LMFDB - Embedded newform 198.4.f.d.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,4,Mod(37,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("198.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	198.f (of order $5$, degree $4$, 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:	$11.6823781811$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 $ x^8 - x^7 + 71x^6 - 141x^5 + 2911x^4 + 2710x^3 + 75340x^2 + 169400x + 5856400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			163.1
Root			$-2.53202 + 7.79275i$ of defining polynomial
Character	$\chi$	$=$	198.163
Dual form			198.4.f.d.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.618034 - 1.90211i) q^{2} +(-3.23607 - 2.35114i) q^{4} +(-4.60996 - 14.1880i) q^{5} +(-17.6106 - 12.7948i) q^{7} +(-6.47214 + 4.70228i) q^{8} +O(q^{10})$	\(q+(0.618034 - 1.90211i) q^{2} +(-3.23607 - 2.35114i) q^{4} +(-4.60996 - 14.1880i) q^{5} +(-17.6106 - 12.7948i) q^{7} +(-6.47214 + 4.70228i) q^{8} -29.8363 q^{10} +(29.3767 + 21.6335i) q^{11} +(-13.6056 + 41.8736i) q^{13} +(-35.2211 + 25.5896i) q^{14} +(4.94427 + 15.2169i) q^{16} +(7.69900 + 23.6951i) q^{17} +(-17.7638 + 12.9061i) q^{19} +(-18.4398 + 56.7520i) q^{20} +(59.3052 - 42.5075i) q^{22} -177.749 q^{23} +(-78.9203 + 57.3389i) q^{25} +(71.2397 + 51.7587i) q^{26} +(26.9065 + 82.8098i) q^{28} +(-120.864 - 87.8130i) q^{29} +(23.2207 - 71.4658i) q^{31} +32.0000 q^{32} +49.8290 q^{34} +(-100.349 + 308.842i) q^{35} +(-179.874 - 130.686i) q^{37} +(13.5703 + 41.7652i) q^{38} +(96.5522 + 70.1493i) q^{40} +(-204.779 + 148.781i) q^{41} +130.623 q^{43} +(-44.2015 - 139.076i) q^{44} +(-109.855 + 338.099i) q^{46} +(403.775 - 293.360i) q^{47} +(40.4316 + 124.436i) q^{49} +(60.2897 + 185.553i) q^{50} +(142.479 - 103.517i) q^{52} +(-3.99933 + 12.3087i) q^{53} +(171.511 - 516.526i) q^{55} +174.143 q^{56} +(-241.728 + 175.626i) q^{58} +(28.7697 + 20.9024i) q^{59} +(166.357 + 511.995i) q^{61} +(-121.585 - 88.3366i) q^{62} +(19.7771 - 60.8676i) q^{64} +656.824 q^{65} -519.621 q^{67} +(30.7960 - 94.7804i) q^{68} +(525.434 + 381.750i) q^{70} +(-24.2420 - 74.6091i) q^{71} +(-925.571 - 672.467i) q^{73} +(-359.748 + 261.372i) q^{74} +87.8290 q^{76} +(-240.543 - 756.848i) q^{77} +(238.730 - 734.735i) q^{79} +(193.104 - 140.299i) q^{80} +(156.438 + 481.465i) q^{82} +(-166.017 - 510.947i) q^{83} +(300.694 - 218.467i) q^{85} +(80.7296 - 248.460i) q^{86} +(-291.857 - 1.87776i) q^{88} -667.089 q^{89} +(775.368 - 563.338i) q^{91} +(575.208 + 417.913i) q^{92} +(-308.457 - 949.332i) q^{94} +(265.003 + 192.536i) q^{95} +(-55.5161 + 170.861i) q^{97} +261.679 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 8 * q^4 - 5 * q^5 - q^7 - 16 * q^8	$ 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8} - 100 q^{10} + 155 q^{11} + 7 q^{13} - 2 q^{14} - 32 q^{16} - 161 q^{17} - 272 q^{19} - 20 q^{20} - 628 q^{23} - 17 q^{25} - 96 q^{26} + 16 q^{28} - 33 q^{29} + 323 q^{31} + 256 q^{32} + 208 q^{34} + 697 q^{35} + 49 q^{37} + 576 q^{38} + 240 q^{40} - 361 q^{41} + 1442 q^{43} - 620 q^{44} - 416 q^{46} + 1069 q^{47} - 709 q^{49} + 76 q^{50} - 192 q^{52} + 281 q^{53} - 7 q^{55} - 48 q^{56} - 66 q^{58} + 128 q^{59} - 617 q^{61} - 1044 q^{62} - 128 q^{64} + 138 q^{65} + 578 q^{67} - 644 q^{68} + 34 q^{70} - 115 q^{71} - 1487 q^{73} + 98 q^{74} - 128 q^{76} - 553 q^{77} + 71 q^{79} + 480 q^{80} + 658 q^{82} - 1942 q^{83} - 329 q^{85} - 2426 q^{86} + 560 q^{88} + 2202 q^{89} + 4523 q^{91} + 2088 q^{92} - 1332 q^{94} + 793 q^{95} - 5128 q^{97} + 3292 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 8 * q^4 - 5 * q^5 - q^7 - 16 * q^8 - 100 * q^10 + 155 * q^11 + 7 * q^13 - 2 * q^14 - 32 * q^16 - 161 * q^17 - 272 * q^19 - 20 * q^20 - 628 * q^23 - 17 * q^25 - 96 * q^26 + 16 * q^28 - 33 * q^29 + 323 * q^31 + 256 * q^32 + 208 * q^34 + 697 * q^35 + 49 * q^37 + 576 * q^38 + 240 * q^40 - 361 * q^41 + 1442 * q^43 - 620 * q^44 - 416 * q^46 + 1069 * q^47 - 709 * q^49 + 76 * q^50 - 192 * q^52 + 281 * q^53 - 7 * q^55 - 48 * q^56 - 66 * q^58 + 128 * q^59 - 617 * q^61 - 1044 * q^62 - 128 * q^64 + 138 * q^65 + 578 * q^67 - 644 * q^68 + 34 * q^70 - 115 * q^71 - 1487 * q^73 + 98 * q^74 - 128 * q^76 - 553 * q^77 + 71 * q^79 + 480 * q^80 + 658 * q^82 - 1942 * q^83 - 329 * q^85 - 2426 * q^86 + 560 * q^88 + 2202 * q^89 + 4523 * q^91 + 2088 * q^92 - 1332 * q^94 + 793 * q^95 - 5128 * q^97 + 3292 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.618034	−	1.90211i	0.218508	−	0.672499i
$2$	0.618034	−	1.90211i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−3.23607	−	2.35114i	−0.404508	−	0.293893i
$5$	−4.60996	−	14.1880i	−0.412327	−	1.26901i	−0.914620	−	0.404315i	$-0.867510\pi$
$5$	−4.60996	−	14.1880i	−0.412327	−	1.26901i	0.502293	−	0.864698i	$-0.332490\pi$
$6$		0			0
$7$	−17.6106	−	12.7948i	−0.950881	−	0.690856i	0.000134039	−	1.00000i	$-0.499957\pi$
$7$	−17.6106	−	12.7948i	−0.950881	−	0.690856i	−0.951015	+	0.309144i	$0.899957\pi$
$8$	−6.47214	+	4.70228i	−0.286031	+	0.207813i
$9$		0			0
$10$	−29.8363			−0.943506
$11$	29.3767	+	21.6335i	0.805219	+	0.592978i
$11$	29.3767	+	21.6335i	0.805219	+	0.592978i
$12$		0			0
$13$	−13.6056	+	41.8736i	−0.290270	+	0.893358i	0.694500	+	0.719493i	$0.255626\pi$
$13$	−13.6056	+	41.8736i	−0.290270	+	0.893358i	−0.984769	+	0.173865i	$0.944374\pi$
$14$	−35.2211	+	25.5896i	−0.672374	+	0.488509i
$15$		0			0
$16$	4.94427	+	15.2169i	0.0772542	+	0.237764i
$17$	7.69900	+	23.6951i	0.109840	+	0.338053i	0.990836	−	0.135071i	$-0.0431262\pi$
$17$	7.69900	+	23.6951i	0.109840	+	0.338053i	−0.880996	+	0.473124i	$0.843126\pi$
$18$		0			0
$19$	−17.7638	+	12.9061i	−0.214489	+	0.155835i	−0.689842	−	0.723960i	$-0.742320\pi$
$19$	−17.7638	+	12.9061i	−0.214489	+	0.155835i	0.475353	+	0.879795i	$0.342320\pi$
$20$	−18.4398	+	56.7520i	−0.206164	+	0.634506i
$21$		0			0
$22$	59.3052	−	42.5075i	0.574724	−	0.411938i
$23$	−177.749			−1.61145			−0.805723	−	0.592293i	$-0.798223\pi$
$23$	−177.749			−1.61145			−0.805723	+	0.592293i	$0.798223\pi$
$24$		0			0
$25$	−78.9203	+	57.3389i	−0.631362	+	0.458711i
$26$	71.2397	+	51.7587i	0.537356	+	0.390412i
$27$		0			0
$28$	26.9065	+	82.8098i	0.181602	+	0.558914i
$29$	−120.864	−	87.8130i	−0.773928	−	0.562292i	0.129223	−	0.991616i	$-0.458752\pi$
$29$	−120.864	−	87.8130i	−0.773928	−	0.562292i	−0.903151	+	0.429324i	$0.858752\pi$
$30$		0			0
$31$	23.2207	−	71.4658i	0.134534	−	0.414053i	−0.860983	−	0.508633i	$-0.830151\pi$
$31$	23.2207	−	71.4658i	0.134534	−	0.414053i	0.995517	+	0.0945803i	$0.0301509\pi$
$32$	32.0000			0.176777
$33$		0			0
$34$	49.8290			0.251341
$35$	−100.349	+	308.842i	−0.484630	+	1.49154i
$36$		0			0
$37$	−179.874	−	130.686i	−0.799219	−	0.580667i	0.111466	−	0.993768i	$-0.464445\pi$
$37$	−179.874	−	130.686i	−0.799219	−	0.580667i	−0.910685	+	0.413102i	$0.864445\pi$
$38$	13.5703	+	41.7652i	0.0579315	+	0.178295i
$39$		0			0
$40$	96.5522	+	70.1493i	0.381656	+	0.277289i
$41$	−204.779	+	148.781i	−0.780029	+	0.566724i	−0.904988	−	0.425438i	$-0.860120\pi$
$41$	−204.779	+	148.781i	−0.780029	+	0.566724i	0.124959	+	0.992162i	$0.460120\pi$
$42$		0			0
$43$	130.623			0.463253			0.231626	−	0.972805i	$-0.425595\pi$
$43$	130.623			0.463253			0.231626	+	0.972805i	$0.425595\pi$
$44$	−44.2015	−	139.076i	−0.151446	−	0.476512i
$45$		0			0
$46$	−109.855	+	338.099i	−0.352114	+	1.08369i
$47$	403.775	−	293.360i	1.25312	−	0.910445i	0.254722	−	0.967014i	$-0.418016\pi$
$47$	403.775	−	293.360i	1.25312	−	0.910445i	0.998399	+	0.0565693i	$0.0180162\pi$
$48$		0			0
$49$	40.4316	+	124.436i	0.117876	+	0.362786i
$50$	60.2897	+	185.553i	0.170525	+	0.524822i
$51$		0			0
$52$	142.479	−	103.517i	0.379968	−	0.276063i
$53$	−3.99933	+	12.3087i	−0.0103651	+	0.0319005i	−0.956105	−	0.293023i	$-0.905339\pi$
$53$	−3.99933	+	12.3087i	−0.0103651	+	0.0319005i	0.945740	+	0.324924i	$0.105339\pi$
$54$		0			0
$55$	171.511	−	516.526i	0.420483	−	1.26633i
$56$	174.143			0.415550
$57$		0			0
$58$	−241.728	+	175.626i	−0.547250	+	0.397600i
$59$	28.7697	+	20.9024i	0.0634831	+	0.0461232i	0.619074	−	0.785332i	$-0.287508\pi$
$59$	28.7697	+	20.9024i	0.0634831	+	0.0461232i	−0.555591	+	0.831456i	$0.687508\pi$
$60$		0			0
$61$	166.357	+	511.995i	0.349178	+	1.07466i	0.959309	+	0.282359i	$0.0911169\pi$
$61$	166.357	+	511.995i	0.349178	+	1.07466i	−0.610131	+	0.792301i	$0.708883\pi$
$62$	−121.585	−	88.3366i	−0.249053	−	0.180948i
$63$		0			0
$64$	19.7771	−	60.8676i	0.0386271	−	0.118882i
$65$	656.824			1.25337
$66$		0			0
$67$	−519.621			−0.947491			−0.473745	−	0.880662i	$-0.657098\pi$
$67$	−519.621			−0.947491			−0.473745	+	0.880662i	$0.657098\pi$
$68$	30.7960	−	94.7804i	0.0549201	−	0.169027i
$69$		0			0
$70$	525.434	+	381.750i	0.897162	+	0.651826i
$71$	−24.2420	−	74.6091i	−0.0405210	−	0.124711i	0.928750	−	0.370708i	$-0.120885\pi$
$71$	−24.2420	−	74.6091i	−0.0405210	−	0.124711i	−0.969271	+	0.245997i	$0.920885\pi$
$72$		0			0
$73$	−925.571	−	672.467i	−1.48397	−	1.07817i	−0.976250	−	0.216648i	$-0.930488\pi$
$73$	−925.571	−	672.467i	−1.48397	−	1.07817i	−0.507722	−	0.861521i	$-0.669512\pi$
$74$	−359.748	+	261.372i	−0.565133	+	0.410593i
$75$		0			0
$76$	87.8290			0.132562
$77$	−240.543	−	756.848i	−0.356005	−	1.12014i
$78$		0			0
$79$	238.730	−	734.735i	0.339990	−	1.04638i	−0.624222	−	0.781247i	$-0.714584\pi$
$79$	238.730	−	734.735i	0.339990	−	1.04638i	0.964212	−	0.265134i	$-0.0854161\pi$
$80$	193.104	−	140.299i	0.269872	−	0.196073i
$81$		0			0
$82$	156.438	+	481.465i	0.210678	+	0.648402i
$83$	−166.017	−	510.947i	−0.219551	−	0.675708i	−0.998799	−	0.0489926i	$-0.984399\pi$
$83$	−166.017	−	510.947i	−0.219551	−	0.675708i	0.779248	−	0.626715i	$-0.215601\pi$
$84$		0			0
$85$	300.694	−	218.467i	0.383704	−	0.278777i
$86$	80.7296	−	248.460i	0.101224	−	0.311537i
$87$		0			0
$88$	−291.857	−	1.87776i	−0.353546	−	0.00227466i
$89$	−667.089			−0.794509			−0.397255	−	0.917708i	$-0.630037\pi$
$89$	−667.089			−0.794509			−0.397255	+	0.917708i	$0.630037\pi$
$90$		0			0
$91$	775.368	−	563.338i	0.893194	−	0.648943i
$92$	575.208	+	417.913i	0.651843	+	0.473592i
$93$		0			0
$94$	−308.457	−	949.332i	−0.338456	−	1.04166i
$95$	265.003	+	192.536i	0.286197	+	0.207934i
$96$		0			0
$97$	−55.5161	+	170.861i	−0.0581114	+	0.178848i	−0.975899	−	0.218224i	$-0.929974\pi$
$97$	−55.5161	+	170.861i	−0.0581114	+	0.178848i	0.917787	+	0.397072i	$0.129974\pi$
$98$	261.679			0.269730
$99$		0			0
$100$	390.203			0.390203
$101$	126.924	−	390.633i	0.125044	−	0.384846i	−0.868865	−	0.495049i	$-0.835150\pi$
$101$	126.924	−	390.633i	0.125044	−	0.384846i	0.993909	+	0.110203i	$0.0351502\pi$
$102$		0			0
$103$	−1106.46	−	803.890i	−1.05847	−	0.769026i	−0.0846679	−	0.996409i	$-0.526983\pi$
$103$	−1106.46	−	803.890i	−1.05847	−	0.769026i	−0.973805	+	0.227383i	$0.926983\pi$
$104$	−108.845	−	334.989i	−0.102626	−	0.315850i
$105$		0			0
$106$	20.9408	+	15.2144i	0.0191882	+	0.0139410i
$107$	−319.756	+	232.317i	−0.288897	+	0.209896i	−0.722789	−	0.691069i	$-0.757140\pi$
$107$	−319.756	+	232.317i	−0.288897	+	0.209896i	0.433892	+	0.900965i	$0.357140\pi$
$108$		0			0
$109$	505.826			0.444490			0.222245	−	0.974991i	$-0.428662\pi$
$109$	505.826			0.444490			0.222245	+	0.974991i	$0.428662\pi$
$110$	−876.491	−	645.464i	−0.759728	−	0.559478i
$111$		0			0
$112$	107.626	−	331.239i	0.0908011	−	0.279457i
$113$	1243.96	−	903.793i	1.03560	−	0.752404i	0.0661744	−	0.997808i	$-0.478921\pi$
$113$	1243.96	−	903.793i	1.03560	−	0.752404i	0.969421	+	0.245404i	$0.0789206\pi$
$114$		0			0
$115$	819.416	+	2521.90i	0.664443	+	2.04494i
$116$	184.664	+	568.337i	0.147807	+	0.454903i
$117$		0			0
$118$	57.5395	−	41.8049i	0.0448893	−	0.0326140i
$119$	167.591	−	515.791i	0.129101	−	0.397332i
$120$		0			0
$121$	394.980	+	1271.04i	0.296754	+	0.954954i
$122$	1076.69			0.799005
$123$		0			0
$124$	−243.170	+	176.673i	−0.176107	+	0.127949i
$125$	−331.285	−	240.693i	−0.237048	−	0.172226i
$126$		0			0
$127$	−215.487	−	663.202i	−0.150562	−	0.463383i	0.847122	−	0.531399i	$-0.178333\pi$
$127$	−215.487	−	663.202i	−0.150562	−	0.463383i	−0.997684	+	0.0680154i	$0.978333\pi$
$128$	−103.554	−	75.2365i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	405.940	−	1249.35i	0.273871	−	0.842889i
$131$	259.910			0.173347			0.0866735	−	0.996237i	$-0.472376\pi$
$131$	259.910			0.173347			0.0866735	+	0.996237i	$0.472376\pi$
$132$		0			0
$133$	477.962			0.311613
$134$	−321.144	+	988.379i	−0.207034	+	0.637186i
$135$		0			0
$136$	−161.250	−	117.155i	−0.101670	−	0.0738673i
$137$	643.856	+	1981.58i	0.401520	+	1.23575i	0.923766	+	0.382958i	$0.125094\pi$
$137$	643.856	+	1981.58i	0.401520	+	1.23575i	−0.522245	+	0.852795i	$0.674906\pi$
$138$		0			0
$139$	−140.307	−	101.939i	−0.0856163	−	0.0622039i	0.544154	−	0.838986i	$-0.316851\pi$
$139$	−140.307	−	101.939i	−0.0856163	−	0.0622039i	−0.629770	+	0.776782i	$0.716851\pi$
$140$	1050.87	−	763.500i	0.634389	−	0.460911i
$141$		0			0
$142$	−156.897			−0.0927220
$143$	−1305.56	+	935.772i	−0.763473	+	0.547225i
$144$		0			0
$145$	−688.711	+	2119.63i	−0.394444	+	1.21397i
$146$	−1851.14	+	1344.93i	−1.04933	+	0.762380i
$147$		0			0
$148$	274.823	+	845.818i	0.152637	+	0.469769i
$149$	138.766	+	427.077i	0.0762961	+	0.234815i	0.981930	−	0.189246i	$-0.0606042\pi$
$149$	138.766	+	427.077i	0.0762961	+	0.234815i	−0.905634	+	0.424061i	$0.860604\pi$
$150$		0			0
$151$	−23.0859	+	16.7729i	−0.0124418	+	0.00903947i	−0.593989	−	0.804473i	$-0.702448\pi$
$151$	−23.0859	+	16.7729i	−0.0124418	+	0.00903947i	0.581547	+	0.813513i	$0.302448\pi$
$152$	54.2813	−	167.061i	0.0289658	−	0.0891474i
$153$		0			0
$154$	−1588.27	−	10.2187i	−0.831083	−	0.00534705i
$155$	−1121.00			−0.580910
$156$		0			0
$157$	−1394.63	+	1013.26i	−0.708941	+	0.515076i	−0.882832	−	0.469689i	$-0.844366\pi$
$157$	−1394.63	+	1013.26i	−0.708941	+	0.515076i	0.173891	+	0.984765i	$0.444366\pi$
$158$	−1250.01	−	908.182i	−0.629399	−	0.457285i
$159$		0			0
$160$	−147.519	−	454.016i	−0.0728898	−	0.224332i
$161$	3130.26	+	2274.27i	1.53229	+	1.11328i
$162$		0			0
$163$	1025.39	−	3155.82i	0.492727	−	1.51646i	−0.327743	−	0.944767i	$-0.606288\pi$
$163$	1025.39	−	3155.82i	0.492727	−	1.51646i	0.820470	−	0.571690i	$-0.193712\pi$
$164$	1012.49			0.482084
$165$		0			0
$166$	−1074.48			−0.502386
$167$	931.871	−	2868.00i	0.431799	−	1.32894i	−0.464533	−	0.885556i	$-0.653778\pi$
$167$	931.871	−	2868.00i	0.431799	−	1.32894i	0.896332	−	0.443384i	$-0.146222\pi$
$168$		0			0
$169$	209.120	+	151.934i	0.0951842	+	0.0691554i
$170$	−229.710	−	706.973i	−0.103635	−	0.318955i
$171$		0			0
$172$	−422.706	−	307.114i	−0.187390	−	0.136147i
$173$	−1787.45	+	1298.66i	−0.785534	+	0.570724i	−0.906635	−	0.421917i	$-0.861357\pi$
$173$	−1787.45	+	1298.66i	−0.785534	+	0.570724i	0.121101	+	0.992640i	$0.461357\pi$
$174$		0			0
$175$	2123.47			0.917254
$176$	−183.949	+	553.984i	−0.0787824	+	0.237262i
$177$		0			0
$178$	−412.284	+	1268.88i	−0.173607	+	0.534306i
$179$	−1837.95	+	1335.35i	−0.767457	+	0.557590i	−0.901189	−	0.433427i	$-0.857304\pi$
$179$	−1837.95	+	1335.35i	−0.767457	+	0.557590i	0.133731	+	0.991018i	$0.457304\pi$
$180$		0			0
$181$	−192.961	−	593.873i	−0.0792413	−	0.243880i	0.903586	−	0.428406i	$-0.140925\pi$
$181$	−192.961	−	593.873i	−0.0792413	−	0.243880i	−0.982828	+	0.184527i	$0.940925\pi$
$182$	−592.328	−	1823.00i	−0.241243	−	0.742471i
$183$		0			0
$184$	1150.42	−	835.826i	0.460923	−	0.334880i
$185$	−1024.96	+	3154.51i	−0.407333	+	1.25364i
$186$		0			0
$187$	−286.438	+	862.640i	−0.112013	+	0.337340i
$188$	−1996.37			−0.774471
$189$		0			0
$190$	530.005	−	385.071i	0.202372	−	0.147032i
$191$	−1087.48	−	790.100i	−0.411975	−	0.299317i	0.362426	−	0.932013i	$-0.381949\pi$
$191$	−1087.48	−	790.100i	−0.411975	−	0.299317i	−0.774401	+	0.632695i	$0.781949\pi$
$192$		0			0
$193$	1428.82	+	4397.46i	0.532895	+	1.64008i	0.748154	+	0.663526i	$0.230941\pi$
$193$	1428.82	+	4397.46i	0.532895	+	1.64008i	−0.215258	+	0.976557i	$0.569059\pi$
$194$	290.686	+	211.196i	0.107578	+	0.0781597i
$195$		0			0
$196$	161.726	−	497.743i	0.0589382	−	0.181393i
$197$	−664.691			−0.240392			−0.120196	−	0.992750i	$-0.538352\pi$
$197$	−664.691			−0.240392			−0.120196	+	0.992750i	$0.538352\pi$
$198$		0			0
$199$	−3042.82			−1.08392			−0.541959	−	0.840405i	$-0.682317\pi$
$199$	−3042.82			−1.08392			−0.541959	+	0.840405i	$0.682317\pi$
$200$	241.159	−	742.211i	0.0852625	−	0.262411i
$201$		0			0
$202$	−664.584	−	482.849i	−0.231485	−	0.168184i
$203$	1004.93	+	3092.87i	0.347451	+	1.06934i
$204$		0			0
$205$	3054.93	+	2219.53i	1.04081	+	0.756190i
$206$	−2212.92	+	1607.78i	−0.748454	+	0.543783i
$207$		0			0
$208$	−704.457			−0.234833
$209$	−801.047	−	5.15380i	−0.265118	−	0.00170572i
$210$		0			0
$211$	800.851	−	2464.77i	0.261293	−	0.804178i	−0.731231	−	0.682130i	$-0.761054\pi$
$211$	800.851	−	2464.77i	0.261293	−	0.804178i	0.992524	−	0.122048i	$-0.0389462\pi$
$212$	41.8815	−	30.4287i	0.0135681	−	0.00985779i
$213$		0			0
$214$	244.272	+	751.792i	0.0780285	+	0.240147i
$215$	−602.168	−	1853.28i	−0.191012	−	0.587873i
$216$		0			0
$217$	−1323.32	+	961.449i	−0.413977	+	0.300772i
$218$	312.618	−	962.139i	0.0971245	−	0.298919i
$219$		0			0
$220$	−1769.45	+	1268.27i	−0.542255	+	0.388666i
$221$	−1096.95			−0.333886
$222$		0			0
$223$	−2133.54	+	1550.11i	−0.640684	+	0.465484i	−0.860085	−	0.510150i	$-0.829590\pi$
$223$	−2133.54	+	1550.11i	−0.640684	+	0.465484i	0.219401	+	0.975635i	$0.429590\pi$
$224$	−563.538	−	409.434i	−0.168094	−	0.122127i
$225$		0			0
$226$	−950.304	−	2924.73i	−0.279705	−	0.860843i
$227$	202.796	+	147.340i	0.0592954	+	0.0430806i	0.617038	−	0.786933i	$-0.288332\pi$
$227$	202.796	+	147.340i	0.0592954	+	0.0430806i	−0.557743	+	0.830014i	$0.688332\pi$
$228$		0			0
$229$	556.018	−	1711.25i	0.160449	−	0.493810i	−0.838224	−	0.545327i	$-0.816406\pi$
$229$	556.018	−	1711.25i	0.160449	−	0.493810i	0.998672	+	0.0515169i	$0.0164056\pi$
$230$	5303.37			1.52041
$231$		0			0
$232$	1195.17			0.338219
$233$	−982.821	+	3024.81i	−0.276338	+	0.850481i	0.712524	+	0.701647i	$0.247552\pi$
$233$	−982.821	+	3024.81i	−0.276338	+	0.850481i	−0.988862	+	0.148833i	$0.952448\pi$
$234$		0			0
$235$	−6023.57	−	4376.38i	−1.67206	−	1.21482i
$236$	−43.9563	−	135.283i	−0.0121242	−	0.0373144i
$237$		0			0
$238$	−877.517	−	637.553i	−0.238996	−	0.173641i
$239$	4056.25	−	2947.04i	1.09781	−	0.797608i	0.117111	−	0.993119i	$-0.462637\pi$
$239$	4056.25	−	2947.04i	1.09781	−	0.797608i	0.980701	+	0.195511i	$0.0626366\pi$
$240$		0			0
$241$	6074.13			1.62352			0.811761	−	0.583990i	$-0.198509\pi$
$241$	6074.13			1.62352			0.811761	+	0.583990i	$0.198509\pi$
$242$	2661.78	+	34.2523i	0.707048	+	0.00909843i
$243$		0			0
$244$	665.429	−	2047.98i	0.174589	−	0.537330i
$245$	1579.10	−	1147.29i	0.411777	−	0.299173i
$246$		0			0
$247$	−298.741	−	919.430i	−0.0769572	−	0.236850i
$248$	185.765	+	571.727i	0.0475649	+	0.146390i
$249$		0			0
$250$	−662.570	+	481.385i	−0.167618	+	0.121782i
$251$	1721.13	−	5297.09i	0.432816	−	1.33207i	−0.462493	−	0.886623i	$-0.653045\pi$
$251$	1721.13	−	5297.09i	0.432816	−	1.33207i	0.895309	−	0.445447i	$-0.146955\pi$
$252$		0			0
$253$	−5221.68	−	3845.34i	−1.29757	−	0.955552i
$254$	−1394.66			−0.344524
$255$		0			0
$256$	−207.108	+	150.473i	−0.0505636	+	0.0367366i
$257$	−4778.90	−	3472.08i	−1.15992	−	0.842732i	−0.170153	−	0.985418i	$-0.554426\pi$
$257$	−4778.90	−	3472.08i	−1.15992	−	0.842732i	−0.989768	+	0.142685i	$0.954426\pi$
$258$		0			0
$259$	1495.58	+	4602.91i	0.358805	+	1.10429i
$260$	−2125.53	−	1544.29i	−0.506998	−	0.368356i
$261$		0			0
$262$	160.633	−	494.379i	0.0378777	−	0.116576i
$263$	6853.74			1.60692			0.803459	−	0.595360i	$-0.202991\pi$
$263$	6853.74			1.60692			0.803459	+	0.595360i	$0.202991\pi$
$264$		0			0
$265$	193.072			0.0447559
$266$	295.397	−	909.138i	0.0680900	−	0.209560i
$267$		0			0
$268$	1681.53	+	1221.70i	0.383268	+	0.278460i
$269$	−340.340	−	1047.46i	−0.0771409	−	0.237415i	0.905049	−	0.425308i	$-0.139834\pi$
$269$	−340.340	−	1047.46i	−0.0771409	−	0.237415i	−0.982190	+	0.187893i	$0.939834\pi$
$270$		0			0
$271$	2080.54	+	1511.60i	0.466362	+	0.338832i	0.796022	−	0.605268i	$-0.206934\pi$
$271$	2080.54	+	1511.60i	0.466362	+	0.338832i	−0.329660	+	0.944100i	$0.606934\pi$
$272$	−322.500	+	234.310i	−0.0718913	+	0.0522321i
$273$		0			0
$274$	4167.12			0.918777
$275$	−3558.86	−	22.8971i	−0.780390	−	0.00502090i
$276$		0			0
$277$	−2268.22	+	6980.85i	−0.492000	+	1.51422i	0.329581	+	0.944127i	$0.393092\pi$
$277$	−2268.22	+	6980.85i	−0.492000	+	1.51422i	−0.821581	+	0.570092i	$0.806908\pi$
$278$	−280.613	+	203.878i	−0.0605398	+	0.0439848i
$279$		0			0
$280$	−802.791	−	2470.74i	−0.171343	−	0.527338i
$281$	2315.45	+	7126.21i	0.491559	+	1.51286i	0.822252	+	0.569124i	$0.192718\pi$
$281$	2315.45	+	7126.21i	0.491559	+	1.51286i	−0.330693	+	0.943738i	$0.607282\pi$
$282$		0			0
$283$	5253.84	−	3817.14i	1.10356	−	0.801785i	0.121925	−	0.992539i	$-0.461093\pi$
$283$	5253.84	−	3817.14i	1.10356	−	0.801785i	0.981638	+	0.190754i	$0.0610933\pi$
$284$	−96.9678	+	298.436i	−0.0202605	+	0.0623554i
$285$		0			0
$286$	973.063	+	3061.67i	0.201183	+	0.633007i
$287$	5509.91			1.13324
$288$		0			0
$289$	3472.52	−	2522.93i	0.706802	−	0.513522i
$290$	3606.14	+	2620.01i	0.730206	+	0.530525i
$291$		0			0
$292$	1414.15	+	4352.30i	0.283413	+	0.872257i
$293$	−2172.11	−	1578.13i	−0.433092	−	0.314660i	0.349792	−	0.936827i	$-0.386252\pi$
$293$	−2172.11	−	1578.13i	−0.433092	−	0.314660i	−0.782884	+	0.622168i	$0.786252\pi$
$294$		0			0
$295$	163.936	−	504.544i	0.0323551	−	0.0995787i
$296$	1778.69			0.349271
$297$		0			0
$298$	898.110			0.174584
$299$	2418.38	−	7443.00i	0.467754	−	1.43960i
$300$		0			0
$301$	−2300.35	−	1671.30i	−0.440498	−	0.320041i
$302$	17.6361	+	54.2783i	0.00336041	+	0.0103423i
$303$		0			0
$304$	−284.221	−	206.498i	−0.0536223	−	0.0389589i
$305$	6497.28	−	4720.55i	1.21978	−	0.886223i
$306$		0			0
$307$	8331.66			1.54890			0.774451	−	0.632633i	$-0.218026\pi$
$307$	8331.66			1.54890			0.774451	+	0.632633i	$0.218026\pi$
$308$	−1001.04	+	3014.76i	−0.185194	+	0.557734i
$309$		0			0
$310$	−692.818	+	2132.27i	−0.126934	+	0.390661i
$311$	−4061.55	+	2950.89i	−0.740545	+	0.538037i	−0.892882	−	0.450292i	$-0.851320\pi$
$311$	−4061.55	+	2950.89i	−0.740545	+	0.538037i	0.152337	+	0.988329i	$0.451320\pi$
$312$		0			0
$313$	933.873	+	2874.16i	0.168644	+	0.519033i	0.999286	−	0.0377733i	$-0.0120265\pi$
$313$	933.873	+	2874.16i	0.168644	+	0.519033i	−0.830642	+	0.556807i	$0.812026\pi$
$314$	1065.40	+	3278.98i	0.191479	+	0.589310i
$315$		0			0
$316$	−2500.01	+	1816.36i	−0.445052	+	0.323350i
$317$	3257.08	−	10024.3i	0.577085	−	1.77609i	−0.0518809	−	0.998653i	$-0.516522\pi$
$317$	3257.08	−	10024.3i	0.577085	−	1.77609i	0.628966	−	0.777433i	$-0.283478\pi$
$318$		0			0
$319$	−1650.88	−	5194.37i	−0.289755	−	0.911690i
$320$	−954.761			−0.166790
$321$		0			0
$322$	6260.52	−	4548.54i	1.08349	−	0.787205i
$323$	−442.576	−	321.550i	−0.0762402	−	0.0553917i
$324$		0			0
$325$	−1327.23	−	4084.81i	−0.226528	−	0.697183i
$326$	−5368.99	−	3900.80i	−0.912150	−	0.662716i
$327$		0			0
$328$	625.750	−	1925.86i	0.105339	−	0.324201i
$329$	−10864.2			−1.82055
$330$		0			0
$331$	309.871			0.0514563			0.0257281	−	0.999669i	$-0.491810\pi$
$331$	309.871			0.0514563			0.0257281	+	0.999669i	$0.491810\pi$
$332$	−664.067	+	2043.79i	−0.109775	+	0.337854i
$333$		0			0
$334$	−4879.34	−	3545.05i	−0.799358	−	0.580768i
$335$	2395.43	+	7372.39i	0.390676	+	1.20238i
$336$		0			0
$337$	−9032.40	−	6562.42i	−1.46002	−	1.06076i	−0.983358	−	0.181677i	$-0.941848\pi$
$337$	−9032.40	−	6562.42i	−1.46002	−	1.06076i	−0.476659	−	0.879088i	$-0.658152\pi$
$338$	418.239	−	303.869i	0.0673054	−	0.0489002i
$339$		0			0
$340$	−1486.71			−0.237142
$341$	2228.20	−	1597.08i	0.353854	−	0.253627i
$342$		0			0
$343$	−1427.13	+	4392.25i	−0.224658	+	0.691425i
$344$	−845.412	+	614.227i	−0.132504	+	0.0962701i
$345$		0			0
$346$	1365.49	+	4202.55i	0.212165	+	0.652978i
$347$	−777.327	−	2392.37i	−0.120257	−	0.370112i	0.872750	−	0.488167i	$-0.162334\pi$
$347$	−777.327	−	2392.37i	−0.120257	−	0.370112i	−0.993007	+	0.118055i	$0.962334\pi$
$348$		0			0
$349$	9203.85	−	6686.99i	1.41166	−	1.02563i	0.418587	−	0.908177i	$-0.362526\pi$
$349$	9203.85	−	6686.99i	1.41166	−	1.02563i	0.993078	−	0.117457i	$-0.0374744\pi$
$350$	1312.38	−	4039.08i	0.200427	−	0.616852i
$351$		0			0
$352$	940.054	+	692.273i	0.142344	+	0.104825i
$353$	−6210.08			−0.936343			−0.468172	−	0.883638i	$-0.655087\pi$
$353$	−6210.08			−0.936343			−0.468172	+	0.883638i	$0.655087\pi$
$354$		0			0
$355$	−946.799	+	687.889i	−0.141552	+	0.102843i
$356$	2158.75	+	1568.42i	0.321386	+	0.233500i
$357$		0			0
$358$	1404.07	+	4321.28i	0.207283	+	0.637952i
$359$	−2012.43	−	1462.12i	−0.295856	−	0.214952i	0.429948	−	0.902854i	$-0.358532\pi$
$359$	−2012.43	−	1462.12i	−0.295856	−	0.214952i	−0.725804	+	0.687902i	$0.758532\pi$
$360$		0			0
$361$	−1970.56	+	6064.77i	−0.287296	+	0.884207i
$362$	−1248.87			−0.181324
$363$		0			0
$364$	−3833.63			−0.552024
$365$	−5274.11	+	16232.0i	−0.756328	+	2.32774i
$366$		0			0
$367$	−5436.21	−	3949.64i	−0.773209	−	0.561770i	0.129724	−	0.991550i	$-0.458591\pi$
$367$	−5436.21	−	3949.64i	−0.773209	−	0.561770i	−0.902933	+	0.429781i	$0.858591\pi$
$368$	−878.840	−	2704.79i	−0.124491	−	0.383144i
$369$		0			0
$370$	5366.77	+	3899.19i	0.754068	+	0.547862i
$371$	227.918	−	165.592i	0.0318946	−	0.0231728i
$372$		0			0
$373$	−8614.37			−1.19580			−0.597902	−	0.801569i	$-0.703999\pi$
$373$	−8614.37			−1.19580			−0.597902	+	0.801569i	$0.703999\pi$
$374$	1463.81	+	1077.98i	0.202385	+	0.149040i
$375$		0			0
$376$	−1233.83	+	3797.33i	−0.169228	+	0.520831i
$377$	5321.47	−	3866.28i	0.726976	−	0.528179i
$378$		0			0
$379$	−2474.95	−	7617.10i	−0.335434	−	1.03236i	−0.966508	−	0.256637i	$-0.917386\pi$
$379$	−2474.95	−	7617.10i	−0.335434	−	1.03236i	0.631074	−	0.775723i	$-0.282614\pi$
$380$	−404.888	−	1246.12i	−0.0546587	−	0.168222i
$381$		0			0
$382$	−2174.96	+	1580.20i	−0.291310	+	0.211649i
$383$	−2475.83	+	7619.82i	−0.330310	+	1.01659i	0.638676	+	0.769476i	$0.279483\pi$
$383$	−2475.83	+	7619.82i	−0.330310	+	1.01659i	−0.968986	+	0.247115i	$0.920517\pi$
$384$		0			0
$385$	−9629.27	+	6901.86i	−1.27468	+	0.913639i
$386$	9247.52			1.21940
$387$		0			0
$388$	581.372	−	422.392i	0.0760688	−	0.0552672i
$389$	6496.09	+	4719.68i	0.846696	+	0.615160i	0.924233	−	0.381829i	$-0.124706\pi$
$389$	6496.09	+	4719.68i	0.846696	+	0.615160i	−0.0775373	+	0.996989i	$0.524706\pi$
$390$		0			0
$391$	−1368.49	−	4211.78i	−0.177001	−	0.544754i
$392$	−846.811	−	615.244i	−0.109108	−	0.0792717i
$393$		0			0
$394$	−410.801	+	1264.32i	−0.0525276	+	0.161663i
$395$	−11524.9			−1.46806
$396$		0			0
$397$	4435.00			0.560670			0.280335	−	0.959902i	$-0.409554\pi$
$397$	4435.00			0.560670			0.280335	+	0.959902i	$0.409554\pi$
$398$	−1880.57	+	5787.79i	−0.236845	+	0.728934i
$399$		0			0
$400$	−1262.72	−	917.423i	−0.157841	−	0.114678i
$401$	1214.19	+	3736.90i	0.151207	+	0.465366i	0.997757	−	0.0669429i	$-0.0213245\pi$
$401$	1214.19	+	3736.90i	0.151207	+	0.465366i	−0.846550	+	0.532309i	$0.821325\pi$
$402$		0			0
$403$	2676.60	+	1944.67i	0.330847	+	0.240374i
$404$	−1329.17	+	965.697i	−0.163685	+	0.118924i
$405$		0			0
$406$	6504.07			0.795054
$407$	−2456.90	−	7730.44i	−0.299223	−	0.941483i
$408$		0			0
$409$	−4500.59	+	13851.4i	−0.544107	+	1.67459i	0.178996	+	0.983850i	$0.442715\pi$
$409$	−4500.59	+	13851.4i	−0.544107	+	1.67459i	−0.723103	+	0.690740i	$0.757285\pi$
$410$	6109.85	−	4439.07i	0.735961	−	0.534707i
$411$		0			0
$412$	1690.52	+	5202.89i	0.202150	+	0.622155i
$413$	−239.208	−	736.208i	−0.0285004	−	0.0877153i
$414$		0			0
$415$	−6483.98	+	4710.89i	−0.766955	+	0.557225i
$416$	−435.378	+	1339.96i	−0.0513129	+	0.157925i
$417$		0			0
$418$	−504.877	+	1520.50i	−0.0590774	+	0.177918i
$419$	−4028.77			−0.469734			−0.234867	−	0.972028i	$-0.575465\pi$
$419$	−4028.77			−0.469734			−0.234867	+	0.972028i	$0.575465\pi$
$420$		0			0
$421$	6898.98	−	5012.40i	0.798659	−	0.580260i	−0.111861	−	0.993724i	$-0.535681\pi$
$421$	6898.98	−	5012.40i	0.798659	−	0.580260i	0.910521	+	0.413464i	$0.135681\pi$
$422$	−4193.31	−	3046.62i	−0.483714	−	0.351439i
$423$		0			0
$424$	−31.9946	−	98.4694i	−0.00366462	−	0.0112785i
$425$	−1966.26	−	1428.57i	−0.224418	−	0.163049i
$426$		0			0
$427$	3621.24	−	11145.0i	0.410408	−	1.26310i
$428$	1580.96			0.178548
$429$		0			0
$430$	−3897.31			−0.437082
$431$	−4145.53	+	12758.6i	−0.463302	+	1.42590i	0.397803	+	0.917471i	$0.369773\pi$
$431$	−4145.53	+	12758.6i	−0.463302	+	1.42590i	−0.861105	+	0.508427i	$0.830227\pi$
$432$		0			0
$433$	−3343.11	−	2428.91i	−0.371038	−	0.269575i	0.386603	−	0.922246i	$-0.373648\pi$
$433$	−3343.11	−	2428.91i	−0.371038	−	0.269575i	−0.757641	+	0.652671i	$0.773648\pi$
$434$	1010.93	+	3111.32i	0.111811	+	0.344120i
$435$		0			0
$436$	−1636.89	−	1189.27i	−0.179800	−	0.130632i
$437$	3157.50	−	2294.06i	0.345637	−	0.251120i
$438$		0			0
$439$	3358.46			0.365126			0.182563	−	0.983194i	$-0.441561\pi$
$439$	3358.46			0.365126			0.182563	+	0.983194i	$0.441561\pi$
$440$	1318.81	+	4149.52i	0.142890	+	0.449592i
$441$		0			0
$442$	−677.952	+	2086.52i	−0.0729568	+	0.224538i
$443$	−357.383	+	259.654i	−0.0383290	+	0.0278477i	−0.606785	−	0.794866i	$-0.707541\pi$
$443$	−357.383	+	259.654i	−0.0383290	+	0.0278477i	0.568456	+	0.822714i	$0.307541\pi$
$444$		0			0
$445$	3075.25	+	9464.66i	0.327598	+	1.00824i
$446$	1629.88	+	5016.26i	0.173043	+	0.532571i
$447$		0			0
$448$	−1127.08	+	818.869i	−0.118860	+	0.0863569i
$449$	126.227	−	388.486i	0.0132673	−	0.0408325i	−0.944204	−	0.329362i	$-0.893166\pi$
$449$	126.227	−	388.486i	0.0132673	−	0.0408325i	0.957471	+	0.288530i	$0.0931663\pi$
$450$		0			0
$451$	−9234.40	−	59.4126i	−0.964148	−	0.00620317i
$452$	−6150.49			−0.640033
$453$		0			0
$454$	405.592	−	294.680i	0.0419282	−	0.0304626i
$455$	−11567.0	−	8403.95i	−1.19181	−	0.865897i
$456$		0			0
$457$	470.585	+	1448.31i	0.0481686	+	0.148248i	0.972248	−	0.233953i	$-0.0751663\pi$
$457$	470.585	+	1448.31i	0.0481686	+	0.148248i	−0.924079	+	0.382201i	$0.875166\pi$
$458$	−2911.35	−	2115.22i	−0.297027	−	0.215803i
$459$		0			0
$460$	3277.66	−	10087.6i	0.332221	−	1.02247i
$461$	13861.4			1.40041			0.700203	−	0.713944i	$-0.253093\pi$
$461$	13861.4			1.40041			0.700203	+	0.713944i	$0.253093\pi$
$462$		0			0
$463$	−6502.26			−0.652669			−0.326334	−	0.945254i	$-0.605814\pi$
$463$	−6502.26			−0.652669			−0.326334	+	0.945254i	$0.605814\pi$
$464$	738.656	−	2273.35i	0.0739036	−	0.227452i
$465$		0			0
$466$	5146.12	+	3738.87i	0.511565	+	0.371674i
$467$	−131.015	−	403.223i	−0.0129821	−	0.0399548i	0.944356	−	0.328926i	$-0.106687\pi$
$467$	−131.015	−	403.223i	−0.0129821	−	0.0399548i	−0.957338	+	0.288971i	$0.906687\pi$
$468$		0			0
$469$	9150.83	+	6648.46i	0.900951	+	0.654579i
$470$	−12047.1	+	8752.76i	−1.18233	+	0.859010i
$471$		0			0
$472$	−284.491			−0.0277431
$473$	3837.28	+	2825.84i	0.373020	+	0.274699i
$474$		0			0
$475$	661.898	−	2037.11i	0.0639368	−	0.196777i
$476$	−1755.03	+	1275.11i	−0.168995	+	0.122782i
$477$		0			0
$478$	−3098.70	−	9536.82i	−0.296509	−	0.912561i
$479$	−1408.29	−	4334.29i	−0.134335	−	0.413442i	0.861151	−	0.508350i	$-0.169744\pi$
$479$	−1408.29	−	4334.29i	−0.134335	−	0.413442i	−0.995486	+	0.0949081i	$0.969744\pi$
$480$		0			0
$481$	7919.59	−	5753.92i	0.750732	−	0.545439i
$482$	3754.02	−	11553.7i	0.354753	−	1.09182i
$483$		0			0
$484$	1710.22	−	5041.84i	0.160614	−	0.473501i
$485$	2680.10			0.250922
$486$		0			0
$487$	5427.63	−	3943.41i	0.505030	−	0.366926i	−0.305905	−	0.952062i	$-0.598959\pi$
$487$	5427.63	−	3943.41i	0.505030	−	0.366926i	0.810935	+	0.585136i	$0.198959\pi$
$488$	−3484.23	−	2531.44i	−0.323204	−	0.234822i
$489$		0			0
$490$	−1206.33	−	3712.70i	−0.111217	−	0.342291i
$491$	11753.1	+	8539.14i	1.08027	+	0.784859i	0.977729	−	0.209870i	$-0.0673040\pi$
$491$	11753.1	+	8539.14i	1.08027	+	0.784859i	0.102537	+	0.994729i	$0.467304\pi$
$492$		0			0
$493$	1150.20	−	3539.96i	0.105076	−	0.323391i
$494$	−1933.49			−0.176097
$495$		0			0
$496$	1202.30			0.108840
$497$	−527.695	+	1624.08i	−0.0476265	+	0.146579i
$498$		0			0
$499$	7847.09	+	5701.24i	0.703976	+	0.511468i	0.881225	−	0.472698i	$-0.156720\pi$
$499$	7847.09	+	5701.24i	0.703976	+	0.511468i	−0.177249	+	0.984166i	$0.556720\pi$
$500$	506.158	+	1557.79i	0.0452722	+	0.139333i
$501$		0			0
$502$	−9011.95	−	6547.57i	−0.801241	−	0.582136i
$503$	12707.4	−	9232.43i	1.12643	−	0.818397i	0.141256	−	0.989973i	$-0.454886\pi$
$503$	12707.4	−	9232.43i	1.12643	−	0.818397i	0.985171	+	0.171576i	$0.0548859\pi$
$504$		0			0
$505$	−6127.41			−0.539933
$506$	−10541.4	+	7555.67i	−0.926136	+	0.663815i
$507$		0			0
$508$	−861.950	+	2652.81i	−0.0752812	+	0.231692i
$509$	−1192.56	+	866.443i	−0.103849	+	0.0754507i	−0.638498	−	0.769624i	$-0.720444\pi$
$509$	−1192.56	+	866.443i	−0.103849	+	0.0754507i	0.534649	+	0.845074i	$0.320444\pi$
$510$		0			0
$511$	7695.74	+	23685.0i	0.666222	+	2.05042i
$512$	158.217	+	486.941i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−9557.81	+	6944.15i	−0.820188	+	0.595902i
$515$	−6304.85	+	19404.3i	−0.539466	+	1.66031i
$516$		0			0
$517$	18208.0	+	117.147i	1.54891	+	0.00996542i
$518$	9679.57			0.821035
$519$		0			0
$520$	−4251.05	+	3088.57i	−0.358502	+	0.260467i
$521$	−7501.89	−	5450.44i	−0.630832	−	0.458326i	0.225856	−	0.974161i	$-0.427482\pi$
$521$	−7501.89	−	5450.44i	−0.630832	−	0.458326i	−0.856688	+	0.515834i	$0.827482\pi$
$522$		0			0
$523$	−1311.01	−	4034.86i	−0.109610	−	0.337346i	0.881174	−	0.472791i	$-0.156754\pi$
$523$	−1311.01	−	4034.86i	−0.109610	−	0.337346i	−0.990785	+	0.135445i	$0.956754\pi$
$524$	−841.087	−	611.085i	−0.0701203	−	0.0509454i
$525$		0			0
$526$	4235.84	−	13036.6i	0.351125	−	1.08065i
$527$	1872.17			0.154749
$528$		0			0
$529$	19427.7			1.59676
$530$	119.325	−	367.245i	0.00977953	−	0.0300983i
$531$		0			0
$532$	−1546.72	−	1123.76i	−0.126050	−	0.0915809i
$533$	−3443.86	−	10599.1i	−0.279869	−	0.861348i
$534$		0			0
$535$	4770.17	+	3465.73i	0.385481	+	0.280068i
$536$	3363.06	−	2443.41i	0.271011	−	0.196901i
$537$		0			0
$538$	−2202.73			−0.176517
$539$	−1504.24	+	4530.19i	−0.120208	+	0.362020i
$540$		0			0
$541$	−2014.87	+	6201.13i	−0.160122	+	0.492805i	−0.998644	−	0.0520633i	$-0.983420\pi$
$541$	−2014.87	+	6201.13i	−0.160122	+	0.492805i	0.838522	+	0.544868i	$0.183420\pi$
$542$	4161.09	−	3023.21i	0.329768	−	0.239590i
$543$		0			0
$544$	246.368	+	758.243i	0.0194172	+	0.0597599i
$545$	−2331.84	−	7176.66i	−0.183275	−	0.564063i
$546$		0			0
$547$	−5154.07	+	3744.65i	−0.402874	+	0.292705i	−0.770711	−	0.637185i	$-0.780099\pi$
$547$	−5154.07	+	3744.65i	−0.402874	+	0.292705i	0.367836	+	0.929890i	$0.380099\pi$
$548$	2575.42	−	7926.34i	0.200760	−	0.617876i
$549$		0			0
$550$	−2243.05	+	6755.20i	−0.173898	+	0.523714i
$551$	3280.33			0.253624
$552$		0			0
$553$	−13605.0	+	9884.59i	−1.04619	+	0.760100i
$554$	11876.5	+	8628.81i	0.910804	+	0.661738i
$555$		0			0
$556$	214.370	+	659.762i	0.0163513	+	0.0503240i
$557$	4938.23	+	3587.84i	0.375655	+	0.272929i	0.759552	−	0.650447i	$-0.225418\pi$
$557$	4938.23	+	3587.84i	0.375655	+	0.272929i	−0.383897	+	0.923376i	$0.625418\pi$
$558$		0			0
$559$	−1777.20	+	5469.67i	−0.134468	+	0.413851i
$560$	−5195.77			−0.392074
$561$		0			0
$562$	14985.9			1.12481
$563$	4200.34	−	12927.3i	0.314429	−	0.967711i	−0.661561	−	0.749892i	$-0.730106\pi$
$563$	4200.34	−	12927.3i	0.314429	−	0.967711i	0.975989	−	0.217820i	$-0.0698945\pi$
$564$		0			0
$565$	−18557.6	−	13482.9i	−1.38181	−	1.00395i
$566$	−4013.57	−	12352.5i	−0.298062	−	0.917341i
$567$		0			0
$568$	507.730	+	368.888i	0.0375068	+	0.0272503i
$569$	13913.1	−	10108.5i	1.02508	−	0.744761i	0.0577589	−	0.998331i	$-0.481605\pi$
$569$	13913.1	−	10108.5i	1.02508	−	0.744761i	0.967317	+	0.253569i	$0.0816045\pi$
$570$		0			0
$571$	2475.65			0.181441			0.0907203	−	0.995876i	$-0.471083\pi$
$571$	2475.65			0.181441			0.0907203	+	0.995876i	$0.471083\pi$
$572$	6425.02	+	41.3375i	0.469657	+	0.00302169i
$573$		0			0
$574$	3405.31	−	10480.5i	0.247622	−	0.762101i
$575$	14028.0	−	10191.9i	1.01741	−	0.739188i
$576$		0			0
$577$	−6285.32	−	19344.2i	−0.453485	−	1.39568i	−0.872904	−	0.487892i	$-0.837766\pi$
$577$	−6285.32	−	19344.2i	−0.453485	−	1.39568i	0.419419	−	0.907793i	$-0.362234\pi$
$578$	−2652.77	−	8164.38i	−0.190901	−	0.587532i
$579$		0			0
$580$	7212.27	−	5240.02i	0.516333	−	0.375138i
$581$	−3613.83	+	11122.2i	−0.258050	+	0.794196i
$582$		0			0
$583$	−383.767	+	275.068i	−0.0272625	+	0.0195406i
$584$	9152.55			0.648519
$585$		0			0
$586$	−4344.22	+	3156.26i	−0.306242	+	0.222498i
$587$	−11988.4	−	8710.07i	−0.842953	−	0.612441i	0.0802411	−	0.996775i	$-0.474431\pi$
$587$	−11988.4	−	8710.07i	−0.842953	−	0.612441i	−0.923194	+	0.384334i	$0.874431\pi$
$588$		0			0
$589$	509.862	+	1569.19i	0.0356681	+	0.109775i
$590$	−858.382	−	623.651i	−0.0598967	−	0.0435175i
$591$		0			0
$592$	1099.29	−	3383.27i	0.0763186	−	0.234885i
$593$	−11123.2			−0.770281			−0.385140	−	0.922858i	$-0.625847\pi$
$593$	−11123.2			−0.770281			−0.385140	+	0.922858i	$0.625847\pi$
$594$		0			0
$595$	−8090.63			−0.557451
$596$	555.062	−	1708.31i	0.0381481	−	0.117408i
$597$		0			0
$598$	−12662.8	−	9200.06i	−0.865920	−	0.629127i
$599$	−2560.26	−	7879.67i	−0.174640	−	0.537487i	0.824977	−	0.565167i	$-0.191188\pi$
$599$	−2560.26	−	7879.67i	−0.174640	−	0.537487i	−0.999617	+	0.0276796i	$0.991188\pi$
$600$		0			0
$601$	−22101.0	−	16057.3i	−1.50003	−	1.08984i	−0.970370	−	0.241625i	$-0.922320\pi$
$601$	−22101.0	−	16057.3i	−1.50003	−	1.08984i	−0.529660	−	0.848210i	$-0.677680\pi$
$602$	−4600.70	+	3342.60i	−0.311479	+	0.226303i
$603$		0			0
$604$	114.143			0.00768944
$605$	16212.7	−	11463.4i	1.08949	−	0.770338i
$606$		0			0
$607$	5045.53	−	15528.6i	0.337384	−	1.03836i	−0.628152	−	0.778091i	$-0.716188\pi$
$607$	5045.53	−	15528.6i	0.337384	−	1.03836i	0.965536	−	0.260270i	$-0.0838115\pi$
$608$	−568.441	+	412.997i	−0.0379167	+	0.0275481i
$609$		0			0
$610$	−4963.48	−	15276.0i	−0.329452	−	1.01395i
$611$	6790.45	+	20898.9i	0.449611	+	1.38376i
$612$		0			0
$613$	17009.8	−	12358.4i	1.12075	−	0.814274i	0.136429	−	0.990650i	$-0.456437\pi$
$613$	17009.8	−	12358.4i	1.12075	−	0.814274i	0.984323	+	0.176376i	$0.0564374\pi$
$614$	5149.25	−	15847.8i	0.338448	−	1.04163i
$615$		0			0
$616$	5115.74	+	3767.33i	0.334609	+	0.246412i
$617$	−871.824			−0.0568854			−0.0284427	−	0.999595i	$-0.509055\pi$
$617$	−871.824			−0.0568854			−0.0284427	+	0.999595i	$0.509055\pi$
$618$		0			0
$619$	−7602.75	+	5523.72i	−0.493668	+	0.358671i	−0.806593	−	0.591107i	$-0.798691\pi$
$619$	−7602.75	+	5523.72i	−0.493668	+	0.358671i	0.312925	+	0.949778i	$0.398691\pi$
$620$	3627.64	+	2635.64i	0.234983	+	0.170725i
$621$		0			0
$622$	3102.75	+	9549.28i	0.200014	+	0.615581i
$623$	11747.8	+	8535.29i	0.755484	+	0.548891i
$624$		0			0
$625$	−5655.84	+	17406.9i	−0.361974	+	1.11404i
$626$	6044.15			0.385899
$627$		0			0
$628$	6895.44			0.438150
$629$	1711.77	−	5268.28i	0.108510	−	0.333959i
$630$		0			0
$631$	11759.8	+	8544.01i	0.741919	+	0.539036i	0.893311	−	0.449438i	$-0.148376\pi$
$631$	11759.8	+	8544.01i	0.741919	+	0.539036i	−0.151393	+	0.988474i	$0.548376\pi$
$632$	1909.84	+	5877.88i	0.120205	+	0.369952i
$633$		0			0
$634$	−17054.3	−	12390.7i	−1.06832	−	0.776178i
$635$	−8416.12	+	6114.67i	−0.525958	+	0.382131i
$636$		0			0
$637$	−5760.67			−0.358314
$638$	−10900.6	−	70.1325i	−0.676424	−	0.00435200i
$639$		0			0
$640$	−590.075	+	1816.06i	−0.0364449	+	0.112166i
$641$	−9238.70	+	6712.31i	−0.569277	+	0.413604i	−0.834843	−	0.550489i	$-0.814441\pi$
$641$	−9238.70	+	6712.31i	−0.569277	+	0.413604i	0.265565	+	0.964093i	$0.414441\pi$
$642$		0			0
$643$	7407.11	+	22796.7i	0.454289	+	1.39816i	0.871968	+	0.489563i	$0.162844\pi$
$643$	7407.11	+	22796.7i	0.454289	+	1.39816i	−0.417679	+	0.908595i	$0.637156\pi$
$644$	−4782.61	−	14719.4i	−0.292642	−	0.900659i
$645$		0			0
$646$	−885.152	+	643.100i	−0.0539100	+	0.0391679i
$647$	−2569.24	+	7907.32i	−0.156117	+	0.480478i	−0.998272	−	0.0587569i	$-0.981286\pi$
$647$	−2569.24	+	7907.32i	−0.156117	+	0.480478i	0.842156	+	0.539234i	$0.181286\pi$
$648$		0			0
$649$	392.966	+	1236.44i	0.0237677	+	0.0747833i
$650$	−8590.04			−0.518353
$651$		0			0
$652$	−10738.0	+	7801.60i	−0.644988	+	0.468611i
$653$	−24334.7	−	17680.2i	−1.45833	−	1.05954i	−0.983794	−	0.179303i	$-0.942616\pi$
$653$	−24334.7	−	17680.2i	−1.45833	−	1.05954i	−0.474536	−	0.880236i	$-0.657384\pi$
$654$		0			0
$655$	−1198.17	−	3687.60i	−0.0714757	−	0.219980i
$656$	−3276.47	−	2380.50i	−0.195007	−	0.141681i
$657$		0			0
$658$	−6714.44	+	20664.9i	−0.397806	+	1.22432i
$659$	10041.6			0.593572			0.296786	−	0.954944i	$-0.404085\pi$
$659$	10041.6			0.593572			0.296786	+	0.954944i	$0.404085\pi$
$660$		0			0
$661$	1402.50			0.0825281			0.0412640	−	0.999148i	$-0.486862\pi$
$661$	1402.50			0.0825281			0.0412640	+	0.999148i	$0.486862\pi$
$662$	191.511	−	589.409i	0.0112436	−	0.0346043i
$663$		0			0
$664$	3477.10	+	2526.26i	0.203219	+	0.147648i
$665$	−2203.39	−	6781.32i	−0.128487	−	0.395441i
$666$		0			0
$667$	21483.5	+	15608.7i	1.24714	+	0.906102i
$668$	−9758.68	+	7090.10i	−0.565232	+	0.410665i
$669$		0			0
$670$	15503.6			0.893963
$671$	−6189.24	+	18639.6i	−0.356085	+	1.07239i
$672$		0			0
$673$	6299.43	−	19387.7i	0.360810	−	1.11046i	−0.591753	−	0.806119i	$-0.701564\pi$
$673$	6299.43	−	19387.7i	0.360810	−	1.11046i	0.952563	−	0.304341i	$-0.0984361\pi$
$674$	−18064.8	+	13124.8i	−1.03239	+	0.750074i
$675$		0			0
$676$	−319.507	−	983.340i	−0.0181786	−	0.0559479i
$677$	2282.09	+	7023.55i	0.129554	+	0.398725i	0.994703	−	0.102789i	$-0.0327766\pi$
$677$	2282.09	+	7023.55i	0.129554	+	0.398725i	−0.865149	+	0.501514i	$0.832777\pi$
$678$		0			0
$679$	3163.81	−	2298.64i	0.178815	−	0.129917i
$680$	−918.838	+	2827.89i	−0.0518174	+	0.159478i
$681$		0			0
$682$	−1660.73	−	5225.35i	−0.0932442	−	0.293386i
$683$	25844.0			1.44787			0.723935	−	0.689868i	$-0.242332\pi$
$683$	25844.0			1.44787			0.723935	+	0.689868i	$0.242332\pi$
$684$		0			0
$685$	25146.5	−	18270.0i	1.40263	−	1.01907i
$686$	7472.53	+	5429.11i	0.415893	+	0.302164i
$687$		0			0
$688$	645.837	+	1987.68i	0.0357882	+	0.110145i
$689$	−460.996	−	334.933i	−0.0254899	−	0.0185195i
$690$		0			0
$691$	2607.73	−	8025.78i	0.143564	−	0.441845i	−0.853259	−	0.521487i	$-0.825378\pi$
$691$	2607.73	−	8025.78i	0.143564	−	0.441845i	0.996824	+	0.0796417i	$0.0253776\pi$
$692$	8837.64			0.485486
$693$		0			0
$694$	−5030.97			−0.275177
$695$	−799.499	+	2460.60i	−0.0436356	+	0.134296i
$696$		0			0
$697$	−5101.98	−	3706.80i	−0.277261	−	0.201442i
$698$	−7031.12	−	21639.6i	−0.381278	−	1.17345i
$699$		0			0
$700$	−6871.70	−	4992.58i	−0.371037	−	0.269574i
$701$	−10503.8	+	7631.43i	−0.565937	+	0.411177i	−0.833627	−	0.552328i	$-0.813740\pi$
$701$	−10503.8	+	7631.43i	−0.565937	+	0.411177i	0.267690	+	0.963505i	$0.413740\pi$
$702$		0			0
$703$	4881.90			0.261912
$704$	1897.77	−	1360.24i	0.101598	−	0.0728210i
$705$		0			0
$706$	−3838.04	+	11812.3i	−0.204598	+	0.629689i
$707$	−7233.28	+	5255.29i	−0.384775	+	0.279555i
$708$		0			0
$709$	−5537.15	−	17041.6i	−0.293303	−	0.902695i	−0.983786	−	0.179346i	$-0.942602\pi$
$709$	−5537.15	−	17041.6i	−0.293303	−	0.902695i	0.690483	−	0.723349i	$-0.257398\pi$
$710$	723.290	+	2226.06i	0.0382318	+	0.117665i
$711$		0			0
$712$	4317.49	−	3136.84i	0.227254	−	0.165110i
$713$	−4127.45	+	12703.0i	−0.216794	+	0.667224i
$714$		0			0
$715$	19295.3	+	14209.4i	1.00924	+	0.743220i
$716$	9087.33			0.474315
$717$		0			0
$718$	−4024.87	+	2924.24i	−0.209202	+	0.151994i
$719$	2845.59	+	2067.45i	0.147598	+	0.107236i	0.659133	−	0.752026i	$-0.270923\pi$
$719$	2845.59	+	2067.45i	0.147598	+	0.107236i	−0.511536	+	0.859262i	$0.670923\pi$
$720$		0			0
$721$	9199.75	+	28313.9i	0.475196	+	1.46250i
$722$	10318.0	+	7496.47i	0.531851	+	0.386412i
$723$		0			0
$724$	−771.844	+	2375.49i	−0.0396207	+	0.121940i
$725$	14573.7			0.746559
$726$		0			0
$727$	−29438.9			−1.50183			−0.750913	−	0.660401i	$-0.770386\pi$
$727$	−29438.9			−1.50183			−0.750913	+	0.660401i	$0.770386\pi$
$728$	−2369.31	+	7292.00i	−0.120622	+	0.371235i
$729$		0			0
$730$	27615.6	+	20063.9i	1.40014	+	1.01726i
$731$	1005.67	+	3095.13i	0.0508837	+	0.156604i
$732$		0			0
$733$	−2779.70	−	2019.57i	−0.140069	−	0.101766i	0.515544	−	0.856863i	$-0.327590\pi$
$733$	−2779.70	−	2019.57i	−0.140069	−	0.101766i	−0.655613	+	0.755097i	$0.727590\pi$
$734$	−10872.4	+	7899.28i	−0.546742	+	0.397231i
$735$		0			0
$736$	−5687.97			−0.284866
$737$	−15264.8	−	11241.3i	−0.762937	−	0.561841i
$738$		0			0
$739$	−10383.5	+	31957.2i	−0.516866	+	1.59075i	0.262995	+	0.964797i	$0.415290\pi$
$739$	−10383.5	+	31957.2i	−0.516866	+	1.59075i	−0.779861	+	0.625953i	$0.784710\pi$
$740$	10733.5	−	7798.37i	0.533206	−	0.387397i
$741$		0			0
$742$	−174.114	−	535.867i	−0.00861444	−	0.0265125i
$743$	368.875	+	1135.28i	0.0182136	+	0.0560557i	0.959750	−	0.280855i	$-0.0906180\pi$
$743$	368.875	+	1135.28i	0.0182136	+	0.0560557i	−0.941537	+	0.336911i	$0.890618\pi$
$744$		0			0
$745$	5419.66	−	3937.61i	0.266525	−	0.193641i
$746$	−5323.97	+	16385.5i	−0.261293	+	0.804177i
$747$		0			0
$748$	2955.12	−	2118.11i	0.144452	−	0.103537i
$749$	8603.54			0.419715
$750$		0			0
$751$	−19828.5	+	14406.2i	−0.963451	+	0.699988i	−0.953950	−	0.299967i	$-0.903024\pi$
$751$	−19828.5	+	14406.2i	−0.963451	+	0.699988i	−0.00950152	+	0.999955i	$0.503024\pi$
$752$	6460.40	+	4693.76i	0.313280	+	0.227611i
$753$		0			0
$754$	−4065.25	−	12511.5i	−0.196349	−	0.604302i
$755$	344.399	+	250.221i	0.0166013	+	0.0120615i
$756$		0			0
$757$	3338.57	−	10275.0i	0.160294	−	0.493333i	−0.838365	−	0.545109i	$-0.816488\pi$
$757$	3338.57	−	10275.0i	0.160294	−	0.493333i	0.998659	+	0.0517762i	$0.0164882\pi$
$758$	−16018.2			−0.767555
$759$		0			0
$760$	−2620.49			−0.125073
$761$	−2526.49	+	7775.75i	−0.120349	+	0.370395i	−0.993025	−	0.117904i	$-0.962383\pi$
$761$	−2526.49	+	7775.75i	−0.120349	+	0.370395i	0.872676	+	0.488299i	$0.162383\pi$
$762$		0			0
$763$	−8907.88	−	6471.96i	−0.422657	−	0.307078i
$764$	1661.52	+	5113.63i	0.0786802	+	0.242153i
$765$		0			0
$766$	12963.6	+	9418.61i	0.611481	+	0.444267i
$767$	−1266.69	+	920.304i	−0.0596317	+	0.0433250i
$768$		0			0
$769$	−28895.9			−1.35502			−0.677511	−	0.735513i	$-0.736941\pi$
$769$	−28895.9			−1.35502			−0.677511	+	0.735513i	$0.736941\pi$
$770$	7176.90	+	22581.5i	0.335893	+	1.05686i
$771$		0			0
$772$	5715.28	−	17589.8i	0.266448	−	0.820041i
$773$	−14559.7	+	10578.3i	−0.677460	+	0.492203i	−0.872514	−	0.488589i	$-0.837512\pi$
$773$	−14559.7	+	10578.3i	−0.677460	+	0.492203i	0.195054	+	0.980792i	$0.437512\pi$
$774$		0			0
$775$	2265.19	+	6971.55i	0.104991	+	0.323130i
$776$	−444.129	−	1366.89i	−0.0205455	−	0.0632325i
$777$		0			0
$778$	12992.2	−	9439.36i	0.598704	−	0.434984i
$779$	1717.47	−	5285.83i	0.0789919	−	0.243112i
$780$		0			0
$781$	901.910	−	2716.21i	0.0413225	−	0.124448i
$782$	−8857.06			−0.405023
$783$		0			0
$784$	−1693.62	+	1230.49i	−0.0771511	+	0.0560536i
$785$	20805.3	+	15115.9i	0.945954	+	0.687276i
$786$		0			0
$787$	−4906.17	−	15099.6i	−0.222219	−	0.683918i	−0.998562	−	0.0536084i	$-0.982928\pi$
$787$	−4906.17	−	15099.6i	−0.222219	−	0.683918i	0.776343	−	0.630310i	$-0.217072\pi$
$788$	2150.98	+	1562.78i	0.0972407	+	0.0706495i
$789$		0			0
$790$	−7122.81	+	21921.7i	−0.320782	+	0.987267i
$791$	−33470.8			−1.50453
$792$		0			0
$793$	−23702.5			−1.06141
$794$	2740.98	−	8435.86i	0.122511	−	0.377050i
$795$		0			0
$796$	9846.78	+	7154.10i	0.438454	+	0.318556i
$797$	−5098.07	−	15690.2i	−0.226578	−	0.697336i	−0.998128	−	0.0611668i	$-0.980518\pi$
$797$	−5098.07	−	15690.2i	−0.226578	−	0.697336i	0.771549	−	0.636170i	$-0.219482\pi$
$798$		0			0
$799$	10059.9	+	7308.91i	0.445422	+	0.323618i
$800$	−2525.45	+	1834.85i	−0.111610	+	0.0810895i
$801$		0			0
$802$	7858.41			0.345998
$803$	−12642.4	−	39778.2i	−0.555591	−	1.74812i
$804$		0			0
$805$	17836.9	−	54896.4i	0.780955	−	2.40353i
$806$	5353.21	−	3889.33i	0.233944	−	0.169970i
$807$		0			0
$808$	1015.39	+	3125.06i	0.0442097	+	0.136063i
$809$	2812.97	+	8657.42i	0.122248	+	0.376241i	0.993390	−	0.114791i	$-0.0366199\pi$
$809$	2812.97	+	8657.42i	0.122248	+	0.376241i	−0.871142	+	0.491032i	$0.836620\pi$
$810$		0			0
$811$	−29590.8	+	21499.0i	−1.28123	+	0.930865i	−0.999589	−	0.0286567i	$-0.990877\pi$
$811$	−29590.8	+	21499.0i	−1.28123	+	0.930865i	−0.281636	+	0.959521i	$0.590877\pi$
$812$	4019.74	−	12371.5i	0.173726	−	0.534672i
$813$		0			0
$814$	−16222.6	−	104.374i	−0.698528	−	0.00449421i
$815$	−49501.7			−2.12757
$816$		0			0
$817$	−2320.36	+	1685.84i	−0.0993626	+	0.0721912i
$818$	23565.4	+	17121.3i	1.00727	+	0.731823i
$819$		0			0
$820$	−4667.51	−	14365.1i	−0.198776	−	0.611771i
$821$	−2948.23	−	2142.01i	−0.125328	−	0.0910558i	0.523356	−	0.852114i	$-0.324680\pi$
$821$	−2948.23	−	2142.01i	−0.125328	−	0.0910558i	−0.648683	+	0.761059i	$0.724680\pi$
$822$		0			0
$823$	−5221.12	+	16068.9i	−0.221138	+	0.680593i	0.777523	+	0.628855i	$0.216476\pi$
$823$	−5221.12	+	16068.9i	−0.221138	+	0.680593i	−0.998661	+	0.0517380i	$0.983524\pi$
$824$	10941.3			0.462570
$825$		0			0
$826$	−1548.19			−0.0652160
$827$	11983.1	−	36880.1i	0.503860	−	1.55072i	−0.298817	−	0.954310i	$-0.596592\pi$
$827$	11983.1	−	36880.1i	0.503860	−	1.55072i	0.802678	−	0.596413i	$-0.203408\pi$
$828$		0			0
$829$	10027.2	+	7285.20i	0.420096	+	0.305218i	0.777677	−	0.628665i	$-0.216398\pi$
$829$	10027.2	+	7285.20i	0.420096	+	0.305218i	−0.357580	+	0.933882i	$0.616398\pi$
$830$	4953.32	+	15244.8i	0.207147	+	0.637534i
$831$		0			0
$832$	2279.67	+	1656.28i	0.0949920	+	0.0690157i
$833$	−2637.23	+	1916.06i	−0.109694	+	0.0796970i
$834$		0			0
$835$	−44987.1			−1.86448
$836$	2580.13	+	1900.05i	0.106741	+	0.0786061i
$837$		0			0
$838$	−2489.92	+	7663.18i	−0.102641	+	0.315895i
$839$	19872.6	−	14438.3i	0.817732	−	0.594117i	−0.0983299	−	0.995154i	$-0.531350\pi$
$839$	19872.6	−	14438.3i	0.817732	−	0.594117i	0.916062	+	0.401037i	$0.131350\pi$
$840$		0			0
$841$	−639.584	−	1968.44i	−0.0262243	−	0.0807100i
$842$	−5270.35	−	16220.5i	−0.215711	−	0.663889i
$843$		0			0
$844$	−8386.62	+	6093.24i	−0.342037	+	0.248505i
$845$	1191.61	−	3667.40i	0.0485120	−	0.149305i
$846$		0			0
$847$	9306.97	−	27437.5i	0.377557	−	1.11306i
$848$	−207.074			−0.00838554
$849$		0			0
$850$	−3932.52	+	2857.14i	−0.158687	+	0.115293i
$851$	31972.4	+	23229.3i	1.28790	+	0.935712i
$852$		0			0
$853$	−3772.37	−	11610.1i	−0.151422	−	0.466030i	0.846358	−	0.532614i	$-0.178790\pi$
$853$	−3772.37	−	11610.1i	−0.151422	−	0.466030i	−0.997781	+	0.0665834i	$0.978790\pi$
$854$	−18961.1	−	13776.0i	−0.759759	−	0.551997i
$855$		0			0
$856$	977.089	−	3007.17i	0.0390143	−	0.120074i
$857$	−7281.72			−0.290244			−0.145122	−	0.989414i	$-0.546357\pi$
$857$	−7281.72			−0.290244			−0.145122	+	0.989414i	$0.546357\pi$
$858$		0			0
$859$	5927.39			0.235437			0.117718	−	0.993047i	$-0.462442\pi$
$859$	5927.39			0.235437			0.117718	+	0.993047i	$0.462442\pi$
$860$	−2408.67	+	7413.13i	−0.0955058	+	0.293937i
$861$		0			0
$862$	21706.3	+	15770.5i	0.857679	+	0.623140i
$863$	11916.3	+	36674.5i	0.470028	+	1.44660i	0.852547	+	0.522651i	$0.175057\pi$
$863$	11916.3	+	36674.5i	0.470028	+	1.44660i	−0.382518	+	0.923948i	$0.624943\pi$
$864$		0			0
$865$	26665.4	+	19373.6i	1.04815	+	0.761527i
$866$	−6686.22	+	4857.82i	−0.262364	+	0.190618i
$867$		0			0
$868$	6542.86			0.255852
$869$	22908.0	−	16419.5i	0.894247	−	0.640959i
$870$		0			0
$871$	7069.75	−	21758.4i	0.275028	−	0.846449i
$872$	−3273.78	+	2378.54i	−0.127138	+	0.0923709i
$873$		0			0
$874$	−2412.11	−	7423.72i	−0.0933535	−	0.287312i
$875$	2754.49	+	8477.46i	0.106422	+	0.327532i
$876$		0			0
$877$	−23067.2	+	16759.3i	−0.888170	+	0.645293i	−0.935400	−	0.353591i	$-0.884961\pi$
$877$	−23067.2	+	16759.3i	−0.888170	+	0.645293i	0.0472301	+	0.998884i	$0.484961\pi$
$878$	2075.64	−	6388.16i	0.0797830	−	0.245547i
$879$		0			0
$880$	8707.92	+	56.0253i	0.333573	+	0.00214615i
$881$	−40747.6			−1.55826			−0.779128	−	0.626865i	$-0.784338\pi$
$881$	−40747.6			−1.55826			−0.779128	+	0.626865i	$0.784338\pi$
$882$		0			0
$883$	2908.89	−	2113.43i	0.110863	−	0.0805467i	−0.530972	−	0.847389i	$-0.678173\pi$
$883$	2908.89	−	2113.43i	0.110863	−	0.0805467i	0.641835	+	0.766842i	$0.278173\pi$
$884$	3549.80	+	2579.08i	0.135060	+	0.0981266i
$885$		0			0
$886$	273.016	+	840.257i	0.0103523	+	0.0318612i
$887$	−6241.81	−	4534.94i	−0.236279	−	0.171667i	0.463345	−	0.886178i	$-0.346649\pi$
$887$	−6241.81	−	4534.94i	−0.236279	−	0.171667i	−0.699624	+	0.714511i	$0.746649\pi$
$888$		0			0
$889$	−4690.70	+	14436.5i	−0.176964	+	0.544639i
$890$	19903.5			0.749624
$891$		0			0
$892$	10548.8			0.395965
$893$	−3386.43	+	10422.4i	−0.126901	+	0.390561i
$894$		0			0
$895$	27418.8	+	19920.9i	1.02403	+	0.744003i
$896$	861.009	+	2649.91i	0.0321030	+	0.0988029i
$897$		0			0
$898$	−660.932	−	480.195i	−0.0245608	−	0.0178445i
$899$	−9082.17	+	6598.58i	−0.336938	+	0.244800i
$900$		0			0
$901$	−322.446			−0.0119226
$902$	−5820.18	+	17528.2i	−0.214846	+	0.647033i
$903$		0			0
$904$	−3801.21	+	11698.9i	−0.139852	+	0.430421i
$905$	−7536.32	+	5475.46i	−0.276813	+	0.201117i
$906$		0			0
$907$	−10418.1	−	32063.6i	−0.381398	−	1.17382i	−0.939060	−	0.343753i	$-0.888302\pi$
$907$	−10418.1	−	32063.6i	−0.381398	−	1.17382i	0.557662	−	0.830068i	$-0.311698\pi$
$908$	−309.845	−	953.605i	−0.0113244	−	0.0348530i
$909$		0			0
$910$	−23134.1	+	16807.9i	−0.842733	+	0.612282i
$911$	−4644.75	+	14295.1i	−0.168922	+	0.519887i	−0.999304	−	0.0373070i	$-0.988122\pi$
$911$	−4644.75	+	14295.1i	−0.168922	+	0.519887i	0.830382	+	0.557194i	$0.188122\pi$
$912$		0			0
$913$	6176.57	−	18601.5i	0.223894	−	0.674281i
$914$	3045.69			0.110222
$915$		0			0
$916$	−5822.70	+	4230.44i	−0.210030	+	0.152596i
$917$	−4577.16	−	3325.50i	−0.164832	−	0.119758i
$918$		0			0
$919$	−5281.31	−	16254.2i	−0.189570	−	0.583435i	0.810428	−	0.585839i	$-0.199235\pi$
$919$	−5281.31	−	16254.2i	−0.189570	−	0.583435i	−0.999997	+	0.00240379i	$0.999235\pi$
$920$	−17162.1	−	12469.0i	−0.615018	−	0.446837i
$921$		0			0
$922$	8566.79	−	26365.9i	0.306000	−	0.941771i
$923$	3453.98			0.123173
$924$		0			0
$925$	21689.1			0.770955
$926$	−4018.62	+	12368.0i	−0.142613	+	0.438919i
$927$		0			0
$928$	−3867.65	−	2810.01i	−0.136812	−	0.0994001i
$929$	−4066.74	−	12516.1i	−0.143623	−	0.442025i	0.853209	−	0.521570i	$-0.174653\pi$
$929$	−4066.74	−	12516.1i	−0.143623	−	0.442025i	−0.996831	+	0.0795446i	$0.974653\pi$
$930$		0			0
$931$	−2324.20	−	1688.63i	−0.0818182	−	0.0594444i
$932$	10292.2	−	7477.75i	0.361731	−	0.262813i
$933$		0			0
$934$	−847.946			−0.0297063
$935$	13559.6	+	87.2401i	0.474274	+	0.00305140i
$936$		0			0
$937$	1253.46	−	3857.76i	0.0437021	−	0.134501i	−0.926825	−	0.375494i	$-0.877473\pi$
$937$	1253.46	−	3857.76i	0.0437021	−	0.134501i	0.970527	+	0.240993i	$0.0774731\pi$
$938$	18301.7	−	13296.9i	0.637068	−	0.462857i
$939$		0			0
$940$	9203.20	+	28324.5i	0.319335	+	0.982813i
$941$	−10320.4	−	31763.0i	−0.357531	−	1.10037i	−0.954527	−	0.298123i	$-0.903639\pi$
$941$	−10320.4	−	31763.0i	−0.357531	−	1.10037i	0.596996	−	0.802244i	$-0.296361\pi$
$942$		0			0
$943$	36399.3	−	26445.7i	1.25697	−	0.913245i
$944$	−175.825	+	541.134i	−0.00606209	+	0.0186572i
$945$		0			0
$946$	7746.64	−	5552.47i	0.266242	−	0.190831i
$947$	−25660.8			−0.880533			−0.440267	−	0.897867i	$-0.645116\pi$
$947$	−25660.8			−0.880533			−0.440267	+	0.897867i	$0.645116\pi$
$948$		0			0
$949$	40751.6	−	29607.8i	1.39394	−	1.01276i
$950$	−3465.74	−	2518.01i	−0.118362	−	0.0859948i
$951$		0			0
$952$	1340.73	+	4126.33i	0.0456441	+	0.140478i
$953$	39522.7	+	28714.9i	1.34341	+	0.976042i	0.999311	+	0.0371079i	$0.0118145\pi$
$953$	39522.7	+	28714.9i	1.34341	+	0.976042i	0.344096	+	0.938935i	$0.388185\pi$
$954$		0			0
$955$	−6196.70	+	19071.5i	−0.209969	+	0.646218i
$956$	−20055.2			−0.678485
$957$		0			0
$958$	−9114.68			−0.307392
$959$	14015.4	−	43134.8i	0.471929	−	1.45245i
$960$		0			0
$961$	19533.3	+	14191.7i	0.655677	+	0.476377i
$962$	−6050.03	−	18620.1i	−0.202766	−	0.624049i
$963$		0			0
$964$	−19656.3	−	14281.1i	−0.656728	−	0.477141i
$965$	55804.3	−	40544.2i	1.86156	−	1.35250i
$966$		0			0
$967$	−48861.8			−1.62491			−0.812456	−	0.583023i	$-0.801870\pi$
$967$	−48861.8			−1.62491			−0.812456	+	0.583023i	$0.801870\pi$
$968$	−8533.17	−	6369.06i	−0.283333	−	0.211477i
$969$		0			0
$970$	1656.39	−	5097.85i	0.0548284	−	0.168745i
$971$	28224.6	−	20506.4i	0.932822	−	0.677735i	−0.0138603	−	0.999904i	$-0.504412\pi$
$971$	28224.6	−	20506.4i	0.932822	−	0.677735i	0.946682	+	0.322169i	$0.104412\pi$
$972$		0			0
$973$	1166.59	+	3590.40i	0.0384370	+	0.118297i
$974$	−4146.34	−	12761.1i	−0.136404	−	0.419808i
$975$		0			0
$976$	−6968.46	+	5062.88i	−0.228540	+	0.166044i
$977$	5875.16	−	18081.9i	0.192388	−	0.592109i	−0.807609	−	0.589718i	$-0.799239\pi$
$977$	5875.16	−	18081.9i	0.192388	−	0.592109i	0.999997	−	0.00239112i	$-0.000761118\pi$
$978$		0			0
$979$	−19596.9	−	14431.5i	−0.639754	−	0.471126i
$980$	−7807.52			−0.254492
$981$		0			0
$982$	23506.2	−	17078.3i	0.763864	−	0.554979i
$983$	−6025.47	−	4377.76i	−0.195506	−	0.142044i	0.485726	−	0.874111i	$-0.338555\pi$
$983$	−6025.47	−	4377.76i	−0.195506	−	0.142044i	−0.681232	+	0.732068i	$0.738555\pi$
$984$		0			0
$985$	3064.20	+	9430.63i	0.0991202	+	0.305061i
$986$	−6022.54	−	4375.63i	−0.194520	−	0.141327i
$987$		0			0
$988$	−1194.96	+	3677.72i	−0.0384786	+	0.118425i
$989$	−23218.2			−0.746506
$990$		0			0
$991$	5313.37			0.170318			0.0851588	−	0.996367i	$-0.472860\pi$
$991$	5313.37			0.170318			0.0851588	+	0.996367i	$0.472860\pi$
$992$	743.061	−	2286.91i	0.0237825	−	0.0731949i
$993$		0			0
$994$	2763.05	+	2007.47i	0.0881676	+	0.0640575i
$995$	14027.3	+	43171.5i	0.446929	+	1.37551i
$996$		0			0
$997$	−43301.8	−	31460.6i	−1.37551	−	0.999365i	−0.997284	−	0.0736504i	$-0.976535\pi$
$997$	−43301.8	−	31460.6i	−1.37551	−	0.999365i	−0.378223	−	0.925714i	$-0.623465\pi$
$998$	15694.2	−	11402.5i	0.497786	−	0.361663i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.4.f.d.163.1		8
3.2	odd	2		22.4.c.b.9.2	yes	8
11.4	even	5		2178.4.a.by.1.1		4
11.5	even	5	inner	198.4.f.d.181.1		8
11.7	odd	10		2178.4.a.bt.1.1		4
12.11	even	2		176.4.m.b.97.1		8
33.2	even	10		242.4.c.n.3.1		8
33.5	odd	10		22.4.c.b.5.2	✓	8
33.8	even	10		242.4.c.n.81.1		8
33.14	odd	10		242.4.c.r.81.1		8
33.17	even	10		242.4.c.q.27.2		8
33.20	odd	10		242.4.c.r.3.1		8
33.26	odd	10		242.4.a.n.1.1		4
33.29	even	10		242.4.a.o.1.1		4
33.32	even	2		242.4.c.q.9.2		8
132.59	even	10		1936.4.a.bn.1.4		4
132.71	even	10		176.4.m.b.49.1		8
132.95	odd	10		1936.4.a.bm.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.5.2	✓	8	33.5	odd	10
22.4.c.b.9.2	yes	8	3.2	odd	2
176.4.m.b.49.1		8	132.71	even	10
176.4.m.b.97.1		8	12.11	even	2
198.4.f.d.163.1		8	1.1	even	1	trivial
198.4.f.d.181.1		8	11.5	even	5	inner
242.4.a.n.1.1		4	33.26	odd	10
242.4.a.o.1.1		4	33.29	even	10
242.4.c.n.3.1		8	33.2	even	10
242.4.c.n.81.1		8	33.8	even	10
242.4.c.q.9.2		8	33.32	even	2
242.4.c.q.27.2		8	33.17	even	10
242.4.c.r.3.1		8	33.20	odd	10
242.4.c.r.81.1		8	33.14	odd	10
1936.4.a.bm.1.4		4	132.95	odd	10
1936.4.a.bn.1.4		4	132.59	even	10
2178.4.a.bt.1.1		4	11.7	odd	10
2178.4.a.by.1.1		4	11.4	even	5

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.618034 - 1.90211i) q^{2} +(-3.23607 - 2.35114i) q^{4} +(-4.60996 - 14.1880i) q^{5} +(-17.6106 - 12.7948i) q^{7} +(-6.47214 + 4.70228i) q^{8} +O(q^{10})\)	\(q+(0.618034 - 1.90211i) q^{2} +(-3.23607 - 2.35114i) q^{4} +(-4.60996 - 14.1880i) q^{5} +(-17.6106 - 12.7948i) q^{7} +(-6.47214 + 4.70228i) q^{8} -29.8363 q^{10} +(29.3767 + 21.6335i) q^{11} +(-13.6056 + 41.8736i) q^{13} +(-35.2211 + 25.5896i) q^{14} +(4.94427 + 15.2169i) q^{16} +(7.69900 + 23.6951i) q^{17} +(-17.7638 + 12.9061i) q^{19} +(-18.4398 + 56.7520i) q^{20} +(59.3052 - 42.5075i) q^{22} -177.749 q^{23} +(-78.9203 + 57.3389i) q^{25} +(71.2397 + 51.7587i) q^{26} +(26.9065 + 82.8098i) q^{28} +(-120.864 - 87.8130i) q^{29} +(23.2207 - 71.4658i) q^{31} +32.0000 q^{32} +49.8290 q^{34} +(-100.349 + 308.842i) q^{35} +(-179.874 - 130.686i) q^{37} +(13.5703 + 41.7652i) q^{38} +(96.5522 + 70.1493i) q^{40} +(-204.779 + 148.781i) q^{41} +130.623 q^{43} +(-44.2015 - 139.076i) q^{44} +(-109.855 + 338.099i) q^{46} +(403.775 - 293.360i) q^{47} +(40.4316 + 124.436i) q^{49} +(60.2897 + 185.553i) q^{50} +(142.479 - 103.517i) q^{52} +(-3.99933 + 12.3087i) q^{53} +(171.511 - 516.526i) q^{55} +174.143 q^{56} +(-241.728 + 175.626i) q^{58} +(28.7697 + 20.9024i) q^{59} +(166.357 + 511.995i) q^{61} +(-121.585 - 88.3366i) q^{62} +(19.7771 - 60.8676i) q^{64} +656.824 q^{65} -519.621 q^{67} +(30.7960 - 94.7804i) q^{68} +(525.434 + 381.750i) q^{70} +(-24.2420 - 74.6091i) q^{71} +(-925.571 - 672.467i) q^{73} +(-359.748 + 261.372i) q^{74} +87.8290 q^{76} +(-240.543 - 756.848i) q^{77} +(238.730 - 734.735i) q^{79} +(193.104 - 140.299i) q^{80} +(156.438 + 481.465i) q^{82} +(-166.017 - 510.947i) q^{83} +(300.694 - 218.467i) q^{85} +(80.7296 - 248.460i) q^{86} +(-291.857 - 1.87776i) q^{88} -667.089 q^{89} +(775.368 - 563.338i) q^{91} +(575.208 + 417.913i) q^{92} +(-308.457 - 949.332i) q^{94} +(265.003 + 192.536i) q^{95} +(-55.5161 + 170.861i) q^{97} +261.679 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 8 * q^4 - 5 * q^5 - q^7 - 16 * q^8	\( 8 q - 4 q^{2} - 8 q^{4} - 5 q^{5} - q^{7} - 16 q^{8} - 100 q^{10} + 155 q^{11} + 7 q^{13} - 2 q^{14} - 32 q^{16} - 161 q^{17} - 272 q^{19} - 20 q^{20} - 628 q^{23} - 17 q^{25} - 96 q^{26} + 16 q^{28} - 33 q^{29} + 323 q^{31} + 256 q^{32} + 208 q^{34} + 697 q^{35} + 49 q^{37} + 576 q^{38} + 240 q^{40} - 361 q^{41} + 1442 q^{43} - 620 q^{44} - 416 q^{46} + 1069 q^{47} - 709 q^{49} + 76 q^{50} - 192 q^{52} + 281 q^{53} - 7 q^{55} - 48 q^{56} - 66 q^{58} + 128 q^{59} - 617 q^{61} - 1044 q^{62} - 128 q^{64} + 138 q^{65} + 578 q^{67} - 644 q^{68} + 34 q^{70} - 115 q^{71} - 1487 q^{73} + 98 q^{74} - 128 q^{76} - 553 q^{77} + 71 q^{79} + 480 q^{80} + 658 q^{82} - 1942 q^{83} - 329 q^{85} - 2426 q^{86} + 560 q^{88} + 2202 q^{89} + 4523 q^{91} + 2088 q^{92} - 1332 q^{94} + 793 q^{95} - 5128 q^{97} + 3292 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^4 - 5 * q^5 - q^7 - 16 * q^8 - 100 * q^10 + 155 * q^11 + 7 * q^13 - 2 * q^14 - 32 * q^16 - 161 * q^17 - 272 * q^19 - 20 * q^20 - 628 * q^23 - 17 * q^25 - 96 * q^26 + 16 * q^28 - 33 * q^29 + 323 * q^31 + 256 * q^32 + 208 * q^34 + 697 * q^35 + 49 * q^37 + 576 * q^38 + 240 * q^40 - 361 * q^41 + 1442 * q^43 - 620 * q^44 - 416 * q^46 + 1069 * q^47 - 709 * q^49 + 76 * q^50 - 192 * q^52 + 281 * q^53 - 7 * q^55 - 48 * q^56 - 66 * q^58 + 128 * q^59 - 617 * q^61 - 1044 * q^62 - 128 * q^64 + 138 * q^65 + 578 * q^67 - 644 * q^68 + 34 * q^70 - 115 * q^71 - 1487 * q^73 + 98 * q^74 - 128 * q^76 - 553 * q^77 + 71 * q^79 + 480 * q^80 + 658 * q^82 - 1942 * q^83 - 329 * q^85 - 2426 * q^86 + 560 * q^88 + 2202 * q^89 + 4523 * q^91 + 2088 * q^92 - 1332 * q^94 + 793 * q^95 - 5128 * q^97 + 3292 * q^98

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