LMFDB - Embedded newform 261.2.k.c.82.1

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			82.1
Root			$-0.353498 + 1.54877i$ of defining polynomial
Character	$\chi$	$=$	261.82
Dual form			261.2.k.c.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61397 - 2.02385i) q^{2} +(-1.04604 + 4.58301i) q^{4} +(0.716354 + 0.898279i) q^{5} +(-0.615328 - 2.69593i) q^{7} +(6.29911 - 3.03349i) q^{8} +(0.661812 - 2.89959i) q^{10} +(-3.92298 - 1.88921i) q^{11} +(-5.07168 - 2.44239i) q^{13} +(-4.46304 + 5.59648i) q^{14} +(-7.83521 - 3.77324i) q^{16} -2.41516 q^{17} +(-0.416772 + 1.82600i) q^{19} +(-4.86616 + 2.34342i) q^{20} +(2.50809 + 10.9886i) q^{22} +(5.49948 - 6.89613i) q^{23} +(0.818862 - 3.58767i) q^{25} +(3.24249 + 14.2063i) q^{26} +12.9991 q^{28} +(-4.53581 + 2.90283i) q^{29} +(0.972977 + 1.22007i) q^{31} +(1.89780 + 8.31482i) q^{32} +(3.89799 + 4.88793i) q^{34} +(1.98091 - 2.48398i) q^{35} +(-6.99449 + 3.36837i) q^{37} +(4.36821 - 2.10362i) q^{38} +(7.23731 + 3.48530i) q^{40} -3.16072 q^{41} +(-0.912772 + 1.14458i) q^{43} +(12.7618 - 16.0028i) q^{44} -22.8327 q^{46} +(0.321962 + 0.155049i) q^{47} +(-0.582626 + 0.280578i) q^{49} +(-8.58252 + 4.13313i) q^{50} +(16.4987 - 20.6887i) q^{52} +(1.01940 + 1.27828i) q^{53} +(-1.11320 - 4.87727i) q^{55} +(-12.0541 - 15.1154i) q^{56} +(13.1955 + 4.49474i) q^{58} +4.85026 q^{59} +(-0.346042 - 1.51611i) q^{61} +(0.898897 - 3.93832i) q^{62} +(2.92070 - 3.66245i) q^{64} +(-1.43917 - 6.30540i) q^{65} +(8.71192 - 4.19544i) q^{67} +(2.52636 - 11.0687i) q^{68} -8.22432 q^{70} +(-7.37090 - 3.54964i) q^{71} +(7.09446 - 8.89617i) q^{73} +(18.1060 + 8.71937i) q^{74} +(-7.93260 - 3.82014i) q^{76} +(-2.67925 + 11.7386i) q^{77} +(7.32556 - 3.52780i) q^{79} +(-2.22336 - 9.74119i) q^{80} +(5.10130 + 6.39683i) q^{82} +(-0.107218 + 0.469754i) q^{83} +(-1.73011 - 2.16949i) q^{85} +3.78965 q^{86} -30.4421 q^{88} +(1.24461 + 1.56070i) q^{89} +(-3.46377 + 15.1758i) q^{91} +(25.8523 + 32.4178i) q^{92} +(-0.205841 - 0.901847i) q^{94} +(-1.93881 + 0.933683i) q^{95} +(-1.03142 + 4.51895i) q^{97} +(1.50819 + 0.726305i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.61397	−	2.02385i	−1.14125	−	1.43108i	−0.885685	−	0.464287i	$-0.846311\pi$
$2$	−1.61397	−	2.02385i	−1.14125	−	1.43108i	−0.255563	−	0.966792i	$-0.582261\pi$
$3$		0			0
$3$		0			0
$4$	−1.04604	+	4.58301i	−0.523021	+	2.29150i
$5$	0.716354	+	0.898279i	0.320363	+	0.401723i	0.915771	−	0.401701i	$-0.131581\pi$
$5$	0.716354	+	0.898279i	0.320363	+	0.401723i	−0.595408	+	0.803424i	$0.703009\pi$
$6$		0			0
$7$	−0.615328	−	2.69593i	−0.232572	−	1.01897i	−0.947497	−	0.319764i	$-0.896396\pi$
$7$	−0.615328	−	2.69593i	−0.232572	−	1.01897i	0.714925	−	0.699201i	$-0.246461\pi$
$8$	6.29911	−	3.03349i	2.22707	−	1.07250i
$9$		0			0
$10$	0.661812	−	2.89959i	0.209283	−	0.916930i
$11$	−3.92298	−	1.88921i	−1.18282	−	0.569617i	−0.264090	−	0.964498i	$-0.585071\pi$
$11$	−3.92298	−	1.88921i	−1.18282	−	0.569617i	−0.918732	+	0.394881i	$0.870786\pi$
$12$		0			0
$13$	−5.07168	−	2.44239i	−1.40663	−	0.677397i	−0.432135	−	0.901809i	$-0.642240\pi$
$13$	−5.07168	−	2.44239i	−1.40663	−	0.677397i	−0.974494	+	0.224411i	$0.927954\pi$
$14$	−4.46304	+	5.59648i	−1.19280	+	1.49572i
$15$		0			0
$16$	−7.83521	−	3.77324i	−1.95880	−	0.943310i
$17$	−2.41516			−0.585763			−0.292881	−	0.956149i	$-0.594614\pi$
$17$	−2.41516			−0.585763			−0.292881	+	0.956149i	$0.594614\pi$
$18$		0			0
$19$	−0.416772	+	1.82600i	−0.0956141	+	0.418913i	−0.999969	−	0.00786845i	$-0.997495\pi$
$19$	−0.416772	+	1.82600i	−0.0956141	+	0.418913i	0.904355	+	0.426781i	$0.140353\pi$
$20$	−4.86616	+	2.34342i	−1.08811	+	0.524004i
$21$		0			0
$22$	2.50809	+	10.9886i	0.534726	+	2.34279i
$23$	5.49948	−	6.89613i	1.14672	−	1.43794i	0.266210	−	0.963915i	$-0.414229\pi$
$23$	5.49948	−	6.89613i	1.14672	−	1.43794i	0.880510	−	0.474027i	$-0.157200\pi$
$24$		0			0
$25$	0.818862	−	3.58767i	0.163772	−	0.717534i
$26$	3.24249	+	14.2063i	0.635904	+	2.78608i
$27$		0			0
$28$	12.9991			2.45660
$29$	−4.53581	+	2.90283i	−0.842279	+	0.539042i
$29$	−4.53581	+	2.90283i	−0.842279	+	0.539042i
$30$		0			0
$31$	0.972977	+	1.22007i	0.174752	+	0.219132i	0.861492	−	0.507771i	$-0.169530\pi$
$31$	0.972977	+	1.22007i	0.174752	+	0.219132i	−0.686740	+	0.726903i	$0.740959\pi$
$32$	1.89780	+	8.31482i	0.335488	+	1.46987i
$33$		0			0
$34$	3.89799	+	4.88793i	0.668500	+	0.838273i
$35$	1.98091	−	2.48398i	0.334834	−	0.419869i
$36$		0			0
$37$	−6.99449	+	3.36837i	−1.14989	+	0.553756i	−0.909000	−	0.416797i	$-0.863153\pi$
$37$	−6.99449	+	3.36837i	−1.14989	+	0.553756i	−0.240887	+	0.970553i	$0.577438\pi$
$38$	4.36821	−	2.10362i	0.708617	−	0.341252i
$39$		0			0
$40$	7.23731	+	3.48530i	1.14432	+	0.551075i
$41$	−3.16072			−0.493622			−0.246811	−	0.969064i	$-0.579383\pi$
$41$	−3.16072			−0.493622			−0.246811	+	0.969064i	$0.579383\pi$
$42$		0			0
$43$	−0.912772	+	1.14458i	−0.139196	+	0.174547i	−0.846543	−	0.532320i	$-0.821320\pi$
$43$	−0.912772	+	1.14458i	−0.139196	+	0.174547i	0.707347	+	0.706867i	$0.249892\pi$
$44$	12.7618	−	16.0028i	1.92392	−	2.41252i
$45$		0			0
$46$	−22.8327			−3.36650
$47$	0.321962	+	0.155049i	0.0469630	+	0.0226162i	0.457218	−	0.889355i	$-0.348846\pi$
$47$	0.321962	+	0.155049i	0.0469630	+	0.0226162i	−0.410255	+	0.911971i	$0.634560\pi$
$48$		0			0
$49$	−0.582626	+	0.280578i	−0.0832323	+	0.0400826i
$50$	−8.58252	+	4.13313i	−1.21375	+	0.584512i
$51$		0			0
$52$	16.4987	−	20.6887i	2.28796	−	2.86901i
$53$	1.01940	+	1.27828i	0.140025	+	0.175586i	0.846899	−	0.531754i	$-0.178467\pi$
$53$	1.01940	+	1.27828i	0.140025	+	0.175586i	−0.706874	+	0.707339i	$0.749895\pi$
$54$		0			0
$55$	−1.11320	−	4.87727i	−0.150104	−	0.657651i
$56$	−12.0541	−	15.1154i	−1.61080	−	2.01987i
$57$		0			0
$58$	13.1955	+	4.49474i	1.73266	+	0.590188i
$59$	4.85026			0.631450			0.315725	−	0.948851i	$-0.397752\pi$
$59$	4.85026			0.631450			0.315725	+	0.948851i	$0.397752\pi$
$60$		0			0
$61$	−0.346042	−	1.51611i	−0.0443062	−	0.194118i	0.947931	−	0.318474i	$-0.103171\pi$
$61$	−0.346042	−	1.51611i	−0.0443062	−	0.194118i	−0.992238	+	0.124356i	$0.960313\pi$
$62$	0.898897	−	3.93832i	0.114160	−	0.500168i
$63$		0			0
$64$	2.92070	−	3.66245i	0.365088	−	0.457806i
$65$	−1.43917	−	6.30540i	−0.178507	−	0.782088i
$66$		0			0
$67$	8.71192	−	4.19544i	1.06433	−	0.512554i	0.182055	−	0.983288i	$-0.441725\pi$
$67$	8.71192	−	4.19544i	1.06433	−	0.512554i	0.882275	+	0.470734i	$0.156011\pi$
$68$	2.52636	−	11.0687i	0.306366	−	1.34228i
$69$		0			0
$70$	−8.22432			−0.982994
$71$	−7.37090	−	3.54964i	−0.874765	−	0.421264i	−0.0580551	−	0.998313i	$-0.518490\pi$
$71$	−7.37090	−	3.54964i	−0.874765	−	0.421264i	−0.816710	+	0.577049i	$0.804204\pi$
$72$		0			0
$73$	7.09446	−	8.89617i	0.830344	−	1.04122i	−0.168117	−	0.985767i	$-0.553769\pi$
$73$	7.09446	−	8.89617i	0.830344	−	1.04122i	0.998461	−	0.0554515i	$-0.0176598\pi$
$74$	18.1060	+	8.71937i	2.10477	+	1.01361i
$75$		0			0
$76$	−7.93260	−	3.82014i	−0.909932	−	0.438200i
$77$	−2.67925	+	11.7386i	−0.305329	+	1.33773i
$78$		0			0
$79$	7.32556	−	3.52780i	0.824189	−	0.396909i	0.0262567	−	0.999655i	$-0.491641\pi$
$79$	7.32556	−	3.52780i	0.824189	−	0.396909i	0.797933	+	0.602747i	$0.205927\pi$
$80$	−2.22336	−	9.74119i	−0.248579	−	1.08910i
$81$		0			0
$82$	5.10130	+	6.39683i	0.563345	+	0.706412i
$83$	−0.107218	+	0.469754i	−0.0117687	+	0.0515622i	−0.980471	−	0.196662i	$-0.936990\pi$
$83$	−0.107218	+	0.469754i	−0.0117687	+	0.0515622i	0.968703	+	0.248224i	$0.0798470\pi$
$84$		0			0
$85$	−1.73011	−	2.16949i	−0.187657	−	0.235314i
$86$	3.78965			0.408648
$87$		0			0
$88$	−30.4421			−3.24514
$89$	1.24461	+	1.56070i	0.131929	+	0.165434i	0.843408	−	0.537274i	$-0.180546\pi$
$89$	1.24461	+	1.56070i	0.131929	+	0.165434i	−0.711479	+	0.702707i	$0.751974\pi$
$90$		0			0
$91$	−3.46377	+	15.1758i	−0.363101	+	1.59085i
$92$	25.8523	+	32.4178i	2.69529	+	3.37979i
$93$		0			0
$94$	−0.205841	−	0.901847i	−0.0212309	−	0.0930184i
$95$	−1.93881	+	0.933683i	−0.198918	+	0.0957938i
$96$		0			0
$97$	−1.03142	+	4.51895i	−0.104725	+	0.458830i	0.895189	+	0.445687i	$0.147041\pi$
$97$	−1.03142	+	4.51895i	−0.104725	+	0.458830i	−0.999914	+	0.0131424i	$0.995817\pi$
$98$	1.50819	+	0.726305i	0.152350	+	0.0733679i
$99$		0			0
$100$	15.5857	+	7.50570i	1.55857	+	0.750570i
$101$	1.18405	−	1.48475i	0.117817	−	0.147738i	−0.719425	−	0.694570i	$-0.755595\pi$
$101$	1.18405	−	1.48475i	0.117817	−	0.147738i	0.837243	+	0.546831i	$0.184166\pi$
$102$		0			0
$103$	7.40706	+	3.56705i	0.729840	+	0.351472i	0.761621	−	0.648023i	$-0.224404\pi$
$103$	7.40706	+	3.56705i	0.729840	+	0.351472i	−0.0317815	+	0.999495i	$0.510118\pi$
$104$	−39.3560			−3.85917
$105$		0			0
$106$	0.941781	−	4.12621i	0.0914739	−	0.400773i
$107$	4.01632	−	1.93416i	0.388273	−	0.186982i	−0.229555	−	0.973296i	$-0.573727\pi$
$107$	4.01632	−	1.93416i	0.388273	−	0.186982i	0.617828	+	0.786313i	$0.288013\pi$
$108$		0			0
$109$	−3.89981	−	17.0862i	−0.373534	−	1.63656i	−0.716768	−	0.697311i	$-0.754380\pi$
$109$	−3.89981	−	17.0862i	−0.373534	−	1.63656i	0.343234	−	0.939250i	$-0.388478\pi$
$110$	−8.07419	+	10.1247i	−0.769844	+	0.965354i
$111$		0			0
$112$	−5.35116	+	23.4450i	−0.505637	+	2.21534i
$113$	1.76485	+	7.73232i	0.166023	+	0.727395i	0.987560	+	0.157240i	$0.0502597\pi$
$113$	1.76485	+	7.73232i	0.166023	+	0.727395i	−0.821537	+	0.570155i	$0.806883\pi$
$114$		0			0
$115$	10.1342			0.945021
$116$	−8.55904	−	23.8241i	−0.794687	−	2.21202i
$117$		0			0
$118$	−7.82817	−	9.81621i	−0.720641	−	0.903655i
$119$	1.48612	+	6.51111i	0.136232	+	0.596872i
$120$		0			0
$121$	4.96226	+	6.22247i	0.451114	+	0.565679i
$122$	−2.50988	+	3.14729i	−0.227234	+	0.284942i
$123$		0			0
$124$	−6.60939	+	3.18291i	−0.593541	+	0.285834i
$125$	8.98513	−	4.32701i	0.803654	−	0.387020i
$126$		0			0
$127$	3.02313	+	1.45586i	0.268259	+	0.129187i	0.563178	−	0.826335i	$-0.309578\pi$
$127$	3.02313	+	1.45586i	0.268259	+	0.129187i	−0.294919	+	0.955522i	$0.595293\pi$
$128$	4.93114			0.435855
$129$		0			0
$130$	−10.4384	+	13.0894i	−0.915510	+	1.14801i
$131$	5.42012	−	6.79661i	0.473558	−	0.593823i	−0.486480	−	0.873692i	$-0.661719\pi$
$131$	5.42012	−	6.79661i	0.473558	−	0.593823i	0.960038	+	0.279869i	$0.0902909\pi$
$132$		0			0
$133$	5.17921			0.449095
$134$	−22.5517	−	10.8603i	−1.94817	−	0.938189i
$135$		0			0
$136$	−15.2134	+	7.32637i	−1.30453	+	0.628231i
$137$	2.90456	−	1.39876i	0.248153	−	0.119504i	−0.305673	−	0.952137i	$-0.598881\pi$
$137$	2.90456	−	1.39876i	0.248153	−	0.119504i	0.553826	+	0.832632i	$0.313167\pi$
$138$		0			0
$139$	−14.0213	+	17.5821i	−1.18927	+	1.49130i	−0.359544	+	0.933128i	$0.617068\pi$
$139$	−14.0213	+	17.5821i	−1.18927	+	1.49130i	−0.829726	+	0.558170i	$0.811504\pi$
$140$	9.31198	+	11.6768i	0.787006	+	0.986874i
$141$		0			0
$142$	4.71245	+	20.6466i	0.395460	+	1.73262i
$143$	15.2819	+	19.1629i	1.27794	+	1.60248i
$144$		0			0
$145$	−5.85680	−	1.99497i	−0.486381	−	0.165674i
$146$	−29.4548			−2.43769
$147$		0			0
$148$	−8.12073	−	35.5792i	−0.667520	−	2.92460i
$149$	0.286904	−	1.25701i	0.0235041	−	0.102978i	−0.961815	−	0.273700i	$-0.911753\pi$
$149$	0.286904	−	1.25701i	0.0235041	−	0.102978i	0.985319	+	0.170721i	$0.0546098\pi$
$150$		0			0
$151$	4.08507	−	5.12252i	0.332439	−	0.416865i	−0.587317	−	0.809357i	$-0.699816\pi$
$151$	4.08507	−	5.12252i	0.332439	−	0.416865i	0.919755	+	0.392492i	$0.128387\pi$
$152$	2.91385	+	12.7664i	0.236345	+	1.03549i
$153$		0			0
$154$	28.0813	−	13.5232i	2.26286	−	1.08973i
$155$	−0.398972	+	1.74801i	−0.0320462	+	0.140404i
$156$		0			0
$157$	−24.1178			−1.92481			−0.962407	−	0.271612i	$-0.912443\pi$
$157$	−24.1178			−1.92481			−0.962407	+	0.271612i	$0.912443\pi$
$158$	−18.9630	−	9.13208i	−1.50861	−	0.726509i
$159$		0			0
$160$	−6.10953	+	7.66111i	−0.483001	+	0.605664i
$161$	−21.9755	−	10.5828i	−1.73191	−	0.834043i
$162$		0			0
$163$	−14.5447	−	7.00435i	−1.13923	−	0.548623i	−0.233446	−	0.972370i	$-0.575000\pi$
$163$	−14.5447	−	7.00435i	−1.13923	−	0.548623i	−0.905781	+	0.423747i	$0.860715\pi$
$164$	3.30625	−	14.4856i	0.258174	−	1.13114i
$165$		0			0
$166$	1.12376	−	0.541174i	0.0872206	−	0.0420032i
$167$	−1.20616	−	5.28454i	−0.0933357	−	0.408930i	0.906578	−	0.422037i	$-0.138685\pi$
$167$	−1.20616	−	5.28454i	−0.0933357	−	0.408930i	−0.999914	+	0.0131071i	$0.995828\pi$
$168$		0			0
$169$	11.6513	+	14.6102i	0.896251	+	1.12386i
$170$	−1.59838	+	7.00297i	−0.122590	+	0.537104i
$171$		0			0
$172$	−4.29082	−	5.38052i	−0.327172	−	0.410261i
$173$	11.2923			0.858537			0.429268	−	0.903177i	$-0.358771\pi$
$173$	11.2923			0.858537			0.429268	+	0.903177i	$0.358771\pi$
$174$		0			0
$175$	−10.1760			−0.769231
$176$	23.6089	+	29.6047i	1.77959	+	2.23154i
$177$		0			0
$178$	1.14985	−	5.03783i	0.0861851	−	0.377601i
$179$	6.64270	+	8.32969i	0.496499	+	0.622590i	0.965436	−	0.260642i	$-0.0839341\pi$
$179$	6.64270	+	8.32969i	0.496499	+	0.622590i	−0.468937	+	0.883232i	$0.655363\pi$
$180$		0			0
$181$	2.73554	+	11.9852i	0.203331	+	0.890853i	0.968891	+	0.247488i	$0.0796051\pi$
$181$	2.73554	+	11.9852i	0.203331	+	0.890853i	−0.765559	+	0.643365i	$0.777538\pi$
$182$	36.3039	−	17.4830i	2.69102	−	1.29593i
$183$		0			0
$184$	13.7225	−	60.1220i	1.01163	−	4.43226i
$185$	−8.03626	−	3.87006i	−0.590838	−	0.284533i
$186$		0			0
$187$	9.47462	+	4.56274i	0.692853	+	0.333660i
$188$	−1.04738	+	1.31337i	−0.0763877	+	0.0957872i
$189$		0			0
$190$	5.01882	+	2.41693i	0.364103	+	0.175343i
$191$	1.68311			0.121786			0.0608929	−	0.998144i	$-0.480605\pi$
$191$	1.68311			0.121786			0.0608929	+	0.998144i	$0.480605\pi$
$192$		0			0
$193$	−2.35340	+	10.3109i	−0.169402	+	0.742197i	0.816837	+	0.576869i	$0.195726\pi$
$193$	−2.35340	+	10.3109i	−0.169402	+	0.742197i	−0.986239	+	0.165328i	$0.947132\pi$
$194$	10.8104	−	5.20599i	0.776138	−	0.373769i
$195$		0			0
$196$	−0.676440	−	2.96368i	−0.0483171	−	0.211691i
$197$	7.55361	−	9.47193i	0.538172	−	0.674847i	−0.436184	−	0.899858i	$-0.643670\pi$
$197$	7.55361	−	9.47193i	0.538172	−	0.674847i	0.974356	+	0.225011i	$0.0722417\pi$
$198$		0			0
$199$	−1.11170	+	4.87066i	−0.0788060	+	0.345272i	−0.998924	−	0.0463686i	$-0.985235\pi$
$199$	−1.11170	+	4.87066i	−0.0788060	+	0.345272i	0.920118	+	0.391640i	$0.128092\pi$
$200$	−5.72505	−	25.0831i	−0.404823	−	1.77364i
$201$		0			0
$202$	−4.91594			−0.345884
$203$	10.6168	+	10.4420i	0.745156	+	0.732887i
$204$		0			0
$205$	−2.26419	−	2.83921i	−0.158138	−	0.198299i
$206$	−4.73557	−	20.7479i	−0.329943	−	1.44558i
$207$		0			0
$208$	30.5219	+	38.2733i	2.11632	+	2.65378i
$209$	5.08467	−	6.37598i	0.351714	−	0.441036i
$210$		0			0
$211$	17.3083	−	8.33526i	1.19156	−	0.573823i	0.270298	−	0.962777i	$-0.412878\pi$
$211$	17.3083	−	8.33526i	1.19156	−	0.573823i	0.921257	+	0.388954i	$0.127163\pi$
$212$	−6.92471	+	3.33476i	−0.475591	+	0.229033i
$213$		0			0
$214$	−10.3967	−	5.00677i	−0.710701	−	0.342256i
$215$	−1.68202			−0.114713
$216$		0			0
$217$	2.69054	−	3.37383i	0.182645	−	0.229030i
$218$	−28.2858	+	35.4692i	−1.91575	+	2.40228i
$219$		0			0
$220$	23.5170			1.58552
$221$	12.2489	+	5.89877i	0.823951	+	0.396794i
$222$		0			0
$223$	19.1403	−	9.21751i	1.28173	−	0.617250i	0.335898	−	0.941898i	$-0.390960\pi$
$223$	19.1403	−	9.21751i	1.28173	−	0.617250i	0.945835	+	0.324649i	$0.105246\pi$
$224$	21.2484	−	10.2327i	1.41972	−	0.683701i
$225$		0			0
$226$	12.8007	−	16.0515i	0.851487	−	1.06773i
$227$	−12.3176	−	15.4458i	−0.817549	−	1.02517i	−0.999126	−	0.0417977i	$-0.986692\pi$
$227$	−12.3176	−	15.4458i	−0.817549	−	1.02517i	0.181577	−	0.983377i	$-0.441880\pi$
$228$		0			0
$229$	−4.60927	−	20.1945i	−0.304589	−	1.33449i	−0.863116	−	0.505005i	$-0.831491\pi$
$229$	−4.60927	−	20.1945i	−0.304589	−	1.33449i	0.558528	−	0.829486i	$-0.311366\pi$
$230$	−16.3563	−	20.5102i	−1.07850	−	1.35240i
$231$		0			0
$232$	−19.7659	+	32.0446i	−1.29769	+	2.10383i
$233$	−20.7745			−1.36098			−0.680492	−	0.732756i	$-0.738234\pi$
$233$	−20.7745			−1.36098			−0.680492	+	0.732756i	$0.738234\pi$
$234$		0			0
$235$	0.0913617	+	0.400282i	0.00595978	+	0.0261115i
$236$	−5.07358	+	22.2288i	−0.330262	+	1.44697i
$237$		0			0
$238$	10.7790	−	13.5164i	0.698697	−	0.876138i
$239$	−0.506194	−	2.21778i	−0.0327430	−	0.143456i	0.955914	−	0.293646i	$-0.0948687\pi$
$239$	−0.506194	−	2.21778i	−0.0327430	−	0.143456i	−0.988657	+	0.150190i	$0.952012\pi$
$240$		0			0
$241$	−10.6119	+	5.11041i	−0.683571	+	0.329190i	−0.743237	−	0.669028i	$-0.766711\pi$
$241$	−10.6119	+	5.11041i	−0.683571	+	0.329190i	0.0596665	+	0.998218i	$0.480996\pi$
$242$	4.58444	−	20.0857i	0.294699	−	1.29116i
$243$		0			0
$244$	7.31032			0.467995
$245$	−0.669404	−	0.322368i	−0.0427666	−	0.0205953i
$246$		0			0
$247$	6.57353	−	8.24295i	0.418264	−	0.524486i
$248$	9.82997	+	4.73386i	0.624204	+	0.300601i
$249$		0			0
$250$	−23.2589	−	11.2009i	−1.47102	−	0.708408i
$251$	−0.317569	+	1.39136i	−0.0200448	+	0.0878219i	−0.983961	−	0.178384i	$-0.942913\pi$
$251$	−0.317569	+	1.39136i	−0.0200448	+	0.0878219i	0.963916	+	0.266206i	$0.0857702\pi$
$252$		0			0
$253$	−34.6025	+	16.6637i	−2.17544	+	1.04764i
$254$	−1.93278	−	8.46808i	−0.121274	−	0.531334i
$255$		0			0
$256$	−13.8001	−	17.3048i	−0.862507	−	1.08155i
$257$	−6.37412	+	27.9268i	−0.397607	+	1.74203i	0.239167	+	0.970978i	$0.423126\pi$
$257$	−6.37412	+	27.9268i	−0.397607	+	1.74203i	−0.636774	+	0.771051i	$0.719732\pi$
$258$		0			0
$259$	13.3848	+	16.7840i	0.831690	+	1.04291i
$260$	30.4031			1.88552
$261$		0			0
$262$	−22.5032			−1.39025
$263$	−11.5360	−	14.4657i	−0.711340	−	0.891993i	0.286473	−	0.958088i	$-0.407517\pi$
$263$	−11.5360	−	14.4657i	−0.711340	−	0.891993i	−0.997813	+	0.0660957i	$0.978946\pi$
$264$		0			0
$265$	−0.418006	+	1.83140i	−0.0256779	+	0.112502i
$266$	−8.35908	−	10.4820i	−0.512528	−	0.642690i
$267$		0			0
$268$	10.1147	+	44.3154i	0.617853	+	2.70699i
$269$	−25.8645	+	12.4557i	−1.57698	+	0.759435i	−0.998419	−	0.0562017i	$-0.982101\pi$
$269$	−25.8645	+	12.4557i	−1.57698	+	0.759435i	−0.578564	+	0.815637i	$0.696387\pi$
$270$		0			0
$271$	−0.401519	+	1.75917i	−0.0243905	+	0.106862i	−0.985658	−	0.168756i	$-0.946025\pi$
$271$	−0.401519	+	1.75917i	−0.0243905	+	0.106862i	0.961267	+	0.275617i	$0.0888823\pi$
$272$	18.9233	+	9.11298i	1.14739	+	0.552556i
$273$		0			0
$274$	−7.51875	−	3.62084i	−0.454224	−	0.218743i
$275$	−9.99022	+	12.5273i	−0.602433	+	0.755427i
$276$		0			0
$277$	12.7892	+	6.15895i	0.768428	+	0.370055i	0.776667	−	0.629911i	$-0.216909\pi$
$277$	12.7892	+	6.15895i	0.768428	+	0.370055i	−0.00823988	+	0.999966i	$0.502623\pi$
$278$	58.2136			3.49142
$279$		0			0
$280$	4.94281	−	21.6559i	0.295390	−	1.29419i
$281$	16.9576	−	8.16637i	1.01161	−	0.487165i	0.146746	−	0.989174i	$-0.453120\pi$
$281$	16.9576	−	8.16637i	1.01161	−	0.487165i	0.864862	+	0.502010i	$0.167406\pi$
$282$		0			0
$283$	−4.86946	−	21.3345i	−0.289460	−	1.26821i	−0.885269	−	0.465079i	$-0.846026\pi$
$283$	−4.86946	−	21.3345i	−0.289460	−	1.26821i	0.595809	−	0.803126i	$-0.296831\pi$
$284$	23.9783	−	30.0678i	1.42285	−	1.78420i
$285$		0			0
$286$	14.1184	−	61.8566i	0.834836	−	3.65765i
$287$	1.94488	+	8.52108i	0.114803	+	0.502983i
$288$		0			0
$289$	−11.1670			−0.656882
$290$	5.41515	+	15.0731i	0.317989	+	0.885124i
$291$		0			0
$292$	33.3501	+	41.8198i	1.95167	+	2.44732i
$293$	0.00172808	+	0.00757121i	0.000100955	+	0.000442315i	0.974978	−	0.222300i	$-0.0713564\pi$
$293$	0.00172808	+	0.00757121i	0.000100955	+	0.000442315i	−0.974877	+	0.222742i	$0.928499\pi$
$294$		0			0
$295$	3.47450	+	4.35689i	0.202293	+	0.253668i
$296$	−33.8411	+	42.4354i	−1.96697	+	2.46651i
$297$		0			0
$298$	−3.00706	+	1.44812i	−0.174194	+	0.0838875i
$299$	−44.7346	+	21.5431i	−2.58707	+	1.24587i
$300$		0			0
$301$	3.64736	+	1.75648i	0.210231	+	0.101242i
$302$	−16.9604			−0.975961
$303$		0			0
$304$	10.1554	−	12.7345i	0.582454	−	0.730374i
$305$	1.11400	−	1.39691i	0.0637876	−	0.0799871i
$306$		0			0
$307$	0.214941			0.0122673			0.00613367	−	0.999981i	$-0.498048\pi$
$307$	0.214941			0.0122673			0.00613367	+	0.999981i	$0.498048\pi$
$308$	−50.9953	−	24.5580i	−2.90573	−	1.39932i
$309$		0			0
$310$	4.18164	−	2.01377i	0.237501	−	0.114375i
$311$	25.4313	−	12.2471i	1.44207	−	0.694467i	0.460876	−	0.887465i	$-0.347535\pi$
$311$	25.4313	−	12.2471i	1.44207	−	0.694467i	0.981199	+	0.192998i	$0.0618211\pi$
$312$		0			0
$313$	−6.37841	+	7.99827i	−0.360529	+	0.452089i	−0.928706	−	0.370817i	$-0.879078\pi$
$313$	−6.37841	+	7.99827i	−0.360529	+	0.452089i	0.568177	+	0.822907i	$0.307649\pi$
$314$	38.9254	+	48.8110i	2.19669	+	2.75456i
$315$		0			0
$316$	8.50511	+	37.2633i	0.478450	+	2.09622i
$317$	−14.8259	−	18.5911i	−0.832704	−	1.04418i	−0.998317	−	0.0579872i	$-0.981532\pi$
$317$	−14.8259	−	18.5911i	−0.832704	−	1.04418i	0.165613	−	0.986191i	$-0.447040\pi$
$318$		0			0
$319$	23.2779	−	2.81864i	1.30331	−	0.157814i
$320$	5.38216			0.300872
$321$		0			0
$322$	14.0496	+	61.5554i	0.782955	+	3.43035i
$323$	1.00657	−	4.41008i	0.0560072	−	0.245383i
$324$		0			0
$325$	−12.9155	+	16.1955i	−0.716422	+	0.898365i
$326$	9.29888	+	40.7411i	0.515017	+	2.25644i
$327$		0			0
$328$	−19.9097	+	9.58801i	−1.09933	+	0.529409i
$329$	0.219888	−	0.963393i	0.0121228	−	0.0531136i
$330$		0			0
$331$	−7.07856			−0.389073			−0.194536	−	0.980895i	$-0.562320\pi$
$331$	−7.07856			−0.389073			−0.194536	+	0.980895i	$0.562320\pi$
$332$	−2.04073	−	0.982764i	−0.112000	−	0.0539362i
$333$		0			0
$334$	−8.74843	+	10.9702i	−0.478693	+	0.600261i
$335$	10.0095	+	4.82032i	0.546877	+	0.263362i
$336$		0			0
$337$	6.32843	+	3.04761i	0.344731	+	0.166014i	0.598235	−	0.801320i	$-0.295869\pi$
$337$	6.32843	+	3.04761i	0.344731	+	0.166014i	−0.253504	+	0.967334i	$0.581583\pi$
$338$	10.7642	−	47.1609i	0.585493	−	2.56521i
$339$		0			0
$340$	11.7526	−	5.65973i	0.637372	−	0.306942i
$341$	−1.51199	−	6.62448i	−0.0818791	−	0.358736i
$342$		0			0
$343$	−10.9539	−	13.7357i	−0.591453	−	0.741658i
$344$	−2.27758	+	9.97872i	−0.122799	+	0.538016i
$345$		0			0
$346$	−18.2254	−	22.8539i	−0.979803	−	1.22863i
$347$	−10.0795			−0.541094			−0.270547	−	0.962707i	$-0.587205\pi$
$347$	−10.0795			−0.541094			−0.270547	+	0.962707i	$0.587205\pi$
$348$		0			0
$349$	−1.64246			−0.0879187			−0.0439593	−	0.999033i	$-0.513997\pi$
$349$	−1.64246			−0.0879187			−0.0439593	+	0.999033i	$0.513997\pi$
$350$	16.4237	+	20.5947i	0.877883	+	1.10083i
$351$		0			0
$352$	8.26337	−	36.2042i	0.440439	−	1.92969i
$353$	−15.0406	−	18.8603i	−0.800530	−	1.00383i	−0.999715	−	0.0238707i	$-0.992401\pi$
$353$	−15.0406	−	18.8603i	−0.800530	−	1.00383i	0.199185	−	0.979962i	$-0.436170\pi$
$354$		0			0
$355$	−2.09161	−	9.16392i	−0.111011	−	0.486370i
$356$	−8.45461	+	4.07153i	−0.448093	+	0.215790i
$357$		0			0
$358$	6.13694	−	26.8877i	0.324347	−	1.42106i
$359$	−11.6187	−	5.59526i	−0.613210	−	0.295307i	0.101382	−	0.994848i	$-0.467674\pi$
$359$	−11.6187	−	5.59526i	−0.613210	−	0.295307i	−0.714592	+	0.699541i	$0.753388\pi$
$360$		0			0
$361$	13.9578	+	6.72174i	0.734623	+	0.353776i
$362$	19.8412	−	24.8801i	1.04283	−	1.30767i
$363$		0			0
$364$	−65.9274	−	31.7489i	−3.45553	−	1.66410i
$365$	13.0734			0.684293
$366$		0			0
$367$	7.06325	−	30.9461i	0.368699	−	1.61537i	−0.361659	−	0.932310i	$-0.617790\pi$
$367$	7.06325	−	30.9461i	0.368699	−	1.61537i	0.730358	−	0.683064i	$-0.239353\pi$
$368$	−69.1103	+	33.2818i	−3.60262	+	1.73493i
$369$		0			0
$370$	5.13784	+	22.5104i	0.267104	+	1.17026i
$371$	2.81890	−	3.53478i	0.146350	−	0.183517i
$372$		0			0
$373$	−1.05811	+	4.63589i	−0.0547869	+	0.240037i	−0.994906	−	0.100810i	$-0.967857\pi$
$373$	−1.05811	+	4.63589i	−0.0547869	+	0.240037i	0.940119	+	0.340847i	$0.110714\pi$
$374$	−6.05743	−	26.5393i	−0.313222	−	1.37232i
$375$		0			0
$376$	2.49841			0.128846
$377$	30.0940	−	3.64398i	1.54992	−	0.187675i
$378$		0			0
$379$	1.32155	+	1.65717i	0.0678834	+	0.0851231i	0.814614	−	0.580004i	$-0.196949\pi$
$379$	1.32155	+	1.65717i	0.0678834	+	0.0851231i	−0.746730	+	0.665127i	$0.768377\pi$
$380$	−2.25100	−	9.86226i	−0.115474	−	0.505924i
$381$		0			0
$382$	−2.71649	−	3.40637i	−0.138988	−	0.174285i
$383$	−9.12830	+	11.4465i	−0.466434	+	0.584890i	−0.958294	−	0.285784i	$-0.907746\pi$
$383$	−9.12830	+	11.4465i	−0.466434	+	0.584890i	0.491860	+	0.870675i	$0.336317\pi$
$384$		0			0
$385$	−12.4638	+	6.00224i	−0.635213	+	0.305903i
$386$	24.6661	−	11.8786i	1.25547	−	0.604604i
$387$		0			0
$388$	−19.6315	−	9.45401i	−0.996636	−	0.479955i
$389$	−1.93401			−0.0980583			−0.0490292	−	0.998797i	$-0.515613\pi$
$389$	−1.93401			−0.0980583			−0.0490292	+	0.998797i	$0.515613\pi$
$390$		0			0
$391$	−13.2821	+	16.6553i	−0.671706	+	0.842293i
$392$	−2.81889	+	3.53478i	−0.142376	+	0.178533i
$393$		0			0
$394$	−31.3611			−1.57995
$395$	8.41664	+	4.05324i	0.423487	+	0.203941i
$396$		0			0
$397$	27.0463	−	13.0248i	1.35742	−	0.653697i	0.393357	−	0.919386i	$-0.371314\pi$
$397$	27.0463	−	13.0248i	1.35742	−	0.653697i	0.964059	+	0.265689i	$0.0855995\pi$
$398$	11.6517	−	5.61118i	0.584048	−	0.281263i
$399$		0			0
$400$	−19.9531	+	25.0204i	−0.997654	+	1.25102i
$401$	−9.79407	−	12.2814i	−0.489093	−	0.613303i	0.474638	−	0.880181i	$-0.342579\pi$
$401$	−9.79407	−	12.2814i	−0.489093	−	0.613303i	−0.963730	+	0.266879i	$0.914008\pi$
$402$		0			0
$403$	−1.95473	−	8.56422i	−0.0973719	−	0.426614i
$404$	5.56607	+	6.97963i	0.276922	+	0.347249i
$405$		0			0
$406$	3.99791	−	38.3400i	0.198413	−	1.90278i
$407$	33.8027			1.67554
$408$		0			0
$409$	1.08416	+	4.75001i	0.0536081	+	0.234873i	0.994633	−	0.103464i	$-0.0329928\pi$
$409$	1.08416	+	4.75001i	0.0536081	+	0.234873i	−0.941025	+	0.338337i	$0.890136\pi$
$410$	−2.09180	+	9.16479i	−0.103307	+	0.452617i
$411$		0			0
$412$	−24.0959	+	30.2153i	−1.18712	+	1.48860i
$413$	−2.98450	−	13.0760i	−0.146858	−	0.643426i
$414$		0			0
$415$	−0.498776	+	0.240198i	−0.0244840	+	0.0117909i
$416$	10.6830	−	46.8053i	0.523777	−	2.29482i
$417$		0			0
$418$	−21.1105			−1.03255
$419$	17.1303	+	8.24949i	0.836867	+	0.403014i	0.802686	−	0.596402i	$-0.203403\pi$
$419$	17.1303	+	8.24949i	0.836867	+	0.403014i	0.0341812	+	0.999416i	$0.489118\pi$
$420$		0			0
$421$	7.80429	−	9.78627i	0.380358	−	0.476954i	−0.554394	−	0.832254i	$-0.687050\pi$
$421$	7.80429	−	9.78627i	0.380358	−	0.476954i	0.934752	+	0.355300i	$0.115621\pi$
$422$	−44.8044	−	21.5767i	−2.18105	−	1.05034i
$423$		0			0
$424$	10.2989	+	4.95971i	0.500161	+	0.240865i
$425$	−1.97768	+	8.66480i	−0.0959317	+	0.420304i
$426$		0			0
$427$	−3.87440	+	1.86581i	−0.187495	+	0.0902929i
$428$	4.66303	+	20.4300i	0.225396	+	0.987524i
$429$		0			0
$430$	2.71473	+	3.40416i	0.130916	+	0.164163i
$431$	7.87657	−	34.5095i	0.379401	−	1.66227i	−0.319910	−	0.947448i	$-0.603653\pi$
$431$	7.87657	−	34.5095i	0.379401	−	1.66227i	0.699311	−	0.714817i	$-0.253490\pi$
$432$		0			0
$433$	3.65050	+	4.57758i	0.175432	+	0.219984i	0.861772	−	0.507297i	$-0.169355\pi$
$433$	3.65050	+	4.57758i	0.175432	+	0.219984i	−0.686340	+	0.727281i	$0.740784\pi$
$434$	−11.1706			−0.536204
$435$		0			0
$436$	82.3856			3.94555
$437$	10.3003	+	12.9161i	0.492729	+	0.617863i
$438$		0			0
$439$	−5.52514	+	24.2072i	−0.263700	+	1.15535i	0.653502	+	0.756925i	$0.273299\pi$
$439$	−5.52514	+	24.2072i	−0.263700	+	1.15535i	−0.917202	+	0.398422i	$0.869558\pi$
$440$	−21.8073	−	27.3455i	−1.03962	−	1.30365i
$441$		0			0
$442$	−7.83113	−	34.3104i	−0.372489	−	1.63198i
$443$	21.3969	−	10.3042i	1.01660	−	0.489568i	0.150060	−	0.988677i	$-0.452053\pi$
$443$	21.3969	−	10.3042i	1.01660	−	0.489568i	0.866539	+	0.499109i	$0.166339\pi$
$444$		0			0
$445$	−0.510358	+	2.23602i	−0.0241933	+	0.105998i
$446$	−49.5468	−	23.8605i	−2.34611	−	1.12983i
$447$		0			0
$448$	−11.6709	−	5.62040i	−0.551398	−	0.265539i
$449$	−4.02060	+	5.04167i	−0.189744	+	0.237931i	−0.867599	−	0.497264i	$-0.834338\pi$
$449$	−4.02060	+	5.04167i	−0.189744	+	0.237931i	0.677856	+	0.735195i	$0.262909\pi$
$450$		0			0
$451$	12.3994	+	5.97125i	0.583866	+	0.281175i
$452$	−37.2834			−1.75366
$453$		0			0
$454$	−11.3798	+	49.8581i	−0.534080	+	2.33996i
$455$	−16.1134	+	7.75978i	−0.755406	+	0.363784i
$456$		0			0
$457$	0.584270	+	2.55985i	0.0273310	+	0.119745i	0.986753	−	0.162228i	$-0.0518682\pi$
$457$	0.584270	+	2.55985i	0.0273310	+	0.119745i	−0.959422	+	0.281973i	$0.909011\pi$
$458$	−33.4315	+	41.9218i	−1.56215	+	1.95888i
$459$		0			0
$460$	−10.6008	+	46.4452i	−0.494266	+	2.16552i
$461$	−1.59279	−	6.97847i	−0.0741837	−	0.325020i	0.924196	−	0.381918i	$-0.124736\pi$
$461$	−1.59279	−	6.97847i	−0.0741837	−	0.325020i	−0.998380	+	0.0568978i	$0.981879\pi$
$462$		0			0
$463$	−18.2411			−0.847737			−0.423868	−	0.905724i	$-0.639328\pi$
$463$	−18.2411			−0.847737			−0.423868	+	0.905724i	$0.639328\pi$
$464$	46.4921	−	5.62957i	2.15834	−	0.261346i
$465$		0			0
$466$	33.5294	+	42.0445i	1.55322	+	1.94768i
$467$	7.89230	+	34.5784i	0.365212	+	1.60010i	0.739746	+	0.672886i	$0.234946\pi$
$467$	7.89230	+	34.5784i	0.365212	+	1.60010i	−0.374534	+	0.927213i	$0.622197\pi$
$468$		0			0
$469$	−16.6713	−	20.9051i	−0.769809	−	0.965310i
$470$	0.662656	−	0.830944i	0.0305660	−	0.0383286i
$471$		0			0
$472$	30.5523	−	14.7132i	1.40628	−	0.677231i
$473$	5.74313	−	2.76575i	0.264070	−	0.127169i
$474$		0			0
$475$	6.20979	+	2.99048i	0.284925	+	0.137213i
$476$	−31.3950			−1.43899
$477$		0			0
$478$	−3.67148	+	4.60389i	−0.167929	+	0.210577i
$479$	−16.2734	+	20.4061i	−0.743548	+	0.932380i	−0.999410	−	0.0343330i	$-0.989069\pi$
$479$	−16.2734	+	20.4061i	−0.743548	+	0.932380i	0.255862	+	0.966713i	$0.417641\pi$
$480$		0			0
$481$	43.7006			1.99258
$482$	27.4699	+	13.2288i	1.25122	+	0.602556i
$483$		0			0
$484$	−33.7084	+	16.2331i	−1.53220	+	0.737868i
$485$	−4.79814	+	2.31066i	−0.217872	+	0.104922i
$486$		0			0
$487$	13.8098	−	17.3170i	0.625783	−	0.784708i	−0.363362	−	0.931648i	$-0.618371\pi$
$487$	13.8098	−	17.3170i	0.625783	−	0.784708i	0.989145	+	0.146940i	$0.0469426\pi$
$488$	−6.77886	−	8.50042i	−0.306865	−	0.384796i
$489$		0			0
$490$	0.427971	+	1.87507i	0.0193338	+	0.0847068i
$491$	7.32494	+	9.18518i	0.330570	+	0.414521i	0.919144	−	0.393922i	$-0.128882\pi$
$491$	7.32494	+	9.18518i	0.330570	+	0.414521i	−0.588574	+	0.808443i	$0.700310\pi$
$492$		0			0
$493$	10.9547	−	7.01080i	0.493376	−	0.315750i
$494$	−27.2920			−1.22792
$495$		0			0
$496$	−3.01985	−	13.2308i	−0.135595	−	0.594082i
$497$	−5.03405	+	22.0556i	−0.225808	+	0.989330i
$498$		0			0
$499$	−10.2098	+	12.8027i	−0.457056	+	0.573130i	−0.955949	−	0.293534i	$-0.905169\pi$
$499$	−10.2098	+	12.8027i	−0.457056	+	0.573130i	0.498893	+	0.866664i	$0.333740\pi$
$500$	10.4319	+	45.7052i	0.466529	+	2.04400i
$501$		0			0
$502$	3.32846	−	1.60290i	0.148556	−	0.0715409i
$503$	3.30118	−	14.4634i	0.147192	−	0.644892i	−0.846465	−	0.532444i	$-0.821274\pi$
$503$	3.30118	−	14.4634i	0.147192	−	0.644892i	0.993658	−	0.112448i	$-0.0358691\pi$
$504$		0			0
$505$	2.18192			0.0970942
$506$	89.5722	+	43.1357i	3.98197	+	1.91762i
$507$		0			0
$508$	−9.83454	+	12.3321i	−0.436337	+	0.547150i
$509$	28.4466	+	13.6992i	1.26087	+	0.607204i	0.940405	−	0.340055i	$-0.110446\pi$
$509$	28.4466	+	13.6992i	1.26087	+	0.607204i	0.320467	+	0.947260i	$0.396160\pi$
$510$		0			0
$511$	−28.3489	−	13.6521i	−1.25408	−	0.603934i
$512$	−10.5548	+	46.2437i	−0.466462	+	2.04370i
$513$		0			0
$514$	66.8074	−	32.1728i	2.94675	−	1.41908i
$515$	2.10187	+	9.20888i	0.0926193	+	0.405792i
$516$		0			0
$517$	−0.970130	−	1.21651i	−0.0426663	−	0.0535018i
$518$	12.3657	−	54.1777i	0.543318	−	2.38043i
$519$		0			0
$520$	−28.1928	−	35.3527i	−1.23634	−	1.55032i
$521$	8.03875			0.352184			0.176092	−	0.984374i	$-0.443654\pi$
$521$	8.03875			0.352184			0.176092	+	0.984374i	$0.443654\pi$
$522$		0			0
$523$	−1.48633			−0.0649927			−0.0324963	−	0.999472i	$-0.510346\pi$
$523$	−1.48633			−0.0649927			−0.0324963	+	0.999472i	$0.510346\pi$
$524$	25.4793	+	31.9500i	1.11307	+	1.39574i
$525$		0			0
$526$	−10.6577	+	46.6943i	−0.464697	+	2.03597i
$527$	−2.34990	−	2.94668i	−0.102363	−	0.128359i
$528$		0			0
$529$	−12.1943	−	53.4268i	−0.530188	−	2.32291i
$530$	4.38114	−	2.10985i	0.190305	−	0.0916459i
$531$		0			0
$532$	−5.41767	+	23.7364i	−0.234886	+	1.02910i
$533$	16.0302	+	7.71971i	0.694343	+	0.334378i
$534$		0			0
$535$	4.61452	+	2.22224i	0.199503	+	0.0960757i
$536$	42.1505	−	52.8550i	1.82062	−	2.28299i
$537$		0			0
$538$	66.9528	+	32.2428i	2.88654	+	1.39008i
$539$	2.81570			0.121281
$540$		0			0
$541$	−8.64061	+	37.8570i	−0.371489	+	1.62760i	0.351112	+	0.936334i	$0.385804\pi$
$541$	−8.64061	+	37.8570i	−0.371489	+	1.62760i	−0.722601	+	0.691266i	$0.757053\pi$
$542$	4.20834	−	2.02663i	0.180764	−	0.0870511i
$543$		0			0
$544$	−4.58350	−	20.0816i	−0.196516	−	0.860993i
$545$	12.5545	−	15.7429i	0.537777	−	0.674351i
$546$		0			0
$547$	3.86062	−	16.9145i	0.165068	−	0.723210i	−0.822853	−	0.568254i	$-0.807619\pi$
$547$	3.86062	−	16.9145i	0.165068	−	0.723210i	0.987921	−	0.154956i	$-0.0495237\pi$
$548$	3.37225	+	14.7748i	0.144055	+	0.631147i
$549$		0			0
$550$	41.4774			1.76860
$551$	−3.41016	−	9.49220i	−0.145278	−	0.404381i
$552$		0			0
$553$	−14.0183	−	17.5784i	−0.596120	−	0.747511i
$554$	−8.17654	−	35.8238i	−0.347388	−	1.52201i
$555$		0			0
$556$	−65.9123	−	82.6514i	−2.79530	−	3.50520i
$557$	−18.9702	+	23.7879i	−0.803794	+	1.00793i	0.195833	+	0.980637i	$0.437259\pi$
$557$	−18.9702	+	23.7879i	−0.803794	+	1.00793i	−0.999628	+	0.0272889i	$0.991313\pi$
$558$		0			0
$559$	7.42480	−	3.57559i	0.314036	−	0.151232i
$560$	−24.8935	+	11.9881i	−1.05194	+	0.506588i
$561$		0			0
$562$	−43.8966	−	21.1395i	−1.85167	−	0.891715i
$563$	12.1911			0.513793			0.256897	−	0.966439i	$-0.417300\pi$
$563$	12.1911			0.513793			0.256897	+	0.966439i	$0.417300\pi$
$564$		0			0
$565$	−5.68152	+	7.12441i	−0.239024	+	0.299726i
$566$	−35.3187	+	44.2883i	−1.48456	+	1.86158i
$567$		0			0
$568$	−57.1978			−2.39997
$569$	−2.84513	−	1.37014i	−0.119274	−	0.0574393i	0.373295	−	0.927713i	$-0.378228\pi$
$569$	−2.84513	−	1.37014i	−0.119274	−	0.0574393i	−0.492569	+	0.870273i	$0.663942\pi$
$570$		0			0
$571$	−21.9308	+	10.5613i	−0.917776	+	0.441977i	−0.832276	−	0.554361i	$-0.812963\pi$
$571$	−21.9308	+	10.5613i	−0.917776	+	0.441977i	−0.0854992	+	0.996338i	$0.527249\pi$
$572$	−103.809	+	49.9918i	−4.34048	+	2.09026i
$573$		0			0
$574$	14.1064	−	17.6889i	0.588791	−	0.738321i
$575$	−20.2377	−	25.3773i	−0.843970	−	1.05831i
$576$		0			0
$577$	−1.77812	−	7.79044i	−0.0740240	−	0.324320i	0.924335	−	0.381581i	$-0.124620\pi$
$577$	−1.77812	−	7.79044i	−0.0740240	−	0.324320i	−0.998359	+	0.0572611i	$0.981763\pi$
$578$	18.0232	+	22.6003i	0.749665	+	0.940050i
$579$		0			0
$580$	15.2694	−	24.7549i	0.634029	−	1.02789i
$581$	1.33240			0.0552772
$582$		0			0
$583$	−1.58413	−	6.94052i	−0.0656079	−	0.287447i
$584$	17.7023	−	77.5589i	0.732527	−	3.20941i
$585$		0			0
$586$	0.0125339	−	0.0157171i	0.000517772	−	0.000649266i
$587$	−9.42720	−	41.3033i	−0.389102	−	1.70477i	−0.667759	−	0.744378i	$-0.732746\pi$
$587$	−9.42720	−	41.3033i	−0.389102	−	1.70477i	0.278657	−	0.960391i	$-0.410111\pi$
$588$		0			0
$589$	−2.63336	+	1.26816i	−0.108506	+	0.0522537i
$590$	3.20996	−	14.0638i	0.132152	−	0.578996i
$591$		0			0
$592$	67.5130			2.77477
$593$	−23.7641	−	11.4442i	−0.975873	−	0.469956i	−0.123189	−	0.992383i	$-0.539312\pi$
$593$	−23.7641	−	11.4442i	−0.975873	−	0.469956i	−0.852684	+	0.522427i	$0.825027\pi$
$594$		0			0
$595$	−4.78421	+	5.99920i	−0.196133	+	0.245943i
$596$	5.46078	+	2.62977i	0.223682	+	0.107720i
$597$		0			0
$598$	115.800	+	55.7664i	4.73542	+	2.28046i
$599$	1.41472	−	6.19828i	0.0578038	−	0.253255i	−0.937768	−	0.347263i	$-0.887111\pi$
$599$	1.41472	−	6.19828i	0.0578038	−	0.253255i	0.995571	+	0.0940086i	$0.0299681\pi$
$600$		0			0
$601$	15.2278	−	7.33332i	0.621155	−	0.299133i	−0.0967123	−	0.995312i	$-0.530833\pi$
$601$	15.2278	−	7.33332i	0.621155	−	0.299133i	0.717867	+	0.696180i	$0.245118\pi$
$602$	−2.33188	−	10.2166i	−0.0950402	−	0.416398i
$603$		0			0
$604$	19.2034	+	24.0803i	0.781375	+	0.979813i
$605$	−2.03479	+	8.91498i	−0.0827259	+	0.362446i
$606$		0			0
$607$	−4.62349	−	5.79767i	−0.187662	−	0.235320i	0.679096	−	0.734049i	$-0.262372\pi$
$607$	−4.62349	−	5.79767i	−0.187662	−	0.235320i	−0.866758	+	0.498729i	$0.833800\pi$
$608$	−15.9738			−0.647823
$609$		0			0
$610$	−4.62511			−0.187265
$611$	−1.25420	−	1.57271i	−0.0507394	−	0.0636252i
$612$		0			0
$613$	6.43653	−	28.2003i	0.259969	−	1.13900i	−0.661315	−	0.750109i	$-0.730001\pi$
$613$	6.43653	−	28.2003i	0.259969	−	1.13900i	0.921284	−	0.388891i	$-0.127142\pi$
$614$	−0.346908	−	0.435009i	−0.0140001	−	0.0175555i
$615$		0			0
$616$	18.7319	+	82.0698i	0.754730	+	3.30669i
$617$	−31.4553	+	15.1481i	−1.26634	+	0.609839i	−0.941845	−	0.336047i	$-0.890910\pi$
$617$	−31.4553	+	15.1481i	−1.26634	+	0.609839i	−0.324499	+	0.945886i	$0.605196\pi$
$618$		0			0
$619$	−10.0433	+	44.0026i	−0.403674	+	1.76861i	0.208635	+	0.977994i	$0.433098\pi$
$619$	−10.0433	+	44.0026i	−0.403674	+	1.76861i	−0.612309	+	0.790618i	$0.709759\pi$
$620$	−7.59381	−	3.65698i	−0.304975	−	0.146868i
$621$		0			0
$622$	−65.8315	−	31.7028i	−2.63960	−	1.27117i
$623$	3.44168	−	4.31574i	0.137888	−	0.172906i
$624$		0			0
$625$	−6.25412	−	3.01183i	−0.250165	−	0.120473i
$626$	26.4819			1.05843
$627$		0			0
$628$	25.2283	−	110.532i	1.00672	−	4.41072i
$629$	16.8928	−	8.13515i	0.673561	−	0.324370i
$630$		0			0
$631$	−6.51100	−	28.5266i	−0.259199	−	1.13562i	−0.922110	−	0.386927i	$-0.873537\pi$
$631$	−6.51100	−	28.5266i	−0.259199	−	1.13562i	0.662912	−	0.748698i	$-0.269321\pi$
$632$	35.4429	−	44.4440i	1.40984	−	1.76789i
$633$		0			0
$634$	−13.6971	+	60.0108i	−0.543980	+	2.38333i
$635$	0.857859	+	3.75853i	0.0340431	+	0.149153i
$636$		0			0
$637$	3.64017			0.144229
$638$	−43.2743	−	42.5619i	−1.71325	−	1.68504i
$639$		0			0
$640$	3.53244	+	4.42954i	0.139632	+	0.175093i
$641$	3.94382	+	17.2790i	0.155772	+	0.682480i	0.991144	+	0.132795i	$0.0423951\pi$
$641$	3.94382	+	17.2790i	0.155772	+	0.682480i	−0.835372	+	0.549685i	$0.814748\pi$
$642$		0			0
$643$	23.9696	+	30.0569i	0.945269	+	1.18533i	0.982545	+	0.186025i	$0.0595605\pi$
$643$	23.9696	+	30.0569i	0.945269	+	1.18533i	−0.0372759	+	0.999305i	$0.511868\pi$
$644$	71.4884	−	89.6436i	2.81704	−	3.53245i
$645$		0			0
$646$	−10.5499	+	5.08057i	−0.415081	+	0.199893i
$647$	36.5712	−	17.6118i	1.43776	−	0.692391i	0.457340	−	0.889292i	$-0.348802\pi$
$647$	36.5712	−	17.6118i	1.43776	−	0.692391i	0.980423	+	0.196901i	$0.0630878\pi$
$648$		0			0
$649$	−19.0275	−	9.16314i	−0.746893	−	0.359685i
$650$	53.6225			2.10325
$651$		0			0
$652$	47.3153	−	59.3315i	1.85301	−	2.32360i
$653$	16.5954	−	20.8099i	0.649427	−	0.814356i	−0.342719	−	0.939438i	$-0.611348\pi$
$653$	16.5954	−	20.8099i	0.649427	−	0.814356i	0.992146	+	0.125082i	$0.0399194\pi$
$654$		0			0
$655$	9.98798			0.390263
$656$	24.7649	+	11.9262i	0.966908	+	0.465638i
$657$		0			0
$658$	−2.30466	+	1.10986i	−0.0898449	+	0.0432670i
$659$	−20.8219	+	10.0273i	−0.811105	+	0.390608i	−0.792995	−	0.609228i	$-0.791479\pi$
$659$	−20.8219	+	10.0273i	−0.811105	+	0.390608i	−0.0181105	+	0.999836i	$0.505765\pi$
$660$		0			0
$661$	14.6279	−	18.3428i	0.568958	−	0.713450i	−0.411228	−	0.911533i	$-0.634900\pi$
$661$	14.6279	−	18.3428i	0.568958	−	0.713450i	0.980185	+	0.198082i	$0.0634713\pi$
$662$	11.4246	+	14.3260i	0.444029	+	0.556794i
$663$		0			0
$664$	0.749614	+	3.28427i	0.0290907	+	0.127455i
$665$	3.71015	+	4.65238i	0.143873	+	0.180412i
$666$		0			0
$667$	−4.92632	+	47.2436i	−0.190748	+	1.82928i
$668$	25.4808			0.985882
$669$		0			0
$670$	−6.39939	−	28.0376i	−0.247230	−	1.08319i
$671$	−1.50673	+	6.60141i	−0.0581666	+	0.254845i
$672$		0			0
$673$	−16.8106	+	21.0798i	−0.648000	+	0.812567i	−0.991978	−	0.126411i	$-0.959654\pi$
$673$	−16.8106	+	21.0798i	−0.648000	+	0.812567i	0.343978	+	0.938978i	$0.388226\pi$
$674$	−4.04597	−	17.7265i	−0.155845	−	0.682801i
$675$		0			0
$676$	−79.1465	+	38.1149i	−3.04409	+	1.46596i
$677$	7.46144	−	32.6907i	0.286766	−	1.25641i	−0.602168	−	0.798370i	$-0.705696\pi$
$677$	7.46144	−	32.6907i	0.286766	−	1.25641i	0.888934	−	0.458035i	$-0.151447\pi$
$678$		0			0
$679$	12.8174			0.491888
$680$	−17.4793	−	8.41757i	−0.670299	−	0.322799i
$681$		0			0
$682$	−10.9667	+	13.7517i	−0.419935	+	0.526582i
$683$	−11.1128	−	5.35164i	−0.425219	−	0.204775i	0.209021	−	0.977911i	$-0.432972\pi$
$683$	−11.1128	−	5.35164i	−0.425219	−	0.204775i	−0.634240	+	0.773137i	$0.718687\pi$
$684$		0			0
$685$	3.33717	+	1.60710i	0.127507	+	0.0614040i
$686$	−10.1199	+	44.3380i	−0.386378	+	1.69283i
$687$		0			0
$688$	11.4705	−	5.52392i	0.437310	−	0.210598i
$689$	−2.04798	−	8.97280i	−0.0780219	−	0.341836i
$690$		0			0
$691$	1.26022	+	1.58026i	0.0479410	+	0.0601161i	0.805224	−	0.592971i	$-0.202045\pi$
$691$	1.26022	+	1.58026i	0.0479410	+	0.0601161i	−0.757283	+	0.653087i	$0.773474\pi$
$692$	−11.8122	+	51.7526i	−0.449033	+	1.96734i
$693$		0			0
$694$	16.2679	+	20.3994i	0.617523	+	0.774349i
$695$	−25.8379			−0.980087
$696$		0			0
$697$	7.63365			0.289145
$698$	2.65087	+	3.32409i	0.100337	+	0.125819i
$699$		0			0
$700$	10.6445	−	46.6366i	0.402324	−	1.76270i
$701$	21.0103	+	26.3461i	0.793549	+	0.995079i	0.999862	+	0.0165931i	$0.00528200\pi$
$701$	21.0103	+	26.3461i	0.793549	+	0.995079i	−0.206313	+	0.978486i	$0.566147\pi$
$702$		0			0
$703$	−3.23552	−	14.1758i	−0.122030	−	0.534649i
$704$	−18.3770	+	8.84988i	−0.692608	+	0.333542i
$705$		0			0
$706$	−13.8954	+	60.8798i	−0.522961	+	2.29124i
$707$	−4.73137	−	2.27851i	−0.177941	−	0.0856921i
$708$		0			0
$709$	−11.4001	−	5.48999i	−0.428139	−	0.206181i	0.207389	−	0.978258i	$-0.433503\pi$
$709$	−11.4001	−	5.48999i	−0.428139	−	0.206181i	−0.635528	+	0.772078i	$0.719218\pi$
$710$	−15.1706	+	19.0234i	−0.569344	+	0.713935i
$711$		0			0
$712$	12.5743	+	6.05547i	0.471243	+	0.226938i
$713$	13.7647			0.515490
$714$		0			0
$715$	−6.26638	+	27.4548i	−0.234349	+	1.02675i
$716$	−45.1236	+	21.7304i	−1.68635	+	0.812102i
$717$		0			0
$718$	7.42820	+	32.5451i	0.277218	+	1.21457i
$719$	−8.31590	+	10.4278i	−0.310131	+	0.388892i	−0.912331	−	0.409453i	$-0.865719\pi$
$719$	−8.31590	+	10.4278i	−0.310131	+	0.388892i	0.602200	+	0.798345i	$0.294291\pi$
$720$		0			0
$721$	5.05875	−	22.1638i	0.188398	−	0.825424i
$722$	−8.92370	−	39.0973i	−0.332106	−	1.45505i
$723$		0			0
$724$	−57.7898			−2.14774
$725$	6.70018	+	18.6500i	0.248838	+	0.692644i
$726$		0			0
$727$	−26.0421	−	32.6558i	−0.965849	−	1.21114i	−0.977442	−	0.211203i	$-0.932262\pi$
$727$	−26.0421	−	32.6558i	−0.965849	−	1.21114i	0.0115932	−	0.999933i	$-0.496310\pi$
$728$	24.2169	+	106.101i	0.897536	+	3.93236i
$729$		0			0
$730$	−21.1000	−	26.4586i	−0.780948	−	0.979277i
$731$	2.20449	−	2.76435i	0.0815361	−	0.102243i
$732$		0			0
$733$	38.3484	−	18.4676i	1.41643	−	0.682116i	0.440009	−	0.897994i	$-0.354975\pi$
$733$	38.3484	−	18.4676i	1.41643	−	0.682116i	0.976420	+	0.215877i	$0.0692611\pi$
$734$	−74.0302	+	35.6511i	−2.73251	+	1.31591i
$735$		0			0
$736$	67.7770	+	32.6397i	2.49829	+	1.20311i
$737$	−42.1027			−1.55087
$738$		0			0
$739$	13.8667	−	17.3883i	0.510095	−	0.639639i	−0.458378	−	0.888757i	$-0.651569\pi$
$739$	13.8667	−	17.3883i	0.510095	−	0.639639i	0.968473	+	0.249118i	$0.0801408\pi$
$740$	26.1428	−	32.7820i	0.961028	−	1.20509i
$741$		0			0
$742$	−11.7035			−0.429648
$743$	−25.2914	−	12.1797i	−0.927853	−	0.446830i	−0.0919847	−	0.995760i	$-0.529321\pi$
$743$	−25.2914	−	12.1797i	−0.927853	−	0.446830i	−0.835868	+	0.548930i	$0.815035\pi$
$744$		0			0
$745$	1.33467	−	0.642744i	0.0488986	−	0.0235483i
$746$	11.0901	−	5.34071i	0.406038	−	0.195537i
$747$		0			0
$748$	−30.8219	+	38.6495i	−1.12696	+	1.41316i
$749$	−7.68571	−	9.63758i	−0.280830	−	0.352149i
$750$		0			0
$751$	−6.35994	−	27.8647i	−0.232077	−	1.01680i	−0.947913	−	0.318529i	$-0.896811\pi$
$751$	−6.35994	−	27.8647i	−0.232077	−	1.01680i	0.715836	−	0.698269i	$-0.246046\pi$
$752$	−1.93761	−	2.42968i	−0.0706572	−	0.0886013i
$753$		0			0
$754$	−55.9456	−	55.0245i	−2.03742	−	2.00388i
$755$	7.52781			0.273965
$756$		0			0
$757$	4.77354	+	20.9142i	0.173497	+	0.760140i	0.984541	+	0.175155i	$0.0560427\pi$
$757$	4.77354	+	20.9142i	0.173497	+	0.760140i	−0.811044	+	0.584985i	$0.801100\pi$
$758$	1.22093	−	5.34924i	0.0443461	−	0.194293i
$759$		0			0
$760$	−9.38047	+	11.7627i	−0.340265	+	0.426679i
$761$	−4.76688	−	20.8851i	−0.172799	−	0.757083i	−0.984838	−	0.173479i	$-0.944499\pi$
$761$	−4.76688	−	20.8851i	−0.172799	−	0.757083i	0.812038	−	0.583604i	$-0.198358\pi$
$762$		0			0
$763$	−43.6635	+	21.0272i	−1.58073	+	0.761237i
$764$	−1.76061	+	7.71372i	−0.0636965	+	0.279072i
$765$		0			0
$766$	37.8989			1.36934
$767$	−24.5990	−	11.8462i	−0.888217	−	0.427743i
$768$		0			0
$769$	−14.1627	+	17.7594i	−0.510719	+	0.640422i	−0.968610	−	0.248587i	$-0.920034\pi$
$769$	−14.1627	+	17.7594i	−0.510719	+	0.640422i	0.457890	+	0.889009i	$0.348605\pi$
$770$	32.2638	+	15.5374i	1.16271	+	0.559930i
$771$		0			0
$772$	−44.7933	−	21.5713i	−1.61215	−	0.776369i
$773$	−0.0401045	+	0.175709i	−0.00144246	+	0.00631983i	−0.975644	−	0.219360i	$-0.929603\pi$
$773$	−0.0401045	+	0.175709i	−0.00144246	+	0.00631983i	0.974202	+	0.225680i	$0.0724603\pi$
$774$		0			0
$775$	5.17396	−	2.49165i	0.185854	−	0.0895026i
$776$	7.21115	+	31.5941i	0.258865	+	1.13416i
$777$		0			0
$778$	3.12143	+	3.91415i	0.111909	+	0.140329i
$779$	1.31730	−	5.77147i	0.0471972	−	0.206784i
$780$		0			0
$781$	22.2099	+	27.8503i	0.794731	+	0.996562i
$782$	55.1447			1.97197
$783$		0			0
$784$	5.62369			0.200846
$785$	−17.2769	−	21.6646i	−0.616640	−	0.773241i
$786$		0			0
$787$	−9.90046	+	43.3768i	−0.352913	+	1.54621i	0.417504	+	0.908675i	$0.362905\pi$
$787$	−9.90046	+	43.3768i	−0.352913	+	1.54621i	−0.770418	+	0.637540i	$0.779952\pi$
$788$	35.5085	+	44.5263i	1.26494	+	1.58618i
$789$		0			0
$790$	−5.38103	−	23.5758i	−0.191448	−	0.838791i
$791$	19.7598	−	9.51583i	0.702578	−	0.338344i
$792$		0			0
$793$	−1.94792	+	8.53439i	−0.0691726	+	0.303065i
$794$	−70.0122	−	33.7161i	−2.48464	−	1.19654i
$795$		0			0
$796$	−21.1594	−	10.1898i	−0.749974	−	0.361169i
$797$	1.42201	−	1.78314i	0.0503700	−	0.0631620i	−0.756008	−	0.654562i	$-0.772853\pi$
$797$	1.42201	−	1.78314i	0.0503700	−	0.0631620i	0.806378	+	0.591400i	$0.201425\pi$
$798$		0			0
$799$	−0.777590	−	0.374468i	−0.0275092	−	0.0132477i
$800$	31.3849			1.10962
$801$		0			0
$802$	−9.04837	+	39.6435i	−0.319509	+	1.39986i
$803$	−44.6381	+	21.4966i	−1.57524	+	0.758598i
$804$		0			0
$805$	−6.23587	−	27.3211i	−0.219786	−	0.962944i
$806$	−14.1778	+	17.7784i	−0.499393	+	0.626219i
$807$		0			0
$808$	2.95448	−	12.9444i	0.103938	−	0.455383i
$809$	2.55396	+	11.1896i	0.0897923	+	0.393406i	0.999774	−	0.0212418i	$-0.00676199\pi$
$809$	2.55396	+	11.1896i	0.0897923	+	0.393406i	−0.909982	+	0.414648i	$0.863905\pi$
$810$		0			0
$811$	27.4524			0.963985			0.481993	−	0.876175i	$-0.339913\pi$
$811$	27.4524			0.963985			0.481993	+	0.876175i	$0.339913\pi$
$812$	−58.9616	+	37.7342i	−2.06915	+	1.32421i
$813$		0			0
$814$	−54.5566	−	68.4118i	−1.91221	−	2.39783i
$815$	−4.12727	−	18.0828i	−0.144572	−	0.633412i
$816$		0			0
$817$	−1.70958	−	2.14375i	−0.0598107	−	0.0750003i
$818$	7.86351	−	9.86053i	0.274941	−	0.344765i
$819$		0			0
$820$	15.3806	−	7.40689i	0.537113	−	0.258660i
$821$	−22.6850	+	10.9245i	−0.791712	+	0.381269i	−0.785617	−	0.618713i	$-0.787654\pi$
$821$	−22.6850	+	10.9245i	−0.791712	+	0.381269i	−0.00609509	+	0.999981i	$0.501940\pi$
$822$		0			0
$823$	−1.91828	−	0.923796i	−0.0668671	−	0.0322015i	0.400151	−	0.916449i	$-0.368958\pi$
$823$	−1.91828	−	0.923796i	−0.0668671	−	0.0322015i	−0.467018	+	0.884248i	$0.654672\pi$
$824$	57.4785			2.00236
$825$		0			0
$826$	−21.6469	+	27.1444i	−0.753193	+	0.944474i
$827$	11.4365	−	14.3409i	0.397685	−	0.498681i	−0.542164	−	0.840273i	$-0.682395\pi$
$827$	11.4365	−	14.3409i	0.397685	−	0.498681i	0.939848	+	0.341592i	$0.110966\pi$
$828$		0			0
$829$	52.9373			1.83859			0.919295	−	0.393570i	$-0.128760\pi$
$829$	52.9373			1.83859			0.919295	+	0.393570i	$0.128760\pi$
$830$	1.29113	+	0.621778i	0.0448159	+	0.0215822i
$831$		0			0
$832$	−23.7580	+	11.4412i	−0.823660	+	0.396654i
$833$	1.40714	−	0.677641i	0.0487544	−	0.0234789i
$834$		0			0
$835$	3.88296	−	4.86907i	0.134375	−	0.168501i
$836$	23.9024	+	29.9726i	0.826681	+	1.03663i
$837$		0			0
$838$	−10.9519	−	47.9835i	−0.378328	−	1.65756i
$839$	16.7410	+	20.9926i	0.577965	+	0.724745i	0.981764	−	0.190102i	$-0.0608820\pi$
$839$	16.7410	+	20.9926i	0.577965	+	0.724745i	−0.403799	+	0.914848i	$0.632311\pi$
$840$		0			0
$841$	12.1472	−	26.3334i	0.418868	−	0.908047i
$842$	−32.4018			−1.11664
$843$		0			0
$844$	20.0953	+	88.0433i	0.691709	+	3.03058i
$845$	−4.77763	+	20.9322i	−0.164356	+	0.720089i
$846$		0			0
$847$	13.7219	−	17.2068i	0.471491	−	0.591231i
$848$	−3.16392	−	13.8620i	−0.108649	−	0.476024i
$849$		0			0
$850$	20.7282	−	9.98217i	0.710971	−	0.342385i
$851$	−15.2373	+	66.7591i	−0.522329	+	2.28847i
$852$		0			0
$853$	39.8554			1.36462			0.682311	−	0.731062i	$-0.260975\pi$
$853$	39.8554			1.36462			0.682311	+	0.731062i	$0.260975\pi$
$854$	10.0293	+	4.82985i	0.343195	+	0.165274i
$855$		0			0
$856$	19.4320	−	24.3669i	0.664172	−	0.832845i
$857$	45.9338	+	22.1206i	1.56907	+	0.755624i	0.997873	−	0.0651893i	$-0.0207651\pi$
$857$	45.9338	+	22.1206i	1.56907	+	0.755624i	0.571197	+	0.820813i	$0.306479\pi$
$858$		0			0
$859$	−13.3986	−	6.45244i	−0.457155	−	0.220154i	0.191111	−	0.981569i	$-0.438791\pi$
$859$	−13.3986	−	6.45244i	−0.457155	−	0.220154i	−0.648266	+	0.761414i	$0.724505\pi$
$860$	1.75946	−	7.70872i	0.0599972	−	0.262865i
$861$		0			0
$862$	−82.5547	+	39.7563i	−2.81182	+	1.35410i
$863$	−4.55285	−	19.9473i	−0.154981	−	0.679016i	−0.991394	−	0.130915i	$-0.958208\pi$
$863$	−4.55285	−	19.9473i	−0.154981	−	0.679016i	0.836413	−	0.548100i	$-0.184649\pi$
$864$		0			0
$865$	8.08927	+	10.1436i	0.275044	+	0.344894i
$866$	3.37255	−	14.7761i	0.114604	−	0.502113i
$867$		0			0
$868$	12.6479	+	15.8599i	0.429296	+	0.538320i
$869$	−35.4027			−1.20096
$870$		0			0
$871$	−54.4309			−1.84432
$872$	−76.3961	−	95.7977i	−2.58710	−	3.24412i
$873$		0			0
$874$	9.51604	−	41.6925i	0.321885	−	1.41027i
$875$	−17.1941	−	21.5607i	−0.581267	−	0.728886i
$876$		0			0
$877$	3.43151	+	15.0344i	0.115874	+	0.507677i	0.999240	+	0.0389921i	$0.0124147\pi$
$877$	3.43151	+	15.0344i	0.115874	+	0.507677i	−0.883366	+	0.468684i	$0.844728\pi$
$878$	57.9092	−	27.8876i	1.95434	−	0.941161i
$879$		0			0
$880$	−9.68091	+	42.4148i	−0.326343	+	1.42980i
$881$	49.5884	+	23.8805i	1.67068	+	0.804555i	0.997904	+	0.0647040i	$0.0206103\pi$
$881$	49.5884	+	23.8805i	1.67068	+	0.804555i	0.672771	+	0.739851i	$0.265104\pi$
$882$		0			0
$883$	−34.2327	−	16.4856i	−1.15202	−	0.554784i	−0.242381	−	0.970181i	$-0.577929\pi$
$883$	−34.2327	−	16.4856i	−1.15202	−	0.554784i	−0.909640	+	0.415397i	$0.863643\pi$
$884$	−39.8470	+	49.9665i	−1.34020	+	1.68056i
$885$		0			0
$886$	−55.3882	−	26.6735i	−1.86080	−	0.896115i
$887$	−18.2699			−0.613444			−0.306722	−	0.951799i	$-0.599232\pi$
$887$	−18.2699			−0.613444			−0.306722	+	0.951799i	$0.599232\pi$
$888$		0			0
$889$	2.06468	−	9.04597i	0.0692473	−	0.303392i
$890$	5.34908	−	2.57598i	0.179302	−	0.0863471i
$891$		0			0
$892$	22.2223	+	97.3623i	0.744058	+	3.25993i
$893$	−0.417303	+	0.523282i	−0.0139645	+	0.0175110i
$894$		0			0
$895$	−2.72386	+	11.9340i	−0.0910486	+	0.398910i
$896$	−3.03427	−	13.2940i	−0.101368	−	0.444122i
$897$		0			0
$898$	16.6927			0.557043
$899$	−7.95491	−	2.70964i	−0.265311	−	0.0903717i
$900$		0			0
$901$	−2.46201	−	3.08726i	−0.0820213	−	0.102851i
$902$	−7.92736	−	34.7320i	−0.263952	−	1.15645i
$903$		0			0
$904$	34.5729	+	43.3530i	1.14988	+	1.44190i
$905$	−8.80644	+	11.0429i	−0.292736	+	0.367079i
$906$		0			0
$907$	−22.7706	+	10.9658i	−0.756086	+	0.364112i	−0.771884	−	0.635763i	$-0.780685\pi$
$907$	−22.7706	+	10.9658i	−0.756086	+	0.364112i	0.0157979	+	0.999875i	$0.494971\pi$
$908$	83.6730	−	40.2948i	2.77679	−	1.33723i
$909$		0			0
$910$	41.7111	+	20.0870i	1.38271	+	0.665877i
$911$	−34.3336			−1.13752			−0.568762	−	0.822502i	$-0.692578\pi$
$911$	−34.3336			−1.13752			−0.568762	+	0.822502i	$0.692578\pi$
$912$		0			0
$913$	1.30808	−	1.64028i	0.0432910	−	0.0542852i
$914$	4.23777	−	5.31400i	0.140173	−	0.175771i
$915$		0			0
$916$	97.3731			3.21730
$917$	−21.6583	−	10.4301i	−0.715222	−	0.344433i
$918$		0			0
$919$	24.2148	−	11.6612i	0.798774	−	0.384669i	0.0104619	−	0.999945i	$-0.496670\pi$
$919$	24.2148	−	11.6612i	0.798774	−	0.384669i	0.788312	+	0.615276i	$0.210956\pi$
$920$	63.8365	−	30.7420i	2.10463	−	1.01354i
$921$		0			0
$922$	−11.5527	+	14.4866i	−0.380467	+	0.477091i
$923$	28.7132	+	36.0052i	0.945107	+	1.18513i
$924$		0			0
$925$	6.35707	+	27.8521i	0.209019	+	0.915772i
$926$	29.4406	+	36.9173i	0.967478	+	1.21318i
$927$		0			0
$928$	−32.7446	−	32.2055i	−1.07489	−	1.05720i
$929$	27.4218			0.899679			0.449839	−	0.893109i	$-0.351481\pi$
$929$	27.4218			0.899679			0.449839	+	0.893109i	$0.351481\pi$
$930$		0			0
$931$	−0.269512	−	1.18081i	−0.00883291	−	0.0386995i
$932$	21.7310	−	95.2098i	0.711823	−	3.11870i
$933$		0			0
$934$	57.2437	−	71.7813i	1.87307	−	2.34876i
$935$	2.68857	+	11.7794i	0.0879256	+	0.385227i
$936$		0			0
$937$	9.28962	−	4.47364i	0.303479	−	0.146148i	−0.275947	−	0.961173i	$-0.588991\pi$
$937$	9.28962	−	4.47364i	0.303479	−	0.146148i	0.579425	+	0.815025i	$0.303277\pi$
$938$	−15.4020	+	67.4805i	−0.502892	+	2.20331i
$939$		0			0
$940$	−1.93006			−0.0629517
$941$	15.2466	+	7.34239i	0.497026	+	0.239355i	0.665565	−	0.746340i	$-0.268191\pi$
$941$	15.2466	+	7.34239i	0.497026	+	0.239355i	−0.168539	+	0.985695i	$0.553905\pi$
$942$		0			0
$943$	−17.3823	+	21.7967i	−0.566046	+	0.709799i
$944$	−38.0028	−	18.3012i	−1.23689	−	0.595653i
$945$		0			0
$946$	−14.8667	−	7.15942i	−0.483358	−	0.232773i
$947$	−4.72259	+	20.6910i	−0.153464	+	0.672368i	0.838399	+	0.545056i	$0.183492\pi$
$947$	−4.72259	+	20.6910i	−0.153464	+	0.672368i	−0.991863	+	0.127311i	$0.959365\pi$
$948$		0			0
$949$	−57.7088	+	27.7911i	−1.87331	+	0.902136i
$950$	−3.97012	−	17.3942i	−0.128808	−	0.564344i
$951$		0			0
$952$	29.1126	+	36.5060i	0.943544	+	1.18317i
$953$	−1.95472	+	8.56419i	−0.0633196	+	0.277421i	−0.996670	−	0.0815464i	$-0.974014\pi$
$953$	−1.95472	+	8.56419i	−0.0633196	+	0.277421i	0.933350	+	0.358968i	$0.116871\pi$
$954$		0			0
$955$	1.20570	+	1.51190i	0.0390157	+	0.0489241i
$956$	10.6936			0.345856
$957$		0			0
$958$	67.5637			2.18288
$959$	−5.55822	−	6.96979i	−0.179484	−	0.225066i
$960$		0			0
$961$	6.35625	−	27.8486i	0.205040	−	0.898340i
$962$	−70.5314	−	88.4436i	−2.27403	−	2.85154i
$963$		0			0
$964$	−12.3206	−	53.9800i	−0.396819	−	1.73858i
$965$	−10.9480	+	5.27226i	−0.352428	+	0.169720i
$966$		0			0
$967$	5.77072	−	25.2832i	0.185574	−	0.813052i	−0.793340	−	0.608779i	$-0.791660\pi$
$967$	5.77072	−	25.2832i	0.185574	−	0.813052i	0.978914	−	0.204273i	$-0.0654832\pi$
$968$	50.1336	+	24.1431i	1.61135	+	0.775987i
$969$		0			0
$970$	12.4205	+	5.98139i	0.398798	+	0.192051i
$971$	36.2491	−	45.4550i	1.16329	−	1.45872i	0.300051	−	0.953923i	$-0.402996\pi$
$971$	36.2491	−	45.4550i	1.16329	−	1.45872i	0.863238	−	0.504796i	$-0.168432\pi$
$972$		0			0
$973$	56.0279	+	26.9816i	1.79617	+	0.864991i
$974$	−57.3357			−1.83715
$975$		0			0
$976$	−3.00933	+	13.1847i	−0.0963264	+	0.422033i
$977$	26.9623	−	12.9844i	0.862600	−	0.415406i	0.0503613	−	0.998731i	$-0.483963\pi$
$977$	26.9623	−	12.9844i	0.862600	−	0.415406i	0.812239	+	0.583325i	$0.198248\pi$
$978$		0			0
$979$	−1.93412	−	8.47391i	−0.0618146	−	0.270827i
$980$	2.17764	−	2.73067i	0.0695621	−	0.0872281i
$981$		0			0
$982$	6.76723	−	29.6492i	0.215951	−	0.946143i
$983$	−8.94737	−	39.2010i	−0.285377	−	1.25032i	−0.890793	−	0.454409i	$-0.849851\pi$
$983$	−8.94737	−	39.2010i	−0.285377	−	1.25032i	0.605417	−	0.795909i	$-0.293007\pi$
$984$		0			0
$985$	13.9195			0.443512
$986$	−31.8694	−	10.8555i	−1.01493	−	0.345710i
$987$		0			0
$988$	30.9013	+	38.7490i	0.983102	+	1.23277i
$989$	2.87340	+	12.5892i	0.0913688	+	0.400313i
$990$		0			0
$991$	24.4225	+	30.6249i	0.775808	+	0.972832i	0.999999	−	0.00171317i	$-0.000545319\pi$
$991$	24.4225	+	30.6249i	0.775808	+	0.972832i	−0.224191	+	0.974545i	$0.571974\pi$
$992$	−8.29819	+	10.4056i	−0.263468	+	0.330378i
$993$		0			0
$994$	52.7621	−	25.4089i	1.67351	−	0.805921i
$995$	−5.17158	+	2.49050i	−0.163950	+	0.0789542i
$996$		0			0
$997$	−31.0615	−	14.9584i	−0.983727	−	0.473738i	−0.128342	−	0.991730i	$-0.540965\pi$
$997$	−31.0615	−	14.9584i	−0.983727	−	0.473738i	−0.855385	+	0.517992i	$0.826680\pi$
$998$	42.3892			1.34181
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.82.1		18
3.2	odd	2		87.2.g.a.82.3	yes	18
29.9	even	14		7569.2.a.bm.1.8		9
29.20	even	7		7569.2.a.bj.1.2		9
29.23	even	7	inner	261.2.k.c.226.1		18
87.20	odd	14		2523.2.a.r.1.8		9
87.23	odd	14		87.2.g.a.52.3	✓	18
87.38	odd	14		2523.2.a.o.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.52.3	✓	18	87.23	odd	14
87.2.g.a.82.3	yes	18	3.2	odd	2
261.2.k.c.82.1		18	1.1	even	1	trivial
261.2.k.c.226.1		18	29.23	even	7	inner
2523.2.a.o.1.2		9	87.38	odd	14
2523.2.a.r.1.8		9	87.20	odd	14
7569.2.a.bj.1.2		9	29.20	even	7
7569.2.a.bm.1.8		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)

\(f(q)\)	\(=\)	\(q+(-1.61397 - 2.02385i) q^{2} +(-1.04604 + 4.58301i) q^{4} +(0.716354 + 0.898279i) q^{5} +(-0.615328 - 2.69593i) q^{7} +(6.29911 - 3.03349i) q^{8} +(0.661812 - 2.89959i) q^{10} +(-3.92298 - 1.88921i) q^{11} +(-5.07168 - 2.44239i) q^{13} +(-4.46304 + 5.59648i) q^{14} +(-7.83521 - 3.77324i) q^{16} -2.41516 q^{17} +(-0.416772 + 1.82600i) q^{19} +(-4.86616 + 2.34342i) q^{20} +(2.50809 + 10.9886i) q^{22} +(5.49948 - 6.89613i) q^{23} +(0.818862 - 3.58767i) q^{25} +(3.24249 + 14.2063i) q^{26} +12.9991 q^{28} +(-4.53581 + 2.90283i) q^{29} +(0.972977 + 1.22007i) q^{31} +(1.89780 + 8.31482i) q^{32} +(3.89799 + 4.88793i) q^{34} +(1.98091 - 2.48398i) q^{35} +(-6.99449 + 3.36837i) q^{37} +(4.36821 - 2.10362i) q^{38} +(7.23731 + 3.48530i) q^{40} -3.16072 q^{41} +(-0.912772 + 1.14458i) q^{43} +(12.7618 - 16.0028i) q^{44} -22.8327 q^{46} +(0.321962 + 0.155049i) q^{47} +(-0.582626 + 0.280578i) q^{49} +(-8.58252 + 4.13313i) q^{50} +(16.4987 - 20.6887i) q^{52} +(1.01940 + 1.27828i) q^{53} +(-1.11320 - 4.87727i) q^{55} +(-12.0541 - 15.1154i) q^{56} +(13.1955 + 4.49474i) q^{58} +4.85026 q^{59} +(-0.346042 - 1.51611i) q^{61} +(0.898897 - 3.93832i) q^{62} +(2.92070 - 3.66245i) q^{64} +(-1.43917 - 6.30540i) q^{65} +(8.71192 - 4.19544i) q^{67} +(2.52636 - 11.0687i) q^{68} -8.22432 q^{70} +(-7.37090 - 3.54964i) q^{71} +(7.09446 - 8.89617i) q^{73} +(18.1060 + 8.71937i) q^{74} +(-7.93260 - 3.82014i) q^{76} +(-2.67925 + 11.7386i) q^{77} +(7.32556 - 3.52780i) q^{79} +(-2.22336 - 9.74119i) q^{80} +(5.10130 + 6.39683i) q^{82} +(-0.107218 + 0.469754i) q^{83} +(-1.73011 - 2.16949i) q^{85} +3.78965 q^{86} -30.4421 q^{88} +(1.24461 + 1.56070i) q^{89} +(-3.46377 + 15.1758i) q^{91} +(25.8523 + 32.4178i) q^{92} +(-0.205841 - 0.901847i) q^{94} +(-1.93881 + 0.933683i) q^{95} +(-1.03142 + 4.51895i) q^{97} +(1.50819 + 0.726305i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) \) 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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