LMFDB - Embedded newform 108.3.f.c.19.2

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			19.2
Root			$-1.26364 + 1.55023i$ of defining polynomial
Character	$\chi$	$=$	108.19
Dual form			108.3.f.c.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26364 + 1.55023i) q^{2} +(-0.806428 - 3.91787i) q^{4} +(-1.35609 - 2.34881i) q^{5} +(10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +O(q^{10})$	\(q+(-1.26364 + 1.55023i) q^{2} +(-0.806428 - 3.91787i) q^{4} +(-1.35609 - 2.34881i) q^{5} +(10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +(5.35481 + 0.865806i) q^{10} +(8.54822 + 4.93532i) q^{11} +(0.296185 + 0.513008i) q^{13} +(-21.6796 + 8.24203i) q^{14} +(-14.6993 + 6.31895i) q^{16} +8.87968 q^{17} +14.0989i q^{19} +(-8.10875 + 7.20712i) q^{20} +(-18.4528 + 7.01525i) q^{22} +(18.2754 - 10.5513i) q^{23} +(8.82205 - 15.2802i) q^{25} +(-1.16955 - 0.189102i) q^{26} +(14.6182 - 44.0234i) q^{28} +(-10.1764 + 17.6260i) q^{29} +(14.3357 - 8.27670i) q^{31} +(8.77885 - 30.7723i) q^{32} +(-11.2207 + 13.7655i) q^{34} -31.4524i q^{35} -40.6557 q^{37} +(-21.8565 - 17.8159i) q^{38} +(-0.926156 - 21.6776i) q^{40} +(-21.2177 - 36.7502i) q^{41} +(-32.2385 - 18.6129i) q^{43} +(12.4424 - 37.4708i) q^{44} +(-6.73658 + 41.6642i) q^{46} +(-1.57134 - 0.907211i) q^{47} +(42.7423 + 74.0318i) q^{49} +(12.5400 + 32.9849i) q^{50} +(1.77105 - 1.57412i) q^{52} +21.1005 q^{53} -26.7709i q^{55} +(49.7742 + 78.2914i) q^{56} +(-14.4651 - 38.0487i) q^{58} +(-76.6879 + 44.2758i) q^{59} +(36.4925 - 63.2069i) q^{61} +(-5.28433 + 32.6823i) q^{62} +(36.6108 + 52.4943i) q^{64} +(0.803307 - 1.39137i) q^{65} +(-38.3110 + 22.1189i) q^{67} +(-7.16082 - 34.7894i) q^{68} +(48.7585 + 39.7446i) q^{70} +111.798i q^{71} -76.2003 q^{73} +(51.3742 - 63.0257i) q^{74} +(55.2375 - 11.3697i) q^{76} +(57.2337 + 99.1316i) q^{77} +(-8.30434 - 4.79451i) q^{79} +(34.7757 + 25.9570i) q^{80} +(83.7828 + 13.5466i) q^{82} +(-73.6244 - 42.5070i) q^{83} +(-12.0416 - 20.8567i) q^{85} +(69.5921 - 26.4571i) q^{86} +(42.3656 + 66.6381i) q^{88} -64.7845 q^{89} +6.86958i q^{91} +(-56.0765 - 63.0918i) q^{92} +(3.39199 - 1.28954i) q^{94} +(33.1157 - 19.1193i) q^{95} +(-3.59139 + 6.22047i) q^{97} +(-168.777 - 27.2892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.26364	+	1.55023i	−0.631820	+	0.775115i
$2$	−1.26364	+	1.55023i	−0.631820	+	0.775115i
$3$		0			0
$3$		0			0
$4$	−0.806428	−	3.91787i	−0.201607	−	0.979467i
$5$	−1.35609	−	2.34881i	−0.271218	−	0.469763i	0.697956	−	0.716140i	$-0.254093\pi$
$5$	−1.35609	−	2.34881i	−0.271218	−	0.469763i	−0.969174	+	0.246378i	$0.920760\pi$
$6$		0			0
$7$	10.0431	+	5.79837i	1.43473	+	0.828339i	0.997476	−	0.0710013i	$-0.0226195\pi$
$7$	10.0431	+	5.79837i	1.43473	+	0.828339i	0.437249	+	0.899340i	$0.355953\pi$
$8$	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	$-0.185233\pi$
$11$	8.54822	+	4.93532i	0.777111	+	0.448665i	−0.0582943	+	0.998299i	$0.518566\pi$
$12$		0			0
$13$	0.296185	+	0.513008i	0.0227835	+	0.0394622i	0.877192	−	0.480139i	$-0.159414\pi$
$13$	0.296185	+	0.513008i	0.0227835	+	0.0394622i	−0.854409	+	0.519601i	$0.826080\pi$
$14$	−21.6796	+	8.24203i	−1.54855	+	0.588716i
$15$		0			0
$16$	−14.6993	+	6.31895i	−0.918709	+	0.394935i
$17$	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	$0.879007\pi$
$20$	−8.10875	+	7.20712i	−0.405438	+	0.360356i
$21$		0			0
$22$	−18.4528	+	7.01525i	−0.838762	+	0.318875i
$23$	18.2754	−	10.5513i	0.794583	−	0.458753i	−0.0469902	−	0.998895i	$-0.514963\pi$
$23$	18.2754	−	10.5513i	0.794583	−	0.458753i	0.841574	+	0.540142i	$0.181630\pi$
$24$		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	−0.986409	−	0.164308i	$-0.947461\pi$
$29$	−10.1764	+	17.6260i	−0.350910	+	0.607793i	0.635499	+	0.772101i	$0.280794\pi$
$30$		0			0
$31$	14.3357	−	8.27670i	0.462441	−	0.266990i	−0.250629	−	0.968083i	$-0.580638\pi$
$31$	14.3357	−	8.27670i	0.462441	−	0.266990i	0.713070	+	0.701093i	$0.247304\pi$
$32$	8.77885	−	30.7723i	0.274339	−	0.961633i
$33$		0			0
$34$	−11.2207	+	13.7655i	−0.330021	+	0.404869i
$35$		−	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	$0.685144\pi$
$38$	−21.8565	−	17.8159i	−0.575171	−	0.468840i
$39$		0			0
$40$	−0.926156	−	21.6776i	−0.0231539	−	0.541941i
$41$	−21.2177	−	36.7502i	−0.517506	−	0.896346i	−0.999793	−	0.0203330i	$-0.993527\pi$
$41$	−21.2177	−	36.7502i	−0.517506	−	0.896346i	0.482288	−	0.876013i	$-0.339806\pi$
$42$		0			0
$43$	−32.2385	−	18.6129i	−0.749732	−	0.432858i	0.0758649	−	0.997118i	$-0.475828\pi$
$43$	−32.2385	−	18.6129i	−0.749732	−	0.432858i	−0.825597	+	0.564260i	$0.809162\pi$
$44$	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	$-0.339478\pi$
$47$	−1.57134	−	0.907211i	−0.0334327	−	0.0193024i	−0.516623	+	0.856213i	$0.672811\pi$
$48$		0			0
$49$	42.7423	+	74.0318i	0.872291	+	1.51085i
$50$	12.5400	+	32.9849i	0.250800	+	0.659698i
$51$		0			0
$52$	1.77105	−	1.57412i	0.0340586	−	0.0302715i
$53$	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
$56$	49.7742	+	78.2914i	0.888826	+	1.39806i
$57$		0			0
$58$	−14.4651	−	38.0487i	−0.249398	−	0.656011i
$59$	−76.6879	+	44.2758i	−1.29980	+	0.750437i	−0.980369	−	0.197174i	$-0.936824\pi$
$59$	−76.6879	+	44.2758i	−1.29980	+	0.750437i	−0.319427	+	0.947611i	$0.603490\pi$
$60$		0			0
$61$	36.4925	−	63.2069i	0.598238	−	1.03618i	−0.394843	−	0.918749i	$-0.629201\pi$
$61$	36.4925	−	63.2069i	0.598238	−	1.03618i	0.993081	−	0.117431i	$-0.0374657\pi$
$62$	−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	$-0.773760\pi$
$67$	−38.3110	+	22.1189i	−0.571807	+	0.330133i	0.186064	+	0.982538i	$0.440427\pi$
$68$	−7.16082	−	34.7894i	−0.105306	−	0.511609i
$69$		0			0
$70$	48.7585	+	39.7446i	0.696550	+	0.567779i
$71$			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	$0.674784\pi$
$74$	51.3742	−	63.0257i	0.694246	−	0.851699i
$75$		0			0
$76$	55.2375	−	11.3697i	0.726810	−	0.149602i
$77$	57.2337	+	99.1316i	0.743294	+	1.28742i
$78$		0			0
$79$	−8.30434	−	4.79451i	−0.105118	−	0.0606901i	0.446519	−	0.894774i	$-0.352663\pi$
$79$	−8.30434	−	4.79451i	−0.105118	−	0.0606901i	−0.551637	+	0.834084i	$0.685997\pi$
$80$	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	$-0.504478\pi$
$83$	−73.6244	−	42.5070i	−0.887041	−	0.512133i	−0.872973	+	0.487768i	$0.837811\pi$
$84$		0			0
$85$	−12.0416	−	20.8567i	−0.141666	−	0.245373i
$86$	69.5921	−	26.4571i	0.809211	−	0.307640i
$87$		0			0
$88$	42.3656	+	66.6381i	0.481428	+	0.757252i
$89$	−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
$92$	−56.0765	−	63.0918i	−0.609527	−	0.685780i
$93$		0			0
$94$	3.39199	−	1.28954i	0.0360850	−	0.0137186i
$95$	33.1157	−	19.1193i	0.348586	−	0.201256i
$96$		0			0
$97$	−3.59139	+	6.22047i	−0.0370246	+	0.0641285i	−0.883944	−	0.467593i	$-0.845121\pi$
$97$	−3.59139	+	6.22047i	−0.0370246	+	0.0641285i	0.846919	+	0.531721i	$0.178455\pi$
$98$	−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	−0.448764	−	0.893650i	$-0.648136\pi$
$101$	55.5037	−	96.1353i	0.549542	−	0.951834i	0.998306	−	0.0581840i	$-0.0185310\pi$
$102$		0			0
$103$	79.6133	−	45.9648i	0.772945	−	0.446260i	−0.0609793	−	0.998139i	$-0.519422\pi$
$103$	79.6133	−	45.9648i	0.772945	−	0.446260i	0.833924	+	0.551879i	$0.186089\pi$
$104$	0.202283	+	4.73465i	0.00194503	+	0.0455255i
$105$		0			0
$106$	−26.6634	+	32.7106i	−0.251541	+	0.308590i
$107$		−	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	$0.370035\pi$
$110$	41.5011	+	33.8288i	0.377283	+	0.307535i
$111$		0			0
$112$	−184.266	−	21.7706i	−1.64524	−	0.194380i
$113$	2.35198	+	4.07376i	0.0208140	+	0.0360509i	0.876245	−	0.481866i	$-0.160041\pi$
$113$	2.35198	+	4.07376i	0.0208140	+	0.0360509i	−0.855431	+	0.517917i	$0.826708\pi$
$114$		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
$122$	51.8719	+	136.443i	0.425179	+	1.11838i
$123$		0			0
$124$	−43.9877	−	49.4906i	−0.354739	−	0.399118i
$125$	−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	$0.989507\pi$
$128$	−127.641	−	9.57876i	−0.997196	−	0.0748341i
$129$		0			0
$130$	1.14185	+	3.00350i	0.00878347	+	0.0231039i
$131$	115.067	−	66.4338i	0.878372	−	0.507129i	0.00825098	−	0.999966i	$-0.497374\pi$
$131$	115.067	−	66.4338i	0.878372	−	0.507129i	0.870121	+	0.492837i	$0.164040\pi$
$132$		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	−0.936533	−	0.350579i	$-0.885985\pi$
$137$	−22.5579	+	39.0715i	−0.164656	+	0.285193i	0.771877	+	0.635772i	$0.219318\pi$
$138$		0			0
$139$	−130.744	+	75.4848i	−0.940601	+	0.543056i	−0.890149	−	0.455670i	$-0.849400\pi$
$139$	−130.744	+	75.4848i	−0.940601	+	0.543056i	−0.0504522	+	0.998726i	$0.516066\pi$
$140$	−123.226	+	25.3641i	−0.880189	+	0.181172i
$141$		0			0
$142$	−173.313	−	141.273i	−1.22051	−	0.994877i
$143$			5.84708i			0.0408887i
$144$		0			0
$145$	55.2003			0.380692
$146$	96.2897	−	118.128i	0.659519	−	0.809096i
$147$		0			0
$148$	32.7859	+	159.284i	0.221526	+	1.07624i
$149$	−71.3914	−	123.653i	−0.479137	−	0.829889i	0.520577	−	0.853815i	$-0.325717\pi$
$149$	−71.3914	−	123.653i	−0.479137	−	0.829889i	−0.999714	+	0.0239255i	$0.992384\pi$
$150$		0			0
$151$	220.027	+	127.033i	1.45713	+	0.841276i	0.998869	−	0.0475407i	$-0.0151384\pi$
$151$	220.027	+	127.033i	1.45713	+	0.841276i	0.458263	+	0.888817i	$0.348472\pi$
$152$	−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	0.874353	−	0.485291i	$-0.161286\pi$
$157$	2.65361	+	4.59618i	0.0169020	+	0.0292751i	−0.857451	+	0.514566i	$0.827953\pi$
$158$	17.9263	−	6.81510i	0.113458	−	0.0431336i
$159$		0			0
$160$	−84.1832	+	21.1100i	−0.526145	+	0.131938i
$161$	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	$0.941523\pi$
$164$	−126.872	+	112.765i	−0.773608	+	0.687589i
$165$		0			0
$166$	158.930	−	60.4211i	0.957412	−	0.363983i
$167$	85.7434	−	49.5040i	0.513434	−	0.296431i	−0.220810	−	0.975317i	$-0.570870\pi$
$167$	85.7434	−	49.5040i	0.513434	−	0.296431i	0.734244	+	0.678886i	$0.237537\pi$
$168$		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	−0.916391	−	0.400283i	$-0.868912\pi$
$173$	−19.2965	+	33.4225i	−0.111540	+	0.193193i	0.804851	+	0.593477i	$0.202245\pi$
$174$		0			0
$175$	177.201	−	102.307i	1.01258	−	0.584612i
$176$	−156.839	−	18.5302i	−0.891133	−	0.105285i
$177$		0			0
$178$	81.8643	−	100.431i	0.459912	−	0.564219i
$179$		−	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	$0.516355\pi$
$182$	−10.6494	−	8.68067i	−0.0585133	−	0.0476960i
$183$		0			0
$184$	168.667	−	7.20614i	0.916670	−	0.0391638i
$185$	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	$-0.0679233\pi$
$191$	244.973	+	141.435i	1.28258	+	0.740497i	0.305260	+	0.952269i	$0.401257\pi$
$192$		0			0
$193$	−151.542	−	262.479i	−0.785193	−	1.35999i	−0.928884	−	0.370372i	$-0.879230\pi$
$193$	−151.542	−	262.479i	−0.785193	−	1.35999i	0.143691	−	0.989623i	$-0.454103\pi$
$194$	−5.10493	−	13.4279i	−0.0263141	−	0.0692160i
$195$		0			0
$196$	255.578	−	227.160i	1.30397	−	1.15898i
$197$	−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	$0.991014\pi$
$200$	119.118	−	75.7300i	0.595590	−	0.378650i
$201$		0			0
$202$	78.8951	+	207.524i	0.390570	+	1.02735i
$203$	−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	$-0.765827\pi$
$211$	−112.017	+	64.6728i	−0.530884	+	0.306506i	0.210492	+	0.977595i	$0.432493\pi$
$212$	−17.0160	−	82.6687i	−0.0802641	−	0.389947i
$213$		0			0
$214$	167.024	+	136.146i	0.780486	+	0.636198i
$215$			100.963i			0.469595i
$216$		0			0
$217$	191.966			0.884634
$218$	−109.376	+	134.182i	−0.501724	+	0.615514i
$219$		0			0
$220$	−104.885	+	21.5888i	−0.476749	+	0.0981310i
$221$	2.63003	+	4.55535i	0.0119006	+	0.0206124i
$222$		0			0
$223$	−209.210	−	120.787i	−0.938159	−	0.541647i	−0.0487765	−	0.998810i	$-0.515532\pi$
$223$	−209.210	−	120.787i	−0.938159	−	0.541647i	−0.889383	+	0.457163i	$0.848866\pi$
$224$	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	$-0.651440\pi$
$227$	−330.710	−	190.936i	−1.45687	−	0.841126i	−0.998856	+	0.0478181i	$0.984773\pi$
$228$		0			0
$229$	74.6642	+	129.322i	0.326044	+	0.564725i	0.981723	−	0.190315i	$-0.0609508\pi$
$229$	74.6642	+	129.322i	0.326044	+	0.564725i	−0.655679	+	0.755040i	$0.727617\pi$
$230$	106.997	−	40.6773i	0.465204	−	0.176858i
$231$		0			0
$232$	−137.404	+	87.3558i	−0.592261	+	0.376534i
$233$	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
$236$	235.310	+	264.748i	0.997076	+	1.12181i
$237$		0			0
$238$	−192.508	+	73.1865i	−0.808858	+	0.307506i
$239$	−218.254	+	126.009i	−0.913197	+	0.527235i	−0.881458	−	0.472262i	$-0.843438\pi$
$239$	−218.254	+	126.009i	−0.913197	+	0.527235i	−0.0317388	+	0.999496i	$0.510104\pi$
$240$		0			0
$241$	−226.014	+	391.467i	−0.937816	+	1.62435i	−0.168282	+	0.985739i	$0.553822\pi$
$241$	−226.014	+	391.467i	−0.937816	+	1.62435i	−0.769534	+	0.638606i	$0.779511\pi$
$242$	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
$248$	132.306	−	5.65266i	0.533494	−	0.0227930i
$249$		0			0
$250$	146.151	−	179.297i	0.584602	−	0.717188i
$251$			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
$254$	−12.9773	−	10.5782i	−0.0510916	−	0.0416463i
$255$		0			0
$256$	176.142	−	185.769i	0.688053	−	0.725660i
$257$	−235.308	−	407.565i	−0.915594	−	1.58586i	−0.806029	−	0.591875i	$-0.798388\pi$
$257$	−235.308	−	407.565i	−0.915594	−	1.58586i	−0.109564	−	0.993980i	$-0.534946\pi$
$258$		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	$-0.348854\pi$
$263$	−22.2028	−	12.8188i	−0.0844214	−	0.0487407i	−0.541616	+	0.840626i	$0.682187\pi$
$264$		0			0
$265$	−28.6141	−	49.5610i	−0.107978	−	0.187023i
$266$	−116.203	−	305.659i	−0.436855	−	1.14909i
$267$		0			0
$268$	117.554	+	132.260i	0.438634	+	0.493508i
$269$	−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	$-0.265961\pi$
$272$	−130.525	+	56.1103i	−0.479873	+	0.206288i
$273$		0			0
$274$	−32.0647	−	84.3423i	−0.117024	−	0.307819i
$275$	150.826	−	87.0792i	0.548457	−	0.316652i
$276$		0			0
$277$	56.2021	−	97.3449i	0.202896	−	0.351426i	−0.746565	−	0.665313i	$-0.768298\pi$
$277$	56.2021	−	97.3449i	0.202896	−	0.351426i	0.949460	+	0.313887i	$0.101631\pi$
$278$	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	−0.226681	+	0.973969i	$0.572788\pi$
$281$	−268.867	+	465.692i	−0.956823	+	1.65727i	−0.730141	+	0.683296i	$0.760546\pi$
$282$		0			0
$283$	−122.303	+	70.6114i	−0.432164	+	0.249510i	−0.700268	−	0.713880i	$-0.746936\pi$
$283$	−122.303	+	70.6114i	−0.432164	+	0.249510i	0.268104	+	0.963390i	$0.413603\pi$
$284$	438.010	−	90.1571i	1.54229	−	0.317454i
$285$		0			0
$286$	−9.06432	−	7.38860i	−0.0316934	−	0.0258343i
$287$		−	492.113i		−	1.71468i
$288$		0			0
$289$	−210.151			−0.727167
$290$	−69.7533	+	85.5732i	−0.240529	+	0.295080i
$291$		0			0
$292$	61.4500	+	298.543i	0.210445	+	1.02241i
$293$	230.291	+	398.875i	0.785975	+	1.36135i	0.928415	+	0.371545i	$0.121172\pi$
$293$	230.291	+	398.875i	0.785975	+	1.36135i	−0.142440	+	0.989803i	$0.545495\pi$
$294$		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
$302$	−474.965	+	180.569i	−1.57273	+	0.597911i
$303$		0			0
$304$	−89.0902	−	207.244i	−0.293060	−	0.681725i
$305$	−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	$-0.111289\pi$
$308$	342.229	−	304.176i	1.11113	−	0.987585i
$309$		0			0
$310$	83.9308	−	31.9082i	0.270744	−	0.102930i
$311$	−110.993	+	64.0821i	−0.356892	+	0.206052i	−0.667717	−	0.744416i	$-0.732728\pi$
$311$	−110.993	+	64.0821i	−0.356892	+	0.206052i	0.310824	+	0.950467i	$0.399395\pi$
$312$		0			0
$313$	−3.62140	+	6.27245i	−0.0115700	+	0.0200398i	−0.871752	−	0.489947i	$-0.837016\pi$
$313$	−3.62140	+	6.27245i	−0.0115700	+	0.0200398i	0.860182	+	0.509986i	$0.170350\pi$
$314$	−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	−0.611911	−	0.790927i	$-0.709599\pi$
$317$	120.145	−	208.098i	0.379007	−	0.656460i	0.990918	+	0.134467i	$0.0429322\pi$
$318$		0			0
$319$	−173.980	+	100.447i	−0.545392	+	0.314882i
$320$	73.6519	−	157.179i	0.230162	−	0.491184i
$321$		0			0
$322$	−309.240	+	379.375i	−0.960374	+	1.17818i
$323$			125.194i			0.387596i
$324$		0			0
$325$	10.4518			0.0321595
$326$	−92.3216	−	75.2541i	−0.283195	−	0.230841i
$327$		0			0
$328$	−14.4909	−	339.174i	−0.0441795	−	1.03407i
$329$	−10.5207	−	18.2224i	−0.0319778	−	0.0553872i
$330$		0			0
$331$	370.385	+	213.842i	1.11899	+	0.646048i	0.941142	−	0.338011i	$-0.109754\pi$
$331$	370.385	+	213.842i	1.11899	+	0.646048i	0.177845	+	0.984058i	$0.443087\pi$
$332$	−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	0.998531	−	0.0541746i	$-0.0172528\pi$
$337$	152.442	+	264.037i	0.452349	+	0.783492i	−0.546182	+	0.837666i	$0.683919\pi$
$338$	119.862	+	315.283i	0.354622	+	0.932789i
$339$		0			0
$340$	−72.0031	+	63.9969i	−0.211774	+	0.188226i
$341$	163.393			0.479157
$342$		0			0
$343$			423.102i			1.23353i
$344$	−159.776	−	251.317i	−0.464466	−	0.730572i
$345$		0			0
$346$	−27.4287	−	72.1480i	−0.0792738	−	0.208520i
$347$	146.406	−	84.5276i	0.421919	−	0.243595i	−0.273979	−	0.961736i	$-0.588340\pi$
$347$	146.406	−	84.5276i	0.421919	−	0.243595i	0.695898	+	0.718140i	$0.255006\pi$
$348$		0			0
$349$	107.298	−	185.846i	0.307444	−	0.532509i	−0.670358	−	0.742037i	$-0.733860\pi$
$349$	107.298	−	185.846i	0.307444	−	0.532509i	0.977802	+	0.209529i	$0.0671930\pi$
$350$	−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	−0.149451	−	0.988769i	$-0.547751\pi$
$353$	275.895	−	477.865i	0.781574	−	1.35373i	0.931025	−	0.364956i	$-0.118916\pi$
$354$		0			0
$355$	262.593	−	151.608i	0.739698	−	0.427065i
$356$	52.2441	+	253.817i	0.146753	+	0.712970i
$357$		0			0
$358$	56.4693	+	46.0299i	0.157736	+	0.128575i
$359$			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
$362$	23.4937	−	28.8220i	0.0648998	−	0.0796189i
$363$		0			0
$364$	26.9141	−	5.53982i	0.0739398	−	0.0152193i
$365$	103.334	+	178.980i	0.283108	+	0.490357i
$366$		0			0
$367$	145.642	+	84.0864i	0.396845	+	0.229118i	0.685122	−	0.728429i	$-0.259749\pi$
$367$	145.642	+	84.0864i	0.396845	+	0.229118i	−0.288277	+	0.957547i	$0.593082\pi$
$368$	−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	0.998977	−	0.0452296i	$-0.0144020\pi$
$373$	171.699	+	297.391i	0.460318	+	0.797295i	−0.538658	+	0.842524i	$0.681069\pi$
$374$	−163.855	+	62.2931i	−0.438114	+	0.166559i
$375$		0			0
$376$	−7.78765	−	12.2494i	−0.0207118	−	0.0325783i
$377$	−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	$0.707621\pi$
$380$	−101.612	−	114.324i	−0.267401	−	0.300854i
$381$		0			0
$382$	−528.814	+	201.041i	−1.38433	+	0.526285i
$383$	315.762	−	182.305i	0.824443	−	0.475992i	−0.0275035	−	0.999622i	$-0.508756\pi$
$383$	315.762	−	182.305i	0.824443	−	0.475992i	0.851946	+	0.523630i	$0.175422\pi$
$384$		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	−0.970362	−	0.241656i	$-0.922310\pi$
$389$	−107.326	+	185.893i	−0.275901	+	0.477875i	0.694461	+	0.719530i	$0.255643\pi$
$390$		0			0
$391$	162.280	−	93.6923i	0.415038	−	0.239622i
$392$	29.1913	+	683.253i	0.0744677	+	1.74299i
$393$		0			0
$394$	175.879	−	215.768i	0.446393	−	0.547634i
$395$			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	$0.830946\pi$
$398$	−17.4148	−	14.1953i	−0.0437557	−	0.0356666i
$399$		0			0
$400$	−33.1233	+	280.356i	−0.0828082	+	0.700889i
$401$	−95.1918	−	164.877i	−0.237386	−	0.411164i	0.722577	−	0.691290i	$-0.242957\pi$
$401$	−95.1918	−	164.877i	−0.237386	−	0.411164i	−0.959963	+	0.280125i	$0.909624\pi$
$402$		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	0.999063	−	0.0432806i	$-0.0137809\pi$
$409$	188.978	+	327.320i	0.462049	+	0.800293i	−0.537014	+	0.843574i	$0.680448\pi$
$410$	−81.7984	−	215.161i	−0.199508	−	0.524782i
$411$		0			0
$412$	−244.286	−	274.847i	−0.592928	−	0.667104i
$413$	−1026.91			−2.48647
$414$		0			0
$415$			230.573i			0.555598i
$416$	18.3866	−	4.61067i	0.0441985	−	0.0110833i
$417$		0			0
$418$	−98.9072	−	260.163i	−0.236620	−	0.622400i
$419$	267.326	−	154.341i	0.638009	−	0.368355i	−0.145838	−	0.989308i	$-0.546588\pi$
$419$	267.326	−	154.341i	0.638009	−	0.368355i	0.783847	+	0.620954i	$0.213255\pi$
$420$		0			0
$421$	176.834	−	306.286i	0.420034	−	0.727521i	−0.575908	−	0.817514i	$-0.695351\pi$
$421$	176.834	−	306.286i	0.420034	−	0.727521i	0.995942	+	0.0899938i	$0.0286847\pi$
$422$	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
$428$	−422.117	+	86.8857i	−0.986254	+	0.203004i
$429$		0			0
$430$	−156.516	−	127.581i	−0.363990	−	0.296700i
$431$		−	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	$0.477406\pi$
$434$	−242.575	+	297.591i	−0.558929	+	0.685693i
$435$		0			0
$436$	−69.8013	−	339.116i	−0.160095	−	0.777788i
$437$	148.762	+	257.663i	0.340416	+	0.589618i
$438$		0			0
$439$	−354.347	−	204.582i	−0.807169	−	0.466019i	0.0388030	−	0.999247i	$-0.487646\pi$
$439$	−354.347	−	204.582i	−0.807169	−	0.466019i	−0.845972	+	0.533228i	$0.820979\pi$
$440$	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	0.999936	+	0.0113360i	$0.00360844\pi$
$443$	668.806	+	386.136i	1.50972	+	0.871638i	0.509785	+	0.860302i	$0.329725\pi$
$444$		0			0
$445$	87.8536	+	152.167i	0.197424	+	0.341948i
$446$	451.613	−	171.691i	1.01259	−	0.384958i
$447$		0			0
$448$	63.3033	+	739.487i	0.141302	+	1.65064i
$449$	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
$452$	14.0637	−	12.4999i	0.0311144	−	0.0276548i
$453$		0			0
$454$	713.892	−	271.403i	1.57245	−	0.597804i
$455$	16.1354	−	9.31575i	0.0354623	−	0.0204742i
$456$		0			0
$457$	138.165	−	239.309i	0.302331	−	0.523653i	−0.674332	−	0.738428i	$-0.735568\pi$
$457$	138.165	−	239.309i	0.302331	−	0.523653i	0.976664	+	0.214775i	$0.0689018\pi$
$458$	−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	−0.348073	−	0.937467i	$-0.613164\pi$
$461$	294.041	−	509.295i	0.637834	−	1.10476i	0.985907	−	0.167293i	$-0.0535027\pi$
$462$		0			0
$463$	−677.285	+	391.031i	−1.46282	+	0.844558i	−0.999141	−	0.0414459i	$-0.986804\pi$
$463$	−677.285	+	391.031i	−1.46282	+	0.844558i	−0.463677	+	0.886004i	$0.653470\pi$
$464$	38.2082	−	323.395i	0.0823454	−	0.696972i
$465$		0			0
$466$	−276.654	+	339.398i	−0.593678	+	0.728322i
$467$		−	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
$470$	−7.62874	−	6.21842i	−0.0162314	−	0.0132307i
$471$		0			0
$472$	−707.767	+	30.2387i	−1.49951	+	0.0640649i
$473$	−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	$-0.570233\pi$
$479$	−562.018	−	324.481i	−1.17331	−	0.677414i	−0.954459	+	0.298344i	$0.903566\pi$
$480$		0			0
$481$	−12.0416	−	20.8567i	−0.0250346	−	0.0433611i
$482$	−321.264	−	845.047i	−0.666524	−	1.75321i
$483$		0			0
$484$	−70.4700	+	62.6343i	−0.145599	+	0.129410i
$485$	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	$-0.0935338\pi$
$488$	492.733	−	313.258i	1.00970	−	0.641923i
$489$		0			0
$490$	164.780	+	433.433i	0.336285	+	0.884557i
$491$	−652.933	+	376.971i	−1.32980	+	0.767762i	−0.985269	−	0.171012i	$-0.945296\pi$
$491$	−652.933	+	376.971i	−1.32980	+	0.767762i	−0.344534	+	0.938774i	$0.611963\pi$
$492$		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	$-0.839329\pi$
$499$	−446.169	+	257.596i	−0.894126	+	0.516224i	−0.0188362	+	0.999823i	$0.505996\pi$
$500$	93.2701	+	453.134i	0.186540	+	0.906268i
$501$		0			0
$502$	−216.146	−	176.187i	−0.430570	−	0.350971i
$503$			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
$506$	−263.212	+	322.908i	−0.520181	+	0.638157i
$507$		0			0
$508$	32.7972	−	6.75075i	0.0645613	−	0.0132889i
$509$	267.685	+	463.645i	0.525905	+	0.910893i	0.999545	+	0.0301749i	$0.00960643\pi$
$509$	267.685	+	463.645i	0.525905	+	0.910893i	−0.473640	+	0.880719i	$0.657060\pi$
$510$		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
$518$	881.402	−	335.085i	1.70155	−	0.646883i
$519$		0			0
$520$	10.8465	−	6.89573i	0.0208586	−	0.0132610i
$521$	−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	$-0.139610\pi$
$524$	−353.072	−	397.242i	−0.673801	−	0.758096i
$525$		0			0
$526$	47.9285	−	18.2211i	0.0911188	−	0.0346409i
$527$	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
$536$	−353.580	+	15.1064i	−0.659664	+	0.0281835i
$537$		0			0
$538$	10.2996	−	12.6355i	0.0191443	−	0.0234861i
$539$			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	$0.322988\pi$
$542$	623.160	+	507.957i	1.14974	+	0.937190i
$543$		0			0
$544$	77.9534	−	273.248i	0.143297	−	0.502294i
$545$	−117.378	−	203.304i	−0.215372	−	0.373036i
$546$		0			0
$547$	139.875	+	80.7569i	0.255713	+	0.147636i	0.622377	−	0.782717i	$-0.286167\pi$
$547$	139.875	+	80.7569i	0.255713	+	0.147636i	−0.366664	+	0.930353i	$0.619500\pi$
$548$	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
$554$	79.8878	+	210.135i	0.144202	+	0.379305i
$555$		0			0
$556$	401.175	+	451.363i	0.721537	+	0.811803i
$557$	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
$560$	198.746	+	462.330i	0.354904	+	0.825590i
$561$		0			0
$562$	−382.178	−	1005.27i	−0.680032	−	1.78874i
$563$	−250.527	+	144.642i	−0.444985	+	0.256912i	−0.705710	−	0.708501i	$-0.749372\pi$
$563$	−250.527	+	144.642i	−0.444985	+	0.256912i	0.260725	+	0.965413i	$0.416038\pi$
$564$		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	−0.600608	−	0.799544i	$-0.705075\pi$
$569$	223.117	−	386.450i	0.392121	−	0.679174i	0.992729	+	0.120370i	$0.0384079\pi$
$570$		0			0
$571$	372.386	−	214.997i	0.652164	−	0.376527i	−0.137121	−	0.990554i	$-0.543785\pi$
$571$	372.386	−	214.997i	0.652164	−	0.376527i	0.789285	+	0.614027i	$0.210451\pi$
$572$	22.9081	−	4.71525i	0.0400491	−	0.00824344i
$573$		0			0
$574$	762.889	+	621.854i	1.32907	+	1.08337i
$575$		−	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	$0.485936\pi$
$578$	265.556	−	325.783i	0.459439	−	0.563638i
$579$		0			0
$580$	−44.5150	−	216.267i	−0.0767501	−	0.372875i
$581$	−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	$-0.115079\pi$
$587$	643.771	+	371.681i	1.09671	+	0.633188i	0.161358	+	0.986896i	$0.448413\pi$
$588$		0			0
$589$	116.692	+	202.117i	0.198119	+	0.343152i
$590$	−448.983	+	170.692i	−0.760989	+	0.289308i
$591$		0			0
$592$	597.612	−	256.902i	1.00948	−	0.433955i
$593$	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
$596$	−426.886	+	379.419i	−0.716251	+	0.636610i
$597$		0			0
$598$	−23.3693	+	8.88440i	−0.0390792	+	0.0148569i
$599$	−856.248	+	494.355i	−1.42946	+	0.825301i	−0.997078	−	0.0763888i	$-0.975661\pi$
$599$	−856.248	+	494.355i	−1.42946	+	0.825301i	−0.432384	+	0.901689i	$0.642328\pi$
$600$		0			0
$601$	−263.280	+	456.015i	−0.438070	+	0.758760i	−0.997541	−	0.0700905i	$-0.977671\pi$
$601$	−263.280	+	456.015i	−0.438070	+	0.758760i	0.559470	+	0.828850i	$0.311005\pi$
$602$	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	$-0.526671\pi$
$607$	447.631	−	258.440i	0.737448	−	0.425766i	0.821141	+	0.570726i	$0.193338\pi$
$608$	433.854	+	123.772i	0.713576	+	0.203572i
$609$		0			0
$610$	250.136	−	306.866i	0.410058	−	0.503059i
$611$		−	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	$0.286193\pi$
$614$	326.048	+	265.772i	0.531023	+	0.432853i
$615$		0			0
$616$	39.0884	+	914.904i	0.0634552	+	1.48523i
$617$	−60.9168	−	105.511i	−0.0987307	−	0.171007i	0.812429	−	0.583060i	$-0.198145\pi$
$617$	−60.9168	−	105.511i	−0.0987307	−	0.171007i	−0.911160	+	0.412054i	$0.864812\pi$
$618$		0			0
$619$	265.675	+	153.388i	0.429200	+	0.247799i	0.699006	−	0.715116i	$-0.253626\pi$
$619$	265.675	+	153.388i	0.429200	+	0.247799i	−0.269806	+	0.962915i	$0.586959\pi$
$620$	−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
$626$	−5.14760	−	13.5401i	−0.00822300	−	0.0216296i
$627$		0			0
$628$	15.8673	−	14.1030i	0.0252664	−	0.0224570i
$629$	−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	$0.677360\pi$
$632$	−41.1569	−	64.7370i	−0.0651217	−	0.102432i
$633$		0			0
$634$	170.779	+	449.214i	0.269368	+	0.708539i
$635$	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	0.0812143	+	0.996697i	$0.474120\pi$
$641$	−527.259	+	913.240i	−0.822557	+	1.42471i	−0.903772	+	0.428015i	$0.859213\pi$
$642$		0			0
$643$	−42.0680	+	24.2880i	−0.0654246	+	0.0377729i	−0.532355	−	0.846521i	$-0.678693\pi$
$643$	−42.0680	+	24.2880i	−0.0654246	+	0.0377729i	0.466931	+	0.884294i	$0.345360\pi$
$644$	−197.351	−	958.788i	−0.306445	−	1.48880i
$645$		0			0
$646$	−194.079	−	158.200i	−0.300432	−	0.244891i
$647$		−	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
$650$	−13.2074	+	16.2028i	−0.0203190	+	0.0249273i
$651$		0			0
$652$	233.322	−	48.0256i	0.357856	−	0.0736588i
$653$	276.457	+	478.838i	0.423365	+	0.733290i	0.996266	−	0.0863348i	$-0.0275155\pi$
$653$	276.457	+	478.838i	0.423365	+	0.733290i	−0.572901	+	0.819624i	$0.694182\pi$
$654$		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	$-0.110940\pi$
$659$	734.162	+	423.869i	1.11406	+	0.643200i	0.174178	+	0.984714i	$0.444273\pi$
$660$		0			0
$661$	−359.447	−	622.580i	−0.543792	−	0.941876i	−0.998682	−	0.0513280i	$-0.983655\pi$
$661$	−359.447	−	622.580i	−0.543792	−	0.941876i	0.454890	−	0.890548i	$-0.349679\pi$
$662$	−799.537	+	303.963i	−1.20776	+	0.459158i
$663$		0			0
$664$	−364.888	−	573.943i	−0.549530	−	0.864372i
$665$	443.444			0.666833
$666$		0			0
$667$			429.497i			0.643923i
$668$	−263.096	−	296.010i	−0.393856	−	0.443129i
$669$		0			0
$670$	−224.299	+	85.2725i	−0.334775	+	0.127272i
$671$	623.893	−	360.205i	0.929796	−	0.536818i
$672$		0			0
$673$	288.488	−	499.675i	0.428659	−	0.742460i	−0.568095	−	0.822963i	$-0.692319\pi$
$673$	288.488	−	499.675i	0.428659	−	0.742460i	0.996754	+	0.0805033i	$0.0256528\pi$
$674$	−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	−0.781720	−	0.623629i	$-0.785657\pi$
$677$	101.021	−	174.974i	0.149219	−	0.258454i	0.930939	+	0.365175i	$0.118991\pi$
$678$		0			0
$679$	−72.1372	+	41.6484i	−0.106240	+	0.0613379i
$680$	−8.22397	−	192.490i	−0.0120941	−	0.283074i
$681$		0			0
$682$	−206.469	+	253.296i	−0.302741	+	0.371402i
$683$			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
$686$	−655.906	−	534.649i	−0.956131	−	0.779371i
$687$		0			0
$688$	591.499	+	69.8840i	0.859737	+	0.101576i
$689$	6.24965	+	10.8247i	0.00907060	+	0.0157107i
$690$		0			0
$691$	−351.376	−	202.867i	−0.508504	−	0.293585i	0.223714	−	0.974655i	$-0.428182\pi$
$691$	−351.376	−	202.867i	−0.508504	−	0.293585i	−0.732218	+	0.681070i	$0.761515\pi$
$692$	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
$698$	152.517	+	401.178i	0.218506	+	0.574754i
$699$		0			0
$700$	−543.725	−	611.747i	−0.776750	−	0.873924i
$701$	−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
$704$	53.8810	+	629.419i	0.0765355	+	0.894061i
$705$		0			0
$706$	392.168	+	1031.55i	0.555479	+	1.46112i
$707$	1114.86	−	643.663i	1.57688	−	0.910414i
$708$		0			0
$709$	−173.908	+	301.217i	−0.245286	+	0.424848i	−0.962212	−	0.272302i	$-0.912215\pi$
$709$	−173.908	+	301.217i	−0.245286	+	0.424848i	0.716926	+	0.697149i	$0.245548\pi$
$710$	−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
$716$	−142.714	+	29.3753i	−0.199321	+	0.0410269i
$717$		0			0
$718$	−860.112	−	701.103i	−1.19793	−	0.976467i
$719$		−	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
$722$	−204.990	+	251.481i	−0.283919	+	0.348311i
$723$		0			0
$724$	14.9932	+	72.8414i	0.0207088	+	0.100610i
$725$	179.553	+	310.995i	0.247659	+	0.428959i
$726$		0			0
$727$	815.055	+	470.573i	1.12112	+	0.647280i	0.941687	−	0.336490i	$-0.109240\pi$
$727$	815.055	+	470.573i	1.12112	+	0.647280i	0.179435	+	0.983770i	$0.442573\pi$
$728$	−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	0.996361	−	0.0852294i	$-0.0271623\pi$
$733$	311.063	+	538.777i	0.424370	+	0.735030i	−0.571991	+	0.820260i	$0.693829\pi$
$734$	−314.392	+	119.524i	−0.428327	+	0.162839i
$735$		0			0
$736$	−164.251	−	655.004i	−0.223167	−	0.889952i
$737$	−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	$-0.0972213\pi$
$740$	329.667	−	293.011i	0.445496	−	0.395960i
$741$		0			0
$742$	−457.450	+	173.910i	−0.616510	+	0.234381i
$743$	66.2270	−	38.2362i	0.0891346	−	0.0514619i	−0.454770	−	0.890609i	$-0.650279\pi$
$743$	66.2270	−	38.2362i	0.0891346	−	0.0514619i	0.543905	+	0.839147i	$0.316945\pi$
$744$		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	$-0.926954\pi$
$751$	−949.025	+	547.920i	−1.26368	+	0.729587i	−0.289897	+	0.957058i	$0.593621\pi$
$752$	28.8302	+	3.40622i	0.0383381	+	0.00452954i
$753$		0			0
$754$	15.2349	−	18.6902i	0.0202055	−	0.0247880i
$755$		−	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	$0.573468\pi$
$758$	−933.847	−	761.207i	−1.23199	−	1.00423i
$759$		0			0
$760$	305.630	−	13.0578i	0.402145	−	0.0171813i
$761$	106.565	+	184.576i	0.140033	+	0.242544i	0.927509	−	0.373802i	$-0.121946\pi$
$761$	106.565	+	184.576i	0.140033	+	0.242544i	−0.787476	+	0.616345i	$0.788613\pi$
$762$		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	0.634495	−	0.772927i	$-0.281208\pi$
$769$	−270.786	−	469.015i	−0.352127	−	0.609902i	−0.986622	+	0.163025i	$0.947875\pi$
$770$	220.647	+	580.384i	0.286554	+	0.753746i
$771$		0			0
$772$	−906.149	+	805.393i	−1.17377	+	1.04325i
$773$	−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
$776$	−48.4920	+	30.8291i	−0.0624897	+	0.0397282i
$777$		0			0
$778$	−152.557	−	401.281i	−0.196088	−	0.515786i
$779$	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	$-0.449517\pi$
$787$	859.448	−	496.202i	1.09206	−	0.630499i	0.934123	+	0.356951i	$0.116184\pi$
$788$	112.242	+	545.306i	0.142439	+	0.692012i
$789$		0			0
$790$	−40.3171	−	32.8637i	−0.0510343	−	0.0415996i
$791$			54.5507i			0.0689643i
$792$		0			0
$793$	43.2342			0.0545198
$794$	865.123	−	1061.33i	1.08958	−	1.33669i
$795$		0			0
$796$	44.0120	−	9.05914i	0.0552914	−	0.0113808i
$797$	−319.262	−	552.978i	−0.400580	−	0.693824i	0.593216	−	0.805043i	$-0.297858\pi$
$797$	−319.262	−	552.978i	−0.400580	−	0.693824i	−0.993796	+	0.111219i	$0.964525\pi$
$798$		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
$806$	−18.3314	+	6.96913i	−0.0227437	+	0.00864656i
$807$		0			0
$808$	749.428	−	476.453i	0.927509	−	0.589670i
$809$	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	$0.740056\pi$
$812$	627.196	+	705.660i	0.772409	+	0.869039i
$813$		0			0
$814$	750.210	−	285.210i	0.921634	−	0.350381i
$815$	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	−0.987634	−	0.156777i	$-0.949890\pi$
$821$	−293.955	+	509.144i	−0.358045	+	0.620151i	0.629590	+	0.776928i	$0.283223\pi$
$822$		0			0
$823$	98.0750	−	56.6236i	0.119168	−	0.0688015i	−0.439231	−	0.898374i	$-0.644749\pi$
$823$	98.0750	−	56.6236i	0.119168	−	0.0688015i	0.558399	+	0.829573i	$0.311416\pi$
$824$	734.766	−	31.3922i	0.891706	−	0.0380973i
$825$		0			0
$826$	1297.64	−	1591.95i	1.57100	−	1.92730i
$827$			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	$0.252573\pi$
$830$	−357.442	−	291.362i	−0.430653	−	0.351038i
$831$		0			0
$832$	−16.0864	+	34.3297i	−0.0193346	+	0.0412616i
$833$	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	0.987912	+	0.155017i	$0.0495432\pi$
$839$	1355.92	+	782.842i	1.61612	+	0.933065i	0.628205	+	0.778048i	$0.283790\pi$
$840$		0			0
$841$	213.383	+	369.590i	0.253725	+	0.439464i
$842$	251.359	+	661.170i	0.298526	+	0.785237i
$843$		0			0
$844$	343.712	+	386.712i	0.407242	+	0.458189i
$845$	−457.406			−0.541309
$846$		0			0
$847$		−	273.341i		−	0.322717i
$848$	−310.163	+	133.333i	−0.365758	+	0.157232i
$849$		0			0
$850$	111.351	+	292.895i	0.131001	+	0.344583i
$851$	−743.000	+	428.971i	−0.873091	+	0.504079i
$852$		0			0
$853$	−68.8088	+	119.180i	−0.0806668	+	0.139719i	−0.903537	−	0.428511i	$-0.859038\pi$
$853$	−68.8088	+	119.180i	−0.0806668	+	0.139719i	0.822870	+	0.568230i	$0.192372\pi$
$854$	−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	−0.549653	−	0.835393i	$-0.685240\pi$
$857$	384.489	−	665.955i	0.448646	−	0.777077i	0.998298	+	0.0583164i	$0.0185732\pi$
$858$		0			0
$859$	178.353	−	102.972i	0.207629	−	0.119875i	−0.392580	−	0.919718i	$-0.628417\pi$
$859$	178.353	−	102.972i	0.207629	−	0.119875i	0.600209	+	0.799843i	$0.295084\pi$
$860$	395.559	−	81.4193i	0.459953	−	0.0946736i
$861$		0			0
$862$	732.912	+	597.419i	0.850246	+	0.693062i
$863$			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
$866$	−77.6112	+	95.2133i	−0.0896204	+	0.109946i
$867$		0			0
$868$	−154.806	−	752.095i	−0.178348	−	0.866469i
$869$	−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	0.729103	−	0.684404i	$-0.239938\pi$
$877$	−200.096	−	346.577i	−0.228160	−	0.395185i	−0.957263	+	0.289219i	$0.906604\pi$
$878$	764.917	−	290.801i	0.871204	−	0.331209i
$879$		0			0
$880$	169.164	+	393.515i	0.192232	+	0.447176i
$881$	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	$-0.0696625\pi$
$884$	15.7263	−	13.9777i	0.0177899	−	0.0158118i
$885$		0			0
$886$	−1443.73	+	548.868i	−1.62949	+	0.619489i
$887$	−1255.91	+	725.098i	−1.41590	+	0.817473i	−0.995936	−	0.0900662i	$-0.971292\pi$
$887$	−1255.91	+	725.098i	−1.41590	+	0.817473i	−0.419968	+	0.907539i	$0.637959\pi$
$888$		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
$896$	−1226.37	−	836.311i	−1.36871	−	0.933383i
$897$		0			0
$898$	−997.059	+	1223.19i	−1.11031	+	1.36213i
$899$			336.907i			0.374758i
$900$		0			0
$901$	187.365			0.207952
$902$	649.337	+	529.295i	0.719886	+	0.586801i
$903$		0			0
$904$	1.60631	+	37.5974i	0.00177690	+	0.0415901i
$905$	25.2125	+	43.6694i	0.0278592	+	0.0482535i
$906$		0			0
$907$	−533.290	−	307.895i	−0.587971	−	0.339465i	0.176324	−	0.984332i	$-0.443580\pi$
$907$	−533.290	−	307.895i	−0.587971	−	0.339465i	−0.764295	+	0.644867i	$0.776913\pi$
$908$	−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	$-0.379292\pi$
$911$	−227.031	−	131.076i	−0.249211	−	0.143882i	−0.619403	+	0.785073i	$0.712625\pi$
$912$		0			0
$913$	−419.572	−	726.720i	−0.459553	−	0.795969i
$914$	196.393	+	516.589i	0.214872	+	0.565196i
$915$		0			0
$916$	446.455	−	396.813i	0.487397	−	0.433202i
$917$	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	$0.900276\pi$
$920$	−245.654	−	386.396i	−0.267015	−	0.419995i
$921$		0			0
$922$	417.961	+	1099.40i	0.453320	+	1.19240i
$923$	−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	−0.980814	−	0.194948i	$-0.937546\pi$
$929$	−298.745	+	517.442i	−0.321577	+	0.556988i	0.659236	+	0.751936i	$0.270880\pi$
$930$		0			0
$931$	−1043.77	+	602.618i	−1.12112	+	0.647281i
$932$	−176.555	−	857.754i	−0.189436	−	0.920337i
$933$		0			0
$934$	1028.12	+	838.050i	1.10077	+	0.897270i
$935$		−	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	$0.421448\pi$
$938$	648.265	−	795.290i	0.691115	−	0.847858i
$939$		0			0
$940$	19.2800	−	3.96846i	0.0205106	−	0.00422176i
$941$	677.858	+	1174.09i	0.720360	+	1.24770i	0.960856	+	0.277049i	$0.0893566\pi$
$941$	677.858	+	1174.09i	0.720360	+	1.24770i	−0.240496	+	0.970650i	$0.577310\pi$
$942$		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	$-0.220791\pi$
$947$	567.925	+	327.891i	0.599709	+	0.346242i	−0.169218	+	0.985579i	$0.554124\pi$
$948$		0			0
$949$	−22.5694	−	39.0914i	−0.0237823	−	0.0411922i
$950$	−465.050	+	176.800i	−0.489527	+	0.186105i
$951$		0			0
$952$	441.979	+	695.202i	0.464264	+	0.730254i
$953$	−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
$956$	669.693	+	753.473i	0.700516	+	0.788152i
$957$		0			0
$958$	1213.21	−	461.230i	1.26640	−	0.481451i
$959$	−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	$-0.569773\pi$
$967$	502.000	−	289.830i	0.519131	−	0.299720i	0.736579	+	0.676351i	$0.236440\pi$
$968$	−8.04887	−	188.392i	−0.00831495	−	0.194620i
$969$		0			0
$970$	−24.6169	+	30.2000i	−0.0253783	+	0.0311340i
$971$		−	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
$974$	437.326	+	356.478i	0.449000	+	0.365994i
$975$		0			0
$976$	−137.015	+	1159.70i	−0.140384	+	1.18821i
$977$	−638.953	−	1106.70i	−0.653995	−	1.13275i	−0.982145	−	0.188127i	$-0.939758\pi$
$977$	−638.953	−	1106.70i	−0.653995	−	1.13275i	0.328149	−	0.944626i	$-0.393575\pi$
$978$		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	$-0.404658\pi$
$983$	−378.325	−	218.426i	−0.384868	−	0.222204i	−0.679934	+	0.733273i	$0.737992\pi$
$984$		0			0
$985$	188.746	+	326.918i	0.191621	+	0.331897i
$986$	−128.445	−	337.860i	−0.130269	−	0.342657i
$987$		0			0
$988$	22.1933	+	24.9698i	0.0224629	+	0.0252730i
$989$	−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	$-0.237307\pi$
$992$	−128.842	−	513.800i	−0.129881	−	0.517944i
$993$		0			0
$994$	−921.443	−	2423.74i	−0.927005	−	2.43837i
$995$	26.3858	−	15.2338i	0.0265184	−	0.0153104i
$996$		0			0
$997$	942.397	−	1632.28i	0.945233	−	1.63719i	0.189949	−	0.981794i	$-0.439168\pi$
$997$	942.397	−	1632.28i	0.945233	−	1.63719i	0.755284	−	0.655398i	$-0.227499\pi$
$998$	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.19.2		16
3.2	odd	2		36.3.f.c.7.7	yes	16
4.3	odd	2	inner	108.3.f.c.19.3		16
8.3	odd	2		1728.3.o.g.127.5		16
8.5	even	2		1728.3.o.g.127.6		16
9.2	odd	6		324.3.d.i.163.1		8
9.4	even	3	inner	108.3.f.c.91.3		16
9.5	odd	6		36.3.f.c.31.6	yes	16
9.7	even	3		324.3.d.g.163.8		8
12.11	even	2		36.3.f.c.7.6	✓	16
24.5	odd	2		576.3.o.g.511.6		16
24.11	even	2		576.3.o.g.511.3		16
36.7	odd	6		324.3.d.g.163.7		8
36.11	even	6		324.3.d.i.163.2		8
36.23	even	6		36.3.f.c.31.7	yes	16
36.31	odd	6	inner	108.3.f.c.91.2		16
72.5	odd	6		576.3.o.g.319.3		16
72.13	even	6		1728.3.o.g.1279.5		16
72.59	even	6		576.3.o.g.319.6		16
72.67	odd	6		1728.3.o.g.1279.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.6	✓	16	12.11	even	2
36.3.f.c.7.7	yes	16	3.2	odd	2
36.3.f.c.31.6	yes	16	9.5	odd	6
36.3.f.c.31.7	yes	16	36.23	even	6
108.3.f.c.19.2		16	1.1	even	1	trivial
108.3.f.c.19.3		16	4.3	odd	2	inner
108.3.f.c.91.2		16	36.31	odd	6	inner
108.3.f.c.91.3		16	9.4	even	3	inner
324.3.d.g.163.7		8	36.7	odd	6
324.3.d.g.163.8		8	9.7	even	3
324.3.d.i.163.1		8	9.2	odd	6
324.3.d.i.163.2		8	36.11	even	6
576.3.o.g.319.3		16	72.5	odd	6
576.3.o.g.319.6		16	72.59	even	6
576.3.o.g.511.3		16	24.11	even	2
576.3.o.g.511.6		16	24.5	odd	2
1728.3.o.g.127.5		16	8.3	odd	2
1728.3.o.g.127.6		16	8.5	even	2
1728.3.o.g.1279.5		16	72.13	even	6
1728.3.o.g.1279.6		16	72.67	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-1.26364 + 1.55023i) q^{2} +(-0.806428 - 3.91787i) q^{4} +(-1.35609 - 2.34881i) q^{5} +(10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +O(q^{10})\)	\(q+(-1.26364 + 1.55023i) q^{2} +(-0.806428 - 3.91787i) q^{4} +(-1.35609 - 2.34881i) q^{5} +(10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +(5.35481 + 0.865806i) q^{10} +(8.54822 + 4.93532i) q^{11} +(0.296185 + 0.513008i) q^{13} +(-21.6796 + 8.24203i) q^{14} +(-14.6993 + 6.31895i) q^{16} +8.87968 q^{17} +14.0989i q^{19} +(-8.10875 + 7.20712i) q^{20} +(-18.4528 + 7.01525i) q^{22} +(18.2754 - 10.5513i) q^{23} +(8.82205 - 15.2802i) q^{25} +(-1.16955 - 0.189102i) q^{26} +(14.6182 - 44.0234i) q^{28} +(-10.1764 + 17.6260i) q^{29} +(14.3357 - 8.27670i) q^{31} +(8.77885 - 30.7723i) q^{32} +(-11.2207 + 13.7655i) q^{34} -31.4524i q^{35} -40.6557 q^{37} +(-21.8565 - 17.8159i) q^{38} +(-0.926156 - 21.6776i) q^{40} +(-21.2177 - 36.7502i) q^{41} +(-32.2385 - 18.6129i) q^{43} +(12.4424 - 37.4708i) q^{44} +(-6.73658 + 41.6642i) q^{46} +(-1.57134 - 0.907211i) q^{47} +(42.7423 + 74.0318i) q^{49} +(12.5400 + 32.9849i) q^{50} +(1.77105 - 1.57412i) q^{52} +21.1005 q^{53} -26.7709i q^{55} +(49.7742 + 78.2914i) q^{56} +(-14.4651 - 38.0487i) q^{58} +(-76.6879 + 44.2758i) q^{59} +(36.4925 - 63.2069i) q^{61} +(-5.28433 + 32.6823i) q^{62} +(36.6108 + 52.4943i) q^{64} +(0.803307 - 1.39137i) q^{65} +(-38.3110 + 22.1189i) q^{67} +(-7.16082 - 34.7894i) q^{68} +(48.7585 + 39.7446i) q^{70} +111.798i q^{71} -76.2003 q^{73} +(51.3742 - 63.0257i) q^{74} +(55.2375 - 11.3697i) q^{76} +(57.2337 + 99.1316i) q^{77} +(-8.30434 - 4.79451i) q^{79} +(34.7757 + 25.9570i) q^{80} +(83.7828 + 13.5466i) q^{82} +(-73.6244 - 42.5070i) q^{83} +(-12.0416 - 20.8567i) q^{85} +(69.5921 - 26.4571i) q^{86} +(42.3656 + 66.6381i) q^{88} -64.7845 q^{89} +6.86958i q^{91} +(-56.0765 - 63.0918i) q^{92} +(3.39199 - 1.28954i) q^{94} +(33.1157 - 19.1193i) q^{95} +(-3.59139 + 6.22047i) q^{97} +(-168.777 - 27.2892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} - 5 q^{4} - 6 q^{5} + 54 q^{8}+O(q^{10}) \) 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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