LMFDB - Embedded newform 108.3.f.c.91.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,3,Mod(19,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("108.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	108.f (of order $6$, degree $2$, not 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:	$2.94278685509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			91.3
Root			$-0.710719 - 1.86946i$ of defining polynomial
Character	$\chi$	$=$	108.91
Dual form			108.3.f.c.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.710719 - 1.86946i) q^{2} +(-2.98976 + 2.65732i) q^{4} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +O(q^{10})$	\(q+(-0.710719 - 1.86946i) q^{2} +(-2.98976 + 2.65732i) q^{4} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +(5.35481 + 0.865806i) q^{10} +(-8.54822 + 4.93532i) q^{11} +(0.296185 - 0.513008i) q^{13} +(17.9776 + 14.6541i) q^{14} +(1.87730 - 15.8895i) q^{16} +8.87968 q^{17} +14.0989i q^{19} +(-2.18718 - 10.6259i) q^{20} +(15.3018 + 12.4729i) q^{22} +(-18.2754 - 10.5513i) q^{23} +(8.82205 + 15.2802i) q^{25} +(-1.16955 - 0.189102i) q^{26} +(14.6182 - 44.0234i) q^{28} +(-10.1764 - 17.6260i) q^{29} +(-14.3357 - 8.27670i) q^{31} +(-31.0390 + 7.78342i) q^{32} +(-6.31095 - 16.6002i) q^{34} -31.4524i q^{35} -40.6557 q^{37} +(26.3573 - 10.0203i) q^{38} +(-18.3103 + 11.6409i) q^{40} +(-21.2177 + 36.7502i) q^{41} +(32.2385 - 18.6129i) q^{43} +(12.4424 - 37.4708i) q^{44} +(-6.73658 + 41.6642i) q^{46} +(1.57134 - 0.907211i) q^{47} +(42.7423 - 74.0318i) q^{49} +(22.2958 - 27.3524i) q^{50} +(0.477704 + 2.32083i) q^{52} +21.1005 q^{53} -26.7709i q^{55} +(-92.6894 + 3.96007i) q^{56} +(-25.7186 + 31.5515i) q^{58} +(76.6879 + 44.2758i) q^{59} +(36.4925 + 63.2069i) q^{61} +(-5.28433 + 32.6823i) q^{62} +(36.6108 + 52.4943i) q^{64} +(0.803307 + 1.39137i) q^{65} +(38.3110 + 22.1189i) q^{67} +(-26.5481 + 23.5961i) q^{68} +(-58.7990 + 22.3538i) q^{70} +111.798i q^{71} -76.2003 q^{73} +(28.8948 + 76.0042i) q^{74} +(-37.4652 - 42.1522i) q^{76} +(57.2337 - 99.1316i) q^{77} +(8.30434 - 4.79451i) q^{79} +(34.7757 + 25.9570i) q^{80} +(83.7828 + 13.5466i) q^{82} +(73.6244 - 42.5070i) q^{83} +(-12.0416 + 20.8567i) q^{85} +(-57.7086 - 47.0400i) q^{86} +(-78.8931 + 3.37063i) q^{88} -64.7845 q^{89} +6.86958i q^{91} +(82.6773 - 17.0178i) q^{92} +(-2.81277 - 2.29278i) q^{94} +(-33.1157 - 19.1193i) q^{95} +(-3.59139 - 6.22047i) q^{97} +(-168.777 - 27.2892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) $ 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8	$ 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8} + 20 q^{10} - 46 q^{13} + 12 q^{14} - 17 q^{16} - 12 q^{17} - 36 q^{20} + 33 q^{22} - 30 q^{25} - 72 q^{26} + 12 q^{28} - 42 q^{29} - 87 q^{32} + 11 q^{34} + 56 q^{37} + 99 q^{38} + 68 q^{40} - 84 q^{41} + 222 q^{44} - 264 q^{46} + 58 q^{49} + 219 q^{50} + 110 q^{52} + 72 q^{53} - 270 q^{56} - 16 q^{58} - 34 q^{61} - 516 q^{62} - 254 q^{64} + 30 q^{65} - 375 q^{68} + 150 q^{70} + 116 q^{73} + 372 q^{74} - 15 q^{76} + 330 q^{77} + 720 q^{80} + 254 q^{82} - 140 q^{85} + 273 q^{86} + 75 q^{88} + 384 q^{89} - 258 q^{92} + 36 q^{94} - 148 q^{97} - 1170 q^{98}+O(q^{100}) $ 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8 + 20 * q^10 - 46 * q^13 + 12 * q^14 - 17 * q^16 - 12 * q^17 - 36 * q^20 + 33 * q^22 - 30 * q^25 - 72 * q^26 + 12 * q^28 - 42 * q^29 - 87 * q^32 + 11 * q^34 + 56 * q^37 + 99 * q^38 + 68 * q^40 - 84 * q^41 + 222 * q^44 - 264 * q^46 + 58 * q^49 + 219 * q^50 + 110 * q^52 + 72 * q^53 - 270 * q^56 - 16 * q^58 - 34 * q^61 - 516 * q^62 - 254 * q^64 + 30 * q^65 - 375 * q^68 + 150 * q^70 + 116 * q^73 + 372 * q^74 - 15 * q^76 + 330 * q^77 + 720 * q^80 + 254 * q^82 - 140 * q^85 + 273 * q^86 + 75 * q^88 + 384 * q^89 - 258 * q^92 + 36 * q^94 - 148 * q^97 - 1170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.710719	−	1.86946i	−0.355359	−	0.934730i
$2$	−0.710719	−	1.86946i	−0.355359	−	0.934730i
$3$		0			0
$3$		0			0
$4$	−2.98976	+	2.65732i	−0.747439	+	0.664330i
$5$	−1.35609	+	2.34881i	−0.271218	+	0.469763i	−0.969174	−	0.246378i	$-0.920760\pi$
$5$	−1.35609	+	2.34881i	−0.271218	+	0.469763i	0.697956	+	0.716140i	$0.254093\pi$
$6$		0			0
$7$	−10.0431	+	5.79837i	−1.43473	+	0.828339i	−0.997476	−	0.0710013i	$-0.977381\pi$
$7$	−10.0431	+	5.79837i	−1.43473	+	0.828339i	−0.437249	+	0.899340i	$0.644047\pi$
$8$	7.09263	+	3.70062i	0.886579	+	0.462578i
$9$		0			0
$10$	5.35481	+	0.865806i	0.535481	+	0.0865806i
$11$	−8.54822	+	4.93532i	−0.777111	+	0.448665i	−0.835406	−	0.549634i	$-0.814767\pi$
$11$	−8.54822	+	4.93532i	−0.777111	+	0.448665i	0.0582943	+	0.998299i	$0.481434\pi$
$12$		0			0
$13$	0.296185	−	0.513008i	0.0227835	−	0.0394622i	−0.854409	−	0.519601i	$-0.826080\pi$
$13$	0.296185	−	0.513008i	0.0227835	−	0.0394622i	0.877192	+	0.480139i	$0.159414\pi$
$14$	17.9776	+	14.6541i	1.28412	+	1.04672i
$15$		0			0
$16$	1.87730	−	15.8895i	0.117331	−	0.993093i
$17$	8.87968			0.522334			0.261167	−	0.965294i	$-0.415893\pi$
$17$	8.87968			0.522334			0.261167	+	0.965294i	$0.415893\pi$
$18$		0			0
$19$			14.0989i			0.742046i	0.928624	+	0.371023i	$0.120993\pi$
$19$			14.0989i			0.742046i	−0.928624	+	0.371023i	$0.879007\pi$
$20$	−2.18718	−	10.6259i	−0.109359	−	0.531297i
$21$		0			0
$22$	15.3018	+	12.4729i	0.695535	+	0.566952i
$23$	−18.2754	−	10.5513i	−0.794583	−	0.458753i	0.0469902	−	0.998895i	$-0.485037\pi$
$23$	−18.2754	−	10.5513i	−0.794583	−	0.458753i	−0.841574	+	0.540142i	$0.818370\pi$
$24$		0			0
$25$	8.82205	+	15.2802i	0.352882	+	0.611209i
$26$	−1.16955	−	0.189102i	−0.0449828	−	0.00727316i
$27$		0			0
$28$	14.6182	−	44.0234i	0.522080	−	1.57226i
$29$	−10.1764	−	17.6260i	−0.350910	−	0.607793i	0.635499	−	0.772101i	$-0.280794\pi$
$29$	−10.1764	−	17.6260i	−0.350910	−	0.607793i	−0.986409	+	0.164308i	$0.947461\pi$
$30$		0			0
$31$	−14.3357	−	8.27670i	−0.462441	−	0.266990i	0.250629	−	0.968083i	$-0.419362\pi$
$31$	−14.3357	−	8.27670i	−0.462441	−	0.266990i	−0.713070	+	0.701093i	$0.752696\pi$
$32$	−31.0390	+	7.78342i	−0.969968	+	0.243232i
$33$		0			0
$34$	−6.31095	−	16.6002i	−0.185616	−	0.488241i
$35$		−	31.4524i		−	0.898641i
$36$		0			0
$37$	−40.6557			−1.09880			−0.549401	−	0.835559i	$-0.685144\pi$
$37$	−40.6557			−1.09880			−0.549401	+	0.835559i	$0.685144\pi$
$38$	26.3573	−	10.0203i	0.693613	−	0.263693i
$39$		0			0
$40$	−18.3103	+	11.6409i	−0.457758	+	0.291022i
$41$	−21.2177	+	36.7502i	−0.517506	+	0.896346i	0.482288	+	0.876013i	$0.339806\pi$
$41$	−21.2177	+	36.7502i	−0.517506	+	0.896346i	−0.999793	+	0.0203330i	$0.993527\pi$
$42$		0			0
$43$	32.2385	−	18.6129i	0.749732	−	0.432858i	−0.0758649	−	0.997118i	$-0.524172\pi$
$43$	32.2385	−	18.6129i	0.749732	−	0.432858i	0.825597	+	0.564260i	$0.190838\pi$
$44$	12.4424	−	37.4708i	0.282782	−	0.851609i
$45$		0			0
$46$	−6.73658	+	41.6642i	−0.146447	+	0.905743i
$47$	1.57134	−	0.907211i	0.0334327	−	0.0193024i	−0.483191	−	0.875515i	$-0.660522\pi$
$47$	1.57134	−	0.907211i	0.0334327	−	0.0193024i	0.516623	+	0.856213i	$0.327189\pi$
$48$		0			0
$49$	42.7423	−	74.0318i	0.872291	−	1.51085i
$50$	22.2958	−	27.3524i	0.445916	−	0.547048i
$51$		0			0
$52$	0.477704	+	2.32083i	0.00918662	+	0.0446313i
$53$	21.1005			0.398122			0.199061	−	0.979987i	$-0.436211\pi$
$53$	21.1005			0.398122			0.199061	+	0.979987i	$0.436211\pi$
$54$		0			0
$55$		−	26.7709i		−	0.486744i
$56$	−92.6894	+	3.96007i	−1.65517	+	0.0707155i
$57$		0			0
$58$	−25.7186	+	31.5515i	−0.443423	+	0.543991i
$59$	76.6879	+	44.2758i	1.29980	+	0.750437i	0.980369	−	0.197174i	$-0.0631764\pi$
$59$	76.6879	+	44.2758i	1.29980	+	0.750437i	0.319427	+	0.947611i	$0.396510\pi$
$60$		0			0
$61$	36.4925	+	63.2069i	0.598238	+	1.03618i	0.993081	+	0.117431i	$0.0374657\pi$
$61$	36.4925	+	63.2069i	0.598238	+	1.03618i	−0.394843	+	0.918749i	$0.629201\pi$
$62$	−5.28433	+	32.6823i	−0.0852311	+	0.527134i
$63$		0			0
$64$	36.6108	+	52.4943i	0.572043	+	0.820223i
$65$	0.803307	+	1.39137i	0.0123586	+	0.0214057i
$66$		0			0
$67$	38.3110	+	22.1189i	0.571807	+	0.330133i	0.757871	−	0.652405i	$-0.226240\pi$
$67$	38.3110	+	22.1189i	0.571807	+	0.330133i	−0.186064	+	0.982538i	$0.559573\pi$
$68$	−26.5481	+	23.5961i	−0.390413	+	0.347002i
$69$		0			0
$70$	−58.7990	+	22.3538i	−0.839986	+	0.319341i
$71$			111.798i			1.57462i	0.616557	+	0.787310i	$0.288527\pi$
$71$			111.798i			1.57462i	−0.616557	+	0.787310i	$0.711473\pi$
$72$		0			0
$73$	−76.2003			−1.04384			−0.521920	−	0.852995i	$-0.674784\pi$
$73$	−76.2003			−1.04384			−0.521920	+	0.852995i	$0.674784\pi$
$74$	28.8948	+	76.0042i	0.390470	+	1.02708i
$75$		0			0
$76$	−37.4652	−	42.1522i	−0.492964	−	0.554635i
$77$	57.2337	−	99.1316i	0.743294	−	1.28742i
$78$		0			0
$79$	8.30434	−	4.79451i	0.105118	−	0.0606901i	−0.446519	−	0.894774i	$-0.647337\pi$
$79$	8.30434	−	4.79451i	0.105118	−	0.0606901i	0.551637	+	0.834084i	$0.314003\pi$
$80$	34.7757	+	25.9570i	0.434696	+	0.324462i
$81$		0			0
$82$	83.7828	+	13.5466i	1.02174	+	0.165203i
$83$	73.6244	−	42.5070i	0.887041	−	0.512133i	0.0140672	−	0.999901i	$-0.495522\pi$
$83$	73.6244	−	42.5070i	0.887041	−	0.512133i	0.872973	+	0.487768i	$0.162189\pi$
$84$		0			0
$85$	−12.0416	+	20.8567i	−0.141666	+	0.245373i
$86$	−57.7086	−	47.0400i	−0.671030	−	0.546977i
$87$		0			0
$88$	−78.8931	+	3.37063i	−0.896513	+	0.0383026i
$89$	−64.7845			−0.727916			−0.363958	−	0.931415i	$-0.618575\pi$
$89$	−64.7845			−0.727916			−0.363958	+	0.931415i	$0.618575\pi$
$90$		0			0
$91$			6.86958i			0.0754898i
$92$	82.6773	−	17.0178i	0.898666	−	0.184976i
$93$		0			0
$94$	−2.81277	−	2.29278i	−0.0299231	−	0.0243912i
$95$	−33.1157	−	19.1193i	−0.348586	−	0.201256i
$96$		0			0
$97$	−3.59139	−	6.22047i	−0.0370246	−	0.0641285i	0.846919	−	0.531721i	$-0.178455\pi$
$97$	−3.59139	−	6.22047i	−0.0370246	−	0.0641285i	−0.883944	+	0.467593i	$0.845121\pi$
$98$	−168.777	−	27.2892i	−1.72222	−	0.278461i
$99$		0			0
$100$	−66.9803	−	22.2412i	−0.669803	−	0.222412i
$101$	55.5037	+	96.1353i	0.549542	+	0.951834i	0.998306	+	0.0581840i	$0.0185310\pi$
$101$	55.5037	+	96.1353i	0.549542	+	0.951834i	−0.448764	+	0.893650i	$0.648136\pi$
$102$		0			0
$103$	−79.6133	−	45.9648i	−0.772945	−	0.446260i	0.0609793	−	0.998139i	$-0.480578\pi$
$103$	−79.6133	−	45.9648i	−0.772945	−	0.446260i	−0.833924	+	0.551879i	$0.813911\pi$
$104$	3.99918	−	2.54251i	0.0384537	−	0.0244472i
$105$		0			0
$106$	−14.9965	−	39.4464i	−0.141476	−	0.372136i
$107$		−	107.741i		−	1.00693i	−0.864016	−	0.503465i	$-0.832058\pi$
$107$		−	107.741i		−	1.00693i	0.864016	−	0.503465i	$-0.167942\pi$
$108$		0			0
$109$	86.5562			0.794093			0.397047	−	0.917798i	$-0.370035\pi$
$109$	86.5562			0.794093			0.397047	+	0.917798i	$0.370035\pi$
$110$	−50.0472	+	19.0266i	−0.454974	+	0.172969i
$111$		0			0
$112$	73.2793	+	170.465i	0.654279	+	1.52201i
$113$	2.35198	−	4.07376i	0.0208140	−	0.0360509i	−0.855431	−	0.517917i	$-0.826708\pi$
$113$	2.35198	−	4.07376i	0.0208140	−	0.0360509i	0.876245	+	0.481866i	$0.160041\pi$
$114$		0			0
$115$	49.5662	−	28.6170i	0.431010	−	0.248844i
$116$	77.2628	+	25.6556i	0.666059	+	0.221169i
$117$		0			0
$118$	28.2682	−	174.833i	0.239561	−	1.48163i
$119$	−89.1793	+	51.4877i	−0.749406	+	0.432670i
$120$		0			0
$121$	−11.7852	+	20.4126i	−0.0973987	+	0.168700i
$122$	92.2269	−	113.144i	0.755958	−	0.927407i
$123$		0			0
$124$	64.8540	−	13.3491i	0.523016	−	0.107654i
$125$	−115.658			−0.925267
$126$		0			0
$127$			8.37118i			0.0659148i	0.999457	+	0.0329574i	$0.0104926\pi$
$127$			8.37118i			0.0659148i	−0.999457	+	0.0329574i	$0.989507\pi$
$128$	72.1160	−	105.751i	0.563406	−	0.826180i
$129$		0			0
$130$	2.03018	−	2.49062i	0.0156168	−	0.0191586i
$131$	−115.067	−	66.4338i	−0.878372	−	0.507129i	−0.00825098	−	0.999966i	$-0.502626\pi$
$131$	−115.067	−	66.4338i	−0.878372	−	0.507129i	−0.870121	+	0.492837i	$0.835960\pi$
$132$		0			0
$133$	−81.7506	−	141.596i	−0.614666	−	1.06463i
$134$	14.1220	−	87.3413i	0.105388	−	0.651800i
$135$		0			0
$136$	62.9803	+	32.8603i	0.463090	+	0.241620i
$137$	−22.5579	−	39.0715i	−0.164656	−	0.285193i	0.771877	−	0.635772i	$-0.219318\pi$
$137$	−22.5579	−	39.0715i	−0.164656	−	0.285193i	−0.936533	+	0.350579i	$0.885985\pi$
$138$		0			0
$139$	130.744	+	75.4848i	0.940601	+	0.543056i	0.890149	−	0.455670i	$-0.150600\pi$
$139$	130.744	+	75.4848i	0.940601	+	0.543056i	0.0504522	+	0.998726i	$0.483934\pi$
$140$	83.5792	+	94.0351i	0.596994	+	0.671680i
$141$		0			0
$142$	209.002	−	79.4570i	1.47184	−	0.559556i
$143$			5.84708i			0.0408887i
$144$		0			0
$145$	55.2003			0.380692
$146$	54.1570	+	142.453i	0.370938	+	0.975708i
$147$		0			0
$148$	121.551	−	108.035i	0.821289	−	0.729968i
$149$	−71.3914	+	123.653i	−0.479137	+	0.829889i	−0.999714	−	0.0239255i	$-0.992384\pi$
$149$	−71.3914	+	123.653i	−0.479137	+	0.829889i	0.520577	+	0.853815i	$0.325717\pi$
$150$		0			0
$151$	−220.027	+	127.033i	−1.45713	+	0.841276i	−0.998869	−	0.0475407i	$-0.984862\pi$
$151$	−220.027	+	127.033i	−1.45713	+	0.841276i	−0.458263	+	0.888817i	$0.651528\pi$
$152$	−52.1746	+	99.9981i	−0.343254	+	0.657882i
$153$		0			0
$154$	−226.000	−	36.5413i	−1.46753	−	0.237281i
$155$	38.8808	−	22.4479i	0.250844	−	0.144825i
$156$		0			0
$157$	2.65361	−	4.59618i	0.0169020	−	0.0292751i	−0.857451	−	0.514566i	$-0.827953\pi$
$157$	2.65361	−	4.59618i	0.0169020	−	0.0292751i	0.874353	+	0.485291i	$0.161286\pi$
$158$	−14.8652	−	12.1171i	−0.0940836	−	0.0766904i
$159$		0			0
$160$	23.8098	−	83.4598i	0.148811	−	0.521624i
$161$	244.722			1.52001
$162$		0			0
$163$			59.5534i			0.365359i	0.983173	+	0.182679i	$0.0584770\pi$
$163$			59.5534i			0.365359i	−0.983173	+	0.182679i	$0.941523\pi$
$164$	−34.2211	−	166.256i	−0.208665	−	1.01376i
$165$		0			0
$166$	−131.791	−	107.427i	−0.793924	−	0.647152i
$167$	−85.7434	−	49.5040i	−0.513434	−	0.296431i	0.220810	−	0.975317i	$-0.429130\pi$
$167$	−85.7434	−	49.5040i	−0.513434	−	0.296431i	−0.734244	+	0.678886i	$0.762463\pi$
$168$		0			0
$169$	84.3245	+	146.054i	0.498962	+	0.864227i
$170$	47.5490	+	7.68808i	0.279700	+	0.0452240i
$171$		0			0
$172$	−46.9248	+	141.316i	−0.272819	+	0.821605i
$173$	−19.2965	−	33.4225i	−0.111540	−	0.193193i	0.804851	−	0.593477i	$-0.202245\pi$
$173$	−19.2965	−	33.4225i	−0.111540	−	0.193193i	−0.916391	+	0.400283i	$0.868912\pi$
$174$		0			0
$175$	−177.201	−	102.307i	−1.01258	−	0.584612i
$176$	62.3721	+	145.092i	0.354387	+	0.824386i
$177$		0			0
$178$	46.0436	+	121.112i	0.258672	+	0.680405i
$179$		−	36.4264i		−	0.203499i	−0.994810	−	0.101750i	$-0.967556\pi$
$179$		−	36.4264i		−	0.203499i	0.994810	−	0.101750i	$-0.0324441\pi$
$180$		0			0
$181$	−18.5921			−0.102719			−0.0513594	−	0.998680i	$-0.516355\pi$
$181$	−18.5921			−0.102719			−0.0513594	+	0.998680i	$0.516355\pi$
$182$	12.8424	−	4.88234i	0.0705626	−	0.0268260i
$183$		0			0
$184$	−90.5743	−	142.467i	−0.492252	−	0.774277i
$185$	55.1327	−	95.4927i	0.298015	−	0.516177i
$186$		0			0
$187$	−75.9055	+	43.8240i	−0.405912	+	0.234353i
$188$	−2.28716	+	6.88788i	−0.0121658	+	0.0366377i
$189$		0			0
$190$	−12.2069	+	75.4968i	−0.0642468	+	0.397352i
$191$	−244.973	+	141.435i	−1.28258	+	0.740497i	−0.977319	−	0.211772i	$-0.932077\pi$
$191$	−244.973	+	141.435i	−1.28258	+	0.740497i	−0.305260	+	0.952269i	$0.598743\pi$
$192$		0			0
$193$	−151.542	+	262.479i	−0.785193	+	1.35999i	0.143691	+	0.989623i	$0.454103\pi$
$193$	−151.542	+	262.479i	−0.785193	+	1.35999i	−0.928884	+	0.370372i	$0.879230\pi$
$194$	−9.07644	+	11.1350i	−0.0467858	+	0.0573967i
$195$		0			0
$196$	68.9371	+	334.917i	0.351720	+	1.70876i
$197$	−139.184			−0.706520			−0.353260	−	0.935525i	$-0.614927\pi$
$197$	−139.184			−0.706520			−0.353260	+	0.935525i	$0.614927\pi$
$198$		0			0
$199$			11.2337i			0.0564505i	0.999602	+	0.0282253i	$0.00898558\pi$
$199$			11.2337i			0.0564505i	−0.999602	+	0.0282253i	$0.991014\pi$
$200$	6.02512	+	141.024i	0.0301256	+	0.705121i
$201$		0			0
$202$	140.273	−	172.087i	0.694423	−	0.851916i
$203$	204.404	+	118.013i	1.00692	+	0.581344i
$204$		0			0
$205$	−57.5462	−	99.6730i	−0.280713	−	0.486210i
$206$	−29.3466	+	181.502i	−0.142459	+	0.881077i
$207$		0			0
$208$	−7.59541	−	5.66930i	−0.0365164	−	0.0272563i
$209$	−69.5825	−	120.520i	−0.332931	−	0.576653i
$210$		0			0
$211$	112.017	+	64.6728i	0.530884	+	0.306506i	0.741376	−	0.671090i	$-0.234173\pi$
$211$	112.017	+	64.6728i	0.530884	+	0.306506i	−0.210492	+	0.977595i	$0.567507\pi$
$212$	−63.0852	+	56.0707i	−0.297572	+	0.264484i
$213$		0			0
$214$	−201.418	+	76.5739i	−0.941207	+	0.357822i
$215$			100.963i			0.469595i
$216$		0			0
$217$	191.966			0.884634
$218$	−61.5171	−	161.813i	−0.282189	−	0.742263i
$219$		0			0
$220$	71.1389	+	80.0386i	0.323359	+	0.363812i
$221$	2.63003	−	4.55535i	0.0119006	−	0.0206124i
$222$		0			0
$223$	209.210	−	120.787i	0.938159	−	0.541647i	0.0487765	−	0.998810i	$-0.484468\pi$
$223$	209.210	−	120.787i	0.938159	−	0.541647i	0.889383	+	0.457163i	$0.151134\pi$
$224$	266.596	−	258.145i	1.19016	−	1.15243i
$225$		0			0
$226$	−9.28732	−	1.50164i	−0.0410943	−	0.00664444i
$227$	330.710	−	190.936i	1.45687	−	0.841126i	0.458016	−	0.888944i	$-0.348560\pi$
$227$	330.710	−	190.936i	1.45687	−	0.841126i	0.998856	+	0.0478181i	$0.0152268\pi$
$228$		0			0
$229$	74.6642	−	129.322i	0.326044	−	0.564725i	−0.655679	−	0.755040i	$-0.727617\pi$
$229$	74.6642	−	129.322i	0.326044	−	0.564725i	0.981723	+	0.190315i	$0.0609508\pi$
$230$	−88.7260	−	72.3233i	−0.385765	−	0.314449i
$231$		0			0
$232$	−6.95007	−	162.674i	−0.0299572	−	0.701180i
$233$	218.934			0.939631			0.469816	−	0.882765i	$-0.344320\pi$
$233$	218.934			0.939631			0.469816	+	0.882765i	$0.344320\pi$
$234$		0			0
$235$			4.92103i			0.0209406i
$236$	−346.933	+	71.4105i	−1.47006	+	0.302587i
$237$		0			0
$238$	159.636	+	130.124i	0.670738	+	0.546739i
$239$	218.254	+	126.009i	0.913197	+	0.527235i	0.881458	−	0.472262i	$-0.156562\pi$
$239$	218.254	+	126.009i	0.913197	+	0.527235i	0.0317388	+	0.999496i	$0.489896\pi$
$240$		0			0
$241$	−226.014	−	391.467i	−0.937816	−	1.62435i	−0.769534	−	0.638606i	$-0.779511\pi$
$241$	−226.014	−	391.467i	−0.937816	−	1.62435i	−0.168282	−	0.985739i	$-0.553822\pi$
$242$	46.5366	+	7.52439i	0.192300	+	0.0310925i
$243$		0			0
$244$	−277.065	−	92.0011i	−1.13551	−	0.377053i
$245$	115.925	+	200.787i	0.473162	+	0.819540i
$246$		0			0
$247$	7.23284	+	4.17588i	0.0292828	+	0.0169064i
$248$	−71.0486	−	111.754i	−0.286486	−	0.450623i
$249$		0			0
$250$	82.2006	+	216.219i	0.328802	+	0.864874i
$251$			139.429i			0.555492i	0.960655	+	0.277746i	$0.0895874\pi$
$251$			139.429i			0.555492i	−0.960655	+	0.277746i	$0.910413\pi$
$252$		0			0
$253$	208.297			0.823306
$254$	15.6496	−	5.94955i	0.0616125	−	0.0234234i
$255$		0			0
$256$	−248.951	−	59.6587i	−0.972467	−	0.233042i
$257$	−235.308	+	407.565i	−0.915594	+	1.58586i	−0.109564	+	0.993980i	$0.534946\pi$
$257$	−235.308	+	407.565i	−0.915594	+	1.58586i	−0.806029	+	0.591875i	$0.798388\pi$
$258$		0			0
$259$	408.308	−	235.737i	1.57648	−	0.910181i
$260$	−6.09901	−	2.02521i	−0.0234577	−	0.00778928i
$261$		0			0
$262$	−42.4152	+	262.328i	−0.161890	+	1.00125i
$263$	22.2028	−	12.8188i	0.0844214	−	0.0487407i	−0.457195	−	0.889366i	$-0.651146\pi$
$263$	22.2028	−	12.8188i	0.0844214	−	0.0487407i	0.541616	+	0.840626i	$0.317813\pi$
$264$		0			0
$265$	−28.6141	+	49.5610i	−0.107978	+	0.187023i
$266$	−206.607	+	253.464i	−0.776717	+	0.952874i
$267$		0			0
$268$	−173.318	+	35.6746i	−0.646708	+	0.133114i
$269$	−8.15075			−0.0303002			−0.0151501	−	0.999885i	$-0.504823\pi$
$269$	−8.15075			−0.0303002			−0.0151501	+	0.999885i	$0.504823\pi$
$270$		0			0
$271$		−	401.979i		−	1.48332i	−0.670777	−	0.741659i	$-0.734039\pi$
$271$		−	401.979i		−	1.48332i	0.670777	−	0.741659i	$-0.265961\pi$
$272$	16.6698	−	141.094i	0.0612861	−	0.518726i
$273$		0			0
$274$	−57.0102	+	69.9400i	−0.208067	+	0.255255i
$275$	−150.826	−	87.0792i	−0.548457	−	0.316652i
$276$		0			0
$277$	56.2021	+	97.3449i	0.202896	+	0.351426i	0.949460	−	0.313887i	$-0.101631\pi$
$277$	56.2021	+	97.3449i	0.202896	+	0.351426i	−0.746565	+	0.665313i	$0.768298\pi$
$278$	48.1939	−	298.068i	0.173359	−	1.07219i
$279$		0			0
$280$	116.394	−	223.080i	0.415691	−	0.796716i
$281$	−268.867	−	465.692i	−0.956823	−	1.65727i	−0.730141	−	0.683296i	$-0.760546\pi$
$281$	−268.867	−	465.692i	−0.956823	−	1.65727i	−0.226681	−	0.973969i	$-0.572788\pi$
$282$		0			0
$283$	122.303	+	70.6114i	0.432164	+	0.249510i	0.700268	−	0.713880i	$-0.253064\pi$
$283$	122.303	+	70.6114i	0.432164	+	0.249510i	−0.268104	+	0.963390i	$0.586397\pi$
$284$	−297.083	−	334.249i	−1.04607	−	1.17693i
$285$		0			0
$286$	10.9309	−	4.15563i	0.0382199	−	0.0145302i
$287$		−	492.113i		−	1.71468i
$288$		0			0
$289$	−210.151			−0.727167
$290$	−39.2319	−	103.195i	−0.135282	−	0.355844i
$291$		0			0
$292$	227.820	−	202.489i	0.780207	−	0.693454i
$293$	230.291	−	398.875i	0.785975	−	1.36135i	−0.142440	−	0.989803i	$-0.545495\pi$
$293$	230.291	−	398.875i	0.785975	−	1.36135i	0.928415	−	0.371545i	$-0.121172\pi$
$294$		0			0
$295$	−207.991	+	120.084i	−0.705055	+	0.407064i
$296$	−288.356	−	150.451i	−0.974175	−	0.508282i
$297$		0			0
$298$	281.904	+	45.5804i	0.945988	+	0.152954i
$299$	−10.8258	+	6.25029i	−0.0362068	+	0.0209040i
$300$		0			0
$301$	−215.849	+	373.862i	−0.717107	+	1.24206i
$302$	393.860	+	321.047i	1.30417	+	1.06307i
$303$		0			0
$304$	224.024	+	26.4678i	0.736921	+	0.0870653i
$305$	−197.948			−0.649011
$306$		0			0
$307$		−	210.322i		−	0.685089i	−0.939502	−	0.342545i	$-0.888711\pi$
$307$		−	210.322i		−	0.685089i	0.939502	−	0.342545i	$-0.111289\pi$
$308$	92.3096	+	448.468i	0.299707	+	1.45606i
$309$		0			0
$310$	−69.5987	−	56.7320i	−0.224512	−	0.183007i
$311$	110.993	+	64.0821i	0.356892	+	0.206052i	0.667717	−	0.744416i	$-0.267272\pi$
$311$	110.993	+	64.0821i	0.356892	+	0.206052i	−0.310824	+	0.950467i	$0.600605\pi$
$312$		0			0
$313$	−3.62140	−	6.27245i	−0.0115700	−	0.0200398i	0.860182	−	0.509986i	$-0.170350\pi$
$313$	−3.62140	−	6.27245i	−0.0115700	−	0.0200398i	−0.871752	+	0.489947i	$0.837016\pi$
$314$	−10.4784	−	1.69422i	−0.0333705	−	0.00539560i
$315$		0			0
$316$	−12.0874	+	36.4017i	−0.0382513	+	0.115195i
$317$	120.145	+	208.098i	0.379007	+	0.656460i	0.990918	−	0.134467i	$-0.0429322\pi$
$317$	120.145	+	208.098i	0.379007	+	0.656460i	−0.611911	+	0.790927i	$0.709599\pi$
$318$		0			0
$319$	173.980	+	100.447i	0.545392	+	0.314882i
$320$	−172.947	+	14.8050i	−0.540459	+	0.0462656i
$321$		0			0
$322$	−173.928	−	457.498i	−0.540151	−	1.42080i
$323$			125.194i			0.387596i
$324$		0			0
$325$	10.4518			0.0321595
$326$	111.333	−	42.3258i	0.341512	−	0.129834i
$327$		0			0
$328$	−286.488	+	182.137i	−0.873439	+	0.555294i
$329$	−10.5207	+	18.2224i	−0.0319778	+	0.0553872i
$330$		0			0
$331$	−370.385	+	213.842i	−1.11899	+	0.646048i	−0.941142	−	0.338011i	$-0.890246\pi$
$331$	−370.385	+	213.842i	−1.11899	+	0.646048i	−0.177845	+	0.984058i	$0.556913\pi$
$332$	−107.164	+	322.729i	−0.322784	+	0.972076i
$333$		0			0
$334$	−31.6062	+	195.477i	−0.0946295	+	0.585261i
$335$	−103.906	+	59.9904i	−0.310168	+	0.179076i
$336$		0			0
$337$	152.442	−	264.037i	0.452349	−	0.783492i	−0.546182	−	0.837666i	$-0.683919\pi$
$337$	152.442	−	264.037i	0.452349	−	0.783492i	0.998531	+	0.0541746i	$0.0172528\pi$
$338$	213.112	−	261.445i	0.630508	−	0.773506i
$339$		0			0
$340$	−19.4214	−	94.3550i	−0.0571218	−	0.277515i
$341$	163.393			0.479157
$342$		0			0
$343$			423.102i			1.23353i
$344$	297.535	−	12.7119i	0.864927	−	0.0369532i
$345$		0			0
$346$	−48.7676	+	59.8280i	−0.140947	+	0.172913i
$347$	−146.406	−	84.5276i	−0.421919	−	0.243595i	0.273979	−	0.961736i	$-0.411660\pi$
$347$	−146.406	−	84.5276i	−0.421919	−	0.243595i	−0.695898	+	0.718140i	$0.744994\pi$
$348$		0			0
$349$	107.298	+	185.846i	0.307444	+	0.532509i	0.977802	−	0.209529i	$-0.0671930\pi$
$349$	107.298	+	185.846i	0.307444	+	0.532509i	−0.670358	+	0.742037i	$0.733860\pi$
$350$	−65.3188	+	403.982i	−0.186625	+	1.15423i
$351$		0			0
$352$	226.915	−	219.722i	0.644644	−	0.624209i
$353$	275.895	+	477.865i	0.781574	+	1.35373i	0.931025	+	0.364956i	$0.118916\pi$
$353$	275.895	+	477.865i	0.781574	+	1.35373i	−0.149451	+	0.988769i	$0.547751\pi$
$354$		0			0
$355$	−262.593	−	151.608i	−0.739698	−	0.427065i
$356$	193.690	−	172.153i	0.544073	−	0.483577i
$357$		0			0
$358$	−68.0977	+	25.8889i	−0.190217	+	0.0723155i
$359$			554.828i			1.54548i	0.634721	+	0.772741i	$0.281115\pi$
$359$			554.828i			1.54548i	−0.634721	+	0.772741i	$0.718885\pi$
$360$		0			0
$361$	162.222			0.449367
$362$	13.2138	+	34.7572i	0.0365021	+	0.0960143i
$363$		0			0
$364$	−18.2547	−	20.5384i	−0.0501502	−	0.0564241i
$365$	103.334	−	178.980i	0.283108	−	0.490357i
$366$		0			0
$367$	−145.642	+	84.0864i	−0.396845	+	0.229118i	−0.685122	−	0.728429i	$-0.740251\pi$
$367$	−145.642	+	84.0864i	−0.396845	+	0.229118i	0.288277	+	0.957547i	$0.406918\pi$
$368$	−201.963	+	270.579i	−0.548814	+	0.735269i
$369$		0			0
$370$	−217.704	−	35.2000i	−0.588388	−	0.0951350i
$371$	−211.913	+	122.348i	−0.571195	+	0.329780i
$372$		0			0
$373$	171.699	−	297.391i	0.460318	−	0.797295i	−0.538658	−	0.842524i	$-0.681069\pi$
$373$	171.699	−	297.391i	0.460318	−	0.797295i	0.998977	+	0.0452296i	$0.0144020\pi$
$374$	135.875	+	110.756i	0.363301	+	0.296138i
$375$		0			0
$376$	14.5021	−	0.619590i	0.0385695	−	0.00164785i
$377$	−12.0564			−0.0319798
$378$		0			0
$379$			602.392i			1.58943i	0.606986	+	0.794713i	$0.292379\pi$
$379$			602.392i			1.58943i	−0.606986	+	0.794713i	$0.707621\pi$
$380$	149.814	−	30.8367i	0.394247	−	0.0811493i
$381$		0			0
$382$	438.514	+	357.446i	1.14794	+	0.935722i
$383$	−315.762	−	182.305i	−0.824443	−	0.475992i	0.0275035	−	0.999622i	$-0.491244\pi$
$383$	−315.762	−	182.305i	−0.824443	−	0.475992i	−0.851946	+	0.523630i	$0.824578\pi$
$384$		0			0
$385$	155.228	+	268.862i	0.403189	+	0.698344i
$386$	598.398	+	96.7534i	1.55025	+	0.250657i
$387$		0			0
$388$	27.2672	+	9.05422i	0.0702762	+	0.0233356i
$389$	−107.326	−	185.893i	−0.275901	−	0.477875i	0.694461	−	0.719530i	$-0.255643\pi$
$389$	−107.326	−	185.893i	−0.275901	−	0.477875i	−0.970362	+	0.241656i	$0.922310\pi$
$390$		0			0
$391$	−162.280	−	93.6923i	−0.415038	−	0.239622i
$392$	577.119	−	366.907i	1.47224	−	0.935987i
$393$		0			0
$394$	98.9209	+	260.200i	0.251068	+	0.660405i
$395$			26.0071i			0.0658409i
$396$		0			0
$397$	−684.628			−1.72450			−0.862251	−	0.506480i	$-0.830946\pi$
$397$	−684.628			−1.72450			−0.862251	+	0.506480i	$0.830946\pi$
$398$	21.0009	−	7.98397i	0.0527660	−	0.0200602i
$399$		0			0
$400$	259.357	−	111.492i	0.648392	−	0.278731i
$401$	−95.1918	+	164.877i	−0.237386	+	0.411164i	−0.959963	−	0.280125i	$-0.909624\pi$
$401$	−95.1918	+	164.877i	−0.237386	+	0.411164i	0.722577	+	0.691290i	$0.242957\pi$
$402$		0			0
$403$	−8.49203	+	4.90287i	−0.0210720	+	0.0121659i
$404$	−421.405	−	139.930i	−1.04308	−	0.346361i
$405$		0			0
$406$	75.3463	−	466.000i	0.185582	−	1.14778i
$407$	347.534	−	200.649i	0.853892	−	0.492995i
$408$		0			0
$409$	188.978	−	327.320i	0.462049	−	0.800293i	−0.537014	−	0.843574i	$-0.680448\pi$
$409$	188.978	−	327.320i	0.462049	−	0.800293i	0.999063	+	0.0432806i	$0.0137809\pi$
$410$	−145.435	+	178.420i	−0.354721	+	0.435170i
$411$		0			0
$412$	360.168	−	74.1345i	0.874193	−	0.179938i
$413$	−1026.91			−2.48647
$414$		0			0
$415$			230.573i			0.555598i
$416$	−5.20034	+	18.2286i	−0.0125008	+	0.0438187i
$417$		0			0
$418$	−175.854	+	215.738i	−0.420704	+	0.516119i
$419$	−267.326	−	154.341i	−0.638009	−	0.368355i	0.145838	−	0.989308i	$-0.453412\pi$
$419$	−267.326	−	154.341i	−0.638009	−	0.368355i	−0.783847	+	0.620954i	$0.786745\pi$
$420$		0			0
$421$	176.834	+	306.286i	0.420034	+	0.727521i	0.995942	−	0.0899938i	$-0.0286847\pi$
$421$	176.834	+	306.286i	0.420034	+	0.727521i	−0.575908	+	0.817514i	$0.695351\pi$
$422$	41.2909	−	255.374i	0.0978457	−	0.605153i
$423$		0			0
$424$	149.658	+	78.0848i	0.352966	+	0.184162i
$425$	78.3369	+	135.684i	0.184322	+	0.319255i
$426$		0			0
$427$	−732.995	−	423.195i	−1.71662	−	0.991088i
$428$	286.304	+	322.121i	0.668934	+	0.752619i
$429$		0			0
$430$	188.746	−	71.7563i	0.438945	−	0.166875i
$431$		−	472.777i		−	1.09693i	−0.836174	−	0.548465i	$-0.815213\pi$
$431$		−	472.777i		−	1.09693i	0.836174	−	0.548465i	$-0.184787\pi$
$432$		0			0
$433$	61.4188			0.141845			0.0709224	−	0.997482i	$-0.477406\pi$
$433$	61.4188			0.141845			0.0709224	+	0.997482i	$0.477406\pi$
$434$	−136.434	−	358.872i	−0.314363	−	0.826893i
$435$		0			0
$436$	−258.782	+	230.007i	−0.593537	+	0.527540i
$437$	148.762	−	257.663i	0.340416	−	0.589618i
$438$		0			0
$439$	354.347	−	204.582i	0.807169	−	0.466019i	−0.0388030	−	0.999247i	$-0.512354\pi$
$439$	354.347	−	204.582i	0.807169	−	0.466019i	0.845972	+	0.533228i	$0.179021\pi$
$440$	99.0691	−	189.876i	0.225157	−	0.431537i
$441$		0			0
$442$	−10.3853	−	1.67917i	−0.0234960	−	0.00379902i
$443$	−668.806	+	386.136i	−1.50972	+	0.871638i	−0.509785	+	0.860302i	$0.670275\pi$
$443$	−668.806	+	386.136i	−1.50972	+	0.871638i	−0.999936	+	0.0113360i	$0.996392\pi$
$444$		0			0
$445$	87.8536	−	152.167i	0.197424	−	0.341948i
$446$	−374.496	−	305.263i	−0.839677	−	0.684446i
$447$		0			0
$448$	−672.066	−	314.921i	−1.50015	−	0.702949i
$449$	789.037			1.75732			0.878660	−	0.477448i	$-0.158438\pi$
$449$	789.037			1.75732			0.878660	+	0.477448i	$0.158438\pi$
$450$		0			0
$451$		−	418.865i		−	0.928747i
$452$	3.79341	+	18.4295i	0.00839250	+	0.0407733i
$453$		0			0
$454$	−591.988	−	482.548i	−1.30394	−	1.06288i
$455$	−16.1354	−	9.31575i	−0.0354623	−	0.0204742i
$456$		0			0
$457$	138.165	+	239.309i	0.302331	+	0.523653i	0.976664	−	0.214775i	$-0.0689018\pi$
$457$	138.165	+	239.309i	0.302331	+	0.523653i	−0.674332	+	0.738428i	$0.735568\pi$
$458$	−294.828	−	47.6700i	−0.643728	−	0.104083i
$459$		0			0
$460$	−72.1462	+	217.271i	−0.156840	+	0.472329i
$461$	294.041	+	509.295i	0.637834	+	1.10476i	0.985907	+	0.167293i	$0.0535027\pi$
$461$	294.041	+	509.295i	0.637834	+	1.10476i	−0.348073	+	0.937467i	$0.613164\pi$
$462$		0			0
$463$	677.285	+	391.031i	1.46282	+	0.844558i	0.999141	−	0.0414459i	$-0.0131964\pi$
$463$	677.285	+	391.031i	1.46282	+	0.844558i	0.463677	+	0.886004i	$0.346530\pi$
$464$	−299.172	+	128.608i	−0.644768	+	0.277173i
$465$		0			0
$466$	−155.601	−	409.288i	−0.333907	−	0.878301i
$467$		−	663.203i		−	1.42014i	−0.704133	−	0.710068i	$-0.748664\pi$
$467$		−	663.203i		−	1.42014i	0.704133	−	0.710068i	$-0.251336\pi$
$468$		0			0
$469$	−513.014			−1.09385
$470$	9.19967	−	3.49747i	0.0195738	−	0.00744143i
$471$		0			0
$472$	380.071	+	597.825i	0.805235	+	1.26658i
$473$	−183.721	+	318.214i	−0.388417	+	0.672758i
$474$		0			0
$475$	−215.434	+	124.381i	−0.453546	+	0.261855i
$476$	129.805	−	390.914i	0.272700	−	0.821247i
$477$		0			0
$478$	80.4516	−	497.574i	0.168309	−	1.04095i
$479$	562.018	−	324.481i	1.17331	−	0.677414i	0.218856	−	0.975757i	$-0.429767\pi$
$479$	562.018	−	324.481i	1.17331	−	0.677414i	0.954459	+	0.298344i	$0.0964341\pi$
$480$		0			0
$481$	−12.0416	+	20.8567i	−0.0250346	+	0.0433611i
$482$	−571.200	+	700.746i	−1.18506	+	1.45383i
$483$		0			0
$484$	−19.0079	−	92.3460i	−0.0392725	−	0.190798i
$485$	19.4810			0.0401669
$486$		0			0
$487$		−	282.104i		−	0.579269i	−0.957137	−	0.289635i	$-0.906466\pi$
$487$		−	282.104i		−	0.579269i	0.957137	−	0.289635i	$-0.0935338\pi$
$488$	24.9230	+	583.348i	0.0510717	+	1.19539i
$489$		0			0
$490$	292.974	−	359.420i	0.597906	−	0.733510i
$491$	652.933	+	376.971i	1.32980	+	0.767762i	0.985269	−	0.171012i	$-0.0547036\pi$
$491$	652.933	+	376.971i	1.32980	+	0.767762i	0.344534	+	0.938774i	$0.388037\pi$
$492$		0			0
$493$	−90.3630	−	156.513i	−0.183292	−	0.317471i
$494$	2.66613	−	16.4894i	0.00539702	−	0.0333793i
$495$		0			0
$496$	−158.425	+	212.248i	−0.319405	+	0.427920i
$497$	−648.247	−	1122.80i	−1.30432	−	2.25915i
$498$		0			0
$499$	446.169	+	257.596i	0.894126	+	0.516224i	0.875290	−	0.483599i	$-0.160671\pi$
$499$	446.169	+	257.596i	0.894126	+	0.516224i	0.0188362	+	0.999823i	$0.494004\pi$
$500$	345.790	−	307.341i	0.691581	−	0.614682i
$501$		0			0
$502$	260.656	−	99.0945i	0.519235	−	0.197399i
$503$			523.660i			1.04107i	0.853839	+	0.520537i	$0.174268\pi$
$503$			523.660i			1.04107i	−0.853839	+	0.520537i	$0.825732\pi$
$504$		0			0
$505$	−301.072			−0.596182
$506$	−148.040	−	389.402i	−0.292570	−	0.769569i
$507$		0			0
$508$	−22.2449	−	25.0278i	−0.0437892	−	0.0492673i
$509$	267.685	−	463.645i	0.525905	−	0.910893i	−0.473640	−	0.880719i	$-0.657060\pi$
$509$	267.685	−	463.645i	0.525905	−	0.910893i	0.999545	−	0.0301749i	$-0.00960643\pi$
$510$		0			0
$511$	765.285	−	441.838i	1.49762	−	0.864653i
$512$	65.4050	+	507.805i	0.127744	+	0.991807i
$513$		0			0
$514$	929.163	+	150.234i	1.80771	+	0.292284i
$515$	215.925	−	124.665i	0.419273	−	0.242067i
$516$		0			0
$517$	−8.95475	+	15.5101i	−0.0173206	+	0.0300002i
$518$	−730.893	−	595.773i	−1.41099	−	1.15014i
$519$		0			0
$520$	0.548628	+	12.8412i	0.00105505	+	0.0246946i
$521$	−177.268			−0.340246			−0.170123	−	0.985423i	$-0.554416\pi$
$521$	−177.268			−0.340246			−0.170123	+	0.985423i	$0.554416\pi$
$522$		0			0
$523$		−	444.206i		−	0.849343i	−0.905347	−	0.424672i	$-0.860390\pi$
$523$		−	444.206i		−	0.849343i	0.905347	−	0.424672i	$-0.139610\pi$
$524$	520.558	−	107.148i	0.993431	−	0.204481i
$525$		0			0
$526$	−39.7442	−	32.3967i	−0.0755593	−	0.0615907i
$527$	−127.296	−	73.4944i	−0.241548	−	0.139458i
$528$		0			0
$529$	−41.8394	−	72.4679i	−0.0790914	−	0.136990i
$530$	112.989	+	18.2689i	0.213187	+	0.0344696i
$531$		0			0
$532$	620.681	+	206.101i	1.16669	+	0.387407i
$533$	12.5688	+	21.7697i	0.0235812	+	0.0408438i
$534$		0			0
$535$	253.065	+	146.107i	0.473018	+	0.273097i
$536$	189.872	+	298.656i	0.354239	+	0.557194i
$537$		0			0
$538$	5.79289	+	15.2375i	0.0107675	+	0.0283225i
$539$			843.787i			1.56547i
$540$		0			0
$541$	571.163			1.05575			0.527877	−	0.849321i	$-0.322988\pi$
$541$	571.163			1.05575			0.527877	+	0.849321i	$0.322988\pi$
$542$	−751.484	+	285.694i	−1.38650	+	0.527111i
$543$		0			0
$544$	−275.616	+	69.1142i	−0.506647	+	0.127048i
$545$	−117.378	+	203.304i	−0.215372	+	0.373036i
$546$		0			0
$547$	−139.875	+	80.7569i	−0.255713	+	0.147636i	−0.622377	−	0.782717i	$-0.713833\pi$
$547$	−139.875	+	80.7569i	−0.255713	+	0.147636i	0.366664	+	0.930353i	$0.380500\pi$
$548$	171.268	+	56.8706i	0.312533	+	0.103779i
$549$		0			0
$550$	−55.5965	+	343.851i	−0.101085	+	0.625184i
$551$	248.507	−	143.476i	0.451011	−	0.260391i
$552$		0			0
$553$	−55.6008	+	96.3034i	−0.100544	+	0.174147i
$554$	142.038	−	174.252i	0.256387	−	0.314535i
$555$		0			0
$556$	−591.479	+	121.746i	−1.06381	+	0.218968i
$557$	568.917			1.02139			0.510697	−	0.859761i	$-0.329387\pi$
$557$	568.917			1.02139			0.510697	+	0.859761i	$0.329387\pi$
$558$		0			0
$559$		−	22.0515i		−	0.0394481i
$560$	−499.763	−	59.0457i	−0.892434	−	0.105439i
$561$		0			0
$562$	−679.503	+	833.612i	−1.20908	+	1.48330i
$563$	250.527	+	144.642i	0.444985	+	0.256912i	0.705710	−	0.708501i	$-0.250628\pi$
$563$	250.527	+	144.642i	0.444985	+	0.256912i	−0.260725	+	0.965413i	$0.583962\pi$
$564$		0			0
$565$	6.37900	+	11.0487i	0.0112903	+	0.0195553i
$566$	45.0824	−	278.824i	0.0796510	−	0.492623i
$567$		0			0
$568$	−413.723	+	792.942i	−0.728385	+	1.39603i
$569$	223.117	+	386.450i	0.392121	+	0.679174i	0.992729	−	0.120370i	$-0.0384079\pi$
$569$	223.117	+	386.450i	0.392121	+	0.679174i	−0.600608	+	0.799544i	$0.705075\pi$
$570$		0			0
$571$	−372.386	−	214.997i	−0.652164	−	0.376527i	0.137121	−	0.990554i	$-0.456215\pi$
$571$	−372.386	−	214.997i	−0.652164	−	0.376527i	−0.789285	+	0.614027i	$0.789549\pi$
$572$	−15.5376	−	17.4813i	−0.0271636	−	0.0305618i
$573$		0			0
$574$	−919.986	+	349.754i	−1.60276	+	0.609328i
$575$		−	372.337i		−	0.647542i
$576$		0			0
$577$	50.9694			0.0883353			0.0441676	−	0.999024i	$-0.485936\pi$
$577$	50.9694			0.0883353			0.0441676	+	0.999024i	$0.485936\pi$
$578$	149.359	+	392.869i	0.258406	+	0.679705i
$579$		0			0
$580$	−165.035	+	146.685i	−0.284544	+	0.252905i
$581$	−492.943	+	853.803i	−0.848440	+	1.46954i
$582$		0			0
$583$	−180.371	+	104.137i	−0.309385	+	0.178623i
$584$	−540.460	−	281.989i	−0.925446	−	0.482857i
$585$		0			0
$586$	−909.353	−	147.031i	−1.55180	−	0.250906i
$587$	−643.771	+	371.681i	−1.09671	+	0.633188i	−0.935356	−	0.353708i	$-0.884921\pi$
$587$	−643.771	+	371.681i	−1.09671	+	0.633188i	−0.161358	+	0.986896i	$0.551587\pi$
$588$		0			0
$589$	116.692	−	202.117i	0.198119	−	0.343152i
$590$	372.315	+	303.485i	0.631042	+	0.514382i
$591$		0			0
$592$	−76.3230	+	645.998i	−0.128924	+	1.09121i
$593$	382.547			0.645104			0.322552	−	0.946552i	$-0.395459\pi$
$593$	382.547			0.645104			0.322552	+	0.946552i	$0.395459\pi$
$594$		0			0
$595$		−	279.287i		−	0.469391i
$596$	−115.144	−	559.404i	−0.193195	−	0.938597i
$597$		0			0
$598$	19.3788	+	15.7962i	0.0324060	+	0.0264151i
$599$	856.248	+	494.355i	1.42946	+	0.825301i	0.997078	−	0.0763888i	$-0.0243390\pi$
$599$	856.248	+	494.355i	1.42946	+	0.825301i	0.432384	+	0.901689i	$0.357672\pi$
$600$		0			0
$601$	−263.280	−	456.015i	−0.438070	−	0.758760i	0.559470	−	0.828850i	$-0.311005\pi$
$601$	−263.280	−	456.015i	−0.438070	−	0.758760i	−0.997541	+	0.0700905i	$0.977671\pi$
$602$	852.327	+	137.811i	1.41583	+	0.228921i
$603$		0			0
$604$	320.261	−	964.479i	0.530233	−	1.59682i
$605$	−31.9637	−	55.3627i	−0.0528325	−	0.0915086i
$606$		0			0
$607$	−447.631	−	258.440i	−0.737448	−	0.425766i	0.0836928	−	0.996492i	$-0.473329\pi$
$607$	−447.631	−	258.440i	−0.737448	−	0.425766i	−0.821141	+	0.570726i	$0.806662\pi$
$608$	−109.737	−	437.615i	−0.180489	−	0.719761i
$609$		0			0
$610$	140.686	+	370.057i	0.230632	+	0.606650i
$611$		−	1.07481i		−	0.00175910i
$612$		0			0
$613$	762.957			1.24463			0.622314	−	0.782768i	$-0.286193\pi$
$613$	762.957			1.24463			0.622314	+	0.782768i	$0.286193\pi$
$614$	−393.189	+	149.480i	−0.640373	+	0.243453i
$615$		0			0
$616$	772.786	−	491.303i	1.25452	−	0.797571i
$617$	−60.9168	+	105.511i	−0.0987307	+	0.171007i	−0.911160	−	0.412054i	$-0.864812\pi$
$617$	−60.9168	+	105.511i	−0.0987307	+	0.171007i	0.812429	+	0.583060i	$0.198145\pi$
$618$		0			0
$619$	−265.675	+	153.388i	−0.429200	+	0.247799i	−0.699006	−	0.715116i	$-0.746374\pi$
$619$	−265.675	+	153.388i	−0.429200	+	0.247799i	0.269806	+	0.962915i	$0.413041\pi$
$620$	−56.5931	+	170.433i	−0.0912793	+	0.274891i
$621$		0			0
$622$	40.9138	−	253.042i	0.0657778	−	0.406820i
$623$	650.636	−	375.645i	1.04436	−	0.602961i
$624$		0			0
$625$	−63.7082	+	110.346i	−0.101933	+	0.176553i
$626$	−9.15230	+	11.2280i	−0.0146203	+	0.0179361i
$627$		0			0
$628$	4.27989	+	20.7930i	0.00681511	+	0.0331098i
$629$	−361.010			−0.573942
$630$		0			0
$631$			1071.11i			1.69749i	0.528805	+	0.848744i	$0.322640\pi$
$631$			1071.11i			1.69749i	−0.528805	+	0.848744i	$0.677360\pi$
$632$	76.6423	−	3.27447i	0.121269	−	0.00518112i
$633$		0			0
$634$	303.641	−	372.506i	0.478929	−	0.587549i
$635$	−19.6623	−	11.3521i	−0.0309643	−	0.0178773i
$636$		0			0
$637$	−25.3193	−	43.8543i	−0.0397477	−	0.0688450i
$638$	64.1315	−	396.638i	0.100520	−	0.621690i
$639$		0			0
$640$	150.594	+	312.795i	0.235303	+	0.488742i
$641$	−527.259	−	913.240i	−0.822557	−	1.42471i	−0.903772	−	0.428015i	$-0.859213\pi$
$641$	−527.259	−	913.240i	−0.822557	−	1.42471i	0.0812143	−	0.996697i	$-0.474120\pi$
$642$		0			0
$643$	42.0680	+	24.2880i	0.0654246	+	0.0377729i	0.532355	−	0.846521i	$-0.321307\pi$
$643$	42.0680	+	24.2880i	0.0654246	+	0.0377729i	−0.466931	+	0.884294i	$0.654640\pi$
$644$	−731.659	+	650.305i	−1.13612	+	1.00979i
$645$		0			0
$646$	234.044	−	88.9774i	0.362298	−	0.137736i
$647$		−	539.373i		−	0.833653i	−0.908986	−	0.416826i	$-0.863142\pi$
$647$		−	539.373i		−	0.833653i	0.908986	−	0.416826i	$-0.136858\pi$
$648$		0			0
$649$	−874.061			−1.34678
$650$	−7.42832	−	19.5393i	−0.0114282	−	0.0300605i
$651$		0			0
$652$	−158.253	−	178.050i	−0.242719	−	0.273083i
$653$	276.457	−	478.838i	0.423365	−	0.733290i	−0.572901	−	0.819624i	$-0.694182\pi$
$653$	276.457	−	478.838i	0.423365	−	0.733290i	0.996266	+	0.0863348i	$0.0275155\pi$
$654$		0			0
$655$	312.081	−	180.180i	0.476460	−	0.275084i
$656$	544.109	+	406.130i	0.829435	+	0.619100i
$657$		0			0
$658$	41.5433	+	6.71703i	0.0631357	+	0.0102082i
$659$	−734.162	+	423.869i	−1.11406	+	0.643200i	−0.939877	−	0.341514i	$-0.889060\pi$
$659$	−734.162	+	423.869i	−1.11406	+	0.643200i	−0.174178	+	0.984714i	$0.555727\pi$
$660$		0			0
$661$	−359.447	+	622.580i	−0.543792	+	0.941876i	0.454890	+	0.890548i	$0.349679\pi$
$661$	−359.447	+	622.580i	−0.543792	+	0.941876i	−0.998682	+	0.0513280i	$0.983655\pi$
$662$	663.008	+	540.438i	1.00152	+	0.816372i
$663$		0			0
$664$	679.493	−	29.0307i	1.02333	−	0.0437209i
$665$	443.444			0.666833
$666$		0			0
$667$			429.497i			0.643923i
$668$	387.900	−	79.8428i	0.580689	−	0.119525i
$669$		0			0
$670$	185.998	+	151.612i	0.277609	+	0.226287i
$671$	−623.893	−	360.205i	−0.929796	−	0.536818i
$672$		0			0
$673$	288.488	+	499.675i	0.428659	+	0.742460i	0.996754	−	0.0805033i	$-0.0256528\pi$
$673$	288.488	+	499.675i	0.428659	+	0.742460i	−0.568095	+	0.822963i	$0.692319\pi$
$674$	−601.949	−	97.3277i	−0.893100	−	0.144403i
$675$		0			0
$676$	−640.223	−	212.590i	−0.947076	−	0.314482i
$677$	101.021	+	174.974i	0.149219	+	0.258454i	0.930939	−	0.365175i	$-0.118991\pi$
$677$	101.021	+	174.974i	0.149219	+	0.258454i	−0.781720	+	0.623629i	$0.785657\pi$
$678$		0			0
$679$	72.1372	+	41.6484i	0.106240	+	0.0613379i
$680$	−162.590	+	103.367i	−0.239102	+	0.152011i
$681$		0			0
$682$	−116.126	−	305.456i	−0.170273	−	0.447882i
$683$			568.249i			0.831990i	0.909367	+	0.415995i	$0.136567\pi$
$683$			568.249i			0.831990i	−0.909367	+	0.415995i	$0.863433\pi$
$684$		0			0
$685$	122.362			0.178631
$686$	790.972	−	300.707i	1.15302	−	0.438348i
$687$		0			0
$688$	−235.228	−	547.195i	−0.341901	−	0.795341i
$689$	6.24965	−	10.8247i	0.00907060	−	0.0157107i
$690$		0			0
$691$	351.376	−	202.867i	0.508504	−	0.293585i	−0.223714	−	0.974655i	$-0.571818\pi$
$691$	351.376	−	202.867i	0.508504	−	0.293585i	0.732218	+	0.681070i	$0.238485\pi$
$692$	146.506	+	48.6482i	0.211714	+	0.0703008i
$693$		0			0
$694$	−53.9673	+	333.775i	−0.0777627	+	0.480945i
$695$	−354.600	+	204.728i	−0.510215	+	0.294573i
$696$		0			0
$697$	−188.407	+	326.330i	−0.270311	+	0.468192i
$698$	271.172	−	332.673i	0.388499	−	0.476609i
$699$		0			0
$700$	801.651	−	165.007i	1.14522	−	0.235724i
$701$	−83.5164			−0.119139			−0.0595695	−	0.998224i	$-0.518973\pi$
$701$	−83.5164			−0.119139			−0.0595695	+	0.998224i	$0.518973\pi$
$702$		0			0
$703$		−	573.200i		−	0.815363i
$704$	−572.033	−	268.047i	−0.812547	−	0.380749i
$705$		0			0
$706$	697.265	−	855.403i	0.987628	−	1.21162i
$707$	−1114.86	−	643.663i	−1.57688	−	0.910414i
$708$		0			0
$709$	−173.908	−	301.217i	−0.245286	−	0.424848i	0.716926	−	0.697149i	$-0.245548\pi$
$709$	−173.908	−	301.217i	−0.245286	−	0.424848i	−0.962212	+	0.272302i	$0.912215\pi$
$710$	−96.7955	+	598.657i	−0.136332	+	0.843180i
$711$		0			0
$712$	−459.493	−	239.743i	−0.645355	−	0.336718i
$713$	174.660	+	302.520i	0.244965	+	0.424292i
$714$		0			0
$715$	−13.7337	−	7.92916i	−0.0192080	−	0.0110897i
$716$	96.7966	+	108.906i	0.135191	+	0.152104i
$717$		0			0
$718$	1037.23	−	394.327i	1.44461	−	0.549202i
$719$		−	536.277i		−	0.745865i	−0.927858	−	0.372933i	$-0.878352\pi$
$719$		−	536.277i		−	0.745865i	0.927858	−	0.372933i	$-0.121648\pi$
$720$		0			0
$721$	1066.08			1.47862
$722$	−115.294	−	303.267i	−0.159687	−	0.420037i
$723$		0			0
$724$	55.5859	−	49.4052i	0.0767761	−	0.0682392i
$725$	179.553	−	310.995i	0.247659	−	0.428959i
$726$		0			0
$727$	−815.055	+	470.573i	−1.12112	+	0.647280i	−0.941687	−	0.336490i	$-0.890760\pi$
$727$	−815.055	+	470.573i	−1.12112	+	0.647280i	−0.179435	+	0.983770i	$0.557427\pi$
$728$	−25.4217	+	48.7233i	−0.0349199	+	0.0669277i
$729$		0			0
$730$	−408.038	−	65.9747i	−0.558956	−	0.0903763i
$731$	286.267	−	165.277i	0.391611	−	0.226096i
$732$		0			0
$733$	311.063	−	538.777i	0.424370	−	0.735030i	−0.571991	−	0.820260i	$-0.693829\pi$
$733$	311.063	−	538.777i	0.424370	−	0.735030i	0.996361	+	0.0852294i	$0.0271623\pi$
$734$	260.707	+	212.510i	0.355186	+	0.289523i
$735$		0			0
$736$	649.376	+	185.257i	0.882304	+	0.251708i
$737$	−436.655			−0.592477
$738$		0			0
$739$		−	444.439i		−	0.601406i	−0.953718	−	0.300703i	$-0.902779\pi$
$739$		−	444.439i		−	0.601406i	0.953718	−	0.300703i	$-0.0972213\pi$
$740$	88.9212	+	432.005i	0.120164	+	0.583791i
$741$		0			0
$742$	379.336	+	309.208i	0.511235	+	0.416723i
$743$	−66.2270	−	38.2362i	−0.0891346	−	0.0514619i	0.454770	−	0.890609i	$-0.349721\pi$
$743$	−66.2270	−	38.2362i	−0.0891346	−	0.0514619i	−0.543905	+	0.839147i	$0.683055\pi$
$744$		0			0
$745$	−193.626	−	335.370i	−0.259901	−	0.450161i
$746$	−677.990	−	109.622i	−0.908833	−	0.146947i
$747$		0			0
$748$	110.484	−	332.728i	0.147706	−	0.444824i
$749$	624.725	+	1082.06i	0.834079	+	1.44467i
$750$		0			0
$751$	949.025	+	547.920i	1.26368	+	0.729587i	0.973785	−	0.227471i	$-0.0730457\pi$
$751$	949.025	+	547.920i	1.26368	+	0.729587i	0.289897	+	0.957058i	$0.406379\pi$
$752$	−11.4652	−	26.6708i	−0.0152463	−	0.0354665i
$753$		0			0
$754$	8.56870	+	22.5389i	0.0113643	+	0.0298925i
$755$		−	689.070i		−	0.912676i
$756$		0			0
$757$	−346.346			−0.457525			−0.228762	−	0.973482i	$-0.573468\pi$
$757$	−346.346			−0.457525			−0.228762	+	0.973482i	$0.573468\pi$
$758$	1126.15	−	428.132i	1.48568	−	0.564817i
$759$		0			0
$760$	−164.124	−	258.155i	−0.215952	−	0.339677i
$761$	106.565	−	184.576i	0.140033	−	0.242544i	−0.787476	−	0.616345i	$-0.788613\pi$
$761$	106.565	−	184.576i	0.140033	−	0.242544i	0.927509	+	0.373802i	$0.121946\pi$
$762$		0			0
$763$	−869.291	+	501.885i	−1.13931	+	0.657779i
$764$	356.571	−	1073.83i	0.466715	−	1.40553i
$765$		0			0
$766$	−116.394	+	719.871i	−0.151951	+	0.939779i
$767$	45.4277	−	26.2277i	0.0592277	−	0.0341952i
$768$		0			0
$769$	−270.786	+	469.015i	−0.352127	+	0.609902i	−0.986622	−	0.163025i	$-0.947875\pi$
$769$	−270.786	+	469.015i	−0.352127	+	0.609902i	0.634495	+	0.772927i	$0.281208\pi$
$770$	392.304	−	481.278i	0.509486	−	0.625036i
$771$		0			0
$772$	−244.416	−	1187.44i	−0.316601	−	1.53814i
$773$	−1255.73			−1.62449			−0.812245	−	0.583317i	$-0.801755\pi$
$773$	−1255.73			−1.62449			−0.812245	+	0.583317i	$0.801755\pi$
$774$		0			0
$775$		−	292.070i		−	0.376864i
$776$	−2.45278	−	57.4098i	−0.00316080	−	0.0739818i
$777$		0			0
$778$	−271.242	+	332.759i	−0.348640	+	0.427710i
$779$	−518.136	−	299.146i	−0.665130	−	0.384013i
$780$		0			0
$781$	−551.759	−	955.675i	−0.706478	−	1.22366i
$782$	−59.8186	+	369.964i	−0.0764944	+	0.473100i
$783$		0			0
$784$	−1096.09	−	818.133i	−1.39807	−	1.04354i
$785$	7.19706	+	12.4657i	0.00916822	+	0.0158798i
$786$		0			0
$787$	−859.448	−	496.202i	−1.09206	−	0.630499i	−0.157933	−	0.987450i	$-0.550483\pi$
$787$	−859.448	−	496.202i	−1.09206	−	0.630499i	−0.934123	+	0.356951i	$0.883816\pi$
$788$	416.127	−	369.857i	0.528081	−	0.469362i
$789$		0			0
$790$	48.6193	−	18.4838i	0.0615434	−	0.0233972i
$791$			54.5507i			0.0689643i
$792$		0			0
$793$	43.2342			0.0545198
$794$	486.578	+	1279.88i	0.612818	+	1.61194i
$795$		0			0
$796$	−29.8514	−	33.5859i	−0.0375018	−	0.0421934i
$797$	−319.262	+	552.978i	−0.400580	+	0.693824i	−0.993796	−	0.111219i	$-0.964525\pi$
$797$	−319.262	+	552.978i	−0.400580	+	0.693824i	0.593216	+	0.805043i	$0.297858\pi$
$798$		0			0
$799$	13.9530	−	8.05574i	0.0174630	−	0.0100823i
$800$	−392.760	−	405.617i	−0.490950	−	0.507022i
$801$		0			0
$802$	375.885	+	60.7760i	0.468685	+	0.0757805i
$803$	651.377	−	376.073i	0.811179	−	0.468335i
$804$		0			0
$805$	−331.865	+	574.806i	−0.412254	+	0.714045i
$806$	15.2012	+	12.3909i	0.0188600	+	0.0153734i
$807$		0			0
$808$	37.9069	+	887.250i	0.0469145	+	1.09808i
$809$	174.260			0.215401			0.107701	−	0.994183i	$-0.465651\pi$
$809$	174.260			0.215401			0.107701	+	0.994183i	$0.465651\pi$
$810$		0			0
$811$			1182.19i			1.45770i	0.684675	+	0.728849i	$0.259944\pi$
$811$			1182.19i			1.45770i	−0.684675	+	0.728849i	$0.740056\pi$
$812$	−924.717	+	190.338i	−1.13881	+	0.234406i
$813$		0			0
$814$	−622.104	−	507.096i	−0.764256	−	0.622968i
$815$	−139.880	−	80.7597i	−0.171632	−	0.0990917i
$816$		0			0
$817$	262.421	+	454.527i	0.321201	+	0.556336i
$818$	−746.222	−	120.655i	−0.912251	−	0.147500i
$819$		0			0
$820$	436.912	+	145.079i	0.532820	+	0.176926i
$821$	−293.955	−	509.144i	−0.358045	−	0.620151i	0.629590	−	0.776928i	$-0.283223\pi$
$821$	−293.955	−	509.144i	−0.358045	−	0.620151i	−0.987634	+	0.156777i	$0.949890\pi$
$822$		0			0
$823$	−98.0750	−	56.6236i	−0.119168	−	0.0688015i	0.439231	−	0.898374i	$-0.355251\pi$
$823$	−98.0750	−	56.6236i	−0.119168	−	0.0688015i	−0.558399	+	0.829573i	$0.688584\pi$
$824$	−394.569	−	620.630i	−0.478846	−	0.753192i
$825$		0			0
$826$	729.844	+	1919.77i	0.883589	+	2.32417i
$827$			800.560i			0.968030i	0.875060	+	0.484015i	$0.160822\pi$
$827$			800.560i			0.968030i	−0.875060	+	0.484015i	$0.839178\pi$
$828$		0			0
$829$	1162.87			1.40274			0.701369	−	0.712798i	$-0.252573\pi$
$829$	1162.87			1.40274			0.701369	+	0.712798i	$0.252573\pi$
$830$	431.047	−	163.873i	0.519334	−	0.197437i
$831$		0			0
$832$	37.7736	−	3.23358i	0.0454009	−	0.00388652i
$833$	379.538	−	657.378i	0.455627	−	0.789170i
$834$		0			0
$835$	232.551	−	134.264i	0.278505	−	0.160795i
$836$	528.296	+	175.424i	0.631933	+	0.209837i
$837$		0			0
$838$	−98.5400	+	609.447i	−0.117590	+	0.727264i
$839$	−1355.92	+	782.842i	−1.61612	+	0.933065i	−0.628205	+	0.778048i	$0.716210\pi$
$839$	−1355.92	+	782.842i	−1.61612	+	0.933065i	−0.987912	+	0.155017i	$0.950457\pi$
$840$		0			0
$841$	213.383	−	369.590i	0.253725	−	0.439464i
$842$	446.910	−	548.268i	0.530772	−	0.651150i
$843$		0			0
$844$	−506.758	+	104.308i	−0.600425	+	0.123587i
$845$	−457.406			−0.541309
$846$		0			0
$847$		−	273.341i		−	0.322717i
$848$	39.6119	−	335.275i	0.0467121	−	0.395372i
$849$		0			0
$850$	197.979	−	242.881i	0.232917	−	0.285742i
$851$	743.000	+	428.971i	0.873091	+	0.504079i
$852$		0			0
$853$	−68.8088	−	119.180i	−0.0806668	−	0.139719i	0.822870	−	0.568230i	$-0.192372\pi$
$853$	−68.8088	−	119.180i	−0.0806668	−	0.139719i	−0.903537	+	0.428511i	$0.859038\pi$
$854$	−270.192	+	1671.08i	−0.316384	+	1.95676i
$855$		0			0
$856$	398.711	−	764.170i	0.465783	−	0.892722i
$857$	384.489	+	665.955i	0.448646	+	0.777077i	0.998298	−	0.0583164i	$-0.0185732\pi$
$857$	384.489	+	665.955i	0.448646	+	0.777077i	−0.549653	+	0.835393i	$0.685240\pi$
$858$		0			0
$859$	−178.353	−	102.972i	−0.207629	−	0.119875i	0.392580	−	0.919718i	$-0.371583\pi$
$859$	−178.353	−	102.972i	−0.207629	−	0.119875i	−0.600209	+	0.799843i	$0.704916\pi$
$860$	−268.291	−	301.855i	−0.311966	−	0.350994i
$861$		0			0
$862$	−883.837	+	336.011i	−1.02533	+	0.389804i
$863$			772.757i			0.895431i	0.894176	+	0.447716i	$0.147762\pi$
$863$			772.757i			0.895431i	−0.894176	+	0.447716i	$0.852238\pi$
$864$		0			0
$865$	104.671			0.121007
$866$	−43.6515	−	114.820i	−0.0504059	−	0.132587i
$867$		0			0
$868$	−573.930	+	510.114i	−0.661210	+	0.587689i
$869$	−47.3249	+	81.9692i	−0.0544591	+	0.0943258i
$870$		0			0
$871$	22.6943	−	13.1026i	0.0260555	−	0.0150432i
$872$	613.911	+	320.312i	0.704026	+	0.367330i
$873$		0			0
$874$	−587.418	−	94.9782i	−0.672103	−	0.108671i
$875$	1161.57	−	670.630i	1.32750	−	0.766435i
$876$		0			0
$877$	−200.096	+	346.577i	−0.228160	+	0.395185i	−0.957263	−	0.289219i	$-0.906604\pi$
$877$	−200.096	+	346.577i	−0.228160	+	0.395185i	0.729103	+	0.684404i	$0.239938\pi$
$878$	−634.300	−	517.037i	−0.722437	−	0.588880i
$879$		0			0
$880$	−425.376	−	50.2571i	−0.483382	−	0.0571103i
$881$	728.323			0.826700			0.413350	−	0.910572i	$-0.364359\pi$
$881$	728.323			0.826700			0.413350	+	0.910572i	$0.364359\pi$
$882$		0			0
$883$		−	383.413i		−	0.434216i	−0.976148	−	0.217108i	$-0.930338\pi$
$883$		−	383.413i		−	0.434216i	0.976148	−	0.217108i	$-0.0696625\pi$
$884$	4.24186	+	20.6082i	0.00479848	+	0.0233125i
$885$		0			0
$886$	1197.20	+	975.873i	1.35124	+	1.10144i
$887$	1255.91	+	725.098i	1.41590	+	0.817473i	0.995936	−	0.0900662i	$-0.0287079\pi$
$887$	1255.91	+	725.098i	1.41590	+	0.817473i	0.419968	+	0.907539i	$0.362041\pi$
$888$		0			0
$889$	−48.5392	−	84.0724i	−0.0545998	−	0.0945696i
$890$	−346.909	−	56.0909i	−0.389785	−	0.0630234i
$891$		0			0
$892$	−304.516	+	917.061i	−0.341385	+	1.02810i
$893$	12.7907	+	22.1541i	0.0143232	+	0.0248086i
$894$		0			0
$895$	85.5589	+	49.3974i	0.0955965	+	0.0551927i
$896$	−111.082	+	1480.22i	−0.123976	+	1.65203i
$897$		0			0
$898$	−560.783	−	1475.07i	−0.624480	−	1.64262i
$899$			336.907i			0.374758i
$900$		0			0
$901$	187.365			0.207952
$902$	−783.051	+	297.695i	−0.868128	+	0.330039i
$903$		0			0
$904$	31.7572	−	20.1898i	0.0351296	−	0.0223339i
$905$	25.2125	−	43.6694i	0.0278592	−	0.0482535i
$906$		0			0
$907$	533.290	−	307.895i	0.587971	−	0.339465i	−0.176324	−	0.984332i	$-0.556420\pi$
$907$	533.290	−	307.895i	0.587971	−	0.339465i	0.764295	+	0.644867i	$0.223087\pi$
$908$	−481.366	+	1449.65i	−0.530139	+	1.59653i
$909$		0			0
$910$	−5.94772	+	36.7853i	−0.00653596	+	0.0404234i
$911$	227.031	−	131.076i	0.249211	−	0.143882i	−0.370192	−	0.928955i	$-0.620708\pi$
$911$	227.031	−	131.076i	0.249211	−	0.143882i	0.619403	+	0.785073i	$0.287375\pi$
$912$		0			0
$913$	−419.572	+	726.720i	−0.459553	+	0.795969i
$914$	349.183	−	428.376i	0.382038	−	0.468683i
$915$		0			0
$916$	120.423	+	585.048i	0.131466	+	0.638699i
$917$	1540.83			1.68030
$918$		0			0
$919$			566.458i			0.616385i	0.951324	+	0.308193i	$0.0997241\pi$
$919$			566.458i			0.616385i	−0.951324	+	0.308193i	$0.900276\pi$
$920$	457.455	−	19.5443i	0.497234	−	0.0212438i
$921$		0			0
$922$	743.125	−	911.664i	0.805992	−	0.988789i
$923$	57.3533	+	33.1130i	0.0621379	+	0.0358754i
$924$		0			0
$925$	−358.667	−	621.229i	−0.387748	−	0.671599i
$926$	249.657	−	1544.07i	0.269608	−	1.66746i
$927$		0			0
$928$	453.055	+	467.886i	0.488206	+	0.504188i
$929$	−298.745	−	517.442i	−0.321577	−	0.556988i	0.659236	−	0.751936i	$-0.270880\pi$
$929$	−298.745	−	517.442i	−0.321577	−	0.556988i	−0.980814	+	0.194948i	$0.937546\pi$
$930$		0			0
$931$	1043.77	+	602.618i	1.12112	+	0.647281i
$932$	−654.560	+	581.778i	−0.702317	+	0.624225i
$933$		0			0
$934$	−1239.83	+	471.351i	−1.32744	+	0.504659i
$935$		−	237.717i		−	0.254243i
$936$		0			0
$937$	457.785			0.488564			0.244282	−	0.969704i	$-0.421448\pi$
$937$	457.785			0.488564			0.244282	+	0.969704i	$0.421448\pi$
$938$	364.609	+	959.060i	0.388709	+	1.02245i
$939$		0			0
$940$	−13.0768	−	14.7127i	−0.0139114	−	0.0156518i
$941$	677.858	−	1174.09i	0.720360	−	1.24770i	−0.240496	−	0.970650i	$-0.577310\pi$
$941$	677.858	−	1174.09i	0.720360	−	1.24770i	0.960856	−	0.277049i	$-0.0893566\pi$
$942$		0			0
$943$	775.526	−	447.750i	0.822403	−	0.474814i
$944$	847.486	−	1135.41i	0.897760	−	1.20277i
$945$		0			0
$946$	725.463	+	117.298i	0.766874	+	0.123994i
$947$	−567.925	+	327.891i	−0.599709	+	0.346242i	−0.768927	−	0.639336i	$-0.779209\pi$
$947$	−567.925	+	327.891i	−0.599709	+	0.346242i	0.169218	+	0.985579i	$0.445876\pi$
$948$		0			0
$949$	−22.5694	+	39.0914i	−0.0237823	+	0.0411922i
$950$	385.638	+	314.346i	0.405935	+	0.330890i
$951$		0			0
$952$	−823.052	+	35.1641i	−0.864551	+	0.0369371i
$953$	−554.778			−0.582139			−0.291069	−	0.956702i	$-0.594011\pi$
$953$	−554.778			−0.582139			−0.291069	+	0.956702i	$0.594011\pi$
$954$		0			0
$955$		−	767.193i		−	0.803344i
$956$	−987.373	+	203.234i	−1.03282	+	0.212588i
$957$		0			0
$958$	−1006.04	−	820.055i	−1.05015	−	0.856007i
$959$	453.102	+	261.599i	0.472474	+	0.272783i
$960$		0			0
$961$	−343.493	−	594.947i	−0.357432	−	0.619091i
$962$	47.5490	+	7.68808i	0.0494272	+	0.00799177i
$963$		0			0
$964$	1715.98	+	569.801i	1.78006	+	0.591080i
$965$	−411.009	−	711.889i	−0.425917	−	0.737709i
$966$		0			0
$967$	−502.000	−	289.830i	−0.519131	−	0.299720i	0.217448	−	0.976072i	$-0.430227\pi$
$967$	−502.000	−	289.830i	−0.519131	−	0.299720i	−0.736579	+	0.676351i	$0.763560\pi$
$968$	−159.128	+	101.167i	−0.164388	+	0.104511i
$969$		0			0
$970$	−13.8455	−	36.4189i	−0.0142737	−	0.0375452i
$971$		−	260.660i		−	0.268445i	−0.990951	−	0.134223i	$-0.957146\pi$
$971$		−	260.660i		−	0.268445i	0.990951	−	0.134223i	$-0.0428537\pi$
$972$		0			0
$973$	−1750.76			−1.79934
$974$	−527.382	+	200.497i	−0.541460	+	0.205849i
$975$		0			0
$976$	1072.83	−	461.189i	1.09921	−	0.472530i
$977$	−638.953	+	1106.70i	−0.653995	+	1.13275i	0.328149	+	0.944626i	$0.393575\pi$
$977$	−638.953	+	1106.70i	−0.653995	+	1.13275i	−0.982145	+	0.188127i	$0.939758\pi$
$978$		0			0
$979$	553.793	−	319.732i	0.565672	−	0.326591i
$980$	−880.143	−	292.257i	−0.898105	−	0.298221i
$981$		0			0
$982$	240.680	−	1488.55i	0.245092	−	1.51584i
$983$	378.325	−	218.426i	0.384868	−	0.222204i	−0.295066	−	0.955477i	$-0.595342\pi$
$983$	378.325	−	218.426i	0.384868	−	0.222204i	0.679934	+	0.733273i	$0.262008\pi$
$984$		0			0
$985$	188.746	−	326.918i	0.191621	−	0.331897i
$986$	−228.373	+	280.167i	−0.231615	+	0.284145i
$987$		0			0
$988$	−32.7211	+	6.73510i	−0.0331185	+	0.00681690i
$989$	−785.562			−0.794300
$990$		0			0
$991$		−	1344.50i		−	1.35671i	−0.734734	−	0.678356i	$-0.762693\pi$
$991$		−	1344.50i		−	1.35671i	0.734734	−	0.678356i	$-0.237307\pi$
$992$	509.385	+	145.320i	0.513493	+	0.146492i
$993$		0			0
$994$	−1638.30	+	2009.86i	−1.64819	+	2.02200i
$995$	−26.3858	−	15.2338i	−0.0265184	−	0.0153104i
$996$		0			0
$997$	942.397	+	1632.28i	0.945233	+	1.63719i	0.755284	+	0.655398i	$0.227499\pi$
$997$	942.397	+	1632.28i	0.945233	+	1.63719i	0.189949	+	0.981794i	$0.439168\pi$
$998$	164.464	−	1017.17i	0.164794	−	1.01921i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.3.f.c.91.3		16
3.2	odd	2		36.3.f.c.31.6	yes	16
4.3	odd	2	inner	108.3.f.c.91.2		16
8.3	odd	2		1728.3.o.g.1279.6		16
8.5	even	2		1728.3.o.g.1279.5		16
9.2	odd	6		36.3.f.c.7.7	yes	16
9.4	even	3		324.3.d.g.163.8		8
9.5	odd	6		324.3.d.i.163.1		8
9.7	even	3	inner	108.3.f.c.19.2		16
12.11	even	2		36.3.f.c.31.7	yes	16
24.5	odd	2		576.3.o.g.319.3		16
24.11	even	2		576.3.o.g.319.6		16
36.7	odd	6	inner	108.3.f.c.19.3		16
36.11	even	6		36.3.f.c.7.6	✓	16
36.23	even	6		324.3.d.i.163.2		8
36.31	odd	6		324.3.d.g.163.7		8
72.11	even	6		576.3.o.g.511.3		16
72.29	odd	6		576.3.o.g.511.6		16
72.43	odd	6		1728.3.o.g.127.5		16
72.61	even	6		1728.3.o.g.127.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.6	✓	16	36.11	even	6
36.3.f.c.7.7	yes	16	9.2	odd	6
36.3.f.c.31.6	yes	16	3.2	odd	2
36.3.f.c.31.7	yes	16	12.11	even	2
108.3.f.c.19.2		16	9.7	even	3	inner
108.3.f.c.19.3		16	36.7	odd	6	inner
108.3.f.c.91.2		16	4.3	odd	2	inner
108.3.f.c.91.3		16	1.1	even	1	trivial
324.3.d.g.163.7		8	36.31	odd	6
324.3.d.g.163.8		8	9.4	even	3
324.3.d.i.163.1		8	9.5	odd	6
324.3.d.i.163.2		8	36.23	even	6
576.3.o.g.319.3		16	24.5	odd	2
576.3.o.g.319.6		16	24.11	even	2
576.3.o.g.511.3		16	72.11	even	6
576.3.o.g.511.6		16	72.29	odd	6
1728.3.o.g.127.5		16	72.43	odd	6
1728.3.o.g.127.6		16	72.61	even	6
1728.3.o.g.1279.5		16	8.5	even	2
1728.3.o.g.1279.6		16	8.3	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	108.f (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.710719 - 1.86946i) q^{2} +(-2.98976 + 2.65732i) q^{4} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +O(q^{10})\)	\(q+(-0.710719 - 1.86946i) q^{2} +(-2.98976 + 2.65732i) q^{4} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +(5.35481 + 0.865806i) q^{10} +(-8.54822 + 4.93532i) q^{11} +(0.296185 - 0.513008i) q^{13} +(17.9776 + 14.6541i) q^{14} +(1.87730 - 15.8895i) q^{16} +8.87968 q^{17} +14.0989i q^{19} +(-2.18718 - 10.6259i) q^{20} +(15.3018 + 12.4729i) q^{22} +(-18.2754 - 10.5513i) q^{23} +(8.82205 + 15.2802i) q^{25} +(-1.16955 - 0.189102i) q^{26} +(14.6182 - 44.0234i) q^{28} +(-10.1764 - 17.6260i) q^{29} +(-14.3357 - 8.27670i) q^{31} +(-31.0390 + 7.78342i) q^{32} +(-6.31095 - 16.6002i) q^{34} -31.4524i q^{35} -40.6557 q^{37} +(26.3573 - 10.0203i) q^{38} +(-18.3103 + 11.6409i) q^{40} +(-21.2177 + 36.7502i) q^{41} +(32.2385 - 18.6129i) q^{43} +(12.4424 - 37.4708i) q^{44} +(-6.73658 + 41.6642i) q^{46} +(1.57134 - 0.907211i) q^{47} +(42.7423 - 74.0318i) q^{49} +(22.2958 - 27.3524i) q^{50} +(0.477704 + 2.32083i) q^{52} +21.1005 q^{53} -26.7709i q^{55} +(-92.6894 + 3.96007i) q^{56} +(-25.7186 + 31.5515i) q^{58} +(76.6879 + 44.2758i) q^{59} +(36.4925 + 63.2069i) q^{61} +(-5.28433 + 32.6823i) q^{62} +(36.6108 + 52.4943i) q^{64} +(0.803307 + 1.39137i) q^{65} +(38.3110 + 22.1189i) q^{67} +(-26.5481 + 23.5961i) q^{68} +(-58.7990 + 22.3538i) q^{70} +111.798i q^{71} -76.2003 q^{73} +(28.8948 + 76.0042i) q^{74} +(-37.4652 - 42.1522i) q^{76} +(57.2337 - 99.1316i) q^{77} +(8.30434 - 4.79451i) q^{79} +(34.7757 + 25.9570i) q^{80} +(83.7828 + 13.5466i) q^{82} +(73.6244 - 42.5070i) q^{83} +(-12.0416 + 20.8567i) q^{85} +(-57.7086 - 47.0400i) q^{86} +(-78.8931 + 3.37063i) q^{88} -64.7845 q^{89} +6.86958i q^{91} +(82.6773 - 17.0178i) q^{92} +(-2.81277 - 2.29278i) q^{94} +(-33.1157 - 19.1193i) q^{95} +(-3.59139 - 6.22047i) q^{97} +(-168.777 - 27.2892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) \) 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8} + 20 q^{10} - 46 q^{13} + 12 q^{14} - 17 q^{16} - 12 q^{17} - 36 q^{20} + 33 q^{22} - 30 q^{25} - 72 q^{26} + 12 q^{28} - 42 q^{29} - 87 q^{32} + 11 q^{34} + 56 q^{37} + 99 q^{38} + 68 q^{40} - 84 q^{41} + 222 q^{44} - 264 q^{46} + 58 q^{49} + 219 q^{50} + 110 q^{52} + 72 q^{53} - 270 q^{56} - 16 q^{58} - 34 q^{61} - 516 q^{62} - 254 q^{64} + 30 q^{65} - 375 q^{68} + 150 q^{70} + 116 q^{73} + 372 q^{74} - 15 q^{76} + 330 q^{77} + 720 q^{80} + 254 q^{82} - 140 q^{85} + 273 q^{86} + 75 q^{88} + 384 q^{89} - 258 q^{92} + 36 q^{94} - 148 q^{97} - 1170 q^{98}+O(q^{100}) \) 16 * q + 3 * q^2 - 5 * q^4 - 6 * q^5 + 54 * q^8 + 20 * q^10 - 46 * q^13 + 12 * q^14 - 17 * q^16 - 12 * q^17 - 36 * q^20 + 33 * q^22 - 30 * q^25 - 72 * q^26 + 12 * q^28 - 42 * q^29 - 87 * q^32 + 11 * q^34 + 56 * q^37 + 99 * q^38 + 68 * q^40 - 84 * q^41 + 222 * q^44 - 264 * q^46 + 58 * q^49 + 219 * q^50 + 110 * q^52 + 72 * q^53 - 270 * q^56 - 16 * q^58 - 34 * q^61 - 516 * q^62 - 254 * q^64 + 30 * q^65 - 375 * q^68 + 150 * q^70 + 116 * q^73 + 372 * q^74 - 15 * q^76 + 330 * q^77 + 720 * q^80 + 254 * q^82 - 140 * q^85 + 273 * q^86 + 75 * q^88 + 384 * q^89 - 258 * q^92 + 36 * q^94 - 148 * q^97 - 1170 * q^98

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