LMFDB - Embedded newform 261.2.k.b.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 $ x^18 - 5x^17 + 15x^16 - 32x^15 + 66x^14 - 115x^13 + 272x^12 - 387x^11 + 762x^10 - 822x^9 + 2349x^8 - 3280x^7 + 7428x^6 - 15449x^5 + 23373x^4 - 19712x^3 + 7938x^2 - 392*x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			190.2
Root			$0.719749 + 0.902536i$ of defining polynomial
Character	$\chi$	$=$	261.190
Dual form			261.2.k.b.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.04007 + 0.500870i) q^{2} +(-0.416111 - 0.521786i) q^{4} +(-3.10796 - 1.49671i) q^{5} +(2.81664 - 3.53195i) q^{7} +(-0.685187 - 3.00200i) q^{8} +(-2.48283 - 3.11337i) q^{10} +(-0.123323 + 0.540315i) q^{11} +(-0.614154 + 2.69078i) q^{13} +(4.69854 - 2.26270i) q^{14} +(0.493954 - 2.16416i) q^{16} +2.99688 q^{17} +(-0.173453 - 0.217503i) q^{19} +(0.512290 + 2.24449i) q^{20} +(-0.398892 + 0.500195i) q^{22} +(0.836001 - 0.402597i) q^{23} +(4.30181 + 5.39430i) q^{25} +(-1.98649 + 2.49098i) q^{26} -3.01496 q^{28} +(5.37860 - 0.265855i) q^{29} +(-8.21748 - 3.95733i) q^{31} +(-2.24199 + 2.81137i) q^{32} +(3.11696 + 1.50105i) q^{34} +(-14.0403 + 6.76146i) q^{35} +(1.52987 + 6.70278i) q^{37} +(-0.0714618 - 0.313095i) q^{38} +(-2.36360 + 10.3556i) q^{40} +2.85317 q^{41} +(10.1079 - 4.86770i) q^{43} +(0.333245 - 0.160482i) q^{44} +1.07115 q^{46} +(0.933590 - 4.09033i) q^{47} +(-2.98359 - 13.0720i) q^{49} +(1.77233 + 7.76508i) q^{50} +(1.65957 - 0.799207i) q^{52} +(-1.87299 - 0.901986i) q^{53} +(1.19198 - 1.49470i) q^{55} +(-12.5328 - 6.03550i) q^{56} +(5.72726 + 2.41747i) q^{58} +14.2670 q^{59} +(-4.50873 + 5.65377i) q^{61} +(-6.56462 - 8.23177i) q^{62} +(-7.73992 + 3.72735i) q^{64} +(5.93610 - 7.44363i) q^{65} +(2.73383 + 11.9777i) q^{67} +(-1.24704 - 1.56373i) q^{68} -17.9895 q^{70} +(-0.530060 + 2.32234i) q^{71} +(0.822693 - 0.396188i) q^{73} +(-1.76606 + 7.73761i) q^{74} +(-0.0413145 + 0.181010i) q^{76} +(1.56101 + 1.95744i) q^{77} +(-0.460193 - 2.01624i) q^{79} +(-4.77431 + 5.98680i) q^{80} +(2.96749 + 1.42907i) q^{82} +(6.83994 + 8.57702i) q^{83} +(-9.31420 - 4.48548i) q^{85} +12.9510 q^{86} +1.70652 q^{88} +(-6.13283 - 2.95341i) q^{89} +(7.77387 + 9.74812i) q^{91} +(-0.557938 - 0.268689i) q^{92} +(3.01972 - 3.78661i) q^{94} +(0.213544 + 0.935599i) q^{95} +(-2.19244 - 2.74924i) q^{97} +(3.44422 - 15.0901i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} - 11 q^{13} + 2 q^{14} + 18 q^{16} + 32 q^{17} + 2 q^{19} - 51 q^{20} + 20 q^{22} + 6 q^{23} + 4 q^{25} + 3 q^{26} - 48 q^{28}+ \cdots + 11 q^{98}+O(q^{100}) $ 18 * q + 2 * q^2 - 6 * q^4 + 7 * q^5 - 4 * q^7 + 3 * q^8 + 6 * q^10 + 6 * q^11 - 11 * q^13 + 2 * q^14 + 18 * q^16 + 32 * q^17 + 2 * q^19 - 51 * q^20 + 20 * q^22 + 6 * q^23 + 4 * q^25 + 3 * q^26 - 48 * q^28 + 10 * q^29 + 8 * q^31 - 55 * q^32 + 6 * q^34 - 31 * q^35 + 20 * q^37 + 20 * q^38 - 59 * q^40 + 68 * q^41 - 3 * q^43 + 10 * q^44 - 12 * q^46 - 19 * q^47 + 17 * q^49 - 23 * q^50 - 4 * q^52 + q^53 + 3 * q^55 - 7 * q^56 - 30 * q^58 - 20 * q^59 + 24 * q^61 - 79 * q^62 - 23 * q^64 - 6 * q^65 - 14 * q^67 + 8 * q^68 + 28 * q^70 + 28 * q^71 + 43 * q^73 + 47 * q^74 + 19 * q^76 - 26 * q^77 + 9 * q^79 + 74 * q^80 - 17 * q^82 - 8 * q^83 - 21 * q^85 + 140 * q^86 - 58 * q^88 + 6 * q^89 - 15 * q^91 - 11 * q^92 + 6 * q^94 + 16 * q^95 - 81 * q^97 + 11 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	1.04007	+	0.500870i	0.735438	+	0.354169i	0.763821	−	0.645429i	$-0.223321\pi$
$2$	1.04007	+	0.500870i	0.735438	+	0.354169i	−0.0283821	+	0.999597i	$0.509036\pi$
$3$		0			0
$3$		0			0
$4$	−0.416111	−	0.521786i	−0.208055	−	0.260893i
$5$	−3.10796	−	1.49671i	−1.38992	−	0.669351i	−0.418831	−	0.908064i	$-0.637560\pi$
$5$	−3.10796	−	1.49671i	−1.38992	−	0.669351i	−0.971090	+	0.238713i	$0.923274\pi$
$6$		0			0
$7$	2.81664	−	3.53195i	1.06459	−	1.33495i	0.125187	−	0.992133i	$-0.460047\pi$
$7$	2.81664	−	3.53195i	1.06459	−	1.33495i	0.939402	−	0.342819i	$-0.111382\pi$
$8$	−0.685187	−	3.00200i	−0.242250	−	1.06137i
$9$		0			0
$10$	−2.48283	−	3.11337i	−0.785139	−	0.984533i
$11$	−0.123323	+	0.540315i	−0.0371834	+	0.162911i	−0.990111	−	0.140287i	$-0.955197\pi$
$11$	−0.123323	+	0.540315i	−0.0371834	+	0.162911i	0.952927	+	0.303198i	$0.0980545\pi$
$12$		0			0
$13$	−0.614154	+	2.69078i	−0.170336	+	0.746289i	0.815525	+	0.578722i	$0.196448\pi$
$13$	−0.614154	+	2.69078i	−0.170336	+	0.746289i	−0.985861	+	0.167567i	$0.946409\pi$
$14$	4.69854	−	2.26270i	1.25574	−	0.604731i
$15$		0			0
$16$	0.493954	−	2.16416i	0.123489	−	0.541039i
$17$	2.99688			0.726851			0.363426	−	0.931623i	$-0.381607\pi$
$17$	2.99688			0.726851			0.363426	+	0.931623i	$0.381607\pi$
$18$		0			0
$19$	−0.173453	−	0.217503i	−0.0397928	−	0.0498985i	0.761537	−	0.648122i	$-0.224445\pi$
$19$	−0.173453	−	0.217503i	−0.0397928	−	0.0498985i	−0.801330	+	0.598223i	$0.795874\pi$
$20$	0.512290	+	2.24449i	0.114552	+	0.501883i
$21$		0			0
$22$	−0.398892	+	0.500195i	−0.0850440	+	0.106642i
$23$	0.836001	−	0.402597i	0.174318	−	0.0839472i	−0.344690	−	0.938717i	$-0.612016\pi$
$23$	0.836001	−	0.402597i	0.174318	−	0.0839472i	0.519008	+	0.854770i	$0.326302\pi$
$24$		0			0
$25$	4.30181	+	5.39430i	0.860362	+	1.07886i
$26$	−1.98649	+	2.49098i	−0.389583	+	0.488522i
$27$		0			0
$28$	−3.01496			−0.569773
$29$	5.37860	−	0.265855i	0.998781	−	0.0493681i
$29$	5.37860	−	0.265855i	0.998781	−	0.0493681i
$30$		0			0
$31$	−8.21748	−	3.95733i	−1.47590	−	0.710757i	−0.489031	−	0.872266i	$-0.662650\pi$
$31$	−8.21748	−	3.95733i	−1.47590	−	0.710757i	−0.986871	+	0.161509i	$0.948364\pi$
$32$	−2.24199	+	2.81137i	−0.396332	+	0.496985i
$33$		0			0
$34$	3.11696	+	1.50105i	0.534554	+	0.257428i
$35$	−14.0403	+	6.76146i	−2.37325	+	1.14290i
$36$		0			0
$37$	1.52987	+	6.70278i	0.251509	+	1.10193i	0.930069	+	0.367386i	$0.119747\pi$
$37$	1.52987	+	6.70278i	0.251509	+	1.10193i	−0.678560	+	0.734545i	$0.737396\pi$
$38$	−0.0714618	−	0.313095i	−0.0115926	−	0.0507907i
$39$		0			0
$40$	−2.36360	+	10.3556i	−0.373718	+	1.63737i
$41$	2.85317			0.445591			0.222795	−	0.974865i	$-0.428482\pi$
$41$	2.85317			0.445591			0.222795	+	0.974865i	$0.428482\pi$
$42$		0			0
$43$	10.1079	−	4.86770i	1.54144	−	0.742317i	0.546004	−	0.837783i	$-0.316148\pi$
$43$	10.1079	−	4.86770i	1.54144	−	0.742317i	0.995433	+	0.0954657i	$0.0304340\pi$
$44$	0.333245	−	0.160482i	0.0502386	−	0.0241936i
$45$		0			0
$46$	1.07115			0.157932
$47$	0.933590	−	4.09033i	0.136178	−	0.596635i	−0.860076	−	0.510165i	$-0.829584\pi$
$47$	0.933590	−	4.09033i	0.136178	−	0.596635i	0.996254	−	0.0864700i	$-0.0275587\pi$
$48$		0			0
$49$	−2.98359	−	13.0720i	−0.426227	−	1.86742i
$50$	1.77233	+	7.76508i	0.250645	+	1.09815i
$51$		0			0
$52$	1.65957	−	0.799207i	0.230141	−	0.110830i
$53$	−1.87299	−	0.901986i	−0.257275	−	0.123897i	0.300801	−	0.953687i	$-0.402746\pi$
$53$	−1.87299	−	0.901986i	−0.257275	−	0.123897i	−0.558076	+	0.829790i	$0.688460\pi$
$54$		0			0
$55$	1.19198	−	1.49470i	0.160727	−	0.201545i
$56$	−12.5328	−	6.03550i	−1.67477	−	0.806527i
$57$		0			0
$58$	5.72726	+	2.41747i	0.752026	+	0.317429i
$59$	14.2670			1.85741			0.928703	−	0.370824i	$-0.120925\pi$
$59$	14.2670			1.85741			0.928703	+	0.370824i	$0.120925\pi$
$60$		0			0
$61$	−4.50873	+	5.65377i	−0.577284	+	0.723891i	−0.981647	−	0.190707i	$-0.938922\pi$
$61$	−4.50873	+	5.65377i	−0.577284	+	0.723891i	0.404363	+	0.914599i	$0.367493\pi$
$62$	−6.56462	−	8.23177i	−0.833708	−	1.04544i
$63$		0			0
$64$	−7.73992	+	3.72735i	−0.967490	+	0.465919i
$65$	5.93610	−	7.44363i	0.736282	−	0.923269i
$66$		0			0
$67$	2.73383	+	11.9777i	0.333990	+	1.46331i	0.811330	+	0.584588i	$0.198744\pi$
$67$	2.73383	+	11.9777i	0.333990	+	1.46331i	−0.477340	+	0.878719i	$0.658399\pi$
$68$	−1.24704	−	1.56373i	−0.151225	−	0.189631i
$69$		0			0
$70$	−17.9895			−2.15015
$71$	−0.530060	+	2.32234i	−0.0629065	+	0.275611i	−0.996593	−	0.0824811i	$-0.973716\pi$
$71$	−0.530060	+	2.32234i	−0.0629065	+	0.275611i	0.933686	+	0.358092i	$0.116573\pi$
$72$		0			0
$73$	0.822693	−	0.396188i	0.0962889	−	0.0463703i	−0.385119	−	0.922867i	$-0.625840\pi$
$73$	0.822693	−	0.396188i	0.0962889	−	0.0463703i	0.481408	+	0.876496i	$0.340125\pi$
$74$	−1.76606	+	7.73761i	−0.205300	+	0.899479i
$75$		0			0
$76$	−0.0413145	+	0.181010i	−0.00473909	+	0.0207633i
$77$	1.56101	+	1.95744i	0.177893	+	0.223071i
$78$		0			0
$79$	−0.460193	−	2.01624i	−0.0517758	−	0.226845i	0.942420	−	0.334432i	$-0.108545\pi$
$79$	−0.460193	−	2.01624i	−0.0517758	−	0.226845i	−0.994196	+	0.107588i	$0.965687\pi$
$80$	−4.77431	+	5.98680i	−0.533784	+	0.669345i
$81$		0			0
$82$	2.96749	+	1.42907i	0.327705	+	0.157814i
$83$	6.83994	+	8.57702i	0.750781	+	0.941450i	0.999633	−	0.0270916i	$-0.00862459\pi$
$83$	6.83994	+	8.57702i	0.750781	+	0.941450i	−0.248852	+	0.968542i	$0.580053\pi$
$84$		0			0
$85$	−9.31420	−	4.48548i	−1.01027	−	0.486519i
$86$	12.9510			1.39654
$87$		0			0
$88$	1.70652			0.181916
$89$	−6.13283	−	2.95341i	−0.650078	−	0.313061i	0.0796253	−	0.996825i	$-0.474628\pi$
$89$	−6.13283	−	2.95341i	−0.650078	−	0.313061i	−0.729703	+	0.683764i	$0.760342\pi$
$90$		0			0
$91$	7.77387	+	9.74812i	0.814923	+	1.02188i
$92$	−0.557938	−	0.268689i	−0.0581691	−	0.0280128i
$93$		0			0
$94$	3.01972	−	3.78661i	0.311460	−	0.390559i
$95$	0.213544	+	0.935599i	0.0219092	+	0.0959904i
$96$		0			0
$97$	−2.19244	−	2.74924i	−0.222609	−	0.279143i	0.657968	−	0.753046i	$-0.271416\pi$
$97$	−2.19244	−	2.74924i	−0.222609	−	0.279143i	−0.880577	+	0.473903i	$0.842845\pi$
$98$	3.44422	−	15.0901i	0.347918	−	1.52433i
$99$		0			0
$100$	1.02464	−	4.48925i	0.102464	−	0.448925i
$101$	−11.4159	+	5.49760i	−1.13592	+	0.547032i	−0.904776	−	0.425887i	$-0.859962\pi$
$101$	−11.4159	+	5.49760i	−1.13592	+	0.547032i	−0.231147	+	0.972919i	$0.574248\pi$
$102$		0			0
$103$	−0.448946	+	1.96696i	−0.0442359	+	0.193810i	−0.992218	−	0.124514i	$-0.960263\pi$
$103$	−0.448946	+	1.96696i	−0.0442359	+	0.193810i	0.947982	+	0.318324i	$0.103120\pi$
$104$	8.49854			0.833350
$105$		0			0
$106$	−1.49626	−	1.87625i	−0.145330	−	0.182238i
$107$	−0.127292	−	0.557702i	−0.0123058	−	0.0539151i	0.968402	−	0.249393i	$-0.0802312\pi$
$107$	−0.127292	−	0.557702i	−0.0123058	−	0.0539151i	−0.980708	+	0.195478i	$0.937374\pi$
$108$		0			0
$109$	12.1384	−	15.2210i	1.16264	−	1.45791i	0.298682	−	0.954353i	$-0.403453\pi$
$109$	12.1384	−	15.2210i	1.16264	−	1.45791i	0.863962	−	0.503557i	$-0.167976\pi$
$110$	1.98839	−	0.957557i	0.189585	−	0.0912995i
$111$		0			0
$112$	−6.25240	−	7.84026i	−0.590797	−	0.740835i
$113$	−1.51936	+	1.90522i	−0.142929	+	0.179228i	−0.848143	−	0.529767i	$-0.822279\pi$
$113$	−1.51936	+	1.90522i	−0.142929	+	0.179228i	0.705214	+	0.708994i	$0.250851\pi$
$114$		0			0
$115$	−3.20083			−0.298479
$116$	−2.37681	−	2.69585i	−0.220681	−	0.250304i
$117$		0			0
$118$	14.8386	+	7.14592i	1.36601	+	0.657835i
$119$	8.44114	−	10.5849i	0.773798	−	0.970312i
$120$		0			0
$121$	9.63393	+	4.63945i	0.875811	+	0.421769i
$122$	−7.52119	+	3.62201i	−0.680936	+	0.327922i
$123$		0			0
$124$	1.35450	+	5.93446i	0.121638	+	0.532930i
$125$	−1.45811	−	6.38840i	−0.130417	−	0.571396i
$126$		0			0
$127$	2.04476	−	8.95869i	0.181443	−	0.794955i	−0.799501	−	0.600665i	$-0.794903\pi$
$127$	2.04476	−	8.95869i	0.181443	−	0.794955i	0.980944	−	0.194290i	$-0.0622403\pi$
$128$	−2.72519			−0.240875
$129$		0			0
$130$	9.90223	−	4.76866i	0.868483	−	0.418240i
$131$	−11.7972	+	5.68123i	−1.03073	+	0.496372i	−0.871255	−	0.490831i	$-0.836693\pi$
$131$	−11.7972	+	5.68123i	−1.03073	+	0.496372i	−0.159471	+	0.987203i	$0.550979\pi$
$132$		0			0
$133$	−1.25676			−0.108975
$134$	−3.15590	+	13.8269i	−0.272628	+	1.19446i
$135$		0			0
$136$	−2.05343	−	8.99665i	−0.176080	−	0.771456i
$137$	−1.69127	−	7.40992i	−0.144495	−	0.633072i	−0.994359	−	0.106070i	$-0.966173\pi$
$137$	−1.69127	−	7.40992i	−0.144495	−	0.633072i	0.849864	−	0.527002i	$-0.176684\pi$
$138$		0			0
$139$	−7.97635	+	3.84121i	−0.676545	+	0.325807i	−0.740414	−	0.672151i	$-0.765370\pi$
$139$	−7.97635	+	3.84121i	−0.676545	+	0.325807i	0.0638687	+	0.997958i	$0.479656\pi$
$140$	9.37036	+	4.51253i	0.791940	+	0.381378i
$141$		0			0
$142$	−1.71449	+	2.14990i	−0.143877	+	0.180416i
$143$	−1.37813	−	0.663673i	−0.115245	−	0.0554991i
$144$		0			0
$145$	−17.1144	−	7.22396i	−1.42127	−	0.599917i
$146$	1.05409			0.0872375
$147$		0			0
$148$	2.86083	−	3.58736i	0.235159	−	0.294879i
$149$	−4.96925	−	6.23124i	−0.407097	−	0.510483i	0.535446	−	0.844570i	$-0.320144\pi$
$149$	−4.96925	−	6.23124i	−0.407097	−	0.510483i	−0.942542	+	0.334087i	$0.891572\pi$
$150$		0			0
$151$	0.0950717	−	0.0457841i	0.00773683	−	0.00372586i	−0.430011	−	0.902823i	$-0.641490\pi$
$151$	0.0950717	−	0.0457841i	0.00773683	−	0.00372586i	0.437748	+	0.899098i	$0.355776\pi$
$152$	−0.534096	+	0.669735i	−0.0433209	+	0.0543226i
$153$		0			0
$154$	0.643129	+	2.81773i	0.0518248	+	0.227059i
$155$	19.6166	+	24.5984i	1.57564	+	1.97579i
$156$		0			0
$157$	−13.5037			−1.07771			−0.538857	−	0.842397i	$-0.681144\pi$
$157$	−13.5037			−1.07771			−0.538857	+	0.842397i	$0.681144\pi$
$158$	0.531241	−	2.32752i	0.0422633	−	0.185168i
$159$		0			0
$160$	11.1758	−	5.38201i	0.883528	−	0.425485i
$161$	0.932758	−	4.08668i	0.0735117	−	0.322076i
$162$		0			0
$163$	0.581624	−	2.54826i	0.0455563	−	0.199595i	−0.947028	−	0.321150i	$-0.895931\pi$
$163$	0.581624	−	2.54826i	0.0455563	−	0.199595i	0.992585	+	0.121554i	$0.0387879\pi$
$164$	−1.18724	−	1.48875i	−0.0927076	−	0.116252i
$165$		0			0
$166$	2.81803	+	12.3466i	0.218722	+	0.958282i
$167$	6.37129	−	7.98935i	0.493026	−	0.618235i	−0.471615	−	0.881805i	$-0.656329\pi$
$167$	6.37129	−	7.98935i	0.493026	−	0.618235i	0.964640	+	0.263570i	$0.0849001\pi$
$168$		0			0
$169$	4.84946	+	2.33538i	0.373036	+	0.179645i
$170$	−7.44075	−	9.33040i	−0.570679	−	0.715609i
$171$		0			0
$172$	−6.74589	−	3.24865i	−0.514370	−	0.247707i
$173$	−23.0919			−1.75564			−0.877822	−	0.478987i	$-0.841004\pi$
$173$	−23.0919			−1.75564			−0.877822	+	0.478987i	$0.841004\pi$
$174$		0			0
$175$	31.1690			2.35616
$176$	1.10841	+	0.533782i	0.0835495	+	0.0402353i
$177$		0			0
$178$	−4.89927	−	6.14350i	−0.367216	−	0.460474i
$179$	13.3241	+	6.41655i	0.995891	+	0.479596i	0.859542	−	0.511065i	$-0.170749\pi$
$179$	13.3241	+	6.41655i	0.995891	+	0.479596i	0.136349	+	0.990661i	$0.456463\pi$
$180$		0			0
$181$	1.80146	−	2.25895i	0.133901	−	0.167907i	−0.710360	−	0.703838i	$-0.751468\pi$
$181$	1.80146	−	2.25895i	0.133901	−	0.167907i	0.844261	+	0.535931i	$0.180039\pi$
$182$	3.20280	+	14.0324i	0.237408	+	1.04015i
$183$		0			0
$184$	−1.78141	−	2.23382i	−0.131327	−	0.164679i
$185$	5.27739	−	23.1218i	0.388001	−	1.69994i
$186$		0			0
$187$	−0.369586	+	1.61926i	−0.0270268	+	0.118412i
$188$	−2.52275	+	1.21489i	−0.183991	+	0.0886052i
$189$		0			0
$190$	−0.246513	+	1.08004i	−0.0178839	+	0.0783546i
$191$	4.66376			0.337458			0.168729	−	0.985663i	$-0.446034\pi$
$191$	4.66376			0.337458			0.168729	+	0.985663i	$0.446034\pi$
$192$		0			0
$193$	−9.09293	−	11.4022i	−0.654523	−	0.820746i	0.338212	−	0.941070i	$-0.390178\pi$
$193$	−9.09293	−	11.4022i	−0.654523	−	0.820746i	−0.992735	+	0.120324i	$0.961607\pi$
$194$	−0.903278	−	3.95752i	−0.0648516	−	0.284133i
$195$		0			0
$196$	−5.57926	+	6.99618i	−0.398519	+	0.499727i
$197$	2.60517	−	1.25458i	0.185611	−	0.0893855i	−0.338770	−	0.940869i	$-0.610011\pi$
$197$	2.60517	−	1.25458i	0.185611	−	0.0893855i	0.524381	+	0.851484i	$0.324297\pi$
$198$		0			0
$199$	2.52561	+	3.16701i	0.179036	+	0.224504i	0.863249	−	0.504778i	$-0.168426\pi$
$199$	2.52561	+	3.16701i	0.179036	+	0.224504i	−0.684213	+	0.729282i	$0.739854\pi$
$200$	13.2461	−	16.6101i	0.936643	−	1.17451i
$201$		0			0
$202$	−14.6269			−1.02914
$203$	14.2106	−	19.7458i	0.997387	−	1.38588i
$204$		0			0
$205$	−8.86755	−	4.27039i	−0.619336	−	0.298257i
$206$	−1.45212	+	1.82091i	−0.101174	+	0.126869i
$207$		0			0
$208$	5.51991	+	2.65825i	0.382737	+	0.184316i
$209$	0.138911	−	0.0668958i	0.00960865	−	0.00462728i
$210$		0			0
$211$	2.93029	+	12.8385i	0.201730	+	0.883836i	0.969883	+	0.243570i	$0.0783186\pi$
$211$	2.93029	+	12.8385i	0.201730	+	0.883836i	−0.768154	+	0.640266i	$0.778824\pi$
$212$	0.308728	+	1.35263i	0.0212036	+	0.0928989i
$213$		0			0
$214$	0.146944	−	0.643805i	0.0100449	−	0.0440096i
$215$	−38.7004			−2.63935
$216$		0			0
$217$	−37.1227	+	17.8774i	−2.52006	+	1.21360i
$218$	20.2485	−	9.75115i	1.37140	−	0.660431i
$219$		0			0
$220$	−1.27591			−0.0860217
$221$	−1.84055	+	8.06397i	−0.123809	+	0.542441i
$222$		0			0
$223$	3.39933	+	14.8934i	0.227636	+	0.997338i	0.951561	+	0.307459i	$0.0994788\pi$
$223$	3.39933	+	14.8934i	0.227636	+	0.997338i	−0.723925	+	0.689878i	$0.757664\pi$
$224$	3.61474	+	15.8372i	0.241520	+	1.05817i
$225$		0			0
$226$	−2.53450	+	1.22055i	−0.168593	+	0.0811899i
$227$	−13.2896	−	6.39993i	−0.882061	−	0.424778i	−0.0626842	−	0.998033i	$-0.519966\pi$
$227$	−13.2896	−	6.39993i	−0.882061	−	0.424778i	−0.819377	+	0.573255i	$0.805680\pi$
$228$		0			0
$229$	6.46791	−	8.11051i	0.427412	−	0.535957i	−0.520765	−	0.853700i	$-0.674353\pi$
$229$	6.46791	−	8.11051i	0.427412	−	0.535957i	0.948177	+	0.317742i	$0.102925\pi$
$230$	−3.32908	−	1.60320i	−0.219513	−	0.105712i
$231$		0			0
$232$	−4.48344	−	15.9644i	−0.294352	−	1.04811i
$233$	−0.280226			−0.0183582			−0.00917911	−	0.999958i	$-0.502922\pi$
$233$	−0.280226			−0.0183582			−0.00917911	+	0.999958i	$0.502922\pi$
$234$		0			0
$235$	−9.02361	+	11.3152i	−0.588635	+	0.738125i
$236$	−5.93666	−	7.44433i	−0.386443	−	0.484585i
$237$		0			0
$238$	14.0810	−	6.78104i	0.912734	−	0.439550i
$239$	−4.01459	+	5.03414i	−0.259682	+	0.325631i	−0.894532	−	0.447005i	$-0.852491\pi$
$239$	−4.01459	+	5.03414i	−0.259682	+	0.325631i	0.634849	+	0.772636i	$0.281062\pi$
$240$		0			0
$241$	3.43240	+	15.0383i	0.221101	+	0.968705i	0.956651	+	0.291235i	$0.0940663\pi$
$241$	3.43240	+	15.0383i	0.221101	+	0.968705i	−0.735551	+	0.677470i	$0.763077\pi$
$242$	7.69617	+	9.65069i	0.494728	+	0.620370i
$243$		0			0
$244$	4.82619			0.308965
$245$	−10.2921	+	45.0927i	−0.657539	+	2.88087i
$246$		0			0
$247$	0.691779	−	0.333143i	0.0440169	−	0.0211974i
$248$	−6.24939	+	27.3804i	−0.396837	+	1.73866i
$249$		0			0
$250$	1.68322	−	7.37469i	0.106456	−	0.466416i
$251$	2.05218	+	2.57336i	0.129533	+	0.162429i	0.842368	−	0.538902i	$-0.181161\pi$
$251$	2.05218	+	2.57336i	0.129533	+	0.162429i	−0.712836	+	0.701331i	$0.752589\pi$
$252$		0			0
$253$	0.114431	+	0.501353i	0.00719419	+	0.0315198i
$254$	6.61383	−	8.29347i	0.414988	−	0.520379i
$255$		0			0
$256$	12.6455	+	6.08973i	0.790341	+	0.380608i
$257$	0.246680	+	0.309326i	0.0153874	+	0.0192953i	0.789466	−	0.613795i	$-0.210358\pi$
$257$	0.246680	+	0.309326i	0.0153874	+	0.0192953i	−0.774078	+	0.633090i	$0.781786\pi$
$258$		0			0
$259$	27.9830	+	13.4759i	1.73878	+	0.837351i
$260$	−6.35406			−0.394062
$261$		0			0
$262$	−15.1154			−0.933835
$263$	−7.33709	−	3.53336i	−0.452425	−	0.217876i	0.193773	−	0.981046i	$-0.437927\pi$
$263$	−7.33709	−	3.53336i	−0.452425	−	0.217876i	−0.646198	+	0.763170i	$0.723642\pi$
$264$		0			0
$265$	4.47117	+	5.60667i	0.274662	+	0.344415i
$266$	−1.30712	−	0.629474i	−0.0801445	−	0.0385955i
$267$		0			0
$268$	5.11222	−	6.41052i	0.312278	−	0.391585i
$269$	1.99769	+	8.75246i	0.121801	+	0.533647i	0.998605	+	0.0527984i	$0.0168141\pi$
$269$	1.99769	+	8.75246i	0.121801	+	0.533647i	−0.876804	+	0.480848i	$0.840329\pi$
$270$		0			0
$271$	3.14213	+	3.94011i	0.190871	+	0.239344i	0.868054	−	0.496470i	$-0.165371\pi$
$271$	3.14213	+	3.94011i	0.190871	+	0.239344i	−0.677183	+	0.735815i	$0.736799\pi$
$272$	1.48032	−	6.48573i	0.0897579	−	0.393255i
$273$		0			0
$274$	1.95238	−	8.55391i	0.117947	−	0.516761i
$275$	−3.44513	+	1.65909i	−0.207749	+	0.100047i
$276$		0			0
$277$	−0.452859	+	1.98410i	−0.0272097	+	0.119213i	−0.986709	−	0.162498i	$-0.948045\pi$
$277$	−0.452859	+	1.98410i	−0.0272097	+	0.119213i	0.959499	+	0.281711i	$0.0909020\pi$
$278$	−10.2199			−0.612948
$279$		0			0
$280$	29.9181	+	37.5162i	1.78795	+	2.24202i
$281$	5.30139	+	23.2269i	0.316255	+	1.38560i	0.844065	+	0.536240i	$0.180156\pi$
$281$	5.30139	+	23.2269i	0.316255	+	1.38560i	−0.527811	+	0.849362i	$0.676987\pi$
$282$		0			0
$283$	−9.34352	+	11.7164i	−0.555414	+	0.696468i	−0.977703	−	0.209994i	$-0.932656\pi$
$283$	−9.34352	+	11.7164i	−0.555414	+	0.696468i	0.422288	+	0.906462i	$0.361227\pi$
$284$	1.43233	−	0.689774i	0.0849932	−	0.0409306i
$285$		0			0
$286$	−1.10093	−	1.38053i	−0.0650996	−	0.0816323i
$287$	8.03636	−	10.0773i	0.474371	−	0.594843i
$288$		0			0
$289$	−8.01868			−0.471687
$290$	−14.1818	−	16.0855i	−0.832786	−	0.944572i
$291$		0			0
$292$	−0.549057	−	0.264412i	−0.0321311	−	0.0154735i
$293$	−18.9354	+	23.7443i	−1.10622	+	1.38715i	−0.192261	+	0.981344i	$0.561582\pi$
$293$	−18.9354	+	23.7443i	−1.10622	+	1.38715i	−0.913957	+	0.405810i	$0.866989\pi$
$294$		0			0
$295$	−44.3413	−	21.3536i	−2.58165	−	1.24326i
$296$	19.0735	−	9.18532i	1.10863	−	0.533886i
$297$		0			0
$298$	−2.04731	−	8.96985i	−0.118598	−	0.519610i
$299$	0.569868	+	2.49675i	0.0329563	+	0.144391i
$300$		0			0
$301$	11.2778	−	49.4111i	0.650039	−	2.84801i
$302$	0.121813			0.00700954
$303$		0			0
$304$	−0.556387	+	0.267942i	−0.0319110	+	0.0153675i
$305$	22.4750	−	10.8234i	1.28692	−	0.619746i
$306$		0			0
$307$	2.10479			0.120127			0.0600635	−	0.998195i	$-0.480870\pi$
$307$	2.10479			0.120127			0.0600635	+	0.998195i	$0.480870\pi$
$308$	0.371814	−	1.62903i	0.0211861	−	0.0928223i
$309$		0			0
$310$	8.08196	+	35.4094i	0.459025	+	2.01112i
$311$	3.75530	+	16.4530i	0.212943	+	0.932965i	0.962555	+	0.271087i	$0.0873832\pi$
$311$	3.75530	+	16.4530i	0.212943	+	0.932965i	−0.749611	+	0.661878i	$0.769760\pi$
$312$		0			0
$313$	−13.3609	+	6.43428i	−0.755203	+	0.363687i	−0.771541	−	0.636180i	$-0.780514\pi$
$313$	−13.3609	+	6.43428i	−0.755203	+	0.363687i	0.0163375	+	0.999867i	$0.494799\pi$
$314$	−14.0448	−	6.76361i	−0.792593	−	0.381693i
$315$		0			0
$316$	−0.860555	+	1.07910i	−0.0484100	+	0.0607042i
$317$	−4.96094	−	2.38906i	−0.278634	−	0.134183i	0.289348	−	0.957224i	$-0.406561\pi$
$317$	−4.96094	−	2.38906i	−0.278634	−	0.134183i	−0.567982	+	0.823041i	$0.692276\pi$
$318$		0			0
$319$	−0.519661	+	2.93892i	−0.0290954	+	0.164548i
$320$	29.6341			1.65660
$321$		0			0
$322$	3.01703	−	3.78323i	0.168132	−	0.210831i
$323$	−0.519818	−	0.651831i	−0.0289234	−	0.0362688i
$324$		0			0
$325$	−17.1569	+	8.26231i	−0.951691	+	0.458310i
$326$	1.88127	−	2.35904i	0.104194	−	0.130655i
$327$		0			0
$328$	−1.95496	−	8.56523i	−0.107944	−	0.472936i
$329$	−11.8172	−	14.8184i	−0.651506	−	0.816963i
$330$		0			0
$331$	−5.88833			−0.323652			−0.161826	−	0.986819i	$-0.551738\pi$
$331$	−5.88833			−0.323652			−0.161826	+	0.986819i	$0.551738\pi$
$332$	1.62920	−	7.13798i	0.0894138	−	0.391747i
$333$		0			0
$334$	10.6282	−	5.11827i	0.581549	−	0.280059i
$335$	9.43054	−	41.3179i	0.515246	−	2.25744i
$336$		0			0
$337$	−3.87848	+	16.9927i	−0.211274	+	0.925652i	0.752428	+	0.658674i	$0.228882\pi$
$337$	−3.87848	+	16.9927i	−0.211274	+	0.925652i	−0.963703	+	0.266978i	$0.913975\pi$
$338$	3.87405	+	4.85790i	0.210720	+	0.264235i
$339$		0			0
$340$	1.53527	+	6.72648i	0.0832619	+	0.364794i
$341$	3.15161	−	3.95199i	0.170669	−	0.214012i
$342$		0			0
$343$	−26.0821	−	12.5605i	−1.40830	−	0.678201i
$344$	−21.5386	−	27.0086i	−1.16128	−	1.45620i
$345$		0			0
$346$	−24.0171	−	11.5660i	−1.29117	−	0.621794i
$347$	2.81562			0.151150			0.0755751	−	0.997140i	$-0.475921\pi$
$347$	2.81562			0.151150			0.0755751	+	0.997140i	$0.475921\pi$
$348$		0			0
$349$	23.4949			1.25765			0.628826	−	0.777546i	$-0.283536\pi$
$349$	23.4949			1.25765			0.628826	+	0.777546i	$0.283536\pi$
$350$	32.4179	+	15.6116i	1.73281	+	0.834477i
$351$		0			0
$352$	−1.24254	−	1.55809i	−0.0662274	−	0.0830465i
$353$	14.5563	+	7.00993i	0.774752	+	0.373101i	0.779108	−	0.626889i	$-0.215672\pi$
$353$	14.5563	+	7.00993i	0.774752	+	0.373101i	−0.00435584	+	0.999991i	$0.501387\pi$
$354$		0			0
$355$	5.12329	−	6.42440i	0.271916	−	0.340972i
$356$	1.01088	+	4.42897i	0.0535767	+	0.234735i
$357$		0			0
$358$	10.6441	+	13.3473i	0.562559	+	0.705426i
$359$	−1.92263	+	8.42361i	−0.101473	+	0.444581i	0.898511	+	0.438950i	$0.144650\pi$
$359$	−1.92263	+	8.42361i	−0.101473	+	0.444581i	−0.999984	+	0.00563099i	$0.998208\pi$
$360$		0			0
$361$	4.21068	−	18.4482i	0.221615	−	0.970957i
$362$	3.00508	−	1.44717i	0.157943	−	0.0760615i
$363$		0			0
$364$	1.85165	−	8.11260i	0.0970527	−	0.425216i
$365$	−3.14988			−0.164872
$366$		0			0
$367$	8.38364	+	10.5127i	0.437622	+	0.548761i	0.950915	−	0.309453i	$-0.100146\pi$
$367$	8.38364	+	10.5127i	0.437622	+	0.548761i	−0.513293	+	0.858214i	$0.671574\pi$
$368$	−0.458336	−	2.00810i	−0.0238924	−	0.104679i
$369$		0			0
$370$	17.0698	−	21.4049i	0.887418	−	1.11279i
$371$	−8.46131	+	4.07475i	−0.439289	+	0.211551i
$372$		0			0
$373$	−1.99095	−	2.49657i	−0.103088	−	0.129268i	0.727611	−	0.685989i	$-0.240630\pi$
$373$	−1.99095	−	2.49657i	−0.103088	−	0.129268i	−0.830699	+	0.556722i	$0.812059\pi$
$374$	−1.19543	+	1.49903i	−0.0618144	+	0.0775128i
$375$		0			0
$376$	−12.9188			−0.666238
$377$	−2.58793	+	14.6359i	−0.133285	+	0.753788i
$378$		0			0
$379$	14.8677	+	7.15991i	0.763703	+	0.367780i	0.774839	−	0.632158i	$-0.217831\pi$
$379$	14.8677	+	7.15991i	0.763703	+	0.367780i	−0.0111367	+	0.999938i	$0.503545\pi$
$380$	0.399325	−	0.500737i	0.0204849	−	0.0256873i
$381$		0			0
$382$	4.85062	+	2.33594i	0.248179	+	0.119517i
$383$	1.42189	−	0.684747i	0.0726553	−	0.0349889i	−0.397203	−	0.917731i	$-0.630019\pi$
$383$	1.42189	−	0.684747i	0.0726553	−	0.0349889i	0.469859	+	0.882742i	$0.344305\pi$
$384$		0			0
$385$	−1.92182	−	8.42003i	−0.0979449	−	0.429125i
$386$	−3.74625	−	16.4134i	−0.190679	−	0.835420i
$387$		0			0
$388$	−0.522215	+	2.28797i	−0.0265114	+	0.116154i
$389$	14.0108			0.710375			0.355188	−	0.934795i	$-0.384417\pi$
$389$	14.0108			0.710375			0.355188	+	0.934795i	$0.384417\pi$
$390$		0			0
$391$	2.50540	−	1.20654i	0.126703	−	0.0610171i
$392$	−37.1977	+	17.9135i	−1.87877	+	0.904766i
$393$		0			0
$394$	3.33794			0.168163
$395$	−1.58747	+	6.95517i	−0.0798744	+	0.349952i
$396$		0			0
$397$	−5.32177	−	23.3162i	−0.267092	−	1.17021i	−0.913378	−	0.407112i	$-0.866536\pi$
$397$	−5.32177	−	23.3162i	−0.267092	−	1.17021i	0.646286	−	0.763095i	$-0.276321\pi$
$398$	1.04054	+	4.55891i	0.0521576	+	0.228517i
$399$		0			0
$400$	13.7990	−	6.64525i	0.689950	−	0.332262i
$401$	−32.3263	−	15.5675i	−1.61430	−	0.777406i	−0.614368	−	0.789019i	$-0.710589\pi$
$401$	−32.3263	−	15.5675i	−1.61430	−	0.777406i	−0.999933	+	0.0116132i	$0.996303\pi$
$402$		0			0
$403$	15.6951	−	19.6810i	0.781829	−	0.980383i
$404$	7.61885	+	3.66904i	0.379052	+	0.182542i
$405$		0			0
$406$	24.6700	−	13.4193i	1.22435	−	0.665987i
$407$	−3.81028			−0.188869
$408$		0			0
$409$	9.36367	−	11.7417i	0.463004	−	0.580588i	−0.494439	−	0.869212i	$-0.664626\pi$
$409$	9.36367	−	11.7417i	0.463004	−	0.580588i	0.957442	+	0.288624i	$0.0931978\pi$
$410$	−7.08394	−	8.88298i	−0.349851	−	0.438699i
$411$		0			0
$412$	1.21314	−	0.584219i	0.0597673	−	0.0287824i
$413$	40.1850	−	50.3904i	1.97737	−	2.47955i
$414$		0			0
$415$	−8.42092	−	36.8945i	−0.413367	−	1.81108i
$416$	−6.18786	−	7.75934i	−0.303385	−	0.380433i
$417$		0			0
$418$	0.177983			0.00870541
$419$	8.22309	−	36.0277i	0.401724	−	1.76007i	−0.218691	−	0.975794i	$-0.570179\pi$
$419$	8.22309	−	36.0277i	0.401724	−	1.76007i	0.620415	−	0.784274i	$-0.286964\pi$
$420$		0			0
$421$	−1.15916	+	0.558222i	−0.0564940	+	0.0272061i	−0.461917	−	0.886923i	$-0.652838\pi$
$421$	−1.15916	+	0.558222i	−0.0564940	+	0.0272061i	0.405423	+	0.914129i	$0.367124\pi$
$422$	−3.38269	+	14.8206i	−0.164667	+	0.721453i
$423$		0			0
$424$	−1.42441	+	6.24075i	−0.0691755	+	0.303078i
$425$	12.8920	+	16.1661i	0.625355	+	0.784170i
$426$		0			0
$427$	7.26938	+	31.8492i	0.351790	+	1.54129i
$428$	−0.238034	+	0.298485i	−0.0115058	+	0.0144278i
$429$		0			0
$430$	−40.2510	−	19.3839i	−1.94108	−	0.934774i
$431$	15.7634	+	19.7667i	0.759298	+	0.952130i	0.999829	−	0.0185118i	$-0.00589284\pi$
$431$	15.7634	+	19.7667i	0.759298	+	0.952130i	−0.240531	+	0.970642i	$0.577321\pi$
$432$		0			0
$433$	9.33295	+	4.49451i	0.448513	+	0.215993i	0.644485	−	0.764617i	$-0.277072\pi$
$433$	9.33295	+	4.49451i	0.448513	+	0.215993i	−0.195972	+	0.980610i	$0.562786\pi$
$434$	−47.5644			−2.28316
$435$		0			0
$436$	−12.9930			−0.622253
$437$	−0.232572	−	0.112001i	−0.0111254	−	0.00535773i
$438$		0			0
$439$	−8.35161	−	10.4726i	−0.398601	−	0.499829i	0.541512	−	0.840693i	$-0.317852\pi$
$439$	−8.35161	−	10.4726i	−0.398601	−	0.499829i	−0.940113	+	0.340864i	$0.889281\pi$
$440$	−5.30381	−	2.55418i	−0.252849	−	0.121766i
$441$		0			0
$442$	−5.95329	+	7.46519i	−0.283169	+	0.355083i
$443$	6.85215	+	30.0213i	0.325556	+	1.42635i	0.827506	+	0.561456i	$0.189759\pi$
$443$	6.85215	+	30.0213i	0.325556	+	1.42635i	−0.501951	+	0.864896i	$0.667384\pi$
$444$		0			0
$445$	14.6402	+	18.3582i	0.694010	+	0.870261i
$446$	−3.92414	+	17.1928i	−0.185813	+	0.814102i
$447$		0			0
$448$	−8.63573	+	37.8356i	−0.408000	+	1.78756i
$449$	5.54036	−	2.66810i	0.261466	−	0.125915i	−0.298559	−	0.954391i	$-0.596506\pi$
$449$	5.54036	−	2.66810i	0.261466	−	0.125915i	0.560025	+	0.828476i	$0.310792\pi$
$450$		0			0
$451$	−0.351863	+	1.54161i	−0.0165686	+	0.0725917i
$452$	1.62634			0.0764965
$453$		0			0
$454$	−10.6165	−	13.3127i	−0.498259	−	0.624797i
$455$	−9.57071	−	41.9320i	−0.448682	−	1.96580i
$456$		0			0
$457$	−10.6275	+	13.3265i	−0.497134	+	0.623386i	−0.965580	−	0.260106i	$-0.916242\pi$
$457$	−10.6275	+	13.3265i	−0.497134	+	0.623386i	0.468446	+	0.883492i	$0.344814\pi$
$458$	10.7894	−	5.19589i	0.504154	−	0.242788i
$459$		0			0
$460$	1.33190	+	1.67015i	0.0621001	+	0.0778711i
$461$	10.3278	−	12.9506i	0.481012	−	0.603170i	−0.480817	−	0.876821i	$-0.659660\pi$
$461$	10.3278	−	12.9506i	0.481012	−	0.603170i	0.961829	+	0.273651i	$0.0882313\pi$
$462$		0			0
$463$	28.9072			1.34343			0.671715	−	0.740809i	$-0.265558\pi$
$463$	28.9072			1.34343			0.671715	+	0.740809i	$0.265558\pi$
$464$	2.08143	−	11.7714i	0.0966280	−	0.546476i
$465$		0			0
$466$	−0.291454	−	0.140357i	−0.0135013	−	0.00650190i
$467$	−14.1479	+	17.7409i	−0.654688	+	0.820953i	−0.992753	−	0.120170i	$-0.961656\pi$
$467$	−14.1479	+	17.7409i	−0.654688	+	0.820953i	0.338065	+	0.941123i	$0.390228\pi$
$468$		0			0
$469$	50.0048	+	24.0810i	2.30901	+	1.11196i
$470$	−15.0526	+	7.24896i	−0.694326	+	0.334370i
$471$		0			0
$472$	−9.77556	−	42.8295i	−0.449957	−	1.97139i
$473$	1.38355	+	6.06173i	0.0636158	+	0.278719i
$474$		0			0
$475$	0.427114	−	1.87131i	0.0195973	−	0.0858616i
$476$	−9.03548			−0.414140
$477$		0			0
$478$	−6.69689	+	3.22505i	−0.306309	+	0.147511i
$479$	5.87751	−	2.83046i	0.268550	−	0.129327i	−0.294763	−	0.955570i	$-0.595241\pi$
$479$	5.87751	−	2.83046i	0.268550	−	0.129327i	0.563313	+	0.826243i	$0.309526\pi$
$480$		0			0
$481$	−18.9753			−0.865200
$482$	−3.96232	+	17.3601i	−0.180479	+	0.790730i
$483$		0			0
$484$	−1.58798	−	6.95738i	−0.0721807	−	0.316244i
$485$	2.69920	+	11.8260i	0.122564	+	0.536990i
$486$		0			0
$487$	21.1411	−	10.1810i	0.957996	−	0.461346i	0.111513	−	0.993763i	$-0.464430\pi$
$487$	21.1411	−	10.1810i	0.957996	−	0.461346i	0.846482	+	0.532417i	$0.178716\pi$
$488$	20.0619	+	9.66132i	0.908161	+	0.437347i
$489$		0			0
$490$	−33.2900	+	41.7444i	−1.50389	+	1.88582i
$491$	−27.0162	−	13.0103i	−1.21923	−	0.587148i	−0.290130	−	0.956987i	$-0.593699\pi$
$491$	−27.0162	−	13.0103i	−1.21923	−	0.587148i	−0.929096	+	0.369839i	$0.879413\pi$
$492$		0			0
$493$	16.1190	−	0.796738i	0.725965	−	0.0358833i
$494$	0.886358			0.0398791
$495$		0			0
$496$	−12.6233	+	15.8292i	−0.566805	+	0.710750i
$497$	6.70942	+	8.41334i	0.300958	+	0.377390i
$498$		0			0
$499$	−13.9764	+	6.73068i	−0.625669	+	0.301307i	−0.719724	−	0.694261i	$-0.755732\pi$
$499$	−13.9764	+	6.73068i	−0.625669	+	0.301307i	0.0940543	+	0.995567i	$0.470017\pi$
$500$	−2.72664	+	3.41910i	−0.121939	+	0.152907i
$501$		0			0
$502$	0.845492	+	3.70434i	0.0377361	+	0.165333i
$503$	9.15733	+	11.4829i	0.408305	+	0.511999i	0.942885	−	0.333120i	$-0.108101\pi$
$503$	9.15733	+	11.4829i	0.408305	+	0.511999i	−0.534579	+	0.845118i	$0.679530\pi$
$504$		0			0
$505$	43.7085			1.94500
$506$	−0.132097	+	0.578755i	−0.00587244	+	0.0257288i
$507$		0			0
$508$	−5.52537	+	2.66088i	−0.245149	+	0.118057i
$509$	7.27387	−	31.8689i	0.322408	−	1.41256i	−0.510845	−	0.859673i	$-0.670667\pi$
$509$	7.27387	−	31.8689i	0.322408	−	1.41256i	0.833254	−	0.552891i	$-0.186475\pi$
$510$		0			0
$511$	0.917911	−	4.02163i	0.0406060	−	0.177906i
$512$	13.5002	+	16.9287i	0.596631	+	0.748151i
$513$		0			0
$514$	0.101631	+	0.445275i	0.00448275	+	0.0196402i
$515$	4.33928	−	5.44129i	0.191212	−	0.239772i
$516$		0			0
$517$	2.09493	+	1.00886i	0.0921349	+	0.0443698i
$518$	22.3545	+	28.0317i	0.982201	+	1.23164i
$519$		0			0
$520$	−26.4131	−	12.7199i	−1.15829	−	0.557804i
$521$	33.5048			1.46787			0.733937	−	0.679218i	$-0.237681\pi$
$521$	33.5048			1.46787			0.733937	+	0.679218i	$0.237681\pi$
$522$		0			0
$523$	−23.3879			−1.02268			−0.511341	−	0.859378i	$-0.670851\pi$
$523$	−23.3879			−1.02268			−0.511341	+	0.859378i	$0.670851\pi$
$524$	7.87333	+	3.79160i	0.343948	+	0.165637i
$525$		0			0
$526$	−5.86132	−	7.34986i	−0.255566	−	0.320469i
$527$	−24.6268	−	11.8597i	−1.07276	−	0.516615i
$528$		0			0
$529$	−13.8035	+	17.3090i	−0.600150	+	0.752564i
$530$	1.84210	+	8.07079i	0.0800159	+	0.350573i
$531$		0			0
$532$	0.522952	+	0.655761i	0.0226729	+	0.0284309i
$533$	−1.75229	+	7.67727i	−0.0759000	+	0.332540i
$534$		0			0
$535$	−0.439103	+	1.92384i	−0.0189841	+	0.0831747i
$536$	34.0838	−	16.4139i	1.47220	−	0.708972i
$537$		0			0
$538$	−2.30611	+	10.1037i	−0.0994234	+	0.435602i
$539$	7.43091			0.320072
$540$		0			0
$541$	−9.10698	−	11.4198i	−0.391540	−	0.490975i	0.546521	−	0.837445i	$-0.315952\pi$
$541$	−9.10698	−	11.4198i	−0.391540	−	0.490975i	−0.938061	+	0.346470i	$0.887380\pi$
$542$	1.29455	+	5.67177i	0.0556055	+	0.243624i
$543$		0			0
$544$	−6.71900	+	8.42536i	−0.288075	+	0.361234i
$545$	−60.5071	+	29.1387i	−2.59184	+	1.24816i
$546$		0			0
$547$	7.68546	+	9.63726i	0.328607	+	0.412060i	0.918500	−	0.395422i	$-0.129402\pi$
$547$	7.68546	+	9.63726i	0.328607	+	0.412060i	−0.589893	+	0.807481i	$0.700830\pi$
$548$	−3.16264	+	3.96583i	−0.135101	+	0.169412i
$549$		0			0
$550$	−4.41415			−0.188220
$551$	−0.990756	−	1.12375i	−0.0422076	−	0.0478732i
$552$		0			0
$553$	−8.41746	−	4.05363i	−0.357947	−	0.172378i
$554$	−1.46478	+	1.83678i	−0.0622326	+	0.0780372i
$555$		0			0
$556$	5.32333	+	2.56358i	0.225760	+	0.108720i
$557$	−22.4253	+	10.7994i	−0.950190	+	0.457587i	−0.843753	−	0.536732i	$-0.819659\pi$
$557$	−22.4253	+	10.7994i	−0.950190	+	0.457587i	−0.106437	+	0.994319i	$0.533944\pi$
$558$		0			0
$559$	6.89013	+	30.1876i	0.291421	+	1.27680i
$560$	7.69758	+	33.7253i	0.325282	+	1.42515i
$561$		0			0
$562$	−6.11986	+	26.8129i	−0.258151	+	1.13103i
$563$	−16.2217			−0.683662			−0.341831	−	0.939762i	$-0.611047\pi$
$563$	−16.2217			−0.683662			−0.341831	+	0.939762i	$0.611047\pi$
$564$		0			0
$565$	7.57368	−	3.64729i	0.318627	−	0.153443i
$566$	−15.5863	+	7.50596i	−0.655140	+	0.315499i
$567$		0			0
$568$	7.33486			0.307764
$569$	−9.97556	+	43.7058i	−0.418197	+	1.83224i	0.124378	+	0.992235i	$0.460307\pi$
$569$	−9.97556	+	43.7058i	−0.418197	+	1.83224i	−0.542575	+	0.840007i	$0.682551\pi$
$570$		0			0
$571$	3.78155	+	16.5681i	0.158253	+	0.693352i	0.990335	+	0.138699i	$0.0442920\pi$
$571$	3.78155	+	16.5681i	0.158253	+	0.693352i	−0.832081	+	0.554653i	$0.812851\pi$
$572$	0.227160	+	0.995251i	0.00949802	+	0.0416135i
$573$		0			0
$574$	13.4058	−	6.45587i	0.559545	−	0.269463i
$575$	5.76804	+	2.77774i	0.240544	+	0.115840i
$576$		0			0
$577$	−3.45830	+	4.33657i	−0.143971	+	0.180534i	−0.848589	−	0.529053i	$-0.822547\pi$
$577$	−3.45830	+	4.33657i	−0.143971	+	0.180534i	0.704618	+	0.709587i	$0.251119\pi$
$578$	−8.33997	−	4.01632i	−0.346897	−	0.167057i
$579$		0			0
$580$	3.35211	+	11.9360i	0.139189	+	0.495616i
$581$	49.5592			2.05606
$582$		0			0
$583$	0.718340	−	0.900769i	0.0297506	−	0.0373061i
$584$	−1.75305	−	2.19826i	−0.0725419	−	0.0909647i
$585$		0			0
$586$	−31.5869	+	15.2114i	−1.30484	+	0.628379i
$587$	11.9358	−	14.9671i	0.492644	−	0.617756i	−0.471908	−	0.881648i	$-0.656435\pi$
$587$	11.9358	−	14.9671i	0.492644	−	0.617756i	0.964552	+	0.263891i	$0.0850060\pi$
$588$		0			0
$589$	0.564613	+	2.47373i	0.0232645	+	0.101928i
$590$	−35.4225	−	44.4184i	−1.45832	−	1.82868i
$591$		0			0
$592$	15.2616			0.627246
$593$	7.05758	−	30.9213i	0.289820	−	1.26978i	−0.594952	−	0.803761i	$-0.702829\pi$
$593$	7.05758	−	30.9213i	0.289820	−	1.26978i	0.884772	−	0.466024i	$-0.154314\pi$
$594$		0			0
$595$	−42.0772	+	20.2633i	−1.72500	+	0.830715i
$596$	−1.18362	+	5.18577i	−0.0484829	+	0.212418i
$597$		0			0
$598$	−0.657848	+	2.88222i	−0.0269014	+	0.117863i
$599$	29.4026	+	36.8696i	1.20136	+	1.50645i	0.810227	+	0.586117i	$0.199344\pi$
$599$	29.4026	+	36.8696i	1.20136	+	1.50645i	0.391129	+	0.920336i	$0.372085\pi$
$600$		0			0
$601$	−3.29442	−	14.4338i	−0.134382	−	0.588766i	−0.996612	−	0.0822488i	$-0.973790\pi$
$601$	−3.29442	−	14.4338i	−0.134382	−	0.588766i	0.862230	−	0.506517i	$-0.169067\pi$
$602$	36.4781	−	45.7421i	1.48674	−	1.86431i
$603$		0			0
$604$	−0.0634499	−	0.0305559i	−0.00258174	−	0.00124330i
$605$	−22.9979	−	28.8385i	−0.934998	−	1.17245i
$606$		0			0
$607$	−10.5442	−	5.07781i	−0.427975	−	0.206102i	0.207481	−	0.978239i	$-0.433474\pi$
$607$	−10.5442	−	5.07781i	−0.427975	−	0.206102i	−0.635456	+	0.772137i	$0.719188\pi$
$608$	1.00036			0.0405700
$609$		0			0
$610$	28.7967			1.16594
$611$	10.4328	+	5.02418i	0.422066	+	0.203256i
$612$		0			0
$613$	−28.6483	−	35.9238i	−1.15709	−	1.45095i	−0.870003	−	0.493046i	$-0.835883\pi$
$613$	−28.6483	−	35.9238i	−1.15709	−	1.45095i	−0.287091	−	0.957903i	$-0.592688\pi$
$614$	2.18913	+	1.05423i	0.0883460	+	0.0425452i
$615$		0			0
$616$	4.80666	−	6.02736i	0.193666	−	0.242849i
$617$	−9.15351	−	40.1041i	−0.368506	−	1.61453i	−0.730885	−	0.682501i	$-0.760892\pi$
$617$	−9.15351	−	40.1041i	−0.368506	−	1.61453i	0.362378	−	0.932031i	$-0.381965\pi$
$618$		0			0
$619$	−1.85196	−	2.32229i	−0.0744367	−	0.0933407i	0.743219	−	0.669048i	$-0.233298\pi$
$619$	−1.85196	−	2.32229i	−0.0744367	−	0.0933407i	−0.817656	+	0.575708i	$0.804727\pi$
$620$	4.67245	−	20.4713i	0.187650	−	0.822149i
$621$		0			0
$622$	−4.33507	+	18.9932i	−0.173820	+	0.761557i
$623$	−27.7053	+	13.3421i	−1.10999	+	0.534542i
$624$		0			0
$625$	2.64663	−	11.5956i	0.105865	−	0.463825i
$626$	−17.1190			−0.684212
$627$		0			0
$628$	5.61905	+	7.04606i	0.224224	+	0.281168i
$629$	4.58483	+	20.0875i	0.182809	+	0.800940i
$630$		0			0
$631$	13.4129	−	16.8192i	0.533959	−	0.669563i	−0.439549	−	0.898219i	$-0.644862\pi$
$631$	13.4129	−	16.8192i	0.533959	−	0.669563i	0.973507	+	0.228656i	$0.0734330\pi$
$632$	−5.73743	+	2.76300i	−0.228223	+	0.109906i
$633$		0			0
$634$	−3.96310	−	4.96957i	−0.157395	−	0.197367i
$635$	−19.7636	+	24.7828i	−0.784296	+	0.983476i
$636$		0			0
$637$	37.0062			1.46624
$638$	−2.01250	+	2.79639i	−0.0796756	+	0.110710i
$639$		0			0
$640$	8.46978	+	4.07883i	0.334797	+	0.161230i
$641$	20.0815	−	25.1814i	0.793172	−	0.994606i	−0.206697	−	0.978405i	$-0.566271\pi$
$641$	20.0815	−	25.1814i	0.793172	−	0.994606i	0.999869	−	0.0162011i	$-0.00515721\pi$
$642$		0			0
$643$	−35.1799	−	16.9417i	−1.38736	−	0.668117i	−0.416803	−	0.908997i	$-0.636850\pi$
$643$	−35.1799	−	16.9417i	−1.38736	−	0.668117i	−0.970555	+	0.240880i	$0.922564\pi$
$644$	−2.52051	+	1.21381i	−0.0993218	+	0.0478309i
$645$		0			0
$646$	−0.214163	−	0.938308i	−0.00842612	−	0.0369173i
$647$	−0.917446	−	4.01959i	−0.0360685	−	0.158027i	0.953687	−	0.300802i	$-0.0972544\pi$
$647$	−0.917446	−	4.01959i	−0.0360685	−	0.158027i	−0.989755	+	0.142776i	$0.954397\pi$
$648$		0			0
$649$	−1.75945	+	7.70867i	−0.0690646	+	0.302592i
$650$	−21.9826			−0.862229
$651$		0			0
$652$	−1.57167	+	0.756875i	−0.0615512	+	0.0296415i
$653$	−13.7671	+	6.62990i	−0.538749	+	0.259448i	−0.683412	−	0.730033i	$-0.739505\pi$
$653$	−13.7671	+	6.62990i	−0.538749	+	0.259448i	0.144663	+	0.989481i	$0.453790\pi$
$654$		0			0
$655$	45.1684			1.76488
$656$	1.40934	−	6.17471i	0.0550254	−	0.241082i
$657$		0			0
$658$	−4.86866	−	21.3310i	−0.189800	−	0.831569i
$659$	−7.68022	−	33.6492i	−0.299179	−	1.31079i	−0.871353	−	0.490656i	$-0.836757\pi$
$659$	−7.68022	−	33.6492i	−0.299179	−	1.31079i	0.572175	−	0.820132i	$-0.306100\pi$
$660$		0			0
$661$	−10.7766	+	5.18973i	−0.419160	+	0.201857i	−0.631562	−	0.775325i	$-0.717586\pi$
$661$	−10.7766	+	5.18973i	−0.419160	+	0.201857i	0.212401	+	0.977182i	$0.431872\pi$
$662$	−6.12425	−	2.94928i	−0.238026	−	0.114627i
$663$		0			0
$664$	21.0616	−	26.4104i	0.817347	−	1.02492i
$665$	3.90597	+	1.88101i	0.151467	+	0.0729426i
$666$		0			0
$667$	4.38948	−	2.38766i	0.169961	−	0.0924506i
$668$	−6.81990			−0.263870
$669$		0			0
$670$	30.5033	−	38.2499i	1.17845	−	1.47772i
$671$	−2.49878	−	3.13338i	−0.0964645	−	0.120963i
$672$		0			0
$673$	15.9364	−	7.67456i	0.614303	−	0.295833i	−0.100741	−	0.994913i	$-0.532121\pi$
$673$	15.9364	−	7.67456i	0.614303	−	0.295833i	0.715043	+	0.699080i	$0.246407\pi$
$674$	−12.5450	+	15.7310i	−0.483216	+	0.605934i
$675$		0			0
$676$	−0.799345	−	3.50216i	−0.0307440	−	0.134698i
$677$	−18.5642	−	23.2788i	−0.713480	−	0.894675i	0.284469	−	0.958685i	$-0.408183\pi$
$677$	−18.5642	−	23.2788i	−0.713480	−	0.894675i	−0.997949	+	0.0640097i	$0.979611\pi$
$678$		0			0
$679$	−15.8855			−0.609629
$680$	−7.08344	+	31.0346i	−0.271638	+	1.19012i
$681$		0			0
$682$	5.25732	−	2.53179i	0.201313	−	0.0969473i
$683$	−3.77624	+	16.5448i	−0.144494	+	0.633069i	0.849865	+	0.527000i	$0.176683\pi$
$683$	−3.77624	+	16.5448i	−0.144494	+	0.633069i	−0.994359	+	0.106068i	$0.966174\pi$
$684$		0			0
$685$	−5.83414	+	25.5611i	−0.222911	+	0.976638i
$686$	−20.8360	−	26.1275i	−0.795520	−	0.997551i
$687$		0			0
$688$	−5.54162	−	24.2794i	−0.211272	−	0.925645i
$689$	3.57735	−	4.48586i	0.136286	−	0.170898i
$690$		0			0
$691$	22.2454	+	10.7128i	0.846254	+	0.407534i	0.806186	−	0.591662i	$-0.201528\pi$
$691$	22.2454	+	10.7128i	0.846254	+	0.407534i	0.0400683	+	0.999197i	$0.487242\pi$
$692$	9.60878	+	12.0490i	0.365271	+	0.458036i
$693$		0			0
$694$	2.92843	+	1.41026i	0.111162	+	0.0535327i
$695$	30.5394			1.15842
$696$		0			0
$697$	8.55063			0.323878
$698$	24.4363	+	11.7679i	0.924926	+	0.445421i
$699$		0			0
$700$	−12.9698	−	16.2636i	−0.490211	−	0.614705i
$701$	22.7891	+	10.9746i	0.860732	+	0.414507i	0.811550	−	0.584283i	$-0.198624\pi$
$701$	22.7891	+	10.9746i	0.860732	+	0.414507i	0.0491820	+	0.998790i	$0.484339\pi$
$702$		0			0
$703$	1.19251	−	1.49537i	0.0449765	−	0.0563988i
$704$	−1.05943	−	4.64166i	−0.0399287	−	0.174939i
$705$		0			0
$706$	11.6284	+	14.5816i	0.437642	+	0.548786i
$707$	−12.7372	+	55.8051i	−0.479030	+	2.09877i
$708$		0			0
$709$	−0.443854	+	1.94465i	−0.0166693	+	0.0730329i	−0.982578	−	0.185848i	$-0.940497\pi$
$709$	−0.443854	+	1.94465i	−0.0166693	+	0.0730329i	0.965909	+	0.258881i	$0.0833538\pi$
$710$	8.54635	−	4.11571i	0.320739	−	0.154460i
$711$		0			0
$712$	−4.66401	+	20.4344i	−0.174791	+	0.765811i
$713$	−8.46302			−0.316943
$714$		0			0
$715$	3.28984	+	4.12533i	0.123033	+	0.154279i
$716$	−2.19624	−	9.62234i	−0.0820772	−	0.359604i
$717$		0			0
$718$	−6.21880	+	7.79813i	−0.232084	+	0.291024i
$719$	5.69960	−	2.74478i	0.212559	−	0.102363i	−0.324575	−	0.945860i	$-0.605221\pi$
$719$	5.69960	−	2.74478i	0.212559	−	0.102363i	0.537134	+	0.843497i	$0.319507\pi$
$720$		0			0
$721$	5.68269	+	7.12586i	0.211634	+	0.265381i
$722$	13.6195	−	17.0783i	0.506866	−	0.635590i
$723$		0			0
$724$	−1.92830			−0.0716646
$725$	24.5718	+	27.8701i	0.912574	+	1.03507i
$726$		0			0
$727$	−16.3885	−	7.89230i	−0.607817	−	0.292709i	0.104547	−	0.994520i	$-0.466661\pi$
$727$	−16.3885	−	7.89230i	−0.607817	−	0.292709i	−0.712363	+	0.701811i	$0.752375\pi$
$728$	23.9373	−	30.0164i	0.887175	−	1.11248i
$729$		0			0
$730$	−3.27608	−	1.57768i	−0.121253	−	0.0583925i
$731$	30.2921	−	14.5879i	1.12040	−	0.539554i
$732$		0			0
$733$	8.06036	+	35.3148i	0.297716	+	1.30438i	0.873518	+	0.486791i	$0.161833\pi$
$733$	8.06036	+	35.3148i	0.297716	+	1.30438i	−0.575802	+	0.817589i	$0.695310\pi$
$734$	3.45403	+	15.1331i	0.127490	+	0.558572i
$735$		0			0
$736$	−0.742460	+	3.25293i	−0.0273674	+	0.119905i
$737$	−6.80886			−0.250808
$738$		0			0
$739$	3.75343	−	1.80755i	0.138072	−	0.0664920i	−0.363572	−	0.931566i	$-0.618443\pi$
$739$	3.75343	−	1.80755i	0.138072	−	0.0664920i	0.501644	+	0.865074i	$0.332729\pi$
$740$	−14.2606	+	6.86754i	−0.524230	+	0.252456i
$741$		0			0
$742$	−10.8412			−0.397995
$743$	5.47368	−	23.9818i	0.200810	−	0.879806i	−0.769635	−	0.638484i	$-0.779562\pi$
$743$	5.47368	−	23.9818i	0.200810	−	0.879806i	0.970445	−	0.241322i	$-0.0775809\pi$
$744$		0			0
$745$	6.11783	+	26.8040i	0.224140	+	0.982022i
$746$	−0.820264	−	3.59381i	−0.0300320	−	0.131579i
$747$		0			0
$748$	0.998697	−	0.480947i	0.0365160	−	0.0175852i
$749$	−2.32831	−	1.12126i	−0.0850747	−	0.0409698i
$750$		0			0
$751$	16.3234	−	20.4689i	0.595651	−	0.746922i	−0.389042	−	0.921220i	$-0.627194\pi$
$751$	16.3234	−	20.4689i	0.595651	−	0.746922i	0.984693	+	0.174297i	$0.0557654\pi$
$752$	−8.39095	−	4.04087i	−0.305987	−	0.147355i
$753$		0			0
$754$	−10.0223	+	13.9261i	−0.364991	+	0.507160i
$755$	−0.364005			−0.0132475
$756$		0			0
$757$	−32.5871	+	40.8630i	−1.18440	+	1.48519i	−0.347632	+	0.937631i	$0.613014\pi$
$757$	−32.5871	+	40.8630i	−1.18440	+	1.48519i	−0.836767	+	0.547559i	$0.815557\pi$
$758$	11.8772	+	14.8936i	0.431400	+	0.540959i
$759$		0			0
$760$	2.66235	−	1.28212i	0.0965735	−	0.0465074i
$761$	−3.05680	+	3.83310i	−0.110809	+	0.138950i	−0.834143	−	0.551548i	$-0.814037\pi$
$761$	−3.05680	+	3.83310i	−0.110809	+	0.138950i	0.723334	+	0.690498i	$0.242609\pi$
$762$		0			0
$763$	−19.5706	−	85.7442i	−0.708502	−	3.10415i
$764$	−1.94064	−	2.43348i	−0.0702099	−	0.0880404i
$765$		0			0
$766$	1.82183			0.0658255
$767$	−8.76214	+	38.3894i	−0.316382	+	1.38616i
$768$		0			0
$769$	−26.1703	+	12.6029i	−0.943725	+	0.454474i	−0.841482	−	0.540285i	$-0.818316\pi$
$769$	−26.1703	+	12.6029i	−0.943725	+	0.454474i	−0.102243	+	0.994759i	$0.532602\pi$
$770$	2.21852	−	9.71998i	0.0799500	−	0.350284i
$771$		0			0
$772$	−2.16583	+	9.48913i	−0.0779500	+	0.341521i
$773$	−33.3981	−	41.8799i	−1.20125	−	1.50632i	−0.810418	−	0.585853i	$-0.800760\pi$
$773$	−33.3981	−	41.8799i	−1.20125	−	1.50632i	−0.390829	−	0.920463i	$-0.627812\pi$
$774$		0			0
$775$	−14.0030	−	61.3512i	−0.503003	−	2.20380i
$776$	−6.75097	+	8.46545i	−0.242346	+	0.303892i
$777$		0			0
$778$	14.5722	+	7.01758i	0.522437	+	0.251593i
$779$	−0.494891	−	0.620573i	−0.0177313	−	0.0222343i
$780$		0			0
$781$	−1.18943	−	0.572798i	−0.0425611	−	0.0204963i
$782$	3.21010			0.114793
$783$		0			0
$784$	−29.7635			−1.06298
$785$	41.9690	+	20.2112i	1.49794	+	0.721370i
$786$		0			0
$787$	−26.7114	−	33.4951i	−0.952160	−	1.19397i	−0.980925	−	0.194384i	$-0.937729\pi$
$787$	−26.7114	−	33.4951i	−0.952160	−	1.19397i	0.0287658	−	0.999586i	$-0.490842\pi$
$788$	−1.73867	−	0.837297i	−0.0619374	−	0.0298275i
$789$		0			0
$790$	−5.13471	+	6.43872i	−0.182685	+	0.229079i
$791$	2.44965	+	10.7326i	0.0870995	+	0.381608i
$792$		0			0
$793$	−12.4440	−	15.6043i	−0.441900	−	0.554125i
$794$	6.14338	−	26.9159i	0.218021	−	0.955210i
$795$		0			0
$796$	0.601571	−	2.63566i	0.0213221	−	0.0934183i
$797$	22.2384	−	10.7094i	0.787724	−	0.379348i	0.00363260	−	0.999993i	$-0.498844\pi$
$797$	22.2384	−	10.7094i	0.787724	−	0.379348i	0.784091	+	0.620646i	$0.213129\pi$
$798$		0			0
$799$	2.79786	−	12.2582i	0.0989812	−	0.433665i
$800$	−24.8100			−0.877166
$801$		0			0
$802$	−25.8243	−	32.3826i	−0.911886	−	1.14347i
$803$	0.112609	+	0.493372i	0.00397389	+	0.0174107i
$804$		0			0
$805$	−9.01557	+	11.3052i	−0.317757	+	0.398455i
$806$	26.1816	−	12.6084i	0.922208	−	0.444112i
$807$		0			0
$808$	24.3258	+	30.5036i	0.855779	+	1.07311i
$809$	−18.8738	+	23.6671i	−0.663569	+	0.832089i	−0.993727	−	0.111837i	$-0.964327\pi$
$809$	−18.8738	+	23.6671i	−0.663569	+	0.832089i	0.330158	+	0.943926i	$0.392898\pi$
$810$		0			0
$811$	33.6697			1.18230			0.591151	−	0.806561i	$-0.298674\pi$
$811$	33.6697			1.18230			0.591151	+	0.806561i	$0.298674\pi$
$812$	−16.2162	+	0.801542i	−0.569079	+	0.0281286i
$813$		0			0
$814$	−3.96295	−	1.90845i	−0.138901	−	0.0668913i
$815$	−5.62168	+	7.04936i	−0.196919	+	0.246928i
$816$		0			0
$817$	−2.81198	−	1.35418i	−0.0983786	−	0.0473766i
$818$	15.6199	−	7.52214i	0.546137	−	0.263006i
$819$		0			0
$820$	1.46165	+	6.40392i	0.0510431	+	0.223635i
$821$	−8.78397	−	38.4851i	−0.306563	−	1.34314i	−0.860019	−	0.510261i	$-0.829549\pi$
$821$	−8.78397	−	38.4851i	−0.306563	−	1.34314i	0.553456	−	0.832878i	$-0.313309\pi$
$822$		0			0
$823$	−6.83426	+	29.9428i	−0.238227	+	1.04374i	0.704376	+	0.709827i	$0.251227\pi$
$823$	−6.83426	+	29.9428i	−0.238227	+	1.04374i	−0.942603	+	0.333915i	$0.891630\pi$
$824$	6.21242			0.216420
$825$		0			0
$826$	67.0341	−	32.2819i	2.33241	−	1.12323i
$827$	45.6520	−	21.9848i	1.58747	−	0.764487i	0.588445	−	0.808537i	$-0.299740\pi$
$827$	45.6520	−	21.9848i	1.58747	−	0.764487i	0.999029	+	0.0440495i	$0.0140259\pi$
$828$		0			0
$829$	17.7320			0.615858			0.307929	−	0.951409i	$-0.400364\pi$
$829$	17.7320			0.615858			0.307929	+	0.951409i	$0.400364\pi$
$830$	9.72100	−	42.5905i	0.337421	−	1.47834i
$831$		0			0
$832$	−5.27599	−	23.1156i	−0.182912	−	0.801390i
$833$	−8.94147	−	39.1751i	−0.309804	−	1.35734i
$834$		0			0
$835$	−31.7595	+	15.2946i	−1.09908	+	0.529290i
$836$	−0.0927076	−	0.0446456i	−0.00320636	−	0.00154410i
$837$		0			0
$838$	26.5977	−	33.3525i	0.918804	−	1.15214i
$839$	21.1502	+	10.1854i	0.730187	+	0.351640i	0.761758	−	0.647862i	$-0.224337\pi$
$839$	21.1502	+	10.1854i	0.730187	+	0.351640i	−0.0315706	+	0.999502i	$0.510051\pi$
$840$		0			0
$841$	28.8586	−	2.85986i	0.995126	−	0.0986158i
$842$	−1.48520			−0.0511834
$843$		0			0
$844$	5.47960	−	6.87121i	0.188616	−	0.236517i
$845$	−11.5765	−	14.5165i	−0.398245	−	0.499384i
$846$		0			0
$847$	43.5216	−	20.9589i	1.49542	−	0.720156i
$848$	−2.87721	+	3.60791i	−0.0988038	+	0.123896i
$849$		0			0
$850$	5.31146	+	23.2710i	0.182182	+	0.798190i
$851$	3.97749	+	4.98761i	0.136347	+	0.170973i
$852$		0			0
$853$	−24.8185			−0.849771			−0.424885	−	0.905247i	$-0.639686\pi$
$853$	−24.8185			−0.849771			−0.424885	+	0.905247i	$0.639686\pi$
$854$	−8.39168	+	36.7664i	−0.287157	+	1.25812i
$855$		0			0
$856$	−1.58700	+	0.764261i	−0.0542427	+	0.0261219i
$857$	−9.42188	+	41.2799i	−0.321845	+	1.41010i	0.512421	+	0.858734i	$0.328749\pi$
$857$	−9.42188	+	41.2799i	−0.321845	+	1.41010i	−0.834266	+	0.551362i	$0.814108\pi$
$858$		0			0
$859$	−4.94998	+	21.6873i	−0.168891	+	0.739960i	0.817552	+	0.575855i	$0.195331\pi$
$859$	−4.94998	+	21.6873i	−0.168891	+	0.739960i	−0.986443	+	0.164105i	$0.947526\pi$
$860$	16.1037	+	20.1934i	0.549130	+	0.688588i
$861$		0			0
$862$	6.49447	+	28.4542i	0.221203	+	0.969152i
$863$	−22.8106	+	28.6036i	−0.776483	+	0.973679i	−0.999999	−	0.00102145i	$-0.999675\pi$
$863$	−22.8106	+	28.6036i	−0.776483	+	0.973679i	0.223517	+	0.974700i	$0.428246\pi$
$864$		0			0
$865$	71.7687	+	34.5620i	2.44021	+	1.17514i
$866$	7.45573	+	9.34919i	0.253356	+	0.317698i
$867$		0			0
$868$	24.7753	+	11.9312i	0.840930	+	0.404971i
$869$	1.14616			0.0388807
$870$		0			0
$871$	−33.9083			−1.14894
$872$	−54.0105	−	26.0101i	−1.82903	−	0.880813i
$873$		0			0
$874$	−0.185793	−	0.232977i	−0.00628454	−	0.00788056i
$875$	−26.6705	−	12.8438i	−0.901627	−	0.434201i
$876$		0			0
$877$	22.4602	−	28.1642i	0.758427	−	0.951037i	−0.241385	−	0.970429i	$-0.577602\pi$
$877$	22.4602	−	28.1642i	0.758427	−	0.951037i	0.999812	+	0.0193923i	$0.00617314\pi$
$878$	−3.44083	−	15.0753i	−0.116122	−	0.508766i
$879$		0			0
$880$	−2.64597	−	3.31794i	−0.0891957	−	0.111848i
$881$	−4.63842	+	20.3222i	−0.156272	+	0.684674i	0.834711	+	0.550688i	$0.185635\pi$
$881$	−4.63842	+	20.3222i	−0.156272	+	0.684674i	−0.990983	+	0.133986i	$0.957222\pi$
$882$		0			0
$883$	−6.21101	+	27.2122i	−0.209017	+	0.915763i	0.756206	+	0.654334i	$0.227051\pi$
$883$	−6.21101	+	27.2122i	−0.209017	+	0.915763i	−0.965223	+	0.261429i	$0.915806\pi$
$884$	4.97354	−	2.39513i	0.167278	−	0.0805570i
$885$		0			0
$886$	−7.91004	+	34.6562i	−0.265743	+	1.16430i
$887$	54.6365			1.83451			0.917257	−	0.398296i	$-0.130398\pi$
$887$	54.6365			1.83451			0.917257	+	0.398296i	$0.130398\pi$
$888$		0			0
$889$	−25.8823	−	32.4554i	−0.868064	−	1.08852i
$890$	6.03169	+	26.4265i	0.202183	+	0.885820i
$891$		0			0
$892$	6.35669	−	7.97104i	0.212838	−	0.266890i
$893$	−1.05159	+	0.506419i	−0.0351901	+	0.0169467i
$894$		0			0
$895$	−31.8071	−	39.8848i	−1.06319	−	1.33320i
$896$	−7.67587	+	9.62524i	−0.256433	+	0.321557i
$897$		0			0
$898$	7.09872			0.236887
$899$	−45.2506	−	19.1002i	−1.50919	−	0.637028i
$900$		0			0
$901$	−5.61314	−	2.70315i	−0.187001	−	0.0900549i
$902$	−1.13811	+	1.42714i	−0.0378949	+	0.0475186i
$903$		0			0
$904$	6.76051	+	3.25569i	0.224851	+	0.108283i
$905$	−8.97986	+	4.32447i	−0.298501	+	0.143750i
$906$		0			0
$907$	−3.58486	−	15.7063i	−0.119033	−	0.521519i	−0.998925	−	0.0463456i	$-0.985242\pi$
$907$	−3.58486	−	15.7063i	−0.119033	−	0.521519i	0.879892	−	0.475173i	$-0.157615\pi$
$908$	2.19055	+	9.59741i	0.0726958	+	0.318501i
$909$		0			0
$910$	11.0483	−	48.4058i	0.366248	−	1.60464i
$911$	−42.9222			−1.42207			−0.711037	−	0.703154i	$-0.751774\pi$
$911$	−42.9222			−1.42207			−0.711037	+	0.703154i	$0.751774\pi$
$912$		0			0
$913$	−5.47781	+	2.63798i	−0.181289	+	0.0873042i
$914$	−17.7281	+	8.53742i	−0.586395	+	0.282393i
$915$		0			0
$916$	−6.92332			−0.228753
$917$	−13.1626	+	57.6691i	−0.434667	+	1.90440i
$918$		0			0
$919$	4.31653	+	18.9120i	0.142389	+	0.623848i	0.994876	+	0.101100i	$0.0322362\pi$
$919$	4.31653	+	18.9120i	0.142389	+	0.623848i	−0.852487	+	0.522749i	$0.824907\pi$
$920$	2.19316	+	9.60888i	0.0723065	+	0.316795i
$921$		0			0
$922$	17.2281	−	8.29664i	0.567379	−	0.273235i
$923$	−5.92338	−	2.85255i	−0.194971	−	0.0938929i
$924$		0			0
$925$	−29.5756	+	37.0866i	−0.972440	+	1.21940i
$926$	30.0654	+	14.4787i	0.988011	+	0.475801i
$927$		0			0
$928$	−11.3114	+	15.7173i	−0.371314	+	0.515945i
$929$	−15.9251			−0.522484			−0.261242	−	0.965273i	$-0.584132\pi$
$929$	−15.9251			−0.522484			−0.261242	+	0.965273i	$0.584132\pi$
$930$		0			0
$931$	−2.32567	+	2.91630i	−0.0762209	+	0.0955780i
$932$	0.116605	+	0.146218i	0.00381953	+	0.00478953i
$933$		0			0
$934$	−23.6007	+	11.3655i	−0.772239	+	0.371891i
$935$	3.57223	−	4.47943i	0.116824	−	0.146493i
$936$		0			0
$937$	8.93124	+	39.1303i	0.291771	+	1.27833i	0.882059	+	0.471139i	$0.156157\pi$
$937$	8.93124	+	39.1303i	0.291771	+	1.27833i	−0.590288	+	0.807193i	$0.700986\pi$
$938$	39.9469	+	50.0918i	1.30431	+	1.63556i
$939$		0			0
$940$	9.65896			0.315041
$941$	0.549269	−	2.40651i	0.0179057	−	0.0784498i	−0.965186	−	0.261566i	$-0.915761\pi$
$941$	0.549269	−	2.40651i	0.0179057	−	0.0784498i	0.983091	+	0.183116i	$0.0586183\pi$
$942$		0			0
$943$	2.38526	−	1.14868i	0.0776746	−	0.0374061i
$944$	7.04725	−	30.8760i	0.229369	−	1.00493i
$945$		0			0
$946$	−1.59715	+	6.99759i	−0.0519280	+	0.227511i
$947$	−16.4220	−	20.5925i	−0.533643	−	0.669167i	0.439801	−	0.898095i	$-0.355049\pi$
$947$	−16.4220	−	20.5925i	−0.533643	−	0.669167i	−0.973443	+	0.228929i	$0.926478\pi$
$948$		0			0
$949$	0.560796	+	2.45701i	0.0182042	+	0.0797579i
$950$	1.38151	−	1.73236i	0.0448221	−	0.0562051i
$951$		0			0
$952$	−37.5595	−	18.0877i	−1.21731	−	0.586225i
$953$	−29.3824	−	36.8443i	−0.951788	−	1.19350i	−0.981015	−	0.193932i	$-0.937876\pi$
$953$	−29.3824	−	36.8443i	−0.951788	−	1.19350i	0.0292271	−	0.999573i	$-0.490695\pi$
$954$		0			0
$955$	−14.4948	−	6.98031i	−0.469040	−	0.225878i
$956$	4.29726			0.138983
$957$		0			0
$958$	7.53070			0.243306
$959$	−30.9351	−	14.8976i	−0.998948	−	0.481068i
$960$		0			0
$961$	32.5383	+	40.8017i	1.04962	+	1.31619i
$962$	−19.7356	−	9.50416i	−0.636301	−	0.306427i
$963$		0			0
$964$	6.41854	−	8.04860i	0.206727	−	0.259228i
$965$	11.1947	+	49.0470i	0.360369	+	1.57888i
$966$		0			0
$967$	−17.7894	−	22.3071i	−0.572067	−	0.717349i	0.408670	−	0.912682i	$-0.365993\pi$
$967$	−17.7894	−	22.3071i	−0.572067	−	0.717349i	−0.980737	+	0.195333i	$0.937421\pi$
$968$	7.32660	−	32.0999i	0.235486	−	1.03173i
$969$		0			0
$970$	−3.11592	+	13.6518i	−0.100046	+	0.438331i
$971$	0.441543	−	0.212636i	0.0141698	−	0.00682381i	−0.426785	−	0.904353i	$-0.640354\pi$
$971$	0.441543	−	0.212636i	0.0141698	−	0.00682381i	0.440955	+	0.897529i	$0.354640\pi$
$972$		0			0
$973$	−8.89952	+	38.9914i	−0.285306	+	1.25001i
$974$	27.0876			0.867941
$975$		0			0
$976$	10.0085	+	12.5503i	0.320365	+	0.401725i
$977$	−4.03733	−	17.6887i	−0.129166	−	0.565911i	−0.997546	−	0.0700129i	$-0.977696\pi$
$977$	−4.03733	−	17.6887i	−0.129166	−	0.565911i	0.868381	−	0.495898i	$-0.165161\pi$
$978$		0			0
$979$	2.35209	−	2.94943i	0.0751732	−	0.0942642i
$980$	27.8114	−	13.3933i	0.888403	−	0.427832i
$981$		0			0
$982$	−21.5822	−	27.0632i	−0.688716	−	0.863623i
$983$	34.7002	−	43.5127i	1.10676	−	1.38784i	0.193193	−	0.981161i	$-0.438116\pi$
$983$	34.7002	−	43.5127i	1.10676	−	1.38784i	0.913571	−	0.406678i	$-0.133313\pi$
$984$		0			0
$985$	−9.97452			−0.317815
$986$	17.1639	+	7.24488i	0.546611	+	0.230724i
$987$		0			0
$988$	−0.461686	−	0.222336i	−0.0146882	−	0.00707347i
$989$	6.49047	−	8.13879i	0.206385	−	0.258799i
$990$		0			0
$991$	−18.2381	−	8.78303i	−0.579354	−	0.279002i	0.121169	−	0.992632i	$-0.461336\pi$
$991$	−18.2381	−	8.78303i	−0.579354	−	0.279002i	−0.700523	+	0.713630i	$0.747050\pi$
$992$	29.5491	−	14.2301i	0.938184	−	0.451806i
$993$		0			0
$994$	2.76425	+	12.1110i	0.0876768	+	0.384137i
$995$	−3.10937	−	13.6231i	−0.0985738	−	0.431880i
$996$		0			0
$997$	−6.50469	+	28.4989i	−0.206005	+	0.902569i	0.761189	+	0.648531i	$0.224616\pi$
$997$	−6.50469	+	28.4989i	−0.206005	+	0.902569i	−0.967194	+	0.254038i	$0.918241\pi$
$998$	−17.9076			−0.566855
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.b.190.2		18
3.2	odd	2		87.2.g.b.16.2	✓	18
29.7	even	7		7569.2.a.bl.1.4		9
29.20	even	7	inner	261.2.k.b.136.2		18
29.22	even	14		7569.2.a.bk.1.6		9
87.20	odd	14		87.2.g.b.49.2	yes	18
87.65	odd	14		2523.2.a.p.1.6		9
87.80	odd	14		2523.2.a.q.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.b.16.2	✓	18	3.2	odd	2
87.2.g.b.49.2	yes	18	87.20	odd	14
261.2.k.b.136.2		18	29.20	even	7	inner
261.2.k.b.190.2		18	1.1	even	1	trivial
2523.2.a.p.1.6		9	87.65	odd	14
2523.2.a.q.1.4		9	87.80	odd	14
7569.2.a.bk.1.6		9	29.22	even	14
7569.2.a.bl.1.4		9	29.7	even	7

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.04007 + 0.500870i) q^{2} +(-0.416111 - 0.521786i) q^{4} +(-3.10796 - 1.49671i) q^{5} +(2.81664 - 3.53195i) q^{7} +(-0.685187 - 3.00200i) q^{8} +(-2.48283 - 3.11337i) q^{10} +(-0.123323 + 0.540315i) q^{11} +(-0.614154 + 2.69078i) q^{13} +(4.69854 - 2.26270i) q^{14} +(0.493954 - 2.16416i) q^{16} +2.99688 q^{17} +(-0.173453 - 0.217503i) q^{19} +(0.512290 + 2.24449i) q^{20} +(-0.398892 + 0.500195i) q^{22} +(0.836001 - 0.402597i) q^{23} +(4.30181 + 5.39430i) q^{25} +(-1.98649 + 2.49098i) q^{26} -3.01496 q^{28} +(5.37860 - 0.265855i) q^{29} +(-8.21748 - 3.95733i) q^{31} +(-2.24199 + 2.81137i) q^{32} +(3.11696 + 1.50105i) q^{34} +(-14.0403 + 6.76146i) q^{35} +(1.52987 + 6.70278i) q^{37} +(-0.0714618 - 0.313095i) q^{38} +(-2.36360 + 10.3556i) q^{40} +2.85317 q^{41} +(10.1079 - 4.86770i) q^{43} +(0.333245 - 0.160482i) q^{44} +1.07115 q^{46} +(0.933590 - 4.09033i) q^{47} +(-2.98359 - 13.0720i) q^{49} +(1.77233 + 7.76508i) q^{50} +(1.65957 - 0.799207i) q^{52} +(-1.87299 - 0.901986i) q^{53} +(1.19198 - 1.49470i) q^{55} +(-12.5328 - 6.03550i) q^{56} +(5.72726 + 2.41747i) q^{58} +14.2670 q^{59} +(-4.50873 + 5.65377i) q^{61} +(-6.56462 - 8.23177i) q^{62} +(-7.73992 + 3.72735i) q^{64} +(5.93610 - 7.44363i) q^{65} +(2.73383 + 11.9777i) q^{67} +(-1.24704 - 1.56373i) q^{68} -17.9895 q^{70} +(-0.530060 + 2.32234i) q^{71} +(0.822693 - 0.396188i) q^{73} +(-1.76606 + 7.73761i) q^{74} +(-0.0413145 + 0.181010i) q^{76} +(1.56101 + 1.95744i) q^{77} +(-0.460193 - 2.01624i) q^{79} +(-4.77431 + 5.98680i) q^{80} +(2.96749 + 1.42907i) q^{82} +(6.83994 + 8.57702i) q^{83} +(-9.31420 - 4.48548i) q^{85} +12.9510 q^{86} +1.70652 q^{88} +(-6.13283 - 2.95341i) q^{89} +(7.77387 + 9.74812i) q^{91} +(-0.557938 - 0.268689i) q^{92} +(3.01972 - 3.78661i) q^{94} +(0.213544 + 0.935599i) q^{95} +(-2.19244 - 2.74924i) q^{97} +(3.44422 - 15.0901i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} - 11 q^{13} + 2 q^{14} + 18 q^{16} + 32 q^{17} + 2 q^{19} - 51 q^{20} + 20 q^{22} + 6 q^{23} + 4 q^{25} + 3 q^{26} - 48 q^{28}+ \cdots + 11 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 - 6 * q^4 + 7 * q^5 - 4 * q^7 + 3 * q^8 + 6 * q^10 + 6 * q^11 - 11 * q^13 + 2 * q^14 + 18 * q^16 + 32 * q^17 + 2 * q^19 - 51 * q^20 + 20 * q^22 + 6 * q^23 + 4 * q^25 + 3 * q^26 - 48 * q^28 + 10 * q^29 + 8 * q^31 - 55 * q^32 + 6 * q^34 - 31 * q^35 + 20 * q^37 + 20 * q^38 - 59 * q^40 + 68 * q^41 - 3 * q^43 + 10 * q^44 - 12 * q^46 - 19 * q^47 + 17 * q^49 - 23 * q^50 - 4 * q^52 + q^53 + 3 * q^55 - 7 * q^56 - 30 * q^58 - 20 * q^59 + 24 * q^61 - 79 * q^62 - 23 * q^64 - 6 * q^65 - 14 * q^67 + 8 * q^68 + 28 * q^70 + 28 * q^71 + 43 * q^73 + 47 * q^74 + 19 * q^76 - 26 * q^77 + 9 * q^79 + 74 * q^80 - 17 * q^82 - 8 * q^83 - 21 * q^85 + 140 * q^86 - 58 * q^88 + 6 * q^89 - 15 * q^91 - 11 * q^92 + 6 * q^94 + 16 * q^95 - 81 * q^97 + 11 * q^98

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