LMFDB - Embedded newform 261.2.k.c.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			199.1
Root			$2.87569 + 1.38486i$ of defining polynomial
Character	$\chi$	$=$	261.199
Dual form			261.2.k.c.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.487716 + 2.13682i) q^{2} +(-2.52621 - 1.21656i) q^{4} +(-0.533332 + 2.33668i) q^{5} +(-1.21803 + 0.586571i) q^{7} +(1.09855 - 1.37753i) q^{8} +(-4.73296 - 2.27927i) q^{10} +(-2.18816 - 2.74387i) q^{11} +(3.76255 + 4.71809i) q^{13} +(-0.659347 - 2.88879i) q^{14} +(-1.08862 - 1.36508i) q^{16} -3.05437 q^{17} +(-5.07762 - 2.44525i) q^{19} +(4.19002 - 5.25412i) q^{20} +(6.93036 - 3.33749i) q^{22} +(0.225809 + 0.989335i) q^{23} +(-0.670784 - 0.323033i) q^{25} +(-11.9168 + 5.73883i) q^{26} +3.79059 q^{28} +(5.14766 + 1.58164i) q^{29} +(-1.80501 + 7.90829i) q^{31} +(6.62277 - 3.18936i) q^{32} +(1.48967 - 6.52665i) q^{34} +(-0.721015 - 3.15897i) q^{35} +(3.42698 - 4.29729i) q^{37} +(7.70151 - 9.65739i) q^{38} +(2.63296 + 3.30163i) q^{40} +6.85782 q^{41} +(1.73610 + 7.60636i) q^{43} +(2.18968 + 9.59361i) q^{44} -2.22416 q^{46} +(0.260777 + 0.327004i) q^{47} +(-3.22491 + 4.04390i) q^{49} +(1.01742 - 1.27580i) q^{50} +(-3.76517 - 16.4963i) q^{52} +(-2.96899 + 13.0080i) q^{53} +(7.57855 - 3.64964i) q^{55} +(-0.530037 + 2.32225i) q^{56} +(-5.89028 + 10.2283i) q^{58} -3.56102 q^{59} +(-6.49557 + 3.12810i) q^{61} +(-16.0183 - 7.71400i) q^{62} +(2.80802 + 12.3027i) q^{64} +(-13.0314 + 6.27557i) q^{65} +(5.18318 - 6.49950i) q^{67} +(7.71599 + 3.71582i) q^{68} +7.10182 q^{70} +(6.10196 + 7.65161i) q^{71} +(0.0675863 + 0.296115i) q^{73} +(7.51117 + 9.41871i) q^{74} +(9.85235 + 12.3545i) q^{76} +(4.27471 + 2.05859i) q^{77} +(2.49794 - 3.13231i) q^{79} +(3.77036 - 1.81571i) q^{80} +(-3.34467 + 14.6540i) q^{82} +(-3.88709 - 1.87192i) q^{83} +(1.62899 - 7.13709i) q^{85} -17.1002 q^{86} -6.18356 q^{88} +(3.11361 - 13.6416i) q^{89} +(-7.35039 - 3.53976i) q^{91} +(0.633143 - 2.77398i) q^{92} +(-0.825935 + 0.397749i) q^{94} +(8.42183 - 10.5606i) q^{95} +(3.42690 + 1.65031i) q^{97} +(-7.06827 - 8.86333i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) $ 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

Character values

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

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.487716	+	2.13682i	−0.344867	+	1.51096i	0.443791	+	0.896130i	$0.353633\pi$
$2$	−0.487716	+	2.13682i	−0.344867	+	1.51096i	−0.788658	+	0.614832i	$0.789224\pi$
$3$		0			0
$3$		0			0
$4$	−2.52621	−	1.21656i	−1.26311	−	0.608280i
$5$	−0.533332	+	2.33668i	−0.238513	+	1.04499i	0.703836	+	0.710363i	$0.251469\pi$
$5$	−0.533332	+	2.33668i	−0.238513	+	1.04499i	−0.942349	+	0.334632i	$0.891388\pi$
$6$		0			0
$7$	−1.21803	+	0.586571i	−0.460371	+	0.221703i	−0.649670	−	0.760217i	$-0.725093\pi$
$7$	−1.21803	+	0.586571i	−0.460371	+	0.221703i	0.189299	+	0.981920i	$0.439378\pi$
$8$	1.09855	−	1.37753i	0.388395	−	0.487031i
$9$		0			0
$10$	−4.73296	−	2.27927i	−1.49669	−	0.720769i
$11$	−2.18816	−	2.74387i	−0.659755	−	0.827307i	0.333561	−	0.942728i	$-0.391750\pi$
$11$	−2.18816	−	2.74387i	−0.659755	−	0.827307i	−0.993317	+	0.115421i	$0.963178\pi$
$12$		0			0
$13$	3.76255	+	4.71809i	1.04354	+	1.30856i	0.949763	+	0.312971i	$0.101324\pi$
$13$	3.76255	+	4.71809i	1.04354	+	1.30856i	0.0937822	+	0.995593i	$0.470104\pi$
$14$	−0.659347	−	2.88879i	−0.176218	−	0.772061i
$15$		0			0
$16$	−1.08862	−	1.36508i	−0.272155	−	0.341271i
$17$	−3.05437			−0.740794			−0.370397	−	0.928874i	$-0.620778\pi$
$17$	−3.05437			−0.740794			−0.370397	+	0.928874i	$0.620778\pi$
$18$		0			0
$19$	−5.07762	−	2.44525i	−1.16489	−	0.560980i	−0.251414	−	0.967880i	$-0.580895\pi$
$19$	−5.07762	−	2.44525i	−1.16489	−	0.560980i	−0.913473	+	0.406900i	$0.866610\pi$
$20$	4.19002	−	5.25412i	0.936916	−	1.17486i
$21$		0			0
$22$	6.93036	−	3.33749i	1.47756	−	0.711555i
$23$	0.225809	+	0.989335i	0.0470845	+	0.206291i	0.992999	−	0.118127i	$-0.0376889\pi$
$23$	0.225809	+	0.989335i	0.0470845	+	0.206291i	−0.945914	+	0.324417i	$0.894832\pi$
$24$		0			0
$25$	−0.670784	−	0.323033i	−0.134157	−	0.0646065i
$26$	−11.9168	+	5.73883i	−2.33708	+	1.12548i
$27$		0			0
$28$	3.79059			0.716354
$29$	5.14766	+	1.58164i	0.955897	+	0.293703i
$29$	5.14766	+	1.58164i	0.955897	+	0.293703i
$30$		0			0
$31$	−1.80501	+	7.90829i	−0.324190	+	1.42037i	0.505828	+	0.862634i	$0.331187\pi$
$31$	−1.80501	+	7.90829i	−0.324190	+	1.42037i	−0.830018	+	0.557736i	$0.811670\pi$
$32$	6.62277	−	3.18936i	1.17075	−	0.563804i
$33$		0			0
$34$	1.48967	−	6.52665i	0.255476	−	1.11931i
$35$	−0.721015	−	3.15897i	−0.121874	−	0.533964i
$36$		0			0
$37$	3.42698	−	4.29729i	0.563392	−	0.706471i	−0.415789	−	0.909461i	$-0.636495\pi$
$37$	3.42698	−	4.29729i	0.563392	−	0.706471i	0.979181	+	0.202990i	$0.0650660\pi$
$38$	7.70151	−	9.65739i	1.24935	−	1.56664i
$39$		0			0
$40$	2.63296	+	3.30163i	0.416308	+	0.522034i
$41$	6.85782			1.07101			0.535506	−	0.844531i	$-0.320121\pi$
$41$	6.85782			1.07101			0.535506	+	0.844531i	$0.320121\pi$
$42$		0			0
$43$	1.73610	+	7.60636i	0.264753	+	1.15996i	0.916027	+	0.401116i	$0.131378\pi$
$43$	1.73610	+	7.60636i	0.264753	+	1.15996i	−0.651274	+	0.758843i	$0.725765\pi$
$44$	2.18968	+	9.59361i	0.330107	+	1.44629i
$45$		0			0
$46$	−2.22416			−0.327935
$47$	0.260777	+	0.327004i	0.0380382	+	0.0476984i	0.800487	−	0.599350i	$-0.204574\pi$
$47$	0.260777	+	0.327004i	0.0380382	+	0.0476984i	−0.762449	+	0.647049i	$0.776003\pi$
$48$		0			0
$49$	−3.22491	+	4.04390i	−0.460701	+	0.577700i
$50$	1.01742	−	1.27580i	0.143884	−	0.180425i
$51$		0			0
$52$	−3.76517	−	16.4963i	−0.522135	−	2.28762i
$53$	−2.96899	+	13.0080i	−0.407821	+	1.78678i	0.186392	+	0.982475i	$0.440320\pi$
$53$	−2.96899	+	13.0080i	−0.407821	+	1.78678i	−0.594214	+	0.804307i	$0.702537\pi$
$54$		0			0
$55$	7.57855	−	3.64964i	1.02189	−	0.492117i
$56$	−0.530037	+	2.32225i	−0.0708292	+	0.310323i
$57$		0			0
$58$	−5.89028	+	10.2283i	−0.773432	+	1.34304i
$59$	−3.56102			−0.463606			−0.231803	−	0.972763i	$-0.574462\pi$
$59$	−3.56102			−0.463606			−0.231803	+	0.972763i	$0.574462\pi$
$60$		0			0
$61$	−6.49557	+	3.12810i	−0.831672	+	0.400512i	−0.800742	−	0.599009i	$-0.795561\pi$
$61$	−6.49557	+	3.12810i	−0.831672	+	0.400512i	−0.0309301	+	0.999522i	$0.509847\pi$
$62$	−16.0183	−	7.71400i	−2.03432	−	0.979679i
$63$		0			0
$64$	2.80802	+	12.3027i	0.351002	+	1.53784i
$65$	−13.0314	+	6.27557i	−1.61634	+	0.778389i
$66$		0			0
$67$	5.18318	−	6.49950i	0.633226	−	0.794040i	−0.356912	−	0.934138i	$-0.616170\pi$
$67$	5.18318	−	6.49950i	0.633226	−	0.794040i	0.990138	+	0.140098i	$0.0447418\pi$
$68$	7.71599	+	3.71582i	0.935701	+	0.450610i
$69$		0			0
$70$	7.10182			0.848830
$71$	6.10196	+	7.65161i	0.724169	+	0.908079i	0.998566	−	0.0535372i	$-0.0170496\pi$
$71$	6.10196	+	7.65161i	0.724169	+	0.908079i	−0.274397	+	0.961617i	$0.588478\pi$
$72$		0			0
$73$	0.0675863	+	0.296115i	0.00791038	+	0.0346577i	0.978729	−	0.205157i	$-0.0657705\pi$
$73$	0.0675863	+	0.296115i	0.00791038	+	0.0346577i	−0.970819	+	0.239815i	$0.922913\pi$
$74$	7.51117	+	9.41871i	0.873156	+	1.09490i
$75$		0			0
$76$	9.85235	+	12.3545i	1.13014	+	1.41715i
$77$	4.27471	+	2.05859i	0.487148	+	0.234598i
$78$		0			0
$79$	2.49794	−	3.13231i	0.281040	−	0.352413i	−0.621196	−	0.783655i	$-0.713353\pi$
$79$	2.49794	−	3.13231i	0.281040	−	0.352413i	0.902236	+	0.431242i	$0.141924\pi$
$80$	3.77036	−	1.81571i	0.421539	−	0.203002i
$81$		0			0
$82$	−3.34467	+	14.6540i	−0.369357	+	1.61826i
$83$	−3.88709	−	1.87192i	−0.426663	−	0.205470i	0.208214	−	0.978083i	$-0.433235\pi$
$83$	−3.88709	−	1.87192i	−0.426663	−	0.205470i	−0.634877	+	0.772613i	$0.718949\pi$
$84$		0			0
$85$	1.62899	−	7.13709i	0.176689	−	0.774126i
$86$	−17.1002			−1.84396
$87$		0			0
$88$	−6.18356			−0.659170
$89$	3.11361	−	13.6416i	0.330042	−	1.44601i	−0.489004	−	0.872282i	$-0.662640\pi$
$89$	3.11361	−	13.6416i	0.330042	−	1.44601i	0.819046	−	0.573728i	$-0.194503\pi$
$90$		0			0
$91$	−7.35039	−	3.53976i	−0.770530	−	0.371068i
$92$	0.633143	−	2.77398i	0.0660097	−	0.289207i
$93$		0			0
$94$	−0.825935	+	0.397749i	−0.0851887	+	0.0410247i
$95$	8.42183	−	10.5606i	0.864062	−	1.08350i
$96$		0			0
$97$	3.42690	+	1.65031i	0.347949	+	0.167563i	0.599692	−	0.800231i	$-0.295290\pi$
$97$	3.42690	+	1.65031i	0.347949	+	0.167563i	−0.251743	+	0.967794i	$0.581004\pi$
$98$	−7.06827	−	8.86333i	−0.714003	−	0.895332i
$99$		0			0
$100$	1.30155	+	1.63210i	0.130155	+	0.163210i
$101$	−0.00939526	−	0.0411633i	−0.000934863	−	0.00409590i	0.974458	−	0.224568i	$-0.0720972\pi$
$101$	−0.00939526	−	0.0411633i	−0.000934863	−	0.00409590i	−0.975393	+	0.220472i	$0.929240\pi$
$102$		0			0
$103$	7.34494	+	9.21026i	0.723718	+	0.907514i	0.998542	−	0.0539808i	$-0.0171910\pi$
$103$	7.34494	+	9.21026i	0.723718	+	0.907514i	−0.274824	+	0.961495i	$0.588620\pi$
$104$	10.6327			1.04262
$105$		0			0
$106$	−26.3477	−	12.6884i	−2.55912	−	1.23241i
$107$	3.90752	−	4.89987i	0.377754	−	0.473688i	−0.556217	−	0.831037i	$-0.687748\pi$
$107$	3.90752	−	4.89987i	0.377754	−	0.473688i	0.933971	+	0.357349i	$0.116319\pi$
$108$		0			0
$109$	13.3409	−	6.42464i	1.27783	−	0.615369i	0.332996	−	0.942928i	$-0.391940\pi$
$109$	13.3409	−	6.42464i	1.27783	−	0.615369i	0.944831	+	0.327559i	$0.106226\pi$
$110$	4.10245	+	17.9740i	0.391154	+	1.71376i
$111$		0			0
$112$	2.12668	+	1.02416i	0.200953	+	0.0967737i
$113$	10.7154	−	5.16029i	1.00802	−	0.485439i	0.144370	−	0.989524i	$-0.453884\pi$
$113$	10.7154	−	5.16029i	1.00802	−	0.485439i	0.863654	+	0.504085i	$0.168170\pi$
$114$		0			0
$115$	−2.43219			−0.226803
$116$	−11.0799	−	10.2580i	−1.02874	−	0.952430i
$117$		0			0
$118$	1.73677	−	7.60928i	0.159883	−	0.700491i
$119$	3.72031	−	1.79160i	0.341040	−	0.164236i
$120$		0			0
$121$	−0.293028	+	1.28384i	−0.0266389	+	0.116713i
$122$	−3.51621	−	15.4055i	−0.318342	−	1.39475i
$123$		0			0
$124$	14.1807	−	17.7821i	1.27347	−	1.59688i
$125$	−6.35924	+	7.97423i	−0.568788	+	0.713237i
$126$		0			0
$127$	−9.41080	−	11.8008i	−0.835074	−	1.04715i	−0.998166	−	0.0605385i	$-0.980718\pi$
$127$	−9.41080	−	11.8008i	−0.835074	−	1.04715i	0.163092	−	0.986611i	$-0.447853\pi$
$128$	−12.9568			−1.14523
$129$		0			0
$130$	−7.05419	−	30.9064i	−0.618693	−	2.71067i
$131$	2.32463	+	10.1849i	0.203103	+	0.889855i	0.969033	+	0.246930i	$0.0794219\pi$
$131$	2.32463	+	10.1849i	0.203103	+	0.889855i	−0.765930	+	0.642924i	$0.777721\pi$
$132$		0			0
$133$	7.61899			0.660650
$134$	11.3604	+	14.2454i	0.981386	+	1.23062i
$135$		0			0
$136$	−3.35537	+	4.20750i	−0.287720	+	0.360790i
$137$	2.28953	−	2.87098i	0.195608	−	0.245284i	−0.674348	−	0.738413i	$-0.735575\pi$
$137$	2.28953	−	2.87098i	0.195608	−	0.245284i	0.869956	+	0.493129i	$0.164147\pi$
$138$		0			0
$139$	−1.28647	−	5.63639i	−0.109117	−	0.478072i	−0.999728	−	0.0233073i	$-0.992580\pi$
$139$	−1.28647	−	5.63639i	−0.109117	−	0.478072i	0.890611	−	0.454765i	$-0.150277\pi$
$140$	−2.02164	+	8.85739i	−0.170860	+	0.748586i
$141$		0			0
$142$	−19.3262	+	9.30699i	−1.62182	+	0.781025i
$143$	4.71275	−	20.6479i	0.394100	−	1.72666i
$144$		0			0
$145$	−6.44120	+	11.1849i	−0.534912	+	0.928855i
$146$	−0.665709			−0.0550944
$147$		0			0
$148$	−13.8852	+	6.68675i	−1.14135	+	0.549648i
$149$	−7.73406	−	3.72453i	−0.633599	−	0.305125i	0.0893774	−	0.995998i	$-0.471512\pi$
$149$	−7.73406	−	3.72453i	−0.633599	−	0.305125i	−0.722977	+	0.690873i	$0.757227\pi$
$150$		0			0
$151$	−2.65704	−	11.6412i	−0.216227	−	0.947351i	−0.960238	−	0.279184i	$-0.909936\pi$
$151$	−2.65704	−	11.6412i	−0.216227	−	0.947351i	0.744011	−	0.668168i	$-0.232921\pi$
$152$	−8.94642	+	4.30837i	−0.725650	+	0.349455i
$153$		0			0
$154$	−6.48369	+	8.13029i	−0.522471	+	0.655158i
$155$	−17.5165	−	8.43548i	−1.40696	−	0.677554i
$156$		0			0
$157$	−12.2535			−0.977936			−0.488968	−	0.872302i	$-0.662626\pi$
$157$	−12.2535			−0.977936			−0.488968	+	0.872302i	$0.662626\pi$
$158$	5.47492	+	6.86533i	0.435561	+	0.546176i
$159$		0			0
$160$	3.92037	+	17.1763i	0.309933	+	1.35790i
$161$	−0.855356	−	1.07258i	−0.0674115	−	0.0845314i
$162$		0			0
$163$	−4.94515	−	6.20102i	−0.387334	−	0.485701i	0.549491	−	0.835499i	$-0.314822\pi$
$163$	−4.94515	−	6.20102i	−0.387334	−	0.485701i	−0.936825	+	0.349798i	$0.886250\pi$
$164$	−17.3243	−	8.34295i	−1.35280	−	0.651475i
$165$		0			0
$166$	5.89576	−	7.39305i	0.457600	−	0.573812i
$167$	11.6445	−	5.60770i	0.901080	−	0.433937i	0.0748008	−	0.997198i	$-0.476168\pi$
$167$	11.6445	−	5.60770i	0.901080	−	0.433937i	0.826279	+	0.563261i	$0.190454\pi$
$168$		0			0
$169$	−5.21082	+	22.8301i	−0.400833	+	1.75616i
$170$	14.4562	+	6.96175i	1.10874	+	0.533941i
$171$		0			0
$172$	4.86783	−	21.3273i	0.371168	−	1.62619i
$173$	−2.65357			−0.201747			−0.100874	−	0.994899i	$-0.532164\pi$
$173$	−2.65357			−0.201747			−0.100874	+	0.994899i	$0.532164\pi$
$174$		0			0
$175$	1.00651			0.0760853
$176$	−1.36354	+	5.97405i	−0.102781	+	0.450311i
$177$		0			0
$178$	27.6312	+	13.3065i	2.07105	+	0.997363i
$179$	−2.98150	+	13.0628i	−0.222848	+	0.976361i	0.732474	+	0.680795i	$0.238365\pi$
$179$	−2.98150	+	13.0628i	−0.222848	+	0.976361i	−0.955322	+	0.295566i	$0.904492\pi$
$180$		0			0
$181$	−1.36397	+	0.656854i	−0.101383	+	0.0488236i	−0.483888	−	0.875130i	$-0.660776\pi$
$181$	−1.36397	+	0.656854i	−0.101383	+	0.0488236i	0.382505	+	0.923953i	$0.375062\pi$
$182$	11.1487	−	13.9801i	0.826400	−	1.03627i
$183$		0			0
$184$	1.61090	+	0.775770i	0.118757	+	0.0571905i
$185$	8.21368	+	10.2996i	0.603882	+	0.757244i
$186$		0			0
$187$	6.68346	+	8.38079i	0.488743	+	0.612864i
$188$	−0.260958	−	1.14333i	−0.0190323	−	0.0833860i
$189$		0			0
$190$	18.4588	+	23.1466i	1.33914	+	1.67923i
$191$	11.6187			0.840696			0.420348	−	0.907363i	$-0.361908\pi$
$191$	11.6187			0.840696			0.420348	+	0.907363i	$0.361908\pi$
$192$		0			0
$193$	5.55158	+	2.67350i	0.399612	+	0.192443i	0.622886	−	0.782313i	$-0.285960\pi$
$193$	5.55158	+	2.67350i	0.399612	+	0.192443i	−0.223274	+	0.974756i	$0.571674\pi$
$194$	−5.19777	+	6.51780i	−0.373178	+	0.467951i
$195$		0			0
$196$	13.0664	−	6.29246i	0.933317	−	0.449462i
$197$	−0.562248	−	2.46337i	−0.0400585	−	0.175508i	0.950941	−	0.309372i	$-0.100119\pi$
$197$	−0.562248	−	2.46337i	−0.0400585	−	0.175508i	−0.991000	+	0.133864i	$0.957262\pi$
$198$		0			0
$199$	−11.9665	−	5.76277i	−0.848284	−	0.408512i	−0.0413438	−	0.999145i	$-0.513164\pi$
$199$	−11.9665	−	5.76277i	−0.848284	−	0.408512i	−0.806940	+	0.590633i	$0.798878\pi$
$200$	−1.18187	+	0.569161i	−0.0835712	+	0.0402458i
$201$		0			0
$202$	0.0925410			0.00651116
$203$	−7.19773	+	1.09299i	−0.505182	+	0.0767128i
$204$		0			0
$205$	−3.65749	+	16.0245i	−0.255451	+	1.11920i
$206$	−23.2629	+	11.2028i	−1.62081	+	0.780539i
$207$		0			0
$208$	2.34461	−	10.2724i	0.162569	−	0.712263i
$209$	4.40120	+	19.2829i	0.304438	+	1.33383i
$210$		0			0
$211$	−5.17794	+	6.49294i	−0.356464	+	0.446992i	−0.927438	−	0.373976i	$-0.877994\pi$
$211$	−5.17794	+	6.49294i	−0.356464	+	0.446992i	0.570974	+	0.820968i	$0.306566\pi$
$212$	23.3253	−	29.2489i	1.60198	−	2.00883i
$213$		0			0
$214$	8.56440	+	10.7394i	0.585450	+	0.734132i
$215$	−18.6995			−1.27530
$216$		0			0
$217$	−2.44021	−	10.6913i	−0.165652	−	0.725771i
$218$	7.22175	+	31.6406i	0.489119	+	2.14297i
$219$		0			0
$220$	−23.5850			−1.59010
$221$	−11.4922	−	14.4108i	−0.773052	−	0.969376i
$222$		0			0
$223$	15.5947	−	19.5551i	1.04430	−	1.30951i	0.0948805	−	0.995489i	$-0.469753\pi$
$223$	15.5947	−	19.5551i	1.04430	−	1.30951i	0.949417	−	0.314019i	$-0.101675\pi$
$224$	−6.19592	+	7.76944i	−0.413983	+	0.519118i
$225$		0			0
$226$	5.80053	+	25.4138i	0.385845	+	1.69050i
$227$	0.677325	−	2.96756i	0.0449556	−	0.196964i	−0.947463	−	0.319865i	$-0.896363\pi$
$227$	0.677325	−	2.96756i	0.0449556	−	0.196964i	0.992419	+	0.122901i	$0.0392197\pi$
$228$		0			0
$229$	19.7389	−	9.50577i	1.30439	−	0.628159i	0.352845	−	0.935682i	$-0.385214\pi$
$229$	19.7389	−	9.50577i	1.30439	−	0.628159i	0.951541	+	0.307523i	$0.0995001\pi$
$230$	1.18622	−	5.19716i	0.0782169	−	0.342691i
$231$		0			0
$232$	7.83370	−	5.35357i	0.514308	−	0.351479i
$233$	−9.96464			−0.652805			−0.326403	−	0.945231i	$-0.605837\pi$
$233$	−9.96464			−0.652805			−0.326403	+	0.945231i	$0.605837\pi$
$234$		0			0
$235$	−0.903184	+	0.434951i	−0.0589173	+	0.0283731i
$236$	8.99590	+	4.33220i	0.585583	+	0.282002i
$237$		0			0
$238$	2.01389	+	8.82343i	0.130541	+	0.571938i
$239$	−7.01041	+	3.37604i	−0.453466	+	0.218378i	−0.646653	−	0.762784i	$-0.723832\pi$
$239$	−7.01041	+	3.37604i	−0.453466	+	0.218378i	0.193187	+	0.981162i	$0.438118\pi$
$240$		0			0
$241$	−14.4582	+	18.1300i	−0.931334	+	1.16786i	0.0542254	+	0.998529i	$0.482731\pi$
$241$	−14.4582	+	18.1300i	−0.931334	+	1.16786i	−0.985560	+	0.169328i	$0.945840\pi$
$242$	−2.60043	−	1.25230i	−0.167162	−	0.0805009i
$243$		0			0
$244$	20.2147			1.29411
$245$	−7.72936	−	9.69231i	−0.493811	−	0.619219i
$246$		0			0
$247$	−7.56789	−	33.1571i	−0.481533	−	2.10974i
$248$	8.91103	+	11.1741i	0.565851	+	0.709555i
$249$		0			0
$250$	−13.9380	−	17.4777i	−0.881518	−	1.10539i
$251$	1.06363	+	0.512217i	0.0671357	+	0.0323308i	0.467150	−	0.884178i	$-0.345281\pi$
$251$	1.06363	+	0.512217i	0.0671357	+	0.0323308i	−0.400015	+	0.916509i	$0.630995\pi$
$252$		0			0
$253$	2.22050	−	2.78441i	0.139601	−	0.175055i
$254$	29.8060	−	14.3538i	1.87019	−	0.900637i
$255$		0			0
$256$	0.703222	−	3.08102i	0.0439514	−	0.192564i
$257$	14.3925	+	6.93107i	0.897781	+	0.432348i	0.825087	−	0.565006i	$-0.191126\pi$
$257$	14.3925	+	6.93107i	0.897781	+	0.432348i	0.0726939	+	0.997354i	$0.476840\pi$
$258$		0			0
$259$	−1.65348	+	7.24438i	−0.102742	+	0.450144i
$260$	40.5546			2.51509
$261$		0			0
$262$	−22.8970			−1.41458
$263$	3.25116	−	14.2443i	0.200475	−	0.878339i	−0.770173	−	0.637835i	$-0.779830\pi$
$263$	3.25116	−	14.2443i	0.200475	−	0.878339i	0.970648	−	0.240504i	$-0.0773126\pi$
$264$		0			0
$265$	−28.8120	−	13.8751i	−1.76991	−	0.852343i
$266$	−3.71590	+	16.2804i	−0.227837	+	0.998218i
$267$		0			0
$268$	−21.0008	+	10.1135i	−1.28283	+	0.617778i
$269$	−13.7882	+	17.2899i	−0.840681	+	1.05418i	0.157099	+	0.987583i	$0.449786\pi$
$269$	−13.7882	+	17.2899i	−0.840681	+	1.05418i	−0.997780	+	0.0665980i	$0.978785\pi$
$270$		0			0
$271$	20.8260	+	10.0293i	1.26509	+	0.609236i	0.941516	−	0.336967i	$-0.109401\pi$
$271$	20.8260	+	10.0293i	1.26509	+	0.609236i	0.323574	+	0.946203i	$0.395115\pi$
$272$	3.32504	+	4.16947i	0.201610	+	0.252812i
$273$		0			0
$274$	5.01814	+	6.29255i	0.303157	+	0.380147i
$275$	0.581425	+	2.54739i	0.0350613	+	0.153613i
$276$		0			0
$277$	11.6674	+	14.6304i	0.701024	+	0.879056i	0.997100	−	0.0761086i	$-0.0242496\pi$
$277$	11.6674	+	14.6304i	0.701024	+	0.879056i	−0.296076	+	0.955164i	$0.595678\pi$
$278$	12.6714			0.759980
$279$		0			0
$280$	−5.14366	−	2.47706i	−0.307392	−	0.148032i
$281$	5.40308	−	6.77525i	0.322321	−	0.404177i	−0.594102	−	0.804390i	$-0.702492\pi$
$281$	5.40308	−	6.77525i	0.322321	−	0.404177i	0.916422	+	0.400213i	$0.131064\pi$
$282$		0			0
$283$	−5.03188	+	2.42322i	−0.299114	+	0.144046i	−0.577421	−	0.816446i	$-0.695941\pi$
$283$	−5.03188	+	2.42322i	−0.299114	+	0.144046i	0.278307	+	0.960492i	$0.410227\pi$
$284$	−6.10619	−	26.7530i	−0.362336	−	1.58750i
$285$		0			0
$286$	41.8224	+	20.1406i	2.47301	+	1.19094i
$287$	−8.35301	+	4.02260i	−0.493063	+	0.237446i
$288$		0			0
$289$	−7.67081			−0.451224
$290$	−20.7587	−	19.2188i	−1.21899	−	1.12856i
$291$		0			0
$292$	0.189504	−	0.830272i	0.0110899	−	0.0485880i
$293$	−4.25166	+	2.04749i	−0.248385	+	0.119616i	−0.553934	−	0.832560i	$-0.686874\pi$
$293$	−4.25166	+	2.04749i	−0.248385	+	0.119616i	0.305549	+	0.952176i	$0.401160\pi$
$294$		0			0
$295$	1.89921	−	8.32097i	0.110576	−	0.484466i
$296$	−2.15497	−	9.44155i	−0.125255	−	0.548779i
$297$		0			0
$298$	11.7307	−	14.7098i	0.679540	−	0.852117i
$299$	−3.81816	+	4.78782i	−0.220810	+	0.276887i
$300$		0			0
$301$	−6.57628	−	8.24640i	−0.379051	−	0.475315i
$302$	26.1712			1.50598
$303$		0			0
$304$	2.18961	+	9.59333i	0.125583	+	0.550215i
$305$	−3.84508	−	16.8464i	−0.220168	−	0.964621i
$306$		0			0
$307$	11.7362			0.669821			0.334910	−	0.942250i	$-0.391294\pi$
$307$	11.7362			0.669821			0.334910	+	0.942250i	$0.391294\pi$
$308$	−8.29442	−	10.4009i	−0.472618	−	0.592645i
$309$		0			0
$310$	26.5682	−	33.3155i	1.50897	−	1.89219i
$311$	−10.4770	+	13.1378i	−0.594097	+	0.744974i	−0.984445	−	0.175693i	$-0.943783\pi$
$311$	−10.4770	+	13.1378i	−0.594097	+	0.744974i	0.390348	+	0.920667i	$0.372355\pi$
$312$		0			0
$313$	2.66132	+	11.6600i	0.150427	+	0.659063i	0.992761	+	0.120107i	$0.0383239\pi$
$313$	2.66132	+	11.6600i	0.150427	+	0.659063i	−0.842334	+	0.538956i	$0.818819\pi$
$314$	5.97623	−	26.1836i	0.337258	−	1.47762i
$315$		0			0
$316$	−10.1210	+	4.87400i	−0.569349	+	0.274184i
$317$	−3.14555	+	13.7815i	−0.176671	+	0.774048i	0.806481	+	0.591260i	$0.201369\pi$
$317$	−3.14555	+	13.7815i	−0.176671	+	0.774048i	−0.983152	+	0.182788i	$0.941488\pi$
$318$		0			0
$319$	−6.92410	−	17.5854i	−0.387675	−	0.984592i
$320$	−30.2451			−1.69075
$321$		0			0
$322$	2.70909	−	1.30463i	0.150972	−	0.0727042i
$323$	15.5089	+	7.46871i	0.862941	+	0.415570i
$324$		0			0
$325$	−0.999763	−	4.38025i	−0.0554569	−	0.242973i
$326$	15.6623	−	7.54257i	0.867455	−	0.417744i
$327$		0			0
$328$	7.53363	−	9.44687i	0.415975	−	0.521616i
$329$	−0.509444	−	0.245335i	−0.0280866	−	0.0135258i
$330$		0			0
$331$	23.0236			1.26549			0.632747	−	0.774359i	$-0.281927\pi$
$331$	23.0236			1.26549			0.632747	+	0.774359i	$0.281927\pi$
$332$	7.54230	+	9.45774i	0.413937	+	0.519061i
$333$		0			0
$334$	6.30346	+	27.6172i	0.344910	+	1.51115i
$335$	12.4229	+	15.5778i	0.678735	+	0.851107i
$336$		0			0
$337$	−1.59382	−	1.99859i	−0.0868212	−	0.108870i	0.736524	−	0.676412i	$-0.236466\pi$
$337$	−1.59382	−	1.99859i	−0.0868212	−	0.108870i	−0.823345	+	0.567542i	$0.807895\pi$
$338$	−46.2425	−	22.2692i	−2.51526	−	1.21129i
$339$		0			0
$340$	−12.7979	+	16.0480i	−0.694062	+	0.870326i
$341$	25.6490	−	12.3519i	1.38897	−	0.668892i
$342$		0			0
$343$	3.66178	−	16.0433i	0.197717	−	0.866257i
$344$	12.3852	+	5.96440i	0.667765	+	0.321579i
$345$		0			0
$346$	1.29419	−	5.67022i	0.0695761	−	0.304833i
$347$	0.891885			0.0478789			0.0239394	−	0.999713i	$-0.492379\pi$
$347$	0.891885			0.0478789			0.0239394	+	0.999713i	$0.492379\pi$
$348$		0			0
$349$	−0.755575			−0.0404450			−0.0202225	−	0.999796i	$-0.506437\pi$
$349$	−0.755575			−0.0404450			−0.0202225	+	0.999796i	$0.506437\pi$
$350$	−0.490893	+	2.15074i	−0.0262393	+	0.114962i
$351$		0			0
$352$	−23.2429	−	11.1932i	−1.23885	−	0.596598i
$353$	4.28143	−	18.7582i	0.227878	−	0.998397i	−0.723489	−	0.690336i	$-0.757463\pi$
$353$	4.28143	−	18.7582i	0.227878	−	0.998397i	0.951367	−	0.308061i	$-0.0996802\pi$
$354$		0			0
$355$	−21.1337	+	10.1775i	−1.12166	+	0.540164i
$356$	−24.4615	+	30.6737i	−1.29646	+	1.62570i
$357$		0			0
$358$	−26.4588	−	12.7419i	−1.39839	−	0.673430i
$359$	−10.9825	−	13.7716i	−0.579634	−	0.726838i	0.402416	−	0.915457i	$-0.368170\pi$
$359$	−10.9825	−	13.7716i	−0.579634	−	0.726838i	−0.982050	+	0.188619i	$0.939599\pi$
$360$		0			0
$361$	7.95667	+	9.97735i	0.418772	+	0.525124i
$362$	−0.738351	−	3.23493i	−0.0388068	−	0.170024i
$363$		0			0
$364$	14.2623	+	17.8844i	0.747548	+	0.937395i
$365$	−0.727972			−0.0381038
$366$		0			0
$367$	−3.42176	−	1.64783i	−0.178614	−	0.0860162i	0.342440	−	0.939540i	$-0.388747\pi$
$367$	−3.42176	−	1.64783i	−0.178614	−	0.0860162i	−0.521054	+	0.853524i	$0.674461\pi$
$368$	1.10471	−	1.38526i	0.0575867	−	0.0722115i
$369$		0			0
$370$	−26.0144	+	12.5279i	−1.35243	+	0.651294i
$371$	−4.01379	−	17.5856i	−0.208386	−	0.912998i
$372$		0			0
$373$	7.47141	+	3.59804i	0.386855	+	0.186299i	0.617194	−	0.786811i	$-0.288269\pi$
$373$	7.47141	+	3.59804i	0.386855	+	0.186299i	−0.230339	+	0.973110i	$0.573984\pi$
$374$	−21.1679	+	10.1939i	−1.09457	+	0.527115i
$375$		0			0
$376$	0.736934			0.0380045
$377$	11.9060	+	30.2382i	0.613192	+	1.55734i
$378$		0			0
$379$	1.98764	−	8.70843i	0.102098	−	0.447322i	−0.897877	−	0.440247i	$-0.854891\pi$
$379$	1.98764	−	8.70843i	0.102098	−	0.447322i	0.999975	−	0.00707478i	$-0.00225199\pi$
$380$	−34.1230	+	16.4328i	−1.75047	+	0.842983i
$381$		0			0
$382$	−5.66660	+	24.8270i	−0.289929	+	1.27026i
$383$	7.97804	+	34.9541i	0.407659	+	1.78607i	0.594947	+	0.803765i	$0.297173\pi$
$383$	7.97804	+	34.9541i	0.407659	+	1.78607i	−0.187288	+	0.982305i	$0.559970\pi$
$384$		0			0
$385$	−7.09011	+	8.89072i	−0.361345	+	0.453113i
$386$	−8.42040	+	10.5588i	−0.428587	+	0.537431i
$387$		0			0
$388$	−6.64938	−	8.33806i	−0.337571	−	0.423301i
$389$	−11.3446			−0.575194			−0.287597	−	0.957752i	$-0.592856\pi$
$389$	−11.3446			−0.575194			−0.287597	+	0.957752i	$0.592856\pi$
$390$		0			0
$391$	−0.689705	−	3.02180i	−0.0348799	−	0.152819i
$392$	2.02790	+	8.88482i	0.102425	+	0.448751i
$393$		0			0
$394$	5.53800			0.279001
$395$	5.98699	+	7.50744i	0.301238	+	0.377740i
$396$		0			0
$397$	−15.0481	+	18.8697i	−0.755242	+	0.947043i	−0.999744	−	0.0226053i	$-0.992804\pi$
$397$	−15.0481	+	18.8697i	−0.755242	+	0.947043i	0.244503	+	0.969649i	$0.421375\pi$
$398$	18.1503	−	22.7598i	0.909792	−	1.14084i
$399$		0			0
$400$	0.289261	+	1.26734i	0.0144631	+	0.0633668i
$401$	4.30720	−	18.8711i	0.215091	−	0.942376i	−0.745957	−	0.665994i	$-0.768008\pi$
$401$	4.30720	−	18.8711i	0.215091	−	0.942376i	0.961048	−	0.276381i	$-0.0891353\pi$
$402$		0			0
$403$	−44.1035	+	21.2391i	−2.19695	+	1.05800i
$404$	−0.0263432	+	0.115417i	−0.00131062	+	0.00574222i
$405$		0			0
$406$	1.17492	−	15.9133i	0.0583105	−	0.789766i
$407$	−19.2900			−0.956169
$408$		0			0
$409$	−10.3124	+	4.96618i	−0.509915	+	0.245562i	−0.671106	−	0.741361i	$-0.734181\pi$
$409$	−10.3124	+	4.96618i	−0.509915	+	0.245562i	0.161192	+	0.986923i	$0.448466\pi$
$410$	−32.4578	−	15.6308i	−1.60298	−	0.771952i
$411$		0			0
$412$	−7.35003	−	32.2026i	−0.362110	−	1.58651i
$413$	4.33742	−	2.08879i	0.213431	−	0.102783i
$414$		0			0
$415$	6.44719	−	8.08452i	0.316480	−	0.396853i
$416$	39.9662	+	19.2467i	1.95951	+	0.943648i
$417$		0			0
$418$	−43.3508			−2.12036
$419$	13.1672	+	16.5111i	0.643259	+	0.806621i	0.991406	−	0.130819i	$-0.0417605\pi$
$419$	13.1672	+	16.5111i	0.643259	+	0.806621i	−0.348147	+	0.937440i	$0.613189\pi$
$420$		0			0
$421$	−6.12223	−	26.8233i	−0.298379	−	1.30729i	−0.872540	−	0.488543i	$-0.837529\pi$
$421$	−6.12223	−	26.8233i	−0.298379	−	1.30729i	0.574161	−	0.818743i	$-0.305329\pi$
$422$	−11.3489	−	14.2311i	−0.552455	−	0.692757i
$423$		0			0
$424$	14.6573	+	18.3797i	0.711823	+	0.892598i
$425$	2.04882	+	0.986662i	0.0993826	+	0.0478601i
$426$		0			0
$427$	6.07692	−	7.62022i	0.294083	−	0.368768i
$428$	−15.8322	+	7.62438i	−0.765278	+	0.368538i
$429$		0			0
$430$	9.12007	−	39.9576i	0.439809	−	1.92693i
$431$	−1.75647	−	0.845873i	−0.0846064	−	0.0407443i	0.391102	−	0.920347i	$-0.372094\pi$
$431$	−1.75647	−	0.845873i	−0.0846064	−	0.0407443i	−0.475708	+	0.879603i	$0.657808\pi$
$432$		0			0
$433$	−1.74340	+	7.63835i	−0.0837826	+	0.367076i	−0.999387	−	0.0350044i	$-0.988855\pi$
$433$	−1.74340	+	7.63835i	−0.0837826	+	0.367076i	0.915605	+	0.402080i	$0.131713\pi$
$434$	24.0355			1.15374
$435$		0			0
$436$	−41.5179			−1.98835
$437$	1.27260	−	5.57563i	0.0608768	−	0.266719i
$438$		0			0
$439$	−2.15322	−	1.03694i	−0.102768	−	0.0494903i	0.381794	−	0.924248i	$-0.375306\pi$
$439$	−2.15322	−	1.03694i	−0.102768	−	0.0494903i	−0.484561	+	0.874757i	$0.661021\pi$
$440$	3.29789	−	14.4490i	0.157221	−	0.688829i
$441$		0			0
$442$	36.3983	−	17.5285i	1.73129	−	0.833746i
$443$	−23.9106	+	29.9830i	−1.13603	+	1.42453i	−0.245623	+	0.969366i	$0.578992\pi$
$443$	−23.9106	+	29.9830i	−1.13603	+	1.42453i	−0.890405	+	0.455168i	$0.849579\pi$
$444$		0			0
$445$	30.2155	+	14.5510i	1.43235	+	0.689785i
$446$	34.1801	+	42.8604i	1.61847	+	2.02950i
$447$		0			0
$448$	−10.6367	−	13.3379i	−0.502535	−	0.630159i
$449$	−6.97471	−	30.5582i	−0.329157	−	1.44213i	−0.820741	−	0.571301i	$-0.806439\pi$
$449$	−6.97471	−	30.5582i	−0.329157	−	1.44213i	0.491584	−	0.870830i	$-0.336418\pi$
$450$		0			0
$451$	−15.0060	−	18.8170i	−0.706606	−	0.886056i
$452$	−33.3473			−1.56852
$453$		0			0
$454$	6.01080	+	2.89465i	0.282101	+	0.135853i
$455$	12.1915	−	15.2876i	0.571545	−	0.716695i
$456$		0			0
$457$	29.0691	−	13.9989i	1.35980	−	0.654843i	0.395204	−	0.918593i	$-0.370674\pi$
$457$	29.0691	−	13.9989i	1.35980	−	0.654843i	0.964591	+	0.263750i	$0.0849595\pi$
$458$	10.6852	+	46.8147i	0.499285	+	2.18751i
$459$		0			0
$460$	6.14422	+	2.95890i	0.286476	+	0.137960i
$461$	−5.11576	+	2.46362i	−0.238265	+	0.114742i	−0.549206	−	0.835687i	$-0.685070\pi$
$461$	−5.11576	+	2.46362i	−0.238265	+	0.114742i	0.310942	+	0.950429i	$0.399356\pi$
$462$		0			0
$463$	23.2339			1.07977			0.539886	−	0.841738i	$-0.318467\pi$
$463$	23.2339			1.07977			0.539886	+	0.841738i	$0.318467\pi$
$464$	−3.44477	−	8.74879i	−0.159919	−	0.406152i
$465$		0			0
$466$	4.85991	−	21.2927i	0.225131	−	0.986364i
$467$	10.8811	−	5.24005i	0.503516	−	0.242481i	−0.164842	−	0.986320i	$-0.552712\pi$
$467$	10.8811	−	5.24005i	0.503516	−	0.242481i	0.668358	+	0.743839i	$0.266997\pi$
$468$		0			0
$469$	−2.50083	+	10.9569i	−0.115478	+	0.505941i
$470$	−0.488915	−	2.14208i	−0.0225520	−	0.0988067i
$471$		0			0
$472$	−3.91195	+	4.90543i	−0.180062	+	0.225791i
$473$	17.0720	−	21.4076i	0.784970	−	0.984321i
$474$		0			0
$475$	2.61609	+	3.28047i	0.120034	+	0.150518i
$476$	−11.5779			−0.530671
$477$		0			0
$478$	−3.79490	−	16.6266i	−0.173575	−	0.760481i
$479$	−6.78931	−	29.7459i	−0.310212	−	1.35913i	−0.854161	−	0.520008i	$-0.825929\pi$
$479$	−6.78931	−	29.7459i	−0.310212	−	1.35913i	0.543950	−	0.839118i	$-0.316928\pi$
$480$		0			0
$481$	33.1692			1.51239
$482$	−31.6891	−	39.7369i	−1.44340	−	1.80997i
$483$		0			0
$484$	2.30212	−	2.88677i	0.104642	−	0.131217i
$485$	−5.68392	+	7.12741i	−0.258093	+	0.323639i
$486$		0			0
$487$	5.23476	+	22.9350i	0.237210	+	1.03928i	0.943503	+	0.331364i	$0.107509\pi$
$487$	5.23476	+	22.9350i	0.237210	+	1.03928i	−0.706293	+	0.707919i	$0.749634\pi$
$488$	−2.82662	+	12.3842i	−0.127955	+	0.560607i
$489$		0			0
$490$	24.4805	−	11.7892i	1.10592	−	0.532581i
$491$	6.13907	−	26.8970i	0.277052	−	1.21385i	−0.624447	−	0.781067i	$-0.714676\pi$
$491$	6.13907	−	26.8970i	0.277052	−	1.21385i	0.901500	−	0.432779i	$-0.142467\pi$
$492$		0			0
$493$	−15.7229	−	4.83091i	−0.708123	−	0.217573i
$494$	74.5419			3.35380
$495$		0			0
$496$	12.7604	−	6.14511i	0.572961	−	0.275924i
$497$	−11.9206	−	5.74064i	−0.534710	−	0.257503i
$498$		0			0
$499$	8.53765	+	37.4059i	0.382198	+	1.67452i	0.690580	+	0.723256i	$0.257355\pi$
$499$	8.53765	+	37.4059i	0.382198	+	1.67452i	−0.308383	+	0.951262i	$0.599788\pi$
$500$	25.7659	−	12.4082i	1.15229	−	0.554912i
$501$		0			0
$502$	−1.61327	+	2.02297i	−0.0720036	+	0.0902896i
$503$	−4.46853	−	2.15193i	−0.199242	−	0.0959498i	0.331602	−	0.943419i	$-0.392411\pi$
$503$	−4.46853	−	2.15193i	−0.199242	−	0.0959498i	−0.530844	+	0.847469i	$0.678125\pi$
$504$		0			0
$505$	0.101196			0.00450318
$506$	4.86683	+	6.10281i	0.216357	+	0.271303i
$507$		0			0
$508$	9.41733	+	41.2600i	0.417827	+	1.83062i
$509$	10.2436	+	12.8450i	0.454038	+	0.569345i	0.955182	−	0.296018i	$-0.0956589\pi$
$509$	10.2436	+	12.8450i	0.454038	+	0.569345i	−0.501144	+	0.865364i	$0.667087\pi$
$510$		0			0
$511$	−0.256014	−	0.321032i	−0.0113254	−	0.0142016i
$512$	−17.1068	−	8.23820i	−0.756020	−	0.364080i
$513$		0			0
$514$	−21.8299	+	27.3739i	−0.962878	+	1.20741i
$515$	−25.4387	+	12.2506i	−1.12096	+	0.539828i
$516$		0			0
$517$	0.326634	−	1.43108i	0.0143653	−	0.0629386i
$518$	−14.6735	−	7.06640i	−0.644718	−	0.310480i
$519$		0			0
$520$	−5.67074	+	24.8451i	−0.248678	+	1.08953i
$521$	30.7040			1.34517			0.672583	−	0.740021i	$-0.265185\pi$
$521$	30.7040			1.34517			0.672583	+	0.740021i	$0.265185\pi$
$522$		0			0
$523$	37.0601			1.62052			0.810262	−	0.586068i	$-0.199325\pi$
$523$	37.0601			1.62052			0.810262	+	0.586068i	$0.199325\pi$
$524$	6.51798	−	28.5571i	0.284739	−	1.24752i
$525$		0			0
$526$	28.8518	+	13.8943i	1.25800	+	0.605821i
$527$	5.51319	−	24.1548i	0.240158	−	1.05220i
$528$		0			0
$529$	19.7945	−	9.53252i	0.860630	−	0.414458i
$530$	43.7008	−	54.7991i	1.89824	−	2.38032i
$531$		0			0
$532$	−19.2472	−	9.26895i	−0.834471	−	0.401860i
$533$	25.8029	+	32.3558i	1.11765	+	1.40149i
$534$		0			0
$535$	9.36542	+	11.7439i	0.404903	+	0.507732i
$536$	−3.25931	−	14.2800i	−0.140781	−	0.616801i
$537$		0			0
$538$	−30.2206	−	37.8955i	−1.30290	−	1.63379i
$539$	18.1525			0.781886
$540$		0			0
$541$	−30.6558	−	14.7631i	−1.31800	−	0.634714i	−0.363128	−	0.931739i	$-0.618291\pi$
$541$	−30.6558	−	14.7631i	−1.31800	−	0.634714i	−0.954870	+	0.297025i	$0.904006\pi$
$542$	−31.5880	+	39.6101i	−1.35682	+	1.70140i
$543$		0			0
$544$	−20.2284	+	9.74148i	−0.867285	+	0.417663i
$545$	7.89720	+	34.5999i	0.338279	+	1.48210i
$546$		0			0
$547$	−15.4934	−	7.46124i	−0.662451	−	0.319020i	0.0722738	−	0.997385i	$-0.476974\pi$
$547$	−15.4934	−	7.46124i	−0.662451	−	0.319020i	−0.734725	+	0.678365i	$0.762689\pi$
$548$	−9.27656	+	4.46735i	−0.396275	+	0.190836i
$549$		0			0
$550$	−5.72689			−0.244196
$551$	−22.2704	−	20.6183i	−0.948750	−	0.878369i
$552$		0			0
$553$	−1.20523	+	5.28046i	−0.0512516	+	0.224548i
$554$	−36.9530	+	17.7956i	−1.56998	+	0.756063i
$555$		0			0
$556$	−3.60711	+	15.8038i	−0.152975	+	0.670229i
$557$	−6.60546	−	28.9404i	−0.279882	−	1.22624i	−0.897942	−	0.440114i	$-0.854938\pi$
$557$	−6.60546	−	28.9404i	−0.279882	−	1.22624i	0.618060	−	0.786131i	$-0.287919\pi$
$558$		0			0
$559$	−29.3553	+	36.8104i	−1.24160	+	1.55692i
$560$	−3.52736	+	4.42316i	−0.149058	+	0.186913i
$561$		0			0
$562$	11.8423	+	14.8498i	0.499539	+	0.626402i
$563$	27.8621			1.17425			0.587125	−	0.809497i	$-0.300260\pi$
$563$	27.8621			1.17425			0.587125	+	0.809497i	$0.300260\pi$
$564$		0			0
$565$	6.34305	+	27.7907i	0.266854	+	1.16916i
$566$	−2.72387	−	11.9341i	−0.114493	−	0.501627i
$567$		0			0
$568$	17.2436			0.723526
$569$	6.10300	+	7.65292i	0.255851	+	0.320827i	0.893124	−	0.449811i	$-0.148509\pi$
$569$	6.10300	+	7.65292i	0.255851	+	0.320827i	−0.637272	+	0.770639i	$0.719937\pi$
$570$		0			0
$571$	−20.1541	+	25.2725i	−0.843424	+	1.05762i	0.154153	+	0.988047i	$0.450735\pi$
$571$	−20.1541	+	25.2725i	−0.843424	+	1.05762i	−0.997577	+	0.0695735i	$0.977836\pi$
$572$	−37.0248	+	46.4276i	−1.54808	+	1.94124i
$573$		0			0
$574$	−4.52168	−	19.8108i	−0.188731	−	0.826886i
$575$	0.168118	−	0.736574i	0.00701101	−	0.0307172i
$576$		0			0
$577$	39.2874	−	18.9198i	1.63555	−	0.787641i	0.635677	−	0.771955i	$-0.280721\pi$
$577$	39.2874	−	18.9198i	1.63555	−	0.787641i	0.999877	−	0.0156861i	$-0.00499325\pi$
$578$	3.74118	−	16.3912i	0.155613	−	0.681783i
$579$		0			0
$580$	29.8789	−	20.4193i	1.24065	−	0.847866i
$581$	5.83259			0.241977
$582$		0			0
$583$	42.1888	−	20.3170i	1.74728	−	0.841446i
$584$	0.482155	+	0.232194i	0.0199517	+	0.00960824i
$585$		0			0
$586$	−2.30153	−	10.0837i	−0.0950752	−	0.416552i
$587$	−39.3393	+	18.9448i	−1.62371	+	0.781935i	−0.623705	+	0.781660i	$0.714373\pi$
$587$	−39.3393	+	18.9448i	−1.62371	+	0.781935i	−1.00000		0.000275397i	$0.999912\pi$
$588$		0			0
$589$	28.5030	−	35.7416i	1.17444	−	1.47271i
$590$	16.8542	+	8.11654i	0.693876	+	0.334153i
$591$		0			0
$592$	−9.59684			−0.394428
$593$	−14.9685	−	18.7699i	−0.614682	−	0.770787i	0.372903	−	0.927870i	$-0.378362\pi$
$593$	−14.9685	−	18.7699i	−0.614682	−	0.770787i	−0.987585	+	0.157083i	$0.949791\pi$
$594$		0			0
$595$	2.20225	+	9.64868i	0.0902834	+	0.395557i
$596$	15.0068	+	18.8179i	0.614701	+	0.770811i
$597$		0			0
$598$	−8.36854	−	10.4938i	−0.342215	−	0.429124i
$599$	3.27503	+	1.57717i	0.133814	+	0.0644415i	0.499593	−	0.866260i	$-0.333483\pi$
$599$	3.27503	+	1.57717i	0.133814	+	0.0644415i	−0.365779	+	0.930702i	$0.619197\pi$
$600$		0			0
$601$	−9.51453	+	11.9308i	−0.388106	+	0.486669i	−0.937053	−	0.349188i	$-0.886458\pi$
$601$	−9.51453	+	11.9308i	−0.388106	+	0.486669i	0.548947	+	0.835857i	$0.315029\pi$
$602$	20.8285	−	10.0305i	0.848905	−	0.408811i
$603$		0			0
$604$	−7.45003	+	32.6407i	−0.303137	+	1.32813i
$605$	−2.84364	−	1.36943i	−0.115611	−	0.0556751i
$606$		0			0
$607$	0.643106	−	2.81763i	0.0261029	−	0.114364i	−0.960198	−	0.279320i	$-0.909891\pi$
$607$	0.643106	−	2.81763i	0.0261029	−	0.114364i	0.986301	+	0.164956i	$0.0527482\pi$
$608$	−41.4267			−1.68007
$609$		0			0
$610$	37.8730			1.53343
$611$	−0.561648	+	2.46074i	−0.0227219	+	0.0995509i
$612$		0			0
$613$	3.96789	+	1.91083i	0.160261	+	0.0771778i	0.512295	−	0.858810i	$-0.328795\pi$
$613$	3.96789	+	1.91083i	0.160261	+	0.0771778i	−0.352034	+	0.935987i	$0.614510\pi$
$614$	−5.72394	+	25.0782i	−0.230999	+	1.01207i
$615$		0			0
$616$	7.53174	−	3.62710i	0.303463	−	0.146140i
$617$	−4.33910	+	5.44106i	−0.174686	+	0.219049i	−0.861465	−	0.507817i	$-0.830453\pi$
$617$	−4.33910	+	5.44106i	−0.174686	+	0.219049i	0.686779	+	0.726866i	$0.259024\pi$
$618$		0			0
$619$	−11.8459	−	5.70468i	−0.476127	−	0.229291i	0.180400	−	0.983593i	$-0.442261\pi$
$619$	−11.8459	−	5.70468i	−0.476127	−	0.229291i	−0.656527	+	0.754303i	$0.727975\pi$
$620$	33.9880	+	42.6196i	1.36499	+	1.71165i
$621$		0			0
$622$	−22.9633	−	28.7950i	−0.920743	−	1.15458i
$623$	4.20932	+	18.4422i	0.168643	+	0.738872i
$624$		0			0
$625$	−17.5626	−	22.0228i	−0.702505	−	0.880914i
$626$	−26.2134			−1.04770
$627$		0			0
$628$	30.9549	+	14.9071i	1.23524	+	0.594858i
$629$	−10.4673	+	13.1255i	−0.417357	+	0.523349i
$630$		0			0
$631$	11.9773	−	5.76796i	0.476808	−	0.229619i	−0.180014	−	0.983664i	$-0.557614\pi$
$631$	11.9773	−	5.76796i	0.476808	−	0.229619i	0.656823	+	0.754045i	$0.271900\pi$
$632$	−1.57077	−	6.88198i	−0.0624818	−	0.273750i
$633$		0			0
$634$	−27.9146	−	13.4430i	−1.10863	−	0.533888i
$635$	32.5937	−	15.6963i	1.29344	−	0.622889i
$636$		0			0
$637$	−31.2134			−1.23672
$638$	40.9539	−	6.21892i	1.62138	−	0.246209i
$639$		0			0
$640$	6.91029	−	30.2760i	0.273153	−	1.19676i
$641$	18.1431	−	8.73725i	0.716609	−	0.345101i	−0.0397927	−	0.999208i	$-0.512670\pi$
$641$	18.1431	−	8.73725i	0.716609	−	0.345101i	0.756402	+	0.654107i	$0.226955\pi$
$642$		0			0
$643$	−9.82444	+	43.0437i	−0.387438	+	1.69748i	0.285997	+	0.958231i	$0.407675\pi$
$643$	−9.82444	+	43.0437i	−0.387438	+	1.69748i	−0.673435	+	0.739247i	$0.735182\pi$
$644$	0.855950	+	3.75016i	0.0337292	+	0.147777i
$645$		0			0
$646$	−23.5233	+	29.4973i	−0.925511	+	1.16055i
$647$	−11.3676	+	14.2546i	−0.446908	+	0.560404i	−0.953349	−	0.301870i	$-0.902389\pi$
$647$	−11.3676	+	14.2546i	−0.446908	+	0.560404i	0.506442	+	0.862274i	$0.330961\pi$
$648$		0			0
$649$	7.79210	+	9.77098i	0.305866	+	0.383544i
$650$	9.84742			0.386248
$651$		0			0
$652$	4.94858	+	21.6811i	0.193801	+	0.849099i
$653$	−3.38155	−	14.8156i	−0.132330	−	0.579778i	−0.996998	−	0.0774324i	$-0.975328\pi$
$653$	−3.38155	−	14.8156i	−0.132330	−	0.579778i	0.864667	−	0.502345i	$-0.167529\pi$
$654$		0			0
$655$	−25.0385			−0.978336
$656$	−7.46555	−	9.36150i	−0.291481	−	0.365505i
$657$		0			0
$658$	0.772703	−	0.968939i	0.0301231	−	0.0377732i
$659$	10.4628	−	13.1200i	0.407574	−	0.511082i	−0.535103	−	0.844787i	$-0.679727\pi$
$659$	10.4628	−	13.1200i	0.407574	−	0.511082i	0.942678	+	0.333704i	$0.108299\pi$
$660$		0			0
$661$	0.299039	+	1.31018i	0.0116313	+	0.0509599i	0.980411	−	0.196965i	$-0.0631085\pi$
$661$	0.299039	+	1.31018i	0.0116313	+	0.0509599i	−0.968779	+	0.247925i	$0.920251\pi$
$662$	−11.2290	+	49.1975i	−0.436428	+	1.91211i
$663$		0			0
$664$	−6.84877	+	3.29820i	−0.265784	+	0.127995i
$665$	−4.06345	+	17.8031i	−0.157574	+	0.690376i
$666$		0			0
$667$	−0.402381	+	5.44991i	−0.0155803	+	0.211021i
$668$	−36.2386			−1.40211
$669$		0			0
$670$	−39.3459	+	18.9480i	−1.52006	+	0.732024i
$671$	22.7964	+	10.9782i	0.880047	+	0.423808i
$672$		0			0
$673$	−2.65230	−	11.6205i	−0.102239	−	0.447937i	−0.999973	−	0.00739895i	$-0.997645\pi$
$673$	−2.65230	−	11.6205i	−0.102239	−	0.447937i	0.897734	−	0.440538i	$-0.145212\pi$
$674$	5.04797	−	2.43098i	0.194441	−	0.0936377i
$675$		0			0
$676$	40.9378	−	51.3344i	1.57453	−	1.97440i
$677$	14.6012	+	7.03155i	0.561169	+	0.270245i	0.692891	−	0.721042i	$-0.256337\pi$
$677$	14.6012	+	7.03155i	0.561169	+	0.270245i	−0.131723	+	0.991287i	$0.542051\pi$
$678$		0			0
$679$	−5.14208			−0.197335
$680$	−8.04205	−	10.0844i	−0.308398	−	0.386719i
$681$		0			0
$682$	13.8844	+	60.8315i	0.531661	+	2.32936i
$683$	17.9645	+	22.5268i	0.687393	+	0.861964i	0.996012	−	0.0892221i	$-0.0284381\pi$
$683$	17.9645	+	22.5268i	0.687393	+	0.861964i	−0.308619	+	0.951186i	$0.599867\pi$
$684$		0			0
$685$	5.48748	+	6.88109i	0.209666	+	0.262913i
$686$	32.4958	+	15.6492i	1.24070	+	0.597487i
$687$		0			0
$688$	8.49337	−	10.6503i	0.323807	−	0.406041i
$689$	−72.5438	+	34.9353i	−2.76370	+	1.33093i
$690$		0			0
$691$	5.64168	−	24.7178i	0.214620	−	0.940310i	−0.746762	−	0.665092i	$-0.768393\pi$
$691$	5.64168	−	24.7178i	0.214620	−	0.940310i	0.961382	−	0.275219i	$-0.0887503\pi$
$692$	6.70349	+	3.22823i	0.254828	+	0.122719i
$693$		0			0
$694$	−0.434987	+	1.90580i	−0.0165119	+	0.0723432i
$695$	13.8566			0.525609
$696$		0			0
$697$	−20.9463			−0.793399
$698$	0.368506	−	1.61453i	0.0139482	−	0.0611109i
$699$		0			0
$700$	−2.54267	−	1.22448i	−0.0961038	−	0.0462811i
$701$	2.93968	−	12.8796i	0.111030	−	0.486455i	−0.888585	−	0.458712i	$-0.848311\pi$
$701$	2.93968	−	12.8796i	0.111030	−	0.486455i	0.999615	−	0.0277426i	$-0.00883188\pi$
$702$		0			0
$703$	−27.9089	+	13.4402i	−1.05260	+	0.506907i
$704$	27.6127	−	34.6252i	1.04069	−	1.30499i
$705$		0			0
$706$	37.9948	+	18.2973i	1.42995	+	0.688629i
$707$	0.0355889	+	0.0446270i	0.00133846	+	0.00167837i
$708$		0			0
$709$	−22.2400	−	27.8881i	−0.835240	−	1.04736i	−0.998155	−	0.0607181i	$-0.980661\pi$
$709$	−22.2400	−	27.8881i	−0.835240	−	1.04736i	0.162915	−	0.986640i	$-0.447911\pi$
$710$	−11.4402	−	50.1228i	−0.429343	−	1.88107i
$711$		0			0
$712$	−15.3713	−	19.2751i	−0.576065	−	0.722363i
$713$	−8.23153			−0.308273
$714$		0			0
$715$	45.7341	+	22.0244i	1.71036	+	0.823665i
$716$	23.4236	−	29.3723i	0.875381	−	1.09769i
$717$		0			0
$718$	34.7839	−	16.7510i	1.29812	−	0.625143i
$719$	0.450188	+	1.97240i	0.0167892	+	0.0735583i	0.982629	−	0.185583i	$-0.0594175\pi$
$719$	0.450188	+	1.97240i	0.0167892	+	0.0735583i	−0.965839	+	0.259142i	$0.916560\pi$
$720$		0			0
$721$	−14.3488	−	6.91002i	−0.534377	−	0.257342i
$722$	−25.2004	+	12.1359i	−0.937863	+	0.451651i
$723$		0			0
$724$	4.24478			0.157756
$725$	−2.94205	−	2.72380i	−0.109265	−	0.101159i
$726$		0			0
$727$	2.34647	−	10.2806i	0.0870258	−	0.381285i	−0.912594	−	0.408868i	$-0.865924\pi$
$727$	2.34647	−	10.2806i	0.0870258	−	0.381285i	0.999620	+	0.0275826i	$0.00878092\pi$
$728$	−12.9509	+	6.23681i	−0.479991	+	0.231152i
$729$		0			0
$730$	0.355044	−	1.55555i	0.0131408	−	0.0575734i
$731$	−5.30270	−	23.2326i	−0.196127	−	0.859291i
$732$		0			0
$733$	−11.8578	+	14.8692i	−0.437979	+	0.549208i	−0.951009	−	0.309162i	$-0.899951\pi$
$733$	−11.8578	+	14.8692i	−0.437979	+	0.549208i	0.513030	+	0.858370i	$0.328523\pi$
$734$	5.18998	−	6.50802i	0.191566	−	0.240216i
$735$		0			0
$736$	4.65083	+	5.83195i	0.171432	+	0.214969i
$737$	−29.1754			−1.07469
$738$		0			0
$739$	9.57638	+	41.9569i	0.352273	+	1.54341i	0.771919	+	0.635721i	$0.219297\pi$
$739$	9.57638	+	41.9569i	0.352273	+	1.54341i	−0.419646	+	0.907688i	$0.637846\pi$
$740$	−8.21938	−	36.0115i	−0.302151	−	1.32381i
$741$		0			0
$742$	39.5349			1.45137
$743$	2.07331	+	2.59985i	0.0760625	+	0.0953794i	0.818407	−	0.574639i	$-0.194858\pi$
$743$	2.07331	+	2.59985i	0.0760625	+	0.0953794i	−0.742344	+	0.670019i	$0.766286\pi$
$744$		0			0
$745$	12.8279	−	16.0856i	0.469976	−	0.589331i
$746$	−11.3323	+	14.2103i	−0.414905	+	0.520275i
$747$		0			0
$748$	−6.68810	−	29.3025i	−0.244541	−	1.07140i
$749$	−1.88534	+	8.26021i	−0.0688888	+	0.301821i
$750$		0			0
$751$	−18.4506	+	8.88532i	−0.673271	+	0.324230i	−0.739095	−	0.673601i	$-0.764747\pi$
$751$	−18.4506	+	8.88532i	−0.673271	+	0.324230i	0.0658243	+	0.997831i	$0.479032\pi$
$752$	0.162501	−	0.711965i	0.00592582	−	0.0259627i
$753$		0			0
$754$	−70.4204	+	10.6935i	−2.56456	+	0.389433i
$755$	28.6190			1.04155
$756$		0			0
$757$	7.59189	−	3.65606i	0.275932	−	0.132882i	−0.290801	−	0.956784i	$-0.593922\pi$
$757$	7.59189	−	3.65606i	0.275932	−	0.132882i	0.566732	+	0.823902i	$0.308207\pi$
$758$	17.6390	+	8.49448i	0.640676	+	0.308533i
$759$		0			0
$760$	−5.29586	−	23.2027i	−0.192101	−	0.841650i
$761$	−23.5526	+	11.3423i	−0.853780	+	0.411159i	−0.808979	−	0.587837i	$-0.799980\pi$
$761$	−23.5526	+	11.3423i	−0.853780	+	0.411159i	−0.0448010	+	0.998996i	$0.514265\pi$
$762$		0			0
$763$	−12.4811	+	15.6508i	−0.451845	+	0.566596i
$764$	−29.3512	−	14.1348i	−1.06189	−	0.511378i
$765$		0			0
$766$	−78.5817			−2.83927
$767$	−13.3985	−	16.8012i	−0.483794	−	0.606658i
$768$		0			0
$769$	−9.15495	−	40.1104i	−0.330136	−	1.44642i	−0.818866	−	0.573985i	$-0.805397\pi$
$769$	−9.15495	−	40.1104i	−0.330136	−	1.44642i	0.488730	−	0.872435i	$-0.337460\pi$
$770$	−15.5399	−	19.4865i	−0.560020	−	0.702243i
$771$		0			0
$772$	−10.7720	−	13.5077i	−0.387693	−	0.486151i
$773$	31.4140	+	15.1282i	1.12988	+	0.544122i	0.902932	−	0.429784i	$-0.141410\pi$
$773$	31.4140	+	15.1282i	1.12988	+	0.544122i	0.226950	+	0.973906i	$0.427125\pi$
$774$		0			0
$775$	3.76541	−	4.72167i	0.135258	−	0.169608i
$776$	6.03796	−	2.90773i	0.216750	−	0.104381i
$777$		0			0
$778$	5.53294	−	24.2414i	0.198365	−	0.869096i
$779$	−34.8214	−	16.7691i	−1.24761	−	0.600816i
$780$		0			0
$781$	7.64294	−	33.4859i	0.273486	−	1.19822i
$782$	6.79343			0.242932
$783$		0			0
$784$	9.03096			0.322534
$785$	6.53518	−	28.6325i	0.233251	−	1.02194i
$786$		0			0
$787$	−14.3756	−	6.92292i	−0.512434	−	0.246775i	0.159752	−	0.987157i	$-0.448930\pi$
$787$	−14.3756	−	6.92292i	−0.512434	−	0.246775i	−0.672187	+	0.740382i	$0.734645\pi$
$788$	−1.57648	+	6.90700i	−0.0561597	+	0.246052i
$789$		0			0
$790$	−18.9620	+	9.13163i	−0.674639	+	0.324889i
$791$	−10.0248	+	12.5707i	−0.356442	+	0.446964i
$792$		0			0
$793$	−39.1986	−	18.8770i	−1.39198	−	0.670344i
$794$	−32.9820	−	41.3582i	−1.17049	−	1.46775i
$795$		0			0
$796$	23.2192	+	29.1160i	0.822983	+	1.03199i
$797$	8.47215	+	37.1189i	0.300099	+	1.31482i	0.869978	+	0.493090i	$0.164133\pi$
$797$	8.47215	+	37.1189i	0.300099	+	1.31482i	−0.569879	+	0.821728i	$0.693010\pi$
$798$		0			0
$799$	−0.796510	−	0.998792i	−0.0281785	−	0.0353347i
$800$	−5.47271			−0.193490
$801$		0			0
$802$	38.2234	+	18.4074i	1.34972	+	0.649989i
$803$	0.664611	−	0.833396i	0.0234536	−	0.0294099i
$804$		0			0
$805$	2.96247	−	1.42665i	0.104413	−	0.0502828i
$806$	−23.8743	−	104.600i	−0.840936	−	3.68438i
$807$		0			0
$808$	−0.0670249	−	0.0322775i	−0.00235793	−	0.00113552i
$809$	−46.9688	+	22.6190i	−1.65133	+	0.795240i	−0.652020	+	0.758202i	$0.726078\pi$
$809$	−46.9688	+	22.6190i	−1.65133	+	0.795240i	−0.999314	+	0.0370382i	$0.988208\pi$
$810$		0			0
$811$	6.35528			0.223164			0.111582	−	0.993755i	$-0.464408\pi$
$811$	6.35528			0.223164			0.111582	+	0.993755i	$0.464408\pi$
$812$	19.5127	+	5.99534i	0.684760	+	0.210395i
$813$		0			0
$814$	9.40804	−	41.2193i	0.329752	−	1.44474i
$815$	17.1272	−	8.24802i	0.599940	−	0.288916i
$816$		0			0
$817$	9.78421	−	42.8674i	0.342306	−	1.49974i
$818$	−5.58234	−	24.4578i	−0.195182	−	0.855148i
$819$		0			0
$820$	28.7344	−	36.0318i	1.00345	−	1.25828i
$821$	−0.133281	+	0.167129i	−0.00465153	+	0.00583283i	−0.784152	−	0.620569i	$-0.786902\pi$
$821$	−0.133281	+	0.167129i	−0.00465153	+	0.00583283i	0.779500	+	0.626402i	$0.215473\pi$
$822$		0			0
$823$	15.8481	+	19.8729i	0.552430	+	0.692726i	0.977138	−	0.212605i	$-0.0681947\pi$
$823$	15.8481	+	19.8729i	0.552430	+	0.692726i	−0.424708	+	0.905330i	$0.639623\pi$
$824$	20.7562			0.723076
$825$		0			0
$826$	2.34795	+	10.2870i	0.0816956	+	0.357932i
$827$	8.75101	+	38.3407i	0.304302	+	1.33324i	0.863562	+	0.504243i	$0.168228\pi$
$827$	8.75101	+	38.3407i	0.304302	+	1.33324i	−0.559260	+	0.828993i	$0.688915\pi$
$828$		0			0
$829$	2.14332			0.0744405			0.0372203	−	0.999307i	$-0.488150\pi$
$829$	2.14332			0.0744405			0.0372203	+	0.999307i	$0.488150\pi$
$830$	14.1308	+	17.7195i	0.490487	+	0.615051i
$831$		0			0
$832$	−47.4801	+	59.5382i	−1.64608	+	2.06411i
$833$	9.85006	−	12.3516i	0.341284	−	0.427957i
$834$		0			0
$835$	6.89301	+	30.2003i	0.238543	+	1.04512i
$836$	12.3405	−	54.0671i	0.426804	−	1.86995i
$837$		0			0
$838$	−41.7032	+	20.0832i	−1.44061	+	0.693763i
$839$	−3.47410	+	15.2210i	−0.119939	+	0.525488i	0.878886	+	0.477032i	$0.158287\pi$
$839$	−3.47410	+	15.2210i	−0.119939	+	0.525488i	−0.998825	+	0.0484563i	$0.984570\pi$
$840$		0			0
$841$	23.9968	+	16.2835i	0.827477	+	0.561500i
$842$	60.3025			2.07816
$843$		0			0
$844$	20.9796	−	10.1033i	0.722148	−	0.347768i
$845$	−50.5675	−	24.3520i	−1.73958	−	0.837736i
$846$		0			0
$847$	−0.396147	−	1.73563i	−0.0136118	−	0.0596371i
$848$	20.9891	−	10.1078i	0.720768	−	0.347103i
$849$		0			0
$850$	−3.10757	+	3.89676i	−0.106589	+	0.133658i
$851$	5.02531	+	2.42006i	0.172265	+	0.0829586i
$852$		0			0
$853$	36.4571			1.24827			0.624133	−	0.781318i	$-0.285452\pi$
$853$	36.4571			1.24827			0.624133	+	0.781318i	$0.285452\pi$
$854$	13.3192	+	16.7018i	0.455775	+	0.571524i
$855$		0			0
$856$	−2.45715	−	10.7655i	−0.0839835	−	0.367956i
$857$	0.305695	+	0.383330i	0.0104424	+	0.0130943i	0.787025	−	0.616921i	$-0.211620\pi$
$857$	0.305695	+	0.383330i	0.0104424	+	0.0130943i	−0.776583	+	0.630015i	$0.783049\pi$
$858$		0			0
$859$	−22.8956	−	28.7102i	−0.781189	−	0.979579i	−0.999993	−	0.00381067i	$-0.998787\pi$
$859$	−22.8956	−	28.7102i	−0.781189	−	0.979579i	0.218804	−	0.975769i	$-0.429784\pi$
$860$	47.2390	+	22.7491i	1.61084	+	0.775738i
$861$		0			0
$862$	2.66414	−	3.34073i	0.0907411	−	0.113786i
$863$	36.1069	−	17.3882i	1.22909	−	0.591901i	0.297264	−	0.954795i	$-0.403926\pi$
$863$	36.1069	−	17.3882i	1.22909	−	0.591901i	0.931830	+	0.362894i	$0.118211\pi$
$864$		0			0
$865$	1.41524	−	6.20055i	0.0481194	−	0.210825i
$866$	−15.4715	−	7.45069i	−0.525744	−	0.253185i
$867$		0			0
$868$	−6.84207	+	29.9771i	−0.232235	+	1.01749i
$869$	−14.0605			−0.476971
$870$		0			0
$871$	50.1672			1.69985
$872$	5.80544	−	25.4353i	0.196597	−	0.861348i
$873$		0			0
$874$	11.2935	+	5.43865i	0.382007	+	0.183965i
$875$	3.06827	−	13.4430i	0.103726	−	0.454455i
$876$		0			0
$877$	−26.3326	+	12.6811i	−0.889189	+	0.428211i	−0.821972	−	0.569528i	$-0.807126\pi$
$877$	−26.3326	+	12.6811i	−0.889189	+	0.428211i	−0.0672167	+	0.997738i	$0.521412\pi$
$878$	3.26591	−	4.09532i	0.110219	−	0.138210i
$879$		0			0
$880$	−13.2322	−	6.37230i	−0.446058	−	0.214810i
$881$	−14.5697	−	18.2698i	−0.490864	−	0.615524i	0.473277	−	0.880914i	$-0.343071\pi$
$881$	−14.5697	−	18.2698i	−0.490864	−	0.615524i	−0.964141	+	0.265389i	$0.914500\pi$
$882$		0			0
$883$	−13.7715	−	17.2689i	−0.463449	−	0.581146i	0.494105	−	0.869402i	$-0.335496\pi$
$883$	−13.7715	−	17.2689i	−0.463449	−	0.581146i	−0.957553	+	0.288256i	$0.906924\pi$
$884$	11.5002	+	50.3857i	0.386794	+	1.69466i
$885$		0			0
$886$	−52.4067	−	65.7160i	−1.76064	−	2.20777i
$887$	−16.2336			−0.545072			−0.272536	−	0.962146i	$-0.587862\pi$
$887$	−16.2336			−0.545072			−0.272536	+	0.962146i	$0.587862\pi$
$888$		0			0
$889$	18.3846	+	8.85355i	0.616599	+	0.296939i
$890$	−45.8296	+	57.4685i	−1.53621	+	1.92635i
$891$		0			0
$892$	−63.1854	+	30.4285i	−2.11560	+	1.01882i
$893$	−0.524519	−	2.29807i	−0.0175524	−	0.0769019i
$894$		0			0
$895$	−28.9335	−	13.9336i	−0.967140	−	0.465750i
$896$	15.7818	−	7.60010i	0.527232	−	0.253901i
$897$		0			0
$898$	68.6992			2.29252
$899$	−21.7997	+	37.8543i	−0.727059	+	1.26251i
$900$		0			0
$901$	9.06838	−	39.7312i	0.302112	−	1.32364i
$902$	47.5272	−	22.8879i	1.58248	−	0.762083i
$903$		0			0
$904$	4.66294	−	20.4297i	0.155087	−	0.679481i
$905$	−0.807408	−	3.53749i	−0.0268392	−	0.117590i
$906$		0			0
$907$	−2.14813	+	2.69367i	−0.0713274	+	0.0894418i	−0.816215	−	0.577748i	$-0.803932\pi$
$907$	−2.14813	+	2.69367i	−0.0713274	+	0.0894418i	0.744888	+	0.667190i	$0.232503\pi$
$908$	−5.32127	+	6.67266i	−0.176593	+	0.221440i
$909$		0			0
$910$	26.7210	+	33.5071i	0.885792	+	1.11075i
$911$	18.9945			0.629315			0.314658	−	0.949205i	$-0.398110\pi$
$911$	18.9945			0.629315			0.314658	+	0.949205i	$0.398110\pi$
$912$		0			0
$913$	3.36927	+	14.7617i	0.111506	+	0.488541i
$914$	15.7358	+	68.9431i	0.520494	+	2.28043i
$915$		0			0
$916$	−61.4290			−2.02967
$917$	−8.80559	−	11.0419i	−0.290786	−	0.364634i
$918$		0			0
$919$	−10.4366	+	13.0871i	−0.344273	+	0.431705i	−0.923581	−	0.383404i	$-0.874752\pi$
$919$	−10.4366	+	13.0871i	−0.344273	+	0.431705i	0.579308	+	0.815109i	$0.303323\pi$
$920$	−2.67187	+	3.35042i	−0.0880890	+	0.110460i
$921$		0			0
$922$	−2.76928	−	12.1330i	−0.0912014	−	0.399580i
$923$	−13.1421	+	57.5792i	−0.432577	+	1.89524i
$924$		0			0
$925$	−3.68693	+	1.77553i	−0.121225	+	0.0583791i
$926$	−11.3316	+	49.6468i	−0.372378	+	1.63150i
$927$		0			0
$928$	39.1362	−	5.94290i	1.28471	−	0.195085i
$929$	57.7025			1.89316			0.946578	−	0.322474i	$-0.104515\pi$
$929$	57.7025			1.89316			0.946578	+	0.322474i	$0.104515\pi$
$930$		0			0
$931$	26.2632	−	12.6477i	0.860742	−	0.414512i
$932$	25.1728	+	12.1226i	0.824562	+	0.397088i
$933$		0			0
$934$	5.89019	+	25.8066i	0.192733	+	0.844417i
$935$	−23.1477	+	11.1474i	−0.757012	+	0.364558i
$936$		0			0
$937$	−25.0122	+	31.3643i	−0.817114	+	1.02463i	0.182031	+	0.983293i	$0.441733\pi$
$937$	−25.0122	+	31.3643i	−0.817114	+	1.02463i	−0.999145	+	0.0413357i	$0.986839\pi$
$938$	−22.1932	−	10.6877i	−0.724633	−	0.348965i
$939$		0			0
$940$	2.81078			0.0916774
$941$	−23.2388	−	29.1406i	−0.757565	−	0.949956i	0.242230	−	0.970219i	$-0.422121\pi$
$941$	−23.2388	−	29.1406i	−0.757565	−	0.949956i	−0.999795	+	0.0202626i	$0.993550\pi$
$942$		0			0
$943$	1.54856	+	6.78468i	0.0504280	+	0.220940i
$944$	3.87660	+	4.86110i	0.126172	+	0.158215i
$945$		0			0
$946$	37.4179	+	46.9206i	1.21656	+	1.52552i
$947$	−24.7428	−	11.9155i	−0.804032	−	0.387201i	−0.0137198	−	0.999906i	$-0.504367\pi$
$947$	−24.7428	−	11.9155i	−0.804032	−	0.387201i	−0.790312	+	0.612705i	$0.790082\pi$
$948$		0			0
$949$	−1.14280	+	1.43303i	−0.0370969	+	0.0465181i
$950$	−8.28571	+	3.99019i	−0.268824	+	0.129459i
$951$		0			0
$952$	1.61893	−	7.09300i	0.0524699	−	0.229886i
$953$	2.18295	+	1.05125i	0.0707126	+	0.0340534i	0.468906	−	0.883248i	$-0.344648\pi$
$953$	2.18295	+	1.05125i	0.0707126	+	0.0340534i	−0.398193	+	0.917302i	$0.630363\pi$
$954$		0			0
$955$	−6.19660	+	27.1491i	−0.200517	+	0.878523i
$956$	21.8169			0.705610
$957$		0			0
$958$	66.8731			2.16057
$959$	−1.10468	+	4.83990i	−0.0356719	+	0.156289i
$960$		0			0
$961$	−31.3529	−	15.0988i	−1.01138	−	0.487057i
$962$	−16.1772	+	70.8768i	−0.521573	+	2.28516i
$963$		0			0
$964$	58.5807	−	28.2110i	1.88676	−	0.908614i
$965$	−9.20795	+	11.5464i	−0.296414	+	0.371692i
$966$		0			0
$967$	−34.1033	−	16.4233i	−1.09669	−	0.528137i	−0.204072	−	0.978956i	$-0.565418\pi$
$967$	−34.1033	−	16.4233i	−1.09669	−	0.528137i	−0.892615	+	0.450819i	$0.851132\pi$
$968$	1.44663	+	1.81401i	0.0464964	+	0.0583046i
$969$		0			0
$970$	−12.4579	−	15.6217i	−0.399998	−	0.501582i
$971$	−2.86612	−	12.5573i	−0.0919781	−	0.402982i	0.907890	−	0.419208i	$-0.137692\pi$
$971$	−2.86612	−	12.5573i	−0.0919781	−	0.402982i	−0.999868	+	0.0162255i	$0.994835\pi$
$972$		0			0
$973$	4.87309	+	6.11067i	0.156224	+	0.195899i
$974$	−51.5611			−1.65212
$975$		0			0
$976$	11.3413	+	5.46169i	0.363027	+	0.174824i
$977$	−0.880437	+	1.10403i	−0.0281677	+	0.0353212i	−0.795716	−	0.605670i	$-0.792905\pi$
$977$	−0.880437	+	1.10403i	−0.0281677	+	0.0353212i	0.767548	+	0.640991i	$0.221477\pi$
$978$		0			0
$979$	−44.2439	+	21.3067i	−1.41404	+	0.680966i
$980$	7.73473	+	33.8880i	0.247077	+	1.08251i
$981$		0			0
$982$	54.4801	+	26.2362i	1.73853	+	0.837232i
$983$	10.8489	−	5.22454i	0.346025	−	0.166637i	−0.252796	−	0.967520i	$-0.581350\pi$
$983$	10.8489	−	5.22454i	0.346025	−	0.166637i	0.598821	+	0.800883i	$0.295636\pi$
$984$		0			0
$985$	6.05597			0.192959
$986$	17.9911	−	31.2409i	0.572954	−	0.994913i
$987$		0			0
$988$	−21.2195	+	92.9686i	−0.675082	+	2.95773i
$989$	−7.13321	+	3.43517i	−0.226823	+	0.109232i
$990$		0			0
$991$	9.99125	−	43.7745i	0.317383	−	1.39054i	−0.524742	−	0.851261i	$-0.675838\pi$
$991$	9.99125	−	43.7745i	0.317383	−	1.39054i	0.842125	−	0.539283i	$-0.181305\pi$
$992$	13.2682	+	58.1316i	0.421264	+	1.84568i
$993$		0			0
$994$	18.0806	−	22.6723i	0.573481	−	0.719123i
$995$	19.8479	−	24.8885i	0.629220	−	0.789017i
$996$		0			0
$997$	11.3546	+	14.2383i	0.359605	+	0.450931i	0.928419	−	0.371536i	$-0.121169\pi$
$997$	11.3546	+	14.2383i	0.359605	+	0.450931i	−0.568813	+	0.822467i	$0.692597\pi$
$998$	−84.0938			−2.66194
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.199.1		18
3.2	odd	2		87.2.g.a.25.3	yes	18
29.6	even	14		7569.2.a.bm.1.1		9
29.7	even	7	inner	261.2.k.c.181.1		18
29.23	even	7		7569.2.a.bj.1.9		9
87.23	odd	14		2523.2.a.r.1.1		9
87.35	odd	14		2523.2.a.o.1.9		9
87.65	odd	14		87.2.g.a.7.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.7.3	✓	18	87.65	odd	14
87.2.g.a.25.3	yes	18	3.2	odd	2
261.2.k.c.181.1		18	29.7	even	7	inner
261.2.k.c.199.1		18	1.1	even	1	trivial
2523.2.a.o.1.9		9	87.35	odd	14
2523.2.a.r.1.1		9	87.23	odd	14
7569.2.a.bj.1.9		9	29.23	even	7
7569.2.a.bm.1.1		9	29.6	even	14

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.487716 + 2.13682i) q^{2} +(-2.52621 - 1.21656i) q^{4} +(-0.533332 + 2.33668i) q^{5} +(-1.21803 + 0.586571i) q^{7} +(1.09855 - 1.37753i) q^{8} +(-4.73296 - 2.27927i) q^{10} +(-2.18816 - 2.74387i) q^{11} +(3.76255 + 4.71809i) q^{13} +(-0.659347 - 2.88879i) q^{14} +(-1.08862 - 1.36508i) q^{16} -3.05437 q^{17} +(-5.07762 - 2.44525i) q^{19} +(4.19002 - 5.25412i) q^{20} +(6.93036 - 3.33749i) q^{22} +(0.225809 + 0.989335i) q^{23} +(-0.670784 - 0.323033i) q^{25} +(-11.9168 + 5.73883i) q^{26} +3.79059 q^{28} +(5.14766 + 1.58164i) q^{29} +(-1.80501 + 7.90829i) q^{31} +(6.62277 - 3.18936i) q^{32} +(1.48967 - 6.52665i) q^{34} +(-0.721015 - 3.15897i) q^{35} +(3.42698 - 4.29729i) q^{37} +(7.70151 - 9.65739i) q^{38} +(2.63296 + 3.30163i) q^{40} +6.85782 q^{41} +(1.73610 + 7.60636i) q^{43} +(2.18968 + 9.59361i) q^{44} -2.22416 q^{46} +(0.260777 + 0.327004i) q^{47} +(-3.22491 + 4.04390i) q^{49} +(1.01742 - 1.27580i) q^{50} +(-3.76517 - 16.4963i) q^{52} +(-2.96899 + 13.0080i) q^{53} +(7.57855 - 3.64964i) q^{55} +(-0.530037 + 2.32225i) q^{56} +(-5.89028 + 10.2283i) q^{58} -3.56102 q^{59} +(-6.49557 + 3.12810i) q^{61} +(-16.0183 - 7.71400i) q^{62} +(2.80802 + 12.3027i) q^{64} +(-13.0314 + 6.27557i) q^{65} +(5.18318 - 6.49950i) q^{67} +(7.71599 + 3.71582i) q^{68} +7.10182 q^{70} +(6.10196 + 7.65161i) q^{71} +(0.0675863 + 0.296115i) q^{73} +(7.51117 + 9.41871i) q^{74} +(9.85235 + 12.3545i) q^{76} +(4.27471 + 2.05859i) q^{77} +(2.49794 - 3.13231i) q^{79} +(3.77036 - 1.81571i) q^{80} +(-3.34467 + 14.6540i) q^{82} +(-3.88709 - 1.87192i) q^{83} +(1.62899 - 7.13709i) q^{85} -17.1002 q^{86} -6.18356 q^{88} +(3.11361 - 13.6416i) q^{89} +(-7.35039 - 3.53976i) q^{91} +(0.633143 - 2.77398i) q^{92} +(-0.825935 + 0.397749i) q^{94} +(8.42183 - 10.5606i) q^{95} +(3.42690 + 1.65031i) q^{97} +(-7.06827 - 8.86333i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) \) 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

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