LMFDB - Embedded newform 261.2.k.c.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(82,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.1
Root			$-1.05678 - 1.32516i$ of defining polynomial
Character	$\chi$	$=$	261.190
Dual form			261.2.k.c.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.626118 - 0.301523i) q^{2} +(-0.945872 - 1.18609i) q^{4} +(-1.81798 - 0.875492i) q^{5} +(-1.49319 + 1.87240i) q^{7} +(0.543873 + 2.38286i) q^{8} +(0.874288 + 1.09632i) q^{10} +(-0.213150 + 0.933871i) q^{11} +(-1.45377 + 6.36940i) q^{13} +(1.49948 - 0.722111i) q^{14} +(-0.297197 + 1.30211i) q^{16} +3.81642 q^{17} +(-2.69251 - 3.37631i) q^{19} +(0.681165 + 2.98438i) q^{20} +(0.415040 - 0.520444i) q^{22} +(-4.85446 + 2.33778i) q^{23} +(-0.578892 - 0.725907i) q^{25} +(2.83075 - 3.54965i) q^{26} +3.63318 q^{28} +(-5.32202 + 0.822256i) q^{29} +(-2.46382 - 1.18651i) q^{31} +(3.62649 - 4.54747i) q^{32} +(-2.38953 - 1.15074i) q^{34} +(4.35384 - 2.09670i) q^{35} +(0.414041 + 1.81403i) q^{37} +(0.667799 + 2.92582i) q^{38} +(1.09743 - 4.80814i) q^{40} -11.8282 q^{41} +(3.33752 - 1.60727i) q^{43} +(1.30926 - 0.630508i) q^{44} +3.74436 q^{46} +(-0.719344 + 3.15165i) q^{47} +(0.281385 + 1.23283i) q^{49} +(0.143577 + 0.629053i) q^{50} +(8.92974 - 4.30034i) q^{52} +(2.04315 + 0.983927i) q^{53} +(1.20510 - 1.51115i) q^{55} +(-5.27376 - 2.53971i) q^{56} +(3.58014 + 1.08988i) q^{58} +9.30726 q^{59} +(1.95684 - 2.45380i) q^{61} +(1.18488 + 1.48579i) q^{62} +(-1.23512 + 0.594802i) q^{64} +(8.21929 - 10.3067i) q^{65} +(-2.69277 - 11.7978i) q^{67} +(-3.60984 - 4.52660i) q^{68} -3.35822 q^{70} +(-1.02436 + 4.48801i) q^{71} +(-8.19102 + 3.94459i) q^{73} +(0.287733 - 1.26064i) q^{74} +(-1.45781 + 6.38710i) q^{76} +(-1.43030 - 1.79354i) q^{77} +(-0.954127 - 4.18030i) q^{79} +(1.68028 - 2.10701i) q^{80} +(7.40582 + 3.56646i) q^{82} +(-10.0888 - 12.6510i) q^{83} +(-6.93816 - 3.34124i) q^{85} -2.57431 q^{86} -2.34121 q^{88} +(13.9137 + 6.70047i) q^{89} +(-9.75529 - 12.2327i) q^{91} +(7.36451 + 3.54656i) q^{92} +(1.40069 - 1.75641i) q^{94} +(1.93900 + 8.49532i) q^{95} +(9.82817 + 12.3241i) q^{97} +(0.195546 - 0.856741i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) $ 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.626118	−	0.301523i	−0.442732	−	0.213209i	0.199218	−	0.979955i	$-0.436160\pi$
$2$	−0.626118	−	0.301523i	−0.442732	−	0.213209i	−0.641950	+	0.766747i	$0.721874\pi$
$3$		0			0
$3$		0			0
$4$	−0.945872	−	1.18609i	−0.472936	−	0.593043i
$5$	−1.81798	−	0.875492i	−0.813024	−	0.391532i	−0.0193032	−	0.999814i	$-0.506145\pi$
$5$	−1.81798	−	0.875492i	−0.813024	−	0.391532i	−0.793721	+	0.608282i	$0.791859\pi$
$6$		0			0
$7$	−1.49319	+	1.87240i	−0.564371	+	0.707699i	−0.979359	−	0.202128i	$-0.935214\pi$
$7$	−1.49319	+	1.87240i	−0.564371	+	0.707699i	0.414988	+	0.909827i	$0.363786\pi$
$8$	0.543873	+	2.38286i	0.192288	+	0.842469i
$9$		0			0
$10$	0.874288	+	1.09632i	0.276474	+	0.346688i
$11$	−0.213150	+	0.933871i	−0.0642671	+	0.281573i	−0.996843	−	0.0794022i	$-0.974699\pi$
$11$	−0.213150	+	0.933871i	−0.0642671	+	0.281573i	0.932576	+	0.360975i	$0.117556\pi$
$12$		0			0
$13$	−1.45377	+	6.36940i	−0.403205	+	1.76655i	0.211078	+	0.977469i	$0.432302\pi$
$13$	−1.45377	+	6.36940i	−0.403205	+	1.76655i	−0.614283	+	0.789086i	$0.710555\pi$
$14$	1.49948	−	0.722111i	0.400753	−	0.192992i
$15$		0			0
$16$	−0.297197	+	1.30211i	−0.0742994	+	0.325527i
$17$	3.81642			0.925617			0.462808	−	0.886458i	$-0.346842\pi$
$17$	3.81642			0.925617			0.462808	+	0.886458i	$0.346842\pi$
$18$		0			0
$19$	−2.69251	−	3.37631i	−0.617705	−	0.774578i	0.370315	−	0.928906i	$-0.379250\pi$
$19$	−2.69251	−	3.37631i	−0.617705	−	0.774578i	−0.988020	+	0.154329i	$0.950678\pi$
$20$	0.681165	+	2.98438i	0.152313	+	0.667328i
$21$		0			0
$22$	0.415040	−	0.520444i	0.0884868	−	0.110959i
$23$	−4.85446	+	2.33778i	−1.01222	+	0.487462i	−0.865070	−	0.501652i	$-0.832726\pi$
$23$	−4.85446	+	2.33778i	−1.01222	+	0.487462i	−0.147155	+	0.989113i	$0.547012\pi$
$24$		0			0
$25$	−0.578892	−	0.725907i	−0.115778	−	0.145181i
$26$	2.83075	−	3.54965i	0.555156	−	0.696144i
$27$		0			0
$28$	3.63318			0.686607
$29$	−5.32202	+	0.822256i	−0.988274	+	0.152689i
$29$	−5.32202	+	0.822256i	−0.988274	+	0.152689i
$30$		0			0
$31$	−2.46382	−	1.18651i	−0.442515	−	0.213104i	0.199339	−	0.979931i	$-0.436120\pi$
$31$	−2.46382	−	1.18651i	−0.442515	−	0.213104i	−0.641855	+	0.766826i	$0.721835\pi$
$32$	3.62649	−	4.54747i	0.641079	−	0.803887i
$33$		0			0
$34$	−2.38953	−	1.15074i	−0.409800	−	0.197349i
$35$	4.35384	−	2.09670i	0.735934	−	0.354407i
$36$		0			0
$37$	0.414041	+	1.81403i	0.0680679	+	0.298225i	0.997491	−	0.0707903i	$-0.0225521\pi$
$37$	0.414041	+	1.81403i	0.0680679	+	0.298225i	−0.929423	+	0.369015i	$0.879695\pi$
$38$	0.667799	+	2.92582i	0.108331	+	0.474631i
$39$		0			0
$40$	1.09743	−	4.80814i	0.173519	−	0.760234i
$41$	−11.8282			−1.84725			−0.923624	−	0.383300i	$-0.874788\pi$
$41$	−11.8282			−1.84725			−0.923624	+	0.383300i	$0.874788\pi$
$42$		0			0
$43$	3.33752	−	1.60727i	0.508967	−	0.245106i	−0.161733	−	0.986835i	$-0.551708\pi$
$43$	3.33752	−	1.60727i	0.508967	−	0.245106i	0.670700	+	0.741729i	$0.265994\pi$
$44$	1.30926	−	0.630508i	0.197379	−	0.0950526i
$45$		0			0
$46$	3.74436			0.552075
$47$	−0.719344	+	3.15165i	−0.104927	+	0.459716i	0.894980	+	0.446106i	$0.147189\pi$
$47$	−0.719344	+	3.15165i	−0.104927	+	0.459716i	−0.999907	+	0.0136100i	$0.995668\pi$
$48$		0			0
$49$	0.281385	+	1.23283i	0.0401979	+	0.176119i
$50$	0.143577	+	0.629053i	0.0203049	+	0.0889615i
$51$		0			0
$52$	8.92974	−	4.30034i	1.23833	−	0.596350i
$53$	2.04315	+	0.983927i	0.280648	+	0.135153i	0.568913	−	0.822398i	$-0.307364\pi$
$53$	2.04315	+	0.983927i	0.280648	+	0.135153i	−0.288265	+	0.957551i	$0.593078\pi$
$54$		0			0
$55$	1.20510	−	1.51115i	0.162495	−	0.203763i
$56$	−5.27376	−	2.53971i	−0.704736	−	0.339383i
$57$		0			0
$58$	3.58014	+	1.08988i	0.470096	+	0.143108i
$59$	9.30726			1.21170			0.605851	−	0.795578i	$-0.292833\pi$
$59$	9.30726			1.21170			0.605851	+	0.795578i	$0.292833\pi$
$60$		0			0
$61$	1.95684	−	2.45380i	0.250547	−	0.314176i	−0.640614	−	0.767863i	$-0.721320\pi$
$61$	1.95684	−	2.45380i	0.250547	−	0.314176i	0.891161	+	0.453687i	$0.149891\pi$
$62$	1.18488	+	1.48579i	0.150480	+	0.188696i
$63$		0			0
$64$	−1.23512	+	0.594802i	−0.154390	+	0.0743503i
$65$	8.21929	−	10.3067i	1.01948	−	1.27838i
$66$		0			0
$67$	−2.69277	−	11.7978i	−0.328975	−	1.44133i	−0.821088	−	0.570801i	$-0.806633\pi$
$67$	−2.69277	−	11.7978i	−0.328975	−	1.44133i	0.492113	−	0.870531i	$-0.336225\pi$
$68$	−3.60984	−	4.52660i	−0.437757	−	0.548930i
$69$		0			0
$70$	−3.35822			−0.401384
$71$	−1.02436	+	4.48801i	−0.121569	+	0.532629i	0.877065	+	0.480373i	$0.159499\pi$
$71$	−1.02436	+	4.48801i	−0.121569	+	0.532629i	−0.998634	+	0.0522567i	$0.983359\pi$
$72$		0			0
$73$	−8.19102	+	3.94459i	−0.958687	+	0.461679i	−0.846723	−	0.532033i	$-0.821428\pi$
$73$	−8.19102	+	3.94459i	−0.958687	+	0.461679i	−0.111963	+	0.993712i	$0.535714\pi$
$74$	0.287733	−	1.26064i	0.0334483	−	0.146547i
$75$		0			0
$76$	−1.45781	+	6.38710i	−0.167223	+	0.732651i
$77$	−1.43030	−	1.79354i	−0.162998	−	0.204393i
$78$		0			0
$79$	−0.954127	−	4.18030i	−0.107348	−	0.470321i	−0.999815	−	0.0192099i	$-0.993885\pi$
$79$	−0.954127	−	4.18030i	−0.107348	−	0.470321i	0.892468	−	0.451111i	$-0.148972\pi$
$80$	1.68028	−	2.10701i	0.187861	−	0.235571i
$81$		0			0
$82$	7.40582	+	3.56646i	0.817836	+	0.393849i
$83$	−10.0888	−	12.6510i	−1.10739	−	1.38863i	−0.913124	−	0.407681i	$-0.866338\pi$
$83$	−10.0888	−	12.6510i	−1.10739	−	1.38863i	−0.194270	−	0.980948i	$-0.562234\pi$
$84$		0			0
$85$	−6.93816	−	3.34124i	−0.752549	−	0.362408i
$86$	−2.57431			−0.277595
$87$		0			0
$88$	−2.34121			−0.249574
$89$	13.9137	+	6.70047i	1.47485	+	0.710248i	0.986706	−	0.162517i	$-0.0519612\pi$
$89$	13.9137	+	6.70047i	1.47485	+	0.710248i	0.488140	+	0.872765i	$0.337675\pi$
$90$		0			0
$91$	−9.75529	−	12.2327i	−1.02263	−	1.28234i
$92$	7.36451	+	3.54656i	0.767803	+	0.369754i
$93$		0			0
$94$	1.40069	−	1.75641i	0.144470	−	0.181160i
$95$	1.93900	+	8.49532i	0.198937	+	0.871602i
$96$		0			0
$97$	9.82817	+	12.3241i	0.997899	+	1.25133i	0.967785	+	0.251780i	$0.0810159\pi$
$97$	9.82817	+	12.3241i	0.997899	+	1.25133i	0.0301150	+	0.999546i	$0.490413\pi$
$98$	0.195546	−	0.856741i	0.0197531	−	0.0865439i
$99$		0			0
$100$	−0.313431	+	1.37323i	−0.0313431	+	0.137323i
$101$	8.33981	−	4.01624i	0.829842	−	0.399631i	0.0297862	−	0.999556i	$-0.490517\pi$
$101$	8.33981	−	4.01624i	0.829842	−	0.399631i	0.800056	+	0.599925i	$0.204803\pi$
$102$		0			0
$103$	−2.35751	+	10.3289i	−0.232292	+	1.01774i	0.715440	+	0.698674i	$0.246226\pi$
$103$	−2.35751	+	10.3289i	−0.232292	+	1.01774i	−0.947733	+	0.319065i	$0.896631\pi$
$104$	−15.9681			−1.56580
$105$		0			0
$106$	−0.982574	−	1.23211i	−0.0954360	−	0.119673i
$107$	−0.0279718	−	0.122553i	−0.00270414	−	0.0118476i	0.973558	−	0.228441i	$-0.0733627\pi$
$107$	−0.0279718	−	0.122553i	−0.00270414	−	0.0118476i	−0.976262	+	0.216593i	$0.930506\pi$
$108$		0			0
$109$	−6.01455	+	7.54201i	−0.576089	+	0.722393i	−0.981440	−	0.191768i	$-0.938578\pi$
$109$	−6.01455	+	7.54201i	−0.576089	+	0.722393i	0.405351	+	0.914161i	$0.367149\pi$
$110$	−1.21018	+	0.582791i	−0.115386	+	0.0555669i
$111$		0			0
$112$	−1.99429	−	2.50076i	−0.188442	−	0.236299i
$113$	−1.93810	+	2.43030i	−0.182321	+	0.228623i	−0.864590	−	0.502478i	$-0.832422\pi$
$113$	−1.93810	+	2.43030i	−0.182321	+	0.228623i	0.682269	+	0.731101i	$0.260993\pi$
$114$		0			0
$115$	10.8720			1.01382
$116$	6.00921	+	5.53462i	0.557941	+	0.513877i
$117$		0			0
$118$	−5.82744	−	2.80635i	−0.536460	−	0.258345i
$119$	−5.69862	+	7.14584i	−0.522391	+	0.655058i
$120$		0			0
$121$	9.08398	+	4.37461i	0.825816	+	0.397692i
$122$	−1.96509	+	0.946336i	−0.177911	+	0.0856772i
$123$		0			0
$124$	0.923152	+	4.04459i	0.0829015	+	0.363215i
$125$	2.66190	+	11.6626i	0.238088	+	1.04313i
$126$		0			0
$127$	0.872287	−	3.82174i	0.0774029	−	0.339124i	−0.921368	−	0.388692i	$-0.872927\pi$
$127$	0.872287	−	3.82174i	0.0774029	−	0.339124i	0.998771	+	0.0495674i	$0.0157843\pi$
$128$	−10.6802			−0.944005
$129$		0			0
$130$	−8.25394	+	3.97489i	−0.723918	+	0.348621i
$131$	−14.8614	+	7.15689i	−1.29845	+	0.625300i	−0.950065	−	0.312052i	$-0.898984\pi$
$131$	−14.8614	+	7.15689i	−1.29845	+	0.625300i	−0.348384	+	0.937352i	$0.613270\pi$
$132$		0			0
$133$	10.3422			0.896782
$134$	−1.87131	+	8.19876i	−0.161657	+	0.708265i
$135$		0			0
$136$	2.07564	+	9.09399i	0.177985	+	0.779803i
$137$	−0.677588	−	2.96871i	−0.0578902	−	0.253634i	0.937700	−	0.347447i	$-0.112951\pi$
$137$	−0.677588	−	2.96871i	−0.0578902	−	0.253634i	−0.995590	+	0.0938135i	$0.970094\pi$
$138$		0			0
$139$	−10.1634	+	4.89444i	−0.862050	+	0.415141i	−0.812036	−	0.583607i	$-0.801641\pi$
$139$	−10.1634	+	4.89444i	−0.862050	+	0.415141i	−0.0500136	+	0.998749i	$0.515926\pi$
$140$	−6.60505	−	3.18082i	−0.558228	−	0.268829i
$141$		0			0
$142$	1.99461	−	2.50116i	0.167384	−	0.209893i
$143$	−5.63833	−	2.71528i	−0.471501	−	0.227063i
$144$		0			0
$145$	10.3952	+	3.16454i	0.863274	+	0.262801i
$146$	6.31793			0.522875
$147$		0			0
$148$	1.75997	−	2.20693i	0.144668	−	0.181408i
$149$	−3.05371	−	3.82923i	−0.250170	−	0.313703i	0.640851	−	0.767665i	$-0.278582\pi$
$149$	−3.05371	−	3.82923i	−0.250170	−	0.313703i	−0.891021	+	0.453962i	$0.850010\pi$
$150$		0			0
$151$	−15.3405	+	7.38759i	−1.24839	+	0.601194i	−0.937080	−	0.349114i	$-0.886483\pi$
$151$	−15.3405	+	7.38759i	−1.24839	+	0.601194i	−0.311312	+	0.950308i	$0.600768\pi$
$152$	6.58088	−	8.25217i	0.533780	−	0.669339i
$153$		0			0
$154$	0.354745	+	1.55424i	0.0285861	+	0.125244i
$155$	3.44039	+	4.31411i	0.276339	+	0.346518i
$156$		0			0
$157$	20.3897			1.62728			0.813639	−	0.581371i	$-0.197483\pi$
$157$	20.3897			1.62728			0.813639	+	0.581371i	$0.197483\pi$
$158$	−0.663060	+	2.90505i	−0.0527502	+	0.231114i
$159$		0			0
$160$	−10.5742	+	5.09224i	−0.835960	+	0.402577i
$161$	2.87135	−	12.5802i	0.226294	−	0.991459i
$162$		0			0
$163$	−1.69789	+	7.43895i	−0.132989	+	0.582664i	0.863887	+	0.503685i	$0.168023\pi$
$163$	−1.69789	+	7.43895i	−0.132989	+	0.582664i	−0.996876	+	0.0789783i	$0.974834\pi$
$164$	11.1879	+	14.0292i	0.873630	+	1.09550i
$165$		0			0
$166$	2.50224	+	10.9630i	0.194212	+	0.850897i
$167$	13.5489	−	16.9898i	1.04845	−	1.31471i	0.100972	−	0.994889i	$-0.467805\pi$
$167$	13.5489	−	16.9898i	1.04845	−	1.31471i	0.947477	−	0.319824i	$-0.103624\pi$
$168$		0			0
$169$	−26.7433	−	12.8789i	−2.05717	−	0.990682i
$170$	3.33665	+	4.18402i	0.255909	+	0.320900i
$171$		0			0
$172$	−5.06322	−	2.43832i	−0.386067	−	0.185920i
$173$	−4.01358			−0.305147			−0.152573	−	0.988292i	$-0.548756\pi$
$173$	−4.01358			−0.305147			−0.152573	+	0.988292i	$0.548756\pi$
$174$		0			0
$175$	2.22358			0.168087
$176$	−1.15265	−	0.555088i	−0.0868844	−	0.0418413i
$177$		0			0
$178$	−6.69126	−	8.39057i	−0.501531	−	0.628900i
$179$	−3.48470	−	1.67814i	−0.260459	−	0.125430i	0.299098	−	0.954222i	$-0.403314\pi$
$179$	−3.48470	−	1.67814i	−0.260459	−	0.125430i	−0.559557	+	0.828792i	$0.689029\pi$
$180$		0			0
$181$	10.3685	−	13.0017i	0.770686	−	0.966410i	−0.229290	−	0.973358i	$-0.573640\pi$
$181$	10.3685	−	13.0017i	0.770686	−	0.966410i	0.999976	+	0.00694853i	$0.00221180\pi$
$182$	2.41951	+	10.6006i	0.179346	+	0.785767i
$183$		0			0
$184$	−8.21082	−	10.2960i	−0.605310	−	0.759034i
$185$	0.835453	−	3.66036i	0.0614237	−	0.269115i
$186$		0			0
$187$	−0.813469	+	3.56404i	−0.0594867	+	0.260628i
$188$	4.41854	−	2.12785i	0.322255	−	0.155190i
$189$		0			0
$190$	1.34749	−	5.90373i	0.0977570	−	0.428301i
$191$	2.64112			0.191105			0.0955525	−	0.995424i	$-0.469538\pi$
$191$	2.64112			0.191105			0.0955525	+	0.995424i	$0.469538\pi$
$192$		0			0
$193$	4.07831	+	5.11404i	0.293563	+	0.368117i	0.906639	−	0.421907i	$-0.138639\pi$
$193$	4.07831	+	5.11404i	0.293563	+	0.368117i	−0.613075	+	0.790024i	$0.710068\pi$
$194$	−2.43759	−	10.6798i	−0.175009	−	0.766763i
$195$		0			0
$196$	1.19609	−	1.49985i	0.0854348	−	0.107132i
$197$	−8.85143	+	4.26262i	−0.630638	+	0.303699i	−0.721763	−	0.692140i	$-0.756668\pi$
$197$	−8.85143	+	4.26262i	−0.630638	+	0.303699i	0.0911250	+	0.995839i	$0.470954\pi$
$198$		0			0
$199$	0.327153	+	0.410236i	0.0231912	+	0.0290809i	0.793292	−	0.608842i	$-0.208365\pi$
$199$	0.327153	+	0.410236i	0.0231912	+	0.0290809i	−0.770101	+	0.637922i	$0.779794\pi$
$200$	1.41489	−	1.77422i	0.100048	−	0.125456i
$201$		0			0
$202$	−6.43269			−0.452603
$203$	6.40717	−	11.1927i	0.449695	−	0.785574i
$204$		0			0
$205$	21.5033	+	10.3555i	1.50186	+	0.723257i
$206$	4.59048	−	5.75628i	0.319834	−	0.401059i
$207$		0			0
$208$	−7.86159	−	3.78594i	−0.545103	−	0.262508i
$209$	3.72694	−	1.79480i	0.257798	−	0.124149i
$210$		0			0
$211$	−3.68219	−	16.1327i	−0.253493	−	1.11062i	−0.928066	−	0.372416i	$-0.878529\pi$
$211$	−3.68219	−	16.1327i	−0.253493	−	1.11062i	0.674573	−	0.738208i	$-0.264328\pi$
$212$	−0.765532	−	3.35401i	−0.0525770	−	0.230355i
$213$		0			0
$214$	−0.0194387	+	0.0851665i	−0.00132880	+	0.00582186i
$215$	−7.47469			−0.509769
$216$		0			0
$217$	5.90056	−	2.84156i	0.400556	−	0.192898i
$218$	6.03990	−	2.90866i	0.409074	−	0.197000i
$219$		0			0
$220$	−2.93222			−0.197690
$221$	−5.54821	+	24.3083i	−0.373213	+	1.63515i
$222$		0			0
$223$	2.61351	+	11.4505i	0.175014	+	0.766785i	0.983885	+	0.178800i	$0.0572215\pi$
$223$	2.61351	+	11.4505i	0.175014	+	0.766785i	−0.808872	+	0.587985i	$0.799921\pi$
$224$	3.09965	+	13.5804i	0.207104	+	0.907381i
$225$		0			0
$226$	1.94627	−	0.937273i	0.129464	−	0.0623465i
$227$	−19.1970	−	9.24479i	−1.27415	−	0.613598i	−0.330270	−	0.943887i	$-0.607140\pi$
$227$	−19.1970	−	9.24479i	−1.27415	−	0.613598i	−0.943880	+	0.330288i	$0.892854\pi$
$228$		0			0
$229$	0.114294	−	0.143320i	0.00755275	−	0.00947084i	−0.778041	−	0.628214i	$-0.783786\pi$
$229$	0.114294	−	0.143320i	0.00755275	−	0.00947084i	0.785594	+	0.618743i	$0.212358\pi$
$230$	−6.80716	−	3.27816i	−0.448851	−	0.216155i
$231$		0			0
$232$	−4.85382	−	12.2344i	−0.318669	−	0.803230i
$233$	23.8810			1.56449			0.782247	−	0.622969i	$-0.214074\pi$
$233$	23.8810			1.56449			0.782247	+	0.622969i	$0.214074\pi$
$234$		0			0
$235$	4.06700	−	5.09985i	0.265302	−	0.332678i
$236$	−8.80347	−	11.0392i	−0.573057	−	0.718591i
$237$		0			0
$238$	5.72264	−	2.75588i	0.370943	−	0.178637i
$239$	5.24316	−	6.57471i	0.339152	−	0.425283i	−0.582783	−	0.812628i	$-0.698036\pi$
$239$	5.24316	−	6.57471i	0.339152	−	0.425283i	0.921935	+	0.387345i	$0.126608\pi$
$240$		0			0
$241$	0.119797	+	0.524865i	0.00771681	+	0.0338095i	0.978640	−	0.205583i	$-0.0659090\pi$
$241$	0.119797	+	0.524865i	0.00771681	+	0.0338095i	−0.970923	+	0.239392i	$0.923052\pi$
$242$	−4.36860	−	5.47805i	−0.280824	−	0.352142i
$243$		0			0
$244$	−4.76133			−0.304813
$245$	0.567780	−	2.48761i	0.0362742	−	0.158927i
$246$		0			0
$247$	25.4194	−	12.2413i	1.61740	−	0.778896i
$248$	1.48729	−	6.51625i	0.0944432	−	0.413783i
$249$		0			0
$250$	1.84986	−	8.10476i	0.116995	−	0.512590i
$251$	1.06622	+	1.33699i	0.0672989	+	0.0843902i	0.814341	−	0.580386i	$-0.197098\pi$
$251$	1.06622	+	1.33699i	0.0672989	+	0.0843902i	−0.747043	+	0.664776i	$0.768527\pi$
$252$		0			0
$253$	−1.14846	−	5.03173i	−0.0722031	−	0.316342i
$254$	−1.69849	+	2.12984i	−0.106573	+	0.133638i
$255$		0			0
$256$	9.15730	+	4.40992i	0.572331	+	0.275620i
$257$	11.2754	+	14.1389i	0.703339	+	0.881959i	0.997268	−	0.0738684i	$-0.0235345\pi$
$257$	11.2754	+	14.1389i	0.703339	+	0.881959i	−0.293929	+	0.955827i	$0.594963\pi$
$258$		0			0
$259$	−4.01482	−	1.93344i	−0.249469	−	0.120138i
$260$	−19.9990			−1.24028
$261$		0			0
$262$	11.4630			0.708185
$263$	0.869873	+	0.418909i	0.0536387	+	0.0258310i	0.460511	−	0.887654i	$-0.347666\pi$
$263$	0.869873	+	0.418909i	0.0536387	+	0.0258310i	−0.406872	+	0.913485i	$0.633381\pi$
$264$		0			0
$265$	−2.85297	−	3.57752i	−0.175257	−	0.219765i
$266$	−6.47544	−	3.11841i	−0.397035	−	0.191202i
$267$		0			0
$268$	−11.4462	+	14.3531i	−0.699188	+	0.876754i
$269$	2.16024	+	9.46463i	0.131712	+	0.577069i	0.997109	+	0.0759819i	$0.0242091\pi$
$269$	2.16024	+	9.46463i	0.131712	+	0.577069i	−0.865397	+	0.501087i	$0.832934\pi$
$270$		0			0
$271$	10.5687	+	13.2527i	0.642002	+	0.805045i	0.991252	−	0.131985i	$-0.0421350\pi$
$271$	10.5687	+	13.2527i	0.642002	+	0.805045i	−0.349250	+	0.937030i	$0.613564\pi$
$272$	−1.13423	+	4.96938i	−0.0687727	+	0.301313i
$273$		0			0
$274$	−0.470882	+	2.06307i	−0.0284470	+	0.124635i
$275$	0.801294	−	0.385883i	0.0483199	−	0.0232696i
$276$		0			0
$277$	4.90011	−	21.4688i	0.294419	−	1.28994i	−0.583886	−	0.811835i	$-0.698469\pi$
$277$	4.90011	−	21.4688i	0.294419	−	1.28994i	0.878306	−	0.478100i	$-0.158674\pi$
$278$	7.83928			0.470169
$279$		0			0
$280$	7.36408	+	9.23427i	0.440088	+	0.551853i
$281$	2.38729	+	10.4594i	0.142414	+	0.623957i	0.994870	+	0.101158i	$0.0322548\pi$
$281$	2.38729	+	10.4594i	0.142414	+	0.623957i	−0.852456	+	0.522798i	$0.824888\pi$
$282$		0			0
$283$	9.48869	−	11.8984i	0.564044	−	0.707289i	−0.415256	−	0.909705i	$-0.636308\pi$
$283$	9.48869	−	11.8984i	0.564044	−	0.707289i	0.979300	+	0.202416i	$0.0648793\pi$
$284$	6.29208	−	3.03011i	0.373366	−	0.179804i
$285$		0			0
$286$	2.71154	+	3.40017i	0.160337	+	0.201056i
$287$	17.6616	−	22.1470i	1.04253	−	1.30730i
$288$		0			0
$289$	−2.43497			−0.143234
$290$	−5.55444	−	5.11576i	−0.326168	−	0.300408i
$291$		0			0
$292$	12.4263	+	5.98418i	0.727193	+	0.350198i
$293$	−14.4563	+	18.1276i	−0.844547	+	1.05903i	0.152944	+	0.988235i	$0.451125\pi$
$293$	−14.4563	+	18.1276i	−0.844547	+	1.05903i	−0.997491	+	0.0707934i	$0.977447\pi$
$294$		0			0
$295$	−16.9204	−	8.14843i	−0.985143	−	0.474420i
$296$	−4.09740	+	1.97320i	−0.238157	+	0.114690i
$297$		0			0
$298$	0.757384	+	3.31832i	0.0438741	+	0.192225i
$299$	−7.83300	−	34.3186i	−0.452994	−	1.98470i
$300$		0			0
$301$	−1.97410	+	8.64910i	−0.113785	+	0.498526i
$302$	11.8325			0.680883
$303$		0			0
$304$	5.19652	−	2.50251i	0.298041	−	0.143529i
$305$	−5.70577	+	2.74775i	−0.326711	+	0.157336i
$306$		0			0
$307$	−18.8555			−1.07614			−0.538070	−	0.842900i	$-0.680846\pi$
$307$	−18.8555			−1.07614			−0.538070	+	0.842900i	$0.680846\pi$
$308$	−0.774413	+	3.39292i	−0.0441262	+	0.193330i
$309$		0			0
$310$	−0.853287	−	3.73850i	−0.0484635	−	0.212332i
$311$	6.04072	+	26.4661i	0.342538	+	1.50076i	0.793698	+	0.608312i	$0.208153\pi$
$311$	6.04072	+	26.4661i	0.342538	+	1.50076i	−0.451160	+	0.892443i	$0.648990\pi$
$312$		0			0
$313$	−6.67788	+	3.21590i	−0.377456	+	0.181773i	−0.612986	−	0.790094i	$-0.710032\pi$
$313$	−6.67788	+	3.21590i	−0.377456	+	0.181773i	0.235530	+	0.971867i	$0.424317\pi$
$314$	−12.7664	−	6.14796i	−0.720448	−	0.346950i
$315$		0			0
$316$	−4.05572	+	5.08571i	−0.228152	+	0.286093i
$317$	2.01091	+	0.968401i	0.112944	+	0.0543908i	0.489502	−	0.872002i	$-0.337178\pi$
$317$	2.01091	+	0.968401i	0.112944	+	0.0543908i	−0.376559	+	0.926393i	$0.622893\pi$
$318$		0			0
$319$	0.366507	−	5.14534i	0.0205205	−	0.288084i
$320$	2.76617			0.154633
$321$		0			0
$322$	−5.59102	+	7.01092i	−0.311575	+	0.390703i
$323$	−10.2758	−	12.8854i	−0.571758	−	0.716962i
$324$		0			0
$325$	5.46518	−	2.63189i	0.303153	−	0.145991i
$326$	3.30609	−	4.14571i	0.183108	−	0.229610i
$327$		0			0
$328$	−6.43301	−	28.1849i	−0.355204	−	1.55625i
$329$	−4.82702	−	6.05290i	−0.266122	−	0.333707i
$330$		0			0
$331$	−23.2235			−1.27648			−0.638241	−	0.769837i	$-0.720337\pi$
$331$	−23.2235			−1.27648			−0.638241	+	0.769837i	$0.720337\pi$
$332$	−5.46243	+	23.9325i	−0.299790	+	1.31346i
$333$		0			0
$334$	−13.6061	+	6.55233i	−0.744491	+	0.358528i
$335$	−5.43349	+	23.8057i	−0.296863	+	1.30064i
$336$		0			0
$337$	−6.02416	+	26.3936i	−0.328157	+	1.43775i	0.494484	+	0.869187i	$0.335357\pi$
$337$	−6.02416	+	26.3936i	−0.328157	+	1.43775i	−0.822641	+	0.568562i	$0.807500\pi$
$338$	12.8612	+	16.1274i	0.699555	+	0.877214i
$339$		0			0
$340$	2.59961	+	11.3896i	0.140984	+	0.617690i
$341$	1.63321	−	2.04798i	0.0884435	−	0.110905i
$342$		0			0
$343$	−17.8325	−	8.58769i	−0.962865	−	0.463691i
$344$	5.64508	+	7.07870i	0.304362	+	0.381658i
$345$		0			0
$346$	2.51297	+	1.21018i	0.135098	+	0.0650599i
$347$	33.0378			1.77356			0.886780	−	0.462191i	$-0.152937\pi$
$347$	33.0378			1.77356			0.886780	+	0.462191i	$0.152937\pi$
$348$		0			0
$349$	6.36434			0.340675			0.170338	−	0.985386i	$-0.445514\pi$
$349$	6.36434			0.340675			0.170338	+	0.985386i	$0.445514\pi$
$350$	−1.39222	−	0.670459i	−0.0744174	−	0.0358375i
$351$		0			0
$352$	3.47377	+	4.35597i	0.185152	+	0.232174i
$353$	15.8323	+	7.62444i	0.842669	+	0.405808i	0.804851	−	0.593477i	$-0.202245\pi$
$353$	15.8323	+	7.62444i	0.842669	+	0.405808i	0.0378175	+	0.999285i	$0.487959\pi$
$354$		0			0
$355$	5.79148	−	7.26229i	0.307380	−	0.385442i
$356$	−5.21322	−	22.8406i	−0.276300	−	1.21055i
$357$		0			0
$358$	1.67584	+	2.10143i	0.0885707	+	0.111064i
$359$	1.74009	−	7.62384i	0.0918385	−	0.402371i	−0.908025	−	0.418917i	$-0.862410\pi$
$359$	1.74009	−	7.62384i	0.0918385	−	0.402371i	0.999863	+	0.0165460i	$0.00526700\pi$
$360$		0			0
$361$	0.0780901	−	0.342135i	0.00411000	−	0.0180071i
$362$	−10.4122	+	5.01426i	−0.547254	+	0.263544i
$363$		0			0
$364$	−5.28183	+	23.1412i	−0.276843	+	1.21293i
$365$	18.3446			0.960198
$366$		0			0
$367$	18.1847	+	22.8028i	0.949231	+	1.19030i	0.981624	+	0.190823i	$0.0611157\pi$
$367$	18.1847	+	22.8028i	0.949231	+	1.19030i	−0.0323932	+	0.999475i	$0.510313\pi$
$368$	−1.60131	−	7.01581i	−0.0834742	−	0.365724i
$369$		0			0
$370$	−1.62677	+	2.03991i	−0.0845719	+	0.106050i
$371$	−4.89310	+	2.35639i	−0.254037	+	0.122338i
$372$		0			0
$373$	−3.65125	−	4.57852i	−0.189054	−	0.237067i	0.678267	−	0.734816i	$-0.262731\pi$
$373$	−3.65125	−	4.57852i	−0.189054	−	0.237067i	−0.867321	+	0.497749i	$0.834160\pi$
$374$	1.58397	−	1.98623i	0.0819049	−	0.102705i
$375$		0			0
$376$	−7.90118			−0.407472
$377$	2.49974	−	35.0935i	0.128743	−	1.80741i
$378$		0			0
$379$	2.08807	+	1.00556i	0.107257	+	0.0516523i	0.486743	−	0.873545i	$-0.338185\pi$
$379$	2.08807	+	1.00556i	0.107257	+	0.0516523i	−0.379486	+	0.925198i	$0.623899\pi$
$380$	8.24213	−	10.3353i	0.422812	−	0.530190i
$381$		0			0
$382$	−1.65366	−	0.796358i	−0.0846084	−	0.0407452i
$383$	−16.4369	+	7.91562i	−0.839889	+	0.404469i	−0.803815	−	0.594880i	$-0.797200\pi$
$383$	−16.4369	+	7.91562i	−0.839889	+	0.404469i	−0.0360743	+	0.999349i	$0.511485\pi$
$384$		0			0
$385$	1.03003	+	4.51284i	0.0524950	+	0.229996i
$386$	−1.01151	−	4.43170i	−0.0514843	−	0.225568i
$387$		0			0
$388$	5.32129	−	23.3141i	0.270148	−	1.18359i
$389$	−29.6576			−1.50370			−0.751850	−	0.659335i	$-0.770838\pi$
$389$	−29.6576			−1.50370			−0.751850	+	0.659335i	$0.770838\pi$
$390$		0			0
$391$	−18.5266	+	8.92195i	−0.936932	+	0.451203i
$392$	−2.78463	+	1.34100i	−0.140645	+	0.0677310i
$393$		0			0
$394$	6.82732			0.343955
$395$	−1.92524	+	8.43503i	−0.0968694	+	0.424413i
$396$		0			0
$397$	−0.452224	−	1.98132i	−0.0226965	−	0.0994398i	0.962311	−	0.271951i	$-0.0876690\pi$
$397$	−0.452224	−	1.98132i	−0.0226965	−	0.0994398i	−0.985008	+	0.172511i	$0.944812\pi$
$398$	−0.0811406	−	0.355500i	−0.00406721	−	0.0178196i
$399$		0			0
$400$	1.11725	−	0.538041i	0.0558627	−	0.0269021i
$401$	−0.128477	−	0.0618714i	−0.00641585	−	0.00308971i	0.430673	−	0.902508i	$-0.358276\pi$
$401$	−0.128477	−	0.0618714i	−0.00641585	−	0.00308971i	−0.437089	+	0.899418i	$0.643990\pi$
$402$		0			0
$403$	11.1392	−	13.9681i	0.554884	−	0.695803i
$404$	−12.6520	−	6.09288i	−0.629460	−	0.303132i
$405$		0			0
$406$	−7.38650	+	5.07605i	−0.366586	+	0.251920i
$407$	−1.78232			−0.0883465
$408$		0			0
$409$	−12.9332	+	16.2178i	−0.639507	+	0.801917i	−0.990941	−	0.134296i	$-0.957123\pi$
$409$	−12.9332	+	16.2178i	−0.639507	+	0.801917i	0.351434	+	0.936213i	$0.385694\pi$
$410$	−10.3412	−	12.9675i	−0.510716	−	0.640418i
$411$		0			0
$412$	14.4809	−	6.97363i	0.713422	−	0.343566i
$413$	−13.8975	+	17.4269i	−0.683849	+	0.857520i
$414$		0			0
$415$	7.26544	+	31.8320i	0.356646	+	1.56257i
$416$	23.6926	+	29.7096i	1.16163	+	1.45663i
$417$		0			0
$418$	−2.87468			−0.140605
$419$	1.45786	−	6.38728i	0.0712209	−	0.312039i	−0.926752	−	0.375673i	$-0.877412\pi$
$419$	1.45786	−	6.38728i	0.0712209	−	0.312039i	0.997973	+	0.0636334i	$0.0202688\pi$
$420$		0			0
$421$	−7.77401	+	3.74377i	−0.378882	+	0.182460i	−0.613625	−	0.789597i	$-0.710289\pi$
$421$	−7.77401	+	3.74377i	−0.378882	+	0.182460i	0.234743	+	0.972057i	$0.424575\pi$
$422$	−2.55890	+	11.2113i	−0.124565	+	0.545756i
$423$		0			0
$424$	−1.23335	+	5.40366i	−0.0598968	+	0.262425i
$425$	−2.20929	−	2.77036i	−0.107166	−	0.134382i
$426$		0			0
$427$	1.67256	+	7.32795i	0.0809406	+	0.354624i
$428$	−0.118900	+	0.149096i	−0.00574725	+	0.00720683i
$429$		0			0
$430$	4.68004	+	2.25379i	0.225691	+	0.108687i
$431$	−19.6857	−	24.6850i	−0.948225	−	1.18904i	−0.981861	−	0.189602i	$-0.939280\pi$
$431$	−19.6857	−	24.6850i	−0.948225	−	1.18904i	0.0336362	−	0.999434i	$-0.489291\pi$
$432$		0			0
$433$	2.83832	+	1.36686i	0.136401	+	0.0656873i	0.500839	−	0.865540i	$-0.333025\pi$
$433$	2.83832	+	1.36686i	0.136401	+	0.0656873i	−0.364438	+	0.931228i	$0.618739\pi$
$434$	−4.55124			−0.218467
$435$		0			0
$436$	14.6345			0.700863
$437$	20.9638	+	10.0956i	1.00283	+	0.482939i
$438$		0			0
$439$	14.2209	+	17.8324i	0.678727	+	0.851096i	0.995236	−	0.0974931i	$-0.0310824\pi$
$439$	14.2209	+	17.8324i	0.678727	+	0.851096i	−0.316510	+	0.948589i	$0.602511\pi$
$440$	4.25627	+	2.04971i	0.202910	+	0.0977161i
$441$		0			0
$442$	10.8033	−	13.5469i	0.513862	−	0.644363i
$443$	4.25594	+	18.6465i	0.202206	+	0.885922i	0.969590	+	0.244735i	$0.0787008\pi$
$443$	4.25594	+	18.6465i	0.202206	+	0.885922i	−0.767384	+	0.641188i	$0.778442\pi$
$444$		0			0
$445$	−19.4285	−	24.3626i	−0.921001	−	1.15490i
$446$	1.81623	−	7.95742i	0.0860010	−	0.376795i
$447$		0			0
$448$	0.730558	−	3.20078i	0.0345156	−	0.151223i
$449$	−35.8493	+	17.2641i	−1.69184	+	0.814745i	−0.696577	+	0.717482i	$0.745294\pi$
$449$	−35.8493	+	17.2641i	−1.69184	+	0.814745i	−0.995259	+	0.0972626i	$0.968991\pi$
$450$		0			0
$451$	2.52117	−	11.0460i	0.118717	−	0.520134i
$452$	4.71573			0.221809
$453$		0			0
$454$	9.23208	+	11.5767i	0.433283	+	0.543320i
$455$	7.02523	+	30.7795i	0.329348	+	1.44297i
$456$		0			0
$457$	18.2165	−	22.8427i	0.852130	−	1.06854i	−0.144739	−	0.989470i	$-0.546234\pi$
$457$	18.2165	−	22.8427i	0.852130	−	1.06854i	0.996869	−	0.0790675i	$-0.0251943\pi$
$458$	−0.114776	+	0.0552730i	−0.00536311	+	0.00258274i
$459$		0			0
$460$	−10.2835	−	12.8951i	−0.479472	−	0.601239i
$461$	−0.612669	+	0.768263i	−0.0285348	+	0.0357816i	−0.795894	−	0.605436i	$-0.792999\pi$
$461$	−0.612669	+	0.768263i	−0.0285348	+	0.0357816i	0.767359	+	0.641217i	$0.221570\pi$
$462$		0			0
$463$	−10.1420			−0.471340			−0.235670	−	0.971833i	$-0.575728\pi$
$463$	−10.1420			−0.471340			−0.235670	+	0.971833i	$0.575728\pi$
$464$	0.511025	−	7.17421i	0.0237238	−	0.333054i
$465$		0			0
$466$	−14.9523	−	7.20065i	−0.692652	−	0.333563i
$467$	−11.2090	+	14.0557i	−0.518692	+	0.650419i	−0.970331	−	0.241782i	$-0.922268\pi$
$467$	−11.2090	+	14.0557i	−0.518692	+	0.650419i	0.451639	+	0.892201i	$0.350840\pi$
$468$		0			0
$469$	26.1110	+	12.5744i	1.20569	+	0.580631i
$470$	−4.08414	+	1.96682i	−0.188387	+	0.0907226i
$471$		0			0
$472$	5.06196	+	22.1779i	0.232996	+	1.02082i
$473$	0.789586	+	3.45940i	0.0363052	+	0.159063i
$474$		0			0
$475$	−0.892211	+	3.90903i	−0.0409374	+	0.179359i
$476$	13.8657			0.635535
$477$		0			0
$478$	−5.26526	+	2.53562i	−0.240827	+	0.115976i
$479$	18.5533	−	8.93481i	0.847723	−	0.408242i	0.0409911	−	0.999160i	$-0.486948\pi$
$479$	18.5533	−	8.93481i	0.847723	−	0.408242i	0.806732	+	0.590918i	$0.201234\pi$
$480$		0			0
$481$	−12.1562			−0.554276
$482$	0.0832516	−	0.364749i	0.00379201	−	0.0166139i
$483$		0			0
$484$	−3.40361	−	14.9122i	−0.154710	−	0.677827i
$485$	−7.07771	−	31.0095i	−0.321382	−	1.40807i
$486$		0			0
$487$	−14.4078	+	6.93844i	−0.652880	+	0.314411i	−0.730843	−	0.682546i	$-0.760873\pi$
$487$	−14.4078	+	6.93844i	−0.652880	+	0.314411i	0.0779626	+	0.996956i	$0.475159\pi$
$488$	6.91133	+	3.32832i	0.312861	+	0.150666i
$489$		0			0
$490$	−1.10557	+	1.38634i	−0.0499444	+	0.0626284i
$491$	−9.19032	−	4.42582i	−0.414753	−	0.199735i	0.214858	−	0.976645i	$-0.431071\pi$
$491$	−9.19032	−	4.42582i	−0.414753	−	0.199735i	−0.629611	+	0.776911i	$0.716786\pi$
$492$		0			0
$493$	−20.3110	+	3.13807i	−0.914763	+	0.141332i
$494$	−19.6066			−0.882141
$495$		0			0
$496$	2.27721	−	2.85553i	0.102250	−	0.128217i
$497$	−6.87378	−	8.61944i	−0.308331	−	0.386635i
$498$		0			0
$499$	5.54276	−	2.66925i	0.248128	−	0.119492i	−0.305687	−	0.952132i	$-0.598886\pi$
$499$	5.54276	−	2.66925i	0.248128	−	0.119492i	0.553815	+	0.832640i	$0.313172\pi$
$500$	11.3150	−	14.1885i	0.506021	−	0.634530i
$501$		0			0
$502$	−0.264443	−	1.15860i	−0.0118027	−	0.0517110i
$503$	12.6166	+	15.8207i	0.562545	+	0.705410i	0.979026	−	0.203735i	$-0.0653081\pi$
$503$	12.6166	+	15.8207i	0.562545	+	0.705410i	−0.416481	+	0.909145i	$0.636737\pi$
$504$		0			0
$505$	−18.6778			−0.831150
$506$	−0.798110	+	3.49675i	−0.0354803	+	0.155449i
$507$		0			0
$508$	−5.35798	+	2.58027i	−0.237722	+	0.114481i
$509$	−0.903261	+	3.95744i	−0.0400363	+	0.175411i	−0.990993	−	0.133913i	$-0.957246\pi$
$509$	−0.903261	+	3.95744i	−0.0400363	+	0.175411i	0.950957	+	0.309324i	$0.100103\pi$
$510$		0			0
$511$	4.84489	−	21.2268i	0.214325	−	0.939020i
$512$	8.91413	+	11.1780i	0.393952	+	0.494001i
$513$		0			0
$514$	−2.79653	−	12.2524i	−0.123350	−	0.540429i
$515$	13.3288	−	16.7138i	0.587337	−	0.736497i
$516$		0			0
$517$	−2.78991	−	1.34355i	−0.122700	−	0.0590892i
$518$	1.93078	+	2.42112i	0.0848335	+	0.106378i
$519$		0			0
$520$	29.0296	+	13.9799i	1.27303	+	0.613060i
$521$	−10.9066			−0.477828			−0.238914	−	0.971041i	$-0.576791\pi$
$521$	−10.9066			−0.477828			−0.238914	+	0.971041i	$0.576791\pi$
$522$		0			0
$523$	3.65147			0.159668			0.0798339	−	0.996808i	$-0.474561\pi$
$523$	3.65147			0.159668			0.0798339	+	0.996808i	$0.474561\pi$
$524$	22.5457	+	10.8574i	0.984913	+	0.474309i
$525$		0			0
$526$	−0.418333	−	0.524573i	−0.0182402	−	0.0228725i
$527$	−9.40296	−	4.52823i	−0.409600	−	0.197253i
$528$		0			0
$529$	3.76026	−	4.71522i	0.163490	−	0.205010i
$530$	0.707596	+	3.10018i	0.0307360	+	0.134663i
$531$		0			0
$532$	−9.78239	−	12.2667i	−0.424121	−	0.531830i
$533$	17.1955	−	75.3383i	0.744819	−	3.26326i
$534$		0			0
$535$	−0.0564416	+	0.247287i	−0.00244018	+	0.0106911i
$536$	26.6480	−	12.8330i	1.15102	−	0.554302i
$537$		0			0
$538$	1.50123	−	6.57734i	0.0647228	−	0.283569i
$539$	−1.21128			−0.0521736
$540$		0			0
$541$	−21.1554	−	26.5281i	−0.909543	−	1.14053i	−0.989615	−	0.143741i	$-0.954087\pi$
$541$	−21.1554	−	26.5281i	−0.909543	−	1.14053i	0.0800725	−	0.996789i	$-0.474485\pi$
$542$	−2.62125	−	11.4845i	−0.112592	−	0.493300i
$543$		0			0
$544$	13.8402	−	17.3550i	0.593393	−	0.744092i
$545$	17.5373	−	8.44551i	0.751215	−	0.361766i
$546$		0			0
$547$	12.2604	+	15.3741i	0.524217	+	0.657347i	0.971498	−	0.237046i	$-0.0761792\pi$
$547$	12.2604	+	15.3741i	0.524217	+	0.657347i	−0.447281	+	0.894393i	$0.647608\pi$
$548$	−2.88023	+	3.61169i	−0.123037	+	0.154284i
$549$		0			0
$550$	−0.618057			−0.0263541
$551$	17.1058	+	15.7548i	0.728731	+	0.671178i
$552$		0			0
$553$	9.25187	+	4.45547i	0.393430	+	0.189466i
$554$	−9.54138	+	11.9645i	−0.405374	+	0.508323i
$555$		0			0
$556$	15.4185	+	7.42517i	0.653891	+	0.314897i
$557$	−34.4588	+	16.5945i	−1.46006	+	0.703130i	−0.984310	−	0.176448i	$-0.943539\pi$
$557$	−34.4588	+	16.5945i	−1.46006	+	0.703130i	−0.475755	+	0.879578i	$0.657825\pi$
$558$		0			0
$559$	5.38532	+	23.5946i	0.227775	+	0.997946i
$560$	1.43618	+	6.29231i	0.0606896	+	0.265898i
$561$		0			0
$562$	1.65902	−	7.26865i	0.0699817	−	0.306610i
$563$	23.4745			0.989330			0.494665	−	0.869084i	$-0.335291\pi$
$563$	23.4745			0.989330			0.494665	+	0.869084i	$0.335291\pi$
$564$		0			0
$565$	5.65113	−	2.72144i	0.237745	−	0.114492i
$566$	−9.52868	+	4.58877i	−0.400520	+	0.192880i
$567$		0			0
$568$	−11.2514			−0.472100
$569$	−0.758682	+	3.32400i	−0.0318056	+	0.139349i	−0.988338	−	0.152277i	$-0.951339\pi$
$569$	−0.758682	+	3.32400i	−0.0318056	+	0.139349i	0.956532	+	0.291627i	$0.0941965\pi$
$570$		0			0
$571$	−5.16346	−	22.6226i	−0.216084	−	0.946726i	−0.960340	−	0.278832i	$-0.910053\pi$
$571$	−5.16346	−	22.6226i	−0.216084	−	0.946726i	0.744256	−	0.667894i	$-0.232804\pi$
$572$	2.11259	+	9.25584i	0.0883316	+	0.387006i
$573$		0			0
$574$	−17.7361	+	8.54125i	−0.740290	+	0.356505i
$575$	4.50722	+	2.17056i	0.187964	+	0.0905187i
$576$		0			0
$577$	−0.183171	+	0.229689i	−0.00762551	+	0.00956209i	−0.785630	−	0.618697i	$-0.787661\pi$
$577$	−0.183171	+	0.229689i	−0.00762551	+	0.00956209i	0.778004	+	0.628259i	$0.216232\pi$
$578$	1.52458	+	0.734199i	0.0634142	+	0.0305387i
$579$		0			0
$580$	−6.07910	−	15.3228i	−0.252421	−	0.636246i
$581$	38.7522			1.60771
$582$		0			0
$583$	−1.35436	+	1.69831i	−0.0560917	+	0.0703368i
$584$	−13.8543	−	17.3727i	−0.573294	−	0.718888i
$585$		0			0
$586$	14.5173	−	6.99114i	0.599702	−	0.288801i
$587$	1.71744	−	2.15360i	0.0708864	−	0.0888888i	−0.745124	−	0.666926i	$-0.767610\pi$
$587$	1.71744	−	2.15360i	0.0708864	−	0.0888888i	0.816010	+	0.578037i	$0.196181\pi$
$588$		0			0
$589$	2.62784	+	11.5133i	0.108278	+	0.474398i
$590$	8.13723	+	10.2038i	0.335004	+	0.420082i
$591$		0			0
$592$	−2.48512			−0.102138
$593$	−4.62823	+	20.2776i	−0.190059	+	0.832701i	0.786524	+	0.617559i	$0.211879\pi$
$593$	−4.62823	+	20.2776i	−0.190059	+	0.832701i	−0.976583	+	0.215142i	$0.930979\pi$
$594$		0			0
$595$	16.6161	−	8.00188i	0.681193	−	0.328045i
$596$	−1.65338	+	7.24393i	−0.0677251	+	0.296723i
$597$		0			0
$598$	−5.44345	+	23.8493i	−0.222599	+	0.975272i
$599$	−21.7810	−	27.3125i	−0.889946	−	1.11596i	−0.992623	−	0.121242i	$-0.961312\pi$
$599$	−21.7810	−	27.3125i	−0.889946	−	1.11596i	0.102677	−	0.994715i	$-0.467259\pi$
$600$		0			0
$601$	−0.641141	−	2.80902i	−0.0261527	−	0.114582i	0.960167	−	0.279428i	$-0.0901447\pi$
$601$	−0.641141	−	2.80902i	−0.0261527	−	0.114582i	−0.986319	+	0.164845i	$0.947288\pi$
$602$	3.84392	−	4.82012i	0.156666	−	0.196454i
$603$		0			0
$604$	23.2725	+	11.2074i	0.946943	+	0.456024i
$605$	−12.6845	−	15.9059i	−0.515699	−	0.646667i
$606$		0			0
$607$	−20.0682	−	9.66435i	−0.814544	−	0.392264i	−0.0202484	−	0.999795i	$-0.506446\pi$
$607$	−20.0682	−	9.66435i	−0.814544	−	0.392264i	−0.794296	+	0.607531i	$0.792160\pi$
$608$	−25.1180			−1.01867
$609$		0			0
$610$	4.40099			0.178191
$611$	−19.0284	−	9.16359i	−0.769806	−	0.370719i
$612$		0			0
$613$	1.04225	+	1.30693i	0.0420959	+	0.0527866i	0.802434	−	0.596741i	$-0.203538\pi$
$613$	1.04225	+	1.30693i	0.0420959	+	0.0527866i	−0.760338	+	0.649528i	$0.774967\pi$
$614$	11.8058	+	5.68536i	0.476442	+	0.229442i
$615$		0			0
$616$	3.49586	−	4.38367i	0.140852	−	0.176623i
$617$	3.20447	+	14.0397i	0.129007	+	0.565216i	0.997572	+	0.0696414i	$0.0221855\pi$
$617$	3.20447	+	14.0397i	0.129007	+	0.565216i	−0.868565	+	0.495575i	$0.834957\pi$
$618$		0			0
$619$	−1.71356	−	2.14873i	−0.0688737	−	0.0863649i	0.746201	−	0.665720i	$-0.231876\pi$
$619$	−1.71356	−	2.14873i	−0.0688737	−	0.0863649i	−0.815075	+	0.579356i	$0.803304\pi$
$620$	1.86274	−	8.16119i	0.0748094	−	0.327761i
$621$		0			0
$622$	4.19793	−	18.3923i	0.168322	−	0.737465i
$623$	−33.3216	+	16.0468i	−1.33500	+	0.642903i
$624$		0			0
$625$	4.33818	−	19.0068i	0.173527	−	0.760272i
$626$	5.15081			0.205868
$627$		0			0
$628$	−19.2861	−	24.1840i	−0.769598	−	0.965045i
$629$	1.58015	+	6.92310i	0.0630048	+	0.276042i
$630$		0			0
$631$	−5.65612	+	7.09255i	−0.225167	+	0.282350i	−0.881563	−	0.472066i	$-0.843508\pi$
$631$	−5.65612	+	7.09255i	−0.225167	+	0.282350i	0.656397	+	0.754416i	$0.272080\pi$
$632$	9.44216	−	4.54711i	0.375589	−	0.180874i
$633$		0			0
$634$	−0.967070	−	1.21267i	−0.0384072	−	0.0481612i
$635$	−4.93170	+	6.18415i	−0.195708	+	0.245411i
$636$		0			0
$637$	−8.26146			−0.327331
$638$	−1.78091	+	3.11108i	−0.0705070	+	0.123169i
$639$		0			0
$640$	19.4164	+	9.35043i	0.767499	+	0.369608i
$641$	7.09852	−	8.90126i	0.280375	−	0.351579i	−0.621625	−	0.783315i	$-0.713527\pi$
$641$	7.09852	−	8.90126i	0.280375	−	0.351579i	0.902000	+	0.431736i	$0.142099\pi$
$642$		0			0
$643$	9.74947	+	4.69510i	0.384482	+	0.185157i	0.616133	−	0.787642i	$-0.288699\pi$
$643$	9.74947	+	4.69510i	0.384482	+	0.185157i	−0.231651	+	0.972799i	$0.574413\pi$
$644$	−17.6371	+	8.49360i	−0.695000	+	0.334695i
$645$		0			0
$646$	2.54860	+	11.1661i	0.100273	+	0.439326i
$647$	−4.91549	−	21.5362i	−0.193248	−	0.846674i	−0.974844	−	0.222889i	$-0.928451\pi$
$647$	−4.91549	−	21.5362i	−0.193248	−	0.846674i	0.781596	−	0.623785i	$-0.214406\pi$
$648$		0			0
$649$	−1.98384	+	8.69178i	−0.0778726	+	0.341182i
$650$	−4.21542			−0.165342
$651$		0			0
$652$	10.4292	−	5.02245i	0.408440	−	0.196694i
$653$	17.4603	−	8.40844i	0.683274	−	0.329048i	−0.0598439	−	0.998208i	$-0.519060\pi$
$653$	17.4603	−	8.40844i	0.683274	−	0.329048i	0.743118	+	0.669160i	$0.233346\pi$
$654$		0			0
$655$	33.2836			1.30050
$656$	3.51530	−	15.4015i	0.137249	−	0.601329i
$657$		0			0
$658$	1.19720	+	5.24528i	0.0466718	+	0.204482i
$659$	1.48867	+	6.52230i	0.0579904	+	0.254073i	0.995611	−	0.0935875i	$-0.0298335\pi$
$659$	1.48867	+	6.52230i	0.0579904	+	0.254073i	−0.937621	+	0.347660i	$0.886976\pi$
$660$		0			0
$661$	40.0727	−	19.2980i	1.55865	−	0.750606i	0.561602	−	0.827407i	$-0.310185\pi$
$661$	40.0727	−	19.2980i	1.55865	−	0.750606i	0.997046	+	0.0768020i	$0.0244709\pi$
$662$	14.5407	+	7.00242i	0.565139	+	0.272157i
$663$		0			0
$664$	24.6586	−	30.9209i	0.956938	−	1.19996i
$665$	−18.8019	−	9.05451i	−0.729106	−	0.351119i
$666$		0			0
$667$	23.9133	−	16.4333i	0.925925	−	0.636301i
$668$	−32.9670			−1.27553
$669$		0			0
$670$	10.5800	−	13.2668i	0.408739	−	0.512543i
$671$	1.87443	+	2.35046i	0.0723615	+	0.0907385i
$672$		0			0
$673$	−18.9884	+	9.14433i	−0.731949	+	0.352488i	−0.762450	−	0.647047i	$-0.776004\pi$
$673$	−18.9884	+	9.14433i	−0.731949	+	0.352488i	0.0305016	+	0.999535i	$0.490290\pi$
$674$	11.7301	−	14.7091i	0.451826	−	0.566572i
$675$		0			0
$676$	10.0202	+	43.9015i	0.385394	+	1.68852i
$677$	−2.23420	−	2.80160i	−0.0858673	−	0.107674i	0.737042	−	0.675847i	$-0.236222\pi$
$677$	−2.23420	−	2.80160i	−0.0858673	−	0.107674i	−0.822909	+	0.568173i	$0.807651\pi$
$678$		0			0
$679$	−37.7509			−1.44875
$680$	4.18824	−	18.3499i	0.160612	−	0.703686i
$681$		0			0
$682$	−1.64010	+	0.789829i	−0.0628026	+	0.0302441i
$683$	−2.99758	+	13.1333i	−0.114699	+	0.502530i	0.884643	+	0.466269i	$0.154402\pi$
$683$	−2.99758	+	13.1333i	−0.114699	+	0.502530i	−0.999342	+	0.0362615i	$0.988455\pi$
$684$		0			0
$685$	−1.36724	+	5.99027i	−0.0522395	+	0.228876i
$686$	8.57588	+	10.7538i	0.327428	+	0.410582i
$687$		0			0
$688$	1.10093	+	4.82348i	0.0419725	+	0.183894i
$689$	−9.23730	+	11.5832i	−0.351913	+	0.441285i
$690$		0			0
$691$	−15.7501	−	7.58486i	−0.599163	−	0.288542i	0.109614	−	0.993974i	$-0.465039\pi$
$691$	−15.7501	−	7.58486i	−0.599163	−	0.288542i	−0.708777	+	0.705432i	$0.750753\pi$
$692$	3.79633	+	4.76045i	0.144315	+	0.180965i
$693$		0			0
$694$	−20.6855	−	9.96163i	−0.785213	−	0.378138i
$695$	22.7619			0.863408
$696$		0			0
$697$	−45.1412			−1.70984
$698$	−3.98483	−	1.91899i	−0.150828	−	0.0726349i
$699$		0			0
$700$	−2.10322	−	2.63735i	−0.0794942	−	0.0996826i
$701$	−26.5799	−	12.8002i	−1.00391	−	0.483458i	−0.141646	−	0.989917i	$-0.545240\pi$
$701$	−26.5799	−	12.8002i	−1.00391	−	0.483458i	−0.862264	+	0.506460i	$0.830954\pi$
$702$		0			0
$703$	5.00991	−	6.28223i	0.188953	−	0.236939i
$704$	−0.292203	−	1.28022i	−0.0110128	−	0.0482503i
$705$		0			0
$706$	−7.61395	−	9.54759i	−0.286555	−	0.359328i
$707$	−4.93289	+	21.6124i	−0.185521	+	0.812818i
$708$		0			0
$709$	−5.48443	+	24.0289i	−0.205972	+	0.902423i	0.761244	+	0.648466i	$0.224589\pi$
$709$	−5.48443	+	24.0289i	−0.205972	+	0.902423i	−0.967216	+	0.253957i	$0.918268\pi$
$710$	−5.81590	+	2.80079i	−0.218267	+	0.105112i
$711$		0			0
$712$	−8.39903	+	36.7985i	−0.314767	+	1.37908i
$713$	14.7343			0.551805
$714$		0			0
$715$	7.87315	+	9.87262i	0.294439	+	0.369215i
$716$	1.30566	+	5.72046i	0.0487948	+	0.213784i
$717$		0			0
$718$	−3.38826	+	4.24875i	−0.126449	+	0.158562i
$719$	−1.24578	+	0.599937i	−0.0464598	+	0.0223739i	−0.456969	−	0.889482i	$-0.651065\pi$
$719$	−1.24578	+	0.599937i	−0.0464598	+	0.0223739i	0.410510	+	0.911856i	$0.365351\pi$
$720$		0			0
$721$	−15.8196	−	19.8372i	−0.589154	−	0.738776i
$722$	−0.152055	+	0.190671i	−0.00565890	+	0.00709604i
$723$		0			0
$724$	−25.2284			−0.937607
$725$	3.67776	+	3.38730i	0.136588	+	0.125801i
$726$		0			0
$727$	−34.0179	−	16.3821i	−1.26165	−	0.607580i	−0.321041	−	0.947065i	$-0.604033\pi$
$727$	−34.0179	−	16.3821i	−1.26165	−	0.607580i	−0.940611	+	0.339485i	$0.889747\pi$
$728$	23.8433	−	29.8985i	0.883691	−	1.10811i
$729$		0			0
$730$	−11.4859	−	5.53130i	−0.425111	−	0.204722i
$731$	12.7374	−	6.13399i	0.471108	−	0.226874i
$732$		0			0
$733$	7.24828	+	31.7568i	0.267721	+	1.17296i	0.912657	+	0.408727i	$0.134027\pi$
$733$	7.24828	+	31.7568i	0.267721	+	1.17296i	−0.644936	+	0.764237i	$0.723116\pi$
$734$	−4.51017	−	19.7603i	−0.166473	−	0.729368i
$735$		0			0
$736$	−6.97363	+	30.5535i	−0.257051	+	1.12622i
$737$	11.5916			0.426982
$738$		0			0
$739$	34.2033	−	16.4714i	1.25819	−	0.605911i	0.318493	−	0.947925i	$-0.396823\pi$
$739$	34.2033	−	16.4714i	1.25819	−	0.605911i	0.939695	+	0.342014i	$0.111109\pi$
$740$	−5.13173	+	2.47131i	−0.188646	+	0.0908472i
$741$		0			0
$742$	3.77416			0.138554
$743$	−2.91935	+	12.7905i	−0.107101	+	0.469238i	0.892726	+	0.450601i	$0.148790\pi$
$743$	−2.91935	+	12.7905i	−0.107101	+	0.469238i	−0.999826	+	0.0186379i	$0.994067\pi$
$744$		0			0
$745$	2.19912	+	9.63496i	0.0805694	+	0.352998i
$746$	0.905585	+	3.96763i	0.0331558	+	0.145265i
$747$		0			0
$748$	4.99669	−	2.40628i	0.182697	−	0.0879823i
$749$	0.271234	+	0.130619i	0.00991067	+	0.00477273i
$750$		0			0
$751$	−17.5307	+	21.9828i	−0.639704	+	0.802163i	−0.990966	−	0.134114i	$-0.957181\pi$
$751$	−17.5307	+	21.9828i	−0.639704	+	0.802163i	0.351262	+	0.936277i	$0.385753\pi$
$752$	−3.89000	−	1.87333i	−0.141854	−	0.0683132i
$753$		0			0
$754$	−12.1466	+	21.2189i	−0.442353	+	0.772748i
$755$	34.3565			1.25036
$756$		0			0
$757$	−11.8885	+	14.9078i	−0.432096	+	0.541831i	−0.949441	−	0.313946i	$-0.898349\pi$
$757$	−11.8885	+	14.9078i	−0.432096	+	0.541831i	0.517345	+	0.855777i	$0.326920\pi$
$758$	−1.00418	−	1.25920i	−0.0364735	−	0.0457363i
$759$		0			0
$760$	−19.1886	+	9.24074i	−0.696044	+	0.335197i
$761$	−5.51450	+	6.91496i	−0.199900	+	0.250667i	−0.871670	−	0.490093i	$-0.836963\pi$
$761$	−5.51450	+	6.91496i	−0.199900	+	0.250667i	0.671770	+	0.740760i	$0.265534\pi$
$762$		0			0
$763$	−5.14078	−	22.5232i	−0.186109	−	0.815395i
$764$	−2.49816	−	3.13260i	−0.0903804	−	0.113333i
$765$		0			0
$766$	12.6782			0.458082
$767$	−13.5307	+	59.2817i	−0.488564	+	2.14054i
$768$		0			0
$769$	12.9746	−	6.24823i	0.467875	−	0.225317i	−0.185065	−	0.982726i	$-0.559250\pi$
$769$	12.9746	−	6.24823i	0.467875	−	0.225317i	0.652940	+	0.757409i	$0.273535\pi$
$770$	0.715805	−	3.13615i	0.0257958	−	0.113019i
$771$		0			0
$772$	2.20813	−	9.67446i	0.0794724	−	0.348191i
$773$	3.56506	+	4.47045i	0.128226	+	0.160791i	0.841800	−	0.539789i	$-0.181496\pi$
$773$	3.56506	+	4.47045i	0.128226	+	0.160791i	−0.713574	+	0.700580i	$0.752925\pi$
$774$		0			0
$775$	0.564987	+	2.47537i	0.0202949	+	0.0889179i
$776$	−24.0214	+	30.1219i	−0.862319	+	1.08131i
$777$		0			0
$778$	18.5691	+	8.94243i	0.665736	+	0.320602i
$779$	31.8475	+	39.9355i	1.14105	+	1.43084i
$780$		0			0
$781$	−3.97288	−	1.91324i	−0.142161	−	0.0684611i
$782$	14.2900			0.511010
$783$		0			0
$784$	−1.68890			−0.0603180
$785$	−37.0681	−	17.8510i	−1.32302	−	0.637131i
$786$		0			0
$787$	24.1684	+	30.3062i	0.861511	+	1.08030i	0.995997	+	0.0893846i	$0.0284900\pi$
$787$	24.1684	+	30.3062i	0.861511	+	1.08030i	−0.134487	+	0.990915i	$0.542939\pi$
$788$	13.4282	+	6.46666i	0.478358	+	0.230365i
$789$		0			0
$790$	3.74878	−	4.70082i	0.133376	−	0.167248i
$791$	−1.65654	−	7.25777i	−0.0588997	−	0.258057i
$792$		0			0
$793$	12.7844	+	16.0312i	0.453988	+	0.569283i
$794$	−0.314268	+	1.37690i	−0.0111530	+	0.0488643i
$795$		0			0
$796$	0.177131	−	0.776062i	0.00627824	−	0.0275068i
$797$	2.84929	−	1.37215i	0.100927	−	0.0486039i	−0.382739	−	0.923856i	$-0.625019\pi$
$797$	2.84929	−	1.37215i	0.100927	−	0.0486039i	0.483666	+	0.875253i	$0.339305\pi$
$798$		0			0
$799$	−2.74532	+	12.0280i	−0.0971223	+	0.425521i
$800$	−5.40039			−0.190933
$801$		0			0
$802$	0.0617863	+	0.0774776i	0.00218175	+	0.00273583i
$803$	−1.93782	−	8.49014i	−0.0683842	−	0.299611i
$804$		0			0
$805$	−16.2339	+	20.3567i	−0.572171	+	0.717479i
$806$	−11.1862	+	5.38698i	−0.394016	+	0.189748i
$807$		0			0
$808$	14.1059	+	17.6883i	0.496245	+	0.622272i
$809$	−7.37667	+	9.25005i	−0.259350	+	0.325215i	−0.894410	−	0.447248i	$-0.852404\pi$
$809$	−7.37667	+	9.25005i	−0.259350	+	0.325215i	0.635060	+	0.772463i	$0.280975\pi$
$810$		0			0
$811$	−11.2027			−0.393381			−0.196691	−	0.980466i	$-0.563019\pi$
$811$	−11.2027			−0.393381			−0.196691	+	0.980466i	$0.563019\pi$
$812$	−19.3359	+	2.98741i	−0.678556	+	0.104837i
$813$		0			0
$814$	1.11595	+	0.537411i	0.0391139	+	0.0188362i
$815$	9.59947	−	12.0374i	0.336255	−	0.421650i
$816$		0			0
$817$	−14.4129	−	6.94091i	−0.504245	−	0.242832i
$818$	12.9878	−	6.25457i	0.454106	−	0.218686i
$819$		0			0
$820$	−8.05693	−	35.2997i	−0.281360	−	1.23272i
$821$	3.30067	+	14.4612i	0.115194	+	0.504699i	0.999300	+	0.0374118i	$0.0119113\pi$
$821$	3.30067	+	14.4612i	0.115194	+	0.504699i	−0.884106	+	0.467287i	$0.845232\pi$
$822$		0			0
$823$	−9.75067	+	42.7205i	−0.339887	+	1.48914i	0.459420	+	0.888219i	$0.348057\pi$
$823$	−9.75067	+	42.7205i	−0.339887	+	1.48914i	−0.799307	+	0.600923i	$0.794800\pi$
$824$	−25.8946			−0.902080
$825$		0			0
$826$	13.9560	−	6.72088i	0.485593	−	0.233849i
$827$	−6.86968	+	3.30826i	−0.238882	+	0.115040i	−0.549495	−	0.835497i	$-0.685180\pi$
$827$	−6.86968	+	3.30826i	−0.238882	+	0.115040i	0.310613	+	0.950536i	$0.399466\pi$
$828$		0			0
$829$	−20.4341			−0.709707			−0.354854	−	0.934922i	$-0.615469\pi$
$829$	−20.4341			−0.709707			−0.354854	+	0.934922i	$0.615469\pi$
$830$	5.04903	−	22.1213i	0.175254	−	0.767840i
$831$		0			0
$832$	−1.99295	−	8.73169i	−0.0690931	−	0.302717i
$833$	1.07388	+	4.70499i	0.0372079	+	0.163018i
$834$		0			0
$835$	−39.5062	+	19.0252i	−1.36717	+	0.658393i
$836$	−5.65400	−	2.72282i	−0.195548	−	0.0941707i
$837$		0			0
$838$	−2.83870	+	3.55962i	−0.0980613	+	0.122965i
$839$	15.2616	+	7.34959i	0.526888	+	0.253736i	0.678365	−	0.734725i	$-0.262689\pi$
$839$	15.2616	+	7.34959i	0.526888	+	0.253736i	−0.151477	+	0.988461i	$0.548403\pi$
$840$		0			0
$841$	27.6478	−	8.75212i	0.953372	−	0.301797i
$842$	5.99628			0.206645
$843$		0			0
$844$	−15.6519	+	19.6269i	−0.538762	+	0.675586i
$845$	37.3433	+	46.8270i	1.28465	+	1.61090i
$846$		0			0
$847$	−21.7551	+	10.4767i	−0.747513	+	0.359983i
$848$	−1.88840	+	2.36797i	−0.0648478	+	0.0813166i
$849$		0			0
$850$	0.547950	+	2.40073i	0.0187945	+	0.0823442i
$851$	−6.25076	−	7.83820i	−0.214273	−	0.268690i
$852$		0			0
$853$	−9.95085			−0.340711			−0.170355	−	0.985383i	$-0.554492\pi$
$853$	−9.95085			−0.340711			−0.170355	+	0.985383i	$0.554492\pi$
$854$	1.16232	−	5.09247i	0.0397739	−	0.174261i
$855$		0			0
$856$	0.276813	−	0.133306i	0.00946126	−	0.00455630i
$857$	7.21912	−	31.6290i	0.246601	−	1.08043i	−0.688274	−	0.725450i	$-0.741631\pi$
$857$	7.21912	−	31.6290i	0.246601	−	1.08043i	0.934875	−	0.354977i	$-0.115511\pi$
$858$		0			0
$859$	11.5600	−	50.6476i	0.394422	−	1.72807i	−0.254368	−	0.967107i	$-0.581868\pi$
$859$	11.5600	−	50.6476i	0.394422	−	1.72807i	0.648790	−	0.760967i	$-0.275275\pi$
$860$	7.07009	+	8.86562i	0.241088	+	0.302315i
$861$		0			0
$862$	4.88245	+	21.3914i	0.166297	+	0.728594i
$863$	−13.0134	+	16.3183i	−0.442983	+	0.555483i	−0.952327	−	0.305080i	$-0.901317\pi$
$863$	−13.0134	+	16.3183i	−0.442983	+	0.555483i	0.509344	+	0.860563i	$0.329888\pi$
$864$		0			0
$865$	7.29660	+	3.51386i	0.248092	+	0.119475i
$866$	−1.36498	−	1.71164i	−0.0463840	−	0.0581638i
$867$		0			0
$868$	−8.95151	−	4.31082i	−0.303834	−	0.146319i
$869$	4.10724			0.139328
$870$		0			0
$871$	79.0597			2.67884
$872$	−21.2427	−	10.2299i	−0.719369	−	0.346430i
$873$		0			0
$874$	−10.0817	−	12.6421i	−0.341020	−	0.427625i
$875$	−25.8116	−	12.4302i	−0.872593	−	0.420218i
$876$		0			0
$877$	−9.39590	+	11.7821i	−0.317277	+	0.397853i	−0.914739	−	0.404044i	$-0.867604\pi$
$877$	−9.39590	+	11.7821i	−0.317277	+	0.397853i	0.597463	+	0.801897i	$0.296176\pi$
$878$	−3.52708	−	15.4531i	−0.119033	−	0.521518i
$879$		0			0
$880$	1.60952	+	2.01828i	0.0542569	+	0.0680360i
$881$	−3.33843	+	14.6266i	−0.112475	+	0.492783i	0.887042	+	0.461689i	$0.152756\pi$
$881$	−3.33843	+	14.6266i	−0.112475	+	0.492783i	−0.999516	+	0.0310944i	$0.990101\pi$
$882$		0			0
$883$	0.911382	−	3.99302i	0.0306704	−	0.134376i	−0.957275	−	0.289180i	$-0.906617\pi$
$883$	0.911382	−	3.99302i	0.0306704	−	0.134376i	0.987945	+	0.154804i	$0.0494746\pi$
$884$	34.0796	−	16.4119i	1.14622	−	0.551991i
$885$		0			0
$886$	2.95762	−	12.9582i	0.0993632	−	0.435338i
$887$	−16.1647			−0.542756			−0.271378	−	0.962473i	$-0.587479\pi$
$887$	−16.1647			−0.542756			−0.271378	+	0.962473i	$0.587479\pi$
$888$		0			0
$889$	5.85332	+	7.33983i	0.196314	+	0.246170i
$890$	4.81868	+	21.1120i	0.161522	+	0.707676i
$891$		0			0
$892$	11.1093	−	13.9306i	0.371966	−	0.466431i
$893$	12.5778	−	6.05714i	0.420899	−	0.202694i
$894$		0			0
$895$	4.86591	+	6.10166i	0.162649	+	0.203956i
$896$	15.9475	−	19.9975i	0.532769	−	0.668071i
$897$		0			0
$898$	27.6514			0.922741
$899$	14.0881	+	4.28876i	0.469865	+	0.143038i
$900$		0			0
$901$	7.79749	+	3.75508i	0.259772	+	0.125100i
$902$	−4.90916	+	6.15589i	−0.163457	+	0.204969i
$903$		0			0
$904$	−6.84514	−	3.29645i	−0.227666	−	0.109638i
$905$	−30.2326	+	14.5593i	−1.00497	+	0.483966i
$906$		0			0
$907$	−9.19510	−	40.2863i	−0.305318	−	1.33769i	−0.861978	−	0.506946i	$-0.830774\pi$
$907$	−9.19510	−	40.2863i	−0.305318	−	1.33769i	0.556660	−	0.830741i	$-0.312083\pi$
$908$	7.19279	+	31.5137i	0.238701	+	1.04582i
$909$		0			0
$910$	4.88210	−	21.3899i	0.161840	−	0.709068i
$911$	−31.3566			−1.03889			−0.519446	−	0.854504i	$-0.673862\pi$
$911$	−31.3566			−1.03889			−0.519446	+	0.854504i	$0.673862\pi$
$912$		0			0
$913$	13.9648	−	6.72512i	0.462169	−	0.222569i
$914$	−18.2932	+	8.80956i	−0.605087	+	0.291394i
$915$		0			0
$916$	−0.278097			−0.00918858
$917$	8.79035	−	38.5130i	0.290283	−	1.27181i
$918$		0			0
$919$	−6.66230	−	29.1894i	−0.219769	−	0.962871i	−0.957649	−	0.287939i	$-0.907030\pi$
$919$	−6.66230	−	29.1894i	−0.219769	−	0.962871i	0.737880	−	0.674932i	$-0.235827\pi$
$920$	5.91299	+	25.9065i	0.194945	+	0.854112i
$921$		0			0
$922$	0.615252	−	0.296290i	0.0202622	−	0.00975778i
$923$	−27.0968	−	13.0491i	−0.891902	−	0.429517i
$924$		0			0
$925$	1.07713	−	1.35068i	0.0354160	−	0.0444102i
$926$	6.35011	+	3.05805i	0.208678	+	0.100494i
$927$		0			0
$928$	−15.5611	+	27.1836i	−0.510817	+	0.892347i
$929$	1.38920			0.0455781			0.0227891	−	0.999740i	$-0.492745\pi$
$929$	1.38920			0.0455781			0.0227891	+	0.999740i	$0.492745\pi$
$930$		0			0
$931$	3.40478	−	4.26945i	0.111587	−	0.139926i
$932$	−22.5883	−	28.3249i	−0.739905	−	0.927812i
$933$		0			0
$934$	11.2563	−	5.42074i	0.368317	−	0.177372i
$935$	4.59916	−	5.76716i	0.150408	−	0.188606i
$936$		0			0
$937$	1.57652	+	6.90720i	0.0515028	+	0.225649i	0.994129	−	0.108202i	$-0.0345092\pi$
$937$	1.57652	+	6.90720i	0.0515028	+	0.225649i	−0.942626	+	0.333850i	$0.891652\pi$
$938$	−12.5571	−	15.7461i	−0.410004	−	0.514128i
$939$		0			0
$940$	−9.89572			−0.322763
$941$	12.5425	−	54.9523i	0.408874	−	1.79139i	−0.180546	−	0.983567i	$-0.557786\pi$
$941$	12.5425	−	54.9523i	0.408874	−	1.79139i	0.589420	−	0.807827i	$-0.299357\pi$
$942$		0			0
$943$	57.4193	−	27.6517i	1.86983	−	0.900462i
$944$	−2.76609	+	12.1190i	−0.0900287	+	0.394441i
$945$		0			0
$946$	0.548714	−	2.40407i	0.0178402	−	0.0781631i
$947$	−14.8344	−	18.6018i	−0.482054	−	0.604477i	0.480022	−	0.877256i	$-0.340629\pi$
$947$	−14.8344	−	18.6018i	−0.482054	−	0.604477i	−0.962077	+	0.272779i	$0.912057\pi$
$948$		0			0
$949$	−13.2168	−	57.9065i	−0.429035	−	1.87972i
$950$	1.73729	−	2.17849i	0.0563651	−	0.0706796i
$951$		0			0
$952$	−20.1269	−	9.69258i	−0.652315	−	0.314138i
$953$	−13.5680	−	17.0137i	−0.439510	−	0.551129i	0.511904	−	0.859043i	$-0.328940\pi$
$953$	−13.5680	−	17.0137i	−0.439510	−	0.551129i	−0.951414	+	0.307914i	$0.900369\pi$
$954$		0			0
$955$	−4.80150	−	2.31228i	−0.155373	−	0.0748237i
$956$	−12.7575			−0.412608
$957$		0			0
$958$	−14.3106			−0.462355
$959$	6.57036	+	3.16412i	0.212168	+	0.102175i
$960$		0			0
$961$	−14.6656	−	18.3901i	−0.473083	−	0.593228i
$962$	7.61123	+	3.66538i	0.245396	+	0.118176i
$963$		0			0
$964$	0.509222	−	0.638545i	0.0164010	−	0.0205661i
$965$	−2.93698	−	12.8678i	−0.0945447	−	0.414228i
$966$		0			0
$967$	15.5078	+	19.4461i	0.498696	+	0.625345i	0.965935	−	0.258786i	$-0.0833225\pi$
$967$	15.5078	+	19.4461i	0.498696	+	0.625345i	−0.467239	+	0.884131i	$0.654751\pi$
$968$	−5.48357	+	24.0251i	−0.176249	+	0.772195i
$969$		0			0
$970$	−4.91858	+	21.5497i	−0.157926	+	0.691919i
$971$	54.0273	−	26.0182i	1.73382	−	0.834962i	0.748737	−	0.662868i	$-0.230661\pi$
$971$	54.0273	−	26.0182i	1.73382	−	0.834962i	0.985080	−	0.172095i	$-0.0550535\pi$
$972$		0			0
$973$	6.01153	−	26.3382i	0.192721	−	0.844365i
$974$	11.1131			0.356086
$975$		0			0
$976$	2.61354	+	3.27727i	0.0836573	+	0.104903i
$977$	−10.2785	−	45.0329i	−0.328837	−	1.44073i	−0.821350	−	0.570425i	$-0.806779\pi$
$977$	−10.2785	−	45.0329i	−0.328837	−	1.44073i	0.492513	−	0.870305i	$-0.336079\pi$
$978$		0			0
$979$	−9.22307	+	11.5654i	−0.294771	+	0.369631i
$980$	−3.48756	+	1.67952i	−0.111406	+	0.0536504i
$981$		0			0
$982$	4.41974	+	5.54217i	0.141039	+	0.176858i
$983$	0.416228	−	0.521933i	0.0132756	−	0.0166471i	−0.775149	−	0.631778i	$-0.782325\pi$
$983$	0.416228	−	0.521933i	0.0132756	−	0.0166471i	0.788425	+	0.615131i	$0.210897\pi$
$984$		0			0
$985$	19.8236			0.631632
$986$	13.6633	+	4.15943i	0.435128	+	0.132463i
$987$		0			0
$988$	−38.5627	−	18.5708i	−1.22684	−	0.590817i
$989$	−12.4444	+	15.6048i	−0.395709	+	0.496204i
$990$		0			0
$991$	40.3777	+	19.4449i	1.28264	+	0.617687i	0.946067	−	0.323971i	$-0.105018\pi$
$991$	40.3777	+	19.4449i	1.28264	+	0.617687i	0.336573	+	0.941658i	$0.390732\pi$
$992$	−14.3307	+	6.90128i	−0.454999	+	0.219116i
$993$		0			0
$994$	1.70484	+	7.46939i	0.0540742	+	0.236915i
$995$	−0.235598	−	1.03222i	−0.00746894	−	0.0327236i
$996$		0			0
$997$	2.48594	−	10.8916i	0.0787306	−	0.344941i	−0.920186	−	0.391482i	$-0.871963\pi$
$997$	2.48594	−	10.8916i	0.0787306	−	0.344941i	0.998916	+	0.0465406i	$0.0148197\pi$
$998$	−4.27526			−0.135331
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.190.1		18
3.2	odd	2		87.2.g.a.16.3	✓	18
29.7	even	7		7569.2.a.bj.1.7		9
29.20	even	7	inner	261.2.k.c.136.1		18
29.22	even	14		7569.2.a.bm.1.3		9
87.20	odd	14		87.2.g.a.49.3	yes	18
87.65	odd	14		2523.2.a.r.1.3		9
87.80	odd	14		2523.2.a.o.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.16.3	✓	18	3.2	odd	2
87.2.g.a.49.3	yes	18	87.20	odd	14
261.2.k.c.136.1		18	29.20	even	7	inner
261.2.k.c.190.1		18	1.1	even	1	trivial
2523.2.a.o.1.7		9	87.80	odd	14
2523.2.a.r.1.3		9	87.65	odd	14
7569.2.a.bj.1.7		9	29.7	even	7
7569.2.a.bm.1.3		9	29.22	even	14

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.626118 - 0.301523i) q^{2} +(-0.945872 - 1.18609i) q^{4} +(-1.81798 - 0.875492i) q^{5} +(-1.49319 + 1.87240i) q^{7} +(0.543873 + 2.38286i) q^{8} +(0.874288 + 1.09632i) q^{10} +(-0.213150 + 0.933871i) q^{11} +(-1.45377 + 6.36940i) q^{13} +(1.49948 - 0.722111i) q^{14} +(-0.297197 + 1.30211i) q^{16} +3.81642 q^{17} +(-2.69251 - 3.37631i) q^{19} +(0.681165 + 2.98438i) q^{20} +(0.415040 - 0.520444i) q^{22} +(-4.85446 + 2.33778i) q^{23} +(-0.578892 - 0.725907i) q^{25} +(2.83075 - 3.54965i) q^{26} +3.63318 q^{28} +(-5.32202 + 0.822256i) q^{29} +(-2.46382 - 1.18651i) q^{31} +(3.62649 - 4.54747i) q^{32} +(-2.38953 - 1.15074i) q^{34} +(4.35384 - 2.09670i) q^{35} +(0.414041 + 1.81403i) q^{37} +(0.667799 + 2.92582i) q^{38} +(1.09743 - 4.80814i) q^{40} -11.8282 q^{41} +(3.33752 - 1.60727i) q^{43} +(1.30926 - 0.630508i) q^{44} +3.74436 q^{46} +(-0.719344 + 3.15165i) q^{47} +(0.281385 + 1.23283i) q^{49} +(0.143577 + 0.629053i) q^{50} +(8.92974 - 4.30034i) q^{52} +(2.04315 + 0.983927i) q^{53} +(1.20510 - 1.51115i) q^{55} +(-5.27376 - 2.53971i) q^{56} +(3.58014 + 1.08988i) q^{58} +9.30726 q^{59} +(1.95684 - 2.45380i) q^{61} +(1.18488 + 1.48579i) q^{62} +(-1.23512 + 0.594802i) q^{64} +(8.21929 - 10.3067i) q^{65} +(-2.69277 - 11.7978i) q^{67} +(-3.60984 - 4.52660i) q^{68} -3.35822 q^{70} +(-1.02436 + 4.48801i) q^{71} +(-8.19102 + 3.94459i) q^{73} +(0.287733 - 1.26064i) q^{74} +(-1.45781 + 6.38710i) q^{76} +(-1.43030 - 1.79354i) q^{77} +(-0.954127 - 4.18030i) q^{79} +(1.68028 - 2.10701i) q^{80} +(7.40582 + 3.56646i) q^{82} +(-10.0888 - 12.6510i) q^{83} +(-6.93816 - 3.34124i) q^{85} -2.57431 q^{86} -2.34121 q^{88} +(13.9137 + 6.70047i) q^{89} +(-9.75529 - 12.2327i) q^{91} +(7.36451 + 3.54656i) q^{92} +(1.40069 - 1.75641i) q^{94} +(1.93900 + 8.49532i) q^{95} +(9.82817 + 12.3241i) q^{97} +(0.195546 - 0.856741i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) \) 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

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