LMFDB - Embedded newform 357.2.d.b.188.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(188,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("357.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.d (of order $2$, degree $1$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.2
Character	$\chi$	$=$	357.188
Dual form			357.2.d.b.188.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62830i q^{2} +(-0.685367 + 1.59068i) q^{3} -4.90796 q^{4} +0.419096 q^{5} +(4.18079 + 1.80135i) q^{6} +(-2.38080 - 1.15403i) q^{7} +7.64298i q^{8} +(-2.06054 - 2.18040i) q^{9} +O(q^{10})$	\(q-2.62830i q^{2} +(-0.685367 + 1.59068i) q^{3} -4.90796 q^{4} +0.419096 q^{5} +(4.18079 + 1.80135i) q^{6} +(-2.38080 - 1.15403i) q^{7} +7.64298i q^{8} +(-2.06054 - 2.18040i) q^{9} -1.10151i q^{10} +3.26816i q^{11} +(3.36375 - 7.80700i) q^{12} +4.15372i q^{13} +(-3.03315 + 6.25745i) q^{14} +(-0.287235 + 0.666649i) q^{15} +10.2721 q^{16} +1.00000 q^{17} +(-5.73075 + 5.41573i) q^{18} +7.62938i q^{19} -2.05691 q^{20} +(3.46742 - 2.99616i) q^{21} +8.58969 q^{22} -1.18901i q^{23} +(-12.1576 - 5.23825i) q^{24} -4.82436 q^{25} +10.9172 q^{26} +(4.88056 - 1.78329i) q^{27} +(11.6849 + 5.66395i) q^{28} -3.03987i q^{29} +(1.75215 + 0.754939i) q^{30} +3.06107i q^{31} -11.7123i q^{32} +(-5.19860 - 2.23989i) q^{33} -2.62830i q^{34} +(-0.997785 - 0.483651i) q^{35} +(10.1131 + 10.7013i) q^{36} -1.78193 q^{37} +20.0523 q^{38} +(-6.60725 - 2.84682i) q^{39} +3.20315i q^{40} -11.8529 q^{41} +(-7.87481 - 9.11343i) q^{42} -3.61369 q^{43} -16.0400i q^{44} +(-0.863567 - 0.913799i) q^{45} -3.12507 q^{46} -6.81792 q^{47} +(-7.04018 + 16.3397i) q^{48} +(4.33641 + 5.49505i) q^{49} +12.6799i q^{50} +(-0.685367 + 1.59068i) q^{51} -20.3863i q^{52} -7.01979i q^{53} +(-4.68703 - 12.8276i) q^{54} +1.36967i q^{55} +(8.82026 - 18.1964i) q^{56} +(-12.1359 - 5.22893i) q^{57} -7.98970 q^{58} +2.59150 q^{59} +(1.40974 - 3.27189i) q^{60} -9.93415i q^{61} +8.04540 q^{62} +(2.38948 + 7.56904i) q^{63} -10.2391 q^{64} +1.74081i q^{65} +(-5.88709 + 13.6635i) q^{66} +7.17696 q^{67} -4.90796 q^{68} +(1.89133 + 0.814907i) q^{69} +(-1.27118 + 2.62248i) q^{70} +6.88987i q^{71} +(16.6648 - 15.7487i) q^{72} +4.99135i q^{73} +4.68345i q^{74} +(3.30646 - 7.67402i) q^{75} -37.4447i q^{76} +(3.77156 - 7.78082i) q^{77} +(-7.48230 + 17.3658i) q^{78} -5.41267 q^{79} +4.30501 q^{80} +(-0.508318 + 8.98563i) q^{81} +31.1530i q^{82} +0.916862 q^{83} +(-17.0180 + 14.7050i) q^{84} +0.419096 q^{85} +9.49786i q^{86} +(4.83547 + 2.08343i) q^{87} -24.9785 q^{88} +1.02907 q^{89} +(-2.40174 + 2.26971i) q^{90} +(4.79353 - 9.88917i) q^{91} +5.83560i q^{92} +(-4.86919 - 2.09795i) q^{93} +17.9195i q^{94} +3.19745i q^{95} +(18.6305 + 8.02720i) q^{96} +11.9067i q^{97} +(14.4426 - 11.3974i) q^{98} +(7.12590 - 6.73418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 8 q^{14} - 4 q^{15} + 20 q^{16} + 22 q^{17} + 8 q^{18} - 30 q^{20} - 4 q^{21} - 12 q^{22} - 44 q^{24} + 14 q^{25} - 24 q^{26} + 6 q^{27} + 8 q^{28} + 5 q^{30} + 28 q^{33} + 10 q^{35} - 3 q^{36} - 16 q^{37} + 88 q^{38} - 14 q^{39} - 16 q^{41} + 19 q^{42} - 24 q^{43} - 46 q^{45} + 4 q^{46} - 16 q^{47} + 25 q^{48} + 6 q^{49} + 36 q^{54} - 40 q^{56} - 6 q^{57} + 24 q^{58} + 24 q^{59} - 21 q^{60} - 20 q^{62} - 6 q^{63} - 20 q^{64} - 116 q^{66} + 8 q^{67} - 24 q^{68} + 6 q^{69} + 4 q^{70} - 7 q^{72} + 54 q^{75} + 6 q^{77} + 2 q^{78} + 16 q^{79} + 128 q^{80} - 4 q^{81} + 8 q^{83} + 42 q^{84} - 48 q^{87} + 32 q^{88} - 100 q^{89} + 47 q^{90} + 18 q^{91} + 20 q^{93} + 88 q^{96} - 8 q^{98} + 18 q^{99}+O(q^{100}) $ 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 8 * q^14 - 4 * q^15 + 20 * q^16 + 22 * q^17 + 8 * q^18 - 30 * q^20 - 4 * q^21 - 12 * q^22 - 44 * q^24 + 14 * q^25 - 24 * q^26 + 6 * q^27 + 8 * q^28 + 5 * q^30 + 28 * q^33 + 10 * q^35 - 3 * q^36 - 16 * q^37 + 88 * q^38 - 14 * q^39 - 16 * q^41 + 19 * q^42 - 24 * q^43 - 46 * q^45 + 4 * q^46 - 16 * q^47 + 25 * q^48 + 6 * q^49 + 36 * q^54 - 40 * q^56 - 6 * q^57 + 24 * q^58 + 24 * q^59 - 21 * q^60 - 20 * q^62 - 6 * q^63 - 20 * q^64 - 116 * q^66 + 8 * q^67 - 24 * q^68 + 6 * q^69 + 4 * q^70 - 7 * q^72 + 54 * q^75 + 6 * q^77 + 2 * q^78 + 16 * q^79 + 128 * q^80 - 4 * q^81 + 8 * q^83 + 42 * q^84 - 48 * q^87 + 32 * q^88 - 100 * q^89 + 47 * q^90 + 18 * q^91 + 20 * q^93 + 88 * q^96 - 8 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	2.62830i		−	1.85849i	−0.369466	−	0.929244i	$-0.620459\pi$
$2$		−	2.62830i		−	1.85849i	0.369466	−	0.929244i	$-0.379541\pi$
$3$	−0.685367	+	1.59068i	−0.395697	+	0.918381i
$3$	−0.685367	+	1.59068i	−0.395697	+	0.918381i
$4$	−4.90796			−2.45398
$5$	0.419096			0.187426			0.0937128	−	0.995599i	$-0.470126\pi$
$5$	0.419096			0.187426			0.0937128	+	0.995599i	$0.470126\pi$
$6$	4.18079	+	1.80135i	1.70680	+	0.735398i
$7$	−2.38080	−	1.15403i	−0.899858	−	0.436184i
$7$	−2.38080	−	1.15403i	−0.899858	−	0.436184i
$8$			7.64298i			2.70220i
$9$	−2.06054	−	2.18040i	−0.686848	−	0.726801i
$10$		−	1.10151i		−	0.348328i
$11$			3.26816i			0.985386i	0.870203	+	0.492693i	$0.163987\pi$
$11$			3.26816i			0.985386i	−0.870203	+	0.492693i	$0.836013\pi$
$12$	3.36375	−	7.80700i	0.971032	−	2.25369i
$13$			4.15372i			1.15203i	0.817438	+	0.576017i	$0.195394\pi$
$13$			4.15372i			1.15203i	−0.817438	+	0.576017i	$0.804606\pi$
$14$	−3.03315	+	6.25745i	−0.810642	+	1.67237i
$15$	−0.287235	+	0.666649i	−0.0741637	+	0.172128i
$16$	10.2721			2.56803
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−5.73075	+	5.41573i	−1.35075	+	1.27650i
$19$			7.62938i			1.75030i	0.483851	+	0.875150i	$0.339238\pi$
$19$			7.62938i			1.75030i	−0.483851	+	0.875150i	$0.660762\pi$
$20$	−2.05691			−0.459938
$21$	3.46742	−	2.99616i	0.756654	−	0.653816i
$22$	8.58969			1.83133
$23$		−	1.18901i		−	0.247925i	−0.992287	−	0.123963i	$-0.960440\pi$
$23$		−	1.18901i		−	0.247925i	0.992287	−	0.123963i	$-0.0395603\pi$
$24$	−12.1576	−	5.23825i	−2.48165	−	1.06925i
$25$	−4.82436			−0.964872
$26$	10.9172			2.14104
$27$	4.88056	−	1.78329i	0.939264	−	0.343195i
$28$	11.6849	+	5.66395i	2.20823	+	1.07039i
$29$		−	3.03987i		−	0.564490i	−0.959342	−	0.282245i	$-0.908921\pi$
$29$		−	3.03987i		−	0.564490i	0.959342	−	0.282245i	$-0.0910792\pi$
$30$	1.75215	+	0.754939i	0.319898	+	0.137832i
$31$			3.06107i			0.549784i	0.961475	+	0.274892i	$0.0886421\pi$
$31$			3.06107i			0.549784i	−0.961475	+	0.274892i	$0.911358\pi$
$32$		−	11.7123i		−	2.07046i
$33$	−5.19860	−	2.23989i	−0.904960	−	0.389914i
$34$		−	2.62830i		−	0.450750i
$35$	−0.997785	−	0.483651i	−0.168656	−	0.0817520i
$36$	10.1131	+	10.7013i	1.68551	+	1.78355i
$37$	−1.78193			−0.292948			−0.146474	−	0.989215i	$-0.546792\pi$
$37$	−1.78193			−0.292948			−0.146474	+	0.989215i	$0.546792\pi$
$38$	20.0523			3.25291
$39$	−6.60725	−	2.84682i	−1.05801	−	0.455856i
$40$			3.20315i			0.506462i
$41$	−11.8529			−1.85111			−0.925556	−	0.378611i	$-0.876402\pi$
$41$	−11.8529			−1.85111			−0.925556	+	0.378611i	$0.876402\pi$
$42$	−7.87481	−	9.11343i	−1.21511	−	1.40623i
$43$	−3.61369			−0.551083			−0.275541	−	0.961289i	$-0.588857\pi$
$43$	−3.61369			−0.551083			−0.275541	+	0.961289i	$0.588857\pi$
$44$		−	16.0400i		−	2.41812i
$45$	−0.863567	−	0.913799i	−0.128733	−	0.136221i
$46$	−3.12507			−0.460766
$47$	−6.81792			−0.994496			−0.497248	−	0.867608i	$-0.665656\pi$
$47$	−6.81792			−0.994496			−0.497248	+	0.867608i	$0.665656\pi$
$48$	−7.04018	+	16.3397i	−1.01616	+	2.35843i
$49$	4.33641	+	5.49505i	0.619488	+	0.785006i
$50$			12.6799i			1.79320i
$51$	−0.685367	+	1.59068i	−0.0959706	+	0.222740i
$52$		−	20.3863i		−	2.82707i
$53$		−	7.01979i		−	0.964243i	−0.876104	−	0.482121i	$-0.839866\pi$
$53$		−	7.01979i		−	0.964243i	0.876104	−	0.482121i	$-0.160134\pi$
$54$	−4.68703	−	12.8276i	−0.637824	−	1.74561i
$55$			1.36967i			0.184687i
$56$	8.82026	−	18.1964i	1.17866	−	2.43160i
$57$	−12.1359	−	5.22893i	−1.60744	−	0.692588i
$58$	−7.98970			−1.04910
$59$	2.59150			0.337385			0.168692	−	0.985669i	$-0.446046\pi$
$59$	2.59150			0.337385			0.168692	+	0.985669i	$0.446046\pi$
$60$	1.40974	−	3.27189i	0.181996	−	0.422399i
$61$		−	9.93415i		−	1.27194i	−0.771715	−	0.635969i	$-0.780601\pi$
$61$		−	9.93415i		−	1.27194i	0.771715	−	0.635969i	$-0.219399\pi$
$62$	8.04540			1.02177
$63$	2.38948	+	7.56904i	0.301047	+	0.953609i
$64$	−10.2391			−1.27989
$65$			1.74081i			0.215921i
$66$	−5.88709	+	13.6635i	−0.724651	+	1.68186i
$67$	7.17696			0.876805			0.438403	−	0.898779i	$-0.355544\pi$
$67$	7.17696			0.876805			0.438403	+	0.898779i	$0.355544\pi$
$68$	−4.90796			−0.595177
$69$	1.89133	+	0.814907i	0.227690	+	0.0981032i
$70$	−1.27118	+	2.62248i	−0.151935	+	0.313446i
$71$			6.88987i			0.817677i	0.912607	+	0.408838i	$0.134066\pi$
$71$			6.88987i			0.817677i	−0.912607	+	0.408838i	$0.865934\pi$
$72$	16.6648	−	15.7487i	1.96396	−	1.85600i
$73$			4.99135i			0.584193i	0.956389	+	0.292096i	$0.0943528\pi$
$73$			4.99135i			0.584193i	−0.956389	+	0.292096i	$0.905647\pi$
$74$			4.68345i			0.544440i
$75$	3.30646	−	7.67402i	0.381797	−	0.886120i
$76$		−	37.4447i		−	4.29520i
$77$	3.77156	−	7.78082i	0.429809	−	0.886707i
$78$	−7.48230	+	17.3658i	−0.847204	+	1.96629i
$79$	−5.41267			−0.608972			−0.304486	−	0.952517i	$-0.598485\pi$
$79$	−5.41267			−0.608972			−0.304486	+	0.952517i	$0.598485\pi$
$80$	4.30501			0.481315
$81$	−0.508318	+	8.98563i	−0.0564798	+	0.998404i
$82$			31.1530i			3.44027i
$83$	0.916862			0.100639			0.0503194	−	0.998733i	$-0.483976\pi$
$83$	0.916862			0.100639			0.0503194	+	0.998733i	$0.483976\pi$
$84$	−17.0180	+	14.7050i	−1.85681	+	1.60445i
$85$	0.419096			0.0454574
$86$			9.49786i			1.02418i
$87$	4.83547	+	2.08343i	0.518417	+	0.223367i
$88$	−24.9785			−2.66271
$89$	1.02907			0.109081			0.0545404	−	0.998512i	$-0.482631\pi$
$89$	1.02907			0.109081			0.0545404	+	0.998512i	$0.482631\pi$
$90$	−2.40174	+	2.26971i	−0.253165	+	0.239249i
$91$	4.79353	−	9.88917i	0.502499	−	1.03667i
$92$			5.83560i			0.608403i
$93$	−4.86919	−	2.09795i	−0.504911	−	0.217548i
$94$			17.9195i			1.84826i
$95$			3.19745i			0.328051i
$96$	18.6305	+	8.02720i	1.90147	+	0.819273i
$97$			11.9067i			1.20894i	0.796629	+	0.604469i	$0.206615\pi$
$97$			11.9067i			1.20894i	−0.796629	+	0.604469i	$0.793385\pi$
$98$	14.4426	−	11.3974i	1.45893	−	1.15131i
$99$	7.12590	−	6.73418i	0.716180	−	0.676810i
$100$	23.6777			2.36777
$101$	15.0983			1.50234			0.751168	−	0.660111i	$-0.229491\pi$
$101$	15.0983			1.50234			0.751168	+	0.660111i	$0.229491\pi$
$102$	4.18079	+	1.80135i	0.413960	+	0.178360i
$103$			5.48877i			0.540825i	0.962745	+	0.270412i	$0.0871600\pi$
$103$			5.48877i			0.540825i	−0.962745	+	0.270412i	$0.912840\pi$
$104$	−31.7468			−3.11303
$105$	1.45318	−	1.25568i	0.141816	−	0.122542i
$106$	−18.4501			−1.79203
$107$			14.3006i			1.38249i	0.722621	+	0.691244i	$0.242937\pi$
$107$			14.3006i			1.38249i	−0.722621	+	0.691244i	$0.757063\pi$
$108$	−23.9536	+	8.75234i	−2.30493	+	0.842194i
$109$	−12.4180			−1.18943			−0.594714	−	0.803938i	$-0.702735\pi$
$109$	−12.4180			−1.18943			−0.594714	+	0.803938i	$0.702735\pi$
$110$	3.59991			0.343238
$111$	1.22128	−	2.83449i	0.115919	−	0.269038i
$112$	−24.4559	−	11.8544i	−2.31086	−	1.12013i
$113$		−	15.7766i		−	1.48414i	−0.670324	−	0.742068i	$-0.733845\pi$
$113$		−	15.7766i		−	1.48414i	0.670324	−	0.742068i	$-0.266155\pi$
$114$	−13.7432	+	31.8969i	−1.28717	+	2.98741i
$115$		−	0.498309i		−	0.0464675i
$116$			14.9196i			1.38525i
$117$	9.05678	−	8.55892i	0.837300	−	0.791272i
$118$		−	6.81125i		−	0.627026i
$119$	−2.38080	−	1.15403i	−0.218248	−	0.105790i
$120$	−5.09519	−	2.19533i	−0.465125	−	0.200405i
$121$	0.319157			0.0290143
$122$	−26.1099			−2.36388
$123$	8.12359	−	18.8542i	0.732479	−	1.70003i
$124$		−	15.0236i		−	1.34916i
$125$	−4.11735			−0.368267
$126$	19.8937	−	6.28028i	1.77227	−	0.559491i
$127$	19.9391			1.76931			0.884655	−	0.466246i	$-0.154394\pi$
$127$	19.9391			1.76931			0.884655	+	0.466246i	$0.154394\pi$
$128$			3.48685i			0.308197i
$129$	2.47670	−	5.74824i	0.218062	−	0.506104i
$130$	4.57537			0.401286
$131$	−21.2915			−1.86025			−0.930123	−	0.367249i	$-0.880300\pi$
$131$	−21.2915			−1.86025			−0.930123	+	0.367249i	$0.880300\pi$
$132$	25.5145	+	10.9933i	2.22075	+	0.956841i
$133$	8.80456	−	18.1640i	0.763453	−	1.57502i
$134$		−	18.8632i		−	1.62953i
$135$	2.04542	−	0.747372i	0.176042	−	0.0643236i
$136$			7.64298i			0.655380i
$137$		−	21.0090i		−	1.79492i	−0.441100	−	0.897458i	$-0.645411\pi$
$137$		−	21.0090i		−	1.79492i	0.441100	−	0.897458i	$-0.354589\pi$
$138$	2.14182	−	4.97099i	0.182324	−	0.423159i
$139$			7.67199i			0.650729i	0.945589	+	0.325365i	$0.105487\pi$
$139$			7.67199i			0.650729i	−0.945589	+	0.325365i	$0.894513\pi$
$140$	4.89708	+	2.37374i	0.413879	+	0.200618i
$141$	4.67278	−	10.8452i	0.393519	−	0.913327i
$142$	18.1086			1.51964
$143$	−13.5750			−1.13520
$144$	−21.1662	−	22.3974i	−1.76385	−	1.86645i
$145$		−	1.27400i		−	0.105800i
$146$	13.1187			1.08572
$147$	−11.7129	+	3.13173i	−0.966064	+	0.258301i
$148$	8.74564			0.718888
$149$			15.4237i			1.26356i	0.775149	+	0.631778i	$0.217675\pi$
$149$			15.4237i			1.26356i	−0.775149	+	0.631778i	$0.782325\pi$
$150$	−20.1696	−	8.69036i	−1.64684	−	0.709565i
$151$	−3.54332			−0.288352			−0.144176	−	0.989552i	$-0.546053\pi$
$151$	−3.54332			−0.288352			−0.144176	+	0.989552i	$0.546053\pi$
$152$	−58.3112			−4.72967
$153$	−2.06054	−	2.18040i	−0.166585	−	0.176275i
$154$	−20.4503	−	9.91279i	−1.64793	−	0.798796i
$155$			1.28288i			0.103044i
$156$	32.4281	+	13.9721i	2.59633	+	1.11866i
$157$			0.290738i			0.0232034i	0.999933	+	0.0116017i	$0.00369302\pi$
$157$			0.290738i			0.0232034i	−0.999933	+	0.0116017i	$0.996307\pi$
$158$			14.2261i			1.13177i
$159$	11.1663	+	4.81113i	0.885542	+	0.381548i
$160$		−	4.90857i		−	0.388056i
$161$	−1.37215	+	2.83079i	−0.108141	+	0.223097i
$162$	23.6169	+	1.33601i	1.85552	+	0.104967i
$163$	4.84774			0.379704			0.189852	−	0.981813i	$-0.439199\pi$
$163$	4.84774			0.379704			0.189852	+	0.981813i	$0.439199\pi$
$164$	58.1735			4.54259
$165$	−2.17871	−	0.938728i	−0.169613	−	0.0730799i
$166$		−	2.40979i		−	0.187036i
$167$	1.44985			0.112193			0.0560965	−	0.998425i	$-0.482135\pi$
$167$	1.44985			0.112193			0.0560965	+	0.998425i	$0.482135\pi$
$168$	22.8996	+	26.5015i	1.76674	+	2.04463i
$169$	−4.25337			−0.327183
$170$		−	1.10151i		−	0.0844820i
$171$	16.6351	−	15.7207i	1.27212	−	1.20219i
$172$	17.7358			1.35235
$173$	7.78298			0.591729			0.295865	−	0.955230i	$-0.404392\pi$
$173$	7.78298			0.591729			0.295865	+	0.955230i	$0.404392\pi$
$174$	5.47588	−	12.7091i	0.415125	−	0.963473i
$175$	11.4858	+	5.56747i	0.868247	+	0.420861i
$176$			33.5709i			2.53050i
$177$	−1.77613	+	4.12226i	−0.133502	+	0.309848i
$178$		−	2.70469i		−	0.202725i
$179$			15.1854i			1.13501i	0.823370	+	0.567505i	$0.192091\pi$
$179$			15.1854i			1.13501i	−0.823370	+	0.567505i	$0.807909\pi$
$180$	4.23835	+	4.48489i	0.315908	+	0.334284i
$181$			5.78668i			0.430121i	0.976601	+	0.215060i	$0.0689948\pi$
$181$			5.78668i			0.430121i	−0.976601	+	0.215060i	$0.931005\pi$
$182$	−25.9917	−	12.5988i	−1.92663	−	0.933888i
$183$	15.8021	+	6.80854i	1.16812	+	0.503302i
$184$	9.08756			0.669944
$185$	−0.746801			−0.0549059
$186$	−5.51405	+	12.7977i	−0.404310	+	0.938371i
$187$			3.26816i			0.238991i
$188$	33.4621			2.44047
$189$	−13.6776	−	1.38666i	−0.994900	−	0.100865i
$190$	8.40385			0.609679
$191$			11.8015i			0.853926i	0.904269	+	0.426963i	$0.140417\pi$
$191$			11.8015i			0.853926i	−0.904269	+	0.426963i	$0.859583\pi$
$192$	7.01753	−	16.2871i	0.506447	−	1.17542i
$193$	1.54021			0.110867			0.0554334	−	0.998462i	$-0.482346\pi$
$193$	1.54021			0.110867			0.0554334	+	0.998462i	$0.482346\pi$
$194$	31.2943			2.24680
$195$	−2.76907	−	1.19309i	−0.198297	−	0.0854391i
$196$	−21.2829	−	26.9694i	−1.52021	−	1.92639i
$197$		−	14.7146i		−	1.04837i	−0.851604	−	0.524186i	$-0.824370\pi$
$197$		−	14.7146i		−	1.04837i	0.851604	−	0.524186i	$-0.175630\pi$
$198$	−17.6994	−	18.7290i	−1.25784	−	1.33101i
$199$		−	12.8226i		−	0.908970i	−0.890754	−	0.454485i	$-0.849823\pi$
$199$		−	12.8226i		−	0.908970i	0.890754	−	0.454485i	$-0.150177\pi$
$200$		−	36.8725i		−	2.60728i
$201$	−4.91885	+	11.4163i	−0.346949	+	0.805242i
$202$		−	39.6828i		−	2.79207i
$203$	−3.50812	+	7.23733i	−0.246222	+	0.507961i
$204$	3.36375	−	7.80700i	0.235510	−	0.546600i
$205$	−4.96751			−0.346946
$206$	14.4261			1.00512
$207$	−2.59252	+	2.45000i	−0.180192	+	0.170287i
$208$			42.6675i			2.95846i
$209$	−24.9340			−1.72472
$210$	−3.30030	−	3.81940i	−0.227743	−	0.263564i
$211$	14.7318			1.01418			0.507091	−	0.861893i	$-0.330721\pi$
$211$	14.7318			1.01418			0.507091	+	0.861893i	$0.330721\pi$
$212$			34.4528i			2.36623i
$213$	−10.9596	−	4.72209i	−0.750939	−	0.323552i
$214$	37.5862			2.56934
$215$	−1.51448			−0.103287
$216$	13.6297	+	37.3020i	0.927383	+	2.53808i
$217$	3.53257	−	7.28779i	0.239807	−	0.494727i
$218$			32.6382i			2.21054i
$219$	−7.93965	−	3.42090i	−0.536512	−	0.231163i
$220$		−	6.72229i		−	0.453217i
$221$			4.15372i			0.279409i
$222$	−7.44988	−	3.20988i	−0.500003	−	0.215433i
$223$		−	15.9206i		−	1.06612i	−0.846076	−	0.533062i	$-0.821041\pi$
$223$		−	15.9206i		−	1.06612i	0.846076	−	0.533062i	$-0.178959\pi$
$224$	−13.5164	+	27.8846i	−0.903099	+	1.86312i
$225$	9.94080	+	10.5190i	0.662720	+	0.701270i
$226$	−41.4656			−2.75825
$227$	2.76671			0.183633			0.0918167	−	0.995776i	$-0.470733\pi$
$227$	2.76671			0.183633			0.0918167	+	0.995776i	$0.470733\pi$
$228$	59.5626	+	25.6634i	3.94463	+	1.69960i
$229$			12.3492i			0.816056i	0.912969	+	0.408028i	$0.133783\pi$
$229$			12.3492i			0.816056i	−0.912969	+	0.408028i	$0.866217\pi$
$230$	−1.30970			−0.0863594
$231$	9.79192	+	11.3321i	0.644261	+	0.745596i
$232$	23.2337			1.52537
$233$		−	12.7552i		−	0.835618i	−0.908535	−	0.417809i	$-0.862798\pi$
$233$		−	12.7552i		−	0.835618i	0.908535	−	0.417809i	$-0.137202\pi$
$234$	−22.4954	−	23.8039i	−1.47057	−	1.55611i
$235$	−2.85737			−0.186394
$236$	−12.7190			−0.827935
$237$	3.70966	−	8.60983i	0.240968	−	0.559269i
$238$	−3.03315	+	6.25745i	−0.196610	+	0.405610i
$239$		−	3.56682i		−	0.230718i	−0.993324	−	0.115359i	$-0.963198\pi$
$239$		−	3.56682i		−	0.230718i	0.993324	−	0.115359i	$-0.0368019\pi$
$240$	−2.95051	+	6.84791i	−0.190455	+	0.442031i
$241$			11.9713i			0.771136i	0.922679	+	0.385568i	$0.125995\pi$
$241$			11.9713i			0.771136i	−0.922679	+	0.385568i	$0.874005\pi$
$242$		−	0.838841i		−	0.0539227i
$243$	−13.9449	−	6.96703i	−0.894566	−	0.446935i
$244$			48.7564i			3.12131i
$245$	1.81737	+	2.30295i	0.116108	+	0.147130i
$246$	−49.5545	−	21.3512i	−3.15948	−	1.36130i
$247$	−31.6903			−2.01641
$248$	−23.3957			−1.48563
$249$	−0.628387	+	1.45844i	−0.0398224	+	0.0924247i
$250$			10.8216i			0.684420i
$251$	9.27569			0.585476			0.292738	−	0.956193i	$-0.405434\pi$
$251$	9.27569			0.585476			0.292738	+	0.956193i	$0.405434\pi$
$252$	−11.7275	−	37.1485i	−0.738762	−	2.34014i
$253$	3.88586			0.244302
$254$		−	52.4060i		−	3.28824i
$255$	−0.287235	+	0.666649i	−0.0179873	+	0.0417472i
$256$	−11.3137			−0.707106
$257$	5.31653			0.331636			0.165818	−	0.986156i	$-0.446974\pi$
$257$	5.31653			0.331636			0.165818	+	0.986156i	$0.446974\pi$
$258$	−15.1081	−	6.50952i	−0.940588	−	0.405265i
$259$	4.24242	+	2.05641i	0.263611	+	0.127779i
$260$		−	8.54381i		−	0.529865i
$261$	−6.62815	+	6.26379i	−0.410272	+	0.387719i
$262$			55.9604i			3.45724i
$263$			12.7247i			0.784640i	0.919829	+	0.392320i	$0.128327\pi$
$263$			12.7247i			0.784640i	−0.919829	+	0.392320i	$0.871673\pi$
$264$	17.1194	−	39.7328i	1.05363	−	2.44538i
$265$		−	2.94197i		−	0.180724i
$266$	−47.7405	−	23.1410i	−2.92716	−	1.41887i
$267$	−0.705288	+	1.63692i	−0.0431629	+	0.100178i
$268$	−35.2242			−2.15166
$269$	−20.7171			−1.26314			−0.631571	−	0.775318i	$-0.717590\pi$
$269$	−20.7171			−1.26314			−0.631571	+	0.775318i	$0.717590\pi$
$270$	−1.96432	−	5.37599i	−0.119545	−	0.327172i
$271$			4.57517i			0.277922i	0.990298	+	0.138961i	$0.0443763\pi$
$271$			4.57517i			0.277922i	−0.990298	+	0.138961i	$0.955624\pi$
$272$	10.2721			0.622839
$273$	12.4452	+	14.4027i	0.753218	+	0.871691i
$274$	−55.2178			−3.33583
$275$		−	15.7668i		−	0.950771i
$276$	−9.28259	−	3.99953i	−0.558746	−	0.240743i
$277$	21.7213			1.30511			0.652555	−	0.757742i	$-0.273697\pi$
$277$	21.7213			1.30511			0.652555	+	0.757742i	$0.273697\pi$
$278$	20.1643			1.20937
$279$	6.67436	−	6.30746i	0.399584	−	0.377618i
$280$	3.69654	−	7.62605i	0.220910	−	0.455744i
$281$			9.51165i			0.567417i	0.958911	+	0.283709i	$0.0915648\pi$
$281$			9.51165i			0.567417i	−0.958911	+	0.283709i	$0.908435\pi$
$282$	−28.5043	−	12.2815i	−1.69741	−	0.731351i
$283$		−	3.12414i		−	0.185711i	−0.995680	−	0.0928555i	$-0.970401\pi$
$283$		−	3.12414i		−	0.185711i	0.995680	−	0.0928555i	$-0.0295995\pi$
$284$		−	33.8152i		−	2.00656i
$285$	−5.08612	−	2.19142i	−0.301276	−	0.129809i
$286$			35.6792i			2.10975i
$287$	28.2194	+	13.6786i	1.66574	+	0.807425i
$288$	−25.5375	+	24.1336i	−1.50481	+	1.42209i
$289$	1.00000			0.0588235
$290$	−3.34845			−0.196628
$291$	−18.9397	−	8.16043i	−1.11027	−	0.478373i
$292$		−	24.4973i		−	1.43360i
$293$	32.5027			1.89883			0.949414	−	0.314026i	$-0.101678\pi$
$293$	32.5027			1.89883			0.949414	+	0.314026i	$0.101678\pi$
$294$	8.23113	+	30.7850i	0.480049	+	1.79542i
$295$	1.08609			0.0632346
$296$		−	13.6193i		−	0.791604i
$297$	5.82809	+	15.9504i	0.338180	+	0.925538i
$298$	40.5380			2.34830
$299$	4.93880			0.285618
$300$	−16.2279	+	37.6638i	−0.936921	+	2.17452i
$301$	8.60347	+	4.17032i	0.495896	+	0.240373i
$302$			9.31291i			0.535898i
$303$	−10.3479	+	24.0166i	−0.594470	+	1.37972i
$304$			78.3700i			4.49483i
$305$		−	4.16337i		−	0.238394i
$306$	−5.73075	+	5.41573i	−0.327605	+	0.309596i
$307$			27.1097i			1.54723i	0.633654	+	0.773617i	$0.281554\pi$
$307$			27.1097i			1.54723i	−0.633654	+	0.773617i	$0.718446\pi$
$308$	−18.5107	+	38.1880i	−1.05474	+	2.17596i
$309$	−8.73090	−	3.76182i	−0.496683	−	0.214003i
$310$	3.37180			0.191505
$311$	−2.60374			−0.147644			−0.0738222	−	0.997271i	$-0.523520\pi$
$311$	−2.60374			−0.147644			−0.0738222	+	0.997271i	$0.523520\pi$
$312$	21.7582	−	50.4991i	1.23182	−	2.85895i
$313$			5.31220i			0.300263i	0.988666	+	0.150132i	$0.0479697\pi$
$313$			5.31220i			0.300263i	−0.988666	+	0.150132i	$0.952030\pi$
$314$	0.764146			0.0431233
$315$	1.00142	+	3.17216i	0.0564238	+	0.178731i
$316$	26.5651			1.49441
$317$			21.0749i			1.18369i	0.806053	+	0.591844i	$0.201600\pi$
$317$			21.0749i			1.18369i	−0.806053	+	0.591844i	$0.798400\pi$
$318$	12.6451	−	29.3483i	0.709102	−	1.64577i
$319$	9.93478			0.556241
$320$	−4.29116			−0.239883
$321$	−22.7477	−	9.80114i	−1.26965	−	0.547046i
$322$	7.44016	+	3.60643i	0.414624	+	0.200979i
$323$			7.62938i			0.424510i
$324$	2.49480	−	44.1011i	0.138600	−	2.45006i
$325$		−	20.0390i		−	1.11157i
$326$		−	12.7413i		−	0.705676i
$327$	8.51088	−	19.7531i	0.470653	−	1.09235i
$328$		−	90.5915i		−	5.00208i
$329$	16.2321	+	7.86811i	0.894905	+	0.433783i
$330$	−2.46726	+	5.72631i	−0.135818	+	0.315223i
$331$	−6.60203			−0.362880			−0.181440	−	0.983402i	$-0.558076\pi$
$331$	−6.60203			−0.362880			−0.181440	+	0.983402i	$0.558076\pi$
$332$	−4.49992			−0.246965
$333$	3.67175	+	3.88533i	0.201211	+	0.212915i
$334$		−	3.81065i		−	0.208509i
$335$	3.00784			0.164336
$336$	35.6178	−	30.7769i	1.94311	−	1.67902i
$337$	11.6070			0.632273			0.316137	−	0.948714i	$-0.397614\pi$
$337$	11.6070			0.632273			0.316137	+	0.948714i	$0.397614\pi$
$338$			11.1791i			0.608065i
$339$	25.0955	+	10.8128i	1.36300	+	0.587268i
$340$	−2.05691			−0.111551
$341$	−10.0040			−0.541749
$342$	−41.3186	−	43.7221i	−2.23426	−	2.36422i
$343$	−3.98266	−	18.0870i	−0.215044	−	0.976604i
$344$		−	27.6194i		−	1.48914i
$345$	0.792651	+	0.341524i	0.0426749	+	0.0183871i
$346$		−	20.4560i		−	1.09972i
$347$		−	21.9356i		−	1.17757i	−0.808291	−	0.588783i	$-0.799607\pi$
$347$		−	21.9356i		−	1.17757i	0.808291	−	0.588783i	$-0.200393\pi$
$348$	−23.7323	−	10.2254i	−1.27219	−	0.548138i
$349$			19.7765i			1.05861i	0.848431	+	0.529306i	$0.177547\pi$
$349$			19.7765i			1.05861i	−0.848431	+	0.529306i	$0.822453\pi$
$350$	14.6330	−	30.1882i	0.782166	−	1.61363i
$351$	7.40730	+	20.2725i	0.395373	+	1.08206i
$352$	38.2775			2.04020
$353$	−30.8652			−1.64279			−0.821394	−	0.570361i	$-0.806803\pi$
$353$	−30.8652			−1.64279			−0.821394	+	0.570361i	$0.806803\pi$
$354$	10.8345	+	4.66820i	0.575849	+	0.248112i
$355$			2.88752i			0.153254i
$356$	−5.05061			−0.267682
$357$	3.46742	−	2.99616i	0.183515	−	0.158574i
$358$	39.9118			2.10940
$359$			18.6374i			0.983642i	0.870696	+	0.491821i	$0.163669\pi$
$359$			18.6374i			0.983642i	−0.870696	+	0.491821i	$0.836331\pi$
$360$	6.98415	−	6.60022i	0.368097	−	0.347862i
$361$	−39.2075			−2.06355
$362$	15.2091			0.799375
$363$	−0.218740	+	0.507678i	−0.0114809	+	0.0266462i
$364$	−23.5264	+	48.5356i	−1.23312	+	2.54396i
$365$			2.09185i			0.109493i
$366$	17.8949	−	41.5326i	0.935381	−	2.17094i
$367$		−	17.2282i		−	0.899304i	−0.893204	−	0.449652i	$-0.851548\pi$
$367$		−	17.2282i		−	0.899304i	0.893204	−	0.449652i	$-0.148452\pi$
$368$		−	12.2136i		−	0.636680i
$369$	24.4234	+	25.8441i	1.27143	+	1.34539i
$370$			1.96282i			0.102042i
$371$	−8.10108	+	16.7127i	−0.420587	+	0.867681i
$372$	23.8978	+	10.2967i	1.23904	+	0.533858i
$373$	−20.0804			−1.03973			−0.519863	−	0.854250i	$-0.674017\pi$
$373$	−20.0804			−1.03973			−0.519863	+	0.854250i	$0.674017\pi$
$374$	8.58969			0.444162
$375$	2.82190	−	6.54940i	0.145722	−	0.338210i
$376$		−	52.1093i		−	2.68733i
$377$	12.6268			0.650312
$378$	−3.64456	+	35.9489i	−0.187456	+	1.84901i
$379$	−19.7985			−1.01698			−0.508491	−	0.861067i	$-0.669797\pi$
$379$	−19.7985			−1.01698			−0.508491	+	0.861067i	$0.669797\pi$
$380$		−	15.6929i		−	0.805030i
$381$	−13.6656	+	31.7168i	−0.700111	+	1.62490i
$382$	31.0179			1.58701
$383$	18.9401			0.967795			0.483897	−	0.875125i	$-0.339221\pi$
$383$	18.9401			0.967795			0.483897	+	0.875125i	$0.339221\pi$
$384$	−5.54647	−	2.38977i	−0.283042	−	0.121952i
$385$	1.58065	−	3.26092i	0.0805573	−	0.166192i
$386$		−	4.04813i		−	0.206045i
$387$	7.44617	+	7.87930i	0.378510	+	0.400528i
$388$		−	58.4374i		−	2.96671i
$389$		−	0.598794i		−	0.0303601i	−0.999885	−	0.0151800i	$-0.995168\pi$
$389$		−	0.598794i		−	0.0303601i	0.999885	−	0.0151800i	$-0.00483214\pi$
$390$	−3.13580	+	7.27795i	−0.158788	+	0.368534i
$391$		−	1.18901i		−	0.0601307i
$392$	−41.9985	+	33.1431i	−2.12125	+	1.67398i
$393$	14.5925	−	33.8680i	0.736093	−	1.70841i
$394$	−38.6744			−1.94839
$395$	−2.26843			−0.114137
$396$	−34.9736	+	33.0511i	−1.75749	+	1.66088i
$397$		−	12.9165i		−	0.648262i	−0.946012	−	0.324131i	$-0.894928\pi$
$397$		−	12.9165i		−	0.648262i	0.946012	−	0.324131i	$-0.105072\pi$
$398$	−33.7016			−1.68931
$399$	22.8589	+	26.4543i	1.14437	+	1.32437i
$400$	−49.5564			−2.47782
$401$			3.61244i			0.180397i	0.995924	+	0.0901984i	$0.0287501\pi$
$401$			3.61244i			0.180397i	−0.995924	+	0.0901984i	$0.971250\pi$
$402$	30.0054	+	12.9282i	1.49653	+	0.644801i
$403$	−12.7148			−0.633370
$404$	−74.1018			−3.68670
$405$	−0.213034	+	3.76585i	−0.0105858	+	0.187126i
$406$	19.0219	+	9.22038i	0.944040	+	0.457600i
$407$		−	5.82363i		−	0.288667i
$408$	−12.1576	−	5.23825i	−0.601889	−	0.259332i
$409$		−	15.3073i		−	0.756895i	−0.925623	−	0.378448i	$-0.876458\pi$
$409$		−	15.3073i		−	0.756895i	0.925623	−	0.378448i	$-0.123542\pi$
$410$			13.0561i			0.644794i
$411$	33.4186	+	14.3988i	1.64842	+	0.710243i
$412$		−	26.9387i		−	1.32717i
$413$	−6.16985	−	2.99068i	−0.303598	−	0.147162i
$414$	6.43934	+	6.81391i	0.316476	+	0.334885i
$415$	0.384254			0.0188623
$416$	48.6495			2.38524
$417$	−12.2037	−	5.25813i	−0.597618	−	0.257492i
$418$			65.5340i			3.20538i
$419$	−17.0774			−0.834286			−0.417143	−	0.908841i	$-0.636969\pi$
$419$	−17.0774			−0.834286			−0.417143	+	0.908841i	$0.636969\pi$
$420$	−7.13217	+	6.16282i	−0.348014	+	0.300715i
$421$	−35.7504			−1.74237			−0.871184	−	0.490957i	$-0.836647\pi$
$421$	−35.7504			−1.74237			−0.871184	+	0.490957i	$0.836647\pi$
$422$		−	38.7197i		−	1.88485i
$423$	14.0486	+	14.8658i	0.683068	+	0.722801i
$424$	53.6521			2.60558
$425$	−4.82436			−0.234016
$426$	−12.4111	+	28.8051i	−0.601318	+	1.39561i
$427$	−11.4643	+	23.6512i	−0.554799	+	1.14456i
$428$		−	70.1866i		−	3.39260i
$429$	9.30386	−	21.5935i	0.449194	−	1.04254i
$430$			3.98052i			0.191958i
$431$		−	8.49145i		−	0.409019i	−0.978865	−	0.204509i	$-0.934440\pi$
$431$		−	8.49145i		−	0.409019i	0.978865	−	0.204509i	$-0.0655599\pi$
$432$	50.1337	−	18.3182i	2.41206	−	0.881337i
$433$			10.7870i			0.518388i	0.965825	+	0.259194i	$0.0834569\pi$
$433$			10.7870i			0.518388i	−0.965825	+	0.259194i	$0.916543\pi$
$434$	−19.1545	−	9.28466i	−0.919445	−	0.445678i
$435$	2.02653	+	0.873158i	0.0971647	+	0.0418647i
$436$	60.9469			2.91883
$437$	9.07139			0.433944
$438$	−8.99116	+	20.8678i	−0.429614	+	0.997101i
$439$		−	11.4818i		−	0.547994i	−0.961730	−	0.273997i	$-0.911654\pi$
$439$		−	11.4818i		−	0.547994i	0.961730	−	0.273997i	$-0.0883459\pi$
$440$	−10.4684			−0.499060
$441$	3.04605	−	20.7779i	0.145050	−	0.989424i
$442$	10.9172			0.519279
$443$			3.74058i			0.177720i	0.996044	+	0.0888601i	$0.0283224\pi$
$443$			3.74058i			0.177720i	−0.996044	+	0.0888601i	$0.971678\pi$
$444$	−5.99398	+	13.9115i	−0.284462	+	0.660213i
$445$	0.431278			0.0204445
$446$	−41.8442			−1.98138
$447$	−24.5342	−	10.5709i	−1.16043	−	0.499985i
$448$	24.3772	+	11.8163i	1.15172	+	0.558265i
$449$			17.2006i			0.811745i	0.913930	+	0.405873i	$0.133032\pi$
$449$			17.2006i			0.811745i	−0.913930	+	0.405873i	$0.866968\pi$
$450$	27.6472	−	26.1274i	1.30330	−	1.23166i
$451$		−	38.7371i		−	1.82406i
$452$			77.4308i			3.64204i
$453$	2.42848	−	5.63630i	0.114100	−	0.264817i
$454$		−	7.27175i		−	0.341280i
$455$	2.00895	−	4.14452i	0.0941811	−	0.194298i
$456$	39.9646	−	92.7547i	1.87151	−	4.34364i
$457$	0.464313			0.0217197			0.0108598	−	0.999941i	$-0.496543\pi$
$457$	0.464313			0.0217197			0.0108598	+	0.999941i	$0.496543\pi$
$458$	32.4573			1.51663
$459$	4.88056	−	1.78329i	0.227805	−	0.0832371i
$460$			2.44568i			0.114030i
$461$	21.3621			0.994930			0.497465	−	0.867484i	$-0.334264\pi$
$461$	21.3621			0.994930			0.497465	+	0.867484i	$0.334264\pi$
$462$	29.7841	−	25.7361i	1.38568	−	1.19735i
$463$	24.3626			1.13223			0.566113	−	0.824328i	$-0.308447\pi$
$463$	24.3626			1.13223			0.566113	+	0.824328i	$0.308447\pi$
$464$		−	31.2260i		−	1.44963i
$465$	−2.04066	−	0.879245i	−0.0946333	−	0.0407740i
$466$	−33.5244			−1.55299
$467$	−38.6049			−1.78642			−0.893211	−	0.449638i	$-0.851553\pi$
$467$	−38.6049			−1.78642			−0.893211	+	0.449638i	$0.851553\pi$
$468$	−44.4503	+	42.0068i	−2.05472	+	1.94177i
$469$	−17.0869	−	8.28246i	−0.789000	−	0.382448i
$470$			7.51002i			0.346411i
$471$	−0.462472	−	0.199262i	−0.0213096	−	0.00918152i
$472$			19.8068i			0.911682i
$473$		−	11.8101i		−	0.543029i
$474$	−22.6292	−	9.75010i	−1.03939	−	0.447837i
$475$		−	36.8069i		−	1.68882i
$476$	11.6849	+	5.66395i	0.535575	+	0.259607i
$477$	−15.3060	+	14.4646i	−0.700813	+	0.662288i
$478$	−9.37466			−0.428787
$479$	−3.00224			−0.137176			−0.0685880	−	0.997645i	$-0.521849\pi$
$479$	−3.00224			−0.137176			−0.0685880	+	0.997645i	$0.521849\pi$
$480$	7.80798	+	3.36417i	0.356384	+	0.153553i
$481$		−	7.40164i		−	0.337486i
$482$	31.4640			1.43315
$483$	−3.56246	−	4.12279i	−0.162097	−	0.187594i
$484$	−1.56641			−0.0712005
$485$			4.99004i			0.226586i
$486$	−18.3114	+	36.6514i	−0.830624	+	1.66254i
$487$	−9.05068			−0.410125			−0.205063	−	0.978749i	$-0.565740\pi$
$487$	−9.05068			−0.410125			−0.205063	+	0.978749i	$0.565740\pi$
$488$	75.9265			3.43703
$489$	−3.32248	+	7.71121i	−0.150248	+	0.348713i
$490$	6.05285	−	4.77661i	0.273440	−	0.215785i
$491$			9.83946i			0.444049i	0.975041	+	0.222024i	$0.0712664\pi$
$491$			9.83946i			0.444049i	−0.975041	+	0.222024i	$0.928734\pi$
$492$	−39.8702	+	92.5356i	−1.79749	+	4.17183i
$493$		−	3.03987i		−	0.136909i
$494$			83.2916i			3.74747i
$495$	2.98644	−	2.82227i	0.134230	−	0.126852i
$496$			31.4437i			1.41186i
$497$	7.95114	−	16.4034i	0.356657	−	0.735792i
$498$	3.83321	+	1.65159i	0.171770	+	0.0740095i
$499$	20.3585			0.911372			0.455686	−	0.890141i	$-0.349394\pi$
$499$	20.3585			0.911372			0.455686	+	0.890141i	$0.349394\pi$
$500$	20.2078			0.903720
$501$	−0.993682	+	2.30626i	−0.0443944	+	0.103036i
$502$		−	24.3793i		−	1.08810i
$503$	21.7975			0.971903			0.485952	−	0.873986i	$-0.338473\pi$
$503$	21.7975			0.971903			0.485952	+	0.873986i	$0.338473\pi$
$504$	−57.8500	+	18.2628i	−2.57685	+	0.813489i
$505$	6.32764			0.281576
$506$		−	10.2132i		−	0.454032i
$507$	2.91512	−	6.76577i	0.129465	−	0.300478i
$508$	−97.8603			−4.34185
$509$	23.0377			1.02113			0.510564	−	0.859840i	$-0.329437\pi$
$509$	23.0377			1.02113			0.510564	+	0.859840i	$0.329437\pi$
$510$	1.75215	+	0.754939i	0.0775867	+	0.0334293i
$511$	5.76018	−	11.8834i	0.254815	−	0.525690i
$512$			36.7095i			1.62234i
$513$	13.6054	+	37.2357i	0.600695	+	1.64399i
$514$		−	13.9734i		−	0.616342i
$515$			2.30032i			0.101364i
$516$	−12.1556	+	28.2121i	−0.535119	+	1.24197i
$517$		−	22.2820i		−	0.979963i
$518$	5.40486	−	11.1504i	0.237476	−	0.489918i
$519$	−5.33420	+	12.3803i	−0.234145	+	0.543433i
$520$	−13.3050			−0.583461
$521$	−43.5894			−1.90969			−0.954843	−	0.297110i	$-0.903977\pi$
$521$	−43.5894			−1.90969			−0.954843	+	0.297110i	$0.903977\pi$
$522$	16.4631	+	17.4208i	0.720571	+	0.762486i
$523$			33.5206i			1.46575i	0.680362	+	0.732876i	$0.261822\pi$
$523$			33.5206i			1.46575i	−0.680362	+	0.732876i	$0.738178\pi$
$524$	104.498			4.56500
$525$	−16.7281	+	14.4546i	−0.730074	+	0.630848i
$526$	33.4444			1.45824
$527$			3.06107i			0.133342i
$528$	−53.4007	−	23.0084i	−2.32397	−	1.00131i
$529$	21.5863			0.938533
$530$	−7.73238			−0.335873
$531$	−5.33991	−	5.65052i	−0.231732	−	0.245212i
$532$	−43.2124	+	89.1483i	−1.87350	+	3.86507i
$533$		−	49.2336i		−	2.13254i
$534$	4.30231	+	1.85371i	0.186179	+	0.0802178i
$535$			5.99332i			0.259114i
$536$			54.8534i			2.36931i
$537$	−24.1551	−	10.4076i	−1.04237	−	0.449120i
$538$			54.4507i			2.34754i
$539$	−17.9587	+	14.1721i	−0.773534	+	0.610434i
$540$	−10.0389	+	3.66807i	−0.432004	+	0.157849i
$541$	−16.5164			−0.710097			−0.355048	−	0.934848i	$-0.615536\pi$
$541$	−16.5164			−0.710097			−0.355048	+	0.934848i	$0.615536\pi$
$542$	12.0249			0.516515
$543$	−9.20478	−	3.96600i	−0.395015	−	0.170197i
$544$		−	11.7123i		−	0.502159i
$545$	−5.20433			−0.222929
$546$	37.8546	−	32.7097i	1.62003	−	1.39985i
$547$	−2.75977			−0.117999			−0.0589997	−	0.998258i	$-0.518791\pi$
$547$	−2.75977			−0.117999			−0.0589997	+	0.998258i	$0.518791\pi$
$548$			103.111i			4.40469i
$549$	−21.6605	+	20.4698i	−0.924446	+	0.873628i
$550$	−41.4398			−1.76700
$551$	23.1924			0.988028
$552$	−6.22832	+	14.4554i	−0.265095	+	0.615264i
$553$	12.8865	+	6.24640i	0.547988	+	0.265624i
$554$		−	57.0902i		−	2.42553i
$555$	0.511833	−	1.18792i	0.0217261	−	0.0504246i
$556$		−	37.6538i		−	1.59688i
$557$		−	22.8197i		−	0.966902i	−0.875371	−	0.483451i	$-0.839383\pi$
$557$		−	22.8197i		−	0.966902i	0.875371	−	0.483451i	$-0.160617\pi$
$558$	−16.5779	−	17.5422i	−0.701798	−	0.742621i
$559$		−	15.0103i		−	0.634866i
$560$	−10.2494	−	4.96813i	−0.433115	−	0.209942i
$561$	−5.19860	−	2.23989i	−0.219485	−	0.0945681i
$562$	24.9995			1.05454
$563$	28.2068			1.18878			0.594388	−	0.804178i	$-0.297394\pi$
$563$	28.2068			1.18878			0.594388	+	0.804178i	$0.297394\pi$
$564$	−22.9338	+	53.2276i	−0.965688	+	2.24128i
$565$		−	6.61191i		−	0.278165i
$566$	−8.21118			−0.345142
$567$	11.5799	−	20.8064i	0.486311	−	0.873786i
$568$	−52.6591			−2.20953
$569$			33.8244i			1.41799i	0.705211	+	0.708997i	$0.250852\pi$
$569$			33.8244i			1.41799i	−0.705211	+	0.708997i	$0.749148\pi$
$570$	−5.75972	+	13.3679i	−0.241248	+	0.559918i
$571$	−22.8959			−0.958165			−0.479082	−	0.877770i	$-0.659030\pi$
$571$	−22.8959			−0.958165			−0.479082	+	0.877770i	$0.659030\pi$
$572$	66.6255			2.78575
$573$	−18.7724	−	8.08836i	−0.784230	−	0.337896i
$574$	35.9516	−	74.1690i	1.50059	−	3.09575i
$575$			5.73620i			0.239216i
$576$	21.0981	+	22.3253i	0.879087	+	0.930223i
$577$		−	11.8036i		−	0.491390i	−0.969347	−	0.245695i	$-0.920984\pi$
$577$		−	11.8036i		−	0.491390i	0.969347	−	0.245695i	$-0.0790161\pi$
$578$		−	2.62830i		−	0.109323i
$579$	−1.05561	+	2.44999i	−0.0438696	+	0.101818i
$580$			6.25274i			0.259631i
$581$	−2.18287	−	1.05809i	−0.0905605	−	0.0438970i
$582$	−21.4481	+	49.7792i	−0.889050	+	2.06342i
$583$	22.9418			0.950151
$584$	−38.1488			−1.57861
$585$	3.79566	−	3.58701i	0.156931	−	0.148305i
$586$		−	85.4268i		−	3.52895i
$587$	−27.1547			−1.12080			−0.560398	−	0.828224i	$-0.689352\pi$
$587$	−27.1547			−1.12080			−0.560398	+	0.828224i	$0.689352\pi$
$588$	57.4865	−	15.3704i	2.37070	−	0.633865i
$589$	−23.3541			−0.962287
$590$		−	2.85457i		−	0.117521i
$591$	23.4063	+	10.0849i	0.962805	+	0.414837i
$592$	−18.3042			−0.752299
$593$	−8.98766			−0.369079			−0.184539	−	0.982825i	$-0.559079\pi$
$593$	−8.98766			−0.369079			−0.184539	+	0.982825i	$0.559079\pi$
$594$	41.9225	−	15.3180i	1.72010	−	0.628503i
$595$	−0.997785	−	0.483651i	−0.0409052	−	0.0198278i
$596$		−	75.6987i		−	3.10074i
$597$	20.3967	+	8.78819i	0.834781	+	0.359677i
$598$		−	12.9806i		−	0.530818i
$599$		−	3.73319i		−	0.152534i	−0.997087	−	0.0762669i	$-0.975700\pi$
$599$		−	3.73319i		−	0.152534i	0.997087	−	0.0762669i	$-0.0243001\pi$
$600$	58.6524	+	25.2712i	2.39448	+	1.03169i
$601$			24.4929i			0.999087i	0.866289	+	0.499544i	$0.166499\pi$
$601$			24.4929i			0.999087i	−0.866289	+	0.499544i	$0.833501\pi$
$602$	10.9609	−	22.6125i	0.446731	−	0.921617i
$603$	−14.7884	−	15.6487i	−0.602232	−	0.637263i
$604$	17.3905			0.707609
$605$	0.133758			0.00543802
$606$	63.1228	+	27.1973i	2.56419	+	1.10482i
$607$			20.8944i			0.848078i	0.905644	+	0.424039i	$0.139388\pi$
$607$			20.8944i			0.848078i	−0.905644	+	0.424039i	$0.860612\pi$
$608$	89.3574			3.62392
$609$	−9.10795	−	10.5405i	−0.369073	−	0.427124i
$610$	−10.9426			−0.443052
$611$		−	28.3197i		−	1.14569i
$612$	10.1131	+	10.7013i	0.408796	+	0.432575i
$613$	27.9090			1.12723			0.563617	−	0.826036i	$-0.309409\pi$
$613$	27.9090			1.12723			0.563617	+	0.826036i	$0.309409\pi$
$614$	71.2525			2.87552
$615$	3.40457	−	7.90173i	0.137285	−	0.318628i
$616$	59.4687	+	28.8260i	2.39606	+	1.16143i
$617$			37.1032i			1.49372i	0.664982	+	0.746860i	$0.268439\pi$
$617$			37.1032i			1.49372i	−0.664982	+	0.746860i	$0.731561\pi$
$618$	−9.88720	+	22.9474i	−0.397721	+	0.923080i
$619$		−	32.2925i		−	1.29795i	−0.760812	−	0.648973i	$-0.775199\pi$
$619$		−	32.2925i		−	1.29795i	0.760812	−	0.648973i	$-0.224801\pi$
$620$		−	6.29633i		−	0.252867i
$621$	−2.12035	−	5.80302i	−0.0850868	−	0.232867i
$622$			6.84340i			0.274396i
$623$	−2.45000	−	1.18758i	−0.0981572	−	0.0475793i
$624$	−67.8705	−	29.2429i	−2.71699	−	1.17065i
$625$	22.3962			0.895849
$626$	13.9620			0.558036
$627$	17.0890	−	39.6621i	0.682467	−	1.58395i
$628$		−	1.42693i		−	0.0569407i
$629$	−1.78193			−0.0710503
$630$	8.33738	−	2.63204i	0.332169	−	0.104863i
$631$	5.04144			0.200696			0.100348	−	0.994952i	$-0.468004\pi$
$631$	5.04144			0.200696			0.100348	+	0.994952i	$0.468004\pi$
$632$		−	41.3689i		−	1.64557i
$633$	−10.0967	+	23.4337i	−0.401309	+	0.931406i
$634$	55.3913			2.19987
$635$	8.35641			0.331614
$636$	−54.8035	−	23.6128i	−2.17310	−	0.936310i
$637$	−22.8249	+	18.0122i	−0.904354	+	0.713671i
$638$		−	26.1116i		−	1.03377i
$639$	15.0227	−	14.1969i	0.594288	−	0.561619i
$640$			1.46133i			0.0577640i
$641$		−	15.2827i		−	0.603632i	−0.953366	−	0.301816i	$-0.902407\pi$
$641$		−	15.2827i		−	0.603632i	0.953366	−	0.301816i	$-0.0975928\pi$
$642$	−25.7603	+	59.7877i	−1.01668	+	2.35963i
$643$			12.8064i			0.505035i	0.967592	+	0.252517i	$0.0812585\pi$
$643$			12.8064i			0.505035i	−0.967592	+	0.252517i	$0.918741\pi$
$644$	6.73448	−	13.8934i	0.265376	−	0.547476i
$645$	1.03798	−	2.40906i	0.0408703	−	0.0948568i
$646$	20.0523			0.788947
$647$	6.14256			0.241489			0.120744	−	0.992684i	$-0.461472\pi$
$647$	6.14256			0.241489			0.120744	+	0.992684i	$0.461472\pi$
$648$	−68.6770	−	3.88507i	−2.69789	−	0.152620i
$649$			8.46944i			0.332454i
$650$	−52.6686			−2.06583
$651$	9.17145	+	10.6140i	0.359457	+	0.415996i
$652$	−23.7925			−0.931786
$653$		−	15.2490i		−	0.596738i	−0.954451	−	0.298369i	$-0.903557\pi$
$653$		−	15.2490i		−	0.596738i	0.954451	−	0.298369i	$-0.0964426\pi$
$654$	−51.9170	−	22.3691i	−2.03012	−	0.874702i
$655$	−8.92318			−0.348658
$656$	−121.754			−4.75371
$657$	10.8831	−	10.2849i	0.424592	−	0.401252i
$658$	20.6798	−	42.6628i	0.806181	−	1.66317i
$659$		−	10.6973i		−	0.416707i	−0.978054	−	0.208353i	$-0.933190\pi$
$659$		−	10.6973i		−	0.416707i	0.978054	−	0.208353i	$-0.0668104\pi$
$660$	10.6930	+	4.60724i	0.416226	+	0.179337i
$661$			42.4332i			1.65046i	0.564796	+	0.825231i	$0.308955\pi$
$661$			42.4332i			1.65046i	−0.564796	+	0.825231i	$0.691045\pi$
$662$			17.3521i			0.674409i
$663$	−6.60725	−	2.84682i	−0.256604	−	0.110561i
$664$			7.00756i			0.271946i
$665$	3.68996	−	7.61248i	0.143091	−	0.295199i
$666$	10.2118	−	9.65045i	0.395700	−	0.373947i
$667$	−3.61443			−0.139951
$668$	−7.11582			−0.275319
$669$	25.3247	+	10.9115i	0.979109	+	0.421862i
$670$		−	7.90550i		−	0.305416i
$671$	32.4664			1.25335
$672$	−35.0918	−	40.6114i	−1.35370	−	1.56662i
$673$	−15.5646			−0.599971			−0.299986	−	0.953944i	$-0.596982\pi$
$673$	−15.5646			−0.599971			−0.299986	+	0.953944i	$0.596982\pi$
$674$		−	30.5066i		−	1.17507i
$675$	−23.5456	+	8.60325i	−0.906269	+	0.331139i
$676$	20.8754			0.802899
$677$	11.1408			0.428176			0.214088	−	0.976814i	$-0.431322\pi$
$677$	11.1408			0.428176			0.214088	+	0.976814i	$0.431322\pi$
$678$	28.4192	−	65.9586i	1.09143	−	2.53313i
$679$	13.7407	−	28.3474i	0.527319	−	1.08787i
$680$			3.20315i			0.122835i
$681$	−1.89622	+	4.40097i	−0.0726631	+	0.168645i
$682$			26.2936i			1.00683i
$683$		−	18.5703i		−	0.710572i	−0.934758	−	0.355286i	$-0.884383\pi$
$683$		−	18.5703i		−	0.710572i	0.934758	−	0.355286i	$-0.115617\pi$
$684$	−81.6445	+	77.1564i	−3.12176	+	2.95015i
$685$		−	8.80478i		−	0.336413i
$686$	−47.5380	+	10.4676i	−1.81501	+	0.399656i
$687$	−19.6436	−	8.46371i	−0.749450	−	0.322911i
$688$	−37.1203			−1.41520
$689$	29.1582			1.11084
$690$	0.897628	−	2.08332i	0.0341721	−	0.0793108i
$691$		−	19.0441i		−	0.724470i	−0.932087	−	0.362235i	$-0.882014\pi$
$691$		−	19.0441i		−	0.724470i	0.932087	−	0.362235i	$-0.117986\pi$
$692$	−38.1985			−1.45209
$693$	−24.7368	+	7.80920i	−0.939673	+	0.296647i
$694$	−57.6533			−2.18849
$695$			3.21530i			0.121963i
$696$	−15.9236	+	36.9574i	−0.603583	+	1.40087i
$697$	−11.8529			−0.448960
$698$	51.9785			1.96742
$699$	20.2894	+	8.74196i	0.767416	+	0.330651i
$700$	−56.3720	−	27.3249i	−2.13066	−	1.03278i
$701$		−	27.7593i		−	1.04845i	−0.851579	−	0.524227i	$-0.824354\pi$
$701$		−	27.7593i		−	1.04845i	0.851579	−	0.524227i	$-0.175646\pi$
$702$	53.2821	−	19.4686i	2.01100	−	0.734795i
$703$		−	13.5950i		−	0.512747i
$704$		−	33.4629i		−	1.26118i
$705$	1.95835	−	4.54517i	0.0737556	−	0.171181i
$706$			81.1229i			3.05310i
$707$	−35.9460	−	17.4239i	−1.35189	−	0.655295i
$708$	8.71717	−	20.2319i	0.327611	−	0.760360i
$709$	46.1627			1.73368			0.866839	−	0.498588i	$-0.166148\pi$
$709$	46.1627			1.73368			0.866839	+	0.498588i	$0.166148\pi$
$710$	7.58926			0.284820
$711$	11.1530	+	11.8018i	0.418271	+	0.442602i
$712$			7.86513i			0.294758i
$713$	3.63963			0.136305
$714$	−7.87481	−	9.11343i	−0.294707	−	0.341061i
$715$	−5.68923			−0.212765
$716$		−	74.5293i		−	2.78529i
$717$	5.67368	+	2.44458i	0.211887	+	0.0912945i
$718$	48.9846			1.82809
$719$	−42.2715			−1.57646			−0.788230	−	0.615381i	$-0.789002\pi$
$719$	−42.2715			−1.57646			−0.788230	+	0.615381i	$0.789002\pi$
$720$	−8.87067	−	9.38666i	−0.330590	−	0.349820i
$721$	6.33423	−	13.0677i	0.235899	−	0.486665i
$722$			103.049i			3.83509i
$723$	−19.0425	−	8.20470i	−0.708197	−	0.305136i
$724$		−	28.4008i		−	1.05551i
$725$			14.6654i			0.544661i
$726$	1.33433	+	0.574914i	0.0495216	+	0.0213371i
$727$			48.9291i			1.81468i	0.420398	+	0.907340i	$0.361891\pi$
$727$			48.9291i			1.81468i	−0.420398	+	0.907340i	$0.638109\pi$
$728$	75.5827	+	36.6369i	2.80128	+	1.35785i
$729$	20.6397	−	17.4070i	0.764434	−	0.644702i
$730$	5.49802			0.203491
$731$	−3.61369			−0.133657
$732$	−77.5560	−	33.4160i	−2.86655	−	1.23509i
$733$		−	9.93444i		−	0.366937i	−0.983026	−	0.183468i	$-0.941267\pi$
$733$		−	9.93444i		−	0.366937i	0.983026	−	0.183468i	$-0.0587325\pi$
$734$	−45.2808			−1.67135
$735$	−4.90884	+	1.31250i	−0.181065	+	0.0484122i
$736$	−13.9260			−0.513318
$737$			23.4554i			0.863992i
$738$	67.9260	−	64.1920i	2.50039	−	2.36294i
$739$	−20.3302			−0.747860			−0.373930	−	0.927457i	$-0.621990\pi$
$739$	−20.3302			−0.747860			−0.373930	+	0.927457i	$0.621990\pi$
$740$	3.66527			0.134738
$741$	21.7195	−	50.4092i	0.797886	−	1.85183i
$742$	43.9260	+	21.2921i	1.61258	+	0.781656i
$743$			27.0454i			0.992201i	0.868265	+	0.496101i	$0.165235\pi$
$743$			27.0454i			0.992201i	−0.868265	+	0.496101i	$0.834765\pi$
$744$	16.0346	−	37.2151i	0.587858	−	1.36437i
$745$			6.46400i			0.236823i
$746$			52.7774i			1.93232i
$747$	−1.88923	−	1.99913i	−0.0691235	−	0.0731443i
$748$		−	16.0400i		−	0.586479i
$749$	16.5033	−	34.0468i	0.603019	−	1.24404i
$750$	−17.2138	−	7.41679i	−0.628559	−	0.270823i
$751$	31.5881			1.15267			0.576333	−	0.817215i	$-0.304483\pi$
$751$	31.5881			1.15267			0.576333	+	0.817215i	$0.304483\pi$
$752$	−70.0346			−2.55390
$753$	−6.35725	+	14.7547i	−0.231671	+	0.537691i
$754$		−	33.1870i		−	1.20860i
$755$	−1.48499			−0.0540445
$756$	67.1292	+	6.80568i	2.44146	+	0.247520i
$757$	43.9393			1.59700			0.798500	−	0.601995i	$-0.205627\pi$
$757$	43.9393			1.59700			0.798500	+	0.601995i	$0.205627\pi$
$758$			52.0365i			1.89005i
$759$	−2.66324	+	6.18117i	−0.0966696	+	0.224362i
$760$	−24.4380			−0.886461
$761$	−39.3775			−1.42743			−0.713716	−	0.700435i	$-0.752989\pi$
$761$	−39.3775			−1.42743			−0.713716	+	0.700435i	$0.752989\pi$
$762$	83.3613	+	35.9173i	3.01986	+	1.30115i
$763$	29.5647	+	14.3308i	1.07032	+	0.518809i
$764$		−	57.9212i		−	2.09552i
$765$	−0.863567	−	0.913799i	−0.0312223	−	0.0330385i
$766$		−	49.7803i		−	1.79863i
$767$			10.7644i			0.388679i
$768$	7.75403	−	17.9965i	0.279800	−	0.649393i
$769$			16.9416i			0.610930i	0.952203	+	0.305465i	$0.0988120\pi$
$769$			16.9416i			0.610930i	−0.952203	+	0.305465i	$0.901188\pi$
$770$	−8.57066	−	4.15442i	−0.308865	−	0.149715i
$771$	−3.64378	+	8.45691i	−0.131227	+	0.304568i
$772$	−7.55929			−0.272065
$773$	−11.7350			−0.422079			−0.211039	−	0.977478i	$-0.567685\pi$
$773$	−11.7350			−0.422079			−0.211039	+	0.977478i	$0.567685\pi$
$774$	20.7092	−	19.5708i	0.744376	−	0.703456i
$775$		−	14.7677i		−	0.530471i
$776$	−91.0024			−3.26679
$777$	−6.17871	+	5.33895i	−0.221660	+	0.191534i
$778$	−1.57381			−0.0564238
$779$		−	90.4303i		−	3.24000i
$780$	13.5905	+	5.85565i	0.486618	+	0.209666i
$781$	−22.5172			−0.805727
$782$	−3.12507			−0.111752
$783$	−5.42099	−	14.8363i	−0.193730	−	0.530206i
$784$	44.5442	+	56.4458i	1.59086	+	2.01592i
$785$			0.121847i			0.00434891i
$786$	−89.0152	−	38.3534i	−3.17507	−	1.36802i
$787$			33.0987i			1.17984i	0.807461	+	0.589921i	$0.200841\pi$
$787$			33.0987i			1.17984i	−0.807461	+	0.589921i	$0.799159\pi$
$788$			72.2186i			2.57268i
$789$	−20.2410	−	8.72110i	−0.720598	−	0.310480i
$790$			5.96211i			0.212122i
$791$	−18.2067	+	37.5609i	−0.647356	+	1.33551i
$792$	51.4692	+	54.4631i	1.82888	+	1.93526i
$793$	41.2637			1.46532
$794$	−33.9485			−1.20479
$795$	4.67974	+	2.01633i	0.165973	+	0.0715118i
$796$			62.9328i			2.23059i
$797$	18.3755			0.650894			0.325447	−	0.945560i	$-0.394485\pi$
$797$	18.3755			0.650894			0.325447	+	0.945560i	$0.394485\pi$
$798$	69.5298	−	60.0799i	2.46133	−	2.12681i
$799$	−6.81792			−0.241201
$800$			56.5042i			1.99772i
$801$	−2.12044	−	2.24378i	−0.0749219	−	0.0792801i
$802$	9.49458			0.335265
$803$	−16.3125			−0.575655
$804$	24.1415	−	56.0306i	0.851406	−	1.97605i
$805$	−0.575065	+	1.18637i	−0.0202684	+	0.0418142i
$806$			33.4183i			1.17711i
$807$	14.1988	−	32.9543i	0.499822	−	1.16005i
$808$			115.396i			4.05962i
$809$		−	11.2846i		−	0.396745i	−0.980127	−	0.198373i	$-0.936434\pi$
$809$		−	11.2846i		−	0.396745i	0.980127	−	0.198373i	$-0.0635656\pi$
$810$	9.89777	+	0.559918i	0.347772	+	0.0196735i
$811$			20.6442i			0.724917i	0.932000	+	0.362458i	$0.118062\pi$
$811$			20.6442i			0.724917i	−0.932000	+	0.362458i	$0.881938\pi$
$812$	17.2177	−	35.5205i	0.604222	−	1.24653i
$813$	−7.27765	−	3.13567i	−0.255238	−	0.109973i
$814$	−15.3062			−0.536484
$815$	2.03167			0.0711663
$816$	−7.04018	+	16.3397i	−0.246456	+	0.572004i
$817$		−	27.5702i		−	0.964560i
$818$	−40.2321			−1.40668
$819$	−31.4397	+	9.92524i	−1.09859	+	0.346816i
$820$	24.3803			0.851397
$821$			8.48441i			0.296108i	0.988979	+	0.148054i	$0.0473010\pi$
$821$			8.48441i			0.296108i	−0.988979	+	0.148054i	$0.952699\pi$
$822$	37.8445	−	87.8340i	1.31998	−	3.06356i
$823$	32.8283			1.14432			0.572161	−	0.820141i	$-0.306105\pi$
$823$	32.8283			1.14432			0.572161	+	0.820141i	$0.306105\pi$
$824$	−41.9506			−1.46142
$825$	25.0799	+	10.8060i	0.873170	+	0.376217i
$826$	−7.86041	+	16.2162i	−0.273499	+	0.564234i
$827$		−	1.63438i		−	0.0568331i	−0.999596	−	0.0284165i	$-0.990954\pi$
$827$		−	1.63438i		−	0.0568331i	0.999596	−	0.0284165i	$-0.00904649\pi$
$828$	12.7240	−	12.0245i	0.442188	−	0.417880i
$829$		−	26.2615i		−	0.912100i	−0.889954	−	0.456050i	$-0.849264\pi$
$829$		−	26.2615i		−	0.912100i	0.889954	−	0.456050i	$-0.150736\pi$
$830$		−	1.00993i		−	0.0350553i
$831$	−14.8871	+	34.5518i	−0.516428	+	1.19859i
$832$		−	42.5303i		−	1.47447i
$833$	4.33641	+	5.49505i	0.150248	+	0.190392i
$834$	−13.8199	+	32.0750i	−0.478545	+	1.11067i
$835$	0.607628			0.0210279
$836$	122.375			4.23243
$837$	5.45879	+	14.9397i	0.188683	+	0.516392i
$838$			44.8845i			1.55051i
$839$	−11.3763			−0.392755			−0.196378	−	0.980528i	$-0.562918\pi$
$839$	−11.3763			−0.392755			−0.196378	+	0.980528i	$0.562918\pi$
$840$	9.59714	+	11.1067i	0.331133	+	0.383216i
$841$	19.7592			0.681351
$842$			93.9628i			3.23817i
$843$	−15.1300	−	6.51897i	−0.521105	−	0.224525i
$844$	−72.3033			−2.48878
$845$	−1.78257			−0.0613224
$846$	39.0718	−	36.9240i	1.34332	−	1.26947i
$847$	−0.759850	−	0.368318i	−0.0261087	−	0.0126556i
$848$		−	72.1082i		−	2.47621i
$849$	4.96952	+	2.14118i	0.170553	+	0.0734852i
$850$			12.6799i			0.434916i
$851$			2.11873i			0.0726291i
$852$	53.7892	+	23.1758i	1.84279	+	0.793990i
$853$			7.35643i			0.251879i	0.992038	+	0.125940i	$0.0401946\pi$
$853$			7.35643i			0.251879i	−0.992038	+	0.125940i	$0.959805\pi$
$854$	62.1625	+	30.1317i	2.12716	+	1.03109i
$855$	6.97172	−	6.58848i	0.238428	−	0.225321i
$856$	−109.299			−3.73576
$857$	19.8228			0.677134			0.338567	−	0.940942i	$-0.390058\pi$
$857$	19.8228			0.677134			0.338567	+	0.940942i	$0.390058\pi$
$858$	−56.7542	−	24.4533i	−1.93756	−	0.834823i
$859$		−	20.0854i		−	0.685306i	−0.939462	−	0.342653i	$-0.888675\pi$
$859$		−	20.0854i		−	0.685306i	0.939462	−	0.342653i	$-0.111325\pi$
$860$	7.43303			0.253464
$861$	−41.0990	+	35.5132i	−1.40065	+	1.21029i
$862$	−22.3181			−0.760156
$863$			1.56572i			0.0532978i	0.999645	+	0.0266489i	$0.00848361\pi$
$863$			1.56572i			0.0532978i	−0.999645	+	0.0266489i	$0.991516\pi$
$864$	−20.8864	−	57.1624i	−0.710571	−	1.94471i
$865$	3.26182			0.110905
$866$	28.3513			0.963418
$867$	−0.685367	+	1.59068i	−0.0232763	+	0.0540224i
$868$	−17.3377	+	35.7681i	−0.588481	+	1.21405i
$869$		−	17.6894i		−	0.600073i
$870$	2.29492	−	5.32633i	0.0778051	−	0.180579i
$871$			29.8111i			1.01011i
$872$		−	94.9104i		−	3.21407i
$873$	25.9613	−	24.5342i	0.878657	−	0.830356i
$874$		−	23.8423i		−	0.806479i
$875$	9.80259	+	4.75156i	0.331388	+	0.160632i
$876$	38.9674	+	16.7897i	1.31659	+	0.567270i
$877$	−40.3002			−1.36084			−0.680421	−	0.732821i	$-0.738203\pi$
$877$	−40.3002			−1.36084			−0.680421	+	0.732821i	$0.738203\pi$
$878$	−30.1775			−1.01844
$879$	−22.2763	+	51.7015i	−0.751361	+	1.74385i
$880$			14.0695i			0.474281i
$881$	10.8561			0.365752			0.182876	−	0.983136i	$-0.441459\pi$
$881$	10.8561			0.365752			0.182876	+	0.983136i	$0.441459\pi$
$882$	−54.6106	−	8.00592i	−1.83883	−	0.269574i
$883$	−29.3748			−0.988540			−0.494270	−	0.869309i	$-0.664565\pi$
$883$	−29.3748			−0.988540			−0.494270	+	0.869309i	$0.664565\pi$
$884$		−	20.3863i		−	0.685664i
$885$	−0.744370	+	1.72762i	−0.0250217	+	0.0580734i
$886$	9.83135			0.330291
$887$	−30.9559			−1.03940			−0.519699	−	0.854349i	$-0.673956\pi$
$887$	−30.9559			−1.03940			−0.519699	+	0.854349i	$0.673956\pi$
$888$	21.6639	+	9.33420i	0.726994	+	0.313235i
$889$	−47.4710	−	23.0104i	−1.59213	−	0.771744i
$890$		−	1.13353i		−	0.0379959i
$891$	−29.3665	−	1.66126i	−0.983813	−	0.0556544i
$892$			78.1378i			2.61625i
$893$		−	52.0166i		−	1.74067i
$894$	−27.7834	+	64.4831i	−0.929216	+	2.15664i
$895$			6.36414i			0.212730i
$896$	4.02394	−	8.30149i	0.134430	−	0.277333i
$897$	−3.38489	+	7.85607i	−0.113018	+	0.262306i
$898$	45.2083			1.50862
$899$	9.30526			0.310348
$900$	−48.7890	−	51.6270i	−1.62630	−	1.72090i
$901$		−	7.01979i		−	0.233863i
$902$	−101.813			−3.38999
$903$	−12.5302	+	10.8272i	−0.416979	+	0.360307i
$904$	120.580			4.01044
$905$			2.42518i			0.0806157i
$906$	−14.8139	−	6.38276i	−0.492159	−	0.212053i
$907$	−39.6198			−1.31555			−0.657777	−	0.753213i	$-0.728503\pi$
$907$	−39.6198			−1.31555			−0.657777	+	0.753213i	$0.728503\pi$
$908$	−13.5789			−0.450632
$909$	−31.1107	−	32.9204i	−1.03188	−	1.09190i
$910$	−10.8930	−	5.28013i	−0.361100	−	0.175034i
$911$			6.12868i			0.203052i	0.994833	+	0.101526i	$0.0323726\pi$
$911$			6.12868i			0.203052i	−0.994833	+	0.101526i	$0.967627\pi$
$912$	−124.662	−	53.7122i	−4.12797	−	1.77859i
$913$			2.99645i			0.0991680i
$914$		−	1.22035i		−	0.0403657i
$915$	6.62260	+	2.85343i	0.218936	+	0.0943316i
$916$		−	60.6092i		−	2.00258i
$917$	50.6907	+	24.5711i	1.67396	+	0.811409i
$918$	−4.68703	−	12.8276i	−0.154695	−	0.423373i
$919$	−23.9964			−0.791569			−0.395784	−	0.918343i	$-0.629527\pi$
$919$	−23.9964			−0.791569			−0.395784	+	0.918343i	$0.629527\pi$
$920$	3.80856			0.125565
$921$	−43.1230	−	18.5801i	−1.42095	−	0.612235i
$922$		−	56.1459i		−	1.84907i
$923$	−28.6186			−0.941991
$924$	−48.0583	−	55.6174i	−1.58100	−	1.82968i
$925$	8.59668			0.282657
$926$		−	64.0322i		−	2.10423i
$927$	11.9677	−	11.3099i	0.393072	−	0.371464i
$928$	−35.6038			−1.16875
$929$	53.6472			1.76011			0.880054	−	0.474873i	$-0.157506\pi$
$929$	53.6472			1.76011			0.880054	+	0.474873i	$0.157506\pi$
$930$	−2.31092	+	5.36346i	−0.0757780	+	0.175875i
$931$	−41.9238	+	33.0842i	−1.37400	+	1.08429i
$932$			62.6017i			2.05059i
$933$	1.78452	−	4.14172i	0.0584225	−	0.135594i
$934$			101.465i			3.32004i
$935$			1.36967i			0.0447931i
$936$	65.4157	+	69.2208i	2.13818	+	2.26255i
$937$		−	19.0332i		−	0.621786i	−0.950445	−	0.310893i	$-0.899372\pi$
$937$		−	19.0332i		−	0.621786i	0.950445	−	0.310893i	$-0.100628\pi$
$938$	−21.7688	+	44.9095i	−0.710776	+	1.46635i
$939$	−8.45002	−	3.64081i	−0.275756	−	0.118813i
$940$	14.0238			0.457407
$941$	57.8182			1.88482			0.942410	−	0.334460i	$-0.108554\pi$
$941$	57.8182			1.88482			0.942410	+	0.334460i	$0.108554\pi$
$942$	−0.523721	+	1.21551i	−0.0170637	+	0.0396036i
$943$			14.0932i			0.458937i
$944$	26.6203			0.866416
$945$	−5.73224	−	0.581145i	−0.186470	−	0.0189046i
$946$	−31.0405			−1.00921
$947$		−	36.3736i		−	1.18198i	−0.806678	−	0.590991i	$-0.798737\pi$
$947$		−	36.3736i		−	1.18198i	0.806678	−	0.590991i	$-0.201263\pi$
$948$	−18.2069	+	42.2567i	−0.591332	+	1.37243i
$949$	−20.7326			−0.673010
$950$	−96.7395			−3.13864
$951$	−33.5236	−	14.4441i	−1.08708	−	0.468381i
$952$	8.82026	−	18.1964i	0.285866	−	0.589749i
$953$		−	2.98919i		−	0.0968293i	−0.998827	−	0.0484146i	$-0.984583\pi$
$953$		−	2.98919i		−	0.0968293i	0.998827	−	0.0484146i	$-0.0154169\pi$
$954$	38.0173	+	40.2287i	1.23085	+	1.30245i
$955$			4.94597i			0.160048i
$956$			17.5058i			0.566178i
$957$	−6.80897	+	15.8031i	−0.220103	+	0.510841i
$958$			7.89080i			0.254940i
$959$	−24.2450	+	50.0181i	−0.782913	+	1.61517i
$960$	2.94102	−	6.82588i	0.0949211	−	0.220304i
$961$	21.6299			0.697738
$962$	−19.4537			−0.627213
$963$	31.1810	−	29.4670i	1.00479	−	0.949560i
$964$		−	58.7544i		−	1.89235i
$965$	0.645497			0.0207793
$966$	−10.8359	+	9.36320i	−0.348640	+	0.301256i
$967$	−42.7342			−1.37424			−0.687120	−	0.726544i	$-0.741125\pi$
$967$	−42.7342			−1.37424			−0.687120	+	0.726544i	$0.741125\pi$
$968$			2.43931i			0.0784025i
$969$	−12.1359	−	5.22893i	−0.389862	−	0.167977i
$970$	13.1153			0.421107
$971$	9.51913			0.305483			0.152742	−	0.988266i	$-0.451190\pi$
$971$	9.51913			0.305483			0.152742	+	0.988266i	$0.451190\pi$
$972$	68.4410	+	34.1939i	2.19525	+	1.09677i
$973$	8.85373	−	18.2655i	0.283838	−	0.585564i
$974$			23.7879i			0.762213i
$975$	31.8757	+	13.7341i	1.02084	+	0.439843i
$976$		−	102.045i		−	3.26638i
$977$		−	35.8308i		−	1.14633i	−0.819440	−	0.573165i	$-0.805716\pi$
$977$		−	35.8308i		−	1.14633i	0.819440	−	0.573165i	$-0.194284\pi$
$978$	20.2674	+	8.73247i	0.648079	+	0.279234i
$979$			3.36315i			0.107487i
$980$	−8.91960	−	11.3028i	−0.284926	−	0.361055i
$981$	25.5878	+	27.0762i	0.816956	+	0.864477i
$982$	25.8610			0.825259
$983$	−37.1208			−1.18397			−0.591985	−	0.805949i	$-0.701656\pi$
$983$	−37.1208			−1.18397			−0.591985	+	0.805949i	$0.701656\pi$
$984$	144.102	+	62.0884i	4.59381	+	1.97931i
$985$		−	6.16684i		−	0.196492i
$986$	−7.98970			−0.254444
$987$	−23.6406	+	20.4276i	−0.752490	+	0.650217i
$988$	155.535			4.94822
$989$			4.29671i			0.136627i
$990$	−7.41777	−	7.84925i	−0.235752	−	0.249466i
$991$	−1.66776			−0.0529780			−0.0264890	−	0.999649i	$-0.508433\pi$
$991$	−1.66776			−0.0529780			−0.0264890	+	0.999649i	$0.508433\pi$
$992$	35.8520			1.13830
$993$	4.52481	−	10.5017i	0.143591	−	0.333262i
$994$	−43.1130	−	20.8980i	−1.36746	−	0.662843i
$995$		−	5.37390i		−	0.170364i
$996$	3.08410	−	7.15795i	0.0977234	−	0.226808i
$997$			27.8345i			0.881528i	0.897623	+	0.440764i	$0.145292\pi$
$997$			27.8345i			0.881528i	−0.897623	+	0.440764i	$0.854708\pi$
$998$		−	53.5082i		−	1.69377i
$999$	−8.69682	+	3.17771i	−0.275155	+	0.100538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.d.b.188.2	yes	22
3.2	odd	2		357.2.d.a.188.21	yes	22
7.6	odd	2		357.2.d.a.188.2	✓	22
21.20	even	2	inner	357.2.d.b.188.21	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.d.a.188.2	✓	22	7.6	odd	2
357.2.d.a.188.21	yes	22	3.2	odd	2
357.2.d.b.188.2	yes	22	1.1	even	1	trivial
357.2.d.b.188.21	yes	22	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.62830i q^{2} +(-0.685367 + 1.59068i) q^{3} -4.90796 q^{4} +0.419096 q^{5} +(4.18079 + 1.80135i) q^{6} +(-2.38080 - 1.15403i) q^{7} +7.64298i q^{8} +(-2.06054 - 2.18040i) q^{9} +O(q^{10})\)	\(q-2.62830i q^{2} +(-0.685367 + 1.59068i) q^{3} -4.90796 q^{4} +0.419096 q^{5} +(4.18079 + 1.80135i) q^{6} +(-2.38080 - 1.15403i) q^{7} +7.64298i q^{8} +(-2.06054 - 2.18040i) q^{9} -1.10151i q^{10} +3.26816i q^{11} +(3.36375 - 7.80700i) q^{12} +4.15372i q^{13} +(-3.03315 + 6.25745i) q^{14} +(-0.287235 + 0.666649i) q^{15} +10.2721 q^{16} +1.00000 q^{17} +(-5.73075 + 5.41573i) q^{18} +7.62938i q^{19} -2.05691 q^{20} +(3.46742 - 2.99616i) q^{21} +8.58969 q^{22} -1.18901i q^{23} +(-12.1576 - 5.23825i) q^{24} -4.82436 q^{25} +10.9172 q^{26} +(4.88056 - 1.78329i) q^{27} +(11.6849 + 5.66395i) q^{28} -3.03987i q^{29} +(1.75215 + 0.754939i) q^{30} +3.06107i q^{31} -11.7123i q^{32} +(-5.19860 - 2.23989i) q^{33} -2.62830i q^{34} +(-0.997785 - 0.483651i) q^{35} +(10.1131 + 10.7013i) q^{36} -1.78193 q^{37} +20.0523 q^{38} +(-6.60725 - 2.84682i) q^{39} +3.20315i q^{40} -11.8529 q^{41} +(-7.87481 - 9.11343i) q^{42} -3.61369 q^{43} -16.0400i q^{44} +(-0.863567 - 0.913799i) q^{45} -3.12507 q^{46} -6.81792 q^{47} +(-7.04018 + 16.3397i) q^{48} +(4.33641 + 5.49505i) q^{49} +12.6799i q^{50} +(-0.685367 + 1.59068i) q^{51} -20.3863i q^{52} -7.01979i q^{53} +(-4.68703 - 12.8276i) q^{54} +1.36967i q^{55} +(8.82026 - 18.1964i) q^{56} +(-12.1359 - 5.22893i) q^{57} -7.98970 q^{58} +2.59150 q^{59} +(1.40974 - 3.27189i) q^{60} -9.93415i q^{61} +8.04540 q^{62} +(2.38948 + 7.56904i) q^{63} -10.2391 q^{64} +1.74081i q^{65} +(-5.88709 + 13.6635i) q^{66} +7.17696 q^{67} -4.90796 q^{68} +(1.89133 + 0.814907i) q^{69} +(-1.27118 + 2.62248i) q^{70} +6.88987i q^{71} +(16.6648 - 15.7487i) q^{72} +4.99135i q^{73} +4.68345i q^{74} +(3.30646 - 7.67402i) q^{75} -37.4447i q^{76} +(3.77156 - 7.78082i) q^{77} +(-7.48230 + 17.3658i) q^{78} -5.41267 q^{79} +4.30501 q^{80} +(-0.508318 + 8.98563i) q^{81} +31.1530i q^{82} +0.916862 q^{83} +(-17.0180 + 14.7050i) q^{84} +0.419096 q^{85} +9.49786i q^{86} +(4.83547 + 2.08343i) q^{87} -24.9785 q^{88} +1.02907 q^{89} +(-2.40174 + 2.26971i) q^{90} +(4.79353 - 9.88917i) q^{91} +5.83560i q^{92} +(-4.86919 - 2.09795i) q^{93} +17.9195i q^{94} +3.19745i q^{95} +(18.6305 + 8.02720i) q^{96} +11.9067i q^{97} +(14.4426 - 11.3974i) q^{98} +(7.12590 - 6.73418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 8 q^{14} - 4 q^{15} + 20 q^{16} + 22 q^{17} + 8 q^{18} - 30 q^{20} - 4 q^{21} - 12 q^{22} - 44 q^{24} + 14 q^{25} - 24 q^{26} + 6 q^{27} + 8 q^{28} + 5 q^{30} + 28 q^{33} + 10 q^{35} - 3 q^{36} - 16 q^{37} + 88 q^{38} - 14 q^{39} - 16 q^{41} + 19 q^{42} - 24 q^{43} - 46 q^{45} + 4 q^{46} - 16 q^{47} + 25 q^{48} + 6 q^{49} + 36 q^{54} - 40 q^{56} - 6 q^{57} + 24 q^{58} + 24 q^{59} - 21 q^{60} - 20 q^{62} - 6 q^{63} - 20 q^{64} - 116 q^{66} + 8 q^{67} - 24 q^{68} + 6 q^{69} + 4 q^{70} - 7 q^{72} + 54 q^{75} + 6 q^{77} + 2 q^{78} + 16 q^{79} + 128 q^{80} - 4 q^{81} + 8 q^{83} + 42 q^{84} - 48 q^{87} + 32 q^{88} - 100 q^{89} + 47 q^{90} + 18 q^{91} + 20 q^{93} + 88 q^{96} - 8 q^{98} + 18 q^{99}+O(q^{100}) \) 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 8 * q^14 - 4 * q^15 + 20 * q^16 + 22 * q^17 + 8 * q^18 - 30 * q^20 - 4 * q^21 - 12 * q^22 - 44 * q^24 + 14 * q^25 - 24 * q^26 + 6 * q^27 + 8 * q^28 + 5 * q^30 + 28 * q^33 + 10 * q^35 - 3 * q^36 - 16 * q^37 + 88 * q^38 - 14 * q^39 - 16 * q^41 + 19 * q^42 - 24 * q^43 - 46 * q^45 + 4 * q^46 - 16 * q^47 + 25 * q^48 + 6 * q^49 + 36 * q^54 - 40 * q^56 - 6 * q^57 + 24 * q^58 + 24 * q^59 - 21 * q^60 - 20 * q^62 - 6 * q^63 - 20 * q^64 - 116 * q^66 + 8 * q^67 - 24 * q^68 + 6 * q^69 + 4 * q^70 - 7 * q^72 + 54 * q^75 + 6 * q^77 + 2 * q^78 + 16 * q^79 + 128 * q^80 - 4 * q^81 + 8 * q^83 + 42 * q^84 - 48 * q^87 + 32 * q^88 - 100 * q^89 + 47 * q^90 + 18 * q^91 + 20 * q^93 + 88 * q^96 - 8 * q^98 + 18 * q^99

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