$
$491$	15.8464	+	27.4468i	0.715138	+	1.23866i	−0.247769	+	0.968819i	$0.579697\pi$
$492$		0			0
$493$	−0.638559	+	1.10602i	−0.0287593	+	0.0498125i
$494$	−9.45788	−	27.4792i	−0.425530	−	1.23635i
$495$		0			0
$496$	−11.4206	+	6.59368i	−0.512800	+	0.296065i
$497$	−24.6355	+	0.651901i	−1.10505	+	0.0292417i
$498$		0			0
$499$	−20.9738	+	12.1092i	−0.938916	+	0.542083i	−0.889620	−	0.456701i	$-0.849031\pi$
$499$	−20.9738	+	12.1092i	−0.938916	+	0.542083i	−0.0492955	+	0.998784i	$0.515698\pi$
$500$	−0.640935	+	0.370044i	−0.0286635	+	0.0165489i
$501$		0			0
$502$	8.04043	−	4.64215i	0.358862	−	0.207189i
$503$	0.427249	−	0.740017i	0.0190501	−	0.0329957i	−0.856343	−	0.516407i	$-0.827269\pi$
$503$	0.427249	−	0.740017i	0.0190501	−	0.0329957i	0.875393	+	0.483411i	$0.160602\pi$
$504$		0			0
$505$	−2.73294	+	1.57786i	−0.121614	+	0.0702139i
$506$	5.83356	+	10.1040i	0.259333	+	0.449179i
$507$		0			0
$508$	−0.0941471	+	0.163068i	−0.00417710	+	0.00723495i
$509$	1.12583	+	0.650000i	0.0499017	+	0.0288108i	0.524743	−	0.851261i	$-0.324161\pi$
$509$	1.12583	+	0.650000i	0.0499017	+	0.0288108i	−0.474842	+	0.880071i	$0.657495\pi$
$510$		0			0
$511$	13.2280	−	0.350037i	0.585171	−	0.0154847i
$512$			24.0616i			1.06338i
$513$		0			0
$514$	−19.7514	+	11.4035i	−0.871199	+	0.502987i
$515$	−5.90051	−	3.40666i	−0.260007	−	0.150115i
$516$		0			0
$517$	−10.1324	−	17.5499i	−0.445624	−	0.771844i
$518$	−3.98291	−	2.16112i	−0.174999	−	0.0949543i
$519$		0			0
$520$	−8.25362	−	1.60545i	−0.361945	−	0.0704034i
$521$	−12.5228	+	21.6901i	−0.548632	+	0.950259i	0.449736	+	0.893161i	$0.351518\pi$
$521$	−12.5228	+	21.6901i	−0.548632	+	0.950259i	−0.998369	+	0.0570974i	$0.981815\pi$
$522$		0			0
$523$	−6.41197	+	11.1059i	−0.280376	+	0.485625i	−0.971477	−	0.237133i	$-0.923792\pi$
$523$	−6.41197	+	11.1059i	−0.280376	+	0.485625i	0.691101	+	0.722758i	$0.257126\pi$
$524$	0.765112	−	1.32521i	0.0334241	−	0.0578922i
$525$		0			0
$526$	11.9701	+	6.91095i	0.521922	+	0.301332i
$527$		−	1.94686i		−	0.0848065i
$528$		0			0
$529$	10.2122	+	17.6880i	0.444008	+	0.769045i
$530$	−3.03122	+	5.25022i	−0.131668	+	0.228055i
$531$		0			0
$532$	−0.724263	+	1.33480i	−0.0314008	+	0.0578711i
$533$	0.638656	−	3.28334i	0.0276632	−	0.142217i
$534$		0			0
$535$		−	7.79773i		−	0.337125i
$536$	−21.2547			−0.918063
$537$		0			0
$538$		−	21.6828i		−	0.934814i
$539$	32.8883	+	16.7346i	1.41660	+	0.720810i
$540$		0			0
$541$	24.8938	−	14.3725i	1.07027	−	0.617920i	0.142014	−	0.989865i	$-0.454642\pi$
$541$	24.8938	−	14.3725i	1.07027	−	0.617920i	0.928255	+	0.371944i	$0.121309\pi$
$542$	−3.59670	−	6.22966i	−0.154491	−	0.267587i
$543$		0			0
$544$	−0.269226	−	0.155438i	−0.0115430	−	0.00666434i
$545$	−11.7376			−0.502785
$546$		0			0
$547$	−8.88085			−0.379718			−0.189859	−	0.981811i	$-0.560803\pi$
$547$	−8.88085			−0.379718			−0.189859	+	0.981811i	$0.560803\pi$
$548$	0.667733	+	0.385516i	0.0285241	+	0.0164684i
$549$		0			0
$550$	−15.8134	−	27.3897i	−0.674287	−	1.16790i
$551$	−11.5413	+	6.66339i	−0.491677	+	0.283870i
$552$		0			0
$553$	26.4378	+	14.3451i	1.12425	+	0.610016i
$554$		−	26.5777i		−	1.12918i
$555$		0			0
$556$	0.974690			0.0413361
$557$			38.7273i			1.64093i	0.571696	+	0.820465i	$0.306286\pi$
$557$			38.7273i			1.64093i	−0.571696	+	0.820465i	$0.693714\pi$
$558$		0			0
$559$	5.21830	+	15.1614i	0.220711	+	0.641259i
$560$	−4.22890	−	6.89666i	−0.178704	−	0.291437i
$561$		0			0
$562$	−1.47754	+	2.55918i	−0.0623263	+	0.107952i
$563$	−3.45441	−	5.98321i	−0.145586	−	0.252162i	0.784005	−	0.620754i	$-0.213173\pi$
$563$	−3.45441	−	5.98321i	−0.145586	−	0.252162i	−0.929591	+	0.368592i	$0.879840\pi$
$564$		0			0
$565$			15.7252i			0.661565i
$566$	18.8105	+	10.8602i	0.790663	+	0.456489i
$567$		0			0
$568$	13.4761	−	23.3413i	0.565444	−	0.979379i
$569$	1.41872	−	2.45730i	0.0594759	−	0.103015i	−0.834754	−	0.550623i	$-0.814390\pi$
$569$	1.41872	−	2.45730i	0.0594759	−	0.103015i	0.894230	+	0.447607i	$0.147724\pi$
$570$		0			0
$571$	−23.3362	+	40.4195i	−0.976589	+	1.69150i	−0.302001	+	0.953307i	$0.597655\pi$
$571$	−23.3362	+	40.4195i	−0.976589	+	1.69150i	−0.674588	+	0.738195i	$0.735679\pi$
$572$	−0.356404	+	1.83228i	−0.0149020	+	0.0766115i
$573$		0			0
$574$	2.88557	−	1.76937i	0.120441	−	0.0738522i
$575$	3.49096	+	6.04653i	0.145583	+	0.252158i
$576$		0			0
$577$	9.88033	+	5.70441i	0.411323	+	0.237478i	0.691358	−	0.722512i	$-0.257013\pi$
$577$	9.88033	+	5.70441i	0.411323	+	0.237478i	−0.280035	+	0.959990i	$0.590346\pi$
$578$	19.9284	−	11.5057i	0.828911	−	0.478572i
$579$		0			0
$580$			0.180474i			0.00749379i
$581$	−8.04867	−	13.1261i	−0.333915	−	0.544563i
$582$		0			0
$583$	24.9017	+	14.3770i	1.03132	+	0.595436i
$584$	−7.23597	+	12.5331i	−0.299426	+	0.518622i
$585$		0			0
$586$	15.9617	+	27.6465i	0.659371	+	1.14206i
$587$	40.2191	−	23.2205i	1.66002	−	0.958413i	0.687318	−	0.726356i	$-0.258788\pi$
$587$	40.2191	−	23.2205i	1.66002	−	0.958413i	0.972702	−	0.232057i	$-0.0745456\pi$
$588$		0			0
$589$	10.1578	−	17.5938i	0.418544	−	0.724939i
$590$	10.5821	−	6.10961i	0.435660	−	0.251529i
$591$		0			0
$592$	4.08064	−	2.35596i	0.167713	−	0.0968292i
$593$	17.5462	−	10.1303i	0.720535	−	0.416001i	−0.0944146	−	0.995533i	$-0.530098\pi$
$593$	17.5462	−	10.1303i	0.720535	−	0.416001i	0.814950	+	0.579532i	$0.196765\pi$
$594$		0			0
$595$	1.19391	−	0.0315930i	0.0489455	−	0.00129519i
$596$	−0.673533	+	0.388864i	−0.0275890	+	0.0159285i
$597$		0			0
$598$	−1.52364	+	7.83304i	−0.0623061	+	0.320317i
$599$	−19.4938	+	33.7642i	−0.796494	+	1.37957i	0.125391	+	0.992107i	$0.459981\pi$
$599$	−19.4938	+	33.7642i	−0.796494	+	1.37957i	−0.921886	+	0.387462i	$0.873352\pi$
$600$		0			0
$601$	−9.56951	−	16.5749i	−0.390348	−	0.676103i	0.602147	−	0.798385i	$-0.294312\pi$
$601$	−9.56951	−	16.5749i	−0.390348	−	0.676103i	−0.992495	+	0.122282i	$0.960979\pi$
$602$	−7.73840	+	14.2617i	−0.315394	+	0.581265i
$603$		0			0
$604$			0.147425i			0.00599865i
$605$	11.7186	−	6.76575i	0.476430	−	0.275067i
$606$		0			0
$607$	43.3336			1.75886			0.879428	−	0.476033i	$-0.157926\pi$
$607$	43.3336			1.75886			0.879428	+	0.476033i	$0.157926\pi$
$608$	−1.62200	−	2.80939i	−0.0657808	−	0.113936i
$609$		0			0
$610$	−8.11595			−0.328605
$611$	2.64644	−	13.6054i	0.107063	−	0.550415i
$612$		0			0
$613$		−	10.3096i		−	0.416399i	−0.978086	−	0.208200i	$-0.933240\pi$
$613$		−	10.3096i		−	0.416399i	0.978086	−	0.208200i	$-0.0667604\pi$
$614$	−2.92077	+	5.05892i	−0.117873	+	0.204161i
$615$		0			0
$616$	−34.4042	+	21.0960i	−1.38619	+	0.849982i
$617$	9.58684	+	5.53497i	0.385952	+	0.222829i	0.680405	−	0.732837i	$-0.261804\pi$
$617$	9.58684	+	5.53497i	0.385952	+	0.222829i	−0.294453	+	0.955666i	$0.595137\pi$
$618$		0			0
$619$	−29.2384	−	16.8808i	−1.17519	−	0.678498i	−0.220295	−	0.975433i	$-0.570702\pi$
$619$	−29.2384	−	16.8808i	−1.17519	−	0.678498i	−0.954897	+	0.296936i	$0.904035\pi$
$620$	−0.137559	−	0.238259i	−0.00552450	−	0.00956871i
$621$		0			0
$622$	−32.5447	+	18.7897i	−1.30492	+	0.753399i
$623$	13.2491	−	0.350597i	0.530816	−	0.0140464i
$624$		0			0
$625$	−7.83931	−	13.5781i	−0.313573	−	0.543124i
$626$		−	3.71927i		−	0.148652i
$627$		0			0
$628$	0.378778			0.0151149
$629$			0.695623i			0.0277363i
$630$		0			0
$631$	33.4264	+	19.2987i	1.33068	+	0.768271i	0.985405	−	0.170229i	$-0.0544507\pi$
$631$	33.4264	+	19.2987i	1.33068	+	0.768271i	0.345280	+	0.938500i	$0.387784\pi$
$632$	−28.4887	+	16.4480i	−1.13322	+	0.654265i
$633$		0			0
$634$	33.1945			1.31832
$635$	1.33823	+	0.772627i	0.0531060	+	0.0306608i
$636$		0			0
$637$	9.46453	+	23.3971i	0.374998	+	0.927025i
$638$	−16.5763			−0.656260
$639$		0			0
$640$	8.38960			0.331628
$641$	−9.76141	−	16.9073i	−0.385553	−	0.667797i	0.606293	−	0.795241i	$-0.292656\pi$
$641$	−9.76141	−	16.9073i	−0.385553	−	0.667797i	−0.991846	+	0.127445i	$0.959322\pi$
$642$		0			0
$643$	10.8009	+	6.23589i	0.425945	+	0.245920i	0.697618	−	0.716470i	$-0.254243\pi$
$643$	10.8009	+	6.23589i	0.425945	+	0.245920i	−0.271673	+	0.962390i	$0.587577\pi$
$644$	0.355490	−	0.217979i	0.0140083	−	0.00858958i
$645$		0			0
$646$	−4.51450			−0.177621
$647$	35.9391			1.41291			0.706455	−	0.707758i	$-0.250293\pi$
$647$	35.9391			1.41291			0.706455	+	0.707758i	$0.250293\pi$
$648$		0			0
$649$	−28.9778	−	50.1910i	−1.13748	−	1.97017i
$650$	4.13023	−	21.2336i	0.162001	−	0.832849i
$651$		0			0
$652$	1.22139	−	0.705171i	0.0478334	−	0.0276166i
$653$	2.42944	−	4.20791i	0.0950713	−	0.164668i	−0.814567	−	0.580069i	$-0.803025\pi$
$653$	2.42944	−	4.20791i	0.0950713	−	0.164668i	0.909638	+	0.415401i	$0.136359\pi$
$654$		0			0
$655$	−10.8755	−	6.27897i	−0.424941	−	0.245340i
$656$			3.51964i			0.137419i
$657$		0			0
$658$	11.9571	−	7.33186i	0.466137	−	0.285826i
$659$	−11.8103	+	20.4560i	−0.460063	+	0.796853i	−0.998964	−	0.0455166i	$-0.985507\pi$
$659$	−11.8103	+	20.4560i	−0.460063	+	0.796853i	0.538900	+	0.842370i	$0.318840\pi$
$660$		0			0
$661$		−	16.3932i		−	0.637623i	−0.947818	−	0.318812i	$-0.896716\pi$
$661$		−	16.3932i		−	0.637623i	0.947818	−	0.318812i	$-0.103284\pi$
$662$	−0.427316	+	0.740134i	−0.0166081	+	0.0287661i
$663$		0			0
$664$	16.8393			0.653492
$665$	10.9542	+	5.94374i	0.424786	+	0.230488i
$666$		0			0
$667$	3.65936			0.141691
$668$	−0.384544	−	0.222016i	−0.0148784	−	0.00859007i
$669$		0			0
$670$			8.16420i			0.315410i
$671$			38.4939i			1.48604i
$672$		0			0
$673$	−7.12678	−	12.3439i	−0.274717	−	0.475824i	0.695347	−	0.718675i	$-0.255251\pi$
$673$	−7.12678	−	12.3439i	−0.274717	−	0.475824i	−0.970064	+	0.242851i	$0.921918\pi$
$674$	−6.83278	−	3.94491i	−0.263189	−	0.151952i
$675$		0			0
$676$	−1.00625	+	0.785753i	−0.0387020	+	0.0302213i
$677$	−5.13574	−	8.89537i	−0.197383	−	0.341877i	0.750296	−	0.661102i	$-0.229911\pi$
$677$	−5.13574	−	8.89537i	−0.197383	−	0.341877i	−0.947679	+	0.319225i	$0.896577\pi$
$678$		0			0
$679$	−28.1629	+	0.745243i	−1.08079	+	0.0285998i
$680$	−0.653092	+	1.13119i	−0.0250449	+	0.0433791i
$681$		0			0
$682$	21.8837	−	12.6345i	0.837969	−	0.483802i
$683$	−1.92432	+	1.11101i	−0.0736321	+	0.0425115i	−0.536364	−	0.843987i	$-0.680203\pi$
$683$	−1.92432	+	1.11101i	−0.0736321	+	0.0425115i	0.462732	+	0.886498i	$0.346869\pi$
$684$		0			0
$685$	3.16377	−	5.47981i	0.120881	−	0.209373i
$686$	−10.9764	+	23.0615i	−0.419080	+	0.880493i
$687$		0			0
$688$	−8.43604	−	14.6117i	−0.321621	−	0.557064i
$689$	6.40044	+	18.5960i	0.243837	+	0.708451i
$690$		0			0
$691$	2.28643	+	1.32007i	0.0869800	+	0.0502179i	0.542859	−	0.839824i	$-0.317342\pi$
$691$	2.28643	+	1.32007i	0.0869800	+	0.0502179i	−0.455879	+	0.890042i	$0.650675\pi$
$692$	0.958402	+	1.66000i	0.0364330	+	0.0631038i
$693$		0			0
$694$		−	2.57174i		−	0.0976220i
$695$		−	7.99889i		−	0.303415i
$696$		0			0
$697$	−0.449993	−	0.259804i	−0.0170447	−	0.00984077i
$698$	−30.7767			−1.16492
$699$		0			0
$700$	−0.963650	+	0.590891i	−0.0364226	+	0.0223336i
$701$	8.89991			0.336145			0.168072	−	0.985775i	$-0.446246\pi$
$701$	8.89991			0.336145			0.168072	+	0.985775i	$0.446246\pi$
$702$		0			0
$703$	−3.62943	+	6.28635i	−0.136886	+	0.237094i
$704$		−	44.0351i		−	1.65964i
$705$		0			0
$706$	−1.60797	+	2.78509i	−0.0605168	+	0.104818i
$707$	−8.83147	+	5.41528i	−0.332142	+	0.203663i
$708$		0			0
$709$		−	40.5944i		−	1.52456i	−0.647250	−	0.762278i	$-0.724081\pi$
$709$		−	40.5944i		−	1.52456i	0.647250	−	0.762278i	$-0.275919\pi$
$710$	−8.96569	−	5.17634i	−0.336476	−	0.194265i
$711$		0			0
$712$	−7.24754	+	12.5531i	−0.271613	+	0.470448i
$713$	−4.83103	+	2.78920i	−0.180923	+	0.104456i
$714$		0			0
$715$	15.0368	+	2.92487i	0.562344	+	0.109384i
$716$	−1.02232	−	1.77071i	−0.0382059	−	0.0661745i
$717$		0			0
$718$	−4.51096			−0.168348
$719$	14.5135			0.541262			0.270631	−	0.962683i	$-0.412768\pi$
$719$	14.5135			0.541262			0.270631	+	0.962683i	$0.412768\pi$
$720$		0			0
$721$	−19.6591	−	10.6670i	−0.732144	−	0.397260i
$722$	−18.1059	−	10.4535i	−0.673834	−	0.389038i
$723$		0			0
$724$	−0.812773	−	1.40776i	−0.0302065	−	0.0523191i
$725$	−9.91969			−0.368408
$726$		0			0
$727$	30.6942			1.13839			0.569193	−	0.822204i	$-0.307256\pi$
$727$	30.6942			1.13839			0.569193	+	0.822204i	$0.307256\pi$
$728$	−27.2248	−	4.55175i	−1.00902	−	0.168699i
$729$		0			0
$730$	4.81411	+	2.77943i	0.178178	+	0.102871i
$731$	2.49084			0.0921269
$732$		0			0
$733$	11.4873	−	6.63218i	0.424292	−	0.244965i	−0.272620	−	0.962122i	$-0.587890\pi$
$733$	11.4873	−	6.63218i	0.424292	−	0.244965i	0.696912	+	0.717157i	$0.254557\pi$
$734$	4.95980	+	2.86354i	0.183069	+	0.105695i
$735$		0			0
$736$			0.890761i			0.0328339i
$737$	38.7227			1.42637
$738$		0			0
$739$			7.25474i			0.266870i	0.991058	+	0.133435i	$0.0426008\pi$
$739$			7.25474i			0.266870i	−0.991058	+	0.133435i	$0.957399\pi$
$740$	0.0491505	+	0.0851312i	0.00180681	+	0.00312948i
$741$		0			0
$742$	−9.49142	+	17.4925i	−0.348441	+	0.642171i
$743$	40.0705	−	23.1347i	1.47004	−	0.848730i	0.470608	−	0.882342i	$-0.344035\pi$
$743$	40.0705	−	23.1347i	1.47004	−	0.848730i	0.999435	+	0.0336128i	$0.0107013\pi$
$744$		0			0
$745$	3.19125	+	5.52741i	0.116918	+	0.202509i
$746$	−13.2673	−	7.65991i	−0.485752	−	0.280449i
$747$		0			0
$748$	0.251121	+	0.144985i	0.00918188	+	0.00530116i
$749$	−0.677140	−	25.5893i	−0.0247421	−	0.935012i
$750$		0			0
$751$	−18.0130	+	31.1995i	−0.657305	+	1.13848i	0.324006	+	0.946055i	$0.394970\pi$
$751$	−18.0130	+	31.1995i	−0.657305	+	1.13848i	−0.981311	+	0.192430i	$0.938363\pi$
$752$			14.5846i			0.531845i
$753$		0			0
$754$	−8.55556	−	7.43917i	−0.311575	−	0.270919i
$755$	1.20986			0.0440313
$756$		0			0
$757$	5.28132	+	9.14751i	0.191953	+	0.332472i	0.945897	−	0.324466i	$-0.105185\pi$
$757$	5.28132	+	9.14751i	0.191953	+	0.332472i	−0.753945	+	0.656938i	$0.771851\pi$
$758$	−6.39923			−0.232430
$759$		0			0
$760$	−11.8040	+	6.81504i	−0.428176	+	0.247207i
$761$		−	7.81202i		−	0.283185i	−0.989925	−	0.141593i	$-0.954778\pi$
$761$		−	7.81202i		−	0.283185i	0.989925	−	0.141593i	$-0.0452223\pi$
$762$		0			0
$763$	−38.5186	+	1.01927i	−1.39447	+	0.0369002i
$764$	−0.208695	−	0.361470i	−0.00755031	−	0.0130775i
$765$		0			0
$766$	−2.53010	+	4.38226i	−0.0914163	+	0.158338i
$767$	7.56855	−	38.9101i	0.273285	−	1.40496i
$768$		0			0
$769$	21.9030	−	12.6457i	0.789844	−	0.456017i	−0.0500637	−	0.998746i	$-0.515942\pi$
$769$	21.9030	−	12.6457i	0.789844	−	0.456017i	0.839908	+	0.542729i	$0.182609\pi$
$770$	8.10324	+	13.2151i	0.292021	+	0.476240i
$771$		0			0
$772$	0.986345	−	0.569467i	0.0354993	−	0.0204956i
$773$	40.3572	−	23.3002i	1.45155	−	0.838051i	0.452977	−	0.891522i	$-0.350362\pi$
$773$	40.3572	−	23.3002i	1.45155	−	0.838051i	0.998569	+	0.0534716i	$0.0170287\pi$
$774$		0			0
$775$	13.0958	−	7.56086i	0.470415	−	0.271594i
$776$	15.4057	−	26.6834i	0.553032	−	0.957879i
$777$		0			0
$778$	−20.1634	+	11.6414i	−0.722895	+	0.417363i
$779$	−2.71106	−	4.69570i	−0.0971339	−	0.168241i
$780$		0			0
$781$	−24.5513	+	42.5241i	−0.878515	+	1.52163i
$782$	1.07355	+	0.619812i	0.0383899	+	0.0221644i
$783$		0			0
$784$	−14.4766	−	22.2651i	−0.517021	−	0.795182i
$785$		−	3.10848i		−	0.110946i
$786$		0			0
$787$	34.4099	−	19.8666i	1.22658	−	0.708167i	0.260268	−	0.965536i	$-0.416189\pi$
$787$	34.4099	−	19.8666i	1.22658	−	0.708167i	0.966313	+	0.257369i	$0.0828556\pi$
$788$	−1.22653	−	0.708140i	−0.0436935	−	0.0252265i
$789$		0			0
$790$	6.31788	+	10.9429i	0.224780	+	0.389330i
$791$	1.36555	+	51.6043i	0.0485532	+	1.83484i
$792$		0			0
$793$	−17.2755	+	19.8680i	−0.613470	+	0.705533i
$794$	11.5210	−	19.9550i	0.408865	−	0.708175i
$795$		0			0
$796$	0.346635	−	0.600389i	0.0122861	−	0.0212802i
$797$	1.39299	−	2.41273i	0.0493422	−	0.0854632i	−0.840299	−	0.542123i	$-0.817621\pi$
$797$	1.39299	−	2.41273i	0.0493422	−	0.0854632i	0.889642	+	0.456659i	$0.150954\pi$
$798$		0			0
$799$	−1.86467	−	1.07656i	−0.0659671	−	0.0380861i
$800$		−	2.41465i		−	0.0853706i
$801$		0			0
$802$	−17.4543	−	30.2317i	−0.616333	−	1.06752i
$803$	13.1828	−	22.8333i	0.465210	−	0.805768i
$804$		0			0
$805$	−1.78887	−	2.91736i	−0.0630493	−	0.102823i
$806$	16.9651	+	3.29995i	0.597570	+	0.116236i
$807$		0			0
$808$		−	11.3298i		−	0.398580i
$809$	41.4586			1.45761			0.728803	−	0.684723i	$-0.240077\pi$
$809$	41.4586			1.45761			0.728803	+	0.684723i	$0.240077\pi$
$810$		0			0
$811$			27.8622i			0.978375i	0.872179	+	0.489188i	$0.162707\pi$
$811$			27.8622i			0.978375i	−0.872179	+	0.489188i	$0.837293\pi$
$812$	0.0156720	+	0.592250i	0.000549981	+	0.0207839i
$813$		0			0
$814$	−7.81915	+	4.51439i	−0.274061	+	0.158229i
$815$	−5.78705	−	10.0235i	−0.202712	−	0.351107i
$816$		0			0
$817$	22.5097	+	12.9960i	0.787515	+	0.454672i
$818$	7.90671			0.276452
$819$		0			0
$820$	−0.0734276			−0.00256420
$821$	19.4164	+	11.2101i	0.677638	+	0.391235i	0.798965	−	0.601378i	$-0.205381\pi$
$821$	19.4164	+	11.2101i	0.677638	+	0.391235i	−0.121326	+	0.992613i	$0.538715\pi$
$822$		0			0
$823$	−1.18083	−	2.04525i	−0.0411611	−	0.0712931i	0.844711	−	0.535223i	$-0.179772\pi$
$823$	−1.18083	−	2.04525i	−0.0411611	−	0.0712931i	−0.885872	+	0.463930i	$0.846439\pi$
$824$	21.1842	−	12.2307i	0.737987	−	0.426077i
$825$		0			0
$826$	34.1962	−	20.9684i	1.18984	−	0.729584i
$827$		−	43.3148i		−	1.50620i	−0.657904	−	0.753102i	$-0.728557\pi$
$827$		−	43.3148i		−	1.50620i	0.657904	−	0.753102i	$-0.271443\pi$
$828$		0			0
$829$	54.9280			1.90773			0.953864	−	0.300239i	$-0.0970665\pi$
$829$	54.9280			1.90773			0.953864	+	0.300239i	$0.0970665\pi$
$830$		−	6.46820i		−	0.224514i
$831$		0			0
$832$	19.7623	−	22.7280i	0.685134	−	0.787951i
$833$	3.91523	−	0.207353i	0.135655	−	0.00718437i
$834$		0			0
$835$	−1.82200	+	3.15579i	−0.0630529	+	0.109211i
$836$	1.51292	+	2.62045i	0.0523254	+	0.0906303i
$837$		0			0
$838$		−	47.3647i		−	1.63619i
$839$	12.7661	+	7.37052i	0.440735	+	0.254459i	0.703910	−	0.710290i	$-0.251436\pi$
$839$	12.7661	+	7.37052i	0.440735	+	0.254459i	−0.263174	+	0.964748i	$0.584769\pi$
$840$		0			0
$841$	11.9004	−	20.6122i	0.410360	−	0.710765i
$842$	2.02837	−	3.51323i	0.0699021	−	0.121074i
$843$		0			0
$844$	1.29745	−	2.24725i	0.0446600	−	0.0773535i
$845$	6.44836	+	8.25791i	0.221830	+	0.284081i
$846$		0			0
$847$	37.8687	−	23.2203i	1.30118	−	0.797860i
$848$	−10.3471	−	17.9217i	−0.355321	−	0.615434i
$849$		0			0
$850$	−2.91013	−	1.68017i	−0.0998168	−	0.0576292i
$851$	1.72615	−	0.996594i	0.0591717	−	0.0341628i
$852$		0			0
$853$			24.1038i			0.825297i	0.910890	+	0.412649i	$0.135396\pi$
$853$			24.1038i			0.825297i	−0.910890	+	0.412649i	$0.864604\pi$
$854$	−26.6336	+	0.704773i	−0.911382	+	0.0241169i
$855$		0			0
$856$	24.2450	+	13.9978i	0.828676	+	0.478436i
$857$	9.29249	−	16.0951i	0.317425	−	0.549797i	−0.662525	−	0.749040i	$-0.730515\pi$
$857$	9.29249	−	16.0951i	0.317425	−	0.549797i	0.979950	+	0.199243i	$0.0638483\pi$
$858$		0			0
$859$	−14.7487	−	25.5456i	−0.503221	−	0.871604i	−0.999993	−	0.00372294i	$-0.998815\pi$
$859$	−14.7487	−	25.5456i	−0.503221	−	0.871604i	0.496772	−	0.867881i	$-0.334518\pi$
$860$	0.304832	−	0.175995i	0.0103947	−	0.00600137i
$861$		0			0
$862$	−27.3712	+	47.4083i	−0.932266	+	1.61473i
$863$	−16.1457	+	9.32173i	−0.549606	+	0.317315i	−0.748963	−	0.662612i	$-0.769448\pi$
$863$	−16.1457	+	9.32173i	−0.549606	+	0.317315i	0.199357	+	0.979927i	$0.436115\pi$
$864$		0			0
$865$	13.6230	−	7.86522i	0.463194	−	0.267425i
$866$	−11.7477	+	6.78256i	−0.399204	+	0.230481i
$867$		0			0
$868$	−0.472108	−	0.769933i	−0.0160244	−	0.0261332i
$869$	51.9020	−	29.9656i	1.76065	−	1.01651i
$870$		0			0
$871$	19.9861	+	17.3782i	0.677203	+	0.588836i
$872$	21.0705	−	36.4951i	0.713536	−	1.23588i
$873$		0			0
$874$	6.46776	+	11.2025i	0.218775	+	0.378930i
$875$	10.4224	+	16.9973i	0.352342	+	0.574615i
$876$		0			0
$877$		−	37.7518i		−	1.27479i	−0.770538	−	0.637395i	$-0.780012\pi$
$877$		−	37.7518i		−	1.27479i	0.770538	−	0.637395i	$-0.219988\pi$
$878$	34.0930	−	19.6836i	1.15058	−	0.664290i
$879$		0			0
$880$	−16.1190			−0.543372
$881$	−14.9149	−	25.8334i	−0.502497	−	0.870350i	−0.999996	−	0.00288515i	$-0.999082\pi$
$881$	−14.9149	−	25.8334i	−0.502497	−	0.870350i	0.497499	−	0.867464i	$-0.334252\pi$
$882$		0			0
$883$	−32.3979			−1.09028			−0.545138	−	0.838346i	$-0.683523\pi$
$883$	−32.3979			−1.09028			−0.545138	+	0.838346i	$0.683523\pi$
$884$	0.0645449	+	0.187531i	0.00217088	+	0.00630734i
$885$		0			0
$886$			4.60468i			0.154697i
$887$	−12.9599	+	22.4472i	−0.435151	+	0.753703i	−0.997308	−	0.0733272i	$-0.976638\pi$
$887$	−12.9599	+	22.4472i	−0.435151	+	0.753703i	0.562157	+	0.827030i	$0.309972\pi$
$888$		0			0
$889$	4.45867	+	2.41927i	0.149539	+	0.0811397i
$890$	4.82181	+	2.78387i	0.161627	+	0.0933156i
$891$		0			0
$892$	−1.95620	−	1.12941i	−0.0654984	−	0.0378155i
$893$	−11.2340	−	19.4579i	−0.375931	−	0.651132i
$894$		0			0
$895$	−14.5315	+	8.38976i	−0.485734	+	0.280439i
$896$	27.5316	−	0.728536i	0.919765	−	0.0243387i
$897$		0			0
$898$	−12.5391	−	21.7184i	−0.418435	−	0.724751i
$899$		−	7.92559i		−	0.264333i
$900$		0			0
$901$	3.05510			0.101780
$902$		−	6.74420i		−	0.224557i
$903$		0			0
$904$	−48.8934	−	28.2286i	−1.62617	−	0.938869i
$905$	−11.5529	+	6.67010i	−0.384033	+	0.221722i
$906$		0			0
$907$	−15.5423			−0.516072			−0.258036	−	0.966135i	$-0.583075\pi$
$907$	−15.5423			−0.516072			−0.258036	+	0.966135i	$0.583075\pi$
$908$	−0.0385589	−	0.0222620i	−0.00127962	−	0.000738791i
$909$		0			0
$910$	−1.74839	+	10.4574i	−0.0579584	+	0.346659i
$911$	−23.6358			−0.783090			−0.391545	−	0.920159i	$-0.628059\pi$
$911$	−23.6358			−0.783090			−0.391545	+	0.920159i	$0.628059\pi$
$912$		0			0
$913$	−30.6786			−1.01531
$914$	6.01911	+	10.4254i	0.199094	+	0.344842i
$915$		0			0
$916$	1.47421	+	0.851138i	0.0487094	+	0.0281224i
$917$	−36.2346	−	19.6609i	−1.19657	−	0.649259i
$918$		0			0
$919$	44.4817			1.46732			0.733659	−	0.679518i	$-0.237811\pi$
$919$	44.4817			1.46732			0.733659	+	0.679518i	$0.237811\pi$
$920$	3.74264			0.123391
$921$		0			0
$922$	1.56608	+	2.71253i	0.0515761	+	0.0893324i
$923$	−31.7560	+	10.9299i	−1.04526	+	0.359761i
$924$		0			0
$925$	−4.67920	+	2.70154i	−0.153851	+	0.0888259i
$926$	3.78086	−	6.54864i	0.124247	−	0.215202i
$927$		0			0
$928$	−1.09601	−	0.632782i	−0.0359783	−	0.0207721i
$929$			2.94270i			0.0965470i	0.998834	+	0.0482735i	$0.0153719\pi$
$929$			2.94270i			0.0965470i	−0.998834	+	0.0482735i	$0.984628\pi$
$930$		0			0
$931$	36.4638	+	18.5539i	1.19505	+	0.608080i
$932$	−0.383751	+	0.664676i	−0.0125702	+	0.0217722i
$933$		0			0
$934$		−	26.0392i		−	0.852028i
$935$	1.18983	−	2.06085i	0.0389116	−	0.0673968i
$936$		0			0
$937$	−0.951020			−0.0310685			−0.0155342	−	0.999879i	$-0.504945\pi$
$937$	−0.951020			−0.0310685			−0.0155342	+	0.999879i	$0.504945\pi$
$938$	0.708963	+	26.7919i	0.0231485	+	0.874786i
$939$		0			0
$940$	−0.304267			−0.00992409
$941$	−19.1125	−	11.0346i	−0.623050	−	0.359718i	0.155006	−	0.987914i	$-0.450460\pi$
$941$	−19.1125	−	11.0346i	−0.623050	−	0.359718i	−0.778056	+	0.628196i	$0.783794\pi$
$942$		0			0
$943$			1.48885i			0.0484835i
$944$			41.7105i			1.35756i
$945$		0			0
$946$	16.1648	+	27.9983i	0.525563	+	0.910302i
$947$	44.3160	+	25.5859i	1.44008	+	0.831429i	0.997854	−	0.0654762i	$-0.0208567\pi$
$947$	44.3160	+	25.5859i	1.44008	+	0.831429i	0.442223	+	0.896905i	$0.354190\pi$
$948$		0			0
$949$	17.0513	−	5.86878i	0.553509	−	0.190509i
$950$	−17.5326	−	30.3674i	−0.568833	−	0.985248i
$951$		0			0
$952$	−2.04498	+	3.76886i	−0.0662781	+	0.122149i
$953$	−22.9235	+	39.7047i	−0.742565	+	1.28616i	0.208758	+	0.977967i	$0.433058\pi$
$953$	−22.9235	+	39.7047i	−0.742565	+	1.28616i	−0.951324	+	0.308194i	$0.900275\pi$
$954$		0			0
$955$	−2.96644	+	1.71267i	−0.0959916	+	0.0554208i
$956$	1.15085	−	0.664444i	0.0372212	−	0.0214896i
$957$		0			0
$958$	22.8478	−	39.5735i	0.738177	−	1.27856i
$959$	9.90647	−	18.2575i	0.319897	−	0.589564i
$960$		0			0
$961$	−9.45905	−	16.3836i	−0.305131	−	0.528502i
$962$	−6.06172	−	1.17909i	−0.195438	−	0.0380154i
$963$		0			0
$964$	1.91866	+	1.10774i	0.0617960	+	0.0356779i
$965$	−4.67338	−	8.09453i	−0.150441	−	0.260572i
$966$		0			0
$967$			19.2609i			0.619387i	0.950836	+	0.309694i	$0.100227\pi$
$967$			19.2609i			0.619387i	−0.950836	+	0.309694i	$0.899773\pi$
$968$			48.5813i			1.56146i
$969$		0			0
$970$	−10.2494	−	5.91752i	−0.329090	−	0.190000i
$971$	−47.3326			−1.51897			−0.759487	−	0.650522i	$-0.774550\pi$
$971$	−47.3326			−1.51897			−0.759487	+	0.650522i	$0.774550\pi$
$972$		0			0
$973$	−0.694608	−	26.2494i	−0.0222681	−	0.841517i
$974$	−22.0046			−0.705072
$975$		0			0
$976$	13.8520	−	23.9923i	0.443390	−	0.767975i
$977$			47.8571i			1.53108i	0.643387	+	0.765541i	$0.277529\pi$
$977$			47.8571i			1.53108i	−0.643387	+	0.765541i	$0.722471\pi$
$978$		0			0
$979$	13.2039	−	22.8698i	0.421998	−	0.730921i
$980$	0.464499	−	0.302014i	0.0148379	−	0.00964747i
$981$		0			0
$982$			43.7061i			1.39472i
$983$	13.6560	+	7.88432i	0.435560	+	0.251471i	0.701712	−	0.712460i	$-0.252419\pi$
$983$	13.6560	+	7.88432i	0.435560	+	0.251471i	−0.266152	+	0.963931i	$0.585752\pi$
$984$		0			0
$985$	−5.81142	+	10.0657i	−0.185167	+	0.320719i
$986$	−1.52526	+	0.880608i	−0.0485741	+	0.0280443i
$987$		0			0
$988$	−0.395151	+	2.03148i	−0.0125714	+	0.0646300i
$989$	−3.56853	−	6.18088i	−0.113473	−	0.196541i
$990$		0			0
$991$	−12.1378			−0.385571			−0.192786	−	0.981241i	$-0.561752\pi$
$991$	−12.1378			−0.385571			−0.192786	+	0.981241i	$0.561752\pi$
$992$	1.92924			0.0612536
$993$		0			0
$994$	−29.8716	−	16.2083i	−0.947469	−	0.514096i
$995$	−4.92715	−	2.84469i	−0.156201	−	0.0901828i
$996$		0			0
$997$	−16.8938	−	29.2609i	−0.535032	−	0.926703i	−0.999162	−	0.0409358i	$-0.986966\pi$
$997$	−16.8938	−	29.2609i	−0.535032	−	0.926703i	0.464129	−	0.885767i	$-0.346367\pi$
$998$	−33.3986			−1.05721
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.e.361.5		12
3.2	odd	2		91.2.u.b.88.2	yes	12
7.2	even	3		819.2.bm.f.478.2		12
13.4	even	6		819.2.bm.f.550.5		12
21.2	odd	6		91.2.k.b.23.5	yes	12
21.5	even	6		637.2.k.i.569.5		12
21.11	odd	6		637.2.q.g.491.5		12
21.17	even	6		637.2.q.i.491.5		12
21.20	even	2		637.2.u.g.361.2		12
39.2	even	12		1183.2.e.j.508.3		24
39.11	even	12		1183.2.e.j.508.10		24
39.17	odd	6		91.2.k.b.4.2	✓	12
91.30	even	6	inner	819.2.do.e.667.5		12
273.2	even	12		1183.2.e.j.170.3		24
273.11	even	12		8281.2.a.cp.1.3		12
273.17	even	6		637.2.q.i.589.5		12
273.80	odd	12		8281.2.a.co.1.10		12
273.95	odd	6		637.2.q.g.589.5		12
273.128	even	12		1183.2.e.j.170.10		24
273.158	even	12		8281.2.a.cp.1.10		12
273.173	even	6		637.2.u.g.30.2		12
273.206	odd	12		8281.2.a.co.1.3		12
273.212	odd	6		91.2.u.b.30.2	yes	12
273.251	even	6		637.2.k.i.459.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.2	✓	12	39.17	odd	6
91.2.k.b.23.5	yes	12	21.2	odd	6
91.2.u.b.30.2	yes	12	273.212	odd	6
91.2.u.b.88.2	yes	12	3.2	odd	2
637.2.k.i.459.2		12	273.251	even	6
637.2.k.i.569.5		12	21.5	even	6
637.2.q.g.491.5		12	21.11	odd	6
637.2.q.g.589.5		12	273.95	odd	6
637.2.q.i.491.5		12	21.17	even	6
637.2.q.i.589.5		12	273.17	even	6
637.2.u.g.30.2		12	273.173	even	6
637.2.u.g.361.2		12	21.20	even	2
819.2.bm.f.478.2		12	7.2	even	3
819.2.bm.f.550.5		12	13.4	even	6
819.2.do.e.361.5		12	1.1	even	1	trivial
819.2.do.e.667.5		12	91.30	even	6	inner
1183.2.e.j.170.3		24	273.2	even	12
1183.2.e.j.170.10		24	273.128	even	12
1183.2.e.j.508.3		24	39.2	even	12
1183.2.e.j.508.10		24	39.11	even	12
8281.2.a.co.1.3		12	273.206	odd	12
8281.2.a.co.1.10		12	273.80	odd	12
8281.2.a.cp.1.3		12	273.11	even	12
8281.2.a.cp.1.10		12	273.158	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.do (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19430 + 0.689527i) q^{2} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(-2.25549 + 1.38302i) q^{7} -2.89354i q^{8} +O(q^{10})\)	\(q+(1.19430 + 0.689527i) q^{2} +(-0.0491037 - 0.0850501i) q^{4} +(-0.697972 + 0.402974i) q^{5} +(-2.25549 + 1.38302i) q^{7} -2.89354i q^{8} -1.11145 q^{10} +5.27158i q^{11} +(-2.36581 + 2.72084i) q^{13} +(-3.64736 + 0.0965159i) q^{14} +(1.89697 - 3.28565i) q^{16} +(0.280051 + 0.485062i) q^{17} +5.84469i q^{19} +(0.0685460 + 0.0395750i) q^{20} +(-3.63490 + 6.29583i) q^{22} +(0.802438 - 1.38986i) q^{23} +(-2.17522 + 3.76760i) q^{25} +(-4.70157 + 1.61820i) q^{26} +(0.228379 + 0.123918i) q^{28} +(1.14008 + 1.97467i) q^{29} +(-3.01022 - 1.73795i) q^{31} +(-0.480674 + 0.277517i) q^{32} +0.772411i q^{34} +(1.01695 - 1.87422i) q^{35} +(1.07557 + 0.620979i) q^{37} +(-4.03007 + 6.98029i) q^{38} +(1.16602 + 2.01961i) q^{40} +(-0.803413 + 0.463851i) q^{41} +(2.22356 - 3.85131i) q^{43} +(0.448348 - 0.258854i) q^{44} +(1.91670 - 1.10661i) q^{46} +(-3.32915 + 1.92209i) q^{47} +(3.17449 - 6.23880i) q^{49} +(-5.19572 + 2.99975i) q^{50} +(0.347577 + 0.0676087i) q^{52} +(2.72727 - 4.72377i) q^{53} +(-2.12431 - 3.67941i) q^{55} +(4.00184 + 6.52637i) q^{56} +3.14446i q^{58} +(-9.52106 + 5.49698i) q^{59} +7.30215 q^{61} +(-2.39673 - 4.15126i) q^{62} -8.35330 q^{64} +(0.554837 - 2.85243i) q^{65} -7.34556i q^{67} +(0.0275031 - 0.0476367i) q^{68} +(2.50686 - 1.53716i) q^{70} +(8.06668 + 4.65730i) q^{71} +(-4.33139 - 2.50073i) q^{73} +(0.856364 + 1.48327i) q^{74} +(0.497091 - 0.286996i) q^{76} +(-7.29072 - 11.8900i) q^{77} +(-5.68437 - 9.84562i) q^{79} +3.05772i q^{80} -1.27935 q^{82} +5.81962i q^{83} +(-0.390935 - 0.225707i) q^{85} +(5.31117 - 3.06641i) q^{86} +15.2535 q^{88} +(-4.33832 - 2.50473i) q^{89} +(1.57307 - 9.40880i) q^{91} -0.157611 q^{92} -5.30133 q^{94} +(-2.35526 - 4.07942i) q^{95} +(9.22171 + 5.32416i) q^{97} +(8.09311 - 5.26207i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7}+O(q^{10}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7	\( 12 q + 4 q^{4} - 3 q^{5} + 3 q^{7} - 24 q^{10} - 2 q^{13} - 4 q^{14} - 8 q^{16} - 17 q^{17} + 3 q^{20} - 15 q^{22} - 3 q^{23} - 5 q^{25} + 9 q^{26} + 27 q^{28} + q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{35} + 15 q^{37} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} - 33 q^{44} - 30 q^{46} - 15 q^{47} + 9 q^{49} - 18 q^{50} + 47 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{59} - 10 q^{61} - 41 q^{62} + 2 q^{64} + 3 q^{65} + 11 q^{68} - 3 q^{70} - 30 q^{71} - 42 q^{73} + 33 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} - 10 q^{82} - 21 q^{85} - 57 q^{86} + 28 q^{88} - 48 q^{89} - 16 q^{91} + 66 q^{92} - 2 q^{94} - 2 q^{95} - 3 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q + 4 * q^4 - 3 * q^5 + 3 * q^7 - 24 * q^10 - 2 * q^13 - 4 * q^14 - 8 * q^16 - 17 * q^17 + 3 * q^20 - 15 * q^22 - 3 * q^23 - 5 * q^25 + 9 * q^26 + 27 * q^28 + q^29 - 18 * q^31 - 18 * q^32 - 18 * q^35 + 15 * q^37 - 19 * q^38 - q^40 + 6 * q^41 + 11 * q^43 - 33 * q^44 - 30 * q^46 - 15 * q^47 + 9 * q^49 - 18 * q^50 + 47 * q^52 + 8 * q^53 - 15 * q^55 - 27 * q^59 - 10 * q^61 - 41 * q^62 + 2 * q^64 + 3 * q^65 + 11 * q^68 - 3 * q^70 - 30 * q^71 - 42 * q^73 + 33 * q^74 - 45 * q^76 + 19 * q^77 - 35 * q^79 - 10 * q^82 - 21 * q^85 - 57 * q^86 + 28 * q^88 - 48 * q^89 - 16 * q^91 + 66 * q^92 - 2 * q^94 - 2 * q^95 - 3 * q^97 + 36 * q^98

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