LMFDB - Embedded newform 225.4.k.a.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.1
Root			$-0.396143 + 1.68614i$ of defining polynomial
Character	$\chi$	$=$	225.49
Dual form			225.4.k.a.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.92048 + 1.68614i) q^{2} +(4.97494 + 1.50000i) q^{3} +(1.68614 - 2.92048i) q^{4} +(-17.0584 + 4.00772i) q^{6} +(1.40965 - 0.813859i) q^{7} -15.6060i q^{8} +(22.5000 + 14.9248i) q^{9} +O(q^{10})$	\(q+(-2.92048 + 1.68614i) q^{2} +(4.97494 + 1.50000i) q^{3} +(1.68614 - 2.92048i) q^{4} +(-17.0584 + 4.00772i) q^{6} +(1.40965 - 0.813859i) q^{7} -15.6060i q^{8} +(22.5000 + 14.9248i) q^{9} +(16.4307 + 28.4588i) q^{11} +(12.7692 - 12.0000i) q^{12} +(-28.5977 - 16.5109i) q^{13} +(-2.74456 + 4.75372i) q^{14} +(39.8030 + 68.9408i) q^{16} +110.307i q^{17} +(-90.8762 - 5.64947i) q^{18} +54.3070 q^{19} +(8.23369 - 1.93443i) q^{21} +(-95.9711 - 55.4090i) q^{22} +(-58.4026 - 33.7188i) q^{23} +(23.4090 - 77.6387i) q^{24} +111.359 q^{26} +(89.5489 + 108.000i) q^{27} -5.48913i q^{28} +(137.259 + 237.740i) q^{29} +(3.00000 - 5.19615i) q^{31} +(-124.366 - 71.8030i) q^{32} +(39.0535 + 166.227i) q^{33} +(-185.993 - 322.150i) q^{34} +(81.5258 - 40.5455i) q^{36} -347.723i q^{37} +(-158.603 + 91.5693i) q^{38} +(-117.505 - 125.037i) q^{39} +(-145.668 + 252.305i) q^{41} +(-20.7846 + 19.5326i) q^{42} +(-174.408 + 100.694i) q^{43} +110.818 q^{44} +227.418 q^{46} +(-417.507 + 241.048i) q^{47} +(94.6062 + 402.681i) q^{48} +(-170.175 + 294.752i) q^{49} +(-165.461 + 548.771i) q^{51} +(-96.4394 + 55.6793i) q^{52} +175.228i q^{53} +(-443.629 - 164.420i) q^{54} +(-12.7011 - 21.9989i) q^{56} +(270.174 + 81.4605i) q^{57} +(-801.728 - 462.878i) q^{58} +(-91.6209 + 158.692i) q^{59} +(-218.297 - 378.102i) q^{61} +20.2337i q^{62} +(43.8637 + 2.72686i) q^{63} -152.568 q^{64} +(-394.337 - 419.613i) q^{66} +(720.100 + 415.750i) q^{67} +(322.150 + 185.993i) q^{68} +(-239.971 - 255.353i) q^{69} -118.951 q^{71} +(232.916 - 351.134i) q^{72} -183.318i q^{73} +(586.310 + 1015.52i) q^{74} +(91.5693 - 158.603i) q^{76} +(46.3229 + 26.7446i) q^{77} +(554.002 + 167.038i) q^{78} +(-319.147 - 552.778i) q^{79} +(283.500 + 671.617i) q^{81} -982.470i q^{82} +(1294.40 - 747.322i) q^{83} +(8.23369 - 27.3081i) q^{84} +(339.569 - 588.151i) q^{86} +(326.247 + 1388.63i) q^{87} +(444.127 - 256.417i) q^{88} +1437.27 q^{89} -53.7501 q^{91} +(-196.950 + 113.709i) q^{92} +(22.7190 - 21.3505i) q^{93} +(812.880 - 1407.95i) q^{94} +(-511.011 - 543.765i) q^{96} +(-772.294 + 445.884i) q^{97} -1147.76i q^{98} +(-55.0516 + 885.548i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 - 102 * q^6 + 180 * q^9	$ 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + 74 q^{11} + 24 q^{14} + 238 q^{16} - 140 q^{19} - 72 q^{21} - 54 q^{24} - 304 q^{26} + 650 q^{29} + 24 q^{31} - 902 q^{34} + 342 q^{36} + 1128 q^{39} - 476 q^{41} + 404 q^{44} - 984 q^{46} - 1258 q^{49} - 462 q^{51} - 1998 q^{54} + 312 q^{56} - 170 q^{59} + 494 q^{61} - 2852 q^{64} - 1776 q^{66} + 3078 q^{69} + 1576 q^{71} + 968 q^{74} + 790 q^{76} - 1680 q^{79} + 2268 q^{81} - 72 q^{84} + 2774 q^{86} + 4260 q^{89} - 2544 q^{91} + 1264 q^{94} + 48 q^{96} + 180 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 - 102 * q^6 + 180 * q^9 + 74 * q^11 + 24 * q^14 + 238 * q^16 - 140 * q^19 - 72 * q^21 - 54 * q^24 - 304 * q^26 + 650 * q^29 + 24 * q^31 - 902 * q^34 + 342 * q^36 + 1128 * q^39 - 476 * q^41 + 404 * q^44 - 984 * q^46 - 1258 * q^49 - 462 * q^51 - 1998 * q^54 + 312 * q^56 - 170 * q^59 + 494 * q^61 - 2852 * q^64 - 1776 * q^66 + 3078 * q^69 + 1576 * q^71 + 968 * q^74 + 790 * q^76 - 1680 * q^79 + 2268 * q^81 - 72 * q^84 + 2774 * q^86 + 4260 * q^89 - 2544 * q^91 + 1264 * q^94 + 48 * q^96 + 180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.92048	+	1.68614i	−1.03255	+	0.596141i	−0.917713	−	0.397244i	$-0.869967\pi$
$2$	−2.92048	+	1.68614i	−1.03255	+	0.596141i	−0.114833	+	0.993385i	$0.536633\pi$
$3$	4.97494	+	1.50000i	0.957427	+	0.288675i
$3$	4.97494	+	1.50000i	0.957427	+	0.288675i
$4$	1.68614	−	2.92048i	0.210768	−	0.365060i
$5$		0			0
$5$		0			0
$6$	−17.0584	+	4.00772i	−1.16068	+	0.272691i
$7$	1.40965	−	0.813859i	0.0761137	−	0.0439443i	−0.461460	−	0.887161i	$-0.652674\pi$
$7$	1.40965	−	0.813859i	0.0761137	−	0.0439443i	0.537574	+	0.843217i	$0.319341\pi$
$8$		−	15.6060i		−	0.689693i
$9$	22.5000	+	14.9248i	0.833333	+	0.552771i
$10$		0			0
$11$	16.4307	+	28.4588i	0.450368	+	0.780060i	0.998409	−	0.0563918i	$-0.0179596\pi$
$11$	16.4307	+	28.4588i	0.450368	+	0.780060i	−0.548041	+	0.836451i	$0.684626\pi$
$12$	12.7692	−	12.0000i	0.307178	−	0.288675i
$13$	−28.5977	−	16.5109i	−0.610121	−	0.352253i	0.162892	−	0.986644i	$-0.447918\pi$
$13$	−28.5977	−	16.5109i	−0.610121	−	0.352253i	−0.773013	+	0.634391i	$0.781251\pi$
$14$	−2.74456	+	4.75372i	−0.0523939	+	0.0907490i
$15$		0			0
$16$	39.8030	+	68.9408i	0.621922	+	1.07720i
$17$			110.307i			1.57373i	0.617126	+	0.786864i	$0.288297\pi$
$17$			110.307i			1.57373i	−0.617126	+	0.786864i	$0.711703\pi$
$18$	−90.8762	−	5.64947i	−1.18998	−	0.0739774i
$19$	54.3070			0.655731			0.327865	−	0.944724i	$-0.393671\pi$
$19$	54.3070			0.655731			0.327865	+	0.944724i	$0.393671\pi$
$20$		0			0
$21$	8.23369	−	1.93443i	0.0855590	−	0.0201013i
$22$	−95.9711	−	55.4090i	−0.930051	−	0.536965i
$23$	−58.4026	−	33.7188i	−0.529469	−	0.305689i	0.211331	−	0.977415i	$-0.432220\pi$
$23$	−58.4026	−	33.7188i	−0.529469	−	0.305689i	−0.740800	+	0.671725i	$0.765553\pi$
$24$	23.4090	−	77.6387i	0.199097	−	0.660331i
$25$		0			0
$26$	111.359			0.839970
$27$	89.5489	+	108.000i	0.638285	+	0.769800i
$28$		−	5.48913i		−	0.0370481i
$29$	137.259	+	237.740i	0.878912	+	1.52232i	0.852536	+	0.522668i	$0.175063\pi$
$29$	137.259	+	237.740i	0.878912	+	1.52232i	0.0263757	+	0.999652i	$0.491603\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.0173812	−	0.0301050i	−0.857204	−	0.514977i	$-0.827800\pi$
$31$	3.00000	−	5.19615i	0.0173812	−	0.0301050i	0.874585	+	0.484872i	$0.161134\pi$
$32$	−124.366	−	71.8030i	−0.687034	−	0.396659i
$33$	39.0535	+	166.227i	0.206010	+	0.876860i
$34$	−185.993	−	322.150i	−0.938164	−	1.62495i
$35$		0			0
$36$	81.5258	−	40.5455i	0.377434	−	0.187711i
$37$		−	347.723i		−	1.54501i	−0.635010	−	0.772504i	$-0.719004\pi$
$37$		−	347.723i		−	1.54501i	0.635010	−	0.772504i	$-0.280996\pi$
$38$	−158.603	+	91.5693i	−0.677072	+	0.390908i
$39$	−117.505	−	125.037i	−0.482459	−	0.513383i
$40$		0			0
$41$	−145.668	+	252.305i	−0.554868	+	0.961060i	0.443046	+	0.896499i	$0.353898\pi$
$41$	−145.668	+	252.305i	−0.554868	+	0.961060i	−0.997914	+	0.0645606i	$0.979435\pi$
$42$	−20.7846	+	19.5326i	−0.0763604	+	0.0717607i
$43$	−174.408	+	100.694i	−0.618533	+	0.357110i	−0.776297	−	0.630367i	$-0.782905\pi$
$43$	−174.408	+	100.694i	−0.618533	+	0.357110i	0.157765	+	0.987477i	$0.449571\pi$
$44$	110.818			0.379692
$45$		0			0
$46$	227.418			0.728935
$47$	−417.507	+	241.048i	−1.29574	+	0.748094i	−0.979665	−	0.200642i	$-0.935697\pi$
$47$	−417.507	+	241.048i	−1.29574	+	0.748094i	−0.316071	+	0.948735i	$0.602364\pi$
$48$	94.6062	+	402.681i	0.284484	+	1.21087i
$49$	−170.175	+	294.752i	−0.496138	+	0.859336i
$50$		0			0
$51$	−165.461	+	548.771i	−0.454296	+	1.50673i
$52$	−96.4394	+	55.6793i	−0.257187	+	0.148487i
$53$			175.228i			0.454140i	0.973878	+	0.227070i	$0.0729147\pi$
$53$			175.228i			0.454140i	−0.973878	+	0.227070i	$0.927085\pi$
$54$	−443.629	−	164.420i	−1.11797	−	0.414347i
$55$		0			0
$56$	−12.7011	−	21.9989i	−0.0303081	−	0.0524951i
$57$	270.174	+	81.4605i	0.627815	+	0.189293i
$58$	−801.728	−	462.878i	−1.81503	−	1.04791i
$59$	−91.6209	+	158.692i	−0.202170	+	0.350169i	−0.949227	−	0.314591i	$-0.898133\pi$
$59$	−91.6209	+	158.692i	−0.202170	+	0.350169i	0.747057	+	0.664760i	$0.231466\pi$
$60$		0			0
$61$	−218.297	−	378.102i	−0.458199	−	0.793623i	0.540667	−	0.841237i	$-0.318172\pi$
$61$	−218.297	−	378.102i	−0.458199	−	0.793623i	−0.998866	+	0.0476132i	$0.984839\pi$
$62$			20.2337i			0.0414465i
$63$	43.8637	+	2.72686i	0.0877192	+	0.00545321i
$64$	−152.568			−0.297984
$65$		0			0
$66$	−394.337	−	419.613i	−0.735447	−	0.782587i
$67$	720.100	+	415.750i	1.31305	+	0.758089i	0.982600	−	0.185736i	$-0.0594668\pi$
$67$	720.100	+	415.750i	1.31305	+	0.758089i	0.330448	+	0.943824i	$0.392800\pi$
$68$	322.150	+	185.993i	0.574506	+	0.331691i
$69$	−239.971	−	255.353i	−0.418683	−	0.445520i
$70$		0			0
$71$	−118.951			−0.198829			−0.0994146	−	0.995046i	$-0.531697\pi$
$71$	−118.951			−0.198829			−0.0994146	+	0.995046i	$0.531697\pi$
$72$	232.916	−	351.134i	0.381242	−	0.574744i
$73$		−	183.318i		−	0.293914i	−0.989143	−	0.146957i	$-0.953052\pi$
$73$		−	183.318i		−	0.293914i	0.989143	−	0.146957i	$-0.0469479\pi$
$74$	586.310	+	1015.52i	0.921042	+	1.59529i
$75$		0			0
$76$	91.5693	−	158.603i	0.138207	−	0.239381i
$77$	46.3229	+	26.7446i	0.0685583	+	0.0395822i
$78$	554.002	+	167.038i	0.804210	+	0.242478i
$79$	−319.147	−	552.778i	−0.454517	−	0.787246i	0.544144	−	0.838992i	$-0.316855\pi$
$79$	−319.147	−	552.778i	−0.454517	−	0.787246i	−0.998660	+	0.0517463i	$0.983521\pi$
$80$		0			0
$81$	283.500	+	671.617i	0.388889	+	0.921285i
$82$		−	982.470i		−	1.32312i
$83$	1294.40	−	747.322i	1.71179	−	0.988304i	0.779647	−	0.626219i	$-0.215398\pi$
$83$	1294.40	−	747.322i	1.71179	−	0.988304i	0.932145	−	0.362085i	$-0.117935\pi$
$84$	8.23369	−	27.3081i	0.0106949	−	0.0354709i
$85$		0			0
$86$	339.569	−	588.151i	0.425776	−	0.737465i
$87$	326.247	+	1388.63i	0.402038	+	1.71123i
$88$	444.127	−	256.417i	0.538002	−	0.310615i
$89$	1437.27			1.71180			0.855900	−	0.517142i	$-0.173004\pi$
$89$	1437.27			1.71180			0.855900	+	0.517142i	$0.173004\pi$
$90$		0			0
$91$	−53.7501			−0.0619181
$92$	−196.950	+	113.709i	−0.223190	+	0.128859i
$93$	22.7190	−	21.3505i	0.0253318	−	0.0238059i
$94$	812.880	−	1407.95i	0.891938	−	1.54488i
$95$		0			0
$96$	−511.011	−	543.765i	−0.543279	−	0.578102i
$97$	−772.294	+	445.884i	−0.808398	+	0.466729i	−0.846399	−	0.532549i	$-0.821234\pi$
$97$	−772.294	+	445.884i	−0.808398	+	0.466729i	0.0380011	+	0.999278i	$0.487901\pi$
$98$		−	1147.76i		−	1.18307i
$99$	−55.0516	+	885.548i	−0.0558878	+	0.899000i
$100$		0			0
$101$	76.8720	+	133.146i	0.0757332	+	0.131174i	0.901405	−	0.432977i	$-0.142537\pi$
$101$	76.8720	+	133.146i	0.0757332	+	0.131174i	−0.825672	+	0.564151i	$0.809204\pi$
$102$	−442.080	−	1881.66i	−0.429142	−	1.82659i
$103$	117.168	+	67.6469i	0.112086	+	0.0647131i	0.554995	−	0.831854i	$-0.312720\pi$
$103$	117.168	+	67.6469i	0.112086	+	0.0647131i	−0.442909	+	0.896567i	$0.646053\pi$
$104$	−257.668	+	446.294i	−0.242947	+	0.420796i
$105$		0			0
$106$	−295.459	−	511.750i	−0.270732	−	0.468921i
$107$		−	718.783i		−	0.649414i	−0.945815	−	0.324707i	$-0.894734\pi$
$107$		−	718.783i		−	0.649414i	0.945815	−	0.324707i	$-0.105266\pi$
$108$	466.404	−	79.4226i	0.415553	−	0.0707634i
$109$	2010.56			1.76676			0.883378	−	0.468661i	$-0.155264\pi$
$109$	2010.56			1.76676			0.883378	+	0.468661i	$0.155264\pi$
$110$		0			0
$111$	521.584	−	1729.90i	0.446005	−	1.47923i
$112$	112.216	+	64.7881i	0.0946735	+	0.0546598i
$113$	−196.367	−	113.372i	−0.163474	−	0.0943820i	0.416031	−	0.909351i	$-0.363421\pi$
$113$	−196.367	−	113.372i	−0.163474	−	0.0943820i	−0.579505	+	0.814969i	$0.696754\pi$
$114$	−926.392	+	217.647i	−0.761093	+	0.178812i
$115$		0			0
$116$	925.755			0.740985
$117$	−397.026	−	798.310i	−0.313718	−	0.630801i
$118$		−	617.943i		−	0.482087i
$119$	89.7744	+	155.494i	0.0691564	+	0.119782i
$120$		0			0
$121$	125.564	−	217.483i	0.0943381	−	0.163398i
$122$	1275.07	+	736.160i	0.946223	+	0.546302i
$123$	−1103.15	+	1036.70i	−0.808680	+	0.759968i
$124$	−10.1168	−	17.5229i	−0.00732677	−	0.0126903i
$125$		0			0
$126$	−132.701	+	65.9967i	−0.0938250	+	0.0466623i
$127$			1132.24i			0.791100i	0.918444	+	0.395550i	$0.129446\pi$
$127$			1132.24i			0.791100i	−0.918444	+	0.395550i	$0.870554\pi$
$128$	1440.50	−	831.675i	0.994717	−	0.574300i
$129$	−1018.71	+	239.336i	−0.695289	+	0.163352i
$130$		0			0
$131$	−388.753	+	673.339i	−0.259278	+	0.449083i	−0.966049	−	0.258360i	$-0.916818\pi$
$131$	−388.753	+	673.339i	−0.259278	+	0.449083i	0.706770	+	0.707443i	$0.250151\pi$
$132$	551.312	+	166.227i	0.363527	+	0.109608i
$133$	76.5537	−	44.1983i	0.0499101	−	0.0288156i
$134$	−2804.05			−1.80771
$135$		0			0
$136$	1721.45			1.08539
$137$	540.087	−	311.819i	0.336808	−	0.194456i	−0.322052	−	0.946722i	$-0.604372\pi$
$137$	540.087	−	311.819i	0.336808	−	0.194456i	0.658860	+	0.752266i	$0.271039\pi$
$138$	1131.39	+	341.127i	0.697902	+	0.210425i
$139$	641.341	−	1110.83i	0.391351	−	0.677840i	−0.601277	−	0.799041i	$-0.705341\pi$
$139$	641.341	−	1110.83i	0.391351	−	0.677840i	0.992628	+	0.121201i	$0.0386745\pi$
$140$		0			0
$141$	−2438.64	+	572.937i	−1.45653	+	0.342198i
$142$	347.394	−	200.568i	0.205300	−	0.118530i
$143$		−	1085.14i		−	0.634574i
$144$	−133.361	+	2145.22i	−0.0771766	+	1.24145i
$145$		0			0
$146$	309.099	+	535.376i	0.175214	+	0.303480i
$147$	−1288.74	+	1211.11i	−0.723085	+	0.679529i
$148$	−1015.52	−	586.310i	−0.564021	−	0.325638i
$149$	762.156	−	1320.09i	0.419049	−	0.725814i	−0.576795	−	0.816889i	$-0.695697\pi$
$149$	762.156	−	1320.09i	0.419049	−	0.725814i	0.995844	+	0.0910749i	$0.0290303\pi$
$150$		0			0
$151$	−1581.28	−	2738.86i	−0.852203	−	1.47606i	−0.879216	−	0.476424i	$-0.841933\pi$
$151$	−1581.28	−	2738.86i	−0.852203	−	1.47606i	0.0270124	−	0.999635i	$-0.491401\pi$
$152$		−	847.514i		−	0.452253i
$153$	−1646.31	+	2481.91i	−0.869911	+	1.31144i
$154$	−180.380			−0.0943861
$155$		0			0
$156$	−563.299	+	132.342i	−0.289103	+	0.0679220i
$157$	2068.67	+	1194.35i	1.05158	+	0.607131i	0.923092	−	0.384580i	$-0.125654\pi$
$157$	2068.67	+	1194.35i	1.05158	+	0.607131i	0.128490	+	0.991711i	$0.458987\pi$
$158$	1864.12	+	1076.25i	0.938619	+	0.541912i
$159$	−262.842	+	871.749i	−0.131099	+	0.434806i
$160$		0			0
$161$	−109.769			−0.0537331
$162$	−1960.40	−	1483.42i	−0.950761	−	0.719436i
$163$			2544.79i			1.22284i	0.791305	+	0.611422i	$0.209402\pi$
$163$			2544.79i			1.22284i	−0.791305	+	0.611422i	$0.790598\pi$
$164$	491.235	+	850.844i	0.233896	+	0.405120i
$165$		0			0
$166$	−2520.18	+	4365.08i	−1.17834	+	2.04094i
$167$	1190.40	+	687.279i	0.551593	+	0.318462i	0.749764	−	0.661705i	$-0.230167\pi$
$167$	1190.40	+	687.279i	0.551593	+	0.318462i	−0.198171	+	0.980167i	$0.563500\pi$
$168$	−30.1887	−	128.495i	−0.0138637	−	0.0590094i
$169$	−553.282	−	958.313i	−0.251835	−	0.436191i
$170$		0			0
$171$	1221.91	+	810.522i	0.546442	+	0.362469i
$172$			679.139i			0.301069i
$173$	−2044.21	+	1180.23i	−0.898372	+	0.518675i	−0.876672	−	0.481089i	$-0.840241\pi$
$173$	−2044.21	+	1180.23i	−0.898372	+	0.518675i	−0.0217005	+	0.999765i	$0.506908\pi$
$174$	−3294.23	−	3505.38i	−1.43526	−	1.52725i
$175$		0			0
$176$	−1307.98	+	2265.49i	−0.560187	+	0.970272i
$177$	−693.846	+	652.052i	−0.294648	+	0.276899i
$178$	−4197.52	+	2423.44i	−1.76751	+	1.02047i
$179$	−1305.11			−0.544963			−0.272482	−	0.962161i	$-0.587844\pi$
$179$	−1305.11			−0.544963			−0.272482	+	0.962161i	$0.587844\pi$
$180$		0			0
$181$	3099.43			1.27281			0.636406	−	0.771355i	$-0.280420\pi$
$181$	3099.43			1.27281			0.636406	+	0.771355i	$0.280420\pi$
$182$	156.976	−	90.6303i	0.0639332	−	0.0369119i
$183$	−518.863	−	2208.48i	−0.209593	−	0.892107i
$184$	−526.214	+	911.429i	−0.210832	+	0.365171i
$185$		0			0
$186$	−30.3505	+	100.661i	−0.0119646	+	0.0396820i
$187$	−3139.21	+	1812.42i	−1.22760	+	0.708756i
$188$			1625.76i			0.630696i
$189$	214.129	+	79.3616i	0.0824105	+	0.0305434i
$190$		0			0
$191$	−190.356	−	329.706i	−0.0721135	−	0.124904i	0.827714	−	0.561150i	$-0.189641\pi$
$191$	−190.356	−	329.706i	−0.0721135	−	0.124904i	−0.899827	+	0.436246i	$0.856308\pi$
$192$	−759.016	−	228.852i	−0.285298	−	0.0860207i
$193$	1338.91	+	773.020i	0.499362	+	0.288307i	0.728450	−	0.685099i	$-0.240241\pi$
$193$	1338.91	+	773.020i	0.499362	+	0.288307i	−0.229088	+	0.973406i	$0.573574\pi$
$194$	1503.65	−	2604.39i	0.556472	−	0.963838i
$195$		0			0
$196$	573.879	+	993.987i	0.209140	+	0.362240i
$197$		−	4284.60i		−	1.54957i	−0.632226	−	0.774784i	$-0.717859\pi$
$197$		−	4284.60i		−	1.54957i	0.632226	−	0.774784i	$-0.282141\pi$
$198$	−1332.38	−	2679.05i	−0.478224	−	0.961576i
$199$	1402.85			0.499727			0.249863	−	0.968281i	$-0.419614\pi$
$199$	1402.85			0.499727			0.249863	+	0.968281i	$0.419614\pi$
$200$		0			0
$201$	2958.83	+	3148.48i	1.03831	+	1.10486i
$202$	−449.007	−	259.234i	−0.156396	−	0.0902953i
$203$	386.974	+	223.420i	0.133795	+	0.0772463i
$204$	1323.68	+	1408.53i	0.454296	+	0.483415i
$205$		0			0
$206$	−456.249			−0.154312
$207$	−810.813	−	1630.32i	−0.272248	−	0.547416i
$208$		−	2628.73i		−	0.876296i
$209$	892.303	+	1545.51i	0.295320	+	0.511509i
$210$		0			0
$211$	1075.23	−	1862.35i	0.350814	−	0.607628i	−0.635578	−	0.772036i	$-0.719238\pi$
$211$	1075.23	−	1862.35i	0.350814	−	0.607628i	0.986392	+	0.164409i	$0.0525716\pi$
$212$	511.750	+	295.459i	0.165789	+	0.0957180i
$213$	−591.773	−	178.426i	−0.190365	−	0.0573971i
$214$	1211.97	+	2099.19i	0.387142	+	0.670550i
$215$		0			0
$216$	1685.44	−	1397.50i	0.530926	−	0.440220i
$217$		−	9.76631i		−	0.00305521i
$218$	−5871.79	+	3390.08i	−1.82426	+	1.05324i
$219$	274.977	−	911.994i	0.0848456	−	0.281401i
$220$		0			0
$221$	1821.27	−	3154.52i	0.554351	−	0.960164i
$222$	1393.58	+	5931.60i	0.421310	+	1.79326i
$223$	2215.42	−	1279.07i	0.665272	−	0.384095i	−0.129011	−	0.991643i	$-0.541180\pi$
$223$	2215.42	−	1279.07i	0.665272	−	0.384095i	0.794283	+	0.607548i	$0.207847\pi$
$224$	−233.750			−0.0697236
$225$		0			0
$226$	764.646			0.225060
$227$	−3537.32	+	2042.27i	−1.03427	+	0.597138i	−0.918206	−	0.396104i	$-0.870362\pi$
$227$	−3537.32	+	2042.27i	−1.03427	+	0.597138i	−0.116067	+	0.993241i	$0.537029\pi$
$228$	693.456	−	651.684i	0.201426	−	0.189293i
$229$	−1370.95	+	2374.56i	−0.395612	+	0.685221i	−0.993179	−	0.116598i	$-0.962801\pi$
$229$	−1370.95	+	2374.56i	−0.395612	+	0.685221i	0.597567	+	0.801819i	$0.296134\pi$
$230$		0			0
$231$	190.337	+	202.537i	0.0542132	+	0.0576881i
$232$	3710.17	−	2142.07i	1.04993	−	0.606179i
$233$		−	5084.70i		−	1.42966i	−0.699300	−	0.714828i	$-0.746505\pi$
$233$		−	5084.70i		−	1.42966i	0.699300	−	0.714828i	$-0.253495\pi$
$234$	2505.57	+	1662.01i	0.699975	+	0.464311i
$235$		0			0
$236$	308.971	+	535.154i	0.0852217	+	0.147608i
$237$	−758.567	−	3228.76i	−0.207908	−	0.884938i
$238$	−524.369	−	302.745i	−0.142814	−	0.0824538i
$239$	738.236	−	1278.66i	0.199801	−	0.346066i	−0.748663	−	0.662951i	$-0.769304\pi$
$239$	738.236	−	1278.66i	0.199801	−	0.346066i	0.948464	+	0.316885i	$0.102637\pi$
$240$		0			0
$241$	−881.728	−	1527.20i	−0.235673	−	0.408197i	0.723795	−	0.690015i	$-0.242396\pi$
$241$	−881.728	−	1527.20i	−0.235673	−	0.408197i	−0.959468	+	0.281818i	$0.909063\pi$
$242$			846.874i			0.224955i
$243$	402.970	+	3766.50i	0.106381	+	0.994325i
$244$	−1472.32			−0.386294
$245$		0			0
$246$	1473.70	−	4887.73i	0.381951	−	1.26679i
$247$	−1553.05	−	896.657i	−0.400075	−	0.230983i
$248$	−81.0910	−	46.8179i	−0.0207632	−	0.0119877i
$249$	7560.54	−	1776.28i	1.92422	−	0.452077i
$250$		0			0
$251$	1705.16			0.428801			0.214400	−	0.976746i	$-0.431220\pi$
$251$	1705.16			0.428801			0.214400	+	0.976746i	$0.431220\pi$
$252$	81.9242	−	123.505i	0.0204791	−	0.0308734i
$253$		−	2216.09i		−	0.550690i
$254$	−1909.11	−	3306.68i	−0.471607	−	0.816848i
$255$		0			0
$256$	−2194.37	+	3800.76i	−0.535735	+	0.927920i
$257$	−197.970	−	114.298i	−0.0480507	−	0.0277421i	0.475782	−	0.879563i	$-0.342165\pi$
$257$	−197.970	−	114.298i	−0.0480507	−	0.0277421i	−0.523833	+	0.851821i	$0.675498\pi$
$258$	2571.56	−	2416.66i	0.620537	−	0.583158i
$259$	−282.997	−	490.166i	−0.0678942	−	0.117596i
$260$		0			0
$261$	−459.892	+	7397.73i	−0.109068	+	1.75444i
$262$		−	2621.97i		−	0.618266i
$263$	1116.10	−	644.380i	0.261679	−	0.151081i	−0.363421	−	0.931625i	$-0.618391\pi$
$263$	1116.10	−	644.380i	0.261679	−	0.151081i	0.625100	+	0.780544i	$0.285058\pi$
$264$	2594.13	−	609.468i	0.604764	−	0.142084i
$265$		0			0
$266$	−149.049	+	258.161i	−0.0343563	+	0.0595069i
$267$	7150.32	+	2155.90i	1.63892	+	0.494154i
$268$	2428.38	−	1402.03i	0.553496	−	0.319561i
$269$	−973.981			−0.220761			−0.110380	−	0.993889i	$-0.535207\pi$
$269$	−973.981			−0.220761			−0.110380	+	0.993889i	$0.535207\pi$
$270$		0			0
$271$	−4021.83			−0.901508			−0.450754	−	0.892648i	$-0.648845\pi$
$271$	−4021.83			−0.901508			−0.450754	+	0.892648i	$0.648845\pi$
$272$	−7604.65	+	4390.55i	−1.69522	+	0.978736i
$273$	−267.403	−	80.6252i	−0.0592820	−	0.0178742i
$274$	−1051.54	+	1821.32i	−0.231847	+	0.401570i
$275$		0			0
$276$	−1150.38	+	270.271i	−0.250886	+	0.0589435i
$277$	−2926.45	+	1689.59i	−0.634777	+	0.366489i	−0.782600	−	0.622525i	$-0.786107\pi$
$277$	−2926.45	+	1689.59i	−0.634777	+	0.366489i	0.147823	+	0.989014i	$0.452773\pi$
$278$			4325.56i			0.933201i
$279$	145.052	−	72.1390i	0.0311255	−	0.0154797i
$280$		0			0
$281$	−366.654	−	635.063i	−0.0778388	−	0.134821i	0.824478	−	0.565893i	$-0.191469\pi$
$281$	−366.654	−	635.063i	−0.0778388	−	0.134821i	−0.902317	+	0.431073i	$0.858135\pi$
$282$	6155.95	−	5785.14i	1.29993	−	1.22163i
$283$	5983.39	+	3454.51i	1.25680	+	0.725617i	0.972452	−	0.233103i	$-0.0748879\pi$
$283$	5983.39	+	3454.51i	1.25680	+	0.725617i	0.284353	+	0.958720i	$0.408221\pi$
$284$	−200.568	+	347.394i	−0.0419068	+	0.0725847i
$285$		0			0
$286$	1829.70	+	3169.13i	0.378295	+	0.655227i
$287$			474.214i			0.0975331i
$288$	−1726.60	−	3471.71i	−0.353267	−	0.710322i
$289$	−7254.64			−1.47662
$290$		0			0
$291$	−4510.94	+	1059.81i	−0.908715	+	0.213494i
$292$	−535.376	−	309.099i	−0.107296	−	0.0619475i
$293$	−4026.57	−	2324.74i	−0.802850	−	0.463525i	0.0416170	−	0.999134i	$-0.486749\pi$
$293$	−4026.57	−	2324.74i	−0.802850	−	0.463525i	−0.844467	+	0.535608i	$0.820082\pi$
$294$	1721.64	−	5710.02i	0.341523	−	1.13271i
$295$		0			0
$296$	−5426.55			−1.06558
$297$	−1602.20	+	4322.97i	−0.313027	+	0.844593i
$298$			5140.41i			0.999248i
$299$	1113.45	+	1928.56i	0.215360	+	0.373014i
$300$		0			0
$301$	−163.902	+	283.886i	−0.0313859	+	0.0543619i
$302$	9236.19	+	5332.52i	1.75988	+	1.01607i
$303$	182.714	+	777.702i	0.0346424	+	0.147452i
$304$	2161.58	+	3743.97i	0.407813	+	0.706353i
$305$		0			0
$306$	623.176	−	10024.3i	0.116420	−	1.87271i
$307$		−	7361.42i		−	1.36853i	−0.729234	−	0.684264i	$-0.760123\pi$
$307$		−	7361.42i		−	1.36853i	0.729234	−	0.684264i	$-0.239877\pi$
$308$	156.214	−	90.1902i	0.0288997	−	0.0166853i
$309$	481.433	+	512.291i	0.0886335	+	0.0943146i
$310$		0			0
$311$	1354.60	−	2346.24i	0.246986	−	0.427792i	−0.715702	−	0.698405i	$-0.753893\pi$
$311$	1354.60	−	2346.24i	0.246986	−	0.427792i	0.962688	+	0.270614i	$0.0872266\pi$
$312$	−1951.32	+	1833.78i	−0.354077	+	0.332749i
$313$	5407.22	−	3121.86i	0.976467	−	0.563763i	0.0752653	−	0.997164i	$-0.476020\pi$
$313$	5407.22	−	3121.86i	0.976467	−	0.563763i	0.901202	+	0.433400i	$0.142686\pi$
$314$	−8055.37			−1.44774
$315$		0			0
$316$	−2152.50			−0.383189
$317$	1804.82	−	1042.02i	0.319776	−	0.184623i	−0.331517	−	0.943449i	$-0.607560\pi$
$317$	1804.82	−	1042.02i	0.319776	−	0.184623i	0.651293	+	0.758827i	$0.274227\pi$
$318$	−702.266	−	2989.12i	−0.123840	−	0.527111i
$319$	−4510.54	+	7812.48i	−0.791667	+	1.37121i
$320$		0			0
$321$	1078.17	−	3575.90i	0.187470	−	0.621767i
$322$	320.579	−	185.087i	0.0554819	−	0.0320325i
$323$			5990.45i			1.03194i
$324$	2439.46	+	304.483i	0.418289	+	0.0522091i
$325$		0			0
$326$	−4290.88	−	7432.02i	−0.728987	−	1.26264i
$327$	10002.4	+	3015.83i	1.69154	+	0.510018i
$328$	3937.47	+	2273.30i	0.662836	+	0.382689i
$329$	−392.358	+	679.583i	−0.0657489	+	0.113880i
$330$		0			0
$331$	113.938	+	197.347i	0.0189203	+	0.0327709i	0.875331	−	0.483525i	$-0.160644\pi$
$331$	113.938	+	197.347i	0.0189203	+	0.0327709i	−0.856410	+	0.516296i	$0.827310\pi$
$332$		−	5040.36i		−	0.833210i
$333$	5189.70	−	7823.76i	0.854035	−	1.28751i
$334$	−4635.39			−0.759394
$335$		0			0
$336$	461.087	+	490.641i	0.0748641	+	0.0796627i
$337$	−2959.62	−	1708.74i	−0.478400	−	0.276205i	0.241349	−	0.970438i	$-0.422410\pi$
$337$	−2959.62	−	1708.74i	−0.478400	−	0.276205i	−0.719750	+	0.694234i	$0.755743\pi$
$338$	3231.70	+	1865.82i	0.520063	+	0.300259i
$339$	−806.853	−	858.570i	−0.129269	−	0.137555i
$340$		0			0
$341$	197.168			0.0313116
$342$	−4935.21	−	306.806i	−0.780309	−	0.0485092i
$343$			1112.30i			0.175098i
$344$	1571.43	+	2721.80i	0.246296	+	0.426598i
$345$		0			0
$346$	3980.05	−	6893.65i	0.618407	−	1.07111i
$347$	−3126.00	−	1804.80i	−0.483610	−	0.279212i	0.238310	−	0.971189i	$-0.423407\pi$
$347$	−3126.00	−	1804.80i	−0.483610	−	0.279212i	−0.721920	+	0.691977i	$0.756740\pi$
$348$	4605.57	+	1388.63i	0.709439	+	0.213904i
$349$	−4400.42	−	7621.74i	−0.674925	−	1.16900i	−0.976491	−	0.215559i	$-0.930843\pi$
$349$	−4400.42	−	7621.74i	−0.674925	−	1.16900i	0.301566	−	0.953445i	$-0.402491\pi$
$350$		0			0
$351$	−777.715	−	4567.08i	−0.118266	−	0.694509i
$352$		−	4719.09i		−	0.714570i
$353$	−7370.30	+	4255.24i	−1.11128	+	0.641597i	−0.939160	−	0.343479i	$-0.888395\pi$
$353$	−7370.30	+	4255.24i	−1.11128	+	0.641597i	−0.172119	+	0.985076i	$0.555061\pi$
$354$	926.914	−	3074.23i	0.139166	−	0.461563i
$355$		0			0
$356$	2423.44	−	4197.52i	0.360792	−	0.624910i
$357$	213.381	+	908.234i	0.0316340	+	0.134647i
$358$	3811.55	−	2200.60i	0.562700	−	0.324875i
$359$	−4320.35			−0.635152			−0.317576	−	0.948233i	$-0.602869\pi$
$359$	−4320.35			−0.635152			−0.317576	+	0.948233i	$0.602869\pi$
$360$		0			0
$361$	−3909.75			−0.570017
$362$	−9051.83	+	5226.08i	−1.31424	+	0.758775i
$363$	950.898	−	893.619i	0.137491	−	0.129209i
$364$	−90.6303	+	156.976i	−0.0130503	+	0.0226038i
$365$		0			0
$366$	5239.14	+	5574.95i	0.748235	+	0.796195i
$367$	5716.10	−	3300.19i	0.813020	−	0.469397i	−0.0349838	−	0.999388i	$-0.511138\pi$
$367$	5716.10	−	3300.19i	0.813020	−	0.469397i	0.848003	+	0.529991i	$0.177805\pi$
$368$		−	5368.43i		−	0.760459i
$369$	−7043.15	+	3502.79i	−0.993636	+	0.494168i
$370$		0			0
$371$	142.611	+	247.010i	0.0199569	+	0.0345663i
$372$	−24.0463	−	102.351i	−0.00335146	−	0.0142651i
$373$	−7455.14	−	4304.23i	−1.03489	−	0.597492i	−0.116506	−	0.993190i	$-0.537169\pi$
$373$	−7455.14	−	4304.23i	−1.03489	−	0.597492i	−0.918381	+	0.395698i	$0.870503\pi$
$374$	6112.00	−	10586.3i	0.845037	−	1.46365i
$375$		0			0
$376$	3761.78	+	6515.60i	0.515955	+	0.893660i
$377$		−	9065.10i		−	1.23840i
$378$	−759.174	+	129.278i	−0.103301	+	0.0175908i
$379$	7129.80			0.966314			0.483157	−	0.875534i	$-0.339490\pi$
$379$	7129.80			0.966314			0.483157	+	0.875534i	$0.339490\pi$
$380$		0			0
$381$	−1698.36	+	5632.81i	−0.228371	+	0.757421i
$382$	1111.86	+	641.934i	0.148921	+	0.0859796i
$383$	5133.33	+	2963.73i	0.684859	+	0.395404i	0.801683	−	0.597749i	$-0.203938\pi$
$383$	5133.33	+	2963.73i	0.684859	+	0.395404i	−0.116824	+	0.993153i	$0.537271\pi$
$384$	8413.93	−	1976.78i	1.11815	−	0.262700i
$385$		0			0
$386$	−5213.68			−0.687486
$387$	−5427.01	−	337.379i	−0.712844	−	0.0443151i
$388$			3007.30i			0.393485i
$389$	519.432	+	899.683i	0.0677024	+	0.117264i	0.897890	−	0.440221i	$-0.145100\pi$
$389$	519.432	+	899.683i	0.0677024	+	0.117264i	−0.830187	+	0.557485i	$0.811766\pi$
$390$		0			0
$391$	3719.42	−	6442.22i	0.481072	−	0.833240i
$392$	4599.89	+	2655.75i	0.592678	+	0.342183i
$393$	−2944.03	+	2766.69i	−0.377879	+	0.355117i
$394$	7224.43	+	12513.1i	0.923761	+	1.60000i
$395$		0			0
$396$	2493.40	+	1653.94i	0.316410	+	0.209882i
$397$			13441.4i			1.69926i	0.527382	+	0.849628i	$0.323174\pi$
$397$			13441.4i			1.69926i	−0.527382	+	0.849628i	$0.676826\pi$
$398$	−4097.01	+	2365.41i	−0.515991	+	0.297907i
$399$	447.147	−	105.053i	0.0561037	−	0.0131810i
$400$		0			0
$401$	−6537.70	+	11323.6i	−0.814157	+	1.41016i	0.0957739	+	0.995403i	$0.469467\pi$
$401$	−6537.70	+	11323.6i	−0.814157	+	1.41016i	−0.909931	+	0.414759i	$0.863866\pi$
$402$	−13950.0	−	4206.08i	−1.73075	−	0.521841i
$403$	−171.586	+	99.0652i	−0.0212092	+	0.0122451i
$404$	518.468			0.0638484
$405$		0			0
$406$	−1506.87			−0.184199
$407$	9895.78	−	5713.33i	1.20520	−	0.695821i
$408$	8564.10	+	2582.17i	1.03918	+	0.313325i
$409$	−2636.59	+	4566.71i	−0.318756	+	0.552101i	−0.980229	−	0.197868i	$-0.936598\pi$
$409$	−2636.59	+	4566.71i	−0.318756	+	0.552101i	0.661473	+	0.749969i	$0.269932\pi$
$410$		0			0
$411$	3154.63	−	741.151i	0.378604	−	0.0889496i
$412$	395.123	−	228.124i	0.0472484	−	0.0272788i
$413$			298.266i			0.0355368i
$414$	5116.91	+	3394.18i	0.607446	+	0.402934i
$415$		0			0
$416$	2371.06	+	4106.80i	0.279449	+	0.484020i
$417$	4856.88	−	4564.32i	0.570366	−	0.536009i
$418$	−5211.91	−	3009.10i	−0.609863	−	0.352105i
$419$	6923.06	−	11991.1i	0.807192	−	1.39810i	−0.107609	−	0.994193i	$-0.534319\pi$
$419$	6923.06	−	11991.1i	0.807192	−	1.39810i	0.914801	−	0.403905i	$-0.132347\pi$
$420$		0			0
$421$	−548.684	−	950.349i	−0.0635184	−	0.110017i	0.832517	−	0.553999i	$-0.186899\pi$
$421$	−548.684	−	950.349i	−0.0635184	−	0.110017i	−0.896036	+	0.443982i	$0.853565\pi$
$422$			7251.94i			0.836538i
$423$	−12991.5	−	807.637i	−1.49330	−	0.0928338i
$424$	2734.60			0.313217
$425$		0			0
$426$	2029.12	−	476.722i	0.230777	−	0.0542189i
$427$	−615.444	−	355.327i	−0.0697504	−	0.0402704i
$428$	−2099.19	−	1211.97i	−0.237075	−	0.136875i
$429$	1627.71	−	5398.51i	0.183186	−	0.607558i
$430$		0			0
$431$	15912.8			1.77841			0.889205	−	0.457509i	$-0.151258\pi$
$431$	15912.8			1.77841			0.889205	+	0.457509i	$0.151258\pi$
$432$	−3881.29	+	10472.3i	−0.432266	+	1.16632i
$433$		−	3566.31i		−	0.395810i	−0.980221	−	0.197905i	$-0.936586\pi$
$433$		−	3566.31i		−	0.395810i	0.980221	−	0.197905i	$-0.0634138\pi$
$434$	16.4674	+	28.5223i	0.00182133	+	0.00315464i
$435$		0			0
$436$	3390.08	−	5871.79i	0.372375	−	0.644972i
$437$	−3171.67	−	1831.17i	−0.347189	−	0.200450i
$438$	734.686	+	3127.11i	0.0801476	+	0.341140i
$439$	−290.411	−	503.007i	−0.0315730	−	0.0546861i	0.849807	−	0.527094i	$-0.176718\pi$
$439$	−290.411	−	503.007i	−0.0315730	−	0.0546861i	−0.881380	+	0.472408i	$0.843385\pi$
$440$		0			0
$441$	−8228.06	+	4092.09i	−0.888464	+	0.441863i
$442$			12283.6i			1.32188i
$443$	9346.82	−	5396.39i	1.00244	−	0.578759i	0.0934706	−	0.995622i	$-0.470204\pi$
$443$	9346.82	−	5396.39i	1.00244	−	0.578759i	0.908969	+	0.416863i	$0.136871\pi$
$444$	−4172.67	−	4440.13i	−0.446005	−	0.474593i
$445$		0			0
$446$	−4313.40	+	7471.03i	−0.457949	+	0.793191i
$447$	5771.82	−	5424.15i	0.610733	−	0.573945i
$448$	−215.067	+	124.169i	−0.0226807	+	0.0130947i
$449$	−2894.01			−0.304180			−0.152090	−	0.988367i	$-0.548600\pi$
$449$	−2894.01			−0.304180			−0.152090	+	0.988367i	$0.548600\pi$
$450$		0			0
$451$	−9573.74			−0.999578
$452$	−662.203	+	382.323i	−0.0689102	+	0.0397853i
$453$	−3758.48	−	15997.6i	−0.389821	−	1.65923i
$454$	6887.11	−	11928.8i	0.711956	−	1.23314i
$455$		0			0
$456$	1271.27	−	4216.33i	0.130554	−	0.432999i
$457$	2771.21	−	1599.96i	0.283658	−	0.163770i	−0.351420	−	0.936218i	$-0.614301\pi$
$457$	2771.21	−	1599.96i	0.283658	−	0.163770i	0.635078	+	0.772448i	$0.280968\pi$
$458$		−	9246.49i		−	0.943363i
$459$	−11913.2	+	9877.87i	−1.21146	+	1.00449i
$460$		0			0
$461$	−3658.19	−	6336.17i	−0.369585	−	0.640141i	0.619915	−	0.784669i	$-0.287167\pi$
$461$	−3658.19	−	6336.17i	−0.369585	−	0.640141i	−0.989501	+	0.144528i	$0.953834\pi$
$462$	−897.381	−	270.571i	−0.0903678	−	0.0272469i
$463$	6072.55	+	3505.99i	0.609536	+	0.351916i	0.772784	−	0.634669i	$-0.218864\pi$
$463$	6072.55	+	3505.99i	0.609536	+	0.351916i	−0.163248	+	0.986585i	$0.552197\pi$
$464$	−10926.7	+	18925.6i	−1.09323	+	1.89353i
$465$		0			0
$466$	8573.53	+	14849.8i	0.852277	+	1.47619i
$467$		−	8002.63i		−	0.792971i	−0.918041	−	0.396485i	$-0.870230\pi$
$467$		−	8002.63i		−	0.792971i	0.918041	−	0.396485i	$-0.129770\pi$
$468$	−3000.89	−	186.555i	−0.296402	−	0.0184263i
$469$	1353.45			0.133255
$470$		0			0
$471$	8500.00	+	9044.83i	0.831549	+	0.884849i
$472$	2476.54	+	1429.83i	0.241509	+	0.139435i
$473$	−5731.28	−	3308.95i	−0.557134	−	0.321661i
$474$	7659.52	+	8150.47i	0.742222	+	0.789797i
$475$		0			0
$476$	605.489			0.0583037
$477$	−2615.25	+	3942.63i	−0.251035	+	0.378450i
$478$			4979.08i			0.476439i
$479$	−1589.42	−	2752.96i	−0.151613	−	0.262601i	0.780208	−	0.625520i	$-0.215113\pi$
$479$	−1589.42	−	2752.96i	−0.151613	−	0.262601i	−0.931820	+	0.362920i	$0.881780\pi$
$480$		0			0
$481$	−5741.21	+	9944.06i	−0.544234	+	0.942641i
$482$	5150.14	+	2973.44i	0.486686	+	0.280988i
$483$	−546.096	−	164.654i	−0.0514456	−	0.0155114i
$484$	−423.437	−	733.414i	−0.0397668	−	0.0688781i
$485$		0			0
$486$	−7527.71	−	10320.5i	−0.702601	−	0.963269i
$487$			13060.3i			1.21523i	0.794232	+	0.607615i	$0.207874\pi$
$487$			13060.3i			1.21523i	−0.794232	+	0.607615i	$0.792126\pi$
$488$	−5900.65	+	3406.74i	−0.547356	+	0.316016i
$489$	−3817.19	+	12660.2i	−0.353005	+	1.17078i
$490$		0			0
$491$	2200.81	−	3811.91i	0.202283	−	0.350365i	−0.746981	−	0.664846i	$-0.768497\pi$
$491$	2200.81	−	3811.91i	0.202283	−	0.350365i	0.949264	+	0.314481i	$0.101831\pi$
$492$	1167.60	+	4969.75i	0.106991	+	0.455393i
$493$	−26224.4	+	15140.7i	−2.39572	+	1.38317i
$494$	6047.56			0.550794
$495$		0			0
$496$	477.636			0.0432389
$497$	−167.679	+	96.8093i	−0.0151336	+	0.00873741i
$498$	−19085.3	+	17935.7i	−1.71734	+	1.61389i
$499$	9362.60	−	16216.5i	0.839935	−	1.45481i	−0.0500129	−	0.998749i	$-0.515926\pi$
$499$	9362.60	−	16216.5i	0.839935	−	1.45481i	0.889948	−	0.456062i	$-0.150740\pi$
$500$		0			0
$501$	4891.26	+	5204.77i	0.436178	+	0.464136i
$502$	−4979.90	+	2875.15i	−0.442757	+	0.255626i
$503$			3811.68i			0.337882i	0.985626	+	0.168941i	$0.0540347\pi$
$503$			3811.68i			0.337882i	−0.985626	+	0.168941i	$0.945965\pi$
$504$	42.5553	−	684.536i	0.00376104	−	0.0604993i
$505$		0			0
$506$	3736.64	+	6472.06i	0.328289	+	0.568613i
$507$	−1315.07	−	5597.47i	−0.115196	−	0.490320i
$508$	3306.68	+	1909.11i	0.288799	+	0.166738i
$509$	2247.74	−	3893.20i	0.195735	−	0.339024i	−0.751406	−	0.659840i	$-0.770624\pi$
$509$	2247.74	−	3893.20i	0.195735	−	0.339024i	0.947141	+	0.320816i	$0.103957\pi$
$510$		0			0
$511$	−149.195	−	258.413i	−0.0129158	−	0.0223709i
$512$		−	1493.27i		−	0.128894i
$513$	4863.13	+	5865.16i	0.418543	+	0.504782i
$514$	770.891			0.0661528
$515$		0			0
$516$	−1018.71	+	3378.67i	−0.0869111	+	0.288251i
$517$	−13719.9	−	7921.16i	−1.16712	−	0.673834i
$518$	1652.98	+	954.347i	0.140208	+	0.0809490i
$519$	−11940.2	+	2805.23i	−1.00985	+	0.237256i
$520$		0			0
$521$	12095.0			1.01706			0.508531	−	0.861043i	$-0.330189\pi$
$521$	12095.0			1.01706			0.508531	+	0.861043i	$0.330189\pi$
$522$	−11130.5	−	22380.4i	−0.933274	−	1.87656i
$523$		−	7385.38i		−	0.617476i	−0.951147	−	0.308738i	$-0.900093\pi$
$523$		−	7385.38i		−	0.617476i	0.951147	−	0.308738i	$-0.0999067\pi$
$524$	1310.98	+	2270.69i	0.109295	+	0.189304i
$525$		0			0
$526$	−2173.03	+	3763.80i	−0.180131	+	0.311995i
$527$	573.172	+	330.921i	0.0473772	+	0.0273532i
$528$	−9905.37	+	9308.70i	−0.816431	+	0.767253i
$529$	−3809.59	−	6598.40i	−0.313108	−	0.542320i
$530$		0			0
$531$	−4429.92	+	2203.15i	−0.362038	+	0.180054i
$532$		−	298.098i		−	0.0242936i
$533$	8331.56	−	4810.23i	0.677073	−	0.390908i
$534$	−24517.5	+	5760.17i	−1.98685	+	0.466792i
$535$		0			0
$536$	6488.18	−	11237.9i	0.522848	−	0.905600i
$537$	−6492.83	−	1957.66i	−0.521763	−	0.157317i
$538$	2844.49	−	1642.27i	0.227946	−	0.131605i
$539$	−11184.4			−0.893778
$540$		0			0
$541$	−5935.19			−0.471670			−0.235835	−	0.971793i	$-0.575783\pi$
$541$	−5935.19			−0.471670			−0.235835	+	0.971793i	$0.575783\pi$
$542$	11745.7	−	6781.37i	0.930849	−	0.537426i
$543$	15419.5	+	4649.15i	1.21862	+	0.367429i
$544$	7920.37	−	13718.5i	0.624234	−	1.08120i
$545$		0			0
$546$	916.892	−	215.416i	0.0718670	−	0.0168845i
$547$	−8796.41	+	5078.61i	−0.687582	+	0.396976i	−0.802705	−	0.596376i	$-0.796607\pi$
$547$	−8796.41	+	5078.61i	−0.687582	+	0.396976i	0.115124	+	0.993351i	$0.463274\pi$
$548$		−	2103.08i		−	0.163940i
$549$	731.413	−	11765.3i	0.0568596	−	0.914632i
$550$		0			0
$551$	7454.16	+	12911.0i	0.576330	+	0.998232i
$552$	−3985.03	+	3744.98i	−0.307272	+	0.288763i
$553$	−899.768	−	519.481i	−0.0691899	−	0.0399468i
$554$	5697.76	−	9868.81i	0.436958	−	0.756833i
$555$		0			0
$556$	−2162.78	−	3746.05i	−0.164968	−	0.285733i
$557$			5709.62i			0.434334i	0.976134	+	0.217167i	$0.0696817\pi$
$557$			5709.62i			0.434334i	−0.976134	+	0.217167i	$0.930318\pi$
$558$	−301.984	+	455.258i	−0.0229104	+	0.0345387i
$559$	6650.20			0.503173
$560$		0			0
$561$	−18336.0	+	4307.88i	−1.37994	+	0.324204i
$562$	2141.61	+	1236.46i	0.160744	+	0.0928058i
$563$	11205.6	+	6469.56i	0.838828	+	0.484297i	0.856866	−	0.515540i	$-0.172409\pi$
$563$	11205.6	+	6469.56i	0.838828	+	0.484297i	−0.0180378	+	0.999837i	$0.505742\pi$
$564$	−2438.64	+	8088.06i	−0.182066	+	0.603845i
$565$		0			0
$566$	−23299.2			−1.73028
$567$	946.236	+	716.012i	0.0700850	+	0.0530330i
$568$			1856.34i			0.137131i
$569$	−3062.71	−	5304.77i	−0.225651	−	0.390839i	0.730863	−	0.682524i	$-0.239118\pi$
$569$	−3062.71	−	5304.77i	−0.225651	−	0.390839i	−0.956515	+	0.291684i	$0.905784\pi$
$570$		0			0
$571$	9641.20	−	16699.0i	0.706605	−	1.22388i	−0.259504	−	0.965742i	$-0.583559\pi$
$571$	9641.20	−	16699.0i	0.706605	−	1.22388i	0.966109	−	0.258134i	$-0.0831076\pi$
$572$	−3169.13	−	1829.70i	−0.231658	−	0.133748i
$573$	−452.450	−	1925.80i	−0.0329867	−	0.140404i
$574$	−799.592	−	1384.93i	−0.0581434	−	0.100707i
$575$		0			0
$576$	−3432.78	−	2277.05i	−0.248320	−	0.164717i
$577$		−	4988.14i		−	0.359894i	−0.983676	−	0.179947i	$-0.942407\pi$
$577$		−	4988.14i		−	0.359894i	0.983676	−	0.179947i	$-0.0575927\pi$
$578$	21187.0	−	12232.3i	1.52468	−	0.880274i
$579$	5501.46	+	5854.09i	0.394876	+	0.420186i
$580$		0			0
$581$	1216.43	−	2106.92i	0.0868606	−	0.150447i
$582$	11387.1	−	10701.2i	0.811018	−	0.762165i
$583$	−4986.78	+	2879.12i	−0.354256	+	0.204530i
$584$	−2860.85			−0.202710
$585$		0			0
$586$	15679.4			1.10531
$587$	−13245.0	+	7647.00i	−0.931311	+	0.537693i	−0.887226	−	0.461335i	$-0.847371\pi$
$587$	−13245.0	+	7647.00i	−0.931311	+	0.537693i	−0.0440852	+	0.999028i	$0.514037\pi$
$588$	1364.03	+	5805.84i	0.0956661	+	0.407192i
$589$	162.921	−	282.188i	0.0113974	−	0.0197408i
$590$		0			0
$591$	6426.90	−	21315.6i	0.447322	−	1.48360i
$592$	23972.3	−	13840.4i	1.66428	−	0.960874i
$593$			11090.9i			0.768040i	0.923325	+	0.384020i	$0.125461\pi$
$593$			11090.9i			0.768040i	−0.923325	+	0.384020i	$0.874539\pi$
$594$	−2609.94	−	15326.7i	−0.180281	−	1.05869i
$595$		0			0
$596$	−2570.21	−	4451.73i	−0.176644	−	0.305956i
$597$	6979.10	+	2104.28i	0.478452	+	0.144259i
$598$	−6503.63	−	3754.88i	−0.444738	−	0.256770i
$599$	−14100.8	+	24423.3i	−0.961840	+	1.66596i	−0.243965	+	0.969784i	$0.578448\pi$
$599$	−14100.8	+	24423.3i	−0.961840	+	1.66596i	−0.717875	+	0.696172i	$0.754885\pi$
$600$		0			0
$601$	−10572.0	−	18311.3i	−0.717539	−	1.24281i	−0.961972	−	0.273148i	$-0.911935\pi$
$601$	−10572.0	−	18311.3i	−0.717539	−	1.24281i	0.244433	−	0.969666i	$-0.421398\pi$
$602$		−	1105.45i		−	0.0748416i
$603$	9997.26	+	20101.7i	0.675157	+	1.35755i
$604$	−10665.0			−0.718467
$605$		0			0
$606$	−1844.93	−	1963.18i	−0.123672	−	0.131599i
$607$	7620.14	+	4399.49i	0.509542	+	0.294184i	0.732645	−	0.680611i	$-0.238285\pi$
$607$	7620.14	+	4399.49i	0.509542	+	0.294184i	−0.223103	+	0.974795i	$0.571619\pi$
$608$	−6753.97	−	3899.41i	−0.450509	−	0.260102i
$609$	1590.04	+	1691.96i	0.105799	+	0.112581i
$610$		0			0
$611$	15919.6			1.05407
$612$	4472.45	+	8992.87i	0.295406	+	0.593979i
$613$		−	19539.8i		−	1.28745i	−0.765257	−	0.643724i	$-0.777388\pi$
$613$		−	19539.8i		−	1.28745i	0.765257	−	0.643724i	$-0.222612\pi$
$614$	12412.4	+	21498.9i	0.815836	+	1.41307i
$615$		0			0
$616$	417.375	−	722.914i	0.0272995	−	0.0472842i
$617$	2835.26	+	1636.94i	0.184997	+	0.106808i	0.589638	−	0.807667i	$-0.299270\pi$
$617$	2835.26	+	1636.94i	0.184997	+	0.106808i	−0.404641	+	0.914475i	$0.632604\pi$
$618$	−2269.81	−	684.373i	−0.147743	−	0.0445462i
$619$	4693.24	+	8128.92i	0.304745	+	0.527834i	0.977205	−	0.212300i	$-0.0680954\pi$
$619$	4693.24	+	8128.92i	0.304745	+	0.527834i	−0.672460	+	0.740134i	$0.734762\pi$
$620$		0			0
$621$	−1588.26	−	9326.96i	−0.102632	−	0.602702i
$622$			9136.21i			0.588953i
$623$	2026.04	−	1169.73i	0.130291	−	0.0752238i
$624$	3943.09	−	13077.8i	0.252965	−	0.838989i
$625$		0			0
$626$	−10527.8	+	18234.7i	−0.672165	+	1.16422i
$627$	2120.88	+	9027.29i	0.135087	+	0.574984i
$628$	6976.15	−	4027.68i	0.443278	−	0.255927i
$629$	38356.3			2.43142
$630$		0			0
$631$	9647.08			0.608628			0.304314	−	0.952572i	$-0.401573\pi$
$631$	9647.08			0.608628			0.304314	+	0.952572i	$0.401573\pi$
$632$	−8626.64	+	4980.59i	−0.542958	+	0.313477i
$633$	8142.72	−	7652.23i	0.511286	−	0.480488i
$634$	−3513.97	+	6086.37i	−0.220122	+	0.381263i
$635$		0			0
$636$	2102.74	+	2237.52i	0.131099	+	0.139502i
$637$	9733.23	−	5619.48i	0.605408	−	0.349532i
$638$		−	30421.6i		−	1.88778i
$639$	−2676.40	−	1775.32i	−0.165691	−	0.109907i
$640$		0			0
$641$	3501.88	+	6065.44i	0.215782	+	0.373745i	0.953514	−	0.301348i	$-0.0974367\pi$
$641$	3501.88	+	6065.44i	0.215782	+	0.373745i	−0.737732	+	0.675093i	$0.764103\pi$
$642$	2880.68	+	12261.3i	0.177089	+	0.753761i
$643$	−5446.34	−	3144.44i	−0.334032	−	0.192853i	0.323598	−	0.946195i	$-0.395108\pi$
$643$	−5446.34	−	3144.44i	−0.334032	−	0.192853i	−0.657630	+	0.753341i	$0.728441\pi$
$644$	−185.087	+	320.579i	−0.0113252	+	0.0196158i
$645$		0			0
$646$	−10100.7	−	17495.0i	−0.615183	−	1.06553i
$647$		−	5900.85i		−	0.358557i	−0.983798	−	0.179279i	$-0.942624\pi$
$647$		−	5900.85i		−	0.358557i	0.983798	−	0.179279i	$-0.0573764\pi$
$648$	10481.2	−	4424.29i	0.635404	−	0.268214i
$649$	−6021.58			−0.364203
$650$		0			0
$651$	14.6495	−	48.5868i	0.000881963	−	0.00292514i
$652$	7432.02	+	4290.88i	0.446412	+	0.257736i
$653$	−6828.74	−	3942.57i	−0.409233	−	0.236271i	0.281227	−	0.959641i	$-0.409259\pi$
$653$	−6828.74	−	3942.57i	−0.409233	−	0.236271i	−0.690460	+	0.723370i	$0.742592\pi$
$654$	−34296.9	+	8057.75i	−2.05064	+	0.481778i
$655$		0			0
$656$	−23192.2			−1.38034
$657$	2735.98	−	4124.65i	0.162467	−	0.244928i
$658$		−	2646.28i		−	0.156782i
$659$	14378.9	+	24905.0i	0.849959	+	1.47217i	0.881244	+	0.472662i	$0.156707\pi$
$659$	14378.9	+	24905.0i	0.849959	+	1.47217i	−0.0312845	+	0.999511i	$0.509960\pi$
$660$		0			0
$661$	−4130.11	+	7153.57i	−0.243030	+	0.420940i	−0.961576	−	0.274539i	$-0.911475\pi$
$661$	−4130.11	+	7153.57i	−0.243030	+	0.420940i	0.718546	+	0.695479i	$0.244808\pi$
$662$	−665.509	−	384.232i	−0.0390721	−	0.0225583i
$663$	13792.5	−	12961.7i	0.807926	−	0.759260i
$664$	−11662.7	−	20200.4i	−0.681626	−	1.18061i
$665$		0			0
$666$	−1964.45	+	31599.7i	−0.114296	+	1.83853i
$667$		−	18512.9i		−	1.07470i
$668$	4014.37	−	2317.70i	0.232516	−	0.134243i
$669$	12940.2	−	3040.18i	0.747828	−	0.175695i
$670$		0			0
$671$	7173.56	−	12425.0i	0.412716	−	0.714845i
$672$	−1162.89	−	350.625i	−0.0667553	−	0.0201275i
$673$	−697.118	+	402.481i	−0.0399285	+	0.0230528i	−0.519831	−	0.854269i	$-0.674005\pi$
$673$	−697.118	+	402.481i	−0.0399285	+	0.0230528i	0.479903	+	0.877322i	$0.340672\pi$
$674$	11524.7			0.658627
$675$		0			0
$676$	−3731.65			−0.212315
$677$	1180.63	−	681.636i	0.0670240	−	0.0386963i	−0.466114	−	0.884725i	$-0.654346\pi$
$677$	1180.63	−	681.636i	0.0670240	−	0.0386963i	0.533137	+	0.846029i	$0.321013\pi$
$678$	3804.07	+	1146.97i	0.215478	+	0.0649692i
$679$	−725.774	+	1257.08i	−0.0410201	+	0.0710489i
$680$		0			0
$681$	−20661.3	+	4854.19i	−1.16262	+	0.273147i
$682$	−575.827	+	332.454i	−0.0323307	+	0.0186661i
$683$			11434.6i			0.640604i	0.947315	+	0.320302i	$0.103784\pi$
$683$			11434.6i			0.640604i	−0.947315	+	0.320302i	$0.896216\pi$
$684$	4427.42	−	2201.91i	0.247495	−	0.123088i
$685$		0			0
$686$	−1875.50	−	3248.46i	−0.104383	−	0.180797i
$687$	−10382.3	+	9756.87i	−0.576576	+	0.541845i
$688$	−13883.9	−	8015.86i	−0.769358	−	0.444189i
$689$	2893.17	−	5011.12i	0.159972	−	0.277080i
$690$		0			0
$691$	9765.29	+	16914.0i	0.537611	+	0.931170i	0.999032	+	0.0439884i	$0.0140065\pi$
$691$	9765.29	+	16914.0i	0.537611	+	0.931170i	−0.461421	+	0.887181i	$0.652660\pi$
$692$			7960.10i			0.437280i
$693$	643.109	+	1293.11i	0.0352521	+	0.0708822i
$694$	12172.6			0.665799
$695$		0			0
$696$	21671.0	−	5091.40i	1.18022	−	0.277283i
$697$	−27831.0	−	16068.3i	−1.51245	−	0.873212i
$698$	25702.7	+	14839.4i	1.39378	+	0.804701i
$699$	7627.06	−	25296.1i	0.412706	−	1.36879i
$700$		0			0
$701$	−11041.4			−0.594903			−0.297452	−	0.954737i	$-0.596137\pi$
$701$	−11041.4			−0.594903			−0.297452	+	0.954737i	$0.596137\pi$
$702$	9972.04	+	12026.7i	0.536140	+	0.646609i
$703$		−	18883.8i		−	1.01311i
$704$	−2506.80	−	4341.90i	−0.134203	−	0.232446i
$705$		0			0
$706$	14349.9	−	24854.7i	0.764964	−	1.32496i
$707$	216.725	+	125.126i	0.0115287	+	0.00665608i
$708$	734.382	+	3125.82i	0.0389827	+	0.165926i
$709$	1969.54	+	3411.34i	0.104327	+	0.180699i	0.913463	−	0.406922i	$-0.133398\pi$
$709$	1969.54	+	3411.34i	0.104327	+	0.180699i	−0.809136	+	0.587621i	$0.800065\pi$
$710$		0			0
$711$	1069.31	−	17200.7i	0.0564027	−	0.907282i
$712$		−	22430.0i		−	1.18062i
$713$	−350.416	+	202.313i	−0.0184056	+	0.0106265i
$714$	−2154.59	−	2292.69i	−0.112932	−	0.120170i
$715$		0			0
$716$	−2200.60	+	3811.55i	−0.114861	+	0.198944i
$717$	5590.67	−	5253.91i	0.291196	−	0.273655i
$718$	12617.5	−	7284.72i	0.655824	−	0.378640i
$719$	23298.2			1.20845			0.604225	−	0.796814i	$-0.293483\pi$
$719$	23298.2			1.20845			0.604225	+	0.796814i	$0.293483\pi$
$720$		0			0
$721$	220.220			0.0113751
$722$	11418.3	−	6592.38i	0.588569	−	0.339810i
$723$	−2095.75	−	8920.31i	−0.107803	−	0.458852i
$724$	5226.08	−	9051.83i	0.268267	−	0.464653i
$725$		0			0
$726$	−1270.31	+	4213.15i	−0.0649389	+	0.215378i
$727$	−8231.12	+	4752.24i	−0.419911	+	0.242436i	−0.695039	−	0.718972i	$-0.744613\pi$
$727$	−8231.12	+	4752.24i	−0.419911	+	0.242436i	0.275128	+	0.961408i	$0.411280\pi$
$728$			838.823i			0.0427044i
$729$	−3645.00	+	19342.6i	−0.185185	+	0.982704i
$730$		0			0
$731$	−11107.3	−	19238.4i	−0.561994	−	0.973402i
$732$	−7324.70	−	2208.48i	−0.369848	−	0.111513i
$733$	6340.01	+	3660.40i	0.319473	+	0.184448i	0.651157	−	0.758943i	$-0.274284\pi$
$733$	6340.01	+	3660.40i	0.319473	+	0.184448i	−0.331685	+	0.943390i	$0.607617\pi$
$734$	−11129.2	+	19276.3i	−0.559653	+	0.969348i
$735$		0			0
$736$	4842.22	+	8386.96i	0.242509	+	0.420037i
$737$			27324.3i			1.36567i
$738$	14663.2	−	22105.6i	0.731381	−	1.10260i
$739$	1274.52			0.0634424			0.0317212	−	0.999497i	$-0.489901\pi$
$739$	1274.52			0.0634424			0.0317212	+	0.999497i	$0.489901\pi$
$740$		0			0
$741$	−6381.37	−	6790.39i	−0.316363	−	0.336641i
$742$	−832.986	−	480.925i	−0.0412128	−	0.0237942i
$743$	1681.09	+	970.576i	0.0830055	+	0.0479232i	0.540928	−	0.841069i	$-0.318073\pi$
$743$	1681.09	+	970.576i	0.0830055	+	0.0479232i	−0.457923	+	0.888992i	$0.651406\pi$
$744$	−333.196	−	354.553i	−0.0164187	−	0.0174711i
$745$		0			0
$746$	29030.1			1.42476
$747$	40277.6	+	2503.93i	1.97280	+	0.122642i
$748$			12224.0i			0.597531i
$749$	−584.988	−	1013.23i	−0.0285380	−	0.0494293i
$750$		0			0
$751$	−8270.01	+	14324.1i	−0.401834	+	0.695996i	−0.993947	−	0.109858i	$-0.964960\pi$
$751$	−8270.01	+	14324.1i	−0.401834	+	0.695996i	0.592114	+	0.805854i	$0.298294\pi$
$752$	−33236.0	−	19188.8i	−1.61169	−	0.930511i
$753$	8483.08	+	2557.75i	0.410545	+	0.123784i
$754$	15285.0	+	26474.4i	0.738260	+	1.27870i
$755$		0			0
$756$	592.826	−	491.545i	0.0285197	−	0.0236472i
$757$			21145.7i			1.01526i	0.861575	+	0.507631i	$0.169479\pi$
$757$			21145.7i			1.01526i	−0.861575	+	0.507631i	$0.830521\pi$
$758$	−20822.4	+	12021.8i	−0.997764	+	0.576059i
$759$	3324.14	−	11024.9i	0.158970	−	0.527245i
$760$		0			0
$761$	10067.1	−	17436.7i	0.479543	−	0.830593i	−0.520181	−	0.854056i	$-0.674136\pi$
$761$	10067.1	−	17436.7i	0.479543	−	0.830593i	0.999725	+	0.0234624i	$0.00746901\pi$
$762$	−4537.69	−	19314.2i	−0.215726	−	0.918213i
$763$	2834.17	−	1636.31i	0.134474	−	0.0776388i
$764$	−1283.87			−0.0607968
$765$		0			0
$766$	−19989.1			−0.942865
$767$	5240.29	−	3025.48i	0.246696	−	0.142430i
$768$	−16618.0	+	15617.0i	−0.780795	+	0.733762i
$769$	1097.36	−	1900.68i	0.0514587	−	0.0891291i	−0.839149	−	0.543902i	$-0.816946\pi$
$769$	1097.36	−	1900.68i	0.0514587	−	0.0891291i	0.890607	+	0.454773i	$0.150280\pi$
$770$		0			0
$771$	−813.442	−	865.581i	−0.0379966	−	0.0404321i
$772$	4515.18	−	2606.84i	0.210499	−	0.121531i
$773$			8327.70i			0.387486i	0.981052	+	0.193743i	$0.0620628\pi$
$773$			8327.70i			0.387486i	−0.981052	+	0.193743i	$0.937937\pi$
$774$	16418.4	−	8165.40i	0.762462	−	0.379198i
$775$		0			0
$776$	6958.46	+	12052.4i	0.321900	+	0.557547i
$777$	−672.646	−	2863.04i	−0.0310567	−	0.132189i
$778$	−3033.98	−	1751.67i	−0.139812	−	0.0807204i
$779$	−7910.82	+	13701.9i	−0.363844	+	0.630196i
$780$		0			0
$781$	−1954.45	−	3385.20i	−0.0895463	−	0.155099i
$782$			25085.8i			1.14715i
$783$	−13384.5	+	36113.4i	−0.610887	+	1.64826i
$784$	−27093.9			−1.23424
$785$		0			0
$786$	3932.95	−	13044.1i	0.178478	−	0.591944i
$787$	16422.7	+	9481.64i	0.743845	+	0.429459i	0.823465	−	0.567366i	$-0.192038\pi$
$787$	16422.7	+	9481.64i	0.743845	+	0.429459i	−0.0796209	+	0.996825i	$0.525371\pi$
$788$	−12513.1	−	7224.43i	−0.565686	−	0.326599i
$789$	6519.10	−	1531.60i	0.294152	−	0.0691084i
$790$		0			0
$791$	−369.076			−0.0165902
$792$	13819.8	+	859.134i	0.620034	+	0.0385454i
$793$			14417.1i			0.645608i
$794$	−22664.1	−	39255.4i	−1.01300	−	1.75456i
$795$		0			0
$796$	2365.41	−	4097.01i	0.105326	−	0.182430i
$797$	−29674.5	−	17132.6i	−1.31885	−	0.761439i	−0.335307	−	0.942109i	$-0.608840\pi$
$797$	−29674.5	−	17132.6i	−1.31885	−	0.761439i	−0.983544	+	0.180670i	$0.942173\pi$
$798$	−1128.75	+	1060.76i	−0.0500718	+	0.0470557i
$799$	−26589.2	−	46053.9i	−1.17730	−	2.03914i
$800$		0			0
$801$	32338.5	+	21451.0i	1.42650	+	0.946233i
$802$		−	44093.9i		−	1.94141i
$803$	5217.00	−	3012.04i	0.229270	−	0.132369i
$804$	14184.1	−	3332.42i	0.622181	−	0.146176i
$805$		0			0
$806$	334.076	−	578.636i	0.0145997	−	0.0252873i
$807$	−4845.49	−	1460.97i	−0.211362	−	0.0637282i
$808$	2077.88	−	1199.66i	0.0904696	−	0.0522327i
$809$	−36425.5			−1.58300			−0.791502	−	0.611166i	$-0.790701\pi$
$809$	−36425.5			−1.58300			−0.791502	+	0.611166i	$0.790701\pi$
$810$		0			0
$811$	45174.0			1.95595			0.977973	−	0.208732i	$-0.0669335\pi$
$811$	45174.0			1.95595			0.977973	+	0.208732i	$0.0669335\pi$
$812$	1304.99	−	753.435i	0.0563991	−	0.0325620i
$813$	−20008.3	−	6032.74i	−0.863128	−	0.260243i
$814$	−19267.0	+	33371.3i	−0.829615	+	1.43694i
$815$		0			0
$816$	−44418.5	+	10435.7i	−1.90559	+	0.447700i
$817$	−9471.56	+	5468.41i	−0.405591	+	0.234168i
$818$		−	17782.7i		−	0.760093i
$819$	−1209.38	−	802.210i	−0.0515984	−	0.0342265i
$820$		0			0
$821$	3459.65	+	5992.29i	0.147068	+	0.254729i	0.930143	−	0.367199i	$-0.119683\pi$
$821$	3459.65	+	5992.29i	0.147068	+	0.254729i	−0.783075	+	0.621928i	$0.786350\pi$
$822$	−7963.34	+	7483.66i	−0.337900	+	0.317546i
$823$	−9871.42	−	5699.26i	−0.418100	−	0.241390i	0.276164	−	0.961110i	$-0.410937\pi$
$823$	−9871.42	−	5699.26i	−0.418100	−	0.241390i	−0.694264	+	0.719721i	$0.744270\pi$
$824$	1055.70	−	1828.52i	0.0446322	−	0.0773052i
$825$		0			0
$826$	−502.919	−	871.080i	−0.0211850	−	0.0366934i
$827$			34712.0i			1.45956i	0.683683	+	0.729779i	$0.260377\pi$
$827$			34712.0i			1.45956i	−0.683683	+	0.729779i	$0.739623\pi$
$828$	−6128.46	−	380.986i	−0.257221	−	0.0159906i
$829$	−2732.97			−0.114500			−0.0572498	−	0.998360i	$-0.518233\pi$
$829$	−2732.97			−0.114500			−0.0572498	+	0.998360i	$0.518233\pi$
$830$		0			0
$831$	−17093.3	+	4015.91i	−0.713549	+	0.167642i
$832$	4363.09	+	2519.03i	0.181806	+	0.104966i
$833$	−32513.2	−	18771.5i	−1.35236	−	0.780786i
$834$	−6488.34	+	21519.4i	−0.269392	+	0.893472i
$835$		0			0
$836$	6018.19			0.248975
$837$	829.831	−	141.310i	0.0342690	−	0.00583557i
$838$			46693.0i			1.92480i
$839$	−4787.89	−	8292.87i	−0.197016	−	0.341242i	0.750544	−	0.660821i	$-0.229792\pi$
$839$	−4787.89	−	8292.87i	−0.197016	−	0.341242i	−0.947560	+	0.319579i	$0.896458\pi$
$840$		0			0
$841$	−25485.8	+	44142.8i	−1.04497	+	1.80995i
$842$	3204.85	+	1850.32i	0.131171	+	0.0757318i
$843$	−871.484	−	3709.38i	−0.0356056	−	0.151551i
$844$	−3625.97	−	6280.37i	−0.147880	−	0.256136i
$845$		0			0
$846$	39303.2	−	19546.8i	1.59725	−	0.794364i
$847$		−	408.766i		−	0.0165825i
$848$	−12080.4	+	6974.60i	−0.489200	+	0.282440i
$849$	24585.2	+	26161.1i	0.993832	+	1.05753i
$850$		0			0
$851$	−11724.8	+	20307.9i	−0.472292	+	0.818034i
$852$	−1518.90	+	1427.41i	−0.0610761	+	0.0573971i
$853$	−7830.51	+	4520.95i	−0.314316	+	0.181470i	−0.648856	−	0.760911i	$-0.724752\pi$
$853$	−7830.51	+	4520.95i	−0.314316	+	0.181470i	0.334540	+	0.942381i	$0.391419\pi$
$854$	2396.52			0.0960274
$855$		0			0
$856$	−11217.3			−0.447896
$857$	−2005.09	+	1157.64i	−0.0799213	+	0.0461426i	−0.539428	−	0.842032i	$-0.681360\pi$
$857$	−2005.09	+	1157.64i	−0.0799213	+	0.0461426i	0.459507	+	0.888174i	$0.348026\pi$
$858$	4348.94	+	18510.8i	0.173043	+	0.736536i
$859$	−15701.6	+	27195.9i	−0.623667	+	1.08022i	0.365130	+	0.930957i	$0.381025\pi$
$859$	−15701.6	+	27195.9i	−0.623667	+	1.08022i	−0.988797	+	0.149266i	$0.952309\pi$
$860$		0			0
$861$	−711.322	+	2359.19i	−0.0281554	+	0.0933808i
$862$	−46473.2	+	26831.3i	−1.83629	+	1.06018i
$863$			40883.5i			1.61262i	0.591493	+	0.806310i	$0.298539\pi$
$863$			40883.5i			1.61262i	−0.591493	+	0.806310i	$0.701461\pi$
$864$	−3382.15	−	19861.4i	−0.133175	−	0.782060i
$865$		0			0
$866$	6013.30	+	10415.3i	0.235959	+	0.408692i
$867$	−36091.4	−	10882.0i	−1.41376	−	0.426264i
$868$	−28.5223	−	16.4674i	−0.00111534	−	0.000643939i
$869$	10487.6	−	18165.1i	0.409399	−	0.709100i
$870$		0			0
$871$	−13728.8	−	23779.0i	−0.534078	−	0.925051i
$872$		−	31376.7i		−	1.21852i
$873$	−24031.4	−	1493.95i	−0.931659	−	0.0579182i
$874$	12350.4			0.477985
$875$		0			0
$876$	−2199.81	−	2340.81i	−0.0848456	−	0.0902840i
$877$	24521.2	+	14157.3i	0.944154	+	0.545107i	0.891260	−	0.453493i	$-0.149822\pi$
$877$	24521.2	+	14157.3i	0.944154	+	0.545107i	0.0528937	+	0.998600i	$0.483156\pi$
$878$	1696.28	+	979.348i	0.0652013	+	0.0376440i
$879$	−16544.8	−	17605.3i	−0.634862	−	0.675554i
$880$		0			0
$881$	6479.51			0.247787			0.123893	−	0.992296i	$-0.460462\pi$
$881$	6479.51			0.247787			0.123893	+	0.992296i	$0.460462\pi$
$882$	17130.1	−	25824.5i	0.653968	−	0.985893i
$883$			17769.0i			0.677208i	0.940929	+	0.338604i	$0.109955\pi$
$883$			17769.0i			0.677208i	−0.940929	+	0.338604i	$0.890045\pi$
$884$	−6141.82	−	10637.9i	−0.233678	−	0.404743i
$885$		0			0
$886$	−18198.1	+	31520.1i	−0.690044	+	1.19519i
$887$	22419.8	+	12944.1i	0.848684	+	0.489988i	0.860207	−	0.509945i	$-0.170334\pi$
$887$	22419.8	+	12944.1i	0.848684	+	0.489988i	−0.0115224	+	0.999934i	$0.503668\pi$
$888$	−26996.8	−	8139.83i	−1.02022	−	0.307607i
$889$	921.481	+	1596.05i	0.0347643	+	0.0602136i
$890$		0			0
$891$	−14455.3	+	19103.2i	−0.543514	+	0.718273i
$892$		−	8626.80i		−	0.323819i
$893$	−22673.5	+	13090.6i	−0.849654	+	0.490548i
$894$	−7710.62	+	25573.2i	−0.288458	+	0.956707i
$895$		0			0
$896$	1353.73	−	2344.73i	0.0504744	−	0.0874242i
$897$	2646.52	+	11264.6i	0.0985115	+	0.419303i
$898$	8451.90	−	4879.71i	0.314080	−	0.181334i
$899$	1647.11			0.0611060
$900$		0			0
$901$	−19328.9			−0.714694
$902$	27959.9	−	16142.7i	1.03211	−	0.595889i
$903$	−1241.23	+	1166.46i	−0.0457426	+	0.0429873i
$904$	−1769.28	+	3064.49i	−0.0650946	+	0.112747i
$905$		0			0
$906$	37950.7	+	40383.2i	1.39164	+	1.48084i
$907$	−39134.2	+	22594.1i	−1.43267	+	0.827150i	−0.997324	−	0.0731143i	$-0.976706\pi$
$907$	−39134.2	+	22594.1i	−1.43267	+	0.827150i	−0.435343	+	0.900265i	$0.643373\pi$
$908$			13774.2i			0.503429i
$909$	−257.562	+	4143.09i	−0.00939802	+	0.151175i
$910$		0			0
$911$	−6587.08	−	11409.2i	−0.239560	−	0.414931i	0.721028	−	0.692906i	$-0.243670\pi$
$911$	−6587.08	−	11409.2i	−0.239560	−	0.414931i	−0.960588	+	0.277975i	$0.910337\pi$
$912$	5137.78	+	21868.4i	0.186545	+	0.794007i
$913$	42535.8	+	24558.0i	1.54187	+	0.890200i
$914$	−5395.51	+	9345.29i	−0.195260	+	0.338200i
$915$		0			0
$916$	4623.24	+	8007.69i	0.166765	+	0.288845i
$917$			1265.56i			0.0455752i
$918$	18136.7	−	48935.4i	0.652069	−	1.75938i
$919$	54078.5			1.94112			0.970558	−	0.240867i	$-0.0774316\pi$
$919$	54078.5			1.94112			0.970558	+	0.240867i	$0.0774316\pi$
$920$		0			0
$921$	11042.1	−	36622.6i	0.395060	−	1.31027i
$922$	21367.3	+	12336.4i	0.763228	+	0.440650i
$923$	3401.72	+	1963.98i	0.121310	+	0.0700383i
$924$	912.440	−	214.370i	0.0324860	−	0.00763229i
$925$		0			0
$926$	−23646.4			−0.839166
$927$	1626.66	+	3270.76i	0.0576338	+	0.115886i
$928$		−	39422.6i		−	1.39451i
$929$	−22858.9	−	39592.8i	−0.807294	−	1.39827i	−0.914732	−	0.404062i	$-0.867598\pi$
$929$	−22858.9	−	39592.8i	−0.807294	−	1.39827i	0.107438	−	0.994212i	$-0.465735\pi$
$930$		0			0
$931$	−9241.71	+	16007.1i	−0.325333	+	0.563493i
$932$	−14849.8	−	8573.53i	−0.521911	−	0.301325i
$933$	10258.4	−	9640.50i	0.359963	−	0.338281i
$934$	13493.6	+	23371.5i	0.472722	+	0.818779i
$935$		0			0
$936$	−12458.4	+	6195.98i	−0.435059	+	0.216369i
$937$		−	5055.54i		−	0.176262i	−0.996109	−	0.0881309i	$-0.971911\pi$
$937$		−	5055.54i		−	0.176262i	0.996109	−	0.0881309i	$-0.0280894\pi$
$938$	−3952.72	+	2282.10i	−0.137592	+	0.0794385i
$939$	31583.4	−	7420.23i	1.09764	−	0.257881i
$940$		0			0
$941$	−14056.0	+	24345.7i	−0.486942	+	0.843407i	−0.999887	−	0.0150136i	$-0.995221\pi$
$941$	−14056.0	+	24345.7i	−0.486942	+	0.843407i	0.512946	+	0.858421i	$0.328554\pi$
$942$	−40075.0	−	12083.1i	−1.38611	−	0.417927i
$943$	17014.8	−	9823.52i	0.587571	−	0.339234i
$944$	−14587.1			−0.502935
$945$		0			0
$946$	22317.4			0.767022
$947$	26085.0	−	15060.2i	0.895090	−	0.516780i	0.0194859	−	0.999810i	$-0.493797\pi$
$947$	26085.0	−	15060.2i	0.895090	−	0.516780i	0.875604	+	0.483030i	$0.160464\pi$
$948$	−10708.6	−	3228.76i	−0.366876	−	0.110617i
$949$	−3026.74	+	5242.46i	−0.103532	+	0.179323i
$950$		0			0
$951$	10541.9	−	2476.73i	0.359458	−	0.0844514i
$952$	2426.63	−	1401.02i	0.0826130	−	0.0476967i
$953$		−	19362.7i		−	0.658154i	−0.944303	−	0.329077i	$-0.893262\pi$
$953$		−	19362.7i		−	0.658154i	0.944303	−	0.329077i	$-0.106738\pi$
$954$	989.946	−	15924.1i	0.0335961	−	0.540420i
$955$		0			0
$956$	−2489.54	−	4312.01i	−0.0842233	−	0.145879i
$957$	−34158.4	+	32100.8i	−1.15380	+	1.08430i
$958$	9283.74	+	5359.97i	0.313094	+	0.180765i
$959$	507.554	−	879.109i	0.0170905	−	0.0296016i
$960$		0			0
$961$	14877.5	+	25768.6i	0.499396	+	0.864979i
$962$		−	38721.9i		−	1.29776i
$963$	10727.7	−	16172.6i	0.358977	−	0.541179i
$964$	−5946.87			−0.198689
$965$		0			0
$966$	1872.49	−	439.925i	0.0623669	−	0.0146525i
$967$	26608.2	+	15362.3i	0.884863	+	0.510876i	0.872259	−	0.489045i	$-0.162654\pi$
$967$	26608.2	+	15362.3i	0.884863	+	0.510876i	0.0126043	+	0.999921i	$0.495988\pi$
$968$	−3394.04	−	1959.55i	−0.112695	−	0.0650643i
$969$	−8985.67	+	29802.1i	−0.297896	+	0.988010i
$970$		0			0
$971$	−49791.0			−1.64559			−0.822796	−	0.568336i	$-0.807587\pi$
$971$	−49791.0			−1.64559			−0.822796	+	0.568336i	$0.807587\pi$
$972$	11679.5	+	5173.98i	0.385410	+	0.170736i
$973$		−	2087.84i		−	0.0687906i
$974$	−22021.4	−	38142.3i	−0.724448	−	1.25478i
$975$		0			0
$976$	17377.8	−	30099.2i	0.569927	−	0.987143i
$977$	19391.9	+	11195.9i	0.635008	+	0.366622i	0.782689	−	0.622413i	$-0.213847\pi$
$977$	19391.9	+	11195.9i	0.635008	+	0.366622i	−0.147681	+	0.989035i	$0.547181\pi$
$978$	−10198.8	−	43410.2i	−0.333458	−	1.41933i
$979$	23615.3	+	40903.0i	0.770939	+	1.33531i
$980$		0			0
$981$	45237.5	+	30007.2i	1.47230	+	0.976611i
$982$			14843.5i			0.482357i
$983$	21321.0	−	12309.7i	0.691794	−	0.399408i	−0.112490	−	0.993653i	$-0.535883\pi$
$983$	21321.0	−	12309.7i	0.691794	−	0.399408i	0.804284	+	0.594245i	$0.202549\pi$
$984$	16178.7	+	17215.7i	0.524144	+	0.557741i
$985$		0			0
$986$	51058.7	−	88436.2i	1.64913	−	2.85637i
$987$	−2971.33	+	2792.35i	−0.0958242	+	0.0900521i
$988$	−5237.34	+	3023.78i	−0.168646	+	0.0973676i
$989$	13581.1			0.436658
$990$		0			0
$991$	24540.3			0.786629			0.393314	−	0.919404i	$-0.371328\pi$
$991$	24540.3			0.786629			0.393314	+	0.919404i	$0.371328\pi$
$992$	−746.199	+	430.818i	−0.0238829	+	0.0137888i
$993$	270.815	+	1152.70i	0.00865465	+	0.0368375i
$994$	326.468	−	565.460i	0.0104175	−	0.0180436i
$995$		0			0
$996$	7560.54	−	25075.5i	0.240527	−	0.797737i
$997$	39799.1	−	22978.0i	1.26424	−	0.729912i	0.290351	−	0.956920i	$-0.406228\pi$
$997$	39799.1	−	22978.0i	1.26424	−	0.729912i	0.973893	+	0.227008i	$0.0728945\pi$
$998$			63146.7i			2.00288i
$999$	37554.1	−	31138.2i	1.18935	−	0.986155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.k.a.49.1		8
5.2	odd	4		225.4.e.a.76.1		4
5.3	odd	4		45.4.e.a.31.2	yes	4
5.4	even	2	inner	225.4.k.a.49.4		8
9.7	even	3	inner	225.4.k.a.124.4		8
15.8	even	4		135.4.e.a.91.1		4
45.7	odd	12		225.4.e.a.151.1		4
45.13	odd	12		405.4.a.d.1.1		2
45.22	odd	12		2025.4.a.l.1.2		2
45.23	even	12		405.4.a.e.1.2		2
45.32	even	12		2025.4.a.j.1.1		2
45.34	even	6	inner	225.4.k.a.124.1		8
45.38	even	12		135.4.e.a.46.1		4
45.43	odd	12		45.4.e.a.16.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.a.16.2	✓	4	45.43	odd	12
45.4.e.a.31.2	yes	4	5.3	odd	4
135.4.e.a.46.1		4	45.38	even	12
135.4.e.a.91.1		4	15.8	even	4
225.4.e.a.76.1		4	5.2	odd	4
225.4.e.a.151.1		4	45.7	odd	12
225.4.k.a.49.1		8	1.1	even	1	trivial
225.4.k.a.49.4		8	5.4	even	2	inner
225.4.k.a.124.1		8	45.34	even	6	inner
225.4.k.a.124.4		8	9.7	even	3	inner
405.4.a.d.1.1		2	45.13	odd	12
405.4.a.e.1.2		2	45.23	even	12
2025.4.a.j.1.1		2	45.32	even	12
2025.4.a.l.1.2		2	45.22	odd	12

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.92048 + 1.68614i) q^{2} +(4.97494 + 1.50000i) q^{3} +(1.68614 - 2.92048i) q^{4} +(-17.0584 + 4.00772i) q^{6} +(1.40965 - 0.813859i) q^{7} -15.6060i q^{8} +(22.5000 + 14.9248i) q^{9} +O(q^{10})\)	\(q+(-2.92048 + 1.68614i) q^{2} +(4.97494 + 1.50000i) q^{3} +(1.68614 - 2.92048i) q^{4} +(-17.0584 + 4.00772i) q^{6} +(1.40965 - 0.813859i) q^{7} -15.6060i q^{8} +(22.5000 + 14.9248i) q^{9} +(16.4307 + 28.4588i) q^{11} +(12.7692 - 12.0000i) q^{12} +(-28.5977 - 16.5109i) q^{13} +(-2.74456 + 4.75372i) q^{14} +(39.8030 + 68.9408i) q^{16} +110.307i q^{17} +(-90.8762 - 5.64947i) q^{18} +54.3070 q^{19} +(8.23369 - 1.93443i) q^{21} +(-95.9711 - 55.4090i) q^{22} +(-58.4026 - 33.7188i) q^{23} +(23.4090 - 77.6387i) q^{24} +111.359 q^{26} +(89.5489 + 108.000i) q^{27} -5.48913i q^{28} +(137.259 + 237.740i) q^{29} +(3.00000 - 5.19615i) q^{31} +(-124.366 - 71.8030i) q^{32} +(39.0535 + 166.227i) q^{33} +(-185.993 - 322.150i) q^{34} +(81.5258 - 40.5455i) q^{36} -347.723i q^{37} +(-158.603 + 91.5693i) q^{38} +(-117.505 - 125.037i) q^{39} +(-145.668 + 252.305i) q^{41} +(-20.7846 + 19.5326i) q^{42} +(-174.408 + 100.694i) q^{43} +110.818 q^{44} +227.418 q^{46} +(-417.507 + 241.048i) q^{47} +(94.6062 + 402.681i) q^{48} +(-170.175 + 294.752i) q^{49} +(-165.461 + 548.771i) q^{51} +(-96.4394 + 55.6793i) q^{52} +175.228i q^{53} +(-443.629 - 164.420i) q^{54} +(-12.7011 - 21.9989i) q^{56} +(270.174 + 81.4605i) q^{57} +(-801.728 - 462.878i) q^{58} +(-91.6209 + 158.692i) q^{59} +(-218.297 - 378.102i) q^{61} +20.2337i q^{62} +(43.8637 + 2.72686i) q^{63} -152.568 q^{64} +(-394.337 - 419.613i) q^{66} +(720.100 + 415.750i) q^{67} +(322.150 + 185.993i) q^{68} +(-239.971 - 255.353i) q^{69} -118.951 q^{71} +(232.916 - 351.134i) q^{72} -183.318i q^{73} +(586.310 + 1015.52i) q^{74} +(91.5693 - 158.603i) q^{76} +(46.3229 + 26.7446i) q^{77} +(554.002 + 167.038i) q^{78} +(-319.147 - 552.778i) q^{79} +(283.500 + 671.617i) q^{81} -982.470i q^{82} +(1294.40 - 747.322i) q^{83} +(8.23369 - 27.3081i) q^{84} +(339.569 - 588.151i) q^{86} +(326.247 + 1388.63i) q^{87} +(444.127 - 256.417i) q^{88} +1437.27 q^{89} -53.7501 q^{91} +(-196.950 + 113.709i) q^{92} +(22.7190 - 21.3505i) q^{93} +(812.880 - 1407.95i) q^{94} +(-511.011 - 543.765i) q^{96} +(-772.294 + 445.884i) q^{97} -1147.76i q^{98} +(-55.0516 + 885.548i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 - 102 * q^6 + 180 * q^9	\( 8 q + 2 q^{4} - 102 q^{6} + 180 q^{9} + 74 q^{11} + 24 q^{14} + 238 q^{16} - 140 q^{19} - 72 q^{21} - 54 q^{24} - 304 q^{26} + 650 q^{29} + 24 q^{31} - 902 q^{34} + 342 q^{36} + 1128 q^{39} - 476 q^{41} + 404 q^{44} - 984 q^{46} - 1258 q^{49} - 462 q^{51} - 1998 q^{54} + 312 q^{56} - 170 q^{59} + 494 q^{61} - 2852 q^{64} - 1776 q^{66} + 3078 q^{69} + 1576 q^{71} + 968 q^{74} + 790 q^{76} - 1680 q^{79} + 2268 q^{81} - 72 q^{84} + 2774 q^{86} + 4260 q^{89} - 2544 q^{91} + 1264 q^{94} + 48 q^{96} + 180 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 - 102 * q^6 + 180 * q^9 + 74 * q^11 + 24 * q^14 + 238 * q^16 - 140 * q^19 - 72 * q^21 - 54 * q^24 - 304 * q^26 + 650 * q^29 + 24 * q^31 - 902 * q^34 + 342 * q^36 + 1128 * q^39 - 476 * q^41 + 404 * q^44 - 984 * q^46 - 1258 * q^49 - 462 * q^51 - 1998 * q^54 + 312 * q^56 - 170 * q^59 + 494 * q^61 - 2852 * q^64 - 1776 * q^66 + 3078 * q^69 + 1576 * q^71 + 968 * q^74 + 790 * q^76 - 1680 * q^79 + 2268 * q^81 - 72 * q^84 + 2774 * q^86 + 4260 * q^89 - 2544 * q^91 + 1264 * q^94 + 48 * q^96 + 180 * q^99

Introduction

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