LMFDB - Embedded newform 261.2.k.c.82.3

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			82.3
Root			$0.491931 - 2.15529i$ of defining polynomial
Character	$\chi$	$=$	261.82
Dual form			261.2.k.c.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.754870 + 0.946578i) q^{2} +(0.118862 - 0.520769i) q^{4} +(-1.12131 - 1.40607i) q^{5} +(-0.951706 - 4.16970i) q^{7} +(2.76431 - 1.33122i) q^{8} +(0.484517 - 2.12281i) q^{10} +(0.951656 + 0.458293i) q^{11} +(4.75885 + 2.29174i) q^{13} +(3.22853 - 4.04845i) q^{14} +(2.38428 + 1.14821i) q^{16} -5.61769 q^{17} +(-1.42675 + 6.25099i) q^{19} +(-0.865520 + 0.416812i) q^{20} +(0.284567 + 1.24677i) q^{22} +(-1.27587 + 1.59988i) q^{23} +(0.392890 - 1.72136i) q^{25} +(1.42300 + 6.23459i) q^{26} -2.28457 q^{28} +(4.54927 - 2.88169i) q^{29} +(2.38467 + 2.99028i) q^{31} +(-0.652504 - 2.85881i) q^{32} +(-4.24063 - 5.31758i) q^{34} +(-4.79575 + 6.01368i) q^{35} +(0.315606 - 0.151988i) q^{37} +(-6.99406 + 3.36816i) q^{38} +(-4.97144 - 2.39412i) q^{40} +3.62240 q^{41} +(1.09049 - 1.36743i) q^{43} +(0.351781 - 0.441119i) q^{44} -2.47753 q^{46} +(6.28881 + 3.02853i) q^{47} +(-10.1739 + 4.89947i) q^{49} +(1.92598 - 0.927505i) q^{50} +(1.75911 - 2.20586i) q^{52} +(4.87488 + 6.11290i) q^{53} +(-0.422703 - 1.85198i) q^{55} +(-8.18161 - 10.2594i) q^{56} +(6.16185 + 2.13093i) q^{58} -0.382668 q^{59} +(1.21640 + 5.32939i) q^{61} +(-1.03041 + 4.51454i) q^{62} +(5.51347 - 6.91367i) q^{64} +(-2.11377 - 9.26104i) q^{65} +(-7.03806 + 3.38935i) q^{67} +(-0.667730 + 2.92552i) q^{68} -9.31258 q^{70} +(-14.0654 - 6.77356i) q^{71} +(-1.58547 + 1.98811i) q^{73} +(0.382110 + 0.184015i) q^{74} +(3.08574 + 1.48601i) q^{76} +(1.00525 - 4.40428i) q^{77} +(-9.25113 + 4.45511i) q^{79} +(-1.05904 - 4.63996i) q^{80} +(2.73445 + 3.42889i) q^{82} +(0.338541 - 1.48324i) q^{83} +(6.29915 + 7.89888i) q^{85} +2.11755 q^{86} +3.24076 q^{88} +(11.1881 + 14.0295i) q^{89} +(5.02684 - 22.0240i) q^{91} +(0.681518 + 0.854597i) q^{92} +(1.88050 + 8.23899i) q^{94} +(10.3892 - 5.00316i) q^{95} +(1.51530 - 6.63895i) q^{97} +(-12.3177 - 5.93188i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{2}{7}\right)$	$1$

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 $

$2$	0.754870	+	0.946578i	0.533774	+	0.669331i	0.973470	−	0.228815i	$-0.0734852\pi$
$2$	0.754870	+	0.946578i	0.533774	+	0.669331i	−0.439696	+	0.898147i	$0.644914\pi$
$3$		0			0
$3$		0			0
$4$	0.118862	−	0.520769i	0.0594310	−	0.260384i
$5$	−1.12131	−	1.40607i	−0.501463	−	0.628815i	0.465095	−	0.885261i	$-0.346020\pi$
$5$	−1.12131	−	1.40607i	−0.501463	−	0.628815i	−0.966559	+	0.256445i	$0.917449\pi$
$6$		0			0
$7$	−0.951706	−	4.16970i	−0.359711	−	1.57600i	−0.753913	−	0.656974i	$-0.771836\pi$
$7$	−0.951706	−	4.16970i	−0.359711	−	1.57600i	0.394202	−	0.919024i	$-0.371021\pi$
$8$	2.76431	−	1.33122i	0.977332	−	0.470658i
$9$		0			0
$10$	0.484517	−	2.12281i	0.153218	−	0.671290i
$11$	0.951656	+	0.458293i	0.286935	+	0.138181i	0.571815	−	0.820383i	$-0.306239\pi$
$11$	0.951656	+	0.458293i	0.286935	+	0.138181i	−0.284880	+	0.958563i	$0.591954\pi$
$12$		0			0
$13$	4.75885	+	2.29174i	1.31987	+	0.635615i	0.955321	−	0.295570i	$-0.0955096\pi$
$13$	4.75885	+	2.29174i	1.31987	+	0.635615i	0.364547	+	0.931185i	$0.381224\pi$
$14$	3.22853	−	4.04845i	0.862860	−	1.08199i
$15$		0			0
$16$	2.38428	+	1.14821i	0.596069	+	0.287052i
$17$	−5.61769			−1.36249			−0.681245	−	0.732056i	$-0.738561\pi$
$17$	−5.61769			−1.36249			−0.681245	+	0.732056i	$0.738561\pi$
$18$		0			0
$19$	−1.42675	+	6.25099i	−0.327319	+	1.43408i	0.496902	+	0.867807i	$0.334471\pi$
$19$	−1.42675	+	6.25099i	−0.327319	+	1.43408i	−0.824220	+	0.566269i	$0.808386\pi$
$20$	−0.865520	+	0.416812i	−0.193536	+	0.0932021i
$21$		0			0
$22$	0.284567	+	1.24677i	0.0606698	+	0.265812i
$23$	−1.27587	+	1.59988i	−0.266036	+	0.333599i	−0.896850	−	0.442336i	$-0.854150\pi$
$23$	−1.27587	+	1.59988i	−0.266036	+	0.333599i	0.630813	+	0.775935i	$0.282721\pi$
$24$		0			0
$25$	0.392890	−	1.72136i	0.0785779	−	0.344272i
$26$	1.42300	+	6.23459i	0.279074	+	1.22270i
$27$		0			0
$28$	−2.28457			−0.431743
$29$	4.54927	−	2.88169i	0.844778	−	0.535117i
$29$	4.54927	−	2.88169i	0.844778	−	0.535117i
$30$		0			0
$31$	2.38467	+	2.99028i	0.428299	+	0.537069i	0.948417	−	0.317025i	$-0.102684\pi$
$31$	2.38467	+	2.99028i	0.428299	+	0.537069i	−0.520119	+	0.854094i	$0.674112\pi$
$32$	−0.652504	−	2.85881i	−0.115348	−	0.505371i
$33$		0			0
$34$	−4.24063	−	5.31758i	−0.727261	−	0.911957i
$35$	−4.79575	+	6.01368i	−0.810629	+	1.01650i
$36$		0			0
$37$	0.315606	−	0.151988i	0.0518854	−	0.0249867i	−0.407761	−	0.913089i	$-0.633690\pi$
$37$	0.315606	−	0.151988i	0.0518854	−	0.0249867i	0.459647	+	0.888102i	$0.347976\pi$
$38$	−6.99406	+	3.36816i	−1.13459	+	0.546388i
$39$		0			0
$40$	−4.97144	−	2.39412i	−0.786053	−	0.378543i
$41$	3.62240			0.565725			0.282862	−	0.959161i	$-0.408716\pi$
$41$	3.62240			0.565725			0.282862	+	0.959161i	$0.408716\pi$
$42$		0			0
$43$	1.09049	−	1.36743i	0.166298	−	0.208530i	−0.691699	−	0.722186i	$-0.743138\pi$
$43$	1.09049	−	1.36743i	0.166298	−	0.208530i	0.857997	+	0.513655i	$0.171709\pi$
$44$	0.351781	−	0.441119i	0.0530329	−	0.0665012i
$45$		0			0
$46$	−2.47753			−0.365292
$47$	6.28881	+	3.02853i	0.917317	+	0.441756i	0.832112	−	0.554607i	$-0.187131\pi$
$47$	6.28881	+	3.02853i	0.917317	+	0.441756i	0.0852043	+	0.996363i	$0.472846\pi$
$48$		0			0
$49$	−10.1739	+	4.89947i	−1.45341	+	0.699924i
$50$	1.92598	−	0.927505i	0.272375	−	0.131169i
$51$		0			0
$52$	1.75911	−	2.20586i	0.243945	−	0.305898i
$53$	4.87488	+	6.11290i	0.669616	+	0.839672i	0.994352	−	0.106133i	$-0.0338469\pi$
$53$	4.87488	+	6.11290i	0.669616	+	0.839672i	−0.324736	+	0.945805i	$0.605276\pi$
$54$		0			0
$55$	−0.422703	−	1.85198i	−0.0569973	−	0.249722i
$56$	−8.18161	−	10.2594i	−1.09331	−	1.37097i
$57$		0			0
$58$	6.16185	+	2.13093i	0.809091	+	0.279805i
$59$	−0.382668			−0.0498191			−0.0249096	−	0.999690i	$-0.507930\pi$
$59$	−0.382668			−0.0498191			−0.0249096	+	0.999690i	$0.507930\pi$
$60$		0			0
$61$	1.21640	+	5.32939i	0.155744	+	0.682358i	0.991152	+	0.132729i	$0.0423740\pi$
$61$	1.21640	+	5.32939i	0.155744	+	0.682358i	−0.835409	+	0.549629i	$0.814769\pi$
$62$	−1.03041	+	4.51454i	−0.130863	+	0.573347i
$63$		0			0
$64$	5.51347	−	6.91367i	0.689184	−	0.864209i
$65$	−2.11377	−	9.26104i	−0.262181	−	1.14869i
$66$		0			0
$67$	−7.03806	+	3.38935i	−0.859836	+	0.414075i	−0.811219	−	0.584742i	$-0.801196\pi$
$67$	−7.03806	+	3.38935i	−0.859836	+	0.414075i	−0.0486169	+	0.998818i	$0.515481\pi$
$68$	−0.667730	+	2.92552i	−0.0809742	+	0.354771i
$69$		0			0
$70$	−9.31258			−1.11307
$71$	−14.0654	−	6.77356i	−1.66926	−	0.803874i	−0.998038	−	0.0626189i	$-0.980055\pi$
$71$	−14.0654	−	6.77356i	−1.66926	−	0.803874i	−0.671224	−	0.741255i	$-0.734231\pi$
$72$		0			0
$73$	−1.58547	+	1.98811i	−0.185565	+	0.232691i	−0.865909	−	0.500202i	$-0.833259\pi$
$73$	−1.58547	+	1.98811i	−0.185565	+	0.232691i	0.680344	+	0.732893i	$0.261830\pi$
$74$	0.382110	+	0.184015i	0.0444194	+	0.0213913i
$75$		0			0
$76$	3.08574	+	1.48601i	0.353958	+	0.170457i
$77$	1.00525	−	4.40428i	0.114559	−	0.501914i
$78$		0			0
$79$	−9.25113	+	4.45511i	−1.04083	+	0.501239i	−0.874599	−	0.484847i	$-0.838875\pi$
$79$	−9.25113	+	4.45511i	−1.04083	+	0.501239i	−0.166235	+	0.986086i	$0.553161\pi$
$80$	−1.05904	−	4.63996i	−0.118404	−	0.518764i
$81$		0			0
$82$	2.73445	+	3.42889i	0.301969	+	0.378657i
$83$	0.338541	−	1.48324i	0.0371597	−	0.162807i	−0.952944	−	0.303148i	$-0.901963\pi$
$83$	0.338541	−	1.48324i	0.0371597	−	0.162807i	0.990103	+	0.140340i	$0.0448197\pi$
$84$		0			0
$85$	6.29915	+	7.89888i	0.683239	+	0.856754i
$86$	2.11755			0.228341
$87$		0			0
$88$	3.24076			0.345467
$89$	11.1881	+	14.0295i	1.18594	+	1.48712i	0.834587	+	0.550876i	$0.185706\pi$
$89$	11.1881	+	14.0295i	1.18594	+	1.48712i	0.351351	+	0.936244i	$0.385722\pi$
$90$		0			0
$91$	5.02684	−	22.0240i	0.526956	−	2.30875i
$92$	0.681518	+	0.854597i	0.0710532	+	0.0890979i
$93$		0			0
$94$	1.88050	+	8.23899i	0.193958	+	0.849787i
$95$	10.3892	−	5.00316i	1.06591	−	0.513314i
$96$		0			0
$97$	1.51530	−	6.63895i	0.153855	−	0.674083i	−0.837888	−	0.545842i	$-0.816210\pi$
$97$	1.51530	−	6.63895i	0.153855	−	0.674083i	0.991743	−	0.128241i	$-0.0409331\pi$
$98$	−12.3177	−	5.93188i	−1.24427	−	0.599210i
$99$		0			0
$100$	−0.849732	−	0.409209i	−0.0849732	−	0.0409209i
$101$	−2.94644	+	3.69472i	−0.293182	+	0.367639i	−0.906506	−	0.422193i	$-0.861261\pi$
$101$	−2.94644	+	3.69472i	−0.293182	+	0.367639i	0.613324	+	0.789831i	$0.289832\pi$
$102$		0			0
$103$	−3.14881	−	1.51639i	−0.310261	−	0.149414i	0.272273	−	0.962220i	$-0.412225\pi$
$103$	−3.14881	−	1.51639i	−0.310261	−	0.149414i	−0.582534	+	0.812806i	$0.697939\pi$
$104$	16.2058			1.58911
$105$		0			0
$106$	−2.10644	+	9.22890i	−0.204595	+	0.896390i
$107$	−4.43449	+	2.13554i	−0.428699	+	0.206450i	−0.635775	−	0.771874i	$-0.719319\pi$
$107$	−4.43449	+	2.13554i	−0.428699	+	0.206450i	0.207076	+	0.978325i	$0.433605\pi$
$108$		0			0
$109$	3.31215	+	14.5115i	0.317246	+	1.38995i	0.842360	+	0.538915i	$0.181166\pi$
$109$	3.31215	+	14.5115i	0.317246	+	1.38995i	−0.525114	+	0.851032i	$0.675977\pi$
$110$	1.43396	−	1.79813i	0.136723	−	0.171445i
$111$		0			0
$112$	2.51855	−	11.0345i	0.237980	−	1.04266i
$113$	−1.41140	−	6.18375i	−0.132773	−	0.581718i	−0.996916	−	0.0784718i	$-0.974996\pi$
$113$	−1.41140	−	6.18375i	−0.132773	−	0.581718i	0.864143	−	0.503246i	$-0.167861\pi$
$114$		0			0
$115$	3.68019			0.343180
$116$	−0.959961	−	2.71164i	−0.0891301	−	0.251770i
$117$		0			0
$118$	−0.288865	−	0.362225i	−0.0265922	−	0.0333455i
$119$	5.34639	+	23.4241i	0.490103	+	2.14728i
$120$		0			0
$121$	−6.16277	−	7.72787i	−0.560252	−	0.702534i
$122$	−4.12646	+	5.17441i	−0.373592	+	0.468469i
$123$		0			0
$124$	1.84069	−	0.886429i	0.165299	−	0.0796037i
$125$	−10.9626	+	5.27930i	−0.980523	+	0.472195i
$126$		0			0
$127$	4.02345	+	1.93759i	0.357023	+	0.171933i	0.603794	−	0.797141i	$-0.293655\pi$
$127$	4.02345	+	1.93759i	0.357023	+	0.171933i	−0.246770	+	0.969074i	$0.579369\pi$
$128$	4.84163			0.427944
$129$		0			0
$130$	7.17067	−	8.99173i	0.628909	−	0.788627i
$131$	−0.00620961	+	0.00778660i	−0.000542536	+	0.000680318i	−0.782103	−	0.623150i	$-0.785853\pi$
$131$	−0.00620961	+	0.00778660i	−0.000542536	+	0.000680318i	0.781560	+	0.623830i	$0.214424\pi$
$132$		0			0
$133$	27.4226			2.37784
$134$	−8.52111	−	4.10355i	−0.736112	−	0.354493i
$135$		0			0
$136$	−15.5290	+	7.47839i	−1.33160	+	0.641267i
$137$	11.0039	−	5.29921i	0.940129	−	0.452742i	0.0999140	−	0.994996i	$-0.468143\pi$
$137$	11.0039	−	5.29921i	0.940129	−	0.452742i	0.840215	+	0.542254i	$0.182429\pi$
$138$		0			0
$139$	3.08354	−	3.86663i	0.261542	−	0.327964i	−0.633670	−	0.773603i	$-0.718452\pi$
$139$	3.08354	−	3.86663i	0.261542	−	0.327964i	0.895212	+	0.445640i	$0.147024\pi$
$140$	2.56170	+	3.21227i	0.216503	+	0.271487i
$141$		0			0
$142$	−4.20589	−	18.4272i	−0.352950	−	1.54638i
$143$	3.47850	+	4.36190i	0.290887	+	0.364760i
$144$		0			0
$145$	−9.15299	−	3.16534i	−0.760115	−	0.262868i
$146$	−3.07873			−0.254797
$147$		0			0
$148$	−0.0416370	−	0.182424i	−0.00342254	−	0.0149951i
$149$	3.11840	−	13.6626i	0.255470	−	1.11929i	−0.670566	−	0.741850i	$-0.733949\pi$
$149$	3.11840	−	13.6626i	0.255470	−	1.11929i	0.926036	−	0.377436i	$-0.123194\pi$
$150$		0			0
$151$	1.82927	−	2.29383i	0.148864	−	0.186669i	−0.701809	−	0.712366i	$-0.747624\pi$
$151$	1.82927	−	2.29383i	0.148864	−	0.186669i	0.850672	+	0.525697i	$0.176195\pi$
$152$	4.37749	+	19.1790i	0.355061	+	1.55562i
$153$		0			0
$154$	4.92782	−	2.37311i	0.397095	−	0.191231i
$155$	1.53061	−	6.70603i	0.122941	−	0.538641i
$156$		0			0
$157$	16.1919			1.29226			0.646128	−	0.763229i	$-0.276387\pi$
$157$	16.1919			1.29226			0.646128	+	0.763229i	$0.276387\pi$
$158$	−11.2005	−	5.39388i	−0.891065	−	0.429114i
$159$		0			0
$160$	−3.28804	+	4.12307i	−0.259942	+	0.325957i
$161$	7.88529	+	3.79735i	0.621448	+	0.299273i
$162$		0			0
$163$	−12.2292	−	5.88927i	−0.957865	−	0.461284i	−0.111428	−	0.993772i	$-0.535543\pi$
$163$	−12.2292	−	5.88927i	−0.957865	−	0.461284i	−0.846437	+	0.532489i	$0.821257\pi$
$164$	0.430567	−	1.88644i	0.0336216	−	0.147306i
$165$		0			0
$166$	1.65956	−	0.799202i	0.128807	−	0.0620301i
$167$	−3.64080	−	15.9514i	−0.281734	−	1.23436i	−0.895569	−	0.444922i	$-0.853231\pi$
$167$	−3.64080	−	15.9514i	−0.281734	−	1.23436i	0.613836	−	0.789434i	$-0.289626\pi$
$168$		0			0
$169$	9.28921	+	11.6483i	0.714555	+	0.896024i
$170$	−2.72186	+	11.9253i	−0.208757	+	0.914626i
$171$		0			0
$172$	−0.582495	−	0.730426i	−0.0444149	−	0.0556945i
$173$	4.46374			0.339372			0.169686	−	0.985498i	$-0.445725\pi$
$173$	4.46374			0.339372			0.169686	+	0.985498i	$0.445725\pi$
$174$		0			0
$175$	−7.55148			−0.570838
$176$	1.74280	+	2.18540i	0.131368	+	0.164730i
$177$		0			0
$178$	−4.83439	+	21.1808i	−0.362353	+	1.58757i
$179$	−2.12026	−	2.65872i	−0.158476	−	0.198722i	0.696254	−	0.717795i	$-0.254849\pi$
$179$	−2.12026	−	2.65872i	−0.158476	−	0.198722i	−0.854730	+	0.519073i	$0.826277\pi$
$180$		0			0
$181$	−1.47339	−	6.45532i	−0.109516	−	0.479820i	−0.999706	−	0.0242319i	$-0.992286\pi$
$181$	−1.47339	−	6.45532i	−0.109516	−	0.479820i	0.890190	−	0.455589i	$-0.150571\pi$
$182$	24.6421	−	11.8670i	1.82659	−	0.879640i
$183$		0			0
$184$	−1.39709	+	6.12104i	−0.102995	+	0.451249i
$185$	−0.567598	−	0.273341i	−0.0417306	−	0.0200964i
$186$		0			0
$187$	−5.34610	−	2.57455i	−0.390946	−	0.188270i
$188$	2.32466	−	2.91504i	0.169544	−	0.212601i
$189$		0			0
$190$	12.5784	+	6.05742i	0.912531	+	0.439452i
$191$	−17.6196			−1.27491			−0.637454	−	0.770489i	$-0.720012\pi$
$191$	−17.6196			−1.27491			−0.637454	+	0.770489i	$0.720012\pi$
$192$		0			0
$193$	2.98147	−	13.0627i	0.214611	−	0.940273i	−0.746776	−	0.665075i	$-0.768399\pi$
$193$	2.98147	−	13.0627i	0.214611	−	0.940273i	0.961388	−	0.275198i	$-0.0887434\pi$
$194$	7.42813	−	3.57720i	0.533309	−	0.256828i
$195$		0			0
$196$	1.34221	+	5.88059i	0.0958719	+	0.420042i
$197$	5.11558	−	6.41474i	0.364470	−	0.457031i	−0.565455	−	0.824779i	$-0.691300\pi$
$197$	5.11558	−	6.41474i	0.364470	−	0.457031i	0.929926	+	0.367748i	$0.119871\pi$
$198$		0			0
$199$	−5.45073	+	23.8812i	−0.386392	+	1.69290i	0.290551	+	0.956860i	$0.406162\pi$
$199$	−5.45073	+	23.8812i	−0.386392	+	1.69290i	−0.676943	+	0.736036i	$0.736696\pi$
$200$	−1.20545	−	5.28141i	−0.0852379	−	0.373452i
$201$		0			0
$202$	−5.72153			−0.402565
$203$	−16.3454	−	16.2266i	−1.14722	−	1.13888i
$204$		0			0
$205$	−4.06182	−	5.09337i	−0.283690	−	0.355736i
$206$	−0.941565	−	4.12527i	−0.0656019	−	0.287421i
$207$		0			0
$208$	8.71503	+	10.9283i	0.604278	+	0.757741i
$209$	−4.22256	+	5.29492i	−0.292081	+	0.366258i
$210$		0			0
$211$	1.99243	−	0.959502i	0.137164	−	0.0660549i	−0.364043	−	0.931382i	$-0.618604\pi$
$211$	1.99243	−	0.959502i	0.137164	−	0.0660549i	0.501207	+	0.865327i	$0.332890\pi$
$212$	3.76285	−	1.81209i	0.258433	−	0.124455i
$213$		0			0
$214$	−5.36892	−	2.58554i	−0.367012	−	0.176744i
$215$	−3.14547			−0.214519
$216$		0			0
$217$	10.1990	−	12.7892i	0.692356	−	0.868187i
$218$	−11.2360	+	14.0895i	−0.760997	+	0.954260i
$219$		0			0
$220$	−1.01470			−0.0684110
$221$	−26.7337	−	12.8743i	−1.79831	−	0.866018i
$222$		0			0
$223$	−2.43655	+	1.17338i	−0.163164	+	0.0785755i	−0.513683	−	0.857980i	$-0.671719\pi$
$223$	−2.43655	+	1.17338i	−0.163164	+	0.0785755i	0.350519	+	0.936555i	$0.386005\pi$
$224$	−11.2994	+	5.44149i	−0.754971	+	0.363575i
$225$		0			0
$226$	4.78798	−	6.00393i	0.318491	−	0.399376i
$227$	−8.99231	−	11.2760i	−0.596840	−	0.748414i	0.388041	−	0.921642i	$-0.373152\pi$
$227$	−8.99231	−	11.2760i	−0.596840	−	0.748414i	−0.984882	+	0.173228i	$0.944580\pi$
$228$		0			0
$229$	−5.72917	−	25.1011i	−0.378594	−	1.65873i	−0.701779	−	0.712394i	$-0.747611\pi$
$229$	−5.72917	−	25.1011i	−0.378594	−	1.65873i	0.323185	−	0.946336i	$-0.395246\pi$
$230$	2.77807	+	3.48359i	0.183180	+	0.229701i
$231$		0			0
$232$	8.73942	−	14.0220i	0.573771	−	0.920589i
$233$	22.6039			1.48083			0.740417	−	0.672148i	$-0.234628\pi$
$233$	22.6039			1.48083			0.740417	+	0.672148i	$0.234628\pi$
$234$		0			0
$235$	−2.79334	−	12.2384i	−0.182218	−	0.798347i
$236$	−0.0454847	+	0.199282i	−0.00296080	+	0.0129721i
$237$		0			0
$238$	−18.1369	+	22.7429i	−1.17564	+	1.47420i
$239$	5.21218	+	22.8361i	0.337148	+	1.47714i	0.804968	+	0.593318i	$0.202182\pi$
$239$	5.21218	+	22.8361i	0.337148	+	1.47714i	−0.467820	+	0.883824i	$0.654960\pi$
$240$		0			0
$241$	−20.1661	+	9.71147i	−1.29901	+	0.625570i	−0.950205	−	0.311625i	$-0.899127\pi$
$241$	−20.1661	+	9.71147i	−1.29901	+	0.625570i	−0.348805	+	0.937195i	$0.613413\pi$
$242$	2.66294	−	11.6671i	0.171180	−	0.749989i
$243$		0			0
$244$	2.91996			0.186932
$245$	18.2970	+	8.81138i	1.16895	+	0.562939i
$246$		0			0
$247$	−21.1153	+	26.4778i	−1.34354	+	1.68474i
$248$	10.5727	+	5.09154i	0.671366	+	0.323313i
$249$		0			0
$250$	−13.2726	−	6.39175i	−0.839433	−	0.404250i
$251$	−1.32618	+	5.81039i	−0.0837079	+	0.366748i	−0.999381	−	0.0351751i	$-0.988801\pi$
$251$	−1.32618	+	5.81039i	−0.0837079	+	0.366748i	0.915673	+	0.401924i	$0.131658\pi$
$252$		0			0
$253$	−1.94740	+	0.937819i	−0.122432	+	0.0589602i
$254$	1.20310	+	5.27114i	0.0754894	+	0.330741i
$255$		0			0
$256$	−7.37214	−	9.24437i	−0.460759	−	0.577773i
$257$	−3.35390	+	14.6944i	−0.209211	+	0.916612i	0.755883	+	0.654707i	$0.227208\pi$
$257$	−3.35390	+	14.6944i	−0.209211	+	0.916612i	−0.965094	+	0.261905i	$0.915649\pi$
$258$		0			0
$259$	−0.934109	−	1.17134i	−0.0580427	−	0.0727832i
$260$	−5.07411			−0.314683
$261$		0			0
$262$	−0.0120581			−0.000744950
$263$	11.6750	+	14.6400i	0.719911	+	0.902740i	0.998333	−	0.0577193i	$-0.0183828\pi$
$263$	11.6750	+	14.6400i	0.719911	+	0.902740i	−0.278422	+	0.960459i	$0.589811\pi$
$264$		0			0
$265$	3.12896	−	13.7089i	0.192210	−	0.842129i
$266$	20.7005	+	25.9576i	1.26923	+	1.59156i
$267$		0			0
$268$	0.928510	+	4.06807i	0.0567178	+	0.248497i
$269$	−20.8357	+	10.0340i	−1.27038	+	0.611781i	−0.942899	−	0.333078i	$-0.891913\pi$
$269$	−20.8357	+	10.0340i	−1.27038	+	0.611781i	−0.327477	+	0.944859i	$0.606198\pi$
$270$		0			0
$271$	−4.75012	+	20.8116i	−0.288549	+	1.26422i	0.597967	+	0.801521i	$0.295975\pi$
$271$	−4.75012	+	20.8116i	−0.288549	+	1.26422i	−0.886517	+	0.462697i	$0.846882\pi$
$272$	−13.3941	−	6.45027i	−0.812138	−	0.391105i
$273$		0			0
$274$	13.3227	+	6.41585i	0.804851	+	0.387596i
$275$	1.16278	−	1.45809i	0.0701185	−	0.0879258i
$276$		0			0
$277$	7.49769	+	3.61070i	0.450493	+	0.216946i	0.645352	−	0.763885i	$-0.276711\pi$
$277$	7.49769	+	3.61070i	0.450493	+	0.216946i	−0.194859	+	0.980831i	$0.562425\pi$
$278$	5.98774			0.359121
$279$		0			0
$280$	−5.25140	+	23.0079i	−0.313831	+	1.37498i
$281$	−26.0562	+	12.5480i	−1.55438	+	0.748552i	−0.996675	−	0.0814850i	$-0.974034\pi$
$281$	−26.0562	+	12.5480i	−1.55438	+	0.748552i	−0.557709	+	0.830037i	$0.688319\pi$
$282$		0			0
$283$	−6.67116	−	29.2282i	−0.396559	−	1.73744i	−0.640785	−	0.767721i	$-0.721391\pi$
$283$	−6.67116	−	29.2282i	−0.396559	−	1.73744i	0.244226	−	0.969718i	$-0.421466\pi$
$284$	−5.19931	+	6.51973i	−0.308522	+	0.386875i
$285$		0			0
$286$	−1.50306	+	6.58534i	−0.0888778	+	0.389399i
$287$	−3.44747	−	15.1043i	−0.203497	−	0.891581i
$288$		0			0
$289$	14.5584			0.856378
$290$	−3.91308	−	11.0534i	−0.229784	−	0.649081i
$291$		0			0
$292$	0.846895	+	1.06197i	0.0495608	+	0.0621473i
$293$	1.94796	+	8.53458i	0.113801	+	0.498595i	0.999416	+	0.0341747i	$0.0108803\pi$
$293$	1.94796	+	8.53458i	0.113801	+	0.498595i	−0.885615	+	0.464421i	$0.846263\pi$
$294$		0			0
$295$	0.429088	+	0.538059i	0.0249825	+	0.0313270i
$296$	0.670105	−	0.840285i	0.0389490	−	0.0488405i
$297$		0			0
$298$	15.2867	−	7.36170i	0.885536	−	0.426452i
$299$	−9.73818	+	4.68966i	−0.563173	+	0.271210i
$300$		0			0
$301$	−6.73958	−	3.24561i	−0.388463	−	0.187074i
$302$	3.55215			0.204403
$303$		0			0
$304$	−10.5792	+	13.2659i	−0.606759	+	0.760852i
$305$	6.12956	−	7.68622i	0.350977	−	0.440112i
$306$		0			0
$307$	−33.9161			−1.93570			−0.967848	−	0.251536i	$-0.919064\pi$
$307$	−33.9161			−1.93570			−0.967848	+	0.251536i	$0.919064\pi$
$308$	−2.17412	−	1.04700i	−0.123882	−	0.0596585i
$309$		0			0
$310$	7.50319	−	3.61334i	0.426152	−	0.205224i
$311$	7.32104	−	3.52563i	0.415138	−	0.199920i	−0.214643	−	0.976693i	$-0.568859\pi$
$311$	7.32104	−	3.52563i	0.415138	−	0.199920i	0.629781	+	0.776773i	$0.283145\pi$
$312$		0			0
$313$	1.57580	−	1.97599i	0.0890693	−	0.111689i	−0.735300	−	0.677742i	$-0.762959\pi$
$313$	1.57580	−	1.97599i	0.0890693	−	0.111689i	0.824369	+	0.566053i	$0.191530\pi$
$314$	12.2228	+	15.3269i	0.689773	+	0.864948i
$315$		0			0
$316$	1.22047	+	5.34724i	0.0686570	+	0.300806i
$317$	−10.3738	−	13.0083i	−0.582651	−	0.730621i	0.399912	−	0.916554i	$-0.369041\pi$
$317$	−10.3738	−	13.0083i	−0.582651	−	0.730621i	−0.982562	+	0.185933i	$0.940469\pi$
$318$		0			0
$319$	5.65000	−	0.657481i	0.316339	−	0.0368119i
$320$	−15.9034			−0.889028
$321$		0			0
$322$	2.35788	+	10.3305i	0.131399	+	0.575699i
$323$	8.01503	−	35.1161i	0.445968	−	1.95391i
$324$		0			0
$325$	5.81462	−	7.29130i	0.322537	−	0.404449i
$326$	−3.65681	−	16.0215i	−0.202532	−	0.887350i
$327$		0			0
$328$	10.0135	−	4.82223i	0.552901	−	0.266263i
$329$	6.64296	−	29.1047i	0.366238	−	1.60459i
$330$		0			0
$331$	12.9286			0.710619			0.355309	−	0.934749i	$-0.384375\pi$
$331$	12.9286			0.710619			0.355309	+	0.934749i	$0.384375\pi$
$332$	−0.732188	−	0.352603i	−0.0401840	−	0.0193516i
$333$		0			0
$334$	12.3509	−	15.4875i	0.675811	−	0.847440i
$335$	12.6575	+	6.09553i	0.691553	+	0.333034i
$336$		0			0
$337$	5.01185	+	2.41358i	0.273013	+	0.131476i	0.565381	−	0.824830i	$-0.308729\pi$
$337$	5.01185	+	2.41358i	0.273013	+	0.131476i	−0.292368	+	0.956306i	$0.594443\pi$
$338$	−4.01387	+	17.5859i	−0.218326	+	0.956548i
$339$		0			0
$340$	4.86222	−	2.34152i	0.263691	−	0.126987i
$341$	0.898957	+	3.93859i	0.0486813	+	0.213286i
$342$		0			0
$343$	11.4455	+	14.3522i	0.617998	+	0.774945i
$344$	1.19409	−	5.23167i	0.0643813	−	0.282073i
$345$		0			0
$346$	3.36955	+	4.22528i	0.181148	+	0.227152i
$347$	8.78686			0.471703			0.235852	−	0.971789i	$-0.424212\pi$
$347$	8.78686			0.471703			0.235852	+	0.971789i	$0.424212\pi$
$348$		0			0
$349$	15.1943			0.813332			0.406666	−	0.913577i	$-0.366691\pi$
$349$	15.1943			0.813332			0.406666	+	0.913577i	$0.366691\pi$
$350$	−5.70039	−	7.14806i	−0.304698	−	0.382080i
$351$		0			0
$352$	0.689213	−	3.01964i	0.0367352	−	0.160947i
$353$	7.71052	+	9.66868i	0.410389	+	0.514612i	0.943473	−	0.331451i	$-0.107538\pi$
$353$	7.71052	+	9.66868i	0.410389	+	0.514612i	−0.533083	+	0.846063i	$0.678967\pi$
$354$		0			0
$355$	6.24754	+	27.3723i	0.331585	+	1.45277i
$356$	8.63595	−	4.15885i	0.457704	−	0.220419i
$357$		0			0
$358$	0.916165	−	4.01398i	0.0484208	−	0.212146i
$359$	−14.4303	−	6.94924i	−0.761600	−	0.366767i	0.0124248	−	0.999923i	$-0.496045\pi$
$359$	−14.4303	−	6.94924i	−0.761600	−	0.366767i	−0.774024	+	0.633156i	$0.781759\pi$
$360$		0			0
$361$	−19.9209	−	9.59340i	−1.04847	−	0.504916i
$362$	4.99825	−	6.26761i	0.262702	−	0.329418i
$363$		0			0
$364$	−10.8719	−	5.23565i	−0.569844	−	0.274422i
$365$	4.57323			0.239374
$366$		0			0
$367$	4.94990	−	21.6869i	0.258383	−	1.13205i	−0.664597	−	0.747202i	$-0.731397\pi$
$367$	4.94990	−	21.6869i	0.258383	−	1.13205i	0.922980	−	0.384847i	$-0.125746\pi$
$368$	−4.87902	+	2.34961i	−0.254336	+	0.122482i
$369$		0			0
$370$	−0.169725	−	0.743612i	−0.00882356	−	0.0386585i
$371$	20.8495	−	26.1445i	1.08245	−	1.35735i
$372$		0			0
$373$	−1.54213	+	6.75653i	−0.0798487	+	0.349840i	−0.999032	−	0.0439901i	$-0.985993\pi$
$373$	−1.54213	+	6.75653i	−0.0798487	+	0.349840i	0.919183	+	0.393830i	$0.128850\pi$
$374$	−1.59861	−	7.00395i	−0.0826620	−	0.362166i
$375$		0			0
$376$	21.4159			1.10444
$377$	28.2534	−	3.28780i	1.45512	−	0.169330i
$378$		0			0
$379$	−4.85604	−	6.08928i	−0.249438	−	0.312785i	0.641311	−	0.767281i	$-0.278391\pi$
$379$	−4.85604	−	6.08928i	−0.249438	−	0.312785i	−0.890749	+	0.454496i	$0.849819\pi$
$380$	−1.37061	−	6.00505i	−0.0703110	−	0.308052i
$381$		0			0
$382$	−13.3005	−	16.6783i	−0.680512	−	0.853335i
$383$	−15.8756	+	19.9074i	−0.811206	+	1.01722i	0.188178	+	0.982135i	$0.439742\pi$
$383$	−15.8756	+	19.9074i	−0.811206	+	1.01722i	−0.999384	+	0.0350856i	$0.988830\pi$
$384$		0			0
$385$	−7.31993	+	3.52509i	−0.373058	+	0.179655i
$386$	14.6155	−	7.03844i	0.743908	−	0.358247i
$387$		0			0
$388$	−3.27725	−	1.57824i	−0.166377	−	0.0801229i
$389$	−10.9838			−0.556902			−0.278451	−	0.960450i	$-0.589821\pi$
$389$	−10.9838			−0.556902			−0.278451	+	0.960450i	$0.589821\pi$
$390$		0			0
$391$	7.16741	−	8.98765i	0.362472	−	0.454525i
$392$	−21.6014	+	27.0873i	−1.09104	+	1.36812i
$393$		0			0
$394$	9.93365			0.500450
$395$	16.6376	+	8.01223i	0.837127	+	0.403139i
$396$		0			0
$397$	−4.59536	+	2.21301i	−0.230635	+	0.111068i	−0.545632	−	0.838025i	$-0.683711\pi$
$397$	−4.59536	+	2.21301i	−0.230635	+	0.111068i	0.314998	+	0.949092i	$0.397996\pi$
$398$	−26.7200	+	12.8677i	−1.33935	+	0.644999i
$399$		0			0
$400$	2.91324	−	3.65309i	0.145662	−	0.182654i
$401$	12.1843	+	15.2786i	0.608455	+	0.762979i	0.986669	−	0.162740i	$-0.0520330\pi$
$401$	12.1843	+	15.2786i	0.608455	+	0.762979i	−0.378214	+	0.925718i	$0.623462\pi$
$402$		0			0
$403$	4.49533	+	19.6953i	0.223928	+	0.981093i
$404$	1.57388	+	1.97358i	0.0783033	+	0.0981892i
$405$		0			0
$406$	3.02106	−	27.7211i	0.149933	−	1.37577i
$407$	0.370004			0.0183404
$408$		0			0
$409$	3.98856	+	17.4750i	0.197221	+	0.864083i	0.972581	+	0.232564i	$0.0747114\pi$
$409$	3.98856	+	17.4750i	0.197221	+	0.864083i	−0.775360	+	0.631520i	$0.782431\pi$
$410$	1.75512	−	7.68966i	0.0866790	−	0.379765i
$411$		0			0
$412$	−1.16396	+	1.45956i	−0.0573442	+	0.0719074i
$413$	0.364188	+	1.59561i	0.0179205	+	0.0785148i
$414$		0			0
$415$	−2.46516	+	1.18716i	−0.121010	+	0.0582753i
$416$	3.44648	−	15.1000i	0.168978	−	0.740339i
$417$		0			0
$418$	−8.19954			−0.401053
$419$	3.36801	+	1.62195i	0.164538	+	0.0792373i	0.514340	−	0.857586i	$-0.328037\pi$
$419$	3.36801	+	1.62195i	0.164538	+	0.0792373i	−0.349802	+	0.936824i	$0.613751\pi$
$420$		0			0
$421$	5.16735	−	6.47965i	0.251841	−	0.315799i	−0.639800	−	0.768541i	$-0.720983\pi$
$421$	5.16735	−	6.47965i	0.251841	−	0.315799i	0.891641	+	0.452742i	$0.149554\pi$
$422$	2.41227	+	1.16169i	0.117427	+	0.0565500i
$423$		0			0
$424$	21.6133	+	10.4084i	1.04964	+	0.505478i
$425$	−2.20713	+	9.67008i	−0.107062	+	0.469068i
$426$		0			0
$427$	21.0643	−	10.1440i	1.01937	−	0.490904i
$428$	0.585029	+	2.56318i	0.0282785	+	0.123896i
$429$		0			0
$430$	−2.37442	−	2.97743i	−0.114505	−	0.143584i
$431$	4.25670	−	18.6498i	0.205038	−	0.898330i	−0.762776	−	0.646663i	$-0.776164\pi$
$431$	4.25670	−	18.6498i	0.205038	−	0.898330i	0.967814	−	0.251667i	$-0.0809787\pi$
$432$		0			0
$433$	−10.0699	−	12.6273i	−0.483929	−	0.606828i	0.478591	−	0.878038i	$-0.341148\pi$
$433$	−10.0699	−	12.6273i	−0.483929	−	0.606828i	−0.962520	+	0.271210i	$0.912576\pi$
$434$	19.8049			0.950667
$435$		0			0
$436$	7.95081			0.380775
$437$	−8.18053	−	10.2581i	−0.391328	−	0.490710i
$438$		0			0
$439$	−0.660522	+	2.89393i	−0.0315250	+	0.138120i	−0.988241	−	0.152902i	$-0.951138\pi$
$439$	−0.660522	+	2.89393i	−0.0315250	+	0.138120i	0.956716	+	0.291022i	$0.0939953\pi$
$440$	−3.63389	−	4.55675i	−0.173239	−	0.217235i
$441$		0			0
$442$	−7.99400	−	35.0240i	−0.380236	−	1.66592i
$443$	9.45260	−	4.55213i	0.449107	−	0.216278i	−0.195638	−	0.980676i	$-0.562678\pi$
$443$	9.45260	−	4.55213i	0.449107	−	0.216278i	0.644745	+	0.764398i	$0.276964\pi$
$444$		0			0
$445$	7.18114	−	31.4626i	0.340419	−	1.49147i
$446$	−2.94998	−	1.42064i	−0.139686	−	0.0672691i
$447$		0			0
$448$	−34.0751	−	16.4097i	−1.60990	−	0.775287i
$449$	2.74538	−	3.44260i	0.129563	−	0.162466i	−0.712819	−	0.701348i	$-0.752582\pi$
$449$	2.74538	−	3.44260i	0.129563	−	0.162466i	0.842381	+	0.538882i	$0.181153\pi$
$450$		0			0
$451$	3.44728	+	1.66012i	0.162326	+	0.0781721i
$452$	−3.38807			−0.159361
$453$		0			0
$454$	3.88558	−	17.0238i	0.182359	−	0.798968i
$455$	−36.6040	+	17.6276i	−1.71602	+	0.826394i
$456$		0			0
$457$	−2.52528	−	11.0640i	−0.118127	−	0.517550i	−0.999021	−	0.0442360i	$-0.985915\pi$
$457$	−2.52528	−	11.0640i	−0.118127	−	0.517550i	0.880894	−	0.473314i	$-0.156943\pi$
$458$	19.4354	−	24.3712i	0.908156	−	1.13879i
$459$		0			0
$460$	0.437435	−	1.91653i	0.0203955	−	0.0893586i
$461$	4.38570	+	19.2150i	0.204262	+	0.894932i	0.968306	+	0.249767i	$0.0803541\pi$
$461$	4.38570	+	19.2150i	0.204262	+	0.894932i	−0.764044	+	0.645165i	$0.776789\pi$
$462$		0			0
$463$	0.753315			0.0350095			0.0175048	−	0.999847i	$-0.494428\pi$
$463$	0.753315			0.0350095			0.0175048	+	0.999847i	$0.494428\pi$
$464$	14.1555	−	1.64725i	0.657153	−	0.0764718i
$465$		0			0
$466$	17.0631	+	21.3964i	0.790431	+	0.991169i
$467$	2.32424	+	10.1832i	0.107553	+	0.471221i	0.999806	+	0.0196852i	$0.00626641\pi$
$467$	2.32424	+	10.1832i	0.107553	+	0.471221i	−0.892253	+	0.451535i	$0.850876\pi$
$468$		0			0
$469$	20.8307	+	26.1209i	0.961874	+	1.20615i
$470$	9.47601	−	11.8825i	0.437096	−	0.548101i
$471$		0			0
$472$	−1.05781	+	0.509416i	−0.0486898	+	0.0234478i
$473$	1.66445	−	0.801556i	0.0765314	−	0.0368556i
$474$		0			0
$475$	10.1997	+	4.91190i	0.467993	+	0.225374i
$476$	12.8340			0.588246
$477$		0			0
$478$	−17.6816	+	22.1720i	−0.808737	+	1.01412i
$479$	8.71517	−	10.9285i	0.398206	−	0.499335i	−0.541793	−	0.840512i	$-0.682254\pi$
$479$	8.71517	−	10.9285i	0.398206	−	0.499335i	0.939999	+	0.341177i	$0.110826\pi$
$480$		0			0
$481$	1.85024			0.0843637
$482$	−24.4154	−	11.7578i	−1.11209	−	0.535555i
$483$		0			0
$484$	−4.75695	+	2.29083i	−0.216225	+	0.104129i
$485$	−11.0340	+	5.31367i	−0.501026	+	0.241282i
$486$		0			0
$487$	−0.910473	+	1.14170i	−0.0412575	+	0.0517352i	−0.802032	−	0.597281i	$-0.796248\pi$
$487$	−0.910473	+	1.14170i	−0.0412575	+	0.0517352i	0.760775	+	0.649016i	$0.224819\pi$
$488$	10.4571	+	13.1128i	0.473371	+	0.593589i
$489$		0			0
$490$	5.47123	+	23.9710i	0.247165	+	1.08290i
$491$	7.57677	+	9.50097i	0.341935	+	0.428773i	0.922831	−	0.385205i	$-0.125869\pi$
$491$	7.57677	+	9.50097i	0.341935	+	0.428773i	−0.580896	+	0.813978i	$0.697298\pi$
$492$		0			0
$493$	−25.5564	+	16.1885i	−1.15100	+	0.729091i
$494$	−41.0027			−1.84480
$495$		0			0
$496$	2.25225	+	9.86774i	0.101129	+	0.443075i
$497$	−14.8575	+	65.0951i	−0.666451	+	2.91991i
$498$		0			0
$499$	−22.4256	+	28.1208i	−1.00391	+	1.25886i	−0.0381883	+	0.999271i	$0.512159\pi$
$499$	−22.4256	+	28.1208i	−1.00391	+	1.25886i	−0.965719	+	0.259589i	$0.916413\pi$
$500$	1.44626	+	6.33648i	0.0646787	+	0.283376i
$501$		0			0
$502$	−6.50108	+	3.13075i	−0.290157	+	0.139732i
$503$	−3.19420	+	13.9947i	−0.142422	+	0.623993i	0.852446	+	0.522815i	$0.175118\pi$
$503$	−3.19420	+	13.9947i	−0.142422	+	0.623993i	−0.994868	+	0.101178i	$0.967739\pi$
$504$		0			0
$505$	8.49892			0.378197
$506$	−2.35775	−	1.13543i	−0.104815	−	0.0504762i
$507$		0			0
$508$	1.48727	−	1.86498i	0.0659871	−	0.0827452i
$509$	−27.9345	−	13.4525i	−1.23817	−	0.596273i	−0.303857	−	0.952718i	$-0.598275\pi$
$509$	−27.9345	−	13.4525i	−1.23817	−	0.596273i	−0.934316	+	0.356445i	$0.883989\pi$
$510$		0			0
$511$	9.79873	+	4.71882i	0.433470	+	0.208748i
$512$	5.34023	−	23.3971i	0.236007	−	1.03401i
$513$		0			0
$514$	−16.4412	+	7.91765i	−0.725189	+	0.349232i
$515$	1.39863	+	6.12779i	0.0616309	+	0.270023i
$516$		0			0
$517$	4.59682	+	5.76423i	0.202168	+	0.253511i
$518$	0.403629	−	1.76841i	0.0177344	−	0.0776996i
$519$		0			0
$520$	−18.1716	−	22.7865i	−0.796879	−	0.999254i
$521$	14.9084			0.653150			0.326575	−	0.945171i	$-0.394105\pi$
$521$	14.9084			0.653150			0.326575	+	0.945171i	$0.394105\pi$
$522$		0			0
$523$	−12.9505			−0.566284			−0.283142	−	0.959078i	$-0.591377\pi$
$523$	−12.9505			−0.566284			−0.283142	+	0.959078i	$0.591377\pi$
$524$	0.00331693	+	0.00415930i	0.000144901	+	0.000181700i
$525$		0			0
$526$	−5.04477	+	22.1026i	−0.219962	+	0.963718i
$527$	−13.3963	−	16.7984i	−0.583552	−	0.731751i
$528$		0			0
$529$	4.18618	+	18.3409i	0.182008	+	0.797429i
$530$	15.3385	−	7.38662i	0.666260	−	0.320854i
$531$		0			0
$532$	3.25951	−	14.2808i	0.141318	−	0.619153i
$533$	17.2385	+	8.30162i	0.746682	+	0.359583i
$534$		0			0
$535$	7.97515	+	3.84063i	0.344796	+	0.166045i
$536$	−14.9434	+	18.7385i	−0.645457	+	0.809378i
$537$		0			0
$538$	−25.2262	−	12.1483i	−1.08758	−	0.523750i
$539$	−11.9274			−0.513750
$540$		0			0
$541$	−2.41951	+	10.6006i	−0.104023	+	0.455754i	0.895911	+	0.444234i	$0.146524\pi$
$541$	−2.41951	+	10.6006i	−0.104023	+	0.455754i	−0.999934	+	0.0115201i	$0.996333\pi$
$542$	−23.2856	+	11.2137i	−1.00020	+	0.481671i
$543$		0			0
$544$	3.66557	+	16.0599i	0.157160	+	0.688562i
$545$	16.6903	−	20.9289i	0.714932	−	0.896497i
$546$		0			0
$547$	5.14692	−	22.5501i	0.220066	−	0.964174i	−0.737361	−	0.675499i	$-0.763928\pi$
$547$	5.14692	−	22.5501i	0.220066	−	0.964174i	0.957427	−	0.288675i	$-0.0932147\pi$
$548$	−1.45171	−	6.36038i	−0.0620142	−	0.271702i
$549$		0			0
$550$	2.25794			0.0962790
$551$	11.5228	+	32.5489i	0.490887	+	1.38663i
$552$		0			0
$553$	27.3808	+	34.3345i	1.16435	+	1.46005i
$554$	2.24198	+	9.82275i	0.0952526	+	0.417329i
$555$		0			0
$556$	−1.64711	−	2.06541i	−0.0698529	−	0.0875928i
$557$	26.8909	−	33.7201i	1.13940	−	1.42877i	0.252029	−	0.967720i	$-0.418902\pi$
$557$	26.8909	−	33.7201i	1.13940	−	1.42877i	0.887375	−	0.461048i	$-0.152526\pi$
$558$		0			0
$559$	8.32325	−	4.00826i	0.352036	−	0.169532i
$560$	−18.3393	+	8.83176i	−0.774979	+	0.373210i
$561$		0			0
$562$	−31.5467	−	15.1921i	−1.33072	−	0.640840i
$563$	−34.1036			−1.43729			−0.718647	−	0.695375i	$-0.755238\pi$
$563$	−34.1036			−1.43729			−0.718647	+	0.695375i	$0.755238\pi$
$564$		0			0
$565$	−7.11219	+	8.91841i	−0.299212	+	0.375200i
$566$	22.6309	−	28.3783i	0.951250	−	1.19283i
$567$		0			0
$568$	−47.8984			−2.00977
$569$	−17.1914	−	8.27893i	−0.720700	−	0.347071i	0.0373190	−	0.999303i	$-0.488118\pi$
$569$	−17.1914	−	8.27893i	−0.720700	−	0.347071i	−0.758019	+	0.652233i	$0.773833\pi$
$570$		0			0
$571$	5.91613	−	2.84906i	0.247582	−	0.119229i	−0.305978	−	0.952039i	$-0.598983\pi$
$571$	5.91613	−	2.84906i	0.247582	−	0.119229i	0.553560	+	0.832809i	$0.313269\pi$
$572$	2.68500	−	1.29303i	0.112266	−	0.0540642i
$573$		0			0
$574$	11.6950	−	14.6651i	0.488141	−	0.612110i
$575$	2.25271	+	2.82480i	0.0939444	+	0.117803i
$576$		0			0
$577$	4.57508	+	20.0447i	0.190463	+	0.834474i	0.976366	+	0.216124i	$0.0693415\pi$
$577$	4.57508	+	20.0447i	0.190463	+	0.834474i	−0.785903	+	0.618350i	$0.787801\pi$
$578$	10.9897	+	13.7807i	0.457112	+	0.573200i
$579$		0			0
$580$	−2.73636	+	4.39036i	−0.113621	+	0.182300i
$581$	−6.50687			−0.269951
$582$		0			0
$583$	1.83770	+	8.05150i	0.0761098	+	0.333459i
$584$	−1.73611	+	7.60637i	−0.0718406	+	0.314754i
$585$		0			0
$586$	−6.60818	+	8.28640i	−0.272981	+	0.342308i
$587$	−2.15654	−	9.44844i	−0.0890101	−	0.389979i	0.910725	−	0.413014i	$-0.135524\pi$
$587$	−2.15654	−	9.44844i	−0.0890101	−	0.389979i	−0.999735	+	0.0230356i	$0.992667\pi$
$588$		0			0
$589$	−22.0945	+	10.6402i	−0.910389	+	0.438420i
$590$	−0.185409	+	0.812330i	−0.00763317	+	0.0334431i
$591$		0			0
$592$	0.927007			0.0380997
$593$	−11.8757	−	5.71902i	−0.487675	−	0.234852i	0.173854	−	0.984771i	$-0.444378\pi$
$593$	−11.8757	−	5.71902i	−0.487675	−	0.234852i	−0.661529	+	0.749919i	$0.730092\pi$
$594$		0			0
$595$	26.9410	−	33.7830i	1.10447	−	1.38497i
$596$	−6.74441	−	3.24794i	−0.276262	−	0.133041i
$597$		0			0
$598$	−11.7902	−	5.67786i	−0.482137	−	0.232185i
$599$	−3.21314	+	14.0777i	−0.131285	+	0.575198i	0.865900	+	0.500218i	$0.166747\pi$
$599$	−3.21314	+	14.0777i	−0.131285	+	0.575198i	−0.997185	+	0.0749808i	$0.976110\pi$
$600$		0			0
$601$	−4.40415	+	2.12093i	−0.179649	+	0.0865143i	−0.521546	−	0.853223i	$-0.674645\pi$
$601$	−4.40415	+	2.12093i	−0.179649	+	0.0865143i	0.341898	+	0.939737i	$0.388930\pi$
$602$	−2.01529	−	8.82955i	−0.0821369	−	0.359865i
$603$		0			0
$604$	−0.977124	−	1.22527i	−0.0397586	−	0.0498557i
$605$	−3.95560	+	17.3306i	−0.160818	+	0.704590i
$606$		0			0
$607$	−7.82778	−	9.81573i	−0.317720	−	0.398408i	0.597168	−	0.802116i	$-0.296293\pi$
$607$	−7.82778	−	9.81573i	−0.317720	−	0.398408i	−0.914888	+	0.403708i	$0.867721\pi$
$608$	18.8014			0.762496
$609$		0			0
$610$	11.9026			0.481923
$611$	22.9869	+	28.8246i	0.929950	+	1.16612i
$612$		0			0
$613$	−0.778292	+	3.40992i	−0.0314349	+	0.137725i	−0.988210	−	0.153102i	$-0.951074\pi$
$613$	−0.778292	+	3.40992i	−0.0314349	+	0.137725i	0.956775	+	0.290828i	$0.0939307\pi$
$614$	−25.6023	−	32.1042i	−1.03322	−	1.29562i
$615$		0			0
$616$	−3.08426	−	13.5130i	−0.124268	−	0.544455i
$617$	−24.5871	+	11.8405i	−0.989838	+	0.476681i	−0.857478	−	0.514521i	$-0.827970\pi$
$617$	−24.5871	+	11.8405i	−0.989838	+	0.476681i	−0.132360	+	0.991202i	$0.542255\pi$
$618$		0			0
$619$	5.68340	−	24.9006i	0.228435	−	1.00084i	−0.722481	−	0.691391i	$-0.756998\pi$
$619$	5.68340	−	24.9006i	0.228435	−	1.00084i	0.950916	−	0.309449i	$-0.100145\pi$
$620$	−3.31036	−	1.59419i	−0.132947	−	0.0640240i
$621$		0			0
$622$	8.86372	+	4.26854i	0.355403	+	0.171153i
$623$	47.8508	−	60.0030i	1.91710	−	2.40397i
$624$		0			0
$625$	11.7616	+	5.66409i	0.470464	+	0.226564i
$626$	3.05995			0.122300
$627$		0			0
$628$	1.92461	−	8.43225i	0.0768002	−	0.336484i
$629$	−1.77298	+	0.853821i	−0.0706933	+	0.0340441i
$630$		0			0
$631$	−4.62745	−	20.2742i	−0.184216	−	0.807102i	−0.979594	−	0.200988i	$-0.935585\pi$
$631$	−4.62745	−	20.2742i	−0.184216	−	0.807102i	0.795378	−	0.606114i	$-0.207272\pi$
$632$	−19.6423	+	24.6306i	−0.781328	+	0.979754i
$633$		0			0
$634$	4.48252	−	19.6392i	0.178024	−	0.779973i
$635$	−1.78712	−	7.82990i	−0.0709198	−	0.310720i
$636$		0			0
$637$	−59.6442			−2.36319
$638$	4.88737	+	4.85185i	0.193493	+	0.192086i
$639$		0			0
$640$	−5.42895	−	6.80769i	−0.214598	−	0.269097i
$641$	−3.14628	−	13.7848i	−0.124271	−	0.544466i	−0.998284	−	0.0585631i	$-0.981348\pi$
$641$	−3.14628	−	13.7848i	−0.124271	−	0.544466i	0.874013	−	0.485903i	$-0.161509\pi$
$642$		0			0
$643$	22.1303	+	27.7505i	0.872734	+	1.09437i	0.994800	+	0.101852i	$0.0324768\pi$
$643$	22.1303	+	27.7505i	0.872734	+	1.09437i	−0.122066	+	0.992522i	$0.538952\pi$
$644$	2.91481	−	3.65505i	0.114859	−	0.144029i
$645$		0			0
$646$	39.2905	−	18.9213i	1.54586	−	0.744448i
$647$	−18.0758	+	8.70484i	−0.710633	+	0.342223i	−0.754034	−	0.656835i	$-0.771895\pi$
$647$	−18.0758	+	8.70484i	−0.710633	+	0.342223i	0.0434016	+	0.999058i	$0.486181\pi$
$648$		0			0
$649$	−0.364168	−	0.175374i	−0.0142948	−	0.00688404i
$650$	11.2911			0.442872
$651$		0			0
$652$	−4.52054	+	5.66858i	−0.177038	+	0.221999i
$653$	−8.32587	+	10.4403i	−0.325816	+	0.408561i	−0.917580	−	0.397550i	$-0.869860\pi$
$653$	−8.32587	+	10.4403i	−0.325816	+	0.408561i	0.591764	+	0.806111i	$0.298432\pi$
$654$		0			0
$655$	0.0179114			0.000699856
$656$	8.63682	+	4.15927i	0.337211	+	0.162392i
$657$		0			0
$658$	32.5644	−	15.6822i	1.26949	−	0.611356i
$659$	10.2522	−	4.93720i	0.399369	−	0.192326i	−0.223408	−	0.974725i	$-0.571718\pi$
$659$	10.2522	−	4.93720i	0.399369	−	0.192326i	0.622778	+	0.782399i	$0.286004\pi$
$660$		0			0
$661$	−23.0877	+	28.9510i	−0.898007	+	1.12606i	0.0934495	+	0.995624i	$0.470211\pi$
$661$	−23.0877	+	28.9510i	−0.898007	+	1.12606i	−0.991456	+	0.130441i	$0.958361\pi$
$662$	9.75940	+	12.2379i	0.379310	+	0.475640i
$663$		0			0
$664$	−1.03870	−	4.55082i	−0.0403092	−	0.176606i
$665$	−30.7491	−	38.5582i	−1.19240	−	1.49522i
$666$		0			0
$667$	−1.19388	+	10.9550i	−0.0462271	+	0.424178i
$668$	−8.73974			−0.338151
$669$		0			0
$670$	3.78488	+	16.5826i	0.146223	+	0.640643i
$671$	−1.28483	+	5.62921i	−0.0496003	+	0.217313i
$672$		0			0
$673$	23.2210	−	29.1182i	0.895103	−	1.12242i	−0.0967842	−	0.995305i	$-0.530856\pi$
$673$	23.2210	−	29.1182i	0.895103	−	1.12242i	0.991888	−	0.127119i	$-0.0405729\pi$
$674$	1.49866	+	6.56604i	0.0577261	+	0.252915i
$675$		0			0
$676$	7.17021	−	3.45299i	0.275777	−	0.132807i
$677$	9.99898	−	43.8084i	0.384292	−	1.68369i	−0.299564	−	0.954076i	$-0.596841\pi$
$677$	9.99898	−	43.8084i	0.384292	−	1.68369i	0.683856	−	0.729617i	$-0.260302\pi$
$678$		0			0
$679$	−29.1245			−1.11770
$680$	27.9280	+	13.4494i	1.07099	+	0.515761i
$681$		0			0
$682$	−3.04958	+	3.82406i	−0.116775	+	0.146431i
$683$	20.3639	+	9.80672i	0.779201	+	0.375244i	0.780821	−	0.624755i	$-0.214801\pi$
$683$	20.3639	+	9.80672i	0.779201	+	0.375244i	−0.00161933	+	0.999999i	$0.500515\pi$
$684$		0			0
$685$	−19.7898	−	9.53029i	−0.756131	−	0.364134i
$686$	−4.94560	+	21.6681i	−0.188824	+	0.827291i
$687$		0			0
$688$	4.17011	−	2.00822i	0.158984	−	0.0765626i
$689$	9.18962	+	40.2623i	0.350097	+	1.53387i
$690$		0			0
$691$	−24.2367	−	30.3919i	−0.922009	−	1.15616i	−0.987391	−	0.158302i	$-0.949398\pi$
$691$	−24.2367	−	30.3919i	−0.922009	−	1.15616i	0.0653818	−	0.997860i	$-0.479173\pi$
$692$	0.530569	−	2.32458i	0.0201692	−	0.0883671i
$693$		0			0
$694$	6.63294	+	8.31744i	0.251783	+	0.315726i
$695$	−8.89436			−0.337382
$696$		0			0
$697$	−20.3495			−0.770794
$698$	11.4697	+	14.3826i	0.434135	+	0.544388i
$699$		0			0
$700$	−0.897584	+	3.93257i	−0.0339255	+	0.148637i
$701$	24.5921	+	30.8375i	0.928831	+	1.16472i	0.986066	+	0.166357i	$0.0532004\pi$
$701$	24.5921	+	30.8375i	0.928831	+	1.16472i	−0.0572342	+	0.998361i	$0.518228\pi$
$702$		0			0
$703$	0.499785	+	2.18970i	0.0188498	+	0.0825862i
$704$	8.41541	−	4.05265i	0.317168	−	0.152740i
$705$		0			0
$706$	−3.33172	+	14.5972i	−0.125391	+	0.549373i
$707$	18.2100	+	8.76949i	0.684859	+	0.329811i
$708$		0			0
$709$	3.67038	+	1.76756i	0.137844	+	0.0663823i	0.501534	−	0.865138i	$-0.332769\pi$
$709$	3.67038	+	1.76756i	0.137844	+	0.0663823i	−0.363690	+	0.931520i	$0.618483\pi$
$710$	−21.1939	+	26.5763i	−0.795393	+	0.997391i
$711$		0			0
$712$	49.6038	+	23.8879i	1.85898	+	0.895238i
$713$	−7.82661			−0.293109
$714$		0			0
$715$	2.23269	−	9.78204i	0.0834978	−	0.365828i
$716$	−1.63660	+	0.788144i	−0.0611625	+	0.0294543i
$717$		0			0
$718$	−4.31497	−	18.9051i	−0.161033	−	0.705533i
$719$	11.4911	−	14.4094i	0.428546	−	0.537380i	−0.519938	−	0.854204i	$-0.674045\pi$
$719$	11.4911	−	14.4094i	0.428546	−	0.537380i	0.948484	+	0.316824i	$0.102616\pi$
$720$		0			0
$721$	−3.32613	+	14.5727i	−0.123872	+	0.542717i
$722$	−5.95680	−	26.0985i	−0.221689	−	0.971284i
$723$		0			0
$724$	−3.53686			−0.131446
$725$	−3.17308	−	8.96313i	−0.117845	−	0.332882i
$726$		0			0
$727$	10.9828	+	13.7720i	0.407330	+	0.510775i	0.942608	−	0.333900i	$-0.108365\pi$
$727$	10.9828	+	13.7720i	0.407330	+	0.510775i	−0.535279	+	0.844675i	$0.679793\pi$
$728$	−15.4231	−	67.5732i	−0.571619	−	2.50443i
$729$		0			0
$730$	3.45219	+	4.32891i	0.127771	+	0.160220i
$731$	−6.12601	+	7.68177i	−0.226579	+	0.284121i
$732$		0			0
$733$	7.41249	−	3.56967i	0.273786	−	0.131849i	−0.291953	−	0.956433i	$-0.594305\pi$
$733$	7.41249	−	3.56967i	0.273786	−	0.131849i	0.565739	+	0.824584i	$0.308591\pi$
$734$	24.2649	−	11.6854i	0.895634	−	0.431315i
$735$		0			0
$736$	5.40627	+	2.60352i	0.199278	+	0.0959671i
$737$	−8.25113			−0.303934
$738$		0			0
$739$	22.3350	−	28.0072i	0.821607	−	1.03026i	−0.177329	−	0.984152i	$-0.556746\pi$
$739$	22.3350	−	28.0072i	0.821607	−	1.03026i	0.998936	−	0.0461112i	$-0.0146829\pi$
$740$	−0.209813	+	0.263097i	−0.00771288	+	0.00967165i
$741$		0			0
$742$	40.4864			1.48630
$743$	8.37415	+	4.03278i	0.307218	+	0.147948i	0.581140	−	0.813803i	$-0.302607\pi$
$743$	8.37415	+	4.03278i	0.307218	+	0.147948i	−0.273922	+	0.961752i	$0.588321\pi$
$744$		0			0
$745$	−22.7073	+	10.9353i	−0.831933	+	0.400638i
$746$	−7.55969	+	3.64056i	−0.276780	+	0.133290i
$747$		0			0
$748$	−1.97619	+	2.47807i	−0.0722568	+	0.0906071i
$749$	13.1249	+	16.4581i	0.479573	+	0.601366i
$750$		0			0
$751$	9.98479	+	43.7462i	0.364350	+	1.59632i	0.742017	+	0.670381i	$0.233869\pi$
$751$	9.98479	+	43.7462i	0.364350	+	1.59632i	−0.377667	+	0.925941i	$0.623274\pi$
$752$	11.5169	+	14.4417i	0.419977	+	0.526635i
$753$		0			0
$754$	24.4398	+	24.2622i	0.890045	+	0.883576i
$755$	−5.27646			−0.192030
$756$		0			0
$757$	−4.81041	−	21.0758i	−0.174837	−	0.766012i	−0.983962	−	0.178376i	$-0.942916\pi$
$757$	−4.81041	−	21.0758i	−0.174837	−	0.766012i	0.809125	−	0.587636i	$-0.199941\pi$
$758$	2.09830	−	9.19323i	0.0762135	−	0.333913i
$759$		0			0
$760$	22.0586	−	27.6606i	0.800150	−	1.00336i
$761$	−8.76193	−	38.3885i	−0.317620	−	1.39158i	−0.841714	−	0.539923i	$-0.818453\pi$
$761$	−8.76193	−	38.3885i	−0.317620	−	1.39158i	0.524094	−	0.851660i	$-0.324404\pi$
$762$		0			0
$763$	57.3563	−	27.6213i	2.07644	−	0.999959i
$764$	−2.09430	+	9.17572i	−0.0757691	+	0.331966i
$765$		0			0
$766$	−30.8279			−1.11386
$767$	−1.82106	−	0.876976i	−0.0657547	−	0.0316658i
$768$		0			0
$769$	2.67820	−	3.35836i	0.0965784	−	0.121105i	−0.731194	−	0.682170i	$-0.761037\pi$
$769$	2.67820	−	3.35836i	0.0965784	−	0.121105i	0.827772	+	0.561064i	$0.189608\pi$
$770$	−8.86237	−	4.26789i	−0.319378	−	0.153804i
$771$		0			0
$772$	−6.44826	−	3.10532i	−0.232078	−	0.111763i
$773$	6.20838	−	27.2007i	0.223300	−	0.978341i	−0.731675	−	0.681654i	$-0.761261\pi$
$773$	6.20838	−	27.2007i	0.223300	−	0.978341i	0.954975	−	0.296687i	$-0.0958819\pi$
$774$		0			0
$775$	6.08426	−	2.93002i	0.218553	−	0.105250i
$776$	−4.64917	−	20.3693i	−0.166895	−	0.731216i
$777$		0			0
$778$	−8.29137	−	10.3970i	−0.297260	−	0.372752i
$779$	−5.16826	+	22.6436i	−0.185172	+	0.811292i
$780$		0			0
$781$	−10.2812	−	12.8922i	−0.367890	−	0.461319i
$782$	13.9180			0.497706
$783$		0			0
$784$	−29.8829			−1.06725
$785$	−18.1561	−	22.7670i	−0.648019	−	0.812591i
$786$		0			0
$787$	1.31441	−	5.75879i	0.0468536	−	0.205279i	−0.946083	−	0.323924i	$-0.894998\pi$
$787$	1.31441	−	5.75879i	0.0468536	−	0.205279i	0.992937	+	0.118645i	$0.0378550\pi$
$788$	−2.73255	−	3.42650i	−0.0973429	−	0.122064i
$789$		0			0
$790$	4.97501	+	21.7969i	0.177003	+	0.775500i
$791$	−24.4411	+	11.7702i	−0.869027	+	0.418501i
$792$		0			0
$793$	−6.42493	+	28.1494i	−0.228156	+	0.999616i
$794$	−5.56369	−	2.67933i	−0.197448	−	0.0950860i
$795$		0			0
$796$	11.7887	+	5.67715i	0.417840	+	0.201221i
$797$	4.73789	−	5.94113i	0.167825	−	0.210446i	−0.690806	−	0.723040i	$-0.742744\pi$
$797$	4.73789	−	5.94113i	0.167825	−	0.210446i	0.858631	+	0.512595i	$0.171316\pi$
$798$		0			0
$799$	−35.3286	−	17.0133i	−1.24983	−	0.601888i
$800$	−5.17741			−0.183049
$801$		0			0
$802$	−5.26484	+	23.0668i	−0.185908	+	0.814516i
$803$	−2.41996	+	1.16539i	−0.0853984	+	0.0411257i
$804$		0			0
$805$	−3.50246	−	15.3453i	−0.123446	−	0.540850i
$806$	−15.2498	+	19.1226i	−0.537150	+	0.673564i
$807$		0			0
$808$	−3.22639	+	14.1357i	−0.113504	+	0.497294i
$809$	−2.19189	−	9.60330i	−0.0770628	−	0.337634i	0.921669	−	0.387977i	$-0.126826\pi$
$809$	−2.19189	−	9.60330i	−0.0770628	−	0.337634i	−0.998732	+	0.0503425i	$0.983969\pi$
$810$		0			0
$811$	46.3250			1.62669			0.813346	−	0.581780i	$-0.197644\pi$
$811$	46.3250			1.62669			0.813346	+	0.581780i	$0.197644\pi$
$812$	−10.3931	+	6.58343i	−0.364727	+	0.231033i
$813$		0			0
$814$	0.279305	+	0.350237i	0.00978963	+	0.0122758i
$815$	5.43193	+	23.7988i	0.190272	+	0.833637i
$816$		0			0
$817$	6.99192	+	8.76759i	0.244616	+	0.306739i
$818$	−13.5306	+	16.9668i	−0.473087	+	0.593232i
$819$		0			0
$820$	−3.13526	+	1.50986i	−0.109488	+	0.0527267i
$821$	16.2673	−	7.83393i	0.567733	−	0.273406i	−0.127919	−	0.991785i	$-0.540830\pi$
$821$	16.2673	−	7.83393i	0.567733	−	0.273406i	0.695652	+	0.718379i	$0.255115\pi$
$822$		0			0
$823$	30.3038	+	14.5936i	1.05633	+	0.508700i	0.879676	−	0.475574i	$-0.157760\pi$
$823$	30.3038	+	14.5936i	1.05633	+	0.508700i	0.176650	+	0.984274i	$0.443474\pi$
$824$	−10.7229			−0.373551
$825$		0			0
$826$	−1.23545	+	1.54921i	−0.0429870	+	0.0539039i
$827$	−25.6465	+	32.1597i	−0.891817	+	1.11830i	0.100544	+	0.994933i	$0.467942\pi$
$827$	−25.6465	+	32.1597i	−0.891817	+	1.11830i	−0.992361	+	0.123370i	$0.960630\pi$
$828$		0			0
$829$	7.95542			0.276303			0.138152	−	0.990411i	$-0.455884\pi$
$829$	7.95542			0.276303			0.138152	+	0.990411i	$0.455884\pi$
$830$	−2.98461	−	1.43731i	−0.103597	−	0.0498899i
$831$		0			0
$832$	42.0821	−	20.2657i	1.45894	−	0.702586i
$833$	57.1536	−	27.5237i	1.98025	−	0.953640i
$834$		0			0
$835$	−18.3464	+	23.0056i	−0.634903	+	0.796143i
$836$	2.25553	+	2.82834i	0.0780091	+	0.0978203i
$837$		0			0
$838$	1.00711	+	4.41244i	0.0347901	+	0.152425i
$839$	7.05968	+	8.85256i	0.243727	+	0.305624i	0.888616	−	0.458652i	$-0.151668\pi$
$839$	7.05968	+	8.85256i	0.243727	+	0.305624i	−0.644889	+	0.764277i	$0.723096\pi$
$840$		0			0
$841$	12.3917	−	26.2192i	0.427299	−	0.904110i
$842$	10.0342			0.345801
$843$		0			0
$844$	−0.262855	−	1.15164i	−0.00904784	−	0.0396412i
$845$	5.96232	−	26.1226i	0.205110	−	0.898646i
$846$		0			0
$847$	−26.3577	+	33.0516i	−0.905663	+	1.13567i
$848$	4.60418	+	20.1722i	0.158108	+	0.692717i
$849$		0			0
$850$	−10.8196	+	5.21043i	−0.371108	+	0.178716i
$851$	−0.159508	+	0.698850i	−0.00546786	+	0.0239563i
$852$		0			0
$853$	14.5146			0.496971			0.248486	−	0.968636i	$-0.420067\pi$
$853$	14.5146			0.496971			0.248486	+	0.968636i	$0.420067\pi$
$854$	25.5029	+	12.2816i	0.872692	+	0.420266i
$855$		0			0
$856$	−9.41545	+	11.8066i	−0.321813	+	0.403541i
$857$	−9.65562	−	4.64990i	−0.329830	−	0.158838i	0.261638	−	0.965166i	$-0.415737\pi$
$857$	−9.65562	−	4.64990i	−0.329830	−	0.158838i	−0.591468	+	0.806328i	$0.701451\pi$
$858$		0			0
$859$	−14.1577	−	6.81799i	−0.483055	−	0.232627i	0.176475	−	0.984305i	$-0.443530\pi$
$859$	−14.1577	−	6.81799i	−0.483055	−	0.232627i	−0.659530	+	0.751678i	$0.729245\pi$
$860$	−0.373877	+	1.63806i	−0.0127491	+	0.0558575i
$861$		0			0
$862$	20.8667	−	10.0489i	0.710724	−	0.342267i
$863$	−3.20755	−	14.0532i	−0.109186	−	0.478377i	−0.999725	−	0.0234684i	$-0.992529\pi$
$863$	−3.20755	−	14.0532i	−0.109186	−	0.478377i	0.890538	−	0.454908i	$-0.150328\pi$
$864$		0			0
$865$	−5.00522	−	6.27635i	−0.170183	−	0.213402i
$866$	4.35122	−	19.0639i	0.147860	−	0.647818i
$867$		0			0
$868$	−5.44794	−	6.83150i	−0.184915	−	0.231876i
$869$	−10.8456			−0.367913
$870$		0			0
$871$	−41.2606			−1.39806
$872$	28.4738	+	35.7050i	0.964245	+	1.20912i
$873$		0			0
$874$	3.53481	−	15.4870i	0.119567	−	0.523856i
$875$	32.4463	+	40.6863i	1.09688	+	1.37545i
$876$		0			0
$877$	−3.02248	−	13.2424i	−0.102062	−	0.447163i	−0.999976	−	0.00699099i	$-0.997775\pi$
$877$	−3.02248	−	13.2424i	−0.102062	−	0.447163i	0.897914	−	0.440172i	$-0.145082\pi$
$878$	−3.23794	+	1.55931i	−0.109275	+	0.0526242i
$879$		0			0
$880$	1.11862	−	4.90100i	0.0377087	−	0.165213i
$881$	19.2804	+	9.28496i	0.649574	+	0.312818i	0.729498	−	0.683983i	$-0.239754\pi$
$881$	19.2804	+	9.28496i	0.649574	+	0.312818i	−0.0799246	+	0.996801i	$0.525468\pi$
$882$		0			0
$883$	10.0207	+	4.82569i	0.337222	+	0.162397i	0.594829	−	0.803852i	$-0.297220\pi$
$883$	10.0207	+	4.82569i	0.337222	+	0.162397i	−0.257607	+	0.966250i	$0.582934\pi$
$884$	−9.88216	+	12.3918i	−0.332373	+	0.416782i
$885$		0			0
$886$	11.4444	+	5.51135i	0.384483	+	0.185157i
$887$	1.53319			0.0514795			0.0257397	−	0.999669i	$-0.491806\pi$
$887$	1.53319			0.0514795			0.0257397	+	0.999669i	$0.491806\pi$
$888$		0			0
$889$	4.25003	−	18.6206i	0.142541	−	0.624514i
$890$	35.2027	−	16.9527i	1.18000	−	0.568256i
$891$		0			0
$892$	0.321447	+	1.40835i	0.0107629	+	0.0471551i
$893$	−27.9039	+	34.9903i	−0.933767	+	1.17091i
$894$		0			0
$895$	−1.36090	+	5.96248i	−0.0454898	+	0.199304i
$896$	−4.60781	−	20.1881i	−0.153936	−	0.674438i
$897$		0			0
$898$	5.33110			0.177901
$899$	19.4655	+	6.73169i	0.649212	+	0.224514i
$900$		0			0
$901$	−27.3855	−	34.3404i	−0.912344	−	1.14404i
$902$	1.03082	+	4.51630i	0.0343224	+	0.150376i
$903$		0			0
$904$	−12.1335	−	15.2149i	−0.403554	−	0.506041i
$905$	−7.42454	+	9.31008i	−0.246800	+	0.309478i
$906$		0			0
$907$	−6.92799	+	3.33634i	−0.230040	+	0.110781i	−0.545354	−	0.838206i	$-0.683605\pi$
$907$	−6.92799	+	3.33634i	−0.230040	+	0.110781i	0.315314	+	0.948988i	$0.397890\pi$
$908$	−6.94103	+	3.34262i	−0.230346	+	0.110929i
$909$		0			0
$910$	−44.3172	−	21.3420i	−1.46910	−	0.707481i
$911$	29.5727			0.979788			0.489894	−	0.871782i	$-0.337036\pi$
$911$	29.5727			0.979788			0.489894	+	0.871782i	$0.337036\pi$
$912$		0			0
$913$	1.00194	−	1.25639i	0.0331592	−	0.0415803i
$914$	8.56664	−	10.7422i	0.283359	−	0.355321i
$915$		0			0
$916$	−13.7529			−0.454408
$917$	0.0383775	+	0.0184816i	0.00126734	+	0.000610317i
$918$		0			0
$919$	30.8397	−	14.8516i	1.01731	−	0.489910i	0.150532	−	0.988605i	$-0.451901\pi$
$919$	30.8397	−	14.8516i	1.01731	−	0.489910i	0.866778	+	0.498695i	$0.166187\pi$
$920$	10.1732	−	4.89915i	0.335400	−	0.161520i
$921$		0			0
$922$	−14.8779	+	18.6562i	−0.489976	+	0.614411i
$923$	−51.4121	−	64.4687i	−1.69225	−	2.12201i
$924$		0			0
$925$	−0.137628	−	0.602987i	−0.00452518	−	0.0198261i
$926$	0.568656	+	0.713072i	0.0186872	+	0.0234330i
$927$		0			0
$928$	−11.2066	−	11.1252i	−0.367876	−	0.365202i
$929$	−48.1477			−1.57967			−0.789837	−	0.613317i	$-0.789835\pi$
$929$	−48.1477			−1.57967			−0.789837	+	0.613317i	$0.789835\pi$
$930$		0			0
$931$	−16.1110	−	70.5870i	−0.528018	−	2.31340i
$932$	2.68675	−	11.7714i	0.0880075	−	0.385586i
$933$		0			0
$934$	−7.88466	+	9.88705i	−0.257994	+	0.323514i
$935$	2.37462	+	10.4039i	0.0776582	+	0.340243i
$936$		0			0
$937$	12.3770	−	5.96047i	0.404340	−	0.194720i	−0.220649	−	0.975353i	$-0.570818\pi$
$937$	12.3770	−	5.96047i	0.404340	−	0.194720i	0.624989	+	0.780633i	$0.285103\pi$
$938$	−9.00097	+	39.4358i	−0.293892	+	1.28763i
$939$		0			0
$940$	−6.70542			−0.218707
$941$	−33.5624	−	16.1628i	−1.09410	−	0.526892i	−0.202303	−	0.979323i	$-0.564843\pi$
$941$	−33.5624	−	16.1628i	−1.09410	−	0.526892i	−0.891800	+	0.452431i	$0.850557\pi$
$942$		0			0
$943$	−4.62170	+	5.79543i	−0.150503	+	0.188725i
$944$	−0.912387	−	0.439382i	−0.0296957	−	0.0143007i
$945$		0			0
$946$	2.01518	+	0.970459i	0.0655191	+	0.0315523i
$947$	3.66686	−	16.0656i	0.119157	−	0.522061i	−0.879755	−	0.475427i	$-0.842294\pi$
$947$	3.66686	−	16.0656i	0.119157	−	0.522061i	0.998912	−	0.0466336i	$-0.0148493\pi$
$948$		0			0
$949$	−12.1012	+	5.82765i	−0.392823	+	0.189174i
$950$	3.04993	+	13.3626i	0.0989529	+	0.433541i
$951$		0			0
$952$	45.9617	+	57.6342i	1.48963	+	1.86794i
$953$	−6.18414	+	27.0945i	−0.200324	+	0.877676i	0.770416	+	0.637542i	$0.220049\pi$
$953$	−6.18414	+	27.0945i	−0.200324	+	0.877676i	−0.970740	+	0.240134i	$0.922808\pi$
$954$		0			0
$955$	19.7569	+	24.7744i	0.639319	+	0.801681i
$956$	12.5118			0.404662
$957$		0			0
$958$	16.9235			0.546773
$959$	−32.5686	−	40.8397i	−1.05170	−	1.31878i
$960$		0			0
$961$	3.64303	−	15.9612i	0.117517	−	0.514876i
$962$	1.39669	+	1.75140i	0.0450312	+	0.0564673i
$963$		0			0
$964$	2.66045	+	11.6562i	0.0856873	+	0.375420i
$965$	−21.7102	+	10.4551i	−0.698878	+	0.336562i
$966$		0			0
$967$	11.5683	−	50.6842i	0.372012	−	1.62989i	−0.349108	−	0.937083i	$-0.613515\pi$
$967$	11.5683	−	50.6842i	0.372012	−	1.62989i	0.721120	−	0.692810i	$-0.243628\pi$
$968$	−27.3233	−	13.1582i	−0.878206	−	0.422922i
$969$		0			0
$970$	−13.3590	−	6.43336i	−0.428932	−	0.206563i
$971$	−16.5938	+	20.8080i	−0.532522	+	0.667761i	−0.973215	−	0.229896i	$-0.926161\pi$
$971$	−16.5938	+	20.8080i	−0.532522	+	0.667761i	0.440693	+	0.897658i	$0.354733\pi$
$972$		0			0
$973$	−19.0573	−	9.17752i	−0.610950	−	0.294218i
$974$	−1.76799			−0.0566502
$975$		0			0
$976$	−3.21901	+	14.1034i	−0.103038	+	0.451440i
$977$	54.8653	−	26.4217i	1.75530	−	0.845306i	0.779568	−	0.626317i	$-0.215438\pi$
$977$	54.8653	−	26.4217i	1.75530	−	0.845306i	0.975727	−	0.218989i	$-0.0702758\pi$
$978$		0			0
$979$	4.21763	+	18.4787i	0.134796	+	0.590580i
$980$	6.76352	−	8.48118i	0.216053	−	0.270921i
$981$		0			0
$982$	−3.27392	+	14.3440i	−0.104475	+	0.457735i
$983$	10.4431	+	45.7541i	0.333083	+	1.45933i	0.813127	+	0.582086i	$0.197763\pi$
$983$	10.4431	+	45.7541i	0.333083	+	1.45933i	−0.480044	+	0.877244i	$0.659379\pi$
$984$		0			0
$985$	−14.7557			−0.470156
$986$	−34.6154	−	11.9709i	−1.10238	−	0.381231i
$987$		0			0
$988$	11.2790	+	14.1434i	0.358833	+	0.449962i
$989$	0.796411	+	3.48930i	0.0253244	+	0.110953i
$990$		0			0
$991$	31.6674	+	39.7096i	1.00595	+	1.26142i	0.964998	+	0.262256i	$0.0844665\pi$
$991$	31.6674	+	39.7096i	1.00595	+	1.26142i	0.0409484	+	0.999161i	$0.486962\pi$
$992$	6.99262	−	8.76847i	0.222016	−	0.278399i
$993$		0			0
$994$	−72.8331	+	35.0746i	−2.31012	+	1.11250i
$995$	39.6907	−	19.1140i	1.25828	−	0.605956i
$996$		0			0
$997$	41.2723	+	19.8757i	1.30711	+	0.629469i	0.952212	−	0.305438i	$-0.0988029\pi$
$997$	41.2723	+	19.8757i	1.30711	+	0.629469i	0.354893	+	0.934907i	$0.384517\pi$
$998$	−43.5469			−1.37845
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.82.3		18
3.2	odd	2		87.2.g.a.82.1	yes	18
29.9	even	14		7569.2.a.bm.1.2		9
29.20	even	7		7569.2.a.bj.1.8		9
29.23	even	7	inner	261.2.k.c.226.3		18
87.20	odd	14		2523.2.a.r.1.2		9
87.23	odd	14		87.2.g.a.52.1	✓	18
87.38	odd	14		2523.2.a.o.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.52.1	✓	18	87.23	odd	14
87.2.g.a.82.1	yes	18	3.2	odd	2
261.2.k.c.82.3		18	1.1	even	1	trivial
261.2.k.c.226.3		18	29.23	even	7	inner
2523.2.a.o.1.8		9	87.38	odd	14
2523.2.a.r.1.2		9	87.20	odd	14
7569.2.a.bj.1.8		9	29.20	even	7
7569.2.a.bm.1.2		9	29.9	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)

\(f(q)\)	\(=\)	\(q+(0.754870 + 0.946578i) q^{2} +(0.118862 - 0.520769i) q^{4} +(-1.12131 - 1.40607i) q^{5} +(-0.951706 - 4.16970i) q^{7} +(2.76431 - 1.33122i) q^{8} +(0.484517 - 2.12281i) q^{10} +(0.951656 + 0.458293i) q^{11} +(4.75885 + 2.29174i) q^{13} +(3.22853 - 4.04845i) q^{14} +(2.38428 + 1.14821i) q^{16} -5.61769 q^{17} +(-1.42675 + 6.25099i) q^{19} +(-0.865520 + 0.416812i) q^{20} +(0.284567 + 1.24677i) q^{22} +(-1.27587 + 1.59988i) q^{23} +(0.392890 - 1.72136i) q^{25} +(1.42300 + 6.23459i) q^{26} -2.28457 q^{28} +(4.54927 - 2.88169i) q^{29} +(2.38467 + 2.99028i) q^{31} +(-0.652504 - 2.85881i) q^{32} +(-4.24063 - 5.31758i) q^{34} +(-4.79575 + 6.01368i) q^{35} +(0.315606 - 0.151988i) q^{37} +(-6.99406 + 3.36816i) q^{38} +(-4.97144 - 2.39412i) q^{40} +3.62240 q^{41} +(1.09049 - 1.36743i) q^{43} +(0.351781 - 0.441119i) q^{44} -2.47753 q^{46} +(6.28881 + 3.02853i) q^{47} +(-10.1739 + 4.89947i) q^{49} +(1.92598 - 0.927505i) q^{50} +(1.75911 - 2.20586i) q^{52} +(4.87488 + 6.11290i) q^{53} +(-0.422703 - 1.85198i) q^{55} +(-8.18161 - 10.2594i) q^{56} +(6.16185 + 2.13093i) q^{58} -0.382668 q^{59} +(1.21640 + 5.32939i) q^{61} +(-1.03041 + 4.51454i) q^{62} +(5.51347 - 6.91367i) q^{64} +(-2.11377 - 9.26104i) q^{65} +(-7.03806 + 3.38935i) q^{67} +(-0.667730 + 2.92552i) q^{68} -9.31258 q^{70} +(-14.0654 - 6.77356i) q^{71} +(-1.58547 + 1.98811i) q^{73} +(0.382110 + 0.184015i) q^{74} +(3.08574 + 1.48601i) q^{76} +(1.00525 - 4.40428i) q^{77} +(-9.25113 + 4.45511i) q^{79} +(-1.05904 - 4.63996i) q^{80} +(2.73445 + 3.42889i) q^{82} +(0.338541 - 1.48324i) q^{83} +(6.29915 + 7.89888i) q^{85} +2.11755 q^{86} +3.24076 q^{88} +(11.1881 + 14.0295i) q^{89} +(5.02684 - 22.0240i) q^{91} +(0.681518 + 0.854597i) q^{92} +(1.88050 + 8.23899i) q^{94} +(10.3892 - 5.00316i) q^{95} +(1.51530 - 6.63895i) q^{97} +(-12.3177 - 5.93188i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) \) 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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