LMFDB - Embedded newform 198.4.f.d.181.1

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			181.1
Root			$-2.53202 - 7.79275i$ of defining polynomial
Character	$\chi$	$=$	198.181
Dual form			198.4.f.d.163.1

$q$-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 $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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	0.502293	+	0.864698i	$0.332490\pi$
$5$	−4.60996	+	14.1880i	−0.412327	+	1.26901i	−0.914620	+	0.404315i	$0.867510\pi$
$6$		0			0
$7$	−17.6106	+	12.7948i	−0.950881	+	0.690856i	−0.951015	−	0.309144i	$-0.899957\pi$
$7$	−17.6106	+	12.7948i	−0.950881	+	0.690856i	0.000134039		1.00000i	$0.499957\pi$
$8$	−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	−0.984769	−	0.173865i	$-0.944374\pi$
$13$	−13.6056	−	41.8736i	−0.290270	−	0.893358i	0.694500	−	0.719493i	$-0.255626\pi$
$14$	−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	−0.880996	−	0.473124i	$-0.843126\pi$
$17$	7.69900	−	23.6951i	0.109840	−	0.338053i	0.990836	+	0.135071i	$0.0431262\pi$
$18$		0			0
$19$	−17.7638	−	12.9061i	−0.214489	−	0.155835i	0.475353	−	0.879795i	$-0.342320\pi$
$19$	−17.7638	−	12.9061i	−0.214489	−	0.155835i	−0.689842	+	0.723960i	$0.742320\pi$
$20$	−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	−0.903151	−	0.429324i	$-0.858752\pi$
$29$	−120.864	+	87.8130i	−0.773928	+	0.562292i	0.129223	+	0.991616i	$0.458752\pi$
$30$		0			0
$31$	23.2207	+	71.4658i	0.134534	+	0.414053i	0.995517	−	0.0945803i	$-0.0301509\pi$
$31$	23.2207	+	71.4658i	0.134534	+	0.414053i	−0.860983	+	0.508633i	$0.830151\pi$
$32$	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	−0.910685	−	0.413102i	$-0.864445\pi$
$37$	−179.874	+	130.686i	−0.799219	+	0.580667i	0.111466	+	0.993768i	$0.464445\pi$
$38$	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	0.124959	−	0.992162i	$-0.460120\pi$
$41$	−204.779	−	148.781i	−0.780029	−	0.566724i	−0.904988	+	0.425438i	$0.860120\pi$
$42$		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	0.998399	−	0.0565693i	$-0.0180162\pi$
$47$	403.775	+	293.360i	1.25312	+	0.910445i	0.254722	+	0.967014i	$0.418016\pi$
$48$		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	0.945740	−	0.324924i	$-0.105339\pi$
$53$	−3.99933	−	12.3087i	−0.0103651	−	0.0319005i	−0.956105	+	0.293023i	$0.905339\pi$
$54$		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	−0.555591	−	0.831456i	$-0.687508\pi$
$59$	28.7697	−	20.9024i	0.0634831	−	0.0461232i	0.619074	+	0.785332i	$0.287508\pi$
$60$		0			0
$61$	166.357	−	511.995i	0.349178	−	1.07466i	−0.610131	−	0.792301i	$-0.708883\pi$
$61$	166.357	−	511.995i	0.349178	−	1.07466i	0.959309	−	0.282359i	$-0.0911169\pi$
$62$	−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	−0.969271	−	0.245997i	$-0.920885\pi$
$71$	−24.2420	+	74.6091i	−0.0405210	+	0.124711i	0.928750	+	0.370708i	$0.120885\pi$
$72$		0			0
$73$	−925.571	+	672.467i	−1.48397	+	1.07817i	−0.507722	+	0.861521i	$0.669512\pi$
$73$	−925.571	+	672.467i	−1.48397	+	1.07817i	−0.976250	+	0.216648i	$0.930488\pi$
$74$	−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	0.964212	+	0.265134i	$0.0854161\pi$
$79$	238.730	+	734.735i	0.339990	+	1.04638i	−0.624222	+	0.781247i	$0.714584\pi$
$80$	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	0.779248	+	0.626715i	$0.215601\pi$
$83$	−166.017	+	510.947i	−0.219551	+	0.675708i	−0.998799	+	0.0489926i	$0.984399\pi$
$84$		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	0.917787	−	0.397072i	$-0.129974\pi$
$97$	−55.5161	−	170.861i	−0.0581114	−	0.178848i	−0.975899	+	0.218224i	$0.929974\pi$
$98$	261.679			0.269730
$99$		0			0
$100$	390.203			0.390203
$101$	126.924	+	390.633i	0.125044	+	0.384846i	0.993909	−	0.110203i	$-0.0351502\pi$
$101$	126.924	+	390.633i	0.125044	+	0.384846i	−0.868865	+	0.495049i	$0.835150\pi$
$102$		0			0
$103$	−1106.46	+	803.890i	−1.05847	+	0.769026i	−0.973805	−	0.227383i	$-0.926983\pi$
$103$	−1106.46	+	803.890i	−1.05847	+	0.769026i	−0.0846679	+	0.996409i	$0.526983\pi$
$104$	−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	0.433892	−	0.900965i	$-0.357140\pi$
$107$	−319.756	−	232.317i	−0.288897	−	0.209896i	−0.722789	+	0.691069i	$0.757140\pi$
$108$		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	0.969421	−	0.245404i	$-0.0789206\pi$
$113$	1243.96	+	903.793i	1.03560	+	0.752404i	0.0661744	+	0.997808i	$0.478921\pi$
$114$		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	−0.997684	−	0.0680154i	$-0.978333\pi$
$127$	−215.487	+	663.202i	−0.150562	+	0.463383i	0.847122	+	0.531399i	$0.178333\pi$
$128$	−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	−0.522245	−	0.852795i	$-0.674906\pi$
$137$	643.856	−	1981.58i	0.401520	−	1.23575i	0.923766	−	0.382958i	$-0.125094\pi$
$138$		0			0
$139$	−140.307	+	101.939i	−0.0856163	+	0.0622039i	−0.629770	−	0.776782i	$-0.716851\pi$
$139$	−140.307	+	101.939i	−0.0856163	+	0.0622039i	0.544154	+	0.838986i	$0.316851\pi$
$140$	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	−0.905634	−	0.424061i	$-0.860604\pi$
$149$	138.766	−	427.077i	0.0762961	−	0.234815i	0.981930	+	0.189246i	$0.0606042\pi$
$150$		0			0
$151$	−23.0859	−	16.7729i	−0.0124418	−	0.00903947i	0.581547	−	0.813513i	$-0.302448\pi$
$151$	−23.0859	−	16.7729i	−0.0124418	−	0.00903947i	−0.593989	+	0.804473i	$0.702448\pi$
$152$	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	0.173891	−	0.984765i	$-0.444366\pi$
$157$	−1394.63	−	1013.26i	−0.708941	−	0.515076i	−0.882832	+	0.469689i	$0.844366\pi$
$158$	−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	0.820470	+	0.571690i	$0.193712\pi$
$163$	1025.39	+	3155.82i	0.492727	+	1.51646i	−0.327743	+	0.944767i	$0.606288\pi$
$164$	1012.49			0.482084
$165$		0			0
$166$	−1074.48			−0.502386
$167$	931.871	+	2868.00i	0.431799	+	1.32894i	0.896332	+	0.443384i	$0.146222\pi$
$167$	931.871	+	2868.00i	0.431799	+	1.32894i	−0.464533	+	0.885556i	$0.653778\pi$
$168$		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	0.121101	−	0.992640i	$-0.461357\pi$
$173$	−1787.45	−	1298.66i	−0.785534	−	0.570724i	−0.906635	+	0.421917i	$0.861357\pi$
$174$		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	0.133731	−	0.991018i	$-0.457304\pi$
$179$	−1837.95	−	1335.35i	−0.767457	−	0.557590i	−0.901189	+	0.433427i	$0.857304\pi$
$180$		0			0
$181$	−192.961	+	593.873i	−0.0792413	+	0.243880i	−0.982828	−	0.184527i	$-0.940925\pi$
$181$	−192.961	+	593.873i	−0.0792413	+	0.243880i	0.903586	+	0.428406i	$0.140925\pi$
$182$	−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	−0.774401	−	0.632695i	$-0.781949\pi$
$191$	−1087.48	+	790.100i	−0.411975	+	0.299317i	0.362426	+	0.932013i	$0.381949\pi$
$192$		0			0
$193$	1428.82	−	4397.46i	0.532895	−	1.64008i	−0.215258	−	0.976557i	$-0.569059\pi$
$193$	1428.82	−	4397.46i	0.532895	−	1.64008i	0.748154	−	0.663526i	$-0.230941\pi$
$194$	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	0.992524	+	0.122048i	$0.0389462\pi$
$211$	800.851	+	2464.77i	0.261293	+	0.804178i	−0.731231	+	0.682130i	$0.761054\pi$
$212$	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	0.219401	−	0.975635i	$-0.429590\pi$
$223$	−2133.54	−	1550.11i	−0.640684	−	0.465484i	−0.860085	+	0.510150i	$0.829590\pi$
$224$	−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	−0.557743	−	0.830014i	$-0.688332\pi$
$227$	202.796	−	147.340i	0.0592954	−	0.0430806i	0.617038	+	0.786933i	$0.288332\pi$
$228$		0			0
$229$	556.018	+	1711.25i	0.160449	+	0.493810i	0.998672	−	0.0515169i	$-0.0164056\pi$
$229$	556.018	+	1711.25i	0.160449	+	0.493810i	−0.838224	+	0.545327i	$0.816406\pi$
$230$	5303.37			1.52041
$231$		0			0
$232$	1195.17			0.338219
$233$	−982.821	−	3024.81i	−0.276338	−	0.850481i	−0.988862	−	0.148833i	$-0.952448\pi$
$233$	−982.821	−	3024.81i	−0.276338	−	0.850481i	0.712524	−	0.701647i	$-0.247552\pi$
$234$		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	0.980701	−	0.195511i	$-0.0626366\pi$
$239$	4056.25	+	2947.04i	1.09781	+	0.797608i	0.117111	+	0.993119i	$0.462637\pi$
$240$		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	0.895309	+	0.445447i	$0.146955\pi$
$251$	1721.13	+	5297.09i	0.432816	+	1.33207i	−0.462493	+	0.886623i	$0.653045\pi$
$252$		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	−0.989768	−	0.142685i	$-0.954426\pi$
$257$	−4778.90	+	3472.08i	−1.15992	+	0.842732i	−0.170153	+	0.985418i	$0.554426\pi$
$258$		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	−0.982190	−	0.187893i	$-0.939834\pi$
$269$	−340.340	+	1047.46i	−0.0771409	+	0.237415i	0.905049	+	0.425308i	$0.139834\pi$
$270$		0			0
$271$	2080.54	−	1511.60i	0.466362	−	0.338832i	−0.329660	−	0.944100i	$-0.606934\pi$
$271$	2080.54	−	1511.60i	0.466362	−	0.338832i	0.796022	+	0.605268i	$0.206934\pi$
$272$	−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	−0.821581	−	0.570092i	$-0.806908\pi$
$277$	−2268.22	−	6980.85i	−0.492000	−	1.51422i	0.329581	−	0.944127i	$-0.393092\pi$
$278$	−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	−0.330693	−	0.943738i	$-0.607282\pi$
$281$	2315.45	−	7126.21i	0.491559	−	1.51286i	0.822252	−	0.569124i	$-0.192718\pi$
$282$		0			0
$283$	5253.84	+	3817.14i	1.10356	+	0.801785i	0.981638	−	0.190754i	$-0.0610933\pi$
$283$	5253.84	+	3817.14i	1.10356	+	0.801785i	0.121925	+	0.992539i	$0.461093\pi$
$284$	−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	−0.782884	−	0.622168i	$-0.786252\pi$
$293$	−2172.11	+	1578.13i	−0.433092	+	0.314660i	0.349792	+	0.936827i	$0.386252\pi$
$294$		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	0.152337	−	0.988329i	$-0.451320\pi$
$311$	−4061.55	−	2950.89i	−0.740545	−	0.538037i	−0.892882	+	0.450292i	$0.851320\pi$
$312$		0			0
$313$	933.873	−	2874.16i	0.168644	−	0.519033i	−0.830642	−	0.556807i	$-0.812026\pi$
$313$	933.873	−	2874.16i	0.168644	−	0.519033i	0.999286	+	0.0377733i	$0.0120265\pi$
$314$	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	0.628966	+	0.777433i	$0.283478\pi$
$317$	3257.08	+	10024.3i	0.577085	+	1.77609i	−0.0518809	+	0.998653i	$0.516522\pi$
$318$		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	−0.476659	+	0.879088i	$0.658152\pi$
$337$	−9032.40	+	6562.42i	−1.46002	+	1.06076i	−0.983358	+	0.181677i	$0.941848\pi$
$338$	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	−0.993007	−	0.118055i	$-0.962334\pi$
$347$	−777.327	+	2392.37i	−0.120257	+	0.370112i	0.872750	+	0.488167i	$0.162334\pi$
$348$		0			0
$349$	9203.85	+	6686.99i	1.41166	+	1.02563i	0.993078	+	0.117457i	$0.0374744\pi$
$349$	9203.85	+	6686.99i	1.41166	+	1.02563i	0.418587	+	0.908177i	$0.362526\pi$
$350$	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	−0.725804	−	0.687902i	$-0.758532\pi$
$359$	−2012.43	+	1462.12i	−0.295856	+	0.214952i	0.429948	+	0.902854i	$0.358532\pi$
$360$		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	−0.902933	−	0.429781i	$-0.858591\pi$
$367$	−5436.21	+	3949.64i	−0.773209	+	0.561770i	0.129724	+	0.991550i	$0.458591\pi$
$368$	−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	0.631074	+	0.775723i	$0.282614\pi$
$379$	−2474.95	+	7617.10i	−0.335434	+	1.03236i	−0.966508	+	0.256637i	$0.917386\pi$
$380$	−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	−0.968986	−	0.247115i	$-0.920517\pi$
$383$	−2475.83	−	7619.82i	−0.330310	−	1.01659i	0.638676	−	0.769476i	$-0.279483\pi$
$384$		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	−0.0775373	−	0.996989i	$-0.524706\pi$
$389$	6496.09	−	4719.68i	0.846696	−	0.615160i	0.924233	+	0.381829i	$0.124706\pi$
$390$		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	−0.846550	−	0.532309i	$-0.821325\pi$
$401$	1214.19	−	3736.90i	0.151207	−	0.465366i	0.997757	+	0.0669429i	$0.0213245\pi$
$402$		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	−0.723103	−	0.690740i	$-0.757285\pi$
$409$	−4500.59	−	13851.4i	−0.544107	−	1.67459i	0.178996	−	0.983850i	$-0.442715\pi$
$410$	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	0.910521	−	0.413464i	$-0.135681\pi$
$421$	6898.98	+	5012.40i	0.798659	+	0.580260i	−0.111861	+	0.993724i	$0.535681\pi$
$422$	−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	−0.861105	−	0.508427i	$-0.830227\pi$
$431$	−4145.53	−	12758.6i	−0.463302	−	1.42590i	0.397803	−	0.917471i	$-0.369773\pi$
$432$		0			0
$433$	−3343.11	+	2428.91i	−0.371038	+	0.269575i	−0.757641	−	0.652671i	$-0.773648\pi$
$433$	−3343.11	+	2428.91i	−0.371038	+	0.269575i	0.386603	+	0.922246i	$0.373648\pi$
$434$	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	0.568456	−	0.822714i	$-0.307541\pi$
$443$	−357.383	−	259.654i	−0.0383290	−	0.0278477i	−0.606785	+	0.794866i	$0.707541\pi$
$444$		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	0.957471	−	0.288530i	$-0.0931663\pi$
$449$	126.227	+	388.486i	0.0132673	+	0.0408325i	−0.944204	+	0.329362i	$0.893166\pi$
$450$		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	−0.924079	−	0.382201i	$-0.875166\pi$
$457$	470.585	−	1448.31i	0.0481686	−	0.148248i	0.972248	+	0.233953i	$0.0751663\pi$
$458$	−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	−0.957338	−	0.288971i	$-0.906687\pi$
$467$	−131.015	+	403.223i	−0.0129821	+	0.0399548i	0.944356	+	0.328926i	$0.106687\pi$
$468$		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	−0.995486	−	0.0949081i	$-0.969744\pi$
$479$	−1408.29	+	4334.29i	−0.134335	+	0.413442i	0.861151	+	0.508350i	$0.169744\pi$
$480$		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	0.810935	−	0.585136i	$-0.198959\pi$
$487$	5427.63	+	3943.41i	0.505030	+	0.366926i	−0.305905	+	0.952062i	$0.598959\pi$
$488$	−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	0.102537	−	0.994729i	$-0.467304\pi$
$491$	11753.1	−	8539.14i	1.08027	−	0.784859i	0.977729	+	0.209870i	$0.0673040\pi$
$492$		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	−0.177249	−	0.984166i	$-0.556720\pi$
$499$	7847.09	−	5701.24i	0.703976	−	0.511468i	0.881225	+	0.472698i	$0.156720\pi$
$500$	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	0.985171	−	0.171576i	$-0.0548859\pi$
$503$	12707.4	+	9232.43i	1.12643	+	0.818397i	0.141256	+	0.989973i	$0.454886\pi$
$504$		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	0.534649	−	0.845074i	$-0.320444\pi$
$509$	−1192.56	−	866.443i	−0.103849	−	0.0754507i	−0.638498	+	0.769624i	$0.720444\pi$
$510$		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	−0.856688	−	0.515834i	$-0.827482\pi$
$521$	−7501.89	+	5450.44i	−0.630832	+	0.458326i	0.225856	+	0.974161i	$0.427482\pi$
$522$		0			0
$523$	−1311.01	+	4034.86i	−0.109610	+	0.337346i	−0.990785	−	0.135445i	$-0.956754\pi$
$523$	−1311.01	+	4034.86i	−0.109610	+	0.337346i	0.881174	+	0.472791i	$0.156754\pi$
$524$	−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	0.838522	−	0.544868i	$-0.183420\pi$
$541$	−2014.87	−	6201.13i	−0.160122	−	0.492805i	−0.998644	+	0.0520633i	$0.983420\pi$
$542$	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	0.367836	−	0.929890i	$-0.380099\pi$
$547$	−5154.07	−	3744.65i	−0.402874	−	0.292705i	−0.770711	+	0.637185i	$0.780099\pi$
$548$	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	−0.383897	−	0.923376i	$-0.625418\pi$
$557$	4938.23	−	3587.84i	0.375655	−	0.272929i	0.759552	+	0.650447i	$0.225418\pi$
$558$		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	0.975989	+	0.217820i	$0.0698945\pi$
$563$	4200.34	+	12927.3i	0.314429	+	0.967711i	−0.661561	+	0.749892i	$0.730106\pi$
$564$		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	0.967317	−	0.253569i	$-0.0816045\pi$
$569$	13913.1	+	10108.5i	1.02508	+	0.744761i	0.0577589	+	0.998331i	$0.481605\pi$
$570$		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	0.419419	+	0.907793i	$0.362234\pi$
$577$	−6285.32	+	19344.2i	−0.453485	+	1.39568i	−0.872904	+	0.487892i	$0.837766\pi$
$578$	−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	−0.923194	−	0.384334i	$-0.874431\pi$
$587$	−11988.4	+	8710.07i	−0.842953	+	0.612441i	0.0802411	+	0.996775i	$0.474431\pi$
$588$		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	−0.999617	−	0.0276796i	$-0.991188\pi$
$599$	−2560.26	+	7879.67i	−0.174640	+	0.537487i	0.824977	+	0.565167i	$0.191188\pi$
$600$		0			0
$601$	−22101.0	+	16057.3i	−1.50003	+	1.08984i	−0.529660	+	0.848210i	$0.677680\pi$
$601$	−22101.0	+	16057.3i	−1.50003	+	1.08984i	−0.970370	+	0.241625i	$0.922320\pi$
$602$	−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	0.965536	+	0.260270i	$0.0838115\pi$
$607$	5045.53	+	15528.6i	0.337384	+	1.03836i	−0.628152	+	0.778091i	$0.716188\pi$
$608$	−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	0.984323	−	0.176376i	$-0.0564374\pi$
$613$	17009.8	+	12358.4i	1.12075	+	0.814274i	0.136429	+	0.990650i	$0.456437\pi$
$614$	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	0.312925	−	0.949778i	$-0.398691\pi$
$619$	−7602.75	−	5523.72i	−0.493668	−	0.358671i	−0.806593	+	0.591107i	$0.798691\pi$
$620$	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	−0.151393	−	0.988474i	$-0.548376\pi$
$631$	11759.8	−	8544.01i	0.741919	−	0.539036i	0.893311	+	0.449438i	$0.148376\pi$
$632$	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	0.265565	−	0.964093i	$-0.414441\pi$
$641$	−9238.70	−	6712.31i	−0.569277	−	0.413604i	−0.834843	+	0.550489i	$0.814441\pi$
$642$		0			0
$643$	7407.11	−	22796.7i	0.454289	−	1.39816i	−0.417679	−	0.908595i	$-0.637156\pi$
$643$	7407.11	−	22796.7i	0.454289	−	1.39816i	0.871968	−	0.489563i	$-0.162844\pi$
$644$	−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	0.842156	−	0.539234i	$-0.181286\pi$
$647$	−2569.24	−	7907.32i	−0.156117	−	0.480478i	−0.998272	+	0.0587569i	$0.981286\pi$
$648$		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	−0.474536	+	0.880236i	$0.657384\pi$
$653$	−24334.7	+	17680.2i	−1.45833	+	1.05954i	−0.983794	+	0.179303i	$0.942616\pi$
$654$		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	0.952563	+	0.304341i	$0.0984361\pi$
$673$	6299.43	+	19387.7i	0.360810	+	1.11046i	−0.591753	+	0.806119i	$0.701564\pi$
$674$	−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	−0.865149	−	0.501514i	$-0.832777\pi$
$677$	2282.09	−	7023.55i	0.129554	−	0.398725i	0.994703	+	0.102789i	$0.0327766\pi$
$678$		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	0.996824	−	0.0796417i	$-0.0253776\pi$
$691$	2607.73	+	8025.78i	0.143564	+	0.441845i	−0.853259	+	0.521487i	$0.825378\pi$
$692$	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	0.267690	−	0.963505i	$-0.413740\pi$
$701$	−10503.8	−	7631.43i	−0.565937	−	0.411177i	−0.833627	+	0.552328i	$0.813740\pi$
$702$		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	0.690483	+	0.723349i	$0.257398\pi$
$709$	−5537.15	+	17041.6i	−0.293303	+	0.902695i	−0.983786	+	0.179346i	$0.942602\pi$
$710$	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	−0.511536	−	0.859262i	$-0.670923\pi$
$719$	2845.59	−	2067.45i	0.147598	−	0.107236i	0.659133	+	0.752026i	$0.270923\pi$
$720$		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	−0.655613	−	0.755097i	$-0.727590\pi$
$733$	−2779.70	+	2019.57i	−0.140069	+	0.101766i	0.515544	+	0.856863i	$0.327590\pi$
$734$	−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	−0.779861	−	0.625953i	$-0.784710\pi$
$739$	−10383.5	−	31957.2i	−0.516866	−	1.59075i	0.262995	−	0.964797i	$-0.415290\pi$
$740$	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	−0.941537	−	0.336911i	$-0.890618\pi$
$743$	368.875	−	1135.28i	0.0182136	−	0.0560557i	0.959750	+	0.280855i	$0.0906180\pi$
$744$		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	−0.00950152	−	0.999955i	$-0.503024\pi$
$751$	−19828.5	−	14406.2i	−0.963451	−	0.699988i	−0.953950	+	0.299967i	$0.903024\pi$
$752$	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	0.998659	−	0.0517762i	$-0.0164882\pi$
$757$	3338.57	+	10275.0i	0.160294	+	0.493333i	−0.838365	+	0.545109i	$0.816488\pi$
$758$	−16018.2			−0.767555
$759$		0			0
$760$	−2620.49			−0.125073
$761$	−2526.49	−	7775.75i	−0.120349	−	0.370395i	0.872676	−	0.488299i	$-0.162383\pi$
$761$	−2526.49	−	7775.75i	−0.120349	−	0.370395i	−0.993025	+	0.117904i	$0.962383\pi$
$762$		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	0.195054	−	0.980792i	$-0.437512\pi$
$773$	−14559.7	−	10578.3i	−0.677460	−	0.492203i	−0.872514	+	0.488589i	$0.837512\pi$
$774$		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	0.776343	+	0.630310i	$0.217072\pi$
$787$	−4906.17	+	15099.6i	−0.222219	+	0.683918i	−0.998562	+	0.0536084i	$0.982928\pi$
$788$	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	0.771549	+	0.636170i	$0.219482\pi$
$797$	−5098.07	+	15690.2i	−0.226578	+	0.697336i	−0.998128	+	0.0611668i	$0.980518\pi$
$798$		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	−0.871142	−	0.491032i	$-0.836620\pi$
$809$	2812.97	−	8657.42i	0.122248	−	0.376241i	0.993390	+	0.114791i	$0.0366199\pi$
$810$		0			0
$811$	−29590.8	−	21499.0i	−1.28123	−	0.930865i	−0.281636	−	0.959521i	$-0.590877\pi$
$811$	−29590.8	−	21499.0i	−1.28123	−	0.930865i	−0.999589	+	0.0286567i	$0.990877\pi$
$812$	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	−0.648683	−	0.761059i	$-0.724680\pi$
$821$	−2948.23	+	2142.01i	−0.125328	+	0.0910558i	0.523356	+	0.852114i	$0.324680\pi$
$822$		0			0
$823$	−5221.12	−	16068.9i	−0.221138	−	0.680593i	−0.998661	−	0.0517380i	$-0.983524\pi$
$823$	−5221.12	−	16068.9i	−0.221138	−	0.680593i	0.777523	−	0.628855i	$-0.216476\pi$
$824$	10941.3			0.462570
$825$		0			0
$826$	−1548.19			−0.0652160
$827$	11983.1	+	36880.1i	0.503860	+	1.55072i	0.802678	+	0.596413i	$0.203408\pi$
$827$	11983.1	+	36880.1i	0.503860	+	1.55072i	−0.298817	+	0.954310i	$0.596592\pi$
$828$		0			0
$829$	10027.2	−	7285.20i	0.420096	−	0.305218i	−0.357580	−	0.933882i	$-0.616398\pi$
$829$	10027.2	−	7285.20i	0.420096	−	0.305218i	0.777677	+	0.628665i	$0.216398\pi$
$830$	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	0.916062	−	0.401037i	$-0.131350\pi$
$839$	19872.6	+	14438.3i	0.817732	+	0.594117i	−0.0983299	+	0.995154i	$0.531350\pi$
$840$		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	−0.997781	−	0.0665834i	$-0.978790\pi$
$853$	−3772.37	+	11610.1i	−0.151422	+	0.466030i	0.846358	+	0.532614i	$0.178790\pi$
$854$	−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	−0.382518	−	0.923948i	$-0.624943\pi$
$863$	11916.3	−	36674.5i	0.470028	−	1.44660i	0.852547	−	0.522651i	$-0.175057\pi$
$864$		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	0.0472301	−	0.998884i	$-0.484961\pi$
$877$	−23067.2	−	16759.3i	−0.888170	−	0.645293i	−0.935400	+	0.353591i	$0.884961\pi$
$878$	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	0.641835	−	0.766842i	$-0.278173\pi$
$883$	2908.89	+	2113.43i	0.110863	+	0.0805467i	−0.530972	+	0.847389i	$0.678173\pi$
$884$	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	−0.699624	−	0.714511i	$-0.746649\pi$
$887$	−6241.81	+	4534.94i	−0.236279	+	0.171667i	0.463345	+	0.886178i	$0.346649\pi$
$888$		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	0.557662	+	0.830068i	$0.311698\pi$
$907$	−10418.1	+	32063.6i	−0.381398	+	1.17382i	−0.939060	+	0.343753i	$0.888302\pi$
$908$	−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	0.830382	−	0.557194i	$-0.188122\pi$
$911$	−4644.75	−	14295.1i	−0.168922	−	0.519887i	−0.999304	+	0.0373070i	$0.988122\pi$
$912$		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	−0.999997	−	0.00240379i	$-0.999235\pi$
$919$	−5281.31	+	16254.2i	−0.189570	+	0.583435i	0.810428	+	0.585839i	$0.199235\pi$
$920$	−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	−0.996831	−	0.0795446i	$-0.974653\pi$
$929$	−4066.74	+	12516.1i	−0.143623	+	0.442025i	0.853209	+	0.521570i	$0.174653\pi$
$930$		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	0.970527	−	0.240993i	$-0.0774731\pi$
$937$	1253.46	+	3857.76i	0.0437021	+	0.134501i	−0.926825	+	0.375494i	$0.877473\pi$
$938$	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	0.596996	+	0.802244i	$0.296361\pi$
$941$	−10320.4	+	31763.0i	−0.357531	+	1.10037i	−0.954527	+	0.298123i	$0.903639\pi$
$942$		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	0.344096	−	0.938935i	$-0.388185\pi$
$953$	39522.7	−	28714.9i	1.34341	−	0.976042i	0.999311	−	0.0371079i	$-0.0118145\pi$
$954$		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	0.946682	−	0.322169i	$-0.104412\pi$
$971$	28224.6	+	20506.4i	0.932822	+	0.677735i	−0.0138603	+	0.999904i	$0.504412\pi$
$972$		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	0.999997	+	0.00239112i	$0.000761118\pi$
$977$	5875.16	+	18081.9i	0.192388	+	0.592109i	−0.807609	+	0.589718i	$0.799239\pi$
$978$		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	−0.681232	−	0.732068i	$-0.738555\pi$
$983$	−6025.47	+	4377.76i	−0.195506	+	0.142044i	0.485726	+	0.874111i	$0.338555\pi$
$984$		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	−0.378223	+	0.925714i	$0.623465\pi$
$997$	−43301.8	+	31460.6i	−1.37551	+	0.999365i	−0.997284	+	0.0736504i	$0.976535\pi$
$998$	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.181.1		8
3.2	odd	2		22.4.c.b.5.2	✓	8
11.3	even	5		2178.4.a.by.1.1		4
11.8	odd	10		2178.4.a.bt.1.1		4
11.9	even	5	inner	198.4.f.d.163.1		8
12.11	even	2		176.4.m.b.49.1		8
33.2	even	10		242.4.c.q.9.2		8
33.5	odd	10		242.4.c.r.81.1		8
33.8	even	10		242.4.a.o.1.1		4
33.14	odd	10		242.4.a.n.1.1		4
33.17	even	10		242.4.c.n.81.1		8
33.20	odd	10		22.4.c.b.9.2	yes	8
33.26	odd	10		242.4.c.r.3.1		8
33.29	even	10		242.4.c.n.3.1		8
33.32	even	2		242.4.c.q.27.2		8
132.47	even	10		1936.4.a.bn.1.4		4
132.107	odd	10		1936.4.a.bm.1.4		4
132.119	even	10		176.4.m.b.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.c.b.5.2	✓	8	3.2	odd	2
22.4.c.b.9.2	yes	8	33.20	odd	10
176.4.m.b.49.1		8	12.11	even	2
176.4.m.b.97.1		8	132.119	even	10
198.4.f.d.163.1		8	11.9	even	5	inner
198.4.f.d.181.1		8	1.1	even	1	trivial
242.4.a.n.1.1		4	33.14	odd	10
242.4.a.o.1.1		4	33.8	even	10
242.4.c.n.3.1		8	33.29	even	10
242.4.c.n.81.1		8	33.17	even	10
242.4.c.q.9.2		8	33.2	even	10
242.4.c.q.27.2		8	33.32	even	2
242.4.c.r.3.1		8	33.26	odd	10
242.4.c.r.81.1		8	33.5	odd	10
1936.4.a.bm.1.4		4	132.107	odd	10
1936.4.a.bn.1.4		4	132.47	even	10
2178.4.a.bt.1.1		4	11.8	odd	10
2178.4.a.by.1.1		4	11.3	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more