LMFDB - Embedded newform 968.2.c.h.485.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(485,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("968.485");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.c (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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 2 x^{16} - 2 x^{15} - 4 x^{14} - 4 x^{13} + 12 x^{12} + 16 x^{11} + 32 x^{9} + \cdots + 1024 $ x^20 - x^18 - 2x^16 - 2x^15 - 4x^14 - 4x^13 + 12x^12 + 16x^11 + 32x^9 + 48x^8 - 32x^7 - 64x^6 - 64x^5 - 128x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			485.14
Root			$0.651763 - 1.25507i$ of defining polynomial
Character	$\chi$	$=$	968.485
Dual form			968.2.c.h.485.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.651763 + 1.25507i) q^{2} -2.44793i q^{3} +(-1.15041 + 1.63602i) q^{4} +0.200474i q^{5} +(3.07232 - 1.59547i) q^{6} -2.34615 q^{7} +(-2.80312 - 0.377551i) q^{8} -2.99235 q^{9} +(-0.251609 + 0.130662i) q^{10} +(4.00485 + 2.81612i) q^{12} +1.63159i q^{13} +(-1.52914 - 2.94459i) q^{14} +0.490746 q^{15} +(-1.35311 - 3.76418i) q^{16} -3.33639 q^{17} +(-1.95030 - 3.75561i) q^{18} +4.92320i q^{19} +(-0.327979 - 0.230627i) q^{20} +5.74321i q^{21} -9.25109 q^{23} +(-0.924218 + 6.86182i) q^{24} +4.95981 q^{25} +(-2.04777 + 1.06341i) q^{26} -0.0187332i q^{27} +(2.69904 - 3.83835i) q^{28} +6.19167i q^{29} +(0.319850 + 0.615922i) q^{30} -8.25919 q^{31} +(3.84241 - 4.15161i) q^{32} +(-2.17453 - 4.18741i) q^{34} -0.470343i q^{35} +(3.44243 - 4.89554i) q^{36} -1.28006i q^{37} +(-6.17897 + 3.20876i) q^{38} +3.99402 q^{39} +(0.0756893 - 0.561952i) q^{40} -6.03055 q^{41} +(-7.20814 + 3.74321i) q^{42} +2.47184i q^{43} -0.599888i q^{45} +(-6.02952 - 11.6108i) q^{46} +4.75897 q^{47} +(-9.21445 + 3.31232i) q^{48} -1.49556 q^{49} +(3.23262 + 6.22492i) q^{50} +8.16724i q^{51} +(-2.66932 - 1.87700i) q^{52} +8.76165i q^{53} +(0.0235115 - 0.0122096i) q^{54} +(6.57654 + 0.885793i) q^{56} +12.0516 q^{57} +(-7.77100 + 4.03550i) q^{58} -1.90497i q^{59} +(-0.564559 + 0.802870i) q^{60} +6.39500i q^{61} +(-5.38303 - 10.3659i) q^{62} +7.02051 q^{63} +(7.71491 + 2.11664i) q^{64} -0.327092 q^{65} -8.27349i q^{67} +(3.83822 - 5.45839i) q^{68} +22.6460i q^{69} +(0.590314 - 0.306552i) q^{70} -1.24836 q^{71} +(8.38789 + 1.12976i) q^{72} +6.89517 q^{73} +(1.60656 - 0.834293i) q^{74} -12.1413i q^{75} +(-8.05444 - 5.66370i) q^{76} +(2.60315 + 5.01278i) q^{78} -14.6219 q^{79} +(0.754622 - 0.271264i) q^{80} -9.02290 q^{81} +(-3.93049 - 7.56878i) q^{82} -9.37255i q^{83} +(-9.39600 - 6.60705i) q^{84} -0.668860i q^{85} +(-3.10234 + 1.61106i) q^{86} +15.1568 q^{87} +5.11129 q^{89} +(0.752903 - 0.390985i) q^{90} -3.82797i q^{91} +(10.6426 - 15.1350i) q^{92} +20.2179i q^{93} +(3.10172 + 5.97285i) q^{94} -0.986974 q^{95} +(-10.1628 - 9.40595i) q^{96} +0.299741 q^{97} +(-0.974753 - 1.87704i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) $ 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	0.651763	+	1.25507i	0.460866	+	0.887470i
$2$	0.651763	+	1.25507i	0.460866	+	0.887470i
$3$		−	2.44793i		−	1.41331i	−0.707558	−	0.706656i	$-0.750203\pi$
$3$		−	2.44793i		−	1.41331i	0.707558	−	0.706656i	$-0.249797\pi$
$4$	−1.15041	+	1.63602i	−0.575205	+	0.818009i
$5$			0.200474i			0.0896548i	0.998995	+	0.0448274i	$0.0142738\pi$
$5$			0.200474i			0.0896548i	−0.998995	+	0.0448274i	$0.985726\pi$
$6$	3.07232	−	1.59547i	1.25427	−	0.651347i
$7$	−2.34615			−0.886763			−0.443381	−	0.896333i	$-0.646221\pi$
$7$	−2.34615			−0.886763			−0.443381	+	0.896333i	$0.646221\pi$
$8$	−2.80312	−	0.377551i	−0.991051	−	0.133485i
$9$	−2.99235			−0.997449
$10$	−0.251609	+	0.130662i	−0.0795659	+	0.0413188i
$11$		0			0
$11$		0			0
$12$	4.00485	+	2.81612i	1.15610	+	0.812944i
$13$			1.63159i			0.452522i	0.974067	+	0.226261i	$0.0726503\pi$
$13$			1.63159i			0.452522i	−0.974067	+	0.226261i	$0.927350\pi$
$14$	−1.52914	−	2.94459i	−0.408679	−	0.786975i
$15$	0.490746			0.126710
$16$	−1.35311	−	3.76418i	−0.338278	−	0.941046i
$17$	−3.33639			−0.809193			−0.404597	−	0.914495i	$-0.632588\pi$
$17$	−3.33639			−0.809193			−0.404597	+	0.914495i	$0.632588\pi$
$18$	−1.95030	−	3.75561i	−0.459690	−	0.885206i
$19$			4.92320i			1.12946i	0.825276	+	0.564729i	$0.191019\pi$
$19$			4.92320i			1.12946i	−0.825276	+	0.564729i	$0.808981\pi$
$20$	−0.327979	−	0.230627i	−0.0733384	−	0.0515699i
$21$			5.74321i			1.25327i
$22$		0			0
$23$	−9.25109			−1.92899			−0.964493	−	0.264108i	$-0.914922\pi$
$23$	−9.25109			−1.92899			−0.964493	+	0.264108i	$0.914922\pi$
$24$	−0.924218	+	6.86182i	−0.188655	+	1.40066i
$25$	4.95981			0.991962
$26$	−2.04777	+	1.06341i	−0.401600	+	0.208552i
$27$		−	0.0187332i		−	0.00360520i
$28$	2.69904	−	3.83835i	0.510070	−	0.725380i
$29$			6.19167i			1.14977i	0.818236	+	0.574883i	$0.194952\pi$
$29$			6.19167i			1.14977i	−0.818236	+	0.574883i	$0.805048\pi$
$30$	0.319850	+	0.615922i	0.0583964	+	0.112451i
$31$	−8.25919			−1.48339			−0.741697	−	0.670735i	$-0.765979\pi$
$31$	−8.25919			−1.48339			−0.741697	+	0.670735i	$0.765979\pi$
$32$	3.84241	−	4.15161i	0.679249	−	0.733908i
$33$		0			0
$34$	−2.17453	−	4.18741i	−0.372930	−	0.718134i
$35$		−	0.470343i		−	0.0795025i
$36$	3.44243	−	4.89554i	0.573738	−	0.815923i
$37$		−	1.28006i		−	0.210440i	−0.994449	−	0.105220i	$-0.966445\pi$
$37$		−	1.28006i		−	0.210440i	0.994449	−	0.105220i	$-0.0335546\pi$
$38$	−6.17897	+	3.20876i	−1.00236	+	0.520529i
$39$	3.99402			0.639555
$40$	0.0756893	−	0.561952i	0.0119675	−	0.0888524i
$41$	−6.03055			−0.941814			−0.470907	−	0.882183i	$-0.656073\pi$
$41$	−6.03055			−0.941814			−0.470907	+	0.882183i	$0.656073\pi$
$42$	−7.20814	+	3.74321i	−1.11224	+	0.577590i
$43$			2.47184i			0.376952i	0.982078	+	0.188476i	$0.0603549\pi$
$43$			2.47184i			0.376952i	−0.982078	+	0.188476i	$0.939645\pi$
$44$		0			0
$45$		−	0.599888i		−	0.0894261i
$46$	−6.02952	−	11.6108i	−0.889004	−	1.71192i
$47$	4.75897			0.694167			0.347084	−	0.937834i	$-0.387172\pi$
$47$	4.75897			0.694167			0.347084	+	0.937834i	$0.387172\pi$
$48$	−9.21445	+	3.31232i	−1.32999	+	0.478092i
$49$	−1.49556			−0.213652
$50$	3.23262	+	6.22492i	0.457162	+	0.880336i
$51$			8.16724i			1.14364i
$52$	−2.66932	−	1.87700i	−0.370167	−	0.260293i
$53$			8.76165i			1.20351i	0.798682	+	0.601753i	$0.205531\pi$
$53$			8.76165i			1.20351i	−0.798682	+	0.601753i	$0.794469\pi$
$54$	0.0235115	−	0.0122096i	0.00319950	−	0.00166151i
$55$		0			0
$56$	6.57654	+	0.885793i	0.878827	+	0.118369i
$57$	12.0516			1.59628
$58$	−7.77100	+	4.03550i	−1.02038	+	0.529888i
$59$		−	1.90497i		−	0.248006i	−0.992282	−	0.124003i	$-0.960427\pi$
$59$		−	1.90497i		−	0.248006i	0.992282	−	0.124003i	$-0.0395732\pi$
$60$	−0.564559	+	0.802870i	−0.0728843	+	0.103650i
$61$			6.39500i			0.818795i	0.912356	+	0.409398i	$0.134261\pi$
$61$			6.39500i			0.818795i	−0.912356	+	0.409398i	$0.865739\pi$
$62$	−5.38303	−	10.3659i	−0.683646	−	1.31647i
$63$	7.02051			0.884501
$64$	7.71491	+	2.11664i	0.964364	+	0.264580i
$65$	−0.327092			−0.0405708
$66$		0			0
$67$		−	8.27349i		−	1.01077i	−0.862895	−	0.505384i	$-0.831351\pi$
$67$		−	8.27349i		−	1.01077i	0.862895	−	0.505384i	$-0.168649\pi$
$68$	3.83822	−	5.45839i	0.465452	−	0.661927i
$69$			22.6460i			2.72626i
$70$	0.590314	−	0.306552i	0.0705561	−	0.0366400i
$71$	−1.24836			−0.148153			−0.0740763	−	0.997253i	$-0.523601\pi$
$71$	−1.24836			−0.148153			−0.0740763	+	0.997253i	$0.523601\pi$
$72$	8.38789	+	1.12976i	0.988523	+	0.133144i
$73$	6.89517			0.807019			0.403510	−	0.914975i	$-0.367790\pi$
$73$	6.89517			0.807019			0.403510	+	0.914975i	$0.367790\pi$
$74$	1.60656	−	0.834293i	0.186759	−	0.0969845i
$75$		−	12.1413i		−	1.40195i
$76$	−8.05444	−	5.66370i	−0.923908	−	0.649670i
$77$		0			0
$78$	2.60315	+	5.01278i	0.294749	+	0.567586i
$79$	−14.6219			−1.64509			−0.822544	−	0.568702i	$-0.807446\pi$
$79$	−14.6219			−1.64509			−0.822544	+	0.568702i	$0.807446\pi$
$80$	0.754622	−	0.271264i	0.0843693	−	0.0303282i
$81$	−9.02290			−1.00254
$82$	−3.93049	−	7.56878i	−0.434050	−	0.835831i
$83$		−	9.37255i		−	1.02877i	−0.857559	−	0.514386i	$-0.828020\pi$
$83$		−	9.37255i		−	1.02877i	0.857559	−	0.514386i	$-0.171980\pi$
$84$	−9.39600	−	6.60705i	−1.02519	−	0.720888i
$85$		−	0.668860i		−	0.0725480i
$86$	−3.10234	+	1.61106i	−0.334534	+	0.173725i
$87$	15.1568			1.62498
$88$		0			0
$89$	5.11129			0.541795			0.270898	−	0.962608i	$-0.412680\pi$
$89$	5.11129			0.541795			0.270898	+	0.962608i	$0.412680\pi$
$90$	0.752903	−	0.390985i	0.0793629	−	0.0412134i
$91$		−	3.82797i		−	0.401280i
$92$	10.6426	−	15.1350i	1.10956	−	1.57793i
$93$			20.2179i			2.09650i
$94$	3.10172	+	5.97285i	0.319918	+	0.616052i
$95$	−0.986974			−0.101261
$96$	−10.1628	−	9.40595i	−1.03724	−	0.959991i
$97$	0.299741			0.0304341			0.0152170	−	0.999884i	$-0.495156\pi$
$97$	0.299741			0.0304341			0.0152170	+	0.999884i	$0.495156\pi$
$98$	−0.974753	−	1.87704i	−0.0984649	−	0.189610i
$99$		0			0
$100$	−5.70582	+	8.11434i	−0.570582	+	0.811434i
$101$		−	15.0198i		−	1.49453i	−0.664527	−	0.747265i	$-0.731367\pi$
$101$		−	15.0198i		−	1.49453i	0.664527	−	0.747265i	$-0.268633\pi$
$102$	−10.2505	+	5.32310i	−1.01495	+	0.527066i
$103$	2.82480			0.278336			0.139168	−	0.990269i	$-0.455557\pi$
$103$	2.82480			0.278336			0.139168	+	0.990269i	$0.455557\pi$
$104$	0.616010	−	4.57354i	0.0604047	−	0.448473i
$105$	−1.15137			−0.112362
$106$	−10.9965	+	5.71052i	−1.06808	+	0.554655i
$107$			0.893354i			0.0863638i	0.999067	+	0.0431819i	$0.0137495\pi$
$107$			0.893354i			0.0863638i	−0.999067	+	0.0431819i	$0.986250\pi$
$108$	0.0306478	+	0.0215508i	0.00294909	+	0.00207373i
$109$		−	1.35318i		−	0.129611i	−0.997898	−	0.0648057i	$-0.979357\pi$
$109$		−	1.35318i		−	0.129611i	0.997898	−	0.0648057i	$-0.0206428\pi$
$110$		0			0
$111$	−3.13348			−0.297417
$112$	3.17461	+	8.83136i	0.299972	+	0.834485i
$113$	−3.76875			−0.354534			−0.177267	−	0.984163i	$-0.556726\pi$
$113$	−3.76875			−0.354534			−0.177267	+	0.984163i	$0.556726\pi$
$114$	7.85480	+	15.1257i	0.735670	+	1.41665i
$115$		−	1.85460i		−	0.172943i
$116$	−10.1297	−	7.12297i	−0.940518	−	0.661351i
$117$		−	4.88229i		−	0.451368i
$118$	2.39087	−	1.24159i	0.220098	−	0.114298i
$119$	7.82768			0.717562
$120$	−1.37562	−	0.185282i	−0.125576	−	0.0169138i
$121$		0			0
$122$	−8.02618	+	4.16802i	−0.726656	+	0.377355i
$123$			14.7624i			1.33108i
$124$	9.50145	−	13.5122i	0.853255	−	1.21343i
$125$			1.99668i			0.178589i
$126$	4.57571	+	8.81124i	0.407636	+	0.784968i
$127$	7.35273			0.652450			0.326225	−	0.945292i	$-0.394223\pi$
$127$	7.35273			0.652450			0.326225	+	0.945292i	$0.394223\pi$
$128$	2.37176	+	11.0623i	0.209636	+	0.977780i
$129$	6.05089			0.532751
$130$	−0.213186	−	0.410524i	−0.0186977	−	0.0360053i
$131$		−	6.85311i		−	0.598759i	−0.954134	−	0.299380i	$-0.903220\pi$
$131$		−	6.85311i		−	0.598759i	0.954134	−	0.299380i	$-0.0967797\pi$
$132$		0			0
$133$		−	11.5506i		−	1.00156i
$134$	10.3838	−	5.39235i	0.897025	−	0.465828i
$135$	0.00375551			0.000323223
$136$	9.35228	+	1.25966i	0.801952	+	0.108015i
$137$	2.80303			0.239479			0.119740	−	0.992805i	$-0.461794\pi$
$137$	2.80303			0.239479			0.119740	+	0.992805i	$0.461794\pi$
$138$	−28.4224	+	14.7598i	−2.41947	+	1.25644i
$139$			8.90509i			0.755320i	0.925944	+	0.377660i	$0.123271\pi$
$139$			8.90509i			0.755320i	−0.925944	+	0.377660i	$0.876729\pi$
$140$	0.769490	+	0.541088i	0.0650338	+	0.0457302i
$141$		−	11.6496i		−	0.981074i
$142$	−0.813632	−	1.56678i	−0.0682785	−	0.131481i
$143$		0			0
$144$	4.04898	+	11.2637i	0.337415	+	0.938646i
$145$	−1.24127			−0.103082
$146$	4.49402	+	8.65394i	0.371928	+	0.716205i
$147$			3.66103i			0.301957i
$148$	2.09419	+	1.47259i	0.172142	+	0.121046i
$149$		−	12.0459i		−	0.986837i	−0.869792	−	0.493418i	$-0.835747\pi$
$149$		−	12.0459i		−	0.986837i	0.869792	−	0.493418i	$-0.164253\pi$
$150$	15.2381	−	7.91322i	1.24419	−	0.646112i
$151$	5.29676			0.431044			0.215522	−	0.976499i	$-0.430855\pi$
$151$	5.29676			0.431044			0.215522	+	0.976499i	$0.430855\pi$
$152$	1.85876	−	13.8003i	0.150765	−	1.11935i
$153$	9.98363			0.807129
$154$		0			0
$155$		−	1.65575i		−	0.132993i
$156$	−4.59476	+	6.53429i	−0.367875	+	0.523162i
$157$			3.95049i			0.315284i	0.987496	+	0.157642i	$0.0503892\pi$
$157$			3.95049i			0.315284i	−0.987496	+	0.157642i	$0.949611\pi$
$158$	−9.52998	−	18.3515i	−0.758165	−	1.45997i
$159$	21.4479			1.70093
$160$	0.832290	+	0.770304i	0.0657983	+	0.0608979i
$161$	21.7045			1.71055
$162$	−5.88079	−	11.3244i	−0.462039	−	0.889728i
$163$		−	16.0588i		−	1.25782i	−0.777477	−	0.628911i	$-0.783501\pi$
$163$		−	16.0588i		−	1.25782i	0.777477	−	0.628911i	$-0.216499\pi$
$164$	6.93761	−	9.86609i	0.541736	−	0.770413i
$165$		0			0
$166$	11.7632	−	6.10868i	0.913003	−	0.474126i
$167$	9.27935			0.718057			0.359029	−	0.933327i	$-0.383108\pi$
$167$	9.27935			0.718057			0.359029	+	0.933327i	$0.383108\pi$
$168$	2.16836	−	16.0989i	0.167292	−	1.24206i
$169$	10.3379			0.795224
$170$	0.839467	−	0.435938i	0.0643842	−	0.0334349i
$171$		−	14.7319i		−	1.12658i
$172$	−4.04398	−	2.84363i	−0.308351	−	0.216825i
$173$			8.84221i			0.672261i	0.941815	+	0.336130i	$0.109118\pi$
$173$			8.84221i			0.672261i	−0.941815	+	0.336130i	$0.890882\pi$
$174$	9.87862	+	19.0228i	0.748896	+	1.44212i
$175$	−11.6365			−0.879635
$176$		0			0
$177$	−4.66323			−0.350510
$178$	3.33135	+	6.41503i	0.249695	+	0.480827i
$179$		−	10.6539i		−	0.796309i	−0.917318	−	0.398154i	$-0.869651\pi$
$179$		−	10.6539i		−	0.796309i	0.917318	−	0.398154i	$-0.130349\pi$
$180$	0.981428	+	0.690118i	0.0731513	+	0.0514383i
$181$		−	13.4165i		−	0.997238i	−0.866821	−	0.498619i	$-0.833841\pi$
$181$		−	13.4165i		−	0.997238i	0.866821	−	0.498619i	$-0.166159\pi$
$182$	4.80437	−	2.49493i	0.356124	−	0.184936i
$183$	15.6545			1.15721
$184$	25.9319	+	3.49276i	1.91172	+	0.257490i
$185$	0.256618			0.0188669
$186$	−25.3749	+	13.1773i	−1.86058	+	0.966204i
$187$		0			0
$188$	−5.47477	+	7.78576i	−0.399289	+	0.567835i
$189$			0.0439509i			0.00319696i
$190$	−0.643273	−	1.23872i	−0.0466679	−	0.0898664i
$191$	−14.8189			−1.07226			−0.536129	−	0.844136i	$-0.680114\pi$
$191$	−14.8189			−1.07226			−0.536129	+	0.844136i	$0.680114\pi$
$192$	5.18138	−	18.8855i	0.373934	−	1.36295i
$193$	−4.47394			−0.322041			−0.161021	−	0.986951i	$-0.551479\pi$
$193$	−4.47394			−0.322041			−0.161021	+	0.986951i	$0.551479\pi$
$194$	0.195360	+	0.376197i	0.0140260	+	0.0270093i
$195$			0.800698i			0.0573391i
$196$	1.72051	−	2.44677i	0.122894	−	0.174769i
$197$			20.3350i			1.44881i	0.689373	+	0.724406i	$0.257886\pi$
$197$			20.3350i			1.44881i	−0.689373	+	0.724406i	$0.742114\pi$
$198$		0			0
$199$	10.4142			0.738245			0.369122	−	0.929381i	$-0.379658\pi$
$199$	10.4142			0.738245			0.369122	+	0.929381i	$0.379658\pi$
$200$	−13.9029	−	1.87258i	−0.983085	−	0.132412i
$201$	−20.2529			−1.42853
$202$	18.8510	−	9.78937i	1.32635	−	0.688778i
$203$		−	14.5266i		−	1.01957i
$204$	−13.3617	−	9.39567i	−0.935510	−	0.657829i
$205$		−	1.20897i		−	0.0844381i
$206$	1.84110	+	3.54532i	0.128275	+	0.247014i
$207$	27.6825			1.92407
$208$	6.14162	−	2.20773i	0.425844	−	0.153078i
$209$		0			0
$210$	−0.750417	−	1.44505i	−0.0517837	−	0.0997177i
$211$			18.7278i			1.28927i	0.764489	+	0.644637i	$0.222992\pi$
$211$			18.7278i			1.28927i	−0.764489	+	0.644637i	$0.777008\pi$
$212$	−14.3342	−	10.0795i	−0.984479	−	0.692263i
$213$			3.05588i			0.209386i
$214$	−1.12122	+	0.582255i	−0.0766453	+	0.0398022i
$215$	−0.495541			−0.0337956
$216$	−0.00707273	+	0.0525112i	−0.000481238	+	0.00357293i
$217$	19.3773			1.31542
$218$	1.69834	−	0.881955i	0.115026	−	0.0597335i
$219$		−	16.8789i		−	1.14057i
$220$		0			0
$221$		−	5.44363i		−	0.366178i
$222$	−2.04229	−	3.93274i	−0.137069	−	0.263949i
$223$	14.5773			0.976172			0.488086	−	0.872796i	$-0.337695\pi$
$223$	14.5773			0.976172			0.488086	+	0.872796i	$0.337695\pi$
$224$	−9.01489	+	9.74031i	−0.602333	+	0.650802i
$225$	−14.8415			−0.989432
$226$	−2.45633	−	4.73005i	−0.163393	−	0.314638i
$227$		−	4.18195i		−	0.277566i	−0.990323	−	0.138783i	$-0.955681\pi$
$227$		−	4.18195i		−	0.277566i	0.990323	−	0.138783i	$-0.0443190\pi$
$228$	−13.8643	+	19.7167i	−0.918187	+	1.30577i
$229$			23.2412i			1.53582i	0.640557	+	0.767911i	$0.278704\pi$
$229$			23.2412i			1.53582i	−0.640557	+	0.767911i	$0.721296\pi$
$230$	2.32766	−	1.20876i	0.153481	−	0.0797034i
$231$		0			0
$232$	2.33767	−	17.3560i	0.153476	−	1.13948i
$233$	−13.9825			−0.916021			−0.458011	−	0.888947i	$-0.651438\pi$
$233$	−13.9825			−0.916021			−0.458011	+	0.888947i	$0.651438\pi$
$234$	6.12763	−	3.18210i	0.400575	−	0.208020i
$235$			0.954051i			0.0622354i
$236$	3.11657	+	2.19150i	0.202871	+	0.142654i
$237$			35.7932i			2.32502i
$238$	5.10179	+	9.82430i	0.330700	+	0.636815i
$239$	−23.9363			−1.54831			−0.774155	−	0.632996i	$-0.781825\pi$
$239$	−23.9363			−1.54831			−0.774155	+	0.632996i	$0.781825\pi$
$240$	−0.664035	−	1.84726i	−0.0428633	−	0.119240i
$241$	−26.1842			−1.68667			−0.843336	−	0.537387i	$-0.819412\pi$
$241$	−26.1842			−1.68667			−0.843336	+	0.537387i	$0.819412\pi$
$242$		0			0
$243$			22.0312i			1.41330i
$244$	−10.4623	−	7.35687i	−0.669782	−	0.470975i
$245$		−	0.299822i		−	0.0191549i
$246$	−18.5278	+	9.62155i	−1.18129	+	0.613448i
$247$	−8.03265			−0.511105
$248$	23.1514	+	3.11827i	1.47012	+	0.198010i
$249$	−22.9433			−1.45397
$250$	−2.50598	+	1.30136i	−0.158492	+	0.0823055i
$251$			19.2762i			1.21671i	0.793667	+	0.608353i	$0.208169\pi$
$251$			19.2762i			1.21671i	−0.793667	+	0.608353i	$0.791831\pi$
$252$	−8.07646	+	11.4857i	−0.508769	+	0.723530i
$253$		0			0
$254$	4.79224	+	9.22821i	0.300692	+	0.579029i
$255$	−1.63732			−0.102533
$256$	−12.3382	+	10.1867i	−0.771136	+	0.636671i
$257$	7.36823			0.459618			0.229809	−	0.973236i	$-0.426190\pi$
$257$	7.36823			0.459618			0.229809	+	0.973236i	$0.426190\pi$
$258$	3.94375	+	7.59430i	0.245527	+	0.472801i
$259$			3.00321i			0.186610i
$260$	0.376290	−	0.535129i	0.0233365	−	0.0331873i
$261$		−	18.5276i		−	1.14683i
$262$	8.60115	−	4.46660i	0.531381	−	0.275948i
$263$	2.69244			0.166023			0.0830114	−	0.996549i	$-0.473546\pi$
$263$	2.69244			0.166023			0.0830114	+	0.996549i	$0.473546\pi$
$264$		0			0
$265$	−1.75649			−0.107900
$266$	14.4968	−	7.52824i	0.888856	−	0.461586i
$267$		−	12.5121i		−	0.765725i
$268$	13.5356	+	9.51790i	0.826817	+	0.581398i
$269$			15.5571i			0.948532i	0.880382	+	0.474266i	$0.157286\pi$
$269$			15.5571i			0.948532i	−0.880382	+	0.474266i	$0.842714\pi$
$270$	0.00244770	+	0.00471344i	0.000148963	+	0.000286851i
$271$	−0.934048			−0.0567393			−0.0283697	−	0.999597i	$-0.509032\pi$
$271$	−0.934048			−0.0567393			−0.0283697	+	0.999597i	$0.509032\pi$
$272$	4.51451	+	12.5588i	0.273732	+	0.761488i
$273$	−9.37058			−0.567133
$274$	1.82691	+	3.51800i	0.110368	+	0.212530i
$275$		0			0
$276$	−37.0493	−	26.0522i	−2.23010	−	1.56816i
$277$		−	13.5603i		−	0.814760i	−0.913259	−	0.407380i	$-0.866442\pi$
$277$		−	13.5603i		−	0.814760i	0.913259	−	0.407380i	$-0.133558\pi$
$278$	−11.1765	+	5.80401i	−0.670324	+	0.348101i
$279$	24.7144			1.47961
$280$	−0.177579	+	1.31843i	−0.0106124	+	0.0787910i
$281$	−15.5472			−0.927470			−0.463735	−	0.885974i	$-0.653491\pi$
$281$	−15.5472			−0.927470			−0.463735	+	0.885974i	$0.653491\pi$
$282$	14.6211	−	7.59279i	0.870674	−	0.452144i
$283$		−	2.34360i		−	0.139313i	−0.997571	−	0.0696564i	$-0.977810\pi$
$283$		−	2.34360i		−	0.139313i	0.997571	−	0.0696564i	$-0.0221903\pi$
$284$	1.43612	−	2.04233i	0.0852181	−	0.121190i
$285$			2.41604i			0.143114i
$286$		0			0
$287$	14.1486			0.835166
$288$	−11.4978	+	12.4231i	−0.677516	+	0.732036i
$289$	−5.86851			−0.345207
$290$	−0.809014	−	1.55788i	−0.0475069	−	0.0914821i
$291$		−	0.733744i		−	0.0430129i
$292$	−7.93228	+	11.2806i	−0.464201	+	0.660149i
$293$		−	18.3947i		−	1.07463i	−0.843381	−	0.537316i	$-0.819438\pi$
$293$		−	18.3947i		−	1.07463i	0.843381	−	0.537316i	$-0.180562\pi$
$294$	−4.59486	+	2.38612i	−0.267977	+	0.139162i
$295$	0.381897			0.0222349
$296$	−0.483286	+	3.58814i	−0.0280905	+	0.208557i
$297$		0			0
$298$	15.1184	−	7.85106i	0.875788	−	0.454800i
$299$		−	15.0940i		−	0.872909i
$300$	19.8633	+	13.9674i	1.14681	+	0.806410i
$301$		−	5.79932i		−	0.334267i
$302$	3.45223	+	6.64781i	0.198654	+	0.382539i
$303$	−36.7675			−2.11224
$304$	18.5318	−	6.66164i	1.06287	−	0.382071i
$305$	−1.28203			−0.0734089
$306$	6.50696	+	12.5302i	0.371978	+	0.716303i
$307$			20.3704i			1.16260i	0.813690	+	0.581299i	$0.197455\pi$
$307$			20.3704i			1.16260i	−0.813690	+	0.581299i	$0.802545\pi$
$308$		0			0
$309$		−	6.91490i		−	0.393375i
$310$	2.07809	−	1.07916i	0.118028	−	0.0612921i
$311$	21.7086			1.23098			0.615492	−	0.788143i	$-0.288957\pi$
$311$	21.7086			1.23098			0.615492	+	0.788143i	$0.288957\pi$
$312$	−11.1957	−	1.50795i	−0.633832	−	0.0853707i
$313$	26.8274			1.51637			0.758186	−	0.652038i	$-0.226086\pi$
$313$	26.8274			1.51637			0.758186	+	0.652038i	$0.226086\pi$
$314$	−4.95815	+	2.57479i	−0.279805	+	0.145304i
$315$			1.40743i			0.0792997i
$316$	16.8211	−	23.9216i	0.946263	−	1.34570i
$317$			3.81008i			0.213995i	0.994259	+	0.106998i	$0.0341237\pi$
$317$			3.81008i			0.213995i	−0.994259	+	0.106998i	$0.965876\pi$
$318$	13.9789	+	26.9186i	0.783900	+	1.50952i
$319$		0			0
$320$	−0.424331	+	1.54664i	−0.0237208	+	0.0864598i
$321$	2.18687			0.122059
$322$	14.1462	+	27.2407i	0.788336	+	1.51806i
$323$		−	16.4257i		−	0.913950i
$324$	10.3800	−	14.7616i	0.576669	−	0.820091i
$325$			8.09239i			0.448885i
$326$	20.1550	−	10.4665i	1.11628	−	0.579688i
$327$	−3.31249			−0.183181
$328$	16.9043	+	2.27684i	0.933386	+	0.125718i
$329$	−11.1653			−0.615562
$330$		0			0
$331$			28.2300i			1.55166i	0.630941	+	0.775831i	$0.282669\pi$
$331$			28.2300i			1.55166i	−0.630941	+	0.775831i	$0.717331\pi$
$332$	15.3337	+	10.7823i	0.841544	+	0.591754i
$333$			3.83037i			0.209903i
$334$	6.04793	+	11.6462i	0.330928	+	0.637254i
$335$	1.65862			0.0906201
$336$	21.6185	−	7.77121i	1.17939	−	0.423954i
$337$	−20.5487			−1.11936			−0.559678	−	0.828710i	$-0.689075\pi$
$337$	−20.5487			−1.11936			−0.559678	+	0.828710i	$0.689075\pi$
$338$	6.73786	+	12.9748i	0.366491	+	0.705737i
$339$			9.22563i			0.501067i
$340$	1.09427	+	0.769463i	0.0593449	+	0.0417300i
$341$		0			0
$342$	18.4896	−	9.60172i	0.999804	−	0.519201i
$343$	19.9319			1.07622
$344$	0.933247	−	6.92886i	0.0503173	−	0.373579i
$345$	−4.53994			−0.244422
$346$	−11.0976	+	5.76302i	−0.596611	+	0.309822i
$347$			3.76822i			0.202289i	0.994872	+	0.101144i	$0.0322504\pi$
$347$			3.76822i			0.202289i	−0.994872	+	0.101144i	$0.967750\pi$
$348$	−17.4365	+	24.7968i	−0.934695	+	1.32925i
$349$			31.4661i			1.68434i	0.539211	+	0.842170i	$0.318722\pi$
$349$			31.4661i			1.68434i	−0.539211	+	0.842170i	$0.681278\pi$
$350$	−7.58422	−	14.6046i	−0.405394	−	0.780649i
$351$	0.0305649			0.00163143
$352$		0			0
$353$	−30.7625			−1.63732			−0.818662	−	0.574276i	$-0.805284\pi$
$353$	−30.7625			−1.63732			−0.818662	+	0.574276i	$0.805284\pi$
$354$	−3.03932	−	5.85269i	−0.161538	−	0.311067i
$355$		−	0.250263i		−	0.0132826i
$356$	−5.88007	+	8.36216i	−0.311643	+	0.443193i
$357$		−	19.1616i		−	1.01414i
$358$	13.3714	−	6.94381i	0.706700	−	0.366992i
$359$	−12.4538			−0.657288			−0.328644	−	0.944454i	$-0.606592\pi$
$359$	−12.4538			−0.657288			−0.328644	+	0.944454i	$0.606592\pi$
$360$	−0.226489	+	1.68156i	−0.0119370	+	0.0886258i
$361$	−5.23787			−0.275677
$362$	16.8386	−	8.74436i	0.885019	−	0.459593i
$363$		0			0
$364$	6.26262	+	4.40373i	0.328251	+	0.230818i
$365$			1.38230i			0.0723531i
$366$	10.2030	+	19.6475i	0.533320	+	1.02699i
$367$	−4.64806			−0.242627			−0.121313	−	0.992614i	$-0.538711\pi$
$367$	−4.64806			−0.242627			−0.121313	+	0.992614i	$0.538711\pi$
$368$	12.5178	+	34.8228i	0.652534	+	1.81526i
$369$	18.0455			0.939412
$370$	0.167254	+	0.322074i	0.00869513	+	0.0167438i
$371$		−	20.5562i		−	1.06722i
$372$	−33.0768	−	23.2589i	−1.71495	−	1.20592i
$373$		−	18.0242i		−	0.933256i	−0.884454	−	0.466628i	$-0.845469\pi$
$373$		−	18.0242i		−	0.933256i	0.884454	−	0.466628i	$-0.154531\pi$
$374$		0			0
$375$	4.88774			0.252402
$376$	−13.3399	−	1.79676i	−0.687955	−	0.0926606i
$377$	−10.1023			−0.520294
$378$	−0.0551615	+	0.0286455i	−0.00283720	+	0.00147337i
$379$			13.9070i			0.714355i	0.934037	+	0.357177i	$0.116261\pi$
$379$			13.9070i			0.714355i	−0.934037	+	0.357177i	$0.883739\pi$
$380$	1.13542	−	1.61471i	0.0582461	−	0.0828327i
$381$		−	17.9990i		−	0.922114i
$382$	−9.65841	−	18.5988i	−0.494167	−	0.951596i
$383$	−22.5740			−1.15348			−0.576739	−	0.816928i	$-0.695675\pi$
$383$	−22.5740			−1.15348			−0.576739	+	0.816928i	$0.695675\pi$
$384$	27.0797	−	5.80589i	1.38191	−	0.296281i
$385$		0			0
$386$	−2.91595	−	5.61512i	−0.148418	−	0.285802i
$387$		−	7.39661i		−	0.375991i
$388$	−0.344825	+	0.490382i	−0.0175058	+	0.0248954i
$389$			23.4650i			1.18972i	0.803829	+	0.594861i	$0.202793\pi$
$389$			23.4650i			1.18972i	−0.803829	+	0.594861i	$0.797207\pi$
$390$	−1.00493	+	0.521865i	−0.0508868	+	0.0264257i
$391$	30.8652			1.56092
$392$	4.19224	+	0.564652i	0.211740	+	0.0285192i
$393$	−16.7759			−0.846233
$394$	−25.5219	+	13.2536i	−1.28578	+	0.667708i
$395$		−	2.93130i		−	0.147490i
$396$		0			0
$397$			29.9901i			1.50516i	0.658500	+	0.752581i	$0.271191\pi$
$397$			29.9901i			1.50516i	−0.658500	+	0.752581i	$0.728809\pi$
$398$	6.78760	+	13.0706i	0.340232	+	0.655170i
$399$	−28.2750			−1.41552
$400$	−6.71118	−	18.6696i	−0.335559	−	0.933482i
$401$	−20.2298			−1.01023			−0.505114	−	0.863052i	$-0.668550\pi$
$401$	−20.2298			−1.01023			−0.505114	+	0.863052i	$0.668550\pi$
$402$	−13.2001	−	25.4188i	−0.658360	−	1.26778i
$403$		−	13.4756i		−	0.671269i
$404$	24.5727	+	17.2790i	1.22254	+	0.859661i
$405$		−	1.80886i		−	0.0898829i
$406$	18.2319	−	9.46791i	0.904836	−	0.469885i
$407$		0			0
$408$	3.08355	−	22.8937i	0.152658	−	1.13341i
$409$	4.43720			0.219405			0.109703	−	0.993964i	$-0.465010\pi$
$409$	4.43720			0.219405			0.109703	+	0.993964i	$0.465010\pi$
$410$	1.51734	−	0.787962i	0.0749363	−	0.0389147i
$411$		−	6.86162i		−	0.338459i
$412$	−3.24968	+	4.62142i	−0.160100	+	0.227681i
$413$			4.46935i			0.219922i
$414$	18.0424	+	34.7435i	0.886736	+	1.70755i
$415$	1.87895			0.0922342
$416$	6.77373	+	6.26925i	0.332110	+	0.307375i
$417$	21.7990			1.06750
$418$		0			0
$419$		−	6.01641i		−	0.293921i	−0.989142	−	0.146960i	$-0.953051\pi$
$419$		−	6.01641i		−	0.293921i	0.989142	−	0.146960i	$-0.0469490\pi$
$420$	1.32454	−	1.88366i	0.0646311	−	0.0919130i
$421$		−	27.4541i		−	1.33803i	−0.743248	−	0.669016i	$-0.766716\pi$
$421$		−	27.4541i		−	1.33803i	0.743248	−	0.669016i	$-0.233284\pi$
$422$	−23.5047	+	12.2061i	−1.14419	+	0.594183i
$423$	−14.2405			−0.692397
$424$	3.30797	−	24.5599i	0.160649	−	1.19274i
$425$	−16.5479			−0.802689
$426$	−3.83535	+	1.99171i	−0.185823	+	0.0964988i
$427$		−	15.0036i		−	0.726077i
$428$	−1.46154	−	1.02772i	−0.0706464	−	0.0496769i
$429$		0			0
$430$	−0.322975	−	0.621939i	−0.0155752	−	0.0299926i
$431$	−24.9012			−1.19945			−0.599723	−	0.800207i	$-0.704723\pi$
$431$	−24.9012			−1.19945			−0.599723	+	0.800207i	$0.704723\pi$
$432$	−0.0705151	+	0.0253481i	−0.00339266	+	0.00121956i
$433$	13.5442			0.650892			0.325446	−	0.945561i	$-0.394486\pi$
$433$	13.5442			0.650892			0.325446	+	0.945561i	$0.394486\pi$
$434$	12.6294	+	24.3199i	0.606231	+	1.16739i
$435$			3.03854i			0.145687i
$436$	2.21383	+	1.55672i	0.106023	+	0.0745532i
$437$		−	45.5449i		−	2.17871i
$438$	21.1842	−	11.0010i	1.01222	−	0.525650i
$439$	−30.1967			−1.44121			−0.720606	−	0.693345i	$-0.756136\pi$
$439$	−30.1967			−1.44121			−0.720606	+	0.693345i	$0.756136\pi$
$440$		0			0
$441$	4.47525			0.213107
$442$	6.83214	−	3.54795i	0.324972	−	0.168759i
$443$		−	13.9387i		−	0.662247i	−0.943587	−	0.331124i	$-0.892572\pi$
$443$		−	13.9387i		−	0.662247i	0.943587	−	0.331124i	$-0.107428\pi$
$444$	3.60479	−	5.12643i	0.171076	−	0.243290i
$445$			1.02468i			0.0485745i
$446$	9.50098	+	18.2956i	0.449884	+	0.866323i
$447$	−29.4874			−1.39471
$448$	−18.1004	−	4.96596i	−0.855162	−	0.234620i
$449$	7.05742			0.333060			0.166530	−	0.986036i	$-0.446744\pi$
$449$	7.05742			0.333060			0.166530	+	0.986036i	$0.446744\pi$
$450$	−9.67312	−	18.6271i	−0.455995	−	0.878091i
$451$		0			0
$452$	4.33561	−	6.16574i	0.203930	−	0.290012i
$453$		−	12.9661i		−	0.609200i
$454$	5.24865	−	2.72564i	0.246331	−	0.127921i
$455$	0.767408			0.0359767
$456$	−33.7821	−	4.55011i	−1.58199	−	0.213078i
$457$	6.26928			0.293265			0.146632	−	0.989191i	$-0.453157\pi$
$457$	6.26928			0.293265			0.146632	+	0.989191i	$0.453157\pi$
$458$	−29.1694	+	15.1478i	−1.36300	+	0.707808i
$459$			0.0625011i			0.00291730i
$460$	3.03417	+	2.13356i	0.141469	+	0.0994776i
$461$		−	18.0857i		−	0.842334i	−0.906983	−	0.421167i	$-0.861621\pi$
$461$		−	18.0857i		−	0.842334i	0.906983	−	0.421167i	$-0.138379\pi$
$462$		0			0
$463$	9.95458			0.462628			0.231314	−	0.972879i	$-0.425697\pi$
$463$	9.95458			0.462628			0.231314	+	0.972879i	$0.425697\pi$
$464$	23.3066	−	8.37803i	1.08198	−	0.388940i
$465$	−4.05316			−0.187961
$466$	−9.11325	−	17.5490i	−0.422163	−	0.812941i
$467$		−	32.6180i		−	1.50938i	−0.656082	−	0.754690i	$-0.727787\pi$
$467$		−	32.6180i		−	1.50938i	0.656082	−	0.754690i	$-0.272213\pi$
$468$	7.98752	+	5.61664i	0.369223	+	0.259629i
$469$			19.4109i			0.896311i
$470$	−1.19740	+	0.621815i	−0.0552320	+	0.0286822i
$471$	9.67052			0.445594
$472$	−0.719224	+	5.33985i	−0.0331050	+	0.245787i
$473$		0			0
$474$	−44.9231	+	23.3287i	−2.06339	+	1.07152i
$475$			24.4181i			1.12038i
$476$	−9.00504	+	12.8062i	−0.412745	+	0.586973i
$477$		−	26.2179i		−	1.20044i
$478$	−15.6008	−	30.0418i	−0.713563	−	1.37408i
$479$	8.51155			0.388903			0.194451	−	0.980912i	$-0.437707\pi$
$479$	8.51155			0.388903			0.194451	+	0.980912i	$0.437707\pi$
$480$	1.88565	−	2.03739i	0.0860677	−	0.0929935i
$481$	2.08853			0.0952287
$482$	−17.0659	−	32.8630i	−0.777330	−	1.49687i
$483$		−	53.1310i		−	2.41754i
$484$		0			0
$485$			0.0600903i			0.00272856i
$486$	−27.6507	+	14.3591i	−1.25426	+	0.651343i
$487$	7.13504			0.323319			0.161660	−	0.986847i	$-0.448315\pi$
$487$	7.13504			0.323319			0.161660	+	0.986847i	$0.448315\pi$
$488$	2.41444	−	17.9259i	0.109296	−	0.811468i
$489$	−39.3108			−1.77770
$490$	0.376298	−	0.195413i	0.0169994	−	0.00882785i
$491$		−	12.1001i		−	0.546069i	−0.962004	−	0.273035i	$-0.911973\pi$
$491$		−	12.1001i		−	0.546069i	0.962004	−	0.273035i	$-0.0880274\pi$
$492$	−24.1515	−	16.9828i	−1.08883	−	0.765642i
$493$		−	20.6578i		−	0.930382i
$494$	−5.23538	−	10.0816i	−0.235551	−	0.453591i
$495$		0			0
$496$	11.1756	+	31.0891i	0.501800	+	1.39594i
$497$	2.92883			0.131376
$498$	−14.9536	−	28.7955i	−0.670087	−	1.29036i
$499$			14.0553i			0.629200i	0.949224	+	0.314600i	$0.101870\pi$
$499$			14.0553i			0.629200i	−0.949224	+	0.314600i	$0.898130\pi$
$500$	−3.26661	−	2.29701i	−0.146087	−	0.102725i
$501$		−	22.7152i		−	1.01484i
$502$	−24.1931	+	12.5635i	−1.07979	+	0.560738i
$503$	−27.5369			−1.22781			−0.613906	−	0.789379i	$-0.710403\pi$
$503$	−27.5369			−1.22781			−0.613906	+	0.789379i	$0.710403\pi$
$504$	−19.6793	−	2.65060i	−0.876585	−	0.118067i
$505$	3.01109			0.133992
$506$		0			0
$507$		−	25.3064i		−	1.12390i
$508$	−8.45866	+	12.0292i	−0.375292	+	0.533710i
$509$			0.301098i			0.0133459i	0.999978	+	0.00667297i	$0.00212409\pi$
$509$			0.301098i			0.0133459i	−0.999978	+	0.00667297i	$0.997876\pi$
$510$	−1.06714	−	2.05495i	−0.0472539	−	0.0909949i
$511$	−16.1771			−0.715634
$512$	−20.8266	−	8.84596i	−0.920416	−	0.390940i
$513$	0.0922270			0.00407192
$514$	4.80234	+	9.24766i	0.211822	+	0.407897i
$515$			0.566299i			0.0249541i
$516$	−6.96101	+	9.89937i	−0.306441	+	0.435795i
$517$		0			0
$518$	−3.76924	+	1.95738i	−0.165611	+	0.0860023i
$519$	21.6451			0.950114
$520$	0.916877	+	0.123494i	0.0402077	+	0.00541557i
$521$	−16.6902			−0.731210			−0.365605	−	0.930770i	$-0.619138\pi$
$521$	−16.6902			−0.731210			−0.365605	+	0.930770i	$0.619138\pi$
$522$	23.2535	−	12.0756i	1.01778	−	0.528536i
$523$			5.73532i			0.250788i	0.992107	+	0.125394i	$0.0400195\pi$
$523$			5.73532i			0.250788i	−0.992107	+	0.125394i	$0.959981\pi$
$524$	11.2118	+	7.88389i	0.489791	+	0.344409i
$525$			28.4852i			1.24320i
$526$	1.75483	+	3.37920i	0.0765142	+	0.147340i
$527$	27.5559			1.20035
$528$		0			0
$529$	62.5827			2.72099
$530$	−1.14481	−	2.20451i	−0.0497274	−	0.0957580i
$531$			5.70033i			0.247373i
$532$	18.8970	+	13.2879i	0.819287	+	0.576104i
$533$		−	9.83940i		−	0.426192i
$534$	15.7035	−	8.15489i	0.679558	−	0.352897i
$535$	−0.179094			−0.00774293
$536$	−3.12367	+	23.1915i	−0.134922	+	1.00172i
$537$	−26.0799			−1.12543
$538$	−19.5252	+	10.1395i	−0.841793	+	0.437146i
$539$		0			0
$540$	−0.00432038	+	0.00614409i	−0.000185920	+	0.000264400i
$541$			24.1196i			1.03698i	0.855083	+	0.518491i	$0.173506\pi$
$541$			24.1196i			1.03698i	−0.855083	+	0.518491i	$0.826494\pi$
$542$	−0.608778	−	1.17230i	−0.0261492	−	0.0503545i
$543$	−32.8425			−1.40941
$544$	−12.8198	+	13.8514i	−0.549644	+	0.593873i
$545$	0.271278			0.0116203
$546$	−6.10740	−	11.7608i	−0.261373	−	0.503314i
$547$		−	7.39628i		−	0.316242i	−0.987420	−	0.158121i	$-0.949456\pi$
$547$		−	7.39628i		−	0.316242i	0.987420	−	0.158121i	$-0.0505436\pi$
$548$	−3.22464	+	4.58581i	−0.137750	+	0.195896i
$549$		−	19.1360i		−	0.816707i
$550$		0			0
$551$	−30.4828			−1.29861
$552$	8.55003	−	63.4793i	0.363913	−	2.70186i
$553$	34.3051			1.45880
$554$	17.0192	−	8.83811i	0.723075	−	0.375495i
$555$		−	0.628182i		−	0.0266648i
$556$	−14.5689	−	10.2445i	−0.617859	−	0.434464i
$557$		−	11.4190i		−	0.483839i	−0.970296	−	0.241920i	$-0.922223\pi$
$557$		−	11.4190i		−	0.483839i	0.970296	−	0.241920i	$-0.0777770\pi$
$558$	16.1079	+	31.0183i	0.681902	+	1.31311i
$559$	−4.03304			−0.170579
$560$	−1.77046	+	0.636427i	−0.0748155	+	0.0268940i
$561$		0			0
$562$	−10.1331	−	19.5129i	−0.427440	−	0.823102i
$563$		−	9.71580i		−	0.409472i	−0.978817	−	0.204736i	$-0.934366\pi$
$563$		−	9.71580i		−	0.409472i	0.978817	−	0.204736i	$-0.0656336\pi$
$564$	19.0590	+	13.4018i	0.802528	+	0.564319i
$565$		−	0.755537i		−	0.0317857i
$566$	2.94139	−	1.52747i	0.123636	−	0.0642045i
$567$	21.1691			0.889019
$568$	3.49929	+	0.471318i	0.146827	+	0.0197761i
$569$	−24.1045			−1.01051			−0.505257	−	0.862969i	$-0.668602\pi$
$569$	−24.1045			−1.01051			−0.505257	+	0.862969i	$0.668602\pi$
$570$	−3.03230	+	1.57468i	−0.127009	+	0.0659563i
$571$			12.8180i			0.536415i	0.963361	+	0.268207i	$0.0864312\pi$
$571$			12.8180i			0.536415i	−0.963361	+	0.268207i	$0.913569\pi$
$572$		0			0
$573$			36.2756i			1.51543i
$574$	9.22153	+	17.7575i	0.384899	+	0.741184i
$575$	−45.8837			−1.91348
$576$	−23.0857	−	6.33372i	−0.961904	−	0.263905i
$577$	22.8507			0.951288			0.475644	−	0.879638i	$-0.342215\pi$
$577$	22.8507			0.951288			0.475644	+	0.879638i	$0.342215\pi$
$578$	−3.82488	−	7.36540i	−0.159094	−	0.306360i
$579$			10.9519i			0.455145i
$580$	1.42797	−	2.03074i	0.0592932	−	0.0843220i
$581$			21.9894i			0.912276i
$582$	0.920902	−	0.478227i	0.0381726	−	0.0198232i
$583$		0			0
$584$	−19.3280	−	2.60328i	−0.799797	−	0.107725i
$585$	0.978773			0.0404673
$586$	23.0867	−	11.9890i	0.953703	−	0.495261i
$587$			29.3027i			1.20945i	0.796433	+	0.604726i	$0.206717\pi$
$587$			29.3027i			1.20945i	−0.796433	+	0.604726i	$0.793283\pi$
$588$	−5.98951	−	4.21169i	−0.247003	−	0.173687i
$589$		−	40.6616i		−	1.67543i
$590$	0.248906	+	0.479308i	0.0102473	+	0.0197328i
$591$	49.7787			2.04762
$592$	−4.81836	+	1.73206i	−0.198034	+	0.0711872i
$593$	10.3694			0.425820			0.212910	−	0.977072i	$-0.431706\pi$
$593$	10.3694			0.425820			0.212910	+	0.977072i	$0.431706\pi$
$594$		0			0
$595$			1.56925i			0.0643329i
$596$	19.7073	+	13.8577i	0.807242	+	0.567634i
$597$		−	25.4933i		−	1.04337i
$598$	18.9441	−	9.83772i	0.774681	−	0.402294i
$599$	−20.8591			−0.852279			−0.426140	−	0.904657i	$-0.640127\pi$
$599$	−20.8591			−0.852279			−0.426140	+	0.904657i	$0.640127\pi$
$600$	−4.58395	+	34.0333i	−0.187139	+	1.38941i
$601$	39.2013			1.59906			0.799528	−	0.600629i	$-0.205083\pi$
$601$	39.2013			1.59906			0.799528	+	0.600629i	$0.205083\pi$
$602$	7.27857	−	3.77978i	0.296652	−	0.154052i
$603$			24.7571i			1.00819i
$604$	−6.09345	+	8.66560i	−0.247939	+	0.352598i
$605$		0			0
$606$	−23.9637	−	46.1458i	−0.973457	−	1.87454i
$607$	−26.6834			−1.08305			−0.541523	−	0.840686i	$-0.682152\pi$
$607$	−26.6834			−1.08305			−0.541523	+	0.840686i	$0.682152\pi$
$608$	20.4392	+	18.9170i	0.828919	+	0.767184i
$609$	−35.5601			−1.44097
$610$	−0.835580	−	1.60904i	−0.0338317	−	0.0651482i
$611$			7.76470i			0.314126i
$612$	−11.4853	+	16.3334i	−0.464265	+	0.660239i
$613$		−	30.7684i		−	1.24272i	−0.783523	−	0.621362i	$-0.786580\pi$
$613$		−	30.7684i		−	1.24272i	0.783523	−	0.621362i	$-0.213420\pi$
$614$	−25.5663	+	13.2767i	−1.03177	+	0.535802i
$615$	−2.95947			−0.119337
$616$		0			0
$617$	10.0183			0.403323			0.201662	−	0.979455i	$-0.435366\pi$
$617$	10.0183			0.403323			0.201662	+	0.979455i	$0.435366\pi$
$618$	8.67869	−	4.50687i	0.349108	−	0.181293i
$619$			32.0971i			1.29009i	0.764144	+	0.645046i	$0.223162\pi$
$619$			32.0971i			1.29009i	−0.764144	+	0.645046i	$0.776838\pi$
$620$	2.70884	+	1.90480i	0.108790	+	0.0764984i
$621$			0.173302i			0.00695438i
$622$	14.1489	+	27.2459i	0.567318	+	1.09246i
$623$	−11.9919			−0.480444
$624$	−5.40436	−	15.0342i	−0.216347	−	0.601851i
$625$	24.3988			0.975951
$626$	17.4851	+	33.6703i	0.698845	+	1.34573i
$627$		0			0
$628$	−6.46308	−	4.54469i	−0.257905	−	0.181353i
$629$			4.27076i			0.170286i
$630$	−1.76643	+	0.917311i	−0.0703761	+	0.0365465i
$631$	−2.80016			−0.111472			−0.0557362	−	0.998446i	$-0.517751\pi$
$631$	−2.80016			−0.111472			−0.0557362	+	0.998446i	$0.517751\pi$
$632$	40.9868	+	5.52050i	1.63037	+	0.219594i
$633$	45.8443			1.82215
$634$	−4.78192	+	2.48327i	−0.189914	+	0.0986232i
$635$			1.47403i			0.0584952i
$636$	−24.6739	+	35.0891i	−0.978383	+	1.39138i
$637$		−	2.44015i		−	0.0966823i
$638$		0			0
$639$	3.73551			0.147775
$640$	−2.21771	+	0.475476i	−0.0876626	+	0.0187948i
$641$	16.8783			0.666652			0.333326	−	0.942812i	$-0.391829\pi$
$641$	16.8783			0.666652			0.333326	+	0.942812i	$0.391829\pi$
$642$	1.42532	+	2.74467i	0.0562528	+	0.108324i
$643$			49.0739i			1.93528i	0.252326	+	0.967642i	$0.418804\pi$
$643$			49.0739i			1.93528i	−0.252326	+	0.967642i	$0.581196\pi$
$644$	−24.9691	+	35.5089i	−0.983919	+	1.39925i
$645$			1.21305i			0.0477637i
$646$	20.6154	−	10.7057i	0.811103	−	0.421209i
$647$	−35.3413			−1.38941			−0.694705	−	0.719295i	$-0.744465\pi$
$647$	−35.3413			−1.38941			−0.694705	+	0.719295i	$0.744465\pi$
$648$	25.2922	+	3.40661i	0.993573	+	0.133824i
$649$		0			0
$650$	−10.1565	+	5.27432i	−0.398372	+	0.206876i
$651$		−	47.4343i		−	1.85910i
$652$	26.2725	+	18.4742i	1.02891	+	0.723506i
$653$		−	0.192213i		−	0.00752186i	−0.999993	−	0.00376093i	$-0.998803\pi$
$653$		−	0.192213i		−	0.00752186i	0.999993	−	0.00376093i	$-0.00119714\pi$
$654$	−2.15896	−	4.15742i	−0.0844220	−	0.162568i
$655$	1.37387			0.0536816
$656$	8.16002	+	22.7001i	0.318595	+	0.886290i
$657$	−20.6328			−0.804960
$658$	−7.27711	−	14.0132i	−0.283691	−	0.546292i
$659$			46.4826i			1.81071i	0.424660	+	0.905353i	$0.360394\pi$
$659$			46.4826i			1.81071i	−0.424660	+	0.905353i	$0.639606\pi$
$660$		0			0
$661$		−	24.0904i		−	0.937007i	−0.883462	−	0.468503i	$-0.844793\pi$
$661$		−	24.0904i		−	0.937007i	0.883462	−	0.468503i	$-0.155207\pi$
$662$	−35.4307	+	18.3993i	−1.37705	+	0.715108i
$663$	−13.3256			−0.517523
$664$	−3.53862	+	26.2723i	−0.137325	+	1.01956i
$665$	2.31559			0.0897948
$666$	−4.80739	+	2.49649i	−0.186283	+	0.0967371i
$667$		−	57.2798i		−	2.21788i
$668$	−10.6751	+	15.1812i	−0.413030	+	0.587378i
$669$		−	35.6843i		−	1.37963i
$670$	1.08103	+	2.08169i	0.0417637	+	0.0804226i
$671$		0			0
$672$	23.8436	+	22.0678i	0.919786	+	0.851284i
$673$	−7.57085			−0.291835			−0.145917	−	0.989297i	$-0.546613\pi$
$673$	−7.57085			−0.291835			−0.145917	+	0.989297i	$0.546613\pi$
$674$	−13.3929	−	25.7900i	−0.515873	−	0.993395i
$675$		−	0.0929129i		−	0.00357622i
$676$	−11.8928	+	16.9130i	−0.457417	+	0.650500i
$677$		−	20.6521i		−	0.793725i	−0.917878	−	0.396862i	$-0.870099\pi$
$677$		−	20.6521i		−	0.793725i	0.917878	−	0.396862i	$-0.129901\pi$
$678$	−11.5788	+	6.01292i	−0.444682	+	0.230925i
$679$	−0.703239			−0.0269878
$680$	−0.252529	+	1.87489i	−0.00968404	+	0.0718988i
$681$	−10.2371			−0.392287
$682$		0			0
$683$		−	14.6272i		−	0.559694i	−0.960045	−	0.279847i	$-0.909716\pi$
$683$		−	14.6272i		−	0.559694i	0.960045	−	0.279847i	$-0.0902837\pi$
$684$	24.1017	+	16.9477i	0.921551	+	0.648013i
$685$			0.561935i			0.0214704i
$686$	12.9909	+	25.0160i	0.495994	+	0.955114i
$687$	56.8928			2.17059
$688$	9.30447	−	3.34468i	0.354730	−	0.127515i
$689$	−14.2954			−0.544613
$690$	−2.95896	−	5.69795i	−0.112646	−	0.216917i
$691$			22.9427i			0.872781i	0.899757	+	0.436390i	$0.143743\pi$
$691$			22.9427i			0.872781i	−0.899757	+	0.436390i	$0.856257\pi$
$692$	−14.4660	−	10.1722i	−0.549915	−	0.386688i
$693$		0			0
$694$	−4.72938	+	2.45598i	−0.179525	+	0.0932279i
$695$	−1.78524			−0.0677181
$696$	−42.4862	−	5.72246i	−1.61043	−	0.216909i
$697$	20.1203			0.762109
$698$	−39.4922	+	20.5084i	−1.49480	+	0.776255i
$699$			34.2280i			1.29462i
$700$	13.3867	−	19.0375i	0.505970	−	0.719549i
$701$			0.700778i			0.0264680i	0.999912	+	0.0132340i	$0.00421264\pi$
$701$			0.700778i			0.0264680i	−0.999912	+	0.0132340i	$0.995787\pi$
$702$	0.0199211	+	0.0383611i	0.000751872	+	0.00144785i
$703$	6.30196			0.237683
$704$		0			0
$705$	2.33545			0.0879580
$706$	−20.0499	−	38.6092i	−0.754587	−	1.45307i
$707$			35.2388i			1.32529i
$708$	5.36462	−	7.62913i	0.201615	−	0.286720i
$709$			4.05276i			0.152205i	0.997100	+	0.0761023i	$0.0242476\pi$
$709$			4.05276i			0.152205i	−0.997100	+	0.0761023i	$0.975752\pi$
$710$	0.314098	−	0.163112i	0.0117879	−	0.00612149i
$711$	43.7537			1.64089
$712$	−14.3275	−	1.92977i	−0.536947	−	0.0723213i
$713$	76.4065			2.86145
$714$	24.0492	−	12.4888i	0.900018	−	0.467382i
$715$		0			0
$716$	17.4299	+	12.2563i	0.651388	+	0.458041i
$717$			58.5943i			2.18824i
$718$	−8.11695	−	15.6305i	−0.302922	−	0.583323i
$719$	10.0908			0.376323			0.188161	−	0.982138i	$-0.439747\pi$
$719$	10.0908			0.376323			0.188161	+	0.982138i	$0.439747\pi$
$720$	−2.25809	+	0.811716i	−0.0841541	+	0.0302509i
$721$	−6.62741			−0.246818
$722$	−3.41385	−	6.57390i	−0.127050	−	0.244655i
$723$			64.0970i			2.38379i
$724$	21.9496	+	15.4344i	0.815750	+	0.573616i
$725$			30.7095i			1.14052i
$726$		0			0
$727$	−13.6615			−0.506675			−0.253338	−	0.967378i	$-0.581528\pi$
$727$	−13.6615			−0.506675			−0.253338	+	0.967378i	$0.581528\pi$
$728$	−1.44525	+	10.7302i	−0.0535647	+	0.397689i
$729$	26.8621			0.994892
$730$	−1.73489	+	0.900934i	−0.0642112	+	0.0333451i
$731$		−	8.24703i		−	0.305027i
$732$	−18.0091	+	25.6110i	−0.665635	+	0.946611i
$733$			17.9204i			0.661906i	0.943647	+	0.330953i	$0.107370\pi$
$733$			17.9204i			0.661906i	−0.943647	+	0.330953i	$0.892630\pi$
$734$	−3.02943	−	5.83364i	−0.111818	−	0.215324i
$735$	−0.733942			−0.0270719
$736$	−35.5465	+	38.4069i	−1.31026	+	1.41570i
$737$		0			0
$738$	11.7614	+	22.6484i	0.432943	+	0.833699i
$739$		−	23.5590i		−	0.866631i	−0.901242	−	0.433316i	$-0.857344\pi$
$739$		−	23.5590i		−	0.866631i	0.901242	−	0.433316i	$-0.142656\pi$
$740$	−0.295216	+	0.419832i	−0.0108524	+	0.0154333i
$741$			19.6633i			0.722351i
$742$	25.7995	−	13.3978i	0.947129	−	0.491847i
$743$	−13.6295			−0.500018			−0.250009	−	0.968244i	$-0.580434\pi$
$743$	−13.6295			−0.500018			−0.250009	+	0.968244i	$0.580434\pi$
$744$	7.63329	−	56.6731i	0.279850	−	2.07774i
$745$	2.41489			0.0884746
$746$	22.6216	−	11.7475i	0.828237	−	0.430106i
$747$			28.0459i			1.02615i
$748$		0			0
$749$		−	2.09595i		−	0.0765842i
$750$	3.18565	+	6.13446i	0.116323	+	0.223999i
$751$	−12.2314			−0.446331			−0.223165	−	0.974781i	$-0.571639\pi$
$751$	−12.2314			−0.446331			−0.223165	+	0.974781i	$0.571639\pi$
$752$	−6.43942	−	17.9136i	−0.234822	−	0.653243i
$753$	47.1868			1.71958
$754$	−6.58430	−	12.6791i	−0.239786	−	0.461745i
$755$			1.06186i			0.0386452i
$756$	−0.0719044	−	0.0505615i	−0.00261514	−	0.00183890i
$757$			21.3405i			0.775634i	0.921736	+	0.387817i	$0.126771\pi$
$757$			21.3405i			0.775634i	−0.921736	+	0.387817i	$0.873229\pi$
$758$	−17.4543	+	9.06407i	−0.633968	+	0.329222i
$759$		0			0
$760$	2.76660	+	0.372633i	0.100355	+	0.0135168i
$761$	11.8300			0.428839			0.214419	−	0.976742i	$-0.431214\pi$
$761$	11.8300			0.428839			0.214419	+	0.976742i	$0.431214\pi$
$762$	22.5900	−	11.7311i	0.818349	−	0.424971i
$763$			3.17478i			0.114935i
$764$	17.0478	−	24.2440i	0.616768	−	0.877117i
$765$			2.00146i			0.0723629i
$766$	−14.7129	−	28.3320i	−0.531599	−	1.02368i
$767$	3.10813			0.112228
$768$	24.9364	+	30.2029i	0.899814	+	1.08985i
$769$	2.94327			0.106137			0.0530685	−	0.998591i	$-0.483100\pi$
$769$	2.94327			0.106137			0.0530685	+	0.998591i	$0.483100\pi$
$770$		0			0
$771$		−	18.0369i		−	0.649583i
$772$	5.14687	−	7.31945i	0.185240	−	0.263433i
$773$			7.95495i			0.286120i	0.989714	+	0.143060i	$0.0456942\pi$
$773$			7.95495i			0.286120i	−0.989714	+	0.143060i	$0.954306\pi$
$774$	9.28328	−	4.82084i	0.333681	−	0.173281i
$775$	−40.9640			−1.47147
$776$	−0.840209	−	0.113168i	−0.0301617	−	0.00406248i
$777$	7.35163			0.263738
$778$	−29.4502	+	15.2936i	−1.05584	+	0.548302i
$779$		−	29.6896i		−	1.06374i
$780$	−1.30996	−	0.921131i	−0.0469039	−	0.0329818i
$781$		0			0
$782$	20.1168	+	38.7381i	0.719376	+	1.38527i
$783$	0.115990			0.00414513
$784$	2.02367	+	5.62958i	0.0722738	+	0.201056i
$785$	−0.791972			−0.0282667
$786$	−10.9339	−	21.0550i	−0.390000	−	0.751006i
$787$			2.72311i			0.0970685i	0.998822	+	0.0485342i	$0.0154550\pi$
$787$			2.72311i			0.0970685i	−0.998822	+	0.0485342i	$0.984545\pi$
$788$	−33.2685	−	23.3936i	−1.18514	−	0.833364i
$789$		−	6.59089i		−	0.234642i
$790$	3.67900	−	1.91052i	0.130893	−	0.0679731i
$791$	8.84207			0.314388
$792$		0			0
$793$	−10.4340			−0.370523
$794$	−37.6398	+	19.5465i	−1.33579	+	0.693678i
$795$			4.29975i			0.152496i
$796$	−11.9806	+	17.0379i	−0.424642	+	0.603891i
$797$		−	28.0588i		−	0.993893i	−0.867781	−	0.496947i	$-0.834454\pi$
$797$		−	28.0588i		−	0.993893i	0.867781	−	0.496947i	$-0.165546\pi$
$798$	−18.4286	−	35.4871i	−0.652364	−	1.25623i
$799$	−15.8778			−0.561715
$800$	19.0576	−	20.5912i	0.673789	−	0.728009i
$801$	−15.2947			−0.540413
$802$	−13.1850	−	25.3899i	−0.465580	−	0.896547i
$803$		0			0
$804$	23.2991	−	33.1341i	0.821697	−	1.16855i
$805$			4.35119i			0.153359i
$806$	16.9129	−	8.78291i	0.595731	−	0.309365i
$807$	38.0826			1.34057
$808$	−5.67076	+	42.1023i	−0.199497	+	1.48115i
$809$	−32.5279			−1.14362			−0.571810	−	0.820386i	$-0.693758\pi$
$809$	−32.5279			−1.14362			−0.571810	+	0.820386i	$0.693758\pi$
$810$	2.27025	−	1.17895i	0.0797683	−	0.0414240i
$811$		−	8.90533i		−	0.312708i	−0.987701	−	0.156354i	$-0.950026\pi$
$811$		−	8.90533i		−	0.312708i	0.987701	−	0.156354i	$-0.0499741\pi$
$812$	23.7658	+	16.7116i	0.834017	+	0.586461i
$813$			2.28648i			0.0801904i
$814$		0			0
$815$	3.21938			0.112770
$816$	30.7430	−	11.0512i	1.07622	−	0.386869i
$817$	−12.1694			−0.425752
$818$	2.89200	+	5.56900i	0.101116	+	0.194716i
$819$			11.4546i			0.400256i
$820$	1.97790	+	1.39081i	0.0690712	+	0.0485692i
$821$			14.3875i			0.502126i	0.967971	+	0.251063i	$0.0807801\pi$
$821$			14.3875i			0.502126i	−0.967971	+	0.251063i	$0.919220\pi$
$822$	8.61182	−	4.47215i	0.300372	−	0.155984i
$823$	−35.3163			−1.23105			−0.615525	−	0.788117i	$-0.711056\pi$
$823$	−35.3163			−1.23105			−0.615525	+	0.788117i	$0.711056\pi$
$824$	−7.91823	−	1.06651i	−0.275845	−	0.0371535i
$825$		0			0
$826$	−5.60936	+	2.91296i	−0.195175	+	0.101355i
$827$		−	12.8333i		−	0.446257i	−0.974789	−	0.223129i	$-0.928373\pi$
$827$		−	12.8333i		−	0.446257i	0.974789	−	0.223129i	$-0.0716270\pi$
$828$	−31.8462	+	45.2890i	−1.10673	+	1.57390i
$829$		−	23.8928i		−	0.829831i	−0.909860	−	0.414916i	$-0.863811\pi$
$829$		−	23.8928i		−	0.829831i	0.909860	−	0.414916i	$-0.136189\pi$
$830$	1.22463	+	2.35822i	0.0425076	+	0.0818551i
$831$	−33.1947			−1.15151
$832$	−3.45349	+	12.5876i	−0.119728	+	0.436396i
$833$	4.98978			0.172886
$834$	14.2078	+	27.3593i	0.491976	+	0.947376i
$835$			1.86027i			0.0643773i
$836$		0			0
$837$			0.154721i			0.00534793i
$838$	7.55103	−	3.92127i	0.260846	−	0.135458i
$839$	23.6213			0.815497			0.407748	−	0.913094i	$-0.366314\pi$
$839$	23.6213			0.815497			0.407748	+	0.913094i	$0.366314\pi$
$840$	3.22741	+	0.434700i	0.111356	+	0.0149986i
$841$	−9.33683			−0.321960
$842$	34.4569	−	17.8936i	1.18746	−	0.616654i
$843$			38.0585i			1.31080i
$844$	−30.6390	−	21.5446i	−1.05464	−	0.741597i
$845$			2.07248i			0.0712956i
$846$	−9.28143	−	17.8728i	−0.319102	−	0.614481i
$847$		0			0
$848$	32.9805	−	11.8555i	1.13255	−	0.407120i
$849$	−5.73697			−0.196892
$850$	−10.7853	−	20.7687i	−0.369932	−	0.712362i
$851$			11.8419i			0.405935i
$852$	−4.99948	−	3.51552i	−0.171279	−	0.120440i
$853$			41.7017i			1.42784i	0.700228	+	0.713919i	$0.253082\pi$
$853$			41.7017i			1.42784i	−0.700228	+	0.713919i	$0.746918\pi$
$854$	18.8306	−	9.77882i	0.644371	−	0.334624i
$855$	2.95337			0.101003
$856$	0.337287	−	2.50418i	0.0115282	−	0.0855910i
$857$	−4.35256			−0.148680			−0.0743402	−	0.997233i	$-0.523685\pi$
$857$	−4.35256			−0.148680			−0.0743402	+	0.997233i	$0.523685\pi$
$858$		0			0
$859$		−	7.91648i		−	0.270107i	−0.990838	−	0.135053i	$-0.956879\pi$
$859$		−	7.91648i		−	0.270107i	0.990838	−	0.135053i	$-0.0431206\pi$
$860$	0.570075	−	0.810713i	0.0194394	−	0.0276451i
$861$		−	34.6347i		−	1.18035i
$862$	−16.2297	−	31.2527i	−0.552784	−	1.06447i
$863$	−12.3382			−0.419996			−0.209998	−	0.977702i	$-0.567346\pi$
$863$	−12.3382			−0.419996			−0.209998	+	0.977702i	$0.567346\pi$
$864$	−0.0777728	−	0.0719805i	−0.00264588	−	0.00244883i
$865$	−1.77263			−0.0602714
$866$	8.82760	+	16.9989i	0.299974	+	0.577647i
$867$			14.3657i			0.487884i
$868$	−22.2919	+	31.7016i	−0.756635	+	1.07602i
$869$		0			0
$870$	−3.81359	+	1.98041i	−0.129293	+	0.0671421i
$871$	13.4990			0.457395
$872$	−0.510896	+	3.79313i	−0.0173011	+	0.128452i
$873$	−0.896929			−0.0303565
$874$	57.1622	−	29.6845i	1.93354	−	1.00409i
$875$		−	4.68453i		−	0.158366i
$876$	27.6142	+	19.4176i	0.932996	+	0.656061i
$877$			58.3261i			1.96953i	0.173887	+	0.984766i	$0.444367\pi$
$877$			58.3261i			1.96953i	−0.173887	+	0.984766i	$0.555633\pi$
$878$	−19.6811	−	37.8991i	−0.664205	−	1.27903i
$879$	−45.0289			−1.51879
$880$		0			0
$881$	−25.8106			−0.869581			−0.434791	−	0.900532i	$-0.643178\pi$
$881$	−25.8106			−0.869581			−0.434791	+	0.900532i	$0.643178\pi$
$882$	2.91680	+	5.61676i	0.0982137	+	0.189126i
$883$		−	36.6024i		−	1.23177i	−0.787836	−	0.615885i	$-0.788799\pi$
$883$		−	36.6024i		−	1.23177i	0.787836	−	0.615885i	$-0.211201\pi$
$884$	8.90587	+	6.26240i	0.299537	+	0.210627i
$885$		−	0.934857i		−	0.0314249i
$886$	17.4941	−	9.08473i	0.587725	−	0.305207i
$887$	21.8922			0.735067			0.367534	−	0.930010i	$-0.380202\pi$
$887$	21.8922			0.735067			0.367534	+	0.930010i	$0.380202\pi$
$888$	8.78351	+	1.18305i	0.294755	+	0.0397006i
$889$	−17.2506			−0.578568
$890$	−1.28605	+	0.667849i	−0.0431084	+	0.0223863i
$891$		0			0
$892$	−16.7699	+	23.8488i	−0.561499	+	0.798517i
$893$			23.4294i			0.784033i
$894$	−19.2188	−	37.0088i	−0.642773	−	1.23776i
$895$	2.13583			0.0713929
$896$	−5.56451	−	25.9539i	−0.185897	−	0.867058i
$897$	−36.9490			−1.23369
$898$	4.59977	+	8.85757i	0.153496	+	0.295581i
$899$		−	51.1382i		−	1.70555i
$900$	17.0738	−	24.2809i	0.569126	−	0.809364i
$901$		−	29.2323i		−	0.973869i
$902$		0			0
$903$	−14.1963			−0.472424
$904$	10.5642	+	1.42290i	0.351361	+	0.0473248i
$905$	2.68965			0.0894071
$906$	16.2734	−	8.45081i	0.540646	−	0.280759i
$907$			28.8065i			0.956503i	0.878223	+	0.478252i	$0.158729\pi$
$907$			28.8065i			0.956503i	−0.878223	+	0.478252i	$0.841271\pi$
$908$	6.84175	+	4.81096i	0.227051	+	0.159657i
$909$			44.9446i			1.49072i
$910$	0.500168	+	0.963152i	0.0165804	+	0.0319282i
$911$	44.2181			1.46501			0.732506	−	0.680760i	$-0.238351\pi$
$911$	44.2181			1.46501			0.732506	+	0.680760i	$0.238351\pi$
$912$	−16.3072	−	45.3646i	−0.539986	−	1.50217i
$913$		0			0
$914$	4.08608	+	7.86840i	0.135156	+	0.260263i
$915$			3.13832i			0.103750i
$916$	−38.0230	−	26.7369i	−1.25632	−	0.883413i
$917$			16.0785i			0.530957i
$918$	−0.0784434	+	0.0407359i	−0.00258902	+	0.00134448i
$919$	−18.9997			−0.626743			−0.313372	−	0.949631i	$-0.601459\pi$
$919$	−18.9997			−0.626743			−0.313372	+	0.949631i	$0.601459\pi$
$920$	−0.700208	+	5.19867i	−0.0230852	+	0.171395i
$921$	49.8652			1.64311
$922$	22.6988	−	11.7876i	0.747546	−	0.388203i
$923$		−	2.03681i		−	0.0670423i
$924$		0			0
$925$		−	6.34883i		−	0.208748i
$926$	6.48802	+	12.4937i	0.213210	+	0.410569i
$927$	−8.45277			−0.277626
$928$	25.7054	+	23.7910i	0.843822	+	0.780977i
$929$	28.0670			0.920850			0.460425	−	0.887699i	$-0.347697\pi$
$929$	28.0670			0.920850			0.460425	+	0.887699i	$0.347697\pi$
$930$	−2.64170	−	5.08701i	−0.0866248	−	0.166810i
$931$		−	7.36295i		−	0.241311i
$932$	16.0856	−	22.8756i	0.526900	−	0.749314i
$933$		−	53.1411i		−	1.73976i
$934$	40.9379	−	21.2592i	1.33953	−	0.695622i
$935$		0			0
$936$	−1.84332	+	13.6856i	−0.0602506	+	0.447329i
$937$	0.293629			0.00959245			0.00479623	−	0.999988i	$-0.498473\pi$
$937$	0.293629			0.00959245			0.00479623	+	0.999988i	$0.498473\pi$
$938$	−24.3620	+	12.6513i	−0.795449	+	0.413079i
$939$		−	65.6715i		−	2.14311i
$940$	−1.56084	−	1.09755i	−0.0509091	−	0.0357981i
$941$		−	16.1292i		−	0.525797i	−0.964823	−	0.262899i	$-0.915322\pi$
$941$		−	16.1292i		−	0.525797i	0.964823	−	0.262899i	$-0.0846785\pi$
$942$	6.30289	+	12.1372i	0.205359	+	0.395451i
$943$	55.7892			1.81675
$944$	−7.17066	+	2.57764i	−0.233385	+	0.0838950i
$945$	−0.00881101			−0.000286622
$946$		0			0
$947$		−	29.0812i		−	0.945011i	−0.881328	−	0.472505i	$-0.843350\pi$
$947$		−	29.0812i		−	0.945011i	0.881328	−	0.472505i	$-0.156650\pi$
$948$	−58.5584	−	41.1769i	−1.90189	−	1.33736i
$949$			11.2501i			0.365194i
$950$	−30.6465	+	15.9148i	−0.994304	+	0.516345i
$951$	9.32680			0.302442
$952$	−21.9419	−	2.95535i	−0.711141	−	0.0957835i
$953$	40.5658			1.31405			0.657027	−	0.753867i	$-0.271814\pi$
$953$	40.5658			1.31405			0.657027	+	0.753867i	$0.271814\pi$
$954$	32.9054	−	17.0879i	1.06535	−	0.553240i
$955$		−	2.97081i		−	0.0961330i
$956$	27.5366	−	39.1602i	0.890596	−	1.26653i
$957$		0			0
$958$	5.54751	+	10.6826i	0.179232	+	0.345139i
$959$	−6.57634			−0.212361
$960$	3.78606	+	1.03873i	0.122195	+	0.0335249i
$961$	37.2141			1.20046
$962$	1.36123	+	2.62125i	0.0438877	+	0.0845126i
$963$		−	2.67323i		−	0.0861435i
$964$	30.1226	−	42.8378i	0.970182	−	1.37971i
$965$		−	0.896909i		−	0.0288725i
$966$	66.6832	−	34.6288i	2.14550	−	1.11416i
$967$	6.42732			0.206689			0.103344	−	0.994646i	$-0.467046\pi$
$967$	6.42732			0.206689			0.103344	+	0.994646i	$0.467046\pi$
$968$		0			0
$969$	−40.2089			−1.29170
$970$	−0.0754177	+	0.0391646i	−0.00242152	+	0.00125750i
$971$			50.7088i			1.62732i	0.581338	+	0.813662i	$0.302529\pi$
$971$			50.7088i			1.62732i	−0.581338	+	0.813662i	$0.697471\pi$
$972$	−36.0435	−	25.3449i	−1.15609	−	0.812939i
$973$		−	20.8927i		−	0.669790i
$974$	4.65035	+	8.95498i	0.149007	+	0.286936i
$975$	19.8096			0.634414
$976$	24.0719	−	8.65315i	0.770524	−	0.276981i
$977$	−0.100545			−0.00321673			−0.00160837	−	0.999999i	$-0.500512\pi$
$977$	−0.100545			−0.00321673			−0.00160837	+	0.999999i	$0.500512\pi$
$978$	−25.6213	−	49.3379i	−0.819279	−	1.57765i
$979$		0			0
$980$	0.490514	+	0.344918i	0.0156689	+	0.0110180i
$981$			4.04919i			0.129281i
$982$	15.1865	−	7.88639i	0.484620	−	0.251665i
$983$	26.3392			0.840091			0.420046	−	0.907503i	$-0.362014\pi$
$983$	26.3392			0.840091			0.420046	+	0.907503i	$0.362014\pi$
$984$	5.57354	−	41.3806i	0.177678	−	1.31916i
$985$	−4.07665			−0.129893
$986$	25.9271	−	13.4640i	0.825686	−	0.428781i
$987$			27.3318i			0.869980i
$988$	9.24084	−	13.1416i	0.293990	−	0.418089i
$989$		−	22.8672i		−	0.727136i
$990$		0			0
$991$	−27.9640			−0.888306			−0.444153	−	0.895951i	$-0.646495\pi$
$991$	−27.9640			−0.888306			−0.444153	+	0.895951i	$0.646495\pi$
$992$	−31.7352	+	34.2889i	−1.00759	+	1.08867i
$993$	69.1050			2.19298
$994$	1.90891	+	3.67590i	0.0605468	+	0.116592i
$995$			2.08778i			0.0661871i
$996$	26.3942	−	37.5357i	0.836333	−	1.18936i
$997$			57.2928i			1.81448i	0.420612	+	0.907241i	$0.361815\pi$
$997$			57.2928i			1.81448i	−0.420612	+	0.907241i	$0.638185\pi$
$998$	−17.6404	+	9.16071i	−0.558396	+	0.289977i
$999$	−0.0239795			−0.000758677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.c.h.485.14		20
4.3	odd	2		3872.2.c.h.1937.17		20
8.3	odd	2		3872.2.c.h.1937.4		20
8.5	even	2	inner	968.2.c.h.485.13		20
11.2	odd	10		968.2.o.i.565.4		40
11.3	even	5		968.2.o.j.493.10		40
11.4	even	5		968.2.o.j.269.2		40
11.5	even	5		88.2.o.a.69.2	yes	40
11.6	odd	10		968.2.o.i.245.9		40
11.7	odd	10		968.2.o.d.269.9		40
11.8	odd	10		968.2.o.d.493.1		40
11.9	even	5		88.2.o.a.37.7	yes	40
11.10	odd	2		968.2.c.i.485.7		20
33.5	odd	10		792.2.br.b.685.9		40
33.20	odd	10		792.2.br.b.37.4		40
44.27	odd	10		352.2.w.a.113.2		40
44.31	odd	10		352.2.w.a.81.9		40
44.43	even	2		3872.2.c.i.1937.17		20
88.5	even	10		88.2.o.a.69.7	yes	40
88.13	odd	10		968.2.o.i.565.9		40
88.21	odd	2		968.2.c.i.485.8		20
88.27	odd	10		352.2.w.a.113.9		40
88.29	odd	10		968.2.o.d.269.1		40
88.37	even	10		968.2.o.j.269.10		40
88.43	even	2		3872.2.c.i.1937.4		20
88.53	even	10		88.2.o.a.37.2	✓	40
88.61	odd	10		968.2.o.i.245.4		40
88.69	even	10		968.2.o.j.493.2		40
88.75	odd	10		352.2.w.a.81.2		40
88.85	odd	10		968.2.o.d.493.9		40
264.5	odd	10		792.2.br.b.685.4		40
264.53	odd	10		792.2.br.b.37.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.2	✓	40	88.53	even	10
88.2.o.a.37.7	yes	40	11.9	even	5
88.2.o.a.69.2	yes	40	11.5	even	5
88.2.o.a.69.7	yes	40	88.5	even	10
352.2.w.a.81.2		40	88.75	odd	10
352.2.w.a.81.9		40	44.31	odd	10
352.2.w.a.113.2		40	44.27	odd	10
352.2.w.a.113.9		40	88.27	odd	10
792.2.br.b.37.4		40	33.20	odd	10
792.2.br.b.37.9		40	264.53	odd	10
792.2.br.b.685.4		40	264.5	odd	10
792.2.br.b.685.9		40	33.5	odd	10
968.2.c.h.485.13		20	8.5	even	2	inner
968.2.c.h.485.14		20	1.1	even	1	trivial
968.2.c.i.485.7		20	11.10	odd	2
968.2.c.i.485.8		20	88.21	odd	2
968.2.o.d.269.1		40	88.29	odd	10
968.2.o.d.269.9		40	11.7	odd	10
968.2.o.d.493.1		40	11.8	odd	10
968.2.o.d.493.9		40	88.85	odd	10
968.2.o.i.245.4		40	88.61	odd	10
968.2.o.i.245.9		40	11.6	odd	10
968.2.o.i.565.4		40	11.2	odd	10
968.2.o.i.565.9		40	88.13	odd	10
968.2.o.j.269.2		40	11.4	even	5
968.2.o.j.269.10		40	88.37	even	10
968.2.o.j.493.2		40	88.69	even	10
968.2.o.j.493.10		40	11.3	even	5
3872.2.c.h.1937.4		20	8.3	odd	2
3872.2.c.h.1937.17		20	4.3	odd	2
3872.2.c.i.1937.4		20	88.43	even	2
3872.2.c.i.1937.17		20	44.43	even	2

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:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.651763 + 1.25507i) q^{2} -2.44793i q^{3} +(-1.15041 + 1.63602i) q^{4} +0.200474i q^{5} +(3.07232 - 1.59547i) q^{6} -2.34615 q^{7} +(-2.80312 - 0.377551i) q^{8} -2.99235 q^{9} +(-0.251609 + 0.130662i) q^{10} +(4.00485 + 2.81612i) q^{12} +1.63159i q^{13} +(-1.52914 - 2.94459i) q^{14} +0.490746 q^{15} +(-1.35311 - 3.76418i) q^{16} -3.33639 q^{17} +(-1.95030 - 3.75561i) q^{18} +4.92320i q^{19} +(-0.327979 - 0.230627i) q^{20} +5.74321i q^{21} -9.25109 q^{23} +(-0.924218 + 6.86182i) q^{24} +4.95981 q^{25} +(-2.04777 + 1.06341i) q^{26} -0.0187332i q^{27} +(2.69904 - 3.83835i) q^{28} +6.19167i q^{29} +(0.319850 + 0.615922i) q^{30} -8.25919 q^{31} +(3.84241 - 4.15161i) q^{32} +(-2.17453 - 4.18741i) q^{34} -0.470343i q^{35} +(3.44243 - 4.89554i) q^{36} -1.28006i q^{37} +(-6.17897 + 3.20876i) q^{38} +3.99402 q^{39} +(0.0756893 - 0.561952i) q^{40} -6.03055 q^{41} +(-7.20814 + 3.74321i) q^{42} +2.47184i q^{43} -0.599888i q^{45} +(-6.02952 - 11.6108i) q^{46} +4.75897 q^{47} +(-9.21445 + 3.31232i) q^{48} -1.49556 q^{49} +(3.23262 + 6.22492i) q^{50} +8.16724i q^{51} +(-2.66932 - 1.87700i) q^{52} +8.76165i q^{53} +(0.0235115 - 0.0122096i) q^{54} +(6.57654 + 0.885793i) q^{56} +12.0516 q^{57} +(-7.77100 + 4.03550i) q^{58} -1.90497i q^{59} +(-0.564559 + 0.802870i) q^{60} +6.39500i q^{61} +(-5.38303 - 10.3659i) q^{62} +7.02051 q^{63} +(7.71491 + 2.11664i) q^{64} -0.327092 q^{65} -8.27349i q^{67} +(3.83822 - 5.45839i) q^{68} +22.6460i q^{69} +(0.590314 - 0.306552i) q^{70} -1.24836 q^{71} +(8.38789 + 1.12976i) q^{72} +6.89517 q^{73} +(1.60656 - 0.834293i) q^{74} -12.1413i q^{75} +(-8.05444 - 5.66370i) q^{76} +(2.60315 + 5.01278i) q^{78} -14.6219 q^{79} +(0.754622 - 0.271264i) q^{80} -9.02290 q^{81} +(-3.93049 - 7.56878i) q^{82} -9.37255i q^{83} +(-9.39600 - 6.60705i) q^{84} -0.668860i q^{85} +(-3.10234 + 1.61106i) q^{86} +15.1568 q^{87} +5.11129 q^{89} +(0.752903 - 0.390985i) q^{90} -3.82797i q^{91} +(10.6426 - 15.1350i) q^{92} +20.2179i q^{93} +(3.10172 + 5.97285i) q^{94} -0.986974 q^{95} +(-10.1628 - 9.40595i) q^{96} +0.299741 q^{97} +(-0.974753 - 1.87704i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - q^{6} + 10 q^{7} - 10 q^{9} - 10 q^{10} - 3 q^{12} - 4 q^{14} - 4 q^{15} + 10 q^{16} + 2 q^{17} - 5 q^{18} - 16 q^{20} - 4 q^{23} + 15 q^{24} - 2 q^{25} + 30 q^{26} - 14 q^{28} + 16 q^{30}+ \cdots - 72 q^{98}+O(q^{100}) \) 20 * q + 2 * q^4 - q^6 + 10 * q^7 - 10 * q^9 - 10 * q^10 - 3 * q^12 - 4 * q^14 - 4 * q^15 + 10 * q^16 + 2 * q^17 - 5 * q^18 - 16 * q^20 - 4 * q^23 + 15 * q^24 - 2 * q^25 + 30 * q^26 - 14 * q^28 + 16 * q^30 + 2 * q^31 + 10 * q^32 + 5 * q^34 + 9 * q^36 + 21 * q^38 + 28 * q^39 + 10 * q^40 - 2 * q^41 - 20 * q^42 + 24 * q^46 + 2 * q^47 - 41 * q^48 - 2 * q^49 - 22 * q^50 - 20 * q^52 + 54 * q^54 - 16 * q^56 + 22 * q^57 + 12 * q^58 - 48 * q^60 + 4 * q^62 - 30 * q^63 + 38 * q^64 - 18 * q^65 - 21 * q^68 - 44 * q^70 - 34 * q^71 + 57 * q^72 + 2 * q^73 - 28 * q^74 - 67 * q^76 - 6 * q^78 - 58 * q^79 + 28 * q^80 - 12 * q^81 - 23 * q^82 - 44 * q^84 + 25 * q^86 + 34 * q^87 - 8 * q^89 - 42 * q^90 + 68 * q^92 + 60 * q^94 - 92 * q^95 + 35 * q^96 + 10 * q^97 - 72 * q^98

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