LMFDB - Embedded newform 315.2.bf.b.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(109,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("315.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 4 x^{13} - 14 x^{12} + 38 x^{11} - 40 x^{10} + 64 x^{9} + 291 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 2x^14 - 4x^13 - 14x^12 + 38x^11 - 40x^10 + 64x^9 + 291x^8 - 630x^7 + 584x^6 - 800x^5 + 734x^4 - 188x^3 + 32x^2 - 8*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.2
Root			$-0.0543258 - 0.202747i$ of defining polynomial
Character	$\chi$	$=$	315.289
Dual form			315.2.bf.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54296 - 0.890827i) q^{2} +(0.587145 + 1.01696i) q^{4} +(1.33920 - 1.79069i) q^{5} +(-2.40898 - 1.09398i) q^{7} +1.47113i q^{8} +O(q^{10})$	\(q+(-1.54296 - 0.890827i) q^{2} +(0.587145 + 1.01696i) q^{4} +(1.33920 - 1.79069i) q^{5} +(-2.40898 - 1.09398i) q^{7} +1.47113i q^{8} +(-3.66151 + 1.56996i) q^{10} +(-1.03925 - 1.80003i) q^{11} -3.13023i q^{13} +(2.74241 + 3.83396i) q^{14} +(2.48481 - 4.30382i) q^{16} +(1.84483 - 1.06512i) q^{17} +(-3.86880 + 6.70095i) q^{19} +(2.60736 + 0.310523i) q^{20} +3.70316i q^{22} +(-4.79479 - 2.76827i) q^{23} +(-1.41311 - 4.79616i) q^{25} +(-2.78849 + 4.82981i) q^{26} +(-0.301877 - 3.09218i) q^{28} -4.01368 q^{29} +(-1.45594 - 2.52177i) q^{31} +(-5.11984 + 2.95594i) q^{32} -3.79533 q^{34} +(-5.18508 + 2.84867i) q^{35} +(-3.04424 - 1.75759i) q^{37} +(11.9388 - 6.89286i) q^{38} +(2.63433 + 1.97013i) q^{40} -7.99038 q^{41} +4.99038i q^{43} +(1.22038 - 2.11376i) q^{44} +(4.93210 + 8.54266i) q^{46} +(2.11376 + 1.22038i) q^{47} +(4.60639 + 5.27078i) q^{49} +(-2.09218 + 8.65910i) q^{50} +(3.18333 - 1.83790i) q^{52} +(8.58394 - 4.95594i) q^{53} +(-4.61504 - 0.549626i) q^{55} +(1.60939 - 3.54393i) q^{56} +(6.19294 + 3.57549i) q^{58} +(-1.47797 - 2.55992i) q^{59} +(5.44729 - 9.43499i) q^{61} +5.18797i q^{62} +0.593684 q^{64} +(-5.60526 - 4.19199i) q^{65} +(3.32501 - 1.91970i) q^{67} +(2.16637 + 1.25075i) q^{68} +(10.5380 + 0.223633i) q^{70} +15.0248 q^{71} +(7.40771 - 4.27684i) q^{73} +(3.13142 + 5.42378i) q^{74} -9.08617 q^{76} +(0.534324 + 5.47316i) q^{77} +(4.05677 - 7.02653i) q^{79} +(-4.37914 - 10.2132i) q^{80} +(12.3288 + 7.11804i) q^{82} -8.75128i q^{83} +(0.563307 - 4.72992i) q^{85} +(4.44556 - 7.69994i) q^{86} +(2.64808 - 1.52887i) q^{88} +(-0.309330 + 0.535776i) q^{89} +(-3.42443 + 7.54067i) q^{91} -6.50151i q^{92} +(-2.17429 - 3.76598i) q^{94} +(6.81823 + 15.9017i) q^{95} -0.296842i q^{97} +(-2.41212 - 12.2361i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) $ 16 * q + 8 * q^4 - 2 * q^5	$ 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.54296	−	0.890827i	−1.09104	−	0.629910i	−0.157184	−	0.987569i	$-0.550241\pi$
$2$	−1.54296	−	0.890827i	−1.09104	−	0.629910i	−0.933852	+	0.357660i	$0.883575\pi$
$3$		0			0
$3$		0			0
$4$	0.587145	+	1.01696i	0.293572	+	0.508482i
$5$	1.33920	−	1.79069i	0.598906	−	0.800819i
$5$	1.33920	−	1.79069i	0.598906	−	0.800819i
$6$		0			0
$7$	−2.40898	−	1.09398i	−0.910510	−	0.413487i
$7$	−2.40898	−	1.09398i	−0.910510	−	0.413487i
$8$			1.47113i			0.520123i
$9$		0			0
$10$	−3.66151	+	1.56996i	−1.15787	+	0.496465i
$11$	−1.03925	−	1.80003i	−0.313345	−	0.542729i	0.665739	−	0.746184i	$-0.268116\pi$
$11$	−1.03925	−	1.80003i	−0.313345	−	0.542729i	−0.979084	+	0.203455i	$0.934783\pi$
$12$		0			0
$13$		−	3.13023i		−	0.868170i	−0.900872	−	0.434085i	$-0.857072\pi$
$13$		−	3.13023i		−	0.868170i	0.900872	−	0.434085i	$-0.142928\pi$
$14$	2.74241	+	3.83396i	0.732939	+	1.02467i
$15$		0			0
$16$	2.48481	−	4.30382i	0.621203	−	1.07596i
$17$	1.84483	−	1.06512i	0.447438	−	0.258329i	−0.259310	−	0.965794i	$-0.583495\pi$
$17$	1.84483	−	1.06512i	0.447438	−	0.258329i	0.706748	+	0.707466i	$0.250162\pi$
$18$		0			0
$19$	−3.86880	+	6.70095i	−0.887563	+	1.53730i	−0.0448157	+	0.998995i	$0.514270\pi$
$19$	−3.86880	+	6.70095i	−0.887563	+	1.53730i	−0.842747	+	0.538309i	$0.819063\pi$
$20$	2.60736	+	0.310523i	0.583024	+	0.0694350i
$21$		0			0
$22$			3.70316i			0.789516i
$23$	−4.79479	−	2.76827i	−0.999783	−	0.577225i	−0.0915990	−	0.995796i	$-0.529198\pi$
$23$	−4.79479	−	2.76827i	−0.999783	−	0.577225i	−0.908184	+	0.418571i	$0.862531\pi$
$24$		0			0
$25$	−1.41311	−	4.79616i	−0.282622	−	0.959231i
$26$	−2.78849	+	4.82981i	−0.546869	+	0.947204i
$27$		0			0
$28$	−0.301877	−	3.09218i	−0.0570495	−	0.584366i
$29$	−4.01368			−0.745322			−0.372661	−	0.927968i	$-0.621555\pi$
$29$	−4.01368			−0.745322			−0.372661	+	0.927968i	$0.621555\pi$
$30$		0			0
$31$	−1.45594	−	2.52177i	−0.261495	−	0.452923i	0.705144	−	0.709064i	$-0.250882\pi$
$31$	−1.45594	−	2.52177i	−0.261495	−	0.452923i	−0.966639	+	0.256141i	$0.917549\pi$
$32$	−5.11984	+	2.95594i	−0.905069	+	0.522542i
$33$		0			0
$34$	−3.79533			−0.650894
$35$	−5.18508	+	2.84867i	−0.876439	+	0.481513i
$36$		0			0
$37$	−3.04424	−	1.75759i	−0.500470	−	0.288947i	0.228437	−	0.973559i	$-0.426638\pi$
$37$	−3.04424	−	1.75759i	−0.500470	−	0.288947i	−0.728908	+	0.684612i	$0.759972\pi$
$38$	11.9388	−	6.89286i	1.93673	−	1.11817i
$39$		0			0
$40$	2.63433	+	1.97013i	0.416525	+	0.311505i
$41$	−7.99038			−1.24789			−0.623944	−	0.781469i	$-0.714471\pi$
$41$	−7.99038			−1.24789			−0.623944	+	0.781469i	$0.714471\pi$
$42$		0			0
$43$			4.99038i			0.761026i	0.924776	+	0.380513i	$0.124253\pi$
$43$			4.99038i			0.761026i	−0.924776	+	0.380513i	$0.875747\pi$
$44$	1.22038	−	2.11376i	0.183979	−	0.318661i
$45$		0			0
$46$	4.93210	+	8.54266i	0.727199	+	1.25955i
$47$	2.11376	+	1.22038i	0.308323	+	0.178010i	0.646176	−	0.763189i	$-0.276367\pi$
$47$	2.11376	+	1.22038i	0.308323	+	0.178010i	−0.337853	+	0.941199i	$0.609701\pi$
$48$		0			0
$49$	4.60639	+	5.27078i	0.658056	+	0.752969i
$50$	−2.09218	+	8.65910i	−0.295878	+	1.22458i
$51$		0			0
$52$	3.18333	−	1.83790i	0.441449	−	0.254871i
$53$	8.58394	−	4.95594i	1.17910	−	0.680751i	0.223290	−	0.974752i	$-0.428320\pi$
$53$	8.58394	−	4.95594i	1.17910	−	0.680751i	0.955805	+	0.294001i	$0.0949869\pi$
$54$		0			0
$55$	−4.61504	−	0.549626i	−0.622292	−	0.0741116i
$56$	1.60939	−	3.54393i	0.215064	−	0.473577i
$57$		0			0
$58$	6.19294	+	3.57549i	0.813173	+	0.469485i
$59$	−1.47797	−	2.55992i	−0.192415	−	0.333273i	0.753635	−	0.657293i	$-0.228299\pi$
$59$	−1.47797	−	2.55992i	−0.192415	−	0.333273i	−0.946050	+	0.324020i	$0.894965\pi$
$60$		0			0
$61$	5.44729	−	9.43499i	0.697454	−	1.20803i	−0.271892	−	0.962328i	$-0.587649\pi$
$61$	5.44729	−	9.43499i	0.697454	−	1.20803i	0.969346	−	0.245699i	$-0.0790174\pi$
$62$			5.18797i			0.658873i
$63$		0			0
$64$	0.593684			0.0742104
$65$	−5.60526	−	4.19199i	−0.695247	−	0.519953i
$66$		0			0
$67$	3.32501	−	1.91970i	0.406215	−	0.234528i	−0.282947	−	0.959135i	$-0.591312\pi$
$67$	3.32501	−	1.91970i	0.406215	−	0.234528i	0.689162	+	0.724607i	$0.257979\pi$
$68$	2.16637	+	1.25075i	0.262711	+	0.151676i
$69$		0			0
$70$	10.5380	+	0.223633i	1.25954	+	0.0267292i
$71$	15.0248			1.78312			0.891559	−	0.452905i	$-0.149612\pi$
$71$	15.0248			1.78312			0.891559	+	0.452905i	$0.149612\pi$
$72$		0			0
$73$	7.40771	−	4.27684i	0.867007	−	0.500567i	0.000654464	−	1.00000i	$-0.499792\pi$
$73$	7.40771	−	4.27684i	0.867007	−	0.500567i	0.866352	+	0.499433i	$0.166458\pi$
$74$	3.13142	+	5.42378i	0.364021	+	0.630502i
$75$		0			0
$76$	−9.08617			−1.04226
$77$	0.534324	+	5.47316i	0.0608919	+	0.623725i
$78$		0			0
$79$	4.05677	−	7.02653i	0.456422	−	0.790546i	−0.542347	−	0.840155i	$-0.682464\pi$
$79$	4.05677	−	7.02653i	0.456422	−	0.790546i	0.998769	+	0.0496086i	$0.0157974\pi$
$80$	−4.37914	−	10.2132i	−0.489603	−	1.14187i
$81$		0			0
$82$	12.3288	+	7.11804i	1.36149	+	0.786056i
$83$		−	8.75128i		−	0.960577i	−0.877110	−	0.480289i	$-0.840532\pi$
$83$		−	8.75128i		−	0.960577i	0.877110	−	0.480289i	$-0.159468\pi$
$84$		0			0
$85$	0.563307	−	4.72992i	0.0610992	−	0.513032i
$86$	4.44556	−	7.69994i	0.479377	−	0.830306i
$87$		0			0
$88$	2.64808	−	1.52887i	0.282286	−	0.162978i
$89$	−0.309330	+	0.535776i	−0.0327890	+	0.0567921i	−0.881954	−	0.471335i	$-0.843772\pi$
$89$	−0.309330	+	0.535776i	−0.0327890	+	0.0567921i	0.849165	+	0.528127i	$0.177106\pi$
$90$		0			0
$91$	−3.42443	+	7.54067i	−0.358977	+	0.790477i
$92$		−	6.50151i		−	0.677829i
$93$		0			0
$94$	−2.17429	−	3.76598i	−0.224261	−	0.388431i
$95$	6.81823	+	15.9017i	0.699535	+	1.63148i
$96$		0			0
$97$		−	0.296842i		−	0.0301397i	−0.999886	−	0.0150699i	$-0.995203\pi$
$97$		−	0.296842i		−	0.0301397i	0.999886	−	0.0150699i	$-0.00479707\pi$
$98$	−2.41212	−	12.2361i	−0.243660	−	1.23603i
$99$		0			0
$100$	4.04782	−	4.25312i	0.404782	−	0.425312i
$101$	4.12939	+	7.15232i	0.410890	+	0.711682i	0.994987	−	0.100001i	$-0.0318847\pi$
$101$	4.12939	+	7.15232i	0.410890	+	0.711682i	−0.584097	+	0.811684i	$0.698551\pi$
$102$		0			0
$103$	−14.7974	−	8.54331i	−1.45804	−	0.841797i	−0.459121	−	0.888374i	$-0.651836\pi$
$103$	−14.7974	−	8.54331i	−1.45804	−	0.841797i	−0.998915	+	0.0465766i	$0.985169\pi$
$104$	4.60498			0.451555
$105$		0			0
$106$	−17.6595			−1.71525
$107$	5.46507	+	3.15526i	0.528329	+	0.305031i	0.740336	−	0.672238i	$-0.234667\pi$
$107$	5.46507	+	3.15526i	0.528329	+	0.305031i	−0.212007	+	0.977268i	$0.568000\pi$
$108$		0			0
$109$	1.22338	+	2.11895i	0.117178	+	0.202959i	0.918648	−	0.395076i	$-0.129282\pi$
$109$	1.22338	+	2.11895i	0.117178	+	0.202959i	−0.801470	+	0.598035i	$0.795948\pi$
$110$	6.63119	+	4.95925i	0.632259	+	0.472846i
$111$		0			0
$112$	−10.6942	+	7.64948i	−1.01051	+	0.722808i
$113$			10.1570i			0.955489i	0.878499	+	0.477745i	$0.158546\pi$
$113$			10.1570i			0.955489i	−0.878499	+	0.477745i	$0.841454\pi$
$114$		0			0
$115$	−11.3783	+	4.87870i	−1.06103	+	0.454941i
$116$	−2.35661	−	4.08177i	−0.218806	−	0.378983i
$117$		0			0
$118$			5.26647i			0.484817i
$119$	−5.60939	+	0.547624i	−0.514212	+	0.0502006i
$120$		0			0
$121$	3.33993	−	5.78493i	0.303630	−	0.525902i
$122$	−16.8099	+	9.70519i	−1.52190	+	0.878667i
$123$		0			0
$124$	1.70970	−	2.96128i	0.153535	−	0.265931i
$125$	−10.4808	−	3.89256i	−0.937435	−	0.348161i
$126$		0			0
$127$			8.86977i			0.787065i	0.919311	+	0.393532i	$0.128747\pi$
$127$			8.86977i			0.787065i	−0.919311	+	0.393532i	$0.871253\pi$
$128$	9.32366	+	5.38302i	0.824103	+	0.475796i
$129$		0			0
$130$	4.91434	+	11.4614i	0.431016	+	1.00523i
$131$	2.67075	−	4.62588i	0.233345	−	0.404165i	−0.725446	−	0.688279i	$-0.758366\pi$
$131$	2.67075	−	4.62588i	0.233345	−	0.404165i	0.958790	+	0.284115i	$0.0916997\pi$
$132$		0			0
$133$	16.6506	−	11.9101i	1.44379	−	1.03273i
$134$	−6.84047			−0.590926
$135$		0			0
$136$	1.56692	+	2.71399i	0.134363	+	0.232723i
$137$	11.3483	−	6.55196i	0.969553	−	0.559772i	0.0704529	−	0.997515i	$-0.477556\pi$
$137$	11.3483	−	6.55196i	0.969553	−	0.559772i	0.899100	+	0.437744i	$0.144222\pi$
$138$		0			0
$139$	−0.243164			−0.0206249			−0.0103125	−	0.999947i	$-0.503283\pi$
$139$	−0.243164			−0.0206249			−0.0103125	+	0.999947i	$0.503283\pi$
$140$	−5.94139	−	3.60046i	−0.502139	−	0.304294i
$141$		0			0
$142$	−23.1827	−	13.3845i	−1.94544	−	1.12320i
$143$	−5.63451	+	3.25309i	−0.471181	+	0.272037i
$144$		0			0
$145$	−5.37510	+	7.18724i	−0.446378	+	0.596868i
$146$	−15.2397			−1.26125
$147$		0			0
$148$		−	4.12785i		−	0.339307i
$149$	−1.16864	+	2.02415i	−0.0957388	+	0.165824i	−0.909917	−	0.414791i	$-0.863855\pi$
$149$	−1.16864	+	2.02415i	−0.0957388	+	0.165824i	0.814178	+	0.580615i	$0.197188\pi$
$150$		0			0
$151$	5.55677	+	9.62460i	0.452203	+	0.783239i	0.998523	−	0.0543378i	$-0.0173048\pi$
$151$	5.55677	+	9.62460i	0.452203	+	0.783239i	−0.546319	+	0.837577i	$0.683971\pi$
$152$	−9.85798	−	5.69151i	−0.799588	−	0.461642i
$153$		0			0
$154$	4.05120	−	8.92084i	0.326455	−	0.718862i
$155$	−6.46548	−	0.770003i	−0.519320	−	0.0618481i
$156$		0			0
$157$	9.80185	−	5.65910i	0.782273	−	0.451645i	−0.0549624	−	0.998488i	$-0.517504\pi$
$157$	9.80185	−	5.65910i	0.782273	−	0.451645i	0.837235	+	0.546843i	$0.184171\pi$
$158$	−12.5188	+	7.22775i	−0.995945	+	0.575009i
$159$		0			0
$160$	−1.56331	+	13.1266i	−0.123590	+	1.03775i
$161$	8.52212	+	11.9142i	0.671637	+	0.938967i
$162$		0			0
$163$	−1.82166	−	1.05174i	−0.142683	−	0.0823783i	0.426959	−	0.904271i	$-0.359585\pi$
$163$	−1.82166	−	1.05174i	−0.142683	−	0.0823783i	−0.569642	+	0.821893i	$0.692918\pi$
$164$	−4.69151	−	8.12593i	−0.366345	−	0.634529i
$165$		0			0
$166$	−7.79587	+	13.5028i	−0.605077	+	1.04802i
$167$			3.58600i			0.277493i	0.990328	+	0.138747i	$0.0443074\pi$
$167$			3.58600i			0.277493i	−0.990328	+	0.138747i	$0.955693\pi$
$168$		0			0
$169$	3.20165			0.246281
$170$	−5.08270	+	6.79625i	−0.389825	+	0.521249i
$171$		0			0
$172$	−5.07504	+	2.93007i	−0.386968	+	0.223416i
$173$	−13.4580	−	7.77000i	−1.02320	−	0.590742i	−0.108168	−	0.994133i	$-0.534498\pi$
$173$	−13.4580	−	7.77000i	−1.02320	−	0.590742i	−0.915028	+	0.403390i	$0.867832\pi$
$174$		0			0
$175$	−1.84277	+	13.0998i	−0.139300	+	0.990250i
$176$	−10.3293			−0.778603
$177$		0			0
$178$	0.954567	−	0.551120i	0.0715478	−	0.0413082i
$179$	−7.86783	−	13.6275i	−0.588069	−	1.01857i	−0.994485	−	0.104877i	$-0.966555\pi$
$179$	−7.86783	−	13.6275i	−0.588069	−	1.01857i	0.406416	−	0.913688i	$-0.366778\pi$
$180$		0			0
$181$	−4.98692			−0.370675			−0.185337	−	0.982675i	$-0.559338\pi$
$181$	−4.98692			−0.370675			−0.185337	+	0.982675i	$0.559338\pi$
$182$	12.0012	−	8.58437i	0.889586	−	0.636315i
$183$		0			0
$184$	4.07249	−	7.05376i	0.300228	−	0.520010i
$185$	−7.22413	+	3.09752i	−0.531129	+	0.227734i
$186$		0			0
$187$	−3.83448	−	2.21384i	−0.280405	−	0.161892i
$188$			2.86615i			0.209036i
$189$		0			0
$190$	3.64542	−	30.6095i	0.264467	−	2.22065i
$191$	5.90421	−	10.2264i	0.427213	−	0.739955i	−0.569411	−	0.822053i	$-0.692829\pi$
$191$	5.90421	−	10.2264i	0.427213	−	0.739955i	0.996624	+	0.0820978i	$0.0261620\pi$
$192$		0			0
$193$	−21.4238	+	12.3690i	−1.54212	+	0.890342i	−0.543412	+	0.839466i	$0.682868\pi$
$193$	−21.4238	+	12.3690i	−1.54212	+	0.890342i	−0.998705	+	0.0508752i	$0.983799\pi$
$194$	−0.264435	+	0.458014i	−0.0189853	+	0.0328835i
$195$		0			0
$196$	−2.65558	+	7.77925i	−0.189684	+	0.555661i
$197$		−	19.5526i		−	1.39307i	−0.717525	−	0.696533i	$-0.754725\pi$
$197$		−	19.5526i		−	1.39307i	0.717525	−	0.696533i	$-0.245275\pi$
$198$		0			0
$199$	−11.1201	−	19.2605i	−0.788281	−	1.36534i	−0.927019	−	0.375014i	$-0.877638\pi$
$199$	−11.1201	−	19.2605i	−0.788281	−	1.36534i	0.138738	−	0.990329i	$-0.455695\pi$
$200$	7.05577	−	2.07887i	0.498919	−	0.146998i
$201$		0			0
$202$		−	14.7143i		−	1.03529i
$203$	9.66889	+	4.39091i	0.678623	+	0.308181i
$204$		0			0
$205$	−10.7007	+	14.3083i	−0.747368	+	0.999332i
$206$	15.2212	+	26.3639i	1.06051	+	1.83686i
$207$		0			0
$208$	−13.4720	−	7.77804i	−0.934112	−	0.539310i
$209$	16.0826			1.11245
$210$		0			0
$211$	23.6191			1.62601			0.813003	−	0.582259i	$-0.197831\pi$
$211$	23.6191			1.62601			0.813003	+	0.582259i	$0.197831\pi$
$212$	10.0800	+	5.81971i	0.692299	+	0.399699i
$213$		0			0
$214$	−5.62158	−	9.73687i	−0.384283	−	0.665598i
$215$	8.93620	+	6.68310i	0.609444	+	0.455783i
$216$		0			0
$217$	0.748566	+	7.66767i	0.0508159	+	0.520515i
$218$		−	4.35927i		−	0.295247i
$219$		0			0
$220$	−2.15075	−	5.01604i	−0.145003	−	0.338182i
$221$	−3.33406	−	5.77476i	−0.224273	−	0.388452i
$222$		0			0
$223$			25.1420i			1.68363i	0.539765	+	0.841815i	$0.318513\pi$
$223$			25.1420i			1.68363i	−0.539765	+	0.841815i	$0.681487\pi$
$224$	15.5674	−	1.51978i	1.04014	−	0.101545i
$225$		0			0
$226$	9.04812	−	15.6718i	0.601872	−	1.04247i
$227$	−20.4990	+	11.8351i	−1.36057	+	0.785524i	−0.989699	−	0.143161i	$-0.954273\pi$
$227$	−20.4990	+	11.8351i	−1.36057	+	0.785524i	−0.370869	+	0.928685i	$0.620940\pi$
$228$		0			0
$229$	0.203158	−	0.351880i	0.0134251	−	0.0232529i	−0.859235	−	0.511581i	$-0.829060\pi$
$229$	0.203158	−	0.351880i	0.0134251	−	0.0232529i	0.872660	+	0.488328i	$0.162393\pi$
$230$	21.9023	+	2.60844i	1.44419	+	0.171995i
$231$		0			0
$232$		−	5.90465i		−	0.387659i
$233$	6.20531	+	3.58264i	0.406523	+	0.234706i	0.689295	−	0.724481i	$-0.257920\pi$
$233$	6.20531	+	3.58264i	0.406523	+	0.234706i	−0.282772	+	0.959187i	$0.591254\pi$
$234$		0			0
$235$	5.01604	−	2.15075i	0.327211	−	0.140299i
$236$	1.73557	−	3.00609i	0.112976	−	0.195680i
$237$		0			0
$238$	9.14289	+	4.15204i	0.592646	+	0.269137i
$239$	10.0922			0.652809			0.326404	−	0.945230i	$-0.394163\pi$
$239$	10.0922			0.652809			0.326404	+	0.945230i	$0.394163\pi$
$240$		0			0
$241$	2.30338	+	3.98957i	0.148374	+	0.256991i	0.930627	−	0.365970i	$-0.119263\pi$
$241$	2.30338	+	3.98957i	0.148374	+	0.256991i	−0.782253	+	0.622961i	$0.785929\pi$
$242$	−10.3067	+	5.95060i	−0.662542	+	0.382519i
$243$		0			0
$244$	12.7934			0.819013
$245$	15.6072	−	1.19000i	0.997106	−	0.0760261i
$246$		0			0
$247$	20.9755	+	12.1102i	1.33464	+	0.770556i
$248$	3.70985	−	2.14188i	0.235576	−	0.136010i
$249$		0			0
$250$	12.7039	+	15.3427i	0.803465	+	0.970355i
$251$	0.311597			0.0196678			0.00983390	−	0.999952i	$-0.496870\pi$
$251$	0.311597			0.0196678			0.00983390	+	0.999952i	$0.496870\pi$
$252$		0			0
$253$			11.5077i			0.723482i
$254$	7.90143	−	13.6857i	0.495780	−	0.858715i
$255$		0			0
$256$	−10.1844	−	17.6398i	−0.636522	−	1.10249i
$257$	−2.16689	−	1.25106i	−0.135167	−	0.0780387i	0.430892	−	0.902404i	$-0.358199\pi$
$257$	−2.16689	−	1.25106i	−0.135167	−	0.0780387i	−0.566059	+	0.824365i	$0.691532\pi$
$258$		0			0
$259$	5.41075	+	7.56437i	0.336207	+	0.470027i
$260$	0.972008	−	8.16165i	0.0602814	−	0.506164i
$261$		0			0
$262$	−8.24171	+	4.75835i	−0.509174	+	0.293972i
$263$	−4.00546	+	2.31255i	−0.246987	+	0.142598i	−0.618384	−	0.785876i	$-0.712212\pi$
$263$	−4.00546	+	2.31255i	−0.246987	+	0.142598i	0.371397	+	0.928474i	$0.378879\pi$
$264$		0			0
$265$	2.62105	−	22.0081i	0.161010	−	1.35195i
$266$	−36.3010	+	3.54393i	−2.22576	+	0.217292i
$267$		0			0
$268$	3.90452	+	2.25428i	0.238507	+	0.137702i
$269$	−6.01165	−	10.4125i	−0.366537	−	0.634860i	0.622485	−	0.782632i	$-0.286123\pi$
$269$	−6.01165	−	10.4125i	−0.366537	−	0.634860i	−0.989022	+	0.147772i	$0.952790\pi$
$270$		0			0
$271$	2.73467	−	4.73660i	0.166120	−	0.287728i	−0.770933	−	0.636917i	$-0.780210\pi$
$271$	2.73467	−	4.73660i	0.166120	−	0.287728i	0.937052	+	0.349189i	$0.113543\pi$
$272$		−	10.5864i		−	0.641898i
$273$		0			0
$274$	−23.3466			−1.41042
$275$	−7.16465	+	7.52803i	−0.432045	+	0.453958i
$276$		0			0
$277$	25.8162	−	14.9050i	1.55114	−	0.895553i	0.553093	−	0.833119i	$-0.313447\pi$
$277$	25.8162	−	14.9050i	1.55114	−	0.895553i	0.998049	−	0.0624333i	$-0.0198861\pi$
$278$	0.375192	+	0.216617i	0.0225025	+	0.0129918i
$279$		0			0
$280$	−4.19077	−	7.62793i	−0.250446	−	0.455856i
$281$	−7.78511			−0.464421			−0.232210	−	0.972666i	$-0.574596\pi$
$281$	−7.78511			−0.464421			−0.232210	+	0.972666i	$0.574596\pi$
$282$		0			0
$283$	2.26417	−	1.30722i	0.134591	−	0.0777062i	−0.431193	−	0.902260i	$-0.641907\pi$
$283$	2.26417	−	1.30722i	0.134591	−	0.0777062i	0.565784	+	0.824554i	$0.308574\pi$
$284$	8.82174	+	15.2797i	0.523474	+	0.906683i
$285$		0			0
$286$	11.5917			0.685434
$287$	19.2487	+	8.74136i	1.13621	+	0.515986i
$288$		0			0
$289$	−6.23106	+	10.7925i	−0.366533	+	0.634853i
$290$	14.6961	−	6.30132i	0.862987	−	0.370026i
$291$		0			0
$292$	8.69879	+	5.02225i	0.509058	+	0.293905i
$293$			12.7559i			0.745210i	0.927990	+	0.372605i	$0.121535\pi$
$293$			12.7559i			0.745210i	−0.927990	+	0.372605i	$0.878465\pi$
$294$		0			0
$295$	−6.56331	−	0.781653i	−0.382131	−	0.0455096i
$296$	2.58565	−	4.47848i	0.150288	−	0.260306i
$297$		0			0
$298$	3.60633	−	2.08211i	0.208909	−	0.120614i
$299$	−8.66534	+	15.0088i	−0.501129	+	0.867982i
$300$		0			0
$301$	5.45940	−	12.0217i	0.314675	−	0.692922i
$302$		−	19.8005i		−	1.13939i
$303$		0			0
$304$	19.2265	+	33.3012i	1.10271	+	1.90996i
$305$	−9.60011	−	22.3897i	−0.549701	−	1.28203i
$306$		0			0
$307$			13.1919i			0.752900i	0.926437	+	0.376450i	$0.122855\pi$
$307$			13.1919i			0.752900i	−0.926437	+	0.376450i	$0.877145\pi$
$308$	−5.25228	+	3.75693i	−0.299277	+	0.214071i
$309$		0			0
$310$	9.29002	+	6.94771i	0.527638	+	0.394603i
$311$	−7.14113	−	12.3688i	−0.404937	−	0.701371i	0.589378	−	0.807858i	$-0.299373\pi$
$311$	−7.14113	−	12.3688i	−0.404937	−	0.701371i	−0.994314	+	0.106487i	$0.966040\pi$
$312$		0			0
$313$	−4.13218	−	2.38572i	−0.233565	−	0.134849i	0.378651	−	0.925540i	$-0.376388\pi$
$313$	−4.13218	−	2.38572i	−0.233565	−	0.134849i	−0.612215	+	0.790691i	$0.709721\pi$
$314$	−20.1651			−1.13798
$315$		0			0
$316$	9.52764			0.535971
$317$	16.2854	+	9.40240i	0.914681	+	0.528091i	0.881934	−	0.471372i	$-0.156241\pi$
$317$	16.2854	+	9.40240i	0.914681	+	0.528091i	0.0327466	+	0.999464i	$0.489575\pi$
$318$		0			0
$319$	4.17121	+	7.22474i	0.233543	+	0.404508i
$320$	0.795058	−	1.06310i	0.0444451	−	0.0594291i
$321$		0			0
$322$	−2.53582	−	25.9748i	−0.141316	−	1.44752i
$323$			16.4829i			0.917131i
$324$		0			0
$325$	−15.0131	+	4.42336i	−0.832776	+	0.245364i
$326$	1.87383	+	3.24557i	0.103782	+	0.179755i
$327$		0			0
$328$		−	11.7549i		−	0.649055i
$329$	−3.75693	−	5.25228i	−0.207126	−	0.289568i
$330$		0			0
$331$	−8.88708	+	15.3929i	−0.488478	+	0.846069i	−0.999912	−	0.0132538i	$-0.995781\pi$
$331$	−8.88708	+	15.3929i	−0.488478	+	0.846069i	0.511434	+	0.859322i	$0.329114\pi$
$332$	8.89973	−	5.13826i	0.488436	−	0.281999i
$333$		0			0
$334$	3.19451	−	5.53305i	0.174796	−	0.302755i
$335$	1.01527	−	8.52490i	0.0554700	−	0.465765i
$336$		0			0
$337$		−	3.86675i		−	0.210635i	−0.994439	−	0.105318i	$-0.966414\pi$
$337$		−	3.86675i		−	0.210635i	0.994439	−	0.105318i	$-0.0335860\pi$
$338$	−4.94001	−	2.85212i	−0.268701	−	0.155135i
$339$		0			0
$340$	5.14090	−	2.20428i	0.278804	−	0.119544i
$341$	−3.02617	+	5.24148i	−0.163876	+	0.283842i
$342$		0			0
$343$	−5.33057	−	17.7365i	−0.287824	−	0.957683i
$344$	−7.34150			−0.395827
$345$		0			0
$346$	13.8435	+	23.9776i	0.744229	+	1.28904i
$347$	8.89622	−	5.13623i	0.477574	−	0.275727i	−0.241831	−	0.970318i	$-0.577748\pi$
$347$	8.89622	−	5.13623i	0.477574	−	0.275727i	0.719405	+	0.694591i	$0.244415\pi$
$348$		0			0
$349$	−23.6180			−1.26424			−0.632122	−	0.774869i	$-0.717816\pi$
$349$	−23.6180			−1.26424			−0.632122	+	0.774869i	$0.717816\pi$
$350$	14.5129	−	18.5708i	0.775749	−	0.992652i
$351$		0			0
$352$	10.6416	+	6.14391i	0.567197	+	0.327472i
$353$	−5.00354	+	2.88880i	−0.266312	+	0.153755i	−0.627210	−	0.778850i	$-0.715803\pi$
$353$	−5.00354	+	2.88880i	−0.266312	+	0.153755i	0.360899	+	0.932605i	$0.382470\pi$
$354$		0			0
$355$	20.1212	−	26.9047i	1.06792	−	1.42795i
$356$	−0.726487			−0.0385037
$357$		0			0
$358$			28.0355i			1.48172i
$359$	−15.6527	+	27.1113i	−0.826118	+	1.43088i	0.0749437	+	0.997188i	$0.476122\pi$
$359$	−15.6527	+	27.1113i	−0.826118	+	1.43088i	−0.901062	+	0.433691i	$0.857211\pi$
$360$		0			0
$361$	−20.4352	−	35.3948i	−1.07554	−	1.86288i
$362$	7.69461	+	4.44248i	0.404420	+	0.233492i
$363$		0			0
$364$	−9.67923	+	0.944946i	−0.507329	+	0.0495286i
$365$	2.26189	−	18.9924i	0.118393	−	0.994108i
$366$		0			0
$367$	−14.3344	+	8.27595i	−0.748248	+	0.432001i	−0.825061	−	0.565044i	$-0.808859\pi$
$367$	−14.3344	+	8.27595i	−0.748248	+	0.432001i	0.0768125	+	0.997046i	$0.475526\pi$
$368$	−23.8283	+	13.7573i	−1.24214	+	0.717148i
$369$		0			0
$370$	13.9059	+	1.65611i	0.722932	+	0.0860972i
$371$	−26.1003	+	2.54807i	−1.35506	+	0.132289i
$372$		0			0
$373$	27.8363	+	16.0713i	1.44131	+	0.832140i	0.997937	−	0.0641985i	$-0.0204491\pi$
$373$	27.8363	+	16.0713i	1.44131	+	0.832140i	0.443371	+	0.896338i	$0.353782\pi$
$374$	3.94429	+	6.83171i	0.203954	+	0.353260i
$375$		0			0
$376$	−1.79533	+	3.10961i	−0.0925873	+	0.160366i
$377$			12.5638i			0.647066i
$378$		0			0
$379$	4.98800			0.256216			0.128108	−	0.991760i	$-0.459110\pi$
$379$	4.98800			0.256216			0.128108	+	0.991760i	$0.459110\pi$
$380$	−12.1682	+	16.2705i	−0.624214	+	0.834658i
$381$		0			0
$382$	−18.2199	+	10.5192i	−0.932210	+	0.538212i
$383$	−22.9123	−	13.2284i	−1.17076	−	0.675940i	−0.216903	−	0.976193i	$-0.569596\pi$
$383$	−22.9123	−	13.2284i	−1.17076	−	0.675940i	−0.953860	+	0.300253i	$0.902929\pi$
$384$		0			0
$385$	10.5163	+	6.37283i	0.535959	+	0.324789i
$386$	44.0746			2.24334
$387$		0			0
$388$	0.301877	−	0.174289i	0.0153255	−	0.00884818i
$389$	6.38580	+	11.0605i	0.323773	+	0.560791i	0.981263	−	0.192672i	$-0.0617154\pi$
$389$	6.38580	+	11.0605i	0.323773	+	0.560791i	−0.657491	+	0.753463i	$0.728382\pi$
$390$		0			0
$391$	−11.7941			−0.596455
$392$	−7.75401	+	6.77661i	−0.391637	+	0.342270i
$393$		0			0
$394$	−17.4180	+	30.1688i	−0.877506	+	1.51988i
$395$	−7.14950	−	16.6743i	−0.359730	−	0.838975i
$396$		0			0
$397$	13.0954	+	7.56061i	0.657237	+	0.379456i	0.791223	−	0.611527i	$-0.209444\pi$
$397$	13.0954	+	7.56061i	0.657237	+	0.379456i	−0.133986	+	0.990983i	$0.542778\pi$
$398$			39.6242i			1.98618i
$399$		0			0
$400$	−24.1531	−	5.83577i	−1.20766	−	0.291789i
$401$	6.18029	−	10.7046i	0.308629	−	0.534561i	−0.669434	−	0.742872i	$-0.733463\pi$
$401$	6.18029	−	10.7046i	0.308629	−	0.534561i	0.978063	+	0.208311i	$0.0667965\pi$
$402$		0			0
$403$	−7.89371	+	4.55744i	−0.393214	+	0.227022i
$404$	−4.84910	+	8.39889i	−0.241252	+	0.417860i
$405$		0			0
$406$	−11.0071	−	15.3883i	−0.546275	−	0.763708i
$407$			7.30630i			0.362160i
$408$		0			0
$409$	−5.26435	−	9.11813i	−0.260306	−	0.450863i	0.706017	−	0.708194i	$-0.250490\pi$
$409$	−5.26435	−	9.11813i	−0.260306	−	0.450863i	−0.966323	+	0.257332i	$0.917157\pi$
$410$	29.2569	−	12.5446i	1.44489	−	0.619533i
$411$		0			0
$412$		−	20.0646i		−	0.988513i
$413$	0.759892	+	7.78368i	0.0373918	+	0.383010i
$414$		0			0
$415$	−15.6708	−	11.7197i	−0.769249	−	0.575296i
$416$	9.25278	+	16.0263i	0.453655	+	0.785754i
$417$		0			0
$418$	−24.8147	−	14.3268i	−1.21373	−	0.700745i
$419$	13.3110			0.650283			0.325142	−	0.945665i	$-0.394588\pi$
$419$	13.3110			0.650283			0.325142	+	0.945665i	$0.394588\pi$
$420$		0			0
$421$	19.1520			0.933413			0.466707	−	0.884412i	$-0.345440\pi$
$421$	19.1520			0.933413			0.466707	+	0.884412i	$0.345440\pi$
$422$	−36.4433	−	21.0405i	−1.77403	−	1.02424i
$423$		0			0
$424$	7.29084	+	12.6281i	0.354074	+	0.613275i
$425$	−7.71542	−	7.34299i	−0.374253	−	0.356187i
$426$		0			0
$427$	−23.4442	+	16.7695i	−1.13454	+	0.811531i
$428$			7.41038i			0.358194i
$429$		0			0
$430$	−7.83470	−	18.2723i	−0.377823	−	0.881170i
$431$	5.44818	+	9.43653i	0.262430	+	0.454542i	0.966887	−	0.255205i	$-0.0821429\pi$
$431$	5.44818	+	9.43653i	0.262430	+	0.454542i	−0.704457	+	0.709746i	$0.748810\pi$
$432$		0			0
$433$		−	19.4869i		−	0.936482i	−0.883601	−	0.468241i	$-0.844888\pi$
$433$		−	19.4869i		−	0.936482i	0.883601	−	0.468241i	$-0.155112\pi$
$434$	5.67556	−	12.4977i	0.272436	−	0.599910i
$435$		0			0
$436$	−1.43660	+	2.48826i	−0.0688006	+	0.119166i
$437$	37.1002	−	21.4198i	1.77474	−	1.02465i
$438$		0			0
$439$	6.76549	−	11.7182i	0.322899	−	0.559278i	−0.658186	−	0.752856i	$-0.728676\pi$
$439$	6.76549	−	11.7182i	0.322899	−	0.559278i	0.981085	+	0.193578i	$0.0620091\pi$
$440$	0.808572	−	6.78933i	0.0385471	−	0.323669i
$441$		0			0
$442$			11.8803i			0.565087i
$443$	−24.9990	−	14.4332i	−1.18774	−	0.685740i	−0.229945	−	0.973204i	$-0.573855\pi$
$443$	−24.9990	−	14.4332i	−1.18774	−	0.685740i	−0.957792	+	0.287463i	$0.907188\pi$
$444$		0			0
$445$	0.545152	+	1.27142i	0.0258427	+	0.0602712i
$446$	22.3971	−	38.7930i	1.06054	−	1.83690i
$447$		0			0
$448$	−1.43017	−	0.649481i	−0.0675693	−	0.0306851i
$449$	23.4298			1.10572			0.552860	−	0.833274i	$-0.313536\pi$
$449$	23.4298			1.10572			0.552860	+	0.833274i	$0.313536\pi$
$450$		0			0
$451$	8.30398	+	14.3829i	0.391019	+	0.677265i
$452$	−10.3293	+	5.96362i	−0.485849	+	0.280505i
$453$		0			0
$454$	42.1722			1.97924
$455$	8.91700	+	16.2305i	0.418035	+	0.760898i
$456$		0			0
$457$	−26.2298	−	15.1438i	−1.22698	−	0.708396i	−0.260582	−	0.965452i	$-0.583914\pi$
$457$	−26.2298	−	15.1438i	−1.22698	−	0.708396i	−0.966397	+	0.257056i	$0.917248\pi$
$458$	−0.626929	+	0.361958i	−0.0292945	+	0.0169132i
$459$		0			0
$460$	−11.6422	−	8.70679i	−0.542818	−	0.405956i
$461$	7.02196			0.327045			0.163523	−	0.986540i	$-0.447714\pi$
$461$	7.02196			0.327045			0.163523	+	0.986540i	$0.447714\pi$
$462$		0			0
$463$		−	2.97324i		−	0.138178i	−0.997610	−	0.0690891i	$-0.977991\pi$
$463$		−	2.97324i		−	0.138178i	0.997610	−	0.0690891i	$-0.0220093\pi$
$464$	−9.97324	+	17.2742i	−0.462996	+	0.801933i
$465$		0			0
$466$	−6.38302	−	11.0557i	−0.295687	−	0.512146i
$467$	20.5723	+	11.8774i	0.951974	+	0.549623i	0.893694	−	0.448678i	$-0.148105\pi$
$467$	20.5723	+	11.8774i	0.951974	+	0.549623i	0.0582807	+	0.998300i	$0.481438\pi$
$468$		0			0
$469$	−10.1100	+	0.987002i	−0.466837	+	0.0455755i
$470$	−9.65548	−	1.14991i	−0.445374	−	0.0530416i
$471$		0			0
$472$	3.76598	−	2.17429i	0.173343	−	0.100080i
$473$	8.98283	−	5.18624i	0.413031	−	0.238464i
$474$		0			0
$475$	37.6059	+	9.08617i	1.72548	+	0.416902i
$476$	−3.85044	−	5.38302i	−0.176485	−	0.246730i
$477$		0			0
$478$	−15.5718	−	8.99038i	−0.712237	−	0.411210i
$479$	3.27211	+	5.66747i	0.149507	+	0.258953i	0.931045	−	0.364904i	$-0.118898\pi$
$479$	3.27211	+	5.66747i	0.149507	+	0.258953i	−0.781539	+	0.623857i	$0.785565\pi$
$480$		0			0
$481$	−5.50168	+	9.52918i	−0.250855	+	0.434493i
$482$		−	8.20765i		−	0.373848i
$483$		0			0
$484$	7.84408			0.356549
$485$	−0.531550	−	0.397529i	−0.0241365	−	0.0180509i
$486$		0			0
$487$	14.1395	−	8.16346i	0.640723	−	0.369922i	−0.144170	−	0.989553i	$-0.546051\pi$
$487$	14.1395	−	8.16346i	0.640723	−	0.369922i	0.784893	+	0.619631i	$0.212718\pi$
$488$	13.8801	+	8.01368i	0.628323	+	0.362762i
$489$		0			0
$490$	−25.1413	−	12.0672i	−1.13577	−	0.545139i
$491$	−24.9009			−1.12376			−0.561882	−	0.827218i	$-0.689922\pi$
$491$	−24.9009			−1.12376			−0.561882	+	0.827218i	$0.689922\pi$
$492$		0			0
$493$	−7.40458	+	4.27503i	−0.333485	+	0.192538i
$494$	−21.5762	−	37.3711i	−0.970761	−	1.68141i
$495$		0			0
$496$	−14.4710			−0.649766
$497$	−36.1945	−	16.4369i	−1.62355	−	0.737297i
$498$		0			0
$499$	−6.10197	+	10.5689i	−0.273161	+	0.473130i	−0.969670	−	0.244419i	$-0.921403\pi$
$499$	−6.10197	+	10.5689i	−0.273161	+	0.473130i	0.696508	+	0.717549i	$0.254736\pi$
$500$	−2.19518	−	12.9441i	−0.0981713	−	0.578879i
$501$		0			0
$502$	−0.480780	−	0.277579i	−0.0214583	−	0.0123889i
$503$		−	27.8165i		−	1.24028i	−0.784492	−	0.620139i	$-0.787076\pi$
$503$		−	27.8165i		−	1.24028i	0.784492	−	0.620139i	$-0.212924\pi$
$504$		0			0
$505$	18.3376	+	2.18391i	0.816013	+	0.0971827i
$506$	10.2514	−	17.7559i	0.455728	−	0.789345i
$507$		0			0
$508$	−9.02024	+	5.20784i	−0.400208	+	0.231060i
$509$	13.9099	−	24.0927i	0.616547	−	1.06789i	−0.373563	−	0.927605i	$-0.621864\pi$
$509$	13.9099	−	24.0927i	0.616547	−	1.06789i	0.990111	−	0.140287i	$-0.0448025\pi$
$510$		0			0
$511$	−22.5238	+	2.19892i	−0.996396	+	0.0972744i
$512$			14.7579i			0.652214i
$513$		0			0
$514$	2.22895	+	3.86065i	0.0983146	+	0.170286i
$515$	−35.1151	+	15.0564i	−1.54735	+	0.663465i
$516$		0			0
$517$		−	5.07310i		−	0.223115i
$518$	−1.61001	−	16.4915i	−0.0707396	−	0.724596i
$519$		0			0
$520$	6.16697	−	8.24607i	0.270439	−	0.361614i
$521$	16.7513	+	29.0141i	0.733887	+	1.27113i	0.955210	+	0.295929i	$0.0956291\pi$
$521$	16.7513	+	29.0141i	0.733887	+	1.27113i	−0.221323	+	0.975200i	$0.571038\pi$
$522$		0			0
$523$	11.0815	+	6.39790i	0.484560	+	0.279761i	0.722315	−	0.691564i	$-0.243078\pi$
$523$	11.0815	+	6.39790i	0.484560	+	0.279761i	−0.237755	+	0.971325i	$0.576412\pi$
$524$	6.27247			0.274014
$525$		0			0
$526$	8.24034			0.359296
$527$	−5.37195	−	3.10149i	−0.234006	−	0.135103i
$528$		0			0
$529$	3.82668	+	6.62801i	0.166377	+	0.288174i
$530$	−23.6496	+	31.6227i	−1.02727	+	1.37360i
$531$		0			0
$532$	21.8884	+	9.94014i	0.948984	+	0.430960i
$533$			25.0117i			1.08338i
$534$		0			0
$535$	12.9689	−	5.56072i	0.560694	−	0.240411i
$536$	2.82412	+	4.89153i	0.121984	+	0.211282i
$537$		0			0
$538$			21.4214i			0.923540i
$539$	4.70038	−	13.7693i	0.202460	−	0.593085i
$540$		0			0
$541$	−12.6283	+	21.8728i	−0.542933	+	0.940387i	0.455801	+	0.890082i	$0.349353\pi$
$541$	−12.6283	+	21.8728i	−0.542933	+	0.940387i	−0.998734	+	0.0503053i	$0.983981\pi$
$542$	−8.43897	+	4.87224i	−0.362485	+	0.209281i
$543$		0			0
$544$	−6.29684	+	10.9064i	−0.269975	+	0.467610i
$545$	5.43272	+	0.647007i	0.232712	+	0.0277147i
$546$		0			0
$547$		−	38.8743i		−	1.66214i	−0.556165	−	0.831072i	$-0.687728\pi$
$547$		−	38.8743i		−	1.66214i	0.556165	−	0.831072i	$-0.312272\pi$
$548$	13.3262	+	7.69389i	0.569268	+	0.328667i
$549$		0			0
$550$	17.7609	−	5.23297i	0.757328	−	0.223135i
$551$	15.5281	−	26.8955i	0.661520	−	1.14579i
$552$		0			0
$553$	−17.4596	+	12.4887i	−0.742458	+	0.531075i
$554$	−53.1110			−2.25647
$555$		0			0
$556$	−0.142773	−	0.247290i	−0.00605491	−	0.0104874i
$557$	1.18106	−	0.681888i	0.0500433	−	0.0288925i	−0.474770	−	0.880110i	$-0.657469\pi$
$557$	1.18106	−	0.681888i	0.0500433	−	0.0288925i	0.524813	+	0.851218i	$0.324135\pi$
$558$		0			0
$559$	15.6210			0.660700
$560$	−0.623786	+	29.3941i	−0.0263598	+	1.24213i
$561$		0			0
$562$	12.0121	+	6.93519i	0.506700	+	0.292543i
$563$	9.15774	−	5.28722i	0.385953	−	0.222830i	−0.294452	−	0.955666i	$-0.595137\pi$
$563$	9.15774	−	5.28722i	0.385953	−	0.222830i	0.680405	+	0.732836i	$0.261804\pi$
$564$		0			0
$565$	18.1880	+	13.6022i	0.765174	+	0.572249i
$566$	−4.65803			−0.195791
$567$		0			0
$568$			22.1035i			0.927441i
$569$	−18.9932	+	32.8973i	−0.796238	+	1.37913i	0.125811	+	0.992054i	$0.459847\pi$
$569$	−18.9932	+	32.8973i	−0.796238	+	1.37913i	−0.922050	+	0.387071i	$0.873487\pi$
$570$		0			0
$571$	7.84550	+	13.5888i	0.328324	+	0.568674i	0.982179	−	0.187946i	$-0.0601829\pi$
$571$	7.84550	+	13.5888i	0.328324	+	0.568674i	−0.653856	+	0.756619i	$0.726850\pi$
$572$	−6.61654	−	3.82006i	−0.276652	−	0.159725i
$573$		0			0
$574$	−21.9129	−	30.6348i	−0.914625	−	1.27867i
$575$	−6.50151	+	26.9084i	−0.271132	+	1.12216i
$576$		0			0
$577$	−2.98614	+	1.72405i	−0.124315	+	0.0717730i	−0.560868	−	0.827905i	$-0.689532\pi$
$577$	−2.98614	+	1.72405i	−0.124315	+	0.0717730i	0.436553	+	0.899678i	$0.356199\pi$
$578$	19.2285	−	11.1016i	0.799800	−	0.461765i
$579$		0			0
$580$	−10.4651	−	1.24634i	−0.434541	−	0.0517514i
$581$	−9.57377	+	21.0817i	−0.397187	+	0.874615i
$582$		0			0
$583$	−17.8417	−	10.3009i	−0.738927	−	0.426620i
$584$	6.29180	+	10.8977i	0.260356	+	0.450950i
$585$		0			0
$586$	11.3633	−	19.6819i	0.469415	−	0.813051i
$587$		−	10.5983i		−	0.437441i	−0.975788	−	0.218720i	$-0.929812\pi$
$587$		−	10.5983i		−	0.437441i	0.975788	−	0.218720i	$-0.0701882\pi$
$588$		0			0
$589$	22.5310			0.928373
$590$	9.43058	+	7.05283i	0.388251	+	0.290360i
$591$		0			0
$592$	−15.1287	+	8.73458i	−0.621787	+	0.358989i
$593$	0.203007	+	0.117206i	0.00833648	+	0.00481307i	0.504162	−	0.863609i	$-0.331801\pi$
$593$	0.203007	+	0.117206i	0.00833648	+	0.00481307i	−0.495826	+	0.868422i	$0.665135\pi$
$594$		0			0
$595$	−6.53145	+	10.7780i	−0.267764	+	0.441857i
$596$	−2.74464			−0.112425
$597$		0			0
$598$	26.7405	−	15.4386i	1.09350	−	0.631333i
$599$	12.9145	+	22.3686i	0.527673	+	0.913956i	0.999480	+	0.0322543i	$0.0102687\pi$
$599$	12.9145	+	22.3686i	0.527673	+	0.913956i	−0.471807	+	0.881702i	$0.656398\pi$
$600$		0			0
$601$	−1.15592			−0.0471508			−0.0235754	−	0.999722i	$-0.507505\pi$
$601$	−1.15592			−0.0471508			−0.0235754	+	0.999722i	$0.507505\pi$
$602$	−19.1329	+	13.6856i	−0.779799	+	0.557785i
$603$		0			0
$604$	−6.52525	+	11.3021i	−0.265509	+	0.459875i
$605$	−5.88617	−	13.7279i	−0.239307	−	0.558119i
$606$		0			0
$607$	−20.1014	−	11.6056i	−0.815891	−	0.471055i	0.0331064	−	0.999452i	$-0.489460\pi$
$607$	−20.1014	−	11.6056i	−0.815891	−	0.471055i	−0.848997	+	0.528397i	$0.822793\pi$
$608$		−	45.7438i		−	1.85516i
$609$		0			0
$610$	−5.13278	+	43.0984i	−0.207820	+	1.74500i
$611$	3.82006	−	6.61654i	0.154543	−	0.267677i
$612$		0			0
$613$	−5.48319	+	3.16572i	−0.221464	+	0.127862i	−0.606628	−	0.794986i	$-0.707478\pi$
$613$	−5.48319	+	3.16572i	−0.221464	+	0.127862i	0.385164	+	0.922848i	$0.374145\pi$
$614$	11.7517	−	20.3545i	0.474259	−	0.821440i
$615$		0			0
$616$	−8.05174	+	0.786061i	−0.324414	+	0.0316713i
$617$			25.9546i			1.04489i	0.852672	+	0.522447i	$0.174981\pi$
$617$			25.9546i			1.04489i	−0.852672	+	0.522447i	$0.825019\pi$
$618$		0			0
$619$	−14.5481	−	25.1981i	−0.584738	−	1.01280i	−0.994908	−	0.100787i	$-0.967864\pi$
$619$	−14.5481	−	25.1981i	−0.584738	−	1.01280i	0.410170	−	0.912009i	$-0.365469\pi$
$620$	−3.01311	−	7.02727i	−0.121009	−	0.282222i
$621$		0			0
$622$			25.4460i			1.02029i
$623$	1.33130	−	0.952272i	0.0533375	−	0.0381520i
$624$		0			0
$625$	−21.0062	+	13.5550i	−0.840250	+	0.542200i
$626$	4.25052	+	7.36211i	0.169885	+	0.294249i
$627$		0			0
$628$	11.5102	+	6.64542i	0.459307	+	0.265181i
$629$	−7.48816			−0.298573
$630$		0			0
$631$	−37.3609			−1.48731			−0.743657	−	0.668561i	$-0.766911\pi$
$631$	−37.3609			−1.48731			−0.743657	+	0.668561i	$0.766911\pi$
$632$	10.3369	+	5.96804i	0.411181	+	0.237396i
$633$		0			0
$634$	−16.7518	−	29.0150i	−0.665300	−	1.15233i
$635$	15.8830	+	11.8784i	0.630296	+	0.471378i
$636$		0			0
$637$	16.4988	−	14.4191i	0.653705	−	0.571305i
$638$		−	14.8633i		−	0.588443i
$639$		0			0
$640$	22.1255	−	9.48683i	0.874587	−	0.375000i
$641$	−13.9268	−	24.1219i	−0.550074	−	0.952756i	−0.998269	−	0.0588199i	$-0.981266\pi$
$641$	−13.9268	−	24.1219i	−0.550074	−	0.952756i	0.448195	−	0.893936i	$-0.352067\pi$
$642$		0			0
$643$		−	20.3104i		−	0.800963i	−0.916305	−	0.400481i	$-0.868843\pi$
$643$		−	20.3104i		−	0.800963i	0.916305	−	0.400481i	$-0.131157\pi$
$644$	−7.11255	+	15.6620i	−0.280274	+	0.617170i
$645$		0			0
$646$	14.6834	−	25.4324i	0.577710	−	1.00062i
$647$	19.4275	−	11.2165i	0.763773	−	0.440964i	−0.0668759	−	0.997761i	$-0.521303\pi$
$647$	19.4275	−	11.2165i	0.763773	−	0.440964i	0.830649	+	0.556797i	$0.187970\pi$
$648$		0			0
$649$	−3.07196	+	5.32078i	−0.120585	+	0.208859i
$650$	27.1050	+	6.54900i	1.06315	+	0.256873i
$651$		0			0
$652$		−	2.47008i		−	0.0967360i
$653$	17.1517	+	9.90257i	0.671200	+	0.387517i	0.796531	−	0.604598i	$-0.206666\pi$
$653$	17.1517	+	9.90257i	0.671200	+	0.387517i	−0.125331	+	0.992115i	$0.539999\pi$
$654$		0			0
$655$	−4.70683	−	10.9774i	−0.183911	−	0.428924i
$656$	−19.8546	+	34.3892i	−0.775192	+	1.34267i
$657$		0			0
$658$	1.11790	+	11.4508i	0.0435803	+	0.446399i
$659$	38.3567			1.49416			0.747082	−	0.664731i	$-0.231454\pi$
$659$	38.3567			1.49416			0.747082	+	0.664731i	$0.231454\pi$
$660$		0			0
$661$	−1.48746	−	2.57635i	−0.0578554	−	0.100209i	0.835647	−	0.549267i	$-0.185093\pi$
$661$	−1.48746	−	2.57635i	−0.0578554	−	0.100209i	−0.893503	+	0.449058i	$0.851760\pi$
$662$	27.4248	−	15.8337i	1.06589	−	0.615394i
$663$		0			0
$664$	12.8743			0.499619
$665$	0.971222	−	45.7659i	0.0376624	−	1.77473i
$666$		0			0
$667$	19.2448	+	11.1110i	0.745160	+	0.430218i
$668$	−3.64684	+	2.10550i	−0.141100	+	0.0814644i
$669$		0			0
$670$	−9.16072	+	12.2491i	−0.353910	+	0.473225i
$671$	−22.6443			−0.874175
$672$		0			0
$673$		−	22.8397i		−	0.880407i	−0.897898	−	0.440203i	$-0.854906\pi$
$673$		−	22.8397i		−	0.880407i	0.897898	−	0.440203i	$-0.145094\pi$
$674$	−3.44461	+	5.96624i	−0.132681	+	0.229811i
$675$		0			0
$676$	1.87983	+	3.25596i	0.0723012	+	0.125229i
$677$	−6.23200	−	3.59805i	−0.239515	−	0.138284i	0.375439	−	0.926847i	$-0.377492\pi$
$677$	−6.23200	−	3.59805i	−0.239515	−	0.138284i	−0.614954	+	0.788563i	$0.710825\pi$
$678$		0			0
$679$	−0.324740	+	0.715087i	−0.0124624	+	0.0274425i
$680$	6.95833	+	0.828698i	0.266840	+	0.0317791i
$681$		0			0
$682$	9.33850	−	5.39159i	0.357590	−	0.206454i
$683$	3.94425	−	2.27721i	0.150922	−	0.0871351i	−0.422637	−	0.906299i	$-0.638895\pi$
$683$	3.94425	−	2.27721i	0.150922	−	0.0871351i	0.573559	+	0.819164i	$0.305562\pi$
$684$		0			0
$685$	3.46513	−	29.0956i	0.132396	−	1.11169i
$686$	−7.57535	+	32.1153i	−0.289228	+	1.22617i
$687$		0			0
$688$	21.4777	+	12.4002i	0.818830	+	0.472751i
$689$	−15.5132	−	26.8697i	−0.591008	−	1.02366i
$690$		0			0
$691$	−1.76948	+	3.06483i	−0.0673142	+	0.116592i	−0.897718	−	0.440570i	$-0.854776\pi$
$691$	−1.76948	+	3.06483i	−0.0673142	+	0.116592i	0.830404	+	0.557162i	$0.188110\pi$
$692$		−	18.2485i		−	0.693702i
$693$		0			0
$694$	−18.3020			−0.694734
$695$	−0.325645	+	0.435431i	−0.0123524	+	0.0165168i
$696$		0			0
$697$	−14.7409	+	8.51068i	−0.558353	+	0.322365i
$698$	36.4416	+	21.0396i	1.37934	+	0.796360i
$699$		0			0
$700$	−14.4040	+	5.81744i	−0.544419	+	0.219878i
$701$	16.8111			0.634948			0.317474	−	0.948267i	$-0.397165\pi$
$701$	16.8111			0.634948			0.317474	+	0.948267i	$0.397165\pi$
$702$		0			0
$703$	23.5551	−	13.5996i	0.888398	−	0.512917i
$704$	−0.616984	−	1.06865i	−0.0232535	−	0.0402762i
$705$		0			0
$706$	10.2937			0.387407
$707$	−2.12311	−	21.7473i	−0.0798477	−	0.817892i
$708$		0			0
$709$	15.9088	−	27.5549i	0.597468	−	1.03484i	−0.395726	−	0.918369i	$-0.629507\pi$
$709$	15.9088	−	27.5549i	0.597468	−	1.03484i	0.993194	−	0.116476i	$-0.0371597\pi$
$710$	−55.0136	+	23.5884i	−2.06462	+	0.885255i
$711$		0			0
$712$	−0.788197	−	0.455066i	−0.0295389	−	0.0170543i
$713$			16.1218i			0.603766i
$714$		0			0
$715$	−1.72046	+	14.4462i	−0.0643414	+	0.540256i
$716$	9.23910	−	16.0026i	0.345282	−	0.598045i
$717$		0			0
$718$	48.3029	−	27.8877i	1.80265	−	1.04076i
$719$	−7.64037	+	13.2335i	−0.284938	+	0.493527i	−0.972594	−	0.232510i	$-0.925306\pi$
$719$	−7.64037	+	13.2335i	−0.284938	+	0.493527i	0.687656	+	0.726036i	$0.258640\pi$
$720$		0			0
$721$	26.3005	+	36.7689i	0.979483	+	1.36934i
$722$			72.8169i			2.70996i
$723$		0			0
$724$	−2.92804	−	5.07152i	−0.108820	−	0.188482i
$725$	5.67177	+	19.2502i	0.210644	+	0.714936i
$726$		0			0
$727$			19.1829i			0.711453i	0.934590	+	0.355726i	$0.115766\pi$
$727$			19.1829i			0.711453i	−0.934590	+	0.355726i	$0.884234\pi$
$728$	−11.0933	−	5.03778i	−0.411146	−	0.186713i
$729$		0			0
$730$	−20.4089	+	27.2895i	−0.755369	+	1.01003i
$731$	5.31533	+	9.20643i	0.196595	+	0.340512i
$732$		0			0
$733$	42.1943	+	24.3609i	1.55848	+	0.899790i	0.997403	+	0.0720283i	$0.0229472\pi$
$733$	42.1943	+	24.3609i	1.55848	+	0.899790i	0.561080	+	0.827762i	$0.310386\pi$
$734$	29.4898			1.08849
$735$		0			0
$736$	32.7314			1.20650
$737$	−6.91102	−	3.99008i	−0.254571	−	0.146976i
$738$		0			0
$739$	−4.74202	−	8.21343i	−0.174438	−	0.302136i	0.765529	−	0.643402i	$-0.222478\pi$
$739$	−4.74202	−	8.21343i	−0.174438	−	0.302136i	−0.939967	+	0.341266i	$0.889144\pi$
$740$	−7.39168	−	5.52799i	−0.271723	−	0.203213i
$741$		0			0
$742$	42.5415	+	19.3193i	1.56175	+	0.709233i
$743$		−	30.2032i		−	1.10805i	−0.832501	−	0.554023i	$-0.813092\pi$
$743$		−	30.2032i		−	1.10805i	0.832501	−	0.554023i	$-0.186908\pi$
$744$		0			0
$745$	2.05957	+	4.80339i	0.0754568	+	0.175983i
$746$	−28.6335	−	49.5946i	−1.04835	−	1.81579i
$747$		0			0
$748$		−	5.19937i		−	0.190108i
$749$	−9.71346	−	13.5797i	−0.354922	−	0.496191i
$750$		0			0
$751$	3.66467	−	6.34739i	0.133726	−	0.231620i	−0.791384	−	0.611319i	$-0.790639\pi$
$751$	3.66467	−	6.34739i	0.133726	−	0.231620i	0.925110	+	0.379699i	$0.123973\pi$
$752$	10.5046	−	6.06481i	0.383062	−	0.221161i
$753$		0			0
$754$	11.1921	−	19.3853i	0.407593	−	0.705972i
$755$	24.6762	+	2.93880i	0.898060	+	0.106954i
$756$		0			0
$757$			14.1603i			0.514666i	0.966323	+	0.257333i	$0.0828438\pi$
$757$			14.1603i			0.514666i	−0.966323	+	0.257333i	$0.917156\pi$
$758$	−7.69626	−	4.44344i	−0.279541	−	0.161393i
$759$		0			0
$760$	−23.3935	+	10.0305i	−0.848570	+	0.363845i
$761$	−11.9592	+	20.7139i	−0.433519	+	0.750878i	−0.997173	−	0.0751333i	$-0.976062\pi$
$761$	−11.9592	+	20.7139i	−0.433519	+	0.750878i	0.563654	+	0.826011i	$0.309395\pi$
$762$		0			0
$763$	−0.628994	−	6.44288i	−0.0227711	−	0.233248i
$764$	13.8665			0.501672
$765$		0			0
$766$	23.5684	+	40.8217i	0.851562	+	1.47495i
$767$	−8.01315	+	4.62639i	−0.289338	+	0.167049i
$768$		0			0
$769$	−14.1358			−0.509750			−0.254875	−	0.966974i	$-0.582034\pi$
$769$	−14.1358			−0.509750			−0.254875	+	0.966974i	$0.582034\pi$
$770$	−10.5491	−	19.2012i	−0.380162	−	0.691962i
$771$		0			0
$772$	−25.1577	−	14.5248i	−0.905445	−	0.522759i
$773$	5.85409	−	3.37986i	0.210557	−	0.121565i	−0.391013	−	0.920385i	$-0.627875\pi$
$773$	5.85409	−	3.37986i	0.210557	−	0.121565i	0.601570	+	0.798820i	$0.294542\pi$
$774$		0			0
$775$	−10.0374	+	10.5465i	−0.360553	+	0.378840i
$776$	0.436693			0.0156764
$777$		0			0
$778$		−	22.7545i		−	0.815790i
$779$	30.9132	−	53.5432i	1.10758	−	1.91838i
$780$		0			0
$781$	−15.6145	−	27.0451i	−0.558731	−	0.967750i
$782$	18.1978	+	10.5065i	0.650753	+	0.375713i
$783$		0			0
$784$	34.1305	−	6.72819i	1.21895	−	0.240293i
$785$	2.99292	−	25.1307i	0.106822	−	0.896952i
$786$		0			0
$787$	13.3152	−	7.68754i	0.474636	−	0.274031i	−0.243543	−	0.969890i	$-0.578310\pi$
$787$	13.3152	−	7.68754i	0.474636	−	0.274031i	0.718178	+	0.695859i	$0.244976\pi$
$788$	19.8843	−	11.4802i	0.708349	−	0.408966i
$789$		0			0
$790$	−3.82254	+	32.0967i	−0.136000	+	1.14195i
$791$	11.1116	−	24.4680i	0.395083	−	0.869982i
$792$		0			0
$793$	−29.5337	−	17.0513i	−1.04877	−	0.605509i
$794$	−13.4704	−	23.3314i	−0.478046	−	0.828000i
$795$		0			0
$796$	13.0582	−	22.6174i	0.462835	−	0.801654i
$797$			9.46785i			0.335369i	0.985841	+	0.167684i	$0.0536289\pi$
$797$			9.46785i			0.335369i	−0.985841	+	0.167684i	$0.946371\pi$
$798$		0			0
$799$	5.19937			0.183941
$800$	21.4121	+	20.3785i	0.757031	+	0.720489i
$801$		0			0
$802$	−19.0718	+	11.0111i	−0.673450	+	0.388817i
$803$	−15.3969	−	8.88940i	−0.543344	−	0.313700i
$804$		0			0
$805$	32.7473	+	0.694947i	1.15419	+	0.0244937i
$806$	16.2395			0.572014
$807$		0			0
$808$	−10.5220	+	6.07488i	−0.370163	+	0.213713i
$809$	−2.81872	−	4.88217i	−0.0991011	−	0.171648i	0.812212	−	0.583363i	$-0.198263\pi$
$809$	−2.81872	−	4.88217i	−0.0991011	−	0.171648i	−0.911313	+	0.411715i	$0.864930\pi$
$810$		0			0
$811$	24.3625			0.855485			0.427742	−	0.903901i	$-0.359309\pi$
$811$	24.3625			0.855485			0.427742	+	0.903901i	$0.359309\pi$
$812$	1.21164	+	12.4110i	0.0425202	+	0.435541i
$813$		0			0
$814$	6.50865	−	11.2733i	0.228128	−	0.395129i
$815$	−4.32289	+	1.85354i	−0.151424	+	0.0649267i
$816$		0			0
$817$	−33.4403	−	19.3068i	−1.16993	−	0.675458i
$818$			18.7585i			0.655876i
$819$		0			0
$820$	−20.8338	−	2.48119i	−0.727549	−	0.0866471i
$821$	−15.8731	+	27.4930i	−0.553974	+	0.959512i	0.444008	+	0.896023i	$0.353556\pi$
$821$	−15.8731	+	27.4930i	−0.553974	+	0.959512i	−0.997983	+	0.0634890i	$0.979777\pi$
$822$		0			0
$823$	3.44299	−	1.98781i	0.120015	−	0.0692908i	−0.438791	−	0.898589i	$-0.644593\pi$
$823$	3.44299	−	1.98781i	0.120015	−	0.0692908i	0.558806	+	0.829299i	$0.311260\pi$
$824$	12.5683	−	21.7690i	0.437838	−	0.758358i
$825$		0			0
$826$	5.76143	−	12.6868i	0.200466	−	0.441431i
$827$		−	6.80348i		−	0.236580i	−0.992979	−	0.118290i	$-0.962259\pi$
$827$		−	6.80348i		−	0.236580i	0.992979	−	0.118290i	$-0.0377413\pi$
$828$		0			0
$829$	11.5303	+	19.9710i	0.400463	+	0.693623i	0.993782	−	0.111345i	$-0.0355159\pi$
$829$	11.5303	+	19.9710i	0.400463	+	0.693623i	−0.593319	+	0.804968i	$0.702183\pi$
$830$	13.7392	+	32.0429i	0.476893	+	1.11223i
$831$		0			0
$832$		−	1.85837i		−	0.0644273i
$833$	14.1120	+	4.81738i	0.488953	+	0.166912i
$834$		0			0
$835$	6.42141	+	4.80236i	0.222222	+	0.166193i
$836$	9.44278	+	16.3554i	0.326586	+	0.565663i
$837$		0			0
$838$	−20.5383	−	11.8578i	−0.709482	−	0.409620i
$839$	−35.0723			−1.21083			−0.605415	−	0.795910i	$-0.706993\pi$
$839$	−35.0723			−1.21083			−0.605415	+	0.795910i	$0.706993\pi$
$840$		0			0
$841$	−12.8904			−0.444495
$842$	−29.5508	−	17.0611i	−1.01839	−	0.587966i
$843$		0			0
$844$	13.8678	+	24.0198i	0.477350	+	0.826795i
$845$	4.28764	−	5.73315i	0.147499	−	0.197226i
$846$		0			0
$847$	−14.3745	+	10.2820i	−0.493912	+	0.353292i
$848$		−	49.2583i		−	1.69154i
$849$		0			0
$850$	5.36323	+	18.2030i	0.183957	+	0.624358i
$851$	9.73100	+	16.8546i	0.333575	+	0.577768i
$852$		0			0
$853$			12.3125i			0.421571i	0.977532	+	0.210785i	$0.0676021\pi$
$853$			12.3125i			0.421571i	−0.977532	+	0.210785i	$0.932398\pi$
$854$	51.1120	−	4.98987i	1.74902	−	0.170750i
$855$		0			0
$856$	−4.64180	+	8.03984i	−0.158654	+	0.274796i
$857$	−28.7952	+	16.6249i	−0.983624	+	0.567896i	−0.903362	−	0.428878i	$-0.858909\pi$
$857$	−28.7952	+	16.6249i	−0.983624	+	0.567896i	−0.0802617	+	0.996774i	$0.525576\pi$
$858$		0			0
$859$	−1.50697	+	2.61015i	−0.0514172	+	0.0890573i	−0.890588	−	0.454810i	$-0.849707\pi$
$859$	−1.50697	+	2.61015i	−0.0514172	+	0.0890573i	0.839171	+	0.543867i	$0.183041\pi$
$860$	−1.54963	+	13.0117i	−0.0528418	+	0.443697i
$861$		0			0
$862$		−	19.4136i		−	0.661228i
$863$	19.2569	+	11.1180i	0.655513	+	0.378460i	0.790565	−	0.612378i	$-0.209787\pi$
$863$	19.2569	+	11.1180i	0.655513	+	0.378460i	−0.135052	+	0.990838i	$0.543120\pi$
$864$		0			0
$865$	−31.9366	+	13.6936i	−1.08588	+	0.465595i
$866$	−17.3595	+	30.0675i	−0.589899	+	1.02174i
$867$		0			0
$868$	−7.35823	+	5.26329i	−0.249755	+	0.178648i
$869$	−16.8639			−0.572070
$870$		0			0
$871$	−6.00909	−	10.4081i	−0.203610	−	0.352663i
$872$	−3.11726	+	1.79975i	−0.105564	+	0.0609472i
$873$		0			0
$874$	−76.3253			−2.58174
$875$	20.9898	+	20.8430i	0.709584	+	0.704621i
$876$		0			0
$877$	12.4033	+	7.16105i	0.418830	+	0.241812i	0.694577	−	0.719419i	$-0.255592\pi$
$877$	12.4033	+	7.16105i	0.418830	+	0.241812i	−0.275747	+	0.961230i	$0.588925\pi$
$878$	−20.8777	+	12.0538i	−0.704589	+	0.406795i
$879$		0			0
$880$	−13.8330	+	18.4966i	−0.466310	+	0.623520i
$881$	−49.9929			−1.68431			−0.842153	−	0.539239i	$-0.818712\pi$
$881$	−49.9929			−1.68431			−0.842153	+	0.539239i	$0.818712\pi$
$882$		0			0
$883$		−	44.3095i		−	1.49113i	−0.666432	−	0.745566i	$-0.732179\pi$
$883$		−	44.3095i		−	1.49113i	0.666432	−	0.745566i	$-0.267821\pi$
$884$	3.91515	−	6.78124i	0.131681	−	0.228078i
$885$		0			0
$886$	25.7149	+	44.5395i	0.863909	+	1.49633i
$887$	−8.91878	−	5.14926i	−0.299463	−	0.172895i	0.342738	−	0.939431i	$-0.388646\pi$
$887$	−8.91878	−	5.14926i	−0.299463	−	0.172895i	−0.642202	+	0.766536i	$0.721979\pi$
$888$		0			0
$889$	9.70339	−	21.3671i	0.325441	−	0.716630i
$890$	0.291470	−	2.44739i	0.00977010	−	0.0820366i
$891$		0			0
$892$	−25.5685	+	14.7620i	−0.856096	+	0.494267i
$893$	−16.3554	+	9.44278i	−0.547312	+	0.315991i
$894$		0			0
$895$	−34.9391	−	4.16105i	−1.16788	−	0.139089i
$896$	−16.5716	−	23.1675i	−0.553618	−	0.773973i
$897$		0			0
$898$	−36.1512	−	20.8719i	−1.20638	−	0.696504i
$899$	5.84369	+	10.1216i	0.194898	+	0.337573i
$900$		0			0
$901$	10.5573	−	18.2858i	0.351715	−	0.609188i
$902$		−	29.5896i		−	0.985227i
$903$		0			0
$904$	−14.9423			−0.496972
$905$	−6.67846	+	8.93001i	−0.222000	+	0.296844i
$906$		0			0
$907$	25.4854	−	14.7140i	0.846228	−	0.488570i	−0.0131487	−	0.999914i	$-0.504185\pi$
$907$	25.4854	−	14.7140i	0.846228	−	0.488570i	0.859376	+	0.511344i	$0.170852\pi$
$908$	−24.0718	−	13.8979i	−0.798850	−	0.461216i
$909$		0			0
$910$	0.700023	−	32.9865i	0.0232055	−	1.09349i
$911$	24.8078			0.821918			0.410959	−	0.911654i	$-0.365194\pi$
$911$	24.8078			0.821918			0.410959	+	0.911654i	$0.365194\pi$
$912$		0			0
$913$	−15.7526	+	9.09474i	−0.521334	+	0.300992i
$914$	26.9810	+	46.7324i	0.892451	+	1.54577i
$915$		0			0
$916$	0.477133			0.0157649
$917$	−11.4944	+	8.22189i	−0.379580	+	0.271511i
$918$		0			0
$919$	6.50466	−	11.2664i	0.214569	−	0.371645i	−0.738570	−	0.674177i	$-0.764499\pi$
$919$	6.50466	−	11.2664i	0.214569	−	0.371645i	0.953139	+	0.302532i	$0.0978320\pi$
$920$	−7.17721	−	16.7389i	−0.236626	−	0.551866i
$921$		0			0
$922$	−10.8346	−	6.25535i	−0.356818	−	0.206009i
$923$		−	47.0312i		−	1.54805i
$924$		0			0
$925$	−4.12785	+	17.0843i	−0.135723	+	0.561730i
$926$	−2.64864	+	4.58758i	−0.0870398	+	0.150757i
$927$		0			0
$928$	20.5494	−	11.8642i	0.674568	−	0.389462i
$929$	−12.4592	+	21.5800i	−0.408775	+	0.708018i	−0.994753	−	0.102309i	$-0.967377\pi$
$929$	−12.4592	+	21.5800i	−0.408775	+	0.708018i	0.585978	+	0.810327i	$0.300710\pi$
$930$		0			0
$931$	−53.1405	+	10.4756i	−1.74161	+	0.343326i
$932$			8.41410i			0.275613i
$933$		0			0
$934$	−21.1615	−	36.6528i	−0.692425	−	1.19932i
$935$	−9.09941	+	3.90159i	−0.297582	+	0.127596i
$936$		0			0
$937$			55.1260i			1.80089i	0.434973	+	0.900444i	$0.356758\pi$
$937$			55.1260i			1.80089i	−0.434973	+	0.900444i	$0.643242\pi$
$938$	16.4786	+	7.48337i	0.538044	+	0.244341i
$939$		0			0
$940$	5.13238	+	3.83834i	0.167400	+	0.125193i
$941$	6.82233	+	11.8166i	0.222402	+	0.385211i	0.955537	−	0.294872i	$-0.0952771\pi$
$941$	6.82233	+	11.8166i	0.222402	+	0.385211i	−0.733135	+	0.680083i	$0.761944\pi$
$942$		0			0
$943$	38.3122	+	22.1196i	1.24762	+	0.720312i
$944$	−14.6899			−0.478116
$945$		0			0
$946$	−18.4802			−0.600842
$947$	0.773437	+	0.446544i	0.0251333	+	0.0145107i	0.512514	−	0.858679i	$-0.328714\pi$
$947$	0.773437	+	0.446544i	0.0251333	+	0.0145107i	−0.487381	+	0.873190i	$0.662048\pi$
$948$		0			0
$949$	−13.3875	−	23.1878i	−0.434577	−	0.752709i
$950$	−49.9300	−	47.5199i	−1.61994	−	1.54175i
$951$		0			0
$952$	−0.805627	−	8.25215i	−0.0261105	−	0.267454i
$953$		−	34.5636i		−	1.11963i	−0.828619	−	0.559813i	$-0.810873\pi$
$953$		−	34.5636i		−	1.11963i	0.828619	−	0.559813i	$-0.189127\pi$
$954$		0			0
$955$	−10.4054	−	24.2677i	−0.336709	−	0.785285i
$956$	5.92557	+	10.2634i	0.191646	+	0.331941i
$957$		0			0
$958$		−	11.6595i		−	0.376703i
$959$	−34.5057	+	3.36866i	−1.11425	+	0.108780i
$960$		0			0
$961$	11.2605	−	19.5037i	0.363241	−	0.629151i
$962$	16.9777	−	9.80208i	0.547383	−	0.316032i
$963$		0			0
$964$	−2.70483	+	4.68491i	−0.0871169	+	0.150891i
$965$	−6.54159	+	54.9278i	−0.210581	+	1.76819i
$966$		0			0
$967$		−	22.1811i		−	0.713296i	−0.934239	−	0.356648i	$-0.883920\pi$
$967$		−	22.1811i		−	0.713296i	0.934239	−	0.356648i	$-0.116080\pi$
$968$	8.51038	+	4.91347i	0.273534	+	0.157925i
$969$		0			0
$970$	0.466030	+	1.08689i	0.0149633	+	0.0348979i
$971$	0.0379659	−	0.0657589i	0.00121839	−	0.00211031i	−0.865416	−	0.501055i	$-0.832946\pi$
$971$	0.0379659	−	0.0657589i	0.00121839	−	0.00211031i	0.866634	+	0.498944i	$0.166279\pi$
$972$		0			0
$973$	0.585779	+	0.266018i	0.0187792	+	0.00852815i
$974$	−29.0889			−0.932069
$975$		0			0
$976$	−27.0710	−	46.8883i	−0.866521	−	1.50086i
$977$	−37.4222	+	21.6057i	−1.19724	+	0.691228i	−0.959940	−	0.280207i	$-0.909597\pi$
$977$	−37.4222	+	21.6057i	−1.19724	+	0.691228i	−0.237303	+	0.971436i	$0.576263\pi$
$978$		0			0
$979$	1.28588			0.0410970
$980$	10.3739	+	15.1732i	0.331381	+	0.484691i
$981$		0			0
$982$	38.4211	+	22.1824i	1.22607	+	0.707869i
$983$	15.8663	−	9.16040i	0.506055	−	0.292171i	−0.225155	−	0.974323i	$-0.572289\pi$
$983$	15.8663	−	9.16040i	0.506055	−	0.292171i	0.731211	+	0.682152i	$0.238956\pi$
$984$		0			0
$985$	−35.0126	−	26.1848i	−1.11559	−	0.834316i
$986$	15.2333			0.485126
$987$		0			0
$988$			28.4418i			0.904855i
$989$	13.8147	−	23.9278i	0.439283	−	0.760861i
$990$		0			0
$991$	15.7888	+	27.3470i	0.501548	+	0.868706i	0.999998	+	0.00178831i	$0.000569236\pi$
$991$	15.7888	+	27.3470i	0.501548	+	0.868706i	−0.498450	+	0.866918i	$0.666097\pi$
$992$	14.9084	+	8.60736i	0.473342	+	0.273284i
$993$		0			0
$994$	41.2041	+	57.6045i	1.30692	+	1.82710i
$995$	−49.3815	−	5.88106i	−1.56550	−	0.186442i
$996$		0			0
$997$	−34.4085	+	19.8657i	−1.08973	+	0.629154i	−0.933504	−	0.358568i	$-0.883265\pi$
$997$	−34.4085	+	19.8657i	−1.08973	+	0.629154i	−0.156223	+	0.987722i	$0.549932\pi$
$998$	18.8301	−	10.8716i	0.596058	−	0.344134i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bf.b.289.2		16
3.2	odd	2		105.2.q.a.79.7	yes	16
5.4	even	2	inner	315.2.bf.b.289.7		16
7.2	even	3		2205.2.d.s.1324.7		8
7.4	even	3	inner	315.2.bf.b.109.7		16
7.5	odd	6		2205.2.d.o.1324.7		8
12.11	even	2		1680.2.di.d.289.2		16
15.2	even	4		525.2.i.k.226.1		8
15.8	even	4		525.2.i.h.226.4		8
15.14	odd	2		105.2.q.a.79.2	yes	16
21.2	odd	6		735.2.d.d.589.2		8
21.5	even	6		735.2.d.e.589.2		8
21.11	odd	6		105.2.q.a.4.2	✓	16
21.17	even	6		735.2.q.g.214.2		16
21.20	even	2		735.2.q.g.79.7		16
35.4	even	6	inner	315.2.bf.b.109.2		16
35.9	even	6		2205.2.d.s.1324.2		8
35.19	odd	6		2205.2.d.o.1324.2		8
60.59	even	2		1680.2.di.d.289.6		16
84.11	even	6		1680.2.di.d.529.6		16
105.2	even	12		3675.2.a.bp.1.4		4
105.23	even	12		3675.2.a.bz.1.1		4
105.32	even	12		525.2.i.k.151.1		8
105.44	odd	6		735.2.d.d.589.7		8
105.47	odd	12		3675.2.a.bn.1.4		4
105.53	even	12		525.2.i.h.151.4		8
105.59	even	6		735.2.q.g.214.7		16
105.68	odd	12		3675.2.a.cb.1.1		4
105.74	odd	6		105.2.q.a.4.7	yes	16
105.89	even	6		735.2.d.e.589.7		8
105.104	even	2		735.2.q.g.79.2		16
420.179	even	6		1680.2.di.d.529.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.2	✓	16	21.11	odd	6
105.2.q.a.4.7	yes	16	105.74	odd	6
105.2.q.a.79.2	yes	16	15.14	odd	2
105.2.q.a.79.7	yes	16	3.2	odd	2
315.2.bf.b.109.2		16	35.4	even	6	inner
315.2.bf.b.109.7		16	7.4	even	3	inner
315.2.bf.b.289.2		16	1.1	even	1	trivial
315.2.bf.b.289.7		16	5.4	even	2	inner
525.2.i.h.151.4		8	105.53	even	12
525.2.i.h.226.4		8	15.8	even	4
525.2.i.k.151.1		8	105.32	even	12
525.2.i.k.226.1		8	15.2	even	4
735.2.d.d.589.2		8	21.2	odd	6
735.2.d.d.589.7		8	105.44	odd	6
735.2.d.e.589.2		8	21.5	even	6
735.2.d.e.589.7		8	105.89	even	6
735.2.q.g.79.2		16	105.104	even	2
735.2.q.g.79.7		16	21.20	even	2
735.2.q.g.214.2		16	21.17	even	6
735.2.q.g.214.7		16	105.59	even	6
1680.2.di.d.289.2		16	12.11	even	2
1680.2.di.d.289.6		16	60.59	even	2
1680.2.di.d.529.2		16	420.179	even	6
1680.2.di.d.529.6		16	84.11	even	6
2205.2.d.o.1324.2		8	35.19	odd	6
2205.2.d.o.1324.7		8	7.5	odd	6
2205.2.d.s.1324.2		8	35.9	even	6
2205.2.d.s.1324.7		8	7.2	even	3
3675.2.a.bn.1.4		4	105.47	odd	12
3675.2.a.bp.1.4		4	105.2	even	12
3675.2.a.bz.1.1		4	105.23	even	12
3675.2.a.cb.1.1		4	105.68	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54296 - 0.890827i) q^{2} +(0.587145 + 1.01696i) q^{4} +(1.33920 - 1.79069i) q^{5} +(-2.40898 - 1.09398i) q^{7} +1.47113i q^{8} +O(q^{10})\)	\(q+(-1.54296 - 0.890827i) q^{2} +(0.587145 + 1.01696i) q^{4} +(1.33920 - 1.79069i) q^{5} +(-2.40898 - 1.09398i) q^{7} +1.47113i q^{8} +(-3.66151 + 1.56996i) q^{10} +(-1.03925 - 1.80003i) q^{11} -3.13023i q^{13} +(2.74241 + 3.83396i) q^{14} +(2.48481 - 4.30382i) q^{16} +(1.84483 - 1.06512i) q^{17} +(-3.86880 + 6.70095i) q^{19} +(2.60736 + 0.310523i) q^{20} +3.70316i q^{22} +(-4.79479 - 2.76827i) q^{23} +(-1.41311 - 4.79616i) q^{25} +(-2.78849 + 4.82981i) q^{26} +(-0.301877 - 3.09218i) q^{28} -4.01368 q^{29} +(-1.45594 - 2.52177i) q^{31} +(-5.11984 + 2.95594i) q^{32} -3.79533 q^{34} +(-5.18508 + 2.84867i) q^{35} +(-3.04424 - 1.75759i) q^{37} +(11.9388 - 6.89286i) q^{38} +(2.63433 + 1.97013i) q^{40} -7.99038 q^{41} +4.99038i q^{43} +(1.22038 - 2.11376i) q^{44} +(4.93210 + 8.54266i) q^{46} +(2.11376 + 1.22038i) q^{47} +(4.60639 + 5.27078i) q^{49} +(-2.09218 + 8.65910i) q^{50} +(3.18333 - 1.83790i) q^{52} +(8.58394 - 4.95594i) q^{53} +(-4.61504 - 0.549626i) q^{55} +(1.60939 - 3.54393i) q^{56} +(6.19294 + 3.57549i) q^{58} +(-1.47797 - 2.55992i) q^{59} +(5.44729 - 9.43499i) q^{61} +5.18797i q^{62} +0.593684 q^{64} +(-5.60526 - 4.19199i) q^{65} +(3.32501 - 1.91970i) q^{67} +(2.16637 + 1.25075i) q^{68} +(10.5380 + 0.223633i) q^{70} +15.0248 q^{71} +(7.40771 - 4.27684i) q^{73} +(3.13142 + 5.42378i) q^{74} -9.08617 q^{76} +(0.534324 + 5.47316i) q^{77} +(4.05677 - 7.02653i) q^{79} +(-4.37914 - 10.2132i) q^{80} +(12.3288 + 7.11804i) q^{82} -8.75128i q^{83} +(0.563307 - 4.72992i) q^{85} +(4.44556 - 7.69994i) q^{86} +(2.64808 - 1.52887i) q^{88} +(-0.309330 + 0.535776i) q^{89} +(-3.42443 + 7.54067i) q^{91} -6.50151i q^{92} +(-2.17429 - 3.76598i) q^{94} +(6.81823 + 15.9017i) q^{95} -0.296842i q^{97} +(-2.41212 - 12.2361i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5}+O(q^{10}) \) 16 * q + 8 * q^4 - 2 * q^5	\( 16 q + 8 q^{4} - 2 q^{5} - 4 q^{10} + 24 q^{14} - 24 q^{19} + 8 q^{20} - 4 q^{25} + 12 q^{26} - 24 q^{29} + 16 q^{31} + 16 q^{34} + 10 q^{35} + 32 q^{40} - 16 q^{41} - 20 q^{44} - 32 q^{46} - 40 q^{49} + 40 q^{50} + 8 q^{55} - 84 q^{56} - 4 q^{59} + 16 q^{61} + 16 q^{64} - 30 q^{65} + 16 q^{70} + 56 q^{71} - 40 q^{74} - 64 q^{76} - 16 q^{79} - 52 q^{80} - 64 q^{85} + 48 q^{86} - 16 q^{89} + 8 q^{91} - 32 q^{94} + 22 q^{95}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 - 4 * q^10 + 24 * q^14 - 24 * q^19 + 8 * q^20 - 4 * q^25 + 12 * q^26 - 24 * q^29 + 16 * q^31 + 16 * q^34 + 10 * q^35 + 32 * q^40 - 16 * q^41 - 20 * q^44 - 32 * q^46 - 40 * q^49 + 40 * q^50 + 8 * q^55 - 84 * q^56 - 4 * q^59 + 16 * q^61 + 16 * q^64 - 30 * q^65 + 16 * q^70 + 56 * q^71 - 40 * q^74 - 64 * q^76 - 16 * q^79 - 52 * q^80 - 64 * q^85 + 48 * q^86 - 16 * q^89 + 8 * q^91 - 32 * q^94 + 22 * q^95

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